LMFDB - Embedded newform 490.4.a.x.1.1

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:	$1$
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			1.1
Root			$4.40086$ 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	$-0.847967\pi$
$3$	−9.22929	−1.77618	−0.888089	+	0.459673i	$0.847967\pi$
$4$	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	$-0.698925\pi$
$13$	−54.8451	−1.17010	−0.585050	+	0.810997i	$0.698925\pi$
$14$	0	0
$15$	46.1464	0.794331
$16$	16.0000	0.250000
$17$	52.8626	0.754180	0.377090	−	0.926177i	$-0.376925\pi$
$17$	52.8626	0.754180	0.377090	+	0.926177i	$0.376925\pi$
$18$	116.359	1.52368
$19$	151.634	1.83091	0.915455	−	0.402421i	$-0.131831\pi$
$19$	151.634	1.83091	0.915455	+	0.402421i	$0.131831\pi$
$20$	−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	$-0.458383\pi$
$31$	45.0046	0.260744	0.130372	+	0.991465i	$0.458383\pi$
$32$	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	$-0.862759\pi$
$41$	−477.005	−1.81697	−0.908483	+	0.417921i	$0.862759\pi$
$42$	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	$-0.573563\pi$
$47$	−147.609	−0.458106	−0.229053	+	0.973414i	$0.573563\pi$
$48$	−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	$-0.597452\pi$
$59$	−273.176	−0.602788	−0.301394	+	0.953500i	$0.597452\pi$
$60$	184.586	0.397165
$61$	−300.712	−0.631184	−0.315592	−	0.948895i	$-0.602203\pi$
$61$	−300.712	−0.631184	−0.315592	+	0.948895i	$0.602203\pi$
$62$	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	$-0.827702\pi$
$73$	−1069.10	−1.71409	−0.857044	+	0.515243i	$0.827702\pi$
$74$	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	$-0.0672133\pi$
$83$	1478.74	1.95558	0.977789	+	0.209591i	$0.0672133\pi$
$84$	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	$-0.483211\pi$
$89$	88.5319	0.105442	0.0527211	+	0.998609i	$0.483211\pi$
$90$	−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	$-0.596558\pi$
$97$	−570.748	−0.597429	−0.298715	+	0.954342i	$0.596558\pi$
$98$	0	0
$99$	1344.72	1.36514
$100$	100.000	0.100000
$101$	−354.028	−0.348783	−0.174392	−	0.984676i	$-0.555796\pi$
$101$	−354.028	−0.348783	−0.174392	+	0.984676i	$0.555796\pi$
$102$	−975.768	−0.947210
$103$	921.368	0.881409	0.440704	−	0.897652i	$-0.354729\pi$
$103$	921.368	0.881409	0.440704	+	0.897652i	$0.354729\pi$
$104$	−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	$-0.365794\pi$
$131$	1227.20	0.818478	0.409239	+	0.912427i	$0.365794\pi$
$132$	−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	$-0.406476\pi$
$139$	949.203	0.579211	0.289605	+	0.957146i	$0.406476\pi$
$140$	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	$-0.814281\pi$
$157$	−3283.52	−1.66913	−0.834566	+	0.550908i	$0.814281\pi$
$158$	−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	$-0.753680\pi$
$167$	−3087.12	−1.43047	−0.715234	+	0.698885i	$0.753680\pi$
$168$	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	$-0.557794\pi$
$173$	−821.763	−0.361141	−0.180571	+	0.983562i	$0.557794\pi$
$174$	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	$-0.276547\pi$
$181$	3144.92	1.29149	0.645745	+	0.763553i	$0.276547\pi$
$182$	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	$-0.595453\pi$
$199$	−1658.52	−0.590801	−0.295401	+	0.955373i	$0.595453\pi$
$200$	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	$-0.652841\pi$
$223$	−3076.51	−0.923850	−0.461925	+	0.886919i	$0.652841\pi$
$224$	0	0
$225$	1454.49	0.430961
$226$	−1498.54	−0.441069
$227$	2338.89	0.683865	0.341933	−	0.939724i	$-0.388919\pi$
$227$	2338.89	0.683865	0.341933	+	0.939724i	$0.388919\pi$
$228$	−5597.90	−1.62601
$229$	3473.28	1.00228	0.501138	−	0.865368i	$-0.332915\pi$
$229$	3473.28	1.00228	0.501138	+	0.865368i	$0.332915\pi$
$230$	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	$-0.456010\pi$
$241$	1030.81	0.275519	0.137759	+	0.990466i	$0.456010\pi$
$242$	−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	$-0.828715\pi$
$251$	−6829.23	−1.71736	−0.858680	+	0.512513i	$0.828715\pi$
$252$	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	$-0.445119\pi$
$257$	1413.68	0.343124	0.171562	+	0.985173i	$0.445119\pi$
$258$	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	$-0.681620\pi$
$269$	−4765.92	−1.08024	−0.540118	+	0.841589i	$0.681620\pi$
$270$	2877.67	0.648627
$271$	−158.724	−0.0355786	−0.0177893	−	0.999842i	$-0.505663\pi$
$271$	−158.724	−0.0355786	−0.0177893	+	0.999842i	$0.505663\pi$
$272$	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	$-0.516561\pi$
$283$	−495.163	−0.104008	−0.0520042	+	0.998647i	$0.516561\pi$
$284$	−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	$-0.759255\pi$
$293$	−7295.98	−1.45473	−0.727364	+	0.686252i	$0.759255\pi$
$294$	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	$-0.248469\pi$
$307$	7643.67	1.42100	0.710500	+	0.703697i	$0.248469\pi$
$308$	0	0
$309$	−8503.57	−1.56554
$310$	−450.046	−0.0824545
$311$	−7579.14	−1.38191	−0.690955	−	0.722898i	$-0.742810\pi$
$311$	−7579.14	−1.38191	−0.690955	+	0.722898i	$0.742810\pi$
$312$	4049.45	0.734792
$313$	−2280.82	−0.411883	−0.205942	−	0.978564i	$-0.566026\pi$
$313$	−2280.82	−0.411883	−0.205942	+	0.978564i	$0.566026\pi$
$314$	−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	$-0.699811\pi$
$349$	−7658.29	−1.17461	−0.587305	+	0.809366i	$0.699811\pi$
$350$	0	0
$351$	15782.6	2.40004
$352$	739.620	0.111994
$353$	−4072.32	−0.614016	−0.307008	−	0.951707i	$-0.599328\pi$
$353$	−4072.32	−0.614016	−0.307008	+	0.951707i	$0.599328\pi$
$354$	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	$-0.318986\pi$
$367$	7572.25	1.07703	0.538513	+	0.842617i	$0.318986\pi$
$368$	−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	$-0.561325\pi$
$383$	−2870.28	−0.382936	−0.191468	+	0.981499i	$0.561325\pi$
$384$	−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	$-0.402428\pi$
$397$	4773.83	0.603506	0.301753	+	0.953386i	$0.402428\pi$
$398$	−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	$-0.363760\pi$
$409$	6866.38	0.830124	0.415062	+	0.909793i	$0.363760\pi$
$410$	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	$-0.400163\pi$
$419$	5292.33	0.617058	0.308529	+	0.951215i	$0.400163\pi$
$420$	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	$-0.459900\pi$
$433$	2264.15	0.251289	0.125645	+	0.992075i	$0.459900\pi$
$434$	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	$-0.642121\pi$
$439$	−7943.41	−0.863595	−0.431798	+	0.901971i	$0.642121\pi$
$440$	−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	$-0.477354\pi$
$461$	1407.19	0.142168	0.0710840	+	0.997470i	$0.477354\pi$
$462$	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	$-0.652465\pi$
$467$	−9302.27	−0.921751	−0.460876	+	0.887465i	$0.652465\pi$
$468$	−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	$-0.779033\pi$
$479$	−16114.6	−1.53715	−0.768574	+	0.639761i	$0.779033\pi$
$480$	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	$-0.447528\pi$
$503$	3702.47	0.328201	0.164100	+	0.986444i	$0.447528\pi$
$504$	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	$-0.691110\pi$
$509$	−12975.6	−1.12993	−0.564963	+	0.825116i	$0.691110\pi$
$510$	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	$-0.429166\pi$
$521$	5249.10	0.441396	0.220698	+	0.975342i	$0.429166\pi$
$522$	−7451.83	−0.624824
$523$	−714.405	−0.0597299	−0.0298650	−	0.999554i	$-0.509508\pi$
$523$	−714.405	−0.0597299	−0.0298650	+	0.999554i	$0.509508\pi$
$524$	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	$-0.315615\pi$
$563$	14625.2	1.09481	0.547406	+	0.836867i	$0.315615\pi$
$564$	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	$-0.388244\pi$
$577$	9533.58	0.687848	0.343924	+	0.938997i	$0.388244\pi$
$578$	−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	$-0.688490\pi$
$587$	−15876.0	−1.11631	−0.558155	+	0.829737i	$0.688490\pi$
$588$	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	$-0.276411\pi$
$593$	18659.2	1.29214	0.646071	+	0.763277i	$0.276411\pi$
$594$	−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	$-0.430211\pi$
$601$	6409.03	0.434991	0.217496	+	0.976061i	$0.430211\pi$
$602$	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	$-0.381797\pi$
$607$	10853.4	0.725741	0.362870	+	0.931840i	$0.381797\pi$
$608$	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	$-0.493450\pi$
$619$	633.763	0.0411520	0.0205760	+	0.999788i	$0.493450\pi$
$620$	−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	$-0.313658\pi$
$643$	18018.2	1.10508	0.552541	+	0.833486i	$0.313658\pi$
$644$	0	0
$645$	−24785.5	−1.51307
$646$	16031.6	0.976398
$647$	−17892.6	−1.08722	−0.543611	−	0.839337i	$-0.682943\pi$
$647$	−17892.6	−1.08722	−0.543611	+	0.839337i	$0.682943\pi$
$648$	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	$-0.652644\pi$
$661$	−15681.5	−0.922754	−0.461377	+	0.887204i	$0.652644\pi$
$662$	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	$-0.611660\pi$
$677$	−12106.5	−0.687282	−0.343641	+	0.939101i	$0.611660\pi$
$678$	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	$-0.347729\pi$
$691$	16723.3	0.920674	0.460337	+	0.887744i	$0.347729\pi$
$692$	−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	$-0.521251\pi$
$719$	−2572.41	−0.133428	−0.0667139	+	0.997772i	$0.521251\pi$
$720$	−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	$-0.217868\pi$
$727$	30374.0	1.54953	0.774765	+	0.632249i	$0.217868\pi$
$728$	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	$-0.207389\pi$
$733$	31560.1	1.59031	0.795157	+	0.606404i	$0.207389\pi$
$734$	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	$-0.551299\pi$
$761$	−6737.26	−0.320927	−0.160464	+	0.987042i	$0.551299\pi$
$762$	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	$-0.345519\pi$
$769$	19895.7	0.932974	0.466487	+	0.884528i	$0.345519\pi$
$770$	0	0
$771$	−13047.2	−0.609449
$772$	784.440	0.0365707
$773$	−25959.7	−1.20790	−0.603950	−	0.797022i	$-0.706407\pi$
$773$	−25959.7	−1.20790	−0.603950	+	0.797022i	$0.706407\pi$
$774$	−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	$-0.497106\pi$
$787$	401.480	0.0181845	0.00909225	+	0.999959i	$0.497106\pi$
$788$	−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	$-0.742827\pi$
$797$	−31095.1	−1.38199	−0.690994	+	0.722860i	$0.742827\pi$
$798$	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	$-0.510345\pi$
$811$	−1500.96	−0.0649888	−0.0324944	+	0.999472i	$0.510345\pi$
$812$	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	$-0.292336\pi$
$829$	28981.1	1.21418	0.607091	+	0.794633i	$0.292336\pi$
$830$	−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	$-0.565664\pi$
$839$	−9955.55	−0.409659	−0.204829	+	0.978798i	$0.565664\pi$
$840$	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	$-0.289210\pi$
$853$	30636.2	1.22973	0.614867	+	0.788631i	$0.289210\pi$
$854$	0	0
$855$	−44110.2	−1.76437
$856$	11760.5	0.469586
$857$	41569.0	1.65691	0.828454	−	0.560058i	$-0.189221\pi$
$857$	41569.0	1.65691	0.828454	+	0.560058i	$0.189221\pi$
$858$	23398.9	0.931031
$859$	5724.34	0.227371	0.113686	−	0.993517i	$-0.463734\pi$
$859$	5724.34	0.227371	0.113686	+	0.993517i	$0.463734\pi$
$860$	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	$-0.455270\pi$
$881$	7325.11	0.280124	0.140062	+	0.990143i	$0.455270\pi$
$882$	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	$-0.381362\pi$
$887$	19239.3	0.728288	0.364144	+	0.931343i	$0.381362\pi$
$888$	−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	$-0.737684\pi$
$929$	−38465.2	−1.35845	−0.679226	+	0.733929i	$0.737684\pi$
$930$	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	$-0.721551\pi$
$937$	−36780.1	−1.28234	−0.641170	+	0.767399i	$0.721551\pi$
$938$	0	0
$939$	21050.3	0.731578
$940$	2952.18	0.102436
$941$	−16379.7	−0.567444	−0.283722	−	0.958907i	$-0.591569\pi$
$941$	−16379.7	−0.567444	−0.283722	+	0.958907i	$0.591569\pi$
$942$	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	$-0.737092\pi$
$971$	−41020.2	−1.35572	−0.677858	+	0.735193i	$0.737092\pi$
$972$	−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	$-0.405600\pi$
$983$	18013.4	0.584475	0.292237	+	0.956346i	$0.405600\pi$
$984$	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	$-0.452746\pi$
$997$	9312.38	0.295814	0.147907	+	0.989001i	$0.452746\pi$
$998$	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.x.1.1	✓	4
5.4	even	2		2450.4.a.cp.1.4		4
7.2	even	3		490.4.e.ba.361.4		8
7.3	odd	6		490.4.e.z.471.1		8
7.4	even	3		490.4.e.ba.471.4		8
7.5	odd	6		490.4.e.z.361.1		8
7.6	odd	2		490.4.a.y.1.4	yes	4
35.34	odd	2		2450.4.a.cj.1.1		4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
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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