LMFDB - Embedded newform 1450.4.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,4,Mod(1,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, 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("1450.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1450.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:	$85.5527695083$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{6}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 6 $ x^2 - 6
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 58)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.44949$ of defining polynomial
Character	$\chi$	$=$	1450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +3.44949 q^{3} +4.00000 q^{4} +6.89898 q^{6} +27.5959 q^{7} +8.00000 q^{8} -15.1010 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.44949 q^{3} +4.00000 q^{4} +6.89898 q^{6} +27.5959 q^{7} +8.00000 q^{8} -15.1010 q^{9} -52.3485 q^{11} +13.7980 q^{12} +5.40408 q^{13} +55.1918 q^{14} +16.0000 q^{16} -17.1918 q^{17} -30.2020 q^{18} +44.2020 q^{19} +95.1918 q^{21} -104.697 q^{22} +205.060 q^{23} +27.5959 q^{24} +10.8082 q^{26} -145.227 q^{27} +110.384 q^{28} +29.0000 q^{29} +299.994 q^{31} +32.0000 q^{32} -180.576 q^{33} -34.3837 q^{34} -60.4041 q^{36} -29.7980 q^{37} +88.4041 q^{38} +18.6413 q^{39} -43.9592 q^{41} +190.384 q^{42} -64.8230 q^{43} -209.394 q^{44} +410.120 q^{46} +499.499 q^{47} +55.1918 q^{48} +418.535 q^{49} -59.3031 q^{51} +21.6163 q^{52} +351.627 q^{53} -290.454 q^{54} +220.767 q^{56} +152.474 q^{57} +58.0000 q^{58} +522.372 q^{59} +484.606 q^{61} +599.989 q^{62} -416.727 q^{63} +64.0000 q^{64} -361.151 q^{66} +504.990 q^{67} -68.7673 q^{68} +707.353 q^{69} +481.283 q^{71} -120.808 q^{72} -3.11019 q^{73} -59.5959 q^{74} +176.808 q^{76} -1444.60 q^{77} +37.2827 q^{78} -1043.27 q^{79} -93.2316 q^{81} -87.9184 q^{82} +1007.08 q^{83} +380.767 q^{84} -129.646 q^{86} +100.035 q^{87} -418.788 q^{88} -295.637 q^{89} +149.131 q^{91} +820.241 q^{92} +1034.83 q^{93} +998.999 q^{94} +110.384 q^{96} -428.949 q^{97} +837.069 q^{98} +790.515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} + 2 q^{3} + 8 q^{4} + 4 q^{6} + 16 q^{7} + 16 q^{8} - 40 q^{9}+O(q^{10}) $ 2 * q + 4 * q^2 + 2 * q^3 + 8 * q^4 + 4 * q^6 + 16 * q^7 + 16 * q^8 - 40 * q^9	$ 2 q + 4 q^{2} + 2 q^{3} + 8 q^{4} + 4 q^{6} + 16 q^{7} + 16 q^{8} - 40 q^{9} - 90 q^{11} + 8 q^{12} + 50 q^{13} + 32 q^{14} + 32 q^{16} + 44 q^{17} - 80 q^{18} + 108 q^{19} + 112 q^{21} - 180 q^{22} + 28 q^{23} + 16 q^{24} + 100 q^{26} - 70 q^{27} + 64 q^{28} + 58 q^{29} + 66 q^{31} + 64 q^{32} - 126 q^{33} + 88 q^{34} - 160 q^{36} - 40 q^{37} + 216 q^{38} - 46 q^{39} + 304 q^{41} + 224 q^{42} + 130 q^{43} - 360 q^{44} + 56 q^{46} + 514 q^{47} + 32 q^{48} + 210 q^{49} - 148 q^{51} + 200 q^{52} + 958 q^{53} - 140 q^{54} + 128 q^{56} + 60 q^{57} + 116 q^{58} - 180 q^{59} + 1028 q^{61} + 132 q^{62} - 128 q^{63} + 128 q^{64} - 252 q^{66} + 912 q^{67} + 176 q^{68} + 964 q^{69} + 796 q^{71} - 320 q^{72} + 856 q^{73} - 80 q^{74} + 432 q^{76} - 1008 q^{77} - 92 q^{78} - 318 q^{79} + 470 q^{81} + 608 q^{82} + 1828 q^{83} + 448 q^{84} + 260 q^{86} + 58 q^{87} - 720 q^{88} - 944 q^{89} - 368 q^{91} + 112 q^{92} + 1374 q^{93} + 1028 q^{94} + 64 q^{96} - 368 q^{97} + 420 q^{98} + 1728 q^{99}+O(q^{100}) $ 2 * q + 4 * q^2 + 2 * q^3 + 8 * q^4 + 4 * q^6 + 16 * q^7 + 16 * q^8 - 40 * q^9 - 90 * q^11 + 8 * q^12 + 50 * q^13 + 32 * q^14 + 32 * q^16 + 44 * q^17 - 80 * q^18 + 108 * q^19 + 112 * q^21 - 180 * q^22 + 28 * q^23 + 16 * q^24 + 100 * q^26 - 70 * q^27 + 64 * q^28 + 58 * q^29 + 66 * q^31 + 64 * q^32 - 126 * q^33 + 88 * q^34 - 160 * q^36 - 40 * q^37 + 216 * q^38 - 46 * q^39 + 304 * q^41 + 224 * q^42 + 130 * q^43 - 360 * q^44 + 56 * q^46 + 514 * q^47 + 32 * q^48 + 210 * q^49 - 148 * q^51 + 200 * q^52 + 958 * q^53 - 140 * q^54 + 128 * q^56 + 60 * q^57 + 116 * q^58 - 180 * q^59 + 1028 * q^61 + 132 * q^62 - 128 * q^63 + 128 * q^64 - 252 * q^66 + 912 * q^67 + 176 * q^68 + 964 * q^69 + 796 * q^71 - 320 * q^72 + 856 * q^73 - 80 * q^74 + 432 * q^76 - 1008 * q^77 - 92 * q^78 - 318 * q^79 + 470 * q^81 + 608 * q^82 + 1828 * q^83 + 448 * q^84 + 260 * q^86 + 58 * q^87 - 720 * q^88 - 944 * q^89 - 368 * q^91 + 112 * q^92 + 1374 * q^93 + 1028 * q^94 + 64 * q^96 - 368 * q^97 + 420 * q^98 + 1728 * 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
$3$	3.44949	0.663855	0.331927	−	0.943305i	$-0.392301\pi$
$3$	3.44949	0.663855	0.331927	+	0.943305i	$0.392301\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	6.89898	0.469416
$7$	27.5959	1.49004	0.745020	−	0.667042i	$-0.232440\pi$
$7$	27.5959	1.49004	0.745020	+	0.667042i	$0.232440\pi$
$8$	8.00000	0.353553
$9$	−15.1010	−0.559297
$10$	0	0
$11$	−52.3485	−1.43488	−0.717439	−	0.696621i	$-0.754686\pi$
$11$	−52.3485	−1.43488	−0.717439	+	0.696621i	$0.754686\pi$
$12$	13.7980	0.331927
$13$	5.40408	0.115294	0.0576470	−	0.998337i	$-0.481640\pi$
$13$	5.40408	0.115294	0.0576470	+	0.998337i	$0.481640\pi$
$14$	55.1918	1.05362
$15$	0	0
$16$	16.0000	0.250000
$17$	−17.1918	−0.245273	−0.122636	−	0.992452i	$-0.539135\pi$
$17$	−17.1918	−0.245273	−0.122636	+	0.992452i	$0.539135\pi$
$18$	−30.2020	−0.395483
$19$	44.2020	0.533718	0.266859	−	0.963736i	$-0.414014\pi$
$19$	44.2020	0.533718	0.266859	+	0.963736i	$0.414014\pi$
$20$	0	0
$21$	95.1918	0.989170
$22$	−104.697	−1.01461
$23$	205.060	1.85904	0.929522	−	0.368767i	$-0.120220\pi$
$23$	205.060	1.85904	0.929522	+	0.368767i	$0.120220\pi$
$24$	27.5959	0.234708
$25$	0	0
$26$	10.8082	0.0815252
$27$	−145.227	−1.03515
$28$	110.384	0.745020
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	0	0
$31$	299.994	1.73808	0.869042	−	0.494739i	$-0.164736\pi$
$31$	299.994	1.73808	0.869042	+	0.494739i	$0.164736\pi$
$32$	32.0000	0.176777
$33$	−180.576	−0.952550
$34$	−34.3837	−0.173434
$35$	0	0
$36$	−60.4041	−0.279649
$37$	−29.7980	−0.132399	−0.0661994	−	0.997806i	$-0.521087\pi$
$37$	−29.7980	−0.132399	−0.0661994	+	0.997806i	$0.521087\pi$
$38$	88.4041	0.377396
$39$	18.6413	0.0765385
$40$	0	0
$41$	−43.9592	−0.167446	−0.0837228	−	0.996489i	$-0.526681\pi$
$41$	−43.9592	−0.167446	−0.0837228	+	0.996489i	$0.526681\pi$
$42$	190.384	0.699449
$43$	−64.8230	−0.229893	−0.114947	−	0.993372i	$-0.536670\pi$
$43$	−64.8230	−0.229893	−0.114947	+	0.993372i	$0.536670\pi$
$44$	−209.394	−0.717439
$45$	0	0
$46$	410.120	1.31454
$47$	499.499	1.55020	0.775101	−	0.631837i	$-0.217699\pi$
$47$	499.499	1.55020	0.775101	+	0.631837i	$0.217699\pi$
$48$	55.1918	0.165964
$49$	418.535	1.22022
$50$	0	0
$51$	−59.3031	−0.162825
$52$	21.6163	0.0576470
$53$	351.627	0.911314	0.455657	−	0.890156i	$-0.349404\pi$
$53$	351.627	0.911314	0.455657	+	0.890156i	$0.349404\pi$
$54$	−290.454	−0.731959
$55$	0	0
$56$	220.767	0.526809
$57$	152.474	0.354311
$58$	58.0000	0.131306
$59$	522.372	1.15266	0.576331	−	0.817216i	$-0.304484\pi$
$59$	522.372	1.15266	0.576331	+	0.817216i	$0.304484\pi$
$60$	0	0
$61$	484.606	1.01717	0.508586	−	0.861011i	$-0.330168\pi$
$61$	484.606	1.01717	0.508586	+	0.861011i	$0.330168\pi$
$62$	599.989	1.22901
$63$	−416.727	−0.833375
$64$	64.0000	0.125000
$65$	0	0
$66$	−361.151	−0.673555
$67$	504.990	0.920811	0.460405	−	0.887709i	$-0.347704\pi$
$67$	504.990	0.920811	0.460405	+	0.887709i	$0.347704\pi$
$68$	−68.7673	−0.122636
$69$	707.353	1.23413
$70$	0	0
$71$	481.283	0.804475	0.402238	−	0.915535i	$-0.368233\pi$
$71$	481.283	0.804475	0.402238	+	0.915535i	$0.368233\pi$
$72$	−120.808	−0.197741
$73$	−3.11019	−0.00498659	−0.00249329	−	0.999997i	$-0.500794\pi$
$73$	−3.11019	−0.00498659	−0.00249329	+	0.999997i	$0.500794\pi$
$74$	−59.5959	−0.0936201
$75$	0	0
$76$	176.808	0.266859
$77$	−1444.60	−2.13802
$78$	37.2827	0.0541209
$79$	−1043.27	−1.48578	−0.742890	−	0.669414i	$-0.766545\pi$
$79$	−1043.27	−1.48578	−0.742890	+	0.669414i	$0.766545\pi$
$80$	0	0
$81$	−93.2316	−0.127890
$82$	−87.9184	−0.118402
$83$	1007.08	1.33182	0.665912	−	0.746030i	$-0.268042\pi$
$83$	1007.08	1.33182	0.665912	+	0.746030i	$0.268042\pi$
$84$	380.767	0.494585
$85$	0	0
$86$	−129.646	−0.162559
$87$	100.035	0.123275
$88$	−418.788	−0.507306
$89$	−295.637	−0.352106	−0.176053	−	0.984381i	$-0.556333\pi$
$89$	−295.637	−0.352106	−0.176053	+	0.984381i	$0.556333\pi$
$90$	0	0
$91$	149.131	0.171793
$92$	820.241	0.929522
$93$	1034.83	1.15383
$94$	998.999	1.09616
$95$	0	0
$96$	110.384	0.117354
$97$	−428.949	−0.449002	−0.224501	−	0.974474i	$-0.572075\pi$
$97$	−428.949	−0.449002	−0.224501	+	0.974474i	$0.572075\pi$
$98$	837.069	0.862824
$99$	790.515	0.802523
$100$	0	0
$101$	−1212.16	−1.19420	−0.597101	−	0.802166i	$-0.703681\pi$
$101$	−1212.16	−1.19420	−0.597101	+	0.802166i	$0.703681\pi$
$102$	−118.606	−0.115135
$103$	−1032.07	−0.987310	−0.493655	−	0.869658i	$-0.664339\pi$
$103$	−1032.07	−0.987310	−0.493655	+	0.869658i	$0.664339\pi$
$104$	43.2327	0.0407626
$105$	0	0
$106$	703.253	0.644396
$107$	1176.06	1.06256	0.531280	−	0.847196i	$-0.321711\pi$
$107$	1176.06	1.06256	0.531280	+	0.847196i	$0.321711\pi$
$108$	−580.908	−0.517573
$109$	−2167.86	−1.90498	−0.952491	−	0.304568i	$-0.901488\pi$
$109$	−2167.86	−1.90498	−0.952491	+	0.304568i	$0.901488\pi$
$110$	0	0
$111$	−102.788	−0.0878935
$112$	441.535	0.372510
$113$	−1623.65	−1.35169	−0.675843	−	0.737046i	$-0.736220\pi$
$113$	−1623.65	−1.35169	−0.675843	+	0.737046i	$0.736220\pi$
$114$	304.949	0.250536
$115$	0	0
$116$	116.000	0.0928477
$117$	−81.6072	−0.0644836
$118$	1044.74	0.815056
$119$	−474.424	−0.365466
$120$	0	0
$121$	1409.36	1.05887
$122$	969.212	0.719249
$123$	−151.637	−0.111160
$124$	1199.98	0.869042
$125$	0	0
$126$	−833.453	−0.589285
$127$	−333.473	−0.233000	−0.116500	−	0.993191i	$-0.537167\pi$
$127$	−333.473	−0.233000	−0.116500	+	0.993191i	$0.537167\pi$
$128$	128.000	0.0883883
$129$	−223.606	−0.152616
$130$	0	0
$131$	−933.492	−0.622592	−0.311296	−	0.950313i	$-0.600763\pi$
$131$	−933.492	−0.622592	−0.311296	+	0.950313i	$0.600763\pi$
$132$	−722.302	−0.476275
$133$	1219.80	0.795261
$134$	1009.98	0.651112
$135$	0	0
$136$	−137.535	−0.0867169
$137$	1090.32	0.679944	0.339972	−	0.940436i	$-0.389582\pi$
$137$	1090.32	0.679944	0.339972	+	0.940436i	$0.389582\pi$
$138$	1414.71	0.872665
$139$	−1924.60	−1.17440	−0.587202	−	0.809440i	$-0.699771\pi$
$139$	−1924.60	−1.17440	−0.587202	+	0.809440i	$0.699771\pi$
$140$	0	0
$141$	1723.02	1.02911
$142$	962.565	0.568850
$143$	−282.895	−0.165433
$144$	−241.616	−0.139824
$145$	0	0
$146$	−6.22039	−0.00352605
$147$	1443.73	0.810047
$148$	−119.192	−0.0661994
$149$	−1703.62	−0.936687	−0.468343	−	0.883546i	$-0.655149\pi$
$149$	−1703.62	−0.936687	−0.468343	+	0.883546i	$0.655149\pi$
$150$	0	0
$151$	1082.81	0.583560	0.291780	−	0.956486i	$-0.405753\pi$
$151$	1082.81	0.583560	0.291780	+	0.956486i	$0.405753\pi$
$152$	353.616	0.188698
$153$	259.614	0.137180
$154$	−2889.21	−1.51181
$155$	0	0
$156$	74.5653	0.0382692
$157$	−2407.90	−1.22402	−0.612010	−	0.790850i	$-0.709639\pi$
$157$	−2407.90	−1.22402	−0.612010	+	0.790850i	$0.709639\pi$
$158$	−2086.53	−1.05060
$159$	1212.93	0.604980
$160$	0	0
$161$	5658.82	2.77005
$162$	−186.463	−0.0904317
$163$	−1061.59	−0.510123	−0.255061	−	0.966925i	$-0.582096\pi$
$163$	−1061.59	−0.510123	−0.255061	+	0.966925i	$0.582096\pi$
$164$	−175.837	−0.0837228
$165$	0	0
$166$	2014.16	0.941742
$167$	−1315.63	−0.609618	−0.304809	−	0.952414i	$-0.598593\pi$
$167$	−1315.63	−0.609618	−0.304809	+	0.952414i	$0.598593\pi$
$168$	761.535	0.349724
$169$	−2167.80	−0.986707
$170$	0	0
$171$	−667.496	−0.298507
$172$	−259.292	−0.114947
$173$	653.800	0.287327	0.143663	−	0.989627i	$-0.454112\pi$
$173$	653.800	0.287327	0.143663	+	0.989627i	$0.454112\pi$
$174$	200.070	0.0871684
$175$	0	0
$176$	−837.576	−0.358719
$177$	1801.92	0.765200
$178$	−591.273	−0.248977
$179$	2055.28	0.858208	0.429104	−	0.903255i	$-0.358829\pi$
$179$	2055.28	0.858208	0.429104	+	0.903255i	$0.358829\pi$
$180$	0	0
$181$	3398.36	1.39557	0.697785	−	0.716307i	$-0.254169\pi$
$181$	3398.36	1.39557	0.697785	+	0.716307i	$0.254169\pi$
$182$	298.261	0.121476
$183$	1671.64	0.675254
$184$	1640.48	0.657271
$185$	0	0
$186$	2069.66	0.815884
$187$	899.966	0.351936
$188$	1998.00	0.775101
$189$	−4007.67	−1.54241
$190$	0	0
$191$	4853.92	1.83883	0.919417	−	0.393285i	$-0.128661\pi$
$191$	4853.92	1.83883	0.919417	+	0.393285i	$0.128661\pi$
$192$	220.767	0.0829818
$193$	4877.24	1.81902	0.909512	−	0.415677i	$-0.136455\pi$
$193$	4877.24	1.81902	0.909512	+	0.415677i	$0.136455\pi$
$194$	−857.898	−0.317492
$195$	0	0
$196$	1674.14	0.610109
$197$	1031.42	0.373022	0.186511	−	0.982453i	$-0.440282\pi$
$197$	1031.42	0.373022	0.186511	+	0.982453i	$0.440282\pi$
$198$	1581.03	0.567469
$199$	−1167.70	−0.415960	−0.207980	−	0.978133i	$-0.566689\pi$
$199$	−1167.70	−0.415960	−0.207980	+	0.978133i	$0.566689\pi$
$200$	0	0
$201$	1741.96	0.611284
$202$	−2424.32	−0.844428
$203$	800.282	0.276693
$204$	−237.212	−0.0814126
$205$	0	0
$206$	−2064.14	−0.698134
$207$	−3096.62	−1.03976
$208$	86.4653	0.0288235
$209$	−2313.91	−0.765820
$210$	0	0
$211$	794.341	0.259169	0.129585	−	0.991568i	$-0.458636\pi$
$211$	794.341	0.259169	0.129585	+	0.991568i	$0.458636\pi$
$212$	1406.51	0.455657
$213$	1660.18	0.534055
$214$	2352.12	0.751343
$215$	0	0
$216$	−1161.82	−0.365980
$217$	8278.62	2.58981
$218$	−4335.71	−1.34703
$219$	−10.7286	−0.00331037
$220$	0	0
$221$	−92.9061	−0.0282785
$222$	−205.576	−0.0621501
$223$	−5136.08	−1.54232	−0.771161	−	0.636641i	$-0.780324\pi$
$223$	−5136.08	−1.54232	−0.771161	+	0.636641i	$0.780324\pi$
$224$	883.069	0.263404
$225$	0	0
$226$	−3247.31	−0.955786
$227$	5032.84	1.47155	0.735774	−	0.677228i	$-0.236819\pi$
$227$	5032.84	1.47155	0.735774	+	0.677228i	$0.236819\pi$
$228$	609.898	0.177156
$229$	−6213.12	−1.79290	−0.896451	−	0.443142i	$-0.853864\pi$
$229$	−6213.12	−1.79290	−0.896451	+	0.443142i	$0.853864\pi$
$230$	0	0
$231$	−4983.15	−1.41934
$232$	232.000	0.0656532
$233$	3117.59	0.876566	0.438283	−	0.898837i	$-0.355587\pi$
$233$	3117.59	0.876566	0.438283	+	0.898837i	$0.355587\pi$
$234$	−163.214	−0.0455968
$235$	0	0
$236$	2089.49	0.576331
$237$	−3598.73	−0.986342
$238$	−948.849	−0.258423
$239$	7193.09	1.94679	0.973394	−	0.229136i	$-0.0735902\pi$
$239$	7193.09	1.94679	0.973394	+	0.229136i	$0.0735902\pi$
$240$	0	0
$241$	−837.347	−0.223810	−0.111905	−	0.993719i	$-0.535695\pi$
$241$	−837.347	−0.223810	−0.111905	+	0.993719i	$0.535695\pi$
$242$	2818.72	0.748737
$243$	3599.53	0.950246
$244$	1938.42	0.508586
$245$	0	0
$246$	−303.273	−0.0786017
$247$	238.871	0.0615345
$248$	2399.96	0.614505
$249$	3473.91	0.884138
$250$	0	0
$251$	4306.56	1.08298	0.541489	−	0.840708i	$-0.317861\pi$
$251$	4306.56	1.08298	0.541489	+	0.840708i	$0.317861\pi$
$252$	−1666.91	−0.416687
$253$	−10734.6	−2.66750
$254$	−666.947	−0.164756
$255$	0	0
$256$	256.000	0.0625000
$257$	−401.238	−0.0973873	−0.0486936	−	0.998814i	$-0.515506\pi$
$257$	−401.238	−0.0973873	−0.0486936	+	0.998814i	$0.515506\pi$
$258$	−447.212	−0.107916
$259$	−822.302	−0.197279
$260$	0	0
$261$	−437.930	−0.103859
$262$	−1866.98	−0.440239
$263$	2682.72	0.628988	0.314494	−	0.949260i	$-0.398165\pi$
$263$	2682.72	0.628988	0.314494	+	0.949260i	$0.398165\pi$
$264$	−1444.60	−0.336777
$265$	0	0
$266$	2439.59	0.562334
$267$	−1019.80	−0.233747
$268$	2019.96	0.460405
$269$	−4732.38	−1.07263	−0.536316	−	0.844017i	$-0.680184\pi$
$269$	−4732.38	−1.07263	−0.536316	+	0.844017i	$0.680184\pi$
$270$	0	0
$271$	4529.66	1.01534	0.507670	−	0.861552i	$-0.330507\pi$
$271$	4529.66	1.01534	0.507670	+	0.861552i	$0.330507\pi$
$272$	−275.069	−0.0613181
$273$	514.424	0.114045
$274$	2180.64	0.480793
$275$	0	0
$276$	2829.41	0.617067
$277$	−7158.69	−1.55279	−0.776397	−	0.630245i	$-0.782955\pi$
$277$	−7158.69	−1.55279	−0.776397	+	0.630245i	$0.782955\pi$
$278$	−3849.19	−0.830429
$279$	−4530.22	−0.972105
$280$	0	0
$281$	−5769.75	−1.22489	−0.612446	−	0.790512i	$-0.709814\pi$
$281$	−5769.75	−1.22489	−0.612446	+	0.790512i	$0.709814\pi$
$282$	3446.04	0.727690
$283$	3815.25	0.801389	0.400694	−	0.916212i	$-0.368769\pi$
$283$	3815.25	0.801389	0.400694	+	0.916212i	$0.368769\pi$
$284$	1925.13	0.402238
$285$	0	0
$286$	−565.791	−0.116979
$287$	−1213.09	−0.249501
$288$	−483.233	−0.0988707
$289$	−4617.44	−0.939841
$290$	0	0
$291$	−1479.66	−0.298072
$292$	−12.4408	−0.00249329
$293$	−5416.66	−1.08002	−0.540008	−	0.841660i	$-0.681579\pi$
$293$	−5416.66	−1.08002	−0.540008	+	0.841660i	$0.681579\pi$
$294$	2887.46	0.572790
$295$	0	0
$296$	−238.384	−0.0468100
$297$	7602.41	1.48531
$298$	−3407.25	−0.662338
$299$	1108.16	0.214337
$300$	0	0
$301$	−1788.85	−0.342550
$302$	2165.61	0.412639
$303$	−4181.33	−0.792776
$304$	707.233	0.133430
$305$	0	0
$306$	519.229	0.0970010
$307$	−4929.06	−0.916339	−0.458169	−	0.888865i	$-0.651495\pi$
$307$	−4929.06	−0.916339	−0.458169	+	0.888865i	$0.651495\pi$
$308$	−5778.42	−1.06901
$309$	−3560.12	−0.655430
$310$	0	0
$311$	1117.93	0.203832	0.101916	−	0.994793i	$-0.467503\pi$
$311$	1117.93	0.203832	0.101916	+	0.994793i	$0.467503\pi$
$312$	149.131	0.0270604
$313$	−2032.21	−0.366988	−0.183494	−	0.983021i	$-0.558741\pi$
$313$	−2032.21	−0.366988	−0.183494	+	0.983021i	$0.558741\pi$
$314$	−4815.79	−0.865512
$315$	0	0
$316$	−4173.06	−0.742890
$317$	−2051.75	−0.363526	−0.181763	−	0.983342i	$-0.558180\pi$
$317$	−2051.75	−0.363526	−0.181763	+	0.983342i	$0.558180\pi$
$318$	2425.86	0.427785
$319$	−1518.11	−0.266450
$320$	0	0
$321$	4056.80	0.705385
$322$	11317.6	1.95872
$323$	−759.914	−0.130906
$324$	−372.927	−0.0639449
$325$	0	0
$326$	−2123.18	−0.360711
$327$	−7478.00	−1.26463
$328$	−351.673	−0.0592010
$329$	13784.1	2.30986
$330$	0	0
$331$	−9652.92	−1.60294	−0.801469	−	0.598036i	$-0.795948\pi$
$331$	−9652.92	−1.60294	−0.801469	+	0.598036i	$0.795948\pi$
$332$	4028.32	0.665912
$333$	449.980	0.0740502
$334$	−2631.25	−0.431065
$335$	0	0
$336$	1523.07	0.247292
$337$	−4277.57	−0.691437	−0.345719	−	0.938338i	$-0.612365\pi$
$337$	−4277.57	−0.691437	−0.345719	+	0.938338i	$0.612365\pi$
$338$	−4335.59	−0.697707
$339$	−5600.77	−0.897322
$340$	0	0
$341$	−15704.2	−2.49394
$342$	−1334.99	−0.211076
$343$	2084.45	0.328133
$344$	−518.584	−0.0812795
$345$	0	0
$346$	1307.60	0.203171
$347$	9475.83	1.46596	0.732982	−	0.680248i	$-0.238128\pi$
$347$	9475.83	1.46596	0.732982	+	0.680248i	$0.238128\pi$
$348$	400.141	0.0616374
$349$	2968.57	0.455313	0.227656	−	0.973742i	$-0.426894\pi$
$349$	2968.57	0.455313	0.227656	+	0.973742i	$0.426894\pi$
$350$	0	0
$351$	−784.819	−0.119346
$352$	−1675.15	−0.253653
$353$	−3969.16	−0.598461	−0.299231	−	0.954181i	$-0.596730\pi$
$353$	−3969.16	−0.598461	−0.299231	+	0.954181i	$0.596730\pi$
$354$	3603.84	0.541078
$355$	0	0
$356$	−1182.55	−0.176053
$357$	−1636.52	−0.242616
$358$	4110.57	0.606845
$359$	−3503.03	−0.514994	−0.257497	−	0.966279i	$-0.582898\pi$
$359$	−3503.03	−0.514994	−0.257497	+	0.966279i	$0.582898\pi$
$360$	0	0
$361$	−4905.18	−0.715145
$362$	6796.72	0.986817
$363$	4861.58	0.702939
$364$	596.522	0.0858963
$365$	0	0
$366$	3343.29	0.477477
$367$	8253.53	1.17393	0.586963	−	0.809614i	$-0.300323\pi$
$367$	8253.53	1.17393	0.586963	+	0.809614i	$0.300323\pi$
$368$	3280.96	0.464761
$369$	663.828	0.0936518
$370$	0	0
$371$	9703.46	1.35789
$372$	4139.31	0.576917
$373$	−1253.95	−0.174067	−0.0870335	−	0.996205i	$-0.527739\pi$
$373$	−1253.95	−0.174067	−0.0870335	+	0.996205i	$0.527739\pi$
$374$	1799.93	0.248856
$375$	0	0
$376$	3996.00	0.548079
$377$	156.718	0.0214096
$378$	−8015.35	−1.09065
$379$	−6966.52	−0.944185	−0.472092	−	0.881549i	$-0.656501\pi$
$379$	−6966.52	−0.944185	−0.472092	+	0.881549i	$0.656501\pi$
$380$	0	0
$381$	−1150.31	−0.154678
$382$	9707.84	1.30025
$383$	9821.84	1.31037	0.655186	−	0.755467i	$-0.272590\pi$
$383$	9821.84	1.31037	0.655186	+	0.755467i	$0.272590\pi$
$384$	441.535	0.0586770
$385$	0	0
$386$	9754.49	1.28624
$387$	978.893	0.128579
$388$	−1715.80	−0.224501
$389$	3942.96	0.513923	0.256962	−	0.966422i	$-0.417279\pi$
$389$	3942.96	0.513923	0.256962	+	0.966422i	$0.417279\pi$
$390$	0	0
$391$	−3525.36	−0.455972
$392$	3348.28	0.431412
$393$	−3220.07	−0.413311
$394$	2062.83	0.263767
$395$	0	0
$396$	3162.06	0.401262
$397$	−8725.50	−1.10307	−0.551537	−	0.834150i	$-0.685959\pi$
$397$	−8725.50	−1.10307	−0.551537	+	0.834150i	$0.685959\pi$
$398$	−2335.40	−0.294128
$399$	4207.67	0.527938
$400$	0	0
$401$	3986.86	0.496494	0.248247	−	0.968697i	$-0.420146\pi$
$401$	3986.86	0.496494	0.248247	+	0.968697i	$0.420146\pi$
$402$	3483.91	0.432243
$403$	1621.19	0.200391
$404$	−4848.64	−0.597101
$405$	0	0
$406$	1600.56	0.195652
$407$	1559.88	0.189976
$408$	−474.424	−0.0575674
$409$	−704.847	−0.0852138	−0.0426069	−	0.999092i	$-0.513566\pi$
$409$	−704.847	−0.0852138	−0.0426069	+	0.999092i	$0.513566\pi$
$410$	0	0
$411$	3761.05	0.451384
$412$	−4128.28	−0.493655
$413$	14415.3	1.71751
$414$	−6193.24	−0.735220
$415$	0	0
$416$	172.931	0.0203813
$417$	−6638.88	−0.779634
$418$	−4627.82	−0.541517
$419$	6705.33	0.781807	0.390903	−	0.920432i	$-0.372163\pi$
$419$	6705.33	0.781807	0.390903	+	0.920432i	$0.372163\pi$
$420$	0	0
$421$	8996.55	1.04148	0.520742	−	0.853714i	$-0.325655\pi$
$421$	8996.55	1.04148	0.520742	+	0.853714i	$0.325655\pi$
$422$	1588.68	0.183260
$423$	−7542.95	−0.867023
$424$	2813.01	0.322198
$425$	0	0
$426$	3320.36	0.377634
$427$	13373.2	1.51563
$428$	4704.24	0.531280
$429$	−975.845	−0.109823
$430$	0	0
$431$	5383.16	0.601619	0.300810	−	0.953684i	$-0.402743\pi$
$431$	5383.16	0.601619	0.300810	+	0.953684i	$0.402743\pi$
$432$	−2323.63	−0.258787
$433$	6901.64	0.765985	0.382993	−	0.923751i	$-0.374893\pi$
$433$	6901.64	0.765985	0.382993	+	0.923751i	$0.374893\pi$
$434$	16557.2	1.83127
$435$	0	0
$436$	−8671.42	−0.952491
$437$	9064.08	0.992205
$438$	−21.4572	−0.00234078
$439$	12119.4	1.31760	0.658802	−	0.752316i	$-0.271063\pi$
$439$	12119.4	1.31760	0.658802	+	0.752316i	$0.271063\pi$
$440$	0	0
$441$	−6320.30	−0.682464
$442$	−185.812	−0.0199959
$443$	−5229.40	−0.560849	−0.280425	−	0.959876i	$-0.590475\pi$
$443$	−5229.40	−0.560849	−0.280425	+	0.959876i	$0.590475\pi$
$444$	−411.151	−0.0439468
$445$	0	0
$446$	−10272.2	−1.09059
$447$	−5876.64	−0.621824
$448$	1766.14	0.186255
$449$	−10220.3	−1.07422	−0.537112	−	0.843511i	$-0.680485\pi$
$449$	−10220.3	−1.07422	−0.537112	+	0.843511i	$0.680485\pi$
$450$	0	0
$451$	2301.20	0.240264
$452$	−6494.61	−0.675843
$453$	3735.13	0.387399
$454$	10065.7	1.04054
$455$	0	0
$456$	1219.80	0.125268
$457$	−12030.6	−1.23143	−0.615717	−	0.787967i	$-0.711134\pi$
$457$	−12030.6	−1.23143	−0.615717	+	0.787967i	$0.711134\pi$
$458$	−12426.2	−1.26777
$459$	2496.72	0.253893
$460$	0	0
$461$	1063.24	0.107418	0.0537092	−	0.998557i	$-0.482896\pi$
$461$	1063.24	0.107418	0.0537092	+	0.998557i	$0.482896\pi$
$462$	−9966.29	−1.00362
$463$	−15498.8	−1.55570	−0.777851	−	0.628449i	$-0.783690\pi$
$463$	−15498.8	−1.55570	−0.777851	+	0.628449i	$0.783690\pi$
$464$	464.000	0.0464238
$465$	0	0
$466$	6235.17	0.619826
$467$	−13215.6	−1.30952	−0.654759	−	0.755838i	$-0.727230\pi$
$467$	−13215.6	−1.30952	−0.654759	+	0.755838i	$0.727230\pi$
$468$	−326.429	−0.0322418
$469$	13935.7	1.37204
$470$	0	0
$471$	−8306.01	−0.812571
$472$	4178.98	0.407528
$473$	3393.38	0.329869
$474$	−7197.47	−0.697449
$475$	0	0
$476$	−1897.70	−0.182733
$477$	−5309.92	−0.509695
$478$	14386.2	1.37659
$479$	−19058.5	−1.81796	−0.908981	−	0.416837i	$-0.863139\pi$
$479$	−19058.5	−1.81796	−0.908981	+	0.416837i	$0.863139\pi$
$480$	0	0
$481$	−161.031	−0.0152648
$482$	−1674.69	−0.158258
$483$	19520.1	1.83891
$484$	5637.45	0.529437
$485$	0	0
$486$	7199.06	0.671926
$487$	487.214	0.0453343	0.0226671	−	0.999743i	$-0.492784\pi$
$487$	487.214	0.0453343	0.0226671	+	0.999743i	$0.492784\pi$
$488$	3876.85	0.359624
$489$	−3661.94	−0.338647
$490$	0	0
$491$	−6462.89	−0.594025	−0.297013	−	0.954874i	$-0.595990\pi$
$491$	−6462.89	−0.594025	−0.297013	+	0.954874i	$0.595990\pi$
$492$	−606.547	−0.0555798
$493$	−498.563	−0.0455460
$494$	477.743	0.0435115
$495$	0	0
$496$	4799.91	0.434521
$497$	13281.4	1.19870
$498$	6947.83	0.625180
$499$	−7947.79	−0.713010	−0.356505	−	0.934293i	$-0.616032\pi$
$499$	−7947.79	−0.713010	−0.356505	+	0.934293i	$0.616032\pi$
$500$	0	0
$501$	−4538.24	−0.404698
$502$	8613.12	0.765781
$503$	2307.81	0.204573	0.102287	−	0.994755i	$-0.467384\pi$
$503$	2307.81	0.204573	0.102287	+	0.994755i	$0.467384\pi$
$504$	−3333.81	−0.294642
$505$	0	0
$506$	−21469.2	−1.88621
$507$	−7477.79	−0.655030
$508$	−1333.89	−0.116500
$509$	−16496.2	−1.43651	−0.718253	−	0.695782i	$-0.755058\pi$
$509$	−16496.2	−1.43651	−0.718253	+	0.695782i	$0.755058\pi$
$510$	0	0
$511$	−85.8287	−0.00743021
$512$	512.000	0.0441942
$513$	−6419.33	−0.552476
$514$	−802.476	−0.0688632
$515$	0	0
$516$	−894.424	−0.0763078
$517$	−26148.0	−2.22435
$518$	−1644.60	−0.139498
$519$	2255.28	0.190743
$520$	0	0
$521$	−10386.5	−0.873398	−0.436699	−	0.899608i	$-0.643853\pi$
$521$	−10386.5	−0.873398	−0.436699	+	0.899608i	$0.643853\pi$
$522$	−875.859	−0.0734393
$523$	918.174	0.0767666	0.0383833	−	0.999263i	$-0.487779\pi$
$523$	918.174	0.0767666	0.0383833	+	0.999263i	$0.487779\pi$
$524$	−3733.97	−0.311296
$525$	0	0
$526$	5365.44	0.444761
$527$	−5157.45	−0.426304
$528$	−2889.21	−0.238138
$529$	29882.7	2.45604
$530$	0	0
$531$	−7888.36	−0.644681
$532$	4879.18	0.397631
$533$	−237.559	−0.0193055
$534$	−2039.59	−0.165284
$535$	0	0
$536$	4039.92	0.325556
$537$	7089.68	0.569725
$538$	−9464.75	−0.758465
$539$	−21909.7	−1.75086
$540$	0	0
$541$	−12860.2	−1.02200	−0.511001	−	0.859580i	$-0.670725\pi$
$541$	−12860.2	−1.02200	−0.511001	+	0.859580i	$0.670725\pi$
$542$	9059.32	0.717954
$543$	11722.6	0.926456
$544$	−550.139	−0.0433585
$545$	0	0
$546$	1028.85	0.0806423
$547$	−4471.84	−0.349547	−0.174774	−	0.984609i	$-0.555919\pi$
$547$	−4471.84	−0.349547	−0.174774	+	0.984609i	$0.555919\pi$
$548$	4361.28	0.339972
$549$	−7318.05	−0.568901
$550$	0	0
$551$	1281.86	0.0991090
$552$	5658.82	0.436333
$553$	−28789.9	−2.21387
$554$	−14317.4	−1.09799
$555$	0	0
$556$	−7698.39	−0.587202
$557$	−2649.40	−0.201542	−0.100771	−	0.994910i	$-0.532131\pi$
$557$	−2649.40	−0.201542	−0.100771	+	0.994910i	$0.532131\pi$
$558$	−9060.44	−0.687382
$559$	−350.309	−0.0265053
$560$	0	0
$561$	3104.42	0.233634
$562$	−11539.5	−0.866130
$563$	−12615.8	−0.944395	−0.472198	−	0.881493i	$-0.656539\pi$
$563$	−12615.8	−0.944395	−0.472198	+	0.881493i	$0.656539\pi$
$564$	6892.07	0.514554
$565$	0	0
$566$	7630.50	0.566667
$567$	−2572.81	−0.190561
$568$	3850.26	0.284425
$569$	617.443	0.0454913	0.0227456	−	0.999741i	$-0.492759\pi$
$569$	617.443	0.0454913	0.0227456	+	0.999741i	$0.492759\pi$
$570$	0	0
$571$	8005.50	0.586725	0.293362	−	0.956001i	$-0.405226\pi$
$571$	8005.50	0.586725	0.293362	+	0.956001i	$0.405226\pi$
$572$	−1131.58	−0.0827164
$573$	16743.5	1.22072
$574$	−2426.19	−0.176424
$575$	0	0
$576$	−966.465	−0.0699121
$577$	−11761.1	−0.848565	−0.424282	−	0.905530i	$-0.639474\pi$
$577$	−11761.1	−0.848565	−0.424282	+	0.905530i	$0.639474\pi$
$578$	−9234.88	−0.664568
$579$	16824.0	1.20757
$580$	0	0
$581$	27791.3	1.98447
$582$	−2959.31	−0.210769
$583$	−18407.1	−1.30762
$584$	−24.8816	−0.00176302
$585$	0	0
$586$	−10833.3	−0.763686
$587$	1211.03	0.0851528	0.0425764	−	0.999093i	$-0.486443\pi$
$587$	1211.03	0.0851528	0.0425764	+	0.999093i	$0.486443\pi$
$588$	5774.92	0.405024
$589$	13260.4	0.927646
$590$	0	0
$591$	3557.86	0.247633
$592$	−476.767	−0.0330997
$593$	−459.376	−0.0318117	−0.0159058	−	0.999873i	$-0.505063\pi$
$593$	−459.376	−0.0318117	−0.0159058	+	0.999873i	$0.505063\pi$
$594$	15204.8	1.05027
$595$	0	0
$596$	−6814.50	−0.468343
$597$	−4027.97	−0.276137
$598$	2216.32	0.151559
$599$	16686.2	1.13820	0.569099	−	0.822269i	$-0.307292\pi$
$599$	16686.2	1.13820	0.569099	+	0.822269i	$0.307292\pi$
$600$	0	0
$601$	11625.9	0.789072	0.394536	−	0.918881i	$-0.370905\pi$
$601$	11625.9	0.789072	0.394536	+	0.918881i	$0.370905\pi$
$602$	−3577.70	−0.242219
$603$	−7625.86	−0.515007
$604$	4331.22	0.291780
$605$	0	0
$606$	−8362.66	−0.560577
$607$	21556.9	1.44146	0.720731	−	0.693215i	$-0.243806\pi$
$607$	21556.9	1.44146	0.720731	+	0.693215i	$0.243806\pi$
$608$	1414.47	0.0943489
$609$	2760.56	0.183684
$610$	0	0
$611$	2699.34	0.178729
$612$	1038.46	0.0685901
$613$	19273.2	1.26988	0.634940	−	0.772561i	$-0.281025\pi$
$613$	19273.2	1.26988	0.634940	+	0.772561i	$0.281025\pi$
$614$	−9858.11	−0.647949
$615$	0	0
$616$	−11556.8	−0.755906
$617$	3270.70	0.213409	0.106704	−	0.994291i	$-0.465970\pi$
$617$	3270.70	0.213409	0.106704	+	0.994291i	$0.465970\pi$
$618$	−7120.23	−0.463459
$619$	75.8068	0.00492234	0.00246117	−	0.999997i	$-0.499217\pi$
$619$	75.8068	0.00492234	0.00246117	+	0.999997i	$0.499217\pi$
$620$	0	0
$621$	−29780.3	−1.92438
$622$	2235.85	0.144131
$623$	−8158.37	−0.524652
$624$	298.261	0.0191346
$625$	0	0
$626$	−4064.41	−0.259499
$627$	−7981.81	−0.508393
$628$	−9631.58	−0.612010
$629$	512.282	0.0324738
$630$	0	0
$631$	−4915.71	−0.310129	−0.155064	−	0.987904i	$-0.549559\pi$
$631$	−4915.71	−0.310129	−0.155064	+	0.987904i	$0.549559\pi$
$632$	−8346.13	−0.525302
$633$	2740.07	0.172051
$634$	−4103.50	−0.257052
$635$	0	0
$636$	4851.73	0.302490
$637$	2261.80	0.140684
$638$	−3036.21	−0.188409
$639$	−7267.86	−0.449941
$640$	0	0
$641$	3317.63	0.204428	0.102214	−	0.994762i	$-0.467407\pi$
$641$	3317.63	0.204428	0.102214	+	0.994762i	$0.467407\pi$
$642$	8113.61	0.498783
$643$	27222.7	1.66961	0.834805	−	0.550546i	$-0.185580\pi$
$643$	27222.7	1.66961	0.834805	+	0.550546i	$0.185580\pi$
$644$	22635.3	1.38502
$645$	0	0
$646$	−1519.83	−0.0925648
$647$	−24433.6	−1.48468	−0.742338	−	0.670025i	$-0.766283\pi$
$647$	−24433.6	−1.48468	−0.742338	+	0.670025i	$0.766283\pi$
$648$	−745.853	−0.0452159
$649$	−27345.4	−1.65393
$650$	0	0
$651$	28557.0	1.71926
$652$	−4246.35	−0.255061
$653$	−5755.36	−0.344907	−0.172454	−	0.985018i	$-0.555170\pi$
$653$	−5755.36	−0.344907	−0.172454	+	0.985018i	$0.555170\pi$
$654$	−14956.0	−0.894229
$655$	0	0
$656$	−703.347	−0.0418614
$657$	46.9671	0.00278898
$658$	27568.3	1.63332
$659$	965.300	0.0570603	0.0285301	−	0.999593i	$-0.490917\pi$
$659$	965.300	0.0570603	0.0285301	+	0.999593i	$0.490917\pi$
$660$	0	0
$661$	−22791.0	−1.34110	−0.670549	−	0.741866i	$-0.733941\pi$
$661$	−22791.0	−1.34110	−0.670549	+	0.741866i	$0.733941\pi$
$662$	−19305.8	−1.13345
$663$	−320.479	−0.0187728
$664$	8056.64	0.470871
$665$	0	0
$666$	899.959	0.0523614
$667$	5946.75	0.345216
$668$	−5262.50	−0.304809
$669$	−17716.9	−1.02388
$670$	0	0
$671$	−25368.4	−1.45952
$672$	3046.14	0.174862
$673$	−12412.1	−0.710925	−0.355463	−	0.934690i	$-0.615677\pi$
$673$	−12412.1	−0.710925	−0.355463	+	0.934690i	$0.615677\pi$
$674$	−8555.15	−0.488920
$675$	0	0
$676$	−8671.18	−0.493354
$677$	−8998.03	−0.510816	−0.255408	−	0.966833i	$-0.582210\pi$
$677$	−8998.03	−0.510816	−0.255408	+	0.966833i	$0.582210\pi$
$678$	−11201.5	−0.634503
$679$	−11837.2	−0.669030
$680$	0	0
$681$	17360.7	0.976893
$682$	−31408.5	−1.76348
$683$	−13439.1	−0.752904	−0.376452	−	0.926436i	$-0.622856\pi$
$683$	−13439.1	−0.752904	−0.376452	+	0.926436i	$0.622856\pi$
$684$	−2669.98	−0.149253
$685$	0	0
$686$	4168.90	0.232025
$687$	−21432.1	−1.19023
$688$	−1037.17	−0.0574733
$689$	1900.22	0.105069
$690$	0	0
$691$	−16220.4	−0.892983	−0.446492	−	0.894788i	$-0.647327\pi$
$691$	−16220.4	−0.892983	−0.446492	+	0.894788i	$0.647327\pi$
$692$	2615.20	0.143663
$693$	21815.0	1.19579
$694$	18951.7	1.03659
$695$	0	0
$696$	800.282	0.0435842
$697$	755.739	0.0410698
$698$	5937.15	0.321955
$699$	10754.1	0.581912
$700$	0	0
$701$	−18919.6	−1.01938	−0.509689	−	0.860359i	$-0.670239\pi$
$701$	−18919.6	−1.01938	−0.509689	+	0.860359i	$0.670239\pi$
$702$	−1569.64	−0.0843905
$703$	−1317.13	−0.0706636
$704$	−3350.30	−0.179360
$705$	0	0
$706$	−7938.31	−0.423176
$707$	−33450.6	−1.77941
$708$	7207.67	0.382600
$709$	−4781.99	−0.253302	−0.126651	−	0.991947i	$-0.540423\pi$
$709$	−4781.99	−0.253302	−0.126651	+	0.991947i	$0.540423\pi$
$710$	0	0
$711$	15754.4	0.830992
$712$	−2365.09	−0.124488
$713$	61516.9	3.23117
$714$	−3273.04	−0.171555
$715$	0	0
$716$	8221.14	0.429104
$717$	24812.5	1.29238
$718$	−7006.06	−0.364156
$719$	13020.1	0.675336	0.337668	−	0.941265i	$-0.390362\pi$
$719$	13020.1	0.675336	0.337668	+	0.941265i	$0.390362\pi$
$720$	0	0
$721$	−28480.9	−1.47113
$722$	−9810.36	−0.505684
$723$	−2888.42	−0.148577
$724$	13593.4	0.697785
$725$	0	0
$726$	9723.16	0.497053
$727$	8738.68	0.445804	0.222902	−	0.974841i	$-0.428447\pi$
$727$	8738.68	0.445804	0.222902	+	0.974841i	$0.428447\pi$
$728$	1193.04	0.0607379
$729$	14933.8	0.758715
$730$	0	0
$731$	1114.43	0.0563865
$732$	6686.58	0.337627
$733$	12775.2	0.643744	0.321872	−	0.946783i	$-0.395688\pi$
$733$	12775.2	0.643744	0.321872	+	0.946783i	$0.395688\pi$
$734$	16507.1	0.830091
$735$	0	0
$736$	6561.93	0.328636
$737$	−26435.4	−1.32125
$738$	1327.66	0.0662219
$739$	5397.68	0.268683	0.134342	−	0.990935i	$-0.457108\pi$
$739$	5397.68	0.268683	0.134342	+	0.990935i	$0.457108\pi$
$740$	0	0
$741$	823.985	0.0408500
$742$	19406.9	0.960176
$743$	37984.2	1.87551	0.937757	−	0.347293i	$-0.112899\pi$
$743$	37984.2	1.87551	0.937757	+	0.347293i	$0.112899\pi$
$744$	8278.62	0.407942
$745$	0	0
$746$	−2507.90	−0.123084
$747$	−15207.9	−0.744886
$748$	3599.87	0.175968
$749$	32454.4	1.58326
$750$	0	0
$751$	26384.8	1.28202	0.641009	−	0.767534i	$-0.278516\pi$
$751$	26384.8	1.28202	0.641009	+	0.767534i	$0.278516\pi$
$752$	7991.99	0.387550
$753$	14855.4	0.718940
$754$	313.437	0.0151389
$755$	0	0
$756$	−16030.7	−0.771205
$757$	−6889.95	−0.330805	−0.165403	−	0.986226i	$-0.552892\pi$
$757$	−6889.95	−0.330805	−0.165403	+	0.986226i	$0.552892\pi$
$758$	−13933.0	−0.667639
$759$	−37028.8	−1.77083
$760$	0	0
$761$	31579.3	1.50427	0.752134	−	0.659010i	$-0.229025\pi$
$761$	31579.3	1.50427	0.752134	+	0.659010i	$0.229025\pi$
$762$	−2300.63	−0.109374
$763$	−59824.0	−2.83850
$764$	19415.7	0.919417
$765$	0	0
$766$	19643.7	0.926574
$767$	2822.94	0.132895
$768$	883.069	0.0414909
$769$	−12232.7	−0.573632	−0.286816	−	0.957986i	$-0.592597\pi$
$769$	−12232.7	−0.573632	−0.286816	+	0.957986i	$0.592597\pi$
$770$	0	0
$771$	−1384.07	−0.0646510
$772$	19509.0	0.909512
$773$	−9958.46	−0.463365	−0.231682	−	0.972792i	$-0.574423\pi$
$773$	−9958.46	−0.463365	−0.231682	+	0.972792i	$0.574423\pi$
$774$	1957.79	0.0909188
$775$	0	0
$776$	−3431.59	−0.158746
$777$	−2836.52	−0.130965
$778$	7885.92	0.363398
$779$	−1943.09	−0.0893688
$780$	0	0
$781$	−25194.4	−1.15432
$782$	−7050.72	−0.322421
$783$	−4211.58	−0.192222
$784$	6696.55	0.305054
$785$	0	0
$786$	−6440.14	−0.292255
$787$	−103.911	−0.00470653	−0.00235326	−	0.999997i	$-0.500749\pi$
$787$	−103.911	−0.00470653	−0.00235326	+	0.999997i	$0.500749\pi$
$788$	4125.67	0.186511
$789$	9254.02	0.417556
$790$	0	0
$791$	−44806.2	−2.01406
$792$	6324.12	0.283735
$793$	2618.85	0.117274
$794$	−17451.0	−0.779991
$795$	0	0
$796$	−4670.80	−0.207980
$797$	−30624.4	−1.36107	−0.680534	−	0.732717i	$-0.738252\pi$
$797$	−30624.4	−1.36107	−0.680534	+	0.732717i	$0.738252\pi$
$798$	8415.35	0.373308
$799$	−8587.31	−0.380222
$800$	0	0
$801$	4464.42	0.196932
$802$	7973.71	0.351074
$803$	162.814	0.00715514
$804$	6967.83	0.305642
$805$	0	0
$806$	3242.39	0.141698
$807$	−16324.3	−0.712072
$808$	−9697.27	−0.422214
$809$	−7737.50	−0.336262	−0.168131	−	0.985765i	$-0.553773\pi$
$809$	−7737.50	−0.336262	−0.168131	+	0.985765i	$0.553773\pi$
$810$	0	0
$811$	−12974.1	−0.561756	−0.280878	−	0.959744i	$-0.590626\pi$
$811$	−12974.1	−0.561756	−0.280878	+	0.959744i	$0.590626\pi$
$812$	3201.13	0.138347
$813$	15625.0	0.674038
$814$	3119.76	0.134333
$815$	0	0
$816$	−948.849	−0.0407063
$817$	−2865.31	−0.122698
$818$	−1409.69	−0.0602552
$819$	−2252.02	−0.0960831
$820$	0	0
$821$	3264.26	0.138762	0.0693809	−	0.997590i	$-0.477898\pi$
$821$	3264.26	0.138762	0.0693809	+	0.997590i	$0.477898\pi$
$822$	7522.10	0.319177
$823$	−23509.7	−0.995745	−0.497872	−	0.867250i	$-0.665885\pi$
$823$	−23509.7	−0.995745	−0.497872	+	0.867250i	$0.665885\pi$
$824$	−8256.56	−0.349067
$825$	0	0
$826$	28830.7	1.21447
$827$	−27116.5	−1.14019	−0.570093	−	0.821580i	$-0.693093\pi$
$827$	−27116.5	−1.14019	−0.570093	+	0.821580i	$0.693093\pi$
$828$	−12386.5	−0.519879
$829$	15393.6	0.644923	0.322462	−	0.946583i	$-0.395490\pi$
$829$	15393.6	0.644923	0.322462	+	0.946583i	$0.395490\pi$
$830$	0	0
$831$	−24693.8	−1.03083
$832$	345.861	0.0144118
$833$	−7195.38	−0.299286
$834$	−13277.8	−0.551284
$835$	0	0
$836$	−9255.64	−0.382910
$837$	−43567.3	−1.79917
$838$	13410.7	0.552821
$839$	−7906.51	−0.325343	−0.162672	−	0.986680i	$-0.552011\pi$
$839$	−7906.51	−0.325343	−0.162672	+	0.986680i	$0.552011\pi$
$840$	0	0
$841$	841.000	0.0344828
$842$	17993.1	0.736441
$843$	−19902.7	−0.813150
$844$	3177.37	0.129585
$845$	0	0
$846$	−15085.9	−0.613078
$847$	38892.6	1.57777
$848$	5626.02	0.227828
$849$	13160.7	0.532005
$850$	0	0
$851$	−6110.38	−0.246135
$852$	6640.72	0.267027
$853$	11887.1	0.477146	0.238573	−	0.971125i	$-0.423320\pi$
$853$	11887.1	0.477146	0.238573	+	0.971125i	$0.423320\pi$
$854$	26746.3	1.07171
$855$	0	0
$856$	9408.47	0.375672
$857$	655.328	0.0261208	0.0130604	−	0.999915i	$-0.495843\pi$
$857$	655.328	0.0261208	0.0130604	+	0.999915i	$0.495843\pi$
$858$	−1951.69	−0.0776569
$859$	−48758.4	−1.93669	−0.968345	−	0.249617i	$-0.919695\pi$
$859$	−48758.4	−1.93669	−0.968345	+	0.249617i	$0.919695\pi$
$860$	0	0
$861$	−4184.55	−0.165632
$862$	10766.3	0.425409
$863$	10398.2	0.410150	0.205075	−	0.978746i	$-0.434256\pi$
$863$	10398.2	0.410150	0.205075	+	0.978746i	$0.434256\pi$
$864$	−4647.27	−0.182990
$865$	0	0
$866$	13803.3	0.541633
$867$	−15927.8	−0.623918
$868$	33114.5	1.29491
$869$	54613.4	2.13191
$870$	0	0
$871$	2729.01	0.106164
$872$	−17342.8	−0.673513
$873$	6477.57	0.251125
$874$	18128.2	0.701595
$875$	0	0
$876$	−42.9143	−0.00165518
$877$	31024.2	1.19454	0.597272	−	0.802039i	$-0.296251\pi$
$877$	31024.2	1.19454	0.597272	+	0.802039i	$0.296251\pi$
$878$	24238.8	0.931687
$879$	−18684.7	−0.716973
$880$	0	0
$881$	−1510.50	−0.0577641	−0.0288821	−	0.999583i	$-0.509195\pi$
$881$	−1510.50	−0.0577641	−0.0288821	+	0.999583i	$0.509195\pi$
$882$	−12640.6	−0.482575
$883$	32376.4	1.23392	0.616961	−	0.786993i	$-0.288363\pi$
$883$	32376.4	1.23392	0.616961	+	0.786993i	$0.288363\pi$
$884$	−371.624	−0.0141392
$885$	0	0
$886$	−10458.8	−0.396580
$887$	−10474.6	−0.396510	−0.198255	−	0.980150i	$-0.563527\pi$
$887$	−10474.6	−0.396510	−0.198255	+	0.980150i	$0.563527\pi$
$888$	−822.302	−0.0310751
$889$	−9202.51	−0.347179
$890$	0	0
$891$	4880.53	0.183506
$892$	−20544.3	−0.771161
$893$	22078.9	0.827371
$894$	−11753.3	−0.439696
$895$	0	0
$896$	3532.28	0.131702
$897$	3822.59	0.142288
$898$	−20440.6	−0.759591
$899$	8699.84	0.322754
$900$	0	0
$901$	−6045.11	−0.223520
$902$	4602.39	0.169892
$903$	−6170.62	−0.227403
$904$	−12989.2	−0.477893
$905$	0	0
$906$	7470.26	0.273932
$907$	34634.3	1.26793	0.633965	−	0.773362i	$-0.281426\pi$
$907$	34634.3	1.26793	0.633965	+	0.773362i	$0.281426\pi$
$908$	20131.4	0.735774
$909$	18304.8	0.667913
$910$	0	0
$911$	1186.14	0.0431377	0.0215688	−	0.999767i	$-0.493134\pi$
$911$	1186.14	0.0431377	0.0215688	+	0.999767i	$0.493134\pi$
$912$	2439.59	0.0885778
$913$	−52719.1	−1.91101
$914$	−24061.1	−0.870755
$915$	0	0
$916$	−24852.5	−0.896451
$917$	−25760.6	−0.927687
$918$	4993.44	0.179529
$919$	−5685.58	−0.204080	−0.102040	−	0.994780i	$-0.532537\pi$
$919$	−5685.58	−0.204080	−0.102040	+	0.994780i	$0.532537\pi$
$920$	0	0
$921$	−17002.7	−0.608316
$922$	2126.47	0.0759563
$923$	2600.89	0.0927512
$924$	−19932.6	−0.709669
$925$	0	0
$926$	−30997.6	−1.10005
$927$	15585.3	0.552200
$928$	928.000	0.0328266
$929$	−19143.7	−0.676087	−0.338044	−	0.941130i	$-0.609765\pi$
$929$	−19143.7	−0.676087	−0.338044	+	0.941130i	$0.609765\pi$
$930$	0	0
$931$	18500.1	0.651252
$932$	12470.3	0.438283
$933$	3856.28	0.135315
$934$	−26431.2	−0.925969
$935$	0	0
$936$	−652.857	−0.0227984
$937$	53623.5	1.86959	0.934794	−	0.355191i	$-0.115584\pi$
$937$	53623.5	1.86959	0.934794	+	0.355191i	$0.115584\pi$
$938$	27871.3	0.970182
$939$	−7010.08	−0.243626
$940$	0	0
$941$	−7947.57	−0.275328	−0.137664	−	0.990479i	$-0.543959\pi$
$941$	−7947.57	−0.275328	−0.137664	+	0.990479i	$0.543959\pi$
$942$	−16612.0	−0.574574
$943$	−9014.28	−0.311289
$944$	8357.96	0.288166
$945$	0	0
$946$	6786.77	0.233252
$947$	41047.8	1.40853	0.704263	−	0.709939i	$-0.251277\pi$
$947$	41047.8	1.40853	0.704263	+	0.709939i	$0.251277\pi$
$948$	−14394.9	−0.493171
$949$	−16.8077	−0.000574924 0
$950$	0	0
$951$	−7077.49	−0.241328
$952$	−3795.40	−0.129212
$953$	12000.8	0.407915	0.203957	−	0.978980i	$-0.434620\pi$
$953$	12000.8	0.407915	0.203957	+	0.978980i	$0.434620\pi$
$954$	−10619.8	−0.360409
$955$	0	0
$956$	28772.4	0.973394
$957$	−5236.69	−0.176884
$958$	−38117.0	−1.28549
$959$	30088.4	1.01314
$960$	0	0
$961$	60205.6	2.02093
$962$	−322.061	−0.0107938
$963$	−17759.7	−0.594287
$964$	−3349.39	−0.111905
$965$	0	0
$966$	39040.1	1.30031
$967$	55391.0	1.84204	0.921021	−	0.389514i	$-0.127357\pi$
$967$	55391.0	1.84204	0.921021	+	0.389514i	$0.127357\pi$
$968$	11274.9	0.374369
$969$	−2621.32	−0.0869028
$970$	0	0
$971$	−23937.0	−0.791117	−0.395558	−	0.918441i	$-0.629449\pi$
$971$	−23937.0	−0.791117	−0.395558	+	0.918441i	$0.629449\pi$
$972$	14398.1	0.475123
$973$	−53111.0	−1.74991
$974$	974.429	0.0320562
$975$	0	0
$976$	7753.70	0.254293
$977$	43982.3	1.44024	0.720122	−	0.693847i	$-0.244086\pi$
$977$	43982.3	1.44024	0.720122	+	0.693847i	$0.244086\pi$
$978$	−7323.88	−0.239460
$979$	15476.1	0.505229
$980$	0	0
$981$	32736.8	1.06545
$982$	−12925.8	−0.420039
$983$	−2724.78	−0.0884100	−0.0442050	−	0.999022i	$-0.514075\pi$
$983$	−2724.78	−0.0884100	−0.0442050	+	0.999022i	$0.514075\pi$
$984$	−1213.09	−0.0393008
$985$	0	0
$986$	−997.126	−0.0322059
$987$	47548.3	1.53341
$988$	955.486	0.0307673
$989$	−13292.6	−0.427382
$990$	0	0
$991$	−23748.6	−0.761250	−0.380625	−	0.924729i	$-0.624291\pi$
$991$	−23748.6	−0.761250	−0.380625	+	0.924729i	$0.624291\pi$
$992$	9599.82	0.307253
$993$	−33297.7	−1.06412
$994$	26562.9	0.847609
$995$	0	0
$996$	13895.7	0.442069
$997$	−24718.0	−0.785182	−0.392591	−	0.919713i	$-0.628421\pi$
$997$	−24718.0	−0.785182	−0.392591	+	0.919713i	$0.628421\pi$
$998$	−15895.6	−0.504174
$999$	4327.47	0.137052

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.4.a.g.1.2		2
5.4	even	2		58.4.a.c.1.1	✓	2
15.14	odd	2		522.4.a.j.1.1		2
20.19	odd	2		464.4.a.e.1.2		2
40.19	odd	2		1856.4.a.i.1.1		2
40.29	even	2		1856.4.a.l.1.2		2
145.144	even	2		1682.4.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.4.a.c.1.1	✓	2	5.4	even	2
464.4.a.e.1.2		2	20.19	odd	2
522.4.a.j.1.1		2	15.14	odd	2
1450.4.a.g.1.2		2	1.1	even	1	trivial
1682.4.a.c.1.2		2	145.144	even	2
1856.4.a.i.1.1		2	40.19	odd	2
1856.4.a.l.1.2		2	40.29	even	2

Overview	Random
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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:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1450.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.44949 q^{3} +4.00000 q^{4} +6.89898 q^{6} +27.5959 q^{7} +8.00000 q^{8} -15.1010 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.44949 q^{3} +4.00000 q^{4} +6.89898 q^{6} +27.5959 q^{7} +8.00000 q^{8} -15.1010 q^{9} -52.3485 q^{11} +13.7980 q^{12} +5.40408 q^{13} +55.1918 q^{14} +16.0000 q^{16} -17.1918 q^{17} -30.2020 q^{18} +44.2020 q^{19} +95.1918 q^{21} -104.697 q^{22} +205.060 q^{23} +27.5959 q^{24} +10.8082 q^{26} -145.227 q^{27} +110.384 q^{28} +29.0000 q^{29} +299.994 q^{31} +32.0000 q^{32} -180.576 q^{33} -34.3837 q^{34} -60.4041 q^{36} -29.7980 q^{37} +88.4041 q^{38} +18.6413 q^{39} -43.9592 q^{41} +190.384 q^{42} -64.8230 q^{43} -209.394 q^{44} +410.120 q^{46} +499.499 q^{47} +55.1918 q^{48} +418.535 q^{49} -59.3031 q^{51} +21.6163 q^{52} +351.627 q^{53} -290.454 q^{54} +220.767 q^{56} +152.474 q^{57} +58.0000 q^{58} +522.372 q^{59} +484.606 q^{61} +599.989 q^{62} -416.727 q^{63} +64.0000 q^{64} -361.151 q^{66} +504.990 q^{67} -68.7673 q^{68} +707.353 q^{69} +481.283 q^{71} -120.808 q^{72} -3.11019 q^{73} -59.5959 q^{74} +176.808 q^{76} -1444.60 q^{77} +37.2827 q^{78} -1043.27 q^{79} -93.2316 q^{81} -87.9184 q^{82} +1007.08 q^{83} +380.767 q^{84} -129.646 q^{86} +100.035 q^{87} -418.788 q^{88} -295.637 q^{89} +149.131 q^{91} +820.241 q^{92} +1034.83 q^{93} +998.999 q^{94} +110.384 q^{96} -428.949 q^{97} +837.069 q^{98} +790.515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} + 2 q^{3} + 8 q^{4} + 4 q^{6} + 16 q^{7} + 16 q^{8} - 40 q^{9}+O(q^{10}) \) 2 * q + 4 * q^2 + 2 * q^3 + 8 * q^4 + 4 * q^6 + 16 * q^7 + 16 * q^8 - 40 * q^9	\( 2 q + 4 q^{2} + 2 q^{3} + 8 q^{4} + 4 q^{6} + 16 q^{7} + 16 q^{8} - 40 q^{9} - 90 q^{11} + 8 q^{12} + 50 q^{13} + 32 q^{14} + 32 q^{16} + 44 q^{17} - 80 q^{18} + 108 q^{19} + 112 q^{21} - 180 q^{22} + 28 q^{23} + 16 q^{24} + 100 q^{26} - 70 q^{27} + 64 q^{28} + 58 q^{29} + 66 q^{31} + 64 q^{32} - 126 q^{33} + 88 q^{34} - 160 q^{36} - 40 q^{37} + 216 q^{38} - 46 q^{39} + 304 q^{41} + 224 q^{42} + 130 q^{43} - 360 q^{44} + 56 q^{46} + 514 q^{47} + 32 q^{48} + 210 q^{49} - 148 q^{51} + 200 q^{52} + 958 q^{53} - 140 q^{54} + 128 q^{56} + 60 q^{57} + 116 q^{58} - 180 q^{59} + 1028 q^{61} + 132 q^{62} - 128 q^{63} + 128 q^{64} - 252 q^{66} + 912 q^{67} + 176 q^{68} + 964 q^{69} + 796 q^{71} - 320 q^{72} + 856 q^{73} - 80 q^{74} + 432 q^{76} - 1008 q^{77} - 92 q^{78} - 318 q^{79} + 470 q^{81} + 608 q^{82} + 1828 q^{83} + 448 q^{84} + 260 q^{86} + 58 q^{87} - 720 q^{88} - 944 q^{89} - 368 q^{91} + 112 q^{92} + 1374 q^{93} + 1028 q^{94} + 64 q^{96} - 368 q^{97} + 420 q^{98} + 1728 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 + 2 * q^3 + 8 * q^4 + 4 * q^6 + 16 * q^7 + 16 * q^8 - 40 * q^9 - 90 * q^11 + 8 * q^12 + 50 * q^13 + 32 * q^14 + 32 * q^16 + 44 * q^17 - 80 * q^18 + 108 * q^19 + 112 * q^21 - 180 * q^22 + 28 * q^23 + 16 * q^24 + 100 * q^26 - 70 * q^27 + 64 * q^28 + 58 * q^29 + 66 * q^31 + 64 * q^32 - 126 * q^33 + 88 * q^34 - 160 * q^36 - 40 * q^37 + 216 * q^38 - 46 * q^39 + 304 * q^41 + 224 * q^42 + 130 * q^43 - 360 * q^44 + 56 * q^46 + 514 * q^47 + 32 * q^48 + 210 * q^49 - 148 * q^51 + 200 * q^52 + 958 * q^53 - 140 * q^54 + 128 * q^56 + 60 * q^57 + 116 * q^58 - 180 * q^59 + 1028 * q^61 + 132 * q^62 - 128 * q^63 + 128 * q^64 - 252 * q^66 + 912 * q^67 + 176 * q^68 + 964 * q^69 + 796 * q^71 - 320 * q^72 + 856 * q^73 - 80 * q^74 + 432 * q^76 - 1008 * q^77 - 92 * q^78 - 318 * q^79 + 470 * q^81 + 608 * q^82 + 1828 * q^83 + 448 * q^84 + 260 * q^86 + 58 * q^87 - 720 * q^88 - 944 * q^89 - 368 * q^91 + 112 * q^92 + 1374 * q^93 + 1028 * q^94 + 64 * q^96 - 368 * q^97 + 420 * q^98 + 1728 * q^99

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