LMFDB - Embedded newform 825.4.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("825.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.6765757547$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.3368.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 15x + 11 $ x^3 - x^2 - 15*x + 11
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.03932$ of defining polynomial
Character	$\chi$	$=$	825.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.03932 q^{2} +3.00000 q^{3} +8.31608 q^{4} -12.1180 q^{6} +6.49923 q^{7} -1.27677 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.03932 q^{2} +3.00000 q^{3} +8.31608 q^{4} -12.1180 q^{6} +6.49923 q^{7} -1.27677 q^{8} +9.00000 q^{9} +11.0000 q^{11} +24.9483 q^{12} -30.5385 q^{13} -26.2524 q^{14} -61.3714 q^{16} +43.1314 q^{17} -36.3539 q^{18} -6.46044 q^{19} +19.4977 q^{21} -44.4325 q^{22} -108.104 q^{23} -3.83030 q^{24} +123.355 q^{26} +27.0000 q^{27} +54.0481 q^{28} -274.857 q^{29} -68.5519 q^{31} +258.113 q^{32} +33.0000 q^{33} -174.221 q^{34} +74.8448 q^{36} +402.200 q^{37} +26.0958 q^{38} -91.6156 q^{39} -268.450 q^{41} -78.7573 q^{42} +30.5334 q^{43} +91.4769 q^{44} +436.666 q^{46} -31.5850 q^{47} -184.114 q^{48} -300.760 q^{49} +129.394 q^{51} -253.961 q^{52} -252.497 q^{53} -109.062 q^{54} -8.29800 q^{56} -19.3813 q^{57} +1110.24 q^{58} -558.331 q^{59} +335.270 q^{61} +276.903 q^{62} +58.4930 q^{63} -551.628 q^{64} -133.297 q^{66} -28.7521 q^{67} +358.684 q^{68} -324.312 q^{69} +89.0081 q^{71} -11.4909 q^{72} +717.622 q^{73} -1624.61 q^{74} -53.7256 q^{76} +71.4915 q^{77} +370.065 q^{78} +200.702 q^{79} +81.0000 q^{81} +1084.36 q^{82} -243.681 q^{83} +162.144 q^{84} -123.334 q^{86} -824.571 q^{87} -14.0444 q^{88} -312.832 q^{89} -198.477 q^{91} -899.002 q^{92} -205.656 q^{93} +127.582 q^{94} +774.338 q^{96} -27.9996 q^{97} +1214.87 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + 9 q^{3} + 7 q^{4} - 3 q^{6} - 16 q^{7} + 3 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q - q^2 + 9 * q^3 + 7 * q^4 - 3 * q^6 - 16 * q^7 + 3 * q^8 + 27 * q^9	$ 3 q - q^{2} + 9 q^{3} + 7 q^{4} - 3 q^{6} - 16 q^{7} + 3 q^{8} + 27 q^{9} + 33 q^{11} + 21 q^{12} - 45 q^{13} - 116 q^{14} - 85 q^{16} + 58 q^{17} - 9 q^{18} - 169 q^{19} - 48 q^{21} - 11 q^{22} - 155 q^{23} + 9 q^{24} + 167 q^{26} + 81 q^{27} - 100 q^{28} - 277 q^{29} - 173 q^{31} - 97 q^{32} + 99 q^{33} - 146 q^{34} + 63 q^{36} - 60 q^{37} - 169 q^{38} - 135 q^{39} + 44 q^{41} - 348 q^{42} + 109 q^{43} + 77 q^{44} + 425 q^{46} - 270 q^{47} - 255 q^{48} - 427 q^{49} + 174 q^{51} - 45 q^{52} + 148 q^{53} - 27 q^{54} + 168 q^{56} - 507 q^{57} + 783 q^{58} - 684 q^{59} - 1038 q^{61} - 953 q^{62} - 144 q^{63} - 1129 q^{64} - 33 q^{66} - 314 q^{67} + 366 q^{68} - 465 q^{69} - 1459 q^{71} + 27 q^{72} + 1170 q^{73} - 1764 q^{74} + 211 q^{76} - 176 q^{77} + 501 q^{78} - 506 q^{79} + 243 q^{81} + 1040 q^{82} + 347 q^{83} - 300 q^{84} - 527 q^{86} - 831 q^{87} + 33 q^{88} - 607 q^{89} - 398 q^{91} - 687 q^{92} - 519 q^{93} - 1822 q^{94} - 291 q^{96} - 1263 q^{97} + 2273 q^{98} + 297 q^{99}+O(q^{100}) $ 3 * q - q^2 + 9 * q^3 + 7 * q^4 - 3 * q^6 - 16 * q^7 + 3 * q^8 + 27 * q^9 + 33 * q^11 + 21 * q^12 - 45 * q^13 - 116 * q^14 - 85 * q^16 + 58 * q^17 - 9 * q^18 - 169 * q^19 - 48 * q^21 - 11 * q^22 - 155 * q^23 + 9 * q^24 + 167 * q^26 + 81 * q^27 - 100 * q^28 - 277 * q^29 - 173 * q^31 - 97 * q^32 + 99 * q^33 - 146 * q^34 + 63 * q^36 - 60 * q^37 - 169 * q^38 - 135 * q^39 + 44 * q^41 - 348 * q^42 + 109 * q^43 + 77 * q^44 + 425 * q^46 - 270 * q^47 - 255 * q^48 - 427 * q^49 + 174 * q^51 - 45 * q^52 + 148 * q^53 - 27 * q^54 + 168 * q^56 - 507 * q^57 + 783 * q^58 - 684 * q^59 - 1038 * q^61 - 953 * q^62 - 144 * q^63 - 1129 * q^64 - 33 * q^66 - 314 * q^67 + 366 * q^68 - 465 * q^69 - 1459 * q^71 + 27 * q^72 + 1170 * q^73 - 1764 * q^74 + 211 * q^76 - 176 * q^77 + 501 * q^78 - 506 * q^79 + 243 * q^81 + 1040 * q^82 + 347 * q^83 - 300 * q^84 - 527 * q^86 - 831 * q^87 + 33 * q^88 - 607 * q^89 - 398 * q^91 - 687 * q^92 - 519 * q^93 - 1822 * q^94 - 291 * q^96 - 1263 * q^97 + 2273 * 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 $

$2$	−4.03932	−1.42811	−0.714057	−	0.700087i	$-0.753144\pi$
$2$	−4.03932	−1.42811	−0.714057	+	0.700087i	$0.753144\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	8.31608	1.03951
$5$	0	0
$5$	0	0
$6$	−12.1180	−0.824522
$7$	6.49923	0.350925	0.175463	−	0.984486i	$-0.443858\pi$
$7$	6.49923	0.350925	0.175463	+	0.984486i	$0.443858\pi$
$8$	−1.27677	−0.0564257
$9$	9.00000	0.333333
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	24.9483	0.600162
$13$	−30.5385	−0.651528	−0.325764	−	0.945451i	$-0.605622\pi$
$13$	−30.5385	−0.651528	−0.325764	+	0.945451i	$0.605622\pi$
$14$	−26.2524	−0.501161
$15$	0	0
$16$	−61.3714	−0.958928
$17$	43.1314	0.615347	0.307674	−	0.951492i	$-0.400450\pi$
$17$	43.1314	0.615347	0.307674	+	0.951492i	$0.400450\pi$
$18$	−36.3539	−0.476038
$19$	−6.46044	−0.0780066	−0.0390033	−	0.999239i	$-0.512418\pi$
$19$	−6.46044	−0.0780066	−0.0390033	+	0.999239i	$0.512418\pi$
$20$	0	0
$21$	19.4977	0.202607
$22$	−44.4325	−0.430593
$23$	−108.104	−0.980054	−0.490027	−	0.871707i	$-0.663013\pi$
$23$	−108.104	−0.980054	−0.490027	+	0.871707i	$0.663013\pi$
$24$	−3.83030	−0.0325774
$25$	0	0
$26$	123.355	0.930457
$27$	27.0000	0.192450
$28$	54.0481	0.364791
$29$	−274.857	−1.75999	−0.879995	−	0.474984i	$-0.842454\pi$
$29$	−274.857	−1.75999	−0.879995	+	0.474984i	$0.842454\pi$
$30$	0	0
$31$	−68.5519	−0.397170	−0.198585	−	0.980084i	$-0.563635\pi$
$31$	−68.5519	−0.397170	−0.198585	+	0.980084i	$0.563635\pi$
$32$	258.113	1.42588
$33$	33.0000	0.174078
$34$	−174.221	−0.878786
$35$	0	0
$36$	74.8448	0.346504
$37$	402.200	1.78706	0.893530	−	0.449004i	$-0.148221\pi$
$37$	402.200	1.78706	0.893530	+	0.449004i	$0.148221\pi$
$38$	26.0958	0.111402
$39$	−91.6156	−0.376160
$40$	0	0
$41$	−268.450	−1.02256	−0.511280	−	0.859414i	$-0.670828\pi$
$41$	−268.450	−1.02256	−0.511280	+	0.859414i	$0.670828\pi$
$42$	−78.7573	−0.289346
$43$	30.5334	0.108286	0.0541431	−	0.998533i	$-0.482757\pi$
$43$	30.5334	0.108286	0.0541431	+	0.998533i	$0.482757\pi$
$44$	91.4769	0.313424
$45$	0	0
$46$	436.666	1.39963
$47$	−31.5850	−0.0980243	−0.0490121	−	0.998798i	$-0.515607\pi$
$47$	−31.5850	−0.0980243	−0.0490121	+	0.998798i	$0.515607\pi$
$48$	−184.114	−0.553638
$49$	−300.760	−0.876851
$50$	0	0
$51$	129.394	0.355271
$52$	−253.961	−0.677271
$53$	−252.497	−0.654398	−0.327199	−	0.944956i	$-0.606105\pi$
$53$	−252.497	−0.654398	−0.327199	+	0.944956i	$0.606105\pi$
$54$	−109.062	−0.274841
$55$	0	0
$56$	−8.29800	−0.0198012
$57$	−19.3813	−0.0450372
$58$	1110.24	2.51347
$59$	−558.331	−1.23201	−0.616004	−	0.787743i	$-0.711250\pi$
$59$	−558.331	−1.23201	−0.616004	+	0.787743i	$0.711250\pi$
$60$	0	0
$61$	335.270	0.703719	0.351860	−	0.936053i	$-0.385549\pi$
$61$	335.270	0.703719	0.351860	+	0.936053i	$0.385549\pi$
$62$	276.903	0.567205
$63$	58.4930	0.116975
$64$	−551.628	−1.07740
$65$	0	0
$66$	−133.297	−0.248603
$67$	−28.7521	−0.0524273	−0.0262136	−	0.999656i	$-0.508345\pi$
$67$	−28.7521	−0.0524273	−0.0262136	+	0.999656i	$0.508345\pi$
$68$	358.684	0.639660
$69$	−324.312	−0.565834
$70$	0	0
$71$	89.0081	0.148779	0.0743895	−	0.997229i	$-0.476299\pi$
$71$	89.0081	0.148779	0.0743895	+	0.997229i	$0.476299\pi$
$72$	−11.4909	−0.0188086
$73$	717.622	1.15057	0.575283	−	0.817954i	$-0.304892\pi$
$73$	717.622	1.15057	0.575283	+	0.817954i	$0.304892\pi$
$74$	−1624.61	−2.55213
$75$	0	0
$76$	−53.7256	−0.0810887
$77$	71.4915	0.105808
$78$	370.065	0.537200
$79$	200.702	0.285832	0.142916	−	0.989735i	$-0.454352\pi$
$79$	200.702	0.285832	0.142916	+	0.989735i	$0.454352\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	1084.36	1.46033
$83$	−243.681	−0.322258	−0.161129	−	0.986933i	$-0.551514\pi$
$83$	−243.681	−0.322258	−0.161129	+	0.986933i	$0.551514\pi$
$84$	162.144	0.210612
$85$	0	0
$86$	−123.334	−0.154645
$87$	−824.571	−1.01613
$88$	−14.0444	−0.0170130
$89$	−312.832	−0.372585	−0.186293	−	0.982494i	$-0.559647\pi$
$89$	−312.832	−0.372585	−0.186293	+	0.982494i	$0.559647\pi$
$90$	0	0
$91$	−198.477	−0.228638
$92$	−899.002	−1.01878
$93$	−205.656	−0.229306
$94$	127.582	0.139990
$95$	0	0
$96$	774.338	0.823235
$97$	−27.9996	−0.0293085	−0.0146543	−	0.999893i	$-0.504665\pi$
$97$	−27.9996	−0.0293085	−0.0146543	+	0.999893i	$0.504665\pi$
$98$	1214.87	1.25224
$99$	99.0000	0.100504
$100$	0	0
$101$	−228.278	−0.224896	−0.112448	−	0.993658i	$-0.535869\pi$
$101$	−228.278	−0.224896	−0.112448	+	0.993658i	$0.535869\pi$
$102$	−522.664	−0.507367
$103$	800.328	0.765618	0.382809	−	0.923827i	$-0.374957\pi$
$103$	800.328	0.765618	0.382809	+	0.923827i	$0.374957\pi$
$104$	38.9906	0.0367629
$105$	0	0
$106$	1019.91	0.934555
$107$	1046.89	0.945857	0.472929	−	0.881101i	$-0.343197\pi$
$107$	1046.89	0.945857	0.472929	+	0.881101i	$0.343197\pi$
$108$	224.534	0.200054
$109$	317.023	0.278581	0.139291	−	0.990252i	$-0.455518\pi$
$109$	317.023	0.278581	0.139291	+	0.990252i	$0.455518\pi$
$110$	0	0
$111$	1206.60	1.03176
$112$	−398.867	−0.336512
$113$	−1333.82	−1.11040	−0.555198	−	0.831718i	$-0.687358\pi$
$113$	−1333.82	−1.11040	−0.555198	+	0.831718i	$0.687358\pi$
$114$	78.2873	0.0643182
$115$	0	0
$116$	−2285.74	−1.82953
$117$	−274.847	−0.217176
$118$	2255.28	1.75945
$119$	280.321	0.215941
$120$	0	0
$121$	121.000	0.0909091
$122$	−1354.26	−1.00499
$123$	−805.351	−0.590375
$124$	−570.083	−0.412863
$125$	0	0
$126$	−236.272	−0.167054
$127$	−564.888	−0.394691	−0.197345	−	0.980334i	$-0.563232\pi$
$127$	−564.888	−0.394691	−0.197345	+	0.980334i	$0.563232\pi$
$128$	163.299	0.112763
$129$	91.6003	0.0625190
$130$	0	0
$131$	−214.082	−0.142782	−0.0713908	−	0.997448i	$-0.522744\pi$
$131$	−214.082	−0.142782	−0.0713908	+	0.997448i	$0.522744\pi$
$132$	274.431	0.180956
$133$	−41.9879	−0.0273745
$134$	116.139	0.0748721
$135$	0	0
$136$	−55.0688	−0.0347214
$137$	65.2288	0.0406779	0.0203389	−	0.999793i	$-0.493525\pi$
$137$	65.2288	0.0406779	0.0203389	+	0.999793i	$0.493525\pi$
$138$	1310.00	0.808076
$139$	−407.084	−0.248406	−0.124203	−	0.992257i	$-0.539637\pi$
$139$	−407.084	−0.248406	−0.124203	+	0.992257i	$0.539637\pi$
$140$	0	0
$141$	−94.7549	−0.0565943
$142$	−359.532	−0.212474
$143$	−335.924	−0.196443
$144$	−552.343	−0.319643
$145$	0	0
$146$	−2898.70	−1.64314
$147$	−902.280	−0.506250
$148$	3344.73	1.85767
$149$	792.092	0.435508	0.217754	−	0.976004i	$-0.430127\pi$
$149$	792.092	0.435508	0.217754	+	0.976004i	$0.430127\pi$
$150$	0	0
$151$	−2861.80	−1.54232	−0.771159	−	0.636642i	$-0.780323\pi$
$151$	−2861.80	−1.54232	−0.771159	+	0.636642i	$0.780323\pi$
$152$	8.24848	0.00440158
$153$	388.183	0.205116
$154$	−288.777	−0.151106
$155$	0	0
$156$	−761.883	−0.391022
$157$	−2991.55	−1.52071	−0.760355	−	0.649507i	$-0.774975\pi$
$157$	−2991.55	−1.52071	−0.760355	+	0.649507i	$0.774975\pi$
$158$	−810.698	−0.408201
$159$	−757.490	−0.377817
$160$	0	0
$161$	−702.592	−0.343926
$162$	−327.185	−0.158679
$163$	−2907.60	−1.39718	−0.698592	−	0.715520i	$-0.746190\pi$
$163$	−2907.60	−1.39718	−0.698592	+	0.715520i	$0.746190\pi$
$164$	−2232.46	−1.06296
$165$	0	0
$166$	984.304	0.460222
$167$	−1100.39	−0.509885	−0.254942	−	0.966956i	$-0.582056\pi$
$167$	−1100.39	−0.509885	−0.254942	+	0.966956i	$0.582056\pi$
$168$	−24.8940	−0.0114322
$169$	−1264.40	−0.575511
$170$	0	0
$171$	−58.1439	−0.0260022
$172$	253.919	0.112565
$173$	−3754.75	−1.65011	−0.825054	−	0.565054i	$-0.808855\pi$
$173$	−3754.75	−1.65011	−0.825054	+	0.565054i	$0.808855\pi$
$174$	3330.71	1.45115
$175$	0	0
$176$	−675.086	−0.289128
$177$	−1674.99	−0.711301
$178$	1263.63	0.532094
$179$	−3218.79	−1.34404	−0.672021	−	0.740532i	$-0.734574\pi$
$179$	−3218.79	−1.34404	−0.672021	+	0.740532i	$0.734574\pi$
$180$	0	0
$181$	−456.885	−0.187624	−0.0938121	−	0.995590i	$-0.529905\pi$
$181$	−456.885	−0.187624	−0.0938121	+	0.995590i	$0.529905\pi$
$182$	801.711	0.326521
$183$	1005.81	0.406292
$184$	138.024	0.0553002
$185$	0	0
$186$	830.709	0.327476
$187$	474.445	0.185534
$188$	−262.663	−0.101897
$189$	175.479	0.0675356
$190$	0	0
$191$	−4907.11	−1.85899	−0.929493	−	0.368841i	$-0.879755\pi$
$191$	−4907.11	−1.85899	−0.929493	+	0.368841i	$0.879755\pi$
$192$	−1654.88	−0.622036
$193$	−1462.17	−0.545333	−0.272667	−	0.962109i	$-0.587906\pi$
$193$	−1462.17	−0.545333	−0.272667	+	0.962109i	$0.587906\pi$
$194$	113.099	0.0418559
$195$	0	0
$196$	−2501.15	−0.911496
$197$	−2210.10	−0.799307	−0.399653	−	0.916666i	$-0.630869\pi$
$197$	−2210.10	−0.799307	−0.399653	+	0.916666i	$0.630869\pi$
$198$	−399.892	−0.143531
$199$	−395.272	−0.140804	−0.0704022	−	0.997519i	$-0.522428\pi$
$199$	−395.272	−0.140804	−0.0704022	+	0.997519i	$0.522428\pi$
$200$	0	0
$201$	−86.2563	−0.0302689
$202$	922.086	0.321177
$203$	−1786.36	−0.617625
$204$	1076.05	0.369308
$205$	0	0
$206$	−3232.78	−1.09339
$207$	−972.936	−0.326685
$208$	1874.19	0.624769
$209$	−71.0648	−0.0235199
$210$	0	0
$211$	1559.98	0.508974	0.254487	−	0.967076i	$-0.418093\pi$
$211$	1559.98	0.508974	0.254487	+	0.967076i	$0.418093\pi$
$212$	−2099.78	−0.680253
$213$	267.024	0.0858976
$214$	−4228.72	−1.35079
$215$	0	0
$216$	−34.4727	−0.0108591
$217$	−445.534	−0.139377
$218$	−1280.56	−0.397846
$219$	2152.87	0.664280
$220$	0	0
$221$	−1317.17	−0.400916
$222$	−4873.84	−1.47347
$223$	−756.215	−0.227085	−0.113542	−	0.993533i	$-0.536220\pi$
$223$	−756.215	−0.227085	−0.113542	+	0.993533i	$0.536220\pi$
$224$	1677.53	0.500379
$225$	0	0
$226$	5387.70	1.58577
$227$	5758.69	1.68378	0.841890	−	0.539649i	$-0.181443\pi$
$227$	5758.69	1.68378	0.841890	+	0.539649i	$0.181443\pi$
$228$	−161.177	−0.0468166
$229$	−1912.63	−0.551921	−0.275961	−	0.961169i	$-0.588996\pi$
$229$	−1912.63	−0.551921	−0.275961	+	0.961169i	$0.588996\pi$
$230$	0	0
$231$	214.474	0.0610882
$232$	350.929	0.0993086
$233$	−1034.86	−0.290970	−0.145485	−	0.989360i	$-0.546474\pi$
$233$	−1034.86	−0.290970	−0.145485	+	0.989360i	$0.546474\pi$
$234$	1110.19	0.310152
$235$	0	0
$236$	−4643.13	−1.28069
$237$	602.105	0.165025
$238$	−1132.30	−0.308388
$239$	2647.23	0.716465	0.358232	−	0.933632i	$-0.383380\pi$
$239$	2647.23	0.716465	0.358232	+	0.933632i	$0.383380\pi$
$240$	0	0
$241$	6734.00	1.79990	0.899948	−	0.435996i	$-0.143604\pi$
$241$	6734.00	1.79990	0.899948	+	0.435996i	$0.143604\pi$
$242$	−488.757	−0.129829
$243$	243.000	0.0641500
$244$	2788.13	0.731523
$245$	0	0
$246$	3253.07	0.843123
$247$	197.292	0.0508235
$248$	87.5248	0.0224106
$249$	−731.043	−0.186056
$250$	0	0
$251$	−5377.57	−1.35231	−0.676154	−	0.736761i	$-0.736354\pi$
$251$	−5377.57	−1.35231	−0.676154	+	0.736761i	$0.736354\pi$
$252$	486.433	0.121597
$253$	−1189.14	−0.295497
$254$	2281.76	0.563663
$255$	0	0
$256$	3753.41	0.916360
$257$	−5882.33	−1.42774	−0.713871	−	0.700278i	$-0.753060\pi$
$257$	−5882.33	−1.42774	−0.713871	+	0.700278i	$0.753060\pi$
$258$	−370.003	−0.0892843
$259$	2613.99	0.627124
$260$	0	0
$261$	−2473.71	−0.586663
$262$	864.744	0.203909
$263$	4001.67	0.938227	0.469113	−	0.883138i	$-0.344574\pi$
$263$	4001.67	0.938227	0.469113	+	0.883138i	$0.344574\pi$
$264$	−42.1333	−0.00982245
$265$	0	0
$266$	169.602	0.0390939
$267$	−938.495	−0.215112
$268$	−239.105	−0.0544987
$269$	−1758.29	−0.398530	−0.199265	−	0.979946i	$-0.563856\pi$
$269$	−1758.29	−0.398530	−0.199265	+	0.979946i	$0.563856\pi$
$270$	0	0
$271$	6018.44	1.34906	0.674528	−	0.738249i	$-0.264347\pi$
$271$	6018.44	1.34906	0.674528	+	0.738249i	$0.264347\pi$
$272$	−2647.03	−0.590074
$273$	−595.431	−0.132004
$274$	−263.480	−0.0580927
$275$	0	0
$276$	−2697.01	−0.588191
$277$	−2910.30	−0.631275	−0.315637	−	0.948880i	$-0.602218\pi$
$277$	−2910.30	−0.631275	−0.315637	+	0.948880i	$0.602218\pi$
$278$	1644.34	0.354752
$279$	−616.967	−0.132390
$280$	0	0
$281$	6893.19	1.46339	0.731697	−	0.681631i	$-0.238729\pi$
$281$	6893.19	1.46339	0.731697	+	0.681631i	$0.238729\pi$
$282$	382.745	0.0808232
$283$	−3120.16	−0.655385	−0.327693	−	0.944784i	$-0.606271\pi$
$283$	−3120.16	−0.655385	−0.327693	+	0.944784i	$0.606271\pi$
$284$	740.199	0.154657
$285$	0	0
$286$	1356.90	0.280543
$287$	−1744.72	−0.358842
$288$	2323.01	0.475295
$289$	−3052.68	−0.621348
$290$	0	0
$291$	−83.9988	−0.0169213
$292$	5967.81	1.19603
$293$	−8869.62	−1.76849	−0.884247	−	0.467020i	$-0.845328\pi$
$293$	−8869.62	−1.76849	−0.884247	+	0.467020i	$0.845328\pi$
$294$	3644.60	0.722983
$295$	0	0
$296$	−513.515	−0.100836
$297$	297.000	0.0580259
$298$	−3199.51	−0.621955
$299$	3301.34	0.638533
$300$	0	0
$301$	198.444	0.0380003
$302$	11559.7	2.20261
$303$	−684.833	−0.129844
$304$	396.486	0.0748028
$305$	0	0
$306$	−1567.99	−0.292929
$307$	5713.42	1.06216	0.531078	−	0.847323i	$-0.321787\pi$
$307$	5713.42	1.06216	0.531078	+	0.847323i	$0.321787\pi$
$308$	594.529	0.109988
$309$	2400.98	0.442030
$310$	0	0
$311$	1984.01	0.361746	0.180873	−	0.983506i	$-0.442108\pi$
$311$	1984.01	0.361746	0.180873	+	0.983506i	$0.442108\pi$
$312$	116.972	0.0212251
$313$	2675.50	0.483156	0.241578	−	0.970381i	$-0.422335\pi$
$313$	2675.50	0.483156	0.241578	+	0.970381i	$0.422335\pi$
$314$	12083.8	2.17175
$315$	0	0
$316$	1669.05	0.297125
$317$	7083.76	1.25509	0.627545	−	0.778580i	$-0.284060\pi$
$317$	7083.76	1.25509	0.627545	+	0.778580i	$0.284060\pi$
$318$	3059.74	0.539565
$319$	−3023.43	−0.530657
$320$	0	0
$321$	3140.67	0.546091
$322$	2837.99	0.491165
$323$	−278.648	−0.0480012
$324$	673.603	0.115501
$325$	0	0
$326$	11744.7	1.99534
$327$	951.070	0.160839
$328$	342.749	0.0576986
$329$	−205.278	−0.0343992
$330$	0	0
$331$	7812.39	1.29730	0.648652	−	0.761085i	$-0.275333\pi$
$331$	7812.39	1.29730	0.648652	+	0.761085i	$0.275333\pi$
$332$	−2026.47	−0.334991
$333$	3619.80	0.595686
$334$	4444.82	0.728173
$335$	0	0
$336$	−1196.60	−0.194285
$337$	11866.4	1.91811	0.959056	−	0.283218i	$-0.0914019\pi$
$337$	11866.4	1.91811	0.959056	+	0.283218i	$0.0914019\pi$
$338$	5107.30	0.821895
$339$	−4001.45	−0.641088
$340$	0	0
$341$	−754.071	−0.119751
$342$	234.862	0.0371341
$343$	−4183.94	−0.658635
$344$	−38.9841	−0.00611012
$345$	0	0
$346$	15166.6	2.35654
$347$	−3485.50	−0.539225	−0.269613	−	0.962969i	$-0.586896\pi$
$347$	−3485.50	−0.539225	−0.269613	+	0.962969i	$0.586896\pi$
$348$	−6857.21	−1.05628
$349$	−6366.76	−0.976518	−0.488259	−	0.872699i	$-0.662368\pi$
$349$	−6366.76	−0.976518	−0.488259	+	0.872699i	$0.662368\pi$
$350$	0	0
$351$	−824.541	−0.125387
$352$	2839.24	0.429920
$353$	−8223.15	−1.23987	−0.619935	−	0.784653i	$-0.712841\pi$
$353$	−8223.15	−1.23987	−0.619935	+	0.784653i	$0.712841\pi$
$354$	6765.83	1.01582
$355$	0	0
$356$	−2601.54	−0.387306
$357$	840.962	0.124674
$358$	13001.7	1.91945
$359$	−9377.54	−1.37863	−0.689314	−	0.724462i	$-0.742088\pi$
$359$	−9377.54	−1.37863	−0.689314	+	0.724462i	$0.742088\pi$
$360$	0	0
$361$	−6817.26	−0.993915
$362$	1845.50	0.267949
$363$	363.000	0.0524864
$364$	−1650.55	−0.237671
$365$	0	0
$366$	−4062.78	−0.580232
$367$	310.895	0.0442196	0.0221098	−	0.999756i	$-0.492962\pi$
$367$	310.895	0.0442196	0.0221098	+	0.999756i	$0.492962\pi$
$368$	6634.49	0.939801
$369$	−2416.05	−0.340853
$370$	0	0
$371$	−1641.03	−0.229645
$372$	−1710.25	−0.238366
$373$	4738.51	0.657777	0.328889	−	0.944369i	$-0.393326\pi$
$373$	4738.51	0.657777	0.328889	+	0.944369i	$0.393326\pi$
$374$	−1916.44	−0.264964
$375$	0	0
$376$	40.3267	0.00553109
$377$	8393.74	1.14668
$378$	−708.816	−0.0964486
$379$	−4735.47	−0.641806	−0.320903	−	0.947112i	$-0.603986\pi$
$379$	−4735.47	−0.641806	−0.320903	+	0.947112i	$0.603986\pi$
$380$	0	0
$381$	−1694.66	−0.227875
$382$	19821.4	2.65484
$383$	−3632.14	−0.484579	−0.242289	−	0.970204i	$-0.577898\pi$
$383$	−3632.14	−0.484579	−0.242289	+	0.970204i	$0.577898\pi$
$384$	489.896	0.0651039
$385$	0	0
$386$	5906.17	0.778798
$387$	274.801	0.0360954
$388$	−232.847	−0.0304665
$389$	6557.50	0.854701	0.427350	−	0.904086i	$-0.359447\pi$
$389$	6557.50	0.854701	0.427350	+	0.904086i	$0.359447\pi$
$390$	0	0
$391$	−4662.68	−0.603073
$392$	384.001	0.0494769
$393$	−642.245	−0.0824350
$394$	8927.31	1.14150
$395$	0	0
$396$	823.292	0.104475
$397$	−4084.97	−0.516420	−0.258210	−	0.966089i	$-0.583133\pi$
$397$	−4084.97	−0.516420	−0.258210	+	0.966089i	$0.583133\pi$
$398$	1596.63	0.201085
$399$	−125.964	−0.0158047
$400$	0	0
$401$	−6676.04	−0.831386	−0.415693	−	0.909505i	$-0.636461\pi$
$401$	−6676.04	−0.831386	−0.415693	+	0.909505i	$0.636461\pi$
$402$	348.417	0.0432275
$403$	2093.47	0.258768
$404$	−1898.38	−0.233782
$405$	0	0
$406$	7215.67	0.882039
$407$	4424.20	0.538819
$408$	−165.206	−0.0200464
$409$	1718.56	0.207769	0.103884	−	0.994589i	$-0.466873\pi$
$409$	1718.56	0.207769	0.103884	+	0.994589i	$0.466873\pi$
$410$	0	0
$411$	195.686	0.0234854
$412$	6655.60	0.795868
$413$	−3628.72	−0.432343
$414$	3930.00	0.466543
$415$	0	0
$416$	−7882.39	−0.929004
$417$	−1221.25	−0.143417
$418$	287.053	0.0335891
$419$	5732.23	0.668348	0.334174	−	0.942511i	$-0.391543\pi$
$419$	5732.23	0.668348	0.334174	+	0.942511i	$0.391543\pi$
$420$	0	0
$421$	−9647.38	−1.11683	−0.558414	−	0.829563i	$-0.688590\pi$
$421$	−9647.38	−1.11683	−0.558414	+	0.829563i	$0.688590\pi$
$422$	−6301.26	−0.726873
$423$	−284.265	−0.0326748
$424$	322.379	0.0369248
$425$	0	0
$426$	−1078.60	−0.122672
$427$	2178.99	0.246953
$428$	8706.03	0.983229
$429$	−1007.77	−0.113417
$430$	0	0
$431$	−3054.57	−0.341376	−0.170688	−	0.985325i	$-0.554599\pi$
$431$	−3054.57	−0.341376	−0.170688	+	0.985325i	$0.554599\pi$
$432$	−1657.03	−0.184546
$433$	−11022.8	−1.22337	−0.611686	−	0.791100i	$-0.709509\pi$
$433$	−11022.8	−1.22337	−0.611686	+	0.791100i	$0.709509\pi$
$434$	1799.65	0.199046
$435$	0	0
$436$	2636.39	0.289588
$437$	698.399	0.0764507
$438$	−8696.11	−0.948667
$439$	−7589.30	−0.825097	−0.412548	−	0.910936i	$-0.635361\pi$
$439$	−7589.30	−0.825097	−0.412548	+	0.910936i	$0.635361\pi$
$440$	0	0
$441$	−2706.84	−0.292284
$442$	5320.47	0.572554
$443$	−4043.30	−0.433641	−0.216821	−	0.976211i	$-0.569569\pi$
$443$	−4043.30	−0.433641	−0.216821	+	0.976211i	$0.569569\pi$
$444$	10034.2	1.07252
$445$	0	0
$446$	3054.59	0.324303
$447$	2376.28	0.251441
$448$	−3585.16	−0.378086
$449$	14619.3	1.53658	0.768291	−	0.640101i	$-0.221107\pi$
$449$	14619.3	1.53658	0.768291	+	0.640101i	$0.221107\pi$
$450$	0	0
$451$	−2952.96	−0.308313
$452$	−11092.1	−1.15427
$453$	−8585.40	−0.890458
$454$	−23261.2	−2.40463
$455$	0	0
$456$	24.7454	0.00254125
$457$	10910.8	1.11682	0.558411	−	0.829565i	$-0.311411\pi$
$457$	10910.8	1.11682	0.558411	+	0.829565i	$0.311411\pi$
$458$	7725.71	0.788207
$459$	1164.55	0.118424
$460$	0	0
$461$	16371.0	1.65395	0.826977	−	0.562236i	$-0.190059\pi$
$461$	16371.0	1.65395	0.826977	+	0.562236i	$0.190059\pi$
$462$	−866.331	−0.0872410
$463$	16023.5	1.60837	0.804186	−	0.594377i	$-0.202601\pi$
$463$	16023.5	1.60837	0.804186	+	0.594377i	$0.202601\pi$
$464$	16868.4	1.68770
$465$	0	0
$466$	4180.13	0.415538
$467$	15097.3	1.49597	0.747985	−	0.663716i	$-0.231022\pi$
$467$	15097.3	1.49597	0.747985	+	0.663716i	$0.231022\pi$
$468$	−2285.65	−0.225757
$469$	−186.866	−0.0183981
$470$	0	0
$471$	−8974.65	−0.877983
$472$	712.859	0.0695170
$473$	335.868	0.0326495
$474$	−2432.09	−0.235675
$475$	0	0
$476$	2331.17	0.224473
$477$	−2272.47	−0.218133
$478$	−10693.0	−1.02319
$479$	−10459.0	−0.997667	−0.498834	−	0.866698i	$-0.666238\pi$
$479$	−10459.0	−0.997667	−0.498834	+	0.866698i	$0.666238\pi$
$480$	0	0
$481$	−12282.6	−1.16432
$482$	−27200.8	−2.57046
$483$	−2107.78	−0.198566
$484$	1006.25	0.0945010
$485$	0	0
$486$	−981.554	−0.0916136
$487$	7939.86	0.738788	0.369394	−	0.929273i	$-0.379565\pi$
$487$	7939.86	0.738788	0.369394	+	0.929273i	$0.379565\pi$
$488$	−428.061	−0.0397078
$489$	−8722.81	−0.806665
$490$	0	0
$491$	11492.7	1.05633	0.528167	−	0.849141i	$-0.322880\pi$
$491$	11492.7	1.05633	0.528167	+	0.849141i	$0.322880\pi$
$492$	−6697.37	−0.613701
$493$	−11855.0	−1.08300
$494$	−796.927	−0.0725818
$495$	0	0
$496$	4207.13	0.380858
$497$	578.484	0.0522103
$498$	2952.91	0.265709
$499$	4813.54	0.431831	0.215915	−	0.976412i	$-0.430726\pi$
$499$	4813.54	0.431831	0.215915	+	0.976412i	$0.430726\pi$
$500$	0	0
$501$	−3301.17	−0.294382
$502$	21721.7	1.93125
$503$	−17756.3	−1.57399	−0.786993	−	0.616962i	$-0.788363\pi$
$503$	−17756.3	−1.57399	−0.786993	+	0.616962i	$0.788363\pi$
$504$	−74.6820	−0.00660040
$505$	0	0
$506$	4803.33	0.422004
$507$	−3793.19	−0.332271
$508$	−4697.66	−0.410285
$509$	3183.05	0.277183	0.138592	−	0.990350i	$-0.455742\pi$
$509$	3183.05	0.277183	0.138592	+	0.990350i	$0.455742\pi$
$510$	0	0
$511$	4663.99	0.403763
$512$	−16467.6	−1.42143
$513$	−174.432	−0.0150124
$514$	23760.6	2.03898
$515$	0	0
$516$	761.756	0.0649892
$517$	−347.435	−0.0295554
$518$	−10558.7	−0.895605
$519$	−11264.3	−0.952690
$520$	0	0
$521$	7246.60	0.609365	0.304683	−	0.952454i	$-0.401450\pi$
$521$	7246.60	0.609365	0.304683	+	0.952454i	$0.401450\pi$
$522$	9992.12	0.837822
$523$	17985.0	1.50369	0.751845	−	0.659340i	$-0.229164\pi$
$523$	17985.0	1.50369	0.751845	+	0.659340i	$0.229164\pi$
$524$	−1780.32	−0.148423
$525$	0	0
$526$	−16164.0	−1.33990
$527$	−2956.74	−0.244398
$528$	−2025.26	−0.166928
$529$	−480.530	−0.0394945
$530$	0	0
$531$	−5024.98	−0.410670
$532$	−349.175	−0.0284561
$533$	8198.09	0.666226
$534$	3790.88	0.307205
$535$	0	0
$536$	36.7097	0.00295825
$537$	−9656.36	−0.775983
$538$	7102.28	0.569147
$539$	−3308.36	−0.264381
$540$	0	0
$541$	−14549.3	−1.15624	−0.578119	−	0.815952i	$-0.696213\pi$
$541$	−14549.3	−1.15624	−0.578119	+	0.815952i	$0.696213\pi$
$542$	−24310.4	−1.92661
$543$	−1370.65	−0.108325
$544$	11132.8	0.877414
$545$	0	0
$546$	2405.13	0.188517
$547$	−5487.29	−0.428920	−0.214460	−	0.976733i	$-0.568799\pi$
$547$	−5487.29	−0.428920	−0.214460	+	0.976733i	$0.568799\pi$
$548$	542.448	0.0422851
$549$	3017.43	0.234573
$550$	0	0
$551$	1775.70	0.137291
$552$	414.071	0.0319276
$553$	1304.41	0.100306
$554$	11755.6	0.901532
$555$	0	0
$556$	−3385.35	−0.258221
$557$	7366.60	0.560382	0.280191	−	0.959944i	$-0.409602\pi$
$557$	7366.60	0.560382	0.280191	+	0.959944i	$0.409602\pi$
$558$	2492.13	0.189068
$559$	−932.446	−0.0705515
$560$	0	0
$561$	1423.34	0.107118
$562$	−27843.8	−2.08989
$563$	4516.14	0.338068	0.169034	−	0.985610i	$-0.445935\pi$
$563$	4516.14	0.338068	0.169034	+	0.985610i	$0.445935\pi$
$564$	−787.990	−0.0588304
$565$	0	0
$566$	12603.3	0.935965
$567$	526.437	0.0389917
$568$	−113.643	−0.00839496
$569$	2174.35	0.160200	0.0800999	−	0.996787i	$-0.474476\pi$
$569$	2174.35	0.160200	0.0800999	+	0.996787i	$0.474476\pi$
$570$	0	0
$571$	−25339.7	−1.85715	−0.928575	−	0.371145i	$-0.878965\pi$
$571$	−25339.7	−1.85715	−0.928575	+	0.371145i	$0.878965\pi$
$572$	−2793.57	−0.204205
$573$	−14721.3	−1.07329
$574$	7047.48	0.512467
$575$	0	0
$576$	−4964.65	−0.359133
$577$	21909.1	1.58074	0.790370	−	0.612630i	$-0.209888\pi$
$577$	21909.1	1.58074	0.790370	+	0.612630i	$0.209888\pi$
$578$	12330.8	0.887356
$579$	−4386.51	−0.314848
$580$	0	0
$581$	−1583.74	−0.113089
$582$	339.298	0.0241655
$583$	−2777.46	−0.197308
$584$	−916.237	−0.0649215
$585$	0	0
$586$	35827.2	2.52561
$587$	922.235	0.0648462	0.0324231	−	0.999474i	$-0.489678\pi$
$587$	922.235	0.0648462	0.0324231	+	0.999474i	$0.489678\pi$
$588$	−7503.44	−0.526253
$589$	442.875	0.0309819
$590$	0	0
$591$	−6630.31	−0.461480
$592$	−24683.6	−1.71366
$593$	9075.86	0.628501	0.314250	−	0.949340i	$-0.398247\pi$
$593$	9075.86	0.628501	0.314250	+	0.949340i	$0.398247\pi$
$594$	−1199.68	−0.0828676
$595$	0	0
$596$	6587.10	0.452715
$597$	−1185.82	−0.0812935
$598$	−13335.2	−0.911898
$599$	19987.0	1.36335	0.681675	−	0.731655i	$-0.261252\pi$
$599$	19987.0	1.36335	0.681675	+	0.731655i	$0.261252\pi$
$600$	0	0
$601$	11116.7	0.754509	0.377255	−	0.926110i	$-0.376868\pi$
$601$	11116.7	0.754509	0.377255	+	0.926110i	$0.376868\pi$
$602$	−801.577	−0.0542688
$603$	−258.769	−0.0174758
$604$	−23799.0	−1.60326
$605$	0	0
$606$	2766.26	0.185432
$607$	−19355.0	−1.29423	−0.647114	−	0.762393i	$-0.724024\pi$
$607$	−19355.0	−1.29423	−0.647114	+	0.762393i	$0.724024\pi$
$608$	−1667.52	−0.111228
$609$	−5359.08	−0.356586
$610$	0	0
$611$	964.559	0.0638656
$612$	3228.16	0.213220
$613$	12325.5	0.812111	0.406056	−	0.913848i	$-0.366904\pi$
$613$	12325.5	0.812111	0.406056	+	0.913848i	$0.366904\pi$
$614$	−23078.3	−1.51688
$615$	0	0
$616$	−91.2780	−0.00597029
$617$	−28207.0	−1.84047	−0.920236	−	0.391363i	$-0.872004\pi$
$617$	−28207.0	−1.84047	−0.920236	+	0.391363i	$0.872004\pi$
$618$	−9698.34	−0.631269
$619$	17236.9	1.11924	0.559621	−	0.828748i	$-0.310947\pi$
$619$	17236.9	1.11924	0.559621	+	0.828748i	$0.310947\pi$
$620$	0	0
$621$	−2918.81	−0.188611
$622$	−8014.06	−0.516615
$623$	−2033.16	−0.130750
$624$	5622.58	0.360711
$625$	0	0
$626$	−10807.2	−0.690003
$627$	−213.194	−0.0135792
$628$	−24878.0	−1.58080
$629$	17347.4	1.09966
$630$	0	0
$631$	−23582.7	−1.48782	−0.743908	−	0.668282i	$-0.767030\pi$
$631$	−23582.7	−1.48782	−0.743908	+	0.668282i	$0.767030\pi$
$632$	−256.250	−0.0161283
$633$	4679.94	0.293856
$634$	−28613.6	−1.79241
$635$	0	0
$636$	−6299.35	−0.392744
$637$	9184.77	0.571294
$638$	12212.6	0.757839
$639$	801.073	0.0495930
$640$	0	0
$641$	−13003.1	−0.801233	−0.400617	−	0.916246i	$-0.631204\pi$
$641$	−13003.1	−0.801233	−0.400617	+	0.916246i	$0.631204\pi$
$642$	−12686.2	−0.779880
$643$	21269.1	1.30446	0.652232	−	0.758019i	$-0.273833\pi$
$643$	21269.1	1.30446	0.652232	+	0.758019i	$0.273833\pi$
$644$	−5842.82	−0.357514
$645$	0	0
$646$	1125.55	0.0685511
$647$	−29247.2	−1.77716	−0.888582	−	0.458717i	$-0.848309\pi$
$647$	−29247.2	−1.77716	−0.888582	+	0.458717i	$0.848309\pi$
$648$	−103.418	−0.00626952
$649$	−6141.64	−0.371465
$650$	0	0
$651$	−1336.60	−0.0804694
$652$	−24179.9	−1.45239
$653$	1678.30	0.100577	0.0502885	−	0.998735i	$-0.483986\pi$
$653$	1678.30	0.100577	0.0502885	+	0.998735i	$0.483986\pi$
$654$	−3841.67	−0.229696
$655$	0	0
$656$	16475.2	0.980561
$657$	6458.60	0.383522
$658$	829.182	0.0491260
$659$	−7620.41	−0.450454	−0.225227	−	0.974306i	$-0.572312\pi$
$659$	−7620.41	−0.450454	−0.225227	+	0.974306i	$0.572312\pi$
$660$	0	0
$661$	−22762.2	−1.33941	−0.669703	−	0.742629i	$-0.733579\pi$
$661$	−22762.2	−1.33941	−0.669703	+	0.742629i	$0.733579\pi$
$662$	−31556.7	−1.85270
$663$	−3951.51	−0.231469
$664$	311.124	0.0181837
$665$	0	0
$666$	−14621.5	−0.850708
$667$	29713.2	1.72488
$668$	−9150.93	−0.530030
$669$	−2268.65	−0.131107
$670$	0	0
$671$	3687.96	0.212179
$672$	5032.60	0.288894
$673$	−698.528	−0.0400093	−0.0200047	−	0.999800i	$-0.506368\pi$
$673$	−698.528	−0.0400093	−0.0200047	+	0.999800i	$0.506368\pi$
$674$	−47932.1	−2.73928
$675$	0	0
$676$	−10514.8	−0.598250
$677$	10860.1	0.616524	0.308262	−	0.951302i	$-0.400253\pi$
$677$	10860.1	0.616524	0.308262	+	0.951302i	$0.400253\pi$
$678$	16163.1	0.915547
$679$	−181.976	−0.0102851
$680$	0	0
$681$	17276.1	0.972131
$682$	3045.93	0.171019
$683$	6534.95	0.366110	0.183055	−	0.983103i	$-0.441401\pi$
$683$	6534.95	0.366110	0.183055	+	0.983103i	$0.441401\pi$
$684$	−483.530	−0.0270296
$685$	0	0
$686$	16900.3	0.940606
$687$	−5737.88	−0.318652
$688$	−1873.88	−0.103839
$689$	7710.88	0.426359
$690$	0	0
$691$	−10915.3	−0.600924	−0.300462	−	0.953794i	$-0.597141\pi$
$691$	−10915.3	−0.600924	−0.300462	+	0.953794i	$0.597141\pi$
$692$	−31224.9	−1.71530
$693$	643.423	0.0352693
$694$	14079.0	0.770076
$695$	0	0
$696$	1052.79	0.0573359
$697$	−11578.6	−0.629229
$698$	25717.3	1.39458
$699$	−3104.58	−0.167991
$700$	0	0
$701$	18405.4	0.991674	0.495837	−	0.868416i	$-0.334861\pi$
$701$	18405.4	0.991674	0.495837	+	0.868416i	$0.334861\pi$
$702$	3330.58	0.179067
$703$	−2598.39	−0.139403
$704$	−6067.91	−0.324848
$705$	0	0
$706$	33215.9	1.77068
$707$	−1483.63	−0.0789217
$708$	−13929.4	−0.739405
$709$	−21436.2	−1.13547	−0.567737	−	0.823210i	$-0.692181\pi$
$709$	−21436.2	−1.13547	−0.567737	+	0.823210i	$0.692181\pi$
$710$	0	0
$711$	1806.32	0.0952773
$712$	399.413	0.0210234
$713$	7410.73	0.389248
$714$	−3396.91	−0.178048
$715$	0	0
$716$	−26767.7	−1.39715
$717$	7941.69	0.413651
$718$	37878.9	1.96884
$719$	28641.7	1.48561	0.742807	−	0.669506i	$-0.233494\pi$
$719$	28641.7	1.48561	0.742807	+	0.669506i	$0.233494\pi$
$720$	0	0
$721$	5201.51	0.268675
$722$	27537.1	1.41942
$723$	20202.0	1.03917
$724$	−3799.49	−0.195037
$725$	0	0
$726$	−1466.27	−0.0749566
$727$	1723.13	0.0879055	0.0439527	−	0.999034i	$-0.486005\pi$
$727$	1723.13	0.0879055	0.0439527	+	0.999034i	$0.486005\pi$
$728$	253.409	0.0129010
$729$	729.000	0.0370370
$730$	0	0
$731$	1316.95	0.0666335
$732$	8364.39	0.422345
$733$	18813.4	0.948005	0.474003	−	0.880523i	$-0.342809\pi$
$733$	18813.4	0.948005	0.474003	+	0.880523i	$0.342809\pi$
$734$	−1255.80	−0.0631506
$735$	0	0
$736$	−27903.0	−1.39744
$737$	−316.273	−0.0158074
$738$	9759.21	0.486777
$739$	−10893.3	−0.542242	−0.271121	−	0.962545i	$-0.587394\pi$
$739$	−10893.3	−0.542242	−0.271121	+	0.962545i	$0.587394\pi$
$740$	0	0
$741$	591.877	0.0293430
$742$	6628.65	0.327959
$743$	−11888.6	−0.587013	−0.293507	−	0.955957i	$-0.594822\pi$
$743$	−11888.6	−0.587013	−0.293507	+	0.955957i	$0.594822\pi$
$744$	262.574	0.0129388
$745$	0	0
$746$	−19140.4	−0.939381
$747$	−2193.13	−0.107419
$748$	3945.53	0.192865
$749$	6803.98	0.331925
$750$	0	0
$751$	−32134.8	−1.56140	−0.780702	−	0.624903i	$-0.785138\pi$
$751$	−32134.8	−1.56140	−0.780702	+	0.624903i	$0.785138\pi$
$752$	1938.41	0.0939982
$753$	−16132.7	−0.780755
$754$	−33905.0	−1.63759
$755$	0	0
$756$	1459.30	0.0702040
$757$	−17366.1	−0.833794	−0.416897	−	0.908954i	$-0.636882\pi$
$757$	−17366.1	−0.833794	−0.416897	+	0.908954i	$0.636882\pi$
$758$	19128.1	0.916573
$759$	−3567.43	−0.170605
$760$	0	0
$761$	−27393.9	−1.30490	−0.652450	−	0.757832i	$-0.726259\pi$
$761$	−27393.9	−1.30490	−0.652450	+	0.757832i	$0.726259\pi$
$762$	6845.28	0.325431
$763$	2060.41	0.0977611
$764$	−40808.0	−1.93243
$765$	0	0
$766$	14671.4	0.692034
$767$	17050.6	0.802689
$768$	11260.2	0.529060
$769$	−12091.3	−0.567000	−0.283500	−	0.958972i	$-0.591496\pi$
$769$	−12091.3	−0.567000	−0.283500	+	0.958972i	$0.591496\pi$
$770$	0	0
$771$	−17647.0	−0.824307
$772$	−12159.5	−0.566879
$773$	−18895.8	−0.879216	−0.439608	−	0.898190i	$-0.644883\pi$
$773$	−18895.8	−0.879216	−0.439608	+	0.898190i	$0.644883\pi$
$774$	−1110.01	−0.0515483
$775$	0	0
$776$	35.7490	0.00165375
$777$	7841.96	0.362070
$778$	−26487.8	−1.22061
$779$	1734.31	0.0797664
$780$	0	0
$781$	979.089	0.0448586
$782$	18834.0	0.861258
$783$	−7421.14	−0.338710
$784$	18458.1	0.840838
$785$	0	0
$786$	2594.23	0.117727
$787$	−23705.9	−1.07373	−0.536863	−	0.843669i	$-0.680391\pi$
$787$	−23705.9	−1.07373	−0.536863	+	0.843669i	$0.680391\pi$
$788$	−18379.4	−0.830888
$789$	12005.0	0.541685
$790$	0	0
$791$	−8668.77	−0.389666
$792$	−126.400	−0.00567100
$793$	−10238.6	−0.458493
$794$	16500.5	0.737507
$795$	0	0
$796$	−3287.11	−0.146368
$797$	37248.0	1.65545	0.827725	−	0.561135i	$-0.189635\pi$
$797$	37248.0	1.65545	0.827725	+	0.561135i	$0.189635\pi$
$798$	508.807	0.0225709
$799$	−1362.30	−0.0603189
$800$	0	0
$801$	−2815.49	−0.124195
$802$	26966.7	1.18731
$803$	7893.84	0.346909
$804$	−717.315	−0.0314648
$805$	0	0
$806$	−8456.21	−0.369550
$807$	−5274.86	−0.230092
$808$	291.458	0.0126899
$809$	−24861.0	−1.08043	−0.540214	−	0.841528i	$-0.681657\pi$
$809$	−24861.0	−1.08043	−0.540214	+	0.841528i	$0.681657\pi$
$810$	0	0
$811$	4131.24	0.178875	0.0894375	−	0.995992i	$-0.471493\pi$
$811$	4131.24	0.178875	0.0894375	+	0.995992i	$0.471493\pi$
$812$	−14855.5	−0.642027
$813$	18055.3	0.778878
$814$	−17870.7	−0.769495
$815$	0	0
$816$	−7941.10	−0.340679
$817$	−197.259	−0.00844704
$818$	−6941.81	−0.296717
$819$	−1786.29	−0.0762126
$820$	0	0
$821$	25297.3	1.07537	0.537687	−	0.843145i	$-0.319298\pi$
$821$	25297.3	1.07537	0.537687	+	0.843145i	$0.319298\pi$
$822$	−790.439	−0.0335398
$823$	18155.5	0.768969	0.384484	−	0.923131i	$-0.374379\pi$
$823$	18155.5	0.768969	0.384484	+	0.923131i	$0.374379\pi$
$824$	−1021.83	−0.0432005
$825$	0	0
$826$	14657.6	0.617435
$827$	29566.8	1.24321	0.621607	−	0.783329i	$-0.286480\pi$
$827$	29566.8	1.24321	0.621607	+	0.783329i	$0.286480\pi$
$828$	−8091.02	−0.339592
$829$	27249.4	1.14163	0.570814	−	0.821079i	$-0.306628\pi$
$829$	27249.4	1.14163	0.570814	+	0.821079i	$0.306628\pi$
$830$	0	0
$831$	−8730.90	−0.364467
$832$	16845.9	0.701956
$833$	−12972.2	−0.539568
$834$	4933.02	0.204816
$835$	0	0
$836$	−590.981	−0.0244492
$837$	−1850.90	−0.0764355
$838$	−23154.3	−0.954478
$839$	−15506.1	−0.638058	−0.319029	−	0.947745i	$-0.603357\pi$
$839$	−15506.1	−0.638058	−0.319029	+	0.947745i	$0.603357\pi$
$840$	0	0
$841$	51157.5	2.09756
$842$	38968.8	1.59496
$843$	20679.6	0.844890
$844$	12972.9	0.529084
$845$	0	0
$846$	1148.24	0.0466633
$847$	786.406	0.0319023
$848$	15496.1	0.627520
$849$	−9360.47	−0.378387
$850$	0	0
$851$	−43479.4	−1.75141
$852$	2220.60	0.0892915
$853$	−8698.16	−0.349143	−0.174572	−	0.984644i	$-0.555854\pi$
$853$	−8698.16	−0.349143	−0.174572	+	0.984644i	$0.555854\pi$
$854$	−8801.64	−0.352677
$855$	0	0
$856$	−1336.64	−0.0533707
$857$	28468.8	1.13474	0.567372	−	0.823462i	$-0.307960\pi$
$857$	28468.8	1.13474	0.567372	+	0.823462i	$0.307960\pi$
$858$	4070.71	0.161972
$859$	−21154.3	−0.840251	−0.420125	−	0.907466i	$-0.638014\pi$
$859$	−21154.3	−0.840251	−0.420125	+	0.907466i	$0.638014\pi$
$860$	0	0
$861$	−5234.16	−0.207177
$862$	12338.4	0.487525
$863$	45959.5	1.81284	0.906420	−	0.422378i	$-0.138805\pi$
$863$	45959.5	1.81284	0.906420	+	0.422378i	$0.138805\pi$
$864$	6969.04	0.274412
$865$	0	0
$866$	44524.5	1.74712
$867$	−9158.05	−0.358735
$868$	−3705.10	−0.144884
$869$	2207.72	0.0861815
$870$	0	0
$871$	878.047	0.0341579
$872$	−404.765	−0.0157191
$873$	−251.996	−0.00976951
$874$	−2821.06	−0.109180
$875$	0	0
$876$	17903.4	0.690526
$877$	7315.10	0.281657	0.140829	−	0.990034i	$-0.455023\pi$
$877$	7315.10	0.281657	0.140829	+	0.990034i	$0.455023\pi$
$878$	30655.6	1.17833
$879$	−26608.9	−1.02104
$880$	0	0
$881$	4652.19	0.177907	0.0889536	−	0.996036i	$-0.471648\pi$
$881$	4652.19	0.177907	0.0889536	+	0.996036i	$0.471648\pi$
$882$	10933.8	0.417415
$883$	38954.3	1.48462	0.742309	−	0.670058i	$-0.233731\pi$
$883$	38954.3	1.48462	0.742309	+	0.670058i	$0.233731\pi$
$884$	−10953.7	−0.416756
$885$	0	0
$886$	16332.2	0.619289
$887$	16917.5	0.640398	0.320199	−	0.947350i	$-0.396250\pi$
$887$	16917.5	0.640398	0.320199	+	0.947350i	$0.396250\pi$
$888$	−1540.55	−0.0582177
$889$	−3671.33	−0.138507
$890$	0	0
$891$	891.000	0.0335013
$892$	−6288.75	−0.236057
$893$	204.053	0.00764654
$894$	−9598.53	−0.359086
$895$	0	0
$896$	1061.32	0.0395715
$897$	9904.01	0.368657
$898$	−59051.8	−2.19441
$899$	18842.0	0.699016
$900$	0	0
$901$	−10890.5	−0.402682
$902$	11927.9	0.440306
$903$	595.331	0.0219395
$904$	1702.97	0.0626549
$905$	0	0
$906$	34679.2	1.27168
$907$	−38985.4	−1.42722	−0.713610	−	0.700543i	$-0.752941\pi$
$907$	−38985.4	−1.42722	−0.713610	+	0.700543i	$0.752941\pi$
$908$	47889.8	1.75031
$909$	−2054.50	−0.0749653
$910$	0	0
$911$	27759.8	1.00957	0.504787	−	0.863244i	$-0.331571\pi$
$911$	27759.8	1.00957	0.504787	+	0.863244i	$0.331571\pi$
$912$	1189.46	0.0431874
$913$	−2680.49	−0.0971646
$914$	−44072.3	−1.59495
$915$	0	0
$916$	−15905.6	−0.573728
$917$	−1391.37	−0.0501057
$918$	−4703.98	−0.169122
$919$	29705.5	1.06626	0.533130	−	0.846033i	$-0.321016\pi$
$919$	29705.5	1.06626	0.533130	+	0.846033i	$0.321016\pi$
$920$	0	0
$921$	17140.3	0.613236
$922$	−66127.6	−2.36204
$923$	−2718.18	−0.0969338
$924$	1783.59	0.0635019
$925$	0	0
$926$	−64724.1	−2.29694
$927$	7202.95	0.255206
$928$	−70944.1	−2.50954
$929$	2940.01	0.103831	0.0519153	−	0.998651i	$-0.483467\pi$
$929$	2940.01	0.103831	0.0519153	+	0.998651i	$0.483467\pi$
$930$	0	0
$931$	1943.04	0.0684002
$932$	−8605.99	−0.302466
$933$	5952.04	0.208854
$934$	−60982.6	−2.13642
$935$	0	0
$936$	350.916	0.0122543
$937$	20041.9	0.698762	0.349381	−	0.936981i	$-0.386392\pi$
$937$	20041.9	0.698762	0.349381	+	0.936981i	$0.386392\pi$
$938$	754.813	0.0262745
$939$	8026.49	0.278951
$940$	0	0
$941$	−14446.1	−0.500457	−0.250229	−	0.968187i	$-0.580506\pi$
$941$	−14446.1	−0.500457	−0.250229	+	0.968187i	$0.580506\pi$
$942$	36251.4	1.25386
$943$	29020.6	1.00216
$944$	34265.6	1.18141
$945$	0	0
$946$	−1356.68	−0.0466272
$947$	−3901.33	−0.133871	−0.0669357	−	0.997757i	$-0.521322\pi$
$947$	−3901.33	−0.133871	−0.0669357	+	0.997757i	$0.521322\pi$
$948$	5007.16	0.171545
$949$	−21915.1	−0.749626
$950$	0	0
$951$	21251.3	0.724627
$952$	−357.904	−0.0121846
$953$	−613.963	−0.0208691	−0.0104345	−	0.999946i	$-0.503321\pi$
$953$	−613.963	−0.0208691	−0.0104345	+	0.999946i	$0.503321\pi$
$954$	9179.22	0.311518
$955$	0	0
$956$	22014.6	0.744773
$957$	−9070.29	−0.306375
$958$	42247.1	1.42478
$959$	423.937	0.0142749
$960$	0	0
$961$	−25091.6	−0.842256
$962$	49613.3	1.66278
$963$	9422.02	0.315286
$964$	56000.5	1.87101
$965$	0	0
$966$	8513.98	0.283574
$967$	20617.4	0.685637	0.342819	−	0.939402i	$-0.388618\pi$
$967$	20617.4	0.685637	0.342819	+	0.939402i	$0.388618\pi$
$968$	−154.489	−0.00512961
$969$	−835.943	−0.0277135
$970$	0	0
$971$	22816.0	0.754069	0.377035	−	0.926199i	$-0.376944\pi$
$971$	22816.0	0.754069	0.377035	+	0.926199i	$0.376944\pi$
$972$	2020.81	0.0666846
$973$	−2645.73	−0.0871719
$974$	−32071.6	−1.05507
$975$	0	0
$976$	−20576.0	−0.674816
$977$	−22650.2	−0.741702	−0.370851	−	0.928692i	$-0.620934\pi$
$977$	−22650.2	−0.741702	−0.370851	+	0.928692i	$0.620934\pi$
$978$	35234.2	1.15201
$979$	−3441.15	−0.112339
$980$	0	0
$981$	2853.21	0.0928604
$982$	−46422.8	−1.50857
$983$	8963.01	0.290820	0.145410	−	0.989372i	$-0.453550\pi$
$983$	8963.01	0.290820	0.145410	+	0.989372i	$0.453550\pi$
$984$	1028.25	0.0333123
$985$	0	0
$986$	47886.0	1.54665
$987$	−615.834	−0.0198604
$988$	1640.70	0.0528316
$989$	−3300.78	−0.106126
$990$	0	0
$991$	422.204	0.0135336	0.00676678	−	0.999977i	$-0.497846\pi$
$991$	422.204	0.0135336	0.00676678	+	0.999977i	$0.497846\pi$
$992$	−17694.1	−0.566319
$993$	23437.2	0.748999
$994$	−2336.68	−0.0745623
$995$	0	0
$996$	−6079.41	−0.193407
$997$	12577.3	0.399524	0.199762	−	0.979844i	$-0.435983\pi$
$997$	12577.3	0.399524	0.199762	+	0.979844i	$0.435983\pi$
$998$	−19443.4	−0.616704
$999$	10859.4	0.343920

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.a.o.1.1	✓	3
3.2	odd	2		2475.4.a.y.1.3		3
5.2	odd	4		825.4.c.n.199.1		6
5.3	odd	4		825.4.c.n.199.6		6
5.4	even	2		825.4.a.q.1.3	yes	3
15.14	odd	2		2475.4.a.v.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.4.a.o.1.1	✓	3	1.1	even	1	trivial
825.4.a.q.1.3	yes	3	5.4	even	2
825.4.c.n.199.1		6	5.2	odd	4
825.4.c.n.199.6		6	5.3	odd	4
2475.4.a.v.1.1		3	15.14	odd	2
2475.4.a.y.1.3		3	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.a (trivial)

\(f(q)\)	\(=\)	\(q-4.03932 q^{2} +3.00000 q^{3} +8.31608 q^{4} -12.1180 q^{6} +6.49923 q^{7} -1.27677 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.03932 q^{2} +3.00000 q^{3} +8.31608 q^{4} -12.1180 q^{6} +6.49923 q^{7} -1.27677 q^{8} +9.00000 q^{9} +11.0000 q^{11} +24.9483 q^{12} -30.5385 q^{13} -26.2524 q^{14} -61.3714 q^{16} +43.1314 q^{17} -36.3539 q^{18} -6.46044 q^{19} +19.4977 q^{21} -44.4325 q^{22} -108.104 q^{23} -3.83030 q^{24} +123.355 q^{26} +27.0000 q^{27} +54.0481 q^{28} -274.857 q^{29} -68.5519 q^{31} +258.113 q^{32} +33.0000 q^{33} -174.221 q^{34} +74.8448 q^{36} +402.200 q^{37} +26.0958 q^{38} -91.6156 q^{39} -268.450 q^{41} -78.7573 q^{42} +30.5334 q^{43} +91.4769 q^{44} +436.666 q^{46} -31.5850 q^{47} -184.114 q^{48} -300.760 q^{49} +129.394 q^{51} -253.961 q^{52} -252.497 q^{53} -109.062 q^{54} -8.29800 q^{56} -19.3813 q^{57} +1110.24 q^{58} -558.331 q^{59} +335.270 q^{61} +276.903 q^{62} +58.4930 q^{63} -551.628 q^{64} -133.297 q^{66} -28.7521 q^{67} +358.684 q^{68} -324.312 q^{69} +89.0081 q^{71} -11.4909 q^{72} +717.622 q^{73} -1624.61 q^{74} -53.7256 q^{76} +71.4915 q^{77} +370.065 q^{78} +200.702 q^{79} +81.0000 q^{81} +1084.36 q^{82} -243.681 q^{83} +162.144 q^{84} -123.334 q^{86} -824.571 q^{87} -14.0444 q^{88} -312.832 q^{89} -198.477 q^{91} -899.002 q^{92} -205.656 q^{93} +127.582 q^{94} +774.338 q^{96} -27.9996 q^{97} +1214.87 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + 9 q^{3} + 7 q^{4} - 3 q^{6} - 16 q^{7} + 3 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q - q^2 + 9 * q^3 + 7 * q^4 - 3 * q^6 - 16 * q^7 + 3 * q^8 + 27 * q^9	\( 3 q - q^{2} + 9 q^{3} + 7 q^{4} - 3 q^{6} - 16 q^{7} + 3 q^{8} + 27 q^{9} + 33 q^{11} + 21 q^{12} - 45 q^{13} - 116 q^{14} - 85 q^{16} + 58 q^{17} - 9 q^{18} - 169 q^{19} - 48 q^{21} - 11 q^{22} - 155 q^{23} + 9 q^{24} + 167 q^{26} + 81 q^{27} - 100 q^{28} - 277 q^{29} - 173 q^{31} - 97 q^{32} + 99 q^{33} - 146 q^{34} + 63 q^{36} - 60 q^{37} - 169 q^{38} - 135 q^{39} + 44 q^{41} - 348 q^{42} + 109 q^{43} + 77 q^{44} + 425 q^{46} - 270 q^{47} - 255 q^{48} - 427 q^{49} + 174 q^{51} - 45 q^{52} + 148 q^{53} - 27 q^{54} + 168 q^{56} - 507 q^{57} + 783 q^{58} - 684 q^{59} - 1038 q^{61} - 953 q^{62} - 144 q^{63} - 1129 q^{64} - 33 q^{66} - 314 q^{67} + 366 q^{68} - 465 q^{69} - 1459 q^{71} + 27 q^{72} + 1170 q^{73} - 1764 q^{74} + 211 q^{76} - 176 q^{77} + 501 q^{78} - 506 q^{79} + 243 q^{81} + 1040 q^{82} + 347 q^{83} - 300 q^{84} - 527 q^{86} - 831 q^{87} + 33 q^{88} - 607 q^{89} - 398 q^{91} - 687 q^{92} - 519 q^{93} - 1822 q^{94} - 291 q^{96} - 1263 q^{97} + 2273 q^{98} + 297 q^{99}+O(q^{100}) \) 3 * q - q^2 + 9 * q^3 + 7 * q^4 - 3 * q^6 - 16 * q^7 + 3 * q^8 + 27 * q^9 + 33 * q^11 + 21 * q^12 - 45 * q^13 - 116 * q^14 - 85 * q^16 + 58 * q^17 - 9 * q^18 - 169 * q^19 - 48 * q^21 - 11 * q^22 - 155 * q^23 + 9 * q^24 + 167 * q^26 + 81 * q^27 - 100 * q^28 - 277 * q^29 - 173 * q^31 - 97 * q^32 + 99 * q^33 - 146 * q^34 + 63 * q^36 - 60 * q^37 - 169 * q^38 - 135 * q^39 + 44 * q^41 - 348 * q^42 + 109 * q^43 + 77 * q^44 + 425 * q^46 - 270 * q^47 - 255 * q^48 - 427 * q^49 + 174 * q^51 - 45 * q^52 + 148 * q^53 - 27 * q^54 + 168 * q^56 - 507 * q^57 + 783 * q^58 - 684 * q^59 - 1038 * q^61 - 953 * q^62 - 144 * q^63 - 1129 * q^64 - 33 * q^66 - 314 * q^67 + 366 * q^68 - 465 * q^69 - 1459 * q^71 + 27 * q^72 + 1170 * q^73 - 1764 * q^74 + 211 * q^76 - 176 * q^77 + 501 * q^78 - 506 * q^79 + 243 * q^81 + 1040 * q^82 + 347 * q^83 - 300 * q^84 - 527 * q^86 - 831 * q^87 + 33 * q^88 - 607 * q^89 - 398 * q^91 - 687 * q^92 - 519 * q^93 - 1822 * q^94 - 291 * q^96 - 1263 * q^97 + 2273 * q^98 + 297 * q^99

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