LMFDB - Embedded newform 289.4.a.f.1.8

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			1.8
Root			$-5.88189$ 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)

$f(q)$	$=$	$q+5.46767 q^{2} +5.57972 q^{3} +21.8954 q^{4} -6.77499 q^{5} +30.5081 q^{6} -4.72009 q^{7} +75.9757 q^{8} +4.13329 q^{9} +O(q^{10})$	\(q+5.46767 q^{2} +5.57972 q^{3} +21.8954 q^{4} -6.77499 q^{5} +30.5081 q^{6} -4.72009 q^{7} +75.9757 q^{8} +4.13329 q^{9} -37.0434 q^{10} -9.47591 q^{11} +122.170 q^{12} +33.7223 q^{13} -25.8079 q^{14} -37.8026 q^{15} +240.247 q^{16} +22.5994 q^{18} +27.4317 q^{19} -148.341 q^{20} -26.3368 q^{21} -51.8112 q^{22} +82.8918 q^{23} +423.923 q^{24} -79.0995 q^{25} +184.382 q^{26} -127.590 q^{27} -103.349 q^{28} -208.027 q^{29} -206.692 q^{30} -223.608 q^{31} +705.786 q^{32} -52.8729 q^{33} +31.9786 q^{35} +90.5001 q^{36} +173.873 q^{37} +149.988 q^{38} +188.161 q^{39} -514.735 q^{40} +86.1730 q^{41} -144.001 q^{42} -258.362 q^{43} -207.479 q^{44} -28.0030 q^{45} +453.225 q^{46} -88.9429 q^{47} +1340.51 q^{48} -320.721 q^{49} -432.490 q^{50} +738.364 q^{52} -541.310 q^{53} -697.620 q^{54} +64.1992 q^{55} -358.613 q^{56} +153.061 q^{57} -1137.43 q^{58} -13.5759 q^{59} -827.704 q^{60} +158.640 q^{61} -1222.62 q^{62} -19.5095 q^{63} +1937.03 q^{64} -228.468 q^{65} -289.092 q^{66} +357.758 q^{67} +462.513 q^{69} +174.848 q^{70} +960.645 q^{71} +314.029 q^{72} +898.274 q^{73} +950.681 q^{74} -441.353 q^{75} +600.630 q^{76} +44.7272 q^{77} +1028.80 q^{78} -451.262 q^{79} -1627.67 q^{80} -823.515 q^{81} +471.166 q^{82} +559.916 q^{83} -576.656 q^{84} -1412.64 q^{86} -1160.74 q^{87} -719.939 q^{88} +602.266 q^{89} -153.111 q^{90} -159.172 q^{91} +1814.95 q^{92} -1247.67 q^{93} -486.311 q^{94} -185.850 q^{95} +3938.09 q^{96} +820.954 q^{97} -1753.60 q^{98} -39.1666 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.46767	1.93311	0.966557	−	0.256451i	$-0.0825534\pi$
$2$	5.46767	1.93311	0.966557	+	0.256451i	$0.0825534\pi$
$3$	5.57972	1.07382	0.536909	−	0.843640i	$-0.319592\pi$
$3$	5.57972	1.07382	0.536909	+	0.843640i	$0.319592\pi$
$4$	21.8954	2.73693
$5$	−6.77499	−0.605974	−0.302987	−	0.952995i	$-0.597984\pi$
$5$	−6.77499	−0.605974	−0.302987	+	0.952995i	$0.597984\pi$
$6$	30.5081	2.07581
$7$	−4.72009	−0.254861	−0.127431	−	0.991848i	$-0.540673\pi$
$7$	−4.72009	−0.254861	−0.127431	+	0.991848i	$0.540673\pi$
$8$	75.9757	3.35769
$9$	4.13329	0.153085
$10$	−37.0434	−1.17142
$11$	−9.47591	−0.259736	−0.129868	−	0.991531i	$-0.541455\pi$
$11$	−9.47591	−0.259736	−0.129868	+	0.991531i	$0.541455\pi$
$12$	122.170	2.93896
$13$	33.7223	0.719452	0.359726	−	0.933058i	$-0.382870\pi$
$13$	33.7223	0.719452	0.359726	+	0.933058i	$0.382870\pi$
$14$	−25.8079	−0.492675
$15$	−37.8026	−0.650705
$16$	240.247	3.75386
$17$	0	0
$17$	0	0
$18$	22.5994	0.295930
$19$	27.4317	0.331225	0.165612	−	0.986191i	$-0.447040\pi$
$19$	27.4317	0.331225	0.165612	+	0.986191i	$0.447040\pi$
$20$	−148.341	−1.65851
$21$	−26.3368	−0.273674
$22$	−51.8112	−0.502099
$23$	82.8918	0.751484	0.375742	−	0.926724i	$-0.377388\pi$
$23$	82.8918	0.751484	0.375742	+	0.926724i	$0.377388\pi$
$24$	423.923	3.60554
$25$	−79.0995	−0.632796
$26$	184.382	1.39078
$27$	−127.590	−0.909433
$28$	−103.349	−0.697537
$29$	−208.027	−1.33206	−0.666030	−	0.745925i	$-0.732008\pi$
$29$	−208.027	−1.33206	−0.666030	+	0.745925i	$0.732008\pi$
$30$	−206.692	−1.25789
$31$	−223.608	−1.29552	−0.647761	−	0.761844i	$-0.724294\pi$
$31$	−223.608	−1.29552	−0.647761	+	0.761844i	$0.724294\pi$
$32$	705.786	3.89895
$33$	−52.8729	−0.278909
$34$	0	0
$35$	31.9786	0.154439
$36$	90.5001	0.418982
$37$	173.873	0.772555	0.386278	−	0.922383i	$-0.373761\pi$
$37$	173.873	0.772555	0.386278	+	0.922383i	$0.373761\pi$
$38$	149.988	0.640296
$39$	188.161	0.772560
$40$	−514.735	−2.03467
$41$	86.1730	0.328243	0.164121	−	0.986440i	$-0.447521\pi$
$41$	86.1730	0.328243	0.164121	+	0.986440i	$0.447521\pi$
$42$	−144.001	−0.529044
$43$	−258.362	−0.916274	−0.458137	−	0.888882i	$-0.651483\pi$
$43$	−258.362	−0.916274	−0.458137	+	0.888882i	$0.651483\pi$
$44$	−207.479	−0.710879
$45$	−28.0030	−0.0927652
$46$	453.225	1.45271
$47$	−88.9429	−0.276035	−0.138018	−	0.990430i	$-0.544073\pi$
$47$	−88.9429	−0.276035	−0.138018	+	0.990430i	$0.544073\pi$
$48$	1340.51	4.03096
$49$	−320.721	−0.935046
$50$	−432.490	−1.22327
$51$	0	0
$52$	738.364	1.96909
$53$	−541.310	−1.40292	−0.701458	−	0.712710i	$-0.747467\pi$
$53$	−541.310	−1.40292	−0.701458	+	0.712710i	$0.747467\pi$
$54$	−697.620	−1.75804
$55$	64.1992	0.157393
$56$	−358.613	−0.855743
$57$	153.061	0.355675
$58$	−1137.43	−2.57502
$59$	−13.5759	−0.0299564	−0.0149782	−	0.999888i	$-0.504768\pi$
$59$	−13.5759	−0.0299564	−0.0149782	+	0.999888i	$0.504768\pi$
$60$	−827.704	−1.78093
$61$	158.640	0.332981	0.166490	−	0.986043i	$-0.446757\pi$
$61$	158.640	0.332981	0.166490	+	0.986043i	$0.446757\pi$
$62$	−1222.62	−2.50439
$63$	−19.5095	−0.0390153
$64$	1937.03	3.78326
$65$	−228.468	−0.435969
$66$	−289.092	−0.539163
$67$	357.758	0.652345	0.326172	−	0.945310i	$-0.394241\pi$
$67$	357.758	0.652345	0.326172	+	0.945310i	$0.394241\pi$
$68$	0	0
$69$	462.513	0.806957
$70$	174.848	0.298548
$71$	960.645	1.60574	0.802870	−	0.596154i	$-0.203305\pi$
$71$	960.645	1.60574	0.802870	+	0.596154i	$0.203305\pi$
$72$	314.029	0.514010
$73$	898.274	1.44021	0.720103	−	0.693868i	$-0.244095\pi$
$73$	898.274	1.44021	0.720103	+	0.693868i	$0.244095\pi$
$74$	950.681	1.49344
$75$	−441.353	−0.679508
$76$	600.630	0.906540
$77$	44.7272	0.0661965
$78$	1028.80	1.49345
$79$	−451.262	−0.642670	−0.321335	−	0.946966i	$-0.604132\pi$
$79$	−451.262	−0.642670	−0.321335	+	0.946966i	$0.604132\pi$
$80$	−1627.67	−2.27474
$81$	−823.515	−1.12965
$82$	471.166	0.634531
$83$	559.916	0.740467	0.370234	−	0.928939i	$-0.379278\pi$
$83$	559.916	0.740467	0.370234	+	0.928939i	$0.379278\pi$
$84$	−576.656	−0.749028
$85$	0	0
$86$	−1412.64	−1.77126
$87$	−1160.74	−1.43039
$88$	−719.939	−0.872111
$89$	602.266	0.717304	0.358652	−	0.933471i	$-0.383237\pi$
$89$	602.266	0.717304	0.358652	+	0.933471i	$0.383237\pi$
$90$	−153.111	−0.179326
$91$	−159.172	−0.183360
$92$	1814.95	2.05676
$93$	−1247.67	−1.39115
$94$	−486.311	−0.533608
$95$	−185.850	−0.200714
$96$	3938.09	4.18676
$97$	820.954	0.859332	0.429666	−	0.902988i	$-0.358631\pi$
$97$	820.954	0.859332	0.429666	+	0.902988i	$0.358631\pi$
$98$	−1753.60	−1.80755
$99$	−39.1666	−0.0397616
$100$	−1731.92	−1.73192
$101$	246.217	0.242570	0.121285	−	0.992618i	$-0.461299\pi$
$101$	246.217	0.242570	0.121285	+	0.992618i	$0.461299\pi$
$102$	0	0
$103$	−102.854	−0.0983931	−0.0491965	−	0.998789i	$-0.515666\pi$
$103$	−102.854	−0.0983931	−0.0491965	+	0.998789i	$0.515666\pi$
$104$	2562.07	2.41569
$105$	178.432	0.165839
$106$	−2959.70	−2.71200
$107$	2044.16	1.84688	0.923441	−	0.383741i	$-0.125365\pi$
$107$	2044.16	1.84688	0.923441	+	0.383741i	$0.125365\pi$
$108$	−2793.64	−2.48905
$109$	262.428	0.230606	0.115303	−	0.993330i	$-0.463216\pi$
$109$	262.428	0.230606	0.115303	+	0.993330i	$0.463216\pi$
$110$	351.020	0.304259
$111$	970.163	0.829584
$112$	−1133.99	−0.956712
$113$	299.445	0.249287	0.124644	−	0.992202i	$-0.460221\pi$
$113$	299.445	0.249287	0.124644	+	0.992202i	$0.460221\pi$
$114$	836.890	0.687561
$115$	−561.591	−0.455380
$116$	−4554.85	−3.64575
$117$	139.384	0.110137
$118$	−74.2284	−0.0579092
$119$	0	0
$120$	−2872.08	−2.18486
$121$	−1241.21	−0.932537
$122$	867.393	0.643689
$123$	480.821	0.352473
$124$	−4896.00	−3.54575
$125$	1382.77	0.989431
$126$	−106.671	−0.0754210
$127$	761.059	0.531757	0.265878	−	0.964007i	$-0.414338\pi$
$127$	761.059	0.531757	0.265878	+	0.964007i	$0.414338\pi$
$128$	4944.76	3.41452
$129$	−1441.59	−0.983911
$130$	−1249.19	−0.842777
$131$	−1448.36	−0.965984	−0.482992	−	0.875625i	$-0.660450\pi$
$131$	−1448.36	−0.965984	−0.482992	+	0.875625i	$0.660450\pi$
$132$	−1157.68	−0.763354
$133$	−129.480	−0.0844163
$134$	1956.10	1.26106
$135$	864.420	0.551092
$136$	0	0
$137$	1902.77	1.18660	0.593301	−	0.804981i	$-0.297824\pi$
$137$	1902.77	1.18660	0.593301	+	0.804981i	$0.297824\pi$
$138$	2528.87	1.55994
$139$	−618.453	−0.377385	−0.188692	−	0.982036i	$-0.560425\pi$
$139$	−618.453	−0.377385	−0.188692	+	0.982036i	$0.560425\pi$
$140$	700.185	0.422689
$141$	−496.277	−0.296412
$142$	5252.49	3.10408
$143$	−319.549	−0.186867
$144$	993.009	0.574658
$145$	1409.38	0.807193
$146$	4911.47	2.78408
$147$	−1789.53	−1.00407
$148$	3807.03	2.11443
$149$	1398.00	0.768647	0.384323	−	0.923199i	$-0.374435\pi$
$149$	1398.00	0.768647	0.384323	+	0.923199i	$0.374435\pi$
$150$	−2413.17	−1.31357
$151$	−2503.54	−1.34924	−0.674619	−	0.738166i	$-0.735692\pi$
$151$	−2503.54	−1.34924	−0.674619	+	0.738166i	$0.735692\pi$
$152$	2084.15	1.11215
$153$	0	0
$154$	244.553	0.127965
$155$	1514.94	0.785052
$156$	4119.86	2.11444
$157$	2715.22	1.38024	0.690121	−	0.723694i	$-0.257557\pi$
$157$	2715.22	1.38024	0.690121	+	0.723694i	$0.257557\pi$
$158$	−2467.35	−1.24235
$159$	−3020.36	−1.50648
$160$	−4781.69	−2.36266
$161$	−391.257	−0.191524
$162$	−4502.71	−2.18374
$163$	−3310.10	−1.59059	−0.795297	−	0.606220i	$-0.792685\pi$
$163$	−3310.10	−1.59059	−0.795297	+	0.606220i	$0.792685\pi$
$164$	1886.80	0.898378
$165$	358.214	0.169011
$166$	3061.44	1.43141
$167$	350.214	0.162278	0.0811389	−	0.996703i	$-0.474144\pi$
$167$	350.214	0.162278	0.0811389	+	0.996703i	$0.474144\pi$
$168$	−2000.96	−0.918912
$169$	−1059.81	−0.482389
$170$	0	0
$171$	113.383	0.0507055
$172$	−5656.94	−2.50778
$173$	−2090.48	−0.918705	−0.459352	−	0.888254i	$-0.651919\pi$
$173$	−2090.48	−0.918705	−0.459352	+	0.888254i	$0.651919\pi$
$174$	−6346.52	−2.76511
$175$	373.357	0.161275
$176$	−2276.56	−0.975011
$177$	−75.7496	−0.0321677
$178$	3292.99	1.38663
$179$	−739.046	−0.308597	−0.154299	−	0.988024i	$-0.549312\pi$
$179$	−739.046	−0.308597	−0.154299	+	0.988024i	$0.549312\pi$
$180$	−613.137	−0.253892
$181$	3262.13	1.33963	0.669813	−	0.742530i	$-0.266374\pi$
$181$	3262.13	1.33963	0.669813	+	0.742530i	$0.266374\pi$
$182$	−870.301	−0.354456
$183$	885.169	0.357560
$184$	6297.77	2.52325
$185$	−1177.99	−0.468148
$186$	−6821.85	−2.68926
$187$	0	0
$188$	−1947.44	−0.755489
$189$	602.236	0.231779
$190$	−1016.17	−0.388002
$191$	265.840	0.100710	0.0503548	−	0.998731i	$-0.483965\pi$
$191$	265.840	0.100710	0.0503548	+	0.998731i	$0.483965\pi$
$192$	10808.1	4.06253
$193$	35.5988	0.0132770	0.00663849	−	0.999978i	$-0.497887\pi$
$193$	35.5988	0.0132770	0.00663849	+	0.999978i	$0.497887\pi$
$194$	4488.71	1.66119
$195$	−1274.79	−0.468151
$196$	−7022.32	−2.55916
$197$	−631.705	−0.228463	−0.114231	−	0.993454i	$-0.536441\pi$
$197$	−631.705	−0.228463	−0.114231	+	0.993454i	$0.536441\pi$
$198$	−214.150	−0.0768636
$199$	−3813.43	−1.35843	−0.679214	−	0.733940i	$-0.737679\pi$
$199$	−3813.43	−1.35843	−0.679214	+	0.733940i	$0.737679\pi$
$200$	−6009.64	−2.12473
$201$	1996.19	0.700499
$202$	1346.24	0.468915
$203$	981.909	0.339490
$204$	0	0
$205$	−583.821	−0.198906
$206$	−562.371	−0.190205
$207$	342.616	0.115041
$208$	8101.67	2.70072
$209$	−259.941	−0.0860310
$210$	975.605	0.320586
$211$	−2357.54	−0.769194	−0.384597	−	0.923085i	$-0.625660\pi$
$211$	−2357.54	−0.769194	−0.384597	+	0.923085i	$0.625660\pi$
$212$	−11852.2	−3.83969
$213$	5360.13	1.72427
$214$	11176.8	3.57023
$215$	1750.40	0.555238
$216$	−9693.74	−3.05359
$217$	1055.45	0.330178
$218$	1434.87	0.445787
$219$	5012.12	1.54652
$220$	1405.67	0.430774
$221$	0	0
$222$	5304.53	1.60368
$223$	5273.08	1.58346	0.791730	−	0.610871i	$-0.209181\pi$
$223$	5273.08	1.58346	0.791730	+	0.610871i	$0.209181\pi$
$224$	−3331.37	−0.993691
$225$	−326.941	−0.0968714
$226$	1637.27	0.481901
$227$	−3496.28	−1.02227	−0.511137	−	0.859499i	$-0.670776\pi$
$227$	−3496.28	−1.02227	−0.511137	+	0.859499i	$0.670776\pi$
$228$	3351.35	0.973458
$229$	1982.99	0.572226	0.286113	−	0.958196i	$-0.407637\pi$
$229$	1982.99	0.572226	0.286113	+	0.958196i	$0.407637\pi$
$230$	−3070.60	−0.880301
$231$	249.565	0.0710830
$232$	−15805.0	−4.47264
$233$	14.5114	0.00408013	0.00204007	−	0.999998i	$-0.499351\pi$
$233$	14.5114	0.00408013	0.00204007	+	0.999998i	$0.499351\pi$
$234$	762.104	0.212907
$235$	602.587	0.167270
$236$	−297.250	−0.0819886
$237$	−2517.92	−0.690111
$238$	0	0
$239$	−5365.31	−1.45210	−0.726052	−	0.687640i	$-0.758647\pi$
$239$	−5365.31	−1.45210	−0.726052	+	0.687640i	$0.758647\pi$
$240$	−9081.95	−2.44265
$241$	−169.604	−0.0453327	−0.0226664	−	0.999743i	$-0.507216\pi$
$241$	−169.604	−0.0453327	−0.0226664	+	0.999743i	$0.507216\pi$
$242$	−6786.51	−1.80270
$243$	−1150.05	−0.303605
$244$	3473.50	0.911345
$245$	2172.88	0.566613
$246$	2628.97	0.681371
$247$	925.060	0.238300
$248$	−16988.8	−4.34996
$249$	3124.18	0.795127
$250$	7560.55	1.91268
$251$	4824.87	1.21332	0.606659	−	0.794962i	$-0.292509\pi$
$251$	4824.87	1.21332	0.606659	+	0.794962i	$0.292509\pi$
$252$	−427.169	−0.106782
$253$	−785.475	−0.195187
$254$	4161.22	1.02795
$255$	0	0
$256$	11540.1	2.81740
$257$	−5583.38	−1.35518	−0.677591	−	0.735439i	$-0.736976\pi$
$257$	−5583.38	−1.35518	−0.677591	+	0.735439i	$0.736976\pi$
$258$	−7882.12	−1.90201
$259$	−820.697	−0.196894
$260$	−5002.41	−1.19322
$261$	−859.837	−0.203918
$262$	−7919.16	−1.86736
$263$	4116.11	0.965059	0.482529	−	0.875880i	$-0.339718\pi$
$263$	4116.11	0.965059	0.482529	+	0.875880i	$0.339718\pi$
$264$	−4017.06	−0.936488
$265$	3667.37	0.850131
$266$	−707.956	−0.163186
$267$	3360.47	0.770254
$268$	7833.27	1.78542
$269$	6049.91	1.37126	0.685631	−	0.727949i	$-0.259526\pi$
$269$	6049.91	1.37126	0.685631	+	0.727949i	$0.259526\pi$
$270$	4726.37	1.06532
$271$	6555.61	1.46947	0.734733	−	0.678357i	$-0.237308\pi$
$271$	6555.61	1.46947	0.734733	+	0.678357i	$0.237308\pi$
$272$	0	0
$273$	−888.136	−0.196895
$274$	10403.7	2.29384
$275$	749.540	0.164360
$276$	10126.9	2.20859
$277$	−2439.98	−0.529257	−0.264628	−	0.964350i	$-0.585249\pi$
$277$	−2439.98	−0.529257	−0.264628	+	0.964350i	$0.585249\pi$
$278$	−3381.50	−0.729528
$279$	−924.236	−0.198325
$280$	2429.60	0.518558
$281$	519.764	0.110343	0.0551717	−	0.998477i	$-0.482429\pi$
$281$	519.764	0.110343	0.0551717	+	0.998477i	$0.482429\pi$
$282$	−2713.48	−0.572997
$283$	4653.11	0.977380	0.488690	−	0.872458i	$-0.337475\pi$
$283$	4653.11	0.977380	0.488690	+	0.872458i	$0.337475\pi$
$284$	21033.7	4.39480
$285$	−1036.99	−0.215530
$286$	−1747.19	−0.361236
$287$	−406.744	−0.0836563
$288$	2917.21	0.596870
$289$	0	0
$290$	7706.05	1.56040
$291$	4580.69	0.922766
$292$	19668.1	3.94174
$293$	−1856.79	−0.370220	−0.185110	−	0.982718i	$-0.559264\pi$
$293$	−1856.79	−0.370220	−0.185110	+	0.982718i	$0.559264\pi$
$294$	−9784.58	−1.94098
$295$	91.9764	0.0181528
$296$	13210.1	2.59400
$297$	1209.03	0.236212
$298$	7643.79	1.48588
$299$	2795.30	0.540657
$300$	−9663.62	−1.85977
$301$	1219.49	0.233522
$302$	−13688.5	−2.60823
$303$	1373.82	0.260476
$304$	6590.39	1.24337
$305$	−1074.79	−0.201777
$306$	0	0
$307$	759.641	0.141221	0.0706107	−	0.997504i	$-0.477505\pi$
$307$	759.641	0.141221	0.0706107	+	0.997504i	$0.477505\pi$
$308$	979.321	0.181175
$309$	−573.895	−0.105656
$310$	8283.21	1.51760
$311$	1022.42	0.186418	0.0932092	−	0.995647i	$-0.470287\pi$
$311$	1022.42	0.186418	0.0932092	+	0.995647i	$0.470287\pi$
$312$	14295.7	2.59401
$313$	3940.99	0.711686	0.355843	−	0.934546i	$-0.384194\pi$
$313$	3940.99	0.711686	0.355843	+	0.934546i	$0.384194\pi$
$314$	14845.9	2.66817
$315$	132.177	0.0236422
$316$	−9880.58	−1.75894
$317$	5383.64	0.953866	0.476933	−	0.878940i	$-0.341748\pi$
$317$	5383.64	0.953866	0.476933	+	0.878940i	$0.341748\pi$
$318$	−16514.3	−2.91219
$319$	1971.25	0.345984
$320$	−13123.4	−2.29256
$321$	11405.8	1.98321
$322$	−2139.27	−0.370238
$323$	0	0
$324$	−18031.2	−3.09177
$325$	−2667.41	−0.455266
$326$	−18098.5	−3.07480
$327$	1464.27	0.247628
$328$	6547.05	1.10214
$329$	419.819	0.0703506
$330$	1958.59	0.326718
$331$	−1697.70	−0.281915	−0.140958	−	0.990016i	$-0.545018\pi$
$331$	−1697.70	−0.281915	−0.140958	+	0.990016i	$0.545018\pi$
$332$	12259.6	2.02661
$333$	718.667	0.118266
$334$	1914.86	0.313702
$335$	−2423.81	−0.395304
$336$	−6327.33	−1.02733
$337$	−11296.6	−1.82601	−0.913006	−	0.407947i	$-0.866245\pi$
$337$	−11296.6	−1.82601	−0.913006	+	0.407947i	$0.866245\pi$
$338$	−5794.69	−0.932514
$339$	1670.82	0.267689
$340$	0	0
$341$	2118.89	0.336493
$342$	619.942	0.0980194
$343$	3132.82	0.493168
$344$	−19629.2	−3.07656
$345$	−3133.52	−0.488995
$346$	−11430.0	−1.77596
$347$	3597.85	0.556607	0.278303	−	0.960493i	$-0.410228\pi$
$347$	3597.85	0.556607	0.278303	+	0.960493i	$0.410228\pi$
$348$	−25414.8	−3.91488
$349$	−3741.37	−0.573842	−0.286921	−	0.957954i	$-0.592632\pi$
$349$	−3741.37	−0.573842	−0.286921	+	0.957954i	$0.592632\pi$
$350$	2041.39	0.311763
$351$	−4302.62	−0.654293
$352$	−6687.96	−1.01270
$353$	5726.82	0.863478	0.431739	−	0.901999i	$-0.357900\pi$
$353$	5726.82	0.863478	0.431739	+	0.901999i	$0.357900\pi$
$354$	−414.174	−0.0621839
$355$	−6508.36	−0.973036
$356$	13186.9	1.96321
$357$	0	0
$358$	−4040.86	−0.596554
$359$	6048.82	0.889260	0.444630	−	0.895714i	$-0.353335\pi$
$359$	6048.82	0.889260	0.444630	+	0.895714i	$0.353335\pi$
$360$	−2127.55	−0.311476
$361$	−6106.50	−0.890290
$362$	17836.3	2.58965
$363$	−6925.59	−1.00138
$364$	−3485.15	−0.501844
$365$	−6085.79	−0.872726
$366$	4839.81	0.691205
$367$	3439.49	0.489210	0.244605	−	0.969623i	$-0.421342\pi$
$367$	3439.49	0.489210	0.244605	+	0.969623i	$0.421342\pi$
$368$	19914.5	2.82097
$369$	356.177	0.0502489
$370$	−6440.85	−0.904984
$371$	2555.03	0.357549
$372$	−27318.3	−3.80749
$373$	−6816.14	−0.946184	−0.473092	−	0.881013i	$-0.656862\pi$
$373$	−6816.14	−0.946184	−0.473092	+	0.881013i	$0.656862\pi$
$374$	0	0
$375$	7715.48	1.06247
$376$	−6757.50	−0.926839
$377$	−7015.16	−0.958353
$378$	3292.83	0.448055
$379$	−5917.75	−0.802043	−0.401022	−	0.916069i	$-0.631345\pi$
$379$	−5917.75	−0.802043	−0.401022	+	0.916069i	$0.631345\pi$
$380$	−4069.26	−0.549339
$381$	4246.50	0.571010
$382$	1453.53	0.194683
$383$	−7584.88	−1.01193	−0.505965	−	0.862554i	$-0.668863\pi$
$383$	−7584.88	−1.01193	−0.505965	+	0.862554i	$0.668863\pi$
$384$	27590.4	3.66658
$385$	−303.026	−0.0401133
$386$	194.643	0.0256659
$387$	−1067.88	−0.140267
$388$	17975.1	2.35193
$389$	−1389.74	−0.181137	−0.0905687	−	0.995890i	$-0.528868\pi$
$389$	−1389.74	−0.181137	−0.0905687	+	0.995890i	$0.528868\pi$
$390$	−6970.12	−0.904989
$391$	0	0
$392$	−24367.0	−3.13959
$393$	−8081.45	−1.03729
$394$	−3453.96	−0.441644
$395$	3057.30	0.389441
$396$	−857.571	−0.108825
$397$	13678.7	1.72926	0.864628	−	0.502412i	$-0.167554\pi$
$397$	13678.7	1.72926	0.864628	+	0.502412i	$0.167554\pi$
$398$	−20850.6	−2.62600
$399$	−722.464	−0.0906478
$400$	−19003.4	−2.37543
$401$	−13292.7	−1.65537	−0.827685	−	0.561193i	$-0.810343\pi$
$401$	−13292.7	−1.65537	−0.827685	+	0.561193i	$0.810343\pi$
$402$	10914.5	1.35415
$403$	−7540.57	−0.932066
$404$	5391.04	0.663897
$405$	5579.30	0.684538
$406$	5368.76	0.656273
$407$	−1647.60	−0.200660
$408$	0	0
$409$	−6570.02	−0.794295	−0.397147	−	0.917755i	$-0.630000\pi$
$409$	−6570.02	−0.794295	−0.397147	+	0.917755i	$0.630000\pi$
$410$	−3192.14	−0.384509
$411$	10616.9	1.27419
$412$	−2252.03	−0.269295
$413$	64.0794	0.00763472
$414$	1873.31	0.222387
$415$	−3793.43	−0.448703
$416$	23800.7	2.80511
$417$	−3450.80	−0.405243
$418$	−1421.27	−0.166308
$419$	−13902.3	−1.62093	−0.810467	−	0.585785i	$-0.800786\pi$
$419$	−13902.3	−1.62093	−0.810467	+	0.585785i	$0.800786\pi$
$420$	3906.84	0.453891
$421$	−3041.18	−0.352062	−0.176031	−	0.984385i	$-0.556326\pi$
$421$	−3041.18	−0.352062	−0.176031	+	0.984385i	$0.556326\pi$
$422$	−12890.3	−1.48694
$423$	−367.626	−0.0422567
$424$	−41126.4	−4.71055
$425$	0	0
$426$	29307.4	3.33322
$427$	−748.797	−0.0848638
$428$	44757.8	5.05479
$429$	−1782.99	−0.200661
$430$	9570.60	1.07334
$431$	6254.26	0.698972	0.349486	−	0.936942i	$-0.386356\pi$
$431$	6254.26	0.698972	0.349486	+	0.936942i	$0.386356\pi$
$432$	−30653.1	−3.41388
$433$	10180.7	1.12992	0.564959	−	0.825119i	$-0.308892\pi$
$433$	10180.7	1.12992	0.564959	+	0.825119i	$0.308892\pi$
$434$	5770.86	0.638272
$435$	7863.97	0.866778
$436$	5745.97	0.631152
$437$	2273.87	0.248910
$438$	27404.6	2.98960
$439$	−9959.89	−1.08282	−0.541412	−	0.840757i	$-0.682110\pi$
$439$	−9959.89	−1.08282	−0.541412	+	0.840757i	$0.682110\pi$
$440$	4877.58	0.528476
$441$	−1325.63	−0.143141
$442$	0	0
$443$	6833.02	0.732836	0.366418	−	0.930450i	$-0.380584\pi$
$443$	6833.02	0.732836	0.366418	+	0.930450i	$0.380584\pi$
$444$	21242.1	2.27051
$445$	−4080.34	−0.434667
$446$	28831.5	3.06101
$447$	7800.43	0.825386
$448$	−9142.96	−0.964206
$449$	−6569.43	−0.690491	−0.345245	−	0.938512i	$-0.612204\pi$
$449$	−6569.43	−0.690491	−0.345245	+	0.938512i	$0.612204\pi$
$450$	−1787.61	−0.187263
$451$	−816.567	−0.0852564
$452$	6556.49	0.682282
$453$	−13969.0	−1.44884
$454$	−19116.5	−1.97617
$455$	1078.39	0.111111
$456$	11629.0	1.19425
$457$	−10031.6	−1.02682	−0.513410	−	0.858144i	$-0.671618\pi$
$457$	−10031.6	−1.02682	−0.513410	+	0.858144i	$0.671618\pi$
$458$	10842.4	1.10618
$459$	0	0
$460$	−12296.3	−1.24634
$461$	1359.04	0.137304	0.0686518	−	0.997641i	$-0.478130\pi$
$461$	1359.04	0.137304	0.0686518	+	0.997641i	$0.478130\pi$
$462$	1364.54	0.137412
$463$	−81.1156	−0.00814203	−0.00407102	−	0.999992i	$-0.501296\pi$
$463$	−81.1156	−0.00814203	−0.00407102	+	0.999992i	$0.501296\pi$
$464$	−49978.0	−5.00036
$465$	8452.95	0.843003
$466$	79.3434	0.00788737
$467$	−10790.7	−1.06924	−0.534618	−	0.845094i	$-0.679545\pi$
$467$	−10790.7	−1.06924	−0.534618	+	0.845094i	$0.679545\pi$
$468$	3051.87	0.301437
$469$	−1688.65	−0.166257
$470$	3294.75	0.323352
$471$	15150.2	1.48213
$472$	−1031.44	−0.100584
$473$	2448.21	0.237989
$474$	−13767.1	−1.33406
$475$	−2169.84	−0.209598
$476$	0	0
$477$	−2237.39	−0.214765
$478$	−29335.7	−2.80708
$479$	−2791.67	−0.266293	−0.133147	−	0.991096i	$-0.542508\pi$
$479$	−2791.67	−0.266293	−0.133147	+	0.991096i	$0.542508\pi$
$480$	−26680.5	−2.53707
$481$	5863.39	0.555816
$482$	−927.342	−0.0876333
$483$	−2183.11	−0.205662
$484$	−27176.8	−2.55229
$485$	−5561.95	−0.520733
$486$	−6288.12	−0.586903
$487$	6470.16	0.602035	0.301018	−	0.953619i	$-0.402674\pi$
$487$	6470.16	0.602035	0.301018	+	0.953619i	$0.402674\pi$
$488$	12052.8	1.11804
$489$	−18469.4	−1.70801
$490$	11880.6	1.09533
$491$	221.719	0.0203789	0.0101895	−	0.999948i	$-0.496757\pi$
$491$	221.719	0.0203789	0.0101895	+	0.999948i	$0.496757\pi$
$492$	10527.8	0.964694
$493$	0	0
$494$	5057.93	0.460662
$495$	265.354	0.0240945
$496$	−53721.1	−4.86321
$497$	−4534.33	−0.409241
$498$	17082.0	1.53707
$499$	−7248.08	−0.650238	−0.325119	−	0.945673i	$-0.605404\pi$
$499$	−7248.08	−0.650238	−0.325119	+	0.945673i	$0.605404\pi$
$500$	30276.4	2.70800
$501$	1954.10	0.174257
$502$	26380.8	2.34548
$503$	7346.69	0.651238	0.325619	−	0.945501i	$-0.394427\pi$
$503$	7346.69	0.651238	0.325619	+	0.945501i	$0.394427\pi$
$504$	−1482.25	−0.131001
$505$	−1668.12	−0.146991
$506$	−4294.72	−0.377320
$507$	−5913.44	−0.517998
$508$	16663.7	1.45538
$509$	−1656.30	−0.144232	−0.0721162	−	0.997396i	$-0.522975\pi$
$509$	−1656.30	−0.144232	−0.0721162	+	0.997396i	$0.522975\pi$
$510$	0	0
$511$	−4239.93	−0.367052
$512$	23539.3	2.03184
$513$	−3500.01	−0.301227
$514$	−30528.1	−2.61972
$515$	696.833	0.0596236
$516$	−31564.2	−2.69290
$517$	842.815	0.0716962
$518$	−4487.30	−0.380619
$519$	−11664.3	−0.986522
$520$	−17358.0	−1.46385
$521$	−17209.6	−1.44715	−0.723575	−	0.690246i	$-0.757502\pi$
$521$	−17209.6	−1.44715	−0.723575	+	0.690246i	$0.757502\pi$
$522$	−4701.31	−0.394197
$523$	−22280.9	−1.86286	−0.931429	−	0.363922i	$-0.881437\pi$
$523$	−22280.9	−1.86286	−0.931429	+	0.363922i	$0.881437\pi$
$524$	−31712.5	−2.64383
$525$	2083.23	0.173180
$526$	22505.6	1.86557
$527$	0	0
$528$	−12702.6	−1.04698
$529$	−5295.94	−0.435271
$530$	20052.0	1.64340
$531$	−56.1130	−0.00458587
$532$	−2835.03	−0.231042
$533$	2905.95	0.236155
$534$	18374.0	1.48899
$535$	−13849.2	−1.11916
$536$	27180.9	2.19037
$537$	−4123.67	−0.331377
$538$	33078.9	2.65081
$539$	3039.12	0.242865
$540$	18926.9	1.50830
$541$	−8492.68	−0.674914	−0.337457	−	0.941341i	$-0.609567\pi$
$541$	−8492.68	−0.674914	−0.337457	+	0.941341i	$0.609567\pi$
$542$	35843.9	2.84064
$543$	18201.8	1.43851
$544$	0	0
$545$	−1777.94	−0.139741
$546$	−4856.04	−0.380621
$547$	12517.8	0.978472	0.489236	−	0.872151i	$-0.337276\pi$
$547$	12517.8	0.978472	0.489236	+	0.872151i	$0.337276\pi$
$548$	41662.0	3.24765
$549$	655.706	0.0509742
$550$	4098.24	0.317726
$551$	−5706.56	−0.441211
$552$	35139.8	2.70951
$553$	2130.00	0.163792
$554$	−13341.0	−1.02311
$555$	−6572.84	−0.502706
$556$	−13541.3	−1.03288
$557$	−21449.2	−1.63165	−0.815827	−	0.578295i	$-0.803718\pi$
$557$	−21449.2	−1.63165	−0.815827	+	0.578295i	$0.803718\pi$
$558$	−5053.42	−0.383384
$559$	−8712.53	−0.659215
$560$	7682.76	0.579742
$561$	0	0
$562$	2841.90	0.213306
$563$	9661.93	0.723271	0.361636	−	0.932319i	$-0.382218\pi$
$563$	9661.93	0.723271	0.361636	+	0.932319i	$0.382218\pi$
$564$	−10866.2	−0.811258
$565$	−2028.74	−0.151061
$566$	25441.7	1.88939
$567$	3887.07	0.287904
$568$	72985.7	5.39157
$569$	22571.3	1.66298	0.831492	−	0.555537i	$-0.187487\pi$
$569$	22571.3	1.66298	0.831492	+	0.555537i	$0.187487\pi$
$570$	−5669.92	−0.416644
$571$	17457.8	1.27948	0.639742	−	0.768590i	$-0.279041\pi$
$571$	17457.8	1.27948	0.639742	+	0.768590i	$0.279041\pi$
$572$	−6996.67	−0.511443
$573$	1483.31	0.108144
$574$	−2223.94	−0.161717
$575$	−6556.70	−0.475536
$576$	8006.29	0.579159
$577$	−22153.0	−1.59834	−0.799168	−	0.601108i	$-0.794726\pi$
$577$	−22153.0	−1.59834	−0.799168	+	0.601108i	$0.794726\pi$
$578$	0	0
$579$	198.631	0.0142571
$580$	30859.1	2.20923
$581$	−2642.86	−0.188716
$582$	25045.7	1.78381
$583$	5129.40	0.364388
$584$	68247.0	4.83576
$585$	−944.323	−0.0667401
$586$	−10152.3	−0.715678
$587$	16152.5	1.13575	0.567873	−	0.823116i	$-0.307766\pi$
$587$	16152.5	1.13575	0.567873	+	0.823116i	$0.307766\pi$
$588$	−39182.6	−2.74807
$589$	−6133.96	−0.429109
$590$	502.897	0.0350914
$591$	−3524.74	−0.245327
$592$	41772.5	2.90006
$593$	8336.26	0.577284	0.288642	−	0.957437i	$-0.406796\pi$
$593$	8336.26	0.577284	0.288642	+	0.957437i	$0.406796\pi$
$594$	6610.58	0.456625
$595$	0	0
$596$	30609.8	2.10373
$597$	−21277.9	−1.45870
$598$	15283.8	1.04515
$599$	9798.73	0.668390	0.334195	−	0.942504i	$-0.391536\pi$
$599$	9798.73	0.668390	0.334195	+	0.942504i	$0.391536\pi$
$600$	−33532.1	−2.28157
$601$	−7719.31	−0.523922	−0.261961	−	0.965078i	$-0.584369\pi$
$601$	−7719.31	−0.523922	−0.261961	+	0.965078i	$0.584369\pi$
$602$	6667.77	0.451426
$603$	1478.72	0.0998640
$604$	−54816.1	−3.69277
$605$	8409.17	0.565093
$606$	7511.62	0.503529
$607$	24275.0	1.62321	0.811607	−	0.584204i	$-0.198593\pi$
$607$	24275.0	1.62321	0.811607	+	0.584204i	$0.198593\pi$
$608$	19360.9	1.29143
$609$	5478.78	0.364551
$610$	−5876.58	−0.390059
$611$	−2999.36	−0.198594
$612$	0	0
$613$	−12662.6	−0.834318	−0.417159	−	0.908833i	$-0.636974\pi$
$613$	−12662.6	−0.834318	−0.417159	+	0.908833i	$0.636974\pi$
$614$	4153.47	0.272997
$615$	−3257.56	−0.213589
$616$	3398.18	0.222267
$617$	−18672.6	−1.21836	−0.609182	−	0.793030i	$-0.708502\pi$
$617$	−18672.6	−1.21836	−0.609182	+	0.793030i	$0.708502\pi$
$618$	−3137.87	−0.204246
$619$	−19355.5	−1.25681	−0.628404	−	0.777887i	$-0.716291\pi$
$619$	−19355.5	−1.25681	−0.628404	+	0.777887i	$0.716291\pi$
$620$	33170.3	2.14863
$621$	−10576.2	−0.683425
$622$	5590.26	0.360368
$623$	−2842.75	−0.182813
$624$	45205.1	2.90008
$625$	519.171	0.0332269
$626$	21548.0	1.37577
$627$	−1450.40	−0.0923816
$628$	59450.9	3.77763
$629$	0	0
$630$	722.698	0.0457032
$631$	6088.34	0.384109	0.192055	−	0.981384i	$-0.438485\pi$
$631$	6088.34	0.384109	0.192055	+	0.981384i	$0.438485\pi$
$632$	−34285.0	−2.15788
$633$	−13154.4	−0.825975
$634$	29436.0	1.84393
$635$	−5156.17	−0.322230
$636$	−66132.1	−4.12312
$637$	−10815.4	−0.672720
$638$	10778.1	0.668826
$639$	3970.62	0.245814
$640$	−33500.7	−2.06911
$641$	−9139.88	−0.563188	−0.281594	−	0.959534i	$-0.590863\pi$
$641$	−9139.88	−0.563188	−0.281594	+	0.959534i	$0.590863\pi$
$642$	62363.4	3.83378
$643$	−24047.0	−1.47484	−0.737420	−	0.675435i	$-0.763956\pi$
$643$	−24047.0	−1.47484	−0.737420	+	0.675435i	$0.763956\pi$
$644$	−8566.75	−0.524188
$645$	9766.73	0.596224
$646$	0	0
$647$	22785.1	1.38451	0.692253	−	0.721655i	$-0.256618\pi$
$647$	22785.1	1.38451	0.692253	+	0.721655i	$0.256618\pi$
$648$	−62567.1	−3.79301
$649$	128.644	0.00778075
$650$	−14584.5	−0.880082
$651$	5889.12	0.354551
$652$	−72476.0	−4.35334
$653$	7404.51	0.443738	0.221869	−	0.975076i	$-0.428784\pi$
$653$	7404.51	0.443738	0.221869	+	0.975076i	$0.428784\pi$
$654$	8006.17	0.478694
$655$	9812.63	0.585361
$656$	20702.8	1.23218
$657$	3712.82	0.220473
$658$	2295.43	0.135996
$659$	18416.5	1.08863	0.544314	−	0.838882i	$-0.316790\pi$
$659$	18416.5	1.08863	0.544314	+	0.838882i	$0.316790\pi$
$660$	7843.24	0.462573
$661$	−23526.7	−1.38439	−0.692197	−	0.721709i	$-0.743357\pi$
$661$	−23526.7	−1.38439	−0.692197	+	0.721709i	$0.743357\pi$
$662$	−9282.45	−0.544974
$663$	0	0
$664$	42540.0	2.48626
$665$	877.228	0.0511541
$666$	3929.43	0.228622
$667$	−17243.8	−1.00102
$668$	7668.10	0.444143
$669$	29422.3	1.70035
$670$	−13252.6	−0.764167
$671$	−1503.26	−0.0864870
$672$	−18588.1	−1.06704
$673$	−20270.7	−1.16104	−0.580520	−	0.814246i	$-0.697151\pi$
$673$	−20270.7	−1.16104	−0.580520	+	0.814246i	$0.697151\pi$
$674$	−61766.2	−3.52989
$675$	10092.3	0.575485
$676$	−23205.0	−1.32027
$677$	33735.8	1.91517	0.957587	−	0.288146i	$-0.0930387\pi$
$677$	33735.8	1.91517	0.957587	+	0.288146i	$0.0930387\pi$
$678$	9135.51	0.517474
$679$	−3874.98	−0.219010
$680$	0	0
$681$	−19508.3	−1.09774
$682$	11585.4	0.650480
$683$	660.167	0.0369848	0.0184924	−	0.999829i	$-0.494113\pi$
$683$	660.167	0.0369848	0.0184924	+	0.999829i	$0.494113\pi$
$684$	2482.58	0.138777
$685$	−12891.2	−0.719049
$686$	17129.3	0.953350
$687$	11064.5	0.614467
$688$	−62070.6	−3.43956
$689$	−18254.2	−1.00933
$690$	−17133.1	−0.945283
$691$	21548.5	1.18631	0.593157	−	0.805087i	$-0.297882\pi$
$691$	21548.5	1.18631	0.593157	+	0.805087i	$0.297882\pi$
$692$	−45771.9	−2.51443
$693$	184.870	0.0101337
$694$	19671.8	1.07598
$695$	4190.01	0.228685
$696$	−88187.7	−4.80280
$697$	0	0
$698$	−20456.6	−1.10930
$699$	80.9694	0.00438132
$700$	8174.82	0.441399
$701$	13156.7	0.708878	0.354439	−	0.935079i	$-0.384672\pi$
$701$	13156.7	0.708878	0.354439	+	0.935079i	$0.384672\pi$
$702$	−23525.3	−1.26482
$703$	4769.64	0.255890
$704$	−18355.1	−0.982648
$705$	3362.27	0.179618
$706$	31312.4	1.66920
$707$	−1162.17	−0.0618216
$708$	−1658.57	−0.0880408
$709$	−32679.3	−1.73102	−0.865512	−	0.500888i	$-0.833007\pi$
$709$	−32679.3	−1.73102	−0.865512	+	0.500888i	$0.833007\pi$
$710$	−35585.6	−1.88099
$711$	−1865.19	−0.0983829
$712$	45757.6	2.40848
$713$	−18535.3	−0.973565
$714$	0	0
$715$	2164.94	0.113237
$716$	−16181.7	−0.844609
$717$	−29936.9	−1.55930
$718$	33073.0	1.71904
$719$	−13465.6	−0.698443	−0.349222	−	0.937040i	$-0.613554\pi$
$719$	−13465.6	−0.698443	−0.349222	+	0.937040i	$0.613554\pi$
$720$	−6727.63	−0.348228
$721$	485.479	0.0250766
$722$	−33388.3	−1.72103
$723$	−946.345	−0.0486791
$724$	71425.8	3.66646
$725$	16454.9	0.842922
$726$	−37866.9	−1.93577
$727$	32562.8	1.66119	0.830596	−	0.556875i	$-0.188000\pi$
$727$	32562.8	1.66119	0.830596	+	0.556875i	$0.188000\pi$
$728$	−12093.2	−0.615666
$729$	15817.9	0.803633
$730$	−33275.1	−1.68708
$731$	0	0
$732$	19381.2	0.978618
$733$	36291.9	1.82875	0.914375	−	0.404869i	$-0.132683\pi$
$733$	36291.9	1.82875	0.914375	+	0.404869i	$0.132683\pi$
$734$	18806.0	0.945699
$735$	12124.1	0.608439
$736$	58503.9	2.93000
$737$	−3390.08	−0.169437
$738$	1947.46	0.0971369
$739$	−13314.8	−0.662776	−0.331388	−	0.943495i	$-0.607517\pi$
$739$	−13314.8	−0.662776	−0.331388	+	0.943495i	$0.607517\pi$
$740$	−25792.6	−1.28129
$741$	5161.58	0.255891
$742$	13970.1	0.691183
$743$	−4223.24	−0.208527	−0.104263	−	0.994550i	$-0.533249\pi$
$743$	−4223.24	−0.208527	−0.104263	+	0.994550i	$0.533249\pi$
$744$	−94792.7	−4.67106
$745$	−9471.41	−0.465779
$746$	−37268.4	−1.82908
$747$	2314.29	0.113354
$748$	0	0
$749$	−9648.62	−0.470698
$750$	42185.7	2.05387
$751$	36696.9	1.78307	0.891537	−	0.452949i	$-0.149628\pi$
$751$	36696.9	1.78307	0.891537	+	0.452949i	$0.149628\pi$
$752$	−21368.3	−1.03620
$753$	26921.4	1.30288
$754$	−38356.6	−1.85260
$755$	16961.4	0.817603
$756$	13186.2	0.634363
$757$	8664.38	0.416000	0.208000	−	0.978129i	$-0.433305\pi$
$757$	8664.38	0.416000	0.208000	+	0.978129i	$0.433305\pi$
$758$	−32356.3	−1.55044
$759$	−4382.73	−0.209596
$760$	−14120.1	−0.673933
$761$	30593.6	1.45731	0.728657	−	0.684879i	$-0.240145\pi$
$761$	30593.6	1.45731	0.728657	+	0.684879i	$0.240145\pi$
$762$	23218.5	1.10383
$763$	−1238.68	−0.0587724
$764$	5820.69	0.275635
$765$	0	0
$766$	−41471.6	−1.95618
$767$	−457.809	−0.0215522
$768$	64390.4	3.02538
$769$	−24560.3	−1.15171	−0.575857	−	0.817550i	$-0.695332\pi$
$769$	−24560.3	−1.15171	−0.575857	+	0.817550i	$0.695332\pi$
$770$	−1656.85	−0.0775437
$771$	−31153.7	−1.45522
$772$	779.452	0.0363382
$773$	−4421.49	−0.205731	−0.102865	−	0.994695i	$-0.532801\pi$
$773$	−4421.49	−0.205731	−0.102865	+	0.994695i	$0.532801\pi$
$774$	−5838.83	−0.271153
$775$	17687.3	0.819801
$776$	62372.6	2.88537
$777$	−4579.26	−0.211429
$778$	−7598.63	−0.350159
$779$	2363.87	0.108722
$780$	−27912.0	−1.28130
$781$	−9102.98	−0.417068
$782$	0	0
$783$	26542.2	1.21142
$784$	−77052.2	−3.51003
$785$	−18395.6	−0.836391
$786$	−44186.7	−2.00520
$787$	−25600.9	−1.15956	−0.579779	−	0.814774i	$-0.696861\pi$
$787$	−25600.9	−1.15956	−0.579779	+	0.814774i	$0.696861\pi$
$788$	−13831.5	−0.625286
$789$	22966.8	1.03630
$790$	16716.3	0.752834
$791$	−1413.41	−0.0635336
$792$	−2975.71	−0.133507
$793$	5349.71	0.239563
$794$	74790.7	3.34285
$795$	20462.9	0.912885
$796$	−83496.8	−3.71792
$797$	29252.2	1.30008	0.650042	−	0.759899i	$-0.274751\pi$
$797$	29252.2	1.30008	0.650042	+	0.759899i	$0.274751\pi$
$798$	−3950.20	−0.175232
$799$	0	0
$800$	−55827.3	−2.46724
$801$	2489.34	0.109808
$802$	−72679.9	−3.20002
$803$	−8511.96	−0.374073
$804$	43707.5	1.91722
$805$	2650.76	0.116059
$806$	−41229.4	−1.80179
$807$	33756.8	1.47249
$808$	18706.5	0.814473
$809$	−29879.3	−1.29852	−0.649259	−	0.760568i	$-0.724921\pi$
$809$	−29879.3	−1.29852	−0.649259	+	0.760568i	$0.724921\pi$
$810$	30505.8	1.32329
$811$	−8123.23	−0.351720	−0.175860	−	0.984415i	$-0.556271\pi$
$811$	−8123.23	−0.351720	−0.175860	+	0.984415i	$0.556271\pi$
$812$	21499.3	0.929161
$813$	36578.5	1.57794
$814$	−9008.56	−0.387899
$815$	22425.9	0.963858
$816$	0	0
$817$	−7087.31	−0.303493
$818$	−35922.7	−1.53546
$819$	−657.904	−0.0280696
$820$	−12783.0	−0.544393
$821$	−27563.3	−1.17170	−0.585851	−	0.810419i	$-0.699240\pi$
$821$	−27563.3	−1.17170	−0.585851	+	0.810419i	$0.699240\pi$
$822$	58049.8	2.46316
$823$	−19682.8	−0.833655	−0.416828	−	0.908986i	$-0.636858\pi$
$823$	−19682.8	−0.833655	−0.416828	+	0.908986i	$0.636858\pi$
$824$	−7814.39	−0.330373
$825$	4182.22	0.176492
$826$	350.365	0.0147588
$827$	30777.1	1.29411	0.647053	−	0.762445i	$-0.276001\pi$
$827$	30777.1	1.29411	0.647053	+	0.762445i	$0.276001\pi$
$828$	7501.72	0.314858
$829$	−29861.7	−1.25108	−0.625538	−	0.780194i	$-0.715120\pi$
$829$	−29861.7	−1.25108	−0.625538	+	0.780194i	$0.715120\pi$
$830$	−20741.2	−0.867395
$831$	−13614.4	−0.568326
$832$	65321.0	2.72187
$833$	0	0
$834$	−18867.8	−0.783380
$835$	−2372.70	−0.0983361
$836$	−5691.52	−0.235461
$837$	28530.1	1.17819
$838$	−76013.2	−3.13345
$839$	−28785.5	−1.18449	−0.592243	−	0.805759i	$-0.701758\pi$
$839$	−28785.5	−1.18449	−0.592243	+	0.805759i	$0.701758\pi$
$840$	13556.5	0.556836
$841$	18886.4	0.774383
$842$	−16628.2	−0.680576
$843$	2900.14	0.118489
$844$	−51619.5	−2.10523
$845$	7180.20	0.292315
$846$	−2010.06	−0.0816871
$847$	5858.61	0.237667
$848$	−130048.	−5.26635
$849$	25963.0	1.04953
$850$	0	0
$851$	14412.7	0.580563
$852$	117362.	4.71921
$853$	2160.76	0.0867328	0.0433664	−	0.999059i	$-0.486192\pi$
$853$	2160.76	0.0867328	0.0433664	+	0.999059i	$0.486192\pi$
$854$	−4094.18	−0.164051
$855$	−768.170	−0.0307262
$856$	155306.	6.20125
$857$	25369.2	1.01120	0.505599	−	0.862769i	$-0.331271\pi$
$857$	25369.2	1.01120	0.505599	+	0.862769i	$0.331271\pi$
$858$	−9748.83	−0.387902
$859$	4878.89	0.193790	0.0968951	−	0.995295i	$-0.469109\pi$
$859$	4878.89	0.193790	0.0968951	+	0.995295i	$0.469109\pi$
$860$	38325.7	1.51965
$861$	−2269.52	−0.0898316
$862$	34196.2	1.35119
$863$	39426.2	1.55514	0.777569	−	0.628797i	$-0.216452\pi$
$863$	39426.2	1.55514	0.777569	+	0.628797i	$0.216452\pi$
$864$	−90051.1	−3.54583
$865$	14163.0	0.556711
$866$	55664.9	2.18426
$867$	0	0
$868$	23109.6	0.903674
$869$	4276.12	0.166924
$870$	42997.6	1.67558
$871$	12064.4	0.469330
$872$	19938.1	0.774301
$873$	3393.24	0.131551
$874$	12432.8	0.481172
$875$	−6526.81	−0.252167
$876$	109743.	4.23271
$877$	−2519.76	−0.0970198	−0.0485099	−	0.998823i	$-0.515447\pi$
$877$	−2519.76	−0.0970198	−0.0485099	+	0.998823i	$0.515447\pi$
$878$	−54457.4	−2.09322
$879$	−10360.3	−0.397549
$880$	15423.7	0.590831
$881$	−3937.23	−0.150566	−0.0752830	−	0.997162i	$-0.523986\pi$
$881$	−3937.23	−0.150566	−0.0752830	+	0.997162i	$0.523986\pi$
$882$	−7248.11	−0.276708
$883$	−8794.76	−0.335184	−0.167592	−	0.985856i	$-0.553599\pi$
$883$	−8794.76	−0.335184	−0.167592	+	0.985856i	$0.553599\pi$
$884$	0	0
$885$	513.203	0.0194928
$886$	37360.7	1.41666
$887$	−545.051	−0.0206325	−0.0103162	−	0.999947i	$-0.503284\pi$
$887$	−545.051	−0.0206325	−0.0103162	+	0.999947i	$0.503284\pi$
$888$	73708.8	2.78548
$889$	−3592.27	−0.135524
$890$	−22310.0	−0.840261
$891$	7803.55	0.293410
$892$	115456.	4.33382
$893$	−2439.86	−0.0914298
$894$	42650.2	1.59557
$895$	5007.03	0.187002
$896$	−23339.7	−0.870229
$897$	15597.0	0.580567
$898$	−35919.5	−1.33480
$899$	46516.6	1.72571
$900$	−7158.51	−0.265130
$901$	0	0
$902$	−4464.72	−0.164810
$903$	6804.42	0.250761
$904$	22750.6	0.837028
$905$	−22100.9	−0.811777
$906$	−76378.1	−2.80077
$907$	2644.96	0.0968294	0.0484147	−	0.998827i	$-0.484583\pi$
$907$	2644.96	0.0968294	0.0484147	+	0.998827i	$0.484583\pi$
$908$	−76552.6	−2.79789
$909$	1017.69	0.0371337
$910$	5896.28	0.214791
$911$	814.772	0.0296318	0.0148159	−	0.999890i	$-0.495284\pi$
$911$	814.772	0.0296318	0.0148159	+	0.999890i	$0.495284\pi$
$912$	36772.6	1.33515
$913$	−5305.71	−0.192326
$914$	−54849.3	−1.98496
$915$	−5997.01	−0.216672
$916$	43418.5	1.56614
$917$	6836.40	0.246192
$918$	0	0
$919$	−44667.9	−1.60333	−0.801664	−	0.597774i	$-0.796052\pi$
$919$	−44667.9	−1.60333	−0.801664	+	0.597774i	$0.796052\pi$
$920$	−42667.3	−1.52902
$921$	4238.58	0.151646
$922$	7430.81	0.265424
$923$	32395.1	1.15525
$924$	5464.34	0.194549
$925$	−13753.3	−0.488870
$926$	−443.514	−0.0157395
$927$	−425.124	−0.0150625
$928$	−146823.	−5.19364
$929$	6971.41	0.246205	0.123102	−	0.992394i	$-0.460716\pi$
$929$	6971.41	0.246205	0.123102	+	0.992394i	$0.460716\pi$
$930$	46218.0	1.62962
$931$	−8797.93	−0.309711
$932$	317.733	0.0111670
$933$	5704.82	0.200179
$934$	−59000.0	−2.06696
$935$	0	0
$936$	10589.8	0.369805
$937$	−46241.3	−1.61221	−0.806103	−	0.591776i	$-0.798427\pi$
$937$	−46241.3	−1.61221	−0.806103	+	0.591776i	$0.798427\pi$
$938$	−9232.99	−0.321394
$939$	21989.6	0.764221
$940$	13193.9	0.457806
$941$	−30844.7	−1.06855	−0.534277	−	0.845310i	$-0.679416\pi$
$941$	−30844.7	−1.06855	−0.534277	+	0.845310i	$0.679416\pi$
$942$	82836.2	2.86512
$943$	7143.03	0.246669
$944$	−3261.56	−0.112452
$945$	−4080.14	−0.140452
$946$	13386.0	0.460060
$947$	25031.3	0.858930	0.429465	−	0.903083i	$-0.358702\pi$
$947$	25031.3	0.858930	0.429465	+	0.903083i	$0.358702\pi$
$948$	−55130.9	−1.88879
$949$	30291.8	1.03616
$950$	−11864.0	−0.405177
$951$	30039.2	1.02428
$952$	0	0
$953$	−8104.79	−0.275488	−0.137744	−	0.990468i	$-0.543985\pi$
$953$	−8104.79	−0.275488	−0.137744	+	0.990468i	$0.543985\pi$
$954$	−12233.3	−0.415165
$955$	−1801.07	−0.0610273
$956$	−117476.	−3.97431
$957$	10999.0	0.371523
$958$	−15263.9	−0.514775
$959$	−8981.24	−0.302419
$960$	−73224.7	−2.46179
$961$	20209.5	0.678377
$962$	32059.1	1.07446
$963$	8449.09	0.282729
$964$	−3713.56	−0.124072
$965$	−241.182	−0.00804550
$966$	−11936.5	−0.397568
$967$	−12592.3	−0.418759	−0.209379	−	0.977834i	$-0.567144\pi$
$967$	−12592.3	−0.418759	−0.209379	+	0.977834i	$0.567144\pi$
$968$	−94301.6	−3.13117
$969$	0	0
$970$	−30410.9	−1.00664
$971$	43998.8	1.45416	0.727080	−	0.686553i	$-0.240877\pi$
$971$	43998.8	1.45416	0.727080	+	0.686553i	$0.240877\pi$
$972$	−25181.0	−0.830946
$973$	2919.16	0.0961807
$974$	35376.7	1.16380
$975$	−14883.4	−0.488873
$976$	38112.9	1.24996
$977$	8709.69	0.285207	0.142604	−	0.989780i	$-0.454453\pi$
$977$	8709.69	0.285207	0.142604	+	0.989780i	$0.454453\pi$
$978$	−100985.	−3.30177
$979$	−5707.01	−0.186309
$980$	47576.2	1.55078
$981$	1084.69	0.0353022
$982$	1212.29	0.0393948
$983$	34612.9	1.12307	0.561536	−	0.827452i	$-0.310211\pi$
$983$	34612.9	1.12307	0.561536	+	0.827452i	$0.310211\pi$
$984$	36530.7	1.18349
$985$	4279.80	0.138442
$986$	0	0
$987$	2342.47	0.0755437
$988$	20254.6	0.652212
$989$	−21416.1	−0.688565
$990$	1450.87	0.0465773
$991$	29600.3	0.948823	0.474412	−	0.880303i	$-0.342661\pi$
$991$	29600.3	0.948823	0.474412	+	0.880303i	$0.342661\pi$
$992$	−157819.	−5.05118
$993$	−9472.68	−0.302725
$994$	−24792.2	−0.791109
$995$	25836.0	0.823171
$996$	68405.2	2.17621
$997$	36506.3	1.15965	0.579823	−	0.814743i	$-0.303122\pi$
$997$	36506.3	1.15965	0.579823	+	0.814743i	$0.303122\pi$
$998$	−39630.1	−1.25698
$999$	−22184.4	−0.702587

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.f.1.8		8
17.2	even	8		17.4.c.a.4.4	✓	8
17.4	even	4		289.4.b.c.288.1		8
17.9	even	8		17.4.c.a.13.1	yes	8
17.13	even	4		289.4.b.c.288.2		8
17.16	even	2	inner	289.4.a.f.1.7		8
51.2	odd	8		153.4.f.a.55.1		8
51.26	odd	8		153.4.f.a.64.4		8
68.19	odd	8		272.4.o.e.225.1		8
68.43	odd	8		272.4.o.e.81.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.c.a.4.4	✓	8	17.2	even	8
17.4.c.a.13.1	yes	8	17.9	even	8
153.4.f.a.55.1		8	51.2	odd	8
153.4.f.a.64.4		8	51.26	odd	8
272.4.o.e.81.1		8	68.43	odd	8
272.4.o.e.225.1		8	68.19	odd	8
289.4.a.f.1.7		8	17.16	even	2	inner
289.4.a.f.1.8		8	1.1	even	1	trivial
289.4.b.c.288.1		8	17.4	even	4
289.4.b.c.288.2		8	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)

\(f(q)\)	\(=\)	\(q+5.46767 q^{2} +5.57972 q^{3} +21.8954 q^{4} -6.77499 q^{5} +30.5081 q^{6} -4.72009 q^{7} +75.9757 q^{8} +4.13329 q^{9} +O(q^{10})\)	\(q+5.46767 q^{2} +5.57972 q^{3} +21.8954 q^{4} -6.77499 q^{5} +30.5081 q^{6} -4.72009 q^{7} +75.9757 q^{8} +4.13329 q^{9} -37.0434 q^{10} -9.47591 q^{11} +122.170 q^{12} +33.7223 q^{13} -25.8079 q^{14} -37.8026 q^{15} +240.247 q^{16} +22.5994 q^{18} +27.4317 q^{19} -148.341 q^{20} -26.3368 q^{21} -51.8112 q^{22} +82.8918 q^{23} +423.923 q^{24} -79.0995 q^{25} +184.382 q^{26} -127.590 q^{27} -103.349 q^{28} -208.027 q^{29} -206.692 q^{30} -223.608 q^{31} +705.786 q^{32} -52.8729 q^{33} +31.9786 q^{35} +90.5001 q^{36} +173.873 q^{37} +149.988 q^{38} +188.161 q^{39} -514.735 q^{40} +86.1730 q^{41} -144.001 q^{42} -258.362 q^{43} -207.479 q^{44} -28.0030 q^{45} +453.225 q^{46} -88.9429 q^{47} +1340.51 q^{48} -320.721 q^{49} -432.490 q^{50} +738.364 q^{52} -541.310 q^{53} -697.620 q^{54} +64.1992 q^{55} -358.613 q^{56} +153.061 q^{57} -1137.43 q^{58} -13.5759 q^{59} -827.704 q^{60} +158.640 q^{61} -1222.62 q^{62} -19.5095 q^{63} +1937.03 q^{64} -228.468 q^{65} -289.092 q^{66} +357.758 q^{67} +462.513 q^{69} +174.848 q^{70} +960.645 q^{71} +314.029 q^{72} +898.274 q^{73} +950.681 q^{74} -441.353 q^{75} +600.630 q^{76} +44.7272 q^{77} +1028.80 q^{78} -451.262 q^{79} -1627.67 q^{80} -823.515 q^{81} +471.166 q^{82} +559.916 q^{83} -576.656 q^{84} -1412.64 q^{86} -1160.74 q^{87} -719.939 q^{88} +602.266 q^{89} -153.111 q^{90} -159.172 q^{91} +1814.95 q^{92} -1247.67 q^{93} -486.311 q^{94} -185.850 q^{95} +3938.09 q^{96} +820.954 q^{97} -1753.60 q^{98} -39.1666 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 36 q^{4} + 96 q^{8} + 8 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

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