LMFDB - Embedded newform 1870.4.a.m.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1870,4,Mod(1,1870)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1870, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1870.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 1870 = 2 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1870.a (trivial)

Newform invariants

comment:select newform

sage:traces = [10,20,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$110.333571711$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 184 x^{8} + 198 x^{7} + 11125 x^{6} - 13769 x^{5} - 258561 x^{4} + 275849 x^{3} + \cdots - 2234586 $ x^10 - x^9 - 184x^8 + 198x^7 + 11125x^6 - 13769x^5 - 258561x^4 + 275849x^3 + 2121305x^2 - 1239587x - 2234586
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.834326$ of defining polynomial
Character	$\chi$	$=$	1870.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} -0.834326 q^{3} +4.00000 q^{4} -5.00000 q^{5} -1.66865 q^{6} +34.7753 q^{7} +8.00000 q^{8} -26.3039 q^{9} -10.0000 q^{10} -11.0000 q^{11} -3.33730 q^{12} +50.4166 q^{13} +69.5507 q^{14} +4.17163 q^{15} +16.0000 q^{16} -17.0000 q^{17} -52.6078 q^{18} -160.203 q^{19} -20.0000 q^{20} -29.0140 q^{21} -22.0000 q^{22} -71.0598 q^{23} -6.67461 q^{24} +25.0000 q^{25} +100.833 q^{26} +44.4728 q^{27} +139.101 q^{28} -135.320 q^{29} +8.34326 q^{30} -228.473 q^{31} +32.0000 q^{32} +9.17758 q^{33} -34.0000 q^{34} -173.877 q^{35} -105.216 q^{36} +144.165 q^{37} -320.406 q^{38} -42.0639 q^{39} -40.0000 q^{40} -29.9628 q^{41} -58.0279 q^{42} -295.320 q^{43} -44.0000 q^{44} +131.520 q^{45} -142.120 q^{46} -556.892 q^{47} -13.3492 q^{48} +866.324 q^{49} +50.0000 q^{50} +14.1835 q^{51} +201.667 q^{52} +474.221 q^{53} +88.9456 q^{54} +55.0000 q^{55} +278.203 q^{56} +133.661 q^{57} -270.640 q^{58} +377.714 q^{59} +16.6865 q^{60} -84.1747 q^{61} -456.946 q^{62} -914.727 q^{63} +64.0000 q^{64} -252.083 q^{65} +18.3552 q^{66} -791.406 q^{67} -68.0000 q^{68} +59.2870 q^{69} -347.753 q^{70} +465.133 q^{71} -210.431 q^{72} +170.945 q^{73} +288.329 q^{74} -20.8581 q^{75} -640.811 q^{76} -382.529 q^{77} -84.1278 q^{78} -365.393 q^{79} -80.0000 q^{80} +673.101 q^{81} -59.9256 q^{82} -6.46028 q^{83} -116.056 q^{84} +85.0000 q^{85} -590.641 q^{86} +112.901 q^{87} -88.0000 q^{88} +238.154 q^{89} +263.039 q^{90} +1753.26 q^{91} -284.239 q^{92} +190.621 q^{93} -1113.78 q^{94} +801.014 q^{95} -26.6984 q^{96} -306.073 q^{97} +1732.65 q^{98} +289.343 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 20 q^{2} + q^{3} + 40 q^{4} - 50 q^{5} + 2 q^{6} + 19 q^{7} + 80 q^{8} + 99 q^{9} - 100 q^{10} - 110 q^{11} + 4 q^{12} - 41 q^{13} + 38 q^{14} - 5 q^{15} + 160 q^{16} - 170 q^{17} + 198 q^{18} - 157 q^{19}+ \cdots - 1089 q^{99}+O(q^{100}) $ 10 * q + 20 * q^2 + q^3 + 40 * q^4 - 50 * q^5 + 2 * q^6 + 19 * q^7 + 80 * q^8 + 99 * q^9 - 100 * q^10 - 110 * q^11 + 4 * q^12 - 41 * q^13 + 38 * q^14 - 5 * q^15 + 160 * q^16 - 170 * q^17 + 198 * q^18 - 157 * q^19 - 200 * q^20 - 288 * q^21 - 220 * q^22 + 56 * q^23 + 8 * q^24 + 250 * q^25 - 82 * q^26 - 95 * q^27 + 76 * q^28 - 212 * q^29 - 10 * q^30 - 171 * q^31 + 320 * q^32 - 11 * q^33 - 340 * q^34 - 95 * q^35 + 396 * q^36 + 20 * q^37 - 314 * q^38 - 447 * q^39 - 400 * q^40 - 393 * q^41 - 576 * q^42 - 294 * q^43 - 440 * q^44 - 495 * q^45 + 112 * q^46 - 1270 * q^47 + 16 * q^48 - 209 * q^49 + 500 * q^50 - 17 * q^51 - 164 * q^52 - 1046 * q^53 - 190 * q^54 + 550 * q^55 + 152 * q^56 - 927 * q^57 - 424 * q^58 - 1766 * q^59 - 20 * q^60 + 505 * q^61 - 342 * q^62 - 2257 * q^63 + 640 * q^64 + 205 * q^65 - 22 * q^66 - 1289 * q^67 - 680 * q^68 - 2942 * q^69 - 190 * q^70 + 411 * q^71 + 792 * q^72 - 216 * q^73 + 40 * q^74 + 25 * q^75 - 628 * q^76 - 209 * q^77 - 894 * q^78 - 612 * q^79 - 800 * q^80 + 558 * q^81 - 786 * q^82 - 1922 * q^83 - 1152 * q^84 + 850 * q^85 - 588 * q^86 - 103 * q^87 - 880 * q^88 - 644 * q^89 - 990 * q^90 + 782 * q^91 + 224 * q^92 - 1803 * q^93 - 2540 * q^94 + 785 * q^95 + 32 * q^96 + 777 * q^97 - 418 * q^98 - 1089 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−0.834326	−0.160566	−0.0802830	−	0.996772i	$-0.525582\pi$
$3$	−0.834326	−0.160566	−0.0802830	+	0.996772i	$0.525582\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−1.66865	−0.113537
$7$	34.7753	1.87769	0.938846	−	0.344337i	$-0.111896\pi$
$7$	34.7753	1.87769	0.938846	+	0.344337i	$0.111896\pi$
$8$	8.00000	0.353553
$9$	−26.3039	−0.974219
$10$	−10.0000	−0.316228
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−3.33730	−0.0802830
$13$	50.4166	1.07562	0.537810	−	0.843066i	$-0.319252\pi$
$13$	50.4166	1.07562	0.537810	+	0.843066i	$0.319252\pi$
$14$	69.5507	1.32773
$15$	4.17163	0.0718073
$16$	16.0000	0.250000
$17$	−17.0000	−0.242536
$17$	−17.0000	−0.242536
$18$	−52.6078	−0.688877
$19$	−160.203	−1.93437	−0.967186	−	0.254071i	$-0.918230\pi$
$19$	−160.203	−1.93437	−0.967186	+	0.254071i	$0.918230\pi$
$20$	−20.0000	−0.223607
$21$	−29.0140	−0.301494
$22$	−22.0000	−0.213201
$23$	−71.0598	−0.644217	−0.322109	−	0.946703i	$-0.604392\pi$
$23$	−71.0598	−0.644217	−0.322109	+	0.946703i	$0.604392\pi$
$24$	−6.67461	−0.0567687
$25$	25.0000	0.200000
$26$	100.833	0.760578
$27$	44.4728	0.316992
$28$	139.101	0.938846
$29$	−135.320	−0.866493	−0.433246	−	0.901275i	$-0.642632\pi$
$29$	−135.320	−0.866493	−0.433246	+	0.901275i	$0.642632\pi$
$30$	8.34326	0.0507754
$31$	−228.473	−1.32371	−0.661854	−	0.749632i	$-0.730230\pi$
$31$	−228.473	−1.32371	−0.661854	+	0.749632i	$0.730230\pi$
$32$	32.0000	0.176777
$33$	9.17758	0.0484125
$34$	−34.0000	−0.171499
$35$	−173.877	−0.839729
$36$	−105.216	−0.487109
$37$	144.165	0.640555	0.320277	−	0.947324i	$-0.396224\pi$
$37$	144.165	0.640555	0.320277	+	0.947324i	$0.396224\pi$
$38$	−320.406	−1.36781
$39$	−42.0639	−0.172708
$40$	−40.0000	−0.158114
$41$	−29.9628	−0.114132	−0.0570659	−	0.998370i	$-0.518175\pi$
$41$	−29.9628	−0.114132	−0.0570659	+	0.998370i	$0.518175\pi$
$42$	−58.0279	−0.213188
$43$	−295.320	−1.04735	−0.523674	−	0.851919i	$-0.675439\pi$
$43$	−295.320	−1.04735	−0.523674	+	0.851919i	$0.675439\pi$
$44$	−44.0000	−0.150756
$45$	131.520	0.435684
$46$	−142.120	−0.455530
$47$	−556.892	−1.72832	−0.864160	−	0.503218i	$-0.832149\pi$
$47$	−556.892	−1.72832	−0.864160	+	0.503218i	$0.832149\pi$
$48$	−13.3492	−0.0401415
$49$	866.324	2.52573
$50$	50.0000	0.141421
$51$	14.1835	0.0389430
$52$	201.667	0.537810
$53$	474.221	1.22904	0.614522	−	0.788900i	$-0.289349\pi$
$53$	474.221	1.22904	0.614522	+	0.788900i	$0.289349\pi$
$54$	88.9456	0.224148
$55$	55.0000	0.134840
$56$	278.203	0.663864
$57$	133.661	0.310594
$58$	−270.640	−0.612703
$59$	377.714	0.833461	0.416730	−	0.909030i	$-0.363176\pi$
$59$	377.714	0.833461	0.416730	+	0.909030i	$0.363176\pi$
$60$	16.6865	0.0359037
$61$	−84.1747	−0.176680	−0.0883399	−	0.996090i	$-0.528156\pi$
$61$	−84.1747	−0.176680	−0.0883399	+	0.996090i	$0.528156\pi$
$62$	−456.946	−0.936003
$63$	−914.727	−1.82928
$64$	64.0000	0.125000
$65$	−252.083	−0.481032
$66$	18.3552	0.0342328
$67$	−791.406	−1.44307	−0.721534	−	0.692379i	$-0.756563\pi$
$67$	−791.406	−1.44307	−0.721534	+	0.692379i	$0.756563\pi$
$68$	−68.0000	−0.121268
$69$	59.2870	0.103439
$70$	−347.753	−0.593778
$71$	465.133	0.777481	0.388741	−	0.921347i	$-0.372910\pi$
$71$	465.133	0.777481	0.388741	+	0.921347i	$0.372910\pi$
$72$	−210.431	−0.344438
$73$	170.945	0.274076	0.137038	−	0.990566i	$-0.456242\pi$
$73$	170.945	0.274076	0.137038	+	0.990566i	$0.456242\pi$
$74$	288.329	0.452941
$75$	−20.8581	−0.0321132
$76$	−640.811	−0.967186
$77$	−382.529	−0.566145
$78$	−84.1278	−0.122123
$79$	−365.393	−0.520379	−0.260189	−	0.965558i	$-0.583785\pi$
$79$	−365.393	−0.520379	−0.260189	+	0.965558i	$0.583785\pi$
$80$	−80.0000	−0.111803
$81$	673.101	0.923320
$82$	−59.9256	−0.0807034
$83$	−6.46028	−0.00854347	−0.00427174	−	0.999991i	$-0.501360\pi$
$83$	−6.46028	−0.00854347	−0.00427174	+	0.999991i	$0.501360\pi$
$84$	−116.056	−0.150747
$85$	85.0000	0.108465
$86$	−590.641	−0.740587
$87$	112.901	0.139129
$88$	−88.0000	−0.106600
$89$	238.154	0.283643	0.141822	−	0.989892i	$-0.454704\pi$
$89$	238.154	0.283643	0.141822	+	0.989892i	$0.454704\pi$
$90$	263.039	0.308075
$91$	1753.26	2.01968
$92$	−284.239	−0.322109
$93$	190.621	0.212543
$94$	−1113.78	−1.22211
$95$	801.014	0.865077
$96$	−26.6984	−0.0283843
$97$	−306.073	−0.320381	−0.160191	−	0.987086i	$-0.551211\pi$
$97$	−306.073	−0.320381	−0.160191	+	0.987086i	$0.551211\pi$
$98$	1732.65	1.78596
$99$	289.343	0.293738
$100$	100.000	0.100000
$101$	−1776.58	−1.75026	−0.875130	−	0.483888i	$-0.839224\pi$
$101$	−1776.58	−1.75026	−0.875130	+	0.483888i	$0.839224\pi$
$102$	28.3671	0.0275369
$103$	158.581	0.151703	0.0758517	−	0.997119i	$-0.475832\pi$
$103$	158.581	0.151703	0.0758517	+	0.997119i	$0.475832\pi$
$104$	403.333	0.380289
$105$	145.070	0.134832
$106$	948.442	0.869065
$107$	−1532.98	−1.38504	−0.692518	−	0.721400i	$-0.743499\pi$
$107$	−1532.98	−1.38504	−0.692518	+	0.721400i	$0.743499\pi$
$108$	177.891	0.158496
$109$	1701.50	1.49518	0.747589	−	0.664161i	$-0.231211\pi$
$109$	1701.50	1.49518	0.747589	+	0.664161i	$0.231211\pi$
$110$	110.000	0.0953463
$111$	−120.280	−0.102851
$112$	556.405	0.469423
$113$	−2008.17	−1.67180	−0.835899	−	0.548884i	$-0.815053\pi$
$113$	−2008.17	−1.67180	−0.835899	+	0.548884i	$0.815053\pi$
$114$	267.323	0.219623
$115$	355.299	0.288103
$116$	−541.280	−0.433246
$117$	−1326.15	−1.04789
$118$	755.428	0.589346
$119$	−591.181	−0.455407
$120$	33.3730	0.0253877
$121$	121.000	0.0909091
$122$	−168.349	−0.124931
$123$	24.9987	0.0183257
$124$	−913.892	−0.661854
$125$	−125.000	−0.0894427
$126$	−1829.45	−1.29350
$127$	462.696	0.323289	0.161644	−	0.986849i	$-0.448320\pi$
$127$	462.696	0.323289	0.161644	+	0.986849i	$0.448320\pi$
$128$	128.000	0.0883883
$129$	246.393	0.168168
$130$	−504.166	−0.340141
$131$	−992.079	−0.661666	−0.330833	−	0.943689i	$-0.607330\pi$
$131$	−992.079	−0.661666	−0.330833	+	0.943689i	$0.607330\pi$
$132$	36.7103	0.0242062
$133$	−5571.11	−3.63215
$134$	−1582.81	−1.02040
$135$	−222.364	−0.141763
$136$	−136.000	−0.0857493
$137$	901.936	0.562464	0.281232	−	0.959640i	$-0.409257\pi$
$137$	901.936	0.562464	0.281232	+	0.959640i	$0.409257\pi$
$138$	118.574	0.0731427
$139$	−1732.43	−1.05714	−0.528572	−	0.848888i	$-0.677272\pi$
$139$	−1732.43	−1.05714	−0.528572	+	0.848888i	$0.677272\pi$
$140$	−695.507	−0.419865
$141$	464.629	0.277509
$142$	930.267	0.549762
$143$	−554.583	−0.324312
$144$	−420.862	−0.243555
$145$	676.600	0.387507
$146$	341.890	0.193801
$147$	−722.797	−0.405546
$148$	576.659	0.320277
$149$	−14.4687	−0.00795519	−0.00397760	−	0.999992i	$-0.501266\pi$
$149$	−14.4687	−0.00795519	−0.00397760	+	0.999992i	$0.501266\pi$
$150$	−41.7163	−0.0227075
$151$	−1833.48	−0.988124	−0.494062	−	0.869427i	$-0.664488\pi$
$151$	−1833.48	−0.988124	−0.494062	+	0.869427i	$0.664488\pi$
$152$	−1281.62	−0.683904
$153$	447.166	0.236283
$154$	−765.058	−0.400325
$155$	1142.37	0.591981
$156$	−168.256	−0.0863540
$157$	−1136.52	−0.577734	−0.288867	−	0.957369i	$-0.593278\pi$
$157$	−1136.52	−0.577734	−0.288867	+	0.957369i	$0.593278\pi$
$158$	−730.786	−0.367964
$159$	−395.655	−0.197343
$160$	−160.000	−0.0790569
$161$	−2471.13	−1.20964
$162$	1346.20	0.652886
$163$	2135.29	1.02607	0.513033	−	0.858369i	$-0.328522\pi$
$163$	2135.29	1.02607	0.513033	+	0.858369i	$0.328522\pi$
$164$	−119.851	−0.0570659
$165$	−45.8879	−0.0216507
$166$	−12.9206	−0.00604115
$167$	3551.10	1.64546	0.822731	−	0.568431i	$-0.192449\pi$
$167$	3551.10	1.64546	0.822731	+	0.568431i	$0.192449\pi$
$168$	−232.112	−0.106594
$169$	344.836	0.156958
$170$	170.000	0.0766965
$171$	4213.96	1.88450
$172$	−1181.28	−0.523674
$173$	−2798.87	−1.23002	−0.615012	−	0.788518i	$-0.710849\pi$
$173$	−2798.87	−1.23002	−0.615012	+	0.788518i	$0.710849\pi$
$174$	225.802	0.0983793
$175$	869.384	0.375538
$176$	−176.000	−0.0753778
$177$	−315.137	−0.133826
$178$	476.308	0.200566
$179$	4020.79	1.67893	0.839464	−	0.543415i	$-0.182869\pi$
$179$	4020.79	1.67893	0.839464	+	0.543415i	$0.182869\pi$
$180$	526.078	0.217842
$181$	302.833	0.124362	0.0621808	−	0.998065i	$-0.480194\pi$
$181$	302.833	0.124362	0.0621808	+	0.998065i	$0.480194\pi$
$182$	3506.51	1.42813
$183$	70.2291	0.0283688
$184$	−568.479	−0.227765
$185$	−720.823	−0.286465
$186$	381.242	0.150290
$187$	187.000	0.0731272
$188$	−2227.57	−0.864160
$189$	1546.56	0.595214
$190$	1602.03	0.611702
$191$	−2095.63	−0.793897	−0.396949	−	0.917841i	$-0.629931\pi$
$191$	−2095.63	−0.793897	−0.396949	+	0.917841i	$0.629931\pi$
$192$	−53.3968	−0.0200708
$193$	−3824.03	−1.42622	−0.713109	−	0.701054i	$-0.752713\pi$
$193$	−3824.03	−1.42622	−0.713109	+	0.701054i	$0.752713\pi$
$194$	−612.145	−0.226544
$195$	210.319	0.0772374
$196$	3465.30	1.26286
$197$	3063.51	1.10795	0.553975	−	0.832533i	$-0.313110\pi$
$197$	3063.51	1.10795	0.553975	+	0.832533i	$0.313110\pi$
$198$	578.686	0.207704
$199$	−234.094	−0.0833895	−0.0416947	−	0.999130i	$-0.513276\pi$
$199$	−234.094	−0.0833895	−0.0416947	+	0.999130i	$0.513276\pi$
$200$	200.000	0.0707107
$201$	660.290	0.231708
$202$	−3553.16	−1.23762
$203$	−4705.80	−1.62701
$204$	56.7341	0.0194715
$205$	149.814	0.0510413
$206$	317.162	0.107270
$207$	1869.15	0.627608
$208$	806.666	0.268905
$209$	1762.23	0.583235
$210$	290.140	0.0953406
$211$	−4632.62	−1.51148	−0.755741	−	0.654870i	$-0.772723\pi$
$211$	−4632.62	−1.51148	−0.755741	+	0.654870i	$0.772723\pi$
$212$	1896.88	0.614522
$213$	−388.073	−0.124837
$214$	−3065.96	−0.979369
$215$	1476.60	0.468388
$216$	355.783	0.112074
$217$	−7945.23	−2.48552
$218$	3403.01	1.05725
$219$	−142.624	−0.0440073
$220$	220.000	0.0674200
$221$	−857.083	−0.260876
$222$	−240.561	−0.0727269
$223$	−1797.35	−0.539728	−0.269864	−	0.962899i	$-0.586979\pi$
$223$	−1797.35	−0.539728	−0.269864	+	0.962899i	$0.586979\pi$
$224$	1112.81	0.331932
$225$	−657.598	−0.194844
$226$	−4016.35	−1.18214
$227$	−3281.44	−0.959459	−0.479729	−	0.877416i	$-0.659265\pi$
$227$	−3281.44	−0.959459	−0.479729	+	0.877416i	$0.659265\pi$
$228$	534.645	0.155297
$229$	6377.08	1.84021	0.920107	−	0.391667i	$-0.128101\pi$
$229$	6377.08	1.84021	0.920107	+	0.391667i	$0.128101\pi$
$230$	710.598	0.203719
$231$	319.154	0.0909037
$232$	−1082.56	−0.306352
$233$	−5803.96	−1.63189	−0.815944	−	0.578131i	$-0.803782\pi$
$233$	−5803.96	−1.63189	−0.815944	+	0.578131i	$0.803782\pi$
$234$	−2652.31	−0.740969
$235$	2784.46	0.772928
$236$	1510.86	0.416730
$237$	304.857	0.0835552
$238$	−1182.36	−0.322022
$239$	−332.323	−0.0899422	−0.0449711	−	0.998988i	$-0.514320\pi$
$239$	−332.323	−0.0899422	−0.0449711	+	0.998988i	$0.514320\pi$
$240$	66.7461	0.0179518
$241$	5988.37	1.60060	0.800300	−	0.599600i	$-0.204673\pi$
$241$	5988.37	1.60060	0.800300	+	0.599600i	$0.204673\pi$
$242$	242.000	0.0642824
$243$	−1762.35	−0.465246
$244$	−336.699	−0.0883399
$245$	−4331.62	−1.12954
$246$	49.9975	0.0129582
$247$	−8076.89	−2.08065
$248$	−1827.78	−0.468002
$249$	5.38998	0.00137179
$250$	−250.000	−0.0632456
$251$	−5937.33	−1.49307	−0.746536	−	0.665345i	$-0.768284\pi$
$251$	−5937.33	−1.49307	−0.746536	+	0.665345i	$0.768284\pi$
$252$	−3658.91	−0.914641
$253$	781.658	0.194239
$254$	925.393	0.228600
$255$	−70.9177	−0.0174158
$256$	256.000	0.0625000
$257$	805.375	0.195478	0.0977392	−	0.995212i	$-0.468839\pi$
$257$	805.375	0.195478	0.0977392	+	0.995212i	$0.468839\pi$
$258$	492.787	0.118913
$259$	5013.38	1.20276
$260$	−1008.33	−0.240516
$261$	3559.44	0.844153
$262$	−1984.16	−0.467869
$263$	2523.16	0.591576	0.295788	−	0.955254i	$-0.404418\pi$
$263$	2523.16	0.591576	0.295788	+	0.955254i	$0.404418\pi$
$264$	73.4207	0.0171164
$265$	−2371.11	−0.549645
$266$	−11142.2	−2.56832
$267$	−198.698	−0.0455435
$268$	−3165.62	−0.721534
$269$	−2048.97	−0.464417	−0.232209	−	0.972666i	$-0.574595\pi$
$269$	−2048.97	−0.464417	−0.232209	+	0.972666i	$0.574595\pi$
$270$	−444.728	−0.100242
$271$	−2717.34	−0.609101	−0.304551	−	0.952496i	$-0.598506\pi$
$271$	−2717.34	−0.609101	−0.304551	+	0.952496i	$0.598506\pi$
$272$	−272.000	−0.0606339
$273$	−1462.79	−0.324292
$274$	1803.87	0.397722
$275$	−275.000	−0.0603023
$276$	237.148	0.0517197
$277$	1405.91	0.304955	0.152478	−	0.988307i	$-0.451275\pi$
$277$	1405.91	0.304955	0.152478	+	0.988307i	$0.451275\pi$
$278$	−3464.87	−0.747514
$279$	6009.73	1.28958
$280$	−1391.01	−0.296889
$281$	−5461.36	−1.15942	−0.579711	−	0.814822i	$-0.696834\pi$
$281$	−5461.36	−1.15942	−0.579711	+	0.814822i	$0.696834\pi$
$282$	929.258	0.196229
$283$	−6324.81	−1.32852	−0.664260	−	0.747502i	$-0.731253\pi$
$283$	−6324.81	−1.32852	−0.664260	+	0.747502i	$0.731253\pi$
$284$	1860.53	0.388741
$285$	−668.307	−0.138902
$286$	−1109.17	−0.229323
$287$	−1041.97	−0.214304
$288$	−841.725	−0.172219
$289$	289.000	0.0588235
$290$	1353.20	0.274009
$291$	255.364	0.0514423
$292$	683.779	0.137038
$293$	−5658.38	−1.12821	−0.564106	−	0.825702i	$-0.690779\pi$
$293$	−5658.38	−1.12821	−0.564106	+	0.825702i	$0.690779\pi$
$294$	−1445.59	−0.286764
$295$	−1888.57	−0.372735
$296$	1153.32	0.226470
$297$	−489.201	−0.0955768
$298$	−28.9374	−0.00562517
$299$	−3582.60	−0.692933
$300$	−83.4326	−0.0160566
$301$	−10269.9	−1.96660
$302$	−3666.97	−0.698709
$303$	1482.25	0.281032
$304$	−2563.25	−0.483593
$305$	420.873	0.0790136
$306$	894.333	0.167077
$307$	6588.64	1.22486	0.612432	−	0.790523i	$-0.290191\pi$
$307$	6588.64	1.22486	0.612432	+	0.790523i	$0.290191\pi$
$308$	−1530.12	−0.283073
$309$	−132.308	−0.0243584
$310$	2284.73	0.418593
$311$	−8479.54	−1.54608	−0.773039	−	0.634358i	$-0.781264\pi$
$311$	−8479.54	−1.54608	−0.773039	+	0.634358i	$0.781264\pi$
$312$	−336.511	−0.0610615
$313$	−632.026	−0.114135	−0.0570674	−	0.998370i	$-0.518175\pi$
$313$	−632.026	−0.114135	−0.0570674	+	0.998370i	$0.518175\pi$
$314$	−2273.04	−0.408519
$315$	4573.64	0.818080
$316$	−1461.57	−0.260189
$317$	−5298.73	−0.938821	−0.469410	−	0.882980i	$-0.655534\pi$
$317$	−5298.73	−0.938821	−0.469410	+	0.882980i	$0.655534\pi$
$318$	−791.310	−0.139542
$319$	1488.52	0.261257
$320$	−320.000	−0.0559017
$321$	1279.01	0.222390
$322$	−4942.26	−0.855346
$323$	2723.45	0.469154
$324$	2692.40	0.461660
$325$	1260.42	0.215124
$326$	4270.58	0.725539
$327$	−1419.61	−0.240075
$328$	−239.702	−0.0403517
$329$	−19366.1	−3.24525
$330$	−91.7758	−0.0153094
$331$	1919.12	0.318684	0.159342	−	0.987223i	$-0.449063\pi$
$331$	1919.12	0.318684	0.159342	+	0.987223i	$0.449063\pi$
$332$	−25.8411	−0.00427174
$333$	−3792.09	−0.624040
$334$	7102.19	1.16352
$335$	3957.03	0.645360
$336$	−464.223	−0.0753734
$337$	10795.6	1.74502	0.872509	−	0.488597i	$-0.162491\pi$
$337$	10795.6	1.74502	0.872509	+	0.488597i	$0.162491\pi$
$338$	689.672	0.110986
$339$	1675.47	0.268434
$340$	340.000	0.0542326
$341$	2513.20	0.399113
$342$	8427.92	1.33254
$343$	18198.8	2.86485
$344$	−2362.56	−0.370293
$345$	−296.435	−0.0462595
$346$	−5597.74	−0.869758
$347$	−2270.73	−0.351295	−0.175648	−	0.984453i	$-0.556202\pi$
$347$	−2270.73	−0.351295	−0.175648	+	0.984453i	$0.556202\pi$
$348$	451.604	0.0695647
$349$	8434.61	1.29368	0.646840	−	0.762626i	$-0.276090\pi$
$349$	8434.61	1.29368	0.646840	+	0.762626i	$0.276090\pi$
$350$	1738.77	0.265546
$351$	2242.17	0.340963
$352$	−352.000	−0.0533002
$353$	2640.82	0.398177	0.199089	−	0.979981i	$-0.436202\pi$
$353$	2640.82	0.398177	0.199089	+	0.979981i	$0.436202\pi$
$354$	−630.273	−0.0946289
$355$	−2325.67	−0.347700
$356$	952.616	0.141822
$357$	493.237	0.0731229
$358$	8041.59	1.18718
$359$	5661.50	0.832319	0.416159	−	0.909292i	$-0.363376\pi$
$359$	5661.50	0.832319	0.416159	+	0.909292i	$0.363376\pi$
$360$	1052.16	0.154037
$361$	18806.0	2.74179
$362$	605.667	0.0879369
$363$	−100.953	−0.0145969
$364$	7013.02	1.00984
$365$	−854.724	−0.122571
$366$	140.458	0.0200598
$367$	3620.95	0.515019	0.257509	−	0.966276i	$-0.417098\pi$
$367$	3620.95	0.515019	0.257509	+	0.966276i	$0.417098\pi$
$368$	−1136.96	−0.161054
$369$	788.139	0.111189
$370$	−1441.65	−0.202561
$371$	16491.2	2.30776
$372$	762.484	0.106271
$373$	563.834	0.0782687	0.0391343	−	0.999234i	$-0.487540\pi$
$373$	563.834	0.0782687	0.0391343	+	0.999234i	$0.487540\pi$
$374$	374.000	0.0517088
$375$	104.291	0.0143615
$376$	−4455.13	−0.611053
$377$	−6822.38	−0.932017
$378$	3093.11	0.420880
$379$	1590.09	0.215507	0.107754	−	0.994178i	$-0.465634\pi$
$379$	1590.09	0.215507	0.107754	+	0.994178i	$0.465634\pi$
$380$	3204.06	0.432539
$381$	−386.040	−0.0519092
$382$	−4191.26	−0.561370
$383$	4891.81	0.652636	0.326318	−	0.945260i	$-0.394192\pi$
$383$	4891.81	0.652636	0.326318	+	0.945260i	$0.394192\pi$
$384$	−106.794	−0.0141922
$385$	1912.64	0.253188
$386$	−7648.07	−1.00849
$387$	7768.08	1.02035
$388$	−1224.29	−0.160191
$389$	−9076.53	−1.18303	−0.591514	−	0.806294i	$-0.701470\pi$
$389$	−9076.53	−1.18303	−0.591514	+	0.806294i	$0.701470\pi$
$390$	420.639	0.0546151
$391$	1208.02	0.156246
$392$	6930.60	0.892979
$393$	827.717	0.106241
$394$	6127.02	0.783439
$395$	1826.97	0.232721
$396$	1157.37	0.146869
$397$	7160.46	0.905222	0.452611	−	0.891708i	$-0.350493\pi$
$397$	7160.46	0.905222	0.452611	+	0.891708i	$0.350493\pi$
$398$	−468.189	−0.0589653
$399$	4648.12	0.583201
$400$	400.000	0.0500000
$401$	−14335.8	−1.78528	−0.892640	−	0.450771i	$-0.851149\pi$
$401$	−14335.8	−1.78528	−0.892640	+	0.450771i	$0.851149\pi$
$402$	1320.58	0.163842
$403$	−11518.8	−1.42381
$404$	−7106.32	−0.875130
$405$	−3365.50	−0.412921
$406$	−9411.60	−1.15047
$407$	−1585.81	−0.193134
$408$	113.468	0.0137684
$409$	10733.6	1.29766	0.648828	−	0.760935i	$-0.275259\pi$
$409$	10733.6	1.29766	0.648828	+	0.760935i	$0.275259\pi$
$410$	299.628	0.0360916
$411$	−752.508	−0.0903127
$412$	634.324	0.0758517
$413$	13135.1	1.56498
$414$	3738.30	0.443786
$415$	32.3014	0.00382076
$416$	1613.33	0.190144
$417$	1445.41	0.169741
$418$	3524.46	0.412409
$419$	−3886.78	−0.453179	−0.226589	−	0.973990i	$-0.572758\pi$
$419$	−3886.78	−0.453179	−0.226589	+	0.973990i	$0.572758\pi$
$420$	580.279	0.0674160
$421$	−3070.71	−0.355480	−0.177740	−	0.984077i	$-0.556879\pi$
$421$	−3070.71	−0.355480	−0.177740	+	0.984077i	$0.556879\pi$
$422$	−9265.24	−1.06878
$423$	14648.4	1.68376
$424$	3793.77	0.434532
$425$	−425.000	−0.0485071
$426$	−776.145	−0.0882732
$427$	−2927.20	−0.331750
$428$	−6131.93	−0.692518
$429$	462.703	0.0520734
$430$	2953.20	0.331200
$431$	26.2187	0.00293018	0.00146509	−	0.999999i	$-0.499534\pi$
$431$	26.2187	0.00293018	0.00146509	+	0.999999i	$0.499534\pi$
$432$	711.565	0.0792481
$433$	−5606.05	−0.622193	−0.311097	−	0.950378i	$-0.600696\pi$
$433$	−5606.05	−0.622193	−0.311097	+	0.950378i	$0.600696\pi$
$434$	−15890.5	−1.75753
$435$	−564.505	−0.0622205
$436$	6806.01	0.747589
$437$	11384.0	1.24616
$438$	−285.247	−0.0311179
$439$	8258.70	0.897873	0.448937	−	0.893564i	$-0.351803\pi$
$439$	8258.70	0.897873	0.448937	+	0.893564i	$0.351803\pi$
$440$	440.000	0.0476731
$441$	−22787.7	−2.46061
$442$	−1714.17	−0.184467
$443$	−10405.2	−1.11595	−0.557975	−	0.829857i	$-0.688422\pi$
$443$	−10405.2	−1.11595	−0.557975	+	0.829857i	$0.688422\pi$
$444$	−481.121	−0.0514257
$445$	−1190.77	−0.126849
$446$	−3594.69	−0.381645
$447$	12.0716	0.00127733
$448$	2225.62	0.234711
$449$	14377.9	1.51121	0.755605	−	0.655027i	$-0.227343\pi$
$449$	14377.9	1.51121	0.755605	+	0.655027i	$0.227343\pi$
$450$	−1315.20	−0.137775
$451$	329.591	0.0344120
$452$	−8032.69	−0.835899
$453$	1529.72	0.158659
$454$	−6562.89	−0.678440
$455$	−8766.28	−0.903229
$456$	1069.29	0.109812
$457$	4037.75	0.413300	0.206650	−	0.978415i	$-0.433744\pi$
$457$	4037.75	0.413300	0.206650	+	0.978415i	$0.433744\pi$
$458$	12754.2	1.30123
$459$	−756.038	−0.0768820
$460$	1421.20	0.144051
$461$	−1655.24	−0.167228	−0.0836142	−	0.996498i	$-0.526646\pi$
$461$	−1655.24	−0.167228	−0.0836142	+	0.996498i	$0.526646\pi$
$462$	638.307	0.0642786
$463$	−628.003	−0.0630362	−0.0315181	−	0.999503i	$-0.510034\pi$
$463$	−628.003	−0.0630362	−0.0315181	+	0.999503i	$0.510034\pi$
$464$	−2165.12	−0.216623
$465$	−953.105	−0.0950520
$466$	−11607.9	−1.15392
$467$	18883.4	1.87114	0.935568	−	0.353147i	$-0.114889\pi$
$467$	18883.4	1.87114	0.935568	+	0.353147i	$0.114889\pi$
$468$	−5304.62	−0.523944
$469$	−27521.4	−2.70964
$470$	5568.92	0.546543
$471$	948.228	0.0927644
$472$	3021.71	0.294673
$473$	3248.53	0.315787
$474$	609.714	0.0590824
$475$	−4005.07	−0.386874
$476$	−2364.72	−0.227704
$477$	−12473.9	−1.19736
$478$	−664.646	−0.0635987
$479$	16757.8	1.59850	0.799251	−	0.600997i	$-0.205230\pi$
$479$	16757.8	1.59850	0.799251	+	0.600997i	$0.205230\pi$
$480$	133.492	0.0126939
$481$	7268.30	0.688993
$482$	11976.7	1.13180
$483$	2061.73	0.194227
$484$	484.000	0.0454545
$485$	1530.36	0.143279
$486$	−3524.70	−0.328979
$487$	408.008	0.0379643	0.0189822	−	0.999820i	$-0.493957\pi$
$487$	408.008	0.0379643	0.0189822	+	0.999820i	$0.493957\pi$
$488$	−673.398	−0.0624657
$489$	−1781.53	−0.164752
$490$	−8663.24	−0.798705
$491$	−3817.39	−0.350868	−0.175434	−	0.984491i	$-0.556133\pi$
$491$	−3817.39	−0.350868	−0.175434	+	0.984491i	$0.556133\pi$
$492$	99.9949	0.00916285
$493$	2300.44	0.210155
$494$	−16153.8	−1.47124
$495$	−1446.71	−0.131364
$496$	−3655.57	−0.330927
$497$	16175.2	1.45987
$498$	10.7800	0.000970003 0
$499$	9090.02	0.815482	0.407741	−	0.913098i	$-0.366317\pi$
$499$	9090.02	0.815482	0.407741	+	0.913098i	$0.366317\pi$
$500$	−500.000	−0.0447214
$501$	−2962.77	−0.264205
$502$	−11874.7	−1.05576
$503$	−2099.33	−0.186093	−0.0930464	−	0.995662i	$-0.529660\pi$
$503$	−2099.33	−0.186093	−0.0930464	+	0.995662i	$0.529660\pi$
$504$	−7317.82	−0.646749
$505$	8882.90	0.782740
$506$	1563.32	0.137348
$507$	−287.706	−0.0252021
$508$	1850.79	0.161644
$509$	−22461.9	−1.95600	−0.978001	−	0.208599i	$-0.933110\pi$
$509$	−22461.9	−1.95600	−0.978001	+	0.208599i	$0.933110\pi$
$510$	−141.835	−0.0123149
$511$	5944.66	0.514631
$512$	512.000	0.0441942
$513$	−7124.67	−0.613181
$514$	1610.75	0.138224
$515$	−792.905	−0.0678438
$516$	985.574	0.0840842
$517$	6125.81	0.521108
$518$	10026.8	0.850483
$519$	2335.17	0.197500
$520$	−2016.67	−0.170070
$521$	−21453.6	−1.80403	−0.902015	−	0.431704i	$-0.857912\pi$
$521$	−21453.6	−1.80403	−0.902015	+	0.431704i	$0.857912\pi$
$522$	7118.89	0.596907
$523$	−9180.58	−0.767569	−0.383784	−	0.923423i	$-0.625379\pi$
$523$	−9180.58	−0.767569	−0.383784	+	0.923423i	$0.625379\pi$
$524$	−3968.31	−0.330833
$525$	−725.349	−0.0602987
$526$	5046.31	0.418307
$527$	3884.04	0.321047
$528$	146.841	0.0121031
$529$	−7117.50	−0.584984
$530$	−4742.21	−0.388658
$531$	−9935.35	−0.811973
$532$	−22284.4	−1.81608
$533$	−1510.62	−0.122762
$534$	−397.396	−0.0322041
$535$	7664.91	0.619407
$536$	−6331.25	−0.510202
$537$	−3354.65	−0.269579
$538$	−4097.95	−0.328393
$539$	−9529.57	−0.761535
$540$	−889.456	−0.0708817
$541$	22252.5	1.76841	0.884205	−	0.467098i	$-0.154701\pi$
$541$	22252.5	1.76841	0.884205	+	0.467098i	$0.154701\pi$
$542$	−5434.67	−0.430700
$543$	−252.662	−0.0199682
$544$	−544.000	−0.0428746
$545$	−8507.52	−0.668664
$546$	−2925.57	−0.229309
$547$	−8091.00	−0.632443	−0.316221	−	0.948685i	$-0.602414\pi$
$547$	−8091.00	−0.632443	−0.316221	+	0.948685i	$0.602414\pi$
$548$	3607.74	0.281232
$549$	2214.12	0.172125
$550$	−550.000	−0.0426401
$551$	21678.7	1.67612
$552$	474.296	0.0365714
$553$	−12706.7	−0.977111
$554$	2811.81	0.215636
$555$	601.401	0.0459965
$556$	−6929.73	−0.528572
$557$	23180.3	1.76334	0.881671	−	0.471864i	$-0.156419\pi$
$557$	23180.3	1.76334	0.881671	+	0.471864i	$0.156419\pi$
$558$	12019.5	0.911872
$559$	−14889.1	−1.12655
$560$	−2782.03	−0.209932
$561$	−156.019	−0.0117418
$562$	−10922.7	−0.819835
$563$	−13655.3	−1.02221	−0.511103	−	0.859520i	$-0.670763\pi$
$563$	−13655.3	−1.02221	−0.511103	+	0.859520i	$0.670763\pi$
$564$	1858.52	0.138755
$565$	10040.9	0.747650
$566$	−12649.6	−0.939405
$567$	23407.3	1.73371
$568$	3721.07	0.274881
$569$	−20683.2	−1.52388	−0.761938	−	0.647650i	$-0.775752\pi$
$569$	−20683.2	−1.52388	−0.761938	+	0.647650i	$0.775752\pi$
$570$	−1336.61	−0.0982186
$571$	15624.8	1.14514	0.572571	−	0.819855i	$-0.305946\pi$
$571$	15624.8	1.14514	0.572571	+	0.819855i	$0.305946\pi$
$572$	−2218.33	−0.162156
$573$	1748.44	0.127473
$574$	−2083.93	−0.151536
$575$	−1776.50	−0.128843
$576$	−1683.45	−0.121777
$577$	−456.814	−0.0329591	−0.0164796	−	0.999864i	$-0.505246\pi$
$577$	−456.814	−0.0329591	−0.0164796	+	0.999864i	$0.505246\pi$
$578$	578.000	0.0415945
$579$	3190.49	0.229002
$580$	2706.40	0.193754
$581$	−224.659	−0.0160420
$582$	510.729	0.0363752
$583$	−5216.43	−0.370570
$584$	1367.56	0.0969006
$585$	6630.77	0.468630
$586$	−11316.8	−0.797766
$587$	−16687.8	−1.17339	−0.586695	−	0.809808i	$-0.699571\pi$
$587$	−16687.8	−1.17339	−0.586695	+	0.809808i	$0.699571\pi$
$588$	−2891.19	−0.202773
$589$	36602.0	2.56054
$590$	−3777.14	−0.263563
$591$	−2555.97	−0.177899
$592$	2306.63	0.160139
$593$	6862.72	0.475241	0.237621	−	0.971358i	$-0.423632\pi$
$593$	6862.72	0.475241	0.237621	+	0.971358i	$0.423632\pi$
$594$	−978.402	−0.0675830
$595$	2955.90	0.203664
$596$	−57.8749	−0.00397760
$597$	195.311	0.0133895
$598$	−7165.19	−0.489977
$599$	20502.6	1.39852	0.699261	−	0.714867i	$-0.253513\pi$
$599$	20502.6	1.39852	0.699261	+	0.714867i	$0.253513\pi$
$600$	−166.865	−0.0113537
$601$	−4174.00	−0.283296	−0.141648	−	0.989917i	$-0.545240\pi$
$601$	−4174.00	−0.283296	−0.141648	+	0.989917i	$0.545240\pi$
$602$	−20539.7	−1.39059
$603$	20817.1	1.40586
$604$	−7333.93	−0.494062
$605$	−605.000	−0.0406558
$606$	2964.49	0.198720
$607$	25795.8	1.72491	0.862453	−	0.506137i	$-0.168927\pi$
$607$	25795.8	1.72491	0.862453	+	0.506137i	$0.168927\pi$
$608$	−5126.49	−0.341952
$609$	3926.17	0.261242
$610$	841.747	0.0558710
$611$	−28076.6	−1.85901
$612$	1788.67	0.118141
$613$	21268.2	1.40133	0.700665	−	0.713490i	$-0.252887\pi$
$613$	21268.2	1.40133	0.700665	+	0.713490i	$0.252887\pi$
$614$	13177.3	0.866110
$615$	−124.994	−0.00819550
$616$	−3060.23	−0.200163
$617$	−21075.2	−1.37513	−0.687567	−	0.726121i	$-0.741321\pi$
$617$	−21075.2	−1.37513	−0.687567	+	0.726121i	$0.741321\pi$
$618$	−264.616	−0.0172240
$619$	−3954.81	−0.256797	−0.128398	−	0.991723i	$-0.540984\pi$
$619$	−3954.81	−0.256797	−0.128398	+	0.991723i	$0.540984\pi$
$620$	4569.46	0.295990
$621$	−3160.23	−0.204212
$622$	−16959.1	−1.09324
$623$	8281.89	0.532595
$624$	−673.022	−0.0431770
$625$	625.000	0.0400000
$626$	−1264.05	−0.0807055
$627$	−1470.27	−0.0936477
$628$	−4546.08	−0.288867
$629$	−2450.80	−0.155357
$630$	9147.27	0.578470
$631$	−156.043	−0.00984464	−0.00492232	−	0.999988i	$-0.501567\pi$
$631$	−156.043	−0.00984464	−0.00492232	+	0.999988i	$0.501567\pi$
$632$	−2923.15	−0.183982
$633$	3865.12	0.242693
$634$	−10597.5	−0.663847
$635$	−2313.48	−0.144579
$636$	−1582.62	−0.0986713
$637$	43677.2	2.71672
$638$	2977.04	0.184737
$639$	−12234.8	−0.757437
$640$	−640.000	−0.0395285
$641$	19554.1	1.20490	0.602450	−	0.798157i	$-0.294191\pi$
$641$	19554.1	1.20490	0.602450	+	0.798157i	$0.294191\pi$
$642$	2558.01	0.157253
$643$	−3372.02	−0.206811	−0.103406	−	0.994639i	$-0.532974\pi$
$643$	−3372.02	−0.206811	−0.103406	+	0.994639i	$0.532974\pi$
$644$	−9884.52	−0.604821
$645$	−1231.97	−0.0752072
$646$	5446.90	0.331742
$647$	−22142.1	−1.34543	−0.672717	−	0.739900i	$-0.734873\pi$
$647$	−22142.1	−1.34543	−0.672717	+	0.739900i	$0.734873\pi$
$648$	5384.80	0.326443
$649$	−4154.86	−0.251298
$650$	2520.83	0.152116
$651$	6628.91	0.399090
$652$	8541.16	0.513033
$653$	−10579.5	−0.634009	−0.317004	−	0.948424i	$-0.602677\pi$
$653$	−10579.5	−0.634009	−0.317004	+	0.948424i	$0.602677\pi$
$654$	−2839.22	−0.169759
$655$	4960.39	0.295906
$656$	−479.405	−0.0285330
$657$	−4496.51	−0.267010
$658$	−38732.2	−2.29474
$659$	−15243.4	−0.901059	−0.450529	−	0.892762i	$-0.648765\pi$
$659$	−15243.4	−0.901059	−0.450529	+	0.892762i	$0.648765\pi$
$660$	−183.552	−0.0108254
$661$	30605.3	1.80092	0.900460	−	0.434939i	$-0.143230\pi$
$661$	30605.3	1.80092	0.900460	+	0.434939i	$0.143230\pi$
$662$	3838.24	0.225344
$663$	715.086	0.0418878
$664$	−51.6823	−0.00302057
$665$	27855.5	1.62435
$666$	−7584.19	−0.441263
$667$	9615.81	0.558210
$668$	14204.4	0.822731
$669$	1499.57	0.0866619
$670$	7914.06	0.456338
$671$	925.922	0.0532710
$672$	−928.447	−0.0532970
$673$	4393.77	0.251660	0.125830	−	0.992052i	$-0.459841\pi$
$673$	4393.77	0.251660	0.125830	+	0.992052i	$0.459841\pi$
$674$	21591.1	1.23391
$675$	1111.82	0.0633985
$676$	1379.34	0.0784789
$677$	26347.3	1.49573	0.747865	−	0.663851i	$-0.231079\pi$
$677$	26347.3	1.49573	0.747865	+	0.663851i	$0.231079\pi$
$678$	3350.94	0.189811
$679$	−10643.8	−0.601577
$680$	680.000	0.0383482
$681$	2737.79	0.154057
$682$	5026.41	0.282216
$683$	9819.09	0.550098	0.275049	−	0.961430i	$-0.411306\pi$
$683$	9819.09	0.550098	0.275049	+	0.961430i	$0.411306\pi$
$684$	16855.8	0.942250
$685$	−4509.68	−0.251542
$686$	36397.6	2.02575
$687$	−5320.56	−0.295476
$688$	−4725.13	−0.261837
$689$	23908.6	1.32198
$690$	−592.870	−0.0327104
$691$	1894.17	0.104280	0.0521401	−	0.998640i	$-0.483396\pi$
$691$	1894.17	0.104280	0.0521401	+	0.998640i	$0.483396\pi$
$692$	−11195.5	−0.615012
$693$	10062.0	0.551549
$694$	−4541.47	−0.248403
$695$	8662.16	0.472769
$696$	903.208	0.0491897
$697$	509.368	0.0276810
$698$	16869.2	0.914770
$699$	4842.39	0.262026
$700$	3477.53	0.187769
$701$	2188.94	0.117939	0.0589695	−	0.998260i	$-0.481219\pi$
$701$	2188.94	0.117939	0.0589695	+	0.998260i	$0.481219\pi$
$702$	4484.34	0.241098
$703$	−23095.6	−1.23907
$704$	−704.000	−0.0376889
$705$	−2323.15	−0.124106
$706$	5281.63	0.281554
$707$	−61781.2	−3.28645
$708$	−1260.55	−0.0669128
$709$	−16246.4	−0.860572	−0.430286	−	0.902693i	$-0.641587\pi$
$709$	−16246.4	−0.860572	−0.430286	+	0.902693i	$0.641587\pi$
$710$	−4651.33	−0.245861
$711$	9611.26	0.506963
$712$	1905.23	0.100283
$713$	16235.3	0.852756
$714$	986.475	0.0517057
$715$	2772.91	0.145037
$716$	16083.2	0.839464
$717$	277.266	0.0144417
$718$	11323.0	0.588538
$719$	9794.19	0.508013	0.254007	−	0.967202i	$-0.418252\pi$
$719$	9794.19	0.508013	0.254007	+	0.967202i	$0.418252\pi$
$720$	2104.31	0.108921
$721$	5514.71	0.284852
$722$	37611.9	1.93874
$723$	−4996.25	−0.257002
$724$	1211.33	0.0621808
$725$	−3383.00	−0.173299
$726$	−201.907	−0.0103216
$727$	−31041.2	−1.58357	−0.791785	−	0.610800i	$-0.790848\pi$
$727$	−31041.2	−1.58357	−0.791785	+	0.610800i	$0.790848\pi$
$728$	14026.0	0.714066
$729$	−16703.3	−0.848618
$730$	−1709.45	−0.0866705
$731$	5020.45	0.254019
$732$	280.916	0.0141844
$733$	−21604.8	−1.08867	−0.544334	−	0.838869i	$-0.683217\pi$
$733$	−21604.8	−1.08867	−0.544334	+	0.838869i	$0.683217\pi$
$734$	7241.89	0.364173
$735$	3613.98	0.181366
$736$	−2273.91	−0.113883
$737$	8705.46	0.435102
$738$	1576.28	0.0786227
$739$	−26874.6	−1.33775	−0.668877	−	0.743373i	$-0.733225\pi$
$739$	−26874.6	−1.33775	−0.668877	+	0.743373i	$0.733225\pi$
$740$	−2883.29	−0.143232
$741$	6738.75	0.334081
$742$	32982.4	1.63184
$743$	17642.1	0.871096	0.435548	−	0.900166i	$-0.356555\pi$
$743$	17642.1	0.871096	0.435548	+	0.900166i	$0.356555\pi$
$744$	1524.97	0.0751452
$745$	72.3436	0.00355767
$746$	1127.67	0.0553443
$747$	169.931	0.00832321
$748$	748.000	0.0365636
$749$	−53310.0	−2.60067
$750$	208.581	0.0101551
$751$	12570.7	0.610799	0.305399	−	0.952224i	$-0.401210\pi$
$751$	12570.7	0.610799	0.305399	+	0.952224i	$0.401210\pi$
$752$	−8910.27	−0.432080
$753$	4953.67	0.239737
$754$	−13644.8	−0.659035
$755$	9167.42	0.441903
$756$	6186.23	0.297607
$757$	24029.8	1.15374	0.576869	−	0.816837i	$-0.304274\pi$
$757$	24029.8	1.15374	0.576869	+	0.816837i	$0.304274\pi$
$758$	3180.17	0.152387
$759$	−652.157	−0.0311882
$760$	6408.11	0.305851
$761$	6132.09	0.292100	0.146050	−	0.989277i	$-0.453344\pi$
$761$	6132.09	0.292100	0.146050	+	0.989277i	$0.453344\pi$
$762$	−772.079	−0.0367053
$763$	59170.4	2.80748
$764$	−8382.51	−0.396949
$765$	−2235.83	−0.105669
$766$	9783.62	0.461484
$767$	19043.1	0.896487
$768$	−213.587	−0.0100354
$769$	26397.7	1.23787	0.618937	−	0.785441i	$-0.287564\pi$
$769$	26397.7	1.23787	0.618937	+	0.785441i	$0.287564\pi$
$770$	3825.29	0.179031
$771$	−671.945	−0.0313872
$772$	−15296.1	−0.713109
$773$	23011.3	1.07071	0.535356	−	0.844626i	$-0.320177\pi$
$773$	23011.3	1.07071	0.535356	+	0.844626i	$0.320177\pi$
$774$	15536.2	0.721493
$775$	−5711.83	−0.264742
$776$	−2448.58	−0.113272
$777$	−4182.79	−0.193123
$778$	−18153.1	−0.836528
$779$	4800.13	0.220773
$780$	841.278	0.0386187
$781$	−5116.47	−0.234419
$782$	2416.03	0.110482
$783$	−6018.06	−0.274672
$784$	13861.2	0.631432
$785$	5682.60	0.258370
$786$	1655.43	0.0751239
$787$	−18753.2	−0.849402	−0.424701	−	0.905334i	$-0.639621\pi$
$787$	−18753.2	−0.849402	−0.424701	+	0.905334i	$0.639621\pi$
$788$	12254.0	0.553975
$789$	−2105.13	−0.0949870
$790$	3653.93	0.164558
$791$	−69834.9	−3.13912
$792$	2314.74	0.103852
$793$	−4243.80	−0.190040
$794$	14320.9	0.640088
$795$	1978.27	0.0882543
$796$	−936.377	−0.0416947
$797$	17996.2	0.799822	0.399911	−	0.916554i	$-0.369041\pi$
$797$	17996.2	0.799822	0.399911	+	0.916554i	$0.369041\pi$
$798$	9296.24	0.412385
$799$	9467.16	0.419179
$800$	800.000	0.0353553
$801$	−6264.38	−0.276331
$802$	−28671.7	−1.26238
$803$	−1880.39	−0.0826371
$804$	2641.16	0.115854
$805$	12355.6	0.540968
$806$	−23037.7	−1.00678
$807$	1709.51	0.0745696
$808$	−14212.6	−0.618810
$809$	6568.05	0.285439	0.142720	−	0.989763i	$-0.454415\pi$
$809$	6568.05	0.285439	0.142720	+	0.989763i	$0.454415\pi$
$810$	−6731.01	−0.291980
$811$	6572.05	0.284557	0.142279	−	0.989827i	$-0.454557\pi$
$811$	6572.05	0.284557	0.142279	+	0.989827i	$0.454557\pi$
$812$	−18823.2	−0.813503
$813$	2267.14	0.0978010
$814$	−3171.62	−0.136567
$815$	−10676.5	−0.458871
$816$	226.937	0.00973575
$817$	47311.2	2.02596
$818$	21467.2	0.917582
$819$	−46117.5	−1.96761
$820$	599.256	0.0255206
$821$	−27186.3	−1.15567	−0.577837	−	0.816152i	$-0.696103\pi$
$821$	−27186.3	−1.15567	−0.577837	+	0.816152i	$0.696103\pi$
$822$	−1505.02	−0.0638607
$823$	23162.2	0.981025	0.490512	−	0.871434i	$-0.336810\pi$
$823$	23162.2	0.981025	0.490512	+	0.871434i	$0.336810\pi$
$824$	1268.65	0.0536352
$825$	229.440	0.00968250
$826$	26270.3	1.10661
$827$	−12560.6	−0.528143	−0.264072	−	0.964503i	$-0.585066\pi$
$827$	−12560.6	−0.528143	−0.264072	+	0.964503i	$0.585066\pi$
$828$	7476.60	0.313804
$829$	38328.7	1.60580	0.802902	−	0.596112i	$-0.203288\pi$
$829$	38328.7	1.60580	0.802902	+	0.596112i	$0.203288\pi$
$830$	64.6028	0.00270168
$831$	−1172.98	−0.0489655
$832$	3226.66	0.134452
$833$	−14727.5	−0.612579
$834$	2890.83	0.120025
$835$	−17755.5	−0.735873
$836$	7048.93	0.291617
$837$	−10160.8	−0.419606
$838$	−7773.57	−0.320446
$839$	34396.1	1.41536	0.707679	−	0.706534i	$-0.249742\pi$
$839$	34396.1	1.41536	0.707679	+	0.706534i	$0.249742\pi$
$840$	1160.56	0.0476703
$841$	−6077.50	−0.249190
$842$	−6141.42	−0.251363
$843$	4556.55	0.186164
$844$	−18530.5	−0.755741
$845$	−1724.18	−0.0701937
$846$	29296.8	1.19060
$847$	4207.82	0.170699
$848$	7587.54	0.307261
$849$	5276.95	0.213315
$850$	−850.000	−0.0342997
$851$	−10244.3	−0.412656
$852$	−1552.29	−0.0624185
$853$	−27513.4	−1.10439	−0.552193	−	0.833717i	$-0.686209\pi$
$853$	−27513.4	−1.10439	−0.552193	+	0.833717i	$0.686209\pi$
$854$	−5854.41	−0.234583
$855$	−21069.8	−0.842774
$856$	−12263.9	−0.489684
$857$	−42515.1	−1.69462	−0.847309	−	0.531100i	$-0.821779\pi$
$857$	−42515.1	−1.69462	−0.847309	+	0.531100i	$0.821779\pi$
$858$	925.406	0.0368215
$859$	22736.2	0.903083	0.451542	−	0.892250i	$-0.350874\pi$
$859$	22736.2	0.903083	0.451542	+	0.892250i	$0.350874\pi$
$860$	5906.41	0.234194
$861$	869.340	0.0344100
$862$	52.4374	0.00207195
$863$	3811.90	0.150358	0.0751788	−	0.997170i	$-0.476047\pi$
$863$	3811.90	0.150358	0.0751788	+	0.997170i	$0.476047\pi$
$864$	1423.13	0.0560369
$865$	13994.3	0.550083
$866$	−11212.1	−0.439957
$867$	−241.120	−0.00944506
$868$	−31780.9	−1.24276
$869$	4019.32	0.156900
$870$	−1129.01	−0.0439966
$871$	−39900.0	−1.55219
$872$	13612.0	0.528625
$873$	8050.91	0.312121
$874$	22768.0	0.881165
$875$	−4346.92	−0.167946
$876$	−570.494	−0.0220037
$877$	36927.0	1.42182	0.710910	−	0.703283i	$-0.248283\pi$
$877$	36927.0	1.42182	0.710910	+	0.703283i	$0.248283\pi$
$878$	16517.4	0.634892
$879$	4720.93	0.181153
$880$	880.000	0.0337100
$881$	25782.3	0.985958	0.492979	−	0.870041i	$-0.335908\pi$
$881$	25782.3	0.985958	0.492979	+	0.870041i	$0.335908\pi$
$882$	−45575.4	−1.73991
$883$	−16980.9	−0.647172	−0.323586	−	0.946199i	$-0.604889\pi$
$883$	−16980.9	−0.647172	−0.323586	+	0.946199i	$0.604889\pi$
$884$	−3428.33	−0.130438
$885$	1575.68	0.0598486
$886$	−20810.4	−0.789096
$887$	3881.01	0.146913	0.0734564	−	0.997298i	$-0.476597\pi$
$887$	3881.01	0.146913	0.0734564	+	0.997298i	$0.476597\pi$
$888$	−962.242	−0.0363634
$889$	16090.4	0.607037
$890$	−2381.54	−0.0896959
$891$	−7404.11	−0.278392
$892$	−7189.39	−0.269864
$893$	89215.6	3.34321
$894$	24.1432	0.000903211 0
$895$	−20104.0	−0.750840
$896$	4451.24	0.165966
$897$	2989.05	0.111261
$898$	28755.7	1.06859
$899$	30917.0	1.14698
$900$	−2630.39	−0.0974219
$901$	−8061.76	−0.298087
$902$	659.182	0.0243330
$903$	8568.42	0.315769
$904$	−16065.4	−0.591070
$905$	−1514.17	−0.0556162
$906$	3059.44	0.112189
$907$	−25533.4	−0.934754	−0.467377	−	0.884058i	$-0.654801\pi$
$907$	−25533.4	−0.934754	−0.467377	+	0.884058i	$0.654801\pi$
$908$	−13125.8	−0.479729
$909$	46731.0	1.70514
$910$	−17532.6	−0.638680
$911$	−10448.6	−0.379997	−0.189998	−	0.981784i	$-0.560848\pi$
$911$	−10448.6	−0.379997	−0.189998	+	0.981784i	$0.560848\pi$
$912$	2138.58	0.0776486
$913$	71.0631	0.00257595
$914$	8075.51	0.292247
$915$	−351.146	−0.0126869
$916$	25508.3	0.920107
$917$	−34499.9	−1.24241
$918$	−1512.08	−0.0543638
$919$	14549.9	0.522261	0.261130	−	0.965304i	$-0.415905\pi$
$919$	14549.9	0.522261	0.261130	+	0.965304i	$0.415905\pi$
$920$	2842.39	0.101860
$921$	−5497.07	−0.196672
$922$	−3310.48	−0.118248
$923$	23450.5	0.836274
$924$	1276.61	0.0454519
$925$	3604.12	0.128111
$926$	−1256.01	−0.0445733
$927$	−4171.30	−0.147792
$928$	−4330.24	−0.153176
$929$	−7738.07	−0.273281	−0.136640	−	0.990621i	$-0.543631\pi$
$929$	−7738.07	−0.273281	−0.136640	+	0.990621i	$0.543631\pi$
$930$	−1906.21	−0.0672119
$931$	−138788.	−4.88569
$932$	−23215.8	−0.815944
$933$	7074.70	0.248248
$934$	37766.8	1.32309
$935$	−935.000	−0.0327035
$936$	−10609.2	−0.370485
$937$	−43885.7	−1.53008	−0.765040	−	0.643983i	$-0.777281\pi$
$937$	−43885.7	−1.53008	−0.765040	+	0.643983i	$0.777281\pi$
$938$	−55042.8	−1.91600
$939$	527.315	0.0183262
$940$	11137.8	0.386464
$941$	241.029	0.00834996	0.00417498	−	0.999991i	$-0.498671\pi$
$941$	241.029	0.00834996	0.00417498	+	0.999991i	$0.498671\pi$
$942$	1896.46	0.0655943
$943$	2129.15	0.0735257
$944$	6043.43	0.208365
$945$	−7732.79	−0.266188
$946$	6497.05	0.223295
$947$	−37617.8	−1.29083	−0.645414	−	0.763833i	$-0.723315\pi$
$947$	−37617.8	−1.29083	−0.645414	+	0.763833i	$0.723315\pi$
$948$	1219.43	0.0417776
$949$	8618.46	0.294802
$950$	−8010.14	−0.273561
$951$	4420.87	0.150743
$952$	−4729.45	−0.161011
$953$	−22141.8	−0.752617	−0.376309	−	0.926494i	$-0.622807\pi$
$953$	−22141.8	−0.752617	−0.376309	+	0.926494i	$0.622807\pi$
$954$	−24947.7	−0.846659
$955$	10478.1	0.355042
$956$	−1329.29	−0.0449711
$957$	−1241.91	−0.0419491
$958$	33515.6	1.13031
$959$	31365.1	1.05613
$960$	266.984	0.00897592
$961$	22408.9	0.752205
$962$	14536.6	0.487192
$963$	40323.4	1.34933
$964$	23953.5	0.800300
$965$	19120.2	0.637824
$966$	4123.45	0.137339
$967$	42716.4	1.42055	0.710273	−	0.703926i	$-0.248571\pi$
$967$	42716.4	1.42055	0.710273	+	0.703926i	$0.248571\pi$
$968$	968.000	0.0321412
$969$	−2272.24	−0.0753302
$970$	3060.73	0.101313
$971$	−46636.5	−1.54134	−0.770668	−	0.637236i	$-0.780077\pi$
$971$	−46636.5	−1.54134	−0.770668	+	0.637236i	$0.780077\pi$
$972$	−7049.40	−0.232623
$973$	−60245.9	−1.98499
$974$	816.016	0.0268448
$975$	−1051.60	−0.0345416
$976$	−1346.80	−0.0441699
$977$	21274.1	0.696641	0.348320	−	0.937376i	$-0.386752\pi$
$977$	21274.1	0.696641	0.348320	+	0.937376i	$0.386752\pi$
$978$	−3563.06	−0.116497
$979$	−2619.69	−0.0855217
$980$	−17326.5	−0.564770
$981$	−44756.2	−1.45663
$982$	−7634.78	−0.248101
$983$	41232.3	1.33785	0.668925	−	0.743330i	$-0.266755\pi$
$983$	41232.3	1.33785	0.668925	+	0.743330i	$0.266755\pi$
$984$	199.990	0.00647911
$985$	−15317.6	−0.495490
$986$	4600.88	0.148602
$987$	16157.6	0.521077
$988$	−32307.5	−1.04032
$989$	20985.4	0.674719
$990$	−2893.43	−0.0928881
$991$	33902.3	1.08672	0.543362	−	0.839499i	$-0.317151\pi$
$991$	33902.3	1.08672	0.543362	+	0.839499i	$0.317151\pi$
$992$	−7311.14	−0.234001
$993$	−1601.17	−0.0511699
$994$	32350.3	1.03228
$995$	1170.47	0.0372929
$996$	21.5599	0.000685896 0
$997$	24532.6	0.779292	0.389646	−	0.920965i	$-0.372597\pi$
$997$	24532.6	0.779292	0.389646	+	0.920965i	$0.372597\pi$
$998$	18180.0	0.576633
$999$	6411.41	0.203051

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1870.4.a.m.1.5	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1870.4.a.m.1.5	✓	10	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1870.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -0.834326 q^{3} +4.00000 q^{4} -5.00000 q^{5} -1.66865 q^{6} +34.7753 q^{7} +8.00000 q^{8} -26.3039 q^{9} -10.0000 q^{10} -11.0000 q^{11} -3.33730 q^{12} +50.4166 q^{13} +69.5507 q^{14} +4.17163 q^{15} +16.0000 q^{16} -17.0000 q^{17} -52.6078 q^{18} -160.203 q^{19} -20.0000 q^{20} -29.0140 q^{21} -22.0000 q^{22} -71.0598 q^{23} -6.67461 q^{24} +25.0000 q^{25} +100.833 q^{26} +44.4728 q^{27} +139.101 q^{28} -135.320 q^{29} +8.34326 q^{30} -228.473 q^{31} +32.0000 q^{32} +9.17758 q^{33} -34.0000 q^{34} -173.877 q^{35} -105.216 q^{36} +144.165 q^{37} -320.406 q^{38} -42.0639 q^{39} -40.0000 q^{40} -29.9628 q^{41} -58.0279 q^{42} -295.320 q^{43} -44.0000 q^{44} +131.520 q^{45} -142.120 q^{46} -556.892 q^{47} -13.3492 q^{48} +866.324 q^{49} +50.0000 q^{50} +14.1835 q^{51} +201.667 q^{52} +474.221 q^{53} +88.9456 q^{54} +55.0000 q^{55} +278.203 q^{56} +133.661 q^{57} -270.640 q^{58} +377.714 q^{59} +16.6865 q^{60} -84.1747 q^{61} -456.946 q^{62} -914.727 q^{63} +64.0000 q^{64} -252.083 q^{65} +18.3552 q^{66} -791.406 q^{67} -68.0000 q^{68} +59.2870 q^{69} -347.753 q^{70} +465.133 q^{71} -210.431 q^{72} +170.945 q^{73} +288.329 q^{74} -20.8581 q^{75} -640.811 q^{76} -382.529 q^{77} -84.1278 q^{78} -365.393 q^{79} -80.0000 q^{80} +673.101 q^{81} -59.9256 q^{82} -6.46028 q^{83} -116.056 q^{84} +85.0000 q^{85} -590.641 q^{86} +112.901 q^{87} -88.0000 q^{88} +238.154 q^{89} +263.039 q^{90} +1753.26 q^{91} -284.239 q^{92} +190.621 q^{93} -1113.78 q^{94} +801.014 q^{95} -26.6984 q^{96} -306.073 q^{97} +1732.65 q^{98} +289.343 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 20 q^{2} + q^{3} + 40 q^{4} - 50 q^{5} + 2 q^{6} + 19 q^{7} + 80 q^{8} + 99 q^{9} - 100 q^{10} - 110 q^{11} + 4 q^{12} - 41 q^{13} + 38 q^{14} - 5 q^{15} + 160 q^{16} - 170 q^{17} + 198 q^{18} - 157 q^{19}+ \cdots - 1089 q^{99}+O(q^{100}) \) 10 * q + 20 * q^2 + q^3 + 40 * q^4 - 50 * q^5 + 2 * q^6 + 19 * q^7 + 80 * q^8 + 99 * q^9 - 100 * q^10 - 110 * q^11 + 4 * q^12 - 41 * q^13 + 38 * q^14 - 5 * q^15 + 160 * q^16 - 170 * q^17 + 198 * q^18 - 157 * q^19 - 200 * q^20 - 288 * q^21 - 220 * q^22 + 56 * q^23 + 8 * q^24 + 250 * q^25 - 82 * q^26 - 95 * q^27 + 76 * q^28 - 212 * q^29 - 10 * q^30 - 171 * q^31 + 320 * q^32 - 11 * q^33 - 340 * q^34 - 95 * q^35 + 396 * q^36 + 20 * q^37 - 314 * q^38 - 447 * q^39 - 400 * q^40 - 393 * q^41 - 576 * q^42 - 294 * q^43 - 440 * q^44 - 495 * q^45 + 112 * q^46 - 1270 * q^47 + 16 * q^48 - 209 * q^49 + 500 * q^50 - 17 * q^51 - 164 * q^52 - 1046 * q^53 - 190 * q^54 + 550 * q^55 + 152 * q^56 - 927 * q^57 - 424 * q^58 - 1766 * q^59 - 20 * q^60 + 505 * q^61 - 342 * q^62 - 2257 * q^63 + 640 * q^64 + 205 * q^65 - 22 * q^66 - 1289 * q^67 - 680 * q^68 - 2942 * q^69 - 190 * q^70 + 411 * q^71 + 792 * q^72 - 216 * q^73 + 40 * q^74 + 25 * q^75 - 628 * q^76 - 209 * q^77 - 894 * q^78 - 612 * q^79 - 800 * q^80 + 558 * q^81 - 786 * q^82 - 1922 * q^83 - 1152 * q^84 + 850 * q^85 - 588 * q^86 - 103 * q^87 - 880 * q^88 - 644 * q^89 - 990 * q^90 + 782 * q^91 + 224 * q^92 - 1803 * q^93 - 2540 * q^94 + 785 * q^95 + 32 * q^96 + 777 * q^97 - 418 * q^98 - 1089 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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