LMFDB - Embedded newform 490.4.a.y.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,4,Mod(1,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, 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("490.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	490.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:	$28.9109359028$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{113})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 59x^{2} + 60x + 674 $ x^4 - 2x^3 - 59x^2 + 60*x + 674
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-3.40086$ of defining polynomial
Character	$\chi$	$=$	490.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +9.22929 q^{3} +4.00000 q^{4} +5.00000 q^{5} +18.4586 q^{6} +8.00000 q^{8} +58.1797 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +9.22929 q^{3} +4.00000 q^{4} +5.00000 q^{5} +18.4586 q^{6} +8.00000 q^{8} +58.1797 q^{9} +10.0000 q^{10} +23.1131 q^{11} +36.9171 q^{12} +54.8451 q^{13} +46.1464 q^{15} +16.0000 q^{16} -52.8626 q^{17} +116.359 q^{18} -151.634 q^{19} +20.0000 q^{20} +46.2263 q^{22} -181.261 q^{23} +73.8343 q^{24} +25.0000 q^{25} +109.690 q^{26} +287.767 q^{27} -64.0415 q^{29} +92.2929 q^{30} -45.0046 q^{31} +32.0000 q^{32} +213.318 q^{33} -105.725 q^{34} +232.719 q^{36} +191.710 q^{37} -303.269 q^{38} +506.181 q^{39} +40.0000 q^{40} +477.005 q^{41} -537.106 q^{43} +92.4525 q^{44} +290.899 q^{45} -362.521 q^{46} +147.609 q^{47} +147.669 q^{48} +50.0000 q^{50} -487.884 q^{51} +219.381 q^{52} -148.905 q^{53} +575.533 q^{54} +115.566 q^{55} -1399.48 q^{57} -128.083 q^{58} +273.176 q^{59} +184.586 q^{60} +300.712 q^{61} -90.0092 q^{62} +64.0000 q^{64} +274.226 q^{65} +426.636 q^{66} +222.085 q^{67} -211.450 q^{68} -1672.91 q^{69} -34.8646 q^{71} +465.438 q^{72} +1069.10 q^{73} +383.420 q^{74} +230.732 q^{75} -606.537 q^{76} +1012.36 q^{78} -1068.60 q^{79} +80.0000 q^{80} +1085.03 q^{81} +954.009 q^{82} -1478.74 q^{83} -264.313 q^{85} -1074.21 q^{86} -591.057 q^{87} +184.905 q^{88} -88.5319 q^{89} +581.797 q^{90} -725.042 q^{92} -415.360 q^{93} +295.218 q^{94} -758.171 q^{95} +295.337 q^{96} +570.748 q^{97} +1344.72 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} + 10 q^{3} + 16 q^{4} + 20 q^{5} + 20 q^{6} + 32 q^{8} + 38 q^{9}+O(q^{10}) $ 4 * q + 8 * q^2 + 10 * q^3 + 16 * q^4 + 20 * q^5 + 20 * q^6 + 32 * q^8 + 38 * q^9	\( 4 q + 8 q^{2} + 10 q^{3} + 16 q^{4} + 20 q^{5} + 20 q^{6} + 32 q^{8} + 38 q^{9} + 40 q^{10} + 18 q^{11} + 40 q^{12} + 130 q^{13} + 50 q^{15} + 64 q^{16} + 110 q^{17} + 76 q^{18} + 40 q^{19} + 80 q^{20} + 36 q^{22} - 164 q^{23} + 80 q^{24} + 100 q^{25} + 260 q^{26} + 430 q^{27} + 94 q^{29} + 100 q^{30} + 180 q^{31} + 128 q^{32} + 650 q^{33} + 220 q^{34} + 152 q^{36} + 16 q^{37} + 80 q^{38} - 10 q^{39} + 160 q^{40} + 540 q^{41} - 560 q^{43} + 72 q^{44} + 190 q^{45} - 328 q^{46} + 1150 q^{47} + 160 q^{48} + 200 q^{50} - 926 q^{51} + 520 q^{52} - 244 q^{53} + 860 q^{54} + 90 q^{55} - 840 q^{57} + 188 q^{58} + 400 q^{59} + 200 q^{60} + 1540 q^{61} + 360 q^{62} + 256 q^{64} + 650 q^{65} + 1300 q^{66} - 760 q^{67} + 440 q^{68} - 1480 q^{69} + 52 q^{71} + 304 q^{72} + 800 q^{73} + 32 q^{74} + 250 q^{75} + 160 q^{76} - 20 q^{78} + 398 q^{79} + 320 q^{80} + 348 q^{81} + 1080 q^{82} - 1220 q^{83} + 550 q^{85} - 1120 q^{86} - 930 q^{87} + 144 q^{88} + 200 q^{89} + 380 q^{90} - 656 q^{92} + 1408 q^{93} + 2300 q^{94} + 200 q^{95} + 320 q^{96} - 670 q^{97} + 2292 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 + 10 * q^3 + 16 * q^4 + 20 * q^5 + 20 * q^6 + 32 * q^8 + 38 * q^9 + 40 * q^10 + 18 * q^11 + 40 * q^12 + 130 * q^13 + 50 * q^15 + 64 * q^16 + 110 * q^17 + 76 * q^18 + 40 * q^19 + 80 * q^20 + 36 * q^22 - 164 * q^23 + 80 * q^24 + 100 * q^25 + 260 * q^26 + 430 * q^27 + 94 * q^29 + 100 * q^30 + 180 * q^31 + 128 * q^32 + 650 * q^33 + 220 * q^34 + 152 * q^36 + 16 * q^37 + 80 * q^38 - 10 * q^39 + 160 * q^40 + 540 * q^41 - 560 * q^43 + 72 * q^44 + 190 * q^45 - 328 * q^46 + 1150 * q^47 + 160 * q^48 + 200 * q^50 - 926 * q^51 + 520 * q^52 - 244 * q^53 + 860 * q^54 + 90 * q^55 - 840 * q^57 + 188 * q^58 + 400 * q^59 + 200 * q^60 + 1540 * q^61 + 360 * q^62 + 256 * q^64 + 650 * q^65 + 1300 * q^66 - 760 * q^67 + 440 * q^68 - 1480 * q^69 + 52 * q^71 + 304 * q^72 + 800 * q^73 + 32 * q^74 + 250 * q^75 + 160 * q^76 - 20 * q^78 + 398 * q^79 + 320 * q^80 + 348 * q^81 + 1080 * q^82 - 1220 * q^83 + 550 * q^85 - 1120 * q^86 - 930 * q^87 + 144 * q^88 + 200 * q^89 + 380 * q^90 - 656 * q^92 + 1408 * q^93 + 2300 * q^94 + 200 * q^95 + 320 * q^96 - 670 * q^97 + 2292 * 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
$3$	9.22929	1.77618	0.888089	−	0.459673i	$-0.152033\pi$
$3$	9.22929	1.77618	0.888089	+	0.459673i	$0.152033\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	18.4586	1.25595
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	58.1797	2.15480
$10$	10.0000	0.316228
$11$	23.1131	0.633534	0.316767	−	0.948503i	$-0.397403\pi$
$11$	23.1131	0.633534	0.316767	+	0.948503i	$0.397403\pi$
$12$	36.9171	0.888089
$13$	54.8451	1.17010	0.585050	−	0.810997i	$-0.301075\pi$
$13$	54.8451	1.17010	0.585050	+	0.810997i	$0.301075\pi$
$14$	0	0
$15$	46.1464	0.794331
$16$	16.0000	0.250000
$17$	−52.8626	−0.754180	−0.377090	−	0.926177i	$-0.623075\pi$
$17$	−52.8626	−0.754180	−0.377090	+	0.926177i	$0.623075\pi$
$18$	116.359	1.52368
$19$	−151.634	−1.83091	−0.915455	−	0.402421i	$-0.868169\pi$
$19$	−151.634	−1.83091	−0.915455	+	0.402421i	$0.868169\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	46.2263	0.447976
$23$	−181.261	−1.64328	−0.821640	−	0.570007i	$-0.806941\pi$
$23$	−181.261	−1.64328	−0.821640	+	0.570007i	$0.806941\pi$
$24$	73.8343	0.627973
$25$	25.0000	0.200000
$26$	109.690	0.827386
$27$	287.767	2.05114
$28$	0	0
$29$	−64.0415	−0.410076	−0.205038	−	0.978754i	$-0.565732\pi$
$29$	−64.0415	−0.410076	−0.205038	+	0.978754i	$0.565732\pi$
$30$	92.2929	0.561676
$31$	−45.0046	−0.260744	−0.130372	−	0.991465i	$-0.541617\pi$
$31$	−45.0046	−0.260744	−0.130372	+	0.991465i	$0.541617\pi$
$32$	32.0000	0.176777
$33$	213.318	1.12527
$34$	−105.725	−0.533286
$35$	0	0
$36$	232.719	1.07740
$37$	191.710	0.851808	0.425904	−	0.904768i	$-0.359956\pi$
$37$	191.710	0.851808	0.425904	+	0.904768i	$0.359956\pi$
$38$	−303.269	−1.29465
$39$	506.181	2.07830
$40$	40.0000	0.158114
$41$	477.005	1.81697	0.908483	−	0.417921i	$-0.137241\pi$
$41$	477.005	1.81697	0.908483	+	0.417921i	$0.137241\pi$
$42$	0	0
$43$	−537.106	−1.90484	−0.952418	−	0.304795i	$-0.901412\pi$
$43$	−537.106	−1.90484	−0.952418	+	0.304795i	$0.901412\pi$
$44$	92.4525	0.316767
$45$	290.899	0.963658
$46$	−362.521	−1.16197
$47$	147.609	0.458106	0.229053	−	0.973414i	$-0.426437\pi$
$47$	147.609	0.458106	0.229053	+	0.973414i	$0.426437\pi$
$48$	147.669	0.444044
$49$	0	0
$50$	50.0000	0.141421
$51$	−487.884	−1.33956
$52$	219.381	0.585050
$53$	−148.905	−0.385918	−0.192959	−	0.981207i	$-0.561808\pi$
$53$	−148.905	−0.385918	−0.192959	+	0.981207i	$0.561808\pi$
$54$	575.533	1.45037
$55$	115.566	0.283325
$56$	0	0
$57$	−1399.48	−3.25202
$58$	−128.083	−0.289968
$59$	273.176	0.602788	0.301394	−	0.953500i	$-0.402548\pi$
$59$	273.176	0.602788	0.301394	+	0.953500i	$0.402548\pi$
$60$	184.586	0.397165
$61$	300.712	0.631184	0.315592	−	0.948895i	$-0.397797\pi$
$61$	300.712	0.631184	0.315592	+	0.948895i	$0.397797\pi$
$62$	−90.0092	−0.184374
$63$	0	0
$64$	64.0000	0.125000
$65$	274.226	0.523285
$66$	426.636	0.795685
$67$	222.085	0.404956	0.202478	−	0.979287i	$-0.435101\pi$
$67$	222.085	0.404956	0.202478	+	0.979287i	$0.435101\pi$
$68$	−211.450	−0.377090
$69$	−1672.91	−2.91876
$70$	0	0
$71$	−34.8646	−0.0582769	−0.0291385	−	0.999575i	$-0.509276\pi$
$71$	−34.8646	−0.0582769	−0.0291385	+	0.999575i	$0.509276\pi$
$72$	465.438	0.761839
$73$	1069.10	1.71409	0.857044	−	0.515243i	$-0.172298\pi$
$73$	1069.10	1.71409	0.857044	+	0.515243i	$0.172298\pi$
$74$	383.420	0.602319
$75$	230.732	0.355235
$76$	−606.537	−0.915455
$77$	0	0
$78$	1012.36	1.46958
$79$	−1068.60	−1.52186	−0.760930	−	0.648834i	$-0.775257\pi$
$79$	−1068.60	−1.52186	−0.760930	+	0.648834i	$0.775257\pi$
$80$	80.0000	0.111803
$81$	1085.03	1.48838
$82$	954.009	1.28479
$83$	−1478.74	−1.95558	−0.977789	−	0.209591i	$-0.932787\pi$
$83$	−1478.74	−1.95558	−0.977789	+	0.209591i	$0.932787\pi$
$84$	0	0
$85$	−264.313	−0.337279
$86$	−1074.21	−1.34692
$87$	−591.057	−0.728368
$88$	184.905	0.223988
$89$	−88.5319	−0.105442	−0.0527211	−	0.998609i	$-0.516789\pi$
$89$	−88.5319	−0.105442	−0.0527211	+	0.998609i	$0.516789\pi$
$90$	581.797	0.681409
$91$	0	0
$92$	−725.042	−0.821640
$93$	−415.360	−0.463127
$94$	295.218	0.323930
$95$	−758.171	−0.818808
$96$	295.337	0.313987
$97$	570.748	0.597429	0.298715	−	0.954342i	$-0.403442\pi$
$97$	570.748	0.597429	0.298715	+	0.954342i	$0.403442\pi$
$98$	0	0
$99$	1344.72	1.36514
$100$	100.000	0.100000
$101$	354.028	0.348783	0.174392	−	0.984676i	$-0.444204\pi$
$101$	354.028	0.348783	0.174392	+	0.984676i	$0.444204\pi$
$102$	−975.768	−0.947210
$103$	−921.368	−0.881409	−0.440704	−	0.897652i	$-0.645271\pi$
$103$	−921.368	−0.881409	−0.440704	+	0.897652i	$0.645271\pi$
$104$	438.761	0.413693
$105$	0	0
$106$	−297.810	−0.272885
$107$	1470.06	1.32819	0.664095	−	0.747648i	$-0.268817\pi$
$107$	1470.06	1.32819	0.664095	+	0.747648i	$0.268817\pi$
$108$	1151.07	1.02557
$109$	−473.135	−0.415762	−0.207881	−	0.978154i	$-0.566657\pi$
$109$	−473.135	−0.415762	−0.207881	+	0.978154i	$0.566657\pi$
$110$	231.131	0.200341
$111$	1769.35	1.51296
$112$	0	0
$113$	−749.272	−0.623766	−0.311883	−	0.950120i	$-0.600960\pi$
$113$	−749.272	−0.623766	−0.311883	+	0.950120i	$0.600960\pi$
$114$	−2798.95	−2.29953
$115$	−906.303	−0.734897
$116$	−256.166	−0.205038
$117$	3190.87	2.52134
$118$	546.352	0.426236
$119$	0	0
$120$	369.171	0.280838
$121$	−796.783	−0.598635
$122$	601.424	0.446314
$123$	4402.41	3.22725
$124$	−180.018	−0.130372
$125$	125.000	0.0894427
$126$	0	0
$127$	−641.638	−0.448316	−0.224158	−	0.974553i	$-0.571963\pi$
$127$	−641.638	−0.448316	−0.224158	+	0.974553i	$0.571963\pi$
$128$	128.000	0.0883883
$129$	−4957.11	−3.38333
$130$	548.451	0.370018
$131$	−1227.20	−0.818478	−0.409239	−	0.912427i	$-0.634206\pi$
$131$	−1227.20	−0.818478	−0.409239	+	0.912427i	$0.634206\pi$
$132$	853.271	0.562634
$133$	0	0
$134$	444.171	0.286347
$135$	1438.83	0.917297
$136$	−422.901	−0.266643
$137$	−1214.50	−0.757387	−0.378693	−	0.925522i	$-0.623626\pi$
$137$	−1214.50	−0.757387	−0.378693	+	0.925522i	$0.623626\pi$
$138$	−3345.81	−2.06387
$139$	−949.203	−0.579211	−0.289605	−	0.957146i	$-0.593524\pi$
$139$	−949.203	−0.579211	−0.289605	+	0.957146i	$0.593524\pi$
$140$	0	0
$141$	1362.33	0.813678
$142$	−69.7291	−0.0412080
$143$	1267.64	0.741298
$144$	930.876	0.538701
$145$	−320.207	−0.183392
$146$	2138.20	1.21204
$147$	0	0
$148$	766.839	0.425904
$149$	−1892.40	−1.04048	−0.520239	−	0.854021i	$-0.674157\pi$
$149$	−1892.40	−1.04048	−0.520239	+	0.854021i	$0.674157\pi$
$150$	461.464	0.251189
$151$	3250.58	1.75185	0.875923	−	0.482451i	$-0.160254\pi$
$151$	3250.58	1.75185	0.875923	+	0.482451i	$0.160254\pi$
$152$	−1213.07	−0.647324
$153$	−3075.53	−1.62511
$154$	0	0
$155$	−225.023	−0.116608
$156$	2024.73	1.03915
$157$	3283.52	1.66913	0.834566	−	0.550908i	$-0.185719\pi$
$157$	3283.52	1.66913	0.834566	+	0.550908i	$0.185719\pi$
$158$	−2137.20	−1.07612
$159$	−1374.28	−0.685458
$160$	160.000	0.0790569
$161$	0	0
$162$	2170.06	1.05244
$163$	1602.64	0.770112	0.385056	−	0.922893i	$-0.374182\pi$
$163$	1602.64	0.770112	0.385056	+	0.922893i	$0.374182\pi$
$164$	1908.02	0.908483
$165$	1066.59	0.503235
$166$	−2957.48	−1.38280
$167$	3087.12	1.43047	0.715234	−	0.698885i	$-0.246320\pi$
$167$	3087.12	1.43047	0.715234	+	0.698885i	$0.246320\pi$
$168$	0	0
$169$	810.988	0.369134
$170$	−528.626	−0.238493
$171$	−8822.04	−3.94525
$172$	−2148.43	−0.952418
$173$	821.763	0.361141	0.180571	−	0.983562i	$-0.442206\pi$
$173$	821.763	0.361141	0.180571	+	0.983562i	$0.442206\pi$
$174$	−1182.11	−0.515034
$175$	0	0
$176$	369.810	0.158383
$177$	2521.22	1.07066
$178$	−177.064	−0.0745589
$179$	−1406.99	−0.587505	−0.293753	−	0.955881i	$-0.594904\pi$
$179$	−1406.99	−0.587505	−0.293753	+	0.955881i	$0.594904\pi$
$180$	1163.59	0.481829
$181$	−3144.92	−1.29149	−0.645745	−	0.763553i	$-0.723453\pi$
$181$	−3144.92	−1.29149	−0.645745	+	0.763553i	$0.723453\pi$
$182$	0	0
$183$	2775.35	1.12109
$184$	−1450.08	−0.580987
$185$	958.549	0.380940
$186$	−830.720	−0.327481
$187$	−1221.82	−0.477798
$188$	590.436	0.229053
$189$	0	0
$190$	−1516.34	−0.578985
$191$	1846.25	0.699423	0.349712	−	0.936857i	$-0.386280\pi$
$191$	1846.25	0.699423	0.349712	+	0.936857i	$0.386280\pi$
$192$	590.674	0.222022
$193$	196.110	0.0731414	0.0365707	−	0.999331i	$-0.488357\pi$
$193$	196.110	0.0731414	0.0365707	+	0.999331i	$0.488357\pi$
$194$	1141.50	0.422446
$195$	2530.91	0.929446
$196$	0	0
$197$	−4030.96	−1.45784	−0.728919	−	0.684600i	$-0.759977\pi$
$197$	−4030.96	−1.45784	−0.728919	+	0.684600i	$0.759977\pi$
$198$	2689.43	0.965301
$199$	1658.52	0.590801	0.295401	−	0.955373i	$-0.404547\pi$
$199$	1658.52	0.590801	0.295401	+	0.955373i	$0.404547\pi$
$200$	200.000	0.0707107
$201$	2049.69	0.719273
$202$	708.056	0.246627
$203$	0	0
$204$	−1951.54	−0.669778
$205$	2385.02	0.812572
$206$	−1842.74	−0.623250
$207$	−10545.7	−3.54095
$208$	877.522	0.292525
$209$	−3504.74	−1.15994
$210$	0	0
$211$	−4566.57	−1.48993	−0.744965	−	0.667103i	$-0.767534\pi$
$211$	−4566.57	−1.48993	−0.744965	+	0.667103i	$0.767534\pi$
$212$	−595.619	−0.192959
$213$	−321.775	−0.103510
$214$	2940.13	0.939172
$215$	−2685.53	−0.851869
$216$	2302.13	0.725187
$217$	0	0
$218$	−946.269	−0.293988
$219$	9867.01	3.04452
$220$	462.263	0.141662
$221$	−2899.25	−0.882466
$222$	3538.69	1.06983
$223$	3076.51	0.923850	0.461925	−	0.886919i	$-0.347159\pi$
$223$	3076.51	0.923850	0.461925	+	0.886919i	$0.347159\pi$
$224$	0	0
$225$	1454.49	0.430961
$226$	−1498.54	−0.441069
$227$	−2338.89	−0.683865	−0.341933	−	0.939724i	$-0.611081\pi$
$227$	−2338.89	−0.683865	−0.341933	+	0.939724i	$0.611081\pi$
$228$	−5597.90	−1.62601
$229$	−3473.28	−1.00228	−0.501138	−	0.865368i	$-0.667085\pi$
$229$	−3473.28	−1.00228	−0.501138	+	0.865368i	$0.667085\pi$
$230$	−1812.61	−0.519651
$231$	0	0
$232$	−512.332	−0.144984
$233$	−2098.22	−0.589952	−0.294976	−	0.955505i	$-0.595312\pi$
$233$	−2098.22	−0.589952	−0.294976	+	0.955505i	$0.595312\pi$
$234$	6381.75	1.78285
$235$	738.045	0.204871
$236$	1092.70	0.301394
$237$	−9862.42	−2.70309
$238$	0	0
$239$	2210.69	0.598317	0.299158	−	0.954203i	$-0.403294\pi$
$239$	2210.69	0.598317	0.299158	+	0.954203i	$0.403294\pi$
$240$	738.343	0.198583
$241$	−1030.81	−0.275519	−0.137759	−	0.990466i	$-0.543990\pi$
$241$	−1030.81	−0.275519	−0.137759	+	0.990466i	$0.543990\pi$
$242$	−1593.57	−0.423299
$243$	2244.34	0.592487
$244$	1202.85	0.315592
$245$	0	0
$246$	8804.83	2.28201
$247$	−8316.40	−2.14235
$248$	−360.037	−0.0921869
$249$	−13647.7	−3.47345
$250$	250.000	0.0632456
$251$	6829.23	1.71736	0.858680	−	0.512513i	$-0.171285\pi$
$251$	6829.23	1.71736	0.858680	+	0.512513i	$0.171285\pi$
$252$	0	0
$253$	−4189.50	−1.04107
$254$	−1283.28	−0.317008
$255$	−2439.42	−0.599068
$256$	256.000	0.0625000
$257$	−1413.68	−0.343124	−0.171562	−	0.985173i	$-0.554881\pi$
$257$	−1413.68	−0.343124	−0.171562	+	0.985173i	$0.554881\pi$
$258$	−9914.22	−2.39237
$259$	0	0
$260$	1096.90	0.261642
$261$	−3725.92	−0.883634
$262$	−2454.39	−0.578751
$263$	−990.301	−0.232185	−0.116092	−	0.993238i	$-0.537037\pi$
$263$	−990.301	−0.232185	−0.116092	+	0.993238i	$0.537037\pi$
$264$	1706.54	0.397842
$265$	−744.524	−0.172588
$266$	0	0
$267$	−817.086	−0.187284
$268$	888.341	0.202478
$269$	4765.92	1.08024	0.540118	−	0.841589i	$-0.318380\pi$
$269$	4765.92	1.08024	0.540118	+	0.841589i	$0.318380\pi$
$270$	2877.67	0.648627
$271$	158.724	0.0355786	0.0177893	−	0.999842i	$-0.494337\pi$
$271$	158.724	0.0355786	0.0177893	+	0.999842i	$0.494337\pi$
$272$	−845.801	−0.188545
$273$	0	0
$274$	−2429.01	−0.535553
$275$	577.828	0.126707
$276$	−6691.62	−1.45938
$277$	5630.75	1.22137	0.610685	−	0.791874i	$-0.290894\pi$
$277$	5630.75	1.22137	0.610685	+	0.791874i	$0.290894\pi$
$278$	−1898.41	−0.409564
$279$	−2618.35	−0.561852
$280$	0	0
$281$	1398.24	0.296840	0.148420	−	0.988924i	$-0.452581\pi$
$281$	1398.24	0.296840	0.148420	+	0.988924i	$0.452581\pi$
$282$	2724.65	0.575357
$283$	495.163	0.104008	0.0520042	−	0.998647i	$-0.483439\pi$
$283$	495.163	0.104008	0.0520042	+	0.998647i	$0.483439\pi$
$284$	−139.458	−0.0291385
$285$	−6997.38	−1.45435
$286$	2535.29	0.524177
$287$	0	0
$288$	1861.75	0.380919
$289$	−2118.55	−0.431213
$290$	−640.415	−0.129677
$291$	5267.59	1.06114
$292$	4276.39	0.857044
$293$	7295.98	1.45473	0.727364	−	0.686252i	$-0.240745\pi$
$293$	7295.98	1.45473	0.727364	+	0.686252i	$0.240745\pi$
$294$	0	0
$295$	1365.88	0.269575
$296$	1533.68	0.301160
$297$	6651.19	1.29947
$298$	−3784.79	−0.735729
$299$	−9941.26	−1.92280
$300$	922.929	0.177618
$301$	0	0
$302$	6501.17	1.23874
$303$	3267.43	0.619501
$304$	−2426.15	−0.457727
$305$	1503.56	0.282274
$306$	−6151.06	−1.14913
$307$	−7643.67	−1.42100	−0.710500	−	0.703697i	$-0.751531\pi$
$307$	−7643.67	−1.42100	−0.710500	+	0.703697i	$0.751531\pi$
$308$	0	0
$309$	−8503.57	−1.56554
$310$	−450.046	−0.0824545
$311$	7579.14	1.38191	0.690955	−	0.722898i	$-0.257190\pi$
$311$	7579.14	1.38191	0.690955	+	0.722898i	$0.257190\pi$
$312$	4049.45	0.734792
$313$	2280.82	0.411883	0.205942	−	0.978564i	$-0.433974\pi$
$313$	2280.82	0.411883	0.205942	+	0.978564i	$0.433974\pi$
$314$	6567.04	1.18025
$315$	0	0
$316$	−4274.40	−0.760930
$317$	161.098	0.0285431	0.0142716	−	0.999898i	$-0.495457\pi$
$317$	161.098	0.0285431	0.0142716	+	0.999898i	$0.495457\pi$
$318$	−2748.57	−0.484692
$319$	−1480.20	−0.259797
$320$	320.000	0.0559017
$321$	13567.6	2.35910
$322$	0	0
$323$	8015.78	1.38084
$324$	4340.11	0.744189
$325$	1371.13	0.234020
$326$	3205.28	0.544552
$327$	−4366.69	−0.738467
$328$	3816.04	0.642395
$329$	0	0
$330$	2133.18	0.355841
$331$	3184.99	0.528890	0.264445	−	0.964401i	$-0.414811\pi$
$331$	3184.99	0.528890	0.264445	+	0.964401i	$0.414811\pi$
$332$	−5914.97	−0.977789
$333$	11153.6	1.83548
$334$	6174.23	1.01149
$335$	1110.43	0.181102
$336$	0	0
$337$	−5914.75	−0.956073	−0.478037	−	0.878340i	$-0.658651\pi$
$337$	−5914.75	−0.956073	−0.478037	+	0.878340i	$0.658651\pi$
$338$	1621.98	0.261017
$339$	−6915.25	−1.10792
$340$	−1057.25	−0.168640
$341$	−1040.20	−0.165190
$342$	−17644.1	−2.78972
$343$	0	0
$344$	−4296.85	−0.673461
$345$	−8364.53	−1.30531
$346$	1643.53	0.255366
$347$	1282.87	0.198467	0.0992335	−	0.995064i	$-0.468361\pi$
$347$	1282.87	0.198467	0.0992335	+	0.995064i	$0.468361\pi$
$348$	−2364.23	−0.364184
$349$	7658.29	1.17461	0.587305	−	0.809366i	$-0.300189\pi$
$349$	7658.29	1.17461	0.587305	+	0.809366i	$0.300189\pi$
$350$	0	0
$351$	15782.6	2.40004
$352$	739.620	0.111994
$353$	4072.32	0.614016	0.307008	−	0.951707i	$-0.400672\pi$
$353$	4072.32	0.614016	0.307008	+	0.951707i	$0.400672\pi$
$354$	5042.44	0.757070
$355$	−174.323	−0.0260622
$356$	−354.127	−0.0527211
$357$	0	0
$358$	−2813.98	−0.415429
$359$	2331.76	0.342801	0.171401	−	0.985201i	$-0.445171\pi$
$359$	2331.76	0.342801	0.171401	+	0.985201i	$0.445171\pi$
$360$	2327.19	0.340705
$361$	16134.0	2.35223
$362$	−6289.83	−0.913222
$363$	−7353.74	−1.06328
$364$	0	0
$365$	5345.49	0.766564
$366$	5550.71	0.792733
$367$	−7572.25	−1.07703	−0.538513	−	0.842617i	$-0.681014\pi$
$367$	−7572.25	−1.07703	−0.538513	+	0.842617i	$0.681014\pi$
$368$	−2900.17	−0.410820
$369$	27752.0	3.91521
$370$	1917.10	0.269365
$371$	0	0
$372$	−1661.44	−0.231564
$373$	8270.43	1.14806	0.574030	−	0.818834i	$-0.305379\pi$
$373$	8270.43	1.14806	0.574030	+	0.818834i	$0.305379\pi$
$374$	−2443.64	−0.337855
$375$	1153.66	0.158866
$376$	1180.87	0.161965
$377$	−3512.36	−0.479830
$378$	0	0
$379$	1809.11	0.245191	0.122596	−	0.992457i	$-0.460878\pi$
$379$	1809.11	0.245191	0.122596	+	0.992457i	$0.460878\pi$
$380$	−3032.69	−0.409404
$381$	−5921.86	−0.796289
$382$	3692.50	0.494567
$383$	2870.28	0.382936	0.191468	−	0.981499i	$-0.438675\pi$
$383$	2870.28	0.382936	0.191468	+	0.981499i	$0.438675\pi$
$384$	1181.35	0.156993
$385$	0	0
$386$	392.220	0.0517188
$387$	−31248.7	−4.10455
$388$	2282.99	0.298715
$389$	3083.98	0.401964	0.200982	−	0.979595i	$-0.435587\pi$
$389$	3083.98	0.401964	0.200982	+	0.979595i	$0.435587\pi$
$390$	5061.81	0.657218
$391$	9581.90	1.23933
$392$	0	0
$393$	−11326.1	−1.45376
$394$	−8061.92	−1.03085
$395$	−5343.00	−0.680597
$396$	5378.86	0.682571
$397$	−4773.83	−0.603506	−0.301753	−	0.953386i	$-0.597572\pi$
$397$	−4773.83	−0.603506	−0.301753	+	0.953386i	$0.597572\pi$
$398$	3317.04	0.417760
$399$	0	0
$400$	400.000	0.0500000
$401$	−10963.1	−1.36526	−0.682632	−	0.730762i	$-0.739165\pi$
$401$	−10963.1	−1.36526	−0.682632	+	0.730762i	$0.739165\pi$
$402$	4099.38	0.508603
$403$	−2468.28	−0.305097
$404$	1416.11	0.174392
$405$	5425.14	0.665623
$406$	0	0
$407$	4431.02	0.539649
$408$	−3903.07	−0.473605
$409$	−6866.38	−0.830124	−0.415062	−	0.909793i	$-0.636240\pi$
$409$	−6866.38	−0.830124	−0.415062	+	0.909793i	$0.636240\pi$
$410$	4770.05	0.574575
$411$	−11209.0	−1.34525
$412$	−3685.47	−0.440704
$413$	0	0
$414$	−21091.4	−2.50383
$415$	−7393.71	−0.874561
$416$	1755.04	0.206846
$417$	−8760.46	−1.02878
$418$	−7009.49	−0.820204
$419$	−5292.33	−0.617058	−0.308529	−	0.951215i	$-0.599837\pi$
$419$	−5292.33	−0.617058	−0.308529	+	0.951215i	$0.599837\pi$
$420$	0	0
$421$	16583.0	1.91973	0.959866	−	0.280457i	$-0.0904861\pi$
$421$	16583.0	1.91973	0.959866	+	0.280457i	$0.0904861\pi$
$422$	−9133.13	−1.05354
$423$	8587.86	0.987130
$424$	−1191.24	−0.136443
$425$	−1321.56	−0.150836
$426$	−643.550	−0.0731927
$427$	0	0
$428$	5880.25	0.664095
$429$	11699.4	1.31668
$430$	−5371.06	−0.602362
$431$	−6724.10	−0.751482	−0.375741	−	0.926725i	$-0.622612\pi$
$431$	−6724.10	−0.751482	−0.375741	+	0.926725i	$0.622612\pi$
$432$	4604.27	0.512784
$433$	−2264.15	−0.251289	−0.125645	−	0.992075i	$-0.540100\pi$
$433$	−2264.15	−0.251289	−0.125645	+	0.992075i	$0.540100\pi$
$434$	0	0
$435$	−2955.29	−0.325736
$436$	−1892.54	−0.207881
$437$	27485.3	3.00870
$438$	19734.0	2.15280
$439$	7943.41	0.863595	0.431798	−	0.901971i	$-0.357879\pi$
$439$	7943.41	0.863595	0.431798	+	0.901971i	$0.357879\pi$
$440$	924.525	0.100171
$441$	0	0
$442$	−5798.51	−0.623998
$443$	4480.91	0.480574	0.240287	−	0.970702i	$-0.422758\pi$
$443$	4480.91	0.480574	0.240287	+	0.970702i	$0.422758\pi$
$444$	7077.38	0.756481
$445$	−442.659	−0.0471552
$446$	6153.02	0.653260
$447$	−17465.5	−1.84807
$448$	0	0
$449$	6145.95	0.645980	0.322990	−	0.946402i	$-0.395312\pi$
$449$	6145.95	0.645980	0.322990	+	0.946402i	$0.395312\pi$
$450$	2908.99	0.304735
$451$	11025.1	1.15111
$452$	−2997.09	−0.311883
$453$	30000.6	3.11159
$454$	−4677.77	−0.483566
$455$	0	0
$456$	−11195.8	−1.14976
$457$	3165.54	0.324021	0.162011	−	0.986789i	$-0.448202\pi$
$457$	3165.54	0.324021	0.162011	+	0.986789i	$0.448202\pi$
$458$	−6946.57	−0.708716
$459$	−15212.1	−1.54693
$460$	−3625.21	−0.367449
$461$	−1407.19	−0.142168	−0.0710840	−	0.997470i	$-0.522646\pi$
$461$	−1407.19	−0.142168	−0.0710840	+	0.997470i	$0.522646\pi$
$462$	0	0
$463$	−14172.9	−1.42261	−0.711306	−	0.702883i	$-0.751896\pi$
$463$	−14172.9	−1.42261	−0.711306	+	0.702883i	$0.751896\pi$
$464$	−1024.66	−0.102519
$465$	−2076.80	−0.207117
$466$	−4196.43	−0.417159
$467$	9302.27	0.921751	0.460876	−	0.887465i	$-0.347535\pi$
$467$	9302.27	0.921751	0.460876	+	0.887465i	$0.347535\pi$
$468$	12763.5	1.26067
$469$	0	0
$470$	1476.09	0.144866
$471$	30304.6	2.96467
$472$	2185.41	0.213118
$473$	−12414.2	−1.20678
$474$	−19724.8	−1.91138
$475$	−3790.86	−0.366182
$476$	0	0
$477$	−8663.24	−0.831577
$478$	4421.38	0.423074
$479$	16114.6	1.53715	0.768574	−	0.639761i	$-0.220967\pi$
$479$	16114.6	1.53715	0.768574	+	0.639761i	$0.220967\pi$
$480$	1476.69	0.140419
$481$	10514.4	0.996701
$482$	−2061.61	−0.194821
$483$	0	0
$484$	−3187.13	−0.299317
$485$	2853.74	0.267179
$486$	4488.67	0.418951
$487$	2011.29	0.187146	0.0935730	−	0.995612i	$-0.470171\pi$
$487$	2011.29	0.187146	0.0935730	+	0.995612i	$0.470171\pi$
$488$	2405.69	0.223157
$489$	14791.2	1.36786
$490$	0	0
$491$	−3505.65	−0.322215	−0.161108	−	0.986937i	$-0.551507\pi$
$491$	−3505.65	−0.322215	−0.161108	+	0.986937i	$0.551507\pi$
$492$	17609.7	1.61363
$493$	3385.40	0.309271
$494$	−16632.8	−1.51487
$495$	6723.58	0.610510
$496$	−720.073	−0.0651860
$497$	0	0
$498$	−27295.5	−2.45610
$499$	5143.82	0.461461	0.230731	−	0.973018i	$-0.425888\pi$
$499$	5143.82	0.461461	0.230731	+	0.973018i	$0.425888\pi$
$500$	500.000	0.0447214
$501$	28491.9	2.54076
$502$	13658.5	1.21436
$503$	−3702.47	−0.328201	−0.164100	−	0.986444i	$-0.552472\pi$
$503$	−3702.47	−0.328201	−0.164100	+	0.986444i	$0.552472\pi$
$504$	0	0
$505$	1770.14	0.155981
$506$	−8379.00	−0.736150
$507$	7484.84	0.655648
$508$	−2566.55	−0.224158
$509$	12975.6	1.12993	0.564963	−	0.825116i	$-0.308890\pi$
$509$	12975.6	1.12993	0.564963	+	0.825116i	$0.308890\pi$
$510$	−4878.84	−0.423605
$511$	0	0
$512$	512.000	0.0441942
$513$	−43635.3	−3.75545
$514$	−2827.36	−0.242625
$515$	−4606.84	−0.394178
$516$	−19828.4	−1.69166
$517$	3411.71	0.290226
$518$	0	0
$519$	7584.28	0.641451
$520$	2193.81	0.185009
$521$	−5249.10	−0.441396	−0.220698	−	0.975342i	$-0.570834\pi$
$521$	−5249.10	−0.441396	−0.220698	+	0.975342i	$0.570834\pi$
$522$	−7451.83	−0.624824
$523$	714.405	0.0597299	0.0298650	−	0.999554i	$-0.490492\pi$
$523$	714.405	0.0597299	0.0298650	+	0.999554i	$0.490492\pi$
$524$	−4908.78	−0.409239
$525$	0	0
$526$	−1980.60	−0.164179
$527$	2379.06	0.196648
$528$	3413.08	0.281317
$529$	20688.4	1.70037
$530$	−1489.05	−0.122038
$531$	15893.3	1.29889
$532$	0	0
$533$	26161.4	2.12603
$534$	−1634.17	−0.132430
$535$	7350.31	0.593985
$536$	1776.68	0.143173
$537$	−12985.5	−1.04351
$538$	9531.84	0.763842
$539$	0	0
$540$	5755.33	0.458648
$541$	−2925.32	−0.232476	−0.116238	−	0.993221i	$-0.537083\pi$
$541$	−2925.32	−0.232476	−0.116238	+	0.993221i	$0.537083\pi$
$542$	317.448	0.0251579
$543$	−29025.3	−2.29392
$544$	−1691.60	−0.133321
$545$	−2365.67	−0.185934
$546$	0	0
$547$	−8641.57	−0.675479	−0.337739	−	0.941240i	$-0.609662\pi$
$547$	−8641.57	−0.675479	−0.337739	+	0.941240i	$0.609662\pi$
$548$	−4858.01	−0.378693
$549$	17495.3	1.36008
$550$	1155.66	0.0895952
$551$	9710.88	0.750812
$552$	−13383.2	−1.03194
$553$	0	0
$554$	11261.5	0.863638
$555$	8846.73	0.676617
$556$	−3796.81	−0.289605
$557$	4282.78	0.325794	0.162897	−	0.986643i	$-0.447916\pi$
$557$	4282.78	0.325794	0.162897	+	0.986643i	$0.447916\pi$
$558$	−5236.71	−0.397290
$559$	−29457.7	−2.22885
$560$	0	0
$561$	−11276.5	−0.848655
$562$	2796.48	0.209897
$563$	−14625.2	−1.09481	−0.547406	−	0.836867i	$-0.684385\pi$
$563$	−14625.2	−1.09481	−0.547406	+	0.836867i	$0.684385\pi$
$564$	5449.31	0.406839
$565$	−3746.36	−0.278957
$566$	990.326	0.0735450
$567$	0	0
$568$	−278.916	−0.0206040
$569$	−1142.97	−0.0842102	−0.0421051	−	0.999113i	$-0.513406\pi$
$569$	−1142.97	−0.0842102	−0.0421051	+	0.999113i	$0.513406\pi$
$570$	−13994.8	−1.02838
$571$	6044.56	0.443007	0.221503	−	0.975160i	$-0.428904\pi$
$571$	6044.56	0.443007	0.221503	+	0.975160i	$0.428904\pi$
$572$	5070.57	0.370649
$573$	17039.6	1.24230
$574$	0	0
$575$	−4531.51	−0.328656
$576$	3723.50	0.269351
$577$	−9533.58	−0.687848	−0.343924	−	0.938997i	$-0.611756\pi$
$577$	−9533.58	−0.687848	−0.343924	+	0.938997i	$0.611756\pi$
$578$	−4237.10	−0.304914
$579$	1809.95	0.129912
$580$	−1280.83	−0.0916958
$581$	0	0
$582$	10535.2	0.750340
$583$	−3441.66	−0.244492
$584$	8552.78	0.606022
$585$	15954.4	1.12758
$586$	14592.0	1.02865
$587$	15876.0	1.11631	0.558155	−	0.829737i	$-0.311510\pi$
$587$	15876.0	1.11631	0.558155	+	0.829737i	$0.311510\pi$
$588$	0	0
$589$	6824.24	0.477399
$590$	2731.76	0.190618
$591$	−37202.9	−2.58938
$592$	3067.36	0.212952
$593$	−18659.2	−1.29214	−0.646071	−	0.763277i	$-0.723589\pi$
$593$	−18659.2	−1.29214	−0.646071	+	0.763277i	$0.723589\pi$
$594$	13302.4	0.918861
$595$	0	0
$596$	−7569.59	−0.520239
$597$	15307.0	1.04937
$598$	−19882.5	−1.35963
$599$	1810.95	0.123528	0.0617640	−	0.998091i	$-0.480327\pi$
$599$	1810.95	0.123528	0.0617640	+	0.998091i	$0.480327\pi$
$600$	1845.86	0.125595
$601$	−6409.03	−0.434991	−0.217496	−	0.976061i	$-0.569789\pi$
$601$	−6409.03	−0.434991	−0.217496	+	0.976061i	$0.569789\pi$
$602$	0	0
$603$	12920.9	0.872601
$604$	13002.3	0.875923
$605$	−3983.91	−0.267718
$606$	6534.85	0.438053
$607$	−10853.4	−0.725741	−0.362870	−	0.931840i	$-0.618203\pi$
$607$	−10853.4	−0.725741	−0.362870	+	0.931840i	$0.618203\pi$
$608$	−4852.30	−0.323662
$609$	0	0
$610$	3007.12	0.199598
$611$	8095.64	0.536030
$612$	−12302.1	−0.812555
$613$	−1457.25	−0.0960158	−0.0480079	−	0.998847i	$-0.515287\pi$
$613$	−1457.25	−0.0960158	−0.0480079	+	0.998847i	$0.515287\pi$
$614$	−15287.3	−1.00480
$615$	22012.1	1.44327
$616$	0	0
$617$	8638.52	0.563653	0.281827	−	0.959465i	$-0.409060\pi$
$617$	8638.52	0.563653	0.281827	+	0.959465i	$0.409060\pi$
$618$	−17007.1	−1.10700
$619$	−633.763	−0.0411520	−0.0205760	−	0.999788i	$-0.506550\pi$
$619$	−633.763	−0.0411520	−0.0205760	+	0.999788i	$0.506550\pi$
$620$	−900.092	−0.0583041
$621$	−52160.7	−3.37059
$622$	15158.3	0.977157
$623$	0	0
$624$	8098.90	0.519576
$625$	625.000	0.0400000
$626$	4561.64	0.291246
$627$	−32346.3	−2.06026
$628$	13134.1	0.834566
$629$	−10134.3	−0.642417
$630$	0	0
$631$	−8206.60	−0.517749	−0.258875	−	0.965911i	$-0.583352\pi$
$631$	−8206.60	−0.517749	−0.258875	+	0.965911i	$0.583352\pi$
$632$	−8548.81	−0.538059
$633$	−42146.2	−2.64638
$634$	322.196	0.0201831
$635$	−3208.19	−0.200493
$636$	−5497.14	−0.342729
$637$	0	0
$638$	−2960.40	−0.183704
$639$	−2028.41	−0.125575
$640$	640.000	0.0395285
$641$	10617.8	0.654253	0.327126	−	0.944981i	$-0.393920\pi$
$641$	10617.8	0.654253	0.327126	+	0.944981i	$0.393920\pi$
$642$	27135.3	1.66814
$643$	−18018.2	−1.10508	−0.552541	−	0.833486i	$-0.686342\pi$
$643$	−18018.2	−1.10508	−0.552541	+	0.833486i	$0.686342\pi$
$644$	0	0
$645$	−24785.5	−1.51307
$646$	16031.6	0.976398
$647$	17892.6	1.08722	0.543611	−	0.839337i	$-0.317057\pi$
$647$	17892.6	1.08722	0.543611	+	0.839337i	$0.317057\pi$
$648$	8680.23	0.526221
$649$	6313.96	0.381887
$650$	2742.26	0.165477
$651$	0	0
$652$	6410.55	0.385056
$653$	31348.7	1.87867	0.939335	−	0.343002i	$-0.111444\pi$
$653$	31348.7	1.87867	0.939335	+	0.343002i	$0.111444\pi$
$654$	−8733.39	−0.522175
$655$	−6135.98	−0.366034
$656$	7632.08	0.454242
$657$	62199.8	3.69353
$658$	0	0
$659$	26724.4	1.57972	0.789859	−	0.613288i	$-0.210154\pi$
$659$	26724.4	1.57972	0.789859	+	0.613288i	$0.210154\pi$
$660$	4266.36	0.251618
$661$	15681.5	0.922754	0.461377	−	0.887204i	$-0.347356\pi$
$661$	15681.5	0.922754	0.461377	+	0.887204i	$0.347356\pi$
$662$	6369.97	0.373982
$663$	−26758.0	−1.56742
$664$	−11829.9	−0.691401
$665$	0	0
$666$	22307.3	1.29788
$667$	11608.2	0.673870
$668$	12348.5	0.715234
$669$	28394.0	1.64092
$670$	2220.85	0.128058
$671$	6950.39	0.399876
$672$	0	0
$673$	13128.8	0.751976	0.375988	−	0.926625i	$-0.377303\pi$
$673$	13128.8	0.751976	0.375988	+	0.926625i	$0.377303\pi$
$674$	−11829.5	−0.676046
$675$	7194.17	0.410228
$676$	3243.95	0.184567
$677$	12106.5	0.687282	0.343641	−	0.939101i	$-0.388340\pi$
$677$	12106.5	0.687282	0.343641	+	0.939101i	$0.388340\pi$
$678$	−13830.5	−0.783417
$679$	0	0
$680$	−2114.50	−0.119246
$681$	−21586.3	−1.21467
$682$	−2080.39	−0.116807
$683$	−25417.3	−1.42396	−0.711981	−	0.702198i	$-0.752202\pi$
$683$	−25417.3	−1.42396	−0.711981	+	0.702198i	$0.752202\pi$
$684$	−35288.2	−1.97263
$685$	−6072.51	−0.338714
$686$	0	0
$687$	−32055.9	−1.78022
$688$	−8593.70	−0.476209
$689$	−8166.70	−0.451562
$690$	−16729.1	−0.922992
$691$	−16723.3	−0.920674	−0.460337	−	0.887744i	$-0.652271\pi$
$691$	−16723.3	−0.920674	−0.460337	+	0.887744i	$0.652271\pi$
$692$	3287.05	0.180571
$693$	0	0
$694$	2565.74	0.140337
$695$	−4746.01	−0.259031
$696$	−4728.46	−0.257517
$697$	−25215.7	−1.37032
$698$	15316.6	0.830575
$699$	−19365.0	−1.04786
$700$	0	0
$701$	30284.7	1.63172	0.815862	−	0.578246i	$-0.196263\pi$
$701$	30284.7	1.63172	0.815862	+	0.578246i	$0.196263\pi$
$702$	31565.2	1.69708
$703$	−29069.8	−1.55958
$704$	1479.24	0.0791917
$705$	6811.63	0.363888
$706$	8144.64	0.434175
$707$	0	0
$708$	10084.9	0.535329
$709$	−22062.4	−1.16865	−0.584323	−	0.811521i	$-0.698640\pi$
$709$	−22062.4	−1.16865	−0.584323	+	0.811521i	$0.698640\pi$
$710$	−348.646	−0.0184288
$711$	−62170.9	−3.27931
$712$	−708.255	−0.0372795
$713$	8157.56	0.428475
$714$	0	0
$715$	6338.21	0.331519
$716$	−5627.96	−0.293753
$717$	20403.1	1.06272
$718$	4663.53	0.242397
$719$	2572.41	0.133428	0.0667139	−	0.997772i	$-0.478749\pi$
$719$	2572.41	0.133428	0.0667139	+	0.997772i	$0.478749\pi$
$720$	4654.38	0.240914
$721$	0	0
$722$	32267.9	1.66328
$723$	−9513.61	−0.489370
$724$	−12579.7	−0.645745
$725$	−1601.04	−0.0820152
$726$	−14707.5	−0.751853
$727$	−30374.0	−1.54953	−0.774765	−	0.632249i	$-0.782132\pi$
$727$	−30374.0	−1.54953	−0.774765	+	0.632249i	$0.782132\pi$
$728$	0	0
$729$	−8582.14	−0.436018
$730$	10691.0	0.542042
$731$	28392.8	1.43659
$732$	11101.4	0.560547
$733$	−31560.1	−1.59031	−0.795157	−	0.606404i	$-0.792611\pi$
$733$	−31560.1	−1.59031	−0.795157	+	0.606404i	$0.792611\pi$
$734$	−15144.5	−0.761572
$735$	0	0
$736$	−5800.34	−0.290494
$737$	5133.09	0.256553
$738$	55504.0	2.76847
$739$	3254.39	0.161996	0.0809978	−	0.996714i	$-0.474189\pi$
$739$	3254.39	0.161996	0.0809978	+	0.996714i	$0.474189\pi$
$740$	3834.20	0.190470
$741$	−76754.4	−3.80519
$742$	0	0
$743$	−22046.5	−1.08857	−0.544286	−	0.838900i	$-0.683199\pi$
$743$	−22046.5	−1.08857	−0.544286	+	0.838900i	$0.683199\pi$
$744$	−3322.88	−0.163740
$745$	−9461.98	−0.465316
$746$	16540.9	0.811801
$747$	−86032.8	−4.21389
$748$	−4887.28	−0.238899
$749$	0	0
$750$	2307.32	0.112335
$751$	19578.7	0.951312	0.475656	−	0.879631i	$-0.342211\pi$
$751$	19578.7	0.951312	0.475656	+	0.879631i	$0.342211\pi$
$752$	2361.75	0.114527
$753$	63028.9	3.05033
$754$	−7024.73	−0.339291
$755$	16252.9	0.783449
$756$	0	0
$757$	−25823.1	−1.23984	−0.619918	−	0.784666i	$-0.712834\pi$
$757$	−25823.1	−1.23984	−0.619918	+	0.784666i	$0.712834\pi$
$758$	3618.21	0.173377
$759$	−38666.1	−1.84913
$760$	−6065.37	−0.289492
$761$	6737.26	0.320927	0.160464	−	0.987042i	$-0.448701\pi$
$761$	6737.26	0.320927	0.160464	+	0.987042i	$0.448701\pi$
$762$	−11843.7	−0.563061
$763$	0	0
$764$	7384.99	0.349712
$765$	−15377.6	−0.726771
$766$	5740.55	0.270776
$767$	14982.4	0.705322
$768$	2362.70	0.111011
$769$	−19895.7	−0.932974	−0.466487	−	0.884528i	$-0.654481\pi$
$769$	−19895.7	−0.932974	−0.466487	+	0.884528i	$0.654481\pi$
$770$	0	0
$771$	−13047.2	−0.609449
$772$	784.440	0.0365707
$773$	25959.7	1.20790	0.603950	−	0.797022i	$-0.293593\pi$
$773$	25959.7	1.20790	0.603950	+	0.797022i	$0.293593\pi$
$774$	−62497.4	−2.90236
$775$	−1125.11	−0.0521488
$776$	4565.98	0.211223
$777$	0	0
$778$	6167.97	0.284232
$779$	−72330.3	−3.32670
$780$	10123.6	0.464723
$781$	−805.829	−0.0369204
$782$	19163.8	0.876338
$783$	−18429.0	−0.841123
$784$	0	0
$785$	16417.6	0.746458
$786$	−22652.3	−1.02796
$787$	−401.480	−0.0181845	−0.00909225	−	0.999959i	$-0.502894\pi$
$787$	−401.480	−0.0181845	−0.00909225	+	0.999959i	$0.502894\pi$
$788$	−16123.8	−0.728919
$789$	−9139.78	−0.412401
$790$	−10686.0	−0.481255
$791$	0	0
$792$	10757.7	0.482651
$793$	16492.6	0.738548
$794$	−9547.67	−0.426743
$795$	−6871.42	−0.306546
$796$	6634.08	0.295401
$797$	31095.1	1.38199	0.690994	−	0.722860i	$-0.257173\pi$
$797$	31095.1	1.38199	0.690994	+	0.722860i	$0.257173\pi$
$798$	0	0
$799$	−7802.99	−0.345494
$800$	800.000	0.0353553
$801$	−5150.76	−0.227207
$802$	−21926.2	−0.965387
$803$	24710.2	1.08593
$804$	8198.75	0.359637
$805$	0	0
$806$	−4936.56	−0.215736
$807$	43986.1	1.91869
$808$	2832.23	0.123314
$809$	−19535.7	−0.848999	−0.424499	−	0.905428i	$-0.639550\pi$
$809$	−19535.7	−0.848999	−0.424499	+	0.905428i	$0.639550\pi$
$810$	10850.3	0.470667
$811$	1500.96	0.0649888	0.0324944	−	0.999472i	$-0.489655\pi$
$811$	1500.96	0.0649888	0.0324944	+	0.999472i	$0.489655\pi$
$812$	0	0
$813$	1464.91	0.0631940
$814$	8862.03	0.381590
$815$	8013.19	0.344405
$816$	−7806.14	−0.334889
$817$	81443.7	3.48758
$818$	−13732.8	−0.586987
$819$	0	0
$820$	9540.09	0.406286
$821$	−226.486	−0.00962780	−0.00481390	−	0.999988i	$-0.501532\pi$
$821$	−226.486	−0.00962780	−0.00481390	+	0.999988i	$0.501532\pi$
$822$	−22418.0	−0.951237
$823$	−17034.1	−0.721473	−0.360736	−	0.932668i	$-0.617475\pi$
$823$	−17034.1	−0.721473	−0.360736	+	0.932668i	$0.617475\pi$
$824$	−7370.95	−0.311625
$825$	5332.94	0.225054
$826$	0	0
$827$	12424.1	0.522403	0.261201	−	0.965284i	$-0.415881\pi$
$827$	12424.1	0.522403	0.261201	+	0.965284i	$0.415881\pi$
$828$	−42182.8	−1.77047
$829$	−28981.1	−1.21418	−0.607091	−	0.794633i	$-0.707664\pi$
$829$	−28981.1	−1.21418	−0.607091	+	0.794633i	$0.707664\pi$
$830$	−14787.4	−0.618408
$831$	51967.8	2.16937
$832$	3510.09	0.146263
$833$	0	0
$834$	−17520.9	−0.727458
$835$	15435.6	0.639725
$836$	−14019.0	−0.579972
$837$	−12950.8	−0.534822
$838$	−10584.7	−0.436326
$839$	9955.55	0.409659	0.204829	−	0.978798i	$-0.434336\pi$
$839$	9955.55	0.409659	0.204829	+	0.978798i	$0.434336\pi$
$840$	0	0
$841$	−20287.7	−0.831838
$842$	33166.1	1.35746
$843$	12904.8	0.527240
$844$	−18266.3	−0.744965
$845$	4054.94	0.165082
$846$	17175.7	0.698006
$847$	0	0
$848$	−2382.48	−0.0964794
$849$	4570.00	0.184737
$850$	−2643.13	−0.106657
$851$	−34749.4	−1.39976
$852$	−1287.10	−0.0517551
$853$	−30636.2	−1.22973	−0.614867	−	0.788631i	$-0.710790\pi$
$853$	−30636.2	−1.22973	−0.614867	+	0.788631i	$0.710790\pi$
$854$	0	0
$855$	−44110.2	−1.76437
$856$	11760.5	0.469586
$857$	−41569.0	−1.65691	−0.828454	−	0.560058i	$-0.810779\pi$
$857$	−41569.0	−1.65691	−0.828454	+	0.560058i	$0.810779\pi$
$858$	23398.9	0.931031
$859$	−5724.34	−0.227371	−0.113686	−	0.993517i	$-0.536266\pi$
$859$	−5724.34	−0.227371	−0.113686	+	0.993517i	$0.536266\pi$
$860$	−10742.1	−0.425934
$861$	0	0
$862$	−13448.2	−0.531378
$863$	18508.7	0.730064	0.365032	−	0.930995i	$-0.381058\pi$
$863$	18508.7	0.730064	0.365032	+	0.930995i	$0.381058\pi$
$864$	9208.53	0.362593
$865$	4108.81	0.161507
$866$	−4528.30	−0.177688
$867$	−19552.7	−0.765910
$868$	0	0
$869$	−24698.7	−0.964150
$870$	−5910.57	−0.230330
$871$	12180.3	0.473839
$872$	−3785.08	−0.146994
$873$	33206.0	1.28734
$874$	54970.6	2.12747
$875$	0	0
$876$	39468.0	1.52226
$877$	−5777.86	−0.222468	−0.111234	−	0.993794i	$-0.535480\pi$
$877$	−5777.86	−0.222468	−0.111234	+	0.993794i	$0.535480\pi$
$878$	15886.8	0.610654
$879$	67336.6	2.58386
$880$	1849.05	0.0708312
$881$	−7325.11	−0.280124	−0.140062	−	0.990143i	$-0.544730\pi$
$881$	−7325.11	−0.280124	−0.140062	+	0.990143i	$0.544730\pi$
$882$	0	0
$883$	49920.5	1.90256	0.951278	−	0.308334i	$-0.0997716\pi$
$883$	49920.5	1.90256	0.951278	+	0.308334i	$0.0997716\pi$
$884$	−11597.0	−0.441233
$885$	12606.1	0.478813
$886$	8961.82	0.339817
$887$	−19239.3	−0.728288	−0.364144	−	0.931343i	$-0.618638\pi$
$887$	−19239.3	−0.728288	−0.364144	+	0.931343i	$0.618638\pi$
$888$	14154.8	0.534913
$889$	0	0
$890$	−885.319	−0.0333438
$891$	25078.4	0.942938
$892$	12306.0	0.461925
$893$	−22382.6	−0.838751
$894$	−34930.9	−1.30678
$895$	−7034.96	−0.262740
$896$	0	0
$897$	−91750.7	−3.41524
$898$	12291.9	0.456777
$899$	2882.16	0.106925
$900$	5817.97	0.215480
$901$	7871.49	0.291051
$902$	22050.2	0.813958
$903$	0	0
$904$	−5994.18	−0.220535
$905$	−15724.6	−0.577572
$906$	60001.1	2.20022
$907$	38618.3	1.41378	0.706891	−	0.707323i	$-0.250097\pi$
$907$	38618.3	1.41378	0.706891	+	0.707323i	$0.250097\pi$
$908$	−9355.55	−0.341933
$909$	20597.3	0.751560
$910$	0	0
$911$	34404.3	1.25123	0.625613	−	0.780134i	$-0.284849\pi$
$911$	34404.3	1.25123	0.625613	+	0.780134i	$0.284849\pi$
$912$	−22391.6	−0.813005
$913$	−34178.4	−1.23893
$914$	6331.08	0.229118
$915$	13876.8	0.501368
$916$	−13893.1	−0.501138
$917$	0	0
$918$	−30424.2	−1.09384
$919$	17950.3	0.644314	0.322157	−	0.946686i	$-0.395592\pi$
$919$	17950.3	0.644314	0.322157	+	0.946686i	$0.395592\pi$
$920$	−7250.42	−0.259825
$921$	−70545.6	−2.52395
$922$	−2814.38	−0.100528
$923$	−1912.15	−0.0681898
$924$	0	0
$925$	4792.75	0.170362
$926$	−28345.7	−1.00594
$927$	−53605.0	−1.89926
$928$	−2049.33	−0.0724919
$929$	38465.2	1.35845	0.679226	−	0.733929i	$-0.262316\pi$
$929$	38465.2	1.35845	0.679226	+	0.733929i	$0.262316\pi$
$930$	−4153.60	−0.146454
$931$	0	0
$932$	−8392.87	−0.294976
$933$	69950.1	2.45452
$934$	18604.5	0.651777
$935$	−6109.10	−0.213678
$936$	25527.0	0.891427
$937$	36780.1	1.28234	0.641170	−	0.767399i	$-0.278449\pi$
$937$	36780.1	1.28234	0.641170	+	0.767399i	$0.278449\pi$
$938$	0	0
$939$	21050.3	0.731578
$940$	2952.18	0.102436
$941$	16379.7	0.567444	0.283722	−	0.958907i	$-0.408431\pi$
$941$	16379.7	0.567444	0.283722	+	0.958907i	$0.408431\pi$
$942$	60609.1	2.09634
$943$	−86462.1	−2.98578
$944$	4370.82	0.150697
$945$	0	0
$946$	−24828.4	−0.853321
$947$	−28887.8	−0.991264	−0.495632	−	0.868532i	$-0.665064\pi$
$947$	−28887.8	−0.991264	−0.495632	+	0.868532i	$0.665064\pi$
$948$	−39449.7	−1.35155
$949$	58634.8	2.00566
$950$	−7581.71	−0.258930
$951$	1486.82	0.0506977
$952$	0	0
$953$	26340.7	0.895340	0.447670	−	0.894199i	$-0.352254\pi$
$953$	26340.7	0.895340	0.447670	+	0.894199i	$0.352254\pi$
$954$	−17326.5	−0.588014
$955$	9231.24	0.312792
$956$	8842.77	0.299158
$957$	−13661.2	−0.461446
$958$	32229.2	1.08693
$959$	0	0
$960$	2953.37	0.0992913
$961$	−27765.6	−0.932013
$962$	21028.7	0.704774
$963$	85527.9	2.86199
$964$	−4123.23	−0.137759
$965$	980.549	0.0327098
$966$	0	0
$967$	44906.4	1.49338	0.746688	−	0.665175i	$-0.231643\pi$
$967$	44906.4	1.49338	0.746688	+	0.665175i	$0.231643\pi$
$968$	−6374.26	−0.211649
$969$	73979.9	2.45261
$970$	5707.48	0.188924
$971$	41020.2	1.35572	0.677858	−	0.735193i	$-0.262908\pi$
$971$	41020.2	1.35572	0.677858	+	0.735193i	$0.262908\pi$
$972$	8977.34	0.296243
$973$	0	0
$974$	4022.57	0.132332
$975$	12654.5	0.415661
$976$	4811.39	0.157796
$977$	41497.4	1.35887	0.679437	−	0.733733i	$-0.262224\pi$
$977$	41497.4	1.35887	0.679437	+	0.733733i	$0.262224\pi$
$978$	29582.4	0.967220
$979$	−2046.25	−0.0668012
$980$	0	0
$981$	−27526.8	−0.895886
$982$	−7011.30	−0.227841
$983$	−18013.4	−0.584475	−0.292237	−	0.956346i	$-0.594400\pi$
$983$	−18013.4	−0.584475	−0.292237	+	0.956346i	$0.594400\pi$
$984$	35219.3	1.14101
$985$	−20154.8	−0.651965
$986$	6770.80	0.218688
$987$	0	0
$988$	−33265.6	−1.07117
$989$	97356.2	3.13018
$990$	13447.2	0.431696
$991$	54047.3	1.73246	0.866231	−	0.499644i	$-0.166536\pi$
$991$	54047.3	1.73246	0.866231	+	0.499644i	$0.166536\pi$
$992$	−1440.15	−0.0460935
$993$	29395.2	0.939403
$994$	0	0
$995$	8292.61	0.264214
$996$	−54590.9	−1.73673
$997$	−9312.38	−0.295814	−0.147907	−	0.989001i	$-0.547254\pi$
$997$	−9312.38	−0.295814	−0.147907	+	0.989001i	$0.547254\pi$
$998$	10287.6	0.326302
$999$	55167.7	1.74718

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.a.y.1.4	yes	4
5.4	even	2		2450.4.a.cj.1.1		4
7.2	even	3		490.4.e.z.361.1		8
7.3	odd	6		490.4.e.ba.471.4		8
7.4	even	3		490.4.e.z.471.1		8
7.5	odd	6		490.4.e.ba.361.4		8
7.6	odd	2		490.4.a.x.1.1	✓	4
35.34	odd	2		2450.4.a.cp.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.4.a.x.1.1	✓	4	7.6	odd	2
490.4.a.y.1.4	yes	4	1.1	even	1	trivial
490.4.e.z.361.1		8	7.2	even	3
490.4.e.z.471.1		8	7.4	even	3
490.4.e.ba.361.4		8	7.5	odd	6
490.4.e.ba.471.4		8	7.3	odd	6
2450.4.a.cj.1.1		4	5.4	even	2
2450.4.a.cp.1.4		4	35.34	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	490.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +9.22929 q^{3} +4.00000 q^{4} +5.00000 q^{5} +18.4586 q^{6} +8.00000 q^{8} +58.1797 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +9.22929 q^{3} +4.00000 q^{4} +5.00000 q^{5} +18.4586 q^{6} +8.00000 q^{8} +58.1797 q^{9} +10.0000 q^{10} +23.1131 q^{11} +36.9171 q^{12} +54.8451 q^{13} +46.1464 q^{15} +16.0000 q^{16} -52.8626 q^{17} +116.359 q^{18} -151.634 q^{19} +20.0000 q^{20} +46.2263 q^{22} -181.261 q^{23} +73.8343 q^{24} +25.0000 q^{25} +109.690 q^{26} +287.767 q^{27} -64.0415 q^{29} +92.2929 q^{30} -45.0046 q^{31} +32.0000 q^{32} +213.318 q^{33} -105.725 q^{34} +232.719 q^{36} +191.710 q^{37} -303.269 q^{38} +506.181 q^{39} +40.0000 q^{40} +477.005 q^{41} -537.106 q^{43} +92.4525 q^{44} +290.899 q^{45} -362.521 q^{46} +147.609 q^{47} +147.669 q^{48} +50.0000 q^{50} -487.884 q^{51} +219.381 q^{52} -148.905 q^{53} +575.533 q^{54} +115.566 q^{55} -1399.48 q^{57} -128.083 q^{58} +273.176 q^{59} +184.586 q^{60} +300.712 q^{61} -90.0092 q^{62} +64.0000 q^{64} +274.226 q^{65} +426.636 q^{66} +222.085 q^{67} -211.450 q^{68} -1672.91 q^{69} -34.8646 q^{71} +465.438 q^{72} +1069.10 q^{73} +383.420 q^{74} +230.732 q^{75} -606.537 q^{76} +1012.36 q^{78} -1068.60 q^{79} +80.0000 q^{80} +1085.03 q^{81} +954.009 q^{82} -1478.74 q^{83} -264.313 q^{85} -1074.21 q^{86} -591.057 q^{87} +184.905 q^{88} -88.5319 q^{89} +581.797 q^{90} -725.042 q^{92} -415.360 q^{93} +295.218 q^{94} -758.171 q^{95} +295.337 q^{96} +570.748 q^{97} +1344.72 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} + 10 q^{3} + 16 q^{4} + 20 q^{5} + 20 q^{6} + 32 q^{8} + 38 q^{9}+O(q^{10}) \) 4 * q + 8 * q^2 + 10 * q^3 + 16 * q^4 + 20 * q^5 + 20 * q^6 + 32 * q^8 + 38 * q^9	\( 4 q + 8 q^{2} + 10 q^{3} + 16 q^{4} + 20 q^{5} + 20 q^{6} + 32 q^{8} + 38 q^{9} + 40 q^{10} + 18 q^{11} + 40 q^{12} + 130 q^{13} + 50 q^{15} + 64 q^{16} + 110 q^{17} + 76 q^{18} + 40 q^{19} + 80 q^{20} + 36 q^{22} - 164 q^{23} + 80 q^{24} + 100 q^{25} + 260 q^{26} + 430 q^{27} + 94 q^{29} + 100 q^{30} + 180 q^{31} + 128 q^{32} + 650 q^{33} + 220 q^{34} + 152 q^{36} + 16 q^{37} + 80 q^{38} - 10 q^{39} + 160 q^{40} + 540 q^{41} - 560 q^{43} + 72 q^{44} + 190 q^{45} - 328 q^{46} + 1150 q^{47} + 160 q^{48} + 200 q^{50} - 926 q^{51} + 520 q^{52} - 244 q^{53} + 860 q^{54} + 90 q^{55} - 840 q^{57} + 188 q^{58} + 400 q^{59} + 200 q^{60} + 1540 q^{61} + 360 q^{62} + 256 q^{64} + 650 q^{65} + 1300 q^{66} - 760 q^{67} + 440 q^{68} - 1480 q^{69} + 52 q^{71} + 304 q^{72} + 800 q^{73} + 32 q^{74} + 250 q^{75} + 160 q^{76} - 20 q^{78} + 398 q^{79} + 320 q^{80} + 348 q^{81} + 1080 q^{82} - 1220 q^{83} + 550 q^{85} - 1120 q^{86} - 930 q^{87} + 144 q^{88} + 200 q^{89} + 380 q^{90} - 656 q^{92} + 1408 q^{93} + 2300 q^{94} + 200 q^{95} + 320 q^{96} - 670 q^{97} + 2292 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 + 10 * q^3 + 16 * q^4 + 20 * q^5 + 20 * q^6 + 32 * q^8 + 38 * q^9 + 40 * q^10 + 18 * q^11 + 40 * q^12 + 130 * q^13 + 50 * q^15 + 64 * q^16 + 110 * q^17 + 76 * q^18 + 40 * q^19 + 80 * q^20 + 36 * q^22 - 164 * q^23 + 80 * q^24 + 100 * q^25 + 260 * q^26 + 430 * q^27 + 94 * q^29 + 100 * q^30 + 180 * q^31 + 128 * q^32 + 650 * q^33 + 220 * q^34 + 152 * q^36 + 16 * q^37 + 80 * q^38 - 10 * q^39 + 160 * q^40 + 540 * q^41 - 560 * q^43 + 72 * q^44 + 190 * q^45 - 328 * q^46 + 1150 * q^47 + 160 * q^48 + 200 * q^50 - 926 * q^51 + 520 * q^52 - 244 * q^53 + 860 * q^54 + 90 * q^55 - 840 * q^57 + 188 * q^58 + 400 * q^59 + 200 * q^60 + 1540 * q^61 + 360 * q^62 + 256 * q^64 + 650 * q^65 + 1300 * q^66 - 760 * q^67 + 440 * q^68 - 1480 * q^69 + 52 * q^71 + 304 * q^72 + 800 * q^73 + 32 * q^74 + 250 * q^75 + 160 * q^76 - 20 * q^78 + 398 * q^79 + 320 * q^80 + 348 * q^81 + 1080 * q^82 - 1220 * q^83 + 550 * q^85 - 1120 * q^86 - 930 * q^87 + 144 * q^88 + 200 * q^89 + 380 * q^90 - 656 * q^92 + 1408 * q^93 + 2300 * q^94 + 200 * q^95 + 320 * q^96 - 670 * q^97 + 2292 * q^99

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