LMFDB - Embedded newform 2535.2.a.bm.1.6

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			1.6
Root			$0.701099$ 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)

$f(q)$	$=$	\(q+1.43598 q^{2} -1.00000 q^{3} +0.0620294 q^{4} -1.00000 q^{5} -1.43598 q^{6} +4.66136 q^{7} -2.78288 q^{8} +1.00000 q^{9} -1.43598 q^{10} -6.18428 q^{11} -0.0620294 q^{12} +6.69361 q^{14} +1.00000 q^{15} -4.12021 q^{16} +4.58791 q^{17} +1.43598 q^{18} +1.10535 q^{19} -0.0620294 q^{20} -4.66136 q^{21} -8.88049 q^{22} +0.468818 q^{23} +2.78288 q^{24} +1.00000 q^{25} -1.00000 q^{27} +0.289142 q^{28} +7.41205 q^{29} +1.43598 q^{30} +1.71209 q^{31} -0.350766 q^{32} +6.18428 q^{33} +6.58813 q^{34} -4.66136 q^{35} +0.0620294 q^{36} +6.88307 q^{37} +1.58726 q^{38} +2.78288 q^{40} +6.47743 q^{41} -6.69361 q^{42} -6.33206 q^{43} -0.383608 q^{44} -1.00000 q^{45} +0.673212 q^{46} -4.57038 q^{47} +4.12021 q^{48} +14.7283 q^{49} +1.43598 q^{50} -4.58791 q^{51} -1.81559 q^{53} -1.43598 q^{54} +6.18428 q^{55} -12.9720 q^{56} -1.10535 q^{57} +10.6435 q^{58} -2.07754 q^{59} +0.0620294 q^{60} -1.70491 q^{61} +2.45852 q^{62} +4.66136 q^{63} +7.73673 q^{64} +8.88049 q^{66} +6.74923 q^{67} +0.284585 q^{68} -0.468818 q^{69} -6.69361 q^{70} +10.3325 q^{71} -2.78288 q^{72} -6.47945 q^{73} +9.88393 q^{74} -1.00000 q^{75} +0.0685643 q^{76} -28.8272 q^{77} +16.4292 q^{79} +4.12021 q^{80} +1.00000 q^{81} +9.30144 q^{82} -3.37171 q^{83} -0.289142 q^{84} -4.58791 q^{85} -9.09269 q^{86} -7.41205 q^{87} +17.2101 q^{88} -9.66236 q^{89} -1.43598 q^{90} +0.0290805 q^{92} -1.71209 q^{93} -6.56295 q^{94} -1.10535 q^{95} +0.350766 q^{96} +19.0665 q^{97} +21.1495 q^{98} -6.18428 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.43598	1.01539	0.507694	−	0.861537i	$-0.330498\pi$
$2$	1.43598	1.01539	0.507694	+	0.861537i	$0.330498\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.0620294	0.0310147
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.43598	−0.586235
$7$	4.66136	1.76183	0.880915	−	0.473275i	$-0.156928\pi$
$7$	4.66136	1.76183	0.880915	+	0.473275i	$0.156928\pi$
$8$	−2.78288	−0.983897
$9$	1.00000	0.333333
$10$	−1.43598	−0.454096
$11$	−6.18428	−1.86463	−0.932316	−	0.361645i	$-0.882215\pi$
$11$	−6.18428	−1.86463	−0.932316	+	0.361645i	$0.882215\pi$
$12$	−0.0620294	−0.0179064
$13$	0	0
$13$	0	0
$14$	6.69361	1.78894
$15$	1.00000	0.258199
$16$	−4.12021	−1.03005
$17$	4.58791	1.11273	0.556366	−	0.830937i	$-0.312195\pi$
$17$	4.58791	1.11273	0.556366	+	0.830937i	$0.312195\pi$
$18$	1.43598	0.338463
$19$	1.10535	0.253585	0.126793	−	0.991929i	$-0.459532\pi$
$19$	1.10535	0.253585	0.126793	+	0.991929i	$0.459532\pi$
$20$	−0.0620294	−0.0138702
$21$	−4.66136	−1.01719
$22$	−8.88049	−1.89333
$23$	0.468818	0.0977553	0.0488777	−	0.998805i	$-0.484436\pi$
$23$	0.468818	0.0977553	0.0488777	+	0.998805i	$0.484436\pi$
$24$	2.78288	0.568053
$25$	1.00000	0.200000
$26$	0	0
$27$	−1.00000	−0.192450
$28$	0.289142	0.0546426
$29$	7.41205	1.37638	0.688191	−	0.725529i	$-0.258405\pi$
$29$	7.41205	1.37638	0.688191	+	0.725529i	$0.258405\pi$
$30$	1.43598	0.262172
$31$	1.71209	0.307500	0.153750	−	0.988110i	$-0.450865\pi$
$31$	1.71209	0.307500	0.153750	+	0.988110i	$0.450865\pi$
$32$	−0.350766	−0.0620073
$33$	6.18428	1.07655
$34$	6.58813	1.12986
$35$	−4.66136	−0.787914
$36$	0.0620294	0.0103382
$37$	6.88307	1.13157	0.565785	−	0.824553i	$-0.308573\pi$
$37$	6.88307	1.13157	0.565785	+	0.824553i	$0.308573\pi$
$38$	1.58726	0.257487
$39$	0	0
$40$	2.78288	0.440012
$41$	6.47743	1.01161	0.505803	−	0.862649i	$-0.331196\pi$
$41$	6.47743	1.01161	0.505803	+	0.862649i	$0.331196\pi$
$42$	−6.69361	−1.03285
$43$	−6.33206	−0.965630	−0.482815	−	0.875722i	$-0.660386\pi$
$43$	−6.33206	−0.965630	−0.482815	+	0.875722i	$0.660386\pi$
$44$	−0.383608	−0.0578310
$45$	−1.00000	−0.149071
$46$	0.673212	0.0992597
$47$	−4.57038	−0.666658	−0.333329	−	0.942811i	$-0.608172\pi$
$47$	−4.57038	−0.666658	−0.333329	+	0.942811i	$0.608172\pi$
$48$	4.12021	0.594701
$49$	14.7283	2.10404
$50$	1.43598	0.203078
$51$	−4.58791	−0.642436
$52$	0	0
$53$	−1.81559	−0.249390	−0.124695	−	0.992195i	$-0.539795\pi$
$53$	−1.81559	−0.249390	−0.124695	+	0.992195i	$0.539795\pi$
$54$	−1.43598	−0.195412
$55$	6.18428	0.833889
$56$	−12.9720	−1.73346
$57$	−1.10535	−0.146407
$58$	10.6435	1.39756
$59$	−2.07754	−0.270472	−0.135236	−	0.990813i	$-0.543179\pi$
$59$	−2.07754	−0.270472	−0.135236	+	0.990813i	$0.543179\pi$
$60$	0.0620294	0.00800796
$61$	−1.70491	−0.218292	−0.109146	−	0.994026i	$-0.534812\pi$
$61$	−1.70491	−0.218292	−0.109146	+	0.994026i	$0.534812\pi$
$62$	2.45852	0.312232
$63$	4.66136	0.587277
$64$	7.73673	0.967091
$65$	0	0
$66$	8.88049	1.09311
$67$	6.74923	0.824550	0.412275	−	0.911060i	$-0.364734\pi$
$67$	6.74923	0.824550	0.412275	+	0.911060i	$0.364734\pi$
$68$	0.284585	0.0345111
$69$	−0.468818	−0.0564391
$70$	−6.69361	−0.800039
$71$	10.3325	1.22624	0.613118	−	0.789991i	$-0.289915\pi$
$71$	10.3325	1.22624	0.613118	+	0.789991i	$0.289915\pi$
$72$	−2.78288	−0.327966
$73$	−6.47945	−0.758362	−0.379181	−	0.925323i	$-0.623794\pi$
$73$	−6.47945	−0.758362	−0.379181	+	0.925323i	$0.623794\pi$
$74$	9.88393	1.14898
$75$	−1.00000	−0.115470
$76$	0.0685643	0.00786487
$77$	−28.8272	−3.28516
$78$	0	0
$79$	16.4292	1.84843	0.924216	−	0.381869i	$-0.124719\pi$
$79$	16.4292	1.84843	0.924216	+	0.381869i	$0.124719\pi$
$80$	4.12021	0.460654
$81$	1.00000	0.111111
$82$	9.30144	1.02717
$83$	−3.37171	−0.370093	−0.185047	−	0.982730i	$-0.559244\pi$
$83$	−3.37171	−0.370093	−0.185047	+	0.982730i	$0.559244\pi$
$84$	−0.289142	−0.0315479
$85$	−4.58791	−0.497629
$86$	−9.09269	−0.980490
$87$	−7.41205	−0.794655
$88$	17.2101	1.83461
$89$	−9.66236	−1.02421	−0.512104	−	0.858923i	$-0.671134\pi$
$89$	−9.66236	−1.02421	−0.512104	+	0.858923i	$0.671134\pi$
$90$	−1.43598	−0.151365
$91$	0	0
$92$	0.0290805	0.00303185
$93$	−1.71209	−0.177535
$94$	−6.56295	−0.676917
$95$	−1.10535	−0.113407
$96$	0.350766	0.0357999
$97$	19.0665	1.93591	0.967956	−	0.251120i	$-0.0807989\pi$
$97$	19.0665	1.93591	0.967956	+	0.251120i	$0.0807989\pi$
$98$	21.1495	2.13642
$99$	−6.18428	−0.621544
$100$	0.0620294	0.00620294
$101$	15.9374	1.58583	0.792916	−	0.609331i	$-0.208562\pi$
$101$	15.9374	1.58583	0.792916	+	0.609331i	$0.208562\pi$
$102$	−6.58813	−0.652322
$103$	6.18951	0.609871	0.304935	−	0.952373i	$-0.401365\pi$
$103$	6.18951	0.609871	0.304935	+	0.952373i	$0.401365\pi$
$104$	0	0
$105$	4.66136	0.454902
$106$	−2.60714	−0.253228
$107$	−2.06493	−0.199625	−0.0998123	−	0.995006i	$-0.531824\pi$
$107$	−2.06493	−0.199625	−0.0998123	+	0.995006i	$0.531824\pi$
$108$	−0.0620294	−0.00596878
$109$	15.3189	1.46728	0.733641	−	0.679537i	$-0.237819\pi$
$109$	15.3189	1.46728	0.733641	+	0.679537i	$0.237819\pi$
$110$	8.88049	0.846721
$111$	−6.88307	−0.653312
$112$	−19.2058	−1.81478
$113$	14.5687	1.37051	0.685256	−	0.728303i	$-0.259690\pi$
$113$	14.5687	1.37051	0.685256	+	0.728303i	$0.259690\pi$
$114$	−1.58726	−0.148660
$115$	−0.468818	−0.0437175
$116$	0.459765	0.0426881
$117$	0	0
$118$	−2.98329	−0.274635
$119$	21.3859	1.96044
$120$	−2.78288	−0.254041
$121$	27.2454	2.47685
$122$	−2.44822	−0.221651
$123$	−6.47743	−0.584050
$124$	0.106200	0.00953703
$125$	−1.00000	−0.0894427
$126$	6.69361	0.596314
$127$	−12.3302	−1.09413	−0.547063	−	0.837091i	$-0.684254\pi$
$127$	−12.3302	−1.09413	−0.547063	+	0.837091i	$0.684254\pi$
$128$	11.8113	1.04398
$129$	6.33206	0.557507
$130$	0	0
$131$	−15.3053	−1.33723	−0.668615	−	0.743609i	$-0.733112\pi$
$131$	−15.3053	−1.33723	−0.668615	+	0.743609i	$0.733112\pi$
$132$	0.383608	0.0333888
$133$	5.15245	0.446774
$134$	9.69174	0.837239
$135$	1.00000	0.0860663
$136$	−12.7676	−1.09481
$137$	−15.1058	−1.29057	−0.645287	−	0.763940i	$-0.723262\pi$
$137$	−15.1058	−1.29057	−0.645287	+	0.763940i	$0.723262\pi$
$138$	−0.673212	−0.0573076
$139$	2.63072	0.223135	0.111567	−	0.993757i	$-0.464413\pi$
$139$	2.63072	0.223135	0.111567	+	0.993757i	$0.464413\pi$
$140$	−0.289142	−0.0244369
$141$	4.57038	0.384895
$142$	14.8372	1.24511
$143$	0	0
$144$	−4.12021	−0.343351
$145$	−7.41205	−0.615537
$146$	−9.30434	−0.770032
$147$	−14.7283	−1.21477
$148$	0.426953	0.0350953
$149$	−19.3002	−1.58113	−0.790567	−	0.612376i	$-0.790214\pi$
$149$	−19.3002	−1.58113	−0.790567	+	0.612376i	$0.790214\pi$
$150$	−1.43598	−0.117247
$151$	9.60278	0.781463	0.390731	−	0.920505i	$-0.372222\pi$
$151$	9.60278	0.781463	0.390731	+	0.920505i	$0.372222\pi$
$152$	−3.07606	−0.249502
$153$	4.58791	0.370911
$154$	−41.3952	−3.33572
$155$	−1.71209	−0.137518
$156$	0	0
$157$	17.7352	1.41542	0.707712	−	0.706501i	$-0.249727\pi$
$157$	17.7352	1.41542	0.707712	+	0.706501i	$0.249727\pi$
$158$	23.5920	1.87688
$159$	1.81559	0.143985
$160$	0.350766	0.0277305
$161$	2.18533	0.172228
$162$	1.43598	0.112821
$163$	−19.1373	−1.49895	−0.749473	−	0.662035i	$-0.769693\pi$
$163$	−19.1373	−1.49895	−0.749473	+	0.662035i	$0.769693\pi$
$164$	0.401791	0.0313746
$165$	−6.18428	−0.481446
$166$	−4.84170	−0.375789
$167$	7.15778	0.553885	0.276943	−	0.960886i	$-0.410679\pi$
$167$	7.15778	0.553885	0.276943	+	0.960886i	$0.410679\pi$
$168$	12.9720	1.00081
$169$	0	0
$170$	−6.58813	−0.505287
$171$	1.10535	0.0845284
$172$	−0.392774	−0.0299487
$173$	5.98501	0.455032	0.227516	−	0.973774i	$-0.426940\pi$
$173$	5.98501	0.455032	0.227516	+	0.973774i	$0.426940\pi$
$174$	−10.6435	−0.806884
$175$	4.66136	0.352366
$176$	25.4806	1.92067
$177$	2.07754	0.156157
$178$	−13.8749	−1.03997
$179$	−9.17996	−0.686142	−0.343071	−	0.939309i	$-0.611467\pi$
$179$	−9.17996	−0.686142	−0.343071	+	0.939309i	$0.611467\pi$
$180$	−0.0620294	−0.00462340
$181$	−7.33835	−0.545455	−0.272728	−	0.962091i	$-0.587926\pi$
$181$	−7.33835	−0.545455	−0.272728	+	0.962091i	$0.587926\pi$
$182$	0	0
$183$	1.70491	0.126031
$184$	−1.30467	−0.0961812
$185$	−6.88307	−0.506053
$186$	−2.45852	−0.180267
$187$	−28.3729	−2.07484
$188$	−0.283498	−0.0206762
$189$	−4.66136	−0.339064
$190$	−1.58726	−0.115152
$191$	12.7239	0.920668	0.460334	−	0.887746i	$-0.347730\pi$
$191$	12.7239	0.920668	0.460334	+	0.887746i	$0.347730\pi$
$192$	−7.73673	−0.558350
$193$	17.0065	1.22416	0.612078	−	0.790798i	$-0.290334\pi$
$193$	17.0065	1.22416	0.612078	+	0.790798i	$0.290334\pi$
$194$	27.3791	1.96570
$195$	0	0
$196$	0.913588	0.0652563
$197$	2.46594	0.175691	0.0878455	−	0.996134i	$-0.472002\pi$
$197$	2.46594	0.175691	0.0878455	+	0.996134i	$0.472002\pi$
$198$	−8.88049	−0.631109
$199$	−6.89365	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$199$	−6.89365	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$200$	−2.78288	−0.196779
$201$	−6.74923	−0.476054
$202$	22.8857	1.61024
$203$	34.5502	2.42495
$204$	−0.284585	−0.0199250
$205$	−6.47743	−0.452404
$206$	8.88800	0.619256
$207$	0.468818	0.0325851
$208$	0	0
$209$	−6.83581	−0.472843
$210$	6.69361	0.461903
$211$	1.95078	0.134297	0.0671485	−	0.997743i	$-0.478610\pi$
$211$	1.95078	0.134297	0.0671485	+	0.997743i	$0.478610\pi$
$212$	−0.112620	−0.00773476
$213$	−10.3325	−0.707968
$214$	−2.96520	−0.202697
$215$	6.33206	0.431843
$216$	2.78288	0.189351
$217$	7.98067	0.541763
$218$	21.9976	1.48986
$219$	6.47945	0.437841
$220$	0.383608	0.0258628
$221$	0	0
$222$	−9.88393	−0.663366
$223$	−13.2382	−0.886496	−0.443248	−	0.896399i	$-0.646174\pi$
$223$	−13.2382	−0.886496	−0.443248	+	0.896399i	$0.646174\pi$
$224$	−1.63505	−0.109246
$225$	1.00000	0.0666667
$226$	20.9204	1.39160
$227$	4.08165	0.270909	0.135454	−	0.990784i	$-0.456751\pi$
$227$	4.08165	0.270909	0.135454	+	0.990784i	$0.456751\pi$
$228$	−0.0685643	−0.00454078
$229$	−23.1885	−1.53234	−0.766171	−	0.642637i	$-0.777840\pi$
$229$	−23.1885	−1.53234	−0.766171	+	0.642637i	$0.777840\pi$
$230$	−0.673212	−0.0443903
$231$	28.8272	1.89669
$232$	−20.6268	−1.35422
$233$	−0.878514	−0.0575534	−0.0287767	−	0.999586i	$-0.509161\pi$
$233$	−0.878514	−0.0575534	−0.0287767	+	0.999586i	$0.509161\pi$
$234$	0	0
$235$	4.57038	0.298138
$236$	−0.128868	−0.00838862
$237$	−16.4292	−1.06719
$238$	30.7097	1.99061
$239$	−18.2068	−1.17770	−0.588849	−	0.808243i	$-0.700419\pi$
$239$	−18.2068	−1.17770	−0.588849	+	0.808243i	$0.700419\pi$
$240$	−4.12021	−0.265958
$241$	−16.4897	−1.06219	−0.531097	−	0.847311i	$-0.678220\pi$
$241$	−16.4897	−1.06219	−0.531097	+	0.847311i	$0.678220\pi$
$242$	39.1237	2.51497
$243$	−1.00000	−0.0641500
$244$	−0.105755	−0.00677026
$245$	−14.7283	−0.940957
$246$	−9.30144	−0.593038
$247$	0	0
$248$	−4.76454	−0.302549
$249$	3.37171	0.213673
$250$	−1.43598	−0.0908191
$251$	24.2256	1.52911	0.764555	−	0.644559i	$-0.222959\pi$
$251$	24.2256	1.52911	0.764555	+	0.644559i	$0.222959\pi$
$252$	0.289142	0.0182142
$253$	−2.89931	−0.182278
$254$	−17.7058	−1.11096
$255$	4.58791	0.287306
$256$	1.48729	0.0929556
$257$	2.13383	0.133105	0.0665524	−	0.997783i	$-0.478800\pi$
$257$	2.13383	0.133105	0.0665524	+	0.997783i	$0.478800\pi$
$258$	9.09269	0.566086
$259$	32.0845	1.99363
$260$	0	0
$261$	7.41205	0.458794
$262$	−21.9780	−1.35781
$263$	4.74578	0.292637	0.146319	−	0.989238i	$-0.453258\pi$
$263$	4.74578	0.292637	0.146319	+	0.989238i	$0.453258\pi$
$264$	−17.2101	−1.05921
$265$	1.81559	0.111531
$266$	7.39879	0.453649
$267$	9.66236	0.591327
$268$	0.418651	0.0255732
$269$	0.699303	0.0426372	0.0213186	−	0.999773i	$-0.493214\pi$
$269$	0.699303	0.0426372	0.0213186	+	0.999773i	$0.493214\pi$
$270$	1.43598	0.0873908
$271$	12.2889	0.746498	0.373249	−	0.927731i	$-0.378244\pi$
$271$	12.2889	0.746498	0.373249	+	0.927731i	$0.378244\pi$
$272$	−18.9032	−1.14617
$273$	0	0
$274$	−21.6916	−1.31044
$275$	−6.18428	−0.372926
$276$	−0.0290805	−0.00175044
$277$	25.8088	1.55070	0.775351	−	0.631531i	$-0.217573\pi$
$277$	25.8088	1.55070	0.775351	+	0.631531i	$0.217573\pi$
$278$	3.77765	0.226569
$279$	1.71209	0.102500
$280$	12.9720	0.775226
$281$	−28.6333	−1.70812	−0.854061	−	0.520173i	$-0.825867\pi$
$281$	−28.6333	−1.70812	−0.854061	+	0.520173i	$0.825867\pi$
$282$	6.56295	0.390818
$283$	23.2312	1.38095	0.690475	−	0.723356i	$-0.257401\pi$
$283$	23.2312	1.38095	0.690475	+	0.723356i	$0.257401\pi$
$284$	0.640916	0.0380314
$285$	1.10535	0.0654754
$286$	0	0
$287$	30.1937	1.78228
$288$	−0.350766	−0.0206691
$289$	4.04892	0.238172
$290$	−10.6435	−0.625010
$291$	−19.0665	−1.11770
$292$	−0.401916	−0.0235204
$293$	−17.7782	−1.03861	−0.519306	−	0.854589i	$-0.673809\pi$
$293$	−17.7782	−1.03861	−0.519306	+	0.854589i	$0.673809\pi$
$294$	−21.1495	−1.23346
$295$	2.07754	0.120959
$296$	−19.1548	−1.11335
$297$	6.18428	0.358849
$298$	−27.7146	−1.60547
$299$	0	0
$300$	−0.0620294	−0.00358127
$301$	−29.5160	−1.70127
$302$	13.7894	0.793489
$303$	−15.9374	−0.915580
$304$	−4.55428	−0.261206
$305$	1.70491	0.0976231
$306$	6.58813	0.376618
$307$	−11.3286	−0.646556	−0.323278	−	0.946304i	$-0.604785\pi$
$307$	−11.3286	−0.646556	−0.323278	+	0.946304i	$0.604785\pi$
$308$	−1.78813	−0.101888
$309$	−6.18951	−0.352109
$310$	−2.45852	−0.139635
$311$	−3.64202	−0.206520	−0.103260	−	0.994654i	$-0.532927\pi$
$311$	−3.64202	−0.206520	−0.103260	+	0.994654i	$0.532927\pi$
$312$	0	0
$313$	−26.9199	−1.52161	−0.760803	−	0.648983i	$-0.775194\pi$
$313$	−26.9199	−1.52161	−0.760803	+	0.648983i	$0.775194\pi$
$314$	25.4674	1.43721
$315$	−4.66136	−0.262638
$316$	1.01910	0.0573286
$317$	−19.0352	−1.06913	−0.534563	−	0.845129i	$-0.679524\pi$
$317$	−19.0352	−1.06913	−0.534563	+	0.845129i	$0.679524\pi$
$318$	2.60714	0.146201
$319$	−45.8382	−2.56645
$320$	−7.73673	−0.432496
$321$	2.06493	0.115253
$322$	3.13809	0.174879
$323$	5.07125	0.282172
$324$	0.0620294	0.00344608
$325$	0	0
$326$	−27.4807	−1.52201
$327$	−15.3189	−0.847136
$328$	−18.0259	−0.995315
$329$	−21.3042	−1.17454
$330$	−8.88049	−0.488855
$331$	−2.98681	−0.164170	−0.0820849	−	0.996625i	$-0.526158\pi$
$331$	−2.98681	−0.164170	−0.0820849	+	0.996625i	$0.526158\pi$
$332$	−0.209145	−0.0114783
$333$	6.88307	0.377190
$334$	10.2784	0.562409
$335$	−6.74923	−0.368750
$336$	19.2058	1.04776
$337$	−16.9655	−0.924168	−0.462084	−	0.886836i	$-0.652898\pi$
$337$	−16.9655	−0.924168	−0.462084	+	0.886836i	$0.652898\pi$
$338$	0	0
$339$	−14.5687	−0.791265
$340$	−0.284585	−0.0154338
$341$	−10.5880	−0.573375
$342$	1.58726	0.0858292
$343$	36.0244	1.94514
$344$	17.6214	0.950080
$345$	0.468818	0.0252403
$346$	8.59433	0.462034
$347$	6.66624	0.357862	0.178931	−	0.983862i	$-0.442736\pi$
$347$	6.66624	0.357862	0.178931	+	0.983862i	$0.442736\pi$
$348$	−0.459765	−0.0246460
$349$	−9.62703	−0.515323	−0.257661	−	0.966235i	$-0.582952\pi$
$349$	−9.62703	−0.515323	−0.257661	+	0.966235i	$0.582952\pi$
$350$	6.69361	0.357788
$351$	0	0
$352$	2.16924	0.115621
$353$	−28.0374	−1.49228	−0.746141	−	0.665788i	$-0.768096\pi$
$353$	−28.0374	−1.49228	−0.746141	+	0.665788i	$0.768096\pi$
$354$	2.98329	0.158560
$355$	−10.3325	−0.548390
$356$	−0.599351	−0.0317655
$357$	−21.3859	−1.13186
$358$	−13.1822	−0.696701
$359$	2.02283	0.106761	0.0533804	−	0.998574i	$-0.483000\pi$
$359$	2.02283	0.106761	0.0533804	+	0.998574i	$0.483000\pi$
$360$	2.78288	0.146671
$361$	−17.7782	−0.935695
$362$	−10.5377	−0.553849
$363$	−27.2454	−1.43001
$364$	0	0
$365$	6.47945	0.339150
$366$	2.44822	0.127970
$367$	−4.70652	−0.245678	−0.122839	−	0.992427i	$-0.539200\pi$
$367$	−4.70652	−0.245678	−0.122839	+	0.992427i	$0.539200\pi$
$368$	−1.93163	−0.100693
$369$	6.47743	0.337202
$370$	−9.88393	−0.513841
$371$	−8.46310	−0.439382
$372$	−0.106200	−0.00550621
$373$	−4.45995	−0.230927	−0.115464	−	0.993312i	$-0.536835\pi$
$373$	−4.45995	−0.230927	−0.115464	+	0.993312i	$0.536835\pi$
$374$	−40.7429	−2.10676
$375$	1.00000	0.0516398
$376$	12.7188	0.655923
$377$	0	0
$378$	−6.69361	−0.344282
$379$	2.06186	0.105910	0.0529552	−	0.998597i	$-0.483136\pi$
$379$	2.06186	0.105910	0.0529552	+	0.998597i	$0.483136\pi$
$380$	−0.0685643	−0.00351728
$381$	12.3302	0.631694
$382$	18.2712	0.934836
$383$	−15.9663	−0.815839	−0.407919	−	0.913018i	$-0.633746\pi$
$383$	−15.9663	−0.815839	−0.407919	+	0.913018i	$0.633746\pi$
$384$	−11.8113	−0.602743
$385$	28.8272	1.46917
$386$	24.4210	1.24299
$387$	−6.33206	−0.321877
$388$	1.18269	0.0600418
$389$	−3.76244	−0.190763	−0.0953816	−	0.995441i	$-0.530407\pi$
$389$	−3.76244	−0.190763	−0.0953816	+	0.995441i	$0.530407\pi$
$390$	0	0
$391$	2.15090	0.108775
$392$	−40.9871	−2.07016
$393$	15.3053	0.772050
$394$	3.54103	0.178395
$395$	−16.4292	−0.826644
$396$	−0.383608	−0.0192770
$397$	29.0906	1.46002	0.730008	−	0.683438i	$-0.239516\pi$
$397$	29.0906	1.46002	0.730008	+	0.683438i	$0.239516\pi$
$398$	−9.89912	−0.496198
$399$	−5.15245	−0.257945
$400$	−4.12021	−0.206011
$401$	−20.1071	−1.00410	−0.502051	−	0.864838i	$-0.667421\pi$
$401$	−20.1071	−1.00410	−0.502051	+	0.864838i	$0.667421\pi$
$402$	−9.69174	−0.483380
$403$	0	0
$404$	0.988588	0.0491841
$405$	−1.00000	−0.0496904
$406$	49.6134	2.46227
$407$	−42.5669	−2.10996
$408$	12.7676	0.632091
$409$	10.7801	0.533041	0.266520	−	0.963829i	$-0.414126\pi$
$409$	10.7801	0.533041	0.266520	+	0.963829i	$0.414126\pi$
$410$	−9.30144	−0.459366
$411$	15.1058	0.745114
$412$	0.383932	0.0189150
$413$	−9.68415	−0.476526
$414$	0.673212	0.0330866
$415$	3.37171	0.165511
$416$	0	0
$417$	−2.63072	−0.128827
$418$	−9.81606	−0.480119
$419$	5.76876	0.281822	0.140911	−	0.990022i	$-0.454997\pi$
$419$	5.76876	0.281822	0.140911	+	0.990022i	$0.454997\pi$
$420$	0.289142	0.0141087
$421$	−8.42888	−0.410799	−0.205399	−	0.978678i	$-0.565849\pi$
$421$	−8.42888	−0.410799	−0.205399	+	0.978678i	$0.565849\pi$
$422$	2.80127	0.136364
$423$	−4.57038	−0.222219
$424$	5.05256	0.245374
$425$	4.58791	0.222546
$426$	−14.8372	−0.718863
$427$	−7.94723	−0.384593
$428$	−0.128087	−0.00619130
$429$	0	0
$430$	9.09269	0.438488
$431$	13.7020	0.660000	0.330000	−	0.943981i	$-0.392951\pi$
$431$	13.7020	0.660000	0.330000	+	0.943981i	$0.392951\pi$
$432$	4.12021	0.198234
$433$	26.3471	1.26616	0.633081	−	0.774086i	$-0.281790\pi$
$433$	26.3471	1.26616	0.633081	+	0.774086i	$0.281790\pi$
$434$	11.4601	0.550100
$435$	7.41205	0.355380
$436$	0.950221	0.0455074
$437$	0.518209	0.0247893
$438$	9.30434	0.444578
$439$	−10.5841	−0.505154	−0.252577	−	0.967577i	$-0.581278\pi$
$439$	−10.5841	−0.505154	−0.252577	+	0.967577i	$0.581278\pi$
$440$	−17.2101	−0.820461
$441$	14.7283	0.701348
$442$	0	0
$443$	−14.5609	−0.691811	−0.345906	−	0.938269i	$-0.612428\pi$
$443$	−14.5609	−0.691811	−0.345906	+	0.938269i	$0.612428\pi$
$444$	−0.426953	−0.0202623
$445$	9.66236	0.458040
$446$	−19.0098	−0.900138
$447$	19.3002	0.912868
$448$	36.0637	1.70385
$449$	−1.82046	−0.0859128	−0.0429564	−	0.999077i	$-0.513678\pi$
$449$	−1.82046	−0.0859128	−0.0429564	+	0.999077i	$0.513678\pi$
$450$	1.43598	0.0676926
$451$	−40.0583	−1.88627
$452$	0.903690	0.0425060
$453$	−9.60278	−0.451178
$454$	5.86116	0.275078
$455$	0	0
$456$	3.07606	0.144050
$457$	−15.6233	−0.730829	−0.365415	−	0.930845i	$-0.619073\pi$
$457$	−15.6233	−0.730829	−0.365415	+	0.930845i	$0.619073\pi$
$458$	−33.2982	−1.55592
$459$	−4.58791	−0.214145
$460$	−0.0290805	−0.00135589
$461$	0.672474	0.0313202	0.0156601	−	0.999877i	$-0.495015\pi$
$461$	0.672474	0.0313202	0.0156601	+	0.999877i	$0.495015\pi$
$462$	41.3952	1.92588
$463$	29.3187	1.36256	0.681279	−	0.732024i	$-0.261424\pi$
$463$	29.3187	1.36256	0.681279	+	0.732024i	$0.261424\pi$
$464$	−30.5392	−1.41775
$465$	1.71209	0.0793962
$466$	−1.26153	−0.0584390
$467$	−12.5039	−0.578611	−0.289305	−	0.957237i	$-0.593424\pi$
$467$	−12.5039	−0.578611	−0.289305	+	0.957237i	$0.593424\pi$
$468$	0	0
$469$	31.4606	1.45272
$470$	6.56295	0.302726
$471$	−17.7352	−0.817196
$472$	5.78154	0.266117
$473$	39.1592	1.80054
$474$	−23.5920	−1.08362
$475$	1.10535	0.0507170
$476$	1.32656	0.0608026
$477$	−1.81559	−0.0831300
$478$	−26.1445	−1.19582
$479$	31.7959	1.45279	0.726396	−	0.687277i	$-0.241194\pi$
$479$	31.7959	1.45279	0.726396	+	0.687277i	$0.241194\pi$
$480$	−0.350766	−0.0160102
$481$	0	0
$482$	−23.6788	−1.07854
$483$	−2.18533	−0.0994360
$484$	1.69002	0.0768189
$485$	−19.0665	−0.865766
$486$	−1.43598	−0.0651372
$487$	37.9782	1.72096	0.860478	−	0.509487i	$-0.170165\pi$
$487$	37.9782	1.72096	0.860478	+	0.509487i	$0.170165\pi$
$488$	4.74457	0.214777
$489$	19.1373	0.865417
$490$	−21.1495	−0.955437
$491$	−11.8063	−0.532811	−0.266405	−	0.963861i	$-0.585836\pi$
$491$	−11.8063	−0.532811	−0.266405	+	0.963861i	$0.585836\pi$
$492$	−0.401791	−0.0181142
$493$	34.0058	1.53154
$494$	0	0
$495$	6.18428	0.277963
$496$	−7.05417	−0.316741
$497$	48.1633	2.16042
$498$	4.84170	0.216962
$499$	−39.9647	−1.78906	−0.894532	−	0.447003i	$-0.852491\pi$
$499$	−39.9647	−1.78906	−0.894532	+	0.447003i	$0.852491\pi$
$500$	−0.0620294	−0.00277404
$501$	−7.15778	−0.319786
$502$	34.7875	1.55264
$503$	−1.68267	−0.0750265	−0.0375133	−	0.999296i	$-0.511944\pi$
$503$	−1.68267	−0.0750265	−0.0375133	+	0.999296i	$0.511944\pi$
$504$	−12.9720	−0.577820
$505$	−15.9374	−0.709205
$506$	−4.16333	−0.185083
$507$	0	0
$508$	−0.764834	−0.0339340
$509$	30.4690	1.35051	0.675257	−	0.737582i	$-0.264033\pi$
$509$	30.4690	1.35051	0.675257	+	0.737582i	$0.264033\pi$
$510$	6.58813	0.291727
$511$	−30.2031	−1.33610
$512$	−21.4869	−0.949595
$513$	−1.10535	−0.0488025
$514$	3.06413	0.135153
$515$	−6.18951	−0.272743
$516$	0.392774	0.0172909
$517$	28.2645	1.24307
$518$	46.0726	2.02431
$519$	−5.98501	−0.262713
$520$	0	0
$521$	23.7603	1.04096	0.520480	−	0.853874i	$-0.325753\pi$
$521$	23.7603	1.04096	0.520480	+	0.853874i	$0.325753\pi$
$522$	10.6435	0.465855
$523$	23.0685	1.00871	0.504357	−	0.863495i	$-0.331730\pi$
$523$	23.0685	1.00871	0.504357	+	0.863495i	$0.331730\pi$
$524$	−0.949378	−0.0414738
$525$	−4.66136	−0.203439
$526$	6.81483	0.297141
$527$	7.85491	0.342165
$528$	−25.4806	−1.10890
$529$	−22.7802	−0.990444
$530$	2.60714	0.113247
$531$	−2.07754	−0.0901574
$532$	0.319603	0.0138566
$533$	0	0
$534$	13.8749	0.600427
$535$	2.06493	0.0892748
$536$	−18.7823	−0.811272
$537$	9.17996	0.396144
$538$	1.00418	0.0432934
$539$	−91.0840	−3.92327
$540$	0.0620294	0.00266932
$541$	18.6879	0.803456	0.401728	−	0.915759i	$-0.368410\pi$
$541$	18.6879	0.803456	0.401728	+	0.915759i	$0.368410\pi$
$542$	17.6466	0.757986
$543$	7.33835	0.314919
$544$	−1.60928	−0.0689975
$545$	−15.3189	−0.656189
$546$	0	0
$547$	−8.14172	−0.348115	−0.174057	−	0.984736i	$-0.555688\pi$
$547$	−8.14172	−0.348115	−0.174057	+	0.984736i	$0.555688\pi$
$548$	−0.937003	−0.0400268
$549$	−1.70491	−0.0727640
$550$	−8.88049	−0.378665
$551$	8.19292	0.349030
$552$	1.30467	0.0555302
$553$	76.5826	3.25662
$554$	37.0609	1.57456
$555$	6.88307	0.292170
$556$	0.163182	0.00692046
$557$	24.4772	1.03713	0.518566	−	0.855037i	$-0.326466\pi$
$557$	24.4772	1.03713	0.518566	+	0.855037i	$0.326466\pi$
$558$	2.45852	0.104077
$559$	0	0
$560$	19.2058	0.811593
$561$	28.3729	1.19791
$562$	−41.1168	−1.73441
$563$	15.5923	0.657136	0.328568	−	0.944480i	$-0.393434\pi$
$563$	15.5923	0.657136	0.328568	+	0.944480i	$0.393434\pi$
$564$	0.283498	0.0119374
$565$	−14.5687	−0.612911
$566$	33.3594	1.40220
$567$	4.66136	0.195759
$568$	−28.7540	−1.20649
$569$	−5.19758	−0.217894	−0.108947	−	0.994048i	$-0.534748\pi$
$569$	−5.19758	−0.217894	−0.108947	+	0.994048i	$0.534748\pi$
$570$	1.58726	0.0664830
$571$	−8.05523	−0.337101	−0.168550	−	0.985693i	$-0.553909\pi$
$571$	−8.05523	−0.337101	−0.168550	+	0.985693i	$0.553909\pi$
$572$	0	0
$573$	−12.7239	−0.531548
$574$	43.3574	1.80970
$575$	0.468818	0.0195511
$576$	7.73673	0.322364
$577$	3.19865	0.133162	0.0665808	−	0.997781i	$-0.478791\pi$
$577$	3.19865	0.133162	0.0665808	+	0.997781i	$0.478791\pi$
$578$	5.81415	0.241837
$579$	−17.0065	−0.706767
$580$	−0.459765	−0.0190907
$581$	−15.7168	−0.652041
$582$	−27.3791	−1.13490
$583$	11.2281	0.465020
$584$	18.0315	0.746150
$585$	0	0
$586$	−25.5290	−1.05459
$587$	−21.0612	−0.869287	−0.434644	−	0.900602i	$-0.643126\pi$
$587$	−21.0612	−0.869287	−0.434644	+	0.900602i	$0.643126\pi$
$588$	−0.913588	−0.0376758
$589$	1.89246	0.0779775
$590$	2.98329	0.122820
$591$	−2.46594	−0.101435
$592$	−28.3597	−1.16558
$593$	−23.9997	−0.985548	−0.492774	−	0.870157i	$-0.664017\pi$
$593$	−23.9997	−0.985548	−0.492774	+	0.870157i	$0.664017\pi$
$594$	8.88049	0.364371
$595$	−21.3859	−0.876737
$596$	−1.19718	−0.0490384
$597$	6.89365	0.282138
$598$	0	0
$599$	16.7394	0.683955	0.341977	−	0.939708i	$-0.388903\pi$
$599$	16.7394	0.683955	0.341977	+	0.939708i	$0.388903\pi$
$600$	2.78288	0.113611
$601$	34.3133	1.39967	0.699834	−	0.714305i	$-0.253257\pi$
$601$	34.3133	1.39967	0.699834	+	0.714305i	$0.253257\pi$
$602$	−42.3843	−1.72746
$603$	6.74923	0.274850
$604$	0.595655	0.0242368
$605$	−27.2454	−1.10768
$606$	−22.8857	−0.929670
$607$	−13.6092	−0.552382	−0.276191	−	0.961103i	$-0.589072\pi$
$607$	−13.6092	−0.552382	−0.276191	+	0.961103i	$0.589072\pi$
$608$	−0.387720	−0.0157241
$609$	−34.5502	−1.40005
$610$	2.44822	0.0991255
$611$	0	0
$612$	0.284585	0.0115037
$613$	21.2349	0.857670	0.428835	−	0.903383i	$-0.358924\pi$
$613$	21.2349	0.857670	0.428835	+	0.903383i	$0.358924\pi$
$614$	−16.2676	−0.656506
$615$	6.47743	0.261195
$616$	80.2227	3.23226
$617$	−7.22102	−0.290707	−0.145354	−	0.989380i	$-0.546432\pi$
$617$	−7.22102	−0.290707	−0.145354	+	0.989380i	$0.546432\pi$
$618$	−8.88800	−0.357528
$619$	6.63029	0.266494	0.133247	−	0.991083i	$-0.457460\pi$
$619$	6.63029	0.266494	0.133247	+	0.991083i	$0.457460\pi$
$620$	−0.106200	−0.00426509
$621$	−0.468818	−0.0188130
$622$	−5.22985	−0.209698
$623$	−45.0398	−1.80448
$624$	0	0
$625$	1.00000	0.0400000
$626$	−38.6564	−1.54502
$627$	6.83581	0.272996
$628$	1.10011	0.0438990
$629$	31.5789	1.25913
$630$	−6.69361	−0.266680
$631$	−6.36730	−0.253478	−0.126739	−	0.991936i	$-0.540451\pi$
$631$	−6.36730	−0.253478	−0.126739	+	0.991936i	$0.540451\pi$
$632$	−45.7206	−1.81867
$633$	−1.95078	−0.0775364
$634$	−27.3342	−1.08558
$635$	12.3302	0.489308
$636$	0.112620	0.00446566
$637$	0	0
$638$	−65.8226	−2.60594
$639$	10.3325	0.408746
$640$	−11.8113	−0.466883
$641$	22.6045	0.892825	0.446413	−	0.894827i	$-0.352701\pi$
$641$	22.6045	0.892825	0.446413	+	0.894827i	$0.352701\pi$
$642$	2.96520	0.117027
$643$	−33.9609	−1.33929	−0.669644	−	0.742682i	$-0.733553\pi$
$643$	−33.9609	−1.33929	−0.669644	+	0.742682i	$0.733553\pi$
$644$	0.135555	0.00534161
$645$	−6.33206	−0.249324
$646$	7.28220	0.286514
$647$	−20.8248	−0.818709	−0.409354	−	0.912375i	$-0.634246\pi$
$647$	−20.8248	−0.818709	−0.409354	+	0.912375i	$0.634246\pi$
$648$	−2.78288	−0.109322
$649$	12.8481	0.504331
$650$	0	0
$651$	−7.98067	−0.312787
$652$	−1.18707	−0.0464894
$653$	24.5455	0.960541	0.480271	−	0.877120i	$-0.340538\pi$
$653$	24.5455	0.960541	0.480271	+	0.877120i	$0.340538\pi$
$654$	−21.9976	−0.860173
$655$	15.3053	0.598027
$656$	−26.6884	−1.04201
$657$	−6.47945	−0.252787
$658$	−30.5923	−1.19261
$659$	12.4224	0.483906	0.241953	−	0.970288i	$-0.422212\pi$
$659$	12.4224	0.483906	0.241953	+	0.970288i	$0.422212\pi$
$660$	−0.383608	−0.0149319
$661$	29.1593	1.13417	0.567083	−	0.823661i	$-0.308072\pi$
$661$	29.1593	1.13417	0.567083	+	0.823661i	$0.308072\pi$
$662$	−4.28899	−0.166696
$663$	0	0
$664$	9.38307	0.364134
$665$	−5.15245	−0.199803
$666$	9.88393	0.382994
$667$	3.47490	0.134549
$668$	0.443993	0.0171786
$669$	13.2382	0.511819
$670$	−9.69174	−0.374425
$671$	10.5437	0.407034
$672$	1.63505	0.0630734
$673$	−0.223030	−0.00859719	−0.00429860	−	0.999991i	$-0.501368\pi$
$673$	−0.223030	−0.00859719	−0.00429860	+	0.999991i	$0.501368\pi$
$674$	−24.3620	−0.938390
$675$	−1.00000	−0.0384900
$676$	0	0
$677$	27.6651	1.06325	0.531627	−	0.846978i	$-0.321581\pi$
$677$	27.6651	1.06325	0.531627	+	0.846978i	$0.321581\pi$
$678$	−20.9204	−0.803442
$679$	88.8760	3.41075
$680$	12.7676	0.489615
$681$	−4.08165	−0.156409
$682$	−15.2042	−0.582198
$683$	42.5702	1.62890	0.814452	−	0.580230i	$-0.197037\pi$
$683$	42.5702	1.62890	0.814452	+	0.580230i	$0.197037\pi$
$684$	0.0685643	0.00262162
$685$	15.1058	0.577162
$686$	51.7303	1.97507
$687$	23.1885	0.884698
$688$	26.0894	0.994649
$689$	0	0
$690$	0.673212	0.0256287
$691$	−40.7207	−1.54909	−0.774543	−	0.632521i	$-0.782020\pi$
$691$	−40.7207	−1.54909	−0.774543	+	0.632521i	$0.782020\pi$
$692$	0.371247	0.0141127
$693$	−28.8272	−1.09505
$694$	9.57256	0.363369
$695$	−2.63072	−0.0997889
$696$	20.6268	0.781859
$697$	29.7179	1.12564
$698$	−13.8242	−0.523253
$699$	0.878514	0.0332284
$700$	0.289142	0.0109285
$701$	−0.483385	−0.0182572	−0.00912861	−	0.999958i	$-0.502906\pi$
$701$	−0.483385	−0.0182572	−0.00912861	+	0.999958i	$0.502906\pi$
$702$	0	0
$703$	7.60821	0.286949
$704$	−47.8461	−1.80327
$705$	−4.57038	−0.172130
$706$	−40.2611	−1.51525
$707$	74.2901	2.79396
$708$	0.128868	0.00484317
$709$	−17.6902	−0.664370	−0.332185	−	0.943214i	$-0.607786\pi$
$709$	−17.6902	−0.664370	−0.332185	+	0.943214i	$0.607786\pi$
$710$	−14.8372	−0.556829
$711$	16.4292	0.616144
$712$	26.8892	1.00772
$713$	0.802658	0.0300598
$714$	−30.7097	−1.14928
$715$	0	0
$716$	−0.569427	−0.0212805
$717$	18.2068	0.679944
$718$	2.90473	0.108404
$719$	12.5472	0.467931	0.233966	−	0.972245i	$-0.424830\pi$
$719$	12.5472	0.467931	0.233966	+	0.972245i	$0.424830\pi$
$720$	4.12021	0.153551
$721$	28.8516	1.07449
$722$	−25.5291	−0.950094
$723$	16.4897	0.613258
$724$	−0.455193	−0.0169171
$725$	7.41205	0.275277
$726$	−39.1237	−1.45202
$727$	−5.26794	−0.195377	−0.0976886	−	0.995217i	$-0.531145\pi$
$727$	−5.26794	−0.195377	−0.0976886	+	0.995217i	$0.531145\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	9.30434	0.344369
$731$	−29.0509	−1.07449
$732$	0.105755	0.00390881
$733$	7.76987	0.286987	0.143493	−	0.989651i	$-0.454166\pi$
$733$	7.76987	0.286987	0.143493	+	0.989651i	$0.454166\pi$
$734$	−6.75846	−0.249459
$735$	14.7283	0.543262
$736$	−0.164446	−0.00606154
$737$	−41.7392	−1.53748
$738$	9.30144	0.342391
$739$	−1.96879	−0.0724232	−0.0362116	−	0.999344i	$-0.511529\pi$
$739$	−1.96879	−0.0724232	−0.0362116	+	0.999344i	$0.511529\pi$
$740$	−0.426953	−0.0156951
$741$	0	0
$742$	−12.1528	−0.446144
$743$	−47.3835	−1.73833	−0.869167	−	0.494520i	$-0.835344\pi$
$743$	−47.3835	−1.73833	−0.869167	+	0.494520i	$0.835344\pi$
$744$	4.76454	0.174676
$745$	19.3002	0.707105
$746$	−6.40438	−0.234481
$747$	−3.37171	−0.123364
$748$	−1.75996	−0.0643504
$749$	−9.62540	−0.351705
$750$	1.43598	0.0524345
$751$	−28.8155	−1.05149	−0.525746	−	0.850642i	$-0.676214\pi$
$751$	−28.8155	−1.05149	−0.525746	+	0.850642i	$0.676214\pi$
$752$	18.8309	0.686693
$753$	−24.2256	−0.882832
$754$	0	0
$755$	−9.60278	−0.349481
$756$	−0.289142	−0.0105160
$757$	4.54992	0.165370	0.0826848	−	0.996576i	$-0.473651\pi$
$757$	4.54992	0.165370	0.0826848	+	0.996576i	$0.473651\pi$
$758$	2.96078	0.107540
$759$	2.89931	0.105238
$760$	3.07606	0.111580
$761$	−15.7565	−0.571173	−0.285586	−	0.958353i	$-0.592188\pi$
$761$	−15.7565	−0.571173	−0.285586	+	0.958353i	$0.592188\pi$
$762$	17.7058	0.641415
$763$	71.4069	2.58510
$764$	0.789255	0.0285542
$765$	−4.58791	−0.165876
$766$	−22.9272	−0.828394
$767$	0	0
$768$	−1.48729	−0.0536679
$769$	−20.7562	−0.748489	−0.374245	−	0.927330i	$-0.622098\pi$
$769$	−20.7562	−0.748489	−0.374245	+	0.927330i	$0.622098\pi$
$770$	41.3952	1.49178
$771$	−2.13383	−0.0768481
$772$	1.05490	0.0379668
$773$	26.6310	0.957852	0.478926	−	0.877855i	$-0.341026\pi$
$773$	26.6310	0.957852	0.478926	+	0.877855i	$0.341026\pi$
$774$	−9.09269	−0.326830
$775$	1.71209	0.0615000
$776$	−53.0599	−1.90474
$777$	−32.0845	−1.15102
$778$	−5.40277	−0.193699
$779$	7.15984	0.256528
$780$	0	0
$781$	−63.8989	−2.28648
$782$	3.08864	0.110449
$783$	−7.41205	−0.264885
$784$	−60.6837	−2.16728
$785$	−17.7352	−0.632997
$786$	21.9780	0.783931
$787$	1.10935	0.0395441	0.0197721	−	0.999805i	$-0.493706\pi$
$787$	1.10935	0.0395441	0.0197721	+	0.999805i	$0.493706\pi$
$788$	0.152961	0.00544901
$789$	−4.74578	−0.168954
$790$	−23.5920	−0.839366
$791$	67.9102	2.41461
$792$	17.2101	0.611535
$793$	0	0
$794$	41.7735	1.48249
$795$	−1.81559	−0.0643922
$796$	−0.427609	−0.0151562
$797$	10.5839	0.374901	0.187451	−	0.982274i	$-0.439978\pi$
$797$	10.5839	0.374901	0.187451	+	0.982274i	$0.439978\pi$
$798$	−7.39879	−0.261914
$799$	−20.9685	−0.741811
$800$	−0.350766	−0.0124015
$801$	−9.66236	−0.341403
$802$	−28.8734	−1.01955
$803$	40.0708	1.41407
$804$	−0.418651	−0.0147647
$805$	−2.18533	−0.0770228
$806$	0	0
$807$	−0.699303	−0.0246166
$808$	−44.3519	−1.56029
$809$	−38.9573	−1.36967	−0.684833	−	0.728700i	$-0.740125\pi$
$809$	−38.9573	−1.36967	−0.684833	+	0.728700i	$0.740125\pi$
$810$	−1.43598	−0.0504551
$811$	−7.30523	−0.256521	−0.128261	−	0.991740i	$-0.540939\pi$
$811$	−7.30523	−0.256521	−0.128261	+	0.991740i	$0.540939\pi$
$812$	2.14313	0.0752092
$813$	−12.2889	−0.430991
$814$	−61.1250	−2.14243
$815$	19.1373	0.670349
$816$	18.9032	0.661743
$817$	−6.99915	−0.244869
$818$	15.4799	0.541244
$819$	0	0
$820$	−0.401791	−0.0140312
$821$	23.3882	0.816255	0.408127	−	0.912925i	$-0.366182\pi$
$821$	23.3882	0.816255	0.408127	+	0.912925i	$0.366182\pi$
$822$	21.6916	0.756580
$823$	−33.0256	−1.15120	−0.575600	−	0.817732i	$-0.695231\pi$
$823$	−33.0256	−1.15120	−0.575600	+	0.817732i	$0.695231\pi$
$824$	−17.2247	−0.600050
$825$	6.18428	0.215309
$826$	−13.9062	−0.483859
$827$	−28.0039	−0.973789	−0.486895	−	0.873461i	$-0.661870\pi$
$827$	−28.0039	−0.973789	−0.486895	+	0.873461i	$0.661870\pi$
$828$	0.0290805	0.00101062
$829$	22.3965	0.777861	0.388931	−	0.921267i	$-0.372845\pi$
$829$	22.3965	0.777861	0.388931	+	0.921267i	$0.372845\pi$
$830$	4.84170	0.168058
$831$	−25.8088	−0.895298
$832$	0	0
$833$	67.5721	2.34124
$834$	−3.77765	−0.130809
$835$	−7.15778	−0.247705
$836$	−0.424021	−0.0146651
$837$	−1.71209	−0.0591784
$838$	8.28381	0.286159
$839$	45.8682	1.58355	0.791773	−	0.610816i	$-0.209158\pi$
$839$	45.8682	1.58355	0.791773	+	0.610816i	$0.209158\pi$
$840$	−12.9720	−0.447577
$841$	25.9385	0.894429
$842$	−12.1037	−0.417120
$843$	28.6333	0.986184
$844$	0.121006	0.00416518
$845$	0	0
$846$	−6.56295	−0.225639
$847$	127.001	4.36379
$848$	7.48060	0.256885
$849$	−23.2312	−0.797292
$850$	6.58813	0.225971
$851$	3.22691	0.110617
$852$	−0.640916	−0.0219574
$853$	−8.06735	−0.276221	−0.138110	−	0.990417i	$-0.544103\pi$
$853$	−8.06735	−0.276221	−0.138110	+	0.990417i	$0.544103\pi$
$854$	−11.4120	−0.390512
$855$	−1.10535	−0.0378022
$856$	5.74646	0.196410
$857$	48.7793	1.66627	0.833134	−	0.553071i	$-0.186544\pi$
$857$	48.7793	1.66627	0.833134	+	0.553071i	$0.186544\pi$
$858$	0	0
$859$	23.7741	0.811161	0.405580	−	0.914059i	$-0.367069\pi$
$859$	23.7741	0.811161	0.405580	+	0.914059i	$0.367069\pi$
$860$	0.392774	0.0133935
$861$	−30.1937	−1.02900
$862$	19.6757	0.670157
$863$	29.6339	1.00875	0.504375	−	0.863485i	$-0.331723\pi$
$863$	29.6339	1.00875	0.504375	+	0.863485i	$0.331723\pi$
$864$	0.350766	0.0119333
$865$	−5.98501	−0.203496
$866$	37.8339	1.28565
$867$	−4.04892	−0.137508
$868$	0.495036	0.0168026
$869$	−101.603	−3.44665
$870$	10.6435	0.360849
$871$	0	0
$872$	−42.6306	−1.44365
$873$	19.0665	0.645304
$874$	0.744136	0.0251708
$875$	−4.66136	−0.157583
$876$	0.401916	0.0135795
$877$	1.32718	0.0448156	0.0224078	−	0.999749i	$-0.492867\pi$
$877$	1.32718	0.0448156	0.0224078	+	0.999749i	$0.492867\pi$
$878$	−15.1986	−0.512928
$879$	17.7782	0.599642
$880$	−25.4806	−0.858949
$881$	47.1336	1.58797	0.793986	−	0.607936i	$-0.208002\pi$
$881$	47.1336	1.58797	0.793986	+	0.607936i	$0.208002\pi$
$882$	21.1495	0.712141
$883$	−24.1882	−0.813999	−0.406999	−	0.913428i	$-0.633425\pi$
$883$	−24.1882	−0.813999	−0.406999	+	0.913428i	$0.633425\pi$
$884$	0	0
$885$	−2.07754	−0.0698356
$886$	−20.9092	−0.702457
$887$	−27.7606	−0.932109	−0.466054	−	0.884756i	$-0.654325\pi$
$887$	−27.7606	−0.932109	−0.466054	+	0.884756i	$0.654325\pi$
$888$	19.1548	0.642792
$889$	−57.4754	−1.92766
$890$	13.8749	0.465089
$891$	−6.18428	−0.207181
$892$	−0.821158	−0.0274944
$893$	−5.05187	−0.169054
$894$	27.7146	0.926916
$895$	9.17996	0.306852
$896$	55.0567	1.83932
$897$	0	0
$898$	−2.61414	−0.0872349
$899$	12.6901	0.423238
$900$	0.0620294	0.00206765
$901$	−8.32974	−0.277504
$902$	−57.5228	−1.91530
$903$	29.5160	0.982232
$904$	−40.5431	−1.34844
$905$	7.33835	0.243935
$906$	−13.7894	−0.458121
$907$	4.74347	0.157504	0.0787522	−	0.996894i	$-0.474906\pi$
$907$	4.74347	0.157504	0.0787522	+	0.996894i	$0.474906\pi$
$908$	0.253183	0.00840216
$909$	15.9374	0.528610
$910$	0	0
$911$	16.9192	0.560560	0.280280	−	0.959918i	$-0.409573\pi$
$911$	16.9192	0.560560	0.280280	+	0.959918i	$0.409573\pi$
$912$	4.55428	0.150807
$913$	20.8516	0.690088
$914$	−22.4348	−0.742076
$915$	−1.70491	−0.0563627
$916$	−1.43837	−0.0475251
$917$	−71.3435	−2.35597
$918$	−6.58813	−0.217441
$919$	38.9332	1.28429	0.642145	−	0.766584i	$-0.278045\pi$
$919$	38.9332	1.28429	0.642145	+	0.766584i	$0.278045\pi$
$920$	1.30467	0.0430135
$921$	11.3286	0.373289
$922$	0.965657	0.0318022
$923$	0	0
$924$	1.78813	0.0588253
$925$	6.88307	0.226314
$926$	42.1010	1.38353
$927$	6.18951	0.203290
$928$	−2.59990	−0.0853457
$929$	29.2709	0.960347	0.480174	−	0.877173i	$-0.340574\pi$
$929$	29.2709	0.960347	0.480174	+	0.877173i	$0.340574\pi$
$930$	2.45852	0.0806180
$931$	16.2800	0.533554
$932$	−0.0544937	−0.00178500
$933$	3.64202	0.119234
$934$	−17.9553	−0.587515
$935$	28.3729	0.927894
$936$	0	0
$937$	55.9440	1.82761	0.913805	−	0.406154i	$-0.133130\pi$
$937$	55.9440	1.82761	0.913805	+	0.406154i	$0.133130\pi$
$938$	45.1767	1.47507
$939$	26.9199	0.878499
$940$	0.283498	0.00924668
$941$	1.75509	0.0572143	0.0286072	−	0.999591i	$-0.490893\pi$
$941$	1.75509	0.0572143	0.0286072	+	0.999591i	$0.490893\pi$
$942$	−25.4674	−0.829771
$943$	3.03674	0.0988898
$944$	8.55989	0.278601
$945$	4.66136	0.151634
$946$	56.2318	1.82825
$947$	−34.3262	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$947$	−34.3262	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$948$	−1.01910	−0.0330987
$949$	0	0
$950$	1.58726	0.0514975
$951$	19.0352	0.617260
$952$	−59.5145	−1.92887
$953$	18.9918	0.615204	0.307602	−	0.951515i	$-0.400473\pi$
$953$	18.9918	0.615204	0.307602	+	0.951515i	$0.400473\pi$
$954$	−2.60714	−0.0844092
$955$	−12.7239	−0.411735
$956$	−1.12935	−0.0365259
$957$	45.8382	1.48174
$958$	45.6582	1.47515
$959$	−70.4136	−2.27377
$960$	7.73673	0.249702
$961$	−28.0688	−0.905444
$962$	0	0
$963$	−2.06493	−0.0665415
$964$	−1.02285	−0.0329436
$965$	−17.0065	−0.547459
$966$	−3.13809	−0.100966
$967$	21.0962	0.678407	0.339203	−	0.940713i	$-0.389842\pi$
$967$	21.0962	0.678407	0.339203	+	0.940713i	$0.389842\pi$
$968$	−75.8206	−2.43697
$969$	−5.07125	−0.162912
$970$	−27.3791	−0.879089
$971$	3.35505	0.107669	0.0538344	−	0.998550i	$-0.482856\pi$
$971$	3.35505	0.107669	0.0538344	+	0.998550i	$0.482856\pi$
$972$	−0.0620294	−0.00198959
$973$	12.2627	0.393125
$974$	54.5358	1.74744
$975$	0	0
$976$	7.02461	0.224852
$977$	−33.8647	−1.08343	−0.541714	−	0.840563i	$-0.682224\pi$
$977$	−33.8647	−1.08343	−0.541714	+	0.840563i	$0.682224\pi$
$978$	27.4807	0.878735
$979$	59.7548	1.90977
$980$	−0.913588	−0.0291835
$981$	15.3189	0.489094
$982$	−16.9536	−0.541010
$983$	4.75377	0.151622	0.0758108	−	0.997122i	$-0.475845\pi$
$983$	4.75377	0.151622	0.0758108	+	0.997122i	$0.475845\pi$
$984$	18.0259	0.574645
$985$	−2.46594	−0.0785714
$986$	48.8316	1.55511
$987$	21.3042	0.678120
$988$	0	0
$989$	−2.96858	−0.0943955
$990$	8.88049	0.282240
$991$	−40.3098	−1.28048	−0.640242	−	0.768173i	$-0.721166\pi$
$991$	−40.3098	−1.28048	−0.640242	+	0.768173i	$0.721166\pi$
$992$	−0.600543	−0.0190673
$993$	2.98681	0.0947835
$994$	69.1614	2.19367
$995$	6.89365	0.218543
$996$	0.209145	0.00662702
$997$	−8.91196	−0.282245	−0.141122	−	0.989992i	$-0.545071\pi$
$997$	−8.91196	−0.282245	−0.141122	+	0.989992i	$0.545071\pi$
$998$	−57.3884	−1.81660
$999$	−6.88307	−0.217771

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2535.2.a.bm.1.6	✓	9
3.2	odd	2		7605.2.a.cr.1.4		9
13.12	even	2		2535.2.a.bn.1.4	yes	9
39.38	odd	2		7605.2.a.cq.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2535.2.a.bm.1.6	✓	9	1.1	even	1	trivial
2535.2.a.bn.1.4	yes	9	13.12	even	2
7605.2.a.cq.1.6		9	39.38	odd	2
7605.2.a.cr.1.4		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)

\(f(q)\)	\(=\)	\(q+1.43598 q^{2} -1.00000 q^{3} +0.0620294 q^{4} -1.00000 q^{5} -1.43598 q^{6} +4.66136 q^{7} -2.78288 q^{8} +1.00000 q^{9} -1.43598 q^{10} -6.18428 q^{11} -0.0620294 q^{12} +6.69361 q^{14} +1.00000 q^{15} -4.12021 q^{16} +4.58791 q^{17} +1.43598 q^{18} +1.10535 q^{19} -0.0620294 q^{20} -4.66136 q^{21} -8.88049 q^{22} +0.468818 q^{23} +2.78288 q^{24} +1.00000 q^{25} -1.00000 q^{27} +0.289142 q^{28} +7.41205 q^{29} +1.43598 q^{30} +1.71209 q^{31} -0.350766 q^{32} +6.18428 q^{33} +6.58813 q^{34} -4.66136 q^{35} +0.0620294 q^{36} +6.88307 q^{37} +1.58726 q^{38} +2.78288 q^{40} +6.47743 q^{41} -6.69361 q^{42} -6.33206 q^{43} -0.383608 q^{44} -1.00000 q^{45} +0.673212 q^{46} -4.57038 q^{47} +4.12021 q^{48} +14.7283 q^{49} +1.43598 q^{50} -4.58791 q^{51} -1.81559 q^{53} -1.43598 q^{54} +6.18428 q^{55} -12.9720 q^{56} -1.10535 q^{57} +10.6435 q^{58} -2.07754 q^{59} +0.0620294 q^{60} -1.70491 q^{61} +2.45852 q^{62} +4.66136 q^{63} +7.73673 q^{64} +8.88049 q^{66} +6.74923 q^{67} +0.284585 q^{68} -0.468818 q^{69} -6.69361 q^{70} +10.3325 q^{71} -2.78288 q^{72} -6.47945 q^{73} +9.88393 q^{74} -1.00000 q^{75} +0.0685643 q^{76} -28.8272 q^{77} +16.4292 q^{79} +4.12021 q^{80} +1.00000 q^{81} +9.30144 q^{82} -3.37171 q^{83} -0.289142 q^{84} -4.58791 q^{85} -9.09269 q^{86} -7.41205 q^{87} +17.2101 q^{88} -9.66236 q^{89} -1.43598 q^{90} +0.0290805 q^{92} -1.71209 q^{93} -6.56295 q^{94} -1.10535 q^{95} +0.350766 q^{96} +19.0665 q^{97} +21.1495 q^{98} -6.18428 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{3} + 10 q^{4} - 9 q^{5} + 10 q^{7} - 3 q^{8} + 9 q^{9} - 11 q^{11} - 10 q^{12} + 10 q^{14} + 9 q^{15} + 8 q^{16} + 18 q^{17} - 10 q^{19} - 10 q^{20} - 10 q^{21} + 17 q^{22} - 7 q^{23} + 3 q^{24}+ \cdots - 11 q^{99}+O(q^{100}) \) 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

Related objects

Downloads

Learn more