LMFDB - Embedded newform 289.4.a.g.1.6

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} - 4 x^{11} - 58 x^{10} + 204 x^{9} + 1191 x^{8} - 3456 x^{7} - 10364 x^{6} + 21448 x^{5} + \cdots + 1156 $ x^12 - 4x^11 - 58x^10 + 204x^9 + 1191x^8 - 3456x^7 - 10364x^6 + 21448x^5 + 38476x^4 - 32336x^3 - 57024x^2 - 15776*x + 1156
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.0598990$ 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)

$f(q)$	$=$	$q-1.70547 q^{2} +4.44379 q^{3} -5.09138 q^{4} -6.80983 q^{5} -7.57875 q^{6} +13.8760 q^{7} +22.3269 q^{8} -7.25269 q^{9} +O(q^{10})$	\(q-1.70547 q^{2} +4.44379 q^{3} -5.09138 q^{4} -6.80983 q^{5} -7.57875 q^{6} +13.8760 q^{7} +22.3269 q^{8} -7.25269 q^{9} +11.6140 q^{10} -30.8361 q^{11} -22.6250 q^{12} +66.0130 q^{13} -23.6651 q^{14} -30.2615 q^{15} +2.65318 q^{16} +12.3692 q^{18} -79.7150 q^{19} +34.6714 q^{20} +61.6622 q^{21} +52.5899 q^{22} -28.8986 q^{23} +99.2163 q^{24} -78.6262 q^{25} -112.583 q^{26} -152.212 q^{27} -70.6481 q^{28} -266.201 q^{29} +51.6100 q^{30} +35.7906 q^{31} -183.140 q^{32} -137.029 q^{33} -94.4935 q^{35} +36.9262 q^{36} +357.875 q^{37} +135.951 q^{38} +293.348 q^{39} -152.043 q^{40} -32.7452 q^{41} -105.163 q^{42} -516.157 q^{43} +156.998 q^{44} +49.3896 q^{45} +49.2857 q^{46} -210.602 q^{47} +11.7902 q^{48} -150.456 q^{49} +134.094 q^{50} -336.097 q^{52} +87.2324 q^{53} +259.593 q^{54} +209.989 q^{55} +309.809 q^{56} -354.237 q^{57} +453.997 q^{58} -310.728 q^{59} +154.073 q^{60} +365.247 q^{61} -61.0397 q^{62} -100.639 q^{63} +291.115 q^{64} -449.537 q^{65} +233.699 q^{66} -660.131 q^{67} -128.420 q^{69} +161.156 q^{70} -398.030 q^{71} -161.930 q^{72} -643.443 q^{73} -610.344 q^{74} -349.399 q^{75} +405.859 q^{76} -427.882 q^{77} -500.296 q^{78} +384.511 q^{79} -18.0677 q^{80} -480.576 q^{81} +55.8460 q^{82} -153.488 q^{83} -313.946 q^{84} +880.289 q^{86} -1182.94 q^{87} -688.475 q^{88} -599.053 q^{89} -84.2324 q^{90} +915.998 q^{91} +147.134 q^{92} +159.046 q^{93} +359.175 q^{94} +542.846 q^{95} -813.838 q^{96} -44.5693 q^{97} +256.598 q^{98} +223.645 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9}+O(q^{10}) $ 12 * q - 8 * q^2 + 16 * q^4 - 96 * q^8 - 36 * q^9	$ 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9} - 8 q^{13} - 192 q^{15} - 184 q^{16} - 352 q^{19} - 256 q^{21} - 492 q^{25} - 784 q^{26} + 744 q^{30} + 24 q^{32} - 1400 q^{33} - 632 q^{35} - 856 q^{36} - 624 q^{38} - 1664 q^{42} - 1200 q^{43} - 1512 q^{47} - 1052 q^{49} - 2856 q^{50} + 792 q^{52} - 2504 q^{53} - 1424 q^{55} - 3408 q^{59} - 2808 q^{60} + 272 q^{64} + 272 q^{66} - 1080 q^{67} - 344 q^{69} + 2600 q^{70} + 248 q^{72} + 896 q^{76} + 848 q^{77} - 2404 q^{81} - 2960 q^{83} + 4768 q^{84} - 1200 q^{86} - 160 q^{87} - 2144 q^{89} + 3800 q^{93} + 5984 q^{94} + 3464 q^{98}+O(q^{100}) $ 12 * q - 8 * q^2 + 16 * q^4 - 96 * q^8 - 36 * q^9 - 8 * q^13 - 192 * q^15 - 184 * q^16 - 352 * q^19 - 256 * q^21 - 492 * q^25 - 784 * q^26 + 744 * q^30 + 24 * q^32 - 1400 * q^33 - 632 * q^35 - 856 * q^36 - 624 * q^38 - 1664 * q^42 - 1200 * q^43 - 1512 * q^47 - 1052 * q^49 - 2856 * q^50 + 792 * q^52 - 2504 * q^53 - 1424 * q^55 - 3408 * q^59 - 2808 * q^60 + 272 * q^64 + 272 * q^66 - 1080 * q^67 - 344 * q^69 + 2600 * q^70 + 248 * q^72 + 896 * q^76 + 848 * q^77 - 2404 * q^81 - 2960 * q^83 + 4768 * q^84 - 1200 * q^86 - 160 * q^87 - 2144 * q^89 + 3800 * q^93 + 5984 * q^94 + 3464 * 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 $

$2$	−1.70547	−0.602974	−0.301487	−	0.953470i	$-0.597483\pi$
$2$	−1.70547	−0.602974	−0.301487	+	0.953470i	$0.597483\pi$
$3$	4.44379	0.855209	0.427604	−	0.903966i	$-0.359358\pi$
$3$	4.44379	0.855209	0.427604	+	0.903966i	$0.359358\pi$
$4$	−5.09138	−0.636422
$5$	−6.80983	−0.609090	−0.304545	−	0.952498i	$-0.598504\pi$
$5$	−6.80983	−0.609090	−0.304545	+	0.952498i	$0.598504\pi$
$6$	−7.57875	−0.515668
$7$	13.8760	0.749235	0.374618	−	0.927179i	$-0.377774\pi$
$7$	13.8760	0.749235	0.374618	+	0.927179i	$0.377774\pi$
$8$	22.3269	0.986720
$9$	−7.25269	−0.268618
$10$	11.6140	0.367265
$11$	−30.8361	−0.845221	−0.422610	−	0.906311i	$-0.638886\pi$
$11$	−30.8361	−0.845221	−0.422610	+	0.906311i	$0.638886\pi$
$12$	−22.6250	−0.544274
$13$	66.0130	1.40836	0.704181	−	0.710021i	$-0.251314\pi$
$13$	66.0130	1.40836	0.704181	+	0.710021i	$0.251314\pi$
$14$	−23.6651	−0.451769
$15$	−30.2615	−0.520899
$16$	2.65318	0.0414559
$17$	0	0
$17$	0	0
$18$	12.3692	0.161970
$19$	−79.7150	−0.962520	−0.481260	−	0.876578i	$-0.659821\pi$
$19$	−79.7150	−0.962520	−0.481260	+	0.876578i	$0.659821\pi$
$20$	34.6714	0.387639
$21$	61.6622	0.640752
$22$	52.5899	0.509646
$23$	−28.8986	−0.261990	−0.130995	−	0.991383i	$-0.541817\pi$
$23$	−28.8986	−0.261990	−0.130995	+	0.991383i	$0.541817\pi$
$24$	99.2163	0.843851
$25$	−78.6262	−0.629009
$26$	−112.583	−0.849205
$27$	−152.212	−1.08493
$28$	−70.6481	−0.476830
$29$	−266.201	−1.70456	−0.852281	−	0.523084i	$-0.824781\pi$
$29$	−266.201	−1.70456	−0.852281	+	0.523084i	$0.824781\pi$
$30$	51.6100	0.314089
$31$	35.7906	0.207361	0.103680	−	0.994611i	$-0.466938\pi$
$31$	35.7906	0.207361	0.103680	+	0.994611i	$0.466938\pi$
$32$	−183.140	−1.01172
$33$	−137.029	−0.722840
$34$	0	0
$35$	−94.4935	−0.456352
$36$	36.9262	0.170955
$37$	357.875	1.59011	0.795057	−	0.606535i	$-0.207441\pi$
$37$	357.875	1.59011	0.795057	+	0.606535i	$0.207441\pi$
$38$	135.951	0.580374
$39$	293.348	1.20444
$40$	−152.043	−0.601001
$41$	−32.7452	−0.124730	−0.0623652	−	0.998053i	$-0.519864\pi$
$41$	−32.7452	−0.124730	−0.0623652	+	0.998053i	$0.519864\pi$
$42$	−105.163	−0.386357
$43$	−516.157	−1.83054	−0.915270	−	0.402841i	$-0.868023\pi$
$43$	−516.157	−1.83054	−0.915270	+	0.402841i	$0.868023\pi$
$44$	156.998	0.537917
$45$	49.3896	0.163613
$46$	49.2857	0.157973
$47$	−210.602	−0.653606	−0.326803	−	0.945093i	$-0.605971\pi$
$47$	−210.602	−0.653606	−0.326803	+	0.945093i	$0.605971\pi$
$48$	11.7902	0.0354534
$49$	−150.456	−0.438647
$50$	134.094	0.379276
$51$	0	0
$52$	−336.097	−0.896313
$53$	87.2324	0.226081	0.113040	−	0.993590i	$-0.463941\pi$
$53$	87.2324	0.226081	0.113040	+	0.993590i	$0.463941\pi$
$54$	259.593	0.654186
$55$	209.989	0.514815
$56$	309.809	0.739285
$57$	−354.237	−0.823155
$58$	453.997	1.02781
$59$	−310.728	−0.685651	−0.342825	−	0.939399i	$-0.611384\pi$
$59$	−310.728	−0.685651	−0.342825	+	0.939399i	$0.611384\pi$
$60$	154.073	0.331512
$61$	365.247	0.766641	0.383321	−	0.923615i	$-0.374780\pi$
$61$	365.247	0.766641	0.383321	+	0.923615i	$0.374780\pi$
$62$	−61.0397	−0.125033
$63$	−100.639	−0.201258
$64$	291.115	0.568583
$65$	−449.537	−0.857819
$66$	233.699	0.435854
$67$	−660.131	−1.20370	−0.601850	−	0.798609i	$-0.705569\pi$
$67$	−660.131	−1.20370	−0.601850	+	0.798609i	$0.705569\pi$
$68$	0	0
$69$	−128.420	−0.224056
$70$	161.156	0.275168
$71$	−398.030	−0.665316	−0.332658	−	0.943047i	$-0.607946\pi$
$71$	−398.030	−0.665316	−0.332658	+	0.943047i	$0.607946\pi$
$72$	−161.930	−0.265051
$73$	−643.443	−1.03163	−0.515817	−	0.856699i	$-0.672511\pi$
$73$	−643.443	−1.03163	−0.515817	+	0.856699i	$0.672511\pi$
$74$	−610.344	−0.958797
$75$	−349.399	−0.537934
$76$	405.859	0.612569
$77$	−427.882	−0.633269
$78$	−500.296	−0.726248
$79$	384.511	0.547605	0.273803	−	0.961786i	$-0.411718\pi$
$79$	384.511	0.547605	0.273803	+	0.961786i	$0.411718\pi$
$80$	−18.0677	−0.0252504
$81$	−480.576	−0.659226
$82$	55.8460	0.0752092
$83$	−153.488	−0.202983	−0.101491	−	0.994836i	$-0.532361\pi$
$83$	−153.488	−0.202983	−0.101491	+	0.994836i	$0.532361\pi$
$84$	−313.946	−0.407789
$85$	0	0
$86$	880.289	1.10377
$87$	−1182.94	−1.45776
$88$	−688.475	−0.833996
$89$	−599.053	−0.713477	−0.356738	−	0.934204i	$-0.616111\pi$
$89$	−599.053	−0.713477	−0.356738	+	0.934204i	$0.616111\pi$
$90$	−84.2324	−0.0986542
$91$	915.998	1.05519
$92$	147.134	0.166737
$93$	159.046	0.177336
$94$	359.175	0.394107
$95$	542.846	0.586261
$96$	−813.838	−0.865229
$97$	−44.5693	−0.0466529	−0.0233265	−	0.999728i	$-0.507426\pi$
$97$	−44.5693	−0.0466529	−0.0233265	+	0.999728i	$0.507426\pi$
$98$	256.598	0.264492
$99$	223.645	0.227042
$100$	400.316	0.400316
$101$	1478.33	1.45643	0.728215	−	0.685348i	$-0.240350\pi$
$101$	1478.33	1.45643	0.728215	+	0.685348i	$0.240350\pi$
$102$	0	0
$103$	618.133	0.591325	0.295662	−	0.955293i	$-0.404460\pi$
$103$	618.133	0.591325	0.295662	+	0.955293i	$0.404460\pi$
$104$	1473.87	1.38966
$105$	−419.909	−0.390276
$106$	−148.772	−0.136321
$107$	−138.979	−0.125567	−0.0627833	−	0.998027i	$-0.519998\pi$
$107$	−138.979	−0.125567	−0.0627833	+	0.998027i	$0.519998\pi$
$108$	774.969	0.690476
$109$	−823.466	−0.723612	−0.361806	−	0.932253i	$-0.617840\pi$
$109$	−823.466	−0.723612	−0.361806	+	0.932253i	$0.617840\pi$
$110$	−358.129	−0.310420
$111$	1590.32	1.35988
$112$	36.8156	0.0310602
$113$	602.474	0.501558	0.250779	−	0.968044i	$-0.419313\pi$
$113$	602.474	0.501558	0.250779	+	0.968044i	$0.419313\pi$
$114$	604.140	0.496341
$115$	196.795	0.159576
$116$	1355.33	1.08482
$117$	−478.772	−0.378312
$118$	529.937	0.413430
$119$	0	0
$120$	−675.646	−0.513982
$121$	−380.136	−0.285602
$122$	−622.917	−0.462265
$123$	−145.513	−0.106671
$124$	−182.223	−0.131969
$125$	1386.66	0.992213
$126$	171.636	0.121354
$127$	1506.98	1.05294	0.526468	−	0.850195i	$-0.323516\pi$
$127$	1506.98	1.05294	0.526468	+	0.850195i	$0.323516\pi$
$128$	968.636	0.668876
$129$	−2293.70	−1.56549
$130$	766.671	0.517243
$131$	2783.58	1.85651	0.928254	−	0.371946i	$-0.121309\pi$
$131$	2783.58	1.85651	0.928254	+	0.371946i	$0.121309\pi$
$132$	697.667	0.460032
$133$	−1106.13	−0.721154
$134$	1125.83	0.725799
$135$	1036.54	0.660822
$136$	0	0
$137$	−629.783	−0.392744	−0.196372	−	0.980529i	$-0.562916\pi$
$137$	−629.783	−0.392744	−0.196372	+	0.980529i	$0.562916\pi$
$138$	219.015	0.135100
$139$	2654.10	1.61955	0.809775	−	0.586740i	$-0.199589\pi$
$139$	2654.10	1.61955	0.809775	+	0.586740i	$0.199589\pi$
$140$	481.102	0.290432
$141$	−935.872	−0.558969
$142$	678.827	0.401168
$143$	−2035.58	−1.19038
$144$	−19.2427	−0.0111358
$145$	1812.78	1.03823
$146$	1097.37	0.622048
$147$	−668.595	−0.375134
$148$	−1822.08	−1.01198
$149$	−2216.30	−1.21857	−0.609283	−	0.792953i	$-0.708543\pi$
$149$	−2216.30	−1.21857	−0.609283	+	0.792953i	$0.708543\pi$
$150$	595.888	0.324360
$151$	2133.15	1.14963	0.574813	−	0.818285i	$-0.305075\pi$
$151$	2133.15	1.14963	0.574813	+	0.818285i	$0.305075\pi$
$152$	−1779.79	−0.949737
$153$	0	0
$154$	729.740	0.381845
$155$	−243.728	−0.126301
$156$	−1493.55	−0.766534
$157$	−345.107	−0.175430	−0.0877152	−	0.996146i	$-0.527957\pi$
$157$	−345.107	−0.175430	−0.0877152	+	0.996146i	$0.527957\pi$
$158$	−655.770	−0.330192
$159$	387.643	0.193346
$160$	1247.16	0.616227
$161$	−400.998	−0.196292
$162$	819.606	0.397496
$163$	678.526	0.326050	0.163025	−	0.986622i	$-0.447875\pi$
$163$	678.526	0.326050	0.163025	+	0.986622i	$0.447875\pi$
$164$	166.718	0.0793812
$165$	933.146	0.440275
$166$	261.770	0.122393
$167$	799.790	0.370596	0.185298	−	0.982682i	$-0.440675\pi$
$167$	799.790	0.370596	0.185298	+	0.982682i	$0.440675\pi$
$168$	1376.73	0.632243
$169$	2160.71	0.983483
$170$	0	0
$171$	578.148	0.258550
$172$	2627.95	1.16500
$173$	−1885.48	−0.828615	−0.414307	−	0.910137i	$-0.635976\pi$
$173$	−1885.48	−0.828615	−0.414307	+	0.910137i	$0.635976\pi$
$174$	2017.47	0.878989
$175$	−1091.02	−0.471276
$176$	−81.8136	−0.0350394
$177$	−1380.81	−0.586374
$178$	1021.66	0.430208
$179$	−3588.86	−1.49857	−0.749286	−	0.662247i	$-0.769603\pi$
$179$	−3588.86	−1.49857	−0.749286	+	0.662247i	$0.769603\pi$
$180$	−251.461	−0.104127
$181$	461.347	0.189457	0.0947284	−	0.995503i	$-0.469802\pi$
$181$	461.347	0.189457	0.0947284	+	0.995503i	$0.469802\pi$
$182$	−1562.20	−0.636255
$183$	1623.08	0.655638
$184$	−645.218	−0.258511
$185$	−2437.07	−0.968522
$186$	−271.248	−0.106929
$187$	0	0
$188$	1072.26	0.415969
$189$	−2112.10	−0.812870
$190$	−925.806	−0.353500
$191$	−4519.91	−1.71230	−0.856149	−	0.516728i	$-0.827150\pi$
$191$	−4519.91	−1.71230	−0.856149	+	0.516728i	$0.827150\pi$
$192$	1293.65	0.486257
$193$	−2928.92	−1.09238	−0.546188	−	0.837663i	$-0.683922\pi$
$193$	−2928.92	−1.09238	−0.546188	+	0.837663i	$0.683922\pi$
$194$	76.0116	0.0281305
$195$	−1997.65	−0.733614
$196$	766.027	0.279165
$197$	1926.13	0.696606	0.348303	−	0.937382i	$-0.386758\pi$
$197$	1926.13	0.696606	0.348303	+	0.937382i	$0.386758\pi$
$198$	−381.419	−0.136900
$199$	3086.61	1.09952	0.549759	−	0.835323i	$-0.314720\pi$
$199$	3086.61	1.09952	0.549759	+	0.835323i	$0.314720\pi$
$200$	−1755.48	−0.620656
$201$	−2933.49	−1.02941
$202$	−2521.25	−0.878190
$203$	−3693.81	−1.27712
$204$	0	0
$205$	222.990	0.0759721
$206$	−1054.21	−0.356553
$207$	209.593	0.0703754
$208$	175.144	0.0583849
$209$	2458.10	0.813541
$210$	716.142	0.235326
$211$	3602.40	1.17535	0.587676	−	0.809097i	$-0.300043\pi$
$211$	3602.40	1.17535	0.587676	+	0.809097i	$0.300043\pi$
$212$	−444.133	−0.143883
$213$	−1768.76	−0.568984
$214$	237.024	0.0757133
$215$	3514.94	1.11496
$216$	−3398.42	−1.07053
$217$	496.631	0.155362
$218$	1404.39	0.436319
$219$	−2859.33	−0.882262
$220$	−1069.13	−0.327640
$221$	0	0
$222$	−2712.24	−0.819972
$223$	−1577.43	−0.473688	−0.236844	−	0.971548i	$-0.576113\pi$
$223$	−1577.43	−0.473688	−0.236844	+	0.971548i	$0.576113\pi$
$224$	−2541.26	−0.758014
$225$	570.252	0.168963
$226$	−1027.50	−0.302426
$227$	−4292.90	−1.25520	−0.627599	−	0.778537i	$-0.715962\pi$
$227$	−4292.90	−1.25520	−0.627599	+	0.778537i	$0.715962\pi$
$228$	1803.55	0.523874
$229$	580.893	0.167627	0.0838133	−	0.996481i	$-0.473290\pi$
$229$	580.893	0.167627	0.0838133	+	0.996481i	$0.473290\pi$
$230$	−335.627	−0.0962200
$231$	−1901.42	−0.541577
$232$	−5943.45	−1.68193
$233$	−671.778	−0.188883	−0.0944413	−	0.995530i	$-0.530106\pi$
$233$	−671.778	−0.188883	−0.0944413	+	0.995530i	$0.530106\pi$
$234$	816.530	0.228112
$235$	1434.16	0.398105
$236$	1582.04	0.436363
$237$	1708.69	0.468317
$238$	0	0
$239$	−273.635	−0.0740584	−0.0370292	−	0.999314i	$-0.511789\pi$
$239$	−273.635	−0.0740584	−0.0370292	+	0.999314i	$0.511789\pi$
$240$	−80.2891	−0.0215943
$241$	6486.56	1.73376	0.866879	−	0.498518i	$-0.166122\pi$
$241$	6486.56	1.73376	0.866879	+	0.498518i	$0.166122\pi$
$242$	648.310	0.172211
$243$	1974.14	0.521158
$244$	−1859.61	−0.487908
$245$	1024.58	0.267175
$246$	248.168	0.0643195
$247$	−5262.22	−1.35558
$248$	799.093	0.204607
$249$	−682.071	−0.173592
$250$	−2364.90	−0.598279
$251$	−2527.58	−0.635615	−0.317808	−	0.948155i	$-0.602947\pi$
$251$	−2527.58	−0.635615	−0.317808	+	0.948155i	$0.602947\pi$
$252$	512.389	0.128085
$253$	891.120	0.221440
$254$	−2570.11	−0.634893
$255$	0	0
$256$	−3980.89	−0.971898
$257$	1702.44	0.413211	0.206605	−	0.978424i	$-0.433758\pi$
$257$	1702.44	0.413211	0.206605	+	0.978424i	$0.433758\pi$
$258$	3911.82	0.943952
$259$	4965.88	1.19137
$260$	2288.76	0.545935
$261$	1930.67	0.457877
$262$	−4747.31	−1.11943
$263$	−4274.40	−1.00217	−0.501085	−	0.865398i	$-0.667066\pi$
$263$	−4274.40	−1.00217	−0.501085	+	0.865398i	$0.667066\pi$
$264$	−3059.44	−0.713241
$265$	−594.038	−0.137704
$266$	1886.46	0.434837
$267$	−2662.07	−0.610172
$268$	3360.98	0.766061
$269$	−7996.34	−1.81244	−0.906218	−	0.422810i	$-0.861044\pi$
$269$	−7996.34	−1.81244	−0.906218	+	0.422810i	$0.861044\pi$
$270$	−1767.78	−0.398458
$271$	474.268	0.106309	0.0531545	−	0.998586i	$-0.483072\pi$
$271$	474.268	0.106309	0.0531545	+	0.998586i	$0.483072\pi$
$272$	0	0
$273$	4070.51	0.902411
$274$	1074.07	0.236815
$275$	2424.52	0.531652
$276$	653.833	0.142595
$277$	2826.25	0.613043	0.306521	−	0.951864i	$-0.400835\pi$
$277$	2826.25	0.613043	0.306521	+	0.951864i	$0.400835\pi$
$278$	−4526.48	−0.976547
$279$	−259.578	−0.0557008
$280$	−2109.75	−0.450291
$281$	−2498.15	−0.530346	−0.265173	−	0.964201i	$-0.585429\pi$
$281$	−2498.15	−0.530346	−0.265173	+	0.964201i	$0.585429\pi$
$282$	1596.10	0.337044
$283$	−2417.07	−0.507704	−0.253852	−	0.967243i	$-0.581698\pi$
$283$	−2417.07	−0.507704	−0.253852	+	0.967243i	$0.581698\pi$
$284$	2026.52	0.423422
$285$	2412.29	0.501375
$286$	3471.62	0.717766
$287$	−454.374	−0.0934524
$288$	1328.26	0.271766
$289$	0	0
$290$	−3091.65	−0.626027
$291$	−198.057	−0.0398980
$292$	3276.01	0.656555
$293$	6652.17	1.32636	0.663181	−	0.748459i	$-0.269206\pi$
$293$	6652.17	1.32636	0.663181	+	0.748459i	$0.269206\pi$
$294$	1140.27	0.226196
$295$	2116.01	0.417623
$296$	7990.24	1.56900
$297$	4693.62	0.917008
$298$	3779.83	0.734764
$299$	−1907.68	−0.368977
$300$	1778.92	0.342353
$301$	−7162.21	−1.37150
$302$	−3638.02	−0.693194
$303$	6569.40	1.24555
$304$	−211.498	−0.0399021
$305$	−2487.27	−0.466954
$306$	0	0
$307$	−2511.18	−0.466842	−0.233421	−	0.972376i	$-0.574992\pi$
$307$	−2511.18	−0.466842	−0.233421	+	0.972376i	$0.574992\pi$
$308$	2178.51	0.403027
$309$	2746.85	0.505706
$310$	415.670	0.0761563
$311$	−3585.10	−0.653674	−0.326837	−	0.945081i	$-0.605983\pi$
$311$	−3585.10	−0.653674	−0.326837	+	0.945081i	$0.605983\pi$
$312$	6549.56	1.18845
$313$	2612.32	0.471747	0.235874	−	0.971784i	$-0.424205\pi$
$313$	2612.32	0.471747	0.235874	+	0.971784i	$0.424205\pi$
$314$	588.570	0.105780
$315$	685.332	0.122584
$316$	−1957.69	−0.348508
$317$	3903.80	0.691669	0.345834	−	0.938296i	$-0.387596\pi$
$317$	3903.80	0.691669	0.345834	+	0.938296i	$0.387596\pi$
$318$	−661.112	−0.116583
$319$	8208.60	1.44073
$320$	−1982.44	−0.346318
$321$	−617.594	−0.107386
$322$	683.890	0.118359
$323$	0	0
$324$	2446.79	0.419546
$325$	−5190.35	−0.885873
$326$	−1157.20	−0.196600
$327$	−3659.31	−0.618839
$328$	−731.101	−0.123074
$329$	−2922.32	−0.489704
$330$	−1591.45	−0.265474
$331$	−6236.03	−1.03554	−0.517769	−	0.855520i	$-0.673237\pi$
$331$	−6236.03	−1.03554	−0.517769	+	0.855520i	$0.673237\pi$
$332$	781.468	0.129183
$333$	−2595.55	−0.427134
$334$	−1364.02	−0.223460
$335$	4495.38	0.733161
$336$	163.601	0.0265630
$337$	−3842.08	−0.621043	−0.310521	−	0.950566i	$-0.600504\pi$
$337$	−3842.08	−0.621043	−0.310521	+	0.950566i	$0.600504\pi$
$338$	−3685.02	−0.593014
$339$	2677.27	0.428936
$340$	0	0
$341$	−1103.64	−0.175265
$342$	−986.014	−0.155899
$343$	−6847.21	−1.07788
$344$	−11524.2	−1.80623
$345$	874.516	0.136471
$346$	3215.62	0.499633
$347$	−8301.86	−1.28434	−0.642172	−	0.766561i	$-0.721966\pi$
$347$	−8301.86	−1.28434	−0.642172	+	0.766561i	$0.721966\pi$
$348$	6022.81	0.927748
$349$	4929.17	0.756024	0.378012	−	0.925801i	$-0.376608\pi$
$349$	4929.17	0.756024	0.378012	+	0.925801i	$0.376608\pi$
$350$	1860.70	0.284167
$351$	−10048.0	−1.52798
$352$	5647.33	0.855124
$353$	−9607.54	−1.44861	−0.724303	−	0.689482i	$-0.757838\pi$
$353$	−9607.54	−1.44861	−0.724303	+	0.689482i	$0.757838\pi$
$354$	2354.93	0.353568
$355$	2710.52	0.405237
$356$	3050.00	0.454073
$357$	0	0
$358$	6120.69	0.903600
$359$	−1962.76	−0.288553	−0.144277	−	0.989537i	$-0.546085\pi$
$359$	−1962.76	−0.288553	−0.144277	+	0.989537i	$0.546085\pi$
$360$	1102.72	0.161440
$361$	−504.522	−0.0735561
$362$	−786.813	−0.114238
$363$	−1689.25	−0.244249
$364$	−4663.69	−0.671549
$365$	4381.74	0.628358
$366$	−2768.12	−0.395333
$367$	−3458.29	−0.491883	−0.245941	−	0.969285i	$-0.579097\pi$
$367$	−3458.29	−0.491883	−0.245941	+	0.969285i	$0.579097\pi$
$368$	−76.6732	−0.0108610
$369$	237.491	0.0335049
$370$	4156.34	0.583994
$371$	1210.44	0.169388
$372$	−809.763	−0.112861
$373$	2661.22	0.369418	0.184709	−	0.982793i	$-0.440866\pi$
$373$	2661.22	0.369418	0.184709	+	0.982793i	$0.440866\pi$
$374$	0	0
$375$	6162.03	0.848549
$376$	−4702.10	−0.644926
$377$	−17572.7	−2.40064
$378$	3602.11	0.490140
$379$	−5583.03	−0.756677	−0.378339	−	0.925667i	$-0.623505\pi$
$379$	−5583.03	−0.756677	−0.378339	+	0.925667i	$0.623505\pi$
$380$	−2763.83	−0.373110
$381$	6696.71	0.900480
$382$	7708.56	1.03247
$383$	7832.13	1.04492	0.522459	−	0.852665i	$-0.325015\pi$
$383$	7832.13	1.04492	0.522459	+	0.852665i	$0.325015\pi$
$384$	4304.42	0.572029
$385$	2913.81	0.385718
$386$	4995.18	0.658674
$387$	3743.53	0.491717
$388$	226.919	0.0296910
$389$	7432.95	0.968807	0.484403	−	0.874845i	$-0.339037\pi$
$389$	7432.95	0.968807	0.484403	+	0.874845i	$0.339037\pi$
$390$	3406.93	0.442350
$391$	0	0
$392$	−3359.22	−0.432821
$393$	12369.7	1.58770
$394$	−3284.96	−0.420035
$395$	−2618.45	−0.333541
$396$	−1138.66	−0.144494
$397$	9540.26	1.20608	0.603038	−	0.797713i	$-0.293957\pi$
$397$	9540.26	1.20608	0.603038	+	0.797713i	$0.293957\pi$
$398$	−5264.12	−0.662981
$399$	−4915.40	−0.616737
$400$	−208.609	−0.0260761
$401$	8663.30	1.07886	0.539432	−	0.842029i	$-0.318639\pi$
$401$	8663.30	1.07886	0.539432	+	0.842029i	$0.318639\pi$
$402$	5002.97	0.620710
$403$	2362.64	0.292039
$404$	−7526.75	−0.926905
$405$	3272.64	0.401528
$406$	6299.68	0.770069
$407$	−11035.4	−1.34400
$408$	0	0
$409$	5279.17	0.638235	0.319117	−	0.947715i	$-0.396614\pi$
$409$	5279.17	0.638235	0.319117	+	0.947715i	$0.396614\pi$
$410$	−380.302	−0.0458092
$411$	−2798.62	−0.335878
$412$	−3147.15	−0.376332
$413$	−4311.68	−0.513714
$414$	−357.454	−0.0424346
$415$	1045.23	0.123635
$416$	−12089.6	−1.42486
$417$	11794.3	1.38505
$418$	−4192.21	−0.490544
$419$	9408.24	1.09695	0.548476	−	0.836166i	$-0.315208\pi$
$419$	9408.24	1.09695	0.548476	+	0.836166i	$0.315208\pi$
$420$	2137.92	0.248380
$421$	−8191.97	−0.948343	−0.474171	−	0.880433i	$-0.657252\pi$
$421$	−8191.97	−0.948343	−0.474171	+	0.880433i	$0.657252\pi$
$422$	−6143.77	−0.708706
$423$	1527.43	0.175570
$424$	1947.63	0.223079
$425$	0	0
$426$	3016.57	0.343083
$427$	5068.18	0.574395
$428$	707.595	0.0799133
$429$	−9045.70	−1.01802
$430$	−5994.62	−0.672294
$431$	1950.29	0.217964	0.108982	−	0.994044i	$-0.465241\pi$
$431$	1950.29	0.217964	0.108982	+	0.994044i	$0.465241\pi$
$432$	−403.845	−0.0449769
$433$	11152.3	1.23775	0.618876	−	0.785489i	$-0.287588\pi$
$433$	11152.3	1.23775	0.618876	+	0.785489i	$0.287588\pi$
$434$	−846.988	−0.0936791
$435$	8055.64	0.887905
$436$	4192.58	0.460523
$437$	2303.65	0.252171
$438$	4876.49	0.531981
$439$	470.158	0.0511149	0.0255574	−	0.999673i	$-0.491864\pi$
$439$	470.158	0.0511149	0.0255574	+	0.999673i	$0.491864\pi$
$440$	4688.40	0.507979
$441$	1091.21	0.117829
$442$	0	0
$443$	−13132.9	−1.40849	−0.704246	−	0.709956i	$-0.748715\pi$
$443$	−13132.9	−1.40849	−0.704246	+	0.709956i	$0.748715\pi$
$444$	−8096.93	−0.865457
$445$	4079.45	0.434572
$446$	2690.25	0.285621
$447$	−9848.78	−1.04213
$448$	4039.51	0.426002
$449$	−10433.0	−1.09658	−0.548291	−	0.836288i	$-0.684721\pi$
$449$	−10433.0	−1.09658	−0.548291	+	0.836288i	$0.684721\pi$
$450$	−972.546	−0.101881
$451$	1009.73	0.105425
$452$	−3067.43	−0.319203
$453$	9479.28	0.983169
$454$	7321.40	0.756851
$455$	−6237.79	−0.642708
$456$	−7909.02	−0.812224
$457$	−253.385	−0.0259362	−0.0129681	−	0.999916i	$-0.504128\pi$
$457$	−253.385	−0.0259362	−0.0129681	+	0.999916i	$0.504128\pi$
$458$	−990.694	−0.101074
$459$	0	0
$460$	−1001.96	−0.101558
$461$	15560.2	1.57204	0.786019	−	0.618202i	$-0.212139\pi$
$461$	15560.2	1.57204	0.786019	+	0.618202i	$0.212139\pi$
$462$	3242.81	0.326557
$463$	10727.9	1.07682	0.538409	−	0.842684i	$-0.319026\pi$
$463$	10727.9	1.07682	0.538409	+	0.842684i	$0.319026\pi$
$464$	−706.279	−0.0706641
$465$	−1083.08	−0.108014
$466$	1145.70	0.113891
$467$	−1960.48	−0.194262	−0.0971308	−	0.995272i	$-0.530967\pi$
$467$	−1960.48	−0.194262	−0.0971308	+	0.995272i	$0.530967\pi$
$468$	2437.61	0.240766
$469$	−9160.00	−0.901854
$470$	−2445.92	−0.240047
$471$	−1533.59	−0.150030
$472$	−6937.61	−0.676545
$473$	15916.3	1.54721
$474$	−2914.11	−0.282383
$475$	6267.68	0.605434
$476$	0	0
$477$	−632.670	−0.0607295
$478$	466.675	0.0446553
$479$	−4294.19	−0.409617	−0.204808	−	0.978802i	$-0.565657\pi$
$479$	−4294.19	−0.409617	−0.204808	+	0.978802i	$0.565657\pi$
$480$	5542.10	0.527002
$481$	23624.4	2.23946
$482$	−11062.6	−1.04541
$483$	−1781.95	−0.167871
$484$	1935.42	0.181764
$485$	303.510	0.0284158
$486$	−3366.84	−0.314244
$487$	−18013.5	−1.67612	−0.838060	−	0.545578i	$-0.816310\pi$
$487$	−18013.5	−1.67612	−0.838060	+	0.545578i	$0.816310\pi$
$488$	8154.85	0.756460
$489$	3015.23	0.278841
$490$	−1747.39	−0.161100
$491$	13733.2	1.26226	0.631129	−	0.775678i	$-0.282592\pi$
$491$	13733.2	1.26226	0.631129	+	0.775678i	$0.282592\pi$
$492$	740.862	0.0678875
$493$	0	0
$494$	8974.55	0.817377
$495$	−1522.98	−0.138289
$496$	94.9587	0.00859632
$497$	−5523.07	−0.498478
$498$	1163.25	0.104672
$499$	7747.71	0.695060	0.347530	−	0.937669i	$-0.387020\pi$
$499$	7747.71	0.695060	0.347530	+	0.937669i	$0.387020\pi$
$500$	−7060.01	−0.631467
$501$	3554.10	0.316937
$502$	4310.71	0.383259
$503$	19203.7	1.70229	0.851143	−	0.524934i	$-0.175910\pi$
$503$	19203.7	1.70229	0.851143	+	0.524934i	$0.175910\pi$
$504$	−2246.95	−0.198586
$505$	−10067.2	−0.887098
$506$	−1519.78	−0.133522
$507$	9601.76	0.841083
$508$	−7672.61	−0.670112
$509$	151.325	0.0131775	0.00658876	−	0.999978i	$-0.497903\pi$
$509$	151.325	0.0131775	0.00658876	+	0.999978i	$0.497903\pi$
$510$	0	0
$511$	−8928.43	−0.772936
$512$	−959.802	−0.0828470
$513$	12133.6	1.04427
$514$	−2903.45	−0.249155
$515$	−4209.38	−0.360170
$516$	11678.1	0.996315
$517$	6494.14	0.552441
$518$	−8469.15	−0.718365
$519$	−8378.68	−0.708638
$520$	−10036.8	−0.846427
$521$	−8548.62	−0.718852	−0.359426	−	0.933174i	$-0.617027\pi$
$521$	−8548.62	−0.718852	−0.359426	+	0.933174i	$0.617027\pi$
$522$	−3292.70	−0.276088
$523$	17874.0	1.49441	0.747205	−	0.664593i	$-0.231395\pi$
$523$	17874.0	1.49441	0.747205	+	0.664593i	$0.231395\pi$
$524$	−14172.3	−1.18152
$525$	−4848.26	−0.403039
$526$	7289.85	0.604283
$527$	0	0
$528$	−363.563	−0.0299660
$529$	−11331.9	−0.931361
$530$	1013.11	0.0830317
$531$	2253.62	0.184178
$532$	5631.71	0.458958
$533$	−2161.61	−0.175666
$534$	4540.07	0.367918
$535$	946.425	0.0764813
$536$	−14738.7	−1.18771
$537$	−15948.2	−1.28159
$538$	13637.5	1.09285
$539$	4639.47	0.370753
$540$	−5277.41	−0.420562
$541$	2122.24	0.168655	0.0843273	−	0.996438i	$-0.473126\pi$
$541$	2122.24	0.168655	0.0843273	+	0.996438i	$0.473126\pi$
$542$	−808.849	−0.0641015
$543$	2050.13	0.162025
$544$	0	0
$545$	5607.67	0.440745
$546$	−6942.12	−0.544130
$547$	284.066	0.0222044	0.0111022	−	0.999938i	$-0.496466\pi$
$547$	284.066	0.0222044	0.0111022	+	0.999938i	$0.496466\pi$
$548$	3206.46	0.249951
$549$	−2649.03	−0.205934
$550$	−4134.95	−0.320572
$551$	21220.2	1.64067
$552$	−2867.21	−0.221081
$553$	5335.48	0.410285
$554$	−4820.08	−0.369649
$555$	−10829.8	−0.828289
$556$	−13513.0	−1.03072
$557$	9915.36	0.754268	0.377134	−	0.926159i	$-0.376910\pi$
$557$	9915.36	0.754268	0.377134	+	0.926159i	$0.376910\pi$
$558$	442.702	0.0335862
$559$	−34073.1	−2.57806
$560$	−250.708	−0.0189185
$561$	0	0
$562$	4260.52	0.319785
$563$	−5048.52	−0.377922	−0.188961	−	0.981985i	$-0.560512\pi$
$563$	−5048.52	−0.377922	−0.188961	+	0.981985i	$0.560512\pi$
$564$	4764.88	0.355741
$565$	−4102.75	−0.305494
$566$	4122.24	0.306132
$567$	−6668.48	−0.493915
$568$	−8886.78	−0.656481
$569$	10964.5	0.807828	0.403914	−	0.914797i	$-0.367650\pi$
$569$	10964.5	0.807828	0.403914	+	0.914797i	$0.367650\pi$
$570$	−4114.09	−0.302316
$571$	6757.57	0.495263	0.247632	−	0.968854i	$-0.420348\pi$
$571$	6757.57	0.495263	0.247632	+	0.968854i	$0.420348\pi$
$572$	10363.9	0.757582
$573$	−20085.5	−1.46437
$574$	774.920	0.0563494
$575$	2272.19	0.164794
$576$	−2111.36	−0.152732
$577$	−18050.9	−1.30237	−0.651187	−	0.758917i	$-0.725729\pi$
$577$	−18050.9	−1.30237	−0.651187	+	0.758917i	$0.725729\pi$
$578$	0	0
$579$	−13015.5	−0.934209
$580$	−9229.57	−0.660754
$581$	−2129.81	−0.152082
$582$	337.780	0.0240574
$583$	−2689.90	−0.191088
$584$	−14366.1	−1.01793
$585$	3260.36	0.230426
$586$	−11345.1	−0.799762
$587$	−7447.06	−0.523634	−0.261817	−	0.965118i	$-0.584322\pi$
$587$	−7447.06	−0.523634	−0.261817	+	0.965118i	$0.584322\pi$
$588$	3404.07	0.238744
$589$	−2853.04	−0.199589
$590$	−3608.78	−0.251816
$591$	8559.34	0.595743
$592$	949.505	0.0659196
$593$	−1229.32	−0.0851298	−0.0425649	−	0.999094i	$-0.513553\pi$
$593$	−1229.32	−0.0851298	−0.0425649	+	0.999094i	$0.513553\pi$
$594$	−8004.82	−0.552932
$595$	0	0
$596$	11284.0	0.775523
$597$	13716.3	0.940317
$598$	3253.49	0.222484
$599$	10655.6	0.726840	0.363420	−	0.931625i	$-0.381609\pi$
$599$	10655.6	0.726840	0.363420	+	0.931625i	$0.381609\pi$
$600$	−7800.99	−0.530790
$601$	2134.49	0.144871	0.0724356	−	0.997373i	$-0.476923\pi$
$601$	2134.49	0.144871	0.0724356	+	0.997373i	$0.476923\pi$
$602$	12214.9	0.826982
$603$	4787.73	0.323336
$604$	−10860.7	−0.731647
$605$	2588.67	0.173957
$606$	−11203.9	−0.751036
$607$	−12364.9	−0.826812	−0.413406	−	0.910547i	$-0.635661\pi$
$607$	−12364.9	−0.826812	−0.413406	+	0.910547i	$0.635661\pi$
$608$	14599.0	0.973797
$609$	−16414.5	−1.09220
$610$	4241.96	0.281561
$611$	−13902.5	−0.920513
$612$	0	0
$613$	4888.87	0.322120	0.161060	−	0.986945i	$-0.448509\pi$
$613$	4888.87	0.322120	0.161060	+	0.986945i	$0.448509\pi$
$614$	4282.73	0.281493
$615$	990.920	0.0649720
$616$	−9553.30	−0.624859
$617$	24750.0	1.61491	0.807453	−	0.589932i	$-0.200845\pi$
$617$	24750.0	1.61491	0.807453	+	0.589932i	$0.200845\pi$
$618$	−4684.67	−0.304927
$619$	10794.8	0.700937	0.350469	−	0.936574i	$-0.386022\pi$
$619$	10794.8	0.700937	0.350469	+	0.936574i	$0.386022\pi$
$620$	1240.91	0.0803809
$621$	4398.72	0.284242
$622$	6114.28	0.394148
$623$	−8312.47	−0.534562
$624$	778.304	0.0499313
$625$	385.346	0.0246621
$626$	−4455.22	−0.284451
$627$	10923.3	0.695748
$628$	1757.07	0.111648
$629$	0	0
$630$	−1168.81	−0.0739152
$631$	−7579.90	−0.478211	−0.239106	−	0.970994i	$-0.576854\pi$
$631$	−7579.90	−0.478211	−0.239106	+	0.970994i	$0.576854\pi$
$632$	8584.94	0.540333
$633$	16008.3	1.00517
$634$	−6657.80	−0.417058
$635$	−10262.3	−0.641333
$636$	−1973.64	−0.123050
$637$	−9932.03	−0.617773
$638$	−13999.5	−0.868723
$639$	2886.79	0.178716
$640$	−6596.25	−0.407406
$641$	−3181.53	−0.196042	−0.0980208	−	0.995184i	$-0.531251\pi$
$641$	−3181.53	−0.196042	−0.0980208	+	0.995184i	$0.531251\pi$
$642$	1053.29	0.0647507
$643$	10552.8	0.647219	0.323609	−	0.946191i	$-0.395104\pi$
$643$	10552.8	0.647219	0.323609	+	0.946191i	$0.395104\pi$
$644$	2041.63	0.124925
$645$	15619.7	0.953526
$646$	0	0
$647$	−10952.0	−0.665483	−0.332742	−	0.943018i	$-0.607974\pi$
$647$	−10952.0	−0.665483	−0.332742	+	0.943018i	$0.607974\pi$
$648$	−10729.8	−0.650471
$649$	9581.64	0.579526
$650$	8851.97	0.534158
$651$	2206.93	0.132867
$652$	−3454.63	−0.207506
$653$	−6526.76	−0.391136	−0.195568	−	0.980690i	$-0.562655\pi$
$653$	−6526.76	−0.391136	−0.195568	+	0.980690i	$0.562655\pi$
$654$	6240.84	0.373144
$655$	−18955.7	−1.13078
$656$	−86.8789	−0.00517081
$657$	4666.69	0.277116
$658$	4983.92	0.295279
$659$	−25717.9	−1.52022	−0.760111	−	0.649793i	$-0.774855\pi$
$659$	−25717.9	−1.52022	−0.760111	+	0.649793i	$0.774855\pi$
$660$	−4751.00	−0.280201
$661$	11808.9	0.694878	0.347439	−	0.937703i	$-0.387051\pi$
$661$	11808.9	0.694878	0.347439	+	0.937703i	$0.387051\pi$
$662$	10635.3	0.624403
$663$	0	0
$664$	−3426.93	−0.200287
$665$	7532.54	0.439247
$666$	4426.64	0.257550
$667$	7692.85	0.446579
$668$	−4072.03	−0.235856
$669$	−7009.76	−0.405102
$670$	−7666.73	−0.442077
$671$	−11262.8	−0.647981
$672$	−11292.8	−0.648260
$673$	−6282.85	−0.359860	−0.179930	−	0.983679i	$-0.557587\pi$
$673$	−6282.85	−0.359860	−0.179930	+	0.983679i	$0.557587\pi$
$674$	6552.54	0.374472
$675$	11967.8	0.682433
$676$	−11001.0	−0.625910
$677$	−18502.8	−1.05040	−0.525200	−	0.850979i	$-0.676009\pi$
$677$	−18502.8	−1.05040	−0.525200	+	0.850979i	$0.676009\pi$
$678$	−4566.00	−0.258638
$679$	−618.446	−0.0349540
$680$	0	0
$681$	−19076.8	−1.07346
$682$	1882.22	0.105680
$683$	137.518	0.00770424	0.00385212	−	0.999993i	$-0.498774\pi$
$683$	137.518	0.00770424	0.00385212	+	0.999993i	$0.498774\pi$
$684$	−2943.57	−0.164547
$685$	4288.71	0.239217
$686$	11677.7	0.649936
$687$	2581.37	0.143356
$688$	−1369.46	−0.0758867
$689$	5758.47	0.318404
$690$	−1491.46	−0.0822882
$691$	303.235	0.0166940	0.00834702	−	0.999965i	$-0.497343\pi$
$691$	303.235	0.0166940	0.00834702	+	0.999965i	$0.497343\pi$
$692$	9599.69	0.527349
$693$	3103.30	0.170108
$694$	14158.6	0.774426
$695$	−18074.0	−0.986452
$696$	−26411.5	−1.43840
$697$	0	0
$698$	−8406.54	−0.455863
$699$	−2985.24	−0.161534
$700$	5554.79	0.299931
$701$	−23434.3	−1.26263	−0.631313	−	0.775528i	$-0.717484\pi$
$701$	−23434.3	−1.26263	−0.631313	+	0.775528i	$0.717484\pi$
$702$	17136.5	0.921331
$703$	−28528.0	−1.53052
$704$	−8976.83	−0.480578
$705$	6373.13	0.340463
$706$	16385.4	0.873472
$707$	20513.4	1.09121
$708$	7030.24	0.373182
$709$	52.1860	0.00276430	0.00138215	−	0.999999i	$-0.499560\pi$
$709$	52.1860	0.00276430	0.00138215	+	0.999999i	$0.499560\pi$
$710$	−4622.70	−0.244348
$711$	−2788.74	−0.147097
$712$	−13375.0	−0.704002
$713$	−1034.30	−0.0543265
$714$	0	0
$715$	13862.0	0.725046
$716$	18272.3	0.953725
$717$	−1215.98	−0.0633354
$718$	3347.43	0.173990
$719$	2244.80	0.116435	0.0582175	−	0.998304i	$-0.481458\pi$
$719$	2244.80	0.116435	0.0582175	+	0.998304i	$0.481458\pi$
$720$	131.039	0.00678271
$721$	8577.23	0.443041
$722$	860.445	0.0443524
$723$	28824.9	1.48272
$724$	−2348.89	−0.120575
$725$	20930.4	1.07219
$726$	2880.96	0.147276
$727$	−2971.90	−0.151612	−0.0758059	−	0.997123i	$-0.524153\pi$
$727$	−2971.90	−0.151612	−0.0758059	+	0.997123i	$0.524153\pi$
$728$	20451.4	1.04118
$729$	21748.2	1.10492
$730$	−7472.91	−0.378883
$731$	0	0
$732$	−8263.73	−0.417263
$733$	31704.8	1.59760	0.798802	−	0.601594i	$-0.205468\pi$
$733$	31704.8	1.59760	0.798802	+	0.601594i	$0.205468\pi$
$734$	5898.00	0.296593
$735$	4553.02	0.228491
$736$	5292.50	0.265060
$737$	20355.9	1.01739
$738$	−405.034	−0.0202026
$739$	−36985.6	−1.84105	−0.920526	−	0.390681i	$-0.872240\pi$
$739$	−36985.6	−1.84105	−0.920526	+	0.390681i	$0.872240\pi$
$740$	12408.0	0.616389
$741$	−23384.2	−1.15930
$742$	−2064.36	−0.102136
$743$	−10601.9	−0.523481	−0.261741	−	0.965138i	$-0.584296\pi$
$743$	−10601.9	−0.523481	−0.261741	+	0.965138i	$0.584296\pi$
$744$	3551.01	0.174981
$745$	15092.6	0.742217
$746$	−4538.63	−0.222750
$747$	1113.21	0.0545248
$748$	0	0
$749$	−1928.48	−0.0940789
$750$	−10509.1	−0.511653
$751$	−29161.5	−1.41694	−0.708468	−	0.705743i	$-0.750613\pi$
$751$	−29161.5	−1.41694	−0.708468	+	0.705743i	$0.750613\pi$
$752$	−558.765	−0.0270958
$753$	−11232.0	−0.543583
$754$	29969.7	1.44752
$755$	−14526.4	−0.700225
$756$	10753.5	0.517329
$757$	−34447.9	−1.65394	−0.826969	−	0.562248i	$-0.809937\pi$
$757$	−34447.9	−1.65394	−0.826969	+	0.562248i	$0.809937\pi$
$758$	9521.67	0.456257
$759$	3959.96	0.189377
$760$	12120.1	0.578476
$761$	−14414.5	−0.686632	−0.343316	−	0.939220i	$-0.611550\pi$
$761$	−14414.5	−0.686632	−0.343316	+	0.939220i	$0.611550\pi$
$762$	−11421.0	−0.542966
$763$	−11426.4	−0.542156
$764$	23012.6	1.08975
$765$	0	0
$766$	−13357.5	−0.630058
$767$	−20512.1	−0.965644
$768$	−17690.3	−0.831175
$769$	−7049.33	−0.330566	−0.165283	−	0.986246i	$-0.552854\pi$
$769$	−7049.33	−0.330566	−0.165283	+	0.986246i	$0.552854\pi$
$770$	−4969.40	−0.232578
$771$	7565.28	0.353381
$772$	14912.3	0.695212
$773$	26768.3	1.24552	0.622760	−	0.782413i	$-0.286011\pi$
$773$	26768.3	1.24552	0.622760	+	0.782413i	$0.286011\pi$
$774$	−6384.47	−0.296492
$775$	−2814.08	−0.130432
$776$	−995.097	−0.0460334
$777$	22067.3	1.01887
$778$	−12676.7	−0.584165
$779$	2610.29	0.120055
$780$	10170.8	0.466889
$781$	12273.7	0.562339
$782$	0	0
$783$	40519.0	1.84934
$784$	−399.186	−0.0181845
$785$	2350.12	0.106853
$786$	−21096.1	−0.957343
$787$	−26085.5	−1.18151	−0.590755	−	0.806851i	$-0.701170\pi$
$787$	−26085.5	−1.18151	−0.590755	+	0.806851i	$0.701170\pi$
$788$	−9806.68	−0.443336
$789$	−18994.6	−0.857065
$790$	4465.69	0.201116
$791$	8359.95	0.375785
$792$	4993.30	0.224027
$793$	24111.1	1.07971
$794$	−16270.6	−0.727232
$795$	−2639.78	−0.117765
$796$	−15715.1	−0.699758
$797$	18108.6	0.804818	0.402409	−	0.915460i	$-0.368173\pi$
$797$	18108.6	0.804818	0.402409	+	0.915460i	$0.368173\pi$
$798$	8383.06	0.371876
$799$	0	0
$800$	14399.6	0.636379
$801$	4344.75	0.191653
$802$	−14775.0	−0.650527
$803$	19841.2	0.871958
$804$	14935.5	0.655142
$805$	2730.73	0.119560
$806$	−4029.41	−0.176092
$807$	−35534.1	−1.55001
$808$	33006.6	1.43709
$809$	7304.62	0.317450	0.158725	−	0.987323i	$-0.449262\pi$
$809$	7304.62	0.317450	0.158725	+	0.987323i	$0.449262\pi$
$810$	−5581.38	−0.242111
$811$	19511.7	0.844817	0.422409	−	0.906405i	$-0.361185\pi$
$811$	19511.7	0.844817	0.422409	+	0.906405i	$0.361185\pi$
$812$	18806.6	0.812786
$813$	2107.55	0.0909163
$814$	18820.6	0.810395
$815$	−4620.65	−0.198594
$816$	0	0
$817$	41145.5	1.76193
$818$	−9003.45	−0.384839
$819$	−6643.45	−0.283444
$820$	−1135.32	−0.0483503
$821$	−29364.3	−1.24826	−0.624131	−	0.781320i	$-0.714547\pi$
$821$	−29364.3	−1.24826	−0.624131	+	0.781320i	$0.714547\pi$
$822$	4772.96	0.202526
$823$	−28112.4	−1.19069	−0.595345	−	0.803470i	$-0.702985\pi$
$823$	−28112.4	−1.19069	−0.595345	+	0.803470i	$0.702985\pi$
$824$	13801.0	0.583472
$825$	10774.1	0.454673
$826$	7353.43	0.309756
$827$	−39360.5	−1.65502	−0.827509	−	0.561453i	$-0.810243\pi$
$827$	−39360.5	−1.65502	−0.827509	+	0.561453i	$0.810243\pi$
$828$	−1067.12	−0.0447885
$829$	15525.3	0.650443	0.325221	−	0.945638i	$-0.394561\pi$
$829$	15525.3	0.650443	0.325221	+	0.945638i	$0.394561\pi$
$830$	−1782.61	−0.0745485
$831$	12559.3	0.524280
$832$	19217.3	0.800771
$833$	0	0
$834$	−20114.7	−0.835151
$835$	−5446.44	−0.225727
$836$	−12515.1	−0.517756
$837$	−5447.75	−0.224972
$838$	−16045.5	−0.661433
$839$	30007.9	1.23479	0.617394	−	0.786654i	$-0.288189\pi$
$839$	30007.9	1.23479	0.617394	+	0.786654i	$0.288189\pi$
$840$	−9375.29	−0.385093
$841$	46474.0	1.90553
$842$	13971.1	0.571826
$843$	−11101.3	−0.453556
$844$	−18341.2	−0.748020
$845$	−14714.1	−0.599029
$846$	−2604.99	−0.105864
$847$	−5274.78	−0.213983
$848$	231.443	0.00937239
$849$	−10741.0	−0.434193
$850$	0	0
$851$	−10342.1	−0.416595
$852$	9005.44	0.362114
$853$	−4351.43	−0.174666	−0.0873331	−	0.996179i	$-0.527834\pi$
$853$	−4351.43	−0.174666	−0.0873331	+	0.996179i	$0.527834\pi$
$854$	−8643.62	−0.346345
$855$	−3937.09	−0.157480
$856$	−3102.98	−0.123899
$857$	25861.5	1.03082	0.515410	−	0.856944i	$-0.327640\pi$
$857$	25861.5	1.03082	0.515410	+	0.856944i	$0.327640\pi$
$858$	15427.2	0.613840
$859$	19084.0	0.758017	0.379009	−	0.925393i	$-0.376265\pi$
$859$	19084.0	0.758017	0.379009	+	0.925393i	$0.376265\pi$
$860$	−17895.9	−0.709588
$861$	−2019.14	−0.0799213
$862$	−3326.16	−0.131426
$863$	24790.2	0.977831	0.488916	−	0.872331i	$-0.337393\pi$
$863$	24790.2	0.977831	0.488916	+	0.872331i	$0.337393\pi$
$864$	27876.1	1.09765
$865$	12839.8	0.504701
$866$	−19019.9	−0.746332
$867$	0	0
$868$	−2528.54	−0.0988757
$869$	−11856.8	−0.462847
$870$	−13738.6	−0.535383
$871$	−43577.2	−1.69524
$872$	−18385.5	−0.714003
$873$	323.248	0.0125318
$874$	−3928.81	−0.152053
$875$	19241.3	0.743401
$876$	14557.9	0.561491
$877$	−14394.0	−0.554219	−0.277109	−	0.960838i	$-0.589376\pi$
$877$	−14394.0	−0.554219	−0.277109	+	0.960838i	$0.589376\pi$
$878$	−801.839	−0.0308209
$879$	29560.9	1.13432
$880$	557.137	0.0213421
$881$	−15328.6	−0.586190	−0.293095	−	0.956083i	$-0.594685\pi$
$881$	−15328.6	−0.586190	−0.293095	+	0.956083i	$0.594685\pi$
$882$	−1861.02	−0.0710475
$883$	8385.90	0.319602	0.159801	−	0.987149i	$-0.448915\pi$
$883$	8385.90	0.319602	0.159801	+	0.987149i	$0.448915\pi$
$884$	0	0
$885$	9403.11	0.357155
$886$	22397.7	0.849283
$887$	9215.90	0.348861	0.174430	−	0.984669i	$-0.444192\pi$
$887$	9215.90	0.348861	0.174430	+	0.984669i	$0.444192\pi$
$888$	35507.0	1.34182
$889$	20910.9	0.788897
$890$	−6957.37	−0.262035
$891$	14819.1	0.557191
$892$	8031.28	0.301465
$893$	16788.1	0.629108
$894$	16796.8	0.628376
$895$	24439.6	0.912765
$896$	13440.8	0.501146
$897$	−8477.36	−0.315553
$898$	17793.2	0.661211
$899$	−9527.49	−0.353459
$900$	−2903.37	−0.107532
$901$	0	0
$902$	−1722.07	−0.0635684
$903$	−31827.4	−1.17292
$904$	13451.4	0.494897
$905$	−3141.70	−0.115396
$906$	−16166.6	−0.592825
$907$	−7468.98	−0.273433	−0.136716	−	0.990610i	$-0.543655\pi$
$907$	−7468.98	−0.273433	−0.136716	+	0.990610i	$0.543655\pi$
$908$	21856.8	0.798836
$909$	−10721.9	−0.391224
$910$	10638.4	0.387536
$911$	−30698.3	−1.11644	−0.558222	−	0.829692i	$-0.688516\pi$
$911$	−30698.3	−1.11644	−0.558222	+	0.829692i	$0.688516\pi$
$912$	−939.854	−0.0341246
$913$	4732.98	0.171565
$914$	432.140	0.0156389
$915$	−11052.9	−0.399343
$916$	−2957.55	−0.106681
$917$	38625.1	1.39096
$918$	0	0
$919$	−24550.8	−0.881237	−0.440619	−	0.897694i	$-0.645241\pi$
$919$	−24550.8	−0.881237	−0.440619	+	0.897694i	$0.645241\pi$
$920$	4393.82	0.157457
$921$	−11159.2	−0.399247
$922$	−26537.4	−0.947898
$923$	−26275.1	−0.937006
$924$	9680.86	0.344672
$925$	−28138.3	−1.00020
$926$	−18296.0	−0.649293
$927$	−4483.13	−0.158841
$928$	48752.1	1.72453
$929$	41655.0	1.47110	0.735552	−	0.677468i	$-0.236923\pi$
$929$	41655.0	1.47110	0.735552	+	0.677468i	$0.236923\pi$
$930$	1847.15	0.0651296
$931$	11993.6	0.422206
$932$	3420.28	0.120209
$933$	−15931.5	−0.559027
$934$	3343.54	0.117135
$935$	0	0
$936$	−10689.5	−0.373288
$937$	83.7368	0.00291949	0.00145975	−	0.999999i	$-0.499535\pi$
$937$	83.7368	0.00291949	0.00145975	+	0.999999i	$0.499535\pi$
$938$	15622.1	0.543795
$939$	11608.6	0.403442
$940$	−7301.88	−0.253363
$941$	49294.1	1.70770	0.853848	−	0.520523i	$-0.174263\pi$
$941$	49294.1	1.70770	0.853848	+	0.520523i	$0.174263\pi$
$942$	2615.48	0.0904639
$943$	946.293	0.0326782
$944$	−824.418	−0.0284243
$945$	14383.0	0.495111
$946$	−27144.7	−0.932927
$947$	9445.27	0.324108	0.162054	−	0.986782i	$-0.448188\pi$
$947$	9445.27	0.324108	0.162054	+	0.986782i	$0.448188\pi$
$948$	−8699.57	−0.298047
$949$	−42475.5	−1.45291
$950$	−10689.3	−0.365061
$951$	17347.7	0.591521
$952$	0	0
$953$	41693.4	1.41719	0.708595	−	0.705616i	$-0.249329\pi$
$953$	41693.4	1.41719	0.708595	+	0.705616i	$0.249329\pi$
$954$	1079.00	0.0366183
$955$	30779.8	1.04294
$956$	1393.18	0.0471324
$957$	36477.3	1.23213
$958$	7323.60	0.246988
$959$	−8738.88	−0.294258
$960$	−8809.56	−0.296174
$961$	−28510.0	−0.957002
$962$	−40290.6	−1.35033
$963$	1007.97	0.0337295
$964$	−33025.5	−1.10340
$965$	19945.5	0.665355
$966$	3039.06	0.101222
$967$	32380.0	1.07681	0.538403	−	0.842688i	$-0.319028\pi$
$967$	32380.0	1.07681	0.538403	+	0.842688i	$0.319028\pi$
$968$	−8487.28	−0.281809
$969$	0	0
$970$	−517.626	−0.0171340
$971$	5401.25	0.178511	0.0892556	−	0.996009i	$-0.471551\pi$
$971$	5401.25	0.178511	0.0892556	+	0.996009i	$0.471551\pi$
$972$	−10051.1	−0.331676
$973$	36828.3	1.21342
$974$	30721.5	1.01066
$975$	−23064.8	−0.757606
$976$	969.066	0.0317818
$977$	−25086.2	−0.821473	−0.410737	−	0.911754i	$-0.634728\pi$
$977$	−25086.2	−0.821473	−0.410737	+	0.911754i	$0.634728\pi$
$978$	−5142.37	−0.168134
$979$	18472.4	0.603045
$980$	−5216.52	−0.170036
$981$	5972.35	0.194375
$982$	−23421.4	−0.761108
$983$	59631.6	1.93485	0.967423	−	0.253166i	$-0.0814720\pi$
$983$	59631.6	1.93485	0.967423	+	0.253166i	$0.0814720\pi$
$984$	−3248.86	−0.105254
$985$	−13116.7	−0.424296
$986$	0	0
$987$	−12986.2	−0.418799
$988$	26792.0	0.862719
$989$	14916.2	0.479584
$990$	2597.40	0.0833846
$991$	40063.8	1.28423	0.642114	−	0.766609i	$-0.278058\pi$
$991$	40063.8	1.28423	0.642114	+	0.766609i	$0.278058\pi$
$992$	−6554.70	−0.209790
$993$	−27711.6	−0.885601
$994$	9419.43	0.300569
$995$	−21019.3	−0.669706
$996$	3472.68	0.110478
$997$	10818.4	0.343652	0.171826	−	0.985127i	$-0.445033\pi$
$997$	10818.4	0.343652	0.171826	+	0.985127i	$0.445033\pi$
$998$	−13213.5	−0.419103
$999$	−54472.8	−1.72517

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.g.1.6		12
17.3	odd	16		17.4.d.a.9.2	yes	12
17.4	even	4		289.4.b.e.288.7		12
17.6	odd	16		17.4.d.a.2.2	✓	12
17.13	even	4		289.4.b.e.288.8		12
17.16	even	2	inner	289.4.a.g.1.5		12
51.20	even	16		153.4.l.a.145.2		12
51.23	even	16		153.4.l.a.19.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.d.a.2.2	✓	12	17.6	odd	16
17.4.d.a.9.2	yes	12	17.3	odd	16
153.4.l.a.19.2		12	51.23	even	16
153.4.l.a.145.2		12	51.20	even	16
289.4.a.g.1.5		12	17.16	even	2	inner
289.4.a.g.1.6		12	1.1	even	1	trivial
289.4.b.e.288.7		12	17.4	even	4
289.4.b.e.288.8		12	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)

\(f(q)\)	\(=\)	\(q-1.70547 q^{2} +4.44379 q^{3} -5.09138 q^{4} -6.80983 q^{5} -7.57875 q^{6} +13.8760 q^{7} +22.3269 q^{8} -7.25269 q^{9} +O(q^{10})\)	\(q-1.70547 q^{2} +4.44379 q^{3} -5.09138 q^{4} -6.80983 q^{5} -7.57875 q^{6} +13.8760 q^{7} +22.3269 q^{8} -7.25269 q^{9} +11.6140 q^{10} -30.8361 q^{11} -22.6250 q^{12} +66.0130 q^{13} -23.6651 q^{14} -30.2615 q^{15} +2.65318 q^{16} +12.3692 q^{18} -79.7150 q^{19} +34.6714 q^{20} +61.6622 q^{21} +52.5899 q^{22} -28.8986 q^{23} +99.2163 q^{24} -78.6262 q^{25} -112.583 q^{26} -152.212 q^{27} -70.6481 q^{28} -266.201 q^{29} +51.6100 q^{30} +35.7906 q^{31} -183.140 q^{32} -137.029 q^{33} -94.4935 q^{35} +36.9262 q^{36} +357.875 q^{37} +135.951 q^{38} +293.348 q^{39} -152.043 q^{40} -32.7452 q^{41} -105.163 q^{42} -516.157 q^{43} +156.998 q^{44} +49.3896 q^{45} +49.2857 q^{46} -210.602 q^{47} +11.7902 q^{48} -150.456 q^{49} +134.094 q^{50} -336.097 q^{52} +87.2324 q^{53} +259.593 q^{54} +209.989 q^{55} +309.809 q^{56} -354.237 q^{57} +453.997 q^{58} -310.728 q^{59} +154.073 q^{60} +365.247 q^{61} -61.0397 q^{62} -100.639 q^{63} +291.115 q^{64} -449.537 q^{65} +233.699 q^{66} -660.131 q^{67} -128.420 q^{69} +161.156 q^{70} -398.030 q^{71} -161.930 q^{72} -643.443 q^{73} -610.344 q^{74} -349.399 q^{75} +405.859 q^{76} -427.882 q^{77} -500.296 q^{78} +384.511 q^{79} -18.0677 q^{80} -480.576 q^{81} +55.8460 q^{82} -153.488 q^{83} -313.946 q^{84} +880.289 q^{86} -1182.94 q^{87} -688.475 q^{88} -599.053 q^{89} -84.2324 q^{90} +915.998 q^{91} +147.134 q^{92} +159.046 q^{93} +359.175 q^{94} +542.846 q^{95} -813.838 q^{96} -44.5693 q^{97} +256.598 q^{98} +223.645 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9}+O(q^{10}) \) 12 * q - 8 * q^2 + 16 * q^4 - 96 * q^8 - 36 * q^9	\( 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9} - 8 q^{13} - 192 q^{15} - 184 q^{16} - 352 q^{19} - 256 q^{21} - 492 q^{25} - 784 q^{26} + 744 q^{30} + 24 q^{32} - 1400 q^{33} - 632 q^{35} - 856 q^{36} - 624 q^{38} - 1664 q^{42} - 1200 q^{43} - 1512 q^{47} - 1052 q^{49} - 2856 q^{50} + 792 q^{52} - 2504 q^{53} - 1424 q^{55} - 3408 q^{59} - 2808 q^{60} + 272 q^{64} + 272 q^{66} - 1080 q^{67} - 344 q^{69} + 2600 q^{70} + 248 q^{72} + 896 q^{76} + 848 q^{77} - 2404 q^{81} - 2960 q^{83} + 4768 q^{84} - 1200 q^{86} - 160 q^{87} - 2144 q^{89} + 3800 q^{93} + 5984 q^{94} + 3464 q^{98}+O(q^{100}) \) 12 * q - 8 * q^2 + 16 * q^4 - 96 * q^8 - 36 * q^9 - 8 * q^13 - 192 * q^15 - 184 * q^16 - 352 * q^19 - 256 * q^21 - 492 * q^25 - 784 * q^26 + 744 * q^30 + 24 * q^32 - 1400 * q^33 - 632 * q^35 - 856 * q^36 - 624 * q^38 - 1664 * q^42 - 1200 * q^43 - 1512 * q^47 - 1052 * q^49 - 2856 * q^50 + 792 * q^52 - 2504 * q^53 - 1424 * q^55 - 3408 * q^59 - 2808 * q^60 + 272 * q^64 + 272 * q^66 - 1080 * q^67 - 344 * q^69 + 2600 * q^70 + 248 * q^72 + 896 * q^76 + 848 * q^77 - 2404 * q^81 - 2960 * q^83 + 4768 * q^84 - 1200 * q^86 - 160 * q^87 - 2144 * q^89 + 3800 * q^93 + 5984 * q^94 + 3464 * q^98

Introduction

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