LMFDB - Embedded newform 1875.4.a.g.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,4,Mod(1,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, 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("1875.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1875.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:	$110.628581261$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 81 x^{12} - 7 x^{11} + 2512 x^{10} + 517 x^{9} - 36970 x^{8} - 12987 x^{7} + 257291 x^{6} + \cdots + 42064 $ x^14 - 81x^12 - 7x^11 + 2512x^10 + 517x^9 - 36970x^8 - 12987x^7 + 257291x^6 + 125779x^5 - 718713x^4 - 371750x^3 + 579848x^2 + 394896x + 42064
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 5^{3} $
Twist minimal:	no (minimal twist has level 75)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$3.90684$ of defining polynomial
Character	$\chi$	$=$	1875.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.90684 q^{2} +3.00000 q^{3} +7.26339 q^{4} +11.7205 q^{6} +22.0918 q^{7} -2.87782 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+3.90684 q^{2} +3.00000 q^{3} +7.26339 q^{4} +11.7205 q^{6} +22.0918 q^{7} -2.87782 q^{8} +9.00000 q^{9} -39.0597 q^{11} +21.7902 q^{12} -68.3943 q^{13} +86.3090 q^{14} -69.3503 q^{16} +100.883 q^{17} +35.1615 q^{18} -94.0468 q^{19} +66.2753 q^{21} -152.600 q^{22} -161.388 q^{23} -8.63347 q^{24} -267.205 q^{26} +27.0000 q^{27} +160.461 q^{28} -51.2792 q^{29} -260.255 q^{31} -247.918 q^{32} -117.179 q^{33} +394.132 q^{34} +65.3705 q^{36} -86.6643 q^{37} -367.426 q^{38} -205.183 q^{39} -52.5039 q^{41} +258.927 q^{42} -53.3748 q^{43} -283.705 q^{44} -630.515 q^{46} +241.996 q^{47} -208.051 q^{48} +145.047 q^{49} +302.648 q^{51} -496.774 q^{52} +59.1547 q^{53} +105.485 q^{54} -63.5763 q^{56} -282.140 q^{57} -200.340 q^{58} -648.190 q^{59} +655.368 q^{61} -1016.78 q^{62} +198.826 q^{63} -413.773 q^{64} -457.799 q^{66} +778.711 q^{67} +732.749 q^{68} -484.163 q^{69} +224.065 q^{71} -25.9004 q^{72} +348.261 q^{73} -338.583 q^{74} -683.098 q^{76} -862.897 q^{77} -801.616 q^{78} +161.563 q^{79} +81.0000 q^{81} -205.124 q^{82} -39.8828 q^{83} +481.383 q^{84} -208.527 q^{86} -153.838 q^{87} +112.407 q^{88} -463.789 q^{89} -1510.95 q^{91} -1172.22 q^{92} -780.766 q^{93} +945.440 q^{94} -743.753 q^{96} +574.441 q^{97} +566.674 q^{98} -351.537 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 42 q^{3} + 50 q^{4} - 27 q^{7} + 21 q^{8} + 126 q^{9}+O(q^{10}) $ 14 * q + 42 * q^3 + 50 * q^4 - 27 * q^7 + 21 * q^8 + 126 * q^9	$ 14 q + 42 q^{3} + 50 q^{4} - 27 q^{7} + 21 q^{8} + 126 q^{9} - 33 q^{11} + 150 q^{12} - 188 q^{13} - 287 q^{14} + 82 q^{16} - 146 q^{17} - 184 q^{19} - 81 q^{21} - 277 q^{22} - 164 q^{23} + 63 q^{24} + 103 q^{26} + 378 q^{27} + 224 q^{28} + 252 q^{29} - 889 q^{31} - 422 q^{32} - 99 q^{33} - 230 q^{34} + 450 q^{36} - 642 q^{37} - 1833 q^{38} - 564 q^{39} - 164 q^{41} - 861 q^{42} - 696 q^{43} - 6 q^{44} - 419 q^{46} + 92 q^{47} + 246 q^{48} + 81 q^{49} - 438 q^{51} - 1956 q^{52} - 949 q^{53} - 2380 q^{56} - 552 q^{57} - 1041 q^{58} - 81 q^{59} - 496 q^{61} - 1454 q^{62} - 243 q^{63} - 3903 q^{64} - 831 q^{66} - 1926 q^{67} - 685 q^{68} - 492 q^{69} + 2498 q^{71} + 189 q^{72} + 1026 q^{73} - 707 q^{74} - 5704 q^{76} - 5434 q^{77} + 309 q^{78} - 695 q^{79} + 1134 q^{81} + 886 q^{82} - 5315 q^{83} + 672 q^{84} + 3997 q^{86} + 756 q^{87} - 2969 q^{88} - 1424 q^{89} - 1194 q^{91} - 1607 q^{92} - 2667 q^{93} - 629 q^{94} - 1266 q^{96} - 291 q^{97} + 1018 q^{98} - 297 q^{99}+O(q^{100}) $ 14 * q + 42 * q^3 + 50 * q^4 - 27 * q^7 + 21 * q^8 + 126 * q^9 - 33 * q^11 + 150 * q^12 - 188 * q^13 - 287 * q^14 + 82 * q^16 - 146 * q^17 - 184 * q^19 - 81 * q^21 - 277 * q^22 - 164 * q^23 + 63 * q^24 + 103 * q^26 + 378 * q^27 + 224 * q^28 + 252 * q^29 - 889 * q^31 - 422 * q^32 - 99 * q^33 - 230 * q^34 + 450 * q^36 - 642 * q^37 - 1833 * q^38 - 564 * q^39 - 164 * q^41 - 861 * q^42 - 696 * q^43 - 6 * q^44 - 419 * q^46 + 92 * q^47 + 246 * q^48 + 81 * q^49 - 438 * q^51 - 1956 * q^52 - 949 * q^53 - 2380 * q^56 - 552 * q^57 - 1041 * q^58 - 81 * q^59 - 496 * q^61 - 1454 * q^62 - 243 * q^63 - 3903 * q^64 - 831 * q^66 - 1926 * q^67 - 685 * q^68 - 492 * q^69 + 2498 * q^71 + 189 * q^72 + 1026 * q^73 - 707 * q^74 - 5704 * q^76 - 5434 * q^77 + 309 * q^78 - 695 * q^79 + 1134 * q^81 + 886 * q^82 - 5315 * q^83 + 672 * q^84 + 3997 * q^86 + 756 * q^87 - 2969 * q^88 - 1424 * q^89 - 1194 * q^91 - 1607 * q^92 - 2667 * q^93 - 629 * q^94 - 1266 * q^96 - 291 * q^97 + 1018 * q^98 - 297 * 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 $

$2$	3.90684	1.38128	0.690638	−	0.723201i	$-0.257330\pi$
$2$	3.90684	1.38128	0.690638	+	0.723201i	$0.257330\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	7.26339	0.907923
$5$	0	0
$5$	0	0
$6$	11.7205	0.797480
$7$	22.0918	1.19284	0.596422	−	0.802671i	$-0.296589\pi$
$7$	22.0918	1.19284	0.596422	+	0.802671i	$0.296589\pi$
$8$	−2.87782	−0.127183
$9$	9.00000	0.333333
$10$	0	0
$11$	−39.0597	−1.07063	−0.535315	−	0.844652i	$-0.679807\pi$
$11$	−39.0597	−1.07063	−0.535315	+	0.844652i	$0.679807\pi$
$12$	21.7902	0.524190
$13$	−68.3943	−1.45917	−0.729583	−	0.683892i	$-0.760286\pi$
$13$	−68.3943	−1.45917	−0.729583	+	0.683892i	$0.760286\pi$
$14$	86.3090	1.64765
$15$	0	0
$16$	−69.3503	−1.08360
$17$	100.883	1.43927	0.719636	−	0.694352i	$-0.244309\pi$
$17$	100.883	1.43927	0.719636	+	0.694352i	$0.244309\pi$
$18$	35.1615	0.460425
$19$	−94.0468	−1.13557	−0.567785	−	0.823177i	$-0.692199\pi$
$19$	−94.0468	−1.13557	−0.567785	+	0.823177i	$0.692199\pi$
$20$	0	0
$21$	66.2753	0.688689
$22$	−152.600	−1.47884
$23$	−161.388	−1.46311	−0.731557	−	0.681780i	$-0.761206\pi$
$23$	−161.388	−1.46311	−0.731557	+	0.681780i	$0.761206\pi$
$24$	−8.63347	−0.0734292
$25$	0	0
$26$	−267.205	−2.01551
$27$	27.0000	0.192450
$28$	160.461	1.08301
$29$	−51.2792	−0.328356	−0.164178	−	0.986431i	$-0.552497\pi$
$29$	−51.2792	−0.328356	−0.164178	+	0.986431i	$0.552497\pi$
$30$	0	0
$31$	−260.255	−1.50785	−0.753923	−	0.656963i	$-0.771841\pi$
$31$	−260.255	−1.50785	−0.753923	+	0.656963i	$0.771841\pi$
$32$	−247.918	−1.36957
$33$	−117.179	−0.618129
$34$	394.132	1.98803
$35$	0	0
$36$	65.3705	0.302641
$37$	−86.6643	−0.385068	−0.192534	−	0.981290i	$-0.561671\pi$
$37$	−86.6643	−0.385068	−0.192534	+	0.981290i	$0.561671\pi$
$38$	−367.426	−1.56853
$39$	−205.183	−0.842450
$40$	0	0
$41$	−52.5039	−0.199993	−0.0999967	−	0.994988i	$-0.531883\pi$
$41$	−52.5039	−0.199993	−0.0999967	+	0.994988i	$0.531883\pi$
$42$	258.927	0.951269
$43$	−53.3748	−0.189293	−0.0946463	−	0.995511i	$-0.530172\pi$
$43$	−53.3748	−0.189293	−0.0946463	+	0.995511i	$0.530172\pi$
$44$	−283.705	−0.972050
$45$	0	0
$46$	−630.515	−2.02096
$47$	241.996	0.751037	0.375519	−	0.926815i	$-0.377465\pi$
$47$	241.996	0.751037	0.375519	+	0.926815i	$0.377465\pi$
$48$	−208.051	−0.625616
$49$	145.047	0.422876
$50$	0	0
$51$	302.648	0.830964
$52$	−496.774	−1.32481
$53$	59.1547	0.153312	0.0766558	−	0.997058i	$-0.475576\pi$
$53$	59.1547	0.153312	0.0766558	+	0.997058i	$0.475576\pi$
$54$	105.485	0.265827
$55$	0	0
$56$	−63.5763	−0.151710
$57$	−282.140	−0.655621
$58$	−200.340	−0.453550
$59$	−648.190	−1.43029	−0.715145	−	0.698976i	$-0.753639\pi$
$59$	−648.190	−1.43029	−0.715145	+	0.698976i	$0.753639\pi$
$60$	0	0
$61$	655.368	1.37560	0.687798	−	0.725902i	$-0.258578\pi$
$61$	655.368	1.37560	0.687798	+	0.725902i	$0.258578\pi$
$62$	−1016.78	−2.08275
$63$	198.826	0.397615
$64$	−413.773	−0.808150
$65$	0	0
$66$	−457.799	−0.853806
$67$	778.711	1.41992	0.709960	−	0.704242i	$-0.248713\pi$
$67$	778.711	1.41992	0.709960	+	0.704242i	$0.248713\pi$
$68$	732.749	1.30675
$69$	−484.163	−0.844729
$70$	0	0
$71$	224.065	0.374529	0.187265	−	0.982309i	$-0.440038\pi$
$71$	224.065	0.374529	0.187265	+	0.982309i	$0.440038\pi$
$72$	−25.9004	−0.0423944
$73$	348.261	0.558368	0.279184	−	0.960238i	$-0.409936\pi$
$73$	348.261	0.558368	0.279184	+	0.960238i	$0.409936\pi$
$74$	−338.583	−0.531886
$75$	0	0
$76$	−683.098	−1.03101
$77$	−862.897	−1.27709
$78$	−801.616	−1.16366
$79$	161.563	0.230092	0.115046	−	0.993360i	$-0.463299\pi$
$79$	161.563	0.230092	0.115046	+	0.993360i	$0.463299\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−205.124	−0.276246
$83$	−39.8828	−0.0527434	−0.0263717	−	0.999652i	$-0.508395\pi$
$83$	−39.8828	−0.0527434	−0.0263717	+	0.999652i	$0.508395\pi$
$84$	481.383	0.625277
$85$	0	0
$86$	−208.527	−0.261465
$87$	−153.838	−0.189576
$88$	112.407	0.136166
$89$	−463.789	−0.552377	−0.276188	−	0.961104i	$-0.589071\pi$
$89$	−463.789	−0.552377	−0.276188	+	0.961104i	$0.589071\pi$
$90$	0	0
$91$	−1510.95	−1.74056
$92$	−1172.22	−1.32840
$93$	−780.766	−0.870555
$94$	945.440	1.03739
$95$	0	0
$96$	−743.753	−0.790719
$97$	574.441	0.601295	0.300647	−	0.953735i	$-0.402797\pi$
$97$	574.441	0.601295	0.300647	+	0.953735i	$0.402797\pi$
$98$	566.674	0.584109
$99$	−351.537	−0.356877
$100$	0	0
$101$	−1074.69	−1.05877	−0.529383	−	0.848383i	$-0.677577\pi$
$101$	−1074.69	−1.05877	−0.529383	+	0.848383i	$0.677577\pi$
$102$	1182.40	1.14779
$103$	932.737	0.892285	0.446142	−	0.894962i	$-0.352797\pi$
$103$	932.737	0.892285	0.446142	+	0.894962i	$0.352797\pi$
$104$	196.827	0.185581
$105$	0	0
$106$	231.108	0.211766
$107$	−1102.95	−0.996511	−0.498255	−	0.867030i	$-0.666026\pi$
$107$	−1102.95	−0.996511	−0.498255	+	0.867030i	$0.666026\pi$
$108$	196.111	0.174730
$109$	−1466.48	−1.28866	−0.644328	−	0.764749i	$-0.722863\pi$
$109$	−1466.48	−1.28866	−0.644328	+	0.764749i	$0.722863\pi$
$110$	0	0
$111$	−259.993	−0.222319
$112$	−1532.07	−1.29256
$113$	−1549.89	−1.29028	−0.645141	−	0.764064i	$-0.723201\pi$
$113$	−1549.89	−1.29028	−0.645141	+	0.764064i	$0.723201\pi$
$114$	−1102.28	−0.905594
$115$	0	0
$116$	−372.461	−0.298122
$117$	−615.549	−0.486389
$118$	−2532.37	−1.97563
$119$	2228.68	1.71683
$120$	0	0
$121$	194.657	0.146249
$122$	2560.42	1.90008
$123$	−157.512	−0.115466
$124$	−1890.33	−1.36901
$125$	0	0
$126$	776.781	0.549216
$127$	971.994	0.679138	0.339569	−	0.940581i	$-0.389719\pi$
$127$	971.994	0.679138	0.339569	+	0.940581i	$0.389719\pi$
$128$	366.800	0.253288
$129$	−160.124	−0.109288
$130$	0	0
$131$	−1168.18	−0.779114	−0.389557	−	0.921002i	$-0.627372\pi$
$131$	−1168.18	−0.779114	−0.389557	+	0.921002i	$0.627372\pi$
$132$	−851.116	−0.561213
$133$	−2077.66	−1.35456
$134$	3042.30	1.96130
$135$	0	0
$136$	−290.322	−0.183051
$137$	1072.74	0.668981	0.334490	−	0.942399i	$-0.391436\pi$
$137$	1072.74	0.668981	0.334490	+	0.942399i	$0.391436\pi$
$138$	−1891.55	−1.16680
$139$	−342.333	−0.208894	−0.104447	−	0.994530i	$-0.533307\pi$
$139$	−342.333	−0.208894	−0.104447	+	0.994530i	$0.533307\pi$
$140$	0	0
$141$	725.988	0.433612
$142$	875.384	0.517328
$143$	2671.46	1.56223
$144$	−624.153	−0.361199
$145$	0	0
$146$	1360.60	0.771260
$147$	435.140	0.244148
$148$	−629.477	−0.349612
$149$	1268.97	0.697704	0.348852	−	0.937178i	$-0.386572\pi$
$149$	1268.97	0.697704	0.348852	+	0.937178i	$0.386572\pi$
$150$	0	0
$151$	−1863.93	−1.00453	−0.502266	−	0.864713i	$-0.667500\pi$
$151$	−1863.93	−1.00453	−0.502266	+	0.864713i	$0.667500\pi$
$152$	270.650	0.144425
$153$	907.943	0.479757
$154$	−3371.20	−1.76402
$155$	0	0
$156$	−1490.32	−0.764880
$157$	−1891.87	−0.961705	−0.480852	−	0.876802i	$-0.659673\pi$
$157$	−1891.87	−0.961705	−0.480852	+	0.876802i	$0.659673\pi$
$158$	631.200	0.317820
$159$	177.464	0.0885145
$160$	0	0
$161$	−3565.34	−1.74527
$162$	316.454	0.153475
$163$	3164.15	1.52046	0.760231	−	0.649653i	$-0.225086\pi$
$163$	3164.15	1.52046	0.760231	+	0.649653i	$0.225086\pi$
$164$	−381.356	−0.181579
$165$	0	0
$166$	−155.816	−0.0728532
$167$	3525.41	1.63356	0.816780	−	0.576949i	$-0.195757\pi$
$167$	3525.41	1.63356	0.816780	+	0.576949i	$0.195757\pi$
$168$	−190.729	−0.0875896
$169$	2480.78	1.12917
$170$	0	0
$171$	−846.421	−0.378523
$172$	−387.682	−0.171863
$173$	3882.26	1.70614	0.853071	−	0.521794i	$-0.174737\pi$
$173$	3882.26	1.70614	0.853071	+	0.521794i	$0.174737\pi$
$174$	−601.019	−0.261857
$175$	0	0
$176$	2708.80	1.16013
$177$	−1944.57	−0.825778
$178$	−1811.95	−0.762985
$179$	499.031	0.208376	0.104188	−	0.994558i	$-0.466776\pi$
$179$	499.031	0.208376	0.104188	+	0.994558i	$0.466776\pi$
$180$	0	0
$181$	−4451.36	−1.82799	−0.913997	−	0.405721i	$-0.867021\pi$
$181$	−4451.36	−1.82799	−0.913997	+	0.405721i	$0.867021\pi$
$182$	−5903.04	−2.40419
$183$	1966.11	0.794201
$184$	464.445	0.186083
$185$	0	0
$186$	−3050.33	−1.20248
$187$	−3940.44	−1.54093
$188$	1757.71	0.681885
$189$	596.478	0.229563
$190$	0	0
$191$	3970.33	1.50410	0.752050	−	0.659106i	$-0.229065\pi$
$191$	3970.33	1.50410	0.752050	+	0.659106i	$0.229065\pi$
$192$	−1241.32	−0.466585
$193$	3115.35	1.16190	0.580952	−	0.813938i	$-0.302680\pi$
$193$	3115.35	1.16190	0.580952	+	0.813938i	$0.302680\pi$
$194$	2244.25	0.830554
$195$	0	0
$196$	1053.53	0.383939
$197$	−1442.80	−0.521802	−0.260901	−	0.965366i	$-0.584020\pi$
$197$	−1442.80	−0.521802	−0.260901	+	0.965366i	$0.584020\pi$
$198$	−1373.40	−0.492945
$199$	−2015.36	−0.717916	−0.358958	−	0.933354i	$-0.616868\pi$
$199$	−2015.36	−0.717916	−0.358958	+	0.933354i	$0.616868\pi$
$200$	0	0
$201$	2336.13	0.819791
$202$	−4198.63	−1.46245
$203$	−1132.85	−0.391677
$204$	2198.25	0.754452
$205$	0	0
$206$	3644.05	1.23249
$207$	−1452.49	−0.487705
$208$	4743.16	1.58115
$209$	3673.44	1.21577
$210$	0	0
$211$	−237.355	−0.0774418	−0.0387209	−	0.999250i	$-0.512328\pi$
$211$	−237.355	−0.0774418	−0.0387209	+	0.999250i	$0.512328\pi$
$212$	429.663	0.139195
$213$	672.194	0.216235
$214$	−4309.07	−1.37646
$215$	0	0
$216$	−77.7013	−0.0244764
$217$	−5749.50	−1.79862
$218$	−5729.31	−1.77999
$219$	1044.78	0.322374
$220$	0	0
$221$	−6899.79	−2.10014
$222$	−1015.75	−0.307084
$223$	−292.812	−0.0879290	−0.0439645	−	0.999033i	$-0.513999\pi$
$223$	−292.812	−0.0879290	−0.0439645	+	0.999033i	$0.513999\pi$
$224$	−5476.95	−1.63368
$225$	0	0
$226$	−6055.19	−1.78223
$227$	213.066	0.0622982	0.0311491	−	0.999515i	$-0.490083\pi$
$227$	213.066	0.0622982	0.0311491	+	0.999515i	$0.490083\pi$
$228$	−2049.30	−0.595254
$229$	−3242.36	−0.935638	−0.467819	−	0.883824i	$-0.654960\pi$
$229$	−3242.36	−0.935638	−0.467819	+	0.883824i	$0.654960\pi$
$230$	0	0
$231$	−2588.69	−0.737331
$232$	147.573	0.0417613
$233$	−3978.24	−1.11855	−0.559277	−	0.828981i	$-0.688921\pi$
$233$	−3978.24	−1.11855	−0.559277	+	0.828981i	$0.688921\pi$
$234$	−2404.85	−0.671837
$235$	0	0
$236$	−4708.05	−1.29859
$237$	484.688	0.132843
$238$	8707.07	2.37141
$239$	−4827.54	−1.30656	−0.653279	−	0.757117i	$-0.726607\pi$
$239$	−4827.54	−1.30656	−0.653279	+	0.757117i	$0.726607\pi$
$240$	0	0
$241$	−2015.36	−0.538675	−0.269338	−	0.963046i	$-0.586805\pi$
$241$	−2015.36	−0.538675	−0.269338	+	0.963046i	$0.586805\pi$
$242$	760.494	0.202010
$243$	243.000	0.0641500
$244$	4760.20	1.24894
$245$	0	0
$246$	−615.373	−0.159491
$247$	6432.26	1.65698
$248$	748.969	0.191772
$249$	−119.648	−0.0304514
$250$	0	0
$251$	−278.293	−0.0699830	−0.0349915	−	0.999388i	$-0.511140\pi$
$251$	−278.293	−0.0699830	−0.0349915	+	0.999388i	$0.511140\pi$
$252$	1444.15	0.361004
$253$	6303.74	1.56645
$254$	3797.42	0.938077
$255$	0	0
$256$	4743.21	1.15801
$257$	−2149.20	−0.521647	−0.260823	−	0.965387i	$-0.583994\pi$
$257$	−2149.20	−0.521647	−0.260823	+	0.965387i	$0.583994\pi$
$258$	−625.580	−0.150957
$259$	−1914.57	−0.459326
$260$	0	0
$261$	−461.513	−0.109452
$262$	−4563.87	−1.07617
$263$	−7143.12	−1.67477	−0.837384	−	0.546616i	$-0.815916\pi$
$263$	−7143.12	−1.67477	−0.837384	+	0.546616i	$0.815916\pi$
$264$	337.221	0.0786155
$265$	0	0
$266$	−8117.09	−1.87102
$267$	−1391.37	−0.318915
$268$	5656.08	1.28918
$269$	886.073	0.200836	0.100418	−	0.994945i	$-0.467982\pi$
$269$	886.073	0.200836	0.100418	+	0.994945i	$0.467982\pi$
$270$	0	0
$271$	−770.402	−0.172689	−0.0863443	−	0.996265i	$-0.527519\pi$
$271$	−770.402	−0.172689	−0.0863443	+	0.996265i	$0.527519\pi$
$272$	−6996.24	−1.55959
$273$	−4532.85	−1.00491
$274$	4191.02	0.924047
$275$	0	0
$276$	−3516.66	−0.766950
$277$	−7492.57	−1.62522	−0.812608	−	0.582810i	$-0.801953\pi$
$277$	−7492.57	−1.62522	−0.812608	+	0.582810i	$0.801953\pi$
$278$	−1337.44	−0.288540
$279$	−2342.30	−0.502615
$280$	0	0
$281$	2195.43	0.466079	0.233039	−	0.972467i	$-0.425133\pi$
$281$	2195.43	0.466079	0.233039	+	0.972467i	$0.425133\pi$
$282$	2836.32	0.598937
$283$	5592.99	1.17480	0.587400	−	0.809297i	$-0.300151\pi$
$283$	5592.99	1.17480	0.587400	+	0.809297i	$0.300151\pi$
$284$	1627.47	0.340044
$285$	0	0
$286$	10437.0	2.15787
$287$	−1159.90	−0.238561
$288$	−2231.26	−0.456522
$289$	5264.29	1.07150
$290$	0	0
$291$	1723.32	0.347158
$292$	2529.55	0.506955
$293$	−2905.73	−0.579367	−0.289684	−	0.957122i	$-0.593550\pi$
$293$	−2905.73	−0.579367	−0.289684	+	0.957122i	$0.593550\pi$
$294$	1700.02	0.337235
$295$	0	0
$296$	249.405	0.0489742
$297$	−1054.61	−0.206043
$298$	4957.65	0.963722
$299$	11038.0	2.13493
$300$	0	0
$301$	−1179.14	−0.225796
$302$	−7282.07	−1.38754
$303$	−3224.06	−0.611279
$304$	6522.17	1.23050
$305$	0	0
$306$	3547.19	0.662677
$307$	−1896.85	−0.352635	−0.176317	−	0.984333i	$-0.556419\pi$
$307$	−1896.85	−0.352635	−0.176317	+	0.984333i	$0.556419\pi$
$308$	−6267.56	−1.15950
$309$	2798.21	0.515161
$310$	0	0
$311$	8821.81	1.60849	0.804243	−	0.594301i	$-0.202571\pi$
$311$	8821.81	1.60849	0.804243	+	0.594301i	$0.202571\pi$
$312$	590.480	0.107145
$313$	−7459.31	−1.34705	−0.673523	−	0.739166i	$-0.735220\pi$
$313$	−7459.31	−1.34705	−0.673523	+	0.739166i	$0.735220\pi$
$314$	−7391.23	−1.32838
$315$	0	0
$316$	1173.49	0.208906
$317$	−5640.05	−0.999296	−0.499648	−	0.866229i	$-0.666537\pi$
$317$	−5640.05	−0.999296	−0.499648	+	0.866229i	$0.666537\pi$
$318$	693.323	0.122263
$319$	2002.95	0.351548
$320$	0	0
$321$	−3308.86	−0.575336
$322$	−13929.2	−2.41070
$323$	−9487.68	−1.63439
$324$	588.334	0.100880
$325$	0	0
$326$	12361.8	2.10018
$327$	−4399.44	−0.744006
$328$	151.097	0.0254358
$329$	5346.12	0.895870
$330$	0	0
$331$	4407.37	0.731876	0.365938	−	0.930639i	$-0.380748\pi$
$331$	4407.37	0.731876	0.365938	+	0.930639i	$0.380748\pi$
$332$	−289.684	−0.0478870
$333$	−779.979	−0.128356
$334$	13773.2	2.25640
$335$	0	0
$336$	−4596.21	−0.746262
$337$	4475.51	0.723432	0.361716	−	0.932288i	$-0.382191\pi$
$337$	4475.51	0.723432	0.361716	+	0.932288i	$0.382191\pi$
$338$	9692.00	1.55969
$339$	−4649.68	−0.744944
$340$	0	0
$341$	10165.5	1.61435
$342$	−3306.83	−0.522845
$343$	−4373.14	−0.688418
$344$	153.603	0.0240748
$345$	0	0
$346$	15167.4	2.35665
$347$	−699.479	−0.108213	−0.0541066	−	0.998535i	$-0.517231\pi$
$347$	−699.479	−0.108213	−0.0541066	+	0.998535i	$0.517231\pi$
$348$	−1117.38	−0.172121
$349$	−7119.97	−1.09204	−0.546022	−	0.837771i	$-0.683858\pi$
$349$	−7119.97	−1.09204	−0.546022	+	0.837771i	$0.683858\pi$
$350$	0	0
$351$	−1846.65	−0.280817
$352$	9683.59	1.46630
$353$	−3541.22	−0.533939	−0.266969	−	0.963705i	$-0.586022\pi$
$353$	−3541.22	−0.533939	−0.266969	+	0.963705i	$0.586022\pi$
$354$	−7597.12	−1.14063
$355$	0	0
$356$	−3368.68	−0.501516
$357$	6686.03	0.991210
$358$	1949.63	0.287825
$359$	11656.7	1.71370	0.856848	−	0.515569i	$-0.172419\pi$
$359$	11656.7	1.71370	0.856848	+	0.515569i	$0.172419\pi$
$360$	0	0
$361$	1985.80	0.289517
$362$	−17390.7	−2.52496
$363$	583.972	0.0844368
$364$	−10974.6	−1.58029
$365$	0	0
$366$	7681.26	1.09701
$367$	73.4995	0.0104541	0.00522703	−	0.999986i	$-0.498336\pi$
$367$	73.4995	0.0104541	0.00522703	+	0.999986i	$0.498336\pi$
$368$	11192.3	1.58543
$369$	−472.535	−0.0666645
$370$	0	0
$371$	1306.83	0.182877
$372$	−5671.00	−0.790398
$373$	2574.61	0.357395	0.178697	−	0.983904i	$-0.442812\pi$
$373$	2574.61	0.357395	0.178697	+	0.983904i	$0.442812\pi$
$374$	−15394.7	−2.12845
$375$	0	0
$376$	−696.422	−0.0955193
$377$	3507.21	0.479126
$378$	2330.34	0.317090
$379$	60.6864	0.00822493	0.00411247	−	0.999992i	$-0.498691\pi$
$379$	60.6864	0.00822493	0.00411247	+	0.999992i	$0.498691\pi$
$380$	0	0
$381$	2915.98	0.392101
$382$	15511.4	2.07758
$383$	3801.09	0.507119	0.253559	−	0.967320i	$-0.418399\pi$
$383$	3801.09	0.507119	0.253559	+	0.967320i	$0.418399\pi$
$384$	1100.40	0.146236
$385$	0	0
$386$	12171.2	1.60491
$387$	−480.373	−0.0630975
$388$	4172.39	0.545930
$389$	9778.93	1.27458	0.637290	−	0.770624i	$-0.280055\pi$
$389$	9778.93	1.27458	0.637290	+	0.770624i	$0.280055\pi$
$390$	0	0
$391$	−16281.2	−2.10582
$392$	−417.419	−0.0537827
$393$	−3504.53	−0.449822
$394$	−5636.77	−0.720753
$395$	0	0
$396$	−2553.35	−0.324017
$397$	−14337.5	−1.81254	−0.906271	−	0.422698i	$-0.861083\pi$
$397$	−14337.5	−1.81254	−0.906271	+	0.422698i	$0.861083\pi$
$398$	−7873.69	−0.991640
$399$	−6232.98	−0.782054
$400$	0	0
$401$	2086.59	0.259849	0.129924	−	0.991524i	$-0.458527\pi$
$401$	2086.59	0.259849	0.129924	+	0.991524i	$0.458527\pi$
$402$	9126.89	1.13236
$403$	17800.0	2.20020
$404$	−7805.87	−0.961279
$405$	0	0
$406$	−4425.86	−0.541014
$407$	3385.08	0.412266
$408$	−870.967	−0.105685
$409$	−417.809	−0.0505118	−0.0252559	−	0.999681i	$-0.508040\pi$
$409$	−417.809	−0.0505118	−0.0252559	+	0.999681i	$0.508040\pi$
$410$	0	0
$411$	3218.22	0.386236
$412$	6774.83	0.810126
$413$	−14319.7	−1.70611
$414$	−5674.64	−0.673655
$415$	0	0
$416$	16956.2	1.99842
$417$	−1027.00	−0.120605
$418$	14351.5	1.67932
$419$	−1247.58	−0.145462	−0.0727309	−	0.997352i	$-0.523171\pi$
$419$	−1247.58	−0.145462	−0.0727309	+	0.997352i	$0.523171\pi$
$420$	0	0
$421$	10541.9	1.22038	0.610191	−	0.792254i	$-0.291092\pi$
$421$	10541.9	1.22038	0.610191	+	0.792254i	$0.291092\pi$
$422$	−927.310	−0.106969
$423$	2177.97	0.250346
$424$	−170.237	−0.0194987
$425$	0	0
$426$	2626.15	0.298680
$427$	14478.3	1.64087
$428$	−8011.19	−0.904755
$429$	8014.37	0.901952
$430$	0	0
$431$	−8929.73	−0.997982	−0.498991	−	0.866607i	$-0.666296\pi$
$431$	−8929.73	−0.997982	−0.498991	+	0.866607i	$0.666296\pi$
$432$	−1872.46	−0.208539
$433$	2428.29	0.269506	0.134753	−	0.990879i	$-0.456976\pi$
$433$	2428.29	0.269506	0.134753	+	0.990879i	$0.456976\pi$
$434$	−22462.4	−2.48440
$435$	0	0
$436$	−10651.6	−1.17000
$437$	15178.0	1.66147
$438$	4081.80	0.445287
$439$	−8825.08	−0.959449	−0.479725	−	0.877419i	$-0.659263\pi$
$439$	−8825.08	−0.959449	−0.479725	+	0.877419i	$0.659263\pi$
$440$	0	0
$441$	1305.42	0.140959
$442$	−26956.4	−2.90087
$443$	−11494.3	−1.23275	−0.616377	−	0.787451i	$-0.711400\pi$
$443$	−11494.3	−1.23275	−0.616377	+	0.787451i	$0.711400\pi$
$444$	−1888.43	−0.201849
$445$	0	0
$446$	−1143.97	−0.121454
$447$	3806.90	0.402820
$448$	−9140.97	−0.963996
$449$	1582.63	0.166345	0.0831727	−	0.996535i	$-0.473495\pi$
$449$	1582.63	0.166345	0.0831727	+	0.996535i	$0.473495\pi$
$450$	0	0
$451$	2050.78	0.214119
$452$	−11257.5	−1.17148
$453$	−5591.79	−0.579967
$454$	832.415	0.0860510
$455$	0	0
$456$	811.951	0.0833839
$457$	6765.77	0.692537	0.346269	−	0.938135i	$-0.387449\pi$
$457$	6765.77	0.692537	0.346269	+	0.938135i	$0.387449\pi$
$458$	−12667.4	−1.29237
$459$	2723.83	0.276988
$460$	0	0
$461$	11612.3	1.17318	0.586592	−	0.809883i	$-0.300469\pi$
$461$	11612.3	1.17318	0.586592	+	0.809883i	$0.300469\pi$
$462$	−10113.6	−1.01846
$463$	−3981.97	−0.399693	−0.199847	−	0.979827i	$-0.564044\pi$
$463$	−3981.97	−0.399693	−0.199847	+	0.979827i	$0.564044\pi$
$464$	3556.23	0.355806
$465$	0	0
$466$	−15542.3	−1.54503
$467$	11069.8	1.09689	0.548447	−	0.836186i	$-0.315219\pi$
$467$	11069.8	1.09689	0.548447	+	0.836186i	$0.315219\pi$
$468$	−4470.97	−0.441604
$469$	17203.1	1.69374
$470$	0	0
$471$	−5675.61	−0.555241
$472$	1865.38	0.181909
$473$	2084.80	0.202662
$474$	1893.60	0.183493
$475$	0	0
$476$	16187.7	1.55875
$477$	532.392	0.0511039
$478$	−18860.4	−1.80472
$479$	−989.051	−0.0943442	−0.0471721	−	0.998887i	$-0.515021\pi$
$479$	−989.051	−0.0943442	−0.0471721	+	0.998887i	$0.515021\pi$
$480$	0	0
$481$	5927.34	0.561879
$482$	−7873.69	−0.744059
$483$	−10696.0	−1.00763
$484$	1413.87	0.132783
$485$	0	0
$486$	949.362	0.0886089
$487$	11838.7	1.10157	0.550784	−	0.834648i	$-0.314329\pi$
$487$	11838.7	1.10157	0.550784	+	0.834648i	$0.314329\pi$
$488$	−1886.04	−0.174953
$489$	9492.45	0.877839
$490$	0	0
$491$	13071.7	1.20146	0.600729	−	0.799453i	$-0.294877\pi$
$491$	13071.7	1.20146	0.600729	+	0.799453i	$0.294877\pi$
$492$	−1144.07	−0.104835
$493$	−5173.18	−0.472593
$494$	25129.8	2.28875
$495$	0	0
$496$	18048.8	1.63390
$497$	4949.99	0.446755
$498$	−467.447	−0.0420618
$499$	107.268	0.00962323	0.00481162	−	0.999988i	$-0.498468\pi$
$499$	107.268	0.00962323	0.00481162	+	0.999988i	$0.498468\pi$
$500$	0	0
$501$	10576.2	0.943137
$502$	−1087.25	−0.0966658
$503$	−5176.94	−0.458903	−0.229451	−	0.973320i	$-0.573693\pi$
$503$	−5176.94	−0.458903	−0.229451	+	0.973320i	$0.573693\pi$
$504$	−572.186	−0.0505699
$505$	0	0
$506$	24627.7	2.16371
$507$	7442.34	0.651925
$508$	7059.97	0.616605
$509$	−4993.51	−0.434840	−0.217420	−	0.976078i	$-0.569764\pi$
$509$	−4993.51	−0.434840	−0.217420	+	0.976078i	$0.569764\pi$
$510$	0	0
$511$	7693.70	0.666046
$512$	15596.6	1.34624
$513$	−2539.26	−0.218540
$514$	−8396.57	−0.720538
$515$	0	0
$516$	−1163.05	−0.0992252
$517$	−9452.29	−0.804083
$518$	−7479.91	−0.634456
$519$	11646.8	0.985042
$520$	0	0
$521$	13780.1	1.15877	0.579384	−	0.815055i	$-0.303293\pi$
$521$	13780.1	1.15877	0.579384	+	0.815055i	$0.303293\pi$
$522$	−1803.06	−0.151183
$523$	21440.1	1.79256	0.896282	−	0.443485i	$-0.146258\pi$
$523$	21440.1	1.79256	0.896282	+	0.443485i	$0.146258\pi$
$524$	−8484.91	−0.707376
$525$	0	0
$526$	−27907.0	−2.31332
$527$	−26255.2	−2.17020
$528$	8126.40	0.669803
$529$	13878.9	1.14070
$530$	0	0
$531$	−5833.71	−0.476763
$532$	−15090.9	−1.22983
$533$	3590.97	0.291824
$534$	−5435.84	−0.440509
$535$	0	0
$536$	−2240.99	−0.180590
$537$	1497.09	0.120306
$538$	3461.75	0.277410
$539$	−5665.47	−0.452744
$540$	0	0
$541$	−23995.2	−1.90690	−0.953451	−	0.301548i	$-0.902497\pi$
$541$	−23995.2	−1.90690	−0.953451	+	0.301548i	$0.902497\pi$
$542$	−3009.84	−0.238531
$543$	−13354.1	−1.05539
$544$	−25010.6	−1.97118
$545$	0	0
$546$	−17709.1	−1.38806
$547$	−22366.9	−1.74834	−0.874169	−	0.485622i	$-0.838593\pi$
$547$	−22366.9	−1.74834	−0.874169	+	0.485622i	$0.838593\pi$
$548$	7791.73	0.607383
$549$	5898.32	0.458532
$550$	0	0
$551$	4822.65	0.372871
$552$	1393.34	0.107435
$553$	3569.21	0.274463
$554$	−29272.3	−2.24487
$555$	0	0
$556$	−2486.49	−0.189660
$557$	5920.24	0.450357	0.225178	−	0.974318i	$-0.427703\pi$
$557$	5920.24	0.450357	0.225178	+	0.974318i	$0.427703\pi$
$558$	−9150.98	−0.694250
$559$	3650.53	0.276209
$560$	0	0
$561$	−11821.3	−0.889655
$562$	8577.18	0.643784
$563$	−3216.97	−0.240816	−0.120408	−	0.992725i	$-0.538420\pi$
$563$	−3216.97	−0.240816	−0.120408	+	0.992725i	$0.538420\pi$
$564$	5273.14	0.393686
$565$	0	0
$566$	21850.9	1.62272
$567$	1789.43	0.132538
$568$	−644.819	−0.0476338
$569$	6048.75	0.445653	0.222827	−	0.974858i	$-0.428472\pi$
$569$	6048.75	0.445653	0.222827	+	0.974858i	$0.428472\pi$
$570$	0	0
$571$	4694.72	0.344077	0.172039	−	0.985090i	$-0.444965\pi$
$571$	4694.72	0.344077	0.172039	+	0.985090i	$0.444965\pi$
$572$	19403.8	1.41838
$573$	11911.0	0.868392
$574$	−4531.56	−0.329518
$575$	0	0
$576$	−3723.95	−0.269383
$577$	−19670.4	−1.41922	−0.709611	−	0.704594i	$-0.751129\pi$
$577$	−19670.4	−1.41922	−0.709611	+	0.704594i	$0.751129\pi$
$578$	20566.7	1.48004
$579$	9346.04	0.670826
$580$	0	0
$581$	−881.081	−0.0629147
$582$	6732.74	0.479521
$583$	−2310.56	−0.164140
$584$	−1002.23	−0.0710150
$585$	0	0
$586$	−11352.2	−0.800266
$587$	−9960.44	−0.700360	−0.350180	−	0.936682i	$-0.613880\pi$
$587$	−9960.44	−0.700360	−0.350180	+	0.936682i	$0.613880\pi$
$588$	3160.59	0.221667
$589$	24476.2	1.71226
$590$	0	0
$591$	−4328.39	−0.301263
$592$	6010.20	0.417259
$593$	−24115.5	−1.66999	−0.834995	−	0.550257i	$-0.814530\pi$
$593$	−24115.5	−1.66999	−0.834995	+	0.550257i	$0.814530\pi$
$594$	−4120.19	−0.284602
$595$	0	0
$596$	9217.01	0.633462
$597$	−6046.09	−0.414489
$598$	43123.6	2.94892
$599$	13381.7	0.912790	0.456395	−	0.889777i	$-0.349140\pi$
$599$	13381.7	0.912790	0.456395	+	0.889777i	$0.349140\pi$
$600$	0	0
$601$	23840.2	1.61807	0.809037	−	0.587758i	$-0.199989\pi$
$601$	23840.2	1.61807	0.809037	+	0.587758i	$0.199989\pi$
$602$	−4606.72	−0.311887
$603$	7008.40	0.473307
$604$	−13538.4	−0.912038
$605$	0	0
$606$	−12595.9	−0.844345
$607$	−17213.0	−1.15100	−0.575499	−	0.817803i	$-0.695192\pi$
$607$	−17213.0	−1.15100	−0.575499	+	0.817803i	$0.695192\pi$
$608$	23315.9	1.55524
$609$	−3398.55	−0.226135
$610$	0	0
$611$	−16551.2	−1.09589
$612$	6594.74	0.435583
$613$	7680.66	0.506067	0.253033	−	0.967458i	$-0.418572\pi$
$613$	7680.66	0.506067	0.253033	+	0.967458i	$0.418572\pi$
$614$	−7410.68	−0.487086
$615$	0	0
$616$	2483.27	0.162425
$617$	18842.2	1.22943	0.614716	−	0.788749i	$-0.289271\pi$
$617$	18842.2	1.22943	0.614716	+	0.788749i	$0.289271\pi$
$618$	10932.2	0.711579
$619$	−28271.6	−1.83576	−0.917878	−	0.396863i	$-0.870099\pi$
$619$	−28271.6	−1.83576	−0.917878	+	0.396863i	$0.870099\pi$
$620$	0	0
$621$	−4357.46	−0.281576
$622$	34465.4	2.22176
$623$	−10245.9	−0.658899
$624$	14229.5	0.912878
$625$	0	0
$626$	−29142.3	−1.86064
$627$	11020.3	0.701928
$628$	−13741.4	−0.873154
$629$	−8742.92	−0.554218
$630$	0	0
$631$	−9058.40	−0.571489	−0.285744	−	0.958306i	$-0.592241\pi$
$631$	−9058.40	−0.571489	−0.285744	+	0.958306i	$0.592241\pi$
$632$	−464.950	−0.0292638
$633$	−712.066	−0.0447111
$634$	−22034.8	−1.38030
$635$	0	0
$636$	1288.99	0.0803644
$637$	−9920.36	−0.617047
$638$	7825.20	0.485584
$639$	2016.58	0.124843
$640$	0	0
$641$	−7737.06	−0.476748	−0.238374	−	0.971173i	$-0.576614\pi$
$641$	−7737.06	−0.476748	−0.238374	+	0.971173i	$0.576614\pi$
$642$	−12927.2	−0.794697
$643$	20694.2	1.26921	0.634604	−	0.772837i	$-0.281163\pi$
$643$	20694.2	1.26921	0.634604	+	0.772837i	$0.281163\pi$
$644$	−25896.4	−1.58457
$645$	0	0
$646$	−37066.8	−2.25755
$647$	8699.16	0.528592	0.264296	−	0.964442i	$-0.414860\pi$
$647$	8699.16	0.528592	0.264296	+	0.964442i	$0.414860\pi$
$648$	−233.104	−0.0141315
$649$	25318.1	1.53131
$650$	0	0
$651$	−17248.5	−1.03844
$652$	22982.4	1.38046
$653$	12108.4	0.725633	0.362816	−	0.931861i	$-0.381815\pi$
$653$	12108.4	0.725633	0.362816	+	0.931861i	$0.381815\pi$
$654$	−17187.9	−1.02768
$655$	0	0
$656$	3641.16	0.216713
$657$	3134.35	0.186123
$658$	20886.4	1.23744
$659$	−1775.52	−0.104953	−0.0524767	−	0.998622i	$-0.516712\pi$
$659$	−1775.52	−0.104953	−0.0524767	+	0.998622i	$0.516712\pi$
$660$	0	0
$661$	−12295.7	−0.723520	−0.361760	−	0.932271i	$-0.617824\pi$
$661$	−12295.7	−0.723520	−0.361760	+	0.932271i	$0.617824\pi$
$662$	17218.9	1.01092
$663$	−20699.4	−1.21251
$664$	114.776	0.00670807
$665$	0	0
$666$	−3047.25	−0.177295
$667$	8275.83	0.480422
$668$	25606.4	1.48315
$669$	−878.437	−0.0507658
$670$	0	0
$671$	−25598.5	−1.47275
$672$	−16430.8	−0.943204
$673$	−29495.8	−1.68942	−0.844710	−	0.535224i	$-0.820227\pi$
$673$	−29495.8	−1.68942	−0.844710	+	0.535224i	$0.820227\pi$
$674$	17485.1	0.999260
$675$	0	0
$676$	18018.9	1.02520
$677$	33797.1	1.91865	0.959326	−	0.282301i	$-0.0910978\pi$
$677$	33797.1	1.91865	0.959326	+	0.282301i	$0.0910978\pi$
$678$	−18165.6	−1.02897
$679$	12690.4	0.717251
$680$	0	0
$681$	639.198	0.0359679
$682$	39714.9	2.22986
$683$	−2135.27	−0.119625	−0.0598123	−	0.998210i	$-0.519050\pi$
$683$	−2135.27	−0.119625	−0.0598123	+	0.998210i	$0.519050\pi$
$684$	−6147.89	−0.343670
$685$	0	0
$686$	−17085.2	−0.950896
$687$	−9727.08	−0.540191
$688$	3701.56	0.205117
$689$	−4045.84	−0.223707
$690$	0	0
$691$	22166.7	1.22035	0.610176	−	0.792266i	$-0.291099\pi$
$691$	22166.7	1.22035	0.610176	+	0.792266i	$0.291099\pi$
$692$	28198.4	1.54905
$693$	−7766.08	−0.425698
$694$	−2732.75	−0.149472
$695$	0	0
$696$	442.718	0.0241109
$697$	−5296.73	−0.287845
$698$	−27816.6	−1.50841
$699$	−11934.7	−0.645797
$700$	0	0
$701$	12304.2	0.662941	0.331471	−	0.943466i	$-0.392455\pi$
$701$	12304.2	0.662941	0.331471	+	0.943466i	$0.392455\pi$
$702$	−7214.55	−0.387885
$703$	8150.50	0.437272
$704$	16161.8	0.865229
$705$	0	0
$706$	−13835.0	−0.737517
$707$	−23741.8	−1.26294
$708$	−14124.2	−0.749743
$709$	11810.2	0.625586	0.312793	−	0.949821i	$-0.398735\pi$
$709$	11810.2	0.625586	0.312793	+	0.949821i	$0.398735\pi$
$710$	0	0
$711$	1454.07	0.0766972
$712$	1334.70	0.0702530
$713$	42002.0	2.20615
$714$	26121.2	1.36913
$715$	0	0
$716$	3624.65	0.189190
$717$	−14482.6	−0.754342
$718$	45540.8	2.36709
$719$	−30376.7	−1.57560	−0.787801	−	0.615930i	$-0.788781\pi$
$719$	−30376.7	−1.57560	−0.787801	+	0.615930i	$0.788781\pi$
$720$	0	0
$721$	20605.8	1.06436
$722$	7758.20	0.399903
$723$	−6046.08	−0.311004
$724$	−32332.0	−1.65968
$725$	0	0
$726$	2281.48	0.116631
$727$	30463.5	1.55410	0.777048	−	0.629442i	$-0.216716\pi$
$727$	30463.5	1.55410	0.777048	+	0.629442i	$0.216716\pi$
$728$	4348.25	0.221369
$729$	729.000	0.0370370
$730$	0	0
$731$	−5384.59	−0.272443
$732$	14280.6	0.721073
$733$	−25466.4	−1.28325	−0.641625	−	0.767018i	$-0.721740\pi$
$733$	−25466.4	−1.28325	−0.641625	+	0.767018i	$0.721740\pi$
$734$	287.151	0.0144399
$735$	0	0
$736$	40010.9	2.00383
$737$	−30416.2	−1.52021
$738$	−1846.12	−0.0920820
$739$	24488.3	1.21897	0.609485	−	0.792798i	$-0.291376\pi$
$739$	24488.3	1.21897	0.609485	+	0.792798i	$0.291376\pi$
$740$	0	0
$741$	19296.8	0.956660
$742$	5105.58	0.252603
$743$	11738.9	0.579622	0.289811	−	0.957084i	$-0.406408\pi$
$743$	11738.9	0.579622	0.289811	+	0.957084i	$0.406408\pi$
$744$	2246.91	0.110720
$745$	0	0
$746$	10058.6	0.493661
$747$	−358.945	−0.0175811
$748$	−28620.9	−1.39904
$749$	−24366.2	−1.18868
$750$	0	0
$751$	−12224.7	−0.593989	−0.296995	−	0.954879i	$-0.595984\pi$
$751$	−12224.7	−0.593989	−0.296995	+	0.954879i	$0.595984\pi$
$752$	−16782.5	−0.813823
$753$	−834.880	−0.0404047
$754$	13702.1	0.661805
$755$	0	0
$756$	4332.45	0.208426
$757$	−22653.2	−1.08764	−0.543822	−	0.839201i	$-0.683023\pi$
$757$	−22653.2	−1.08764	−0.543822	+	0.839201i	$0.683023\pi$
$758$	237.092	0.0113609
$759$	18911.2	0.904393
$760$	0	0
$761$	7709.57	0.367243	0.183621	−	0.982997i	$-0.441218\pi$
$761$	7709.57	0.367243	0.183621	+	0.982997i	$0.441218\pi$
$762$	11392.3	0.541599
$763$	−32397.2	−1.53716
$764$	28838.0	1.36561
$765$	0	0
$766$	14850.2	0.700471
$767$	44332.5	2.08703
$768$	14229.6	0.668577
$769$	27961.8	1.31122	0.655611	−	0.755099i	$-0.272411\pi$
$769$	27961.8	1.31122	0.655611	+	0.755099i	$0.272411\pi$
$770$	0	0
$771$	−6447.59	−0.301173
$772$	22628.0	1.05492
$773$	39376.1	1.83216	0.916081	−	0.400993i	$-0.131335\pi$
$773$	39376.1	1.83216	0.916081	+	0.400993i	$0.131335\pi$
$774$	−1876.74	−0.0871551
$775$	0	0
$776$	−1653.14	−0.0764746
$777$	−5743.71	−0.265192
$778$	38204.7	1.76055
$779$	4937.82	0.227106
$780$	0	0
$781$	−8751.89	−0.400982
$782$	−63608.0	−2.90872
$783$	−1384.54	−0.0631921
$784$	−10059.0	−0.458228
$785$	0	0
$786$	−13691.6	−0.621328
$787$	−20996.4	−0.951007	−0.475503	−	0.879714i	$-0.657734\pi$
$787$	−20996.4	−0.951007	−0.475503	+	0.879714i	$0.657734\pi$
$788$	−10479.6	−0.473756
$789$	−21429.4	−0.966927
$790$	0	0
$791$	−34239.9	−1.53910
$792$	1011.66	0.0453887
$793$	−44823.5	−2.00722
$794$	−56014.3	−2.50362
$795$	0	0
$796$	−14638.4	−0.651812
$797$	27645.2	1.22866	0.614331	−	0.789049i	$-0.289426\pi$
$797$	27645.2	1.22866	0.614331	+	0.789049i	$0.289426\pi$
$798$	−24351.3	−1.08023
$799$	24413.2	1.08095
$800$	0	0
$801$	−4174.10	−0.184126
$802$	8151.97	0.358923
$803$	−13603.0	−0.597805
$804$	16968.2	0.744308
$805$	0	0
$806$	69541.6	3.03908
$807$	2658.22	0.115953
$808$	3092.76	0.134657
$809$	18691.6	0.812311	0.406156	−	0.913804i	$-0.366869\pi$
$809$	18691.6	0.812311	0.406156	+	0.913804i	$0.366869\pi$
$810$	0	0
$811$	−25423.3	−1.10078	−0.550389	−	0.834908i	$-0.685521\pi$
$811$	−25423.3	−1.10078	−0.550389	+	0.834908i	$0.685521\pi$
$812$	−8228.33	−0.355613
$813$	−2311.21	−0.0997018
$814$	13225.0	0.569453
$815$	0	0
$816$	−20988.7	−0.900431
$817$	5019.73	0.214955
$818$	−1632.31	−0.0697707
$819$	−13598.6	−0.580186
$820$	0	0
$821$	7415.63	0.315234	0.157617	−	0.987500i	$-0.449619\pi$
$821$	7415.63	0.315234	0.157617	+	0.987500i	$0.449619\pi$
$822$	12573.1	0.533499
$823$	−1457.31	−0.0617239	−0.0308620	−	0.999524i	$-0.509825\pi$
$823$	−1457.31	−0.0617239	−0.0308620	+	0.999524i	$0.509825\pi$
$824$	−2684.25	−0.113484
$825$	0	0
$826$	−55944.6	−2.35661
$827$	12929.7	0.543662	0.271831	−	0.962345i	$-0.412371\pi$
$827$	12929.7	0.543662	0.271831	+	0.962345i	$0.412371\pi$
$828$	−10550.0	−0.442799
$829$	−24201.6	−1.01394	−0.506970	−	0.861964i	$-0.669234\pi$
$829$	−24201.6	−1.01394	−0.506970	+	0.861964i	$0.669234\pi$
$830$	0	0
$831$	−22477.7	−0.938319
$832$	28299.7	1.17922
$833$	14632.7	0.608634
$834$	−4012.31	−0.166589
$835$	0	0
$836$	26681.6	1.10383
$837$	−7026.89	−0.290185
$838$	−4874.11	−0.200923
$839$	−6478.33	−0.266576	−0.133288	−	0.991077i	$-0.542553\pi$
$839$	−6478.33	−0.266576	−0.133288	+	0.991077i	$0.542553\pi$
$840$	0	0
$841$	−21759.4	−0.892183
$842$	41185.5	1.68569
$843$	6586.28	0.269091
$844$	−1724.00	−0.0703112
$845$	0	0
$846$	8508.96	0.345797
$847$	4300.32	0.174452
$848$	−4102.39	−0.166128
$849$	16779.0	0.678271
$850$	0	0
$851$	13986.5	0.563399
$852$	4882.41	0.196324
$853$	−2086.22	−0.0837405	−0.0418703	−	0.999123i	$-0.513332\pi$
$853$	−2086.22	−0.0837405	−0.0418703	+	0.999123i	$0.513332\pi$
$854$	56564.2	2.26650
$855$	0	0
$856$	3174.11	0.126739
$857$	19021.1	0.758167	0.379083	−	0.925363i	$-0.376239\pi$
$857$	19021.1	0.758167	0.379083	+	0.925363i	$0.376239\pi$
$858$	31310.9	1.24585
$859$	−32398.1	−1.28686	−0.643428	−	0.765506i	$-0.722489\pi$
$859$	−32398.1	−1.28686	−0.643428	+	0.765506i	$0.722489\pi$
$860$	0	0
$861$	−3479.71	−0.137733
$862$	−34887.0	−1.37849
$863$	−18352.7	−0.723908	−0.361954	−	0.932196i	$-0.617890\pi$
$863$	−18352.7	−0.723908	−0.361954	+	0.932196i	$0.617890\pi$
$864$	−6693.78	−0.263573
$865$	0	0
$866$	9486.93	0.372262
$867$	15792.9	0.618632
$868$	−41760.9	−1.63301
$869$	−6310.59	−0.246343
$870$	0	0
$871$	−53259.4	−2.07190
$872$	4220.28	0.163895
$873$	5169.97	0.200432
$874$	59297.9	2.29495
$875$	0	0
$876$	7588.66	0.292691
$877$	−14742.1	−0.567625	−0.283812	−	0.958880i	$-0.591599\pi$
$877$	−14742.1	−0.567625	−0.283812	+	0.958880i	$0.591599\pi$
$878$	−34478.2	−1.32526
$879$	−8717.19	−0.334498
$880$	0	0
$881$	5381.71	0.205805	0.102903	−	0.994691i	$-0.467187\pi$
$881$	5381.71	0.205805	0.102903	+	0.994691i	$0.467187\pi$
$882$	5100.06	0.194703
$883$	−21034.9	−0.801677	−0.400839	−	0.916149i	$-0.631281\pi$
$883$	−21034.9	−0.801677	−0.400839	+	0.916149i	$0.631281\pi$
$884$	−50115.9	−1.90676
$885$	0	0
$886$	−44906.3	−1.70277
$887$	6406.18	0.242501	0.121251	−	0.992622i	$-0.461310\pi$
$887$	6406.18	0.242501	0.121251	+	0.992622i	$0.461310\pi$
$888$	748.214	0.0282752
$889$	21473.1	0.810106
$890$	0	0
$891$	−3163.83	−0.118959
$892$	−2126.81	−0.0798328
$893$	−22759.0	−0.852855
$894$	14873.0	0.556405
$895$	0	0
$896$	8103.27	0.302133
$897$	33114.0	1.23260
$898$	6183.09	0.229769
$899$	13345.7	0.495110
$900$	0	0
$901$	5967.68	0.220657
$902$	8012.08	0.295757
$903$	−3537.43	−0.130364
$904$	4460.32	0.164102
$905$	0	0
$906$	−21846.2	−0.801094
$907$	21808.6	0.798392	0.399196	−	0.916866i	$-0.369289\pi$
$907$	21808.6	0.798392	0.399196	+	0.916866i	$0.369289\pi$
$908$	1547.58	0.0565620
$909$	−9672.19	−0.352922
$910$	0	0
$911$	32569.8	1.18451	0.592253	−	0.805752i	$-0.298239\pi$
$911$	32569.8	1.18451	0.592253	+	0.805752i	$0.298239\pi$
$912$	19566.5	0.710430
$913$	1557.81	0.0564687
$914$	26432.8	0.956585
$915$	0	0
$916$	−23550.5	−0.849488
$917$	−25807.1	−0.929362
$918$	10641.6	0.382597
$919$	12013.0	0.431200	0.215600	−	0.976482i	$-0.430829\pi$
$919$	12013.0	0.431200	0.215600	+	0.976482i	$0.430829\pi$
$920$	0	0
$921$	−5690.55	−0.203594
$922$	45367.3	1.62049
$923$	−15324.7	−0.546501
$924$	−18802.7	−0.669440
$925$	0	0
$926$	−15556.9	−0.552086
$927$	8394.64	0.297428
$928$	12713.0	0.449705
$929$	4760.87	0.168137	0.0840684	−	0.996460i	$-0.473209\pi$
$929$	4760.87	0.168137	0.0840684	+	0.996460i	$0.473209\pi$
$930$	0	0
$931$	−13641.2	−0.480205
$932$	−28895.5	−1.01556
$933$	26465.4	0.928660
$934$	43247.9	1.51511
$935$	0	0
$936$	1771.44	0.0618604
$937$	7124.36	0.248391	0.124196	−	0.992258i	$-0.460365\pi$
$937$	7124.36	0.248391	0.124196	+	0.992258i	$0.460365\pi$
$938$	67209.7	2.33953
$939$	−22377.9	−0.777717
$940$	0	0
$941$	−7208.66	−0.249730	−0.124865	−	0.992174i	$-0.539850\pi$
$941$	−7208.66	−0.249730	−0.124865	+	0.992174i	$0.539850\pi$
$942$	−22173.7	−0.766940
$943$	8473.47	0.292613
$944$	44952.1	1.54986
$945$	0	0
$946$	8144.98	0.279933
$947$	7802.80	0.267748	0.133874	−	0.990998i	$-0.457258\pi$
$947$	7802.80	0.267748	0.133874	+	0.990998i	$0.457258\pi$
$948$	3520.48	0.120612
$949$	−23819.1	−0.814752
$950$	0	0
$951$	−16920.1	−0.576944
$952$	−6413.74	−0.218351
$953$	4495.22	0.152796	0.0763979	−	0.997077i	$-0.475658\pi$
$953$	4495.22	0.152796	0.0763979	+	0.997077i	$0.475658\pi$
$954$	2079.97	0.0705886
$955$	0	0
$956$	−35064.3	−1.18625
$957$	6008.85	0.202966
$958$	−3864.06	−0.130315
$959$	23698.7	0.797990
$960$	0	0
$961$	37941.8	1.27360
$962$	23157.2	0.776110
$963$	−9926.59	−0.332170
$964$	−14638.3	−0.489076
$965$	0	0
$966$	−41787.6	−1.39182
$967$	12693.8	0.422137	0.211069	−	0.977471i	$-0.432306\pi$
$967$	12693.8	0.422137	0.211069	+	0.977471i	$0.432306\pi$
$968$	−560.189	−0.0186004
$969$	−28463.0	−0.943617
$970$	0	0
$971$	−35363.0	−1.16875	−0.584373	−	0.811485i	$-0.698659\pi$
$971$	−35363.0	−1.16875	−0.584373	+	0.811485i	$0.698659\pi$
$972$	1765.00	0.0582433
$973$	−7562.73	−0.249178
$974$	46251.9	1.52157
$975$	0	0
$976$	−45450.0	−1.49059
$977$	−26497.7	−0.867694	−0.433847	−	0.900987i	$-0.642844\pi$
$977$	−26497.7	−0.867694	−0.433847	+	0.900987i	$0.642844\pi$
$978$	37085.5	1.21254
$979$	18115.4	0.591391
$980$	0	0
$981$	−13198.3	−0.429552
$982$	51068.8	1.65954
$983$	−34795.4	−1.12899	−0.564497	−	0.825435i	$-0.690930\pi$
$983$	−34795.4	−1.12899	−0.564497	+	0.825435i	$0.690930\pi$
$984$	453.291	0.0146854
$985$	0	0
$986$	−20210.8	−0.652782
$987$	16038.4	0.517231
$988$	46720.0	1.50442
$989$	8614.03	0.276957
$990$	0	0
$991$	−6309.89	−0.202261	−0.101130	−	0.994873i	$-0.532246\pi$
$991$	−6309.89	−0.202261	−0.101130	+	0.994873i	$0.532246\pi$
$992$	64521.9	2.06509
$993$	13222.1	0.422549
$994$	19338.8	0.617092
$995$	0	0
$996$	−869.052	−0.0276476
$997$	−3021.16	−0.0959690	−0.0479845	−	0.998848i	$-0.515280\pi$
$997$	−3021.16	−0.0959690	−0.0479845	+	0.998848i	$0.515280\pi$
$998$	419.080	0.0132923
$999$	−2339.94	−0.0741064

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.4.a.g.1.11		14
5.4	even	2		1875.4.a.f.1.4		14
25.6	even	5		75.4.g.b.61.2	yes	28
25.21	even	5		75.4.g.b.16.2	✓	28
75.56	odd	10		225.4.h.a.136.6		28
75.71	odd	10		225.4.h.a.91.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.16.2	✓	28	25.21	even	5
75.4.g.b.61.2	yes	28	25.6	even	5
225.4.h.a.91.6		28	75.71	odd	10
225.4.h.a.136.6		28	75.56	odd	10
1875.4.a.f.1.4		14	5.4	even	2
1875.4.a.g.1.11		14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1875.a (trivial)

\(f(q)\)	\(=\)	\(q+3.90684 q^{2} +3.00000 q^{3} +7.26339 q^{4} +11.7205 q^{6} +22.0918 q^{7} -2.87782 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+3.90684 q^{2} +3.00000 q^{3} +7.26339 q^{4} +11.7205 q^{6} +22.0918 q^{7} -2.87782 q^{8} +9.00000 q^{9} -39.0597 q^{11} +21.7902 q^{12} -68.3943 q^{13} +86.3090 q^{14} -69.3503 q^{16} +100.883 q^{17} +35.1615 q^{18} -94.0468 q^{19} +66.2753 q^{21} -152.600 q^{22} -161.388 q^{23} -8.63347 q^{24} -267.205 q^{26} +27.0000 q^{27} +160.461 q^{28} -51.2792 q^{29} -260.255 q^{31} -247.918 q^{32} -117.179 q^{33} +394.132 q^{34} +65.3705 q^{36} -86.6643 q^{37} -367.426 q^{38} -205.183 q^{39} -52.5039 q^{41} +258.927 q^{42} -53.3748 q^{43} -283.705 q^{44} -630.515 q^{46} +241.996 q^{47} -208.051 q^{48} +145.047 q^{49} +302.648 q^{51} -496.774 q^{52} +59.1547 q^{53} +105.485 q^{54} -63.5763 q^{56} -282.140 q^{57} -200.340 q^{58} -648.190 q^{59} +655.368 q^{61} -1016.78 q^{62} +198.826 q^{63} -413.773 q^{64} -457.799 q^{66} +778.711 q^{67} +732.749 q^{68} -484.163 q^{69} +224.065 q^{71} -25.9004 q^{72} +348.261 q^{73} -338.583 q^{74} -683.098 q^{76} -862.897 q^{77} -801.616 q^{78} +161.563 q^{79} +81.0000 q^{81} -205.124 q^{82} -39.8828 q^{83} +481.383 q^{84} -208.527 q^{86} -153.838 q^{87} +112.407 q^{88} -463.789 q^{89} -1510.95 q^{91} -1172.22 q^{92} -780.766 q^{93} +945.440 q^{94} -743.753 q^{96} +574.441 q^{97} +566.674 q^{98} -351.537 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 42 q^{3} + 50 q^{4} - 27 q^{7} + 21 q^{8} + 126 q^{9}+O(q^{10}) \) 14 * q + 42 * q^3 + 50 * q^4 - 27 * q^7 + 21 * q^8 + 126 * q^9	\( 14 q + 42 q^{3} + 50 q^{4} - 27 q^{7} + 21 q^{8} + 126 q^{9} - 33 q^{11} + 150 q^{12} - 188 q^{13} - 287 q^{14} + 82 q^{16} - 146 q^{17} - 184 q^{19} - 81 q^{21} - 277 q^{22} - 164 q^{23} + 63 q^{24} + 103 q^{26} + 378 q^{27} + 224 q^{28} + 252 q^{29} - 889 q^{31} - 422 q^{32} - 99 q^{33} - 230 q^{34} + 450 q^{36} - 642 q^{37} - 1833 q^{38} - 564 q^{39} - 164 q^{41} - 861 q^{42} - 696 q^{43} - 6 q^{44} - 419 q^{46} + 92 q^{47} + 246 q^{48} + 81 q^{49} - 438 q^{51} - 1956 q^{52} - 949 q^{53} - 2380 q^{56} - 552 q^{57} - 1041 q^{58} - 81 q^{59} - 496 q^{61} - 1454 q^{62} - 243 q^{63} - 3903 q^{64} - 831 q^{66} - 1926 q^{67} - 685 q^{68} - 492 q^{69} + 2498 q^{71} + 189 q^{72} + 1026 q^{73} - 707 q^{74} - 5704 q^{76} - 5434 q^{77} + 309 q^{78} - 695 q^{79} + 1134 q^{81} + 886 q^{82} - 5315 q^{83} + 672 q^{84} + 3997 q^{86} + 756 q^{87} - 2969 q^{88} - 1424 q^{89} - 1194 q^{91} - 1607 q^{92} - 2667 q^{93} - 629 q^{94} - 1266 q^{96} - 291 q^{97} + 1018 q^{98} - 297 q^{99}+O(q^{100}) \) 14 * q + 42 * q^3 + 50 * q^4 - 27 * q^7 + 21 * q^8 + 126 * q^9 - 33 * q^11 + 150 * q^12 - 188 * q^13 - 287 * q^14 + 82 * q^16 - 146 * q^17 - 184 * q^19 - 81 * q^21 - 277 * q^22 - 164 * q^23 + 63 * q^24 + 103 * q^26 + 378 * q^27 + 224 * q^28 + 252 * q^29 - 889 * q^31 - 422 * q^32 - 99 * q^33 - 230 * q^34 + 450 * q^36 - 642 * q^37 - 1833 * q^38 - 564 * q^39 - 164 * q^41 - 861 * q^42 - 696 * q^43 - 6 * q^44 - 419 * q^46 + 92 * q^47 + 246 * q^48 + 81 * q^49 - 438 * q^51 - 1956 * q^52 - 949 * q^53 - 2380 * q^56 - 552 * q^57 - 1041 * q^58 - 81 * q^59 - 496 * q^61 - 1454 * q^62 - 243 * q^63 - 3903 * q^64 - 831 * q^66 - 1926 * q^67 - 685 * q^68 - 492 * q^69 + 2498 * q^71 + 189 * q^72 + 1026 * q^73 - 707 * q^74 - 5704 * q^76 - 5434 * q^77 + 309 * q^78 - 695 * q^79 + 1134 * q^81 + 886 * q^82 - 5315 * q^83 + 672 * q^84 + 3997 * q^86 + 756 * q^87 - 2969 * q^88 - 1424 * q^89 - 1194 * q^91 - 1607 * q^92 - 2667 * q^93 - 629 * q^94 - 1266 * q^96 - 291 * q^97 + 1018 * q^98 - 297 * q^99

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