LMFDB - Embedded newform 4011.2.a.j.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.95690 q^{2} -1.00000 q^{3} +1.82947 q^{4} -3.69601 q^{5} +1.95690 q^{6} -1.00000 q^{7} +0.333702 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.95690 q^{2} -1.00000 q^{3} +1.82947 q^{4} -3.69601 q^{5} +1.95690 q^{6} -1.00000 q^{7} +0.333702 q^{8} +1.00000 q^{9} +7.23273 q^{10} -1.37257 q^{11} -1.82947 q^{12} -1.91776 q^{13} +1.95690 q^{14} +3.69601 q^{15} -4.31197 q^{16} -2.07474 q^{17} -1.95690 q^{18} +6.94405 q^{19} -6.76175 q^{20} +1.00000 q^{21} +2.68599 q^{22} +2.64993 q^{23} -0.333702 q^{24} +8.66046 q^{25} +3.75287 q^{26} -1.00000 q^{27} -1.82947 q^{28} -4.43171 q^{29} -7.23273 q^{30} -5.32582 q^{31} +7.77071 q^{32} +1.37257 q^{33} +4.06007 q^{34} +3.69601 q^{35} +1.82947 q^{36} +1.70486 q^{37} -13.5888 q^{38} +1.91776 q^{39} -1.23337 q^{40} -9.08204 q^{41} -1.95690 q^{42} -3.79696 q^{43} -2.51109 q^{44} -3.69601 q^{45} -5.18567 q^{46} -0.337396 q^{47} +4.31197 q^{48} +1.00000 q^{49} -16.9477 q^{50} +2.07474 q^{51} -3.50849 q^{52} -4.43646 q^{53} +1.95690 q^{54} +5.07304 q^{55} -0.333702 q^{56} -6.94405 q^{57} +8.67244 q^{58} -7.11860 q^{59} +6.76175 q^{60} -4.27392 q^{61} +10.4221 q^{62} -1.00000 q^{63} -6.58260 q^{64} +7.08804 q^{65} -2.68599 q^{66} +7.63898 q^{67} -3.79568 q^{68} -2.64993 q^{69} -7.23273 q^{70} -7.55733 q^{71} +0.333702 q^{72} -0.633412 q^{73} -3.33624 q^{74} -8.66046 q^{75} +12.7040 q^{76} +1.37257 q^{77} -3.75287 q^{78} +12.8862 q^{79} +15.9371 q^{80} +1.00000 q^{81} +17.7727 q^{82} -11.2560 q^{83} +1.82947 q^{84} +7.66825 q^{85} +7.43029 q^{86} +4.43171 q^{87} -0.458031 q^{88} +4.72479 q^{89} +7.23273 q^{90} +1.91776 q^{91} +4.84799 q^{92} +5.32582 q^{93} +0.660253 q^{94} -25.6653 q^{95} -7.77071 q^{96} -15.6874 q^{97} -1.95690 q^{98} -1.37257 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) $ 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9	$ 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) $ 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9 - q^10 + 13 * q^11 - 34 * q^12 - q^13 - 2 * q^15 + 54 * q^16 + q^19 - 22 * q^20 + 26 * q^21 + 17 * q^22 - 3 * q^23 + 48 * q^25 + 6 * q^26 - 26 * q^27 - 34 * q^28 + 23 * q^29 + q^30 + 18 * q^31 + 10 * q^32 - 13 * q^33 - 19 * q^34 - 2 * q^35 + 34 * q^36 + 23 * q^37 - 15 * q^38 + q^39 + 14 * q^40 - 4 * q^41 + 5 * q^43 + 60 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^47 - 54 * q^48 + 26 * q^49 + 26 * q^50 + 19 * q^52 + 31 * q^53 + 41 * q^55 - q^57 + 19 * q^58 - 2 * q^59 + 22 * q^60 - 2 * q^61 - 35 * q^62 - 26 * q^63 + 132 * q^64 + 40 * q^65 - 17 * q^66 + 47 * q^67 - 60 * q^68 + 3 * q^69 + q^70 + 16 * q^71 - 23 * q^73 + 34 * q^74 - 48 * q^75 + 72 * q^76 - 13 * q^77 - 6 * q^78 + 14 * q^79 - 21 * q^80 + 26 * q^81 + 60 * q^82 - 4 * q^83 + 34 * q^84 + 36 * q^85 + 21 * q^86 - 23 * q^87 + 67 * q^88 + 14 * q^89 - q^90 + q^91 + 20 * q^92 - 18 * q^93 + 58 * q^94 - 4 * q^95 - 10 * q^96 + 48 * q^97 + 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.95690	−1.38374	−0.691870	−	0.722022i	$-0.743213\pi$
$2$	−1.95690	−1.38374	−0.691870	+	0.722022i	$0.743213\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.82947	0.914737
$5$	−3.69601	−1.65290	−0.826452	−	0.563007i	$-0.809644\pi$
$5$	−3.69601	−1.65290	−0.826452	+	0.563007i	$0.809644\pi$
$6$	1.95690	0.798903
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.333702	0.117982
$9$	1.00000	0.333333
$10$	7.23273	2.28719
$11$	−1.37257	−0.413846	−0.206923	−	0.978357i	$-0.566345\pi$
$11$	−1.37257	−0.413846	−0.206923	+	0.978357i	$0.566345\pi$
$12$	−1.82947	−0.528124
$13$	−1.91776	−0.531890	−0.265945	−	0.963988i	$-0.585684\pi$
$13$	−1.91776	−0.531890	−0.265945	+	0.963988i	$0.585684\pi$
$14$	1.95690	0.523005
$15$	3.69601	0.954305
$16$	−4.31197	−1.07799
$17$	−2.07474	−0.503198	−0.251599	−	0.967832i	$-0.580956\pi$
$17$	−2.07474	−0.503198	−0.251599	+	0.967832i	$0.580956\pi$
$18$	−1.95690	−0.461247
$19$	6.94405	1.59307	0.796537	−	0.604589i	$-0.206663\pi$
$19$	6.94405	1.59307	0.796537	+	0.604589i	$0.206663\pi$
$20$	−6.76175	−1.51197
$21$	1.00000	0.218218
$22$	2.68599	0.572656
$23$	2.64993	0.552549	0.276275	−	0.961079i	$-0.410900\pi$
$23$	2.64993	0.552549	0.276275	+	0.961079i	$0.410900\pi$
$24$	−0.333702	−0.0681167
$25$	8.66046	1.73209
$26$	3.75287	0.735998
$27$	−1.00000	−0.192450
$28$	−1.82947	−0.345738
$29$	−4.43171	−0.822949	−0.411474	−	0.911421i	$-0.634986\pi$
$29$	−4.43171	−0.822949	−0.411474	+	0.911421i	$0.634986\pi$
$30$	−7.23273	−1.32051
$31$	−5.32582	−0.956545	−0.478273	−	0.878211i	$-0.658737\pi$
$31$	−5.32582	−0.956545	−0.478273	+	0.878211i	$0.658737\pi$
$32$	7.77071	1.37368
$33$	1.37257	0.238934
$34$	4.06007	0.696296
$35$	3.69601	0.624739
$36$	1.82947	0.304912
$37$	1.70486	0.280277	0.140138	−	0.990132i	$-0.455245\pi$
$37$	1.70486	0.280277	0.140138	+	0.990132i	$0.455245\pi$
$38$	−13.5888	−2.20440
$39$	1.91776	0.307087
$40$	−1.23337	−0.195012
$41$	−9.08204	−1.41838	−0.709188	−	0.705019i	$-0.750938\pi$
$41$	−9.08204	−1.41838	−0.709188	+	0.705019i	$0.750938\pi$
$42$	−1.95690	−0.301957
$43$	−3.79696	−0.579031	−0.289516	−	0.957173i	$-0.593494\pi$
$43$	−3.79696	−0.579031	−0.289516	+	0.957173i	$0.593494\pi$
$44$	−2.51109	−0.378561
$45$	−3.69601	−0.550968
$46$	−5.18567	−0.764585
$47$	−0.337396	−0.0492143	−0.0246072	−	0.999697i	$-0.507833\pi$
$47$	−0.337396	−0.0492143	−0.0246072	+	0.999697i	$0.507833\pi$
$48$	4.31197	0.622380
$49$	1.00000	0.142857
$50$	−16.9477	−2.39677
$51$	2.07474	0.290522
$52$	−3.50849	−0.486540
$53$	−4.43646	−0.609395	−0.304698	−	0.952449i	$-0.598555\pi$
$53$	−4.43646	−0.609395	−0.304698	+	0.952449i	$0.598555\pi$
$54$	1.95690	0.266301
$55$	5.07304	0.684048
$56$	−0.333702	−0.0445928
$57$	−6.94405	−0.919762
$58$	8.67244	1.13875
$59$	−7.11860	−0.926763	−0.463381	−	0.886159i	$-0.653364\pi$
$59$	−7.11860	−0.926763	−0.463381	+	0.886159i	$0.653364\pi$
$60$	6.76175	0.872938
$61$	−4.27392	−0.547220	−0.273610	−	0.961841i	$-0.588218\pi$
$61$	−4.27392	−0.547220	−0.273610	+	0.961841i	$0.588218\pi$
$62$	10.4221	1.32361
$63$	−1.00000	−0.125988
$64$	−6.58260	−0.822825
$65$	7.08804	0.879163
$66$	−2.68599	−0.330623
$67$	7.63898	0.933250	0.466625	−	0.884455i	$-0.345470\pi$
$67$	7.63898	0.933250	0.466625	+	0.884455i	$0.345470\pi$
$68$	−3.79568	−0.460294
$69$	−2.64993	−0.319014
$70$	−7.23273	−0.864477
$71$	−7.55733	−0.896890	−0.448445	−	0.893810i	$-0.648022\pi$
$71$	−7.55733	−0.896890	−0.448445	+	0.893810i	$0.648022\pi$
$72$	0.333702	0.0393272
$73$	−0.633412	−0.0741352	−0.0370676	−	0.999313i	$-0.511802\pi$
$73$	−0.633412	−0.0741352	−0.0370676	+	0.999313i	$0.511802\pi$
$74$	−3.33624	−0.387830
$75$	−8.66046	−1.00002
$76$	12.7040	1.45724
$77$	1.37257	0.156419
$78$	−3.75287	−0.424928
$79$	12.8862	1.44981	0.724903	−	0.688851i	$-0.241885\pi$
$79$	12.8862	1.44981	0.724903	+	0.688851i	$0.241885\pi$
$80$	15.9371	1.78182
$81$	1.00000	0.111111
$82$	17.7727	1.96266
$83$	−11.2560	−1.23551	−0.617753	−	0.786372i	$-0.711957\pi$
$83$	−11.2560	−1.23551	−0.617753	+	0.786372i	$0.711957\pi$
$84$	1.82947	0.199612
$85$	7.66825	0.831739
$86$	7.43029	0.801229
$87$	4.43171	0.475130
$88$	−0.458031	−0.0488262
$89$	4.72479	0.500827	0.250414	−	0.968139i	$-0.419433\pi$
$89$	4.72479	0.500827	0.250414	+	0.968139i	$0.419433\pi$
$90$	7.23273	0.762397
$91$	1.91776	0.201036
$92$	4.84799	0.505437
$93$	5.32582	0.552262
$94$	0.660253	0.0680998
$95$	−25.6653	−2.63320
$96$	−7.77071	−0.793095
$97$	−15.6874	−1.59281	−0.796405	−	0.604764i	$-0.793267\pi$
$97$	−15.6874	−1.59281	−0.796405	+	0.604764i	$0.793267\pi$
$98$	−1.95690	−0.197677
$99$	−1.37257	−0.137949
$100$	15.8441	1.58441
$101$	−7.21773	−0.718191	−0.359095	−	0.933301i	$-0.616915\pi$
$101$	−7.21773	−0.718191	−0.359095	+	0.933301i	$0.616915\pi$
$102$	−4.06007	−0.402007
$103$	−17.1866	−1.69344	−0.846721	−	0.532037i	$-0.821427\pi$
$103$	−17.1866	−1.69344	−0.846721	+	0.532037i	$0.821427\pi$
$104$	−0.639960	−0.0627532
$105$	−3.69601	−0.360693
$106$	8.68173	0.843244
$107$	−1.80323	−0.174325	−0.0871625	−	0.996194i	$-0.527780\pi$
$107$	−1.80323	−0.174325	−0.0871625	+	0.996194i	$0.527780\pi$
$108$	−1.82947	−0.176041
$109$	−3.82223	−0.366104	−0.183052	−	0.983103i	$-0.558598\pi$
$109$	−3.82223	−0.366104	−0.183052	+	0.983103i	$0.558598\pi$
$110$	−9.92745	−0.946545
$111$	−1.70486	−0.161818
$112$	4.31197	0.407443
$113$	−17.7125	−1.66626	−0.833128	−	0.553080i	$-0.813452\pi$
$113$	−17.7125	−1.66626	−0.833128	+	0.553080i	$0.813452\pi$
$114$	13.5888	1.27271
$115$	−9.79417	−0.913311
$116$	−8.10771	−0.752782
$117$	−1.91776	−0.177297
$118$	13.9304	1.28240
$119$	2.07474	0.190191
$120$	1.23337	0.112590
$121$	−9.11604	−0.828731
$122$	8.36366	0.757210
$123$	9.08204	0.818900
$124$	−9.74345	−0.874988
$125$	−13.5291	−1.21008
$126$	1.95690	0.174335
$127$	−2.49097	−0.221038	−0.110519	−	0.993874i	$-0.535251\pi$
$127$	−2.49097	−0.221038	−0.110519	+	0.993874i	$0.535251\pi$
$128$	−2.65991	−0.235105
$129$	3.79696	0.334304
$130$	−13.8706	−1.21653
$131$	5.98606	0.523004	0.261502	−	0.965203i	$-0.415782\pi$
$131$	5.98606	0.523004	0.261502	+	0.965203i	$0.415782\pi$
$132$	2.51109	0.218562
$133$	−6.94405	−0.602126
$134$	−14.9487	−1.29138
$135$	3.69601	0.318102
$136$	−0.692345	−0.0593681
$137$	−3.07821	−0.262990	−0.131495	−	0.991317i	$-0.541978\pi$
$137$	−3.07821	−0.262990	−0.131495	+	0.991317i	$0.541978\pi$
$138$	5.18567	0.441433
$139$	5.96581	0.506014	0.253007	−	0.967464i	$-0.418580\pi$
$139$	5.96581	0.506014	0.253007	+	0.967464i	$0.418580\pi$
$140$	6.76175	0.571472
$141$	0.337396	0.0284139
$142$	14.7890	1.24106
$143$	2.63226	0.220121
$144$	−4.31197	−0.359331
$145$	16.3796	1.36026
$146$	1.23953	0.102584
$147$	−1.00000	−0.0824786
$148$	3.11899	0.256380
$149$	17.1652	1.40623	0.703113	−	0.711078i	$-0.251793\pi$
$149$	17.1652	1.40623	0.703113	+	0.711078i	$0.251793\pi$
$150$	16.9477	1.38377
$151$	20.4263	1.66227	0.831133	−	0.556073i	$-0.187693\pi$
$151$	20.4263	1.66227	0.831133	+	0.556073i	$0.187693\pi$
$152$	2.31725	0.187953
$153$	−2.07474	−0.167733
$154$	−2.68599	−0.216444
$155$	19.6843	1.58108
$156$	3.50849	0.280904
$157$	0.158692	0.0126650	0.00633251	−	0.999980i	$-0.497984\pi$
$157$	0.158692	0.0126650	0.00633251	+	0.999980i	$0.497984\pi$
$158$	−25.2170	−2.00615
$159$	4.43646	0.351834
$160$	−28.7206	−2.27056
$161$	−2.64993	−0.208844
$162$	−1.95690	−0.153749
$163$	11.3437	0.888507	0.444253	−	0.895901i	$-0.353469\pi$
$163$	11.3437	0.888507	0.444253	+	0.895901i	$0.353469\pi$
$164$	−16.6154	−1.29744
$165$	−5.07304	−0.394935
$166$	22.0269	1.70962
$167$	−12.8720	−0.996068	−0.498034	−	0.867157i	$-0.665945\pi$
$167$	−12.8720	−0.996068	−0.498034	+	0.867157i	$0.665945\pi$
$168$	0.333702	0.0257457
$169$	−9.32221	−0.717093
$170$	−15.0060	−1.15091
$171$	6.94405	0.531025
$172$	−6.94644	−0.529661
$173$	4.16669	0.316788	0.158394	−	0.987376i	$-0.449368\pi$
$173$	4.16669	0.316788	0.158394	+	0.987376i	$0.449368\pi$
$174$	−8.67244	−0.657456
$175$	−8.66046	−0.654669
$176$	5.91850	0.446123
$177$	7.11860	0.535067
$178$	−9.24597	−0.693015
$179$	−13.2993	−0.994038	−0.497019	−	0.867740i	$-0.665572\pi$
$179$	−13.2993	−0.994038	−0.497019	+	0.867740i	$0.665572\pi$
$180$	−6.76175	−0.503991
$181$	5.71679	0.424926	0.212463	−	0.977169i	$-0.431851\pi$
$181$	5.71679	0.424926	0.212463	+	0.977169i	$0.431851\pi$
$182$	−3.75287	−0.278181
$183$	4.27392	0.315937
$184$	0.884289	0.0651906
$185$	−6.30116	−0.463271
$186$	−10.4221	−0.764187
$187$	2.84773	0.208247
$188$	−0.617258	−0.0450182
$189$	1.00000	0.0727393
$190$	50.2245	3.64366
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	6.58260	0.475058
$193$	−19.5494	−1.40720	−0.703598	−	0.710599i	$-0.748424\pi$
$193$	−19.5494	−1.40720	−0.703598	+	0.710599i	$0.748424\pi$
$194$	30.6986	2.20403
$195$	−7.08804	−0.507585
$196$	1.82947	0.130677
$197$	−4.52178	−0.322164	−0.161082	−	0.986941i	$-0.551498\pi$
$197$	−4.52178	−0.322164	−0.161082	+	0.986941i	$0.551498\pi$
$198$	2.68599	0.190885
$199$	10.6775	0.756907	0.378454	−	0.925620i	$-0.376456\pi$
$199$	10.6775	0.756907	0.378454	+	0.925620i	$0.376456\pi$
$200$	2.89001	0.204355
$201$	−7.63898	−0.538812
$202$	14.1244	0.993789
$203$	4.43171	0.311045
$204$	3.79568	0.265751
$205$	33.5673	2.34444
$206$	33.6325	2.34328
$207$	2.64993	0.184183
$208$	8.26931	0.573374
$209$	−9.53122	−0.659288
$210$	7.23273	0.499106
$211$	−12.6823	−0.873088	−0.436544	−	0.899683i	$-0.643798\pi$
$211$	−12.6823	−0.873088	−0.436544	+	0.899683i	$0.643798\pi$
$212$	−8.11639	−0.557436
$213$	7.55733	0.517820
$214$	3.52875	0.241221
$215$	14.0336	0.957083
$216$	−0.333702	−0.0227056
$217$	5.32582	0.361540
$218$	7.47974	0.506592
$219$	0.633412	0.0428020
$220$	9.28099	0.625724
$221$	3.97885	0.267646
$222$	3.33624	0.223914
$223$	14.5175	0.972161	0.486080	−	0.873914i	$-0.338426\pi$
$223$	14.5175	0.972161	0.486080	+	0.873914i	$0.338426\pi$
$224$	−7.77071	−0.519203
$225$	8.66046	0.577364
$226$	34.6618	2.30567
$227$	−16.1163	−1.06968	−0.534839	−	0.844954i	$-0.679628\pi$
$227$	−16.1163	−1.06968	−0.534839	+	0.844954i	$0.679628\pi$
$228$	−12.7040	−0.841341
$229$	−10.5894	−0.699769	−0.349884	−	0.936793i	$-0.613779\pi$
$229$	−10.5894	−0.699769	−0.349884	+	0.936793i	$0.613779\pi$
$230$	19.1663	1.26379
$231$	−1.37257	−0.0903087
$232$	−1.47887	−0.0970927
$233$	−19.4052	−1.27128	−0.635639	−	0.771986i	$-0.719263\pi$
$233$	−19.4052	−1.27128	−0.635639	+	0.771986i	$0.719263\pi$
$234$	3.75287	0.245333
$235$	1.24702	0.0813466
$236$	−13.0233	−0.847744
$237$	−12.8862	−0.837046
$238$	−4.06007	−0.263175
$239$	21.4653	1.38847	0.694236	−	0.719748i	$-0.255742\pi$
$239$	21.4653	1.38847	0.694236	+	0.719748i	$0.255742\pi$
$240$	−15.9371	−1.02873
$241$	−12.8406	−0.827136	−0.413568	−	0.910473i	$-0.635718\pi$
$241$	−12.8406	−0.827136	−0.413568	+	0.910473i	$0.635718\pi$
$242$	17.8392	1.14675
$243$	−1.00000	−0.0641500
$244$	−7.81903	−0.500562
$245$	−3.69601	−0.236129
$246$	−17.7727	−1.13314
$247$	−13.3170	−0.847340
$248$	−1.77724	−0.112855
$249$	11.2560	0.713320
$250$	26.4751	1.67443
$251$	10.6849	0.674424	0.337212	−	0.941429i	$-0.390516\pi$
$251$	10.6849	0.674424	0.337212	+	0.941429i	$0.390516\pi$
$252$	−1.82947	−0.115246
$253$	−3.63723	−0.228670
$254$	4.87460	0.305860
$255$	−7.66825	−0.480205
$256$	18.3704	1.14815
$257$	14.2766	0.890551	0.445275	−	0.895394i	$-0.353106\pi$
$257$	14.2766	0.890551	0.445275	+	0.895394i	$0.353106\pi$
$258$	−7.43029	−0.462590
$259$	−1.70486	−0.105935
$260$	12.9674	0.804203
$261$	−4.43171	−0.274316
$262$	−11.7141	−0.723702
$263$	0.804406	0.0496018	0.0248009	−	0.999692i	$-0.492105\pi$
$263$	0.804406	0.0496018	0.0248009	+	0.999692i	$0.492105\pi$
$264$	0.458031	0.0281898
$265$	16.3972	1.00727
$266$	13.5888	0.833186
$267$	−4.72479	−0.289153
$268$	13.9753	0.853678
$269$	27.3535	1.66777	0.833887	−	0.551936i	$-0.186111\pi$
$269$	27.3535	1.66777	0.833887	+	0.551936i	$0.186111\pi$
$270$	−7.23273	−0.440170
$271$	20.2290	1.22882	0.614411	−	0.788986i	$-0.289394\pi$
$271$	20.2290	1.22882	0.614411	+	0.788986i	$0.289394\pi$
$272$	8.94622	0.542444
$273$	−1.91776	−0.116068
$274$	6.02377	0.363909
$275$	−11.8871	−0.716820
$276$	−4.84799	−0.291814
$277$	11.0000	0.660927	0.330464	−	0.943819i	$-0.392795\pi$
$277$	11.0000	0.660927	0.330464	+	0.943819i	$0.392795\pi$
$278$	−11.6745	−0.700191
$279$	−5.32582	−0.318848
$280$	1.23337	0.0737077
$281$	−8.74547	−0.521711	−0.260856	−	0.965378i	$-0.584005\pi$
$281$	−8.74547	−0.521711	−0.260856	+	0.965378i	$0.584005\pi$
$282$	−0.660253	−0.0393175
$283$	3.04708	0.181130	0.0905652	−	0.995891i	$-0.471133\pi$
$283$	3.04708	0.181130	0.0905652	+	0.995891i	$0.471133\pi$
$284$	−13.8259	−0.820419
$285$	25.6653	1.52028
$286$	−5.15108	−0.304590
$287$	9.08204	0.536096
$288$	7.77071	0.457894
$289$	−12.6955	−0.746791
$290$	−32.0534	−1.88224
$291$	15.6874	0.919609
$292$	−1.15881	−0.0678143
$293$	−13.6918	−0.799882	−0.399941	−	0.916541i	$-0.630969\pi$
$293$	−13.6918	−0.799882	−0.399941	+	0.916541i	$0.630969\pi$
$294$	1.95690	0.114129
$295$	26.3104	1.53185
$296$	0.568915	0.0330675
$297$	1.37257	0.0796448
$298$	−33.5906	−1.94585
$299$	−5.08193	−0.293895
$300$	−15.8441	−0.914759
$301$	3.79696	0.218853
$302$	−39.9723	−2.30014
$303$	7.21773	0.414648
$304$	−29.9426	−1.71732
$305$	15.7964	0.904502
$306$	4.06007	0.232099
$307$	0.518453	0.0295897	0.0147948	−	0.999891i	$-0.495290\pi$
$307$	0.518453	0.0295897	0.0147948	+	0.999891i	$0.495290\pi$
$308$	2.51109	0.143082
$309$	17.1866	0.977710
$310$	−38.5202	−2.18780
$311$	0.516257	0.0292742	0.0146371	−	0.999893i	$-0.495341\pi$
$311$	0.516257	0.0292742	0.0146371	+	0.999893i	$0.495341\pi$
$312$	0.639960	0.0362306
$313$	21.8262	1.23369	0.616845	−	0.787085i	$-0.288411\pi$
$313$	21.8262	1.23369	0.616845	+	0.787085i	$0.288411\pi$
$314$	−0.310546	−0.0175251
$315$	3.69601	0.208246
$316$	23.5749	1.32619
$317$	10.2827	0.577533	0.288767	−	0.957400i	$-0.406755\pi$
$317$	10.2827	0.577533	0.288767	+	0.957400i	$0.406755\pi$
$318$	−8.68173	−0.486847
$319$	6.08285	0.340574
$320$	24.3293	1.36005
$321$	1.80323	0.100647
$322$	5.18567	0.288986
$323$	−14.4071	−0.801633
$324$	1.82947	0.101637
$325$	−16.6087	−0.921282
$326$	−22.1985	−1.22946
$327$	3.82223	0.211370
$328$	−3.03070	−0.167342
$329$	0.337396	0.0186013
$330$	9.92745	0.546488
$331$	9.95388	0.547115	0.273557	−	0.961856i	$-0.411800\pi$
$331$	9.95388	0.547115	0.273557	+	0.961856i	$0.411800\pi$
$332$	−20.5926	−1.13016
$333$	1.70486	0.0934256
$334$	25.1893	1.37830
$335$	−28.2337	−1.54257
$336$	−4.31197	−0.235237
$337$	−23.7349	−1.29292	−0.646460	−	0.762948i	$-0.723751\pi$
$337$	−23.7349	−1.29292	−0.646460	+	0.762948i	$0.723751\pi$
$338$	18.2427	0.992271
$339$	17.7125	0.962014
$340$	14.0289	0.760822
$341$	7.31007	0.395863
$342$	−13.5888	−0.734801
$343$	−1.00000	−0.0539949
$344$	−1.26705	−0.0683150
$345$	9.79417	0.527300
$346$	−8.15381	−0.438352
$347$	17.3007	0.928748	0.464374	−	0.885639i	$-0.346279\pi$
$347$	17.3007	0.928748	0.464374	+	0.885639i	$0.346279\pi$
$348$	8.10771	0.434619
$349$	18.8805	1.01065	0.505325	−	0.862929i	$-0.331373\pi$
$349$	18.8805	1.01065	0.505325	+	0.862929i	$0.331373\pi$
$350$	16.9477	0.905892
$351$	1.91776	0.102362
$352$	−10.6659	−0.568493
$353$	7.60875	0.404973	0.202487	−	0.979285i	$-0.435098\pi$
$353$	7.60875	0.404973	0.202487	+	0.979285i	$0.435098\pi$
$354$	−13.9304	−0.740393
$355$	27.9319	1.48247
$356$	8.64389	0.458125
$357$	−2.07474	−0.109807
$358$	26.0255	1.37549
$359$	4.05694	0.214117	0.107059	−	0.994253i	$-0.465857\pi$
$359$	4.05694	0.214117	0.107059	+	0.994253i	$0.465857\pi$
$360$	−1.23337	−0.0650041
$361$	29.2199	1.53789
$362$	−11.1872	−0.587987
$363$	9.11604	0.478468
$364$	3.50849	0.183895
$365$	2.34109	0.122538
$366$	−8.36366	−0.437175
$367$	−20.9076	−1.09137	−0.545684	−	0.837991i	$-0.683730\pi$
$367$	−20.9076	−1.09137	−0.545684	+	0.837991i	$0.683730\pi$
$368$	−11.4264	−0.595644
$369$	−9.08204	−0.472792
$370$	12.3308	0.641046
$371$	4.43646	0.230330
$372$	9.74345	0.505174
$373$	24.8992	1.28923	0.644617	−	0.764506i	$-0.277017\pi$
$373$	24.8992	1.28923	0.644617	+	0.764506i	$0.277017\pi$
$374$	−5.57274	−0.288160
$375$	13.5291	0.698639
$376$	−0.112590	−0.00580638
$377$	8.49895	0.437718
$378$	−1.95690	−0.100652
$379$	−8.97189	−0.460855	−0.230428	−	0.973089i	$-0.574012\pi$
$379$	−8.97189	−0.460855	−0.230428	+	0.973089i	$0.574012\pi$
$380$	−46.9539	−2.40869
$381$	2.49097	0.127616
$382$	−1.95690	−0.100124
$383$	−20.1063	−1.02739	−0.513693	−	0.857974i	$-0.671723\pi$
$383$	−20.1063	−1.02739	−0.513693	+	0.857974i	$0.671723\pi$
$384$	2.65991	0.135738
$385$	−5.07304	−0.258546
$386$	38.2563	1.94719
$387$	−3.79696	−0.193010
$388$	−28.6996	−1.45700
$389$	18.5733	0.941703	0.470851	−	0.882213i	$-0.343947\pi$
$389$	18.5733	0.941703	0.470851	+	0.882213i	$0.343947\pi$
$390$	13.8706	0.702366
$391$	−5.49792	−0.278042
$392$	0.333702	0.0168545
$393$	−5.98606	−0.301957
$394$	8.84870	0.445791
$395$	−47.6273	−2.39639
$396$	−2.51109	−0.126187
$397$	7.80115	0.391529	0.195764	−	0.980651i	$-0.437281\pi$
$397$	7.80115	0.391529	0.195764	+	0.980651i	$0.437281\pi$
$398$	−20.8948	−1.04736
$399$	6.94405	0.347637
$400$	−37.3437	−1.86718
$401$	24.3411	1.21554	0.607769	−	0.794114i	$-0.292065\pi$
$401$	24.3411	1.21554	0.607769	+	0.794114i	$0.292065\pi$
$402$	14.9487	0.745576
$403$	10.2136	0.508777
$404$	−13.2046	−0.656956
$405$	−3.69601	−0.183656
$406$	−8.67244	−0.430406
$407$	−2.34004	−0.115992
$408$	0.692345	0.0342762
$409$	−38.4678	−1.90211	−0.951056	−	0.309019i	$-0.899999\pi$
$409$	−38.4678	−1.90211	−0.951056	+	0.309019i	$0.899999\pi$
$410$	−65.6879	−3.24410
$411$	3.07821	0.151837
$412$	−31.4424	−1.54906
$413$	7.11860	0.350283
$414$	−5.18567	−0.254862
$415$	41.6022	2.04217
$416$	−14.9023	−0.730647
$417$	−5.96581	−0.292147
$418$	18.6517	0.912284
$419$	9.89129	0.483221	0.241611	−	0.970373i	$-0.422324\pi$
$419$	9.89129	0.483221	0.241611	+	0.970373i	$0.422324\pi$
$420$	−6.76175	−0.329940
$421$	4.59520	0.223956	0.111978	−	0.993711i	$-0.464281\pi$
$421$	4.59520	0.223956	0.111978	+	0.993711i	$0.464281\pi$
$422$	24.8181	1.20813
$423$	−0.337396	−0.0164048
$424$	−1.48046	−0.0718974
$425$	−17.9682	−0.871586
$426$	−14.7890	−0.716528
$427$	4.27392	0.206830
$428$	−3.29897	−0.159462
$429$	−2.63226	−0.127087
$430$	−27.4624	−1.32435
$431$	21.7871	1.04945	0.524723	−	0.851273i	$-0.324169\pi$
$431$	21.7871	1.04945	0.524723	+	0.851273i	$0.324169\pi$
$432$	4.31197	0.207460
$433$	15.9551	0.766755	0.383377	−	0.923592i	$-0.374761\pi$
$433$	15.9551	0.766755	0.383377	+	0.923592i	$0.374761\pi$
$434$	−10.4221	−0.500278
$435$	−16.3796	−0.785344
$436$	−6.99268	−0.334889
$437$	18.4013	0.880252
$438$	−1.23953	−0.0592269
$439$	−32.1585	−1.53484	−0.767420	−	0.641144i	$-0.778460\pi$
$439$	−32.1585	−1.53484	−0.767420	+	0.641144i	$0.778460\pi$
$440$	1.69288	0.0807051
$441$	1.00000	0.0476190
$442$	−7.78622	−0.370353
$443$	−31.3243	−1.48826	−0.744132	−	0.668032i	$-0.767137\pi$
$443$	−31.3243	−1.48826	−0.744132	+	0.668032i	$0.767137\pi$
$444$	−3.11899	−0.148021
$445$	−17.4629	−0.827819
$446$	−28.4093	−1.34522
$447$	−17.1652	−0.811886
$448$	6.58260	0.310998
$449$	25.3616	1.19689	0.598443	−	0.801165i	$-0.295786\pi$
$449$	25.3616	1.19689	0.598443	+	0.801165i	$0.295786\pi$
$450$	−16.9477	−0.798922
$451$	12.4658	0.586990
$452$	−32.4047	−1.52419
$453$	−20.4263	−0.959710
$454$	31.5381	1.48016
$455$	−7.08804	−0.332292
$456$	−2.31725	−0.108515
$457$	18.0314	0.843475	0.421737	−	0.906718i	$-0.361420\pi$
$457$	18.0314	0.843475	0.421737	+	0.906718i	$0.361420\pi$
$458$	20.7225	0.968298
$459$	2.07474	0.0968406
$460$	−17.9182	−0.835440
$461$	36.6709	1.70793	0.853967	−	0.520327i	$-0.174190\pi$
$461$	36.6709	1.70793	0.853967	+	0.520327i	$0.174190\pi$
$462$	2.68599	0.124964
$463$	2.40420	0.111733	0.0558664	−	0.998438i	$-0.482208\pi$
$463$	2.40420	0.111733	0.0558664	+	0.998438i	$0.482208\pi$
$464$	19.1094	0.887133
$465$	−19.6843	−0.912836
$466$	37.9742	1.75912
$467$	1.61209	0.0745987	0.0372993	−	0.999304i	$-0.488125\pi$
$467$	1.61209	0.0745987	0.0372993	+	0.999304i	$0.488125\pi$
$468$	−3.50849	−0.162180
$469$	−7.63898	−0.352735
$470$	−2.44030	−0.112563
$471$	−0.158692	−0.00731216
$472$	−2.37549	−0.109341
$473$	5.21161	0.239630
$474$	25.2170	1.15825
$475$	60.1387	2.75935
$476$	3.79568	0.173975
$477$	−4.43646	−0.203132
$478$	−42.0054	−1.92128
$479$	−12.2014	−0.557498	−0.278749	−	0.960364i	$-0.589920\pi$
$479$	−12.2014	−0.557498	−0.278749	+	0.960364i	$0.589920\pi$
$480$	28.7206	1.31091
$481$	−3.26950	−0.149076
$482$	25.1278	1.14454
$483$	2.64993	0.120576
$484$	−16.6776	−0.758071
$485$	57.9805	2.63276
$486$	1.95690	0.0887670
$487$	−5.44246	−0.246621	−0.123311	−	0.992368i	$-0.539351\pi$
$487$	−5.44246	−0.246621	−0.123311	+	0.992368i	$0.539351\pi$
$488$	−1.42622	−0.0645618
$489$	−11.3437	−0.512980
$490$	7.23273	0.326741
$491$	11.6528	0.525884	0.262942	−	0.964812i	$-0.415307\pi$
$491$	11.6528	0.525884	0.262942	+	0.964812i	$0.415307\pi$
$492$	16.6154	0.749078
$493$	9.19466	0.414106
$494$	26.0601	1.17250
$495$	5.07304	0.228016
$496$	22.9648	1.03115
$497$	7.55733	0.338993
$498$	−22.0269	−0.987049
$499$	44.2836	1.98241	0.991204	−	0.132344i	$-0.0422503\pi$
$499$	44.2836	1.98241	0.991204	+	0.132344i	$0.0422503\pi$
$500$	−24.7511	−1.10690
$501$	12.8720	0.575080
$502$	−20.9093	−0.933227
$503$	7.32728	0.326707	0.163354	−	0.986568i	$-0.447769\pi$
$503$	7.32728	0.326707	0.163354	+	0.986568i	$0.447769\pi$
$504$	−0.333702	−0.0148643
$505$	26.6768	1.18710
$506$	7.11770	0.316421
$507$	9.32221	0.414014
$508$	−4.55717	−0.202192
$509$	32.1056	1.42306	0.711529	−	0.702657i	$-0.248003\pi$
$509$	32.1056	1.42306	0.711529	+	0.702657i	$0.248003\pi$
$510$	15.0060	0.664478
$511$	0.633412	0.0280205
$512$	−30.6293	−1.35364
$513$	−6.94405	−0.306587
$514$	−27.9380	−1.23229
$515$	63.5217	2.79910
$516$	6.94644	0.305800
$517$	0.463101	0.0203672
$518$	3.33624	0.146586
$519$	−4.16669	−0.182897
$520$	2.36529	0.103725
$521$	0.948137	0.0415386	0.0207693	−	0.999784i	$-0.493388\pi$
$521$	0.948137	0.0415386	0.0207693	+	0.999784i	$0.493388\pi$
$522$	8.67244	0.379582
$523$	−10.7711	−0.470989	−0.235495	−	0.971876i	$-0.575671\pi$
$523$	−10.7711	−0.470989	−0.235495	+	0.971876i	$0.575671\pi$
$524$	10.9513	0.478412
$525$	8.66046	0.377973
$526$	−1.57415	−0.0686360
$527$	11.0497	0.481332
$528$	−5.91850	−0.257569
$529$	−15.9779	−0.694689
$530$	−32.0877	−1.39380
$531$	−7.11860	−0.308921
$532$	−12.7040	−0.550787
$533$	17.4171	0.754420
$534$	9.24597	0.400112
$535$	6.66476	0.288143
$536$	2.54914	0.110106
$537$	13.2993	0.573908
$538$	−53.5282	−2.30777
$539$	−1.37257	−0.0591209
$540$	6.76175	0.290979
$541$	−17.3420	−0.745590	−0.372795	−	0.927914i	$-0.621601\pi$
$541$	−17.3420	−0.745590	−0.372795	+	0.927914i	$0.621601\pi$
$542$	−39.5862	−1.70037
$543$	−5.71679	−0.245331
$544$	−16.1222	−0.691234
$545$	14.1270	0.605134
$546$	3.75287	0.160608
$547$	−18.8804	−0.807267	−0.403633	−	0.914921i	$-0.632253\pi$
$547$	−18.8804	−0.807267	−0.403633	+	0.914921i	$0.632253\pi$
$548$	−5.63151	−0.240566
$549$	−4.27392	−0.182407
$550$	23.2619	0.991893
$551$	−30.7741	−1.31102
$552$	−0.884289	−0.0376378
$553$	−12.8862	−0.547975
$554$	−21.5260	−0.914552
$555$	6.30116	0.267470
$556$	10.9143	0.462869
$557$	24.2880	1.02911	0.514557	−	0.857456i	$-0.327956\pi$
$557$	24.2880	1.02911	0.514557	+	0.857456i	$0.327956\pi$
$558$	10.4221	0.441203
$559$	7.28165	0.307981
$560$	−15.9371	−0.673464
$561$	−2.84773	−0.120231
$562$	17.1141	0.721913
$563$	8.04390	0.339010	0.169505	−	0.985529i	$-0.445783\pi$
$563$	8.04390	0.339010	0.169505	+	0.985529i	$0.445783\pi$
$564$	0.617258	0.0259913
$565$	65.4657	2.75416
$566$	−5.96285	−0.250637
$567$	−1.00000	−0.0419961
$568$	−2.52190	−0.105816
$569$	5.57506	0.233718	0.116859	−	0.993148i	$-0.462717\pi$
$569$	5.57506	0.233718	0.116859	+	0.993148i	$0.462717\pi$
$570$	−50.2245	−2.10367
$571$	10.4112	0.435693	0.217847	−	0.975983i	$-0.430097\pi$
$571$	10.4112	0.435693	0.217847	+	0.975983i	$0.430097\pi$
$572$	4.81565	0.201353
$573$	−1.00000	−0.0417756
$574$	−17.7727	−0.741817
$575$	22.9496	0.957066
$576$	−6.58260	−0.274275
$577$	−29.9770	−1.24796	−0.623979	−	0.781441i	$-0.714485\pi$
$577$	−29.9770	−1.24796	−0.623979	+	0.781441i	$0.714485\pi$
$578$	24.8438	1.03337
$579$	19.5494	0.812445
$580$	29.9661	1.24428
$581$	11.2560	0.466977
$582$	−30.6986	−1.27250
$583$	6.08937	0.252196
$584$	−0.211371	−0.00874659
$585$	7.08804	0.293054
$586$	26.7935	1.10683
$587$	5.22993	0.215862	0.107931	−	0.994158i	$-0.465577\pi$
$587$	5.22993	0.215862	0.107931	+	0.994158i	$0.465577\pi$
$588$	−1.82947	−0.0754463
$589$	−36.9828	−1.52385
$590$	−51.4869	−2.11968
$591$	4.52178	0.186001
$592$	−7.35130	−0.302137
$593$	−8.70083	−0.357300	−0.178650	−	0.983913i	$-0.557173\pi$
$593$	−8.70083	−0.357300	−0.178650	+	0.983913i	$0.557173\pi$
$594$	−2.68599	−0.110208
$595$	−7.66825	−0.314368
$596$	31.4033	1.28633
$597$	−10.6775	−0.437001
$598$	9.94484	0.406675
$599$	10.6752	0.436178	0.218089	−	0.975929i	$-0.430018\pi$
$599$	10.6752	0.436178	0.218089	+	0.975929i	$0.430018\pi$
$600$	−2.89001	−0.117984
$601$	−14.5972	−0.595433	−0.297716	−	0.954654i	$-0.596225\pi$
$601$	−14.5972	−0.595433	−0.297716	+	0.954654i	$0.596225\pi$
$602$	−7.43029	−0.302836
$603$	7.63898	0.311083
$604$	37.3693	1.52054
$605$	33.6930	1.36981
$606$	−14.1244	−0.573765
$607$	13.9165	0.564852	0.282426	−	0.959289i	$-0.408861\pi$
$607$	13.9165	0.564852	0.282426	+	0.959289i	$0.408861\pi$
$608$	53.9602	2.18838
$609$	−4.43171	−0.179582
$610$	−30.9121	−1.25160
$611$	0.647044	0.0261766
$612$	−3.79568	−0.153431
$613$	24.0981	0.973314	0.486657	−	0.873593i	$-0.338216\pi$
$613$	24.0981	0.973314	0.486657	+	0.873593i	$0.338216\pi$
$614$	−1.01456	−0.0409444
$615$	−33.5673	−1.35356
$616$	0.458031	0.0184546
$617$	−11.2395	−0.452484	−0.226242	−	0.974071i	$-0.572644\pi$
$617$	−11.2395	−0.452484	−0.226242	+	0.974071i	$0.572644\pi$
$618$	−33.6325	−1.35290
$619$	3.30478	0.132830	0.0664152	−	0.997792i	$-0.478844\pi$
$619$	3.30478	0.132830	0.0664152	+	0.997792i	$0.478844\pi$
$620$	36.0118	1.44627
$621$	−2.64993	−0.106338
$622$	−1.01026	−0.0405079
$623$	−4.72479	−0.189295
$624$	−8.26931	−0.331037
$625$	6.70126	0.268050
$626$	−42.7118	−1.70711
$627$	9.53122	0.380640
$628$	0.290324	0.0115852
$629$	−3.53714	−0.141035
$630$	−7.23273	−0.288159
$631$	2.38073	0.0947755	0.0473878	−	0.998877i	$-0.484910\pi$
$631$	2.38073	0.0947755	0.0473878	+	0.998877i	$0.484910\pi$
$632$	4.30014	0.171050
$633$	12.6823	0.504078
$634$	−20.1222	−0.799156
$635$	9.20666	0.365355
$636$	8.11639	0.321836
$637$	−1.91776	−0.0759843
$638$	−11.9036	−0.471266
$639$	−7.55733	−0.298963
$640$	9.83106	0.388607
$641$	−10.2015	−0.402936	−0.201468	−	0.979495i	$-0.564571\pi$
$641$	−10.2015	−0.402936	−0.201468	+	0.979495i	$0.564571\pi$
$642$	−3.52875	−0.139269
$643$	−30.6371	−1.20821	−0.604105	−	0.796905i	$-0.706469\pi$
$643$	−30.6371	−1.20821	−0.604105	+	0.796905i	$0.706469\pi$
$644$	−4.84799	−0.191037
$645$	−14.0336	−0.552572
$646$	28.1933	1.10925
$647$	15.4893	0.608946	0.304473	−	0.952521i	$-0.401520\pi$
$647$	15.4893	0.608946	0.304473	+	0.952521i	$0.401520\pi$
$648$	0.333702	0.0131091
$649$	9.77080	0.383537
$650$	32.5015	1.27482
$651$	−5.32582	−0.208735
$652$	20.7530	0.812750
$653$	−44.9163	−1.75771	−0.878856	−	0.477087i	$-0.841693\pi$
$653$	−44.9163	−1.75771	−0.878856	+	0.477087i	$0.841693\pi$
$654$	−7.47974	−0.292481
$655$	−22.1245	−0.864476
$656$	39.1615	1.52900
$657$	−0.633412	−0.0247117
$658$	−0.660253	−0.0257393
$659$	15.5951	0.607497	0.303749	−	0.952752i	$-0.401762\pi$
$659$	15.5951	0.607497	0.303749	+	0.952752i	$0.401762\pi$
$660$	−9.28099	−0.361262
$661$	−11.8425	−0.460621	−0.230311	−	0.973117i	$-0.573974\pi$
$661$	−11.8425	−0.460621	−0.230311	+	0.973117i	$0.573974\pi$
$662$	−19.4788	−0.757065
$663$	−3.97885	−0.154526
$664$	−3.75615	−0.145767
$665$	25.6653	0.995256
$666$	−3.33624	−0.129277
$667$	−11.7437	−0.454720
$668$	−23.5491	−0.911141
$669$	−14.5175	−0.561277
$670$	55.2507	2.13452
$671$	5.86627	0.226465
$672$	7.77071	0.299762
$673$	−39.0528	−1.50537	−0.752687	−	0.658378i	$-0.771243\pi$
$673$	−39.0528	−1.50537	−0.752687	+	0.658378i	$0.771243\pi$
$674$	46.4468	1.78907
$675$	−8.66046	−0.333341
$676$	−17.0547	−0.655952
$677$	−44.0940	−1.69467	−0.847336	−	0.531058i	$-0.821795\pi$
$677$	−44.0940	−1.69467	−0.847336	+	0.531058i	$0.821795\pi$
$678$	−34.6618	−1.33118
$679$	15.6874	0.602025
$680$	2.55891	0.0981298
$681$	16.1163	0.617579
$682$	−14.3051	−0.547771
$683$	21.3325	0.816267	0.408133	−	0.912922i	$-0.366180\pi$
$683$	21.3325	0.816267	0.408133	+	0.912922i	$0.366180\pi$
$684$	12.7040	0.485748
$685$	11.3771	0.434696
$686$	1.95690	0.0747150
$687$	10.5894	0.404012
$688$	16.3724	0.624192
$689$	8.50805	0.324131
$690$	−19.1663	−0.729647
$691$	−43.7536	−1.66447	−0.832233	−	0.554426i	$-0.812938\pi$
$691$	−43.7536	−1.66447	−0.832233	+	0.554426i	$0.812938\pi$
$692$	7.62285	0.289777
$693$	1.37257	0.0521397
$694$	−33.8557	−1.28515
$695$	−22.0497	−0.836392
$696$	1.47887	0.0560565
$697$	18.8429	0.713725
$698$	−36.9474	−1.39848
$699$	19.4052	0.733973
$700$	−15.8441	−0.598850
$701$	36.7290	1.38724	0.693618	−	0.720343i	$-0.256015\pi$
$701$	36.7290	1.38724	0.693618	+	0.720343i	$0.256015\pi$
$702$	−3.75287	−0.141643
$703$	11.8386	0.446502
$704$	9.03509	0.340523
$705$	−1.24702	−0.0469655
$706$	−14.8896	−0.560378
$707$	7.21773	0.271451
$708$	13.0233	0.489445
$709$	−16.4956	−0.619507	−0.309753	−	0.950817i	$-0.600246\pi$
$709$	−16.4956	−0.619507	−0.309753	+	0.950817i	$0.600246\pi$
$710$	−54.6601	−2.05136
$711$	12.8862	0.483269
$712$	1.57667	0.0590884
$713$	−14.1131	−0.528538
$714$	4.06007	0.151944
$715$	−9.72885	−0.363838
$716$	−24.3308	−0.909284
$717$	−21.4653	−0.801634
$718$	−7.93904	−0.296282
$719$	−32.7336	−1.22076	−0.610378	−	0.792110i	$-0.708982\pi$
$719$	−32.7336	−1.22076	−0.610378	+	0.792110i	$0.708982\pi$
$720$	15.9371	0.593940
$721$	17.1866	0.640061
$722$	−57.1805	−2.12804
$723$	12.8406	0.477547
$724$	10.4587	0.388696
$725$	−38.3807	−1.42542
$726$	−17.8392	−0.662076
$727$	44.7911	1.66121	0.830605	−	0.556862i	$-0.187995\pi$
$727$	44.7911	1.66121	0.830605	+	0.556862i	$0.187995\pi$
$728$	0.639960	0.0237185
$729$	1.00000	0.0370370
$730$	−4.58130	−0.169561
$731$	7.87771	0.291368
$732$	7.81903	0.289000
$733$	8.14502	0.300843	0.150422	−	0.988622i	$-0.451937\pi$
$733$	8.14502	0.300843	0.150422	+	0.988622i	$0.451937\pi$
$734$	40.9141	1.51017
$735$	3.69601	0.136329
$736$	20.5919	0.759026
$737$	−10.4851	−0.386222
$738$	17.7727	0.654221
$739$	47.1735	1.73530	0.867652	−	0.497172i	$-0.165628\pi$
$739$	47.1735	1.73530	0.867652	+	0.497172i	$0.165628\pi$
$740$	−11.5278	−0.423771
$741$	13.3170	0.489212
$742$	−8.68173	−0.318716
$743$	34.9665	1.28280	0.641398	−	0.767208i	$-0.278355\pi$
$743$	34.9665	1.28280	0.641398	+	0.767208i	$0.278355\pi$
$744$	1.77724	0.0651567
$745$	−63.4426	−2.32436
$746$	−48.7254	−1.78396
$747$	−11.2560	−0.411835
$748$	5.20985	0.190491
$749$	1.80323	0.0658887
$750$	−26.4751	−0.966734
$751$	26.9193	0.982300	0.491150	−	0.871075i	$-0.336577\pi$
$751$	26.9193	0.982300	0.491150	+	0.871075i	$0.336577\pi$
$752$	1.45484	0.0530527
$753$	−10.6849	−0.389379
$754$	−16.6316	−0.605688
$755$	−75.4956	−2.74757
$756$	1.82947	0.0665373
$757$	37.7422	1.37176	0.685881	−	0.727714i	$-0.259417\pi$
$757$	37.7422	1.37176	0.685881	+	0.727714i	$0.259417\pi$
$758$	17.5571	0.637704
$759$	3.63723	0.132023
$760$	−8.56455	−0.310669
$761$	−1.22056	−0.0442454	−0.0221227	−	0.999755i	$-0.507042\pi$
$761$	−1.22056	−0.0442454	−0.0221227	+	0.999755i	$0.507042\pi$
$762$	−4.87460	−0.176588
$763$	3.82223	0.138374
$764$	1.82947	0.0661881
$765$	7.66825	0.277246
$766$	39.3462	1.42163
$767$	13.6517	0.492936
$768$	−18.3704	−0.662884
$769$	13.4303	0.484308	0.242154	−	0.970238i	$-0.422146\pi$
$769$	13.4303	0.484308	0.242154	+	0.970238i	$0.422146\pi$
$770$	9.92745	0.357760
$771$	−14.2766	−0.514160
$772$	−35.7651	−1.28721
$773$	−5.68620	−0.204518	−0.102259	−	0.994758i	$-0.532607\pi$
$773$	−5.68620	−0.204518	−0.102259	+	0.994758i	$0.532607\pi$
$774$	7.43029	0.267076
$775$	−46.1240	−1.65682
$776$	−5.23490	−0.187922
$777$	1.70486	0.0611614
$778$	−36.3461	−1.30307
$779$	−63.0661	−2.25958
$780$	−12.9674	−0.464307
$781$	10.3730	0.371175
$782$	10.7589	0.384738
$783$	4.43171	0.158377
$784$	−4.31197	−0.153999
$785$	−0.586528	−0.0209341
$786$	11.7141	0.417830
$787$	−27.5259	−0.981191	−0.490596	−	0.871387i	$-0.663221\pi$
$787$	−27.5259	−0.981191	−0.490596	+	0.871387i	$0.663221\pi$
$788$	−8.27249	−0.294695
$789$	−0.804406	−0.0286376
$790$	93.2021	3.31598
$791$	17.7125	0.629786
$792$	−0.458031	−0.0162754
$793$	8.19634	0.291061
$794$	−15.2661	−0.541774
$795$	−16.3972	−0.581548
$796$	19.5342	0.692371
$797$	−43.7606	−1.55008	−0.775040	−	0.631912i	$-0.782270\pi$
$797$	−43.7606	−1.55008	−0.775040	+	0.631912i	$0.782270\pi$
$798$	−13.5888	−0.481040
$799$	0.700010	0.0247646
$800$	67.2979	2.37934
$801$	4.72479	0.166942
$802$	−47.6333	−1.68199
$803$	0.869404	0.0306806
$804$	−13.9753	−0.492871
$805$	9.79417	0.345199
$806$	−19.9871	−0.704015
$807$	−27.3535	−0.962889
$808$	−2.40857	−0.0847333
$809$	31.9967	1.12494	0.562472	−	0.826817i	$-0.309851\pi$
$809$	31.9967	1.12494	0.562472	+	0.826817i	$0.309851\pi$
$810$	7.23273	0.254132
$811$	−0.501485	−0.0176095	−0.00880476	−	0.999961i	$-0.502803\pi$
$811$	−0.501485	−0.0176095	−0.00880476	+	0.999961i	$0.502803\pi$
$812$	8.10771	0.284525
$813$	−20.2290	−0.709461
$814$	4.57924	0.160502
$815$	−41.9264	−1.46862
$816$	−8.94622	−0.313180
$817$	−26.3663	−0.922440
$818$	75.2779	2.63203
$819$	1.91776	0.0670118
$820$	61.4105	2.14455
$821$	−8.61707	−0.300738	−0.150369	−	0.988630i	$-0.548046\pi$
$821$	−8.61707	−0.300738	−0.150369	+	0.988630i	$0.548046\pi$
$822$	−6.02377	−0.210103
$823$	39.5377	1.37820	0.689098	−	0.724668i	$-0.258007\pi$
$823$	39.5377	1.37820	0.689098	+	0.724668i	$0.258007\pi$
$824$	−5.73520	−0.199795
$825$	11.8871	0.413856
$826$	−13.9304	−0.484701
$827$	−27.9158	−0.970728	−0.485364	−	0.874312i	$-0.661313\pi$
$827$	−27.9158	−0.970728	−0.485364	+	0.874312i	$0.661313\pi$
$828$	4.84799	0.168479
$829$	−31.9274	−1.10888	−0.554441	−	0.832223i	$-0.687068\pi$
$829$	−31.9274	−1.10888	−0.554441	+	0.832223i	$0.687068\pi$
$830$	−81.4116	−2.82584
$831$	−11.0000	−0.381587
$832$	12.6238	0.437652
$833$	−2.07474	−0.0718855
$834$	11.6745	0.404256
$835$	47.5751	1.64641
$836$	−17.4371	−0.603075
$837$	5.32582	0.184087
$838$	−19.3563	−0.668652
$839$	−7.62505	−0.263246	−0.131623	−	0.991300i	$-0.542019\pi$
$839$	−7.62505	−0.263246	−0.131623	+	0.991300i	$0.542019\pi$
$840$	−1.23337	−0.0425551
$841$	−9.35991	−0.322756
$842$	−8.99236	−0.309897
$843$	8.74547	0.301210
$844$	−23.2020	−0.798646
$845$	34.4549	1.18529
$846$	0.660253	0.0226999
$847$	9.11604	0.313231
$848$	19.1299	0.656924
$849$	−3.04708	−0.104576
$850$	35.1621	1.20605
$851$	4.51776	0.154867
$852$	13.8259	0.473669
$853$	45.0571	1.54273	0.771363	−	0.636395i	$-0.219575\pi$
$853$	45.0571	1.54273	0.771363	+	0.636395i	$0.219575\pi$
$854$	−8.36366	−0.286198
$855$	−25.6653	−0.877733
$856$	−0.601743	−0.0205671
$857$	19.3631	0.661432	0.330716	−	0.943730i	$-0.392710\pi$
$857$	19.3631	0.661432	0.330716	+	0.943730i	$0.392710\pi$
$858$	5.15108	0.175855
$859$	−47.7045	−1.62766	−0.813829	−	0.581105i	$-0.802621\pi$
$859$	−47.7045	−1.62766	−0.813829	+	0.581105i	$0.802621\pi$
$860$	25.6741	0.875479
$861$	−9.08204	−0.309515
$862$	−42.6352	−1.45216
$863$	22.2933	0.758872	0.379436	−	0.925218i	$-0.376118\pi$
$863$	22.2933	0.758872	0.379436	+	0.925218i	$0.376118\pi$
$864$	−7.77071	−0.264365
$865$	−15.4001	−0.523619
$866$	−31.2227	−1.06099
$867$	12.6955	0.431160
$868$	9.74345	0.330714
$869$	−17.6872	−0.599997
$870$	32.0534	1.08671
$871$	−14.6497	−0.496386
$872$	−1.27549	−0.0431935
$873$	−15.6874	−0.530936
$874$	−36.0095	−1.21804
$875$	13.5291	0.457366
$876$	1.15881	0.0391526
$877$	24.6151	0.831194	0.415597	−	0.909549i	$-0.363573\pi$
$877$	24.6151	0.831194	0.415597	+	0.909549i	$0.363573\pi$
$878$	62.9311	2.12382
$879$	13.6918	0.461812
$880$	−21.8748	−0.737399
$881$	−0.394221	−0.0132817	−0.00664083	−	0.999978i	$-0.502114\pi$
$881$	−0.394221	−0.0132817	−0.00664083	+	0.999978i	$0.502114\pi$
$882$	−1.95690	−0.0658924
$883$	−27.8564	−0.937442	−0.468721	−	0.883346i	$-0.655285\pi$
$883$	−27.8564	−0.937442	−0.468721	+	0.883346i	$0.655285\pi$
$884$	7.27920	0.244826
$885$	−26.3104	−0.884414
$886$	61.2987	2.05937
$887$	−41.2461	−1.38491	−0.692455	−	0.721461i	$-0.743471\pi$
$887$	−41.2461	−1.38491	−0.692455	+	0.721461i	$0.743471\pi$
$888$	−0.568915	−0.0190915
$889$	2.49097	0.0835446
$890$	34.1732	1.14549
$891$	−1.37257	−0.0459829
$892$	26.5593	0.889272
$893$	−2.34290	−0.0784021
$894$	33.5906	1.12344
$895$	49.1544	1.64305
$896$	2.65991	0.0888615
$897$	5.08193	0.169681
$898$	−49.6302	−1.65618
$899$	23.6025	0.787188
$900$	15.8441	0.528136
$901$	9.20451	0.306647
$902$	−24.3943	−0.812241
$903$	−3.79696	−0.126355
$904$	−5.91072	−0.196588
$905$	−21.1293	−0.702362
$906$	39.9723	1.32799
$907$	−14.3202	−0.475496	−0.237748	−	0.971327i	$-0.576409\pi$
$907$	−14.3202	−0.475496	−0.237748	+	0.971327i	$0.576409\pi$
$908$	−29.4844	−0.978474
$909$	−7.21773	−0.239397
$910$	13.8706	0.459806
$911$	15.0465	0.498512	0.249256	−	0.968438i	$-0.419814\pi$
$911$	15.0465	0.498512	0.249256	+	0.968438i	$0.419814\pi$
$912$	29.9426	0.991497
$913$	15.4497	0.511309
$914$	−35.2858	−1.16715
$915$	−15.7964	−0.522214
$916$	−19.3731	−0.640105
$917$	−5.98606	−0.197677
$918$	−4.06007	−0.134002
$919$	−25.1408	−0.829319	−0.414660	−	0.909977i	$-0.636099\pi$
$919$	−25.1408	−0.829319	−0.414660	+	0.909977i	$0.636099\pi$
$920$	−3.26834	−0.107754
$921$	−0.518453	−0.0170836
$922$	−71.7614	−2.36334
$923$	14.4931	0.477047
$924$	−2.51109	−0.0826087
$925$	14.7649	0.485465
$926$	−4.70479	−0.154609
$927$	−17.1866	−0.564481
$928$	−34.4376	−1.13047
$929$	−16.1312	−0.529248	−0.264624	−	0.964352i	$-0.585248\pi$
$929$	−16.1312	−0.529248	−0.264624	+	0.964352i	$0.585248\pi$
$930$	38.5202	1.26313
$931$	6.94405	0.227582
$932$	−35.5014	−1.16289
$933$	−0.516257	−0.0169015
$934$	−3.15471	−0.103225
$935$	−10.5252	−0.344212
$936$	−0.639960	−0.0209177
$937$	−28.7188	−0.938201	−0.469101	−	0.883145i	$-0.655422\pi$
$937$	−28.7188	−0.938201	−0.469101	+	0.883145i	$0.655422\pi$
$938$	14.9487	0.488094
$939$	−21.8262	−0.712271
$940$	2.28139	0.0744107
$941$	−44.5358	−1.45182	−0.725912	−	0.687787i	$-0.758582\pi$
$941$	−44.5358	−1.45182	−0.725912	+	0.687787i	$0.758582\pi$
$942$	0.310546	0.0101181
$943$	−24.0668	−0.783723
$944$	30.6952	0.999044
$945$	−3.69601	−0.120231
$946$	−10.1986	−0.331586
$947$	−14.5474	−0.472728	−0.236364	−	0.971665i	$-0.575956\pi$
$947$	−14.5474	−0.472728	−0.236364	+	0.971665i	$0.575956\pi$
$948$	−23.5749	−0.765677
$949$	1.21473	0.0394318
$950$	−117.686	−3.81823
$951$	−10.2827	−0.333439
$952$	0.692345	0.0224390
$953$	27.2840	0.883817	0.441908	−	0.897060i	$-0.354302\pi$
$953$	27.2840	0.883817	0.441908	+	0.897060i	$0.354302\pi$
$954$	8.68173	0.281081
$955$	−3.69601	−0.119600
$956$	39.2701	1.27009
$957$	−6.08285	−0.196631
$958$	23.8771	0.771433
$959$	3.07821	0.0994007
$960$	−24.3293	−0.785225
$961$	−2.63566	−0.0850212
$962$	6.39810	0.206283
$963$	−1.80323	−0.0581083
$964$	−23.4915	−0.756612
$965$	72.2546	2.32596
$966$	−5.18567	−0.166846
$967$	−3.58901	−0.115415	−0.0577074	−	0.998334i	$-0.518379\pi$
$967$	−3.58901	−0.115415	−0.0577074	+	0.998334i	$0.518379\pi$
$968$	−3.04204	−0.0977750
$969$	14.4071	0.462823
$970$	−113.462	−3.64306
$971$	−49.5389	−1.58978	−0.794890	−	0.606754i	$-0.792471\pi$
$971$	−49.5389	−1.58978	−0.794890	+	0.606754i	$0.792471\pi$
$972$	−1.82947	−0.0586804
$973$	−5.96581	−0.191255
$974$	10.6504	0.341260
$975$	16.6087	0.531903
$976$	18.4290	0.589899
$977$	−10.1391	−0.324378	−0.162189	−	0.986760i	$-0.551855\pi$
$977$	−10.1391	−0.324378	−0.162189	+	0.986760i	$0.551855\pi$
$978$	22.1985	0.709831
$979$	−6.48512	−0.207265
$980$	−6.76175	−0.215996
$981$	−3.82223	−0.122035
$982$	−22.8034	−0.727687
$983$	−42.2642	−1.34802	−0.674010	−	0.738722i	$-0.735429\pi$
$983$	−42.2642	−1.34802	−0.674010	+	0.738722i	$0.735429\pi$
$984$	3.03070	0.0966151
$985$	16.7125	0.532506
$986$	−17.9931	−0.573016
$987$	−0.337396	−0.0107394
$988$	−24.3631	−0.775094
$989$	−10.0617	−0.319943
$990$	−9.92745	−0.315515
$991$	−44.6634	−1.41878	−0.709389	−	0.704817i	$-0.751029\pi$
$991$	−44.6634	−1.41878	−0.709389	+	0.704817i	$0.751029\pi$
$992$	−41.3854	−1.31399
$993$	−9.95388	−0.315877
$994$	−14.7890	−0.469078
$995$	−39.4641	−1.25110
$996$	20.5926	0.652500
$997$	54.7745	1.73473	0.867363	−	0.497677i	$-0.165813\pi$
$997$	54.7745	1.73473	0.867363	+	0.497677i	$0.165813\pi$
$998$	−86.6588	−2.74314
$999$	−1.70486	−0.0539393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.j.1.5	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.j.1.5	✓	26	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-1.95690 q^{2} -1.00000 q^{3} +1.82947 q^{4} -3.69601 q^{5} +1.95690 q^{6} -1.00000 q^{7} +0.333702 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.95690 q^{2} -1.00000 q^{3} +1.82947 q^{4} -3.69601 q^{5} +1.95690 q^{6} -1.00000 q^{7} +0.333702 q^{8} +1.00000 q^{9} +7.23273 q^{10} -1.37257 q^{11} -1.82947 q^{12} -1.91776 q^{13} +1.95690 q^{14} +3.69601 q^{15} -4.31197 q^{16} -2.07474 q^{17} -1.95690 q^{18} +6.94405 q^{19} -6.76175 q^{20} +1.00000 q^{21} +2.68599 q^{22} +2.64993 q^{23} -0.333702 q^{24} +8.66046 q^{25} +3.75287 q^{26} -1.00000 q^{27} -1.82947 q^{28} -4.43171 q^{29} -7.23273 q^{30} -5.32582 q^{31} +7.77071 q^{32} +1.37257 q^{33} +4.06007 q^{34} +3.69601 q^{35} +1.82947 q^{36} +1.70486 q^{37} -13.5888 q^{38} +1.91776 q^{39} -1.23337 q^{40} -9.08204 q^{41} -1.95690 q^{42} -3.79696 q^{43} -2.51109 q^{44} -3.69601 q^{45} -5.18567 q^{46} -0.337396 q^{47} +4.31197 q^{48} +1.00000 q^{49} -16.9477 q^{50} +2.07474 q^{51} -3.50849 q^{52} -4.43646 q^{53} +1.95690 q^{54} +5.07304 q^{55} -0.333702 q^{56} -6.94405 q^{57} +8.67244 q^{58} -7.11860 q^{59} +6.76175 q^{60} -4.27392 q^{61} +10.4221 q^{62} -1.00000 q^{63} -6.58260 q^{64} +7.08804 q^{65} -2.68599 q^{66} +7.63898 q^{67} -3.79568 q^{68} -2.64993 q^{69} -7.23273 q^{70} -7.55733 q^{71} +0.333702 q^{72} -0.633412 q^{73} -3.33624 q^{74} -8.66046 q^{75} +12.7040 q^{76} +1.37257 q^{77} -3.75287 q^{78} +12.8862 q^{79} +15.9371 q^{80} +1.00000 q^{81} +17.7727 q^{82} -11.2560 q^{83} +1.82947 q^{84} +7.66825 q^{85} +7.43029 q^{86} +4.43171 q^{87} -0.458031 q^{88} +4.72479 q^{89} +7.23273 q^{90} +1.91776 q^{91} +4.84799 q^{92} +5.32582 q^{93} +0.660253 q^{94} -25.6653 q^{95} -7.77071 q^{96} -15.6874 q^{97} -1.95690 q^{98} -1.37257 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) \) 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) \) 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9 - q^10 + 13 * q^11 - 34 * q^12 - q^13 - 2 * q^15 + 54 * q^16 + q^19 - 22 * q^20 + 26 * q^21 + 17 * q^22 - 3 * q^23 + 48 * q^25 + 6 * q^26 - 26 * q^27 - 34 * q^28 + 23 * q^29 + q^30 + 18 * q^31 + 10 * q^32 - 13 * q^33 - 19 * q^34 - 2 * q^35 + 34 * q^36 + 23 * q^37 - 15 * q^38 + q^39 + 14 * q^40 - 4 * q^41 + 5 * q^43 + 60 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^47 - 54 * q^48 + 26 * q^49 + 26 * q^50 + 19 * q^52 + 31 * q^53 + 41 * q^55 - q^57 + 19 * q^58 - 2 * q^59 + 22 * q^60 - 2 * q^61 - 35 * q^62 - 26 * q^63 + 132 * q^64 + 40 * q^65 - 17 * q^66 + 47 * q^67 - 60 * q^68 + 3 * q^69 + q^70 + 16 * q^71 - 23 * q^73 + 34 * q^74 - 48 * q^75 + 72 * q^76 - 13 * q^77 - 6 * q^78 + 14 * q^79 - 21 * q^80 + 26 * q^81 + 60 * q^82 - 4 * q^83 + 34 * q^84 + 36 * q^85 + 21 * q^86 - 23 * q^87 + 67 * q^88 + 14 * q^89 - q^90 + q^91 + 20 * q^92 - 18 * q^93 + 58 * q^94 - 4 * q^95 - 10 * q^96 + 48 * q^97 + 13 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more