LMFDB - Embedded newform 4235.2.a.y.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.173513.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 3x^{2} + 3x - 1 $ x^5 - 2x^4 - 5x^3 + 3x^2 + 3x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.812660$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23053 q^{2} +2.39311 q^{3} +2.97525 q^{4} -1.00000 q^{5} -5.33790 q^{6} +1.00000 q^{7} -2.17531 q^{8} +2.72699 q^{9} +O(q^{10})$	\(q-2.23053 q^{2} +2.39311 q^{3} +2.97525 q^{4} -1.00000 q^{5} -5.33790 q^{6} +1.00000 q^{7} -2.17531 q^{8} +2.72699 q^{9} +2.23053 q^{10} +7.12010 q^{12} -2.48205 q^{13} -2.23053 q^{14} -2.39311 q^{15} -1.09840 q^{16} -4.59486 q^{17} -6.08262 q^{18} -6.44696 q^{19} -2.97525 q^{20} +2.39311 q^{21} +3.74472 q^{23} -5.20577 q^{24} +1.00000 q^{25} +5.53629 q^{26} -0.653344 q^{27} +2.97525 q^{28} +5.59150 q^{29} +5.33790 q^{30} +7.48276 q^{31} +6.80064 q^{32} +10.2490 q^{34} -1.00000 q^{35} +8.11347 q^{36} +2.42684 q^{37} +14.3801 q^{38} -5.93984 q^{39} +2.17531 q^{40} -1.74136 q^{41} -5.33790 q^{42} -4.05760 q^{43} -2.72699 q^{45} -8.35270 q^{46} +10.9512 q^{47} -2.62859 q^{48} +1.00000 q^{49} -2.23053 q^{50} -10.9960 q^{51} -7.38472 q^{52} -8.45098 q^{53} +1.45730 q^{54} -2.17531 q^{56} -15.4283 q^{57} -12.4720 q^{58} -13.0244 q^{59} -7.12010 q^{60} +1.25223 q^{61} -16.6905 q^{62} +2.72699 q^{63} -12.9722 q^{64} +2.48205 q^{65} -2.18239 q^{67} -13.6709 q^{68} +8.96154 q^{69} +2.23053 q^{70} +0.903671 q^{71} -5.93206 q^{72} -0.771063 q^{73} -5.41314 q^{74} +2.39311 q^{75} -19.1813 q^{76} +13.2490 q^{78} -9.68456 q^{79} +1.09840 q^{80} -9.74450 q^{81} +3.88414 q^{82} -4.58420 q^{83} +7.12010 q^{84} +4.59486 q^{85} +9.05057 q^{86} +13.3811 q^{87} -3.91301 q^{89} +6.08262 q^{90} -2.48205 q^{91} +11.1415 q^{92} +17.9071 q^{93} -24.4269 q^{94} +6.44696 q^{95} +16.2747 q^{96} -17.9552 q^{97} -2.23053 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} + 5 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 + 5 * q^7 + 6 * q^8 + 3 * q^9	$ 5 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} + 5 q^{7} + 6 q^{8} + 3 q^{9} + 2 q^{10} + 11 q^{12} - 12 q^{13} - 2 q^{14} + 2 q^{15} + 2 q^{16} - 14 q^{17} - 7 q^{18} - 9 q^{19} - 4 q^{20} - 2 q^{21} + 17 q^{23} - 6 q^{24} + 5 q^{25} - 11 q^{26} - 11 q^{27} + 4 q^{28} - 3 q^{29} + 5 q^{30} + 2 q^{31} + 5 q^{32} + 16 q^{34} - 5 q^{35} - 15 q^{36} + 4 q^{37} - 11 q^{38} - 2 q^{39} - 6 q^{40} + 15 q^{41} - 5 q^{42} - 4 q^{43} - 3 q^{45} + 10 q^{46} - 2 q^{47} - 10 q^{48} + 5 q^{49} - 2 q^{50} + 18 q^{51} - 4 q^{52} + 6 q^{53} - 4 q^{54} + 6 q^{56} - 32 q^{58} - 6 q^{59} - 11 q^{60} - 20 q^{61} - 21 q^{62} + 3 q^{63} - 26 q^{64} + 12 q^{65} + 3 q^{67} - 5 q^{68} + 2 q^{70} - 6 q^{71} - 34 q^{72} - 11 q^{73} + 15 q^{74} - 2 q^{75} - 47 q^{76} + 31 q^{78} - 19 q^{79} - 2 q^{80} + 33 q^{81} - 8 q^{83} + 11 q^{84} + 14 q^{85} + 27 q^{86} + 30 q^{87} + q^{89} + 7 q^{90} - 12 q^{91} + 44 q^{92} + 3 q^{93} - 28 q^{94} + 9 q^{95} + 4 q^{96} - 7 q^{97} - 2 q^{98}+O(q^{100}) $ 5 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 + 5 * q^7 + 6 * q^8 + 3 * q^9 + 2 * q^10 + 11 * q^12 - 12 * q^13 - 2 * q^14 + 2 * q^15 + 2 * q^16 - 14 * q^17 - 7 * q^18 - 9 * q^19 - 4 * q^20 - 2 * q^21 + 17 * q^23 - 6 * q^24 + 5 * q^25 - 11 * q^26 - 11 * q^27 + 4 * q^28 - 3 * q^29 + 5 * q^30 + 2 * q^31 + 5 * q^32 + 16 * q^34 - 5 * q^35 - 15 * q^36 + 4 * q^37 - 11 * q^38 - 2 * q^39 - 6 * q^40 + 15 * q^41 - 5 * q^42 - 4 * q^43 - 3 * q^45 + 10 * q^46 - 2 * q^47 - 10 * q^48 + 5 * q^49 - 2 * q^50 + 18 * q^51 - 4 * q^52 + 6 * q^53 - 4 * q^54 + 6 * q^56 - 32 * q^58 - 6 * q^59 - 11 * q^60 - 20 * q^61 - 21 * q^62 + 3 * q^63 - 26 * q^64 + 12 * q^65 + 3 * q^67 - 5 * q^68 + 2 * q^70 - 6 * q^71 - 34 * q^72 - 11 * q^73 + 15 * q^74 - 2 * q^75 - 47 * q^76 + 31 * q^78 - 19 * q^79 - 2 * q^80 + 33 * q^81 - 8 * q^83 + 11 * q^84 + 14 * q^85 + 27 * q^86 + 30 * q^87 + q^89 + 7 * q^90 - 12 * q^91 + 44 * q^92 + 3 * q^93 - 28 * q^94 + 9 * q^95 + 4 * q^96 - 7 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.23053	−1.57722	−0.788610	−	0.614894i	$-0.789199\pi$
$2$	−2.23053	−1.57722	−0.788610	+	0.614894i	$0.789199\pi$
$3$	2.39311	1.38166	0.690832	−	0.723015i	$-0.257244\pi$
$3$	2.39311	1.38166	0.690832	+	0.723015i	$0.257244\pi$
$4$	2.97525	1.48762
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−5.33790	−2.17919
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.17531	−0.769090
$9$	2.72699	0.908997
$10$	2.23053	0.705354
$11$	0	0
$11$	0	0
$12$	7.12010	2.05540
$13$	−2.48205	−0.688398	−0.344199	−	0.938897i	$-0.611849\pi$
$13$	−2.48205	−0.688398	−0.344199	+	0.938897i	$0.611849\pi$
$14$	−2.23053	−0.596133
$15$	−2.39311	−0.617899
$16$	−1.09840	−0.274600
$17$	−4.59486	−1.11442	−0.557209	−	0.830372i	$-0.688128\pi$
$17$	−4.59486	−1.11442	−0.557209	+	0.830372i	$0.688128\pi$
$18$	−6.08262	−1.43369
$19$	−6.44696	−1.47903	−0.739517	−	0.673138i	$-0.764946\pi$
$19$	−6.44696	−1.47903	−0.739517	+	0.673138i	$0.764946\pi$
$20$	−2.97525	−0.665286
$21$	2.39311	0.522220
$22$	0	0
$23$	3.74472	0.780828	0.390414	−	0.920639i	$-0.372332\pi$
$23$	3.74472	0.780828	0.390414	+	0.920639i	$0.372332\pi$
$24$	−5.20577	−1.06262
$25$	1.00000	0.200000
$26$	5.53629	1.08576
$27$	−0.653344	−0.125736
$28$	2.97525	0.562269
$29$	5.59150	1.03832	0.519158	−	0.854679i	$-0.326246\pi$
$29$	5.59150	1.03832	0.519158	+	0.854679i	$0.326246\pi$
$30$	5.33790	0.974563
$31$	7.48276	1.34394	0.671971	−	0.740577i	$-0.265448\pi$
$31$	7.48276	1.34394	0.671971	+	0.740577i	$0.265448\pi$
$32$	6.80064	1.20219
$33$	0	0
$34$	10.2490	1.75768
$35$	−1.00000	−0.169031
$36$	8.11347	1.35224
$37$	2.42684	0.398970	0.199485	−	0.979901i	$-0.436073\pi$
$37$	2.42684	0.398970	0.199485	+	0.979901i	$0.436073\pi$
$38$	14.3801	2.33276
$39$	−5.93984	−0.951135
$40$	2.17531	0.343947
$41$	−1.74136	−0.271954	−0.135977	−	0.990712i	$-0.543417\pi$
$41$	−1.74136	−0.271954	−0.135977	+	0.990712i	$0.543417\pi$
$42$	−5.33790	−0.823656
$43$	−4.05760	−0.618778	−0.309389	−	0.950936i	$-0.600124\pi$
$43$	−4.05760	−0.618778	−0.309389	+	0.950936i	$0.600124\pi$
$44$	0	0
$45$	−2.72699	−0.406516
$46$	−8.35270	−1.23154
$47$	10.9512	1.59740	0.798698	−	0.601732i	$-0.205522\pi$
$47$	10.9512	1.59740	0.798698	+	0.601732i	$0.205522\pi$
$48$	−2.62859	−0.379404
$49$	1.00000	0.142857
$50$	−2.23053	−0.315444
$51$	−10.9960	−1.53975
$52$	−7.38472	−1.02408
$53$	−8.45098	−1.16083	−0.580416	−	0.814320i	$-0.697110\pi$
$53$	−8.45098	−1.16083	−0.580416	+	0.814320i	$0.697110\pi$
$54$	1.45730	0.198314
$55$	0	0
$56$	−2.17531	−0.290689
$57$	−15.4283	−2.04353
$58$	−12.4720	−1.63765
$59$	−13.0244	−1.69563	−0.847814	−	0.530294i	$-0.822082\pi$
$59$	−13.0244	−1.69563	−0.847814	+	0.530294i	$0.822082\pi$
$60$	−7.12010	−0.919201
$61$	1.25223	0.160332	0.0801659	−	0.996782i	$-0.474455\pi$
$61$	1.25223	0.160332	0.0801659	+	0.996782i	$0.474455\pi$
$62$	−16.6905	−2.11969
$63$	2.72699	0.343568
$64$	−12.9722	−1.62152
$65$	2.48205	0.307861
$66$	0	0
$67$	−2.18239	−0.266621	−0.133311	−	0.991074i	$-0.542561\pi$
$67$	−2.18239	−0.266621	−0.133311	+	0.991074i	$0.542561\pi$
$68$	−13.6709	−1.65783
$69$	8.96154	1.07884
$70$	2.23053	0.266599
$71$	0.903671	0.107246	0.0536230	−	0.998561i	$-0.482923\pi$
$71$	0.903671	0.107246	0.0536230	+	0.998561i	$0.482923\pi$
$72$	−5.93206	−0.699100
$73$	−0.771063	−0.0902461	−0.0451230	−	0.998981i	$-0.514368\pi$
$73$	−0.771063	−0.0902461	−0.0451230	+	0.998981i	$0.514368\pi$
$74$	−5.41314	−0.629264
$75$	2.39311	0.276333
$76$	−19.1813	−2.20025
$77$	0	0
$78$	13.2490	1.50015
$79$	−9.68456	−1.08960	−0.544799	−	0.838567i	$-0.683394\pi$
$79$	−9.68456	−1.08960	−0.544799	+	0.838567i	$0.683394\pi$
$80$	1.09840	0.122805
$81$	−9.74450	−1.08272
$82$	3.88414	0.428932
$83$	−4.58420	−0.503182	−0.251591	−	0.967834i	$-0.580954\pi$
$83$	−4.58420	−0.503182	−0.251591	+	0.967834i	$0.580954\pi$
$84$	7.12010	0.776867
$85$	4.59486	0.498383
$86$	9.05057	0.975949
$87$	13.3811	1.43460
$88$	0	0
$89$	−3.91301	−0.414779	−0.207389	−	0.978258i	$-0.566497\pi$
$89$	−3.91301	−0.414779	−0.207389	+	0.978258i	$0.566497\pi$
$90$	6.08262	0.641165
$91$	−2.48205	−0.260190
$92$	11.1415	1.16158
$93$	17.9071	1.85688
$94$	−24.4269	−2.51945
$95$	6.44696	0.661444
$96$	16.2747	1.66103
$97$	−17.9552	−1.82307	−0.911536	−	0.411221i	$-0.865102\pi$
$97$	−17.9552	−1.82307	−0.911536	+	0.411221i	$0.865102\pi$
$98$	−2.23053	−0.225317
$99$	0	0
$100$	2.97525	0.297525
$101$	13.3422	1.32760	0.663801	−	0.747909i	$-0.268942\pi$
$101$	13.3422	1.32760	0.663801	+	0.747909i	$0.268942\pi$
$102$	24.5269	2.42853
$103$	−8.11347	−0.799444	−0.399722	−	0.916636i	$-0.630893\pi$
$103$	−8.11347	−0.799444	−0.399722	+	0.916636i	$0.630893\pi$
$104$	5.39925	0.529440
$105$	−2.39311	−0.233544
$106$	18.8501	1.83089
$107$	13.1526	1.27151	0.635756	−	0.771890i	$-0.280688\pi$
$107$	13.1526	1.27151	0.635756	+	0.771890i	$0.280688\pi$
$108$	−1.94386	−0.187048
$109$	−10.7146	−1.02628	−0.513139	−	0.858306i	$-0.671517\pi$
$109$	−10.7146	−1.02628	−0.513139	+	0.858306i	$0.671517\pi$
$110$	0	0
$111$	5.80771	0.551243
$112$	−1.09840	−0.103789
$113$	−16.6587	−1.56712	−0.783561	−	0.621315i	$-0.786599\pi$
$113$	−16.6587	−1.56712	−0.783561	+	0.621315i	$0.786599\pi$
$114$	34.4132	3.22309
$115$	−3.74472	−0.349197
$116$	16.6361	1.54462
$117$	−6.76854	−0.625751
$118$	29.0512	2.67438
$119$	−4.59486	−0.421210
$120$	5.20577	0.475220
$121$	0	0
$122$	−2.79313	−0.252878
$123$	−4.16727	−0.375750
$124$	22.2631	1.99928
$125$	−1.00000	−0.0894427
$126$	−6.08262	−0.541883
$127$	−3.44969	−0.306111	−0.153055	−	0.988218i	$-0.548911\pi$
$127$	−3.44969	−0.306111	−0.153055	+	0.988218i	$0.548911\pi$
$128$	15.3336	1.35531
$129$	−9.71029	−0.854943
$130$	−5.53629	−0.485564
$131$	−7.99168	−0.698237	−0.349118	−	0.937079i	$-0.613519\pi$
$131$	−7.99168	−0.698237	−0.349118	+	0.937079i	$0.613519\pi$
$132$	0	0
$133$	−6.44696	−0.559022
$134$	4.86787	0.420520
$135$	0.653344	0.0562309
$136$	9.99527	0.857087
$137$	−1.22482	−0.104643	−0.0523217	−	0.998630i	$-0.516662\pi$
$137$	−1.22482	−0.104643	−0.0523217	+	0.998630i	$0.516662\pi$
$138$	−19.9890	−1.70157
$139$	−1.27116	−0.107819	−0.0539093	−	0.998546i	$-0.517168\pi$
$139$	−1.27116	−0.107819	−0.0539093	+	0.998546i	$0.517168\pi$
$140$	−2.97525	−0.251454
$141$	26.2075	2.20707
$142$	−2.01566	−0.169151
$143$	0	0
$144$	−2.99532	−0.249610
$145$	−5.59150	−0.464349
$146$	1.71988	0.142338
$147$	2.39311	0.197381
$148$	7.22046	0.593518
$149$	1.16670	0.0955801	0.0477901	−	0.998857i	$-0.484782\pi$
$149$	1.16670	0.0955801	0.0477901	+	0.998857i	$0.484782\pi$
$150$	−5.33790	−0.435838
$151$	−10.5333	−0.857190	−0.428595	−	0.903497i	$-0.640991\pi$
$151$	−10.5333	−0.857190	−0.428595	+	0.903497i	$0.640991\pi$
$152$	14.0242	1.13751
$153$	−12.5301	−1.01300
$154$	0	0
$155$	−7.48276	−0.601029
$156$	−17.6725	−1.41493
$157$	−22.5221	−1.79746	−0.898728	−	0.438506i	$-0.855508\pi$
$157$	−22.5221	−1.79746	−0.898728	+	0.438506i	$0.855508\pi$
$158$	21.6017	1.71854
$159$	−20.2242	−1.60388
$160$	−6.80064	−0.537637
$161$	3.74472	0.295125
$162$	21.7354	1.70769
$163$	22.1428	1.73436	0.867180	−	0.497994i	$-0.165930\pi$
$163$	22.1428	1.73436	0.867180	+	0.497994i	$0.165930\pi$
$164$	−5.18097	−0.404566
$165$	0	0
$166$	10.2252	0.793628
$167$	−25.2875	−1.95680	−0.978402	−	0.206714i	$-0.933723\pi$
$167$	−25.2875	−1.95680	−0.978402	+	0.206714i	$0.933723\pi$
$168$	−5.20577	−0.401634
$169$	−6.83941	−0.526108
$170$	−10.2490	−0.786059
$171$	−17.5808	−1.34444
$172$	−12.0724	−0.920508
$173$	24.4240	1.85692	0.928460	−	0.371434i	$-0.121134\pi$
$173$	24.4240	1.85692	0.928460	+	0.371434i	$0.121134\pi$
$174$	−29.8469	−2.26269
$175$	1.00000	0.0755929
$176$	0	0
$177$	−31.1688	−2.34279
$178$	8.72808	0.654197
$179$	−10.9621	−0.819348	−0.409674	−	0.912232i	$-0.634358\pi$
$179$	−10.9621	−0.819348	−0.409674	+	0.912232i	$0.634358\pi$
$180$	−8.11347	−0.604742
$181$	9.79520	0.728072	0.364036	−	0.931385i	$-0.381399\pi$
$181$	9.79520	0.728072	0.364036	+	0.931385i	$0.381399\pi$
$182$	5.53629	0.410377
$183$	2.99673	0.221525
$184$	−8.14595	−0.600527
$185$	−2.42684	−0.178425
$186$	−39.9422	−2.92871
$187$	0	0
$188$	32.5825	2.37632
$189$	−0.653344	−0.0475238
$190$	−14.3801	−1.04324
$191$	11.5140	0.833125	0.416562	−	0.909107i	$-0.363235\pi$
$191$	11.5140	0.833125	0.416562	+	0.909107i	$0.363235\pi$
$192$	−31.0439	−2.24040
$193$	−15.0974	−1.08674	−0.543368	−	0.839495i	$-0.682851\pi$
$193$	−15.0974	−1.08674	−0.543368	+	0.839495i	$0.682851\pi$
$194$	40.0495	2.87538
$195$	5.93984	0.425360
$196$	2.97525	0.212518
$197$	−3.07387	−0.219004	−0.109502	−	0.993987i	$-0.534926\pi$
$197$	−3.07387	−0.219004	−0.109502	+	0.993987i	$0.534926\pi$
$198$	0	0
$199$	−20.2497	−1.43546	−0.717730	−	0.696321i	$-0.754819\pi$
$199$	−20.2497	−1.43546	−0.717730	+	0.696321i	$0.754819\pi$
$200$	−2.17531	−0.153818
$201$	−5.22270	−0.368381
$202$	−29.7602	−2.09392
$203$	5.59150	0.392446
$204$	−32.7159	−2.29057
$205$	1.74136	0.121622
$206$	18.0973	1.26090
$207$	10.2118	0.709770
$208$	2.72628	0.189034
$209$	0	0
$210$	5.33790	0.368350
$211$	−0.955354	−0.0657693	−0.0328846	−	0.999459i	$-0.510469\pi$
$211$	−0.955354	−0.0657693	−0.0328846	+	0.999459i	$0.510469\pi$
$212$	−25.1438	−1.72688
$213$	2.16259	0.148178
$214$	−29.3373	−2.00546
$215$	4.05760	0.276726
$216$	1.42123	0.0967024
$217$	7.48276	0.507963
$218$	23.8993	1.61867
$219$	−1.84524	−0.124690
$220$	0	0
$221$	11.4047	0.767163
$222$	−12.9542	−0.869432
$223$	−18.8703	−1.26365	−0.631823	−	0.775113i	$-0.717693\pi$
$223$	−18.8703	−1.26365	−0.631823	+	0.775113i	$0.717693\pi$
$224$	6.80064	0.454387
$225$	2.72699	0.181799
$226$	37.1577	2.47170
$227$	0.250864	0.0166504	0.00832521	−	0.999965i	$-0.497350\pi$
$227$	0.250864	0.0166504	0.00832521	+	0.999965i	$0.497350\pi$
$228$	−45.9030	−3.04000
$229$	−3.62257	−0.239386	−0.119693	−	0.992811i	$-0.538191\pi$
$229$	−3.62257	−0.239386	−0.119693	+	0.992811i	$0.538191\pi$
$230$	8.35270	0.550761
$231$	0	0
$232$	−12.1633	−0.798558
$233$	17.3971	1.13972	0.569862	−	0.821740i	$-0.306997\pi$
$233$	17.3971	1.13972	0.569862	+	0.821740i	$0.306997\pi$
$234$	15.0974	0.986948
$235$	−10.9512	−0.714377
$236$	−38.7507	−2.52246
$237$	−23.1762	−1.50546
$238$	10.2490	0.664341
$239$	25.8333	1.67102	0.835510	−	0.549475i	$-0.185172\pi$
$239$	25.8333	1.67102	0.835510	+	0.549475i	$0.185172\pi$
$240$	2.62859	0.169675
$241$	10.3898	0.669265	0.334633	−	0.942349i	$-0.391388\pi$
$241$	10.3898	0.669265	0.334633	+	0.942349i	$0.391388\pi$
$242$	0	0
$243$	−21.3596	−1.37022
$244$	3.72570	0.238513
$245$	−1.00000	−0.0638877
$246$	9.29520	0.592640
$247$	16.0017	1.01816
$248$	−16.2773	−1.03361
$249$	−10.9705	−0.695228
$250$	2.23053	0.141071
$251$	3.80830	0.240378	0.120189	−	0.992751i	$-0.461650\pi$
$251$	3.80830	0.240378	0.120189	+	0.992751i	$0.461650\pi$
$252$	8.11347	0.511101
$253$	0	0
$254$	7.69463	0.482804
$255$	10.9960	0.688598
$256$	−8.25751	−0.516094
$257$	−18.6564	−1.16375	−0.581877	−	0.813277i	$-0.697681\pi$
$257$	−18.6564	−1.16375	−0.581877	+	0.813277i	$0.697681\pi$
$258$	21.6590	1.34843
$259$	2.42684	0.150797
$260$	7.38472	0.457981
$261$	15.2480	0.943825
$262$	17.8257	1.10127
$263$	−17.9440	−1.10647	−0.553236	−	0.833024i	$-0.686607\pi$
$263$	−17.9440	−1.10647	−0.553236	+	0.833024i	$0.686607\pi$
$264$	0	0
$265$	8.45098	0.519140
$266$	14.3801	0.881701
$267$	−9.36428	−0.573085
$268$	−6.49314	−0.396632
$269$	8.44707	0.515027	0.257514	−	0.966275i	$-0.417097\pi$
$269$	8.44707	0.515027	0.257514	+	0.966275i	$0.417097\pi$
$270$	−1.45730	−0.0886885
$271$	29.4963	1.79177	0.895887	−	0.444282i	$-0.146541\pi$
$271$	29.4963	1.79177	0.895887	+	0.444282i	$0.146541\pi$
$272$	5.04699	0.306019
$273$	−5.93984	−0.359495
$274$	2.73199	0.165046
$275$	0	0
$276$	26.6628	1.60491
$277$	−23.7318	−1.42591	−0.712953	−	0.701212i	$-0.752643\pi$
$277$	−23.7318	−1.42591	−0.712953	+	0.701212i	$0.752643\pi$
$278$	2.83536	0.170054
$279$	20.4054	1.22164
$280$	2.17531	0.130000
$281$	2.14849	0.128168	0.0640842	−	0.997944i	$-0.479587\pi$
$281$	2.14849	0.128168	0.0640842	+	0.997944i	$0.479587\pi$
$282$	−58.4564	−3.48103
$283$	−15.5938	−0.926958	−0.463479	−	0.886108i	$-0.653399\pi$
$283$	−15.5938	−0.926958	−0.463479	+	0.886108i	$0.653399\pi$
$284$	2.68864	0.159542
$285$	15.4283	0.913894
$286$	0	0
$287$	−1.74136	−0.102789
$288$	18.5453	1.09279
$289$	4.11276	0.241927
$290$	12.4720	0.732380
$291$	−42.9688	−2.51887
$292$	−2.29410	−0.134252
$293$	−18.8272	−1.09989	−0.549947	−	0.835199i	$-0.685352\pi$
$293$	−18.8272	−1.09989	−0.549947	+	0.835199i	$0.685352\pi$
$294$	−5.33790	−0.311313
$295$	13.0244	0.758308
$296$	−5.27915	−0.306844
$297$	0	0
$298$	−2.60236	−0.150751
$299$	−9.29460	−0.537521
$300$	7.12010	0.411079
$301$	−4.05760	−0.233876
$302$	23.4949	1.35198
$303$	31.9295	1.83430
$304$	7.08133	0.406142
$305$	−1.25223	−0.0717025
$306$	27.9488	1.59773
$307$	1.13588	0.0648280	0.0324140	−	0.999475i	$-0.489680\pi$
$307$	1.13588	0.0648280	0.0324140	+	0.999475i	$0.489680\pi$
$308$	0	0
$309$	−19.4164	−1.10456
$310$	16.6905	0.947956
$311$	16.0759	0.911581	0.455791	−	0.890087i	$-0.349357\pi$
$311$	16.0759	0.911581	0.455791	+	0.890087i	$0.349357\pi$
$312$	12.9210	0.731508
$313$	18.1314	1.02485	0.512424	−	0.858732i	$-0.328748\pi$
$313$	18.1314	1.02485	0.512424	+	0.858732i	$0.328748\pi$
$314$	50.2360	2.83498
$315$	−2.72699	−0.153648
$316$	−28.8140	−1.62091
$317$	4.87233	0.273657	0.136829	−	0.990595i	$-0.456309\pi$
$317$	4.87233	0.273657	0.136829	+	0.990595i	$0.456309\pi$
$318$	45.1105	2.52967
$319$	0	0
$320$	12.9722	0.725168
$321$	31.4757	1.75680
$322$	−8.35270	−0.465478
$323$	29.6229	1.64826
$324$	−28.9923	−1.61068
$325$	−2.48205	−0.137680
$326$	−49.3902	−2.73547
$327$	−25.6414	−1.41797
$328$	3.78800	0.209157
$329$	10.9512	0.603759
$330$	0	0
$331$	−34.2613	−1.88317	−0.941585	−	0.336775i	$-0.890664\pi$
$331$	−34.2613	−1.88317	−0.941585	+	0.336775i	$0.890664\pi$
$332$	−13.6391	−0.748545
$333$	6.61797	0.362663
$334$	56.4044	3.08631
$335$	2.18239	0.119237
$336$	−2.62859	−0.143401
$337$	17.6252	0.960106	0.480053	−	0.877239i	$-0.340617\pi$
$337$	17.6252	0.960106	0.480053	+	0.877239i	$0.340617\pi$
$338$	15.2555	0.829789
$339$	−39.8662	−2.16524
$340$	13.6709	0.741406
$341$	0	0
$342$	39.2144	2.12047
$343$	1.00000	0.0539949
$344$	8.82655	0.475896
$345$	−8.96154	−0.482473
$346$	−54.4783	−2.92877
$347$	15.4233	0.827964	0.413982	−	0.910285i	$-0.364138\pi$
$347$	15.4233	0.827964	0.413982	+	0.910285i	$0.364138\pi$
$348$	39.8120	2.13415
$349$	−30.5524	−1.63543	−0.817717	−	0.575621i	$-0.804761\pi$
$349$	−30.5524	−1.63543	−0.817717	+	0.575621i	$0.804761\pi$
$350$	−2.23053	−0.119227
$351$	1.62164	0.0865565
$352$	0	0
$353$	32.5324	1.73152	0.865761	−	0.500457i	$-0.166835\pi$
$353$	32.5324	1.73152	0.865761	+	0.500457i	$0.166835\pi$
$354$	69.5228	3.69509
$355$	−0.903671	−0.0479619
$356$	−11.6422	−0.617035
$357$	−10.9960	−0.581971
$358$	24.4513	1.29229
$359$	17.4092	0.918820	0.459410	−	0.888224i	$-0.348061\pi$
$359$	17.4092	0.918820	0.459410	+	0.888224i	$0.348061\pi$
$360$	5.93206	0.312647
$361$	22.5633	1.18754
$362$	−21.8485	−1.14833
$363$	0	0
$364$	−7.38472	−0.387065
$365$	0.771063	0.0403593
$366$	−6.68428	−0.349393
$367$	−33.8986	−1.76949	−0.884747	−	0.466072i	$-0.845669\pi$
$367$	−33.8986	−1.76949	−0.884747	+	0.466072i	$0.845669\pi$
$368$	−4.11320	−0.214415
$369$	−4.74866	−0.247206
$370$	5.41314	0.281416
$371$	−8.45098	−0.438753
$372$	53.2780	2.76234
$373$	−26.9006	−1.39286	−0.696431	−	0.717624i	$-0.745230\pi$
$373$	−26.9006	−1.39286	−0.696431	+	0.717624i	$0.745230\pi$
$374$	0	0
$375$	−2.39311	−0.123580
$376$	−23.8223	−1.22854
$377$	−13.8784	−0.714774
$378$	1.45730	0.0749555
$379$	11.2691	0.578854	0.289427	−	0.957200i	$-0.406535\pi$
$379$	11.2691	0.578854	0.289427	+	0.957200i	$0.406535\pi$
$380$	19.1813	0.983980
$381$	−8.25550	−0.422942
$382$	−25.6823	−1.31402
$383$	−35.5421	−1.81612	−0.908058	−	0.418845i	$-0.862435\pi$
$383$	−35.5421	−1.81612	−0.908058	+	0.418845i	$0.862435\pi$
$384$	36.6949	1.87258
$385$	0	0
$386$	33.6752	1.71402
$387$	−11.0650	−0.562467
$388$	−53.4211	−2.71204
$389$	23.3032	1.18152	0.590761	−	0.806847i	$-0.298828\pi$
$389$	23.3032	1.18152	0.590761	+	0.806847i	$0.298828\pi$
$390$	−13.2490	−0.670887
$391$	−17.2065	−0.870169
$392$	−2.17531	−0.109870
$393$	−19.1250	−0.964729
$394$	6.85634	0.345418
$395$	9.68456	0.487283
$396$	0	0
$397$	−15.8445	−0.795212	−0.397606	−	0.917556i	$-0.630159\pi$
$397$	−15.8445	−0.795212	−0.397606	+	0.917556i	$0.630159\pi$
$398$	45.1674	2.26404
$399$	−15.4283	−0.772381
$400$	−1.09840	−0.0549199
$401$	34.6690	1.73129	0.865644	−	0.500661i	$-0.166910\pi$
$401$	34.6690	1.73129	0.865644	+	0.500661i	$0.166910\pi$
$402$	11.6494	0.581018
$403$	−18.5726	−0.925167
$404$	39.6965	1.97497
$405$	9.74450	0.484208
$406$	−12.4720	−0.618974
$407$	0	0
$408$	23.9198	1.18421
$409$	14.6150	0.722663	0.361332	−	0.932437i	$-0.382322\pi$
$409$	14.6150	0.722663	0.361332	+	0.932437i	$0.382322\pi$
$410$	−3.88414	−0.191824
$411$	−2.93113	−0.144582
$412$	−24.1396	−1.18927
$413$	−13.0244	−0.640887
$414$	−22.7777	−1.11946
$415$	4.58420	0.225030
$416$	−16.8795	−0.827588
$417$	−3.04204	−0.148969
$418$	0	0
$419$	14.5242	0.709552	0.354776	−	0.934951i	$-0.384557\pi$
$419$	14.5242	0.709552	0.354776	+	0.934951i	$0.384557\pi$
$420$	−7.12010	−0.347425
$421$	2.60838	0.127125	0.0635624	−	0.997978i	$-0.479754\pi$
$421$	2.60838	0.127125	0.0635624	+	0.997978i	$0.479754\pi$
$422$	2.13094	0.103733
$423$	29.8638	1.45203
$424$	18.3835	0.892784
$425$	−4.59486	−0.222884
$426$	−4.82371	−0.233709
$427$	1.25223	0.0605997
$428$	39.1323	1.89153
$429$	0	0
$430$	−9.05057	−0.436457
$431$	2.24167	0.107977	0.0539886	−	0.998542i	$-0.482807\pi$
$431$	2.24167	0.107977	0.0539886	+	0.998542i	$0.482807\pi$
$432$	0.717632	0.0345271
$433$	−4.95709	−0.238222	−0.119111	−	0.992881i	$-0.538004\pi$
$433$	−4.95709	−0.238222	−0.119111	+	0.992881i	$0.538004\pi$
$434$	−16.6905	−0.801169
$435$	−13.3811	−0.641574
$436$	−31.8787	−1.52671
$437$	−24.1421	−1.15487
$438$	4.11586	0.196663
$439$	−28.9152	−1.38005	−0.690025	−	0.723786i	$-0.742400\pi$
$439$	−28.9152	−1.38005	−0.690025	+	0.723786i	$0.742400\pi$
$440$	0	0
$441$	2.72699	0.129857
$442$	−25.4385	−1.20998
$443$	−12.5910	−0.598216	−0.299108	−	0.954219i	$-0.596689\pi$
$443$	−12.5910	−0.598216	−0.299108	+	0.954219i	$0.596689\pi$
$444$	17.2794	0.820043
$445$	3.91301	0.185495
$446$	42.0906	1.99305
$447$	2.79205	0.132060
$448$	−12.9722	−0.612879
$449$	−29.9941	−1.41551	−0.707756	−	0.706457i	$-0.750292\pi$
$449$	−29.9941	−1.41551	−0.707756	+	0.706457i	$0.750292\pi$
$450$	−6.08262	−0.286738
$451$	0	0
$452$	−49.5638	−2.33129
$453$	−25.2075	−1.18435
$454$	−0.559559	−0.0262614
$455$	2.48205	0.116360
$456$	33.5614	1.57166
$457$	40.7774	1.90749	0.953743	−	0.300624i	$-0.0971950\pi$
$457$	40.7774	1.90749	0.953743	+	0.300624i	$0.0971950\pi$
$458$	8.08024	0.377565
$459$	3.00203	0.140123
$460$	−11.1415	−0.519474
$461$	12.0834	0.562781	0.281390	−	0.959593i	$-0.409204\pi$
$461$	12.0834	0.562781	0.281390	+	0.959593i	$0.409204\pi$
$462$	0	0
$463$	29.5664	1.37407	0.687033	−	0.726626i	$-0.258913\pi$
$463$	29.5664	1.37407	0.687033	+	0.726626i	$0.258913\pi$
$464$	−6.14169	−0.285121
$465$	−17.9071	−0.830421
$466$	−38.8048	−1.79760
$467$	−22.7528	−1.05287	−0.526436	−	0.850215i	$-0.676472\pi$
$467$	−22.7528	−1.05287	−0.526436	+	0.850215i	$0.676472\pi$
$468$	−20.1381	−0.930883
$469$	−2.18239	−0.100773
$470$	24.4269	1.12673
$471$	−53.8978	−2.48348
$472$	28.3321	1.30409
$473$	0	0
$474$	51.6952	2.37444
$475$	−6.44696	−0.295807
$476$	−13.6709	−0.626602
$477$	−23.0457	−1.05519
$478$	−57.6220	−2.63557
$479$	20.5483	0.938874	0.469437	−	0.882966i	$-0.344457\pi$
$479$	20.5483	0.938874	0.469437	+	0.882966i	$0.344457\pi$
$480$	−16.2747	−0.742835
$481$	−6.02355	−0.274650
$482$	−23.1747	−1.05558
$483$	8.96154	0.407764
$484$	0	0
$485$	17.9552	0.815302
$486$	47.6433	2.16114
$487$	12.3320	0.558817	0.279409	−	0.960172i	$-0.409862\pi$
$487$	12.3320	0.558817	0.279409	+	0.960172i	$0.409862\pi$
$488$	−2.72400	−0.123309
$489$	52.9903	2.39630
$490$	2.23053	0.100765
$491$	−11.2148	−0.506119	−0.253059	−	0.967451i	$-0.581437\pi$
$491$	−11.2148	−0.506119	−0.253059	+	0.967451i	$0.581437\pi$
$492$	−12.3986	−0.558974
$493$	−25.6922	−1.15712
$494$	−35.6922	−1.60587
$495$	0	0
$496$	−8.21905	−0.369046
$497$	0.903671	0.0405352
$498$	24.4700	1.09653
$499$	7.74584	0.346751	0.173376	−	0.984856i	$-0.444533\pi$
$499$	7.74584	0.346751	0.173376	+	0.984856i	$0.444533\pi$
$500$	−2.97525	−0.133057
$501$	−60.5158	−2.70365
$502$	−8.49451	−0.379128
$503$	9.86950	0.440059	0.220030	−	0.975493i	$-0.429385\pi$
$503$	9.86950	0.440059	0.220030	+	0.975493i	$0.429385\pi$
$504$	−5.93206	−0.264235
$505$	−13.3422	−0.593722
$506$	0	0
$507$	−16.3675	−0.726905
$508$	−10.2637	−0.455377
$509$	27.7747	1.23109	0.615547	−	0.788100i	$-0.288935\pi$
$509$	27.7747	1.23109	0.615547	+	0.788100i	$0.288935\pi$
$510$	−24.5269	−1.08607
$511$	−0.771063	−0.0341098
$512$	−12.2485	−0.541314
$513$	4.21208	0.185968
$514$	41.6136	1.83550
$515$	8.11347	0.357522
$516$	−28.8905	−1.27183
$517$	0	0
$518$	−5.41314	−0.237840
$519$	58.4493	2.56564
$520$	−5.39925	−0.236773
$521$	−24.2447	−1.06218	−0.531090	−	0.847316i	$-0.678217\pi$
$521$	−24.2447	−1.06218	−0.531090	+	0.847316i	$0.678217\pi$
$522$	−34.0110	−1.48862
$523$	−19.3581	−0.846473	−0.423236	−	0.906019i	$-0.639106\pi$
$523$	−19.3581	−0.846473	−0.423236	+	0.906019i	$0.639106\pi$
$524$	−23.7772	−1.03871
$525$	2.39311	0.104444
$526$	40.0245	1.74515
$527$	−34.3822	−1.49771
$528$	0	0
$529$	−8.97706	−0.390307
$530$	−18.8501	−0.818798
$531$	−35.5173	−1.54132
$532$	−19.1813	−0.831615
$533$	4.32214	0.187213
$534$	20.8873	0.903881
$535$	−13.1526	−0.568638
$536$	4.74738	0.205056
$537$	−26.2336	−1.13206
$538$	−18.8414	−0.812311
$539$	0	0
$540$	1.94386	0.0836504
$541$	15.0511	0.647099	0.323549	−	0.946211i	$-0.395124\pi$
$541$	15.0511	0.647099	0.323549	+	0.946211i	$0.395124\pi$
$542$	−65.7923	−2.82602
$543$	23.4410	1.00595
$544$	−31.2480	−1.33975
$545$	10.7146	0.458965
$546$	13.2490	0.567003
$547$	23.4658	1.00332	0.501662	−	0.865064i	$-0.332722\pi$
$547$	23.4658	1.00332	0.501662	+	0.865064i	$0.332722\pi$
$548$	−3.64414	−0.155670
$549$	3.41482	0.145741
$550$	0	0
$551$	−36.0482	−1.53570
$552$	−19.4942	−0.829727
$553$	−9.68456	−0.411829
$554$	52.9344	2.24897
$555$	−5.80771	−0.246523
$556$	−3.78202	−0.160394
$557$	5.72855	0.242727	0.121363	−	0.992608i	$-0.461273\pi$
$557$	5.72855	0.242727	0.121363	+	0.992608i	$0.461273\pi$
$558$	−45.5148	−1.92679
$559$	10.0712	0.425965
$560$	1.09840	0.0464158
$561$	0	0
$562$	−4.79227	−0.202150
$563$	−41.3412	−1.74232	−0.871162	−	0.490996i	$-0.836633\pi$
$563$	−41.3412	−1.74232	−0.871162	+	0.490996i	$0.836633\pi$
$564$	77.9736	3.28328
$565$	16.6587	0.700838
$566$	34.7825	1.46202
$567$	−9.74450	−0.409230
$568$	−1.96577	−0.0824818
$569$	6.17814	0.259001	0.129501	−	0.991579i	$-0.458663\pi$
$569$	6.17814	0.259001	0.129501	+	0.991579i	$0.458663\pi$
$570$	−34.4132	−1.44141
$571$	−2.50833	−0.104970	−0.0524852	−	0.998622i	$-0.516714\pi$
$571$	−2.50833	−0.104970	−0.0524852	+	0.998622i	$0.516714\pi$
$572$	0	0
$573$	27.5543	1.15110
$574$	3.88414	0.162121
$575$	3.74472	0.156166
$576$	−35.3751	−1.47396
$577$	0.367523	0.0153002	0.00765009	−	0.999971i	$-0.497565\pi$
$577$	0.367523	0.0153002	0.00765009	+	0.999971i	$0.497565\pi$
$578$	−9.17361	−0.381572
$579$	−36.1298	−1.50150
$580$	−16.6361	−0.690776
$581$	−4.58420	−0.190185
$582$	95.8429	3.97282
$583$	0	0
$584$	1.67730	0.0694073
$585$	6.76854	0.279845
$586$	41.9945	1.73478
$587$	18.6747	0.770786	0.385393	−	0.922753i	$-0.374066\pi$
$587$	18.6747	0.770786	0.385393	+	0.922753i	$0.374066\pi$
$588$	7.12010	0.293628
$589$	−48.2410	−1.98774
$590$	−29.0512	−1.19602
$591$	−7.35611	−0.302590
$592$	−2.66564	−0.109557
$593$	−32.0456	−1.31595	−0.657977	−	0.753038i	$-0.728588\pi$
$593$	−32.0456	−1.31595	−0.657977	+	0.753038i	$0.728588\pi$
$594$	0	0
$595$	4.59486	0.188371
$596$	3.47123	0.142187
$597$	−48.4597	−1.98332
$598$	20.7318	0.847788
$599$	23.3157	0.952654	0.476327	−	0.879268i	$-0.341968\pi$
$599$	23.3157	0.952654	0.476327	+	0.879268i	$0.341968\pi$
$600$	−5.20577	−0.212525
$601$	5.43279	0.221608	0.110804	−	0.993842i	$-0.464657\pi$
$601$	5.43279	0.221608	0.110804	+	0.993842i	$0.464657\pi$
$602$	9.05057	0.368874
$603$	−5.95135	−0.242358
$604$	−31.3393	−1.27518
$605$	0	0
$606$	−71.2196	−2.89310
$607$	−13.7235	−0.557019	−0.278509	−	0.960434i	$-0.589840\pi$
$607$	−13.7235	−0.557019	−0.278509	+	0.960434i	$0.589840\pi$
$608$	−43.8434	−1.77809
$609$	13.3811	0.542229
$610$	2.79313	0.113091
$611$	−27.1815	−1.09964
$612$	−37.2803	−1.50697
$613$	−36.4729	−1.47313	−0.736563	−	0.676369i	$-0.763553\pi$
$613$	−36.4729	−1.47313	−0.736563	+	0.676369i	$0.763553\pi$
$614$	−2.53361	−0.102248
$615$	4.16727	0.168040
$616$	0	0
$617$	−17.6223	−0.709445	−0.354723	−	0.934972i	$-0.615425\pi$
$617$	−17.6223	−0.709445	−0.354723	+	0.934972i	$0.615425\pi$
$618$	43.3089	1.74214
$619$	26.0827	1.04835	0.524176	−	0.851610i	$-0.324374\pi$
$619$	26.0827	1.04835	0.524176	+	0.851610i	$0.324374\pi$
$620$	−22.2631	−0.894106
$621$	−2.44659	−0.0981783
$622$	−35.8577	−1.43776
$623$	−3.91301	−0.156772
$624$	6.52431	0.261181
$625$	1.00000	0.0400000
$626$	−40.4426	−1.61641
$627$	0	0
$628$	−67.0087	−2.67394
$629$	−11.1510	−0.444620
$630$	6.08262	0.242337
$631$	28.3522	1.12868	0.564342	−	0.825541i	$-0.309130\pi$
$631$	28.3522	1.12868	0.564342	+	0.825541i	$0.309130\pi$
$632$	21.0670	0.837999
$633$	−2.28627	−0.0908711
$634$	−10.8679	−0.431617
$635$	3.44969	0.136897
$636$	−60.1719	−2.38597
$637$	−2.48205	−0.0983426
$638$	0	0
$639$	2.46430	0.0974863
$640$	−15.3336	−0.606112
$641$	4.41661	0.174446	0.0872229	−	0.996189i	$-0.472201\pi$
$641$	4.41661	0.174446	0.0872229	+	0.996189i	$0.472201\pi$
$642$	−70.2074	−2.77087
$643$	−15.6291	−0.616351	−0.308176	−	0.951330i	$-0.599718\pi$
$643$	−15.6291	−0.616351	−0.308176	+	0.951330i	$0.599718\pi$
$644$	11.1415	0.439035
$645$	9.71029	0.382342
$646$	−66.0746	−2.59967
$647$	1.33648	0.0525426	0.0262713	−	0.999655i	$-0.491637\pi$
$647$	1.33648	0.0525426	0.0262713	+	0.999655i	$0.491637\pi$
$648$	21.1973	0.832710
$649$	0	0
$650$	5.53629	0.217151
$651$	17.9071	0.701834
$652$	65.8804	2.58008
$653$	−13.8173	−0.540711	−0.270356	−	0.962761i	$-0.587141\pi$
$653$	−13.8173	−0.540711	−0.270356	+	0.962761i	$0.587141\pi$
$654$	57.1937	2.23645
$655$	7.99168	0.312261
$656$	1.91270	0.0746786
$657$	−2.10268	−0.0820334
$658$	−24.4269	−0.952261
$659$	−34.3826	−1.33936	−0.669679	−	0.742651i	$-0.733568\pi$
$659$	−34.3826	−1.33936	−0.669679	+	0.742651i	$0.733568\pi$
$660$	0	0
$661$	17.0926	0.664827	0.332413	−	0.943134i	$-0.392137\pi$
$661$	17.0926	0.664827	0.332413	+	0.943134i	$0.392137\pi$
$662$	76.4207	2.97017
$663$	27.2927	1.05996
$664$	9.97208	0.386992
$665$	6.44696	0.250002
$666$	−14.7616	−0.571999
$667$	20.9386	0.810746
$668$	−75.2365	−2.91099
$669$	−45.1587	−1.74593
$670$	−4.86787	−0.188062
$671$	0	0
$672$	16.2747	0.627810
$673$	44.4681	1.71412	0.857059	−	0.515219i	$-0.172289\pi$
$673$	44.4681	1.71412	0.857059	+	0.515219i	$0.172289\pi$
$674$	−39.3135	−1.51430
$675$	−0.653344	−0.0251472
$676$	−20.3489	−0.782651
$677$	3.99943	0.153711	0.0768553	−	0.997042i	$-0.475512\pi$
$677$	3.99943	0.153711	0.0768553	+	0.997042i	$0.475512\pi$
$678$	88.9227	3.41505
$679$	−17.9552	−0.689056
$680$	−9.99527	−0.383301
$681$	0.600346	0.0230053
$682$	0	0
$683$	−37.7958	−1.44622	−0.723108	−	0.690735i	$-0.757287\pi$
$683$	−37.7958	−1.44622	−0.723108	+	0.690735i	$0.757287\pi$
$684$	−52.3072	−2.00002
$685$	1.22482	0.0467980
$686$	−2.23053	−0.0851619
$687$	−8.66922	−0.330751
$688$	4.45686	0.169916
$689$	20.9758	0.799114
$690$	19.9890	0.760966
$691$	18.2039	0.692509	0.346255	−	0.938141i	$-0.387453\pi$
$691$	18.2039	0.692509	0.346255	+	0.938141i	$0.387453\pi$
$692$	72.6673	2.76240
$693$	0	0
$694$	−34.4020	−1.30588
$695$	1.27116	0.0482180
$696$	−29.1081	−1.10334
$697$	8.00130	0.303071
$698$	68.1480	2.57944
$699$	41.6333	1.57472
$700$	2.97525	0.112454
$701$	−19.3813	−0.732021	−0.366010	−	0.930611i	$-0.619276\pi$
$701$	−19.3813	−0.732021	−0.366010	+	0.930611i	$0.619276\pi$
$702$	−3.61710	−0.136519
$703$	−15.6458	−0.590091
$704$	0	0
$705$	−26.2075	−0.987030
$706$	−72.5643	−2.73099
$707$	13.3422	0.501787
$708$	−92.7348	−3.48519
$709$	37.6738	1.41487	0.707435	−	0.706778i	$-0.249852\pi$
$709$	37.6738	1.41487	0.707435	+	0.706778i	$0.249852\pi$
$710$	2.01566	0.0756464
$711$	−26.4097	−0.990441
$712$	8.51204	0.319002
$713$	28.0208	1.04939
$714$	24.5269	0.917897
$715$	0	0
$716$	−32.6150	−1.21888
$717$	61.8221	2.30879
$718$	−38.8316	−1.44918
$719$	−26.1737	−0.976113	−0.488057	−	0.872812i	$-0.662294\pi$
$719$	−26.1737	−0.976113	−0.488057	+	0.872812i	$0.662294\pi$
$720$	2.99532	0.111629
$721$	−8.11347	−0.302161
$722$	−50.3280	−1.87301
$723$	24.8639	0.924700
$724$	29.1431	1.08310
$725$	5.59150	0.207663
$726$	0	0
$727$	−35.2900	−1.30883	−0.654416	−	0.756134i	$-0.727086\pi$
$727$	−35.2900	−1.30883	−0.654416	+	0.756134i	$0.727086\pi$
$728$	5.39925	0.200109
$729$	−21.8826	−0.810465
$730$	−1.71988	−0.0636554
$731$	18.6441	0.689577
$732$	8.91601	0.329545
$733$	20.2930	0.749538	0.374769	−	0.927118i	$-0.377722\pi$
$733$	20.2930	0.749538	0.374769	+	0.927118i	$0.377722\pi$
$734$	75.6118	2.79088
$735$	−2.39311	−0.0882713
$736$	25.4665	0.938707
$737$	0	0
$738$	10.5920	0.389898
$739$	18.3773	0.676021	0.338011	−	0.941142i	$-0.390246\pi$
$739$	18.3773	0.676021	0.338011	+	0.941142i	$0.390246\pi$
$740$	−7.22046	−0.265429
$741$	38.2939	1.40676
$742$	18.8501	0.692010
$743$	−6.28566	−0.230599	−0.115299	−	0.993331i	$-0.536783\pi$
$743$	−6.28566	−0.230599	−0.115299	+	0.993331i	$0.536783\pi$
$744$	−38.9535	−1.42811
$745$	−1.16670	−0.0427447
$746$	60.0025	2.19685
$747$	−12.5011	−0.457390
$748$	0	0
$749$	13.1526	0.480587
$750$	5.33790	0.194913
$751$	49.6832	1.81297	0.906483	−	0.422242i	$-0.138757\pi$
$751$	49.6832	1.81297	0.906483	+	0.422242i	$0.138757\pi$
$752$	−12.0288	−0.438644
$753$	9.11368	0.332121
$754$	30.9561	1.12736
$755$	10.5333	0.383347
$756$	−1.94386	−0.0706975
$757$	−6.48438	−0.235679	−0.117839	−	0.993033i	$-0.537597\pi$
$757$	−6.48438	−0.235679	−0.117839	+	0.993033i	$0.537597\pi$
$758$	−25.1360	−0.912980
$759$	0	0
$760$	−14.0242	−0.508710
$761$	9.10052	0.329894	0.164947	−	0.986302i	$-0.447255\pi$
$761$	9.10052	0.329894	0.164947	+	0.986302i	$0.447255\pi$
$762$	18.4141	0.667073
$763$	−10.7146	−0.387896
$764$	34.2570	1.23938
$765$	12.5301	0.453028
$766$	79.2775	2.86441
$767$	32.3272	1.16727
$768$	−19.7611	−0.713069
$769$	16.4987	0.594957	0.297478	−	0.954729i	$-0.403854\pi$
$769$	16.4987	0.594957	0.297478	+	0.954729i	$0.403854\pi$
$770$	0	0
$771$	−44.6468	−1.60792
$772$	−44.9186	−1.61665
$773$	48.7475	1.75333	0.876663	−	0.481105i	$-0.159764\pi$
$773$	48.7475	1.75333	0.876663	+	0.481105i	$0.159764\pi$
$774$	24.6808	0.887134
$775$	7.48276	0.268789
$776$	39.0581	1.40211
$777$	5.80771	0.208350
$778$	−51.9785	−1.86352
$779$	11.2265	0.402230
$780$	17.6725	0.632776
$781$	0	0
$782$	38.3795	1.37245
$783$	−3.65317	−0.130554
$784$	−1.09840	−0.0392285
$785$	22.5221	0.803847
$786$	42.6588	1.52159
$787$	42.0547	1.49909	0.749544	−	0.661954i	$-0.230273\pi$
$787$	42.0547	1.49909	0.749544	+	0.661954i	$0.230273\pi$
$788$	−9.14552	−0.325796
$789$	−42.9420	−1.52877
$790$	−21.6017	−0.768553
$791$	−16.6587	−0.592316
$792$	0	0
$793$	−3.10810	−0.110372
$794$	35.3415	1.25422
$795$	20.2242	0.717277
$796$	−60.2478	−2.13542
$797$	−4.46584	−0.158188	−0.0790941	−	0.996867i	$-0.525203\pi$
$797$	−4.46584	−0.158188	−0.0790941	+	0.996867i	$0.525203\pi$
$798$	34.4132	1.21821
$799$	−50.3192	−1.78017
$800$	6.80064	0.240439
$801$	−10.6707	−0.377032
$802$	−77.3301	−2.73062
$803$	0	0
$804$	−15.5388	−0.548012
$805$	−3.74472	−0.131984
$806$	41.4267	1.45919
$807$	20.2148	0.711595
$808$	−29.0236	−1.02105
$809$	52.1612	1.83389	0.916945	−	0.399013i	$-0.130647\pi$
$809$	52.1612	1.83389	0.916945	+	0.399013i	$0.130647\pi$
$810$	−21.7354	−0.763702
$811$	5.66828	0.199040	0.0995202	−	0.995036i	$-0.468269\pi$
$811$	5.66828	0.199040	0.0995202	+	0.995036i	$0.468269\pi$
$812$	16.6361	0.583812
$813$	70.5880	2.47563
$814$	0	0
$815$	−22.1428	−0.775630
$816$	12.0780	0.422815
$817$	26.1592	0.915193
$818$	−32.5990	−1.13980
$819$	−6.76854	−0.236512
$820$	5.18097	0.180927
$821$	−5.02300	−0.175304	−0.0876519	−	0.996151i	$-0.527936\pi$
$821$	−5.02300	−0.175304	−0.0876519	+	0.996151i	$0.527936\pi$
$822$	6.53797	0.228038
$823$	33.1797	1.15657	0.578286	−	0.815834i	$-0.303722\pi$
$823$	33.1797	1.15657	0.578286	+	0.815834i	$0.303722\pi$
$824$	17.6493	0.614844
$825$	0	0
$826$	29.0512	1.01082
$827$	−39.3806	−1.36940	−0.684699	−	0.728826i	$-0.740066\pi$
$827$	−39.3806	−1.36940	−0.684699	+	0.728826i	$0.740066\pi$
$828$	30.3827	1.05587
$829$	−38.9511	−1.35283	−0.676414	−	0.736521i	$-0.736467\pi$
$829$	−38.9511	−1.35283	−0.676414	+	0.736521i	$0.736467\pi$
$830$	−10.2252	−0.354921
$831$	−56.7929	−1.97012
$832$	32.1977	1.11625
$833$	−4.59486	−0.159203
$834$	6.78534	0.234957
$835$	25.2875	0.875109
$836$	0	0
$837$	−4.88882	−0.168982
$838$	−32.3965	−1.11912
$839$	−6.83346	−0.235917	−0.117959	−	0.993019i	$-0.537635\pi$
$839$	−6.83346	−0.235917	−0.117959	+	0.993019i	$0.537635\pi$
$840$	5.20577	0.179616
$841$	2.26486	0.0780985
$842$	−5.81807	−0.200504
$843$	5.14159	0.177086
$844$	−2.84241	−0.0978399
$845$	6.83941	0.235283
$846$	−66.6120	−2.29017
$847$	0	0
$848$	9.28255	0.318764
$849$	−37.3178	−1.28074
$850$	10.2490	0.351536
$851$	9.08785	0.311527
$852$	6.43423	0.220433
$853$	−23.2284	−0.795324	−0.397662	−	0.917532i	$-0.630178\pi$
$853$	−23.2284	−0.795324	−0.397662	+	0.917532i	$0.630178\pi$
$854$	−2.79313	−0.0955791
$855$	17.5808	0.601250
$856$	−28.6111	−0.977908
$857$	46.1262	1.57564	0.787820	−	0.615905i	$-0.211210\pi$
$857$	46.1262	1.57564	0.787820	+	0.615905i	$0.211210\pi$
$858$	0	0
$859$	28.5681	0.974731	0.487366	−	0.873198i	$-0.337958\pi$
$859$	28.5681	0.974731	0.487366	+	0.873198i	$0.337958\pi$
$860$	12.0724	0.411664
$861$	−4.16727	−0.142020
$862$	−5.00009	−0.170304
$863$	−9.86868	−0.335934	−0.167967	−	0.985793i	$-0.553720\pi$
$863$	−9.86868	−0.335934	−0.167967	+	0.985793i	$0.553720\pi$
$864$	−4.44316	−0.151159
$865$	−24.4240	−0.830439
$866$	11.0569	0.375729
$867$	9.84229	0.334262
$868$	22.2631	0.755657
$869$	0	0
$870$	29.8469	1.01190
$871$	5.41680	0.183541
$872$	23.3077	0.789299
$873$	−48.9636	−1.65717
$874$	53.8495	1.82149
$875$	−1.00000	−0.0338062
$876$	−5.49005	−0.185491
$877$	−33.1521	−1.11947	−0.559733	−	0.828673i	$-0.689096\pi$
$877$	−33.1521	−1.11947	−0.559733	+	0.828673i	$0.689096\pi$
$878$	64.4962	2.17664
$879$	−45.0555	−1.51969
$880$	0	0
$881$	6.32109	0.212963	0.106481	−	0.994315i	$-0.466042\pi$
$881$	6.32109	0.212963	0.106481	+	0.994315i	$0.466042\pi$
$882$	−6.08262	−0.204813
$883$	40.5101	1.36327	0.681637	−	0.731691i	$-0.261269\pi$
$883$	40.5101	1.36327	0.681637	+	0.731691i	$0.261269\pi$
$884$	33.9318	1.14125
$885$	31.1688	1.04773
$886$	28.0846	0.943519
$887$	−24.6009	−0.826019	−0.413009	−	0.910727i	$-0.635522\pi$
$887$	−24.6009	−0.826019	−0.413009	+	0.910727i	$0.635522\pi$
$888$	−12.6336	−0.423956
$889$	−3.44969	−0.115699
$890$	−8.72808	−0.292566
$891$	0	0
$892$	−56.1437	−1.87983
$893$	−70.6019	−2.36260
$894$	−6.22775	−0.208287
$895$	10.9621	0.366424
$896$	15.3336	0.512258
$897$	−22.2430	−0.742673
$898$	66.9027	2.23257
$899$	41.8398	1.39544
$900$	8.11347	0.270449
$901$	38.8311	1.29365
$902$	0	0
$903$	−9.71029	−0.323138
$904$	36.2380	1.20526
$905$	−9.79520	−0.325604
$906$	56.2259	1.86798
$907$	−51.1544	−1.69855	−0.849277	−	0.527948i	$-0.822962\pi$
$907$	−51.1544	−1.69855	−0.849277	+	0.527948i	$0.822962\pi$
$908$	0.746382	0.0247696
$909$	36.3842	1.20679
$910$	−5.53629	−0.183526
$911$	−52.2932	−1.73255	−0.866275	−	0.499567i	$-0.833493\pi$
$911$	−52.2932	−1.73255	−0.866275	+	0.499567i	$0.833493\pi$
$912$	16.9464	0.561152
$913$	0	0
$914$	−90.9550	−3.00852
$915$	−2.99673	−0.0990688
$916$	−10.7780	−0.356117
$917$	−7.99168	−0.263909
$918$	−6.69610	−0.221004
$919$	−44.3573	−1.46321	−0.731606	−	0.681728i	$-0.761229\pi$
$919$	−44.3573	−1.46321	−0.731606	+	0.681728i	$0.761229\pi$
$920$	8.14595	0.268564
$921$	2.71829	0.0895706
$922$	−26.9524	−0.887629
$923$	−2.24296	−0.0738279
$924$	0	0
$925$	2.42684	0.0797941
$926$	−65.9486	−2.16721
$927$	−22.1253	−0.726692
$928$	38.0257	1.24826
$929$	21.6930	0.711725	0.355862	−	0.934538i	$-0.384187\pi$
$929$	21.6930	0.711725	0.355862	+	0.934538i	$0.384187\pi$
$930$	39.9422	1.30976
$931$	−6.44696	−0.211291
$932$	51.7608	1.69548
$933$	38.4715	1.25950
$934$	50.7507	1.66061
$935$	0	0
$936$	14.7237	0.481259
$937$	−42.9154	−1.40198	−0.700992	−	0.713169i	$-0.747259\pi$
$937$	−42.9154	−1.40198	−0.700992	+	0.713169i	$0.747259\pi$
$938$	4.86787	0.158942
$939$	43.3905	1.41600
$940$	−32.5825	−1.06272
$941$	44.1858	1.44041	0.720207	−	0.693759i	$-0.244047\pi$
$941$	44.1858	1.44041	0.720207	+	0.693759i	$0.244047\pi$
$942$	120.221	3.91700
$943$	−6.52090	−0.212350
$944$	14.3059	0.465619
$945$	0.653344	0.0212533
$946$	0	0
$947$	−7.70679	−0.250437	−0.125219	−	0.992129i	$-0.539963\pi$
$947$	−7.70679	−0.250437	−0.125219	+	0.992129i	$0.539963\pi$
$948$	−68.9550	−2.23956
$949$	1.91382	0.0621252
$950$	14.3801	0.466552
$951$	11.6600	0.378102
$952$	9.99527	0.323949
$953$	−6.90767	−0.223762	−0.111881	−	0.993722i	$-0.535687\pi$
$953$	−6.90767	−0.223762	−0.111881	+	0.993722i	$0.535687\pi$
$954$	51.4041	1.66427
$955$	−11.5140	−0.372585
$956$	76.8606	2.48585
$957$	0	0
$958$	−45.8334	−1.48081
$959$	−1.22482	−0.0395515
$960$	31.0439	1.00194
$961$	24.9917	0.806182
$962$	13.4357	0.433184
$963$	35.8671	1.15580
$964$	30.9122	0.995615
$965$	15.0974	0.486003
$966$	−19.9890	−0.643134
$967$	−7.32107	−0.235430	−0.117715	−	0.993047i	$-0.537557\pi$
$967$	−7.32107	−0.235430	−0.117715	+	0.993047i	$0.537557\pi$
$968$	0	0
$969$	70.8909	2.27734
$970$	−40.0495	−1.28591
$971$	7.03591	0.225793	0.112897	−	0.993607i	$-0.463987\pi$
$971$	7.03591	0.225793	0.112897	+	0.993607i	$0.463987\pi$
$972$	−63.5502	−2.03837
$973$	−1.27116	−0.0407516
$974$	−27.5069	−0.881378
$975$	−5.93984	−0.190227
$976$	−1.37545	−0.0440270
$977$	27.8375	0.890601	0.445300	−	0.895381i	$-0.353097\pi$
$977$	27.8375	0.890601	0.445300	+	0.895381i	$0.353097\pi$
$978$	−118.196	−3.77950
$979$	0	0
$980$	−2.97525	−0.0950408
$981$	−29.2187	−0.932883
$982$	25.0150	0.798261
$983$	2.40546	0.0767221	0.0383611	−	0.999264i	$-0.487786\pi$
$983$	2.40546	0.0767221	0.0383611	+	0.999264i	$0.487786\pi$
$984$	9.06511	0.288985
$985$	3.07387	0.0979416
$986$	57.3070	1.82503
$987$	26.2075	0.834192
$988$	47.6090	1.51464
$989$	−15.1946	−0.483159
$990$	0	0
$991$	25.4300	0.807810	0.403905	−	0.914801i	$-0.367653\pi$
$991$	25.4300	0.807810	0.403905	+	0.914801i	$0.367653\pi$
$992$	50.8875	1.61568
$993$	−81.9911	−2.60191
$994$	−2.01566	−0.0639329
$995$	20.2497	0.641957
$996$	−32.6400	−1.03424
$997$	3.07667	0.0974391	0.0487196	−	0.998812i	$-0.484486\pi$
$997$	3.07667	0.0974391	0.0487196	+	0.998812i	$0.484486\pi$
$998$	−17.2773	−0.546903
$999$	−1.58556	−0.0501650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.y.1.1	✓	5
11.10	odd	2		4235.2.a.be.1.5	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.y.1.1	✓	5	1.1	even	1	trivial
4235.2.a.be.1.5	yes	5	11.10	odd	2

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:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23053 q^{2} +2.39311 q^{3} +2.97525 q^{4} -1.00000 q^{5} -5.33790 q^{6} +1.00000 q^{7} -2.17531 q^{8} +2.72699 q^{9} +O(q^{10})\)	\(q-2.23053 q^{2} +2.39311 q^{3} +2.97525 q^{4} -1.00000 q^{5} -5.33790 q^{6} +1.00000 q^{7} -2.17531 q^{8} +2.72699 q^{9} +2.23053 q^{10} +7.12010 q^{12} -2.48205 q^{13} -2.23053 q^{14} -2.39311 q^{15} -1.09840 q^{16} -4.59486 q^{17} -6.08262 q^{18} -6.44696 q^{19} -2.97525 q^{20} +2.39311 q^{21} +3.74472 q^{23} -5.20577 q^{24} +1.00000 q^{25} +5.53629 q^{26} -0.653344 q^{27} +2.97525 q^{28} +5.59150 q^{29} +5.33790 q^{30} +7.48276 q^{31} +6.80064 q^{32} +10.2490 q^{34} -1.00000 q^{35} +8.11347 q^{36} +2.42684 q^{37} +14.3801 q^{38} -5.93984 q^{39} +2.17531 q^{40} -1.74136 q^{41} -5.33790 q^{42} -4.05760 q^{43} -2.72699 q^{45} -8.35270 q^{46} +10.9512 q^{47} -2.62859 q^{48} +1.00000 q^{49} -2.23053 q^{50} -10.9960 q^{51} -7.38472 q^{52} -8.45098 q^{53} +1.45730 q^{54} -2.17531 q^{56} -15.4283 q^{57} -12.4720 q^{58} -13.0244 q^{59} -7.12010 q^{60} +1.25223 q^{61} -16.6905 q^{62} +2.72699 q^{63} -12.9722 q^{64} +2.48205 q^{65} -2.18239 q^{67} -13.6709 q^{68} +8.96154 q^{69} +2.23053 q^{70} +0.903671 q^{71} -5.93206 q^{72} -0.771063 q^{73} -5.41314 q^{74} +2.39311 q^{75} -19.1813 q^{76} +13.2490 q^{78} -9.68456 q^{79} +1.09840 q^{80} -9.74450 q^{81} +3.88414 q^{82} -4.58420 q^{83} +7.12010 q^{84} +4.59486 q^{85} +9.05057 q^{86} +13.3811 q^{87} -3.91301 q^{89} +6.08262 q^{90} -2.48205 q^{91} +11.1415 q^{92} +17.9071 q^{93} -24.4269 q^{94} +6.44696 q^{95} +16.2747 q^{96} -17.9552 q^{97} -2.23053 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} + 5 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 + 5 * q^7 + 6 * q^8 + 3 * q^9	\( 5 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} + 5 q^{7} + 6 q^{8} + 3 q^{9} + 2 q^{10} + 11 q^{12} - 12 q^{13} - 2 q^{14} + 2 q^{15} + 2 q^{16} - 14 q^{17} - 7 q^{18} - 9 q^{19} - 4 q^{20} - 2 q^{21} + 17 q^{23} - 6 q^{24} + 5 q^{25} - 11 q^{26} - 11 q^{27} + 4 q^{28} - 3 q^{29} + 5 q^{30} + 2 q^{31} + 5 q^{32} + 16 q^{34} - 5 q^{35} - 15 q^{36} + 4 q^{37} - 11 q^{38} - 2 q^{39} - 6 q^{40} + 15 q^{41} - 5 q^{42} - 4 q^{43} - 3 q^{45} + 10 q^{46} - 2 q^{47} - 10 q^{48} + 5 q^{49} - 2 q^{50} + 18 q^{51} - 4 q^{52} + 6 q^{53} - 4 q^{54} + 6 q^{56} - 32 q^{58} - 6 q^{59} - 11 q^{60} - 20 q^{61} - 21 q^{62} + 3 q^{63} - 26 q^{64} + 12 q^{65} + 3 q^{67} - 5 q^{68} + 2 q^{70} - 6 q^{71} - 34 q^{72} - 11 q^{73} + 15 q^{74} - 2 q^{75} - 47 q^{76} + 31 q^{78} - 19 q^{79} - 2 q^{80} + 33 q^{81} - 8 q^{83} + 11 q^{84} + 14 q^{85} + 27 q^{86} + 30 q^{87} + q^{89} + 7 q^{90} - 12 q^{91} + 44 q^{92} + 3 q^{93} - 28 q^{94} + 9 q^{95} + 4 q^{96} - 7 q^{97} - 2 q^{98}+O(q^{100}) \) 5 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 + 5 * q^7 + 6 * q^8 + 3 * q^9 + 2 * q^10 + 11 * q^12 - 12 * q^13 - 2 * q^14 + 2 * q^15 + 2 * q^16 - 14 * q^17 - 7 * q^18 - 9 * q^19 - 4 * q^20 - 2 * q^21 + 17 * q^23 - 6 * q^24 + 5 * q^25 - 11 * q^26 - 11 * q^27 + 4 * q^28 - 3 * q^29 + 5 * q^30 + 2 * q^31 + 5 * q^32 + 16 * q^34 - 5 * q^35 - 15 * q^36 + 4 * q^37 - 11 * q^38 - 2 * q^39 - 6 * q^40 + 15 * q^41 - 5 * q^42 - 4 * q^43 - 3 * q^45 + 10 * q^46 - 2 * q^47 - 10 * q^48 + 5 * q^49 - 2 * q^50 + 18 * q^51 - 4 * q^52 + 6 * q^53 - 4 * q^54 + 6 * q^56 - 32 * q^58 - 6 * q^59 - 11 * q^60 - 20 * q^61 - 21 * q^62 + 3 * q^63 - 26 * q^64 + 12 * q^65 + 3 * q^67 - 5 * q^68 + 2 * q^70 - 6 * q^71 - 34 * q^72 - 11 * q^73 + 15 * q^74 - 2 * q^75 - 47 * q^76 + 31 * q^78 - 19 * q^79 - 2 * q^80 + 33 * q^81 - 8 * q^83 + 11 * q^84 + 14 * q^85 + 27 * q^86 + 30 * q^87 + q^89 + 7 * q^90 - 12 * q^91 + 44 * q^92 + 3 * q^93 - 28 * q^94 + 9 * q^95 + 4 * q^96 - 7 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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