LMFDB - Embedded newform 1150.4.a.p.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,4,Mod(1,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, 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("1150.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1150.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:	$67.8521965066$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 68x^{2} - 111x + 342 $ x^4 - 68x^2 - 111x + 342
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-3.74869$ of defining polynomial
Character	$\chi$	$=$	1150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +4.74869 q^{3} +4.00000 q^{4} +9.49738 q^{6} -29.3684 q^{7} +8.00000 q^{8} -4.44993 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +4.74869 q^{3} +4.00000 q^{4} +9.49738 q^{6} -29.3684 q^{7} +8.00000 q^{8} -4.44993 q^{9} -38.1645 q^{11} +18.9948 q^{12} +22.5396 q^{13} -58.7368 q^{14} +16.0000 q^{16} +104.049 q^{17} -8.89986 q^{18} +142.000 q^{19} -139.461 q^{21} -76.3291 q^{22} +23.0000 q^{23} +37.9895 q^{24} +45.0792 q^{26} -149.346 q^{27} -117.474 q^{28} +241.429 q^{29} +99.2706 q^{31} +32.0000 q^{32} -181.232 q^{33} +208.097 q^{34} -17.7997 q^{36} -59.9452 q^{37} +284.000 q^{38} +107.034 q^{39} +249.248 q^{41} -278.923 q^{42} +163.863 q^{43} -152.658 q^{44} +46.0000 q^{46} +205.591 q^{47} +75.9791 q^{48} +519.502 q^{49} +494.095 q^{51} +90.1584 q^{52} -491.274 q^{53} -298.692 q^{54} -234.947 q^{56} +674.313 q^{57} +482.858 q^{58} +433.734 q^{59} +660.902 q^{61} +198.541 q^{62} +130.687 q^{63} +64.0000 q^{64} -362.463 q^{66} +323.564 q^{67} +416.195 q^{68} +109.220 q^{69} +893.243 q^{71} -35.5994 q^{72} -196.273 q^{73} -119.890 q^{74} +567.999 q^{76} +1120.83 q^{77} +214.067 q^{78} -500.211 q^{79} -589.050 q^{81} +498.496 q^{82} -800.944 q^{83} -557.846 q^{84} +327.726 q^{86} +1146.47 q^{87} -305.316 q^{88} -729.016 q^{89} -661.952 q^{91} +92.0000 q^{92} +471.405 q^{93} +411.181 q^{94} +151.958 q^{96} -1139.96 q^{97} +1039.00 q^{98} +169.829 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} + 4 q^{3} + 16 q^{4} + 8 q^{6} + q^{7} + 32 q^{8} + 32 q^{9}+O(q^{10}) $ 4 * q + 8 * q^2 + 4 * q^3 + 16 * q^4 + 8 * q^6 + q^7 + 32 * q^8 + 32 * q^9	$ 4 q + 8 q^{2} + 4 q^{3} + 16 q^{4} + 8 q^{6} + q^{7} + 32 q^{8} + 32 q^{9} - 39 q^{11} + 16 q^{12} + 20 q^{13} + 2 q^{14} + 64 q^{16} + 23 q^{17} + 64 q^{18} + 53 q^{19} + 300 q^{21} - 78 q^{22} + 92 q^{23} + 32 q^{24} + 40 q^{26} - 137 q^{27} + 4 q^{28} + 161 q^{29} + 388 q^{31} + 128 q^{32} - 87 q^{33} + 46 q^{34} + 128 q^{36} - 466 q^{37} + 106 q^{38} + 1047 q^{39} + 484 q^{41} + 600 q^{42} - 894 q^{43} - 156 q^{44} + 184 q^{46} + 265 q^{47} + 64 q^{48} + 1643 q^{49} + 1825 q^{51} + 80 q^{52} - 576 q^{53} - 274 q^{54} + 8 q^{56} - 178 q^{57} + 322 q^{58} - 94 q^{59} + 1153 q^{61} + 776 q^{62} - 60 q^{63} + 256 q^{64} - 174 q^{66} + 1472 q^{67} + 92 q^{68} + 92 q^{69} + 200 q^{71} + 256 q^{72} - 1147 q^{73} - 932 q^{74} + 212 q^{76} + 2176 q^{77} + 2094 q^{78} - 908 q^{79} - 1056 q^{81} + 968 q^{82} + 1048 q^{83} + 1200 q^{84} - 1788 q^{86} + 2167 q^{87} - 312 q^{88} - 1784 q^{89} + 2329 q^{91} + 368 q^{92} - 1483 q^{93} + 530 q^{94} + 128 q^{96} + 2047 q^{97} + 3286 q^{98} - 2665 q^{99}+O(q^{100}) $ 4 * q + 8 * q^2 + 4 * q^3 + 16 * q^4 + 8 * q^6 + q^7 + 32 * q^8 + 32 * q^9 - 39 * q^11 + 16 * q^12 + 20 * q^13 + 2 * q^14 + 64 * q^16 + 23 * q^17 + 64 * q^18 + 53 * q^19 + 300 * q^21 - 78 * q^22 + 92 * q^23 + 32 * q^24 + 40 * q^26 - 137 * q^27 + 4 * q^28 + 161 * q^29 + 388 * q^31 + 128 * q^32 - 87 * q^33 + 46 * q^34 + 128 * q^36 - 466 * q^37 + 106 * q^38 + 1047 * q^39 + 484 * q^41 + 600 * q^42 - 894 * q^43 - 156 * q^44 + 184 * q^46 + 265 * q^47 + 64 * q^48 + 1643 * q^49 + 1825 * q^51 + 80 * q^52 - 576 * q^53 - 274 * q^54 + 8 * q^56 - 178 * q^57 + 322 * q^58 - 94 * q^59 + 1153 * q^61 + 776 * q^62 - 60 * q^63 + 256 * q^64 - 174 * q^66 + 1472 * q^67 + 92 * q^68 + 92 * q^69 + 200 * q^71 + 256 * q^72 - 1147 * q^73 - 932 * q^74 + 212 * q^76 + 2176 * q^77 + 2094 * q^78 - 908 * q^79 - 1056 * q^81 + 968 * q^82 + 1048 * q^83 + 1200 * q^84 - 1788 * q^86 + 2167 * q^87 - 312 * q^88 - 1784 * q^89 + 2329 * q^91 + 368 * q^92 - 1483 * q^93 + 530 * q^94 + 128 * q^96 + 2047 * q^97 + 3286 * q^98 - 2665 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	4.74869	0.913886	0.456943	−	0.889496i	$-0.348944\pi$
$3$	4.74869	0.913886	0.456943	+	0.889496i	$0.348944\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	9.49738	0.646215
$7$	−29.3684	−1.58574	−0.792872	−	0.609388i	$-0.791415\pi$
$7$	−29.3684	−1.58574	−0.792872	+	0.609388i	$0.791415\pi$
$8$	8.00000	0.353553
$9$	−4.44993	−0.164812
$10$	0	0
$11$	−38.1645	−1.04609	−0.523047	−	0.852304i	$-0.675205\pi$
$11$	−38.1645	−1.04609	−0.523047	+	0.852304i	$0.675205\pi$
$12$	18.9948	0.456943
$13$	22.5396	0.480874	0.240437	−	0.970665i	$-0.422709\pi$
$13$	22.5396	0.480874	0.240437	+	0.970665i	$0.422709\pi$
$14$	−58.7368	−1.12129
$15$	0	0
$16$	16.0000	0.250000
$17$	104.049	1.48444	0.742221	−	0.670155i	$-0.233772\pi$
$17$	104.049	1.48444	0.742221	+	0.670155i	$0.233772\pi$
$18$	−8.89986	−0.116540
$19$	142.000	1.71458	0.857289	−	0.514835i	$-0.172147\pi$
$19$	142.000	1.71458	0.857289	+	0.514835i	$0.172147\pi$
$20$	0	0
$21$	−139.461	−1.44919
$22$	−76.3291	−0.739701
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	37.9895	0.323108
$25$	0	0
$26$	45.0792	0.340029
$27$	−149.346	−1.06451
$28$	−117.474	−0.792872
$29$	241.429	1.54594	0.772969	−	0.634444i	$-0.218771\pi$
$29$	241.429	1.54594	0.772969	+	0.634444i	$0.218771\pi$
$30$	0	0
$31$	99.2706	0.575146	0.287573	−	0.957759i	$-0.407152\pi$
$31$	99.2706	0.575146	0.287573	+	0.957759i	$0.407152\pi$
$32$	32.0000	0.176777
$33$	−181.232	−0.956011
$34$	208.097	1.04966
$35$	0	0
$36$	−17.7997	−0.0824061
$37$	−59.9452	−0.266349	−0.133175	−	0.991093i	$-0.542517\pi$
$37$	−59.9452	−0.266349	−0.133175	+	0.991093i	$0.542517\pi$
$38$	284.000	1.21239
$39$	107.034	0.439464
$40$	0	0
$41$	249.248	0.949414	0.474707	−	0.880144i	$-0.342554\pi$
$41$	249.248	0.949414	0.474707	+	0.880144i	$0.342554\pi$
$42$	−278.923	−1.02473
$43$	163.863	0.581136	0.290568	−	0.956854i	$-0.406156\pi$
$43$	163.863	0.581136	0.290568	+	0.956854i	$0.406156\pi$
$44$	−152.658	−0.523047
$45$	0	0
$46$	46.0000	0.147442
$47$	205.591	0.638052	0.319026	−	0.947746i	$-0.396644\pi$
$47$	205.591	0.638052	0.319026	+	0.947746i	$0.396644\pi$
$48$	75.9791	0.228472
$49$	519.502	1.51458
$50$	0	0
$51$	494.095	1.35661
$52$	90.1584	0.240437
$53$	−491.274	−1.27324	−0.636620	−	0.771178i	$-0.719668\pi$
$53$	−491.274	−1.27324	−0.636620	+	0.771178i	$0.719668\pi$
$54$	−298.692	−0.752719
$55$	0	0
$56$	−234.947	−0.560645
$57$	674.313	1.56693
$58$	482.858	1.09314
$59$	433.734	0.957074	0.478537	−	0.878067i	$-0.341167\pi$
$59$	433.734	0.957074	0.478537	+	0.878067i	$0.341167\pi$
$60$	0	0
$61$	660.902	1.38721	0.693605	−	0.720355i	$-0.256021\pi$
$61$	660.902	1.38721	0.693605	+	0.720355i	$0.256021\pi$
$62$	198.541	0.406690
$63$	130.687	0.261350
$64$	64.0000	0.125000
$65$	0	0
$66$	−362.463	−0.676002
$67$	323.564	0.589995	0.294997	−	0.955498i	$-0.404681\pi$
$67$	323.564	0.589995	0.294997	+	0.955498i	$0.404681\pi$
$68$	416.195	0.742221
$69$	109.220	0.190558
$70$	0	0
$71$	893.243	1.49308	0.746538	−	0.665342i	$-0.231714\pi$
$71$	893.243	1.49308	0.746538	+	0.665342i	$0.231714\pi$
$72$	−35.5994	−0.0582699
$73$	−196.273	−0.314685	−0.157343	−	0.987544i	$-0.550293\pi$
$73$	−196.273	−0.314685	−0.157343	+	0.987544i	$0.550293\pi$
$74$	−119.890	−0.188337
$75$	0	0
$76$	567.999	0.857289
$77$	1120.83	1.65884
$78$	214.067	0.310748
$79$	−500.211	−0.712381	−0.356191	−	0.934413i	$-0.615925\pi$
$79$	−500.211	−0.712381	−0.356191	+	0.934413i	$0.615925\pi$
$80$	0	0
$81$	−589.050	−0.808025
$82$	498.496	0.671337
$83$	−800.944	−1.05922	−0.529609	−	0.848242i	$-0.677661\pi$
$83$	−800.944	−1.05922	−0.529609	+	0.848242i	$0.677661\pi$
$84$	−557.846	−0.724595
$85$	0	0
$86$	327.726	0.410925
$87$	1146.47	1.41281
$88$	−305.316	−0.369850
$89$	−729.016	−0.868264	−0.434132	−	0.900849i	$-0.642945\pi$
$89$	−729.016	−0.868264	−0.434132	+	0.900849i	$0.642945\pi$
$90$	0	0
$91$	−661.952	−0.762543
$92$	92.0000	0.104257
$93$	471.405	0.525618
$94$	411.181	0.451171
$95$	0	0
$96$	151.958	0.161554
$97$	−1139.96	−1.19325	−0.596626	−	0.802520i	$-0.703492\pi$
$97$	−1139.96	−1.19325	−0.596626	+	0.802520i	$0.703492\pi$
$98$	1039.00	1.07097
$99$	169.829	0.172409
$100$	0	0
$101$	−1669.38	−1.64465	−0.822326	−	0.569017i	$-0.807324\pi$
$101$	−1669.38	−1.64465	−0.822326	+	0.569017i	$0.807324\pi$
$102$	988.190	0.959269
$103$	1110.63	1.06246	0.531229	−	0.847228i	$-0.321730\pi$
$103$	1110.63	1.06246	0.531229	+	0.847228i	$0.321730\pi$
$104$	180.317	0.170015
$105$	0	0
$106$	−982.549	−0.900317
$107$	−39.1892	−0.0354071	−0.0177036	−	0.999843i	$-0.505636\pi$
$107$	−39.1892	−0.0354071	−0.0177036	+	0.999843i	$0.505636\pi$
$108$	−597.384	−0.532253
$109$	807.545	0.709622	0.354811	−	0.934938i	$-0.384545\pi$
$109$	807.545	0.709622	0.354811	+	0.934938i	$0.384545\pi$
$110$	0	0
$111$	−284.661	−0.243413
$112$	−469.894	−0.396436
$113$	−1066.58	−0.887923	−0.443961	−	0.896046i	$-0.646427\pi$
$113$	−1066.58	−0.887923	−0.443961	+	0.896046i	$0.646427\pi$
$114$	1348.63	1.10799
$115$	0	0
$116$	965.715	0.772969
$117$	−100.300	−0.0792539
$118$	867.468	0.676753
$119$	−3055.74	−2.35395
$120$	0	0
$121$	125.532	0.0943139
$122$	1321.80	0.980906
$123$	1183.60	0.867657
$124$	397.082	0.287573
$125$	0	0
$126$	261.374	0.184802
$127$	641.707	0.448364	0.224182	−	0.974547i	$-0.428029\pi$
$127$	641.707	0.448364	0.224182	+	0.974547i	$0.428029\pi$
$128$	128.000	0.0883883
$129$	778.134	0.531092
$130$	0	0
$131$	2389.92	1.59396	0.796979	−	0.604007i	$-0.206430\pi$
$131$	2389.92	1.59396	0.796979	+	0.604007i	$0.206430\pi$
$132$	−724.926	−0.478006
$133$	−4170.31	−2.71888
$134$	647.128	0.417189
$135$	0	0
$136$	832.390	0.524830
$137$	−899.291	−0.560814	−0.280407	−	0.959881i	$-0.590470\pi$
$137$	−899.291	−0.560814	−0.280407	+	0.959881i	$0.590470\pi$
$138$	218.440	0.134745
$139$	309.341	0.188762	0.0943811	−	0.995536i	$-0.469913\pi$
$139$	309.341	0.188762	0.0943811	+	0.995536i	$0.469913\pi$
$140$	0	0
$141$	976.286	0.583107
$142$	1786.49	1.05576
$143$	−860.214	−0.503040
$144$	−71.1989	−0.0412030
$145$	0	0
$146$	−392.546	−0.222516
$147$	2466.96	1.38416
$148$	−239.781	−0.133175
$149$	2560.87	1.40802	0.704010	−	0.710190i	$-0.251391\pi$
$149$	2560.87	1.40802	0.704010	+	0.710190i	$0.251391\pi$
$150$	0	0
$151$	−2463.15	−1.32747	−0.663737	−	0.747966i	$-0.731031\pi$
$151$	−2463.15	−1.32747	−0.663737	+	0.747966i	$0.731031\pi$
$152$	1136.00	0.606195
$153$	−463.009	−0.244654
$154$	2241.66	1.17298
$155$	0	0
$156$	428.135	0.219732
$157$	566.720	0.288084	0.144042	−	0.989572i	$-0.453990\pi$
$157$	566.720	0.288084	0.144042	+	0.989572i	$0.453990\pi$
$158$	−1000.42	−0.503730
$159$	−2332.91	−1.16360
$160$	0	0
$161$	−675.473	−0.330650
$162$	−1178.10	−0.571360
$163$	−960.902	−0.461740	−0.230870	−	0.972985i	$-0.574157\pi$
$163$	−960.902	−0.461740	−0.230870	+	0.972985i	$0.574157\pi$
$164$	996.992	0.474707
$165$	0	0
$166$	−1601.89	−0.748980
$167$	4224.70	1.95759	0.978794	−	0.204847i	$-0.0656696\pi$
$167$	4224.70	1.95759	0.978794	+	0.204847i	$0.0656696\pi$
$168$	−1115.69	−0.512366
$169$	−1688.97	−0.768760
$170$	0	0
$171$	−631.889	−0.282583
$172$	655.451	0.290568
$173$	−3448.98	−1.51573	−0.757865	−	0.652412i	$-0.773757\pi$
$173$	−3448.98	−1.51573	−0.757865	+	0.652412i	$0.773757\pi$
$174$	2292.94	0.999008
$175$	0	0
$176$	−610.633	−0.261524
$177$	2059.67	0.874657
$178$	−1458.03	−0.613955
$179$	1457.82	0.608728	0.304364	−	0.952556i	$-0.401556\pi$
$179$	1457.82	0.608728	0.304364	+	0.952556i	$0.401556\pi$
$180$	0	0
$181$	−3634.97	−1.49274	−0.746368	−	0.665534i	$-0.768204\pi$
$181$	−3634.97	−1.49274	−0.746368	+	0.665534i	$0.768204\pi$
$182$	−1323.90	−0.539199
$183$	3138.42	1.26775
$184$	184.000	0.0737210
$185$	0	0
$186$	942.811	0.371668
$187$	−3970.97	−1.55287
$188$	822.362	0.319026
$189$	4386.05	1.68803
$190$	0	0
$191$	448.811	0.170025	0.0850127	−	0.996380i	$-0.472907\pi$
$191$	448.811	0.170025	0.0850127	+	0.996380i	$0.472907\pi$
$192$	303.916	0.114236
$193$	−4259.35	−1.58857	−0.794286	−	0.607544i	$-0.792155\pi$
$193$	−4259.35	−1.58857	−0.794286	+	0.607544i	$0.792155\pi$
$194$	−2279.92	−0.843756
$195$	0	0
$196$	2078.01	0.757292
$197$	1767.37	0.639189	0.319594	−	0.947554i	$-0.396453\pi$
$197$	1767.37	0.639189	0.319594	+	0.947554i	$0.396453\pi$
$198$	339.659	0.121912
$199$	1004.29	0.357750	0.178875	−	0.983872i	$-0.442754\pi$
$199$	1004.29	0.357750	0.178875	+	0.983872i	$0.442754\pi$
$200$	0	0
$201$	1536.51	0.539188
$202$	−3338.76	−1.16294
$203$	−7090.37	−2.45146
$204$	1976.38	0.678305
$205$	0	0
$206$	2221.25	0.751272
$207$	−102.348	−0.0343657
$208$	360.634	0.120218
$209$	−5419.36	−1.79361
$210$	0	0
$211$	5395.17	1.76028	0.880140	−	0.474714i	$-0.157449\pi$
$211$	5395.17	1.76028	0.880140	+	0.474714i	$0.157449\pi$
$212$	−1965.10	−0.636620
$213$	4241.74	1.36450
$214$	−78.3783	−0.0250366
$215$	0	0
$216$	−1194.77	−0.376360
$217$	−2915.42	−0.912034
$218$	1615.09	0.501779
$219$	−932.041	−0.287587
$220$	0	0
$221$	2345.22	0.713830
$222$	−569.322	−0.172119
$223$	1504.79	0.451876	0.225938	−	0.974142i	$-0.427455\pi$
$223$	1504.79	0.451876	0.225938	+	0.974142i	$0.427455\pi$
$224$	−939.788	−0.280323
$225$	0	0
$226$	−2133.16	−0.627856
$227$	1779.44	0.520288	0.260144	−	0.965570i	$-0.416230\pi$
$227$	1779.44	0.520288	0.260144	+	0.965570i	$0.416230\pi$
$228$	2697.25	0.783465
$229$	3976.16	1.14739	0.573694	−	0.819070i	$-0.305510\pi$
$229$	3976.16	1.14739	0.573694	+	0.819070i	$0.305510\pi$
$230$	0	0
$231$	5322.48	1.51599
$232$	1931.43	0.546572
$233$	2311.12	0.649815	0.324907	−	0.945746i	$-0.394667\pi$
$233$	2311.12	0.649815	0.324907	+	0.945746i	$0.394667\pi$
$234$	−200.599	−0.0560410
$235$	0	0
$236$	1734.94	0.478537
$237$	−2375.35	−0.651035
$238$	−6111.49	−1.66449
$239$	824.267	0.223085	0.111543	−	0.993760i	$-0.464421\pi$
$239$	824.267	0.223085	0.111543	+	0.993760i	$0.464421\pi$
$240$	0	0
$241$	3641.83	0.973406	0.486703	−	0.873567i	$-0.338199\pi$
$241$	3641.83	0.973406	0.486703	+	0.873567i	$0.338199\pi$
$242$	251.064	0.0666900
$243$	1235.13	0.326063
$244$	2643.61	0.693605
$245$	0	0
$246$	2367.20	0.613526
$247$	3200.62	0.824496
$248$	794.165	0.203345
$249$	−3803.44	−0.968004
$250$	0	0
$251$	−7767.51	−1.95331	−0.976655	−	0.214813i	$-0.931086\pi$
$251$	−7767.51	−1.95331	−0.976655	+	0.214813i	$0.931086\pi$
$252$	522.749	0.130675
$253$	−877.784	−0.218126
$254$	1283.41	0.317042
$255$	0	0
$256$	256.000	0.0625000
$257$	1501.17	0.364359	0.182179	−	0.983265i	$-0.441685\pi$
$257$	1501.17	0.364359	0.182179	+	0.983265i	$0.441685\pi$
$258$	1556.27	0.375539
$259$	1760.49	0.422362
$260$	0	0
$261$	−1074.34	−0.254789
$262$	4779.84	1.12710
$263$	5430.98	1.27334	0.636671	−	0.771136i	$-0.280311\pi$
$263$	5430.98	1.27334	0.636671	+	0.771136i	$0.280311\pi$
$264$	−1449.85	−0.338001
$265$	0	0
$266$	−8340.61	−1.92254
$267$	−3461.87	−0.793494
$268$	1294.26	0.294997
$269$	−5014.20	−1.13651	−0.568255	−	0.822852i	$-0.692381\pi$
$269$	−5014.20	−1.13651	−0.568255	+	0.822852i	$0.692381\pi$
$270$	0	0
$271$	7215.54	1.61739	0.808695	−	0.588228i	$-0.200174\pi$
$271$	7215.54	1.61739	0.808695	+	0.588228i	$0.200174\pi$
$272$	1664.78	0.371111
$273$	−3143.41	−0.696877
$274$	−1798.58	−0.396556
$275$	0	0
$276$	436.880	0.0952792
$277$	7439.60	1.61373	0.806863	−	0.590738i	$-0.201163\pi$
$277$	7439.60	1.61373	0.806863	+	0.590738i	$0.201163\pi$
$278$	618.681	0.133475
$279$	−441.747	−0.0947910
$280$	0	0
$281$	−2605.59	−0.553155	−0.276578	−	0.960992i	$-0.589200\pi$
$281$	−2605.59	−0.553155	−0.276578	+	0.960992i	$0.589200\pi$
$282$	1952.57	0.412319
$283$	7162.57	1.50449	0.752245	−	0.658884i	$-0.228971\pi$
$283$	7162.57	1.50449	0.752245	+	0.658884i	$0.228971\pi$
$284$	3572.97	0.746538
$285$	0	0
$286$	−1720.43	−0.355703
$287$	−7320.01	−1.50553
$288$	−142.398	−0.0291349
$289$	5913.13	1.20357
$290$	0	0
$291$	−5413.32	−1.09050
$292$	−785.093	−0.157343
$293$	−9310.55	−1.85641	−0.928205	−	0.372069i	$-0.878649\pi$
$293$	−9310.55	−1.85641	−0.928205	+	0.372069i	$0.878649\pi$
$294$	4933.91	0.978747
$295$	0	0
$296$	−479.562	−0.0941687
$297$	5699.72	1.11357
$298$	5121.74	0.995620
$299$	518.411	0.100269
$300$	0	0
$301$	−4812.39	−0.921533
$302$	−4926.31	−0.938666
$303$	−7927.38	−1.50302
$304$	2272.00	0.428645
$305$	0	0
$306$	−926.018	−0.172997
$307$	−3359.07	−0.624470	−0.312235	−	0.950005i	$-0.601078\pi$
$307$	−3359.07	−0.624470	−0.312235	+	0.950005i	$0.601078\pi$
$308$	4483.32	0.829419
$309$	5274.02	0.970966
$310$	0	0
$311$	−5509.20	−1.00450	−0.502248	−	0.864724i	$-0.667493\pi$
$311$	−5509.20	−1.00450	−0.502248	+	0.864724i	$0.667493\pi$
$312$	856.269	0.155374
$313$	−2401.42	−0.433661	−0.216831	−	0.976209i	$-0.569572\pi$
$313$	−2401.42	−0.433661	−0.216831	+	0.976209i	$0.569572\pi$
$314$	1133.44	0.203706
$315$	0	0
$316$	−2000.84	−0.356191
$317$	1057.36	0.187341	0.0936704	−	0.995603i	$-0.470140\pi$
$317$	1057.36	0.187341	0.0936704	+	0.995603i	$0.470140\pi$
$318$	−4665.82	−0.822787
$319$	−9214.02	−1.61720
$320$	0	0
$321$	−186.097	−0.0323581
$322$	−1350.95	−0.233805
$323$	14774.9	2.54519
$324$	−2356.20	−0.404012
$325$	0	0
$326$	−1921.80	−0.326500
$327$	3834.78	0.648514
$328$	1993.98	0.335669
$329$	−6037.86	−1.01179
$330$	0	0
$331$	−9680.21	−1.60747	−0.803735	−	0.594987i	$-0.797157\pi$
$331$	−9680.21	−1.60747	−0.803735	+	0.594987i	$0.797157\pi$
$332$	−3203.78	−0.529609
$333$	266.752	0.0438976
$334$	8449.40	1.38422
$335$	0	0
$336$	−2231.38	−0.362297
$337$	−467.694	−0.0755991	−0.0377996	−	0.999285i	$-0.512035\pi$
$337$	−467.694	−0.0755991	−0.0377996	+	0.999285i	$0.512035\pi$
$338$	−3377.93	−0.543596
$339$	−5064.85	−0.811460
$340$	0	0
$341$	−3788.62	−0.601657
$342$	−1263.78	−0.199817
$343$	−5183.59	−0.815998
$344$	1310.90	0.205463
$345$	0	0
$346$	−6897.96	−1.07178
$347$	−3371.55	−0.521597	−0.260798	−	0.965393i	$-0.583986\pi$
$347$	−3371.55	−0.521597	−0.260798	+	0.965393i	$0.583986\pi$
$348$	4585.88	0.706406
$349$	10958.7	1.68082	0.840412	−	0.541947i	$-0.182313\pi$
$349$	10958.7	1.68082	0.840412	+	0.541947i	$0.182313\pi$
$350$	0	0
$351$	−3366.20	−0.511893
$352$	−1221.27	−0.184925
$353$	1584.76	0.238947	0.119474	−	0.992837i	$-0.461879\pi$
$353$	1584.76	0.238947	0.119474	+	0.992837i	$0.461879\pi$
$354$	4119.34	0.618476
$355$	0	0
$356$	−2916.06	−0.434132
$357$	−14510.8	−2.15124
$358$	2915.63	0.430436
$359$	5130.67	0.754280	0.377140	−	0.926156i	$-0.376908\pi$
$359$	5130.67	0.754280	0.377140	+	0.926156i	$0.376908\pi$
$360$	0	0
$361$	13304.9	1.93978
$362$	−7269.94	−1.05552
$363$	596.112	0.0861922
$364$	−2647.81	−0.381271
$365$	0	0
$366$	6276.84	0.896437
$367$	−2811.27	−0.399856	−0.199928	−	0.979811i	$-0.564071\pi$
$367$	−2811.27	−0.399856	−0.199928	+	0.979811i	$0.564071\pi$
$368$	368.000	0.0521286
$369$	−1109.14	−0.156475
$370$	0	0
$371$	14427.9	2.01903
$372$	1885.62	0.262809
$373$	1952.42	0.271026	0.135513	−	0.990776i	$-0.456732\pi$
$373$	1952.42	0.271026	0.135513	+	0.990776i	$0.456732\pi$
$374$	−7941.94	−1.09804
$375$	0	0
$376$	1644.72	0.225586
$377$	5441.71	0.743401
$378$	8772.10	1.19362
$379$	9609.27	1.30236	0.651181	−	0.758923i	$-0.274274\pi$
$379$	9609.27	1.30236	0.651181	+	0.758923i	$0.274274\pi$
$380$	0	0
$381$	3047.27	0.409754
$382$	897.623	0.120226
$383$	−5027.44	−0.670732	−0.335366	−	0.942088i	$-0.608860\pi$
$383$	−5027.44	−0.670732	−0.335366	+	0.942088i	$0.608860\pi$
$384$	607.833	0.0807769
$385$	0	0
$386$	−8518.70	−1.12329
$387$	−729.178	−0.0957783
$388$	−4559.84	−0.596626
$389$	5892.29	0.767997	0.383999	−	0.923334i	$-0.374547\pi$
$389$	5892.29	0.767997	0.383999	+	0.923334i	$0.374547\pi$
$390$	0	0
$391$	2393.12	0.309528
$392$	4156.02	0.535486
$393$	11349.0	1.45670
$394$	3534.75	0.451975
$395$	0	0
$396$	679.318	0.0862046
$397$	2454.41	0.310285	0.155143	−	0.987892i	$-0.450416\pi$
$397$	2454.41	0.310285	0.155143	+	0.987892i	$0.450416\pi$
$398$	2008.58	0.252967
$399$	−19803.5	−2.48475
$400$	0	0
$401$	9458.39	1.17788	0.588939	−	0.808177i	$-0.299546\pi$
$401$	9458.39	1.17788	0.588939	+	0.808177i	$0.299546\pi$
$402$	3073.01	0.381264
$403$	2237.52	0.276573
$404$	−6677.53	−0.822326
$405$	0	0
$406$	−14180.7	−1.73345
$407$	2287.78	0.278627
$408$	3952.76	0.479634
$409$	−5857.25	−0.708123	−0.354062	−	0.935222i	$-0.615200\pi$
$409$	−5857.25	−0.708123	−0.354062	+	0.935222i	$0.615200\pi$
$410$	0	0
$411$	−4270.45	−0.512521
$412$	4442.51	0.531229
$413$	−12738.1	−1.51767
$414$	−204.697	−0.0243002
$415$	0	0
$416$	721.267	0.0850073
$417$	1468.96	0.172507
$418$	−10838.7	−1.26827
$419$	−5252.61	−0.612426	−0.306213	−	0.951963i	$-0.599062\pi$
$419$	−5252.61	−0.612426	−0.306213	+	0.951963i	$0.599062\pi$
$420$	0	0
$421$	−203.517	−0.0235602	−0.0117801	−	0.999931i	$-0.503750\pi$
$421$	−203.517	−0.0235602	−0.0117801	+	0.999931i	$0.503750\pi$
$422$	10790.3	1.24471
$423$	−914.863	−0.105159
$424$	−3930.20	−0.450158
$425$	0	0
$426$	8483.47	0.964849
$427$	−19409.6	−2.19976
$428$	−156.757	−0.0177036
$429$	−4084.89	−0.459721
$430$	0	0
$431$	3107.72	0.347317	0.173659	−	0.984806i	$-0.444441\pi$
$431$	3107.72	0.347317	0.173659	+	0.984806i	$0.444441\pi$
$432$	−2389.54	−0.266126
$433$	5713.46	0.634114	0.317057	−	0.948406i	$-0.397305\pi$
$433$	5713.46	0.634114	0.317057	+	0.948406i	$0.397305\pi$
$434$	−5830.83	−0.644905
$435$	0	0
$436$	3230.18	0.354811
$437$	3266.00	0.357514
$438$	−1864.08	−0.203354
$439$	−4587.14	−0.498706	−0.249353	−	0.968413i	$-0.580218\pi$
$439$	−4587.14	−0.498706	−0.249353	+	0.968413i	$0.580218\pi$
$440$	0	0
$441$	−2311.75	−0.249622
$442$	4690.43	0.504754
$443$	−5268.01	−0.564990	−0.282495	−	0.959269i	$-0.591162\pi$
$443$	−5268.01	−0.564990	−0.282495	+	0.959269i	$0.591162\pi$
$444$	−1138.64	−0.121707
$445$	0	0
$446$	3009.58	0.319525
$447$	12160.8	1.28677
$448$	−1879.58	−0.198218
$449$	16866.8	1.77282	0.886409	−	0.462902i	$-0.153192\pi$
$449$	16866.8	1.77282	0.886409	+	0.462902i	$0.153192\pi$
$450$	0	0
$451$	−9512.43	−0.993177
$452$	−4266.31	−0.443961
$453$	−11696.8	−1.21316
$454$	3558.87	0.367899
$455$	0	0
$456$	5394.51	0.553993
$457$	−9124.25	−0.933948	−0.466974	−	0.884271i	$-0.654656\pi$
$457$	−9124.25	−0.933948	−0.466974	+	0.884271i	$0.654656\pi$
$458$	7952.31	0.811326
$459$	−15539.3	−1.58020
$460$	0	0
$461$	6011.92	0.607382	0.303691	−	0.952771i	$-0.401781\pi$
$461$	6011.92	0.607382	0.303691	+	0.952771i	$0.401781\pi$
$462$	10645.0	1.07197
$463$	8584.09	0.861634	0.430817	−	0.902439i	$-0.358225\pi$
$463$	8584.09	0.861634	0.430817	+	0.902439i	$0.358225\pi$
$464$	3862.86	0.386484
$465$	0	0
$466$	4622.25	0.459488
$467$	−3954.09	−0.391806	−0.195903	−	0.980623i	$-0.562764\pi$
$467$	−3954.09	−0.391806	−0.195903	+	0.980623i	$0.562764\pi$
$468$	−401.198	−0.0396269
$469$	−9502.56	−0.935581
$470$	0	0
$471$	2691.18	0.263276
$472$	3469.87	0.338377
$473$	−6253.75	−0.607923
$474$	−4750.69	−0.460351
$475$	0	0
$476$	−12223.0	−1.17697
$477$	2186.14	0.209845
$478$	1648.53	0.157745
$479$	−95.3377	−0.00909413	−0.00454707	−	0.999990i	$-0.501447\pi$
$479$	−95.3377	−0.00909413	−0.00454707	+	0.999990i	$0.501447\pi$
$480$	0	0
$481$	−1351.14	−0.128080
$482$	7283.66	0.688302
$483$	−3207.61	−0.302177
$484$	502.127	0.0471570
$485$	0	0
$486$	2470.25	0.230561
$487$	−13915.2	−1.29478	−0.647391	−	0.762158i	$-0.724140\pi$
$487$	−13915.2	−1.29478	−0.647391	+	0.762158i	$0.724140\pi$
$488$	5287.22	0.490453
$489$	−4563.03	−0.421978
$490$	0	0
$491$	6291.33	0.578256	0.289128	−	0.957290i	$-0.406635\pi$
$491$	6291.33	0.578256	0.289128	+	0.957290i	$0.406635\pi$
$492$	4734.41	0.433828
$493$	25120.3	2.29486
$494$	6401.24	0.583007
$495$	0	0
$496$	1588.33	0.143786
$497$	−26233.1	−2.36764
$498$	−7606.87	−0.684482
$499$	−638.332	−0.0572658	−0.0286329	−	0.999590i	$-0.509115\pi$
$499$	−638.332	−0.0572658	−0.0286329	+	0.999590i	$0.509115\pi$
$500$	0	0
$501$	20061.8	1.78901
$502$	−15535.0	−1.38120
$503$	−15063.4	−1.33527	−0.667637	−	0.744487i	$-0.732694\pi$
$503$	−15063.4	−1.33527	−0.667637	+	0.744487i	$0.732694\pi$
$504$	1045.50	0.0924011
$505$	0	0
$506$	−1755.57	−0.154238
$507$	−8020.38	−0.702559
$508$	2566.83	0.224182
$509$	−13623.1	−1.18631	−0.593157	−	0.805087i	$-0.702119\pi$
$509$	−13623.1	−1.18631	−0.593157	+	0.805087i	$0.702119\pi$
$510$	0	0
$511$	5764.23	0.499010
$512$	512.000	0.0441942
$513$	−21207.1	−1.82518
$514$	3002.33	0.257640
$515$	0	0
$516$	3112.54	0.265546
$517$	−7846.27	−0.667463
$518$	3520.99	0.298655
$519$	−16378.2	−1.38520
$520$	0	0
$521$	−21659.4	−1.82133	−0.910666	−	0.413143i	$-0.864431\pi$
$521$	−21659.4	−1.82133	−0.910666	+	0.413143i	$0.864431\pi$
$522$	−2148.68	−0.180163
$523$	3813.85	0.318868	0.159434	−	0.987209i	$-0.449033\pi$
$523$	3813.85	0.318868	0.159434	+	0.987209i	$0.449033\pi$
$524$	9559.69	0.796979
$525$	0	0
$526$	10862.0	0.900388
$527$	10329.0	0.853771
$528$	−2899.71	−0.239003
$529$	529.000	0.0434783
$530$	0	0
$531$	−1930.09	−0.157737
$532$	−16681.2	−1.35944
$533$	5617.95	0.456549
$534$	−6923.74	−0.561085
$535$	0	0
$536$	2588.51	0.208595
$537$	6922.72	0.556308
$538$	−10028.4	−0.803634
$539$	−19826.6	−1.58440
$540$	0	0
$541$	9727.32	0.773031	0.386516	−	0.922283i	$-0.373679\pi$
$541$	9727.32	0.773031	0.386516	+	0.922283i	$0.373679\pi$
$542$	14431.1	1.14367
$543$	−17261.3	−1.36419
$544$	3329.56	0.262415
$545$	0	0
$546$	−6286.81	−0.492767
$547$	−782.647	−0.0611766	−0.0305883	−	0.999532i	$-0.509738\pi$
$547$	−782.647	−0.0611766	−0.0305883	+	0.999532i	$0.509738\pi$
$548$	−3597.16	−0.280407
$549$	−2940.97	−0.228629
$550$	0	0
$551$	34282.8	2.65063
$552$	873.759	0.0673726
$553$	14690.4	1.12965
$554$	14879.2	1.14108
$555$	0	0
$556$	1237.36	0.0943811
$557$	−3472.87	−0.264184	−0.132092	−	0.991237i	$-0.542169\pi$
$557$	−3472.87	−0.264184	−0.132092	+	0.991237i	$0.542169\pi$
$558$	−883.494	−0.0670274
$559$	3693.40	0.279453
$560$	0	0
$561$	−18856.9	−1.41914
$562$	−5211.18	−0.391140
$563$	−7544.75	−0.564784	−0.282392	−	0.959299i	$-0.591128\pi$
$563$	−7544.75	−0.564784	−0.282392	+	0.959299i	$0.591128\pi$
$564$	3905.14	0.291554
$565$	0	0
$566$	14325.1	1.06383
$567$	17299.5	1.28132
$568$	7145.94	0.527882
$569$	13222.5	0.974193	0.487096	−	0.873348i	$-0.338056\pi$
$569$	13222.5	0.974193	0.487096	+	0.873348i	$0.338056\pi$
$570$	0	0
$571$	4069.49	0.298254	0.149127	−	0.988818i	$-0.452354\pi$
$571$	4069.49	0.298254	0.149127	+	0.988818i	$0.452354\pi$
$572$	−3440.85	−0.251520
$573$	2131.27	0.155384
$574$	−14640.0	−1.06457
$575$	0	0
$576$	−284.795	−0.0206015
$577$	−846.627	−0.0610841	−0.0305421	−	0.999533i	$-0.509723\pi$
$577$	−846.627	−0.0610841	−0.0305421	+	0.999533i	$0.509723\pi$
$578$	11826.3	0.851051
$579$	−20226.3	−1.45177
$580$	0	0
$581$	23522.4	1.67965
$582$	−10826.6	−0.771097
$583$	18749.3	1.33193
$584$	−1570.19	−0.111258
$585$	0	0
$586$	−18621.1	−1.31268
$587$	−4702.77	−0.330672	−0.165336	−	0.986237i	$-0.552871\pi$
$587$	−4702.77	−0.330672	−0.165336	+	0.986237i	$0.552871\pi$
$588$	9867.82	0.692079
$589$	14096.4	0.986133
$590$	0	0
$591$	8392.71	0.584146
$592$	−959.123	−0.0665874
$593$	14016.5	0.970640	0.485320	−	0.874337i	$-0.338703\pi$
$593$	14016.5	0.970640	0.485320	+	0.874337i	$0.338703\pi$
$594$	11399.4	0.787415
$595$	0	0
$596$	10243.5	0.704010
$597$	4769.07	0.326943
$598$	1036.82	0.0709010
$599$	12885.0	0.878910	0.439455	−	0.898265i	$-0.355172\pi$
$599$	12885.0	0.878910	0.439455	+	0.898265i	$0.355172\pi$
$600$	0	0
$601$	−4753.41	−0.322622	−0.161311	−	0.986904i	$-0.551572\pi$
$601$	−4753.41	−0.322622	−0.161311	+	0.986904i	$0.551572\pi$
$602$	−9624.77	−0.651622
$603$	−1439.84	−0.0972383
$604$	−9852.61	−0.663737
$605$	0	0
$606$	−15854.8	−1.06280
$607$	6800.06	0.454705	0.227352	−	0.973813i	$-0.426993\pi$
$607$	6800.06	0.454705	0.227352	+	0.973813i	$0.426993\pi$
$608$	4543.99	0.303097
$609$	−33670.0	−2.24036
$610$	0	0
$611$	4633.93	0.306823
$612$	−1852.04	−0.122327
$613$	−20842.3	−1.37327	−0.686634	−	0.727003i	$-0.740913\pi$
$613$	−20842.3	−1.37327	−0.686634	+	0.727003i	$0.740913\pi$
$614$	−6718.14	−0.441567
$615$	0	0
$616$	8966.65	0.586488
$617$	−18917.7	−1.23436	−0.617179	−	0.786823i	$-0.711724\pi$
$617$	−18917.7	−1.23436	−0.617179	+	0.786823i	$0.711724\pi$
$618$	10548.0	0.686577
$619$	−28044.8	−1.82103	−0.910513	−	0.413480i	$-0.864313\pi$
$619$	−28044.8	−1.82103	−0.910513	+	0.413480i	$0.864313\pi$
$620$	0	0
$621$	−3434.96	−0.221965
$622$	−11018.4	−0.710285
$623$	21410.0	1.37684
$624$	1712.54	0.109866
$625$	0	0
$626$	−4802.83	−0.306645
$627$	−25734.9	−1.63916
$628$	2266.88	0.144042
$629$	−6237.22	−0.395380
$630$	0	0
$631$	−25796.2	−1.62746	−0.813732	−	0.581241i	$-0.802567\pi$
$631$	−25796.2	−1.62746	−0.813732	+	0.581241i	$0.802567\pi$
$632$	−4001.69	−0.251865
$633$	25620.0	1.60870
$634$	2114.71	0.132470
$635$	0	0
$636$	−9331.64	−0.581798
$637$	11709.4	0.728324
$638$	−18428.0	−1.14353
$639$	−3974.87	−0.246077
$640$	0	0
$641$	−26482.3	−1.63181	−0.815903	−	0.578188i	$-0.803760\pi$
$641$	−26482.3	−1.63181	−0.815903	+	0.578188i	$0.803760\pi$
$642$	−372.195	−0.0228806
$643$	−30458.1	−1.86804	−0.934020	−	0.357219i	$-0.883725\pi$
$643$	−30458.1	−1.86804	−0.934020	+	0.357219i	$0.883725\pi$
$644$	−2701.89	−0.165325
$645$	0	0
$646$	29549.8	1.79972
$647$	6746.24	0.409926	0.204963	−	0.978770i	$-0.434293\pi$
$647$	6746.24	0.409926	0.204963	+	0.978770i	$0.434293\pi$
$648$	−4712.40	−0.285680
$649$	−16553.3	−1.00119
$650$	0	0
$651$	−13844.4	−0.833495
$652$	−3843.61	−0.230870
$653$	−12976.2	−0.777640	−0.388820	−	0.921314i	$-0.627117\pi$
$653$	−12976.2	−0.777640	−0.388820	+	0.921314i	$0.627117\pi$
$654$	7669.57	0.458569
$655$	0	0
$656$	3987.97	0.237354
$657$	873.401	0.0518640
$658$	−12075.7	−0.715442
$659$	−6538.56	−0.386504	−0.193252	−	0.981149i	$-0.561903\pi$
$659$	−6538.56	−0.386504	−0.193252	+	0.981149i	$0.561903\pi$
$660$	0	0
$661$	−25177.1	−1.48151	−0.740753	−	0.671777i	$-0.765531\pi$
$661$	−25177.1	−1.48151	−0.740753	+	0.671777i	$0.765531\pi$
$662$	−19360.4	−1.13665
$663$	11136.7	0.652359
$664$	−6407.55	−0.374490
$665$	0	0
$666$	533.504	0.0310403
$667$	5552.86	0.322350
$668$	16898.8	0.978794
$669$	7145.79	0.412963
$670$	0	0
$671$	−25223.0	−1.45115
$672$	−4462.77	−0.256183
$673$	−18339.3	−1.05041	−0.525207	−	0.850975i	$-0.676012\pi$
$673$	−18339.3	−1.05041	−0.525207	+	0.850975i	$0.676012\pi$
$674$	−935.388	−0.0534567
$675$	0	0
$676$	−6755.86	−0.384380
$677$	−31876.9	−1.80965	−0.904823	−	0.425789i	$-0.859997\pi$
$677$	−31876.9	−1.80965	−0.904823	+	0.425789i	$0.859997\pi$
$678$	−10129.7	−0.573789
$679$	33478.8	1.89219
$680$	0	0
$681$	8450.00	0.475484
$682$	−7577.23	−0.425436
$683$	28843.7	1.61592	0.807959	−	0.589239i	$-0.200572\pi$
$683$	28843.7	1.61592	0.807959	+	0.589239i	$0.200572\pi$
$684$	−2527.56	−0.141292
$685$	0	0
$686$	−10367.2	−0.576998
$687$	18881.5	1.04858
$688$	2621.80	0.145284
$689$	−11073.1	−0.612268
$690$	0	0
$691$	−18327.7	−1.00900	−0.504499	−	0.863413i	$-0.668323\pi$
$691$	−18327.7	−1.00900	−0.504499	+	0.863413i	$0.668323\pi$
$692$	−13795.9	−0.757865
$693$	−4987.62	−0.273397
$694$	−6743.09	−0.368825
$695$	0	0
$696$	9171.77	0.499504
$697$	25933.9	1.40935
$698$	21917.5	1.18852
$699$	10974.8	0.593857
$700$	0	0
$701$	−8329.48	−0.448788	−0.224394	−	0.974499i	$-0.572040\pi$
$701$	−8329.48	−0.448788	−0.224394	+	0.974499i	$0.572040\pi$
$702$	−6732.40	−0.361963
$703$	−8512.20	−0.456677
$704$	−2442.53	−0.130762
$705$	0	0
$706$	3169.52	0.168961
$707$	49027.1	2.60800
$708$	8238.68	0.437328
$709$	−6169.85	−0.326818	−0.163409	−	0.986558i	$-0.552249\pi$
$709$	−6169.85	−0.326818	−0.163409	+	0.986558i	$0.552249\pi$
$710$	0	0
$711$	2225.90	0.117409
$712$	−5832.12	−0.306978
$713$	2283.22	0.119926
$714$	−29021.6	−1.52115
$715$	0	0
$716$	5831.27	0.304364
$717$	3914.19	0.203875
$718$	10261.3	0.533356
$719$	28740.8	1.49075	0.745377	−	0.666644i	$-0.232270\pi$
$719$	28740.8	1.49075	0.745377	+	0.666644i	$0.232270\pi$
$720$	0	0
$721$	−32617.3	−1.68479
$722$	26609.9	1.37163
$723$	17293.9	0.889583
$724$	−14539.9	−0.746368
$725$	0	0
$726$	1192.22	0.0609471
$727$	−11174.0	−0.570041	−0.285021	−	0.958521i	$-0.592000\pi$
$727$	−11174.0	−0.570041	−0.285021	+	0.958521i	$0.592000\pi$
$728$	−5295.62	−0.269600
$729$	21769.6	1.10601
$730$	0	0
$731$	17049.7	0.862663
$732$	12553.7	0.633876
$733$	23560.7	1.18722	0.593612	−	0.804751i	$-0.297701\pi$
$733$	23560.7	1.18722	0.593612	+	0.804751i	$0.297701\pi$
$734$	−5622.54	−0.282741
$735$	0	0
$736$	736.000	0.0368605
$737$	−12348.7	−0.617191
$738$	−2218.27	−0.110645
$739$	22713.6	1.13063	0.565313	−	0.824877i	$-0.308755\pi$
$739$	22713.6	1.13063	0.565313	+	0.824877i	$0.308755\pi$
$740$	0	0
$741$	15198.8	0.753495
$742$	28855.9	1.42767
$743$	15882.7	0.784224	0.392112	−	0.919917i	$-0.371745\pi$
$743$	15882.7	0.784224	0.392112	+	0.919917i	$0.371745\pi$
$744$	3771.24	0.185834
$745$	0	0
$746$	3904.84	0.191644
$747$	3564.14	0.174572
$748$	−15883.9	−0.776433
$749$	1150.92	0.0561466
$750$	0	0
$751$	−30250.6	−1.46985	−0.734927	−	0.678146i	$-0.762784\pi$
$751$	−30250.6	−1.46985	−0.734927	+	0.678146i	$0.762784\pi$
$752$	3289.45	0.159513
$753$	−36885.5	−1.78510
$754$	10883.4	0.525664
$755$	0	0
$756$	17544.2	0.844017
$757$	9611.05	0.461453	0.230726	−	0.973019i	$-0.425890\pi$
$757$	9611.05	0.461453	0.230726	+	0.973019i	$0.425890\pi$
$758$	19218.5	0.920908
$759$	−4168.33	−0.199342
$760$	0	0
$761$	5892.64	0.280694	0.140347	−	0.990102i	$-0.455178\pi$
$761$	5892.64	0.280694	0.140347	+	0.990102i	$0.455178\pi$
$762$	6094.54	0.289740
$763$	−23716.3	−1.12528
$764$	1795.25	0.0850127
$765$	0	0
$766$	−10054.9	−0.474279
$767$	9776.19	0.460232
$768$	1215.67	0.0571179
$769$	1683.72	0.0789553	0.0394777	−	0.999220i	$-0.487431\pi$
$769$	1683.72	0.0789553	0.0394777	+	0.999220i	$0.487431\pi$
$770$	0	0
$771$	7128.57	0.332982
$772$	−17037.4	−0.794286
$773$	−19880.8	−0.925048	−0.462524	−	0.886607i	$-0.653056\pi$
$773$	−19880.8	−0.925048	−0.462524	+	0.886607i	$0.653056\pi$
$774$	−1458.36	−0.0677255
$775$	0	0
$776$	−9119.68	−0.421878
$777$	8360.04	0.385991
$778$	11784.6	0.543056
$779$	35393.2	1.62785
$780$	0	0
$781$	−34090.2	−1.56190
$782$	4786.24	0.218869
$783$	−36056.4	−1.64566
$784$	8312.04	0.378646
$785$	0	0
$786$	22698.0	1.03004
$787$	7622.64	0.345258	0.172629	−	0.984987i	$-0.444774\pi$
$787$	7622.64	0.345258	0.172629	+	0.984987i	$0.444774\pi$
$788$	7069.50	0.319594
$789$	25790.1	1.16369
$790$	0	0
$791$	31323.7	1.40802
$792$	1358.64	0.0609558
$793$	14896.5	0.667074
$794$	4908.82	0.219405
$795$	0	0
$796$	4017.16	0.178875
$797$	22380.9	0.994693	0.497347	−	0.867552i	$-0.334308\pi$
$797$	22380.9	0.994693	0.497347	+	0.867552i	$0.334308\pi$
$798$	−39607.0	−1.75698
$799$	21391.4	0.947152
$800$	0	0
$801$	3244.07	0.143100
$802$	18916.8	0.832886
$803$	7490.67	0.329191
$804$	6146.03	0.269594
$805$	0	0
$806$	4475.04	0.195566
$807$	−23810.9	−1.03864
$808$	−13355.1	−0.581472
$809$	8117.18	0.352762	0.176381	−	0.984322i	$-0.443561\pi$
$809$	8117.18	0.352762	0.176381	+	0.984322i	$0.443561\pi$
$810$	0	0
$811$	7221.05	0.312658	0.156329	−	0.987705i	$-0.450034\pi$
$811$	7221.05	0.312658	0.156329	+	0.987705i	$0.450034\pi$
$812$	−28361.5	−1.22573
$813$	34264.4	1.47811
$814$	4575.56	0.197019
$815$	0	0
$816$	7905.52	0.339153
$817$	23268.5	0.996403
$818$	−11714.5	−0.500719
$819$	2945.64	0.125676
$820$	0	0
$821$	34803.3	1.47947	0.739735	−	0.672899i	$-0.234951\pi$
$821$	34803.3	1.47947	0.739735	+	0.672899i	$0.234951\pi$
$822$	−8540.91	−0.362407
$823$	−490.883	−0.0207911	−0.0103956	−	0.999946i	$-0.503309\pi$
$823$	−490.883	−0.0207911	−0.0103956	+	0.999946i	$0.503309\pi$
$824$	8885.01	0.375636
$825$	0	0
$826$	−25476.1	−1.07316
$827$	−30952.0	−1.30146	−0.650729	−	0.759310i	$-0.725537\pi$
$827$	−30952.0	−1.30146	−0.650729	+	0.759310i	$0.725537\pi$
$828$	−409.393	−0.0171829
$829$	8587.63	0.359784	0.179892	−	0.983686i	$-0.442425\pi$
$829$	8587.63	0.359784	0.179892	+	0.983686i	$0.442425\pi$
$830$	0	0
$831$	35328.4	1.47476
$832$	1442.53	0.0601092
$833$	54053.5	2.24831
$834$	2937.93	0.121981
$835$	0	0
$836$	−21677.4	−0.896806
$837$	−14825.7	−0.612246
$838$	−10505.2	−0.433051
$839$	3077.94	0.126653	0.0633267	−	0.997993i	$-0.479829\pi$
$839$	3077.94	0.126653	0.0633267	+	0.997993i	$0.479829\pi$
$840$	0	0
$841$	33898.9	1.38992
$842$	−407.035	−0.0166596
$843$	−12373.2	−0.505521
$844$	21580.7	0.880140
$845$	0	0
$846$	−1829.73	−0.0743585
$847$	−3686.67	−0.149558
$848$	−7860.39	−0.318310
$849$	34012.8	1.37493
$850$	0	0
$851$	−1378.74	−0.0555377
$852$	16966.9	0.682251
$853$	9193.14	0.369012	0.184506	−	0.982831i	$-0.440932\pi$
$853$	9193.14	0.369012	0.184506	+	0.982831i	$0.440932\pi$
$854$	−38819.3	−1.55547
$855$	0	0
$856$	−313.513	−0.0125183
$857$	−21445.8	−0.854813	−0.427407	−	0.904059i	$-0.640573\pi$
$857$	−21445.8	−0.854813	−0.427407	+	0.904059i	$0.640573\pi$
$858$	−8169.78	−0.325072
$859$	−40276.7	−1.59979	−0.799897	−	0.600137i	$-0.795113\pi$
$859$	−40276.7	−1.59979	−0.799897	+	0.600137i	$0.795113\pi$
$860$	0	0
$861$	−34760.5	−1.37588
$862$	6215.44	0.245590
$863$	−43713.4	−1.72424	−0.862120	−	0.506703i	$-0.830864\pi$
$863$	−43713.4	−1.72424	−0.862120	+	0.506703i	$0.830864\pi$
$864$	−4779.07	−0.188180
$865$	0	0
$866$	11426.9	0.448386
$867$	28079.6	1.09992
$868$	−11661.7	−0.456017
$869$	19090.3	0.745218
$870$	0	0
$871$	7293.01	0.283713
$872$	6460.36	0.250889
$873$	5072.74	0.196662
$874$	6531.99	0.252801
$875$	0	0
$876$	−3728.16	−0.143793
$877$	−24740.5	−0.952596	−0.476298	−	0.879284i	$-0.658022\pi$
$877$	−24740.5	−0.952596	−0.476298	+	0.879284i	$0.658022\pi$
$878$	−9174.27	−0.352639
$879$	−44212.9	−1.69655
$880$	0	0
$881$	−44027.2	−1.68367	−0.841835	−	0.539735i	$-0.818524\pi$
$881$	−44027.2	−1.68367	−0.841835	+	0.539735i	$0.818524\pi$
$882$	−4623.50	−0.176509
$883$	−30245.0	−1.15269	−0.576344	−	0.817207i	$-0.695521\pi$
$883$	−30245.0	−1.15269	−0.576344	+	0.817207i	$0.695521\pi$
$884$	9380.87	0.356915
$885$	0	0
$886$	−10536.0	−0.399509
$887$	7317.82	0.277010	0.138505	−	0.990362i	$-0.455770\pi$
$887$	7317.82	0.277010	0.138505	+	0.990362i	$0.455770\pi$
$888$	−2277.29	−0.0860595
$889$	−18845.9	−0.710991
$890$	0	0
$891$	22480.8	0.845270
$892$	6019.17	0.225938
$893$	29193.8	1.09399
$894$	24321.6	0.909883
$895$	0	0
$896$	−3759.15	−0.140161
$897$	2461.77	0.0916346
$898$	33733.7	1.25357
$899$	23966.8	0.889140
$900$	0	0
$901$	−51116.5	−1.89005
$902$	−19024.9	−0.702282
$903$	−22852.5	−0.842176
$904$	−8532.63	−0.313928
$905$	0	0
$906$	−23393.5	−0.857834
$907$	35436.0	1.29728	0.648640	−	0.761096i	$-0.275338\pi$
$907$	35436.0	1.29728	0.648640	+	0.761096i	$0.275338\pi$
$908$	7117.75	0.260144
$909$	7428.63	0.271058
$910$	0	0
$911$	−11359.1	−0.413112	−0.206556	−	0.978435i	$-0.566225\pi$
$911$	−11359.1	−0.413112	−0.206556	+	0.978435i	$0.566225\pi$
$912$	10789.0	0.391732
$913$	30567.7	1.10804
$914$	−18248.5	−0.660401
$915$	0	0
$916$	15904.6	0.573694
$917$	−70188.2	−2.52761
$918$	−31078.5	−1.11737
$919$	40517.5	1.45435	0.727175	−	0.686452i	$-0.240833\pi$
$919$	40517.5	1.45435	0.727175	+	0.686452i	$0.240833\pi$
$920$	0	0
$921$	−15951.2	−0.570695
$922$	12023.8	0.429484
$923$	20133.3	0.717982
$924$	21289.9	0.757995
$925$	0	0
$926$	17168.2	0.609267
$927$	−4942.21	−0.175106
$928$	7725.72	0.273286
$929$	16242.2	0.573614	0.286807	−	0.957988i	$-0.407406\pi$
$929$	16242.2	0.573614	0.286807	+	0.957988i	$0.407406\pi$
$930$	0	0
$931$	73769.2	2.59687
$932$	9244.50	0.324907
$933$	−26161.5	−0.917994
$934$	−7908.19	−0.277049
$935$	0	0
$936$	−802.397	−0.0280205
$937$	47445.0	1.65417	0.827087	−	0.562074i	$-0.189996\pi$
$937$	47445.0	1.65417	0.827087	+	0.562074i	$0.189996\pi$
$938$	−19005.1	−0.661556
$939$	−11403.6	−0.396317
$940$	0	0
$941$	−48063.5	−1.66506	−0.832532	−	0.553976i	$-0.813110\pi$
$941$	−48063.5	−1.66506	−0.832532	+	0.553976i	$0.813110\pi$
$942$	5382.36	0.186164
$943$	5732.70	0.197967
$944$	6939.74	0.239268
$945$	0	0
$946$	−12507.5	−0.429867
$947$	−13745.4	−0.471663	−0.235831	−	0.971794i	$-0.575781\pi$
$947$	−13745.4	−0.471663	−0.235831	+	0.971794i	$0.575781\pi$
$948$	−9501.39	−0.325518
$949$	−4423.92	−0.151324
$950$	0	0
$951$	5021.06	0.171208
$952$	−24445.9	−0.832245
$953$	13999.1	0.475839	0.237920	−	0.971285i	$-0.423535\pi$
$953$	13999.1	0.475839	0.237920	+	0.971285i	$0.423535\pi$
$954$	4372.27	0.148383
$955$	0	0
$956$	3297.07	0.111543
$957$	−43754.5	−1.47793
$958$	−190.675	−0.00643052
$959$	26410.7	0.889308
$960$	0	0
$961$	−19936.4	−0.669207
$962$	−2702.28	−0.0905666
$963$	174.389	0.00583552
$964$	14567.3	0.486703
$965$	0	0
$966$	−6415.23	−0.213671
$967$	800.187	0.0266104	0.0133052	−	0.999911i	$-0.495765\pi$
$967$	800.187	0.0266104	0.0133052	+	0.999911i	$0.495765\pi$
$968$	1004.25	0.0333450
$969$	70161.4	2.32602
$970$	0	0
$971$	−11363.5	−0.375563	−0.187782	−	0.982211i	$-0.560130\pi$
$971$	−11363.5	−0.375563	−0.187782	+	0.982211i	$0.560130\pi$
$972$	4940.50	0.163032
$973$	−9084.84	−0.299328
$974$	−27830.4	−0.915549
$975$	0	0
$976$	10574.4	0.346803
$977$	17444.0	0.571220	0.285610	−	0.958346i	$-0.407804\pi$
$977$	17444.0	0.571220	0.285610	+	0.958346i	$0.407804\pi$
$978$	−9126.06	−0.298384
$979$	27822.5	0.908286
$980$	0	0
$981$	−3593.52	−0.116954
$982$	12582.7	0.408889
$983$	54032.7	1.75318	0.876590	−	0.481237i	$-0.159812\pi$
$983$	54032.7	1.75318	0.876590	+	0.481237i	$0.159812\pi$
$984$	9468.81	0.306763
$985$	0	0
$986$	50240.7	1.62271
$987$	−28671.9	−0.924659
$988$	12802.5	0.412248
$989$	3768.84	0.121175
$990$	0	0
$991$	28869.3	0.925392	0.462696	−	0.886517i	$-0.346882\pi$
$991$	28869.3	0.925392	0.462696	+	0.886517i	$0.346882\pi$
$992$	3176.66	0.101672
$993$	−45968.3	−1.46904
$994$	−52466.2	−1.67417
$995$	0	0
$996$	−15213.7	−0.484002
$997$	−3358.78	−0.106694	−0.0533469	−	0.998576i	$-0.516989\pi$
$997$	−3358.78	−0.106694	−0.0533469	+	0.998576i	$0.516989\pi$
$998$	−1276.66	−0.0404931
$999$	8952.57	0.283530

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.4.a.p.1.3		4
5.2	odd	4		1150.4.b.n.599.6		8
5.3	odd	4		1150.4.b.n.599.3		8
5.4	even	2		230.4.a.h.1.2	✓	4
15.14	odd	2		2070.4.a.bj.1.4		4
20.19	odd	2		1840.4.a.m.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.h.1.2	✓	4	5.4	even	2
1150.4.a.p.1.3		4	1.1	even	1	trivial
1150.4.b.n.599.3		8	5.3	odd	4
1150.4.b.n.599.6		8	5.2	odd	4
1840.4.a.m.1.3		4	20.19	odd	2
2070.4.a.bj.1.4		4	15.14	odd	2

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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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +4.74869 q^{3} +4.00000 q^{4} +9.49738 q^{6} -29.3684 q^{7} +8.00000 q^{8} -4.44993 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +4.74869 q^{3} +4.00000 q^{4} +9.49738 q^{6} -29.3684 q^{7} +8.00000 q^{8} -4.44993 q^{9} -38.1645 q^{11} +18.9948 q^{12} +22.5396 q^{13} -58.7368 q^{14} +16.0000 q^{16} +104.049 q^{17} -8.89986 q^{18} +142.000 q^{19} -139.461 q^{21} -76.3291 q^{22} +23.0000 q^{23} +37.9895 q^{24} +45.0792 q^{26} -149.346 q^{27} -117.474 q^{28} +241.429 q^{29} +99.2706 q^{31} +32.0000 q^{32} -181.232 q^{33} +208.097 q^{34} -17.7997 q^{36} -59.9452 q^{37} +284.000 q^{38} +107.034 q^{39} +249.248 q^{41} -278.923 q^{42} +163.863 q^{43} -152.658 q^{44} +46.0000 q^{46} +205.591 q^{47} +75.9791 q^{48} +519.502 q^{49} +494.095 q^{51} +90.1584 q^{52} -491.274 q^{53} -298.692 q^{54} -234.947 q^{56} +674.313 q^{57} +482.858 q^{58} +433.734 q^{59} +660.902 q^{61} +198.541 q^{62} +130.687 q^{63} +64.0000 q^{64} -362.463 q^{66} +323.564 q^{67} +416.195 q^{68} +109.220 q^{69} +893.243 q^{71} -35.5994 q^{72} -196.273 q^{73} -119.890 q^{74} +567.999 q^{76} +1120.83 q^{77} +214.067 q^{78} -500.211 q^{79} -589.050 q^{81} +498.496 q^{82} -800.944 q^{83} -557.846 q^{84} +327.726 q^{86} +1146.47 q^{87} -305.316 q^{88} -729.016 q^{89} -661.952 q^{91} +92.0000 q^{92} +471.405 q^{93} +411.181 q^{94} +151.958 q^{96} -1139.96 q^{97} +1039.00 q^{98} +169.829 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} + 4 q^{3} + 16 q^{4} + 8 q^{6} + q^{7} + 32 q^{8} + 32 q^{9}+O(q^{10}) \) 4 * q + 8 * q^2 + 4 * q^3 + 16 * q^4 + 8 * q^6 + q^7 + 32 * q^8 + 32 * q^9	\( 4 q + 8 q^{2} + 4 q^{3} + 16 q^{4} + 8 q^{6} + q^{7} + 32 q^{8} + 32 q^{9} - 39 q^{11} + 16 q^{12} + 20 q^{13} + 2 q^{14} + 64 q^{16} + 23 q^{17} + 64 q^{18} + 53 q^{19} + 300 q^{21} - 78 q^{22} + 92 q^{23} + 32 q^{24} + 40 q^{26} - 137 q^{27} + 4 q^{28} + 161 q^{29} + 388 q^{31} + 128 q^{32} - 87 q^{33} + 46 q^{34} + 128 q^{36} - 466 q^{37} + 106 q^{38} + 1047 q^{39} + 484 q^{41} + 600 q^{42} - 894 q^{43} - 156 q^{44} + 184 q^{46} + 265 q^{47} + 64 q^{48} + 1643 q^{49} + 1825 q^{51} + 80 q^{52} - 576 q^{53} - 274 q^{54} + 8 q^{56} - 178 q^{57} + 322 q^{58} - 94 q^{59} + 1153 q^{61} + 776 q^{62} - 60 q^{63} + 256 q^{64} - 174 q^{66} + 1472 q^{67} + 92 q^{68} + 92 q^{69} + 200 q^{71} + 256 q^{72} - 1147 q^{73} - 932 q^{74} + 212 q^{76} + 2176 q^{77} + 2094 q^{78} - 908 q^{79} - 1056 q^{81} + 968 q^{82} + 1048 q^{83} + 1200 q^{84} - 1788 q^{86} + 2167 q^{87} - 312 q^{88} - 1784 q^{89} + 2329 q^{91} + 368 q^{92} - 1483 q^{93} + 530 q^{94} + 128 q^{96} + 2047 q^{97} + 3286 q^{98} - 2665 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 + 4 * q^3 + 16 * q^4 + 8 * q^6 + q^7 + 32 * q^8 + 32 * q^9 - 39 * q^11 + 16 * q^12 + 20 * q^13 + 2 * q^14 + 64 * q^16 + 23 * q^17 + 64 * q^18 + 53 * q^19 + 300 * q^21 - 78 * q^22 + 92 * q^23 + 32 * q^24 + 40 * q^26 - 137 * q^27 + 4 * q^28 + 161 * q^29 + 388 * q^31 + 128 * q^32 - 87 * q^33 + 46 * q^34 + 128 * q^36 - 466 * q^37 + 106 * q^38 + 1047 * q^39 + 484 * q^41 + 600 * q^42 - 894 * q^43 - 156 * q^44 + 184 * q^46 + 265 * q^47 + 64 * q^48 + 1643 * q^49 + 1825 * q^51 + 80 * q^52 - 576 * q^53 - 274 * q^54 + 8 * q^56 - 178 * q^57 + 322 * q^58 - 94 * q^59 + 1153 * q^61 + 776 * q^62 - 60 * q^63 + 256 * q^64 - 174 * q^66 + 1472 * q^67 + 92 * q^68 + 92 * q^69 + 200 * q^71 + 256 * q^72 - 1147 * q^73 - 932 * q^74 + 212 * q^76 + 2176 * q^77 + 2094 * q^78 - 908 * q^79 - 1056 * q^81 + 968 * q^82 + 1048 * q^83 + 1200 * q^84 - 1788 * q^86 + 2167 * q^87 - 312 * q^88 - 1784 * q^89 + 2329 * q^91 + 368 * q^92 - 1483 * q^93 + 530 * q^94 + 128 * q^96 + 2047 * q^97 + 3286 * q^98 - 2665 * q^99

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