LMFDB - Embedded newform 798.4.a.q.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,4,Mod(1,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, 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("798.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	798.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:	$47.0835241846$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 350x^{2} - 180x + 19400 $ x^4 - 2x^3 - 350x^2 - 180*x + 19400
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-14.8333$ of defining polynomial
Character	$\chi$	$=$	798.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +12.8333 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +12.8333 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +25.6667 q^{10} +28.1555 q^{11} -12.0000 q^{12} +87.5917 q^{13} +14.0000 q^{14} -38.5000 q^{15} +16.0000 q^{16} -23.4250 q^{17} +18.0000 q^{18} -19.0000 q^{19} +51.3333 q^{20} -21.0000 q^{21} +56.3109 q^{22} -81.2414 q^{23} -24.0000 q^{24} +39.6945 q^{25} +175.183 q^{26} -27.0000 q^{27} +28.0000 q^{28} +36.2471 q^{29} -77.0000 q^{30} +92.4586 q^{31} +32.0000 q^{32} -84.4664 q^{33} -46.8500 q^{34} +89.8333 q^{35} +36.0000 q^{36} -86.1083 q^{37} -38.0000 q^{38} -262.775 q^{39} +102.667 q^{40} -353.928 q^{41} -42.0000 q^{42} +228.166 q^{43} +112.622 q^{44} +115.500 q^{45} -162.483 q^{46} +473.277 q^{47} -48.0000 q^{48} +49.0000 q^{49} +79.3890 q^{50} +70.2749 q^{51} +350.367 q^{52} -524.041 q^{53} -54.0000 q^{54} +361.329 q^{55} +56.0000 q^{56} +57.0000 q^{57} +72.4942 q^{58} +393.790 q^{59} -154.000 q^{60} -593.295 q^{61} +184.917 q^{62} +63.0000 q^{63} +64.0000 q^{64} +1124.09 q^{65} -168.933 q^{66} +552.032 q^{67} -93.6999 q^{68} +243.724 q^{69} +179.667 q^{70} +1096.94 q^{71} +72.0000 q^{72} -385.261 q^{73} -172.217 q^{74} -119.083 q^{75} -76.0000 q^{76} +197.088 q^{77} -525.550 q^{78} -217.001 q^{79} +205.333 q^{80} +81.0000 q^{81} -707.856 q^{82} -472.071 q^{83} -84.0000 q^{84} -300.621 q^{85} +456.333 q^{86} -108.741 q^{87} +225.244 q^{88} -405.558 q^{89} +231.000 q^{90} +613.142 q^{91} -324.965 q^{92} -277.376 q^{93} +946.553 q^{94} -243.833 q^{95} -96.0000 q^{96} -540.291 q^{97} +98.0000 q^{98} +253.399 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} - 12 q^{3} + 16 q^{4} - 10 q^{5} - 24 q^{6} + 28 q^{7} + 32 q^{8} + 36 q^{9}+O(q^{10}) $ 4 * q + 8 * q^2 - 12 * q^3 + 16 * q^4 - 10 * q^5 - 24 * q^6 + 28 * q^7 + 32 * q^8 + 36 * q^9	\( 4 q + 8 q^{2} - 12 q^{3} + 16 q^{4} - 10 q^{5} - 24 q^{6} + 28 q^{7} + 32 q^{8} + 36 q^{9} - 20 q^{10} + 48 q^{11} - 48 q^{12} + 46 q^{13} + 56 q^{14} + 30 q^{15} + 64 q^{16} - 96 q^{17} + 72 q^{18} - 76 q^{19} - 40 q^{20} - 84 q^{21} + 96 q^{22} + 46 q^{23} - 96 q^{24} + 228 q^{25} + 92 q^{26} - 108 q^{27} + 112 q^{28} + 328 q^{29} + 60 q^{30} + 14 q^{31} + 128 q^{32} - 144 q^{33} - 192 q^{34} - 70 q^{35} + 144 q^{36} + 78 q^{37} - 152 q^{38} - 138 q^{39} - 80 q^{40} - 216 q^{41} - 168 q^{42} + 728 q^{43} + 192 q^{44} - 90 q^{45} + 92 q^{46} + 158 q^{47} - 192 q^{48} + 196 q^{49} + 456 q^{50} + 288 q^{51} + 184 q^{52} + 432 q^{53} - 216 q^{54} + 756 q^{55} + 224 q^{56} + 228 q^{57} + 656 q^{58} + 1120 q^{59} + 120 q^{60} + 412 q^{61} + 28 q^{62} + 252 q^{63} + 256 q^{64} + 1284 q^{65} - 288 q^{66} + 1248 q^{67} - 384 q^{68} - 138 q^{69} - 140 q^{70} + 848 q^{71} + 288 q^{72} + 1376 q^{73} + 156 q^{74} - 684 q^{75} - 304 q^{76} + 336 q^{77} - 276 q^{78} + 2102 q^{79} - 160 q^{80} + 324 q^{81} - 432 q^{82} + 484 q^{83} - 336 q^{84} + 2356 q^{85} + 1456 q^{86} - 984 q^{87} + 384 q^{88} + 792 q^{89} - 180 q^{90} + 322 q^{91} + 184 q^{92} - 42 q^{93} + 316 q^{94} + 190 q^{95} - 384 q^{96} + 1788 q^{97} + 392 q^{98} + 432 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 - 12 * q^3 + 16 * q^4 - 10 * q^5 - 24 * q^6 + 28 * q^7 + 32 * q^8 + 36 * q^9 - 20 * q^10 + 48 * q^11 - 48 * q^12 + 46 * q^13 + 56 * q^14 + 30 * q^15 + 64 * q^16 - 96 * q^17 + 72 * q^18 - 76 * q^19 - 40 * q^20 - 84 * q^21 + 96 * q^22 + 46 * q^23 - 96 * q^24 + 228 * q^25 + 92 * q^26 - 108 * q^27 + 112 * q^28 + 328 * q^29 + 60 * q^30 + 14 * q^31 + 128 * q^32 - 144 * q^33 - 192 * q^34 - 70 * q^35 + 144 * q^36 + 78 * q^37 - 152 * q^38 - 138 * q^39 - 80 * q^40 - 216 * q^41 - 168 * q^42 + 728 * q^43 + 192 * q^44 - 90 * q^45 + 92 * q^46 + 158 * q^47 - 192 * q^48 + 196 * q^49 + 456 * q^50 + 288 * q^51 + 184 * q^52 + 432 * q^53 - 216 * q^54 + 756 * q^55 + 224 * q^56 + 228 * q^57 + 656 * q^58 + 1120 * q^59 + 120 * q^60 + 412 * q^61 + 28 * q^62 + 252 * q^63 + 256 * q^64 + 1284 * q^65 - 288 * q^66 + 1248 * q^67 - 384 * q^68 - 138 * q^69 - 140 * q^70 + 848 * q^71 + 288 * q^72 + 1376 * q^73 + 156 * q^74 - 684 * q^75 - 304 * q^76 + 336 * q^77 - 276 * q^78 + 2102 * q^79 - 160 * q^80 + 324 * q^81 - 432 * q^82 + 484 * q^83 - 336 * q^84 + 2356 * q^85 + 1456 * q^86 - 984 * q^87 + 384 * q^88 + 792 * q^89 - 180 * q^90 + 322 * q^91 + 184 * q^92 - 42 * q^93 + 316 * q^94 + 190 * q^95 - 384 * q^96 + 1788 * q^97 + 392 * q^98 + 432 * 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
$5$	12.8333	1.14785	0.573924	−	0.818908i	$-0.305420\pi$
$5$	12.8333	1.14785	0.573924	+	0.818908i	$0.305420\pi$
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	25.6667	0.811651
$11$	28.1555	0.771745	0.385872	−	0.922552i	$-0.373900\pi$
$11$	28.1555	0.771745	0.385872	+	0.922552i	$0.373900\pi$
$12$	−12.0000	−0.288675
$13$	87.5917	1.86874	0.934368	−	0.356311i	$-0.115966\pi$
$13$	87.5917	1.86874	0.934368	+	0.356311i	$0.115966\pi$
$14$	14.0000	0.267261
$15$	−38.5000	−0.662711
$16$	16.0000	0.250000
$17$	−23.4250	−0.334200	−0.167100	−	0.985940i	$-0.553440\pi$
$17$	−23.4250	−0.334200	−0.167100	+	0.985940i	$0.553440\pi$
$18$	18.0000	0.235702
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	51.3333	0.573924
$21$	−21.0000	−0.218218
$22$	56.3109	0.545706
$23$	−81.2414	−0.736522	−0.368261	−	0.929723i	$-0.620047\pi$
$23$	−81.2414	−0.736522	−0.368261	+	0.929723i	$0.620047\pi$
$24$	−24.0000	−0.204124
$25$	39.6945	0.317556
$26$	175.183	1.32140
$27$	−27.0000	−0.192450
$28$	28.0000	0.188982
$29$	36.2471	0.232101	0.116050	−	0.993243i	$-0.462977\pi$
$29$	36.2471	0.232101	0.116050	+	0.993243i	$0.462977\pi$
$30$	−77.0000	−0.468607
$31$	92.4586	0.535679	0.267840	−	0.963464i	$-0.413690\pi$
$31$	92.4586	0.535679	0.267840	+	0.963464i	$0.413690\pi$
$32$	32.0000	0.176777
$33$	−84.4664	−0.445567
$34$	−46.8500	−0.236315
$35$	89.8333	0.433846
$36$	36.0000	0.166667
$37$	−86.1083	−0.382598	−0.191299	−	0.981532i	$-0.561270\pi$
$37$	−86.1083	−0.382598	−0.191299	+	0.981532i	$0.561270\pi$
$38$	−38.0000	−0.162221
$39$	−262.775	−1.07891
$40$	102.667	0.405826
$41$	−353.928	−1.34815	−0.674077	−	0.738661i	$-0.735458\pi$
$41$	−353.928	−1.34815	−0.674077	+	0.738661i	$0.735458\pi$
$42$	−42.0000	−0.154303
$43$	228.166	0.809187	0.404593	−	0.914497i	$-0.367413\pi$
$43$	228.166	0.809187	0.404593	+	0.914497i	$0.367413\pi$
$44$	112.622	0.385872
$45$	115.500	0.382616
$46$	−162.483	−0.520799
$47$	473.277	1.46882	0.734410	−	0.678706i	$-0.237459\pi$
$47$	473.277	1.46882	0.734410	+	0.678706i	$0.237459\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	79.3890	0.224546
$51$	70.2749	0.192950
$52$	350.367	0.934368
$53$	−524.041	−1.35816	−0.679081	−	0.734064i	$-0.737621\pi$
$53$	−524.041	−1.35816	−0.679081	+	0.734064i	$0.737621\pi$
$54$	−54.0000	−0.136083
$55$	361.329	0.885846
$56$	56.0000	0.133631
$57$	57.0000	0.132453
$58$	72.4942	0.164120
$59$	393.790	0.868933	0.434466	−	0.900688i	$-0.356937\pi$
$59$	393.790	0.868933	0.434466	+	0.900688i	$0.356937\pi$
$60$	−154.000	−0.331355
$61$	−593.295	−1.24530	−0.622652	−	0.782498i	$-0.713945\pi$
$61$	−593.295	−1.24530	−0.622652	+	0.782498i	$0.713945\pi$
$62$	184.917	0.378782
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	1124.09	2.14502
$66$	−168.933	−0.315064
$67$	552.032	1.00659	0.503294	−	0.864115i	$-0.332121\pi$
$67$	552.032	1.00659	0.503294	+	0.864115i	$0.332121\pi$
$68$	−93.6999	−0.167100
$69$	243.724	0.425231
$70$	179.667	0.306775
$71$	1096.94	1.83356	0.916780	−	0.399392i	$-0.130779\pi$
$71$	1096.94	1.83356	0.916780	+	0.399392i	$0.130779\pi$
$72$	72.0000	0.117851
$73$	−385.261	−0.617691	−0.308846	−	0.951112i	$-0.599943\pi$
$73$	−385.261	−0.617691	−0.308846	+	0.951112i	$0.599943\pi$
$74$	−172.217	−0.270537
$75$	−119.083	−0.183341
$76$	−76.0000	−0.114708
$77$	197.088	0.291692
$78$	−525.550	−0.762908
$79$	−217.001	−0.309045	−0.154522	−	0.987989i	$-0.549384\pi$
$79$	−217.001	−0.309045	−0.154522	+	0.987989i	$0.549384\pi$
$80$	205.333	0.286962
$81$	81.0000	0.111111
$82$	−707.856	−0.953288
$83$	−472.071	−0.624296	−0.312148	−	0.950033i	$-0.601048\pi$
$83$	−472.071	−0.624296	−0.312148	+	0.950033i	$0.601048\pi$
$84$	−84.0000	−0.109109
$85$	−300.621	−0.383610
$86$	456.333	0.572182
$87$	−108.741	−0.134003
$88$	225.244	0.272853
$89$	−405.558	−0.483023	−0.241511	−	0.970398i	$-0.577643\pi$
$89$	−405.558	−0.483023	−0.241511	+	0.970398i	$0.577643\pi$
$90$	231.000	0.270550
$91$	613.142	0.706315
$92$	−324.965	−0.368261
$93$	−277.376	−0.309274
$94$	946.553	1.03861
$95$	−243.833	−0.263334
$96$	−96.0000	−0.102062
$97$	−540.291	−0.565548	−0.282774	−	0.959186i	$-0.591255\pi$
$97$	−540.291	−0.565548	−0.282774	+	0.959186i	$0.591255\pi$
$98$	98.0000	0.101015
$99$	253.399	0.257248
$100$	158.778	0.158778
$101$	1668.24	1.64352	0.821761	−	0.569832i	$-0.192992\pi$
$101$	1668.24	1.64352	0.821761	+	0.569832i	$0.192992\pi$
$102$	140.550	0.136436
$103$	1513.27	1.44764	0.723818	−	0.689991i	$-0.242385\pi$
$103$	1513.27	1.44764	0.723818	+	0.689991i	$0.242385\pi$
$104$	700.733	0.660698
$105$	−269.500	−0.250481
$106$	−1048.08	−0.960365
$107$	−1273.65	−1.15073	−0.575364	−	0.817897i	$-0.695140\pi$
$107$	−1273.65	−1.15073	−0.575364	+	0.817897i	$0.695140\pi$
$108$	−108.000	−0.0962250
$109$	768.539	0.675345	0.337673	−	0.941264i	$-0.390360\pi$
$109$	768.539	0.675345	0.337673	+	0.941264i	$0.390360\pi$
$110$	722.657	0.626388
$111$	258.325	0.220893
$112$	112.000	0.0944911
$113$	374.980	0.312170	0.156085	−	0.987744i	$-0.450113\pi$
$113$	374.980	0.312170	0.156085	+	0.987744i	$0.450113\pi$
$114$	114.000	0.0936586
$115$	−1042.60	−0.845415
$116$	144.988	0.116050
$117$	788.325	0.622912
$118$	787.579	0.614428
$119$	−163.975	−0.126316
$120$	−308.000	−0.234304
$121$	−538.270	−0.404410
$122$	−1186.59	−0.880564
$123$	1061.78	0.778357
$124$	369.834	0.267840
$125$	−1094.75	−0.783342
$126$	126.000	0.0890871
$127$	−50.7343	−0.0354484	−0.0177242	−	0.999843i	$-0.505642\pi$
$127$	−50.7343	−0.0354484	−0.0177242	+	0.999843i	$0.505642\pi$
$128$	128.000	0.0883883
$129$	−684.499	−0.467184
$130$	2248.19	1.51676
$131$	458.099	0.305529	0.152764	−	0.988263i	$-0.451182\pi$
$131$	458.099	0.305529	0.152764	+	0.988263i	$0.451182\pi$
$132$	−337.866	−0.222784
$133$	−133.000	−0.0867110
$134$	1104.06	0.711766
$135$	−346.500	−0.220904
$136$	−187.400	−0.118157
$137$	2554.24	1.59287	0.796436	−	0.604723i	$-0.206716\pi$
$137$	2554.24	1.59287	0.796436	+	0.604723i	$0.206716\pi$
$138$	487.448	0.300684
$139$	−365.735	−0.223175	−0.111587	−	0.993755i	$-0.535593\pi$
$139$	−365.735	−0.223175	−0.111587	+	0.993755i	$0.535593\pi$
$140$	359.333	0.216923
$141$	−1419.83	−0.848023
$142$	2193.88	1.29652
$143$	2466.18	1.44219
$144$	144.000	0.0833333
$145$	465.171	0.266416
$146$	−770.523	−0.436773
$147$	−147.000	−0.0824786
$148$	−344.433	−0.191299
$149$	894.349	0.491731	0.245865	−	0.969304i	$-0.420928\pi$
$149$	894.349	0.491731	0.245865	+	0.969304i	$0.420928\pi$
$150$	−238.167	−0.129642
$151$	1214.60	0.654590	0.327295	−	0.944922i	$-0.393863\pi$
$151$	1214.60	0.654590	0.327295	+	0.944922i	$0.393863\pi$
$152$	−152.000	−0.0811107
$153$	−210.825	−0.111400
$154$	394.177	0.206257
$155$	1186.55	0.614878
$156$	−1051.10	−0.539457
$157$	398.426	0.202534	0.101267	−	0.994859i	$-0.467710\pi$
$157$	398.426	0.202534	0.101267	+	0.994859i	$0.467710\pi$
$158$	−434.002	−0.218528
$159$	1572.12	0.784135
$160$	410.667	0.202913
$161$	−568.690	−0.278379
$162$	162.000	0.0785674
$163$	576.659	0.277101	0.138550	−	0.990355i	$-0.455756\pi$
$163$	576.659	0.277101	0.138550	+	0.990355i	$0.455756\pi$
$164$	−1415.71	−0.674077
$165$	−1083.99	−0.511443
$166$	−944.143	−0.441444
$167$	−3329.84	−1.54294	−0.771470	−	0.636265i	$-0.780478\pi$
$167$	−3329.84	−1.54294	−0.771470	+	0.636265i	$0.780478\pi$
$168$	−168.000	−0.0771517
$169$	5475.30	2.49217
$170$	−601.241	−0.271254
$171$	−171.000	−0.0764719
$172$	912.665	0.404593
$173$	−378.675	−0.166417	−0.0832084	−	0.996532i	$-0.526517\pi$
$173$	−378.675	−0.166417	−0.0832084	+	0.996532i	$0.526517\pi$
$174$	−217.483	−0.0947547
$175$	277.861	0.120025
$176$	450.488	0.192936
$177$	−1181.37	−0.501679
$178$	−811.115	−0.341549
$179$	2066.06	0.862709	0.431354	−	0.902183i	$-0.358036\pi$
$179$	2066.06	0.862709	0.431354	+	0.902183i	$0.358036\pi$
$180$	462.000	0.191308
$181$	−3868.02	−1.58844	−0.794220	−	0.607631i	$-0.792120\pi$
$181$	−3868.02	−1.58844	−0.794220	+	0.607631i	$0.792120\pi$
$182$	1226.28	0.499440
$183$	1779.88	0.718977
$184$	−649.931	−0.260400
$185$	−1105.06	−0.439164
$186$	−554.752	−0.218690
$187$	−659.541	−0.257917
$188$	1893.11	0.734410
$189$	−189.000	−0.0727393
$190$	−487.667	−0.186206
$191$	−1733.30	−0.656634	−0.328317	−	0.944568i	$-0.606481\pi$
$191$	−1733.30	−0.656634	−0.328317	+	0.944568i	$0.606481\pi$
$192$	−192.000	−0.0721688
$193$	3851.79	1.43657	0.718285	−	0.695749i	$-0.244927\pi$
$193$	3851.79	1.43657	0.718285	+	0.695749i	$0.244927\pi$
$194$	−1080.58	−0.399903
$195$	−3372.28	−1.23843
$196$	196.000	0.0714286
$197$	−2333.63	−0.843982	−0.421991	−	0.906600i	$-0.638669\pi$
$197$	−2333.63	−0.843982	−0.421991	+	0.906600i	$0.638669\pi$
$198$	506.798	0.181902
$199$	1307.85	0.465884	0.232942	−	0.972491i	$-0.425165\pi$
$199$	1307.85	0.465884	0.232942	+	0.972491i	$0.425165\pi$
$200$	317.556	0.112273
$201$	−1656.10	−0.581154
$202$	3336.47	1.16215
$203$	253.730	0.0877258
$204$	281.100	0.0964751
$205$	−4542.08	−1.54748
$206$	3026.53	1.02363
$207$	−731.172	−0.245507
$208$	1401.47	0.467184
$209$	−534.954	−0.177050
$210$	−539.000	−0.177117
$211$	−4381.59	−1.42958	−0.714789	−	0.699340i	$-0.753477\pi$
$211$	−4381.59	−1.42958	−0.714789	+	0.699340i	$0.753477\pi$
$212$	−2096.16	−0.679081
$213$	−3290.82	−1.05861
$214$	−2547.29	−0.813688
$215$	2928.14	0.928824
$216$	−216.000	−0.0680414
$217$	647.210	0.202468
$218$	1537.08	0.477541
$219$	1155.78	0.356624
$220$	1445.31	0.442923
$221$	−2051.83	−0.624530
$222$	516.650	0.156195
$223$	2358.55	0.708253	0.354127	−	0.935197i	$-0.384778\pi$
$223$	2358.55	0.708253	0.354127	+	0.935197i	$0.384778\pi$
$224$	224.000	0.0668153
$225$	357.250	0.105852
$226$	749.961	0.220737
$227$	−2895.35	−0.846570	−0.423285	−	0.905997i	$-0.639123\pi$
$227$	−2895.35	−0.846570	−0.423285	+	0.905997i	$0.639123\pi$
$228$	228.000	0.0662266
$229$	−5054.66	−1.45861	−0.729304	−	0.684190i	$-0.760156\pi$
$229$	−5054.66	−1.45861	−0.729304	+	0.684190i	$0.760156\pi$
$230$	−2085.20	−0.597799
$231$	−591.265	−0.168409
$232$	289.977	0.0820600
$233$	−3684.97	−1.03610	−0.518049	−	0.855351i	$-0.673341\pi$
$233$	−3684.97	−1.03610	−0.518049	+	0.855351i	$0.673341\pi$
$234$	1576.65	0.440465
$235$	6073.72	1.68598
$236$	1575.16	0.434466
$237$	651.003	0.178427
$238$	−327.950	−0.0893186
$239$	−7208.86	−1.95106	−0.975528	−	0.219873i	$-0.929436\pi$
$239$	−7208.86	−1.95106	−0.975528	+	0.219873i	$0.929436\pi$
$240$	−616.000	−0.165678
$241$	1827.06	0.488344	0.244172	−	0.969732i	$-0.421484\pi$
$241$	1827.06	0.488344	0.244172	+	0.969732i	$0.421484\pi$
$242$	−1076.54	−0.285961
$243$	−243.000	−0.0641500
$244$	−2373.18	−0.622652
$245$	628.833	0.163978
$246$	2123.57	0.550381
$247$	−1664.24	−0.428717
$248$	739.669	0.189391
$249$	1416.21	0.360438
$250$	−2189.51	−0.553907
$251$	−3478.76	−0.874811	−0.437405	−	0.899264i	$-0.644103\pi$
$251$	−3478.76	−0.874811	−0.437405	+	0.899264i	$0.644103\pi$
$252$	252.000	0.0629941
$253$	−2287.39	−0.568407
$254$	−101.469	−0.0250658
$255$	901.862	0.221478
$256$	256.000	0.0625000
$257$	509.953	0.123774	0.0618872	−	0.998083i	$-0.480288\pi$
$257$	509.953	0.123774	0.0618872	+	0.998083i	$0.480288\pi$
$258$	−1369.00	−0.330349
$259$	−602.758	−0.144608
$260$	4496.37	1.07251
$261$	326.224	0.0773669
$262$	916.197	0.216041
$263$	−233.799	−0.0548163	−0.0274081	−	0.999624i	$-0.508725\pi$
$263$	−233.799	−0.0548163	−0.0274081	+	0.999624i	$0.508725\pi$
$264$	−675.731	−0.157532
$265$	−6725.19	−1.55896
$266$	−266.000	−0.0613139
$267$	1216.67	0.278873
$268$	2208.13	0.503294
$269$	−3508.81	−0.795300	−0.397650	−	0.917537i	$-0.630174\pi$
$269$	−3508.81	−0.795300	−0.397650	+	0.917537i	$0.630174\pi$
$270$	−693.000	−0.156202
$271$	−5333.33	−1.19549	−0.597743	−	0.801688i	$-0.703936\pi$
$271$	−5333.33	−1.19549	−0.597743	+	0.801688i	$0.703936\pi$
$272$	−374.800	−0.0835499
$273$	−1839.42	−0.407791
$274$	5108.48	1.12633
$275$	1117.62	0.245072
$276$	974.896	0.212615
$277$	2334.60	0.506399	0.253200	−	0.967414i	$-0.418517\pi$
$277$	2334.60	0.506399	0.253200	+	0.967414i	$0.418517\pi$
$278$	−731.471	−0.157808
$279$	832.127	0.178560
$280$	718.667	0.153388
$281$	4114.01	0.873386	0.436693	−	0.899611i	$-0.356150\pi$
$281$	4114.01	0.873386	0.436693	+	0.899611i	$0.356150\pi$
$282$	−2839.66	−0.599643
$283$	−3641.40	−0.764872	−0.382436	−	0.923982i	$-0.624915\pi$
$283$	−3641.40	−0.764872	−0.382436	+	0.923982i	$0.624915\pi$
$284$	4387.76	0.916780
$285$	731.500	0.152036
$286$	4932.37	1.01978
$287$	−2477.50	−0.509554
$288$	288.000	0.0589256
$289$	−4364.27	−0.888311
$290$	930.343	0.188385
$291$	1620.87	0.326520
$292$	−1541.05	−0.308846
$293$	−6776.79	−1.35121	−0.675605	−	0.737264i	$-0.736117\pi$
$293$	−6776.79	−1.35121	−0.675605	+	0.737264i	$0.736117\pi$
$294$	−294.000	−0.0583212
$295$	5053.63	0.997403
$296$	−688.866	−0.135269
$297$	−760.198	−0.148522
$298$	1788.70	0.347706
$299$	−7116.07	−1.37636
$300$	−476.334	−0.0916705
$301$	1597.16	0.305844
$302$	2429.21	0.462865
$303$	−5004.71	−0.948888
$304$	−304.000	−0.0573539
$305$	−7613.95	−1.42942
$306$	−421.650	−0.0787716
$307$	−1454.51	−0.270401	−0.135201	−	0.990818i	$-0.543168\pi$
$307$	−1454.51	−0.270401	−0.135201	+	0.990818i	$0.543168\pi$
$308$	788.353	0.145846
$309$	−4539.80	−0.835793
$310$	2373.10	0.434785
$311$	3967.91	0.723470	0.361735	−	0.932281i	$-0.382184\pi$
$311$	3967.91	0.723470	0.361735	+	0.932281i	$0.382184\pi$
$312$	−2102.20	−0.381454
$313$	−10319.0	−1.86346	−0.931729	−	0.363154i	$-0.881700\pi$
$313$	−10319.0	−1.86346	−0.931729	+	0.363154i	$0.881700\pi$
$314$	796.852	0.143213
$315$	808.500	0.144615
$316$	−868.005	−0.154522
$317$	−5483.66	−0.971586	−0.485793	−	0.874074i	$-0.661469\pi$
$317$	−5483.66	−0.971586	−0.485793	+	0.874074i	$0.661469\pi$
$318$	3144.25	0.554467
$319$	1020.55	0.179123
$320$	821.333	0.143481
$321$	3820.94	0.664373
$322$	−1137.38	−0.196844
$323$	445.075	0.0766706
$324$	324.000	0.0555556
$325$	3476.91	0.593428
$326$	1153.32	0.195940
$327$	−2305.62	−0.389911
$328$	−2831.42	−0.476644
$329$	3312.94	0.555162
$330$	−2167.97	−0.361645
$331$	8980.51	1.49128	0.745640	−	0.666349i	$-0.232144\pi$
$331$	8980.51	1.49128	0.745640	+	0.666349i	$0.232144\pi$
$332$	−1888.29	−0.312148
$333$	−774.975	−0.127533
$334$	−6659.69	−1.09102
$335$	7084.41	1.15541
$336$	−336.000	−0.0545545
$337$	−57.2743	−0.00925795	−0.00462897	−	0.999989i	$-0.501473\pi$
$337$	−57.2743	−0.00925795	−0.00462897	+	0.999989i	$0.501473\pi$
$338$	10950.6	1.76223
$339$	−1124.94	−0.180231
$340$	−1202.48	−0.191805
$341$	2603.22	0.413408
$342$	−342.000	−0.0540738
$343$	343.000	0.0539949
$344$	1825.33	0.286091
$345$	3127.79	0.488101
$346$	−757.350	−0.117674
$347$	−6927.30	−1.07169	−0.535846	−	0.844316i	$-0.680007\pi$
$347$	−6927.30	−1.07169	−0.535846	+	0.844316i	$0.680007\pi$
$348$	−434.965	−0.0670017
$349$	7092.23	1.08779	0.543894	−	0.839154i	$-0.316949\pi$
$349$	7092.23	1.08779	0.543894	+	0.839154i	$0.316949\pi$
$350$	555.723	0.0848704
$351$	−2364.97	−0.359638
$352$	900.975	0.136427
$353$	−1813.33	−0.273410	−0.136705	−	0.990612i	$-0.543651\pi$
$353$	−1813.33	−0.273410	−0.136705	+	0.990612i	$0.543651\pi$
$354$	−2362.74	−0.354740
$355$	14077.4	2.10465
$356$	−1622.23	−0.241511
$357$	491.925	0.0729283
$358$	4132.13	0.610027
$359$	12181.9	1.79090	0.895451	−	0.445160i	$-0.146853\pi$
$359$	12181.9	1.79090	0.895451	+	0.445160i	$0.146853\pi$
$360$	924.000	0.135275
$361$	361.000	0.0526316
$362$	−7736.04	−1.12320
$363$	1614.81	0.233486
$364$	2452.57	0.353158
$365$	−4944.19	−0.709016
$366$	3559.77	0.508394
$367$	6388.49	0.908655	0.454328	−	0.890835i	$-0.349880\pi$
$367$	6388.49	0.908655	0.454328	+	0.890835i	$0.349880\pi$
$368$	−1299.86	−0.184130
$369$	−3185.35	−0.449384
$370$	−2210.11	−0.310536
$371$	−3668.29	−0.513337
$372$	−1109.50	−0.154637
$373$	6036.25	0.837923	0.418962	−	0.908004i	$-0.362394\pi$
$373$	6036.25	0.837923	0.418962	+	0.908004i	$0.362394\pi$
$374$	−1319.08	−0.182375
$375$	3284.26	0.452263
$376$	3786.21	0.519306
$377$	3174.94	0.433735
$378$	−378.000	−0.0514344
$379$	8019.36	1.08688	0.543439	−	0.839448i	$-0.317122\pi$
$379$	8019.36	1.08688	0.543439	+	0.839448i	$0.317122\pi$
$380$	−975.333	−0.131667
$381$	152.203	0.0204661
$382$	−3466.60	−0.464310
$383$	−7707.77	−1.02832	−0.514162	−	0.857693i	$-0.671897\pi$
$383$	−7707.77	−1.02832	−0.514162	+	0.857693i	$0.671897\pi$
$384$	−384.000	−0.0510310
$385$	2529.30	0.334818
$386$	7703.58	1.01581
$387$	2053.50	0.269729
$388$	−2161.16	−0.282774
$389$	−5927.54	−0.772592	−0.386296	−	0.922375i	$-0.626246\pi$
$389$	−5927.54	−0.772592	−0.386296	+	0.922375i	$0.626246\pi$
$390$	−6744.56	−0.875703
$391$	1903.08	0.246145
$392$	392.000	0.0505076
$393$	−1374.30	−0.176397
$394$	−4667.27	−0.596786
$395$	−2784.85	−0.354737
$396$	1013.60	0.128624
$397$	−4891.32	−0.618358	−0.309179	−	0.951004i	$-0.600054\pi$
$397$	−4891.32	−0.618358	−0.309179	+	0.951004i	$0.600054\pi$
$398$	2615.70	0.329430
$399$	399.000	0.0500626
$400$	635.112	0.0793890
$401$	−5122.13	−0.637873	−0.318936	−	0.947776i	$-0.603326\pi$
$401$	−5122.13	−0.637873	−0.318936	+	0.947776i	$0.603326\pi$
$402$	−3312.19	−0.410938
$403$	8098.60	1.00104
$404$	6672.94	0.821761
$405$	1039.50	0.127539
$406$	507.460	0.0620315
$407$	−2424.42	−0.295268
$408$	562.200	0.0682182
$409$	−5244.22	−0.634010	−0.317005	−	0.948424i	$-0.602677\pi$
$409$	−5244.22	−0.634010	−0.317005	+	0.948424i	$0.602677\pi$
$410$	−9084.16	−1.09423
$411$	−7662.72	−0.919645
$412$	6053.06	0.723818
$413$	2756.53	0.328426
$414$	−1462.34	−0.173600
$415$	−6058.25	−0.716597
$416$	2802.93	0.330349
$417$	1097.21	0.128850
$418$	−1069.91	−0.125194
$419$	−2156.07	−0.251386	−0.125693	−	0.992069i	$-0.540116\pi$
$419$	−2156.07	−0.251386	−0.125693	+	0.992069i	$0.540116\pi$
$420$	−1078.00	−0.125241
$421$	10287.9	1.19097	0.595487	−	0.803365i	$-0.296959\pi$
$421$	10287.9	1.19097	0.595487	+	0.803365i	$0.296959\pi$
$422$	−8763.17	−1.01086
$423$	4259.49	0.489606
$424$	−4192.33	−0.480183
$425$	−929.843	−0.106127
$426$	−6581.64	−0.748548
$427$	−4153.06	−0.470681
$428$	−5094.58	−0.575364
$429$	−7398.55	−0.832647
$430$	5856.27	0.656778
$431$	1451.93	0.162267	0.0811336	−	0.996703i	$-0.474146\pi$
$431$	1451.93	0.162267	0.0811336	+	0.996703i	$0.474146\pi$
$432$	−432.000	−0.0481125
$433$	12852.0	1.42639	0.713195	−	0.700966i	$-0.247247\pi$
$433$	12852.0	1.42639	0.713195	+	0.700966i	$0.247247\pi$
$434$	1294.42	0.143166
$435$	−1395.51	−0.153816
$436$	3074.15	0.337673
$437$	1543.59	0.168970
$438$	2311.57	0.252171
$439$	1432.75	0.155766	0.0778829	−	0.996963i	$-0.475184\pi$
$439$	1432.75	0.155766	0.0778829	+	0.996963i	$0.475184\pi$
$440$	2890.63	0.313194
$441$	441.000	0.0476190
$442$	−4103.67	−0.441610
$443$	9042.91	0.969846	0.484923	−	0.874557i	$-0.338848\pi$
$443$	9042.91	0.969846	0.484923	+	0.874557i	$0.338848\pi$
$444$	1033.30	0.110446
$445$	−5204.66	−0.554437
$446$	4717.11	0.500811
$447$	−2683.05	−0.283901
$448$	448.000	0.0472456
$449$	−8455.69	−0.888750	−0.444375	−	0.895841i	$-0.646574\pi$
$449$	−8455.69	−0.888750	−0.444375	+	0.895841i	$0.646574\pi$
$450$	714.501	0.0748487
$451$	−9965.01	−1.04043
$452$	1499.92	0.156085
$453$	−3643.81	−0.377928
$454$	−5790.71	−0.598615
$455$	7868.65	0.810743
$456$	456.000	0.0468293
$457$	−3714.55	−0.380217	−0.190109	−	0.981763i	$-0.560884\pi$
$457$	−3714.55	−0.380217	−0.190109	+	0.981763i	$0.560884\pi$
$458$	−10109.3	−1.03139
$459$	632.475	0.0643167
$460$	−4170.39	−0.422708
$461$	−12032.1	−1.21560	−0.607801	−	0.794089i	$-0.707948\pi$
$461$	−12032.1	−1.21560	−0.607801	+	0.794089i	$0.707948\pi$
$462$	−1182.53	−0.119083
$463$	−7738.23	−0.776730	−0.388365	−	0.921506i	$-0.626960\pi$
$463$	−7738.23	−0.776730	−0.388365	+	0.921506i	$0.626960\pi$
$464$	579.954	0.0580252
$465$	−3559.66	−0.355000
$466$	−7369.95	−0.732631
$467$	11547.1	1.14419	0.572094	−	0.820188i	$-0.306131\pi$
$467$	11547.1	1.14419	0.572094	+	0.820188i	$0.306131\pi$
$468$	3153.30	0.311456
$469$	3864.22	0.380455
$470$	12147.4	1.19217
$471$	−1195.28	−0.116933
$472$	3150.32	0.307214
$473$	6424.13	0.624486
$474$	1302.01	0.126167
$475$	−754.195	−0.0728523
$476$	−655.900	−0.0631578
$477$	−4716.37	−0.452720
$478$	−14417.7	−1.37961
$479$	−14223.1	−1.35672	−0.678360	−	0.734730i	$-0.737309\pi$
$479$	−14223.1	−1.35672	−0.678360	+	0.734730i	$0.737309\pi$
$480$	−1232.00	−0.117152
$481$	−7542.37	−0.714974
$482$	3654.11	0.345312
$483$	1706.07	0.160722
$484$	−2153.08	−0.202205
$485$	−6933.73	−0.649164
$486$	−486.000	−0.0453609
$487$	17495.0	1.62788	0.813938	−	0.580951i	$-0.197319\pi$
$487$	17495.0	1.62788	0.813938	+	0.580951i	$0.197319\pi$
$488$	−4746.36	−0.440282
$489$	−1729.98	−0.159984
$490$	1257.67	0.115950
$491$	4382.61	0.402820	0.201410	−	0.979507i	$-0.435448\pi$
$491$	4382.61	0.402820	0.201410	+	0.979507i	$0.435448\pi$
$492$	4247.14	0.389178
$493$	−849.088	−0.0775679
$494$	−3328.48	−0.303149
$495$	3251.96	0.295282
$496$	1479.34	0.133920
$497$	7678.58	0.693021
$498$	2832.43	0.254868
$499$	8555.37	0.767517	0.383758	−	0.923434i	$-0.374630\pi$
$499$	8555.37	0.767517	0.383758	+	0.923434i	$0.374630\pi$
$500$	−4379.02	−0.391671
$501$	9989.53	0.890817
$502$	−6957.53	−0.618585
$503$	−17988.8	−1.59460	−0.797298	−	0.603586i	$-0.793738\pi$
$503$	−17988.8	−1.59460	−0.797298	+	0.603586i	$0.793738\pi$
$504$	504.000	0.0445435
$505$	21409.0	1.88651
$506$	−4574.78	−0.401924
$507$	−16425.9	−1.43886
$508$	−202.937	−0.0177242
$509$	−18400.2	−1.60231	−0.801155	−	0.598456i	$-0.795781\pi$
$509$	−18400.2	−1.60231	−0.801155	+	0.598456i	$0.795781\pi$
$510$	1803.72	0.156608
$511$	−2696.83	−0.233465
$512$	512.000	0.0441942
$513$	513.000	0.0441511
$514$	1019.91	0.0875217
$515$	19420.3	1.66167
$516$	−2738.00	−0.233592
$517$	13325.3	1.13355
$518$	−1205.52	−0.102254
$519$	1136.02	0.0960808
$520$	8992.75	0.758381
$521$	−9614.64	−0.808493	−0.404247	−	0.914650i	$-0.632466\pi$
$521$	−9614.64	−0.808493	−0.404247	+	0.914650i	$0.632466\pi$
$522$	652.448	0.0547067
$523$	3881.53	0.324527	0.162263	−	0.986747i	$-0.448121\pi$
$523$	3881.53	0.324527	0.162263	+	0.986747i	$0.448121\pi$
$524$	1832.39	0.152764
$525$	−833.584	−0.0692964
$526$	−467.598	−0.0387609
$527$	−2165.84	−0.179024
$528$	−1351.46	−0.111392
$529$	−5566.84	−0.457536
$530$	−13450.4	−1.10235
$531$	3544.11	0.289644
$532$	−532.000	−0.0433555
$533$	−31001.1	−2.51934
$534$	2433.35	0.197193
$535$	−16345.1	−1.32086
$536$	4416.26	0.355883
$537$	−6198.19	−0.498085
$538$	−7017.61	−0.562362
$539$	1379.62	0.110249
$540$	−1386.00	−0.110452
$541$	−15016.9	−1.19339	−0.596696	−	0.802467i	$-0.703520\pi$
$541$	−15016.9	−1.19339	−0.596696	+	0.802467i	$0.703520\pi$
$542$	−10666.7	−0.845336
$543$	11604.1	0.917086
$544$	−749.599	−0.0590787
$545$	9862.91	0.775194
$546$	−3678.85	−0.288352
$547$	6627.69	0.518062	0.259031	−	0.965869i	$-0.416597\pi$
$547$	6627.69	0.518062	0.259031	+	0.965869i	$0.416597\pi$
$548$	10217.0	0.796436
$549$	−5339.65	−0.415102
$550$	2235.23	0.173292
$551$	−688.695	−0.0532475
$552$	1949.79	0.150342
$553$	−1519.01	−0.116808
$554$	4669.20	0.358078
$555$	3315.17	0.253552
$556$	−1462.94	−0.111587
$557$	4660.68	0.354541	0.177271	−	0.984162i	$-0.443273\pi$
$557$	4660.68	0.354541	0.177271	+	0.984162i	$0.443273\pi$
$558$	1664.25	0.126261
$559$	19985.5	1.51216
$560$	1437.33	0.108461
$561$	1978.62	0.148908
$562$	8228.03	0.617577
$563$	−11242.6	−0.841599	−0.420799	−	0.907154i	$-0.638250\pi$
$563$	−11242.6	−0.841599	−0.420799	+	0.907154i	$0.638250\pi$
$564$	−5679.32	−0.424012
$565$	4812.25	0.358324
$566$	−7282.80	−0.540846
$567$	567.000	0.0419961
$568$	8775.52	0.648262
$569$	13063.0	0.962439	0.481219	−	0.876600i	$-0.340194\pi$
$569$	13063.0	0.962439	0.481219	+	0.876600i	$0.340194\pi$
$570$	1463.00	0.107506
$571$	−17686.1	−1.29622	−0.648111	−	0.761546i	$-0.724441\pi$
$571$	−17686.1	−1.29622	−0.648111	+	0.761546i	$0.724441\pi$
$572$	9864.74	0.721093
$573$	5199.90	0.379108
$574$	−4954.99	−0.360309
$575$	−3224.84	−0.233887
$576$	576.000	0.0416667
$577$	21553.1	1.55506	0.777530	−	0.628846i	$-0.216472\pi$
$577$	21553.1	1.55506	0.777530	+	0.628846i	$0.216472\pi$
$578$	−8728.54	−0.628130
$579$	−11555.4	−0.829404
$580$	1860.69	0.133208
$581$	−3304.50	−0.235962
$582$	3241.74	0.230884
$583$	−14754.6	−1.04815
$584$	−3082.09	−0.218387
$585$	10116.8	0.715008
$586$	−13553.6	−0.955449
$587$	−15818.5	−1.11227	−0.556133	−	0.831093i	$-0.687716\pi$
$587$	−15818.5	−1.11227	−0.556133	+	0.831093i	$0.687716\pi$
$588$	−588.000	−0.0412393
$589$	−1756.71	−0.122893
$590$	10107.3	0.705270
$591$	7000.90	0.487273
$592$	−1377.73	−0.0956494
$593$	−25180.3	−1.74373	−0.871866	−	0.489745i	$-0.837090\pi$
$593$	−25180.3	−1.74373	−0.871866	+	0.489745i	$0.837090\pi$
$594$	−1520.40	−0.105021
$595$	−2104.34	−0.144991
$596$	3577.39	0.245865
$597$	−3923.55	−0.268978
$598$	−14232.1	−0.973236
$599$	7982.59	0.544507	0.272254	−	0.962226i	$-0.412231\pi$
$599$	7982.59	0.544507	0.272254	+	0.962226i	$0.412231\pi$
$600$	−952.668	−0.0648208
$601$	20633.5	1.40043	0.700216	−	0.713931i	$-0.253087\pi$
$601$	20633.5	1.40043	0.700216	+	0.713931i	$0.253087\pi$
$602$	3194.33	0.216264
$603$	4968.29	0.335530
$604$	4858.42	0.327295
$605$	−6907.79	−0.464201
$606$	−10009.4	−0.670965
$607$	15327.8	1.02493	0.512466	−	0.858707i	$-0.328732\pi$
$607$	15327.8	1.02493	0.512466	+	0.858707i	$0.328732\pi$
$608$	−608.000	−0.0405554
$609$	−761.189	−0.0506485
$610$	−15227.9	−1.01075
$611$	41455.1	2.74483
$612$	−843.299	−0.0556999
$613$	18662.9	1.22967	0.614835	−	0.788655i	$-0.289222\pi$
$613$	18662.9	1.22967	0.614835	+	0.788655i	$0.289222\pi$
$614$	−2909.02	−0.191202
$615$	13626.2	0.893435
$616$	1576.71	0.103129
$617$	11297.2	0.737129	0.368565	−	0.929602i	$-0.379849\pi$
$617$	11297.2	0.737129	0.368565	+	0.929602i	$0.379849\pi$
$618$	−9079.60	−0.590995
$619$	−21382.4	−1.38842	−0.694209	−	0.719773i	$-0.744246\pi$
$619$	−21382.4	−1.38842	−0.694209	+	0.719773i	$0.744246\pi$
$620$	4746.21	0.307439
$621$	2193.52	0.141744
$622$	7935.81	0.511571
$623$	−2838.90	−0.182565
$624$	−4204.40	−0.269729
$625$	−19011.2	−1.21671
$626$	−20637.9	−1.31766
$627$	1604.86	0.102220
$628$	1593.70	0.101267
$629$	2017.09	0.127864
$630$	1617.00	0.102258
$631$	−11187.1	−0.705784	−0.352892	−	0.935664i	$-0.614802\pi$
$631$	−11187.1	−0.705784	−0.352892	+	0.935664i	$0.614802\pi$
$632$	−1736.01	−0.109264
$633$	13144.8	0.825367
$634$	−10967.3	−0.687015
$635$	−651.090	−0.0406893
$636$	6288.49	0.392067
$637$	4291.99	0.266962
$638$	2041.11	0.126659
$639$	9872.46	0.611187
$640$	1642.67	0.101456
$641$	23324.6	1.43723	0.718616	−	0.695407i	$-0.244776\pi$
$641$	23324.6	1.43723	0.718616	+	0.695407i	$0.244776\pi$
$642$	7641.87	0.469783
$643$	22566.1	1.38401	0.692006	−	0.721892i	$-0.256727\pi$
$643$	22566.1	1.38401	0.692006	+	0.721892i	$0.256727\pi$
$644$	−2274.76	−0.139189
$645$	−8784.41	−0.536257
$646$	890.149	0.0542143
$647$	−4281.78	−0.260177	−0.130088	−	0.991502i	$-0.541526\pi$
$647$	−4281.78	−0.260177	−0.130088	+	0.991502i	$0.541526\pi$
$648$	648.000	0.0392837
$649$	11087.3	0.670594
$650$	6953.81	0.419617
$651$	−1941.63	−0.116895
$652$	2306.63	0.138550
$653$	−27888.6	−1.67131	−0.835654	−	0.549257i	$-0.814911\pi$
$653$	−27888.6	−1.67131	−0.835654	+	0.549257i	$0.814911\pi$
$654$	−4611.23	−0.275709
$655$	5878.93	0.350701
$656$	−5662.85	−0.337038
$657$	−3467.35	−0.205897
$658$	6625.87	0.392558
$659$	1533.20	0.0906300	0.0453150	−	0.998973i	$-0.485571\pi$
$659$	1533.20	0.0906300	0.0453150	+	0.998973i	$0.485571\pi$
$660$	−4335.94	−0.255722
$661$	26818.5	1.57809	0.789045	−	0.614335i	$-0.210576\pi$
$661$	26818.5	1.57809	0.789045	+	0.614335i	$0.210576\pi$
$662$	17961.0	1.05449
$663$	6155.50	0.360573
$664$	−3776.57	−0.220722
$665$	−1706.83	−0.0995311
$666$	−1549.95	−0.0901792
$667$	−2944.76	−0.170947
$668$	−13319.4	−0.771470
$669$	−7075.66	−0.408910
$670$	14168.8	0.816999
$671$	−16704.5	−0.961058
$672$	−672.000	−0.0385758
$673$	19654.9	1.12577	0.562883	−	0.826537i	$-0.309692\pi$
$673$	19654.9	1.12577	0.562883	+	0.826537i	$0.309692\pi$
$674$	−114.549	−0.00654636
$675$	−1071.75	−0.0611137
$676$	21901.2	1.24609
$677$	−208.999	−0.0118648	−0.00593241	−	0.999982i	$-0.501888\pi$
$677$	−208.999	−0.0118648	−0.00593241	+	0.999982i	$0.501888\pi$
$678$	−2249.88	−0.127443
$679$	−3782.03	−0.213757
$680$	−2404.97	−0.135627
$681$	8686.06	0.488767
$682$	5206.43	0.292323
$683$	−8505.27	−0.476493	−0.238247	−	0.971205i	$-0.576573\pi$
$683$	−8505.27	−0.476493	−0.238247	+	0.971205i	$0.576573\pi$
$684$	−684.000	−0.0382360
$685$	32779.4	1.82838
$686$	686.000	0.0381802
$687$	15164.0	0.842127
$688$	3650.66	0.202297
$689$	−45901.6	−2.53804
$690$	6255.59	0.345139
$691$	3139.83	0.172858	0.0864289	−	0.996258i	$-0.472454\pi$
$691$	3139.83	0.172858	0.0864289	+	0.996258i	$0.472454\pi$
$692$	−1514.70	−0.0832084
$693$	1773.79	0.0972307
$694$	−13854.6	−0.757800
$695$	−4693.60	−0.256171
$696$	−869.931	−0.0473774
$697$	8290.76	0.450552
$698$	14184.5	0.769183
$699$	11054.9	0.598191
$700$	1111.45	0.0600124
$701$	−1099.68	−0.0592502	−0.0296251	−	0.999561i	$-0.509431\pi$
$701$	−1099.68	−0.0592502	−0.0296251	+	0.999561i	$0.509431\pi$
$702$	−4729.95	−0.254303
$703$	1636.06	0.0877739
$704$	1801.95	0.0964681
$705$	−18221.2	−0.973402
$706$	−3626.66	−0.193330
$707$	11677.7	0.621193
$708$	−4725.47	−0.250839
$709$	18247.7	0.966580	0.483290	−	0.875460i	$-0.339442\pi$
$709$	18247.7	0.966580	0.483290	+	0.875460i	$0.339442\pi$
$710$	28154.8	1.48821
$711$	−1953.01	−0.103015
$712$	−3244.46	−0.170774
$713$	−7511.46	−0.394539
$714$	983.849	0.0515681
$715$	31649.4	1.65541
$716$	8264.26	0.431354
$717$	21626.6	1.12644
$718$	24363.7	1.26636
$719$	−8401.90	−0.435797	−0.217899	−	0.975971i	$-0.569920\pi$
$719$	−8401.90	−0.435797	−0.217899	+	0.975971i	$0.569920\pi$
$720$	1848.00	0.0956540
$721$	10592.9	0.547155
$722$	722.000	0.0372161
$723$	−5481.17	−0.281946
$724$	−15472.1	−0.794220
$725$	1438.81	0.0737050
$726$	3229.62	0.165100
$727$	−31186.3	−1.59097	−0.795485	−	0.605973i	$-0.792784\pi$
$727$	−31186.3	−1.59097	−0.795485	+	0.605973i	$0.792784\pi$
$728$	4905.13	0.249720
$729$	729.000	0.0370370
$730$	−9888.38	−0.501350
$731$	−5344.79	−0.270430
$732$	7119.54	0.359489
$733$	−10029.6	−0.505393	−0.252697	−	0.967546i	$-0.581317\pi$
$733$	−10029.6	−0.505393	−0.252697	+	0.967546i	$0.581317\pi$
$734$	12777.0	0.642516
$735$	−1886.50	−0.0946729
$736$	−2599.72	−0.130200
$737$	15542.7	0.776830
$738$	−6370.71	−0.317763
$739$	−1143.38	−0.0569148	−0.0284574	−	0.999595i	$-0.509059\pi$
$739$	−1143.38	−0.0569148	−0.0284574	+	0.999595i	$0.509059\pi$
$740$	−4420.23	−0.219582
$741$	4992.72	0.247520
$742$	−7336.57	−0.362984
$743$	4301.87	0.212410	0.106205	−	0.994344i	$-0.466130\pi$
$743$	4301.87	0.212410	0.106205	+	0.994344i	$0.466130\pi$
$744$	−2219.01	−0.109345
$745$	11477.5	0.564432
$746$	12072.5	0.592501
$747$	−4248.64	−0.208099
$748$	−2638.17	−0.128958
$749$	−8915.52	−0.434934
$750$	6568.52	0.319798
$751$	−26742.9	−1.29942	−0.649708	−	0.760184i	$-0.725109\pi$
$751$	−26742.9	−1.29942	−0.649708	+	0.760184i	$0.725109\pi$
$752$	7572.43	0.367205
$753$	10436.3	0.505072
$754$	6349.89	0.306697
$755$	15587.4	0.751370
$756$	−756.000	−0.0363696
$757$	1192.08	0.0572351	0.0286176	−	0.999590i	$-0.490890\pi$
$757$	1192.08	0.0572351	0.0286176	+	0.999590i	$0.490890\pi$
$758$	16038.7	0.768539
$759$	6862.17	0.328170
$760$	−1950.67	−0.0931028
$761$	9519.44	0.453455	0.226728	−	0.973958i	$-0.427197\pi$
$761$	9519.44	0.453455	0.226728	+	0.973958i	$0.427197\pi$
$762$	304.406	0.0144717
$763$	5379.77	0.255257
$764$	−6933.19	−0.328317
$765$	−2705.59	−0.127870
$766$	−15415.5	−0.727136
$767$	34492.7	1.62381
$768$	−768.000	−0.0360844
$769$	2191.58	0.102770	0.0513852	−	0.998679i	$-0.483636\pi$
$769$	2191.58	0.102770	0.0513852	+	0.998679i	$0.483636\pi$
$770$	5058.60	0.236752
$771$	−1529.86	−0.0714612
$772$	15407.2	0.718285
$773$	17922.1	0.833909	0.416955	−	0.908927i	$-0.363097\pi$
$773$	17922.1	0.833909	0.416955	+	0.908927i	$0.363097\pi$
$774$	4106.99	0.190727
$775$	3670.10	0.170108
$776$	−4322.33	−0.199952
$777$	1808.27	0.0834897
$778$	−11855.1	−0.546305
$779$	6724.63	0.309288
$780$	−13489.1	−0.619215
$781$	30884.9	1.41504
$782$	3806.16	0.174051
$783$	−978.672	−0.0446678
$784$	784.000	0.0357143
$785$	5113.13	0.232478
$786$	−2748.59	−0.124732
$787$	42648.2	1.93169	0.965847	−	0.259113i	$-0.0834302\pi$
$787$	42648.2	1.93169	0.965847	+	0.259113i	$0.0834302\pi$
$788$	−9334.54	−0.421991
$789$	701.398	0.0316482
$790$	−5569.70	−0.250837
$791$	2624.86	0.117989
$792$	2027.19	0.0909510
$793$	−51967.7	−2.32715
$794$	−9782.64	−0.437245
$795$	20175.6	0.900068
$796$	5231.40	0.232942
$797$	19316.8	0.858515	0.429258	−	0.903182i	$-0.358775\pi$
$797$	19316.8	0.858515	0.429258	+	0.903182i	$0.358775\pi$
$798$	798.000	0.0353996
$799$	−11086.5	−0.490879
$800$	1270.22	0.0561365
$801$	−3650.02	−0.161008
$802$	−10244.3	−0.451044
$803$	−10847.2	−0.476700
$804$	−6624.38	−0.290577
$805$	−7298.18	−0.319537
$806$	16197.2	0.707844
$807$	10526.4	0.459167
$808$	13345.9	0.581073
$809$	−8869.95	−0.385477	−0.192738	−	0.981250i	$-0.561737\pi$
$809$	−8869.95	−0.385477	−0.192738	+	0.981250i	$0.561737\pi$
$810$	2079.00	0.0901835
$811$	−18437.3	−0.798300	−0.399150	−	0.916886i	$-0.630695\pi$
$811$	−18437.3	−0.798300	−0.399150	+	0.916886i	$0.630695\pi$
$812$	1014.92	0.0438629
$813$	16000.0	0.690214
$814$	−4848.84	−0.208786
$815$	7400.45	0.318069
$816$	1124.40	0.0482376
$817$	−4335.16	−0.185640
$818$	−10488.4	−0.448313
$819$	5518.27	0.235438
$820$	−18168.3	−0.773738
$821$	−5475.97	−0.232780	−0.116390	−	0.993204i	$-0.537132\pi$
$821$	−5475.97	−0.232780	−0.116390	+	0.993204i	$0.537132\pi$
$822$	−15325.4	−0.650287
$823$	−38150.5	−1.61585	−0.807924	−	0.589287i	$-0.799409\pi$
$823$	−38150.5	−1.61585	−0.807924	+	0.589287i	$0.799409\pi$
$824$	12106.1	0.511817
$825$	−3352.85	−0.141492
$826$	5513.05	0.232232
$827$	3329.19	0.139985	0.0699924	−	0.997548i	$-0.477703\pi$
$827$	3329.19	0.139985	0.0699924	+	0.997548i	$0.477703\pi$
$828$	−2924.69	−0.122754
$829$	−42923.4	−1.79830	−0.899150	−	0.437640i	$-0.855815\pi$
$829$	−42923.4	−1.79830	−0.899150	+	0.437640i	$0.855815\pi$
$830$	−12116.5	−0.506711
$831$	−7003.80	−0.292370
$832$	5605.87	0.233592
$833$	−1147.82	−0.0477428
$834$	2194.41	0.0911106
$835$	−42733.0	−1.77106
$836$	−2139.82	−0.0885252
$837$	−2496.38	−0.103091
$838$	−4312.14	−0.177757
$839$	−4562.76	−0.187752	−0.0938760	−	0.995584i	$-0.529926\pi$
$839$	−4562.76	−0.187752	−0.0938760	+	0.995584i	$0.529926\pi$
$840$	−2156.00	−0.0885584
$841$	−23075.1	−0.946129
$842$	20575.8	0.842146
$843$	−12342.0	−0.504250
$844$	−17526.3	−0.714789
$845$	70266.3	2.86063
$846$	8518.98	0.346204
$847$	−3767.89	−0.152853
$848$	−8384.65	−0.339540
$849$	10924.2	0.441599
$850$	−1859.69	−0.0750432
$851$	6995.56	0.281791
$852$	−13163.3	−0.529303
$853$	−7119.05	−0.285758	−0.142879	−	0.989740i	$-0.545636\pi$
$853$	−7119.05	−0.285758	−0.142879	+	0.989740i	$0.545636\pi$
$854$	−8306.13	−0.332822
$855$	−2194.50	−0.0877782
$856$	−10189.2	−0.406844
$857$	−16518.8	−0.658425	−0.329213	−	0.944256i	$-0.606783\pi$
$857$	−16518.8	−0.658425	−0.329213	+	0.944256i	$0.606783\pi$
$858$	−14797.1	−0.588770
$859$	−4096.82	−0.162726	−0.0813631	−	0.996685i	$-0.525927\pi$
$859$	−4096.82	−0.162726	−0.0813631	+	0.996685i	$0.525927\pi$
$860$	11712.5	0.464412
$861$	7432.49	0.294191
$862$	2903.87	0.114740
$863$	−26706.2	−1.05341	−0.526703	−	0.850050i	$-0.676572\pi$
$863$	−26706.2	−1.05341	−0.526703	+	0.850050i	$0.676572\pi$
$864$	−864.000	−0.0340207
$865$	−4859.66	−0.191021
$866$	25704.0	1.00861
$867$	13092.8	0.512866
$868$	2588.84	0.101234
$869$	−6109.77	−0.238504
$870$	−2791.03	−0.108764
$871$	48353.4	1.88105
$872$	6148.31	0.238771
$873$	−4862.62	−0.188516
$874$	3087.17	0.119480
$875$	−7663.28	−0.296076
$876$	4623.14	0.178312
$877$	−10452.6	−0.402464	−0.201232	−	0.979544i	$-0.564494\pi$
$877$	−10452.6	−0.402464	−0.201232	+	0.979544i	$0.564494\pi$
$878$	2865.49	0.110143
$879$	20330.4	0.780121
$880$	5781.26	0.221462
$881$	24982.0	0.955352	0.477676	−	0.878536i	$-0.341479\pi$
$881$	24982.0	0.955352	0.477676	+	0.878536i	$0.341479\pi$
$882$	882.000	0.0336718
$883$	41259.6	1.57247	0.786237	−	0.617924i	$-0.212026\pi$
$883$	41259.6	1.57247	0.786237	+	0.617924i	$0.212026\pi$
$884$	−8207.33	−0.312265
$885$	−15160.9	−0.575851
$886$	18085.8	0.685785
$887$	−22406.9	−0.848197	−0.424099	−	0.905616i	$-0.639409\pi$
$887$	−22406.9	−0.848197	−0.424099	+	0.905616i	$0.639409\pi$
$888$	2066.60	0.0780974
$889$	−355.140	−0.0133982
$890$	−10409.3	−0.392046
$891$	2280.59	0.0857494
$892$	9434.22	0.354127
$893$	−8992.26	−0.336970
$894$	−5366.09	−0.200748
$895$	26514.5	0.990259
$896$	896.000	0.0334077
$897$	21348.2	0.794644
$898$	−16911.4	−0.628441
$899$	3351.36	0.124331
$900$	1429.00	0.0529260
$901$	12275.6	0.453897
$902$	−19930.0	−0.735695
$903$	−4791.49	−0.176579
$904$	2999.84	0.110369
$905$	−49639.6	−1.82329
$906$	−7287.62	−0.267235
$907$	42804.0	1.56702	0.783508	−	0.621382i	$-0.213428\pi$
$907$	42804.0	1.56702	0.783508	+	0.621382i	$0.213428\pi$
$908$	−11581.4	−0.423285
$909$	15014.1	0.547841
$910$	15737.3	0.573282
$911$	29813.3	1.08426	0.542129	−	0.840295i	$-0.317618\pi$
$911$	29813.3	1.08426	0.542129	+	0.840295i	$0.317618\pi$
$912$	912.000	0.0331133
$913$	−13291.4	−0.481797
$914$	−7429.10	−0.268854
$915$	22841.9	0.825277
$916$	−20218.6	−0.729304
$917$	3206.69	0.115479
$918$	1264.95	0.0454788
$919$	9486.12	0.340499	0.170249	−	0.985401i	$-0.445543\pi$
$919$	9486.12	0.340499	0.170249	+	0.985401i	$0.445543\pi$
$920$	−8340.78	−0.298899
$921$	4363.52	0.156116
$922$	−24064.3	−0.859561
$923$	96082.8	3.42644
$924$	−2365.06	−0.0842043
$925$	−3418.03	−0.121496
$926$	−15476.5	−0.549231
$927$	13619.4	0.482545
$928$	1159.91	0.0410300
$929$	44384.5	1.56750	0.783750	−	0.621077i	$-0.213305\pi$
$929$	44384.5	1.56750	0.783750	+	0.621077i	$0.213305\pi$
$930$	−7119.31	−0.251023
$931$	−931.000	−0.0327737
$932$	−14739.9	−0.518049
$933$	−11903.7	−0.417696
$934$	23094.2	0.809063
$935$	−8464.12	−0.296049
$936$	6306.60	0.220233
$937$	−32995.3	−1.15038	−0.575191	−	0.818019i	$-0.695072\pi$
$937$	−32995.3	−1.15038	−0.575191	+	0.818019i	$0.695072\pi$
$938$	7728.45	0.269022
$939$	30956.9	1.07587
$940$	24294.9	0.842991
$941$	−10443.4	−0.361791	−0.180896	−	0.983502i	$-0.557900\pi$
$941$	−10443.4	−0.361791	−0.180896	+	0.983502i	$0.557900\pi$
$942$	−2390.55	−0.0826842
$943$	28753.6	0.992944
$944$	6300.63	0.217233
$945$	−2425.50	−0.0834937
$946$	12848.3	0.441578
$947$	14459.1	0.496155	0.248078	−	0.968740i	$-0.420201\pi$
$947$	14459.1	0.496155	0.248078	+	0.968740i	$0.420201\pi$
$948$	2604.01	0.0892135
$949$	−33745.7	−1.15430
$950$	−1508.39	−0.0515144
$951$	16451.0	0.560945
$952$	−1311.80	−0.0446593
$953$	−32962.3	−1.12041	−0.560207	−	0.828353i	$-0.689278\pi$
$953$	−32962.3	−1.12041	−0.560207	+	0.828353i	$0.689278\pi$
$954$	−9432.74	−0.320122
$955$	−22244.0	−0.753716
$956$	−28835.5	−0.975528
$957$	−3061.66	−0.103416
$958$	−28446.1	−0.959345
$959$	17879.7	0.602049
$960$	−2464.00	−0.0828388
$961$	−21242.4	−0.713048
$962$	−15084.7	−0.505563
$963$	−11462.8	−0.383576
$964$	7308.22	0.244172
$965$	49431.3	1.64896
$966$	3412.14	0.113648
$967$	16064.5	0.534229	0.267114	−	0.963665i	$-0.413930\pi$
$967$	16064.5	0.534229	0.267114	+	0.963665i	$0.413930\pi$
$968$	−4306.16	−0.142980
$969$	−1335.22	−0.0442658
$970$	−13867.5	−0.459028
$971$	3475.19	0.114855	0.0574274	−	0.998350i	$-0.481710\pi$
$971$	3475.19	0.114855	0.0574274	+	0.998350i	$0.481710\pi$
$972$	−972.000	−0.0320750
$973$	−2560.15	−0.0843521
$974$	34990.1	1.15108
$975$	−10430.7	−0.342616
$976$	−9492.72	−0.311326
$977$	41972.8	1.37444	0.687221	−	0.726449i	$-0.258831\pi$
$977$	41972.8	1.37444	0.687221	+	0.726449i	$0.258831\pi$
$978$	−3459.95	−0.113126
$979$	−11418.7	−0.372770
$980$	2515.33	0.0819892
$981$	6916.85	0.225115
$982$	8765.22	0.284837
$983$	1746.56	0.0566701	0.0283351	−	0.999598i	$-0.490979\pi$
$983$	1746.56	0.0566701	0.0283351	+	0.999598i	$0.490979\pi$
$984$	8494.27	0.275191
$985$	−29948.3	−0.968764
$986$	−1698.18	−0.0548488
$987$	−9938.81	−0.320523
$988$	−6656.97	−0.214359
$989$	−18536.5	−0.595984
$990$	6503.91	0.208796
$991$	−47117.1	−1.51032	−0.755159	−	0.655541i	$-0.772440\pi$
$991$	−47117.1	−1.51032	−0.755159	+	0.655541i	$0.772440\pi$
$992$	2958.67	0.0946956
$993$	−26941.5	−0.860990
$994$	15357.2	0.490040
$995$	16784.1	0.534764
$996$	5664.86	0.180219
$997$	2957.02	0.0939317	0.0469658	−	0.998896i	$-0.485045\pi$
$997$	2957.02	0.0939317	0.0469658	+	0.998896i	$0.485045\pi$
$998$	17110.7	0.542716
$999$	2324.92	0.0736310

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.4.a.q.1.4	✓	4
3.2	odd	2		2394.4.a.r.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.4.a.q.1.4	✓	4	1.1	even	1	trivial
2394.4.a.r.1.1		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	798.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +12.8333 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +12.8333 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +25.6667 q^{10} +28.1555 q^{11} -12.0000 q^{12} +87.5917 q^{13} +14.0000 q^{14} -38.5000 q^{15} +16.0000 q^{16} -23.4250 q^{17} +18.0000 q^{18} -19.0000 q^{19} +51.3333 q^{20} -21.0000 q^{21} +56.3109 q^{22} -81.2414 q^{23} -24.0000 q^{24} +39.6945 q^{25} +175.183 q^{26} -27.0000 q^{27} +28.0000 q^{28} +36.2471 q^{29} -77.0000 q^{30} +92.4586 q^{31} +32.0000 q^{32} -84.4664 q^{33} -46.8500 q^{34} +89.8333 q^{35} +36.0000 q^{36} -86.1083 q^{37} -38.0000 q^{38} -262.775 q^{39} +102.667 q^{40} -353.928 q^{41} -42.0000 q^{42} +228.166 q^{43} +112.622 q^{44} +115.500 q^{45} -162.483 q^{46} +473.277 q^{47} -48.0000 q^{48} +49.0000 q^{49} +79.3890 q^{50} +70.2749 q^{51} +350.367 q^{52} -524.041 q^{53} -54.0000 q^{54} +361.329 q^{55} +56.0000 q^{56} +57.0000 q^{57} +72.4942 q^{58} +393.790 q^{59} -154.000 q^{60} -593.295 q^{61} +184.917 q^{62} +63.0000 q^{63} +64.0000 q^{64} +1124.09 q^{65} -168.933 q^{66} +552.032 q^{67} -93.6999 q^{68} +243.724 q^{69} +179.667 q^{70} +1096.94 q^{71} +72.0000 q^{72} -385.261 q^{73} -172.217 q^{74} -119.083 q^{75} -76.0000 q^{76} +197.088 q^{77} -525.550 q^{78} -217.001 q^{79} +205.333 q^{80} +81.0000 q^{81} -707.856 q^{82} -472.071 q^{83} -84.0000 q^{84} -300.621 q^{85} +456.333 q^{86} -108.741 q^{87} +225.244 q^{88} -405.558 q^{89} +231.000 q^{90} +613.142 q^{91} -324.965 q^{92} -277.376 q^{93} +946.553 q^{94} -243.833 q^{95} -96.0000 q^{96} -540.291 q^{97} +98.0000 q^{98} +253.399 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} - 12 q^{3} + 16 q^{4} - 10 q^{5} - 24 q^{6} + 28 q^{7} + 32 q^{8} + 36 q^{9}+O(q^{10}) \) 4 * q + 8 * q^2 - 12 * q^3 + 16 * q^4 - 10 * q^5 - 24 * q^6 + 28 * q^7 + 32 * q^8 + 36 * q^9	\( 4 q + 8 q^{2} - 12 q^{3} + 16 q^{4} - 10 q^{5} - 24 q^{6} + 28 q^{7} + 32 q^{8} + 36 q^{9} - 20 q^{10} + 48 q^{11} - 48 q^{12} + 46 q^{13} + 56 q^{14} + 30 q^{15} + 64 q^{16} - 96 q^{17} + 72 q^{18} - 76 q^{19} - 40 q^{20} - 84 q^{21} + 96 q^{22} + 46 q^{23} - 96 q^{24} + 228 q^{25} + 92 q^{26} - 108 q^{27} + 112 q^{28} + 328 q^{29} + 60 q^{30} + 14 q^{31} + 128 q^{32} - 144 q^{33} - 192 q^{34} - 70 q^{35} + 144 q^{36} + 78 q^{37} - 152 q^{38} - 138 q^{39} - 80 q^{40} - 216 q^{41} - 168 q^{42} + 728 q^{43} + 192 q^{44} - 90 q^{45} + 92 q^{46} + 158 q^{47} - 192 q^{48} + 196 q^{49} + 456 q^{50} + 288 q^{51} + 184 q^{52} + 432 q^{53} - 216 q^{54} + 756 q^{55} + 224 q^{56} + 228 q^{57} + 656 q^{58} + 1120 q^{59} + 120 q^{60} + 412 q^{61} + 28 q^{62} + 252 q^{63} + 256 q^{64} + 1284 q^{65} - 288 q^{66} + 1248 q^{67} - 384 q^{68} - 138 q^{69} - 140 q^{70} + 848 q^{71} + 288 q^{72} + 1376 q^{73} + 156 q^{74} - 684 q^{75} - 304 q^{76} + 336 q^{77} - 276 q^{78} + 2102 q^{79} - 160 q^{80} + 324 q^{81} - 432 q^{82} + 484 q^{83} - 336 q^{84} + 2356 q^{85} + 1456 q^{86} - 984 q^{87} + 384 q^{88} + 792 q^{89} - 180 q^{90} + 322 q^{91} + 184 q^{92} - 42 q^{93} + 316 q^{94} + 190 q^{95} - 384 q^{96} + 1788 q^{97} + 392 q^{98} + 432 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 - 12 * q^3 + 16 * q^4 - 10 * q^5 - 24 * q^6 + 28 * q^7 + 32 * q^8 + 36 * q^9 - 20 * q^10 + 48 * q^11 - 48 * q^12 + 46 * q^13 + 56 * q^14 + 30 * q^15 + 64 * q^16 - 96 * q^17 + 72 * q^18 - 76 * q^19 - 40 * q^20 - 84 * q^21 + 96 * q^22 + 46 * q^23 - 96 * q^24 + 228 * q^25 + 92 * q^26 - 108 * q^27 + 112 * q^28 + 328 * q^29 + 60 * q^30 + 14 * q^31 + 128 * q^32 - 144 * q^33 - 192 * q^34 - 70 * q^35 + 144 * q^36 + 78 * q^37 - 152 * q^38 - 138 * q^39 - 80 * q^40 - 216 * q^41 - 168 * q^42 + 728 * q^43 + 192 * q^44 - 90 * q^45 + 92 * q^46 + 158 * q^47 - 192 * q^48 + 196 * q^49 + 456 * q^50 + 288 * q^51 + 184 * q^52 + 432 * q^53 - 216 * q^54 + 756 * q^55 + 224 * q^56 + 228 * q^57 + 656 * q^58 + 1120 * q^59 + 120 * q^60 + 412 * q^61 + 28 * q^62 + 252 * q^63 + 256 * q^64 + 1284 * q^65 - 288 * q^66 + 1248 * q^67 - 384 * q^68 - 138 * q^69 - 140 * q^70 + 848 * q^71 + 288 * q^72 + 1376 * q^73 + 156 * q^74 - 684 * q^75 - 304 * q^76 + 336 * q^77 - 276 * q^78 + 2102 * q^79 - 160 * q^80 + 324 * q^81 - 432 * q^82 + 484 * q^83 - 336 * q^84 + 2356 * q^85 + 1456 * q^86 - 984 * q^87 + 384 * q^88 + 792 * q^89 - 180 * q^90 + 322 * q^91 + 184 * q^92 - 42 * q^93 + 316 * q^94 + 190 * q^95 - 384 * q^96 + 1788 * q^97 + 392 * q^98 + 432 * q^99

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