LMFDB - Embedded newform 289.4.a.g.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$17.0515519917$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 58 x^{10} + 204 x^{9} + 1191 x^{8} - 3456 x^{7} - 10364 x^{6} + 21448 x^{5} + 38476 x^{4} - 32336 x^{3} - 57024 x^{2} - 15776 x + 1156 $ x^12 - 4x^11 - 58x^10 + 204x^9 + 1191x^8 - 3456x^7 - 10364x^6 + 21448x^5 + 38476x^4 - 32336x^3 - 57024x^2 - 15776*x + 1156
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$4.91828$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.15292 q^{2} -1.99138 q^{3} +1.94089 q^{4} +5.00761 q^{5} -6.27866 q^{6} -2.78516 q^{7} -19.1039 q^{8} -23.0344 q^{9} +O(q^{10})$	\(q+3.15292 q^{2} -1.99138 q^{3} +1.94089 q^{4} +5.00761 q^{5} -6.27866 q^{6} -2.78516 q^{7} -19.1039 q^{8} -23.0344 q^{9} +15.7886 q^{10} +27.2453 q^{11} -3.86505 q^{12} -59.7352 q^{13} -8.78140 q^{14} -9.97206 q^{15} -75.7601 q^{16} -72.6256 q^{18} +33.2605 q^{19} +9.71922 q^{20} +5.54633 q^{21} +85.9023 q^{22} -210.884 q^{23} +38.0431 q^{24} -99.9239 q^{25} -188.340 q^{26} +99.6376 q^{27} -5.40570 q^{28} +20.0521 q^{29} -31.4411 q^{30} -133.659 q^{31} -86.0343 q^{32} -54.2559 q^{33} -13.9470 q^{35} -44.7072 q^{36} +152.772 q^{37} +104.868 q^{38} +118.956 q^{39} -95.6647 q^{40} +261.840 q^{41} +17.4871 q^{42} -316.820 q^{43} +52.8802 q^{44} -115.347 q^{45} -664.899 q^{46} +329.443 q^{47} +150.867 q^{48} -335.243 q^{49} -315.052 q^{50} -115.939 q^{52} -310.540 q^{53} +314.149 q^{54} +136.434 q^{55} +53.2074 q^{56} -66.2344 q^{57} +63.2227 q^{58} -54.7388 q^{59} -19.3547 q^{60} -818.751 q^{61} -421.417 q^{62} +64.1546 q^{63} +334.822 q^{64} -299.130 q^{65} -171.064 q^{66} +731.181 q^{67} +419.950 q^{69} -43.9738 q^{70} +629.179 q^{71} +440.046 q^{72} +496.481 q^{73} +481.678 q^{74} +198.987 q^{75} +64.5550 q^{76} -75.8828 q^{77} +375.057 q^{78} -90.0262 q^{79} -379.377 q^{80} +423.512 q^{81} +825.559 q^{82} +364.025 q^{83} +10.7648 q^{84} -998.907 q^{86} -39.9315 q^{87} -520.492 q^{88} -192.079 q^{89} -363.680 q^{90} +166.372 q^{91} -409.302 q^{92} +266.167 q^{93} +1038.71 q^{94} +166.556 q^{95} +171.327 q^{96} +1350.20 q^{97} -1056.99 q^{98} -627.580 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9}+O(q^{10}) $ 12 * q - 8 * q^2 + 16 * q^4 - 96 * q^8 - 36 * q^9	$ 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9} - 8 q^{13} - 192 q^{15} - 184 q^{16} - 352 q^{19} - 256 q^{21} - 492 q^{25} - 784 q^{26} + 744 q^{30} + 24 q^{32} - 1400 q^{33} - 632 q^{35} - 856 q^{36} - 624 q^{38} - 1664 q^{42} - 1200 q^{43} - 1512 q^{47} - 1052 q^{49} - 2856 q^{50} + 792 q^{52} - 2504 q^{53} - 1424 q^{55} - 3408 q^{59} - 2808 q^{60} + 272 q^{64} + 272 q^{66} - 1080 q^{67} - 344 q^{69} + 2600 q^{70} + 248 q^{72} + 896 q^{76} + 848 q^{77} - 2404 q^{81} - 2960 q^{83} + 4768 q^{84} - 1200 q^{86} - 160 q^{87} - 2144 q^{89} + 3800 q^{93} + 5984 q^{94} + 3464 q^{98}+O(q^{100}) $ 12 * q - 8 * q^2 + 16 * q^4 - 96 * q^8 - 36 * q^9 - 8 * q^13 - 192 * q^15 - 184 * q^16 - 352 * q^19 - 256 * q^21 - 492 * q^25 - 784 * q^26 + 744 * q^30 + 24 * q^32 - 1400 * q^33 - 632 * q^35 - 856 * q^36 - 624 * q^38 - 1664 * q^42 - 1200 * q^43 - 1512 * q^47 - 1052 * q^49 - 2856 * q^50 + 792 * q^52 - 2504 * q^53 - 1424 * q^55 - 3408 * q^59 - 2808 * q^60 + 272 * q^64 + 272 * q^66 - 1080 * q^67 - 344 * q^69 + 2600 * q^70 + 248 * q^72 + 896 * q^76 + 848 * q^77 - 2404 * q^81 - 2960 * q^83 + 4768 * q^84 - 1200 * q^86 - 160 * q^87 - 2144 * q^89 + 3800 * q^93 + 5984 * q^94 + 3464 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	3.15292	1.11472	0.557362	−	0.830269i	$-0.311813\pi$
$2$	3.15292	1.11472	0.557362	+	0.830269i	$0.311813\pi$
$3$	−1.99138	−0.383242	−0.191621	−	0.981469i	$-0.561374\pi$
$3$	−1.99138	−0.383242	−0.191621	+	0.981469i	$0.561374\pi$
$4$	1.94089	0.242611
$5$	5.00761	0.447894	0.223947	−	0.974601i	$-0.428106\pi$
$5$	5.00761	0.447894	0.223947	+	0.974601i	$0.428106\pi$
$6$	−6.27866	−0.427209
$7$	−2.78516	−0.150385	−0.0751924	−	0.997169i	$-0.523957\pi$
$7$	−2.78516	−0.150385	−0.0751924	+	0.997169i	$0.523957\pi$
$8$	−19.1039	−0.844280
$9$	−23.0344	−0.853126
$10$	15.7886	0.499279
$11$	27.2453	0.746798	0.373399	−	0.927671i	$-0.378192\pi$
$11$	27.2453	0.746798	0.373399	+	0.927671i	$0.378192\pi$
$12$	−3.86505	−0.0929787
$13$	−59.7352	−1.27443	−0.637214	−	0.770687i	$-0.719913\pi$
$13$	−59.7352	−1.27443	−0.637214	+	0.770687i	$0.719913\pi$
$14$	−8.78140	−0.167638
$15$	−9.97206	−0.171652
$16$	−75.7601	−1.18375
$17$	0	0
$17$	0	0
$18$	−72.6256	−0.951000
$19$	33.2605	0.401604	0.200802	−	0.979632i	$-0.435645\pi$
$19$	33.2605	0.401604	0.200802	+	0.979632i	$0.435645\pi$
$20$	9.71922	0.108664
$21$	5.54633	0.0576337
$22$	85.9023	0.832475
$23$	−210.884	−1.91184	−0.955919	−	0.293630i	$-0.905137\pi$
$23$	−210.884	−1.91184	−0.955919	+	0.293630i	$0.905137\pi$
$24$	38.0431	0.323563
$25$	−99.9239	−0.799391
$26$	−188.340	−1.42064
$27$	99.6376	0.710195
$28$	−5.40570	−0.0364850
$29$	20.0521	0.128400	0.0641998	−	0.997937i	$-0.479551\pi$
$29$	20.0521	0.128400	0.0641998	+	0.997937i	$0.479551\pi$
$30$	−31.4411	−0.191344
$31$	−133.659	−0.774385	−0.387192	−	0.921999i	$-0.626555\pi$
$31$	−133.659	−0.774385	−0.387192	+	0.921999i	$0.626555\pi$
$32$	−86.0343	−0.475277
$33$	−54.2559	−0.286204
$34$	0	0
$35$	−13.9470	−0.0673565
$36$	−44.7072	−0.206978
$37$	152.772	0.678800	0.339400	−	0.940642i	$-0.389776\pi$
$37$	152.772	0.678800	0.339400	+	0.940642i	$0.389776\pi$
$38$	104.868	0.447678
$39$	118.956	0.488414
$40$	−95.6647	−0.378148
$41$	261.840	0.997377	0.498689	−	0.866781i	$-0.333815\pi$
$41$	261.840	0.997377	0.498689	+	0.866781i	$0.333815\pi$
$42$	17.4871	0.0642457
$43$	−316.820	−1.12359	−0.561797	−	0.827275i	$-0.689890\pi$
$43$	−316.820	−1.12359	−0.561797	+	0.827275i	$0.689890\pi$
$44$	52.8802	0.181182
$45$	−115.347	−0.382110
$46$	−664.899	−2.13117
$47$	329.443	1.02243	0.511215	−	0.859453i	$-0.329196\pi$
$47$	329.443	1.02243	0.511215	+	0.859453i	$0.329196\pi$
$48$	150.867	0.453663
$49$	−335.243	−0.977384
$50$	−315.052	−0.891101
$51$	0	0
$52$	−115.939	−0.309190
$53$	−310.540	−0.804829	−0.402415	−	0.915458i	$-0.631829\pi$
$53$	−310.540	−0.804829	−0.402415	+	0.915458i	$0.631829\pi$
$54$	314.149	0.791672
$55$	136.434	0.334487
$56$	53.2074	0.126967
$57$	−66.2344	−0.153911
$58$	63.2227	0.143130
$59$	−54.7388	−0.120786	−0.0603931	−	0.998175i	$-0.519235\pi$
$59$	−54.7388	−0.120786	−0.0603931	+	0.998175i	$0.519235\pi$
$60$	−19.3547	−0.0416446
$61$	−818.751	−1.71853	−0.859265	−	0.511531i	$-0.829079\pi$
$61$	−818.751	−1.71853	−0.859265	+	0.511531i	$0.829079\pi$
$62$	−421.417	−0.863226
$63$	64.1546	0.128297
$64$	334.822	0.653948
$65$	−299.130	−0.570808
$66$	−171.064	−0.319039
$67$	731.181	1.33325	0.666627	−	0.745392i	$-0.267738\pi$
$67$	731.181	1.33325	0.666627	+	0.745392i	$0.267738\pi$
$68$	0	0
$69$	419.950	0.732696
$70$	−43.9738	−0.0750839
$71$	629.179	1.05169	0.525844	−	0.850581i	$-0.323750\pi$
$71$	629.179	1.05169	0.525844	+	0.850581i	$0.323750\pi$
$72$	440.046	0.720277
$73$	496.481	0.796010	0.398005	−	0.917383i	$-0.369703\pi$
$73$	496.481	0.796010	0.398005	+	0.917383i	$0.369703\pi$
$74$	481.678	0.756675
$75$	198.987	0.306360
$76$	64.5550	0.0974337
$77$	−75.8828	−0.112307
$78$	375.057	0.544447
$79$	−90.0262	−0.128212	−0.0641059	−	0.997943i	$-0.520420\pi$
$79$	−90.0262	−0.128212	−0.0641059	+	0.997943i	$0.520420\pi$
$80$	−379.377	−0.530195
$81$	423.512	0.580950
$82$	825.559	1.11180
$83$	364.025	0.481409	0.240704	−	0.970599i	$-0.422622\pi$
$83$	364.025	0.481409	0.240704	+	0.970599i	$0.422622\pi$
$84$	10.7648	0.0139826
$85$	0	0
$86$	−998.907	−1.25250
$87$	−39.9315	−0.0492081
$88$	−520.492	−0.630507
$89$	−192.079	−0.228767	−0.114384	−	0.993437i	$-0.536489\pi$
$89$	−192.079	−0.228767	−0.114384	+	0.993437i	$0.536489\pi$
$90$	−363.680	−0.425948
$91$	166.372	0.191654
$92$	−409.302	−0.463833
$93$	266.167	0.296776
$94$	1038.71	1.13973
$95$	166.556	0.179876
$96$	171.327	0.182146
$97$	1350.20	1.41332	0.706659	−	0.707554i	$-0.250202\pi$
$97$	1350.20	1.41332	0.706659	+	0.707554i	$0.250202\pi$
$98$	−1056.99	−1.08951
$99$	−627.580	−0.637113
$100$	−193.941	−0.193941
$101$	−304.020	−0.299516	−0.149758	−	0.988723i	$-0.547850\pi$
$101$	−304.020	−0.299516	−0.149758	+	0.988723i	$0.547850\pi$
$102$	0	0
$103$	988.515	0.945643	0.472822	−	0.881158i	$-0.343236\pi$
$103$	988.515	0.945643	0.472822	+	0.881158i	$0.343236\pi$
$104$	1141.17	1.07597
$105$	27.7738	0.0258138
$106$	−979.107	−0.897163
$107$	−1175.01	−1.06162	−0.530808	−	0.847492i	$-0.678111\pi$
$107$	−1175.01	−1.06162	−0.530808	+	0.847492i	$0.678111\pi$
$108$	193.386	0.172301
$109$	−838.865	−0.737144	−0.368572	−	0.929599i	$-0.620153\pi$
$109$	−838.865	−0.737144	−0.368572	+	0.929599i	$0.620153\pi$
$110$	430.165	0.372860
$111$	−304.228	−0.260144
$112$	211.004	0.178018
$113$	2026.81	1.68731	0.843655	−	0.536885i	$-0.180399\pi$
$113$	2026.81	1.68731	0.843655	+	0.536885i	$0.180399\pi$
$114$	−208.831	−0.171569
$115$	−1056.02	−0.856301
$116$	38.9190	0.0311512
$117$	1375.96	1.08725
$118$	−172.587	−0.134643
$119$	0	0
$120$	190.505	0.144922
$121$	−588.691	−0.442292
$122$	−2581.45	−1.91569
$123$	−521.423	−0.382237
$124$	−259.418	−0.187874
$125$	−1126.33	−0.805937
$126$	202.274	0.143016
$127$	−1600.30	−1.11814	−0.559070	−	0.829120i	$-0.688842\pi$
$127$	−1600.30	−1.11814	−0.559070	+	0.829120i	$0.688842\pi$
$128$	1743.94	1.20425
$129$	630.909	0.430608
$130$	−943.133	−0.636294
$131$	2615.07	1.74412	0.872061	−	0.489397i	$-0.162783\pi$
$131$	2615.07	1.74412	0.872061	+	0.489397i	$0.162783\pi$
$132$	−105.305	−0.0694364
$133$	−92.6360	−0.0603952
$134$	2305.35	1.48621
$135$	498.946	0.318092
$136$	0	0
$137$	745.711	0.465039	0.232520	−	0.972592i	$-0.425303\pi$
$137$	745.711	0.465039	0.232520	+	0.972592i	$0.425303\pi$
$138$	1324.07	0.816754
$139$	−2532.45	−1.54532	−0.772661	−	0.634818i	$-0.781075\pi$
$139$	−2532.45	−1.54532	−0.772661	+	0.634818i	$0.781075\pi$
$140$	−27.0696	−0.0163414
$141$	−656.047	−0.391837
$142$	1983.75	1.17234
$143$	−1627.51	−0.951740
$144$	1745.09	1.00989
$145$	100.413	0.0575094
$146$	1565.36	0.887332
$147$	667.597	0.374574
$148$	296.514	0.164684
$149$	−1816.70	−0.998858	−0.499429	−	0.866355i	$-0.666457\pi$
$149$	−1816.70	−0.998858	−0.499429	+	0.866355i	$0.666457\pi$
$150$	627.388	0.341507
$151$	−2120.50	−1.14280	−0.571402	−	0.820670i	$-0.693600\pi$
$151$	−2120.50	−1.14280	−0.571402	+	0.820670i	$0.693600\pi$
$152$	−635.404	−0.339066
$153$	0	0
$154$	−239.252	−0.125191
$155$	−669.314	−0.346842
$156$	230.880	0.118495
$157$	−1607.82	−0.817314	−0.408657	−	0.912688i	$-0.634003\pi$
$157$	−1607.82	−0.817314	−0.408657	+	0.912688i	$0.634003\pi$
$158$	−283.845	−0.142921
$159$	618.404	0.308444
$160$	−430.826	−0.212874
$161$	587.346	0.287511
$162$	1335.30	0.647599
$163$	−2278.00	−1.09464	−0.547322	−	0.836922i	$-0.684353\pi$
$163$	−2278.00	−1.09464	−0.547322	+	0.836922i	$0.684353\pi$
$164$	508.202	0.241975
$165$	−271.692	−0.128189
$166$	1147.74	0.536638
$167$	−1652.12	−0.765538	−0.382769	−	0.923844i	$-0.625029\pi$
$167$	−1652.12	−0.765538	−0.382769	+	0.923844i	$0.625029\pi$
$168$	−105.956	−0.0486590
$169$	1371.29	0.624165
$170$	0	0
$171$	−766.135	−0.342619
$172$	−614.912	−0.272597
$173$	2210.82	0.971595	0.485797	−	0.874071i	$-0.338529\pi$
$173$	2210.82	0.971595	0.485797	+	0.874071i	$0.338529\pi$
$174$	−125.901	−0.0548534
$175$	278.304	0.120216
$176$	−2064.11	−0.884023
$177$	109.006	0.0462903
$178$	−605.608	−0.255013
$179$	20.7548	0.00866640	0.00433320	−	0.999991i	$-0.498621\pi$
$179$	20.7548	0.00866640	0.00433320	+	0.999991i	$0.498621\pi$
$180$	−223.876	−0.0927042
$181$	−436.498	−0.179252	−0.0896262	−	0.995975i	$-0.528567\pi$
$181$	−436.498	−0.179252	−0.0896262	+	0.995975i	$0.528567\pi$
$182$	524.558	0.213642
$183$	1630.45	0.658612
$184$	4028.69	1.61413
$185$	765.023	0.304030
$186$	839.202	0.330824
$187$	0	0
$188$	639.412	0.248053
$189$	−277.507	−0.106803
$190$	525.136	0.200512
$191$	787.808	0.298449	0.149225	−	0.988803i	$-0.452322\pi$
$191$	787.808	0.298449	0.149225	+	0.988803i	$0.452322\pi$
$192$	−666.758	−0.250620
$193$	3726.86	1.38998	0.694988	−	0.719021i	$-0.255410\pi$
$193$	3726.86	1.38998	0.694988	+	0.719021i	$0.255410\pi$
$194$	4257.06	1.57546
$195$	595.683	0.218758
$196$	−650.669	−0.237124
$197$	451.885	0.163429	0.0817144	−	0.996656i	$-0.473960\pi$
$197$	451.885	0.163429	0.0817144	+	0.996656i	$0.473960\pi$
$198$	−1978.71	−0.710206
$199$	−3480.16	−1.23971	−0.619855	−	0.784716i	$-0.712809\pi$
$199$	−3480.16	−1.23971	−0.619855	+	0.784716i	$0.712809\pi$
$200$	1908.93	0.674910
$201$	−1456.06	−0.510958
$202$	−958.551	−0.333878
$203$	−55.8485	−0.0193093
$204$	0	0
$205$	1311.19	0.446719
$206$	3116.71	1.05413
$207$	4857.58	1.63104
$208$	4525.54	1.50860
$209$	906.194	0.299917
$210$	87.5686	0.0287753
$211$	−1818.51	−0.593323	−0.296661	−	0.954983i	$-0.595873\pi$
$211$	−1818.51	−0.593323	−0.296661	+	0.954983i	$0.595873\pi$
$212$	−602.724	−0.195261
$213$	−1252.94	−0.403051
$214$	−3704.72	−1.18341
$215$	−1586.51	−0.503251
$216$	−1903.46	−0.599603
$217$	372.263	0.116456
$218$	−2644.87	−0.821712
$219$	−988.684	−0.305064
$220$	264.803	0.0811502
$221$	0	0
$222$	−959.205	−0.289989
$223$	−6507.83	−1.95425	−0.977123	−	0.212676i	$-0.931782\pi$
$223$	−6507.83	−1.95425	−0.977123	+	0.212676i	$0.931782\pi$
$224$	239.620	0.0714744
$225$	2301.69	0.681981
$226$	6390.36	1.88089
$227$	−2427.16	−0.709676	−0.354838	−	0.934928i	$-0.615464\pi$
$227$	−2427.16	−0.709676	−0.354838	+	0.934928i	$0.615464\pi$
$228$	−128.554	−0.0373407
$229$	655.706	0.189215	0.0946076	−	0.995515i	$-0.469840\pi$
$229$	655.706	0.189215	0.0946076	+	0.995515i	$0.469840\pi$
$230$	−3329.55	−0.954540
$231$	151.112	0.0430408
$232$	−383.073	−0.108405
$233$	−1171.70	−0.329445	−0.164723	−	0.986340i	$-0.552673\pi$
$233$	−1171.70	−0.329445	−0.164723	+	0.986340i	$0.552673\pi$
$234$	4338.30	1.21198
$235$	1649.72	0.457940
$236$	−106.242	−0.0293041
$237$	179.277	0.0491361
$238$	0	0
$239$	−5281.06	−1.42930	−0.714651	−	0.699481i	$-0.753415\pi$
$239$	−5281.06	−1.42930	−0.714651	+	0.699481i	$0.753415\pi$
$240$	755.484	0.203193
$241$	1327.84	0.354912	0.177456	−	0.984129i	$-0.443213\pi$
$241$	1327.84	0.354912	0.177456	+	0.984129i	$0.443213\pi$
$242$	−1856.09	−0.493034
$243$	−3533.59	−0.932839
$244$	−1589.11	−0.416935
$245$	−1678.77	−0.437765
$246$	−1644.00	−0.426089
$247$	−1986.82	−0.511815
$248$	2553.41	0.653797
$249$	−724.912	−0.184496
$250$	−3551.23	−0.898397
$251$	−4280.39	−1.07640	−0.538198	−	0.842818i	$-0.680895\pi$
$251$	−4280.39	−1.07640	−0.538198	+	0.842818i	$0.680895\pi$
$252$	124.517	0.0311263
$253$	−5745.60	−1.42776
$254$	−5045.62	−1.24642
$255$	0	0
$256$	2819.92	0.688458
$257$	242.890	0.0589536	0.0294768	−	0.999565i	$-0.490616\pi$
$257$	242.890	0.0589536	0.0294768	+	0.999565i	$0.490616\pi$
$258$	1989.20	0.480010
$259$	−425.496	−0.102081
$260$	−580.579	−0.138485
$261$	−461.889	−0.109541
$262$	8245.11	1.94422
$263$	−3153.49	−0.739364	−0.369682	−	0.929158i	$-0.620533\pi$
$263$	−3153.49	−0.739364	−0.369682	+	0.929158i	$0.620533\pi$
$264$	1036.50	0.241636
$265$	−1555.06	−0.360478
$266$	−292.074	−0.0673240
$267$	382.502	0.0876732
$268$	1419.14	0.323462
$269$	210.898	0.0478018	0.0239009	−	0.999714i	$-0.492391\pi$
$269$	210.898	0.0478018	0.0239009	+	0.999714i	$0.492391\pi$
$270$	1573.14	0.354585
$271$	−1627.36	−0.364780	−0.182390	−	0.983226i	$-0.558383\pi$
$271$	−1627.36	−0.364780	−0.182390	+	0.983226i	$0.558383\pi$
$272$	0	0
$273$	−331.311	−0.0734500
$274$	2351.16	0.518391
$275$	−2722.46	−0.596984
$276$	815.076	0.177760
$277$	4626.89	1.00362	0.501810	−	0.864978i	$-0.332668\pi$
$277$	4626.89	1.00362	0.501810	+	0.864978i	$0.332668\pi$
$278$	−7984.62	−1.72261
$279$	3078.76	0.660648
$280$	266.442	0.0568677
$281$	−5076.28	−1.07767	−0.538836	−	0.842411i	$-0.681136\pi$
$281$	−5076.28	−1.07767	−0.538836	+	0.842411i	$0.681136\pi$
$282$	−2068.46	−0.436791
$283$	2437.04	0.511898	0.255949	−	0.966690i	$-0.417612\pi$
$283$	2437.04	0.511898	0.255949	+	0.966690i	$0.417612\pi$
$284$	1221.17	0.255151
$285$	−331.676	−0.0689360
$286$	−5131.39	−1.06093
$287$	−729.266	−0.149990
$288$	1981.75	0.405471
$289$	0	0
$290$	316.595	0.0641072
$291$	−2688.76	−0.541642
$292$	963.616	0.193121
$293$	−3300.30	−0.658041	−0.329020	−	0.944323i	$-0.606718\pi$
$293$	−3300.30	−0.658041	−0.329020	+	0.944323i	$0.606718\pi$
$294$	2104.88	0.417547
$295$	−274.111	−0.0540994
$296$	−2918.54	−0.573097
$297$	2714.66	0.530372
$298$	−5727.91	−1.11345
$299$	12597.2	2.43650
$300$	386.211	0.0743263
$301$	882.395	0.168971
$302$	−6685.75	−1.27391
$303$	605.420	0.114787
$304$	−2519.82	−0.475399
$305$	−4099.98	−0.769719
$306$	0	0
$307$	−1186.40	−0.220558	−0.110279	−	0.993901i	$-0.535174\pi$
$307$	−1186.40	−0.220558	−0.110279	+	0.993901i	$0.535174\pi$
$308$	−147.280	−0.0272470
$309$	−1968.51	−0.362410
$310$	−2110.29	−0.386634
$311$	−657.473	−0.119877	−0.0599387	−	0.998202i	$-0.519091\pi$
$311$	−657.473	−0.119877	−0.0599387	+	0.998202i	$0.519091\pi$
$312$	−2272.51	−0.412358
$313$	−6073.66	−1.09682	−0.548408	−	0.836211i	$-0.684766\pi$
$313$	−6073.66	−1.09682	−0.548408	+	0.836211i	$0.684766\pi$
$314$	−5069.34	−0.911080
$315$	321.261	0.0574635
$316$	−174.731	−0.0311056
$317$	5753.26	1.01935	0.509677	−	0.860366i	$-0.329765\pi$
$317$	5753.26	1.01935	0.509677	+	0.860366i	$0.329765\pi$
$318$	1949.78	0.343830
$319$	546.327	0.0958886
$320$	1676.66	0.292900
$321$	2339.90	0.406855
$322$	1851.85	0.320496
$323$	0	0
$324$	821.991	0.140945
$325$	5968.97	1.01877
$326$	−7182.35	−1.22023
$327$	1670.50	0.282504
$328$	−5002.15	−0.842066
$329$	−917.553	−0.153758
$330$	−856.623	−0.142896
$331$	−89.8427	−0.0149190	−0.00745952	−	0.999972i	$-0.502374\pi$
$331$	−89.8427	−0.0149190	−0.00745952	+	0.999972i	$0.502374\pi$
$332$	706.532	0.116795
$333$	−3519.01	−0.579101
$334$	−5209.00	−0.853364
$335$	3661.47	0.597156
$336$	−420.190	−0.0682240
$337$	−847.308	−0.136961	−0.0684804	−	0.997652i	$-0.521815\pi$
$337$	−847.308	−0.136961	−0.0684804	+	0.997652i	$0.521815\pi$
$338$	4323.56	0.695772
$339$	−4036.15	−0.646648
$340$	0	0
$341$	−3641.60	−0.578309
$342$	−2415.56	−0.381926
$343$	1889.02	0.297369
$344$	6052.48	0.948628
$345$	2102.94	0.328170
$346$	6970.55	1.08306
$347$	590.322	0.0913260	0.0456630	−	0.998957i	$-0.485460\pi$
$347$	590.322	0.0913260	0.0456630	+	0.998957i	$0.485460\pi$
$348$	−77.5026	−0.0119384
$349$	9387.68	1.43986	0.719930	−	0.694047i	$-0.244174\pi$
$349$	9387.68	1.43986	0.719930	+	0.694047i	$0.244174\pi$
$350$	877.471	0.134008
$351$	−5951.87	−0.905092
$352$	−2344.03	−0.354936
$353$	−6176.09	−0.931218	−0.465609	−	0.884990i	$-0.654165\pi$
$353$	−6176.09	−0.931218	−0.465609	+	0.884990i	$0.654165\pi$
$354$	343.687	0.0516009
$355$	3150.68	0.471045
$356$	−372.804	−0.0555015
$357$	0	0
$358$	65.4382	0.00966066
$359$	7151.14	1.05132	0.525658	−	0.850696i	$-0.323819\pi$
$359$	7151.14	1.05132	0.525658	+	0.850696i	$0.323819\pi$
$360$	2203.58	0.322608
$361$	−5752.74	−0.838714
$362$	−1376.24	−0.199817
$363$	1172.31	0.169505
$364$	322.910	0.0464975
$365$	2486.18	0.356528
$366$	5140.66	0.734171
$367$	−3358.05	−0.477626	−0.238813	−	0.971066i	$-0.576758\pi$
$367$	−3358.05	−0.477626	−0.238813	+	0.971066i	$0.576758\pi$
$368$	15976.6	2.26314
$369$	−6031.32	−0.850888
$370$	2412.05	0.338910
$371$	864.905	0.121034
$372$	516.600	0.0720013
$373$	8379.14	1.16315	0.581576	−	0.813492i	$-0.302436\pi$
$373$	8379.14	1.16315	0.581576	+	0.813492i	$0.302436\pi$
$374$	0	0
$375$	2242.95	0.308868
$376$	−6293.64	−0.863217
$377$	−1197.82	−0.163636
$378$	−874.957	−0.119055
$379$	−6395.71	−0.866821	−0.433411	−	0.901196i	$-0.642690\pi$
$379$	−6395.71	−0.866821	−0.433411	+	0.901196i	$0.642690\pi$
$380$	323.266	0.0436400
$381$	3186.81	0.428518
$382$	2483.89	0.332689
$383$	−204.687	−0.0273081	−0.0136541	−	0.999907i	$-0.504346\pi$
$383$	−204.687	−0.0273081	−0.0136541	+	0.999907i	$0.504346\pi$
$384$	−3472.85	−0.461518
$385$	−379.991	−0.0503017
$386$	11750.5	1.54944
$387$	7297.75	0.958567
$388$	2620.59	0.342887
$389$	5770.56	0.752131	0.376066	−	0.926593i	$-0.377277\pi$
$389$	5770.56	0.752131	0.376066	+	0.926593i	$0.377277\pi$
$390$	1878.14	0.243854
$391$	0	0
$392$	6404.44	0.825186
$393$	−5207.61	−0.668420
$394$	1424.76	0.182178
$395$	−450.816	−0.0574253
$396$	−1218.06	−0.154571
$397$	7144.37	0.903188	0.451594	−	0.892223i	$-0.350855\pi$
$397$	7144.37	0.903188	0.451594	+	0.892223i	$0.350855\pi$
$398$	−10972.7	−1.38194
$399$	184.474	0.0231459
$400$	7570.24	0.946280
$401$	−6364.52	−0.792591	−0.396296	−	0.918123i	$-0.629704\pi$
$401$	−6364.52	−0.792591	−0.396296	+	0.918123i	$0.629704\pi$
$402$	−4590.84	−0.569578
$403$	7984.16	0.986897
$404$	−590.070	−0.0726660
$405$	2120.78	0.260204
$406$	−176.086	−0.0215246
$407$	4162.33	0.506926
$408$	0	0
$409$	2997.87	0.362433	0.181217	−	0.983443i	$-0.441997\pi$
$409$	2997.87	0.362433	0.181217	+	0.983443i	$0.441997\pi$
$410$	4134.07	0.497969
$411$	−1485.00	−0.178222
$412$	1918.60	0.229424
$413$	152.457	0.0181644
$414$	15315.5	1.81816
$415$	1822.89	0.215620
$416$	5139.27	0.605705
$417$	5043.08	0.592232
$418$	2857.15	0.334325
$419$	−11747.3	−1.36967	−0.684835	−	0.728698i	$-0.740126\pi$
$419$	−11747.3	−1.36967	−0.684835	+	0.728698i	$0.740126\pi$
$420$	53.9060	0.00626272
$421$	8842.15	1.02361	0.511805	−	0.859102i	$-0.328977\pi$
$421$	8842.15	1.02361	0.511805	+	0.859102i	$0.328977\pi$
$422$	−5733.60	−0.661391
$423$	−7588.52	−0.872261
$424$	5932.52	0.679501
$425$	0	0
$426$	−3950.41	−0.449291
$427$	2280.36	0.258441
$428$	−2280.57	−0.257560
$429$	3240.98	0.364746
$430$	−5002.13	−0.560987
$431$	3099.38	0.346385	0.173192	−	0.984888i	$-0.444592\pi$
$431$	3099.38	0.346385	0.173192	+	0.984888i	$0.444592\pi$
$432$	−7548.55	−0.840694
$433$	10072.8	1.11794	0.558970	−	0.829188i	$-0.311197\pi$
$433$	10072.8	1.11794	0.558970	+	0.829188i	$0.311197\pi$
$434$	1173.72	0.129816
$435$	−199.961	−0.0220400
$436$	−1628.14	−0.178839
$437$	−7014.09	−0.767802
$438$	−3117.24	−0.340063
$439$	17357.9	1.88712	0.943561	−	0.331199i	$-0.107453\pi$
$439$	17357.9	1.88712	0.943561	+	0.331199i	$0.107453\pi$
$440$	−2606.42	−0.282400
$441$	7722.12	0.833832
$442$	0	0
$443$	6979.90	0.748589	0.374295	−	0.927310i	$-0.377885\pi$
$443$	6979.90	0.748589	0.374295	+	0.927310i	$0.377885\pi$
$444$	−590.472	−0.0631139
$445$	−961.855	−0.102464
$446$	−20518.7	−2.17845
$447$	3617.74	0.382804
$448$	−932.533	−0.0983439
$449$	9230.50	0.970188	0.485094	−	0.874462i	$-0.338785\pi$
$449$	9230.50	0.970188	0.485094	+	0.874462i	$0.338785\pi$
$450$	7257.03	0.760221
$451$	7133.91	0.744840
$452$	3933.81	0.409361
$453$	4222.72	0.437970
$454$	−7652.64	−0.791093
$455$	833.127	0.0858409
$456$	1265.33	0.129944
$457$	12250.6	1.25396	0.626979	−	0.779036i	$-0.284291\pi$
$457$	12250.6	1.25396	0.626979	+	0.779036i	$0.284291\pi$
$458$	2067.39	0.210923
$459$	0	0
$460$	−2049.62	−0.207748
$461$	6259.50	0.632395	0.316198	−	0.948693i	$-0.397594\pi$
$461$	6259.50	0.632395	0.316198	+	0.948693i	$0.397594\pi$
$462$	476.442	0.0479786
$463$	10195.0	1.02333	0.511665	−	0.859185i	$-0.329029\pi$
$463$	10195.0	1.02333	0.511665	+	0.859185i	$0.329029\pi$
$464$	−1519.15	−0.151993
$465$	1332.86	0.132924
$466$	−3694.28	−0.367241
$467$	−14783.0	−1.46483	−0.732417	−	0.680856i	$-0.761608\pi$
$467$	−14783.0	−1.46483	−0.732417	+	0.680856i	$0.761608\pi$
$468$	2670.59	0.263778
$469$	−2036.46	−0.200501
$470$	5201.43	0.510477
$471$	3201.79	0.313229
$472$	1045.72	0.101977
$473$	−8631.86	−0.839098
$474$	565.244	0.0547732
$475$	−3323.52	−0.321039
$476$	0	0
$477$	7153.10	0.686620
$478$	−16650.7	−1.59328
$479$	−16370.0	−1.56152	−0.780758	−	0.624834i	$-0.785167\pi$
$479$	−16370.0	−1.56152	−0.780758	+	0.624834i	$0.785167\pi$
$480$	857.939	0.0815820
$481$	−9125.87	−0.865081
$482$	4186.57	0.395629
$483$	−1169.63	−0.110186
$484$	−1142.58	−0.107305
$485$	6761.26	0.633017
$486$	−11141.1	−1.03986
$487$	−4106.31	−0.382084	−0.191042	−	0.981582i	$-0.561187\pi$
$487$	−4106.31	−0.382084	−0.191042	+	0.981582i	$0.561187\pi$
$488$	15641.3	1.45092
$489$	4536.37	0.419513
$490$	−5293.01	−0.487987
$491$	−878.001	−0.0806999	−0.0403499	−	0.999186i	$-0.512847\pi$
$491$	−878.001	−0.0806999	−0.0403499	+	0.999186i	$0.512847\pi$
$492$	−1012.02	−0.0927349
$493$	0	0
$494$	−6264.28	−0.570533
$495$	−3142.68	−0.285359
$496$	10126.0	0.916679
$497$	−1752.37	−0.158158
$498$	−2285.59	−0.205662
$499$	−13819.6	−1.23978	−0.619892	−	0.784687i	$-0.712824\pi$
$499$	−13819.6	−1.23978	−0.619892	+	0.784687i	$0.712824\pi$
$500$	−2186.08	−0.195529
$501$	3290.00	0.293386
$502$	−13495.7	−1.19989
$503$	4721.43	0.418525	0.209263	−	0.977859i	$-0.432894\pi$
$503$	4721.43	0.418525	0.209263	+	0.977859i	$0.432894\pi$
$504$	−1225.60	−0.108319
$505$	−1522.41	−0.134152
$506$	−18115.4	−1.59156
$507$	−2730.76	−0.239206
$508$	−3106.01	−0.271273
$509$	−16554.3	−1.44156	−0.720782	−	0.693161i	$-0.756217\pi$
$509$	−16554.3	−1.44156	−0.720782	+	0.693161i	$0.756217\pi$
$510$	0	0
$511$	−1382.78	−0.119708
$512$	−5060.53	−0.436808
$513$	3314.00	0.285217
$514$	765.813	0.0657171
$515$	4950.09	0.423548
$516$	1224.53	0.104470
$517$	8975.79	0.763548
$518$	−1341.55	−0.113792
$519$	−4402.60	−0.372356
$520$	5714.55	0.481922
$521$	14755.5	1.24079	0.620394	−	0.784290i	$-0.286973\pi$
$521$	14755.5	1.24079	0.620394	+	0.784290i	$0.286973\pi$
$522$	−1456.30	−0.122108
$523$	7800.86	0.652214	0.326107	−	0.945333i	$-0.394263\pi$
$523$	7800.86	0.652214	0.326107	+	0.945333i	$0.394263\pi$
$524$	5075.57	0.423144
$525$	−554.210	−0.0460719
$526$	−9942.71	−0.824188
$527$	0	0
$528$	4110.43	0.338795
$529$	32304.9	2.65512
$530$	−4902.98	−0.401834
$531$	1260.88	0.103046
$532$	−179.796	−0.0146525
$533$	−15641.0	−1.27108
$534$	1206.00	0.0977315
$535$	−5884.01	−0.475491
$536$	−13968.4	−1.12564
$537$	−41.3307	−0.00332133
$538$	664.944	0.0532859
$539$	−9133.81	−0.729909
$540$	968.399	0.0771727
$541$	−23028.5	−1.83007	−0.915037	−	0.403369i	$-0.867839\pi$
$541$	−23028.5	−1.83007	−0.915037	+	0.403369i	$0.867839\pi$
$542$	−5130.95	−0.406629
$543$	869.235	0.0686970
$544$	0	0
$545$	−4200.71	−0.330162
$546$	−1044.60	−0.0818765
$547$	−2641.77	−0.206497	−0.103249	−	0.994656i	$-0.532924\pi$
$547$	−2641.77	−0.206497	−0.103249	+	0.994656i	$0.532924\pi$
$548$	1447.34	0.112824
$549$	18859.4	1.46612
$550$	−8583.69	−0.665473
$551$	666.944	0.0515658
$552$	−8022.67	−0.618601
$553$	250.738	0.0192811
$554$	14588.2	1.11876
$555$	−1523.45	−0.116517
$556$	−4915.21	−0.374913
$557$	−19800.8	−1.50626	−0.753129	−	0.657873i	$-0.771456\pi$
$557$	−19800.8	−1.50626	−0.753129	+	0.657873i	$0.771456\pi$
$558$	9707.08	0.736440
$559$	18925.3	1.43194
$560$	1056.63	0.0797333
$561$	0	0
$562$	−16005.1	−1.20131
$563$	−9733.93	−0.728661	−0.364331	−	0.931270i	$-0.618702\pi$
$563$	−9733.93	−0.728661	−0.364331	+	0.931270i	$0.618702\pi$
$564$	−1273.31	−0.0950642
$565$	10149.5	0.755736
$566$	7683.80	0.570626
$567$	−1179.55	−0.0873660
$568$	−12019.8	−0.887919
$569$	6340.67	0.467161	0.233581	−	0.972337i	$-0.424956\pi$
$569$	6340.67	0.467161	0.233581	+	0.972337i	$0.424956\pi$
$570$	−1045.75	−0.0768447
$571$	12377.7	0.907166	0.453583	−	0.891214i	$-0.350146\pi$
$571$	12377.7	0.907166	0.453583	+	0.891214i	$0.350146\pi$
$572$	−3158.81	−0.230903
$573$	−1568.83	−0.114378
$574$	−2299.32	−0.167198
$575$	21072.3	1.52831
$576$	−7712.41	−0.557900
$577$	−36.6040	−0.00264098	−0.00132049	−	0.999999i	$-0.500420\pi$
$577$	−36.6040	−0.00264098	−0.00132049	+	0.999999i	$0.500420\pi$
$578$	0	0
$579$	−7421.61	−0.532697
$580$	194.891	0.0139524
$581$	−1013.87	−0.0723965
$582$	−8477.44	−0.603782
$583$	−8460.77	−0.601045
$584$	−9484.72	−0.672055
$585$	6890.29	0.486971
$586$	−10405.6	−0.733534
$587$	−20350.4	−1.43092	−0.715462	−	0.698651i	$-0.753784\pi$
$587$	−20350.4	−1.43092	−0.715462	+	0.698651i	$0.753784\pi$
$588$	1295.73	0.0908760
$589$	−4445.58	−0.310996
$590$	−864.248	−0.0603060
$591$	−899.876	−0.0626328
$592$	−11574.0	−0.803530
$593$	−20387.4	−1.41182	−0.705910	−	0.708301i	$-0.749462\pi$
$593$	−20387.4	−1.41182	−0.705910	+	0.708301i	$0.749462\pi$
$594$	8559.10	0.591219
$595$	0	0
$596$	−3526.02	−0.242334
$597$	6930.33	0.475108
$598$	39717.8	2.71603
$599$	316.417	0.0215834	0.0107917	−	0.999942i	$-0.496565\pi$
$599$	316.417	0.0215834	0.0107917	+	0.999942i	$0.496565\pi$
$600$	−3801.41	−0.258653
$601$	1331.85	0.0903950	0.0451975	−	0.998978i	$-0.485608\pi$
$601$	1331.85	0.0903950	0.0451975	+	0.998978i	$0.485608\pi$
$602$	2782.12	0.188357
$603$	−16842.3	−1.13743
$604$	−4115.65	−0.277257
$605$	−2947.93	−0.198100
$606$	1908.84	0.127956
$607$	13873.2	0.927668	0.463834	−	0.885922i	$-0.346473\pi$
$607$	13873.2	0.927668	0.463834	+	0.885922i	$0.346473\pi$
$608$	−2861.54	−0.190873
$609$	111.216	0.00740014
$610$	−12926.9	−0.858025
$611$	−19679.3	−1.30301
$612$	0	0
$613$	15297.0	1.00790	0.503948	−	0.863734i	$-0.331880\pi$
$613$	15297.0	1.00790	0.503948	+	0.863734i	$0.331880\pi$
$614$	−3740.61	−0.245861
$615$	−2611.08	−0.171201
$616$	1449.66	0.0948186
$617$	15116.8	0.986354	0.493177	−	0.869929i	$-0.335835\pi$
$617$	15116.8	0.986354	0.493177	+	0.869929i	$0.335835\pi$
$618$	−6206.55	−0.403987
$619$	22412.1	1.45528	0.727639	−	0.685960i	$-0.240618\pi$
$619$	22412.1	1.45528	0.727639	+	0.685960i	$0.240618\pi$
$620$	−1299.06	−0.0841479
$621$	−21011.9	−1.35778
$622$	−2072.96	−0.133630
$623$	534.971	0.0344031
$624$	−9012.08	−0.578160
$625$	6850.26	0.438417
$626$	−19149.7	−1.22265
$627$	−1804.58	−0.114941
$628$	−3120.61	−0.198290
$629$	0	0
$630$	1012.91	0.0640560
$631$	−4830.94	−0.304781	−0.152390	−	0.988320i	$-0.548697\pi$
$631$	−4830.94	−0.304781	−0.152390	+	0.988320i	$0.548697\pi$
$632$	1719.85	0.108247
$633$	3621.34	0.227386
$634$	18139.6	1.13630
$635$	−8013.68	−0.500808
$636$	1200.25	0.0748320
$637$	20025.8	1.24561
$638$	1722.53	0.106889
$639$	−14492.8	−0.897222
$640$	8732.96	0.539376
$641$	−23007.3	−1.41768	−0.708839	−	0.705370i	$-0.750781\pi$
$641$	−23007.3	−1.41768	−0.708839	+	0.705370i	$0.750781\pi$
$642$	7377.52	0.453532
$643$	5689.90	0.348970	0.174485	−	0.984660i	$-0.444174\pi$
$643$	5689.90	0.348970	0.174485	+	0.984660i	$0.444174\pi$
$644$	1139.97	0.0697535
$645$	3159.35	0.192867
$646$	0	0
$647$	−15949.0	−0.969122	−0.484561	−	0.874758i	$-0.661021\pi$
$647$	−15949.0	−0.969122	−0.484561	+	0.874758i	$0.661021\pi$
$648$	−8090.72	−0.490484
$649$	−1491.38	−0.0902029
$650$	18819.7	1.13564
$651$	−741.318	−0.0446307
$652$	−4421.35	−0.265573
$653$	−10764.6	−0.645101	−0.322550	−	0.946552i	$-0.604540\pi$
$653$	−10764.6	−0.645101	−0.322550	+	0.946552i	$0.604540\pi$
$654$	5266.95	0.314914
$655$	13095.3	0.781182
$656$	−19837.0	−1.18065
$657$	−11436.1	−0.679097
$658$	−2892.97	−0.171398
$659$	25208.2	1.49010	0.745048	−	0.667011i	$-0.232427\pi$
$659$	25208.2	1.49010	0.745048	+	0.667011i	$0.232427\pi$
$660$	−527.325	−0.0311001
$661$	14419.5	0.848492	0.424246	−	0.905547i	$-0.360539\pi$
$661$	14419.5	0.848492	0.424246	+	0.905547i	$0.360539\pi$
$662$	−283.267	−0.0166306
$663$	0	0
$664$	−6954.28	−0.406444
$665$	−463.885	−0.0270506
$666$	−11095.2	−0.645539
$667$	−4228.67	−0.245479
$668$	−3206.58	−0.185728
$669$	12959.6	0.748948
$670$	11544.3	0.665665
$671$	−22307.2	−1.28339
$672$	−477.174	−0.0273920
$673$	−2110.64	−0.120890	−0.0604451	−	0.998172i	$-0.519252\pi$
$673$	−2110.64	−0.120890	−0.0604451	+	0.998172i	$0.519252\pi$
$674$	−2671.49	−0.152674
$675$	−9956.17	−0.567723
$676$	2661.52	0.151429
$677$	11944.5	0.678087	0.339043	−	0.940771i	$-0.389897\pi$
$677$	11944.5	0.678087	0.339043	+	0.940771i	$0.389897\pi$
$678$	−12725.6	−0.720834
$679$	−3760.52	−0.212541
$680$	0	0
$681$	4833.41	0.271977
$682$	−11481.6	−0.644656
$683$	19085.8	1.06925	0.534626	−	0.845089i	$-0.320453\pi$
$683$	19085.8	1.06925	0.534626	+	0.845089i	$0.320453\pi$
$684$	−1486.98	−0.0831232
$685$	3734.23	0.208288
$686$	5955.92	0.331484
$687$	−1305.76	−0.0725152
$688$	24002.3	1.33006
$689$	18550.2	1.02570
$690$	6630.41	0.365819
$691$	−28316.8	−1.55893	−0.779465	−	0.626445i	$-0.784509\pi$
$691$	−28316.8	−1.55893	−0.779465	+	0.626445i	$0.784509\pi$
$692$	4290.97	0.235720
$693$	1747.91	0.0958121
$694$	1861.24	0.101803
$695$	−12681.5	−0.692141
$696$	762.846	0.0415454
$697$	0	0
$698$	29598.6	1.60505
$699$	2333.31	0.126257
$700$	540.158	0.0291658
$701$	−5916.75	−0.318791	−0.159396	−	0.987215i	$-0.550955\pi$
$701$	−5916.75	−0.318791	−0.159396	+	0.987215i	$0.550955\pi$
$702$	−18765.8	−1.00893
$703$	5081.28	0.272609
$704$	9122.33	0.488368
$705$	−3285.22	−0.175502
$706$	−19472.7	−1.03805
$707$	846.747	0.0450427
$708$	211.568	0.0112305
$709$	−18499.8	−0.979936	−0.489968	−	0.871740i	$-0.662992\pi$
$709$	−18499.8	−0.979936	−0.489968	+	0.871740i	$0.662992\pi$
$710$	9933.85	0.525085
$711$	2073.70	0.109381
$712$	3669.45	0.193144
$713$	28186.6	1.48050
$714$	0	0
$715$	−8149.91	−0.426279
$716$	40.2828	0.00210257
$717$	10516.6	0.547768
$718$	22546.9	1.17193
$719$	−22206.5	−1.15182	−0.575912	−	0.817511i	$-0.695353\pi$
$719$	−22206.5	−1.15182	−0.575912	+	0.817511i	$0.695353\pi$
$720$	8738.72	0.452323
$721$	−2753.18	−0.142210
$722$	−18137.9	−0.934935
$723$	−2644.24	−0.136017
$724$	−847.195	−0.0434886
$725$	−2003.69	−0.102641
$726$	3696.19	0.188951
$727$	3777.02	0.192685	0.0963424	−	0.995348i	$-0.469286\pi$
$727$	3777.02	0.192685	0.0963424	+	0.995348i	$0.469286\pi$
$728$	−3178.36	−0.161810
$729$	−4398.10	−0.223447
$730$	7838.73	0.397431
$731$	0	0
$732$	3164.52	0.159787
$733$	−19956.4	−1.00560	−0.502801	−	0.864402i	$-0.667697\pi$
$733$	−19956.4	−1.00560	−0.502801	+	0.864402i	$0.667697\pi$
$734$	−10587.7	−0.532422
$735$	3343.06	0.167770
$736$	18143.2	0.908652
$737$	19921.3	0.995671
$738$	−19016.2	−0.948506
$739$	23268.4	1.15824	0.579121	−	0.815241i	$-0.303396\pi$
$739$	23268.4	1.15824	0.579121	+	0.815241i	$0.303396\pi$
$740$	1484.83	0.0737612
$741$	3956.52	0.196149
$742$	2726.97	0.134920
$743$	12587.1	0.621502	0.310751	−	0.950491i	$-0.399420\pi$
$743$	12587.1	0.621502	0.310751	+	0.950491i	$0.399420\pi$
$744$	−5084.82	−0.250562
$745$	−9097.32	−0.447383
$746$	26418.7	1.29659
$747$	−8385.09	−0.410702
$748$	0	0
$749$	3272.61	0.159651
$750$	7071.85	0.344303
$751$	2662.79	0.129383	0.0646914	−	0.997905i	$-0.479394\pi$
$751$	2662.79	0.129383	0.0646914	+	0.997905i	$0.479394\pi$
$752$	−24958.6	−1.21030
$753$	8523.89	0.412520
$754$	−3776.62	−0.182409
$755$	−10618.6	−0.511855
$756$	−538.611	−0.0259115
$757$	26430.2	1.26899	0.634493	−	0.772929i	$-0.281209\pi$
$757$	26430.2	1.26899	0.634493	+	0.772929i	$0.281209\pi$
$758$	−20165.1	−0.966267
$759$	11441.7	0.547176
$760$	−3181.86	−0.151866
$761$	−8469.75	−0.403454	−0.201727	−	0.979442i	$-0.564655\pi$
$761$	−8469.75	−0.403454	−0.201727	+	0.979442i	$0.564655\pi$
$762$	10047.8	0.477680
$763$	2336.38	0.110855
$764$	1529.05	0.0724071
$765$	0	0
$766$	−645.361	−0.0304410
$767$	3269.83	0.153933
$768$	−5615.54	−0.263846
$769$	−8452.54	−0.396367	−0.198184	−	0.980165i	$-0.563504\pi$
$769$	−8452.54	−0.396367	−0.198184	+	0.980165i	$0.563504\pi$
$770$	−1198.08	−0.0560725
$771$	−483.687	−0.0225935
$772$	7233.43	0.337224
$773$	33936.2	1.57904	0.789521	−	0.613724i	$-0.210329\pi$
$773$	33936.2	1.57904	0.789521	+	0.613724i	$0.210329\pi$
$774$	23009.2	1.06854
$775$	13355.8	0.619036
$776$	−25794.0	−1.19324
$777$	847.324	0.0391217
$778$	18194.1	0.838419
$779$	8708.91	0.400551
$780$	1156.15	0.0530730
$781$	17142.2	0.785399
$782$	0	0
$783$	1997.95	0.0911887
$784$	25398.0	1.15698
$785$	−8051.35	−0.366070
$786$	−16419.2	−0.745105
$787$	−34379.1	−1.55716	−0.778578	−	0.627547i	$-0.784059\pi$
$787$	−34379.1	−1.55716	−0.778578	+	0.627547i	$0.784059\pi$
$788$	877.059	0.0396497
$789$	6279.81	0.283355
$790$	−1421.39	−0.0640134
$791$	−5645.00	−0.253746
$792$	11989.2	0.537902
$793$	48908.2	2.19014
$794$	22525.6	1.00681
$795$	3096.72	0.138150
$796$	−6754.61	−0.300768
$797$	−3329.26	−0.147965	−0.0739826	−	0.997260i	$-0.523571\pi$
$797$	−3329.26	−0.147965	−0.0739826	+	0.997260i	$0.523571\pi$
$798$	581.630	0.0258014
$799$	0	0
$800$	8596.87	0.379932
$801$	4424.42	0.195167
$802$	−20066.8	−0.883521
$803$	13526.8	0.594459
$804$	−2826.05	−0.123964
$805$	2941.20	0.128775
$806$	25173.4	1.10012
$807$	−419.979	−0.0183196
$808$	5807.97	0.252876
$809$	−7217.64	−0.313670	−0.156835	−	0.987625i	$-0.550129\pi$
$809$	−7217.64	−0.313670	−0.156835	+	0.987625i	$0.550129\pi$
$810$	6686.66	0.290056
$811$	36564.1	1.58316	0.791579	−	0.611067i	$-0.209259\pi$
$811$	36564.1	1.58316	0.791579	+	0.611067i	$0.209259\pi$
$812$	−108.396	−0.00468466
$813$	3240.70	0.139799
$814$	13123.5	0.565083
$815$	−11407.3	−0.490284
$816$	0	0
$817$	−10537.6	−0.451240
$818$	9452.04	0.404013
$819$	−3832.29	−0.163505
$820$	2544.88	0.108379
$821$	23140.5	0.983691	0.491845	−	0.870683i	$-0.336323\pi$
$821$	23140.5	0.983691	0.491845	+	0.870683i	$0.336323\pi$
$822$	−4682.07	−0.198669
$823$	−41287.9	−1.74873	−0.874365	−	0.485269i	$-0.838722\pi$
$823$	−41287.9	−1.74873	−0.874365	+	0.485269i	$0.838722\pi$
$824$	−18884.5	−0.798388
$825$	5421.46	0.228789
$826$	480.683	0.0202483
$827$	−10008.0	−0.420811	−0.210405	−	0.977614i	$-0.567478\pi$
$827$	−10008.0	−0.420811	−0.210405	+	0.977614i	$0.567478\pi$
$828$	9428.02	0.395708
$829$	−44643.6	−1.87037	−0.935185	−	0.354159i	$-0.884767\pi$
$829$	−44643.6	−1.87037	−0.935185	+	0.354159i	$0.884767\pi$
$830$	5747.43	0.240357
$831$	−9213.90	−0.384629
$832$	−20000.6	−0.833410
$833$	0	0
$834$	15900.4	0.660176
$835$	−8273.17	−0.342880
$836$	1758.82	0.0727633
$837$	−13317.5	−0.549964
$838$	−37038.2	−1.52681
$839$	14235.3	0.585765	0.292882	−	0.956148i	$-0.405386\pi$
$839$	14235.3	0.585765	0.292882	+	0.956148i	$0.405386\pi$
$840$	−530.588	−0.0217941
$841$	−23986.9	−0.983514
$842$	27878.6	1.14104
$843$	10108.8	0.413008
$844$	−3529.52	−0.143947
$845$	6866.88	0.279560
$846$	−23926.0	−0.972331
$847$	1639.60	0.0665140
$848$	23526.5	0.952717
$849$	−4853.08	−0.196181
$850$	0	0
$851$	−32217.1	−1.29775
$852$	−2431.81	−0.0977846
$853$	−27729.0	−1.11304	−0.556520	−	0.830834i	$-0.687864\pi$
$853$	−27729.0	−1.11304	−0.556520	+	0.830834i	$0.687864\pi$
$854$	7189.78	0.288090
$855$	−3836.51	−0.153457
$856$	22447.3	0.896301
$857$	−31280.7	−1.24682	−0.623411	−	0.781894i	$-0.714254\pi$
$857$	−31280.7	−1.24682	−0.623411	+	0.781894i	$0.714254\pi$
$858$	10218.6	0.406592
$859$	−55.2890	−0.00219608	−0.00109804	−	0.999999i	$-0.500350\pi$
$859$	−55.2890	−0.00219608	−0.00109804	+	0.999999i	$0.500350\pi$
$860$	−3079.24	−0.122094
$861$	1452.25	0.0574826
$862$	9772.09	0.386124
$863$	−22900.4	−0.903291	−0.451646	−	0.892197i	$-0.649163\pi$
$863$	−22900.4	−0.903291	−0.451646	+	0.892197i	$0.649163\pi$
$864$	−8572.25	−0.337539
$865$	11070.9	0.435172
$866$	31758.7	1.24620
$867$	0	0
$868$	722.522	0.0282535
$869$	−2452.79	−0.0957484
$870$	−630.461	−0.0245685
$871$	−43677.2	−1.69913
$872$	16025.6	0.622356
$873$	−31101.0	−1.20574
$874$	−22114.9	−0.855888
$875$	3137.02	0.121201
$876$	−1918.93	−0.0740120
$877$	−1782.50	−0.0686326	−0.0343163	−	0.999411i	$-0.510925\pi$
$877$	−1782.50	−0.0686326	−0.0343163	+	0.999411i	$0.510925\pi$
$878$	54728.0	2.10362
$879$	6572.17	0.252189
$880$	−10336.3	−0.395949
$881$	−17232.6	−0.659001	−0.329500	−	0.944155i	$-0.606880\pi$
$881$	−17232.6	−0.659001	−0.329500	+	0.944155i	$0.606880\pi$
$882$	24347.2	0.929493
$883$	10188.2	0.388291	0.194145	−	0.980973i	$-0.437807\pi$
$883$	10188.2	0.388291	0.194145	+	0.980973i	$0.437807\pi$
$884$	0	0
$885$	545.859	0.0207332
$886$	22007.1	0.834471
$887$	−15671.6	−0.593238	−0.296619	−	0.954996i	$-0.595859\pi$
$887$	−15671.6	−0.593238	−0.296619	+	0.954996i	$0.595859\pi$
$888$	5811.93	0.219635
$889$	4457.10	0.168151
$890$	−3032.65	−0.114219
$891$	11538.7	0.433852
$892$	−12631.0	−0.474122
$893$	10957.4	0.410612
$894$	11406.4	0.426721
$895$	103.932	0.00388163
$896$	−4857.16	−0.181101
$897$	−25085.8	−0.933768
$898$	29103.0	1.08149
$899$	−2680.15	−0.0994307
$900$	4467.32	0.165456
$901$	0	0
$902$	22492.6	0.830291
$903$	−1757.19	−0.0647569
$904$	−38719.9	−1.42456
$905$	−2185.81	−0.0802861
$906$	13313.9	0.488216
$907$	16908.3	0.618999	0.309500	−	0.950900i	$-0.399838\pi$
$907$	16908.3	0.618999	0.309500	+	0.950900i	$0.399838\pi$
$908$	−4710.86	−0.172175
$909$	7002.92	0.255525
$910$	2626.78	0.0956890
$911$	36100.6	1.31292	0.656458	−	0.754362i	$-0.272054\pi$
$911$	36100.6	1.31292	0.656458	+	0.754362i	$0.272054\pi$
$912$	5017.92	0.182193
$913$	9917.98	0.359515
$914$	38625.1	1.39782
$915$	8164.63	0.294988
$916$	1272.65	0.0459057
$917$	−7283.41	−0.262290
$918$	0	0
$919$	20016.2	0.718470	0.359235	−	0.933247i	$-0.383038\pi$
$919$	20016.2	0.718470	0.359235	+	0.933247i	$0.383038\pi$
$920$	20174.1	0.722958
$921$	2362.57	0.0845269
$922$	19735.7	0.704947
$923$	−37584.1	−1.34030
$924$	293.291	0.0104422
$925$	−15265.6	−0.542626
$926$	32144.0	1.14073
$927$	−22769.8	−0.806753
$928$	−1725.17	−0.0610253
$929$	−30630.3	−1.08175	−0.540875	−	0.841103i	$-0.681907\pi$
$929$	−30630.3	−1.08175	−0.540875	+	0.841103i	$0.681907\pi$
$930$	4202.40	0.148174
$931$	−11150.3	−0.392522
$932$	−2274.15	−0.0799272
$933$	1309.28	0.0459420
$934$	−46609.7	−1.63289
$935$	0	0
$936$	−26286.2	−0.917941
$937$	3883.68	0.135405	0.0677025	−	0.997706i	$-0.478433\pi$
$937$	3883.68	0.135405	0.0677025	+	0.997706i	$0.478433\pi$
$938$	−6420.79	−0.223503
$939$	12095.0	0.420346
$940$	3201.93	0.111101
$941$	21696.0	0.751613	0.375807	−	0.926698i	$-0.377366\pi$
$941$	21696.0	0.751613	0.375807	+	0.926698i	$0.377366\pi$
$942$	10095.0	0.349164
$943$	−55217.7	−1.90682
$944$	4147.02	0.142981
$945$	−1389.65	−0.0478362
$946$	−27215.6	−0.935364
$947$	−15904.8	−0.545763	−0.272882	−	0.962048i	$-0.587977\pi$
$947$	−15904.8	−0.545763	−0.272882	+	0.962048i	$0.587977\pi$
$948$	347.956	0.0119210
$949$	−29657.4	−1.01446
$950$	−10478.8	−0.357870
$951$	−11456.9	−0.390659
$952$	0	0
$953$	−81.8493	−0.00278212	−0.00139106	−	0.999999i	$-0.500443\pi$
$953$	−81.8493	−0.00278212	−0.00139106	+	0.999999i	$0.500443\pi$
$954$	22553.1	0.765393
$955$	3945.03	0.133674
$956$	−10250.0	−0.346765
$957$	−1087.95	−0.0367485
$958$	−51613.4	−1.74066
$959$	−2076.93	−0.0699348
$960$	−3338.86	−0.112251
$961$	−11926.2	−0.400328
$962$	−28773.1	−0.964327
$963$	27065.7	0.905692
$964$	2577.19	0.0861056
$965$	18662.7	0.622562
$966$	−3687.75	−0.122827
$967$	−19279.7	−0.641151	−0.320576	−	0.947223i	$-0.603876\pi$
$967$	−19279.7	−0.641151	−0.320576	+	0.947223i	$0.603876\pi$
$968$	11246.3	0.373419
$969$	0	0
$970$	21317.7	0.705639
$971$	−53776.3	−1.77731	−0.888653	−	0.458581i	$-0.848358\pi$
$971$	−53776.3	−1.77731	−0.888653	+	0.458581i	$0.848358\pi$
$972$	−6858.31	−0.226317
$973$	7053.30	0.232393
$974$	−12946.9	−0.425918
$975$	−11886.5	−0.390433
$976$	62028.6	2.03431
$977$	54738.2	1.79246	0.896228	−	0.443594i	$-0.146297\pi$
$977$	54738.2	1.79246	0.896228	+	0.443594i	$0.146297\pi$
$978$	14302.8	0.467641
$979$	−5233.25	−0.170843
$980$	−3258.30	−0.106207
$981$	19322.7	0.628876
$982$	−2768.27	−0.0899581
$983$	3405.32	0.110491	0.0552456	−	0.998473i	$-0.482406\pi$
$983$	3405.32	0.110491	0.0552456	+	0.998473i	$0.482406\pi$
$984$	9961.19	0.322715
$985$	2262.86	0.0731988
$986$	0	0
$987$	1827.20	0.0589264
$988$	−3856.20	−0.124172
$989$	66812.1	2.14813
$990$	−9908.60	−0.318097
$991$	29925.7	0.959256	0.479628	−	0.877472i	$-0.340772\pi$
$991$	29925.7	0.959256	0.479628	+	0.877472i	$0.340772\pi$
$992$	11499.3	0.368047
$993$	178.911	0.00571759
$994$	−5525.07	−0.176302
$995$	−17427.3	−0.555259
$996$	−1406.98	−0.0447608
$997$	32714.5	1.03920	0.519598	−	0.854411i	$-0.326082\pi$
$997$	32714.5	1.03920	0.519598	+	0.854411i	$0.326082\pi$
$998$	−43572.2	−1.38202
$999$	15221.8	0.482080

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.g.1.11		12
17.3	odd	16		17.4.d.a.9.3	yes	12
17.4	even	4		289.4.b.e.288.2		12
17.6	odd	16		17.4.d.a.2.3	✓	12
17.13	even	4		289.4.b.e.288.1		12
17.16	even	2	inner	289.4.a.g.1.12		12
51.20	even	16		153.4.l.a.145.1		12
51.23	even	16		153.4.l.a.19.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.d.a.2.3	✓	12	17.6	odd	16
17.4.d.a.9.3	yes	12	17.3	odd	16
153.4.l.a.19.1		12	51.23	even	16
153.4.l.a.145.1		12	51.20	even	16
289.4.a.g.1.11		12	1.1	even	1	trivial
289.4.a.g.1.12		12	17.16	even	2	inner
289.4.b.e.288.1		12	17.13	even	4
289.4.b.e.288.2		12	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)

\(f(q)\)	\(=\)	\(q+3.15292 q^{2} -1.99138 q^{3} +1.94089 q^{4} +5.00761 q^{5} -6.27866 q^{6} -2.78516 q^{7} -19.1039 q^{8} -23.0344 q^{9} +O(q^{10})\)	\(q+3.15292 q^{2} -1.99138 q^{3} +1.94089 q^{4} +5.00761 q^{5} -6.27866 q^{6} -2.78516 q^{7} -19.1039 q^{8} -23.0344 q^{9} +15.7886 q^{10} +27.2453 q^{11} -3.86505 q^{12} -59.7352 q^{13} -8.78140 q^{14} -9.97206 q^{15} -75.7601 q^{16} -72.6256 q^{18} +33.2605 q^{19} +9.71922 q^{20} +5.54633 q^{21} +85.9023 q^{22} -210.884 q^{23} +38.0431 q^{24} -99.9239 q^{25} -188.340 q^{26} +99.6376 q^{27} -5.40570 q^{28} +20.0521 q^{29} -31.4411 q^{30} -133.659 q^{31} -86.0343 q^{32} -54.2559 q^{33} -13.9470 q^{35} -44.7072 q^{36} +152.772 q^{37} +104.868 q^{38} +118.956 q^{39} -95.6647 q^{40} +261.840 q^{41} +17.4871 q^{42} -316.820 q^{43} +52.8802 q^{44} -115.347 q^{45} -664.899 q^{46} +329.443 q^{47} +150.867 q^{48} -335.243 q^{49} -315.052 q^{50} -115.939 q^{52} -310.540 q^{53} +314.149 q^{54} +136.434 q^{55} +53.2074 q^{56} -66.2344 q^{57} +63.2227 q^{58} -54.7388 q^{59} -19.3547 q^{60} -818.751 q^{61} -421.417 q^{62} +64.1546 q^{63} +334.822 q^{64} -299.130 q^{65} -171.064 q^{66} +731.181 q^{67} +419.950 q^{69} -43.9738 q^{70} +629.179 q^{71} +440.046 q^{72} +496.481 q^{73} +481.678 q^{74} +198.987 q^{75} +64.5550 q^{76} -75.8828 q^{77} +375.057 q^{78} -90.0262 q^{79} -379.377 q^{80} +423.512 q^{81} +825.559 q^{82} +364.025 q^{83} +10.7648 q^{84} -998.907 q^{86} -39.9315 q^{87} -520.492 q^{88} -192.079 q^{89} -363.680 q^{90} +166.372 q^{91} -409.302 q^{92} +266.167 q^{93} +1038.71 q^{94} +166.556 q^{95} +171.327 q^{96} +1350.20 q^{97} -1056.99 q^{98} -627.580 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9}+O(q^{10}) \) 12 * q - 8 * q^2 + 16 * q^4 - 96 * q^8 - 36 * q^9	\( 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9} - 8 q^{13} - 192 q^{15} - 184 q^{16} - 352 q^{19} - 256 q^{21} - 492 q^{25} - 784 q^{26} + 744 q^{30} + 24 q^{32} - 1400 q^{33} - 632 q^{35} - 856 q^{36} - 624 q^{38} - 1664 q^{42} - 1200 q^{43} - 1512 q^{47} - 1052 q^{49} - 2856 q^{50} + 792 q^{52} - 2504 q^{53} - 1424 q^{55} - 3408 q^{59} - 2808 q^{60} + 272 q^{64} + 272 q^{66} - 1080 q^{67} - 344 q^{69} + 2600 q^{70} + 248 q^{72} + 896 q^{76} + 848 q^{77} - 2404 q^{81} - 2960 q^{83} + 4768 q^{84} - 1200 q^{86} - 160 q^{87} - 2144 q^{89} + 3800 q^{93} + 5984 q^{94} + 3464 q^{98}+O(q^{100}) \) 12 * q - 8 * q^2 + 16 * q^4 - 96 * q^8 - 36 * q^9 - 8 * q^13 - 192 * q^15 - 184 * q^16 - 352 * q^19 - 256 * q^21 - 492 * q^25 - 784 * q^26 + 744 * q^30 + 24 * q^32 - 1400 * q^33 - 632 * q^35 - 856 * q^36 - 624 * q^38 - 1664 * q^42 - 1200 * q^43 - 1512 * q^47 - 1052 * q^49 - 2856 * q^50 + 792 * q^52 - 2504 * q^53 - 1424 * q^55 - 3408 * q^59 - 2808 * q^60 + 272 * q^64 + 272 * q^66 - 1080 * q^67 - 344 * q^69 + 2600 * q^70 + 248 * q^72 + 896 * q^76 + 848 * q^77 - 2404 * q^81 - 2960 * q^83 + 4768 * q^84 - 1200 * q^86 - 160 * q^87 - 2144 * q^89 + 3800 * q^93 + 5984 * q^94 + 3464 * q^98

Introduction

L-functions

Modular forms

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Database

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