LMFDB - Embedded newform 6897.2.a.bc.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [6897,2,Mod(1,6897)] 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("6897.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6897, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 6897 = 3 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6897.a (trivial)

Newform invariants

comment:select newform

sage:traces = [8,-1,-8,9,-2,1,-6,-6,8,-3,0,-9,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	yes
Analytic conductor:	$55.0728222741$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 12x^{6} + 9x^{5} + 40x^{4} - 22x^{3} - 28x^{2} + 12x - 1 $ x^8 - x^7 - 12x^6 + 9x^5 + 40x^4 - 22x^3 - 28x^2 + 12x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.118442$ of defining polynomial
Character	$\chi$	$=$	6897.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.118442 q^{2} -1.00000 q^{3} -1.98597 q^{4} +1.83342 q^{5} +0.118442 q^{6} +2.90053 q^{7} +0.472107 q^{8} +1.00000 q^{9} -0.217154 q^{10} +1.98597 q^{12} -0.118442 q^{13} -0.343545 q^{14} -1.83342 q^{15} +3.91603 q^{16} +3.52582 q^{17} -0.118442 q^{18} +1.00000 q^{19} -3.64113 q^{20} -2.90053 q^{21} -3.54008 q^{23} -0.472107 q^{24} -1.63856 q^{25} +0.0140285 q^{26} -1.00000 q^{27} -5.76037 q^{28} -0.0586159 q^{29} +0.217154 q^{30} -7.39303 q^{31} -1.40804 q^{32} -0.417605 q^{34} +5.31790 q^{35} -1.98597 q^{36} -4.84494 q^{37} -0.118442 q^{38} +0.118442 q^{39} +0.865571 q^{40} -9.00894 q^{41} +0.343545 q^{42} -9.93882 q^{43} +1.83342 q^{45} +0.419294 q^{46} +9.30165 q^{47} -3.91603 q^{48} +1.41309 q^{49} +0.194074 q^{50} -3.52582 q^{51} +0.235223 q^{52} -2.88129 q^{53} +0.118442 q^{54} +1.36936 q^{56} -1.00000 q^{57} +0.00694258 q^{58} -13.3060 q^{59} +3.64113 q^{60} +5.62925 q^{61} +0.875646 q^{62} +2.90053 q^{63} -7.66528 q^{64} -0.217154 q^{65} +3.37041 q^{67} -7.00217 q^{68} +3.54008 q^{69} -0.629863 q^{70} +2.37046 q^{71} +0.472107 q^{72} +10.8925 q^{73} +0.573845 q^{74} +1.63856 q^{75} -1.98597 q^{76} -0.0140285 q^{78} -10.6322 q^{79} +7.17973 q^{80} +1.00000 q^{81} +1.06704 q^{82} -11.0325 q^{83} +5.76037 q^{84} +6.46432 q^{85} +1.17717 q^{86} +0.0586159 q^{87} -11.9376 q^{89} -0.217154 q^{90} -0.343545 q^{91} +7.03049 q^{92} +7.39303 q^{93} -1.10171 q^{94} +1.83342 q^{95} +1.40804 q^{96} -2.30245 q^{97} -0.167369 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 8 q^{3} + 9 q^{4} - 2 q^{5} + q^{6} - 6 q^{7} - 6 q^{8} + 8 q^{9} - 3 q^{10} - 9 q^{12} - q^{13} + 7 q^{14} + 2 q^{15} + 23 q^{16} - 15 q^{17} - q^{18} + 8 q^{19} - 4 q^{20} + 6 q^{21}+ \cdots - 55 q^{98}+O(q^{100}) $ 8 * q - q^2 - 8 * q^3 + 9 * q^4 - 2 * q^5 + q^6 - 6 * q^7 - 6 * q^8 + 8 * q^9 - 3 * q^10 - 9 * q^12 - q^13 + 7 * q^14 + 2 * q^15 + 23 * q^16 - 15 * q^17 - q^18 + 8 * q^19 - 4 * q^20 + 6 * q^21 - 5 * q^23 + 6 * q^24 + 4 * q^25 + 25 * q^26 - 8 * q^27 - 8 * q^28 - 17 * q^29 + 3 * q^30 - 4 * q^31 - 38 * q^32 - 18 * q^34 - 2 * q^35 + 9 * q^36 - 4 * q^37 - q^38 + q^39 - 14 * q^40 - 2 * q^41 - 7 * q^42 - 10 * q^43 - 2 * q^45 + 10 * q^46 + 5 * q^47 - 23 * q^48 + 28 * q^49 - 7 * q^50 + 15 * q^51 - 8 * q^52 - 19 * q^53 + q^54 - 49 * q^56 - 8 * q^57 + 35 * q^58 + 12 * q^59 + 4 * q^60 + 5 * q^61 - 22 * q^62 - 6 * q^63 + 24 * q^64 - 3 * q^65 - 12 * q^67 + 3 * q^68 + 5 * q^69 - 22 * q^70 + 40 * q^71 - 6 * q^72 + 12 * q^73 + 7 * q^74 - 4 * q^75 + 9 * q^76 - 25 * q^78 - 14 * q^79 + 37 * q^80 + 8 * q^81 + 31 * q^82 - 17 * q^83 + 8 * q^84 + 35 * q^85 - q^86 + 17 * q^87 - 9 * q^89 - 3 * q^90 + 7 * q^91 + 12 * q^92 + 4 * q^93 - 51 * q^94 - 2 * q^95 + 38 * q^96 + 8 * q^97 - 55 * q^98

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 $

$2$	−0.118442	−0.0837512	−0.0418756	−	0.999123i	$-0.513333\pi$
$2$	−0.118442	−0.0837512	−0.0418756	+	0.999123i	$0.513333\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.98597	−0.992986
$5$	1.83342	0.819932	0.409966	−	0.912101i	$-0.365541\pi$
$5$	1.83342	0.819932	0.409966	+	0.912101i	$0.365541\pi$
$6$	0.118442	0.0483538
$7$	2.90053	1.09630	0.548149	−	0.836381i	$-0.315333\pi$
$7$	2.90053	1.09630	0.548149	+	0.836381i	$0.315333\pi$
$8$	0.472107	0.166915
$9$	1.00000	0.333333
$10$	−0.217154	−0.0686703
$11$	0	0
$11$	0	0
$12$	1.98597	0.573301
$13$	−0.118442	−0.0328499	−0.0164250	−	0.999865i	$-0.505228\pi$
$13$	−0.118442	−0.0328499	−0.0164250	+	0.999865i	$0.505228\pi$
$14$	−0.343545	−0.0918163
$15$	−1.83342	−0.473388
$16$	3.91603	0.979006
$17$	3.52582	0.855136	0.427568	−	0.903983i	$-0.359370\pi$
$17$	3.52582	0.855136	0.427568	+	0.903983i	$0.359370\pi$
$18$	−0.118442	−0.0279171
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−3.64113	−0.814181
$21$	−2.90053	−0.632948
$22$	0	0
$23$	−3.54008	−0.738157	−0.369079	−	0.929398i	$-0.620327\pi$
$23$	−3.54008	−0.738157	−0.369079	+	0.929398i	$0.620327\pi$
$24$	−0.472107	−0.0963684
$25$	−1.63856	−0.327712
$26$	0.0140285	0.00275122
$27$	−1.00000	−0.192450
$28$	−5.76037	−1.08861
$29$	−0.0586159	−0.0108847	−0.00544235	−	0.999985i	$-0.501732\pi$
$29$	−0.0586159	−0.0108847	−0.00544235	+	0.999985i	$0.501732\pi$
$30$	0.217154	0.0396468
$31$	−7.39303	−1.32783	−0.663914	−	0.747809i	$-0.731106\pi$
$31$	−7.39303	−1.32783	−0.663914	+	0.747809i	$0.731106\pi$
$32$	−1.40804	−0.248908
$33$	0	0
$34$	−0.417605	−0.0716187
$35$	5.31790	0.898890
$36$	−1.98597	−0.330995
$37$	−4.84494	−0.796504	−0.398252	−	0.917276i	$-0.630383\pi$
$37$	−4.84494	−0.796504	−0.398252	+	0.917276i	$0.630383\pi$
$38$	−0.118442	−0.0192138
$39$	0.118442	0.0189659
$40$	0.865571	0.136859
$41$	−9.00894	−1.40696	−0.703480	−	0.710715i	$-0.748372\pi$
$41$	−9.00894	−1.40696	−0.703480	+	0.710715i	$0.748372\pi$
$42$	0.343545	0.0530101
$43$	−9.93882	−1.51566	−0.757828	−	0.652455i	$-0.773739\pi$
$43$	−9.93882	−1.51566	−0.757828	+	0.652455i	$0.773739\pi$
$44$	0	0
$45$	1.83342	0.273311
$46$	0.419294	0.0618215
$47$	9.30165	1.35678	0.678392	−	0.734700i	$-0.262677\pi$
$47$	9.30165	1.35678	0.678392	+	0.734700i	$0.262677\pi$
$48$	−3.91603	−0.565230
$49$	1.41309	0.201870
$50$	0.194074	0.0274462
$51$	−3.52582	−0.493713
$52$	0.235223	0.0326195
$53$	−2.88129	−0.395775	−0.197888	−	0.980225i	$-0.563408\pi$
$53$	−2.88129	−0.395775	−0.197888	+	0.980225i	$0.563408\pi$
$54$	0.118442	0.0161179
$55$	0	0
$56$	1.36936	0.182989
$57$	−1.00000	−0.132453
$58$	0.00694258	0.000911606 0
$59$	−13.3060	−1.73229	−0.866147	−	0.499790i	$-0.833411\pi$
$59$	−13.3060	−1.73229	−0.866147	+	0.499790i	$0.833411\pi$
$60$	3.64113	0.470067
$61$	5.62925	0.720752	0.360376	−	0.932807i	$-0.382648\pi$
$61$	5.62925	0.720752	0.360376	+	0.932807i	$0.382648\pi$
$62$	0.875646	0.111207
$63$	2.90053	0.365433
$64$	−7.66528	−0.958160
$65$	−0.217154	−0.0269347
$66$	0	0
$67$	3.37041	0.411761	0.205881	−	0.978577i	$-0.433994\pi$
$67$	3.37041	0.411761	0.205881	+	0.978577i	$0.433994\pi$
$68$	−7.00217	−0.849138
$69$	3.54008	0.426175
$70$	−0.629863	−0.0752831
$71$	2.37046	0.281322	0.140661	−	0.990058i	$-0.455077\pi$
$71$	2.37046	0.281322	0.140661	+	0.990058i	$0.455077\pi$
$72$	0.472107	0.0556383
$73$	10.8925	1.27487	0.637433	−	0.770505i	$-0.279996\pi$
$73$	10.8925	1.27487	0.637433	+	0.770505i	$0.279996\pi$
$74$	0.573845	0.0667081
$75$	1.63856	0.189204
$76$	−1.98597	−0.227807
$77$	0	0
$78$	−0.0140285	−0.00158842
$79$	−10.6322	−1.19621	−0.598107	−	0.801416i	$-0.704080\pi$
$79$	−10.6322	−1.19621	−0.598107	+	0.801416i	$0.704080\pi$
$80$	7.17973	0.802719
$81$	1.00000	0.111111
$82$	1.06704	0.117835
$83$	−11.0325	−1.21097	−0.605485	−	0.795857i	$-0.707021\pi$
$83$	−11.0325	−1.21097	−0.605485	+	0.795857i	$0.707021\pi$
$84$	5.76037	0.628508
$85$	6.46432	0.701154
$86$	1.17717	0.126938
$87$	0.0586159	0.00628428
$88$	0	0
$89$	−11.9376	−1.26539	−0.632693	−	0.774403i	$-0.718050\pi$
$89$	−11.9376	−1.26539	−0.632693	+	0.774403i	$0.718050\pi$
$90$	−0.217154	−0.0228901
$91$	−0.343545	−0.0360133
$92$	7.03049	0.732980
$93$	7.39303	0.766622
$94$	−1.10171	−0.113632
$95$	1.83342	0.188105
$96$	1.40804	0.143707
$97$	−2.30245	−0.233778	−0.116889	−	0.993145i	$-0.537292\pi$
$97$	−2.30245	−0.233778	−0.116889	+	0.993145i	$0.537292\pi$
$98$	−0.167369	−0.0169068
$99$	0	0
$100$	3.25413	0.325413
$101$	5.80306	0.577426	0.288713	−	0.957416i	$-0.406773\pi$
$101$	5.80306	0.577426	0.288713	+	0.957416i	$0.406773\pi$
$102$	0.417605	0.0413491
$103$	7.00302	0.690028	0.345014	−	0.938598i	$-0.387874\pi$
$103$	7.00302	0.690028	0.345014	+	0.938598i	$0.387874\pi$
$104$	−0.0559173	−0.00548314
$105$	−5.31790	−0.518974
$106$	0.341266	0.0331467
$107$	10.3108	0.996782	0.498391	−	0.866953i	$-0.333924\pi$
$107$	10.3108	0.996782	0.498391	+	0.866953i	$0.333924\pi$
$108$	1.98597	0.191100
$109$	−9.04469	−0.866324	−0.433162	−	0.901316i	$-0.642602\pi$
$109$	−9.04469	−0.866324	−0.433162	+	0.901316i	$0.642602\pi$
$110$	0	0
$111$	4.84494	0.459862
$112$	11.3586	1.07328
$113$	−12.2908	−1.15622	−0.578109	−	0.815960i	$-0.696209\pi$
$113$	−12.2908	−1.15622	−0.578109	+	0.815960i	$0.696209\pi$
$114$	0.118442	0.0110931
$115$	−6.49046	−0.605239
$116$	0.116409	0.0108083
$117$	−0.118442	−0.0109500
$118$	1.57599	0.145082
$119$	10.2267	0.937484
$120$	−0.865571	−0.0790155
$121$	0	0
$122$	−0.666740	−0.0603638
$123$	9.00894	0.812309
$124$	14.6824	1.31851
$125$	−12.1713	−1.08863
$126$	−0.343545	−0.0306054
$127$	4.45512	0.395328	0.197664	−	0.980270i	$-0.436664\pi$
$127$	4.45512	0.395328	0.197664	+	0.980270i	$0.436664\pi$
$128$	3.72396	0.329155
$129$	9.93882	0.875064
$130$	0.0257202	0.00225581
$131$	2.79790	0.244454	0.122227	−	0.992502i	$-0.460996\pi$
$131$	2.79790	0.244454	0.122227	+	0.992502i	$0.460996\pi$
$132$	0	0
$133$	2.90053	0.251508
$134$	−0.399199	−0.0344855
$135$	−1.83342	−0.157796
$136$	1.66456	0.142735
$137$	8.31687	0.710558	0.355279	−	0.934760i	$-0.384386\pi$
$137$	8.31687	0.710558	0.355279	+	0.934760i	$0.384386\pi$
$138$	−0.419294	−0.0356927
$139$	−21.0079	−1.78187	−0.890935	−	0.454131i	$-0.849950\pi$
$139$	−21.0079	−1.78187	−0.890935	+	0.454131i	$0.849950\pi$
$140$	−10.5612	−0.892585
$141$	−9.30165	−0.783340
$142$	−0.280762	−0.0235610
$143$	0	0
$144$	3.91603	0.326335
$145$	−0.107468	−0.00892470
$146$	−1.29013	−0.106772
$147$	−1.41309	−0.116549
$148$	9.62192	0.790917
$149$	3.65477	0.299410	0.149705	−	0.988731i	$-0.452168\pi$
$149$	3.65477	0.299410	0.149705	+	0.988731i	$0.452168\pi$
$150$	−0.194074	−0.0158461
$151$	7.89399	0.642404	0.321202	−	0.947011i	$-0.395913\pi$
$151$	7.89399	0.642404	0.321202	+	0.947011i	$0.395913\pi$
$152$	0.472107	0.0382929
$153$	3.52582	0.285045
$154$	0	0
$155$	−13.5546	−1.08873
$156$	−0.235223	−0.0188329
$157$	12.9439	1.03304	0.516518	−	0.856276i	$-0.327228\pi$
$157$	12.9439	1.03304	0.516518	+	0.856276i	$0.327228\pi$
$158$	1.25930	0.100184
$159$	2.88129	0.228501
$160$	−2.58153	−0.204087
$161$	−10.2681	−0.809240
$162$	−0.118442	−0.00930569
$163$	−4.12394	−0.323012	−0.161506	−	0.986872i	$-0.551635\pi$
$163$	−4.12394	−0.323012	−0.161506	+	0.986872i	$0.551635\pi$
$164$	17.8915	1.39709
$165$	0	0
$166$	1.30671	0.101420
$167$	−11.6083	−0.898274	−0.449137	−	0.893463i	$-0.648268\pi$
$167$	−11.6083	−0.898274	−0.449137	+	0.893463i	$0.648268\pi$
$168$	−1.36936	−0.105648
$169$	−12.9860	−0.998921
$170$	−0.765647	−0.0587224
$171$	1.00000	0.0764719
$172$	19.7382	1.50502
$173$	14.3167	1.08848	0.544240	−	0.838929i	$-0.316818\pi$
$173$	14.3167	1.08848	0.544240	+	0.838929i	$0.316818\pi$
$174$	−0.00694258	−0.000526316 0
$175$	−4.75269	−0.359270
$176$	0	0
$177$	13.3060	1.00014
$178$	1.41392	0.105977
$179$	2.17541	0.162598	0.0812989	−	0.996690i	$-0.474093\pi$
$179$	2.17541	0.162598	0.0812989	+	0.996690i	$0.474093\pi$
$180$	−3.64113	−0.271394
$181$	15.9423	1.18498	0.592491	−	0.805577i	$-0.298144\pi$
$181$	15.9423	1.18498	0.592491	+	0.805577i	$0.298144\pi$
$182$	0.0406902	0.00301616
$183$	−5.62925	−0.416126
$184$	−1.67129	−0.123209
$185$	−8.88283	−0.653079
$186$	−0.875646	−0.0642055
$187$	0	0
$188$	−18.4728	−1.34727
$189$	−2.90053	−0.210983
$190$	−0.217154	−0.0157540
$191$	5.37883	0.389198	0.194599	−	0.980883i	$-0.437659\pi$
$191$	5.37883	0.389198	0.194599	+	0.980883i	$0.437659\pi$
$192$	7.66528	0.553194
$193$	−14.7818	−1.06401	−0.532007	−	0.846740i	$-0.678562\pi$
$193$	−14.7818	−1.06401	−0.532007	+	0.846740i	$0.678562\pi$
$194$	0.272707	0.0195792
$195$	0.217154	0.0155508
$196$	−2.80635	−0.200454
$197$	13.6539	0.972800	0.486400	−	0.873736i	$-0.338310\pi$
$197$	13.6539	0.972800	0.486400	+	0.873736i	$0.338310\pi$
$198$	0	0
$199$	−7.49231	−0.531116	−0.265558	−	0.964095i	$-0.585556\pi$
$199$	−7.49231	−0.531116	−0.265558	+	0.964095i	$0.585556\pi$
$200$	−0.773574	−0.0547000
$201$	−3.37041	−0.237731
$202$	−0.687326	−0.0483601
$203$	−0.170017	−0.0119329
$204$	7.00217	0.490250
$205$	−16.5172	−1.15361
$206$	−0.829452	−0.0577906
$207$	−3.54008	−0.246052
$208$	−0.463822	−0.0321603
$209$	0	0
$210$	0.629863	0.0434647
$211$	−21.4286	−1.47520	−0.737602	−	0.675236i	$-0.764042\pi$
$211$	−21.4286	−1.47520	−0.737602	+	0.675236i	$0.764042\pi$
$212$	5.72216	0.392999
$213$	−2.37046	−0.162421
$214$	−1.22123	−0.0834816
$215$	−18.2221	−1.24273
$216$	−0.472107	−0.0321228
$217$	−21.4437	−1.45570
$218$	1.07127	0.0725557
$219$	−10.8925	−0.736045
$220$	0	0
$221$	−0.417605	−0.0280912
$222$	−0.573845	−0.0385140
$223$	10.4775	0.701623	0.350812	−	0.936446i	$-0.385906\pi$
$223$	10.4775	0.701623	0.350812	+	0.936446i	$0.385906\pi$
$224$	−4.08405	−0.272877
$225$	−1.63856	−0.109237
$226$	1.45574	0.0968346
$227$	−16.4746	−1.09346	−0.546728	−	0.837311i	$-0.684127\pi$
$227$	−16.4746	−1.09346	−0.546728	+	0.837311i	$0.684127\pi$
$228$	1.98597	0.131524
$229$	12.6714	0.837349	0.418675	−	0.908136i	$-0.362495\pi$
$229$	12.6714	0.837349	0.418675	+	0.908136i	$0.362495\pi$
$230$	0.768744	0.0506895
$231$	0	0
$232$	−0.0276729	−0.00181682
$233$	−8.31460	−0.544707	−0.272354	−	0.962197i	$-0.587802\pi$
$233$	−8.31460	−0.544707	−0.272354	+	0.962197i	$0.587802\pi$
$234$	0.0140285	0.000917073 0
$235$	17.0539	1.11247
$236$	26.4253	1.72014
$237$	10.6322	0.690634
$238$	−1.21128	−0.0785154
$239$	5.93440	0.383865	0.191932	−	0.981408i	$-0.438525\pi$
$239$	5.93440	0.383865	0.191932	+	0.981408i	$0.438525\pi$
$240$	−7.17973	−0.463450
$241$	5.25880	0.338749	0.169374	−	0.985552i	$-0.445825\pi$
$241$	5.25880	0.338749	0.169374	+	0.985552i	$0.445825\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	−11.1795	−0.715696
$245$	2.59079	0.165519
$246$	−1.06704	−0.0680318
$247$	−0.118442	−0.00753629
$248$	−3.49030	−0.221634
$249$	11.0325	0.699154
$250$	1.44159	0.0911743
$251$	25.4857	1.60865	0.804323	−	0.594193i	$-0.202528\pi$
$251$	25.4857	1.60865	0.804323	+	0.594193i	$0.202528\pi$
$252$	−5.76037	−0.362869
$253$	0	0
$254$	−0.527674	−0.0331092
$255$	−6.46432	−0.404811
$256$	14.8895	0.930593
$257$	−4.30259	−0.268388	−0.134194	−	0.990955i	$-0.542845\pi$
$257$	−4.30259	−0.268388	−0.134194	+	0.990955i	$0.542845\pi$
$258$	−1.17717	−0.0732876
$259$	−14.0529	−0.873205
$260$	0.431263	0.0267458
$261$	−0.0586159	−0.00362823
$262$	−0.331390	−0.0204733
$263$	−3.76883	−0.232396	−0.116198	−	0.993226i	$-0.537071\pi$
$263$	−3.76883	−0.232396	−0.116198	+	0.993226i	$0.537071\pi$
$264$	0	0
$265$	−5.28262	−0.324509
$266$	−0.343545	−0.0210641
$267$	11.9376	0.730570
$268$	−6.69354	−0.408873
$269$	−11.5259	−0.702750	−0.351375	−	0.936235i	$-0.614286\pi$
$269$	−11.5259	−0.702750	−0.351375	+	0.936235i	$0.614286\pi$
$270$	0.217154	0.0132156
$271$	−1.49560	−0.0908512	−0.0454256	−	0.998968i	$-0.514464\pi$
$271$	−1.49560	−0.0908512	−0.0454256	+	0.998968i	$0.514464\pi$
$272$	13.8072	0.837184
$273$	0.343545	0.0207923
$274$	−0.985068	−0.0595101
$275$	0	0
$276$	−7.03049	−0.423186
$277$	1.74878	0.105074	0.0525370	−	0.998619i	$-0.483269\pi$
$277$	1.74878	0.105074	0.0525370	+	0.998619i	$0.483269\pi$
$278$	2.48822	0.149234
$279$	−7.39303	−0.442609
$280$	2.51062	0.150038
$281$	−20.6292	−1.23064	−0.615318	−	0.788279i	$-0.710972\pi$
$281$	−20.6292	−1.23064	−0.615318	+	0.788279i	$0.710972\pi$
$282$	1.10171	0.0656057
$283$	−28.1002	−1.67039	−0.835193	−	0.549957i	$-0.814644\pi$
$283$	−28.1002	−1.67039	−0.835193	+	0.549957i	$0.814644\pi$
$284$	−4.70766	−0.279348
$285$	−1.83342	−0.108603
$286$	0	0
$287$	−26.1307	−1.54245
$288$	−1.40804	−0.0829693
$289$	−4.56861	−0.268742
$290$	0.0127287	0.000747455 0
$291$	2.30245	0.134972
$292$	−21.6321	−1.26592
$293$	−8.19850	−0.478961	−0.239481	−	0.970901i	$-0.576977\pi$
$293$	−8.19850	−0.478961	−0.239481	+	0.970901i	$0.576977\pi$
$294$	0.167369	0.00976116
$295$	−24.3955	−1.42036
$296$	−2.28733	−0.132948
$297$	0	0
$298$	−0.432878	−0.0250760
$299$	0.419294	0.0242484
$300$	−3.25413	−0.187877
$301$	−28.8279	−1.66161
$302$	−0.934981	−0.0538021
$303$	−5.80306	−0.333377
$304$	3.91603	0.224599
$305$	10.3208	0.590968
$306$	−0.417605	−0.0238729
$307$	−13.3073	−0.759487	−0.379744	−	0.925092i	$-0.623988\pi$
$307$	−13.3073	−0.759487	−0.379744	+	0.925092i	$0.623988\pi$
$308$	0	0
$309$	−7.00302	−0.398388
$310$	1.60543	0.0911823
$311$	31.5423	1.78860	0.894299	−	0.447470i	$-0.147675\pi$
$311$	31.5423	1.78860	0.894299	+	0.447470i	$0.147675\pi$
$312$	0.0559173	0.00316569
$313$	6.33158	0.357882	0.178941	−	0.983860i	$-0.442733\pi$
$313$	6.33158	0.357882	0.178941	+	0.983860i	$0.442733\pi$
$314$	−1.53310	−0.0865181
$315$	5.31790	0.299630
$316$	21.1152	1.18782
$317$	23.3234	1.30997	0.654987	−	0.755641i	$-0.272674\pi$
$317$	23.3234	1.30997	0.654987	+	0.755641i	$0.272674\pi$
$318$	−0.341266	−0.0191372
$319$	0	0
$320$	−14.0537	−0.785626
$321$	−10.3108	−0.575492
$322$	1.21618	0.0677748
$323$	3.52582	0.196182
$324$	−1.98597	−0.110332
$325$	0.194074	0.0107653
$326$	0.488448	0.0270526
$327$	9.04469	0.500173
$328$	−4.25318	−0.234843
$329$	26.9797	1.48744
$330$	0	0
$331$	10.5241	0.578455	0.289227	−	0.957260i	$-0.406602\pi$
$331$	10.5241	0.578455	0.289227	+	0.957260i	$0.406602\pi$
$332$	21.9102	1.20248
$333$	−4.84494	−0.265501
$334$	1.37491	0.0752315
$335$	6.17939	0.337616
$336$	−11.3586	−0.619660
$337$	−20.8955	−1.13825	−0.569124	−	0.822251i	$-0.692718\pi$
$337$	−20.8955	−1.13825	−0.569124	+	0.822251i	$0.692718\pi$
$338$	1.53809	0.0836608
$339$	12.2908	0.667543
$340$	−12.8379	−0.696236
$341$	0	0
$342$	−0.118442	−0.00640461
$343$	−16.2050	−0.874989
$344$	−4.69218	−0.252985
$345$	6.49046	0.349435
$346$	−1.69570	−0.0911615
$347$	−6.45651	−0.346603	−0.173302	−	0.984869i	$-0.555444\pi$
$347$	−6.45651	−0.346603	−0.173302	+	0.984869i	$0.555444\pi$
$348$	−0.116409	−0.00624020
$349$	25.3975	1.35950	0.679748	−	0.733446i	$-0.262089\pi$
$349$	25.3975	1.35950	0.679748	+	0.733446i	$0.262089\pi$
$350$	0.562919	0.0300893
$351$	0.118442	0.00632197
$352$	0	0
$353$	−25.5676	−1.36083	−0.680413	−	0.732829i	$-0.738200\pi$
$353$	−25.5676	−1.36083	−0.680413	+	0.732829i	$0.738200\pi$
$354$	−1.57599	−0.0837629
$355$	4.34605	0.230665
$356$	23.7078	1.25651
$357$	−10.2267	−0.541257
$358$	−0.257660	−0.0136178
$359$	−29.4298	−1.55325	−0.776624	−	0.629965i	$-0.783069\pi$
$359$	−29.4298	−1.55325	−0.776624	+	0.629965i	$0.783069\pi$
$360$	0.865571	0.0456196
$361$	1.00000	0.0526316
$362$	−1.88824	−0.0992437
$363$	0	0
$364$	0.682271	0.0357607
$365$	19.9705	1.04530
$366$	0.666740	0.0348511
$367$	−4.69002	−0.244817	−0.122409	−	0.992480i	$-0.539062\pi$
$367$	−4.69002	−0.244817	−0.122409	+	0.992480i	$0.539062\pi$
$368$	−13.8630	−0.722661
$369$	−9.00894	−0.468987
$370$	1.05210	0.0546961
$371$	−8.35727	−0.433888
$372$	−14.6824	−0.761245
$373$	4.85976	0.251629	0.125814	−	0.992054i	$-0.459846\pi$
$373$	4.85976	0.251629	0.125814	+	0.992054i	$0.459846\pi$
$374$	0	0
$375$	12.1713	0.628523
$376$	4.39137	0.226468
$377$	0.00694258	0.000357561 0
$378$	0.343545	0.0176700
$379$	6.45445	0.331543	0.165771	−	0.986164i	$-0.446989\pi$
$379$	6.45445	0.331543	0.165771	+	0.986164i	$0.446989\pi$
$380$	−3.64113	−0.186786
$381$	−4.45512	−0.228243
$382$	−0.637079	−0.0325958
$383$	27.0398	1.38167	0.690835	−	0.723012i	$-0.257243\pi$
$383$	27.0398	1.38167	0.690835	+	0.723012i	$0.257243\pi$
$384$	−3.72396	−0.190038
$385$	0	0
$386$	1.75078	0.0891124
$387$	−9.93882	−0.505218
$388$	4.57260	0.232138
$389$	−17.1214	−0.868089	−0.434044	−	0.900891i	$-0.642914\pi$
$389$	−17.1214	−0.868089	−0.434044	+	0.900891i	$0.642914\pi$
$390$	−0.0257202	−0.00130239
$391$	−12.4817	−0.631225
$392$	0.667128	0.0336950
$393$	−2.79790	−0.141136
$394$	−1.61720	−0.0814732
$395$	−19.4933	−0.980814
$396$	0	0
$397$	21.1664	1.06231	0.531157	−	0.847274i	$-0.321758\pi$
$397$	21.1664	1.06231	0.531157	+	0.847274i	$0.321758\pi$
$398$	0.887404	0.0444816
$399$	−2.90053	−0.145208
$400$	−6.41664	−0.320832
$401$	−28.6350	−1.42996	−0.714981	−	0.699144i	$-0.753565\pi$
$401$	−28.6350	−1.42996	−0.714981	+	0.699144i	$0.753565\pi$
$402$	0.399199	0.0199102
$403$	0.875646	0.0436190
$404$	−11.5247	−0.573376
$405$	1.83342	0.0911035
$406$	0.0201372	0.000999392 0
$407$	0	0
$408$	−1.66456	−0.0824081
$409$	−3.18177	−0.157328	−0.0786641	−	0.996901i	$-0.525065\pi$
$409$	−3.18177	−0.157328	−0.0786641	+	0.996901i	$0.525065\pi$
$410$	1.95633	0.0966163
$411$	−8.31687	−0.410241
$412$	−13.9078	−0.685188
$413$	−38.5945	−1.89911
$414$	0.419294	0.0206072
$415$	−20.2272	−0.992913
$416$	0.166771	0.00817660
$417$	21.0079	1.02876
$418$	0	0
$419$	−25.2231	−1.23223	−0.616114	−	0.787657i	$-0.711294\pi$
$419$	−25.2231	−1.23223	−0.616114	+	0.787657i	$0.711294\pi$
$420$	10.5612	0.515334
$421$	14.9814	0.730148	0.365074	−	0.930979i	$-0.381044\pi$
$421$	14.9814	0.730148	0.365074	+	0.930979i	$0.381044\pi$
$422$	2.53805	0.123550
$423$	9.30165	0.452262
$424$	−1.36028	−0.0660608
$425$	−5.77726	−0.280238
$426$	0.280762	0.0136030
$427$	16.3278	0.790159
$428$	−20.4769	−0.989790
$429$	0	0
$430$	2.15826	0.104080
$431$	7.99053	0.384890	0.192445	−	0.981308i	$-0.438358\pi$
$431$	7.99053	0.384890	0.192445	+	0.981308i	$0.438358\pi$
$432$	−3.91603	−0.188410
$433$	25.2031	1.21118	0.605592	−	0.795775i	$-0.292936\pi$
$433$	25.2031	1.21118	0.605592	+	0.795775i	$0.292936\pi$
$434$	2.53984	0.121916
$435$	0.107468	0.00515268
$436$	17.9625	0.860248
$437$	−3.54008	−0.169345
$438$	1.29013	0.0616446
$439$	14.6035	0.696986	0.348493	−	0.937311i	$-0.386693\pi$
$439$	14.6035	0.696986	0.348493	+	0.937311i	$0.386693\pi$
$440$	0	0
$441$	1.41309	0.0672899
$442$	0.0494620	0.00235267
$443$	14.5766	0.692555	0.346277	−	0.938132i	$-0.387446\pi$
$443$	14.5766	0.692555	0.346277	+	0.938132i	$0.387446\pi$
$444$	−9.62192	−0.456636
$445$	−21.8867	−1.03753
$446$	−1.24097	−0.0587618
$447$	−3.65477	−0.172865
$448$	−22.2334	−1.05043
$449$	38.1066	1.79836	0.899181	−	0.437578i	$-0.144163\pi$
$449$	38.1066	1.79836	0.899181	+	0.437578i	$0.144163\pi$
$450$	0.194074	0.00914875
$451$	0	0
$452$	24.4091	1.14811
$453$	−7.89399	−0.370892
$454$	1.95128	0.0915782
$455$	−0.629863	−0.0295285
$456$	−0.472107	−0.0221084
$457$	−13.3399	−0.624013	−0.312006	−	0.950080i	$-0.601001\pi$
$457$	−13.3399	−0.624013	−0.312006	+	0.950080i	$0.601001\pi$
$458$	−1.50083	−0.0701290
$459$	−3.52582	−0.164571
$460$	12.8899	0.600993
$461$	−19.8340	−0.923760	−0.461880	−	0.886942i	$-0.652825\pi$
$461$	−19.8340	−0.923760	−0.461880	+	0.886942i	$0.652825\pi$
$462$	0	0
$463$	−27.9282	−1.29793	−0.648966	−	0.760818i	$-0.724798\pi$
$463$	−27.9282	−1.29793	−0.648966	+	0.760818i	$0.724798\pi$
$464$	−0.229541	−0.0106562
$465$	13.5546	0.628578
$466$	0.984798	0.0456199
$467$	−8.57031	−0.396587	−0.198293	−	0.980143i	$-0.563540\pi$
$467$	−8.57031	−0.396587	−0.198293	+	0.980143i	$0.563540\pi$
$468$	0.235223	0.0108732
$469$	9.77599	0.451413
$470$	−2.01989	−0.0931708
$471$	−12.9439	−0.596424
$472$	−6.28185	−0.289146
$473$	0	0
$474$	−1.25930	−0.0578414
$475$	−1.63856	−0.0751822
$476$	−20.3100	−0.930909
$477$	−2.88129	−0.131925
$478$	−0.702883	−0.0321491
$479$	−18.4518	−0.843085	−0.421543	−	0.906809i	$-0.638511\pi$
$479$	−18.4518	−0.843085	−0.421543	+	0.906809i	$0.638511\pi$
$480$	2.58153	0.117830
$481$	0.573845	0.0261651
$482$	−0.622863	−0.0283706
$483$	10.2681	0.467215
$484$	0	0
$485$	−4.22136	−0.191682
$486$	0.118442	0.00537264
$487$	2.34389	0.106212	0.0531060	−	0.998589i	$-0.483088\pi$
$487$	2.34389	0.106212	0.0531060	+	0.998589i	$0.483088\pi$
$488$	2.65761	0.120304
$489$	4.12394	0.186491
$490$	−0.306858	−0.0138624
$491$	−11.8598	−0.535226	−0.267613	−	0.963526i	$-0.586235\pi$
$491$	−11.8598	−0.535226	−0.267613	+	0.963526i	$0.586235\pi$
$492$	−17.8915	−0.806611
$493$	−0.206669	−0.00930789
$494$	0.0140285	0.000631173 0
$495$	0	0
$496$	−28.9513	−1.29995
$497$	6.87559	0.308412
$498$	−1.30671	−0.0585550
$499$	−28.1695	−1.26104	−0.630521	−	0.776172i	$-0.717159\pi$
$499$	−28.1695	−1.26104	−0.630521	+	0.776172i	$0.717159\pi$
$500$	24.1718	1.08100
$501$	11.6083	0.518619
$502$	−3.01858	−0.134726
$503$	−27.4292	−1.22301	−0.611503	−	0.791242i	$-0.709435\pi$
$503$	−27.4292	−1.22301	−0.611503	+	0.791242i	$0.709435\pi$
$504$	1.36936	0.0609962
$505$	10.6395	0.473450
$506$	0	0
$507$	12.9860	0.576727
$508$	−8.84775	−0.392555
$509$	−43.8230	−1.94242	−0.971210	−	0.238223i	$-0.923435\pi$
$509$	−43.8230	−1.94242	−0.971210	+	0.238223i	$0.923435\pi$
$510$	0.765647	0.0339034
$511$	31.5939	1.39763
$512$	−9.21147	−0.407093
$513$	−1.00000	−0.0441511
$514$	0.509608	0.0224779
$515$	12.8395	0.565776
$516$	−19.7382	−0.868926
$517$	0	0
$518$	1.66446	0.0731320
$519$	−14.3167	−0.628435
$520$	−0.102520	−0.00449580
$521$	5.33941	0.233924	0.116962	−	0.993136i	$-0.462684\pi$
$521$	5.33941	0.233924	0.116962	+	0.993136i	$0.462684\pi$
$522$	0.00694258	0.000303869 0
$523$	36.7522	1.60706	0.803530	−	0.595265i	$-0.202953\pi$
$523$	36.7522	1.60706	0.803530	+	0.595265i	$0.202953\pi$
$524$	−5.55656	−0.242739
$525$	4.75269	0.207424
$526$	0.446388	0.0194635
$527$	−26.0665	−1.13547
$528$	0	0
$529$	−10.4678	−0.455124
$530$	0.625685	0.0271780
$531$	−13.3060	−0.577431
$532$	−5.76037	−0.249744
$533$	1.06704	0.0462185
$534$	−1.41392	−0.0611861
$535$	18.9040	0.817293
$536$	1.59119	0.0687291
$537$	−2.17541	−0.0938759
$538$	1.36516	0.0588561
$539$	0	0
$540$	3.64113	0.156689
$541$	−9.45964	−0.406701	−0.203351	−	0.979106i	$-0.565183\pi$
$541$	−9.45964	−0.406701	−0.203351	+	0.979106i	$0.565183\pi$
$542$	0.177142	0.00760890
$543$	−15.9423	−0.684150
$544$	−4.96448	−0.212850
$545$	−16.5828	−0.710327
$546$	−0.0406902	−0.00174138
$547$	40.1673	1.71743	0.858715	−	0.512454i	$-0.171264\pi$
$547$	40.1673	1.71743	0.858715	+	0.512454i	$0.171264\pi$
$548$	−16.5171	−0.705574
$549$	5.62925	0.240251
$550$	0	0
$551$	−0.0586159	−0.00249712
$552$	1.67129	0.0711350
$553$	−30.8390	−1.31141
$554$	−0.207129	−0.00880008
$555$	8.88283	0.377055
$556$	41.7212	1.76937
$557$	−7.44492	−0.315451	−0.157726	−	0.987483i	$-0.550416\pi$
$557$	−7.44492	−0.315451	−0.157726	+	0.987483i	$0.550416\pi$
$558$	0.875646	0.0370691
$559$	1.17717	0.0497891
$560$	20.8250	0.880019
$561$	0	0
$562$	2.44337	0.103067
$563$	−9.34015	−0.393640	−0.196820	−	0.980440i	$-0.563061\pi$
$563$	−9.34015	−0.393640	−0.196820	+	0.980440i	$0.563061\pi$
$564$	18.4728	0.777846
$565$	−22.5342	−0.948020
$566$	3.32825	0.139897
$567$	2.90053	0.121811
$568$	1.11911	0.0469568
$569$	−31.7113	−1.32941	−0.664704	−	0.747107i	$-0.731442\pi$
$569$	−31.7113	−1.32941	−0.664704	+	0.747107i	$0.731442\pi$
$570$	0.217154	0.00909560
$571$	3.24336	0.135731	0.0678653	−	0.997694i	$-0.478381\pi$
$571$	3.24336	0.135731	0.0678653	+	0.997694i	$0.478381\pi$
$572$	0	0
$573$	−5.37883	−0.224704
$574$	3.09498	0.129182
$575$	5.80063	0.241903
$576$	−7.66528	−0.319387
$577$	−16.2972	−0.678463	−0.339231	−	0.940703i	$-0.610167\pi$
$577$	−16.2972	−0.678463	−0.339231	+	0.940703i	$0.610167\pi$
$578$	0.541116	0.0225074
$579$	14.7818	0.614309
$580$	0.213428	0.00886210
$581$	−32.0000	−1.32758
$582$	−0.272707	−0.0113041
$583$	0	0
$584$	5.14241	0.212794
$585$	−0.217154	−0.00897823
$586$	0.971047	0.0401136
$587$	−34.2542	−1.41382	−0.706912	−	0.707301i	$-0.749912\pi$
$587$	−34.2542	−1.41382	−0.706912	+	0.707301i	$0.749912\pi$
$588$	2.80635	0.115732
$589$	−7.39303	−0.304625
$590$	2.88946	0.118957
$591$	−13.6539	−0.561646
$592$	−18.9729	−0.779782
$593$	−11.9214	−0.489551	−0.244776	−	0.969580i	$-0.578714\pi$
$593$	−11.9214	−0.489551	−0.244776	+	0.969580i	$0.578714\pi$
$594$	0	0
$595$	18.7500	0.768673
$596$	−7.25827	−0.297310
$597$	7.49231	0.306640
$598$	−0.0496621	−0.00203083
$599$	−35.7926	−1.46245	−0.731223	−	0.682139i	$-0.761050\pi$
$599$	−35.7926	−1.46245	−0.731223	+	0.682139i	$0.761050\pi$
$600$	0.773574	0.0315810
$601$	19.3338	0.788642	0.394321	−	0.918973i	$-0.370980\pi$
$601$	19.3338	0.788642	0.394321	+	0.918973i	$0.370980\pi$
$602$	3.41443	0.139162
$603$	3.37041	0.137254
$604$	−15.6772	−0.637898
$605$	0	0
$606$	0.687326	0.0279207
$607$	−4.34106	−0.176198	−0.0880992	−	0.996112i	$-0.528079\pi$
$607$	−4.34106	−0.176198	−0.0880992	+	0.996112i	$0.528079\pi$
$608$	−1.40804	−0.0571034
$609$	0.170017	0.00688944
$610$	−1.22242	−0.0494942
$611$	−1.10171	−0.0445703
$612$	−7.00217	−0.283046
$613$	25.7765	1.04110	0.520552	−	0.853830i	$-0.325726\pi$
$613$	25.7765	1.04110	0.520552	+	0.853830i	$0.325726\pi$
$614$	1.57614	0.0636080
$615$	16.5172	0.666038
$616$	0	0
$617$	24.4016	0.982370	0.491185	−	0.871055i	$-0.336564\pi$
$617$	24.4016	0.982370	0.491185	+	0.871055i	$0.336564\pi$
$618$	0.829452	0.0333654
$619$	−36.3458	−1.46086	−0.730431	−	0.682987i	$-0.760681\pi$
$619$	−36.3458	−1.46086	−0.730431	+	0.682987i	$0.760681\pi$
$620$	26.9190	1.08109
$621$	3.54008	0.142058
$622$	−3.73593	−0.149797
$623$	−34.6254	−1.38724
$624$	0.463822	0.0185677
$625$	−14.1223	−0.564893
$626$	−0.749926	−0.0299731
$627$	0	0
$628$	−25.7062	−1.02579
$629$	−17.0824	−0.681119
$630$	−0.629863	−0.0250944
$631$	−28.5702	−1.13736	−0.568681	−	0.822558i	$-0.692546\pi$
$631$	−28.5702	−1.13736	−0.568681	+	0.822558i	$0.692546\pi$
$632$	−5.01952	−0.199666
$633$	21.4286	0.851710
$634$	−2.76247	−0.109712
$635$	8.16813	0.324142
$636$	−5.72216	−0.226898
$637$	−0.167369	−0.00663140
$638$	0	0
$639$	2.37046	0.0937739
$640$	6.82760	0.269885
$641$	−33.6278	−1.32822	−0.664108	−	0.747636i	$-0.731189\pi$
$641$	−33.6278	−1.32822	−0.664108	+	0.747636i	$0.731189\pi$
$642$	1.22123	0.0481981
$643$	33.8028	1.33305	0.666527	−	0.745481i	$-0.267780\pi$
$643$	33.8028	1.33305	0.666527	+	0.745481i	$0.267780\pi$
$644$	20.3922	0.803564
$645$	18.2221	0.717493
$646$	−0.417605	−0.0164305
$647$	8.52256	0.335056	0.167528	−	0.985867i	$-0.446421\pi$
$647$	8.52256	0.335056	0.167528	+	0.985867i	$0.446421\pi$
$648$	0.472107	0.0185461
$649$	0	0
$650$	−0.0229866	−0.000901607 0
$651$	21.4437	0.840446
$652$	8.19003	0.320746
$653$	25.7025	1.00582	0.502908	−	0.864340i	$-0.332263\pi$
$653$	25.7025	1.00582	0.502908	+	0.864340i	$0.332263\pi$
$654$	−1.07127	−0.0418901
$655$	5.12974	0.200436
$656$	−35.2792	−1.37742
$657$	10.8925	0.424956
$658$	−3.19553	−0.124575
$659$	−30.0864	−1.17200	−0.586001	−	0.810311i	$-0.699298\pi$
$659$	−30.0864	−1.17200	−0.586001	+	0.810311i	$0.699298\pi$
$660$	0	0
$661$	29.8953	1.16279	0.581396	−	0.813621i	$-0.302507\pi$
$661$	29.8953	1.16279	0.581396	+	0.813621i	$0.302507\pi$
$662$	−1.24649	−0.0484463
$663$	0.417605	0.0162184
$664$	−5.20850	−0.202129
$665$	5.31790	0.206219
$666$	0.573845	0.0222360
$667$	0.207505	0.00803461
$668$	23.0537	0.891973
$669$	−10.4775	−0.405082
$670$	−0.731900	−0.0282758
$671$	0	0
$672$	4.08405	0.157546
$673$	−8.47423	−0.326658	−0.163329	−	0.986572i	$-0.552223\pi$
$673$	−8.47423	−0.326658	−0.163329	+	0.986572i	$0.552223\pi$
$674$	2.47490	0.0953297
$675$	1.63856	0.0630681
$676$	25.7898	0.991914
$677$	−42.3588	−1.62798	−0.813991	−	0.580878i	$-0.802709\pi$
$677$	−42.3588	−1.62798	−0.813991	+	0.580878i	$0.802709\pi$
$678$	−1.45574	−0.0559075
$679$	−6.67833	−0.256291
$680$	3.05185	0.117033
$681$	16.4746	0.631307
$682$	0	0
$683$	9.47454	0.362533	0.181267	−	0.983434i	$-0.441980\pi$
$683$	9.47454	0.362533	0.181267	+	0.983434i	$0.441980\pi$
$684$	−1.98597	−0.0759355
$685$	15.2483	0.582609
$686$	1.91936	0.0732814
$687$	−12.6714	−0.483444
$688$	−38.9207	−1.48384
$689$	0.341266	0.0130012
$690$	−0.768744	−0.0292656
$691$	13.0056	0.494757	0.247379	−	0.968919i	$-0.420431\pi$
$691$	13.0056	0.494757	0.247379	+	0.968919i	$0.420431\pi$
$692$	−28.4326	−1.08085
$693$	0	0
$694$	0.764722	0.0290284
$695$	−38.5164	−1.46101
$696$	0.0276729	0.00104894
$697$	−31.7639	−1.20314
$698$	−3.00813	−0.113859
$699$	8.31460	0.314487
$700$	9.43871	0.356750
$701$	−15.5410	−0.586976	−0.293488	−	0.955963i	$-0.594816\pi$
$701$	−15.5410	−0.586976	−0.293488	+	0.955963i	$0.594816\pi$
$702$	−0.0140285	−0.000529472 0
$703$	−4.84494	−0.182730
$704$	0	0
$705$	−17.0539	−0.642286
$706$	3.02828	0.113971
$707$	16.8320	0.633031
$708$	−26.4253	−0.993125
$709$	35.8661	1.34698	0.673490	−	0.739196i	$-0.264795\pi$
$709$	35.8661	1.34698	0.673490	+	0.739196i	$0.264795\pi$
$710$	−0.514755	−0.0193184
$711$	−10.6322	−0.398738
$712$	−5.63583	−0.211212
$713$	26.1719	0.980146
$714$	1.21128	0.0453309
$715$	0	0
$716$	−4.32030	−0.161457
$717$	−5.93440	−0.221624
$718$	3.48573	0.130086
$719$	−4.08302	−0.152271	−0.0761355	−	0.997097i	$-0.524258\pi$
$719$	−4.08302	−0.152271	−0.0761355	+	0.997097i	$0.524258\pi$
$720$	7.17973	0.267573
$721$	20.3125	0.756476
$722$	−0.118442	−0.00440796
$723$	−5.25880	−0.195577
$724$	−31.6610	−1.17667
$725$	0.0960455	0.00356704
$726$	0	0
$727$	36.3803	1.34927	0.674635	−	0.738151i	$-0.264301\pi$
$727$	36.3803	1.34927	0.674635	+	0.738151i	$0.264301\pi$
$728$	−0.162190	−0.00601116
$729$	1.00000	0.0370370
$730$	−2.36535	−0.0875454
$731$	−35.0425	−1.29609
$732$	11.1795	0.413208
$733$	−22.5237	−0.831932	−0.415966	−	0.909380i	$-0.636557\pi$
$733$	−22.5237	−0.831932	−0.415966	+	0.909380i	$0.636557\pi$
$734$	0.555496	0.0205037
$735$	−2.59079	−0.0955626
$736$	4.98456	0.183733
$737$	0	0
$738$	1.06704	0.0392782
$739$	−28.3381	−1.04243	−0.521217	−	0.853424i	$-0.674522\pi$
$739$	−28.3381	−1.04243	−0.521217	+	0.853424i	$0.674522\pi$
$740$	17.6410	0.648498
$741$	0.118442	0.00435108
$742$	0.989852	0.0363386
$743$	6.39794	0.234718	0.117359	−	0.993090i	$-0.462557\pi$
$743$	6.39794	0.234718	0.117359	+	0.993090i	$0.462557\pi$
$744$	3.49030	0.127961
$745$	6.70074	0.245496
$746$	−0.575600	−0.0210742
$747$	−11.0325	−0.403657
$748$	0	0
$749$	29.9068	1.09277
$750$	−1.44159	−0.0526395
$751$	−30.5006	−1.11298	−0.556492	−	0.830853i	$-0.687853\pi$
$751$	−30.5006	−1.11298	−0.556492	+	0.830853i	$0.687853\pi$
$752$	36.4255	1.32830
$753$	−25.4857	−0.928752
$754$	−0.000822294 0	−2.99462e−5 0
$755$	14.4730	0.526727
$756$	5.76037	0.209503
$757$	34.6488	1.25933	0.629665	−	0.776866i	$-0.283192\pi$
$757$	34.6488	1.25933	0.629665	+	0.776866i	$0.283192\pi$
$758$	−0.764478	−0.0277671
$759$	0	0
$760$	0.865571	0.0313976
$761$	20.3899	0.739134	0.369567	−	0.929204i	$-0.379506\pi$
$761$	20.3899	0.739134	0.369567	+	0.929204i	$0.379506\pi$
$762$	0.527674	0.0191156
$763$	−26.2344	−0.949750
$764$	−10.6822	−0.386468
$765$	6.46432	0.233718
$766$	−3.20265	−0.115717
$767$	1.57599	0.0569057
$768$	−14.8895	−0.537278
$769$	30.2294	1.09010	0.545050	−	0.838403i	$-0.316511\pi$
$769$	30.2294	1.09010	0.545050	+	0.838403i	$0.316511\pi$
$770$	0	0
$771$	4.30259	0.154954
$772$	29.3561	1.05655
$773$	20.6425	0.742459	0.371229	−	0.928541i	$-0.378936\pi$
$773$	20.6425	0.742459	0.371229	+	0.928541i	$0.378936\pi$
$774$	1.17717	0.0423126
$775$	12.1139	0.435145
$776$	−1.08700	−0.0390211
$777$	14.0529	0.504145
$778$	2.02789	0.0727035
$779$	−9.00894	−0.322779
$780$	−0.431263	−0.0154417
$781$	0	0
$782$	1.47835	0.0528659
$783$	0.0586159	0.00209476
$784$	5.53369	0.197632
$785$	23.7317	0.847020
$786$	0.331390	0.0118203
$787$	6.75105	0.240649	0.120324	−	0.992735i	$-0.461607\pi$
$787$	6.75105	0.240649	0.120324	+	0.992735i	$0.461607\pi$
$788$	−27.1163	−0.965977
$789$	3.76883	0.134174
$790$	2.30883	0.0821443
$791$	−35.6498	−1.26756
$792$	0	0
$793$	−0.666740	−0.0236766
$794$	−2.50700	−0.0889700
$795$	5.28262	0.187355
$796$	14.8795	0.527390
$797$	32.4238	1.14851	0.574256	−	0.818676i	$-0.305292\pi$
$797$	32.4238	1.14851	0.574256	+	0.818676i	$0.305292\pi$
$798$	0.343545	0.0121614
$799$	32.7959	1.16024
$800$	2.30715	0.0815700
$801$	−11.9376	−0.421795
$802$	3.39159	0.119761
$803$	0	0
$804$	6.69354	0.236063
$805$	−18.8258	−0.663522
$806$	−0.103713	−0.00365315
$807$	11.5259	0.405733
$808$	2.73966	0.0963810
$809$	29.5856	1.04018	0.520088	−	0.854113i	$-0.325899\pi$
$809$	29.5856	1.04018	0.520088	+	0.854113i	$0.325899\pi$
$810$	−0.217154	−0.00763003
$811$	−33.3643	−1.17158	−0.585789	−	0.810464i	$-0.699215\pi$
$811$	−33.3643	−1.17158	−0.585789	+	0.810464i	$0.699215\pi$
$812$	0.337649	0.0118492
$813$	1.49560	0.0524530
$814$	0	0
$815$	−7.56093	−0.264848
$816$	−13.8072	−0.483348
$817$	−9.93882	−0.347715
$818$	0.376855	0.0131764
$819$	−0.343545	−0.0120044
$820$	32.8027	1.14552
$821$	20.4307	0.713035	0.356518	−	0.934289i	$-0.383964\pi$
$821$	20.4307	0.713035	0.356518	+	0.934289i	$0.383964\pi$
$822$	0.985068	0.0343582
$823$	−18.4284	−0.642374	−0.321187	−	0.947016i	$-0.604082\pi$
$823$	−18.4284	−0.642374	−0.321187	+	0.947016i	$0.604082\pi$
$824$	3.30617	0.115176
$825$	0	0
$826$	4.57121	0.159053
$827$	−42.1448	−1.46552	−0.732760	−	0.680487i	$-0.761768\pi$
$827$	−42.1448	−1.46552	−0.732760	+	0.680487i	$0.761768\pi$
$828$	7.03049	0.244327
$829$	41.0101	1.42434	0.712170	−	0.702007i	$-0.247712\pi$
$829$	41.0101	1.42434	0.712170	+	0.702007i	$0.247712\pi$
$830$	2.39575	0.0831577
$831$	−1.74878	−0.0606646
$832$	0.907892	0.0314755
$833$	4.98229	0.172626
$834$	−2.48822	−0.0861601
$835$	−21.2828	−0.736523
$836$	0	0
$837$	7.39303	0.255541
$838$	2.98747	0.103201
$839$	−20.0533	−0.692316	−0.346158	−	0.938176i	$-0.612514\pi$
$839$	−20.0533	−0.692316	−0.346158	+	0.938176i	$0.612514\pi$
$840$	−2.51062	−0.0866245
$841$	−28.9966	−0.999882
$842$	−1.77443	−0.0611508
$843$	20.6292	0.710508
$844$	42.5565	1.46486
$845$	−23.8088	−0.819047
$846$	−1.10171	−0.0378774
$847$	0	0
$848$	−11.2832	−0.387467
$849$	28.1002	0.964398
$850$	0.684270	0.0234703
$851$	17.1515	0.587945
$852$	4.70766	0.161282
$853$	−16.5563	−0.566879	−0.283439	−	0.958990i	$-0.591475\pi$
$853$	−16.5563	−0.566879	−0.283439	+	0.958990i	$0.591475\pi$
$854$	−1.93390	−0.0661768
$855$	1.83342	0.0627018
$856$	4.86779	0.166378
$857$	18.1051	0.618459	0.309229	−	0.950987i	$-0.399929\pi$
$857$	18.1051	0.618459	0.309229	+	0.950987i	$0.399929\pi$
$858$	0	0
$859$	50.6794	1.72916	0.864580	−	0.502495i	$-0.167584\pi$
$859$	50.6794	1.72916	0.864580	+	0.502495i	$0.167584\pi$
$860$	36.1885	1.23402
$861$	26.1307	0.890533
$862$	−0.946415	−0.0322350
$863$	34.7723	1.18366	0.591832	−	0.806061i	$-0.298405\pi$
$863$	34.7723	1.18366	0.591832	+	0.806061i	$0.298405\pi$
$864$	1.40804	0.0479023
$865$	26.2486	0.892480
$866$	−2.98511	−0.101438
$867$	4.56861	0.155158
$868$	42.5866	1.44548
$869$	0	0
$870$	−0.0127287	−0.000431543 0
$871$	−0.399199	−0.0135263
$872$	−4.27006	−0.144602
$873$	−2.30245	−0.0779261
$874$	0.419294	0.0141828
$875$	−35.3032	−1.19347
$876$	21.6321	0.730882
$877$	−2.09613	−0.0707814	−0.0353907	−	0.999374i	$-0.511268\pi$
$877$	−2.09613	−0.0707814	−0.0353907	+	0.999374i	$0.511268\pi$
$878$	−1.72967	−0.0583734
$879$	8.19850	0.276529
$880$	0	0
$881$	−20.9706	−0.706519	−0.353259	−	0.935525i	$-0.614927\pi$
$881$	−20.9706	−0.706519	−0.353259	+	0.935525i	$0.614927\pi$
$882$	−0.167369	−0.00563561
$883$	55.8049	1.87798	0.938992	−	0.343938i	$-0.111761\pi$
$883$	55.8049	1.87798	0.938992	+	0.343938i	$0.111761\pi$
$884$	0.829352	0.0278941
$885$	24.3955	0.820047
$886$	−1.72648	−0.0580023
$887$	24.9321	0.837139	0.418569	−	0.908185i	$-0.362532\pi$
$887$	24.9321	0.837139	0.418569	+	0.908185i	$0.362532\pi$
$888$	2.28733	0.0767578
$889$	12.9222	0.433398
$890$	2.59231	0.0868943
$891$	0	0
$892$	−20.8080	−0.696702
$893$	9.30165	0.311268
$894$	0.432878	0.0144776
$895$	3.98845	0.133319
$896$	10.8015	0.360852
$897$	−0.419294	−0.0139998
$898$	−4.51342	−0.150615
$899$	0.433349	0.0144530
$900$	3.25413	0.108471
$901$	−10.1589	−0.338442
$902$	0	0
$903$	28.8279	0.959331
$904$	−5.80255	−0.192990
$905$	29.2290	0.971605
$906$	0.934981	0.0310627
$907$	−10.6516	−0.353679	−0.176840	−	0.984240i	$-0.556587\pi$
$907$	−10.6516	−0.353679	−0.176840	+	0.984240i	$0.556587\pi$
$908$	32.7180	1.08579
$909$	5.80306	0.192475
$910$	0.0746023	0.00247304
$911$	−16.9428	−0.561340	−0.280670	−	0.959804i	$-0.590557\pi$
$911$	−16.9428	−0.561340	−0.280670	+	0.959804i	$0.590557\pi$
$912$	−3.91603	−0.129673
$913$	0	0
$914$	1.58000	0.0522618
$915$	−10.3208	−0.341195
$916$	−25.1650	−0.831476
$917$	8.11541	0.267995
$918$	0.417605	0.0137830
$919$	42.8514	1.41354	0.706769	−	0.707445i	$-0.250152\pi$
$919$	42.8514	1.41354	0.706769	+	0.707445i	$0.250152\pi$
$920$	−3.06419	−0.101023
$921$	13.3073	0.438490
$922$	2.34918	0.0773660
$923$	−0.280762	−0.00924139
$924$	0	0
$925$	7.93872	0.261024
$926$	3.30787	0.108703
$927$	7.00302	0.230009
$928$	0.0825332	0.00270929
$929$	40.4540	1.32725	0.663626	−	0.748065i	$-0.269017\pi$
$929$	40.4540	1.32725	0.663626	+	0.748065i	$0.269017\pi$
$930$	−1.60543	−0.0526441
$931$	1.41309	0.0463121
$932$	16.5126	0.540887
$933$	−31.5423	−1.03265
$934$	1.01508	0.0332146
$935$	0	0
$936$	−0.0559173	−0.00182771
$937$	19.2679	0.629455	0.314727	−	0.949182i	$-0.398087\pi$
$937$	19.2679	0.629455	0.314727	+	0.949182i	$0.398087\pi$
$938$	−1.15789	−0.0378064
$939$	−6.33158	−0.206623
$940$	−33.8685	−1.10467
$941$	0.336424	0.0109671	0.00548356	−	0.999985i	$-0.498255\pi$
$941$	0.336424	0.0109671	0.00548356	+	0.999985i	$0.498255\pi$
$942$	1.53310	0.0499512
$943$	31.8924	1.03856
$944$	−52.1066	−1.69593
$945$	−5.31790	−0.172991
$946$	0	0
$947$	−40.6522	−1.32102	−0.660510	−	0.750817i	$-0.729660\pi$
$947$	−40.6522	−1.32102	−0.660510	+	0.750817i	$0.729660\pi$
$948$	−21.1152	−0.685790
$949$	−1.29013	−0.0418793
$950$	0.194074	0.00629660
$951$	−23.3234	−0.756313
$952$	4.82812	0.156480
$953$	−38.5751	−1.24957	−0.624785	−	0.780797i	$-0.714813\pi$
$953$	−38.5751	−1.24957	−0.624785	+	0.780797i	$0.714813\pi$
$954$	0.341266	0.0110489
$955$	9.86166	0.319116
$956$	−11.7856	−0.381172
$957$	0	0
$958$	2.18547	0.0706094
$959$	24.1234	0.778984
$960$	14.0537	0.453581
$961$	23.6570	0.763128
$962$	−0.0679674	−0.00219136
$963$	10.3108	0.332261
$964$	−10.4438	−0.336373
$965$	−27.1012	−0.872419
$966$	−1.21618	−0.0391298
$967$	48.7854	1.56883	0.784417	−	0.620234i	$-0.212962\pi$
$967$	48.7854	1.56883	0.784417	+	0.620234i	$0.212962\pi$
$968$	0	0
$969$	−3.52582	−0.113266
$970$	0.499987	0.0160536
$971$	−55.8127	−1.79111	−0.895557	−	0.444946i	$-0.853223\pi$
$971$	−55.8127	−1.79111	−0.895557	+	0.444946i	$0.853223\pi$
$972$	1.98597	0.0637001
$973$	−60.9342	−1.95346
$974$	−0.277616	−0.00889538
$975$	−0.194074	−0.00621535
$976$	22.0443	0.705621
$977$	40.1849	1.28563	0.642815	−	0.766021i	$-0.277766\pi$
$977$	40.1849	1.28563	0.642815	+	0.766021i	$0.277766\pi$
$978$	−0.488448	−0.0156188
$979$	0	0
$980$	−5.14523	−0.164358
$981$	−9.04469	−0.288775
$982$	1.40470	0.0448258
$983$	18.9467	0.604306	0.302153	−	0.953260i	$-0.402295\pi$
$983$	18.9467	0.604306	0.302153	+	0.953260i	$0.402295\pi$
$984$	4.25318	0.135586
$985$	25.0334	0.797630
$986$	0.0244783	0.000779547 0
$987$	−26.9797	−0.858774
$988$	0.235223	0.00748343
$989$	35.1842	1.11879
$990$	0	0
$991$	19.5972	0.622525	0.311263	−	0.950324i	$-0.399248\pi$
$991$	19.5972	0.622525	0.311263	+	0.950324i	$0.399248\pi$
$992$	10.4097	0.330507
$993$	−10.5241	−0.333971
$994$	−0.814359	−0.0258299
$995$	−13.7366	−0.435479
$996$	−21.9102	−0.694250
$997$	0.612212	0.0193889	0.00969447	−	0.999953i	$-0.496914\pi$
$997$	0.612212	0.0193889	0.00969447	+	0.999953i	$0.496914\pi$
$998$	3.33646	0.105614
$999$	4.84494	0.153287

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6897.2.a.bc.1.5	✓	8
11.10	odd	2		6897.2.a.bd.1.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6897.2.a.bc.1.5	✓	8	1.1	even	1	trivial
6897.2.a.bd.1.4	yes	8	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6897 = 3 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6897.a (trivial)

\(f(q)\)	\(=\)	\(q-0.118442 q^{2} -1.00000 q^{3} -1.98597 q^{4} +1.83342 q^{5} +0.118442 q^{6} +2.90053 q^{7} +0.472107 q^{8} +1.00000 q^{9} -0.217154 q^{10} +1.98597 q^{12} -0.118442 q^{13} -0.343545 q^{14} -1.83342 q^{15} +3.91603 q^{16} +3.52582 q^{17} -0.118442 q^{18} +1.00000 q^{19} -3.64113 q^{20} -2.90053 q^{21} -3.54008 q^{23} -0.472107 q^{24} -1.63856 q^{25} +0.0140285 q^{26} -1.00000 q^{27} -5.76037 q^{28} -0.0586159 q^{29} +0.217154 q^{30} -7.39303 q^{31} -1.40804 q^{32} -0.417605 q^{34} +5.31790 q^{35} -1.98597 q^{36} -4.84494 q^{37} -0.118442 q^{38} +0.118442 q^{39} +0.865571 q^{40} -9.00894 q^{41} +0.343545 q^{42} -9.93882 q^{43} +1.83342 q^{45} +0.419294 q^{46} +9.30165 q^{47} -3.91603 q^{48} +1.41309 q^{49} +0.194074 q^{50} -3.52582 q^{51} +0.235223 q^{52} -2.88129 q^{53} +0.118442 q^{54} +1.36936 q^{56} -1.00000 q^{57} +0.00694258 q^{58} -13.3060 q^{59} +3.64113 q^{60} +5.62925 q^{61} +0.875646 q^{62} +2.90053 q^{63} -7.66528 q^{64} -0.217154 q^{65} +3.37041 q^{67} -7.00217 q^{68} +3.54008 q^{69} -0.629863 q^{70} +2.37046 q^{71} +0.472107 q^{72} +10.8925 q^{73} +0.573845 q^{74} +1.63856 q^{75} -1.98597 q^{76} -0.0140285 q^{78} -10.6322 q^{79} +7.17973 q^{80} +1.00000 q^{81} +1.06704 q^{82} -11.0325 q^{83} +5.76037 q^{84} +6.46432 q^{85} +1.17717 q^{86} +0.0586159 q^{87} -11.9376 q^{89} -0.217154 q^{90} -0.343545 q^{91} +7.03049 q^{92} +7.39303 q^{93} -1.10171 q^{94} +1.83342 q^{95} +1.40804 q^{96} -2.30245 q^{97} -0.167369 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 8 q^{3} + 9 q^{4} - 2 q^{5} + q^{6} - 6 q^{7} - 6 q^{8} + 8 q^{9} - 3 q^{10} - 9 q^{12} - q^{13} + 7 q^{14} + 2 q^{15} + 23 q^{16} - 15 q^{17} - q^{18} + 8 q^{19} - 4 q^{20} + 6 q^{21}+ \cdots - 55 q^{98}+O(q^{100}) \) 8 * q - q^2 - 8 * q^3 + 9 * q^4 - 2 * q^5 + q^6 - 6 * q^7 - 6 * q^8 + 8 * q^9 - 3 * q^10 - 9 * q^12 - q^13 + 7 * q^14 + 2 * q^15 + 23 * q^16 - 15 * q^17 - q^18 + 8 * q^19 - 4 * q^20 + 6 * q^21 - 5 * q^23 + 6 * q^24 + 4 * q^25 + 25 * q^26 - 8 * q^27 - 8 * q^28 - 17 * q^29 + 3 * q^30 - 4 * q^31 - 38 * q^32 - 18 * q^34 - 2 * q^35 + 9 * q^36 - 4 * q^37 - q^38 + q^39 - 14 * q^40 - 2 * q^41 - 7 * q^42 - 10 * q^43 - 2 * q^45 + 10 * q^46 + 5 * q^47 - 23 * q^48 + 28 * q^49 - 7 * q^50 + 15 * q^51 - 8 * q^52 - 19 * q^53 + q^54 - 49 * q^56 - 8 * q^57 + 35 * q^58 + 12 * q^59 + 4 * q^60 + 5 * q^61 - 22 * q^62 - 6 * q^63 + 24 * q^64 - 3 * q^65 - 12 * q^67 + 3 * q^68 + 5 * q^69 - 22 * q^70 + 40 * q^71 - 6 * q^72 + 12 * q^73 + 7 * q^74 - 4 * q^75 + 9 * q^76 - 25 * q^78 - 14 * q^79 + 37 * q^80 + 8 * q^81 + 31 * q^82 - 17 * q^83 + 8 * q^84 + 35 * q^85 - q^86 + 17 * q^87 - 9 * q^89 - 3 * q^90 + 7 * q^91 + 12 * q^92 + 4 * q^93 - 51 * q^94 - 2 * q^95 + 38 * q^96 + 8 * q^97 - 55 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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