LMFDB - Embedded newform 1859.2.a.s.1.7

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			1.7
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)

$f(q)$	$=$	$q-1.43463 q^{2} +0.655312 q^{3} +0.0581570 q^{4} -1.45609 q^{5} -0.940129 q^{6} -3.21683 q^{7} +2.78582 q^{8} -2.57057 q^{9} +O(q^{10})$	\(q-1.43463 q^{2} +0.655312 q^{3} +0.0581570 q^{4} -1.45609 q^{5} -0.940129 q^{6} -3.21683 q^{7} +2.78582 q^{8} -2.57057 q^{9} +2.08894 q^{10} -1.00000 q^{11} +0.0381110 q^{12} +4.61496 q^{14} -0.954190 q^{15} -4.11293 q^{16} +2.77570 q^{17} +3.68781 q^{18} -6.77395 q^{19} -0.0846816 q^{20} -2.10803 q^{21} +1.43463 q^{22} +7.11072 q^{23} +1.82558 q^{24} -2.87981 q^{25} -3.65046 q^{27} -0.187081 q^{28} -3.39343 q^{29} +1.36891 q^{30} -10.2964 q^{31} +0.328883 q^{32} -0.655312 q^{33} -3.98210 q^{34} +4.68398 q^{35} -0.149497 q^{36} +2.07211 q^{37} +9.71809 q^{38} -4.05640 q^{40} -3.73696 q^{41} +3.02424 q^{42} +5.99390 q^{43} -0.0581570 q^{44} +3.74297 q^{45} -10.2012 q^{46} +10.9686 q^{47} -2.69525 q^{48} +3.34801 q^{49} +4.13146 q^{50} +1.81895 q^{51} -1.46322 q^{53} +5.23705 q^{54} +1.45609 q^{55} -8.96152 q^{56} -4.43905 q^{57} +4.86831 q^{58} -9.94003 q^{59} -0.0554929 q^{60} +2.55646 q^{61} +14.7715 q^{62} +8.26908 q^{63} +7.75404 q^{64} +0.940129 q^{66} +11.6323 q^{67} +0.161426 q^{68} +4.65974 q^{69} -6.71977 q^{70} -9.44195 q^{71} -7.16114 q^{72} +7.67100 q^{73} -2.97271 q^{74} -1.88718 q^{75} -0.393953 q^{76} +3.21683 q^{77} +8.09605 q^{79} +5.98878 q^{80} +5.31951 q^{81} +5.36114 q^{82} +2.39011 q^{83} -0.122597 q^{84} -4.04166 q^{85} -8.59902 q^{86} -2.22376 q^{87} -2.78582 q^{88} +13.1321 q^{89} -5.36976 q^{90} +0.413538 q^{92} -6.74735 q^{93} -15.7358 q^{94} +9.86345 q^{95} +0.215521 q^{96} +9.77821 q^{97} -4.80315 q^{98} +2.57057 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.43463	−1.01444	−0.507218	−	0.861818i	$-0.669326\pi$
$2$	−1.43463	−1.01444	−0.507218	+	0.861818i	$0.669326\pi$
$3$	0.655312	0.378344	0.189172	−	0.981944i	$-0.439420\pi$
$3$	0.655312	0.378344	0.189172	+	0.981944i	$0.439420\pi$
$4$	0.0581570	0.0290785
$5$	−1.45609	−0.651181	−0.325591	−	0.945511i	$-0.605563\pi$
$5$	−1.45609	−0.651181	−0.325591	+	0.945511i	$0.605563\pi$
$6$	−0.940129	−0.383806
$7$	−3.21683	−1.21585	−0.607924	−	0.793995i	$-0.707998\pi$
$7$	−3.21683	−1.21585	−0.607924	+	0.793995i	$0.707998\pi$
$8$	2.78582	0.984937
$9$	−2.57057	−0.856855
$10$	2.08894	0.660581
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.0381110	0.0110017
$13$	0	0
$13$	0	0
$14$	4.61496	1.23340
$15$	−0.954190	−0.246371
$16$	−4.11293	−1.02823
$17$	2.77570	0.673206	0.336603	−	0.941647i	$-0.390722\pi$
$17$	2.77570	0.673206	0.336603	+	0.941647i	$0.390722\pi$
$18$	3.68781	0.869224
$19$	−6.77395	−1.55405	−0.777025	−	0.629470i	$-0.783272\pi$
$19$	−6.77395	−1.55405	−0.777025	+	0.629470i	$0.783272\pi$
$20$	−0.0846816	−0.0189354
$21$	−2.10803	−0.460009
$22$	1.43463	0.305864
$23$	7.11072	1.48269	0.741344	−	0.671125i	$-0.234189\pi$
$23$	7.11072	1.48269	0.741344	+	0.671125i	$0.234189\pi$
$24$	1.82558	0.372645
$25$	−2.87981	−0.575963
$26$	0	0
$27$	−3.65046	−0.702531
$28$	−0.187081	−0.0353551
$29$	−3.39343	−0.630145	−0.315072	−	0.949068i	$-0.602029\pi$
$29$	−3.39343	−0.630145	−0.315072	+	0.949068i	$0.602029\pi$
$30$	1.36891	0.249927
$31$	−10.2964	−1.84929	−0.924643	−	0.380834i	$-0.875637\pi$
$31$	−10.2964	−1.84929	−0.924643	+	0.380834i	$0.875637\pi$
$32$	0.328883	0.0581388
$33$	−0.655312	−0.114075
$34$	−3.98210	−0.682924
$35$	4.68398	0.791738
$36$	−0.149497	−0.0249161
$37$	2.07211	0.340653	0.170327	−	0.985388i	$-0.445518\pi$
$37$	2.07211	0.340653	0.170327	+	0.985388i	$0.445518\pi$
$38$	9.71809	1.57648
$39$	0	0
$40$	−4.05640	−0.641372
$41$	−3.73696	−0.583615	−0.291807	−	0.956477i	$-0.594257\pi$
$41$	−3.73696	−0.583615	−0.291807	+	0.956477i	$0.594257\pi$
$42$	3.02424	0.466650
$43$	5.99390	0.914062	0.457031	−	0.889451i	$-0.348913\pi$
$43$	5.99390	0.914062	0.457031	+	0.889451i	$0.348913\pi$
$44$	−0.0581570	−0.00876750
$45$	3.74297	0.557968
$46$	−10.2012	−1.50409
$47$	10.9686	1.59993	0.799965	−	0.600047i	$-0.204851\pi$
$47$	10.9686	1.59993	0.799965	+	0.600047i	$0.204851\pi$
$48$	−2.69525	−0.389026
$49$	3.34801	0.478287
$50$	4.13146	0.584277
$51$	1.81895	0.254704
$52$	0	0
$53$	−1.46322	−0.200988	−0.100494	−	0.994938i	$-0.532042\pi$
$53$	−1.46322	−0.200988	−0.100494	+	0.994938i	$0.532042\pi$
$54$	5.23705	0.712672
$55$	1.45609	0.196339
$56$	−8.96152	−1.19753
$57$	−4.43905	−0.587966
$58$	4.86831	0.639241
$59$	−9.94003	−1.29408	−0.647041	−	0.762455i	$-0.723994\pi$
$59$	−9.94003	−1.29408	−0.647041	+	0.762455i	$0.723994\pi$
$60$	−0.0554929	−0.00716410
$61$	2.55646	0.327321	0.163660	−	0.986517i	$-0.447670\pi$
$61$	2.55646	0.327321	0.163660	+	0.986517i	$0.447670\pi$
$62$	14.7715	1.87598
$63$	8.26908	1.04181
$64$	7.75404	0.969255
$65$	0	0
$66$	0.940129	0.115722
$67$	11.6323	1.42111	0.710555	−	0.703641i	$-0.248444\pi$
$67$	11.6323	1.42111	0.710555	+	0.703641i	$0.248444\pi$
$68$	0.161426	0.0195758
$69$	4.65974	0.560967
$70$	−6.71977	−0.803166
$71$	−9.44195	−1.12055	−0.560277	−	0.828305i	$-0.689305\pi$
$71$	−9.44195	−1.12055	−0.560277	+	0.828305i	$0.689305\pi$
$72$	−7.16114	−0.843949
$73$	7.67100	0.897823	0.448911	−	0.893576i	$-0.351812\pi$
$73$	7.67100	0.897823	0.448911	+	0.893576i	$0.351812\pi$
$74$	−2.97271	−0.345571
$75$	−1.88718	−0.217912
$76$	−0.393953	−0.0451895
$77$	3.21683	0.366592
$78$	0	0
$79$	8.09605	0.910877	0.455438	−	0.890267i	$-0.349483\pi$
$79$	8.09605	0.910877	0.455438	+	0.890267i	$0.349483\pi$
$80$	5.98878	0.669566
$81$	5.31951	0.591057
$82$	5.36114	0.592039
$83$	2.39011	0.262348	0.131174	−	0.991359i	$-0.458125\pi$
$83$	2.39011	0.262348	0.131174	+	0.991359i	$0.458125\pi$
$84$	−0.122597	−0.0133764
$85$	−4.04166	−0.438379
$86$	−8.59902	−0.927256
$87$	−2.22376	−0.238412
$88$	−2.78582	−0.296970
$89$	13.1321	1.39200	0.696000	−	0.718041i	$-0.254961\pi$
$89$	13.1321	1.39200	0.696000	+	0.718041i	$0.254961\pi$
$90$	−5.36976	−0.566023
$91$	0	0
$92$	0.413538	0.0431144
$93$	−6.74735	−0.699667
$94$	−15.7358	−1.62302
$95$	9.86345	1.01197
$96$	0.215521	0.0219965
$97$	9.77821	0.992827	0.496413	−	0.868086i	$-0.334650\pi$
$97$	9.77821	0.992827	0.496413	+	0.868086i	$0.334650\pi$
$98$	−4.80315	−0.485191
$99$	2.57057	0.258352
$100$	−0.167482	−0.0167482
$101$	−8.08592	−0.804579	−0.402290	−	0.915512i	$-0.631786\pi$
$101$	−8.08592	−0.804579	−0.402290	+	0.915512i	$0.631786\pi$
$102$	−2.60951	−0.258380
$103$	−8.01086	−0.789334	−0.394667	−	0.918824i	$-0.629140\pi$
$103$	−8.01086	−0.789334	−0.394667	+	0.918824i	$0.629140\pi$
$104$	0	0
$105$	3.06947	0.299550
$106$	2.09917	0.203890
$107$	3.26352	0.315496	0.157748	−	0.987479i	$-0.449577\pi$
$107$	3.26352	0.315496	0.157748	+	0.987479i	$0.449577\pi$
$108$	−0.212300	−0.0204286
$109$	17.0047	1.62876	0.814378	−	0.580334i	$-0.197078\pi$
$109$	17.0047	1.62876	0.814378	+	0.580334i	$0.197078\pi$
$110$	−2.08894	−0.199173
$111$	1.35788	0.128884
$112$	13.2306	1.25018
$113$	−10.0429	−0.944753	−0.472377	−	0.881397i	$-0.656604\pi$
$113$	−10.0429	−0.944753	−0.472377	+	0.881397i	$0.656604\pi$
$114$	6.36838	0.596453
$115$	−10.3538	−0.965498
$116$	−0.197352	−0.0183237
$117$	0	0
$118$	14.2602	1.31276
$119$	−8.92896	−0.818516
$120$	−2.65820	−0.242660
$121$	1.00000	0.0909091
$122$	−3.66757	−0.332046
$123$	−2.44887	−0.220807
$124$	−0.598808	−0.0537745
$125$	11.4737	1.02624
$126$	−11.8631	−1.05684
$127$	−2.23609	−0.198420	−0.0992102	−	0.995066i	$-0.531632\pi$
$127$	−2.23609	−0.198420	−0.0992102	+	0.995066i	$0.531632\pi$
$128$	−11.7819	−1.04138
$129$	3.92788	0.345830
$130$	0	0
$131$	1.52746	0.133455	0.0667273	−	0.997771i	$-0.478744\pi$
$131$	1.52746	0.133455	0.0667273	+	0.997771i	$0.478744\pi$
$132$	−0.0381110	−0.00331714
$133$	21.7906	1.88949
$134$	−16.6880	−1.44162
$135$	5.31538	0.457475
$136$	7.73260	0.663065
$137$	6.07861	0.519331	0.259665	−	0.965699i	$-0.416388\pi$
$137$	6.07861	0.519331	0.259665	+	0.965699i	$0.416388\pi$
$138$	−6.68499	−0.569064
$139$	16.8529	1.42944	0.714721	−	0.699410i	$-0.246554\pi$
$139$	16.8529	1.42944	0.714721	+	0.699410i	$0.246554\pi$
$140$	0.272407	0.0230226
$141$	7.18783	0.605325
$142$	13.5457	1.13673
$143$	0	0
$144$	10.5726	0.881047
$145$	4.94113	0.410338
$146$	−11.0050	−0.910783
$147$	2.19399	0.180957
$148$	0.120508	0.00990569
$149$	6.57344	0.538517	0.269259	−	0.963068i	$-0.413221\pi$
$149$	6.57344	0.538517	0.269259	+	0.963068i	$0.413221\pi$
$150$	2.70740	0.221058
$151$	−19.0261	−1.54832	−0.774162	−	0.632988i	$-0.781828\pi$
$151$	−19.0261	−1.54832	−0.774162	+	0.632988i	$0.781828\pi$
$152$	−18.8710	−1.53064
$153$	−7.13512	−0.576840
$154$	−4.61496	−0.371884
$155$	14.9924	1.20422
$156$	0	0
$157$	−3.54317	−0.282776	−0.141388	−	0.989954i	$-0.545156\pi$
$157$	−3.54317	−0.282776	−0.141388	+	0.989954i	$0.545156\pi$
$158$	−11.6148	−0.924025
$159$	−0.958864	−0.0760429
$160$	−0.478881	−0.0378589
$161$	−22.8740	−1.80272
$162$	−7.63152	−0.599589
$163$	−8.25772	−0.646795	−0.323397	−	0.946263i	$-0.604825\pi$
$163$	−8.25772	−0.646795	−0.323397	+	0.946263i	$0.604825\pi$
$164$	−0.217330	−0.0169707
$165$	0.954190	0.0742836
$166$	−3.42891	−0.266135
$167$	4.90041	0.379205	0.189602	−	0.981861i	$-0.439280\pi$
$167$	4.90041	0.379205	0.189602	+	0.981861i	$0.439280\pi$
$168$	−5.87259	−0.453080
$169$	0	0
$170$	5.79827	0.444707
$171$	17.4129	1.33160
$172$	0.348588	0.0265796
$173$	0.662919	0.0504008	0.0252004	−	0.999682i	$-0.491978\pi$
$173$	0.662919	0.0504008	0.0252004	+	0.999682i	$0.491978\pi$
$174$	3.19026	0.241853
$175$	9.26388	0.700284
$176$	4.11293	0.310024
$177$	−6.51382	−0.489609
$178$	−18.8397	−1.41209
$179$	−10.8625	−0.811901	−0.405950	−	0.913895i	$-0.633059\pi$
$179$	−10.8625	−0.811901	−0.405950	+	0.913895i	$0.633059\pi$
$180$	0.217680	0.0162249
$181$	13.6608	1.01540	0.507698	−	0.861535i	$-0.330496\pi$
$181$	13.6608	1.01540	0.507698	+	0.861535i	$0.330496\pi$
$182$	0	0
$183$	1.67528	0.123840
$184$	19.8092	1.46035
$185$	−3.01717	−0.221827
$186$	9.67993	0.709767
$187$	−2.77570	−0.202979
$188$	0.637899	0.0465236
$189$	11.7429	0.854171
$190$	−14.1504	−1.02658
$191$	−18.5405	−1.34154	−0.670772	−	0.741664i	$-0.734037\pi$
$191$	−18.5405	−1.34154	−0.670772	+	0.741664i	$0.734037\pi$
$192$	5.08131	0.366712
$193$	−7.01456	−0.504919	−0.252460	−	0.967607i	$-0.581240\pi$
$193$	−7.01456	−0.504919	−0.252460	+	0.967607i	$0.581240\pi$
$194$	−14.0281	−1.00716
$195$	0	0
$196$	0.194710	0.0139079
$197$	−11.3461	−0.808376	−0.404188	−	0.914676i	$-0.632446\pi$
$197$	−11.3461	−0.808376	−0.404188	+	0.914676i	$0.632446\pi$
$198$	−3.68781	−0.262081
$199$	9.41305	0.667273	0.333637	−	0.942702i	$-0.391724\pi$
$199$	9.41305	0.667273	0.333637	+	0.942702i	$0.391724\pi$
$200$	−8.02265	−0.567287
$201$	7.62278	0.537669
$202$	11.6003	0.816193
$203$	10.9161	0.766160
$204$	0.105785	0.00740641
$205$	5.44133	0.380039
$206$	11.4926	0.800728
$207$	−18.2786	−1.27045
$208$	0	0
$209$	6.77395	0.468564
$210$	−4.40355	−0.303874
$211$	5.60589	0.385925	0.192963	−	0.981206i	$-0.438190\pi$
$211$	5.60589	0.385925	0.192963	+	0.981206i	$0.438190\pi$
$212$	−0.0850964	−0.00584445
$213$	−6.18742	−0.423955
$214$	−4.68194	−0.320051
$215$	−8.72764	−0.595220
$216$	−10.1695	−0.691949
$217$	33.1218	2.24845
$218$	−24.3954	−1.65227
$219$	5.02690	0.339686
$220$	0.0846816	0.00570924
$221$	0	0
$222$	−1.94805	−0.130745
$223$	14.8767	0.996215	0.498108	−	0.867115i	$-0.334028\pi$
$223$	14.8767	0.996215	0.498108	+	0.867115i	$0.334028\pi$
$224$	−1.05796	−0.0706879
$225$	7.40275	0.493517
$226$	14.4078	0.958391
$227$	18.6696	1.23915	0.619574	−	0.784938i	$-0.287305\pi$
$227$	18.6696	1.23915	0.619574	+	0.784938i	$0.287305\pi$
$228$	−0.258162	−0.0170972
$229$	2.65371	0.175362	0.0876811	−	0.996149i	$-0.472054\pi$
$229$	2.65371	0.175362	0.0876811	+	0.996149i	$0.472054\pi$
$230$	14.8539	0.979436
$231$	2.10803	0.138698
$232$	−9.45350	−0.620653
$233$	29.7930	1.95180	0.975902	−	0.218211i	$-0.0700220\pi$
$233$	29.7930	1.95180	0.975902	+	0.218211i	$0.0700220\pi$
$234$	0	0
$235$	−15.9712	−1.04184
$236$	−0.578083	−0.0376300
$237$	5.30544	0.344625
$238$	12.8097	0.830332
$239$	24.4485	1.58144	0.790720	−	0.612179i	$-0.209707\pi$
$239$	24.4485	1.58144	0.790720	+	0.612179i	$0.209707\pi$
$240$	3.92452	0.253327
$241$	11.8300	0.762036	0.381018	−	0.924568i	$-0.375574\pi$
$241$	11.8300	0.762036	0.381018	+	0.924568i	$0.375574\pi$
$242$	−1.43463	−0.0922214
$243$	14.4373	0.926154
$244$	0.148676	0.00951801
$245$	−4.87499	−0.311452
$246$	3.51322	0.223995
$247$	0	0
$248$	−28.6839	−1.82143
$249$	1.56626	0.0992580
$250$	−16.4605	−1.04105
$251$	11.2327	0.709001	0.354500	−	0.935056i	$-0.384651\pi$
$251$	11.2327	0.709001	0.354500	+	0.935056i	$0.384651\pi$
$252$	0.480905	0.0302942
$253$	−7.11072	−0.447047
$254$	3.20795	0.201285
$255$	−2.64854	−0.165858
$256$	1.39460	0.0871625
$257$	−23.0023	−1.43484	−0.717422	−	0.696639i	$-0.754678\pi$
$257$	−23.0023	−1.43484	−0.717422	+	0.696639i	$0.754678\pi$
$258$	−5.63504	−0.350822
$259$	−6.66564	−0.414183
$260$	0	0
$261$	8.72304	0.539943
$262$	−2.19133	−0.135381
$263$	21.9165	1.35143	0.675714	−	0.737163i	$-0.263835\pi$
$263$	21.9165	1.35143	0.675714	+	0.737163i	$0.263835\pi$
$264$	−1.82558	−0.112357
$265$	2.13057	0.130880
$266$	−31.2615	−1.91676
$267$	8.60563	0.526656
$268$	0.676500	0.0413238
$269$	2.52774	0.154119	0.0770594	−	0.997027i	$-0.475447\pi$
$269$	2.52774	0.154119	0.0770594	+	0.997027i	$0.475447\pi$
$270$	−7.62559	−0.464079
$271$	−10.4276	−0.633430	−0.316715	−	0.948521i	$-0.602580\pi$
$271$	−10.4276	−0.633430	−0.316715	+	0.948521i	$0.602580\pi$
$272$	−11.4163	−0.692213
$273$	0	0
$274$	−8.72054	−0.526827
$275$	2.87981	0.173659
$276$	0.270997	0.0163121
$277$	−17.4391	−1.04781	−0.523907	−	0.851776i	$-0.675526\pi$
$277$	−17.4391	−1.04781	−0.523907	+	0.851776i	$0.675526\pi$
$278$	−24.1776	−1.45008
$279$	26.4676	1.58457
$280$	13.0487	0.779812
$281$	13.3162	0.794380	0.397190	−	0.917736i	$-0.369985\pi$
$281$	13.3162	0.794380	0.397190	+	0.917736i	$0.369985\pi$
$282$	−10.3119	−0.614062
$283$	−8.64894	−0.514126	−0.257063	−	0.966395i	$-0.582755\pi$
$283$	−8.64894	−0.514126	−0.257063	+	0.966395i	$0.582755\pi$
$284$	−0.549116	−0.0325840
$285$	6.46363	0.382873
$286$	0	0
$287$	12.0212	0.709587
$288$	−0.845415	−0.0498165
$289$	−9.29549	−0.546794
$290$	−7.08868	−0.416262
$291$	6.40778	0.375631
$292$	0.446123	0.0261074
$293$	10.2809	0.600616	0.300308	−	0.953842i	$-0.402911\pi$
$293$	10.2809	0.600616	0.300308	+	0.953842i	$0.402911\pi$
$294$	−3.14756	−0.183569
$295$	14.4735	0.842682
$296$	5.77254	0.335522
$297$	3.65046	0.211821
$298$	−9.43044	−0.546291
$299$	0	0
$300$	−0.109753	−0.00633657
$301$	−19.2814	−1.11136
$302$	27.2954	1.57067
$303$	−5.29880	−0.304408
$304$	27.8608	1.59793
$305$	−3.72242	−0.213145
$306$	10.2362	0.585167
$307$	27.4584	1.56714	0.783568	−	0.621307i	$-0.213398\pi$
$307$	27.4584	1.56714	0.783568	+	0.621307i	$0.213398\pi$
$308$	0.187081	0.0106600
$309$	−5.24961	−0.298640
$310$	−21.5086	−1.22160
$311$	−30.2258	−1.71395	−0.856974	−	0.515360i	$-0.827658\pi$
$311$	−30.2258	−1.71395	−0.856974	+	0.515360i	$0.827658\pi$
$312$	0	0
$313$	−19.7213	−1.11472	−0.557358	−	0.830272i	$-0.688185\pi$
$313$	−19.7213	−1.11472	−0.557358	+	0.830272i	$0.688185\pi$
$314$	5.08313	0.286857
$315$	−12.0405	−0.678405
$316$	0.470842	0.0264870
$317$	−0.586819	−0.0329590	−0.0164795	−	0.999864i	$-0.505246\pi$
$317$	−0.586819	−0.0329590	−0.0164795	+	0.999864i	$0.505246\pi$
$318$	1.37561	0.0771405
$319$	3.39343	0.189996
$320$	−11.2905	−0.631161
$321$	2.13862	0.119366
$322$	32.8157	1.82875
$323$	−18.8024	−1.04620
$324$	0.309367	0.0171871
$325$	0	0
$326$	11.8468	0.656131
$327$	11.1434	0.616231
$328$	−10.4105	−0.574824
$329$	−35.2840	−1.94527
$330$	−1.36891	−0.0753559
$331$	−33.7665	−1.85598	−0.927988	−	0.372611i	$-0.878463\pi$
$331$	−33.7665	−1.85598	−0.927988	+	0.372611i	$0.878463\pi$
$332$	0.139002	0.00762870
$333$	−5.32650	−0.291891
$334$	−7.03026	−0.384679
$335$	−16.9376	−0.925401
$336$	8.67018	0.472997
$337$	−30.2231	−1.64636	−0.823179	−	0.567781i	$-0.807802\pi$
$337$	−30.2231	−1.64636	−0.823179	+	0.567781i	$0.807802\pi$
$338$	0	0
$339$	−6.58121	−0.357442
$340$	−0.235051	−0.0127474
$341$	10.2964	0.557581
$342$	−24.9810	−1.35082
$343$	11.7478	0.634324
$344$	16.6979	0.900293
$345$	−6.78498	−0.365291
$346$	−0.951042	−0.0511283
$347$	−10.9572	−0.588213	−0.294107	−	0.955773i	$-0.595022\pi$
$347$	−10.9572	−0.588213	−0.294107	+	0.955773i	$0.595022\pi$
$348$	−0.129327	−0.00693266
$349$	37.0347	1.98242	0.991211	−	0.132293i	$-0.0422341\pi$
$349$	37.0347	1.98242	0.991211	+	0.132293i	$0.0422341\pi$
$350$	−13.2902	−0.710392
$351$	0	0
$352$	−0.328883	−0.0175295
$353$	−10.2718	−0.546711	−0.273356	−	0.961913i	$-0.588134\pi$
$353$	−10.2718	−0.546711	−0.273356	+	0.961913i	$0.588134\pi$
$354$	9.34491	0.496676
$355$	13.7483	0.729683
$356$	0.763725	0.0404773
$357$	−5.85125	−0.309681
$358$	15.5836	0.823620
$359$	11.6703	0.615935	0.307968	−	0.951397i	$-0.400351\pi$
$359$	11.6703	0.615935	0.307968	+	0.951397i	$0.400351\pi$
$360$	10.4272	0.549563
$361$	26.8863	1.41507
$362$	−19.5981	−1.03005
$363$	0.655312	0.0343949
$364$	0	0
$365$	−11.1696	−0.584645
$366$	−2.40340	−0.125628
$367$	−18.8743	−0.985229	−0.492615	−	0.870248i	$-0.663959\pi$
$367$	−18.8743	−0.985229	−0.492615	+	0.870248i	$0.663959\pi$
$368$	−29.2459	−1.52455
$369$	9.60610	0.500074
$370$	4.32852	0.225029
$371$	4.70693	0.244371
$372$	−0.392406	−0.0203453
$373$	−0.390809	−0.0202353	−0.0101177	−	0.999949i	$-0.503221\pi$
$373$	−0.390809	−0.0202353	−0.0101177	+	0.999949i	$0.503221\pi$
$374$	3.98210	0.205909
$375$	7.51884	0.388271
$376$	30.5565	1.57583
$377$	0	0
$378$	−16.8467	−0.866501
$379$	−26.0803	−1.33966	−0.669828	−	0.742516i	$-0.733632\pi$
$379$	−26.0803	−1.33966	−0.669828	+	0.742516i	$0.733632\pi$
$380$	0.573629	0.0294265
$381$	−1.46533	−0.0750713
$382$	26.5987	1.36091
$383$	1.49911	0.0766008	0.0383004	−	0.999266i	$-0.487806\pi$
$383$	1.49911	0.0766008	0.0383004	+	0.999266i	$0.487806\pi$
$384$	−7.72084	−0.394002
$385$	−4.68398	−0.238718
$386$	10.0633	0.512208
$387$	−15.4077	−0.783219
$388$	0.568672	0.0288699
$389$	−5.04180	−0.255630	−0.127815	−	0.991798i	$-0.540796\pi$
$389$	−5.04180	−0.255630	−0.127815	+	0.991798i	$0.540796\pi$
$390$	0	0
$391$	19.7372	0.998154
$392$	9.32696	0.471083
$393$	1.00096	0.0504918
$394$	16.2774	0.820045
$395$	−11.7885	−0.593146
$396$	0.149497	0.00751248
$397$	9.30731	0.467121	0.233560	−	0.972342i	$-0.424962\pi$
$397$	9.30731	0.467121	0.233560	+	0.972342i	$0.424962\pi$
$398$	−13.5042	−0.676905
$399$	14.2797	0.714878
$400$	11.8445	0.592224
$401$	−24.4114	−1.21905	−0.609523	−	0.792769i	$-0.708639\pi$
$401$	−24.4114	−1.21905	−0.609523	+	0.792769i	$0.708639\pi$
$402$	−10.9359	−0.545431
$403$	0	0
$404$	−0.470253	−0.0233960
$405$	−7.74566	−0.384885
$406$	−15.6605	−0.777220
$407$	−2.07211	−0.102711
$408$	5.06727	0.250867
$409$	6.36177	0.314569	0.157285	−	0.987553i	$-0.449726\pi$
$409$	6.36177	0.314569	0.157285	+	0.987553i	$0.449726\pi$
$410$	−7.80629	−0.385525
$411$	3.98338	0.196486
$412$	−0.465888	−0.0229527
$413$	31.9754	1.57341
$414$	26.2230	1.28879
$415$	−3.48020	−0.170836
$416$	0	0
$417$	11.0439	0.540821
$418$	−9.71809	−0.475327
$419$	2.57848	0.125967	0.0629835	−	0.998015i	$-0.479938\pi$
$419$	2.57848	0.125967	0.0629835	+	0.998015i	$0.479938\pi$
$420$	0.178511	0.00871046
$421$	24.8155	1.20943	0.604716	−	0.796441i	$-0.293287\pi$
$421$	24.8155	1.20943	0.604716	+	0.796441i	$0.293287\pi$
$422$	−8.04236	−0.391496
$423$	−28.1954	−1.37091
$424$	−4.07626	−0.197961
$425$	−7.99350	−0.387742
$426$	8.87665	0.430075
$427$	−8.22370	−0.397973
$428$	0.189797	0.00917417
$429$	0	0
$430$	12.5209	0.603812
$431$	−41.0457	−1.97710	−0.988550	−	0.150893i	$-0.951785\pi$
$431$	−41.0457	−1.97710	−0.988550	+	0.150893i	$0.951785\pi$
$432$	15.0141	0.722365
$433$	32.5278	1.56319	0.781593	−	0.623789i	$-0.214408\pi$
$433$	32.5278	1.56319	0.781593	+	0.623789i	$0.214408\pi$
$434$	−47.5174	−2.28091
$435$	3.23798	0.155249
$436$	0.988944	0.0473618
$437$	−48.1676	−2.30417
$438$	−7.21173	−0.344590
$439$	1.98368	0.0946757	0.0473378	−	0.998879i	$-0.484926\pi$
$439$	1.98368	0.0946757	0.0473378	+	0.998879i	$0.484926\pi$
$440$	4.05640	0.193381
$441$	−8.60628	−0.409823
$442$	0	0
$443$	−30.0670	−1.42853	−0.714264	−	0.699877i	$-0.753238\pi$
$443$	−30.0670	−1.42853	−0.714264	+	0.699877i	$0.753238\pi$
$444$	0.0789703	0.00374776
$445$	−19.1215	−0.906445
$446$	−21.3425	−1.01060
$447$	4.30765	0.203745
$448$	−24.9434	−1.17847
$449$	17.9192	0.845659	0.422829	−	0.906209i	$-0.361037\pi$
$449$	17.9192	0.845659	0.422829	+	0.906209i	$0.361037\pi$
$450$	−10.6202	−0.500641
$451$	3.73696	0.175967
$452$	−0.584063	−0.0274720
$453$	−12.4680	−0.585800
$454$	−26.7840	−1.25704
$455$	0	0
$456$	−12.3664	−0.579109
$457$	−26.8996	−1.25831	−0.629156	−	0.777279i	$-0.716599\pi$
$457$	−26.8996	−1.25831	−0.629156	+	0.777279i	$0.716599\pi$
$458$	−3.80709	−0.177894
$459$	−10.1326	−0.472948
$460$	−0.602147	−0.0280753
$461$	−33.5938	−1.56462	−0.782310	−	0.622889i	$-0.785959\pi$
$461$	−33.5938	−1.56462	−0.782310	+	0.622889i	$0.785959\pi$
$462$	−3.02424	−0.140700
$463$	19.5065	0.906543	0.453271	−	0.891373i	$-0.350257\pi$
$463$	19.5065	0.906543	0.453271	+	0.891373i	$0.350257\pi$
$464$	13.9570	0.647935
$465$	9.82472	0.455610
$466$	−42.7418	−1.97998
$467$	32.6367	1.51025	0.755124	−	0.655582i	$-0.227577\pi$
$467$	32.6367	1.51025	0.755124	+	0.655582i	$0.227577\pi$
$468$	0	0
$469$	−37.4191	−1.72786
$470$	22.9127	1.05688
$471$	−2.32188	−0.106987
$472$	−27.6912	−1.27459
$473$	−5.99390	−0.275600
$474$	−7.61133	−0.349600
$475$	19.5077	0.895075
$476$	−0.519282	−0.0238012
$477$	3.76130	0.172218
$478$	−35.0744	−1.60427
$479$	2.04138	0.0932732	0.0466366	−	0.998912i	$-0.485150\pi$
$479$	2.04138	0.0932732	0.0466366	+	0.998912i	$0.485150\pi$
$480$	−0.313817	−0.0143237
$481$	0	0
$482$	−16.9716	−0.773036
$483$	−14.9896	−0.682050
$484$	0.0581570	0.00264350
$485$	−14.2379	−0.646510
$486$	−20.7122	−0.939523
$487$	−1.42608	−0.0646216	−0.0323108	−	0.999478i	$-0.510287\pi$
$487$	−1.42608	−0.0646216	−0.0323108	+	0.999478i	$0.510287\pi$
$488$	7.12184	0.322390
$489$	−5.41138	−0.244711
$490$	6.99380	0.315947
$491$	−22.8208	−1.02989	−0.514944	−	0.857224i	$-0.672187\pi$
$491$	−22.8208	−1.02989	−0.514944	+	0.857224i	$0.672187\pi$
$492$	−0.142419	−0.00642075
$493$	−9.41915	−0.424217
$494$	0	0
$495$	−3.74297	−0.168234
$496$	42.3484	1.90150
$497$	30.3732	1.36242
$498$	−2.24701	−0.100691
$499$	−30.2658	−1.35488	−0.677441	−	0.735577i	$-0.736911\pi$
$499$	−30.2658	−1.35488	−0.677441	+	0.735577i	$0.736911\pi$
$500$	0.667276	0.0298415
$501$	3.21129	0.143470
$502$	−16.1147	−0.719235
$503$	16.2023	0.722423	0.361212	−	0.932484i	$-0.382363\pi$
$503$	16.2023	0.722423	0.361212	+	0.932484i	$0.382363\pi$
$504$	23.0362	1.02611
$505$	11.7738	0.523927
$506$	10.2012	0.453500
$507$	0	0
$508$	−0.130044	−0.00576978
$509$	−35.6080	−1.57830	−0.789148	−	0.614203i	$-0.789478\pi$
$509$	−35.6080	−1.57830	−0.789148	+	0.614203i	$0.789478\pi$
$510$	3.79968	0.168252
$511$	−24.6763	−1.09162
$512$	21.5631	0.952964
$513$	24.7280	1.09177
$514$	32.9998	1.45556
$515$	11.6645	0.513999
$516$	0.228434	0.0100562
$517$	−10.9686	−0.482397
$518$	9.56271	0.420161
$519$	0.434419	0.0190689
$520$	0	0
$521$	−22.1588	−0.970794	−0.485397	−	0.874294i	$-0.661325\pi$
$521$	−22.1588	−0.970794	−0.485397	+	0.874294i	$0.661325\pi$
$522$	−12.5143	−0.547737
$523$	5.06169	0.221332	0.110666	−	0.993858i	$-0.464702\pi$
$523$	5.06169	0.221332	0.110666	+	0.993858i	$0.464702\pi$
$524$	0.0888325	0.00388067
$525$	6.07073	0.264948
$526$	−31.4420	−1.37094
$527$	−28.5797	−1.24495
$528$	2.69525	0.117296
$529$	27.5623	1.19836
$530$	−3.05658	−0.132769
$531$	25.5515	1.10884
$532$	1.26728	0.0549435
$533$	0	0
$534$	−12.3459	−0.534258
$535$	−4.75196	−0.205445
$536$	32.4055	1.39970
$537$	−7.11832	−0.307178
$538$	−3.62636	−0.156344
$539$	−3.34801	−0.144209
$540$	0.309127	0.0133027
$541$	17.5776	0.755719	0.377859	−	0.925863i	$-0.376660\pi$
$541$	17.5776	0.755719	0.377859	+	0.925863i	$0.376660\pi$
$542$	14.9597	0.642573
$543$	8.95206	0.384170
$544$	0.912879	0.0391394
$545$	−24.7603	−1.06062
$546$	0	0
$547$	44.3094	1.89453	0.947267	−	0.320444i	$-0.103832\pi$
$547$	44.3094	1.89453	0.947267	+	0.320444i	$0.103832\pi$
$548$	0.353514	0.0151014
$549$	−6.57155	−0.280467
$550$	−4.13146	−0.176166
$551$	22.9869	0.979276
$552$	12.9812	0.552517
$553$	−26.0436	−1.10749
$554$	25.0186	1.06294
$555$	−1.97719	−0.0839270
$556$	0.980113	0.0415661
$557$	24.1276	1.02232	0.511160	−	0.859486i	$-0.329216\pi$
$557$	24.1276	1.02232	0.511160	+	0.859486i	$0.329216\pi$
$558$	−37.9711	−1.60745
$559$	0	0
$560$	−19.2649	−0.814091
$561$	−1.81895	−0.0767961
$562$	−19.1038	−0.805847
$563$	3.82022	0.161003	0.0805016	−	0.996754i	$-0.474348\pi$
$563$	3.82022	0.161003	0.0805016	+	0.996754i	$0.474348\pi$
$564$	0.418023	0.0176019
$565$	14.6233	0.615206
$566$	12.4080	0.521548
$567$	−17.1120	−0.718635
$568$	−26.3036	−1.10367
$569$	−10.4948	−0.439964	−0.219982	−	0.975504i	$-0.570600\pi$
$569$	−10.4948	−0.439964	−0.219982	+	0.975504i	$0.570600\pi$
$570$	−9.27291	−0.388399
$571$	−40.0219	−1.67487	−0.837433	−	0.546540i	$-0.815945\pi$
$571$	−40.0219	−1.67487	−0.837433	+	0.546540i	$0.815945\pi$
$572$	0	0
$573$	−12.1498	−0.507566
$574$	−17.2459	−0.719830
$575$	−20.4776	−0.853973
$576$	−19.9323	−0.830511
$577$	−28.4941	−1.18623	−0.593113	−	0.805119i	$-0.702101\pi$
$577$	−28.4941	−1.18623	−0.593113	+	0.805119i	$0.702101\pi$
$578$	13.3356	0.554687
$579$	−4.59673	−0.191033
$580$	0.287361	0.0119320
$581$	−7.68857	−0.318976
$582$	−9.19278	−0.381053
$583$	1.46322	0.0606003
$584$	21.3700	0.884299
$585$	0	0
$586$	−14.7493	−0.609286
$587$	−5.30994	−0.219165	−0.109582	−	0.993978i	$-0.534951\pi$
$587$	−5.30994	−0.219165	−0.109582	+	0.993978i	$0.534951\pi$
$588$	0.127596	0.00526197
$589$	69.7472	2.87388
$590$	−20.7641	−0.854846
$591$	−7.43523	−0.305845
$592$	−8.52246	−0.350271
$593$	−27.5649	−1.13195	−0.565977	−	0.824421i	$-0.691501\pi$
$593$	−27.5649	−1.13195	−0.565977	+	0.824421i	$0.691501\pi$
$594$	−5.23705	−0.214879
$595$	13.0013	0.533003
$596$	0.382292	0.0156593
$597$	6.16848	0.252459
$598$	0	0
$599$	37.2112	1.52041	0.760205	−	0.649683i	$-0.225098\pi$
$599$	37.2112	1.52041	0.760205	+	0.649683i	$0.225098\pi$
$600$	−5.25734	−0.214630
$601$	18.4580	0.752919	0.376459	−	0.926433i	$-0.377141\pi$
$601$	18.4580	0.752919	0.376459	+	0.926433i	$0.377141\pi$
$602$	27.6616	1.12740
$603$	−29.9016	−1.21769
$604$	−1.10650	−0.0450230
$605$	−1.45609	−0.0591983
$606$	7.60181	0.308802
$607$	25.1059	1.01902	0.509508	−	0.860466i	$-0.329827\pi$
$607$	25.1059	1.01902	0.509508	+	0.860466i	$0.329827\pi$
$608$	−2.22783	−0.0903506
$609$	7.15345	0.289872
$610$	5.34029	0.216222
$611$	0	0
$612$	−0.414957	−0.0167737
$613$	29.3930	1.18717	0.593586	−	0.804771i	$-0.297712\pi$
$613$	29.3930	1.18717	0.593586	+	0.804771i	$0.297712\pi$
$614$	−39.3926	−1.58976
$615$	3.56577	0.143786
$616$	8.96152	0.361070
$617$	−27.9655	−1.12585	−0.562923	−	0.826509i	$-0.690323\pi$
$617$	−27.9655	−1.12585	−0.562923	+	0.826509i	$0.690323\pi$
$618$	7.53124	0.302951
$619$	−9.84634	−0.395758	−0.197879	−	0.980226i	$-0.563405\pi$
$619$	−9.84634	−0.395758	−0.197879	+	0.980226i	$0.563405\pi$
$620$	0.871916	0.0350170
$621$	−25.9574	−1.04163
$622$	43.3628	1.73869
$623$	−42.2438	−1.69246
$624$	0	0
$625$	−2.30760	−0.0923039
$626$	28.2928	1.13081
$627$	4.43905	0.177278
$628$	−0.206060	−0.00822270
$629$	5.75156	0.229330
$630$	17.2736	0.688198
$631$	−6.68062	−0.265951	−0.132976	−	0.991119i	$-0.542453\pi$
$631$	−6.68062	−0.265951	−0.132976	+	0.991119i	$0.542453\pi$
$632$	22.5542	0.897156
$633$	3.67360	0.146013
$634$	0.841867	0.0334348
$635$	3.25593	0.129208
$636$	−0.0557647	−0.00221121
$637$	0	0
$638$	−4.86831	−0.192738
$639$	24.2712	0.960152
$640$	17.1555	0.678130
$641$	31.3725	1.23914	0.619570	−	0.784941i	$-0.287307\pi$
$641$	31.3725	1.23914	0.619570	+	0.784941i	$0.287307\pi$
$642$	−3.06813	−0.121089
$643$	−35.8394	−1.41337	−0.706684	−	0.707529i	$-0.749810\pi$
$643$	−35.8394	−1.41337	−0.706684	+	0.707529i	$0.749810\pi$
$644$	−1.33028	−0.0524205
$645$	−5.71932	−0.225198
$646$	26.9745	1.06130
$647$	−23.3917	−0.919621	−0.459811	−	0.888017i	$-0.652083\pi$
$647$	−23.3917	−0.919621	−0.459811	+	0.888017i	$0.652083\pi$
$648$	14.8192	0.582154
$649$	9.94003	0.390180
$650$	0	0
$651$	21.7051	0.850689
$652$	−0.480245	−0.0188078
$653$	9.33883	0.365457	0.182728	−	0.983163i	$-0.441507\pi$
$653$	9.33883	0.365457	0.182728	+	0.983163i	$0.441507\pi$
$654$	−15.9866	−0.625126
$655$	−2.22411	−0.0869032
$656$	15.3699	0.600092
$657$	−19.7188	−0.769304
$658$	50.6195	1.97335
$659$	−37.2441	−1.45083	−0.725413	−	0.688314i	$-0.758351\pi$
$659$	−37.2441	−1.45083	−0.725413	+	0.688314i	$0.758351\pi$
$660$	0.0554929	0.00216006
$661$	−14.6427	−0.569536	−0.284768	−	0.958596i	$-0.591917\pi$
$661$	−14.6427	−0.569536	−0.284768	+	0.958596i	$0.591917\pi$
$662$	48.4424	1.88277
$663$	0	0
$664$	6.65841	0.258396
$665$	−31.7290	−1.23040
$666$	7.64155	0.296104
$667$	−24.1297	−0.934307
$668$	0.284993	0.0110267
$669$	9.74886	0.376913
$670$	24.2992	0.938759
$671$	−2.55646	−0.0986910
$672$	−0.693294	−0.0267444
$673$	35.5677	1.37103	0.685517	−	0.728057i	$-0.259576\pi$
$673$	35.5677	1.37103	0.685517	+	0.728057i	$0.259576\pi$
$674$	43.3589	1.67012
$675$	10.5126	0.404632
$676$	0	0
$677$	34.4663	1.32465	0.662325	−	0.749217i	$-0.269570\pi$
$677$	34.4663	1.32465	0.662325	+	0.749217i	$0.269570\pi$
$678$	9.44159	0.362602
$679$	−31.4549	−1.20713
$680$	−11.2593	−0.431776
$681$	12.2344	0.468825
$682$	−14.7715	−0.565630
$683$	1.02390	0.0391785	0.0195893	−	0.999808i	$-0.493764\pi$
$683$	1.02390	0.0391785	0.0195893	+	0.999808i	$0.493764\pi$
$684$	1.01268	0.0387208
$685$	−8.85098	−0.338178
$686$	−16.8538	−0.643480
$687$	1.73901	0.0663473
$688$	−24.6525	−0.939868
$689$	0	0
$690$	9.73392	0.370564
$691$	−6.15763	−0.234247	−0.117124	−	0.993117i	$-0.537367\pi$
$691$	−6.15763	−0.234247	−0.117124	+	0.993117i	$0.537367\pi$
$692$	0.0385534	0.00146558
$693$	−8.26908	−0.314116
$694$	15.7195	0.596704
$695$	−24.5392	−0.930826
$696$	−6.19499	−0.234820
$697$	−10.3727	−0.392893
$698$	−53.1310	−2.01104
$699$	19.5237	0.738454
$700$	0.538760	0.0203632
$701$	31.0865	1.17412	0.587060	−	0.809543i	$-0.300285\pi$
$701$	31.0865	1.17412	0.587060	+	0.809543i	$0.300285\pi$
$702$	0	0
$703$	−14.0364	−0.529392
$704$	−7.75404	−0.292241
$705$	−10.4661	−0.394176
$706$	14.7362	0.554603
$707$	26.0111	0.978246
$708$	−0.378825	−0.0142371
$709$	21.4453	0.805395	0.402698	−	0.915333i	$-0.368073\pi$
$709$	21.4453	0.805395	0.402698	+	0.915333i	$0.368073\pi$
$710$	−19.7237	−0.740217
$711$	−20.8114	−0.780490
$712$	36.5837	1.37103
$713$	−73.2148	−2.74191
$714$	8.39437	0.314151
$715$	0	0
$716$	−0.631730	−0.0236089
$717$	16.0214	0.598329
$718$	−16.7426	−0.624826
$719$	−21.7883	−0.812568	−0.406284	−	0.913747i	$-0.633176\pi$
$719$	−21.7883	−0.812568	−0.406284	+	0.913747i	$0.633176\pi$
$720$	−15.3946	−0.573721
$721$	25.7696	0.959710
$722$	−38.5719	−1.43550
$723$	7.75233	0.288312
$724$	0.794470	0.0295262
$725$	9.77245	0.362940
$726$	−0.940129	−0.0348914
$727$	19.3982	0.719441	0.359720	−	0.933060i	$-0.382872\pi$
$727$	19.3982	0.719441	0.359720	+	0.933060i	$0.382872\pi$
$728$	0	0
$729$	−6.49759	−0.240652
$730$	16.0243	0.593085
$731$	16.6373	0.615352
$732$	0.0974292	0.00360109
$733$	45.1048	1.66599	0.832993	−	0.553284i	$-0.186626\pi$
$733$	45.1048	1.66599	0.832993	+	0.553284i	$0.186626\pi$
$734$	27.0776	0.999451
$735$	−3.19464	−0.117836
$736$	2.33859	0.0862017
$737$	−11.6323	−0.428481
$738$	−13.7812	−0.507292
$739$	−36.1403	−1.32944	−0.664722	−	0.747091i	$-0.731450\pi$
$739$	−36.1403	−1.32944	−0.664722	+	0.747091i	$0.731450\pi$
$740$	−0.175470	−0.00645040
$741$	0	0
$742$	−6.75269	−0.247899
$743$	49.3704	1.81122	0.905611	−	0.424108i	$-0.139412\pi$
$743$	49.3704	1.81122	0.905611	+	0.424108i	$0.139412\pi$
$744$	−18.7969	−0.689128
$745$	−9.57149	−0.350672
$746$	0.560665	0.0205274
$747$	−6.14393	−0.224795
$748$	−0.161426	−0.00590234
$749$	−10.4982	−0.383596
$750$	−10.7867	−0.393876
$751$	7.50381	0.273818	0.136909	−	0.990584i	$-0.456283\pi$
$751$	7.50381	0.273818	0.136909	+	0.990584i	$0.456283\pi$
$752$	−45.1130	−1.64510
$753$	7.36091	0.268246
$754$	0	0
$755$	27.7037	1.00824
$756$	0.682933	0.0248380
$757$	40.2759	1.46385	0.731926	−	0.681384i	$-0.238621\pi$
$757$	40.2759	1.46385	0.731926	+	0.681384i	$0.238621\pi$
$758$	37.4156	1.35899
$759$	−4.65974	−0.169138
$760$	27.4778	0.996725
$761$	13.0491	0.473029	0.236514	−	0.971628i	$-0.423995\pi$
$761$	13.0491	0.473029	0.236514	+	0.971628i	$0.423995\pi$
$762$	2.10221	0.0761550
$763$	−54.7013	−1.98032
$764$	−1.07826	−0.0390101
$765$	10.3893	0.375628
$766$	−2.15066	−0.0777065
$767$	0	0
$768$	0.913898	0.0329775
$769$	28.2107	1.01730	0.508652	−	0.860972i	$-0.330144\pi$
$769$	28.2107	1.01730	0.508652	+	0.860972i	$0.330144\pi$
$770$	6.71977	0.242164
$771$	−15.0737	−0.542865
$772$	−0.407946	−0.0146823
$773$	39.3054	1.41372	0.706858	−	0.707355i	$-0.250112\pi$
$773$	39.3054	1.41372	0.706858	+	0.707355i	$0.250112\pi$
$774$	22.1044	0.794525
$775$	29.6517	1.06512
$776$	27.2404	0.977872
$777$	−4.36807	−0.156704
$778$	7.23311	0.259320
$779$	25.3140	0.906967
$780$	0	0
$781$	9.44195	0.337860
$782$	−28.3156	−1.01256
$783$	12.3876	0.442696
$784$	−13.7701	−0.491791
$785$	5.15916	0.184138
$786$	−1.43601	−0.0512207
$787$	−0.462301	−0.0164793	−0.00823963	−	0.999966i	$-0.502623\pi$
$787$	−0.462301	−0.0164793	−0.00823963	+	0.999966i	$0.502623\pi$
$788$	−0.659856	−0.0235064
$789$	14.3621	0.511306
$790$	16.9122	0.601708
$791$	32.3062	1.14868
$792$	7.16114	0.254460
$793$	0	0
$794$	−13.3525	−0.473863
$795$	1.39619	0.0495177
$796$	0.547435	0.0194033
$797$	10.4672	0.370766	0.185383	−	0.982666i	$-0.440647\pi$
$797$	10.4672	0.370766	0.185383	+	0.982666i	$0.440647\pi$
$798$	−20.4860	−0.725197
$799$	30.4454	1.07708
$800$	−0.947121	−0.0334858
$801$	−33.7570	−1.19274
$802$	35.0212	1.23664
$803$	−7.67100	−0.270704
$804$	0.443318	0.0156346
$805$	33.3065	1.17390
$806$	0	0
$807$	1.65646	0.0583100
$808$	−22.5259	−0.792460
$809$	−12.5180	−0.440108	−0.220054	−	0.975488i	$-0.570623\pi$
$809$	−12.5180	−0.440108	−0.220054	+	0.975488i	$0.570623\pi$
$810$	11.1121	0.390441
$811$	5.70313	0.200264	0.100132	−	0.994974i	$-0.468074\pi$
$811$	5.70313	0.200264	0.100132	+	0.994974i	$0.468074\pi$
$812$	0.634848	0.0222788
$813$	−6.83331	−0.239655
$814$	2.97271	0.104193
$815$	12.0239	0.421181
$816$	−7.48121	−0.261895
$817$	−40.6024	−1.42050
$818$	−9.12677	−0.319110
$819$	0	0
$820$	0.316452	0.0110510
$821$	14.1529	0.493939	0.246969	−	0.969023i	$-0.420565\pi$
$821$	14.1529	0.493939	0.246969	+	0.969023i	$0.420565\pi$
$822$	−5.71467	−0.199322
$823$	26.4939	0.923519	0.461760	−	0.887005i	$-0.347218\pi$
$823$	26.4939	0.923519	0.461760	+	0.887005i	$0.347218\pi$
$824$	−22.3168	−0.777444
$825$	1.88718	0.0657030
$826$	−45.8728	−1.59612
$827$	10.9079	0.379306	0.189653	−	0.981851i	$-0.439264\pi$
$827$	10.9079	0.379306	0.189653	+	0.981851i	$0.439264\pi$
$828$	−1.06303	−0.0369428
$829$	26.4466	0.918527	0.459263	−	0.888300i	$-0.348113\pi$
$829$	26.4466	0.918527	0.459263	+	0.888300i	$0.348113\pi$
$830$	4.99279	0.173302
$831$	−11.4280	−0.396434
$832$	0	0
$833$	9.29307	0.321986
$834$	−15.8439	−0.548628
$835$	−7.13541	−0.246931
$836$	0.393953	0.0136251
$837$	37.5866	1.29918
$838$	−3.69916	−0.127785
$839$	3.76688	0.130047	0.0650236	−	0.997884i	$-0.479288\pi$
$839$	3.76688	0.130047	0.0650236	+	0.997884i	$0.479288\pi$
$840$	8.55100	0.295037
$841$	−17.4846	−0.602918
$842$	−35.6010	−1.22689
$843$	8.72628	0.300549
$844$	0.326022	0.0112221
$845$	0	0
$846$	40.4499	1.39070
$847$	−3.21683	−0.110532
$848$	6.01812	0.206663
$849$	−5.66775	−0.194517
$850$	11.4677	0.393339
$851$	14.7342	0.505082
$852$	−0.359842	−0.0123280
$853$	−6.21698	−0.212865	−0.106433	−	0.994320i	$-0.533943\pi$
$853$	−6.21698	−0.212865	−0.106433	+	0.994320i	$0.533943\pi$
$854$	11.7979	0.403717
$855$	−25.3546	−0.867110
$856$	9.09158	0.310744
$857$	−19.7791	−0.675643	−0.337821	−	0.941210i	$-0.609690\pi$
$857$	−19.7791	−0.675643	−0.337821	+	0.941210i	$0.609690\pi$
$858$	0	0
$859$	39.4374	1.34559	0.672793	−	0.739831i	$-0.265095\pi$
$859$	39.4374	1.34559	0.672793	+	0.739831i	$0.265095\pi$
$860$	−0.507574	−0.0173081
$861$	7.87761	0.268468
$862$	58.8853	2.00564
$863$	−9.53372	−0.324532	−0.162266	−	0.986747i	$-0.551880\pi$
$863$	−9.53372	−0.324532	−0.162266	+	0.986747i	$0.551880\pi$
$864$	−1.20057	−0.0408443
$865$	−0.965267	−0.0328201
$866$	−46.6652	−1.58575
$867$	−6.09145	−0.206876
$868$	1.92626	0.0653817
$869$	−8.09605	−0.274640
$870$	−4.64530	−0.157490
$871$	0	0
$872$	47.3721	1.60422
$873$	−25.1355	−0.850709
$874$	69.1026	2.33743
$875$	−36.9089	−1.24775
$876$	0.292350	0.00987758
$877$	−16.0771	−0.542885	−0.271443	−	0.962455i	$-0.587501\pi$
$877$	−16.0771	−0.542885	−0.271443	+	0.962455i	$0.587501\pi$
$878$	−2.84584	−0.0960423
$879$	6.73719	0.227240
$880$	−5.98878	−0.201882
$881$	2.42443	0.0816811	0.0408405	−	0.999166i	$-0.486996\pi$
$881$	2.42443	0.0816811	0.0408405	+	0.999166i	$0.486996\pi$
$882$	12.3468	0.415739
$883$	0.684622	0.0230394	0.0115197	−	0.999934i	$-0.496333\pi$
$883$	0.684622	0.0230394	0.0115197	+	0.999934i	$0.496333\pi$
$884$	0	0
$885$	9.48468	0.318824
$886$	43.1350	1.44915
$887$	−33.8117	−1.13529	−0.567643	−	0.823275i	$-0.692145\pi$
$887$	−33.8117	−1.13529	−0.567643	+	0.823275i	$0.692145\pi$
$888$	3.78281	0.126943
$889$	7.19311	0.241249
$890$	27.4322	0.919530
$891$	−5.31951	−0.178210
$892$	0.865183	0.0289685
$893$	−74.3005	−2.48637
$894$	−6.17988	−0.206686
$895$	15.8167	0.528694
$896$	37.9005	1.26617
$897$	0	0
$898$	−25.7074	−0.857866
$899$	34.9401	1.16532
$900$	0.430522	0.0143507
$901$	−4.06145	−0.135307
$902$	−5.36114	−0.178507
$903$	−12.6353	−0.420477
$904$	−27.9776	−0.930522
$905$	−19.8912	−0.661207
$906$	17.8870	0.594256
$907$	13.3167	0.442173	0.221086	−	0.975254i	$-0.429040\pi$
$907$	13.3167	0.442173	0.221086	+	0.975254i	$0.429040\pi$
$908$	1.08577	0.0360326
$909$	20.7854	0.689408
$910$	0	0
$911$	2.04780	0.0678466	0.0339233	−	0.999424i	$-0.489200\pi$
$911$	2.04780	0.0678466	0.0339233	+	0.999424i	$0.489200\pi$
$912$	18.2575	0.604566
$913$	−2.39011	−0.0791010
$914$	38.5909	1.27647
$915$	−2.43935	−0.0806423
$916$	0.154332	0.00509927
$917$	−4.91358	−0.162261
$918$	14.5365	0.479775
$919$	53.8585	1.77663	0.888314	−	0.459237i	$-0.151877\pi$
$919$	53.8585	1.77663	0.888314	+	0.459237i	$0.151877\pi$
$920$	−28.8439	−0.950955
$921$	17.9938	0.592917
$922$	48.1947	1.58721
$923$	0	0
$924$	0.122597	0.00403314
$925$	−5.96730	−0.196204
$926$	−27.9845	−0.919629
$927$	20.5925	0.676345
$928$	−1.11604	−0.0366358
$929$	48.4345	1.58908	0.794542	−	0.607209i	$-0.207711\pi$
$929$	48.4345	1.58908	0.794542	+	0.607209i	$0.207711\pi$
$930$	−14.0948	−0.462187
$931$	−22.6792	−0.743282
$932$	1.73267	0.0567556
$933$	−19.8073	−0.648463
$934$	−46.8216	−1.53205
$935$	4.04166	0.132176
$936$	0	0
$937$	−11.2715	−0.368225	−0.184112	−	0.982905i	$-0.558941\pi$
$937$	−11.2715	−0.368225	−0.184112	+	0.982905i	$0.558941\pi$
$938$	53.6825	1.75280
$939$	−12.9236	−0.421747
$940$	−0.928836	−0.0302953
$941$	−9.41907	−0.307053	−0.153526	−	0.988145i	$-0.549063\pi$
$941$	−9.41907	−0.307053	−0.153526	+	0.988145i	$0.549063\pi$
$942$	3.33103	0.108531
$943$	−26.5725	−0.865319
$944$	40.8827	1.33062
$945$	−17.0987	−0.556220
$946$	8.59902	0.279578
$947$	35.7478	1.16165	0.580823	−	0.814030i	$-0.302731\pi$
$947$	35.7478	1.16165	0.580823	+	0.814030i	$0.302731\pi$
$948$	0.308549	0.0100212
$949$	0	0
$950$	−27.9863	−0.907995
$951$	−0.384549	−0.0124699
$952$	−24.8745	−0.806187
$953$	20.9956	0.680114	0.340057	−	0.940405i	$-0.389554\pi$
$953$	20.9956	0.680114	0.340057	+	0.940405i	$0.389554\pi$
$954$	−5.39606	−0.174704
$955$	26.9966	0.873588
$956$	1.42185	0.0459859
$957$	2.22376	0.0718838
$958$	−2.92863	−0.0946196
$959$	−19.5539	−0.631427
$960$	−7.39883	−0.238796
$961$	75.0157	2.41986
$962$	0	0
$963$	−8.38909	−0.270335
$964$	0.687997	0.0221589
$965$	10.2138	0.328794
$966$	21.5045	0.691896
$967$	−29.7216	−0.955783	−0.477891	−	0.878419i	$-0.658599\pi$
$967$	−29.7216	−0.955783	−0.477891	+	0.878419i	$0.658599\pi$
$968$	2.78582	0.0895397
$969$	−12.3215	−0.395822
$970$	20.4261	0.655843
$971$	−7.84457	−0.251744	−0.125872	−	0.992046i	$-0.540173\pi$
$971$	−7.84457	−0.251744	−0.125872	+	0.992046i	$0.540173\pi$
$972$	0.839631	0.0269312
$973$	−54.2129	−1.73798
$974$	2.04589	0.0655545
$975$	0	0
$976$	−10.5145	−0.336562
$977$	9.57173	0.306227	0.153113	−	0.988209i	$-0.451070\pi$
$977$	9.57173	0.306227	0.153113	+	0.988209i	$0.451070\pi$
$978$	7.76332	0.248244
$979$	−13.1321	−0.419704
$980$	−0.283515	−0.00905655
$981$	−43.7118	−1.39561
$982$	32.7394	1.04476
$983$	39.3971	1.25657	0.628285	−	0.777983i	$-0.283757\pi$
$983$	39.3971	1.25657	0.628285	+	0.777983i	$0.283757\pi$
$984$	−6.82212	−0.217481
$985$	16.5209	0.526399
$986$	13.5130	0.430341
$987$	−23.1220	−0.735983
$988$	0	0
$989$	42.6210	1.35527
$990$	5.36976	0.170662
$991$	−21.6676	−0.688293	−0.344147	−	0.938916i	$-0.611832\pi$
$991$	−21.6676	−0.688293	−0.344147	+	0.938916i	$0.611832\pi$
$992$	−3.38630	−0.107515
$993$	−22.1276	−0.702198
$994$	−43.5742	−1.38209
$995$	−13.7062	−0.434516
$996$	0.0910893	0.00288628
$997$	38.4863	1.21887	0.609437	−	0.792835i	$-0.291396\pi$
$997$	38.4863	1.21887	0.609437	+	0.792835i	$0.291396\pi$
$998$	43.4201	1.37444
$999$	−7.56416	−0.239319

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.s.1.7	✓	21
13.12	even	2		1859.2.a.t.1.15	yes	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.s.1.7	✓	21	1.1	even	1	trivial
1859.2.a.t.1.15	yes	21	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-1.43463 q^{2} +0.655312 q^{3} +0.0581570 q^{4} -1.45609 q^{5} -0.940129 q^{6} -3.21683 q^{7} +2.78582 q^{8} -2.57057 q^{9} +O(q^{10})\)	\(q-1.43463 q^{2} +0.655312 q^{3} +0.0581570 q^{4} -1.45609 q^{5} -0.940129 q^{6} -3.21683 q^{7} +2.78582 q^{8} -2.57057 q^{9} +2.08894 q^{10} -1.00000 q^{11} +0.0381110 q^{12} +4.61496 q^{14} -0.954190 q^{15} -4.11293 q^{16} +2.77570 q^{17} +3.68781 q^{18} -6.77395 q^{19} -0.0846816 q^{20} -2.10803 q^{21} +1.43463 q^{22} +7.11072 q^{23} +1.82558 q^{24} -2.87981 q^{25} -3.65046 q^{27} -0.187081 q^{28} -3.39343 q^{29} +1.36891 q^{30} -10.2964 q^{31} +0.328883 q^{32} -0.655312 q^{33} -3.98210 q^{34} +4.68398 q^{35} -0.149497 q^{36} +2.07211 q^{37} +9.71809 q^{38} -4.05640 q^{40} -3.73696 q^{41} +3.02424 q^{42} +5.99390 q^{43} -0.0581570 q^{44} +3.74297 q^{45} -10.2012 q^{46} +10.9686 q^{47} -2.69525 q^{48} +3.34801 q^{49} +4.13146 q^{50} +1.81895 q^{51} -1.46322 q^{53} +5.23705 q^{54} +1.45609 q^{55} -8.96152 q^{56} -4.43905 q^{57} +4.86831 q^{58} -9.94003 q^{59} -0.0554929 q^{60} +2.55646 q^{61} +14.7715 q^{62} +8.26908 q^{63} +7.75404 q^{64} +0.940129 q^{66} +11.6323 q^{67} +0.161426 q^{68} +4.65974 q^{69} -6.71977 q^{70} -9.44195 q^{71} -7.16114 q^{72} +7.67100 q^{73} -2.97271 q^{74} -1.88718 q^{75} -0.393953 q^{76} +3.21683 q^{77} +8.09605 q^{79} +5.98878 q^{80} +5.31951 q^{81} +5.36114 q^{82} +2.39011 q^{83} -0.122597 q^{84} -4.04166 q^{85} -8.59902 q^{86} -2.22376 q^{87} -2.78582 q^{88} +13.1321 q^{89} -5.36976 q^{90} +0.413538 q^{92} -6.74735 q^{93} -15.7358 q^{94} +9.86345 q^{95} +0.215521 q^{96} +9.77821 q^{97} -4.80315 q^{98} +2.57057 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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