LMFDB - Embedded newform 966.4.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,4,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	966.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:	$56.9958450655$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.65101.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 28x - 29 $ x^3 - 28*x - 29
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-4.66766$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +14.1224 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +14.1224 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +28.2447 q^{10} -26.4547 q^{11} -12.0000 q^{12} +8.09359 q^{13} -14.0000 q^{14} -42.3671 q^{15} +16.0000 q^{16} -91.8079 q^{17} +18.0000 q^{18} -113.434 q^{19} +56.4894 q^{20} +21.0000 q^{21} -52.9094 q^{22} -23.0000 q^{23} -24.0000 q^{24} +74.4408 q^{25} +16.1872 q^{26} -27.0000 q^{27} -28.0000 q^{28} -191.092 q^{29} -84.7341 q^{30} +47.5116 q^{31} +32.0000 q^{32} +79.3641 q^{33} -183.616 q^{34} -98.8565 q^{35} +36.0000 q^{36} -80.9441 q^{37} -226.867 q^{38} -24.2808 q^{39} +112.979 q^{40} +141.469 q^{41} +42.0000 q^{42} -223.196 q^{43} -105.819 q^{44} +127.101 q^{45} -46.0000 q^{46} +33.0423 q^{47} -48.0000 q^{48} +49.0000 q^{49} +148.882 q^{50} +275.424 q^{51} +32.3744 q^{52} +76.0827 q^{53} -54.0000 q^{54} -373.602 q^{55} -56.0000 q^{56} +340.301 q^{57} -382.183 q^{58} -548.415 q^{59} -169.468 q^{60} +533.017 q^{61} +95.0232 q^{62} -63.0000 q^{63} +64.0000 q^{64} +114.301 q^{65} +158.728 q^{66} +625.568 q^{67} -367.231 q^{68} +69.0000 q^{69} -197.713 q^{70} +247.335 q^{71} +72.0000 q^{72} -956.751 q^{73} -161.888 q^{74} -223.322 q^{75} -453.734 q^{76} +185.183 q^{77} -48.5615 q^{78} -984.717 q^{79} +225.958 q^{80} +81.0000 q^{81} +282.938 q^{82} +188.927 q^{83} +84.0000 q^{84} -1296.54 q^{85} -446.392 q^{86} +573.275 q^{87} -211.638 q^{88} -532.128 q^{89} +254.202 q^{90} -56.6551 q^{91} -92.0000 q^{92} -142.535 q^{93} +66.0846 q^{94} -1601.95 q^{95} -96.0000 q^{96} -115.772 q^{97} +98.0000 q^{98} -238.092 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 5 q^{5} - 18 q^{6} - 21 q^{7} + 24 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 5 * q^5 - 18 * q^6 - 21 * q^7 + 24 * q^8 + 27 * q^9	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 5 q^{5} - 18 q^{6} - 21 q^{7} + 24 q^{8} + 27 q^{9} + 10 q^{10} - 56 q^{11} - 36 q^{12} + 29 q^{13} - 42 q^{14} - 15 q^{15} + 48 q^{16} + 28 q^{17} + 54 q^{18} - 18 q^{19} + 20 q^{20} + 63 q^{21} - 112 q^{22} - 69 q^{23} - 72 q^{24} + 32 q^{25} + 58 q^{26} - 81 q^{27} - 84 q^{28} - 242 q^{29} - 30 q^{30} - 86 q^{31} + 96 q^{32} + 168 q^{33} + 56 q^{34} - 35 q^{35} + 108 q^{36} - 70 q^{37} - 36 q^{38} - 87 q^{39} + 40 q^{40} - 402 q^{41} + 126 q^{42} - 553 q^{43} - 224 q^{44} + 45 q^{45} - 138 q^{46} - 368 q^{47} - 144 q^{48} + 147 q^{49} + 64 q^{50} - 84 q^{51} + 116 q^{52} + 23 q^{53} - 162 q^{54} - 467 q^{55} - 168 q^{56} + 54 q^{57} - 484 q^{58} - 861 q^{59} - 60 q^{60} - 311 q^{61} - 172 q^{62} - 189 q^{63} + 192 q^{64} - 624 q^{65} + 336 q^{66} - 215 q^{67} + 112 q^{68} + 207 q^{69} - 70 q^{70} + 121 q^{71} + 216 q^{72} - 588 q^{73} - 140 q^{74} - 96 q^{75} - 72 q^{76} + 392 q^{77} - 174 q^{78} - 1418 q^{79} + 80 q^{80} + 243 q^{81} - 804 q^{82} - 352 q^{83} + 252 q^{84} - 827 q^{85} - 1106 q^{86} + 726 q^{87} - 448 q^{88} + 1275 q^{89} + 90 q^{90} - 203 q^{91} - 276 q^{92} + 258 q^{93} - 736 q^{94} - 3593 q^{95} - 288 q^{96} - 602 q^{97} + 294 q^{98} - 504 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 5 * q^5 - 18 * q^6 - 21 * q^7 + 24 * q^8 + 27 * q^9 + 10 * q^10 - 56 * q^11 - 36 * q^12 + 29 * q^13 - 42 * q^14 - 15 * q^15 + 48 * q^16 + 28 * q^17 + 54 * q^18 - 18 * q^19 + 20 * q^20 + 63 * q^21 - 112 * q^22 - 69 * q^23 - 72 * q^24 + 32 * q^25 + 58 * q^26 - 81 * q^27 - 84 * q^28 - 242 * q^29 - 30 * q^30 - 86 * q^31 + 96 * q^32 + 168 * q^33 + 56 * q^34 - 35 * q^35 + 108 * q^36 - 70 * q^37 - 36 * q^38 - 87 * q^39 + 40 * q^40 - 402 * q^41 + 126 * q^42 - 553 * q^43 - 224 * q^44 + 45 * q^45 - 138 * q^46 - 368 * q^47 - 144 * q^48 + 147 * q^49 + 64 * q^50 - 84 * q^51 + 116 * q^52 + 23 * q^53 - 162 * q^54 - 467 * q^55 - 168 * q^56 + 54 * q^57 - 484 * q^58 - 861 * q^59 - 60 * q^60 - 311 * q^61 - 172 * q^62 - 189 * q^63 + 192 * q^64 - 624 * q^65 + 336 * q^66 - 215 * q^67 + 112 * q^68 + 207 * q^69 - 70 * q^70 + 121 * q^71 + 216 * q^72 - 588 * q^73 - 140 * q^74 - 96 * q^75 - 72 * q^76 + 392 * q^77 - 174 * q^78 - 1418 * q^79 + 80 * q^80 + 243 * q^81 - 804 * q^82 - 352 * q^83 + 252 * q^84 - 827 * q^85 - 1106 * q^86 + 726 * q^87 - 448 * q^88 + 1275 * q^89 + 90 * q^90 - 203 * q^91 - 276 * q^92 + 258 * q^93 - 736 * q^94 - 3593 * q^95 - 288 * q^96 - 602 * q^97 + 294 * q^98 - 504 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	14.1224	1.26314	0.631571	−	0.775318i	$-0.282411\pi$
$5$	14.1224	1.26314	0.631571	+	0.775318i	$0.282411\pi$
$6$	−6.00000	−0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	28.2447	0.893176
$11$	−26.4547	−0.725126	−0.362563	−	0.931959i	$-0.618098\pi$
$11$	−26.4547	−0.725126	−0.362563	+	0.931959i	$0.618098\pi$
$12$	−12.0000	−0.288675
$13$	8.09359	0.172674	0.0863368	−	0.996266i	$-0.472484\pi$
$13$	8.09359	0.172674	0.0863368	+	0.996266i	$0.472484\pi$
$14$	−14.0000	−0.267261
$15$	−42.3671	−0.729275
$16$	16.0000	0.250000
$17$	−91.8079	−1.30980	−0.654902	−	0.755714i	$-0.727290\pi$
$17$	−91.8079	−1.30980	−0.654902	+	0.755714i	$0.727290\pi$
$18$	18.0000	0.235702
$19$	−113.434	−1.36965	−0.684827	−	0.728706i	$-0.740122\pi$
$19$	−113.434	−1.36965	−0.684827	+	0.728706i	$0.740122\pi$
$20$	56.4894	0.631571
$21$	21.0000	0.218218
$22$	−52.9094	−0.512742
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−24.0000	−0.204124
$25$	74.4408	0.595526
$26$	16.1872	0.122099
$27$	−27.0000	−0.192450
$28$	−28.0000	−0.188982
$29$	−191.092	−1.22361	−0.611807	−	0.791007i	$-0.709557\pi$
$29$	−191.092	−1.22361	−0.611807	+	0.791007i	$0.709557\pi$
$30$	−84.7341	−0.515675
$31$	47.5116	0.275269	0.137634	−	0.990483i	$-0.456050\pi$
$31$	47.5116	0.275269	0.137634	+	0.990483i	$0.456050\pi$
$32$	32.0000	0.176777
$33$	79.3641	0.418652
$34$	−183.616	−0.926172
$35$	−98.8565	−0.477423
$36$	36.0000	0.166667
$37$	−80.9441	−0.359652	−0.179826	−	0.983698i	$-0.557553\pi$
$37$	−80.9441	−0.359652	−0.179826	+	0.983698i	$0.557553\pi$
$38$	−226.867	−0.968492
$39$	−24.2808	−0.0996932
$40$	112.979	0.446588
$41$	141.469	0.538873	0.269436	−	0.963018i	$-0.413163\pi$
$41$	141.469	0.538873	0.269436	+	0.963018i	$0.413163\pi$
$42$	42.0000	0.154303
$43$	−223.196	−0.791560	−0.395780	−	0.918345i	$-0.629526\pi$
$43$	−223.196	−0.791560	−0.395780	+	0.918345i	$0.629526\pi$
$44$	−105.819	−0.362563
$45$	127.101	0.421047
$46$	−46.0000	−0.147442
$47$	33.0423	0.102547	0.0512735	−	0.998685i	$-0.483672\pi$
$47$	33.0423	0.102547	0.0512735	+	0.998685i	$0.483672\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	148.882	0.421101
$51$	275.424	0.756216
$52$	32.3744	0.0863368
$53$	76.0827	0.197184	0.0985921	−	0.995128i	$-0.468566\pi$
$53$	76.0827	0.197184	0.0985921	+	0.995128i	$0.468566\pi$
$54$	−54.0000	−0.136083
$55$	−373.602	−0.915937
$56$	−56.0000	−0.133631
$57$	340.301	0.790770
$58$	−382.183	−0.865226
$59$	−548.415	−1.21013	−0.605064	−	0.796177i	$-0.706852\pi$
$59$	−548.415	−1.21013	−0.605064	+	0.796177i	$0.706852\pi$
$60$	−169.468	−0.364638
$61$	533.017	1.11878	0.559392	−	0.828903i	$-0.311034\pi$
$61$	533.017	1.11878	0.559392	+	0.828903i	$0.311034\pi$
$62$	95.0232	0.194644
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	114.301	0.218111
$66$	158.728	0.296032
$67$	625.568	1.14068	0.570338	−	0.821410i	$-0.306812\pi$
$67$	625.568	1.14068	0.570338	+	0.821410i	$0.306812\pi$
$68$	−367.231	−0.654902
$69$	69.0000	0.120386
$70$	−197.713	−0.337589
$71$	247.335	0.413426	0.206713	−	0.978402i	$-0.433723\pi$
$71$	247.335	0.413426	0.206713	+	0.978402i	$0.433723\pi$
$72$	72.0000	0.117851
$73$	−956.751	−1.53396	−0.766981	−	0.641670i	$-0.778242\pi$
$73$	−956.751	−1.53396	−0.766981	+	0.641670i	$0.778242\pi$
$74$	−161.888	−0.254312
$75$	−223.322	−0.343827
$76$	−453.734	−0.684827
$77$	185.183	0.274072
$78$	−48.5615	−0.0704937
$79$	−984.717	−1.40240	−0.701198	−	0.712967i	$-0.747351\pi$
$79$	−984.717	−1.40240	−0.701198	+	0.712967i	$0.747351\pi$
$80$	225.958	0.315785
$81$	81.0000	0.111111
$82$	282.938	0.381040
$83$	188.927	0.249849	0.124924	−	0.992166i	$-0.460131\pi$
$83$	188.927	0.249849	0.124924	+	0.992166i	$0.460131\pi$
$84$	84.0000	0.109109
$85$	−1296.54	−1.65447
$86$	−446.392	−0.559718
$87$	573.275	0.706454
$88$	−211.638	−0.256371
$89$	−532.128	−0.633769	−0.316884	−	0.948464i	$-0.602637\pi$
$89$	−532.128	−0.633769	−0.316884	+	0.948464i	$0.602637\pi$
$90$	254.202	0.297725
$91$	−56.6551	−0.0652645
$92$	−92.0000	−0.104257
$93$	−142.535	−0.158927
$94$	66.0846	0.0725117
$95$	−1601.95	−1.73007
$96$	−96.0000	−0.102062
$97$	−115.772	−0.121184	−0.0605921	−	0.998163i	$-0.519299\pi$
$97$	−115.772	−0.121184	−0.0605921	+	0.998163i	$0.519299\pi$
$98$	98.0000	0.101015
$99$	−238.092	−0.241709
$100$	297.763	0.297763
$101$	1795.29	1.76870	0.884348	−	0.466829i	$-0.154604\pi$
$101$	1795.29	1.76870	0.884348	+	0.466829i	$0.154604\pi$
$102$	550.847	0.534725
$103$	−474.877	−0.454282	−0.227141	−	0.973862i	$-0.572938\pi$
$103$	−474.877	−0.454282	−0.227141	+	0.973862i	$0.572938\pi$
$104$	64.7487	0.0610494
$105$	296.569	0.275640
$106$	152.165	0.139430
$107$	−1113.03	−1.00562	−0.502808	−	0.864398i	$-0.667700\pi$
$107$	−1113.03	−1.00562	−0.502808	+	0.864398i	$0.667700\pi$
$108$	−108.000	−0.0962250
$109$	−240.002	−0.210899	−0.105450	−	0.994425i	$-0.533628\pi$
$109$	−240.002	−0.210899	−0.105450	+	0.994425i	$0.533628\pi$
$110$	−747.205	−0.647665
$111$	242.832	0.207645
$112$	−112.000	−0.0944911
$113$	1253.18	1.04327	0.521634	−	0.853169i	$-0.325323\pi$
$113$	1253.18	1.04327	0.521634	+	0.853169i	$0.325323\pi$
$114$	680.601	0.559159
$115$	−324.814	−0.263383
$116$	−764.366	−0.611807
$117$	72.8423	0.0575579
$118$	−1096.83	−0.855689
$119$	642.655	0.495060
$120$	−338.936	−0.257838
$121$	−631.149	−0.474192
$122$	1066.03	0.791100
$123$	−424.408	−0.311118
$124$	190.046	0.137634
$125$	−714.015	−0.510907
$126$	−126.000	−0.0890871
$127$	−1957.84	−1.36796	−0.683979	−	0.729502i	$-0.739752\pi$
$127$	−1957.84	−1.36796	−0.683979	+	0.729502i	$0.739752\pi$
$128$	128.000	0.0883883
$129$	669.588	0.457007
$130$	228.601	0.154228
$131$	−1169.85	−0.780232	−0.390116	−	0.920766i	$-0.627565\pi$
$131$	−1169.85	−0.780232	−0.390116	+	0.920766i	$0.627565\pi$
$132$	317.456	0.209326
$133$	794.035	0.517681
$134$	1251.14	0.806580
$135$	−381.303	−0.243092
$136$	−734.463	−0.463086
$137$	2110.94	1.31642	0.658211	−	0.752834i	$-0.271314\pi$
$137$	2110.94	1.31642	0.658211	+	0.752834i	$0.271314\pi$
$138$	138.000	0.0851257
$139$	−1159.49	−0.707528	−0.353764	−	0.935335i	$-0.615098\pi$
$139$	−1159.49	−0.707528	−0.353764	+	0.935335i	$0.615098\pi$
$140$	−395.426	−0.238711
$141$	−99.1269	−0.0592056
$142$	494.670	0.292336
$143$	−214.113	−0.125210
$144$	144.000	0.0833333
$145$	−2698.66	−1.54560
$146$	−1913.50	−1.08467
$147$	−147.000	−0.0824786
$148$	−323.776	−0.179826
$149$	2327.79	1.27987	0.639934	−	0.768430i	$-0.278962\pi$
$149$	2327.79	1.27987	0.639934	+	0.768430i	$0.278962\pi$
$150$	−446.645	−0.243123
$151$	−1155.46	−0.622716	−0.311358	−	0.950293i	$-0.600784\pi$
$151$	−1155.46	−0.622716	−0.311358	+	0.950293i	$0.600784\pi$
$152$	−907.468	−0.484246
$153$	−826.271	−0.436602
$154$	370.366	0.193798
$155$	670.975	0.347703
$156$	−97.1231	−0.0498466
$157$	2712.33	1.37877	0.689386	−	0.724394i	$-0.257880\pi$
$157$	2712.33	1.37877	0.689386	+	0.724394i	$0.257880\pi$
$158$	−1969.43	−0.991644
$159$	−228.248	−0.113844
$160$	451.915	0.223294
$161$	161.000	0.0788110
$162$	162.000	0.0785674
$163$	1698.54	0.816195	0.408098	−	0.912938i	$-0.366192\pi$
$163$	1698.54	0.816195	0.408098	+	0.912938i	$0.366192\pi$
$164$	565.877	0.269436
$165$	1120.81	0.528817
$166$	377.854	0.176670
$167$	−3546.67	−1.64341	−0.821705	−	0.569913i	$-0.806977\pi$
$167$	−3546.67	−1.64341	−0.821705	+	0.569913i	$0.806977\pi$
$168$	168.000	0.0771517
$169$	−2131.49	−0.970184
$170$	−2593.09	−1.16989
$171$	−1020.90	−0.456551
$172$	−892.784	−0.395780
$173$	−3647.95	−1.60317	−0.801585	−	0.597880i	$-0.796010\pi$
$173$	−3647.95	−1.60317	−0.801585	+	0.597880i	$0.796010\pi$
$174$	1146.55	0.499539
$175$	−521.086	−0.225088
$176$	−423.275	−0.181282
$177$	1645.24	0.698667
$178$	−1064.26	−0.448142
$179$	−983.805	−0.410799	−0.205399	−	0.978678i	$-0.565849\pi$
$179$	−983.805	−0.410799	−0.205399	+	0.978678i	$0.565849\pi$
$180$	508.405	0.210524
$181$	−126.446	−0.0519262	−0.0259631	−	0.999663i	$-0.508265\pi$
$181$	−126.446	−0.0519262	−0.0259631	+	0.999663i	$0.508265\pi$
$182$	−113.310	−0.0461490
$183$	−1599.05	−0.645931
$184$	−184.000	−0.0737210
$185$	−1143.12	−0.454291
$186$	−285.070	−0.112378
$187$	2428.75	0.949774
$188$	132.169	0.0512735
$189$	189.000	0.0727393
$190$	−3203.90	−1.22334
$191$	−1069.67	−0.405228	−0.202614	−	0.979259i	$-0.564944\pi$
$191$	−1069.67	−0.405228	−0.202614	+	0.979259i	$0.564944\pi$
$192$	−192.000	−0.0721688
$193$	2401.54	0.895684	0.447842	−	0.894113i	$-0.352193\pi$
$193$	2401.54	0.895684	0.447842	+	0.894113i	$0.352193\pi$
$194$	−231.544	−0.0856901
$195$	−342.902	−0.125927
$196$	196.000	0.0714286
$197$	−4170.53	−1.50832	−0.754158	−	0.656694i	$-0.771955\pi$
$197$	−4170.53	−1.50832	−0.754158	+	0.656694i	$0.771955\pi$
$198$	−476.184	−0.170914
$199$	5479.81	1.95203	0.976013	−	0.217712i	$-0.0698594\pi$
$199$	5479.81	1.95203	0.976013	+	0.217712i	$0.0698594\pi$
$200$	595.526	0.210550
$201$	−1876.70	−0.658570
$202$	3590.58	1.25066
$203$	1337.64	0.462483
$204$	1101.69	0.378108
$205$	1997.88	0.680672
$206$	−949.754	−0.321226
$207$	−207.000	−0.0695048
$208$	129.497	0.0431684
$209$	3000.85	0.993172
$210$	593.139	0.194907
$211$	−4022.86	−1.31254	−0.656268	−	0.754528i	$-0.727866\pi$
$211$	−4022.86	−1.31254	−0.656268	+	0.754528i	$0.727866\pi$
$212$	304.331	0.0985921
$213$	−742.005	−0.238692
$214$	−2226.06	−0.711078
$215$	−3152.05	−0.999852
$216$	−216.000	−0.0680414
$217$	−332.581	−0.104042
$218$	−480.004	−0.149128
$219$	2870.25	0.885633
$220$	−1494.41	−0.457969
$221$	−743.055	−0.226169
$222$	485.665	0.146827
$223$	−3130.06	−0.939929	−0.469965	−	0.882685i	$-0.655733\pi$
$223$	−3130.06	−0.939929	−0.469965	+	0.882685i	$0.655733\pi$
$224$	−224.000	−0.0668153
$225$	669.967	0.198509
$226$	2506.36	0.737702
$227$	602.812	0.176256	0.0881278	−	0.996109i	$-0.471912\pi$
$227$	602.812	0.176256	0.0881278	+	0.996109i	$0.471912\pi$
$228$	1361.20	0.395385
$229$	−2273.31	−0.656003	−0.328001	−	0.944677i	$-0.606375\pi$
$229$	−2273.31	−0.656003	−0.328001	+	0.944677i	$0.606375\pi$
$230$	−649.628	−0.186240
$231$	−555.549	−0.158236
$232$	−1528.73	−0.432613
$233$	−2954.99	−0.830848	−0.415424	−	0.909628i	$-0.636367\pi$
$233$	−2954.99	−0.830848	−0.415424	+	0.909628i	$0.636367\pi$
$234$	145.685	0.0406996
$235$	466.635	0.129531
$236$	−2193.66	−0.605064
$237$	2954.15	0.809674
$238$	1285.31	0.350060
$239$	−1653.84	−0.447606	−0.223803	−	0.974634i	$-0.571847\pi$
$239$	−1653.84	−0.447606	−0.223803	+	0.974634i	$0.571847\pi$
$240$	−677.873	−0.182319
$241$	3808.39	1.01792	0.508962	−	0.860789i	$-0.330029\pi$
$241$	3808.39	1.01792	0.508962	+	0.860789i	$0.330029\pi$
$242$	−1262.30	−0.335304
$243$	−243.000	−0.0641500
$244$	2132.07	0.559392
$245$	691.995	0.180449
$246$	−848.815	−0.219994
$247$	−918.084	−0.236503
$248$	380.093	0.0973222
$249$	−566.781	−0.144250
$250$	−1428.03	−0.361266
$251$	2215.87	0.557229	0.278614	−	0.960403i	$-0.410125\pi$
$251$	2215.87	0.557229	0.278614	+	0.960403i	$0.410125\pi$
$252$	−252.000	−0.0629941
$253$	608.458	0.151199
$254$	−3915.69	−0.967292
$255$	3889.63	0.955208
$256$	256.000	0.0625000
$257$	5877.88	1.42666	0.713331	−	0.700827i	$-0.247186\pi$
$257$	5877.88	1.42666	0.713331	+	0.700827i	$0.247186\pi$
$258$	1339.18	0.323153
$259$	566.609	0.135936
$260$	457.202	0.109056
$261$	−1719.82	−0.407871
$262$	−2339.70	−0.551707
$263$	−1127.30	−0.264305	−0.132152	−	0.991229i	$-0.542189\pi$
$263$	−1127.30	−0.264305	−0.132152	+	0.991229i	$0.542189\pi$
$264$	634.913	0.148016
$265$	1074.47	0.249071
$266$	1588.07	0.366055
$267$	1596.38	0.365907
$268$	2502.27	0.570338
$269$	3949.40	0.895165	0.447583	−	0.894243i	$-0.352285\pi$
$269$	3949.40	0.895165	0.447583	+	0.894243i	$0.352285\pi$
$270$	−762.607	−0.171892
$271$	6787.62	1.52147	0.760736	−	0.649062i	$-0.224838\pi$
$271$	6787.62	1.52147	0.760736	+	0.649062i	$0.224838\pi$
$272$	−1468.93	−0.327451
$273$	169.965	0.0376805
$274$	4221.88	0.930851
$275$	−1969.31	−0.431832
$276$	276.000	0.0601929
$277$	3593.19	0.779400	0.389700	−	0.920942i	$-0.372579\pi$
$277$	3593.19	0.779400	0.389700	+	0.920942i	$0.372579\pi$
$278$	−2318.97	−0.500298
$279$	427.604	0.0917563
$280$	−790.852	−0.168794
$281$	−696.963	−0.147962	−0.0739810	−	0.997260i	$-0.523570\pi$
$281$	−696.963	−0.147962	−0.0739810	+	0.997260i	$0.523570\pi$
$282$	−198.254	−0.0418647
$283$	819.216	0.172075	0.0860377	−	0.996292i	$-0.472579\pi$
$283$	819.216	0.172075	0.0860377	+	0.996292i	$0.472579\pi$
$284$	989.340	0.206713
$285$	4805.84	0.998855
$286$	−428.227	−0.0885370
$287$	−990.284	−0.203675
$288$	288.000	0.0589256
$289$	3515.68	0.715588
$290$	−5397.33	−1.09290
$291$	347.316	0.0699657
$292$	−3827.00	−0.766981
$293$	6694.15	1.33473	0.667366	−	0.744730i	$-0.267422\pi$
$293$	6694.15	1.33473	0.667366	+	0.744730i	$0.267422\pi$
$294$	−294.000	−0.0583212
$295$	−7744.90	−1.52856
$296$	−647.553	−0.127156
$297$	714.277	0.139551
$298$	4655.59	0.905003
$299$	−186.153	−0.0360049
$300$	−893.290	−0.171914
$301$	1562.37	0.299182
$302$	−2310.92	−0.440327
$303$	−5385.88	−1.02116
$304$	−1814.94	−0.342414
$305$	7527.46	1.41318
$306$	−1652.54	−0.308724
$307$	2181.57	0.405566	0.202783	−	0.979224i	$-0.435001\pi$
$307$	2181.57	0.405566	0.202783	+	0.979224i	$0.435001\pi$
$308$	740.731	0.137036
$309$	1424.63	0.262280
$310$	1341.95	0.245863
$311$	6568.11	1.19757	0.598784	−	0.800911i	$-0.295651\pi$
$311$	6568.11	1.19757	0.598784	+	0.800911i	$0.295651\pi$
$312$	−194.246	−0.0352469
$313$	8879.68	1.60354	0.801772	−	0.597630i	$-0.203891\pi$
$313$	8879.68	1.60354	0.801772	+	0.597630i	$0.203891\pi$
$314$	5424.65	0.974939
$315$	−889.708	−0.159141
$316$	−3938.87	−0.701198
$317$	3939.74	0.698037	0.349018	−	0.937116i	$-0.386515\pi$
$317$	3939.74	0.698037	0.349018	+	0.937116i	$0.386515\pi$
$318$	−456.496	−0.0805001
$319$	5055.27	0.887275
$320$	903.830	0.157893
$321$	3339.10	0.580593
$322$	322.000	0.0557278
$323$	10414.1	1.79398
$324$	324.000	0.0555556
$325$	602.493	0.102832
$326$	3397.08	0.577137
$327$	720.006	0.121763
$328$	1131.75	0.190520
$329$	−231.296	−0.0387592
$330$	2241.61	0.373930
$331$	−458.540	−0.0761440	−0.0380720	−	0.999275i	$-0.512122\pi$
$331$	−458.540	−0.0761440	−0.0380720	+	0.999275i	$0.512122\pi$
$332$	755.708	0.124924
$333$	−728.497	−0.119884
$334$	−7093.34	−1.16207
$335$	8834.49	1.44084
$336$	336.000	0.0545545
$337$	−1678.49	−0.271315	−0.135657	−	0.990756i	$-0.543315\pi$
$337$	−1678.49	−0.271315	−0.135657	+	0.990756i	$0.543315\pi$
$338$	−4262.99	−0.686024
$339$	−3759.54	−0.602331
$340$	−5186.17	−0.827234
$341$	−1256.90	−0.199605
$342$	−2041.80	−0.322831
$343$	−343.000	−0.0539949
$344$	−1785.57	−0.279859
$345$	974.442	0.152064
$346$	−7295.90	−1.13361
$347$	−3047.76	−0.471505	−0.235753	−	0.971813i	$-0.575756\pi$
$347$	−3047.76	−0.471505	−0.235753	+	0.971813i	$0.575756\pi$
$348$	2293.10	0.353227
$349$	10995.9	1.68653	0.843264	−	0.537499i	$-0.180631\pi$
$349$	10995.9	1.68653	0.843264	+	0.537499i	$0.180631\pi$
$350$	−1042.17	−0.159161
$351$	−218.527	−0.0332311
$352$	−846.550	−0.128185
$353$	3460.09	0.521706	0.260853	−	0.965379i	$-0.415996\pi$
$353$	3460.09	0.521706	0.260853	+	0.965379i	$0.415996\pi$
$354$	3290.49	0.494032
$355$	3492.95	0.522216
$356$	−2128.51	−0.316884
$357$	−1927.97	−0.285823
$358$	−1967.61	−0.290479
$359$	−5273.32	−0.775251	−0.387625	−	0.921817i	$-0.626705\pi$
$359$	−5273.32	−0.775251	−0.387625	+	0.921817i	$0.626705\pi$
$360$	1016.81	0.148863
$361$	6008.16	0.875953
$362$	−252.892	−0.0367174
$363$	1893.45	0.273775
$364$	−226.620	−0.0326323
$365$	−13511.6	−1.93761
$366$	−3198.10	−0.456742
$367$	9327.41	1.32667	0.663334	−	0.748324i	$-0.269141\pi$
$367$	9327.41	1.32667	0.663334	+	0.748324i	$0.269141\pi$
$368$	−368.000	−0.0521286
$369$	1273.22	0.179624
$370$	−2286.24	−0.321233
$371$	−532.579	−0.0745286
$372$	−570.139	−0.0794633
$373$	−7520.85	−1.04401	−0.522004	−	0.852943i	$-0.674815\pi$
$373$	−7520.85	−1.04401	−0.522004	+	0.852943i	$0.674815\pi$
$374$	4857.50	0.671591
$375$	2142.04	0.294972
$376$	264.338	0.0362559
$377$	−1546.62	−0.211286
$378$	378.000	0.0514344
$379$	508.496	0.0689174	0.0344587	−	0.999406i	$-0.489029\pi$
$379$	508.496	0.0689174	0.0344587	+	0.999406i	$0.489029\pi$
$380$	−6407.79	−0.865034
$381$	5873.53	0.789791
$382$	−2139.34	−0.286539
$383$	−2568.46	−0.342669	−0.171335	−	0.985213i	$-0.554808\pi$
$383$	−2568.46	−0.342669	−0.171335	+	0.985213i	$0.554808\pi$
$384$	−384.000	−0.0510310
$385$	2615.22	0.346192
$386$	4803.09	0.633344
$387$	−2008.76	−0.263853
$388$	−463.088	−0.0605921
$389$	−14463.5	−1.88516	−0.942579	−	0.333983i	$-0.891607\pi$
$389$	−14463.5	−1.88516	−0.942579	+	0.333983i	$0.891607\pi$
$390$	−685.803	−0.0890436
$391$	2111.58	0.273113
$392$	392.000	0.0505076
$393$	3509.55	0.450467
$394$	−8341.06	−1.06654
$395$	−13906.5	−1.77142
$396$	−952.369	−0.120854
$397$	−10102.2	−1.27712	−0.638558	−	0.769574i	$-0.720469\pi$
$397$	−10102.2	−1.27712	−0.638558	+	0.769574i	$0.720469\pi$
$398$	10959.6	1.38029
$399$	−2382.10	−0.298883
$400$	1191.05	0.148882
$401$	−1338.94	−0.166741	−0.0833707	−	0.996519i	$-0.526569\pi$
$401$	−1338.94	−0.166741	−0.0833707	+	0.996519i	$0.526569\pi$
$402$	−3753.41	−0.465679
$403$	384.539	0.0475317
$404$	7181.17	0.884348
$405$	1143.91	0.140349
$406$	2675.28	0.327025
$407$	2141.35	0.260793
$408$	2203.39	0.267363
$409$	14639.9	1.76992	0.884961	−	0.465665i	$-0.154185\pi$
$409$	14639.9	1.76992	0.884961	+	0.465665i	$0.154185\pi$
$410$	3995.76	0.481308
$411$	−6332.82	−0.760036
$412$	−1899.51	−0.227141
$413$	3838.90	0.457385
$414$	−414.000	−0.0491473
$415$	2668.09	0.315594
$416$	258.995	0.0305247
$417$	3478.46	0.408491
$418$	6001.70	0.702279
$419$	−6892.43	−0.803621	−0.401810	−	0.915723i	$-0.631619\pi$
$419$	−6892.43	−0.803621	−0.401810	+	0.915723i	$0.631619\pi$
$420$	1186.28	0.137820
$421$	−8467.62	−0.980253	−0.490126	−	0.871651i	$-0.663049\pi$
$421$	−8467.62	−0.980253	−0.490126	+	0.871651i	$0.663049\pi$
$422$	−8045.72	−0.928104
$423$	297.381	0.0341824
$424$	608.661	0.0697151
$425$	−6834.25	−0.780023
$426$	−1484.01	−0.168781
$427$	−3731.12	−0.422861
$428$	−4452.13	−0.502808
$429$	642.340	0.0722902
$430$	−6304.11	−0.707002
$431$	−9591.02	−1.07189	−0.535943	−	0.844254i	$-0.680044\pi$
$431$	−9591.02	−1.07189	−0.535943	+	0.844254i	$0.680044\pi$
$432$	−432.000	−0.0481125
$433$	6893.34	0.765064	0.382532	−	0.923942i	$-0.375052\pi$
$433$	6893.34	0.765064	0.382532	+	0.923942i	$0.375052\pi$
$434$	−665.162	−0.0735687
$435$	8095.99	0.892352
$436$	−960.008	−0.105450
$437$	2608.97	0.285593
$438$	5740.51	0.626237
$439$	4125.51	0.448519	0.224259	−	0.974530i	$-0.428004\pi$
$439$	4125.51	0.448519	0.224259	+	0.974530i	$0.428004\pi$
$440$	−2988.82	−0.323833
$441$	441.000	0.0476190
$442$	−1486.11	−0.159925
$443$	2265.00	0.242920	0.121460	−	0.992596i	$-0.461242\pi$
$443$	2265.00	0.242920	0.121460	+	0.992596i	$0.461242\pi$
$444$	971.329	0.103823
$445$	−7514.90	−0.800540
$446$	−6260.12	−0.664630
$447$	−6983.38	−0.738932
$448$	−448.000	−0.0472456
$449$	−7845.57	−0.824622	−0.412311	−	0.911043i	$-0.635278\pi$
$449$	−7845.57	−0.824622	−0.412311	+	0.911043i	$0.635278\pi$
$450$	1339.93	0.140367
$451$	−3742.52	−0.390751
$452$	5012.72	0.521634
$453$	3466.39	0.359526
$454$	1205.62	0.124632
$455$	−800.104	−0.0824383
$456$	2722.40	0.279579
$457$	8825.65	0.903384	0.451692	−	0.892174i	$-0.350821\pi$
$457$	8825.65	0.903384	0.451692	+	0.892174i	$0.350821\pi$
$458$	−4546.62	−0.463864
$459$	2478.81	0.252072
$460$	−1299.26	−0.131692
$461$	−10666.9	−1.07768	−0.538838	−	0.842409i	$-0.681137\pi$
$461$	−10666.9	−1.07768	−0.538838	+	0.842409i	$0.681137\pi$
$462$	−1111.10	−0.111889
$463$	−8226.78	−0.825768	−0.412884	−	0.910784i	$-0.635479\pi$
$463$	−8226.78	−0.825768	−0.412884	+	0.910784i	$0.635479\pi$
$464$	−3057.47	−0.305904
$465$	−2012.93	−0.200747
$466$	−5909.97	−0.587498
$467$	−2548.90	−0.252567	−0.126284	−	0.991994i	$-0.540305\pi$
$467$	−2548.90	−0.252567	−0.126284	+	0.991994i	$0.540305\pi$
$468$	291.369	0.0287789
$469$	−4378.98	−0.431135
$470$	933.270	0.0915926
$471$	−8136.98	−0.796034
$472$	−4387.32	−0.427845
$473$	5904.58	0.573981
$474$	5908.30	0.572526
$475$	−8444.08	−0.815665
$476$	2570.62	0.247530
$477$	684.744	0.0657280
$478$	−3307.68	−0.316506
$479$	19288.1	1.83987	0.919935	−	0.392071i	$-0.128241\pi$
$479$	19288.1	1.83987	0.919935	+	0.392071i	$0.128241\pi$
$480$	−1355.75	−0.128919
$481$	−655.128	−0.0621024
$482$	7616.77	0.719781
$483$	−483.000	−0.0455016
$484$	−2524.60	−0.237096
$485$	−1634.97	−0.153073
$486$	−486.000	−0.0453609
$487$	−8023.03	−0.746526	−0.373263	−	0.927725i	$-0.621761\pi$
$487$	−8023.03	−0.746526	−0.373263	+	0.927725i	$0.621761\pi$
$488$	4264.14	0.395550
$489$	−5095.62	−0.471230
$490$	1383.99	0.127597
$491$	14160.5	1.30153	0.650766	−	0.759278i	$-0.274448\pi$
$491$	14160.5	1.30153	0.650766	+	0.759278i	$0.274448\pi$
$492$	−1697.63	−0.155559
$493$	17543.7	1.60270
$494$	−1836.17	−0.167233
$495$	−3362.42	−0.305312
$496$	760.185	0.0688172
$497$	−1731.34	−0.156260
$498$	−1133.56	−0.102000
$499$	4554.91	0.408629	0.204315	−	0.978905i	$-0.434503\pi$
$499$	4554.91	0.408629	0.204315	+	0.978905i	$0.434503\pi$
$500$	−2856.06	−0.255454
$501$	10640.0	0.948823
$502$	4431.74	0.394020
$503$	−7050.45	−0.624978	−0.312489	−	0.949921i	$-0.601163\pi$
$503$	−7050.45	−0.624978	−0.312489	+	0.949921i	$0.601163\pi$
$504$	−504.000	−0.0445435
$505$	25353.7	2.23411
$506$	1216.92	0.106914
$507$	6394.48	0.560136
$508$	−7831.38	−0.683979
$509$	−9491.19	−0.826502	−0.413251	−	0.910617i	$-0.635607\pi$
$509$	−9491.19	−0.826502	−0.413251	+	0.910617i	$0.635607\pi$
$510$	7779.26	0.675434
$511$	6697.26	0.579783
$512$	512.000	0.0441942
$513$	3062.70	0.263590
$514$	11755.8	1.00880
$515$	−6706.38	−0.573822
$516$	2678.35	0.228504
$517$	−874.123	−0.0743596
$518$	1133.22	0.0961211
$519$	10943.9	0.925591
$520$	914.404	0.0771140
$521$	−5942.93	−0.499740	−0.249870	−	0.968279i	$-0.580388\pi$
$521$	−5942.93	−0.499740	−0.249870	+	0.968279i	$0.580388\pi$
$522$	−3439.65	−0.288409
$523$	10643.0	0.889840	0.444920	−	0.895570i	$-0.353232\pi$
$523$	10643.0	0.889840	0.444920	+	0.895570i	$0.353232\pi$
$524$	−4679.40	−0.390116
$525$	1563.26	0.129955
$526$	−2254.60	−0.186892
$527$	−4361.94	−0.360548
$528$	1269.83	0.104663
$529$	529.000	0.0434783
$530$	2148.93	0.176120
$531$	−4935.73	−0.403376
$532$	3176.14	0.258840
$533$	1144.99	0.0930491
$534$	3192.77	0.258735
$535$	−15718.6	−1.27023
$536$	5004.54	0.403290
$537$	2951.41	0.237175
$538$	7898.81	0.632977
$539$	−1296.28	−0.103589
$540$	−1525.21	−0.121546
$541$	71.2013	0.00565838	0.00282919	−	0.999996i	$-0.499099\pi$
$541$	71.2013	0.00565838	0.00282919	+	0.999996i	$0.499099\pi$
$542$	13575.2	1.07584
$543$	379.337	0.0299796
$544$	−2937.85	−0.231543
$545$	−3389.39	−0.266396
$546$	339.931	0.0266441
$547$	17752.5	1.38764	0.693822	−	0.720146i	$-0.255925\pi$
$547$	17752.5	1.38764	0.693822	+	0.720146i	$0.255925\pi$
$548$	8443.76	0.658211
$549$	4797.16	0.372928
$550$	−3938.62	−0.305351
$551$	21676.2	1.67593
$552$	552.000	0.0425628
$553$	6893.02	0.530056
$554$	7186.38	0.551119
$555$	3429.36	0.262285
$556$	−4637.95	−0.353764
$557$	−5569.30	−0.423660	−0.211830	−	0.977307i	$-0.567942\pi$
$557$	−5569.30	−0.423660	−0.211830	+	0.977307i	$0.567942\pi$
$558$	855.209	0.0648815
$559$	−1806.46	−0.136682
$560$	−1581.70	−0.119356
$561$	−7286.25	−0.548352
$562$	−1393.93	−0.104625
$563$	−15341.9	−1.14846	−0.574231	−	0.818693i	$-0.694699\pi$
$563$	−15341.9	−1.14846	−0.574231	+	0.818693i	$0.694699\pi$
$564$	−396.507	−0.0296028
$565$	17697.9	1.31780
$566$	1638.43	0.121676
$567$	−567.000	−0.0419961
$568$	1978.68	0.146168
$569$	−15530.0	−1.14420	−0.572102	−	0.820182i	$-0.693872\pi$
$569$	−15530.0	−1.14420	−0.572102	+	0.820182i	$0.693872\pi$
$570$	9611.69	0.706297
$571$	−13666.3	−1.00160	−0.500802	−	0.865562i	$-0.666961\pi$
$571$	−13666.3	−1.00160	−0.500802	+	0.865562i	$0.666961\pi$
$572$	−856.454	−0.0626051
$573$	3209.01	0.233958
$574$	−1980.57	−0.144020
$575$	−1712.14	−0.124176
$576$	576.000	0.0416667
$577$	−3109.53	−0.224353	−0.112176	−	0.993688i	$-0.535782\pi$
$577$	−3109.53	−0.224353	−0.112176	+	0.993688i	$0.535782\pi$
$578$	7031.37	0.505997
$579$	−7204.63	−0.517123
$580$	−10794.7	−0.772799
$581$	−1322.49	−0.0944339
$582$	694.632	0.0494732
$583$	−2012.74	−0.142983
$584$	−7654.01	−0.542337
$585$	1028.70	0.0727038
$586$	13388.3	0.943798
$587$	19448.8	1.36753	0.683764	−	0.729703i	$-0.260342\pi$
$587$	19448.8	1.36753	0.683764	+	0.729703i	$0.260342\pi$
$588$	−588.000	−0.0412393
$589$	−5389.41	−0.377023
$590$	−15489.8	−1.08086
$591$	12511.6	0.870826
$592$	−1295.11	−0.0899130
$593$	−10439.2	−0.722911	−0.361456	−	0.932389i	$-0.617720\pi$
$593$	−10439.2	−0.722911	−0.361456	+	0.932389i	$0.617720\pi$
$594$	1428.55	0.0986772
$595$	9075.80	0.625330
$596$	9311.17	0.639934
$597$	−16439.4	−1.12700
$598$	−372.305	−0.0254593
$599$	−14193.9	−0.968189	−0.484095	−	0.875016i	$-0.660851\pi$
$599$	−14193.9	−0.968189	−0.484095	+	0.875016i	$0.660851\pi$
$600$	−1786.58	−0.121561
$601$	3753.28	0.254741	0.127371	−	0.991855i	$-0.459346\pi$
$601$	3753.28	0.254741	0.127371	+	0.991855i	$0.459346\pi$
$602$	3124.75	0.211553
$603$	5630.11	0.380225
$604$	−4621.85	−0.311358
$605$	−8913.31	−0.598971
$606$	−10771.8	−0.722067
$607$	−2494.32	−0.166789	−0.0833947	−	0.996517i	$-0.526576\pi$
$607$	−2494.32	−0.166789	−0.0833947	+	0.996517i	$0.526576\pi$
$608$	−3629.87	−0.242123
$609$	−4012.92	−0.267015
$610$	15054.9	0.999272
$611$	267.431	0.0177072
$612$	−3305.08	−0.218301
$613$	1919.03	0.126442	0.0632210	−	0.998000i	$-0.479863\pi$
$613$	1919.03	0.126442	0.0632210	+	0.998000i	$0.479863\pi$
$614$	4363.14	0.286779
$615$	−5993.63	−0.392986
$616$	1481.46	0.0968991
$617$	−9250.73	−0.603598	−0.301799	−	0.953372i	$-0.597587\pi$
$617$	−9250.73	−0.603598	−0.301799	+	0.953372i	$0.597587\pi$
$618$	2849.26	0.185460
$619$	12574.8	0.816520	0.408260	−	0.912866i	$-0.366136\pi$
$619$	12574.8	0.816520	0.408260	+	0.912866i	$0.366136\pi$
$620$	2683.90	0.173852
$621$	621.000	0.0401286
$622$	13136.2	0.846808
$623$	3724.89	0.239542
$624$	−388.492	−0.0249233
$625$	−19388.7	−1.24087
$626$	17759.4	1.13388
$627$	−9002.55	−0.573408
$628$	10849.3	0.689386
$629$	7431.30	0.471074
$630$	−1779.42	−0.112530
$631$	24675.4	1.55675	0.778376	−	0.627798i	$-0.216044\pi$
$631$	24675.4	1.55675	0.778376	+	0.627798i	$0.216044\pi$
$632$	−7877.73	−0.495822
$633$	12068.6	0.757793
$634$	7879.47	0.493586
$635$	−27649.4	−1.72792
$636$	−912.992	−0.0569222
$637$	396.586	0.0246677
$638$	10110.5	0.627398
$639$	2226.01	0.137809
$640$	1807.66	0.111647
$641$	6195.13	0.381736	0.190868	−	0.981616i	$-0.438870\pi$
$641$	6195.13	0.381736	0.190868	+	0.981616i	$0.438870\pi$
$642$	6678.19	0.410541
$643$	−10508.5	−0.644503	−0.322252	−	0.946654i	$-0.604440\pi$
$643$	−10508.5	−0.644503	−0.322252	+	0.946654i	$0.604440\pi$
$644$	644.000	0.0394055
$645$	9456.16	0.577265
$646$	20828.2	1.26853
$647$	−26059.5	−1.58347	−0.791735	−	0.610865i	$-0.790822\pi$
$647$	−26059.5	−1.58347	−0.791735	+	0.610865i	$0.790822\pi$
$648$	648.000	0.0392837
$649$	14508.1	0.877495
$650$	1204.99	0.0727130
$651$	997.743	0.0600686
$652$	6794.15	0.408098
$653$	3976.42	0.238299	0.119150	−	0.992876i	$-0.461983\pi$
$653$	3976.42	0.238299	0.119150	+	0.992876i	$0.461983\pi$
$654$	1440.01	0.0860993
$655$	−16521.0	−0.985543
$656$	2263.51	0.134718
$657$	−8610.76	−0.511321
$658$	−462.592	−0.0274069
$659$	11556.7	0.683135	0.341568	−	0.939857i	$-0.389042\pi$
$659$	11556.7	0.683135	0.341568	+	0.939857i	$0.389042\pi$
$660$	4483.23	0.264408
$661$	8759.94	0.515465	0.257732	−	0.966216i	$-0.417025\pi$
$661$	8759.94	0.515465	0.257732	+	0.966216i	$0.417025\pi$
$662$	−917.081	−0.0538419
$663$	2229.17	0.130579
$664$	1511.42	0.0883348
$665$	11213.6	0.653904
$666$	−1456.99	−0.0847708
$667$	4395.11	0.255141
$668$	−14186.7	−0.821705
$669$	9390.18	0.542668
$670$	17669.0	1.01882
$671$	−14100.8	−0.811260
$672$	672.000	0.0385758
$673$	19384.0	1.11025	0.555125	−	0.831767i	$-0.312670\pi$
$673$	19384.0	1.11025	0.555125	+	0.831767i	$0.312670\pi$
$674$	−3356.98	−0.191849
$675$	−2009.90	−0.114609
$676$	−8525.98	−0.485092
$677$	−32955.2	−1.87086	−0.935429	−	0.353514i	$-0.884987\pi$
$677$	−32955.2	−1.87086	−0.935429	+	0.353514i	$0.884987\pi$
$678$	−7519.09	−0.425913
$679$	810.404	0.0458033
$680$	−10372.3	−0.584943
$681$	−1808.44	−0.101761
$682$	−2513.81	−0.141142
$683$	10338.1	0.579177	0.289588	−	0.957151i	$-0.406482\pi$
$683$	10338.1	0.579177	0.289588	+	0.957151i	$0.406482\pi$
$684$	−4083.61	−0.228276
$685$	29811.4	1.66283
$686$	−686.000	−0.0381802
$687$	6819.93	0.378743
$688$	−3571.14	−0.197890
$689$	615.782	0.0340485
$690$	1948.88	0.107526
$691$	−15022.8	−0.827052	−0.413526	−	0.910492i	$-0.635703\pi$
$691$	−15022.8	−0.827052	−0.413526	+	0.910492i	$0.635703\pi$
$692$	−14591.8	−0.801585
$693$	1666.65	0.0913573
$694$	−6095.52	−0.333405
$695$	−16374.7	−0.893708
$696$	4586.20	0.249769
$697$	−12988.0	−0.705818
$698$	21991.9	1.19256
$699$	8864.96	0.479690
$700$	−2084.34	−0.112544
$701$	−1370.50	−0.0738416	−0.0369208	−	0.999318i	$-0.511755\pi$
$701$	−1370.50	−0.0738416	−0.0369208	+	0.999318i	$0.511755\pi$
$702$	−437.054	−0.0234979
$703$	9181.77	0.492599
$704$	−1693.10	−0.0906408
$705$	−1399.90	−0.0747850
$706$	6920.19	0.368902
$707$	−12567.0	−0.668504
$708$	6580.98	0.349334
$709$	−1743.85	−0.0923719	−0.0461860	−	0.998933i	$-0.514707\pi$
$709$	−1743.85	−0.0923719	−0.0461860	+	0.998933i	$0.514707\pi$
$710$	6985.90	0.369262
$711$	−8862.45	−0.467465
$712$	−4257.02	−0.224071
$713$	−1092.77	−0.0573975
$714$	−3855.93	−0.202107
$715$	−3023.78	−0.158158
$716$	−3935.22	−0.205399
$717$	4961.52	0.258426
$718$	−10546.6	−0.548185
$719$	−8844.69	−0.458764	−0.229382	−	0.973336i	$-0.573671\pi$
$719$	−8844.69	−0.458764	−0.229382	+	0.973336i	$0.573671\pi$
$720$	2033.62	0.105262
$721$	3324.14	0.171702
$722$	12016.3	0.619392
$723$	−11425.2	−0.587699
$724$	−505.783	−0.0259631
$725$	−14225.0	−0.728695
$726$	3786.90	0.193588
$727$	30789.8	1.57074	0.785372	−	0.619024i	$-0.212472\pi$
$727$	30789.8	1.57074	0.785372	+	0.619024i	$0.212472\pi$
$728$	−453.241	−0.0230745
$729$	729.000	0.0370370
$730$	−27023.1	−1.37010
$731$	20491.2	1.03679
$732$	−6396.21	−0.322965
$733$	−858.096	−0.0432394	−0.0216197	−	0.999766i	$-0.506882\pi$
$733$	−858.096	−0.0432394	−0.0216197	+	0.999766i	$0.506882\pi$
$734$	18654.8	0.938095
$735$	−2075.99	−0.104182
$736$	−736.000	−0.0368605
$737$	−16549.2	−0.827134
$738$	2546.45	0.127013
$739$	−35680.0	−1.77606	−0.888031	−	0.459783i	$-0.847927\pi$
$739$	−35680.0	−1.77606	−0.888031	+	0.459783i	$0.847927\pi$
$740$	−4572.48	−0.227146
$741$	2754.25	0.136545
$742$	−1065.16	−0.0526997
$743$	−19004.5	−0.938370	−0.469185	−	0.883100i	$-0.655452\pi$
$743$	−19004.5	−0.938370	−0.469185	+	0.883100i	$0.655452\pi$
$744$	−1140.28	−0.0561890
$745$	32873.9	1.61665
$746$	−15041.7	−0.738225
$747$	1700.34	0.0832828
$748$	9715.00	0.474887
$749$	7791.23	0.380087
$750$	4284.09	0.208577
$751$	6432.31	0.312541	0.156271	−	0.987714i	$-0.450053\pi$
$751$	6432.31	0.312541	0.156271	+	0.987714i	$0.450053\pi$
$752$	528.677	0.0256368
$753$	−6647.61	−0.321716
$754$	−3093.23	−0.149402
$755$	−16317.8	−0.786579
$756$	756.000	0.0363696
$757$	−6511.07	−0.312614	−0.156307	−	0.987709i	$-0.549959\pi$
$757$	−6511.07	−0.312614	−0.156307	+	0.987709i	$0.549959\pi$
$758$	1016.99	0.0487319
$759$	−1825.37	−0.0872950
$760$	−12815.6	−0.611671
$761$	−32639.6	−1.55478	−0.777388	−	0.629021i	$-0.783456\pi$
$761$	−32639.6	−1.55478	−0.777388	+	0.629021i	$0.783456\pi$
$762$	11747.1	0.558466
$763$	1680.01	0.0797125
$764$	−4278.68	−0.202614
$765$	−11668.9	−0.551489
$766$	−5136.93	−0.242304
$767$	−4438.64	−0.208957
$768$	−768.000	−0.0360844
$769$	−7106.99	−0.333270	−0.166635	−	0.986019i	$-0.553290\pi$
$769$	−7106.99	−0.333270	−0.166635	+	0.986019i	$0.553290\pi$
$770$	5230.43	0.244795
$771$	−17633.6	−0.823684
$772$	9606.18	0.447842
$773$	24521.4	1.14097	0.570486	−	0.821307i	$-0.306755\pi$
$773$	24521.4	1.14097	0.570486	+	0.821307i	$0.306755\pi$
$774$	−4017.53	−0.186573
$775$	3536.80	0.163930
$776$	−926.176	−0.0428451
$777$	−1699.83	−0.0784825
$778$	−28926.9	−1.33301
$779$	−16047.3	−0.738069
$780$	−1371.61	−0.0629633
$781$	−6543.17	−0.299786
$782$	4223.16	0.193120
$783$	5159.47	0.235485
$784$	784.000	0.0357143
$785$	38304.4	1.74158
$786$	7019.10	0.318528
$787$	−15034.2	−0.680957	−0.340478	−	0.940252i	$-0.610589\pi$
$787$	−15034.2	−0.680957	−0.340478	+	0.940252i	$0.610589\pi$
$788$	−16682.1	−0.754158
$789$	3381.89	0.152596
$790$	−27813.0	−1.25259
$791$	−8772.27	−0.394318
$792$	−1904.74	−0.0854570
$793$	4314.02	0.193185
$794$	−20204.4	−0.903057
$795$	−3223.40	−0.143801
$796$	21919.2	0.976013
$797$	16316.2	0.725155	0.362577	−	0.931954i	$-0.381897\pi$
$797$	16316.2	0.725155	0.362577	+	0.931954i	$0.381897\pi$
$798$	−4764.21	−0.211342
$799$	−3033.54	−0.134317
$800$	2382.11	0.105275
$801$	−4789.15	−0.211256
$802$	−2677.87	−0.117904
$803$	25310.6	1.11232
$804$	−7506.82	−0.329285
$805$	2273.70	0.0995495
$806$	769.078	0.0336100
$807$	−11848.2	−0.516824
$808$	14362.3	0.625328
$809$	−16328.0	−0.709593	−0.354797	−	0.934944i	$-0.615450\pi$
$809$	−16328.0	−0.709593	−0.354797	+	0.934944i	$0.615450\pi$
$810$	2287.82	0.0992418
$811$	26975.3	1.16798	0.583989	−	0.811762i	$-0.301491\pi$
$811$	26975.3	1.16798	0.583989	+	0.811762i	$0.301491\pi$
$812$	5350.56	0.231241
$813$	−20362.9	−0.878422
$814$	4282.70	0.184409
$815$	23987.4	1.03097
$816$	4406.78	0.189054
$817$	25317.9	1.08416
$818$	29279.9	1.25152
$819$	−509.896	−0.0217548
$820$	7991.51	0.340336
$821$	17249.6	0.733271	0.366635	−	0.930365i	$-0.380510\pi$
$821$	17249.6	0.733271	0.366635	+	0.930365i	$0.380510\pi$
$822$	−12665.6	−0.537427
$823$	21106.7	0.893966	0.446983	−	0.894542i	$-0.352498\pi$
$823$	21106.7	0.893966	0.446983	+	0.894542i	$0.352498\pi$
$824$	−3799.02	−0.160613
$825$	5907.93	0.249318
$826$	7677.81	0.323420
$827$	28630.8	1.20386	0.601929	−	0.798549i	$-0.294399\pi$
$827$	28630.8	1.20386	0.601929	+	0.798549i	$0.294399\pi$
$828$	−828.000	−0.0347524
$829$	−22196.8	−0.929949	−0.464975	−	0.885324i	$-0.653937\pi$
$829$	−22196.8	−0.929949	−0.464975	+	0.885324i	$0.653937\pi$
$830$	5336.19	0.223159
$831$	−10779.6	−0.449987
$832$	517.990	0.0215842
$833$	−4498.59	−0.187115
$834$	6956.92	0.288847
$835$	−50087.3	−2.07586
$836$	12003.4	0.496586
$837$	−1282.81	−0.0529755
$838$	−13784.9	−0.568246
$839$	−34606.8	−1.42403	−0.712014	−	0.702166i	$-0.752217\pi$
$839$	−34606.8	−1.42403	−0.712014	+	0.702166i	$0.752217\pi$
$840$	2372.56	0.0974535
$841$	12127.0	0.497232
$842$	−16935.2	−0.693143
$843$	2090.89	0.0854259
$844$	−16091.4	−0.656268
$845$	−30101.7	−1.22548
$846$	594.761	0.0241706
$847$	4418.04	0.179228
$848$	1217.32	0.0492960
$849$	−2457.65	−0.0993478
$850$	−13668.5	−0.551560
$851$	1861.71	0.0749926
$852$	−2968.02	−0.119346
$853$	−46163.3	−1.85299	−0.926495	−	0.376308i	$-0.877194\pi$
$853$	−46163.3	−1.85299	−0.926495	+	0.376308i	$0.877194\pi$
$854$	−7462.24	−0.299008
$855$	−14417.5	−0.576689
$856$	−8904.26	−0.355539
$857$	17078.5	0.680737	0.340369	−	0.940292i	$-0.389448\pi$
$857$	17078.5	0.680737	0.340369	+	0.940292i	$0.389448\pi$
$858$	1284.68	0.0511169
$859$	11810.0	0.469093	0.234546	−	0.972105i	$-0.424640\pi$
$859$	11810.0	0.469093	0.234546	+	0.972105i	$0.424640\pi$
$860$	−12608.2	−0.499926
$861$	2970.85	0.117592
$862$	−19182.0	−0.757938
$863$	−10288.1	−0.405808	−0.202904	−	0.979199i	$-0.565038\pi$
$863$	−10288.1	−0.405808	−0.202904	+	0.979199i	$0.565038\pi$
$864$	−864.000	−0.0340207
$865$	−51517.6	−2.02503
$866$	13786.7	0.540982
$867$	−10547.0	−0.413145
$868$	−1330.32	−0.0520209
$869$	26050.4	1.01691
$870$	16192.0	0.630988
$871$	5063.09	0.196965
$872$	−1920.02	−0.0745642
$873$	−1041.95	−0.0403947
$874$	5217.94	0.201944
$875$	4998.10	0.193105
$876$	11481.0	0.442817
$877$	43757.9	1.68483	0.842417	−	0.538826i	$-0.181132\pi$
$877$	43757.9	1.68483	0.842417	+	0.538826i	$0.181132\pi$
$878$	8251.01	0.317151
$879$	−20082.5	−0.770608
$880$	−5977.64	−0.228984
$881$	−25295.0	−0.967322	−0.483661	−	0.875256i	$-0.660693\pi$
$881$	−25295.0	−0.967322	−0.483661	+	0.875256i	$0.660693\pi$
$882$	882.000	0.0336718
$883$	−37402.0	−1.42545	−0.712727	−	0.701441i	$-0.752540\pi$
$883$	−37402.0	−1.42545	−0.712727	+	0.701441i	$0.752540\pi$
$884$	−2972.22	−0.113084
$885$	23234.7	0.882516
$886$	4530.00	0.171770
$887$	16891.1	0.639401	0.319700	−	0.947519i	$-0.396418\pi$
$887$	16891.1	0.639401	0.319700	+	0.947519i	$0.396418\pi$
$888$	1942.66	0.0734137
$889$	13704.9	0.517039
$890$	−15029.8	−0.566067
$891$	−2142.83	−0.0805696
$892$	−12520.2	−0.469965
$893$	−3748.10	−0.140454
$894$	−13966.8	−0.522504
$895$	−13893.6	−0.518897
$896$	−896.000	−0.0334077
$897$	558.458	0.0207875
$898$	−15691.1	−0.583096
$899$	−9079.06	−0.336823
$900$	2679.87	0.0992544
$901$	−6984.99	−0.258273
$902$	−7485.05	−0.276303
$903$	−4687.12	−0.172733
$904$	10025.4	0.368851
$905$	−1785.71	−0.0655902
$906$	6932.77	0.254223
$907$	42640.1	1.56102	0.780508	−	0.625145i	$-0.214960\pi$
$907$	42640.1	1.56102	0.780508	+	0.625145i	$0.214960\pi$
$908$	2411.25	0.0881278
$909$	16157.6	0.589565
$910$	−1600.21	−0.0582927
$911$	−44680.1	−1.62494	−0.812468	−	0.583005i	$-0.801877\pi$
$911$	−44680.1	−1.62494	−0.812468	+	0.583005i	$0.801877\pi$
$912$	5444.81	0.197693
$913$	−4998.00	−0.181172
$914$	17651.3	0.638789
$915$	−22582.4	−0.815902
$916$	−9093.24	−0.328001
$917$	8188.96	0.294900
$918$	4957.62	0.178242
$919$	2563.38	0.0920110	0.0460055	−	0.998941i	$-0.485351\pi$
$919$	2563.38	0.0920110	0.0460055	+	0.998941i	$0.485351\pi$
$920$	−2598.51	−0.0931200
$921$	−6544.71	−0.234154
$922$	−21333.9	−0.762032
$923$	2001.83	0.0713878
$924$	−2222.19	−0.0791178
$925$	−6025.54	−0.214182
$926$	−16453.6	−0.583906
$927$	−4273.89	−0.151427
$928$	−6114.93	−0.216307
$929$	−40797.1	−1.44081	−0.720403	−	0.693556i	$-0.756043\pi$
$929$	−40797.1	−1.44081	−0.720403	+	0.693556i	$0.756043\pi$
$930$	−4025.85	−0.141949
$931$	−5558.24	−0.195665
$932$	−11819.9	−0.415424
$933$	−19704.3	−0.691416
$934$	−5097.80	−0.178592
$935$	34299.6	1.19970
$936$	582.738	0.0203498
$937$	11273.3	0.393044	0.196522	−	0.980499i	$-0.437035\pi$
$937$	11273.3	0.393044	0.196522	+	0.980499i	$0.437035\pi$
$938$	−8757.95	−0.304859
$939$	−26639.1	−0.925807
$940$	1866.54	0.0647657
$941$	4530.75	0.156959	0.0784793	−	0.996916i	$-0.474994\pi$
$941$	4530.75	0.156959	0.0784793	+	0.996916i	$0.474994\pi$
$942$	−16274.0	−0.562881
$943$	−3253.79	−0.112363
$944$	−8774.63	−0.302532
$945$	2669.12	0.0918800
$946$	11809.2	0.405866
$947$	5805.46	0.199210	0.0996052	−	0.995027i	$-0.468242\pi$
$947$	5805.46	0.199210	0.0996052	+	0.995027i	$0.468242\pi$
$948$	11816.6	0.404837
$949$	−7743.55	−0.264875
$950$	−16888.2	−0.576762
$951$	−11819.2	−0.403012
$952$	5141.24	0.175030
$953$	13447.4	0.457088	0.228544	−	0.973534i	$-0.426604\pi$
$953$	13447.4	0.457088	0.228544	+	0.973534i	$0.426604\pi$
$954$	1369.49	0.0464767
$955$	−15106.2	−0.511860
$956$	−6615.35	−0.223803
$957$	−15165.8	−0.512269
$958$	38576.3	1.30098
$959$	−14776.6	−0.497561
$960$	−2711.49	−0.0911594
$961$	−27533.6	−0.924227
$962$	−1310.26	−0.0439131
$963$	−10017.3	−0.335205
$964$	15233.5	0.508962
$965$	33915.4	1.13138
$966$	−966.000	−0.0321745
$967$	−6959.70	−0.231447	−0.115723	−	0.993281i	$-0.536919\pi$
$967$	−6959.70	−0.231447	−0.115723	+	0.993281i	$0.536919\pi$
$968$	−5049.19	−0.167652
$969$	−31242.3	−1.03575
$970$	−3269.95	−0.108239
$971$	26466.2	0.874708	0.437354	−	0.899290i	$-0.355916\pi$
$971$	26466.2	0.874708	0.437354	+	0.899290i	$0.355916\pi$
$972$	−972.000	−0.0320750
$973$	8116.41	0.267420
$974$	−16046.1	−0.527874
$975$	−1807.48	−0.0593699
$976$	8528.28	0.279696
$977$	−3620.40	−0.118554	−0.0592768	−	0.998242i	$-0.518879\pi$
$977$	−3620.40	−0.118554	−0.0592768	+	0.998242i	$0.518879\pi$
$978$	−10191.2	−0.333210
$979$	14077.3	0.459563
$980$	2767.98	0.0902244
$981$	−2160.02	−0.0702998
$982$	28320.9	0.920322
$983$	−37274.2	−1.20942	−0.604712	−	0.796444i	$-0.706712\pi$
$983$	−37274.2	−1.20942	−0.604712	+	0.796444i	$0.706712\pi$
$984$	−3395.26	−0.109997
$985$	−58897.7	−1.90522
$986$	35087.4	1.13328
$987$	693.888	0.0223776
$988$	−3672.34	−0.118252
$989$	5133.51	0.165052
$990$	−6724.84	−0.215888
$991$	20684.6	0.663035	0.331517	−	0.943449i	$-0.392439\pi$
$991$	20684.6	0.663035	0.331517	+	0.943449i	$0.392439\pi$
$992$	1520.37	0.0486611
$993$	1375.62	0.0439617
$994$	−3462.69	−0.110493
$995$	77387.8	2.46569
$996$	−2267.12	−0.0721251
$997$	2841.13	0.0902501	0.0451251	−	0.998981i	$-0.485631\pi$
$997$	2841.13	0.0902501	0.0451251	+	0.998981i	$0.485631\pi$
$998$	9109.83	0.288944
$999$	2185.49	0.0692151

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.e.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.e.1.3	✓	3	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +14.1224 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +14.1224 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +28.2447 q^{10} -26.4547 q^{11} -12.0000 q^{12} +8.09359 q^{13} -14.0000 q^{14} -42.3671 q^{15} +16.0000 q^{16} -91.8079 q^{17} +18.0000 q^{18} -113.434 q^{19} +56.4894 q^{20} +21.0000 q^{21} -52.9094 q^{22} -23.0000 q^{23} -24.0000 q^{24} +74.4408 q^{25} +16.1872 q^{26} -27.0000 q^{27} -28.0000 q^{28} -191.092 q^{29} -84.7341 q^{30} +47.5116 q^{31} +32.0000 q^{32} +79.3641 q^{33} -183.616 q^{34} -98.8565 q^{35} +36.0000 q^{36} -80.9441 q^{37} -226.867 q^{38} -24.2808 q^{39} +112.979 q^{40} +141.469 q^{41} +42.0000 q^{42} -223.196 q^{43} -105.819 q^{44} +127.101 q^{45} -46.0000 q^{46} +33.0423 q^{47} -48.0000 q^{48} +49.0000 q^{49} +148.882 q^{50} +275.424 q^{51} +32.3744 q^{52} +76.0827 q^{53} -54.0000 q^{54} -373.602 q^{55} -56.0000 q^{56} +340.301 q^{57} -382.183 q^{58} -548.415 q^{59} -169.468 q^{60} +533.017 q^{61} +95.0232 q^{62} -63.0000 q^{63} +64.0000 q^{64} +114.301 q^{65} +158.728 q^{66} +625.568 q^{67} -367.231 q^{68} +69.0000 q^{69} -197.713 q^{70} +247.335 q^{71} +72.0000 q^{72} -956.751 q^{73} -161.888 q^{74} -223.322 q^{75} -453.734 q^{76} +185.183 q^{77} -48.5615 q^{78} -984.717 q^{79} +225.958 q^{80} +81.0000 q^{81} +282.938 q^{82} +188.927 q^{83} +84.0000 q^{84} -1296.54 q^{85} -446.392 q^{86} +573.275 q^{87} -211.638 q^{88} -532.128 q^{89} +254.202 q^{90} -56.6551 q^{91} -92.0000 q^{92} -142.535 q^{93} +66.0846 q^{94} -1601.95 q^{95} -96.0000 q^{96} -115.772 q^{97} +98.0000 q^{98} -238.092 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 5 q^{5} - 18 q^{6} - 21 q^{7} + 24 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 5 * q^5 - 18 * q^6 - 21 * q^7 + 24 * q^8 + 27 * q^9	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 5 q^{5} - 18 q^{6} - 21 q^{7} + 24 q^{8} + 27 q^{9} + 10 q^{10} - 56 q^{11} - 36 q^{12} + 29 q^{13} - 42 q^{14} - 15 q^{15} + 48 q^{16} + 28 q^{17} + 54 q^{18} - 18 q^{19} + 20 q^{20} + 63 q^{21} - 112 q^{22} - 69 q^{23} - 72 q^{24} + 32 q^{25} + 58 q^{26} - 81 q^{27} - 84 q^{28} - 242 q^{29} - 30 q^{30} - 86 q^{31} + 96 q^{32} + 168 q^{33} + 56 q^{34} - 35 q^{35} + 108 q^{36} - 70 q^{37} - 36 q^{38} - 87 q^{39} + 40 q^{40} - 402 q^{41} + 126 q^{42} - 553 q^{43} - 224 q^{44} + 45 q^{45} - 138 q^{46} - 368 q^{47} - 144 q^{48} + 147 q^{49} + 64 q^{50} - 84 q^{51} + 116 q^{52} + 23 q^{53} - 162 q^{54} - 467 q^{55} - 168 q^{56} + 54 q^{57} - 484 q^{58} - 861 q^{59} - 60 q^{60} - 311 q^{61} - 172 q^{62} - 189 q^{63} + 192 q^{64} - 624 q^{65} + 336 q^{66} - 215 q^{67} + 112 q^{68} + 207 q^{69} - 70 q^{70} + 121 q^{71} + 216 q^{72} - 588 q^{73} - 140 q^{74} - 96 q^{75} - 72 q^{76} + 392 q^{77} - 174 q^{78} - 1418 q^{79} + 80 q^{80} + 243 q^{81} - 804 q^{82} - 352 q^{83} + 252 q^{84} - 827 q^{85} - 1106 q^{86} + 726 q^{87} - 448 q^{88} + 1275 q^{89} + 90 q^{90} - 203 q^{91} - 276 q^{92} + 258 q^{93} - 736 q^{94} - 3593 q^{95} - 288 q^{96} - 602 q^{97} + 294 q^{98} - 504 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 5 * q^5 - 18 * q^6 - 21 * q^7 + 24 * q^8 + 27 * q^9 + 10 * q^10 - 56 * q^11 - 36 * q^12 + 29 * q^13 - 42 * q^14 - 15 * q^15 + 48 * q^16 + 28 * q^17 + 54 * q^18 - 18 * q^19 + 20 * q^20 + 63 * q^21 - 112 * q^22 - 69 * q^23 - 72 * q^24 + 32 * q^25 + 58 * q^26 - 81 * q^27 - 84 * q^28 - 242 * q^29 - 30 * q^30 - 86 * q^31 + 96 * q^32 + 168 * q^33 + 56 * q^34 - 35 * q^35 + 108 * q^36 - 70 * q^37 - 36 * q^38 - 87 * q^39 + 40 * q^40 - 402 * q^41 + 126 * q^42 - 553 * q^43 - 224 * q^44 + 45 * q^45 - 138 * q^46 - 368 * q^47 - 144 * q^48 + 147 * q^49 + 64 * q^50 - 84 * q^51 + 116 * q^52 + 23 * q^53 - 162 * q^54 - 467 * q^55 - 168 * q^56 + 54 * q^57 - 484 * q^58 - 861 * q^59 - 60 * q^60 - 311 * q^61 - 172 * q^62 - 189 * q^63 + 192 * q^64 - 624 * q^65 + 336 * q^66 - 215 * q^67 + 112 * q^68 + 207 * q^69 - 70 * q^70 + 121 * q^71 + 216 * q^72 - 588 * q^73 - 140 * q^74 - 96 * q^75 - 72 * q^76 + 392 * q^77 - 174 * q^78 - 1418 * q^79 + 80 * q^80 + 243 * q^81 - 804 * q^82 - 352 * q^83 + 252 * q^84 - 827 * q^85 - 1106 * q^86 + 726 * q^87 - 448 * q^88 + 1275 * q^89 + 90 * q^90 - 203 * q^91 - 276 * q^92 + 258 * q^93 - 736 * q^94 - 3593 * q^95 - 288 * q^96 - 602 * q^97 + 294 * q^98 - 504 * q^99

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