LMFDB - Embedded newform 2303.4.a.e.1.5

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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 130 x^{18} + 379 x^{17} + 6970 x^{16} - 19652 x^{15} - 199330 x^{14} + \cdots - 19267584 $ x^20 - 3x^19 - 130x^18 + 379x^17 + 6970x^16 - 19652x^15 - 199330x^14 + 540440x^13 + 3283799x^12 - 8520033x^11 - 31283236x^10 + 77759541x^9 + 161161774x^8 - 391970848x^7 - 357939064x^6 + 946653568x^5 + 47744512x^4 - 707974144x^3 + 258494464x^2 + 38535168*x - 19267584
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 329)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-3.29728$ of defining polynomial
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)

$f(q)$	$=$	$q-3.29728 q^{2} -4.34822 q^{3} +2.87207 q^{4} -10.4624 q^{5} +14.3373 q^{6} +16.9082 q^{8} -8.09301 q^{9} +O(q^{10})$	\(q-3.29728 q^{2} -4.34822 q^{3} +2.87207 q^{4} -10.4624 q^{5} +14.3373 q^{6} +16.9082 q^{8} -8.09301 q^{9} +34.4975 q^{10} +26.9209 q^{11} -12.4884 q^{12} -12.5358 q^{13} +45.4928 q^{15} -78.7278 q^{16} -38.7618 q^{17} +26.6849 q^{18} -53.3344 q^{19} -30.0487 q^{20} -88.7659 q^{22} +89.5137 q^{23} -73.5207 q^{24} -15.5381 q^{25} +41.3339 q^{26} +152.592 q^{27} +155.960 q^{29} -150.003 q^{30} +49.9507 q^{31} +124.322 q^{32} -117.058 q^{33} +127.808 q^{34} -23.2437 q^{36} -190.310 q^{37} +175.859 q^{38} +54.5082 q^{39} -176.901 q^{40} -81.5494 q^{41} +197.857 q^{43} +77.3187 q^{44} +84.6724 q^{45} -295.152 q^{46} +47.0000 q^{47} +342.325 q^{48} +51.2334 q^{50} +168.545 q^{51} -36.0036 q^{52} +716.802 q^{53} -503.139 q^{54} -281.658 q^{55} +231.910 q^{57} -514.244 q^{58} +90.8772 q^{59} +130.658 q^{60} -143.539 q^{61} -164.701 q^{62} +219.898 q^{64} +131.154 q^{65} +385.973 q^{66} +431.908 q^{67} -111.326 q^{68} -389.225 q^{69} +284.770 q^{71} -136.839 q^{72} -1018.40 q^{73} +627.506 q^{74} +67.5628 q^{75} -153.180 q^{76} -179.729 q^{78} -116.373 q^{79} +823.682 q^{80} -444.992 q^{81} +268.891 q^{82} -1060.75 q^{83} +405.541 q^{85} -652.392 q^{86} -678.148 q^{87} +455.185 q^{88} -242.413 q^{89} -279.189 q^{90} +257.090 q^{92} -217.196 q^{93} -154.972 q^{94} +558.006 q^{95} -540.578 q^{96} -1241.28 q^{97} -217.871 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 3 q^{2} - 2 q^{3} + 109 q^{4} + 4 q^{5} - q^{6} + 12 q^{8} + 278 q^{9}+O(q^{10}) $ 20 * q + 3 * q^2 - 2 * q^3 + 109 * q^4 + 4 * q^5 - q^6 + 12 * q^8 + 278 * q^9	\( 20 q + 3 q^{2} - 2 q^{3} + 109 q^{4} + 4 q^{5} - q^{6} + 12 q^{8} + 278 q^{9} - 68 q^{10} + 62 q^{11} + 6 q^{13} + 420 q^{15} + 957 q^{16} + 138 q^{17} + 120 q^{18} - 182 q^{19} - 787 q^{20} + 521 q^{22} + 326 q^{23} + 18 q^{24} + 678 q^{25} - 118 q^{26} - 68 q^{27} + 528 q^{29} + 877 q^{30} - 1092 q^{31} + 254 q^{32} + 424 q^{33} - 234 q^{34} + 2608 q^{36} + 904 q^{37} + 166 q^{38} + 606 q^{39} - 323 q^{40} + 8 q^{41} - 18 q^{43} + 98 q^{44} - 316 q^{45} + 1382 q^{46} + 940 q^{47} - 937 q^{48} + 892 q^{50} + 756 q^{51} - 761 q^{52} + 992 q^{53} - 384 q^{54} - 1060 q^{55} + 1554 q^{57} - 938 q^{58} - 2140 q^{59} + 5830 q^{60} + 186 q^{61} - 69 q^{62} + 7086 q^{64} + 662 q^{65} - 3617 q^{66} + 2852 q^{67} - 1163 q^{68} - 628 q^{69} + 3448 q^{71} - 355 q^{72} + 304 q^{73} + 1512 q^{74} - 4930 q^{75} - 339 q^{76} + 1054 q^{78} + 4248 q^{79} - 5945 q^{80} + 5696 q^{81} - 3665 q^{82} + 274 q^{83} + 232 q^{85} - 5730 q^{86} - 3756 q^{87} + 1976 q^{88} + 3168 q^{89} + 13306 q^{90} - 4214 q^{92} - 374 q^{93} + 141 q^{94} + 6100 q^{95} + 11433 q^{96} + 4112 q^{97} + 7252 q^{99}+O(q^{100}) \) 20 * q + 3 * q^2 - 2 * q^3 + 109 * q^4 + 4 * q^5 - q^6 + 12 * q^8 + 278 * q^9 - 68 * q^10 + 62 * q^11 + 6 * q^13 + 420 * q^15 + 957 * q^16 + 138 * q^17 + 120 * q^18 - 182 * q^19 - 787 * q^20 + 521 * q^22 + 326 * q^23 + 18 * q^24 + 678 * q^25 - 118 * q^26 - 68 * q^27 + 528 * q^29 + 877 * q^30 - 1092 * q^31 + 254 * q^32 + 424 * q^33 - 234 * q^34 + 2608 * q^36 + 904 * q^37 + 166 * q^38 + 606 * q^39 - 323 * q^40 + 8 * q^41 - 18 * q^43 + 98 * q^44 - 316 * q^45 + 1382 * q^46 + 940 * q^47 - 937 * q^48 + 892 * q^50 + 756 * q^51 - 761 * q^52 + 992 * q^53 - 384 * q^54 - 1060 * q^55 + 1554 * q^57 - 938 * q^58 - 2140 * q^59 + 5830 * q^60 + 186 * q^61 - 69 * q^62 + 7086 * q^64 + 662 * q^65 - 3617 * q^66 + 2852 * q^67 - 1163 * q^68 - 628 * q^69 + 3448 * q^71 - 355 * q^72 + 304 * q^73 + 1512 * q^74 - 4930 * q^75 - 339 * q^76 + 1054 * q^78 + 4248 * q^79 - 5945 * q^80 + 5696 * q^81 - 3665 * q^82 + 274 * q^83 + 232 * q^85 - 5730 * q^86 - 3756 * q^87 + 1976 * q^88 + 3168 * q^89 + 13306 * q^90 - 4214 * q^92 - 374 * q^93 + 141 * q^94 + 6100 * q^95 + 11433 * q^96 + 4112 * q^97 + 7252 * 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 $

$2$	−3.29728	−1.16577	−0.582883	−	0.812556i	$-0.698075\pi$
$2$	−3.29728	−1.16577	−0.582883	+	0.812556i	$0.698075\pi$
$3$	−4.34822	−0.836815	−0.418407	−	0.908259i	$-0.637412\pi$
$3$	−4.34822	−0.836815	−0.418407	+	0.908259i	$0.637412\pi$
$4$	2.87207	0.359009
$5$	−10.4624	−0.935786	−0.467893	−	0.883785i	$-0.654987\pi$
$5$	−10.4624	−0.935786	−0.467893	+	0.883785i	$0.654987\pi$
$6$	14.3373	0.975529
$7$	0	0
$7$	0	0
$8$	16.9082	0.747246
$9$	−8.09301	−0.299741
$10$	34.4975	1.09091
$11$	26.9209	0.737906	0.368953	−	0.929448i	$-0.379716\pi$
$11$	26.9209	0.737906	0.368953	+	0.929448i	$0.379716\pi$
$12$	−12.4884	−0.300424
$13$	−12.5358	−0.267446	−0.133723	−	0.991019i	$-0.542693\pi$
$13$	−12.5358	−0.267446	−0.133723	+	0.991019i	$0.542693\pi$
$14$	0	0
$15$	45.4928	0.783080
$16$	−78.7278	−1.23012
$17$	−38.7618	−0.553007	−0.276503	−	0.961013i	$-0.589176\pi$
$17$	−38.7618	−0.553007	−0.276503	+	0.961013i	$0.589176\pi$
$18$	26.6849	0.349428
$19$	−53.3344	−0.643987	−0.321994	−	0.946742i	$-0.604353\pi$
$19$	−53.3344	−0.643987	−0.321994	+	0.946742i	$0.604353\pi$
$20$	−30.0487	−0.335955
$21$	0	0
$22$	−88.7659	−0.860225
$23$	89.5137	0.811518	0.405759	−	0.913980i	$-0.367007\pi$
$23$	89.5137	0.811518	0.405759	+	0.913980i	$0.367007\pi$
$24$	−73.5207	−0.625306
$25$	−15.5381	−0.124304
$26$	41.3339	0.311779
$27$	152.592	1.08764
$28$	0	0
$29$	155.960	0.998656	0.499328	−	0.866413i	$-0.333580\pi$
$29$	155.960	0.998656	0.499328	+	0.866413i	$0.333580\pi$
$30$	−150.003	−0.912887
$31$	49.9507	0.289400	0.144700	−	0.989476i	$-0.453778\pi$
$31$	49.9507	0.289400	0.144700	+	0.989476i	$0.453778\pi$
$32$	124.322	0.686787
$33$	−117.058	−0.617490
$34$	127.808	0.644676
$35$	0	0
$36$	−23.2437	−0.107610
$37$	−190.310	−0.845589	−0.422794	−	0.906226i	$-0.638951\pi$
$37$	−190.310	−0.845589	−0.422794	+	0.906226i	$0.638951\pi$
$38$	175.859	0.750738
$39$	54.5082	0.223802
$40$	−176.901	−0.699262
$41$	−81.5494	−0.310631	−0.155316	−	0.987865i	$-0.549639\pi$
$41$	−81.5494	−0.310631	−0.155316	+	0.987865i	$0.549639\pi$
$42$	0	0
$43$	197.857	0.701697	0.350848	−	0.936432i	$-0.385893\pi$
$43$	197.857	0.701697	0.350848	+	0.936432i	$0.385893\pi$
$44$	77.3187	0.264915
$45$	84.6724	0.280494
$46$	−295.152	−0.946039
$47$	47.0000	0.145865
$47$	47.0000	0.145865
$48$	342.325	1.02938
$49$	0	0
$50$	51.2334	0.144910
$51$	168.545	0.462764
$52$	−36.0036	−0.0960153
$53$	716.802	1.85774	0.928871	−	0.370404i	$-0.120781\pi$
$53$	716.802	1.85774	0.928871	+	0.370404i	$0.120781\pi$
$54$	−503.139	−1.26794
$55$	−281.658	−0.690522
$56$	0	0
$57$	231.910	0.538898
$58$	−514.244	−1.16420
$59$	90.8772	0.200529	0.100264	−	0.994961i	$-0.468031\pi$
$59$	90.8772	0.200529	0.100264	+	0.994961i	$0.468031\pi$
$60$	130.658	0.281132
$61$	−143.539	−0.301284	−0.150642	−	0.988588i	$-0.548134\pi$
$61$	−143.539	−0.301284	−0.150642	+	0.988588i	$0.548134\pi$
$62$	−164.701	−0.337373
$63$	0	0
$64$	219.898	0.429489
$65$	131.154	0.250272
$66$	385.973	0.719849
$67$	431.908	0.787552	0.393776	−	0.919206i	$-0.371169\pi$
$67$	431.908	0.787552	0.393776	+	0.919206i	$0.371169\pi$
$68$	−111.326	−0.198534
$69$	−389.225	−0.679090
$70$	0	0
$71$	284.770	0.475999	0.237999	−	0.971265i	$-0.423508\pi$
$71$	284.770	0.475999	0.237999	+	0.971265i	$0.423508\pi$
$72$	−136.839	−0.223980
$73$	−1018.40	−1.63280	−0.816401	−	0.577485i	$-0.804034\pi$
$73$	−1018.40	−1.63280	−0.816401	+	0.577485i	$0.804034\pi$
$74$	627.506	0.985758
$75$	67.5628	0.104020
$76$	−153.180	−0.231197
$77$	0	0
$78$	−179.729	−0.260901
$79$	−116.373	−0.165734	−0.0828670	−	0.996561i	$-0.526408\pi$
$79$	−116.373	−0.165734	−0.0828670	+	0.996561i	$0.526408\pi$
$80$	823.682	1.15113
$81$	−444.992	−0.610414
$82$	268.891	0.362123
$83$	−1060.75	−1.40280	−0.701401	−	0.712766i	$-0.747442\pi$
$83$	−1060.75	−1.40280	−0.701401	+	0.712766i	$0.747442\pi$
$84$	0	0
$85$	405.541	0.517496
$86$	−652.392	−0.818014
$87$	−678.148	−0.835690
$88$	455.185	0.551397
$89$	−242.413	−0.288716	−0.144358	−	0.989525i	$-0.546112\pi$
$89$	−242.413	−0.288716	−0.144358	+	0.989525i	$0.546112\pi$
$90$	−279.189	−0.326990
$91$	0	0
$92$	257.090	0.291342
$93$	−217.196	−0.242174
$94$	−154.972	−0.170044
$95$	558.006	0.602634
$96$	−540.578	−0.574714
$97$	−1241.28	−1.29931	−0.649653	−	0.760231i	$-0.725086\pi$
$97$	−1241.28	−1.29931	−0.649653	+	0.760231i	$0.725086\pi$
$98$	0	0
$99$	−217.871	−0.221181
$100$	−44.6264	−0.0446264
$101$	−216.456	−0.213249	−0.106625	−	0.994299i	$-0.534004\pi$
$101$	−216.456	−0.213249	−0.106625	+	0.994299i	$0.534004\pi$
$102$	−555.739	−0.539474
$103$	−330.249	−0.315927	−0.157963	−	0.987445i	$-0.550493\pi$
$103$	−330.249	−0.315927	−0.157963	+	0.987445i	$0.550493\pi$
$104$	−211.958	−0.199848
$105$	0	0
$106$	−2363.50	−2.16569
$107$	−1038.57	−0.938342	−0.469171	−	0.883107i	$-0.655447\pi$
$107$	−1038.57	−0.938342	−0.469171	+	0.883107i	$0.655447\pi$
$108$	438.255	0.390473
$109$	−167.275	−0.146991	−0.0734954	−	0.997296i	$-0.523415\pi$
$109$	−167.275	−0.146991	−0.0734954	+	0.997296i	$0.523415\pi$
$110$	928.705	0.804986
$111$	827.510	0.707601
$112$	0	0
$113$	−1073.37	−0.893578	−0.446789	−	0.894639i	$-0.647433\pi$
$113$	−1073.37	−0.893578	−0.446789	+	0.894639i	$0.647433\pi$
$114$	−764.672	−0.628229
$115$	−936.529	−0.759407
$116$	447.928	0.358526
$117$	101.452	0.0801645
$118$	−299.648	−0.233769
$119$	0	0
$120$	769.203	0.585153
$121$	−606.264	−0.455495
$122$	473.290	0.351227
$123$	354.594	0.259941
$124$	143.462	0.103897
$125$	1470.37	1.05211
$126$	0	0
$127$	−1100.37	−0.768834	−0.384417	−	0.923160i	$-0.625598\pi$
$127$	−1100.37	−0.768834	−0.384417	+	0.923160i	$0.625598\pi$
$128$	−1719.64	−1.18747
$129$	−860.327	−0.587190
$130$	−432.452	−0.291758
$131$	−1175.87	−0.784245	−0.392123	−	0.919913i	$-0.628259\pi$
$131$	−1175.87	−0.784245	−0.392123	+	0.919913i	$0.628259\pi$
$132$	−336.199	−0.221684
$133$	0	0
$134$	−1424.12	−0.918100
$135$	−1596.48	−1.01780
$136$	−655.393	−0.413232
$137$	−1372.67	−0.856020	−0.428010	−	0.903774i	$-0.640785\pi$
$137$	−1372.67	−0.856020	−0.428010	+	0.903774i	$0.640785\pi$
$138$	1283.39	0.791659
$139$	2035.65	1.24217	0.621084	−	0.783744i	$-0.286693\pi$
$139$	2035.65	1.24217	0.621084	+	0.783744i	$0.286693\pi$
$140$	0	0
$141$	−204.366	−0.122062
$142$	−938.965	−0.554903
$143$	−337.474	−0.197350
$144$	637.145	0.368718
$145$	−1631.72	−0.934529
$146$	3357.95	1.90346
$147$	0	0
$148$	−546.584	−0.303574
$149$	−2510.42	−1.38028	−0.690139	−	0.723676i	$-0.742451\pi$
$149$	−2510.42	−1.38028	−0.690139	+	0.723676i	$0.742451\pi$
$150$	−222.774	−0.121263
$151$	3678.20	1.98230	0.991150	−	0.132745i	$-0.0423793\pi$
$151$	3678.20	1.98230	0.991150	+	0.132745i	$0.0423793\pi$
$152$	−901.791	−0.481217
$153$	313.699	0.165759
$154$	0	0
$155$	−522.604	−0.270817
$156$	156.551	0.0803470
$157$	−1484.00	−0.754372	−0.377186	−	0.926138i	$-0.623108\pi$
$157$	−1484.00	−0.754372	−0.377186	+	0.926138i	$0.623108\pi$
$158$	383.715	0.193207
$159$	−3116.81	−1.55459
$160$	−1300.70	−0.642686
$161$	0	0
$162$	1467.26	0.711600
$163$	1554.79	0.747120	0.373560	−	0.927606i	$-0.378137\pi$
$163$	1554.79	0.747120	0.373560	+	0.927606i	$0.378137\pi$
$164$	−234.215	−0.111519
$165$	1224.71	0.577839
$166$	3497.60	1.63534
$167$	2542.66	1.17819	0.589093	−	0.808065i	$-0.299485\pi$
$167$	2542.66	1.17819	0.589093	+	0.808065i	$0.299485\pi$
$168$	0	0
$169$	−2039.85	−0.928473
$170$	−1337.18	−0.603279
$171$	431.636	0.193029
$172$	568.260	0.251915
$173$	1907.58	0.838326	0.419163	−	0.907911i	$-0.362324\pi$
$173$	1907.58	0.838326	0.419163	+	0.907911i	$0.362324\pi$
$174$	2236.04	0.974219
$175$	0	0
$176$	−2119.42	−0.907714
$177$	−395.154	−0.167805
$178$	799.305	0.336576
$179$	574.706	0.239975	0.119988	−	0.992775i	$-0.461715\pi$
$179$	574.706	0.239975	0.119988	+	0.992775i	$0.461715\pi$
$180$	243.185	0.100700
$181$	580.331	0.238319	0.119159	−	0.992875i	$-0.461980\pi$
$181$	580.331	0.238319	0.119159	+	0.992875i	$0.461980\pi$
$182$	0	0
$183$	624.141	0.252119
$184$	1513.52	0.606403
$185$	1991.10	0.791290
$186$	716.158	0.282318
$187$	−1043.50	−0.408067
$188$	134.987	0.0523668
$189$	0	0
$190$	−1839.90	−0.702530
$191$	−219.308	−0.0830816	−0.0415408	−	0.999137i	$-0.513227\pi$
$191$	−219.308	−0.0830816	−0.0415408	+	0.999137i	$0.513227\pi$
$192$	−956.165	−0.359402
$193$	−1449.47	−0.540597	−0.270299	−	0.962777i	$-0.587122\pi$
$193$	−1449.47	−0.540597	−0.270299	+	0.962777i	$0.587122\pi$
$194$	4092.85	1.51469
$195$	−570.287	−0.209431
$196$	0	0
$197$	−1216.55	−0.439978	−0.219989	−	0.975502i	$-0.570602\pi$
$197$	−1216.55	−0.439978	−0.219989	+	0.975502i	$0.570602\pi$
$198$	718.383	0.257845
$199$	660.371	0.235239	0.117619	−	0.993059i	$-0.462474\pi$
$199$	660.371	0.235239	0.117619	+	0.993059i	$0.462474\pi$
$200$	−262.721	−0.0928859
$201$	−1878.03	−0.659035
$202$	713.716	0.248598
$203$	0	0
$204$	484.072	0.166136
$205$	853.203	0.290684
$206$	1088.93	0.368296
$207$	−724.436	−0.243245
$208$	986.912	0.328991
$209$	−1435.81	−0.475202
$210$	0	0
$211$	−2972.01	−0.969675	−0.484838	−	0.874604i	$-0.661121\pi$
$211$	−2972.01	−0.969675	−0.484838	+	0.874604i	$0.661121\pi$
$212$	2058.70	0.666945
$213$	−1238.24	−0.398323
$214$	3424.47	1.09389
$215$	−2070.06	−0.656638
$216$	2580.06	0.812736
$217$	0	0
$218$	551.551	0.171357
$219$	4428.22	1.36635
$220$	−808.940	−0.247903
$221$	485.908	0.147899
$222$	−2728.53	−0.824897
$223$	586.428	0.176099	0.0880497	−	0.996116i	$-0.471937\pi$
$223$	586.428	0.176099	0.0880497	+	0.996116i	$0.471937\pi$
$224$	0	0
$225$	125.750	0.0372592
$226$	3539.21	1.04170
$227$	−3132.01	−0.915767	−0.457883	−	0.889012i	$-0.651392\pi$
$227$	−3132.01	−0.915767	−0.457883	+	0.889012i	$0.651392\pi$
$228$	666.060	0.193469
$229$	−3748.51	−1.08170	−0.540849	−	0.841120i	$-0.681897\pi$
$229$	−3748.51	−1.08170	−0.540849	+	0.841120i	$0.681897\pi$
$230$	3088.00	0.885290
$231$	0	0
$232$	2637.01	0.746242
$233$	−3044.82	−0.856105	−0.428053	−	0.903754i	$-0.640800\pi$
$233$	−3044.82	−0.856105	−0.428053	+	0.903754i	$0.640800\pi$
$234$	−334.516	−0.0934530
$235$	−491.733	−0.136498
$236$	261.005	0.0719916
$237$	506.015	0.138689
$238$	0	0
$239$	1344.43	0.363866	0.181933	−	0.983311i	$-0.441765\pi$
$239$	1344.43	0.363866	0.181933	+	0.983311i	$0.441765\pi$
$240$	−3581.55	−0.963283
$241$	−4655.35	−1.24431	−0.622153	−	0.782896i	$-0.713742\pi$
$241$	−4655.35	−1.24431	−0.622153	+	0.782896i	$0.713742\pi$
$242$	1999.02	0.531000
$243$	−2185.06	−0.576839
$244$	−412.255	−0.108164
$245$	0	0
$246$	−1169.20	−0.303030
$247$	668.588	0.172232
$248$	844.578	0.216253
$249$	4612.38	1.17389
$250$	−4848.21	−1.22651
$251$	777.995	0.195644	0.0978219	−	0.995204i	$-0.468812\pi$
$251$	777.995	0.195644	0.0978219	+	0.995204i	$0.468812\pi$
$252$	0	0
$253$	2409.79	0.598824
$254$	3628.23	0.896280
$255$	−1763.38	−0.433048
$256$	3910.95	0.954823
$257$	−2183.78	−0.530042	−0.265021	−	0.964243i	$-0.585379\pi$
$257$	−2183.78	−0.530042	−0.265021	+	0.964243i	$0.585379\pi$
$258$	2836.74	0.684526
$259$	0	0
$260$	376.684	0.0898498
$261$	−1262.19	−0.299338
$262$	3877.17	0.914246
$263$	−2487.05	−0.583111	−0.291555	−	0.956554i	$-0.594173\pi$
$263$	−2487.05	−0.583111	−0.291555	+	0.956554i	$0.594173\pi$
$264$	−1979.24	−0.461417
$265$	−7499.47	−1.73845
$266$	0	0
$267$	1054.07	0.241602
$268$	1240.47	0.282738
$269$	−3860.99	−0.875126	−0.437563	−	0.899188i	$-0.644158\pi$
$269$	−3860.99	−0.875126	−0.437563	+	0.899188i	$0.644158\pi$
$270$	5264.04	1.18652
$271$	5453.27	1.22237	0.611185	−	0.791488i	$-0.290693\pi$
$271$	5453.27	1.22237	0.611185	+	0.791488i	$0.290693\pi$
$272$	3051.63	0.680265
$273$	0	0
$274$	4526.07	0.997918
$275$	−418.299	−0.0917250
$276$	−1117.88	−0.243799
$277$	4411.32	0.956861	0.478430	−	0.878125i	$-0.341206\pi$
$277$	4411.32	0.956861	0.478430	+	0.878125i	$0.341206\pi$
$278$	−6712.10	−1.44808
$279$	−404.251	−0.0867451
$280$	0	0
$281$	−4272.09	−0.906944	−0.453472	−	0.891270i	$-0.649815\pi$
$281$	−4272.09	−0.906944	−0.453472	+	0.891270i	$0.649815\pi$
$282$	673.853	0.142296
$283$	1483.54	0.311616	0.155808	−	0.987787i	$-0.450202\pi$
$283$	1483.54	0.311616	0.155808	+	0.987787i	$0.450202\pi$
$284$	817.878	0.170888
$285$	−2426.33	−0.504293
$286$	1112.75	0.230063
$287$	0	0
$288$	−1006.14	−0.205858
$289$	−3410.53	−0.694184
$290$	5380.23	1.08944
$291$	5397.35	1.08728
$292$	−2924.91	−0.586190
$293$	3216.25	0.641281	0.320641	−	0.947201i	$-0.396102\pi$
$293$	3216.25	0.641281	0.320641	+	0.947201i	$0.396102\pi$
$294$	0	0
$295$	−950.794	−0.187652
$296$	−3217.81	−0.631863
$297$	4107.92	0.802578
$298$	8277.56	1.60908
$299$	−1122.12	−0.217037
$300$	194.045	0.0373440
$301$	0	0
$302$	−12128.0	−2.31090
$303$	941.197	0.178450
$304$	4198.90	0.792183
$305$	1501.77	0.281938
$306$	−1034.36	−0.193236
$307$	6136.32	1.14078	0.570388	−	0.821376i	$-0.306793\pi$
$307$	6136.32	1.14078	0.570388	+	0.821376i	$0.306793\pi$
$308$	0	0
$309$	1436.00	0.264372
$310$	1723.17	0.315709
$311$	7906.25	1.44155	0.720776	−	0.693169i	$-0.243786\pi$
$311$	7906.25	1.44155	0.720776	+	0.693169i	$0.243786\pi$
$312$	921.637	0.167235
$313$	8828.69	1.59434	0.797168	−	0.603757i	$-0.206330\pi$
$313$	8828.69	1.59434	0.797168	+	0.603757i	$0.206330\pi$
$314$	4893.18	0.879420
$315$	0	0
$316$	−334.231	−0.0595000
$317$	−1229.10	−0.217770	−0.108885	−	0.994054i	$-0.534728\pi$
$317$	−1229.10	−0.217770	−0.108885	+	0.994054i	$0.534728\pi$
$318$	10277.0	1.81228
$319$	4198.59	0.736914
$320$	−2300.66	−0.401910
$321$	4515.94	0.785219
$322$	0	0
$323$	2067.34	0.356129
$324$	−1278.05	−0.219144
$325$	194.781	0.0332447
$326$	−5126.58	−0.870967
$327$	727.346	0.123004
$328$	−1378.86	−0.232118
$329$	0	0
$330$	−4038.21	−0.673625
$331$	−4658.04	−0.773501	−0.386751	−	0.922184i	$-0.626403\pi$
$331$	−4658.04	−0.773501	−0.386751	+	0.922184i	$0.626403\pi$
$332$	−3046.55	−0.503618
$333$	1540.18	0.253458
$334$	−8383.87	−1.37349
$335$	−4518.80	−0.736980
$336$	0	0
$337$	−10221.0	−1.65215	−0.826075	−	0.563561i	$-0.809431\pi$
$337$	−10221.0	−1.65215	−0.826075	+	0.563561i	$0.809431\pi$
$338$	6725.98	1.08238
$339$	4667.25	0.747760
$340$	1164.74	0.185785
$341$	1344.72	0.213550
$342$	−1423.23	−0.225027
$343$	0	0
$344$	3345.42	0.524340
$345$	4072.23	0.635483
$346$	−6289.82	−0.977292
$347$	3737.15	0.578158	0.289079	−	0.957305i	$-0.406651\pi$
$347$	3737.15	0.578158	0.289079	+	0.957305i	$0.406651\pi$
$348$	−1947.69	−0.300020
$349$	1421.34	0.218002	0.109001	−	0.994042i	$-0.465235\pi$
$349$	1421.34	0.218002	0.109001	+	0.994042i	$0.465235\pi$
$350$	0	0
$351$	−1912.86	−0.290885
$352$	3346.86	0.506784
$353$	3287.96	0.495752	0.247876	−	0.968792i	$-0.420267\pi$
$353$	3287.96	0.495752	0.247876	+	0.968792i	$0.420267\pi$
$354$	1302.93	0.195622
$355$	−2979.37	−0.445433
$356$	−696.228	−0.103652
$357$	0	0
$358$	−1894.97	−0.279755
$359$	3133.84	0.460718	0.230359	−	0.973106i	$-0.426010\pi$
$359$	3133.84	0.460718	0.230359	+	0.973106i	$0.426010\pi$
$360$	1431.66	0.209598
$361$	−4014.44	−0.585280
$362$	−1913.52	−0.277824
$363$	2636.17	0.381165
$364$	0	0
$365$	10654.9	1.52795
$366$	−2057.97	−0.293912
$367$	1346.55	0.191525	0.0957623	−	0.995404i	$-0.469471\pi$
$367$	1346.55	0.191525	0.0957623	+	0.995404i	$0.469471\pi$
$368$	−7047.22	−0.998265
$369$	659.980	0.0931089
$370$	−6565.22	−0.922459
$371$	0	0
$372$	−623.803	−0.0869427
$373$	−2604.00	−0.361474	−0.180737	−	0.983531i	$-0.557848\pi$
$373$	−2604.00	−0.361474	−0.180737	+	0.983531i	$0.557848\pi$
$374$	3440.72	0.475710
$375$	−6393.47	−0.880420
$376$	794.687	0.108997
$377$	−1955.08	−0.267086
$378$	0	0
$379$	13910.2	1.88527	0.942635	−	0.333825i	$-0.108339\pi$
$379$	13910.2	1.88527	0.942635	+	0.333825i	$0.108339\pi$
$380$	1602.63	0.216351
$381$	4784.64	0.643372
$382$	723.121	0.0968537
$383$	8548.15	1.14044	0.570222	−	0.821491i	$-0.306857\pi$
$383$	8548.15	1.14044	0.570222	+	0.821491i	$0.306857\pi$
$384$	7477.37	0.993693
$385$	0	0
$386$	4779.32	0.630209
$387$	−1601.26	−0.210327
$388$	−3565.04	−0.466462
$389$	2347.69	0.305996	0.152998	−	0.988227i	$-0.451107\pi$
$389$	2347.69	0.305996	0.152998	+	0.988227i	$0.451107\pi$
$390$	1880.40	0.244148
$391$	−3469.71	−0.448775
$392$	0	0
$393$	5112.93	0.656268
$394$	4011.32	0.512912
$395$	1217.54	0.155092
$396$	−625.741	−0.0794058
$397$	−551.018	−0.0696594	−0.0348297	−	0.999393i	$-0.511089\pi$
$397$	−551.018	−0.0696594	−0.0348297	+	0.999393i	$0.511089\pi$
$398$	−2177.43	−0.274233
$399$	0	0
$400$	1223.28	0.152910
$401$	−5115.45	−0.637041	−0.318520	−	0.947916i	$-0.603186\pi$
$401$	−5115.45	−0.637041	−0.318520	+	0.947916i	$0.603186\pi$
$402$	6192.39	0.768280
$403$	−626.169	−0.0773988
$404$	−621.676	−0.0765583
$405$	4655.69	0.571217
$406$	0	0
$407$	−5123.32	−0.623965
$408$	2849.79	0.345798
$409$	6336.62	0.766078	0.383039	−	0.923732i	$-0.374877\pi$
$409$	6336.62	0.766078	0.383039	+	0.923732i	$0.374877\pi$
$410$	−2813.25	−0.338870
$411$	5968.65	0.716330
$412$	−948.499	−0.113420
$413$	0	0
$414$	2388.67	0.283567
$415$	11098.0	1.31272
$416$	−1558.47	−0.183678
$417$	−8851.43	−1.03946
$418$	4734.28	0.553974
$419$	−10494.5	−1.22361	−0.611803	−	0.791010i	$-0.709556\pi$
$419$	−10494.5	−1.22361	−0.611803	+	0.791010i	$0.709556\pi$
$420$	0	0
$421$	5517.60	0.638744	0.319372	−	0.947629i	$-0.396528\pi$
$421$	5517.60	0.638744	0.319372	+	0.947629i	$0.396528\pi$
$422$	9799.55	1.13041
$423$	−380.372	−0.0437217
$424$	12119.9	1.38819
$425$	602.283	0.0687412
$426$	4082.83	0.464351
$427$	0	0
$428$	−2982.85	−0.336873
$429$	1467.41	0.165145
$430$	6825.59	0.765486
$431$	−15848.7	−1.77124	−0.885622	−	0.464407i	$-0.846268\pi$
$431$	−15848.7	−1.77124	−0.885622	+	0.464407i	$0.846268\pi$
$432$	−12013.2	−1.33793
$433$	1118.53	0.124141	0.0620707	−	0.998072i	$-0.480230\pi$
$433$	1118.53	0.124141	0.0620707	+	0.998072i	$0.480230\pi$
$434$	0	0
$435$	7095.06	0.782027
$436$	−480.424	−0.0527710
$437$	−4774.16	−0.522607
$438$	−14601.1	−1.59285
$439$	2985.00	0.324524	0.162262	−	0.986748i	$-0.448121\pi$
$439$	2985.00	0.324524	0.162262	+	0.986748i	$0.448121\pi$
$440$	−4762.33	−0.515989
$441$	0	0
$442$	−1602.18	−0.172416
$443$	9797.82	1.05081	0.525405	−	0.850852i	$-0.323914\pi$
$443$	9797.82	1.05081	0.525405	+	0.850852i	$0.323914\pi$
$444$	2376.66	0.254035
$445$	2536.23	0.270177
$446$	−1933.62	−0.205290
$447$	10915.8	1.15504
$448$	0	0
$449$	1316.77	0.138401	0.0692006	−	0.997603i	$-0.477955\pi$
$449$	1316.77	0.138401	0.0692006	+	0.997603i	$0.477955\pi$
$450$	−414.632	−0.0434354
$451$	−2195.38	−0.229216
$452$	−3082.80	−0.320802
$453$	−15993.6	−1.65882
$454$	10327.1	1.06757
$455$	0	0
$456$	3921.18	0.402689
$457$	5964.54	0.610524	0.305262	−	0.952268i	$-0.401256\pi$
$457$	5964.54	0.610524	0.305262	+	0.952268i	$0.401256\pi$
$458$	12359.9	1.26100
$459$	−5914.74	−0.601473
$460$	−2689.78	−0.272634
$461$	2460.33	0.248566	0.124283	−	0.992247i	$-0.460337\pi$
$461$	2460.33	0.248566	0.124283	+	0.992247i	$0.460337\pi$
$462$	0	0
$463$	5509.22	0.552992	0.276496	−	0.961015i	$-0.410827\pi$
$463$	5509.22	0.552992	0.276496	+	0.961015i	$0.410827\pi$
$464$	−12278.4	−1.22847
$465$	2272.40	0.226623
$466$	10039.6	0.998018
$467$	7203.57	0.713794	0.356897	−	0.934144i	$-0.383835\pi$
$467$	7203.57	0.713794	0.356897	+	0.934144i	$0.383835\pi$
$468$	291.377	0.0287797
$469$	0	0
$470$	1621.38	0.159125
$471$	6452.77	0.631269
$472$	1536.57	0.149844
$473$	5326.50	0.517786
$474$	−1668.48	−0.161678
$475$	828.713	0.0800505
$476$	0	0
$477$	−5801.08	−0.556842
$478$	−4432.96	−0.424182
$479$	−18101.6	−1.72669	−0.863344	−	0.504616i	$-0.831634\pi$
$479$	−18101.6	−1.72669	−0.863344	+	0.504616i	$0.831634\pi$
$480$	5655.75	0.537809
$481$	2385.68	0.226149
$482$	15350.0	1.45057
$483$	0	0
$484$	−1741.23	−0.163527
$485$	12986.8	1.21587
$486$	7204.77	0.672459
$487$	19716.9	1.83462	0.917310	−	0.398173i	$-0.130356\pi$
$487$	19716.9	1.83462	0.917310	+	0.398173i	$0.130356\pi$
$488$	−2427.00	−0.225133
$489$	−6760.57	−0.625201
$490$	0	0
$491$	9031.19	0.830085	0.415043	−	0.909802i	$-0.363767\pi$
$491$	9031.19	0.830085	0.415043	+	0.909802i	$0.363767\pi$
$492$	1018.42	0.0933209
$493$	−6045.28	−0.552264
$494$	−2204.52	−0.200782
$495$	2279.46	0.206978
$496$	−3932.50	−0.355997
$497$	0	0
$498$	−15208.3	−1.36848
$499$	−4997.41	−0.448327	−0.224163	−	0.974552i	$-0.571965\pi$
$499$	−4997.41	−0.448327	−0.224163	+	0.974552i	$0.571965\pi$
$500$	4222.99	0.377716
$501$	−11056.0	−0.985924
$502$	−2565.27	−0.228075
$503$	9925.08	0.879796	0.439898	−	0.898048i	$-0.355015\pi$
$503$	9925.08	0.879796	0.439898	+	0.898048i	$0.355015\pi$
$504$	0	0
$505$	2264.65	0.199556
$506$	−7945.77	−0.698088
$507$	8869.73	0.776960
$508$	−3160.33	−0.276018
$509$	1605.73	0.139829	0.0699143	−	0.997553i	$-0.477727\pi$
$509$	1605.73	0.139829	0.0699143	+	0.997553i	$0.477727\pi$
$510$	5814.37	0.504832
$511$	0	0
$512$	861.605	0.0743710
$513$	−8138.41	−0.700428
$514$	7200.55	0.617904
$515$	3455.20	0.295640
$516$	−2470.92	−0.210806
$517$	1265.28	0.107635
$518$	0	0
$519$	−8294.56	−0.701524
$520$	2217.59	0.187015
$521$	−20817.6	−1.75055	−0.875275	−	0.483625i	$-0.839320\pi$
$521$	−20817.6	−1.75055	−0.875275	+	0.483625i	$0.839320\pi$
$522$	4161.78	0.348958
$523$	3951.34	0.330363	0.165182	−	0.986263i	$-0.447179\pi$
$523$	3951.34	0.330363	0.165182	+	0.986263i	$0.447179\pi$
$524$	−3377.18	−0.281551
$525$	0	0
$526$	8200.51	0.679770
$527$	−1936.18	−0.160040
$528$	9215.72	0.759588
$529$	−4154.29	−0.341439
$530$	24727.9	2.02662
$531$	−735.470	−0.0601067
$532$	0	0
$533$	1022.28	0.0830769
$534$	−3475.55	−0.281651
$535$	10866.0	0.878088
$536$	7302.80	0.588495
$537$	−2498.95	−0.200815
$538$	12730.8	1.02019
$539$	0	0
$540$	−4585.20	−0.365399
$541$	14829.6	1.17851	0.589257	−	0.807946i	$-0.299421\pi$
$541$	14829.6	1.17851	0.589257	+	0.807946i	$0.299421\pi$
$542$	−17981.0	−1.42500
$543$	−2523.41	−0.199429
$544$	−4818.93	−0.379798
$545$	1750.09	0.137552
$546$	0	0
$547$	−1553.95	−0.121466	−0.0607331	−	0.998154i	$-0.519344\pi$
$547$	−1553.95	−0.121466	−0.0607331	+	0.998154i	$0.519344\pi$
$548$	−3942.39	−0.307318
$549$	1161.67	0.0903073
$550$	1379.25	0.106930
$551$	−8318.04	−0.643122
$552$	−6581.11	−0.507447
$553$	0	0
$554$	−14545.4	−1.11548
$555$	−8657.74	−0.662163
$556$	5846.51	0.445949
$557$	2570.55	0.195544	0.0977718	−	0.995209i	$-0.468828\pi$
$557$	2570.55	0.195544	0.0977718	+	0.995209i	$0.468828\pi$
$558$	1332.93	0.101124
$559$	−2480.29	−0.187666
$560$	0	0
$561$	4537.38	0.341476
$562$	14086.3	1.05728
$563$	2614.22	0.195695	0.0978476	−	0.995201i	$-0.468804\pi$
$563$	2614.22	0.195695	0.0978476	+	0.995201i	$0.468804\pi$
$564$	−586.954	−0.0438213
$565$	11230.1	0.836198
$566$	−4891.64	−0.363271
$567$	0	0
$568$	4814.95	0.355688
$569$	21599.4	1.59138	0.795688	−	0.605707i	$-0.207110\pi$
$569$	21599.4	1.59138	0.795688	+	0.605707i	$0.207110\pi$
$570$	8000.30	0.587888
$571$	6114.50	0.448133	0.224067	−	0.974574i	$-0.428067\pi$
$571$	6114.50	0.448133	0.224067	+	0.974574i	$0.428067\pi$
$572$	−969.249	−0.0708502
$573$	953.600	0.0695239
$574$	0	0
$575$	−1390.87	−0.100875
$576$	−1779.64	−0.128735
$577$	17937.2	1.29417	0.647085	−	0.762418i	$-0.275988\pi$
$577$	17937.2	1.29417	0.647085	+	0.762418i	$0.275988\pi$
$578$	11245.5	0.809255
$579$	6302.62	0.452380
$580$	−4686.40	−0.335504
$581$	0	0
$582$	−17796.6	−1.26751
$583$	19297.0	1.37084
$584$	−17219.3	−1.22010
$585$	−1061.43	−0.0750168
$586$	−10604.9	−0.747583
$587$	−18428.1	−1.29576	−0.647880	−	0.761743i	$-0.724344\pi$
$587$	−18428.1	−1.29576	−0.647880	+	0.761743i	$0.724344\pi$
$588$	0	0
$589$	−2664.09	−0.186370
$590$	3135.04	0.218758
$591$	5289.83	0.368180
$592$	14982.7	1.04018
$593$	24771.5	1.71542	0.857711	−	0.514132i	$-0.171886\pi$
$593$	24771.5	1.71542	0.857711	+	0.514132i	$0.171886\pi$
$594$	−13545.0	−0.935617
$595$	0	0
$596$	−7210.10	−0.495532
$597$	−2871.44	−0.196851
$598$	3699.96	0.253014
$599$	−2379.64	−0.162320	−0.0811600	−	0.996701i	$-0.525862\pi$
$599$	−2379.64	−0.162320	−0.0811600	+	0.996701i	$0.525862\pi$
$600$	1142.37	0.0777283
$601$	18573.5	1.26062	0.630308	−	0.776346i	$-0.282929\pi$
$601$	18573.5	1.26062	0.630308	+	0.776346i	$0.282929\pi$
$602$	0	0
$603$	−3495.44	−0.236062
$604$	10564.0	0.711663
$605$	6342.98	0.426246
$606$	−3103.39	−0.208031
$607$	14727.7	0.984805	0.492403	−	0.870367i	$-0.336119\pi$
$607$	14727.7	0.984805	0.492403	+	0.870367i	$0.336119\pi$
$608$	−6630.63	−0.442282
$609$	0	0
$610$	−4951.75	−0.328673
$611$	−589.181	−0.0390110
$612$	900.966	0.0595088
$613$	−8473.86	−0.558330	−0.279165	−	0.960243i	$-0.590058\pi$
$613$	−8473.86	−0.558330	−0.279165	+	0.960243i	$0.590058\pi$
$614$	−20233.2	−1.32988
$615$	−3709.91	−0.243249
$616$	0	0
$617$	−26608.6	−1.73618	−0.868088	−	0.496410i	$-0.834651\pi$
$617$	−26608.6	−1.73618	−0.868088	+	0.496410i	$0.834651\pi$
$618$	−4734.88	−0.308196
$619$	−19807.6	−1.28616	−0.643081	−	0.765798i	$-0.722344\pi$
$619$	−19807.6	−1.28616	−0.643081	+	0.765798i	$0.722344\pi$
$620$	−1500.96	−0.0972255
$621$	13659.1	0.882641
$622$	−26069.1	−1.68051
$623$	0	0
$624$	−4291.31	−0.275304
$625$	−13441.3	−0.860244
$626$	−29110.7	−1.85862
$627$	6243.22	0.397656
$628$	−4262.16	−0.270826
$629$	7376.76	0.467616
$630$	0	0
$631$	5744.96	0.362446	0.181223	−	0.983442i	$-0.441994\pi$
$631$	5744.96	0.362446	0.181223	+	0.983442i	$0.441994\pi$
$632$	−1967.66	−0.123844
$633$	12922.9	0.811439
$634$	4052.69	0.253869
$635$	11512.5	0.719464
$636$	−8951.69	−0.558110
$637$	0	0
$638$	−13843.9	−0.859069
$639$	−2304.64	−0.142676
$640$	17991.6	1.11122
$641$	−3078.97	−0.189722	−0.0948612	−	0.995491i	$-0.530241\pi$
$641$	−3078.97	−0.189722	−0.0948612	+	0.995491i	$0.530241\pi$
$642$	−14890.3	−0.915381
$643$	7185.80	0.440716	0.220358	−	0.975419i	$-0.429277\pi$
$643$	7185.80	0.440716	0.220358	+	0.975419i	$0.429277\pi$
$644$	0	0
$645$	9001.09	0.549484
$646$	−6816.59	−0.415163
$647$	−7400.94	−0.449708	−0.224854	−	0.974393i	$-0.572190\pi$
$647$	−7400.94	−0.449708	−0.224854	+	0.974393i	$0.572190\pi$
$648$	−7524.03	−0.456129
$649$	2446.50	0.147971
$650$	−642.249	−0.0387555
$651$	0	0
$652$	4465.47	0.268223
$653$	−8237.98	−0.493686	−0.246843	−	0.969055i	$-0.579393\pi$
$653$	−8237.98	−0.493686	−0.246843	+	0.969055i	$0.579393\pi$
$654$	−2398.27	−0.143394
$655$	12302.4	0.733886
$656$	6420.20	0.382114
$657$	8241.91	0.489418
$658$	0	0
$659$	27054.8	1.59925	0.799625	−	0.600500i	$-0.205032\pi$
$659$	27054.8	1.59925	0.799625	+	0.600500i	$0.205032\pi$
$660$	3517.45	0.207449
$661$	−13360.3	−0.786165	−0.393083	−	0.919503i	$-0.628591\pi$
$661$	−13360.3	−0.786165	−0.393083	+	0.919503i	$0.628591\pi$
$662$	15358.9	0.901721
$663$	−2112.83	−0.123764
$664$	−17935.4	−1.04824
$665$	0	0
$666$	−5078.41	−0.295472
$667$	13960.6	0.810427
$668$	7302.70	0.422979
$669$	−2549.92	−0.147363
$670$	14899.8	0.859146
$671$	−3864.21	−0.222319
$672$	0	0
$673$	−25983.8	−1.48827	−0.744133	−	0.668032i	$-0.767137\pi$
$673$	−25983.8	−1.48827	−0.744133	+	0.668032i	$0.767137\pi$
$674$	33701.6	1.92602
$675$	−2370.98	−0.135199
$676$	−5858.60	−0.333330
$677$	12596.7	0.715110	0.357555	−	0.933892i	$-0.383610\pi$
$677$	12596.7	0.715110	0.357555	+	0.933892i	$0.383610\pi$
$678$	−15389.3	−0.871712
$679$	0	0
$680$	6856.99	0.386696
$681$	13618.7	0.766327
$682$	−4433.91	−0.248949
$683$	−9931.03	−0.556369	−0.278185	−	0.960528i	$-0.589733\pi$
$683$	−9931.03	−0.556369	−0.278185	+	0.960528i	$0.589733\pi$
$684$	1239.69	0.0692992
$685$	14361.4	0.801051
$686$	0	0
$687$	16299.3	0.905180
$688$	−15576.9	−0.863172
$689$	−8985.65	−0.496845
$690$	−13427.3	−0.740824
$691$	−23896.1	−1.31556	−0.657778	−	0.753212i	$-0.728503\pi$
$691$	−23896.1	−1.31556	−0.657778	+	0.753212i	$0.728503\pi$
$692$	5478.69	0.300966
$693$	0	0
$694$	−12322.4	−0.673997
$695$	−21297.8	−1.16240
$696$	−11466.3	−0.624466
$697$	3161.00	0.171781
$698$	−4686.57	−0.254139
$699$	13239.5	0.716401
$700$	0	0
$701$	−8701.49	−0.468832	−0.234416	−	0.972136i	$-0.575318\pi$
$701$	−8701.49	−0.468832	−0.234416	+	0.972136i	$0.575318\pi$
$702$	6307.23	0.339104
$703$	10150.1	0.544548
$704$	5919.86	0.316922
$705$	2138.16	0.114224
$706$	−10841.3	−0.577931
$707$	0	0
$708$	−1134.91	−0.0602436
$709$	29153.8	1.54428	0.772140	−	0.635452i	$-0.219186\pi$
$709$	29153.8	1.54428	0.772140	+	0.635452i	$0.219186\pi$
$710$	9823.84	0.519271
$711$	941.808	0.0496773
$712$	−4098.78	−0.215742
$713$	4471.27	0.234853
$714$	0	0
$715$	3530.79	0.184677
$716$	1650.60	0.0861532
$717$	−5845.87	−0.304488
$718$	−10333.2	−0.537089
$719$	−4722.15	−0.244933	−0.122466	−	0.992473i	$-0.539080\pi$
$719$	−4722.15	−0.244933	−0.122466	+	0.992473i	$0.539080\pi$
$720$	−6666.07	−0.345041
$721$	0	0
$722$	13236.7	0.682300
$723$	20242.5	1.04125
$724$	1666.75	0.0855585
$725$	−2423.31	−0.124137
$726$	−8692.19	−0.444349
$727$	−28254.6	−1.44141	−0.720704	−	0.693243i	$-0.756181\pi$
$727$	−28254.6	−1.44141	−0.720704	+	0.693243i	$0.756181\pi$
$728$	0	0
$729$	21515.9	1.09312
$730$	−35132.2	−1.78124
$731$	−7669.30	−0.388043
$732$	1792.57	0.0905129
$733$	28572.7	1.43978	0.719889	−	0.694090i	$-0.244193\pi$
$733$	28572.7	1.43978	0.719889	+	0.694090i	$0.244193\pi$
$734$	−4439.97	−0.223273
$735$	0	0
$736$	11128.5	0.557340
$737$	11627.4	0.581139
$738$	−2176.14	−0.108543
$739$	10742.7	0.534747	0.267374	−	0.963593i	$-0.413844\pi$
$739$	10742.7	0.534747	0.267374	+	0.963593i	$0.413844\pi$
$740$	5718.58	0.284080
$741$	−2907.16	−0.144126
$742$	0	0
$743$	9474.33	0.467806	0.233903	−	0.972260i	$-0.424850\pi$
$743$	9474.33	0.467806	0.233903	+	0.972260i	$0.424850\pi$
$744$	−3672.41	−0.180964
$745$	26265.0	1.29165
$746$	8586.11	0.421394
$747$	8584.68	0.420478
$748$	−2997.01	−0.146499
$749$	0	0
$750$	21081.1	1.02636
$751$	−8327.26	−0.404615	−0.202308	−	0.979322i	$-0.564844\pi$
$751$	−8327.26	−0.404615	−0.202308	+	0.979322i	$0.564844\pi$
$752$	−3700.21	−0.179432
$753$	−3382.89	−0.163718
$754$	6446.44	0.311360
$755$	−38482.8	−1.85501
$756$	0	0
$757$	−22448.3	−1.07780	−0.538902	−	0.842368i	$-0.681161\pi$
$757$	−22448.3	−1.07780	−0.538902	+	0.842368i	$0.681161\pi$
$758$	−45865.8	−2.19778
$759$	−10478.3	−0.501104
$760$	9434.91	0.450316
$761$	14903.9	0.709942	0.354971	−	0.934877i	$-0.384491\pi$
$761$	14903.9	0.709942	0.354971	+	0.934877i	$0.384491\pi$
$762$	−15776.3	−0.750020
$763$	0	0
$764$	−629.869	−0.0298270
$765$	−3282.05	−0.155115
$766$	−28185.7	−1.32949
$767$	−1139.21	−0.0536306
$768$	−17005.7	−0.799010
$769$	−9384.83	−0.440085	−0.220043	−	0.975490i	$-0.570620\pi$
$769$	−9384.83	−0.440085	−0.220043	+	0.975490i	$0.570620\pi$
$770$	0	0
$771$	9495.57	0.443547
$772$	−4162.98	−0.194079
$773$	−1077.26	−0.0501248	−0.0250624	−	0.999686i	$-0.507978\pi$
$773$	−1077.26	−0.0501248	−0.0250624	+	0.999686i	$0.507978\pi$
$774$	5279.81	0.245192
$775$	−776.136	−0.0359737
$776$	−20987.8	−0.970901
$777$	0	0
$778$	−7740.98	−0.356719
$779$	4349.39	0.200042
$780$	−1637.90	−0.0751876
$781$	7666.26	0.351242
$782$	11440.6	0.523166
$783$	23798.2	1.08618
$784$	0	0
$785$	15526.2	0.705931
$786$	−16858.8	−0.765054
$787$	36579.2	1.65681	0.828405	−	0.560130i	$-0.189249\pi$
$787$	36579.2	1.65681	0.828405	+	0.560130i	$0.189249\pi$
$788$	−3494.02	−0.157956
$789$	10814.2	0.487956
$790$	−4014.58	−0.180800
$791$	0	0
$792$	−3683.82	−0.165276
$793$	1799.38	0.0805772
$794$	1816.86	0.0812065
$795$	32609.3	1.45476
$796$	1896.63	0.0844527
$797$	2238.71	0.0994973	0.0497487	−	0.998762i	$-0.484158\pi$
$797$	2238.71	0.0994973	0.0497487	+	0.998762i	$0.484158\pi$
$798$	0	0
$799$	−1821.80	−0.0806643
$800$	−1931.72	−0.0853707
$801$	1961.85	0.0865402
$802$	16867.1	0.742640
$803$	−27416.2	−1.20485
$804$	−5393.83	−0.236599
$805$	0	0
$806$	2064.66	0.0902288
$807$	16788.4	0.732319
$808$	−3659.89	−0.159349
$809$	−22879.8	−0.994329	−0.497165	−	0.867656i	$-0.665626\pi$
$809$	−22879.8	−0.994329	−0.497165	+	0.867656i	$0.665626\pi$
$810$	−15351.1	−0.665905
$811$	−33441.6	−1.44796	−0.723979	−	0.689822i	$-0.757689\pi$
$811$	−33441.6	−1.44796	−0.723979	+	0.689822i	$0.757689\pi$
$812$	0	0
$813$	−23712.0	−1.02290
$814$	16893.0	0.727397
$815$	−16266.9	−0.699145
$816$	−13269.1	−0.569256
$817$	−10552.6	−0.451884
$818$	−20893.6	−0.893067
$819$	0	0
$820$	2450.46	0.104358
$821$	−13048.2	−0.554671	−0.277336	−	0.960773i	$-0.589451\pi$
$821$	−13048.2	−0.554671	−0.277336	+	0.960773i	$0.589451\pi$
$822$	−19680.3	−0.835073
$823$	−15998.1	−0.677593	−0.338797	−	0.940860i	$-0.610020\pi$
$823$	−15998.1	−0.677593	−0.338797	+	0.940860i	$0.610020\pi$
$824$	−5583.93	−0.236075
$825$	1818.85	0.0767568
$826$	0	0
$827$	25626.2	1.07752	0.538761	−	0.842459i	$-0.318893\pi$
$827$	25626.2	1.07752	0.538761	+	0.842459i	$0.318893\pi$
$828$	−2080.63	−0.0873271
$829$	−18680.5	−0.782630	−0.391315	−	0.920257i	$-0.627980\pi$
$829$	−18680.5	−0.782630	−0.391315	+	0.920257i	$0.627980\pi$
$830$	−36593.3	−1.53033
$831$	−19181.4	−0.800715
$832$	−2756.59	−0.114865
$833$	0	0
$834$	29185.7	1.21177
$835$	−26602.4	−1.10253
$836$	−4123.75	−0.170602
$837$	7622.07	0.314764
$838$	34603.4	1.42644
$839$	30840.9	1.26907	0.634534	−	0.772895i	$-0.281192\pi$
$839$	30840.9	1.26907	0.634534	+	0.772895i	$0.281192\pi$
$840$	0	0
$841$	−65.4922	−0.00268532
$842$	−18193.1	−0.744626
$843$	18576.0	0.758944
$844$	−8535.81	−0.348122
$845$	21341.8	0.868852
$846$	1254.19	0.0509693
$847$	0	0
$848$	−56432.2	−2.28525
$849$	−6450.75	−0.260765
$850$	−1985.90	−0.0801361
$851$	−17035.4	−0.686210
$852$	−3556.31	−0.143001
$853$	32950.2	1.32262	0.661309	−	0.750114i	$-0.270001\pi$
$853$	32950.2	1.32262	0.661309	+	0.750114i	$0.270001\pi$
$854$	0	0
$855$	−4515.95	−0.180634
$856$	−17560.4	−0.701172
$857$	−26728.6	−1.06538	−0.532691	−	0.846310i	$-0.678819\pi$
$857$	−26728.6	−1.06538	−0.532691	+	0.846310i	$0.678819\pi$
$858$	−4838.47	−0.192520
$859$	16190.4	0.643085	0.321543	−	0.946895i	$-0.395799\pi$
$859$	16190.4	0.643085	0.321543	+	0.946895i	$0.395799\pi$
$860$	−5945.37	−0.235739
$861$	0	0
$862$	52257.7	2.06485
$863$	13793.1	0.544059	0.272029	−	0.962289i	$-0.412305\pi$
$863$	13793.1	0.544059	0.272029	+	0.962289i	$0.412305\pi$
$864$	18970.5	0.746979
$865$	−19957.9	−0.784494
$866$	−3688.11	−0.144720
$867$	14829.7	0.580903
$868$	0	0
$869$	−3132.87	−0.122296
$870$	−23394.4	−0.911660
$871$	−5414.30	−0.210627
$872$	−2828.32	−0.109838
$873$	10045.7	0.389456
$874$	15741.8	0.609237
$875$	0	0
$876$	12718.1	0.490532
$877$	−12065.7	−0.464571	−0.232285	−	0.972648i	$-0.574620\pi$
$877$	−12065.7	−0.464571	−0.232285	+	0.972648i	$0.574620\pi$
$878$	−9842.38	−0.378319
$879$	−13985.0	−0.536633
$880$	22174.3	0.849426
$881$	7139.80	0.273038	0.136519	−	0.990637i	$-0.456409\pi$
$881$	7139.80	0.273038	0.136519	+	0.990637i	$0.456409\pi$
$882$	0	0
$883$	24731.9	0.942575	0.471287	−	0.881980i	$-0.343790\pi$
$883$	24731.9	0.942575	0.471287	+	0.881980i	$0.343790\pi$
$884$	1395.56	0.0530971
$885$	4134.26	0.157030
$886$	−32306.2	−1.22500
$887$	10626.5	0.402259	0.201130	−	0.979565i	$-0.435539\pi$
$887$	10626.5	0.402259	0.201130	+	0.979565i	$0.435539\pi$
$888$	13991.7	0.528752
$889$	0	0
$890$	−8362.66	−0.314963
$891$	−11979.6	−0.450428
$892$	1684.26	0.0632212
$893$	−2506.72	−0.0939352
$894$	−35992.6	−1.34650
$895$	−6012.81	−0.224565
$896$	0	0
$897$	4879.23	0.181620
$898$	−4341.76	−0.161343
$899$	7790.30	0.289011
$900$	361.162	0.0133764
$901$	−27784.5	−1.02734
$902$	7238.80	0.267213
$903$	0	0
$904$	−18148.8	−0.667722
$905$	−6071.66	−0.223015
$906$	52735.4	1.93379
$907$	19584.3	0.716965	0.358482	−	0.933537i	$-0.383294\pi$
$907$	19584.3	0.716965	0.358482	+	0.933537i	$0.383294\pi$
$908$	−8995.36	−0.328768
$909$	1751.78	0.0639195
$910$	0	0
$911$	31269.7	1.13722	0.568611	−	0.822606i	$-0.307481\pi$
$911$	31269.7	1.13722	0.568611	+	0.822606i	$0.307481\pi$
$912$	−18257.7	−0.662910
$913$	−28556.4	−1.03514
$914$	−19666.8	−0.711728
$915$	−6530.01	−0.235930
$916$	−10766.0	−0.388339
$917$	0	0
$918$	19502.6	0.701177
$919$	43505.4	1.56160	0.780801	−	0.624780i	$-0.214811\pi$
$919$	43505.4	1.56160	0.780801	+	0.624780i	$0.214811\pi$
$920$	−15835.1	−0.567463
$921$	−26682.0	−0.954618
$922$	−8112.40	−0.289770
$923$	−3569.80	−0.127304
$924$	0	0
$925$	2957.05	0.105110
$926$	−18165.5	−0.644659
$927$	2672.71	0.0946962
$928$	19389.2	0.685865
$929$	33060.8	1.16759	0.583794	−	0.811902i	$-0.301568\pi$
$929$	33060.8	1.16759	0.583794	+	0.811902i	$0.301568\pi$
$930$	−7492.73	−0.264190
$931$	0	0
$932$	−8744.92	−0.307349
$933$	−34378.1	−1.20631
$934$	−23752.2	−0.832116
$935$	10917.5	0.381863
$936$	1715.37	0.0599025
$937$	3664.88	0.127776	0.0638882	−	0.997957i	$-0.479650\pi$
$937$	3664.88	0.127776	0.0638882	+	0.997957i	$0.479650\pi$
$938$	0	0
$939$	−38389.1	−1.33416
$940$	−1412.29	−0.0490041
$941$	−14469.8	−0.501278	−0.250639	−	0.968081i	$-0.580641\pi$
$941$	−14469.8	−0.501278	−0.250639	+	0.968081i	$0.580641\pi$
$942$	−21276.6	−0.735912
$943$	−7299.79	−0.252083
$944$	−7154.56	−0.246675
$945$	0	0
$946$	−17563.0	−0.603617
$947$	−45212.2	−1.55142	−0.775712	−	0.631088i	$-0.782609\pi$
$947$	−45212.2	−1.55142	−0.775712	+	0.631088i	$0.782609\pi$
$948$	1453.31	0.0497904
$949$	12766.4	0.436686
$950$	−2732.50	−0.0933201
$951$	5344.39	0.182233
$952$	0	0
$953$	−42755.6	−1.45329	−0.726647	−	0.687011i	$-0.758922\pi$
$953$	−42755.6	−1.45329	−0.726647	+	0.687011i	$0.758922\pi$
$954$	19127.8	0.649147
$955$	2294.49	0.0777466
$956$	3861.29	0.130631
$957$	−18256.4	−0.616661
$958$	59686.1	2.01291
$959$	0	0
$960$	10003.8	0.336324
$961$	−27295.9	−0.916248
$962$	−7866.27	−0.263637
$963$	8405.18	0.281260
$964$	−13370.5	−0.446717
$965$	15165.0	0.505883
$966$	0	0
$967$	−3475.40	−0.115575	−0.0577877	−	0.998329i	$-0.518405\pi$
$967$	−3475.40	−0.115575	−0.0577877	+	0.998329i	$0.518405\pi$
$968$	−10250.9	−0.340367
$969$	−8989.23	−0.298014
$970$	−42821.0	−1.41742
$971$	−37977.1	−1.25514	−0.627571	−	0.778559i	$-0.715951\pi$
$971$	−37977.1	−1.25514	−0.627571	+	0.778559i	$0.715951\pi$
$972$	−6275.65	−0.207090
$973$	0	0
$974$	−65012.3	−2.13874
$975$	−846.951	−0.0278196
$976$	11300.5	0.370616
$977$	−26515.4	−0.868274	−0.434137	−	0.900847i	$-0.642947\pi$
$977$	−26515.4	−0.868274	−0.434137	+	0.900847i	$0.642947\pi$
$978$	22291.5	0.728838
$979$	−6525.99	−0.213046
$980$	0	0
$981$	1353.75	0.0440592
$982$	−29778.4	−0.967685
$983$	12527.8	0.406485	0.203243	−	0.979128i	$-0.434852\pi$
$983$	12527.8	0.406485	0.203243	+	0.979128i	$0.434852\pi$
$984$	5995.57	0.194239
$985$	12728.1	0.411726
$986$	19933.0	0.643810
$987$	0	0
$988$	1920.23	0.0618326
$989$	17711.0	0.569439
$990$	−7516.02	−0.241288
$991$	−36506.6	−1.17020	−0.585102	−	0.810960i	$-0.698945\pi$
$991$	−36506.6	−1.17020	−0.585102	+	0.810960i	$0.698945\pi$
$992$	6209.96	0.198756
$993$	20254.2	0.647277
$994$	0	0
$995$	−6909.07	−0.220133
$996$	13247.1	0.421435
$997$	−35131.6	−1.11598	−0.557989	−	0.829848i	$-0.688427\pi$
$997$	−35131.6	−1.11598	−0.557989	+	0.829848i	$0.688427\pi$
$998$	16477.9	0.522643
$999$	−29039.8	−0.919698

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.e.1.5		20
7.6	odd	2		329.4.a.c.1.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
329.4.a.c.1.5	✓	20	7.6	odd	2
2303.4.a.e.1.5		20	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)

\(f(q)\)	\(=\)	\(q-3.29728 q^{2} -4.34822 q^{3} +2.87207 q^{4} -10.4624 q^{5} +14.3373 q^{6} +16.9082 q^{8} -8.09301 q^{9} +O(q^{10})\)	\(q-3.29728 q^{2} -4.34822 q^{3} +2.87207 q^{4} -10.4624 q^{5} +14.3373 q^{6} +16.9082 q^{8} -8.09301 q^{9} +34.4975 q^{10} +26.9209 q^{11} -12.4884 q^{12} -12.5358 q^{13} +45.4928 q^{15} -78.7278 q^{16} -38.7618 q^{17} +26.6849 q^{18} -53.3344 q^{19} -30.0487 q^{20} -88.7659 q^{22} +89.5137 q^{23} -73.5207 q^{24} -15.5381 q^{25} +41.3339 q^{26} +152.592 q^{27} +155.960 q^{29} -150.003 q^{30} +49.9507 q^{31} +124.322 q^{32} -117.058 q^{33} +127.808 q^{34} -23.2437 q^{36} -190.310 q^{37} +175.859 q^{38} +54.5082 q^{39} -176.901 q^{40} -81.5494 q^{41} +197.857 q^{43} +77.3187 q^{44} +84.6724 q^{45} -295.152 q^{46} +47.0000 q^{47} +342.325 q^{48} +51.2334 q^{50} +168.545 q^{51} -36.0036 q^{52} +716.802 q^{53} -503.139 q^{54} -281.658 q^{55} +231.910 q^{57} -514.244 q^{58} +90.8772 q^{59} +130.658 q^{60} -143.539 q^{61} -164.701 q^{62} +219.898 q^{64} +131.154 q^{65} +385.973 q^{66} +431.908 q^{67} -111.326 q^{68} -389.225 q^{69} +284.770 q^{71} -136.839 q^{72} -1018.40 q^{73} +627.506 q^{74} +67.5628 q^{75} -153.180 q^{76} -179.729 q^{78} -116.373 q^{79} +823.682 q^{80} -444.992 q^{81} +268.891 q^{82} -1060.75 q^{83} +405.541 q^{85} -652.392 q^{86} -678.148 q^{87} +455.185 q^{88} -242.413 q^{89} -279.189 q^{90} +257.090 q^{92} -217.196 q^{93} -154.972 q^{94} +558.006 q^{95} -540.578 q^{96} -1241.28 q^{97} -217.871 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 3 q^{2} - 2 q^{3} + 109 q^{4} + 4 q^{5} - q^{6} + 12 q^{8} + 278 q^{9}+O(q^{10}) \) 20 * q + 3 * q^2 - 2 * q^3 + 109 * q^4 + 4 * q^5 - q^6 + 12 * q^8 + 278 * q^9	\( 20 q + 3 q^{2} - 2 q^{3} + 109 q^{4} + 4 q^{5} - q^{6} + 12 q^{8} + 278 q^{9} - 68 q^{10} + 62 q^{11} + 6 q^{13} + 420 q^{15} + 957 q^{16} + 138 q^{17} + 120 q^{18} - 182 q^{19} - 787 q^{20} + 521 q^{22} + 326 q^{23} + 18 q^{24} + 678 q^{25} - 118 q^{26} - 68 q^{27} + 528 q^{29} + 877 q^{30} - 1092 q^{31} + 254 q^{32} + 424 q^{33} - 234 q^{34} + 2608 q^{36} + 904 q^{37} + 166 q^{38} + 606 q^{39} - 323 q^{40} + 8 q^{41} - 18 q^{43} + 98 q^{44} - 316 q^{45} + 1382 q^{46} + 940 q^{47} - 937 q^{48} + 892 q^{50} + 756 q^{51} - 761 q^{52} + 992 q^{53} - 384 q^{54} - 1060 q^{55} + 1554 q^{57} - 938 q^{58} - 2140 q^{59} + 5830 q^{60} + 186 q^{61} - 69 q^{62} + 7086 q^{64} + 662 q^{65} - 3617 q^{66} + 2852 q^{67} - 1163 q^{68} - 628 q^{69} + 3448 q^{71} - 355 q^{72} + 304 q^{73} + 1512 q^{74} - 4930 q^{75} - 339 q^{76} + 1054 q^{78} + 4248 q^{79} - 5945 q^{80} + 5696 q^{81} - 3665 q^{82} + 274 q^{83} + 232 q^{85} - 5730 q^{86} - 3756 q^{87} + 1976 q^{88} + 3168 q^{89} + 13306 q^{90} - 4214 q^{92} - 374 q^{93} + 141 q^{94} + 6100 q^{95} + 11433 q^{96} + 4112 q^{97} + 7252 q^{99}+O(q^{100}) \) 20 * q + 3 * q^2 - 2 * q^3 + 109 * q^4 + 4 * q^5 - q^6 + 12 * q^8 + 278 * q^9 - 68 * q^10 + 62 * q^11 + 6 * q^13 + 420 * q^15 + 957 * q^16 + 138 * q^17 + 120 * q^18 - 182 * q^19 - 787 * q^20 + 521 * q^22 + 326 * q^23 + 18 * q^24 + 678 * q^25 - 118 * q^26 - 68 * q^27 + 528 * q^29 + 877 * q^30 - 1092 * q^31 + 254 * q^32 + 424 * q^33 - 234 * q^34 + 2608 * q^36 + 904 * q^37 + 166 * q^38 + 606 * q^39 - 323 * q^40 + 8 * q^41 - 18 * q^43 + 98 * q^44 - 316 * q^45 + 1382 * q^46 + 940 * q^47 - 937 * q^48 + 892 * q^50 + 756 * q^51 - 761 * q^52 + 992 * q^53 - 384 * q^54 - 1060 * q^55 + 1554 * q^57 - 938 * q^58 - 2140 * q^59 + 5830 * q^60 + 186 * q^61 - 69 * q^62 + 7086 * q^64 + 662 * q^65 - 3617 * q^66 + 2852 * q^67 - 1163 * q^68 - 628 * q^69 + 3448 * q^71 - 355 * q^72 + 304 * q^73 + 1512 * q^74 - 4930 * q^75 - 339 * q^76 + 1054 * q^78 + 4248 * q^79 - 5945 * q^80 + 5696 * q^81 - 3665 * q^82 + 274 * q^83 + 232 * q^85 - 5730 * q^86 - 3756 * q^87 + 1976 * q^88 + 3168 * q^89 + 13306 * q^90 - 4214 * q^92 - 374 * q^93 + 141 * q^94 + 6100 * q^95 + 11433 * q^96 + 4112 * q^97 + 7252 * q^99

Introduction

L-functions

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Database

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