LMFDB - Embedded newform 1859.2.a.t.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, 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("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1859.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:	$14.8441897358$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.23194 q^{2} +1.36188 q^{3} +2.98154 q^{4} +4.28736 q^{5} +3.03963 q^{6} +0.384100 q^{7} +2.19073 q^{8} -1.14528 q^{9} +O(q^{10})$	\(q+2.23194 q^{2} +1.36188 q^{3} +2.98154 q^{4} +4.28736 q^{5} +3.03963 q^{6} +0.384100 q^{7} +2.19073 q^{8} -1.14528 q^{9} +9.56911 q^{10} +1.00000 q^{11} +4.06050 q^{12} +0.857286 q^{14} +5.83888 q^{15} -1.07351 q^{16} -4.75294 q^{17} -2.55618 q^{18} -2.17281 q^{19} +12.7829 q^{20} +0.523099 q^{21} +2.23194 q^{22} +2.70390 q^{23} +2.98352 q^{24} +13.3814 q^{25} -5.64538 q^{27} +1.14521 q^{28} -10.2556 q^{29} +13.0320 q^{30} +3.64487 q^{31} -6.77746 q^{32} +1.36188 q^{33} -10.6083 q^{34} +1.64677 q^{35} -3.41468 q^{36} -4.30010 q^{37} -4.84956 q^{38} +9.39245 q^{40} +6.28472 q^{41} +1.16752 q^{42} +0.639237 q^{43} +2.98154 q^{44} -4.91021 q^{45} +6.03493 q^{46} +4.82001 q^{47} -1.46199 q^{48} -6.85247 q^{49} +29.8665 q^{50} -6.47295 q^{51} +3.32193 q^{53} -12.6001 q^{54} +4.28736 q^{55} +0.841459 q^{56} -2.95911 q^{57} -22.8898 q^{58} -8.90125 q^{59} +17.4088 q^{60} +8.06080 q^{61} +8.13512 q^{62} -0.439900 q^{63} -12.9798 q^{64} +3.03963 q^{66} +14.7519 q^{67} -14.1711 q^{68} +3.68239 q^{69} +3.67549 q^{70} -13.9356 q^{71} -2.50899 q^{72} -11.4254 q^{73} -9.59755 q^{74} +18.2240 q^{75} -6.47830 q^{76} +0.384100 q^{77} +7.58183 q^{79} -4.60251 q^{80} -4.25252 q^{81} +14.0271 q^{82} -13.8004 q^{83} +1.55964 q^{84} -20.3776 q^{85} +1.42674 q^{86} -13.9669 q^{87} +2.19073 q^{88} +4.74761 q^{89} -10.9593 q^{90} +8.06178 q^{92} +4.96389 q^{93} +10.7580 q^{94} -9.31560 q^{95} -9.23010 q^{96} +15.3780 q^{97} -15.2943 q^{98} -1.14528 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) $ 21 * q + 6 * q^3 + 32 * q^4 + 7 * q^5 - 19 * q^6 + q^7 - 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9} + 18 q^{10} + 21 q^{11} + 23 q^{12} + 20 q^{14} + 16 q^{15} + 50 q^{16} + 16 q^{17} + 3 q^{18} - 11 q^{19} + 24 q^{20} - 5 q^{21} - 9 q^{23} - 54 q^{24} + 36 q^{25} - 11 q^{28} + 28 q^{29} + 21 q^{30} + 15 q^{31} - 61 q^{32} + 6 q^{33} - 6 q^{34} - 3 q^{35} + 45 q^{36} - 12 q^{37} + q^{38} + 55 q^{40} - 4 q^{41} - 34 q^{42} + 17 q^{43} + 32 q^{44} + 9 q^{45} + 11 q^{46} + 36 q^{47} + 24 q^{48} + 72 q^{49} - 9 q^{50} + 2 q^{51} + 19 q^{53} + q^{54} + 7 q^{55} + 44 q^{56} - 4 q^{57} - 33 q^{58} + 54 q^{59} + 64 q^{60} + 98 q^{61} - 29 q^{62} - 81 q^{63} + 63 q^{64} - 19 q^{66} + 25 q^{67} + 4 q^{68} + 89 q^{69} + 65 q^{70} + 37 q^{71} + 55 q^{72} + 8 q^{73} - 11 q^{74} + 24 q^{75} + 13 q^{76} + q^{77} + 24 q^{79} + 26 q^{80} + 81 q^{81} + 26 q^{82} - 34 q^{83} - 103 q^{84} - 11 q^{85} + 30 q^{86} + 32 q^{87} - 3 q^{88} + 6 q^{89} + 47 q^{90} - 80 q^{92} + 41 q^{93} + 40 q^{94} + 20 q^{95} - 98 q^{96} - 5 q^{98} + 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 + 7 * q^5 - 19 * q^6 + q^7 - 3 * q^8 + 33 * q^9 + 18 * q^10 + 21 * q^11 + 23 * q^12 + 20 * q^14 + 16 * q^15 + 50 * q^16 + 16 * q^17 + 3 * q^18 - 11 * q^19 + 24 * q^20 - 5 * q^21 - 9 * q^23 - 54 * q^24 + 36 * q^25 - 11 * q^28 + 28 * q^29 + 21 * q^30 + 15 * q^31 - 61 * q^32 + 6 * q^33 - 6 * q^34 - 3 * q^35 + 45 * q^36 - 12 * q^37 + q^38 + 55 * q^40 - 4 * q^41 - 34 * q^42 + 17 * q^43 + 32 * q^44 + 9 * q^45 + 11 * q^46 + 36 * q^47 + 24 * q^48 + 72 * q^49 - 9 * q^50 + 2 * q^51 + 19 * q^53 + q^54 + 7 * q^55 + 44 * q^56 - 4 * q^57 - 33 * q^58 + 54 * q^59 + 64 * q^60 + 98 * q^61 - 29 * q^62 - 81 * q^63 + 63 * q^64 - 19 * q^66 + 25 * q^67 + 4 * q^68 + 89 * q^69 + 65 * q^70 + 37 * q^71 + 55 * q^72 + 8 * q^73 - 11 * q^74 + 24 * q^75 + 13 * q^76 + q^77 + 24 * q^79 + 26 * q^80 + 81 * q^81 + 26 * q^82 - 34 * q^83 - 103 * q^84 - 11 * q^85 + 30 * q^86 + 32 * q^87 - 3 * q^88 + 6 * q^89 + 47 * q^90 - 80 * q^92 + 41 * q^93 + 40 * q^94 + 20 * q^95 - 98 * q^96 - 5 * q^98 + 33 * 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 $

$2$	2.23194	1.57822	0.789109	−	0.614254i	$-0.210543\pi$
$2$	2.23194	1.57822	0.789109	+	0.614254i	$0.210543\pi$
$3$	1.36188	0.786283	0.393142	−	0.919478i	$-0.371388\pi$
$3$	1.36188	0.786283	0.393142	+	0.919478i	$0.371388\pi$
$4$	2.98154	1.49077
$5$	4.28736	1.91737	0.958683	−	0.284478i	$-0.0918202\pi$
$5$	4.28736	1.91737	0.958683	+	0.284478i	$0.0918202\pi$
$6$	3.03963	1.24093
$7$	0.384100	0.145176	0.0725880	−	0.997362i	$-0.476874\pi$
$7$	0.384100	0.145176	0.0725880	+	0.997362i	$0.476874\pi$
$8$	2.19073	0.774540
$9$	−1.14528	−0.381759
$10$	9.56911	3.02602
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	4.06050	1.17217
$13$	0	0
$13$	0	0
$14$	0.857286	0.229119
$15$	5.83888	1.50759
$16$	−1.07351	−0.268377
$17$	−4.75294	−1.15276	−0.576379	−	0.817182i	$-0.695535\pi$
$17$	−4.75294	−1.15276	−0.576379	+	0.817182i	$0.695535\pi$
$18$	−2.55618	−0.602498
$19$	−2.17281	−0.498476	−0.249238	−	0.968442i	$-0.580180\pi$
$19$	−2.17281	−0.498476	−0.249238	+	0.968442i	$0.580180\pi$
$20$	12.7829	2.85835
$21$	0.523099	0.114149
$22$	2.23194	0.475850
$23$	2.70390	0.563802	0.281901	−	0.959444i	$-0.409035\pi$
$23$	2.70390	0.563802	0.281901	+	0.959444i	$0.409035\pi$
$24$	2.98352	0.609008
$25$	13.3814	2.67629
$26$	0	0
$27$	−5.64538	−1.08645
$28$	1.14521	0.216424
$29$	−10.2556	−1.90442	−0.952209	−	0.305449i	$-0.901194\pi$
$29$	−10.2556	−1.90442	−0.952209	+	0.305449i	$0.901194\pi$
$30$	13.0320	2.37931
$31$	3.64487	0.654638	0.327319	−	0.944914i	$-0.393855\pi$
$31$	3.64487	0.654638	0.327319	+	0.944914i	$0.393855\pi$
$32$	−6.77746	−1.19810
$33$	1.36188	0.237073
$34$	−10.6083	−1.81930
$35$	1.64677	0.278355
$36$	−3.41468	−0.569114
$37$	−4.30010	−0.706932	−0.353466	−	0.935447i	$-0.614997\pi$
$37$	−4.30010	−0.706932	−0.353466	+	0.935447i	$0.614997\pi$
$38$	−4.84956	−0.786703
$39$	0	0
$40$	9.39245	1.48508
$41$	6.28472	0.981508	0.490754	−	0.871298i	$-0.336721\pi$
$41$	6.28472	0.981508	0.490754	+	0.871298i	$0.336721\pi$
$42$	1.16752	0.180153
$43$	0.639237	0.0974827	0.0487414	−	0.998811i	$-0.484479\pi$
$43$	0.639237	0.0974827	0.0487414	+	0.998811i	$0.484479\pi$
$44$	2.98154	0.449484
$45$	−4.91021	−0.731971
$46$	6.03493	0.889801
$47$	4.82001	0.703071	0.351536	−	0.936174i	$-0.385660\pi$
$47$	4.82001	0.703071	0.351536	+	0.936174i	$0.385660\pi$
$48$	−1.46199	−0.211020
$49$	−6.85247	−0.978924
$50$	29.8665	4.22377
$51$	−6.47295	−0.906395
$52$	0	0
$53$	3.32193	0.456302	0.228151	−	0.973626i	$-0.426732\pi$
$53$	3.32193	0.456302	0.228151	+	0.973626i	$0.426732\pi$
$54$	−12.6001	−1.71466
$55$	4.28736	0.578107
$56$	0.841459	0.112445
$57$	−2.95911	−0.391943
$58$	−22.8898	−3.00558
$59$	−8.90125	−1.15884	−0.579422	−	0.815028i	$-0.696722\pi$
$59$	−8.90125	−1.15884	−0.579422	+	0.815028i	$0.696722\pi$
$60$	17.4088	2.24747
$61$	8.06080	1.03208	0.516040	−	0.856565i	$-0.327406\pi$
$61$	8.06080	1.03208	0.516040	+	0.856565i	$0.327406\pi$
$62$	8.13512	1.03316
$63$	−0.439900	−0.0554222
$64$	−12.9798	−1.62248
$65$	0	0
$66$	3.03963	0.374153
$67$	14.7519	1.80223	0.901114	−	0.433583i	$-0.142751\pi$
$67$	14.7519	1.80223	0.901114	+	0.433583i	$0.142751\pi$
$68$	−14.1711	−1.71850
$69$	3.68239	0.443308
$70$	3.67549	0.439305
$71$	−13.9356	−1.65385	−0.826927	−	0.562309i	$-0.809913\pi$
$71$	−13.9356	−1.65385	−0.826927	+	0.562309i	$0.809913\pi$
$72$	−2.50899	−0.295687
$73$	−11.4254	−1.33725	−0.668623	−	0.743602i	$-0.733116\pi$
$73$	−11.4254	−1.33725	−0.668623	+	0.743602i	$0.733116\pi$
$74$	−9.59755	−1.11569
$75$	18.2240	2.10432
$76$	−6.47830	−0.743112
$77$	0.384100	0.0437722
$78$	0	0
$79$	7.58183	0.853023	0.426511	−	0.904482i	$-0.359742\pi$
$79$	7.58183	0.853023	0.426511	+	0.904482i	$0.359742\pi$
$80$	−4.60251	−0.514576
$81$	−4.25252	−0.472502
$82$	14.0271	1.54903
$83$	−13.8004	−1.51479	−0.757394	−	0.652958i	$-0.773528\pi$
$83$	−13.8004	−1.51479	−0.757394	+	0.652958i	$0.773528\pi$
$84$	1.55964	0.170171
$85$	−20.3776	−2.21026
$86$	1.42674	0.153849
$87$	−13.9669	−1.49741
$88$	2.19073	0.233533
$89$	4.74761	0.503245	0.251623	−	0.967825i	$-0.419036\pi$
$89$	4.74761	0.503245	0.251623	+	0.967825i	$0.419036\pi$
$90$	−10.9593	−1.15521
$91$	0	0
$92$	8.06178	0.840498
$93$	4.96389	0.514731
$94$	10.7580	1.10960
$95$	−9.31560	−0.955760
$96$	−9.23010	−0.942044
$97$	15.3780	1.56140	0.780700	−	0.624906i	$-0.214863\pi$
$97$	15.3780	1.56140	0.780700	+	0.624906i	$0.214863\pi$
$98$	−15.2943	−1.54495
$99$	−1.14528	−0.115105
$100$	39.8973	3.98973
$101$	5.03341	0.500843	0.250422	−	0.968137i	$-0.419431\pi$
$101$	5.03341	0.500843	0.250422	+	0.968137i	$0.419431\pi$
$102$	−14.4472	−1.43049
$103$	11.2981	1.11323	0.556617	−	0.830769i	$-0.312099\pi$
$103$	11.2981	1.11323	0.556617	+	0.830769i	$0.312099\pi$
$104$	0	0
$105$	2.24271	0.218866
$106$	7.41433	0.720143
$107$	10.3551	1.00106	0.500532	−	0.865718i	$-0.333138\pi$
$107$	10.3551	1.00106	0.500532	+	0.865718i	$0.333138\pi$
$108$	−16.8319	−1.61965
$109$	0.406377	0.0389239	0.0194619	−	0.999811i	$-0.493805\pi$
$109$	0.406377	0.0389239	0.0194619	+	0.999811i	$0.493805\pi$
$110$	9.56911	0.912379
$111$	−5.85623	−0.555849
$112$	−0.412334	−0.0389619
$113$	−0.904703	−0.0851073	−0.0425536	−	0.999094i	$-0.513549\pi$
$113$	−0.904703	−0.0851073	−0.0425536	+	0.999094i	$0.513549\pi$
$114$	−6.60453	−0.618571
$115$	11.5926	1.08101
$116$	−30.5775	−2.83905
$117$	0	0
$118$	−19.8670	−1.82891
$119$	−1.82560	−0.167353
$120$	12.7914	1.16769
$121$	1.00000	0.0909091
$122$	17.9912	1.62885
$123$	8.55905	0.771743
$124$	10.8673	0.975915
$125$	35.9343	3.21406
$126$	−0.981829	−0.0874682
$127$	0.830064	0.0736563	0.0368281	−	0.999322i	$-0.488275\pi$
$127$	0.830064	0.0736563	0.0368281	+	0.999322i	$0.488275\pi$
$128$	−15.4153	−1.36253
$129$	0.870566	0.0766490
$130$	0	0
$131$	1.61595	0.141187	0.0705933	−	0.997505i	$-0.477511\pi$
$131$	1.61595	0.141187	0.0705933	+	0.997505i	$0.477511\pi$
$132$	4.06050	0.353422
$133$	−0.834574	−0.0723667
$134$	32.9252	2.84431
$135$	−24.2038	−2.08313
$136$	−10.4124	−0.892858
$137$	2.65513	0.226843	0.113421	−	0.993547i	$-0.463819\pi$
$137$	2.65513	0.226843	0.113421	+	0.993547i	$0.463819\pi$
$138$	8.21886	0.699636
$139$	0.619987	0.0525866	0.0262933	−	0.999654i	$-0.491630\pi$
$139$	0.619987	0.0525866	0.0262933	+	0.999654i	$0.491630\pi$
$140$	4.90992	0.414964
$141$	6.56429	0.552813
$142$	−31.1034	−2.61014
$143$	0	0
$144$	1.22946	0.102455
$145$	−43.9694	−3.65146
$146$	−25.5008	−2.11046
$147$	−9.33226	−0.769712
$148$	−12.8209	−1.05387
$149$	3.82208	0.313117	0.156559	−	0.987669i	$-0.449960\pi$
$149$	3.82208	0.313117	0.156559	+	0.987669i	$0.449960\pi$
$150$	40.6747	3.32108
$151$	−17.1470	−1.39540	−0.697702	−	0.716388i	$-0.745794\pi$
$151$	−17.1470	−1.39540	−0.697702	+	0.716388i	$0.745794\pi$
$152$	−4.76003	−0.386089
$153$	5.44343	0.440075
$154$	0.857286	0.0690821
$155$	15.6269	1.25518
$156$	0	0
$157$	−10.0397	−0.801254	−0.400627	−	0.916241i	$-0.631208\pi$
$157$	−10.0397	−0.801254	−0.400627	+	0.916241i	$0.631208\pi$
$158$	16.9222	1.34626
$159$	4.52407	0.358782
$160$	−29.0574	−2.29719
$161$	1.03857	0.0818505
$162$	−9.49135	−0.745711
$163$	7.10088	0.556184	0.278092	−	0.960554i	$-0.410298\pi$
$163$	7.10088	0.556184	0.278092	+	0.960554i	$0.410298\pi$
$164$	18.7381	1.46320
$165$	5.83888	0.454556
$166$	−30.8016	−2.39066
$167$	−18.1467	−1.40423	−0.702116	−	0.712062i	$-0.747761\pi$
$167$	−18.1467	−1.40423	−0.702116	+	0.712062i	$0.747761\pi$
$168$	1.14597	0.0884133
$169$	0	0
$170$	−45.4815	−3.48827
$171$	2.48846	0.190297
$172$	1.90591	0.145324
$173$	10.1392	0.770866	0.385433	−	0.922736i	$-0.374052\pi$
$173$	10.1392	0.770866	0.385433	+	0.922736i	$0.374052\pi$
$174$	−31.1733	−2.36324
$175$	5.13981	0.388533
$176$	−1.07351	−0.0809186
$177$	−12.1225	−0.911180
$178$	10.5964	0.794230
$179$	−14.5995	−1.09122	−0.545610	−	0.838039i	$-0.683702\pi$
$179$	−14.5995	−1.09122	−0.545610	+	0.838039i	$0.683702\pi$
$180$	−14.6400	−1.09120
$181$	15.2448	1.13313	0.566567	−	0.824016i	$-0.308271\pi$
$181$	15.2448	1.13313	0.566567	+	0.824016i	$0.308271\pi$
$182$	0	0
$183$	10.9779	0.811507
$184$	5.92351	0.436687
$185$	−18.4361	−1.35545
$186$	11.0791	0.812358
$187$	−4.75294	−0.347570
$188$	14.3711	1.04812
$189$	−2.16839	−0.157727
$190$	−20.7918	−1.50840
$191$	16.1594	1.16926	0.584628	−	0.811301i	$-0.301240\pi$
$191$	16.1594	1.16926	0.584628	+	0.811301i	$0.301240\pi$
$192$	−17.6770	−1.27573
$193$	4.84928	0.349059	0.174529	−	0.984652i	$-0.444160\pi$
$193$	4.84928	0.349059	0.174529	+	0.984652i	$0.444160\pi$
$194$	34.3227	2.46423
$195$	0	0
$196$	−20.4309	−1.45935
$197$	19.1751	1.36617	0.683084	−	0.730340i	$-0.260638\pi$
$197$	19.1751	1.36617	0.683084	+	0.730340i	$0.260638\pi$
$198$	−2.55618	−0.181660
$199$	3.42451	0.242757	0.121379	−	0.992606i	$-0.461269\pi$
$199$	3.42451	0.242757	0.121379	+	0.992606i	$0.461269\pi$
$200$	29.3151	2.07289
$201$	20.0903	1.41706
$202$	11.2343	0.790440
$203$	−3.93917	−0.276476
$204$	−19.2994	−1.35123
$205$	26.9448	1.88191
$206$	25.2166	1.75692
$207$	−3.09671	−0.215236
$208$	0	0
$209$	−2.17281	−0.150296
$210$	5.00559	0.345418
$211$	22.3140	1.53616	0.768079	−	0.640355i	$-0.221213\pi$
$211$	22.3140	1.53616	0.768079	+	0.640355i	$0.221213\pi$
$212$	9.90445	0.680240
$213$	−18.9787	−1.30040
$214$	23.1119	1.57990
$215$	2.74064	0.186910
$216$	−12.3675	−0.841502
$217$	1.39999	0.0950378
$218$	0.907008	0.0614303
$219$	−15.5601	−1.05145
$220$	12.7829	0.861825
$221$	0	0
$222$	−13.0707	−0.877250
$223$	4.73412	0.317020	0.158510	−	0.987357i	$-0.449331\pi$
$223$	4.73412	0.317020	0.158510	+	0.987357i	$0.449331\pi$
$224$	−2.60322	−0.173935
$225$	−15.3254	−1.02170
$226$	−2.01924	−0.134318
$227$	−5.54598	−0.368100	−0.184050	−	0.982917i	$-0.558921\pi$
$227$	−5.54598	−0.368100	−0.184050	+	0.982917i	$0.558921\pi$
$228$	−8.82269	−0.584297
$229$	−9.51261	−0.628611	−0.314305	−	0.949322i	$-0.601772\pi$
$229$	−9.51261	−0.628611	−0.314305	+	0.949322i	$0.601772\pi$
$230$	25.8739	1.70607
$231$	0.523099	0.0344174
$232$	−22.4672	−1.47505
$233$	4.49964	0.294781	0.147391	−	0.989078i	$-0.452913\pi$
$233$	4.49964	0.294781	0.147391	+	0.989078i	$0.452913\pi$
$234$	0	0
$235$	20.6651	1.34804
$236$	−26.5394	−1.72757
$237$	10.3256	0.670718
$238$	−4.07463	−0.264119
$239$	−2.97813	−0.192639	−0.0963196	−	0.995350i	$-0.530707\pi$
$239$	−2.97813	−0.192639	−0.0963196	+	0.995350i	$0.530707\pi$
$240$	−6.26808	−0.404603
$241$	−17.6425	−1.13645	−0.568227	−	0.822872i	$-0.692370\pi$
$241$	−17.6425	−1.13645	−0.568227	+	0.822872i	$0.692370\pi$
$242$	2.23194	0.143474
$243$	11.1447	0.714933
$244$	24.0336	1.53859
$245$	−29.3790	−1.87695
$246$	19.1032	1.21798
$247$	0	0
$248$	7.98493	0.507044
$249$	−18.7945	−1.19105
$250$	80.2030	5.07248
$251$	11.9658	0.755273	0.377636	−	0.925954i	$-0.376737\pi$
$251$	11.9658	0.755273	0.377636	+	0.925954i	$0.376737\pi$
$252$	−1.31158	−0.0826217
$253$	2.70390	0.169993
$254$	1.85265	0.116246
$255$	−27.7519	−1.73789
$256$	−8.44618	−0.527886
$257$	4.13033	0.257643	0.128822	−	0.991668i	$-0.458881\pi$
$257$	4.13033	0.257643	0.128822	+	0.991668i	$0.458881\pi$
$258$	1.94305	0.120969
$259$	−1.65167	−0.102630
$260$	0	0
$261$	11.7455	0.727027
$262$	3.60671	0.222823
$263$	−10.0479	−0.619581	−0.309790	−	0.950805i	$-0.600259\pi$
$263$	−10.0479	−0.619581	−0.309790	+	0.950805i	$0.600259\pi$
$264$	2.98352	0.183623
$265$	14.2423	0.874897
$266$	−1.86272	−0.114210
$267$	6.46568	0.395693
$268$	43.9832	2.68670
$269$	−7.95591	−0.485080	−0.242540	−	0.970141i	$-0.577981\pi$
$269$	−7.95591	−0.485080	−0.242540	+	0.970141i	$0.577981\pi$
$270$	−54.0213	−3.28763
$271$	−29.1531	−1.77092	−0.885462	−	0.464712i	$-0.846158\pi$
$271$	−29.1531	−1.77092	−0.885462	+	0.464712i	$0.846158\pi$
$272$	5.10232	0.309374
$273$	0	0
$274$	5.92607	0.358007
$275$	13.3814	0.806932
$276$	10.9792	0.660870
$277$	2.20405	0.132428	0.0662142	−	0.997805i	$-0.478908\pi$
$277$	2.20405	0.132428	0.0662142	+	0.997805i	$0.478908\pi$
$278$	1.38377	0.0829931
$279$	−4.17438	−0.249914
$280$	3.60764	0.215597
$281$	28.6515	1.70920	0.854602	−	0.519284i	$-0.173801\pi$
$281$	28.6515	1.70920	0.854602	+	0.519284i	$0.173801\pi$
$282$	14.6511	0.872459
$283$	−3.89684	−0.231643	−0.115821	−	0.993270i	$-0.536950\pi$
$283$	−3.89684	−0.231643	−0.115821	+	0.993270i	$0.536950\pi$
$284$	−41.5496	−2.46552
$285$	−12.6867	−0.751498
$286$	0	0
$287$	2.41396	0.142491
$288$	7.76206	0.457384
$289$	5.59049	0.328852
$290$	−98.1370	−5.76280
$291$	20.9430	1.22770
$292$	−34.0654	−1.99352
$293$	−7.85353	−0.458808	−0.229404	−	0.973331i	$-0.573678\pi$
$293$	−7.85353	−0.458808	−0.229404	+	0.973331i	$0.573678\pi$
$294$	−20.8290	−1.21477
$295$	−38.1629	−2.22193
$296$	−9.42036	−0.547547
$297$	−5.64538	−0.327578
$298$	8.53065	0.494167
$299$	0	0
$300$	54.3354	3.13706
$301$	0.245531	0.0141522
$302$	−38.2710	−2.20225
$303$	6.85492	0.393805
$304$	2.33252	0.133779
$305$	34.5595	1.97887
$306$	12.1494	0.694534
$307$	−19.3947	−1.10691	−0.553456	−	0.832878i	$-0.686691\pi$
$307$	−19.3947	−1.10691	−0.553456	+	0.832878i	$0.686691\pi$
$308$	1.14521	0.0652543
$309$	15.3867	0.875317
$310$	34.8782	1.98095
$311$	−23.4655	−1.33060	−0.665302	−	0.746574i	$-0.731697\pi$
$311$	−23.4655	−1.33060	−0.665302	+	0.746574i	$0.731697\pi$
$312$	0	0
$313$	7.41942	0.419370	0.209685	−	0.977769i	$-0.432756\pi$
$313$	7.41942	0.419370	0.209685	+	0.977769i	$0.432756\pi$
$314$	−22.4079	−1.26455
$315$	−1.88601	−0.106265
$316$	22.6055	1.27166
$317$	6.18430	0.347345	0.173672	−	0.984803i	$-0.444437\pi$
$317$	6.18430	0.347345	0.173672	+	0.984803i	$0.444437\pi$
$318$	10.0974	0.566236
$319$	−10.2556	−0.574203
$320$	−55.6492	−3.11089
$321$	14.1024	0.787120
$322$	2.31801	0.129178
$323$	10.3272	0.574622
$324$	−12.6790	−0.704391
$325$	0	0
$326$	15.8487	0.877779
$327$	0.553438	0.0306052
$328$	13.7681	0.760217
$329$	1.85137	0.102069
$330$	13.0320	0.717388
$331$	−13.7493	−0.755730	−0.377865	−	0.925861i	$-0.623342\pi$
$331$	−13.7493	−0.755730	−0.377865	+	0.925861i	$0.623342\pi$
$332$	−41.1463	−2.25820
$333$	4.92480	0.269877
$334$	−40.5022	−2.21618
$335$	63.2465	3.45553
$336$	−0.561550	−0.0306351
$337$	−8.57461	−0.467089	−0.233544	−	0.972346i	$-0.575032\pi$
$337$	−8.57461	−0.467089	−0.233544	+	0.972346i	$0.575032\pi$
$338$	0	0
$339$	−1.23210	−0.0669184
$340$	−60.7565	−3.29499
$341$	3.64487	0.197381
$342$	5.55409	0.300331
$343$	−5.32073	−0.287292
$344$	1.40040	0.0755043
$345$	15.7877	0.849983
$346$	22.6300	1.21659
$347$	9.73625	0.522669	0.261335	−	0.965248i	$-0.415837\pi$
$347$	9.73625	0.522669	0.261335	+	0.965248i	$0.415837\pi$
$348$	−41.6429	−2.23229
$349$	10.3236	0.552608	0.276304	−	0.961070i	$-0.410890\pi$
$349$	10.3236	0.552608	0.276304	+	0.961070i	$0.410890\pi$
$350$	11.4717	0.613190
$351$	0	0
$352$	−6.77746	−0.361240
$353$	−3.38311	−0.180065	−0.0900324	−	0.995939i	$-0.528697\pi$
$353$	−3.38311	−0.180065	−0.0900324	+	0.995939i	$0.528697\pi$
$354$	−27.0565	−1.43804
$355$	−59.7470	−3.17104
$356$	14.1552	0.750222
$357$	−2.48626	−0.131587
$358$	−32.5852	−1.72218
$359$	−14.4639	−0.763376	−0.381688	−	0.924291i	$-0.624657\pi$
$359$	−14.4639	−0.763376	−0.381688	+	0.924291i	$0.624657\pi$
$360$	−10.7569	−0.566940
$361$	−14.2789	−0.751522
$362$	34.0253	1.78833
$363$	1.36188	0.0714803
$364$	0	0
$365$	−48.9849	−2.56399
$366$	24.5019	1.28073
$367$	−21.5437	−1.12457	−0.562286	−	0.826943i	$-0.690078\pi$
$367$	−21.5437	−1.12457	−0.562286	+	0.826943i	$0.690078\pi$
$368$	−2.90265	−0.151311
$369$	−7.19773	−0.374699
$370$	−41.1481	−2.13919
$371$	1.27595	0.0662441
$372$	14.8000	0.767345
$373$	−25.6291	−1.32703	−0.663513	−	0.748165i	$-0.730935\pi$
$373$	−25.6291	−1.32703	−0.663513	+	0.748165i	$0.730935\pi$
$374$	−10.6083	−0.548541
$375$	48.9383	2.52716
$376$	10.5593	0.544557
$377$	0	0
$378$	−4.83970	−0.248927
$379$	−9.41163	−0.483443	−0.241722	−	0.970346i	$-0.577712\pi$
$379$	−9.41163	−0.483443	−0.241722	+	0.970346i	$0.577712\pi$
$380$	−27.7748	−1.42482
$381$	1.13045	0.0579147
$382$	36.0668	1.84534
$383$	−9.95412	−0.508632	−0.254316	−	0.967121i	$-0.581850\pi$
$383$	−9.95412	−0.508632	−0.254316	+	0.967121i	$0.581850\pi$
$384$	−20.9938	−1.07133
$385$	1.64677	0.0839273
$386$	10.8233	0.550891
$387$	−0.732102	−0.0372149
$388$	45.8501	2.32769
$389$	−3.75782	−0.190529	−0.0952646	−	0.995452i	$-0.530370\pi$
$389$	−3.75782	−0.190529	−0.0952646	+	0.995452i	$0.530370\pi$
$390$	0	0
$391$	−12.8515	−0.649927
$392$	−15.0119	−0.758216
$393$	2.20074	0.111013
$394$	42.7975	2.15611
$395$	32.5060	1.63556
$396$	−3.41468	−0.171594
$397$	−16.9510	−0.850748	−0.425374	−	0.905018i	$-0.639857\pi$
$397$	−16.9510	−0.850748	−0.425374	+	0.905018i	$0.639857\pi$
$398$	7.64329	0.383123
$399$	−1.13659	−0.0569007
$400$	−14.3651	−0.718254
$401$	14.0800	0.703120	0.351560	−	0.936165i	$-0.385651\pi$
$401$	14.0800	0.703120	0.351560	+	0.936165i	$0.385651\pi$
$402$	44.8403	2.23643
$403$	0	0
$404$	15.0073	0.746642
$405$	−18.2321	−0.905959
$406$	−8.79198	−0.436339
$407$	−4.30010	−0.213148
$408$	−14.1805	−0.702039
$409$	34.6483	1.71325	0.856624	−	0.515941i	$-0.172557\pi$
$409$	34.6483	1.71325	0.856624	+	0.515941i	$0.172557\pi$
$410$	60.1391	2.97006
$411$	3.61597	0.178363
$412$	33.6857	1.65957
$413$	−3.41897	−0.168236
$414$	−6.91166	−0.339689
$415$	−59.1672	−2.90440
$416$	0	0
$417$	0.844350	0.0413480
$418$	−4.84956	−0.237200
$419$	−0.846364	−0.0413476	−0.0206738	−	0.999786i	$-0.506581\pi$
$419$	−0.846364	−0.0413476	−0.0206738	+	0.999786i	$0.506581\pi$
$420$	6.68673	0.326279
$421$	11.2318	0.547406	0.273703	−	0.961814i	$-0.411751\pi$
$421$	11.2318	0.547406	0.273703	+	0.961814i	$0.411751\pi$
$422$	49.8034	2.42439
$423$	−5.52024	−0.268403
$424$	7.27744	0.353424
$425$	−63.6013	−3.08512
$426$	−42.3592	−2.05231
$427$	3.09615	0.149833
$428$	30.8741	1.49236
$429$	0	0
$430$	6.11693	0.294985
$431$	−11.6680	−0.562030	−0.281015	−	0.959703i	$-0.590671\pi$
$431$	−11.6680	−0.562030	−0.281015	+	0.959703i	$0.590671\pi$
$432$	6.06035	0.291579
$433$	−4.80473	−0.230901	−0.115450	−	0.993313i	$-0.536831\pi$
$433$	−4.80473	−0.230901	−0.115450	+	0.993313i	$0.536831\pi$
$434$	3.12470	0.149990
$435$	−59.8812	−2.87108
$436$	1.21163	0.0580265
$437$	−5.87504	−0.281041
$438$	−34.7291	−1.65942
$439$	14.8238	0.707504	0.353752	−	0.935339i	$-0.384906\pi$
$439$	14.8238	0.707504	0.353752	+	0.935339i	$0.384906\pi$
$440$	9.39245	0.447767
$441$	7.84796	0.373713
$442$	0	0
$443$	11.2007	0.532162	0.266081	−	0.963951i	$-0.414271\pi$
$443$	11.2007	0.532162	0.266081	+	0.963951i	$0.414271\pi$
$444$	−17.4606	−0.828642
$445$	20.3547	0.964905
$446$	10.5662	0.500326
$447$	5.20523	0.246199
$448$	−4.98555	−0.235545
$449$	27.5634	1.30080	0.650399	−	0.759593i	$-0.274602\pi$
$449$	27.5634	1.30080	0.650399	+	0.759593i	$0.274602\pi$
$450$	−34.2054	−1.61246
$451$	6.28472	0.295936
$452$	−2.69741	−0.126875
$453$	−23.3522	−1.09718
$454$	−12.3783	−0.580941
$455$	0	0
$456$	−6.48260	−0.303576
$457$	36.7079	1.71712	0.858562	−	0.512710i	$-0.171358\pi$
$457$	36.7079	1.71712	0.858562	+	0.512710i	$0.171358\pi$
$458$	−21.2315	−0.992084
$459$	26.8322	1.25242
$460$	34.5637	1.61154
$461$	1.28568	0.0598803	0.0299401	−	0.999552i	$-0.490468\pi$
$461$	1.28568	0.0598803	0.0299401	+	0.999552i	$0.490468\pi$
$462$	1.16752	0.0543181
$463$	25.8691	1.20224	0.601120	−	0.799159i	$-0.294721\pi$
$463$	25.8691	1.20224	0.601120	+	0.799159i	$0.294721\pi$
$464$	11.0095	0.511101
$465$	21.2820	0.986928
$466$	10.0429	0.465228
$467$	−19.9050	−0.921095	−0.460548	−	0.887635i	$-0.652347\pi$
$467$	−19.9050	−0.921095	−0.460548	+	0.887635i	$0.652347\pi$
$468$	0	0
$469$	5.66619	0.261640
$470$	46.1232	2.12751
$471$	−13.6729	−0.630013
$472$	−19.5002	−0.897571
$473$	0.639237	0.0293921
$474$	23.0460	1.05854
$475$	−29.0753	−1.33407
$476$	−5.44311	−0.249485
$477$	−3.80452	−0.174197
$478$	−6.64699	−0.304026
$479$	−41.7901	−1.90944	−0.954720	−	0.297507i	$-0.903845\pi$
$479$	−41.7901	−1.90944	−0.954720	+	0.297507i	$0.903845\pi$
$480$	−39.5728	−1.80624
$481$	0	0
$482$	−39.3770	−1.79357
$483$	1.41441	0.0643577
$484$	2.98154	0.135524
$485$	65.9310	2.99377
$486$	24.8743	1.12832
$487$	−25.1408	−1.13924	−0.569619	−	0.821909i	$-0.692909\pi$
$487$	−25.1408	−1.13924	−0.569619	+	0.821909i	$0.692909\pi$
$488$	17.6590	0.799387
$489$	9.67057	0.437318
$490$	−65.5720	−2.96224
$491$	−33.4637	−1.51020	−0.755098	−	0.655612i	$-0.772411\pi$
$491$	−33.4637	−1.51020	−0.755098	+	0.655612i	$0.772411\pi$
$492$	25.5191	1.15049
$493$	48.7443	2.19533
$494$	0	0
$495$	−4.91021	−0.220697
$496$	−3.91280	−0.175690
$497$	−5.35267	−0.240100
$498$	−41.9481	−1.87974
$499$	−32.1808	−1.44061	−0.720305	−	0.693657i	$-0.755998\pi$
$499$	−32.1808	−1.44061	−0.720305	+	0.693657i	$0.755998\pi$
$500$	107.139	4.79142
$501$	−24.7137	−1.10412
$502$	26.7068	1.19198
$503$	25.3959	1.13235	0.566173	−	0.824287i	$-0.308424\pi$
$503$	25.3959	1.13235	0.566173	+	0.824287i	$0.308424\pi$
$504$	−0.963702	−0.0429267
$505$	21.5801	0.960300
$506$	6.03493	0.268285
$507$	0	0
$508$	2.47487	0.109805
$509$	−40.0559	−1.77545	−0.887723	−	0.460378i	$-0.847714\pi$
$509$	−40.0559	−1.77545	−0.887723	+	0.460378i	$0.847714\pi$
$510$	−61.9404	−2.74277
$511$	−4.38850	−0.194136
$512$	11.9792	0.529410
$513$	12.2663	0.541571
$514$	9.21864	0.406617
$515$	48.4389	2.13447
$516$	2.59562	0.114266
$517$	4.82001	0.211984
$518$	−3.68641	−0.161972
$519$	13.8084	0.606119
$520$	0	0
$521$	9.99187	0.437752	0.218876	−	0.975753i	$-0.429761\pi$
$521$	9.99187	0.437752	0.218876	+	0.975753i	$0.429761\pi$
$522$	26.2152	1.14741
$523$	16.7831	0.733873	0.366937	−	0.930246i	$-0.380407\pi$
$523$	16.7831	0.733873	0.366937	+	0.930246i	$0.380407\pi$
$524$	4.81803	0.210477
$525$	6.99982	0.305497
$526$	−22.4263	−0.977833
$527$	−17.3239	−0.754640
$528$	−1.46199	−0.0636250
$529$	−15.6889	−0.682128
$530$	31.7879	1.38078
$531$	10.1944	0.442399
$532$	−2.48831	−0.107882
$533$	0	0
$534$	14.4310	0.624490
$535$	44.3960	1.91941
$536$	32.3174	1.39590
$537$	−19.8829	−0.858009
$538$	−17.7571	−0.765562
$539$	−6.85247	−0.295157
$540$	−72.1645	−3.10546
$541$	9.22570	0.396644	0.198322	−	0.980137i	$-0.436451\pi$
$541$	9.22570	0.396644	0.198322	+	0.980137i	$0.436451\pi$
$542$	−65.0678	−2.79490
$543$	20.7616	0.890965
$544$	32.2129	1.38112
$545$	1.74228	0.0746313
$546$	0	0
$547$	−39.1085	−1.67216	−0.836079	−	0.548609i	$-0.815158\pi$
$547$	−39.1085	−1.67216	−0.836079	+	0.548609i	$0.815158\pi$
$548$	7.91636	0.338170
$549$	−9.23183	−0.394005
$550$	29.8665	1.27351
$551$	22.2834	0.949306
$552$	8.06713	0.343360
$553$	2.91218	0.123838
$554$	4.91929	0.209001
$555$	−25.1078	−1.06577
$556$	1.84852	0.0783945
$557$	−23.3254	−0.988327	−0.494164	−	0.869369i	$-0.664526\pi$
$557$	−23.3254	−0.988327	−0.494164	+	0.869369i	$0.664526\pi$
$558$	−9.31696	−0.394418
$559$	0	0
$560$	−1.76782	−0.0747041
$561$	−6.47295	−0.273288
$562$	63.9482	2.69749
$563$	8.48003	0.357391	0.178695	−	0.983904i	$-0.442812\pi$
$563$	8.48003	0.357391	0.178695	+	0.983904i	$0.442812\pi$
$564$	19.5717	0.824117
$565$	−3.87879	−0.163182
$566$	−8.69749	−0.365583
$567$	−1.63339	−0.0685959
$568$	−30.5292	−1.28098
$569$	6.74179	0.282630	0.141315	−	0.989965i	$-0.454867\pi$
$569$	6.74179	0.282630	0.141315	+	0.989965i	$0.454867\pi$
$570$	−28.3160	−1.18603
$571$	16.4075	0.686632	0.343316	−	0.939220i	$-0.388450\pi$
$571$	16.4075	0.686632	0.343316	+	0.939220i	$0.388450\pi$
$572$	0	0
$573$	22.0073	0.919367
$574$	5.38780	0.224882
$575$	36.1821	1.50890
$576$	14.8655	0.619396
$577$	12.7296	0.529939	0.264969	−	0.964257i	$-0.414638\pi$
$577$	12.7296	0.529939	0.264969	+	0.964257i	$0.414638\pi$
$578$	12.4776	0.519000
$579$	6.60415	0.274459
$580$	−131.097	−5.44349
$581$	−5.30072	−0.219911
$582$	46.7435	1.93758
$583$	3.32193	0.137580
$584$	−25.0300	−1.03575
$585$	0	0
$586$	−17.5286	−0.724099
$587$	32.3761	1.33630	0.668152	−	0.744025i	$-0.267085\pi$
$587$	32.3761	1.33630	0.668152	+	0.744025i	$0.267085\pi$
$588$	−27.8245	−1.14746
$589$	−7.91960	−0.326321
$590$	−85.1770	−3.50668
$591$	26.1142	1.07419
$592$	4.61619	0.189724
$593$	26.6848	1.09581	0.547907	−	0.836539i	$-0.315425\pi$
$593$	26.6848	1.09581	0.547907	+	0.836539i	$0.315425\pi$
$594$	−12.6001	−0.516989
$595$	−7.82702	−0.320877
$596$	11.3957	0.466786
$597$	4.66378	0.190876
$598$	0	0
$599$	16.3472	0.667928	0.333964	−	0.942586i	$-0.391614\pi$
$599$	16.3472	0.667928	0.333964	+	0.942586i	$0.391614\pi$
$600$	39.9238	1.62988
$601$	−15.9276	−0.649700	−0.324850	−	0.945766i	$-0.605314\pi$
$601$	−15.9276	−0.649700	−0.324850	+	0.945766i	$0.605314\pi$
$602$	0.548009	0.0223352
$603$	−16.8950	−0.688016
$604$	−51.1245	−2.08023
$605$	4.28736	0.174306
$606$	15.2997	0.621509
$607$	−33.1705	−1.34635	−0.673175	−	0.739483i	$-0.735070\pi$
$607$	−33.1705	−1.34635	−0.673175	+	0.739483i	$0.735070\pi$
$608$	14.7261	0.597222
$609$	−5.36469	−0.217388
$610$	77.1347	3.12309
$611$	0	0
$612$	16.2298	0.656051
$613$	15.0843	0.609251	0.304626	−	0.952472i	$-0.401469\pi$
$613$	15.0843	0.609251	0.304626	+	0.952472i	$0.401469\pi$
$614$	−43.2876	−1.74695
$615$	36.6957	1.47971
$616$	0.841459	0.0339033
$617$	12.1043	0.487302	0.243651	−	0.969863i	$-0.421655\pi$
$617$	12.1043	0.487302	0.243651	+	0.969863i	$0.421655\pi$
$618$	34.3421	1.38144
$619$	−9.71704	−0.390561	−0.195280	−	0.980747i	$-0.562562\pi$
$619$	−9.71704	−0.390561	−0.195280	+	0.980747i	$0.562562\pi$
$620$	46.5921	1.87118
$621$	−15.2645	−0.612544
$622$	−52.3734	−2.09998
$623$	1.82355	0.0730591
$624$	0	0
$625$	87.1559	3.48624
$626$	16.5597	0.661858
$627$	−2.95911	−0.118175
$628$	−29.9337	−1.19449
$629$	20.4381	0.814922
$630$	−4.20945	−0.167709
$631$	38.4391	1.53024	0.765118	−	0.643890i	$-0.222680\pi$
$631$	38.4391	1.53024	0.765118	+	0.643890i	$0.222680\pi$
$632$	16.6097	0.660700
$633$	30.3890	1.20786
$634$	13.8030	0.548185
$635$	3.55878	0.141226
$636$	13.4887	0.534862
$637$	0	0
$638$	−22.8898	−0.906217
$639$	15.9601	0.631373
$640$	−66.0907	−2.61247
$641$	−2.30218	−0.0909308	−0.0454654	−	0.998966i	$-0.514477\pi$
$641$	−2.30218	−0.0909308	−0.0454654	+	0.998966i	$0.514477\pi$
$642$	31.4757	1.24225
$643$	13.5933	0.536067	0.268033	−	0.963410i	$-0.413626\pi$
$643$	13.5933	0.536067	0.268033	+	0.963410i	$0.413626\pi$
$644$	3.09653	0.122020
$645$	3.73243	0.146964
$646$	23.0497	0.906878
$647$	−25.3906	−0.998209	−0.499104	−	0.866542i	$-0.666338\pi$
$647$	−25.3906	−0.998209	−0.499104	+	0.866542i	$0.666338\pi$
$648$	−9.31612	−0.365972
$649$	−8.90125	−0.349405
$650$	0	0
$651$	1.90663	0.0747266
$652$	21.1715	0.829142
$653$	−24.1446	−0.944853	−0.472426	−	0.881370i	$-0.656622\pi$
$653$	−24.1446	−0.944853	−0.472426	+	0.881370i	$0.656622\pi$
$654$	1.23524	0.0483016
$655$	6.92817	0.270706
$656$	−6.74669	−0.263414
$657$	13.0853	0.510505
$658$	4.13213	0.161087
$659$	34.3980	1.33996	0.669978	−	0.742381i	$-0.266304\pi$
$659$	34.3980	1.33996	0.669978	+	0.742381i	$0.266304\pi$
$660$	17.4088	0.677638
$661$	17.4355	0.678163	0.339081	−	0.940757i	$-0.389884\pi$
$661$	17.4355	0.678163	0.339081	+	0.940757i	$0.389884\pi$
$662$	−30.6876	−1.19271
$663$	0	0
$664$	−30.2329	−1.17326
$665$	−3.57812	−0.138753
$666$	10.9918	0.425925
$667$	−27.7301	−1.07371
$668$	−54.1050	−2.09339
$669$	6.44731	0.249267
$670$	141.162	5.45357
$671$	8.06080	0.311184
$672$	−3.54528	−0.136762
$673$	−43.1928	−1.66496	−0.832479	−	0.554056i	$-0.813079\pi$
$673$	−43.1928	−1.66496	−0.832479	+	0.554056i	$0.813079\pi$
$674$	−19.1380	−0.737167
$675$	−75.5433	−2.90766
$676$	0	0
$677$	22.7599	0.874732	0.437366	−	0.899284i	$-0.355911\pi$
$677$	22.7599	0.874732	0.437366	+	0.899284i	$0.355911\pi$
$678$	−2.74997	−0.105612
$679$	5.90669	0.226678
$680$	−44.6418	−1.71193
$681$	−7.55297	−0.289431
$682$	8.13512	0.311510
$683$	−16.9629	−0.649066	−0.324533	−	0.945874i	$-0.605207\pi$
$683$	−16.9629	−0.649066	−0.324533	+	0.945874i	$0.605207\pi$
$684$	7.41944	0.283689
$685$	11.3835	0.434940
$686$	−11.8755	−0.453410
$687$	−12.9551	−0.494266
$688$	−0.686225	−0.0261621
$689$	0	0
$690$	35.2372	1.34146
$691$	4.52167	0.172012	0.0860061	−	0.996295i	$-0.472590\pi$
$691$	4.52167	0.172012	0.0860061	+	0.996295i	$0.472590\pi$
$692$	30.2303	1.14918
$693$	−0.439900	−0.0167104
$694$	21.7307	0.824885
$695$	2.65811	0.100828
$696$	−30.5978	−1.15981
$697$	−29.8709	−1.13144
$698$	23.0415	0.872135
$699$	6.12798	0.231781
$700$	15.3245	0.579213
$701$	38.4564	1.45248	0.726239	−	0.687442i	$-0.241267\pi$
$701$	38.4564	1.45248	0.726239	+	0.687442i	$0.241267\pi$
$702$	0	0
$703$	9.34328	0.352388
$704$	−12.9798	−0.489196
$705$	28.1435	1.05994
$706$	−7.55089	−0.284181
$707$	1.93333	0.0727105
$708$	−36.1436	−1.35836
$709$	37.4050	1.40477	0.702386	−	0.711796i	$-0.252118\pi$
$709$	37.4050	1.40477	0.702386	+	0.711796i	$0.252118\pi$
$710$	−133.352	−5.00459
$711$	−8.68329	−0.325649
$712$	10.4007	0.389784
$713$	9.85536	0.369086
$714$	−5.54917	−0.207673
$715$	0	0
$716$	−43.5291	−1.62676
$717$	−4.05586	−0.151469
$718$	−32.2825	−1.20477
$719$	30.7619	1.14722	0.573612	−	0.819127i	$-0.305542\pi$
$719$	30.7619	1.14722	0.573612	+	0.819127i	$0.305542\pi$
$720$	5.27114	0.196444
$721$	4.33959	0.161615
$722$	−31.8696	−1.18606
$723$	−24.0270	−0.893575
$724$	45.4528	1.68924
$725$	−137.235	−5.09677
$726$	3.03963	0.112811
$727$	22.7199	0.842636	0.421318	−	0.906913i	$-0.361568\pi$
$727$	22.7199	0.842636	0.421318	+	0.906913i	$0.361568\pi$
$728$	0	0
$729$	27.9353	1.03464
$730$	−109.331	−4.04653
$731$	−3.03826	−0.112374
$732$	32.7309	1.20977
$733$	18.1398	0.670008	0.335004	−	0.942217i	$-0.391262\pi$
$733$	18.1398	0.670008	0.335004	+	0.942217i	$0.391262\pi$
$734$	−48.0842	−1.77482
$735$	−40.0107	−1.47582
$736$	−18.3256	−0.675489
$737$	14.7519	0.543392
$738$	−16.0649	−0.591356
$739$	−38.3992	−1.41254	−0.706268	−	0.707945i	$-0.749623\pi$
$739$	−38.3992	−1.41254	−0.706268	+	0.707945i	$0.749623\pi$
$740$	−54.9679	−2.02066
$741$	0	0
$742$	2.84784	0.104548
$743$	−36.1752	−1.32714	−0.663571	−	0.748114i	$-0.730960\pi$
$743$	−36.1752	−1.32714	−0.663571	+	0.748114i	$0.730960\pi$
$744$	10.8745	0.398680
$745$	16.3866	0.600360
$746$	−57.2026	−2.09434
$747$	15.8052	0.578283
$748$	−14.1711	−0.518146
$749$	3.97739	0.145331
$750$	109.227	3.98841
$751$	−12.5624	−0.458408	−0.229204	−	0.973378i	$-0.573612\pi$
$751$	−12.5624	−0.458408	−0.229204	+	0.973378i	$0.573612\pi$
$752$	−5.17432	−0.188688
$753$	16.2960	0.593858
$754$	0	0
$755$	−73.5154	−2.67550
$756$	−6.46513	−0.235135
$757$	32.0717	1.16566	0.582832	−	0.812593i	$-0.301945\pi$
$757$	32.0717	1.16566	0.582832	+	0.812593i	$0.301945\pi$
$758$	−21.0062	−0.762978
$759$	3.68239	0.133662
$760$	−20.4080	−0.740274
$761$	−2.45600	−0.0890300	−0.0445150	−	0.999009i	$-0.514174\pi$
$761$	−2.45600	−0.0890300	−0.0445150	+	0.999009i	$0.514174\pi$
$762$	2.52309	0.0914020
$763$	0.156089	0.00565081
$764$	48.1800	1.74309
$765$	23.3379	0.843785
$766$	−22.2170	−0.802732
$767$	0	0
$768$	−11.5027	−0.415068
$769$	1.97248	0.0711296	0.0355648	−	0.999367i	$-0.488677\pi$
$769$	1.97248	0.0711296	0.0355648	+	0.999367i	$0.488677\pi$
$770$	3.67549	0.132456
$771$	5.62503	0.202581
$772$	14.4583	0.520366
$773$	−25.9419	−0.933064	−0.466532	−	0.884504i	$-0.654497\pi$
$773$	−25.9419	−0.933064	−0.466532	+	0.884504i	$0.654497\pi$
$774$	−1.63401	−0.0587331
$775$	48.7737	1.75200
$776$	33.6891	1.20937
$777$	−2.24938	−0.0806959
$778$	−8.38722	−0.300696
$779$	−13.6555	−0.489258
$780$	0	0
$781$	−13.9356	−0.498656
$782$	−28.6837	−1.02573
$783$	57.8967	2.06906
$784$	7.35617	0.262720
$785$	−43.0438	−1.53630
$786$	4.91191	0.175202
$787$	45.8214	1.63336	0.816679	−	0.577093i	$-0.195813\pi$
$787$	45.8214	1.63336	0.816679	+	0.577093i	$0.195813\pi$
$788$	57.1712	2.03664
$789$	−13.6841	−0.487166
$790$	72.5514	2.58126
$791$	−0.347496	−0.0123555
$792$	−2.50899	−0.0891531
$793$	0	0
$794$	−37.8336	−1.34267
$795$	19.3963	0.687917
$796$	10.2103	0.361895
$797$	25.4970	0.903152	0.451576	−	0.892233i	$-0.350862\pi$
$797$	25.4970	0.903152	0.451576	+	0.892233i	$0.350862\pi$
$798$	−2.53680	−0.0898017
$799$	−22.9093	−0.810471
$800$	−90.6922	−3.20645
$801$	−5.43732	−0.192118
$802$	31.4256	1.10968
$803$	−11.4254	−0.403195
$804$	59.9000	2.11251
$805$	4.45271	0.156937
$806$	0	0
$807$	−10.8350	−0.381411
$808$	11.0269	0.387923
$809$	46.8717	1.64792	0.823960	−	0.566648i	$-0.191760\pi$
$809$	46.8717	1.64792	0.823960	+	0.566648i	$0.191760\pi$
$810$	−40.6928	−1.42980
$811$	−2.41983	−0.0849717	−0.0424859	−	0.999097i	$-0.513528\pi$
$811$	−2.41983	−0.0849717	−0.0424859	+	0.999097i	$0.513528\pi$
$812$	−11.7448	−0.412161
$813$	−39.7031	−1.39245
$814$	−9.59755	−0.336394
$815$	30.4440	1.06641
$816$	6.94876	0.243255
$817$	−1.38894	−0.0485928
$818$	77.3328	2.70388
$819$	0	0
$820$	80.3370	2.80549
$821$	−8.76673	−0.305961	−0.152980	−	0.988229i	$-0.548887\pi$
$821$	−8.76673	−0.305961	−0.152980	+	0.988229i	$0.548887\pi$
$822$	8.07061	0.281495
$823$	−41.7652	−1.45584	−0.727921	−	0.685661i	$-0.759513\pi$
$823$	−41.7652	−1.45584	−0.727921	+	0.685661i	$0.759513\pi$
$824$	24.7511	0.862244
$825$	18.2240	0.634477
$826$	−7.63091	−0.265513
$827$	38.4530	1.33714	0.668570	−	0.743649i	$-0.266907\pi$
$827$	38.4530	1.33714	0.668570	+	0.743649i	$0.266907\pi$
$828$	−9.23295	−0.320867
$829$	1.12630	0.0391179	0.0195590	−	0.999809i	$-0.493774\pi$
$829$	1.12630	0.0391179	0.0195590	+	0.999809i	$0.493774\pi$
$830$	−132.057	−4.58378
$831$	3.00165	0.104126
$832$	0	0
$833$	32.5694	1.12846
$834$	1.88453	0.0652561
$835$	−77.8014	−2.69243
$836$	−6.47830	−0.224057
$837$	−20.5767	−0.711234
$838$	−1.88903	−0.0652555
$839$	−8.13825	−0.280964	−0.140482	−	0.990083i	$-0.544865\pi$
$839$	−8.13825	−0.280964	−0.140482	+	0.990083i	$0.544865\pi$
$840$	4.91318	0.169521
$841$	76.1773	2.62680
$842$	25.0688	0.863926
$843$	39.0199	1.34392
$844$	66.5300	2.29006
$845$	0	0
$846$	−12.3208	−0.423599
$847$	0.384100	0.0131978
$848$	−3.56611	−0.122461
$849$	−5.30704	−0.182137
$850$	−141.954	−4.86898
$851$	−11.6270	−0.398570
$852$	−56.5857	−1.93859
$853$	23.5017	0.804682	0.402341	−	0.915490i	$-0.368197\pi$
$853$	23.5017	0.804682	0.402341	+	0.915490i	$0.368197\pi$
$854$	6.91041	0.236469
$855$	10.6689	0.364870
$856$	22.6852	0.775364
$857$	−26.1485	−0.893217	−0.446608	−	0.894730i	$-0.647368\pi$
$857$	−26.1485	−0.893217	−0.446608	+	0.894730i	$0.647368\pi$
$858$	0	0
$859$	14.9787	0.511065	0.255533	−	0.966800i	$-0.417749\pi$
$859$	14.9787	0.511065	0.255533	+	0.966800i	$0.417749\pi$
$860$	8.17132	0.278640
$861$	3.28753	0.112039
$862$	−26.0423	−0.887005
$863$	45.0286	1.53279	0.766396	−	0.642369i	$-0.222048\pi$
$863$	45.0286	1.53279	0.766396	+	0.642369i	$0.222048\pi$
$864$	38.2613	1.30168
$865$	43.4702	1.47803
$866$	−10.7238	−0.364411
$867$	7.61359	0.258571
$868$	4.17414	0.141679
$869$	7.58183	0.257196
$870$	−133.651	−4.53119
$871$	0	0
$872$	0.890262	0.0301481
$873$	−17.6121	−0.596078
$874$	−13.1127	−0.443544
$875$	13.8023	0.466604
$876$	−46.3930	−1.56748
$877$	−15.9277	−0.537839	−0.268920	−	0.963163i	$-0.586667\pi$
$877$	−15.9277	−0.537839	−0.268920	+	0.963163i	$0.586667\pi$
$878$	33.0859	1.11659
$879$	−10.6956	−0.360753
$880$	−4.60251	−0.155151
$881$	47.6435	1.60515	0.802575	−	0.596551i	$-0.203463\pi$
$881$	47.6435	1.60515	0.802575	+	0.596551i	$0.203463\pi$
$882$	17.5162	0.589800
$883$	23.9450	0.805815	0.402907	−	0.915241i	$-0.368000\pi$
$883$	23.9450	0.805815	0.402907	+	0.915241i	$0.368000\pi$
$884$	0	0
$885$	−51.9733	−1.74706
$886$	24.9993	0.839867
$887$	26.8935	0.902996	0.451498	−	0.892272i	$-0.350890\pi$
$887$	26.8935	0.902996	0.451498	+	0.892272i	$0.350890\pi$
$888$	−12.8294	−0.430527
$889$	0.318827	0.0106931
$890$	45.4304	1.52283
$891$	−4.25252	−0.142465
$892$	14.1150	0.472604
$893$	−10.4730	−0.350464
$894$	11.6177	0.388555
$895$	−62.5935	−2.09227
$896$	−5.92099	−0.197807
$897$	0	0
$898$	61.5197	2.05294
$899$	−37.3804	−1.24670
$900$	−45.6934	−1.52311
$901$	−15.7889	−0.526006
$902$	14.0271	0.467051
$903$	0.334384	0.0111276
$904$	−1.98196	−0.0659190
$905$	65.3598	2.17263
$906$	−52.1207	−1.73159
$907$	31.8951	1.05906	0.529530	−	0.848291i	$-0.322368\pi$
$907$	31.8951	1.05906	0.529530	+	0.848291i	$0.322368\pi$
$908$	−16.5355	−0.548751
$909$	−5.76465	−0.191201
$910$	0	0
$911$	−14.6773	−0.486280	−0.243140	−	0.969991i	$-0.578177\pi$
$911$	−14.6773	−0.486280	−0.243140	+	0.969991i	$0.578177\pi$
$912$	3.17662	0.105188
$913$	−13.8004	−0.456726
$914$	81.9297	2.70999
$915$	47.0660	1.55595
$916$	−28.3622	−0.937114
$917$	0.620687	0.0204969
$918$	59.8877	1.97659
$919$	28.8671	0.952239	0.476119	−	0.879381i	$-0.342043\pi$
$919$	28.8671	0.952239	0.476119	+	0.879381i	$0.342043\pi$
$920$	25.3962	0.837288
$921$	−26.4133	−0.870346
$922$	2.86956	0.0945041
$923$	0	0
$924$	1.55964	0.0513083
$925$	−57.5416	−1.89195
$926$	57.7382	1.89740
$927$	−12.9394	−0.424986
$928$	69.5069	2.28168
$929$	−50.7771	−1.66594	−0.832972	−	0.553316i	$-0.813362\pi$
$929$	−50.7771	−1.66594	−0.832972	+	0.553316i	$0.813362\pi$
$930$	47.5000	1.55759
$931$	14.8891	0.487970
$932$	13.4158	0.439450
$933$	−31.9572	−1.04623
$934$	−44.4268	−1.45369
$935$	−20.3776	−0.666418
$936$	0	0
$937$	19.2380	0.628478	0.314239	−	0.949344i	$-0.398251\pi$
$937$	19.2380	0.628478	0.314239	+	0.949344i	$0.398251\pi$
$938$	12.6466	0.412925
$939$	10.1044	0.329744
$940$	61.6139	2.00962
$941$	−9.69418	−0.316021	−0.158011	−	0.987437i	$-0.550508\pi$
$941$	−9.69418	−0.316021	−0.158011	+	0.987437i	$0.550508\pi$
$942$	−30.5170	−0.994297
$943$	16.9932	0.553376
$944$	9.55555	0.311007
$945$	−9.29666	−0.302420
$946$	1.42674	0.0463872
$947$	−50.0296	−1.62574	−0.812871	−	0.582444i	$-0.802097\pi$
$947$	−50.0296	−1.62574	−0.812871	+	0.582444i	$0.802097\pi$
$948$	30.7861	0.999885
$949$	0	0
$950$	−64.8942	−2.10544
$951$	8.42229	0.273111
$952$	−3.99941	−0.129622
$953$	−41.2685	−1.33682	−0.668409	−	0.743794i	$-0.733024\pi$
$953$	−41.2685	−1.33682	−0.668409	+	0.743794i	$0.733024\pi$
$954$	−8.49145	−0.274921
$955$	69.2813	2.24189
$956$	−8.87941	−0.287181
$957$	−13.9669	−0.451487
$958$	−93.2729	−3.01351
$959$	1.01983	0.0329321
$960$	−75.7877	−2.44604
$961$	−17.7149	−0.571449
$962$	0	0
$963$	−11.8594	−0.382165
$964$	−52.6018	−1.69419
$965$	20.7906	0.669273
$966$	3.15686	0.101570
$967$	−9.89332	−0.318148	−0.159074	−	0.987267i	$-0.550851\pi$
$967$	−9.89332	−0.318148	−0.159074	+	0.987267i	$0.550851\pi$
$968$	2.19073	0.0704127
$969$	14.0645	0.451816
$970$	147.154	4.72482
$971$	−0.640473	−0.0205537	−0.0102769	−	0.999947i	$-0.503271\pi$
$971$	−0.640473	−0.0205537	−0.0102769	+	0.999947i	$0.503271\pi$
$972$	33.2284	1.06580
$973$	0.238137	0.00763432
$974$	−56.1126	−1.79796
$975$	0	0
$976$	−8.65332	−0.276986
$977$	19.9838	0.639338	0.319669	−	0.947529i	$-0.396428\pi$
$977$	19.9838	0.639338	0.319669	+	0.947529i	$0.396428\pi$
$978$	21.5841	0.690183
$979$	4.74761	0.151734
$980$	−87.5946	−2.79811
$981$	−0.465414	−0.0148595
$982$	−74.6889	−2.38342
$983$	50.7308	1.61806	0.809031	−	0.587766i	$-0.199993\pi$
$983$	50.7308	1.61806	0.809031	+	0.587766i	$0.199993\pi$
$984$	18.7506	0.597746
$985$	82.2104	2.61944
$986$	108.794	3.46471
$987$	2.52134	0.0802552
$988$	0	0
$989$	1.72843	0.0549609
$990$	−10.9593	−0.348308
$991$	27.3294	0.868147	0.434073	−	0.900878i	$-0.357076\pi$
$991$	27.3294	0.868147	0.434073	+	0.900878i	$0.357076\pi$
$992$	−24.7030	−0.784320
$993$	−18.7249	−0.594218
$994$	−11.9468	−0.378930
$995$	14.6821	0.465454
$996$	−56.0365	−1.77558
$997$	28.7308	0.909915	0.454958	−	0.890513i	$-0.349654\pi$
$997$	28.7308	0.909915	0.454958	+	0.890513i	$0.349654\pi$
$998$	−71.8255	−2.27360
$999$	24.2757	0.768049

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.t.1.18	yes	21
13.12	even	2		1859.2.a.s.1.4	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.s.1.4	✓	21	13.12	even	2
1859.2.a.t.1.18	yes	21	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+2.23194 q^{2} +1.36188 q^{3} +2.98154 q^{4} +4.28736 q^{5} +3.03963 q^{6} +0.384100 q^{7} +2.19073 q^{8} -1.14528 q^{9} +O(q^{10})\)	\(q+2.23194 q^{2} +1.36188 q^{3} +2.98154 q^{4} +4.28736 q^{5} +3.03963 q^{6} +0.384100 q^{7} +2.19073 q^{8} -1.14528 q^{9} +9.56911 q^{10} +1.00000 q^{11} +4.06050 q^{12} +0.857286 q^{14} +5.83888 q^{15} -1.07351 q^{16} -4.75294 q^{17} -2.55618 q^{18} -2.17281 q^{19} +12.7829 q^{20} +0.523099 q^{21} +2.23194 q^{22} +2.70390 q^{23} +2.98352 q^{24} +13.3814 q^{25} -5.64538 q^{27} +1.14521 q^{28} -10.2556 q^{29} +13.0320 q^{30} +3.64487 q^{31} -6.77746 q^{32} +1.36188 q^{33} -10.6083 q^{34} +1.64677 q^{35} -3.41468 q^{36} -4.30010 q^{37} -4.84956 q^{38} +9.39245 q^{40} +6.28472 q^{41} +1.16752 q^{42} +0.639237 q^{43} +2.98154 q^{44} -4.91021 q^{45} +6.03493 q^{46} +4.82001 q^{47} -1.46199 q^{48} -6.85247 q^{49} +29.8665 q^{50} -6.47295 q^{51} +3.32193 q^{53} -12.6001 q^{54} +4.28736 q^{55} +0.841459 q^{56} -2.95911 q^{57} -22.8898 q^{58} -8.90125 q^{59} +17.4088 q^{60} +8.06080 q^{61} +8.13512 q^{62} -0.439900 q^{63} -12.9798 q^{64} +3.03963 q^{66} +14.7519 q^{67} -14.1711 q^{68} +3.68239 q^{69} +3.67549 q^{70} -13.9356 q^{71} -2.50899 q^{72} -11.4254 q^{73} -9.59755 q^{74} +18.2240 q^{75} -6.47830 q^{76} +0.384100 q^{77} +7.58183 q^{79} -4.60251 q^{80} -4.25252 q^{81} +14.0271 q^{82} -13.8004 q^{83} +1.55964 q^{84} -20.3776 q^{85} +1.42674 q^{86} -13.9669 q^{87} +2.19073 q^{88} +4.74761 q^{89} -10.9593 q^{90} +8.06178 q^{92} +4.96389 q^{93} +10.7580 q^{94} -9.31560 q^{95} -9.23010 q^{96} +15.3780 q^{97} -15.2943 q^{98} -1.14528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) \) 21 * q + 6 * q^3 + 32 * q^4 + 7 * q^5 - 19 * q^6 + q^7 - 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9} + 18 q^{10} + 21 q^{11} + 23 q^{12} + 20 q^{14} + 16 q^{15} + 50 q^{16} + 16 q^{17} + 3 q^{18} - 11 q^{19} + 24 q^{20} - 5 q^{21} - 9 q^{23} - 54 q^{24} + 36 q^{25} - 11 q^{28} + 28 q^{29} + 21 q^{30} + 15 q^{31} - 61 q^{32} + 6 q^{33} - 6 q^{34} - 3 q^{35} + 45 q^{36} - 12 q^{37} + q^{38} + 55 q^{40} - 4 q^{41} - 34 q^{42} + 17 q^{43} + 32 q^{44} + 9 q^{45} + 11 q^{46} + 36 q^{47} + 24 q^{48} + 72 q^{49} - 9 q^{50} + 2 q^{51} + 19 q^{53} + q^{54} + 7 q^{55} + 44 q^{56} - 4 q^{57} - 33 q^{58} + 54 q^{59} + 64 q^{60} + 98 q^{61} - 29 q^{62} - 81 q^{63} + 63 q^{64} - 19 q^{66} + 25 q^{67} + 4 q^{68} + 89 q^{69} + 65 q^{70} + 37 q^{71} + 55 q^{72} + 8 q^{73} - 11 q^{74} + 24 q^{75} + 13 q^{76} + q^{77} + 24 q^{79} + 26 q^{80} + 81 q^{81} + 26 q^{82} - 34 q^{83} - 103 q^{84} - 11 q^{85} + 30 q^{86} + 32 q^{87} - 3 q^{88} + 6 q^{89} + 47 q^{90} - 80 q^{92} + 41 q^{93} + 40 q^{94} + 20 q^{95} - 98 q^{96} - 5 q^{98} + 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 + 7 * q^5 - 19 * q^6 + q^7 - 3 * q^8 + 33 * q^9 + 18 * q^10 + 21 * q^11 + 23 * q^12 + 20 * q^14 + 16 * q^15 + 50 * q^16 + 16 * q^17 + 3 * q^18 - 11 * q^19 + 24 * q^20 - 5 * q^21 - 9 * q^23 - 54 * q^24 + 36 * q^25 - 11 * q^28 + 28 * q^29 + 21 * q^30 + 15 * q^31 - 61 * q^32 + 6 * q^33 - 6 * q^34 - 3 * q^35 + 45 * q^36 - 12 * q^37 + q^38 + 55 * q^40 - 4 * q^41 - 34 * q^42 + 17 * q^43 + 32 * q^44 + 9 * q^45 + 11 * q^46 + 36 * q^47 + 24 * q^48 + 72 * q^49 - 9 * q^50 + 2 * q^51 + 19 * q^53 + q^54 + 7 * q^55 + 44 * q^56 - 4 * q^57 - 33 * q^58 + 54 * q^59 + 64 * q^60 + 98 * q^61 - 29 * q^62 - 81 * q^63 + 63 * q^64 - 19 * q^66 + 25 * q^67 + 4 * q^68 + 89 * q^69 + 65 * q^70 + 37 * q^71 + 55 * q^72 + 8 * q^73 - 11 * q^74 + 24 * q^75 + 13 * q^76 + q^77 + 24 * q^79 + 26 * q^80 + 81 * q^81 + 26 * q^82 - 34 * q^83 - 103 * q^84 - 11 * q^85 + 30 * q^86 + 32 * q^87 - 3 * q^88 + 6 * q^89 + 47 * q^90 - 80 * q^92 + 41 * q^93 + 40 * q^94 + 20 * q^95 - 98 * q^96 - 5 * q^98 + 33 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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