LMFDB - Embedded newform 490.4.a.v.1.2

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:	$3$
Coefficient field:	3.3.115880.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 66x + 90 $ x^3 - x^2 - 66*x + 90
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.37435$ 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)

$f(q)$	$=$	$q+2.00000 q^{2} -2.37435 q^{3} +4.00000 q^{4} -5.00000 q^{5} -4.74870 q^{6} +8.00000 q^{8} -21.3625 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -2.37435 q^{3} +4.00000 q^{4} -5.00000 q^{5} -4.74870 q^{6} +8.00000 q^{8} -21.3625 q^{9} -10.0000 q^{10} +49.8651 q^{11} -9.49740 q^{12} -42.1112 q^{13} +11.8717 q^{15} +16.0000 q^{16} -22.4922 q^{17} -42.7249 q^{18} +106.836 q^{19} -20.0000 q^{20} +99.7301 q^{22} +189.200 q^{23} -18.9948 q^{24} +25.0000 q^{25} -84.2223 q^{26} +114.829 q^{27} -52.5744 q^{29} +23.7435 q^{30} -154.199 q^{31} +32.0000 q^{32} -118.397 q^{33} -44.9844 q^{34} -85.4499 q^{36} +317.609 q^{37} +213.672 q^{38} +99.9866 q^{39} -40.0000 q^{40} -145.500 q^{41} +427.284 q^{43} +199.460 q^{44} +106.812 q^{45} +378.400 q^{46} +498.805 q^{47} -37.9896 q^{48} +50.0000 q^{50} +53.4043 q^{51} -168.445 q^{52} -524.170 q^{53} +229.659 q^{54} -249.325 q^{55} -253.666 q^{57} -105.149 q^{58} +310.413 q^{59} +47.4870 q^{60} +653.519 q^{61} -308.397 q^{62} +64.0000 q^{64} +210.556 q^{65} -236.794 q^{66} +403.740 q^{67} -89.9688 q^{68} -449.227 q^{69} +199.303 q^{71} -170.900 q^{72} +222.207 q^{73} +635.217 q^{74} -59.3587 q^{75} +427.344 q^{76} +199.973 q^{78} +34.7398 q^{79} -80.0000 q^{80} +304.141 q^{81} -290.999 q^{82} -679.483 q^{83} +112.461 q^{85} +854.569 q^{86} +124.830 q^{87} +398.921 q^{88} -1051.75 q^{89} +213.625 q^{90} +756.800 q^{92} +366.121 q^{93} +997.610 q^{94} -534.180 q^{95} -75.9792 q^{96} -69.1939 q^{97} -1065.24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6 q^{2} - 4 q^{3} + 12 q^{4} - 15 q^{5} - 8 q^{6} + 24 q^{8} + 57 q^{9}+O(q^{10}) $ 3 * q + 6 * q^2 - 4 * q^3 + 12 * q^4 - 15 * q^5 - 8 * q^6 + 24 * q^8 + 57 * q^9	\( 3 q + 6 q^{2} - 4 q^{3} + 12 q^{4} - 15 q^{5} - 8 q^{6} + 24 q^{8} + 57 q^{9} - 30 q^{10} + 41 q^{11} - 16 q^{12} + q^{13} + 20 q^{15} + 48 q^{16} - 30 q^{17} + 114 q^{18} - 49 q^{19} - 60 q^{20} + 82 q^{22} + 145 q^{23} - 32 q^{24} + 75 q^{25} + 2 q^{26} - 118 q^{27} + 268 q^{29} + 40 q^{30} + 28 q^{31} + 96 q^{32} + 626 q^{33} - 60 q^{34} + 228 q^{36} + 813 q^{37} - 98 q^{38} + 114 q^{39} - 120 q^{40} - 313 q^{41} + 360 q^{43} + 164 q^{44} - 285 q^{45} + 290 q^{46} + 977 q^{47} - 64 q^{48} + 150 q^{50} + 1632 q^{51} + 4 q^{52} + 325 q^{53} - 236 q^{54} - 205 q^{55} + 250 q^{57} + 536 q^{58} + 272 q^{59} + 80 q^{60} + 902 q^{61} + 56 q^{62} + 192 q^{64} - 5 q^{65} + 1252 q^{66} - 170 q^{67} - 120 q^{68} - 2264 q^{69} - 1080 q^{71} + 456 q^{72} + 584 q^{73} + 1626 q^{74} - 100 q^{75} - 196 q^{76} + 228 q^{78} - 310 q^{79} - 240 q^{80} + 147 q^{81} - 626 q^{82} - 626 q^{83} + 150 q^{85} + 720 q^{86} + 1846 q^{87} + 328 q^{88} + 400 q^{89} - 570 q^{90} + 580 q^{92} - 372 q^{93} + 1954 q^{94} + 245 q^{95} - 128 q^{96} - 1626 q^{97} - 2611 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 4 * q^3 + 12 * q^4 - 15 * q^5 - 8 * q^6 + 24 * q^8 + 57 * q^9 - 30 * q^10 + 41 * q^11 - 16 * q^12 + q^13 + 20 * q^15 + 48 * q^16 - 30 * q^17 + 114 * q^18 - 49 * q^19 - 60 * q^20 + 82 * q^22 + 145 * q^23 - 32 * q^24 + 75 * q^25 + 2 * q^26 - 118 * q^27 + 268 * q^29 + 40 * q^30 + 28 * q^31 + 96 * q^32 + 626 * q^33 - 60 * q^34 + 228 * q^36 + 813 * q^37 - 98 * q^38 + 114 * q^39 - 120 * q^40 - 313 * q^41 + 360 * q^43 + 164 * q^44 - 285 * q^45 + 290 * q^46 + 977 * q^47 - 64 * q^48 + 150 * q^50 + 1632 * q^51 + 4 * q^52 + 325 * q^53 - 236 * q^54 - 205 * q^55 + 250 * q^57 + 536 * q^58 + 272 * q^59 + 80 * q^60 + 902 * q^61 + 56 * q^62 + 192 * q^64 - 5 * q^65 + 1252 * q^66 - 170 * q^67 - 120 * q^68 - 2264 * q^69 - 1080 * q^71 + 456 * q^72 + 584 * q^73 + 1626 * q^74 - 100 * q^75 - 196 * q^76 + 228 * q^78 - 310 * q^79 - 240 * q^80 + 147 * q^81 - 626 * q^82 - 626 * q^83 + 150 * q^85 + 720 * q^86 + 1846 * q^87 + 328 * q^88 + 400 * q^89 - 570 * q^90 + 580 * q^92 - 372 * q^93 + 1954 * q^94 + 245 * q^95 - 128 * q^96 - 1626 * q^97 - 2611 * 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
$3$	−2.37435	−0.456944	−0.228472	−	0.973551i	$-0.573373\pi$
$3$	−2.37435	−0.456944	−0.228472	+	0.973551i	$0.573373\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−4.74870	−0.323108
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	−21.3625	−0.791202
$10$	−10.0000	−0.316228
$11$	49.8651	1.36681	0.683404	−	0.730041i	$-0.260499\pi$
$11$	49.8651	1.36681	0.683404	+	0.730041i	$0.260499\pi$
$12$	−9.49740	−0.228472
$13$	−42.1112	−0.898426	−0.449213	−	0.893425i	$-0.648296\pi$
$13$	−42.1112	−0.898426	−0.449213	+	0.893425i	$0.648296\pi$
$14$	0	0
$15$	11.8717	0.204351
$16$	16.0000	0.250000
$17$	−22.4922	−0.320892	−0.160446	−	0.987045i	$-0.551293\pi$
$17$	−22.4922	−0.320892	−0.160446	+	0.987045i	$0.551293\pi$
$18$	−42.7249	−0.559465
$19$	106.836	1.28999	0.644997	−	0.764185i	$-0.276859\pi$
$19$	106.836	1.28999	0.644997	+	0.764185i	$0.276859\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	99.7301	0.966479
$23$	189.200	1.71526	0.857629	−	0.514269i	$-0.171937\pi$
$23$	189.200	1.71526	0.857629	+	0.514269i	$0.171937\pi$
$24$	−18.9948	−0.161554
$25$	25.0000	0.200000
$26$	−84.2223	−0.635283
$27$	114.829	0.818479
$28$	0	0
$29$	−52.5744	−0.336649	−0.168324	−	0.985732i	$-0.553836\pi$
$29$	−52.5744	−0.336649	−0.168324	+	0.985732i	$0.553836\pi$
$30$	23.7435	0.144498
$31$	−154.199	−0.893383	−0.446692	−	0.894688i	$-0.647398\pi$
$31$	−154.199	−0.893383	−0.446692	+	0.894688i	$0.647398\pi$
$32$	32.0000	0.176777
$33$	−118.397	−0.624554
$34$	−44.9844	−0.226905
$35$	0	0
$36$	−85.4499	−0.395601
$37$	317.609	1.41120	0.705602	−	0.708609i	$-0.250677\pi$
$37$	317.609	1.41120	0.705602	+	0.708609i	$0.250677\pi$
$38$	213.672	0.912163
$39$	99.9866	0.410530
$40$	−40.0000	−0.158114
$41$	−145.500	−0.554225	−0.277113	−	0.960837i	$-0.589377\pi$
$41$	−145.500	−0.554225	−0.277113	+	0.960837i	$0.589377\pi$
$42$	0	0
$43$	427.284	1.51536	0.757678	−	0.652629i	$-0.226334\pi$
$43$	427.284	1.51536	0.757678	+	0.652629i	$0.226334\pi$
$44$	199.460	0.683404
$45$	106.812	0.353836
$46$	378.400	1.21287
$47$	498.805	1.54805	0.774023	−	0.633157i	$-0.218241\pi$
$47$	498.805	1.54805	0.774023	+	0.633157i	$0.218241\pi$
$48$	−37.9896	−0.114236
$49$	0	0
$50$	50.0000	0.141421
$51$	53.4043	0.146629
$52$	−168.445	−0.449213
$53$	−524.170	−1.35850	−0.679248	−	0.733909i	$-0.737694\pi$
$53$	−524.170	−1.35850	−0.679248	+	0.733909i	$0.737694\pi$
$54$	229.659	0.578752
$55$	−249.325	−0.611255
$56$	0	0
$57$	−253.666	−0.589455
$58$	−105.149	−0.238047
$59$	310.413	0.684956	0.342478	−	0.939526i	$-0.388734\pi$
$59$	310.413	0.684956	0.342478	+	0.939526i	$0.388734\pi$
$60$	47.4870	0.102176
$61$	653.519	1.37171	0.685856	−	0.727737i	$-0.259428\pi$
$61$	653.519	1.37171	0.685856	+	0.727737i	$0.259428\pi$
$62$	−308.397	−0.631717
$63$	0	0
$64$	64.0000	0.125000
$65$	210.556	0.401788
$66$	−236.794	−0.441627
$67$	403.740	0.736189	0.368094	−	0.929788i	$-0.380010\pi$
$67$	403.740	0.736189	0.368094	+	0.929788i	$0.380010\pi$
$68$	−89.9688	−0.160446
$69$	−449.227	−0.783777
$70$	0	0
$71$	199.303	0.333139	0.166570	−	0.986030i	$-0.446731\pi$
$71$	199.303	0.333139	0.166570	+	0.986030i	$0.446731\pi$
$72$	−170.900	−0.279732
$73$	222.207	0.356266	0.178133	−	0.984006i	$-0.442994\pi$
$73$	222.207	0.356266	0.178133	+	0.984006i	$0.442994\pi$
$74$	635.217	0.997871
$75$	−59.3587	−0.0913888
$76$	427.344	0.644997
$77$	0	0
$78$	199.973	0.290289
$79$	34.7398	0.0494751	0.0247375	−	0.999694i	$-0.492125\pi$
$79$	34.7398	0.0494751	0.0247375	+	0.999694i	$0.492125\pi$
$80$	−80.0000	−0.111803
$81$	304.141	0.417203
$82$	−290.999	−0.391896
$83$	−679.483	−0.898590	−0.449295	−	0.893384i	$-0.648325\pi$
$83$	−679.483	−0.898590	−0.449295	+	0.893384i	$0.648325\pi$
$84$	0	0
$85$	112.461	0.143507
$86$	854.569	1.07152
$87$	124.830	0.153830
$88$	398.921	0.483239
$89$	−1051.75	−1.25265	−0.626323	−	0.779564i	$-0.715441\pi$
$89$	−1051.75	−1.25265	−0.626323	+	0.779564i	$0.715441\pi$
$90$	213.625	0.250200
$91$	0	0
$92$	756.800	0.857629
$93$	366.121	0.408226
$94$	997.610	1.09463
$95$	−534.180	−0.576903
$96$	−75.9792	−0.0807770
$97$	−69.1939	−0.0724286	−0.0362143	−	0.999344i	$-0.511530\pi$
$97$	−69.1939	−0.0724286	−0.0362143	+	0.999344i	$0.511530\pi$
$98$	0	0
$99$	−1065.24	−1.08142
$100$	100.000	0.100000
$101$	1400.59	1.37984	0.689922	−	0.723884i	$-0.257645\pi$
$101$	1400.59	1.37984	0.689922	+	0.723884i	$0.257645\pi$
$102$	106.809	0.103683
$103$	154.878	0.148161	0.0740804	−	0.997252i	$-0.476398\pi$
$103$	154.878	0.148161	0.0740804	+	0.997252i	$0.476398\pi$
$104$	−336.889	−0.317641
$105$	0	0
$106$	−1048.34	−0.960602
$107$	23.8049	0.0215075	0.0107537	−	0.999942i	$-0.496577\pi$
$107$	23.8049	0.0215075	0.0107537	+	0.999942i	$0.496577\pi$
$108$	459.318	0.409239
$109$	173.703	0.152640	0.0763198	−	0.997083i	$-0.475683\pi$
$109$	173.703	0.152640	0.0763198	+	0.997083i	$0.475683\pi$
$110$	−498.651	−0.432222
$111$	−754.114	−0.644841
$112$	0	0
$113$	−757.568	−0.630672	−0.315336	−	0.948980i	$-0.602117\pi$
$113$	−757.568	−0.630672	−0.315336	+	0.948980i	$0.602117\pi$
$114$	−507.332	−0.416807
$115$	−946.000	−0.767087
$116$	−210.298	−0.168324
$117$	899.598	0.710837
$118$	620.827	0.484337
$119$	0	0
$120$	94.9740	0.0722492
$121$	1155.52	0.868163
$122$	1307.04	0.969948
$123$	345.467	0.253250
$124$	−616.794	−0.446692
$125$	−125.000	−0.0894427
$126$	0	0
$127$	−373.607	−0.261041	−0.130521	−	0.991446i	$-0.541665\pi$
$127$	−373.607	−0.261041	−0.130521	+	0.991446i	$0.541665\pi$
$128$	128.000	0.0883883
$129$	−1014.52	−0.692432
$130$	421.112	0.284107
$131$	1374.32	0.916600	0.458300	−	0.888797i	$-0.348458\pi$
$131$	1374.32	0.916600	0.458300	+	0.888797i	$0.348458\pi$
$132$	−473.588	−0.312277
$133$	0	0
$134$	807.479	0.520564
$135$	−574.147	−0.366035
$136$	−179.938	−0.113452
$137$	412.806	0.257434	0.128717	−	0.991681i	$-0.458914\pi$
$137$	412.806	0.257434	0.128717	+	0.991681i	$0.458914\pi$
$138$	−898.454	−0.554214
$139$	−1063.98	−0.649251	−0.324625	−	0.945843i	$-0.605238\pi$
$139$	−1063.98	−0.649251	−0.324625	+	0.945843i	$0.605238\pi$
$140$	0	0
$141$	−1184.34	−0.707370
$142$	398.605	0.235565
$143$	−2099.88	−1.22798
$144$	−341.799	−0.197801
$145$	262.872	0.150554
$146$	444.415	0.251918
$147$	0	0
$148$	1270.43	0.705602
$149$	−2303.52	−1.26652	−0.633262	−	0.773938i	$-0.718284\pi$
$149$	−2303.52	−1.26652	−0.633262	+	0.773938i	$0.718284\pi$
$150$	−118.717	−0.0646216
$151$	−3470.20	−1.87020	−0.935101	−	0.354380i	$-0.884692\pi$
$151$	−3470.20	−1.87020	−0.935101	+	0.354380i	$0.884692\pi$
$152$	854.689	0.456082
$153$	480.489	0.253890
$154$	0	0
$155$	770.993	0.399533
$156$	399.947	0.205265
$157$	1909.13	0.970477	0.485238	−	0.874382i	$-0.338733\pi$
$157$	1909.13	0.970477	0.485238	+	0.874382i	$0.338733\pi$
$158$	69.4796	0.0349842
$159$	1244.56	0.620756
$160$	−160.000	−0.0790569
$161$	0	0
$162$	608.283	0.295007
$163$	−2291.37	−1.10107	−0.550533	−	0.834813i	$-0.685576\pi$
$163$	−2291.37	−1.10107	−0.550533	+	0.834813i	$0.685576\pi$
$164$	−581.999	−0.277113
$165$	591.986	0.279309
$166$	−1358.97	−0.635399
$167$	4080.39	1.89072	0.945360	−	0.326028i	$-0.105710\pi$
$167$	4080.39	1.89072	0.945360	+	0.326028i	$0.105710\pi$
$168$	0	0
$169$	−423.650	−0.192831
$170$	224.922	0.101475
$171$	−2282.28	−1.02065
$172$	1709.14	0.757678
$173$	−668.731	−0.293888	−0.146944	−	0.989145i	$-0.546944\pi$
$173$	−668.731	−0.293888	−0.146944	+	0.989145i	$0.546944\pi$
$174$	249.660	0.108774
$175$	0	0
$176$	797.841	0.341702
$177$	−737.030	−0.312986
$178$	−2103.50	−0.885755
$179$	−1567.72	−0.654621	−0.327311	−	0.944917i	$-0.606142\pi$
$179$	−1567.72	−0.654621	−0.327311	+	0.944917i	$0.606142\pi$
$180$	427.249	0.176918
$181$	−4669.21	−1.91746	−0.958728	−	0.284324i	$-0.908231\pi$
$181$	−4669.21	−1.91746	−0.958728	+	0.284324i	$0.908231\pi$
$182$	0	0
$183$	−1551.68	−0.626796
$184$	1513.60	0.606435
$185$	−1588.04	−0.631109
$186$	732.243	0.288659
$187$	−1121.57	−0.438597
$188$	1995.22	0.774023
$189$	0	0
$190$	−1068.36	−0.407932
$191$	1680.74	0.636721	0.318361	−	0.947970i	$-0.396868\pi$
$191$	1680.74	0.636721	0.318361	+	0.947970i	$0.396868\pi$
$192$	−151.958	−0.0571180
$193$	−2006.53	−0.748358	−0.374179	−	0.927357i	$-0.622075\pi$
$193$	−2006.53	−0.748358	−0.374179	+	0.927357i	$0.622075\pi$
$194$	−138.388	−0.0512148
$195$	−499.933	−0.183595
$196$	0	0
$197$	3066.18	1.10892	0.554458	−	0.832211i	$-0.312925\pi$
$197$	3066.18	1.10892	0.554458	+	0.832211i	$0.312925\pi$
$198$	−2130.48	−0.764680
$199$	3409.96	1.21470	0.607351	−	0.794433i	$-0.292232\pi$
$199$	3409.96	1.21470	0.607351	+	0.794433i	$0.292232\pi$
$200$	200.000	0.0707107
$201$	−958.619	−0.336397
$202$	2801.19	0.975697
$203$	0	0
$204$	213.617	0.0733147
$205$	727.498	0.247857
$206$	309.756	0.104766
$207$	−4041.78	−1.35712
$208$	−673.779	−0.224606
$209$	5327.39	1.76317
$210$	0	0
$211$	−4870.61	−1.58913	−0.794565	−	0.607179i	$-0.792301\pi$
$211$	−4870.61	−1.58913	−0.794565	+	0.607179i	$0.792301\pi$
$212$	−2096.68	−0.679248
$213$	−473.214	−0.152226
$214$	47.6097	0.0152081
$215$	−2136.42	−0.677687
$216$	918.635	0.289376
$217$	0	0
$218$	347.406	0.107933
$219$	−527.598	−0.162794
$220$	−997.301	−0.305627
$221$	947.173	0.288297
$222$	−1508.23	−0.455971
$223$	−418.142	−0.125564	−0.0627822	−	0.998027i	$-0.519997\pi$
$223$	−418.142	−0.125564	−0.0627822	+	0.998027i	$0.519997\pi$
$224$	0	0
$225$	−534.062	−0.158240
$226$	−1515.14	−0.445953
$227$	−206.782	−0.0604608	−0.0302304	−	0.999543i	$-0.509624\pi$
$227$	−206.782	−0.0604608	−0.0302304	+	0.999543i	$0.509624\pi$
$228$	−1014.66	−0.294727
$229$	4038.80	1.16546	0.582732	−	0.812665i	$-0.301984\pi$
$229$	4038.80	1.16546	0.582732	+	0.812665i	$0.301984\pi$
$230$	−1892.00	−0.542412
$231$	0	0
$232$	−420.595	−0.119023
$233$	−1784.29	−0.501686	−0.250843	−	0.968028i	$-0.580708\pi$
$233$	−1784.29	−0.501686	−0.250843	+	0.968028i	$0.580708\pi$
$234$	1799.20	0.502637
$235$	−2494.02	−0.692307
$236$	1241.65	0.342478
$237$	−82.4844	−0.0226073
$238$	0	0
$239$	773.433	0.209327	0.104664	−	0.994508i	$-0.466623\pi$
$239$	773.433	0.209327	0.104664	+	0.994508i	$0.466623\pi$
$240$	189.948	0.0510879
$241$	−5323.07	−1.42278	−0.711388	−	0.702799i	$-0.751933\pi$
$241$	−5323.07	−1.42278	−0.711388	+	0.702799i	$0.751933\pi$
$242$	2311.05	0.613884
$243$	−3822.53	−1.00912
$244$	2614.07	0.685856
$245$	0	0
$246$	690.934	0.179075
$247$	−4498.99	−1.15896
$248$	−1233.59	−0.315859
$249$	1613.33	0.410605
$250$	−250.000	−0.0632456
$251$	3438.23	0.864617	0.432308	−	0.901726i	$-0.357699\pi$
$251$	3438.23	0.864617	0.432308	+	0.901726i	$0.357699\pi$
$252$	0	0
$253$	9434.47	2.34443
$254$	−747.214	−0.184584
$255$	−267.022	−0.0655747
$256$	256.000	0.0625000
$257$	5847.17	1.41921	0.709604	−	0.704600i	$-0.248874\pi$
$257$	5847.17	1.41921	0.709604	+	0.704600i	$0.248874\pi$
$258$	−2029.05	−0.489623
$259$	0	0
$260$	842.223	0.200894
$261$	1123.12	0.266357
$262$	2748.63	0.648134
$263$	4487.93	1.05223	0.526117	−	0.850412i	$-0.323647\pi$
$263$	4487.93	1.05223	0.526117	+	0.850412i	$0.323647\pi$
$264$	−947.177	−0.220813
$265$	2620.85	0.607538
$266$	0	0
$267$	2497.23	0.572389
$268$	1614.96	0.368094
$269$	−1392.07	−0.315523	−0.157762	−	0.987477i	$-0.550428\pi$
$269$	−1392.07	−0.315523	−0.157762	+	0.987477i	$0.550428\pi$
$270$	−1148.29	−0.258826
$271$	2381.62	0.533850	0.266925	−	0.963717i	$-0.413992\pi$
$271$	2381.62	0.533850	0.266925	+	0.963717i	$0.413992\pi$
$272$	−359.875	−0.0802229
$273$	0	0
$274$	825.612	0.182033
$275$	1246.63	0.273361
$276$	−1796.91	−0.391888
$277$	1894.66	0.410972	0.205486	−	0.978660i	$-0.434122\pi$
$277$	1894.66	0.410972	0.205486	+	0.978660i	$0.434122\pi$
$278$	−2127.97	−0.459090
$279$	3294.06	0.706847
$280$	0	0
$281$	−3296.31	−0.699792	−0.349896	−	0.936789i	$-0.613783\pi$
$281$	−3296.31	−0.699792	−0.349896	+	0.936789i	$0.613783\pi$
$282$	−2368.67	−0.500186
$283$	1573.59	0.330530	0.165265	−	0.986249i	$-0.447152\pi$
$283$	1573.59	0.330530	0.165265	+	0.986249i	$0.447152\pi$
$284$	797.211	0.166570
$285$	1268.33	0.263612
$286$	−4199.75	−0.868310
$287$	0	0
$288$	−683.599	−0.139866
$289$	−4407.10	−0.897029
$290$	525.744	0.106458
$291$	164.291	0.0330958
$292$	888.830	0.178133
$293$	−1540.15	−0.307086	−0.153543	−	0.988142i	$-0.549068\pi$
$293$	−1540.15	−0.307086	−0.153543	+	0.988142i	$0.549068\pi$
$294$	0	0
$295$	−1552.07	−0.306322
$296$	2540.87	0.498936
$297$	5725.98	1.11870
$298$	−4607.05	−0.895567
$299$	−7967.43	−1.54103
$300$	−237.435	−0.0456944
$301$	0	0
$302$	−6940.39	−1.32243
$303$	−3325.50	−0.630511
$304$	1709.38	0.322498
$305$	−3267.59	−0.613449
$306$	960.977	0.179528
$307$	3833.99	0.712760	0.356380	−	0.934341i	$-0.384011\pi$
$307$	3833.99	0.712760	0.356380	+	0.934341i	$0.384011\pi$
$308$	0	0
$309$	−367.734	−0.0677012
$310$	1541.99	0.282513
$311$	−10550.2	−1.92362	−0.961809	−	0.273722i	$-0.911745\pi$
$311$	−10550.2	−1.92362	−0.961809	+	0.273722i	$0.911745\pi$
$312$	799.893	0.145144
$313$	−1472.76	−0.265959	−0.132980	−	0.991119i	$-0.542455\pi$
$313$	−1472.76	−0.265959	−0.132980	+	0.991119i	$0.542455\pi$
$314$	3818.25	0.686231
$315$	0	0
$316$	138.959	0.0247375
$317$	−2806.94	−0.497330	−0.248665	−	0.968590i	$-0.579992\pi$
$317$	−2806.94	−0.497330	−0.248665	+	0.968590i	$0.579992\pi$
$318$	2489.13	0.438941
$319$	−2621.63	−0.460134
$320$	−320.000	−0.0559017
$321$	−56.5211	−0.00982772
$322$	0	0
$323$	−2402.98	−0.413948
$324$	1216.57	0.208602
$325$	−1052.78	−0.179685
$326$	−4582.74	−0.778572
$327$	−412.432	−0.0697477
$328$	−1164.00	−0.195948
$329$	0	0
$330$	1183.97	0.197501
$331$	9835.02	1.63318	0.816589	−	0.577220i	$-0.195862\pi$
$331$	9835.02	1.63318	0.816589	+	0.577220i	$0.195862\pi$
$332$	−2717.93	−0.449295
$333$	−6784.90	−1.11655
$334$	8160.79	1.33694
$335$	−2018.70	−0.329234
$336$	0	0
$337$	−7739.51	−1.25103	−0.625516	−	0.780211i	$-0.715112\pi$
$337$	−7739.51	−1.25103	−0.625516	+	0.780211i	$0.715112\pi$
$338$	−847.300	−0.136352
$339$	1798.73	0.288182
$340$	449.844	0.0717536
$341$	−7689.12	−1.22108
$342$	−4564.56	−0.721706
$343$	0	0
$344$	3418.28	0.535759
$345$	2246.14	0.350516
$346$	−1337.46	−0.207810
$347$	3952.03	0.611401	0.305700	−	0.952128i	$-0.401109\pi$
$347$	3952.03	0.611401	0.305700	+	0.952128i	$0.401109\pi$
$348$	499.320	0.0769148
$349$	−12173.7	−1.86717	−0.933585	−	0.358356i	$-0.883337\pi$
$349$	−12173.7	−1.86717	−0.933585	+	0.358356i	$0.883337\pi$
$350$	0	0
$351$	−4835.60	−0.735343
$352$	1595.68	0.241620
$353$	10676.7	1.60982	0.804908	−	0.593400i	$-0.202215\pi$
$353$	10676.7	1.60982	0.804908	+	0.593400i	$0.202215\pi$
$354$	−1474.06	−0.221315
$355$	−996.514	−0.148984
$356$	−4207.01	−0.626323
$357$	0	0
$358$	−3135.45	−0.462887
$359$	−3357.06	−0.493534	−0.246767	−	0.969075i	$-0.579368\pi$
$359$	−3357.06	−0.493534	−0.246767	+	0.969075i	$0.579368\pi$
$360$	854.499	0.125100
$361$	4554.95	0.664084
$362$	−9338.42	−1.35585
$363$	−2743.62	−0.396702
$364$	0	0
$365$	−1111.04	−0.159327
$366$	−3103.36	−0.443212
$367$	10872.9	1.54649	0.773245	−	0.634107i	$-0.218632\pi$
$367$	10872.9	1.54649	0.773245	+	0.634107i	$0.218632\pi$
$368$	3027.20	0.428815
$369$	3108.23	0.438504
$370$	−3176.09	−0.446262
$371$	0	0
$372$	1464.49	0.204113
$373$	13045.1	1.81085	0.905427	−	0.424501i	$-0.139551\pi$
$373$	13045.1	1.81085	0.905427	+	0.424501i	$0.139551\pi$
$374$	−2243.15	−0.310135
$375$	296.794	0.0408703
$376$	3990.44	0.547317
$377$	2213.97	0.302454
$378$	0	0
$379$	6319.40	0.856480	0.428240	−	0.903665i	$-0.359134\pi$
$379$	6319.40	0.856480	0.428240	+	0.903665i	$0.359134\pi$
$380$	−2136.72	−0.288451
$381$	887.074	0.119281
$382$	3361.47	0.450230
$383$	1164.76	0.155395	0.0776975	−	0.996977i	$-0.475243\pi$
$383$	1164.76	0.155395	0.0776975	+	0.996977i	$0.475243\pi$
$384$	−303.917	−0.0403885
$385$	0	0
$386$	−4013.05	−0.529169
$387$	−9127.85	−1.19895
$388$	−276.776	−0.0362143
$389$	12126.6	1.58057	0.790284	−	0.612741i	$-0.209933\pi$
$389$	12126.6	1.58057	0.790284	+	0.612741i	$0.209933\pi$
$390$	−999.866	−0.129821
$391$	−4255.52	−0.550412
$392$	0	0
$393$	−3263.11	−0.418835
$394$	6132.37	0.784123
$395$	−173.699	−0.0221259
$396$	−4260.96	−0.540711
$397$	5122.37	0.647568	0.323784	−	0.946131i	$-0.395045\pi$
$397$	5122.37	0.647568	0.323784	+	0.946131i	$0.395045\pi$
$398$	6819.92	0.858924
$399$	0	0
$400$	400.000	0.0500000
$401$	12964.0	1.61444	0.807219	−	0.590253i	$-0.200972\pi$
$401$	12964.0	1.61444	0.807219	+	0.590253i	$0.200972\pi$
$402$	−1917.24	−0.237868
$403$	6493.48	0.802638
$404$	5602.37	0.689922
$405$	−1520.71	−0.186579
$406$	0	0
$407$	15837.6	1.92884
$408$	427.235	0.0518414
$409$	521.974	0.0631051	0.0315525	−	0.999502i	$-0.489955\pi$
$409$	521.974	0.0631051	0.0315525	+	0.999502i	$0.489955\pi$
$410$	1455.00	0.175261
$411$	−980.146	−0.117633
$412$	619.512	0.0740804
$413$	0	0
$414$	−8083.56	−0.959626
$415$	3397.42	0.401862
$416$	−1347.56	−0.158821
$417$	2526.27	0.296671
$418$	10654.8	1.24675
$419$	2345.23	0.273441	0.136721	−	0.990610i	$-0.456344\pi$
$419$	2345.23	0.273441	0.136721	+	0.990610i	$0.456344\pi$
$420$	0	0
$421$	4103.59	0.475052	0.237526	−	0.971381i	$-0.423663\pi$
$421$	4103.59	0.475052	0.237526	+	0.971381i	$0.423663\pi$
$422$	−9741.22	−1.12369
$423$	−10655.7	−1.22482
$424$	−4193.36	−0.480301
$425$	−562.305	−0.0641783
$426$	−946.429	−0.107640
$427$	0	0
$428$	95.2194	0.0107537
$429$	4985.84	0.561116
$430$	−4272.84	−0.479197
$431$	4481.23	0.500820	0.250410	−	0.968140i	$-0.419435\pi$
$431$	4481.23	0.500820	0.250410	+	0.968140i	$0.419435\pi$
$432$	1837.27	0.204620
$433$	−8906.27	−0.988471	−0.494235	−	0.869328i	$-0.664552\pi$
$433$	−8906.27	−0.988471	−0.494235	+	0.869328i	$0.664552\pi$
$434$	0	0
$435$	−624.150	−0.0687947
$436$	694.812	0.0763198
$437$	20213.4	2.21267
$438$	−1055.20	−0.115112
$439$	−1796.37	−0.195299	−0.0976494	−	0.995221i	$-0.531132\pi$
$439$	−1796.37	−0.195299	−0.0976494	+	0.995221i	$0.531132\pi$
$440$	−1994.60	−0.216111
$441$	0	0
$442$	1894.35	0.203857
$443$	−3982.18	−0.427085	−0.213543	−	0.976934i	$-0.568500\pi$
$443$	−3982.18	−0.427085	−0.213543	+	0.976934i	$0.568500\pi$
$444$	−3016.46	−0.322420
$445$	5258.76	0.560200
$446$	−836.284	−0.0887875
$447$	5469.37	0.578730
$448$	0	0
$449$	8581.51	0.901975	0.450987	−	0.892530i	$-0.351072\pi$
$449$	8581.51	0.901975	0.450987	+	0.892530i	$0.351072\pi$
$450$	−1068.12	−0.111893
$451$	−7255.35	−0.757519
$452$	−3030.27	−0.315336
$453$	8239.46	0.854578
$454$	−413.564	−0.0427522
$455$	0	0
$456$	−2029.33	−0.208404
$457$	13035.5	1.33430	0.667150	−	0.744924i	$-0.267514\pi$
$457$	13035.5	1.33430	0.667150	+	0.744924i	$0.267514\pi$
$458$	8077.59	0.824107
$459$	−2582.77	−0.262643
$460$	−3784.00	−0.383543
$461$	−17709.8	−1.78921	−0.894605	−	0.446858i	$-0.852543\pi$
$461$	−17709.8	−1.78921	−0.894605	+	0.446858i	$0.852543\pi$
$462$	0	0
$463$	−5261.70	−0.528146	−0.264073	−	0.964503i	$-0.585066\pi$
$463$	−5261.70	−0.528146	−0.264073	+	0.964503i	$0.585066\pi$
$464$	−841.190	−0.0841622
$465$	−1830.61	−0.182564
$466$	−3568.58	−0.354746
$467$	−176.703	−0.0175093	−0.00875463	−	0.999962i	$-0.502787\pi$
$467$	−176.703	−0.0175093	−0.00875463	+	0.999962i	$0.502787\pi$
$468$	3598.39	0.355418
$469$	0	0
$470$	−4988.05	−0.489535
$471$	−4532.93	−0.443453
$472$	2483.31	0.242168
$473$	21306.6	2.07120
$474$	−164.969	−0.0159858
$475$	2670.90	0.257999
$476$	0	0
$477$	11197.6	1.07485
$478$	1546.87	0.148017
$479$	9541.00	0.910104	0.455052	−	0.890465i	$-0.349621\pi$
$479$	9541.00	0.910104	0.455052	+	0.890465i	$0.349621\pi$
$480$	379.896	0.0361246
$481$	−13374.9	−1.26786
$482$	−10646.1	−1.00606
$483$	0	0
$484$	4622.10	0.434081
$485$	345.970	0.0323911
$486$	−7645.06	−0.713554
$487$	−5618.04	−0.522747	−0.261373	−	0.965238i	$-0.584175\pi$
$487$	−5618.04	−0.522747	−0.261373	+	0.965238i	$0.584175\pi$
$488$	5228.15	0.484974
$489$	5440.51	0.503126
$490$	0	0
$491$	9290.23	0.853894	0.426947	−	0.904277i	$-0.359589\pi$
$491$	9290.23	0.853894	0.426947	+	0.904277i	$0.359589\pi$
$492$	1381.87	0.126625
$493$	1182.51	0.108028
$494$	−8997.98	−0.819511
$495$	5326.20	0.483626
$496$	−2467.18	−0.223346
$497$	0	0
$498$	3226.66	0.290342
$499$	−11090.7	−0.994968	−0.497484	−	0.867473i	$-0.665743\pi$
$499$	−11090.7	−0.994968	−0.497484	+	0.867473i	$0.665743\pi$
$500$	−500.000	−0.0447214
$501$	−9688.28	−0.863953
$502$	6876.45	0.611377
$503$	17220.2	1.52646	0.763230	−	0.646127i	$-0.223612\pi$
$503$	17220.2	1.52646	0.763230	+	0.646127i	$0.223612\pi$
$504$	0	0
$505$	−7002.96	−0.617085
$506$	18868.9	1.65776
$507$	1005.89	0.0881130
$508$	−1494.43	−0.130521
$509$	−19166.4	−1.66903	−0.834514	−	0.550987i	$-0.814251\pi$
$509$	−19166.4	−1.66903	−0.834514	+	0.550987i	$0.814251\pi$
$510$	−534.043	−0.0463683
$511$	0	0
$512$	512.000	0.0441942
$513$	12267.9	1.05583
$514$	11694.3	1.00353
$515$	−774.389	−0.0662596
$516$	−4058.09	−0.346216
$517$	24872.9	2.11588
$518$	0	0
$519$	1587.80	0.134290
$520$	1684.45	0.142054
$521$	2547.23	0.214196	0.107098	−	0.994248i	$-0.465844\pi$
$521$	2547.23	0.214196	0.107098	+	0.994248i	$0.465844\pi$
$522$	2246.24	0.188343
$523$	8673.48	0.725172	0.362586	−	0.931950i	$-0.381894\pi$
$523$	8673.48	0.725172	0.362586	+	0.931950i	$0.381894\pi$
$524$	5497.27	0.458300
$525$	0	0
$526$	8975.86	0.744042
$527$	3468.26	0.286679
$528$	−1894.35	−0.156139
$529$	23629.7	1.94211
$530$	5241.70	0.429594
$531$	−6631.20	−0.541939
$532$	0	0
$533$	6127.16	0.497930
$534$	4994.46	0.404740
$535$	−119.024	−0.00961845
$536$	3229.92	0.260282
$537$	3722.32	0.299125
$538$	−2784.13	−0.223109
$539$	0	0
$540$	−2296.59	−0.183017
$541$	6658.86	0.529181	0.264590	−	0.964361i	$-0.414763\pi$
$541$	6658.86	0.529181	0.264590	+	0.964361i	$0.414763\pi$
$542$	4763.25	0.377489
$543$	11086.3	0.876170
$544$	−719.750	−0.0567262
$545$	−868.515	−0.0682625
$546$	0	0
$547$	−13393.4	−1.04691	−0.523457	−	0.852052i	$-0.675358\pi$
$547$	−13393.4	−1.04691	−0.523457	+	0.852052i	$0.675358\pi$
$548$	1651.22	0.128717
$549$	−13960.8	−1.08530
$550$	2493.25	0.193296
$551$	−5616.84	−0.434275
$552$	−3593.82	−0.277107
$553$	0	0
$554$	3789.33	0.290601
$555$	3770.57	0.288382
$556$	−4255.93	−0.324625
$557$	−3955.20	−0.300875	−0.150437	−	0.988620i	$-0.548068\pi$
$557$	−3955.20	−0.300875	−0.150437	+	0.988620i	$0.548068\pi$
$558$	6588.12	0.499816
$559$	−17993.4	−1.36143
$560$	0	0
$561$	2663.01	0.200414
$562$	−6592.63	−0.494828
$563$	−4330.71	−0.324188	−0.162094	−	0.986775i	$-0.551825\pi$
$563$	−4330.71	−0.324188	−0.162094	+	0.986775i	$0.551825\pi$
$564$	−4737.35	−0.353685
$565$	3787.84	0.282045
$566$	3147.17	0.233720
$567$	0	0
$568$	1594.42	0.117782
$569$	13819.1	1.01815	0.509073	−	0.860723i	$-0.329988\pi$
$569$	13819.1	1.01815	0.509073	+	0.860723i	$0.329988\pi$
$570$	2536.66	0.186402
$571$	−16699.5	−1.22391	−0.611955	−	0.790893i	$-0.709616\pi$
$571$	−16699.5	−1.22391	−0.611955	+	0.790893i	$0.709616\pi$
$572$	−8399.50	−0.613988
$573$	−3990.65	−0.290946
$574$	0	0
$575$	4730.00	0.343052
$576$	−1367.20	−0.0989003
$577$	−16461.8	−1.18772	−0.593859	−	0.804569i	$-0.702397\pi$
$577$	−16461.8	−1.18772	−0.593859	+	0.804569i	$0.702397\pi$
$578$	−8814.20	−0.634295
$579$	4764.20	0.341957
$580$	1051.49	0.0752770
$581$	0	0
$582$	328.581	0.0234023
$583$	−26137.8	−1.85680
$584$	1777.66	0.125959
$585$	−4497.99	−0.317896
$586$	−3080.29	−0.217143
$587$	3920.44	0.275662	0.137831	−	0.990456i	$-0.455987\pi$
$587$	3920.44	0.275662	0.137831	+	0.990456i	$0.455987\pi$
$588$	0	0
$589$	−16474.0	−1.15246
$590$	−3104.13	−0.216602
$591$	−7280.19	−0.506713
$592$	5081.74	0.352801
$593$	−12135.2	−0.840358	−0.420179	−	0.907441i	$-0.638033\pi$
$593$	−12135.2	−0.840358	−0.420179	+	0.907441i	$0.638033\pi$
$594$	11452.0	0.791043
$595$	0	0
$596$	−9214.09	−0.633262
$597$	−8096.44	−0.555051
$598$	−15934.9	−1.08967
$599$	11749.0	0.801423	0.400712	−	0.916204i	$-0.368763\pi$
$599$	11749.0	0.801423	0.400712	+	0.916204i	$0.368763\pi$
$600$	−474.870	−0.0323108
$601$	−8963.69	−0.608381	−0.304190	−	0.952611i	$-0.598386\pi$
$601$	−8963.69	−0.608381	−0.304190	+	0.952611i	$0.598386\pi$
$602$	0	0
$603$	−8624.87	−0.582474
$604$	−13880.8	−0.935101
$605$	−5777.62	−0.388254
$606$	−6650.99	−0.445839
$607$	−3726.27	−0.249168	−0.124584	−	0.992209i	$-0.539760\pi$
$607$	−3726.27	−0.249168	−0.124584	+	0.992209i	$0.539760\pi$
$608$	3418.75	0.228041
$609$	0	0
$610$	−6535.19	−0.433774
$611$	−21005.3	−1.39080
$612$	1921.95	0.126945
$613$	−15107.3	−0.995395	−0.497697	−	0.867351i	$-0.665821\pi$
$613$	−15107.3	−0.995395	−0.497697	+	0.867351i	$0.665821\pi$
$614$	7667.98	0.503997
$615$	−1727.34	−0.113257
$616$	0	0
$617$	27266.1	1.77908	0.889540	−	0.456857i	$-0.151025\pi$
$617$	27266.1	1.77908	0.889540	+	0.456857i	$0.151025\pi$
$618$	−735.469	−0.0478720
$619$	4360.27	0.283125	0.141562	−	0.989929i	$-0.454787\pi$
$619$	4360.27	0.283125	0.141562	+	0.989929i	$0.454787\pi$
$620$	3083.97	0.199767
$621$	21725.7	1.40390
$622$	−21100.3	−1.36020
$623$	0	0
$624$	1599.79	0.102633
$625$	625.000	0.0400000
$626$	−2945.52	−0.188062
$627$	−12649.1	−0.805671
$628$	7636.50	0.485238
$629$	−7143.71	−0.452843
$630$	0	0
$631$	8907.37	0.561960	0.280980	−	0.959714i	$-0.409341\pi$
$631$	8907.37	0.561960	0.280980	+	0.959714i	$0.409341\pi$
$632$	277.918	0.0174921
$633$	11564.5	0.726143
$634$	−5613.88	−0.351665
$635$	1868.04	0.116741
$636$	4978.25	0.310378
$637$	0	0
$638$	−5243.25	−0.325364
$639$	−4257.60	−0.263581
$640$	−640.000	−0.0395285
$641$	−11739.7	−0.723388	−0.361694	−	0.932297i	$-0.617802\pi$
$641$	−11739.7	−0.723388	−0.361694	+	0.932297i	$0.617802\pi$
$642$	−113.042	−0.00694925
$643$	22965.2	1.40849	0.704244	−	0.709958i	$-0.251286\pi$
$643$	22965.2	1.40849	0.704244	+	0.709958i	$0.251286\pi$
$644$	0	0
$645$	5072.61	0.309665
$646$	−4805.96	−0.292706
$647$	−13326.5	−0.809768	−0.404884	−	0.914368i	$-0.632688\pi$
$647$	−13326.5	−0.809768	−0.404884	+	0.914368i	$0.632688\pi$
$648$	2433.13	0.147504
$649$	15478.8	0.936203
$650$	−2105.56	−0.127057
$651$	0	0
$652$	−9165.48	−0.550533
$653$	815.690	0.0488827	0.0244414	−	0.999701i	$-0.492219\pi$
$653$	815.690	0.0488827	0.0244414	+	0.999701i	$0.492219\pi$
$654$	−824.863	−0.0493191
$655$	−6871.59	−0.409916
$656$	−2327.99	−0.138556
$657$	−4746.90	−0.281878
$658$	0	0
$659$	−20626.2	−1.21925	−0.609624	−	0.792691i	$-0.708680\pi$
$659$	−20626.2	−1.21925	−0.609624	+	0.792691i	$0.708680\pi$
$660$	2367.94	0.139655
$661$	−7206.83	−0.424075	−0.212037	−	0.977262i	$-0.568010\pi$
$661$	−7206.83	−0.424075	−0.212037	+	0.977262i	$0.568010\pi$
$662$	19670.0	1.15483
$663$	−2248.92	−0.131736
$664$	−5435.86	−0.317699
$665$	0	0
$666$	−13569.8	−0.789518
$667$	−9947.08	−0.577440
$668$	16321.6	0.945360
$669$	992.816	0.0573759
$670$	−4037.40	−0.232803
$671$	32587.8	1.87487
$672$	0	0
$673$	−26998.7	−1.54639	−0.773197	−	0.634166i	$-0.781343\pi$
$673$	−26998.7	−1.54639	−0.773197	+	0.634166i	$0.781343\pi$
$674$	−15479.0	−0.884614
$675$	2870.74	0.163696
$676$	−1694.60	−0.0964156
$677$	−24327.3	−1.38105	−0.690527	−	0.723307i	$-0.742621\pi$
$677$	−24327.3	−1.38105	−0.690527	+	0.723307i	$0.742621\pi$
$678$	3597.46	0.203775
$679$	0	0
$680$	899.688	0.0507374
$681$	490.972	0.0276272
$682$	−15378.2	−0.863436
$683$	−16784.5	−0.940326	−0.470163	−	0.882580i	$-0.655805\pi$
$683$	−16784.5	−0.940326	−0.470163	+	0.882580i	$0.655805\pi$
$684$	−9129.13	−0.510323
$685$	−2064.03	−0.115128
$686$	0	0
$687$	−9589.51	−0.532551
$688$	6836.55	0.378839
$689$	22073.4	1.22051
$690$	4492.27	0.247852
$691$	−24712.9	−1.36052	−0.680262	−	0.732969i	$-0.738134\pi$
$691$	−24712.9	−1.36052	−0.680262	+	0.732969i	$0.738134\pi$
$692$	−2674.92	−0.146944
$693$	0	0
$694$	7904.06	0.432326
$695$	5319.92	0.290354
$696$	998.640	0.0543870
$697$	3272.61	0.177846
$698$	−24347.4	−1.32029
$699$	4236.53	0.229242
$700$	0	0
$701$	−2916.83	−0.157157	−0.0785785	−	0.996908i	$-0.525038\pi$
$701$	−2916.83	−0.157157	−0.0785785	+	0.996908i	$0.525038\pi$
$702$	−9671.20	−0.519966
$703$	33932.1	1.82044
$704$	3191.36	0.170851
$705$	5921.69	0.316346
$706$	21353.4	1.13831
$707$	0	0
$708$	−2948.12	−0.156493
$709$	−24554.5	−1.30066	−0.650328	−	0.759654i	$-0.725368\pi$
$709$	−24554.5	−1.30066	−0.650328	+	0.759654i	$0.725368\pi$
$710$	−1993.03	−0.105348
$711$	−742.128	−0.0391448
$712$	−8414.02	−0.442877
$713$	−29174.4	−1.53238
$714$	0	0
$715$	10499.4	0.549167
$716$	−6270.90	−0.327311
$717$	−1836.40	−0.0956508
$718$	−6714.11	−0.348981
$719$	−22943.2	−1.19004	−0.595020	−	0.803711i	$-0.702856\pi$
$719$	−22943.2	−1.19004	−0.595020	+	0.803711i	$0.702856\pi$
$720$	1709.00	0.0884591
$721$	0	0
$722$	9109.90	0.469578
$723$	12638.8	0.650129
$724$	−18676.8	−0.958728
$725$	−1314.36	−0.0673298
$726$	−5487.24	−0.280510
$727$	32954.2	1.68116	0.840581	−	0.541685i	$-0.182214\pi$
$727$	32954.2	1.68116	0.840581	+	0.541685i	$0.182214\pi$
$728$	0	0
$729$	864.212	0.0439065
$730$	−2222.07	−0.112661
$731$	−9610.57	−0.486265
$732$	−6206.73	−0.313398
$733$	427.748	0.0215542	0.0107771	−	0.999942i	$-0.496569\pi$
$733$	427.748	0.0215542	0.0107771	+	0.999942i	$0.496569\pi$
$734$	21745.9	1.09353
$735$	0	0
$736$	6054.40	0.303218
$737$	20132.5	1.00623
$738$	6216.46	0.310069
$739$	−31196.6	−1.55289	−0.776445	−	0.630186i	$-0.782979\pi$
$739$	−31196.6	−1.55289	−0.776445	+	0.630186i	$0.782979\pi$
$740$	−6352.17	−0.315555
$741$	10682.2	0.529581
$742$	0	0
$743$	11230.8	0.554534	0.277267	−	0.960793i	$-0.410571\pi$
$743$	11230.8	0.554534	0.277267	+	0.960793i	$0.410571\pi$
$744$	2928.97	0.144330
$745$	11517.6	0.566407
$746$	26090.2	1.28047
$747$	14515.4	0.710966
$748$	−4486.30	−0.219299
$749$	0	0
$750$	593.587	0.0288997
$751$	−7632.99	−0.370881	−0.185440	−	0.982655i	$-0.559371\pi$
$751$	−7632.99	−0.370881	−0.185440	+	0.982655i	$0.559371\pi$
$752$	7980.88	0.387012
$753$	−8163.55	−0.395081
$754$	4427.94	0.213867
$755$	17351.0	0.836380
$756$	0	0
$757$	−2052.39	−0.0985406	−0.0492703	−	0.998785i	$-0.515690\pi$
$757$	−2052.39	−0.0985406	−0.0492703	+	0.998785i	$0.515690\pi$
$758$	12638.8	0.605623
$759$	−22400.7	−1.07127
$760$	−4273.44	−0.203966
$761$	19373.7	0.922860	0.461430	−	0.887177i	$-0.347337\pi$
$761$	19373.7	0.922860	0.461430	+	0.887177i	$0.347337\pi$
$762$	1774.15	0.0843446
$763$	0	0
$764$	6722.94	0.318361
$765$	−2402.44	−0.113543
$766$	2329.51	0.109881
$767$	−13071.9	−0.615382
$768$	−607.834	−0.0285590
$769$	−15119.5	−0.709003	−0.354502	−	0.935055i	$-0.615349\pi$
$769$	−15119.5	−0.709003	−0.354502	+	0.935055i	$0.615349\pi$
$770$	0	0
$771$	−13883.2	−0.648499
$772$	−8026.11	−0.374179
$773$	−28086.5	−1.30686	−0.653430	−	0.756987i	$-0.726671\pi$
$773$	−28086.5	−1.30686	−0.653430	+	0.756987i	$0.726671\pi$
$774$	−18255.7	−0.847787
$775$	−3854.96	−0.178677
$776$	−553.551	−0.0256074
$777$	0	0
$778$	24253.1	1.11763
$779$	−15544.6	−0.714947
$780$	−1999.73	−0.0917973
$781$	9938.24	0.455337
$782$	−8511.05	−0.389200
$783$	−6037.09	−0.275540
$784$	0	0
$785$	−9545.63	−0.434010
$786$	−6526.22	−0.296161
$787$	−1356.30	−0.0614319	−0.0307160	−	0.999528i	$-0.509779\pi$
$787$	−1356.30	−0.0614319	−0.0307160	+	0.999528i	$0.509779\pi$
$788$	12264.7	0.554458
$789$	−10655.9	−0.480812
$790$	−347.398	−0.0156454
$791$	0	0
$792$	−8521.92	−0.382340
$793$	−27520.4	−1.23238
$794$	10244.7	0.457900
$795$	−6222.82	−0.277611
$796$	13639.8	0.607351
$797$	6087.69	0.270561	0.135280	−	0.990807i	$-0.456806\pi$
$797$	6087.69	0.270561	0.135280	+	0.990807i	$0.456806\pi$
$798$	0	0
$799$	−11219.2	−0.496755
$800$	800.000	0.0353553
$801$	22468.0	0.991097
$802$	25927.9	1.14158
$803$	11080.4	0.486947
$804$	−3834.48	−0.168198
$805$	0	0
$806$	12987.0	0.567551
$807$	3305.25	0.144176
$808$	11204.7	0.487848
$809$	4958.65	0.215497	0.107748	−	0.994178i	$-0.465636\pi$
$809$	4958.65	0.215497	0.107748	+	0.994178i	$0.465636\pi$
$810$	−3041.41	−0.131931
$811$	−32083.6	−1.38916	−0.694580	−	0.719416i	$-0.744410\pi$
$811$	−32083.6	−1.38916	−0.694580	+	0.719416i	$0.744410\pi$
$812$	0	0
$813$	−5654.81	−0.243940
$814$	31675.1	1.36390
$815$	11456.8	0.492412
$816$	854.470	0.0366574
$817$	45649.4	1.95480
$818$	1043.95	0.0446220
$819$	0	0
$820$	2909.99	0.123928
$821$	−40959.3	−1.74116	−0.870578	−	0.492031i	$-0.836255\pi$
$821$	−40959.3	−1.74116	−0.870578	+	0.492031i	$0.836255\pi$
$822$	−1960.29	−0.0831789
$823$	−23352.1	−0.989069	−0.494534	−	0.869158i	$-0.664661\pi$
$823$	−23352.1	−0.989069	−0.494534	+	0.869158i	$0.664661\pi$
$824$	1239.02	0.0523828
$825$	−2959.93	−0.124911
$826$	0	0
$827$	−19365.6	−0.814276	−0.407138	−	0.913367i	$-0.633473\pi$
$827$	−19365.6	−0.814276	−0.407138	+	0.913367i	$0.633473\pi$
$828$	−16167.1	−0.678558
$829$	−17963.9	−0.752607	−0.376304	−	0.926496i	$-0.622805\pi$
$829$	−17963.9	−0.752607	−0.376304	+	0.926496i	$0.622805\pi$
$830$	6794.83	0.284159
$831$	−4498.59	−0.187791
$832$	−2695.11	−0.112303
$833$	0	0
$834$	5052.54	0.209778
$835$	−20402.0	−0.845556
$836$	21309.6	0.881587
$837$	−17706.5	−0.731215
$838$	4690.46	0.193352
$839$	10265.4	0.422407	0.211204	−	0.977442i	$-0.432262\pi$
$839$	10265.4	0.422407	0.211204	+	0.977442i	$0.432262\pi$
$840$	0	0
$841$	−21624.9	−0.886668
$842$	8207.19	0.335913
$843$	7826.60	0.319766
$844$	−19482.4	−0.794565
$845$	2118.25	0.0862367
$846$	−21311.4	−0.866077
$847$	0	0
$848$	−8386.72	−0.339624
$849$	−3736.24	−0.151034
$850$	−1124.61	−0.0453809
$851$	60091.6	2.42058
$852$	−1892.86	−0.0761130
$853$	−2485.01	−0.0997480	−0.0498740	−	0.998756i	$-0.515882\pi$
$853$	−2485.01	−0.0997480	−0.0498740	+	0.998756i	$0.515882\pi$
$854$	0	0
$855$	11411.4	0.456447
$856$	190.439	0.00760405
$857$	−36004.3	−1.43510	−0.717552	−	0.696505i	$-0.754737\pi$
$857$	−36004.3	−1.43510	−0.717552	+	0.696505i	$0.754737\pi$
$858$	9971.68	0.396769
$859$	−21882.4	−0.869170	−0.434585	−	0.900631i	$-0.643105\pi$
$859$	−21882.4	−0.869170	−0.434585	+	0.900631i	$0.643105\pi$
$860$	−8545.69	−0.338844
$861$	0	0
$862$	8962.47	0.354133
$863$	−15308.7	−0.603841	−0.301921	−	0.953333i	$-0.597628\pi$
$863$	−15308.7	−0.603841	−0.301921	+	0.953333i	$0.597628\pi$
$864$	3674.54	0.144688
$865$	3343.66	0.131431
$866$	−17812.5	−0.698954
$867$	10464.0	0.409892
$868$	0	0
$869$	1732.30	0.0676229
$870$	−1248.30	−0.0486452
$871$	−17001.9	−0.661411
$872$	1389.62	0.0539663
$873$	1478.15	0.0573057
$874$	40426.8	1.56460
$875$	0	0
$876$	−2110.39	−0.0813968
$877$	26945.8	1.03751	0.518754	−	0.854924i	$-0.326396\pi$
$877$	26945.8	1.03751	0.518754	+	0.854924i	$0.326396\pi$
$878$	−3592.75	−0.138097
$879$	3656.85	0.140321
$880$	−3989.21	−0.152814
$881$	11575.1	0.442651	0.221325	−	0.975200i	$-0.428962\pi$
$881$	11575.1	0.442651	0.221325	+	0.975200i	$0.428962\pi$
$882$	0	0
$883$	−46.8449	−0.00178534	−0.000892671	−	1.00000i	$-0.500284\pi$
$883$	−46.8449	−0.00178534	−0.000892671		1.00000i	$0.500284\pi$
$884$	3788.69	0.144149
$885$	3685.15	0.139972
$886$	−7964.35	−0.301995
$887$	27372.3	1.03616	0.518080	−	0.855332i	$-0.326647\pi$
$887$	27372.3	1.03616	0.518080	+	0.855332i	$0.326647\pi$
$888$	−6032.91	−0.227986
$889$	0	0
$890$	10517.5	0.396122
$891$	15166.0	0.570237
$892$	−1672.57	−0.0627822
$893$	53290.4	1.99697
$894$	10938.7	0.409224
$895$	7838.62	0.292755
$896$	0	0
$897$	18917.5	0.704165
$898$	17163.0	0.637793
$899$	8106.89	0.300756
$900$	−2136.25	−0.0791202
$901$	11789.7	0.435930
$902$	−14510.7	−0.535647
$903$	0	0
$904$	−6060.54	−0.222976
$905$	23346.1	0.857513
$906$	16478.9	0.604278
$907$	−45290.7	−1.65805	−0.829025	−	0.559211i	$-0.811104\pi$
$907$	−45290.7	−1.65805	−0.829025	+	0.559211i	$0.811104\pi$
$908$	−827.127	−0.0302304
$909$	−29920.1	−1.09174
$910$	0	0
$911$	26077.5	0.948394	0.474197	−	0.880419i	$-0.342739\pi$
$911$	26077.5	0.948394	0.474197	+	0.880419i	$0.342739\pi$
$912$	−4058.66	−0.147364
$913$	−33882.5	−1.22820
$914$	26071.0	0.943492
$915$	7758.41	0.280312
$916$	16155.2	0.582732
$917$	0	0
$918$	−5165.53	−0.185717
$919$	33214.5	1.19222	0.596108	−	0.802905i	$-0.296713\pi$
$919$	33214.5	1.19222	0.596108	+	0.802905i	$0.296713\pi$
$920$	−7568.00	−0.271206
$921$	−9103.23	−0.325691
$922$	−35419.5	−1.26516
$923$	−8392.87	−0.299301
$924$	0	0
$925$	7940.21	0.282241
$926$	−10523.4	−0.373456
$927$	−3308.57	−0.117225
$928$	−1682.38	−0.0595117
$929$	42280.9	1.49321	0.746604	−	0.665269i	$-0.231683\pi$
$929$	42280.9	1.49321	0.746604	+	0.665269i	$0.231683\pi$
$930$	−3661.21	−0.129092
$931$	0	0
$932$	−7137.17	−0.250843
$933$	25049.8	0.878985
$934$	−353.406	−0.0123809
$935$	5607.87	0.196147
$936$	7196.79	0.251319
$937$	−36113.1	−1.25909	−0.629543	−	0.776965i	$-0.716758\pi$
$937$	−36113.1	−1.25909	−0.629543	+	0.776965i	$0.716758\pi$
$938$	0	0
$939$	3496.85	0.121528
$940$	−9976.10	−0.346154
$941$	44978.3	1.55818	0.779091	−	0.626910i	$-0.215681\pi$
$941$	44978.3	1.55818	0.779091	+	0.626910i	$0.215681\pi$
$942$	−9065.87	−0.313569
$943$	−27528.5	−0.950639
$944$	4966.62	0.171239
$945$	0	0
$946$	42613.1	1.46456
$947$	20954.4	0.719036	0.359518	−	0.933138i	$-0.382941\pi$
$947$	20954.4	0.719036	0.359518	+	0.933138i	$0.382941\pi$
$948$	−329.938	−0.0113037
$949$	−9357.41	−0.320079
$950$	5341.80	0.182433
$951$	6664.66	0.227252
$952$	0	0
$953$	27330.5	0.928984	0.464492	−	0.885577i	$-0.346237\pi$
$953$	27330.5	0.928984	0.464492	+	0.885577i	$0.346237\pi$
$954$	22395.1	0.760030
$955$	−8403.68	−0.284750
$956$	3093.73	0.104664
$957$	6224.65	0.210256
$958$	19082.0	0.643540
$959$	0	0
$960$	759.792	0.0255439
$961$	−6013.81	−0.201867
$962$	−26749.7	−0.896513
$963$	−508.530	−0.0170168
$964$	−21292.3	−0.711388
$965$	10032.6	0.334676
$966$	0	0
$967$	−9481.13	−0.315298	−0.157649	−	0.987495i	$-0.550391\pi$
$967$	−9481.13	−0.315298	−0.157649	+	0.987495i	$0.550391\pi$
$968$	9244.20	0.306942
$969$	5705.51	0.189151
$970$	691.939	0.0229039
$971$	−2141.84	−0.0707878	−0.0353939	−	0.999373i	$-0.511269\pi$
$971$	−2141.84	−0.0707878	−0.0353939	+	0.999373i	$0.511269\pi$
$972$	−15290.1	−0.504559
$973$	0	0
$974$	−11236.1	−0.369638
$975$	2499.67	0.0821060
$976$	10456.3	0.342928
$977$	−16348.4	−0.535345	−0.267672	−	0.963510i	$-0.586255\pi$
$977$	−16348.4	−0.535345	−0.267672	+	0.963510i	$0.586255\pi$
$978$	10881.0	0.355764
$979$	−52445.7	−1.71213
$980$	0	0
$981$	−3710.72	−0.120769
$982$	18580.5	0.603795
$983$	−52338.2	−1.69820	−0.849099	−	0.528234i	$-0.822854\pi$
$983$	−52338.2	−1.69820	−0.849099	+	0.528234i	$0.822854\pi$
$984$	2763.74	0.0895373
$985$	−15330.9	−0.495923
$986$	2365.03	0.0763872
$987$	0	0
$988$	−17996.0	−0.579482
$989$	80842.2	2.59922
$990$	10652.4	0.341975
$991$	−48538.8	−1.55589	−0.777944	−	0.628334i	$-0.783737\pi$
$991$	−48538.8	−1.55589	−0.777944	+	0.628334i	$0.783737\pi$
$992$	−4934.35	−0.157929
$993$	−23351.8	−0.746270
$994$	0	0
$995$	−17049.8	−0.543232
$996$	6453.32	0.205303
$997$	47659.2	1.51392	0.756962	−	0.653459i	$-0.226683\pi$
$997$	47659.2	1.51392	0.756962	+	0.653459i	$0.226683\pi$
$998$	−22181.4	−0.703548
$999$	36470.8	1.15504

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.a.v.1.2		3
5.4	even	2		2450.4.a.ce.1.2		3
7.2	even	3		490.4.e.y.361.2		6
7.3	odd	6		70.4.e.e.51.2	yes	6
7.4	even	3		490.4.e.y.471.2		6
7.5	odd	6		70.4.e.e.11.2	✓	6
7.6	odd	2		490.4.a.w.1.2		3
21.5	even	6		630.4.k.r.361.2		6
21.17	even	6		630.4.k.r.541.2		6
28.3	even	6		560.4.q.m.401.2		6
28.19	even	6		560.4.q.m.81.2		6
35.3	even	12		350.4.j.i.149.5		12
35.12	even	12		350.4.j.i.249.5		12
35.17	even	12		350.4.j.i.149.2		12
35.19	odd	6		350.4.e.k.151.2		6
35.24	odd	6		350.4.e.k.51.2		6
35.33	even	12		350.4.j.i.249.2		12
35.34	odd	2		2450.4.a.cb.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.e.e.11.2	✓	6	7.5	odd	6
70.4.e.e.51.2	yes	6	7.3	odd	6
350.4.e.k.51.2		6	35.24	odd	6
350.4.e.k.151.2		6	35.19	odd	6
350.4.j.i.149.2		12	35.17	even	12
350.4.j.i.149.5		12	35.3	even	12
350.4.j.i.249.2		12	35.33	even	12
350.4.j.i.249.5		12	35.12	even	12
490.4.a.v.1.2		3	1.1	even	1	trivial
490.4.a.w.1.2		3	7.6	odd	2
490.4.e.y.361.2		6	7.2	even	3
490.4.e.y.471.2		6	7.4	even	3
560.4.q.m.81.2		6	28.19	even	6
560.4.q.m.401.2		6	28.3	even	6
630.4.k.r.361.2		6	21.5	even	6
630.4.k.r.541.2		6	21.17	even	6
2450.4.a.cb.1.2		3	35.34	odd	2
2450.4.a.ce.1.2		3	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)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -2.37435 q^{3} +4.00000 q^{4} -5.00000 q^{5} -4.74870 q^{6} +8.00000 q^{8} -21.3625 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -2.37435 q^{3} +4.00000 q^{4} -5.00000 q^{5} -4.74870 q^{6} +8.00000 q^{8} -21.3625 q^{9} -10.0000 q^{10} +49.8651 q^{11} -9.49740 q^{12} -42.1112 q^{13} +11.8717 q^{15} +16.0000 q^{16} -22.4922 q^{17} -42.7249 q^{18} +106.836 q^{19} -20.0000 q^{20} +99.7301 q^{22} +189.200 q^{23} -18.9948 q^{24} +25.0000 q^{25} -84.2223 q^{26} +114.829 q^{27} -52.5744 q^{29} +23.7435 q^{30} -154.199 q^{31} +32.0000 q^{32} -118.397 q^{33} -44.9844 q^{34} -85.4499 q^{36} +317.609 q^{37} +213.672 q^{38} +99.9866 q^{39} -40.0000 q^{40} -145.500 q^{41} +427.284 q^{43} +199.460 q^{44} +106.812 q^{45} +378.400 q^{46} +498.805 q^{47} -37.9896 q^{48} +50.0000 q^{50} +53.4043 q^{51} -168.445 q^{52} -524.170 q^{53} +229.659 q^{54} -249.325 q^{55} -253.666 q^{57} -105.149 q^{58} +310.413 q^{59} +47.4870 q^{60} +653.519 q^{61} -308.397 q^{62} +64.0000 q^{64} +210.556 q^{65} -236.794 q^{66} +403.740 q^{67} -89.9688 q^{68} -449.227 q^{69} +199.303 q^{71} -170.900 q^{72} +222.207 q^{73} +635.217 q^{74} -59.3587 q^{75} +427.344 q^{76} +199.973 q^{78} +34.7398 q^{79} -80.0000 q^{80} +304.141 q^{81} -290.999 q^{82} -679.483 q^{83} +112.461 q^{85} +854.569 q^{86} +124.830 q^{87} +398.921 q^{88} -1051.75 q^{89} +213.625 q^{90} +756.800 q^{92} +366.121 q^{93} +997.610 q^{94} -534.180 q^{95} -75.9792 q^{96} -69.1939 q^{97} -1065.24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{2} - 4 q^{3} + 12 q^{4} - 15 q^{5} - 8 q^{6} + 24 q^{8} + 57 q^{9}+O(q^{10}) \) 3 * q + 6 * q^2 - 4 * q^3 + 12 * q^4 - 15 * q^5 - 8 * q^6 + 24 * q^8 + 57 * q^9	\( 3 q + 6 q^{2} - 4 q^{3} + 12 q^{4} - 15 q^{5} - 8 q^{6} + 24 q^{8} + 57 q^{9} - 30 q^{10} + 41 q^{11} - 16 q^{12} + q^{13} + 20 q^{15} + 48 q^{16} - 30 q^{17} + 114 q^{18} - 49 q^{19} - 60 q^{20} + 82 q^{22} + 145 q^{23} - 32 q^{24} + 75 q^{25} + 2 q^{26} - 118 q^{27} + 268 q^{29} + 40 q^{30} + 28 q^{31} + 96 q^{32} + 626 q^{33} - 60 q^{34} + 228 q^{36} + 813 q^{37} - 98 q^{38} + 114 q^{39} - 120 q^{40} - 313 q^{41} + 360 q^{43} + 164 q^{44} - 285 q^{45} + 290 q^{46} + 977 q^{47} - 64 q^{48} + 150 q^{50} + 1632 q^{51} + 4 q^{52} + 325 q^{53} - 236 q^{54} - 205 q^{55} + 250 q^{57} + 536 q^{58} + 272 q^{59} + 80 q^{60} + 902 q^{61} + 56 q^{62} + 192 q^{64} - 5 q^{65} + 1252 q^{66} - 170 q^{67} - 120 q^{68} - 2264 q^{69} - 1080 q^{71} + 456 q^{72} + 584 q^{73} + 1626 q^{74} - 100 q^{75} - 196 q^{76} + 228 q^{78} - 310 q^{79} - 240 q^{80} + 147 q^{81} - 626 q^{82} - 626 q^{83} + 150 q^{85} + 720 q^{86} + 1846 q^{87} + 328 q^{88} + 400 q^{89} - 570 q^{90} + 580 q^{92} - 372 q^{93} + 1954 q^{94} + 245 q^{95} - 128 q^{96} - 1626 q^{97} - 2611 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 4 * q^3 + 12 * q^4 - 15 * q^5 - 8 * q^6 + 24 * q^8 + 57 * q^9 - 30 * q^10 + 41 * q^11 - 16 * q^12 + q^13 + 20 * q^15 + 48 * q^16 - 30 * q^17 + 114 * q^18 - 49 * q^19 - 60 * q^20 + 82 * q^22 + 145 * q^23 - 32 * q^24 + 75 * q^25 + 2 * q^26 - 118 * q^27 + 268 * q^29 + 40 * q^30 + 28 * q^31 + 96 * q^32 + 626 * q^33 - 60 * q^34 + 228 * q^36 + 813 * q^37 - 98 * q^38 + 114 * q^39 - 120 * q^40 - 313 * q^41 + 360 * q^43 + 164 * q^44 - 285 * q^45 + 290 * q^46 + 977 * q^47 - 64 * q^48 + 150 * q^50 + 1632 * q^51 + 4 * q^52 + 325 * q^53 - 236 * q^54 - 205 * q^55 + 250 * q^57 + 536 * q^58 + 272 * q^59 + 80 * q^60 + 902 * q^61 + 56 * q^62 + 192 * q^64 - 5 * q^65 + 1252 * q^66 - 170 * q^67 - 120 * q^68 - 2264 * q^69 - 1080 * q^71 + 456 * q^72 + 584 * q^73 + 1626 * q^74 - 100 * q^75 - 196 * q^76 + 228 * q^78 - 310 * q^79 - 240 * q^80 + 147 * q^81 - 626 * q^82 - 626 * q^83 + 150 * q^85 + 720 * q^86 + 1846 * q^87 + 328 * q^88 + 400 * q^89 - 570 * q^90 + 580 * q^92 - 372 * q^93 + 1954 * q^94 + 245 * q^95 - 128 * q^96 - 1626 * q^97 - 2611 * q^99

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