LMFDB - Embedded newform 289.4.a.h.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,4,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	289.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:	$17.0515519917$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 72 x^{10} - 17 x^{9} + 1872 x^{8} + 627 x^{7} - 20922 x^{6} - 5163 x^{5} + 93255 x^{4} + \cdots + 29352 $ x^12 - 72x^10 - 17x^9 + 1872x^8 + 627x^7 - 20922x^6 - 5163x^5 + 93255x^4 - 4607x^3 - 117822x^2 + 21960x + 29352
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 17^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-3.25752$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.25752 q^{2} +6.51757 q^{3} +2.61146 q^{4} -19.1073 q^{5} +21.2311 q^{6} -22.0995 q^{7} -17.5533 q^{8} +15.4787 q^{9} +O(q^{10})$	\(q+3.25752 q^{2} +6.51757 q^{3} +2.61146 q^{4} -19.1073 q^{5} +21.2311 q^{6} -22.0995 q^{7} -17.5533 q^{8} +15.4787 q^{9} -62.2426 q^{10} +8.25972 q^{11} +17.0204 q^{12} -0.398269 q^{13} -71.9898 q^{14} -124.533 q^{15} -78.0720 q^{16} +50.4221 q^{18} +103.371 q^{19} -49.8980 q^{20} -144.035 q^{21} +26.9062 q^{22} -138.311 q^{23} -114.405 q^{24} +240.090 q^{25} -1.29737 q^{26} -75.0910 q^{27} -57.7120 q^{28} -222.296 q^{29} -405.670 q^{30} -49.1520 q^{31} -113.895 q^{32} +53.8333 q^{33} +422.263 q^{35} +40.4219 q^{36} -61.3077 q^{37} +336.734 q^{38} -2.59575 q^{39} +335.397 q^{40} +387.391 q^{41} -469.198 q^{42} -20.3847 q^{43} +21.5699 q^{44} -295.756 q^{45} -450.553 q^{46} +44.1322 q^{47} -508.839 q^{48} +145.389 q^{49} +782.100 q^{50} -1.04006 q^{52} +59.6456 q^{53} -244.611 q^{54} -157.821 q^{55} +387.920 q^{56} +673.728 q^{57} -724.134 q^{58} +238.069 q^{59} -325.214 q^{60} +595.816 q^{61} -160.114 q^{62} -342.071 q^{63} +253.561 q^{64} +7.60987 q^{65} +175.363 q^{66} -408.815 q^{67} -901.454 q^{69} +1375.53 q^{70} -1037.38 q^{71} -271.702 q^{72} -22.3789 q^{73} -199.711 q^{74} +1564.80 q^{75} +269.949 q^{76} -182.536 q^{77} -8.45571 q^{78} +682.688 q^{79} +1491.75 q^{80} -907.335 q^{81} +1261.93 q^{82} -312.352 q^{83} -376.142 q^{84} -66.4037 q^{86} -1448.83 q^{87} -144.985 q^{88} -904.392 q^{89} -963.433 q^{90} +8.80157 q^{91} -361.195 q^{92} -320.351 q^{93} +143.762 q^{94} -1975.15 q^{95} -742.317 q^{96} -1006.72 q^{97} +473.610 q^{98} +127.849 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) $ 12 * q - 18 * q^3 + 48 * q^4 - 30 * q^5 + 9 * q^6 - 24 * q^7 - 51 * q^8 + 108 * q^9	\( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9} - 60 q^{10} - 162 q^{11} - 216 q^{12} - 72 q^{13} - 267 q^{14} - 138 q^{15} + 192 q^{16} + 189 q^{18} - 66 q^{19} - 129 q^{20} + 246 q^{21} - 456 q^{22} - 282 q^{23} - 72 q^{24} + 444 q^{25} + 528 q^{26} - 1092 q^{27} - 120 q^{28} - 648 q^{29} - 1890 q^{30} - 504 q^{31} - 1353 q^{32} + 966 q^{33} - 66 q^{35} - 663 q^{36} + 30 q^{37} - 60 q^{38} - 1758 q^{39} + 450 q^{40} - 318 q^{41} + 804 q^{42} + 486 q^{43} - 2448 q^{44} - 486 q^{45} - 1617 q^{46} - 888 q^{47} - 1257 q^{48} - 570 q^{49} + 435 q^{50} + 225 q^{52} + 1026 q^{53} - 933 q^{54} + 972 q^{55} - 2661 q^{56} + 156 q^{57} - 201 q^{58} - 792 q^{59} + 1458 q^{60} - 1212 q^{61} - 2817 q^{62} - 2112 q^{63} - 1857 q^{64} - 2742 q^{65} - 594 q^{66} + 624 q^{67} - 1506 q^{69} - 1650 q^{70} - 2802 q^{71} + 1455 q^{72} - 726 q^{73} - 270 q^{74} + 264 q^{75} + 675 q^{76} - 1008 q^{77} + 3090 q^{78} + 444 q^{79} + 1143 q^{80} + 2520 q^{81} + 4950 q^{82} + 672 q^{83} - 777 q^{84} + 2778 q^{86} + 726 q^{87} + 3750 q^{88} - 906 q^{89} + 7755 q^{90} - 2280 q^{91} - 87 q^{92} + 132 q^{93} + 735 q^{94} - 966 q^{95} + 5046 q^{96} + 3246 q^{97} + 1911 q^{98} + 282 q^{99}+O(q^{100}) \) 12 * q - 18 * q^3 + 48 * q^4 - 30 * q^5 + 9 * q^6 - 24 * q^7 - 51 * q^8 + 108 * q^9 - 60 * q^10 - 162 * q^11 - 216 * q^12 - 72 * q^13 - 267 * q^14 - 138 * q^15 + 192 * q^16 + 189 * q^18 - 66 * q^19 - 129 * q^20 + 246 * q^21 - 456 * q^22 - 282 * q^23 - 72 * q^24 + 444 * q^25 + 528 * q^26 - 1092 * q^27 - 120 * q^28 - 648 * q^29 - 1890 * q^30 - 504 * q^31 - 1353 * q^32 + 966 * q^33 - 66 * q^35 - 663 * q^36 + 30 * q^37 - 60 * q^38 - 1758 * q^39 + 450 * q^40 - 318 * q^41 + 804 * q^42 + 486 * q^43 - 2448 * q^44 - 486 * q^45 - 1617 * q^46 - 888 * q^47 - 1257 * q^48 - 570 * q^49 + 435 * q^50 + 225 * q^52 + 1026 * q^53 - 933 * q^54 + 972 * q^55 - 2661 * q^56 + 156 * q^57 - 201 * q^58 - 792 * q^59 + 1458 * q^60 - 1212 * q^61 - 2817 * q^62 - 2112 * q^63 - 1857 * q^64 - 2742 * q^65 - 594 * q^66 + 624 * q^67 - 1506 * q^69 - 1650 * q^70 - 2802 * q^71 + 1455 * q^72 - 726 * q^73 - 270 * q^74 + 264 * q^75 + 675 * q^76 - 1008 * q^77 + 3090 * q^78 + 444 * q^79 + 1143 * q^80 + 2520 * q^81 + 4950 * q^82 + 672 * q^83 - 777 * q^84 + 2778 * q^86 + 726 * q^87 + 3750 * q^88 - 906 * q^89 + 7755 * q^90 - 2280 * q^91 - 87 * q^92 + 132 * q^93 + 735 * q^94 - 966 * q^95 + 5046 * q^96 + 3246 * q^97 + 1911 * q^98 + 282 * 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 $

$2$	3.25752	1.15171	0.575854	−	0.817552i	$-0.304670\pi$
$2$	3.25752	1.15171	0.575854	+	0.817552i	$0.304670\pi$
$3$	6.51757	1.25431	0.627153	−	0.778896i	$-0.284220\pi$
$3$	6.51757	1.25431	0.627153	+	0.778896i	$0.284220\pi$
$4$	2.61146	0.326432
$5$	−19.1073	−1.70901	−0.854506	−	0.519441i	$-0.826140\pi$
$5$	−19.1073	−1.70901	−0.854506	+	0.519441i	$0.826140\pi$
$6$	21.2311	1.44460
$7$	−22.0995	−1.19326	−0.596631	−	0.802515i	$-0.703495\pi$
$7$	−22.0995	−1.19326	−0.596631	+	0.802515i	$0.703495\pi$
$8$	−17.5533	−0.775753
$9$	15.4787	0.573284
$10$	−62.2426	−1.96828
$11$	8.25972	0.226400	0.113200	−	0.993572i	$-0.463890\pi$
$11$	8.25972	0.226400	0.113200	+	0.993572i	$0.463890\pi$
$12$	17.0204	0.409446
$13$	−0.398269	−0.00849693	−0.00424846	−	0.999991i	$-0.501352\pi$
$13$	−0.398269	−0.00849693	−0.00424846	+	0.999991i	$0.501352\pi$
$14$	−71.9898	−1.37429
$15$	−124.533	−2.14362
$16$	−78.0720	−1.21987
$17$	0	0
$17$	0	0
$18$	50.4221	0.660256
$19$	103.371	1.24816	0.624078	−	0.781362i	$-0.285475\pi$
$19$	103.371	1.24816	0.624078	+	0.781362i	$0.285475\pi$
$20$	−49.8980	−0.557877
$21$	−144.035	−1.49672
$22$	26.9062	0.260747
$23$	−138.311	−1.25391	−0.626955	−	0.779056i	$-0.715699\pi$
$23$	−138.311	−1.25391	−0.626955	+	0.779056i	$0.715699\pi$
$24$	−114.405	−0.973032
$25$	240.090	1.92072
$26$	−1.29737	−0.00978598
$27$	−75.0910	−0.535233
$28$	−57.7120	−0.389520
$29$	−222.296	−1.42342	−0.711712	−	0.702471i	$-0.752080\pi$
$29$	−222.296	−1.42342	−0.711712	+	0.702471i	$0.752080\pi$
$30$	−405.670	−2.46883
$31$	−49.1520	−0.284773	−0.142386	−	0.989811i	$-0.545478\pi$
$31$	−49.1520	−0.284773	−0.142386	+	0.989811i	$0.545478\pi$
$32$	−113.895	−0.629186
$33$	53.8333	0.283975
$34$	0	0
$35$	422.263	2.03930
$36$	40.4219	0.187138
$37$	−61.3077	−0.272403	−0.136202	−	0.990681i	$-0.543490\pi$
$37$	−61.3077	−0.272403	−0.136202	+	0.990681i	$0.543490\pi$
$38$	336.734	1.43751
$39$	−2.59575	−0.0106577
$40$	335.397	1.32577
$41$	387.391	1.47562	0.737808	−	0.675011i	$-0.235861\pi$
$41$	387.391	1.47562	0.737808	+	0.675011i	$0.235861\pi$
$42$	−469.198	−1.72378
$43$	−20.3847	−0.0722939	−0.0361470	−	0.999346i	$-0.511508\pi$
$43$	−20.3847	−0.0722939	−0.0361470	+	0.999346i	$0.511508\pi$
$44$	21.5699	0.0739043
$45$	−295.756	−0.979749
$46$	−450.553	−1.44414
$47$	44.1322	0.136965	0.0684824	−	0.997652i	$-0.478184\pi$
$47$	44.1322	0.136965	0.0684824	+	0.997652i	$0.478184\pi$
$48$	−508.839	−1.53010
$49$	145.389	0.423876
$50$	782.100	2.21211
$51$	0	0
$52$	−1.04006	−0.00277367
$53$	59.6456	0.154584	0.0772920	−	0.997009i	$-0.475373\pi$
$53$	59.6456	0.154584	0.0772920	+	0.997009i	$0.475373\pi$
$54$	−244.611	−0.616432
$55$	−157.821	−0.386920
$56$	387.920	0.925678
$57$	673.728	1.56557
$58$	−724.134	−1.63937
$59$	238.069	0.525321	0.262660	−	0.964888i	$-0.415400\pi$
$59$	238.069	0.525321	0.262660	+	0.964888i	$0.415400\pi$
$60$	−325.214	−0.699749
$61$	595.816	1.25060	0.625298	−	0.780386i	$-0.284977\pi$
$61$	595.816	1.25060	0.625298	+	0.780386i	$0.284977\pi$
$62$	−160.114	−0.327975
$63$	−342.071	−0.684078
$64$	253.561	0.495235
$65$	7.60987	0.0145214
$66$	175.363	0.327056
$67$	−408.815	−0.745442	−0.372721	−	0.927943i	$-0.621575\pi$
$67$	−408.815	−0.745442	−0.372721	+	0.927943i	$0.621575\pi$
$68$	0	0
$69$	−901.454	−1.57279
$70$	1375.53	2.34868
$71$	−1037.38	−1.73400	−0.866999	−	0.498309i	$-0.833954\pi$
$71$	−1037.38	−1.73400	−0.866999	+	0.498309i	$0.833954\pi$
$72$	−271.702	−0.444727
$73$	−22.3789	−0.0358802	−0.0179401	−	0.999839i	$-0.505711\pi$
$73$	−22.3789	−0.0358802	−0.0179401	+	0.999839i	$0.505711\pi$
$74$	−199.711	−0.313729
$75$	1564.80	2.40917
$76$	269.949	0.407438
$77$	−182.536	−0.270155
$78$	−8.45571	−0.0122746
$79$	682.688	0.972259	0.486129	−	0.873887i	$-0.338408\pi$
$79$	682.688	0.972259	0.486129	+	0.873887i	$0.338408\pi$
$80$	1491.75	2.08478
$81$	−907.335	−1.24463
$82$	1261.93	1.69948
$83$	−312.352	−0.413073	−0.206536	−	0.978439i	$-0.566219\pi$
$83$	−312.352	−0.413073	−0.206536	+	0.978439i	$0.566219\pi$
$84$	−376.142	−0.488577
$85$	0	0
$86$	−66.4037	−0.0832616
$87$	−1448.83	−1.78541
$88$	−144.985	−0.175630
$89$	−904.392	−1.07714	−0.538570	−	0.842581i	$-0.681035\pi$
$89$	−904.392	−1.07714	−0.538570	+	0.842581i	$0.681035\pi$
$90$	−963.433	−1.12839
$91$	8.80157	0.0101391
$92$	−361.195	−0.409317
$93$	−320.351	−0.357192
$94$	143.762	0.157744
$95$	−1975.15	−2.13311
$96$	−742.317	−0.789192
$97$	−1006.72	−1.05378	−0.526891	−	0.849933i	$-0.676642\pi$
$97$	−1006.72	−1.05378	−0.526891	+	0.849933i	$0.676642\pi$
$98$	473.610	0.488182
$99$	127.849	0.129791
$100$	626.986	0.626986
$101$	−1124.60	−1.10794	−0.553968	−	0.832538i	$-0.686887\pi$
$101$	−1124.60	−1.10794	−0.553968	+	0.832538i	$0.686887\pi$
$102$	0	0
$103$	−396.677	−0.379473	−0.189736	−	0.981835i	$-0.560763\pi$
$103$	−396.677	−0.379473	−0.189736	+	0.981835i	$0.560763\pi$
$104$	6.99094	0.00659152
$105$	2752.13	2.55791
$106$	194.297	0.178036
$107$	288.906	0.261024	0.130512	−	0.991447i	$-0.458338\pi$
$107$	288.906	0.261024	0.130512	+	0.991447i	$0.458338\pi$
$108$	−196.097	−0.174717
$109$	−1379.15	−1.21191	−0.605955	−	0.795499i	$-0.707209\pi$
$109$	−1379.15	−1.21191	−0.605955	+	0.795499i	$0.707209\pi$
$110$	−514.106	−0.445619
$111$	−399.577	−0.341677
$112$	1725.35	1.45563
$113$	1364.42	1.13587	0.567937	−	0.823072i	$-0.307742\pi$
$113$	1364.42	1.13587	0.567937	+	0.823072i	$0.307742\pi$
$114$	2194.68	1.80308
$115$	2642.76	2.14295
$116$	−580.517	−0.464652
$117$	−6.16468	−0.00487115
$118$	775.515	0.605016
$119$	0	0
$120$	2185.97	1.66292
$121$	−1262.78	−0.948743
$122$	1940.88	1.44032
$123$	2524.84	1.85087
$124$	−128.358	−0.0929591
$125$	−2199.07	−1.57353
$126$	−1114.31	−0.787859
$127$	1003.33	0.701032	0.350516	−	0.936557i	$-0.386006\pi$
$127$	1003.33	0.701032	0.350516	+	0.936557i	$0.386006\pi$
$128$	1737.14	1.19955
$129$	−132.859	−0.0906787
$130$	24.7893	0.0167244
$131$	218.014	0.145404	0.0727022	−	0.997354i	$-0.476838\pi$
$131$	218.014	0.145404	0.0727022	+	0.997354i	$0.476838\pi$
$132$	140.583	0.0926986
$133$	−2284.45	−1.48938
$134$	−1331.72	−0.858532
$135$	1434.79	0.914719
$136$	0	0
$137$	−1625.34	−1.01359	−0.506797	−	0.862066i	$-0.669171\pi$
$137$	−1625.34	−1.01359	−0.506797	+	0.862066i	$0.669171\pi$
$138$	−2936.51	−1.81139
$139$	−1034.35	−0.631166	−0.315583	−	0.948898i	$-0.602200\pi$
$139$	−1034.35	−0.631166	−0.315583	+	0.948898i	$0.602200\pi$
$140$	1102.72	0.665694
$141$	287.635	0.171796
$142$	−3379.28	−1.99706
$143$	−3.28959	−0.00192370
$144$	−1208.45	−0.699334
$145$	4247.48	2.43265
$146$	−72.8999	−0.0413236
$147$	947.585	0.531670
$148$	−160.103	−0.0889213
$149$	−650.200	−0.357493	−0.178747	−	0.983895i	$-0.557204\pi$
$149$	−650.200	−0.357493	−0.178747	+	0.983895i	$0.557204\pi$
$150$	5097.39	2.77467
$151$	1023.67	0.551689	0.275845	−	0.961202i	$-0.411042\pi$
$151$	1023.67	0.551689	0.275845	+	0.961202i	$0.411042\pi$
$152$	−1814.50	−0.968261
$153$	0	0
$154$	−594.615	−0.311139
$155$	939.164	0.486680
$156$	−6.77869	−0.00347903
$157$	671.612	0.341404	0.170702	−	0.985323i	$-0.445396\pi$
$157$	671.612	0.341404	0.170702	+	0.985323i	$0.445396\pi$
$158$	2223.87	1.11976
$159$	388.744	0.193896
$160$	2176.23	1.07529
$161$	3056.62	1.49624
$162$	−2955.66	−1.43345
$163$	1893.45	0.909857	0.454929	−	0.890528i	$-0.349665\pi$
$163$	1893.45	0.909857	0.454929	+	0.890528i	$0.349665\pi$
$164$	1011.65	0.481689
$165$	−1028.61	−0.485316
$166$	−1017.49	−0.475739
$167$	−290.246	−0.134491	−0.0672453	−	0.997736i	$-0.521421\pi$
$167$	−290.246	−0.134491	−0.0672453	+	0.997736i	$0.521421\pi$
$168$	2528.29	1.16108
$169$	−2196.84	−0.999928
$170$	0	0
$171$	1600.05	0.715547
$172$	−53.2339	−0.0235991
$173$	3665.86	1.61104	0.805521	−	0.592567i	$-0.201886\pi$
$173$	3665.86	1.61104	0.805521	+	0.592567i	$0.201886\pi$
$174$	−4719.59	−2.05627
$175$	−5305.89	−2.29193
$176$	−644.852	−0.276179
$177$	1551.63	0.658913
$178$	−2946.08	−1.24055
$179$	−3628.67	−1.51519	−0.757597	−	0.652723i	$-0.773627\pi$
$179$	−3628.67	−1.51519	−0.757597	+	0.652723i	$0.773627\pi$
$180$	−772.355	−0.319822
$181$	−3827.78	−1.57191	−0.785957	−	0.618281i	$-0.787829\pi$
$181$	−3827.78	−1.57191	−0.785957	+	0.618281i	$0.787829\pi$
$182$	28.6713	0.0116773
$183$	3883.27	1.56863
$184$	2427.82	0.972725
$185$	1171.43	0.465541
$186$	−1043.55	−0.411382
$187$	0	0
$188$	115.249	0.0447097
$189$	1659.48	0.638673
$190$	−6434.08	−2.45672
$191$	−877.247	−0.332332	−0.166166	−	0.986098i	$-0.553139\pi$
$191$	−877.247	−0.332332	−0.166166	+	0.986098i	$0.553139\pi$
$192$	1652.60	0.621177
$193$	4769.70	1.77891	0.889457	−	0.457018i	$-0.151083\pi$
$193$	4769.70	1.77891	0.889457	+	0.457018i	$0.151083\pi$
$194$	−3279.41	−1.21365
$195$	49.5978	0.0182142
$196$	379.679	0.138367
$197$	−1492.97	−0.539949	−0.269974	−	0.962867i	$-0.587015\pi$
$197$	−1492.97	−0.539949	−0.269974	+	0.962867i	$0.587015\pi$
$198$	416.473	0.149482
$199$	3091.28	1.10118	0.550591	−	0.834775i	$-0.314402\pi$
$199$	3091.28	1.10118	0.550591	+	0.834775i	$0.314402\pi$
$200$	−4214.38	−1.49001
$201$	−2664.48	−0.935013
$202$	−3663.40	−1.27602
$203$	4912.63	1.69852
$204$	0	0
$205$	−7402.00	−2.52185
$206$	−1292.18	−0.437042
$207$	−2140.88	−0.718846
$208$	31.0937	0.0103652
$209$	853.816	0.282582
$210$	8965.12	2.94596
$211$	2776.38	0.905848	0.452924	−	0.891549i	$-0.350381\pi$
$211$	2776.38	0.905848	0.452924	+	0.891549i	$0.350381\pi$
$212$	155.762	0.0504612
$213$	−6761.17	−2.17497
$214$	941.118	0.300624
$215$	389.498	0.123551
$216$	1318.10	0.415209
$217$	1086.24	0.339809
$218$	−4492.60	−1.39577
$219$	−145.856	−0.0450048
$220$	−412.144	−0.126303
$221$	0	0
$222$	−1301.63	−0.393513
$223$	4641.22	1.39372	0.696859	−	0.717209i	$-0.254581\pi$
$223$	4641.22	1.39372	0.696859	+	0.717209i	$0.254581\pi$
$224$	2517.02	0.750784
$225$	3716.28	1.10112
$226$	4444.63	1.30820
$227$	−1712.30	−0.500658	−0.250329	−	0.968161i	$-0.580539\pi$
$227$	−1712.30	−0.500658	−0.250329	+	0.968161i	$0.580539\pi$
$228$	1759.41	0.511052
$229$	−6028.18	−1.73954	−0.869768	−	0.493461i	$-0.835731\pi$
$229$	−6028.18	−1.73954	−0.869768	+	0.493461i	$0.835731\pi$
$230$	8608.86	2.46805
$231$	−1189.69	−0.338857
$232$	3902.02	1.10423
$233$	−2663.60	−0.748919	−0.374459	−	0.927243i	$-0.622172\pi$
$233$	−2663.60	−0.748919	−0.374459	+	0.927243i	$0.622172\pi$
$234$	−20.0816	−0.00561015
$235$	−843.249	−0.234075
$236$	621.707	0.171482
$237$	4449.47	1.21951
$238$	0	0
$239$	6020.73	1.62949	0.814747	−	0.579817i	$-0.196876\pi$
$239$	6020.73	1.62949	0.814747	+	0.579817i	$0.196876\pi$
$240$	9722.56	2.61495
$241$	−6080.97	−1.62535	−0.812676	−	0.582716i	$-0.801990\pi$
$241$	−6080.97	−1.62535	−0.812676	+	0.582716i	$0.801990\pi$
$242$	−4113.53	−1.09268
$243$	−3886.16	−1.02591
$244$	1555.95	0.408235
$245$	−2778.01	−0.724409
$246$	8224.74	2.13167
$247$	−41.1695	−0.0106055
$248$	862.780	0.220914
$249$	−2035.77	−0.518120
$250$	−7163.52	−1.81224
$251$	−3296.82	−0.829058	−0.414529	−	0.910036i	$-0.636054\pi$
$251$	−3296.82	−0.829058	−0.414529	+	0.910036i	$0.636054\pi$
$252$	−893.305	−0.223305
$253$	−1142.41	−0.283885
$254$	3268.37	0.807384
$255$	0	0
$256$	3630.28	0.886300
$257$	−1243.37	−0.301786	−0.150893	−	0.988550i	$-0.548215\pi$
$257$	−1243.37	−0.301786	−0.150893	+	0.988550i	$0.548215\pi$
$258$	−432.790	−0.104435
$259$	1354.87	0.325049
$260$	19.8729	0.00474024
$261$	−3440.84	−0.816026
$262$	710.186	0.167463
$263$	4523.81	1.06065	0.530324	−	0.847795i	$-0.322070\pi$
$263$	4523.81	1.06065	0.530324	+	0.847795i	$0.322070\pi$
$264$	−944.951	−0.220294
$265$	−1139.67	−0.264186
$266$	−7441.66	−1.71533
$267$	−5894.44	−1.35106
$268$	−1067.60	−0.243337
$269$	2155.56	0.488576	0.244288	−	0.969703i	$-0.421446\pi$
$269$	2155.56	0.488576	0.244288	+	0.969703i	$0.421446\pi$
$270$	4673.86	1.05349
$271$	−5433.12	−1.21785	−0.608927	−	0.793226i	$-0.708400\pi$
$271$	−5433.12	−1.21785	−0.608927	+	0.793226i	$0.708400\pi$
$272$	0	0
$273$	57.3648	0.0127175
$274$	−5294.59	−1.16736
$275$	1983.08	0.434851
$276$	−2354.11	−0.513408
$277$	3349.75	0.726595	0.363297	−	0.931673i	$-0.381651\pi$
$277$	3349.75	0.726595	0.363297	+	0.931673i	$0.381651\pi$
$278$	−3369.40	−0.726919
$279$	−760.807	−0.163256
$280$	−7412.11	−1.58199
$281$	−2668.18	−0.566441	−0.283221	−	0.959055i	$-0.591403\pi$
$281$	−2668.18	−0.566441	−0.283221	+	0.959055i	$0.591403\pi$
$282$	936.977	0.197859
$283$	−5452.65	−1.14532	−0.572662	−	0.819792i	$-0.694089\pi$
$283$	−5452.65	−1.14532	−0.572662	+	0.819792i	$0.694089\pi$
$284$	−2709.07	−0.566033
$285$	−12873.1	−2.67558
$286$	−10.7159	−0.00221555
$287$	−8561.15	−1.76080
$288$	−1762.94	−0.360702
$289$	0	0
$290$	13836.3	2.80170
$291$	−6561.36	−1.32177
$292$	−58.4417	−0.0117125
$293$	6341.24	1.26437	0.632183	−	0.774819i	$-0.282159\pi$
$293$	6341.24	1.26437	0.632183	+	0.774819i	$0.282159\pi$
$294$	3086.78	0.612329
$295$	−4548.86	−0.897780
$296$	1076.15	0.211318
$297$	−620.231	−0.121177
$298$	−2118.04	−0.411728
$299$	55.0852	0.0106544
$300$	4086.42	0.786433
$301$	450.493	0.0862657
$302$	3334.63	0.635385
$303$	−7329.63	−1.38969
$304$	−8070.38	−1.52259
$305$	−11384.5	−2.13729
$306$	0	0
$307$	820.602	0.152555	0.0762773	−	0.997087i	$-0.475697\pi$
$307$	820.602	0.152555	0.0762773	+	0.997087i	$0.475697\pi$
$308$	−476.685	−0.0881872
$309$	−2585.37	−0.475975
$310$	3059.35	0.560514
$311$	−7492.46	−1.36610	−0.683052	−	0.730369i	$-0.739348\pi$
$311$	−7492.46	−1.36610	−0.683052	+	0.730369i	$0.739348\pi$
$312$	45.5639	0.00826779
$313$	−1217.76	−0.219910	−0.109955	−	0.993937i	$-0.535071\pi$
$313$	−1217.76	−0.219910	−0.109955	+	0.993937i	$0.535071\pi$
$314$	2187.79	0.393198
$315$	6536.07	1.16910
$316$	1782.81	0.317377
$317$	5682.18	1.00676	0.503380	−	0.864065i	$-0.332090\pi$
$317$	5682.18	1.00676	0.503380	+	0.864065i	$0.332090\pi$
$318$	1266.34	0.223311
$319$	−1836.10	−0.322263
$320$	−4844.87	−0.846363
$321$	1882.96	0.327404
$322$	9957.00	1.72324
$323$	0	0
$324$	−2369.47	−0.406287
$325$	−95.6206	−0.0163202
$326$	6167.97	1.04789
$327$	−8988.68	−1.52011
$328$	−6799.98	−1.14471
$329$	−975.301	−0.163435
$330$	−3350.72	−0.558943
$331$	7387.94	1.22682	0.613411	−	0.789764i	$-0.289797\pi$
$331$	7387.94	1.22682	0.613411	+	0.789764i	$0.289797\pi$
$332$	−815.693	−0.134840
$333$	−948.962	−0.156165
$334$	−945.483	−0.154894
$335$	7811.36	1.27397
$336$	11245.1	1.82581
$337$	5104.29	0.825069	0.412534	−	0.910942i	$-0.364644\pi$
$337$	5104.29	0.825069	0.412534	+	0.910942i	$0.364644\pi$
$338$	−7156.26	−1.15163
$339$	8892.69	1.42473
$340$	0	0
$341$	−405.982	−0.0644725
$342$	5212.19	0.824102
$343$	4367.10	0.687467
$344$	357.819	0.0560823
$345$	17224.4	2.68791
$346$	11941.6	1.85545
$347$	−8986.15	−1.39021	−0.695103	−	0.718910i	$-0.744641\pi$
$347$	−8986.15	−1.39021	−0.695103	+	0.718910i	$0.744641\pi$
$348$	−3783.55	−0.582816
$349$	1924.65	0.295198	0.147599	−	0.989047i	$-0.452845\pi$
$349$	1924.65	0.295198	0.147599	+	0.989047i	$0.452845\pi$
$350$	−17284.0	−2.63963
$351$	29.9065	0.00454783
$352$	−940.739	−0.142448
$353$	4574.33	0.689709	0.344854	−	0.938656i	$-0.387928\pi$
$353$	4574.33	0.689709	0.344854	+	0.938656i	$0.387928\pi$
$354$	5054.47	0.758876
$355$	19821.5	2.96343
$356$	−2361.78	−0.351613
$357$	0	0
$358$	−11820.5	−1.74506
$359$	9358.89	1.37589	0.687943	−	0.725765i	$-0.258514\pi$
$359$	9358.89	1.37589	0.687943	+	0.725765i	$0.258514\pi$
$360$	5191.50	0.760044
$361$	3826.58	0.557892
$362$	−12469.1	−1.81039
$363$	−8230.23	−1.19001
$364$	22.9849	0.00330972
$365$	427.602	0.0613198
$366$	12649.8	1.80661
$367$	1596.51	0.227077	0.113539	−	0.993534i	$-0.463781\pi$
$367$	1596.51	0.227077	0.113539	+	0.993534i	$0.463781\pi$
$368$	10798.2	1.52961
$369$	5996.29	0.845947
$370$	3815.95	0.536167
$371$	−1318.14	−0.184459
$372$	−836.585	−0.116599
$373$	−10884.6	−1.51094	−0.755471	−	0.655182i	$-0.772592\pi$
$373$	−10884.6	−1.51094	−0.755471	+	0.655182i	$0.772592\pi$
$374$	0	0
$375$	−14332.6	−1.97368
$376$	−774.666	−0.106251
$377$	88.5336	0.0120947
$378$	5405.79	0.735565
$379$	1561.47	0.211629	0.105814	−	0.994386i	$-0.466255\pi$
$379$	1561.47	0.211629	0.105814	+	0.994386i	$0.466255\pi$
$380$	−5158.01	−0.696317
$381$	6539.26	0.879308
$382$	−2857.65	−0.382749
$383$	−4409.48	−0.588287	−0.294143	−	0.955761i	$-0.595034\pi$
$383$	−4409.48	−0.588287	−0.294143	+	0.955761i	$0.595034\pi$
$384$	11321.9	1.50461
$385$	3487.78	0.461697
$386$	15537.4	2.04879
$387$	−315.528	−0.0414450
$388$	−2629.01	−0.343989
$389$	−8017.21	−1.04496	−0.522479	−	0.852652i	$-0.674993\pi$
$389$	−8017.21	−1.04496	−0.522479	+	0.852652i	$0.674993\pi$
$390$	161.566	0.0209775
$391$	0	0
$392$	−2552.06	−0.328823
$393$	1420.92	0.182382
$394$	−4863.39	−0.621864
$395$	−13044.4	−1.66160
$396$	333.874	0.0423681
$397$	9437.12	1.19304	0.596519	−	0.802599i	$-0.296550\pi$
$397$	9437.12	1.19304	0.596519	+	0.802599i	$0.296550\pi$
$398$	10069.9	1.26824
$399$	−14889.1	−1.86814
$400$	−18744.3	−2.34304
$401$	−4509.28	−0.561553	−0.280777	−	0.959773i	$-0.590592\pi$
$401$	−4509.28	−0.561553	−0.280777	+	0.959773i	$0.590592\pi$
$402$	−8679.59	−1.07686
$403$	19.5757	0.00241969
$404$	−2936.84	−0.361666
$405$	17336.8	2.12709
$406$	16003.0	1.95620
$407$	−506.384	−0.0616721
$408$	0	0
$409$	12446.9	1.50480	0.752398	−	0.658709i	$-0.228897\pi$
$409$	12446.9	1.50480	0.752398	+	0.658709i	$0.228897\pi$
$410$	−24112.2	−2.90443
$411$	−10593.3	−1.27136
$412$	−1035.91	−0.123872
$413$	−5261.21	−0.626846
$414$	−6973.95	−0.827901
$415$	5968.21	0.705946
$416$	45.3608	0.00534615
$417$	−6741.41	−0.791675
$418$	2781.33	0.325452
$419$	−1648.22	−0.192173	−0.0960867	−	0.995373i	$-0.530633\pi$
$419$	−1648.22	−0.192173	−0.0960867	+	0.995373i	$0.530633\pi$
$420$	7187.07	0.834984
$421$	14395.5	1.66649	0.833247	−	0.552901i	$-0.186479\pi$
$421$	14395.5	1.66649	0.833247	+	0.552901i	$0.186479\pi$
$422$	9044.13	1.04327
$423$	683.108	0.0785197
$424$	−1046.98	−0.119919
$425$	0	0
$426$	−22024.7	−2.50493
$427$	−13167.3	−1.49229
$428$	754.466	0.0852068
$429$	−21.4401	−0.00241291
$430$	1268.80	0.142295
$431$	5351.92	0.598127	0.299064	−	0.954233i	$-0.403326\pi$
$431$	5351.92	0.598127	0.299064	+	0.954233i	$0.403326\pi$
$432$	5862.50	0.652916
$433$	15578.0	1.72894	0.864472	−	0.502680i	$-0.167653\pi$
$433$	15578.0	1.72894	0.864472	+	0.502680i	$0.167653\pi$
$434$	3538.44	0.391361
$435$	27683.2	3.05129
$436$	−3601.58	−0.395607
$437$	−14297.4	−1.56507
$438$	−475.130	−0.0518324
$439$	16584.8	1.80307	0.901535	−	0.432707i	$-0.142442\pi$
$439$	16584.8	1.80307	0.901535	+	0.432707i	$0.142442\pi$
$440$	2770.28	0.300155
$441$	2250.44	0.243001
$442$	0	0
$443$	5163.31	0.553761	0.276881	−	0.960904i	$-0.410699\pi$
$443$	5163.31	0.553761	0.276881	+	0.960904i	$0.410699\pi$
$444$	−1043.48	−0.111535
$445$	17280.5	1.84084
$446$	15118.9	1.60516
$447$	−4237.72	−0.448406
$448$	−5603.57	−0.590946
$449$	−10771.9	−1.13220	−0.566099	−	0.824337i	$-0.691548\pi$
$449$	−10771.9	−1.13220	−0.566099	+	0.824337i	$0.691548\pi$
$450$	12105.9	1.26817
$451$	3199.74	0.334079
$452$	3563.13	0.370786
$453$	6671.84	0.691987
$454$	−5577.86	−0.576612
$455$	−168.175	−0.0173278
$456$	−11826.1	−1.21450
$457$	5024.59	0.514312	0.257156	−	0.966370i	$-0.417215\pi$
$457$	5024.59	0.514312	0.257156	+	0.966370i	$0.417215\pi$
$458$	−19636.9	−2.00344
$459$	0	0
$460$	6901.47	0.699527
$461$	−2366.96	−0.239133	−0.119567	−	0.992826i	$-0.538151\pi$
$461$	−2366.96	−0.239133	−0.119567	+	0.992826i	$0.538151\pi$
$462$	−3875.44	−0.390264
$463$	−17712.9	−1.77795	−0.888974	−	0.457958i	$-0.848581\pi$
$463$	−17712.9	−1.77795	−0.888974	+	0.457958i	$0.848581\pi$
$464$	17355.1	1.73640
$465$	6121.06	0.610446
$466$	−8676.73	−0.862536
$467$	−19592.7	−1.94141	−0.970707	−	0.240267i	$-0.922765\pi$
$467$	−19592.7	−1.94141	−0.970707	+	0.240267i	$0.922765\pi$
$468$	−16.0988	−0.00159010
$469$	9034.61	0.889509
$470$	−2746.90	−0.269586
$471$	4377.27	0.428225
$472$	−4178.89	−0.407519
$473$	−168.372	−0.0163673
$474$	14494.2	1.40452
$475$	24818.4	2.39736
$476$	0	0
$477$	923.234	0.0886205
$478$	19612.7	1.87670
$479$	4060.41	0.387317	0.193659	−	0.981069i	$-0.437965\pi$
$479$	4060.41	0.387317	0.193659	+	0.981069i	$0.437965\pi$
$480$	14183.7	1.34874
$481$	24.4170	0.00231459
$482$	−19808.9	−1.87193
$483$	19921.7	1.87675
$484$	−3297.69	−0.309701
$485$	19235.7	1.80093
$486$	−12659.2	−1.18155
$487$	7256.96	0.675244	0.337622	−	0.941282i	$-0.390377\pi$
$487$	7256.96	0.675244	0.337622	+	0.941282i	$0.390377\pi$
$488$	−10458.5	−0.970155
$489$	12340.7	1.14124
$490$	−9049.42	−0.834308
$491$	−769.855	−0.0707598	−0.0353799	−	0.999374i	$-0.511264\pi$
$491$	−769.855	−0.0707598	−0.0353799	+	0.999374i	$0.511264\pi$
$492$	6593.53	0.604185
$493$	0	0
$494$	−134.111	−0.0122144
$495$	−2442.86	−0.221815
$496$	3837.39	0.347387
$497$	22925.5	2.06912
$498$	−6631.58	−0.596723
$499$	−1432.66	−0.128526	−0.0642630	−	0.997933i	$-0.520470\pi$
$499$	−1432.66	−0.128526	−0.0642630	+	0.997933i	$0.520470\pi$
$500$	−5742.78	−0.513650
$501$	−1891.70	−0.168692
$502$	−10739.5	−0.954833
$503$	−16206.3	−1.43659	−0.718295	−	0.695739i	$-0.755077\pi$
$503$	−16206.3	−1.43659	−0.718295	+	0.695739i	$0.755077\pi$
$504$	6004.48	0.530676
$505$	21488.0	1.89348
$506$	−3721.44	−0.326953
$507$	−14318.1	−1.25422
$508$	2620.15	0.228839
$509$	15009.4	1.30703	0.653517	−	0.756912i	$-0.273293\pi$
$509$	15009.4	1.30703	0.653517	+	0.756912i	$0.273293\pi$
$510$	0	0
$511$	494.564	0.0428145
$512$	−2071.37	−0.178794
$513$	−7762.24	−0.668053
$514$	−4050.29	−0.347570
$515$	7579.44	0.648524
$516$	−346.955	−0.0296005
$517$	364.520	0.0310088
$518$	4413.53	0.374361
$519$	23892.5	2.02074
$520$	−133.578	−0.0112650
$521$	−19626.5	−1.65039	−0.825196	−	0.564846i	$-0.808936\pi$
$521$	−19626.5	−1.65039	−0.825196	+	0.564846i	$0.808936\pi$
$522$	−11208.6	−0.939824
$523$	−9267.41	−0.774829	−0.387414	−	0.921906i	$-0.626632\pi$
$523$	−9267.41	−0.774829	−0.387414	+	0.921906i	$0.626632\pi$
$524$	569.335	0.0474647
$525$	−34581.5	−2.87478
$526$	14736.4	1.22156
$527$	0	0
$528$	−4202.87	−0.346414
$529$	6963.04	0.572289
$530$	−3712.50	−0.304265
$531$	3684.99	0.301158
$532$	−5965.76	−0.486181
$533$	−154.286	−0.0125382
$534$	−19201.3	−1.55603
$535$	−5520.22	−0.446094
$536$	7176.04	0.578280
$537$	−23650.1	−1.90052
$538$	7021.79	0.562697
$539$	1200.88	0.0959655
$540$	3746.90	0.298594
$541$	907.733	0.0721377	0.0360689	−	0.999349i	$-0.488516\pi$
$541$	907.733	0.0721377	0.0360689	+	0.999349i	$0.488516\pi$
$542$	−17698.5	−1.40261
$543$	−24947.8	−1.97166
$544$	0	0
$545$	26351.8	2.07117
$546$	186.867	0.0146468
$547$	11197.7	0.875281	0.437640	−	0.899150i	$-0.355814\pi$
$547$	11197.7	0.875281	0.437640	+	0.899150i	$0.355814\pi$
$548$	−4244.51	−0.330870
$549$	9222.44	0.716947
$550$	6459.92	0.500822
$551$	−22979.0	−1.77665
$552$	15823.5	1.22009
$553$	−15087.1	−1.16016
$554$	10911.9	0.836825
$555$	7634.85	0.583931
$556$	−2701.15	−0.206033
$557$	−3207.25	−0.243978	−0.121989	−	0.992531i	$-0.538927\pi$
$557$	−3207.25	−0.243978	−0.121989	+	0.992531i	$0.538927\pi$
$558$	−2478.35	−0.188023
$559$	8.11861	0.000614276 0
$560$	−32966.9	−2.48769
$561$	0	0
$562$	−8691.64	−0.652375
$563$	−6522.79	−0.488282	−0.244141	−	0.969740i	$-0.578506\pi$
$563$	−6522.79	−0.488282	−0.244141	+	0.969740i	$0.578506\pi$
$564$	751.146	0.0560797
$565$	−26070.4	−1.94122
$566$	−17762.2	−1.31908
$567$	20051.7	1.48517
$568$	18209.4	1.34516
$569$	−3040.50	−0.224015	−0.112007	−	0.993707i	$-0.535728\pi$
$569$	−3040.50	−0.224015	−0.112007	+	0.993707i	$0.535728\pi$
$570$	−41934.6	−3.08148
$571$	−17273.2	−1.26596	−0.632979	−	0.774169i	$-0.718168\pi$
$571$	−17273.2	−1.26596	−0.632979	+	0.774169i	$0.718168\pi$
$572$	−8.59064	−0.000627959 0
$573$	−5717.51	−0.416846
$574$	−27888.2	−2.02793
$575$	−33207.2	−2.40841
$576$	3924.78	0.283910
$577$	−5804.29	−0.418779	−0.209390	−	0.977832i	$-0.567148\pi$
$577$	−5804.29	−0.418779	−0.209390	+	0.977832i	$0.567148\pi$
$578$	0	0
$579$	31086.8	2.23130
$580$	11092.1	0.794096
$581$	6902.83	0.492904
$582$	−21373.8	−1.52229
$583$	492.656	0.0349978
$584$	392.824	0.0278342
$585$	117.791	0.00832486
$586$	20656.8	1.45618
$587$	12862.4	0.904407	0.452204	−	0.891915i	$-0.350638\pi$
$587$	12862.4	0.904407	0.452204	+	0.891915i	$0.350638\pi$
$588$	2474.58	0.173554
$589$	−5080.89	−0.355441
$590$	−14818.0	−1.03398
$591$	−9730.55	−0.677261
$592$	4786.41	0.332298
$593$	1319.33	0.0913631	0.0456816	−	0.998956i	$-0.485454\pi$
$593$	1319.33	0.0913631	0.0456816	+	0.998956i	$0.485454\pi$
$594$	−2020.42	−0.139560
$595$	0	0
$596$	−1697.97	−0.116697
$597$	20147.6	1.38122
$598$	179.441	0.0122707
$599$	−16269.3	−1.10976	−0.554881	−	0.831930i	$-0.687236\pi$
$599$	−16269.3	−1.10976	−0.554881	+	0.831930i	$0.687236\pi$
$600$	−27467.5	−1.86893
$601$	7427.38	0.504108	0.252054	−	0.967713i	$-0.418894\pi$
$601$	7427.38	0.504108	0.252054	+	0.967713i	$0.418894\pi$
$602$	1467.49	0.0993529
$603$	−6327.90	−0.427350
$604$	2673.27	0.180089
$605$	24128.3	1.62141
$606$	−23876.4	−1.60052
$607$	7212.10	0.482257	0.241129	−	0.970493i	$-0.422482\pi$
$607$	7212.10	0.482257	0.241129	+	0.970493i	$0.422482\pi$
$608$	−11773.4	−0.785322
$609$	32018.4	2.13046
$610$	−37085.1	−2.46153
$611$	−17.5765	−0.00116378
$612$	0	0
$613$	−15446.5	−1.01775	−0.508873	−	0.860842i	$-0.669938\pi$
$613$	−15446.5	−1.01775	−0.508873	+	0.860842i	$0.669938\pi$
$614$	2673.13	0.175698
$615$	−48243.1	−3.16317
$616$	3204.11	0.209573
$617$	8746.54	0.570701	0.285350	−	0.958423i	$-0.407890\pi$
$617$	8746.54	0.570701	0.285350	+	0.958423i	$0.407890\pi$
$618$	−8421.89	−0.548185
$619$	−4740.09	−0.307787	−0.153894	−	0.988087i	$-0.549181\pi$
$619$	−4740.09	−0.307787	−0.153894	+	0.988087i	$0.549181\pi$
$620$	2452.59	0.158868
$621$	10385.9	0.671133
$622$	−24406.9	−1.57335
$623$	19986.7	1.28531
$624$	202.655	0.0130011
$625$	12007.1	0.768453
$626$	−3966.89	−0.253273
$627$	5564.80	0.354445
$628$	1753.89	0.111445
$629$	0	0
$630$	21291.4	1.34646
$631$	−17055.1	−1.07600	−0.537998	−	0.842946i	$-0.680819\pi$
$631$	−17055.1	−1.07600	−0.537998	+	0.842946i	$0.680819\pi$
$632$	−11983.4	−0.754233
$633$	18095.2	1.13621
$634$	18509.8	1.15949
$635$	−19170.9	−1.19807
$636$	1015.19	0.0632938
$637$	−57.9042	−0.00360164
$638$	−5981.14	−0.371153
$639$	−16057.2	−0.994074
$640$	−33192.1	−2.05005
$641$	−16050.5	−0.989012	−0.494506	−	0.869174i	$-0.664651\pi$
$641$	−16050.5	−0.989012	−0.494506	+	0.869174i	$0.664651\pi$
$642$	6133.80	0.377074
$643$	−14821.5	−0.909027	−0.454514	−	0.890740i	$-0.650187\pi$
$643$	−14821.5	−0.909027	−0.454514	+	0.890740i	$0.650187\pi$
$644$	7982.23	0.488422
$645$	2538.58	0.154971
$646$	0	0
$647$	−30527.0	−1.85493	−0.927465	−	0.373910i	$-0.878017\pi$
$647$	−30527.0	−1.85493	−0.927465	+	0.373910i	$0.878017\pi$
$648$	15926.7	0.965526
$649$	1966.38	0.118933
$650$	−311.486	−0.0187962
$651$	7079.62	0.426224
$652$	4944.68	0.297007
$653$	20173.6	1.20897	0.604483	−	0.796618i	$-0.293380\pi$
$653$	20173.6	1.20897	0.604483	+	0.796618i	$0.293380\pi$
$654$	−29280.8	−1.75072
$655$	−4165.67	−0.248498
$656$	−30244.3	−1.80007
$657$	−346.396	−0.0205696
$658$	−3177.07	−0.188229
$659$	−21503.0	−1.27107	−0.635537	−	0.772071i	$-0.719221\pi$
$659$	−21503.0	−1.27107	−0.635537	+	0.772071i	$0.719221\pi$
$660$	−2686.17	−0.158423
$661$	−1772.12	−0.104278	−0.0521389	−	0.998640i	$-0.516604\pi$
$661$	−1772.12	−0.104278	−0.0521389	+	0.998640i	$0.516604\pi$
$662$	24066.4	1.41294
$663$	0	0
$664$	5482.80	0.320443
$665$	43649.8	2.54536
$666$	−3091.26	−0.179856
$667$	30746.0	1.78485
$668$	−757.966	−0.0439021
$669$	30249.4	1.74815
$670$	25445.7	1.46724
$671$	4921.27	0.283135
$672$	16404.9	0.941713
$673$	33449.4	1.91587	0.957936	−	0.286983i	$-0.0926523\pi$
$673$	33449.4	1.91587	0.957936	+	0.286983i	$0.0926523\pi$
$674$	16627.3	0.950239
$675$	−18028.6	−1.02803
$676$	−5736.96	−0.326409
$677$	−805.765	−0.0457431	−0.0228716	−	0.999738i	$-0.507281\pi$
$677$	−805.765	−0.0457431	−0.0228716	+	0.999738i	$0.507281\pi$
$678$	28968.2	1.64088
$679$	22248.0	1.25744
$680$	0	0
$681$	−11160.0	−0.627978
$682$	−1322.49	−0.0742536
$683$	993.802	0.0556761	0.0278380	−	0.999612i	$-0.491138\pi$
$683$	993.802	0.0556761	0.0278380	+	0.999612i	$0.491138\pi$
$684$	4178.46	0.233578
$685$	31056.0	1.73224
$686$	14225.9	0.791762
$687$	−39289.1	−2.18191
$688$	1591.47	0.0881895
$689$	−23.7550	−0.00131349
$690$	56108.8	3.09569
$691$	33450.1	1.84154	0.920768	−	0.390111i	$-0.127563\pi$
$691$	33450.1	1.84154	0.920768	+	0.390111i	$0.127563\pi$
$692$	9573.25	0.525896
$693$	−2825.41	−0.154875
$694$	−29272.6	−1.60111
$695$	19763.6	1.07867
$696$	25431.7	1.38504
$697$	0	0
$698$	6269.59	0.339982
$699$	−17360.2	−0.939373
$700$	−13856.1	−0.748159
$701$	−18290.5	−0.985481	−0.492740	−	0.870176i	$-0.664005\pi$
$701$	−18290.5	−0.985481	−0.492740	+	0.870176i	$0.664005\pi$
$702$	97.4210	0.00523778
$703$	−6337.44	−0.340002
$704$	2094.34	0.112121
$705$	−5495.93	−0.293601
$706$	14901.0	0.794343
$707$	24853.1	1.32206
$708$	4052.02	0.215091
$709$	6780.00	0.359137	0.179569	−	0.983745i	$-0.442530\pi$
$709$	6780.00	0.359137	0.179569	+	0.983745i	$0.442530\pi$
$710$	64569.0	3.41300
$711$	10567.1	0.557380
$712$	15875.1	0.835595
$713$	6798.28	0.357079
$714$	0	0
$715$	62.8554	0.00328763
$716$	−9476.13	−0.494608
$717$	39240.5	2.04388
$718$	30486.8	1.58462
$719$	−24591.0	−1.27551	−0.637754	−	0.770240i	$-0.720136\pi$
$719$	−24591.0	−1.27551	−0.637754	+	0.770240i	$0.720136\pi$
$720$	23090.3	1.19517
$721$	8766.37	0.452811
$722$	12465.2	0.642528
$723$	−39633.1	−2.03869
$724$	−9996.08	−0.513124
$725$	−53371.1	−2.73400
$726$	−26810.2	−1.37055
$727$	−9819.79	−0.500957	−0.250479	−	0.968122i	$-0.580588\pi$
$727$	−9819.79	−0.500957	−0.250479	+	0.968122i	$0.580588\pi$
$728$	−154.497	−0.00786542
$729$	−830.242	−0.0421806
$730$	1392.92	0.0706225
$731$	0	0
$732$	10141.0	0.512052
$733$	−10751.8	−0.541783	−0.270892	−	0.962610i	$-0.587318\pi$
$733$	−10751.8	−0.541783	−0.270892	+	0.962610i	$0.587318\pi$
$734$	5200.68	0.261527
$735$	−18105.8	−0.908631
$736$	15753.0	0.788942
$737$	−3376.69	−0.168768
$738$	19533.1	0.974284
$739$	−1809.70	−0.0900823	−0.0450412	−	0.998985i	$-0.514342\pi$
$739$	−1809.70	−0.0900823	−0.0450412	+	0.998985i	$0.514342\pi$
$740$	3059.13	0.151968
$741$	−268.325	−0.0133025
$742$	−4293.87	−0.212443
$743$	−895.790	−0.0442306	−0.0221153	−	0.999755i	$-0.507040\pi$
$743$	−895.790	−0.0442306	−0.0221153	+	0.999755i	$0.507040\pi$
$744$	5623.22	0.277093
$745$	12423.6	0.610960
$746$	−35456.7	−1.74016
$747$	−4834.79	−0.236808
$748$	0	0
$749$	−6384.69	−0.311470
$750$	−46688.7	−2.27311
$751$	−11683.1	−0.567672	−0.283836	−	0.958873i	$-0.591607\pi$
$751$	−11683.1	−0.567672	−0.283836	+	0.958873i	$0.591607\pi$
$752$	−3445.49	−0.167080
$753$	−21487.2	−1.03989
$754$	288.400	0.0139296
$755$	−19559.6	−0.942844
$756$	4333.66	0.208484
$757$	−12621.2	−0.605976	−0.302988	−	0.952994i	$-0.597984\pi$
$757$	−12621.2	−0.605976	−0.302988	+	0.952994i	$0.597984\pi$
$758$	5086.53	0.243735
$759$	−7445.75	−0.356079
$760$	34670.3	1.65477
$761$	−5759.46	−0.274350	−0.137175	−	0.990547i	$-0.543802\pi$
$761$	−5759.46	−0.274350	−0.137175	+	0.990547i	$0.543802\pi$
$762$	21301.8	1.01271
$763$	30478.5	1.44613
$764$	−2290.89	−0.108484
$765$	0	0
$766$	−14364.0	−0.677535
$767$	−94.8156	−0.00446361
$768$	23660.6	1.11169
$769$	3245.56	0.152195	0.0760975	−	0.997100i	$-0.475754\pi$
$769$	3245.56	0.152195	0.0760975	+	0.997100i	$0.475754\pi$
$770$	11361.5	0.531741
$771$	−8103.72	−0.378532
$772$	12455.9	0.580695
$773$	−2500.27	−0.116337	−0.0581684	−	0.998307i	$-0.518526\pi$
$773$	−2500.27	−0.116337	−0.0581684	+	0.998307i	$0.518526\pi$
$774$	−1027.84	−0.0477325
$775$	−11800.9	−0.546970
$776$	17671.2	0.817475
$777$	8830.47	0.407711
$778$	−26116.2	−1.20349
$779$	40045.0	1.84180
$780$	129.523	0.00594571
$781$	−8568.44	−0.392577
$782$	0	0
$783$	16692.4	0.761863
$784$	−11350.8	−0.517075
$785$	−12832.7	−0.583464
$786$	4628.68	0.210050
$787$	15270.8	0.691671	0.345835	−	0.938295i	$-0.387596\pi$
$787$	15270.8	0.691671	0.345835	+	0.938295i	$0.387596\pi$
$788$	−3898.84	−0.176257
$789$	29484.2	1.33038
$790$	−42492.3	−1.91368
$791$	−30153.0	−1.35540
$792$	−2244.18	−0.100686
$793$	−237.295	−0.0106262
$794$	30741.7	1.37403
$795$	−7427.86	−0.331370
$796$	8072.76	0.359462
$797$	6885.20	0.306006	0.153003	−	0.988226i	$-0.451106\pi$
$797$	6885.20	0.306006	0.153003	+	0.988226i	$0.451106\pi$
$798$	−48501.5	−2.15155
$799$	0	0
$800$	−27345.1	−1.20849
$801$	−13998.8	−0.617507
$802$	−14689.1	−0.646746
$803$	−184.844	−0.00812328
$804$	−6958.17	−0.305219
$805$	−58403.8	−2.55710
$806$	63.7684	0.00278678
$807$	14049.0	0.612824
$808$	19740.4	0.859485
$809$	−13606.4	−0.591318	−0.295659	−	0.955294i	$-0.595539\pi$
$809$	−13606.4	−0.591318	−0.295659	+	0.955294i	$0.595539\pi$
$810$	56474.9	2.44978
$811$	−12718.7	−0.550694	−0.275347	−	0.961345i	$-0.588793\pi$
$811$	−12718.7	−0.550694	−0.275347	+	0.961345i	$0.588793\pi$
$812$	12829.1	0.554452
$813$	−35410.7	−1.52756
$814$	−1649.56	−0.0710283
$815$	−36178.9	−1.55496
$816$	0	0
$817$	−2107.19	−0.0902341
$818$	40546.2	1.73309
$819$	136.237	0.00581257
$820$	−19330.0	−0.823212
$821$	−29119.6	−1.23786	−0.618929	−	0.785447i	$-0.712433\pi$
$821$	−29119.6	−1.23786	−0.618929	+	0.785447i	$0.712433\pi$
$822$	−34507.8	−1.46423
$823$	6284.88	0.266193	0.133097	−	0.991103i	$-0.457508\pi$
$823$	6284.88	0.266193	0.133097	+	0.991103i	$0.457508\pi$
$824$	6962.98	0.294377
$825$	12924.8	0.545437
$826$	−17138.5	−0.721944
$827$	−5383.60	−0.226368	−0.113184	−	0.993574i	$-0.536105\pi$
$827$	−5383.60	−0.226368	−0.113184	+	0.993574i	$0.536105\pi$
$828$	−5590.81	−0.234655
$829$	25382.6	1.06342	0.531709	−	0.846927i	$-0.321550\pi$
$829$	25382.6	1.06342	0.531709	+	0.846927i	$0.321550\pi$
$830$	19441.6	0.813045
$831$	21832.2	0.911372
$832$	−100.985	−0.00420798
$833$	0	0
$834$	−21960.3	−0.911779
$835$	5545.83	0.229846
$836$	2229.71	0.0922440
$837$	3690.88	0.152420
$838$	−5369.10	−0.221328
$839$	−2499.44	−0.102849	−0.0514246	−	0.998677i	$-0.516376\pi$
$839$	−2499.44	−0.102849	−0.0514246	+	0.998677i	$0.516376\pi$
$840$	−48308.9	−1.98431
$841$	25026.4	1.02614
$842$	46893.7	1.91932
$843$	−17390.0	−0.710491
$844$	7250.41	0.295698
$845$	41975.8	1.70889
$846$	2225.24	0.0904318
$847$	27906.8	1.13210
$848$	−4656.65	−0.188573
$849$	−35538.0	−1.43659
$850$	0	0
$851$	8479.55	0.341569
$852$	−17656.5	−0.709979
$853$	38293.9	1.53711	0.768557	−	0.639781i	$-0.220975\pi$
$853$	38293.9	1.53711	0.768557	+	0.639781i	$0.220975\pi$
$854$	−42892.6	−1.71868
$855$	−30572.6	−1.22288
$856$	−5071.25	−0.202490
$857$	−426.303	−0.0169921	−0.00849606	−	0.999964i	$-0.502704\pi$
$857$	−426.303	−0.0169921	−0.00849606	+	0.999964i	$0.502704\pi$
$858$	−69.8418	−0.00277897
$859$	30976.1	1.23037	0.615186	−	0.788382i	$-0.289081\pi$
$859$	30976.1	1.23037	0.615186	+	0.788382i	$0.289081\pi$
$860$	1017.16	0.0403311
$861$	−55797.9	−2.20858
$862$	17434.0	0.688868
$863$	38201.4	1.50682	0.753412	−	0.657549i	$-0.228407\pi$
$863$	38201.4	1.50682	0.753412	+	0.657549i	$0.228407\pi$
$864$	8552.48	0.336761
$865$	−70044.8	−2.75329
$866$	50745.8	1.99124
$867$	0	0
$868$	2836.66	0.110925
$869$	5638.81	0.220119
$870$	90178.8	3.51419
$871$	162.818	0.00633397
$872$	24208.6	0.940144
$873$	−15582.7	−0.604116
$874$	−46574.1	−1.80251
$875$	48598.4	1.87763
$876$	−380.898	−0.0146910
$877$	−13461.8	−0.518327	−0.259163	−	0.965833i	$-0.583447\pi$
$877$	−13461.8	−0.518327	−0.259163	+	0.965833i	$0.583447\pi$
$878$	54025.2	2.07661
$879$	41329.5	1.58590
$880$	12321.4	0.471994
$881$	13867.4	0.530310	0.265155	−	0.964206i	$-0.414577\pi$
$881$	13867.4	0.530310	0.265155	+	0.964206i	$0.414577\pi$
$882$	7330.85	0.279867
$883$	−330.794	−0.0126072	−0.00630358	−	0.999980i	$-0.502007\pi$
$883$	−330.794	−0.0126072	−0.00630358	+	0.999980i	$0.502007\pi$
$884$	0	0
$885$	−29647.5	−1.12609
$886$	16819.6	0.637772
$887$	−42906.5	−1.62419	−0.812097	−	0.583523i	$-0.801674\pi$
$887$	−42906.5	−1.62419	−0.812097	+	0.583523i	$0.801674\pi$
$888$	7013.90	0.265057
$889$	−22173.1	−0.836515
$890$	56291.7	2.12012
$891$	−7494.33	−0.281784
$892$	12120.4	0.454954
$893$	4561.99	0.170953
$894$	−13804.5	−0.516433
$895$	69334.3	2.58948
$896$	−38389.9	−1.43138
$897$	359.021	0.0133639
$898$	−35089.7	−1.30396
$899$	10926.3	0.405353
$900$	9704.91	0.359441
$901$	0	0
$902$	10423.2	0.384762
$903$	2936.12	0.108204
$904$	−23950.1	−0.881158
$905$	73138.6	2.68642
$906$	21733.7	0.796968
$907$	−6908.93	−0.252930	−0.126465	−	0.991971i	$-0.540363\pi$
$907$	−6908.93	−0.252930	−0.126465	+	0.991971i	$0.540363\pi$
$908$	−4471.60	−0.163431
$909$	−17407.2	−0.635162
$910$	−547.833	−0.0199566
$911$	33032.6	1.20134	0.600669	−	0.799497i	$-0.294901\pi$
$911$	33032.6	1.20134	0.600669	+	0.799497i	$0.294901\pi$
$912$	−52599.2	−1.90980
$913$	−2579.94	−0.0935196
$914$	16367.7	0.592337
$915$	−74198.9	−2.68081
$916$	−15742.4	−0.567841
$917$	−4818.01	−0.173506
$918$	0	0
$919$	8167.05	0.293151	0.146576	−	0.989199i	$-0.453175\pi$
$919$	8167.05	0.293151	0.146576	+	0.989199i	$0.453175\pi$
$920$	−46389.2	−1.66240
$921$	5348.33	0.191350
$922$	−7710.44	−0.275412
$923$	413.155	0.0147337
$924$	−3106.83	−0.110614
$925$	−14719.4	−0.523211
$926$	−57700.3	−2.04768
$927$	−6140.03	−0.217546
$928$	25318.3	0.895599
$929$	1864.03	0.0658308	0.0329154	−	0.999458i	$-0.489521\pi$
$929$	1864.03	0.0658308	0.0329154	+	0.999458i	$0.489521\pi$
$930$	19939.5	0.703056
$931$	15029.1	0.529063
$932$	−6955.87	−0.244471
$933$	−48832.6	−1.71351
$934$	−63823.6	−2.23594
$935$	0	0
$936$	108.210	0.00377881
$937$	−44071.0	−1.53654	−0.768270	−	0.640126i	$-0.778882\pi$
$937$	−44071.0	−1.53654	−0.768270	+	0.640126i	$0.778882\pi$
$938$	29430.5	1.02445
$939$	−7936.84	−0.275835
$940$	−2202.11	−0.0764095
$941$	−33030.1	−1.14426	−0.572131	−	0.820162i	$-0.693883\pi$
$941$	−33030.1	−1.14426	−0.572131	+	0.820162i	$0.693883\pi$
$942$	14259.1	0.493191
$943$	−53580.5	−1.85029
$944$	−18586.5	−0.640825
$945$	−31708.2	−1.09150
$946$	−548.476	−0.0188504
$947$	9340.37	0.320508	0.160254	−	0.987076i	$-0.448769\pi$
$947$	9340.37	0.320508	0.160254	+	0.987076i	$0.448769\pi$
$948$	11619.6	0.398088
$949$	8.91285	0.000304872 0
$950$	80846.5	2.76106
$951$	37034.0	1.26278
$952$	0	0
$953$	21211.2	0.720984	0.360492	−	0.932762i	$-0.382609\pi$
$953$	21211.2	0.720984	0.360492	+	0.932762i	$0.382609\pi$
$954$	3007.46	0.102065
$955$	16761.9	0.567959
$956$	15722.9	0.531919
$957$	−11966.9	−0.404217
$958$	13226.9	0.446077
$959$	35919.3	1.20948
$960$	−31576.7	−1.06160
$961$	−27375.1	−0.918904
$962$	79.5389	0.00266574
$963$	4471.88	0.149641
$964$	−15880.2	−0.530567
$965$	−91136.3	−3.04019
$966$	64895.4	2.16147
$967$	21688.1	0.721242	0.360621	−	0.932712i	$-0.382565\pi$
$967$	21688.1	0.721242	0.360621	+	0.932712i	$0.382565\pi$
$968$	22165.9	0.735991
$969$	0	0
$970$	62660.8	2.07414
$971$	−22478.6	−0.742918	−0.371459	−	0.928449i	$-0.621142\pi$
$971$	−22478.6	−0.742918	−0.371459	+	0.928449i	$0.621142\pi$
$972$	−10148.5	−0.334892
$973$	22858.5	0.753146
$974$	23639.7	0.777685
$975$	−623.214	−0.0204706
$976$	−46516.5	−1.52557
$977$	21731.7	0.711626	0.355813	−	0.934557i	$-0.384204\pi$
$977$	21731.7	0.711626	0.355813	+	0.934557i	$0.384204\pi$
$978$	40200.2	1.31438
$979$	−7470.03	−0.243864
$980$	−7254.65	−0.236471
$981$	−21347.3	−0.694769
$982$	−2507.82	−0.0814947
$983$	−34128.8	−1.10737	−0.553683	−	0.832728i	$-0.686778\pi$
$983$	−34128.8	−1.10737	−0.553683	+	0.832728i	$0.686778\pi$
$984$	−44319.3	−1.43582
$985$	28526.7	0.922779
$986$	0	0
$987$	−6356.59	−0.204998
$988$	−107.513	−0.00346197
$989$	2819.44	0.0906501
$990$	−7957.68	−0.255466
$991$	−39750.8	−1.27419	−0.637097	−	0.770784i	$-0.719865\pi$
$991$	−39750.8	−1.27419	−0.637097	+	0.770784i	$0.719865\pi$
$992$	5598.16	0.179175
$993$	48151.4	1.53881
$994$	74680.5	2.38302
$995$	−59066.2	−1.88193
$996$	−5316.34	−0.169131
$997$	−54112.0	−1.71890	−0.859450	−	0.511219i	$-0.829194\pi$
$997$	−54112.0	−1.71890	−0.859450	+	0.511219i	$0.829194\pi$
$998$	−4666.91	−0.148024
$999$	4603.66	0.145799

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.h.1.9	✓	12
17.4	even	4		289.4.b.f.288.7		24
17.13	even	4		289.4.b.f.288.8		24
17.16	even	2		289.4.a.i.1.9	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.4.a.h.1.9	✓	12	1.1	even	1	trivial
289.4.a.i.1.9	yes	12	17.16	even	2
289.4.b.f.288.7		24	17.4	even	4
289.4.b.f.288.8		24	17.13	even	4

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+3.25752 q^{2} +6.51757 q^{3} +2.61146 q^{4} -19.1073 q^{5} +21.2311 q^{6} -22.0995 q^{7} -17.5533 q^{8} +15.4787 q^{9} +O(q^{10})\)	\(q+3.25752 q^{2} +6.51757 q^{3} +2.61146 q^{4} -19.1073 q^{5} +21.2311 q^{6} -22.0995 q^{7} -17.5533 q^{8} +15.4787 q^{9} -62.2426 q^{10} +8.25972 q^{11} +17.0204 q^{12} -0.398269 q^{13} -71.9898 q^{14} -124.533 q^{15} -78.0720 q^{16} +50.4221 q^{18} +103.371 q^{19} -49.8980 q^{20} -144.035 q^{21} +26.9062 q^{22} -138.311 q^{23} -114.405 q^{24} +240.090 q^{25} -1.29737 q^{26} -75.0910 q^{27} -57.7120 q^{28} -222.296 q^{29} -405.670 q^{30} -49.1520 q^{31} -113.895 q^{32} +53.8333 q^{33} +422.263 q^{35} +40.4219 q^{36} -61.3077 q^{37} +336.734 q^{38} -2.59575 q^{39} +335.397 q^{40} +387.391 q^{41} -469.198 q^{42} -20.3847 q^{43} +21.5699 q^{44} -295.756 q^{45} -450.553 q^{46} +44.1322 q^{47} -508.839 q^{48} +145.389 q^{49} +782.100 q^{50} -1.04006 q^{52} +59.6456 q^{53} -244.611 q^{54} -157.821 q^{55} +387.920 q^{56} +673.728 q^{57} -724.134 q^{58} +238.069 q^{59} -325.214 q^{60} +595.816 q^{61} -160.114 q^{62} -342.071 q^{63} +253.561 q^{64} +7.60987 q^{65} +175.363 q^{66} -408.815 q^{67} -901.454 q^{69} +1375.53 q^{70} -1037.38 q^{71} -271.702 q^{72} -22.3789 q^{73} -199.711 q^{74} +1564.80 q^{75} +269.949 q^{76} -182.536 q^{77} -8.45571 q^{78} +682.688 q^{79} +1491.75 q^{80} -907.335 q^{81} +1261.93 q^{82} -312.352 q^{83} -376.142 q^{84} -66.4037 q^{86} -1448.83 q^{87} -144.985 q^{88} -904.392 q^{89} -963.433 q^{90} +8.80157 q^{91} -361.195 q^{92} -320.351 q^{93} +143.762 q^{94} -1975.15 q^{95} -742.317 q^{96} -1006.72 q^{97} +473.610 q^{98} +127.849 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) \) 12 * q - 18 * q^3 + 48 * q^4 - 30 * q^5 + 9 * q^6 - 24 * q^7 - 51 * q^8 + 108 * q^9	\( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9} - 60 q^{10} - 162 q^{11} - 216 q^{12} - 72 q^{13} - 267 q^{14} - 138 q^{15} + 192 q^{16} + 189 q^{18} - 66 q^{19} - 129 q^{20} + 246 q^{21} - 456 q^{22} - 282 q^{23} - 72 q^{24} + 444 q^{25} + 528 q^{26} - 1092 q^{27} - 120 q^{28} - 648 q^{29} - 1890 q^{30} - 504 q^{31} - 1353 q^{32} + 966 q^{33} - 66 q^{35} - 663 q^{36} + 30 q^{37} - 60 q^{38} - 1758 q^{39} + 450 q^{40} - 318 q^{41} + 804 q^{42} + 486 q^{43} - 2448 q^{44} - 486 q^{45} - 1617 q^{46} - 888 q^{47} - 1257 q^{48} - 570 q^{49} + 435 q^{50} + 225 q^{52} + 1026 q^{53} - 933 q^{54} + 972 q^{55} - 2661 q^{56} + 156 q^{57} - 201 q^{58} - 792 q^{59} + 1458 q^{60} - 1212 q^{61} - 2817 q^{62} - 2112 q^{63} - 1857 q^{64} - 2742 q^{65} - 594 q^{66} + 624 q^{67} - 1506 q^{69} - 1650 q^{70} - 2802 q^{71} + 1455 q^{72} - 726 q^{73} - 270 q^{74} + 264 q^{75} + 675 q^{76} - 1008 q^{77} + 3090 q^{78} + 444 q^{79} + 1143 q^{80} + 2520 q^{81} + 4950 q^{82} + 672 q^{83} - 777 q^{84} + 2778 q^{86} + 726 q^{87} + 3750 q^{88} - 906 q^{89} + 7755 q^{90} - 2280 q^{91} - 87 q^{92} + 132 q^{93} + 735 q^{94} - 966 q^{95} + 5046 q^{96} + 3246 q^{97} + 1911 q^{98} + 282 q^{99}+O(q^{100}) \) 12 * q - 18 * q^3 + 48 * q^4 - 30 * q^5 + 9 * q^6 - 24 * q^7 - 51 * q^8 + 108 * q^9 - 60 * q^10 - 162 * q^11 - 216 * q^12 - 72 * q^13 - 267 * q^14 - 138 * q^15 + 192 * q^16 + 189 * q^18 - 66 * q^19 - 129 * q^20 + 246 * q^21 - 456 * q^22 - 282 * q^23 - 72 * q^24 + 444 * q^25 + 528 * q^26 - 1092 * q^27 - 120 * q^28 - 648 * q^29 - 1890 * q^30 - 504 * q^31 - 1353 * q^32 + 966 * q^33 - 66 * q^35 - 663 * q^36 + 30 * q^37 - 60 * q^38 - 1758 * q^39 + 450 * q^40 - 318 * q^41 + 804 * q^42 + 486 * q^43 - 2448 * q^44 - 486 * q^45 - 1617 * q^46 - 888 * q^47 - 1257 * q^48 - 570 * q^49 + 435 * q^50 + 225 * q^52 + 1026 * q^53 - 933 * q^54 + 972 * q^55 - 2661 * q^56 + 156 * q^57 - 201 * q^58 - 792 * q^59 + 1458 * q^60 - 1212 * q^61 - 2817 * q^62 - 2112 * q^63 - 1857 * q^64 - 2742 * q^65 - 594 * q^66 + 624 * q^67 - 1506 * q^69 - 1650 * q^70 - 2802 * q^71 + 1455 * q^72 - 726 * q^73 - 270 * q^74 + 264 * q^75 + 675 * q^76 - 1008 * q^77 + 3090 * q^78 + 444 * q^79 + 1143 * q^80 + 2520 * q^81 + 4950 * q^82 + 672 * q^83 - 777 * q^84 + 2778 * q^86 + 726 * q^87 + 3750 * q^88 - 906 * q^89 + 7755 * q^90 - 2280 * q^91 - 87 * q^92 + 132 * q^93 + 735 * q^94 - 966 * q^95 + 5046 * q^96 + 3246 * q^97 + 1911 * q^98 + 282 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more