LMFDB - Embedded newform 2303.4.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2303,4,Mod(1,2303)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2303, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2303.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2303 = 7^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2303.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$135.881398743$
Analytic rank:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	2303.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.92815 q^{2} -4.29114 q^{3} +16.2866 q^{4} +2.55035 q^{5} +21.1474 q^{6} -40.8377 q^{8} -8.58611 q^{9} +O(q^{10})$	\(q-4.92815 q^{2} -4.29114 q^{3} +16.2866 q^{4} +2.55035 q^{5} +21.1474 q^{6} -40.8377 q^{8} -8.58611 q^{9} -12.5685 q^{10} +30.6844 q^{11} -69.8882 q^{12} -6.03822 q^{13} -10.9439 q^{15} +70.9613 q^{16} -70.2408 q^{17} +42.3136 q^{18} -127.304 q^{19} +41.5366 q^{20} -151.217 q^{22} -58.0155 q^{23} +175.241 q^{24} -118.496 q^{25} +29.7573 q^{26} +152.705 q^{27} -127.399 q^{29} +53.9332 q^{30} -150.236 q^{31} -23.0059 q^{32} -131.671 q^{33} +346.157 q^{34} -139.839 q^{36} -346.869 q^{37} +627.372 q^{38} +25.9109 q^{39} -104.151 q^{40} -147.065 q^{41} -418.228 q^{43} +499.745 q^{44} -21.8976 q^{45} +285.909 q^{46} +47.0000 q^{47} -304.505 q^{48} +583.964 q^{50} +301.413 q^{51} -98.3423 q^{52} -561.350 q^{53} -752.553 q^{54} +78.2559 q^{55} +546.278 q^{57} +627.841 q^{58} +227.276 q^{59} -178.240 q^{60} -760.844 q^{61} +740.384 q^{62} -454.314 q^{64} -15.3996 q^{65} +648.894 q^{66} +486.037 q^{67} -1143.99 q^{68} +248.953 q^{69} +111.669 q^{71} +350.637 q^{72} +711.251 q^{73} +1709.42 q^{74} +508.482 q^{75} -2073.35 q^{76} -127.693 q^{78} +193.350 q^{79} +180.976 q^{80} -423.454 q^{81} +724.758 q^{82} -372.102 q^{83} -179.139 q^{85} +2061.09 q^{86} +546.687 q^{87} -1253.08 q^{88} -960.731 q^{89} +107.915 q^{90} -944.877 q^{92} +644.683 q^{93} -231.623 q^{94} -324.669 q^{95} +98.7217 q^{96} +344.174 q^{97} -263.459 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) $ 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9} + 100 q^{10} + 40 q^{11} + 144 q^{12} + 328 q^{13} + 20 q^{15} + 643 q^{16} + 152 q^{17} + 51 q^{18} + 266 q^{19} + 1064 q^{20} - 168 q^{22} - 134 q^{23} + 288 q^{24} + 1137 q^{25} + 156 q^{26} + 672 q^{27} + 248 q^{29} - 216 q^{30} + 276 q^{31} + 347 q^{32} + 1056 q^{33} + 908 q^{34} + 909 q^{36} - 418 q^{37} + 164 q^{38} - 548 q^{39} + 1200 q^{40} + 918 q^{41} + 608 q^{43} + 1288 q^{44} + 876 q^{45} - 972 q^{46} + 1645 q^{47} + 1252 q^{48} - 367 q^{50} - 464 q^{51} + 3798 q^{52} - 218 q^{53} - 744 q^{54} + 1004 q^{55} - 436 q^{57} - 1270 q^{58} + 3760 q^{59} - 424 q^{60} + 956 q^{61} + 84 q^{62} + 2189 q^{64} - 596 q^{65} + 5500 q^{66} - 476 q^{67} + 256 q^{68} + 444 q^{69} + 852 q^{71} - 883 q^{72} + 6250 q^{73} + 1366 q^{74} - 2568 q^{75} + 1742 q^{76} - 1460 q^{78} + 632 q^{79} + 10124 q^{80} + 1267 q^{81} + 792 q^{82} + 796 q^{83} - 1228 q^{85} - 2864 q^{86} + 8360 q^{87} - 50 q^{88} + 908 q^{89} - 1858 q^{90} + 1696 q^{92} + 644 q^{93} + 235 q^{94} + 1320 q^{95} + 2688 q^{96} + 6184 q^{97} - 1812 q^{99}+O(q^{100}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9 + 100 * q^10 + 40 * q^11 + 144 * q^12 + 328 * q^13 + 20 * q^15 + 643 * q^16 + 152 * q^17 + 51 * q^18 + 266 * q^19 + 1064 * q^20 - 168 * q^22 - 134 * q^23 + 288 * q^24 + 1137 * q^25 + 156 * q^26 + 672 * q^27 + 248 * q^29 - 216 * q^30 + 276 * q^31 + 347 * q^32 + 1056 * q^33 + 908 * q^34 + 909 * q^36 - 418 * q^37 + 164 * q^38 - 548 * q^39 + 1200 * q^40 + 918 * q^41 + 608 * q^43 + 1288 * q^44 + 876 * q^45 - 972 * q^46 + 1645 * q^47 + 1252 * q^48 - 367 * q^50 - 464 * q^51 + 3798 * q^52 - 218 * q^53 - 744 * q^54 + 1004 * q^55 - 436 * q^57 - 1270 * q^58 + 3760 * q^59 - 424 * q^60 + 956 * q^61 + 84 * q^62 + 2189 * q^64 - 596 * q^65 + 5500 * q^66 - 476 * q^67 + 256 * q^68 + 444 * q^69 + 852 * q^71 - 883 * q^72 + 6250 * q^73 + 1366 * q^74 - 2568 * q^75 + 1742 * q^76 - 1460 * q^78 + 632 * q^79 + 10124 * q^80 + 1267 * q^81 + 792 * q^82 + 796 * q^83 - 1228 * q^85 - 2864 * q^86 + 8360 * q^87 - 50 * q^88 + 908 * q^89 - 1858 * q^90 + 1696 * q^92 + 644 * q^93 + 235 * q^94 + 1320 * q^95 + 2688 * q^96 + 6184 * q^97 - 1812 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−4.92815	−1.74236	−0.871182	−	0.490961i	$-0.836646\pi$
$2$	−4.92815	−1.74236	−0.871182	+	0.490961i	$0.836646\pi$
$3$	−4.29114	−0.825830	−0.412915	−	0.910769i	$-0.635489\pi$
$3$	−4.29114	−0.825830	−0.412915	+	0.910769i	$0.635489\pi$
$4$	16.2866	2.03583
$5$	2.55035	0.228110	0.114055	−	0.993474i	$-0.463616\pi$
$5$	2.55035	0.228110	0.114055	+	0.993474i	$0.463616\pi$
$6$	21.1474	1.43890
$7$	0	0
$7$	0	0
$8$	−40.8377	−1.80479
$9$	−8.58611	−0.318004
$10$	−12.5685	−0.397451
$11$	30.6844	0.841062	0.420531	−	0.907278i	$-0.361844\pi$
$11$	30.6844	0.841062	0.420531	+	0.907278i	$0.361844\pi$
$12$	−69.8882	−1.68125
$13$	−6.03822	−0.128823	−0.0644116	−	0.997923i	$-0.520517\pi$
$13$	−6.03822	−0.128823	−0.0644116	+	0.997923i	$0.520517\pi$
$14$	0	0
$15$	−10.9439	−0.188380
$16$	70.9613	1.10877
$17$	−70.2408	−1.00211	−0.501056	−	0.865415i	$-0.667055\pi$
$17$	−70.2408	−1.00211	−0.501056	+	0.865415i	$0.667055\pi$
$18$	42.3136	0.554079
$19$	−127.304	−1.53713	−0.768566	−	0.639771i	$-0.779029\pi$
$19$	−127.304	−1.53713	−0.768566	+	0.639771i	$0.779029\pi$
$20$	41.5366	0.464394
$21$	0	0
$22$	−151.217	−1.46544
$23$	−58.0155	−0.525959	−0.262980	−	0.964801i	$-0.584705\pi$
$23$	−58.0155	−0.525959	−0.262980	+	0.964801i	$0.584705\pi$
$24$	175.241	1.49045
$25$	−118.496	−0.947966
$26$	29.7573	0.224457
$27$	152.705	1.08845
$28$	0	0
$29$	−127.399	−0.815772	−0.407886	−	0.913033i	$-0.633734\pi$
$29$	−127.399	−0.815772	−0.407886	+	0.913033i	$0.633734\pi$
$30$	53.9332	0.328227
$31$	−150.236	−0.870424	−0.435212	−	0.900328i	$-0.643327\pi$
$31$	−150.236	−0.870424	−0.435212	+	0.900328i	$0.643327\pi$
$32$	−23.0059	−0.127091
$33$	−131.671	−0.694575
$34$	346.157	1.74604
$35$	0	0
$36$	−139.839	−0.647402
$37$	−346.869	−1.54121	−0.770606	−	0.637311i	$-0.780046\pi$
$37$	−346.869	−1.54121	−0.770606	+	0.637311i	$0.780046\pi$
$38$	627.372	2.67824
$39$	25.9109	0.106386
$40$	−104.151	−0.411691
$41$	−147.065	−0.560187	−0.280094	−	0.959973i	$-0.590366\pi$
$41$	−147.065	−0.560187	−0.280094	+	0.959973i	$0.590366\pi$
$42$	0	0
$43$	−418.228	−1.48324	−0.741619	−	0.670822i	$-0.765942\pi$
$43$	−418.228	−1.48324	−0.741619	+	0.670822i	$0.765942\pi$
$44$	499.745	1.71226
$45$	−21.8976	−0.0725400
$46$	285.909	0.916412
$47$	47.0000	0.145865
$47$	47.0000	0.145865
$48$	−304.505	−0.915657
$49$	0	0
$50$	583.964	1.65170
$51$	301.413	0.827575
$52$	−98.3423	−0.262262
$53$	−561.350	−1.45486	−0.727428	−	0.686184i	$-0.759285\pi$
$53$	−561.350	−1.45486	−0.727428	+	0.686184i	$0.759285\pi$
$54$	−752.553	−1.89647
$55$	78.2559	0.191855
$56$	0	0
$57$	546.278	1.26941
$58$	627.841	1.42137
$59$	227.276	0.501505	0.250753	−	0.968051i	$-0.419322\pi$
$59$	227.276	0.501505	0.250753	+	0.968051i	$0.419322\pi$
$60$	−178.240	−0.383510
$61$	−760.844	−1.59699	−0.798493	−	0.602005i	$-0.794369\pi$
$61$	−760.844	−1.59699	−0.798493	+	0.602005i	$0.794369\pi$
$62$	740.384	1.51659
$63$	0	0
$64$	−454.314	−0.887332
$65$	−15.3996	−0.0293859
$66$	648.894	1.21020
$67$	486.037	0.886251	0.443126	−	0.896460i	$-0.353870\pi$
$67$	486.037	0.886251	0.443126	+	0.896460i	$0.353870\pi$
$68$	−1143.99	−2.04013
$69$	248.953	0.434353
$70$	0	0
$71$	111.669	0.186657	0.0933284	−	0.995635i	$-0.470249\pi$
$71$	111.669	0.186657	0.0933284	+	0.995635i	$0.470249\pi$
$72$	350.637	0.573931
$73$	711.251	1.14035	0.570176	−	0.821523i	$-0.306875\pi$
$73$	711.251	1.14035	0.570176	+	0.821523i	$0.306875\pi$
$74$	1709.42	2.68535
$75$	508.482	0.782859
$76$	−2073.35	−3.12934
$77$	0	0
$78$	−127.693	−0.185363
$79$	193.350	0.275362	0.137681	−	0.990477i	$-0.456035\pi$
$79$	193.350	0.275362	0.137681	+	0.990477i	$0.456035\pi$
$80$	180.976	0.252922
$81$	−423.454	−0.580869
$82$	724.758	0.976050
$83$	−372.102	−0.492090	−0.246045	−	0.969258i	$-0.579131\pi$
$83$	−372.102	−0.492090	−0.246045	+	0.969258i	$0.579131\pi$
$84$	0	0
$85$	−179.139	−0.228592
$86$	2061.09	2.58434
$87$	546.687	0.673690
$88$	−1253.08	−1.51794
$89$	−960.731	−1.14424	−0.572119	−	0.820170i	$-0.693879\pi$
$89$	−960.731	−1.14424	−0.572119	+	0.820170i	$0.693879\pi$
$90$	107.915	0.126391
$91$	0	0
$92$	−944.877	−1.07076
$93$	644.683	0.718822
$94$	−231.623	−0.254150
$95$	−324.669	−0.350635
$96$	98.7217	0.104956
$97$	344.174	0.360264	0.180132	−	0.983642i	$-0.442348\pi$
$97$	344.174	0.360264	0.180132	+	0.983642i	$0.442348\pi$
$98$	0	0
$99$	−263.459	−0.267461
$100$	−1929.90	−1.92990
$101$	177.170	0.174545	0.0872725	−	0.996184i	$-0.472185\pi$
$101$	177.170	0.174545	0.0872725	+	0.996184i	$0.472185\pi$
$102$	−1485.41	−1.44194
$103$	1523.39	1.45732	0.728662	−	0.684874i	$-0.240143\pi$
$103$	1523.39	1.45732	0.728662	+	0.684874i	$0.240143\pi$
$104$	246.587	0.232499
$105$	0	0
$106$	2766.42	2.53489
$107$	127.082	0.114817	0.0574087	−	0.998351i	$-0.481716\pi$
$107$	127.082	0.114817	0.0574087	+	0.998351i	$0.481716\pi$
$108$	2487.05	2.21589
$109$	757.628	0.665758	0.332879	−	0.942970i	$-0.391980\pi$
$109$	757.628	0.665758	0.332879	+	0.942970i	$0.391980\pi$
$110$	−385.657	−0.334281
$111$	1488.46	1.27278
$112$	0	0
$113$	−1448.49	−1.20586	−0.602930	−	0.797794i	$-0.706000\pi$
$113$	−1448.49	−1.20586	−0.602930	+	0.797794i	$0.706000\pi$
$114$	−2692.14	−2.21177
$115$	−147.960	−0.119977
$116$	−2074.90	−1.66077
$117$	51.8449	0.0409663
$118$	−1120.05	−0.873804
$119$	0	0
$120$	446.925	0.339987
$121$	−389.469	−0.292614
$122$	3749.55	2.78253
$123$	631.076	0.462620
$124$	−2446.83	−1.77203
$125$	−620.999	−0.444351
$126$	0	0
$127$	971.726	0.678950	0.339475	−	0.940615i	$-0.389751\pi$
$127$	971.726	0.678950	0.339475	+	0.940615i	$0.389751\pi$
$128$	2422.97	1.67315
$129$	1794.68	1.22490
$130$	75.8914	0.0512009
$131$	−41.8014	−0.0278794	−0.0139397	−	0.999903i	$-0.504437\pi$
$131$	−41.8014	−0.0278794	−0.0139397	+	0.999903i	$0.504437\pi$
$132$	−2144.48	−1.41404
$133$	0	0
$134$	−2395.26	−1.54417
$135$	389.451	0.248286
$136$	2868.48	1.80860
$137$	257.354	0.160491	0.0802454	−	0.996775i	$-0.474430\pi$
$137$	257.354	0.160491	0.0802454	+	0.996775i	$0.474430\pi$
$138$	−1226.87	−0.756801
$139$	323.338	0.197303	0.0986517	−	0.995122i	$-0.468547\pi$
$139$	323.338	0.197303	0.0986517	+	0.995122i	$0.468547\pi$
$140$	0	0
$141$	−201.684	−0.120460
$142$	−550.320	−0.325224
$143$	−185.279	−0.108348
$144$	−609.282	−0.352594
$145$	−324.912	−0.186086
$146$	−3505.15	−1.98691
$147$	0	0
$148$	−5649.32	−3.13765
$149$	−739.794	−0.406754	−0.203377	−	0.979101i	$-0.565192\pi$
$149$	−739.794	−0.406754	−0.203377	+	0.979101i	$0.565192\pi$
$150$	−2505.87	−1.36402
$151$	1198.64	0.645985	0.322993	−	0.946402i	$-0.395311\pi$
$151$	1198.64	0.645985	0.322993	+	0.946402i	$0.395311\pi$
$152$	5198.80	2.77420
$153$	603.096	0.318676
$154$	0	0
$155$	−383.154	−0.198553
$156$	422.001	0.216584
$157$	3176.69	1.61483	0.807413	−	0.589986i	$-0.200867\pi$
$157$	3176.69	1.61483	0.807413	+	0.589986i	$0.200867\pi$
$158$	−952.859	−0.479781
$159$	2408.83	1.20146
$160$	−58.6732	−0.0289908
$161$	0	0
$162$	2086.84	1.01209
$163$	−3622.46	−1.74069	−0.870346	−	0.492440i	$-0.836105\pi$
$163$	−3622.46	−1.74069	−0.870346	+	0.492440i	$0.836105\pi$
$164$	−2395.19	−1.14045
$165$	−335.807	−0.158440
$166$	1833.77	0.857400
$167$	−4078.58	−1.88988	−0.944940	−	0.327242i	$-0.893881\pi$
$167$	−4078.58	−1.88988	−0.944940	+	0.327242i	$0.893881\pi$
$168$	0	0
$169$	−2160.54	−0.983405
$170$	882.822	0.398290
$171$	1093.04	0.488814
$172$	−6811.53	−3.01962
$173$	−2060.20	−0.905399	−0.452700	−	0.891663i	$-0.649539\pi$
$173$	−2060.20	−0.905399	−0.452700	+	0.891663i	$0.649539\pi$
$174$	−2694.15	−1.17381
$175$	0	0
$176$	2177.40	0.932545
$177$	−975.273	−0.414158
$178$	4734.62	1.99368
$179$	−830.833	−0.346924	−0.173462	−	0.984841i	$-0.555495\pi$
$179$	−830.833	−0.346924	−0.173462	+	0.984841i	$0.555495\pi$
$180$	−356.638	−0.147679
$181$	−2918.24	−1.19840	−0.599202	−	0.800598i	$-0.704515\pi$
$181$	−2918.24	−1.19840	−0.599202	+	0.800598i	$0.704515\pi$
$182$	0	0
$183$	3264.89	1.31884
$184$	2369.22	0.949246
$185$	−884.637	−0.351566
$186$	−3177.09	−1.25245
$187$	−2155.30	−0.842839
$188$	765.472	0.296956
$189$	0	0
$190$	1600.02	0.610934
$191$	−3839.87	−1.45468	−0.727338	−	0.686280i	$-0.759243\pi$
$191$	−3839.87	−1.45468	−0.727338	+	0.686280i	$0.759243\pi$
$192$	1949.53	0.732786
$193$	1624.22	0.605771	0.302885	−	0.953027i	$-0.402050\pi$
$193$	1624.22	0.605771	0.302885	+	0.953027i	$0.402050\pi$
$194$	−1696.14	−0.627710
$195$	66.0818	0.0242678
$196$	0	0
$197$	−500.158	−0.180887	−0.0904436	−	0.995902i	$-0.528828\pi$
$197$	−500.158	−0.180887	−0.0904436	+	0.995902i	$0.528828\pi$
$198$	1298.37	0.466015
$199$	4237.83	1.50961	0.754804	−	0.655951i	$-0.227732\pi$
$199$	4237.83	1.50961	0.754804	+	0.655951i	$0.227732\pi$
$200$	4839.10	1.71088
$201$	−2085.65	−0.731893
$202$	−873.119	−0.304121
$203$	0	0
$204$	4909.01	1.68480
$205$	−375.067	−0.127785
$206$	−7507.50	−2.53919
$207$	498.127	0.167257
$208$	−428.480	−0.142835
$209$	−3906.24	−1.29282
$210$	0	0
$211$	−2480.95	−0.809458	−0.404729	−	0.914437i	$-0.632634\pi$
$211$	−2480.95	−0.809458	−0.404729	+	0.914437i	$0.632634\pi$
$212$	−9142.51	−2.96184
$213$	−479.186	−0.154147
$214$	−626.278	−0.200054
$215$	−1066.63	−0.338342
$216$	−6236.13	−1.96442
$217$	0	0
$218$	−3733.70	−1.15999
$219$	−3052.08	−0.941737
$220$	1274.53	0.390584
$221$	424.130	0.129095
$222$	−7335.36	−2.21765
$223$	−1720.64	−0.516694	−0.258347	−	0.966052i	$-0.583178\pi$
$223$	−1720.64	−0.516694	−0.258347	+	0.966052i	$0.583178\pi$
$224$	0	0
$225$	1017.42	0.301457
$226$	7138.35	2.10105
$227$	−5717.01	−1.67159	−0.835795	−	0.549041i	$-0.814993\pi$
$227$	−5717.01	−1.67159	−0.835795	+	0.549041i	$0.814993\pi$
$228$	8897.04	2.58430
$229$	−337.388	−0.0973590	−0.0486795	−	0.998814i	$-0.515501\pi$
$229$	−337.388	−0.0973590	−0.0486795	+	0.998814i	$0.515501\pi$
$230$	729.168	0.209043
$231$	0	0
$232$	5202.69	1.47230
$233$	3191.97	0.897479	0.448740	−	0.893662i	$-0.351873\pi$
$233$	3191.97	0.897479	0.448740	+	0.893662i	$0.351873\pi$
$234$	−255.499	−0.0713782
$235$	119.866	0.0332733
$236$	3701.56	1.02098
$237$	−829.694	−0.227402
$238$	0	0
$239$	−2316.68	−0.627001	−0.313501	−	0.949588i	$-0.601502\pi$
$239$	−2316.68	−0.627001	−0.313501	+	0.949588i	$0.601502\pi$
$240$	−776.595	−0.208871
$241$	−5779.19	−1.54469	−0.772345	−	0.635204i	$-0.780916\pi$
$241$	−5779.19	−1.54469	−0.772345	+	0.635204i	$0.780916\pi$
$242$	1919.36	0.509840
$243$	−2305.94	−0.608748
$244$	−12391.6	−3.25119
$245$	0	0
$246$	−3110.04	−0.806052
$247$	768.689	0.198018
$248$	6135.29	1.57093
$249$	1596.74	0.406383
$250$	3060.38	0.774221
$251$	5491.04	1.38084	0.690421	−	0.723408i	$-0.257426\pi$
$251$	5491.04	1.38084	0.690421	+	0.723408i	$0.257426\pi$
$252$	0	0
$253$	−1780.17	−0.442364
$254$	−4788.81	−1.18298
$255$	768.710	0.188778
$256$	−8306.26	−2.02790
$257$	560.398	0.136018	0.0680091	−	0.997685i	$-0.478335\pi$
$257$	560.398	0.136018	0.0680091	+	0.997685i	$0.478335\pi$
$258$	−8844.43	−2.13423
$259$	0	0
$260$	−250.807	−0.0598247
$261$	1093.86	0.259419
$262$	206.004	0.0485761
$263$	−593.712	−0.139201	−0.0696005	−	0.997575i	$-0.522172\pi$
$263$	−593.712	−0.139201	−0.0696005	+	0.997575i	$0.522172\pi$
$264$	5377.14	1.25356
$265$	−1431.64	−0.331868
$266$	0	0
$267$	4122.63	0.944947
$268$	7915.90	1.80426
$269$	−5744.61	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$269$	−5744.61	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$270$	−1919.27	−0.432605
$271$	1703.37	0.381817	0.190909	−	0.981608i	$-0.438857\pi$
$271$	1703.37	0.381817	0.190909	+	0.981608i	$0.438857\pi$
$272$	−4984.38	−1.11111
$273$	0	0
$274$	−1268.28	−0.279633
$275$	−3635.97	−0.797298
$276$	4054.60	0.884269
$277$	−3113.54	−0.675360	−0.337680	−	0.941261i	$-0.609642\pi$
$277$	−3113.54	−0.675360	−0.337680	+	0.941261i	$0.609642\pi$
$278$	−1593.46	−0.343774
$279$	1289.94	0.276798
$280$	0	0
$281$	−1855.05	−0.393818	−0.196909	−	0.980422i	$-0.563090\pi$
$281$	−1855.05	−0.393818	−0.196909	+	0.980422i	$0.563090\pi$
$282$	993.927	0.209885
$283$	3364.29	0.706665	0.353333	−	0.935498i	$-0.385048\pi$
$283$	3364.29	0.706665	0.353333	+	0.935498i	$0.385048\pi$
$284$	1818.71	0.380001
$285$	1393.20	0.289565
$286$	913.083	0.188782
$287$	0	0
$288$	197.532	0.0404155
$289$	20.7757	0.00422872
$290$	1601.21	0.324229
$291$	−1476.90	−0.297517
$292$	11583.9	2.32156
$293$	5756.15	1.14771	0.573853	−	0.818958i	$-0.305448\pi$
$293$	5756.15	1.14771	0.573853	+	0.818958i	$0.305448\pi$
$294$	0	0
$295$	579.633	0.114398
$296$	14165.3	2.78157
$297$	4685.66	0.915453
$298$	3645.81	0.708713
$299$	350.310	0.0677558
$300$	8281.46	1.59377
$301$	0	0
$302$	−5907.06	−1.12554
$303$	−760.261	−0.144145
$304$	−9033.65	−1.70433
$305$	−1940.42	−0.364289
$306$	−2972.14	−0.555249
$307$	4266.59	0.793183	0.396591	−	0.917995i	$-0.370193\pi$
$307$	4266.59	0.793183	0.396591	+	0.917995i	$0.370193\pi$
$308$	0	0
$309$	−6537.09	−1.20350
$310$	1888.24	0.345951
$311$	−7342.40	−1.33874	−0.669372	−	0.742928i	$-0.733437\pi$
$311$	−7342.40	−1.33874	−0.669372	+	0.742928i	$0.733437\pi$
$312$	−1058.14	−0.192005
$313$	8026.97	1.44956	0.724778	−	0.688982i	$-0.241942\pi$
$313$	8026.97	1.44956	0.724778	+	0.688982i	$0.241942\pi$
$314$	−15655.2	−2.81361
$315$	0	0
$316$	3149.03	0.560590
$317$	3673.84	0.650926	0.325463	−	0.945555i	$-0.394480\pi$
$317$	3673.84	0.650926	0.325463	+	0.945555i	$0.394480\pi$
$318$	−11871.1	−2.09339
$319$	−3909.16	−0.686115
$320$	−1158.66	−0.202410
$321$	−545.326	−0.0948197
$322$	0	0
$323$	8941.92	1.54038
$324$	−6896.64	−1.18255
$325$	715.504	0.122120
$326$	17852.0	3.03292
$327$	−3251.09	−0.549803
$328$	6005.80	1.01102
$329$	0	0
$330$	1654.91	0.276059
$331$	−4375.48	−0.726581	−0.363291	−	0.931676i	$-0.618347\pi$
$331$	−4375.48	−0.726581	−0.363291	+	0.931676i	$0.618347\pi$
$332$	−6060.29	−1.00181
$333$	2978.25	0.490112
$334$	20099.8	3.29286
$335$	1239.56	0.202163
$336$	0	0
$337$	1433.48	0.231711	0.115856	−	0.993266i	$-0.463039\pi$
$337$	1433.48	0.231711	0.115856	+	0.993266i	$0.463039\pi$
$338$	10647.5	1.71345
$339$	6215.66	0.995836
$340$	−2917.57	−0.465374
$341$	−4609.89	−0.732081
$342$	−5386.68	−0.851691
$343$	0	0
$344$	17079.5	2.67693
$345$	634.916	0.0990804
$346$	10153.0	1.57753
$347$	3475.98	0.537753	0.268877	−	0.963175i	$-0.413348\pi$
$347$	3475.98	0.537753	0.268877	+	0.963175i	$0.413348\pi$
$348$	8903.69	1.37152
$349$	3778.14	0.579482	0.289741	−	0.957105i	$-0.406431\pi$
$349$	3778.14	0.579482	0.289741	+	0.957105i	$0.406431\pi$
$350$	0	0
$351$	−922.067	−0.140217
$352$	−705.923	−0.106892
$353$	4747.95	0.715886	0.357943	−	0.933743i	$-0.383478\pi$
$353$	4747.95	0.715886	0.357943	+	0.933743i	$0.383478\pi$
$354$	4806.29	0.721614
$355$	284.794	0.0425784
$356$	−15647.1	−2.32947
$357$	0	0
$358$	4094.47	0.604467
$359$	5893.76	0.866464	0.433232	−	0.901282i	$-0.357373\pi$
$359$	5893.76	0.866464	0.433232	+	0.901282i	$0.357373\pi$
$360$	894.248	0.130919
$361$	9347.25	1.36277
$362$	14381.5	2.08806
$363$	1671.27	0.241650
$364$	0	0
$365$	1813.94	0.260126
$366$	−16089.9	−2.29790
$367$	−124.773	−0.0177469	−0.00887346	−	0.999961i	$-0.502825\pi$
$367$	−124.773	−0.0177469	−0.00887346	+	0.999961i	$0.502825\pi$
$368$	−4116.85	−0.583168
$369$	1262.72	0.178142
$370$	4359.62	0.612556
$371$	0	0
$372$	10499.7	1.46340
$373$	−2790.13	−0.387313	−0.193656	−	0.981069i	$-0.562035\pi$
$373$	−2790.13	−0.387313	−0.193656	+	0.981069i	$0.562035\pi$
$374$	10621.6	1.46853
$375$	2664.80	0.366959
$376$	−1919.37	−0.263256
$377$	769.263	0.105090
$378$	0	0
$379$	2685.78	0.364009	0.182004	−	0.983298i	$-0.441741\pi$
$379$	2685.78	0.364009	0.182004	+	0.983298i	$0.441741\pi$
$380$	−5287.77	−0.713834
$381$	−4169.81	−0.560698
$382$	18923.4	2.53457
$383$	−2366.81	−0.315767	−0.157883	−	0.987458i	$-0.550467\pi$
$383$	−2366.81	−0.315767	−0.157883	+	0.987458i	$0.550467\pi$
$384$	−10397.3	−1.38173
$385$	0	0
$386$	−8004.39	−1.05547
$387$	3590.95	0.471676
$388$	5605.44	0.733436
$389$	2376.46	0.309746	0.154873	−	0.987934i	$-0.450503\pi$
$389$	2376.46	0.309746	0.154873	+	0.987934i	$0.450503\pi$
$390$	−325.661	−0.0422833
$391$	4075.05	0.527070
$392$	0	0
$393$	179.376	0.0230237
$394$	2464.85	0.315171
$395$	493.111	0.0628130
$396$	−4290.87	−0.544505
$397$	−2906.18	−0.367398	−0.183699	−	0.982983i	$-0.558807\pi$
$397$	−2906.18	−0.367398	−0.183699	+	0.982983i	$0.558807\pi$
$398$	−20884.7	−2.63028
$399$	0	0
$400$	−8408.61	−1.05108
$401$	−4975.18	−0.619573	−0.309786	−	0.950806i	$-0.600258\pi$
$401$	−4975.18	−0.619573	−0.309786	+	0.950806i	$0.600258\pi$
$402$	10278.4	1.27522
$403$	907.157	0.112131
$404$	2885.50	0.355344
$405$	−1079.96	−0.132502
$406$	0	0
$407$	−10643.4	−1.29626
$408$	−12309.0	−1.49360
$409$	9615.88	1.16253	0.581265	−	0.813714i	$-0.302558\pi$
$409$	9615.88	1.16253	0.581265	+	0.813714i	$0.302558\pi$
$410$	1848.39	0.222647
$411$	−1104.34	−0.132538
$412$	24810.9	2.96686
$413$	0	0
$414$	−2454.84	−0.291423
$415$	−948.990	−0.112251
$416$	138.915	0.0163723
$417$	−1387.49	−0.162939
$418$	19250.5	2.25257
$419$	15186.8	1.77070	0.885348	−	0.464929i	$-0.153920\pi$
$419$	15186.8	1.77070	0.885348	+	0.464929i	$0.153920\pi$
$420$	0	0
$421$	−10397.8	−1.20370	−0.601849	−	0.798610i	$-0.705569\pi$
$421$	−10397.8	−1.20370	−0.601849	+	0.798610i	$0.705569\pi$
$422$	12226.5	1.41037
$423$	−403.547	−0.0463857
$424$	22924.3	2.62571
$425$	8323.24	0.949968
$426$	2361.50	0.268580
$427$	0	0
$428$	2069.73	0.233749
$429$	795.059	0.0894774
$430$	5256.50	0.589514
$431$	−16563.1	−1.85108	−0.925539	−	0.378652i	$-0.876388\pi$
$431$	−16563.1	−1.85108	−0.925539	+	0.378652i	$0.876388\pi$
$432$	10836.2	1.20684
$433$	10316.3	1.14497	0.572485	−	0.819915i	$-0.305979\pi$
$433$	10316.3	1.14497	0.572485	+	0.819915i	$0.305979\pi$
$434$	0	0
$435$	1394.24	0.153676
$436$	12339.2	1.35537
$437$	7385.59	0.808468
$438$	15041.1	1.64085
$439$	−4664.95	−0.507166	−0.253583	−	0.967314i	$-0.581609\pi$
$439$	−4664.95	−0.507166	−0.253583	+	0.967314i	$0.581609\pi$
$440$	−3195.79	−0.346258
$441$	0	0
$442$	−2090.17	−0.224931
$443$	7755.17	0.831736	0.415868	−	0.909425i	$-0.363478\pi$
$443$	7755.17	0.831736	0.415868	+	0.909425i	$0.363478\pi$
$444$	24242.0	2.59116
$445$	−2450.20	−0.261013
$446$	8479.57	0.900268
$447$	3174.56	0.335910
$448$	0	0
$449$	12395.6	1.30287	0.651433	−	0.758706i	$-0.274168\pi$
$449$	12395.6	1.30287	0.651433	+	0.758706i	$0.274168\pi$
$450$	−5013.98	−0.525247
$451$	−4512.60	−0.471153
$452$	−23591.0	−2.45492
$453$	−5143.52	−0.533474
$454$	28174.2	2.91252
$455$	0	0
$456$	−22308.8	−2.29102
$457$	−10905.8	−1.11631	−0.558155	−	0.829737i	$-0.688491\pi$
$457$	−10905.8	−1.11631	−0.558155	+	0.829737i	$0.688491\pi$
$458$	1662.70	0.169635
$459$	−10726.1	−1.09075
$460$	−2409.77	−0.244252
$461$	−9382.39	−0.947899	−0.473950	−	0.880552i	$-0.657172\pi$
$461$	−9382.39	−0.947899	−0.473950	+	0.880552i	$0.657172\pi$
$462$	0	0
$463$	5227.14	0.524677	0.262339	−	0.964976i	$-0.415506\pi$
$463$	5227.14	0.524677	0.262339	+	0.964976i	$0.415506\pi$
$464$	−9040.40	−0.904504
$465$	1644.17	0.163971
$466$	−15730.5	−1.56374
$467$	−825.414	−0.0817893	−0.0408947	−	0.999163i	$-0.513021\pi$
$467$	−825.414	−0.0817893	−0.0408947	+	0.999163i	$0.513021\pi$
$468$	844.378	0.0834004
$469$	0	0
$470$	−590.720	−0.0579742
$471$	−13631.6	−1.33357
$472$	−9281.43	−0.905111
$473$	−12833.1	−1.24750
$474$	4088.85	0.396218
$475$	15085.0	1.45715
$476$	0	0
$477$	4819.82	0.462650
$478$	11416.9	1.09246
$479$	11558.7	1.10257	0.551285	−	0.834317i	$-0.314138\pi$
$479$	11558.7	1.10257	0.551285	+	0.834317i	$0.314138\pi$
$480$	251.775	0.0239415
$481$	2094.47	0.198544
$482$	28480.7	2.69141
$483$	0	0
$484$	−6343.14	−0.595712
$485$	877.765	0.0821799
$486$	11364.0	1.06066
$487$	−15826.3	−1.47260	−0.736300	−	0.676655i	$-0.763429\pi$
$487$	−15826.3	−1.47260	−0.736300	+	0.676655i	$0.763429\pi$
$488$	31071.2	2.88222
$489$	15544.5	1.43752
$490$	0	0
$491$	−15421.9	−1.41748	−0.708739	−	0.705471i	$-0.750736\pi$
$491$	−15421.9	−1.41748	−0.708739	+	0.705471i	$0.750736\pi$
$492$	10278.1	0.941815
$493$	8948.61	0.817495
$494$	−3788.21	−0.345020
$495$	−671.914	−0.0610107
$496$	−10660.9	−0.965100
$497$	0	0
$498$	−7868.98	−0.708067
$499$	−16790.4	−1.50629	−0.753147	−	0.657853i	$-0.771465\pi$
$499$	−16790.4	−1.50629	−0.753147	+	0.657853i	$0.771465\pi$
$500$	−10114.0	−0.904623
$501$	17501.8	1.56072
$502$	−27060.6	−2.40593
$503$	8690.21	0.770333	0.385166	−	0.922847i	$-0.374144\pi$
$503$	8690.21	0.770333	0.385166	+	0.922847i	$0.374144\pi$
$504$	0	0
$505$	451.845	0.0398155
$506$	8772.93	0.770760
$507$	9271.18	0.812125
$508$	15826.1	1.38223
$509$	−17012.5	−1.48146	−0.740731	−	0.671802i	$-0.765521\pi$
$509$	−17012.5	−1.48146	−0.740731	+	0.671802i	$0.765521\pi$
$510$	−3788.31	−0.328920
$511$	0	0
$512$	21550.7	1.86018
$513$	−19439.9	−1.67309
$514$	−2761.73	−0.236993
$515$	3885.19	0.332431
$516$	29229.2	2.49369
$517$	1442.17	0.122682
$518$	0	0
$519$	8840.61	0.747706
$520$	628.884	0.0530354
$521$	12742.3	1.07150	0.535748	−	0.844378i	$-0.320030\pi$
$521$	12742.3	1.07150	0.535748	+	0.844378i	$0.320030\pi$
$522$	−5390.71	−0.452002
$523$	18250.1	1.52585	0.762927	−	0.646485i	$-0.223762\pi$
$523$	18250.1	1.52585	0.762927	+	0.646485i	$0.223762\pi$
$524$	−680.804	−0.0567578
$525$	0	0
$526$	2925.90	0.242539
$527$	10552.7	0.872262
$528$	−9343.55	−0.770124
$529$	−8801.21	−0.723367
$530$	7055.33	0.578234
$531$	−1951.42	−0.159481
$532$	0	0
$533$	888.011	0.0721651
$534$	−20316.9	−1.64644
$535$	324.103	0.0261910
$536$	−19848.6	−1.59950
$537$	3565.22	0.286500
$538$	28310.3	2.26867
$539$	0	0
$540$	6342.85	0.505468
$541$	16139.2	1.28259	0.641293	−	0.767296i	$-0.278398\pi$
$541$	16139.2	1.28259	0.641293	+	0.767296i	$0.278398\pi$
$542$	−8394.46	−0.665264
$543$	12522.6	0.989679
$544$	1615.96	0.127359
$545$	1932.22	0.151866
$546$	0	0
$547$	4901.60	0.383139	0.191570	−	0.981479i	$-0.438642\pi$
$547$	4901.60	0.383139	0.191570	+	0.981479i	$0.438642\pi$
$548$	4191.43	0.326732
$549$	6532.69	0.507848
$550$	17918.6	1.38918
$551$	16218.4	1.25395
$552$	−10166.7	−0.783916
$553$	0	0
$554$	15344.0	1.17672
$555$	3796.10	0.290334
$556$	5266.08	0.401676
$557$	−9780.83	−0.744034	−0.372017	−	0.928226i	$-0.621334\pi$
$557$	−9780.83	−0.744034	−0.372017	+	0.928226i	$0.621334\pi$
$558$	−6357.02	−0.482283
$559$	2525.36	0.191075
$560$	0	0
$561$	9248.68	0.696042
$562$	9141.96	0.686175
$563$	−2355.00	−0.176290	−0.0881452	−	0.996108i	$-0.528094\pi$
$563$	−2355.00	−0.176290	−0.0881452	+	0.996108i	$0.528094\pi$
$564$	−3284.75	−0.245235
$565$	−3694.15	−0.275069
$566$	−16579.7	−1.23127
$567$	0	0
$568$	−4560.30	−0.336877
$569$	8208.45	0.604774	0.302387	−	0.953185i	$-0.402217\pi$
$569$	8208.45	0.604774	0.302387	+	0.953185i	$0.402217\pi$
$570$	−6865.90	−0.504528
$571$	−11011.5	−0.807036	−0.403518	−	0.914972i	$-0.632213\pi$
$571$	−11011.5	−0.807036	−0.403518	+	0.914972i	$0.632213\pi$
$572$	−3017.57	−0.220579
$573$	16477.4	1.20132
$574$	0	0
$575$	6874.58	0.498591
$576$	3900.79	0.282175
$577$	1630.34	0.117629	0.0588145	−	0.998269i	$-0.481268\pi$
$577$	1630.34	0.117629	0.0588145	+	0.998269i	$0.481268\pi$
$578$	−102.386	−0.00736797
$579$	−6969.75	−0.500264
$580$	−5291.72	−0.378839
$581$	0	0
$582$	7278.38	0.518382
$583$	−17224.7	−1.22363
$584$	−29045.9	−2.05810
$585$	132.223	0.00934484
$586$	−28367.2	−1.99972
$587$	14394.1	1.01211	0.506055	−	0.862501i	$-0.331103\pi$
$587$	14394.1	1.01211	0.506055	+	0.862501i	$0.331103\pi$
$588$	0	0
$589$	19125.6	1.33796
$590$	−2856.52	−0.199324
$591$	2146.25	0.149382
$592$	−24614.3	−1.70885
$593$	−11113.3	−0.769591	−0.384795	−	0.923002i	$-0.625728\pi$
$593$	−11113.3	−0.769591	−0.384795	+	0.923002i	$0.625728\pi$
$594$	−23091.6	−1.59505
$595$	0	0
$596$	−12048.8	−0.828081
$597$	−18185.1	−1.24668
$598$	−1726.38	−0.118055
$599$	−19701.4	−1.34387	−0.671934	−	0.740611i	$-0.734536\pi$
$599$	−19701.4	−1.34387	−0.671934	+	0.740611i	$0.734536\pi$
$600$	−20765.2	−1.41290
$601$	17656.8	1.19839	0.599197	−	0.800602i	$-0.295487\pi$
$601$	17656.8	1.19839	0.599197	+	0.800602i	$0.295487\pi$
$602$	0	0
$603$	−4173.16	−0.281831
$604$	19521.8	1.31512
$605$	−993.283	−0.0667483
$606$	3746.68	0.251152
$607$	24012.1	1.60564	0.802818	−	0.596225i	$-0.203333\pi$
$607$	24012.1	1.60564	0.802818	+	0.596225i	$0.203333\pi$
$608$	2928.74	0.195356
$609$	0	0
$610$	9562.67	0.634723
$611$	−283.797	−0.0187908
$612$	9822.40	0.648769
$613$	456.703	0.0300915	0.0150457	−	0.999887i	$-0.495211\pi$
$613$	456.703	0.0300915	0.0150457	+	0.999887i	$0.495211\pi$
$614$	−21026.4	−1.38201
$615$	1609.47	0.105528
$616$	0	0
$617$	−23661.0	−1.54385	−0.771925	−	0.635714i	$-0.780706\pi$
$617$	−23661.0	−1.54385	−0.771925	+	0.635714i	$0.780706\pi$
$618$	32215.8	2.09694
$619$	−17899.8	−1.16228	−0.581141	−	0.813803i	$-0.697394\pi$
$619$	−17899.8	−1.16228	−0.581141	+	0.813803i	$0.697394\pi$
$620$	−6240.28	−0.404219
$621$	−8859.25	−0.572479
$622$	36184.4	2.33258
$623$	0	0
$624$	1838.67	0.117958
$625$	13228.2	0.846605
$626$	−39558.1	−2.52565
$627$	16762.2	1.06765
$628$	51737.6	3.28751
$629$	24364.4	1.54447
$630$	0	0
$631$	12150.1	0.766542	0.383271	−	0.923636i	$-0.374797\pi$
$631$	12150.1	0.766542	0.383271	+	0.923636i	$0.374797\pi$
$632$	−7895.99	−0.496971
$633$	10646.1	0.668475
$634$	−18105.2	−1.13415
$635$	2478.24	0.154876
$636$	39231.8	2.44598
$637$	0	0
$638$	19264.9	1.19546
$639$	−958.800	−0.0593576
$640$	6179.43	0.381662
$641$	−16145.1	−0.994844	−0.497422	−	0.867509i	$-0.665720\pi$
$641$	−16145.1	−0.994844	−0.497422	+	0.867509i	$0.665720\pi$
$642$	2687.45	0.165210
$643$	3860.59	0.236776	0.118388	−	0.992967i	$-0.462227\pi$
$643$	3860.59	0.236776	0.118388	+	0.992967i	$0.462227\pi$
$644$	0	0
$645$	4577.05	0.279413
$646$	−44067.1	−2.68390
$647$	−6831.04	−0.415079	−0.207539	−	0.978227i	$-0.566546\pi$
$647$	−6831.04	−0.415079	−0.207539	+	0.978227i	$0.566546\pi$
$648$	17292.9	1.04835
$649$	6973.82	0.421797
$650$	−3526.11	−0.212777
$651$	0	0
$652$	−58997.7	−3.54375
$653$	−17915.8	−1.07366	−0.536829	−	0.843691i	$-0.680378\pi$
$653$	−17915.8	−1.07366	−0.536829	+	0.843691i	$0.680378\pi$
$654$	16021.8	0.957957
$655$	−106.608	−0.00635959
$656$	−10435.9	−0.621119
$657$	−6106.88	−0.362637
$658$	0	0
$659$	−3920.03	−0.231719	−0.115859	−	0.993266i	$-0.536962\pi$
$659$	−3920.03	−0.231719	−0.115859	+	0.993266i	$0.536962\pi$
$660$	−5469.17	−0.322556
$661$	−16153.2	−0.950510	−0.475255	−	0.879848i	$-0.657644\pi$
$661$	−16153.2	−0.950510	−0.475255	+	0.879848i	$0.657644\pi$
$662$	21563.0	1.26597
$663$	−1820.00	−0.106611
$664$	15195.8	0.888120
$665$	0	0
$666$	−14677.3	−0.853953
$667$	7391.11	0.429063
$668$	−66426.4	−3.84747
$669$	7383.51	0.426701
$670$	−6108.75	−0.352241
$671$	−23346.0	−1.34316
$672$	0	0
$673$	−20598.4	−1.17981	−0.589903	−	0.807474i	$-0.700834\pi$
$673$	−20598.4	−1.17981	−0.589903	+	0.807474i	$0.700834\pi$
$674$	−7064.40	−0.403725
$675$	−18094.9	−1.03181
$676$	−35187.9	−2.00204
$677$	−21455.6	−1.21803	−0.609015	−	0.793159i	$-0.708435\pi$
$677$	−21455.6	−1.21803	−0.609015	+	0.793159i	$0.708435\pi$
$678$	−30631.7	−1.73511
$679$	0	0
$680$	7315.62	0.412561
$681$	24532.5	1.38045
$682$	22718.2	1.27555
$683$	21184.1	1.18680	0.593401	−	0.804907i	$-0.297785\pi$
$683$	21184.1	1.18680	0.593401	+	0.804907i	$0.297785\pi$
$684$	17802.0	0.995142
$685$	656.343	0.0366096
$686$	0	0
$687$	1447.78	0.0804020
$688$	−29678.0	−1.64457
$689$	3389.56	0.187419
$690$	−3128.96	−0.172634
$691$	−9148.10	−0.503632	−0.251816	−	0.967775i	$-0.581028\pi$
$691$	−9148.10	−0.503632	−0.251816	+	0.967775i	$0.581028\pi$
$692$	−33553.7	−1.84324
$693$	0	0
$694$	−17130.1	−0.936961
$695$	824.625	0.0450069
$696$	−22325.5	−1.21587
$697$	10330.0	0.561371
$698$	−18619.2	−1.00967
$699$	−13697.2	−0.741166
$700$	0	0
$701$	15761.6	0.849224	0.424612	−	0.905375i	$-0.360410\pi$
$701$	15761.6	0.849224	0.424612	+	0.905375i	$0.360410\pi$
$702$	4544.08	0.244310
$703$	44157.7	2.36905
$704$	−13940.3	−0.746302
$705$	−514.364	−0.0274781
$706$	−23398.6	−1.24733
$707$	0	0
$708$	−15883.9	−0.843155
$709$	21586.3	1.14343	0.571713	−	0.820453i	$-0.306279\pi$
$709$	21586.3	1.14343	0.571713	+	0.820453i	$0.306279\pi$
$710$	−1403.51	−0.0741870
$711$	−1660.13	−0.0875663
$712$	39234.1	2.06511
$713$	8716.00	0.457807
$714$	0	0
$715$	−472.527	−0.0247154
$716$	−13531.5	−0.706278
$717$	9941.18	0.517797
$718$	−29045.3	−1.50969
$719$	−32500.7	−1.68578	−0.842888	−	0.538089i	$-0.819146\pi$
$719$	−32500.7	−1.68578	−0.842888	+	0.538089i	$0.819146\pi$
$720$	−1553.88	−0.0804302
$721$	0	0
$722$	−46064.6	−2.37444
$723$	24799.3	1.27565
$724$	−47528.3	−2.43975
$725$	15096.2	0.773324
$726$	−8236.25	−0.421041
$727$	14309.6	0.730004	0.365002	−	0.931007i	$-0.381068\pi$
$727$	14309.6	0.730004	0.365002	+	0.931007i	$0.381068\pi$
$728$	0	0
$729$	21328.3	1.08359
$730$	−8939.37	−0.453234
$731$	29376.7	1.48637
$732$	53174.0	2.68493
$733$	−2077.27	−0.104673	−0.0523367	−	0.998629i	$-0.516667\pi$
$733$	−2077.27	−0.104673	−0.0523367	+	0.998629i	$0.516667\pi$
$734$	614.902	0.0309216
$735$	0	0
$736$	1334.70	0.0668447
$737$	14913.7	0.745392
$738$	−6222.85	−0.310388
$739$	18738.4	0.932753	0.466376	−	0.884586i	$-0.345559\pi$
$739$	18738.4	0.932753	0.466376	+	0.884586i	$0.345559\pi$
$740$	−14407.8	−0.715729
$741$	−3298.55	−0.163529
$742$	0	0
$743$	27206.2	1.34333	0.671667	−	0.740853i	$-0.265578\pi$
$743$	27206.2	1.34333	0.671667	+	0.740853i	$0.265578\pi$
$744$	−26327.4	−1.29732
$745$	−1886.73	−0.0927847
$746$	13750.2	0.674840
$747$	3194.91	0.156487
$748$	−35102.5	−1.71588
$749$	0	0
$750$	−13132.5	−0.639375
$751$	−15140.4	−0.735659	−0.367829	−	0.929893i	$-0.619899\pi$
$751$	−15140.4	−0.735659	−0.367829	+	0.929893i	$0.619899\pi$
$752$	3335.18	0.161731
$753$	−23562.8	−1.14034
$754$	−3791.04	−0.183106
$755$	3056.95	0.147356
$756$	0	0
$757$	18039.2	0.866112	0.433056	−	0.901367i	$-0.357435\pi$
$757$	18039.2	0.866112	0.433056	+	0.901367i	$0.357435\pi$
$758$	−13235.9	−0.634235
$759$	7638.95	0.365318
$760$	13258.8	0.632823
$761$	−8344.90	−0.397506	−0.198753	−	0.980050i	$-0.563689\pi$
$761$	−8344.90	−0.397506	−0.198753	+	0.980050i	$0.563689\pi$
$762$	20549.4	0.976939
$763$	0	0
$764$	−62538.5	−2.96147
$765$	1538.11	0.0726932
$766$	11664.0	0.550180
$767$	−1372.34	−0.0646055
$768$	35643.3	1.67470
$769$	18528.0	0.868840	0.434420	−	0.900710i	$-0.356953\pi$
$769$	18528.0	0.868840	0.434420	+	0.900710i	$0.356953\pi$
$770$	0	0
$771$	−2404.75	−0.112328
$772$	26453.0	1.23325
$773$	22415.9	1.04301	0.521503	−	0.853249i	$-0.325371\pi$
$773$	22415.9	1.04301	0.521503	+	0.853249i	$0.325371\pi$
$774$	−17696.7	−0.821830
$775$	17802.3	0.825132
$776$	−14055.3	−0.650201
$777$	0	0
$778$	−11711.5	−0.539691
$779$	18721.9	0.861081
$780$	1076.25	0.0494050
$781$	3426.48	0.156990
$782$	−20082.5	−0.918347
$783$	−19454.5	−0.887926
$784$	0	0
$785$	8101.68	0.368359
$786$	−883.990	−0.0401156
$787$	−10200.2	−0.462005	−0.231003	−	0.972953i	$-0.574201\pi$
$787$	−10200.2	−0.462005	−0.231003	+	0.972953i	$0.574201\pi$
$788$	−8145.89	−0.368255
$789$	2547.70	0.114956
$790$	−2430.12	−0.109443
$791$	0	0
$792$	10759.1	0.482711
$793$	4594.15	0.205729
$794$	14322.1	0.640140
$795$	6143.37	0.274067
$796$	69020.0	3.07330
$797$	−12157.5	−0.540328	−0.270164	−	0.962814i	$-0.587078\pi$
$797$	−12157.5	−0.540328	−0.270164	+	0.962814i	$0.587078\pi$
$798$	0	0
$799$	−3301.32	−0.146173
$800$	2726.11	0.120478
$801$	8248.94	0.363873
$802$	24518.4	1.07952
$803$	21824.3	0.959107
$804$	−33968.2	−1.49001
$805$	0	0
$806$	−4470.60	−0.195373
$807$	24650.9	1.07528
$808$	−7235.21	−0.315017
$809$	20578.1	0.894299	0.447149	−	0.894459i	$-0.352439\pi$
$809$	20578.1	0.894299	0.447149	+	0.894459i	$0.352439\pi$
$810$	5322.18	0.230867
$811$	17357.1	0.751530	0.375765	−	0.926715i	$-0.377380\pi$
$811$	17357.1	0.751530	0.375765	+	0.926715i	$0.377380\pi$
$812$	0	0
$813$	−7309.41	−0.315316
$814$	52452.5	2.25855
$815$	−9238.54	−0.397070
$816$	21388.7	0.917591
$817$	53242.0	2.27993
$818$	−47388.5	−2.02555
$819$	0	0
$820$	−6108.58	−0.260147
$821$	−29419.1	−1.25059	−0.625295	−	0.780389i	$-0.715021\pi$
$821$	−29419.1	−1.25059	−0.625295	+	0.780389i	$0.715021\pi$
$822$	5442.36	0.230930
$823$	−1833.32	−0.0776497	−0.0388248	−	0.999246i	$-0.512361\pi$
$823$	−1833.32	−0.0776497	−0.0388248	+	0.999246i	$0.512361\pi$
$824$	−62211.9	−2.63016
$825$	15602.4	0.658433
$826$	0	0
$827$	−25007.8	−1.05152	−0.525761	−	0.850633i	$-0.676219\pi$
$827$	−25007.8	−1.05152	−0.525761	+	0.850633i	$0.676219\pi$
$828$	8112.81	0.340507
$829$	−17478.1	−0.732256	−0.366128	−	0.930564i	$-0.619317\pi$
$829$	−17478.1	−0.732256	−0.366128	+	0.930564i	$0.619317\pi$
$830$	4676.76	0.195582
$831$	13360.7	0.557733
$832$	2743.25	0.114309
$833$	0	0
$834$	6837.75	0.283899
$835$	−10401.8	−0.431101
$836$	−63619.4	−2.63197
$837$	−22941.7	−0.947411
$838$	−74842.6	−3.08519
$839$	−1959.72	−0.0806402	−0.0403201	−	0.999187i	$-0.512838\pi$
$839$	−1959.72	−0.0806402	−0.0403201	+	0.999187i	$0.512838\pi$
$840$	0	0
$841$	−8158.50	−0.334516
$842$	51241.8	2.09728
$843$	7960.28	0.325227
$844$	−40406.3	−1.64792
$845$	−5510.13	−0.224325
$846$	1988.74	0.0808207
$847$	0	0
$848$	−39834.2	−1.61310
$849$	−14436.6	−0.583586
$850$	−41018.1	−1.65519
$851$	20123.7	0.810615
$852$	−7804.33	−0.313817
$853$	3957.80	0.158866	0.0794329	−	0.996840i	$-0.474689\pi$
$853$	3957.80	0.158866	0.0794329	+	0.996840i	$0.474689\pi$
$854$	0	0
$855$	2787.65	0.111503
$856$	−5189.73	−0.207221
$857$	−36482.5	−1.45417	−0.727083	−	0.686550i	$-0.759124\pi$
$857$	−36482.5	−1.45417	−0.727083	+	0.686550i	$0.759124\pi$
$858$	−3918.17	−0.155902
$859$	12030.0	0.477831	0.238915	−	0.971040i	$-0.423208\pi$
$859$	12030.0	0.477831	0.238915	+	0.971040i	$0.423208\pi$
$860$	−17371.8	−0.688806
$861$	0	0
$862$	81625.2	3.22525
$863$	29023.0	1.14479	0.572396	−	0.819977i	$-0.306014\pi$
$863$	29023.0	1.14479	0.572396	+	0.819977i	$0.306014\pi$
$864$	−3513.12	−0.138332
$865$	−5254.23	−0.206531
$866$	−50840.5	−1.99495
$867$	−89.1515	−0.00349221
$868$	0	0
$869$	5932.83	0.231597
$870$	−6871.04	−0.267759
$871$	−2934.80	−0.114170
$872$	−30939.8	−1.20155
$873$	−2955.12	−0.114565
$874$	−36397.3	−1.40865
$875$	0	0
$876$	−49708.1	−1.91722
$877$	14126.3	0.543913	0.271957	−	0.962310i	$-0.412329\pi$
$877$	14126.3	0.543913	0.271957	+	0.962310i	$0.412329\pi$
$878$	22989.5	0.883667
$879$	−24700.5	−0.947811
$880$	5553.14	0.212723
$881$	8558.96	0.327308	0.163654	−	0.986518i	$-0.447672\pi$
$881$	8558.96	0.327308	0.163654	+	0.986518i	$0.447672\pi$
$882$	0	0
$883$	−14157.8	−0.539579	−0.269790	−	0.962919i	$-0.586954\pi$
$883$	−14157.8	−0.539579	−0.269790	+	0.962919i	$0.586954\pi$
$884$	6907.65	0.262816
$885$	−2487.29	−0.0944737
$886$	−38218.6	−1.44919
$887$	33674.5	1.27472	0.637362	−	0.770564i	$-0.280026\pi$
$887$	33674.5	1.27472	0.637362	+	0.770564i	$0.280026\pi$
$888$	−60785.5	−2.29710
$889$	0	0
$890$	12074.9	0.454779
$891$	−12993.4	−0.488547
$892$	−28023.5	−1.05190
$893$	−5983.28	−0.224214
$894$	−15644.7	−0.585276
$895$	−2118.92	−0.0791369
$896$	0	0
$897$	−1503.23	−0.0559548
$898$	−61087.6	−2.27006
$899$	19139.9	0.710067
$900$	16570.3	0.613715
$901$	39429.7	1.45793
$902$	22238.7	0.820919
$903$	0	0
$904$	59152.9	2.17632
$905$	−7442.54	−0.273368
$906$	25348.0	0.929506
$907$	5123.01	0.187549	0.0937743	−	0.995593i	$-0.470107\pi$
$907$	5123.01	0.187549	0.0937743	+	0.995593i	$0.470107\pi$
$908$	−93110.8	−3.40307
$909$	−1521.20	−0.0555060
$910$	0	0
$911$	−40081.1	−1.45768	−0.728840	−	0.684684i	$-0.759940\pi$
$911$	−40081.1	−1.45768	−0.728840	+	0.684684i	$0.759940\pi$
$912$	38764.6	1.40748
$913$	−11417.7	−0.413879
$914$	53745.6	1.94502
$915$	8326.61	0.300841
$916$	−5494.91	−0.198206
$917$	0	0
$918$	52859.9	1.90048
$919$	24668.2	0.885452	0.442726	−	0.896657i	$-0.354012\pi$
$919$	24668.2	0.885452	0.442726	+	0.896657i	$0.354012\pi$
$920$	6042.34	0.216533
$921$	−18308.5	−0.655034
$922$	46237.8	1.65158
$923$	−674.281	−0.0240457
$924$	0	0
$925$	41102.5	1.46102
$926$	−25760.1	−0.914178
$927$	−13080.0	−0.463435
$928$	2930.93	0.103677
$929$	−17640.0	−0.622980	−0.311490	−	0.950249i	$-0.600828\pi$
$929$	−17640.0	−0.622980	−0.311490	+	0.950249i	$0.600828\pi$
$930$	−8102.70	−0.285697
$931$	0	0
$932$	51986.4	1.82711
$933$	31507.3	1.10557
$934$	4067.76	0.142507
$935$	−5496.76	−0.192260
$936$	−2117.23	−0.0739356
$937$	−5589.13	−0.194866	−0.0974328	−	0.995242i	$-0.531063\pi$
$937$	−5589.13	−0.194866	−0.0974328	+	0.995242i	$0.531063\pi$
$938$	0	0
$939$	−34444.9	−1.19709
$940$	1952.22	0.0677388
$941$	51584.2	1.78703	0.893516	−	0.449032i	$-0.148231\pi$
$941$	51584.2	1.78703	0.893516	+	0.449032i	$0.148231\pi$
$942$	67178.7	2.32357
$943$	8532.04	0.294636
$944$	16127.8	0.556054
$945$	0	0
$946$	63243.3	2.17359
$947$	−41914.6	−1.43827	−0.719135	−	0.694871i	$-0.755462\pi$
$947$	−41914.6	−1.43827	−0.719135	+	0.694871i	$0.755462\pi$
$948$	−13512.9	−0.462953
$949$	−4294.70	−0.146904
$950$	−74340.9	−2.53888
$951$	−15765.0	−0.537554
$952$	0	0
$953$	38682.2	1.31484	0.657418	−	0.753526i	$-0.271649\pi$
$953$	38682.2	1.31484	0.657418	+	0.753526i	$0.271649\pi$
$954$	−23752.8	−0.806105
$955$	−9793.01	−0.331826
$956$	−37730.9	−1.27647
$957$	16774.7	0.566615
$958$	−56963.0	−1.92108
$959$	0	0
$960$	4971.97	0.167156
$961$	−7220.23	−0.242363
$962$	−10321.9	−0.345936
$963$	−1091.14	−0.0365124
$964$	−94123.5	−3.14472
$965$	4142.33	0.138183
$966$	0	0
$967$	−37652.6	−1.25215	−0.626074	−	0.779764i	$-0.715339\pi$
$967$	−37652.6	−1.25215	−0.626074	+	0.779764i	$0.715339\pi$
$968$	15905.0	0.528107
$969$	−38371.1	−1.27209
$970$	−4325.75	−0.143187
$971$	6897.62	0.227966	0.113983	−	0.993483i	$-0.463639\pi$
$971$	6897.62	0.227966	0.113983	+	0.993483i	$0.463639\pi$
$972$	−37555.9	−1.23931
$973$	0	0
$974$	77994.1	2.56580
$975$	−3070.33	−0.100850
$976$	−53990.5	−1.77069
$977$	−54998.8	−1.80099	−0.900495	−	0.434865i	$-0.856796\pi$
$977$	−54998.8	−1.80099	−0.900495	+	0.434865i	$0.856796\pi$
$978$	−76605.5	−2.50468
$979$	−29479.4	−0.962376
$980$	0	0
$981$	−6505.08	−0.211714
$982$	76001.5	2.46976
$983$	−36883.9	−1.19676	−0.598379	−	0.801213i	$-0.704188\pi$
$983$	−36883.9	−1.19676	−0.598379	+	0.801213i	$0.704188\pi$
$984$	−25771.7	−0.834932
$985$	−1275.58	−0.0412622
$986$	−44100.1	−1.42437
$987$	0	0
$988$	12519.4	0.403131
$989$	24263.7	0.780122
$990$	3311.29	0.106303
$991$	−24747.1	−0.793257	−0.396629	−	0.917979i	$-0.629820\pi$
$991$	−24747.1	−0.793257	−0.396629	+	0.917979i	$0.629820\pi$
$992$	3456.31	0.110623
$993$	18775.8	0.600033
$994$	0	0
$995$	10808.0	0.344357
$996$	26005.5	0.827327
$997$	−13881.7	−0.440960	−0.220480	−	0.975392i	$-0.570762\pi$
$997$	−13881.7	−0.440960	−0.220480	+	0.975392i	$0.570762\pi$
$998$	82745.4	2.62451
$999$	−52968.6	−1.67753

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.h.1.3	yes	35
7.6	odd	2		2303.4.a.g.1.3	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.g.1.3	✓	35	7.6	odd	2
2303.4.a.h.1.3	yes	35	1.1	even	1	trivial

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 2303 = 7^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2303.a (trivial)

\(f(q)\)	\(=\)	\(q-4.92815 q^{2} -4.29114 q^{3} +16.2866 q^{4} +2.55035 q^{5} +21.1474 q^{6} -40.8377 q^{8} -8.58611 q^{9} +O(q^{10})\)	\(q-4.92815 q^{2} -4.29114 q^{3} +16.2866 q^{4} +2.55035 q^{5} +21.1474 q^{6} -40.8377 q^{8} -8.58611 q^{9} -12.5685 q^{10} +30.6844 q^{11} -69.8882 q^{12} -6.03822 q^{13} -10.9439 q^{15} +70.9613 q^{16} -70.2408 q^{17} +42.3136 q^{18} -127.304 q^{19} +41.5366 q^{20} -151.217 q^{22} -58.0155 q^{23} +175.241 q^{24} -118.496 q^{25} +29.7573 q^{26} +152.705 q^{27} -127.399 q^{29} +53.9332 q^{30} -150.236 q^{31} -23.0059 q^{32} -131.671 q^{33} +346.157 q^{34} -139.839 q^{36} -346.869 q^{37} +627.372 q^{38} +25.9109 q^{39} -104.151 q^{40} -147.065 q^{41} -418.228 q^{43} +499.745 q^{44} -21.8976 q^{45} +285.909 q^{46} +47.0000 q^{47} -304.505 q^{48} +583.964 q^{50} +301.413 q^{51} -98.3423 q^{52} -561.350 q^{53} -752.553 q^{54} +78.2559 q^{55} +546.278 q^{57} +627.841 q^{58} +227.276 q^{59} -178.240 q^{60} -760.844 q^{61} +740.384 q^{62} -454.314 q^{64} -15.3996 q^{65} +648.894 q^{66} +486.037 q^{67} -1143.99 q^{68} +248.953 q^{69} +111.669 q^{71} +350.637 q^{72} +711.251 q^{73} +1709.42 q^{74} +508.482 q^{75} -2073.35 q^{76} -127.693 q^{78} +193.350 q^{79} +180.976 q^{80} -423.454 q^{81} +724.758 q^{82} -372.102 q^{83} -179.139 q^{85} +2061.09 q^{86} +546.687 q^{87} -1253.08 q^{88} -960.731 q^{89} +107.915 q^{90} -944.877 q^{92} +644.683 q^{93} -231.623 q^{94} -324.669 q^{95} +98.7217 q^{96} +344.174 q^{97} -263.459 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9} + 100 q^{10} + 40 q^{11} + 144 q^{12} + 328 q^{13} + 20 q^{15} + 643 q^{16} + 152 q^{17} + 51 q^{18} + 266 q^{19} + 1064 q^{20} - 168 q^{22} - 134 q^{23} + 288 q^{24} + 1137 q^{25} + 156 q^{26} + 672 q^{27} + 248 q^{29} - 216 q^{30} + 276 q^{31} + 347 q^{32} + 1056 q^{33} + 908 q^{34} + 909 q^{36} - 418 q^{37} + 164 q^{38} - 548 q^{39} + 1200 q^{40} + 918 q^{41} + 608 q^{43} + 1288 q^{44} + 876 q^{45} - 972 q^{46} + 1645 q^{47} + 1252 q^{48} - 367 q^{50} - 464 q^{51} + 3798 q^{52} - 218 q^{53} - 744 q^{54} + 1004 q^{55} - 436 q^{57} - 1270 q^{58} + 3760 q^{59} - 424 q^{60} + 956 q^{61} + 84 q^{62} + 2189 q^{64} - 596 q^{65} + 5500 q^{66} - 476 q^{67} + 256 q^{68} + 444 q^{69} + 852 q^{71} - 883 q^{72} + 6250 q^{73} + 1366 q^{74} - 2568 q^{75} + 1742 q^{76} - 1460 q^{78} + 632 q^{79} + 10124 q^{80} + 1267 q^{81} + 792 q^{82} + 796 q^{83} - 1228 q^{85} - 2864 q^{86} + 8360 q^{87} - 50 q^{88} + 908 q^{89} - 1858 q^{90} + 1696 q^{92} + 644 q^{93} + 235 q^{94} + 1320 q^{95} + 2688 q^{96} + 6184 q^{97} - 1812 q^{99}+O(q^{100}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9 + 100 * q^10 + 40 * q^11 + 144 * q^12 + 328 * q^13 + 20 * q^15 + 643 * q^16 + 152 * q^17 + 51 * q^18 + 266 * q^19 + 1064 * q^20 - 168 * q^22 - 134 * q^23 + 288 * q^24 + 1137 * q^25 + 156 * q^26 + 672 * q^27 + 248 * q^29 - 216 * q^30 + 276 * q^31 + 347 * q^32 + 1056 * q^33 + 908 * q^34 + 909 * q^36 - 418 * q^37 + 164 * q^38 - 548 * q^39 + 1200 * q^40 + 918 * q^41 + 608 * q^43 + 1288 * q^44 + 876 * q^45 - 972 * q^46 + 1645 * q^47 + 1252 * q^48 - 367 * q^50 - 464 * q^51 + 3798 * q^52 - 218 * q^53 - 744 * q^54 + 1004 * q^55 - 436 * q^57 - 1270 * q^58 + 3760 * q^59 - 424 * q^60 + 956 * q^61 + 84 * q^62 + 2189 * q^64 - 596 * q^65 + 5500 * q^66 - 476 * q^67 + 256 * q^68 + 444 * q^69 + 852 * q^71 - 883 * q^72 + 6250 * q^73 + 1366 * q^74 - 2568 * q^75 + 1742 * q^76 - 1460 * q^78 + 632 * q^79 + 10124 * q^80 + 1267 * q^81 + 792 * q^82 + 796 * q^83 - 1228 * q^85 - 2864 * q^86 + 8360 * q^87 - 50 * q^88 + 908 * q^89 - 1858 * q^90 + 1696 * q^92 + 644 * q^93 + 235 * q^94 + 1320 * q^95 + 2688 * q^96 + 6184 * q^97 - 1812 * q^99

Introduction

L-functions

Modular forms

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Database

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