LMFDB - Embedded newform 9386.2.a.bw.1.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9386,2,Mod(1,9386)] 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("9386.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9386, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 9386 = 2 \cdot 13 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9386.a (trivial)

Newform invariants

comment:select newform

sage:traces = [15,-15,-3,15,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$74.9475873372$
Analytic rank:	$1$
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} - 3 x^{14} - 27 x^{13} + 70 x^{12} + 306 x^{11} - 609 x^{10} - 1854 x^{9} + 2346 x^{8} + \cdots - 24 $ x^15 - 3x^14 - 27x^13 + 70x^12 + 306x^11 - 609x^10 - 1854x^9 + 2346x^8 + 6129x^7 - 3442x^6 - 9735x^5 + 222x^4 + 5181x^3 + 1422x^2 - 36x - 24
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 494)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.276311$ of defining polynomial
Character	$\chi$	$=$	9386.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +0.276311 q^{3} +1.00000 q^{4} -3.22926 q^{5} -0.276311 q^{6} -1.92690 q^{7} -1.00000 q^{8} -2.92365 q^{9} +3.22926 q^{10} -1.72726 q^{11} +0.276311 q^{12} +1.00000 q^{13} +1.92690 q^{14} -0.892279 q^{15} +1.00000 q^{16} -2.47761 q^{17} +2.92365 q^{18} -3.22926 q^{20} -0.532424 q^{21} +1.72726 q^{22} -5.45322 q^{23} -0.276311 q^{24} +5.42811 q^{25} -1.00000 q^{26} -1.63677 q^{27} -1.92690 q^{28} +6.22398 q^{29} +0.892279 q^{30} -5.87659 q^{31} -1.00000 q^{32} -0.477260 q^{33} +2.47761 q^{34} +6.22247 q^{35} -2.92365 q^{36} +9.94375 q^{37} +0.276311 q^{39} +3.22926 q^{40} +8.58938 q^{41} +0.532424 q^{42} +6.66422 q^{43} -1.72726 q^{44} +9.44123 q^{45} +5.45322 q^{46} +6.47020 q^{47} +0.276311 q^{48} -3.28704 q^{49} -5.42811 q^{50} -0.684589 q^{51} +1.00000 q^{52} +13.4108 q^{53} +1.63677 q^{54} +5.57776 q^{55} +1.92690 q^{56} -6.22398 q^{58} +11.5500 q^{59} -0.892279 q^{60} -1.76476 q^{61} +5.87659 q^{62} +5.63360 q^{63} +1.00000 q^{64} -3.22926 q^{65} +0.477260 q^{66} -3.85273 q^{67} -2.47761 q^{68} -1.50678 q^{69} -6.22247 q^{70} +6.95717 q^{71} +2.92365 q^{72} +3.75939 q^{73} -9.94375 q^{74} +1.49985 q^{75} +3.32826 q^{77} -0.276311 q^{78} -14.9841 q^{79} -3.22926 q^{80} +8.31870 q^{81} -8.58938 q^{82} -9.76103 q^{83} -0.532424 q^{84} +8.00083 q^{85} -6.66422 q^{86} +1.71975 q^{87} +1.72726 q^{88} +8.18396 q^{89} -9.44123 q^{90} -1.92690 q^{91} -5.45322 q^{92} -1.62377 q^{93} -6.47020 q^{94} -0.276311 q^{96} -10.1177 q^{97} +3.28704 q^{98} +5.04990 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} - 3 q^{3} + 15 q^{4} + 3 q^{5} + 3 q^{6} - 15 q^{8} + 18 q^{9} - 3 q^{10} - 3 q^{11} - 3 q^{12} + 15 q^{13} + 15 q^{16} + 3 q^{17} - 18 q^{18} + 3 q^{20} - 33 q^{21} + 3 q^{22} + 9 q^{23}+ \cdots + 3 q^{98}+O(q^{100}) $ 15 * q - 15 * q^2 - 3 * q^3 + 15 * q^4 + 3 * q^5 + 3 * q^6 - 15 * q^8 + 18 * q^9 - 3 * q^10 - 3 * q^11 - 3 * q^12 + 15 * q^13 + 15 * q^16 + 3 * q^17 - 18 * q^18 + 3 * q^20 - 33 * q^21 + 3 * q^22 + 9 * q^23 + 3 * q^24 + 24 * q^25 - 15 * q^26 - 42 * q^27 - 12 * q^29 - 24 * q^31 - 15 * q^32 + 3 * q^33 - 3 * q^34 + 6 * q^35 + 18 * q^36 - 30 * q^37 - 3 * q^39 - 3 * q^40 + 24 * q^41 + 33 * q^42 - 12 * q^43 - 3 * q^44 + 21 * q^45 - 9 * q^46 - 6 * q^47 - 3 * q^48 - 3 * q^49 - 24 * q^50 - 48 * q^51 + 15 * q^52 - 9 * q^53 + 42 * q^54 - 60 * q^55 + 12 * q^58 - 12 * q^59 - 12 * q^61 + 24 * q^62 + 15 * q^63 + 15 * q^64 + 3 * q^65 - 3 * q^66 - 48 * q^67 + 3 * q^68 - 18 * q^69 - 6 * q^70 - 21 * q^71 - 18 * q^72 + 21 * q^73 + 30 * q^74 - 21 * q^75 - 9 * q^77 + 3 * q^78 - 45 * q^79 + 3 * q^80 + 15 * q^81 - 24 * q^82 - 33 * q^83 - 33 * q^84 - 6 * q^85 + 12 * q^86 + 9 * q^87 + 3 * q^88 + 12 * q^89 - 21 * q^90 + 9 * q^92 - 3 * q^93 + 6 * q^94 + 3 * q^96 + 24 * q^97 + 3 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.276311	0.159528	0.0797640	−	0.996814i	$-0.474583\pi$
$3$	0.276311	0.159528	0.0797640	+	0.996814i	$0.474583\pi$
$4$	1.00000	0.500000
$5$	−3.22926	−1.44417	−0.722084	−	0.691805i	$-0.756816\pi$
$5$	−3.22926	−1.44417	−0.722084	+	0.691805i	$0.756816\pi$
$6$	−0.276311	−0.112803
$7$	−1.92690	−0.728301	−0.364151	−	0.931340i	$-0.618641\pi$
$7$	−1.92690	−0.728301	−0.364151	+	0.931340i	$0.618641\pi$
$8$	−1.00000	−0.353553
$9$	−2.92365	−0.974551
$10$	3.22926	1.02118
$11$	−1.72726	−0.520788	−0.260394	−	0.965502i	$-0.583852\pi$
$11$	−1.72726	−0.520788	−0.260394	+	0.965502i	$0.583852\pi$
$12$	0.276311	0.0797640
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.92690	0.514987
$15$	−0.892279	−0.230385
$16$	1.00000	0.250000
$17$	−2.47761	−0.600908	−0.300454	−	0.953796i	$-0.597138\pi$
$17$	−2.47761	−0.600908	−0.300454	+	0.953796i	$0.597138\pi$
$18$	2.92365	0.689111
$19$	0	0
$19$	0	0
$20$	−3.22926	−0.722084
$21$	−0.532424	−0.116185
$22$	1.72726	0.368253
$23$	−5.45322	−1.13707	−0.568537	−	0.822658i	$-0.692490\pi$
$23$	−5.45322	−1.13707	−0.568537	+	0.822658i	$0.692490\pi$
$24$	−0.276311	−0.0564017
$25$	5.42811	1.08562
$26$	−1.00000	−0.196116
$27$	−1.63677	−0.314996
$28$	−1.92690	−0.364151
$29$	6.22398	1.15576	0.577882	−	0.816120i	$-0.303879\pi$
$29$	6.22398	1.15576	0.577882	+	0.816120i	$0.303879\pi$
$30$	0.892279	0.162907
$31$	−5.87659	−1.05547	−0.527733	−	0.849410i	$-0.676958\pi$
$31$	−5.87659	−1.05547	−0.527733	+	0.849410i	$0.676958\pi$
$32$	−1.00000	−0.176777
$33$	−0.477260	−0.0830803
$34$	2.47761	0.424906
$35$	6.22247	1.05179
$36$	−2.92365	−0.487275
$37$	9.94375	1.63474	0.817371	−	0.576112i	$-0.195431\pi$
$37$	9.94375	1.63474	0.817371	+	0.576112i	$0.195431\pi$
$38$	0	0
$39$	0.276311	0.0442451
$40$	3.22926	0.510591
$41$	8.58938	1.34144	0.670718	−	0.741712i	$-0.265986\pi$
$41$	8.58938	1.34144	0.670718	+	0.741712i	$0.265986\pi$
$42$	0.532424	0.0821549
$43$	6.66422	1.01628	0.508142	−	0.861273i	$-0.330333\pi$
$43$	6.66422	1.01628	0.508142	+	0.861273i	$0.330333\pi$
$44$	−1.72726	−0.260394
$45$	9.44123	1.40742
$46$	5.45322	0.804033
$47$	6.47020	0.943775	0.471888	−	0.881659i	$-0.343573\pi$
$47$	6.47020	0.943775	0.471888	+	0.881659i	$0.343573\pi$
$48$	0.276311	0.0398820
$49$	−3.28704	−0.469577
$50$	−5.42811	−0.767651
$51$	−0.684589	−0.0958617
$52$	1.00000	0.138675
$53$	13.4108	1.84212	0.921060	−	0.389421i	$-0.127325\pi$
$53$	13.4108	1.84212	0.921060	+	0.389421i	$0.127325\pi$
$54$	1.63677	0.222736
$55$	5.57776	0.752105
$56$	1.92690	0.257493
$57$	0	0
$58$	−6.22398	−0.817249
$59$	11.5500	1.50369	0.751843	−	0.659342i	$-0.229165\pi$
$59$	11.5500	1.50369	0.751843	+	0.659342i	$0.229165\pi$
$60$	−0.892279	−0.115193
$61$	−1.76476	−0.225954	−0.112977	−	0.993598i	$-0.536039\pi$
$61$	−1.76476	−0.225954	−0.112977	+	0.993598i	$0.536039\pi$
$62$	5.87659	0.746328
$63$	5.63360	0.709767
$64$	1.00000	0.125000
$65$	−3.22926	−0.400540
$66$	0.477260	0.0587466
$67$	−3.85273	−0.470686	−0.235343	−	0.971912i	$-0.575621\pi$
$67$	−3.85273	−0.470686	−0.235343	+	0.971912i	$0.575621\pi$
$68$	−2.47761	−0.300454
$69$	−1.50678	−0.181395
$70$	−6.22247	−0.743728
$71$	6.95717	0.825664	0.412832	−	0.910807i	$-0.364540\pi$
$71$	6.95717	0.825664	0.412832	+	0.910807i	$0.364540\pi$
$72$	2.92365	0.344556
$73$	3.75939	0.440003	0.220001	−	0.975500i	$-0.429394\pi$
$73$	3.75939	0.440003	0.220001	+	0.975500i	$0.429394\pi$
$74$	−9.94375	−1.15594
$75$	1.49985	0.173187
$76$	0	0
$77$	3.32826	0.379290
$78$	−0.276311	−0.0312860
$79$	−14.9841	−1.68585	−0.842924	−	0.538033i	$-0.819168\pi$
$79$	−14.9841	−1.68585	−0.842924	+	0.538033i	$0.819168\pi$
$80$	−3.22926	−0.361042
$81$	8.31870	0.924300
$82$	−8.58938	−0.948539
$83$	−9.76103	−1.07141	−0.535706	−	0.844405i	$-0.679954\pi$
$83$	−9.76103	−1.07141	−0.535706	+	0.844405i	$0.679954\pi$
$84$	−0.532424	−0.0580923
$85$	8.00083	0.867812
$86$	−6.66422	−0.718621
$87$	1.71975	0.184377
$88$	1.72726	0.184126
$89$	8.18396	0.867498	0.433749	−	0.901034i	$-0.357190\pi$
$89$	8.18396	0.867498	0.433749	+	0.901034i	$0.357190\pi$
$90$	−9.44123	−0.995193
$91$	−1.92690	−0.201994
$92$	−5.45322	−0.568537
$93$	−1.62377	−0.168377
$94$	−6.47020	−0.667350
$95$	0	0
$96$	−0.276311	−0.0282008
$97$	−10.1177	−1.02730	−0.513651	−	0.857999i	$-0.671707\pi$
$97$	−10.1177	−1.02730	−0.513651	+	0.857999i	$0.671707\pi$
$98$	3.28704	0.332041
$99$	5.04990	0.507534
$100$	5.42811	0.542811
$101$	−15.3074	−1.52314	−0.761572	−	0.648081i	$-0.775572\pi$
$101$	−15.3074	−1.52314	−0.761572	+	0.648081i	$0.775572\pi$
$102$	0.684589	0.0677844
$103$	−15.4225	−1.51962	−0.759811	−	0.650144i	$-0.774709\pi$
$103$	−15.4225	−1.51962	−0.759811	+	0.650144i	$0.774709\pi$
$104$	−1.00000	−0.0980581
$105$	1.71934	0.167790
$106$	−13.4108	−1.30258
$107$	−7.98507	−0.771946	−0.385973	−	0.922510i	$-0.626134\pi$
$107$	−7.98507	−0.771946	−0.385973	+	0.922510i	$0.626134\pi$
$108$	−1.63677	−0.157498
$109$	−1.45984	−0.139827	−0.0699134	−	0.997553i	$-0.522272\pi$
$109$	−1.45984	−0.139827	−0.0699134	+	0.997553i	$0.522272\pi$
$110$	−5.57776	−0.531819
$111$	2.74756	0.260787
$112$	−1.92690	−0.182075
$113$	17.0707	1.60587	0.802937	−	0.596064i	$-0.203270\pi$
$113$	17.0707	1.60587	0.802937	+	0.596064i	$0.203270\pi$
$114$	0	0
$115$	17.6098	1.64213
$116$	6.22398	0.577882
$117$	−2.92365	−0.270292
$118$	−11.5500	−1.06327
$119$	4.77411	0.437642
$120$	0.892279	0.0814535
$121$	−8.01658	−0.728780
$122$	1.76476	0.159773
$123$	2.37334	0.213997
$124$	−5.87659	−0.527733
$125$	−1.38248	−0.123653
$126$	−5.63360	−0.501881
$127$	−9.74384	−0.864626	−0.432313	−	0.901724i	$-0.642303\pi$
$127$	−9.74384	−0.864626	−0.432313	+	0.901724i	$0.642303\pi$
$128$	−1.00000	−0.0883883
$129$	1.84139	0.162126
$130$	3.22926	0.283225
$131$	8.05727	0.703967	0.351984	−	0.936006i	$-0.385507\pi$
$131$	8.05727	0.703967	0.351984	+	0.936006i	$0.385507\pi$
$132$	−0.477260	−0.0415401
$133$	0	0
$134$	3.85273	0.332826
$135$	5.28555	0.454908
$136$	2.47761	0.212453
$137$	−5.87887	−0.502266	−0.251133	−	0.967953i	$-0.580803\pi$
$137$	−5.87887	−0.502266	−0.251133	+	0.967953i	$0.580803\pi$
$138$	1.50678	0.128266
$139$	2.76234	0.234299	0.117149	−	0.993114i	$-0.462624\pi$
$139$	2.76234	0.234299	0.117149	+	0.993114i	$0.462624\pi$
$140$	6.22247	0.525895
$141$	1.78779	0.150559
$142$	−6.95717	−0.583833
$143$	−1.72726	−0.144441
$144$	−2.92365	−0.243638
$145$	−20.0989	−1.66912
$146$	−3.75939	−0.311129
$147$	−0.908244	−0.0749107
$148$	9.94375	0.817371
$149$	21.8995	1.79408	0.897040	−	0.441950i	$-0.145713\pi$
$149$	21.8995	1.79408	0.897040	+	0.441950i	$0.145713\pi$
$150$	−1.49985	−0.122462
$151$	−6.09089	−0.495670	−0.247835	−	0.968802i	$-0.579719\pi$
$151$	−6.09089	−0.495670	−0.247835	+	0.968802i	$0.579719\pi$
$152$	0	0
$153$	7.24366	0.585615
$154$	−3.32826	−0.268199
$155$	18.9770	1.52427
$156$	0.276311	0.0221226
$157$	13.7890	1.10048	0.550240	−	0.835007i	$-0.314536\pi$
$157$	13.7890	1.10048	0.550240	+	0.835007i	$0.314536\pi$
$158$	14.9841	1.19207
$159$	3.70556	0.293870
$160$	3.22926	0.255295
$161$	10.5078	0.828133
$162$	−8.31870	−0.653579
$163$	−6.16062	−0.482537	−0.241268	−	0.970458i	$-0.577563\pi$
$163$	−6.16062	−0.482537	−0.241268	+	0.970458i	$0.577563\pi$
$164$	8.58938	0.670718
$165$	1.54120	0.119982
$166$	9.76103	0.757603
$167$	−4.05262	−0.313601	−0.156801	−	0.987630i	$-0.550118\pi$
$167$	−4.05262	−0.313601	−0.156801	+	0.987630i	$0.550118\pi$
$168$	0.532424	0.0410774
$169$	1.00000	0.0769231
$170$	−8.00083	−0.613636
$171$	0	0
$172$	6.66422	0.508142
$173$	−2.19689	−0.167027	−0.0835133	−	0.996507i	$-0.526614\pi$
$173$	−2.19689	−0.167027	−0.0835133	+	0.996507i	$0.526614\pi$
$174$	−1.71975	−0.130374
$175$	−10.4595	−0.790660
$176$	−1.72726	−0.130197
$177$	3.19140	0.239880
$178$	−8.18396	−0.613414
$179$	−25.8048	−1.92874	−0.964371	−	0.264555i	$-0.914775\pi$
$179$	−25.8048	−1.92874	−0.964371	+	0.264555i	$0.914775\pi$
$180$	9.44123	0.703708
$181$	10.5212	0.782033	0.391016	−	0.920384i	$-0.372124\pi$
$181$	10.5212	0.782033	0.391016	+	0.920384i	$0.372124\pi$
$182$	1.92690	0.142832
$183$	−0.487621	−0.0360460
$184$	5.45322	0.402016
$185$	−32.1109	−2.36084
$186$	1.62377	0.119060
$187$	4.27947	0.312945
$188$	6.47020	0.471888
$189$	3.15390	0.229412
$190$	0	0
$191$	−13.1671	−0.952739	−0.476369	−	0.879245i	$-0.658047\pi$
$191$	−13.1671	−0.952739	−0.476369	+	0.879245i	$0.658047\pi$
$192$	0.276311	0.0199410
$193$	−3.26304	−0.234879	−0.117439	−	0.993080i	$-0.537469\pi$
$193$	−3.26304	−0.234879	−0.117439	+	0.993080i	$0.537469\pi$
$194$	10.1177	0.726412
$195$	−0.892279	−0.0638974
$196$	−3.28704	−0.234789
$197$	16.5424	1.17860	0.589300	−	0.807914i	$-0.299404\pi$
$197$	16.5424	1.17860	0.589300	+	0.807914i	$0.299404\pi$
$198$	−5.04990	−0.358881
$199$	−14.0766	−0.997864	−0.498932	−	0.866641i	$-0.666274\pi$
$199$	−14.0766	−0.997864	−0.498932	+	0.866641i	$0.666274\pi$
$200$	−5.42811	−0.383825
$201$	−1.06455	−0.0750877
$202$	15.3074	1.07702
$203$	−11.9930	−0.841745
$204$	−0.684589	−0.0479308
$205$	−27.7373	−1.93726
$206$	15.4225	1.07453
$207$	15.9433	1.10814
$208$	1.00000	0.0693375
$209$	0	0
$210$	−1.71934	−0.118645
$211$	8.92749	0.614594	0.307297	−	0.951614i	$-0.400576\pi$
$211$	8.92749	0.614594	0.307297	+	0.951614i	$0.400576\pi$
$212$	13.4108	0.921060
$213$	1.92234	0.131717
$214$	7.98507	0.545848
$215$	−21.5205	−1.46768
$216$	1.63677	0.111368
$217$	11.3236	0.768698
$218$	1.45984	0.0988725
$219$	1.03876	0.0701928
$220$	5.57776	0.376053
$221$	−2.47761	−0.166662
$222$	−2.74756	−0.184404
$223$	−1.66977	−0.111816	−0.0559080	−	0.998436i	$-0.517805\pi$
$223$	−1.66977	−0.111816	−0.0559080	+	0.998436i	$0.517805\pi$
$224$	1.92690	0.128747
$225$	−15.8699	−1.05799
$226$	−17.0707	−1.13552
$227$	0.198601	0.0131816	0.00659079	−	0.999978i	$-0.497902\pi$
$227$	0.198601	0.0131816	0.00659079	+	0.999978i	$0.497902\pi$
$228$	0	0
$229$	9.34936	0.617823	0.308912	−	0.951091i	$-0.400035\pi$
$229$	9.34936	0.617823	0.308912	+	0.951091i	$0.400035\pi$
$230$	−17.6098	−1.16116
$231$	0.919634	0.0605075
$232$	−6.22398	−0.408625
$233$	−0.0118010	−0.000773106 0	−0.000386553	−	1.00000i	$-0.500123\pi$
$233$	−0.0118010	−0.000773106 0	−0.000386553		1.00000i	$0.500123\pi$
$234$	2.92365	0.191125
$235$	−20.8939	−1.36297
$236$	11.5500	0.751843
$237$	−4.14028	−0.268940
$238$	−4.77411	−0.309460
$239$	12.3396	0.798182	0.399091	−	0.916911i	$-0.369326\pi$
$239$	12.3396	0.798182	0.399091	+	0.916911i	$0.369326\pi$
$240$	−0.892279	−0.0575964
$241$	−6.83547	−0.440311	−0.220156	−	0.975465i	$-0.570656\pi$
$241$	−6.83547	−0.440311	−0.220156	+	0.975465i	$0.570656\pi$
$242$	8.01658	0.515325
$243$	7.20885	0.462448
$244$	−1.76476	−0.112977
$245$	10.6147	0.678148
$246$	−2.37334	−0.151319
$247$	0	0
$248$	5.87659	0.373164
$249$	−2.69708	−0.170920
$250$	1.38248	0.0874360
$251$	20.5068	1.29438	0.647190	−	0.762329i	$-0.275944\pi$
$251$	20.5068	1.29438	0.647190	+	0.762329i	$0.275944\pi$
$252$	5.63360	0.354883
$253$	9.41911	0.592174
$254$	9.74384	0.611383
$255$	2.21072	0.138440
$256$	1.00000	0.0625000
$257$	−4.11725	−0.256827	−0.128413	−	0.991721i	$-0.540988\pi$
$257$	−4.11725	−0.256827	−0.128413	+	0.991721i	$0.540988\pi$
$258$	−1.84139	−0.114640
$259$	−19.1606	−1.19058
$260$	−3.22926	−0.200270
$261$	−18.1968	−1.12635
$262$	−8.05727	−0.497780
$263$	9.44613	0.582473	0.291237	−	0.956651i	$-0.405933\pi$
$263$	9.44613	0.582473	0.291237	+	0.956651i	$0.405933\pi$
$264$	0.477260	0.0293733
$265$	−43.3070	−2.66033
$266$	0	0
$267$	2.26132	0.138390
$268$	−3.85273	−0.235343
$269$	15.1222	0.922015	0.461007	−	0.887396i	$-0.347488\pi$
$269$	15.1222	0.922015	0.461007	+	0.887396i	$0.347488\pi$
$270$	−5.28555	−0.321668
$271$	−15.3658	−0.933406	−0.466703	−	0.884414i	$-0.654558\pi$
$271$	−15.3658	−0.933406	−0.466703	+	0.884414i	$0.654558\pi$
$272$	−2.47761	−0.150227
$273$	−0.532424	−0.0322238
$274$	5.87887	0.355156
$275$	−9.37575	−0.565379
$276$	−1.50678	−0.0906976
$277$	−31.6325	−1.90061	−0.950307	−	0.311316i	$-0.899230\pi$
$277$	−31.6325	−1.90061	−0.950307	+	0.311316i	$0.899230\pi$
$278$	−2.76234	−0.165674
$279$	17.1811	1.02861
$280$	−6.22247	−0.371864
$281$	7.80476	0.465593	0.232797	−	0.972525i	$-0.425212\pi$
$281$	7.80476	0.465593	0.232797	+	0.972525i	$0.425212\pi$
$282$	−1.78779	−0.106461
$283$	4.73088	0.281222	0.140611	−	0.990065i	$-0.455093\pi$
$283$	4.73088	0.281222	0.140611	+	0.990065i	$0.455093\pi$
$284$	6.95717	0.412832
$285$	0	0
$286$	1.72726	0.102135
$287$	−16.5509	−0.976970
$288$	2.92365	0.172278
$289$	−10.8615	−0.638910
$290$	20.0989	1.18025
$291$	−2.79564	−0.163883
$292$	3.75939	0.220001
$293$	1.31373	0.0767492	0.0383746	−	0.999263i	$-0.487782\pi$
$293$	1.31373	0.0767492	0.0383746	+	0.999263i	$0.487782\pi$
$294$	0.908244	0.0529699
$295$	−37.2981	−2.17158
$296$	−9.94375	−0.577969
$297$	2.82712	0.164046
$298$	−21.8995	−1.26861
$299$	−5.45322	−0.315368
$300$	1.49985	0.0865936
$301$	−12.8413	−0.740161
$302$	6.09089	0.350491
$303$	−4.22960	−0.242984
$304$	0	0
$305$	5.69885	0.326315
$306$	−7.24366	−0.414092
$307$	12.8112	0.731176	0.365588	−	0.930777i	$-0.380868\pi$
$307$	12.8112	0.731176	0.365588	+	0.930777i	$0.380868\pi$
$308$	3.32826	0.189645
$309$	−4.26140	−0.242422
$310$	−18.9770	−1.07782
$311$	30.6450	1.73772	0.868861	−	0.495057i	$-0.164853\pi$
$311$	30.6450	1.73772	0.868861	+	0.495057i	$0.164853\pi$
$312$	−0.276311	−0.0156430
$313$	−15.3927	−0.870045	−0.435022	−	0.900420i	$-0.643260\pi$
$313$	−15.3927	−0.870045	−0.435022	+	0.900420i	$0.643260\pi$
$314$	−13.7890	−0.778157
$315$	−18.1923	−1.02502
$316$	−14.9841	−0.842924
$317$	16.1848	0.909031	0.454515	−	0.890739i	$-0.349812\pi$
$317$	16.1848	0.909031	0.454515	+	0.890739i	$0.349812\pi$
$318$	−3.70556	−0.207797
$319$	−10.7504	−0.601908
$320$	−3.22926	−0.180521
$321$	−2.20636	−0.123147
$322$	−10.5078	−0.585578
$323$	0	0
$324$	8.31870	0.462150
$325$	5.42811	0.301097
$326$	6.16062	0.341205
$327$	−0.403368	−0.0223063
$328$	−8.58938	−0.474269
$329$	−12.4675	−0.687353
$330$	−1.54120	−0.0848400
$331$	−4.00824	−0.220313	−0.110156	−	0.993914i	$-0.535135\pi$
$331$	−4.00824	−0.220313	−0.110156	+	0.993914i	$0.535135\pi$
$332$	−9.76103	−0.535706
$333$	−29.0721	−1.59314
$334$	4.05262	0.221750
$335$	12.4415	0.679750
$336$	−0.532424	−0.0290461
$337$	−0.818998	−0.0446137	−0.0223068	−	0.999751i	$-0.507101\pi$
$337$	−0.818998	−0.0446137	−0.0223068	+	0.999751i	$0.507101\pi$
$338$	−1.00000	−0.0543928
$339$	4.71681	0.256182
$340$	8.00083	0.433906
$341$	10.1504	0.549674
$342$	0	0
$343$	19.8221	1.07030
$344$	−6.66422	−0.359311
$345$	4.86579	0.261965
$346$	2.19689	0.118106
$347$	−27.9171	−1.49867	−0.749333	−	0.662193i	$-0.769626\pi$
$347$	−27.9171	−1.49867	−0.749333	+	0.662193i	$0.769626\pi$
$348$	1.71975	0.0921885
$349$	8.33854	0.446352	0.223176	−	0.974778i	$-0.428358\pi$
$349$	8.33854	0.446352	0.223176	+	0.974778i	$0.428358\pi$
$350$	10.4595	0.559081
$351$	−1.63677	−0.0873643
$352$	1.72726	0.0920632
$353$	17.4488	0.928704	0.464352	−	0.885651i	$-0.346287\pi$
$353$	17.4488	0.928704	0.464352	+	0.885651i	$0.346287\pi$
$354$	−3.19140	−0.169621
$355$	−22.4665	−1.19240
$356$	8.18396	0.433749
$357$	1.31914	0.0698162
$358$	25.8048	1.36383
$359$	3.29874	0.174101	0.0870505	−	0.996204i	$-0.472256\pi$
$359$	3.29874	0.174101	0.0870505	+	0.996204i	$0.472256\pi$
$360$	−9.44123	−0.497597
$361$	0	0
$362$	−10.5212	−0.552981
$363$	−2.21507	−0.116261
$364$	−1.92690	−0.100997
$365$	−12.1400	−0.635438
$366$	0.487621	0.0254883
$367$	−14.1051	−0.736280	−0.368140	−	0.929770i	$-0.620005\pi$
$367$	−14.1051	−0.736280	−0.368140	+	0.929770i	$0.620005\pi$
$368$	−5.45322	−0.284269
$369$	−25.1124	−1.30730
$370$	32.1109	1.66937
$371$	−25.8414	−1.34162
$372$	−1.62377	−0.0841883
$373$	−22.5858	−1.16945	−0.584724	−	0.811232i	$-0.698797\pi$
$373$	−22.5858	−1.16945	−0.584724	+	0.811232i	$0.698797\pi$
$374$	−4.27947	−0.221286
$375$	−0.381995	−0.0197261
$376$	−6.47020	−0.333675
$377$	6.22398	0.320552
$378$	−3.15390	−0.162219
$379$	18.3572	0.942944	0.471472	−	0.881881i	$-0.343723\pi$
$379$	18.3572	0.942944	0.471472	+	0.881881i	$0.343723\pi$
$380$	0	0
$381$	−2.69233	−0.137932
$382$	13.1671	0.673688
$383$	−3.58115	−0.182988	−0.0914941	−	0.995806i	$-0.529164\pi$
$383$	−3.58115	−0.182988	−0.0914941	+	0.995806i	$0.529164\pi$
$384$	−0.276311	−0.0141004
$385$	−10.7478	−0.547759
$386$	3.26304	0.166084
$387$	−19.4839	−0.990420
$388$	−10.1177	−0.513651
$389$	−22.6537	−1.14859	−0.574294	−	0.818649i	$-0.694723\pi$
$389$	−22.6537	−1.14859	−0.574294	+	0.818649i	$0.694723\pi$
$390$	0.892279	0.0451823
$391$	13.5109	0.683277
$392$	3.28704	0.166021
$393$	2.22631	0.112303
$394$	−16.5424	−0.833396
$395$	48.3877	2.43465
$396$	5.04990	0.253767
$397$	−3.30516	−0.165881	−0.0829406	−	0.996554i	$-0.526431\pi$
$397$	−3.30516	−0.165881	−0.0829406	+	0.996554i	$0.526431\pi$
$398$	14.0766	0.705597
$399$	0	0
$400$	5.42811	0.271406
$401$	−20.5487	−1.02615	−0.513077	−	0.858342i	$-0.671495\pi$
$401$	−20.5487	−1.02615	−0.513077	+	0.858342i	$0.671495\pi$
$402$	1.06455	0.0530950
$403$	−5.87659	−0.292734
$404$	−15.3074	−0.761572
$405$	−26.8632	−1.33484
$406$	11.9930	0.595204
$407$	−17.1754	−0.851354
$408$	0.684589	0.0338922
$409$	−6.76400	−0.334458	−0.167229	−	0.985918i	$-0.553482\pi$
$409$	−6.76400	−0.334458	−0.167229	+	0.985918i	$0.553482\pi$
$410$	27.7373	1.36985
$411$	−1.62440	−0.0801255
$412$	−15.4225	−0.759811
$413$	−22.2558	−1.09514
$414$	−15.9433	−0.783571
$415$	31.5209	1.54730
$416$	−1.00000	−0.0490290
$417$	0.763265	0.0373773
$418$	0	0
$419$	−1.77080	−0.0865090	−0.0432545	−	0.999064i	$-0.513773\pi$
$419$	−1.77080	−0.0865090	−0.0432545	+	0.999064i	$0.513773\pi$
$420$	1.71934	0.0838950
$421$	32.2098	1.56981	0.784904	−	0.619618i	$-0.212712\pi$
$421$	32.2098	1.56981	0.784904	+	0.619618i	$0.212712\pi$
$422$	−8.92749	−0.434583
$423$	−18.9166	−0.919757
$424$	−13.4108	−0.651288
$425$	−13.4487	−0.652359
$426$	−1.92234	−0.0931377
$427$	3.40051	0.164562
$428$	−7.98507	−0.385973
$429$	−0.477260	−0.0230423
$430$	21.5205	1.03781
$431$	−10.3497	−0.498530	−0.249265	−	0.968435i	$-0.580189\pi$
$431$	−10.3497	−0.498530	−0.249265	+	0.968435i	$0.580189\pi$
$432$	−1.63677	−0.0787491
$433$	28.7793	1.38305	0.691523	−	0.722354i	$-0.256940\pi$
$433$	28.7793	1.38305	0.691523	+	0.722354i	$0.256940\pi$
$434$	−11.3236	−0.543552
$435$	−5.55353	−0.266271
$436$	−1.45984	−0.0699134
$437$	0	0
$438$	−1.03876	−0.0496338
$439$	6.47174	0.308879	0.154440	−	0.988002i	$-0.450643\pi$
$439$	6.47174	0.308879	0.154440	+	0.988002i	$0.450643\pi$
$440$	−5.57776	−0.265909
$441$	9.61016	0.457627
$442$	2.47761	0.117848
$443$	3.51346	0.166930	0.0834648	−	0.996511i	$-0.473401\pi$
$443$	3.51346	0.166930	0.0834648	+	0.996511i	$0.473401\pi$
$444$	2.74756	0.130394
$445$	−26.4281	−1.25281
$446$	1.66977	0.0790659
$447$	6.05108	0.286206
$448$	−1.92690	−0.0910377
$449$	−22.3130	−1.05302	−0.526509	−	0.850170i	$-0.676499\pi$
$449$	−22.3130	−1.05302	−0.526509	+	0.850170i	$0.676499\pi$
$450$	15.8699	0.748115
$451$	−14.8361	−0.698604
$452$	17.0707	0.802937
$453$	−1.68298	−0.0790732
$454$	−0.198601	−0.00932079
$455$	6.22247	0.291714
$456$	0	0
$457$	3.84010	0.179632	0.0898161	−	0.995958i	$-0.471372\pi$
$457$	3.84010	0.179632	0.0898161	+	0.995958i	$0.471372\pi$
$458$	−9.34936	−0.436867
$459$	4.05527	0.189284
$460$	17.6098	0.821063
$461$	−14.7910	−0.688884	−0.344442	−	0.938808i	$-0.611932\pi$
$461$	−14.7910	−0.688884	−0.344442	+	0.938808i	$0.611932\pi$
$462$	−0.919634	−0.0427853
$463$	19.7642	0.918519	0.459260	−	0.888302i	$-0.348115\pi$
$463$	19.7642	0.918519	0.459260	+	0.888302i	$0.348115\pi$
$464$	6.22398	0.288941
$465$	5.24356	0.243164
$466$	0.0118010	0.000546668 0
$467$	34.0785	1.57696	0.788482	−	0.615058i	$-0.210867\pi$
$467$	34.0785	1.57696	0.788482	+	0.615058i	$0.210867\pi$
$468$	−2.92365	−0.135146
$469$	7.42385	0.342802
$470$	20.8939	0.963766
$471$	3.81004	0.175557
$472$	−11.5500	−0.531634
$473$	−11.5108	−0.529268
$474$	4.14028	0.190169
$475$	0	0
$476$	4.77411	0.218821
$477$	−39.2086	−1.79524
$478$	−12.3396	−0.564400
$479$	−38.1612	−1.74363	−0.871814	−	0.489837i	$-0.837056\pi$
$479$	−38.1612	−1.74363	−0.871814	+	0.489837i	$0.837056\pi$
$480$	0.892279	0.0407268
$481$	9.94375	0.453396
$482$	6.83547	0.311347
$483$	2.90343	0.132110
$484$	−8.01658	−0.364390
$485$	32.6728	1.48360
$486$	−7.20885	−0.327000
$487$	−28.4320	−1.28838	−0.644190	−	0.764866i	$-0.722805\pi$
$487$	−28.4320	−1.28838	−0.644190	+	0.764866i	$0.722805\pi$
$488$	1.76476	0.0798867
$489$	−1.70224	−0.0769781
$490$	−10.6147	−0.479523
$491$	−44.0285	−1.98698	−0.993488	−	0.113933i	$-0.963655\pi$
$491$	−44.0285	−1.98698	−0.993488	+	0.113933i	$0.963655\pi$
$492$	2.37334	0.106998
$493$	−15.4206	−0.694508
$494$	0	0
$495$	−16.3074	−0.732965
$496$	−5.87659	−0.263867
$497$	−13.4058	−0.601332
$498$	2.69708	0.120859
$499$	15.7478	0.704969	0.352485	−	0.935818i	$-0.385337\pi$
$499$	15.7478	0.704969	0.352485	+	0.935818i	$0.385337\pi$
$500$	−1.38248	−0.0618266
$501$	−1.11978	−0.0500282
$502$	−20.5068	−0.915264
$503$	31.8584	1.42049	0.710247	−	0.703953i	$-0.248583\pi$
$503$	31.8584	1.42049	0.710247	+	0.703953i	$0.248583\pi$
$504$	−5.63360	−0.250940
$505$	49.4316	2.19968
$506$	−9.41911	−0.418731
$507$	0.276311	0.0122714
$508$	−9.74384	−0.432313
$509$	24.3510	1.07934	0.539670	−	0.841877i	$-0.318549\pi$
$509$	24.3510	1.07934	0.539670	+	0.841877i	$0.318549\pi$
$510$	−2.21072	−0.0978921
$511$	−7.24398	−0.320455
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	4.11725	0.181604
$515$	49.8032	2.19459
$516$	1.84139	0.0810629
$517$	−11.1757	−0.491507
$518$	19.1606	0.841871
$519$	−0.607025	−0.0266454
$520$	3.22926	0.141612
$521$	−30.0183	−1.31513	−0.657563	−	0.753400i	$-0.728413\pi$
$521$	−30.0183	−1.31513	−0.657563	+	0.753400i	$0.728413\pi$
$522$	18.1968	0.796451
$523$	21.7114	0.949374	0.474687	−	0.880155i	$-0.342561\pi$
$523$	21.7114	0.949374	0.474687	+	0.880155i	$0.342561\pi$
$524$	8.05727	0.351984
$525$	−2.89006	−0.126133
$526$	−9.44613	−0.411871
$527$	14.5599	0.634238
$528$	−0.477260	−0.0207701
$529$	6.73757	0.292938
$530$	43.3070	1.88114
$531$	−33.7683	−1.46542
$532$	0	0
$533$	8.58938	0.372047
$534$	−2.26132	−0.0978567
$535$	25.7859	1.11482
$536$	3.85273	0.166413
$537$	−7.13014	−0.307688
$538$	−15.1222	−0.651963
$539$	5.67757	0.244550
$540$	5.28555	0.227454
$541$	0.485991	0.0208944	0.0104472	−	0.999945i	$-0.496674\pi$
$541$	0.485991	0.0208944	0.0104472	+	0.999945i	$0.496674\pi$
$542$	15.3658	0.660018
$543$	2.90711	0.124756
$544$	2.47761	0.106227
$545$	4.71419	0.201934
$546$	0.532424	0.0227857
$547$	21.2491	0.908546	0.454273	−	0.890863i	$-0.349899\pi$
$547$	21.2491	0.908546	0.454273	+	0.890863i	$0.349899\pi$
$548$	−5.87887	−0.251133
$549$	5.15953	0.220203
$550$	9.37575	0.399783
$551$	0	0
$552$	1.50678	0.0641329
$553$	28.8730	1.22781
$554$	31.6325	1.34394
$555$	−8.87260	−0.376621
$556$	2.76234	0.117149
$557$	−4.29477	−0.181975	−0.0909875	−	0.995852i	$-0.529002\pi$
$557$	−4.29477	−0.181975	−0.0909875	+	0.995852i	$0.529002\pi$
$558$	−17.1811	−0.727334
$559$	6.66422	0.281866
$560$	6.22247	0.262947
$561$	1.18246	0.0499236
$562$	−7.80476	−0.329224
$563$	14.2007	0.598487	0.299243	−	0.954177i	$-0.403266\pi$
$563$	14.2007	0.598487	0.299243	+	0.954177i	$0.403266\pi$
$564$	1.78779	0.0752793
$565$	−55.1256	−2.31915
$566$	−4.73088	−0.198854
$567$	−16.0293	−0.673169
$568$	−6.95717	−0.291916
$569$	−26.1253	−1.09523	−0.547614	−	0.836731i	$-0.684464\pi$
$569$	−26.1253	−1.09523	−0.547614	+	0.836731i	$0.684464\pi$
$570$	0	0
$571$	−31.4721	−1.31707	−0.658533	−	0.752552i	$-0.728823\pi$
$571$	−31.4721	−1.31707	−0.658533	+	0.752552i	$0.728823\pi$
$572$	−1.72726	−0.0722203
$573$	−3.63821	−0.151989
$574$	16.5509	0.690822
$575$	−29.6007	−1.23443
$576$	−2.92365	−0.121819
$577$	−28.9964	−1.20714	−0.603568	−	0.797312i	$-0.706255\pi$
$577$	−28.9964	−1.20714	−0.603568	+	0.797312i	$0.706255\pi$
$578$	10.8615	0.451777
$579$	−0.901613	−0.0374698
$580$	−20.0989	−0.834560
$581$	18.8086	0.780311
$582$	2.79564	0.115883
$583$	−23.1640	−0.959353
$584$	−3.75939	−0.155564
$585$	9.44123	0.390347
$586$	−1.31373	−0.0542699
$587$	13.8961	0.573555	0.286777	−	0.957997i	$-0.407416\pi$
$587$	13.8961	0.573555	0.286777	+	0.957997i	$0.407416\pi$
$588$	−0.908244	−0.0374554
$589$	0	0
$590$	37.2981	1.53554
$591$	4.57085	0.188020
$592$	9.94375	0.408685
$593$	−48.4492	−1.98957	−0.994785	−	0.101997i	$-0.967477\pi$
$593$	−48.4492	−1.98957	−0.994785	+	0.101997i	$0.967477\pi$
$594$	−2.82712	−0.115998
$595$	−15.4168	−0.632029
$596$	21.8995	0.897040
$597$	−3.88952	−0.159187
$598$	5.45322	0.222999
$599$	−42.7274	−1.74579	−0.872897	−	0.487905i	$-0.837761\pi$
$599$	−42.7274	−1.74579	−0.872897	+	0.487905i	$0.837761\pi$
$600$	−1.49985	−0.0612309
$601$	3.20221	0.130621	0.0653104	−	0.997865i	$-0.479196\pi$
$601$	3.20221	0.130621	0.0653104	+	0.997865i	$0.479196\pi$
$602$	12.8413	0.523373
$603$	11.2641	0.458708
$604$	−6.09089	−0.247835
$605$	25.8876	1.05248
$606$	4.22960	0.171816
$607$	43.0384	1.74687	0.873437	−	0.486938i	$-0.161886\pi$
$607$	43.0384	1.74687	0.873437	+	0.486938i	$0.161886\pi$
$608$	0	0
$609$	−3.31380	−0.134282
$610$	−5.69885	−0.230740
$611$	6.47020	0.261756
$612$	7.24366	0.292808
$613$	−5.58776	−0.225687	−0.112844	−	0.993613i	$-0.535996\pi$
$613$	−5.58776	−0.225687	−0.112844	+	0.993613i	$0.535996\pi$
$614$	−12.8112	−0.517020
$615$	−7.66412	−0.309047
$616$	−3.32826	−0.134099
$617$	−11.2298	−0.452096	−0.226048	−	0.974116i	$-0.572581\pi$
$617$	−11.2298	−0.452096	−0.226048	+	0.974116i	$0.572581\pi$
$618$	4.26140	0.171419
$619$	5.41866	0.217794	0.108897	−	0.994053i	$-0.465268\pi$
$619$	5.41866	0.217794	0.108897	+	0.994053i	$0.465268\pi$
$620$	18.9770	0.762136
$621$	8.92565	0.358174
$622$	−30.6450	−1.22875
$623$	−15.7697	−0.631800
$624$	0.276311	0.0110613
$625$	−22.6762	−0.907046
$626$	15.3927	0.615215
$627$	0	0
$628$	13.7890	0.550240
$629$	−24.6367	−0.982329
$630$	18.1923	0.724800
$631$	−3.08072	−0.122642	−0.0613208	−	0.998118i	$-0.519531\pi$
$631$	−3.08072	−0.122642	−0.0613208	+	0.998118i	$0.519531\pi$
$632$	14.9841	0.596037
$633$	2.46676	0.0980449
$634$	−16.1848	−0.642782
$635$	31.4654	1.24867
$636$	3.70556	0.146935
$637$	−3.28704	−0.130237
$638$	10.7504	0.425613
$639$	−20.3403	−0.804652
$640$	3.22926	0.127648
$641$	36.5937	1.44537	0.722683	−	0.691180i	$-0.242909\pi$
$641$	36.5937	1.44537	0.722683	+	0.691180i	$0.242909\pi$
$642$	2.20636	0.0870781
$643$	16.8901	0.666080	0.333040	−	0.942913i	$-0.391926\pi$
$643$	16.8901	0.666080	0.333040	+	0.942913i	$0.391926\pi$
$644$	10.5078	0.414066
$645$	−5.94634	−0.234137
$646$	0	0
$647$	−34.3958	−1.35224	−0.676119	−	0.736793i	$-0.736339\pi$
$647$	−34.3958	−1.35224	−0.676119	+	0.736793i	$0.736339\pi$
$648$	−8.31870	−0.326789
$649$	−19.9499	−0.783102
$650$	−5.42811	−0.212908
$651$	3.12884	0.122629
$652$	−6.16062	−0.241268
$653$	44.8741	1.75606	0.878030	−	0.478606i	$-0.158858\pi$
$653$	44.8741	1.75606	0.878030	+	0.478606i	$0.158858\pi$
$654$	0.403368	0.0157729
$655$	−26.0190	−1.01665
$656$	8.58938	0.335359
$657$	−10.9911	−0.428805
$658$	12.4675	0.486032
$659$	−8.42070	−0.328024	−0.164012	−	0.986458i	$-0.552444\pi$
$659$	−8.42070	−0.328024	−0.164012	+	0.986458i	$0.552444\pi$
$660$	1.54120	0.0599910
$661$	3.90934	0.152056	0.0760278	−	0.997106i	$-0.475776\pi$
$661$	3.90934	0.152056	0.0760278	+	0.997106i	$0.475776\pi$
$662$	4.00824	0.155785
$663$	−0.684589	−0.0265872
$664$	9.76103	0.378801
$665$	0	0
$666$	29.0721	1.12652
$667$	−33.9407	−1.31419
$668$	−4.05262	−0.156801
$669$	−0.461375	−0.0178378
$670$	−12.4415	−0.480656
$671$	3.04819	0.117674
$672$	0.532424	0.0205387
$673$	−14.7146	−0.567205	−0.283603	−	0.958942i	$-0.591530\pi$
$673$	−14.7146	−0.567205	−0.283603	+	0.958942i	$0.591530\pi$
$674$	0.818998	0.0315466
$675$	−8.88456	−0.341967
$676$	1.00000	0.0384615
$677$	−7.23755	−0.278162	−0.139081	−	0.990281i	$-0.544415\pi$
$677$	−7.23755	−0.278162	−0.139081	+	0.990281i	$0.544415\pi$
$678$	−4.71681	−0.181148
$679$	19.4959	0.748185
$680$	−8.00083	−0.306818
$681$	0.0548755	0.00210283
$682$	−10.1504	−0.388678
$683$	11.5050	0.440228	0.220114	−	0.975474i	$-0.429357\pi$
$683$	11.5050	0.440228	0.220114	+	0.975474i	$0.429357\pi$
$684$	0	0
$685$	18.9844	0.725356
$686$	−19.8221	−0.756813
$687$	2.58333	0.0985602
$688$	6.66422	0.254071
$689$	13.4108	0.510912
$690$	−4.86579	−0.185237
$691$	−41.2049	−1.56751	−0.783754	−	0.621071i	$-0.786698\pi$
$691$	−41.2049	−1.56751	−0.783754	+	0.621071i	$0.786698\pi$
$692$	−2.19689	−0.0835133
$693$	−9.73068	−0.369638
$694$	27.9171	1.05972
$695$	−8.92032	−0.338367
$696$	−1.71975	−0.0651871
$697$	−21.2811	−0.806079
$698$	−8.33854	−0.315618
$699$	−0.00326073	−0.000123332 0
$700$	−10.4595	−0.395330
$701$	7.79854	0.294547	0.147273	−	0.989096i	$-0.452950\pi$
$701$	7.79854	0.294547	0.147273	+	0.989096i	$0.452950\pi$
$702$	1.63677	0.0617759
$703$	0	0
$704$	−1.72726	−0.0650985
$705$	−5.77322	−0.217432
$706$	−17.4488	−0.656693
$707$	29.4959	1.10931
$708$	3.19140	0.119940
$709$	32.1720	1.20825	0.604123	−	0.796891i	$-0.293524\pi$
$709$	32.1720	1.20825	0.604123	+	0.796891i	$0.293524\pi$
$710$	22.4665	0.843153
$711$	43.8084	1.64294
$712$	−8.18396	−0.306707
$713$	32.0463	1.20014
$714$	−1.31914	−0.0493675
$715$	5.57776	0.208596
$716$	−25.8048	−0.964371
$717$	3.40956	0.127333
$718$	−3.29874	−0.123108
$719$	−3.10751	−0.115890	−0.0579452	−	0.998320i	$-0.518455\pi$
$719$	−3.10751	−0.115890	−0.0579452	+	0.998320i	$0.518455\pi$
$720$	9.44123	0.351854
$721$	29.7176	1.10674
$722$	0	0
$723$	−1.88871	−0.0702420
$724$	10.5212	0.391016
$725$	33.7845	1.25472
$726$	2.21507	0.0822089
$727$	6.08806	0.225794	0.112897	−	0.993607i	$-0.463987\pi$
$727$	6.08806	0.225794	0.112897	+	0.993607i	$0.463987\pi$
$728$	1.92690	0.0714158
$729$	−22.9642	−0.850527
$730$	12.1400	0.449323
$731$	−16.5113	−0.610693
$732$	−0.487621	−0.0180230
$733$	−42.4333	−1.56731	−0.783654	−	0.621197i	$-0.786647\pi$
$733$	−42.4333	−1.56731	−0.783654	+	0.621197i	$0.786647\pi$
$734$	14.1051	0.520629
$735$	2.93296	0.108184
$736$	5.45322	0.201008
$737$	6.65466	0.245128
$738$	25.1124	0.924399
$739$	37.8382	1.39190	0.695950	−	0.718090i	$-0.254984\pi$
$739$	37.8382	1.39190	0.695950	+	0.718090i	$0.254984\pi$
$740$	−32.1109	−1.18042
$741$	0	0
$742$	25.8414	0.948667
$743$	17.2309	0.632141	0.316070	−	0.948736i	$-0.397636\pi$
$743$	17.2309	0.632141	0.316070	+	0.948736i	$0.397636\pi$
$744$	1.62377	0.0595301
$745$	−70.7192	−2.59095
$746$	22.5858	0.826925
$747$	28.5379	1.04415
$748$	4.27947	0.156473
$749$	15.3865	0.562209
$750$	0.381995	0.0139485
$751$	22.1918	0.809789	0.404894	−	0.914363i	$-0.367308\pi$
$751$	22.1918	0.809789	0.404894	+	0.914363i	$0.367308\pi$
$752$	6.47020	0.235944
$753$	5.66626	0.206490
$754$	−6.22398	−0.226664
$755$	19.6691	0.715830
$756$	3.15390	0.114706
$757$	−37.0445	−1.34641	−0.673203	−	0.739458i	$-0.735082\pi$
$757$	−37.0445	−1.34641	−0.673203	+	0.739458i	$0.735082\pi$
$758$	−18.3572	−0.666762
$759$	2.60260	0.0944684
$760$	0	0
$761$	−15.2357	−0.552294	−0.276147	−	0.961115i	$-0.589058\pi$
$761$	−15.2357	−0.552294	−0.276147	+	0.961115i	$0.589058\pi$
$762$	2.69233	0.0975328
$763$	2.81296	0.101836
$764$	−13.1671	−0.476369
$765$	−23.3917	−0.845727
$766$	3.58115	0.129392
$767$	11.5500	0.417048
$768$	0.276311	0.00997051
$769$	18.7931	0.677696	0.338848	−	0.940841i	$-0.389963\pi$
$769$	18.7931	0.677696	0.338848	+	0.940841i	$0.389963\pi$
$770$	10.7478	0.387324
$771$	−1.13764	−0.0409711
$772$	−3.26304	−0.117439
$773$	−23.8080	−0.856315	−0.428157	−	0.903704i	$-0.640837\pi$
$773$	−23.8080	−0.856315	−0.428157	+	0.903704i	$0.640837\pi$
$774$	19.4839	0.700333
$775$	−31.8988	−1.14584
$776$	10.1177	0.363206
$777$	−5.29429	−0.189932
$778$	22.6537	0.812174
$779$	0	0
$780$	−0.892279	−0.0319487
$781$	−12.0168	−0.429996
$782$	−13.5109	−0.483150
$783$	−10.1872	−0.364062
$784$	−3.28704	−0.117394
$785$	−44.5282	−1.58928
$786$	−2.22631	−0.0794099
$787$	24.4686	0.872212	0.436106	−	0.899895i	$-0.356357\pi$
$787$	24.4686	0.872212	0.436106	+	0.899895i	$0.356357\pi$
$788$	16.5424	0.589300
$789$	2.61007	0.0929209
$790$	−48.3877	−1.72156
$791$	−32.8935	−1.16956
$792$	−5.04990	−0.179440
$793$	−1.76476	−0.0626683
$794$	3.30516	0.117296
$795$	−11.9662	−0.424397
$796$	−14.0766	−0.498932
$797$	17.5583	0.621946	0.310973	−	0.950419i	$-0.399345\pi$
$797$	17.5583	0.621946	0.310973	+	0.950419i	$0.399345\pi$
$798$	0	0
$799$	−16.0306	−0.567122
$800$	−5.42811	−0.191913
$801$	−23.9270	−0.845421
$802$	20.5487	0.725601
$803$	−6.49343	−0.229148
$804$	−1.06455	−0.0375438
$805$	−33.9325	−1.19596
$806$	5.87659	0.206994
$807$	4.17842	0.147087
$808$	15.3074	0.538512
$809$	−11.7959	−0.414720	−0.207360	−	0.978265i	$-0.566487\pi$
$809$	−11.7959	−0.414720	−0.207360	+	0.978265i	$0.566487\pi$
$810$	26.8632	0.943878
$811$	2.00999	0.0705803	0.0352901	−	0.999377i	$-0.488764\pi$
$811$	2.00999	0.0705803	0.0352901	+	0.999377i	$0.488764\pi$
$812$	−11.9930	−0.420873
$813$	−4.24574	−0.148905
$814$	17.1754	0.601998
$815$	19.8942	0.696864
$816$	−0.684589	−0.0239654
$817$	0	0
$818$	6.76400	0.236498
$819$	5.63360	0.196854
$820$	−27.7373	−0.968630
$821$	7.38073	0.257589	0.128795	−	0.991671i	$-0.458889\pi$
$821$	7.38073	0.257589	0.128795	+	0.991671i	$0.458889\pi$
$822$	1.62440	0.0566573
$823$	2.07397	0.0722942	0.0361471	−	0.999346i	$-0.488492\pi$
$823$	2.07397	0.0722942	0.0361471	+	0.999346i	$0.488492\pi$
$824$	15.4225	0.537267
$825$	−2.59062	−0.0901938
$826$	22.2558	0.774379
$827$	−21.3025	−0.740760	−0.370380	−	0.928880i	$-0.620773\pi$
$827$	−21.3025	−0.740760	−0.370380	+	0.928880i	$0.620773\pi$
$828$	15.9433	0.554068
$829$	−26.5490	−0.922086	−0.461043	−	0.887378i	$-0.652525\pi$
$829$	−26.5490	−0.922086	−0.461043	+	0.887378i	$0.652525\pi$
$830$	−31.5209	−1.09411
$831$	−8.74040	−0.303201
$832$	1.00000	0.0346688
$833$	8.14399	0.282173
$834$	−0.763265	−0.0264297
$835$	13.0870	0.452893
$836$	0	0
$837$	9.61862	0.332468
$838$	1.77080	0.0611711
$839$	−40.8842	−1.41148	−0.705740	−	0.708471i	$-0.749385\pi$
$839$	−40.8842	−1.41148	−0.705740	+	0.708471i	$0.749385\pi$
$840$	−1.71934	−0.0593227
$841$	9.73798	0.335792
$842$	−32.2098	−1.11002
$843$	2.15654	0.0742752
$844$	8.92749	0.307297
$845$	−3.22926	−0.111090
$846$	18.9166	0.650366
$847$	15.4472	0.530772
$848$	13.4108	0.460530
$849$	1.30719	0.0448628
$850$	13.4487	0.461287
$851$	−54.2254	−1.85882
$852$	1.92234	0.0658583
$853$	5.85098	0.200334	0.100167	−	0.994971i	$-0.468062\pi$
$853$	5.85098	0.200334	0.100167	+	0.994971i	$0.468062\pi$
$854$	−3.40051	−0.116363
$855$	0	0
$856$	7.98507	0.272924
$857$	23.3634	0.798079	0.399039	−	0.916934i	$-0.369344\pi$
$857$	23.3634	0.798079	0.399039	+	0.916934i	$0.369344\pi$
$858$	0.477260	0.0162934
$859$	42.8689	1.46267	0.731334	−	0.682019i	$-0.238898\pi$
$859$	42.8689	1.46267	0.731334	+	0.682019i	$0.238898\pi$
$860$	−21.5205	−0.733842
$861$	−4.57320	−0.155854
$862$	10.3497	0.352514
$863$	−47.9658	−1.63277	−0.816387	−	0.577505i	$-0.804026\pi$
$863$	−47.9658	−1.63277	−0.816387	+	0.577505i	$0.804026\pi$
$864$	1.63677	0.0556840
$865$	7.09434	0.241215
$866$	−28.7793	−0.977962
$867$	−3.00114	−0.101924
$868$	11.3236	0.384349
$869$	25.8815	0.877969
$870$	5.55353	0.188282
$871$	−3.85273	−0.130545
$872$	1.45984	0.0494363
$873$	29.5808	1.00116
$874$	0	0
$875$	2.66391	0.0900567
$876$	1.03876	0.0350964
$877$	−6.62271	−0.223633	−0.111817	−	0.993729i	$-0.535667\pi$
$877$	−6.62271	−0.223633	−0.111817	+	0.993729i	$0.535667\pi$
$878$	−6.47174	−0.218411
$879$	0.362999	0.0122437
$880$	5.57776	0.188026
$881$	−50.7597	−1.71014	−0.855068	−	0.518515i	$-0.826485\pi$
$881$	−50.7597	−1.71014	−0.855068	+	0.518515i	$0.826485\pi$
$882$	−9.61016	−0.323591
$883$	6.69751	0.225389	0.112694	−	0.993630i	$-0.464052\pi$
$883$	6.69751	0.225389	0.112694	+	0.993630i	$0.464052\pi$
$884$	−2.47761	−0.0833309
$885$	−10.3059	−0.346428
$886$	−3.51346	−0.118037
$887$	6.03875	0.202761	0.101381	−	0.994848i	$-0.467674\pi$
$887$	6.03875	0.202761	0.101381	+	0.994848i	$0.467674\pi$
$888$	−2.74756	−0.0922022
$889$	18.7755	0.629709
$890$	26.4281	0.885872
$891$	−14.3685	−0.481364
$892$	−1.66977	−0.0559080
$893$	0	0
$894$	−6.05108	−0.202378
$895$	83.3304	2.78543
$896$	1.92690	0.0643734
$897$	−1.50678	−0.0503100
$898$	22.3130	0.744596
$899$	−36.5758	−1.21987
$900$	−15.8699	−0.528997
$901$	−33.2268	−1.10694
$902$	14.8361	0.493987
$903$	−3.54819	−0.118076
$904$	−17.0707	−0.567762
$905$	−33.9756	−1.12939
$906$	1.68298	0.0559132
$907$	29.1315	0.967295	0.483647	−	0.875263i	$-0.339312\pi$
$907$	29.1315	0.967295	0.483647	+	0.875263i	$0.339312\pi$
$908$	0.198601	0.00659079
$909$	44.7535	1.48438
$910$	−6.22247	−0.206273
$911$	15.5852	0.516360	0.258180	−	0.966097i	$-0.416877\pi$
$911$	15.5852	0.516360	0.258180	+	0.966097i	$0.416877\pi$
$912$	0	0
$913$	16.8598	0.557978
$914$	−3.84010	−0.127019
$915$	1.57465	0.0520564
$916$	9.34936	0.308912
$917$	−15.5256	−0.512700
$918$	−4.05527	−0.133844
$919$	29.9657	0.988477	0.494239	−	0.869326i	$-0.335447\pi$
$919$	29.9657	0.988477	0.494239	+	0.869326i	$0.335447\pi$
$920$	−17.6098	−0.580579
$921$	3.53988	0.116643
$922$	14.7910	0.487115
$923$	6.95717	0.228998
$924$	0.919634	0.0302537
$925$	53.9758	1.77471
$926$	−19.7642	−0.649491
$927$	45.0900	1.48095
$928$	−6.22398	−0.204312
$929$	−0.907211	−0.0297646	−0.0148823	−	0.999889i	$-0.504737\pi$
$929$	−0.907211	−0.0297646	−0.0148823	+	0.999889i	$0.504737\pi$
$930$	−5.24356	−0.171943
$931$	0	0
$932$	−0.0118010	−0.000386553 0
$933$	8.46756	0.277215
$934$	−34.0785	−1.11508
$935$	−13.8195	−0.451946
$936$	2.92365	0.0955626
$937$	−36.5835	−1.19513	−0.597565	−	0.801820i	$-0.703865\pi$
$937$	−36.5835	−1.19513	−0.597565	+	0.801820i	$0.703865\pi$
$938$	−7.42385	−0.242397
$939$	−4.25316	−0.138797
$940$	−20.8939	−0.681485
$941$	30.2431	0.985898	0.492949	−	0.870058i	$-0.335919\pi$
$941$	30.2431	0.985898	0.492949	+	0.870058i	$0.335919\pi$
$942$	−3.81004	−0.124138
$943$	−46.8398	−1.52531
$944$	11.5500	0.375922
$945$	−10.1847	−0.331310
$946$	11.5108	0.374249
$947$	31.1032	1.01072	0.505359	−	0.862909i	$-0.331360\pi$
$947$	31.1032	1.01072	0.505359	+	0.862909i	$0.331360\pi$
$948$	−4.14028	−0.134470
$949$	3.75939	0.122035
$950$	0	0
$951$	4.47204	0.145016
$952$	−4.77411	−0.154730
$953$	−29.7160	−0.962596	−0.481298	−	0.876557i	$-0.659835\pi$
$953$	−29.7160	−0.962596	−0.481298	+	0.876557i	$0.659835\pi$
$954$	39.2086	1.26943
$955$	42.5200	1.37592
$956$	12.3396	0.399091
$957$	−2.97046	−0.0960213
$958$	38.1612	1.23293
$959$	11.3280	0.365801
$960$	−0.892279	−0.0287982
$961$	3.53431	0.114010
$962$	−9.94375	−0.320599
$963$	23.3456	0.752301
$964$	−6.83547	−0.220156
$965$	10.5372	0.339205
$966$	−2.90343	−0.0934162
$967$	57.3280	1.84354	0.921771	−	0.387734i	$-0.126742\pi$
$967$	57.3280	1.84354	0.921771	+	0.387734i	$0.126742\pi$
$968$	8.01658	0.257663
$969$	0	0
$970$	−32.6728	−1.04906
$971$	−45.5484	−1.46172	−0.730859	−	0.682529i	$-0.760880\pi$
$971$	−45.5484	−1.46172	−0.730859	+	0.682529i	$0.760880\pi$
$972$	7.20885	0.231224
$973$	−5.32277	−0.170640
$974$	28.4320	0.911022
$975$	1.49985	0.0480335
$976$	−1.76476	−0.0564884
$977$	42.2238	1.35086	0.675430	−	0.737424i	$-0.263958\pi$
$977$	42.2238	1.35086	0.675430	+	0.737424i	$0.263958\pi$
$978$	1.70224	0.0544318
$979$	−14.1358	−0.451782
$980$	10.6147	0.339074
$981$	4.26805	0.136268
$982$	44.0285	1.40500
$983$	2.11220	0.0673687	0.0336844	−	0.999433i	$-0.489276\pi$
$983$	2.11220	0.0673687	0.0336844	+	0.999433i	$0.489276\pi$
$984$	−2.37334	−0.0756593
$985$	−53.4198	−1.70210
$986$	15.4206	0.491091
$987$	−3.44489	−0.109652
$988$	0	0
$989$	−36.3414	−1.15559
$990$	16.3074	0.518284
$991$	−28.7171	−0.912229	−0.456114	−	0.889921i	$-0.650759\pi$
$991$	−28.7171	−0.912229	−0.456114	+	0.889921i	$0.650759\pi$
$992$	5.87659	0.186582
$993$	−1.10752	−0.0351461
$994$	13.4058	0.425206
$995$	45.4570	1.44108
$996$	−2.69708	−0.0854601
$997$	14.1738	0.448888	0.224444	−	0.974487i	$-0.427943\pi$
$997$	14.1738	0.448888	0.224444	+	0.974487i	$0.427943\pi$
$998$	−15.7478	−0.498489
$999$	−16.2756	−0.514938

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9386.2.a.bw.1.9		15
19.3	odd	18		494.2.x.d.313.3	yes	30
19.13	odd	18		494.2.x.d.131.3	✓	30
19.18	odd	2		9386.2.a.bz.1.7		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.x.d.131.3	✓	30	19.13	odd	18
494.2.x.d.313.3	yes	30	19.3	odd	18
9386.2.a.bw.1.9		15	1.1	even	1	trivial
9386.2.a.bz.1.7		15	19.18	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:	\( N \)	\(=\)	\( 9386 = 2 \cdot 13 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9386.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.276311 q^{3} +1.00000 q^{4} -3.22926 q^{5} -0.276311 q^{6} -1.92690 q^{7} -1.00000 q^{8} -2.92365 q^{9} +3.22926 q^{10} -1.72726 q^{11} +0.276311 q^{12} +1.00000 q^{13} +1.92690 q^{14} -0.892279 q^{15} +1.00000 q^{16} -2.47761 q^{17} +2.92365 q^{18} -3.22926 q^{20} -0.532424 q^{21} +1.72726 q^{22} -5.45322 q^{23} -0.276311 q^{24} +5.42811 q^{25} -1.00000 q^{26} -1.63677 q^{27} -1.92690 q^{28} +6.22398 q^{29} +0.892279 q^{30} -5.87659 q^{31} -1.00000 q^{32} -0.477260 q^{33} +2.47761 q^{34} +6.22247 q^{35} -2.92365 q^{36} +9.94375 q^{37} +0.276311 q^{39} +3.22926 q^{40} +8.58938 q^{41} +0.532424 q^{42} +6.66422 q^{43} -1.72726 q^{44} +9.44123 q^{45} +5.45322 q^{46} +6.47020 q^{47} +0.276311 q^{48} -3.28704 q^{49} -5.42811 q^{50} -0.684589 q^{51} +1.00000 q^{52} +13.4108 q^{53} +1.63677 q^{54} +5.57776 q^{55} +1.92690 q^{56} -6.22398 q^{58} +11.5500 q^{59} -0.892279 q^{60} -1.76476 q^{61} +5.87659 q^{62} +5.63360 q^{63} +1.00000 q^{64} -3.22926 q^{65} +0.477260 q^{66} -3.85273 q^{67} -2.47761 q^{68} -1.50678 q^{69} -6.22247 q^{70} +6.95717 q^{71} +2.92365 q^{72} +3.75939 q^{73} -9.94375 q^{74} +1.49985 q^{75} +3.32826 q^{77} -0.276311 q^{78} -14.9841 q^{79} -3.22926 q^{80} +8.31870 q^{81} -8.58938 q^{82} -9.76103 q^{83} -0.532424 q^{84} +8.00083 q^{85} -6.66422 q^{86} +1.71975 q^{87} +1.72726 q^{88} +8.18396 q^{89} -9.44123 q^{90} -1.92690 q^{91} -5.45322 q^{92} -1.62377 q^{93} -6.47020 q^{94} -0.276311 q^{96} -10.1177 q^{97} +3.28704 q^{98} +5.04990 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} - 3 q^{3} + 15 q^{4} + 3 q^{5} + 3 q^{6} - 15 q^{8} + 18 q^{9} - 3 q^{10} - 3 q^{11} - 3 q^{12} + 15 q^{13} + 15 q^{16} + 3 q^{17} - 18 q^{18} + 3 q^{20} - 33 q^{21} + 3 q^{22} + 9 q^{23}+ \cdots + 3 q^{98}+O(q^{100}) \) 15 * q - 15 * q^2 - 3 * q^3 + 15 * q^4 + 3 * q^5 + 3 * q^6 - 15 * q^8 + 18 * q^9 - 3 * q^10 - 3 * q^11 - 3 * q^12 + 15 * q^13 + 15 * q^16 + 3 * q^17 - 18 * q^18 + 3 * q^20 - 33 * q^21 + 3 * q^22 + 9 * q^23 + 3 * q^24 + 24 * q^25 - 15 * q^26 - 42 * q^27 - 12 * q^29 - 24 * q^31 - 15 * q^32 + 3 * q^33 - 3 * q^34 + 6 * q^35 + 18 * q^36 - 30 * q^37 - 3 * q^39 - 3 * q^40 + 24 * q^41 + 33 * q^42 - 12 * q^43 - 3 * q^44 + 21 * q^45 - 9 * q^46 - 6 * q^47 - 3 * q^48 - 3 * q^49 - 24 * q^50 - 48 * q^51 + 15 * q^52 - 9 * q^53 + 42 * q^54 - 60 * q^55 + 12 * q^58 - 12 * q^59 - 12 * q^61 + 24 * q^62 + 15 * q^63 + 15 * q^64 + 3 * q^65 - 3 * q^66 - 48 * q^67 + 3 * q^68 - 18 * q^69 - 6 * q^70 - 21 * q^71 - 18 * q^72 + 21 * q^73 + 30 * q^74 - 21 * q^75 - 9 * q^77 + 3 * q^78 - 45 * q^79 + 3 * q^80 + 15 * q^81 - 24 * q^82 - 33 * q^83 - 33 * q^84 - 6 * q^85 + 12 * q^86 + 9 * q^87 + 3 * q^88 + 12 * q^89 - 21 * q^90 + 9 * q^92 - 3 * q^93 + 6 * q^94 + 3 * q^96 + 24 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

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Groups

Database

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