LMFDB - Embedded newform 1875.4.a.f.1.4

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:	$0$
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			1.4
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	$-0.742670\pi$
$2$	−3.90684	−1.38128	−0.690638	+	0.723201i	$0.742670\pi$
$3$	−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	$-0.703411\pi$
$7$	−22.0918	−1.19284	−0.596422	+	0.802671i	$0.703411\pi$
$8$	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	$-0.239714\pi$
$13$	68.3943	1.45917	0.729583	+	0.683892i	$0.239714\pi$
$14$	86.3090	1.64765
$15$	0	0
$16$	−69.3503	−1.08360
$17$	−100.883	−1.43927	−0.719636	−	0.694352i	$-0.755691\pi$
$17$	−100.883	−1.43927	−0.719636	+	0.694352i	$0.755691\pi$
$18$	−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	$-0.238794\pi$
$23$	161.388	1.46311	0.731557	+	0.681780i	$0.238794\pi$
$24$	−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	$-0.438329\pi$
$37$	86.6643	0.385068	0.192534	+	0.981290i	$0.438329\pi$
$38$	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	$-0.469828\pi$
$43$	53.3748	0.189293	0.0946463	+	0.995511i	$0.469828\pi$
$44$	−283.705	−0.972050
$45$	0	0
$46$	−630.515	−2.02096
$47$	−241.996	−0.751037	−0.375519	−	0.926815i	$-0.622535\pi$
$47$	−241.996	−0.751037	−0.375519	+	0.926815i	$0.622535\pi$
$48$	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	$-0.524424\pi$
$53$	−59.1547	−0.153312	−0.0766558	+	0.997058i	$0.524424\pi$
$54$	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	$-0.751287\pi$
$67$	−778.711	−1.41992	−0.709960	+	0.704242i	$0.751287\pi$
$68$	−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	$-0.590064\pi$
$73$	−348.261	−0.558368	−0.279184	+	0.960238i	$0.590064\pi$
$74$	−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	$-0.491605\pi$
$83$	39.8828	0.0527434	0.0263717	+	0.999652i	$0.491605\pi$
$84$	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	$-0.597203\pi$
$97$	−574.441	−0.601295	−0.300647	+	0.953735i	$0.597203\pi$
$98$	−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	$-0.647203\pi$
$103$	−932.737	−0.892285	−0.446142	+	0.894962i	$0.647203\pi$
$104$	196.827	0.185581
$105$	0	0
$106$	231.108	0.211766
$107$	1102.95	0.996511	0.498255	−	0.867030i	$-0.333974\pi$
$107$	1102.95	0.996511	0.498255	+	0.867030i	$0.333974\pi$
$108$	−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	$-0.276799\pi$
$113$	1549.89	1.29028	0.645141	+	0.764064i	$0.276799\pi$
$114$	−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	$-0.610281\pi$
$127$	−971.994	−0.679138	−0.339569	+	0.940581i	$0.610281\pi$
$128$	−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	$-0.608564\pi$
$137$	−1072.74	−0.668981	−0.334490	+	0.942399i	$0.608564\pi$
$138$	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	$-0.340327\pi$
$157$	1891.87	0.961705	0.480852	+	0.876802i	$0.340327\pi$
$158$	−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	$-0.774914\pi$
$163$	−3164.15	−1.52046	−0.760231	+	0.649653i	$0.774914\pi$
$164$	−381.356	−0.181579
$165$	0	0
$166$	−155.816	−0.0728532
$167$	−3525.41	−1.63356	−0.816780	−	0.576949i	$-0.804243\pi$
$167$	−3525.41	−1.63356	−0.816780	+	0.576949i	$0.804243\pi$
$168$	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	$-0.825263\pi$
$173$	−3882.26	−1.70614	−0.853071	+	0.521794i	$0.825263\pi$
$174$	−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	$-0.697320\pi$
$193$	−3115.35	−1.16190	−0.580952	+	0.813938i	$0.697320\pi$
$194$	2244.25	0.830554
$195$	0	0
$196$	1053.53	0.383939
$197$	1442.80	0.521802	0.260901	−	0.965366i	$-0.415980\pi$
$197$	1442.80	0.521802	0.260901	+	0.965366i	$0.415980\pi$
$198$	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	$-0.486001\pi$
$223$	292.812	0.0879290	0.0439645	+	0.999033i	$0.486001\pi$
$224$	−5476.95	−1.63368
$225$	0	0
$226$	−6055.19	−1.78223
$227$	−213.066	−0.0622982	−0.0311491	−	0.999515i	$-0.509917\pi$
$227$	−213.066	−0.0622982	−0.0311491	+	0.999515i	$0.509917\pi$
$228$	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	$-0.311079\pi$
$233$	3978.24	1.11855	0.559277	+	0.828981i	$0.311079\pi$
$234$	−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	$-0.416006\pi$
$257$	2149.20	0.521647	0.260823	+	0.965387i	$0.416006\pi$
$258$	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	$-0.184084\pi$
$263$	7143.12	1.67477	0.837384	+	0.546616i	$0.184084\pi$
$264$	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	$-0.198047\pi$
$277$	7492.57	1.62522	0.812608	+	0.582810i	$0.198047\pi$
$278$	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	$-0.699849\pi$
$283$	−5592.99	−1.17480	−0.587400	+	0.809297i	$0.699849\pi$
$284$	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	$-0.406450\pi$
$293$	2905.73	0.579367	0.289684	+	0.957122i	$0.406450\pi$
$294$	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	$-0.443581\pi$
$307$	1896.85	0.352635	0.176317	+	0.984333i	$0.443581\pi$
$308$	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	$-0.264780\pi$
$313$	7459.31	1.34705	0.673523	+	0.739166i	$0.264780\pi$
$314$	−7391.23	−1.32838
$315$	0	0
$316$	1173.49	0.208906
$317$	5640.05	0.999296	0.499648	−	0.866229i	$-0.333463\pi$
$317$	5640.05	0.999296	0.499648	+	0.866229i	$0.333463\pi$
$318$	−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	$-0.617809\pi$
$337$	−4475.51	−0.723432	−0.361716	+	0.932288i	$0.617809\pi$
$338$	−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	$-0.482769\pi$
$347$	699.479	0.108213	0.0541066	+	0.998535i	$0.482769\pi$
$348$	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	$-0.413978\pi$
$353$	3541.22	0.533939	0.266969	+	0.963705i	$0.413978\pi$
$354$	−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	$-0.501664\pi$
$367$	−73.4995	−0.0104541	−0.00522703	+	0.999986i	$0.501664\pi$
$368$	−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	$-0.557188\pi$
$373$	−2574.61	−0.357395	−0.178697	+	0.983904i	$0.557188\pi$
$374$	−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	$-0.581601\pi$
$383$	−3801.09	−0.507119	−0.253559	+	0.967320i	$0.581601\pi$
$384$	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	$-0.138917\pi$
$397$	14337.5	1.81254	0.906271	+	0.422698i	$0.138917\pi$
$398$	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	$-0.543024\pi$
$433$	−2428.29	−0.269506	−0.134753	+	0.990879i	$0.543024\pi$
$434$	−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	$-0.288600\pi$
$443$	11494.3	1.23275	0.616377	+	0.787451i	$0.288600\pi$
$444$	−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	$-0.612551\pi$
$457$	−6765.77	−0.692537	−0.346269	+	0.938135i	$0.612551\pi$
$458$	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	$-0.435956\pi$
$463$	3981.97	0.399693	0.199847	+	0.979827i	$0.435956\pi$
$464$	3556.23	0.355806
$465$	0	0
$466$	−15542.3	−1.54503
$467$	−11069.8	−1.09689	−0.548447	−	0.836186i	$-0.684781\pi$
$467$	−11069.8	−1.09689	−0.548447	+	0.836186i	$0.684781\pi$
$468$	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	$-0.685671\pi$
$487$	−11838.7	−1.10157	−0.550784	+	0.834648i	$0.685671\pi$
$488$	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	$-0.426307\pi$
$503$	5176.94	0.458903	0.229451	+	0.973320i	$0.426307\pi$
$504$	−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	$-0.853742\pi$
$523$	−21440.1	−1.79256	−0.896282	+	0.443485i	$0.853742\pi$
$524$	−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	$-0.161407\pi$
$547$	22366.9	1.74834	0.874169	+	0.485622i	$0.161407\pi$
$548$	−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	$-0.572297\pi$
$557$	−5920.24	−0.450357	−0.225178	+	0.974318i	$0.572297\pi$
$558$	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	$-0.461580\pi$
$563$	3216.97	0.240816	0.120408	+	0.992725i	$0.461580\pi$
$564$	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	$-0.248871\pi$
$577$	19670.4	1.41922	0.709611	+	0.704594i	$0.248871\pi$
$578$	−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	$-0.386120\pi$
$587$	9960.44	0.700360	0.350180	+	0.936682i	$0.386120\pi$
$588$	−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	$-0.185470\pi$
$593$	24115.5	1.66999	0.834995	+	0.550257i	$0.185470\pi$
$594$	−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	$-0.304808\pi$
$607$	17213.0	1.15100	0.575499	+	0.817803i	$0.304808\pi$
$608$	−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	$-0.581428\pi$
$613$	−7680.66	−0.506067	−0.253033	+	0.967458i	$0.581428\pi$
$614$	−7410.68	−0.487086
$615$	0	0
$616$	2483.27	0.162425
$617$	−18842.2	−1.22943	−0.614716	−	0.788749i	$-0.710729\pi$
$617$	−18842.2	−1.22943	−0.614716	+	0.788749i	$0.710729\pi$
$618$	−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	$-0.718837\pi$
$643$	−20694.2	−1.26921	−0.634604	+	0.772837i	$0.718837\pi$
$644$	−25896.4	−1.58457
$645$	0	0
$646$	−37066.8	−2.25755
$647$	−8699.16	−0.528592	−0.264296	−	0.964442i	$-0.585140\pi$
$647$	−8699.16	−0.528592	−0.264296	+	0.964442i	$0.585140\pi$
$648$	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	$-0.618185\pi$
$653$	−12108.4	−0.725633	−0.362816	+	0.931861i	$0.618185\pi$
$654$	−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	$-0.179773\pi$
$673$	29495.8	1.68942	0.844710	+	0.535224i	$0.179773\pi$
$674$	17485.1	0.999260
$675$	0	0
$676$	18018.9	1.02520
$677$	−33797.1	−1.91865	−0.959326	−	0.282301i	$-0.908902\pi$
$677$	−33797.1	−1.91865	−0.959326	+	0.282301i	$0.908902\pi$
$678$	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	$-0.480950\pi$
$683$	2135.27	0.119625	0.0598123	+	0.998210i	$0.480950\pi$
$684$	−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	$-0.783284\pi$
$727$	−30463.5	−1.55410	−0.777048	+	0.629442i	$0.783284\pi$
$728$	−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	$-0.278260\pi$
$733$	25466.4	1.28325	0.641625	+	0.767018i	$0.278260\pi$
$734$	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	$-0.593592\pi$
$743$	−11738.9	−0.579622	−0.289811	+	0.957084i	$0.593592\pi$
$744$	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	$-0.316977\pi$
$757$	22653.2	1.08764	0.543822	+	0.839201i	$0.316977\pi$
$758$	−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	$-0.868665\pi$
$773$	−39376.1	−1.83216	−0.916081	+	0.400993i	$0.868665\pi$
$774$	−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	$-0.342266\pi$
$787$	20996.4	0.951007	0.475503	+	0.879714i	$0.342266\pi$
$788$	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	$-0.710574\pi$
$797$	−27645.2	−1.22866	−0.614331	+	0.789049i	$0.710574\pi$
$798$	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	$-0.490175\pi$
$823$	1457.31	0.0617239	0.0308620	+	0.999524i	$0.490175\pi$
$824$	−2684.25	−0.113484
$825$	0	0
$826$	−55944.6	−2.35661
$827$	−12929.7	−0.543662	−0.271831	−	0.962345i	$-0.587629\pi$
$827$	−12929.7	−0.543662	−0.271831	+	0.962345i	$0.587629\pi$
$828$	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	$-0.486668\pi$
$853$	2086.22	0.0837405	0.0418703	+	0.999123i	$0.486668\pi$
$854$	56564.2	2.26650
$855$	0	0
$856$	3174.11	0.126739
$857$	−19021.1	−0.758167	−0.379083	−	0.925363i	$-0.623761\pi$
$857$	−19021.1	−0.758167	−0.379083	+	0.925363i	$0.623761\pi$
$858$	−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	$-0.382110\pi$
$863$	18352.7	0.723908	0.361954	+	0.932196i	$0.382110\pi$
$864$	−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	$-0.408401\pi$
$877$	14742.1	0.567625	0.283812	+	0.958880i	$0.408401\pi$
$878$	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	$-0.368719\pi$
$883$	21034.9	0.801677	0.400839	+	0.916149i	$0.368719\pi$
$884$	−50115.9	−1.90676
$885$	0	0
$886$	−44906.3	−1.70277
$887$	−6406.18	−0.242501	−0.121251	−	0.992622i	$-0.538690\pi$
$887$	−6406.18	−0.242501	−0.121251	+	0.992622i	$0.538690\pi$
$888$	−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	$-0.630711\pi$
$907$	−21808.6	−0.798392	−0.399196	+	0.916866i	$0.630711\pi$
$908$	−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	$-0.539635\pi$
$937$	−7124.36	−0.248391	−0.124196	+	0.992258i	$0.539635\pi$
$938$	−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	$-0.542742\pi$
$947$	−7802.80	−0.267748	−0.133874	+	0.990998i	$0.542742\pi$
$948$	−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	$-0.524342\pi$
$953$	−4495.22	−0.152796	−0.0763979	+	0.997077i	$0.524342\pi$
$954$	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	$-0.567694\pi$
$967$	−12693.8	−0.422137	−0.211069	+	0.977471i	$0.567694\pi$
$968$	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	$-0.357156\pi$
$977$	26497.7	0.867694	0.433847	+	0.900987i	$0.357156\pi$
$978$	−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	$-0.309070\pi$
$983$	34795.4	1.12899	0.564497	+	0.825435i	$0.309070\pi$
$984$	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	$-0.484720\pi$
$997$	3021.16	0.0959690	0.0479845	+	0.998848i	$0.484720\pi$
$998$	−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.f.1.4		14
5.4	even	2		1875.4.a.g.1.11		14
25.4	even	10		75.4.g.b.16.2	✓	28
25.19	even	10		75.4.g.b.61.2	yes	28
75.29	odd	10		225.4.h.a.91.6		28
75.44	odd	10		225.4.h.a.136.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.16.2	✓	28	25.4	even	10
75.4.g.b.61.2	yes	28	25.19	even	10
225.4.h.a.91.6		28	75.29	odd	10
225.4.h.a.136.6		28	75.44	odd	10
1875.4.a.f.1.4		14	1.1	even	1	trivial
1875.4.a.g.1.11		14	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
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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