LMFDB - Embedded newform 1295.2.a.j.1.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1295,2,Mod(1,1295)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1295.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1295, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1295 = 5 \cdot 7 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1295.a (trivial)

Newform invariants

comment:select newform

sage:traces = [15,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$10.3406270618$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - x^{14} - 26 x^{13} + 24 x^{12} + 266 x^{11} - 222 x^{10} - 1368 x^{9} + 998 x^{8} + 3770 x^{7} + \cdots - 158 $ x^15 - x^14 - 26x^13 + 24x^12 + 266x^11 - 222x^10 - 1368x^9 + 998x^8 + 3770x^7 - 2257x^6 - 5537x^5 + 2394x^4 + 3982x^3 - 824x^2 - 1058*x - 158
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.217863$ of defining polynomial
Character	$\chi$	$=$	1295.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.217863 q^{2} -1.49352 q^{3} -1.95254 q^{4} -1.00000 q^{5} -0.325383 q^{6} -1.00000 q^{7} -0.861110 q^{8} -0.769386 q^{9} -0.217863 q^{10} +3.38659 q^{11} +2.91616 q^{12} -5.83649 q^{13} -0.217863 q^{14} +1.49352 q^{15} +3.71747 q^{16} -6.73222 q^{17} -0.167621 q^{18} -6.04339 q^{19} +1.95254 q^{20} +1.49352 q^{21} +0.737812 q^{22} +1.87057 q^{23} +1.28609 q^{24} +1.00000 q^{25} -1.27155 q^{26} +5.62967 q^{27} +1.95254 q^{28} +2.09751 q^{29} +0.325383 q^{30} +6.03431 q^{31} +2.53212 q^{32} -5.05796 q^{33} -1.46670 q^{34} +1.00000 q^{35} +1.50225 q^{36} +1.00000 q^{37} -1.31663 q^{38} +8.71693 q^{39} +0.861110 q^{40} -5.53198 q^{41} +0.325383 q^{42} -9.02220 q^{43} -6.61245 q^{44} +0.769386 q^{45} +0.407528 q^{46} -2.22013 q^{47} -5.55213 q^{48} +1.00000 q^{49} +0.217863 q^{50} +10.0547 q^{51} +11.3959 q^{52} +10.5060 q^{53} +1.22649 q^{54} -3.38659 q^{55} +0.861110 q^{56} +9.02595 q^{57} +0.456969 q^{58} +12.2350 q^{59} -2.91616 q^{60} +4.32755 q^{61} +1.31465 q^{62} +0.769386 q^{63} -6.88328 q^{64} +5.83649 q^{65} -1.10194 q^{66} -3.52898 q^{67} +13.1449 q^{68} -2.79375 q^{69} +0.217863 q^{70} +16.7576 q^{71} +0.662526 q^{72} +15.9462 q^{73} +0.217863 q^{74} -1.49352 q^{75} +11.7999 q^{76} -3.38659 q^{77} +1.89909 q^{78} -5.87020 q^{79} -3.71747 q^{80} -6.09989 q^{81} -1.20521 q^{82} +0.349330 q^{83} -2.91616 q^{84} +6.73222 q^{85} -1.96560 q^{86} -3.13268 q^{87} -2.91623 q^{88} +4.91332 q^{89} +0.167621 q^{90} +5.83649 q^{91} -3.65236 q^{92} -9.01239 q^{93} -0.483683 q^{94} +6.04339 q^{95} -3.78178 q^{96} -16.3416 q^{97} +0.217863 q^{98} -2.60560 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - q^{2} - q^{3} + 23 q^{4} - 15 q^{5} + 6 q^{6} - 15 q^{7} - 3 q^{8} + 30 q^{9} + q^{10} + 17 q^{11} + 8 q^{12} - 5 q^{13} + q^{14} + q^{15} + 39 q^{16} - 7 q^{17} + 12 q^{18} + 6 q^{19} - 23 q^{20}+ \cdots + 90 q^{99}+O(q^{100}) $ 15 * q - q^2 - q^3 + 23 * q^4 - 15 * q^5 + 6 * q^6 - 15 * q^7 - 3 * q^8 + 30 * q^9 + q^10 + 17 * q^11 + 8 * q^12 - 5 * q^13 + q^14 + q^15 + 39 * q^16 - 7 * q^17 + 12 * q^18 + 6 * q^19 - 23 * q^20 + q^21 + 18 * q^22 - 2 * q^23 + 4 * q^24 + 15 * q^25 + 4 * q^26 + 5 * q^27 - 23 * q^28 + 13 * q^29 - 6 * q^30 - 4 * q^31 - 7 * q^32 + 7 * q^33 + 38 * q^34 + 15 * q^35 + 49 * q^36 + 15 * q^37 - 26 * q^38 + 33 * q^39 + 3 * q^40 + 22 * q^41 - 6 * q^42 + 10 * q^43 + 58 * q^44 - 30 * q^45 + 32 * q^46 - 9 * q^47 + 43 * q^48 + 15 * q^49 - q^50 + 39 * q^51 + 6 * q^52 - 16 * q^53 + 30 * q^54 - 17 * q^55 + 3 * q^56 + 16 * q^57 + 44 * q^58 + 6 * q^59 - 8 * q^60 - 11 * q^62 - 30 * q^63 + 119 * q^64 + 5 * q^65 + 3 * q^66 + 4 * q^67 - 70 * q^68 + 14 * q^69 - q^70 + 48 * q^71 - 25 * q^72 + 38 * q^73 - q^74 - q^75 - 3 * q^76 - 17 * q^77 - 40 * q^78 + 7 * q^79 - 39 * q^80 + 111 * q^81 + 6 * q^82 - 6 * q^83 - 8 * q^84 + 7 * q^85 - 40 * q^86 - 47 * q^87 + 23 * q^88 - 2 * q^89 - 12 * q^90 + 5 * q^91 + 7 * q^92 - 26 * q^94 - 6 * q^95 - 29 * q^96 + 79 * q^97 - q^98 + 90 * q^99

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 $

$2$	0.217863	0.154052	0.0770261	−	0.997029i	$-0.475458\pi$
$2$	0.217863	0.154052	0.0770261	+	0.997029i	$0.475458\pi$
$3$	−1.49352	−0.862286	−0.431143	−	0.902284i	$-0.641890\pi$
$3$	−1.49352	−0.862286	−0.431143	+	0.902284i	$0.641890\pi$
$4$	−1.95254	−0.976268
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.325383	−0.132837
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.861110	−0.304448
$9$	−0.769386	−0.256462
$10$	−0.217863	−0.0688942
$11$	3.38659	1.02110	0.510548	−	0.859849i	$-0.329442\pi$
$11$	3.38659	1.02110	0.510548	+	0.859849i	$0.329442\pi$
$12$	2.91616	0.841823
$13$	−5.83649	−1.61875	−0.809375	−	0.587292i	$-0.800194\pi$
$13$	−5.83649	−1.61875	−0.809375	+	0.587292i	$0.800194\pi$
$14$	−0.217863	−0.0582262
$15$	1.49352	0.385626
$16$	3.71747	0.929367
$17$	−6.73222	−1.63280	−0.816402	−	0.577484i	$-0.804034\pi$
$17$	−6.73222	−1.63280	−0.816402	+	0.577484i	$0.804034\pi$
$18$	−0.167621	−0.0395086
$19$	−6.04339	−1.38645	−0.693225	−	0.720721i	$-0.743811\pi$
$19$	−6.04339	−1.38645	−0.693225	+	0.720721i	$0.743811\pi$
$20$	1.95254	0.436600
$21$	1.49352	0.325914
$22$	0.737812	0.157302
$23$	1.87057	0.390042	0.195021	−	0.980799i	$-0.437523\pi$
$23$	1.87057	0.390042	0.195021	+	0.980799i	$0.437523\pi$
$24$	1.28609	0.262522
$25$	1.00000	0.200000
$26$	−1.27155	−0.249372
$27$	5.62967	1.08343
$28$	1.95254	0.368995
$29$	2.09751	0.389498	0.194749	−	0.980853i	$-0.437611\pi$
$29$	2.09751	0.389498	0.194749	+	0.980853i	$0.437611\pi$
$30$	0.325383	0.0594066
$31$	6.03431	1.08379	0.541897	−	0.840445i	$-0.317706\pi$
$31$	6.03431	1.08379	0.541897	+	0.840445i	$0.317706\pi$
$32$	2.53212	0.447619
$33$	−5.05796	−0.880478
$34$	−1.46670	−0.251537
$35$	1.00000	0.169031
$36$	1.50225	0.250376
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−1.31663	−0.213586
$39$	8.71693	1.39583
$40$	0.861110	0.136153
$41$	−5.53198	−0.863950	−0.431975	−	0.901886i	$-0.642183\pi$
$41$	−5.53198	−0.863950	−0.431975	+	0.901886i	$0.642183\pi$
$42$	0.325383	0.0502077
$43$	−9.02220	−1.37587	−0.687936	−	0.725771i	$-0.741483\pi$
$43$	−9.02220	−1.37587	−0.687936	+	0.725771i	$0.741483\pi$
$44$	−6.61245	−0.996864
$45$	0.769386	0.114693
$46$	0.407528	0.0600868
$47$	−2.22013	−0.323839	−0.161919	−	0.986804i	$-0.551768\pi$
$47$	−2.22013	−0.323839	−0.161919	+	0.986804i	$0.551768\pi$
$48$	−5.55213	−0.801381
$49$	1.00000	0.142857
$50$	0.217863	0.0308104
$51$	10.0547	1.40794
$52$	11.3959	1.58033
$53$	10.5060	1.44311	0.721553	−	0.692360i	$-0.243429\pi$
$53$	10.5060	1.44311	0.721553	+	0.692360i	$0.243429\pi$
$54$	1.22649	0.166905
$55$	−3.38659	−0.456648
$56$	0.861110	0.115071
$57$	9.02595	1.19552
$58$	0.456969	0.0600030
$59$	12.2350	1.59286	0.796428	−	0.604734i	$-0.206721\pi$
$59$	12.2350	1.59286	0.796428	+	0.604734i	$0.206721\pi$
$60$	−2.91616	−0.376474
$61$	4.32755	0.554086	0.277043	−	0.960858i	$-0.410646\pi$
$61$	4.32755	0.554086	0.277043	+	0.960858i	$0.410646\pi$
$62$	1.31465	0.166961
$63$	0.769386	0.0969336
$64$	−6.88328	−0.860410
$65$	5.83649	0.723927
$66$	−1.10194	−0.135639
$67$	−3.52898	−0.431134	−0.215567	−	0.976489i	$-0.569160\pi$
$67$	−3.52898	−0.431134	−0.215567	+	0.976489i	$0.569160\pi$
$68$	13.1449	1.59405
$69$	−2.79375	−0.336328
$70$	0.217863	0.0260396
$71$	16.7576	1.98876	0.994381	−	0.105856i	$-0.0337583\pi$
$71$	16.7576	1.98876	0.994381	+	0.105856i	$0.0337583\pi$
$72$	0.662526	0.0780795
$73$	15.9462	1.86636	0.933181	−	0.359406i	$-0.117021\pi$
$73$	15.9462	1.86636	0.933181	+	0.359406i	$0.117021\pi$
$74$	0.217863	0.0253260
$75$	−1.49352	−0.172457
$76$	11.7999	1.35355
$77$	−3.38659	−0.385938
$78$	1.89909	0.215030
$79$	−5.87020	−0.660449	−0.330224	−	0.943903i	$-0.607124\pi$
$79$	−5.87020	−0.660449	−0.330224	+	0.943903i	$0.607124\pi$
$80$	−3.71747	−0.415626
$81$	−6.09989	−0.677765
$82$	−1.20521	−0.133093
$83$	0.349330	0.0383440	0.0191720	−	0.999816i	$-0.493897\pi$
$83$	0.349330	0.0383440	0.0191720	+	0.999816i	$0.493897\pi$
$84$	−2.91616	−0.318179
$85$	6.73222	0.730212
$86$	−1.96560	−0.211956
$87$	−3.13268	−0.335859
$88$	−2.91623	−0.310871
$89$	4.91332	0.520811	0.260405	−	0.965499i	$-0.416144\pi$
$89$	4.91332	0.520811	0.260405	+	0.965499i	$0.416144\pi$
$90$	0.167621	0.0176688
$91$	5.83649	0.611830
$92$	−3.65236	−0.380785
$93$	−9.01239	−0.934541
$94$	−0.483683	−0.0498880
$95$	6.04339	0.620039
$96$	−3.78178	−0.385976
$97$	−16.3416	−1.65924	−0.829620	−	0.558328i	$-0.811443\pi$
$97$	−16.3416	−1.65924	−0.829620	+	0.558328i	$0.811443\pi$
$98$	0.217863	0.0220075
$99$	−2.60560	−0.261873
$100$	−1.95254	−0.195254
$101$	−4.90859	−0.488423	−0.244212	−	0.969722i	$-0.578529\pi$
$101$	−4.90859	−0.488423	−0.244212	+	0.969722i	$0.578529\pi$
$102$	2.19055	0.216897
$103$	6.89151	0.679040	0.339520	−	0.940599i	$-0.389735\pi$
$103$	6.89151	0.679040	0.339520	+	0.940599i	$0.389735\pi$
$104$	5.02586	0.492826
$105$	−1.49352	−0.145753
$106$	2.28886	0.222314
$107$	14.3715	1.38935	0.694674	−	0.719325i	$-0.255549\pi$
$107$	14.3715	1.38935	0.694674	+	0.719325i	$0.255549\pi$
$108$	−10.9921	−1.05772
$109$	−3.28497	−0.314643	−0.157321	−	0.987547i	$-0.550286\pi$
$109$	−3.28497	−0.314643	−0.157321	+	0.987547i	$0.550286\pi$
$110$	−0.737812	−0.0703477
$111$	−1.49352	−0.141759
$112$	−3.71747	−0.351268
$113$	−11.2517	−1.05847	−0.529237	−	0.848474i	$-0.677522\pi$
$113$	−11.2517	−1.05847	−0.529237	+	0.848474i	$0.677522\pi$
$114$	1.96642	0.184172
$115$	−1.87057	−0.174432
$116$	−4.09546	−0.380254
$117$	4.49051	0.415148
$118$	2.66554	0.245383
$119$	6.73222	0.617142
$120$	−1.28609	−0.117403
$121$	0.469017	0.0426380
$122$	0.942811	0.0853581
$123$	8.26214	0.744973
$124$	−11.7822	−1.05807
$125$	−1.00000	−0.0894427
$126$	0.167621	0.0149328
$127$	6.97972	0.619350	0.309675	−	0.950842i	$-0.399780\pi$
$127$	6.97972	0.619350	0.309675	+	0.950842i	$0.399780\pi$
$128$	−6.56385	−0.580167
$129$	13.4749	1.18640
$130$	1.27155	0.111523
$131$	−16.6490	−1.45463	−0.727315	−	0.686303i	$-0.759232\pi$
$131$	−16.6490	−1.45463	−0.727315	+	0.686303i	$0.759232\pi$
$132$	9.87585	0.859582
$133$	6.04339	0.524029
$134$	−0.768834	−0.0664171
$135$	−5.62967	−0.484525
$136$	5.79718	0.497104
$137$	2.78390	0.237845	0.118922	−	0.992904i	$-0.462056\pi$
$137$	2.78390	0.237845	0.118922	+	0.992904i	$0.462056\pi$
$138$	−0.608653	−0.0518120
$139$	−6.67857	−0.566469	−0.283234	−	0.959051i	$-0.591407\pi$
$139$	−6.67857	−0.566469	−0.283234	+	0.959051i	$0.591407\pi$
$140$	−1.95254	−0.165019
$141$	3.31581	0.279242
$142$	3.65086	0.306373
$143$	−19.7658	−1.65290
$144$	−2.86017	−0.238347
$145$	−2.09751	−0.174189
$146$	3.47408	0.287517
$147$	−1.49352	−0.123184
$148$	−1.95254	−0.160497
$149$	−11.3078	−0.926373	−0.463186	−	0.886261i	$-0.653294\pi$
$149$	−11.3078	−0.926373	−0.463186	+	0.886261i	$0.653294\pi$
$150$	−0.325383	−0.0265674
$151$	3.41835	0.278181	0.139091	−	0.990280i	$-0.455582\pi$
$151$	3.41835	0.278181	0.139091	+	0.990280i	$0.455582\pi$
$152$	5.20403	0.422102
$153$	5.17968	0.418752
$154$	−0.737812	−0.0594546
$155$	−6.03431	−0.484687
$156$	−17.0201	−1.36270
$157$	12.1170	0.967044	0.483522	−	0.875332i	$-0.339357\pi$
$157$	12.1170	0.967044	0.483522	+	0.875332i	$0.339357\pi$
$158$	−1.27890	−0.101744
$159$	−15.6909	−1.24437
$160$	−2.53212	−0.200181
$161$	−1.87057	−0.147422
$162$	−1.32894	−0.104411
$163$	−19.0212	−1.48986	−0.744929	−	0.667143i	$-0.767517\pi$
$163$	−19.0212	−1.48986	−0.744929	+	0.667143i	$0.767517\pi$
$164$	10.8014	0.843447
$165$	5.05796	0.393762
$166$	0.0761060	0.00590697
$167$	−3.66541	−0.283638	−0.141819	−	0.989893i	$-0.545295\pi$
$167$	−3.66541	−0.283638	−0.141819	+	0.989893i	$0.545295\pi$
$168$	−1.28609	−0.0992239
$169$	21.0646	1.62035
$170$	1.46670	0.112491
$171$	4.64971	0.355572
$172$	17.6162	1.34322
$173$	4.03343	0.306656	0.153328	−	0.988175i	$-0.451001\pi$
$173$	4.03343	0.306656	0.153328	+	0.988175i	$0.451001\pi$
$174$	−0.682495	−0.0517398
$175$	−1.00000	−0.0755929
$176$	12.5896	0.948973
$177$	−18.2732	−1.37350
$178$	1.07043	0.0802320
$179$	5.88554	0.439906	0.219953	−	0.975511i	$-0.429410\pi$
$179$	5.88554	0.439906	0.219953	+	0.975511i	$0.429410\pi$
$180$	−1.50225	−0.111971
$181$	12.4436	0.924929	0.462464	−	0.886638i	$-0.346965\pi$
$181$	12.4436	0.924929	0.462464	+	0.886638i	$0.346965\pi$
$182$	1.27155	0.0942537
$183$	−6.46329	−0.477780
$184$	−1.61077	−0.118748
$185$	−1.00000	−0.0735215
$186$	−1.96346	−0.143968
$187$	−22.7993	−1.66725
$188$	4.33487	0.316153
$189$	−5.62967	−0.409498
$190$	1.31663	0.0955184
$191$	−13.0389	−0.943462	−0.471731	−	0.881743i	$-0.656371\pi$
$191$	−13.0389	−0.943462	−0.471731	+	0.881743i	$0.656371\pi$
$192$	10.2803	0.741920
$193$	8.61139	0.619861	0.309931	−	0.950759i	$-0.399694\pi$
$193$	8.61139	0.619861	0.309931	+	0.950759i	$0.399694\pi$
$194$	−3.56023	−0.255610
$195$	−8.71693	−0.624232
$196$	−1.95254	−0.139467
$197$	−7.23661	−0.515587	−0.257794	−	0.966200i	$-0.582995\pi$
$197$	−7.23661	−0.515587	−0.257794	+	0.966200i	$0.582995\pi$
$198$	−0.567663	−0.0403420
$199$	12.0025	0.850833	0.425417	−	0.904998i	$-0.360128\pi$
$199$	12.0025	0.850833	0.425417	+	0.904998i	$0.360128\pi$
$200$	−0.861110	−0.0608897
$201$	5.27062	0.371761
$202$	−1.06940	−0.0752427
$203$	−2.09751	−0.147216
$204$	−19.6322	−1.37453
$205$	5.53198	0.386370
$206$	1.50140	0.104608
$207$	−1.43919	−0.100031
$208$	−21.6969	−1.50441
$209$	−20.4665	−1.41570
$210$	−0.325383	−0.0224536
$211$	6.91538	0.476074	0.238037	−	0.971256i	$-0.423496\pi$
$211$	6.91538	0.476074	0.238037	+	0.971256i	$0.423496\pi$
$212$	−20.5133	−1.40886
$213$	−25.0279	−1.71488
$214$	3.13102	0.214032
$215$	9.02220	0.615309
$216$	−4.84776	−0.329849
$217$	−6.03431	−0.409636
$218$	−0.715672	−0.0484714
$219$	−23.8160	−1.60934
$220$	6.61245	0.445811
$221$	39.2925	2.64310
$222$	−0.325383	−0.0218383
$223$	−23.2218	−1.55505	−0.777524	−	0.628853i	$-0.783525\pi$
$223$	−23.2218	−1.55505	−0.777524	+	0.628853i	$0.783525\pi$
$224$	−2.53212	−0.169184
$225$	−0.769386	−0.0512924
$226$	−2.45133	−0.163060
$227$	−26.0532	−1.72921	−0.864605	−	0.502452i	$-0.832431\pi$
$227$	−26.0532	−1.72921	−0.864605	+	0.502452i	$0.832431\pi$
$228$	−17.6235	−1.16714
$229$	23.5530	1.55642	0.778212	−	0.628002i	$-0.216127\pi$
$229$	23.5530	1.55642	0.778212	+	0.628002i	$0.216127\pi$
$230$	−0.407528	−0.0268716
$231$	5.05796	0.332789
$232$	−1.80619	−0.118582
$233$	−3.48049	−0.228014	−0.114007	−	0.993480i	$-0.536369\pi$
$233$	−3.48049	−0.228014	−0.114007	+	0.993480i	$0.536369\pi$
$234$	0.978315	0.0639545
$235$	2.22013	0.144825
$236$	−23.8892	−1.55505
$237$	8.76728	0.569496
$238$	1.46670	0.0950720
$239$	12.7795	0.826639	0.413320	−	0.910586i	$-0.364369\pi$
$239$	12.7795	0.826639	0.413320	+	0.910586i	$0.364369\pi$
$240$	5.55213	0.358388
$241$	7.87741	0.507429	0.253714	−	0.967279i	$-0.418348\pi$
$241$	7.87741	0.507429	0.253714	+	0.967279i	$0.418348\pi$
$242$	0.102181	0.00656847
$243$	−7.77868	−0.499003
$244$	−8.44969	−0.540936
$245$	−1.00000	−0.0638877
$246$	1.80001	0.114765
$247$	35.2722	2.24432
$248$	−5.19620	−0.329959
$249$	−0.521733	−0.0330635
$250$	−0.217863	−0.0137788
$251$	0.295312	0.0186399	0.00931997	−	0.999957i	$-0.497033\pi$
$251$	0.295312	0.0186399	0.00931997	+	0.999957i	$0.497033\pi$
$252$	−1.50225	−0.0946331
$253$	6.33487	0.398270
$254$	1.52062	0.0954122
$255$	−10.0547	−0.629652
$256$	12.3365	0.771034
$257$	14.8383	0.925586	0.462793	−	0.886466i	$-0.346847\pi$
$257$	14.8383	0.925586	0.462793	+	0.886466i	$0.346847\pi$
$258$	2.93567	0.182767
$259$	−1.00000	−0.0621370
$260$	−11.3959	−0.706747
$261$	−1.61380	−0.0998915
$262$	−3.62720	−0.224089
$263$	17.5280	1.08082	0.540411	−	0.841401i	$-0.318269\pi$
$263$	17.5280	1.08082	0.540411	+	0.841401i	$0.318269\pi$
$264$	4.35546	0.268060
$265$	−10.5060	−0.645376
$266$	1.31663	0.0807278
$267$	−7.33816	−0.449088
$268$	6.89047	0.420902
$269$	23.6619	1.44269	0.721346	−	0.692575i	$-0.243524\pi$
$269$	23.6619	1.44269	0.721346	+	0.692575i	$0.243524\pi$
$270$	−1.22649	−0.0746421
$271$	−17.4543	−1.06027	−0.530136	−	0.847913i	$-0.677859\pi$
$271$	−17.4543	−1.06027	−0.530136	+	0.847913i	$0.677859\pi$
$272$	−25.0268	−1.51747
$273$	−8.71693	−0.527573
$274$	0.606508	0.0366405
$275$	3.38659	0.204219
$276$	5.45489	0.328346
$277$	−18.3589	−1.10308	−0.551541	−	0.834148i	$-0.685960\pi$
$277$	−18.3589	−1.10308	−0.551541	+	0.834148i	$0.685960\pi$
$278$	−1.45501	−0.0872657
$279$	−4.64272	−0.277952
$280$	−0.861110	−0.0514612
$281$	20.1014	1.19915	0.599574	−	0.800319i	$-0.295337\pi$
$281$	20.1014	1.19915	0.599574	+	0.800319i	$0.295337\pi$
$282$	0.722391	0.0430178
$283$	−6.73193	−0.400172	−0.200086	−	0.979778i	$-0.564122\pi$
$283$	−6.73193	−0.400172	−0.200086	+	0.979778i	$0.564122\pi$
$284$	−32.7198	−1.94157
$285$	−9.02595	−0.534651
$286$	−4.30623	−0.254633
$287$	5.53198	0.326542
$288$	−1.94818	−0.114797
$289$	28.3228	1.66605
$290$	−0.456969	−0.0268342
$291$	24.4066	1.43074
$292$	−31.1355	−1.82207
$293$	−26.6297	−1.55572	−0.777861	−	0.628437i	$-0.783695\pi$
$293$	−26.6297	−1.55572	−0.777861	+	0.628437i	$0.783695\pi$
$294$	−0.325383	−0.0189767
$295$	−12.2350	−0.712346
$296$	−0.861110	−0.0500510
$297$	19.0654	1.10629
$298$	−2.46355	−0.142710
$299$	−10.9176	−0.631380
$300$	2.91616	0.168365
$301$	9.02220	0.520031
$302$	0.744730	0.0428544
$303$	7.33110	0.421161
$304$	−22.4661	−1.28852
$305$	−4.32755	−0.247795
$306$	1.12846	0.0645097
$307$	16.8453	0.961412	0.480706	−	0.876882i	$-0.340380\pi$
$307$	16.8453	0.961412	0.480706	+	0.876882i	$0.340380\pi$
$308$	6.61245	0.376779
$309$	−10.2926	−0.585527
$310$	−1.31465	−0.0746672
$311$	4.94377	0.280336	0.140168	−	0.990128i	$-0.455236\pi$
$311$	4.94377	0.280336	0.140168	+	0.990128i	$0.455236\pi$
$312$	−7.50624	−0.424957
$313$	−21.0958	−1.19241	−0.596203	−	0.802834i	$-0.703325\pi$
$313$	−21.0958	−1.19241	−0.596203	+	0.802834i	$0.703325\pi$
$314$	2.63985	0.148975
$315$	−0.769386	−0.0433500
$316$	11.4618	0.644775
$317$	−11.6927	−0.656726	−0.328363	−	0.944552i	$-0.606497\pi$
$317$	−11.6927	−0.656726	−0.328363	+	0.944552i	$0.606497\pi$
$318$	−3.41846	−0.191698
$319$	7.10342	0.397715
$320$	6.88328	0.384787
$321$	−21.4642	−1.19802
$322$	−0.407528	−0.0227107
$323$	40.6855	2.26380
$324$	11.9102	0.661680
$325$	−5.83649	−0.323750
$326$	−4.14402	−0.229516
$327$	4.90618	0.271312
$328$	4.76364	0.263028
$329$	2.22013	0.122399
$330$	1.10194	0.0606598
$331$	25.8826	1.42263	0.711317	−	0.702872i	$-0.248099\pi$
$331$	25.8826	1.42263	0.711317	+	0.702872i	$0.248099\pi$
$332$	−0.682080	−0.0374340
$333$	−0.769386	−0.0421621
$334$	−0.798557	−0.0436951
$335$	3.52898	0.192809
$336$	5.55213	0.302893
$337$	24.8397	1.35311	0.676553	−	0.736394i	$-0.263473\pi$
$337$	24.8397	1.35311	0.676553	+	0.736394i	$0.263473\pi$
$338$	4.58918	0.249619
$339$	16.8047	0.912707
$340$	−13.1449	−0.712882
$341$	20.4358	1.10666
$342$	1.01300	0.0547766
$343$	−1.00000	−0.0539949
$344$	7.76911	0.418882
$345$	2.79375	0.150410
$346$	0.878733	0.0472410
$347$	−8.07883	−0.433695	−0.216847	−	0.976206i	$-0.569577\pi$
$347$	−8.07883	−0.433695	−0.216847	+	0.976206i	$0.569577\pi$
$348$	6.11667	0.327888
$349$	10.7292	0.574319	0.287160	−	0.957883i	$-0.407289\pi$
$349$	10.7292	0.574319	0.287160	+	0.957883i	$0.407289\pi$
$350$	−0.217863	−0.0116452
$351$	−32.8575	−1.75380
$352$	8.57525	0.457063
$353$	13.6499	0.726510	0.363255	−	0.931690i	$-0.381665\pi$
$353$	13.6499	0.726510	0.363255	+	0.931690i	$0.381665\pi$
$354$	−3.98105	−0.211590
$355$	−16.7576	−0.889402
$356$	−9.59343	−0.508451
$357$	−10.0547	−0.532153
$358$	1.28224	0.0677684
$359$	−19.6097	−1.03496	−0.517481	−	0.855695i	$-0.673130\pi$
$359$	−19.6097	−1.03496	−0.517481	+	0.855695i	$0.673130\pi$
$360$	−0.662526	−0.0349182
$361$	17.5226	0.922242
$362$	2.71101	0.142487
$363$	−0.700489	−0.0367661
$364$	−11.3959	−0.597310
$365$	−15.9462	−0.834663
$366$	−1.40811	−0.0736031
$367$	−12.0754	−0.630332	−0.315166	−	0.949037i	$-0.602060\pi$
$367$	−12.0754	−0.630332	−0.315166	+	0.949037i	$0.602060\pi$
$368$	6.95380	0.362492
$369$	4.25623	0.221571
$370$	−0.217863	−0.0113261
$371$	−10.5060	−0.545443
$372$	17.5970	0.912362
$373$	10.3739	0.537141	0.268570	−	0.963260i	$-0.413449\pi$
$373$	10.3739	0.537141	0.268570	+	0.963260i	$0.413449\pi$
$374$	−4.96712	−0.256843
$375$	1.49352	0.0771252
$376$	1.91177	0.0985921
$377$	−12.2421	−0.630500
$378$	−1.22649	−0.0630841
$379$	15.2882	0.785303	0.392652	−	0.919687i	$-0.371558\pi$
$379$	15.2882	0.785303	0.392652	+	0.919687i	$0.371558\pi$
$380$	−11.7999	−0.605324
$381$	−10.4244	−0.534057
$382$	−2.84069	−0.145342
$383$	−32.3354	−1.65226	−0.826131	−	0.563477i	$-0.809463\pi$
$383$	−32.3354	−1.65226	−0.826131	+	0.563477i	$0.809463\pi$
$384$	9.80326	0.500271
$385$	3.38659	0.172597
$386$	1.87610	0.0954910
$387$	6.94156	0.352859
$388$	31.9076	1.61986
$389$	−8.03491	−0.407386	−0.203693	−	0.979035i	$-0.565294\pi$
$389$	−8.03491	−0.407386	−0.203693	+	0.979035i	$0.565294\pi$
$390$	−1.89909	−0.0961644
$391$	−12.5931	−0.636861
$392$	−0.861110	−0.0434926
$393$	24.8657	1.25431
$394$	−1.57659	−0.0794274
$395$	5.87020	0.295362
$396$	5.08753	0.255658
$397$	18.7558	0.941324	0.470662	−	0.882313i	$-0.344015\pi$
$397$	18.7558	0.941324	0.470662	+	0.882313i	$0.344015\pi$
$398$	2.61489	0.131073
$399$	−9.02595	−0.451863
$400$	3.71747	0.185873
$401$	30.0494	1.50060	0.750298	−	0.661100i	$-0.229910\pi$
$401$	30.0494	1.50060	0.750298	+	0.661100i	$0.229910\pi$
$402$	1.14827	0.0572706
$403$	−35.2192	−1.75439
$404$	9.58420	0.476832
$405$	6.09989	0.303106
$406$	−0.456969	−0.0226790
$407$	3.38659	0.167867
$408$	−8.65823	−0.428646
$409$	37.3232	1.84551	0.922756	−	0.385385i	$-0.125931\pi$
$409$	37.3232	1.84551	0.922756	+	0.385385i	$0.125931\pi$
$410$	1.20521	0.0595212
$411$	−4.15782	−0.205090
$412$	−13.4559	−0.662925
$413$	−12.2350	−0.602043
$414$	−0.313547	−0.0154100
$415$	−0.349330	−0.0171479
$416$	−14.7787	−0.724584
$417$	9.97460	0.488458
$418$	−4.45889	−0.218091
$419$	−29.3732	−1.43498	−0.717488	−	0.696571i	$-0.754708\pi$
$419$	−29.3732	−1.43498	−0.717488	+	0.696571i	$0.754708\pi$
$420$	2.91616	0.142294
$421$	1.46201	0.0712541	0.0356271	−	0.999365i	$-0.488657\pi$
$421$	1.46201	0.0712541	0.0356271	+	0.999365i	$0.488657\pi$
$422$	1.50660	0.0733403
$423$	1.70813	0.0830523
$424$	−9.04679	−0.439351
$425$	−6.73222	−0.326561
$426$	−5.45264	−0.264181
$427$	−4.32755	−0.209425
$428$	−28.0609	−1.35638
$429$	29.5207	1.42527
$430$	1.96560	0.0947897
$431$	−26.5945	−1.28101	−0.640506	−	0.767953i	$-0.721275\pi$
$431$	−26.5945	−1.28101	−0.640506	+	0.767953i	$0.721275\pi$
$432$	20.9281	1.00690
$433$	22.3197	1.07261	0.536307	−	0.844023i	$-0.319819\pi$
$433$	22.3197	1.07261	0.536307	+	0.844023i	$0.319819\pi$
$434$	−1.31465	−0.0631053
$435$	3.13268	0.150201
$436$	6.41402	0.307176
$437$	−11.3046	−0.540773
$438$	−5.18863	−0.247922
$439$	2.38539	0.113848	0.0569242	−	0.998379i	$-0.481871\pi$
$439$	2.38539	0.113848	0.0569242	+	0.998379i	$0.481871\pi$
$440$	2.91623	0.139026
$441$	−0.769386	−0.0366374
$442$	8.56037	0.407175
$443$	−5.89075	−0.279878	−0.139939	−	0.990160i	$-0.544691\pi$
$443$	−5.89075	−0.279878	−0.139939	+	0.990160i	$0.544691\pi$
$444$	2.91616	0.138395
$445$	−4.91332	−0.232914
$446$	−5.05917	−0.239558
$447$	16.8885	0.798799
$448$	6.88328	0.325205
$449$	20.6587	0.974943	0.487472	−	0.873139i	$-0.337919\pi$
$449$	20.6587	0.974943	0.487472	+	0.873139i	$0.337919\pi$
$450$	−0.167621	−0.00790171
$451$	−18.7346	−0.882176
$452$	21.9694	1.03335
$453$	−5.10538	−0.239872
$454$	−5.67601	−0.266389
$455$	−5.83649	−0.273619
$456$	−7.77234	−0.363973
$457$	1.41072	0.0659909	0.0329954	−	0.999456i	$-0.489495\pi$
$457$	1.41072	0.0659909	0.0329954	+	0.999456i	$0.489495\pi$
$458$	5.13131	0.239770
$459$	−37.9002	−1.76903
$460$	3.65236	0.170292
$461$	−11.6513	−0.542657	−0.271328	−	0.962487i	$-0.587463\pi$
$461$	−11.6513	−0.542657	−0.271328	+	0.962487i	$0.587463\pi$
$462$	1.10194	0.0512669
$463$	36.5630	1.69923	0.849613	−	0.527406i	$-0.176835\pi$
$463$	36.5630	1.69923	0.849613	+	0.527406i	$0.176835\pi$
$464$	7.79743	0.361987
$465$	9.01239	0.417939
$466$	−0.758268	−0.0351261
$467$	40.8668	1.89109	0.945546	−	0.325489i	$-0.105529\pi$
$467$	40.8668	1.89109	0.945546	+	0.325489i	$0.105529\pi$
$468$	−8.76789	−0.405296
$469$	3.52898	0.162953
$470$	0.483683	0.0223106
$471$	−18.0971	−0.833869
$472$	−10.5356	−0.484942
$473$	−30.5545	−1.40490
$474$	1.91006	0.0877321
$475$	−6.04339	−0.277290
$476$	−13.1449	−0.602496
$477$	−8.08315	−0.370102
$478$	2.78418	0.127346
$479$	25.7716	1.17753	0.588767	−	0.808303i	$-0.299614\pi$
$479$	25.7716	1.17753	0.588767	+	0.808303i	$0.299614\pi$
$480$	3.78178	0.172614
$481$	−5.83649	−0.266121
$482$	1.71619	0.0781705
$483$	2.79375	0.127120
$484$	−0.915773	−0.0416261
$485$	16.3416	0.742035
$486$	−1.69468	−0.0768724
$487$	9.17920	0.415949	0.207975	−	0.978134i	$-0.433313\pi$
$487$	9.17920	0.415949	0.207975	+	0.978134i	$0.433313\pi$
$488$	−3.72649	−0.168690
$489$	28.4087	1.28469
$490$	−0.217863	−0.00984203
$491$	−7.48276	−0.337692	−0.168846	−	0.985642i	$-0.554004\pi$
$491$	−7.48276	−0.337692	−0.168846	+	0.985642i	$0.554004\pi$
$492$	−16.1321	−0.727293
$493$	−14.1209	−0.635974
$494$	7.68449	0.345742
$495$	2.60560	0.117113
$496$	22.4324	1.00724
$497$	−16.7576	−0.751682
$498$	−0.113666	−0.00509350
$499$	5.58693	0.250105	0.125053	−	0.992150i	$-0.460090\pi$
$499$	5.58693	0.250105	0.125053	+	0.992150i	$0.460090\pi$
$500$	1.95254	0.0873201
$501$	5.47438	0.244577
$502$	0.0643375	0.00287152
$503$	−15.6151	−0.696242	−0.348121	−	0.937450i	$-0.613180\pi$
$503$	−15.6151	−0.696242	−0.348121	+	0.937450i	$0.613180\pi$
$504$	−0.662526	−0.0295113
$505$	4.90859	0.218430
$506$	1.38013	0.0613544
$507$	−31.4604	−1.39721
$508$	−13.6282	−0.604652
$509$	16.1873	0.717489	0.358745	−	0.933436i	$-0.383205\pi$
$509$	16.1873	0.717489	0.358745	+	0.933436i	$0.383205\pi$
$510$	−2.19055	−0.0969992
$511$	−15.9462	−0.705419
$512$	15.8154	0.698947
$513$	−34.0223	−1.50212
$514$	3.23271	0.142589
$515$	−6.89151	−0.303676
$516$	−26.3102	−1.15824
$517$	−7.51866	−0.330670
$518$	−0.217863	−0.00957234
$519$	−6.02402	−0.264425
$520$	−5.02586	−0.220398
$521$	−9.69133	−0.424585	−0.212293	−	0.977206i	$-0.568093\pi$
$521$	−9.69133	−0.424585	−0.212293	+	0.977206i	$0.568093\pi$
$522$	−0.351586	−0.0153885
$523$	−11.2897	−0.493662	−0.246831	−	0.969058i	$-0.579389\pi$
$523$	−11.2897	−0.493662	−0.246831	+	0.969058i	$0.579389\pi$
$524$	32.5078	1.42011
$525$	1.49352	0.0651827
$526$	3.81869	0.166503
$527$	−40.6243	−1.76962
$528$	−18.8028	−0.818287
$529$	−19.5010	−0.847868
$530$	−2.28886	−0.0994216
$531$	−9.41341	−0.408507
$532$	−11.7999	−0.511592
$533$	32.2873	1.39852
$534$	−1.59871	−0.0691830
$535$	−14.3715	−0.621335
$536$	3.03884	0.131258
$537$	−8.79019	−0.379325
$538$	5.15504	0.222250
$539$	3.38659	0.145871
$540$	10.9921	0.473026
$541$	−21.2851	−0.915120	−0.457560	−	0.889179i	$-0.651276\pi$
$541$	−21.2851	−0.915120	−0.457560	+	0.889179i	$0.651276\pi$
$542$	−3.80263	−0.163337
$543$	−18.5849	−0.797553
$544$	−17.0468	−0.730874
$545$	3.28497	0.140713
$546$	−1.89909	−0.0812737
$547$	5.41351	0.231465	0.115732	−	0.993280i	$-0.463078\pi$
$547$	5.41351	0.231465	0.115732	+	0.993280i	$0.463078\pi$
$548$	−5.43566	−0.232200
$549$	−3.32956	−0.142102
$550$	0.737812	0.0314604
$551$	−12.6761	−0.540019
$552$	2.40572	0.102394
$553$	5.87020	0.249626
$554$	−3.99973	−0.169932
$555$	1.49352	0.0633966
$556$	13.0401	0.553025
$557$	22.9573	0.972732	0.486366	−	0.873755i	$-0.338322\pi$
$557$	22.9573	0.972732	0.486366	+	0.873755i	$0.338322\pi$
$558$	−1.01147	−0.0428191
$559$	52.6579	2.22719
$560$	3.71747	0.157092
$561$	34.0513	1.43765
$562$	4.37934	0.184731
$563$	28.4981	1.20105	0.600525	−	0.799606i	$-0.294958\pi$
$563$	28.4981	1.20105	0.600525	+	0.799606i	$0.294958\pi$
$564$	−6.47424	−0.272615
$565$	11.2517	0.473364
$566$	−1.46664	−0.0616473
$567$	6.09989	0.256171
$568$	−14.4301	−0.605476
$569$	21.3568	0.895322	0.447661	−	0.894203i	$-0.352257\pi$
$569$	21.3568	0.895322	0.447661	+	0.894203i	$0.352257\pi$
$570$	−1.96642	−0.0823642
$571$	−6.48995	−0.271596	−0.135798	−	0.990737i	$-0.543360\pi$
$571$	−6.48995	−0.271596	−0.135798	+	0.990737i	$0.543360\pi$
$572$	38.5934	1.61367
$573$	19.4739	0.813534
$574$	1.20521	0.0503046
$575$	1.87057	0.0780083
$576$	5.29590	0.220663
$577$	38.6544	1.60920	0.804602	−	0.593815i	$-0.202379\pi$
$577$	38.6544	1.60920	0.804602	+	0.593815i	$0.202379\pi$
$578$	6.17048	0.256658
$579$	−12.8613	−0.534498
$580$	4.09546	0.170055
$581$	−0.349330	−0.0144927
$582$	5.31729	0.220409
$583$	35.5794	1.47355
$584$	−13.7314	−0.568211
$585$	−4.49051	−0.185660
$586$	−5.80161	−0.239662
$587$	−5.41348	−0.223438	−0.111719	−	0.993740i	$-0.535636\pi$
$587$	−5.41348	−0.223438	−0.111719	+	0.993740i	$0.535636\pi$
$588$	2.91616	0.120260
$589$	−36.4677	−1.50263
$590$	−2.66554	−0.109739
$591$	10.8081	0.444584
$592$	3.71747	0.152787
$593$	26.1907	1.07552	0.537762	−	0.843097i	$-0.319270\pi$
$593$	26.1907	1.07552	0.537762	+	0.843097i	$0.319270\pi$
$594$	4.15364	0.170426
$595$	−6.73222	−0.275994
$596$	22.0789	0.904388
$597$	−17.9260	−0.733662
$598$	−2.37853	−0.0972654
$599$	11.4005	0.465814	0.232907	−	0.972499i	$-0.425176\pi$
$599$	11.4005	0.465814	0.232907	+	0.972499i	$0.425176\pi$
$600$	1.28609	0.0525043
$601$	32.8167	1.33862	0.669311	−	0.742983i	$-0.266590\pi$
$601$	32.8167	1.33862	0.669311	+	0.742983i	$0.266590\pi$
$602$	1.96560	0.0801119
$603$	2.71515	0.110570
$604$	−6.67445	−0.271579
$605$	−0.469017	−0.0190683
$606$	1.59717	0.0648807
$607$	41.3132	1.67685	0.838426	−	0.545016i	$-0.183476\pi$
$607$	41.3132	1.67685	0.838426	+	0.545016i	$0.183476\pi$
$608$	−15.3026	−0.620602
$609$	3.13268	0.126943
$610$	−0.942811	−0.0381733
$611$	12.9577	0.524214
$612$	−10.1135	−0.408814
$613$	−22.9322	−0.926225	−0.463112	−	0.886300i	$-0.653267\pi$
$613$	−22.9322	−0.926225	−0.463112	+	0.886300i	$0.653267\pi$
$614$	3.66996	0.148108
$615$	−8.26214	−0.333162
$616$	2.91623	0.117498
$617$	−12.8588	−0.517674	−0.258837	−	0.965921i	$-0.583339\pi$
$617$	−12.8588	−0.517674	−0.258837	+	0.965921i	$0.583339\pi$
$618$	−2.24238	−0.0902017
$619$	27.7662	1.11602	0.558009	−	0.829835i	$-0.311565\pi$
$619$	27.7662	1.11602	0.558009	+	0.829835i	$0.311565\pi$
$620$	11.7822	0.473185
$621$	10.5307	0.422583
$622$	1.07706	0.0431863
$623$	−4.91332	−0.196848
$624$	32.4049	1.29723
$625$	1.00000	0.0400000
$626$	−4.59599	−0.183693
$627$	30.5672	1.22074
$628$	−23.6589	−0.944094
$629$	−6.73222	−0.268431
$630$	−0.167621	−0.00667816
$631$	−39.3607	−1.56693	−0.783463	−	0.621439i	$-0.786548\pi$
$631$	−39.3607	−1.56693	−0.783463	+	0.621439i	$0.786548\pi$
$632$	5.05488	0.201072
$633$	−10.3283	−0.410512
$634$	−2.54740	−0.101170
$635$	−6.97972	−0.276982
$636$	30.6371	1.21484
$637$	−5.83649	−0.231250
$638$	1.54757	0.0612689
$639$	−12.8931	−0.510042
$640$	6.56385	0.259459
$641$	20.0941	0.793669	0.396834	−	0.917890i	$-0.370109\pi$
$641$	20.0941	0.793669	0.396834	+	0.917890i	$0.370109\pi$
$642$	−4.67625	−0.184557
$643$	7.75553	0.305848	0.152924	−	0.988238i	$-0.451131\pi$
$643$	7.75553	0.305848	0.152924	+	0.988238i	$0.451131\pi$
$644$	3.65236	0.143923
$645$	−13.4749	−0.530573
$646$	8.86384	0.348743
$647$	12.6001	0.495362	0.247681	−	0.968842i	$-0.420332\pi$
$647$	12.6001	0.495362	0.247681	+	0.968842i	$0.420332\pi$
$648$	5.25267	0.206344
$649$	41.4348	1.62646
$650$	−1.27155	−0.0498744
$651$	9.01239	0.353223
$652$	37.1397	1.45450
$653$	−7.33941	−0.287213	−0.143607	−	0.989635i	$-0.545870\pi$
$653$	−7.33941	−0.287213	−0.143607	+	0.989635i	$0.545870\pi$
$654$	1.06887	0.0417962
$655$	16.6490	0.650531
$656$	−20.5650	−0.802927
$657$	−12.2688	−0.478651
$658$	0.483683	0.0188559
$659$	−43.8743	−1.70910	−0.854550	−	0.519370i	$-0.826167\pi$
$659$	−43.8743	−1.70910	−0.854550	+	0.519370i	$0.826167\pi$
$660$	−9.87585	−0.384417
$661$	−3.62074	−0.140830	−0.0704152	−	0.997518i	$-0.522432\pi$
$661$	−3.62074	−0.140830	−0.0704152	+	0.997518i	$0.522432\pi$
$662$	5.63884	0.219160
$663$	−58.6843	−2.27911
$664$	−0.300812	−0.0116738
$665$	−6.04339	−0.234353
$666$	−0.167621	−0.00649517
$667$	3.92355	0.151920
$668$	7.15685	0.276907
$669$	34.6823	1.34090
$670$	0.768834	0.0297027
$671$	14.6556	0.565775
$672$	3.78178	0.145885
$673$	41.1003	1.58430	0.792151	−	0.610326i	$-0.208961\pi$
$673$	41.1003	1.58430	0.792151	+	0.610326i	$0.208961\pi$
$674$	5.41165	0.208449
$675$	5.62967	0.216686
$676$	−41.1293	−1.58190
$677$	−9.33150	−0.358639	−0.179319	−	0.983791i	$-0.557390\pi$
$677$	−9.33150	−0.358639	−0.179319	+	0.983791i	$0.557390\pi$
$678$	3.66112	0.140604
$679$	16.3416	0.627134
$680$	−5.79718	−0.222312
$681$	38.9110	1.49107
$682$	4.45219	0.170483
$683$	−4.22754	−0.161762	−0.0808811	−	0.996724i	$-0.525773\pi$
$683$	−4.22754	−0.161762	−0.0808811	+	0.996724i	$0.525773\pi$
$684$	−9.07872	−0.347133
$685$	−2.78390	−0.106367
$686$	−0.217863	−0.00831804
$687$	−35.1769	−1.34208
$688$	−33.5397	−1.27869
$689$	−61.3179	−2.33603
$690$	0.608653	0.0231710
$691$	11.2190	0.426792	0.213396	−	0.976966i	$-0.431548\pi$
$691$	11.2190	0.426792	0.213396	+	0.976966i	$0.431548\pi$
$692$	−7.87541	−0.299378
$693$	2.60560	0.0989785
$694$	−1.76008	−0.0668116
$695$	6.67857	0.253332
$696$	2.69758	0.102252
$697$	37.2425	1.41066
$698$	2.33749	0.0884751
$699$	5.19819	0.196614
$700$	1.95254	0.0737989
$701$	−45.8362	−1.73121	−0.865604	−	0.500729i	$-0.833065\pi$
$701$	−45.8362	−1.73121	−0.865604	+	0.500729i	$0.833065\pi$
$702$	−7.15842	−0.270177
$703$	−6.04339	−0.227931
$704$	−23.3109	−0.878562
$705$	−3.31581	−0.124881
$706$	2.97380	0.111920
$707$	4.90859	0.184607
$708$	35.6791	1.34090
$709$	−5.50415	−0.206713	−0.103356	−	0.994644i	$-0.532958\pi$
$709$	−5.50415	−0.206713	−0.103356	+	0.994644i	$0.532958\pi$
$710$	−3.65086	−0.137014
$711$	4.51645	0.169380
$712$	−4.23091	−0.158560
$713$	11.2876	0.422725
$714$	−2.19055	−0.0819793
$715$	19.7658	0.739199
$716$	−11.4917	−0.429466
$717$	−19.0865	−0.712800
$718$	−4.27223	−0.159438
$719$	−11.1224	−0.414795	−0.207398	−	0.978257i	$-0.566499\pi$
$719$	−11.1224	−0.414795	−0.207398	+	0.978257i	$0.566499\pi$
$720$	2.86017	0.106592
$721$	−6.89151	−0.256653
$722$	3.81752	0.142073
$723$	−11.7651	−0.437549
$724$	−24.2967	−0.902978
$725$	2.09751	0.0778996
$726$	−0.152610	−0.00566390
$727$	−42.2530	−1.56708	−0.783538	−	0.621344i	$-0.786587\pi$
$727$	−42.2530	−1.56708	−0.783538	+	0.621344i	$0.786587\pi$
$728$	−5.02586	−0.186271
$729$	29.9173	1.10805
$730$	−3.47408	−0.128582
$731$	60.7394	2.24653
$732$	12.6198	0.466442
$733$	38.0314	1.40472	0.702361	−	0.711821i	$-0.252129\pi$
$733$	38.0314	1.40472	0.702361	+	0.711821i	$0.252129\pi$
$734$	−2.63079	−0.0971040
$735$	1.49352	0.0550895
$736$	4.73651	0.174590
$737$	−11.9512	−0.440230
$738$	0.927274	0.0341334
$739$	−31.6847	−1.16554	−0.582770	−	0.812637i	$-0.698031\pi$
$739$	−31.6847	−1.16554	−0.582770	+	0.812637i	$0.698031\pi$
$740$	1.95254	0.0717766
$741$	−52.6798	−1.93524
$742$	−2.28886	−0.0840266
$743$	19.8357	0.727702	0.363851	−	0.931457i	$-0.381462\pi$
$743$	19.8357	0.727702	0.363851	+	0.931457i	$0.381462\pi$
$744$	7.76066	0.284519
$745$	11.3078	0.414287
$746$	2.26009	0.0827477
$747$	−0.268770	−0.00983378
$748$	44.5164	1.62768
$749$	−14.3715	−0.525124
$750$	0.325383	0.0118813
$751$	−15.2445	−0.556281	−0.278141	−	0.960540i	$-0.589718\pi$
$751$	−15.2445	−0.556281	−0.278141	+	0.960540i	$0.589718\pi$
$752$	−8.25325	−0.300965
$753$	−0.441056	−0.0160730
$754$	−2.66709	−0.0971299
$755$	−3.41835	−0.124406
$756$	10.9921	0.399780
$757$	44.9317	1.63307	0.816535	−	0.577296i	$-0.195892\pi$
$757$	44.9317	1.63307	0.816535	+	0.577296i	$0.195892\pi$
$758$	3.33073	0.120978
$759$	−9.46128	−0.343423
$760$	−5.20403	−0.188770
$761$	−38.3101	−1.38874	−0.694369	−	0.719619i	$-0.744317\pi$
$761$	−38.3101	−1.38874	−0.694369	+	0.719619i	$0.744317\pi$
$762$	−2.27108	−0.0822727
$763$	3.28497	0.118924
$764$	25.4589	0.921071
$765$	−5.17968	−0.187272
$766$	−7.04468	−0.254535
$767$	−71.4091	−2.57843
$768$	−18.4249	−0.664852
$769$	−21.9991	−0.793309	−0.396655	−	0.917968i	$-0.629829\pi$
$769$	−21.9991	−0.793309	−0.396655	+	0.917968i	$0.629829\pi$
$770$	0.737812	0.0265889
$771$	−22.1613	−0.798121
$772$	−16.8140	−0.605151
$773$	−17.8465	−0.641894	−0.320947	−	0.947097i	$-0.604001\pi$
$773$	−17.8465	−0.641894	−0.320947	+	0.947097i	$0.604001\pi$
$774$	1.51231	0.0543587
$775$	6.03431	0.216759
$776$	14.0719	0.505153
$777$	1.49352	0.0535799
$778$	−1.75051	−0.0627587
$779$	33.4319	1.19782
$780$	17.0201	0.609418
$781$	56.7512	2.03072
$782$	−2.74357	−0.0981099
$783$	11.8083	0.421994
$784$	3.71747	0.132767
$785$	−12.1170	−0.432475
$786$	5.41731	0.193229
$787$	−26.3236	−0.938335	−0.469167	−	0.883109i	$-0.655446\pi$
$787$	−26.3236	−0.938335	−0.469167	+	0.883109i	$0.655446\pi$
$788$	14.1297	0.503351
$789$	−26.1785	−0.931978
$790$	1.27890	0.0455011
$791$	11.2517	0.400065
$792$	2.24371	0.0797267
$793$	−25.2577	−0.896926
$794$	4.08618	0.145013
$795$	15.6909	0.556499
$796$	−23.4353	−0.830641
$797$	−8.11182	−0.287335	−0.143668	−	0.989626i	$-0.545890\pi$
$797$	−8.11182	−0.287335	−0.143668	+	0.989626i	$0.545890\pi$
$798$	−1.96642	−0.0696104
$799$	14.9464	0.528765
$800$	2.53212	0.0895239
$801$	−3.78024	−0.133568
$802$	6.54665	0.231170
$803$	54.0033	1.90574
$804$	−10.2911	−0.362938
$805$	1.87057	0.0659291
$806$	−7.67294	−0.270268
$807$	−35.3396	−1.24401
$808$	4.22684	0.148700
$809$	19.4596	0.684162	0.342081	−	0.939670i	$-0.388868\pi$
$809$	19.4596	0.684162	0.342081	+	0.939670i	$0.388868\pi$
$810$	1.32894	0.0466941
$811$	48.8378	1.71493	0.857464	−	0.514544i	$-0.172039\pi$
$811$	48.8378	1.71493	0.857464	+	0.514544i	$0.172039\pi$
$812$	4.09546	0.143723
$813$	26.0684	0.914258
$814$	0.737812	0.0258603
$815$	19.0212	0.666285
$816$	37.3781	1.30850
$817$	54.5247	1.90758
$818$	8.13133	0.284305
$819$	−4.49051	−0.156911
$820$	−10.8014	−0.377201
$821$	−3.45147	−0.120457	−0.0602286	−	0.998185i	$-0.519183\pi$
$821$	−3.45147	−0.120457	−0.0602286	+	0.998185i	$0.519183\pi$
$822$	−0.905834	−0.0315946
$823$	38.5885	1.34511	0.672555	−	0.740047i	$-0.265197\pi$
$823$	38.5885	1.34511	0.672555	+	0.740047i	$0.265197\pi$
$824$	−5.93434	−0.206733
$825$	−5.05796	−0.176096
$826$	−2.66554	−0.0927460
$827$	−28.0738	−0.976220	−0.488110	−	0.872782i	$-0.662314\pi$
$827$	−28.0738	−0.976220	−0.488110	+	0.872782i	$0.662314\pi$
$828$	2.81008	0.0976570
$829$	−55.9601	−1.94357	−0.971787	−	0.235859i	$-0.924210\pi$
$829$	−55.9601	−1.94357	−0.971787	+	0.235859i	$0.924210\pi$
$830$	−0.0761060	−0.00264168
$831$	27.4195	0.951172
$832$	40.1742	1.39279
$833$	−6.73222	−0.233258
$834$	2.17309	0.0752480
$835$	3.66541	0.126847
$836$	39.9616	1.38210
$837$	33.9712	1.17422
$838$	−6.39933	−0.221061
$839$	−36.8044	−1.27063	−0.635314	−	0.772254i	$-0.719129\pi$
$839$	−36.8044	−1.27063	−0.635314	+	0.772254i	$0.719129\pi$
$840$	1.28609	0.0443743
$841$	−24.6004	−0.848291
$842$	0.318518	0.0109769
$843$	−30.0219	−1.03401
$844$	−13.5025	−0.464776
$845$	−21.0646	−0.724643
$846$	0.372139	0.0127944
$847$	−0.469017	−0.0161156
$848$	39.0556	1.34117
$849$	10.0543	0.345063
$850$	−1.46670	−0.0503074
$851$	1.87057	0.0641224
$852$	48.8679	1.67419
$853$	15.8751	0.543553	0.271776	−	0.962360i	$-0.412389\pi$
$853$	15.8751	0.543553	0.271776	+	0.962360i	$0.412389\pi$
$854$	−0.942811	−0.0322623
$855$	−4.64971	−0.159017
$856$	−12.3755	−0.422985
$857$	−11.5952	−0.396086	−0.198043	−	0.980193i	$-0.563459\pi$
$857$	−11.5952	−0.396086	−0.198043	+	0.980193i	$0.563459\pi$
$858$	6.43146	0.219566
$859$	25.3500	0.864931	0.432465	−	0.901651i	$-0.357644\pi$
$859$	25.3500	0.864931	0.432465	+	0.901651i	$0.357644\pi$
$860$	−17.6162	−0.600706
$861$	−8.26214	−0.281573
$862$	−5.79395	−0.197343
$863$	25.4598	0.866661	0.433330	−	0.901235i	$-0.357338\pi$
$863$	25.4598	0.866661	0.433330	+	0.901235i	$0.357338\pi$
$864$	14.2550	0.484964
$865$	−4.03343	−0.137141
$866$	4.86262	0.165239
$867$	−42.3008	−1.43661
$868$	11.7822	0.399914
$869$	−19.8800	−0.674382
$870$	0.682495	0.0231387
$871$	20.5969	0.697898
$872$	2.82872	0.0957925
$873$	12.5730	0.425532
$874$	−2.46285	−0.0833073
$875$	1.00000	0.0338062
$876$	46.5017	1.57115
$877$	−20.7406	−0.700360	−0.350180	−	0.936682i	$-0.613880\pi$
$877$	−20.7406	−0.700360	−0.350180	+	0.936682i	$0.613880\pi$
$878$	0.519687	0.0175386
$879$	39.7720	1.34148
$880$	−12.5896	−0.424394
$881$	12.8811	0.433976	0.216988	−	0.976174i	$-0.430377\pi$
$881$	12.8811	0.433976	0.216988	+	0.976174i	$0.430377\pi$
$882$	−0.167621	−0.00564408
$883$	23.7354	0.798760	0.399380	−	0.916786i	$-0.369225\pi$
$883$	23.7354	0.798760	0.399380	+	0.916786i	$0.369225\pi$
$884$	−76.7200	−2.58037
$885$	18.2732	0.614247
$886$	−1.28337	−0.0431158
$887$	−32.8026	−1.10140	−0.550702	−	0.834702i	$-0.685640\pi$
$887$	−32.8026	−1.10140	−0.550702	+	0.834702i	$0.685640\pi$
$888$	1.28609	0.0431583
$889$	−6.97972	−0.234092
$890$	−1.07043	−0.0358808
$891$	−20.6578	−0.692063
$892$	45.3414	1.51814
$893$	13.4171	0.448986
$894$	3.67937	0.123057
$895$	−5.88554	−0.196732
$896$	6.56385	0.219283
$897$	16.3057	0.544430
$898$	4.50075	0.150192
$899$	12.6570	0.422136
$900$	1.50225	0.0500752
$901$	−70.7285	−2.35631
$902$	−4.08156	−0.135901
$903$	−13.4749	−0.448416
$904$	9.68897	0.322250
$905$	−12.4436	−0.413641
$906$	−1.11227	−0.0369528
$907$	16.8914	0.560871	0.280436	−	0.959873i	$-0.409521\pi$
$907$	16.8914	0.560871	0.280436	+	0.959873i	$0.409521\pi$
$908$	50.8698	1.68817
$909$	3.77661	0.125262
$910$	−1.27155	−0.0421516
$911$	8.36024	0.276987	0.138494	−	0.990363i	$-0.455774\pi$
$911$	8.36024	0.276987	0.138494	+	0.990363i	$0.455774\pi$
$912$	33.5537	1.11107
$913$	1.18304	0.0391529
$914$	0.307344	0.0101660
$915$	6.46329	0.213670
$916$	−45.9880	−1.51949
$917$	16.6490	0.549799
$918$	−8.25703	−0.272523
$919$	47.7444	1.57494	0.787472	−	0.616350i	$-0.211389\pi$
$919$	47.7444	1.57494	0.787472	+	0.616350i	$0.211389\pi$
$920$	1.61077	0.0531055
$921$	−25.1589	−0.829012
$922$	−2.53839	−0.0835974
$923$	−97.8056	−3.21931
$924$	−9.87585	−0.324891
$925$	1.00000	0.0328798
$926$	7.96571	0.261769
$927$	−5.30223	−0.174148
$928$	5.31114	0.174347
$929$	12.7769	0.419196	0.209598	−	0.977788i	$-0.432784\pi$
$929$	12.7769	0.419196	0.209598	+	0.977788i	$0.432784\pi$
$930$	1.96346	0.0643845
$931$	−6.04339	−0.198064
$932$	6.79578	0.222603
$933$	−7.38364	−0.241730
$934$	8.90336	0.291327
$935$	22.7993	0.745617
$936$	−3.86683	−0.126391
$937$	40.0276	1.30764	0.653822	−	0.756648i	$-0.273164\pi$
$937$	40.0276	1.30764	0.653822	+	0.756648i	$0.273164\pi$
$938$	0.768834	0.0251033
$939$	31.5071	1.02820
$940$	−4.33487	−0.141388
$941$	4.88944	0.159391	0.0796955	−	0.996819i	$-0.474605\pi$
$941$	4.88944	0.159391	0.0796955	+	0.996819i	$0.474605\pi$
$942$	−3.94268	−0.128459
$943$	−10.3480	−0.336976
$944$	45.4830	1.48035
$945$	5.62967	0.183133
$946$	−6.65669	−0.216428
$947$	51.9445	1.68797	0.843985	−	0.536367i	$-0.180204\pi$
$947$	51.9445	1.68797	0.843985	+	0.536367i	$0.180204\pi$
$948$	−17.1184	−0.555980
$949$	−93.0698	−3.02117
$950$	−1.31663	−0.0427171
$951$	17.4633	0.566286
$952$	−5.79718	−0.187888
$953$	−20.4519	−0.662502	−0.331251	−	0.943543i	$-0.607471\pi$
$953$	−20.4519	−0.662502	−0.331251	+	0.943543i	$0.607471\pi$
$954$	−1.76102	−0.0570150
$955$	13.0389	0.421929
$956$	−24.9525	−0.807021
$957$	−10.6091	−0.342944
$958$	5.61466	0.181402
$959$	−2.78390	−0.0898968
$960$	−10.2803	−0.331797
$961$	5.41290	0.174610
$962$	−1.27155	−0.0409965
$963$	−11.0573	−0.356315
$964$	−15.3809	−0.495386
$965$	−8.61139	−0.277210
$966$	0.608653	0.0195831
$967$	29.7143	0.955547	0.477773	−	0.878483i	$-0.341444\pi$
$967$	29.7143	0.955547	0.477773	+	0.878483i	$0.341444\pi$
$968$	−0.403876	−0.0129811
$969$	−60.7647	−1.95204
$970$	3.56023	0.114312
$971$	37.3665	1.19915	0.599574	−	0.800319i	$-0.295337\pi$
$971$	37.3665	1.19915	0.599574	+	0.800319i	$0.295337\pi$
$972$	15.1882	0.487160
$973$	6.67857	0.214105
$974$	1.99981	0.0640779
$975$	8.71693	0.279165
$976$	16.0875	0.514949
$977$	−21.6934	−0.694032	−0.347016	−	0.937859i	$-0.612805\pi$
$977$	−21.6934	−0.694032	−0.347016	+	0.937859i	$0.612805\pi$
$978$	6.18919	0.197909
$979$	16.6394	0.531798
$980$	1.95254	0.0623715
$981$	2.52741	0.0806940
$982$	−1.63021	−0.0520222
$983$	−18.4925	−0.589820	−0.294910	−	0.955525i	$-0.595290\pi$
$983$	−18.4925	−0.589820	−0.294910	+	0.955525i	$0.595290\pi$
$984$	−7.11462	−0.226806
$985$	7.23661	0.230578
$986$	−3.07642	−0.0979731
$987$	−3.31581	−0.105543
$988$	−68.8702	−2.19105
$989$	−16.8767	−0.536648
$990$	0.567663	0.0180415
$991$	6.04331	0.191972	0.0959860	−	0.995383i	$-0.469400\pi$
$991$	6.04331	0.191972	0.0959860	+	0.995383i	$0.469400\pi$
$992$	15.2796	0.485127
$993$	−38.6562	−1.22672
$994$	−3.65086	−0.115798
$995$	−12.0025	−0.380504
$996$	1.01870	0.0322788
$997$	9.16494	0.290257	0.145128	−	0.989413i	$-0.453640\pi$
$997$	9.16494	0.290257	0.145128	+	0.989413i	$0.453640\pi$
$998$	1.21718	0.0385293
$999$	5.62967	0.178115

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1295.2.a.j.1.8	✓	15
5.4	even	2		6475.2.a.u.1.8		15
7.6	odd	2		9065.2.a.o.1.8		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1295.2.a.j.1.8	✓	15	1.1	even	1	trivial
6475.2.a.u.1.8		15	5.4	even	2
9065.2.a.o.1.8		15	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1295 = 5 \cdot 7 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1295.a (trivial)

\(f(q)\)	\(=\)	\(q+0.217863 q^{2} -1.49352 q^{3} -1.95254 q^{4} -1.00000 q^{5} -0.325383 q^{6} -1.00000 q^{7} -0.861110 q^{8} -0.769386 q^{9} -0.217863 q^{10} +3.38659 q^{11} +2.91616 q^{12} -5.83649 q^{13} -0.217863 q^{14} +1.49352 q^{15} +3.71747 q^{16} -6.73222 q^{17} -0.167621 q^{18} -6.04339 q^{19} +1.95254 q^{20} +1.49352 q^{21} +0.737812 q^{22} +1.87057 q^{23} +1.28609 q^{24} +1.00000 q^{25} -1.27155 q^{26} +5.62967 q^{27} +1.95254 q^{28} +2.09751 q^{29} +0.325383 q^{30} +6.03431 q^{31} +2.53212 q^{32} -5.05796 q^{33} -1.46670 q^{34} +1.00000 q^{35} +1.50225 q^{36} +1.00000 q^{37} -1.31663 q^{38} +8.71693 q^{39} +0.861110 q^{40} -5.53198 q^{41} +0.325383 q^{42} -9.02220 q^{43} -6.61245 q^{44} +0.769386 q^{45} +0.407528 q^{46} -2.22013 q^{47} -5.55213 q^{48} +1.00000 q^{49} +0.217863 q^{50} +10.0547 q^{51} +11.3959 q^{52} +10.5060 q^{53} +1.22649 q^{54} -3.38659 q^{55} +0.861110 q^{56} +9.02595 q^{57} +0.456969 q^{58} +12.2350 q^{59} -2.91616 q^{60} +4.32755 q^{61} +1.31465 q^{62} +0.769386 q^{63} -6.88328 q^{64} +5.83649 q^{65} -1.10194 q^{66} -3.52898 q^{67} +13.1449 q^{68} -2.79375 q^{69} +0.217863 q^{70} +16.7576 q^{71} +0.662526 q^{72} +15.9462 q^{73} +0.217863 q^{74} -1.49352 q^{75} +11.7999 q^{76} -3.38659 q^{77} +1.89909 q^{78} -5.87020 q^{79} -3.71747 q^{80} -6.09989 q^{81} -1.20521 q^{82} +0.349330 q^{83} -2.91616 q^{84} +6.73222 q^{85} -1.96560 q^{86} -3.13268 q^{87} -2.91623 q^{88} +4.91332 q^{89} +0.167621 q^{90} +5.83649 q^{91} -3.65236 q^{92} -9.01239 q^{93} -0.483683 q^{94} +6.04339 q^{95} -3.78178 q^{96} -16.3416 q^{97} +0.217863 q^{98} -2.60560 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - q^{2} - q^{3} + 23 q^{4} - 15 q^{5} + 6 q^{6} - 15 q^{7} - 3 q^{8} + 30 q^{9} + q^{10} + 17 q^{11} + 8 q^{12} - 5 q^{13} + q^{14} + q^{15} + 39 q^{16} - 7 q^{17} + 12 q^{18} + 6 q^{19} - 23 q^{20}+ \cdots + 90 q^{99}+O(q^{100}) \) 15 * q - q^2 - q^3 + 23 * q^4 - 15 * q^5 + 6 * q^6 - 15 * q^7 - 3 * q^8 + 30 * q^9 + q^10 + 17 * q^11 + 8 * q^12 - 5 * q^13 + q^14 + q^15 + 39 * q^16 - 7 * q^17 + 12 * q^18 + 6 * q^19 - 23 * q^20 + q^21 + 18 * q^22 - 2 * q^23 + 4 * q^24 + 15 * q^25 + 4 * q^26 + 5 * q^27 - 23 * q^28 + 13 * q^29 - 6 * q^30 - 4 * q^31 - 7 * q^32 + 7 * q^33 + 38 * q^34 + 15 * q^35 + 49 * q^36 + 15 * q^37 - 26 * q^38 + 33 * q^39 + 3 * q^40 + 22 * q^41 - 6 * q^42 + 10 * q^43 + 58 * q^44 - 30 * q^45 + 32 * q^46 - 9 * q^47 + 43 * q^48 + 15 * q^49 - q^50 + 39 * q^51 + 6 * q^52 - 16 * q^53 + 30 * q^54 - 17 * q^55 + 3 * q^56 + 16 * q^57 + 44 * q^58 + 6 * q^59 - 8 * q^60 - 11 * q^62 - 30 * q^63 + 119 * q^64 + 5 * q^65 + 3 * q^66 + 4 * q^67 - 70 * q^68 + 14 * q^69 - q^70 + 48 * q^71 - 25 * q^72 + 38 * q^73 - q^74 - q^75 - 3 * q^76 - 17 * q^77 - 40 * q^78 + 7 * q^79 - 39 * q^80 + 111 * q^81 + 6 * q^82 - 6 * q^83 - 8 * q^84 + 7 * q^85 - 40 * q^86 - 47 * q^87 + 23 * q^88 - 2 * q^89 - 12 * q^90 + 5 * q^91 + 7 * q^92 - 26 * q^94 - 6 * q^95 - 29 * q^96 + 79 * q^97 - q^98 + 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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