LMFDB - Embedded newform 825.4.a.bd.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(1,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("825.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.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:	$48.6765757547$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 31x^{5} + 50x^{4} + 272x^{3} - 322x^{2} - 704x + 512 $ x^7 - 2x^6 - 31x^5 + 50x^4 + 272x^3 - 322x^2 - 704x + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 5 $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.20690$ of defining polynomial
Character	$\chi$	$=$	825.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20690 q^{2} -3.00000 q^{3} -3.12958 q^{4} +6.62071 q^{6} +1.50972 q^{7} +24.5619 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.20690 q^{2} -3.00000 q^{3} -3.12958 q^{4} +6.62071 q^{6} +1.50972 q^{7} +24.5619 q^{8} +9.00000 q^{9} +11.0000 q^{11} +9.38875 q^{12} -68.3212 q^{13} -3.33181 q^{14} -29.1690 q^{16} +113.151 q^{17} -19.8621 q^{18} -72.3208 q^{19} -4.52917 q^{21} -24.2759 q^{22} +144.617 q^{23} -73.6857 q^{24} +150.778 q^{26} -27.0000 q^{27} -4.72480 q^{28} -133.492 q^{29} +177.784 q^{31} -132.122 q^{32} -33.0000 q^{33} -249.713 q^{34} -28.1663 q^{36} +39.8169 q^{37} +159.605 q^{38} +204.964 q^{39} -366.404 q^{41} +9.99542 q^{42} -427.219 q^{43} -34.4254 q^{44} -319.156 q^{46} -340.290 q^{47} +87.5071 q^{48} -340.721 q^{49} -339.453 q^{51} +213.817 q^{52} +659.877 q^{53} +59.5863 q^{54} +37.0816 q^{56} +216.963 q^{57} +294.603 q^{58} -525.541 q^{59} -462.358 q^{61} -392.353 q^{62} +13.5875 q^{63} +524.933 q^{64} +72.8278 q^{66} +514.730 q^{67} -354.115 q^{68} -433.852 q^{69} -848.333 q^{71} +221.057 q^{72} +987.550 q^{73} -87.8721 q^{74} +226.334 q^{76} +16.6069 q^{77} -452.335 q^{78} +442.561 q^{79} +81.0000 q^{81} +808.617 q^{82} +603.960 q^{83} +14.1744 q^{84} +942.831 q^{86} +400.475 q^{87} +270.181 q^{88} +1001.29 q^{89} -103.146 q^{91} -452.592 q^{92} -533.353 q^{93} +750.987 q^{94} +396.366 q^{96} -468.418 q^{97} +751.937 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 5 q^{2} - 21 q^{3} + 13 q^{4} - 15 q^{6} + 34 q^{7} + 75 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q + 5 * q^2 - 21 * q^3 + 13 * q^4 - 15 * q^6 + 34 * q^7 + 75 * q^8 + 63 * q^9	\( 7 q + 5 q^{2} - 21 q^{3} + 13 q^{4} - 15 q^{6} + 34 q^{7} + 75 q^{8} + 63 q^{9} + 77 q^{11} - 39 q^{12} + 80 q^{13} + 42 q^{14} - 43 q^{16} + 162 q^{17} + 45 q^{18} + 58 q^{19} - 102 q^{21} + 55 q^{22} + 324 q^{23} - 225 q^{24} - 200 q^{26} - 189 q^{27} - 168 q^{28} + 64 q^{29} - 348 q^{31} - 75 q^{32} - 231 q^{33} + 206 q^{34} + 117 q^{36} + 664 q^{37} + 334 q^{38} - 240 q^{39} - 332 q^{41} - 126 q^{42} + 774 q^{43} + 143 q^{44} - 328 q^{46} + 872 q^{47} + 129 q^{48} - 417 q^{49} - 486 q^{51} + 134 q^{52} + 1628 q^{53} - 135 q^{54} - 1618 q^{56} - 174 q^{57} + 1568 q^{58} - 332 q^{59} + 22 q^{61} - 260 q^{62} + 306 q^{63} + 561 q^{64} - 165 q^{66} + 1524 q^{67} + 2324 q^{68} - 972 q^{69} - 516 q^{71} + 675 q^{72} + 1700 q^{73} + 1628 q^{74} + 2794 q^{76} + 374 q^{77} + 600 q^{78} + 1746 q^{79} + 567 q^{81} + 364 q^{82} + 2344 q^{83} + 504 q^{84} + 1270 q^{86} - 192 q^{87} + 825 q^{88} - 2226 q^{89} + 1072 q^{91} + 4184 q^{92} + 1044 q^{93} + 4736 q^{94} + 225 q^{96} + 1048 q^{97} + 3057 q^{98} + 693 q^{99}+O(q^{100}) \) 7 * q + 5 * q^2 - 21 * q^3 + 13 * q^4 - 15 * q^6 + 34 * q^7 + 75 * q^8 + 63 * q^9 + 77 * q^11 - 39 * q^12 + 80 * q^13 + 42 * q^14 - 43 * q^16 + 162 * q^17 + 45 * q^18 + 58 * q^19 - 102 * q^21 + 55 * q^22 + 324 * q^23 - 225 * q^24 - 200 * q^26 - 189 * q^27 - 168 * q^28 + 64 * q^29 - 348 * q^31 - 75 * q^32 - 231 * q^33 + 206 * q^34 + 117 * q^36 + 664 * q^37 + 334 * q^38 - 240 * q^39 - 332 * q^41 - 126 * q^42 + 774 * q^43 + 143 * q^44 - 328 * q^46 + 872 * q^47 + 129 * q^48 - 417 * q^49 - 486 * q^51 + 134 * q^52 + 1628 * q^53 - 135 * q^54 - 1618 * q^56 - 174 * q^57 + 1568 * q^58 - 332 * q^59 + 22 * q^61 - 260 * q^62 + 306 * q^63 + 561 * q^64 - 165 * q^66 + 1524 * q^67 + 2324 * q^68 - 972 * q^69 - 516 * q^71 + 675 * q^72 + 1700 * q^73 + 1628 * q^74 + 2794 * q^76 + 374 * q^77 + 600 * q^78 + 1746 * q^79 + 567 * q^81 + 364 * q^82 + 2344 * q^83 + 504 * q^84 + 1270 * q^86 - 192 * q^87 + 825 * q^88 - 2226 * q^89 + 1072 * q^91 + 4184 * q^92 + 1044 * q^93 + 4736 * q^94 + 225 * q^96 + 1048 * q^97 + 3057 * q^98 + 693 * 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 $

$2$	−2.20690	−0.780258	−0.390129	−	0.920760i	$-0.627570\pi$
$2$	−2.20690	−0.780258	−0.390129	+	0.920760i	$0.627570\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−3.12958	−0.391198
$5$	0	0
$5$	0	0
$6$	6.62071	0.450482
$7$	1.50972	0.0815173	0.0407587	−	0.999169i	$-0.487023\pi$
$7$	1.50972	0.0815173	0.0407587	+	0.999169i	$0.487023\pi$
$8$	24.5619	1.08549
$9$	9.00000	0.333333
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	9.38875	0.225858
$13$	−68.3212	−1.45761	−0.728804	−	0.684723i	$-0.759923\pi$
$13$	−68.3212	−1.45761	−0.728804	+	0.684723i	$0.759923\pi$
$14$	−3.33181	−0.0636045
$15$	0	0
$16$	−29.1690	−0.455766
$17$	113.151	1.61430	0.807151	−	0.590345i	$-0.201008\pi$
$17$	113.151	1.61430	0.807151	+	0.590345i	$0.201008\pi$
$18$	−19.8621	−0.260086
$19$	−72.3208	−0.873239	−0.436619	−	0.899646i	$-0.643824\pi$
$19$	−72.3208	−0.873239	−0.436619	+	0.899646i	$0.643824\pi$
$20$	0	0
$21$	−4.52917	−0.0470640
$22$	−24.2759	−0.235257
$23$	144.617	1.31108	0.655539	−	0.755162i	$-0.272442\pi$
$23$	144.617	1.31108	0.655539	+	0.755162i	$0.272442\pi$
$24$	−73.6857	−0.626710
$25$	0	0
$26$	150.778	1.13731
$27$	−27.0000	−0.192450
$28$	−4.72480	−0.0318894
$29$	−133.492	−0.854785	−0.427393	−	0.904066i	$-0.640568\pi$
$29$	−133.492	−0.854785	−0.427393	+	0.904066i	$0.640568\pi$
$30$	0	0
$31$	177.784	1.03003	0.515016	−	0.857180i	$-0.327786\pi$
$31$	177.784	1.03003	0.515016	+	0.857180i	$0.327786\pi$
$32$	−132.122	−0.729878
$33$	−33.0000	−0.174078
$34$	−249.713	−1.25957
$35$	0	0
$36$	−28.1663	−0.130399
$37$	39.8169	0.176915	0.0884576	−	0.996080i	$-0.471806\pi$
$37$	39.8169	0.176915	0.0884576	+	0.996080i	$0.471806\pi$
$38$	159.605	0.681351
$39$	204.964	0.841550
$40$	0	0
$41$	−366.404	−1.39568	−0.697838	−	0.716256i	$-0.745854\pi$
$41$	−366.404	−1.39568	−0.697838	+	0.716256i	$0.745854\pi$
$42$	9.99542	0.0367221
$43$	−427.219	−1.51512	−0.757562	−	0.652763i	$-0.773610\pi$
$43$	−427.219	−1.51512	−0.757562	+	0.652763i	$0.773610\pi$
$44$	−34.4254	−0.117951
$45$	0	0
$46$	−319.156	−1.02298
$47$	−340.290	−1.05609	−0.528047	−	0.849215i	$-0.677076\pi$
$47$	−340.290	−1.05609	−0.528047	+	0.849215i	$0.677076\pi$
$48$	87.5071	0.263137
$49$	−340.721	−0.993355
$50$	0	0
$51$	−339.453	−0.932018
$52$	213.817	0.570213
$53$	659.877	1.71021	0.855105	−	0.518455i	$-0.173493\pi$
$53$	659.877	1.71021	0.855105	+	0.518455i	$0.173493\pi$
$54$	59.5863	0.150161
$55$	0	0
$56$	37.0816	0.0884865
$57$	216.963	0.504165
$58$	294.603	0.666953
$59$	−525.541	−1.15965	−0.579827	−	0.814740i	$-0.696880\pi$
$59$	−525.541	−1.15965	−0.579827	+	0.814740i	$0.696880\pi$
$60$	0	0
$61$	−462.358	−0.970473	−0.485237	−	0.874383i	$-0.661267\pi$
$61$	−462.358	−0.970473	−0.485237	+	0.874383i	$0.661267\pi$
$62$	−392.353	−0.803691
$63$	13.5875	0.0271724
$64$	524.933	1.02526
$65$	0	0
$66$	72.8278	0.135825
$67$	514.730	0.938571	0.469285	−	0.883047i	$-0.344512\pi$
$67$	514.730	0.938571	0.469285	+	0.883047i	$0.344512\pi$
$68$	−354.115	−0.631512
$69$	−433.852	−0.756951
$70$	0	0
$71$	−848.333	−1.41801	−0.709004	−	0.705204i	$-0.750855\pi$
$71$	−848.333	−1.41801	−0.709004	+	0.705204i	$0.750855\pi$
$72$	221.057	0.361831
$73$	987.550	1.58334	0.791671	−	0.610947i	$-0.209211\pi$
$73$	987.550	1.58334	0.791671	+	0.610947i	$0.209211\pi$
$74$	−87.8721	−0.138039
$75$	0	0
$76$	226.334	0.341609
$77$	16.6069	0.0245784
$78$	−452.335	−0.656626
$79$	442.561	0.630279	0.315139	−	0.949045i	$-0.397949\pi$
$79$	442.561	0.630279	0.315139	+	0.949045i	$0.397949\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	808.617	1.08899
$83$	603.960	0.798713	0.399357	−	0.916796i	$-0.369234\pi$
$83$	603.960	0.798713	0.399357	+	0.916796i	$0.369234\pi$
$84$	14.1744	0.0184114
$85$	0	0
$86$	942.831	1.18219
$87$	400.475	0.493511
$88$	270.181	0.327288
$89$	1001.29	1.19254	0.596270	−	0.802784i	$-0.296649\pi$
$89$	1001.29	1.19254	0.596270	+	0.802784i	$0.296649\pi$
$90$	0	0
$91$	−103.146	−0.118820
$92$	−452.592	−0.512891
$93$	−533.353	−0.594690
$94$	750.987	0.824025
$95$	0	0
$96$	396.366	0.421395
$97$	−468.418	−0.490315	−0.245158	−	0.969483i	$-0.578840\pi$
$97$	−468.418	−0.490315	−0.245158	+	0.969483i	$0.578840\pi$
$98$	751.937	0.775073
$99$	99.0000	0.100504
$100$	0	0
$101$	1577.43	1.55406	0.777031	−	0.629462i	$-0.216725\pi$
$101$	1577.43	1.55406	0.777031	+	0.629462i	$0.216725\pi$
$102$	749.139	0.727214
$103$	776.371	0.742700	0.371350	−	0.928493i	$-0.378895\pi$
$103$	776.371	0.742700	0.371350	+	0.928493i	$0.378895\pi$
$104$	−1678.10	−1.58222
$105$	0	0
$106$	−1456.28	−1.33440
$107$	−409.524	−0.370002	−0.185001	−	0.982738i	$-0.559229\pi$
$107$	−409.524	−0.370002	−0.185001	+	0.982738i	$0.559229\pi$
$108$	84.4988	0.0752861
$109$	374.126	0.328760	0.164380	−	0.986397i	$-0.447438\pi$
$109$	374.126	0.328760	0.164380	+	0.986397i	$0.447438\pi$
$110$	0	0
$111$	−119.451	−0.102142
$112$	−44.0371	−0.0371528
$113$	1477.62	1.23012	0.615058	−	0.788482i	$-0.289133\pi$
$113$	1477.62	1.23012	0.615058	+	0.788482i	$0.289133\pi$
$114$	−478.815	−0.393378
$115$	0	0
$116$	417.773	0.334390
$117$	−614.891	−0.485869
$118$	1159.82	0.904828
$119$	170.826	0.131594
$120$	0	0
$121$	121.000	0.0909091
$122$	1020.38	0.757219
$123$	1099.21	0.805793
$124$	−556.391	−0.402947
$125$	0	0
$126$	−29.9863	−0.0212015
$127$	566.909	0.396103	0.198051	−	0.980192i	$-0.436539\pi$
$127$	566.909	0.396103	0.198051	+	0.980192i	$0.436539\pi$
$128$	−101.498	−0.0700880
$129$	1281.66	0.874758
$130$	0	0
$131$	328.369	0.219006	0.109503	−	0.993986i	$-0.465074\pi$
$131$	328.369	0.219006	0.109503	+	0.993986i	$0.465074\pi$
$132$	103.276	0.0680988
$133$	−109.184	−0.0711841
$134$	−1135.96	−0.732327
$135$	0	0
$136$	2779.20	1.75231
$137$	−635.136	−0.396082	−0.198041	−	0.980194i	$-0.563458\pi$
$137$	−635.136	−0.396082	−0.198041	+	0.980194i	$0.563458\pi$
$138$	957.468	0.590617
$139$	−573.459	−0.349929	−0.174965	−	0.984575i	$-0.555981\pi$
$139$	−573.459	−0.349929	−0.174965	+	0.984575i	$0.555981\pi$
$140$	0	0
$141$	1020.87	0.609736
$142$	1872.19	1.10641
$143$	−751.533	−0.439485
$144$	−262.521	−0.151922
$145$	0	0
$146$	−2179.43	−1.23542
$147$	1022.16	0.573514
$148$	−124.610	−0.0692089
$149$	−844.518	−0.464333	−0.232167	−	0.972676i	$-0.574581\pi$
$149$	−844.518	−0.464333	−0.232167	+	0.972676i	$0.574581\pi$
$150$	0	0
$151$	25.5488	0.0137691	0.00688455	−	0.999976i	$-0.497809\pi$
$151$	25.5488	0.0137691	0.00688455	+	0.999976i	$0.497809\pi$
$152$	−1776.34	−0.947895
$153$	1018.36	0.538101
$154$	−36.6499	−0.0191775
$155$	0	0
$156$	−641.451	−0.329213
$157$	−964.739	−0.490411	−0.245206	−	0.969471i	$-0.578855\pi$
$157$	−964.739	−0.490411	−0.245206	+	0.969471i	$0.578855\pi$
$158$	−976.689	−0.491780
$159$	−1979.63	−0.987390
$160$	0	0
$161$	218.332	0.106876
$162$	−178.759	−0.0866953
$163$	1619.81	0.778363	0.389182	−	0.921161i	$-0.372758\pi$
$163$	1619.81	0.778363	0.389182	+	0.921161i	$0.372758\pi$
$164$	1146.69	0.545985
$165$	0	0
$166$	−1332.88	−0.623202
$167$	2814.68	1.30423	0.652116	−	0.758119i	$-0.273881\pi$
$167$	2814.68	1.30423	0.652116	+	0.758119i	$0.273881\pi$
$168$	−111.245	−0.0510877
$169$	2470.79	1.12462
$170$	0	0
$171$	−650.888	−0.291080
$172$	1337.02	0.592714
$173$	−3386.43	−1.48824	−0.744119	−	0.668047i	$-0.767130\pi$
$173$	−3386.43	−1.48824	−0.744119	+	0.668047i	$0.767130\pi$
$174$	−883.809	−0.385065
$175$	0	0
$176$	−320.859	−0.137419
$177$	1576.62	0.669526
$178$	−2209.74	−0.930489
$179$	2759.40	1.15222	0.576110	−	0.817372i	$-0.304570\pi$
$179$	2759.40	1.15222	0.576110	+	0.817372i	$0.304570\pi$
$180$	0	0
$181$	2520.55	1.03509	0.517544	−	0.855657i	$-0.326847\pi$
$181$	2520.55	1.03509	0.517544	+	0.855657i	$0.326847\pi$
$182$	227.633	0.0927104
$183$	1387.07	0.560303
$184$	3552.07	1.42317
$185$	0	0
$186$	1177.06	0.464011
$187$	1244.66	0.486730
$188$	1064.97	0.413142
$189$	−40.7625	−0.0156880
$190$	0	0
$191$	3747.78	1.41979	0.709894	−	0.704308i	$-0.248743\pi$
$191$	3747.78	1.41979	0.709894	+	0.704308i	$0.248743\pi$
$192$	−1574.80	−0.591933
$193$	2544.51	0.949004	0.474502	−	0.880254i	$-0.342628\pi$
$193$	2544.51	0.949004	0.474502	+	0.880254i	$0.342628\pi$
$194$	1033.75	0.382572
$195$	0	0
$196$	1066.31	0.388599
$197$	−2239.70	−0.810011	−0.405005	−	0.914314i	$-0.632730\pi$
$197$	−2239.70	−0.810011	−0.405005	+	0.914314i	$0.632730\pi$
$198$	−218.483	−0.0784188
$199$	1074.20	0.382654	0.191327	−	0.981526i	$-0.438721\pi$
$199$	1074.20	0.382654	0.191327	+	0.981526i	$0.438721\pi$
$200$	0	0
$201$	−1544.19	−0.541884
$202$	−3481.24	−1.21257
$203$	−201.535	−0.0696798
$204$	1062.35	0.364603
$205$	0	0
$206$	−1713.38	−0.579498
$207$	1301.56	0.437026
$208$	1992.86	0.664328
$209$	−795.529	−0.263291
$210$	0	0
$211$	4873.15	1.58996	0.794980	−	0.606636i	$-0.207482\pi$
$211$	4873.15	1.58996	0.794980	+	0.606636i	$0.207482\pi$
$212$	−2065.14	−0.669031
$213$	2545.00	0.818688
$214$	903.779	0.288697
$215$	0	0
$216$	−663.171	−0.208903
$217$	268.405	0.0839655
$218$	−825.660	−0.256517
$219$	−2962.65	−0.914143
$220$	0	0
$221$	−7730.61	−2.35302
$222$	263.616	0.0796971
$223$	−1941.68	−0.583069	−0.291534	−	0.956560i	$-0.594166\pi$
$223$	−1941.68	−0.583069	−0.291534	+	0.956560i	$0.594166\pi$
$224$	−199.468	−0.0594977
$225$	0	0
$226$	−3260.97	−0.959807
$227$	−1347.48	−0.393987	−0.196994	−	0.980405i	$-0.563118\pi$
$227$	−1347.48	−0.393987	−0.196994	+	0.980405i	$0.563118\pi$
$228$	−679.003	−0.197228
$229$	−818.085	−0.236072	−0.118036	−	0.993009i	$-0.537660\pi$
$229$	−818.085	−0.236072	−0.118036	+	0.993009i	$0.537660\pi$
$230$	0	0
$231$	−49.8208	−0.0141903
$232$	−3278.81	−0.927863
$233$	−217.090	−0.0610389	−0.0305195	−	0.999534i	$-0.509716\pi$
$233$	−217.090	−0.0610389	−0.0305195	+	0.999534i	$0.509716\pi$
$234$	1357.00	0.379103
$235$	0	0
$236$	1644.72	0.453654
$237$	−1327.68	−0.363891
$238$	−376.997	−0.102677
$239$	3964.48	1.07297	0.536487	−	0.843909i	$-0.319751\pi$
$239$	3964.48	1.07297	0.536487	+	0.843909i	$0.319751\pi$
$240$	0	0
$241$	3973.08	1.06194	0.530972	−	0.847390i	$-0.321827\pi$
$241$	3973.08	1.06194	0.530972	+	0.847390i	$0.321827\pi$
$242$	−267.035	−0.0709325
$243$	−243.000	−0.0641500
$244$	1446.99	0.379647
$245$	0	0
$246$	−2425.85	−0.628726
$247$	4941.05	1.27284
$248$	4366.72	1.11809
$249$	−1811.88	−0.461137
$250$	0	0
$251$	−4308.81	−1.08355	−0.541773	−	0.840525i	$-0.682247\pi$
$251$	−4308.81	−1.08355	−0.541773	+	0.840525i	$0.682247\pi$
$252$	−42.5232	−0.0106298
$253$	1590.79	0.395305
$254$	−1251.11	−0.309062
$255$	0	0
$256$	−3975.46	−0.970572
$257$	6343.46	1.53967	0.769833	−	0.638245i	$-0.220339\pi$
$257$	6343.46	1.53967	0.769833	+	0.638245i	$0.220339\pi$
$258$	−2828.49	−0.682536
$259$	60.1125	0.0144217
$260$	0	0
$261$	−1201.42	−0.284928
$262$	−724.679	−0.170881
$263$	−4404.34	−1.03264	−0.516318	−	0.856397i	$-0.672698\pi$
$263$	−4404.34	−1.03264	−0.516318	+	0.856397i	$0.672698\pi$
$264$	−810.543	−0.188960
$265$	0	0
$266$	240.959	0.0555419
$267$	−3003.86	−0.688514
$268$	−1610.89	−0.367167
$269$	−4817.34	−1.09189	−0.545945	−	0.837821i	$-0.683829\pi$
$269$	−4817.34	−1.09189	−0.545945	+	0.837821i	$0.683829\pi$
$270$	0	0
$271$	−2171.29	−0.486702	−0.243351	−	0.969938i	$-0.578247\pi$
$271$	−2171.29	−0.486702	−0.243351	+	0.969938i	$0.578247\pi$
$272$	−3300.50	−0.735744
$273$	309.438	0.0686009
$274$	1401.68	0.309046
$275$	0	0
$276$	1357.78	0.296118
$277$	−1351.39	−0.293131	−0.146565	−	0.989201i	$-0.546822\pi$
$277$	−1351.39	−0.293131	−0.146565	+	0.989201i	$0.546822\pi$
$278$	1265.57	0.273035
$279$	1600.06	0.343344
$280$	0	0
$281$	−3118.19	−0.661978	−0.330989	−	0.943635i	$-0.607382\pi$
$281$	−3118.19	−0.661978	−0.330989	+	0.943635i	$0.607382\pi$
$282$	−2252.96	−0.475751
$283$	4164.03	0.874651	0.437325	−	0.899303i	$-0.355926\pi$
$283$	4164.03	0.874651	0.437325	+	0.899303i	$0.355926\pi$
$284$	2654.93	0.554722
$285$	0	0
$286$	1658.56	0.342912
$287$	−553.168	−0.113772
$288$	−1189.10	−0.243293
$289$	7890.13	1.60597
$290$	0	0
$291$	1405.25	0.283084
$292$	−3090.62	−0.619401
$293$	−1431.01	−0.285326	−0.142663	−	0.989771i	$-0.545567\pi$
$293$	−1431.01	−0.285326	−0.142663	+	0.989771i	$0.545567\pi$
$294$	−2255.81	−0.447488
$295$	0	0
$296$	977.980	0.192040
$297$	−297.000	−0.0580259
$298$	1863.77	0.362299
$299$	−9880.43	−1.91104
$300$	0	0
$301$	−644.982	−0.123509
$302$	−56.3837	−0.0107434
$303$	−4732.29	−0.897238
$304$	2109.53	0.397993
$305$	0	0
$306$	−2247.42	−0.419857
$307$	8616.73	1.60190	0.800949	−	0.598733i	$-0.204329\pi$
$307$	8616.73	1.60190	0.800949	+	0.598733i	$0.204329\pi$
$308$	−51.9728	−0.00961502
$309$	−2329.11	−0.428798
$310$	0	0
$311$	6469.81	1.17964	0.589822	−	0.807534i	$-0.299198\pi$
$311$	6469.81	1.17964	0.589822	+	0.807534i	$0.299198\pi$
$312$	5034.30	0.913497
$313$	−3751.51	−0.677470	−0.338735	−	0.940882i	$-0.609999\pi$
$313$	−3751.51	−0.677470	−0.338735	+	0.940882i	$0.609999\pi$
$314$	2129.09	0.382647
$315$	0	0
$316$	−1385.03	−0.246564
$317$	4014.08	0.711208	0.355604	−	0.934637i	$-0.384275\pi$
$317$	4014.08	0.711208	0.355604	+	0.934637i	$0.384275\pi$
$318$	4368.85	0.770419
$319$	−1468.41	−0.257727
$320$	0	0
$321$	1228.57	0.213620
$322$	−481.837	−0.0833904
$323$	−8183.17	−1.40967
$324$	−253.496	−0.0434665
$325$	0	0
$326$	−3574.76	−0.607324
$327$	−1122.38	−0.189809
$328$	−8999.58	−1.51500
$329$	−513.743	−0.0860899
$330$	0	0
$331$	7277.84	1.20854	0.604269	−	0.796780i	$-0.293465\pi$
$331$	7277.84	1.20854	0.604269	+	0.796780i	$0.293465\pi$
$332$	−1890.14	−0.312455
$333$	358.352	0.0589718
$334$	−6211.73	−1.01764
$335$	0	0
$336$	132.111	0.0214502
$337$	839.290	0.135665	0.0678324	−	0.997697i	$-0.478392\pi$
$337$	839.290	0.135665	0.0678324	+	0.997697i	$0.478392\pi$
$338$	−5452.79	−0.877493
$339$	−4432.87	−0.710208
$340$	0	0
$341$	1955.63	0.310566
$342$	1436.44	0.227117
$343$	−1032.23	−0.162493
$344$	−10493.3	−1.64466
$345$	0	0
$346$	7473.51	1.16121
$347$	2255.56	0.348948	0.174474	−	0.984662i	$-0.444178\pi$
$347$	2255.56	0.348948	0.174474	+	0.984662i	$0.444178\pi$
$348$	−1253.32	−0.193060
$349$	10347.5	1.58708	0.793540	−	0.608518i	$-0.208236\pi$
$349$	10347.5	1.58708	0.793540	+	0.608518i	$0.208236\pi$
$350$	0	0
$351$	1844.67	0.280517
$352$	−1453.34	−0.220066
$353$	2178.70	0.328500	0.164250	−	0.986419i	$-0.447480\pi$
$353$	2178.70	0.328500	0.164250	+	0.986419i	$0.447480\pi$
$354$	−3479.45	−0.522403
$355$	0	0
$356$	−3133.61	−0.466520
$357$	−512.479	−0.0759756
$358$	−6089.72	−0.899028
$359$	−6432.48	−0.945665	−0.472832	−	0.881152i	$-0.656768\pi$
$359$	−6432.48	−0.945665	−0.472832	+	0.881152i	$0.656768\pi$
$360$	0	0
$361$	−1628.70	−0.237454
$362$	−5562.60	−0.807635
$363$	−363.000	−0.0524864
$364$	322.804	0.0464823
$365$	0	0
$366$	−3061.14	−0.437181
$367$	−7654.12	−1.08867	−0.544335	−	0.838868i	$-0.683218\pi$
$367$	−7654.12	−1.08867	−0.544335	+	0.838868i	$0.683218\pi$
$368$	−4218.34	−0.597544
$369$	−3297.64	−0.465225
$370$	0	0
$371$	996.231	0.139412
$372$	1669.17	0.232641
$373$	361.440	0.0501734	0.0250867	−	0.999685i	$-0.492014\pi$
$373$	361.440	0.0501734	0.0250867	+	0.999685i	$0.492014\pi$
$374$	−2746.84	−0.379775
$375$	0	0
$376$	−8358.17	−1.14638
$377$	9120.31	1.24594
$378$	89.9588	0.0122407
$379$	−8972.22	−1.21602	−0.608010	−	0.793929i	$-0.708032\pi$
$379$	−8972.22	−1.21602	−0.608010	+	0.793929i	$0.708032\pi$
$380$	0	0
$381$	−1700.73	−0.228690
$382$	−8270.98	−1.10780
$383$	8031.77	1.07155	0.535776	−	0.844360i	$-0.320019\pi$
$383$	8031.77	1.07155	0.535776	+	0.844360i	$0.320019\pi$
$384$	304.495	0.0404653
$385$	0	0
$386$	−5615.48	−0.740468
$387$	−3844.97	−0.505041
$388$	1465.95	0.191810
$389$	−1091.68	−0.142289	−0.0711443	−	0.997466i	$-0.522665\pi$
$389$	−1091.68	−0.142289	−0.0711443	+	0.997466i	$0.522665\pi$
$390$	0	0
$391$	16363.6	2.11647
$392$	−8368.75	−1.07828
$393$	−985.108	−0.126443
$394$	4942.80	0.632017
$395$	0	0
$396$	−309.829	−0.0393169
$397$	545.504	0.0689623	0.0344812	−	0.999405i	$-0.489022\pi$
$397$	545.504	0.0689623	0.0344812	+	0.999405i	$0.489022\pi$
$398$	−2370.66	−0.298569
$399$	327.553	0.0410981
$400$	0	0
$401$	6886.67	0.857616	0.428808	−	0.903396i	$-0.358934\pi$
$401$	6886.67	0.857616	0.428808	+	0.903396i	$0.358934\pi$
$402$	3407.87	0.422809
$403$	−12146.4	−1.50138
$404$	−4936.70	−0.607946
$405$	0	0
$406$	444.768	0.0543682
$407$	437.986	0.0533420
$408$	−8337.61	−1.01170
$409$	9815.16	1.18662	0.593311	−	0.804973i	$-0.297820\pi$
$409$	9815.16	1.18662	0.593311	+	0.804973i	$0.297820\pi$
$410$	0	0
$411$	1905.41	0.228678
$412$	−2429.72	−0.290543
$413$	−793.420	−0.0945318
$414$	−2872.40	−0.340993
$415$	0	0
$416$	9026.74	1.06388
$417$	1720.38	0.202032
$418$	1755.65	0.205435
$419$	−2666.80	−0.310935	−0.155467	−	0.987841i	$-0.549688\pi$
$419$	−2666.80	−0.310935	−0.155467	+	0.987841i	$0.549688\pi$
$420$	0	0
$421$	−8269.30	−0.957295	−0.478647	−	0.878007i	$-0.658873\pi$
$421$	−8269.30	−0.957295	−0.478647	+	0.878007i	$0.658873\pi$
$422$	−10754.6	−1.24058
$423$	−3062.61	−0.352031
$424$	16207.8	1.85642
$425$	0	0
$426$	−5616.56	−0.638787
$427$	−698.032	−0.0791104
$428$	1281.64	0.144744
$429$	2254.60	0.253737
$430$	0	0
$431$	11805.7	1.31940	0.659698	−	0.751531i	$-0.270684\pi$
$431$	11805.7	1.31940	0.659698	+	0.751531i	$0.270684\pi$
$432$	787.564	0.0877122
$433$	−12938.9	−1.43604	−0.718020	−	0.696023i	$-0.754951\pi$
$433$	−12938.9	−1.43604	−0.718020	+	0.696023i	$0.754951\pi$
$434$	−592.343	−0.0655147
$435$	0	0
$436$	−1170.86	−0.128610
$437$	−10458.8	−1.14488
$438$	6538.28	0.713267
$439$	−474.875	−0.0516277	−0.0258138	−	0.999667i	$-0.508218\pi$
$439$	−474.875	−0.0516277	−0.0258138	+	0.999667i	$0.508218\pi$
$440$	0	0
$441$	−3066.49	−0.331118
$442$	17060.7	1.83596
$443$	3691.55	0.395916	0.197958	−	0.980210i	$-0.436569\pi$
$443$	3691.55	0.395916	0.197958	+	0.980210i	$0.436569\pi$
$444$	373.831	0.0399578
$445$	0	0
$446$	4285.09	0.454944
$447$	2533.56	0.268083
$448$	792.502	0.0835763
$449$	15741.4	1.65453	0.827266	−	0.561811i	$-0.189895\pi$
$449$	15741.4	1.65453	0.827266	+	0.561811i	$0.189895\pi$
$450$	0	0
$451$	−4030.44	−0.420812
$452$	−4624.35	−0.481219
$453$	−76.6465	−0.00794959
$454$	2973.75	0.307412
$455$	0	0
$456$	5329.01	0.547267
$457$	−3995.03	−0.408927	−0.204463	−	0.978874i	$-0.565545\pi$
$457$	−3995.03	−0.408927	−0.204463	+	0.978874i	$0.565545\pi$
$458$	1805.43	0.184197
$459$	−3055.07	−0.310673
$460$	0	0
$461$	−11467.6	−1.15856	−0.579281	−	0.815128i	$-0.696667\pi$
$461$	−11467.6	−1.15856	−0.579281	+	0.815128i	$0.696667\pi$
$462$	109.950	0.0110721
$463$	14675.0	1.47301	0.736507	−	0.676430i	$-0.236474\pi$
$463$	14675.0	1.47301	0.736507	+	0.676430i	$0.236474\pi$
$464$	3893.82	0.389582
$465$	0	0
$466$	479.097	0.0476261
$467$	−1509.15	−0.149540	−0.0747700	−	0.997201i	$-0.523822\pi$
$467$	−1509.15	−0.149540	−0.0747700	+	0.997201i	$0.523822\pi$
$468$	1924.35	0.190071
$469$	777.098	0.0765097
$470$	0	0
$471$	2894.22	0.283139
$472$	−12908.3	−1.25880
$473$	−4699.41	−0.456827
$474$	2930.07	0.283929
$475$	0	0
$476$	−534.616	−0.0514791
$477$	5938.90	0.570070
$478$	−8749.22	−0.837196
$479$	−2021.17	−0.192797	−0.0963986	−	0.995343i	$-0.530732\pi$
$479$	−2021.17	−0.192797	−0.0963986	+	0.995343i	$0.530732\pi$
$480$	0	0
$481$	−2720.34	−0.257873
$482$	−8768.19	−0.828589
$483$	−654.995	−0.0617046
$484$	−378.680	−0.0355635
$485$	0	0
$486$	536.277	0.0500535
$487$	5048.84	0.469784	0.234892	−	0.972021i	$-0.424526\pi$
$487$	5048.84	0.469784	0.234892	+	0.972021i	$0.424526\pi$
$488$	−11356.4	−1.05344
$489$	−4859.42	−0.449388
$490$	0	0
$491$	−18950.5	−1.74180	−0.870899	−	0.491462i	$-0.836463\pi$
$491$	−18950.5	−1.74180	−0.870899	+	0.491462i	$0.836463\pi$
$492$	−3440.08	−0.315225
$493$	−15104.7	−1.37988
$494$	−10904.4	−0.993143
$495$	0	0
$496$	−5185.79	−0.469454
$497$	−1280.75	−0.115592
$498$	3998.64	0.359806
$499$	8942.71	0.802266	0.401133	−	0.916020i	$-0.368617\pi$
$499$	8942.71	0.802266	0.401133	+	0.916020i	$0.368617\pi$
$500$	0	0
$501$	−8444.05	−0.752999
$502$	9509.13	0.845445
$503$	6281.34	0.556801	0.278401	−	0.960465i	$-0.410196\pi$
$503$	6281.34	0.556801	0.278401	+	0.960465i	$0.410196\pi$
$504$	333.735	0.0294955
$505$	0	0
$506$	−3510.72	−0.308439
$507$	−7412.37	−0.649300
$508$	−1774.19	−0.154955
$509$	−3877.32	−0.337641	−0.168820	−	0.985647i	$-0.553996\pi$
$509$	−3877.32	−0.337641	−0.168820	+	0.985647i	$0.553996\pi$
$510$	0	0
$511$	1490.93	0.129070
$512$	9585.44	0.827384
$513$	1952.66	0.168055
$514$	−13999.4	−1.20134
$515$	0	0
$516$	−4011.06	−0.342203
$517$	−3743.19	−0.318424
$518$	−132.662	−0.0112526
$519$	10159.3	0.859235
$520$	0	0
$521$	−19738.2	−1.65978	−0.829892	−	0.557923i	$-0.811598\pi$
$521$	−19738.2	−1.65978	−0.829892	+	0.557923i	$0.811598\pi$
$522$	2651.43	0.222318
$523$	21804.4	1.82302	0.911512	−	0.411274i	$-0.134916\pi$
$523$	21804.4	1.82302	0.911512	+	0.411274i	$0.134916\pi$
$524$	−1027.66	−0.0856747
$525$	0	0
$526$	9719.95	0.805722
$527$	20116.5	1.66278
$528$	962.578	0.0793387
$529$	8747.15	0.718924
$530$	0	0
$531$	−4729.87	−0.386551
$532$	341.702	0.0278471
$533$	25033.2	2.03435
$534$	6629.22	0.537218
$535$	0	0
$536$	12642.7	1.01881
$537$	−8278.20	−0.665234
$538$	10631.4	0.851956
$539$	−3747.93	−0.299508
$540$	0	0
$541$	6332.36	0.503234	0.251617	−	0.967827i	$-0.419038\pi$
$541$	6332.36	0.503234	0.251617	+	0.967827i	$0.419038\pi$
$542$	4791.81	0.379753
$543$	−7561.64	−0.597608
$544$	−14949.7	−1.17824
$545$	0	0
$546$	−682.900	−0.0535264
$547$	−1049.90	−0.0820669	−0.0410334	−	0.999158i	$-0.513065\pi$
$547$	−1049.90	−0.0820669	−0.0410334	+	0.999158i	$0.513065\pi$
$548$	1987.71	0.154947
$549$	−4161.22	−0.323491
$550$	0	0
$551$	9654.23	0.746432
$552$	−10656.2	−0.821665
$553$	668.144	0.0513786
$554$	2982.39	0.228718
$555$	0	0
$556$	1794.69	0.136892
$557$	7763.68	0.590588	0.295294	−	0.955406i	$-0.404582\pi$
$557$	7763.68	0.590588	0.295294	+	0.955406i	$0.404582\pi$
$558$	−3531.17	−0.267897
$559$	29188.2	2.20846
$560$	0	0
$561$	−3733.98	−0.281014
$562$	6881.55	0.516514
$563$	−5779.52	−0.432642	−0.216321	−	0.976322i	$-0.569406\pi$
$563$	−5779.52	−0.432642	−0.216321	+	0.976322i	$0.569406\pi$
$564$	−3194.90	−0.238528
$565$	0	0
$566$	−9189.61	−0.682453
$567$	122.287	0.00905748
$568$	−20836.7	−1.53924
$569$	7128.46	0.525203	0.262601	−	0.964904i	$-0.415420\pi$
$569$	7128.46	0.525203	0.262601	+	0.964904i	$0.415420\pi$
$570$	0	0
$571$	−13775.0	−1.00957	−0.504784	−	0.863245i	$-0.668428\pi$
$571$	−13775.0	−1.00957	−0.504784	+	0.863245i	$0.668428\pi$
$572$	2351.99	0.171926
$573$	−11243.3	−0.819715
$574$	1220.79	0.0887712
$575$	0	0
$576$	4724.39	0.341753
$577$	−14483.4	−1.04498	−0.522488	−	0.852646i	$-0.674996\pi$
$577$	−14483.4	−1.04498	−0.522488	+	0.852646i	$0.674996\pi$
$578$	−17412.7	−1.25307
$579$	−7633.53	−0.547908
$580$	0	0
$581$	911.811	0.0651090
$582$	−3101.25	−0.220878
$583$	7258.65	0.515648
$584$	24256.1	1.71871
$585$	0	0
$586$	3158.10	0.222628
$587$	18694.1	1.31446	0.657228	−	0.753691i	$-0.271729\pi$
$587$	18694.1	1.31446	0.657228	+	0.753691i	$0.271729\pi$
$588$	−3198.94	−0.224357
$589$	−12857.5	−0.899464
$590$	0	0
$591$	6719.10	0.467660
$592$	−1161.42	−0.0806320
$593$	15320.9	1.06097	0.530486	−	0.847694i	$-0.322010\pi$
$593$	15320.9	1.06097	0.530486	+	0.847694i	$0.322010\pi$
$594$	655.450	0.0452751
$595$	0	0
$596$	2642.99	0.181646
$597$	−3222.61	−0.220926
$598$	21805.1	1.49110
$599$	14142.5	0.964684	0.482342	−	0.875983i	$-0.339786\pi$
$599$	14142.5	0.964684	0.482342	+	0.875983i	$0.339786\pi$
$600$	0	0
$601$	−15024.9	−1.01977	−0.509883	−	0.860244i	$-0.670311\pi$
$601$	−15024.9	−1.01977	−0.509883	+	0.860244i	$0.670311\pi$
$602$	1423.41	0.0963687
$603$	4632.57	0.312857
$604$	−79.9572	−0.00538644
$605$	0	0
$606$	10443.7	0.700077
$607$	8612.72	0.575913	0.287957	−	0.957643i	$-0.407024\pi$
$607$	8612.72	0.575913	0.287957	+	0.957643i	$0.407024\pi$
$608$	9555.18	0.637358
$609$	604.606	0.0402297
$610$	0	0
$611$	23249.0	1.53937
$612$	−3187.04	−0.210504
$613$	1215.02	0.0800558	0.0400279	−	0.999199i	$-0.487255\pi$
$613$	1215.02	0.0800558	0.0400279	+	0.999199i	$0.487255\pi$
$614$	−19016.3	−1.24989
$615$	0	0
$616$	407.898	0.0266797
$617$	17602.6	1.14855	0.574275	−	0.818662i	$-0.305284\pi$
$617$	17602.6	1.14855	0.574275	+	0.818662i	$0.305284\pi$
$618$	5140.13	0.334573
$619$	−2312.91	−0.150184	−0.0750920	−	0.997177i	$-0.523925\pi$
$619$	−2312.91	−0.150184	−0.0750920	+	0.997177i	$0.523925\pi$
$620$	0	0
$621$	−3904.67	−0.252317
$622$	−14278.2	−0.920426
$623$	1511.66	0.0972127
$624$	−5978.59	−0.383550
$625$	0	0
$626$	8279.22	0.528601
$627$	2386.59	0.152011
$628$	3019.23	0.191848
$629$	4505.32	0.285595
$630$	0	0
$631$	22763.2	1.43612	0.718059	−	0.695982i	$-0.245031\pi$
$631$	22763.2	1.43612	0.718059	+	0.695982i	$0.245031\pi$
$632$	10870.1	0.684163
$633$	−14619.4	−0.917963
$634$	−8858.67	−0.554926
$635$	0	0
$636$	6195.43	0.386265
$637$	23278.5	1.44792
$638$	3240.63	0.201094
$639$	−7635.00	−0.472670
$640$	0	0
$641$	−519.128	−0.0319880	−0.0159940	−	0.999872i	$-0.505091\pi$
$641$	−519.128	−0.0319880	−0.0159940	+	0.999872i	$0.505091\pi$
$642$	−2711.34	−0.166679
$643$	12006.6	0.736382	0.368191	−	0.929750i	$-0.379977\pi$
$643$	12006.6	0.736382	0.368191	+	0.929750i	$0.379977\pi$
$644$	−683.288	−0.0418095
$645$	0	0
$646$	18059.5	1.09991
$647$	9014.17	0.547734	0.273867	−	0.961768i	$-0.411697\pi$
$647$	9014.17	0.547734	0.273867	+	0.961768i	$0.411697\pi$
$648$	1989.51	0.120610
$649$	−5780.95	−0.349649
$650$	0	0
$651$	−805.215	−0.0484775
$652$	−5069.33	−0.304494
$653$	26556.4	1.59148	0.795738	−	0.605641i	$-0.207083\pi$
$653$	26556.4	1.59148	0.795738	+	0.605641i	$0.207083\pi$
$654$	2476.98	0.148100
$655$	0	0
$656$	10687.6	0.636101
$657$	8887.95	0.527781
$658$	1133.78	0.0671723
$659$	−8015.80	−0.473826	−0.236913	−	0.971531i	$-0.576136\pi$
$659$	−8015.80	−0.473826	−0.236913	+	0.971531i	$0.576136\pi$
$660$	0	0
$661$	2593.17	0.152591	0.0762953	−	0.997085i	$-0.475691\pi$
$661$	2593.17	0.152591	0.0762953	+	0.997085i	$0.475691\pi$
$662$	−16061.5	−0.942971
$663$	23191.8	1.35852
$664$	14834.4	0.866998
$665$	0	0
$666$	−790.849	−0.0460132
$667$	−19305.2	−1.12069
$668$	−8808.79	−0.510213
$669$	5825.03	0.336635
$670$	0	0
$671$	−5085.94	−0.292609
$672$	598.403	0.0343510
$673$	−17727.8	−1.01539	−0.507694	−	0.861537i	$-0.669502\pi$
$673$	−17727.8	−1.01539	−0.507694	+	0.861537i	$0.669502\pi$
$674$	−1852.23	−0.105853
$675$	0	0
$676$	−7732.55	−0.439949
$677$	3681.04	0.208972	0.104486	−	0.994526i	$-0.466680\pi$
$677$	3681.04	0.208972	0.104486	+	0.994526i	$0.466680\pi$
$678$	9782.90	0.554145
$679$	−707.180	−0.0399692
$680$	0	0
$681$	4042.43	0.227469
$682$	−4315.88	−0.242322
$683$	−7829.21	−0.438619	−0.219309	−	0.975655i	$-0.570380\pi$
$683$	−7829.21	−0.438619	−0.219309	+	0.975655i	$0.570380\pi$
$684$	2037.01	0.113870
$685$	0	0
$686$	2278.03	0.126786
$687$	2454.26	0.136296
$688$	12461.6	0.690542
$689$	−45083.6	−2.49281
$690$	0	0
$691$	4983.99	0.274385	0.137192	−	0.990544i	$-0.456192\pi$
$691$	4983.99	0.274385	0.137192	+	0.990544i	$0.456192\pi$
$692$	10598.1	0.582196
$693$	149.462	0.00819280
$694$	−4977.80	−0.272269
$695$	0	0
$696$	9836.43	0.535702
$697$	−41458.9	−2.25304
$698$	−22836.0	−1.23833
$699$	651.271	0.0352408
$700$	0	0
$701$	1748.60	0.0942135	0.0471068	−	0.998890i	$-0.485000\pi$
$701$	1748.60	0.0942135	0.0471068	+	0.998890i	$0.485000\pi$
$702$	−4071.01	−0.218875
$703$	−2879.59	−0.154489
$704$	5774.26	0.309127
$705$	0	0
$706$	−4808.18	−0.256315
$707$	2381.48	0.126683
$708$	−4934.17	−0.261917
$709$	22959.1	1.21614	0.608072	−	0.793882i	$-0.291943\pi$
$709$	22959.1	1.21614	0.608072	+	0.793882i	$0.291943\pi$
$710$	0	0
$711$	3983.05	0.210093
$712$	24593.5	1.29449
$713$	25710.7	1.35045
$714$	1130.99	0.0592805
$715$	0	0
$716$	−8635.78	−0.450746
$717$	−11893.4	−0.619482
$718$	14195.9	0.737862
$719$	23344.8	1.21087	0.605435	−	0.795895i	$-0.292999\pi$
$719$	23344.8	1.21087	0.605435	+	0.795895i	$0.292999\pi$
$720$	0	0
$721$	1172.10	0.0605429
$722$	3594.37	0.185275
$723$	−11919.2	−0.613113
$724$	−7888.27	−0.404924
$725$	0	0
$726$	801.105	0.0409529
$727$	16238.3	0.828400	0.414200	−	0.910186i	$-0.364061\pi$
$727$	16238.3	0.828400	0.414200	+	0.910186i	$0.364061\pi$
$728$	−2533.46	−0.128979
$729$	729.000	0.0370370
$730$	0	0
$731$	−48340.3	−2.44587
$732$	−4340.97	−0.219189
$733$	−36830.4	−1.85588	−0.927940	−	0.372729i	$-0.878422\pi$
$733$	−36830.4	−1.85588	−0.927940	+	0.372729i	$0.878422\pi$
$734$	16891.9	0.849442
$735$	0	0
$736$	−19107.1	−0.956926
$737$	5662.03	0.282990
$738$	7277.56	0.362995
$739$	33393.1	1.66223	0.831114	−	0.556102i	$-0.187704\pi$
$739$	33393.1	1.66223	0.831114	+	0.556102i	$0.187704\pi$
$740$	0	0
$741$	−14823.1	−0.734874
$742$	−2198.58	−0.108777
$743$	−17151.0	−0.846850	−0.423425	−	0.905931i	$-0.639172\pi$
$743$	−17151.0	−0.846850	−0.423425	+	0.905931i	$0.639172\pi$
$744$	−13100.2	−0.645531
$745$	0	0
$746$	−797.663	−0.0391482
$747$	5435.64	0.266238
$748$	−3895.27	−0.190408
$749$	−618.267	−0.0301615
$750$	0	0
$751$	23603.0	1.14685	0.573425	−	0.819258i	$-0.305614\pi$
$751$	23603.0	1.14685	0.573425	+	0.819258i	$0.305614\pi$
$752$	9925.93	0.481332
$753$	12926.4	0.625585
$754$	−20127.6	−0.972155
$755$	0	0
$756$	127.570	0.00613712
$757$	40304.2	1.93511	0.967556	−	0.252655i	$-0.0813038\pi$
$757$	40304.2	1.93511	0.967556	+	0.252655i	$0.0813038\pi$
$758$	19800.8	0.948809
$759$	−4772.37	−0.228229
$760$	0	0
$761$	−12908.2	−0.614876	−0.307438	−	0.951568i	$-0.599472\pi$
$761$	−12908.2	−0.614876	−0.307438	+	0.951568i	$0.599472\pi$
$762$	3753.34	0.178437
$763$	564.826	0.0267996
$764$	−11729.0	−0.555419
$765$	0	0
$766$	−17725.3	−0.836087
$767$	35905.6	1.69032
$768$	11926.4	0.560360
$769$	4151.97	0.194700	0.0973498	−	0.995250i	$-0.468963\pi$
$769$	4151.97	0.194700	0.0973498	+	0.995250i	$0.468963\pi$
$770$	0	0
$771$	−19030.4	−0.888927
$772$	−7963.26	−0.371249
$773$	34207.0	1.59164	0.795822	−	0.605531i	$-0.207039\pi$
$773$	34207.0	1.59164	0.795822	+	0.605531i	$0.207039\pi$
$774$	8485.48	0.394062
$775$	0	0
$776$	−11505.2	−0.532234
$777$	−180.338	−0.00832635
$778$	2409.22	0.111022
$779$	26498.6	1.21876
$780$	0	0
$781$	−9331.66	−0.427546
$782$	−36112.8	−1.65140
$783$	3604.27	0.164504
$784$	9938.49	0.452737
$785$	0	0
$786$	2174.04	0.0986582
$787$	−7957.51	−0.360425	−0.180213	−	0.983628i	$-0.557679\pi$
$787$	−7957.51	−0.360425	−0.180213	+	0.983628i	$0.557679\pi$
$788$	7009.34	0.316875
$789$	13213.0	0.596193
$790$	0	0
$791$	2230.80	0.100276
$792$	2431.63	0.109096
$793$	31588.9	1.41457
$794$	−1203.87	−0.0538084
$795$	0	0
$796$	−3361.81	−0.149694
$797$	−23524.5	−1.04552	−0.522762	−	0.852479i	$-0.675098\pi$
$797$	−23524.5	−1.04552	−0.522762	+	0.852479i	$0.675098\pi$
$798$	−722.877	−0.0320671
$799$	−38504.1	−1.70485
$800$	0	0
$801$	9011.57	0.397513
$802$	−15198.2	−0.669162
$803$	10863.1	0.477396
$804$	4832.67	0.211984
$805$	0	0
$806$	26806.0	1.17147
$807$	14452.0	0.630404
$808$	38744.7	1.68692
$809$	−11428.3	−0.496659	−0.248329	−	0.968676i	$-0.579882\pi$
$809$	−11428.3	−0.496659	−0.248329	+	0.968676i	$0.579882\pi$
$810$	0	0
$811$	−16762.6	−0.725789	−0.362895	−	0.931830i	$-0.618211\pi$
$811$	−16762.6	−0.725789	−0.362895	+	0.931830i	$0.618211\pi$
$812$	630.722	0.0272586
$813$	6513.86	0.280997
$814$	−966.593	−0.0416205
$815$	0	0
$816$	9901.51	0.424782
$817$	30896.9	1.32307
$818$	−21661.1	−0.925871
$819$	−928.314	−0.0396068
$820$	0	0
$821$	4391.15	0.186665	0.0933326	−	0.995635i	$-0.470248\pi$
$821$	4391.15	0.186665	0.0933326	+	0.995635i	$0.470248\pi$
$822$	−4205.05	−0.178428
$823$	28052.8	1.18816	0.594082	−	0.804404i	$-0.297515\pi$
$823$	28052.8	1.18816	0.594082	+	0.804404i	$0.297515\pi$
$824$	19069.2	0.806196
$825$	0	0
$826$	1751.00	0.0737592
$827$	−5791.95	−0.243538	−0.121769	−	0.992558i	$-0.538857\pi$
$827$	−5791.95	−0.243538	−0.121769	+	0.992558i	$0.538857\pi$
$828$	−4073.33	−0.170964
$829$	−37447.0	−1.56886	−0.784432	−	0.620215i	$-0.787045\pi$
$829$	−37447.0	−1.56886	−0.784432	+	0.620215i	$0.787045\pi$
$830$	0	0
$831$	4054.17	0.169239
$832$	−35864.0	−1.49443
$833$	−38552.9	−1.60357
$834$	−3796.71	−0.157637
$835$	0	0
$836$	2489.68	0.102999
$837$	−4800.18	−0.198230
$838$	5885.37	0.242609
$839$	6001.17	0.246941	0.123470	−	0.992348i	$-0.460598\pi$
$839$	6001.17	0.246941	0.123470	+	0.992348i	$0.460598\pi$
$840$	0	0
$841$	−6568.98	−0.269342
$842$	18249.5	0.746936
$843$	9354.58	0.382193
$844$	−15250.9	−0.621989
$845$	0	0
$846$	6758.88	0.274675
$847$	182.676	0.00741066
$848$	−19248.0	−0.779455
$849$	−12492.1	−0.504980
$850$	0	0
$851$	5758.22	0.231950
$852$	−7964.79	−0.320269
$853$	1272.58	0.0510812	0.0255406	−	0.999674i	$-0.491869\pi$
$853$	1272.58	0.0510812	0.0255406	+	0.999674i	$0.491869\pi$
$854$	1540.49	0.0617265
$855$	0	0
$856$	−10058.7	−0.401634
$857$	−21932.2	−0.874201	−0.437100	−	0.899413i	$-0.643995\pi$
$857$	−21932.2	−0.874201	−0.437100	+	0.899413i	$0.643995\pi$
$858$	−4975.68	−0.197980
$859$	−23911.6	−0.949770	−0.474885	−	0.880048i	$-0.657510\pi$
$859$	−23911.6	−0.949770	−0.474885	+	0.880048i	$0.657510\pi$
$860$	0	0
$861$	1659.50	0.0656861
$862$	−26054.0	−1.02947
$863$	−12447.1	−0.490967	−0.245484	−	0.969401i	$-0.578947\pi$
$863$	−12447.1	−0.490967	−0.245484	+	0.969401i	$0.578947\pi$
$864$	3567.29	0.140465
$865$	0	0
$866$	28554.9	1.12048
$867$	−23670.4	−0.927207
$868$	−839.996	−0.0328471
$869$	4868.17	0.190036
$870$	0	0
$871$	−35167.0	−1.36807
$872$	9189.25	0.356866
$873$	−4215.76	−0.163438
$874$	23081.6	0.893304
$875$	0	0
$876$	9271.87	0.357611
$877$	−29036.8	−1.11802	−0.559011	−	0.829160i	$-0.688819\pi$
$877$	−29036.8	−1.11802	−0.559011	+	0.829160i	$0.688819\pi$
$878$	1048.00	0.0402829
$879$	4293.03	0.164733
$880$	0	0
$881$	40243.9	1.53899	0.769495	−	0.638652i	$-0.220508\pi$
$881$	40243.9	1.53899	0.769495	+	0.638652i	$0.220508\pi$
$882$	6767.43	0.258358
$883$	40042.9	1.52610	0.763052	−	0.646337i	$-0.223700\pi$
$883$	40042.9	1.52610	0.763052	+	0.646337i	$0.223700\pi$
$884$	24193.6	0.920496
$885$	0	0
$886$	−8146.89	−0.308917
$887$	−21075.4	−0.797793	−0.398896	−	0.916996i	$-0.630607\pi$
$887$	−21075.4	−0.797793	−0.398896	+	0.916996i	$0.630607\pi$
$888$	−2933.94	−0.110875
$889$	855.875	0.0322892
$890$	0	0
$891$	891.000	0.0335013
$892$	6076.64	0.228095
$893$	24610.1	0.922222
$894$	−5591.31	−0.209174
$895$	0	0
$896$	−153.234	−0.00571339
$897$	29641.3	1.10334
$898$	−34739.8	−1.29096
$899$	−23732.7	−0.880457
$900$	0	0
$901$	74665.7	2.76079
$902$	8894.79	0.328342
$903$	1934.95	0.0713079
$904$	36293.2	1.33528
$905$	0	0
$906$	169.151	0.00620273
$907$	31049.7	1.13670	0.568351	−	0.822786i	$-0.307581\pi$
$907$	31049.7	1.13670	0.568351	+	0.822786i	$0.307581\pi$
$908$	4217.04	0.154127
$909$	14196.9	0.518021
$910$	0	0
$911$	−17625.2	−0.640996	−0.320498	−	0.947249i	$-0.603850\pi$
$911$	−17625.2	−0.640996	−0.320498	+	0.947249i	$0.603850\pi$
$912$	−6328.58	−0.229781
$913$	6643.56	0.240821
$914$	8816.64	0.319068
$915$	0	0
$916$	2560.27	0.0923511
$917$	495.747	0.0178528
$918$	6742.25	0.242405
$919$	−51856.3	−1.86135	−0.930675	−	0.365848i	$-0.880779\pi$
$919$	−51856.3	−1.86135	−0.930675	+	0.365848i	$0.880779\pi$
$920$	0	0
$921$	−25850.2	−0.924856
$922$	25307.8	0.903977
$923$	57959.2	2.06690
$924$	155.918	0.00555123
$925$	0	0
$926$	−32386.3	−1.14933
$927$	6987.34	0.247567
$928$	17637.2	0.623889
$929$	−24369.1	−0.860628	−0.430314	−	0.902679i	$-0.641597\pi$
$929$	−24369.1	−0.860628	−0.430314	+	0.902679i	$0.641597\pi$
$930$	0	0
$931$	24641.2	0.867436
$932$	679.403	0.0238783
$933$	−19409.4	−0.681067
$934$	3330.55	0.116680
$935$	0	0
$936$	−15102.9	−0.527408
$937$	31621.9	1.10250	0.551249	−	0.834341i	$-0.314151\pi$
$937$	31621.9	1.10250	0.551249	+	0.834341i	$0.314151\pi$
$938$	−1714.98	−0.0596973
$939$	11254.5	0.391137
$940$	0	0
$941$	−8576.25	−0.297107	−0.148554	−	0.988904i	$-0.547462\pi$
$941$	−8576.25	−0.297107	−0.148554	+	0.988904i	$0.547462\pi$
$942$	−6387.26	−0.220921
$943$	−52988.3	−1.82984
$944$	15329.5	0.528531
$945$	0	0
$946$	10371.1	0.356443
$947$	24802.7	0.851087	0.425544	−	0.904938i	$-0.360083\pi$
$947$	24802.7	0.851087	0.425544	+	0.904938i	$0.360083\pi$
$948$	4155.10	0.142354
$949$	−67470.6	−2.30789
$950$	0	0
$951$	−12042.2	−0.410616
$952$	4195.82	0.142844
$953$	−34824.6	−1.18371	−0.591857	−	0.806043i	$-0.701605\pi$
$953$	−34824.6	−1.18371	−0.591857	+	0.806043i	$0.701605\pi$
$954$	−13106.6	−0.444801
$955$	0	0
$956$	−12407.2	−0.419745
$957$	4405.22	0.148799
$958$	4460.53	0.150431
$959$	−958.878	−0.0322876
$960$	0	0
$961$	1816.26	0.0609669
$962$	6003.53	0.201207
$963$	−3685.71	−0.123334
$964$	−12434.1	−0.415430
$965$	0	0
$966$	1445.51	0.0481455
$967$	−11980.0	−0.398399	−0.199199	−	0.979959i	$-0.563834\pi$
$967$	−11980.0	−0.398399	−0.199199	+	0.979959i	$0.563834\pi$
$968$	2971.99	0.0986812
$969$	24549.5	0.813874
$970$	0	0
$971$	−32808.5	−1.08432	−0.542161	−	0.840275i	$-0.682394\pi$
$971$	−32808.5	−1.08432	−0.542161	+	0.840275i	$0.682394\pi$
$972$	760.489	0.0250954
$973$	−865.764	−0.0285253
$974$	−11142.3	−0.366553
$975$	0	0
$976$	13486.5	0.442309
$977$	−46876.8	−1.53503	−0.767514	−	0.641032i	$-0.778507\pi$
$977$	−46876.8	−1.53503	−0.767514	+	0.641032i	$0.778507\pi$
$978$	10724.3	0.350638
$979$	11014.1	0.359564
$980$	0	0
$981$	3367.14	0.109587
$982$	41821.8	1.35905
$983$	−9569.95	−0.310513	−0.155256	−	0.987874i	$-0.549620\pi$
$983$	−9569.95	−0.310513	−0.155256	+	0.987874i	$0.549620\pi$
$984$	26998.7	0.874683
$985$	0	0
$986$	33334.6	1.07666
$987$	1541.23	0.0497041
$988$	−15463.4	−0.497932
$989$	−61783.3	−1.98645
$990$	0	0
$991$	1528.89	0.0490077	0.0245039	−	0.999700i	$-0.492199\pi$
$991$	1528.89	0.0490077	0.0245039	+	0.999700i	$0.492199\pi$
$992$	−23489.2	−0.751798
$993$	−21833.5	−0.697750
$994$	2826.48	0.0901917
$995$	0	0
$996$	5670.43	0.180396
$997$	46090.7	1.46410	0.732050	−	0.681251i	$-0.238564\pi$
$997$	46090.7	1.46410	0.732050	+	0.681251i	$0.238564\pi$
$998$	−19735.7	−0.625974
$999$	−1075.06	−0.0340474

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.a.bd.1.2		7
3.2	odd	2		2475.4.a.bo.1.6		7
5.2	odd	4		165.4.c.b.34.5	✓	14
5.3	odd	4		165.4.c.b.34.10	yes	14
5.4	even	2		825.4.a.ba.1.6		7
15.2	even	4		495.4.c.d.199.10		14
15.8	even	4		495.4.c.d.199.5		14
15.14	odd	2		2475.4.a.bs.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.c.b.34.5	✓	14	5.2	odd	4
165.4.c.b.34.10	yes	14	5.3	odd	4
495.4.c.d.199.5		14	15.8	even	4
495.4.c.d.199.10		14	15.2	even	4
825.4.a.ba.1.6		7	5.4	even	2
825.4.a.bd.1.2		7	1.1	even	1	trivial
2475.4.a.bo.1.6		7	3.2	odd	2
2475.4.a.bs.1.2		7	15.14	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20690 q^{2} -3.00000 q^{3} -3.12958 q^{4} +6.62071 q^{6} +1.50972 q^{7} +24.5619 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.20690 q^{2} -3.00000 q^{3} -3.12958 q^{4} +6.62071 q^{6} +1.50972 q^{7} +24.5619 q^{8} +9.00000 q^{9} +11.0000 q^{11} +9.38875 q^{12} -68.3212 q^{13} -3.33181 q^{14} -29.1690 q^{16} +113.151 q^{17} -19.8621 q^{18} -72.3208 q^{19} -4.52917 q^{21} -24.2759 q^{22} +144.617 q^{23} -73.6857 q^{24} +150.778 q^{26} -27.0000 q^{27} -4.72480 q^{28} -133.492 q^{29} +177.784 q^{31} -132.122 q^{32} -33.0000 q^{33} -249.713 q^{34} -28.1663 q^{36} +39.8169 q^{37} +159.605 q^{38} +204.964 q^{39} -366.404 q^{41} +9.99542 q^{42} -427.219 q^{43} -34.4254 q^{44} -319.156 q^{46} -340.290 q^{47} +87.5071 q^{48} -340.721 q^{49} -339.453 q^{51} +213.817 q^{52} +659.877 q^{53} +59.5863 q^{54} +37.0816 q^{56} +216.963 q^{57} +294.603 q^{58} -525.541 q^{59} -462.358 q^{61} -392.353 q^{62} +13.5875 q^{63} +524.933 q^{64} +72.8278 q^{66} +514.730 q^{67} -354.115 q^{68} -433.852 q^{69} -848.333 q^{71} +221.057 q^{72} +987.550 q^{73} -87.8721 q^{74} +226.334 q^{76} +16.6069 q^{77} -452.335 q^{78} +442.561 q^{79} +81.0000 q^{81} +808.617 q^{82} +603.960 q^{83} +14.1744 q^{84} +942.831 q^{86} +400.475 q^{87} +270.181 q^{88} +1001.29 q^{89} -103.146 q^{91} -452.592 q^{92} -533.353 q^{93} +750.987 q^{94} +396.366 q^{96} -468.418 q^{97} +751.937 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 5 q^{2} - 21 q^{3} + 13 q^{4} - 15 q^{6} + 34 q^{7} + 75 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q + 5 * q^2 - 21 * q^3 + 13 * q^4 - 15 * q^6 + 34 * q^7 + 75 * q^8 + 63 * q^9	\( 7 q + 5 q^{2} - 21 q^{3} + 13 q^{4} - 15 q^{6} + 34 q^{7} + 75 q^{8} + 63 q^{9} + 77 q^{11} - 39 q^{12} + 80 q^{13} + 42 q^{14} - 43 q^{16} + 162 q^{17} + 45 q^{18} + 58 q^{19} - 102 q^{21} + 55 q^{22} + 324 q^{23} - 225 q^{24} - 200 q^{26} - 189 q^{27} - 168 q^{28} + 64 q^{29} - 348 q^{31} - 75 q^{32} - 231 q^{33} + 206 q^{34} + 117 q^{36} + 664 q^{37} + 334 q^{38} - 240 q^{39} - 332 q^{41} - 126 q^{42} + 774 q^{43} + 143 q^{44} - 328 q^{46} + 872 q^{47} + 129 q^{48} - 417 q^{49} - 486 q^{51} + 134 q^{52} + 1628 q^{53} - 135 q^{54} - 1618 q^{56} - 174 q^{57} + 1568 q^{58} - 332 q^{59} + 22 q^{61} - 260 q^{62} + 306 q^{63} + 561 q^{64} - 165 q^{66} + 1524 q^{67} + 2324 q^{68} - 972 q^{69} - 516 q^{71} + 675 q^{72} + 1700 q^{73} + 1628 q^{74} + 2794 q^{76} + 374 q^{77} + 600 q^{78} + 1746 q^{79} + 567 q^{81} + 364 q^{82} + 2344 q^{83} + 504 q^{84} + 1270 q^{86} - 192 q^{87} + 825 q^{88} - 2226 q^{89} + 1072 q^{91} + 4184 q^{92} + 1044 q^{93} + 4736 q^{94} + 225 q^{96} + 1048 q^{97} + 3057 q^{98} + 693 q^{99}+O(q^{100}) \) 7 * q + 5 * q^2 - 21 * q^3 + 13 * q^4 - 15 * q^6 + 34 * q^7 + 75 * q^8 + 63 * q^9 + 77 * q^11 - 39 * q^12 + 80 * q^13 + 42 * q^14 - 43 * q^16 + 162 * q^17 + 45 * q^18 + 58 * q^19 - 102 * q^21 + 55 * q^22 + 324 * q^23 - 225 * q^24 - 200 * q^26 - 189 * q^27 - 168 * q^28 + 64 * q^29 - 348 * q^31 - 75 * q^32 - 231 * q^33 + 206 * q^34 + 117 * q^36 + 664 * q^37 + 334 * q^38 - 240 * q^39 - 332 * q^41 - 126 * q^42 + 774 * q^43 + 143 * q^44 - 328 * q^46 + 872 * q^47 + 129 * q^48 - 417 * q^49 - 486 * q^51 + 134 * q^52 + 1628 * q^53 - 135 * q^54 - 1618 * q^56 - 174 * q^57 + 1568 * q^58 - 332 * q^59 + 22 * q^61 - 260 * q^62 + 306 * q^63 + 561 * q^64 - 165 * q^66 + 1524 * q^67 + 2324 * q^68 - 972 * q^69 - 516 * q^71 + 675 * q^72 + 1700 * q^73 + 1628 * q^74 + 2794 * q^76 + 374 * q^77 + 600 * q^78 + 1746 * q^79 + 567 * q^81 + 364 * q^82 + 2344 * q^83 + 504 * q^84 + 1270 * q^86 - 192 * q^87 + 825 * q^88 - 2226 * q^89 + 1072 * q^91 + 4184 * q^92 + 1044 * q^93 + 4736 * q^94 + 225 * q^96 + 1048 * q^97 + 3057 * q^98 + 693 * q^99

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