LMFDB - Embedded newform 289.4.a.f.1.7

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			1.7
Root			$-3.05346$ 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	$-0.680408\pi$
$3$	−5.57972	−1.07382	−0.536909	+	0.843640i	$0.680408\pi$
$4$	21.8954	2.73693
$5$	6.77499	0.605974	0.302987	−	0.952995i	$-0.402016\pi$
$5$	6.77499	0.605974	0.302987	+	0.952995i	$0.402016\pi$
$6$	−30.5081	−2.07581
$7$	4.72009	0.254861	0.127431	−	0.991848i	$-0.459327\pi$
$7$	4.72009	0.254861	0.127431	+	0.991848i	$0.459327\pi$
$8$	75.9757	3.35769
$9$	4.13329	0.153085
$10$	37.0434	1.17142
$11$	9.47591	0.259736	0.129868	−	0.991531i	$-0.458545\pi$
$11$	9.47591	0.259736	0.129868	+	0.991531i	$0.458545\pi$
$12$	−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	$-0.622612\pi$
$23$	−82.8918	−0.751484	−0.375742	+	0.926724i	$0.622612\pi$
$24$	−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	$-0.267992\pi$
$29$	208.027	1.33206	0.666030	+	0.745925i	$0.267992\pi$
$30$	−206.692	−1.25789
$31$	223.608	1.29552	0.647761	−	0.761844i	$-0.275706\pi$
$31$	223.608	1.29552	0.647761	+	0.761844i	$0.275706\pi$
$32$	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	$-0.626239\pi$
$37$	−173.873	−0.772555	−0.386278	+	0.922383i	$0.626239\pi$
$38$	149.988	0.640296
$39$	−188.161	−0.772560
$40$	514.735	2.03467
$41$	−86.1730	−0.328243	−0.164121	−	0.986440i	$-0.552479\pi$
$41$	−86.1730	−0.328243	−0.164121	+	0.986440i	$0.552479\pi$
$42$	−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	$-0.553243\pi$
$61$	−158.640	−0.332981	−0.166490	+	0.986043i	$0.553243\pi$
$62$	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	$-0.796695\pi$
$71$	−960.645	−1.60574	−0.802870	+	0.596154i	$0.796695\pi$
$72$	314.029	0.514010
$73$	−898.274	−1.44021	−0.720103	−	0.693868i	$-0.755905\pi$
$73$	−898.274	−1.44021	−0.720103	+	0.693868i	$0.755905\pi$
$74$	−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	$-0.395868\pi$
$79$	451.262	0.642670	0.321335	+	0.946966i	$0.395868\pi$
$80$	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	$-0.641369\pi$
$97$	−820.954	−0.859332	−0.429666	+	0.902988i	$0.641369\pi$
$98$	−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	$-0.874635\pi$
$107$	−2044.16	−1.84688	−0.923441	+	0.383741i	$0.874635\pi$
$108$	2793.64	2.48905
$109$	−262.428	−0.230606	−0.115303	−	0.993330i	$-0.536784\pi$
$109$	−262.428	−0.230606	−0.115303	+	0.993330i	$0.536784\pi$
$110$	351.020	0.304259
$111$	970.163	0.829584
$112$	1133.99	0.956712
$113$	−299.445	−0.249287	−0.124644	−	0.992202i	$-0.539779\pi$
$113$	−299.445	−0.249287	−0.124644	+	0.992202i	$0.539779\pi$
$114$	−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	$-0.339550\pi$
$131$	1448.36	0.965984	0.482992	+	0.875625i	$0.339550\pi$
$132$	−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	$-0.439575\pi$
$139$	618.453	0.377385	0.188692	+	0.982036i	$0.439575\pi$
$140$	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	$-0.207315\pi$
$163$	3310.10	1.59059	0.795297	+	0.606220i	$0.207315\pi$
$164$	−1886.80	−0.898378
$165$	−358.214	−0.169011
$166$	3061.44	1.43141
$167$	−350.214	−0.162278	−0.0811389	−	0.996703i	$-0.525856\pi$
$167$	−350.214	−0.162278	−0.0811389	+	0.996703i	$0.525856\pi$
$168$	−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	$-0.348081\pi$
$173$	2090.48	0.918705	0.459352	+	0.888254i	$0.348081\pi$
$174$	−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	$-0.733626\pi$
$181$	−3262.13	−1.33963	−0.669813	+	0.742530i	$0.733626\pi$
$182$	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	$-0.502113\pi$
$193$	−35.5988	−0.0132770	−0.00663849	+	0.999978i	$0.502113\pi$
$194$	−4488.71	−1.66119
$195$	−1274.79	−0.468151
$196$	−7022.32	−2.55916
$197$	631.705	0.228463	0.114231	−	0.993454i	$-0.463559\pi$
$197$	631.705	0.228463	0.114231	+	0.993454i	$0.463559\pi$
$198$	214.150	0.0768636
$199$	3813.43	1.35843	0.679214	−	0.733940i	$-0.262321\pi$
$199$	3813.43	1.35843	0.679214	+	0.733940i	$0.262321\pi$
$200$	−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	$-0.374340\pi$
$211$	2357.54	0.769194	0.384597	+	0.923085i	$0.374340\pi$
$212$	−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	$-0.329224\pi$
$227$	3496.28	1.02227	0.511137	+	0.859499i	$0.329224\pi$
$228$	−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	$-0.500649\pi$
$233$	−14.5114	−0.00408013	−0.00204007	+	0.999998i	$0.500649\pi$
$234$	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	$-0.492784\pi$
$241$	169.604	0.0453327	0.0226664	+	0.999743i	$0.492784\pi$
$242$	−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	$-0.740474\pi$
$269$	−6049.91	−1.37126	−0.685631	+	0.727949i	$0.740474\pi$
$270$	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	$-0.414751\pi$
$277$	2439.98	0.529257	0.264628	+	0.964350i	$0.414751\pi$
$278$	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	$-0.662525\pi$
$283$	−4653.11	−0.977380	−0.488690	+	0.872458i	$0.662525\pi$
$284$	−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	$-0.529713\pi$
$311$	−1022.42	−0.186418	−0.0932092	+	0.995647i	$0.529713\pi$
$312$	−14295.7	−2.59401
$313$	−3940.99	−0.711686	−0.355843	−	0.934546i	$-0.615806\pi$
$313$	−3940.99	−0.711686	−0.355843	+	0.934546i	$0.615806\pi$
$314$	14845.9	2.66817
$315$	132.177	0.0236422
$316$	9880.58	1.75894
$317$	−5383.64	−0.953866	−0.476933	−	0.878940i	$-0.658252\pi$
$317$	−5383.64	−0.953866	−0.476933	+	0.878940i	$0.658252\pi$
$318$	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	$-0.133755\pi$
$337$	11296.6	1.82601	0.913006	+	0.407947i	$0.133755\pi$
$338$	−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	$-0.589772\pi$
$347$	−3597.85	−0.556607	−0.278303	+	0.960493i	$0.589772\pi$
$348$	−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	$-0.578658\pi$
$367$	−3439.49	−0.489210	−0.244605	+	0.969623i	$0.578658\pi$
$368$	−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	$-0.368655\pi$
$379$	5917.75	0.802043	0.401022	+	0.916069i	$0.368655\pi$
$380$	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	$-0.832446\pi$
$397$	−13678.7	−1.72926	−0.864628	+	0.502412i	$0.832446\pi$
$398$	20850.6	2.62600
$399$	−722.464	−0.0906478
$400$	−19003.4	−2.37543
$401$	13292.7	1.65537	0.827685	−	0.561193i	$-0.189657\pi$
$401$	13292.7	1.65537	0.827685	+	0.561193i	$0.189657\pi$
$402$	−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	$-0.199214\pi$
$419$	13902.3	1.62093	0.810467	+	0.585785i	$0.199214\pi$
$420$	−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	$-0.613644\pi$
$431$	−6254.26	−0.698972	−0.349486	+	0.936942i	$0.613644\pi$
$432$	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	$-0.317890\pi$
$439$	9959.89	1.08282	0.541412	+	0.840757i	$0.317890\pi$
$440$	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	$-0.387796\pi$
$449$	6569.43	0.690491	0.345245	+	0.938512i	$0.387796\pi$
$450$	−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	$-0.457492\pi$
$479$	2791.67	0.266293	0.133147	+	0.991096i	$0.457492\pi$
$480$	−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	$-0.597326\pi$
$487$	−6470.16	−0.602035	−0.301018	+	0.953619i	$0.597326\pi$
$488$	−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	$-0.394596\pi$
$499$	7248.08	0.650238	0.325119	+	0.945673i	$0.394596\pi$
$500$	−30276.4	−2.70800
$501$	1954.10	0.174257
$502$	26380.8	2.34548
$503$	−7346.69	−0.651238	−0.325619	−	0.945501i	$-0.605573\pi$
$503$	−7346.69	−0.651238	−0.325619	+	0.945501i	$0.605573\pi$
$504$	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	$-0.242498\pi$
$521$	17209.6	1.44715	0.723575	+	0.690246i	$0.242498\pi$
$522$	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	$-0.390433\pi$
$541$	8492.68	0.674914	0.337457	+	0.941341i	$0.390433\pi$
$542$	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	$-0.662724\pi$
$547$	−12517.8	−0.978472	−0.489236	+	0.872151i	$0.662724\pi$
$548$	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	$-0.720959\pi$
$571$	−17457.8	−1.27948	−0.639742	+	0.768590i	$0.720959\pi$
$572$	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	$-0.415631\pi$
$601$	7719.31	0.523922	0.261961	+	0.965078i	$0.415631\pi$
$602$	−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	$-0.801407\pi$
$607$	−24275.0	−1.62321	−0.811607	+	0.584204i	$0.801407\pi$
$608$	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	$-0.291498\pi$
$617$	18672.6	1.21836	0.609182	+	0.793030i	$0.291498\pi$
$618$	3137.87	0.204246
$619$	19355.5	1.25681	0.628404	−	0.777887i	$-0.283709\pi$
$619$	19355.5	1.25681	0.628404	+	0.777887i	$0.283709\pi$
$620$	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	$-0.409137\pi$
$641$	9139.88	0.563188	0.281594	+	0.959534i	$0.409137\pi$
$642$	62363.4	3.83378
$643$	24047.0	1.47484	0.737420	−	0.675435i	$-0.236044\pi$
$643$	24047.0	1.47484	0.737420	+	0.675435i	$0.236044\pi$
$644$	−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	$-0.571216\pi$
$653$	−7404.51	−0.443738	−0.221869	+	0.975076i	$0.571216\pi$
$654$	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	$-0.302849\pi$
$673$	20270.7	1.16104	0.580520	+	0.814246i	$0.302849\pi$
$674$	61766.2	3.52989
$675$	−10092.3	−0.575485
$676$	−23205.0	−1.32027
$677$	−33735.8	−1.91517	−0.957587	−	0.288146i	$-0.906961\pi$
$677$	−33735.8	−1.91517	−0.957587	+	0.288146i	$0.906961\pi$
$678$	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	$-0.505887\pi$
$683$	−660.167	−0.0369848	−0.0184924	+	0.999829i	$0.505887\pi$
$684$	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	$-0.702118\pi$
$691$	−21548.5	−1.18631	−0.593157	+	0.805087i	$0.702118\pi$
$692$	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	$-0.166993\pi$
$709$	32679.3	1.73102	0.865512	+	0.500888i	$0.166993\pi$
$710$	−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	$-0.386446\pi$
$719$	13465.6	0.698443	0.349222	+	0.937040i	$0.386446\pi$
$720$	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	$-0.466751\pi$
$743$	4223.24	0.208527	0.104263	+	0.994550i	$0.466751\pi$
$744$	−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	$-0.850372\pi$
$751$	−36696.9	−1.78307	−0.891537	+	0.452949i	$0.850372\pi$
$752$	−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	$-0.303139\pi$
$787$	25600.9	1.15956	0.579779	+	0.814774i	$0.303139\pi$
$788$	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	$-0.275079\pi$
$809$	29879.3	1.29852	0.649259	+	0.760568i	$0.275079\pi$
$810$	−30505.8	−1.32329
$811$	8123.23	0.351720	0.175860	−	0.984415i	$-0.443729\pi$
$811$	8123.23	0.351720	0.175860	+	0.984415i	$0.443729\pi$
$812$	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	$-0.300760\pi$
$821$	27563.3	1.17170	0.585851	+	0.810419i	$0.300760\pi$
$822$	−58049.8	−2.46316
$823$	19682.8	0.833655	0.416828	−	0.908986i	$-0.363142\pi$
$823$	19682.8	0.833655	0.416828	+	0.908986i	$0.363142\pi$
$824$	−7814.39	−0.330373
$825$	4182.22	0.176492
$826$	−350.365	−0.0147588
$827$	−30777.1	−1.29411	−0.647053	−	0.762445i	$-0.723999\pi$
$827$	−30777.1	−1.29411	−0.647053	+	0.762445i	$0.723999\pi$
$828$	−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	$-0.298242\pi$
$839$	28785.5	1.18449	0.592243	+	0.805759i	$0.298242\pi$
$840$	−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	$-0.513808\pi$
$853$	−2160.76	−0.0867328	−0.0433664	+	0.999059i	$0.513808\pi$
$854$	−4094.18	−0.164051
$855$	768.170	0.0307262
$856$	−155306.	−6.20125
$857$	−25369.2	−1.01120	−0.505599	−	0.862769i	$-0.668729\pi$
$857$	−25369.2	−1.01120	−0.505599	+	0.862769i	$0.668729\pi$
$858$	−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	$-0.484553\pi$
$877$	2519.76	0.0970198	0.0485099	+	0.998823i	$0.484553\pi$
$878$	54457.4	2.09322
$879$	10360.3	0.397549
$880$	15423.7	0.590831
$881$	3937.23	0.150566	0.0752830	−	0.997162i	$-0.476014\pi$
$881$	3937.23	0.150566	0.0752830	+	0.997162i	$0.476014\pi$
$882$	−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	$-0.496716\pi$
$887$	545.051	0.0206325	0.0103162	+	0.999947i	$0.496716\pi$
$888$	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	$-0.515417\pi$
$907$	−2644.96	−0.0968294	−0.0484147	+	0.998827i	$0.515417\pi$
$908$	76552.6	2.79789
$909$	1017.69	0.0371337
$910$	5896.28	0.214791
$911$	−814.772	−0.0296318	−0.0148159	−	0.999890i	$-0.504716\pi$
$911$	−814.772	−0.0296318	−0.0148159	+	0.999890i	$0.504716\pi$
$912$	−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	$-0.539284\pi$
$929$	−6971.41	−0.246205	−0.123102	+	0.992394i	$0.539284\pi$
$930$	−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	$-0.320584\pi$
$941$	30844.7	1.06855	0.534277	+	0.845310i	$0.320584\pi$
$942$	−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	$-0.641298\pi$
$947$	−25031.3	−0.858930	−0.429465	+	0.903083i	$0.641298\pi$
$948$	−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	$-0.689789\pi$
$983$	−34612.9	−1.12307	−0.561536	+	0.827452i	$0.689789\pi$
$984$	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	$-0.657339\pi$
$991$	−29600.3	−0.948823	−0.474412	+	0.880303i	$0.657339\pi$
$992$	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	$-0.696878\pi$
$997$	−36506.3	−1.15965	−0.579823	+	0.814743i	$0.696878\pi$
$998$	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.1.7		8
17.4	even	4		289.4.b.c.288.2		8
17.8	even	8		17.4.c.a.13.1	yes	8
17.13	even	4		289.4.b.c.288.1		8
17.15	even	8		17.4.c.a.4.4	✓	8
17.16	even	2	inner	289.4.a.f.1.8		8
51.8	odd	8		153.4.f.a.64.4		8
51.32	odd	8		153.4.f.a.55.1		8
68.15	odd	8		272.4.o.e.225.1		8
68.59	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	17.15	even	8
17.4.c.a.13.1	yes	8	17.8	even	8
153.4.f.a.55.1		8	51.32	odd	8
153.4.f.a.64.4		8	51.8	odd	8
272.4.o.e.81.1		8	68.59	odd	8
272.4.o.e.225.1		8	68.15	odd	8
289.4.a.f.1.7		8	1.1	even	1	trivial
289.4.a.f.1.8		8	17.16	even	2	inner
289.4.b.c.288.1		8	17.13	even	4
289.4.b.c.288.2		8	17.4	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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