LMFDB - Embedded newform 6033.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47960 q^{2} -1.00000 q^{3} +4.14839 q^{4} -2.94703 q^{5} +2.47960 q^{6} -3.66351 q^{7} -5.32715 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.47960 q^{2} -1.00000 q^{3} +4.14839 q^{4} -2.94703 q^{5} +2.47960 q^{6} -3.66351 q^{7} -5.32715 q^{8} +1.00000 q^{9} +7.30744 q^{10} +0.762326 q^{11} -4.14839 q^{12} -0.524844 q^{13} +9.08403 q^{14} +2.94703 q^{15} +4.91239 q^{16} +6.46193 q^{17} -2.47960 q^{18} +3.82814 q^{19} -12.2254 q^{20} +3.66351 q^{21} -1.89026 q^{22} +7.02404 q^{23} +5.32715 q^{24} +3.68497 q^{25} +1.30140 q^{26} -1.00000 q^{27} -15.1977 q^{28} +10.0227 q^{29} -7.30744 q^{30} -4.48215 q^{31} -1.52644 q^{32} -0.762326 q^{33} -16.0230 q^{34} +10.7965 q^{35} +4.14839 q^{36} +7.06200 q^{37} -9.49223 q^{38} +0.524844 q^{39} +15.6993 q^{40} -8.59228 q^{41} -9.08403 q^{42} +12.9553 q^{43} +3.16243 q^{44} -2.94703 q^{45} -17.4168 q^{46} +6.17872 q^{47} -4.91239 q^{48} +6.42133 q^{49} -9.13724 q^{50} -6.46193 q^{51} -2.17726 q^{52} +3.74581 q^{53} +2.47960 q^{54} -2.24660 q^{55} +19.5161 q^{56} -3.82814 q^{57} -24.8523 q^{58} +2.86700 q^{59} +12.2254 q^{60} -8.13652 q^{61} +11.1139 q^{62} -3.66351 q^{63} -6.03983 q^{64} +1.54673 q^{65} +1.89026 q^{66} +5.61825 q^{67} +26.8066 q^{68} -7.02404 q^{69} -26.7709 q^{70} -2.35881 q^{71} -5.32715 q^{72} -9.74309 q^{73} -17.5109 q^{74} -3.68497 q^{75} +15.8806 q^{76} -2.79279 q^{77} -1.30140 q^{78} -5.64573 q^{79} -14.4769 q^{80} +1.00000 q^{81} +21.3054 q^{82} -1.39582 q^{83} +15.1977 q^{84} -19.0435 q^{85} -32.1239 q^{86} -10.0227 q^{87} -4.06103 q^{88} -6.93447 q^{89} +7.30744 q^{90} +1.92277 q^{91} +29.1385 q^{92} +4.48215 q^{93} -15.3207 q^{94} -11.2816 q^{95} +1.52644 q^{96} +14.9713 q^{97} -15.9223 q^{98} +0.762326 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) $ 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9} - 9 q^{10} + 28 q^{11} - 87 q^{12} - 14 q^{13} + 21 q^{14} - 7 q^{15} + 93 q^{16} + 25 q^{17} + 13 q^{18} - 7 q^{19} + 40 q^{20} - 30 q^{21} + 31 q^{22} + 97 q^{23} - 39 q^{24} + 83 q^{25} + 22 q^{26} - 82 q^{27} + 53 q^{28} + 45 q^{29} + 9 q^{30} - 11 q^{31} + 86 q^{32} - 28 q^{33} - 30 q^{34} + 69 q^{35} + 87 q^{36} + 8 q^{37} + 33 q^{38} + 14 q^{39} - 38 q^{40} + 12 q^{41} - 21 q^{42} + 68 q^{43} + 77 q^{44} + 7 q^{45} - 14 q^{46} + 85 q^{47} - 93 q^{48} + 68 q^{49} + 56 q^{50} - 25 q^{51} - 18 q^{52} + 58 q^{53} - 13 q^{54} + 68 q^{55} + 59 q^{56} + 7 q^{57} + 27 q^{58} + 40 q^{59} - 40 q^{60} - 116 q^{61} + 79 q^{62} + 30 q^{63} + 127 q^{64} + 66 q^{65} - 31 q^{66} + 51 q^{67} + 94 q^{68} - 97 q^{69} + q^{70} + 101 q^{71} + 39 q^{72} + 12 q^{73} + 72 q^{74} - 83 q^{75} - 3 q^{76} + 101 q^{77} - 22 q^{78} + 26 q^{79} + 61 q^{80} + 82 q^{81} + 31 q^{82} + 94 q^{83} - 53 q^{84} - 8 q^{85} + 68 q^{86} - 45 q^{87} + 91 q^{88} + 40 q^{89} - 9 q^{90} - 6 q^{91} + 180 q^{92} + 11 q^{93} - 31 q^{94} + 153 q^{95} - 86 q^{96} - 39 q^{97} + 115 q^{98} + 28 q^{99}+O(q^{100}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9 - 9 * q^10 + 28 * q^11 - 87 * q^12 - 14 * q^13 + 21 * q^14 - 7 * q^15 + 93 * q^16 + 25 * q^17 + 13 * q^18 - 7 * q^19 + 40 * q^20 - 30 * q^21 + 31 * q^22 + 97 * q^23 - 39 * q^24 + 83 * q^25 + 22 * q^26 - 82 * q^27 + 53 * q^28 + 45 * q^29 + 9 * q^30 - 11 * q^31 + 86 * q^32 - 28 * q^33 - 30 * q^34 + 69 * q^35 + 87 * q^36 + 8 * q^37 + 33 * q^38 + 14 * q^39 - 38 * q^40 + 12 * q^41 - 21 * q^42 + 68 * q^43 + 77 * q^44 + 7 * q^45 - 14 * q^46 + 85 * q^47 - 93 * q^48 + 68 * q^49 + 56 * q^50 - 25 * q^51 - 18 * q^52 + 58 * q^53 - 13 * q^54 + 68 * q^55 + 59 * q^56 + 7 * q^57 + 27 * q^58 + 40 * q^59 - 40 * q^60 - 116 * q^61 + 79 * q^62 + 30 * q^63 + 127 * q^64 + 66 * q^65 - 31 * q^66 + 51 * q^67 + 94 * q^68 - 97 * q^69 + q^70 + 101 * q^71 + 39 * q^72 + 12 * q^73 + 72 * q^74 - 83 * q^75 - 3 * q^76 + 101 * q^77 - 22 * q^78 + 26 * q^79 + 61 * q^80 + 82 * q^81 + 31 * q^82 + 94 * q^83 - 53 * q^84 - 8 * q^85 + 68 * q^86 - 45 * q^87 + 91 * q^88 + 40 * q^89 - 9 * q^90 - 6 * q^91 + 180 * q^92 + 11 * q^93 - 31 * q^94 + 153 * q^95 - 86 * q^96 - 39 * q^97 + 115 * q^98 + 28 * 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 $

$2$	−2.47960	−1.75334	−0.876669	−	0.481093i	$-0.840240\pi$
$2$	−2.47960	−1.75334	−0.876669	+	0.481093i	$0.840240\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.14839	2.07420
$5$	−2.94703	−1.31795	−0.658975	−	0.752164i	$-0.729010\pi$
$5$	−2.94703	−1.31795	−0.658975	+	0.752164i	$0.729010\pi$
$6$	2.47960	1.01229
$7$	−3.66351	−1.38468	−0.692339	−	0.721573i	$-0.743420\pi$
$7$	−3.66351	−1.38468	−0.692339	+	0.721573i	$0.743420\pi$
$8$	−5.32715	−1.88343
$9$	1.00000	0.333333
$10$	7.30744	2.31081
$11$	0.762326	0.229850	0.114925	−	0.993374i	$-0.463337\pi$
$11$	0.762326	0.229850	0.114925	+	0.993374i	$0.463337\pi$
$12$	−4.14839	−1.19754
$13$	−0.524844	−0.145565	−0.0727827	−	0.997348i	$-0.523188\pi$
$13$	−0.524844	−0.145565	−0.0727827	+	0.997348i	$0.523188\pi$
$14$	9.08403	2.42781
$15$	2.94703	0.760919
$16$	4.91239	1.22810
$17$	6.46193	1.56725	0.783624	−	0.621235i	$-0.213369\pi$
$17$	6.46193	1.56725	0.783624	+	0.621235i	$0.213369\pi$
$18$	−2.47960	−0.584446
$19$	3.82814	0.878235	0.439117	−	0.898430i	$-0.355291\pi$
$19$	3.82814	0.878235	0.439117	+	0.898430i	$0.355291\pi$
$20$	−12.2254	−2.73369
$21$	3.66351	0.799444
$22$	−1.89026	−0.403005
$23$	7.02404	1.46461	0.732306	−	0.680975i	$-0.238444\pi$
$23$	7.02404	1.46461	0.732306	+	0.680975i	$0.238444\pi$
$24$	5.32715	1.08740
$25$	3.68497	0.736994
$26$	1.30140	0.255226
$27$	−1.00000	−0.192450
$28$	−15.1977	−2.87209
$29$	10.0227	1.86117	0.930586	−	0.366074i	$-0.119298\pi$
$29$	10.0227	1.86117	0.930586	+	0.366074i	$0.119298\pi$
$30$	−7.30744	−1.33415
$31$	−4.48215	−0.805018	−0.402509	−	0.915416i	$-0.631862\pi$
$31$	−4.48215	−0.805018	−0.402509	+	0.915416i	$0.631862\pi$
$32$	−1.52644	−0.269839
$33$	−0.762326	−0.132704
$34$	−16.0230	−2.74792
$35$	10.7965	1.82494
$36$	4.14839	0.691399
$37$	7.06200	1.16099	0.580493	−	0.814265i	$-0.302860\pi$
$37$	7.06200	1.16099	0.580493	+	0.814265i	$0.302860\pi$
$38$	−9.49223	−1.53984
$39$	0.524844	0.0840423
$40$	15.6993	2.48227
$41$	−8.59228	−1.34189	−0.670945	−	0.741508i	$-0.734111\pi$
$41$	−8.59228	−1.34189	−0.670945	+	0.741508i	$0.734111\pi$
$42$	−9.08403	−1.40170
$43$	12.9553	1.97566	0.987831	−	0.155532i	$-0.0497092\pi$
$43$	12.9553	1.97566	0.987831	+	0.155532i	$0.0497092\pi$
$44$	3.16243	0.476754
$45$	−2.94703	−0.439317
$46$	−17.4168	−2.56796
$47$	6.17872	0.901260	0.450630	−	0.892711i	$-0.351199\pi$
$47$	6.17872	0.901260	0.450630	+	0.892711i	$0.351199\pi$
$48$	−4.91239	−0.709042
$49$	6.42133	0.917332
$50$	−9.13724	−1.29220
$51$	−6.46193	−0.904852
$52$	−2.17726	−0.301932
$53$	3.74581	0.514526	0.257263	−	0.966341i	$-0.417179\pi$
$53$	3.74581	0.514526	0.257263	+	0.966341i	$0.417179\pi$
$54$	2.47960	0.337430
$55$	−2.24660	−0.302931
$56$	19.5161	2.60795
$57$	−3.82814	−0.507049
$58$	−24.8523	−3.26326
$59$	2.86700	0.373252	0.186626	−	0.982431i	$-0.440245\pi$
$59$	2.86700	0.373252	0.186626	+	0.982431i	$0.440245\pi$
$60$	12.2254	1.57830
$61$	−8.13652	−1.04177	−0.520887	−	0.853625i	$-0.674399\pi$
$61$	−8.13652	−1.04177	−0.520887	+	0.853625i	$0.674399\pi$
$62$	11.1139	1.41147
$63$	−3.66351	−0.461559
$64$	−6.03983	−0.754978
$65$	1.54673	0.191848
$66$	1.89026	0.232675
$67$	5.61825	0.686378	0.343189	−	0.939266i	$-0.388493\pi$
$67$	5.61825	0.686378	0.343189	+	0.939266i	$0.388493\pi$
$68$	26.8066	3.25078
$69$	−7.02404	−0.845595
$70$	−26.7709	−3.19973
$71$	−2.35881	−0.279939	−0.139969	−	0.990156i	$-0.544700\pi$
$71$	−2.35881	−0.279939	−0.139969	+	0.990156i	$0.544700\pi$
$72$	−5.32715	−0.627811
$73$	−9.74309	−1.14034	−0.570172	−	0.821526i	$-0.693123\pi$
$73$	−9.74309	−1.14034	−0.570172	+	0.821526i	$0.693123\pi$
$74$	−17.5109	−2.03560
$75$	−3.68497	−0.425504
$76$	15.8806	1.82163
$77$	−2.79279	−0.318268
$78$	−1.30140	−0.147355
$79$	−5.64573	−0.635194	−0.317597	−	0.948226i	$-0.602876\pi$
$79$	−5.64573	−0.635194	−0.317597	+	0.948226i	$0.602876\pi$
$80$	−14.4769	−1.61857
$81$	1.00000	0.111111
$82$	21.3054	2.35279
$83$	−1.39582	−0.153211	−0.0766057	−	0.997061i	$-0.524408\pi$
$83$	−1.39582	−0.153211	−0.0766057	+	0.997061i	$0.524408\pi$
$84$	15.1977	1.65820
$85$	−19.0435	−2.06556
$86$	−32.1239	−3.46400
$87$	−10.0227	−1.07455
$88$	−4.06103	−0.432907
$89$	−6.93447	−0.735053	−0.367526	−	0.930013i	$-0.619795\pi$
$89$	−6.93447	−0.735053	−0.367526	+	0.930013i	$0.619795\pi$
$90$	7.30744	0.770271
$91$	1.92277	0.201561
$92$	29.1385	3.03790
$93$	4.48215	0.464777
$94$	−15.3207	−1.58021
$95$	−11.2816	−1.15747
$96$	1.52644	0.155792
$97$	14.9713	1.52010	0.760052	−	0.649863i	$-0.225174\pi$
$97$	14.9713	1.52010	0.760052	+	0.649863i	$0.225174\pi$
$98$	−15.9223	−1.60839
$99$	0.762326	0.0766166
$100$	15.2867	1.52867
$101$	10.2761	1.02251	0.511255	−	0.859429i	$-0.329181\pi$
$101$	10.2761	1.02251	0.511255	+	0.859429i	$0.329181\pi$
$102$	16.0230	1.58651
$103$	−17.1791	−1.69271	−0.846354	−	0.532620i	$-0.821207\pi$
$103$	−17.1791	−1.69271	−0.846354	+	0.532620i	$0.821207\pi$
$104$	2.79592	0.274163
$105$	−10.7965	−1.05363
$106$	−9.28809	−0.902139
$107$	−3.35481	−0.324322	−0.162161	−	0.986764i	$-0.551846\pi$
$107$	−3.35481	−0.324322	−0.162161	+	0.986764i	$0.551846\pi$
$108$	−4.14839	−0.399179
$109$	3.88501	0.372117	0.186058	−	0.982539i	$-0.440429\pi$
$109$	3.88501	0.372117	0.186058	+	0.982539i	$0.440429\pi$
$110$	5.57065	0.531141
$111$	−7.06200	−0.670295
$112$	−17.9966	−1.70052
$113$	13.1886	1.24068	0.620339	−	0.784334i	$-0.286995\pi$
$113$	13.1886	1.24068	0.620339	+	0.784334i	$0.286995\pi$
$114$	9.49223	0.889029
$115$	−20.7000	−1.93029
$116$	41.5782	3.86044
$117$	−0.524844	−0.0485218
$118$	−7.10900	−0.654437
$119$	−23.6734	−2.17013
$120$	−15.6993	−1.43314
$121$	−10.4189	−0.947169
$122$	20.1753	1.82658
$123$	8.59228	0.774740
$124$	−18.5937	−1.66977
$125$	3.87542	0.346628
$126$	9.08403	0.809270
$127$	2.94625	0.261437	0.130719	−	0.991419i	$-0.458272\pi$
$127$	2.94625	0.261437	0.130719	+	0.991419i	$0.458272\pi$
$128$	18.0292	1.59357
$129$	−12.9553	−1.14065
$130$	−3.83526	−0.336375
$131$	0.647211	0.0565471	0.0282735	−	0.999600i	$-0.490999\pi$
$131$	0.647211	0.0565471	0.0282735	+	0.999600i	$0.490999\pi$
$132$	−3.16243	−0.275254
$133$	−14.0244	−1.21607
$134$	−13.9310	−1.20345
$135$	2.94703	0.253640
$136$	−34.4237	−2.95181
$137$	2.40188	0.205207	0.102603	−	0.994722i	$-0.467283\pi$
$137$	2.40188	0.205207	0.102603	+	0.994722i	$0.467283\pi$
$138$	17.4168	1.48261
$139$	−20.9021	−1.77289	−0.886447	−	0.462831i	$-0.846834\pi$
$139$	−20.9021	−1.77289	−0.886447	+	0.462831i	$0.846834\pi$
$140$	44.7880	3.78528
$141$	−6.17872	−0.520342
$142$	5.84889	0.490828
$143$	−0.400102	−0.0334582
$144$	4.91239	0.409366
$145$	−29.5372	−2.45293
$146$	24.1589	1.99941
$147$	−6.42133	−0.529622
$148$	29.2960	2.40811
$149$	6.49226	0.531867	0.265933	−	0.963991i	$-0.414320\pi$
$149$	6.49226	0.531867	0.265933	+	0.963991i	$0.414320\pi$
$150$	9.13724	0.746053
$151$	20.3023	1.65218	0.826089	−	0.563539i	$-0.190561\pi$
$151$	20.3023	1.65218	0.826089	+	0.563539i	$0.190561\pi$
$152$	−20.3931	−1.65410
$153$	6.46193	0.522416
$154$	6.92499	0.558032
$155$	13.2090	1.06097
$156$	2.17726	0.174320
$157$	−4.87679	−0.389210	−0.194605	−	0.980882i	$-0.562343\pi$
$157$	−4.87679	−0.389210	−0.194605	+	0.980882i	$0.562343\pi$
$158$	13.9991	1.11371
$159$	−3.74581	−0.297062
$160$	4.49846	0.355635
$161$	−25.7326	−2.02802
$162$	−2.47960	−0.194815
$163$	−2.84119	−0.222539	−0.111269	−	0.993790i	$-0.535492\pi$
$163$	−2.84119	−0.222539	−0.111269	+	0.993790i	$0.535492\pi$
$164$	−35.6442	−2.78334
$165$	2.24660	0.174897
$166$	3.46108	0.268632
$167$	10.6413	0.823448	0.411724	−	0.911308i	$-0.364927\pi$
$167$	10.6413	0.823448	0.411724	+	0.911308i	$0.364927\pi$
$168$	−19.5161	−1.50570
$169$	−12.7245	−0.978811
$170$	47.2202	3.62162
$171$	3.82814	0.292745
$172$	53.7436	4.09791
$173$	7.82678	0.595059	0.297529	−	0.954713i	$-0.403837\pi$
$173$	7.82678	0.595059	0.297529	+	0.954713i	$0.403837\pi$
$174$	24.8523	1.88405
$175$	−13.4999	−1.02050
$176$	3.74484	0.282278
$177$	−2.86700	−0.215497
$178$	17.1947	1.28880
$179$	24.2254	1.81069	0.905346	−	0.424675i	$-0.139612\pi$
$179$	24.2254	1.81069	0.905346	+	0.424675i	$0.139612\pi$
$180$	−12.2254	−0.911230
$181$	1.41828	0.105420	0.0527098	−	0.998610i	$-0.483214\pi$
$181$	1.41828	0.105420	0.0527098	+	0.998610i	$0.483214\pi$
$182$	−4.76770	−0.353405
$183$	8.13652	0.601469
$184$	−37.4181	−2.75850
$185$	−20.8119	−1.53012
$186$	−11.1139	−0.814912
$187$	4.92610	0.360232
$188$	25.6318	1.86939
$189$	3.66351	0.266481
$190$	27.9739	2.02944
$191$	25.9357	1.87664	0.938322	−	0.345763i	$-0.112380\pi$
$191$	25.9357	1.87664	0.938322	+	0.345763i	$0.112380\pi$
$192$	6.03983	0.435887
$193$	−0.404825	−0.0291400	−0.0145700	−	0.999894i	$-0.504638\pi$
$193$	−0.404825	−0.0291400	−0.0145700	+	0.999894i	$0.504638\pi$
$194$	−37.1227	−2.66526
$195$	−1.54673	−0.110764
$196$	26.6382	1.90273
$197$	0.600114	0.0427564	0.0213782	−	0.999771i	$-0.493195\pi$
$197$	0.600114	0.0427564	0.0213782	+	0.999771i	$0.493195\pi$
$198$	−1.89026	−0.134335
$199$	1.26905	0.0899607	0.0449803	−	0.998988i	$-0.485677\pi$
$199$	1.26905	0.0899607	0.0449803	+	0.998988i	$0.485677\pi$
$200$	−19.6304	−1.38808
$201$	−5.61825	−0.396280
$202$	−25.4805	−1.79280
$203$	−36.7183	−2.57712
$204$	−26.8066	−1.87684
$205$	25.3217	1.76854
$206$	42.5973	2.96789
$207$	7.02404	0.488204
$208$	−2.57824	−0.178769
$209$	2.91829	0.201862
$210$	26.7709	1.84737
$211$	28.7933	1.98221	0.991107	−	0.133068i	$-0.0424828\pi$
$211$	28.7933	1.98221	0.991107	+	0.133068i	$0.0424828\pi$
$212$	15.5391	1.06723
$213$	2.35881	0.161623
$214$	8.31858	0.568646
$215$	−38.1796	−2.60382
$216$	5.32715	0.362467
$217$	16.4204	1.11469
$218$	−9.63327	−0.652447
$219$	9.74309	0.658377
$220$	−9.31977	−0.628339
$221$	−3.39151	−0.228137
$222$	17.5109	1.17525
$223$	−1.97684	−0.132379	−0.0661895	−	0.997807i	$-0.521084\pi$
$223$	−1.97684	−0.132379	−0.0661895	+	0.997807i	$0.521084\pi$
$224$	5.59213	0.373640
$225$	3.68497	0.245665
$226$	−32.7023	−2.17533
$227$	−19.8520	−1.31762	−0.658811	−	0.752309i	$-0.728940\pi$
$227$	−19.8520	−1.31762	−0.658811	+	0.752309i	$0.728940\pi$
$228$	−15.8806	−1.05172
$229$	−4.62908	−0.305898	−0.152949	−	0.988234i	$-0.548877\pi$
$229$	−4.62908	−0.305898	−0.152949	+	0.988234i	$0.548877\pi$
$230$	51.3277	3.38445
$231$	2.79279	0.183752
$232$	−53.3925	−3.50539
$233$	3.28012	0.214888	0.107444	−	0.994211i	$-0.465733\pi$
$233$	3.28012	0.214888	0.107444	+	0.994211i	$0.465733\pi$
$234$	1.30140	0.0850752
$235$	−18.2089	−1.18782
$236$	11.8934	0.774198
$237$	5.64573	0.366729
$238$	58.7004	3.80498
$239$	−24.7531	−1.60115	−0.800573	−	0.599236i	$-0.795471\pi$
$239$	−24.7531	−1.60115	−0.800573	+	0.599236i	$0.795471\pi$
$240$	14.4769	0.934483
$241$	−3.75403	−0.241819	−0.120909	−	0.992664i	$-0.538581\pi$
$241$	−3.75403	−0.241819	−0.120909	+	0.992664i	$0.538581\pi$
$242$	25.8346	1.66071
$243$	−1.00000	−0.0641500
$244$	−33.7535	−2.16085
$245$	−18.9238	−1.20900
$246$	−21.3054	−1.35838
$247$	−2.00917	−0.127841
$248$	23.8771	1.51620
$249$	1.39582	0.0884567
$250$	−9.60949	−0.607757
$251$	−7.86502	−0.496436	−0.248218	−	0.968704i	$-0.579845\pi$
$251$	−7.86502	−0.496436	−0.248218	+	0.968704i	$0.579845\pi$
$252$	−15.1977	−0.957365
$253$	5.35461	0.336641
$254$	−7.30551	−0.458388
$255$	19.0435	1.19255
$256$	−32.6255	−2.03909
$257$	−16.8170	−1.04902	−0.524509	−	0.851405i	$-0.675751\pi$
$257$	−16.8170	−1.04902	−0.524509	+	0.851405i	$0.675751\pi$
$258$	32.1239	1.99994
$259$	−25.8717	−1.60759
$260$	6.41644	0.397931
$261$	10.0227	0.620391
$262$	−1.60482	−0.0991462
$263$	20.5677	1.26826	0.634129	−	0.773228i	$-0.281359\pi$
$263$	20.5677	1.26826	0.634129	+	0.773228i	$0.281359\pi$
$264$	4.06103	0.249939
$265$	−11.0390	−0.678120
$266$	34.7749	2.13219
$267$	6.93447	0.424383
$268$	23.3067	1.42368
$269$	−18.9273	−1.15402	−0.577009	−	0.816738i	$-0.695780\pi$
$269$	−18.9273	−1.15402	−0.577009	+	0.816738i	$0.695780\pi$
$270$	−7.30744	−0.444716
$271$	−1.77103	−0.107582	−0.0537911	−	0.998552i	$-0.517131\pi$
$271$	−1.77103	−0.107582	−0.0537911	+	0.998552i	$0.517131\pi$
$272$	31.7435	1.92473
$273$	−1.92277	−0.116371
$274$	−5.95570	−0.359797
$275$	2.80915	0.169398
$276$	−29.1385	−1.75393
$277$	29.6064	1.77888	0.889440	−	0.457053i	$-0.151095\pi$
$277$	29.6064	1.77888	0.889440	+	0.457053i	$0.151095\pi$
$278$	51.8288	3.10848
$279$	−4.48215	−0.268339
$280$	−57.5144	−3.43715
$281$	−20.8712	−1.24507	−0.622537	−	0.782591i	$-0.713898\pi$
$281$	−20.8712	−1.24507	−0.622537	+	0.782591i	$0.713898\pi$
$282$	15.3207	0.912337
$283$	6.29401	0.374140	0.187070	−	0.982347i	$-0.440101\pi$
$283$	6.29401	0.374140	0.187070	+	0.982347i	$0.440101\pi$
$284$	−9.78527	−0.580649
$285$	11.2816	0.668266
$286$	0.992091	0.0586636
$287$	31.4779	1.85808
$288$	−1.52644	−0.0899463
$289$	24.7566	1.45627
$290$	73.2404	4.30082
$291$	−14.9713	−0.877632
$292$	−40.4182	−2.36530
$293$	15.3531	0.896938	0.448469	−	0.893798i	$-0.351969\pi$
$293$	15.3531	0.896938	0.448469	+	0.893798i	$0.351969\pi$
$294$	15.9223	0.928607
$295$	−8.44913	−0.491927
$296$	−37.6203	−2.18664
$297$	−0.762326	−0.0442346
$298$	−16.0982	−0.932543
$299$	−3.68652	−0.213197
$300$	−15.2867	−0.882579
$301$	−47.4618	−2.73565
$302$	−50.3415	−2.89683
$303$	−10.2761	−0.590346
$304$	18.8053	1.07856
$305$	23.9786	1.37301
$306$	−16.0230	−0.915973
$307$	−1.59570	−0.0910717	−0.0455358	−	0.998963i	$-0.514500\pi$
$307$	−1.59570	−0.0910717	−0.0455358	+	0.998963i	$0.514500\pi$
$308$	−11.5856	−0.660151
$309$	17.1791	0.977286
$310$	−32.7530	−1.86025
$311$	6.21429	0.352380	0.176190	−	0.984356i	$-0.443623\pi$
$311$	6.21429	0.352380	0.176190	+	0.984356i	$0.443623\pi$
$312$	−2.79592	−0.158288
$313$	−15.5194	−0.877207	−0.438604	−	0.898681i	$-0.644527\pi$
$313$	−15.5194	−0.877207	−0.438604	+	0.898681i	$0.644527\pi$
$314$	12.0925	0.682418
$315$	10.7965	0.608312
$316$	−23.4207	−1.31752
$317$	20.5977	1.15688	0.578442	−	0.815724i	$-0.303661\pi$
$317$	20.5977	1.15688	0.578442	+	0.815724i	$0.303661\pi$
$318$	9.28809	0.520850
$319$	7.64058	0.427790
$320$	17.7995	0.995024
$321$	3.35481	0.187247
$322$	63.8066	3.55580
$323$	24.7372	1.37641
$324$	4.14839	0.230466
$325$	−1.93403	−0.107281
$326$	7.04499	0.390186
$327$	−3.88501	−0.214842
$328$	45.7724	2.52736
$329$	−22.6358	−1.24795
$330$	−5.57065	−0.306654
$331$	28.9951	1.59371	0.796857	−	0.604168i	$-0.206494\pi$
$331$	28.9951	1.59371	0.796857	+	0.604168i	$0.206494\pi$
$332$	−5.79043	−0.317791
$333$	7.06200	0.386995
$334$	−26.3861	−1.44378
$335$	−16.5571	−0.904612
$336$	17.9966	0.981795
$337$	1.67789	0.0914006	0.0457003	−	0.998955i	$-0.485448\pi$
$337$	1.67789	0.0914006	0.0457003	+	0.998955i	$0.485448\pi$
$338$	31.5517	1.71619
$339$	−13.1886	−0.716305
$340$	−78.9999	−4.28437
$341$	−3.41686	−0.185033
$342$	−9.49223	−0.513281
$343$	2.11998	0.114468
$344$	−69.0147	−3.72102
$345$	20.7000	1.11445
$346$	−19.4072	−1.04334
$347$	−27.8178	−1.49334	−0.746669	−	0.665196i	$-0.768348\pi$
$347$	−27.8178	−1.49334	−0.746669	+	0.665196i	$0.768348\pi$
$348$	−41.5782	−2.22882
$349$	4.02376	0.215387	0.107693	−	0.994184i	$-0.465654\pi$
$349$	4.02376	0.215387	0.107693	+	0.994184i	$0.465654\pi$
$350$	33.4744	1.78928
$351$	0.524844	0.0280141
$352$	−1.16365	−0.0620225
$353$	−34.2534	−1.82312	−0.911562	−	0.411163i	$-0.865123\pi$
$353$	−34.2534	−1.82312	−0.911562	+	0.411163i	$0.865123\pi$
$354$	7.10900	0.377839
$355$	6.95147	0.368946
$356$	−28.7669	−1.52464
$357$	23.6734	1.25293
$358$	−60.0692	−3.17476
$359$	−10.9644	−0.578679	−0.289339	−	0.957227i	$-0.593436\pi$
$359$	−10.9644	−0.578679	−0.289339	+	0.957227i	$0.593436\pi$
$360$	15.6993	0.827424
$361$	−4.34538	−0.228704
$362$	−3.51675	−0.184836
$363$	10.4189	0.546848
$364$	7.97642	0.418078
$365$	28.7132	1.50292
$366$	−20.1753	−1.05458
$367$	35.4160	1.84870	0.924350	−	0.381546i	$-0.124608\pi$
$367$	35.4160	1.84870	0.924350	+	0.381546i	$0.124608\pi$
$368$	34.5048	1.79869
$369$	−8.59228	−0.447296
$370$	51.6051	2.68282
$371$	−13.7228	−0.712453
$372$	18.5937	0.964040
$373$	−20.7820	−1.07605	−0.538025	−	0.842929i	$-0.680829\pi$
$373$	−20.7820	−1.07605	−0.538025	+	0.842929i	$0.680829\pi$
$374$	−12.2147	−0.631609
$375$	−3.87542	−0.200126
$376$	−32.9150	−1.69746
$377$	−5.26036	−0.270922
$378$	−9.08403	−0.467232
$379$	−38.3093	−1.96782	−0.983908	−	0.178677i	$-0.942818\pi$
$379$	−38.3093	−1.96782	−0.983908	+	0.178677i	$0.942818\pi$
$380$	−46.8006	−2.40082
$381$	−2.94625	−0.150941
$382$	−64.3101	−3.29039
$383$	−17.1140	−0.874484	−0.437242	−	0.899344i	$-0.644045\pi$
$383$	−17.1140	−0.874484	−0.437242	+	0.899344i	$0.644045\pi$
$384$	−18.0292	−0.920049
$385$	8.23043	0.419462
$386$	1.00380	0.0510922
$387$	12.9553	0.658554
$388$	62.1068	3.15299
$389$	18.2530	0.925462	0.462731	−	0.886499i	$-0.346870\pi$
$389$	18.2530	0.925462	0.462731	+	0.886499i	$0.346870\pi$
$390$	3.83526	0.194206
$391$	45.3888	2.29541
$392$	−34.2074	−1.72773
$393$	−0.647211	−0.0326475
$394$	−1.48804	−0.0749664
$395$	16.6381	0.837155
$396$	3.16243	0.158918
$397$	15.6544	0.785673	0.392837	−	0.919608i	$-0.371494\pi$
$397$	15.6544	0.785673	0.392837	+	0.919608i	$0.371494\pi$
$398$	−3.14673	−0.157732
$399$	14.0244	0.702099
$400$	18.1020	0.905101
$401$	−10.0463	−0.501687	−0.250843	−	0.968028i	$-0.580708\pi$
$401$	−10.0463	−0.501687	−0.250843	+	0.968028i	$0.580708\pi$
$402$	13.9310	0.694814
$403$	2.35243	0.117183
$404$	42.6293	2.12089
$405$	−2.94703	−0.146439
$406$	91.0467	4.51857
$407$	5.38355	0.266852
$408$	34.4237	1.70423
$409$	−4.83082	−0.238869	−0.119434	−	0.992842i	$-0.538108\pi$
$409$	−4.83082	−0.238869	−0.119434	+	0.992842i	$0.538108\pi$
$410$	−62.7876	−3.10086
$411$	−2.40188	−0.118476
$412$	−71.2658	−3.51101
$413$	−10.5033	−0.516833
$414$	−17.4168	−0.855987
$415$	4.11353	0.201925
$416$	0.801143	0.0392792
$417$	20.9021	1.02358
$418$	−7.23617	−0.353933
$419$	2.92841	0.143062	0.0715312	−	0.997438i	$-0.477211\pi$
$419$	2.92841	0.143062	0.0715312	+	0.997438i	$0.477211\pi$
$420$	−44.7880	−2.18543
$421$	−37.7795	−1.84126	−0.920630	−	0.390437i	$-0.872324\pi$
$421$	−37.7795	−1.84126	−0.920630	+	0.390437i	$0.872324\pi$
$422$	−71.3958	−3.47549
$423$	6.17872	0.300420
$424$	−19.9545	−0.969075
$425$	23.8120	1.15505
$426$	−5.84889	−0.283380
$427$	29.8083	1.44252
$428$	−13.9171	−0.672708
$429$	0.400102	0.0193171
$430$	94.6699	4.56539
$431$	37.7217	1.81699	0.908494	−	0.417897i	$-0.137233\pi$
$431$	37.7217	1.81699	0.908494	+	0.417897i	$0.137233\pi$
$432$	−4.91239	−0.236347
$433$	−17.6083	−0.846202	−0.423101	−	0.906082i	$-0.639058\pi$
$433$	−17.6083	−0.846202	−0.423101	+	0.906082i	$0.639058\pi$
$434$	−40.7160	−1.95443
$435$	29.5372	1.41620
$436$	16.1166	0.771844
$437$	26.8890	1.28627
$438$	−24.1589	−1.15436
$439$	34.2050	1.63252	0.816259	−	0.577687i	$-0.196044\pi$
$439$	34.2050	1.63252	0.816259	+	0.577687i	$0.196044\pi$
$440$	11.9680	0.570550
$441$	6.42133	0.305777
$442$	8.40956	0.400002
$443$	−35.2937	−1.67686	−0.838428	−	0.545013i	$-0.816525\pi$
$443$	−35.2937	−1.67686	−0.838428	+	0.545013i	$0.816525\pi$
$444$	−29.2960	−1.39032
$445$	20.4361	0.968764
$446$	4.90176	0.232105
$447$	−6.49226	−0.307073
$448$	22.1270	1.04540
$449$	−22.6667	−1.06971	−0.534853	−	0.844945i	$-0.679633\pi$
$449$	−22.6667	−1.06971	−0.534853	+	0.844945i	$0.679633\pi$
$450$	−9.13724	−0.430734
$451$	−6.55012	−0.308433
$452$	54.7114	2.57341
$453$	−20.3023	−0.953886
$454$	49.2249	2.31024
$455$	−5.66646	−0.265648
$456$	20.3931	0.954992
$457$	4.19532	0.196249	0.0981243	−	0.995174i	$-0.468716\pi$
$457$	4.19532	0.196249	0.0981243	+	0.995174i	$0.468716\pi$
$458$	11.4783	0.536344
$459$	−6.46193	−0.301617
$460$	−85.8719	−4.00380
$461$	−28.5821	−1.33120	−0.665601	−	0.746307i	$-0.731825\pi$
$461$	−28.5821	−1.33120	−0.665601	+	0.746307i	$0.731825\pi$
$462$	−6.92499	−0.322180
$463$	33.6570	1.56418	0.782088	−	0.623168i	$-0.214155\pi$
$463$	33.6570	1.56418	0.782088	+	0.623168i	$0.214155\pi$
$464$	49.2355	2.28570
$465$	−13.2090	−0.612554
$466$	−8.13338	−0.376772
$467$	9.60195	0.444325	0.222163	−	0.975010i	$-0.428688\pi$
$467$	9.60195	0.444325	0.222163	+	0.975010i	$0.428688\pi$
$468$	−2.17726	−0.100644
$469$	−20.5825	−0.950412
$470$	45.1506	2.08264
$471$	4.87679	0.224711
$472$	−15.2729	−0.702994
$473$	9.87615	0.454106
$474$	−13.9991	−0.643001
$475$	14.1066	0.647254
$476$	−98.2065	−4.50129
$477$	3.74581	0.171509
$478$	61.3777	2.80735
$479$	7.37946	0.337176	0.168588	−	0.985687i	$-0.446079\pi$
$479$	7.37946	0.337176	0.168588	+	0.985687i	$0.446079\pi$
$480$	−4.49846	−0.205326
$481$	−3.70645	−0.168999
$482$	9.30849	0.423990
$483$	25.7326	1.17088
$484$	−43.2215	−1.96462
$485$	−44.1208	−2.00342
$486$	2.47960	0.112477
$487$	−2.60383	−0.117991	−0.0589953	−	0.998258i	$-0.518790\pi$
$487$	−2.60383	−0.117991	−0.0589953	+	0.998258i	$0.518790\pi$
$488$	43.3445	1.96211
$489$	2.84119	0.128483
$490$	46.9234	2.11978
$491$	−23.6770	−1.06853	−0.534264	−	0.845318i	$-0.679411\pi$
$491$	−23.6770	−1.06853	−0.534264	+	0.845318i	$0.679411\pi$
$492$	35.6442	1.60696
$493$	64.7661	2.91692
$494$	4.98194	0.224148
$495$	−2.24660	−0.100977
$496$	−22.0181	−0.988641
$497$	8.64152	0.387625
$498$	−3.46108	−0.155095
$499$	−22.8837	−1.02441	−0.512206	−	0.858862i	$-0.671172\pi$
$499$	−22.8837	−1.02441	−0.512206	+	0.858862i	$0.671172\pi$
$500$	16.0768	0.718976
$501$	−10.6413	−0.475418
$502$	19.5021	0.870420
$503$	4.79832	0.213947	0.106973	−	0.994262i	$-0.465884\pi$
$503$	4.79832	0.213947	0.106973	+	0.994262i	$0.465884\pi$
$504$	19.5161	0.869316
$505$	−30.2839	−1.34762
$506$	−13.2773	−0.590246
$507$	12.7245	0.565117
$508$	12.2222	0.542273
$509$	4.37720	0.194016	0.0970080	−	0.995284i	$-0.469073\pi$
$509$	4.37720	0.194016	0.0970080	+	0.995284i	$0.469073\pi$
$510$	−47.2202	−2.09094
$511$	35.6940	1.57901
$512$	44.8396	1.98165
$513$	−3.82814	−0.169016
$514$	41.6994	1.83928
$515$	50.6273	2.23091
$516$	−53.7436	−2.36593
$517$	4.71020	0.207154
$518$	64.1514	2.81865
$519$	−7.82678	−0.343557
$520$	−8.23966	−0.361333
$521$	−2.32162	−0.101712	−0.0508560	−	0.998706i	$-0.516195\pi$
$521$	−2.32162	−0.101712	−0.0508560	+	0.998706i	$0.516195\pi$
$522$	−24.8523	−1.08775
$523$	−13.4558	−0.588382	−0.294191	−	0.955747i	$-0.595050\pi$
$523$	−13.4558	−0.588382	−0.294191	+	0.955747i	$0.595050\pi$
$524$	2.68489	0.117290
$525$	13.4999	0.589186
$526$	−50.9995	−2.22369
$527$	−28.9634	−1.26166
$528$	−3.74484	−0.162973
$529$	26.3371	1.14509
$530$	27.3723	1.18897
$531$	2.86700	0.124417
$532$	−58.1789	−2.52237
$533$	4.50961	0.195333
$534$	−17.1947	−0.744087
$535$	9.88673	0.427440
$536$	−29.9292	−1.29275
$537$	−24.2254	−1.04540
$538$	46.9320	2.02338
$539$	4.89514	0.210849
$540$	12.2254	0.526099
$541$	−10.5727	−0.454555	−0.227277	−	0.973830i	$-0.572982\pi$
$541$	−10.5727	−0.454555	−0.227277	+	0.973830i	$0.572982\pi$
$542$	4.39143	0.188628
$543$	−1.41828	−0.0608640
$544$	−9.86375	−0.422905
$545$	−11.4492	−0.490432
$546$	4.76770	0.204039
$547$	−18.5624	−0.793672	−0.396836	−	0.917889i	$-0.629892\pi$
$547$	−18.5624	−0.793672	−0.396836	+	0.917889i	$0.629892\pi$
$548$	9.96396	0.425639
$549$	−8.13652	−0.347258
$550$	−6.96556	−0.297012
$551$	38.3683	1.63455
$552$	37.4181	1.59262
$553$	20.6832	0.879539
$554$	−73.4120	−3.11898
$555$	20.8119	0.883416
$556$	−86.7102	−3.67733
$557$	6.44162	0.272940	0.136470	−	0.990644i	$-0.456424\pi$
$557$	6.44162	0.272940	0.136470	+	0.990644i	$0.456424\pi$
$558$	11.1139	0.470490
$559$	−6.79950	−0.287588
$560$	53.0365	2.24120
$561$	−4.92610	−0.207980
$562$	51.7522	2.18304
$563$	−24.9408	−1.05113	−0.525564	−	0.850754i	$-0.676146\pi$
$563$	−24.9408	−1.05113	−0.525564	+	0.850754i	$0.676146\pi$
$564$	−25.6318	−1.07929
$565$	−38.8671	−1.63515
$566$	−15.6066	−0.655995
$567$	−3.66351	−0.153853
$568$	12.5657	0.527246
$569$	25.8991	1.08575	0.542874	−	0.839814i	$-0.317336\pi$
$569$	25.8991	1.08575	0.542874	+	0.839814i	$0.317336\pi$
$570$	−27.9739	−1.17170
$571$	0.971587	0.0406596	0.0203298	−	0.999793i	$-0.493528\pi$
$571$	0.971587	0.0406596	0.0203298	+	0.999793i	$0.493528\pi$
$572$	−1.65978	−0.0693989
$573$	−25.9357	−1.08348
$574$	−78.0526	−3.25785
$575$	25.8834	1.07941
$576$	−6.03983	−0.251659
$577$	34.0214	1.41633	0.708165	−	0.706047i	$-0.249523\pi$
$577$	34.0214	1.41633	0.708165	+	0.706047i	$0.249523\pi$
$578$	−61.3863	−2.55333
$579$	0.404825	0.0168240
$580$	−122.532	−5.08787
$581$	5.11362	0.212149
$582$	37.1227	1.53879
$583$	2.85553	0.118264
$584$	51.9029	2.14776
$585$	1.54673	0.0639494
$586$	−38.0695	−1.57264
$587$	36.5685	1.50934	0.754671	−	0.656103i	$-0.227796\pi$
$587$	36.5685	1.50934	0.754671	+	0.656103i	$0.227796\pi$
$588$	−26.6382	−1.09854
$589$	−17.1583	−0.706995
$590$	20.9504	0.862515
$591$	−0.600114	−0.0246854
$592$	34.6913	1.42580
$593$	23.4970	0.964905	0.482453	−	0.875922i	$-0.339746\pi$
$593$	23.4970	0.964905	0.482453	+	0.875922i	$0.339746\pi$
$594$	1.89026	0.0775583
$595$	69.7661	2.86013
$596$	26.9325	1.10320
$597$	−1.26905	−0.0519388
$598$	9.14108	0.373807
$599$	21.3677	0.873060	0.436530	−	0.899690i	$-0.356207\pi$
$599$	21.3677	0.873060	0.436530	+	0.899690i	$0.356207\pi$
$600$	19.6304	0.801408
$601$	−38.3475	−1.56423	−0.782115	−	0.623135i	$-0.785859\pi$
$601$	−38.3475	−1.56423	−0.782115	+	0.623135i	$0.785859\pi$
$602$	117.686	4.79653
$603$	5.61825	0.228793
$604$	84.2220	3.42695
$605$	30.7047	1.24832
$606$	25.4805	1.03508
$607$	−30.1227	−1.22264	−0.611322	−	0.791382i	$-0.709362\pi$
$607$	−30.1227	−1.22264	−0.611322	+	0.791382i	$0.709362\pi$
$608$	−5.84342	−0.236982
$609$	36.7183	1.48790
$610$	−59.4571	−2.40735
$611$	−3.24286	−0.131192
$612$	26.8066	1.08359
$613$	12.5114	0.505330	0.252665	−	0.967554i	$-0.418693\pi$
$613$	12.5114	0.505330	0.252665	+	0.967554i	$0.418693\pi$
$614$	3.95670	0.159679
$615$	−25.3217	−1.02107
$616$	14.8776	0.599436
$617$	−4.26392	−0.171659	−0.0858294	−	0.996310i	$-0.527354\pi$
$617$	−4.26392	−0.171659	−0.0858294	+	0.996310i	$0.527354\pi$
$618$	−42.5973	−1.71351
$619$	43.1051	1.73254	0.866269	−	0.499577i	$-0.166511\pi$
$619$	43.1051	1.73254	0.866269	+	0.499577i	$0.166511\pi$
$620$	54.7962	2.20067
$621$	−7.02404	−0.281865
$622$	−15.4089	−0.617841
$623$	25.4045	1.01781
$624$	2.57824	0.103212
$625$	−29.8458	−1.19383
$626$	38.4818	1.53804
$627$	−2.91829	−0.116545
$628$	−20.2309	−0.807299
$629$	45.6342	1.81955
$630$	−26.7709	−1.06658
$631$	23.8744	0.950426	0.475213	−	0.879871i	$-0.342371\pi$
$631$	23.8744	0.950426	0.475213	+	0.879871i	$0.342371\pi$
$632$	30.0756	1.19634
$633$	−28.7933	−1.14443
$634$	−51.0740	−2.02841
$635$	−8.68268	−0.344562
$636$	−15.5391	−0.616165
$637$	−3.37019	−0.133532
$638$	−18.9455	−0.750061
$639$	−2.35881	−0.0933130
$640$	−53.1326	−2.10025
$641$	24.4875	0.967197	0.483598	−	0.875290i	$-0.339330\pi$
$641$	24.4875	0.967197	0.483598	+	0.875290i	$0.339330\pi$
$642$	−8.31858	−0.328308
$643$	21.2840	0.839359	0.419680	−	0.907672i	$-0.362142\pi$
$643$	21.2840	0.839359	0.419680	+	0.907672i	$0.362142\pi$
$644$	−106.749	−4.20651
$645$	38.1796	1.50332
$646$	−61.3381	−2.41332
$647$	16.3268	0.641874	0.320937	−	0.947101i	$-0.396002\pi$
$647$	16.3268	0.641874	0.320937	+	0.947101i	$0.396002\pi$
$648$	−5.32715	−0.209270
$649$	2.18559	0.0857919
$650$	4.79562	0.188100
$651$	−16.4204	−0.643567
$652$	−11.7864	−0.461590
$653$	−7.18408	−0.281135	−0.140567	−	0.990071i	$-0.544893\pi$
$653$	−7.18408	−0.281135	−0.140567	+	0.990071i	$0.544893\pi$
$654$	9.63327	0.376690
$655$	−1.90735	−0.0745262
$656$	−42.2086	−1.64797
$657$	−9.74309	−0.380114
$658$	56.1277	2.18809
$659$	5.67110	0.220915	0.110457	−	0.993881i	$-0.464768\pi$
$659$	5.67110	0.220915	0.110457	+	0.993881i	$0.464768\pi$
$660$	9.31977	0.362771
$661$	−7.34916	−0.285849	−0.142925	−	0.989734i	$-0.545651\pi$
$661$	−7.34916	−0.285849	−0.142925	+	0.989734i	$0.545651\pi$
$662$	−71.8961	−2.79432
$663$	3.39151	0.131715
$664$	7.43576	0.288563
$665$	41.3304	1.60272
$666$	−17.5109	−0.678534
$667$	70.3999	2.72590
$668$	44.1443	1.70799
$669$	1.97684	0.0764290
$670$	41.0550	1.58609
$671$	−6.20268	−0.239452
$672$	−5.59213	−0.215721
$673$	28.2247	1.08798	0.543991	−	0.839091i	$-0.316912\pi$
$673$	28.2247	1.08798	0.543991	+	0.839091i	$0.316912\pi$
$674$	−4.16050	−0.160256
$675$	−3.68497	−0.141835
$676$	−52.7864	−2.03025
$677$	28.2965	1.08752	0.543761	−	0.839240i	$-0.317000\pi$
$677$	28.2965	1.08752	0.543761	+	0.839240i	$0.317000\pi$
$678$	32.7023	1.25593
$679$	−54.8475	−2.10485
$680$	101.448	3.89034
$681$	19.8520	0.760729
$682$	8.47243	0.324426
$683$	−46.1072	−1.76424	−0.882121	−	0.471023i	$-0.843885\pi$
$683$	−46.1072	−1.76424	−0.882121	+	0.471023i	$0.843885\pi$
$684$	15.8806	0.607211
$685$	−7.07842	−0.270452
$686$	−5.25669	−0.200701
$687$	4.62908	0.176611
$688$	63.6414	2.42631
$689$	−1.96596	−0.0748973
$690$	−51.3277	−1.95401
$691$	−8.45587	−0.321676	−0.160838	−	0.986981i	$-0.551420\pi$
$691$	−8.45587	−0.321676	−0.160838	+	0.986981i	$0.551420\pi$
$692$	32.4686	1.23427
$693$	−2.79279	−0.106089
$694$	68.9769	2.61833
$695$	61.5991	2.33659
$696$	53.3925	2.02384
$697$	−55.5228	−2.10307
$698$	−9.97729	−0.377646
$699$	−3.28012	−0.124066
$700$	−56.0031	−2.11672
$701$	2.56950	0.0970487	0.0485244	−	0.998822i	$-0.484548\pi$
$701$	2.56950	0.0970487	0.0485244	+	0.998822i	$0.484548\pi$
$702$	−1.30140	−0.0491182
$703$	27.0343	1.01962
$704$	−4.60432	−0.173532
$705$	18.2089	0.685786
$706$	84.9345	3.19655
$707$	−37.6466	−1.41585
$708$	−11.8934	−0.446983
$709$	−21.2078	−0.796475	−0.398237	−	0.917282i	$-0.630378\pi$
$709$	−21.2078	−0.796475	−0.398237	+	0.917282i	$0.630378\pi$
$710$	−17.2368	−0.646887
$711$	−5.64573	−0.211731
$712$	36.9410	1.38442
$713$	−31.4828	−1.17904
$714$	−58.7004	−2.19681
$715$	1.17911	0.0440963
$716$	100.497	3.75573
$717$	24.7531	0.924422
$718$	27.1873	1.01462
$719$	4.98987	0.186091	0.0930454	−	0.995662i	$-0.470340\pi$
$719$	4.98987	0.186091	0.0930454	+	0.995662i	$0.470340\pi$
$720$	−14.4769	−0.539524
$721$	62.9359	2.34386
$722$	10.7748	0.400996
$723$	3.75403	0.139614
$724$	5.88357	0.218661
$725$	36.9334	1.37167
$726$	−25.8346	−0.958810
$727$	8.66643	0.321420	0.160710	−	0.987002i	$-0.448622\pi$
$727$	8.66643	0.321420	0.160710	+	0.987002i	$0.448622\pi$
$728$	−10.2429	−0.379627
$729$	1.00000	0.0370370
$730$	−71.1971	−2.63512
$731$	83.7161	3.09635
$732$	33.7535	1.24757
$733$	23.3012	0.860651	0.430326	−	0.902674i	$-0.358399\pi$
$733$	23.3012	0.860651	0.430326	+	0.902674i	$0.358399\pi$
$734$	−87.8174	−3.24140
$735$	18.9238	0.698016
$736$	−10.7218	−0.395210
$737$	4.28293	0.157764
$738$	21.3054	0.784262
$739$	35.1341	1.29243	0.646214	−	0.763156i	$-0.276351\pi$
$739$	35.1341	1.29243	0.646214	+	0.763156i	$0.276351\pi$
$740$	−86.3360	−3.17377
$741$	2.00917	0.0738088
$742$	34.0270	1.24917
$743$	−0.441742	−0.0162059	−0.00810297	−	0.999967i	$-0.502579\pi$
$743$	−0.441742	−0.0162059	−0.00810297	+	0.999967i	$0.502579\pi$
$744$	−23.8771	−0.875377
$745$	−19.1329	−0.700974
$746$	51.5309	1.88668
$747$	−1.39582	−0.0510705
$748$	20.4354	0.747192
$749$	12.2904	0.449081
$750$	9.60949	0.350889
$751$	50.6605	1.84863	0.924314	−	0.381632i	$-0.124638\pi$
$751$	50.6605	1.84863	0.924314	+	0.381632i	$0.124638\pi$
$752$	30.3523	1.10683
$753$	7.86502	0.286617
$754$	13.0436	0.475019
$755$	−59.8315	−2.17749
$756$	15.1977	0.552735
$757$	−5.91609	−0.215024	−0.107512	−	0.994204i	$-0.534288\pi$
$757$	−5.91609	−0.215024	−0.107512	+	0.994204i	$0.534288\pi$
$758$	94.9915	3.45025
$759$	−5.35461	−0.194360
$760$	60.0989	2.18002
$761$	50.7327	1.83906	0.919529	−	0.393023i	$-0.128571\pi$
$761$	50.7327	1.83906	0.919529	+	0.393023i	$0.128571\pi$
$762$	7.30551	0.264651
$763$	−14.2328	−0.515262
$764$	107.592	3.89253
$765$	−19.0435	−0.688519
$766$	42.4358	1.53327
$767$	−1.50473	−0.0543326
$768$	32.6255	1.17727
$769$	25.9745	0.936664	0.468332	−	0.883553i	$-0.344855\pi$
$769$	25.9745	0.936664	0.468332	+	0.883553i	$0.344855\pi$
$770$	−20.4081	−0.735459
$771$	16.8170	0.605651
$772$	−1.67938	−0.0604420
$773$	14.0412	0.505027	0.252514	−	0.967593i	$-0.418743\pi$
$773$	14.0412	0.505027	0.252514	+	0.967593i	$0.418743\pi$
$774$	−32.1239	−1.15467
$775$	−16.5166	−0.593294
$776$	−79.7543	−2.86301
$777$	25.8717	0.928143
$778$	−45.2600	−1.62265
$779$	−32.8924	−1.17849
$780$	−6.41644	−0.229746
$781$	−1.79818	−0.0643440
$782$	−112.546	−4.02464
$783$	−10.0227	−0.358183
$784$	31.5441	1.12657
$785$	14.3720	0.512960
$786$	1.60482	0.0572421
$787$	−3.54359	−0.126315	−0.0631576	−	0.998004i	$-0.520117\pi$
$787$	−3.54359	−0.126315	−0.0631576	+	0.998004i	$0.520117\pi$
$788$	2.48951	0.0886852
$789$	−20.5677	−0.732229
$790$	−41.2558	−1.46782
$791$	−48.3165	−1.71794
$792$	−4.06103	−0.144302
$793$	4.27040	0.151646
$794$	−38.8166	−1.37755
$795$	11.0390	0.391513
$796$	5.26453	0.186596
$797$	9.41578	0.333524	0.166762	−	0.985997i	$-0.446669\pi$
$797$	9.41578	0.333524	0.166762	+	0.985997i	$0.446669\pi$
$798$	−34.7749	−1.23102
$799$	39.9265	1.41250
$800$	−5.62489	−0.198870
$801$	−6.93447	−0.245018
$802$	24.9107	0.879627
$803$	−7.42741	−0.262108
$804$	−23.3067	−0.821964
$805$	75.8348	2.67283
$806$	−5.83307	−0.205461
$807$	18.9273	0.666272
$808$	−54.7423	−1.92583
$809$	15.0530	0.529237	0.264618	−	0.964353i	$-0.414754\pi$
$809$	15.0530	0.529237	0.264618	+	0.964353i	$0.414754\pi$
$810$	7.30744	0.256757
$811$	−23.0387	−0.809000	−0.404500	−	0.914538i	$-0.632554\pi$
$811$	−23.0387	−0.809000	−0.404500	+	0.914538i	$0.632554\pi$
$812$	−152.322	−5.34546
$813$	1.77103	0.0621127
$814$	−13.3490	−0.467883
$815$	8.37306	0.293295
$816$	−31.7435	−1.11125
$817$	49.5946	1.73509
$818$	11.9785	0.418818
$819$	1.92277	0.0671871
$820$	105.044	3.66831
$821$	−24.6817	−0.861397	−0.430699	−	0.902496i	$-0.641733\pi$
$821$	−24.6817	−0.861397	−0.430699	+	0.902496i	$0.641733\pi$
$822$	5.95570	0.207729
$823$	−37.2913	−1.29989	−0.649947	−	0.759980i	$-0.725209\pi$
$823$	−37.2913	−1.29989	−0.649947	+	0.759980i	$0.725209\pi$
$824$	91.5157	3.18810
$825$	−2.80915	−0.0978020
$826$	26.0439	0.906184
$827$	−53.9013	−1.87433	−0.937165	−	0.348886i	$-0.886560\pi$
$827$	−53.9013	−1.87433	−0.937165	+	0.348886i	$0.886560\pi$
$828$	29.1385	1.01263
$829$	16.2051	0.562825	0.281412	−	0.959587i	$-0.409197\pi$
$829$	16.2051	0.562825	0.281412	+	0.959587i	$0.409197\pi$
$830$	−10.1999	−0.354043
$831$	−29.6064	−1.02704
$832$	3.16996	0.109899
$833$	41.4942	1.43769
$834$	−51.8288	−1.79468
$835$	−31.3602	−1.08526
$836$	12.1062	0.418702
$837$	4.48215	0.154926
$838$	−7.26128	−0.250837
$839$	11.1516	0.384995	0.192498	−	0.981297i	$-0.438341\pi$
$839$	11.1516	0.384995	0.192498	+	0.981297i	$0.438341\pi$
$840$	57.5144	1.98444
$841$	71.4548	2.46396
$842$	93.6779	3.22835
$843$	20.8712	0.718843
$844$	119.446	4.11150
$845$	37.4996	1.29002
$846$	−15.3207	−0.526738
$847$	38.1696	1.31152
$848$	18.4009	0.631889
$849$	−6.29401	−0.216010
$850$	−59.0442	−2.02520
$851$	49.6037	1.70039
$852$	9.78527	0.335238
$853$	−40.7568	−1.39549	−0.697743	−	0.716349i	$-0.745812\pi$
$853$	−40.7568	−1.39549	−0.697743	+	0.716349i	$0.745812\pi$
$854$	−73.9124	−2.52923
$855$	−11.2816	−0.385823
$856$	17.8716	0.610839
$857$	−31.5015	−1.07607	−0.538035	−	0.842923i	$-0.680833\pi$
$857$	−31.5015	−1.07607	−0.538035	+	0.842923i	$0.680833\pi$
$858$	−0.992091	−0.0338694
$859$	55.4752	1.89279	0.946394	−	0.323013i	$-0.104696\pi$
$859$	55.4752	1.89279	0.946394	+	0.323013i	$0.104696\pi$
$860$	−158.384	−5.40085
$861$	−31.4779	−1.07277
$862$	−93.5345	−3.18580
$863$	−26.3719	−0.897709	−0.448855	−	0.893605i	$-0.648168\pi$
$863$	−26.3719	−0.897709	−0.448855	+	0.893605i	$0.648168\pi$
$864$	1.52644	0.0519305
$865$	−23.0657	−0.784258
$866$	43.6615	1.48368
$867$	−24.7566	−0.840777
$868$	68.1184	2.31209
$869$	−4.30389	−0.145999
$870$	−73.2404	−2.48308
$871$	−2.94870	−0.0999129
$872$	−20.6961	−0.700857
$873$	14.9713	0.506701
$874$	−66.6738	−2.25527
$875$	−14.1977	−0.479969
$876$	40.4182	1.36560
$877$	−40.3971	−1.36411	−0.682057	−	0.731299i	$-0.738914\pi$
$877$	−40.3971	−1.36411	−0.682057	+	0.731299i	$0.738914\pi$
$878$	−84.8146	−2.86236
$879$	−15.3531	−0.517847
$880$	−11.0362	−0.372029
$881$	−7.72960	−0.260417	−0.130208	−	0.991487i	$-0.541565\pi$
$881$	−7.72960	−0.260417	−0.130208	+	0.991487i	$0.541565\pi$
$882$	−15.9223	−0.536132
$883$	10.2559	0.345138	0.172569	−	0.984997i	$-0.444793\pi$
$883$	10.2559	0.345138	0.172569	+	0.984997i	$0.444793\pi$
$884$	−14.0693	−0.473202
$885$	8.44913	0.284014
$886$	87.5142	2.94010
$887$	47.7214	1.60233	0.801163	−	0.598446i	$-0.204215\pi$
$887$	47.7214	1.60233	0.801163	+	0.598446i	$0.204215\pi$
$888$	37.6203	1.26246
$889$	−10.7936	−0.362007
$890$	−50.6732	−1.69857
$891$	0.762326	0.0255389
$892$	−8.20071	−0.274580
$893$	23.6530	0.791517
$894$	16.0982	0.538404
$895$	−71.3929	−2.38640
$896$	−66.0502	−2.20658
$897$	3.68652	0.123089
$898$	56.2042	1.87556
$899$	−44.9233	−1.49828
$900$	15.2867	0.509557
$901$	24.2052	0.806391
$902$	16.2417	0.540788
$903$	47.4618	1.57943
$904$	−70.2575	−2.33673
$905$	−4.17970	−0.138938
$906$	50.3415	1.67249
$907$	−0.581201	−0.0192985	−0.00964923	−	0.999953i	$-0.503071\pi$
$907$	−0.581201	−0.0192985	−0.00964923	+	0.999953i	$0.503071\pi$
$908$	−82.3538	−2.73301
$909$	10.2761	0.340836
$910$	14.0505	0.465771
$911$	41.0455	1.35990	0.679949	−	0.733259i	$-0.262002\pi$
$911$	41.0455	1.35990	0.679949	+	0.733259i	$0.262002\pi$
$912$	−18.8053	−0.622706
$913$	−1.06407	−0.0352157
$914$	−10.4027	−0.344090
$915$	−23.9786	−0.792707
$916$	−19.2033	−0.634494
$917$	−2.37106	−0.0782995
$918$	16.0230	0.528837
$919$	39.1111	1.29016	0.645078	−	0.764117i	$-0.276825\pi$
$919$	39.1111	1.29016	0.645078	+	0.764117i	$0.276825\pi$
$920$	110.272	3.63557
$921$	1.59570	0.0525802
$922$	70.8721	2.33405
$923$	1.23801	0.0407495
$924$	11.5856	0.381138
$925$	26.0233	0.855640
$926$	−83.4559	−2.74253
$927$	−17.1791	−0.564236
$928$	−15.2991	−0.502217
$929$	−22.1601	−0.727049	−0.363524	−	0.931585i	$-0.618427\pi$
$929$	−22.1601	−0.727049	−0.363524	+	0.931585i	$0.618427\pi$
$930$	32.7530	1.07401
$931$	24.5817	0.805633
$932$	13.6073	0.445720
$933$	−6.21429	−0.203447
$934$	−23.8090	−0.779053
$935$	−14.5174	−0.474768
$936$	2.79592	0.0913876
$937$	−11.3355	−0.370315	−0.185158	−	0.982709i	$-0.559280\pi$
$937$	−11.3355	−0.370315	−0.185158	+	0.982709i	$0.559280\pi$
$938$	51.0363	1.66639
$939$	15.5194	0.506456
$940$	−75.5376	−2.46376
$941$	−16.4249	−0.535436	−0.267718	−	0.963497i	$-0.586270\pi$
$941$	−16.4249	−0.535436	−0.267718	+	0.963497i	$0.586270\pi$
$942$	−12.0925	−0.393994
$943$	−60.3525	−1.96535
$944$	14.0838	0.458389
$945$	−10.7965	−0.351209
$946$	−24.4889	−0.796201
$947$	43.4293	1.41126	0.705631	−	0.708579i	$-0.250664\pi$
$947$	43.4293	1.41126	0.705631	+	0.708579i	$0.250664\pi$
$948$	23.4207	0.760669
$949$	5.11360	0.165995
$950$	−34.9786	−1.13486
$951$	−20.5977	−0.667927
$952$	126.112	4.08730
$953$	32.1114	1.04019	0.520095	−	0.854109i	$-0.325897\pi$
$953$	32.1114	1.04019	0.520095	+	0.854109i	$0.325897\pi$
$954$	−9.28809	−0.300713
$955$	−76.4333	−2.47332
$956$	−102.686	−3.32109
$957$	−7.64058	−0.246985
$958$	−18.2981	−0.591184
$959$	−8.79933	−0.284145
$960$	−17.7995	−0.574477
$961$	−10.9103	−0.351946
$962$	9.19049	0.296313
$963$	−3.35481	−0.108107
$964$	−15.5732	−0.501580
$965$	1.19303	0.0384050
$966$	−63.8066	−2.05294
$967$	−27.7507	−0.892404	−0.446202	−	0.894932i	$-0.647224\pi$
$967$	−27.7507	−0.892404	−0.446202	+	0.894932i	$0.647224\pi$
$968$	55.5028	1.78393
$969$	−24.7372	−0.794672
$970$	109.402	3.51268
$971$	−46.2892	−1.48549	−0.742745	−	0.669575i	$-0.766476\pi$
$971$	−46.2892	−1.48549	−0.742745	+	0.669575i	$0.766476\pi$
$972$	−4.14839	−0.133060
$973$	76.5751	2.45489
$974$	6.45644	0.206878
$975$	1.93403	0.0619387
$976$	−39.9698	−1.27940
$977$	21.2040	0.678376	0.339188	−	0.940719i	$-0.389848\pi$
$977$	21.2040	0.678376	0.339188	+	0.940719i	$0.389848\pi$
$978$	−7.04499	−0.225274
$979$	−5.28633	−0.168952
$980$	−78.5035	−2.50770
$981$	3.88501	0.124039
$982$	58.7094	1.87349
$983$	−3.80566	−0.121382	−0.0606908	−	0.998157i	$-0.519330\pi$
$983$	−3.80566	−0.121382	−0.0606908	+	0.998157i	$0.519330\pi$
$984$	−45.7724	−1.45917
$985$	−1.76855	−0.0563508
$986$	−160.594	−5.11435
$987$	22.6358	0.720507
$988$	−8.33484	−0.265167
$989$	90.9984	2.89358
$990$	5.57065	0.177047
$991$	−35.1469	−1.11648	−0.558239	−	0.829680i	$-0.688523\pi$
$991$	−35.1469	−1.11648	−0.558239	+	0.829680i	$0.688523\pi$
$992$	6.84173	0.217225
$993$	−28.9951	−0.920131
$994$	−21.4275	−0.679638
$995$	−3.73993	−0.118564
$996$	5.79043	0.183477
$997$	−51.6181	−1.63476	−0.817380	−	0.576099i	$-0.804574\pi$
$997$	−51.6181	−1.63476	−0.817380	+	0.576099i	$0.804574\pi$
$998$	56.7422	1.79614
$999$	−7.06200	−0.223432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.c.1.5	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.c.1.5	✓	82	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47960 q^{2} -1.00000 q^{3} +4.14839 q^{4} -2.94703 q^{5} +2.47960 q^{6} -3.66351 q^{7} -5.32715 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.47960 q^{2} -1.00000 q^{3} +4.14839 q^{4} -2.94703 q^{5} +2.47960 q^{6} -3.66351 q^{7} -5.32715 q^{8} +1.00000 q^{9} +7.30744 q^{10} +0.762326 q^{11} -4.14839 q^{12} -0.524844 q^{13} +9.08403 q^{14} +2.94703 q^{15} +4.91239 q^{16} +6.46193 q^{17} -2.47960 q^{18} +3.82814 q^{19} -12.2254 q^{20} +3.66351 q^{21} -1.89026 q^{22} +7.02404 q^{23} +5.32715 q^{24} +3.68497 q^{25} +1.30140 q^{26} -1.00000 q^{27} -15.1977 q^{28} +10.0227 q^{29} -7.30744 q^{30} -4.48215 q^{31} -1.52644 q^{32} -0.762326 q^{33} -16.0230 q^{34} +10.7965 q^{35} +4.14839 q^{36} +7.06200 q^{37} -9.49223 q^{38} +0.524844 q^{39} +15.6993 q^{40} -8.59228 q^{41} -9.08403 q^{42} +12.9553 q^{43} +3.16243 q^{44} -2.94703 q^{45} -17.4168 q^{46} +6.17872 q^{47} -4.91239 q^{48} +6.42133 q^{49} -9.13724 q^{50} -6.46193 q^{51} -2.17726 q^{52} +3.74581 q^{53} +2.47960 q^{54} -2.24660 q^{55} +19.5161 q^{56} -3.82814 q^{57} -24.8523 q^{58} +2.86700 q^{59} +12.2254 q^{60} -8.13652 q^{61} +11.1139 q^{62} -3.66351 q^{63} -6.03983 q^{64} +1.54673 q^{65} +1.89026 q^{66} +5.61825 q^{67} +26.8066 q^{68} -7.02404 q^{69} -26.7709 q^{70} -2.35881 q^{71} -5.32715 q^{72} -9.74309 q^{73} -17.5109 q^{74} -3.68497 q^{75} +15.8806 q^{76} -2.79279 q^{77} -1.30140 q^{78} -5.64573 q^{79} -14.4769 q^{80} +1.00000 q^{81} +21.3054 q^{82} -1.39582 q^{83} +15.1977 q^{84} -19.0435 q^{85} -32.1239 q^{86} -10.0227 q^{87} -4.06103 q^{88} -6.93447 q^{89} +7.30744 q^{90} +1.92277 q^{91} +29.1385 q^{92} +4.48215 q^{93} -15.3207 q^{94} -11.2816 q^{95} +1.52644 q^{96} +14.9713 q^{97} -15.9223 q^{98} +0.762326 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9} - 9 q^{10} + 28 q^{11} - 87 q^{12} - 14 q^{13} + 21 q^{14} - 7 q^{15} + 93 q^{16} + 25 q^{17} + 13 q^{18} - 7 q^{19} + 40 q^{20} - 30 q^{21} + 31 q^{22} + 97 q^{23} - 39 q^{24} + 83 q^{25} + 22 q^{26} - 82 q^{27} + 53 q^{28} + 45 q^{29} + 9 q^{30} - 11 q^{31} + 86 q^{32} - 28 q^{33} - 30 q^{34} + 69 q^{35} + 87 q^{36} + 8 q^{37} + 33 q^{38} + 14 q^{39} - 38 q^{40} + 12 q^{41} - 21 q^{42} + 68 q^{43} + 77 q^{44} + 7 q^{45} - 14 q^{46} + 85 q^{47} - 93 q^{48} + 68 q^{49} + 56 q^{50} - 25 q^{51} - 18 q^{52} + 58 q^{53} - 13 q^{54} + 68 q^{55} + 59 q^{56} + 7 q^{57} + 27 q^{58} + 40 q^{59} - 40 q^{60} - 116 q^{61} + 79 q^{62} + 30 q^{63} + 127 q^{64} + 66 q^{65} - 31 q^{66} + 51 q^{67} + 94 q^{68} - 97 q^{69} + q^{70} + 101 q^{71} + 39 q^{72} + 12 q^{73} + 72 q^{74} - 83 q^{75} - 3 q^{76} + 101 q^{77} - 22 q^{78} + 26 q^{79} + 61 q^{80} + 82 q^{81} + 31 q^{82} + 94 q^{83} - 53 q^{84} - 8 q^{85} + 68 q^{86} - 45 q^{87} + 91 q^{88} + 40 q^{89} - 9 q^{90} - 6 q^{91} + 180 q^{92} + 11 q^{93} - 31 q^{94} + 153 q^{95} - 86 q^{96} - 39 q^{97} + 115 q^{98} + 28 q^{99}+O(q^{100}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9 - 9 * q^10 + 28 * q^11 - 87 * q^12 - 14 * q^13 + 21 * q^14 - 7 * q^15 + 93 * q^16 + 25 * q^17 + 13 * q^18 - 7 * q^19 + 40 * q^20 - 30 * q^21 + 31 * q^22 + 97 * q^23 - 39 * q^24 + 83 * q^25 + 22 * q^26 - 82 * q^27 + 53 * q^28 + 45 * q^29 + 9 * q^30 - 11 * q^31 + 86 * q^32 - 28 * q^33 - 30 * q^34 + 69 * q^35 + 87 * q^36 + 8 * q^37 + 33 * q^38 + 14 * q^39 - 38 * q^40 + 12 * q^41 - 21 * q^42 + 68 * q^43 + 77 * q^44 + 7 * q^45 - 14 * q^46 + 85 * q^47 - 93 * q^48 + 68 * q^49 + 56 * q^50 - 25 * q^51 - 18 * q^52 + 58 * q^53 - 13 * q^54 + 68 * q^55 + 59 * q^56 + 7 * q^57 + 27 * q^58 + 40 * q^59 - 40 * q^60 - 116 * q^61 + 79 * q^62 + 30 * q^63 + 127 * q^64 + 66 * q^65 - 31 * q^66 + 51 * q^67 + 94 * q^68 - 97 * q^69 + q^70 + 101 * q^71 + 39 * q^72 + 12 * q^73 + 72 * q^74 - 83 * q^75 - 3 * q^76 + 101 * q^77 - 22 * q^78 + 26 * q^79 + 61 * q^80 + 82 * q^81 + 31 * q^82 + 94 * q^83 - 53 * q^84 - 8 * q^85 + 68 * q^86 - 45 * q^87 + 91 * q^88 + 40 * q^89 - 9 * q^90 - 6 * q^91 + 180 * q^92 + 11 * q^93 - 31 * q^94 + 153 * q^95 - 86 * q^96 - 39 * q^97 + 115 * q^98 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more