LMFDB - Embedded newform 1859.4.a.e.1.9

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			1.9
Root			$3.59635$ 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)

$f(q)$	$=$	$q+2.59635 q^{2} +4.20666 q^{3} -1.25897 q^{4} -11.3514 q^{5} +10.9220 q^{6} -3.36670 q^{7} -24.0395 q^{8} -9.30403 q^{9} +O(q^{10})$	\(q+2.59635 q^{2} +4.20666 q^{3} -1.25897 q^{4} -11.3514 q^{5} +10.9220 q^{6} -3.36670 q^{7} -24.0395 q^{8} -9.30403 q^{9} -29.4723 q^{10} -11.0000 q^{11} -5.29607 q^{12} -8.74113 q^{14} -47.7516 q^{15} -52.3432 q^{16} +24.8548 q^{17} -24.1565 q^{18} -23.3785 q^{19} +14.2911 q^{20} -14.1626 q^{21} -28.5598 q^{22} +153.932 q^{23} -101.126 q^{24} +3.85509 q^{25} -152.719 q^{27} +4.23858 q^{28} +235.740 q^{29} -123.980 q^{30} -343.410 q^{31} +56.4149 q^{32} -46.2732 q^{33} +64.5316 q^{34} +38.2169 q^{35} +11.7135 q^{36} -27.1453 q^{37} -60.6987 q^{38} +272.883 q^{40} -334.480 q^{41} -36.7709 q^{42} +184.608 q^{43} +13.8487 q^{44} +105.614 q^{45} +399.661 q^{46} +392.620 q^{47} -220.190 q^{48} -331.665 q^{49} +10.0092 q^{50} +104.555 q^{51} -227.922 q^{53} -396.511 q^{54} +124.866 q^{55} +80.9339 q^{56} -98.3452 q^{57} +612.063 q^{58} +767.215 q^{59} +60.1180 q^{60} -234.105 q^{61} -891.611 q^{62} +31.3239 q^{63} +565.219 q^{64} -120.141 q^{66} -25.9764 q^{67} -31.2915 q^{68} +647.538 q^{69} +99.2244 q^{70} +490.348 q^{71} +223.664 q^{72} -27.0719 q^{73} -70.4787 q^{74} +16.2171 q^{75} +29.4328 q^{76} +37.0337 q^{77} +748.726 q^{79} +594.171 q^{80} -391.226 q^{81} -868.427 q^{82} +1334.30 q^{83} +17.8303 q^{84} -282.137 q^{85} +479.307 q^{86} +991.678 q^{87} +264.435 q^{88} +1379.00 q^{89} +274.211 q^{90} -193.796 q^{92} -1444.61 q^{93} +1019.38 q^{94} +265.379 q^{95} +237.318 q^{96} -101.717 q^{97} -861.119 q^{98} +102.344 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.59635	0.917948	0.458974	−	0.888450i	$-0.348217\pi$
$2$	2.59635	0.917948	0.458974	+	0.888450i	$0.348217\pi$
$3$	4.20666	0.809572	0.404786	−	0.914412i	$-0.367346\pi$
$3$	4.20666	0.809572	0.404786	+	0.914412i	$0.367346\pi$
$4$	−1.25897	−0.157372
$5$	−11.3514	−1.01530	−0.507652	−	0.861562i	$-0.669486\pi$
$5$	−11.3514	−1.01530	−0.507652	+	0.861562i	$0.669486\pi$
$6$	10.9220	0.743145
$7$	−3.36670	−0.181785	−0.0908924	−	0.995861i	$-0.528972\pi$
$7$	−3.36670	−0.181785	−0.0908924	+	0.995861i	$0.528972\pi$
$8$	−24.0395	−1.06241
$9$	−9.30403	−0.344594
$10$	−29.4723	−0.931996
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−5.29607	−0.127404
$13$	0	0
$13$	0	0
$14$	−8.74113	−0.166869
$15$	−47.7516	−0.821961
$16$	−52.3432	−0.817863
$17$	24.8548	0.354598	0.177299	−	0.984157i	$-0.443264\pi$
$17$	24.8548	0.354598	0.177299	+	0.984157i	$0.443264\pi$
$18$	−24.1565	−0.316319
$19$	−23.3785	−0.282284	−0.141142	−	0.989989i	$-0.545077\pi$
$19$	−23.3785	−0.282284	−0.141142	+	0.989989i	$0.545077\pi$
$20$	14.2911	0.159780
$21$	−14.1626	−0.147168
$22$	−28.5598	−0.276772
$23$	153.932	1.39552	0.697761	−	0.716331i	$-0.254180\pi$
$23$	153.932	1.39552	0.697761	+	0.716331i	$0.254180\pi$
$24$	−101.126	−0.860095
$25$	3.85509	0.0308408
$26$	0	0
$27$	−152.719	−1.08854
$28$	4.23858	0.0286077
$29$	235.740	1.50951	0.754756	−	0.656006i	$-0.227755\pi$
$29$	235.740	1.50951	0.754756	+	0.656006i	$0.227755\pi$
$30$	−123.980	−0.754517
$31$	−343.410	−1.98962	−0.994810	−	0.101755i	$-0.967554\pi$
$31$	−343.410	−1.98962	−0.994810	+	0.101755i	$0.967554\pi$
$32$	56.4149	0.311651
$33$	−46.2732	−0.244095
$34$	64.5316	0.325502
$35$	38.2169	0.184567
$36$	11.7135	0.0542292
$37$	−27.1453	−0.120612	−0.0603062	−	0.998180i	$-0.519208\pi$
$37$	−27.1453	−0.120612	−0.0603062	+	0.998180i	$0.519208\pi$
$38$	−60.6987	−0.259122
$39$	0	0
$40$	272.883	1.07867
$41$	−334.480	−1.27407	−0.637037	−	0.770834i	$-0.719840\pi$
$41$	−334.480	−1.27407	−0.637037	+	0.770834i	$0.719840\pi$
$42$	−36.7709	−0.135092
$43$	184.608	0.654709	0.327354	−	0.944902i	$-0.393843\pi$
$43$	184.608	0.654709	0.327354	+	0.944902i	$0.393843\pi$
$44$	13.8487	0.0474493
$45$	105.614	0.349867
$46$	399.661	1.28102
$47$	392.620	1.21850	0.609249	−	0.792979i	$-0.291471\pi$
$47$	392.620	1.21850	0.609249	+	0.792979i	$0.291471\pi$
$48$	−220.190	−0.662118
$49$	−331.665	−0.966954
$50$	10.0092	0.0283102
$51$	104.555	0.287072
$52$	0	0
$53$	−227.922	−0.590707	−0.295353	−	0.955388i	$-0.595437\pi$
$53$	−227.922	−0.590707	−0.295353	+	0.955388i	$0.595437\pi$
$54$	−396.511	−0.999228
$55$	124.866	0.306125
$56$	80.9339	0.193129
$57$	−98.3452	−0.228529
$58$	612.063	1.38565
$59$	767.215	1.69293	0.846465	−	0.532444i	$-0.178726\pi$
$59$	767.215	1.69293	0.846465	+	0.532444i	$0.178726\pi$
$60$	60.1180	0.129353
$61$	−234.105	−0.491379	−0.245689	−	0.969349i	$-0.579014\pi$
$61$	−234.105	−0.491379	−0.245689	+	0.969349i	$0.579014\pi$
$62$	−891.611	−1.82637
$63$	31.3239	0.0626419
$64$	565.219	1.10394
$65$	0	0
$66$	−120.141	−0.224067
$67$	−25.9764	−0.0473660	−0.0236830	−	0.999720i	$-0.507539\pi$
$67$	−25.9764	−0.0473660	−0.0236830	+	0.999720i	$0.507539\pi$
$68$	−31.2915	−0.0558036
$69$	647.538	1.12977
$70$	99.2244	0.169423
$71$	490.348	0.819628	0.409814	−	0.912169i	$-0.365594\pi$
$71$	490.348	0.819628	0.409814	+	0.912169i	$0.365594\pi$
$72$	223.664	0.366099
$73$	−27.0719	−0.0434045	−0.0217023	−	0.999764i	$-0.506909\pi$
$73$	−27.0719	−0.0434045	−0.0217023	+	0.999764i	$0.506909\pi$
$74$	−70.4787	−0.110716
$75$	16.2171	0.0249678
$76$	29.4328	0.0444234
$77$	37.0337	0.0548102
$78$	0	0
$79$	748.726	1.06631	0.533154	−	0.846018i	$-0.321007\pi$
$79$	748.726	1.06631	0.533154	+	0.846018i	$0.321007\pi$
$80$	594.171	0.830379
$81$	−391.226	−0.536662
$82$	−868.427	−1.16953
$83$	1334.30	1.76456	0.882282	−	0.470721i	$-0.156006\pi$
$83$	1334.30	1.76456	0.882282	+	0.470721i	$0.156006\pi$
$84$	17.8303	0.0231600
$85$	−282.137	−0.360024
$86$	479.307	0.600988
$87$	991.678	1.22206
$88$	264.435	0.320328
$89$	1379.00	1.64241	0.821203	−	0.570636i	$-0.193303\pi$
$89$	1379.00	1.64241	0.821203	+	0.570636i	$0.193303\pi$
$90$	274.211	0.321160
$91$	0	0
$92$	−193.796	−0.219615
$93$	−1444.61	−1.61074
$94$	1019.38	1.11852
$95$	265.379	0.286604
$96$	237.318	0.252304
$97$	−101.717	−0.106472	−0.0532361	−	0.998582i	$-0.516954\pi$
$97$	−101.717	−0.106472	−0.0532361	+	0.998582i	$0.516954\pi$
$98$	−861.119	−0.887614
$99$	102.344	0.103899
$100$	−4.85346	−0.00485346
$101$	1122.41	1.10579	0.552893	−	0.833253i	$-0.313524\pi$
$101$	1122.41	1.10579	0.552893	+	0.833253i	$0.313524\pi$
$102$	271.462	0.263518
$103$	710.083	0.679287	0.339644	−	0.940554i	$-0.389694\pi$
$103$	710.083	0.679287	0.339644	+	0.940554i	$0.389694\pi$
$104$	0	0
$105$	160.765	0.149420
$106$	−591.764	−0.542238
$107$	1072.59	0.969081	0.484540	−	0.874769i	$-0.338987\pi$
$107$	1072.59	0.969081	0.484540	+	0.874769i	$0.338987\pi$
$108$	192.269	0.171306
$109$	−569.497	−0.500440	−0.250220	−	0.968189i	$-0.580503\pi$
$109$	−569.497	−0.500440	−0.250220	+	0.968189i	$0.580503\pi$
$110$	324.195	0.281007
$111$	−114.191	−0.0976444
$112$	176.224	0.148675
$113$	1006.23	0.837686	0.418843	−	0.908059i	$-0.362436\pi$
$113$	1006.23	0.837686	0.418843	+	0.908059i	$0.362436\pi$
$114$	−255.339	−0.209778
$115$	−1747.35	−1.41688
$116$	−296.790	−0.237554
$117$	0	0
$118$	1991.96	1.55402
$119$	−83.6785	−0.0644605
$120$	1147.93	0.873257
$121$	121.000	0.0909091
$122$	−607.819	−0.451060
$123$	−1407.04	−1.03145
$124$	432.343	0.313109
$125$	1375.17	0.983991
$126$	81.3277	0.0575020
$127$	−2272.97	−1.58814	−0.794069	−	0.607827i	$-0.792041\pi$
$127$	−2272.97	−1.58814	−0.794069	+	0.607827i	$0.792041\pi$
$128$	1016.19	0.701710
$129$	776.583	0.530033
$130$	0	0
$131$	−2087.21	−1.39206	−0.696031	−	0.718012i	$-0.745052\pi$
$131$	−2087.21	−1.39206	−0.696031	+	0.718012i	$0.745052\pi$
$132$	58.2567	0.0384136
$133$	78.7083	0.0513149
$134$	−67.4438	−0.0434795
$135$	1733.58	1.10520
$136$	−597.496	−0.376727
$137$	1856.04	1.15746	0.578731	−	0.815519i	$-0.303548\pi$
$137$	1856.04	1.15746	0.578731	+	0.815519i	$0.303548\pi$
$138$	1681.24	1.03707
$139$	−320.276	−0.195435	−0.0977176	−	0.995214i	$-0.531154\pi$
$139$	−320.276	−0.195435	−0.0977176	+	0.995214i	$0.531154\pi$
$140$	−48.1140	−0.0290455
$141$	1651.62	0.986462
$142$	1273.11	0.752376
$143$	0	0
$144$	487.003	0.281830
$145$	−2675.99	−1.53261
$146$	−70.2882	−0.0398431
$147$	−1395.20	−0.782819
$148$	34.1752	0.0189810
$149$	504.089	0.277158	0.138579	−	0.990351i	$-0.455747\pi$
$149$	504.089	0.277158	0.138579	+	0.990351i	$0.455747\pi$
$150$	42.1052	0.0229191
$151$	541.167	0.291652	0.145826	−	0.989310i	$-0.453416\pi$
$151$	541.167	0.291652	0.145826	+	0.989310i	$0.453416\pi$
$152$	562.007	0.299900
$153$	−231.249	−0.122192
$154$	96.1524	0.0503129
$155$	3898.19	2.02007
$156$	0	0
$157$	−1357.62	−0.690126	−0.345063	−	0.938579i	$-0.612143\pi$
$157$	−1357.62	−0.690126	−0.345063	+	0.938579i	$0.612143\pi$
$158$	1943.95	0.978815
$159$	−958.789	−0.478219
$160$	−640.391	−0.316421
$161$	−518.242	−0.253685
$162$	−1015.76	−0.492627
$163$	−1132.23	−0.544070	−0.272035	−	0.962287i	$-0.587697\pi$
$163$	−1132.23	−0.544070	−0.272035	+	0.962287i	$0.587697\pi$
$164$	421.101	0.200503
$165$	525.268	0.247831
$166$	3464.32	1.61978
$167$	1278.19	0.592270	0.296135	−	0.955146i	$-0.404302\pi$
$167$	1278.19	0.592270	0.296135	+	0.955146i	$0.404302\pi$
$168$	340.461	0.156352
$169$	0	0
$170$	−732.527	−0.330484
$171$	217.514	0.0972732
$172$	−232.416	−0.103032
$173$	−116.772	−0.0513181	−0.0256590	−	0.999671i	$-0.508168\pi$
$173$	−116.772	−0.0513181	−0.0256590	+	0.999671i	$0.508168\pi$
$174$	2574.74	1.12179
$175$	−12.9789	−0.00560638
$176$	575.775	0.246595
$177$	3227.41	1.37055
$178$	3580.38	1.50764
$179$	2762.55	1.15354	0.576768	−	0.816908i	$-0.304314\pi$
$179$	2762.55	1.15354	0.576768	+	0.816908i	$0.304314\pi$
$180$	−132.965	−0.0550591
$181$	1466.98	0.602428	0.301214	−	0.953557i	$-0.402608\pi$
$181$	1466.98	0.602428	0.301214	+	0.953557i	$0.402608\pi$
$182$	0	0
$183$	−984.800	−0.397806
$184$	−3700.45	−1.48261
$185$	308.138	0.122458
$186$	−3750.70	−1.47857
$187$	−273.402	−0.106915
$188$	−494.297	−0.191757
$189$	514.158	0.197881
$190$	689.017	0.263087
$191$	−3879.20	−1.46958	−0.734788	−	0.678297i	$-0.762718\pi$
$191$	−3879.20	−1.46958	−0.734788	+	0.678297i	$0.762718\pi$
$192$	2377.68	0.893721
$193$	2442.88	0.911101	0.455550	−	0.890210i	$-0.349443\pi$
$193$	2442.88	0.911101	0.455550	+	0.890210i	$0.349443\pi$
$194$	−264.093	−0.0977360
$195$	0	0
$196$	417.557	0.152171
$197$	−3449.26	−1.24746	−0.623730	−	0.781640i	$-0.714383\pi$
$197$	−3449.26	−1.24746	−0.623730	+	0.781640i	$0.714383\pi$
$198$	265.722	0.0953738
$199$	−1635.75	−0.582690	−0.291345	−	0.956618i	$-0.594103\pi$
$199$	−1635.75	−0.582690	−0.291345	+	0.956618i	$0.594103\pi$
$200$	−92.6746	−0.0327654
$201$	−109.274	−0.0383462
$202$	2914.18	1.01505
$203$	−793.666	−0.274406
$204$	−131.632	−0.0451770
$205$	3796.83	1.29357
$206$	1843.62	0.623550
$207$	−1432.19	−0.480888
$208$	0	0
$209$	257.163	0.0851117
$210$	417.403	0.137160
$211$	−1107.44	−0.361324	−0.180662	−	0.983545i	$-0.557824\pi$
$211$	−1107.44	−0.361324	−0.180662	+	0.983545i	$0.557824\pi$
$212$	286.947	0.0929604
$213$	2062.73	0.663547
$214$	2784.83	0.889566
$215$	−2095.57	−0.664728
$216$	3671.28	1.15648
$217$	1156.16	0.361682
$218$	−1478.61	−0.459378
$219$	−113.882	−0.0351391
$220$	−157.203	−0.0481754
$221$	0	0
$222$	−296.480	−0.0896325
$223$	−3767.20	−1.13126	−0.565629	−	0.824660i	$-0.691366\pi$
$223$	−3767.20	−1.13126	−0.565629	+	0.824660i	$0.691366\pi$
$224$	−189.932	−0.0566535
$225$	−35.8679	−0.0106275
$226$	2612.53	0.768952
$227$	3104.30	0.907662	0.453831	−	0.891088i	$-0.350057\pi$
$227$	3104.30	0.907662	0.453831	+	0.891088i	$0.350057\pi$
$228$	123.814	0.0359639
$229$	−288.999	−0.0833956	−0.0416978	−	0.999130i	$-0.513277\pi$
$229$	−288.999	−0.0833956	−0.0416978	+	0.999130i	$0.513277\pi$
$230$	−4536.72	−1.30062
$231$	155.788	0.0443728
$232$	−5667.08	−1.60371
$233$	−2150.50	−0.604653	−0.302326	−	0.953204i	$-0.597763\pi$
$233$	−2150.50	−0.604653	−0.302326	+	0.953204i	$0.597763\pi$
$234$	0	0
$235$	−4456.80	−1.23715
$236$	−965.903	−0.266419
$237$	3149.63	0.863252
$238$	−217.259	−0.0591714
$239$	−4371.75	−1.18320	−0.591600	−	0.806232i	$-0.701503\pi$
$239$	−4371.75	−1.18320	−0.591600	+	0.806232i	$0.701503\pi$
$240$	2499.47	0.672251
$241$	1119.32	0.299177	0.149589	−	0.988748i	$-0.452205\pi$
$241$	1119.32	0.299177	0.149589	+	0.988748i	$0.452205\pi$
$242$	314.158	0.0834498
$243$	2477.65	0.654079
$244$	294.732	0.0773290
$245$	3764.88	0.981752
$246$	−3653.17	−0.946821
$247$	0	0
$248$	8255.40	2.11378
$249$	5612.96	1.42854
$250$	3570.42	0.903252
$251$	−3388.89	−0.852211	−0.426106	−	0.904673i	$-0.640115\pi$
$251$	−3388.89	−0.852211	−0.426106	+	0.904673i	$0.640115\pi$
$252$	−39.4359	−0.00985805
$253$	−1693.25	−0.420766
$254$	−5901.43	−1.45783
$255$	−1186.85	−0.291466
$256$	−1883.38	−0.459809
$257$	5255.85	1.27568	0.637842	−	0.770167i	$-0.279827\pi$
$257$	5255.85	1.27568	0.637842	+	0.770167i	$0.279827\pi$
$258$	2016.28	0.486543
$259$	91.3901	0.0219255
$260$	0	0
$261$	−2193.33	−0.520168
$262$	−5419.11	−1.27784
$263$	−638.903	−0.149796	−0.0748981	−	0.997191i	$-0.523863\pi$
$263$	−638.903	−0.149796	−0.0748981	+	0.997191i	$0.523863\pi$
$264$	1112.39	0.259328
$265$	2587.24	0.599746
$266$	204.354	0.0471044
$267$	5801.00	1.32965
$268$	32.7035	0.00745406
$269$	−1485.59	−0.336721	−0.168360	−	0.985726i	$-0.553847\pi$
$269$	−1485.59	−0.336721	−0.168360	+	0.985726i	$0.553847\pi$
$270$	4500.97	1.01452
$271$	6399.27	1.43442	0.717210	−	0.696857i	$-0.245419\pi$
$271$	6399.27	1.43442	0.717210	+	0.696857i	$0.245419\pi$
$272$	−1300.98	−0.290012
$273$	0	0
$274$	4818.93	1.06249
$275$	−42.4060	−0.00929884
$276$	−815.233	−0.177794
$277$	1312.00	0.284586	0.142293	−	0.989825i	$-0.454553\pi$
$277$	1312.00	0.284586	0.142293	+	0.989825i	$0.454553\pi$
$278$	−831.549	−0.179399
$279$	3195.09	0.685610
$280$	−918.716	−0.196085
$281$	−5443.78	−1.15569	−0.577845	−	0.816146i	$-0.696106\pi$
$281$	−5443.78	−1.15569	−0.577845	+	0.816146i	$0.696106\pi$
$282$	4288.17	0.905521
$283$	3081.57	0.647281	0.323640	−	0.946180i	$-0.395093\pi$
$283$	3081.57	0.647281	0.323640	+	0.946180i	$0.395093\pi$
$284$	−617.334	−0.128986
$285$	1116.36	0.232026
$286$	0	0
$287$	1126.09	0.231607
$288$	−524.886	−0.107393
$289$	−4295.24	−0.874260
$290$	−6947.80	−1.40686
$291$	−427.889	−0.0861969
$292$	34.0828	0.00683064
$293$	−7888.58	−1.57289	−0.786443	−	0.617662i	$-0.788080\pi$
$293$	−7888.58	−1.57289	−0.786443	+	0.617662i	$0.788080\pi$
$294$	−3622.43	−0.718587
$295$	−8708.99	−1.71884
$296$	652.560	0.128140
$297$	1679.90	0.328209
$298$	1308.79	0.254417
$299$	0	0
$300$	−20.4168	−0.00392922
$301$	−621.520	−0.119016
$302$	1405.06	0.267722
$303$	4721.61	0.895212
$304$	1223.70	0.230869
$305$	2657.43	0.498898
$306$	−600.404	−0.112166
$307$	5284.98	0.982507	0.491253	−	0.871017i	$-0.336539\pi$
$307$	5284.98	0.982507	0.491253	+	0.871017i	$0.336539\pi$
$308$	−46.6244	−0.00862556
$309$	2987.08	0.549932
$310$	10121.1	1.85432
$311$	−6664.49	−1.21514	−0.607570	−	0.794266i	$-0.707856\pi$
$311$	−6664.49	−1.21514	−0.607570	+	0.794266i	$0.707856\pi$
$312$	0	0
$313$	9790.03	1.76794	0.883970	−	0.467544i	$-0.154861\pi$
$313$	9790.03	1.76794	0.883970	+	0.467544i	$0.154861\pi$
$314$	−3524.85	−0.633500
$315$	−355.571	−0.0636005
$316$	−942.626	−0.167806
$317$	−1734.26	−0.307273	−0.153636	−	0.988127i	$-0.549098\pi$
$317$	−1734.26	−0.307273	−0.153636	+	0.988127i	$0.549098\pi$
$318$	−2489.35	−0.438981
$319$	−2593.14	−0.455135
$320$	−6416.04	−1.12084
$321$	4512.04	0.784540
$322$	−1345.54	−0.232869
$323$	−581.066	−0.100097
$324$	492.543	0.0844552
$325$	0	0
$326$	−2939.67	−0.499428
$327$	−2395.68	−0.405142
$328$	8040.74	1.35358
$329$	−1321.83	−0.221505
$330$	1363.78	0.227496
$331$	6728.44	1.11731	0.558653	−	0.829401i	$-0.311318\pi$
$331$	6728.44	1.11731	0.558653	+	0.829401i	$0.311318\pi$
$332$	−1679.85	−0.277692
$333$	252.561	0.0415623
$334$	3318.62	0.543673
$335$	294.869	0.0480908
$336$	741.314	0.120363
$337$	2627.07	0.424645	0.212323	−	0.977200i	$-0.431897\pi$
$337$	2627.07	0.424645	0.212323	+	0.977200i	$0.431897\pi$
$338$	0	0
$339$	4232.88	0.678167
$340$	355.203	0.0566576
$341$	3777.51	0.599893
$342$	564.742	0.0892917
$343$	2271.40	0.357562
$344$	−4437.89	−0.695567
$345$	−7350.49	−1.14706
$346$	−303.181	−0.0471073
$347$	−8915.13	−1.37922	−0.689610	−	0.724181i	$-0.742218\pi$
$347$	−8915.13	−1.37922	−0.689610	+	0.724181i	$0.742218\pi$
$348$	−1248.49	−0.192317
$349$	−9262.42	−1.42065	−0.710323	−	0.703875i	$-0.751451\pi$
$349$	−9262.42	−1.42065	−0.710323	+	0.703875i	$0.751451\pi$
$350$	−33.6979	−0.00514636
$351$	0	0
$352$	−620.564	−0.0939665
$353$	−5776.58	−0.870982	−0.435491	−	0.900193i	$-0.643425\pi$
$353$	−5776.58	−0.870982	−0.435491	+	0.900193i	$0.643425\pi$
$354$	8379.49	1.25809
$355$	−5566.15	−0.832171
$356$	−1736.13	−0.258468
$357$	−352.007	−0.0521854
$358$	7172.56	1.05889
$359$	6646.88	0.977184	0.488592	−	0.872512i	$-0.337511\pi$
$359$	6646.88	0.977184	0.488592	+	0.872512i	$0.337511\pi$
$360$	−2538.91	−0.371701
$361$	−6312.45	−0.920316
$362$	3808.78	0.552998
$363$	509.006	0.0735974
$364$	0	0
$365$	307.305	0.0440688
$366$	−2556.88	−0.365165
$367$	12891.5	1.83361	0.916803	−	0.399340i	$-0.130761\pi$
$367$	12891.5	1.83361	0.916803	+	0.399340i	$0.130761\pi$
$368$	−8057.28	−1.14135
$369$	3112.01	0.439038
$370$	800.034	0.112410
$371$	767.344	0.107381
$372$	1818.72	0.253485
$373$	1126.32	0.156350	0.0781749	−	0.996940i	$-0.475091\pi$
$373$	1126.32	0.156350	0.0781749	+	0.996940i	$0.475091\pi$
$374$	−709.848	−0.0981427
$375$	5784.86	0.796611
$376$	−9438.39	−1.29454
$377$	0	0
$378$	1334.93	0.181644
$379$	−1885.79	−0.255585	−0.127792	−	0.991801i	$-0.540789\pi$
$379$	−1885.79	−0.255585	−0.127792	+	0.991801i	$0.540789\pi$
$380$	−334.105	−0.0451032
$381$	−9561.61	−1.28571
$382$	−10071.8	−1.34899
$383$	13490.6	1.79984	0.899918	−	0.436060i	$-0.143626\pi$
$383$	13490.6	1.79984	0.899918	+	0.436060i	$0.143626\pi$
$384$	4274.74	0.568085
$385$	−420.386	−0.0556489
$386$	6342.57	0.836343
$387$	−1717.60	−0.225608
$388$	128.059	0.0167557
$389$	−235.854	−0.0307410	−0.0153705	−	0.999882i	$-0.504893\pi$
$389$	−235.854	−0.0307410	−0.0153705	+	0.999882i	$0.504893\pi$
$390$	0	0
$391$	3825.94	0.494849
$392$	7973.08	1.02730
$393$	−8780.16	−1.12697
$394$	−8955.48	−1.14510
$395$	−8499.12	−1.08263
$396$	−128.849	−0.0163507
$397$	−12157.2	−1.53691	−0.768457	−	0.639902i	$-0.778975\pi$
$397$	−12157.2	−1.53691	−0.768457	+	0.639902i	$0.778975\pi$
$398$	−4246.98	−0.534879
$399$	331.099	0.0415431
$400$	−201.788	−0.0252235
$401$	−1875.31	−0.233538	−0.116769	−	0.993159i	$-0.537254\pi$
$401$	−1875.31	−0.233538	−0.116769	+	0.993159i	$0.537254\pi$
$402$	−283.713	−0.0351998
$403$	0	0
$404$	−1413.09	−0.174019
$405$	4440.98	0.544874
$406$	−2060.63	−0.251891
$407$	298.598	0.0363660
$408$	−2513.46	−0.304988
$409$	−6745.46	−0.815505	−0.407752	−	0.913093i	$-0.633687\pi$
$409$	−6745.46	−0.815505	−0.407752	+	0.913093i	$0.633687\pi$
$410$	9857.89	1.18743
$411$	7807.73	0.937048
$412$	−893.975	−0.106900
$413$	−2582.98	−0.307749
$414$	−3718.45	−0.441430
$415$	−15146.3	−1.79157
$416$	0	0
$417$	−1347.29	−0.158219
$418$	667.685	0.0781281
$419$	−8135.10	−0.948510	−0.474255	−	0.880387i	$-0.657283\pi$
$419$	−8135.10	−0.948510	−0.474255	+	0.880387i	$0.657283\pi$
$420$	−202.399	−0.0235144
$421$	5745.91	0.665175	0.332587	−	0.943072i	$-0.392078\pi$
$421$	5745.91	0.665175	0.332587	+	0.943072i	$0.392078\pi$
$422$	−2875.30	−0.331676
$423$	−3652.94	−0.419887
$424$	5479.13	0.627571
$425$	95.8174	0.0109361
$426$	5355.55	0.609102
$427$	788.162	0.0893251
$428$	−1350.37	−0.152506
$429$	0	0
$430$	−5440.82	−0.610185
$431$	13316.2	1.48822	0.744108	−	0.668060i	$-0.232875\pi$
$431$	13316.2	1.48822	0.744108	+	0.668060i	$0.232875\pi$
$432$	7993.78	0.890280
$433$	3194.42	0.354536	0.177268	−	0.984163i	$-0.443274\pi$
$433$	3194.42	0.354536	0.177268	+	0.984163i	$0.443274\pi$
$434$	3001.79	0.332006
$435$	−11257.0	−1.24076
$436$	716.982	0.0787550
$437$	−3598.69	−0.393933
$438$	−295.678	−0.0322559
$439$	3297.75	0.358526	0.179263	−	0.983801i	$-0.442629\pi$
$439$	3297.75	0.358526	0.179263	+	0.983801i	$0.442629\pi$
$440$	−3001.71	−0.325230
$441$	3085.82	0.333206
$442$	0	0
$443$	1280.16	0.137296	0.0686481	−	0.997641i	$-0.478131\pi$
$443$	1280.16	0.137296	0.0686481	+	0.997641i	$0.478131\pi$
$444$	143.763	0.0153665
$445$	−15653.7	−1.66754
$446$	−9780.97	−1.03844
$447$	2120.53	0.224379
$448$	−1902.92	−0.200680
$449$	−11560.3	−1.21506	−0.607531	−	0.794296i	$-0.707840\pi$
$449$	−11560.3	−1.21506	−0.607531	+	0.794296i	$0.707840\pi$
$450$	−93.1256	−0.00975552
$451$	3679.28	0.384147
$452$	−1266.82	−0.131828
$453$	2276.50	0.236114
$454$	8059.83	0.833187
$455$	0	0
$456$	2364.17	0.242791
$457$	4490.67	0.459660	0.229830	−	0.973231i	$-0.426183\pi$
$457$	4490.67	0.459660	0.229830	+	0.973231i	$0.426183\pi$
$458$	−750.342	−0.0765528
$459$	−3795.78	−0.385996
$460$	2199.86	0.222976
$461$	−16130.9	−1.62969	−0.814847	−	0.579676i	$-0.803179\pi$
$461$	−16130.9	−1.62969	−0.814847	+	0.579676i	$0.803179\pi$
$462$	404.480	0.0407319
$463$	2838.88	0.284955	0.142477	−	0.989798i	$-0.454493\pi$
$463$	2838.88	0.284955	0.142477	+	0.989798i	$0.454493\pi$
$464$	−12339.4	−1.23457
$465$	16398.4	1.63539
$466$	−5583.45	−0.555040
$467$	6321.60	0.626400	0.313200	−	0.949687i	$-0.398599\pi$
$467$	6321.60	0.626400	0.313200	+	0.949687i	$0.398599\pi$
$468$	0	0
$469$	87.4547	0.00861041
$470$	−11571.4	−1.13564
$471$	−5711.04	−0.558707
$472$	−18443.5	−1.79858
$473$	−2030.69	−0.197402
$474$	8177.55	0.792421
$475$	−90.1262	−0.00870584
$476$	105.349	0.0101442
$477$	2120.59	0.203554
$478$	−11350.6	−1.08612
$479$	17498.9	1.66919	0.834596	−	0.550862i	$-0.185701\pi$
$479$	17498.9	1.66919	0.834596	+	0.550862i	$0.185701\pi$
$480$	−2693.90	−0.256165
$481$	0	0
$482$	2906.14	0.274629
$483$	−2180.07	−0.205376
$484$	−152.336	−0.0143065
$485$	1154.64	0.108102
$486$	6432.84	0.600410
$487$	15551.0	1.44699	0.723495	−	0.690330i	$-0.242535\pi$
$487$	15551.0	1.44699	0.723495	+	0.690330i	$0.242535\pi$
$488$	5627.78	0.522044
$489$	−4762.92	−0.440464
$490$	9774.94	0.901197
$491$	5414.52	0.497666	0.248833	−	0.968546i	$-0.419953\pi$
$491$	5414.52	0.497666	0.248833	+	0.968546i	$0.419953\pi$
$492$	1771.43	0.162321
$493$	5859.26	0.535269
$494$	0	0
$495$	−1161.76	−0.105489
$496$	17975.2	1.62724
$497$	−1650.85	−0.148996
$498$	14573.2	1.31133
$499$	−11547.9	−1.03598	−0.517990	−	0.855387i	$-0.673320\pi$
$499$	−11547.9	−1.03598	−0.517990	+	0.855387i	$0.673320\pi$
$500$	−1731.30	−0.154852
$501$	5376.89	0.479485
$502$	−8798.75	−0.782285
$503$	−132.562	−0.0117508	−0.00587541	−	0.999983i	$-0.501870\pi$
$503$	−132.562	−0.0117508	−0.00587541	+	0.999983i	$0.501870\pi$
$504$	−753.011	−0.0665512
$505$	−12741.0	−1.12271
$506$	−4396.27	−0.386241
$507$	0	0
$508$	2861.61	0.249928
$509$	14127.6	1.23025	0.615123	−	0.788431i	$-0.289107\pi$
$509$	14127.6	1.23025	0.615123	+	0.788431i	$0.289107\pi$
$510$	−3081.49	−0.267550
$511$	91.1431	0.00789028
$512$	−13019.4	−1.12379
$513$	3570.33	0.307278
$514$	13646.0	1.17101
$515$	−8060.46	−0.689683
$516$	−977.696	−0.0834122
$517$	−4318.82	−0.367391
$518$	237.281	0.0201265
$519$	−491.221	−0.0415457
$520$	0	0
$521$	17312.1	1.45577	0.727884	−	0.685701i	$-0.240504\pi$
$521$	17312.1	1.45577	0.727884	+	0.685701i	$0.240504\pi$
$522$	−5694.66	−0.477487
$523$	−16404.1	−1.37151	−0.685757	−	0.727830i	$-0.740529\pi$
$523$	−16404.1	−1.37151	−0.685757	+	0.727830i	$0.740529\pi$
$524$	2627.73	0.219071
$525$	−54.5980	−0.00453877
$526$	−1658.81	−0.137505
$527$	−8535.36	−0.705515
$528$	2422.09	0.199636
$529$	11528.0	0.947481
$530$	6717.37	0.550536
$531$	−7138.19	−0.583373
$532$	−99.0916	−0.00807550
$533$	0	0
$534$	15061.4	1.22055
$535$	−12175.5	−0.983911
$536$	624.460	0.0503219
$537$	11621.1	0.933870
$538$	−3857.10	−0.309092
$539$	3648.32	0.291548
$540$	−2182.52	−0.173928
$541$	12414.2	0.986558	0.493279	−	0.869871i	$-0.335798\pi$
$541$	12414.2	0.986558	0.493279	+	0.869871i	$0.335798\pi$
$542$	16614.7	1.31672
$543$	6171.07	0.487709
$544$	1402.18	0.110511
$545$	6464.61	0.508098
$546$	0	0
$547$	19490.3	1.52348	0.761740	−	0.647883i	$-0.224345\pi$
$547$	19490.3	1.52348	0.761740	+	0.647883i	$0.224345\pi$
$548$	−2336.70	−0.182152
$549$	2178.12	0.169326
$550$	−110.101	−0.00853585
$551$	−5511.24	−0.426110
$552$	−15566.5	−1.20028
$553$	−2520.74	−0.193838
$554$	3406.40	0.261235
$555$	1296.23	0.0991387
$556$	403.219	0.0307559
$557$	−13841.0	−1.05290	−0.526449	−	0.850207i	$-0.676477\pi$
$557$	−13841.0	−1.05290	−0.526449	+	0.850207i	$0.676477\pi$
$558$	8295.58	0.629354
$559$	0	0
$560$	−2000.39	−0.150950
$561$	−1150.11	−0.0865556
$562$	−14134.0	−1.06086
$563$	6392.68	0.478542	0.239271	−	0.970953i	$-0.423092\pi$
$563$	6392.68	0.478542	0.239271	+	0.970953i	$0.423092\pi$
$564$	−2079.34	−0.155241
$565$	−11422.2	−0.850505
$566$	8000.83	0.594170
$567$	1317.14	0.0975569
$568$	−11787.7	−0.870778
$569$	−24231.8	−1.78532	−0.892661	−	0.450728i	$-0.851164\pi$
$569$	−24231.8	−1.78532	−0.892661	+	0.450728i	$0.851164\pi$
$570$	2898.46	0.212988
$571$	17935.1	1.31447	0.657235	−	0.753686i	$-0.271726\pi$
$571$	17935.1	1.31447	0.657235	+	0.753686i	$0.271726\pi$
$572$	0	0
$573$	−16318.5	−1.18973
$574$	2923.73	0.212603
$575$	593.422	0.0430389
$576$	−5258.81	−0.380412
$577$	13344.1	0.962774	0.481387	−	0.876508i	$-0.340133\pi$
$577$	13344.1	0.962774	0.481387	+	0.876508i	$0.340133\pi$
$578$	−11151.9	−0.802526
$579$	10276.4	0.737601
$580$	3368.99	0.241189
$581$	−4492.20	−0.320771
$582$	−1110.95	−0.0791243
$583$	2507.14	0.178105
$584$	650.797	0.0461133
$585$	0	0
$586$	−20481.5	−1.44383
$587$	10795.6	0.759086	0.379543	−	0.925174i	$-0.376081\pi$
$587$	10795.6	0.759086	0.379543	+	0.925174i	$0.376081\pi$
$588$	1756.52	0.123193
$589$	8028.39	0.561637
$590$	−22611.6	−1.57780
$591$	−14509.8	−1.00991
$592$	1420.87	0.0986444
$593$	15483.7	1.07224	0.536122	−	0.844140i	$-0.319889\pi$
$593$	15483.7	1.07224	0.536122	+	0.844140i	$0.319889\pi$
$594$	4361.62	0.301278
$595$	949.871	0.0654469
$596$	−634.634	−0.0436168
$597$	−6881.05	−0.471729
$598$	0	0
$599$	11396.8	0.777395	0.388697	−	0.921366i	$-0.372925\pi$
$599$	11396.8	0.777395	0.388697	+	0.921366i	$0.372925\pi$
$600$	−389.850	−0.0265260
$601$	20399.2	1.38453	0.692263	−	0.721645i	$-0.256614\pi$
$601$	20399.2	1.38453	0.692263	+	0.721645i	$0.256614\pi$
$602$	−1613.68	−0.109251
$603$	241.685	0.0163220
$604$	−681.314	−0.0458978
$605$	−1373.52	−0.0923003
$606$	12258.9	0.821758
$607$	20209.8	1.35138	0.675692	−	0.737184i	$-0.263845\pi$
$607$	20209.8	1.35138	0.675692	+	0.737184i	$0.263845\pi$
$608$	−1318.90	−0.0879741
$609$	−3338.68	−0.222151
$610$	6899.61	0.457963
$611$	0	0
$612$	291.137	0.0192296
$613$	3861.58	0.254434	0.127217	−	0.991875i	$-0.459396\pi$
$613$	3861.58	0.254434	0.127217	+	0.991875i	$0.459396\pi$
$614$	13721.6	0.901890
$615$	15972.0	1.04724
$616$	−890.273	−0.0582307
$617$	27771.0	1.81203	0.906013	−	0.423250i	$-0.139111\pi$
$617$	27771.0	1.81203	0.906013	+	0.423250i	$0.139111\pi$
$618$	7755.49	0.504809
$619$	2995.88	0.194531	0.0972653	−	0.995258i	$-0.468990\pi$
$619$	2995.88	0.194531	0.0972653	+	0.995258i	$0.468990\pi$
$620$	−4907.72	−0.317901
$621$	−23508.3	−1.51909
$622$	−17303.3	−1.11544
$623$	−4642.70	−0.298564
$624$	0	0
$625$	−16092.0	−1.02989
$626$	25418.3	1.62288
$627$	1081.80	0.0689040
$628$	1709.21	0.108606
$629$	−674.690	−0.0427689
$630$	−923.187	−0.0583820
$631$	−4620.28	−0.291490	−0.145745	−	0.989322i	$-0.546558\pi$
$631$	−4620.28	−0.291490	−0.145745	+	0.989322i	$0.546558\pi$
$632$	−17999.0	−1.13285
$633$	−4658.62	−0.292517
$634$	−4502.73	−0.282060
$635$	25801.5	1.61244
$636$	1207.09	0.0752581
$637$	0	0
$638$	−6732.70	−0.417790
$639$	−4562.21	−0.282439
$640$	−11535.2	−0.712449
$641$	22027.6	1.35731	0.678656	−	0.734457i	$-0.262563\pi$
$641$	22027.6	1.35731	0.678656	+	0.734457i	$0.262563\pi$
$642$	11714.8	0.720167
$643$	5260.09	0.322609	0.161304	−	0.986905i	$-0.448430\pi$
$643$	5260.09	0.322609	0.161304	+	0.986905i	$0.448430\pi$
$644$	652.453	0.0399227
$645$	−8815.33	−0.538145
$646$	−1508.65	−0.0918840
$647$	13931.0	0.846499	0.423250	−	0.906013i	$-0.360889\pi$
$647$	13931.0	0.846499	0.423250	+	0.906013i	$0.360889\pi$
$648$	9404.89	0.570153
$649$	−8439.37	−0.510438
$650$	0	0
$651$	4863.56	0.292808
$652$	1425.45	0.0856211
$653$	−2488.07	−0.149105	−0.0745525	−	0.997217i	$-0.523753\pi$
$653$	−2488.07	−0.149105	−0.0745525	+	0.997217i	$0.523753\pi$
$654$	−6220.02	−0.371899
$655$	23692.8	1.41336
$656$	17507.8	1.04202
$657$	251.878	0.0149569
$658$	−3431.94	−0.203330
$659$	−2626.69	−0.155268	−0.0776338	−	0.996982i	$-0.524737\pi$
$659$	−2626.69	−0.155268	−0.0776338	+	0.996982i	$0.524737\pi$
$660$	−661.297	−0.0390015
$661$	26813.8	1.57781	0.788907	−	0.614512i	$-0.210647\pi$
$661$	26813.8	1.57781	0.788907	+	0.614512i	$0.210647\pi$
$662$	17469.4	1.02563
$663$	0	0
$664$	−32076.0	−1.87468
$665$	−893.452	−0.0521002
$666$	655.736	0.0381520
$667$	36287.9	2.10656
$668$	−1609.20	−0.0932064
$669$	−15847.3	−0.915834
$670$	765.583	0.0441449
$671$	2575.16	0.148156
$672$	−798.980	−0.0458651
$673$	1211.46	0.0693886	0.0346943	−	0.999398i	$-0.488954\pi$
$673$	1211.46	0.0693886	0.0346943	+	0.999398i	$0.488954\pi$
$674$	6820.78	0.389802
$675$	−588.745	−0.0335715
$676$	0	0
$677$	7986.00	0.453363	0.226682	−	0.973969i	$-0.427212\pi$
$677$	7986.00	0.453363	0.226682	+	0.973969i	$0.427212\pi$
$678$	10990.0	0.622522
$679$	342.451	0.0193550
$680$	6782.44	0.382492
$681$	13058.7	0.734818
$682$	9807.72	0.550670
$683$	423.898	0.0237482	0.0118741	−	0.999930i	$-0.496220\pi$
$683$	423.898	0.0237482	0.0118741	+	0.999930i	$0.496220\pi$
$684$	−273.844	−0.0153080
$685$	−21068.7	−1.17517
$686$	5897.34	0.328224
$687$	−1215.72	−0.0675147
$688$	−9662.98	−0.535462
$689$	0	0
$690$	−19084.4	−1.05295
$691$	−1096.57	−0.0603696	−0.0301848	−	0.999544i	$-0.509610\pi$
$691$	−1096.57	−0.0603696	−0.0301848	+	0.999544i	$0.509610\pi$
$692$	147.013	0.00807600
$693$	−344.563	−0.0188872
$694$	−23146.8	−1.26605
$695$	3635.60	0.198426
$696$	−23839.5	−1.29832
$697$	−8313.42	−0.451784
$698$	−24048.5	−1.30408
$699$	−9046.42	−0.489510
$700$	16.3401	0.000882284 0
$701$	−35315.3	−1.90277	−0.951384	−	0.308006i	$-0.900338\pi$
$701$	−35315.3	−1.90277	−0.951384	+	0.308006i	$0.900338\pi$
$702$	0	0
$703$	634.616	0.0340469
$704$	−6217.40	−0.332851
$705$	−18748.2	−1.00156
$706$	−14998.0	−0.799516
$707$	−3778.83	−0.201015
$708$	−4063.22	−0.215685
$709$	1647.13	0.0872486	0.0436243	−	0.999048i	$-0.486110\pi$
$709$	1647.13	0.0872486	0.0436243	+	0.999048i	$0.486110\pi$
$710$	−14451.7	−0.763889
$711$	−6966.17	−0.367443
$712$	−33150.6	−1.74490
$713$	−52861.7	−2.77656
$714$	−913.933	−0.0479035
$715$	0	0
$716$	−3477.98	−0.181534
$717$	−18390.4	−0.957885
$718$	17257.6	0.897004
$719$	2098.87	0.108866	0.0544330	−	0.998517i	$-0.482665\pi$
$719$	2098.87	0.108866	0.0544330	+	0.998517i	$0.482665\pi$
$720$	−5528.18	−0.286143
$721$	−2390.64	−0.123484
$722$	−16389.3	−0.844802
$723$	4708.59	0.242205
$724$	−1846.88	−0.0948050
$725$	908.800	0.0465545
$726$	1321.56	0.0675586
$727$	6870.65	0.350506	0.175253	−	0.984523i	$-0.443926\pi$
$727$	6870.65	0.350506	0.175253	+	0.984523i	$0.443926\pi$
$728$	0	0
$729$	20985.7	1.06619
$730$	797.872	0.0404528
$731$	4588.39	0.232158
$732$	1239.84	0.0626034
$733$	11252.4	0.567009	0.283505	−	0.958971i	$-0.408503\pi$
$733$	11252.4	0.567009	0.283505	+	0.958971i	$0.408503\pi$
$734$	33471.0	1.68315
$735$	15837.6	0.794799
$736$	8684.05	0.434916
$737$	285.740	0.0142814
$738$	8079.87	0.403014
$739$	−10823.9	−0.538788	−0.269394	−	0.963030i	$-0.586823\pi$
$739$	−10823.9	−0.538788	−0.269394	+	0.963030i	$0.586823\pi$
$740$	−387.938	−0.0192714
$741$	0	0
$742$	1992.29	0.0985706
$743$	−7754.93	−0.382908	−0.191454	−	0.981502i	$-0.561320\pi$
$743$	−7754.93	−0.382908	−0.191454	+	0.981502i	$0.561320\pi$
$744$	34727.7	1.71126
$745$	−5722.13	−0.281399
$746$	2924.31	0.143521
$747$	−12414.4	−0.608058
$748$	344.206	0.0168254
$749$	−3611.11	−0.176164
$750$	15019.5	0.731247
$751$	−18101.8	−0.879554	−0.439777	−	0.898107i	$-0.644943\pi$
$751$	−18101.8	−0.879554	−0.439777	+	0.898107i	$0.644943\pi$
$752$	−20551.0	−0.996565
$753$	−14255.9	−0.689926
$754$	0	0
$755$	−6143.02	−0.296116
$756$	−647.311	−0.0311408
$757$	20134.9	0.966731	0.483366	−	0.875419i	$-0.339414\pi$
$757$	20134.9	0.966731	0.483366	+	0.875419i	$0.339414\pi$
$758$	−4896.18	−0.234614
$759$	−7122.92	−0.340640
$760$	−6379.59	−0.304490
$761$	10431.9	0.496919	0.248459	−	0.968642i	$-0.420076\pi$
$761$	10431.9	0.496919	0.248459	+	0.968642i	$0.420076\pi$
$762$	−24825.3	−1.18022
$763$	1917.33	0.0909724
$764$	4883.80	0.231269
$765$	2625.01	0.124062
$766$	35026.3	1.65216
$767$	0	0
$768$	−7922.73	−0.372248
$769$	−12971.9	−0.608296	−0.304148	−	0.952625i	$-0.598372\pi$
$769$	−12971.9	−0.608296	−0.304148	+	0.952625i	$0.598372\pi$
$770$	−1091.47	−0.0510828
$771$	22109.6	1.03276
$772$	−3075.52	−0.143381
$773$	14706.3	0.684282	0.342141	−	0.939649i	$-0.388848\pi$
$773$	14706.3	0.684282	0.342141	+	0.939649i	$0.388848\pi$
$774$	−4459.49	−0.207097
$775$	−1323.88	−0.0613613
$776$	2445.23	0.113117
$777$	384.447	0.0177503
$778$	−612.359	−0.0282187
$779$	7819.63	0.359650
$780$	0	0
$781$	−5393.83	−0.247127
$782$	9933.47	0.454246
$783$	−36001.9	−1.64317
$784$	17360.4	0.790836
$785$	15410.9	0.700688
$786$	−22796.4	−1.03450
$787$	15127.4	0.685178	0.342589	−	0.939485i	$-0.388696\pi$
$787$	15127.4	0.685178	0.342589	+	0.939485i	$0.388696\pi$
$788$	4342.52	0.196315
$789$	−2687.64	−0.121271
$790$	−22066.7	−0.993794
$791$	−3387.69	−0.152279
$792$	−2460.31	−0.110383
$793$	0	0
$794$	−31564.4	−1.41081
$795$	10883.6	0.485538
$796$	2059.37	0.0916988
$797$	12787.0	0.568303	0.284152	−	0.958779i	$-0.408288\pi$
$797$	12787.0	0.568303	0.284152	+	0.958779i	$0.408288\pi$
$798$	859.648	0.0381344
$799$	9758.46	0.432077
$800$	217.485	0.00961157
$801$	−12830.3	−0.565963
$802$	−4868.97	−0.214376
$803$	297.791	0.0130870
$804$	137.573	0.00603459
$805$	5882.79	0.257567
$806$	0	0
$807$	−6249.36	−0.272599
$808$	−26982.3	−1.17479
$809$	−32145.2	−1.39699	−0.698495	−	0.715615i	$-0.746147\pi$
$809$	−32145.2	−1.39699	−0.698495	+	0.715615i	$0.746147\pi$
$810$	11530.3	0.500166
$811$	−6262.27	−0.271144	−0.135572	−	0.990767i	$-0.543287\pi$
$811$	−6262.27	−0.271144	−0.135572	+	0.990767i	$0.543287\pi$
$812$	999.204	0.0431837
$813$	26919.5	1.16127
$814$	775.266	0.0333821
$815$	12852.5	0.552396
$816$	−5472.77	−0.234786
$817$	−4315.85	−0.184814
$818$	−17513.6	−0.748591
$819$	0	0
$820$	−4780.10	−0.203571
$821$	30294.3	1.28779	0.643896	−	0.765113i	$-0.277317\pi$
$821$	30294.3	1.28779	0.643896	+	0.765113i	$0.277317\pi$
$822$	20271.6	0.860162
$823$	−1706.90	−0.0722951	−0.0361476	−	0.999346i	$-0.511509\pi$
$823$	−1706.90	−0.0722951	−0.0361476	+	0.999346i	$0.511509\pi$
$824$	−17070.1	−0.721679
$825$	−178.388	−0.00752807
$826$	−6706.33	−0.282498
$827$	−15062.0	−0.633322	−0.316661	−	0.948539i	$-0.602562\pi$
$827$	−15062.0	−0.633322	−0.316661	+	0.948539i	$0.602562\pi$
$828$	1803.08	0.0756781
$829$	−20868.7	−0.874305	−0.437153	−	0.899387i	$-0.644013\pi$
$829$	−20868.7	−0.874305	−0.437153	+	0.899387i	$0.644013\pi$
$830$	−39325.0	−1.64457
$831$	5519.12	0.230392
$832$	0	0
$833$	−8243.46	−0.342880
$834$	−3498.04	−0.145237
$835$	−14509.2	−0.601333
$836$	−323.761	−0.0133942
$837$	52445.0	2.16579
$838$	−21121.6	−0.870683
$839$	−12865.3	−0.529393	−0.264697	−	0.964332i	$-0.585272\pi$
$839$	−12865.3	−0.529393	−0.264697	+	0.964332i	$0.585272\pi$
$840$	−3864.72	−0.158745
$841$	31184.4	1.27862
$842$	14918.4	0.610596
$843$	−22900.1	−0.935614
$844$	1394.24	0.0568621
$845$	0	0
$846$	−9484.32	−0.385434
$847$	−407.371	−0.0165259
$848$	11930.2	0.483117
$849$	12963.1	0.524020
$850$	248.775	0.0100387
$851$	−4178.53	−0.168317
$852$	−2596.91	−0.104423
$853$	2524.90	0.101349	0.0506747	−	0.998715i	$-0.483863\pi$
$853$	2524.90	0.101349	0.0506747	+	0.998715i	$0.483863\pi$
$854$	2046.34	0.0819958
$855$	−2469.10	−0.0987618
$856$	−25784.7	−1.02956
$857$	−3223.37	−0.128481	−0.0642405	−	0.997934i	$-0.520462\pi$
$857$	−3223.37	−0.128481	−0.0642405	+	0.997934i	$0.520462\pi$
$858$	0	0
$859$	−26676.6	−1.05960	−0.529799	−	0.848123i	$-0.677733\pi$
$859$	−26676.6	−1.05960	−0.529799	+	0.848123i	$0.677733\pi$
$860$	2638.26	0.104609
$861$	4737.09	0.187503
$862$	34573.6	1.36610
$863$	25734.3	1.01507	0.507535	−	0.861631i	$-0.330557\pi$
$863$	25734.3	1.01507	0.507535	+	0.861631i	$0.330557\pi$
$864$	−8615.61	−0.339247
$865$	1325.53	0.0521034
$866$	8293.83	0.325446
$867$	−18068.6	−0.707776
$868$	−1455.57	−0.0569185
$869$	−8235.99	−0.321504
$870$	−29227.0	−1.13895
$871$	0	0
$872$	13690.4	0.531671
$873$	946.379	0.0366897
$874$	−9343.46	−0.361610
$875$	−4629.78	−0.178874
$876$	143.375	0.00552989
$877$	31883.5	1.22763	0.613813	−	0.789451i	$-0.289635\pi$
$877$	31883.5	1.22763	0.613813	+	0.789451i	$0.289635\pi$
$878$	8562.12	0.329109
$879$	−33184.6	−1.27336
$880$	−6535.88	−0.250369
$881$	7420.77	0.283782	0.141891	−	0.989882i	$-0.454682\pi$
$881$	7420.77	0.283782	0.141891	+	0.989882i	$0.454682\pi$
$882$	8011.88	0.305866
$883$	38153.5	1.45410	0.727048	−	0.686586i	$-0.240892\pi$
$883$	38153.5	1.45410	0.727048	+	0.686586i	$0.240892\pi$
$884$	0	0
$885$	−36635.8	−1.39152
$886$	3323.74	0.126031
$887$	−37254.9	−1.41026	−0.705128	−	0.709081i	$-0.749110\pi$
$887$	−37254.9	−1.41026	−0.705128	+	0.709081i	$0.749110\pi$
$888$	2745.10	0.103738
$889$	7652.42	0.288699
$890$	−40642.4	−1.53072
$891$	4303.49	0.161810
$892$	4742.80	0.178028
$893$	−9178.85	−0.343962
$894$	5505.63	0.205969
$895$	−31359.0	−1.17119
$896$	−3421.19	−0.127560
$897$	0	0
$898$	−30014.5	−1.11536
$899$	−80955.4	−3.00335
$900$	45.1567	0.00167247
$901$	−5664.94	−0.209463
$902$	9552.69	0.352627
$903$	−2614.52	−0.0963520
$904$	−24189.4	−0.889963
$905$	−16652.3	−0.611647
$906$	5910.60	0.216740
$907$	−12247.3	−0.448363	−0.224181	−	0.974547i	$-0.571971\pi$
$907$	−12247.3	−0.448363	−0.224181	+	0.974547i	$0.571971\pi$
$908$	−3908.22	−0.142840
$909$	−10443.0	−0.381047
$910$	0	0
$911$	22969.8	0.835373	0.417686	−	0.908591i	$-0.362841\pi$
$911$	22969.8	0.835373	0.417686	+	0.908591i	$0.362841\pi$
$912$	5147.71	0.186905
$913$	−14677.3	−0.532036
$914$	11659.3	0.421944
$915$	11178.9	0.403894
$916$	363.842	0.0131241
$917$	7027.00	0.253055
$918$	−9855.18	−0.354324
$919$	−27919.7	−1.00216	−0.501080	−	0.865401i	$-0.667064\pi$
$919$	−27919.7	−1.00216	−0.501080	+	0.865401i	$0.667064\pi$
$920$	42005.4	1.50530
$921$	22232.1	0.795410
$922$	−41881.3	−1.49597
$923$	0	0
$924$	−196.133	−0.00698301
$925$	−104.648	−0.00371978
$926$	7370.72	0.261573
$927$	−6606.64	−0.234078
$928$	13299.3	0.470441
$929$	−2424.14	−0.0856120	−0.0428060	−	0.999083i	$-0.513630\pi$
$929$	−2424.14	−0.0856120	−0.0428060	+	0.999083i	$0.513630\pi$
$930$	42575.9	1.50120
$931$	7753.83	0.272955
$932$	2707.42	0.0951551
$933$	−28035.2	−0.983743
$934$	16413.1	0.575002
$935$	3103.51	0.108551
$936$	0	0
$937$	−17186.0	−0.599192	−0.299596	−	0.954066i	$-0.596852\pi$
$937$	−17186.0	−0.599192	−0.299596	+	0.954066i	$0.596852\pi$
$938$	227.063	0.00790391
$939$	41183.3	1.43127
$940$	5610.98	0.194692
$941$	−29765.0	−1.03115	−0.515575	−	0.856845i	$-0.672422\pi$
$941$	−29765.0	−1.03115	−0.515575	+	0.856845i	$0.672422\pi$
$942$	−14827.9	−0.512864
$943$	−51487.1	−1.77800
$944$	−40158.5	−1.38458
$945$	−5836.43	−0.200909
$946$	−5272.38	−0.181205
$947$	20203.3	0.693263	0.346632	−	0.938001i	$-0.387325\pi$
$947$	20203.3	0.693263	0.346632	+	0.938001i	$0.387325\pi$
$948$	−3965.30	−0.135851
$949$	0	0
$950$	−233.999	−0.00799151
$951$	−7295.42	−0.248759
$952$	2011.59	0.0684833
$953$	32928.0	1.11925	0.559623	−	0.828747i	$-0.310946\pi$
$953$	32928.0	1.11925	0.559623	+	0.828747i	$0.310946\pi$
$954$	5505.79	0.186852
$955$	44034.5	1.49207
$956$	5503.91	0.186202
$957$	−10908.5	−0.368464
$958$	45433.1	1.53223
$959$	−6248.73	−0.210409
$960$	−26990.1	−0.907397
$961$	88139.2	2.95858
$962$	0	0
$963$	−9979.45	−0.333939
$964$	−1409.19	−0.0470820
$965$	−27730.2	−0.925043
$966$	−5660.22	−0.188524
$967$	12157.2	0.404289	0.202145	−	0.979356i	$-0.435209\pi$
$967$	12157.2	0.404289	0.202145	+	0.979356i	$0.435209\pi$
$968$	−2908.78	−0.0965824
$969$	−2444.35	−0.0810358
$970$	2997.84	0.0992317
$971$	−41378.5	−1.36756	−0.683779	−	0.729690i	$-0.739665\pi$
$971$	−41378.5	−1.36756	−0.683779	+	0.729690i	$0.739665\pi$
$972$	−3119.29	−0.102933
$973$	1078.28	0.0355271
$974$	40375.9	1.32826
$975$	0	0
$976$	12253.8	0.401880
$977$	−42191.3	−1.38160	−0.690798	−	0.723048i	$-0.742741\pi$
$977$	−42191.3	−1.38160	−0.690798	+	0.723048i	$0.742741\pi$
$978$	−12366.2	−0.404323
$979$	−15169.0	−0.495204
$980$	−4739.88	−0.154500
$981$	5298.62	0.172448
$982$	14058.0	0.456831
$983$	23017.8	0.746849	0.373425	−	0.927661i	$-0.378183\pi$
$983$	23017.8	0.746849	0.373425	+	0.927661i	$0.378183\pi$
$984$	33824.6	1.09582
$985$	39154.0	1.26655
$986$	15212.7	0.491349
$987$	−5560.50	−0.179324
$988$	0	0
$989$	28417.1	0.913660
$990$	−3016.32	−0.0968333
$991$	−28320.0	−0.907784	−0.453892	−	0.891057i	$-0.649965\pi$
$991$	−28320.0	−0.907784	−0.453892	+	0.891057i	$0.649965\pi$
$992$	−19373.4	−0.620068
$993$	28304.2	0.904540
$994$	−4286.19	−0.136770
$995$	18568.1	0.591607
$996$	−7066.56	−0.224812
$997$	25122.9	0.798045	0.399023	−	0.916941i	$-0.369349\pi$
$997$	25122.9	0.798045	0.399023	+	0.916941i	$0.369349\pi$
$998$	−29982.3	−0.950976
$999$	4145.59	0.131292

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.e.1.9		11
13.12	even	2		143.4.a.d.1.3	✓	11
39.38	odd	2		1287.4.a.m.1.9		11
52.51	odd	2		2288.4.a.u.1.4		11
143.142	odd	2		1573.4.a.f.1.9		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.d.1.3	✓	11	13.12	even	2
1287.4.a.m.1.9		11	39.38	odd	2
1573.4.a.f.1.9		11	143.142	odd	2
1859.4.a.e.1.9		11	1.1	even	1	trivial
2288.4.a.u.1.4		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)

\(f(q)\)	\(=\)	\(q+2.59635 q^{2} +4.20666 q^{3} -1.25897 q^{4} -11.3514 q^{5} +10.9220 q^{6} -3.36670 q^{7} -24.0395 q^{8} -9.30403 q^{9} +O(q^{10})\)	\(q+2.59635 q^{2} +4.20666 q^{3} -1.25897 q^{4} -11.3514 q^{5} +10.9220 q^{6} -3.36670 q^{7} -24.0395 q^{8} -9.30403 q^{9} -29.4723 q^{10} -11.0000 q^{11} -5.29607 q^{12} -8.74113 q^{14} -47.7516 q^{15} -52.3432 q^{16} +24.8548 q^{17} -24.1565 q^{18} -23.3785 q^{19} +14.2911 q^{20} -14.1626 q^{21} -28.5598 q^{22} +153.932 q^{23} -101.126 q^{24} +3.85509 q^{25} -152.719 q^{27} +4.23858 q^{28} +235.740 q^{29} -123.980 q^{30} -343.410 q^{31} +56.4149 q^{32} -46.2732 q^{33} +64.5316 q^{34} +38.2169 q^{35} +11.7135 q^{36} -27.1453 q^{37} -60.6987 q^{38} +272.883 q^{40} -334.480 q^{41} -36.7709 q^{42} +184.608 q^{43} +13.8487 q^{44} +105.614 q^{45} +399.661 q^{46} +392.620 q^{47} -220.190 q^{48} -331.665 q^{49} +10.0092 q^{50} +104.555 q^{51} -227.922 q^{53} -396.511 q^{54} +124.866 q^{55} +80.9339 q^{56} -98.3452 q^{57} +612.063 q^{58} +767.215 q^{59} +60.1180 q^{60} -234.105 q^{61} -891.611 q^{62} +31.3239 q^{63} +565.219 q^{64} -120.141 q^{66} -25.9764 q^{67} -31.2915 q^{68} +647.538 q^{69} +99.2244 q^{70} +490.348 q^{71} +223.664 q^{72} -27.0719 q^{73} -70.4787 q^{74} +16.2171 q^{75} +29.4328 q^{76} +37.0337 q^{77} +748.726 q^{79} +594.171 q^{80} -391.226 q^{81} -868.427 q^{82} +1334.30 q^{83} +17.8303 q^{84} -282.137 q^{85} +479.307 q^{86} +991.678 q^{87} +264.435 q^{88} +1379.00 q^{89} +274.211 q^{90} -193.796 q^{92} -1444.61 q^{93} +1019.38 q^{94} +265.379 q^{95} +237.318 q^{96} -101.717 q^{97} -861.119 q^{98} +102.344 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

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