LMFDB - Embedded newform 1859.4.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$109.684550701$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 64 x^{9} + 268 x^{8} + 1564 x^{7} - 4963 x^{6} - 16942 x^{5} + 37082 x^{4} + \cdots + 16256 $ x^11 - 5x^10 - 64x^9 + 268x^8 + 1564x^7 - 4963x^6 - 16942x^5 + 37082x^4 + 68209x^3 - 90926x^2 - 1672x + 16256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-3.37601$ 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)

$f(q)$	$=$	$q-4.37601 q^{2} +4.08546 q^{3} +11.1495 q^{4} -1.30050 q^{5} -17.8780 q^{6} -14.9266 q^{7} -13.7821 q^{8} -10.3090 q^{9} +O(q^{10})$	\(q-4.37601 q^{2} +4.08546 q^{3} +11.1495 q^{4} -1.30050 q^{5} -17.8780 q^{6} -14.9266 q^{7} -13.7821 q^{8} -10.3090 q^{9} +5.69101 q^{10} -11.0000 q^{11} +45.5508 q^{12} +65.3192 q^{14} -5.31315 q^{15} -28.8850 q^{16} -127.838 q^{17} +45.1122 q^{18} -113.242 q^{19} -14.4999 q^{20} -60.9823 q^{21} +48.1361 q^{22} +104.237 q^{23} -56.3065 q^{24} -123.309 q^{25} -152.425 q^{27} -166.424 q^{28} -76.5628 q^{29} +23.2504 q^{30} +8.10035 q^{31} +236.658 q^{32} -44.9401 q^{33} +559.420 q^{34} +19.4121 q^{35} -114.940 q^{36} -345.749 q^{37} +495.549 q^{38} +17.9237 q^{40} +466.793 q^{41} +266.859 q^{42} -45.7776 q^{43} -122.644 q^{44} +13.4068 q^{45} -456.140 q^{46} -301.735 q^{47} -118.009 q^{48} -120.195 q^{49} +539.600 q^{50} -522.277 q^{51} -471.496 q^{53} +667.011 q^{54} +14.3055 q^{55} +205.721 q^{56} -462.647 q^{57} +335.040 q^{58} -600.995 q^{59} -59.2389 q^{60} +933.526 q^{61} -35.4472 q^{62} +153.878 q^{63} -804.539 q^{64} +196.658 q^{66} -23.7598 q^{67} -1425.33 q^{68} +425.855 q^{69} -84.9477 q^{70} +285.593 q^{71} +142.080 q^{72} +459.363 q^{73} +1513.00 q^{74} -503.773 q^{75} -1262.59 q^{76} +164.193 q^{77} -92.6658 q^{79} +37.5650 q^{80} -344.383 q^{81} -2042.69 q^{82} -843.087 q^{83} -679.921 q^{84} +166.253 q^{85} +200.323 q^{86} -312.795 q^{87} +151.604 q^{88} +692.372 q^{89} -58.6685 q^{90} +1162.18 q^{92} +33.0937 q^{93} +1320.39 q^{94} +147.272 q^{95} +966.859 q^{96} +190.600 q^{97} +525.976 q^{98} +113.399 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9}+O(q^{10}) $ 11 * q - 6 * q^2 + 6 * q^3 + 66 * q^4 + 4 * q^5 + 14 * q^6 - 45 * q^7 - 78 * q^8 + 135 * q^9	\( 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9} + 48 q^{10} - 121 q^{11} + 105 q^{12} - 48 q^{14} + 125 q^{15} + 394 q^{16} + 265 q^{17} - 405 q^{18} - 127 q^{19} + 46 q^{20} + 287 q^{21} + 66 q^{22} + 42 q^{23} + 83 q^{24} + 737 q^{25} + 69 q^{27} - 675 q^{28} + 435 q^{29} + 785 q^{30} + 174 q^{31} - 315 q^{32} - 66 q^{33} - 497 q^{34} + 844 q^{35} + 1572 q^{36} - 187 q^{37} - 1813 q^{38} - 1470 q^{40} - 128 q^{41} - 2630 q^{42} + 696 q^{43} - 726 q^{44} + 1537 q^{45} - 785 q^{46} + 355 q^{47} - 516 q^{48} + 1758 q^{49} + 3414 q^{50} - 25 q^{51} - 693 q^{53} + 4150 q^{54} - 44 q^{55} - 3123 q^{56} - 99 q^{57} + 287 q^{58} + 609 q^{59} + 5013 q^{60} + 1625 q^{61} - 882 q^{62} - 1365 q^{63} - 914 q^{64} - 154 q^{66} - 633 q^{67} + 2873 q^{68} - 2192 q^{69} + 2054 q^{70} + 1937 q^{71} - 3242 q^{72} - 404 q^{73} - 447 q^{74} + 1781 q^{75} + 1814 q^{76} + 495 q^{77} + 1670 q^{79} + 1568 q^{80} + 2619 q^{81} + 1283 q^{82} - 785 q^{83} + 11750 q^{84} - 3189 q^{85} + 5950 q^{86} + 46 q^{87} + 858 q^{88} - 1464 q^{89} + 401 q^{90} - 3786 q^{92} - 1826 q^{93} - 2597 q^{94} - 2356 q^{95} - 4513 q^{96} - 1184 q^{97} - 2823 q^{98} - 1485 q^{99}+O(q^{100}) \) 11 * q - 6 * q^2 + 6 * q^3 + 66 * q^4 + 4 * q^5 + 14 * q^6 - 45 * q^7 - 78 * q^8 + 135 * q^9 + 48 * q^10 - 121 * q^11 + 105 * q^12 - 48 * q^14 + 125 * q^15 + 394 * q^16 + 265 * q^17 - 405 * q^18 - 127 * q^19 + 46 * q^20 + 287 * q^21 + 66 * q^22 + 42 * q^23 + 83 * q^24 + 737 * q^25 + 69 * q^27 - 675 * q^28 + 435 * q^29 + 785 * q^30 + 174 * q^31 - 315 * q^32 - 66 * q^33 - 497 * q^34 + 844 * q^35 + 1572 * q^36 - 187 * q^37 - 1813 * q^38 - 1470 * q^40 - 128 * q^41 - 2630 * q^42 + 696 * q^43 - 726 * q^44 + 1537 * q^45 - 785 * q^46 + 355 * q^47 - 516 * q^48 + 1758 * q^49 + 3414 * q^50 - 25 * q^51 - 693 * q^53 + 4150 * q^54 - 44 * q^55 - 3123 * q^56 - 99 * q^57 + 287 * q^58 + 609 * q^59 + 5013 * q^60 + 1625 * q^61 - 882 * q^62 - 1365 * q^63 - 914 * q^64 - 154 * q^66 - 633 * q^67 + 2873 * q^68 - 2192 * q^69 + 2054 * q^70 + 1937 * q^71 - 3242 * q^72 - 404 * q^73 - 447 * q^74 + 1781 * q^75 + 1814 * q^76 + 495 * q^77 + 1670 * q^79 + 1568 * q^80 + 2619 * q^81 + 1283 * q^82 - 785 * q^83 + 11750 * q^84 - 3189 * q^85 + 5950 * q^86 + 46 * q^87 + 858 * q^88 - 1464 * q^89 + 401 * q^90 - 3786 * q^92 - 1826 * q^93 - 2597 * q^94 - 2356 * q^95 - 4513 * q^96 - 1184 * q^97 - 2823 * q^98 - 1485 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−4.37601	−1.54715	−0.773577	−	0.633703i	$-0.781534\pi$
$2$	−4.37601	−1.54715	−0.773577	+	0.633703i	$0.781534\pi$
$3$	4.08546	0.786248	0.393124	−	0.919485i	$-0.371394\pi$
$3$	4.08546	0.786248	0.393124	+	0.919485i	$0.371394\pi$
$4$	11.1495	1.39368
$5$	−1.30050	−0.116320	−0.0581602	−	0.998307i	$-0.518523\pi$
$5$	−1.30050	−0.116320	−0.0581602	+	0.998307i	$0.518523\pi$
$6$	−17.8780	−1.21645
$7$	−14.9266	−0.805963	−0.402982	−	0.915208i	$-0.632026\pi$
$7$	−14.9266	−0.805963	−0.402982	+	0.915208i	$0.632026\pi$
$8$	−13.7821	−0.609090
$9$	−10.3090	−0.381814
$10$	5.69101	0.179966
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	45.5508	1.09578
$13$	0	0
$13$	0	0
$14$	65.3192	1.24695
$15$	−5.31315	−0.0914567
$16$	−28.8850	−0.451328
$17$	−127.838	−1.82384	−0.911919	−	0.410371i	$-0.865399\pi$
$17$	−127.838	−1.82384	−0.911919	+	0.410371i	$0.865399\pi$
$18$	45.1122	0.590725
$19$	−113.242	−1.36734	−0.683672	−	0.729789i	$-0.739618\pi$
$19$	−113.242	−1.36734	−0.683672	+	0.729789i	$0.739618\pi$
$20$	−14.4999	−0.162114
$21$	−60.9823	−0.633687
$22$	48.1361	0.466484
$23$	104.237	0.944992	0.472496	−	0.881333i	$-0.343353\pi$
$23$	104.237	0.944992	0.472496	+	0.881333i	$0.343353\pi$
$24$	−56.3065	−0.478896
$25$	−123.309	−0.986470
$26$	0	0
$27$	−152.425	−1.08645
$28$	−166.424	−1.12326
$29$	−76.5628	−0.490254	−0.245127	−	0.969491i	$-0.578830\pi$
$29$	−76.5628	−0.490254	−0.245127	+	0.969491i	$0.578830\pi$
$30$	23.2504	0.141498
$31$	8.10035	0.0469312	0.0234656	−	0.999725i	$-0.492530\pi$
$31$	8.10035	0.0469312	0.0234656	+	0.999725i	$0.492530\pi$
$32$	236.658	1.30736
$33$	−44.9401	−0.237063
$34$	559.420	2.82176
$35$	19.4121	0.0937500
$36$	−114.940	−0.532128
$37$	−345.749	−1.53624	−0.768120	−	0.640306i	$-0.778807\pi$
$37$	−345.749	−1.53624	−0.768120	+	0.640306i	$0.778807\pi$
$38$	495.549	2.11549
$39$	0	0
$40$	17.9237	0.0708497
$41$	466.793	1.77807	0.889034	−	0.457842i	$-0.151377\pi$
$41$	466.793	1.77807	0.889034	+	0.457842i	$0.151377\pi$
$42$	266.859	0.980411
$43$	−45.7776	−0.162349	−0.0811747	−	0.996700i	$-0.525867\pi$
$43$	−45.7776	−0.162349	−0.0811747	+	0.996700i	$0.525867\pi$
$44$	−122.644	−0.420212
$45$	13.4068	0.0444128
$46$	−456.140	−1.46205
$47$	−301.735	−0.936437	−0.468218	−	0.883613i	$-0.655104\pi$
$47$	−301.735	−0.936437	−0.468218	+	0.883613i	$0.655104\pi$
$48$	−118.009	−0.354856
$49$	−120.195	−0.350423
$50$	539.600	1.52622
$51$	−522.277	−1.43399
$52$	0	0
$53$	−471.496	−1.22198	−0.610990	−	0.791638i	$-0.709229\pi$
$53$	−471.496	−1.22198	−0.610990	+	0.791638i	$0.709229\pi$
$54$	667.011	1.68090
$55$	14.3055	0.0350719
$56$	205.721	0.490904
$57$	−462.647	−1.07507
$58$	335.040	0.758498
$59$	−600.995	−1.32615	−0.663075	−	0.748553i	$-0.730749\pi$
$59$	−600.995	−1.32615	−0.663075	+	0.748553i	$0.730749\pi$
$60$	−59.2389	−0.127462
$61$	933.526	1.95944	0.979719	−	0.200377i	$-0.0642166\pi$
$61$	933.526	1.95944	0.979719	+	0.200377i	$0.0642166\pi$
$62$	−35.4472	−0.0726098
$63$	153.878	0.307728
$64$	−804.539	−1.57137
$65$	0	0
$66$	196.658	0.366772
$67$	−23.7598	−0.0433242	−0.0216621	−	0.999765i	$-0.506896\pi$
$67$	−23.7598	−0.0433242	−0.0216621	+	0.999765i	$0.506896\pi$
$68$	−1425.33	−2.54185
$69$	425.855	0.742998
$70$	−84.9477	−0.145046
$71$	285.593	0.477375	0.238687	−	0.971096i	$-0.423283\pi$
$71$	285.593	0.477375	0.238687	+	0.971096i	$0.423283\pi$
$72$	142.080	0.232559
$73$	459.363	0.736499	0.368249	−	0.929727i	$-0.379957\pi$
$73$	459.363	0.736499	0.368249	+	0.929727i	$0.379957\pi$
$74$	1513.00	2.37680
$75$	−503.773	−0.775610
$76$	−1262.59	−1.90565
$77$	164.193	0.243007
$78$	0	0
$79$	−92.6658	−0.131971	−0.0659856	−	0.997821i	$-0.521019\pi$
$79$	−92.6658	−0.131971	−0.0659856	+	0.997821i	$0.521019\pi$
$80$	37.5650	0.0524987
$81$	−344.383	−0.472404
$82$	−2042.69	−2.75094
$83$	−843.087	−1.11495	−0.557475	−	0.830194i	$-0.688230\pi$
$83$	−843.087	−1.11495	−0.557475	+	0.830194i	$0.688230\pi$
$84$	−679.921	−0.883160
$85$	166.253	0.212150
$86$	200.323	0.251179
$87$	−312.795	−0.385461
$88$	151.604	0.183648
$89$	692.372	0.824621	0.412311	−	0.911043i	$-0.364722\pi$
$89$	692.372	0.824621	0.412311	+	0.911043i	$0.364722\pi$
$90$	−58.6685	−0.0687134
$91$	0	0
$92$	1162.18	1.31702
$93$	33.0937	0.0368996
$94$	1320.39	1.44881
$95$	147.272	0.159050
$96$	966.859	1.02791
$97$	190.600	0.199510	0.0997551	−	0.995012i	$-0.468194\pi$
$97$	190.600	0.199510	0.0997551	+	0.995012i	$0.468194\pi$
$98$	525.976	0.542159
$99$	113.399	0.115121
$100$	−1374.83	−1.37483
$101$	−42.0029	−0.0413807	−0.0206903	−	0.999786i	$-0.506586\pi$
$101$	−42.0029	−0.0413807	−0.0206903	+	0.999786i	$0.506586\pi$
$102$	2285.49	2.21860
$103$	528.478	0.505558	0.252779	−	0.967524i	$-0.418655\pi$
$103$	528.478	0.505558	0.252779	+	0.967524i	$0.418655\pi$
$104$	0	0
$105$	79.3076	0.0737107
$106$	2063.27	1.89059
$107$	2062.70	1.86363	0.931816	−	0.362932i	$-0.118224\pi$
$107$	2062.70	1.86363	0.931816	+	0.362932i	$0.118224\pi$
$108$	−1699.45	−1.51417
$109$	−102.719	−0.0902632	−0.0451316	−	0.998981i	$-0.514371\pi$
$109$	−102.719	−0.0902632	−0.0451316	+	0.998981i	$0.514371\pi$
$110$	−62.6011	−0.0542617
$111$	−1412.55	−1.20787
$112$	431.156	0.363754
$113$	434.064	0.361356	0.180678	−	0.983542i	$-0.442171\pi$
$113$	434.064	0.361356	0.180678	+	0.983542i	$0.442171\pi$
$114$	2024.55	1.66330
$115$	−135.560	−0.109922
$116$	−853.635	−0.683259
$117$	0	0
$118$	2629.96	2.05176
$119$	1908.19	1.46995
$120$	73.2267	0.0557054
$121$	121.000	0.0909091
$122$	−4085.12	−3.03155
$123$	1907.07	1.39800
$124$	90.3147	0.0654073
$125$	322.926	0.231067
$126$	−673.374	−0.476103
$127$	152.353	0.106450	0.0532249	−	0.998583i	$-0.483050\pi$
$127$	152.353	0.106450	0.0532249	+	0.998583i	$0.483050\pi$
$128$	1627.41	1.12378
$129$	−187.023	−0.127647
$130$	0	0
$131$	2639.78	1.76060	0.880300	−	0.474418i	$-0.157341\pi$
$131$	2639.78	1.76060	0.880300	+	0.474418i	$0.157341\pi$
$132$	−501.059	−0.330391
$133$	1690.33	1.10203
$134$	103.973	0.0670292
$135$	198.228	0.126376
$136$	1761.88	1.11088
$137$	−2019.40	−1.25933	−0.629667	−	0.776865i	$-0.716809\pi$
$137$	−2019.40	−1.25933	−0.629667	+	0.776865i	$0.716809\pi$
$138$	−1863.54	−1.14953
$139$	−341.826	−0.208585	−0.104293	−	0.994547i	$-0.533258\pi$
$139$	−341.826	−0.208585	−0.104293	+	0.994547i	$0.533258\pi$
$140$	216.435	0.130658
$141$	−1232.73	−0.736272
$142$	−1249.76	−0.738572
$143$	0	0
$144$	297.775	0.172323
$145$	99.5701	0.0570265
$146$	−2010.18	−1.13948
$147$	−491.053	−0.275520
$148$	−3854.92	−2.14103
$149$	−2290.67	−1.25946	−0.629730	−	0.776814i	$-0.716834\pi$
$149$	−2290.67	−1.25946	−0.629730	+	0.776814i	$0.716834\pi$
$150$	2204.52	1.19999
$151$	−3284.81	−1.77029	−0.885145	−	0.465316i	$-0.845941\pi$
$151$	−3284.81	−1.77029	−0.885145	+	0.465316i	$0.845941\pi$
$152$	1560.72	0.832836
$153$	1317.88	0.696367
$154$	−718.511	−0.375969
$155$	−10.5345	−0.00545906
$156$	0	0
$157$	773.990	0.393447	0.196723	−	0.980459i	$-0.436970\pi$
$157$	773.990	0.393447	0.196723	+	0.980459i	$0.436970\pi$
$158$	405.507	0.204180
$159$	−1926.28	−0.960780
$160$	−307.774	−0.152073
$161$	−1555.90	−0.761629
$162$	1507.02	0.730882
$163$	−332.420	−0.159737	−0.0798685	−	0.996805i	$-0.525450\pi$
$163$	−332.420	−0.159737	−0.0798685	+	0.996805i	$0.525450\pi$
$164$	5204.49	2.47807
$165$	58.4447	0.0275752
$166$	3689.36	1.72500
$167$	1582.39	0.733226	0.366613	−	0.930374i	$-0.380517\pi$
$167$	1582.39	0.733226	0.366613	+	0.930374i	$0.380517\pi$
$168$	840.467	0.385973
$169$	0	0
$170$	−727.527	−0.328228
$171$	1167.41	0.522071
$172$	−510.397	−0.226264
$173$	−3951.29	−1.73648	−0.868241	−	0.496143i	$-0.834749\pi$
$173$	−3951.29	−1.73648	−0.868241	+	0.496143i	$0.834749\pi$
$174$	1368.79	0.596367
$175$	1840.59	0.795058
$176$	317.735	0.136081
$177$	−2455.34	−1.04268
$178$	−3029.83	−1.27582
$179$	−1912.00	−0.798376	−0.399188	−	0.916869i	$-0.630708\pi$
$179$	−1912.00	−0.798376	−0.399188	+	0.916869i	$0.630708\pi$
$180$	149.479	0.0618974
$181$	−328.347	−0.134839	−0.0674195	−	0.997725i	$-0.521477\pi$
$181$	−328.347	−0.134839	−0.0674195	+	0.997725i	$0.521477\pi$
$182$	0	0
$183$	3813.89	1.54060
$184$	−1436.60	−0.575586
$185$	449.648	0.178696
$186$	−144.818	−0.0570893
$187$	1406.22	0.549908
$188$	−3364.18	−1.30510
$189$	2275.19	0.875638
$190$	−644.462	−0.246075
$191$	237.620	0.0900188	0.0450094	−	0.998987i	$-0.485668\pi$
$191$	237.620	0.0900188	0.0450094	+	0.998987i	$0.485668\pi$
$192$	−3286.92	−1.23548
$193$	3625.07	1.35201	0.676006	−	0.736896i	$-0.263709\pi$
$193$	3625.07	1.35201	0.676006	+	0.736896i	$0.263709\pi$
$194$	−834.068	−0.308673
$195$	0	0
$196$	−1340.11	−0.488380
$197$	−3252.19	−1.17619	−0.588094	−	0.808793i	$-0.700122\pi$
$197$	−3252.19	−1.17619	−0.588094	+	0.808793i	$0.700122\pi$
$198$	−496.234	−0.178110
$199$	−2274.47	−0.810214	−0.405107	−	0.914269i	$-0.632766\pi$
$199$	−2274.47	−0.810214	−0.405107	+	0.914269i	$0.632766\pi$
$200$	1699.46	0.600849
$201$	−97.0698	−0.0340636
$202$	183.805	0.0640223
$203$	1142.83	0.395126
$204$	−5823.12	−1.99853
$205$	−607.065	−0.206826
$206$	−2312.62	−0.782176
$207$	−1074.57	−0.360811
$208$	0	0
$209$	1245.66	0.412270
$210$	−347.051	−0.114042
$211$	586.925	0.191496	0.0957479	−	0.995406i	$-0.469476\pi$
$211$	586.925	0.191496	0.0957479	+	0.995406i	$0.469476\pi$
$212$	−5256.94	−1.70306
$213$	1166.78	0.375335
$214$	−9026.39	−2.88332
$215$	59.5339	0.0188846
$216$	2100.74	0.661745
$217$	−120.911	−0.0378248
$218$	449.499	0.139651
$219$	1876.71	0.579071
$220$	159.499	0.0488792
$221$	0	0
$222$	6181.32	1.86875
$223$	3730.52	1.12024	0.560121	−	0.828411i	$-0.310755\pi$
$223$	3730.52	1.12024	0.560121	+	0.828411i	$0.310755\pi$
$224$	−3532.51	−1.05369
$225$	1271.19	0.376648
$226$	−1899.47	−0.559074
$227$	5758.34	1.68368	0.841839	−	0.539729i	$-0.181473\pi$
$227$	5758.34	1.68368	0.841839	+	0.539729i	$0.181473\pi$
$228$	−5158.27	−1.49831
$229$	1313.16	0.378935	0.189468	−	0.981887i	$-0.439324\pi$
$229$	1313.16	0.378935	0.189468	+	0.981887i	$0.439324\pi$
$230$	593.211	0.170066
$231$	670.805	0.191064
$232$	1055.20	0.298609
$233$	−6860.84	−1.92905	−0.964525	−	0.263992i	$-0.914961\pi$
$233$	−6860.84	−1.92905	−0.964525	+	0.263992i	$0.914961\pi$
$234$	0	0
$235$	392.407	0.108927
$236$	−6700.78	−1.84823
$237$	−378.583	−0.103762
$238$	−8350.27	−2.27423
$239$	1484.44	0.401760	0.200880	−	0.979616i	$-0.435620\pi$
$239$	1484.44	0.401760	0.200880	+	0.979616i	$0.435620\pi$
$240$	153.470	0.0412770
$241$	−562.199	−0.150267	−0.0751337	−	0.997173i	$-0.523938\pi$
$241$	−562.199	−0.150267	−0.0751337	+	0.997173i	$0.523938\pi$
$242$	−529.497	−0.140650
$243$	2708.50	0.715022
$244$	10408.3	2.73084
$245$	156.314	0.0407614
$246$	−8345.34	−2.16292
$247$	0	0
$248$	−111.640	−0.0285853
$249$	−3444.40	−0.876627
$250$	−1413.13	−0.357496
$251$	−7212.01	−1.81362	−0.906809	−	0.421542i	$-0.861489\pi$
$251$	−7212.01	−1.81362	−0.906809	+	0.421542i	$0.861489\pi$
$252$	1715.66	0.428876
$253$	−1146.60	−0.284926
$254$	−666.698	−0.164694
$255$	679.222	0.166802
$256$	−685.237	−0.167294
$257$	−5258.99	−1.27645	−0.638223	−	0.769852i	$-0.720330\pi$
$257$	−5258.99	−1.27645	−0.638223	+	0.769852i	$0.720330\pi$
$258$	818.415	0.197489
$259$	5160.88	1.23815
$260$	0	0
$261$	789.284	0.187186
$262$	−11551.7	−2.72392
$263$	−4071.92	−0.954698	−0.477349	−	0.878714i	$-0.658402\pi$
$263$	−4071.92	−0.954698	−0.477349	+	0.878714i	$0.658402\pi$
$264$	619.371	0.144393
$265$	613.182	0.142141
$266$	−7396.89	−1.70501
$267$	2828.66	0.648357
$268$	−264.909	−0.0603803
$269$	−6619.65	−1.50040	−0.750200	−	0.661211i	$-0.770043\pi$
$269$	−6619.65	−1.50040	−0.750200	+	0.661211i	$0.770043\pi$
$270$	−867.450	−0.195523
$271$	−2938.20	−0.658608	−0.329304	−	0.944224i	$-0.606814\pi$
$271$	−2938.20	−0.658608	−0.329304	+	0.944224i	$0.606814\pi$
$272$	3692.60	0.823149
$273$	0	0
$274$	8836.91	1.94838
$275$	1356.40	0.297432
$276$	4748.06	1.03551
$277$	5897.25	1.27917	0.639587	−	0.768718i	$-0.279105\pi$
$277$	5897.25	1.27917	0.639587	+	0.768718i	$0.279105\pi$
$278$	1495.84	0.322713
$279$	−83.5064	−0.0179190
$280$	−267.541	−0.0571022
$281$	−924.577	−0.196284	−0.0981418	−	0.995172i	$-0.531290\pi$
$281$	−924.577	−0.196284	−0.0981418	+	0.995172i	$0.531290\pi$
$282$	5394.43	1.13913
$283$	4754.32	0.998639	0.499320	−	0.866418i	$-0.333583\pi$
$283$	4754.32	0.998639	0.499320	+	0.866418i	$0.333583\pi$
$284$	3184.21	0.665310
$285$	601.673	0.125053
$286$	0	0
$287$	−6967.65	−1.43306
$288$	−2439.70	−0.499170
$289$	11429.5	2.32638
$290$	−435.720	−0.0882288
$291$	778.690	0.156865
$292$	5121.66	1.02645
$293$	−182.036	−0.0362958	−0.0181479	−	0.999835i	$-0.505777\pi$
$293$	−182.036	−0.0362958	−0.0181479	+	0.999835i	$0.505777\pi$
$294$	2148.85	0.426271
$295$	781.595	0.154258
$296$	4765.17	0.935709
$297$	1676.67	0.327577
$298$	10024.0	1.94858
$299$	0	0
$300$	−5616.81	−1.08096
$301$	683.307	0.130848
$302$	14374.4	2.73891
$303$	−171.602	−0.0325355
$304$	3271.00	0.617121
$305$	−1214.05	−0.227923
$306$	−5767.05	−1.07739
$307$	−4511.46	−0.838705	−0.419353	−	0.907823i	$-0.637743\pi$
$307$	−4511.46	−0.838705	−0.419353	+	0.907823i	$0.637743\pi$
$308$	1830.67	0.338675
$309$	2159.08	0.397494
$310$	46.0992	0.00844600
$311$	3051.26	0.556338	0.278169	−	0.960532i	$-0.410273\pi$
$311$	3051.26	0.556338	0.278169	+	0.960532i	$0.410273\pi$
$312$	0	0
$313$	−4686.91	−0.846389	−0.423194	−	0.906039i	$-0.639091\pi$
$313$	−4686.91	−0.846389	−0.423194	+	0.906039i	$0.639091\pi$
$314$	−3386.99	−0.608722
$315$	−200.119	−0.0357951
$316$	−1033.18	−0.183926
$317$	8233.82	1.45886	0.729428	−	0.684057i	$-0.239786\pi$
$317$	8233.82	1.45886	0.729428	+	0.684057i	$0.239786\pi$
$318$	8429.43	1.48647
$319$	842.191	0.147817
$320$	1046.30	0.182782
$321$	8427.08	1.46528
$322$	6808.64	1.17836
$323$	14476.6	2.49381
$324$	−3839.69	−0.658382
$325$	0	0
$326$	1454.67	0.247138
$327$	−419.655	−0.0709693
$328$	−6433.40	−1.08300
$329$	4503.89	0.754734
$330$	−255.755	−0.0426631
$331$	2576.26	0.427807	0.213904	−	0.976855i	$-0.431382\pi$
$331$	2576.26	0.427807	0.213904	+	0.976855i	$0.431382\pi$
$332$	−9399.98	−1.55389
$333$	3564.32	0.586558
$334$	−6924.54	−1.13441
$335$	30.8997	0.00503949
$336$	1761.47	0.286001
$337$	4759.04	0.769263	0.384631	−	0.923070i	$-0.374329\pi$
$337$	4759.04	0.769263	0.384631	+	0.923070i	$0.374329\pi$
$338$	0	0
$339$	1773.35	0.284116
$340$	1853.64	0.295670
$341$	−89.1039	−0.0141503
$342$	−5108.60	−0.807724
$343$	6913.95	1.08839
$344$	630.914	0.0988855
$345$	−553.825	−0.0864259
$346$	17290.9	2.68660
$347$	2502.13	0.387093	0.193546	−	0.981091i	$-0.438001\pi$
$347$	2502.13	0.387093	0.193546	+	0.981091i	$0.438001\pi$
$348$	−3487.50	−0.537211
$349$	−8206.05	−1.25862	−0.629312	−	0.777153i	$-0.716663\pi$
$349$	−8206.05	−1.25862	−0.629312	+	0.777153i	$0.716663\pi$
$350$	−8054.42	−1.23008
$351$	0	0
$352$	−2603.24	−0.394185
$353$	3907.05	0.589097	0.294548	−	0.955637i	$-0.404831\pi$
$353$	3907.05	0.589097	0.294548	+	0.955637i	$0.404831\pi$
$354$	10744.6	1.61319
$355$	−371.414	−0.0555285
$356$	7719.58	1.14926
$357$	7795.85	1.15574
$358$	8366.92	1.23521
$359$	−4522.95	−0.664936	−0.332468	−	0.943114i	$-0.607881\pi$
$359$	−4522.95	−0.664936	−0.332468	+	0.943114i	$0.607881\pi$
$360$	−184.775	−0.0270514
$361$	5964.79	0.869629
$362$	1436.85	0.208617
$363$	494.341	0.0714771
$364$	0	0
$365$	−597.403	−0.0856698
$366$	−16689.6	−2.38355
$367$	−9072.56	−1.29042	−0.645210	−	0.764006i	$-0.723230\pi$
$367$	−9072.56	−1.29042	−0.645210	+	0.764006i	$0.723230\pi$
$368$	−3010.87	−0.426501
$369$	−4812.15	−0.678891
$370$	−1967.66	−0.276470
$371$	7037.86	0.984872
$372$	368.978	0.0514263
$373$	7802.13	1.08305	0.541527	−	0.840684i	$-0.317846\pi$
$373$	7802.13	1.08305	0.541527	+	0.840684i	$0.317846\pi$
$374$	−6153.62	−0.850792
$375$	1319.30	0.181676
$376$	4158.55	0.570375
$377$	0	0
$378$	−9956.24	−1.35475
$379$	9107.90	1.23441	0.617205	−	0.786802i	$-0.288265\pi$
$379$	9107.90	1.23441	0.617205	+	0.786802i	$0.288265\pi$
$380$	1642.00	0.221666
$381$	622.432	0.0836960
$382$	−1039.83	−0.139273
$383$	5972.74	0.796848	0.398424	−	0.917201i	$-0.369557\pi$
$383$	5972.74	0.796848	0.398424	+	0.917201i	$0.369557\pi$
$384$	6648.71	0.883569
$385$	−213.533	−0.0282667
$386$	−15863.4	−2.09177
$387$	471.921	0.0619873
$388$	2125.09	0.278054
$389$	12668.3	1.65118	0.825591	−	0.564269i	$-0.190842\pi$
$389$	12668.3	1.65118	0.825591	+	0.564269i	$0.190842\pi$
$390$	0	0
$391$	−13325.4	−1.72351
$392$	1656.55	0.213439
$393$	10784.7	1.38427
$394$	14231.6	1.81974
$395$	120.512	0.0153509
$396$	1264.34	0.160443
$397$	−2888.18	−0.365123	−0.182561	−	0.983194i	$-0.558439\pi$
$397$	−2888.18	−0.365123	−0.182561	+	0.983194i	$0.558439\pi$
$398$	9953.09	1.25353
$399$	6905.77	0.866468
$400$	3561.77	0.445221
$401$	3951.26	0.492061	0.246031	−	0.969262i	$-0.420874\pi$
$401$	3951.26	0.492061	0.246031	+	0.969262i	$0.420874\pi$
$402$	424.779	0.0527016
$403$	0	0
$404$	−468.311	−0.0576716
$405$	447.870	0.0549503
$406$	−5001.02	−0.611321
$407$	3803.24	0.463194
$408$	7198.10	0.873429
$409$	1662.27	0.200963	0.100482	−	0.994939i	$-0.467962\pi$
$409$	1662.27	0.200963	0.100482	+	0.994939i	$0.467962\pi$
$410$	2656.52	0.319991
$411$	−8250.18	−0.990150
$412$	5892.25	0.704588
$413$	8970.84	1.06883
$414$	4702.34	0.558230
$415$	1096.44	0.129691
$416$	0	0
$417$	−1396.52	−0.164000
$418$	−5451.04	−0.637845
$419$	−1031.74	−0.120295	−0.0601477	−	0.998189i	$-0.519157\pi$
$419$	−1031.74	−0.120295	−0.0601477	+	0.998189i	$0.519157\pi$
$420$	884.238	0.102730
$421$	−2268.11	−0.262567	−0.131284	−	0.991345i	$-0.541910\pi$
$421$	−2268.11	−0.262567	−0.131284	+	0.991345i	$0.541910\pi$
$422$	−2568.39	−0.296273
$423$	3110.58	0.357545
$424$	6498.23	0.744297
$425$	15763.5	1.79916
$426$	−5105.84	−0.580701
$427$	−13934.4	−1.57923
$428$	22998.0	2.59731
$429$	0	0
$430$	−260.521	−0.0292173
$431$	−5332.68	−0.595977	−0.297988	−	0.954570i	$-0.596316\pi$
$431$	−5332.68	−0.595977	−0.297988	+	0.954570i	$0.596316\pi$
$432$	4402.78	0.490345
$433$	−4276.63	−0.474646	−0.237323	−	0.971431i	$-0.576270\pi$
$433$	−4276.63	−0.474646	−0.237323	+	0.971431i	$0.576270\pi$
$434$	529.109	0.0585208
$435$	406.790	0.0448370
$436$	−1145.26	−0.125798
$437$	−11804.0	−1.29213
$438$	−8212.52	−0.895911
$439$	−680.029	−0.0739317	−0.0369658	−	0.999317i	$-0.511769\pi$
$439$	−680.029	−0.0739317	−0.0369658	+	0.999317i	$0.511769\pi$
$440$	−197.161	−0.0213620
$441$	1239.09	0.133797
$442$	0	0
$443$	−5330.21	−0.571661	−0.285830	−	0.958280i	$-0.592269\pi$
$443$	−5330.21	−0.571661	−0.285830	+	0.958280i	$0.592269\pi$
$444$	−15749.2	−1.68338
$445$	−900.431	−0.0959203
$446$	−16324.8	−1.73319
$447$	−9358.47	−0.990247
$448$	12009.1	1.26646
$449$	−4616.55	−0.485230	−0.242615	−	0.970123i	$-0.578005\pi$
$449$	−4616.55	−0.485230	−0.242615	+	0.970123i	$0.578005\pi$
$450$	−5562.73	−0.582732
$451$	−5134.72	−0.536108
$452$	4839.58	0.503617
$453$	−13420.0	−1.39189
$454$	−25198.6	−2.60491
$455$	0	0
$456$	6376.27	0.654816
$457$	2597.22	0.265849	0.132924	−	0.991126i	$-0.457563\pi$
$457$	2597.22	0.265849	0.132924	+	0.991126i	$0.457563\pi$
$458$	−5746.41	−0.586271
$459$	19485.6	1.98151
$460$	−1511.42	−0.153196
$461$	8926.69	0.901860	0.450930	−	0.892559i	$-0.351092\pi$
$461$	8926.69	0.901860	0.450930	+	0.892559i	$0.351092\pi$
$462$	−2935.45	−0.295605
$463$	8914.66	0.894815	0.447408	−	0.894330i	$-0.352347\pi$
$463$	8914.66	0.894815	0.447408	+	0.894330i	$0.352347\pi$
$464$	2211.52	0.221265
$465$	−43.0384	−0.00429217
$466$	30023.1	2.98454
$467$	11839.9	1.17320	0.586599	−	0.809877i	$-0.300466\pi$
$467$	11839.9	1.17320	0.586599	+	0.809877i	$0.300466\pi$
$468$	0	0
$469$	354.654	0.0349177
$470$	−1717.18	−0.168526
$471$	3162.11	0.309347
$472$	8282.99	0.807745
$473$	503.554	0.0489502
$474$	1656.68	0.160536
$475$	13963.7	1.34884
$476$	21275.3	2.04864
$477$	4860.64	0.466569
$478$	−6495.94	−0.621584
$479$	18069.7	1.72365	0.861824	−	0.507207i	$-0.169322\pi$
$479$	18069.7	1.72365	0.861824	+	0.507207i	$0.169322\pi$
$480$	−1257.40	−0.119567
$481$	0	0
$482$	2460.19	0.232487
$483$	−6356.58	−0.598829
$484$	1349.09	0.126699
$485$	−247.876	−0.0232071
$486$	−11852.4	−1.10625
$487$	−6820.29	−0.634614	−0.317307	−	0.948323i	$-0.602779\pi$
$487$	−6820.29	−0.634614	−0.317307	+	0.948323i	$0.602779\pi$
$488$	−12866.0	−1.19347
$489$	−1358.09	−0.125593
$490$	−684.032	−0.0630641
$491$	11106.6	1.02084	0.510422	−	0.859924i	$-0.329489\pi$
$491$	11106.6	1.02084	0.510422	+	0.859924i	$0.329489\pi$
$492$	21262.8	1.94837
$493$	9787.62	0.894143
$494$	0	0
$495$	−147.475	−0.0133910
$496$	−233.979	−0.0211814
$497$	−4262.94	−0.384747
$498$	15072.7	1.35628
$499$	−2492.47	−0.223603	−0.111802	−	0.993731i	$-0.535662\pi$
$499$	−2492.47	−0.223603	−0.111802	+	0.993731i	$0.535662\pi$
$500$	3600.45	0.322034
$501$	6464.78	0.576497
$502$	31559.8	2.80595
$503$	−5402.29	−0.478879	−0.239440	−	0.970911i	$-0.576964\pi$
$503$	−5402.29	−0.478879	−0.239440	+	0.970911i	$0.576964\pi$
$504$	−2120.77	−0.187434
$505$	54.6249	0.00481342
$506$	5017.54	0.440824
$507$	0	0
$508$	1698.65	0.148358
$509$	2321.48	0.202157	0.101078	−	0.994878i	$-0.467771\pi$
$509$	2321.48	0.202157	0.101078	+	0.994878i	$0.467771\pi$
$510$	−2972.29	−0.258069
$511$	−6856.75	−0.593591
$512$	−10020.6	−0.864950
$513$	17260.9	1.48555
$514$	23013.4	1.97486
$515$	−687.286	−0.0588067
$516$	−2085.21	−0.177900
$517$	3319.08	0.282346
$518$	−22584.1	−1.91561
$519$	−16142.9	−1.36531
$520$	0	0
$521$	−7589.78	−0.638223	−0.319112	−	0.947717i	$-0.603385\pi$
$521$	−7589.78	−0.638223	−0.319112	+	0.947717i	$0.603385\pi$
$522$	−3453.92	−0.289605
$523$	20117.6	1.68199	0.840995	−	0.541043i	$-0.181970\pi$
$523$	20117.6	1.68199	0.840995	+	0.541043i	$0.181970\pi$
$524$	29432.2	2.45372
$525$	7519.65	0.625113
$526$	17818.8	1.47706
$527$	−1035.53	−0.0855949
$528$	1298.09	0.106993
$529$	−1301.75	−0.106990
$530$	−2683.29	−0.219915
$531$	6195.64	0.506343
$532$	18846.2	1.53588
$533$	0	0
$534$	−12378.3	−1.00311
$535$	−2682.54	−0.216778
$536$	327.461	0.0263884
$537$	−7811.39	−0.627721
$538$	28967.7	2.32135
$539$	1322.15	0.105657
$540$	2210.14	0.176128
$541$	10420.7	0.828137	0.414068	−	0.910246i	$-0.364107\pi$
$541$	10420.7	0.828137	0.414068	+	0.910246i	$0.364107\pi$
$542$	12857.6	1.01897
$543$	−1341.45	−0.106017
$544$	−30253.9	−2.38442
$545$	133.586	0.0104995
$546$	0	0
$547$	4305.56	0.336549	0.168274	−	0.985740i	$-0.446181\pi$
$547$	4305.56	0.336549	0.168274	+	0.985740i	$0.446181\pi$
$548$	−22515.2	−1.75512
$549$	−9623.69	−0.748141
$550$	−5935.60	−0.460173
$551$	8670.14	0.670345
$552$	−5869.19	−0.452553
$553$	1383.19	0.106364
$554$	−25806.4	−1.97908
$555$	1837.02	0.140499
$556$	−3811.18	−0.290702
$557$	−19978.6	−1.51978	−0.759891	−	0.650050i	$-0.774748\pi$
$557$	−19978.6	−1.51978	−0.759891	+	0.650050i	$0.774748\pi$
$558$	365.425	0.0277234
$559$	0	0
$560$	−560.719	−0.0423120
$561$	5745.05	0.432364
$562$	4045.96	0.303681
$563$	−21049.6	−1.57573	−0.787863	−	0.615850i	$-0.788813\pi$
$563$	−21049.6	−1.57573	−0.787863	+	0.615850i	$0.788813\pi$
$564$	−13744.3	−1.02613
$565$	−564.501	−0.0420331
$566$	−20805.0	−1.54505
$567$	5140.48	0.380740
$568$	−3936.08	−0.290765
$569$	12124.3	0.893282	0.446641	−	0.894713i	$-0.352620\pi$
$569$	12124.3	0.893282	0.446641	+	0.894713i	$0.352620\pi$
$570$	−2632.93	−0.193476
$571$	24710.2	1.81102	0.905509	−	0.424327i	$-0.139489\pi$
$571$	24710.2	1.81102	0.905509	+	0.424327i	$0.139489\pi$
$572$	0	0
$573$	970.789	0.0707771
$574$	30490.5	2.21716
$575$	−12853.3	−0.932206
$576$	8293.97	0.599969
$577$	−14825.1	−1.06963	−0.534816	−	0.844969i	$-0.679619\pi$
$577$	−14825.1	−1.06963	−0.534816	+	0.844969i	$0.679619\pi$
$578$	−50015.7	−3.59927
$579$	14810.1	1.06302
$580$	1110.15	0.0794770
$581$	12584.5	0.898609
$582$	−3407.55	−0.242694
$583$	5186.46	0.368441
$584$	−6331.01	−0.448594
$585$	0	0
$586$	796.592	0.0561552
$587$	−13048.1	−0.917466	−0.458733	−	0.888574i	$-0.651697\pi$
$587$	−13048.1	−0.917466	−0.458733	+	0.888574i	$0.651697\pi$
$588$	−5474.99	−0.383987
$589$	−917.302	−0.0641711
$590$	−3420.27	−0.238661
$591$	−13286.7	−0.924776
$592$	9986.97	0.693348
$593$	−967.774	−0.0670181	−0.0335090	−	0.999438i	$-0.510668\pi$
$593$	−967.774	−0.0670181	−0.0335090	+	0.999438i	$0.510668\pi$
$594$	−7337.13	−0.506811
$595$	−2481.61	−0.170985
$596$	−25539.8	−1.75529
$597$	−9292.25	−0.637029
$598$	0	0
$599$	2513.00	0.171417	0.0857083	−	0.996320i	$-0.472685\pi$
$599$	2513.00	0.171417	0.0857083	+	0.996320i	$0.472685\pi$
$600$	6943.08	0.472417
$601$	−3660.57	−0.248449	−0.124225	−	0.992254i	$-0.539644\pi$
$601$	−3660.57	−0.248449	−0.124225	+	0.992254i	$0.539644\pi$
$602$	−2990.16	−0.202441
$603$	244.939	0.0165418
$604$	−36623.9	−2.46723
$605$	−157.361	−0.0105746
$606$	750.930	0.0503374
$607$	2026.84	0.135530	0.0677651	−	0.997701i	$-0.478413\pi$
$607$	2026.84	0.135530	0.0677651	+	0.997701i	$0.478413\pi$
$608$	−26799.7	−1.78762
$609$	4668.97	0.310667
$610$	5312.70	0.352631
$611$	0	0
$612$	14693.6	0.970515
$613$	17261.2	1.13732	0.568658	−	0.822574i	$-0.307463\pi$
$613$	17261.2	1.13732	0.568658	+	0.822574i	$0.307463\pi$
$614$	19742.2	1.29761
$615$	−2480.14	−0.162616
$616$	−2262.93	−0.148013
$617$	−21380.6	−1.39506	−0.697530	−	0.716556i	$-0.745717\pi$
$617$	−21380.6	−1.39506	−0.697530	+	0.716556i	$0.745717\pi$
$618$	−9448.15	−0.614984
$619$	−14380.5	−0.933769	−0.466884	−	0.884318i	$-0.654624\pi$
$619$	−14380.5	−0.933769	−0.466884	+	0.884318i	$0.654624\pi$
$620$	−117.454	−0.00760820
$621$	−15888.2	−1.02669
$622$	−13352.3	−0.860740
$623$	−10334.8	−0.664614
$624$	0	0
$625$	14993.6	0.959592
$626$	20510.0	1.30949
$627$	5089.12	0.324146
$628$	8629.58	0.548340
$629$	44199.9	2.80185
$630$	875.724	0.0553804
$631$	−2443.26	−0.154144	−0.0770719	−	0.997026i	$-0.524557\pi$
$631$	−2443.26	−0.154144	−0.0770719	+	0.997026i	$0.524557\pi$
$632$	1277.13	0.0803824
$633$	2397.86	0.150563
$634$	−36031.3	−2.25708
$635$	−198.135	−0.0123823
$636$	−21477.0	−1.33902
$637$	0	0
$638$	−3685.44	−0.228696
$639$	−2944.17	−0.182268
$640$	−2116.45	−0.130719
$641$	1510.86	0.0930971	0.0465486	−	0.998916i	$-0.485178\pi$
$641$	1510.86	0.0930971	0.0465486	+	0.998916i	$0.485178\pi$
$642$	−36877.0	−2.26701
$643$	11573.1	0.709797	0.354899	−	0.934905i	$-0.384515\pi$
$643$	11573.1	0.709797	0.354899	+	0.934905i	$0.384515\pi$
$644$	−17347.5	−1.06147
$645$	243.224	0.0148479
$646$	−63349.9	−3.85831
$647$	−17117.6	−1.04012	−0.520062	−	0.854128i	$-0.674091\pi$
$647$	−17117.6	−1.04012	−0.520062	+	0.854128i	$0.674091\pi$
$648$	4746.33	0.287737
$649$	6610.94	0.399849
$650$	0	0
$651$	−493.978	−0.0297397
$652$	−3706.31	−0.222623
$653$	−7433.40	−0.445469	−0.222735	−	0.974879i	$-0.571498\pi$
$653$	−7433.40	−0.445469	−0.222735	+	0.974879i	$0.571498\pi$
$654$	1836.41	0.109800
$655$	−3433.04	−0.204794
$656$	−13483.3	−0.802492
$657$	−4735.57	−0.281205
$658$	−19709.1	−1.16769
$659$	15051.1	0.889692	0.444846	−	0.895607i	$-0.353258\pi$
$659$	15051.1	0.889692	0.444846	+	0.895607i	$0.353258\pi$
$660$	651.628	0.0384312
$661$	22416.8	1.31908	0.659541	−	0.751669i	$-0.270751\pi$
$661$	22416.8	1.31908	0.659541	+	0.751669i	$0.270751\pi$
$662$	−11273.8	−0.661883
$663$	0	0
$664$	11619.5	0.679105
$665$	−2198.27	−0.128188
$666$	−15597.5	−0.907495
$667$	−7980.64	−0.463286
$668$	17642.8	1.02189
$669$	15240.9	0.880788
$670$	−135.217	−0.00779686
$671$	−10268.8	−0.590793
$672$	−14432.0	−0.828460
$673$	8319.03	0.476486	0.238243	−	0.971206i	$-0.423429\pi$
$673$	8319.03	0.476486	0.238243	+	0.971206i	$0.423429\pi$
$674$	−20825.6	−1.19017
$675$	18795.3	1.07175
$676$	0	0
$677$	7461.95	0.423613	0.211806	−	0.977312i	$-0.432065\pi$
$677$	7461.95	0.423613	0.211806	+	0.977312i	$0.432065\pi$
$678$	−7760.21	−0.439571
$679$	−2845.02	−0.160798
$680$	−2291.33	−0.129218
$681$	23525.5	1.32379
$682$	389.920	0.0218927
$683$	12428.9	0.696309	0.348155	−	0.937437i	$-0.386808\pi$
$683$	12428.9	0.696309	0.348155	+	0.937437i	$0.386808\pi$
$684$	13016.0	0.727602
$685$	2626.23	0.146486
$686$	−30255.5	−1.68391
$687$	5364.88	0.297937
$688$	1322.29	0.0732728
$689$	0	0
$690$	2423.54	0.133714
$691$	4967.81	0.273494	0.136747	−	0.990606i	$-0.456335\pi$
$691$	4967.81	0.273494	0.136747	+	0.990606i	$0.456335\pi$
$692$	−44054.9	−2.42011
$693$	−1692.66	−0.0927835
$694$	−10949.3	−0.598892
$695$	444.546	0.0242627
$696$	4310.98	0.234781
$697$	−59673.8	−3.24291
$698$	35909.8	1.94728
$699$	−28029.7	−1.51671
$700$	20521.6	1.10806
$701$	−5532.15	−0.298069	−0.149035	−	0.988832i	$-0.547617\pi$
$701$	−5532.15	−0.298069	−0.149035	+	0.988832i	$0.547617\pi$
$702$	0	0
$703$	39153.4	2.10057
$704$	8849.93	0.473784
$705$	1603.16	0.0856434
$706$	−17097.3	−0.911423
$707$	626.963	0.0333513
$708$	−27375.8	−1.45317
$709$	34720.9	1.83917	0.919585	−	0.392891i	$-0.128525\pi$
$709$	34720.9	1.83917	0.919585	+	0.392891i	$0.128525\pi$
$710$	1625.31	0.0859111
$711$	955.290	0.0503884
$712$	−9542.37	−0.502269
$713$	844.353	0.0443496
$714$	−34114.7	−1.78811
$715$	0	0
$716$	−21317.8	−1.11268
$717$	6064.64	0.315883
$718$	19792.5	1.02876
$719$	−751.841	−0.0389972	−0.0194986	−	0.999810i	$-0.506207\pi$
$719$	−751.841	−0.0389972	−0.0194986	+	0.999810i	$0.506207\pi$
$720$	−387.257	−0.0200447
$721$	−7888.40	−0.407461
$722$	−26102.0	−1.34545
$723$	−2296.85	−0.118147
$724$	−3660.90	−0.187923
$725$	9440.86	0.483620
$726$	−2163.24	−0.110586
$727$	17179.1	0.876393	0.438197	−	0.898879i	$-0.355617\pi$
$727$	17179.1	0.876393	0.438197	+	0.898879i	$0.355617\pi$
$728$	0	0
$729$	20363.8	1.03459
$730$	2614.24	0.132544
$731$	5852.12	0.296099
$732$	42522.8	2.14712
$733$	−26427.7	−1.33169	−0.665845	−	0.746090i	$-0.731929\pi$
$733$	−26427.7	−1.33169	−0.665845	+	0.746090i	$0.731929\pi$
$734$	39701.6	1.99648
$735$	638.616	0.0320486
$736$	24668.4	1.23545
$737$	261.358	0.0130627
$738$	21058.0	1.05035
$739$	−11912.1	−0.592955	−0.296477	−	0.955040i	$-0.595812\pi$
$739$	−11912.1	−0.592955	−0.296477	+	0.955040i	$0.595812\pi$
$740$	5013.34	0.249046
$741$	0	0
$742$	−30797.7	−1.52375
$743$	−19638.9	−0.969691	−0.484845	−	0.874600i	$-0.661124\pi$
$743$	−19638.9	−0.969691	−0.484845	+	0.874600i	$0.661124\pi$
$744$	−456.102	−0.0224752
$745$	2979.03	0.146501
$746$	−34142.2	−1.67565
$747$	8691.37	0.425703
$748$	15678.6	0.766398
$749$	−30789.2	−1.50202
$750$	−5773.28	−0.281081
$751$	22313.5	1.08420	0.542098	−	0.840316i	$-0.317630\pi$
$751$	22313.5	1.08420	0.542098	+	0.840316i	$0.317630\pi$
$752$	8715.60	0.422640
$753$	−29464.4	−1.42595
$754$	0	0
$755$	4271.90	0.205921
$756$	25367.1	1.22036
$757$	−37754.4	−1.81269	−0.906346	−	0.422537i	$-0.861140\pi$
$757$	−37754.4	−1.81269	−0.906346	+	0.422537i	$0.861140\pi$
$758$	−39856.3	−1.90982
$759$	−4684.40	−0.224022
$760$	−2029.72	−0.0968758
$761$	36350.4	1.73154	0.865770	−	0.500443i	$-0.166829\pi$
$761$	36350.4	1.73154	0.865770	+	0.500443i	$0.166829\pi$
$762$	−2723.77	−0.129491
$763$	1533.25	0.0727489
$764$	2649.34	0.125458
$765$	−1713.90	−0.0810017
$766$	−26136.8	−1.23285
$767$	0	0
$768$	−2799.51	−0.131535
$769$	30660.4	1.43777	0.718883	−	0.695131i	$-0.244654\pi$
$769$	30660.4	1.43777	0.718883	+	0.695131i	$0.244654\pi$
$770$	934.425	0.0437329
$771$	−21485.4	−1.00360
$772$	40417.6	1.88428
$773$	8029.33	0.373603	0.186801	−	0.982398i	$-0.440188\pi$
$773$	8029.33	0.373603	0.186801	+	0.982398i	$0.440188\pi$
$774$	−2065.13	−0.0959038
$775$	−998.844	−0.0462962
$776$	−2626.88	−0.121520
$777$	21084.6	0.973495
$778$	−55436.7	−2.55463
$779$	−52860.6	−2.43123
$780$	0	0
$781$	−3141.52	−0.143934
$782$	58312.0	2.66654
$783$	11670.0	0.532635
$784$	3471.84	0.158156
$785$	−1006.58	−0.0457659
$786$	−47194.1	−2.14168
$787$	−42914.5	−1.94375	−0.971877	−	0.235487i	$-0.924331\pi$
$787$	−42914.5	−1.94375	−0.971877	+	0.235487i	$0.924331\pi$
$788$	−36260.2	−1.63924
$789$	−16635.7	−0.750629
$790$	−527.362	−0.0237503
$791$	−6479.11	−0.291240
$792$	−1562.88	−0.0701192
$793$	0	0
$794$	12638.7	0.564901
$795$	2505.13	0.111758
$796$	−25359.1	−1.12918
$797$	−36942.7	−1.64188	−0.820938	−	0.571017i	$-0.806549\pi$
$797$	−36942.7	−1.64188	−0.820938	+	0.571017i	$0.806549\pi$
$798$	−30219.7	−1.34056
$799$	38573.1	1.70791
$800$	−29182.0	−1.28967
$801$	−7137.65	−0.314852
$802$	−17290.8	−0.761294
$803$	−5053.00	−0.222063
$804$	−1082.28	−0.0474739
$805$	2023.45	0.0885930
$806$	0	0
$807$	−27044.4	−1.17969
$808$	578.890	0.0252046
$809$	−24696.7	−1.07329	−0.536644	−	0.843809i	$-0.680308\pi$
$809$	−24696.7	−1.07329	−0.536644	+	0.843809i	$0.680308\pi$
$810$	−1959.89	−0.0850165
$811$	−6548.91	−0.283555	−0.141778	−	0.989899i	$-0.545282\pi$
$811$	−6548.91	−0.283555	−0.141778	+	0.989899i	$0.545282\pi$
$812$	12741.9	0.550681
$813$	−12003.9	−0.517829
$814$	−16643.0	−0.716632
$815$	432.313	0.0185807
$816$	15086.0	0.647199
$817$	5183.96	0.221987
$818$	−7274.12	−0.310921
$819$	0	0
$820$	−6768.45	−0.288250
$821$	8760.09	0.372386	0.186193	−	0.982513i	$-0.440385\pi$
$821$	8760.09	0.372386	0.186193	+	0.982513i	$0.440385\pi$
$822$	36102.9	1.53191
$823$	17706.6	0.749957	0.374979	−	0.927033i	$-0.377650\pi$
$823$	17706.6	0.749957	0.374979	+	0.927033i	$0.377650\pi$
$824$	−7283.56	−0.307930
$825$	5541.51	0.233855
$826$	−39256.5	−1.65364
$827$	−9743.57	−0.409694	−0.204847	−	0.978794i	$-0.565670\pi$
$827$	−9743.57	−0.409694	−0.204847	+	0.978794i	$0.565670\pi$
$828$	−11980.9	−0.502857
$829$	−22351.6	−0.936432	−0.468216	−	0.883614i	$-0.655103\pi$
$829$	−22351.6	−0.936432	−0.468216	+	0.883614i	$0.655103\pi$
$830$	−4798.02	−0.200653
$831$	24093.0	1.00575
$832$	0	0
$833$	15365.5	0.639115
$834$	6111.18	0.253733
$835$	−2057.90	−0.0852891
$836$	13888.5	0.574574
$837$	−1234.69	−0.0509883
$838$	4514.90	0.186115
$839$	−36827.6	−1.51541	−0.757706	−	0.652596i	$-0.773680\pi$
$839$	−36827.6	−1.51541	−0.757706	+	0.652596i	$0.773680\pi$
$840$	−1093.03	−0.0448965
$841$	−18527.1	−0.759651
$842$	9925.27	0.406232
$843$	−3777.33	−0.154328
$844$	6543.91	0.266885
$845$	0	0
$846$	−13611.9	−0.553176
$847$	−1806.12	−0.0732694
$848$	13619.2	0.551514
$849$	19423.6	0.785178
$850$	−68981.3	−2.78358
$851$	−36039.7	−1.45173
$852$	13009.0	0.523099
$853$	−35688.7	−1.43254	−0.716271	−	0.697822i	$-0.754152\pi$
$853$	−35688.7	−1.43254	−0.716271	+	0.697822i	$0.754152\pi$
$854$	60977.1	2.44332
$855$	−1518.22	−0.0607275
$856$	−28428.4	−1.13512
$857$	−20711.8	−0.825557	−0.412778	−	0.910831i	$-0.635442\pi$
$857$	−20711.8	−0.825557	−0.412778	+	0.910831i	$0.635442\pi$
$858$	0	0
$859$	−5468.42	−0.217206	−0.108603	−	0.994085i	$-0.534638\pi$
$859$	−5468.42	−0.217206	−0.108603	+	0.994085i	$0.534638\pi$
$860$	663.772	0.0263191
$861$	−28466.1	−1.12674
$862$	23335.8	0.922068
$863$	−16797.3	−0.662557	−0.331278	−	0.943533i	$-0.607480\pi$
$863$	−16797.3	−0.662557	−0.331278	+	0.943533i	$0.607480\pi$
$864$	−36072.5	−1.42038
$865$	5138.67	0.201988
$866$	18714.6	0.734350
$867$	46694.9	1.82911
$868$	−1348.10	−0.0527158
$869$	1019.32	0.0397908
$870$	−1780.12	−0.0693697
$871$	0	0
$872$	1415.69	0.0549785
$873$	−1964.89	−0.0761758
$874$	51654.3	1.99912
$875$	−4820.20	−0.186231
$876$	20924.4	0.807042
$877$	37042.0	1.42625	0.713124	−	0.701038i	$-0.247280\pi$
$877$	37042.0	1.42625	0.713124	+	0.701038i	$0.247280\pi$
$878$	2975.81	0.114384
$879$	−743.702	−0.0285375
$880$	−413.215	−0.0158289
$881$	−37307.3	−1.42669	−0.713345	−	0.700813i	$-0.752821\pi$
$881$	−37307.3	−1.42669	−0.713345	+	0.700813i	$0.752821\pi$
$882$	−5422.27	−0.207004
$883$	30657.2	1.16840	0.584201	−	0.811609i	$-0.301408\pi$
$883$	30657.2	1.16840	0.584201	+	0.811609i	$0.301408\pi$
$884$	0	0
$885$	3193.18	0.121285
$886$	23325.0	0.884447
$887$	−34102.4	−1.29092	−0.645461	−	0.763793i	$-0.723335\pi$
$887$	−34102.4	−1.29092	−0.645461	+	0.763793i	$0.723335\pi$
$888$	19467.9	0.735699
$889$	−2274.12	−0.0857947
$890$	3940.30	0.148403
$891$	3788.21	0.142435
$892$	41593.3	1.56126
$893$	34169.1	1.28043
$894$	40952.8	1.53206
$895$	2486.55	0.0928674
$896$	−24291.7	−0.905725
$897$	0	0
$898$	20202.1	0.750726
$899$	−620.186	−0.0230082
$900$	14173.1	0.524928
$901$	60275.1	2.22869
$902$	22469.6	0.829441
$903$	2791.63	0.102879
$904$	−5982.33	−0.220099
$905$	427.016	0.0156845
$906$	58725.9	2.15346
$907$	8578.06	0.314035	0.157017	−	0.987596i	$-0.449812\pi$
$907$	8578.06	0.314035	0.157017	+	0.987596i	$0.449812\pi$
$908$	64202.5	2.34651
$909$	433.007	0.0157997
$910$	0	0
$911$	8170.11	0.297133	0.148566	−	0.988902i	$-0.452534\pi$
$911$	8170.11	0.297133	0.148566	+	0.988902i	$0.452534\pi$
$912$	13363.6	0.485210
$913$	9273.96	0.336170
$914$	−11365.5	−0.411309
$915$	−4959.97	−0.179204
$916$	14641.1	0.528116
$917$	−39403.0	−1.41898
$918$	−85269.3	−3.06569
$919$	−52538.4	−1.88584	−0.942918	−	0.333025i	$-0.891931\pi$
$919$	−52538.4	−1.88584	−0.942918	+	0.333025i	$0.891931\pi$
$920$	1868.30	0.0669524
$921$	−18431.4	−0.659430
$922$	−39063.3	−1.39532
$923$	0	0
$924$	7479.13	0.266283
$925$	42633.9	1.51545
$926$	−39010.7	−1.38442
$927$	−5448.06	−0.193029
$928$	−18119.2	−0.640940
$929$	−5617.07	−0.198375	−0.0991874	−	0.995069i	$-0.531624\pi$
$929$	−5617.07	−0.198375	−0.0991874	+	0.995069i	$0.531624\pi$
$930$	188.337	0.00664065
$931$	13611.2	0.479149
$932$	−76494.8	−2.68849
$933$	12465.8	0.437419
$934$	−51811.4	−1.81512
$935$	−1828.79	−0.0639655
$936$	0	0
$937$	34510.8	1.20322	0.601610	−	0.798790i	$-0.294526\pi$
$937$	34510.8	1.20322	0.601610	+	0.798790i	$0.294526\pi$
$938$	−1551.97	−0.0540231
$939$	−19148.2	−0.665472
$940$	4375.13	0.151809
$941$	12330.0	0.427149	0.213575	−	0.976927i	$-0.431489\pi$
$941$	12330.0	0.427149	0.213575	+	0.976927i	$0.431489\pi$
$942$	−13837.4	−0.478607
$943$	48656.8	1.68026
$944$	17359.7	0.598529
$945$	−2958.89	−0.101855
$946$	−2203.56	−0.0757335
$947$	−24499.2	−0.840671	−0.420336	−	0.907369i	$-0.638088\pi$
$947$	−24499.2	−0.840671	−0.420336	+	0.907369i	$0.638088\pi$
$948$	−4221.00	−0.144612
$949$	0	0
$950$	−61105.5	−2.08687
$951$	33639.0	1.14702
$952$	−26299.0	−0.895330
$953$	13726.0	0.466558	0.233279	−	0.972410i	$-0.425054\pi$
$953$	13726.0	0.466558	0.233279	+	0.972410i	$0.425054\pi$
$954$	−21270.2	−0.721855
$955$	−309.025	−0.0104710
$956$	16550.8	0.559926
$957$	3440.74	0.116221
$958$	−79073.4	−2.66675
$959$	30142.8	1.01498
$960$	4274.64	0.143712
$961$	−29725.4	−0.997797
$962$	0	0
$963$	−21264.3	−0.711561
$964$	−6268.23	−0.209425
$965$	−4714.41	−0.157267
$966$	27816.5	0.926481
$967$	−15458.9	−0.514088	−0.257044	−	0.966400i	$-0.582749\pi$
$967$	−15458.9	−0.514088	−0.257044	+	0.966400i	$0.582749\pi$
$968$	−1667.64	−0.0553719
$969$	59143.8	1.96076
$970$	1084.71	0.0359050
$971$	−22467.5	−0.742552	−0.371276	−	0.928523i	$-0.621080\pi$
$971$	−22467.5	−0.742552	−0.371276	+	0.928523i	$0.621080\pi$
$972$	30198.3	0.996515
$973$	5102.32	0.168112
$974$	29845.7	0.981845
$975$	0	0
$976$	−26964.9	−0.884349
$977$	−41930.0	−1.37304	−0.686519	−	0.727112i	$-0.740862\pi$
$977$	−41930.0	−1.37304	−0.686519	+	0.727112i	$0.740862\pi$
$978$	5943.02	0.194312
$979$	−7616.09	−0.248633
$980$	1742.82	0.0568085
$981$	1058.93	0.0344638
$982$	−48602.7	−1.57940
$983$	−25528.9	−0.828328	−0.414164	−	0.910202i	$-0.635926\pi$
$983$	−25528.9	−0.828328	−0.414164	+	0.910202i	$0.635926\pi$
$984$	−26283.4	−0.851510
$985$	4229.48	0.136815
$986$	−42830.8	−1.38338
$987$	18400.5	0.593408
$988$	0	0
$989$	−4771.70	−0.153419
$990$	645.354	0.0207179
$991$	48670.3	1.56010	0.780052	−	0.625715i	$-0.215193\pi$
$991$	48670.3	1.56010	0.780052	+	0.625715i	$0.215193\pi$
$992$	1917.02	0.0613561
$993$	10525.2	0.336363
$994$	18654.7	0.595262
$995$	2957.95	0.0942444
$996$	−38403.3	−1.22174
$997$	−29133.5	−0.925444	−0.462722	−	0.886503i	$-0.653127\pi$
$997$	−29133.5	−0.925444	−0.462722	+	0.886503i	$0.653127\pi$
$998$	10907.1	0.345949
$999$	52700.7	1.66905

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.e.1.3		11
13.12	even	2		143.4.a.d.1.9	✓	11
39.38	odd	2		1287.4.a.m.1.3		11
52.51	odd	2		2288.4.a.u.1.5		11
143.142	odd	2		1573.4.a.f.1.3		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.d.1.9	✓	11	13.12	even	2
1287.4.a.m.1.3		11	39.38	odd	2
1573.4.a.f.1.3		11	143.142	odd	2
1859.4.a.e.1.3		11	1.1	even	1	trivial
2288.4.a.u.1.5		11	52.51	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-4.37601 q^{2} +4.08546 q^{3} +11.1495 q^{4} -1.30050 q^{5} -17.8780 q^{6} -14.9266 q^{7} -13.7821 q^{8} -10.3090 q^{9} +O(q^{10})\)	\(q-4.37601 q^{2} +4.08546 q^{3} +11.1495 q^{4} -1.30050 q^{5} -17.8780 q^{6} -14.9266 q^{7} -13.7821 q^{8} -10.3090 q^{9} +5.69101 q^{10} -11.0000 q^{11} +45.5508 q^{12} +65.3192 q^{14} -5.31315 q^{15} -28.8850 q^{16} -127.838 q^{17} +45.1122 q^{18} -113.242 q^{19} -14.4999 q^{20} -60.9823 q^{21} +48.1361 q^{22} +104.237 q^{23} -56.3065 q^{24} -123.309 q^{25} -152.425 q^{27} -166.424 q^{28} -76.5628 q^{29} +23.2504 q^{30} +8.10035 q^{31} +236.658 q^{32} -44.9401 q^{33} +559.420 q^{34} +19.4121 q^{35} -114.940 q^{36} -345.749 q^{37} +495.549 q^{38} +17.9237 q^{40} +466.793 q^{41} +266.859 q^{42} -45.7776 q^{43} -122.644 q^{44} +13.4068 q^{45} -456.140 q^{46} -301.735 q^{47} -118.009 q^{48} -120.195 q^{49} +539.600 q^{50} -522.277 q^{51} -471.496 q^{53} +667.011 q^{54} +14.3055 q^{55} +205.721 q^{56} -462.647 q^{57} +335.040 q^{58} -600.995 q^{59} -59.2389 q^{60} +933.526 q^{61} -35.4472 q^{62} +153.878 q^{63} -804.539 q^{64} +196.658 q^{66} -23.7598 q^{67} -1425.33 q^{68} +425.855 q^{69} -84.9477 q^{70} +285.593 q^{71} +142.080 q^{72} +459.363 q^{73} +1513.00 q^{74} -503.773 q^{75} -1262.59 q^{76} +164.193 q^{77} -92.6658 q^{79} +37.5650 q^{80} -344.383 q^{81} -2042.69 q^{82} -843.087 q^{83} -679.921 q^{84} +166.253 q^{85} +200.323 q^{86} -312.795 q^{87} +151.604 q^{88} +692.372 q^{89} -58.6685 q^{90} +1162.18 q^{92} +33.0937 q^{93} +1320.39 q^{94} +147.272 q^{95} +966.859 q^{96} +190.600 q^{97} +525.976 q^{98} +113.399 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9}+O(q^{10}) \) 11 * q - 6 * q^2 + 6 * q^3 + 66 * q^4 + 4 * q^5 + 14 * q^6 - 45 * q^7 - 78 * q^8 + 135 * q^9	\( 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9} + 48 q^{10} - 121 q^{11} + 105 q^{12} - 48 q^{14} + 125 q^{15} + 394 q^{16} + 265 q^{17} - 405 q^{18} - 127 q^{19} + 46 q^{20} + 287 q^{21} + 66 q^{22} + 42 q^{23} + 83 q^{24} + 737 q^{25} + 69 q^{27} - 675 q^{28} + 435 q^{29} + 785 q^{30} + 174 q^{31} - 315 q^{32} - 66 q^{33} - 497 q^{34} + 844 q^{35} + 1572 q^{36} - 187 q^{37} - 1813 q^{38} - 1470 q^{40} - 128 q^{41} - 2630 q^{42} + 696 q^{43} - 726 q^{44} + 1537 q^{45} - 785 q^{46} + 355 q^{47} - 516 q^{48} + 1758 q^{49} + 3414 q^{50} - 25 q^{51} - 693 q^{53} + 4150 q^{54} - 44 q^{55} - 3123 q^{56} - 99 q^{57} + 287 q^{58} + 609 q^{59} + 5013 q^{60} + 1625 q^{61} - 882 q^{62} - 1365 q^{63} - 914 q^{64} - 154 q^{66} - 633 q^{67} + 2873 q^{68} - 2192 q^{69} + 2054 q^{70} + 1937 q^{71} - 3242 q^{72} - 404 q^{73} - 447 q^{74} + 1781 q^{75} + 1814 q^{76} + 495 q^{77} + 1670 q^{79} + 1568 q^{80} + 2619 q^{81} + 1283 q^{82} - 785 q^{83} + 11750 q^{84} - 3189 q^{85} + 5950 q^{86} + 46 q^{87} + 858 q^{88} - 1464 q^{89} + 401 q^{90} - 3786 q^{92} - 1826 q^{93} - 2597 q^{94} - 2356 q^{95} - 4513 q^{96} - 1184 q^{97} - 2823 q^{98} - 1485 q^{99}+O(q^{100}) \) 11 * q - 6 * q^2 + 6 * q^3 + 66 * q^4 + 4 * q^5 + 14 * q^6 - 45 * q^7 - 78 * q^8 + 135 * q^9 + 48 * q^10 - 121 * q^11 + 105 * q^12 - 48 * q^14 + 125 * q^15 + 394 * q^16 + 265 * q^17 - 405 * q^18 - 127 * q^19 + 46 * q^20 + 287 * q^21 + 66 * q^22 + 42 * q^23 + 83 * q^24 + 737 * q^25 + 69 * q^27 - 675 * q^28 + 435 * q^29 + 785 * q^30 + 174 * q^31 - 315 * q^32 - 66 * q^33 - 497 * q^34 + 844 * q^35 + 1572 * q^36 - 187 * q^37 - 1813 * q^38 - 1470 * q^40 - 128 * q^41 - 2630 * q^42 + 696 * q^43 - 726 * q^44 + 1537 * q^45 - 785 * q^46 + 355 * q^47 - 516 * q^48 + 1758 * q^49 + 3414 * q^50 - 25 * q^51 - 693 * q^53 + 4150 * q^54 - 44 * q^55 - 3123 * q^56 - 99 * q^57 + 287 * q^58 + 609 * q^59 + 5013 * q^60 + 1625 * q^61 - 882 * q^62 - 1365 * q^63 - 914 * q^64 - 154 * q^66 - 633 * q^67 + 2873 * q^68 - 2192 * q^69 + 2054 * q^70 + 1937 * q^71 - 3242 * q^72 - 404 * q^73 - 447 * q^74 + 1781 * q^75 + 1814 * q^76 + 495 * q^77 + 1670 * q^79 + 1568 * q^80 + 2619 * q^81 + 1283 * q^82 - 785 * q^83 + 11750 * q^84 - 3189 * q^85 + 5950 * q^86 + 46 * q^87 + 858 * q^88 - 1464 * q^89 + 401 * q^90 - 3786 * q^92 - 1826 * q^93 - 2597 * q^94 - 2356 * q^95 - 4513 * q^96 - 1184 * q^97 - 2823 * q^98 - 1485 * q^99

Introduction

L-functions

Modular forms

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Database

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