LMFDB - Embedded newform 161.4.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,4,Mod(1,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("161.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.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:	$9.49930751092$
Analytic rank:	$1$
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} - 44x^{6} - 23x^{5} + 587x^{4} + 594x^{3} - 2430x^{2} - 3403x + 110 $ x^8 - 44x^6 - 23x^5 + 587x^4 + 594x^3 - 2430x^2 - 3403x + 110
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.78325$ of defining polynomial
Character	$\chi$	$=$	161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.78325 q^{2} -9.05000 q^{3} +6.31297 q^{4} -4.56958 q^{5} +34.2384 q^{6} -7.00000 q^{7} +6.38246 q^{8} +54.9026 q^{9} +17.2879 q^{10} -4.84425 q^{11} -57.1324 q^{12} +67.7189 q^{13} +26.4827 q^{14} +41.3547 q^{15} -74.6502 q^{16} +67.9787 q^{17} -207.710 q^{18} -72.3091 q^{19} -28.8476 q^{20} +63.3500 q^{21} +18.3270 q^{22} +23.0000 q^{23} -57.7613 q^{24} -104.119 q^{25} -256.197 q^{26} -252.518 q^{27} -44.1908 q^{28} +110.369 q^{29} -156.455 q^{30} -155.459 q^{31} +231.360 q^{32} +43.8405 q^{33} -257.180 q^{34} +31.9871 q^{35} +346.598 q^{36} +13.3091 q^{37} +273.563 q^{38} -612.856 q^{39} -29.1651 q^{40} -310.511 q^{41} -239.669 q^{42} +364.413 q^{43} -30.5816 q^{44} -250.882 q^{45} -87.0147 q^{46} +134.720 q^{47} +675.584 q^{48} +49.0000 q^{49} +393.908 q^{50} -615.208 q^{51} +427.507 q^{52} +590.866 q^{53} +955.340 q^{54} +22.1362 q^{55} -44.6772 q^{56} +654.398 q^{57} -417.552 q^{58} -415.205 q^{59} +261.071 q^{60} -322.759 q^{61} +588.141 q^{62} -384.318 q^{63} -278.093 q^{64} -309.447 q^{65} -165.859 q^{66} -589.265 q^{67} +429.147 q^{68} -208.150 q^{69} -121.015 q^{70} +786.036 q^{71} +350.413 q^{72} -758.113 q^{73} -50.3517 q^{74} +942.277 q^{75} -456.485 q^{76} +33.9097 q^{77} +2318.59 q^{78} +446.730 q^{79} +341.120 q^{80} +802.923 q^{81} +1174.74 q^{82} -1478.21 q^{83} +399.927 q^{84} -310.634 q^{85} -1378.67 q^{86} -998.837 q^{87} -30.9182 q^{88} +237.223 q^{89} +949.148 q^{90} -474.032 q^{91} +145.198 q^{92} +1406.91 q^{93} -509.679 q^{94} +330.422 q^{95} -2093.81 q^{96} -340.246 q^{97} -185.379 q^{98} -265.962 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{3} + 24 q^{4} - 24 q^{5} - 41 q^{6} - 56 q^{7} - 69 q^{8} + 95 q^{9} - 30 q^{10} - 98 q^{11} - 131 q^{12} - 145 q^{13} - 232 q^{15} - 76 q^{16} - 96 q^{17} - 69 q^{18} - 226 q^{19} - 22 q^{20}+ \cdots - 1676 q^{99}+O(q^{100}) $ 8 * q - 3 * q^3 + 24 * q^4 - 24 * q^5 - 41 * q^6 - 56 * q^7 - 69 * q^8 + 95 * q^9 - 30 * q^10 - 98 * q^11 - 131 * q^12 - 145 * q^13 - 232 * q^15 - 76 * q^16 - 96 * q^17 - 69 * q^18 - 226 * q^19 - 22 * q^20 + 21 * q^21 - 98 * q^22 + 184 * q^23 - 216 * q^24 + 60 * q^25 - 185 * q^26 - 531 * q^27 - 168 * q^28 + 73 * q^29 - 416 * q^30 - 987 * q^31 + 118 * q^32 + 16 * q^33 - 846 * q^34 + 168 * q^35 - 69 * q^36 - 2 * q^37 - 454 * q^38 - 675 * q^39 - 640 * q^40 - 907 * q^41 + 287 * q^42 + 636 * q^43 + 126 * q^44 - 126 * q^45 + 421 * q^47 + 2165 * q^48 + 392 * q^49 + 2308 * q^50 - 408 * q^51 - 931 * q^52 + 138 * q^53 + 1717 * q^54 - 90 * q^55 + 483 * q^56 + 984 * q^57 + 1329 * q^58 - 924 * q^59 + 2642 * q^60 - 890 * q^61 + 2175 * q^62 - 665 * q^63 + 303 * q^64 - 392 * q^65 + 408 * q^66 - 1392 * q^67 + 2592 * q^68 - 69 * q^69 + 210 * q^70 + 259 * q^71 + 141 * q^72 - 297 * q^73 + 2314 * q^74 - 851 * q^75 - 428 * q^76 + 686 * q^77 + 6789 * q^78 - 1788 * q^79 - 2104 * q^80 + 2300 * q^81 - 219 * q^82 + 2114 * q^83 + 917 * q^84 + 528 * q^85 - 2360 * q^86 - 2441 * q^87 + 2144 * q^88 - 1040 * q^89 + 4872 * q^90 + 1015 * q^91 + 552 * q^92 - 621 * q^93 - 1009 * q^94 + 1268 * q^95 - 1163 * q^96 - 1452 * q^97 - 1676 * q^99

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 $

$2$	−3.78325	−1.33758	−0.668790	−	0.743451i	$-0.733188\pi$
$2$	−3.78325	−1.33758	−0.668790	+	0.743451i	$0.733188\pi$
$3$	−9.05000	−1.74167	−0.870837	−	0.491572i	$-0.836423\pi$
$3$	−9.05000	−1.74167	−0.870837	+	0.491572i	$0.836423\pi$
$4$	6.31297	0.789121
$5$	−4.56958	−0.408716	−0.204358	−	0.978896i	$-0.565511\pi$
$5$	−4.56958	−0.408716	−0.204358	+	0.978896i	$0.565511\pi$
$6$	34.2384	2.32963
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	6.38246	0.282067
$9$	54.9026	2.03343
$10$	17.2879	0.546690
$11$	−4.84425	−0.132781	−0.0663907	−	0.997794i	$-0.521148\pi$
$11$	−4.84425	−0.132781	−0.0663907	+	0.997794i	$0.521148\pi$
$12$	−57.1324	−1.37439
$13$	67.7189	1.44476	0.722378	−	0.691498i	$-0.243049\pi$
$13$	67.7189	1.44476	0.722378	+	0.691498i	$0.243049\pi$
$14$	26.4827	0.505558
$15$	41.3547	0.711849
$16$	−74.6502	−1.16641
$17$	67.9787	0.969839	0.484919	−	0.874559i	$-0.338849\pi$
$17$	67.9787	0.969839	0.484919	+	0.874559i	$0.338849\pi$
$18$	−207.710	−2.71987
$19$	−72.3091	−0.873097	−0.436549	−	0.899681i	$-0.643799\pi$
$19$	−72.3091	−0.873097	−0.436549	+	0.899681i	$0.643799\pi$
$20$	−28.8476	−0.322526
$21$	63.3500	0.658291
$22$	18.3270	0.177606
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−57.7613	−0.491270
$25$	−104.119	−0.832952
$26$	−256.197	−1.93248
$27$	−252.518	−1.79990
$28$	−44.1908	−0.298260
$29$	110.369	0.706723	0.353361	−	0.935487i	$-0.385039\pi$
$29$	110.369	0.706723	0.353361	+	0.935487i	$0.385039\pi$
$30$	−156.455	−0.952156
$31$	−155.459	−0.900688	−0.450344	−	0.892855i	$-0.648699\pi$
$31$	−155.459	−0.900688	−0.450344	+	0.892855i	$0.648699\pi$
$32$	231.360	1.27810
$33$	43.8405	0.231262
$34$	−257.180	−1.29724
$35$	31.9871	0.154480
$36$	346.598	1.60462
$37$	13.3091	0.0591353	0.0295677	−	0.999563i	$-0.490587\pi$
$37$	13.3091	0.0591353	0.0295677	+	0.999563i	$0.490587\pi$
$38$	273.563	1.16784
$39$	−612.856	−2.51630
$40$	−29.1651	−0.115285
$41$	−310.511	−1.18277	−0.591386	−	0.806389i	$-0.701419\pi$
$41$	−310.511	−1.18277	−0.591386	+	0.806389i	$0.701419\pi$
$42$	−239.669	−0.880517
$43$	364.413	1.29238	0.646192	−	0.763175i	$-0.276360\pi$
$43$	364.413	1.29238	0.646192	+	0.763175i	$0.276360\pi$
$44$	−30.5816	−0.104781
$45$	−250.882	−0.831094
$46$	−87.0147	−0.278905
$47$	134.720	0.418105	0.209052	−	0.977904i	$-0.432962\pi$
$47$	134.720	0.418105	0.209052	+	0.977904i	$0.432962\pi$
$48$	675.584	2.03150
$49$	49.0000	0.142857
$50$	393.908	1.11414
$51$	−615.208	−1.68914
$52$	427.507	1.14009
$53$	590.866	1.53135	0.765676	−	0.643226i	$-0.222405\pi$
$53$	590.866	1.53135	0.765676	+	0.643226i	$0.222405\pi$
$54$	955.340	2.40751
$55$	22.1362	0.0542699
$56$	−44.6772	−0.106611
$57$	654.398	1.52065
$58$	−417.552	−0.945298
$59$	−415.205	−0.916188	−0.458094	−	0.888904i	$-0.651468\pi$
$59$	−415.205	−0.916188	−0.458094	+	0.888904i	$0.651468\pi$
$60$	261.071	0.561735
$61$	−322.759	−0.677459	−0.338730	−	0.940884i	$-0.609997\pi$
$61$	−322.759	−0.677459	−0.338730	+	0.940884i	$0.609997\pi$
$62$	588.141	1.20474
$63$	−384.318	−0.768564
$64$	−278.093	−0.543150
$65$	−309.447	−0.590495
$66$	−165.859	−0.309332
$67$	−589.265	−1.07448	−0.537241	−	0.843429i	$-0.680533\pi$
$67$	−589.265	−1.07448	−0.537241	+	0.843429i	$0.680533\pi$
$68$	429.147	0.765320
$69$	−208.150	−0.363164
$70$	−121.015	−0.206629
$71$	786.036	1.31388	0.656939	−	0.753944i	$-0.271851\pi$
$71$	786.036	1.31388	0.656939	+	0.753944i	$0.271851\pi$
$72$	350.413	0.573564
$73$	−758.113	−1.21548	−0.607742	−	0.794134i	$-0.707925\pi$
$73$	−758.113	−1.21548	−0.607742	+	0.794134i	$0.707925\pi$
$74$	−50.3517	−0.0790982
$75$	942.277	1.45073
$76$	−456.485	−0.688979
$77$	33.9097	0.0501867
$78$	2318.59	3.36575
$79$	446.730	0.636216	0.318108	−	0.948054i	$-0.396952\pi$
$79$	446.730	0.636216	0.318108	+	0.948054i	$0.396952\pi$
$80$	341.120	0.476730
$81$	802.923	1.10140
$82$	1174.74	1.58205
$83$	−1478.21	−1.95487	−0.977437	−	0.211227i	$-0.932254\pi$
$83$	−1478.21	−1.95487	−0.977437	+	0.211227i	$0.932254\pi$
$84$	399.927	0.519471
$85$	−310.634	−0.396388
$86$	−1378.67	−1.72867
$87$	−998.837	−1.23088
$88$	−30.9182	−0.0374533
$89$	237.223	0.282534	0.141267	−	0.989972i	$-0.454882\pi$
$89$	237.223	0.282534	0.141267	+	0.989972i	$0.454882\pi$
$90$	949.148	1.11165
$91$	−474.032	−0.546067
$92$	145.198	0.164543
$93$	1406.91	1.56870
$94$	−509.679	−0.559249
$95$	330.422	0.356848
$96$	−2093.81	−2.22603
$97$	−340.246	−0.356152	−0.178076	−	0.984017i	$-0.556987\pi$
$97$	−340.246	−0.356152	−0.178076	+	0.984017i	$0.556987\pi$
$98$	−185.379	−0.191083
$99$	−265.962	−0.270002
$100$	−657.300	−0.657300
$101$	432.577	0.426169	0.213084	−	0.977034i	$-0.431649\pi$
$101$	432.577	0.426169	0.213084	+	0.977034i	$0.431649\pi$
$102$	2327.48	2.25936
$103$	−2043.55	−1.95492	−0.977462	−	0.211111i	$-0.932292\pi$
$103$	−2043.55	−1.95492	−0.977462	+	0.211111i	$0.932292\pi$
$104$	432.213	0.407519
$105$	−289.483	−0.269054
$106$	−2235.39	−2.04831
$107$	1328.50	1.20029	0.600143	−	0.799893i	$-0.295110\pi$
$107$	1328.50	1.20029	0.600143	+	0.799893i	$0.295110\pi$
$108$	−1594.14	−1.42034
$109$	−1278.56	−1.12352	−0.561761	−	0.827299i	$-0.689876\pi$
$109$	−1278.56	−1.12352	−0.561761	+	0.827299i	$0.689876\pi$
$110$	−83.7467	−0.0725903
$111$	−120.448	−0.102994
$112$	522.551	0.440861
$113$	−602.412	−0.501506	−0.250753	−	0.968051i	$-0.580678\pi$
$113$	−602.412	−0.501506	−0.250753	+	0.968051i	$0.580678\pi$
$114$	−2475.75	−2.03399
$115$	−105.100	−0.0852231
$116$	696.754	0.557690
$117$	3717.94	2.93781
$118$	1570.82	1.22547
$119$	−475.851	−0.366565
$120$	263.945	0.200790
$121$	−1307.53	−0.982369
$122$	1221.08	0.906156
$123$	2810.12	2.06000
$124$	−981.410	−0.710752
$125$	1046.98	0.749156
$126$	1453.97	1.02802
$127$	−1697.57	−1.18610	−0.593052	−	0.805164i	$-0.702077\pi$
$127$	−1697.57	−1.18610	−0.593052	+	0.805164i	$0.702077\pi$
$128$	−798.790	−0.551591
$129$	−3297.94	−2.25091
$130$	1170.71	0.789834
$131$	1050.46	0.700604	0.350302	−	0.936637i	$-0.386079\pi$
$131$	1050.46	0.700604	0.350302	+	0.936637i	$0.386079\pi$
$132$	276.764	0.182494
$133$	506.164	0.330000
$134$	2229.34	1.43720
$135$	1153.90	0.735645
$136$	433.871	0.273560
$137$	−1969.92	−1.22848	−0.614241	−	0.789119i	$-0.710538\pi$
$137$	−1969.92	−1.22848	−0.614241	+	0.789119i	$0.710538\pi$
$138$	787.484	0.485761
$139$	−1548.94	−0.945178	−0.472589	−	0.881283i	$-0.656680\pi$
$139$	−1548.94	−0.945178	−0.472589	+	0.881283i	$0.656680\pi$
$140$	201.933	0.121903
$141$	−1219.22	−0.728202
$142$	−2973.77	−1.75742
$143$	−328.047	−0.191837
$144$	−4098.49	−2.37181
$145$	−504.339	−0.288849
$146$	2868.13	1.62581
$147$	−443.450	−0.248811
$148$	84.0201	0.0466649
$149$	−1280.07	−0.703811	−0.351905	−	0.936036i	$-0.614466\pi$
$149$	−1280.07	−0.703811	−0.351905	+	0.936036i	$0.614466\pi$
$150$	−3564.87	−1.94047
$151$	−1822.48	−0.982196	−0.491098	−	0.871104i	$-0.663404\pi$
$151$	−1822.48	−0.982196	−0.491098	+	0.871104i	$0.663404\pi$
$152$	−461.510	−0.246272
$153$	3732.21	1.97210
$154$	−128.289	−0.0671287
$155$	710.384	0.368125
$156$	−3868.94	−1.98566
$157$	1938.19	0.985249	0.492624	−	0.870242i	$-0.336038\pi$
$157$	1938.19	0.985249	0.492624	+	0.870242i	$0.336038\pi$
$158$	−1690.09	−0.850991
$159$	−5347.34	−2.66712
$160$	−1057.22	−0.522379
$161$	−161.000	−0.0788110
$162$	−3037.66	−1.47322
$163$	1177.55	0.565844	0.282922	−	0.959143i	$-0.408696\pi$
$163$	1177.55	0.565844	0.282922	+	0.959143i	$0.408696\pi$
$164$	−1960.24	−0.933350
$165$	−200.333	−0.0945204
$166$	5592.43	2.61480
$167$	−1059.81	−0.491080	−0.245540	−	0.969386i	$-0.578965\pi$
$167$	−1059.81	−0.491080	−0.245540	+	0.969386i	$0.578965\pi$
$168$	404.329	0.185682
$169$	2388.85	1.08732
$170$	1175.21	0.530201
$171$	−3969.96	−1.77538
$172$	2300.53	1.01985
$173$	−924.034	−0.406087	−0.203043	−	0.979170i	$-0.565083\pi$
$173$	−924.034	−0.406087	−0.203043	+	0.979170i	$0.565083\pi$
$174$	3778.85	1.64640
$175$	728.833	0.314826
$176$	361.624	0.154878
$177$	3757.61	1.59570
$178$	−897.472	−0.377912
$179$	−1223.97	−0.511082	−0.255541	−	0.966798i	$-0.582254\pi$
$179$	−1223.97	−0.511082	−0.255541	+	0.966798i	$0.582254\pi$
$180$	−1583.81	−0.655834
$181$	2806.42	1.15248	0.576242	−	0.817279i	$-0.304519\pi$
$181$	2806.42	1.15248	0.576242	+	0.817279i	$0.304519\pi$
$182$	1793.38	0.730408
$183$	2920.97	1.17991
$184$	146.797	0.0588151
$185$	−60.8171	−0.0241695
$186$	−5322.68	−2.09827
$187$	−329.306	−0.128777
$188$	850.483	0.329935
$189$	1767.63	0.680297
$190$	−1250.07	−0.477313
$191$	−233.238	−0.0883586	−0.0441793	−	0.999024i	$-0.514067\pi$
$191$	−233.238	−0.0883586	−0.0441793	+	0.999024i	$0.514067\pi$
$192$	2516.74	0.945990
$193$	4808.96	1.79356	0.896778	−	0.442481i	$-0.145902\pi$
$193$	4808.96	1.79356	0.896778	+	0.442481i	$0.145902\pi$
$194$	1287.24	0.476382
$195$	2800.49	1.02845
$196$	309.335	0.112732
$197$	4546.05	1.64412	0.822062	−	0.569398i	$-0.192824\pi$
$197$	4546.05	1.64412	0.822062	+	0.569398i	$0.192824\pi$
$198$	1006.20	0.361149
$199$	1465.84	0.522163	0.261081	−	0.965317i	$-0.415921\pi$
$199$	1465.84	0.522163	0.261081	+	0.965317i	$0.415921\pi$
$200$	−664.535	−0.234949
$201$	5332.85	1.87140
$202$	−1636.55	−0.570035
$203$	−772.581	−0.267116
$204$	−3883.79	−1.33294
$205$	1418.90	0.483417
$206$	7731.27	2.61487
$207$	1262.76	0.423999
$208$	−5055.23	−1.68518
$209$	350.283	0.115931
$210$	1095.19	0.359881
$211$	2992.67	0.976415	0.488208	−	0.872728i	$-0.337651\pi$
$211$	2992.67	0.976415	0.488208	+	0.872728i	$0.337651\pi$
$212$	3730.12	1.20842
$213$	−7113.63	−2.28835
$214$	−5026.03	−1.60548
$215$	−1665.22	−0.528218
$216$	−1611.69	−0.507692
$217$	1088.22	0.340428
$218$	4837.12	1.50280
$219$	6860.92	2.11698
$220$	139.745	0.0428255
$221$	4603.44	1.40118
$222$	455.683	0.137763
$223$	−2558.55	−0.768309	−0.384154	−	0.923269i	$-0.625507\pi$
$223$	−2558.55	−0.768309	−0.384154	+	0.923269i	$0.625507\pi$
$224$	−1619.52	−0.483076
$225$	−5716.40	−1.69375
$226$	2279.08	0.670805
$227$	1915.04	0.559937	0.279968	−	0.960009i	$-0.409676\pi$
$227$	1915.04	0.559937	0.279968	+	0.960009i	$0.409676\pi$
$228$	4131.19	1.19998
$229$	−4612.32	−1.33096	−0.665482	−	0.746414i	$-0.731774\pi$
$229$	−4612.32	−1.33096	−0.665482	+	0.746414i	$0.731774\pi$
$230$	397.621	0.113993
$231$	−306.883	−0.0874088
$232$	704.424	0.199343
$233$	−5894.34	−1.65730	−0.828651	−	0.559766i	$-0.810891\pi$
$233$	−5894.34	−1.65730	−0.828651	+	0.559766i	$0.810891\pi$
$234$	−14065.9	−3.92956
$235$	−615.613	−0.170886
$236$	−2621.18	−0.722983
$237$	−4042.91	−1.10808
$238$	1800.26	0.490310
$239$	−6769.93	−1.83226	−0.916130	−	0.400881i	$-0.868704\pi$
$239$	−6769.93	−1.83226	−0.916130	+	0.400881i	$0.868704\pi$
$240$	−3087.14	−0.830307
$241$	1199.61	0.320639	0.160319	−	0.987065i	$-0.448748\pi$
$241$	1199.61	0.320639	0.160319	+	0.987065i	$0.448748\pi$
$242$	4946.72	1.31400
$243$	−448.459	−0.118390
$244$	−2037.57	−0.534597
$245$	−223.909	−0.0583879
$246$	−10631.4	−2.75542
$247$	−4896.69	−1.26141
$248$	−992.213	−0.254055
$249$	13377.8	3.40475
$250$	−3960.97	−1.00206
$251$	−5410.12	−1.36049	−0.680247	−	0.732983i	$-0.738127\pi$
$251$	−5410.12	−1.36049	−0.680247	+	0.732983i	$0.738127\pi$
$252$	−2426.19	−0.606490
$253$	−111.418	−0.0276869
$254$	6422.34	1.58651
$255$	2811.24	0.690379
$256$	5246.76	1.28095
$257$	4412.16	1.07091	0.535453	−	0.844565i	$-0.320141\pi$
$257$	4412.16	1.07091	0.535453	+	0.844565i	$0.320141\pi$
$258$	12476.9	3.01078
$259$	−93.1639	−0.0223510
$260$	−1953.53	−0.465972
$261$	6059.53	1.43707
$262$	−3974.15	−0.937114
$263$	617.492	0.144776	0.0723882	−	0.997377i	$-0.476938\pi$
$263$	617.492	0.144776	0.0723882	+	0.997377i	$0.476938\pi$
$264$	279.810	0.0652315
$265$	−2700.01	−0.625888
$266$	−1914.94	−0.441401
$267$	−2146.87	−0.492083
$268$	−3720.01	−0.847896
$269$	4413.54	1.00036	0.500182	−	0.865920i	$-0.333266\pi$
$269$	4413.54	1.00036	0.500182	+	0.865920i	$0.333266\pi$
$270$	−4365.50	−0.983985
$271$	−4540.10	−1.01768	−0.508841	−	0.860861i	$-0.669926\pi$
$271$	−4540.10	−1.01768	−0.508841	+	0.860861i	$0.669926\pi$
$272$	−5074.62	−1.13123
$273$	4289.99	0.951070
$274$	7452.71	1.64319
$275$	504.378	0.110601
$276$	−1314.05	−0.286580
$277$	3713.29	0.805451	0.402726	−	0.915321i	$-0.368063\pi$
$277$	3713.29	0.805451	0.402726	+	0.915321i	$0.368063\pi$
$278$	5860.04	1.26425
$279$	−8535.12	−1.83148
$280$	204.156	0.0435738
$281$	−8256.83	−1.75289	−0.876443	−	0.481505i	$-0.840090\pi$
$281$	−8256.83	−1.75289	−0.876443	+	0.481505i	$0.840090\pi$
$282$	4612.60	0.974029
$283$	−1391.40	−0.292262	−0.146131	−	0.989265i	$-0.546682\pi$
$283$	−1391.40	−0.292262	−0.146131	+	0.989265i	$0.546682\pi$
$284$	4962.22	1.03681
$285$	−2990.32	−0.621514
$286$	1241.08	0.256597
$287$	2173.57	0.447045
$288$	12702.3	2.59892
$289$	−291.896	−0.0594129
$290$	1908.04	0.386358
$291$	3079.23	0.620301
$292$	−4785.94	−0.959165
$293$	−8477.87	−1.69038	−0.845192	−	0.534463i	$-0.820514\pi$
$293$	−8477.87	−1.69038	−0.845192	+	0.534463i	$0.820514\pi$
$294$	1677.68	0.332804
$295$	1897.31	0.374460
$296$	84.9449	0.0166801
$297$	1223.26	0.238993
$298$	4842.84	0.941403
$299$	1557.53	0.301253
$300$	5948.56	1.14480
$301$	−2550.89	−0.488475
$302$	6894.91	1.31377
$303$	−3914.83	−0.742247
$304$	5397.89	1.01839
$305$	1474.87	0.276888
$306$	−14119.9	−2.63784
$307$	−10382.3	−1.93013	−0.965067	−	0.262004i	$-0.915617\pi$
$307$	−10382.3	−1.93013	−0.965067	+	0.262004i	$0.915617\pi$
$308$	214.071	0.0396034
$309$	18494.2	3.40484
$310$	−2687.56	−0.492397
$311$	2039.97	0.371949	0.185974	−	0.982555i	$-0.440456\pi$
$311$	2039.97	0.371949	0.185974	+	0.982555i	$0.440456\pi$
$312$	−3911.53	−0.709765
$313$	−2677.77	−0.483567	−0.241784	−	0.970330i	$-0.577732\pi$
$313$	−2677.77	−0.483567	−0.241784	+	0.970330i	$0.577732\pi$
$314$	−7332.64	−1.31785
$315$	1756.17	0.314124
$316$	2820.20	0.502052
$317$	−2581.29	−0.457350	−0.228675	−	0.973503i	$-0.573439\pi$
$317$	−2581.29	−0.457350	−0.228675	+	0.973503i	$0.573439\pi$
$318$	20230.3	3.56748
$319$	−534.654	−0.0938397
$320$	1270.77	0.221994
$321$	−12022.9	−2.09051
$322$	609.103	0.105416
$323$	−4915.48	−0.846763
$324$	5068.83	0.869140
$325$	−7050.82	−1.20341
$326$	−4454.95	−0.756862
$327$	11571.0	1.95681
$328$	−1981.82	−0.333621
$329$	−943.040	−0.158029
$330$	757.908	0.126429
$331$	−2719.32	−0.451564	−0.225782	−	0.974178i	$-0.572494\pi$
$331$	−2719.32	−0.451564	−0.225782	+	0.974178i	$0.572494\pi$
$332$	−9331.89	−1.54263
$333$	730.705	0.120247
$334$	4009.51	0.656859
$335$	2692.69	0.439157
$336$	−4729.09	−0.767836
$337$	−571.658	−0.0924041	−0.0462021	−	0.998932i	$-0.514712\pi$
$337$	−571.658	−0.0924041	−0.0462021	+	0.998932i	$0.514712\pi$
$338$	−9037.60	−1.45438
$339$	5451.83	0.873460
$340$	−1961.02	−0.312798
$341$	753.084	0.119595
$342$	15019.3	2.37471
$343$	−343.000	−0.0539949
$344$	2325.85	0.364540
$345$	951.158	0.148431
$346$	3495.85	0.543174
$347$	−1444.25	−0.223434	−0.111717	−	0.993740i	$-0.535635\pi$
$347$	−1444.25	−0.223434	−0.111717	+	0.993740i	$0.535635\pi$
$348$	−6305.63	−0.971314
$349$	6055.83	0.928829	0.464414	−	0.885618i	$-0.346265\pi$
$349$	6055.83	0.928829	0.464414	+	0.885618i	$0.346265\pi$
$350$	−2757.35	−0.421105
$351$	−17100.3	−2.60041
$352$	−1120.77	−0.169708
$353$	−6726.97	−1.01428	−0.507139	−	0.861864i	$-0.669297\pi$
$353$	−6726.97	−1.01428	−0.507139	+	0.861864i	$0.669297\pi$
$354$	−14216.0	−2.13438
$355$	−3591.85	−0.537002
$356$	1497.58	0.222954
$357$	4306.45	0.638436
$358$	4630.57	0.683613
$359$	8865.95	1.30342	0.651709	−	0.758469i	$-0.274052\pi$
$359$	8865.95	1.30342	0.651709	+	0.758469i	$0.274052\pi$
$360$	−1601.24	−0.234425
$361$	−1630.39	−0.237701
$362$	−10617.4	−1.54154
$363$	11833.2	1.71097
$364$	−2992.55	−0.430913
$365$	3464.26	0.496787
$366$	−11050.7	−1.57823
$367$	6921.55	0.984474	0.492237	−	0.870461i	$-0.336179\pi$
$367$	6921.55	0.984474	0.492237	+	0.870461i	$0.336179\pi$
$368$	−1716.95	−0.243213
$369$	−17047.8	−2.40508
$370$	230.086	0.0323287
$371$	−4136.06	−0.578797
$372$	8881.77	1.23790
$373$	−8441.89	−1.17186	−0.585931	−	0.810361i	$-0.699271\pi$
$373$	−8441.89	−1.17186	−0.585931	+	0.810361i	$0.699271\pi$
$374$	1245.85	0.172249
$375$	−9475.15	−1.30479
$376$	859.844	0.117934
$377$	7474.04	1.02104
$378$	−6687.38	−0.909951
$379$	8366.99	1.13399	0.566996	−	0.823720i	$-0.308105\pi$
$379$	8366.99	1.13399	0.566996	+	0.823720i	$0.308105\pi$
$380$	2085.95	0.281597
$381$	15363.0	2.06581
$382$	882.397	0.118187
$383$	5063.95	0.675603	0.337802	−	0.941217i	$-0.390317\pi$
$383$	5063.95	0.675603	0.337802	+	0.941217i	$0.390317\pi$
$384$	7229.05	0.960692
$385$	−154.953	−0.0205121
$386$	−18193.5	−2.39902
$387$	20007.2	2.62797
$388$	−2147.96	−0.281047
$389$	−5601.27	−0.730066	−0.365033	−	0.930995i	$-0.618942\pi$
$389$	−5601.27	−0.730066	−0.365033	+	0.930995i	$0.618942\pi$
$390$	−10595.0	−1.37563
$391$	1563.51	0.202225
$392$	312.740	0.0402953
$393$	−9506.67	−1.22022
$394$	−17198.8	−2.19915
$395$	−2041.37	−0.260032
$396$	−1679.01	−0.213064
$397$	15436.0	1.95142	0.975709	−	0.219070i	$-0.0703023\pi$
$397$	15436.0	1.95142	0.975709	+	0.219070i	$0.0703023\pi$
$398$	−5545.62	−0.698434
$399$	−4580.78	−0.574752
$400$	7772.50	0.971562
$401$	−9034.43	−1.12508	−0.562541	−	0.826769i	$-0.690176\pi$
$401$	−9034.43	−1.12508	−0.562541	+	0.826769i	$0.690176\pi$
$402$	−20175.5	−2.50314
$403$	−10527.5	−1.30127
$404$	2730.85	0.336299
$405$	−3669.02	−0.450161
$406$	2922.87	0.357289
$407$	−64.4727	−0.00785207
$408$	−3926.54	−0.476452
$409$	1988.19	0.240366	0.120183	−	0.992752i	$-0.461652\pi$
$409$	1988.19	0.240366	0.120183	+	0.992752i	$0.461652\pi$
$410$	−5368.06	−0.646609
$411$	17827.8	2.13961
$412$	−12900.9	−1.54267
$413$	2906.43	0.346286
$414$	−4777.33	−0.567133
$415$	6754.79	0.798988
$416$	15667.5	1.84654
$417$	14018.0	1.64619
$418$	−1325.21	−0.155067
$419$	−11899.2	−1.38738	−0.693691	−	0.720273i	$-0.744017\pi$
$419$	−11899.2	−1.38738	−0.693691	+	0.720273i	$0.744017\pi$
$420$	−1827.50	−0.212316
$421$	−5809.77	−0.672567	−0.336284	−	0.941761i	$-0.609170\pi$
$421$	−5809.77	−0.672567	−0.336284	+	0.941761i	$0.609170\pi$
$422$	−11322.0	−1.30603
$423$	7396.47	0.850186
$424$	3771.18	0.431945
$425$	−7077.87	−0.807829
$426$	26912.6	3.06085
$427$	2259.31	0.256056
$428$	8386.76	0.947171
$429$	2968.83	0.334117
$430$	6299.93	0.706533
$431$	−2165.59	−0.242025	−0.121013	−	0.992651i	$-0.538614\pi$
$431$	−2165.59	−0.242025	−0.121013	+	0.992651i	$0.538614\pi$
$432$	18850.5	2.09941
$433$	−13371.3	−1.48402	−0.742011	−	0.670388i	$-0.766128\pi$
$433$	−13371.3	−1.48402	−0.742011	+	0.670388i	$0.766128\pi$
$434$	−4116.99	−0.455350
$435$	4564.27	0.503080
$436$	−8071.52	−0.886595
$437$	−1663.11	−0.182053
$438$	−25956.6	−2.83163
$439$	−12889.5	−1.40132	−0.700662	−	0.713494i	$-0.747112\pi$
$439$	−12889.5	−1.40132	−0.700662	+	0.713494i	$0.747112\pi$
$440$	141.283	0.0153078
$441$	2690.23	0.290490
$442$	−17416.0	−1.87419
$443$	−1108.70	−0.118908	−0.0594539	−	0.998231i	$-0.518936\pi$
$443$	−1108.70	−0.118908	−0.0594539	+	0.998231i	$0.518936\pi$
$444$	−760.382	−0.0812751
$445$	−1084.01	−0.115476
$446$	9679.61	1.02767
$447$	11584.7	1.22581
$448$	1946.65	0.205291
$449$	−11525.5	−1.21141	−0.605705	−	0.795690i	$-0.707109\pi$
$449$	−11525.5	−1.21141	−0.605705	+	0.795690i	$0.707109\pi$
$450$	21626.6	2.26552
$451$	1504.19	0.157050
$452$	−3803.01	−0.395749
$453$	16493.5	1.71067
$454$	−7245.07	−0.748960
$455$	2166.13	0.223186
$456$	4176.67	0.428926
$457$	8740.83	0.894702	0.447351	−	0.894358i	$-0.352367\pi$
$457$	8740.83	0.894702	0.447351	+	0.894358i	$0.352367\pi$
$458$	17449.6	1.78027
$459$	−17165.9	−1.74561
$460$	−663.495	−0.0672513
$461$	−4066.14	−0.410800	−0.205400	−	0.978678i	$-0.565850\pi$
$461$	−4066.14	−0.410800	−0.205400	+	0.978678i	$0.565850\pi$
$462$	1161.02	0.116916
$463$	11258.3	1.13006	0.565031	−	0.825070i	$-0.308864\pi$
$463$	11258.3	1.13006	0.565031	+	0.825070i	$0.308864\pi$
$464$	−8239.04	−0.824328
$465$	−6428.98	−0.641154
$466$	22299.8	2.21677
$467$	10961.4	1.08615	0.543076	−	0.839684i	$-0.317260\pi$
$467$	10961.4	1.08615	0.543076	+	0.839684i	$0.317260\pi$
$468$	23471.2	2.31829
$469$	4124.86	0.406116
$470$	2329.02	0.228574
$471$	−17540.6	−1.71598
$472$	−2650.03	−0.258427
$473$	−1765.31	−0.171605
$474$	15295.3	1.48215
$475$	7528.75	0.727248
$476$	−3004.03	−0.289264
$477$	32440.1	3.11390
$478$	25612.3	2.45079
$479$	13529.8	1.29059	0.645294	−	0.763934i	$-0.276735\pi$
$479$	13529.8	1.29059	0.645294	+	0.763934i	$0.276735\pi$
$480$	9567.85	0.909813
$481$	901.279	0.0854361
$482$	−4538.44	−0.428880
$483$	1457.05	0.137263
$484$	−8254.42	−0.775208
$485$	1554.78	0.145565
$486$	1696.63	0.158355
$487$	14377.0	1.33775	0.668875	−	0.743375i	$-0.266776\pi$
$487$	14377.0	1.33775	0.668875	+	0.743375i	$0.266776\pi$
$488$	−2059.99	−0.191089
$489$	−10656.8	−0.985517
$490$	847.105	0.0780986
$491$	11982.1	1.10131	0.550655	−	0.834733i	$-0.314378\pi$
$491$	11982.1	1.10131	0.550655	+	0.834733i	$0.314378\pi$
$492$	17740.2	1.62559
$493$	7502.72	0.685407
$494$	18525.4	1.68724
$495$	1215.33	0.110354
$496$	11605.1	1.05057
$497$	−5502.25	−0.496599
$498$	−50611.5	−4.55413
$499$	16885.3	1.51481	0.757405	−	0.652946i	$-0.226467\pi$
$499$	16885.3	1.51481	0.757405	+	0.652946i	$0.226467\pi$
$500$	6609.53	0.591175
$501$	9591.26	0.855301
$502$	20467.8	1.81977
$503$	−244.700	−0.0216912	−0.0108456	−	0.999941i	$-0.503452\pi$
$503$	−244.700	−0.0216912	−0.0108456	+	0.999941i	$0.503452\pi$
$504$	−2452.89	−0.216787
$505$	−1976.70	−0.174182
$506$	421.521	0.0370334
$507$	−21619.1	−1.89376
$508$	−10716.7	−0.935980
$509$	3721.25	0.324050	0.162025	−	0.986787i	$-0.448197\pi$
$509$	3721.25	0.324050	0.162025	+	0.986787i	$0.448197\pi$
$510$	−10635.6	−0.923437
$511$	5306.79	0.459410
$512$	−13459.5	−1.16178
$513$	18259.4	1.57148
$514$	−16692.3	−1.43242
$515$	9338.17	0.799008
$516$	−20819.8	−1.77624
$517$	−652.617	−0.0555166
$518$	352.462	0.0298963
$519$	8362.51	0.707271
$520$	−1975.03	−0.166559
$521$	−1616.30	−0.135914	−0.0679571	−	0.997688i	$-0.521648\pi$
$521$	−1616.30	−0.135914	−0.0679571	+	0.997688i	$0.521648\pi$
$522$	−22924.7	−1.92220
$523$	−19142.4	−1.60046	−0.800230	−	0.599693i	$-0.795289\pi$
$523$	−19142.4	−1.60046	−0.800230	+	0.599693i	$0.795289\pi$
$524$	6631.52	0.552861
$525$	−6595.94	−0.548324
$526$	−2336.13	−0.193650
$527$	−10567.9	−0.873522
$528$	−3272.70	−0.269746
$529$	529.000	0.0434783
$530$	10214.8	0.837175
$531$	−22795.8	−1.86300
$532$	3195.40	0.260410
$533$	−21027.4	−1.70882
$534$	8122.13	0.658200
$535$	−6070.67	−0.490576
$536$	−3760.96	−0.303076
$537$	11076.9	0.890138
$538$	−16697.5	−1.33807
$539$	−237.368	−0.0189688
$540$	7284.55	0.580513
$541$	−6518.72	−0.518044	−0.259022	−	0.965871i	$-0.583400\pi$
$541$	−6518.72	−0.518044	−0.259022	+	0.965871i	$0.583400\pi$
$542$	17176.3	1.36123
$543$	−25398.1	−2.00725
$544$	15727.6	1.23955
$545$	5842.49	0.459201
$546$	−16230.1	−1.27213
$547$	−16336.5	−1.27696	−0.638481	−	0.769637i	$-0.720437\pi$
$547$	−16336.5	−1.27696	−0.638481	+	0.769637i	$0.720437\pi$
$548$	−12436.1	−0.969421
$549$	−17720.3	−1.37756
$550$	−1908.19	−0.147937
$551$	−7980.66	−0.617038
$552$	−1328.51	−0.102437
$553$	−3127.11	−0.240467
$554$	−14048.3	−1.07736
$555$	550.395	0.0420954
$556$	−9778.44	−0.745860
$557$	−11949.3	−0.908993	−0.454496	−	0.890749i	$-0.650181\pi$
$557$	−11949.3	−0.908993	−0.454496	+	0.890749i	$0.650181\pi$
$558$	32290.5	2.44976
$559$	24677.7	1.86718
$560$	−2387.84	−0.180187
$561$	2980.22	0.224287
$562$	31237.6	2.34463
$563$	6148.58	0.460270	0.230135	−	0.973159i	$-0.426083\pi$
$563$	6148.58	0.460270	0.230135	+	0.973159i	$0.426083\pi$
$564$	−7696.87	−0.574640
$565$	2752.77	0.204973
$566$	5264.02	0.390925
$567$	−5620.46	−0.416291
$568$	5016.84	0.370602
$569$	4009.95	0.295441	0.147720	−	0.989029i	$-0.452806\pi$
$569$	4009.95	0.295441	0.147720	+	0.989029i	$0.452806\pi$
$570$	11313.1	0.831324
$571$	13301.0	0.974831	0.487416	−	0.873170i	$-0.337940\pi$
$571$	13301.0	0.974831	0.487416	+	0.873170i	$0.337940\pi$
$572$	−2070.95	−0.151383
$573$	2110.80	0.153892
$574$	−8223.17	−0.597959
$575$	−2394.74	−0.173682
$576$	−15268.0	−1.10446
$577$	17209.0	1.24163	0.620814	−	0.783958i	$-0.286802\pi$
$577$	17209.0	1.24163	0.620814	+	0.783958i	$0.286802\pi$
$578$	1104.31	0.0794695
$579$	−43521.1	−3.12379
$580$	−3183.87	−0.227936
$581$	10347.5	0.738873
$582$	−11649.5	−0.829703
$583$	−2862.30	−0.203335
$584$	−4838.62	−0.342849
$585$	−16989.4	−1.20073
$586$	32073.9	2.26102
$587$	24505.2	1.72306	0.861531	−	0.507704i	$-0.169506\pi$
$587$	24505.2	1.72306	0.861531	+	0.507704i	$0.169506\pi$
$588$	−2799.49	−0.196342
$589$	11241.1	0.786388
$590$	−7178.00	−0.500871
$591$	−41141.7	−2.86353
$592$	−993.529	−0.0689760
$593$	13119.0	0.908488	0.454244	−	0.890877i	$-0.349910\pi$
$593$	13119.0	0.908488	0.454244	+	0.890877i	$0.349910\pi$
$594$	−4627.90	−0.319672
$595$	2174.44	0.149821
$596$	−8081.07	−0.555392
$597$	−13265.8	−0.909437
$598$	−5892.54	−0.402950
$599$	−23171.7	−1.58058	−0.790292	−	0.612730i	$-0.790071\pi$
$599$	−23171.7	−1.58058	−0.790292	+	0.612730i	$0.790071\pi$
$600$	6014.04	0.409204
$601$	−14118.2	−0.958227	−0.479113	−	0.877753i	$-0.659042\pi$
$601$	−14118.2	−0.958227	−0.479113	+	0.877753i	$0.659042\pi$
$602$	9650.66	0.653375
$603$	−32352.2	−2.18488
$604$	−11505.3	−0.775072
$605$	5974.88	0.401510
$606$	14810.8	0.992815
$607$	−9761.28	−0.652715	−0.326357	−	0.945246i	$-0.605821\pi$
$607$	−9761.28	−0.652715	−0.326357	+	0.945246i	$0.605821\pi$
$608$	−16729.5	−1.11590
$609$	6991.86	0.465229
$610$	−5579.80	−0.370360
$611$	9123.08	0.604060
$612$	23561.3	1.55622
$613$	−16066.2	−1.05858	−0.529288	−	0.848442i	$-0.677541\pi$
$613$	−16066.2	−1.05858	−0.529288	+	0.848442i	$0.677541\pi$
$614$	39278.9	2.58171
$615$	−12841.1	−0.841955
$616$	216.428	0.0141560
$617$	7725.09	0.504052	0.252026	−	0.967720i	$-0.418903\pi$
$617$	7725.09	0.504052	0.252026	+	0.967720i	$0.418903\pi$
$618$	−69968.0	−4.55425
$619$	−15861.2	−1.02991	−0.514955	−	0.857217i	$-0.672192\pi$
$619$	−15861.2	−1.02991	−0.514955	+	0.857217i	$0.672192\pi$
$620$	4484.63	0.290495
$621$	−5807.92	−0.375304
$622$	−7717.71	−0.497511
$623$	−1660.56	−0.106788
$624$	45749.8	2.93503
$625$	8230.62	0.526760
$626$	10130.7	0.646810
$627$	−3170.07	−0.201914
$628$	12235.7	0.777481
$629$	904.737	0.0573517
$630$	−6644.03	−0.420166
$631$	−15676.7	−0.989032	−0.494516	−	0.869169i	$-0.664655\pi$
$631$	−15676.7	−0.989032	−0.494516	+	0.869169i	$0.664655\pi$
$632$	2851.24	0.179456
$633$	−27083.6	−1.70060
$634$	9765.68	0.611742
$635$	7757.19	0.484779
$636$	−33757.6	−2.10468
$637$	3318.22	0.206394
$638$	2022.73	0.125518
$639$	43155.4	2.67168
$640$	3650.13	0.225444
$641$	−24437.6	−1.50582	−0.752908	−	0.658126i	$-0.771349\pi$
$641$	−24437.6	−1.50582	−0.752908	+	0.658126i	$0.771349\pi$
$642$	45485.6	2.79622
$643$	−6427.17	−0.394188	−0.197094	−	0.980385i	$-0.563150\pi$
$643$	−6427.17	−0.394188	−0.197094	+	0.980385i	$0.563150\pi$
$644$	−1016.39	−0.0621915
$645$	15070.2	0.919983
$646$	18596.5	1.13261
$647$	4215.13	0.256127	0.128063	−	0.991766i	$-0.459124\pi$
$647$	4215.13	0.256127	0.128063	+	0.991766i	$0.459124\pi$
$648$	5124.62	0.310670
$649$	2011.36	0.121653
$650$	26675.0	1.60966
$651$	−9848.35	−0.592915
$652$	7433.82	0.446520
$653$	24079.4	1.44303	0.721517	−	0.692397i	$-0.243445\pi$
$653$	24079.4	1.44303	0.721517	+	0.692397i	$0.243445\pi$
$654$	−43775.9	−2.61739
$655$	−4800.16	−0.286348
$656$	23179.7	1.37959
$657$	−41622.3	−2.47160
$658$	3567.75	0.211376
$659$	−17107.1	−1.01123	−0.505614	−	0.862760i	$-0.668734\pi$
$659$	−17107.1	−1.01123	−0.505614	+	0.862760i	$0.668734\pi$
$660$	−1264.69	−0.0745880
$661$	16609.1	0.977338	0.488669	−	0.872469i	$-0.337483\pi$
$661$	16609.1	0.977338	0.488669	+	0.872469i	$0.337483\pi$
$662$	10287.9	0.604002
$663$	−41661.2	−2.44040
$664$	−9434.61	−0.551406
$665$	−2312.96	−0.134876
$666$	−2764.44	−0.160841
$667$	2538.48	0.147362
$668$	−6690.53	−0.387521
$669$	23154.8	1.33814
$670$	−10187.1	−0.587408
$671$	1563.52	0.0899540
$672$	14656.7	0.841360
$673$	−18095.9	−1.03647	−0.518237	−	0.855237i	$-0.673412\pi$
$673$	−18095.9	−1.03647	−0.518237	+	0.855237i	$0.673412\pi$
$674$	2162.72	0.123598
$675$	26291.9	1.49923
$676$	15080.7	0.858028
$677$	−24604.0	−1.39676	−0.698381	−	0.715727i	$-0.746096\pi$
$677$	−24604.0	−1.39676	−0.698381	+	0.715727i	$0.746096\pi$
$678$	−20625.6	−1.16832
$679$	2381.72	0.134613
$680$	−1982.61	−0.111808
$681$	−17331.1	−0.975227
$682$	−2849.10	−0.159967
$683$	−3505.60	−0.196396	−0.0981978	−	0.995167i	$-0.531308\pi$
$683$	−3505.60	−0.196396	−0.0981978	+	0.995167i	$0.531308\pi$
$684$	−25062.2	−1.40099
$685$	9001.73	0.502100
$686$	1297.65	0.0722225
$687$	41741.5	2.31811
$688$	−27203.5	−1.50745
$689$	40012.8	2.21243
$690$	−3598.47	−0.198538
$691$	−13973.7	−0.769299	−0.384649	−	0.923063i	$-0.625678\pi$
$691$	−13973.7	−0.769299	−0.384649	+	0.923063i	$0.625678\pi$
$692$	−5833.40	−0.320452
$693$	1861.73	0.102051
$694$	5463.97	0.298861
$695$	7078.02	0.386309
$696$	−6375.04	−0.347191
$697$	−21108.1	−1.14710
$698$	−22910.7	−1.24238
$699$	53343.8	2.88648
$700$	4601.10	0.248436
$701$	−13863.7	−0.746967	−0.373483	−	0.927637i	$-0.621837\pi$
$701$	−13863.7	−0.746967	−0.373483	+	0.927637i	$0.621837\pi$
$702$	64694.5	3.47826
$703$	−962.371	−0.0516309
$704$	1347.15	0.0721203
$705$	5571.30	0.297628
$706$	25449.8	1.35668
$707$	−3028.04	−0.161077
$708$	23721.7	1.25920
$709$	−32762.4	−1.73542	−0.867712	−	0.497067i	$-0.834410\pi$
$709$	−32762.4	−1.73542	−0.867712	+	0.497067i	$0.834410\pi$
$710$	13588.9	0.718284
$711$	24526.6	1.29370
$712$	1514.06	0.0796937
$713$	−3575.57	−0.187806
$714$	−16292.4	−0.853959
$715$	1499.04	0.0784067
$716$	−7726.87	−0.403305
$717$	61267.9	3.19120
$718$	−33542.1	−1.74343
$719$	−9404.55	−0.487803	−0.243902	−	0.969800i	$-0.578427\pi$
$719$	−9404.55	−0.487803	−0.243902	+	0.969800i	$0.578427\pi$
$720$	18728.4	0.969395
$721$	14304.9	0.738892
$722$	6168.18	0.317945
$723$	−10856.5	−0.558448
$724$	17716.8	0.909449
$725$	−11491.5	−0.588666
$726$	−44767.9	−2.28856
$727$	24724.0	1.26130	0.630648	−	0.776069i	$-0.282789\pi$
$727$	24724.0	1.26130	0.630648	+	0.776069i	$0.282789\pi$
$728$	−3025.49	−0.154028
$729$	−17620.4	−0.895207
$730$	−13106.1	−0.664493
$731$	24772.4	1.25340
$732$	18440.0	0.931094
$733$	25332.2	1.27649	0.638245	−	0.769833i	$-0.279661\pi$
$733$	25332.2	1.27649	0.638245	+	0.769833i	$0.279661\pi$
$734$	−26185.9	−1.31681
$735$	2026.38	0.101693
$736$	5321.29	0.266502
$737$	2854.55	0.142671
$738$	64496.2	3.21699
$739$	−6708.25	−0.333920	−0.166960	−	0.985964i	$-0.553395\pi$
$739$	−6708.25	−0.333920	−0.166960	+	0.985964i	$0.553395\pi$
$740$	−383.936	−0.0190727
$741$	44315.1	2.19697
$742$	15647.7	0.774187
$743$	−28884.6	−1.42621	−0.713105	−	0.701057i	$-0.752712\pi$
$743$	−28884.6	−1.42621	−0.713105	+	0.701057i	$0.752712\pi$
$744$	8979.53	0.442481
$745$	5849.40	0.287658
$746$	31937.8	1.56746
$747$	−81157.5	−3.97510
$748$	−2078.90	−0.101620
$749$	−9299.47	−0.453665
$750$	35846.8	1.74526
$751$	−15823.4	−0.768848	−0.384424	−	0.923157i	$-0.625600\pi$
$751$	−15823.4	−0.768848	−0.384424	+	0.923157i	$0.625600\pi$
$752$	−10056.9	−0.487681
$753$	48961.6	2.36954
$754$	−28276.2	−1.36573
$755$	8327.99	0.401439
$756$	11159.0	0.536836
$757$	18547.6	0.890518	0.445259	−	0.895402i	$-0.353112\pi$
$757$	18547.6	0.890518	0.445259	+	0.895402i	$0.353112\pi$
$758$	−31654.4	−1.51681
$759$	1008.33	0.0482215
$760$	2108.91	0.100655
$761$	−30235.5	−1.44026	−0.720128	−	0.693841i	$-0.755917\pi$
$761$	−30235.5	−1.44026	−0.720128	+	0.693841i	$0.755917\pi$
$762$	−58122.2	−2.76318
$763$	8949.93	0.424652
$764$	−1472.42	−0.0697257
$765$	−17054.6	−0.806027
$766$	−19158.2	−0.903673
$767$	−28117.2	−1.32367
$768$	−47483.2	−2.23099
$769$	21255.4	0.996737	0.498368	−	0.866965i	$-0.333933\pi$
$769$	21255.4	0.996737	0.498368	+	0.866965i	$0.333933\pi$
$770$	586.227	0.0274366
$771$	−39930.1	−1.86517
$772$	30358.8	1.41533
$773$	18701.5	0.870177	0.435089	−	0.900388i	$-0.356717\pi$
$773$	18701.5	0.870177	0.435089	+	0.900388i	$0.356717\pi$
$774$	−75692.3	−3.51512
$775$	16186.3	0.750229
$776$	−2171.61	−0.100459
$777$	843.133	0.0389282
$778$	21191.0	0.976522
$779$	22452.7	1.03267
$780$	17679.4	0.811571
$781$	−3807.76	−0.174459
$782$	−5915.15	−0.270493
$783$	−27870.1	−1.27203
$784$	−3657.86	−0.166630
$785$	−8856.69	−0.402687
$786$	35966.1	1.63215
$787$	−32672.6	−1.47987	−0.739933	−	0.672681i	$-0.765143\pi$
$787$	−32672.6	−1.47987	−0.739933	+	0.672681i	$0.765143\pi$
$788$	28699.0	1.29741
$789$	−5588.30	−0.252153
$790$	7723.01	0.347813
$791$	4216.89	0.189551
$792$	−1697.49	−0.0761587
$793$	−21856.9	−0.978764
$794$	−58398.4	−2.61018
$795$	24435.1	1.09009
$796$	9253.78	0.412050
$797$	14216.8	0.631851	0.315926	−	0.948784i	$-0.397685\pi$
$797$	14216.8	0.631851	0.315926	+	0.948784i	$0.397685\pi$
$798$	17330.2	0.768777
$799$	9158.09	0.405494
$800$	−24089.0	−1.06459
$801$	13024.1	0.574513
$802$	34179.5	1.50489
$803$	3672.49	0.161394
$804$	33666.1	1.47676
$805$	735.702	0.0322113
$806$	39828.3	1.74056
$807$	−39942.5	−1.74231
$808$	2760.91	0.120208
$809$	31047.8	1.34930	0.674650	−	0.738138i	$-0.264295\pi$
$809$	31047.8	1.34930	0.674650	+	0.738138i	$0.264295\pi$
$810$	13880.8	0.602126
$811$	1425.65	0.0617280	0.0308640	−	0.999524i	$-0.490174\pi$
$811$	1425.65	0.0617280	0.0308640	+	0.999524i	$0.490174\pi$
$812$	−4877.28	−0.210787
$813$	41088.0	1.77247
$814$	243.916	0.0105028
$815$	−5380.90	−0.231269
$816$	45925.4	1.97023
$817$	−26350.4	−1.12838
$818$	−7521.82	−0.321509
$819$	−26025.6	−1.11039
$820$	8957.49	0.381475
$821$	46004.3	1.95562	0.977808	−	0.209502i	$-0.0671842\pi$
$821$	46004.3	1.95562	0.977808	+	0.209502i	$0.0671842\pi$
$822$	−67447.1	−2.86191
$823$	−7394.38	−0.313186	−0.156593	−	0.987663i	$-0.550051\pi$
$823$	−7394.38	−0.313186	−0.156593	+	0.987663i	$0.550051\pi$
$824$	−13042.9	−0.551420
$825$	−4564.62	−0.192630
$826$	−10995.8	−0.463186
$827$	24938.4	1.04860	0.524301	−	0.851533i	$-0.324327\pi$
$827$	24938.4	1.04860	0.524301	+	0.851533i	$0.324327\pi$
$828$	7971.76	0.334587
$829$	−10899.8	−0.456654	−0.228327	−	0.973585i	$-0.573325\pi$
$829$	−10899.8	−0.456654	−0.228327	+	0.973585i	$0.573325\pi$
$830$	−25555.1	−1.06871
$831$	−33605.3	−1.40283
$832$	−18832.1	−0.784720
$833$	3330.96	0.138548
$834$	−53033.4	−2.20191
$835$	4842.87	0.200712
$836$	2211.33	0.0914837
$837$	39256.3	1.62114
$838$	45017.6	1.85573
$839$	12453.6	0.512451	0.256226	−	0.966617i	$-0.417521\pi$
$839$	12453.6	0.512451	0.256226	+	0.966617i	$0.417521\pi$
$840$	−1847.61	−0.0758913
$841$	−12207.7	−0.500543
$842$	21979.8	0.899613
$843$	74724.3	3.05296
$844$	18892.6	0.770510
$845$	−10916.0	−0.444405
$846$	−27982.7	−1.13719
$847$	9152.73	0.371301
$848$	−44108.2	−1.78618
$849$	12592.2	0.509026
$850$	26777.3	1.08054
$851$	306.110	0.0123306
$852$	−44908.1	−1.80578
$853$	−25419.1	−1.02032	−0.510161	−	0.860079i	$-0.670414\pi$
$853$	−25419.1	−1.02032	−0.510161	+	0.860079i	$0.670414\pi$
$854$	−8547.53	−0.342495
$855$	18141.0	0.725626
$856$	8479.07	0.338562
$857$	13111.6	0.522618	0.261309	−	0.965255i	$-0.415846\pi$
$857$	13111.6	0.522618	0.261309	+	0.965255i	$0.415846\pi$
$858$	−11231.8	−0.446909
$859$	17402.8	0.691242	0.345621	−	0.938374i	$-0.387668\pi$
$859$	17402.8	0.691242	0.345621	+	0.938374i	$0.387668\pi$
$860$	−10512.5	−0.416828
$861$	−19670.9	−0.778607
$862$	8192.98	0.323728
$863$	20393.5	0.804406	0.402203	−	0.915551i	$-0.368245\pi$
$863$	20393.5	0.804406	0.402203	+	0.915551i	$0.368245\pi$
$864$	−58422.8	−2.30044
$865$	4222.45	0.165974
$866$	50586.8	1.98500
$867$	2641.66	0.103478
$868$	6869.87	0.268639
$869$	−2164.07	−0.0844778
$870$	−17267.8	−0.672910
$871$	−39904.4	−1.55236
$872$	−8160.36	−0.316909
$873$	−18680.4	−0.724211
$874$	6291.96	0.243511
$875$	−7328.84	−0.283154
$876$	43312.8	1.67055
$877$	−34176.3	−1.31591	−0.657954	−	0.753058i	$-0.728578\pi$
$877$	−34176.3	−1.31591	−0.657954	+	0.753058i	$0.728578\pi$
$878$	48764.1	1.87438
$879$	76724.8	2.94410
$880$	−1652.47	−0.0633009
$881$	−43679.4	−1.67037	−0.835186	−	0.549968i	$-0.814640\pi$
$881$	−43679.4	−1.67037	−0.835186	+	0.549968i	$0.814640\pi$
$882$	−10177.8	−0.388553
$883$	33948.9	1.29385	0.646926	−	0.762553i	$-0.276054\pi$
$883$	33948.9	1.29385	0.646926	+	0.762553i	$0.276054\pi$
$884$	29061.4	1.10570
$885$	−17170.7	−0.652188
$886$	4194.50	0.159049
$887$	34720.7	1.31432	0.657162	−	0.753749i	$-0.271757\pi$
$887$	34720.7	1.31432	0.657162	+	0.753749i	$0.271757\pi$
$888$	−768.752	−0.0290514
$889$	11883.0	0.448305
$890$	4101.07	0.154459
$891$	−3889.56	−0.146246
$892$	−16152.0	−0.606289
$893$	−9741.48	−0.365046
$894$	−43827.7	−1.63962
$895$	5593.02	0.208887
$896$	5591.53	0.208482
$897$	−14095.7	−0.524684
$898$	43603.9	1.62036
$899$	−17157.8	−0.636536
$900$	−36087.4	−1.33657
$901$	40166.3	1.48516
$902$	−5690.73	−0.210067
$903$	23085.6	0.850765
$904$	−3844.87	−0.141459
$905$	−12824.2	−0.471038
$906$	−62399.0	−2.28815
$907$	−15596.4	−0.570972	−0.285486	−	0.958383i	$-0.592155\pi$
$907$	−15596.4	−0.570972	−0.285486	+	0.958383i	$0.592155\pi$
$908$	12089.6	0.441858
$909$	23749.6	0.866584
$910$	−8195.00	−0.298529
$911$	2980.74	0.108404	0.0542021	−	0.998530i	$-0.482738\pi$
$911$	2980.74	0.108404	0.0542021	+	0.998530i	$0.482738\pi$
$912$	−48850.9	−1.77370
$913$	7160.81	0.259571
$914$	−33068.7	−1.19674
$915$	−13347.6	−0.482249
$916$	−29117.4	−1.05029
$917$	−7353.22	−0.264803
$918$	64942.8	2.33489
$919$	49093.6	1.76219	0.881093	−	0.472944i	$-0.156809\pi$
$919$	49093.6	1.76219	0.881093	+	0.472944i	$0.156809\pi$
$920$	−670.798	−0.0240387
$921$	93960.2	3.36166
$922$	15383.2	0.549478
$923$	53229.5	1.89823
$924$	−1937.35	−0.0689762
$925$	−1385.73	−0.0492569
$926$	−42593.0	−1.51155
$927$	−112196.	−3.97520
$928$	25535.0	0.903261
$929$	−25012.3	−0.883345	−0.441672	−	0.897176i	$-0.645615\pi$
$929$	−25012.3	−0.883345	−0.441672	+	0.897176i	$0.645615\pi$
$930$	24322.4	0.857595
$931$	−3543.15	−0.124728
$932$	−37210.8	−1.30781
$933$	−18461.7	−0.647813
$934$	−41469.7	−1.45281
$935$	1504.79	0.0526330
$936$	23729.6	0.828660
$937$	−20661.6	−0.720370	−0.360185	−	0.932881i	$-0.617286\pi$
$937$	−20661.6	−0.720370	−0.360185	+	0.932881i	$0.617286\pi$
$938$	−15605.4	−0.543212
$939$	24233.8	0.842217
$940$	−3886.35	−0.134850
$941$	25865.8	0.896069	0.448035	−	0.894016i	$-0.352124\pi$
$941$	25865.8	0.896069	0.448035	+	0.894016i	$0.352124\pi$
$942$	66360.4	2.29526
$943$	−7141.74	−0.246625
$944$	30995.1	1.06865
$945$	−8077.32	−0.278048
$946$	6678.60	0.229535
$947$	−29129.1	−0.999544	−0.499772	−	0.866157i	$-0.666583\pi$
$947$	−29129.1	−0.999544	−0.499772	+	0.866157i	$0.666583\pi$
$948$	−25522.8	−0.874411
$949$	−51338.5	−1.75608
$950$	−28483.1	−0.972752
$951$	23360.7	0.796554
$952$	−3037.10	−0.103396
$953$	16.9264	0.000575340 0	0.000287670	−	1.00000i	$-0.499908\pi$
$953$	16.9264	0.000575340 0	0.000287670		1.00000i	$0.499908\pi$
$954$	−122729.	−4.16509
$955$	1065.80	0.0361136
$956$	−42738.3	−1.44588
$957$	4838.62	0.163438
$958$	−51186.6	−1.72627
$959$	13789.5	0.464322
$960$	−11500.4	−0.386641
$961$	−5623.39	−0.188761
$962$	−3409.76	−0.114278
$963$	72937.9	2.44070
$964$	7573.12	0.253023
$965$	−21974.9	−0.733054
$966$	−5512.38	−0.183600
$967$	31926.9	1.06174	0.530869	−	0.847454i	$-0.321866\pi$
$967$	31926.9	1.06174	0.530869	+	0.847454i	$0.321866\pi$
$968$	−8345.28	−0.277094
$969$	44485.1	1.47479
$970$	−5882.13	−0.194705
$971$	46315.0	1.53071	0.765355	−	0.643608i	$-0.222563\pi$
$971$	46315.0	1.53071	0.765355	+	0.643608i	$0.222563\pi$
$972$	−2831.11	−0.0934237
$973$	10842.6	0.357244
$974$	−54391.8	−1.78935
$975$	63809.9	2.09595
$976$	24094.0	0.790195
$977$	11114.5	0.363954	0.181977	−	0.983303i	$-0.441750\pi$
$977$	11114.5	0.363954	0.181977	+	0.983303i	$0.441750\pi$
$978$	40317.4	1.31821
$979$	−1149.17	−0.0375153
$980$	−1413.53	−0.0460752
$981$	−70196.3	−2.28460
$982$	−45331.2	−1.47309
$983$	−9246.02	−0.300002	−0.150001	−	0.988686i	$-0.547928\pi$
$983$	−9246.02	−0.300002	−0.150001	+	0.988686i	$0.547928\pi$
$984$	17935.5	0.581059
$985$	−20773.5	−0.671979
$986$	−28384.7	−0.916787
$987$	8534.51	0.275235
$988$	−30912.7	−0.995408
$989$	8381.51	0.269481
$990$	−4597.91	−0.147607
$991$	16539.1	0.530152	0.265076	−	0.964228i	$-0.414603\pi$
$991$	16539.1	0.530152	0.265076	+	0.964228i	$0.414603\pi$
$992$	−35967.2	−1.15117
$993$	24609.9	0.786476
$994$	20816.4	0.664241
$995$	−6698.25	−0.213416
$996$	84453.6	2.68676
$997$	−8326.03	−0.264481	−0.132241	−	0.991218i	$-0.542217\pi$
$997$	−8326.03	−0.264481	−0.132241	+	0.991218i	$0.542217\pi$
$998$	−63881.3	−2.02618
$999$	−3360.80	−0.106437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.a.b.1.2	✓	8
3.2	odd	2		1449.4.a.i.1.7		8
7.6	odd	2		1127.4.a.e.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.a.b.1.2	✓	8	1.1	even	1	trivial
1127.4.a.e.1.2		8	7.6	odd	2
1449.4.a.i.1.7		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.a (trivial)

\(f(q)\)	\(=\)	\(q-3.78325 q^{2} -9.05000 q^{3} +6.31297 q^{4} -4.56958 q^{5} +34.2384 q^{6} -7.00000 q^{7} +6.38246 q^{8} +54.9026 q^{9} +17.2879 q^{10} -4.84425 q^{11} -57.1324 q^{12} +67.7189 q^{13} +26.4827 q^{14} +41.3547 q^{15} -74.6502 q^{16} +67.9787 q^{17} -207.710 q^{18} -72.3091 q^{19} -28.8476 q^{20} +63.3500 q^{21} +18.3270 q^{22} +23.0000 q^{23} -57.7613 q^{24} -104.119 q^{25} -256.197 q^{26} -252.518 q^{27} -44.1908 q^{28} +110.369 q^{29} -156.455 q^{30} -155.459 q^{31} +231.360 q^{32} +43.8405 q^{33} -257.180 q^{34} +31.9871 q^{35} +346.598 q^{36} +13.3091 q^{37} +273.563 q^{38} -612.856 q^{39} -29.1651 q^{40} -310.511 q^{41} -239.669 q^{42} +364.413 q^{43} -30.5816 q^{44} -250.882 q^{45} -87.0147 q^{46} +134.720 q^{47} +675.584 q^{48} +49.0000 q^{49} +393.908 q^{50} -615.208 q^{51} +427.507 q^{52} +590.866 q^{53} +955.340 q^{54} +22.1362 q^{55} -44.6772 q^{56} +654.398 q^{57} -417.552 q^{58} -415.205 q^{59} +261.071 q^{60} -322.759 q^{61} +588.141 q^{62} -384.318 q^{63} -278.093 q^{64} -309.447 q^{65} -165.859 q^{66} -589.265 q^{67} +429.147 q^{68} -208.150 q^{69} -121.015 q^{70} +786.036 q^{71} +350.413 q^{72} -758.113 q^{73} -50.3517 q^{74} +942.277 q^{75} -456.485 q^{76} +33.9097 q^{77} +2318.59 q^{78} +446.730 q^{79} +341.120 q^{80} +802.923 q^{81} +1174.74 q^{82} -1478.21 q^{83} +399.927 q^{84} -310.634 q^{85} -1378.67 q^{86} -998.837 q^{87} -30.9182 q^{88} +237.223 q^{89} +949.148 q^{90} -474.032 q^{91} +145.198 q^{92} +1406.91 q^{93} -509.679 q^{94} +330.422 q^{95} -2093.81 q^{96} -340.246 q^{97} -185.379 q^{98} -265.962 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{3} + 24 q^{4} - 24 q^{5} - 41 q^{6} - 56 q^{7} - 69 q^{8} + 95 q^{9} - 30 q^{10} - 98 q^{11} - 131 q^{12} - 145 q^{13} - 232 q^{15} - 76 q^{16} - 96 q^{17} - 69 q^{18} - 226 q^{19} - 22 q^{20}+ \cdots - 1676 q^{99}+O(q^{100}) \) 8 * q - 3 * q^3 + 24 * q^4 - 24 * q^5 - 41 * q^6 - 56 * q^7 - 69 * q^8 + 95 * q^9 - 30 * q^10 - 98 * q^11 - 131 * q^12 - 145 * q^13 - 232 * q^15 - 76 * q^16 - 96 * q^17 - 69 * q^18 - 226 * q^19 - 22 * q^20 + 21 * q^21 - 98 * q^22 + 184 * q^23 - 216 * q^24 + 60 * q^25 - 185 * q^26 - 531 * q^27 - 168 * q^28 + 73 * q^29 - 416 * q^30 - 987 * q^31 + 118 * q^32 + 16 * q^33 - 846 * q^34 + 168 * q^35 - 69 * q^36 - 2 * q^37 - 454 * q^38 - 675 * q^39 - 640 * q^40 - 907 * q^41 + 287 * q^42 + 636 * q^43 + 126 * q^44 - 126 * q^45 + 421 * q^47 + 2165 * q^48 + 392 * q^49 + 2308 * q^50 - 408 * q^51 - 931 * q^52 + 138 * q^53 + 1717 * q^54 - 90 * q^55 + 483 * q^56 + 984 * q^57 + 1329 * q^58 - 924 * q^59 + 2642 * q^60 - 890 * q^61 + 2175 * q^62 - 665 * q^63 + 303 * q^64 - 392 * q^65 + 408 * q^66 - 1392 * q^67 + 2592 * q^68 - 69 * q^69 + 210 * q^70 + 259 * q^71 + 141 * q^72 - 297 * q^73 + 2314 * q^74 - 851 * q^75 - 428 * q^76 + 686 * q^77 + 6789 * q^78 - 1788 * q^79 - 2104 * q^80 + 2300 * q^81 - 219 * q^82 + 2114 * q^83 + 917 * q^84 + 528 * q^85 - 2360 * q^86 - 2441 * q^87 + 2144 * q^88 - 1040 * q^89 + 4872 * q^90 + 1015 * q^91 + 552 * q^92 - 621 * q^93 - 1009 * q^94 + 1268 * q^95 - 1163 * q^96 - 1452 * q^97 - 1676 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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