LMFDB - Embedded newform 289.4.a.f.1.2

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:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 54x^{6} - 20x^{5} + 677x^{4} + 380x^{3} - 2216x^{2} - 1000x + 476 $ x^8 - 54x^6 - 20x^5 + 677x^4 + 380x^3 - 2216x^2 - 1000x + 476
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$6.35073$ 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)

$f(q)$	$=$	$q-3.93651 q^{2} +0.423991 q^{3} +7.49613 q^{4} +1.95080 q^{5} -1.66905 q^{6} +25.4345 q^{7} +1.98349 q^{8} -26.8202 q^{9} +O(q^{10})$	\(q-3.93651 q^{2} +0.423991 q^{3} +7.49613 q^{4} +1.95080 q^{5} -1.66905 q^{6} +25.4345 q^{7} +1.98349 q^{8} -26.8202 q^{9} -7.67934 q^{10} +32.4303 q^{11} +3.17829 q^{12} +54.6855 q^{13} -100.123 q^{14} +0.827121 q^{15} -67.7771 q^{16} +105.578 q^{18} -46.1336 q^{19} +14.6234 q^{20} +10.7840 q^{21} -127.662 q^{22} +75.2978 q^{23} +0.840984 q^{24} -121.194 q^{25} -215.270 q^{26} -22.8193 q^{27} +190.660 q^{28} +157.040 q^{29} -3.25597 q^{30} -252.606 q^{31} +250.937 q^{32} +13.7502 q^{33} +49.6175 q^{35} -201.048 q^{36} +226.214 q^{37} +181.606 q^{38} +23.1862 q^{39} +3.86940 q^{40} -231.163 q^{41} -42.4513 q^{42} +119.642 q^{43} +243.102 q^{44} -52.3209 q^{45} -296.411 q^{46} +188.319 q^{47} -28.7369 q^{48} +303.913 q^{49} +477.083 q^{50} +409.930 q^{52} +468.212 q^{53} +89.8285 q^{54} +63.2650 q^{55} +50.4491 q^{56} -19.5603 q^{57} -618.188 q^{58} +751.217 q^{59} +6.20021 q^{60} +483.210 q^{61} +994.385 q^{62} -682.159 q^{63} -445.601 q^{64} +106.680 q^{65} -54.1277 q^{66} +533.879 q^{67} +31.9256 q^{69} -195.320 q^{70} -78.1521 q^{71} -53.1977 q^{72} +383.013 q^{73} -890.494 q^{74} -51.3854 q^{75} -345.824 q^{76} +824.848 q^{77} -91.2727 q^{78} -1278.85 q^{79} -132.219 q^{80} +714.471 q^{81} +909.975 q^{82} +591.376 q^{83} +80.8382 q^{84} -470.973 q^{86} +66.5834 q^{87} +64.3253 q^{88} +609.729 q^{89} +205.962 q^{90} +1390.90 q^{91} +564.442 q^{92} -107.103 q^{93} -741.321 q^{94} -89.9974 q^{95} +106.395 q^{96} +1592.06 q^{97} -1196.36 q^{98} -869.788 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 36 q^{4} + 96 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 36 * q^4 + 96 * q^8 + 8 * q^9	$ 8 q + 8 q^{2} + 36 q^{4} + 96 q^{8} + 8 q^{9} + 88 q^{13} + 252 q^{15} + 420 q^{16} + 428 q^{18} - 52 q^{19} + 260 q^{21} - 140 q^{25} - 268 q^{26} + 120 q^{30} + 2336 q^{32} + 816 q^{33} + 1172 q^{35} - 264 q^{36} + 768 q^{38} - 136 q^{42} - 752 q^{43} + 368 q^{47} + 852 q^{49} + 468 q^{50} + 2564 q^{52} - 1156 q^{53} + 1996 q^{55} + 192 q^{59} - 3160 q^{60} + 3044 q^{64} + 1052 q^{66} + 764 q^{67} + 1812 q^{69} + 544 q^{70} - 1404 q^{72} + 896 q^{76} + 3084 q^{77} - 280 q^{81} + 496 q^{83} - 2952 q^{84} - 4244 q^{86} - 2860 q^{87} + 2156 q^{89} - 4012 q^{93} - 3392 q^{94} - 6728 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 + 36 * q^4 + 96 * q^8 + 8 * q^9 + 88 * q^13 + 252 * q^15 + 420 * q^16 + 428 * q^18 - 52 * q^19 + 260 * q^21 - 140 * q^25 - 268 * q^26 + 120 * q^30 + 2336 * q^32 + 816 * q^33 + 1172 * q^35 - 264 * q^36 + 768 * q^38 - 136 * q^42 - 752 * q^43 + 368 * q^47 + 852 * q^49 + 468 * q^50 + 2564 * q^52 - 1156 * q^53 + 1996 * q^55 + 192 * q^59 - 3160 * q^60 + 3044 * q^64 + 1052 * q^66 + 764 * q^67 + 1812 * q^69 + 544 * q^70 - 1404 * q^72 + 896 * q^76 + 3084 * q^77 - 280 * q^81 + 496 * q^83 - 2952 * q^84 - 4244 * q^86 - 2860 * q^87 + 2156 * q^89 - 4012 * q^93 - 3392 * q^94 - 6728 * 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 $

$2$	−3.93651	−1.39177	−0.695884	−	0.718155i	$-0.744987\pi$
$2$	−3.93651	−1.39177	−0.695884	+	0.718155i	$0.744987\pi$
$3$	0.423991	0.0815972	0.0407986	−	0.999167i	$-0.487010\pi$
$3$	0.423991	0.0815972	0.0407986	+	0.999167i	$0.487010\pi$
$4$	7.49613	0.937016
$5$	1.95080	0.174485	0.0872423	−	0.996187i	$-0.472195\pi$
$5$	1.95080	0.174485	0.0872423	+	0.996187i	$0.472195\pi$
$6$	−1.66905	−0.113564
$7$	25.4345	1.37333	0.686667	−	0.726973i	$-0.259073\pi$
$7$	25.4345	1.37333	0.686667	+	0.726973i	$0.259073\pi$
$8$	1.98349	0.0876588
$9$	−26.8202	−0.993342
$10$	−7.67934	−0.242842
$11$	32.4303	0.888918	0.444459	−	0.895799i	$-0.353396\pi$
$11$	32.4303	0.888918	0.444459	+	0.895799i	$0.353396\pi$
$12$	3.17829	0.0764579
$13$	54.6855	1.16669	0.583347	−	0.812223i	$-0.301743\pi$
$13$	54.6855	1.16669	0.583347	+	0.812223i	$0.301743\pi$
$14$	−100.123	−1.91136
$15$	0.827121	0.0142375
$16$	−67.7771	−1.05902
$17$	0	0
$17$	0	0
$18$	105.578	1.38250
$19$	−46.1336	−0.557041	−0.278521	−	0.960430i	$-0.589844\pi$
$19$	−46.1336	−0.557041	−0.278521	+	0.960430i	$0.589844\pi$
$20$	14.6234	0.163495
$21$	10.7840	0.112060
$22$	−127.662	−1.23717
$23$	75.2978	0.682638	0.341319	−	0.939948i	$-0.389126\pi$
$23$	75.2978	0.682638	0.341319	+	0.939948i	$0.389126\pi$
$24$	0.840984	0.00715271
$25$	−121.194	−0.969555
$26$	−215.270	−1.62377
$27$	−22.8193	−0.162651
$28$	190.660	1.28684
$29$	157.040	1.00557	0.502785	−	0.864412i	$-0.332309\pi$
$29$	157.040	1.00557	0.502785	+	0.864412i	$0.332309\pi$
$30$	−3.25597	−0.0198152
$31$	−252.606	−1.46353	−0.731763	−	0.681559i	$-0.761302\pi$
$31$	−252.606	−1.46353	−0.731763	+	0.681559i	$0.761302\pi$
$32$	250.937	1.38625
$33$	13.7502	0.0725332
$34$	0	0
$35$	49.6175	0.239626
$36$	−201.048	−0.930777
$37$	226.214	1.00512	0.502559	−	0.864543i	$-0.332392\pi$
$37$	226.214	1.00512	0.502559	+	0.864543i	$0.332392\pi$
$38$	181.606	0.775272
$39$	23.1862	0.0951990
$40$	3.86940	0.0152951
$41$	−231.163	−0.880526	−0.440263	−	0.897869i	$-0.645115\pi$
$41$	−231.163	−0.880526	−0.440263	+	0.897869i	$0.645115\pi$
$42$	−42.4513	−0.155962
$43$	119.642	0.424309	0.212154	−	0.977236i	$-0.431952\pi$
$43$	119.642	0.424309	0.212154	+	0.977236i	$0.431952\pi$
$44$	243.102	0.832931
$45$	−52.3209	−0.173323
$46$	−296.411	−0.950073
$47$	188.319	0.584451	0.292225	−	0.956349i	$-0.405604\pi$
$47$	188.319	0.584451	0.292225	+	0.956349i	$0.405604\pi$
$48$	−28.7369	−0.0864128
$49$	303.913	0.886044
$50$	477.083	1.34940
$51$	0	0
$52$	409.930	1.09321
$53$	468.212	1.21347	0.606734	−	0.794905i	$-0.292479\pi$
$53$	468.212	1.21347	0.606734	+	0.794905i	$0.292479\pi$
$54$	89.8285	0.226372
$55$	63.2650	0.155103
$56$	50.4491	0.120385
$57$	−19.5603	−0.0454530
$58$	−618.188	−1.39952
$59$	751.217	1.65763	0.828815	−	0.559523i	$-0.189016\pi$
$59$	751.217	1.65763	0.828815	+	0.559523i	$0.189016\pi$
$60$	6.20021	0.0133407
$61$	483.210	1.01424	0.507121	−	0.861875i	$-0.330710\pi$
$61$	483.210	1.01424	0.507121	+	0.861875i	$0.330710\pi$
$62$	994.385	2.03689
$63$	−682.159	−1.36419
$64$	−445.601	−0.870315
$65$	106.680	0.203570
$66$	−54.1277	−0.100949
$67$	533.879	0.973487	0.486744	−	0.873545i	$-0.338185\pi$
$67$	533.879	0.973487	0.486744	+	0.873545i	$0.338185\pi$
$68$	0	0
$69$	31.9256	0.0557013
$70$	−195.320	−0.333503
$71$	−78.1521	−0.130633	−0.0653165	−	0.997865i	$-0.520806\pi$
$71$	−78.1521	−0.130633	−0.0653165	+	0.997865i	$0.520806\pi$
$72$	−53.1977	−0.0870752
$73$	383.013	0.614085	0.307043	−	0.951696i	$-0.400661\pi$
$73$	383.013	0.614085	0.307043	+	0.951696i	$0.400661\pi$
$74$	−890.494	−1.39889
$75$	−51.3854	−0.0791129
$76$	−345.824	−0.521957
$77$	824.848	1.22078
$78$	−91.2727	−0.132495
$79$	−1278.85	−1.82129	−0.910646	−	0.413187i	$-0.864416\pi$
$79$	−1278.85	−1.82129	−0.910646	+	0.413187i	$0.864416\pi$
$80$	−132.219	−0.184782
$81$	714.471	0.980070
$82$	909.975	1.22549
$83$	591.376	0.782071	0.391036	−	0.920376i	$-0.372117\pi$
$83$	591.376	0.782071	0.391036	+	0.920376i	$0.372117\pi$
$84$	80.8382	0.105002
$85$	0	0
$86$	−470.973	−0.590539
$87$	66.5834	0.0820516
$88$	64.3253	0.0779215
$89$	609.729	0.726192	0.363096	−	0.931752i	$-0.381720\pi$
$89$	609.729	0.726192	0.363096	+	0.931752i	$0.381720\pi$
$90$	205.962	0.241225
$91$	1390.90	1.60226
$92$	564.442	0.639643
$93$	−107.103	−0.119420
$94$	−741.321	−0.813420
$95$	−89.9974	−0.0971952
$96$	106.395	0.113114
$97$	1592.06	1.66648	0.833242	−	0.552908i	$-0.186482\pi$
$97$	1592.06	1.66648	0.833242	+	0.552908i	$0.186482\pi$
$98$	−1196.36	−1.23317
$99$	−869.788	−0.883000
$100$	−908.489	−0.908489
$101$	−666.897	−0.657017	−0.328508	−	0.944501i	$-0.606546\pi$
$101$	−666.897	−0.657017	−0.328508	+	0.944501i	$0.606546\pi$
$102$	0	0
$103$	−872.373	−0.834538	−0.417269	−	0.908783i	$-0.637013\pi$
$103$	−872.373	−0.834538	−0.417269	+	0.908783i	$0.637013\pi$
$104$	108.468	0.102271
$105$	21.0374	0.0195528
$106$	−1843.12	−1.68887
$107$	−346.327	−0.312904	−0.156452	−	0.987686i	$-0.550006\pi$
$107$	−346.327	−0.312904	−0.156452	+	0.987686i	$0.550006\pi$
$108$	−171.056	−0.152407
$109$	−135.821	−0.119351	−0.0596757	−	0.998218i	$-0.519007\pi$
$109$	−135.821	−0.119351	−0.0596757	+	0.998218i	$0.519007\pi$
$110$	−249.043	−0.215867
$111$	95.9128	0.0820147
$112$	−1723.88	−1.45438
$113$	−885.947	−0.737548	−0.368774	−	0.929519i	$-0.620222\pi$
$113$	−885.947	−0.737548	−0.368774	+	0.929519i	$0.620222\pi$
$114$	76.9992	0.0632600
$115$	146.891	0.119110
$116$	1177.19	0.942235
$117$	−1466.68	−1.15893
$118$	−2957.18	−2.30703
$119$	0	0
$120$	1.64059	0.00124804
$121$	−279.276	−0.209824
$122$	−1902.16	−1.41159
$123$	−98.0110	−0.0718484
$124$	−1893.56	−1.37135
$125$	−480.276	−0.343657
$126$	2685.33	1.89863
$127$	−1971.07	−1.37720	−0.688598	−	0.725144i	$-0.741773\pi$
$127$	−1971.07	−1.37720	−0.688598	+	0.725144i	$0.741773\pi$
$128$	−253.384	−0.174970
$129$	50.7273	0.0346224
$130$	−419.949	−0.283323
$131$	250.787	0.167262	0.0836312	−	0.996497i	$-0.473348\pi$
$131$	250.787	0.167262	0.0836312	+	0.996497i	$0.473348\pi$
$132$	103.073	0.0679648
$133$	−1173.39	−0.765003
$134$	−2101.62	−1.35487
$135$	−44.5159	−0.0283801
$136$	0	0
$137$	436.372	0.272130	0.136065	−	0.990700i	$-0.456554\pi$
$137$	436.372	0.272130	0.136065	+	0.990700i	$0.456554\pi$
$138$	−125.676	−0.0775233
$139$	83.7228	0.0510883	0.0255441	−	0.999674i	$-0.491868\pi$
$139$	83.7228	0.0510883	0.0255441	+	0.999674i	$0.491868\pi$
$140$	371.940	0.224533
$141$	79.8457	0.0476895
$142$	307.647	0.181811
$143$	1773.47	1.03710
$144$	1817.80	1.05197
$145$	306.353	0.175457
$146$	−1507.73	−0.854664
$147$	128.856	0.0722986
$148$	1695.73	0.941811
$149$	2357.45	1.29617	0.648085	−	0.761568i	$-0.275570\pi$
$149$	2357.45	1.29617	0.648085	+	0.761568i	$0.275570\pi$
$150$	202.279	0.110107
$151$	149.746	0.0807031	0.0403515	−	0.999186i	$-0.487152\pi$
$151$	149.746	0.0807031	0.0403515	+	0.999186i	$0.487152\pi$
$152$	−91.5058	−0.0488296
$153$	0	0
$154$	−3247.02	−1.69904
$155$	−492.783	−0.255363
$156$	173.807	0.0892030
$157$	119.280	0.0606343	0.0303172	−	0.999540i	$-0.490348\pi$
$157$	119.280	0.0606343	0.0303172	+	0.999540i	$0.490348\pi$
$158$	5034.22	2.53481
$159$	198.518	0.0990156
$160$	489.528	0.241879
$161$	1915.16	0.937489
$162$	−2812.52	−1.36403
$163$	152.626	0.0733411	0.0366705	−	0.999327i	$-0.488325\pi$
$163$	152.626	0.0733411	0.0366705	+	0.999327i	$0.488325\pi$
$164$	−1732.83	−0.825067
$165$	26.8238	0.0126559
$166$	−2327.96	−1.08846
$167$	2525.07	1.17003	0.585017	−	0.811021i	$-0.301088\pi$
$167$	2525.07	1.17003	0.585017	+	0.811021i	$0.301088\pi$
$168$	21.3900	0.00982306
$169$	793.506	0.361177
$170$	0	0
$171$	1237.31	0.553332
$172$	896.854	0.397584
$173$	−328.274	−0.144267	−0.0721335	−	0.997395i	$-0.522981\pi$
$173$	−328.274	−0.144267	−0.0721335	+	0.997395i	$0.522981\pi$
$174$	−262.106	−0.114197
$175$	−3082.52	−1.33152
$176$	−2198.03	−0.941379
$177$	318.509	0.135258
$178$	−2400.20	−1.01069
$179$	4155.11	1.73501	0.867506	−	0.497427i	$-0.165722\pi$
$179$	4155.11	1.73501	0.867506	+	0.497427i	$0.165722\pi$
$180$	−392.204	−0.162406
$181$	−955.425	−0.392355	−0.196177	−	0.980568i	$-0.562853\pi$
$181$	−955.425	−0.392355	−0.196177	+	0.980568i	$0.562853\pi$
$182$	−5475.29	−2.22997
$183$	204.877	0.0827592
$184$	149.353	0.0598393
$185$	441.298	0.175378
$186$	421.611	0.166204
$187$	0	0
$188$	1411.67	0.547640
$189$	−580.397	−0.223374
$190$	354.276	0.135273
$191$	889.758	0.337072	0.168536	−	0.985696i	$-0.446096\pi$
$191$	889.758	0.337072	0.168536	+	0.985696i	$0.446096\pi$
$192$	−188.931	−0.0710152
$193$	1732.07	0.645997	0.322999	−	0.946399i	$-0.395309\pi$
$193$	1732.07	0.645997	0.322999	+	0.946399i	$0.395309\pi$
$194$	−6267.16	−2.31936
$195$	45.2316	0.0166108
$196$	2278.17	0.830237
$197$	4443.91	1.60718	0.803592	−	0.595181i	$-0.202919\pi$
$197$	4443.91	1.60718	0.803592	+	0.595181i	$0.202919\pi$
$198$	3423.93	1.22893
$199$	3118.38	1.11083	0.555417	−	0.831572i	$-0.312559\pi$
$199$	3118.38	1.11083	0.555417	+	0.831572i	$0.312559\pi$
$200$	−240.388	−0.0849901
$201$	226.360	0.0794338
$202$	2625.25	0.914415
$203$	3994.22	1.38098
$204$	0	0
$205$	−450.952	−0.153638
$206$	3434.11	1.16148
$207$	−2019.50	−0.678093
$208$	−3706.42	−1.23555
$209$	−1496.13	−0.495164
$210$	−82.8140	−0.0272129
$211$	−4532.53	−1.47883	−0.739413	−	0.673252i	$-0.764897\pi$
$211$	−4532.53	−1.47883	−0.739413	+	0.673252i	$0.764897\pi$
$212$	3509.78	1.13704
$213$	−33.1358	−0.0106593
$214$	1363.32	0.435489
$215$	233.398	0.0740354
$216$	−45.2619	−0.0142578
$217$	−6424.89	−2.00991
$218$	534.661	0.166109
$219$	162.394	0.0501076
$220$	474.242	0.145334
$221$	0	0
$222$	−377.562	−0.114145
$223$	123.574	0.0371082	0.0185541	−	0.999828i	$-0.494094\pi$
$223$	123.574	0.0371082	0.0185541	+	0.999828i	$0.494094\pi$
$224$	6382.46	1.90378
$225$	3250.46	0.963100
$226$	3487.54	1.02649
$227$	−780.134	−0.228103	−0.114051	−	0.993475i	$-0.536383\pi$
$227$	−780.134	−0.228103	−0.114051	+	0.993475i	$0.536383\pi$
$228$	−146.626	−0.0425902
$229$	−2776.64	−0.801247	−0.400624	−	0.916243i	$-0.631206\pi$
$229$	−2776.64	−0.801247	−0.400624	+	0.916243i	$0.631206\pi$
$230$	−578.237	−0.165773
$231$	349.728	0.0996122
$232$	311.487	0.0881471
$233$	−5047.60	−1.41922	−0.709612	−	0.704593i	$-0.751130\pi$
$233$	−5047.60	−1.41922	−0.709612	+	0.704593i	$0.751130\pi$
$234$	5773.60	1.61296
$235$	367.373	0.101978
$236$	5631.22	1.55323
$237$	−542.222	−0.148612
$238$	0	0
$239$	2254.20	0.610092	0.305046	−	0.952338i	$-0.401328\pi$
$239$	2254.20	0.610092	0.305046	+	0.952338i	$0.401328\pi$
$240$	−56.0599	−0.0150777
$241$	1729.12	0.462168	0.231084	−	0.972934i	$-0.425773\pi$
$241$	1729.12	0.462168	0.231084	+	0.972934i	$0.425773\pi$
$242$	1099.37	0.292027
$243$	919.051	0.242622
$244$	3622.21	0.950360
$245$	592.873	0.154601
$246$	385.821	0.0999962
$247$	−2522.84	−0.649897
$248$	−501.042	−0.128291
$249$	250.738	0.0638148
$250$	1890.61	0.478291
$251$	1314.25	0.330496	0.165248	−	0.986252i	$-0.447158\pi$
$251$	1314.25	0.330496	0.165248	+	0.986252i	$0.447158\pi$
$252$	−5113.55	−1.27827
$253$	2441.93	0.606809
$254$	7759.13	1.91674
$255$	0	0
$256$	4562.26	1.11383
$257$	−6039.96	−1.46600	−0.733001	−	0.680228i	$-0.761881\pi$
$257$	−6039.96	−1.46600	−0.733001	+	0.680228i	$0.761881\pi$
$258$	−199.689	−0.0481863
$259$	5753.64	1.38036
$260$	799.690	0.190749
$261$	−4211.84	−0.998874
$262$	−987.226	−0.232790
$263$	990.368	0.232201	0.116100	−	0.993237i	$-0.462961\pi$
$263$	990.368	0.232201	0.116100	+	0.993237i	$0.462961\pi$
$264$	27.2733	0.00635818
$265$	913.386	0.211732
$266$	4619.05	1.06471
$267$	258.520	0.0592552
$268$	4002.02	0.912173
$269$	−3390.55	−0.768497	−0.384248	−	0.923230i	$-0.625539\pi$
$269$	−3390.55	−0.768497	−0.384248	+	0.923230i	$0.625539\pi$
$270$	175.237	0.0394985
$271$	−3706.24	−0.830767	−0.415383	−	0.909646i	$-0.636353\pi$
$271$	−3706.24	−0.830767	−0.415383	+	0.909646i	$0.636353\pi$
$272$	0	0
$273$	589.729	0.130740
$274$	−1717.79	−0.378742
$275$	−3930.37	−0.861855
$276$	239.318	0.0521930
$277$	−7651.83	−1.65976	−0.829880	−	0.557942i	$-0.811591\pi$
$277$	−7651.83	−1.65976	−0.829880	+	0.557942i	$0.811591\pi$
$278$	−329.576	−0.0711030
$279$	6774.94	1.45378
$280$	98.4161	0.0210053
$281$	−3194.87	−0.678256	−0.339128	−	0.940740i	$-0.610132\pi$
$281$	−3194.87	−0.678256	−0.339128	+	0.940740i	$0.610132\pi$
$282$	−314.314	−0.0663727
$283$	5989.81	1.25815	0.629076	−	0.777344i	$-0.283433\pi$
$283$	5989.81	1.25815	0.629076	+	0.777344i	$0.283433\pi$
$284$	−585.838	−0.122405
$285$	−38.1581	−0.00793085
$286$	−6981.27	−1.44340
$287$	−5879.50	−1.20925
$288$	−6730.20	−1.37702
$289$	0	0
$290$	−1205.96	−0.244195
$291$	675.019	0.135980
$292$	2871.11	0.575408
$293$	−5372.44	−1.07120	−0.535600	−	0.844472i	$-0.679914\pi$
$293$	−5372.44	−1.07120	−0.535600	+	0.844472i	$0.679914\pi$
$294$	−507.245	−0.100623
$295$	1465.47	0.289231
$296$	448.694	0.0881074
$297$	−740.037	−0.144583
$298$	−9280.11	−1.80397
$299$	4117.70	0.796430
$300$	−385.191	−0.0741301
$301$	3043.04	0.582717
$302$	−589.477	−0.112320
$303$	−282.758	−0.0536107
$304$	3126.80	0.589916
$305$	942.645	0.176970
$306$	0	0
$307$	7020.91	1.30523	0.652613	−	0.757692i	$-0.273673\pi$
$307$	7020.91	1.30523	0.652613	+	0.757692i	$0.273673\pi$
$308$	6183.16	1.14389
$309$	−369.878	−0.0680960
$310$	1939.84	0.355406
$311$	−1026.01	−0.187072	−0.0935362	−	0.995616i	$-0.529817\pi$
$311$	−1026.01	−0.187072	−0.0935362	+	0.995616i	$0.529817\pi$
$312$	45.9896	0.00834503
$313$	−2490.87	−0.449815	−0.224907	−	0.974380i	$-0.572208\pi$
$313$	−2490.87	−0.449815	−0.224907	+	0.974380i	$0.572208\pi$
$314$	−469.548	−0.0843889
$315$	−1330.75	−0.238030
$316$	−9586.44	−1.70658
$317$	2775.18	0.491702	0.245851	−	0.969308i	$-0.420933\pi$
$317$	2775.18	0.491702	0.245851	+	0.969308i	$0.420933\pi$
$318$	−781.467	−0.137807
$319$	5092.84	0.893869
$320$	−869.278	−0.151857
$321$	−146.840	−0.0255321
$322$	−7539.05	−1.30477
$323$	0	0
$324$	5355.77	0.918341
$325$	−6627.58	−1.13117
$326$	−600.815	−0.102074
$327$	−57.5870	−0.00973873
$328$	−458.510	−0.0771859
$329$	4789.80	0.802646
$330$	−105.592	−0.0176141
$331$	−6017.90	−0.999317	−0.499659	−	0.866222i	$-0.666541\pi$
$331$	−6017.90	−0.999317	−0.499659	+	0.866222i	$0.666541\pi$
$332$	4433.03	0.732813
$333$	−6067.11	−0.998425
$334$	−9939.96	−1.62841
$335$	1041.49	0.169859
$336$	−730.908	−0.118674
$337$	−474.374	−0.0766789	−0.0383395	−	0.999265i	$-0.512207\pi$
$337$	−474.374	−0.0766789	−0.0383395	+	0.999265i	$0.512207\pi$
$338$	−3123.64	−0.502674
$339$	−375.634	−0.0601818
$340$	0	0
$341$	−8192.07	−1.30095
$342$	−4870.71	−0.770110
$343$	−994.158	−0.156500
$344$	237.310	0.0371944
$345$	62.2804	0.00971903
$346$	1292.25	0.200786
$347$	1475.45	0.228261	0.114130	−	0.993466i	$-0.463592\pi$
$347$	1475.45	0.228261	0.114130	+	0.993466i	$0.463592\pi$
$348$	499.118	0.0768837
$349$	6855.25	1.05144	0.525721	−	0.850657i	$-0.323796\pi$
$349$	6855.25	1.05144	0.525721	+	0.850657i	$0.323796\pi$
$350$	12134.4	1.85317
$351$	−1247.89	−0.189764
$352$	8137.97	1.23226
$353$	−7485.74	−1.12868	−0.564342	−	0.825541i	$-0.690870\pi$
$353$	−7485.74	−1.12868	−0.564342	+	0.825541i	$0.690870\pi$
$354$	−1253.82	−0.188247
$355$	−152.459	−0.0227935
$356$	4570.60	0.680454
$357$	0	0
$358$	−16356.6	−2.41473
$359$	7169.54	1.05402	0.527011	−	0.849859i	$-0.323313\pi$
$359$	7169.54	1.05402	0.527011	+	0.849859i	$0.323313\pi$
$360$	−103.778	−0.0151933
$361$	−4730.69	−0.689705
$362$	3761.04	0.546067
$363$	−118.411	−0.0171211
$364$	10426.4	1.50134
$365$	747.180	0.107149
$366$	−806.500	−0.115182
$367$	−6608.80	−0.939991	−0.469995	−	0.882669i	$-0.655744\pi$
$367$	−6608.80	−0.939991	−0.469995	+	0.882669i	$0.655744\pi$
$368$	−5103.46	−0.722925
$369$	6199.84	0.874663
$370$	−1737.17	−0.244085
$371$	11908.7	1.66650
$372$	−802.855	−0.111898
$373$	−1602.91	−0.222508	−0.111254	−	0.993792i	$-0.535487\pi$
$373$	−1602.91	−0.222508	−0.111254	+	0.993792i	$0.535487\pi$
$374$	0	0
$375$	−203.633	−0.0280415
$376$	373.530	0.0512323
$377$	8587.79	1.17319
$378$	2284.74	0.310885
$379$	1743.08	0.236243	0.118121	−	0.992999i	$-0.462313\pi$
$379$	1743.08	0.236243	0.118121	+	0.992999i	$0.462313\pi$
$380$	−674.632	−0.0910734
$381$	−835.715	−0.112375
$382$	−3502.55	−0.469125
$383$	−1155.24	−0.154125	−0.0770627	−	0.997026i	$-0.524554\pi$
$383$	−1155.24	−0.154125	−0.0770627	+	0.997026i	$0.524554\pi$
$384$	−107.432	−0.0142771
$385$	1609.11	0.213008
$386$	−6818.33	−0.899078
$387$	−3208.83	−0.421484
$388$	11934.3	1.56152
$389$	3698.95	0.482119	0.241060	−	0.970510i	$-0.422505\pi$
$389$	3698.95	0.482119	0.241060	+	0.970510i	$0.422505\pi$
$390$	−178.055	−0.0231183
$391$	0	0
$392$	602.809	0.0776696
$393$	106.332	0.0136481
$394$	−17493.5	−2.23683
$395$	−2494.78	−0.317788
$396$	−6520.04	−0.827385
$397$	−13587.9	−1.71778	−0.858891	−	0.512159i	$-0.828846\pi$
$397$	−13587.9	−1.71778	−0.858891	+	0.512159i	$0.828846\pi$
$398$	−12275.5	−1.54602
$399$	−497.505	−0.0624221
$400$	8214.20	1.02678
$401$	−2664.34	−0.331798	−0.165899	−	0.986143i	$-0.553053\pi$
$401$	−2664.34	−0.331798	−0.165899	+	0.986143i	$0.553053\pi$
$402$	−891.068	−0.110553
$403$	−13813.9	−1.70749
$404$	−4999.14	−0.615635
$405$	1393.79	0.171007
$406$	−15723.3	−1.92201
$407$	7336.19	0.893467
$408$	0	0
$409$	4145.86	0.501222	0.250611	−	0.968088i	$-0.419368\pi$
$409$	4145.86	0.501222	0.250611	+	0.968088i	$0.419368\pi$
$410$	1775.18	0.213829
$411$	185.018	0.0222050
$412$	−6539.42	−0.781976
$413$	19106.8	2.27648
$414$	7949.80	0.943748
$415$	1153.65	0.136459
$416$	13722.6	1.61733
$417$	35.4977	0.00416866
$418$	5889.52	0.689153
$419$	−14247.5	−1.66118	−0.830592	−	0.556882i	$-0.811997\pi$
$419$	−14247.5	−1.66118	−0.830592	+	0.556882i	$0.811997\pi$
$420$	157.699	0.0183213
$421$	3191.61	0.369477	0.184738	−	0.982788i	$-0.440856\pi$
$421$	3191.61	0.369477	0.184738	+	0.982788i	$0.440856\pi$
$422$	17842.4	2.05818
$423$	−5050.77	−0.580560
$424$	928.695	0.106371
$425$	0	0
$426$	130.439	0.0148352
$427$	12290.2	1.39289
$428$	−2596.11	−0.293196
$429$	751.935	0.0846241
$430$	−918.774	−0.103040
$431$	1639.42	0.183220	0.0916101	−	0.995795i	$-0.470799\pi$
$431$	1639.42	0.183220	0.0916101	+	0.995795i	$0.470799\pi$
$432$	1546.63	0.172250
$433$	16579.9	1.84013	0.920066	−	0.391764i	$-0.128135\pi$
$433$	16579.9	1.84013	0.920066	+	0.391764i	$0.128135\pi$
$434$	25291.7	2.79732
$435$	129.891	0.0143168
$436$	−1018.13	−0.111834
$437$	−3473.76	−0.380258
$438$	−639.266	−0.0697382
$439$	−7347.09	−0.798764	−0.399382	−	0.916785i	$-0.630775\pi$
$439$	−7347.09	−0.798764	−0.399382	+	0.916785i	$0.630775\pi$
$440$	125.486	0.0135961
$441$	−8151.02	−0.880144
$442$	0	0
$443$	−13325.5	−1.42915	−0.714575	−	0.699559i	$-0.753380\pi$
$443$	−13325.5	−1.42915	−0.714575	+	0.699559i	$0.753380\pi$
$444$	718.974	0.0768491
$445$	1189.46	0.126709
$446$	−486.451	−0.0516460
$447$	999.536	0.105764
$448$	−11333.6	−1.19523
$449$	−9686.35	−1.01810	−0.509050	−	0.860737i	$-0.670003\pi$
$449$	−9686.35	−1.01810	−0.509050	+	0.860737i	$0.670003\pi$
$450$	−12795.5	−1.34041
$451$	−7496.67	−0.782715
$452$	−6641.17	−0.691094
$453$	63.4910	0.00658514
$454$	3071.01	0.317466
$455$	2713.36	0.279570
$456$	−38.7976	−0.00398436
$457$	698.065	0.0714532	0.0357266	−	0.999362i	$-0.488625\pi$
$457$	698.065	0.0714532	0.0357266	+	0.999362i	$0.488625\pi$
$458$	10930.3	1.11515
$459$	0	0
$460$	1101.11	0.111608
$461$	6505.58	0.657256	0.328628	−	0.944459i	$-0.393414\pi$
$461$	6505.58	0.657256	0.328628	+	0.944459i	$0.393414\pi$
$462$	−1376.71	−0.138637
$463$	−1181.74	−0.118618	−0.0593089	−	0.998240i	$-0.518890\pi$
$463$	−1181.74	−0.118618	−0.0593089	+	0.998240i	$0.518890\pi$
$464$	−10643.7	−1.06492
$465$	−208.935	−0.0208369
$466$	19869.9	1.97523
$467$	2950.96	0.292407	0.146204	−	0.989255i	$-0.453295\pi$
$467$	2950.96	0.292407	0.146204	+	0.989255i	$0.453295\pi$
$468$	−10994.4	−1.08593
$469$	13578.9	1.33692
$470$	−1446.17	−0.141929
$471$	50.5737	0.00494759
$472$	1490.03	0.145306
$473$	3880.03	0.377176
$474$	2134.46	0.206834
$475$	5591.14	0.540082
$476$	0	0
$477$	−12557.5	−1.20539
$478$	−8873.69	−0.849107
$479$	−8890.21	−0.848025	−0.424013	−	0.905656i	$-0.639379\pi$
$479$	−8890.21	−0.848025	−0.424013	+	0.905656i	$0.639379\pi$
$480$	207.556	0.0197366
$481$	12370.6	1.17267
$482$	−6806.70	−0.643230
$483$	812.011	0.0764965
$484$	−2093.49	−0.196609
$485$	3105.78	0.290776
$486$	−3617.85	−0.337673
$487$	7104.47	0.661056	0.330528	−	0.943796i	$-0.392773\pi$
$487$	7104.47	0.661056	0.330528	+	0.943796i	$0.392773\pi$
$488$	958.444	0.0889072
$489$	64.7121	0.00598442
$490$	−2333.85	−0.215169
$491$	7638.33	0.702063	0.351031	−	0.936364i	$-0.385831\pi$
$491$	7638.33	0.702063	0.351031	+	0.936364i	$0.385831\pi$
$492$	−734.703	−0.0673231
$493$	0	0
$494$	9931.20	0.904505
$495$	−1696.78	−0.154070
$496$	17120.9	1.54990
$497$	−1987.76	−0.179403
$498$	−987.033	−0.0888153
$499$	20202.5	1.81241	0.906203	−	0.422843i	$-0.138968\pi$
$499$	20202.5	1.81241	0.906203	+	0.422843i	$0.138968\pi$
$500$	−3600.21	−0.322012
$501$	1070.61	0.0954714
$502$	−5173.54	−0.459973
$503$	−20469.5	−1.81449	−0.907244	−	0.420604i	$-0.861818\pi$
$503$	−20469.5	−1.81449	−0.907244	+	0.420604i	$0.861818\pi$
$504$	−1353.06	−0.119583
$505$	−1300.98	−0.114639
$506$	−9612.68	−0.844537
$507$	336.439	0.0294710
$508$	−14775.4	−1.29045
$509$	−19503.1	−1.69835	−0.849173	−	0.528116i	$-0.822899\pi$
$509$	−19503.1	−1.69835	−0.849173	+	0.528116i	$0.822899\pi$
$510$	0	0
$511$	9741.73	0.843344
$512$	−15932.3	−1.37523
$513$	1052.74	0.0906033
$514$	23776.4	2.04033
$515$	−1701.82	−0.145614
$516$	380.258	0.0324417
$517$	6107.25	0.519529
$518$	−22649.3	−1.92114
$519$	−139.185	−0.0117718
$520$	211.600	0.0178447
$521$	−6963.51	−0.585561	−0.292780	−	0.956180i	$-0.594580\pi$
$521$	−6963.51	−0.585561	−0.292780	+	0.956180i	$0.594580\pi$
$522$	16580.0	1.39020
$523$	2507.22	0.209623	0.104812	−	0.994492i	$-0.466576\pi$
$523$	2507.22	0.209623	0.104812	+	0.994492i	$0.466576\pi$
$524$	1879.93	0.156728
$525$	−1306.96	−0.108648
$526$	−3898.60	−0.323169
$527$	0	0
$528$	−931.946	−0.0768139
$529$	−6497.24	−0.534005
$530$	−3595.56	−0.294681
$531$	−20147.8	−1.64659
$532$	−8795.85	−0.716820
$533$	−12641.3	−1.02730
$534$	−1017.67	−0.0824695
$535$	−675.614	−0.0545969
$536$	1058.94	0.0853348
$537$	1761.73	0.141572
$538$	13346.9	1.06957
$539$	9855.99	0.787620
$540$	−333.697	−0.0265926
$541$	−19376.1	−1.53982	−0.769912	−	0.638149i	$-0.779700\pi$
$541$	−19376.1	−1.53982	−0.769912	+	0.638149i	$0.779700\pi$
$542$	14589.6	1.15623
$543$	−405.092	−0.0320150
$544$	0	0
$545$	−264.960	−0.0208250
$546$	−2321.47	−0.181960
$547$	2956.31	0.231083	0.115542	−	0.993303i	$-0.463140\pi$
$547$	2956.31	0.231083	0.115542	+	0.993303i	$0.463140\pi$
$548$	3271.10	0.254990
$549$	−12959.8	−1.00749
$550$	15471.9	1.19950
$551$	−7244.81	−0.560144
$552$	63.3242	0.00488271
$553$	−32526.9	−2.50124
$554$	30121.5	2.31000
$555$	187.106	0.0143103
$556$	627.597	0.0478706
$557$	3920.00	0.298197	0.149099	−	0.988822i	$-0.452363\pi$
$557$	3920.00	0.298197	0.149099	+	0.988822i	$0.452363\pi$
$558$	−26669.6	−2.02333
$559$	6542.70	0.495039
$560$	−3362.93	−0.253768
$561$	0	0
$562$	12576.6	0.943975
$563$	20821.5	1.55865	0.779326	−	0.626618i	$-0.215561\pi$
$563$	20821.5	1.55865	0.779326	+	0.626618i	$0.215561\pi$
$564$	598.534	0.0446859
$565$	−1728.30	−0.128691
$566$	−23579.0	−1.75106
$567$	18172.2	1.34596
$568$	−155.014	−0.0114511
$569$	−7849.66	−0.578339	−0.289170	−	0.957278i	$-0.593379\pi$
$569$	−7849.66	−0.578339	−0.289170	+	0.957278i	$0.593379\pi$
$570$	150.210	0.0110379
$571$	−24535.7	−1.79822	−0.899112	−	0.437719i	$-0.855786\pi$
$571$	−24535.7	−1.79822	−0.899112	+	0.437719i	$0.855786\pi$
$572$	13294.1	0.971776
$573$	377.250	0.0275041
$574$	23144.7	1.68300
$575$	−9125.67	−0.661855
$576$	11951.1	0.864521
$577$	−7549.37	−0.544687	−0.272343	−	0.962200i	$-0.587799\pi$
$577$	−7549.37	−0.544687	−0.272343	+	0.962200i	$0.587799\pi$
$578$	0	0
$579$	734.384	0.0527115
$580$	2296.46	0.164406
$581$	15041.3	1.07404
$582$	−2657.22	−0.189253
$583$	15184.2	1.07867
$584$	759.703	0.0538300
$585$	−2861.19	−0.202215
$586$	21148.7	1.49086
$587$	6451.77	0.453651	0.226826	−	0.973935i	$-0.427165\pi$
$587$	6451.77	0.453651	0.226826	+	0.973935i	$0.427165\pi$
$588$	965.925	0.0677450
$589$	11653.6	0.815244
$590$	−5768.85	−0.402542
$591$	1884.18	0.131142
$592$	−15332.1	−1.06444
$593$	176.420	0.0122170	0.00610850	−	0.999981i	$-0.498056\pi$
$593$	176.420	0.0122170	0.00610850	+	0.999981i	$0.498056\pi$
$594$	2913.16	0.201227
$595$	0	0
$596$	17671.7	1.21453
$597$	1322.16	0.0906408
$598$	−16209.4	−1.10845
$599$	11248.7	0.767292	0.383646	−	0.923480i	$-0.374668\pi$
$599$	11248.7	0.767292	0.383646	+	0.923480i	$0.374668\pi$
$600$	−101.923	−0.00693495
$601$	−25418.5	−1.72519	−0.862596	−	0.505893i	$-0.831163\pi$
$601$	−25418.5	−1.72519	−0.862596	+	0.505893i	$0.831163\pi$
$602$	−11979.0	−0.811007
$603$	−14318.7	−0.967006
$604$	1122.52	0.0756201
$605$	−544.812	−0.0366112
$606$	1113.08	0.0746136
$607$	−19680.4	−1.31599	−0.657993	−	0.753024i	$-0.728594\pi$
$607$	−19680.4	−1.31599	−0.657993	+	0.753024i	$0.728594\pi$
$608$	−11576.7	−0.772196
$609$	1693.51	0.112684
$610$	−3710.74	−0.246300
$611$	10298.3	0.681876
$612$	0	0
$613$	3619.34	0.238473	0.119236	−	0.992866i	$-0.461955\pi$
$613$	3619.34	0.238473	0.119236	+	0.992866i	$0.461955\pi$
$614$	−27637.9	−1.81657
$615$	−191.200	−0.0125364
$616$	1636.08	0.107012
$617$	19744.9	1.28833	0.644164	−	0.764887i	$-0.277205\pi$
$617$	19744.9	1.28833	0.644164	+	0.764887i	$0.277205\pi$
$618$	1456.03	0.0947737
$619$	18695.9	1.21397	0.606987	−	0.794712i	$-0.292378\pi$
$619$	18695.9	1.21397	0.606987	+	0.794712i	$0.292378\pi$
$620$	−3693.96	−0.239279
$621$	−1718.24	−0.111032
$622$	4038.89	0.260361
$623$	15508.1	0.997304
$624$	−1571.49	−0.100817
$625$	14212.4	0.909592
$626$	9805.33	0.626038
$627$	−634.345	−0.0404040
$628$	894.139	0.0568153
$629$	0	0
$630$	5238.53	0.331283
$631$	−10087.2	−0.636394	−0.318197	−	0.948025i	$-0.603077\pi$
$631$	−10087.2	−0.636394	−0.318197	+	0.948025i	$0.603077\pi$
$632$	−2536.59	−0.159652
$633$	−1921.75	−0.120668
$634$	−10924.5	−0.684335
$635$	−3845.15	−0.240300
$636$	1488.11	0.0927792
$637$	16619.6	1.03374
$638$	−20048.0	−1.24406
$639$	2096.06	0.129763
$640$	−494.300	−0.0305296
$641$	10265.1	0.632523	0.316261	−	0.948672i	$-0.397572\pi$
$641$	10265.1	0.632523	0.316261	+	0.948672i	$0.397572\pi$
$642$	578.036	0.0355347
$643$	7778.26	0.477052	0.238526	−	0.971136i	$-0.423336\pi$
$643$	7778.26	0.477052	0.238526	+	0.971136i	$0.423336\pi$
$644$	14356.3	0.878443
$645$	98.9587	0.00604108
$646$	0	0
$647$	5015.28	0.304746	0.152373	−	0.988323i	$-0.451308\pi$
$647$	5015.28	0.304746	0.152373	+	0.988323i	$0.451308\pi$
$648$	1417.15	0.0859118
$649$	24362.2	1.47350
$650$	26089.5	1.57433
$651$	−2724.10	−0.164003
$652$	1144.10	0.0687218
$653$	−14563.9	−0.872784	−0.436392	−	0.899757i	$-0.643744\pi$
$653$	−14563.9	−0.872784	−0.436392	+	0.899757i	$0.643744\pi$
$654$	226.692	0.0135541
$655$	489.235	0.0291847
$656$	15667.5	0.932491
$657$	−10272.5	−0.609997
$658$	−18855.1	−1.11710
$659$	−6199.21	−0.366445	−0.183222	−	0.983072i	$-0.558653\pi$
$659$	−6199.21	−0.366445	−0.183222	+	0.983072i	$0.558653\pi$
$660$	201.075	0.0118588
$661$	15131.8	0.890406	0.445203	−	0.895430i	$-0.353132\pi$
$661$	15131.8	0.890406	0.445203	+	0.895430i	$0.353132\pi$
$662$	23689.6	1.39082
$663$	0	0
$664$	1172.99	0.0685554
$665$	−2289.04	−0.133481
$666$	23883.3	1.38958
$667$	11824.7	0.686440
$668$	18928.2	1.09634
$669$	52.3943	0.00302792
$670$	−4099.84	−0.236404
$671$	15670.6	0.901577
$672$	2706.11	0.155343
$673$	27043.8	1.54898	0.774488	−	0.632589i	$-0.218008\pi$
$673$	27043.8	1.54898	0.774488	+	0.632589i	$0.218008\pi$
$674$	1867.38	0.106719
$675$	2765.57	0.157699
$676$	5948.22	0.338429
$677$	−2671.45	−0.151658	−0.0758288	−	0.997121i	$-0.524160\pi$
$677$	−2671.45	−0.151658	−0.0758288	+	0.997121i	$0.524160\pi$
$678$	1478.69	0.0837591
$679$	40493.2	2.28864
$680$	0	0
$681$	−330.770	−0.0186125
$682$	32248.2	1.81063
$683$	−14786.6	−0.828393	−0.414197	−	0.910187i	$-0.635937\pi$
$683$	−14786.6	−0.828393	−0.414197	+	0.910187i	$0.635937\pi$
$684$	9275.07	0.518481
$685$	851.274	0.0474825
$686$	3913.52	0.217812
$687$	−1177.27	−0.0653795
$688$	−8109.01	−0.449350
$689$	25604.4	1.41575
$690$	−245.168	−0.0135266
$691$	18670.1	1.02785	0.513924	−	0.857836i	$-0.328191\pi$
$691$	18670.1	1.02785	0.513924	+	0.857836i	$0.328191\pi$
$692$	−2460.78	−0.135181
$693$	−22122.6	−1.21265
$694$	−5808.14	−0.317686
$695$	163.326	0.00891413
$696$	132.068	0.00719255
$697$	0	0
$698$	−26985.8	−1.46336
$699$	−2140.14	−0.115805
$700$	−23106.9	−1.24766
$701$	−27668.5	−1.49076	−0.745381	−	0.666638i	$-0.767733\pi$
$701$	−27668.5	−1.49076	−0.745381	+	0.666638i	$0.767733\pi$
$702$	4912.32	0.264107
$703$	−10436.1	−0.559892
$704$	−14451.0	−0.773639
$705$	155.763	0.00832109
$706$	29467.7	1.57087
$707$	−16962.2	−0.902303
$708$	2387.59	0.126739
$709$	−10439.9	−0.553002	−0.276501	−	0.961014i	$-0.589175\pi$
$709$	−10439.9	−0.553002	−0.276501	+	0.961014i	$0.589175\pi$
$710$	600.157	0.0317232
$711$	34299.1	1.80917
$712$	1209.39	0.0636572
$713$	−19020.6	−0.999059
$714$	0	0
$715$	3459.68	0.180957
$716$	31147.2	1.62573
$717$	955.761	0.0497818
$718$	−28223.0	−1.46695
$719$	−17815.1	−0.924050	−0.462025	−	0.886867i	$-0.652877\pi$
$719$	−17815.1	−0.924050	−0.462025	+	0.886867i	$0.652877\pi$
$720$	3546.16	0.183552
$721$	−22188.4	−1.14610
$722$	18622.4	0.959909
$723$	733.132	0.0377116
$724$	−7161.99	−0.367643
$725$	−19032.3	−0.974955
$726$	466.125	0.0238286
$727$	4296.42	0.219182	0.109591	−	0.993977i	$-0.465046\pi$
$727$	4296.42	0.219182	0.109591	+	0.993977i	$0.465046\pi$
$728$	2758.84	0.140452
$729$	−18901.0	−0.960273
$730$	−2941.28	−0.149126
$731$	0	0
$732$	1535.78	0.0775467
$733$	−28559.1	−1.43909	−0.719546	−	0.694445i	$-0.755650\pi$
$733$	−28559.1	−1.43909	−0.719546	+	0.694445i	$0.755650\pi$
$734$	26015.6	1.30825
$735$	251.373	0.0126150
$736$	18895.0	0.946304
$737$	17313.8	0.865351
$738$	−24405.7	−1.21733
$739$	−10646.9	−0.529974	−0.264987	−	0.964252i	$-0.585368\pi$
$739$	−10646.9	−0.529974	−0.264987	+	0.964252i	$0.585368\pi$
$740$	3308.03	0.164332
$741$	−1069.66	−0.0530298
$742$	−46878.8	−2.31937
$743$	−13964.7	−0.689521	−0.344760	−	0.938691i	$-0.612040\pi$
$743$	−13964.7	−0.689521	−0.344760	+	0.938691i	$0.612040\pi$
$744$	−212.437	−0.0104682
$745$	4598.90	0.226162
$746$	6309.87	0.309679
$747$	−15860.8	−0.776864
$748$	0	0
$749$	−8808.65	−0.429721
$750$	801.602	0.0390272
$751$	−26761.0	−1.30030	−0.650149	−	0.759807i	$-0.725293\pi$
$751$	−26761.0	−1.30030	−0.650149	+	0.759807i	$0.725293\pi$
$752$	−12763.7	−0.618943
$753$	557.229	0.0269675
$754$	−33805.9	−1.63281
$755$	292.124	0.0140815
$756$	−4350.73	−0.209305
$757$	−1399.40	−0.0671889	−0.0335945	−	0.999436i	$-0.510695\pi$
$757$	−1399.40	−0.0671889	−0.0335945	+	0.999436i	$0.510695\pi$
$758$	−6861.66	−0.328795
$759$	1035.36	0.0495139
$760$	−178.509	−0.00852002
$761$	−29282.9	−1.39488	−0.697440	−	0.716644i	$-0.745677\pi$
$761$	−29282.9	−1.39488	−0.697440	+	0.716644i	$0.745677\pi$
$762$	3289.80	0.156400
$763$	−3454.54	−0.163909
$764$	6669.74	0.315841
$765$	0	0
$766$	4547.62	0.214507
$767$	41080.7	1.93395
$768$	1934.36	0.0908856
$769$	11804.9	0.553571	0.276786	−	0.960932i	$-0.410731\pi$
$769$	11804.9	0.553571	0.276786	+	0.960932i	$0.410731\pi$
$770$	−6334.29	−0.296457
$771$	−2560.89	−0.119622
$772$	12983.9	0.605310
$773$	−18421.7	−0.857155	−0.428578	−	0.903505i	$-0.640985\pi$
$773$	−18421.7	−0.857155	−0.428578	+	0.903505i	$0.640985\pi$
$774$	12631.6	0.586607
$775$	30614.4	1.41897
$776$	3157.84	0.146082
$777$	2439.49	0.112634
$778$	−14561.0	−0.670998
$779$	10664.4	0.490489
$780$	339.062	0.0155646
$781$	−2534.49	−0.116122
$782$	0	0
$783$	−3583.53	−0.163557
$784$	−20598.3	−0.938335
$785$	232.691	0.0105798
$786$	−418.575	−0.0189950
$787$	−22391.5	−1.01419	−0.507096	−	0.861889i	$-0.669281\pi$
$787$	−22391.5	−1.01419	−0.507096	+	0.861889i	$0.669281\pi$
$788$	33312.1	1.50596
$789$	419.908	0.0189469
$790$	9820.74	0.442286
$791$	−22533.6	−1.01290
$792$	−1725.22	−0.0774027
$793$	26424.6	1.18331
$794$	53489.1	2.39075
$795$	387.268	0.0172767
$796$	23375.7	1.04087
$797$	−13676.1	−0.607818	−0.303909	−	0.952701i	$-0.598292\pi$
$797$	−13676.1	−0.607818	−0.303909	+	0.952701i	$0.598292\pi$
$798$	1958.43	0.0868770
$799$	0	0
$800$	−30412.2	−1.34404
$801$	−16353.1	−0.721357
$802$	10488.2	0.461786
$803$	12421.2	0.545872
$804$	1696.82	0.0744308
$805$	3736.09	0.163578
$806$	54378.5	2.37643
$807$	−1437.56	−0.0627071
$808$	−1322.79	−0.0575933
$809$	−100.880	−0.00438410	−0.00219205	−	0.999998i	$-0.500698\pi$
$809$	−100.880	−0.00438410	−0.00219205	+	0.999998i	$0.500698\pi$
$810$	−5486.67	−0.238002
$811$	16719.6	0.723926	0.361963	−	0.932192i	$-0.382107\pi$
$811$	16719.6	0.723926	0.361963	+	0.932192i	$0.382107\pi$
$812$	29941.2	1.29400
$813$	−1571.41	−0.0677882
$814$	−28879.0	−1.24350
$815$	297.743	0.0127969
$816$	0	0
$817$	−5519.54	−0.236358
$818$	−16320.2	−0.697584
$819$	−37304.2	−1.59159
$820$	−3380.39	−0.143962
$821$	−4932.52	−0.209679	−0.104839	−	0.994489i	$-0.533433\pi$
$821$	−4932.52	−0.209679	−0.104839	+	0.994489i	$0.533433\pi$
$822$	−728.326	−0.0309042
$823$	26576.3	1.12563	0.562814	−	0.826583i	$-0.309719\pi$
$823$	26576.3	1.12563	0.562814	+	0.826583i	$0.309719\pi$
$824$	−1730.35	−0.0731547
$825$	−1666.44	−0.0703249
$826$	−75214.2	−3.16833
$827$	−31136.7	−1.30923	−0.654613	−	0.755965i	$-0.727168\pi$
$827$	−31136.7	−1.30923	−0.654613	+	0.755965i	$0.727168\pi$
$828$	−15138.5	−0.635384
$829$	−17274.9	−0.723742	−0.361871	−	0.932228i	$-0.617862\pi$
$829$	−17274.9	−0.723742	−0.361871	+	0.932228i	$0.617862\pi$
$830$	−4541.37	−0.189920
$831$	−3244.31	−0.135432
$832$	−24367.9	−1.01539
$833$	0	0
$834$	−139.737	−0.00580180
$835$	4925.90	0.204153
$836$	−11215.2	−0.463977
$837$	5764.28	0.238044
$838$	56085.4	2.31198
$839$	−5614.44	−0.231027	−0.115514	−	0.993306i	$-0.536851\pi$
$839$	−5614.44	−0.231027	−0.115514	+	0.993306i	$0.536851\pi$
$840$	41.7276	0.00171397
$841$	272.434	0.0111704
$842$	−12563.8	−0.514226
$843$	−1354.60	−0.0553438
$844$	−33976.4	−1.38568
$845$	1547.97	0.0630198
$846$	19882.4	0.808004
$847$	−7103.25	−0.288159
$848$	−31734.0	−1.28508
$849$	2539.63	0.102662
$850$	0	0
$851$	17033.4	0.686132
$852$	−248.390	−0.00998792
$853$	−3799.83	−0.152525	−0.0762625	−	0.997088i	$-0.524299\pi$
$853$	−3799.83	−0.152525	−0.0762625	+	0.997088i	$0.524299\pi$
$854$	−48380.5	−1.93858
$855$	2413.75	0.0965480
$856$	−686.938	−0.0274288
$857$	42210.3	1.68247	0.841235	−	0.540669i	$-0.181829\pi$
$857$	42210.3	1.68247	0.841235	+	0.540669i	$0.181829\pi$
$858$	−2960.00	−0.117777
$859$	3132.98	0.124442	0.0622212	−	0.998062i	$-0.480182\pi$
$859$	3132.98	0.124442	0.0622212	+	0.998062i	$0.480182\pi$
$860$	1749.58	0.0693724
$861$	−2492.86	−0.0986718
$862$	−6453.58	−0.255000
$863$	31934.9	1.25965	0.629824	−	0.776738i	$-0.283127\pi$
$863$	31934.9	1.25965	0.629824	+	0.776738i	$0.283127\pi$
$864$	−5726.22	−0.225474
$865$	−640.396	−0.0251724
$866$	−65266.8	−2.56104
$867$	0	0
$868$	−48161.8	−1.88332
$869$	−41473.5	−1.61898
$870$	−511.317	−0.0199256
$871$	29195.4	1.13576
$872$	−269.400	−0.0104622
$873$	−42699.4	−1.65539
$874$	13674.5	0.529230
$875$	−12215.6	−0.471956
$876$	1217.33	0.0469517
$877$	−15340.7	−0.590670	−0.295335	−	0.955394i	$-0.595431\pi$
$877$	−15340.7	−0.590670	−0.295335	+	0.955394i	$0.595431\pi$
$878$	28921.9	1.11169
$879$	−2277.87	−0.0874068
$880$	−4287.91	−0.164256
$881$	−46287.9	−1.77012	−0.885062	−	0.465472i	$-0.845884\pi$
$881$	−46287.9	−1.77012	−0.885062	+	0.465472i	$0.845884\pi$
$882$	32086.6	1.22496
$883$	−26455.9	−1.00828	−0.504140	−	0.863622i	$-0.668190\pi$
$883$	−26455.9	−1.00828	−0.504140	+	0.863622i	$0.668190\pi$
$884$	0	0
$885$	621.348	0.0236004
$886$	52456.0	1.98904
$887$	18030.9	0.682546	0.341273	−	0.939964i	$-0.389142\pi$
$887$	18030.9	0.682546	0.341273	+	0.939964i	$0.389142\pi$
$888$	190.242	0.00718932
$889$	−50133.0	−1.89135
$890$	−4682.31	−0.176350
$891$	23170.5	0.871202
$892$	926.327	0.0347710
$893$	−8687.85	−0.325563
$894$	−3934.69	−0.147199
$895$	8105.77	0.302733
$896$	−6444.68	−0.240292
$897$	1745.87	0.0649864
$898$	38130.4	1.41696
$899$	−39669.1	−1.47168
$900$	24365.9	0.902440
$901$	0	0
$902$	29510.7	1.08936
$903$	1290.22	0.0475481
$904$	−1757.27	−0.0646526
$905$	−1863.84	−0.0684599
$906$	−249.933	−0.00916498
$907$	45743.1	1.67461	0.837307	−	0.546733i	$-0.184129\pi$
$907$	45743.1	1.67461	0.837307	+	0.546733i	$0.184129\pi$
$908$	−5847.99	−0.213736
$909$	17886.3	0.652642
$910$	−10681.2	−0.389096
$911$	−1701.39	−0.0618766	−0.0309383	−	0.999521i	$-0.509850\pi$
$911$	−1701.39	−0.0618766	−0.0309383	+	0.999521i	$0.509850\pi$
$912$	1325.74	0.0481355
$913$	19178.5	0.695197
$914$	−2747.94	−0.0994462
$915$	399.673	0.0144402
$916$	−20814.1	−0.750782
$917$	6378.64	0.229707
$918$	0	0
$919$	30814.5	1.10607	0.553035	−	0.833158i	$-0.313470\pi$
$919$	30814.5	1.10607	0.553035	+	0.833158i	$0.313470\pi$
$920$	291.357	0.0104410
$921$	2976.80	0.106503
$922$	−25609.3	−0.914747
$923$	−4273.79	−0.152409
$924$	2621.61	0.0933383
$925$	−27415.9	−0.974517
$926$	4651.93	0.165088
$927$	23397.2	0.828982
$928$	39407.1	1.39397
$929$	−4093.21	−0.144558	−0.0722788	−	0.997384i	$-0.523027\pi$
$929$	−4093.21	−0.144558	−0.0722788	+	0.997384i	$0.523027\pi$
$930$	822.477	0.0290001
$931$	−14020.6	−0.493563
$932$	−37837.4	−1.32984
$933$	−435.018	−0.0152646
$934$	−11616.5	−0.406963
$935$	0	0
$936$	−2909.15	−0.101590
$937$	−16517.3	−0.575877	−0.287939	−	0.957649i	$-0.592970\pi$
$937$	−16517.3	−0.575877	−0.287939	+	0.957649i	$0.592970\pi$
$938$	−53453.6	−1.86068
$939$	−1056.11	−0.0367036
$940$	2753.88	0.0955548
$941$	6860.74	0.237677	0.118838	−	0.992914i	$-0.462083\pi$
$941$	6860.74	0.237677	0.118838	+	0.992914i	$0.462083\pi$
$942$	−199.084	−0.00688589
$943$	−17406.0	−0.601080
$944$	−50915.3	−1.75546
$945$	−1132.24	−0.0389754
$946$	−15273.8	−0.524941
$947$	33298.8	1.14262	0.571312	−	0.820733i	$-0.306435\pi$
$947$	33298.8	1.14262	0.571312	+	0.820733i	$0.306435\pi$
$948$	−4064.57	−0.139252
$949$	20945.2	0.716450
$950$	−22009.6	−0.751669
$951$	1176.65	0.0401215
$952$	0	0
$953$	−24857.5	−0.844925	−0.422462	−	0.906380i	$-0.638834\pi$
$953$	−24857.5	−0.844925	−0.422462	+	0.906380i	$0.638834\pi$
$954$	49432.9	1.67762
$955$	1735.74	0.0588138
$956$	16897.8	0.571666
$957$	2159.32	0.0729372
$958$	34996.4	1.18025
$959$	11098.9	0.373725
$960$	−368.566	−0.0123911
$961$	34018.6	1.14191
$962$	−48697.1	−1.63208
$963$	9288.57	0.310820
$964$	12961.7	0.433059
$965$	3378.93	0.112717
$966$	−3196.49	−0.106465
$967$	15832.2	0.526504	0.263252	−	0.964727i	$-0.415205\pi$
$967$	15832.2	0.526504	0.263252	+	0.964727i	$0.415205\pi$
$968$	−553.943	−0.0183930
$969$	0	0
$970$	−12226.0	−0.404693
$971$	−39521.9	−1.30620	−0.653098	−	0.757273i	$-0.726531\pi$
$971$	−39521.9	−1.30620	−0.653098	+	0.757273i	$0.726531\pi$
$972$	6889.32	0.227341
$973$	2129.45	0.0701612
$974$	−27966.8	−0.920036
$975$	−2810.03	−0.0923007
$976$	−32750.6	−1.07410
$977$	−11587.3	−0.379438	−0.189719	−	0.981838i	$-0.560758\pi$
$977$	−11587.3	−0.379438	−0.189719	+	0.981838i	$0.560758\pi$
$978$	−254.740	−0.00832893
$979$	19773.7	0.645525
$980$	4444.25	0.144864
$981$	3642.75	0.118557
$982$	−30068.4	−0.977108
$983$	32119.5	1.04217	0.521085	−	0.853505i	$-0.325528\pi$
$983$	32119.5	1.04217	0.521085	+	0.853505i	$0.325528\pi$
$984$	−194.404	−0.00629815
$985$	8669.17	0.280429
$986$	0	0
$987$	2030.83	0.0654936
$988$	−18911.5	−0.608964
$989$	9008.80	0.289649
$990$	6679.40	0.214429
$991$	−18717.3	−0.599976	−0.299988	−	0.953943i	$-0.596983\pi$
$991$	−18717.3	−0.599976	−0.299988	+	0.953943i	$0.596983\pi$
$992$	−63388.2	−2.02881
$993$	−2551.54	−0.0815414
$994$	7824.83	0.249687
$995$	6083.32	0.193823
$996$	1879.56	0.0597955
$997$	11611.3	0.368840	0.184420	−	0.982848i	$-0.440959\pi$
$997$	11611.3	0.368840	0.184420	+	0.982848i	$0.440959\pi$
$998$	−79527.6	−2.52245
$999$	−5162.05	−0.163483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.f.1.2		8
17.4	even	4		289.4.b.c.288.7		8
17.8	even	8		17.4.c.a.13.4	yes	8
17.13	even	4		289.4.b.c.288.8		8
17.15	even	8		17.4.c.a.4.1	✓	8
17.16	even	2	inner	289.4.a.f.1.1		8
51.8	odd	8		153.4.f.a.64.1		8
51.32	odd	8		153.4.f.a.55.4		8
68.15	odd	8		272.4.o.e.225.3		8
68.59	odd	8		272.4.o.e.81.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.c.a.4.1	✓	8	17.15	even	8
17.4.c.a.13.4	yes	8	17.8	even	8
153.4.f.a.55.4		8	51.32	odd	8
153.4.f.a.64.1		8	51.8	odd	8
272.4.o.e.81.3		8	68.59	odd	8
272.4.o.e.225.3		8	68.15	odd	8
289.4.a.f.1.1		8	17.16	even	2	inner
289.4.a.f.1.2		8	1.1	even	1	trivial
289.4.b.c.288.7		8	17.4	even	4
289.4.b.c.288.8		8	17.13	even	4

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q-3.93651 q^{2} +0.423991 q^{3} +7.49613 q^{4} +1.95080 q^{5} -1.66905 q^{6} +25.4345 q^{7} +1.98349 q^{8} -26.8202 q^{9} +O(q^{10})\)	\(q-3.93651 q^{2} +0.423991 q^{3} +7.49613 q^{4} +1.95080 q^{5} -1.66905 q^{6} +25.4345 q^{7} +1.98349 q^{8} -26.8202 q^{9} -7.67934 q^{10} +32.4303 q^{11} +3.17829 q^{12} +54.6855 q^{13} -100.123 q^{14} +0.827121 q^{15} -67.7771 q^{16} +105.578 q^{18} -46.1336 q^{19} +14.6234 q^{20} +10.7840 q^{21} -127.662 q^{22} +75.2978 q^{23} +0.840984 q^{24} -121.194 q^{25} -215.270 q^{26} -22.8193 q^{27} +190.660 q^{28} +157.040 q^{29} -3.25597 q^{30} -252.606 q^{31} +250.937 q^{32} +13.7502 q^{33} +49.6175 q^{35} -201.048 q^{36} +226.214 q^{37} +181.606 q^{38} +23.1862 q^{39} +3.86940 q^{40} -231.163 q^{41} -42.4513 q^{42} +119.642 q^{43} +243.102 q^{44} -52.3209 q^{45} -296.411 q^{46} +188.319 q^{47} -28.7369 q^{48} +303.913 q^{49} +477.083 q^{50} +409.930 q^{52} +468.212 q^{53} +89.8285 q^{54} +63.2650 q^{55} +50.4491 q^{56} -19.5603 q^{57} -618.188 q^{58} +751.217 q^{59} +6.20021 q^{60} +483.210 q^{61} +994.385 q^{62} -682.159 q^{63} -445.601 q^{64} +106.680 q^{65} -54.1277 q^{66} +533.879 q^{67} +31.9256 q^{69} -195.320 q^{70} -78.1521 q^{71} -53.1977 q^{72} +383.013 q^{73} -890.494 q^{74} -51.3854 q^{75} -345.824 q^{76} +824.848 q^{77} -91.2727 q^{78} -1278.85 q^{79} -132.219 q^{80} +714.471 q^{81} +909.975 q^{82} +591.376 q^{83} +80.8382 q^{84} -470.973 q^{86} +66.5834 q^{87} +64.3253 q^{88} +609.729 q^{89} +205.962 q^{90} +1390.90 q^{91} +564.442 q^{92} -107.103 q^{93} -741.321 q^{94} -89.9974 q^{95} +106.395 q^{96} +1592.06 q^{97} -1196.36 q^{98} -869.788 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 36 q^{4} + 96 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 36 * q^4 + 96 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 36 q^{4} + 96 q^{8} + 8 q^{9} + 88 q^{13} + 252 q^{15} + 420 q^{16} + 428 q^{18} - 52 q^{19} + 260 q^{21} - 140 q^{25} - 268 q^{26} + 120 q^{30} + 2336 q^{32} + 816 q^{33} + 1172 q^{35} - 264 q^{36} + 768 q^{38} - 136 q^{42} - 752 q^{43} + 368 q^{47} + 852 q^{49} + 468 q^{50} + 2564 q^{52} - 1156 q^{53} + 1996 q^{55} + 192 q^{59} - 3160 q^{60} + 3044 q^{64} + 1052 q^{66} + 764 q^{67} + 1812 q^{69} + 544 q^{70} - 1404 q^{72} + 896 q^{76} + 3084 q^{77} - 280 q^{81} + 496 q^{83} - 2952 q^{84} - 4244 q^{86} - 2860 q^{87} + 2156 q^{89} - 4012 q^{93} - 3392 q^{94} - 6728 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 + 36 * q^4 + 96 * q^8 + 8 * q^9 + 88 * q^13 + 252 * q^15 + 420 * q^16 + 428 * q^18 - 52 * q^19 + 260 * q^21 - 140 * q^25 - 268 * q^26 + 120 * q^30 + 2336 * q^32 + 816 * q^33 + 1172 * q^35 - 264 * q^36 + 768 * q^38 - 136 * q^42 - 752 * q^43 + 368 * q^47 + 852 * q^49 + 468 * q^50 + 2564 * q^52 - 1156 * q^53 + 1996 * q^55 + 192 * q^59 - 3160 * q^60 + 3044 * q^64 + 1052 * q^66 + 764 * q^67 + 1812 * q^69 + 544 * q^70 - 1404 * q^72 + 896 * q^76 + 3084 * q^77 - 280 * q^81 + 496 * q^83 - 2952 * q^84 - 4244 * q^86 - 2860 * q^87 + 2156 * q^89 - 4012 * q^93 - 3392 * q^94 - 6728 * q^98

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