LMFDB - Embedded newform 798.4.a.o.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} - x^{3} - 98x^{2} + 87x + 335 $ x^4 - x^3 - 98x^2 + 87x + 335
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$9.76424$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +21.5285 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +21.5285 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -43.0570 q^{10} -33.5191 q^{11} +12.0000 q^{12} -46.6997 q^{13} -14.0000 q^{14} +64.5855 q^{15} +16.0000 q^{16} -41.8988 q^{17} -18.0000 q^{18} -19.0000 q^{19} +86.1140 q^{20} +21.0000 q^{21} +67.0382 q^{22} +52.5535 q^{23} -24.0000 q^{24} +338.476 q^{25} +93.3994 q^{26} +27.0000 q^{27} +28.0000 q^{28} +198.558 q^{29} -129.171 q^{30} +117.908 q^{31} -32.0000 q^{32} -100.557 q^{33} +83.7975 q^{34} +150.699 q^{35} +36.0000 q^{36} +240.118 q^{37} +38.0000 q^{38} -140.099 q^{39} -172.228 q^{40} -3.25316 q^{41} -42.0000 q^{42} +486.614 q^{43} -134.076 q^{44} +193.756 q^{45} -105.107 q^{46} -176.661 q^{47} +48.0000 q^{48} +49.0000 q^{49} -676.952 q^{50} -125.696 q^{51} -186.799 q^{52} +751.469 q^{53} -54.0000 q^{54} -721.616 q^{55} -56.0000 q^{56} -57.0000 q^{57} -397.115 q^{58} +306.076 q^{59} +258.342 q^{60} +39.2724 q^{61} -235.815 q^{62} +63.0000 q^{63} +64.0000 q^{64} -1005.37 q^{65} +201.115 q^{66} +582.219 q^{67} -167.595 q^{68} +157.660 q^{69} -301.399 q^{70} +586.000 q^{71} -72.0000 q^{72} -759.825 q^{73} -480.236 q^{74} +1015.43 q^{75} -76.0000 q^{76} -234.634 q^{77} +280.198 q^{78} -300.059 q^{79} +344.456 q^{80} +81.0000 q^{81} +6.50632 q^{82} -826.385 q^{83} +84.0000 q^{84} -902.017 q^{85} -973.229 q^{86} +595.673 q^{87} +268.153 q^{88} +455.987 q^{89} -387.513 q^{90} -326.898 q^{91} +210.214 q^{92} +353.723 q^{93} +353.323 q^{94} -409.041 q^{95} -96.0000 q^{96} -528.107 q^{97} -98.0000 q^{98} -301.672 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} + 10 q^{5} - 24 q^{6} + 28 q^{7} - 32 q^{8} + 36 q^{9} - 20 q^{10} + 48 q^{11} + 48 q^{12} - 30 q^{13} - 56 q^{14} + 30 q^{15} + 64 q^{16} + 128 q^{17} - 72 q^{18} - 76 q^{19} + 40 q^{20} + 84 q^{21} - 96 q^{22} + 98 q^{23} - 96 q^{24} + 312 q^{25} + 60 q^{26} + 108 q^{27} + 112 q^{28} + 144 q^{29} - 60 q^{30} + 10 q^{31} - 128 q^{32} + 144 q^{33} - 256 q^{34} + 70 q^{35} + 144 q^{36} + 222 q^{37} + 152 q^{38} - 90 q^{39} - 80 q^{40} + 256 q^{41} - 168 q^{42} + 188 q^{43} + 192 q^{44} + 90 q^{45} - 196 q^{46} + 522 q^{47} + 192 q^{48} + 196 q^{49} - 624 q^{50} + 384 q^{51} - 120 q^{52} + 1088 q^{53} - 216 q^{54} - 1092 q^{55} - 224 q^{56} - 228 q^{57} - 288 q^{58} + 1456 q^{59} + 120 q^{60} - 108 q^{61} - 20 q^{62} + 252 q^{63} + 256 q^{64} + 836 q^{65} - 288 q^{66} + 296 q^{67} + 512 q^{68} + 294 q^{69} - 140 q^{70} + 808 q^{71} - 288 q^{72} - 1384 q^{73} - 444 q^{74} + 936 q^{75} - 304 q^{76} + 336 q^{77} + 180 q^{78} + 582 q^{79} + 160 q^{80} + 324 q^{81} - 512 q^{82} - 1236 q^{83} + 336 q^{84} - 2216 q^{85} - 376 q^{86} + 432 q^{87} - 384 q^{88} + 2528 q^{89} - 180 q^{90} - 210 q^{91} + 392 q^{92} + 30 q^{93} - 1044 q^{94} - 190 q^{95} - 384 q^{96} - 1028 q^{97} - 392 q^{98} + 432 q^{99}+O(q^{100}) \) 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 - 30 * q^13 - 56 * q^14 + 30 * q^15 + 64 * q^16 + 128 * q^17 - 72 * q^18 - 76 * q^19 + 40 * q^20 + 84 * q^21 - 96 * q^22 + 98 * q^23 - 96 * q^24 + 312 * q^25 + 60 * q^26 + 108 * q^27 + 112 * q^28 + 144 * q^29 - 60 * q^30 + 10 * q^31 - 128 * q^32 + 144 * q^33 - 256 * q^34 + 70 * q^35 + 144 * q^36 + 222 * q^37 + 152 * q^38 - 90 * q^39 - 80 * q^40 + 256 * q^41 - 168 * q^42 + 188 * q^43 + 192 * q^44 + 90 * q^45 - 196 * q^46 + 522 * q^47 + 192 * q^48 + 196 * q^49 - 624 * q^50 + 384 * q^51 - 120 * q^52 + 1088 * q^53 - 216 * q^54 - 1092 * q^55 - 224 * q^56 - 228 * q^57 - 288 * q^58 + 1456 * q^59 + 120 * q^60 - 108 * q^61 - 20 * q^62 + 252 * q^63 + 256 * q^64 + 836 * q^65 - 288 * q^66 + 296 * q^67 + 512 * q^68 + 294 * q^69 - 140 * q^70 + 808 * q^71 - 288 * q^72 - 1384 * q^73 - 444 * q^74 + 936 * q^75 - 304 * q^76 + 336 * q^77 + 180 * q^78 + 582 * q^79 + 160 * q^80 + 324 * q^81 - 512 * q^82 - 1236 * q^83 + 336 * q^84 - 2216 * q^85 - 376 * q^86 + 432 * q^87 - 384 * q^88 + 2528 * q^89 - 180 * q^90 - 210 * q^91 + 392 * q^92 + 30 * q^93 - 1044 * q^94 - 190 * q^95 - 384 * q^96 - 1028 * 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
$5$	21.5285	1.92557	0.962783	−	0.270275i	$-0.0871145\pi$
$5$	21.5285	1.92557	0.962783	+	0.270275i	$0.0871145\pi$
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−43.0570	−1.36158
$11$	−33.5191	−0.918763	−0.459381	−	0.888239i	$-0.651929\pi$
$11$	−33.5191	−0.918763	−0.459381	+	0.888239i	$0.651929\pi$
$12$	12.0000	0.288675
$13$	−46.6997	−0.996320	−0.498160	−	0.867085i	$-0.665991\pi$
$13$	−46.6997	−0.996320	−0.498160	+	0.867085i	$0.665991\pi$
$14$	−14.0000	−0.267261
$15$	64.5855	1.11173
$16$	16.0000	0.250000
$17$	−41.8988	−0.597761	−0.298881	−	0.954291i	$-0.596613\pi$
$17$	−41.8988	−0.597761	−0.298881	+	0.954291i	$0.596613\pi$
$18$	−18.0000	−0.235702
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	86.1140	0.962783
$21$	21.0000	0.218218
$22$	67.0382	0.649663
$23$	52.5535	0.476442	0.238221	−	0.971211i	$-0.423436\pi$
$23$	52.5535	0.476442	0.238221	+	0.971211i	$0.423436\pi$
$24$	−24.0000	−0.204124
$25$	338.476	2.70781
$26$	93.3994	0.704505
$27$	27.0000	0.192450
$28$	28.0000	0.188982
$29$	198.558	1.27142	0.635711	−	0.771927i	$-0.280707\pi$
$29$	198.558	1.27142	0.635711	+	0.771927i	$0.280707\pi$
$30$	−129.171	−0.786109
$31$	117.908	0.683124	0.341562	−	0.939859i	$-0.389044\pi$
$31$	117.908	0.683124	0.341562	+	0.939859i	$0.389044\pi$
$32$	−32.0000	−0.176777
$33$	−100.557	−0.530448
$34$	83.7975	0.422681
$35$	150.699	0.727796
$36$	36.0000	0.166667
$37$	240.118	1.06690	0.533448	−	0.845833i	$-0.320896\pi$
$37$	240.118	1.06690	0.533448	+	0.845833i	$0.320896\pi$
$38$	38.0000	0.162221
$39$	−140.099	−0.575226
$40$	−172.228	−0.680791
$41$	−3.25316	−0.0123917	−0.00619583	−	0.999981i	$-0.501972\pi$
$41$	−3.25316	−0.0123917	−0.00619583	+	0.999981i	$0.501972\pi$
$42$	−42.0000	−0.154303
$43$	486.614	1.72577	0.862884	−	0.505402i	$-0.168656\pi$
$43$	486.614	1.72577	0.862884	+	0.505402i	$0.168656\pi$
$44$	−134.076	−0.459381
$45$	193.756	0.641856
$46$	−105.107	−0.336895
$47$	−176.661	−0.548270	−0.274135	−	0.961691i	$-0.588392\pi$
$47$	−176.661	−0.548270	−0.274135	+	0.961691i	$0.588392\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	−676.952	−1.91471
$51$	−125.696	−0.345118
$52$	−186.799	−0.498160
$53$	751.469	1.94759	0.973794	−	0.227432i	$-0.0730329\pi$
$53$	751.469	1.94759	0.973794	+	0.227432i	$0.0730329\pi$
$54$	−54.0000	−0.136083
$55$	−721.616	−1.76914
$56$	−56.0000	−0.133631
$57$	−57.0000	−0.132453
$58$	−397.115	−0.899031
$59$	306.076	0.675386	0.337693	−	0.941256i	$-0.390353\pi$
$59$	306.076	0.675386	0.337693	+	0.941256i	$0.390353\pi$
$60$	258.342	0.555863
$61$	39.2724	0.0824315	0.0412157	−	0.999150i	$-0.486877\pi$
$61$	39.2724	0.0824315	0.0412157	+	0.999150i	$0.486877\pi$
$62$	−235.815	−0.483041
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	−1005.37	−1.91848
$66$	201.115	0.375083
$67$	582.219	1.06163	0.530816	−	0.847487i	$-0.321886\pi$
$67$	582.219	1.06163	0.530816	+	0.847487i	$0.321886\pi$
$68$	−167.595	−0.298881
$69$	157.660	0.275074
$70$	−301.399	−0.514629
$71$	586.000	0.979513	0.489756	−	0.871859i	$-0.337086\pi$
$71$	586.000	0.979513	0.489756	+	0.871859i	$0.337086\pi$
$72$	−72.0000	−0.117851
$73$	−759.825	−1.21823	−0.609115	−	0.793082i	$-0.708475\pi$
$73$	−759.825	−1.21823	−0.609115	+	0.793082i	$0.708475\pi$
$74$	−480.236	−0.754409
$75$	1015.43	1.56335
$76$	−76.0000	−0.114708
$77$	−234.634	−0.347260
$78$	280.198	0.406746
$79$	−300.059	−0.427333	−0.213666	−	0.976907i	$-0.568541\pi$
$79$	−300.059	−0.427333	−0.213666	+	0.976907i	$0.568541\pi$
$80$	344.456	0.481392
$81$	81.0000	0.111111
$82$	6.50632	0.00876223
$83$	−826.385	−1.09286	−0.546431	−	0.837504i	$-0.684014\pi$
$83$	−826.385	−1.09286	−0.546431	+	0.837504i	$0.684014\pi$
$84$	84.0000	0.109109
$85$	−902.017	−1.15103
$86$	−973.229	−1.22030
$87$	595.673	0.734055
$88$	268.153	0.324832
$89$	455.987	0.543085	0.271542	−	0.962427i	$-0.412466\pi$
$89$	455.987	0.543085	0.271542	+	0.962427i	$0.412466\pi$
$90$	−387.513	−0.453860
$91$	−326.898	−0.376574
$92$	210.214	0.238221
$93$	353.723	0.394402
$94$	353.323	0.387686
$95$	−409.041	−0.441755
$96$	−96.0000	−0.102062
$97$	−528.107	−0.552795	−0.276397	−	0.961043i	$-0.589141\pi$
$97$	−528.107	−0.552795	−0.276397	+	0.961043i	$0.589141\pi$
$98$	−98.0000	−0.101015
$99$	−301.672	−0.306254
$100$	1353.90	1.35390
$101$	297.593	0.293184	0.146592	−	0.989197i	$-0.453170\pi$
$101$	297.593	0.293184	0.146592	+	0.989197i	$0.453170\pi$
$102$	251.393	0.244035
$103$	−912.306	−0.872739	−0.436370	−	0.899767i	$-0.643736\pi$
$103$	−912.306	−0.872739	−0.436370	+	0.899767i	$0.643736\pi$
$104$	373.597	0.352252
$105$	452.098	0.420193
$106$	−1502.94	−1.37715
$107$	90.8700	0.0821003	0.0410501	−	0.999157i	$-0.486930\pi$
$107$	90.8700	0.0821003	0.0410501	+	0.999157i	$0.486930\pi$
$108$	108.000	0.0962250
$109$	1446.90	1.27145	0.635723	−	0.771917i	$-0.280702\pi$
$109$	1446.90	1.27145	0.635723	+	0.771917i	$0.280702\pi$
$110$	1443.23	1.25097
$111$	720.353	0.615972
$112$	112.000	0.0944911
$113$	751.734	0.625815	0.312908	−	0.949784i	$-0.398697\pi$
$113$	751.734	0.625815	0.312908	+	0.949784i	$0.398697\pi$
$114$	114.000	0.0936586
$115$	1131.40	0.917420
$116$	794.230	0.635711
$117$	−420.297	−0.332107
$118$	−612.153	−0.477570
$119$	−293.291	−0.225932
$120$	−516.684	−0.393055
$121$	−207.469	−0.155875
$122$	−78.5449	−0.0582878
$123$	−9.75948	−0.00715433
$124$	471.630	0.341562
$125$	4595.81	3.28849
$126$	−126.000	−0.0890871
$127$	27.9713	0.0195437	0.00977185	−	0.999952i	$-0.496889\pi$
$127$	27.9713	0.0195437	0.00977185	+	0.999952i	$0.496889\pi$
$128$	−128.000	−0.0883883
$129$	1459.84	0.996372
$130$	2010.75	1.35657
$131$	−138.762	−0.0925472	−0.0462736	−	0.998929i	$-0.514735\pi$
$131$	−138.762	−0.0925472	−0.0462736	+	0.998929i	$0.514735\pi$
$132$	−402.229	−0.265224
$133$	−133.000	−0.0867110
$134$	−1164.44	−0.750687
$135$	581.269	0.370575
$136$	335.190	0.211341
$137$	666.561	0.415680	0.207840	−	0.978163i	$-0.433357\pi$
$137$	666.561	0.415680	0.207840	+	0.978163i	$0.433357\pi$
$138$	−315.321	−0.194506
$139$	−3240.58	−1.97742	−0.988712	−	0.149827i	$-0.952128\pi$
$139$	−3240.58	−1.97742	−0.988712	+	0.149827i	$0.952128\pi$
$140$	602.798	0.363898
$141$	−529.984	−0.316544
$142$	−1172.00	−0.692620
$143$	1565.33	0.915382
$144$	144.000	0.0833333
$145$	4274.64	2.44821
$146$	1519.65	0.861419
$147$	147.000	0.0824786
$148$	960.471	0.533448
$149$	−3337.04	−1.83477	−0.917385	−	0.398001i	$-0.869704\pi$
$149$	−3337.04	−1.83477	−0.917385	+	0.398001i	$0.869704\pi$
$150$	−2030.85	−1.10546
$151$	−936.880	−0.504916	−0.252458	−	0.967608i	$-0.581239\pi$
$151$	−936.880	−0.504916	−0.252458	+	0.967608i	$0.581239\pi$
$152$	152.000	0.0811107
$153$	−377.089	−0.199254
$154$	469.267	0.245550
$155$	2538.37	1.31540
$156$	−560.396	−0.287613
$157$	−851.201	−0.432696	−0.216348	−	0.976316i	$-0.569415\pi$
$157$	−851.201	−0.432696	−0.216348	+	0.976316i	$0.569415\pi$
$158$	600.118	0.302170
$159$	2254.41	1.12444
$160$	−688.912	−0.340395
$161$	367.874	0.180078
$162$	−162.000	−0.0785674
$163$	−1642.27	−0.789155	−0.394577	−	0.918863i	$-0.629109\pi$
$163$	−1642.27	−0.789155	−0.394577	+	0.918863i	$0.629109\pi$
$164$	−13.0126	−0.00619583
$165$	−2164.85	−1.02141
$166$	1652.77	0.772770
$167$	1114.15	0.516259	0.258129	−	0.966110i	$-0.416894\pi$
$167$	1114.15	0.516259	0.258129	+	0.966110i	$0.416894\pi$
$168$	−168.000	−0.0771517
$169$	−16.1396	−0.00734620
$170$	1804.03	0.813900
$171$	−171.000	−0.0764719
$172$	1946.46	0.862884
$173$	704.921	0.309793	0.154896	−	0.987931i	$-0.450496\pi$
$173$	704.921	0.309793	0.154896	+	0.987931i	$0.450496\pi$
$174$	−1191.35	−0.519056
$175$	2369.33	1.02345
$176$	−536.306	−0.229691
$177$	918.229	0.389934
$178$	−911.974	−0.384019
$179$	−3717.71	−1.55237	−0.776186	−	0.630504i	$-0.782848\pi$
$179$	−3717.71	−1.55237	−0.776186	+	0.630504i	$0.782848\pi$
$180$	775.026	0.320928
$181$	−349.542	−0.143543	−0.0717713	−	0.997421i	$-0.522865\pi$
$181$	−349.542	−0.143543	−0.0717713	+	0.997421i	$0.522865\pi$
$182$	653.796	0.266278
$183$	117.817	0.0475918
$184$	−420.428	−0.168448
$185$	5169.37	2.05438
$186$	−707.446	−0.278884
$187$	1404.41	0.549201
$188$	−706.645	−0.274135
$189$	189.000	0.0727393
$190$	818.083	0.312368
$191$	3138.16	1.18884	0.594422	−	0.804154i	$-0.297381\pi$
$191$	3138.16	1.18884	0.594422	+	0.804154i	$0.297381\pi$
$192$	192.000	0.0721688
$193$	−204.898	−0.0764189	−0.0382095	−	0.999270i	$-0.512165\pi$
$193$	−204.898	−0.0764189	−0.0382095	+	0.999270i	$0.512165\pi$
$194$	1056.21	0.390885
$195$	−3016.12	−1.10764
$196$	196.000	0.0714286
$197$	4709.16	1.70312	0.851558	−	0.524260i	$-0.175658\pi$
$197$	4709.16	1.70312	0.851558	+	0.524260i	$0.175658\pi$
$198$	603.344	0.216554
$199$	−3994.92	−1.42308	−0.711539	−	0.702647i	$-0.752001\pi$
$199$	−3994.92	−1.42308	−0.711539	+	0.702647i	$0.752001\pi$
$200$	−2707.81	−0.957354
$201$	1746.66	0.612934
$202$	−595.186	−0.207313
$203$	1389.90	0.480552
$204$	−502.785	−0.172559
$205$	−70.0356	−0.0238610
$206$	1824.61	0.617120
$207$	472.981	0.158814
$208$	−747.195	−0.249080
$209$	636.863	0.210779
$210$	−904.196	−0.297121
$211$	−204.623	−0.0667623	−0.0333811	−	0.999443i	$-0.510628\pi$
$211$	−204.623	−0.0667623	−0.0333811	+	0.999443i	$0.510628\pi$
$212$	3005.87	0.973794
$213$	1758.00	0.565522
$214$	−181.740	−0.0580537
$215$	10476.1	3.32308
$216$	−216.000	−0.0680414
$217$	825.353	0.258196
$218$	−2893.79	−0.899048
$219$	−2279.47	−0.703345
$220$	−2886.46	−0.884569
$221$	1956.66	0.595562
$222$	−1440.71	−0.435558
$223$	−5163.25	−1.55048	−0.775239	−	0.631668i	$-0.782371\pi$
$223$	−5163.25	−1.55048	−0.775239	+	0.631668i	$0.782371\pi$
$224$	−224.000	−0.0668153
$225$	3046.28	0.902602
$226$	−1503.47	−0.442518
$227$	−1212.76	−0.354597	−0.177298	−	0.984157i	$-0.556736\pi$
$227$	−1212.76	−0.354597	−0.177298	+	0.984157i	$0.556736\pi$
$228$	−228.000	−0.0662266
$229$	4103.96	1.18427	0.592135	−	0.805839i	$-0.298285\pi$
$229$	4103.96	1.18427	0.592135	+	0.805839i	$0.298285\pi$
$230$	−2262.79	−0.648714
$231$	−703.901	−0.200490
$232$	−1588.46	−0.449515
$233$	−3421.57	−0.962038	−0.481019	−	0.876710i	$-0.659733\pi$
$233$	−3421.57	−0.962038	−0.481019	+	0.876710i	$0.659733\pi$
$234$	840.594	0.234835
$235$	−3803.25	−1.05573
$236$	1224.31	0.337693
$237$	−900.177	−0.246721
$238$	586.583	0.159758
$239$	−1946.65	−0.526854	−0.263427	−	0.964679i	$-0.584853\pi$
$239$	−1946.65	−0.526854	−0.263427	+	0.964679i	$0.584853\pi$
$240$	1033.37	0.277932
$241$	−1908.58	−0.510135	−0.255068	−	0.966923i	$-0.582098\pi$
$241$	−1908.58	−0.510135	−0.255068	+	0.966923i	$0.582098\pi$
$242$	414.939	0.110220
$243$	243.000	0.0641500
$244$	157.090	0.0412157
$245$	1054.90	0.275081
$246$	19.5190	0.00505888
$247$	887.294	0.228572
$248$	−943.261	−0.241521
$249$	−2479.16	−0.630964
$250$	−9191.62	−2.32532
$251$	−970.268	−0.243995	−0.121998	−	0.992530i	$-0.538930\pi$
$251$	−970.268	−0.243995	−0.121998	+	0.992530i	$0.538930\pi$
$252$	252.000	0.0629941
$253$	−1761.55	−0.437737
$254$	−55.9426	−0.0138195
$255$	−2706.05	−0.664547
$256$	256.000	0.0625000
$257$	1032.35	0.250568	0.125284	−	0.992121i	$-0.460016\pi$
$257$	1032.35	0.250568	0.125284	+	0.992121i	$0.460016\pi$
$258$	−2919.69	−0.704542
$259$	1680.82	0.403248
$260$	−4021.49	−0.959240
$261$	1787.02	0.423807
$262$	277.524	0.0654408
$263$	1655.04	0.388039	0.194019	−	0.980998i	$-0.437848\pi$
$263$	1655.04	0.388039	0.194019	+	0.980998i	$0.437848\pi$
$264$	804.459	0.187542
$265$	16178.0	3.75021
$266$	266.000	0.0613139
$267$	1367.96	0.313550
$268$	2328.88	0.530816
$269$	736.875	0.167019	0.0835094	−	0.996507i	$-0.473387\pi$
$269$	736.875	0.167019	0.0835094	+	0.996507i	$0.473387\pi$
$270$	−1162.54	−0.262036
$271$	−6182.97	−1.38594	−0.692968	−	0.720968i	$-0.743697\pi$
$271$	−6182.97	−1.38594	−0.692968	+	0.720968i	$0.743697\pi$
$272$	−670.380	−0.149440
$273$	−980.693	−0.217415
$274$	−1333.12	−0.293930
$275$	−11345.4	−2.48783
$276$	630.642	0.137537
$277$	−7452.72	−1.61657	−0.808286	−	0.588790i	$-0.799605\pi$
$277$	−7452.72	−1.61657	−0.808286	+	0.588790i	$0.799605\pi$
$278$	6481.15	1.39825
$279$	1061.17	0.227708
$280$	−1205.60	−0.257315
$281$	−1249.11	−0.265180	−0.132590	−	0.991171i	$-0.542329\pi$
$281$	−1249.11	−0.265180	−0.132590	+	0.991171i	$0.542329\pi$
$282$	1059.97	0.223830
$283$	−6140.75	−1.28986	−0.644929	−	0.764243i	$-0.723113\pi$
$283$	−6140.75	−1.28986	−0.644929	+	0.764243i	$0.723113\pi$
$284$	2344.00	0.489756
$285$	−1227.12	−0.255048
$286$	−3130.66	−0.647273
$287$	−22.7721	−0.00468361
$288$	−288.000	−0.0589256
$289$	−3157.49	−0.642682
$290$	−8549.29	−1.73114
$291$	−1584.32	−0.319156
$292$	−3039.30	−0.609115
$293$	7804.10	1.55604	0.778022	−	0.628238i	$-0.216223\pi$
$293$	7804.10	1.55604	0.778022	+	0.628238i	$0.216223\pi$
$294$	−294.000	−0.0583212
$295$	6589.36	1.30050
$296$	−1920.94	−0.377204
$297$	−905.016	−0.176816
$298$	6674.07	1.29738
$299$	−2454.23	−0.474688
$300$	4061.71	0.781676
$301$	3406.30	0.652279
$302$	1873.76	0.357029
$303$	892.779	0.169270
$304$	−304.000	−0.0573539
$305$	845.476	0.158727
$306$	754.178	0.140894
$307$	−5832.56	−1.08431	−0.542153	−	0.840280i	$-0.682391\pi$
$307$	−5832.56	−1.08431	−0.542153	+	0.840280i	$0.682391\pi$
$308$	−938.535	−0.173630
$309$	−2736.92	−0.503876
$310$	−5076.75	−0.930128
$311$	9955.13	1.81512	0.907562	−	0.419918i	$-0.137941\pi$
$311$	9955.13	1.81512	0.907562	+	0.419918i	$0.137941\pi$
$312$	1120.79	0.203373
$313$	−7677.21	−1.38639	−0.693197	−	0.720748i	$-0.743799\pi$
$313$	−7677.21	−1.38639	−0.693197	+	0.720748i	$0.743799\pi$
$314$	1702.40	0.305962
$315$	1356.29	0.242599
$316$	−1200.24	−0.213666
$317$	−9617.75	−1.70406	−0.852030	−	0.523493i	$-0.824629\pi$
$317$	−9617.75	−1.70406	−0.852030	+	0.523493i	$0.824629\pi$
$318$	−4508.81	−0.795099
$319$	−6655.47	−1.16813
$320$	1377.82	0.240696
$321$	272.610	0.0474006
$322$	−735.749	−0.127334
$323$	796.076	0.137136
$324$	324.000	0.0555556
$325$	−15806.7	−2.69784
$326$	3284.53	0.558017
$327$	4340.69	0.734069
$328$	26.0253	0.00438111
$329$	−1236.63	−0.207227
$330$	4329.69	0.722248
$331$	−1001.26	−0.166266	−0.0831330	−	0.996538i	$-0.526493\pi$
$331$	−1001.26	−0.166266	−0.0831330	+	0.996538i	$0.526493\pi$
$332$	−3305.54	−0.546431
$333$	2161.06	0.355632
$334$	−2228.29	−0.365050
$335$	12534.3	2.04424
$336$	336.000	0.0545545
$337$	−1583.59	−0.255975	−0.127988	−	0.991776i	$-0.540852\pi$
$337$	−1583.59	−0.255975	−0.127988	+	0.991776i	$0.540852\pi$
$338$	32.2792	0.00519454
$339$	2255.20	0.361315
$340$	−3608.07	−0.575514
$341$	−3952.16	−0.627629
$342$	342.000	0.0540738
$343$	343.000	0.0539949
$344$	−3892.92	−0.610151
$345$	3394.19	0.529673
$346$	−1409.84	−0.219057
$347$	7278.96	1.12609	0.563047	−	0.826425i	$-0.309629\pi$
$347$	7278.96	1.12609	0.563047	+	0.826425i	$0.309629\pi$
$348$	2382.69	0.367028
$349$	8340.47	1.27924	0.639620	−	0.768691i	$-0.279092\pi$
$349$	8340.47	1.27924	0.639620	+	0.768691i	$0.279092\pi$
$350$	−4738.66	−0.723692
$351$	−1260.89	−0.191742
$352$	1072.61	0.162416
$353$	−6145.47	−0.926602	−0.463301	−	0.886201i	$-0.653335\pi$
$353$	−6145.47	−0.926602	−0.463301	+	0.886201i	$0.653335\pi$
$354$	−1836.46	−0.275725
$355$	12615.7	1.88612
$356$	1823.95	0.271542
$357$	−879.874	−0.130442
$358$	7435.42	1.09769
$359$	9753.89	1.43396	0.716979	−	0.697095i	$-0.245525\pi$
$359$	9753.89	1.43396	0.716979	+	0.697095i	$0.245525\pi$
$360$	−1550.05	−0.226930
$361$	361.000	0.0526316
$362$	699.083	0.101500
$363$	−622.408	−0.0899944
$364$	−1307.59	−0.188287
$365$	−16357.9	−2.34578
$366$	−235.635	−0.0336525
$367$	−8940.02	−1.27157	−0.635784	−	0.771867i	$-0.719323\pi$
$367$	−8940.02	−1.27157	−0.635784	+	0.771867i	$0.719323\pi$
$368$	840.856	0.119110
$369$	−29.2784	−0.00413055
$370$	−10338.7	−1.45266
$371$	5260.28	0.736119
$372$	1414.89	0.197201
$373$	8972.19	1.24548	0.622738	−	0.782431i	$-0.286020\pi$
$373$	8972.19	1.24548	0.622738	+	0.782431i	$0.286020\pi$
$374$	−2808.82	−0.388344
$375$	13787.4	1.89861
$376$	1413.29	0.193843
$377$	−9272.58	−1.26674
$378$	−378.000	−0.0514344
$379$	455.027	0.0616706	0.0308353	−	0.999524i	$-0.490183\pi$
$379$	455.027	0.0616706	0.0308353	+	0.999524i	$0.490183\pi$
$380$	−1636.17	−0.220878
$381$	83.9139	0.0112836
$382$	−6276.31	−0.840639
$383$	−8516.36	−1.13620	−0.568101	−	0.822959i	$-0.692322\pi$
$383$	−8516.36	−1.13620	−0.568101	+	0.822959i	$0.692322\pi$
$384$	−384.000	−0.0510310
$385$	−5051.31	−0.668672
$386$	409.795	0.0540363
$387$	4379.53	0.575256
$388$	−2112.43	−0.276397
$389$	−12203.2	−1.59056	−0.795280	−	0.606242i	$-0.792676\pi$
$389$	−12203.2	−1.59056	−0.795280	+	0.606242i	$0.792676\pi$
$390$	6032.24	0.783216
$391$	−2201.93	−0.284798
$392$	−392.000	−0.0505076
$393$	−416.286	−0.0534322
$394$	−9418.32	−1.20429
$395$	−6459.82	−0.822857
$396$	−1206.69	−0.153127
$397$	11075.9	1.40022	0.700108	−	0.714037i	$-0.253135\pi$
$397$	11075.9	1.40022	0.700108	+	0.714037i	$0.253135\pi$
$398$	7989.84	1.00627
$399$	−399.000	−0.0500626
$400$	5415.61	0.676952
$401$	−10478.3	−1.30489	−0.652444	−	0.757837i	$-0.726256\pi$
$401$	−10478.3	−1.30489	−0.652444	+	0.757837i	$0.726256\pi$
$402$	−3493.31	−0.433409
$403$	−5506.25	−0.680610
$404$	1190.37	0.146592
$405$	1743.81	0.213952
$406$	−2779.81	−0.339802
$407$	−8048.53	−0.980224
$408$	1005.57	0.122017
$409$	10792.7	1.30480	0.652399	−	0.757876i	$-0.273763\pi$
$409$	10792.7	1.30480	0.652399	+	0.757876i	$0.273763\pi$
$410$	140.071	0.0168723
$411$	1999.68	0.239993
$412$	−3649.22	−0.436370
$413$	2142.54	0.255272
$414$	−945.963	−0.112298
$415$	−17790.8	−2.10438
$416$	1494.39	0.176126
$417$	−9721.73	−1.14167
$418$	−1273.73	−0.149043
$419$	−5723.37	−0.667315	−0.333658	−	0.942694i	$-0.608283\pi$
$419$	−5723.37	−0.667315	−0.333658	+	0.942694i	$0.608283\pi$
$420$	1808.39	0.210097
$421$	14546.9	1.68402	0.842010	−	0.539461i	$-0.181372\pi$
$421$	14546.9	1.68402	0.842010	+	0.539461i	$0.181372\pi$
$422$	409.246	0.0472080
$423$	−1589.95	−0.182757
$424$	−6011.75	−0.688576
$425$	−14181.7	−1.61862
$426$	−3516.00	−0.399884
$427$	274.907	0.0311562
$428$	363.480	0.0410501
$429$	4696.00	0.528496
$430$	−20952.1	−2.34977
$431$	3911.19	0.437112	0.218556	−	0.975824i	$-0.429865\pi$
$431$	3911.19	0.437112	0.218556	+	0.975824i	$0.429865\pi$
$432$	432.000	0.0481125
$433$	−2101.49	−0.233236	−0.116618	−	0.993177i	$-0.537205\pi$
$433$	−2101.49	−0.233236	−0.116618	+	0.993177i	$0.537205\pi$
$434$	−1650.71	−0.182572
$435$	12823.9	1.41347
$436$	5787.59	0.635723
$437$	−998.516	−0.109303
$438$	4558.95	0.497340
$439$	−683.929	−0.0743557	−0.0371778	−	0.999309i	$-0.511837\pi$
$439$	−683.929	−0.0743557	−0.0371778	+	0.999309i	$0.511837\pi$
$440$	5772.93	0.625485
$441$	441.000	0.0476190
$442$	−3913.32	−0.421126
$443$	4500.53	0.482679	0.241339	−	0.970441i	$-0.422413\pi$
$443$	4500.53	0.482679	0.241339	+	0.970441i	$0.422413\pi$
$444$	2881.41	0.307986
$445$	9816.71	1.04575
$446$	10326.5	1.09635
$447$	−10011.1	−1.05930
$448$	448.000	0.0472456
$449$	3060.38	0.321667	0.160833	−	0.986982i	$-0.448582\pi$
$449$	3060.38	0.321667	0.160833	+	0.986982i	$0.448582\pi$
$450$	−6092.56	−0.638236
$451$	109.043	0.0113850
$452$	3006.93	0.312908
$453$	−2810.64	−0.291513
$454$	2425.51	0.250738
$455$	−7037.61	−0.725118
$456$	456.000	0.0468293
$457$	−2314.52	−0.236911	−0.118456	−	0.992959i	$-0.537794\pi$
$457$	−2314.52	−0.236911	−0.118456	+	0.992959i	$0.537794\pi$
$458$	−8207.93	−0.837405
$459$	−1131.27	−0.115039
$460$	4525.59	0.458710
$461$	12856.3	1.29887	0.649435	−	0.760417i	$-0.275006\pi$
$461$	12856.3	1.29887	0.649435	+	0.760417i	$0.275006\pi$
$462$	1407.80	0.141768
$463$	2163.36	0.217148	0.108574	−	0.994088i	$-0.465371\pi$
$463$	2163.36	0.217148	0.108574	+	0.994088i	$0.465371\pi$
$464$	3176.92	0.317855
$465$	7615.12	0.759447
$466$	6843.15	0.680263
$467$	−17759.9	−1.75981	−0.879905	−	0.475150i	$-0.842394\pi$
$467$	−17759.9	−1.75981	−0.879905	+	0.475150i	$0.842394\pi$
$468$	−1681.19	−0.166053
$469$	4075.53	0.401259
$470$	7606.50	0.746515
$471$	−2553.60	−0.249817
$472$	−2448.61	−0.238785
$473$	−16310.9	−1.58557
$474$	1800.35	0.174458
$475$	−6431.04	−0.621213
$476$	−1173.17	−0.112966
$477$	6763.22	0.649196
$478$	3893.29	0.372542
$479$	−15496.9	−1.47823	−0.739113	−	0.673582i	$-0.764755\pi$
$479$	−15496.9	−1.47823	−0.739113	+	0.673582i	$0.764755\pi$
$480$	−2066.73	−0.196527
$481$	−11213.4	−1.06297
$482$	3817.16	0.360720
$483$	1103.62	0.103968
$484$	−829.878	−0.0779374
$485$	−11369.3	−1.06444
$486$	−486.000	−0.0453609
$487$	8548.82	0.795449	0.397725	−	0.917505i	$-0.369800\pi$
$487$	8548.82	0.795449	0.397725	+	0.917505i	$0.369800\pi$
$488$	−314.179	−0.0291439
$489$	−4926.80	−0.455619
$490$	−2109.79	−0.194512
$491$	−7130.65	−0.655400	−0.327700	−	0.944782i	$-0.606274\pi$
$491$	−7130.65	−0.655400	−0.327700	+	0.944782i	$0.606274\pi$
$492$	−39.0379	−0.00357717
$493$	−8319.31	−0.760006
$494$	−1774.59	−0.161624
$495$	−6494.54	−0.589713
$496$	1886.52	0.170781
$497$	4102.00	0.370221
$498$	4958.31	0.446159
$499$	5580.74	0.500658	0.250329	−	0.968161i	$-0.419461\pi$
$499$	5580.74	0.500658	0.250329	+	0.968161i	$0.419461\pi$
$500$	18383.2	1.64425
$501$	3342.44	0.298062
$502$	1940.54	0.172531
$503$	13740.6	1.21802	0.609009	−	0.793163i	$-0.291567\pi$
$503$	13740.6	1.21802	0.609009	+	0.793163i	$0.291567\pi$
$504$	−504.000	−0.0445435
$505$	6406.73	0.564546
$506$	3523.09	0.309527
$507$	−48.4188	−0.00424133
$508$	111.885	0.00977185
$509$	−9650.64	−0.840387	−0.420194	−	0.907434i	$-0.638038\pi$
$509$	−9650.64	−0.840387	−0.420194	+	0.907434i	$0.638038\pi$
$510$	5412.10	0.469906
$511$	−5318.77	−0.460448
$512$	−512.000	−0.0441942
$513$	−513.000	−0.0441511
$514$	−2064.69	−0.177178
$515$	−19640.6	−1.68052
$516$	5839.37	0.498186
$517$	5921.53	0.503730
$518$	−3361.65	−0.285140
$519$	2114.76	0.178859
$520$	8042.99	0.678285
$521$	−15284.5	−1.28527	−0.642636	−	0.766172i	$-0.722159\pi$
$521$	−15284.5	−1.28527	−0.642636	+	0.766172i	$0.722159\pi$
$522$	−3574.04	−0.299677
$523$	12423.3	1.03869	0.519345	−	0.854565i	$-0.326176\pi$
$523$	12423.3	1.03869	0.519345	+	0.854565i	$0.326176\pi$
$524$	−555.048	−0.0462736
$525$	7107.99	0.590892
$526$	−3310.08	−0.274385
$527$	−4940.18	−0.408345
$528$	−1608.92	−0.132612
$529$	−9405.13	−0.773003
$530$	−32356.0	−2.65180
$531$	2754.69	0.225129
$532$	−532.000	−0.0433555
$533$	151.922	0.0123461
$534$	−2735.92	−0.221713
$535$	1956.29	0.158090
$536$	−4657.75	−0.375344
$537$	−11153.1	−0.896262
$538$	−1473.75	−0.118100
$539$	−1642.44	−0.131252
$540$	2325.08	0.185288
$541$	11827.0	0.939893	0.469946	−	0.882695i	$-0.344273\pi$
$541$	11827.0	0.939893	0.469946	+	0.882695i	$0.344273\pi$
$542$	12365.9	0.980005
$543$	−1048.62	−0.0828744
$544$	1340.76	0.105670
$545$	31149.5	2.44825
$546$	1961.39	0.153736
$547$	14379.4	1.12399	0.561993	−	0.827142i	$-0.310035\pi$
$547$	14379.4	1.12399	0.561993	+	0.827142i	$0.310035\pi$
$548$	2666.24	0.207840
$549$	353.452	0.0274772
$550$	22690.8	1.75916
$551$	−3772.59	−0.291684
$552$	−1261.28	−0.0972532
$553$	−2100.41	−0.161517
$554$	14905.4	1.14309
$555$	15508.1	1.18610
$556$	−12962.3	−0.988712
$557$	21350.5	1.62415	0.812074	−	0.583555i	$-0.198339\pi$
$557$	21350.5	1.62415	0.812074	+	0.583555i	$0.198339\pi$
$558$	−2122.34	−0.161014
$559$	−22724.7	−1.71942
$560$	2411.19	0.181949
$561$	4213.23	0.317081
$562$	2498.21	0.187510
$563$	−4919.09	−0.368233	−0.184116	−	0.982904i	$-0.558942\pi$
$563$	−4919.09	−0.368233	−0.184116	+	0.982904i	$0.558942\pi$
$564$	−2119.94	−0.158272
$565$	16183.7	1.20505
$566$	12281.5	0.912067
$567$	567.000	0.0419961
$568$	−4688.00	−0.346310
$569$	16559.0	1.22002	0.610010	−	0.792394i	$-0.291166\pi$
$569$	16559.0	1.22002	0.610010	+	0.792394i	$0.291166\pi$
$570$	2454.25	0.180346
$571$	−21476.5	−1.57402	−0.787008	−	0.616943i	$-0.788371\pi$
$571$	−21476.5	−1.57402	−0.787008	+	0.616943i	$0.788371\pi$
$572$	6261.33	0.457691
$573$	9414.47	0.686379
$574$	45.5442	0.00331181
$575$	17788.1	1.29011
$576$	576.000	0.0416667
$577$	−14569.0	−1.05115	−0.525576	−	0.850747i	$-0.676150\pi$
$577$	−14569.0	−1.05115	−0.525576	+	0.850747i	$0.676150\pi$
$578$	6314.99	0.454444
$579$	−614.693	−0.0441205
$580$	17098.6	1.22410
$581$	−5784.70	−0.413063
$582$	3168.64	0.225678
$583$	−25188.6	−1.78937
$584$	6078.60	0.430709
$585$	−9048.36	−0.639494
$586$	−15608.2	−1.10029
$587$	24314.9	1.70968	0.854841	−	0.518890i	$-0.173655\pi$
$587$	24314.9	1.70968	0.854841	+	0.518890i	$0.173655\pi$
$588$	588.000	0.0412393
$589$	−2240.24	−0.156719
$590$	−13178.7	−0.919593
$591$	14127.5	0.983295
$592$	3841.88	0.266724
$593$	13316.1	0.922136	0.461068	−	0.887365i	$-0.347466\pi$
$593$	13316.1	0.922136	0.461068	+	0.887365i	$0.347466\pi$
$594$	1810.03	0.125028
$595$	−6314.12	−0.435048
$596$	−13348.1	−0.917385
$597$	−11984.8	−0.821614
$598$	4908.46	0.335655
$599$	21012.4	1.43329	0.716647	−	0.697436i	$-0.245676\pi$
$599$	21012.4	1.43329	0.716647	+	0.697436i	$0.245676\pi$
$600$	−8123.42	−0.552729
$601$	−3109.35	−0.211036	−0.105518	−	0.994417i	$-0.533650\pi$
$601$	−3109.35	−0.211036	−0.105518	+	0.994417i	$0.533650\pi$
$602$	−6812.60	−0.461231
$603$	5239.97	0.353877
$604$	−3747.52	−0.252458
$605$	−4466.50	−0.300147
$606$	−1785.56	−0.119692
$607$	16836.8	1.12584	0.562921	−	0.826511i	$-0.309678\pi$
$607$	16836.8	1.12584	0.562921	+	0.826511i	$0.309678\pi$
$608$	608.000	0.0405554
$609$	4169.71	0.277447
$610$	−1690.95	−0.112237
$611$	8250.03	0.546253
$612$	−1508.36	−0.0996269
$613$	−8214.63	−0.541249	−0.270625	−	0.962685i	$-0.587230\pi$
$613$	−8214.63	−0.541249	−0.270625	+	0.962685i	$0.587230\pi$
$614$	11665.1	0.766720
$615$	−210.107	−0.0137761
$616$	1877.07	0.122775
$617$	11755.9	0.767061	0.383530	−	0.923528i	$-0.374708\pi$
$617$	11755.9	0.767061	0.383530	+	0.923528i	$0.374708\pi$
$618$	5473.83	0.356294
$619$	23263.4	1.51056	0.755278	−	0.655404i	$-0.227502\pi$
$619$	23263.4	1.51056	0.755278	+	0.655404i	$0.227502\pi$
$620$	10153.5	0.657700
$621$	1418.94	0.0916912
$622$	−19910.3	−1.28349
$623$	3191.91	0.205267
$624$	−2241.58	−0.143806
$625$	56631.4	3.62441
$626$	15354.4	0.980329
$627$	1910.59	0.121693
$628$	−3404.80	−0.216348
$629$	−10060.6	−0.637749
$630$	−2712.59	−0.171543
$631$	−6706.23	−0.423091	−0.211546	−	0.977368i	$-0.567850\pi$
$631$	−6706.23	−0.423091	−0.211546	+	0.977368i	$0.567850\pi$
$632$	2400.47	0.151085
$633$	−613.869	−0.0385452
$634$	19235.5	1.20495
$635$	602.180	0.0376327
$636$	9017.62	0.562220
$637$	−2288.28	−0.142331
$638$	13310.9	0.825996
$639$	5274.00	0.326504
$640$	−2755.65	−0.170198
$641$	17304.8	1.06630	0.533151	−	0.846020i	$-0.321008\pi$
$641$	17304.8	1.06630	0.533151	+	0.846020i	$0.321008\pi$
$642$	−545.220	−0.0335173
$643$	19832.1	1.21633	0.608167	−	0.793809i	$-0.291905\pi$
$643$	19832.1	1.21633	0.608167	+	0.793809i	$0.291905\pi$
$644$	1471.50	0.0900390
$645$	31428.2	1.91858
$646$	−1592.15	−0.0969697
$647$	18518.3	1.12524	0.562620	−	0.826716i	$-0.309793\pi$
$647$	18518.3	1.12524	0.562620	+	0.826716i	$0.309793\pi$
$648$	−648.000	−0.0392837
$649$	−10259.4	−0.620519
$650$	31613.4	1.90766
$651$	2476.06	0.149070
$652$	−6569.06	−0.394577
$653$	14733.5	0.882951	0.441476	−	0.897273i	$-0.354455\pi$
$653$	14733.5	0.882951	0.441476	+	0.897273i	$0.354455\pi$
$654$	−8681.38	−0.519065
$655$	−2987.34	−0.178206
$656$	−52.0506	−0.00309792
$657$	−6838.42	−0.406077
$658$	2473.26	0.146531
$659$	−33432.6	−1.97625	−0.988126	−	0.153643i	$-0.950900\pi$
$659$	−33432.6	−1.97625	−0.988126	+	0.153643i	$0.950900\pi$
$660$	−8659.39	−0.510706
$661$	5426.93	0.319339	0.159669	−	0.987171i	$-0.448957\pi$
$661$	5426.93	0.319339	0.159669	+	0.987171i	$0.448957\pi$
$662$	2002.51	0.117568
$663$	5869.98	0.343848
$664$	6611.08	0.386385
$665$	−2863.29	−0.166968
$666$	−4322.12	−0.251470
$667$	10434.9	0.605758
$668$	4456.58	0.258129
$669$	−15489.7	−0.895169
$670$	−25068.6	−1.44550
$671$	−1316.38	−0.0757350
$672$	−672.000	−0.0385758
$673$	26516.1	1.51875	0.759376	−	0.650652i	$-0.225504\pi$
$673$	26516.1	1.51875	0.759376	+	0.650652i	$0.225504\pi$
$674$	3167.18	0.181002
$675$	9138.85	0.521118
$676$	−64.5584	−0.00367310
$677$	−6540.84	−0.371322	−0.185661	−	0.982614i	$-0.559443\pi$
$677$	−6540.84	−0.371322	−0.185661	+	0.982614i	$0.559443\pi$
$678$	−4510.40	−0.255488
$679$	−3696.75	−0.208937
$680$	7216.13	0.406950
$681$	−3638.27	−0.204727
$682$	7904.32	0.443800
$683$	−15123.7	−0.847280	−0.423640	−	0.905831i	$-0.639248\pi$
$683$	−15123.7	−0.847280	−0.423640	+	0.905831i	$0.639248\pi$
$684$	−684.000	−0.0382360
$685$	14350.0	0.800419
$686$	−686.000	−0.0381802
$687$	12311.9	0.683738
$688$	7785.83	0.431442
$689$	−35093.4	−1.94042
$690$	−6788.38	−0.374535
$691$	−28017.2	−1.54244	−0.771218	−	0.636571i	$-0.780352\pi$
$691$	−28017.2	−1.54244	−0.771218	+	0.636571i	$0.780352\pi$
$692$	2819.68	0.154896
$693$	−2111.70	−0.115753
$694$	−14557.9	−0.796269
$695$	−69764.7	−3.80766
$696$	−4765.38	−0.259528
$697$	136.303	0.00740726
$698$	−16680.9	−0.904560
$699$	−10264.7	−0.555433
$700$	9477.32	0.511727
$701$	8523.70	0.459252	0.229626	−	0.973279i	$-0.426250\pi$
$701$	8523.70	0.459252	0.229626	+	0.973279i	$0.426250\pi$
$702$	2521.78	0.135582
$703$	−4562.24	−0.244763
$704$	−2145.22	−0.114845
$705$	−11409.8	−0.609527
$706$	12290.9	0.655207
$707$	2083.15	0.110813
$708$	3672.92	0.194967
$709$	−24092.8	−1.27620	−0.638099	−	0.769954i	$-0.720279\pi$
$709$	−24092.8	−1.27620	−0.638099	+	0.769954i	$0.720279\pi$
$710$	−25231.4	−1.33369
$711$	−2700.53	−0.142444
$712$	−3647.90	−0.192009
$713$	6196.46	0.325469
$714$	1759.75	0.0922366
$715$	33699.2	1.76263
$716$	−14870.8	−0.776186
$717$	−5839.94	−0.304179
$718$	−19507.8	−1.01396
$719$	26706.2	1.38522	0.692611	−	0.721311i	$-0.256460\pi$
$719$	26706.2	1.38522	0.692611	+	0.721311i	$0.256460\pi$
$720$	3100.10	0.160464
$721$	−6386.14	−0.329864
$722$	−722.000	−0.0372161
$723$	−5725.75	−0.294527
$724$	−1398.17	−0.0717713
$725$	67206.9	3.44276
$726$	1244.82	0.0636357
$727$	−3997.69	−0.203942	−0.101971	−	0.994787i	$-0.532515\pi$
$727$	−3997.69	−0.203942	−0.101971	+	0.994787i	$0.532515\pi$
$728$	2615.18	0.133139
$729$	729.000	0.0370370
$730$	32715.8	1.65872
$731$	−20388.5	−1.03160
$732$	471.269	0.0237959
$733$	13829.0	0.696843	0.348422	−	0.937338i	$-0.386718\pi$
$733$	13829.0	0.696843	0.348422	+	0.937338i	$0.386718\pi$
$734$	17880.0	0.899134
$735$	3164.69	0.158818
$736$	−1681.71	−0.0842238
$737$	−19515.5	−0.975388
$738$	58.5569	0.00292074
$739$	−298.096	−0.0148385	−0.00741923	−	0.999972i	$-0.502362\pi$
$739$	−298.096	−0.0148385	−0.00741923	+	0.999972i	$0.502362\pi$
$740$	20677.5	1.02719
$741$	2661.88	0.131966
$742$	−10520.6	−0.520515
$743$	405.736	0.0200337	0.0100168	−	0.999950i	$-0.496811\pi$
$743$	405.736	0.0200337	0.0100168	+	0.999950i	$0.496811\pi$
$744$	−2829.78	−0.139442
$745$	−71841.4	−3.53297
$746$	−17944.4	−0.880684
$747$	−7437.47	−0.364287
$748$	5617.64	0.274600
$749$	636.090	0.0310310
$750$	−27574.9	−1.34252
$751$	−30988.8	−1.50572	−0.752862	−	0.658179i	$-0.771327\pi$
$751$	−30988.8	−1.50572	−0.752862	+	0.658179i	$0.771327\pi$
$752$	−2826.58	−0.137068
$753$	−2910.80	−0.140871
$754$	18545.2	0.895722
$755$	−20169.6	−0.972248
$756$	756.000	0.0363696
$757$	−7026.79	−0.337375	−0.168688	−	0.985670i	$-0.553953\pi$
$757$	−7026.79	−0.337375	−0.168688	+	0.985670i	$0.553953\pi$
$758$	−910.054	−0.0436077
$759$	−5284.64	−0.252727
$760$	3272.33	0.156184
$761$	28041.7	1.33576	0.667879	−	0.744270i	$-0.267202\pi$
$761$	28041.7	1.33576	0.667879	+	0.744270i	$0.267202\pi$
$762$	−167.828	−0.00797869
$763$	10128.3	0.480561
$764$	12552.6	0.594422
$765$	−8118.15	−0.383676
$766$	17032.7	0.803417
$767$	−14293.7	−0.672900
$768$	768.000	0.0360844
$769$	12854.4	0.602784	0.301392	−	0.953500i	$-0.402549\pi$
$769$	12854.4	0.602784	0.301392	+	0.953500i	$0.402549\pi$
$770$	10102.6	0.472822
$771$	3097.04	0.144666
$772$	−819.590	−0.0382095
$773$	33240.5	1.54667	0.773335	−	0.633997i	$-0.218587\pi$
$773$	33240.5	1.54667	0.773335	+	0.633997i	$0.218587\pi$
$774$	−8759.06	−0.406767
$775$	39908.9	1.84977
$776$	4224.85	0.195443
$777$	5042.47	0.232816
$778$	24406.4	1.12470
$779$	61.8100	0.00284284
$780$	−12064.5	−0.553818
$781$	−19642.2	−0.899940
$782$	4403.85	0.201383
$783$	5361.05	0.244685
$784$	784.000	0.0357143
$785$	−18325.1	−0.833184
$786$	832.572	0.0377823
$787$	−32021.7	−1.45038	−0.725190	−	0.688549i	$-0.758248\pi$
$787$	−32021.7	−1.45038	−0.725190	+	0.688549i	$0.758248\pi$
$788$	18836.6	0.851558
$789$	4965.12	0.224034
$790$	12919.6	0.581848
$791$	5262.14	0.236536
$792$	2413.38	0.108277
$793$	−1834.01	−0.0821281
$794$	−22151.9	−0.990102
$795$	48534.0	2.16518
$796$	−15979.7	−0.711539
$797$	−36571.0	−1.62536	−0.812680	−	0.582711i	$-0.801992\pi$
$797$	−36571.0	−1.62536	−0.812680	+	0.582711i	$0.801992\pi$
$798$	798.000	0.0353996
$799$	7401.89	0.327735
$800$	−10831.2	−0.478677
$801$	4103.88	0.181028
$802$	20956.5	0.922695
$803$	25468.7	1.11926
$804$	6986.63	0.306467
$805$	7919.78	0.346752
$806$	11012.5	0.481264
$807$	2210.62	0.0964283
$808$	−2380.74	−0.103656
$809$	4065.58	0.176685	0.0883424	−	0.996090i	$-0.471843\pi$
$809$	4065.58	0.176685	0.0883424	+	0.996090i	$0.471843\pi$
$810$	−3487.62	−0.151287
$811$	−40894.5	−1.77065	−0.885327	−	0.464969i	$-0.846065\pi$
$811$	−40894.5	−1.77065	−0.885327	+	0.464969i	$0.846065\pi$
$812$	5559.61	0.240276
$813$	−18548.9	−0.800171
$814$	16097.1	0.693123
$815$	−35355.5	−1.51957
$816$	−2011.14	−0.0862794
$817$	−9245.67	−0.395918
$818$	−21585.3	−0.922631
$819$	−2942.08	−0.125525
$820$	−280.142	−0.0119305
$821$	16308.9	0.693281	0.346640	−	0.937998i	$-0.387322\pi$
$821$	16308.9	0.693281	0.346640	+	0.937998i	$0.387322\pi$
$822$	−3999.36	−0.169701
$823$	23326.7	0.987992	0.493996	−	0.869464i	$-0.335536\pi$
$823$	23326.7	0.987992	0.493996	+	0.869464i	$0.335536\pi$
$824$	7298.45	0.308560
$825$	−34036.2	−1.43635
$826$	−4285.07	−0.180504
$827$	−17902.6	−0.752763	−0.376381	−	0.926465i	$-0.622832\pi$
$827$	−17902.6	−0.752763	−0.376381	+	0.926465i	$0.622832\pi$
$828$	1891.93	0.0794069
$829$	794.825	0.0332996	0.0166498	−	0.999861i	$-0.494700\pi$
$829$	794.825	0.0332996	0.0166498	+	0.999861i	$0.494700\pi$
$830$	35581.7	1.48802
$831$	−22358.2	−0.933329
$832$	−2988.78	−0.124540
$833$	−2053.04	−0.0853945
$834$	19443.5	0.807280
$835$	23985.9	0.994091
$836$	2547.45	0.105389
$837$	3183.51	0.131467
$838$	11446.7	0.471863
$839$	−2463.54	−0.101372	−0.0506859	−	0.998715i	$-0.516141\pi$
$839$	−2463.54	−0.101372	−0.0506859	+	0.998715i	$0.516141\pi$
$840$	−3616.79	−0.148561
$841$	15036.1	0.616512
$842$	−29093.8	−1.19078
$843$	−3747.32	−0.153102
$844$	−818.492	−0.0333811
$845$	−347.461	−0.0141456
$846$	3179.90	0.129229
$847$	−1452.29	−0.0589152
$848$	12023.5	0.486897
$849$	−18422.3	−0.744700
$850$	28363.4	1.14454
$851$	12619.0	0.508313
$852$	7032.00	0.282761
$853$	−19077.4	−0.765766	−0.382883	−	0.923797i	$-0.625069\pi$
$853$	−19077.4	−0.765766	−0.382883	+	0.923797i	$0.625069\pi$
$854$	−549.814	−0.0220307
$855$	−3681.37	−0.147252
$856$	−726.960	−0.0290268
$857$	−43989.5	−1.75339	−0.876694	−	0.481048i	$-0.840256\pi$
$857$	−43989.5	−1.75339	−0.876694	+	0.481048i	$0.840256\pi$
$858$	−9391.99	−0.373703
$859$	3111.47	0.123588	0.0617940	−	0.998089i	$-0.480318\pi$
$859$	3111.47	0.123588	0.0617940	+	0.998089i	$0.480318\pi$
$860$	41904.3	1.66154
$861$	−68.3164	−0.00270408
$862$	−7822.38	−0.309085
$863$	−26146.2	−1.03132	−0.515658	−	0.856794i	$-0.672453\pi$
$863$	−26146.2	−1.03132	−0.515658	+	0.856794i	$0.672453\pi$
$864$	−864.000	−0.0340207
$865$	15175.9	0.596527
$866$	4202.98	0.164923
$867$	−9472.48	−0.371052
$868$	3301.41	0.129098
$869$	10057.7	0.392617
$870$	−25647.9	−0.999476
$871$	−27189.4	−1.05773
$872$	−11575.2	−0.449524
$873$	−4752.96	−0.184265
$874$	1997.03	0.0772890
$875$	32170.7	1.24293
$876$	−9117.90	−0.351673
$877$	−15546.5	−0.598596	−0.299298	−	0.954160i	$-0.596753\pi$
$877$	−15546.5	−0.598596	−0.299298	+	0.954160i	$0.596753\pi$
$878$	1367.86	0.0525774
$879$	23412.3	0.898382
$880$	−11545.9	−0.442285
$881$	−27221.7	−1.04100	−0.520500	−	0.853862i	$-0.674255\pi$
$881$	−27221.7	−1.04100	−0.520500	+	0.853862i	$0.674255\pi$
$882$	−882.000	−0.0336718
$883$	−35711.4	−1.36102	−0.680512	−	0.732737i	$-0.738243\pi$
$883$	−35711.4	−1.36102	−0.680512	+	0.732737i	$0.738243\pi$
$884$	7826.63	0.297781
$885$	19768.1	0.750844
$886$	−9001.06	−0.341305
$887$	−40082.5	−1.51729	−0.758647	−	0.651502i	$-0.774139\pi$
$887$	−40082.5	−1.51729	−0.758647	+	0.651502i	$0.774139\pi$
$888$	−5762.83	−0.217779
$889$	195.799	0.00738683
$890$	−19633.4	−0.739454
$891$	−2715.05	−0.102085
$892$	−20653.0	−0.775239
$893$	3356.57	0.125782
$894$	20022.2	0.749042
$895$	−80036.6	−2.98919
$896$	−896.000	−0.0334077
$897$	−7362.69	−0.274061
$898$	−6120.77	−0.227453
$899$	23411.4	0.868538
$900$	12185.1	0.451301
$901$	−31485.6	−1.16419
$902$	−218.086	−0.00805041
$903$	10218.9	0.376593
$904$	−6013.87	−0.221259
$905$	−7525.10	−0.276401
$906$	5621.28	0.206131
$907$	26634.4	0.975061	0.487530	−	0.873106i	$-0.337898\pi$
$907$	26634.4	0.975061	0.487530	+	0.873106i	$0.337898\pi$
$908$	−4851.03	−0.177298
$909$	2678.34	0.0977281
$910$	14075.2	0.512736
$911$	19637.0	0.714164	0.357082	−	0.934073i	$-0.383772\pi$
$911$	19637.0	0.714164	0.357082	+	0.934073i	$0.383772\pi$
$912$	−912.000	−0.0331133
$913$	27699.7	1.00408
$914$	4629.03	0.167522
$915$	2536.43	0.0916412
$916$	16415.9	0.592135
$917$	−971.334	−0.0349796
$918$	2262.53	0.0813450
$919$	−2180.60	−0.0782713	−0.0391356	−	0.999234i	$-0.512460\pi$
$919$	−2180.60	−0.0782713	−0.0391356	+	0.999234i	$0.512460\pi$
$920$	−9051.18	−0.324357
$921$	−17497.7	−0.626024
$922$	−25712.7	−0.918440
$923$	−27366.0	−0.975908
$924$	−2815.60	−0.100245
$925$	81274.1	2.88895
$926$	−4326.71	−0.153547
$927$	−8210.75	−0.290913
$928$	−6353.84	−0.224758
$929$	−5251.19	−0.185453	−0.0927266	−	0.995692i	$-0.529558\pi$
$929$	−5251.19	−0.185453	−0.0927266	+	0.995692i	$0.529558\pi$
$930$	−15230.2	−0.537010
$931$	−931.000	−0.0327737
$932$	−13686.3	−0.481019
$933$	29865.4	1.04796
$934$	35519.8	1.24437
$935$	30234.8	1.05752
$936$	3362.38	0.117417
$937$	21707.1	0.756820	0.378410	−	0.925638i	$-0.376471\pi$
$937$	21707.1	0.756820	0.378410	+	0.925638i	$0.376471\pi$
$938$	−8151.06	−0.283733
$939$	−23031.6	−0.800435
$940$	−15213.0	−0.527866
$941$	−53415.8	−1.85049	−0.925243	−	0.379376i	$-0.876139\pi$
$941$	−53415.8	−1.85049	−0.925243	+	0.379376i	$0.876139\pi$
$942$	5107.21	0.176647
$943$	−170.965	−0.00590390
$944$	4897.22	0.168846
$945$	4068.88	0.140064
$946$	32621.8	1.12117
$947$	2490.27	0.0854517	0.0427258	−	0.999087i	$-0.486396\pi$
$947$	2490.27	0.0854517	0.0427258	+	0.999087i	$0.486396\pi$
$948$	−3600.71	−0.123360
$949$	35483.6	1.21375
$950$	12862.1	0.439264
$951$	−28853.3	−0.983839
$952$	2346.33	0.0798792
$953$	−14208.3	−0.482952	−0.241476	−	0.970407i	$-0.577631\pi$
$953$	−14208.3	−0.482952	−0.241476	+	0.970407i	$0.577631\pi$
$954$	−13526.4	−0.459051
$955$	67559.8	2.28920
$956$	−7786.59	−0.263427
$957$	−19966.4	−0.674423
$958$	30993.7	1.04526
$959$	4665.93	0.157112
$960$	4133.47	0.138966
$961$	−15888.8	−0.533342
$962$	22426.9	0.751633
$963$	817.830	0.0273668
$964$	−7634.33	−0.255068
$965$	−4411.14	−0.147150
$966$	−2207.25	−0.0735165
$967$	−10896.2	−0.362354	−0.181177	−	0.983450i	$-0.557991\pi$
$967$	−10896.2	−0.362354	−0.181177	+	0.983450i	$0.557991\pi$
$968$	1659.76	0.0551101
$969$	2388.23	0.0791754
$970$	22738.7	0.752675
$971$	−19983.7	−0.660459	−0.330230	−	0.943901i	$-0.607126\pi$
$971$	−19983.7	−0.660459	−0.330230	+	0.943901i	$0.607126\pi$
$972$	972.000	0.0320750
$973$	−22684.0	−0.747396
$974$	−17097.6	−0.562468
$975$	−47420.1	−1.55760
$976$	628.359	0.0206079
$977$	17431.4	0.570810	0.285405	−	0.958407i	$-0.407872\pi$
$977$	17431.4	0.570810	0.285405	+	0.958407i	$0.407872\pi$
$978$	9853.60	0.322171
$979$	−15284.3	−0.498966
$980$	4219.58	0.137540
$981$	13022.1	0.423815
$982$	14261.3	0.463438
$983$	−13482.9	−0.437474	−0.218737	−	0.975784i	$-0.570194\pi$
$983$	−13482.9	−0.437474	−0.218737	+	0.975784i	$0.570194\pi$
$984$	78.0758	0.00252944
$985$	101381.	3.27946
$986$	16638.6	0.537406
$987$	−3709.89	−0.119642
$988$	3549.18	0.114286
$989$	25573.3	0.822228
$990$	12989.1	0.416990
$991$	−15875.8	−0.508892	−0.254446	−	0.967087i	$-0.581893\pi$
$991$	−15875.8	−0.508892	−0.254446	+	0.967087i	$0.581893\pi$
$992$	−3773.04	−0.120760
$993$	−3003.77	−0.0959938
$994$	−8204.00	−0.261786
$995$	−86004.6	−2.74023
$996$	−9916.62	−0.315482
$997$	27056.0	0.859450	0.429725	−	0.902960i	$-0.358611\pi$
$997$	27056.0	0.859450	0.429725	+	0.902960i	$0.358611\pi$
$998$	−11161.5	−0.354019
$999$	6483.18	0.205324

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.4.a.o.1.4	✓	4	1.1	even	1	trivial
2394.4.a.u.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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +21.5285 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +21.5285 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -43.0570 q^{10} -33.5191 q^{11} +12.0000 q^{12} -46.6997 q^{13} -14.0000 q^{14} +64.5855 q^{15} +16.0000 q^{16} -41.8988 q^{17} -18.0000 q^{18} -19.0000 q^{19} +86.1140 q^{20} +21.0000 q^{21} +67.0382 q^{22} +52.5535 q^{23} -24.0000 q^{24} +338.476 q^{25} +93.3994 q^{26} +27.0000 q^{27} +28.0000 q^{28} +198.558 q^{29} -129.171 q^{30} +117.908 q^{31} -32.0000 q^{32} -100.557 q^{33} +83.7975 q^{34} +150.699 q^{35} +36.0000 q^{36} +240.118 q^{37} +38.0000 q^{38} -140.099 q^{39} -172.228 q^{40} -3.25316 q^{41} -42.0000 q^{42} +486.614 q^{43} -134.076 q^{44} +193.756 q^{45} -105.107 q^{46} -176.661 q^{47} +48.0000 q^{48} +49.0000 q^{49} -676.952 q^{50} -125.696 q^{51} -186.799 q^{52} +751.469 q^{53} -54.0000 q^{54} -721.616 q^{55} -56.0000 q^{56} -57.0000 q^{57} -397.115 q^{58} +306.076 q^{59} +258.342 q^{60} +39.2724 q^{61} -235.815 q^{62} +63.0000 q^{63} +64.0000 q^{64} -1005.37 q^{65} +201.115 q^{66} +582.219 q^{67} -167.595 q^{68} +157.660 q^{69} -301.399 q^{70} +586.000 q^{71} -72.0000 q^{72} -759.825 q^{73} -480.236 q^{74} +1015.43 q^{75} -76.0000 q^{76} -234.634 q^{77} +280.198 q^{78} -300.059 q^{79} +344.456 q^{80} +81.0000 q^{81} +6.50632 q^{82} -826.385 q^{83} +84.0000 q^{84} -902.017 q^{85} -973.229 q^{86} +595.673 q^{87} +268.153 q^{88} +455.987 q^{89} -387.513 q^{90} -326.898 q^{91} +210.214 q^{92} +353.723 q^{93} +353.323 q^{94} -409.041 q^{95} -96.0000 q^{96} -528.107 q^{97} -98.0000 q^{98} -301.672 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} + 10 q^{5} - 24 q^{6} + 28 q^{7} - 32 q^{8} + 36 q^{9}+O(q^{10}) \) 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	\( 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} + 10 q^{5} - 24 q^{6} + 28 q^{7} - 32 q^{8} + 36 q^{9} - 20 q^{10} + 48 q^{11} + 48 q^{12} - 30 q^{13} - 56 q^{14} + 30 q^{15} + 64 q^{16} + 128 q^{17} - 72 q^{18} - 76 q^{19} + 40 q^{20} + 84 q^{21} - 96 q^{22} + 98 q^{23} - 96 q^{24} + 312 q^{25} + 60 q^{26} + 108 q^{27} + 112 q^{28} + 144 q^{29} - 60 q^{30} + 10 q^{31} - 128 q^{32} + 144 q^{33} - 256 q^{34} + 70 q^{35} + 144 q^{36} + 222 q^{37} + 152 q^{38} - 90 q^{39} - 80 q^{40} + 256 q^{41} - 168 q^{42} + 188 q^{43} + 192 q^{44} + 90 q^{45} - 196 q^{46} + 522 q^{47} + 192 q^{48} + 196 q^{49} - 624 q^{50} + 384 q^{51} - 120 q^{52} + 1088 q^{53} - 216 q^{54} - 1092 q^{55} - 224 q^{56} - 228 q^{57} - 288 q^{58} + 1456 q^{59} + 120 q^{60} - 108 q^{61} - 20 q^{62} + 252 q^{63} + 256 q^{64} + 836 q^{65} - 288 q^{66} + 296 q^{67} + 512 q^{68} + 294 q^{69} - 140 q^{70} + 808 q^{71} - 288 q^{72} - 1384 q^{73} - 444 q^{74} + 936 q^{75} - 304 q^{76} + 336 q^{77} + 180 q^{78} + 582 q^{79} + 160 q^{80} + 324 q^{81} - 512 q^{82} - 1236 q^{83} + 336 q^{84} - 2216 q^{85} - 376 q^{86} + 432 q^{87} - 384 q^{88} + 2528 q^{89} - 180 q^{90} - 210 q^{91} + 392 q^{92} + 30 q^{93} - 1044 q^{94} - 190 q^{95} - 384 q^{96} - 1028 q^{97} - 392 q^{98} + 432 q^{99}+O(q^{100}) \) 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 - 30 * q^13 - 56 * q^14 + 30 * q^15 + 64 * q^16 + 128 * q^17 - 72 * q^18 - 76 * q^19 + 40 * q^20 + 84 * q^21 - 96 * q^22 + 98 * q^23 - 96 * q^24 + 312 * q^25 + 60 * q^26 + 108 * q^27 + 112 * q^28 + 144 * q^29 - 60 * q^30 + 10 * q^31 - 128 * q^32 + 144 * q^33 - 256 * q^34 + 70 * q^35 + 144 * q^36 + 222 * q^37 + 152 * q^38 - 90 * q^39 - 80 * q^40 + 256 * q^41 - 168 * q^42 + 188 * q^43 + 192 * q^44 + 90 * q^45 - 196 * q^46 + 522 * q^47 + 192 * q^48 + 196 * q^49 - 624 * q^50 + 384 * q^51 - 120 * q^52 + 1088 * q^53 - 216 * q^54 - 1092 * q^55 - 224 * q^56 - 228 * q^57 - 288 * q^58 + 1456 * q^59 + 120 * q^60 - 108 * q^61 - 20 * q^62 + 252 * q^63 + 256 * q^64 + 836 * q^65 - 288 * q^66 + 296 * q^67 + 512 * q^68 + 294 * q^69 - 140 * q^70 + 808 * q^71 - 288 * q^72 - 1384 * q^73 - 444 * q^74 + 936 * q^75 - 304 * q^76 + 336 * q^77 + 180 * q^78 + 582 * q^79 + 160 * q^80 + 324 * q^81 - 512 * q^82 - 1236 * q^83 + 336 * q^84 - 2216 * q^85 - 376 * q^86 + 432 * q^87 - 384 * q^88 + 2528 * q^89 - 180 * q^90 - 210 * q^91 + 392 * q^92 + 30 * q^93 - 1044 * q^94 - 190 * q^95 - 384 * q^96 - 1028 * q^97 - 392 * q^98 + 432 * q^99

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