LMFDB - Embedded newform 1859.4.a.i.1.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1859,4,Mod(1,1859)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1859.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1859, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.a (trivial)

Newform invariants

comment:select newform

sage:traces = [17,4,-6,78,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$109.684550701$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 4 x^{16} - 99 x^{15} + 375 x^{14} + 3949 x^{13} - 13998 x^{12} - 81750 x^{11} + 267574 x^{10} + \cdots + 2596992 $ x^17 - 4x^16 - 99x^15 + 375x^14 + 3949x^13 - 13998x^12 - 81750x^11 + 267574x^10 + 941923x^9 - 2799440x^8 - 6021311x^7 + 15765187x^6 + 20197463x^5 - 42560950x^4 - 32766128x^3 + 37775816x^2 + 27375104x + 2596992
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 5 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$3.98991$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.98991 q^{2} +1.67407 q^{3} +7.91939 q^{4} -20.8270 q^{5} +6.67941 q^{6} +9.96761 q^{7} -0.321630 q^{8} -24.1975 q^{9} -83.0979 q^{10} -11.0000 q^{11} +13.2576 q^{12} +39.7699 q^{14} -34.8659 q^{15} -64.6384 q^{16} -10.2521 q^{17} -96.5458 q^{18} +99.7472 q^{19} -164.937 q^{20} +16.6865 q^{21} -43.8890 q^{22} -41.1988 q^{23} -0.538432 q^{24} +308.764 q^{25} -85.7084 q^{27} +78.9374 q^{28} +79.6896 q^{29} -139.112 q^{30} +19.9662 q^{31} -255.328 q^{32} -18.4148 q^{33} -40.9050 q^{34} -207.595 q^{35} -191.629 q^{36} -64.5829 q^{37} +397.983 q^{38} +6.69858 q^{40} -196.862 q^{41} +66.5778 q^{42} +306.839 q^{43} -87.1133 q^{44} +503.961 q^{45} -164.379 q^{46} -107.239 q^{47} -108.209 q^{48} -243.647 q^{49} +1231.94 q^{50} -17.1628 q^{51} -216.118 q^{53} -341.969 q^{54} +229.097 q^{55} -3.20588 q^{56} +166.984 q^{57} +317.955 q^{58} +234.392 q^{59} -276.117 q^{60} +529.608 q^{61} +79.6635 q^{62} -241.191 q^{63} -501.630 q^{64} -73.4735 q^{66} +222.613 q^{67} -81.1904 q^{68} -68.9698 q^{69} -828.287 q^{70} +1011.21 q^{71} +7.78263 q^{72} +968.334 q^{73} -257.680 q^{74} +516.893 q^{75} +789.937 q^{76} -109.644 q^{77} +1057.84 q^{79} +1346.22 q^{80} +509.850 q^{81} -785.462 q^{82} -175.936 q^{83} +132.147 q^{84} +213.521 q^{85} +1224.26 q^{86} +133.406 q^{87} +3.53793 q^{88} +512.958 q^{89} +2010.76 q^{90} -326.269 q^{92} +33.4250 q^{93} -427.872 q^{94} -2077.43 q^{95} -427.439 q^{96} +1414.73 q^{97} -972.129 q^{98} +266.172 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 4 q^{2} - 6 q^{3} + 78 q^{4} + 16 q^{5} + 14 q^{6} - 6 q^{7} + 63 q^{8} + 135 q^{9} + 2 q^{10} - 187 q^{11} - 95 q^{12} - 60 q^{14} - 28 q^{15} + 350 q^{16} + 118 q^{17} + 478 q^{18} + 403 q^{19}+ \cdots - 1485 q^{99}+O(q^{100}) $ 17 * q + 4 * q^2 - 6 * q^3 + 78 * q^4 + 16 * q^5 + 14 * q^6 - 6 * q^7 + 63 * q^8 + 135 * q^9 + 2 * q^10 - 187 * q^11 - 95 * q^12 - 60 * q^14 - 28 * q^15 + 350 * q^16 + 118 * q^17 + 478 * q^18 + 403 * q^19 + 98 * q^20 + 220 * q^21 - 44 * q^22 - 215 * q^23 + 26 * q^24 + 319 * q^25 - 384 * q^27 - 396 * q^28 - 7 * q^29 - 1269 * q^30 + 682 * q^31 + 813 * q^32 + 66 * q^33 + 738 * q^34 + 10 * q^35 + 560 * q^36 + 1084 * q^37 + 410 * q^38 + 95 * q^40 + 240 * q^41 + 393 * q^42 - 435 * q^43 - 858 * q^44 + 1242 * q^45 + 1671 * q^46 + 549 * q^47 + 894 * q^48 + 403 * q^49 - 651 * q^50 + 1552 * q^51 - 566 * q^53 + 311 * q^54 - 176 * q^55 - 1925 * q^56 - 534 * q^57 + 618 * q^58 + 2010 * q^59 - 411 * q^60 + 460 * q^61 - 823 * q^62 + 820 * q^63 + 3171 * q^64 - 154 * q^66 - 232 * q^67 + 1795 * q^68 - 1608 * q^69 + 207 * q^70 + 489 * q^71 + 2556 * q^72 + 290 * q^73 + 2653 * q^74 - 2852 * q^75 + 2421 * q^76 + 66 * q^77 - 732 * q^79 + 4915 * q^80 + 2393 * q^81 - 1772 * q^82 - 117 * q^83 + 4161 * q^84 + 4858 * q^85 + 1034 * q^86 + 3032 * q^87 - 693 * q^88 + 4113 * q^89 + 15145 * q^90 - 3554 * q^92 + 802 * q^93 + 2325 * q^94 - 3924 * q^95 + 2601 * q^96 + 2793 * q^97 + 533 * q^98 - 1485 * 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 $

$2$	3.98991	1.41065	0.705323	−	0.708886i	$-0.250802\pi$
$2$	3.98991	1.41065	0.705323	+	0.708886i	$0.250802\pi$
$3$	1.67407	0.322176	0.161088	−	0.986940i	$-0.448500\pi$
$3$	1.67407	0.322176	0.161088	+	0.986940i	$0.448500\pi$
$4$	7.91939	0.989924
$5$	−20.8270	−1.86282	−0.931411	−	0.363968i	$-0.881422\pi$
$5$	−20.8270	−1.86282	−0.931411	+	0.363968i	$0.881422\pi$
$6$	6.67941	0.454476
$7$	9.96761	0.538201	0.269100	−	0.963112i	$-0.413274\pi$
$7$	9.96761	0.538201	0.269100	+	0.963112i	$0.413274\pi$
$8$	−0.321630	−0.0142142
$9$	−24.1975	−0.896203
$10$	−83.0979	−2.62778
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	13.2576	0.318929
$13$	0	0
$13$	0	0
$14$	39.7699	0.759211
$15$	−34.8659	−0.600156
$16$	−64.6384	−1.00997
$17$	−10.2521	−0.146265	−0.0731324	−	0.997322i	$-0.523300\pi$
$17$	−10.2521	−0.146265	−0.0731324	+	0.997322i	$0.523300\pi$
$18$	−96.5458	−1.26423
$19$	99.7472	1.20440	0.602200	−	0.798346i	$-0.294291\pi$
$19$	99.7472	1.20440	0.602200	+	0.798346i	$0.294291\pi$
$20$	−164.937	−1.84405
$21$	16.6865	0.173395
$22$	−43.8890	−0.425326
$23$	−41.1988	−0.373502	−0.186751	−	0.982407i	$-0.559796\pi$
$23$	−41.1988	−0.373502	−0.186751	+	0.982407i	$0.559796\pi$
$24$	−0.538432	−0.00457946
$25$	308.764	2.47011
$26$	0	0
$27$	−85.7084	−0.610911
$28$	78.9374	0.532777
$29$	79.6896	0.510276	0.255138	−	0.966905i	$-0.417879\pi$
$29$	79.6896	0.510276	0.255138	+	0.966905i	$0.417879\pi$
$30$	−139.112	−0.846609
$31$	19.9662	0.115679	0.0578394	−	0.998326i	$-0.481579\pi$
$31$	19.9662	0.115679	0.0578394	+	0.998326i	$0.481579\pi$
$32$	−255.328	−1.41050
$33$	−18.4148	−0.0971396
$34$	−40.9050	−0.206328
$35$	−207.595	−1.00257
$36$	−191.629	−0.887172
$37$	−64.5829	−0.286956	−0.143478	−	0.989654i	$-0.545829\pi$
$37$	−64.5829	−0.286956	−0.143478	+	0.989654i	$0.545829\pi$
$38$	397.983	1.69898
$39$	0	0
$40$	6.69858	0.0264785
$41$	−196.862	−0.749870	−0.374935	−	0.927051i	$-0.622335\pi$
$41$	−196.862	−0.749870	−0.374935	+	0.927051i	$0.622335\pi$
$42$	66.5778	0.244599
$43$	306.839	1.08820	0.544100	−	0.839021i	$-0.316871\pi$
$43$	306.839	1.08820	0.544100	+	0.839021i	$0.316871\pi$
$44$	−87.1133	−0.298473
$45$	503.961	1.66947
$46$	−164.379	−0.526879
$47$	−107.239	−0.332816	−0.166408	−	0.986057i	$-0.553217\pi$
$47$	−107.239	−0.332816	−0.166408	+	0.986057i	$0.553217\pi$
$48$	−108.209	−0.325389
$49$	−243.647	−0.710340
$50$	1231.94	3.48445
$51$	−17.1628	−0.0471230
$52$	0	0
$53$	−216.118	−0.560116	−0.280058	−	0.959983i	$-0.590354\pi$
$53$	−216.118	−0.560116	−0.280058	+	0.959983i	$0.590354\pi$
$54$	−341.969	−0.861779
$55$	229.097	0.561662
$56$	−3.20588	−0.00765007
$57$	166.984	0.388028
$58$	317.955	0.719819
$59$	234.392	0.517208	0.258604	−	0.965983i	$-0.416737\pi$
$59$	234.392	0.517208	0.258604	+	0.965983i	$0.416737\pi$
$60$	−276.117	−0.594109
$61$	529.608	1.11163	0.555815	−	0.831306i	$-0.312406\pi$
$61$	529.608	1.11163	0.555815	+	0.831306i	$0.312406\pi$
$62$	79.6635	0.163182
$63$	−241.191	−0.482337
$64$	−501.630	−0.979747
$65$	0	0
$66$	−73.4735	−0.137030
$67$	222.613	0.405918	0.202959	−	0.979187i	$-0.434944\pi$
$67$	222.613	0.405918	0.202959	+	0.979187i	$0.434944\pi$
$68$	−81.1904	−0.144791
$69$	−68.9698	−0.120333
$70$	−828.287	−1.41428
$71$	1011.21	1.69027	0.845133	−	0.534555i	$-0.179521\pi$
$71$	1011.21	1.69027	0.845133	+	0.534555i	$0.179521\pi$
$72$	7.78263	0.0127388
$73$	968.334	1.55253	0.776267	−	0.630405i	$-0.217111\pi$
$73$	968.334	1.55253	0.776267	+	0.630405i	$0.217111\pi$
$74$	−257.680	−0.404793
$75$	516.893	0.795809
$76$	789.937	1.19226
$77$	−109.644	−0.162274
$78$	0	0
$79$	1057.84	1.50653	0.753267	−	0.657714i	$-0.228477\pi$
$79$	1057.84	1.50653	0.753267	+	0.657714i	$0.228477\pi$
$80$	1346.22	1.88140
$81$	509.850	0.699382
$82$	−785.462	−1.05780
$83$	−175.936	−0.232668	−0.116334	−	0.993210i	$-0.537114\pi$
$83$	−175.936	−0.232668	−0.116334	+	0.993210i	$0.537114\pi$
$84$	132.147	0.171648
$85$	213.521	0.272465
$86$	1224.26	1.53506
$87$	133.406	0.164398
$88$	3.53793	0.00428573
$89$	512.958	0.610937	0.305469	−	0.952202i	$-0.401187\pi$
$89$	512.958	0.610937	0.305469	+	0.952202i	$0.401187\pi$
$90$	2010.76	2.35503
$91$	0	0
$92$	−326.269	−0.369738
$93$	33.4250	0.0372689
$94$	−427.872	−0.469486
$95$	−2077.43	−2.24358
$96$	−427.439	−0.454430
$97$	1414.73	1.48087	0.740435	−	0.672128i	$-0.234620\pi$
$97$	1414.73	1.48087	0.740435	+	0.672128i	$0.234620\pi$
$98$	−972.129	−1.00204
$99$	266.172	0.270215
$100$	2445.22	2.44522
$101$	−104.380	−0.102834	−0.0514169	−	0.998677i	$-0.516374\pi$
$101$	−104.380	−0.102834	−0.0514169	+	0.998677i	$0.516374\pi$
$102$	−68.4780	−0.0664739
$103$	−1087.04	−1.03989	−0.519946	−	0.854199i	$-0.674048\pi$
$103$	−1087.04	−1.03989	−0.519946	+	0.854199i	$0.674048\pi$
$104$	0	0
$105$	−347.530	−0.323005
$106$	−862.293	−0.790126
$107$	−626.190	−0.565758	−0.282879	−	0.959156i	$-0.591289\pi$
$107$	−626.190	−0.565758	−0.282879	+	0.959156i	$0.591289\pi$
$108$	−678.758	−0.604755
$109$	2004.14	1.76112	0.880560	−	0.473934i	$-0.157167\pi$
$109$	2004.14	1.76112	0.880560	+	0.473934i	$0.157167\pi$
$110$	914.076	0.792307
$111$	−108.117	−0.0924501
$112$	−644.291	−0.543569
$113$	−1831.55	−1.52476	−0.762380	−	0.647130i	$-0.775969\pi$
$113$	−1831.55	−1.52476	−0.762380	+	0.647130i	$0.775969\pi$
$114$	666.252	0.547371
$115$	858.047	0.695767
$116$	631.093	0.505134
$117$	0	0
$118$	935.205	0.729598
$119$	−102.189	−0.0787198
$120$	11.2139	0.00853072
$121$	121.000	0.0909091
$122$	2113.09	1.56812
$123$	−329.562	−0.241590
$124$	158.120	0.114513
$125$	−3827.25	−2.73855
$126$	−962.331	−0.680407
$127$	1599.80	1.11779	0.558896	−	0.829238i	$-0.311225\pi$
$127$	1599.80	1.11779	0.558896	+	0.829238i	$0.311225\pi$
$128$	41.1665	0.0284269
$129$	513.672	0.350592
$130$	0	0
$131$	500.858	0.334047	0.167024	−	0.985953i	$-0.446584\pi$
$131$	500.858	0.334047	0.167024	+	0.985953i	$0.446584\pi$
$132$	−145.834	−0.0961608
$133$	994.242	0.648208
$134$	888.206	0.572607
$135$	1785.05	1.13802
$136$	3.29738	0.00207903
$137$	912.430	0.569009	0.284504	−	0.958675i	$-0.408171\pi$
$137$	912.430	0.569009	0.284504	+	0.958675i	$0.408171\pi$
$138$	−275.183	−0.169748
$139$	2193.70	1.33861	0.669306	−	0.742987i	$-0.266592\pi$
$139$	2193.70	1.33861	0.669306	+	0.742987i	$0.266592\pi$
$140$	−1644.03	−0.992470
$141$	−179.525	−0.107225
$142$	4034.65	2.38437
$143$	0	0
$144$	1564.09	0.905142
$145$	−1659.70	−0.950553
$146$	3863.57	2.19008
$147$	−407.883	−0.228854
$148$	−511.457	−0.284064
$149$	2189.56	1.20387	0.601933	−	0.798546i	$-0.294397\pi$
$149$	2189.56	1.20387	0.601933	+	0.798546i	$0.294397\pi$
$150$	2062.36	1.12261
$151$	−3273.48	−1.76419	−0.882093	−	0.471075i	$-0.843866\pi$
$151$	−3273.48	−1.76419	−0.882093	+	0.471075i	$0.843866\pi$
$152$	−32.0817	−0.0171195
$153$	248.075	0.131083
$154$	−437.469	−0.228911
$155$	−415.837	−0.215489
$156$	0	0
$157$	456.309	0.231958	0.115979	−	0.993252i	$-0.462999\pi$
$157$	456.309	0.231958	0.115979	+	0.993252i	$0.462999\pi$
$158$	4220.69	2.12519
$159$	−361.798	−0.180456
$160$	5317.72	2.62752
$161$	−410.653	−0.201019
$162$	2034.25	0.986581
$163$	−3304.85	−1.58807	−0.794036	−	0.607871i	$-0.792024\pi$
$163$	−3304.85	−1.58807	−0.794036	+	0.607871i	$0.792024\pi$
$164$	−1559.03	−0.742314
$165$	383.525	0.180954
$166$	−701.968	−0.328213
$167$	−3488.01	−1.61623	−0.808114	−	0.589026i	$-0.799512\pi$
$167$	−3488.01	−1.61623	−0.808114	+	0.589026i	$0.799512\pi$
$168$	−5.36688	−0.00246467
$169$	0	0
$170$	851.928	0.384352
$171$	−2413.63	−1.07939
$172$	2429.98	1.07723
$173$	−3861.94	−1.69721	−0.848607	−	0.529023i	$-0.822559\pi$
$173$	−3861.94	−1.69721	−0.848607	+	0.529023i	$0.822559\pi$
$174$	532.280	0.231908
$175$	3077.64	1.32941
$176$	711.022	0.304519
$177$	392.390	0.166632
$178$	2046.66	0.861817
$179$	−3878.93	−1.61969	−0.809845	−	0.586643i	$-0.800449\pi$
$179$	−3878.93	−1.61969	−0.809845	+	0.586643i	$0.800449\pi$
$180$	3991.06	1.65265
$181$	−4409.64	−1.81086	−0.905430	−	0.424495i	$-0.860452\pi$
$181$	−4409.64	−1.81086	−0.905430	+	0.424495i	$0.860452\pi$
$182$	0	0
$183$	886.604	0.358140
$184$	13.2508	0.00530901
$185$	1345.07	0.534547
$186$	133.363	0.0525733
$187$	112.773	0.0441005
$188$	−849.264	−0.329462
$189$	−854.308	−0.328792
$190$	−8288.78	−3.16490
$191$	1885.54	0.714307	0.357154	−	0.934046i	$-0.383747\pi$
$191$	1885.54	0.714307	0.357154	+	0.934046i	$0.383747\pi$
$192$	−839.767	−0.315651
$193$	574.922	0.214424	0.107212	−	0.994236i	$-0.465808\pi$
$193$	574.922	0.214424	0.107212	+	0.994236i	$0.465808\pi$
$194$	5644.66	2.08898
$195$	0	0
$196$	−1929.53	−0.703183
$197$	3952.45	1.42945	0.714723	−	0.699408i	$-0.246553\pi$
$197$	3952.45	1.42945	0.714723	+	0.699408i	$0.246553\pi$
$198$	1062.00	0.381178
$199$	2117.35	0.754248	0.377124	−	0.926163i	$-0.376913\pi$
$199$	2117.35	0.754248	0.377124	+	0.926163i	$0.376913\pi$
$200$	−99.3076	−0.0351105
$201$	372.671	0.130777
$202$	−416.467	−0.145062
$203$	794.316	0.274631
$204$	−135.919	−0.0466481
$205$	4100.04	1.39688
$206$	−4337.18	−1.46692
$207$	996.906	0.334733
$208$	0	0
$209$	−1097.22	−0.363140
$210$	−1386.61	−0.455645
$211$	−3200.46	−1.04421	−0.522106	−	0.852881i	$-0.674853\pi$
$211$	−3200.46	−1.04421	−0.522106	+	0.852881i	$0.674853\pi$
$212$	−1711.53	−0.554472
$213$	1692.85	0.544563
$214$	−2498.44	−0.798084
$215$	−6390.54	−2.02712
$216$	27.5664	0.00868358
$217$	199.016	0.0622584
$218$	7996.35	2.48432
$219$	1621.06	0.500189
$220$	1814.31	0.556003
$221$	0	0
$222$	−431.375	−0.130414
$223$	4286.80	1.28729	0.643645	−	0.765324i	$-0.277421\pi$
$223$	4286.80	1.28729	0.643645	+	0.765324i	$0.277421\pi$
$224$	−2545.01	−0.759134
$225$	−7471.30	−2.21372
$226$	−7307.73	−2.15090
$227$	−1065.70	−0.311600	−0.155800	−	0.987789i	$-0.549796\pi$
$227$	−1065.70	−0.311600	−0.155800	+	0.987789i	$0.549796\pi$
$228$	1322.41	0.384118
$229$	−931.338	−0.268753	−0.134377	−	0.990930i	$-0.542903\pi$
$229$	−931.338	−0.268753	−0.134377	+	0.990930i	$0.542903\pi$
$230$	3423.53	0.981482
$231$	−183.552	−0.0522806
$232$	−25.6306	−0.00725314
$233$	1105.63	0.310869	0.155434	−	0.987846i	$-0.450322\pi$
$233$	1105.63	0.310869	0.155434	+	0.987846i	$0.450322\pi$
$234$	0	0
$235$	2233.46	0.619977
$236$	1856.24	0.511997
$237$	1770.90	0.485369
$238$	−407.725	−0.111046
$239$	2857.97	0.773501	0.386750	−	0.922184i	$-0.373598\pi$
$239$	2857.97	0.773501	0.386750	+	0.922184i	$0.373598\pi$
$240$	2253.68	0.606143
$241$	−1778.91	−0.475477	−0.237738	−	0.971329i	$-0.576406\pi$
$241$	−1778.91	−0.475477	−0.237738	+	0.971329i	$0.576406\pi$
$242$	482.779	0.128241
$243$	3167.65	0.836235
$244$	4194.17	1.10043
$245$	5074.43	1.32324
$246$	−1314.92	−0.340798
$247$	0	0
$248$	−6.42174	−0.00164428
$249$	−294.530	−0.0749601
$250$	−15270.4	−3.86313
$251$	6026.17	1.51541	0.757706	−	0.652596i	$-0.226320\pi$
$251$	6026.17	1.51541	0.757706	+	0.652596i	$0.226320\pi$
$252$	−1910.09	−0.477477
$253$	453.187	0.112615
$254$	6383.07	1.57681
$255$	357.449	0.0877818
$256$	4177.29	1.01985
$257$	−4981.07	−1.20899	−0.604495	−	0.796609i	$-0.706625\pi$
$257$	−4981.07	−1.20899	−0.604495	+	0.796609i	$0.706625\pi$
$258$	2049.51	0.494561
$259$	−643.737	−0.154440
$260$	0	0
$261$	−1928.29	−0.457311
$262$	1998.38	0.471223
$263$	−2756.17	−0.646209	−0.323104	−	0.946363i	$-0.604726\pi$
$263$	−2756.17	−0.646209	−0.323104	+	0.946363i	$0.604726\pi$
$264$	5.92275	0.00138076
$265$	4501.10	1.04340
$266$	3966.94	0.914393
$267$	858.730	0.196829
$268$	1762.96	0.401828
$269$	6043.67	1.36985	0.684924	−	0.728615i	$-0.259836\pi$
$269$	6043.67	1.36985	0.684924	+	0.728615i	$0.259836\pi$
$270$	7122.18	1.60534
$271$	1911.18	0.428398	0.214199	−	0.976790i	$-0.431286\pi$
$271$	1911.18	0.428398	0.214199	+	0.976790i	$0.431286\pi$
$272$	662.680	0.147724
$273$	0	0
$274$	3640.52	0.802670
$275$	−3396.40	−0.744766
$276$	−546.199	−0.119121
$277$	441.829	0.0958372	0.0479186	−	0.998851i	$-0.484741\pi$
$277$	441.829	0.0958372	0.0479186	+	0.998851i	$0.484741\pi$
$278$	8752.66	1.88831
$279$	−483.133	−0.103672
$280$	66.7689	0.0142507
$281$	9369.87	1.98918	0.994590	−	0.103880i	$-0.0331257\pi$
$281$	9369.87	1.98918	0.994590	+	0.103880i	$0.0331257\pi$
$282$	−716.290	−0.151257
$283$	−7193.95	−1.51108	−0.755541	−	0.655102i	$-0.772626\pi$
$283$	−7193.95	−1.51108	−0.755541	+	0.655102i	$0.772626\pi$
$284$	8008.19	1.67324
$285$	−3477.78	−0.722828
$286$	0	0
$287$	−1962.24	−0.403581
$288$	6178.30	1.26410
$289$	−4807.89	−0.978607
$290$	−6622.04	−1.34089
$291$	2368.37	0.477100
$292$	7668.61	1.53689
$293$	6031.95	1.20270	0.601349	−	0.798987i	$-0.294630\pi$
$293$	6031.95	1.20270	0.601349	+	0.798987i	$0.294630\pi$
$294$	−1627.42	−0.322833
$295$	−4881.69	−0.963468
$296$	20.7718	0.00407883
$297$	942.792	0.184196
$298$	8736.17	1.69823
$299$	0	0
$300$	4093.48	0.787791
$301$	3058.46	0.585670
$302$	−13060.9	−2.48864
$303$	−174.740	−0.0331306
$304$	−6447.50	−1.21641
$305$	−11030.2	−2.07077
$306$	989.798	0.184912
$307$	677.018	0.125861	0.0629307	−	0.998018i	$-0.479955\pi$
$307$	677.018	0.125861	0.0629307	+	0.998018i	$0.479955\pi$
$308$	−868.312	−0.160638
$309$	−1819.78	−0.335028
$310$	−1659.15	−0.303979
$311$	2466.20	0.449663	0.224832	−	0.974398i	$-0.427817\pi$
$311$	2466.20	0.449663	0.224832	+	0.974398i	$0.427817\pi$
$312$	0	0
$313$	175.679	0.0317251	0.0158626	−	0.999874i	$-0.494951\pi$
$313$	175.679	0.0317251	0.0158626	+	0.999874i	$0.494951\pi$
$314$	1820.63	0.327211
$315$	5023.29	0.898508
$316$	8377.44	1.49135
$317$	−10787.5	−1.91131	−0.955653	−	0.294495i	$-0.904849\pi$
$317$	−10787.5	−1.91131	−0.955653	+	0.294495i	$0.904849\pi$
$318$	−1443.54	−0.254559
$319$	−876.586	−0.153854
$320$	10447.5	1.82509
$321$	−1048.29	−0.182273
$322$	−1638.47	−0.283566
$323$	−1022.62	−0.176161
$324$	4037.70	0.692335
$325$	0	0
$326$	−13186.1	−2.24021
$327$	3355.08	0.567390
$328$	63.3167	0.0106588
$329$	−1068.91	−0.179122
$330$	1530.23	0.255262
$331$	9415.77	1.56356	0.781779	−	0.623556i	$-0.214313\pi$
$331$	9415.77	1.56356	0.781779	+	0.623556i	$0.214313\pi$
$332$	−1393.30	−0.230324
$333$	1562.74	0.257170
$334$	−13916.8	−2.27993
$335$	−4636.36	−0.756153
$336$	−1078.59	−0.175125
$337$	−2553.22	−0.412708	−0.206354	−	0.978477i	$-0.566160\pi$
$337$	−2553.22	−0.412708	−0.206354	+	0.978477i	$0.566160\pi$
$338$	0	0
$339$	−3066.15	−0.491241
$340$	1690.95	0.269720
$341$	−219.629	−0.0348785
$342$	−9630.17	−1.52263
$343$	−5847.47	−0.920506
$344$	−98.6887	−0.0154678
$345$	1436.43	0.224159
$346$	−15408.8	−2.39417
$347$	2355.29	0.364377	0.182188	−	0.983264i	$-0.441682\pi$
$347$	2355.29	0.364377	0.182188	+	0.983264i	$0.441682\pi$
$348$	1056.50	0.162742
$349$	1877.70	0.287997	0.143999	−	0.989578i	$-0.454004\pi$
$349$	1877.70	0.287997	0.143999	+	0.989578i	$0.454004\pi$
$350$	12279.5	1.87533
$351$	0	0
$352$	2808.61	0.425283
$353$	−2382.83	−0.359278	−0.179639	−	0.983733i	$-0.557493\pi$
$353$	−2382.83	−0.359278	−0.179639	+	0.983733i	$0.557493\pi$
$354$	1565.60	0.235059
$355$	−21060.5	−3.14867
$356$	4062.31	0.604781
$357$	−171.072	−0.0253616
$358$	−15476.6	−2.28481
$359$	9552.64	1.40437	0.702185	−	0.711995i	$-0.252208\pi$
$359$	9552.64	1.40437	0.702185	+	0.711995i	$0.252208\pi$
$360$	−162.089	−0.0237301
$361$	3090.51	0.450577
$362$	−17594.1	−2.55448
$363$	202.563	0.0292887
$364$	0	0
$365$	−20167.5	−2.89209
$366$	3537.47	0.505209
$367$	1892.40	0.269163	0.134581	−	0.990903i	$-0.457031\pi$
$367$	1892.40	0.269163	0.134581	+	0.990903i	$0.457031\pi$
$368$	2663.02	0.377227
$369$	4763.56	0.672036
$370$	5366.70	0.754057
$371$	−2154.18	−0.301455
$372$	264.705	0.0368934
$373$	−6605.65	−0.916964	−0.458482	−	0.888704i	$-0.651607\pi$
$373$	−6605.65	−0.916964	−0.458482	+	0.888704i	$0.651607\pi$
$374$	449.955	0.0622102
$375$	−6407.09	−0.882296
$376$	34.4911	0.00473070
$377$	0	0
$378$	−3408.61	−0.463810
$379$	11736.6	1.59068	0.795341	−	0.606162i	$-0.207292\pi$
$379$	11736.6	1.59068	0.795341	+	0.606162i	$0.207292\pi$
$380$	−16452.0	−2.22098
$381$	2678.19	0.360125
$382$	7523.13	1.00764
$383$	7361.16	0.982082	0.491041	−	0.871136i	$-0.336616\pi$
$383$	7361.16	0.982082	0.491041	+	0.871136i	$0.336616\pi$
$384$	68.9158	0.00915845
$385$	2283.55	0.302287
$386$	2293.89	0.302476
$387$	−7424.74	−0.975247
$388$	11203.8	1.46595
$389$	−6587.34	−0.858590	−0.429295	−	0.903164i	$-0.641238\pi$
$389$	−6587.34	−0.858590	−0.429295	+	0.903164i	$0.641238\pi$
$390$	0	0
$391$	422.374	0.0546301
$392$	78.3640	0.0100969
$393$	838.474	0.107622
$394$	15769.9	2.01644
$395$	−22031.6	−2.80641
$396$	2107.92	0.267493
$397$	256.809	0.0324657	0.0162329	−	0.999868i	$-0.494833\pi$
$397$	256.809	0.0324657	0.0162329	+	0.999868i	$0.494833\pi$
$398$	8448.05	1.06398
$399$	1664.43	0.208837
$400$	−19958.0	−2.49475
$401$	−7440.06	−0.926531	−0.463266	−	0.886219i	$-0.653322\pi$
$401$	−7440.06	−0.926531	−0.463266	+	0.886219i	$0.653322\pi$
$402$	1486.92	0.184480
$403$	0	0
$404$	−826.627	−0.101798
$405$	−10618.6	−1.30283
$406$	3169.25	0.387407
$407$	710.411	0.0865204
$408$	5.52006	0.000669813 0
$409$	−5133.83	−0.620664	−0.310332	−	0.950628i	$-0.600440\pi$
$409$	−5133.83	−0.620664	−0.310332	+	0.950628i	$0.600440\pi$
$410$	16358.8	1.97050
$411$	1527.48	0.183321
$412$	−8608.67	−1.02941
$413$	2336.33	0.278362
$414$	3977.57	0.472190
$415$	3664.22	0.433420
$416$	0	0
$417$	3672.41	0.431268
$418$	−4377.81	−0.512262
$419$	7954.17	0.927415	0.463707	−	0.885988i	$-0.346519\pi$
$419$	7954.17	0.927415	0.463707	+	0.885988i	$0.346519\pi$
$420$	−2752.23	−0.319750
$421$	−16008.8	−1.85325	−0.926626	−	0.375984i	$-0.877305\pi$
$421$	−16008.8	−1.85325	−0.926626	+	0.375984i	$0.877305\pi$
$422$	−12769.5	−1.47301
$423$	2594.90	0.298270
$424$	69.5101	0.00796158
$425$	−3165.48	−0.361290
$426$	6754.31	0.768186
$427$	5278.93	0.598280
$428$	−4959.04	−0.560057
$429$	0	0
$430$	−25497.7	−2.85955
$431$	9917.78	1.10841	0.554203	−	0.832382i	$-0.313023\pi$
$431$	9917.78	1.10841	0.554203	+	0.832382i	$0.313023\pi$
$432$	5540.05	0.617004
$433$	3790.36	0.420677	0.210338	−	0.977629i	$-0.432543\pi$
$433$	3790.36	0.420677	0.210338	+	0.977629i	$0.432543\pi$
$434$	794.055	0.0878246
$435$	−2778.45	−0.306245
$436$	15871.6	1.74337
$437$	−4109.46	−0.449845
$438$	6467.90	0.705589
$439$	4648.60	0.505388	0.252694	−	0.967546i	$-0.418683\pi$
$439$	4648.60	0.505388	0.252694	+	0.967546i	$0.418683\pi$
$440$	−73.6844	−0.00798356
$441$	5895.63	0.636609
$442$	0	0
$443$	1479.09	0.158632	0.0793159	−	0.996850i	$-0.474726\pi$
$443$	1479.09	0.158632	0.0793159	+	0.996850i	$0.474726\pi$
$444$	−856.217	−0.0915186
$445$	−10683.4	−1.13807
$446$	17104.0	1.81591
$447$	3665.49	0.387857
$448$	−5000.06	−0.527300
$449$	5046.75	0.530447	0.265224	−	0.964187i	$-0.414554\pi$
$449$	5046.75	0.530447	0.265224	+	0.964187i	$0.414554\pi$
$450$	−29809.8	−3.12278
$451$	2165.48	0.226094
$452$	−14504.8	−1.50940
$453$	−5480.05	−0.568378
$454$	−4252.06	−0.439558
$455$	0	0
$456$	−53.7071	−0.00551550
$457$	−7765.04	−0.794821	−0.397410	−	0.917641i	$-0.630091\pi$
$457$	−7765.04	−0.794821	−0.397410	+	0.917641i	$0.630091\pi$
$458$	−3715.95	−0.379116
$459$	878.692	0.0893547
$460$	6795.21	0.688757
$461$	3234.31	0.326761	0.163380	−	0.986563i	$-0.447760\pi$
$461$	3234.31	0.326761	0.163380	+	0.986563i	$0.447760\pi$
$462$	−732.355	−0.0737495
$463$	10228.1	1.02666	0.513329	−	0.858192i	$-0.328412\pi$
$463$	10228.1	1.02666	0.513329	+	0.858192i	$0.328412\pi$
$464$	−5151.01	−0.515366
$465$	−696.142	−0.0694254
$466$	4411.37	0.438526
$467$	−646.021	−0.0640135	−0.0320067	−	0.999488i	$-0.510190\pi$
$467$	−646.021	−0.0640135	−0.0320067	+	0.999488i	$0.510190\pi$
$468$	0	0
$469$	2218.92	0.218465
$470$	8911.29	0.874568
$471$	763.896	0.0747314
$472$	−75.3876	−0.00735168
$473$	−3375.23	−0.328104
$474$	7065.74	0.684684
$475$	30798.3	2.97500
$476$	−809.275	−0.0779266
$477$	5229.52	0.501977
$478$	11403.0	1.09114
$479$	−6535.42	−0.623405	−0.311703	−	0.950180i	$-0.600899\pi$
$479$	−6535.42	−0.623405	−0.311703	+	0.950180i	$0.600899\pi$
$480$	8902.26	0.846523
$481$	0	0
$482$	−7097.71	−0.670730
$483$	−687.464	−0.0647634
$484$	958.246	0.0899931
$485$	−29464.6	−2.75860
$486$	12638.7	1.17963
$487$	−11975.1	−1.11426	−0.557128	−	0.830426i	$-0.688097\pi$
$487$	−11975.1	−1.11426	−0.557128	+	0.830426i	$0.688097\pi$
$488$	−170.338	−0.0158009
$489$	−5532.56	−0.511638
$490$	20246.5	1.86662
$491$	1270.34	0.116761	0.0583805	−	0.998294i	$-0.481406\pi$
$491$	1270.34	0.116761	0.0583805	+	0.998294i	$0.481406\pi$
$492$	−2609.93	−0.239156
$493$	−816.987	−0.0746354
$494$	0	0
$495$	−5543.57	−0.503363
$496$	−1290.59	−0.116833
$497$	10079.4	0.909703
$498$	−1175.15	−0.105742
$499$	20645.1	1.85210	0.926052	−	0.377396i	$-0.123180\pi$
$499$	20645.1	1.85210	0.926052	+	0.377396i	$0.123180\pi$
$500$	−30309.4	−2.71096
$501$	−5839.19	−0.520710
$502$	24043.9	2.13771
$503$	7902.74	0.700529	0.350264	−	0.936651i	$-0.386092\pi$
$503$	7902.74	0.700529	0.350264	+	0.936651i	$0.386092\pi$
$504$	77.5742	0.00685601
$505$	2173.92	0.191561
$506$	1808.17	0.158860
$507$	0	0
$508$	12669.5	1.10653
$509$	2677.65	0.233173	0.116586	−	0.993181i	$-0.462805\pi$
$509$	2677.65	0.233173	0.116586	+	0.993181i	$0.462805\pi$
$510$	1426.19	0.123829
$511$	9651.98	0.835574
$512$	16337.7	1.41022
$513$	−8549.17	−0.735780
$514$	−19874.0	−1.70546
$515$	22639.7	1.93714
$516$	4067.97	0.347059
$517$	1179.62	0.100348
$518$	−2568.45	−0.217860
$519$	−6465.18	−0.546802
$520$	0	0
$521$	−15013.4	−1.26248	−0.631239	−	0.775588i	$-0.717453\pi$
$521$	−15013.4	−1.26248	−0.631239	+	0.775588i	$0.717453\pi$
$522$	−7693.70	−0.645104
$523$	−7571.54	−0.633041	−0.316521	−	0.948586i	$-0.602515\pi$
$523$	−7571.54	−0.633041	−0.316521	+	0.948586i	$0.602515\pi$
$524$	3966.49	0.330681
$525$	5152.19	0.428305
$526$	−10996.9	−0.911572
$527$	−204.696	−0.0169197
$528$	1190.30	0.0981086
$529$	−10469.7	−0.860497
$530$	17959.0	1.47186
$531$	−5671.70	−0.463524
$532$	7873.79	0.641677
$533$	0	0
$534$	3426.25	0.277656
$535$	13041.7	1.05391
$536$	−71.5989	−0.00576978
$537$	−6493.61	−0.521825
$538$	24113.7	1.93237
$539$	2680.11	0.214176
$540$	14136.5	1.12655
$541$	6565.46	0.521758	0.260879	−	0.965371i	$-0.415988\pi$
$541$	6565.46	0.521758	0.260879	+	0.965371i	$0.415988\pi$
$542$	7625.43	0.604318
$543$	−7382.06	−0.583415
$544$	2617.65	0.206307
$545$	−41740.3	−3.28066
$546$	0	0
$547$	−18563.4	−1.45103	−0.725514	−	0.688208i	$-0.758398\pi$
$547$	−18563.4	−1.45103	−0.725514	+	0.688208i	$0.758398\pi$
$548$	7225.89	0.563275
$549$	−12815.2	−0.996246
$550$	−13551.3	−1.05060
$551$	7948.82	0.614576
$552$	22.1827	0.00171044
$553$	10544.1	0.810818
$554$	1762.86	0.135192
$555$	2251.74	0.172218
$556$	17372.8	1.32512
$557$	−13379.7	−1.01780	−0.508902	−	0.860825i	$-0.669948\pi$
$557$	−13379.7	−1.01780	−0.508902	+	0.860825i	$0.669948\pi$
$558$	−1927.66	−0.146244
$559$	0	0
$560$	13418.6	1.01257
$561$	188.791	0.0142081
$562$	37384.9	2.80603
$563$	11070.8	0.828738	0.414369	−	0.910109i	$-0.364002\pi$
$563$	11070.8	0.828738	0.414369	+	0.910109i	$0.364002\pi$
$564$	−1421.73	−0.106145
$565$	38145.7	2.84036
$566$	−28703.2	−2.13160
$567$	5081.98	0.376408
$568$	−325.236	−0.0240257
$569$	16024.2	1.18061	0.590307	−	0.807179i	$-0.299007\pi$
$569$	16024.2	1.18061	0.590307	+	0.807179i	$0.299007\pi$
$570$	−13876.0	−1.01965
$571$	14927.3	1.09402	0.547012	−	0.837125i	$-0.315765\pi$
$571$	14927.3	1.09402	0.547012	+	0.837125i	$0.315765\pi$
$572$	0	0
$573$	3156.53	0.230133
$574$	−7829.18	−0.569310
$575$	−12720.7	−0.922590
$576$	12138.2	0.878052
$577$	7279.04	0.525182	0.262591	−	0.964907i	$-0.415423\pi$
$577$	7279.04	0.525182	0.262591	+	0.964907i	$0.415423\pi$
$578$	−19183.1	−1.38047
$579$	962.461	0.0690821
$580$	−13143.8	−0.940975
$581$	−1753.66	−0.125222
$582$	9449.58	0.673020
$583$	2377.30	0.168881
$584$	−311.445	−0.0220680
$585$	0	0
$586$	24067.0	1.69658
$587$	18192.4	1.27918	0.639591	−	0.768715i	$-0.279104\pi$
$587$	18192.4	1.27918	0.639591	+	0.768715i	$0.279104\pi$
$588$	−3230.18	−0.226548
$589$	1991.58	0.139323
$590$	−19477.5	−1.35911
$591$	6616.70	0.460533
$592$	4174.53	0.289818
$593$	−17189.1	−1.19034	−0.595172	−	0.803599i	$-0.702916\pi$
$593$	−17189.1	−1.19034	−0.595172	+	0.803599i	$0.702916\pi$
$594$	3761.66	0.259836
$595$	2128.29	0.146641
$596$	17340.0	1.19174
$597$	3544.61	0.243000
$598$	0	0
$599$	15773.3	1.07593	0.537963	−	0.842969i	$-0.319194\pi$
$599$	15773.3	1.07593	0.537963	+	0.842969i	$0.319194\pi$
$600$	−166.248	−0.0113118
$601$	9916.19	0.673028	0.336514	−	0.941679i	$-0.390752\pi$
$601$	9916.19	0.673028	0.336514	+	0.941679i	$0.390752\pi$
$602$	12203.0	0.826173
$603$	−5386.67	−0.363785
$604$	−25924.0	−1.74641
$605$	−2520.07	−0.169348
$606$	−697.198	−0.0467355
$607$	7522.34	0.503002	0.251501	−	0.967857i	$-0.419076\pi$
$607$	7522.34	0.503002	0.251501	+	0.967857i	$0.419076\pi$
$608$	−25468.3	−1.69881
$609$	1329.74	0.0884794
$610$	−44009.3	−2.92112
$611$	0	0
$612$	1964.60	0.129762
$613$	10397.0	0.685040	0.342520	−	0.939510i	$-0.388719\pi$
$613$	10397.0	0.685040	0.342520	+	0.939510i	$0.388719\pi$
$614$	2701.24	0.177546
$615$	6863.78	0.450040
$616$	35.2647	0.00230658
$617$	−7775.64	−0.507351	−0.253675	−	0.967289i	$-0.581639\pi$
$617$	−7775.64	−0.507351	−0.253675	+	0.967289i	$0.581639\pi$
$618$	−7260.76	−0.472606
$619$	27006.4	1.75360	0.876801	−	0.480853i	$-0.159673\pi$
$619$	27006.4	1.75360	0.876801	+	0.480853i	$0.159673\pi$
$620$	−3293.17	−0.213318
$621$	3531.08	0.228176
$622$	9839.91	0.634316
$623$	5112.97	0.328807
$624$	0	0
$625$	41114.6	2.63133
$626$	700.943	0.0447529
$627$	−1836.83	−0.116995
$628$	3613.69	0.229621
$629$	662.110	0.0419715
$630$	20042.5	1.26748
$631$	13093.9	0.826083	0.413042	−	0.910712i	$-0.364466\pi$
$631$	13093.9	0.826083	0.413042	+	0.910712i	$0.364466\pi$
$632$	−340.233	−0.0214141
$633$	−5357.80	−0.336420
$634$	−43041.0	−2.69618
$635$	−33319.1	−2.08225
$636$	−2865.22	−0.178637
$637$	0	0
$638$	−3497.50	−0.217033
$639$	−24468.8	−1.51482
$640$	−857.375	−0.0529542
$641$	22003.5	1.35583	0.677913	−	0.735142i	$-0.262885\pi$
$641$	22003.5	1.35583	0.677913	+	0.735142i	$0.262885\pi$
$642$	−4182.58	−0.257123
$643$	27204.8	1.66851	0.834254	−	0.551380i	$-0.185899\pi$
$643$	27204.8	1.66851	0.834254	+	0.551380i	$0.185899\pi$
$644$	−3252.12	−0.198993
$645$	−10698.2	−0.653090
$646$	−4080.16	−0.248501
$647$	1142.76	0.0694385	0.0347192	−	0.999397i	$-0.488946\pi$
$647$	1142.76	0.0694385	0.0347192	+	0.999397i	$0.488946\pi$
$648$	−163.983	−0.00994113
$649$	−2578.32	−0.155944
$650$	0	0
$651$	333.167	0.0200581
$652$	−26172.4	−1.57207
$653$	−3664.24	−0.219591	−0.109795	−	0.993954i	$-0.535020\pi$
$653$	−3664.24	−0.219591	−0.109795	+	0.993954i	$0.535020\pi$
$654$	13386.5	0.800387
$655$	−10431.4	−0.622271
$656$	12724.8	0.757350
$657$	−23431.2	−1.39138
$658$	−4264.86	−0.252677
$659$	−3953.10	−0.233674	−0.116837	−	0.993151i	$-0.537275\pi$
$659$	−3953.10	−0.233674	−0.116837	+	0.993151i	$0.537275\pi$
$660$	3037.29	0.179131
$661$	31581.7	1.85838	0.929188	−	0.369608i	$-0.120508\pi$
$661$	31581.7	1.85838	0.929188	+	0.369608i	$0.120508\pi$
$662$	37568.1	2.20563
$663$	0	0
$664$	56.5862	0.00330718
$665$	−20707.1	−1.20750
$666$	6235.20	0.362777
$667$	−3283.12	−0.190589
$668$	−27622.9	−1.59994
$669$	7176.43	0.414733
$670$	−18498.7	−1.06666
$671$	−5825.69	−0.335169
$672$	−4260.54	−0.244574
$673$	26922.9	1.54205	0.771027	−	0.636802i	$-0.219743\pi$
$673$	26922.9	1.54205	0.771027	+	0.636802i	$0.219743\pi$
$674$	−10187.1	−0.582185
$675$	−26463.6	−1.50902
$676$	0	0
$677$	697.353	0.0395886	0.0197943	−	0.999804i	$-0.493699\pi$
$677$	697.353	0.0395886	0.0197943	+	0.999804i	$0.493699\pi$
$678$	−12233.7	−0.692967
$679$	14101.5	0.797005
$680$	−68.6746	−0.00387287
$681$	−1784.07	−0.100390
$682$	−876.299	−0.0492012
$683$	−20810.4	−1.16587	−0.582933	−	0.812520i	$-0.698095\pi$
$683$	−20810.4	−1.16587	−0.582933	+	0.812520i	$0.698095\pi$
$684$	−19114.5	−1.06851
$685$	−19003.2	−1.05996
$686$	−23330.9	−1.29851
$687$	−1559.13	−0.0865858
$688$	−19833.6	−1.09905
$689$	0	0
$690$	5731.24	0.316210
$691$	32183.1	1.77179	0.885893	−	0.463890i	$-0.153547\pi$
$691$	32183.1	1.77179	0.885893	+	0.463890i	$0.153547\pi$
$692$	−30584.2	−1.68011
$693$	2653.10	0.145430
$694$	9397.40	0.514007
$695$	−45688.1	−2.49360
$696$	−42.9075	−0.00233679
$697$	2018.25	0.109680
$698$	7491.86	0.406262
$699$	1850.91	0.100154
$700$	24373.0	1.31602
$701$	−6160.64	−0.331932	−0.165966	−	0.986131i	$-0.553074\pi$
$701$	−6160.64	−0.331932	−0.165966	+	0.986131i	$0.553074\pi$
$702$	0	0
$703$	−6441.96	−0.345609
$704$	5517.93	0.295405
$705$	3738.97	0.199742
$706$	−9507.27	−0.506814
$707$	−1040.42	−0.0553452
$708$	3107.49	0.164953
$709$	−2601.97	−0.137827	−0.0689134	−	0.997623i	$-0.521953\pi$
$709$	−2601.97	−0.137827	−0.0689134	+	0.997623i	$0.521953\pi$
$710$	−84029.7	−4.44166
$711$	−25597.0	−1.35016
$712$	−164.983	−0.00868396
$713$	−822.585	−0.0432062
$714$	−682.562	−0.0357763
$715$	0	0
$716$	−30718.7	−1.60337
$717$	4784.45	0.249203
$718$	38114.2	1.98107
$719$	−1195.65	−0.0620168	−0.0310084	−	0.999519i	$-0.509872\pi$
$719$	−1195.65	−0.0620168	−0.0310084	+	0.999519i	$0.509872\pi$
$720$	−32575.2	−1.68612
$721$	−10835.2	−0.559671
$722$	12330.9	0.635605
$723$	−2978.03	−0.153187
$724$	−34921.6	−1.79261
$725$	24605.3	1.26044
$726$	808.208	0.0413160
$727$	12799.5	0.652968	0.326484	−	0.945203i	$-0.394136\pi$
$727$	12799.5	0.652968	0.326484	+	0.945203i	$0.394136\pi$
$728$	0	0
$729$	−8463.05	−0.429968
$730$	−80466.5	−4.07972
$731$	−3145.75	−0.159165
$732$	7021.36	0.354531
$733$	−3924.79	−0.197770	−0.0988850	−	0.995099i	$-0.531528\pi$
$733$	−3924.79	−0.197770	−0.0988850	+	0.995099i	$0.531528\pi$
$734$	7550.52	0.379693
$735$	8494.97	0.426315
$736$	10519.2	0.526825
$737$	−2448.74	−0.122389
$738$	19006.2	0.948005
$739$	−21672.0	−1.07878	−0.539389	−	0.842057i	$-0.681345\pi$
$739$	−21672.0	−1.07878	−0.539389	+	0.842057i	$0.681345\pi$
$740$	10652.1	0.529161
$741$	0	0
$742$	−8595.01	−0.425246
$743$	26790.1	1.32279	0.661396	−	0.750037i	$-0.269964\pi$
$743$	26790.1	1.32279	0.661396	+	0.750037i	$0.269964\pi$
$744$	−10.7505	−0.000529746 0
$745$	−45602.0	−2.24259
$746$	−26355.9	−1.29351
$747$	4257.20	0.208518
$748$	893.095	0.0436561
$749$	−6241.62	−0.304491
$750$	−25563.7	−1.24461
$751$	12312.5	0.598257	0.299128	−	0.954213i	$-0.403304\pi$
$751$	12312.5	0.598257	0.299128	+	0.954213i	$0.403304\pi$
$752$	6931.72	0.336136
$753$	10088.3	0.488229
$754$	0	0
$755$	68176.8	3.28637
$756$	−6765.60	−0.325479
$757$	6127.02	0.294175	0.147087	−	0.989124i	$-0.453010\pi$
$757$	6127.02	0.294175	0.147087	+	0.989124i	$0.453010\pi$
$758$	46828.0	2.24389
$759$	758.668	0.0362818
$760$	668.165	0.0318906
$761$	782.672	0.0372823	0.0186412	−	0.999826i	$-0.494066\pi$
$761$	782.672	0.0372823	0.0186412	+	0.999826i	$0.494066\pi$
$762$	10685.7	0.508009
$763$	19976.5	0.947836
$764$	14932.3	0.707110
$765$	−5166.66	−0.244184
$766$	29370.4	1.38537
$767$	0	0
$768$	6993.10	0.328570
$769$	−19785.0	−0.927784	−0.463892	−	0.885892i	$-0.653547\pi$
$769$	−19785.0	−0.927784	−0.463892	+	0.885892i	$0.653547\pi$
$770$	9111.16	0.426420
$771$	−8338.68	−0.389507
$772$	4553.03	0.212263
$773$	28038.9	1.30464	0.652321	−	0.757943i	$-0.273795\pi$
$773$	28038.9	1.30464	0.652321	+	0.757943i	$0.273795\pi$
$774$	−29624.1	−1.37573
$775$	6164.85	0.285739
$776$	−455.020	−0.0210493
$777$	−1077.66	−0.0497567
$778$	−26282.9	−1.21117
$779$	−19636.4	−0.903143
$780$	0	0
$781$	−11123.3	−0.509635
$782$	1685.24	0.0770638
$783$	−6830.07	−0.311733
$784$	15748.9	0.717426
$785$	−9503.55	−0.432097
$786$	3345.44	0.151817
$787$	−32661.4	−1.47936	−0.739679	−	0.672960i	$-0.765022\pi$
$787$	−32661.4	−1.47936	−0.739679	+	0.672960i	$0.765022\pi$
$788$	31301.0	1.41504
$789$	−4614.04	−0.208193
$790$	−87904.2	−3.95885
$791$	−18256.2	−0.820627
$792$	−85.6089	−0.00384088
$793$	0	0
$794$	1024.65	0.0457976
$795$	7535.17	0.336157
$796$	16768.2	0.746647
$797$	−18169.1	−0.807506	−0.403753	−	0.914868i	$-0.632295\pi$
$797$	−18169.1	−0.807506	−0.403753	+	0.914868i	$0.632295\pi$
$798$	6640.95	0.294595
$799$	1099.42	0.0486792
$800$	−78836.1	−3.48410
$801$	−12412.3	−0.547524
$802$	−29685.2	−1.30701
$803$	−10651.7	−0.468106
$804$	2951.32	0.129459
$805$	8552.68	0.374462
$806$	0	0
$807$	10117.5	0.441332
$808$	33.5718	0.00146170
$809$	−33500.0	−1.45587	−0.727934	−	0.685647i	$-0.759519\pi$
$809$	−33500.0	−1.45587	−0.727934	+	0.685647i	$0.759519\pi$
$810$	−42367.4	−1.83783
$811$	−39882.2	−1.72682	−0.863411	−	0.504501i	$-0.831676\pi$
$811$	−39882.2	−1.72682	−0.863411	+	0.504501i	$0.831676\pi$
$812$	6290.49	0.271863
$813$	3199.46	0.138019
$814$	2834.48	0.122050
$815$	68830.1	2.95830
$816$	1109.38	0.0475930
$817$	30606.4	1.31063
$818$	−20483.5	−0.875537
$819$	0	0
$820$	32469.8	1.38280
$821$	−10675.7	−0.453816	−0.226908	−	0.973916i	$-0.572862\pi$
$821$	−10675.7	−0.453816	−0.226908	+	0.973916i	$0.572862\pi$
$822$	6094.49	0.258601
$823$	−10242.5	−0.433819	−0.216909	−	0.976192i	$-0.569598\pi$
$823$	−10242.5	−0.433819	−0.216909	+	0.976192i	$0.569598\pi$
$824$	349.623	0.0147812
$825$	−5685.83	−0.239946
$826$	9321.76	0.392670
$827$	19343.7	0.813359	0.406680	−	0.913571i	$-0.366687\pi$
$827$	19343.7	0.813359	0.406680	+	0.913571i	$0.366687\pi$
$828$	7894.89	0.331360
$829$	6854.35	0.287167	0.143584	−	0.989638i	$-0.454137\pi$
$829$	6854.35	0.287167	0.143584	+	0.989638i	$0.454137\pi$
$830$	14619.9	0.611402
$831$	739.654	0.0308764
$832$	0	0
$833$	2497.89	0.103898
$834$	14652.6	0.608367
$835$	72644.7	3.01075
$836$	−8689.31	−0.359481
$837$	−1711.27	−0.0706694
$838$	31736.4	1.30825
$839$	−17749.2	−0.730358	−0.365179	−	0.930937i	$-0.618992\pi$
$839$	−17749.2	−0.730358	−0.365179	+	0.930937i	$0.618992\pi$
$840$	111.776	0.00459124
$841$	−18038.6	−0.739619
$842$	−63873.5	−2.61428
$843$	15685.9	0.640866
$844$	−25345.7	−1.03369
$845$	0	0
$846$	10353.4	0.420754
$847$	1206.08	0.0489273
$848$	13969.5	0.565703
$849$	−12043.2	−0.486834
$850$	−12630.0	−0.509653
$851$	2660.73	0.107178
$852$	13406.3	0.539076
$853$	−12586.4	−0.505217	−0.252608	−	0.967569i	$-0.581288\pi$
$853$	−12586.4	−0.505217	−0.252608	+	0.967569i	$0.581288\pi$
$854$	21062.5	0.843961
$855$	50268.7	2.01070
$856$	201.401	0.00804177
$857$	−16185.5	−0.645141	−0.322570	−	0.946545i	$-0.604547\pi$
$857$	−16185.5	−0.645141	−0.322570	+	0.946545i	$0.604547\pi$
$858$	0	0
$859$	−24377.9	−0.968293	−0.484147	−	0.874987i	$-0.660870\pi$
$859$	−24377.9	−0.968293	−0.484147	+	0.874987i	$0.660870\pi$
$860$	−50609.2	−2.00670
$861$	−3284.94	−0.130024
$862$	39571.1	1.56357
$863$	−1535.01	−0.0605474	−0.0302737	−	0.999542i	$-0.509638\pi$
$863$	−1535.01	−0.0605474	−0.0302737	+	0.999542i	$0.509638\pi$
$864$	21883.8	0.861691
$865$	80432.7	3.16161
$866$	15123.2	0.593426
$867$	−8048.77	−0.315283
$868$	1576.08	0.0616311
$869$	−11636.2	−0.454237
$870$	−11085.8	−0.432004
$871$	0	0
$872$	−644.592	−0.0250328
$873$	−34233.0	−1.32716
$874$	−16396.4	−0.634572
$875$	−38148.5	−1.47389
$876$	12837.8	0.495148
$877$	−11405.0	−0.439131	−0.219566	−	0.975598i	$-0.570464\pi$
$877$	−11405.0	−0.439131	−0.219566	+	0.975598i	$0.570464\pi$
$878$	18547.5	0.712924
$879$	10097.9	0.387480
$880$	−14808.5	−0.567265
$881$	8252.61	0.315593	0.157796	−	0.987472i	$-0.449561\pi$
$881$	8252.61	0.315593	0.157796	+	0.987472i	$0.449561\pi$
$882$	23523.1	0.898030
$883$	11884.7	0.452945	0.226473	−	0.974018i	$-0.427281\pi$
$883$	11884.7	0.452945	0.226473	+	0.974018i	$0.427281\pi$
$884$	0	0
$885$	−8172.31	−0.310406
$886$	5901.45	0.223773
$887$	20904.6	0.791329	0.395664	−	0.918395i	$-0.370514\pi$
$887$	20904.6	0.791329	0.395664	+	0.918395i	$0.370514\pi$
$888$	34.7735	0.00131410
$889$	15946.2	0.601596
$890$	−42625.7	−1.60541
$891$	−5608.35	−0.210872
$892$	33948.9	1.27432
$893$	−10696.7	−0.400843
$894$	14625.0	0.547129
$895$	80786.4	3.01720
$896$	410.332	0.0152994
$897$	0	0
$898$	20136.1	0.748274
$899$	1591.10	0.0590281
$900$	−59168.1	−2.19141
$901$	2215.67	0.0819252
$902$	8640.08	0.318939
$903$	5120.08	0.188689
$904$	589.081	0.0216732
$905$	91839.5	3.37331
$906$	−21864.9	−0.801781
$907$	37869.9	1.38638	0.693192	−	0.720753i	$-0.256204\pi$
$907$	37869.9	1.38638	0.693192	+	0.720753i	$0.256204\pi$
$908$	−8439.73	−0.308460
$909$	2525.74	0.0921599
$910$	0	0
$911$	36633.8	1.33231	0.666154	−	0.745814i	$-0.267939\pi$
$911$	36633.8	1.33231	0.666154	+	0.745814i	$0.267939\pi$
$912$	−10793.6	−0.391899
$913$	1935.29	0.0701521
$914$	−30981.8	−1.12121
$915$	−18465.3	−0.667152
$916$	−7375.63	−0.266045
$917$	4992.36	0.179784
$918$	3505.90	0.126048
$919$	−2386.32	−0.0856556	−0.0428278	−	0.999082i	$-0.513637\pi$
$919$	−2386.32	−0.0856556	−0.0428278	+	0.999082i	$0.513637\pi$
$920$	−275.973	−0.00988975
$921$	1133.38	0.0405495
$922$	12904.6	0.460944
$923$	0	0
$924$	−1453.62	−0.0517538
$925$	−19940.8	−0.708812
$926$	40809.4	1.44825
$927$	26303.5	0.931954
$928$	−20347.0	−0.719746
$929$	24671.8	0.871320	0.435660	−	0.900111i	$-0.356515\pi$
$929$	24671.8	0.871320	0.435660	+	0.900111i	$0.356515\pi$
$930$	−2777.54	−0.0979347
$931$	−24303.1	−0.855533
$932$	8755.93	0.307736
$933$	4128.60	0.144871
$934$	−2577.57	−0.0903004
$935$	−2348.73	−0.0821514
$936$	0	0
$937$	3045.78	0.106191	0.0530956	−	0.998589i	$-0.483091\pi$
$937$	3045.78	0.106191	0.0530956	+	0.998589i	$0.483091\pi$
$938$	8853.29	0.308177
$939$	294.100	0.0102211
$940$	17687.6	0.613730
$941$	40232.6	1.39378	0.696889	−	0.717179i	$-0.254567\pi$
$941$	40232.6	1.39378	0.696889	+	0.717179i	$0.254567\pi$
$942$	3047.88	0.105420
$943$	8110.47	0.280078
$944$	−15150.7	−0.522367
$945$	17792.7	0.612482
$946$	−13466.9	−0.462839
$947$	6768.36	0.232252	0.116126	−	0.993235i	$-0.462952\pi$
$947$	6768.36	0.232252	0.116126	+	0.993235i	$0.462952\pi$
$948$	14024.5	0.480478
$949$	0	0
$950$	122883.	4.19667
$951$	−18059.0	−0.615776
$952$	32.8670	0.00111894
$953$	4770.35	0.162148	0.0810739	−	0.996708i	$-0.474165\pi$
$953$	4770.35	0.162148	0.0810739	+	0.996708i	$0.474165\pi$
$954$	20865.3	0.708113
$955$	−39270.1	−1.33063
$956$	22633.4	0.765707
$957$	−1467.47	−0.0495680
$958$	−26075.8	−0.879405
$959$	9094.75	0.306241
$960$	17489.8	0.588001
$961$	−29392.3	−0.986618
$962$	0	0
$963$	15152.2	0.507034
$964$	−14087.9	−0.470686
$965$	−11973.9	−0.399433
$966$	−2742.92	−0.0913582
$967$	−6004.49	−0.199681	−0.0998404	−	0.995003i	$-0.531833\pi$
$967$	−6004.49	−0.199681	−0.0998404	+	0.995003i	$0.531833\pi$
$968$	−38.9172	−0.00129220
$969$	−1711.94	−0.0567549
$970$	−117561.	−3.89141
$971$	12670.2	0.418750	0.209375	−	0.977835i	$-0.432857\pi$
$971$	12670.2	0.418750	0.209375	+	0.977835i	$0.432857\pi$
$972$	25085.9	0.827808
$973$	21865.9	0.720442
$974$	−47779.5	−1.57182
$975$	0	0
$976$	−34233.0	−1.12272
$977$	−16673.3	−0.545983	−0.272992	−	0.962016i	$-0.588013\pi$
$977$	−16673.3	−0.545983	−0.272992	+	0.962016i	$0.588013\pi$
$978$	−22074.4	−0.721741
$979$	−5642.54	−0.184205
$980$	40186.4	1.30990
$981$	−48495.2	−1.57832
$982$	5068.55	0.164709
$983$	11945.8	0.387602	0.193801	−	0.981041i	$-0.437918\pi$
$983$	11945.8	0.387602	0.193801	+	0.981041i	$0.437918\pi$
$984$	105.997	0.00343400
$985$	−82317.7	−2.66280
$986$	−3259.70	−0.105284
$987$	−1789.44	−0.0577087
$988$	0	0
$989$	−12641.4	−0.406444
$990$	−22118.3	−0.710068
$991$	13371.6	0.428619	0.214310	−	0.976766i	$-0.431250\pi$
$991$	13371.6	0.428619	0.214310	+	0.976766i	$0.431250\pi$
$992$	−5097.95	−0.163165
$993$	15762.7	0.503740
$994$	40215.8	1.28327
$995$	−44098.1	−1.40503
$996$	−2332.50	−0.0742048
$997$	37713.0	1.19798	0.598988	−	0.800758i	$-0.295570\pi$
$997$	37713.0	1.19798	0.598988	+	0.800758i	$0.295570\pi$
$998$	82372.0	2.61266
$999$	5535.29	0.175304

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.i.1.14		17
13.3	even	3		143.4.e.a.100.4	✓	34
13.9	even	3		143.4.e.a.133.4	yes	34
13.12	even	2		1859.4.a.f.1.4		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.a.100.4	✓	34	13.3	even	3
143.4.e.a.133.4	yes	34	13.9	even	3
1859.4.a.f.1.4		17	13.12	even	2
1859.4.a.i.1.14		17	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+3.98991 q^{2} +1.67407 q^{3} +7.91939 q^{4} -20.8270 q^{5} +6.67941 q^{6} +9.96761 q^{7} -0.321630 q^{8} -24.1975 q^{9} -83.0979 q^{10} -11.0000 q^{11} +13.2576 q^{12} +39.7699 q^{14} -34.8659 q^{15} -64.6384 q^{16} -10.2521 q^{17} -96.5458 q^{18} +99.7472 q^{19} -164.937 q^{20} +16.6865 q^{21} -43.8890 q^{22} -41.1988 q^{23} -0.538432 q^{24} +308.764 q^{25} -85.7084 q^{27} +78.9374 q^{28} +79.6896 q^{29} -139.112 q^{30} +19.9662 q^{31} -255.328 q^{32} -18.4148 q^{33} -40.9050 q^{34} -207.595 q^{35} -191.629 q^{36} -64.5829 q^{37} +397.983 q^{38} +6.69858 q^{40} -196.862 q^{41} +66.5778 q^{42} +306.839 q^{43} -87.1133 q^{44} +503.961 q^{45} -164.379 q^{46} -107.239 q^{47} -108.209 q^{48} -243.647 q^{49} +1231.94 q^{50} -17.1628 q^{51} -216.118 q^{53} -341.969 q^{54} +229.097 q^{55} -3.20588 q^{56} +166.984 q^{57} +317.955 q^{58} +234.392 q^{59} -276.117 q^{60} +529.608 q^{61} +79.6635 q^{62} -241.191 q^{63} -501.630 q^{64} -73.4735 q^{66} +222.613 q^{67} -81.1904 q^{68} -68.9698 q^{69} -828.287 q^{70} +1011.21 q^{71} +7.78263 q^{72} +968.334 q^{73} -257.680 q^{74} +516.893 q^{75} +789.937 q^{76} -109.644 q^{77} +1057.84 q^{79} +1346.22 q^{80} +509.850 q^{81} -785.462 q^{82} -175.936 q^{83} +132.147 q^{84} +213.521 q^{85} +1224.26 q^{86} +133.406 q^{87} +3.53793 q^{88} +512.958 q^{89} +2010.76 q^{90} -326.269 q^{92} +33.4250 q^{93} -427.872 q^{94} -2077.43 q^{95} -427.439 q^{96} +1414.73 q^{97} -972.129 q^{98} +266.172 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 4 q^{2} - 6 q^{3} + 78 q^{4} + 16 q^{5} + 14 q^{6} - 6 q^{7} + 63 q^{8} + 135 q^{9} + 2 q^{10} - 187 q^{11} - 95 q^{12} - 60 q^{14} - 28 q^{15} + 350 q^{16} + 118 q^{17} + 478 q^{18} + 403 q^{19}+ \cdots - 1485 q^{99}+O(q^{100}) \) 17 * q + 4 * q^2 - 6 * q^3 + 78 * q^4 + 16 * q^5 + 14 * q^6 - 6 * q^7 + 63 * q^8 + 135 * q^9 + 2 * q^10 - 187 * q^11 - 95 * q^12 - 60 * q^14 - 28 * q^15 + 350 * q^16 + 118 * q^17 + 478 * q^18 + 403 * q^19 + 98 * q^20 + 220 * q^21 - 44 * q^22 - 215 * q^23 + 26 * q^24 + 319 * q^25 - 384 * q^27 - 396 * q^28 - 7 * q^29 - 1269 * q^30 + 682 * q^31 + 813 * q^32 + 66 * q^33 + 738 * q^34 + 10 * q^35 + 560 * q^36 + 1084 * q^37 + 410 * q^38 + 95 * q^40 + 240 * q^41 + 393 * q^42 - 435 * q^43 - 858 * q^44 + 1242 * q^45 + 1671 * q^46 + 549 * q^47 + 894 * q^48 + 403 * q^49 - 651 * q^50 + 1552 * q^51 - 566 * q^53 + 311 * q^54 - 176 * q^55 - 1925 * q^56 - 534 * q^57 + 618 * q^58 + 2010 * q^59 - 411 * q^60 + 460 * q^61 - 823 * q^62 + 820 * q^63 + 3171 * q^64 - 154 * q^66 - 232 * q^67 + 1795 * q^68 - 1608 * q^69 + 207 * q^70 + 489 * q^71 + 2556 * q^72 + 290 * q^73 + 2653 * q^74 - 2852 * q^75 + 2421 * q^76 + 66 * q^77 - 732 * q^79 + 4915 * q^80 + 2393 * q^81 - 1772 * q^82 - 117 * q^83 + 4161 * q^84 + 4858 * q^85 + 1034 * q^86 + 3032 * q^87 - 693 * q^88 + 4113 * q^89 + 15145 * q^90 - 3554 * q^92 + 802 * q^93 + 2325 * q^94 - 3924 * q^95 + 2601 * q^96 + 2793 * q^97 + 533 * q^98 - 1485 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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