LMFDB - Embedded newform 1573.4.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1573,4,Mod(1,1573)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1573, 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("1573.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1573 = 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1573.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:	$92.8100044390$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 34x^{4} - 26x^{3} + 249x^{2} + 274x - 200 $ x^6 - 34x^4 - 26x^3 + 249x^2 + 274x - 200
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-4.30719$ of defining polynomial
Character	$\chi$	$=$	1573.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.30719 q^{2} +4.61773 q^{3} +20.1662 q^{4} +5.13365 q^{5} +24.5072 q^{6} +25.3474 q^{7} +64.5685 q^{8} -5.67656 q^{9} +O(q^{10})$	\(q+5.30719 q^{2} +4.61773 q^{3} +20.1662 q^{4} +5.13365 q^{5} +24.5072 q^{6} +25.3474 q^{7} +64.5685 q^{8} -5.67656 q^{9} +27.2453 q^{10} +93.1223 q^{12} +13.0000 q^{13} +134.523 q^{14} +23.7058 q^{15} +181.347 q^{16} +33.4620 q^{17} -30.1266 q^{18} +79.5721 q^{19} +103.527 q^{20} +117.047 q^{21} +28.3682 q^{23} +298.160 q^{24} -98.6456 q^{25} +68.9934 q^{26} -150.892 q^{27} +511.161 q^{28} -248.189 q^{29} +125.811 q^{30} -104.834 q^{31} +445.897 q^{32} +177.589 q^{34} +130.125 q^{35} -114.475 q^{36} -377.610 q^{37} +422.304 q^{38} +60.0305 q^{39} +331.473 q^{40} +263.301 q^{41} +621.192 q^{42} -320.858 q^{43} -29.1415 q^{45} +150.555 q^{46} -328.795 q^{47} +837.414 q^{48} +299.489 q^{49} -523.531 q^{50} +154.519 q^{51} +262.161 q^{52} -452.030 q^{53} -800.810 q^{54} +1636.64 q^{56} +367.442 q^{57} -1317.18 q^{58} +504.608 q^{59} +478.058 q^{60} +61.1162 q^{61} -556.371 q^{62} -143.886 q^{63} +915.677 q^{64} +66.7375 q^{65} -72.0712 q^{67} +674.804 q^{68} +130.997 q^{69} +690.596 q^{70} +423.212 q^{71} -366.527 q^{72} +623.580 q^{73} -2004.05 q^{74} -455.519 q^{75} +1604.67 q^{76} +318.593 q^{78} +1325.65 q^{79} +930.975 q^{80} -543.509 q^{81} +1397.39 q^{82} -697.928 q^{83} +2360.41 q^{84} +171.783 q^{85} -1702.85 q^{86} -1146.07 q^{87} +994.203 q^{89} -154.659 q^{90} +329.516 q^{91} +572.080 q^{92} -484.093 q^{93} -1744.98 q^{94} +408.496 q^{95} +2059.03 q^{96} +1094.12 q^{97} +1589.45 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 6 q^{3} + 26 q^{4} - 8 q^{5} + 15 q^{6} + 53 q^{7} + 36 q^{8}+O(q^{10}) $ 6 * q + 6 * q^2 - 6 * q^3 + 26 * q^4 - 8 * q^5 + 15 * q^6 + 53 * q^7 + 36 * q^8	\( 6 q + 6 q^{2} - 6 q^{3} + 26 q^{4} - 8 q^{5} + 15 q^{6} + 53 q^{7} + 36 q^{8} + 52 q^{10} - 19 q^{12} + 78 q^{13} - 120 q^{14} - 23 q^{15} + 26 q^{16} + 117 q^{17} + 27 q^{18} + 67 q^{19} + 10 q^{20} - 19 q^{21} - 158 q^{23} + 609 q^{24} - 234 q^{25} + 78 q^{26} - 531 q^{27} + 670 q^{28} + 145 q^{29} + 211 q^{30} - 58 q^{31} + 364 q^{32} + 43 q^{34} + 210 q^{35} + 383 q^{36} - 753 q^{37} + 738 q^{38} - 78 q^{39} - 4 q^{40} + 232 q^{41} + 1593 q^{42} + 390 q^{43} - 107 q^{45} - 5 q^{46} - 205 q^{47} + 1625 q^{48} + 491 q^{49} - 938 q^{50} - 363 q^{51} + 338 q^{52} - 65 q^{53} - 1917 q^{54} + 1816 q^{56} + 1657 q^{57} - 1685 q^{58} + 1735 q^{59} + 871 q^{60} - 421 q^{61} - 3394 q^{62} + 125 q^{63} + 570 q^{64} - 104 q^{65} - 703 q^{67} - 209 q^{68} - 272 q^{69} + 1968 q^{70} + 445 q^{71} - 1035 q^{72} + 2340 q^{73} - 1135 q^{74} + 1941 q^{75} + 1208 q^{76} + 195 q^{78} + 1234 q^{79} + 2766 q^{80} + 606 q^{81} - 897 q^{82} + 1601 q^{83} + 7 q^{84} + 2245 q^{85} - 1146 q^{86} - 2462 q^{87} - 442 q^{89} - 113 q^{90} + 689 q^{91} + 2737 q^{92} - 982 q^{93} - 2733 q^{94} + 504 q^{95} + 1153 q^{96} - 2682 q^{97} - 2036 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 26 * q^4 - 8 * q^5 + 15 * q^6 + 53 * q^7 + 36 * q^8 + 52 * q^10 - 19 * q^12 + 78 * q^13 - 120 * q^14 - 23 * q^15 + 26 * q^16 + 117 * q^17 + 27 * q^18 + 67 * q^19 + 10 * q^20 - 19 * q^21 - 158 * q^23 + 609 * q^24 - 234 * q^25 + 78 * q^26 - 531 * q^27 + 670 * q^28 + 145 * q^29 + 211 * q^30 - 58 * q^31 + 364 * q^32 + 43 * q^34 + 210 * q^35 + 383 * q^36 - 753 * q^37 + 738 * q^38 - 78 * q^39 - 4 * q^40 + 232 * q^41 + 1593 * q^42 + 390 * q^43 - 107 * q^45 - 5 * q^46 - 205 * q^47 + 1625 * q^48 + 491 * q^49 - 938 * q^50 - 363 * q^51 + 338 * q^52 - 65 * q^53 - 1917 * q^54 + 1816 * q^56 + 1657 * q^57 - 1685 * q^58 + 1735 * q^59 + 871 * q^60 - 421 * q^61 - 3394 * q^62 + 125 * q^63 + 570 * q^64 - 104 * q^65 - 703 * q^67 - 209 * q^68 - 272 * q^69 + 1968 * q^70 + 445 * q^71 - 1035 * q^72 + 2340 * q^73 - 1135 * q^74 + 1941 * q^75 + 1208 * q^76 + 195 * q^78 + 1234 * q^79 + 2766 * q^80 + 606 * q^81 - 897 * q^82 + 1601 * q^83 + 7 * q^84 + 2245 * q^85 - 1146 * q^86 - 2462 * q^87 - 442 * q^89 - 113 * q^90 + 689 * q^91 + 2737 * q^92 - 982 * q^93 - 2733 * q^94 + 504 * q^95 + 1153 * q^96 - 2682 * q^97 - 2036 * q^98

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 $

$2$	5.30719	1.87637	0.938187	−	0.346128i	$-0.112504\pi$
$2$	5.30719	1.87637	0.938187	+	0.346128i	$0.112504\pi$
$3$	4.61773	0.888683	0.444341	−	0.895858i	$-0.353438\pi$
$3$	4.61773	0.888683	0.444341	+	0.895858i	$0.353438\pi$
$4$	20.1662	2.52078
$5$	5.13365	0.459168	0.229584	−	0.973289i	$-0.426263\pi$
$5$	5.13365	0.459168	0.229584	+	0.973289i	$0.426263\pi$
$6$	24.5072	1.66750
$7$	25.3474	1.36863	0.684315	−	0.729187i	$-0.260101\pi$
$7$	25.3474	1.36863	0.684315	+	0.729187i	$0.260101\pi$
$8$	64.5685	2.85355
$9$	−5.67656	−0.210243
$10$	27.2453	0.861571
$11$	0	0
$11$	0	0
$12$	93.1223	2.24017
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	134.523	2.56806
$15$	23.7058	0.408055
$16$	181.347	2.83355
$17$	33.4620	0.477396	0.238698	−	0.971094i	$-0.423279\pi$
$17$	33.4620	0.477396	0.238698	+	0.971094i	$0.423279\pi$
$18$	−30.1266	−0.394495
$19$	79.5721	0.960794	0.480397	−	0.877051i	$-0.340493\pi$
$19$	79.5721	0.960794	0.480397	+	0.877051i	$0.340493\pi$
$20$	103.527	1.15746
$21$	117.047	1.21628
$22$	0	0
$23$	28.3682	0.257182	0.128591	−	0.991698i	$-0.458955\pi$
$23$	28.3682	0.257182	0.128591	+	0.991698i	$0.458955\pi$
$24$	298.160	2.53590
$25$	−98.6456	−0.789165
$26$	68.9934	0.520413
$27$	−150.892	−1.07552
$28$	511.161	3.45001
$29$	−248.189	−1.58922	−0.794612	−	0.607117i	$-0.792326\pi$
$29$	−248.189	−1.58922	−0.794612	+	0.607117i	$0.792326\pi$
$30$	125.811	0.765663
$31$	−104.834	−0.607376	−0.303688	−	0.952771i	$-0.598218\pi$
$31$	−104.834	−0.607376	−0.303688	+	0.952771i	$0.598218\pi$
$32$	445.897	2.46325
$33$	0	0
$34$	177.589	0.895774
$35$	130.125	0.628431
$36$	−114.475	−0.529976
$37$	−377.610	−1.67780	−0.838901	−	0.544284i	$-0.816802\pi$
$37$	−377.610	−1.67780	−0.838901	+	0.544284i	$0.816802\pi$
$38$	422.304	1.80281
$39$	60.0305	0.246476
$40$	331.473	1.31026
$41$	263.301	1.00294	0.501472	−	0.865174i	$-0.332792\pi$
$41$	263.301	1.00294	0.501472	+	0.865174i	$0.332792\pi$
$42$	621.192	2.28219
$43$	−320.858	−1.13791	−0.568957	−	0.822367i	$-0.692653\pi$
$43$	−320.858	−1.13791	−0.568957	+	0.822367i	$0.692653\pi$
$44$	0	0
$45$	−29.1415	−0.0965369
$46$	150.555	0.482569
$47$	−328.795	−1.02042	−0.510210	−	0.860050i	$-0.670432\pi$
$47$	−328.795	−1.02042	−0.510210	+	0.860050i	$0.670432\pi$
$48$	837.414	2.51813
$49$	299.489	0.873147
$50$	−523.531	−1.48077
$51$	154.519	0.424254
$52$	262.161	0.699139
$53$	−452.030	−1.17153	−0.585765	−	0.810481i	$-0.699206\pi$
$53$	−452.030	−1.17153	−0.585765	+	0.810481i	$0.699206\pi$
$54$	−800.810	−2.01808
$55$	0	0
$56$	1636.64	3.90546
$57$	367.442	0.853841
$58$	−1317.18	−2.98198
$59$	504.608	1.11346	0.556732	−	0.830692i	$-0.312055\pi$
$59$	504.608	1.11346	0.556732	+	0.830692i	$0.312055\pi$
$60$	478.058	1.02862
$61$	61.1162	0.128281	0.0641404	−	0.997941i	$-0.479569\pi$
$61$	61.1162	0.128281	0.0641404	+	0.997941i	$0.479569\pi$
$62$	−556.371	−1.13967
$63$	−143.886	−0.287745
$64$	915.677	1.78843
$65$	66.7375	0.127350
$66$	0	0
$67$	−72.0712	−0.131416	−0.0657082	−	0.997839i	$-0.520931\pi$
$67$	−72.0712	−0.131416	−0.0657082	+	0.997839i	$0.520931\pi$
$68$	674.804	1.20341
$69$	130.997	0.228553
$70$	690.596	1.17917
$71$	423.212	0.707410	0.353705	−	0.935357i	$-0.384922\pi$
$71$	423.212	0.707410	0.353705	+	0.935357i	$0.384922\pi$
$72$	−366.527	−0.599940
$73$	623.580	0.999789	0.499894	−	0.866086i	$-0.333372\pi$
$73$	623.580	0.999789	0.499894	+	0.866086i	$0.333372\pi$
$74$	−2004.05	−3.14819
$75$	−455.519	−0.701317
$76$	1604.67	2.42195
$77$	0	0
$78$	318.593	0.462482
$79$	1325.65	1.88794	0.943972	−	0.330026i	$-0.107058\pi$
$79$	1325.65	1.88794	0.943972	+	0.330026i	$0.107058\pi$
$80$	930.975	1.30108
$81$	−543.509	−0.745555
$82$	1397.39	1.88190
$83$	−697.928	−0.922983	−0.461491	−	0.887145i	$-0.652686\pi$
$83$	−697.928	−0.922983	−0.461491	+	0.887145i	$0.652686\pi$
$84$	2360.41	3.06597
$85$	171.783	0.219205
$86$	−1702.85	−2.13515
$87$	−1146.07	−1.41232
$88$	0	0
$89$	994.203	1.18410	0.592052	−	0.805900i	$-0.298318\pi$
$89$	994.203	1.18410	0.592052	+	0.805900i	$0.298318\pi$
$90$	−154.659	−0.181139
$91$	329.516	0.379590
$92$	572.080	0.648299
$93$	−484.093	−0.539765
$94$	−1744.98	−1.91469
$95$	408.496	0.441166
$96$	2059.03	2.18905
$97$	1094.12	1.14526	0.572632	−	0.819812i	$-0.305922\pi$
$97$	1094.12	1.14526	0.572632	+	0.819812i	$0.305922\pi$
$98$	1589.45	1.63835
$99$	0	0
$100$	−1989.31	−1.98931
$101$	−182.929	−0.180219	−0.0901093	−	0.995932i	$-0.528722\pi$
$101$	−182.929	−0.180219	−0.0901093	+	0.995932i	$0.528722\pi$
$102$	820.060	0.796059
$103$	229.184	0.219244	0.109622	−	0.993973i	$-0.465036\pi$
$103$	229.184	0.219244	0.109622	+	0.993973i	$0.465036\pi$
$104$	839.391	0.791433
$105$	600.881	0.558476
$106$	−2399.01	−2.19823
$107$	1673.53	1.51202	0.756010	−	0.654560i	$-0.227146\pi$
$107$	1673.53	1.51202	0.756010	+	0.654560i	$0.227146\pi$
$108$	−3042.92	−2.71115
$109$	−1049.20	−0.921973	−0.460986	−	0.887407i	$-0.652504\pi$
$109$	−1049.20	−0.921973	−0.460986	+	0.887407i	$0.652504\pi$
$110$	0	0
$111$	−1743.70	−1.49103
$112$	4596.68	3.87809
$113$	335.067	0.278942	0.139471	−	0.990226i	$-0.455460\pi$
$113$	335.067	0.278942	0.139471	+	0.990226i	$0.455460\pi$
$114$	1950.09	1.60213
$115$	145.633	0.118090
$116$	−5005.04	−4.00609
$117$	−73.7953	−0.0583109
$118$	2678.05	2.08928
$119$	848.175	0.653379
$120$	1530.65	1.16441
$121$	0	0
$122$	324.355	0.240703
$123$	1215.85	0.891299
$124$	−2114.10	−1.53106
$125$	−1148.12	−0.821527
$126$	−763.630	−0.539917
$127$	−2542.22	−1.77627	−0.888133	−	0.459586i	$-0.847998\pi$
$127$	−2542.22	−1.77627	−0.888133	+	0.459586i	$0.847998\pi$
$128$	1292.50	0.892515
$129$	−1481.63	−1.01124
$130$	354.189	0.238957
$131$	512.054	0.341514	0.170757	−	0.985313i	$-0.445379\pi$
$131$	512.054	0.341514	0.170757	+	0.985313i	$0.445379\pi$
$132$	0	0
$133$	2016.94	1.31497
$134$	−382.495	−0.246586
$135$	−774.625	−0.493845
$136$	2160.59	1.36228
$137$	−1139.91	−0.710869	−0.355435	−	0.934701i	$-0.615667\pi$
$137$	−1139.91	−0.710869	−0.355435	+	0.934701i	$0.615667\pi$
$138$	695.225	0.428851
$139$	1154.97	0.704770	0.352385	−	0.935855i	$-0.385371\pi$
$139$	1154.97	0.704770	0.352385	+	0.935855i	$0.385371\pi$
$140$	2624.13	1.58414
$141$	−1518.29	−0.906829
$142$	2246.07	1.32737
$143$	0	0
$144$	−1029.43	−0.595735
$145$	−1274.12	−0.729721
$146$	3309.46	1.87598
$147$	1382.96	0.775951
$148$	−7614.97	−4.22937
$149$	−2691.89	−1.48006	−0.740028	−	0.672576i	$-0.765188\pi$
$149$	−2691.89	−1.48006	−0.740028	+	0.672576i	$0.765188\pi$
$150$	−2417.52	−1.31593
$151$	−3221.34	−1.73608	−0.868042	−	0.496492i	$-0.834621\pi$
$151$	−3221.34	−1.73608	−0.868042	+	0.496492i	$0.834621\pi$
$152$	5137.85	2.74168
$153$	−189.949	−0.100369
$154$	0	0
$155$	−538.179	−0.278888
$156$	1210.59	0.621312
$157$	1475.65	0.750126	0.375063	−	0.926999i	$-0.377621\pi$
$157$	1475.65	0.750126	0.375063	+	0.926999i	$0.377621\pi$
$158$	7035.49	3.54249
$159$	−2087.35	−1.04112
$160$	2289.08	1.13105
$161$	719.060	0.351987
$162$	−2884.51	−1.39894
$163$	−1080.37	−0.519146	−0.259573	−	0.965723i	$-0.583582\pi$
$163$	−1080.37	−0.519146	−0.259573	+	0.965723i	$0.583582\pi$
$164$	5309.79	2.52820
$165$	0	0
$166$	−3704.04	−1.73186
$167$	−4082.38	−1.89164	−0.945820	−	0.324691i	$-0.894740\pi$
$167$	−4082.38	−1.89164	−0.945820	+	0.324691i	$0.894740\pi$
$168$	7557.58	3.47071
$169$	169.000	0.0769231
$170$	911.682	0.411311
$171$	−451.696	−0.202000
$172$	−6470.49	−2.86843
$173$	2979.93	1.30959	0.654797	−	0.755805i	$-0.272754\pi$
$173$	2979.93	1.30959	0.654797	+	0.755805i	$0.272754\pi$
$174$	−6082.40	−2.65003
$175$	−2500.41	−1.08007
$176$	0	0
$177$	2330.15	0.989517
$178$	5276.42	2.22182
$179$	469.115	0.195884	0.0979422	−	0.995192i	$-0.468774\pi$
$179$	469.115	0.195884	0.0979422	+	0.995192i	$0.468774\pi$
$180$	−587.675	−0.243348
$181$	−1155.75	−0.474620	−0.237310	−	0.971434i	$-0.576266\pi$
$181$	−1155.75	−0.474620	−0.237310	+	0.971434i	$0.576266\pi$
$182$	1748.80	0.712252
$183$	282.218	0.114001
$184$	1831.69	0.733882
$185$	−1938.52	−0.770393
$186$	−2569.17	−1.01280
$187$	0	0
$188$	−6630.56	−2.57225
$189$	−3824.71	−1.47199
$190$	2167.96	0.827792
$191$	−2968.67	−1.12464	−0.562318	−	0.826921i	$-0.690090\pi$
$191$	−2968.67	−1.12464	−0.562318	+	0.826921i	$0.690090\pi$
$192$	4228.35	1.58935
$193$	5282.89	1.97031	0.985157	−	0.171655i	$-0.0549116\pi$
$193$	5282.89	1.97031	0.985157	+	0.171655i	$0.0549116\pi$
$194$	5806.68	2.14895
$195$	308.176	0.113174
$196$	6039.58	2.20101
$197$	2152.73	0.778558	0.389279	−	0.921120i	$-0.372724\pi$
$197$	2152.73	0.778558	0.389279	+	0.921120i	$0.372724\pi$
$198$	0	0
$199$	4790.13	1.70635	0.853174	−	0.521626i	$-0.174674\pi$
$199$	4790.13	1.70635	0.853174	+	0.521626i	$0.174674\pi$
$200$	−6369.40	−2.25192
$201$	−332.805	−0.116787
$202$	−970.836	−0.338157
$203$	−6290.93	−2.17506
$204$	3116.06	1.06945
$205$	1351.70	0.460520
$206$	1216.32	0.411384
$207$	−161.034	−0.0540707
$208$	2357.52	0.785886
$209$	0	0
$210$	3188.99	1.04791
$211$	4741.30	1.54694	0.773471	−	0.633832i	$-0.218519\pi$
$211$	4741.30	1.54694	0.773471	+	0.633832i	$0.218519\pi$
$212$	−9115.74	−2.95317
$213$	1954.28	0.628663
$214$	8881.73	2.83711
$215$	−1647.17	−0.522494
$216$	−9742.85	−3.06906
$217$	−2657.26	−0.831273
$218$	−5568.30	−1.72997
$219$	2879.53	0.888495
$220$	0	0
$221$	435.006	0.132406
$222$	−9254.15	−2.79774
$223$	2279.21	0.684426	0.342213	−	0.939622i	$-0.388824\pi$
$223$	2279.21	0.684426	0.342213	+	0.939622i	$0.388824\pi$
$224$	11302.3	3.37128
$225$	559.968	0.165916
$226$	1778.26	0.523399
$227$	5286.81	1.54581	0.772903	−	0.634524i	$-0.218804\pi$
$227$	5286.81	1.54581	0.772903	+	0.634524i	$0.218804\pi$
$228$	7409.93	2.15235
$229$	−906.243	−0.261512	−0.130756	−	0.991415i	$-0.541740\pi$
$229$	−906.243	−0.261512	−0.130756	+	0.991415i	$0.541740\pi$
$230$	772.900	0.221580
$231$	0	0
$232$	−16025.2	−4.53494
$233$	−960.037	−0.269932	−0.134966	−	0.990850i	$-0.543092\pi$
$233$	−960.037	−0.269932	−0.134966	+	0.990850i	$0.543092\pi$
$234$	−391.646	−0.109413
$235$	−1687.92	−0.468544
$236$	10176.1	2.80680
$237$	6121.51	1.67778
$238$	4501.42	1.22598
$239$	1475.35	0.399299	0.199650	−	0.979867i	$-0.436020\pi$
$239$	1475.35	0.399299	0.199650	+	0.979867i	$0.436020\pi$
$240$	4298.99	1.15624
$241$	4054.32	1.08366	0.541829	−	0.840489i	$-0.317732\pi$
$241$	4054.32	1.08366	0.541829	+	0.840489i	$0.317732\pi$
$242$	0	0
$243$	1564.29	0.412960
$244$	1232.48	0.323368
$245$	1537.48	0.400921
$246$	6452.76	1.67241
$247$	1034.44	0.266476
$248$	−6768.95	−1.73318
$249$	−3222.85	−0.820239
$250$	−6093.28	−1.54149
$251$	5951.50	1.49663	0.748317	−	0.663341i	$-0.230862\pi$
$251$	5951.50	1.49663	0.748317	+	0.663341i	$0.230862\pi$
$252$	−2901.64	−0.725342
$253$	0	0
$254$	−13492.1	−3.33294
$255$	793.246	0.194804
$256$	−465.882	−0.113741
$257$	1199.56	0.291153	0.145577	−	0.989347i	$-0.453496\pi$
$257$	1199.56	0.291153	0.145577	+	0.989347i	$0.453496\pi$
$258$	−7863.31	−1.89747
$259$	−9571.42	−2.29629
$260$	1345.84	0.321022
$261$	1408.86	0.334123
$262$	2717.57	0.640809
$263$	−4206.58	−0.986270	−0.493135	−	0.869953i	$-0.664149\pi$
$263$	−4206.58	−0.986270	−0.493135	+	0.869953i	$0.664149\pi$
$264$	0	0
$265$	−2320.56	−0.537929
$266$	10704.3	2.46738
$267$	4590.96	1.05229
$268$	−1453.41	−0.331272
$269$	−2482.72	−0.562728	−0.281364	−	0.959601i	$-0.590787\pi$
$269$	−2482.72	−0.562728	−0.281364	+	0.959601i	$0.590787\pi$
$270$	−4111.08	−0.926639
$271$	−8757.29	−1.96298	−0.981489	−	0.191516i	$-0.938660\pi$
$271$	−8757.29	−1.96298	−0.981489	+	0.191516i	$0.938660\pi$
$272$	6068.25	1.35273
$273$	1521.62	0.337335
$274$	−6049.72	−1.33386
$275$	0	0
$276$	2641.71	0.576132
$277$	3877.23	0.841012	0.420506	−	0.907290i	$-0.361853\pi$
$277$	3877.23	0.841012	0.420506	+	0.907290i	$0.361853\pi$
$278$	6129.63	1.32241
$279$	595.094	0.127697
$280$	8401.96	1.79326
$281$	−5016.86	−1.06506	−0.532528	−	0.846412i	$-0.678758\pi$
$281$	−5016.86	−1.06506	−0.532528	+	0.846412i	$0.678758\pi$
$282$	−8057.84	−1.70155
$283$	−5498.11	−1.15487	−0.577436	−	0.816436i	$-0.695947\pi$
$283$	−5498.11	−1.15487	−0.577436	+	0.816436i	$0.695947\pi$
$284$	8534.60	1.78322
$285$	1886.32	0.392057
$286$	0	0
$287$	6673.99	1.37266
$288$	−2531.16	−0.517882
$289$	−3793.29	−0.772093
$290$	−6761.97	−1.36923
$291$	5052.34	1.01778
$292$	12575.3	2.52025
$293$	5050.99	1.00711	0.503553	−	0.863965i	$-0.332026\pi$
$293$	5050.99	1.00711	0.503553	+	0.863965i	$0.332026\pi$
$294$	7339.64	1.45597
$295$	2590.49	0.511267
$296$	−24381.7	−4.78770
$297$	0	0
$298$	−14286.4	−2.77714
$299$	368.787	0.0713294
$300$	−9186.10	−1.76787
$301$	−8132.90	−1.55738
$302$	−17096.2	−3.25754
$303$	−844.715	−0.160157
$304$	14430.2	2.72246
$305$	313.749	0.0589024
$306$	−1008.10	−0.188330
$307$	4499.69	0.836518	0.418259	−	0.908328i	$-0.362641\pi$
$307$	4499.69	0.836518	0.418259	+	0.908328i	$0.362641\pi$
$308$	0	0
$309$	1058.31	0.194839
$310$	−2856.22	−0.523298
$311$	−3800.20	−0.692893	−0.346446	−	0.938070i	$-0.612612\pi$
$311$	−3800.20	−0.692893	−0.346446	+	0.938070i	$0.612612\pi$
$312$	3876.08	0.703333
$313$	−6595.05	−1.19097	−0.595486	−	0.803366i	$-0.703040\pi$
$313$	−6595.05	−1.19097	−0.595486	+	0.803366i	$0.703040\pi$
$314$	7831.56	1.40752
$315$	−738.661	−0.132123
$316$	26733.4	4.75909
$317$	−1941.46	−0.343984	−0.171992	−	0.985098i	$-0.555020\pi$
$317$	−1941.46	−0.343984	−0.171992	+	0.985098i	$0.555020\pi$
$318$	−11078.0	−1.95353
$319$	0	0
$320$	4700.77	0.821191
$321$	7727.90	1.34371
$322$	3816.19	0.660459
$323$	2662.64	0.458679
$324$	−10960.5	−1.87938
$325$	−1282.39	−0.218875
$326$	−5733.71	−0.974112
$327$	−4844.92	−0.819341
$328$	17001.0	2.86195
$329$	−8334.09	−1.39658
$330$	0	0
$331$	1.93737	0.000321715 0	0.000160857	−	1.00000i	$-0.499949\pi$
$331$	1.93737	0.000321715 0	0.000160857		1.00000i	$0.499949\pi$
$332$	−14074.6	−2.32664
$333$	2143.53	0.352746
$334$	−21665.9	−3.54943
$335$	−369.989	−0.0603422
$336$	21226.2	3.44639
$337$	1488.93	0.240674	0.120337	−	0.992733i	$-0.461602\pi$
$337$	1488.93	0.240674	0.120337	+	0.992733i	$0.461602\pi$
$338$	896.915	0.144336
$339$	1547.25	0.247891
$340$	3464.21	0.552568
$341$	0	0
$342$	−2397.23	−0.379028
$343$	−1102.88	−0.173615
$344$	−20717.3	−3.24710
$345$	672.492	0.104944
$346$	15815.0	2.45729
$347$	5329.54	0.824509	0.412254	−	0.911069i	$-0.364741\pi$
$347$	5329.54	0.824509	0.412254	+	0.911069i	$0.364741\pi$
$348$	−23111.9	−3.56014
$349$	−5077.47	−0.778770	−0.389385	−	0.921075i	$-0.627312\pi$
$349$	−5077.47	−0.778770	−0.389385	+	0.921075i	$0.627312\pi$
$350$	−13270.1	−2.02662
$351$	−1961.59	−0.298296
$352$	0	0
$353$	1385.36	0.208881	0.104441	−	0.994531i	$-0.466695\pi$
$353$	1385.36	0.208881	0.104441	+	0.994531i	$0.466695\pi$
$354$	12366.5	1.85670
$355$	2172.63	0.324820
$356$	20049.3	2.98487
$357$	3916.64	0.580646
$358$	2489.68	0.367552
$359$	672.605	0.0988822	0.0494411	−	0.998777i	$-0.484256\pi$
$359$	672.605	0.0988822	0.0494411	+	0.998777i	$0.484256\pi$
$360$	−1881.62	−0.275473
$361$	−527.283	−0.0768746
$362$	−6133.78	−0.890564
$363$	0	0
$364$	6645.10	0.956862
$365$	3201.25	0.459071
$366$	1497.78	0.213908
$367$	−3226.94	−0.458978	−0.229489	−	0.973311i	$-0.573705\pi$
$367$	−3226.94	−0.458978	−0.229489	+	0.973311i	$0.573705\pi$
$368$	5144.50	0.728738
$369$	−1494.64	−0.210862
$370$	−10288.1	−1.44555
$371$	−11457.8	−1.60339
$372$	−9762.34	−1.36063
$373$	7233.83	1.00416	0.502082	−	0.864820i	$-0.332568\pi$
$373$	7233.83	1.00416	0.502082	+	0.864820i	$0.332568\pi$
$374$	0	0
$375$	−5301.71	−0.730077
$376$	−21229.8	−2.91182
$377$	−3226.45	−0.440771
$378$	−20298.4	−2.76201
$379$	−2271.87	−0.307911	−0.153956	−	0.988078i	$-0.549201\pi$
$379$	−2271.87	−0.307911	−0.153956	+	0.988078i	$0.549201\pi$
$380$	8237.82	1.11208
$381$	−11739.3	−1.57854
$382$	−15755.3	−2.11024
$383$	630.510	0.0841190	0.0420595	−	0.999115i	$-0.486608\pi$
$383$	630.510	0.0841190	0.0420595	+	0.999115i	$0.486608\pi$
$384$	5968.41	0.793162
$385$	0	0
$386$	28037.3	3.69705
$387$	1821.37	0.239239
$388$	22064.2	2.88696
$389$	−2027.27	−0.264233	−0.132117	−	0.991234i	$-0.542177\pi$
$389$	−2027.27	−0.264233	−0.132117	+	0.991234i	$0.542177\pi$
$390$	1635.55	0.212357
$391$	949.258	0.122778
$392$	19337.6	2.49157
$393$	2364.53	0.303498
$394$	11425.0	1.46087
$395$	6805.44	0.866883
$396$	0	0
$397$	12483.4	1.57814	0.789072	−	0.614301i	$-0.210562\pi$
$397$	12483.4	1.57814	0.789072	+	0.614301i	$0.210562\pi$
$398$	25422.1	3.20175
$399$	9313.70	1.16859
$400$	−17889.1	−2.23614
$401$	−8877.78	−1.10557	−0.552787	−	0.833323i	$-0.686436\pi$
$401$	−8877.78	−1.10557	−0.552787	+	0.833323i	$0.686436\pi$
$402$	−1766.26	−0.219137
$403$	−1362.84	−0.168456
$404$	−3688.98	−0.454291
$405$	−2790.19	−0.342335
$406$	−33387.2	−4.08123
$407$	0	0
$408$	9977.04	1.21063
$409$	12566.8	1.51928	0.759642	−	0.650342i	$-0.225374\pi$
$409$	12566.8	1.51928	0.759642	+	0.650342i	$0.225374\pi$
$410$	7173.71	0.864107
$411$	−5263.80	−0.631737
$412$	4621.78	0.552667
$413$	12790.5	1.52392
$414$	−854.637	−0.101457
$415$	−3582.92	−0.423804
$416$	5796.65	0.683184
$417$	5333.33	0.626317
$418$	0	0
$419$	−5389.40	−0.628376	−0.314188	−	0.949361i	$-0.601732\pi$
$419$	−5389.40	−0.628376	−0.314188	+	0.949361i	$0.601732\pi$
$420$	12117.5	1.40779
$421$	−1450.59	−0.167927	−0.0839636	−	0.996469i	$-0.526758\pi$
$421$	−1450.59	−0.167927	−0.0839636	+	0.996469i	$0.526758\pi$
$422$	25163.0	2.90264
$423$	1866.43	0.214536
$424$	−29186.9	−3.34302
$425$	−3300.88	−0.376744
$426$	10371.7	1.17961
$427$	1549.13	0.175569
$428$	33748.8	3.81147
$429$	0	0
$430$	−8741.85	−0.980394
$431$	−10952.4	−1.22404	−0.612019	−	0.790843i	$-0.709642\pi$
$431$	−10952.4	−1.22404	−0.612019	+	0.790843i	$0.709642\pi$
$432$	−27363.8	−3.04755
$433$	−3961.80	−0.439705	−0.219852	−	0.975533i	$-0.570558\pi$
$433$	−3961.80	−0.439705	−0.219852	+	0.975533i	$0.570558\pi$
$434$	−14102.6	−1.55978
$435$	−5883.52	−0.648490
$436$	−21158.4	−2.32409
$437$	2257.32	0.247099
$438$	15282.2	1.66715
$439$	1137.14	0.123628	0.0618139	−	0.998088i	$-0.480311\pi$
$439$	1137.14	0.123628	0.0618139	+	0.998088i	$0.480311\pi$
$440$	0	0
$441$	−1700.07	−0.183573
$442$	2308.66	0.248443
$443$	12242.6	1.31301	0.656507	−	0.754320i	$-0.272033\pi$
$443$	12242.6	1.31301	0.656507	+	0.754320i	$0.272033\pi$
$444$	−35163.9	−3.75857
$445$	5103.89	0.543703
$446$	12096.2	1.28424
$447$	−12430.4	−1.31530
$448$	23210.0	2.44770
$449$	4360.33	0.458300	0.229150	−	0.973391i	$-0.426405\pi$
$449$	4360.33	0.458300	0.229150	+	0.973391i	$0.426405\pi$
$450$	2971.85	0.311321
$451$	0	0
$452$	6757.03	0.703151
$453$	−14875.3	−1.54283
$454$	28058.1	2.90051
$455$	1691.62	0.174295
$456$	23725.2	2.43648
$457$	2779.55	0.284511	0.142256	−	0.989830i	$-0.454564\pi$
$457$	2779.55	0.284511	0.142256	+	0.989830i	$0.454564\pi$
$458$	−4809.60	−0.490694
$459$	−5049.14	−0.513450
$460$	2936.86	0.297678
$461$	11722.8	1.18435	0.592176	−	0.805808i	$-0.298269\pi$
$461$	11722.8	1.18435	0.592176	+	0.805808i	$0.298269\pi$
$462$	0	0
$463$	−13289.6	−1.33395	−0.666976	−	0.745080i	$-0.732411\pi$
$463$	−13289.6	−1.33395	−0.666976	+	0.745080i	$0.732411\pi$
$464$	−45008.4	−4.50315
$465$	−2485.17	−0.247843
$466$	−5095.10	−0.506493
$467$	−12299.9	−1.21878	−0.609391	−	0.792870i	$-0.708586\pi$
$467$	−12299.9	−1.21878	−0.609391	+	0.792870i	$0.708586\pi$
$468$	−1488.17	−0.146989
$469$	−1826.82	−0.179860
$470$	−8958.11	−0.879164
$471$	6814.16	0.666624
$472$	32581.8	3.17733
$473$	0	0
$474$	32488.0	3.14815
$475$	−7849.44	−0.758225
$476$	17104.5	1.64702
$477$	2565.97	0.246306
$478$	7829.97	0.749235
$479$	4120.96	0.393093	0.196547	−	0.980494i	$-0.437027\pi$
$479$	4120.96	0.393093	0.196547	+	0.980494i	$0.437027\pi$
$480$	10570.3	1.00514
$481$	−4908.93	−0.465339
$482$	21517.0	2.03335
$483$	3320.42	0.312804
$484$	0	0
$485$	5616.82	0.525869
$486$	8301.99	0.774868
$487$	−11817.4	−1.09959	−0.549793	−	0.835301i	$-0.685293\pi$
$487$	−11817.4	−1.09959	−0.549793	+	0.835301i	$0.685293\pi$
$488$	3946.18	0.366056
$489$	−4988.84	−0.461356
$490$	8159.67	0.752278
$491$	−4311.90	−0.396320	−0.198160	−	0.980170i	$-0.563497\pi$
$491$	−4311.90	−0.396320	−0.198160	+	0.980170i	$0.563497\pi$
$492$	24519.2	2.24677
$493$	−8304.90	−0.758690
$494$	5489.95	0.500009
$495$	0	0
$496$	−19011.3	−1.72103
$497$	10727.3	0.968182
$498$	−17104.2	−1.53908
$499$	−4441.37	−0.398443	−0.199222	−	0.979954i	$-0.563841\pi$
$499$	−4441.37	−0.398443	−0.199222	+	0.979954i	$0.563841\pi$
$500$	−23153.3	−2.07089
$501$	−18851.3	−1.68107
$502$	31585.7	2.80825
$503$	26.9872	0.00239225	0.00119612	−	0.999999i	$-0.499619\pi$
$503$	26.9872	0.00239225	0.00119612	+	0.999999i	$0.499619\pi$
$504$	−9290.50	−0.821095
$505$	−939.092	−0.0827506
$506$	0	0
$507$	780.397	0.0683602
$508$	−51267.1	−4.47758
$509$	−9236.28	−0.804304	−0.402152	−	0.915573i	$-0.631738\pi$
$509$	−9236.28	−0.804304	−0.402152	+	0.915573i	$0.631738\pi$
$510$	4209.90	0.365525
$511$	15806.1	1.36834
$512$	−12812.5	−1.10593
$513$	−12006.8	−1.03336
$514$	6366.28	0.546312
$515$	1176.55	0.100670
$516$	−29879.0	−2.54913
$517$	0	0
$518$	−50797.3	−4.30870
$519$	13760.5	1.16381
$520$	4309.14	0.363401
$521$	−11817.5	−0.993735	−0.496867	−	0.867827i	$-0.665516\pi$
$521$	−11817.5	−0.993735	−0.496867	+	0.867827i	$0.665516\pi$
$522$	7477.08	0.626940
$523$	−16935.2	−1.41591	−0.707957	−	0.706256i	$-0.750383\pi$
$523$	−16935.2	−1.41591	−0.707957	+	0.706256i	$0.750383\pi$
$524$	10326.2	0.860883
$525$	−11546.2	−0.959843
$526$	−22325.1	−1.85061
$527$	−3507.94	−0.289959
$528$	0	0
$529$	−11362.2	−0.933858
$530$	−12315.7	−1.00936
$531$	−2864.44	−0.234098
$532$	40674.2	3.31475
$533$	3422.91	0.278167
$534$	24365.1	1.97450
$535$	8591.32	0.694271
$536$	−4653.53	−0.375004
$537$	2166.25	0.174079
$538$	−13176.2	−1.05589
$539$	0	0
$540$	−15621.3	−1.24488
$541$	13506.6	1.07337	0.536686	−	0.843782i	$-0.319676\pi$
$541$	13506.6	1.07337	0.536686	+	0.843782i	$0.319676\pi$
$542$	−46476.6	−3.68328
$543$	−5336.94	−0.421786
$544$	14920.6	1.17595
$545$	−5386.23	−0.423340
$546$	8075.50	0.632966
$547$	−1981.49	−0.154886	−0.0774428	−	0.996997i	$-0.524676\pi$
$547$	−1981.49	−0.154886	−0.0774428	+	0.996997i	$0.524676\pi$
$548$	−22987.7	−1.79195
$549$	−346.930	−0.0269701
$550$	0	0
$551$	−19748.9	−1.52692
$552$	8458.27	0.652188
$553$	33601.8	2.58390
$554$	20577.2	1.57805
$555$	−8951.56	−0.684635
$556$	23291.3	1.77657
$557$	4004.82	0.304649	0.152325	−	0.988331i	$-0.451324\pi$
$557$	4004.82	0.304649	0.152325	+	0.988331i	$0.451324\pi$
$558$	3158.28	0.239607
$559$	−4171.15	−0.315601
$560$	23597.8	1.78069
$561$	0	0
$562$	−26625.4	−1.99845
$563$	15066.8	1.12787	0.563935	−	0.825819i	$-0.309287\pi$
$563$	15066.8	1.12787	0.563935	+	0.825819i	$0.309287\pi$
$564$	−30618.2	−2.28592
$565$	1720.12	0.128081
$566$	−29179.5	−2.16697
$567$	−13776.5	−1.02039
$568$	27326.2	2.01863
$569$	2037.33	0.150104	0.0750522	−	0.997180i	$-0.476088\pi$
$569$	2037.33	0.150104	0.0750522	+	0.997180i	$0.476088\pi$
$570$	10011.1	0.735645
$571$	17246.9	1.26403	0.632015	−	0.774956i	$-0.282228\pi$
$571$	17246.9	1.26403	0.632015	+	0.774956i	$0.282228\pi$
$572$	0	0
$573$	−13708.5	−0.999444
$574$	35420.1	2.57562
$575$	−2798.40	−0.202959
$576$	−5197.90	−0.376005
$577$	−24835.2	−1.79186	−0.895928	−	0.444199i	$-0.853488\pi$
$577$	−24835.2	−1.79186	−0.895928	+	0.444199i	$0.853488\pi$
$578$	−20131.7	−1.44874
$579$	24395.0	1.75098
$580$	−25694.1	−1.83947
$581$	−17690.7	−1.26322
$582$	26813.7	1.90973
$583$	0	0
$584$	40263.7	2.85295
$585$	−378.840	−0.0267745
$586$	26806.5	1.88971
$587$	16695.4	1.17392	0.586961	−	0.809615i	$-0.300324\pi$
$587$	16695.4	1.17392	0.586961	+	0.809615i	$0.300324\pi$
$588$	27889.1	1.95600
$589$	−8341.83	−0.583564
$590$	13748.2	0.959329
$591$	9940.74	0.691891
$592$	−68478.6	−4.75414
$593$	15968.5	1.10581	0.552907	−	0.833243i	$-0.313518\pi$
$593$	15968.5	1.10581	0.552907	+	0.833243i	$0.313518\pi$
$594$	0	0
$595$	4354.24	0.300011
$596$	−54285.4	−3.73090
$597$	22119.5	1.51640
$598$	1957.22	0.133841
$599$	17197.9	1.17310	0.586549	−	0.809914i	$-0.300486\pi$
$599$	17197.9	1.17310	0.586549	+	0.809914i	$0.300486\pi$
$600$	−29412.2	−2.00125
$601$	18775.2	1.27430	0.637152	−	0.770738i	$-0.280112\pi$
$601$	18775.2	1.27430	0.637152	+	0.770738i	$0.280112\pi$
$602$	−43162.8	−2.92223
$603$	409.117	0.0276294
$604$	−64962.2	−4.37628
$605$	0	0
$606$	−4483.06	−0.300515
$607$	−16839.7	−1.12603	−0.563016	−	0.826446i	$-0.690359\pi$
$607$	−16839.7	−1.12603	−0.563016	+	0.826446i	$0.690359\pi$
$608$	35480.9	2.36668
$609$	−29049.8	−1.93294
$610$	1665.13	0.110523
$611$	−4274.34	−0.283013
$612$	−3830.56	−0.253009
$613$	−23364.9	−1.53948	−0.769739	−	0.638358i	$-0.779614\pi$
$613$	−23364.9	−1.53948	−0.769739	+	0.638358i	$0.779614\pi$
$614$	23880.7	1.56962
$615$	6241.77	0.409256
$616$	0	0
$617$	27460.3	1.79175	0.895876	−	0.444304i	$-0.146549\pi$
$617$	27460.3	1.79175	0.895876	+	0.444304i	$0.146549\pi$
$618$	5616.65	0.365590
$619$	−13032.5	−0.846234	−0.423117	−	0.906075i	$-0.639064\pi$
$619$	−13032.5	−0.846234	−0.423117	+	0.906075i	$0.639064\pi$
$620$	−10853.1	−0.703015
$621$	−4280.52	−0.276605
$622$	−20168.4	−1.30013
$623$	25200.4	1.62060
$624$	10886.4	0.698404
$625$	6436.65	0.411946
$626$	−35001.2	−2.23471
$627$	0	0
$628$	29758.4	1.89090
$629$	−12635.6	−0.800977
$630$	−3920.21	−0.247913
$631$	−17203.7	−1.08537	−0.542686	−	0.839936i	$-0.682593\pi$
$631$	−17203.7	−1.08537	−0.542686	+	0.839936i	$0.682593\pi$
$632$	85595.4	5.38735
$633$	21894.1	1.37474
$634$	−10303.7	−0.645443
$635$	−13050.9	−0.815605
$636$	−42094.0	−2.62443
$637$	3893.36	0.242167
$638$	0	0
$639$	−2402.39	−0.148728
$640$	6635.24	0.409814
$641$	21794.3	1.34294	0.671470	−	0.741032i	$-0.265663\pi$
$641$	21794.3	1.34294	0.671470	+	0.741032i	$0.265663\pi$
$642$	41013.4	2.52130
$643$	−20959.7	−1.28549	−0.642746	−	0.766080i	$-0.722205\pi$
$643$	−20959.7	−1.28549	−0.642746	+	0.766080i	$0.722205\pi$
$644$	14500.7	0.887281
$645$	−7606.20	−0.464331
$646$	14131.2	0.860654
$647$	7163.17	0.435260	0.217630	−	0.976031i	$-0.430167\pi$
$647$	7163.17	0.435260	0.217630	+	0.976031i	$0.430167\pi$
$648$	−35093.6	−2.12748
$649$	0	0
$650$	−6805.90	−0.410691
$651$	−12270.5	−0.738738
$652$	−21786.9	−1.30865
$653$	10701.5	0.641320	0.320660	−	0.947194i	$-0.396095\pi$
$653$	10701.5	0.641320	0.320660	+	0.947194i	$0.396095\pi$
$654$	−25712.9	−1.53739
$655$	2628.71	0.156812
$656$	47748.9	2.84190
$657$	−3539.79	−0.210199
$658$	−44230.6	−2.62050
$659$	1643.84	0.0971697	0.0485848	−	0.998819i	$-0.484529\pi$
$659$	1643.84	0.0971697	0.0485848	+	0.998819i	$0.484529\pi$
$660$	0	0
$661$	11036.9	0.649451	0.324726	−	0.945808i	$-0.394728\pi$
$661$	11036.9	0.649451	0.324726	+	0.945808i	$0.394728\pi$
$662$	10.2820	0.000603657 0
$663$	2008.74	0.117667
$664$	−45064.2	−2.63378
$665$	10354.3	0.603793
$666$	11376.1	0.661884
$667$	−7040.67	−0.408720
$668$	−82326.2	−4.76841
$669$	10524.8	0.608237
$670$	−1963.60	−0.113225
$671$	0	0
$672$	52191.0	2.99600
$673$	13422.4	0.768792	0.384396	−	0.923168i	$-0.374410\pi$
$673$	13422.4	0.768792	0.384396	+	0.923168i	$0.374410\pi$
$674$	7902.03	0.451594
$675$	14884.8	0.848764
$676$	3408.10	0.193906
$677$	−8927.32	−0.506802	−0.253401	−	0.967361i	$-0.581549\pi$
$677$	−8927.32	−0.506802	−0.253401	+	0.967361i	$0.581549\pi$
$678$	8211.53	0.465136
$679$	27733.0	1.56744
$680$	11091.7	0.625513
$681$	24413.1	1.37373
$682$	0	0
$683$	1189.95	0.0666647	0.0333324	−	0.999444i	$-0.489388\pi$
$683$	1189.95	0.0666647	0.0333324	+	0.999444i	$0.489388\pi$
$684$	−9109.01	−0.509198
$685$	−5851.91	−0.326408
$686$	−5853.18	−0.325766
$687$	−4184.79	−0.232401
$688$	−58186.7	−3.22434
$689$	−5876.39	−0.324924
$690$	3569.04	0.196915
$691$	853.797	0.0470043	0.0235022	−	0.999724i	$-0.492518\pi$
$691$	853.797	0.0470043	0.0235022	+	0.999724i	$0.492518\pi$
$692$	60094.0	3.30120
$693$	0	0
$694$	28284.9	1.54709
$695$	5929.20	0.323608
$696$	−74000.0	−4.03012
$697$	8810.59	0.478802
$698$	−26947.1	−1.46126
$699$	−4433.19	−0.239884
$700$	−50423.8	−2.72263
$701$	28917.3	1.55805	0.779023	−	0.626995i	$-0.215715\pi$
$701$	28917.3	1.55805	0.779023	+	0.626995i	$0.215715\pi$
$702$	−10410.5	−0.559715
$703$	−30047.2	−1.61202
$704$	0	0
$705$	−7794.36	−0.416387
$706$	7352.35	0.391939
$707$	−4636.76	−0.246652
$708$	46990.3	2.49436
$709$	−23256.4	−1.23189	−0.615947	−	0.787787i	$-0.711227\pi$
$709$	−23256.4	−1.23189	−0.615947	+	0.787787i	$0.711227\pi$
$710$	11530.5	0.609484
$711$	−7525.15	−0.396927
$712$	64194.2	3.37890
$713$	−2973.94	−0.156206
$714$	20786.4	1.08951
$715$	0	0
$716$	9460.29	0.493781
$717$	6812.78	0.354851
$718$	3569.64	0.185540
$719$	−3093.49	−0.160456	−0.0802278	−	0.996777i	$-0.525565\pi$
$719$	−3093.49	−0.160456	−0.0802278	+	0.996777i	$0.525565\pi$
$720$	−5284.74	−0.273542
$721$	5809.21	0.300064
$722$	−2798.39	−0.144246
$723$	18721.8	0.963028
$724$	−23307.1	−1.19641
$725$	24482.7	1.25416
$726$	0	0
$727$	30538.0	1.55790	0.778949	−	0.627088i	$-0.215753\pi$
$727$	30538.0	1.55790	0.778949	+	0.627088i	$0.215753\pi$
$728$	21276.4	1.08318
$729$	21898.2	1.11255
$730$	16989.6	0.861389
$731$	−10736.5	−0.543236
$732$	5691.28	0.287371
$733$	33455.3	1.68581	0.842906	−	0.538061i	$-0.180843\pi$
$733$	33455.3	1.68581	0.842906	+	0.538061i	$0.180843\pi$
$734$	−17126.0	−0.861214
$735$	7099.65	0.356292
$736$	12649.3	0.633504
$737$	0	0
$738$	−7932.36	−0.395656
$739$	1598.95	0.0795920	0.0397960	−	0.999208i	$-0.487329\pi$
$739$	1598.95	0.0795920	0.0397960	+	0.999208i	$0.487329\pi$
$740$	−39092.6	−1.94199
$741$	4776.75	0.236813
$742$	−60808.5	−3.00856
$743$	−36061.5	−1.78058	−0.890288	−	0.455398i	$-0.849497\pi$
$743$	−36061.5	−1.78058	−0.890288	+	0.455398i	$0.849497\pi$
$744$	−31257.2	−1.54025
$745$	−13819.2	−0.679595
$746$	38391.3	1.88419
$747$	3961.83	0.194051
$748$	0	0
$749$	42419.6	2.06940
$750$	−28137.1	−1.36990
$751$	10315.2	0.501206	0.250603	−	0.968090i	$-0.419371\pi$
$751$	10315.2	0.501206	0.250603	+	0.968090i	$0.419371\pi$
$752$	−59626.2	−2.89141
$753$	27482.4	1.33003
$754$	−17123.4	−0.827052
$755$	−16537.2	−0.797154
$756$	−77129.9	−3.71057
$757$	−4875.63	−0.234092	−0.117046	−	0.993126i	$-0.537343\pi$
$757$	−4875.63	−0.234092	−0.117046	+	0.993126i	$0.537343\pi$
$758$	−12057.3	−0.577757
$759$	0	0
$760$	26376.0	1.25889
$761$	36160.3	1.72248	0.861241	−	0.508197i	$-0.169688\pi$
$761$	36160.3	1.72248	0.861241	+	0.508197i	$0.169688\pi$
$762$	−62302.7	−2.96193
$763$	−26594.4	−1.26184
$764$	−59866.9	−2.83496
$765$	−975.134	−0.0460863
$766$	3346.24	0.157839
$767$	6559.91	0.308820
$768$	−2151.32	−0.101080
$769$	−1446.71	−0.0678409	−0.0339204	−	0.999425i	$-0.510799\pi$
$769$	−1446.71	−0.0678409	−0.0339204	+	0.999425i	$0.510799\pi$
$770$	0	0
$771$	5539.23	0.258743
$772$	106536.	4.96673
$773$	23535.3	1.09509	0.547545	−	0.836776i	$-0.315562\pi$
$773$	23535.3	1.09509	0.547545	+	0.836776i	$0.315562\pi$
$774$	9666.34	0.448901
$775$	10341.4	0.479320
$776$	70645.5	3.26807
$777$	−44198.2	−2.04067
$778$	−10759.1	−0.495801
$779$	20951.4	0.963623
$780$	6214.75	0.285287
$781$	0	0
$782$	5037.89	0.230377
$783$	37449.6	1.70925
$784$	54311.6	2.47411
$785$	7575.49	0.344434
$786$	12549.0	0.569476
$787$	−19738.9	−0.894046	−0.447023	−	0.894522i	$-0.647516\pi$
$787$	−19738.9	−0.894046	−0.447023	+	0.894522i	$0.647516\pi$
$788$	43412.5	1.96257
$789$	−19424.9	−0.876481
$790$	36117.8	1.62660
$791$	8493.06	0.381768
$792$	0	0
$793$	794.510	0.0355787
$794$	66251.7	2.96119
$795$	−10715.7	−0.478048
$796$	96599.0	4.30133
$797$	15133.5	0.672592	0.336296	−	0.941756i	$-0.390826\pi$
$797$	15133.5	0.672592	0.336296	+	0.941756i	$0.390826\pi$
$798$	49429.6	2.19272
$799$	−11002.2	−0.487144
$800$	−43985.7	−1.94391
$801$	−5643.65	−0.248950
$802$	−47116.0	−2.07447
$803$	0	0
$804$	−6711.43	−0.294396
$805$	3691.40	0.161621
$806$	−7232.83	−0.316086
$807$	−11464.5	−0.500087
$808$	−11811.4	−0.514263
$809$	23565.6	1.02413	0.512065	−	0.858947i	$-0.328881\pi$
$809$	23565.6	1.02413	0.512065	+	0.858947i	$0.328881\pi$
$810$	−14808.1	−0.642349
$811$	9896.86	0.428515	0.214258	−	0.976777i	$-0.431267\pi$
$811$	9896.86	0.428515	0.214258	+	0.976777i	$0.431267\pi$
$812$	−126865.	−5.48285
$813$	−40438.8	−1.74447
$814$	0	0
$815$	−5546.23	−0.238375
$816$	28021.6	1.20215
$817$	−25531.3	−1.09330
$818$	66694.2	2.85074
$819$	−1870.52	−0.0798061
$820$	27258.6	1.16087
$821$	−33812.2	−1.43734	−0.718669	−	0.695352i	$-0.755249\pi$
$821$	−33812.2	−1.43734	−0.718669	+	0.695352i	$0.755249\pi$
$822$	−27936.0	−1.18538
$823$	−8303.91	−0.351708	−0.175854	−	0.984416i	$-0.556269\pi$
$823$	−8303.91	−0.351708	−0.175854	+	0.984416i	$0.556269\pi$
$824$	14798.1	0.625625
$825$	0	0
$826$	67881.6	2.85945
$827$	6445.69	0.271026	0.135513	−	0.990776i	$-0.456732\pi$
$827$	6445.69	0.271026	0.135513	+	0.990776i	$0.456732\pi$
$828$	−3247.45	−0.136300
$829$	4568.94	0.191419	0.0957093	−	0.995409i	$-0.469488\pi$
$829$	4568.94	0.191419	0.0957093	+	0.995409i	$0.469488\pi$
$830$	−19015.2	−0.795215
$831$	17904.0	0.747393
$832$	11903.8	0.496022
$833$	10021.5	0.416837
$834$	28305.0	1.17520
$835$	−20957.5	−0.868581
$836$	0	0
$837$	15818.5	0.653247
$838$	−28602.6	−1.17907
$839$	18726.7	0.770581	0.385290	−	0.922795i	$-0.374101\pi$
$839$	18726.7	0.770581	0.385290	+	0.922795i	$0.374101\pi$
$840$	38798.0	1.59364
$841$	37208.7	1.52563
$842$	−7698.55	−0.315094
$843$	−23166.5	−0.946498
$844$	95614.3	3.89950
$845$	867.588	0.0353206
$846$	9905.47	0.402550
$847$	0	0
$848$	−81974.4	−3.31959
$849$	−25388.8	−1.02632
$850$	−17518.4	−0.706913
$851$	−10712.1	−0.431500
$852$	39410.5	1.58472
$853$	−5700.90	−0.228834	−0.114417	−	0.993433i	$-0.536500\pi$
$853$	−5700.90	−0.228834	−0.114417	+	0.993433i	$0.536500\pi$
$854$	8221.55	0.329433
$855$	−2318.85	−0.0927521
$856$	108057.	4.31463
$857$	−34915.4	−1.39170	−0.695851	−	0.718186i	$-0.744972\pi$
$857$	−34915.4	−1.39170	−0.695851	+	0.718186i	$0.744972\pi$
$858$	0	0
$859$	−12387.9	−0.492048	−0.246024	−	0.969264i	$-0.579124\pi$
$859$	−12387.9	−0.492048	−0.246024	+	0.969264i	$0.579124\pi$
$860$	−33217.3	−1.31709
$861$	30818.7	1.21986
$862$	−58126.6	−2.29675
$863$	9285.36	0.366254	0.183127	−	0.983089i	$-0.441378\pi$
$863$	9285.36	0.366254	0.183127	+	0.983089i	$0.441378\pi$
$864$	−67282.0	−2.64928
$865$	15297.9	0.601324
$866$	−21026.0	−0.825051
$867$	−17516.4	−0.686146
$868$	−53586.9	−2.09546
$869$	0	0
$870$	−31225.0	−1.21681
$871$	−936.925	−0.0364483
$872$	−67745.3	−2.63090
$873$	−6210.82	−0.240784
$874$	11980.0	0.463650
$875$	−29101.8	−1.12437
$876$	58069.2	2.23970
$877$	−7761.34	−0.298839	−0.149419	−	0.988774i	$-0.547740\pi$
$877$	−7761.34	−0.298839	−0.149419	+	0.988774i	$0.547740\pi$
$878$	6035.00	0.231972
$879$	23324.1	0.894997
$880$	0	0
$881$	−24308.1	−0.929581	−0.464790	−	0.885421i	$-0.653870\pi$
$881$	−24308.1	−0.929581	−0.464790	+	0.885421i	$0.653870\pi$
$882$	−9022.59	−0.344452
$883$	3876.23	0.147730	0.0738649	−	0.997268i	$-0.476467\pi$
$883$	3876.23	0.147730	0.0738649	+	0.997268i	$0.476467\pi$
$884$	8772.45	0.333766
$885$	11962.2	0.454355
$886$	64974.0	2.46371
$887$	11107.2	0.420455	0.210228	−	0.977652i	$-0.432579\pi$
$887$	11107.2	0.420455	0.210228	+	0.977652i	$0.432579\pi$
$888$	−112588.	−4.25474
$889$	−64438.7	−2.43105
$890$	27087.3	1.02019
$891$	0	0
$892$	45963.0	1.72529
$893$	−26162.9	−0.980413
$894$	−65970.7	−2.46800
$895$	2408.27	0.0899438
$896$	32761.5	1.22152
$897$	1702.96	0.0633892
$898$	23141.1	0.859942
$899$	26018.5	0.965257
$900$	11292.4	0.418239
$901$	−15125.8	−0.559284
$902$	0	0
$903$	−37555.5	−1.38402
$904$	21634.8	0.795975
$905$	−5933.22	−0.217930
$906$	−78945.8	−2.89492
$907$	38754.9	1.41878	0.709391	−	0.704815i	$-0.248970\pi$
$907$	38754.9	1.41878	0.709391	+	0.704815i	$0.248970\pi$
$908$	106615.	3.89664
$909$	1038.41	0.0378897
$910$	8977.75	0.327043
$911$	37191.3	1.35258	0.676291	−	0.736635i	$-0.263586\pi$
$911$	37191.3	1.35258	0.676291	+	0.736635i	$0.263586\pi$
$912$	66634.7	2.41940
$913$	0	0
$914$	14751.6	0.533850
$915$	1448.81	0.0523456
$916$	−18275.5	−0.659214
$917$	12979.2	0.467407
$918$	−26796.7	−0.963425
$919$	−23959.9	−0.860025	−0.430012	−	0.902823i	$-0.641491\pi$
$919$	−23959.9	−0.860025	−0.430012	+	0.902823i	$0.641491\pi$
$920$	9403.29	0.336975
$921$	20778.4	0.743399
$922$	62215.3	2.22229
$923$	5501.76	0.196200
$924$	0	0
$925$	37249.6	1.32406
$926$	−70530.3	−2.50299
$927$	−1300.98	−0.0460946
$928$	−110667.	−3.91466
$929$	3622.70	0.127941	0.0639704	−	0.997952i	$-0.479624\pi$
$929$	3622.70	0.127941	0.0639704	+	0.997952i	$0.479624\pi$
$930$	−13189.3	−0.465046
$931$	23831.0	0.838915
$932$	−19360.3	−0.680439
$933$	−17548.3	−0.615762
$934$	−65277.9	−2.28689
$935$	0	0
$936$	−4764.85	−0.166393
$937$	−23974.0	−0.835855	−0.417928	−	0.908480i	$-0.637243\pi$
$937$	−23974.0	−0.835855	−0.417928	+	0.908480i	$0.637243\pi$
$938$	−9695.25	−0.337485
$939$	−30454.2	−1.05840
$940$	−34039.0	−1.18110
$941$	−30208.2	−1.04650	−0.523251	−	0.852179i	$-0.675281\pi$
$941$	−30208.2	−1.04650	−0.523251	+	0.852179i	$0.675281\pi$
$942$	36164.0	1.25084
$943$	7469.38	0.257939
$944$	91509.4	3.15506
$945$	−19634.7	−0.675891
$946$	0	0
$947$	−21182.8	−0.726872	−0.363436	−	0.931619i	$-0.618396\pi$
$947$	−21182.8	−0.726872	−0.363436	+	0.931619i	$0.618396\pi$
$948$	123448.	4.22932
$949$	8106.55	0.277291
$950$	−41658.4	−1.42271
$951$	−8965.12	−0.305693
$952$	54765.4	1.86445
$953$	−18371.4	−0.624458	−0.312229	−	0.950007i	$-0.601076\pi$
$953$	−18371.4	−0.624458	−0.312229	+	0.950007i	$0.601076\pi$
$954$	13618.1	0.462162
$955$	−15240.1	−0.516397
$956$	29752.3	1.00655
$957$	0	0
$958$	21870.7	0.737590
$959$	−28893.7	−0.972917
$960$	21706.9	0.729778
$961$	−18800.9	−0.631094
$962$	−26052.6	−0.873149
$963$	−9499.89	−0.317892
$964$	81760.4	2.73166
$965$	27120.5	0.904705
$966$	17622.1	0.586938
$967$	14257.5	0.474137	0.237069	−	0.971493i	$-0.423813\pi$
$967$	14257.5	0.474137	0.237069	+	0.971493i	$0.423813\pi$
$968$	0	0
$969$	12295.4	0.407621
$970$	29809.5	0.986727
$971$	−5160.59	−0.170557	−0.0852787	−	0.996357i	$-0.527178\pi$
$971$	−5160.59	−0.170557	−0.0852787	+	0.996357i	$0.527178\pi$
$972$	31545.9	1.04098
$973$	29275.4	0.964569
$974$	−62717.3	−2.06324
$975$	−5921.74	−0.194510
$976$	11083.3	0.363490
$977$	−18922.9	−0.619650	−0.309825	−	0.950794i	$-0.600271\pi$
$977$	−18922.9	−0.619650	−0.309825	+	0.950794i	$0.600271\pi$
$978$	−26476.7	−0.865677
$979$	0	0
$980$	31005.1	1.01063
$981$	5955.84	0.193838
$982$	−22884.1	−0.743645
$983$	−13472.7	−0.437144	−0.218572	−	0.975821i	$-0.570140\pi$
$983$	−13472.7	−0.437144	−0.218572	+	0.975821i	$0.570140\pi$
$984$	78505.8	2.54337
$985$	11051.4	0.357489
$986$	−44075.7	−1.42359
$987$	−38484.6	−1.24111
$988$	20860.7	0.671728
$989$	−9102.16	−0.292651
$990$	0	0
$991$	30136.5	0.966011	0.483005	−	0.875617i	$-0.339545\pi$
$991$	30136.5	0.966011	0.483005	+	0.875617i	$0.339545\pi$
$992$	−46744.9	−1.49612
$993$	8.94626	0.000285902 0
$994$	56931.9	1.81667
$995$	24590.9	0.783501
$996$	−64992.7	−2.06764
$997$	18832.5	0.598226	0.299113	−	0.954218i	$-0.403309\pi$
$997$	18832.5	0.598226	0.299113	+	0.954218i	$0.403309\pi$
$998$	−23571.2	−0.747629
$999$	56978.2	1.80451

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.d.1.6		6
11.10	odd	2		143.4.a.b.1.1	✓	6
33.32	even	2		1287.4.a.f.1.6		6
44.43	even	2		2288.4.a.m.1.1		6
143.142	odd	2		1859.4.a.c.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.b.1.1	✓	6	11.10	odd	2
1287.4.a.f.1.6		6	33.32	even	2
1573.4.a.d.1.6		6	1.1	even	1	trivial
1859.4.a.c.1.6		6	143.142	odd	2
2288.4.a.m.1.1		6	44.43	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1573 = 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1573.a (trivial)

\(f(q)\)	\(=\)	\(q+5.30719 q^{2} +4.61773 q^{3} +20.1662 q^{4} +5.13365 q^{5} +24.5072 q^{6} +25.3474 q^{7} +64.5685 q^{8} -5.67656 q^{9} +O(q^{10})\)	\(q+5.30719 q^{2} +4.61773 q^{3} +20.1662 q^{4} +5.13365 q^{5} +24.5072 q^{6} +25.3474 q^{7} +64.5685 q^{8} -5.67656 q^{9} +27.2453 q^{10} +93.1223 q^{12} +13.0000 q^{13} +134.523 q^{14} +23.7058 q^{15} +181.347 q^{16} +33.4620 q^{17} -30.1266 q^{18} +79.5721 q^{19} +103.527 q^{20} +117.047 q^{21} +28.3682 q^{23} +298.160 q^{24} -98.6456 q^{25} +68.9934 q^{26} -150.892 q^{27} +511.161 q^{28} -248.189 q^{29} +125.811 q^{30} -104.834 q^{31} +445.897 q^{32} +177.589 q^{34} +130.125 q^{35} -114.475 q^{36} -377.610 q^{37} +422.304 q^{38} +60.0305 q^{39} +331.473 q^{40} +263.301 q^{41} +621.192 q^{42} -320.858 q^{43} -29.1415 q^{45} +150.555 q^{46} -328.795 q^{47} +837.414 q^{48} +299.489 q^{49} -523.531 q^{50} +154.519 q^{51} +262.161 q^{52} -452.030 q^{53} -800.810 q^{54} +1636.64 q^{56} +367.442 q^{57} -1317.18 q^{58} +504.608 q^{59} +478.058 q^{60} +61.1162 q^{61} -556.371 q^{62} -143.886 q^{63} +915.677 q^{64} +66.7375 q^{65} -72.0712 q^{67} +674.804 q^{68} +130.997 q^{69} +690.596 q^{70} +423.212 q^{71} -366.527 q^{72} +623.580 q^{73} -2004.05 q^{74} -455.519 q^{75} +1604.67 q^{76} +318.593 q^{78} +1325.65 q^{79} +930.975 q^{80} -543.509 q^{81} +1397.39 q^{82} -697.928 q^{83} +2360.41 q^{84} +171.783 q^{85} -1702.85 q^{86} -1146.07 q^{87} +994.203 q^{89} -154.659 q^{90} +329.516 q^{91} +572.080 q^{92} -484.093 q^{93} -1744.98 q^{94} +408.496 q^{95} +2059.03 q^{96} +1094.12 q^{97} +1589.45 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 6 q^{3} + 26 q^{4} - 8 q^{5} + 15 q^{6} + 53 q^{7} + 36 q^{8}+O(q^{10}) \) 6 * q + 6 * q^2 - 6 * q^3 + 26 * q^4 - 8 * q^5 + 15 * q^6 + 53 * q^7 + 36 * q^8	\( 6 q + 6 q^{2} - 6 q^{3} + 26 q^{4} - 8 q^{5} + 15 q^{6} + 53 q^{7} + 36 q^{8} + 52 q^{10} - 19 q^{12} + 78 q^{13} - 120 q^{14} - 23 q^{15} + 26 q^{16} + 117 q^{17} + 27 q^{18} + 67 q^{19} + 10 q^{20} - 19 q^{21} - 158 q^{23} + 609 q^{24} - 234 q^{25} + 78 q^{26} - 531 q^{27} + 670 q^{28} + 145 q^{29} + 211 q^{30} - 58 q^{31} + 364 q^{32} + 43 q^{34} + 210 q^{35} + 383 q^{36} - 753 q^{37} + 738 q^{38} - 78 q^{39} - 4 q^{40} + 232 q^{41} + 1593 q^{42} + 390 q^{43} - 107 q^{45} - 5 q^{46} - 205 q^{47} + 1625 q^{48} + 491 q^{49} - 938 q^{50} - 363 q^{51} + 338 q^{52} - 65 q^{53} - 1917 q^{54} + 1816 q^{56} + 1657 q^{57} - 1685 q^{58} + 1735 q^{59} + 871 q^{60} - 421 q^{61} - 3394 q^{62} + 125 q^{63} + 570 q^{64} - 104 q^{65} - 703 q^{67} - 209 q^{68} - 272 q^{69} + 1968 q^{70} + 445 q^{71} - 1035 q^{72} + 2340 q^{73} - 1135 q^{74} + 1941 q^{75} + 1208 q^{76} + 195 q^{78} + 1234 q^{79} + 2766 q^{80} + 606 q^{81} - 897 q^{82} + 1601 q^{83} + 7 q^{84} + 2245 q^{85} - 1146 q^{86} - 2462 q^{87} - 442 q^{89} - 113 q^{90} + 689 q^{91} + 2737 q^{92} - 982 q^{93} - 2733 q^{94} + 504 q^{95} + 1153 q^{96} - 2682 q^{97} - 2036 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 26 * q^4 - 8 * q^5 + 15 * q^6 + 53 * q^7 + 36 * q^8 + 52 * q^10 - 19 * q^12 + 78 * q^13 - 120 * q^14 - 23 * q^15 + 26 * q^16 + 117 * q^17 + 27 * q^18 + 67 * q^19 + 10 * q^20 - 19 * q^21 - 158 * q^23 + 609 * q^24 - 234 * q^25 + 78 * q^26 - 531 * q^27 + 670 * q^28 + 145 * q^29 + 211 * q^30 - 58 * q^31 + 364 * q^32 + 43 * q^34 + 210 * q^35 + 383 * q^36 - 753 * q^37 + 738 * q^38 - 78 * q^39 - 4 * q^40 + 232 * q^41 + 1593 * q^42 + 390 * q^43 - 107 * q^45 - 5 * q^46 - 205 * q^47 + 1625 * q^48 + 491 * q^49 - 938 * q^50 - 363 * q^51 + 338 * q^52 - 65 * q^53 - 1917 * q^54 + 1816 * q^56 + 1657 * q^57 - 1685 * q^58 + 1735 * q^59 + 871 * q^60 - 421 * q^61 - 3394 * q^62 + 125 * q^63 + 570 * q^64 - 104 * q^65 - 703 * q^67 - 209 * q^68 - 272 * q^69 + 1968 * q^70 + 445 * q^71 - 1035 * q^72 + 2340 * q^73 - 1135 * q^74 + 1941 * q^75 + 1208 * q^76 + 195 * q^78 + 1234 * q^79 + 2766 * q^80 + 606 * q^81 - 897 * q^82 + 1601 * q^83 + 7 * q^84 + 2245 * q^85 - 1146 * q^86 - 2462 * q^87 - 442 * q^89 - 113 * q^90 + 689 * q^91 + 2737 * q^92 - 982 * q^93 - 2733 * q^94 + 504 * q^95 + 1153 * q^96 - 2682 * q^97 - 2036 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more