LMFDB - Embedded newform 1859.4.a.g.1.17

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:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 93 x^{15} - 7 x^{14} + 3449 x^{13} + 406 x^{12} - 65242 x^{11} - 7942 x^{10} + 669163 x^{9} + \cdots - 2210688 $ x^17 - 93x^15 - 7x^14 + 3449x^13 + 406x^12 - 65242x^11 - 7942x^10 + 669163x^9 + 59532x^8 - 3663297x^7 - 79027x^6 + 9967603x^5 - 984554x^4 - 12177120x^3 + 3207432x^2 + 5215872*x - 2210688
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$-5.11519$ 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)

$f(q)$	$=$	$q+5.11519 q^{2} -3.58195 q^{3} +18.1651 q^{4} -2.16776 q^{5} -18.3223 q^{6} +20.9807 q^{7} +51.9966 q^{8} -14.1696 q^{9} +O(q^{10})$	\(q+5.11519 q^{2} -3.58195 q^{3} +18.1651 q^{4} -2.16776 q^{5} -18.3223 q^{6} +20.9807 q^{7} +51.9966 q^{8} -14.1696 q^{9} -11.0885 q^{10} +11.0000 q^{11} -65.0666 q^{12} +107.320 q^{14} +7.76481 q^{15} +120.651 q^{16} -100.760 q^{17} -72.4803 q^{18} -163.980 q^{19} -39.3777 q^{20} -75.1519 q^{21} +56.2671 q^{22} -47.5254 q^{23} -186.249 q^{24} -120.301 q^{25} +147.468 q^{27} +381.118 q^{28} -245.239 q^{29} +39.7185 q^{30} -29.8659 q^{31} +201.181 q^{32} -39.4015 q^{33} -515.408 q^{34} -45.4812 q^{35} -257.393 q^{36} +195.724 q^{37} -838.789 q^{38} -112.716 q^{40} +197.154 q^{41} -384.416 q^{42} -9.07360 q^{43} +199.817 q^{44} +30.7164 q^{45} -243.101 q^{46} +449.261 q^{47} -432.167 q^{48} +97.1910 q^{49} -615.361 q^{50} +360.918 q^{51} -296.513 q^{53} +754.324 q^{54} -23.8454 q^{55} +1090.93 q^{56} +587.369 q^{57} -1254.44 q^{58} -707.988 q^{59} +141.049 q^{60} -253.314 q^{61} -152.770 q^{62} -297.289 q^{63} +63.8689 q^{64} -201.546 q^{66} +440.328 q^{67} -1830.32 q^{68} +170.234 q^{69} -232.645 q^{70} +339.149 q^{71} -736.773 q^{72} +188.512 q^{73} +1001.17 q^{74} +430.912 q^{75} -2978.72 q^{76} +230.788 q^{77} +252.516 q^{79} -261.543 q^{80} -145.641 q^{81} +1008.48 q^{82} -710.703 q^{83} -1365.15 q^{84} +218.424 q^{85} -46.4132 q^{86} +878.433 q^{87} +571.963 q^{88} +1383.30 q^{89} +157.120 q^{90} -863.306 q^{92} +106.978 q^{93} +2298.05 q^{94} +355.470 q^{95} -720.621 q^{96} -373.164 q^{97} +497.150 q^{98} -155.866 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9}+O(q^{10}) $ 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 127 q^{12} - 148 q^{15} + 126 q^{16} - 74 q^{17} + 90 q^{18} - 159 q^{19} - 222 q^{20} - 184 q^{21} - 215 q^{23} + 214 q^{24} + 95 q^{25} - 192 q^{27} - 358 q^{28} - 157 q^{29} + 829 q^{30} - 394 q^{31} - 553 q^{32} - 66 q^{33} - 702 q^{34} + 58 q^{35} - 700 q^{36} + 88 q^{37} - 1318 q^{38} + 733 q^{40} - 512 q^{41} + 337 q^{42} + 927 q^{43} + 550 q^{44} - 1482 q^{45} - 1361 q^{46} - 143 q^{47} - 178 q^{48} + 1835 q^{49} - 583 q^{50} - 568 q^{51} + 106 q^{53} - 67 q^{54} - 264 q^{55} + 2059 q^{56} + 1298 q^{57} - 1690 q^{58} - 266 q^{59} + 37 q^{60} - 624 q^{61} + 643 q^{62} - 2360 q^{63} - 1589 q^{64} + 176 q^{66} - 676 q^{67} - 413 q^{68} + 764 q^{69} - 1061 q^{70} - 763 q^{71} - 1366 q^{72} - 2374 q^{73} - 1649 q^{74} + 2420 q^{75} - 2101 q^{76} - 682 q^{77} + 2164 q^{79} - 1013 q^{80} + 537 q^{81} + 3152 q^{82} + 777 q^{83} - 3381 q^{84} - 1690 q^{85} + 2894 q^{86} - 4200 q^{87} - 231 q^{88} - 1687 q^{89} - 5399 q^{90} + 5542 q^{92} - 4310 q^{93} + 1777 q^{94} + 1124 q^{95} - 3465 q^{96} - 2047 q^{97} + 1553 q^{98} + 1485 q^{99}+O(q^{100}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 127 * q^12 - 148 * q^15 + 126 * q^16 - 74 * q^17 + 90 * q^18 - 159 * q^19 - 222 * q^20 - 184 * q^21 - 215 * q^23 + 214 * q^24 + 95 * q^25 - 192 * q^27 - 358 * q^28 - 157 * q^29 + 829 * q^30 - 394 * q^31 - 553 * q^32 - 66 * q^33 - 702 * q^34 + 58 * q^35 - 700 * q^36 + 88 * q^37 - 1318 * q^38 + 733 * q^40 - 512 * q^41 + 337 * q^42 + 927 * q^43 + 550 * q^44 - 1482 * q^45 - 1361 * q^46 - 143 * q^47 - 178 * q^48 + 1835 * q^49 - 583 * q^50 - 568 * q^51 + 106 * q^53 - 67 * q^54 - 264 * q^55 + 2059 * q^56 + 1298 * q^57 - 1690 * q^58 - 266 * q^59 + 37 * q^60 - 624 * q^61 + 643 * q^62 - 2360 * q^63 - 1589 * q^64 + 176 * q^66 - 676 * q^67 - 413 * q^68 + 764 * q^69 - 1061 * q^70 - 763 * q^71 - 1366 * q^72 - 2374 * q^73 - 1649 * q^74 + 2420 * q^75 - 2101 * q^76 - 682 * q^77 + 2164 * q^79 - 1013 * q^80 + 537 * q^81 + 3152 * q^82 + 777 * q^83 - 3381 * q^84 - 1690 * q^85 + 2894 * q^86 - 4200 * q^87 - 231 * q^88 - 1687 * q^89 - 5399 * q^90 + 5542 * q^92 - 4310 * q^93 + 1777 * q^94 + 1124 * q^95 - 3465 * q^96 - 2047 * q^97 + 1553 * 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 $

$2$	5.11519	1.80849	0.904246	−	0.427012i	$-0.140434\pi$
$2$	5.11519	1.80849	0.904246	+	0.427012i	$0.140434\pi$
$3$	−3.58195	−0.689347	−0.344673	−	0.938723i	$-0.612010\pi$
$3$	−3.58195	−0.689347	−0.344673	+	0.938723i	$0.612010\pi$
$4$	18.1651	2.27064
$5$	−2.16776	−0.193890	−0.0969452	−	0.995290i	$-0.530907\pi$
$5$	−2.16776	−0.193890	−0.0969452	+	0.995290i	$0.530907\pi$
$6$	−18.3223	−1.24668
$7$	20.9807	1.13285	0.566426	−	0.824112i	$-0.308326\pi$
$7$	20.9807	1.13285	0.566426	+	0.824112i	$0.308326\pi$
$8$	51.9966	2.29795
$9$	−14.1696	−0.524801
$10$	−11.0885	−0.350649
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−65.0666	−1.56526
$13$	0	0
$13$	0	0
$14$	107.320	2.04876
$15$	7.76481	0.133658
$16$	120.651	1.88518
$17$	−100.760	−1.43753	−0.718763	−	0.695255i	$-0.755292\pi$
$17$	−100.760	−1.43753	−0.718763	+	0.695255i	$0.755292\pi$
$18$	−72.4803	−0.949099
$19$	−163.980	−1.97998	−0.989990	−	0.141136i	$-0.954924\pi$
$19$	−163.980	−1.97998	−0.989990	+	0.141136i	$0.954924\pi$
$20$	−39.3777	−0.440256
$21$	−75.1519	−0.780928
$22$	56.2671	0.545281
$23$	−47.5254	−0.430858	−0.215429	−	0.976520i	$-0.569115\pi$
$23$	−47.5254	−0.430858	−0.215429	+	0.976520i	$0.569115\pi$
$24$	−186.249	−1.58408
$25$	−120.301	−0.962406
$26$	0	0
$27$	147.468	1.05112
$28$	381.118	2.57230
$29$	−245.239	−1.57033	−0.785167	−	0.619284i	$-0.787423\pi$
$29$	−245.239	−1.57033	−0.785167	+	0.619284i	$0.787423\pi$
$30$	39.7185	0.241719
$31$	−29.8659	−0.173034	−0.0865172	−	0.996250i	$-0.527574\pi$
$31$	−29.8659	−0.173034	−0.0865172	+	0.996250i	$0.527574\pi$
$32$	201.181	1.11138
$33$	−39.4015	−0.207846
$34$	−515.408	−2.59976
$35$	−45.4812	−0.219649
$36$	−257.393	−1.19164
$37$	195.724	0.869645	0.434822	−	0.900516i	$-0.356811\pi$
$37$	195.724	0.869645	0.434822	+	0.900516i	$0.356811\pi$
$38$	−838.789	−3.58078
$39$	0	0
$40$	−112.716	−0.445550
$41$	197.154	0.750983	0.375491	−	0.926826i	$-0.377474\pi$
$41$	197.154	0.750983	0.375491	+	0.926826i	$0.377474\pi$
$42$	−384.416	−1.41230
$43$	−9.07360	−0.0321793	−0.0160897	−	0.999871i	$-0.505122\pi$
$43$	−9.07360	−0.0321793	−0.0160897	+	0.999871i	$0.505122\pi$
$44$	199.817	0.684625
$45$	30.7164	0.101754
$46$	−243.101	−0.779203
$47$	449.261	1.39429	0.697143	−	0.716932i	$-0.254454\pi$
$47$	449.261	1.39429	0.697143	+	0.716932i	$0.254454\pi$
$48$	−432.167	−1.29954
$49$	97.1910	0.283356
$50$	−615.361	−1.74050
$51$	360.918	0.990954
$52$	0	0
$53$	−296.513	−0.768474	−0.384237	−	0.923234i	$-0.625535\pi$
$53$	−296.513	−0.768474	−0.384237	+	0.923234i	$0.625535\pi$
$54$	754.324	1.90094
$55$	−23.8454	−0.0584602
$56$	1090.93	2.60324
$57$	587.369	1.36489
$58$	−1254.44	−2.83994
$59$	−707.988	−1.56224	−0.781120	−	0.624380i	$-0.785352\pi$
$59$	−707.988	−1.56224	−0.781120	+	0.624380i	$0.785352\pi$
$60$	141.049	0.303489
$61$	−253.314	−0.531696	−0.265848	−	0.964015i	$-0.585652\pi$
$61$	−253.314	−0.531696	−0.265848	+	0.964015i	$0.585652\pi$
$62$	−152.770	−0.312931
$63$	−297.289	−0.594523
$64$	63.8689	0.124744
$65$	0	0
$66$	−201.546	−0.375888
$67$	440.328	0.802904	0.401452	−	0.915880i	$-0.368506\pi$
$67$	440.328	0.802904	0.401452	+	0.915880i	$0.368506\pi$
$68$	−1830.32	−3.26411
$69$	170.234	0.297010
$70$	−232.645	−0.397234
$71$	339.149	0.566895	0.283447	−	0.958988i	$-0.408522\pi$
$71$	339.149	0.566895	0.283447	+	0.958988i	$0.408522\pi$
$72$	−736.773	−1.20597
$73$	188.512	0.302242	0.151121	−	0.988515i	$-0.451712\pi$
$73$	188.512	0.302242	0.151121	+	0.988515i	$0.451712\pi$
$74$	1001.17	1.57275
$75$	430.912	0.663432
$76$	−2978.72	−4.49583
$77$	230.788	0.341568
$78$	0	0
$79$	252.516	0.359624	0.179812	−	0.983701i	$-0.442451\pi$
$79$	252.516	0.359624	0.179812	+	0.983701i	$0.442451\pi$
$80$	−261.543	−0.365518
$81$	−145.641	−0.199782
$82$	1008.48	1.35815
$83$	−710.703	−0.939877	−0.469939	−	0.882699i	$-0.655724\pi$
$83$	−710.703	−0.939877	−0.469939	+	0.882699i	$0.655724\pi$
$84$	−1365.15	−1.77321
$85$	218.424	0.278723
$86$	−46.4132	−0.0581961
$87$	878.433	1.08251
$88$	571.963	0.692857
$89$	1383.30	1.64752	0.823762	−	0.566936i	$-0.191871\pi$
$89$	1383.30	1.64752	0.823762	+	0.566936i	$0.191871\pi$
$90$	157.120	0.184021
$91$	0	0
$92$	−863.306	−0.978325
$93$	106.978	0.119281
$94$	2298.05	2.52155
$95$	355.470	0.383899
$96$	−720.621	−0.766126
$97$	−373.164	−0.390609	−0.195304	−	0.980743i	$-0.562569\pi$
$97$	−373.164	−0.390609	−0.195304	+	0.980743i	$0.562569\pi$
$98$	497.150	0.512447
$99$	−155.866	−0.158234
$100$	−2185.28	−2.18528
$101$	−506.149	−0.498651	−0.249326	−	0.968420i	$-0.580209\pi$
$101$	−506.149	−0.498651	−0.249326	+	0.968420i	$0.580209\pi$
$102$	1846.16	1.79213
$103$	−1161.94	−1.11154	−0.555771	−	0.831335i	$-0.687577\pi$
$103$	−1161.94	−1.11154	−0.555771	+	0.831335i	$0.687577\pi$
$104$	0	0
$105$	162.911	0.151415
$106$	−1516.72	−1.38978
$107$	−1078.72	−0.974617	−0.487309	−	0.873230i	$-0.662021\pi$
$107$	−1078.72	−0.974617	−0.487309	+	0.873230i	$0.662021\pi$
$108$	2678.77	2.38671
$109$	677.905	0.595702	0.297851	−	0.954612i	$-0.403730\pi$
$109$	677.905	0.595702	0.297851	+	0.954612i	$0.403730\pi$
$110$	−121.974	−0.105725
$111$	−701.074	−0.599487
$112$	2531.35	2.13563
$113$	752.745	0.626657	0.313329	−	0.949645i	$-0.398556\pi$
$113$	752.745	0.626657	0.313329	+	0.949645i	$0.398556\pi$
$114$	3004.50	2.46840
$115$	103.024	0.0835392
$116$	−4454.80	−3.56567
$117$	0	0
$118$	−3621.49	−2.82530
$119$	−2114.02	−1.62851
$120$	403.744	0.307138
$121$	121.000	0.0909091
$122$	−1295.75	−0.961569
$123$	−706.196	−0.517687
$124$	−542.518	−0.392900
$125$	531.754	0.380492
$126$	−1520.69	−1.07519
$127$	−1408.35	−0.984024	−0.492012	−	0.870589i	$-0.663738\pi$
$127$	−1408.35	−0.984024	−0.492012	+	0.870589i	$0.663738\pi$
$128$	−1282.75	−0.885781
$129$	32.5012	0.0221827
$130$	0	0
$131$	747.620	0.498625	0.249312	−	0.968423i	$-0.419795\pi$
$131$	747.620	0.498625	0.249312	+	0.968423i	$0.419795\pi$
$132$	−715.733	−0.471944
$133$	−3440.42	−2.24303
$134$	2252.36	1.45205
$135$	−319.674	−0.203801
$136$	−5239.19	−3.30336
$137$	2557.96	1.59519	0.797595	−	0.603193i	$-0.206105\pi$
$137$	2557.96	1.59519	0.797595	+	0.603193i	$0.206105\pi$
$138$	870.777	0.537141
$139$	−2405.56	−1.46789	−0.733946	−	0.679208i	$-0.762324\pi$
$139$	−2405.56	−1.46789	−0.733946	+	0.679208i	$0.762324\pi$
$140$	−826.173	−0.498745
$141$	−1609.23	−0.961146
$142$	1734.81	1.02523
$143$	0	0
$144$	−1709.58	−0.989343
$145$	531.619	0.304473
$146$	964.274	0.546602
$147$	−348.133	−0.195330
$148$	3555.36	1.97465
$149$	−1518.06	−0.834658	−0.417329	−	0.908755i	$-0.637034\pi$
$149$	−1518.06	−0.834658	−0.417329	+	0.908755i	$0.637034\pi$
$150$	2204.19	1.19981
$151$	−1058.05	−0.570219	−0.285109	−	0.958495i	$-0.592030\pi$
$151$	−1058.05	−0.570219	−0.285109	+	0.958495i	$0.592030\pi$
$152$	−8526.41	−4.54989
$153$	1427.74	0.754416
$154$	1180.52	0.617723
$155$	64.7421	0.0335497
$156$	0	0
$157$	−3240.36	−1.64719	−0.823594	−	0.567179i	$-0.808035\pi$
$157$	−3240.36	−1.64719	−0.823594	+	0.567179i	$0.808035\pi$
$158$	1291.67	0.650377
$159$	1062.09	0.529745
$160$	−436.113	−0.215486
$161$	−997.118	−0.488099
$162$	−744.983	−0.361305
$163$	1408.43	0.676792	0.338396	−	0.941004i	$-0.390116\pi$
$163$	1408.43	0.676792	0.338396	+	0.941004i	$0.390116\pi$
$164$	3581.33	1.70521
$165$	85.4129	0.0402993
$166$	−3635.38	−1.69976
$167$	1658.11	0.768313	0.384156	−	0.923268i	$-0.374492\pi$
$167$	1658.11	0.768313	0.384156	+	0.923268i	$0.374492\pi$
$168$	−3907.65	−1.79453
$169$	0	0
$170$	1117.28	0.504068
$171$	2323.54	1.03910
$172$	−164.823	−0.0730678
$173$	−2055.90	−0.903508	−0.451754	−	0.892143i	$-0.649202\pi$
$173$	−2055.90	−0.903508	−0.451754	+	0.892143i	$0.649202\pi$
$174$	4493.35	1.95770
$175$	−2524.00	−1.09027
$176$	1327.16	0.568402
$177$	2535.98	1.07693
$178$	7075.84	2.97953
$179$	−4610.14	−1.92502	−0.962509	−	0.271249i	$-0.912563\pi$
$179$	−4610.14	−1.92502	−0.962509	+	0.271249i	$0.912563\pi$
$180$	557.967	0.231047
$181$	3125.73	1.28361	0.641805	−	0.766868i	$-0.278186\pi$
$181$	3125.73	1.28361	0.641805	+	0.766868i	$0.278186\pi$
$182$	0	0
$183$	907.357	0.366523
$184$	−2471.16	−0.990089
$185$	−424.283	−0.168616
$186$	547.213	0.215718
$187$	−1108.36	−0.433431
$188$	8160.89	3.16593
$189$	3093.98	1.19076
$190$	1818.29	0.694279
$191$	−2153.65	−0.815877	−0.407938	−	0.913009i	$-0.633752\pi$
$191$	−2153.65	−0.815877	−0.407938	+	0.913009i	$0.633752\pi$
$192$	−228.775	−0.0859918
$193$	564.361	0.210485	0.105243	−	0.994447i	$-0.466438\pi$
$193$	564.361	0.210485	0.105243	+	0.994447i	$0.466438\pi$
$194$	−1908.80	−0.706412
$195$	0	0
$196$	1765.49	0.643400
$197$	1241.52	0.449009	0.224504	−	0.974473i	$-0.427924\pi$
$197$	1241.52	0.449009	0.224504	+	0.974473i	$0.427924\pi$
$198$	−797.284	−0.286164
$199$	−1900.50	−0.677000	−0.338500	−	0.940966i	$-0.609920\pi$
$199$	−1900.50	−0.677000	−0.338500	+	0.940966i	$0.609920\pi$
$200$	−6255.24	−2.21156
$201$	−1577.23	−0.553479
$202$	−2589.05	−0.901806
$203$	−5145.29	−1.77896
$204$	6556.13	2.25010
$205$	−427.383	−0.145608
$206$	−5943.52	−2.01022
$207$	673.418	0.226115
$208$	0	0
$209$	−1803.78	−0.596987
$210$	833.323	0.273832
$211$	3545.42	1.15676	0.578380	−	0.815767i	$-0.303685\pi$
$211$	3545.42	1.15676	0.578380	+	0.815767i	$0.303685\pi$
$212$	−5386.19	−1.74493
$213$	−1214.81	−0.390787
$214$	−5517.87	−1.76259
$215$	19.6694	0.00623927
$216$	7667.82	2.41541
$217$	−626.608	−0.196023
$218$	3467.61	1.07732
$219$	−675.240	−0.208349
$220$	−433.155	−0.132742
$221$	0	0
$222$	−3586.13	−1.08417
$223$	−1491.27	−0.447816	−0.223908	−	0.974610i	$-0.571882\pi$
$223$	−1491.27	−0.447816	−0.223908	+	0.974610i	$0.571882\pi$
$224$	4220.93	1.25903
$225$	1704.62	0.505072
$226$	3850.43	1.13330
$227$	1888.56	0.552193	0.276097	−	0.961130i	$-0.410959\pi$
$227$	1888.56	0.552193	0.276097	+	0.961130i	$0.410959\pi$
$228$	10669.6	3.09918
$229$	−2300.70	−0.663906	−0.331953	−	0.943296i	$-0.607708\pi$
$229$	−2300.70	−0.663906	−0.331953	+	0.943296i	$0.607708\pi$
$230$	526.986	0.151080
$231$	−826.671	−0.235459
$232$	−12751.6	−3.60855
$233$	1680.29	0.472445	0.236223	−	0.971699i	$-0.424091\pi$
$233$	1680.29	0.472445	0.236223	+	0.971699i	$0.424091\pi$
$234$	0	0
$235$	−973.890	−0.270339
$236$	−12860.7	−3.54729
$237$	−904.500	−0.247906
$238$	−10813.6	−2.94514
$239$	5621.13	1.52134	0.760671	−	0.649138i	$-0.224870\pi$
$239$	5621.13	1.52134	0.760671	+	0.649138i	$0.224870\pi$
$240$	936.835	0.251968
$241$	3570.85	0.954433	0.477217	−	0.878786i	$-0.341646\pi$
$241$	3570.85	0.954433	0.477217	+	0.878786i	$0.341646\pi$
$242$	618.938	0.164408
$243$	−3459.94	−0.913397
$244$	−4601.48	−1.20729
$245$	−210.687	−0.0549400
$246$	−3612.32	−0.936233
$247$	0	0
$248$	−1552.92	−0.397624
$249$	2545.70	0.647901
$250$	2720.02	0.688117
$251$	−2159.29	−0.543000	−0.271500	−	0.962438i	$-0.587520\pi$
$251$	−2159.29	−0.543000	−0.271500	+	0.962438i	$0.587520\pi$
$252$	−5400.30	−1.34995
$253$	−522.779	−0.129909
$254$	−7203.98	−1.77960
$255$	−782.385	−0.192137
$256$	−7072.45	−1.72667
$257$	−8173.44	−1.98383	−0.991916	−	0.126895i	$-0.959499\pi$
$257$	−8173.44	−1.98383	−0.991916	+	0.126895i	$0.959499\pi$
$258$	166.250	0.0401173
$259$	4106.44	0.985180
$260$	0	0
$261$	3474.94	0.824114
$262$	3824.22	0.901759
$263$	5776.10	1.35426	0.677129	−	0.735865i	$-0.263224\pi$
$263$	5776.10	1.35426	0.677129	+	0.735865i	$0.263224\pi$
$264$	−2048.74	−0.477619
$265$	642.768	0.149000
$266$	−17598.4	−4.05650
$267$	−4954.91	−1.13571
$268$	7998.62	1.82311
$269$	2247.94	0.509514	0.254757	−	0.967005i	$-0.418005\pi$
$269$	2247.94	0.509514	0.254757	+	0.967005i	$0.418005\pi$
$270$	−1635.19	−0.368573
$271$	−372.277	−0.0834473	−0.0417236	−	0.999129i	$-0.513285\pi$
$271$	−372.277	−0.0834473	−0.0417236	+	0.999129i	$0.513285\pi$
$272$	−12156.9	−2.70999
$273$	0	0
$274$	13084.4	2.88489
$275$	−1323.31	−0.290176
$276$	3092.32	0.674405
$277$	7452.77	1.61658	0.808292	−	0.588782i	$-0.200392\pi$
$277$	7452.77	1.61658	0.808292	+	0.588782i	$0.200392\pi$
$278$	−12304.9	−2.65467
$279$	423.188	0.0908087
$280$	−2364.87	−0.504743
$281$	3561.16	0.756018	0.378009	−	0.925802i	$-0.376609\pi$
$281$	3561.16	0.756018	0.378009	+	0.925802i	$0.376609\pi$
$282$	−8231.51	−1.73823
$283$	4734.42	0.994460	0.497230	−	0.867619i	$-0.334350\pi$
$283$	4734.42	0.994460	0.497230	+	0.867619i	$0.334350\pi$
$284$	6160.68	1.28722
$285$	−1273.28	−0.264640
$286$	0	0
$287$	4136.44	0.850753
$288$	−2850.66	−0.583253
$289$	5239.63	1.06648
$290$	2719.33	0.550637
$291$	1336.65	0.269265
$292$	3424.35	0.686283
$293$	512.588	0.102204	0.0511019	−	0.998693i	$-0.483727\pi$
$293$	512.588	0.102204	0.0511019	+	0.998693i	$0.483727\pi$
$294$	−1780.77	−0.353253
$295$	1534.75	0.302904
$296$	10177.0	1.99840
$297$	1622.14	0.316924
$298$	−7765.15	−1.50947
$299$	0	0
$300$	7827.57	1.50642
$301$	−190.371	−0.0364545
$302$	−5412.13	−1.03124
$303$	1813.00	0.343743
$304$	−19784.4	−3.73261
$305$	549.123	0.103091
$306$	7303.14	1.36435
$307$	−1313.04	−0.244102	−0.122051	−	0.992524i	$-0.538947\pi$
$307$	−1313.04	−0.244102	−0.122051	+	0.992524i	$0.538947\pi$
$308$	4192.30	0.775579
$309$	4162.00	0.766238
$310$	331.168	0.0606744
$311$	9832.07	1.79269	0.896343	−	0.443361i	$-0.146214\pi$
$311$	9832.07	1.79269	0.896343	+	0.443361i	$0.146214\pi$
$312$	0	0
$313$	−5987.25	−1.08121	−0.540606	−	0.841276i	$-0.681805\pi$
$313$	−5987.25	−1.08121	−0.540606	+	0.841276i	$0.681805\pi$
$314$	−16575.0	−2.97893
$315$	644.452	0.115272
$316$	4586.99	0.816578
$317$	4038.80	0.715589	0.357794	−	0.933800i	$-0.383529\pi$
$317$	4038.80	0.715589	0.357794	+	0.933800i	$0.383529\pi$
$318$	5432.81	0.958040
$319$	−2697.63	−0.473474
$320$	−138.452	−0.0241867
$321$	3863.93	0.671849
$322$	−5100.44	−0.882722
$323$	16522.7	2.84627
$324$	−2645.60	−0.453635
$325$	0	0
$326$	7204.40	1.22397
$327$	−2428.22	−0.410645
$328$	10251.3	1.72572
$329$	9425.82	1.57952
$330$	436.903	0.0728810
$331$	10671.7	1.77212	0.886059	−	0.463573i	$-0.153433\pi$
$331$	10671.7	1.77212	0.886059	+	0.463573i	$0.153433\pi$
$332$	−12910.0	−2.13413
$333$	−2773.34	−0.456391
$334$	8481.53	1.38949
$335$	−954.525	−0.155676
$336$	−9067.18	−1.47219
$337$	888.621	0.143639	0.0718194	−	0.997418i	$-0.477119\pi$
$337$	888.621	0.143639	0.0718194	+	0.997418i	$0.477119\pi$
$338$	0	0
$339$	−2696.29	−0.431984
$340$	3967.71	0.632880
$341$	−328.525	−0.0521719
$342$	11885.3	1.87920
$343$	−5157.25	−0.811853
$344$	−471.797	−0.0739464
$345$	−369.026	−0.0575875
$346$	−10516.3	−1.63399
$347$	−4641.53	−0.718070	−0.359035	−	0.933324i	$-0.616894\pi$
$347$	−4641.53	−0.718070	−0.359035	+	0.933324i	$0.616894\pi$
$348$	15956.9	2.45798
$349$	−1492.57	−0.228927	−0.114463	−	0.993427i	$-0.536515\pi$
$349$	−1492.57	−0.228927	−0.114463	+	0.993427i	$0.536515\pi$
$350$	−12910.7	−1.97174
$351$	0	0
$352$	2212.99	0.335094
$353$	−7503.90	−1.13142	−0.565711	−	0.824603i	$-0.691398\pi$
$353$	−7503.90	−1.13142	−0.565711	+	0.824603i	$0.691398\pi$
$354$	12972.0	1.94761
$355$	−735.193	−0.109916
$356$	25127.9	3.74094
$357$	7572.33	1.12261
$358$	−23581.7	−3.48138
$359$	−2648.70	−0.389396	−0.194698	−	0.980863i	$-0.562373\pi$
$359$	−2648.70	−0.389396	−0.194698	+	0.980863i	$0.562373\pi$
$360$	1597.15	0.233825
$361$	20030.5	2.92032
$362$	15988.7	2.32140
$363$	−433.416	−0.0626679
$364$	0	0
$365$	−408.649	−0.0586018
$366$	4641.30	0.662854
$367$	−12777.8	−1.81743	−0.908714	−	0.417420i	$-0.862934\pi$
$367$	−12777.8	−1.81743	−0.908714	+	0.417420i	$0.862934\pi$
$368$	−5734.00	−0.812243
$369$	−2793.60	−0.394117
$370$	−2170.29	−0.304940
$371$	−6221.05	−0.870568
$372$	1943.27	0.270844
$373$	319.960	0.0444152	0.0222076	−	0.999753i	$-0.492931\pi$
$373$	319.960	0.0444152	0.0222076	+	0.999753i	$0.492931\pi$
$374$	−5669.48	−0.783856
$375$	−1904.71	−0.262291
$376$	23360.0	3.20400
$377$	0	0
$378$	15826.3	2.15348
$379$	−2490.46	−0.337536	−0.168768	−	0.985656i	$-0.553979\pi$
$379$	−2490.46	−0.337536	−0.168768	+	0.985656i	$0.553979\pi$
$380$	6457.16	0.871698
$381$	5044.64	0.678333
$382$	−11016.3	−1.47551
$383$	−5347.18	−0.713390	−0.356695	−	0.934221i	$-0.616096\pi$
$383$	−5347.18	−0.713390	−0.356695	+	0.934221i	$0.616096\pi$
$384$	4594.74	0.610610
$385$	−500.293	−0.0662268
$386$	2886.81	0.380660
$387$	128.570	0.0168878
$388$	−6778.57	−0.886933
$389$	−1245.73	−0.162367	−0.0811837	−	0.996699i	$-0.525870\pi$
$389$	−1245.73	−0.162367	−0.0811837	+	0.996699i	$0.525870\pi$
$390$	0	0
$391$	4788.67	0.619370
$392$	5053.60	0.651137
$393$	−2677.94	−0.343725
$394$	6350.61	0.812029
$395$	−547.395	−0.0697276
$396$	−2831.33	−0.359292
$397$	429.976	0.0543574	0.0271787	−	0.999631i	$-0.491348\pi$
$397$	429.976	0.0543574	0.0271787	+	0.999631i	$0.491348\pi$
$398$	−9721.43	−1.22435
$399$	12323.4	1.54622
$400$	−14514.5	−1.81431
$401$	−5456.28	−0.679485	−0.339743	−	0.940518i	$-0.610340\pi$
$401$	−5456.28	−0.679485	−0.339743	+	0.940518i	$0.610340\pi$
$402$	−8067.84	−1.00096
$403$	0	0
$404$	−9194.28	−1.13226
$405$	315.716	0.0387359
$406$	−26319.1	−3.21723
$407$	2152.97	0.262208
$408$	18766.5	2.27716
$409$	−10559.8	−1.27665	−0.638323	−	0.769769i	$-0.720372\pi$
$409$	−10559.8	−1.27665	−0.638323	+	0.769769i	$0.720372\pi$
$410$	−2186.14	−0.263332
$411$	−9162.47	−1.09964
$412$	−21106.7	−2.52392
$413$	−14854.1	−1.76979
$414$	3444.66	0.408927
$415$	1540.63	0.182233
$416$	0	0
$417$	8616.60	1.01189
$418$	−9226.68	−1.07965
$419$	−5430.06	−0.633116	−0.316558	−	0.948573i	$-0.602527\pi$
$419$	−5430.06	−0.633116	−0.316558	+	0.948573i	$0.602527\pi$
$420$	2959.31	0.343808
$421$	7025.98	0.813362	0.406681	−	0.913570i	$-0.366686\pi$
$421$	7025.98	0.813362	0.406681	+	0.913570i	$0.366686\pi$
$422$	18135.5	2.09199
$423$	−6365.86	−0.731723
$424$	−15417.7	−1.76591
$425$	12121.5	1.38349
$426$	−6214.00	−0.706735
$427$	−5314.70	−0.602334
$428$	−19595.1	−2.21301
$429$	0	0
$430$	100.613	0.0112837
$431$	2946.46	0.329294	0.164647	−	0.986353i	$-0.447351\pi$
$431$	2946.46	0.329294	0.164647	+	0.986353i	$0.447351\pi$
$432$	17792.2	1.98154
$433$	−1906.21	−0.211563	−0.105782	−	0.994389i	$-0.533734\pi$
$433$	−1906.21	−0.211563	−0.105782	+	0.994389i	$0.533734\pi$
$434$	−3205.22	−0.354505
$435$	−1904.23	−0.209887
$436$	12314.2	1.35263
$437$	7793.22	0.853090
$438$	−3453.98	−0.376798
$439$	16294.1	1.77147	0.885737	−	0.464187i	$-0.153653\pi$
$439$	16294.1	1.77147	0.885737	+	0.464187i	$0.153653\pi$
$440$	−1239.88	−0.134338
$441$	−1377.16	−0.148705
$442$	0	0
$443$	−757.392	−0.0812298	−0.0406149	−	0.999175i	$-0.512932\pi$
$443$	−757.392	−0.0812298	−0.0406149	+	0.999175i	$0.512932\pi$
$444$	−12735.1	−1.36122
$445$	−2998.67	−0.319439
$446$	−7628.14	−0.809872
$447$	5437.61	0.575369
$448$	1340.02	0.141316
$449$	4381.31	0.460505	0.230252	−	0.973131i	$-0.426045\pi$
$449$	4381.31	0.460505	0.230252	+	0.973131i	$0.426045\pi$
$450$	8719.44	0.913419
$451$	2168.69	0.226430
$452$	13673.7	1.42291
$453$	3789.89	0.393078
$454$	9660.32	0.998637
$455$	0	0
$456$	30541.2	3.13645
$457$	−10979.6	−1.12386	−0.561931	−	0.827184i	$-0.689941\pi$
$457$	−10979.6	−1.12386	−0.561931	+	0.827184i	$0.689941\pi$
$458$	−11768.5	−1.20067
$459$	−14858.9	−1.51101
$460$	1871.44	0.189688
$461$	7454.38	0.753113	0.376557	−	0.926394i	$-0.377108\pi$
$461$	7454.38	0.753113	0.376557	+	0.926394i	$0.377108\pi$
$462$	−4228.58	−0.425825
$463$	−5694.35	−0.571574	−0.285787	−	0.958293i	$-0.592255\pi$
$463$	−5694.35	−0.571574	−0.285787	+	0.958293i	$0.592255\pi$
$464$	−29588.4	−2.96036
$465$	−231.903	−0.0231274
$466$	8595.02	0.854413
$467$	−4784.89	−0.474129	−0.237064	−	0.971494i	$-0.576185\pi$
$467$	−4784.89	−0.474129	−0.237064	+	0.971494i	$0.576185\pi$
$468$	0	0
$469$	9238.40	0.909573
$470$	−4981.63	−0.488905
$471$	11606.8	1.13548
$472$	−36813.0	−3.58995
$473$	−99.8096	−0.00970244
$474$	−4626.69	−0.448335
$475$	19726.9	1.90555
$476$	−38401.6	−3.69776
$477$	4201.47	0.403296
$478$	28753.1	2.75133
$479$	5371.02	0.512334	0.256167	−	0.966632i	$-0.417540\pi$
$479$	5371.02	0.512334	0.256167	+	0.966632i	$0.417540\pi$
$480$	1562.13	0.148544
$481$	0	0
$482$	18265.5	1.72608
$483$	3571.63	0.336469
$484$	2197.98	0.206422
$485$	808.930	0.0757353
$486$	−17698.3	−1.65187
$487$	−11110.5	−1.03380	−0.516902	−	0.856044i	$-0.672915\pi$
$487$	−11110.5	−1.03380	−0.516902	+	0.856044i	$0.672915\pi$
$488$	−13171.5	−1.22181
$489$	−5044.94	−0.466544
$490$	−1077.70	−0.0993585
$491$	−8615.57	−0.791885	−0.395942	−	0.918275i	$-0.629582\pi$
$491$	−8615.57	−0.791885	−0.395942	+	0.918275i	$0.629582\pi$
$492$	−12828.2	−1.17548
$493$	24710.3	2.25740
$494$	0	0
$495$	337.880	0.0306800
$496$	−3603.36	−0.326201
$497$	7115.59	0.642209
$498$	13021.8	1.17172
$499$	6406.12	0.574704	0.287352	−	0.957825i	$-0.407225\pi$
$499$	6406.12	0.574704	0.287352	+	0.957825i	$0.407225\pi$
$500$	9659.38	0.863961
$501$	−5939.26	−0.529634
$502$	−11045.2	−0.982011
$503$	−4437.41	−0.393349	−0.196675	−	0.980469i	$-0.563014\pi$
$503$	−4437.41	−0.393349	−0.196675	+	0.980469i	$0.563014\pi$
$504$	−15458.0	−1.36618
$505$	1097.21	0.0966837
$506$	−2674.12	−0.234939
$507$	0	0
$508$	−25582.9	−2.23437
$509$	−16266.2	−1.41647	−0.708237	−	0.705975i	$-0.750509\pi$
$509$	−16266.2	−1.41647	−0.708237	+	0.705975i	$0.750509\pi$
$510$	−4002.04	−0.347477
$511$	3955.12	0.342395
$512$	−25914.9	−2.23689
$513$	−24181.8	−2.08119
$514$	−41808.7	−3.58774
$515$	2518.80	0.215518
$516$	590.389	0.0503690
$517$	4941.87	0.420393
$518$	21005.2	1.78169
$519$	7364.12	0.622830
$520$	0	0
$521$	−18667.0	−1.56970	−0.784851	−	0.619684i	$-0.787261\pi$
$521$	−18667.0	−1.56970	−0.784851	+	0.619684i	$0.787261\pi$
$522$	17775.0	1.49040
$523$	−8795.44	−0.735368	−0.367684	−	0.929951i	$-0.619849\pi$
$523$	−8795.44	−0.735368	−0.367684	+	0.929951i	$0.619849\pi$
$524$	13580.6	1.13220
$525$	9040.84	0.751571
$526$	29545.8	2.44916
$527$	3009.29	0.248742
$528$	−4753.84	−0.391826
$529$	−9908.34	−0.814361
$530$	3287.88	0.269465
$531$	10031.9	0.819866
$532$	−62495.8	−5.09311
$533$	0	0
$534$	−25345.3	−2.05393
$535$	2338.41	0.188969
$536$	22895.6	1.84503
$537$	16513.3	1.32700
$538$	11498.6	0.921452
$539$	1069.10	0.0854350
$540$	−5806.93	−0.462760
$541$	−20229.3	−1.60763	−0.803813	−	0.594882i	$-0.797199\pi$
$541$	−20229.3	−1.60763	−0.803813	+	0.594882i	$0.797199\pi$
$542$	−1904.27	−0.150914
$543$	−11196.2	−0.884853
$544$	−20271.1	−1.59764
$545$	−1469.54	−0.115501
$546$	0	0
$547$	−6508.23	−0.508724	−0.254362	−	0.967109i	$-0.581865\pi$
$547$	−6508.23	−0.508724	−0.254362	+	0.967109i	$0.581865\pi$
$548$	46465.7	3.62211
$549$	3589.36	0.279035
$550$	−6768.97	−0.524782
$551$	40214.3	3.10923
$552$	8851.57	0.682515
$553$	5297.97	0.407401
$554$	38122.3	2.92358
$555$	1519.76	0.116235
$556$	−43697.4	−3.33306
$557$	7329.05	0.557526	0.278763	−	0.960360i	$-0.410076\pi$
$557$	7329.05	0.557526	0.278763	+	0.960360i	$0.410076\pi$
$558$	2164.69	0.164227
$559$	0	0
$560$	−5487.37	−0.414078
$561$	3970.10	0.298784
$562$	18216.0	1.36725
$563$	8186.50	0.612824	0.306412	−	0.951899i	$-0.400871\pi$
$563$	8186.50	0.612824	0.306412	+	0.951899i	$0.400871\pi$
$564$	−29231.9	−2.18242
$565$	−1631.77	−0.121503
$566$	24217.5	1.79847
$567$	−3055.66	−0.226324
$568$	17634.6	1.30270
$569$	−4368.66	−0.321870	−0.160935	−	0.986965i	$-0.551451\pi$
$569$	−4368.66	−0.321870	−0.160935	+	0.986965i	$0.551451\pi$
$570$	−6513.04	−0.478599
$571$	7386.75	0.541376	0.270688	−	0.962667i	$-0.412749\pi$
$571$	7386.75	0.541376	0.270688	+	0.962667i	$0.412749\pi$
$572$	0	0
$573$	7714.26	0.562422
$574$	21158.6	1.53858
$575$	5717.34	0.414660
$576$	−904.999	−0.0654658
$577$	−9363.28	−0.675561	−0.337780	−	0.941225i	$-0.609676\pi$
$577$	−9363.28	−0.675561	−0.337780	+	0.941225i	$0.609676\pi$
$578$	26801.7	1.92873
$579$	−2021.51	−0.145097
$580$	9656.94	0.691349
$581$	−14911.1	−1.06474
$582$	6837.23	0.486963
$583$	−3261.64	−0.231704
$584$	9801.98	0.694536
$585$	0	0
$586$	2621.98	0.184835
$587$	−6516.22	−0.458182	−0.229091	−	0.973405i	$-0.573575\pi$
$587$	−6516.22	−0.458182	−0.229091	+	0.973405i	$0.573575\pi$
$588$	−6323.89	−0.443525
$589$	4897.41	0.342605
$590$	7850.53	0.547799
$591$	−4447.07	−0.309523
$592$	23614.4	1.63943
$593$	18704.6	1.29529	0.647643	−	0.761944i	$-0.275755\pi$
$593$	18704.6	1.29529	0.647643	+	0.761944i	$0.275755\pi$
$594$	8297.57	0.573154
$595$	4582.70	0.315752
$596$	−27575.7	−1.89521
$597$	6807.51	0.466688
$598$	0	0
$599$	6285.10	0.428718	0.214359	−	0.976755i	$-0.431234\pi$
$599$	6285.10	0.428718	0.214359	+	0.976755i	$0.431234\pi$
$600$	22405.9	1.52453
$601$	22144.7	1.50300	0.751499	−	0.659734i	$-0.229331\pi$
$601$	22144.7	1.50300	0.751499	+	0.659734i	$0.229331\pi$
$602$	−973.782	−0.0659276
$603$	−6239.28	−0.421365
$604$	−19219.7	−1.29476
$605$	−262.299	−0.0176264
$606$	9273.85	0.621657
$607$	−613.760	−0.0410408	−0.0205204	−	0.999789i	$-0.506532\pi$
$607$	−613.760	−0.0410408	−0.0205204	+	0.999789i	$0.506532\pi$
$608$	−32989.7	−2.20051
$609$	18430.2	1.22632
$610$	2808.87	0.186439
$611$	0	0
$612$	25935.0	1.71301
$613$	6125.61	0.403607	0.201804	−	0.979426i	$-0.435320\pi$
$613$	6125.61	0.403607	0.201804	+	0.979426i	$0.435320\pi$
$614$	−6716.47	−0.441457
$615$	1530.86	0.100375
$616$	12000.2	0.784905
$617$	3508.29	0.228912	0.114456	−	0.993428i	$-0.463488\pi$
$617$	3508.29	0.228912	0.114456	+	0.993428i	$0.463488\pi$
$618$	21289.4	1.38574
$619$	30039.5	1.95055	0.975275	−	0.220993i	$-0.0709299\pi$
$619$	30039.5	1.95055	0.975275	+	0.220993i	$0.0709299\pi$
$620$	1176.05	0.0761795
$621$	−7008.46	−0.452882
$622$	50292.9	3.24206
$623$	29022.7	1.86640
$624$	0	0
$625$	13884.9	0.888633
$626$	−30625.9	−1.95536
$627$	6461.06	0.411531
$628$	−58861.5	−3.74018
$629$	−19721.2	−1.25014
$630$	3296.49	0.208469
$631$	−17070.8	−1.07698	−0.538492	−	0.842630i	$-0.681006\pi$
$631$	−17070.8	−1.07698	−0.538492	+	0.842630i	$0.681006\pi$
$632$	13130.0	0.826397
$633$	−12699.5	−0.797409
$634$	20659.2	1.29414
$635$	3052.97	0.190793
$636$	19293.1	1.20286
$637$	0	0
$638$	−13798.9	−0.856273
$639$	−4805.61	−0.297507
$640$	2780.69	0.171745
$641$	24951.3	1.53747	0.768734	−	0.639568i	$-0.220887\pi$
$641$	24951.3	1.53747	0.768734	+	0.639568i	$0.220887\pi$
$642$	19764.7	1.21503
$643$	16031.1	0.983211	0.491606	−	0.870818i	$-0.336410\pi$
$643$	16031.1	0.983211	0.491606	+	0.870818i	$0.336410\pi$
$644$	−18112.8	−1.10830
$645$	−70.4548	−0.00430102
$646$	84516.6	5.14746
$647$	7626.55	0.463417	0.231708	−	0.972785i	$-0.425568\pi$
$647$	7626.55	0.463417	0.231708	+	0.972785i	$0.425568\pi$
$648$	−7572.86	−0.459090
$649$	−7787.87	−0.471033
$650$	0	0
$651$	2244.48	0.135128
$652$	25584.4	1.53675
$653$	22378.2	1.34108	0.670540	−	0.741873i	$-0.266062\pi$
$653$	22378.2	1.34108	0.670540	+	0.741873i	$0.266062\pi$
$654$	−12420.8	−0.742648
$655$	−1620.66	−0.0966786
$656$	23786.9	1.41574
$657$	−2671.14	−0.158617
$658$	48214.8	2.85655
$659$	204.306	0.0120769	0.00603843	−	0.999982i	$-0.498078\pi$
$659$	204.306	0.0120769	0.00603843	+	0.999982i	$0.498078\pi$
$660$	1551.54	0.0915054
$661$	−22005.4	−1.29487	−0.647436	−	0.762120i	$-0.724159\pi$
$661$	−22005.4	−1.29487	−0.647436	+	0.762120i	$0.724159\pi$
$662$	54587.8	3.20486
$663$	0	0
$664$	−36954.2	−2.15979
$665$	7458.02	0.434901
$666$	−14186.2	−0.825379
$667$	11655.1	0.676591
$668$	30119.8	1.74456
$669$	5341.66	0.308700
$670$	−4882.58	−0.281538
$671$	−2786.45	−0.160313
$672$	−15119.2	−0.867908
$673$	2434.90	0.139463	0.0697314	−	0.997566i	$-0.477786\pi$
$673$	2434.90	0.139463	0.0697314	+	0.997566i	$0.477786\pi$
$674$	4545.47	0.259770
$675$	−17740.5	−1.01160
$676$	0	0
$677$	4776.11	0.271138	0.135569	−	0.990768i	$-0.456714\pi$
$677$	4776.11	0.271138	0.135569	+	0.990768i	$0.456714\pi$
$678$	−13792.0	−0.781240
$679$	−7829.25	−0.442502
$680$	11357.3	0.640490
$681$	−6764.72	−0.380653
$682$	−1680.46	−0.0943524
$683$	13988.4	0.783678	0.391839	−	0.920034i	$-0.371839\pi$
$683$	13988.4	0.783678	0.391839	+	0.920034i	$0.371839\pi$
$684$	42207.4	2.35942
$685$	−5545.04	−0.309292
$686$	−26380.3	−1.46823
$687$	8240.99	0.457662
$688$	−1094.74	−0.0606637
$689$	0	0
$690$	−1887.64	−0.104147
$691$	−24068.6	−1.32506	−0.662529	−	0.749037i	$-0.730517\pi$
$691$	−24068.6	−1.32506	−0.662529	+	0.749037i	$0.730517\pi$
$692$	−37345.7	−2.05154
$693$	−3270.18	−0.179255
$694$	−23742.3	−1.29862
$695$	5214.68	0.284610
$696$	45675.6	2.48754
$697$	−19865.3	−1.07956
$698$	−7634.77	−0.414012
$699$	−6018.73	−0.325678
$700$	−45848.8	−2.47560
$701$	36641.1	1.97420	0.987102	−	0.160095i	$-0.0511801\pi$
$701$	36641.1	1.97420	0.987102	+	0.160095i	$0.0511801\pi$
$702$	0	0
$703$	−32094.9	−1.72188
$704$	702.558	0.0376117
$705$	3488.43	0.186357
$706$	−38383.9	−2.04617
$707$	−10619.4	−0.564898
$708$	46066.4	2.44531
$709$	−11371.4	−0.602341	−0.301171	−	0.953570i	$-0.597377\pi$
$709$	−11371.4	−0.602341	−0.301171	+	0.953570i	$0.597377\pi$
$710$	−3760.65	−0.198781
$711$	−3578.06	−0.188731
$712$	71927.0	3.78592
$713$	1419.39	0.0745533
$714$	38733.9	2.03022
$715$	0	0
$716$	−83743.9	−4.37103
$717$	−20134.6	−1.04873
$718$	−13548.6	−0.704220
$719$	−16917.3	−0.877481	−0.438741	−	0.898614i	$-0.644575\pi$
$719$	−16917.3	−0.877481	−0.438741	+	0.898614i	$0.644575\pi$
$720$	3705.97	0.191824
$721$	−24378.3	−1.25921
$722$	102460.	5.28138
$723$	−12790.6	−0.657935
$724$	56779.3	2.91462
$725$	29502.4	1.51130
$726$	−2217.00	−0.113334
$727$	3856.69	0.196749	0.0983745	−	0.995149i	$-0.468636\pi$
$727$	3856.69	0.196749	0.0983745	+	0.995149i	$0.468636\pi$
$728$	0	0
$729$	16325.7	0.829430
$730$	−2090.31	−0.105981
$731$	914.259	0.0462587
$732$	16482.3	0.832243
$733$	−24883.8	−1.25390	−0.626948	−	0.779061i	$-0.715696\pi$
$733$	−24883.8	−1.25390	−0.626948	+	0.779061i	$0.715696\pi$
$734$	−65360.9	−3.28680
$735$	754.670	0.0378727
$736$	−9561.22	−0.478847
$737$	4843.61	0.242085
$738$	−14289.8	−0.712757
$739$	−18534.9	−0.922623	−0.461311	−	0.887238i	$-0.652621\pi$
$739$	−18534.9	−0.922623	−0.461311	+	0.887238i	$0.652621\pi$
$740$	−7707.17	−0.382866
$741$	0	0
$742$	−31821.8	−1.57442
$743$	−31108.0	−1.53599	−0.767997	−	0.640454i	$-0.778746\pi$
$743$	−31108.0	−1.53599	−0.767997	+	0.640454i	$0.778746\pi$
$744$	5562.50	0.274101
$745$	3290.79	0.161832
$746$	1636.65	0.0803246
$747$	10070.4	0.493249
$748$	−20133.6	−0.984166
$749$	−22632.4	−1.10410
$750$	−9742.97	−0.474351
$751$	−6637.64	−0.322518	−0.161259	−	0.986912i	$-0.551555\pi$
$751$	−6637.64	−0.322518	−0.161259	+	0.986912i	$0.551555\pi$
$752$	54203.9	2.62848
$753$	7734.45	0.374315
$754$	0	0
$755$	2293.60	0.110560
$756$	56202.5	2.70379
$757$	−4132.13	−0.198395	−0.0991973	−	0.995068i	$-0.531628\pi$
$757$	−4132.13	−0.198395	−0.0991973	+	0.995068i	$0.531628\pi$
$758$	−12739.2	−0.610432
$759$	1872.57	0.0895520
$760$	18483.2	0.882181
$761$	1494.59	0.0711944	0.0355972	−	0.999366i	$-0.488667\pi$
$761$	1494.59	0.0711944	0.0355972	+	0.999366i	$0.488667\pi$
$762$	25804.3	1.22676
$763$	14222.9	0.674842
$764$	−39121.3	−1.85256
$765$	−3094.99	−0.146274
$766$	−27351.8	−1.29016
$767$	0	0
$768$	25333.2	1.19028
$769$	11227.7	0.526504	0.263252	−	0.964727i	$-0.415205\pi$
$769$	11227.7	0.526504	0.263252	+	0.964727i	$0.415205\pi$
$770$	−2559.09	−0.119771
$771$	29276.8	1.36755
$772$	10251.7	0.477936
$773$	22126.9	1.02956	0.514780	−	0.857322i	$-0.327874\pi$
$773$	22126.9	1.02956	0.514780	+	0.857322i	$0.327874\pi$
$774$	657.658	0.0305414
$775$	3592.89	0.166530
$776$	−19403.3	−0.897598
$777$	−14709.0	−0.679130
$778$	−6372.14	−0.293640
$779$	−32329.3	−1.48693
$780$	0	0
$781$	3730.64	0.170925
$782$	24495.0	1.12013
$783$	−36164.8	−1.65060
$784$	11726.2	0.534176
$785$	7024.32	0.319374
$786$	−13698.2	−0.621625
$787$	−17041.5	−0.771875	−0.385938	−	0.922525i	$-0.626122\pi$
$787$	−17041.5	−0.771875	−0.385938	+	0.922525i	$0.626122\pi$
$788$	22552.4	1.01954
$789$	−20689.7	−0.933553
$790$	−2800.03	−0.126102
$791$	15793.1	0.709910
$792$	−8104.50	−0.363612
$793$	0	0
$794$	2199.41	0.0983049
$795$	−2302.36	−0.102713
$796$	−34522.9	−1.53723
$797$	17504.3	0.777960	0.388980	−	0.921246i	$-0.372828\pi$
$797$	17504.3	0.777960	0.388980	+	0.921246i	$0.372828\pi$
$798$	63036.6	2.79633
$799$	−45267.6	−2.00432
$800$	−24202.3	−1.06960
$801$	−19600.9	−0.864622
$802$	−27909.9	−1.22884
$803$	2073.63	0.0911293
$804$	−28650.6	−1.25675
$805$	2161.51	0.0946377
$806$	0	0
$807$	−8052.00	−0.351232
$808$	−26318.1	−1.14587
$809$	5491.89	0.238670	0.119335	−	0.992854i	$-0.461924\pi$
$809$	5491.89	0.238670	0.119335	+	0.992854i	$0.461924\pi$
$810$	1614.95	0.0700536
$811$	21887.8	0.947699	0.473849	−	0.880606i	$-0.342864\pi$
$811$	21887.8	0.947699	0.473849	+	0.880606i	$0.342864\pi$
$812$	−93464.9	−4.03938
$813$	1333.48	0.0575241
$814$	11012.8	0.474201
$815$	−3053.15	−0.131223
$816$	43545.3	1.86812
$817$	1487.89	0.0637145
$818$	−54015.3	−2.30880
$819$	0	0
$820$	−7763.47	−0.330625
$821$	20611.7	0.876193	0.438096	−	0.898928i	$-0.355653\pi$
$821$	20611.7	0.876193	0.438096	+	0.898928i	$0.355653\pi$
$822$	−46867.8	−1.98869
$823$	30946.7	1.31073	0.655366	−	0.755311i	$-0.272514\pi$
$823$	30946.7	1.31073	0.655366	+	0.755311i	$0.272514\pi$
$824$	−60416.7	−2.55427
$825$	4740.03	0.200032
$826$	−75981.5	−3.20065
$827$	−435.745	−0.0183221	−0.00916104	−	0.999958i	$-0.502916\pi$
$827$	−435.745	−0.0183221	−0.00916104	+	0.999958i	$0.502916\pi$
$828$	12232.7	0.513426
$829$	−34150.3	−1.43075	−0.715374	−	0.698742i	$-0.753744\pi$
$829$	−34150.3	−1.43075	−0.715374	+	0.698742i	$0.753744\pi$
$830$	7880.64	0.329567
$831$	−26695.5	−1.11439
$832$	0	0
$833$	−9792.99	−0.407331
$834$	44075.5	1.82999
$835$	−3594.38	−0.148969
$836$	−32766.0	−1.35554
$837$	−4404.25	−0.181879
$838$	−27775.8	−1.14499
$839$	29430.7	1.21104	0.605519	−	0.795831i	$-0.292966\pi$
$839$	29430.7	1.21104	0.605519	+	0.795831i	$0.292966\pi$
$840$	8470.84	0.347943
$841$	35753.1	1.46595
$842$	35939.2	1.47096
$843$	−12755.9	−0.521158
$844$	64403.0	2.62659
$845$	0	0
$846$	−32562.6	−1.32331
$847$	2538.67	0.102987
$848$	−35774.6	−1.44871
$849$	−16958.5	−0.685528
$850$	62004.0	2.50202
$851$	−9301.87	−0.374693
$852$	−22067.3	−0.887338
$853$	−5380.99	−0.215992	−0.107996	−	0.994151i	$-0.534443\pi$
$853$	−5380.99	−0.215992	−0.107996	+	0.994151i	$0.534443\pi$
$854$	−27185.7	−1.08932
$855$	−5036.88	−0.201471
$856$	−56089.9	−2.23962
$857$	19052.3	0.759409	0.379705	−	0.925108i	$-0.376026\pi$
$857$	19052.3	0.759409	0.379705	+	0.925108i	$0.376026\pi$
$858$	0	0
$859$	−32175.1	−1.27800	−0.639000	−	0.769207i	$-0.720652\pi$
$859$	−32175.1	−1.27800	−0.639000	+	0.769207i	$0.720652\pi$
$860$	357.298	0.0141671
$861$	−14816.5	−0.586464
$862$	15071.7	0.595526
$863$	−8470.66	−0.334119	−0.167059	−	0.985947i	$-0.553427\pi$
$863$	−8470.66	−0.334119	−0.167059	+	0.985947i	$0.553427\pi$
$864$	29667.7	1.16819
$865$	4456.69	0.175182
$866$	−9750.65	−0.382610
$867$	−18768.1	−0.735177
$868$	−11382.4	−0.445097
$869$	2777.68	0.108431
$870$	−9740.51	−0.379580
$871$	0	0
$872$	35248.8	1.36889
$873$	5287.59	0.204992
$874$	39863.8	1.54281
$875$	11156.6	0.431041
$876$	−12265.8	−0.473087
$877$	41900.2	1.61330	0.806652	−	0.591026i	$-0.201277\pi$
$877$	41900.2	1.61330	0.806652	+	0.591026i	$0.201277\pi$
$878$	83347.6	3.20370
$879$	−1836.06	−0.0704538
$880$	−2876.98	−0.110208
$881$	19207.7	0.734532	0.367266	−	0.930116i	$-0.380294\pi$
$881$	19207.7	0.734532	0.367266	+	0.930116i	$0.380294\pi$
$882$	−7044.44	−0.268933
$883$	29638.5	1.12957	0.564787	−	0.825237i	$-0.308958\pi$
$883$	29638.5	1.12957	0.564787	+	0.825237i	$0.308958\pi$
$884$	0	0
$885$	−5497.40	−0.208806
$886$	−3874.20	−0.146903
$887$	−42482.3	−1.60814	−0.804068	−	0.594538i	$-0.797335\pi$
$887$	−42482.3	−1.60814	−0.804068	+	0.594538i	$0.797335\pi$
$888$	−36453.5	−1.37759
$889$	−29548.2	−1.11475
$890$	−15338.7	−0.577703
$891$	−1602.06	−0.0602367
$892$	−27089.2	−1.01683
$893$	−73669.9	−2.76066
$894$	27814.4	1.04055
$895$	9993.69	0.373243
$896$	−26913.0	−1.00346
$897$	0	0
$898$	22411.2	0.832820
$899$	7324.27	0.271722
$900$	30964.6	1.14684
$901$	29876.7	1.10470
$902$	11093.3	0.409496
$903$	681.899	0.0251298
$904$	39140.2	1.44003
$905$	−6775.83	−0.248880
$906$	19386.0	0.710879
$907$	−51525.3	−1.88630	−0.943148	−	0.332373i	$-0.892151\pi$
$907$	−51525.3	−1.88630	−0.943148	+	0.332373i	$0.892151\pi$
$908$	34305.9	1.25383
$909$	7171.95	0.261693
$910$	0	0
$911$	−9999.32	−0.363658	−0.181829	−	0.983330i	$-0.558202\pi$
$911$	−9999.32	−0.363658	−0.181829	+	0.983330i	$0.558202\pi$
$912$	70866.8	2.57306
$913$	−7817.73	−0.283384
$914$	−56162.8	−2.03249
$915$	−1966.93	−0.0710653
$916$	−41792.6	−1.50749
$917$	15685.6	0.564869
$918$	−76005.9	−2.73265
$919$	49505.6	1.77697	0.888487	−	0.458902i	$-0.151757\pi$
$919$	49505.6	1.77697	0.888487	+	0.458902i	$0.151757\pi$
$920$	5356.89	0.191969
$921$	4703.26	0.168271
$922$	38130.6	1.36200
$923$	0	0
$924$	−15016.6	−0.534643
$925$	−23545.8	−0.836952
$926$	−29127.6	−1.03369
$927$	16464.2	0.583339
$928$	−49337.4	−1.74524
$929$	−39331.9	−1.38906	−0.694530	−	0.719464i	$-0.744388\pi$
$929$	−39331.9	−1.38906	−0.694530	+	0.719464i	$0.744388\pi$
$930$	−1186.23	−0.0418257
$931$	−15937.4	−0.561039
$932$	30522.8	1.07275
$933$	−35218.0	−1.23578
$934$	−24475.6	−0.857458
$935$	2402.67	0.0840381
$936$	0	0
$937$	−14333.0	−0.499720	−0.249860	−	0.968282i	$-0.580385\pi$
$937$	−14333.0	−0.499720	−0.249860	+	0.968282i	$0.580385\pi$
$938$	47256.1	1.64495
$939$	21446.0	0.745329
$940$	−17690.9	−0.613843
$941$	56634.2	1.96198	0.980990	−	0.194057i	$-0.0621646\pi$
$941$	56634.2	1.96198	0.980990	+	0.194057i	$0.0621646\pi$
$942$	59370.9	2.05351
$943$	−9369.83	−0.323567
$944$	−85419.7	−2.94510
$945$	−6707.00	−0.230877
$946$	−510.545	−0.0175468
$947$	12631.3	0.433434	0.216717	−	0.976234i	$-0.430465\pi$
$947$	12631.3	0.433434	0.216717	+	0.976234i	$0.430465\pi$
$948$	−16430.4	−0.562905
$949$	0	0
$950$	100907.	3.44616
$951$	−14466.8	−0.493289
$952$	−109922.	−3.74222
$953$	−33571.1	−1.14111	−0.570554	−	0.821260i	$-0.693271\pi$
$953$	−33571.1	−1.14111	−0.570554	+	0.821260i	$0.693271\pi$
$954$	21491.3	0.729358
$955$	4668.59	0.158191
$956$	102109.	3.45442
$957$	9662.77	0.326388
$958$	27473.8	0.926553
$959$	53667.8	1.80712
$960$	495.930	0.0166730
$961$	−28899.0	−0.970059
$962$	0	0
$963$	15285.1	0.511480
$964$	64864.9	2.16718
$965$	−1223.40	−0.0408110
$966$	18269.5	0.608502
$967$	−12984.6	−0.431806	−0.215903	−	0.976415i	$-0.569269\pi$
$967$	−12984.6	−0.431806	−0.215903	+	0.976415i	$0.569269\pi$
$968$	6291.59	0.208904
$969$	−59183.4	−1.96207
$970$	4137.83	0.136967
$971$	−40020.8	−1.32269	−0.661343	−	0.750084i	$-0.730013\pi$
$971$	−40020.8	−1.32269	−0.661343	+	0.750084i	$0.730013\pi$
$972$	−62850.4	−2.07400
$973$	−50470.4	−1.66291
$974$	−56832.1	−1.86963
$975$	0	0
$976$	−30562.6	−1.00234
$977$	29379.9	0.962073	0.481037	−	0.876700i	$-0.340260\pi$
$977$	29379.9	0.962073	0.481037	+	0.876700i	$0.340260\pi$
$978$	−25805.8	−0.843741
$979$	15216.3	0.496747
$980$	−3827.16	−0.124749
$981$	−9605.66	−0.312625
$982$	−44070.3	−1.43212
$983$	−35077.8	−1.13816	−0.569078	−	0.822284i	$-0.692700\pi$
$983$	−35077.8	−1.13816	−0.569078	+	0.822284i	$0.692700\pi$
$984$	−36719.8	−1.18962
$985$	−2691.32	−0.0870585
$986$	126398.	4.08249
$987$	−33762.8	−1.08884
$988$	0	0
$989$	431.227	0.0138647
$990$	1728.32	0.0554845
$991$	−18598.3	−0.596159	−0.298079	−	0.954541i	$-0.596346\pi$
$991$	−18598.3	−0.596159	−0.298079	+	0.954541i	$0.596346\pi$
$992$	−6008.45	−0.192307
$993$	−38225.6	−1.22160
$994$	36397.6	1.16143
$995$	4119.84	0.131264
$996$	46243.1	1.47115
$997$	−5466.87	−0.173659	−0.0868293	−	0.996223i	$-0.527673\pi$
$997$	−5466.87	−0.173659	−0.0868293	+	0.996223i	$0.527673\pi$
$998$	32768.5	1.03935
$999$	28863.0	0.914098

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.g.1.17		17
13.3	even	3		143.4.e.b.100.1	✓	34
13.9	even	3		143.4.e.b.133.1	yes	34
13.12	even	2		1859.4.a.h.1.1		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.1	✓	34	13.3	even	3
143.4.e.b.133.1	yes	34	13.9	even	3
1859.4.a.g.1.17		17	1.1	even	1	trivial
1859.4.a.h.1.1		17	13.12	even	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)

\(f(q)\)	\(=\)	\(q+5.11519 q^{2} -3.58195 q^{3} +18.1651 q^{4} -2.16776 q^{5} -18.3223 q^{6} +20.9807 q^{7} +51.9966 q^{8} -14.1696 q^{9} +O(q^{10})\)	\(q+5.11519 q^{2} -3.58195 q^{3} +18.1651 q^{4} -2.16776 q^{5} -18.3223 q^{6} +20.9807 q^{7} +51.9966 q^{8} -14.1696 q^{9} -11.0885 q^{10} +11.0000 q^{11} -65.0666 q^{12} +107.320 q^{14} +7.76481 q^{15} +120.651 q^{16} -100.760 q^{17} -72.4803 q^{18} -163.980 q^{19} -39.3777 q^{20} -75.1519 q^{21} +56.2671 q^{22} -47.5254 q^{23} -186.249 q^{24} -120.301 q^{25} +147.468 q^{27} +381.118 q^{28} -245.239 q^{29} +39.7185 q^{30} -29.8659 q^{31} +201.181 q^{32} -39.4015 q^{33} -515.408 q^{34} -45.4812 q^{35} -257.393 q^{36} +195.724 q^{37} -838.789 q^{38} -112.716 q^{40} +197.154 q^{41} -384.416 q^{42} -9.07360 q^{43} +199.817 q^{44} +30.7164 q^{45} -243.101 q^{46} +449.261 q^{47} -432.167 q^{48} +97.1910 q^{49} -615.361 q^{50} +360.918 q^{51} -296.513 q^{53} +754.324 q^{54} -23.8454 q^{55} +1090.93 q^{56} +587.369 q^{57} -1254.44 q^{58} -707.988 q^{59} +141.049 q^{60} -253.314 q^{61} -152.770 q^{62} -297.289 q^{63} +63.8689 q^{64} -201.546 q^{66} +440.328 q^{67} -1830.32 q^{68} +170.234 q^{69} -232.645 q^{70} +339.149 q^{71} -736.773 q^{72} +188.512 q^{73} +1001.17 q^{74} +430.912 q^{75} -2978.72 q^{76} +230.788 q^{77} +252.516 q^{79} -261.543 q^{80} -145.641 q^{81} +1008.48 q^{82} -710.703 q^{83} -1365.15 q^{84} +218.424 q^{85} -46.4132 q^{86} +878.433 q^{87} +571.963 q^{88} +1383.30 q^{89} +157.120 q^{90} -863.306 q^{92} +106.978 q^{93} +2298.05 q^{94} +355.470 q^{95} -720.621 q^{96} -373.164 q^{97} +497.150 q^{98} -155.866 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9}+O(q^{10}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 127 q^{12} - 148 q^{15} + 126 q^{16} - 74 q^{17} + 90 q^{18} - 159 q^{19} - 222 q^{20} - 184 q^{21} - 215 q^{23} + 214 q^{24} + 95 q^{25} - 192 q^{27} - 358 q^{28} - 157 q^{29} + 829 q^{30} - 394 q^{31} - 553 q^{32} - 66 q^{33} - 702 q^{34} + 58 q^{35} - 700 q^{36} + 88 q^{37} - 1318 q^{38} + 733 q^{40} - 512 q^{41} + 337 q^{42} + 927 q^{43} + 550 q^{44} - 1482 q^{45} - 1361 q^{46} - 143 q^{47} - 178 q^{48} + 1835 q^{49} - 583 q^{50} - 568 q^{51} + 106 q^{53} - 67 q^{54} - 264 q^{55} + 2059 q^{56} + 1298 q^{57} - 1690 q^{58} - 266 q^{59} + 37 q^{60} - 624 q^{61} + 643 q^{62} - 2360 q^{63} - 1589 q^{64} + 176 q^{66} - 676 q^{67} - 413 q^{68} + 764 q^{69} - 1061 q^{70} - 763 q^{71} - 1366 q^{72} - 2374 q^{73} - 1649 q^{74} + 2420 q^{75} - 2101 q^{76} - 682 q^{77} + 2164 q^{79} - 1013 q^{80} + 537 q^{81} + 3152 q^{82} + 777 q^{83} - 3381 q^{84} - 1690 q^{85} + 2894 q^{86} - 4200 q^{87} - 231 q^{88} - 1687 q^{89} - 5399 q^{90} + 5542 q^{92} - 4310 q^{93} + 1777 q^{94} + 1124 q^{95} - 3465 q^{96} - 2047 q^{97} + 1553 q^{98} + 1485 q^{99}+O(q^{100}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 127 * q^12 - 148 * q^15 + 126 * q^16 - 74 * q^17 + 90 * q^18 - 159 * q^19 - 222 * q^20 - 184 * q^21 - 215 * q^23 + 214 * q^24 + 95 * q^25 - 192 * q^27 - 358 * q^28 - 157 * q^29 + 829 * q^30 - 394 * q^31 - 553 * q^32 - 66 * q^33 - 702 * q^34 + 58 * q^35 - 700 * q^36 + 88 * q^37 - 1318 * q^38 + 733 * q^40 - 512 * q^41 + 337 * q^42 + 927 * q^43 + 550 * q^44 - 1482 * q^45 - 1361 * q^46 - 143 * q^47 - 178 * q^48 + 1835 * q^49 - 583 * q^50 - 568 * q^51 + 106 * q^53 - 67 * q^54 - 264 * q^55 + 2059 * q^56 + 1298 * q^57 - 1690 * q^58 - 266 * q^59 + 37 * q^60 - 624 * q^61 + 643 * q^62 - 2360 * q^63 - 1589 * q^64 + 176 * q^66 - 676 * q^67 - 413 * q^68 + 764 * q^69 - 1061 * q^70 - 763 * q^71 - 1366 * q^72 - 2374 * q^73 - 1649 * q^74 + 2420 * q^75 - 2101 * q^76 - 682 * q^77 + 2164 * q^79 - 1013 * q^80 + 537 * q^81 + 3152 * q^82 + 777 * q^83 - 3381 * q^84 - 1690 * q^85 + 2894 * q^86 - 4200 * q^87 - 231 * q^88 - 1687 * q^89 - 5399 * q^90 + 5542 * q^92 - 4310 * q^93 + 1777 * q^94 + 1124 * q^95 - 3465 * q^96 - 2047 * q^97 + 1553 * q^98 + 1485 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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