LMFDB - Embedded newform 2535.2.a.bm.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2535,2,Mod(1,2535)] 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("2535.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2535, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2535 = 3 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2535.a (trivial)

Newform invariants

comment:select newform

sage:traces = [9,0,-9,10,-9,0,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$20.2420769124$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 9x^{7} + 29x^{6} + 17x^{5} - 83x^{4} + 17x^{3} + 70x^{2} - 48x + 8 $ x^9 - 3x^8 - 9x^7 + 29x^6 + 17x^5 - 83x^4 + 17x^3 + 70x^2 - 48x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.813006$ of defining polynomial
Character	$\chi$	$=$	2535.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.16585 q^{2} -1.00000 q^{3} -0.640788 q^{4} -1.00000 q^{5} +1.16585 q^{6} +0.957202 q^{7} +3.07877 q^{8} +1.00000 q^{9} +1.16585 q^{10} -5.05761 q^{11} +0.640788 q^{12} -1.11596 q^{14} +1.00000 q^{15} -2.30781 q^{16} -1.25739 q^{17} -1.16585 q^{18} +2.44704 q^{19} +0.640788 q^{20} -0.957202 q^{21} +5.89643 q^{22} -5.45555 q^{23} -3.07877 q^{24} +1.00000 q^{25} -1.00000 q^{27} -0.613364 q^{28} +10.2006 q^{29} -1.16585 q^{30} -1.02783 q^{31} -3.46697 q^{32} +5.05761 q^{33} +1.46593 q^{34} -0.957202 q^{35} -0.640788 q^{36} -0.939148 q^{37} -2.85289 q^{38} -3.07877 q^{40} -7.55650 q^{41} +1.11596 q^{42} +0.259367 q^{43} +3.24086 q^{44} -1.00000 q^{45} +6.36037 q^{46} +0.115292 q^{47} +2.30781 q^{48} -6.08376 q^{49} -1.16585 q^{50} +1.25739 q^{51} -2.43698 q^{53} +1.16585 q^{54} +5.05761 q^{55} +2.94700 q^{56} -2.44704 q^{57} -11.8924 q^{58} -8.32438 q^{59} -0.640788 q^{60} +13.1657 q^{61} +1.19830 q^{62} +0.957202 q^{63} +8.65760 q^{64} -5.89643 q^{66} -11.8247 q^{67} +0.805722 q^{68} +5.45555 q^{69} +1.11596 q^{70} +0.977874 q^{71} +3.07877 q^{72} +7.06112 q^{73} +1.09491 q^{74} -1.00000 q^{75} -1.56804 q^{76} -4.84116 q^{77} -13.0206 q^{79} +2.30781 q^{80} +1.00000 q^{81} +8.80977 q^{82} -3.76930 q^{83} +0.613364 q^{84} +1.25739 q^{85} -0.302384 q^{86} -10.2006 q^{87} -15.5712 q^{88} -17.9201 q^{89} +1.16585 q^{90} +3.49585 q^{92} +1.02783 q^{93} -0.134414 q^{94} -2.44704 q^{95} +3.46697 q^{96} +8.42595 q^{97} +7.09277 q^{98} -5.05761 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{3} + 10 q^{4} - 9 q^{5} + 10 q^{7} - 3 q^{8} + 9 q^{9} - 11 q^{11} - 10 q^{12} + 10 q^{14} + 9 q^{15} + 8 q^{16} + 18 q^{17} - 10 q^{19} - 10 q^{20} - 10 q^{21} + 17 q^{22} - 7 q^{23} + 3 q^{24}+ \cdots - 11 q^{99}+O(q^{100}) $ 9 * q - 9 * q^3 + 10 * q^4 - 9 * q^5 + 10 * q^7 - 3 * q^8 + 9 * q^9 - 11 * q^11 - 10 * q^12 + 10 * q^14 + 9 * q^15 + 8 * q^16 + 18 * q^17 - 10 * q^19 - 10 * q^20 - 10 * q^21 + 17 * q^22 - 7 * q^23 + 3 * q^24 + 9 * q^25 - 9 * q^27 + 43 * q^28 - 9 * q^29 - 17 * q^31 - 11 * q^32 + 11 * q^33 + 4 * q^34 - 10 * q^35 + 10 * q^36 - 3 * q^37 + 21 * q^38 + 3 * q^40 - 4 * q^41 - 10 * q^42 + 14 * q^43 - 13 * q^44 - 9 * q^45 - 3 * q^46 + 2 * q^47 - 8 * q^48 + 43 * q^49 - 18 * q^51 + 5 * q^53 + 11 * q^55 + q^56 + 10 * q^57 + 14 * q^58 - 3 * q^59 + 10 * q^60 + 48 * q^61 - 7 * q^62 + 10 * q^63 + 41 * q^64 - 17 * q^66 + 40 * q^67 + 40 * q^68 + 7 * q^69 - 10 * q^70 - 12 * q^71 - 3 * q^72 + 38 * q^73 - 4 * q^74 - 9 * q^75 - 51 * q^76 + 8 * q^77 + 22 * q^79 - 8 * q^80 + 9 * q^81 + 38 * q^82 - 11 * q^83 - 43 * q^84 - 18 * q^85 - 56 * q^86 + 9 * q^87 + 50 * q^88 - 2 * q^89 - 36 * q^92 + 17 * q^93 + 42 * q^94 + 10 * q^95 + 11 * q^96 + 23 * q^97 + 79 * q^98 - 11 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.16585	−0.824382	−0.412191	−	0.911097i	$-0.635236\pi$
$2$	−1.16585	−0.824382	−0.412191	+	0.911097i	$0.635236\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.640788	−0.320394
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.16585	0.475957
$7$	0.957202	0.361788	0.180894	−	0.983503i	$-0.442101\pi$
$7$	0.957202	0.361788	0.180894	+	0.983503i	$0.442101\pi$
$8$	3.07877	1.08851
$9$	1.00000	0.333333
$10$	1.16585	0.368675
$11$	−5.05761	−1.52493	−0.762464	−	0.647031i	$-0.776011\pi$
$11$	−5.05761	−1.52493	−0.762464	+	0.647031i	$0.776011\pi$
$12$	0.640788	0.184980
$13$	0	0
$13$	0	0
$14$	−1.11596	−0.298252
$15$	1.00000	0.258199
$16$	−2.30781	−0.576954
$17$	−1.25739	−0.304962	−0.152481	−	0.988306i	$-0.548726\pi$
$17$	−1.25739	−0.304962	−0.152481	+	0.988306i	$0.548726\pi$
$18$	−1.16585	−0.274794
$19$	2.44704	0.561390	0.280695	−	0.959797i	$-0.409435\pi$
$19$	2.44704	0.561390	0.280695	+	0.959797i	$0.409435\pi$
$20$	0.640788	0.143285
$21$	−0.957202	−0.208879
$22$	5.89643	1.25712
$23$	−5.45555	−1.13756	−0.568781	−	0.822489i	$-0.692585\pi$
$23$	−5.45555	−1.13756	−0.568781	+	0.822489i	$0.692585\pi$
$24$	−3.07877	−0.628451
$25$	1.00000	0.200000
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−0.613364	−0.115915
$29$	10.2006	1.89421	0.947103	−	0.320929i	$-0.103995\pi$
$29$	10.2006	1.89421	0.947103	+	0.320929i	$0.103995\pi$
$30$	−1.16585	−0.212855
$31$	−1.02783	−0.184604	−0.0923022	−	0.995731i	$-0.529423\pi$
$31$	−1.02783	−0.184604	−0.0923022	+	0.995731i	$0.529423\pi$
$32$	−3.46697	−0.612879
$33$	5.05761	0.880418
$34$	1.46593	0.251405
$35$	−0.957202	−0.161797
$36$	−0.640788	−0.106798
$37$	−0.939148	−0.154395	−0.0771975	−	0.997016i	$-0.524597\pi$
$37$	−0.939148	−0.154395	−0.0771975	+	0.997016i	$0.524597\pi$
$38$	−2.85289	−0.462800
$39$	0	0
$40$	−3.07877	−0.486796
$41$	−7.55650	−1.18013	−0.590064	−	0.807357i	$-0.700897\pi$
$41$	−7.55650	−1.18013	−0.590064	+	0.807357i	$0.700897\pi$
$42$	1.11596	0.172196
$43$	0.259367	0.0395531	0.0197765	−	0.999804i	$-0.493705\pi$
$43$	0.259367	0.0395531	0.0197765	+	0.999804i	$0.493705\pi$
$44$	3.24086	0.488578
$45$	−1.00000	−0.149071
$46$	6.36037	0.937786
$47$	0.115292	0.0168171	0.00840855	−	0.999965i	$-0.497323\pi$
$47$	0.115292	0.0168171	0.00840855	+	0.999965i	$0.497323\pi$
$48$	2.30781	0.333104
$49$	−6.08376	−0.869109
$50$	−1.16585	−0.164876
$51$	1.25739	0.176070
$52$	0	0
$53$	−2.43698	−0.334745	−0.167372	−	0.985894i	$-0.553528\pi$
$53$	−2.43698	−0.334745	−0.167372	+	0.985894i	$0.553528\pi$
$54$	1.16585	0.158652
$55$	5.05761	0.681969
$56$	2.94700	0.393810
$57$	−2.44704	−0.324119
$58$	−11.8924	−1.56155
$59$	−8.32438	−1.08374	−0.541871	−	0.840461i	$-0.682284\pi$
$59$	−8.32438	−1.08374	−0.541871	+	0.840461i	$0.682284\pi$
$60$	−0.640788	−0.0827254
$61$	13.1657	1.68569	0.842845	−	0.538156i	$-0.180879\pi$
$61$	13.1657	1.68569	0.842845	+	0.538156i	$0.180879\pi$
$62$	1.19830	0.152185
$63$	0.957202	0.120596
$64$	8.65760	1.08220
$65$	0	0
$66$	−5.89643	−0.725801
$67$	−11.8247	−1.44462	−0.722311	−	0.691569i	$-0.756920\pi$
$67$	−11.8247	−1.44462	−0.722311	+	0.691569i	$0.756920\pi$
$68$	0.805722	0.0977081
$69$	5.45555	0.656772
$70$	1.11596	0.133382
$71$	0.977874	0.116052	0.0580261	−	0.998315i	$-0.481519\pi$
$71$	0.977874	0.116052	0.0580261	+	0.998315i	$0.481519\pi$
$72$	3.07877	0.362836
$73$	7.06112	0.826442	0.413221	−	0.910631i	$-0.364404\pi$
$73$	7.06112	0.826442	0.413221	+	0.910631i	$0.364404\pi$
$74$	1.09491	0.127280
$75$	−1.00000	−0.115470
$76$	−1.56804	−0.179866
$77$	−4.84116	−0.551701
$78$	0	0
$79$	−13.0206	−1.46493	−0.732467	−	0.680803i	$-0.761631\pi$
$79$	−13.0206	−1.46493	−0.732467	+	0.680803i	$0.761631\pi$
$80$	2.30781	0.258022
$81$	1.00000	0.111111
$82$	8.80977	0.972876
$83$	−3.76930	−0.413734	−0.206867	−	0.978369i	$-0.566327\pi$
$83$	−3.76930	−0.413734	−0.206867	+	0.978369i	$0.566327\pi$
$84$	0.613364	0.0669235
$85$	1.25739	0.136383
$86$	−0.302384	−0.0326069
$87$	−10.2006	−1.09362
$88$	−15.5712	−1.65990
$89$	−17.9201	−1.89952	−0.949762	−	0.312972i	$-0.898675\pi$
$89$	−17.9201	−1.89952	−0.949762	+	0.312972i	$0.898675\pi$
$90$	1.16585	0.122892
$91$	0	0
$92$	3.49585	0.364468
$93$	1.02783	0.106581
$94$	−0.134414	−0.0138637
$95$	−2.44704	−0.251061
$96$	3.46697	0.353846
$97$	8.42595	0.855525	0.427763	−	0.903891i	$-0.359302\pi$
$97$	8.42595	0.855525	0.427763	+	0.903891i	$0.359302\pi$
$98$	7.09277	0.716478
$99$	−5.05761	−0.508309
$100$	−0.640788	−0.0640788
$101$	4.78493	0.476118	0.238059	−	0.971251i	$-0.423489\pi$
$101$	4.78493	0.476118	0.238059	+	0.971251i	$0.423489\pi$
$102$	−1.46593	−0.145149
$103$	10.6406	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$103$	10.6406	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$104$	0	0
$105$	0.957202	0.0934134
$106$	2.84116	0.275958
$107$	16.5805	1.60290	0.801449	−	0.598063i	$-0.204063\pi$
$107$	16.5805	1.60290	0.801449	+	0.598063i	$0.204063\pi$
$108$	0.640788	0.0616599
$109$	−12.8615	−1.23191	−0.615953	−	0.787783i	$-0.711229\pi$
$109$	−12.8615	−1.23191	−0.615953	+	0.787783i	$0.711229\pi$
$110$	−5.89643	−0.562203
$111$	0.939148	0.0891400
$112$	−2.20905	−0.208735
$113$	13.2710	1.24843	0.624213	−	0.781254i	$-0.285420\pi$
$113$	13.2710	1.24843	0.624213	+	0.781254i	$0.285420\pi$
$114$	2.85289	0.267198
$115$	5.45555	0.508733
$116$	−6.53643	−0.606892
$117$	0	0
$118$	9.70500	0.893418
$119$	−1.20358	−0.110332
$120$	3.07877	0.281052
$121$	14.5795	1.32541
$122$	−15.3492	−1.38965
$123$	7.55650	0.681347
$124$	0.658624	0.0591462
$125$	−1.00000	−0.0894427
$126$	−1.11596	−0.0994173
$127$	13.4321	1.19191	0.595953	−	0.803020i	$-0.296775\pi$
$127$	13.4321	1.19191	0.595953	+	0.803020i	$0.296775\pi$
$128$	−3.15955	−0.279268
$129$	−0.259367	−0.0228360
$130$	0	0
$131$	8.09375	0.707154	0.353577	−	0.935405i	$-0.384965\pi$
$131$	8.09375	0.707154	0.353577	+	0.935405i	$0.384965\pi$
$132$	−3.24086	−0.282081
$133$	2.34231	0.203104
$134$	13.7859	1.19092
$135$	1.00000	0.0860663
$136$	−3.87122	−0.331954
$137$	17.5189	1.49674	0.748372	−	0.663279i	$-0.230836\pi$
$137$	17.5189	1.49674	0.748372	+	0.663279i	$0.230836\pi$
$138$	−6.36037	−0.541431
$139$	−8.84347	−0.750094	−0.375047	−	0.927006i	$-0.622373\pi$
$139$	−8.84347	−0.750094	−0.375047	+	0.927006i	$0.622373\pi$
$140$	0.613364	0.0518387
$141$	−0.115292	−0.00970935
$142$	−1.14006	−0.0956714
$143$	0	0
$144$	−2.30781	−0.192318
$145$	−10.2006	−0.847115
$146$	−8.23223	−0.681304
$147$	6.08376	0.501780
$148$	0.601795	0.0494672
$149$	−7.44717	−0.610096	−0.305048	−	0.952337i	$-0.598673\pi$
$149$	−7.44717	−0.610096	−0.305048	+	0.952337i	$0.598673\pi$
$150$	1.16585	0.0951915
$151$	18.9412	1.54141	0.770705	−	0.637192i	$-0.219904\pi$
$151$	18.9412	1.54141	0.770705	+	0.637192i	$0.219904\pi$
$152$	7.53388	0.611078
$153$	−1.25739	−0.101654
$154$	5.64408	0.454813
$155$	1.02783	0.0825576
$156$	0	0
$157$	20.1480	1.60799	0.803993	−	0.594638i	$-0.202705\pi$
$157$	20.1480	1.60799	0.803993	+	0.594638i	$0.202705\pi$
$158$	15.1801	1.20766
$159$	2.43698	0.193265
$160$	3.46697	0.274088
$161$	−5.22207	−0.411557
$162$	−1.16585	−0.0915980
$163$	9.33184	0.730926	0.365463	−	0.930826i	$-0.380911\pi$
$163$	9.33184	0.730926	0.365463	+	0.930826i	$0.380911\pi$
$164$	4.84212	0.378106
$165$	−5.05761	−0.393735
$166$	4.39444	0.341075
$167$	−0.308104	−0.0238418	−0.0119209	−	0.999929i	$-0.503795\pi$
$167$	−0.308104	−0.0238418	−0.0119209	+	0.999929i	$0.503795\pi$
$168$	−2.94700	−0.227366
$169$	0	0
$170$	−1.46593	−0.112432
$171$	2.44704	0.187130
$172$	−0.166199	−0.0126726
$173$	−9.83812	−0.747978	−0.373989	−	0.927433i	$-0.622010\pi$
$173$	−9.83812	−0.747978	−0.373989	+	0.927433i	$0.622010\pi$
$174$	11.8924	0.901562
$175$	0.957202	0.0723577
$176$	11.6720	0.879813
$177$	8.32438	0.625699
$178$	20.8922	1.56593
$179$	−3.92634	−0.293469	−0.146734	−	0.989176i	$-0.546876\pi$
$179$	−3.92634	−0.293469	−0.146734	+	0.989176i	$0.546876\pi$
$180$	0.640788	0.0477615
$181$	21.3537	1.58721	0.793603	−	0.608436i	$-0.208203\pi$
$181$	21.3537	1.58721	0.793603	+	0.608436i	$0.208203\pi$
$182$	0	0
$183$	−13.1657	−0.973234
$184$	−16.7964	−1.23825
$185$	0.939148	0.0690475
$186$	−1.19830	−0.0878638
$187$	6.35940	0.465046
$188$	−0.0738779	−0.00538810
$189$	−0.957202	−0.0696262
$190$	2.85289	0.206970
$191$	2.06081	0.149115	0.0745577	−	0.997217i	$-0.476246\pi$
$191$	2.06081	0.149115	0.0745577	+	0.997217i	$0.476246\pi$
$192$	−8.65760	−0.624809
$193$	10.6654	0.767709	0.383855	−	0.923394i	$-0.374596\pi$
$193$	10.6654	0.767709	0.383855	+	0.923394i	$0.374596\pi$
$194$	−9.82341	−0.705280
$195$	0	0
$196$	3.89840	0.278457
$197$	17.2608	1.22978	0.614889	−	0.788613i	$-0.289201\pi$
$197$	17.2608	1.22978	0.614889	+	0.788613i	$0.289201\pi$
$198$	5.89643	0.419041
$199$	1.48323	0.105143	0.0525716	−	0.998617i	$-0.483258\pi$
$199$	1.48323	0.105143	0.0525716	+	0.998617i	$0.483258\pi$
$200$	3.07877	0.217702
$201$	11.8247	0.834053
$202$	−5.57852	−0.392503
$203$	9.76405	0.685302
$204$	−0.805722	−0.0564118
$205$	7.55650	0.527769
$206$	−12.4053	−0.864319
$207$	−5.45555	−0.379187
$208$	0	0
$209$	−12.3762	−0.856080
$210$	−1.11596	−0.0770083
$211$	4.95941	0.341420	0.170710	−	0.985321i	$-0.445394\pi$
$211$	4.95941	0.341420	0.170710	+	0.985321i	$0.445394\pi$
$212$	1.56159	0.107250
$213$	−0.977874	−0.0670028
$214$	−19.3304	−1.32140
$215$	−0.259367	−0.0176887
$216$	−3.07877	−0.209484
$217$	−0.983845	−0.0667878
$218$	14.9946	1.01556
$219$	−7.06112	−0.477146
$220$	−3.24086	−0.218499
$221$	0	0
$222$	−1.09491	−0.0734854
$223$	28.1738	1.88666	0.943329	−	0.331860i	$-0.107676\pi$
$223$	28.1738	1.88666	0.943329	+	0.331860i	$0.107676\pi$
$224$	−3.31859	−0.221732
$225$	1.00000	0.0666667
$226$	−15.4720	−1.02918
$227$	−21.1618	−1.40456	−0.702280	−	0.711901i	$-0.747835\pi$
$227$	−21.1618	−1.40456	−0.702280	+	0.711901i	$0.747835\pi$
$228$	1.56804	0.103846
$229$	24.2688	1.60373	0.801865	−	0.597506i	$-0.203841\pi$
$229$	24.2688	1.60373	0.801865	+	0.597506i	$0.203841\pi$
$230$	−6.36037	−0.419391
$231$	4.84116	0.318525
$232$	31.4053	2.06186
$233$	−24.5751	−1.60997	−0.804983	−	0.593298i	$-0.797826\pi$
$233$	−24.5751	−1.60997	−0.804983	+	0.593298i	$0.797826\pi$
$234$	0	0
$235$	−0.115292	−0.00752083
$236$	5.33417	0.347225
$237$	13.0206	0.845780
$238$	1.40319	0.0909556
$239$	25.0729	1.62183	0.810916	−	0.585163i	$-0.198969\pi$
$239$	25.0729	1.62183	0.810916	+	0.585163i	$0.198969\pi$
$240$	−2.30781	−0.148969
$241$	−1.78188	−0.114781	−0.0573904	−	0.998352i	$-0.518278\pi$
$241$	−1.78188	−0.114781	−0.0573904	+	0.998352i	$0.518278\pi$
$242$	−16.9975	−1.09264
$243$	−1.00000	−0.0641500
$244$	−8.43640	−0.540085
$245$	6.08376	0.388677
$246$	−8.80977	−0.561690
$247$	0	0
$248$	−3.16446	−0.200944
$249$	3.76930	0.238870
$250$	1.16585	0.0737350
$251$	−17.7480	−1.12024	−0.560122	−	0.828410i	$-0.689246\pi$
$251$	−17.7480	−1.12024	−0.560122	+	0.828410i	$0.689246\pi$
$252$	−0.613364	−0.0386383
$253$	27.5921	1.73470
$254$	−15.6598	−0.982585
$255$	−1.25739	−0.0787409
$256$	−13.6316	−0.851977
$257$	27.8765	1.73889	0.869445	−	0.494031i	$-0.164477\pi$
$257$	27.8765	1.73889	0.869445	+	0.494031i	$0.164477\pi$
$258$	0.302384	0.0188256
$259$	−0.898955	−0.0558583
$260$	0	0
$261$	10.2006	0.631402
$262$	−9.43612	−0.582965
$263$	11.9705	0.738134	0.369067	−	0.929403i	$-0.379677\pi$
$263$	11.9705	0.738134	0.369067	+	0.929403i	$0.379677\pi$
$264$	15.5712	0.958343
$265$	2.43698	0.149702
$266$	−2.73079	−0.167436
$267$	17.9201	1.09669
$268$	7.57715	0.462848
$269$	−17.0425	−1.03910	−0.519551	−	0.854440i	$-0.673901\pi$
$269$	−17.0425	−1.03910	−0.519551	+	0.854440i	$0.673901\pi$
$270$	−1.16585	−0.0709515
$271$	−12.3515	−0.750301	−0.375151	−	0.926964i	$-0.622409\pi$
$271$	−12.3515	−0.750301	−0.375151	+	0.926964i	$0.622409\pi$
$272$	2.90183	0.175949
$273$	0	0
$274$	−20.4245	−1.23389
$275$	−5.05761	−0.304986
$276$	−3.49585	−0.210426
$277$	−1.71328	−0.102941	−0.0514705	−	0.998675i	$-0.516391\pi$
$277$	−1.71328	−0.102941	−0.0514705	+	0.998675i	$0.516391\pi$
$278$	10.3102	0.618364
$279$	−1.02783	−0.0615348
$280$	−2.94700	−0.176117
$281$	−0.221037	−0.0131860	−0.00659299	−	0.999978i	$-0.502099\pi$
$281$	−0.221037	−0.0131860	−0.00659299	+	0.999978i	$0.502099\pi$
$282$	0.134414	0.00800422
$283$	9.44547	0.561475	0.280737	−	0.959785i	$-0.409421\pi$
$283$	9.44547	0.561475	0.280737	+	0.959785i	$0.409421\pi$
$284$	−0.626610	−0.0371825
$285$	2.44704	0.144950
$286$	0	0
$287$	−7.23310	−0.426956
$288$	−3.46697	−0.204293
$289$	−15.4190	−0.906998
$290$	11.8924	0.698347
$291$	−8.42595	−0.493938
$292$	−4.52468	−0.264787
$293$	−13.5832	−0.793539	−0.396769	−	0.917918i	$-0.629869\pi$
$293$	−13.5832	−0.793539	−0.396769	+	0.917918i	$0.629869\pi$
$294$	−7.09277	−0.413659
$295$	8.32438	0.484664
$296$	−2.89142	−0.168060
$297$	5.05761	0.293473
$298$	8.68230	0.502952
$299$	0	0
$300$	0.640788	0.0369959
$301$	0.248267	0.0143098
$302$	−22.0826	−1.27071
$303$	−4.78493	−0.274887
$304$	−5.64732	−0.323896
$305$	−13.1657	−0.753864
$306$	1.46593	0.0838018
$307$	−8.65595	−0.494021	−0.247011	−	0.969013i	$-0.579448\pi$
$307$	−8.65595	−0.494021	−0.247011	+	0.969013i	$0.579448\pi$
$308$	3.10216	0.176762
$309$	−10.6406	−0.605320
$310$	−1.19830	−0.0680590
$311$	−8.06452	−0.457297	−0.228649	−	0.973509i	$-0.573431\pi$
$311$	−8.06452	−0.457297	−0.228649	+	0.973509i	$0.573431\pi$
$312$	0	0
$313$	22.0529	1.24650	0.623251	−	0.782022i	$-0.285811\pi$
$313$	22.0529	1.24650	0.623251	+	0.782022i	$0.285811\pi$
$314$	−23.4896	−1.32560
$315$	−0.957202	−0.0539322
$316$	8.34345	0.469356
$317$	−20.8086	−1.16873	−0.584364	−	0.811492i	$-0.698656\pi$
$317$	−20.8086	−1.16873	−0.584364	+	0.811492i	$0.698656\pi$
$318$	−2.84116	−0.159324
$319$	−51.5908	−2.88853
$320$	−8.65760	−0.483975
$321$	−16.5805	−0.925433
$322$	6.08816	0.339280
$323$	−3.07689	−0.171203
$324$	−0.640788	−0.0355993
$325$	0	0
$326$	−10.8795	−0.602562
$327$	12.8615	0.711241
$328$	−23.2647	−1.28458
$329$	0.110358	0.00608423
$330$	5.89643	0.324588
$331$	10.3654	0.569732	0.284866	−	0.958567i	$-0.408051\pi$
$331$	10.3654	0.569732	0.284866	+	0.958567i	$0.408051\pi$
$332$	2.41532	0.132558
$333$	−0.939148	−0.0514650
$334$	0.359204	0.0196548
$335$	11.8247	0.646054
$336$	2.20905	0.120513
$337$	15.4304	0.840546	0.420273	−	0.907398i	$-0.361934\pi$
$337$	15.4304	0.840546	0.420273	+	0.907398i	$0.361934\pi$
$338$	0	0
$339$	−13.2710	−0.720779
$340$	−0.805722	−0.0436964
$341$	5.19839	0.281509
$342$	−2.85289	−0.154267
$343$	−12.5238	−0.676222
$344$	0.798531	0.0430539
$345$	−5.45555	−0.293717
$346$	11.4698	0.616620
$347$	−24.6928	−1.32558	−0.662789	−	0.748806i	$-0.730627\pi$
$347$	−24.6928	−1.32558	−0.662789	+	0.748806i	$0.730627\pi$
$348$	6.53643	0.350390
$349$	15.4777	0.828505	0.414252	−	0.910162i	$-0.364043\pi$
$349$	15.4777	0.828505	0.414252	+	0.910162i	$0.364043\pi$
$350$	−1.11596	−0.0596504
$351$	0	0
$352$	17.5346	0.934596
$353$	14.6323	0.778796	0.389398	−	0.921069i	$-0.372683\pi$
$353$	14.6323	0.778796	0.389398	+	0.921069i	$0.372683\pi$
$354$	−9.70500	−0.515815
$355$	−0.977874	−0.0519002
$356$	11.4830	0.608596
$357$	1.20358	0.0637001
$358$	4.57754	0.241930
$359$	18.1306	0.956898	0.478449	−	0.878115i	$-0.341199\pi$
$359$	18.1306	0.956898	0.478449	+	0.878115i	$0.341199\pi$
$360$	−3.07877	−0.162265
$361$	−13.0120	−0.684841
$362$	−24.8952	−1.30846
$363$	−14.5795	−0.765223
$364$	0	0
$365$	−7.06112	−0.369596
$366$	15.3492	0.802317
$367$	−9.19781	−0.480122	−0.240061	−	0.970758i	$-0.577167\pi$
$367$	−9.19781	−0.480122	−0.240061	+	0.970758i	$0.577167\pi$
$368$	12.5904	0.656320
$369$	−7.55650	−0.393376
$370$	−1.09491	−0.0569216
$371$	−2.33268	−0.121107
$372$	−0.658624	−0.0341481
$373$	28.5940	1.48054	0.740270	−	0.672310i	$-0.234698\pi$
$373$	28.5940	1.48054	0.740270	+	0.672310i	$0.234698\pi$
$374$	−7.41413	−0.383375
$375$	1.00000	0.0516398
$376$	0.354958	0.0183056
$377$	0	0
$378$	1.11596	0.0573986
$379$	−18.7115	−0.961147	−0.480573	−	0.876955i	$-0.659571\pi$
$379$	−18.7115	−0.961147	−0.480573	+	0.876955i	$0.659571\pi$
$380$	1.56804	0.0804385
$381$	−13.4321	−0.688147
$382$	−2.40261	−0.122928
$383$	34.2009	1.74759	0.873793	−	0.486299i	$-0.161653\pi$
$383$	34.2009	1.74759	0.873793	+	0.486299i	$0.161653\pi$
$384$	3.15955	0.161235
$385$	4.84116	0.246728
$386$	−12.4342	−0.632886
$387$	0.259367	0.0131844
$388$	−5.39925	−0.274105
$389$	14.5536	0.737896	0.368948	−	0.929450i	$-0.379718\pi$
$389$	14.5536	0.737896	0.368948	+	0.929450i	$0.379718\pi$
$390$	0	0
$391$	6.85977	0.346913
$392$	−18.7305	−0.946033
$393$	−8.09375	−0.408276
$394$	−20.1235	−1.01381
$395$	13.0206	0.655138
$396$	3.24086	0.162859
$397$	−8.07706	−0.405376	−0.202688	−	0.979243i	$-0.564968\pi$
$397$	−8.07706	−0.405376	−0.202688	+	0.979243i	$0.564968\pi$
$398$	−1.72923	−0.0866782
$399$	−2.34231	−0.117262
$400$	−2.30781	−0.115391
$401$	14.1755	0.707889	0.353944	−	0.935266i	$-0.384840\pi$
$401$	14.1755	0.707889	0.353944	+	0.935266i	$0.384840\pi$
$402$	−13.7859	−0.687578
$403$	0	0
$404$	−3.06612	−0.152545
$405$	−1.00000	−0.0496904
$406$	−11.3834	−0.564951
$407$	4.74985	0.235441
$408$	3.87122	0.191654
$409$	1.93570	0.0957144	0.0478572	−	0.998854i	$-0.484761\pi$
$409$	1.93570	0.0957144	0.0478572	+	0.998854i	$0.484761\pi$
$410$	−8.80977	−0.435083
$411$	−17.5189	−0.864146
$412$	−6.81834	−0.335915
$413$	−7.96812	−0.392085
$414$	6.36037	0.312595
$415$	3.76930	0.185028
$416$	0	0
$417$	8.84347	0.433067
$418$	14.4288	0.705737
$419$	26.1769	1.27883	0.639413	−	0.768863i	$-0.279177\pi$
$419$	26.1769	1.27883	0.639413	+	0.768863i	$0.279177\pi$
$420$	−0.613364	−0.0299291
$421$	−12.6661	−0.617309	−0.308655	−	0.951174i	$-0.599879\pi$
$421$	−12.6661	−0.617309	−0.308655	+	0.951174i	$0.599879\pi$
$422$	−5.78194	−0.281460
$423$	0.115292	0.00560570
$424$	−7.50289	−0.364373
$425$	−1.25739	−0.0609925
$426$	1.14006	0.0552359
$427$	12.6022	0.609863
$428$	−10.6246	−0.513559
$429$	0	0
$430$	0.302384	0.0145822
$431$	28.3470	1.36543	0.682713	−	0.730687i	$-0.260800\pi$
$431$	28.3470	1.36543	0.682713	+	0.730687i	$0.260800\pi$
$432$	2.30781	0.111035
$433$	−9.98885	−0.480033	−0.240017	−	0.970769i	$-0.577153\pi$
$433$	−9.98885	−0.480033	−0.240017	+	0.970769i	$0.577153\pi$
$434$	1.14702	0.0550586
$435$	10.2006	0.489082
$436$	8.24148	0.394695
$437$	−13.3500	−0.638616
$438$	8.23223	0.393351
$439$	19.3922	0.925540	0.462770	−	0.886478i	$-0.346856\pi$
$439$	19.3922	0.925540	0.462770	+	0.886478i	$0.346856\pi$
$440$	15.5712	0.742329
$441$	−6.08376	−0.289703
$442$	0	0
$443$	5.82980	0.276982	0.138491	−	0.990364i	$-0.455775\pi$
$443$	5.82980	0.276982	0.138491	+	0.990364i	$0.455775\pi$
$444$	−0.601795	−0.0285599
$445$	17.9201	0.849493
$446$	−32.8465	−1.55533
$447$	7.44717	0.352239
$448$	8.28707	0.391527
$449$	−27.2523	−1.28612	−0.643058	−	0.765818i	$-0.722335\pi$
$449$	−27.2523	−1.28612	−0.643058	+	0.765818i	$0.722335\pi$
$450$	−1.16585	−0.0549588
$451$	38.2179	1.79961
$452$	−8.50387	−0.399988
$453$	−18.9412	−0.889934
$454$	24.6716	1.15789
$455$	0	0
$456$	−7.53388	−0.352806
$457$	23.7369	1.11036	0.555182	−	0.831729i	$-0.312648\pi$
$457$	23.7369	1.11036	0.555182	+	0.831729i	$0.312648\pi$
$458$	−28.2939	−1.32209
$459$	1.25739	0.0586900
$460$	−3.49585	−0.162995
$461$	17.3059	0.806014	0.403007	−	0.915197i	$-0.367965\pi$
$461$	17.3059	0.806014	0.403007	+	0.915197i	$0.367965\pi$
$462$	−5.64408	−0.262586
$463$	−34.5377	−1.60510	−0.802552	−	0.596582i	$-0.796525\pi$
$463$	−34.5377	−1.60510	−0.802552	+	0.596582i	$0.796525\pi$
$464$	−23.5411	−1.09287
$465$	−1.02783	−0.0476647
$466$	28.6509	1.32723
$467$	13.7597	0.636724	0.318362	−	0.947969i	$-0.396867\pi$
$467$	13.7597	0.636724	0.318362	+	0.947969i	$0.396867\pi$
$468$	0	0
$469$	−11.3187	−0.522647
$470$	0.134414	0.00620004
$471$	−20.1480	−0.928372
$472$	−25.6289	−1.17966
$473$	−1.31178	−0.0603156
$474$	−15.1801	−0.697246
$475$	2.44704	0.112278
$476$	0.771238	0.0353497
$477$	−2.43698	−0.111582
$478$	−29.2313	−1.33701
$479$	−2.32088	−0.106044	−0.0530219	−	0.998593i	$-0.516885\pi$
$479$	−2.32088	−0.106044	−0.0530219	+	0.998593i	$0.516885\pi$
$480$	−3.46697	−0.158245
$481$	0	0
$482$	2.07741	0.0946232
$483$	5.22207	0.237612
$484$	−9.34235	−0.424652
$485$	−8.42595	−0.382603
$486$	1.16585	0.0528841
$487$	14.7251	0.667257	0.333629	−	0.942705i	$-0.391727\pi$
$487$	14.7251	0.667257	0.333629	+	0.942705i	$0.391727\pi$
$488$	40.5340	1.83489
$489$	−9.33184	−0.422000
$490$	−7.09277	−0.320419
$491$	−39.3204	−1.77451	−0.887253	−	0.461283i	$-0.847389\pi$
$491$	−39.3204	−1.77451	−0.887253	+	0.461283i	$0.847389\pi$
$492$	−4.84212	−0.218299
$493$	−12.8262	−0.577662
$494$	0	0
$495$	5.05761	0.227323
$496$	2.37205	0.106508
$497$	0.936023	0.0419864
$498$	−4.39444	−0.196920
$499$	21.0832	0.943814	0.471907	−	0.881648i	$-0.343566\pi$
$499$	21.0832	0.943814	0.471907	+	0.881648i	$0.343566\pi$
$500$	0.640788	0.0286569
$501$	0.308104	0.0137651
$502$	20.6916	0.923510
$503$	−6.33407	−0.282422	−0.141211	−	0.989980i	$-0.545100\pi$
$503$	−6.33407	−0.282422	−0.141211	+	0.989980i	$0.545100\pi$
$504$	2.94700	0.131270
$505$	−4.78493	−0.212927
$506$	−32.1683	−1.43006
$507$	0	0
$508$	−8.60712	−0.381879
$509$	11.0119	0.488092	0.244046	−	0.969764i	$-0.421525\pi$
$509$	11.0119	0.488092	0.244046	+	0.969764i	$0.421525\pi$
$510$	1.46593	0.0649126
$511$	6.75892	0.298997
$512$	22.2116	0.981622
$513$	−2.44704	−0.108040
$514$	−32.4999	−1.43351
$515$	−10.6406	−0.468879
$516$	0.166199	0.00731651
$517$	−0.583104	−0.0256449
$518$	1.04805	0.0460486
$519$	9.83812	0.431846
$520$	0	0
$521$	24.2840	1.06390	0.531951	−	0.846775i	$-0.321459\pi$
$521$	24.2840	1.06390	0.531951	+	0.846775i	$0.321459\pi$
$522$	−11.8924	−0.520517
$523$	−25.8888	−1.13204	−0.566018	−	0.824393i	$-0.691517\pi$
$523$	−25.8888	−1.13204	−0.566018	+	0.824393i	$0.691517\pi$
$524$	−5.18638	−0.226568
$525$	−0.957202	−0.0417757
$526$	−13.9559	−0.608504
$527$	1.29239	0.0562974
$528$	−11.6720	−0.507960
$529$	6.76308	0.294047
$530$	−2.84116	−0.123412
$531$	−8.32438	−0.361248
$532$	−1.50093	−0.0650734
$533$	0	0
$534$	−20.8922	−0.904093
$535$	−16.5805	−0.716838
$536$	−36.4056	−1.57248
$537$	3.92634	0.169434
$538$	19.8691	0.856617
$539$	30.7693	1.32533
$540$	−0.640788	−0.0275751
$541$	−3.67904	−0.158174	−0.0790871	−	0.996868i	$-0.525201\pi$
$541$	−3.67904	−0.158174	−0.0790871	+	0.996868i	$0.525201\pi$
$542$	14.4000	0.618535
$543$	−21.3537	−0.916374
$544$	4.35934	0.186905
$545$	12.8615	0.550925
$546$	0	0
$547$	33.0031	1.41111	0.705554	−	0.708656i	$-0.250698\pi$
$547$	33.0031	1.41111	0.705554	+	0.708656i	$0.250698\pi$
$548$	−11.2259	−0.479548
$549$	13.1657	0.561897
$550$	5.89643	0.251425
$551$	24.9613	1.06339
$552$	16.7964	0.714902
$553$	−12.4634	−0.529996
$554$	1.99743	0.0848627
$555$	−0.939148	−0.0398646
$556$	5.66679	0.240326
$557$	25.6886	1.08846	0.544230	−	0.838936i	$-0.316822\pi$
$557$	25.6886	1.08846	0.544230	+	0.838936i	$0.316822\pi$
$558$	1.19830	0.0507282
$559$	0	0
$560$	2.20905	0.0933492
$561$	−6.35940	−0.268494
$562$	0.257697	0.0108703
$563$	−43.7560	−1.84410	−0.922048	−	0.387075i	$-0.873485\pi$
$563$	−43.7560	−1.84410	−0.922048	+	0.387075i	$0.873485\pi$
$564$	0.0738779	0.00311082
$565$	−13.2710	−0.558313
$566$	−11.0120	−0.462870
$567$	0.957202	0.0401987
$568$	3.01065	0.126324
$569$	−24.5255	−1.02816	−0.514082	−	0.857741i	$-0.671867\pi$
$569$	−24.5255	−1.02816	−0.514082	+	0.857741i	$0.671867\pi$
$570$	−2.85289	−0.119494
$571$	4.90263	0.205169	0.102584	−	0.994724i	$-0.467289\pi$
$571$	4.90263	0.205169	0.102584	+	0.994724i	$0.467289\pi$
$572$	0	0
$573$	−2.06081	−0.0860918
$574$	8.43273	0.351975
$575$	−5.45555	−0.227512
$576$	8.65760	0.360733
$577$	19.1780	0.798391	0.399195	−	0.916866i	$-0.369290\pi$
$577$	19.1780	0.798391	0.399195	+	0.916866i	$0.369290\pi$
$578$	17.9762	0.747713
$579$	−10.6654	−0.443237
$580$	6.53643	0.271411
$581$	−3.60798	−0.149684
$582$	9.82341	0.407194
$583$	12.3253	0.510462
$584$	21.7396	0.899590
$585$	0	0
$586$	15.8360	0.654179
$587$	14.8326	0.612209	0.306104	−	0.951998i	$-0.400974\pi$
$587$	14.8326	0.612209	0.306104	+	0.951998i	$0.400974\pi$
$588$	−3.89840	−0.160767
$589$	−2.51515	−0.103635
$590$	−9.70500	−0.399549
$591$	−17.2608	−0.710013
$592$	2.16738	0.0890788
$593$	6.61437	0.271620	0.135810	−	0.990735i	$-0.456636\pi$
$593$	6.61437	0.271620	0.135810	+	0.990735i	$0.456636\pi$
$594$	−5.89643	−0.241934
$595$	1.20358	0.0493419
$596$	4.77206	0.195471
$597$	−1.48323	−0.0607045
$598$	0	0
$599$	−6.94677	−0.283837	−0.141919	−	0.989878i	$-0.545327\pi$
$599$	−6.94677	−0.283837	−0.141919	+	0.989878i	$0.545327\pi$
$600$	−3.07877	−0.125690
$601$	18.3658	0.749157	0.374579	−	0.927195i	$-0.377787\pi$
$601$	18.3658	0.749157	0.374579	+	0.927195i	$0.377787\pi$
$602$	−0.289442	−0.0117968
$603$	−11.8247	−0.481541
$604$	−12.1373	−0.493859
$605$	−14.5795	−0.592740
$606$	5.57852	0.226612
$607$	−31.6416	−1.28429	−0.642147	−	0.766582i	$-0.721956\pi$
$607$	−31.6416	−1.28429	−0.642147	+	0.766582i	$0.721956\pi$
$608$	−8.48382	−0.344064
$609$	−9.76405	−0.395659
$610$	15.3492	0.621472
$611$	0	0
$612$	0.805722	0.0325694
$613$	−43.9923	−1.77683	−0.888417	−	0.459037i	$-0.848194\pi$
$613$	−43.9923	−1.77683	−0.888417	+	0.459037i	$0.848194\pi$
$614$	10.0916	0.407262
$615$	−7.55650	−0.304708
$616$	−14.9048	−0.600532
$617$	−5.08640	−0.204771	−0.102385	−	0.994745i	$-0.532647\pi$
$617$	−5.08640	−0.204771	−0.102385	+	0.994745i	$0.532647\pi$
$618$	12.4053	0.499015
$619$	−44.5174	−1.78931	−0.894653	−	0.446762i	$-0.852577\pi$
$619$	−44.5174	−1.78931	−0.894653	+	0.446762i	$0.852577\pi$
$620$	−0.658624	−0.0264510
$621$	5.45555	0.218924
$622$	9.40204	0.376988
$623$	−17.1531	−0.687226
$624$	0	0
$625$	1.00000	0.0400000
$626$	−25.7104	−1.02759
$627$	12.3762	0.494258
$628$	−12.9106	−0.515189
$629$	1.18088	0.0470847
$630$	1.11596	0.0444608
$631$	25.4933	1.01487	0.507437	−	0.861689i	$-0.330593\pi$
$631$	25.4933	1.01487	0.507437	+	0.861689i	$0.330593\pi$
$632$	−40.0875	−1.59459
$633$	−4.95941	−0.197119
$634$	24.2598	0.963478
$635$	−13.4321	−0.533036
$636$	−1.56159	−0.0619209
$637$	0	0
$638$	60.1472	2.38125
$639$	0.977874	0.0386841
$640$	3.15955	0.124892
$641$	16.9617	0.669948	0.334974	−	0.942227i	$-0.391273\pi$
$641$	16.9617	0.669948	0.334974	+	0.942227i	$0.391273\pi$
$642$	19.3304	0.762911
$643$	−11.7358	−0.462814	−0.231407	−	0.972857i	$-0.574333\pi$
$643$	−11.7358	−0.462814	−0.231407	+	0.972857i	$0.574333\pi$
$644$	3.34624	0.131860
$645$	0.259367	0.0102126
$646$	3.58720	0.141137
$647$	16.4828	0.648007	0.324004	−	0.946056i	$-0.394971\pi$
$647$	16.4828	0.648007	0.324004	+	0.946056i	$0.394971\pi$
$648$	3.07877	0.120945
$649$	42.1015	1.65263
$650$	0	0
$651$	0.983845	0.0385599
$652$	−5.97973	−0.234184
$653$	−11.3795	−0.445316	−0.222658	−	0.974897i	$-0.571473\pi$
$653$	−11.3795	−0.445316	−0.222658	+	0.974897i	$0.571473\pi$
$654$	−14.9946	−0.586335
$655$	−8.09375	−0.316249
$656$	17.4390	0.680879
$657$	7.06112	0.275481
$658$	−0.128661	−0.00501573
$659$	−31.5912	−1.23062	−0.615310	−	0.788285i	$-0.710969\pi$
$659$	−31.5912	−1.23062	−0.615310	+	0.788285i	$0.710969\pi$
$660$	3.24086	0.126150
$661$	−41.2523	−1.60453	−0.802265	−	0.596968i	$-0.796372\pi$
$661$	−41.2523	−1.60453	−0.802265	+	0.596968i	$0.796372\pi$
$662$	−12.0845	−0.469677
$663$	0	0
$664$	−11.6048	−0.450353
$665$	−2.34231	−0.0908311
$666$	1.09491	0.0424268
$667$	−55.6500	−2.15478
$668$	0.197429	0.00763877
$669$	−28.1738	−1.08926
$670$	−13.7859	−0.532596
$671$	−66.5868	−2.57056
$672$	3.31859	0.128017
$673$	31.1149	1.19939	0.599695	−	0.800229i	$-0.295289\pi$
$673$	31.1149	1.19939	0.599695	+	0.800229i	$0.295289\pi$
$674$	−17.9895	−0.692931
$675$	−1.00000	−0.0384900
$676$	0	0
$677$	−33.9996	−1.30671	−0.653356	−	0.757051i	$-0.726640\pi$
$677$	−33.9996	−1.30671	−0.653356	+	0.757051i	$0.726640\pi$
$678$	15.4720	0.594198
$679$	8.06534	0.309519
$680$	3.87122	0.148454
$681$	21.1618	0.810923
$682$	−6.06056	−0.232071
$683$	39.2385	1.50142	0.750710	−	0.660632i	$-0.229711\pi$
$683$	39.2385	1.50142	0.750710	+	0.660632i	$0.229711\pi$
$684$	−1.56804	−0.0599553
$685$	−17.5189	−0.669365
$686$	14.6009	0.557465
$687$	−24.2688	−0.925914
$688$	−0.598571	−0.0228203
$689$	0	0
$690$	6.36037	0.242135
$691$	3.87229	0.147309	0.0736544	−	0.997284i	$-0.476534\pi$
$691$	3.87229	0.147309	0.0736544	+	0.997284i	$0.476534\pi$
$692$	6.30415	0.239648
$693$	−4.84116	−0.183900
$694$	28.7881	1.09278
$695$	8.84347	0.335452
$696$	−31.4053	−1.19042
$697$	9.50148	0.359894
$698$	−18.0448	−0.683005
$699$	24.5751	0.929515
$700$	−0.613364	−0.0231830
$701$	43.7894	1.65390	0.826952	−	0.562273i	$-0.190073\pi$
$701$	43.7894	1.65390	0.826952	+	0.562273i	$0.190073\pi$
$702$	0	0
$703$	−2.29814	−0.0866758
$704$	−43.7868	−1.65028
$705$	0.115292	0.00434216
$706$	−17.0591	−0.642026
$707$	4.58014	0.172254
$708$	−5.33417	−0.200470
$709$	−43.3413	−1.62772	−0.813859	−	0.581062i	$-0.802637\pi$
$709$	−43.3413	−1.62772	−0.813859	+	0.581062i	$0.802637\pi$
$710$	1.14006	0.0427856
$711$	−13.0206	−0.488311
$712$	−55.1718	−2.06765
$713$	5.60741	0.209999
$714$	−1.40319	−0.0525132
$715$	0	0
$716$	2.51595	0.0940256
$717$	−25.0729	−0.936365
$718$	−21.1376	−0.788850
$719$	0.135145	0.00504005	0.00252003	−	0.999997i	$-0.499198\pi$
$719$	0.135145	0.00504005	0.00252003	+	0.999997i	$0.499198\pi$
$720$	2.30781	0.0860072
$721$	10.1852	0.379315
$722$	15.1701	0.564571
$723$	1.78188	0.0662687
$724$	−13.6832	−0.508531
$725$	10.2006	0.378841
$726$	16.9975	0.630837
$727$	−7.02528	−0.260553	−0.130277	−	0.991478i	$-0.541587\pi$
$727$	−7.02528	−0.260553	−0.130277	+	0.991478i	$0.541587\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	8.23223	0.304688
$731$	−0.326126	−0.0120622
$732$	8.43640	0.311818
$733$	−21.2839	−0.786140	−0.393070	−	0.919509i	$-0.628587\pi$
$733$	−21.2839	−0.786140	−0.393070	+	0.919509i	$0.628587\pi$
$734$	10.7233	0.395804
$735$	−6.08376	−0.224403
$736$	18.9142	0.697188
$737$	59.8050	2.20294
$738$	8.80977	0.324292
$739$	−9.68852	−0.356398	−0.178199	−	0.983994i	$-0.557027\pi$
$739$	−9.68852	−0.356398	−0.178199	+	0.983994i	$0.557027\pi$
$740$	−0.601795	−0.0221224
$741$	0	0
$742$	2.71956	0.0998382
$743$	44.8866	1.64673	0.823364	−	0.567513i	$-0.192095\pi$
$743$	44.8866	1.64673	0.823364	+	0.567513i	$0.192095\pi$
$744$	3.16446	0.116015
$745$	7.44717	0.272843
$746$	−33.3364	−1.22053
$747$	−3.76930	−0.137911
$748$	−4.07503	−0.148998
$749$	15.8709	0.579910
$750$	−1.16585	−0.0425709
$751$	3.50781	0.128002	0.0640009	−	0.997950i	$-0.479614\pi$
$751$	3.50781	0.128002	0.0640009	+	0.997950i	$0.479614\pi$
$752$	−0.266073	−0.00970269
$753$	17.7480	0.646774
$754$	0	0
$755$	−18.9412	−0.689340
$756$	0.613364	0.0223078
$757$	−22.0135	−0.800095	−0.400048	−	0.916494i	$-0.631006\pi$
$757$	−22.0135	−0.800095	−0.400048	+	0.916494i	$0.631006\pi$
$758$	21.8149	0.792352
$759$	−27.5921	−1.00153
$760$	−7.53388	−0.273283
$761$	10.9054	0.395321	0.197661	−	0.980271i	$-0.436666\pi$
$761$	10.9054	0.395321	0.197661	+	0.980271i	$0.436666\pi$
$762$	15.6598	0.567296
$763$	−12.3110	−0.445689
$764$	−1.32055	−0.0477757
$765$	1.25739	0.0454611
$766$	−39.8732	−1.44068
$767$	0	0
$768$	13.6316	0.491889
$769$	−29.5569	−1.06585	−0.532925	−	0.846163i	$-0.678907\pi$
$769$	−29.5569	−1.06585	−0.532925	+	0.846163i	$0.678907\pi$
$770$	−5.64408	−0.203398
$771$	−27.8765	−1.00395
$772$	−6.83423	−0.245969
$773$	−10.0137	−0.360169	−0.180085	−	0.983651i	$-0.557637\pi$
$773$	−10.0137	−0.360169	−0.180085	+	0.983651i	$0.557637\pi$
$774$	−0.302384	−0.0108690
$775$	−1.02783	−0.0369209
$776$	25.9416	0.931247
$777$	0.898955	0.0322498
$778$	−16.9673	−0.608309
$779$	−18.4911	−0.662512
$780$	0	0
$781$	−4.94571	−0.176971
$782$	−7.99748	−0.285989
$783$	−10.2006	−0.364540
$784$	14.0402	0.501436
$785$	−20.1480	−0.719114
$786$	9.43612	0.336575
$787$	−29.9935	−1.06915	−0.534576	−	0.845121i	$-0.679529\pi$
$787$	−29.9935	−1.06915	−0.534576	+	0.845121i	$0.679529\pi$
$788$	−11.0605	−0.394014
$789$	−11.9705	−0.426162
$790$	−15.1801	−0.540084
$791$	12.7030	0.451666
$792$	−15.5712	−0.553300
$793$	0	0
$794$	9.41665	0.334185
$795$	−2.43698	−0.0864307
$796$	−0.950435	−0.0336873
$797$	28.8344	1.02137	0.510684	−	0.859768i	$-0.329392\pi$
$797$	28.8344	1.02137	0.510684	+	0.859768i	$0.329392\pi$
$798$	2.73079	0.0966690
$799$	−0.144967	−0.00512858
$800$	−3.46697	−0.122576
$801$	−17.9201	−0.633175
$802$	−16.5265	−0.583571
$803$	−35.7124	−1.26026
$804$	−7.57715	−0.267225
$805$	5.22207	0.184054
$806$	0	0
$807$	17.0425	0.599926
$808$	14.7317	0.518259
$809$	37.0934	1.30414	0.652068	−	0.758161i	$-0.273902\pi$
$809$	37.0934	1.30414	0.652068	+	0.758161i	$0.273902\pi$
$810$	1.16585	0.0409639
$811$	19.6091	0.688568	0.344284	−	0.938866i	$-0.388122\pi$
$811$	19.6091	0.688568	0.344284	+	0.938866i	$0.388122\pi$
$812$	−6.25669	−0.219567
$813$	12.3515	0.433187
$814$	−5.53762	−0.194094
$815$	−9.33184	−0.326880
$816$	−2.90183	−0.101584
$817$	0.634682	0.0222047
$818$	−2.25674	−0.0789052
$819$	0	0
$820$	−4.84212	−0.169094
$821$	−2.89699	−0.101106	−0.0505528	−	0.998721i	$-0.516098\pi$
$821$	−2.89699	−0.101106	−0.0505528	+	0.998721i	$0.516098\pi$
$822$	20.4245	0.712386
$823$	−28.6695	−0.999356	−0.499678	−	0.866211i	$-0.666548\pi$
$823$	−28.6695	−0.999356	−0.499678	+	0.866211i	$0.666548\pi$
$824$	32.7598	1.14124
$825$	5.05761	0.176084
$826$	9.28965	0.323228
$827$	−30.8087	−1.07132	−0.535662	−	0.844432i	$-0.679938\pi$
$827$	−30.8087	−1.07132	−0.535662	+	0.844432i	$0.679938\pi$
$828$	3.49585	0.121489
$829$	2.42720	0.0843003	0.0421501	−	0.999111i	$-0.486579\pi$
$829$	2.42720	0.0843003	0.0421501	+	0.999111i	$0.486579\pi$
$830$	−4.39444	−0.152533
$831$	1.71328	0.0594330
$832$	0	0
$833$	7.64968	0.265046
$834$	−10.3102	−0.357013
$835$	0.308104	0.0106624
$836$	7.93052	0.274283
$837$	1.02783	0.0355271
$838$	−30.5184	−1.05424
$839$	4.26940	0.147396	0.0736981	−	0.997281i	$-0.476520\pi$
$839$	4.26940	0.147396	0.0736981	+	0.997281i	$0.476520\pi$
$840$	2.94700	0.101681
$841$	75.0526	2.58802
$842$	14.7668	0.508899
$843$	0.221037	0.00761293
$844$	−3.17793	−0.109389
$845$	0	0
$846$	−0.134414	−0.00462124
$847$	13.9555	0.479516
$848$	5.62409	0.193132
$849$	−9.44547	−0.324168
$850$	1.46593	0.0502811
$851$	5.12357	0.175634
$852$	0.626610	0.0214673
$853$	21.5257	0.737025	0.368513	−	0.929623i	$-0.379867\pi$
$853$	21.5257	0.737025	0.368513	+	0.929623i	$0.379867\pi$
$854$	−14.6923	−0.502760
$855$	−2.44704	−0.0836871
$856$	51.0475	1.74477
$857$	42.2276	1.44247	0.721234	−	0.692691i	$-0.243575\pi$
$857$	42.2276	1.44247	0.721234	+	0.692691i	$0.243575\pi$
$858$	0	0
$859$	35.9388	1.22622	0.613108	−	0.789999i	$-0.289919\pi$
$859$	35.9388	1.22622	0.613108	+	0.789999i	$0.289919\pi$
$860$	0.166199	0.00566735
$861$	7.23310	0.246503
$862$	−33.0484	−1.12563
$863$	−23.5593	−0.801970	−0.400985	−	0.916085i	$-0.631332\pi$
$863$	−23.5593	−0.801970	−0.400985	+	0.916085i	$0.631332\pi$
$864$	3.46697	0.117949
$865$	9.83812	0.334506
$866$	11.6455	0.395731
$867$	15.4190	0.523656
$868$	0.630436	0.0213984
$869$	65.8532	2.23392
$870$	−11.8924	−0.403191
$871$	0	0
$872$	−39.5975	−1.34094
$873$	8.42595	0.285175
$874$	15.5641	0.526464
$875$	−0.957202	−0.0323593
$876$	4.52468	0.152875
$877$	15.0874	0.509464	0.254732	−	0.967012i	$-0.418013\pi$
$877$	15.0874	0.509464	0.254732	+	0.967012i	$0.418013\pi$
$878$	−22.6085	−0.762999
$879$	13.5832	0.458150
$880$	−11.6720	−0.393464
$881$	1.03462	0.0348573	0.0174287	−	0.999848i	$-0.494452\pi$
$881$	1.03462	0.0348573	0.0174287	+	0.999848i	$0.494452\pi$
$882$	7.09277	0.238826
$883$	2.06340	0.0694389	0.0347194	−	0.999397i	$-0.488946\pi$
$883$	2.06340	0.0694389	0.0347194	+	0.999397i	$0.488946\pi$
$884$	0	0
$885$	−8.32438	−0.279821
$886$	−6.79669	−0.228339
$887$	−53.8193	−1.80707	−0.903537	−	0.428511i	$-0.859038\pi$
$887$	−53.8193	−1.80707	−0.903537	+	0.428511i	$0.859038\pi$
$888$	2.89142	0.0970297
$889$	12.8572	0.431217
$890$	−20.8922	−0.700307
$891$	−5.05761	−0.169436
$892$	−18.0534	−0.604474
$893$	0.282125	0.00944095
$894$	−8.68230	−0.290380
$895$	3.92634	0.131243
$896$	−3.02433	−0.101036
$897$	0	0
$898$	31.7722	1.06025
$899$	−10.4845	−0.349679
$900$	−0.640788	−0.0213596
$901$	3.06424	0.102085
$902$	−44.5564	−1.48357
$903$	−0.248267	−0.00826180
$904$	40.8582	1.35892
$905$	−21.3537	−0.709820
$906$	22.0826	0.733646
$907$	26.4675	0.878839	0.439420	−	0.898282i	$-0.355184\pi$
$907$	26.4675	0.878839	0.439420	+	0.898282i	$0.355184\pi$
$908$	13.5602	0.450013
$909$	4.78493	0.158706
$910$	0	0
$911$	−4.13621	−0.137039	−0.0685193	−	0.997650i	$-0.521827\pi$
$911$	−4.13621	−0.137039	−0.0685193	+	0.997650i	$0.521827\pi$
$912$	5.64732	0.187002
$913$	19.0637	0.630915
$914$	−27.6737	−0.915365
$915$	13.1657	0.435243
$916$	−15.5512	−0.513825
$917$	7.74735	0.255840
$918$	−1.46593	−0.0483830
$919$	4.30934	0.142152	0.0710761	−	0.997471i	$-0.477357\pi$
$919$	4.30934	0.142152	0.0710761	+	0.997471i	$0.477357\pi$
$920$	16.7964	0.553761
$921$	8.65595	0.285223
$922$	−20.1761	−0.664463
$923$	0	0
$924$	−3.10216	−0.102053
$925$	−0.939148	−0.0308790
$926$	40.2659	1.32322
$927$	10.6406	0.349482
$928$	−35.3652	−1.16092
$929$	−43.7707	−1.43607	−0.718035	−	0.696007i	$-0.754958\pi$
$929$	−43.7707	−1.43607	−0.718035	+	0.696007i	$0.754958\pi$
$930$	1.19830	0.0392939
$931$	−14.8872	−0.487909
$932$	15.7474	0.515824
$933$	8.06452	0.264021
$934$	−16.0418	−0.524904
$935$	−6.35940	−0.207975
$936$	0	0
$937$	2.17755	0.0711374	0.0355687	−	0.999367i	$-0.488676\pi$
$937$	2.17755	0.0711374	0.0355687	+	0.999367i	$0.488676\pi$
$938$	13.1959	0.430861
$939$	−22.0529	−0.719669
$940$	0.0738779	0.00240963
$941$	18.6557	0.608158	0.304079	−	0.952647i	$-0.401651\pi$
$941$	18.6557	0.608158	0.304079	+	0.952647i	$0.401651\pi$
$942$	23.4896	0.765333
$943$	41.2249	1.34247
$944$	19.2111	0.625269
$945$	0.957202	0.0311378
$946$	1.52934	0.0497231
$947$	0.281211	0.00913813	0.00456907	−	0.999990i	$-0.498546\pi$
$947$	0.281211	0.00913813	0.00456907	+	0.999990i	$0.498546\pi$
$948$	−8.34345	−0.270983
$949$	0	0
$950$	−2.85289	−0.0925600
$951$	20.8086	0.674765
$952$	−3.70554	−0.120097
$953$	29.2264	0.946737	0.473368	−	0.880865i	$-0.343038\pi$
$953$	29.2264	0.946737	0.473368	+	0.880865i	$0.343038\pi$
$954$	2.84116	0.0919858
$955$	−2.06081	−0.0666864
$956$	−16.0664	−0.519625
$957$	51.5908	1.66769
$958$	2.70580	0.0874206
$959$	16.7692	0.541505
$960$	8.65760	0.279423
$961$	−29.9436	−0.965921
$962$	0	0
$963$	16.5805	0.534299
$964$	1.14181	0.0367751
$965$	−10.6654	−0.343330
$966$	−6.08816	−0.195883
$967$	13.1700	0.423519	0.211760	−	0.977322i	$-0.432081\pi$
$967$	13.1700	0.423519	0.211760	+	0.977322i	$0.432081\pi$
$968$	44.8868	1.44272
$969$	3.07689	0.0988440
$970$	9.82341	0.315411
$971$	−27.3988	−0.879270	−0.439635	−	0.898176i	$-0.644892\pi$
$971$	−27.3988	−0.879270	−0.439635	+	0.898176i	$0.644892\pi$
$972$	0.640788	0.0205533
$973$	−8.46499	−0.271375
$974$	−17.1673	−0.550075
$975$	0	0
$976$	−30.3839	−0.972565
$977$	28.1077	0.899245	0.449622	−	0.893219i	$-0.351559\pi$
$977$	28.1077	0.899245	0.449622	+	0.893219i	$0.351559\pi$
$978$	10.8795	0.347889
$979$	90.6329	2.89664
$980$	−3.89840	−0.124530
$981$	−12.8615	−0.410635
$982$	45.8418	1.46287
$983$	37.5892	1.19891	0.599455	−	0.800409i	$-0.295384\pi$
$983$	37.5892	1.19891	0.599455	+	0.800409i	$0.295384\pi$
$984$	23.2647	0.741652
$985$	−17.2608	−0.549974
$986$	14.9534	0.476214
$987$	−0.110358	−0.00351273
$988$	0	0
$989$	−1.41499	−0.0449941
$990$	−5.89643	−0.187401
$991$	53.2906	1.69283	0.846416	−	0.532522i	$-0.178756\pi$
$991$	53.2906	1.69283	0.846416	+	0.532522i	$0.178756\pi$
$992$	3.56347	0.113140
$993$	−10.3654	−0.328935
$994$	−1.09126	−0.0346128
$995$	−1.48323	−0.0470215
$996$	−2.41532	−0.0765324
$997$	−13.2842	−0.420715	−0.210357	−	0.977625i	$-0.567463\pi$
$997$	−13.2842	−0.420715	−0.210357	+	0.977625i	$0.567463\pi$
$998$	−24.5799	−0.778063
$999$	0.939148	0.0297133

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2535.2.a.bm.1.3	✓	9
3.2	odd	2		7605.2.a.cr.1.7		9
13.12	even	2		2535.2.a.bn.1.7	yes	9
39.38	odd	2		7605.2.a.cq.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2535.2.a.bm.1.3	✓	9	1.1	even	1	trivial
2535.2.a.bn.1.7	yes	9	13.12	even	2
7605.2.a.cq.1.3		9	39.38	odd	2
7605.2.a.cr.1.7		9	3.2	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:	\( N \)	\(=\)	\( 2535 = 3 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2535.a (trivial)

\(f(q)\)	\(=\)	\(q-1.16585 q^{2} -1.00000 q^{3} -0.640788 q^{4} -1.00000 q^{5} +1.16585 q^{6} +0.957202 q^{7} +3.07877 q^{8} +1.00000 q^{9} +1.16585 q^{10} -5.05761 q^{11} +0.640788 q^{12} -1.11596 q^{14} +1.00000 q^{15} -2.30781 q^{16} -1.25739 q^{17} -1.16585 q^{18} +2.44704 q^{19} +0.640788 q^{20} -0.957202 q^{21} +5.89643 q^{22} -5.45555 q^{23} -3.07877 q^{24} +1.00000 q^{25} -1.00000 q^{27} -0.613364 q^{28} +10.2006 q^{29} -1.16585 q^{30} -1.02783 q^{31} -3.46697 q^{32} +5.05761 q^{33} +1.46593 q^{34} -0.957202 q^{35} -0.640788 q^{36} -0.939148 q^{37} -2.85289 q^{38} -3.07877 q^{40} -7.55650 q^{41} +1.11596 q^{42} +0.259367 q^{43} +3.24086 q^{44} -1.00000 q^{45} +6.36037 q^{46} +0.115292 q^{47} +2.30781 q^{48} -6.08376 q^{49} -1.16585 q^{50} +1.25739 q^{51} -2.43698 q^{53} +1.16585 q^{54} +5.05761 q^{55} +2.94700 q^{56} -2.44704 q^{57} -11.8924 q^{58} -8.32438 q^{59} -0.640788 q^{60} +13.1657 q^{61} +1.19830 q^{62} +0.957202 q^{63} +8.65760 q^{64} -5.89643 q^{66} -11.8247 q^{67} +0.805722 q^{68} +5.45555 q^{69} +1.11596 q^{70} +0.977874 q^{71} +3.07877 q^{72} +7.06112 q^{73} +1.09491 q^{74} -1.00000 q^{75} -1.56804 q^{76} -4.84116 q^{77} -13.0206 q^{79} +2.30781 q^{80} +1.00000 q^{81} +8.80977 q^{82} -3.76930 q^{83} +0.613364 q^{84} +1.25739 q^{85} -0.302384 q^{86} -10.2006 q^{87} -15.5712 q^{88} -17.9201 q^{89} +1.16585 q^{90} +3.49585 q^{92} +1.02783 q^{93} -0.134414 q^{94} -2.44704 q^{95} +3.46697 q^{96} +8.42595 q^{97} +7.09277 q^{98} -5.05761 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{3} + 10 q^{4} - 9 q^{5} + 10 q^{7} - 3 q^{8} + 9 q^{9} - 11 q^{11} - 10 q^{12} + 10 q^{14} + 9 q^{15} + 8 q^{16} + 18 q^{17} - 10 q^{19} - 10 q^{20} - 10 q^{21} + 17 q^{22} - 7 q^{23} + 3 q^{24}+ \cdots - 11 q^{99}+O(q^{100}) \) 9 * q - 9 * q^3 + 10 * q^4 - 9 * q^5 + 10 * q^7 - 3 * q^8 + 9 * q^9 - 11 * q^11 - 10 * q^12 + 10 * q^14 + 9 * q^15 + 8 * q^16 + 18 * q^17 - 10 * q^19 - 10 * q^20 - 10 * q^21 + 17 * q^22 - 7 * q^23 + 3 * q^24 + 9 * q^25 - 9 * q^27 + 43 * q^28 - 9 * q^29 - 17 * q^31 - 11 * q^32 + 11 * q^33 + 4 * q^34 - 10 * q^35 + 10 * q^36 - 3 * q^37 + 21 * q^38 + 3 * q^40 - 4 * q^41 - 10 * q^42 + 14 * q^43 - 13 * q^44 - 9 * q^45 - 3 * q^46 + 2 * q^47 - 8 * q^48 + 43 * q^49 - 18 * q^51 + 5 * q^53 + 11 * q^55 + q^56 + 10 * q^57 + 14 * q^58 - 3 * q^59 + 10 * q^60 + 48 * q^61 - 7 * q^62 + 10 * q^63 + 41 * q^64 - 17 * q^66 + 40 * q^67 + 40 * q^68 + 7 * q^69 - 10 * q^70 - 12 * q^71 - 3 * q^72 + 38 * q^73 - 4 * q^74 - 9 * q^75 - 51 * q^76 + 8 * q^77 + 22 * q^79 - 8 * q^80 + 9 * q^81 + 38 * q^82 - 11 * q^83 - 43 * q^84 - 18 * q^85 - 56 * q^86 + 9 * q^87 + 50 * q^88 - 2 * q^89 - 36 * q^92 + 17 * q^93 + 42 * q^94 + 10 * q^95 + 11 * q^96 + 23 * q^97 + 79 * q^98 - 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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