LMFDB - Embedded newform 798.4.a.n.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} - 149x^{2} - 30x + 190 $ x^4 - 149x^2 - 30x + 190
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.03645$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +22.1981 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +22.1981 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -44.3962 q^{10} +61.0073 q^{11} +12.0000 q^{12} +46.9344 q^{13} +14.0000 q^{14} +66.5944 q^{15} +16.0000 q^{16} -82.7402 q^{17} -18.0000 q^{18} +19.0000 q^{19} +88.7925 q^{20} -21.0000 q^{21} -122.015 q^{22} -20.7157 q^{23} -24.0000 q^{24} +367.756 q^{25} -93.8687 q^{26} +27.0000 q^{27} -28.0000 q^{28} -145.512 q^{29} -133.189 q^{30} +86.6717 q^{31} -32.0000 q^{32} +183.022 q^{33} +165.480 q^{34} -155.387 q^{35} +36.0000 q^{36} +159.190 q^{37} -38.0000 q^{38} +140.803 q^{39} -177.585 q^{40} +181.027 q^{41} +42.0000 q^{42} -61.8047 q^{43} +244.029 q^{44} +199.783 q^{45} +41.4313 q^{46} +446.590 q^{47} +48.0000 q^{48} +49.0000 q^{49} -735.513 q^{50} -248.220 q^{51} +187.737 q^{52} -314.611 q^{53} -54.0000 q^{54} +1354.25 q^{55} +56.0000 q^{56} +57.0000 q^{57} +291.023 q^{58} -597.722 q^{59} +266.377 q^{60} -759.492 q^{61} -173.343 q^{62} -63.0000 q^{63} +64.0000 q^{64} +1041.85 q^{65} -366.044 q^{66} -665.153 q^{67} -330.961 q^{68} -62.1470 q^{69} +310.774 q^{70} +77.0628 q^{71} -72.0000 q^{72} +81.4826 q^{73} -318.379 q^{74} +1103.27 q^{75} +76.0000 q^{76} -427.051 q^{77} -281.606 q^{78} -1207.27 q^{79} +355.170 q^{80} +81.0000 q^{81} -362.055 q^{82} -226.474 q^{83} -84.0000 q^{84} -1836.68 q^{85} +123.609 q^{86} -436.535 q^{87} -488.058 q^{88} +1112.49 q^{89} -399.566 q^{90} -328.541 q^{91} -82.8626 q^{92} +260.015 q^{93} -893.180 q^{94} +421.764 q^{95} -96.0000 q^{96} -1117.95 q^{97} -98.0000 q^{98} +549.065 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} + 10 q^{5} - 24 q^{6} - 28 q^{7} - 32 q^{8} + 36 q^{9} - 20 q^{10} + 64 q^{11} + 48 q^{12} + 16 q^{13} + 56 q^{14} + 30 q^{15} + 64 q^{16} - 78 q^{17} - 72 q^{18} + 76 q^{19} + 40 q^{20} - 84 q^{21} - 128 q^{22} + 64 q^{23} - 96 q^{24} + 124 q^{25} - 32 q^{26} + 108 q^{27} - 112 q^{28} + 70 q^{29} - 60 q^{30} - 28 q^{31} - 128 q^{32} + 192 q^{33} + 156 q^{34} - 70 q^{35} + 144 q^{36} + 224 q^{37} - 152 q^{38} + 48 q^{39} - 80 q^{40} + 568 q^{41} + 168 q^{42} + 348 q^{43} + 256 q^{44} + 90 q^{45} - 128 q^{46} + 886 q^{47} + 192 q^{48} + 196 q^{49} - 248 q^{50} - 234 q^{51} + 64 q^{52} + 382 q^{53} - 216 q^{54} + 1232 q^{55} + 224 q^{56} + 228 q^{57} - 140 q^{58} + 552 q^{59} + 120 q^{60} - 744 q^{61} + 56 q^{62} - 252 q^{63} + 256 q^{64} + 1288 q^{65} - 384 q^{66} + 92 q^{67} - 312 q^{68} + 192 q^{69} + 140 q^{70} + 1154 q^{71} - 288 q^{72} + 508 q^{73} - 448 q^{74} + 372 q^{75} + 304 q^{76} - 448 q^{77} - 96 q^{78} - 2320 q^{79} + 160 q^{80} + 324 q^{81} - 1136 q^{82} + 1318 q^{83} - 336 q^{84} - 1640 q^{85} - 696 q^{86} + 210 q^{87} - 512 q^{88} - 56 q^{89} - 180 q^{90} - 112 q^{91} + 256 q^{92} - 84 q^{93} - 1772 q^{94} + 190 q^{95} - 384 q^{96} - 504 q^{97} - 392 q^{98} + 576 q^{99}+O(q^{100}) \) 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 + 64 * q^11 + 48 * q^12 + 16 * q^13 + 56 * q^14 + 30 * q^15 + 64 * q^16 - 78 * q^17 - 72 * q^18 + 76 * q^19 + 40 * q^20 - 84 * q^21 - 128 * q^22 + 64 * q^23 - 96 * q^24 + 124 * q^25 - 32 * q^26 + 108 * q^27 - 112 * q^28 + 70 * q^29 - 60 * q^30 - 28 * q^31 - 128 * q^32 + 192 * q^33 + 156 * q^34 - 70 * q^35 + 144 * q^36 + 224 * q^37 - 152 * q^38 + 48 * q^39 - 80 * q^40 + 568 * q^41 + 168 * q^42 + 348 * q^43 + 256 * q^44 + 90 * q^45 - 128 * q^46 + 886 * q^47 + 192 * q^48 + 196 * q^49 - 248 * q^50 - 234 * q^51 + 64 * q^52 + 382 * q^53 - 216 * q^54 + 1232 * q^55 + 224 * q^56 + 228 * q^57 - 140 * q^58 + 552 * q^59 + 120 * q^60 - 744 * q^61 + 56 * q^62 - 252 * q^63 + 256 * q^64 + 1288 * q^65 - 384 * q^66 + 92 * q^67 - 312 * q^68 + 192 * q^69 + 140 * q^70 + 1154 * q^71 - 288 * q^72 + 508 * q^73 - 448 * q^74 + 372 * q^75 + 304 * q^76 - 448 * q^77 - 96 * q^78 - 2320 * q^79 + 160 * q^80 + 324 * q^81 - 1136 * q^82 + 1318 * q^83 - 336 * q^84 - 1640 * q^85 - 696 * q^86 + 210 * q^87 - 512 * q^88 - 56 * q^89 - 180 * q^90 - 112 * q^91 + 256 * q^92 - 84 * q^93 - 1772 * q^94 + 190 * q^95 - 384 * q^96 - 504 * q^97 - 392 * q^98 + 576 * 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
$5$	22.1981	1.98546	0.992730	−	0.120362i	$-0.0384056\pi$
$5$	22.1981	1.98546	0.992730	+	0.120362i	$0.0384056\pi$
$6$	−6.00000	−0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−44.3962	−1.40393
$11$	61.0073	1.67222	0.836108	−	0.548564i	$-0.184825\pi$
$11$	61.0073	1.67222	0.836108	+	0.548564i	$0.184825\pi$
$12$	12.0000	0.288675
$13$	46.9344	1.00133	0.500663	−	0.865642i	$-0.333089\pi$
$13$	46.9344	1.00133	0.500663	+	0.865642i	$0.333089\pi$
$14$	14.0000	0.267261
$15$	66.5944	1.14631
$16$	16.0000	0.250000
$17$	−82.7402	−1.18044	−0.590219	−	0.807243i	$-0.700959\pi$
$17$	−82.7402	−1.18044	−0.590219	+	0.807243i	$0.700959\pi$
$18$	−18.0000	−0.235702
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	88.7925	0.992730
$21$	−21.0000	−0.218218
$22$	−122.015	−1.18244
$23$	−20.7157	−0.187805	−0.0939025	−	0.995581i	$-0.529934\pi$
$23$	−20.7157	−0.187805	−0.0939025	+	0.995581i	$0.529934\pi$
$24$	−24.0000	−0.204124
$25$	367.756	2.94205
$26$	−93.8687	−0.708045
$27$	27.0000	0.192450
$28$	−28.0000	−0.188982
$29$	−145.512	−0.931752	−0.465876	−	0.884850i	$-0.654261\pi$
$29$	−145.512	−0.931752	−0.465876	+	0.884850i	$0.654261\pi$
$30$	−133.189	−0.810561
$31$	86.6717	0.502151	0.251076	−	0.967967i	$-0.419216\pi$
$31$	86.6717	0.502151	0.251076	+	0.967967i	$0.419216\pi$
$32$	−32.0000	−0.176777
$33$	183.022	0.965455
$34$	165.480	0.834695
$35$	−155.387	−0.750433
$36$	36.0000	0.166667
$37$	159.190	0.707314	0.353657	−	0.935375i	$-0.384938\pi$
$37$	159.190	0.707314	0.353657	+	0.935375i	$0.384938\pi$
$38$	−38.0000	−0.162221
$39$	140.803	0.578116
$40$	−177.585	−0.701966
$41$	181.027	0.689554	0.344777	−	0.938685i	$-0.387955\pi$
$41$	181.027	0.689554	0.344777	+	0.938685i	$0.387955\pi$
$42$	42.0000	0.154303
$43$	−61.8047	−0.219189	−0.109594	−	0.993976i	$-0.534955\pi$
$43$	−61.8047	−0.219189	−0.109594	+	0.993976i	$0.534955\pi$
$44$	244.029	0.836108
$45$	199.783	0.661820
$46$	41.4313	0.132798
$47$	446.590	1.38600	0.692998	−	0.720939i	$-0.256289\pi$
$47$	446.590	1.38600	0.692998	+	0.720939i	$0.256289\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	−735.513	−2.08034
$51$	−248.220	−0.681526
$52$	187.737	0.500663
$53$	−314.611	−0.815381	−0.407690	−	0.913120i	$-0.633666\pi$
$53$	−314.611	−0.815381	−0.407690	+	0.913120i	$0.633666\pi$
$54$	−54.0000	−0.136083
$55$	1354.25	3.32012
$56$	56.0000	0.133631
$57$	57.0000	0.132453
$58$	291.023	0.658848
$59$	−597.722	−1.31893	−0.659464	−	0.751736i	$-0.729217\pi$
$59$	−597.722	−1.31893	−0.659464	+	0.751736i	$0.729217\pi$
$60$	266.377	0.573153
$61$	−759.492	−1.59415	−0.797073	−	0.603883i	$-0.793620\pi$
$61$	−759.492	−1.59415	−0.797073	+	0.603883i	$0.793620\pi$
$62$	−173.343	−0.355075
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	1041.85	1.98809
$66$	−366.044	−0.682680
$67$	−665.153	−1.21286	−0.606428	−	0.795138i	$-0.707398\pi$
$67$	−665.153	−1.21286	−0.606428	+	0.795138i	$0.707398\pi$
$68$	−330.961	−0.590219
$69$	−62.1470	−0.108429
$70$	310.774	0.530637
$71$	77.0628	0.128812	0.0644062	−	0.997924i	$-0.479485\pi$
$71$	77.0628	0.128812	0.0644062	+	0.997924i	$0.479485\pi$
$72$	−72.0000	−0.117851
$73$	81.4826	0.130641	0.0653207	−	0.997864i	$-0.479193\pi$
$73$	81.4826	0.130641	0.0653207	+	0.997864i	$0.479193\pi$
$74$	−318.379	−0.500147
$75$	1103.27	1.69859
$76$	76.0000	0.114708
$77$	−427.051	−0.632038
$78$	−281.606	−0.408790
$79$	−1207.27	−1.71935	−0.859673	−	0.510845i	$-0.829332\pi$
$79$	−1207.27	−1.71935	−0.859673	+	0.510845i	$0.829332\pi$
$80$	355.170	0.496365
$81$	81.0000	0.111111
$82$	−362.055	−0.487588
$83$	−226.474	−0.299504	−0.149752	−	0.988724i	$-0.547847\pi$
$83$	−226.474	−0.299504	−0.149752	+	0.988724i	$0.547847\pi$
$84$	−84.0000	−0.109109
$85$	−1836.68	−2.34371
$86$	123.609	0.154990
$87$	−436.535	−0.537947
$88$	−488.058	−0.591218
$89$	1112.49	1.32499	0.662495	−	0.749066i	$-0.269498\pi$
$89$	1112.49	1.32499	0.662495	+	0.749066i	$0.269498\pi$
$90$	−399.566	−0.467977
$91$	−328.541	−0.378466
$92$	−82.8626	−0.0939025
$93$	260.015	0.289917
$94$	−893.180	−0.980048
$95$	421.764	0.455496
$96$	−96.0000	−0.102062
$97$	−1117.95	−1.17021	−0.585106	−	0.810957i	$-0.698947\pi$
$97$	−1117.95	−1.17021	−0.585106	+	0.810957i	$0.698947\pi$
$98$	−98.0000	−0.101015
$99$	549.065	0.557406
$100$	1471.03	1.47103
$101$	−477.193	−0.470123	−0.235062	−	0.971980i	$-0.575529\pi$
$101$	−477.193	−0.470123	−0.235062	+	0.971980i	$0.575529\pi$
$102$	496.441	0.481912
$103$	1023.86	0.979457	0.489728	−	0.871875i	$-0.337096\pi$
$103$	1023.86	0.979457	0.489728	+	0.871875i	$0.337096\pi$
$104$	−375.475	−0.354023
$105$	−466.160	−0.433263
$106$	629.223	0.576561
$107$	231.548	0.209202	0.104601	−	0.994514i	$-0.466643\pi$
$107$	231.548	0.209202	0.104601	+	0.994514i	$0.466643\pi$
$108$	108.000	0.0962250
$109$	−821.904	−0.722239	−0.361120	−	0.932519i	$-0.617605\pi$
$109$	−821.904	−0.722239	−0.361120	+	0.932519i	$0.617605\pi$
$110$	−2708.49	−2.34768
$111$	477.569	0.408368
$112$	−112.000	−0.0944911
$113$	1296.77	1.07956	0.539780	−	0.841806i	$-0.318507\pi$
$113$	1296.77	1.07956	0.539780	+	0.841806i	$0.318507\pi$
$114$	−114.000	−0.0936586
$115$	−459.849	−0.372879
$116$	−582.046	−0.465876
$117$	422.409	0.333776
$118$	1195.44	0.932624
$119$	579.181	0.446163
$120$	−532.755	−0.405280
$121$	2390.89	1.79631
$122$	1518.98	1.12723
$123$	543.082	0.398114
$124$	346.687	0.251076
$125$	5388.74	3.85587
$126$	126.000	0.0890871
$127$	2017.14	1.40939	0.704695	−	0.709510i	$-0.251084\pi$
$127$	2017.14	1.40939	0.704695	+	0.709510i	$0.251084\pi$
$128$	−128.000	−0.0883883
$129$	−185.414	−0.126549
$130$	−2083.71	−1.40580
$131$	−2417.35	−1.61225	−0.806127	−	0.591743i	$-0.798440\pi$
$131$	−2417.35	−1.61225	−0.806127	+	0.591743i	$0.798440\pi$
$132$	732.087	0.482727
$133$	−133.000	−0.0867110
$134$	1330.31	0.857619
$135$	599.349	0.382102
$136$	661.921	0.417348
$137$	1884.92	1.17547	0.587737	−	0.809052i	$-0.300019\pi$
$137$	1884.92	1.17547	0.587737	+	0.809052i	$0.300019\pi$
$138$	124.294	0.0766710
$139$	2056.80	1.25508	0.627539	−	0.778585i	$-0.284062\pi$
$139$	2056.80	1.25508	0.627539	+	0.778585i	$0.284062\pi$
$140$	−621.547	−0.375217
$141$	1339.77	0.800205
$142$	−154.126	−0.0910841
$143$	2863.34	1.67444
$144$	144.000	0.0833333
$145$	−3230.08	−1.84996
$146$	−162.965	−0.0923774
$147$	147.000	0.0824786
$148$	636.759	0.353657
$149$	1623.43	0.892596	0.446298	−	0.894884i	$-0.352742\pi$
$149$	1623.43	0.892596	0.446298	+	0.894884i	$0.352742\pi$
$150$	−2206.54	−1.20109
$151$	−2613.68	−1.40860	−0.704299	−	0.709904i	$-0.748738\pi$
$151$	−2613.68	−1.40860	−0.704299	+	0.709904i	$0.748738\pi$
$152$	−152.000	−0.0811107
$153$	−744.661	−0.393479
$154$	854.102	0.446919
$155$	1923.95	0.997002
$156$	563.212	0.289058
$157$	1653.75	0.840660	0.420330	−	0.907371i	$-0.361914\pi$
$157$	1653.75	0.840660	0.420330	+	0.907371i	$0.361914\pi$
$158$	2414.54	1.21576
$159$	−943.834	−0.470760
$160$	−710.340	−0.350983
$161$	145.010	0.0709836
$162$	−162.000	−0.0785674
$163$	101.488	0.0487680	0.0243840	−	0.999703i	$-0.492238\pi$
$163$	101.488	0.0487680	0.0243840	+	0.999703i	$0.492238\pi$
$164$	724.109	0.344777
$165$	4062.74	1.91687
$166$	452.949	0.211781
$167$	−2358.13	−1.09268	−0.546339	−	0.837564i	$-0.683979\pi$
$167$	−2358.13	−1.09268	−0.546339	+	0.837564i	$0.683979\pi$
$168$	168.000	0.0771517
$169$	5.83457	0.00265570
$170$	3673.35	1.65725
$171$	171.000	0.0764719
$172$	−247.219	−0.109594
$173$	1386.27	0.609226	0.304613	−	0.952476i	$-0.401473\pi$
$173$	1386.27	0.609226	0.304613	+	0.952476i	$0.401473\pi$
$174$	873.069	0.380386
$175$	−2574.30	−1.11199
$176$	976.116	0.418054
$177$	−1793.17	−0.761484
$178$	−2224.99	−0.936909
$179$	−1063.77	−0.444191	−0.222096	−	0.975025i	$-0.571290\pi$
$179$	−1063.77	−0.444191	−0.222096	+	0.975025i	$0.571290\pi$
$180$	799.132	0.330910
$181$	−1146.20	−0.470699	−0.235349	−	0.971911i	$-0.575623\pi$
$181$	−1146.20	−0.470699	−0.235349	+	0.971911i	$0.575623\pi$
$182$	657.081	0.267616
$183$	−2278.48	−0.920381
$184$	165.725	0.0663991
$185$	3533.71	1.40434
$186$	−520.030	−0.205002
$187$	−5047.75	−1.97395
$188$	1786.36	0.692998
$189$	−189.000	−0.0727393
$190$	−843.529	−0.322084
$191$	−3991.63	−1.51217	−0.756085	−	0.654474i	$-0.772890\pi$
$191$	−3991.63	−1.51217	−0.756085	+	0.654474i	$0.772890\pi$
$192$	192.000	0.0721688
$193$	3867.38	1.44238	0.721192	−	0.692735i	$-0.243594\pi$
$193$	3867.38	1.44238	0.721192	+	0.692735i	$0.243594\pi$
$194$	2235.90	0.827465
$195$	3125.56	1.14783
$196$	196.000	0.0714286
$197$	4286.17	1.55014	0.775068	−	0.631878i	$-0.217716\pi$
$197$	4286.17	1.55014	0.775068	+	0.631878i	$0.217716\pi$
$198$	−1098.13	−0.394145
$199$	73.4349	0.0261591	0.0130796	−	0.999914i	$-0.495837\pi$
$199$	73.4349	0.0261591	0.0130796	+	0.999914i	$0.495837\pi$
$200$	−2942.05	−1.04017
$201$	−1995.46	−0.700243
$202$	954.385	0.332427
$203$	1018.58	0.352169
$204$	−992.882	−0.340763
$205$	4018.47	1.36908
$206$	−2047.72	−0.692581
$207$	−186.441	−0.0626016
$208$	750.950	0.250332
$209$	1159.14	0.383633
$210$	932.321	0.306363
$211$	−1379.42	−0.450063	−0.225032	−	0.974351i	$-0.572249\pi$
$211$	−1379.42	−0.450063	−0.225032	+	0.974351i	$0.572249\pi$
$212$	−1258.45	−0.407690
$213$	231.188	0.0743698
$214$	−463.097	−0.147928
$215$	−1371.95	−0.435191
$216$	−216.000	−0.0680414
$217$	−606.702	−0.189795
$218$	1643.81	0.510700
$219$	244.448	0.0754258
$220$	5416.99	1.66006
$221$	−3883.36	−1.18200
$222$	−955.138	−0.288760
$223$	292.523	0.0878422	0.0439211	−	0.999035i	$-0.486015\pi$
$223$	292.523	0.0878422	0.0439211	+	0.999035i	$0.486015\pi$
$224$	224.000	0.0668153
$225$	3309.81	0.980684
$226$	−2593.55	−0.763364
$227$	−4612.34	−1.34860	−0.674298	−	0.738459i	$-0.735554\pi$
$227$	−4612.34	−1.34860	−0.674298	+	0.738459i	$0.735554\pi$
$228$	228.000	0.0662266
$229$	−2249.71	−0.649193	−0.324597	−	0.945853i	$-0.605229\pi$
$229$	−2249.71	−0.649193	−0.324597	+	0.945853i	$0.605229\pi$
$230$	919.697	0.263665
$231$	−1281.15	−0.364908
$232$	1164.09	0.329424
$233$	6364.02	1.78936	0.894679	−	0.446709i	$-0.147404\pi$
$233$	6364.02	1.78936	0.894679	+	0.446709i	$0.147404\pi$
$234$	−844.819	−0.236015
$235$	9913.46	2.75184
$236$	−2390.89	−0.659464
$237$	−3621.80	−0.992664
$238$	−1158.36	−0.315485
$239$	−2442.91	−0.661166	−0.330583	−	0.943777i	$-0.607245\pi$
$239$	−2442.91	−0.661166	−0.330583	+	0.943777i	$0.607245\pi$
$240$	1065.51	0.286576
$241$	−2061.01	−0.550877	−0.275439	−	0.961319i	$-0.588823\pi$
$241$	−2061.01	−0.550877	−0.275439	+	0.961319i	$0.588823\pi$
$242$	−4781.77	−1.27018
$243$	243.000	0.0641500
$244$	−3037.97	−0.797073
$245$	1087.71	0.283637
$246$	−1086.16	−0.281509
$247$	891.753	0.229720
$248$	−693.374	−0.177537
$249$	−679.423	−0.172918
$250$	−10777.5	−2.72651
$251$	−373.282	−0.0938700	−0.0469350	−	0.998898i	$-0.514945\pi$
$251$	−373.282	−0.0938700	−0.0469350	+	0.998898i	$0.514945\pi$
$252$	−252.000	−0.0629941
$253$	−1263.81	−0.314051
$254$	−4034.29	−0.996590
$255$	−5510.03	−1.35314
$256$	256.000	0.0625000
$257$	532.978	0.129363	0.0646814	−	0.997906i	$-0.479397\pi$
$257$	532.978	0.129363	0.0646814	+	0.997906i	$0.479397\pi$
$258$	370.828	0.0894835
$259$	−1114.33	−0.267340
$260$	4167.42	0.994047
$261$	−1309.60	−0.310584
$262$	4834.71	1.14004
$263$	3974.19	0.931784	0.465892	−	0.884842i	$-0.345734\pi$
$263$	3974.19	0.931784	0.465892	+	0.884842i	$0.345734\pi$
$264$	−1464.17	−0.341340
$265$	−6983.78	−1.61891
$266$	266.000	0.0613139
$267$	3337.48	0.764983
$268$	−2660.61	−0.606428
$269$	3959.13	0.897369	0.448685	−	0.893690i	$-0.351893\pi$
$269$	3959.13	0.897369	0.448685	+	0.893690i	$0.351893\pi$
$270$	−1198.70	−0.270187
$271$	2268.96	0.508595	0.254298	−	0.967126i	$-0.418156\pi$
$271$	2268.96	0.508595	0.254298	+	0.967126i	$0.418156\pi$
$272$	−1323.84	−0.295109
$273$	−985.622	−0.218507
$274$	−3769.85	−0.831185
$275$	22435.8	4.91975
$276$	−248.588	−0.0542146
$277$	4164.51	0.903326	0.451663	−	0.892189i	$-0.350831\pi$
$277$	4164.51	0.903326	0.451663	+	0.892189i	$0.350831\pi$
$278$	−4113.61	−0.887474
$279$	780.045	0.167384
$280$	1243.09	0.265318
$281$	7286.46	1.54688	0.773441	−	0.633868i	$-0.218534\pi$
$281$	7286.46	1.54688	0.773441	+	0.633868i	$0.218534\pi$
$282$	−2679.54	−0.565831
$283$	−5855.00	−1.22984	−0.614918	−	0.788591i	$-0.710811\pi$
$283$	−5855.00	−1.22984	−0.614918	+	0.788591i	$0.710811\pi$
$284$	308.251	0.0644062
$285$	1265.29	0.262981
$286$	−5726.67	−1.18400
$287$	−1267.19	−0.260627
$288$	−288.000	−0.0589256
$289$	1932.93	0.393433
$290$	6460.16	1.30812
$291$	−3353.85	−0.675622
$292$	325.930	0.0653207
$293$	−5513.84	−1.09939	−0.549697	−	0.835364i	$-0.685257\pi$
$293$	−5513.84	−1.09939	−0.549697	+	0.835364i	$0.685257\pi$
$294$	−294.000	−0.0583212
$295$	−13268.3	−2.61868
$296$	−1273.52	−0.250073
$297$	1647.20	0.321818
$298$	−3246.87	−0.631161
$299$	−972.276	−0.188054
$300$	4413.08	0.849297
$301$	432.633	0.0828457
$302$	5227.36	0.996029
$303$	−1431.58	−0.271426
$304$	304.000	0.0573539
$305$	−16859.3	−3.16511
$306$	1489.32	0.278232
$307$	−3021.71	−0.561753	−0.280877	−	0.959744i	$-0.590625\pi$
$307$	−3021.71	−0.561753	−0.280877	+	0.959744i	$0.590625\pi$
$308$	−1708.20	−0.316019
$309$	3071.58	0.565490
$310$	−3847.90	−0.704987
$311$	1384.20	0.252381	0.126191	−	0.992006i	$-0.459725\pi$
$311$	1384.20	0.252381	0.126191	+	0.992006i	$0.459725\pi$
$312$	−1126.42	−0.204395
$313$	6066.44	1.09551	0.547756	−	0.836638i	$-0.315482\pi$
$313$	6066.44	1.09551	0.547756	+	0.836638i	$0.315482\pi$
$314$	−3307.50	−0.594436
$315$	−1398.48	−0.250144
$316$	−4829.07	−0.859673
$317$	−6016.56	−1.06601	−0.533003	−	0.846114i	$-0.678936\pi$
$317$	−6016.56	−1.06601	−0.533003	+	0.846114i	$0.678936\pi$
$318$	1887.67	0.332878
$319$	−8877.26	−1.55809
$320$	1420.68	0.248183
$321$	694.645	0.120783
$322$	−290.019	−0.0501930
$323$	−1572.06	−0.270811
$324$	324.000	0.0555556
$325$	17260.4	2.94596
$326$	−202.977	−0.0344842
$327$	−2465.71	−0.416985
$328$	−1448.22	−0.243794
$329$	−3126.13	−0.523857
$330$	−8125.48	−1.35543
$331$	6889.76	1.14410	0.572048	−	0.820220i	$-0.306149\pi$
$331$	6889.76	1.14410	0.572048	+	0.820220i	$0.306149\pi$
$332$	−905.898	−0.149752
$333$	1432.71	0.235771
$334$	4716.25	0.772640
$335$	−14765.2	−2.40808
$336$	−336.000	−0.0545545
$337$	−12193.5	−1.97098	−0.985492	−	0.169723i	$-0.945713\pi$
$337$	−12193.5	−1.97098	−0.985492	+	0.169723i	$0.945713\pi$
$338$	−11.6691	−0.00187786
$339$	3890.32	0.623284
$340$	−7346.70	−1.17186
$341$	5287.60	0.839706
$342$	−342.000	−0.0540738
$343$	−343.000	−0.0539949
$344$	494.438	0.0774950
$345$	−1379.55	−0.215282
$346$	−2772.54	−0.430788
$347$	7147.32	1.10573	0.552865	−	0.833271i	$-0.313534\pi$
$347$	7147.32	1.10573	0.552865	+	0.833271i	$0.313534\pi$
$348$	−1746.14	−0.268974
$349$	−2246.77	−0.344604	−0.172302	−	0.985044i	$-0.555121\pi$
$349$	−2246.77	−0.344604	−0.172302	+	0.985044i	$0.555121\pi$
$350$	5148.59	0.786296
$351$	1267.23	0.192705
$352$	−1952.23	−0.295609
$353$	736.382	0.111030	0.0555151	−	0.998458i	$-0.482320\pi$
$353$	736.382	0.111030	0.0555151	+	0.998458i	$0.482320\pi$
$354$	3586.33	0.538450
$355$	1710.65	0.255752
$356$	4449.98	0.662495
$357$	1737.54	0.257593
$358$	2127.55	0.314091
$359$	7799.59	1.14665	0.573324	−	0.819329i	$-0.305654\pi$
$359$	7799.59	1.14665	0.573324	+	0.819329i	$0.305654\pi$
$360$	−1598.26	−0.233989
$361$	361.000	0.0526316
$362$	2292.40	0.332834
$363$	7172.66	1.03710
$364$	−1314.16	−0.189233
$365$	1808.76	0.259383
$366$	4556.95	0.650808
$367$	6218.32	0.884451	0.442226	−	0.896904i	$-0.354189\pi$
$367$	6218.32	0.884451	0.442226	+	0.896904i	$0.354189\pi$
$368$	−331.451	−0.0469512
$369$	1629.25	0.229851
$370$	−7067.43	−0.993022
$371$	2202.28	0.308185
$372$	1040.06	0.144959
$373$	−4430.62	−0.615037	−0.307519	−	0.951542i	$-0.599499\pi$
$373$	−4430.62	−0.615037	−0.307519	+	0.951542i	$0.599499\pi$
$374$	10095.5	1.39579
$375$	16166.2	2.22619
$376$	−3572.72	−0.490024
$377$	−6829.49	−0.932989
$378$	378.000	0.0514344
$379$	−14675.3	−1.98898	−0.994488	−	0.104854i	$-0.966562\pi$
$379$	−14675.3	−1.98898	−0.994488	+	0.104854i	$0.966562\pi$
$380$	1687.06	0.227748
$381$	6051.43	0.813712
$382$	7983.27	1.06927
$383$	4442.34	0.592670	0.296335	−	0.955084i	$-0.404235\pi$
$383$	4442.34	0.592670	0.296335	+	0.955084i	$0.404235\pi$
$384$	−384.000	−0.0510310
$385$	−9479.73	−1.25489
$386$	−7734.76	−1.01992
$387$	−556.242	−0.0730630
$388$	−4471.80	−0.585106
$389$	−1408.74	−0.183614	−0.0918071	−	0.995777i	$-0.529264\pi$
$389$	−1408.74	−0.183614	−0.0918071	+	0.995777i	$0.529264\pi$
$390$	−6251.13	−0.811636
$391$	1714.02	0.221692
$392$	−392.000	−0.0505076
$393$	−7252.06	−0.930835
$394$	−8572.33	−1.09611
$395$	−26799.1	−3.41369
$396$	2196.26	0.278703
$397$	−11789.6	−1.49044	−0.745218	−	0.666821i	$-0.767654\pi$
$397$	−11789.6	−1.49044	−0.745218	+	0.666821i	$0.767654\pi$
$398$	−146.870	−0.0184973
$399$	−399.000	−0.0500626
$400$	5884.10	0.735513
$401$	−3108.69	−0.387134	−0.193567	−	0.981087i	$-0.562006\pi$
$401$	−3108.69	−0.387134	−0.193567	+	0.981087i	$0.562006\pi$
$402$	3990.92	0.495147
$403$	4067.88	0.502818
$404$	−1908.77	−0.235062
$405$	1798.05	0.220607
$406$	−2037.16	−0.249021
$407$	9711.73	1.18278
$408$	1985.76	0.240956
$409$	3414.66	0.412822	0.206411	−	0.978465i	$-0.433822\pi$
$409$	3414.66	0.412822	0.206411	+	0.978465i	$0.433822\pi$
$410$	−8036.93	−0.968087
$411$	5654.77	0.678660
$412$	4095.45	0.489728
$413$	4184.06	0.498508
$414$	372.882	0.0442660
$415$	−5027.31	−0.594652
$416$	−1501.90	−0.177011
$417$	6170.41	0.724619
$418$	−2318.28	−0.271269
$419$	−12757.3	−1.48744	−0.743718	−	0.668493i	$-0.766940\pi$
$419$	−12757.3	−1.48744	−0.743718	+	0.668493i	$0.766940\pi$
$420$	−1864.64	−0.216631
$421$	−12821.2	−1.48424	−0.742120	−	0.670267i	$-0.766180\pi$
$421$	−12821.2	−1.48424	−0.742120	+	0.670267i	$0.766180\pi$
$422$	2758.84	0.318243
$423$	4019.31	0.461999
$424$	2516.89	0.288281
$425$	−30428.2	−3.47291
$426$	−462.377	−0.0525874
$427$	5316.44	0.602531
$428$	926.193	0.104601
$429$	8590.01	0.966736
$430$	2743.90	0.307727
$431$	2016.00	0.225306	0.112653	−	0.993634i	$-0.464065\pi$
$431$	2016.00	0.225306	0.112653	+	0.993634i	$0.464065\pi$
$432$	432.000	0.0481125
$433$	−1743.00	−0.193449	−0.0967246	−	0.995311i	$-0.530837\pi$
$433$	−1743.00	−0.193449	−0.0967246	+	0.995311i	$0.530837\pi$
$434$	1213.40	0.134206
$435$	−9690.25	−1.06807
$436$	−3287.61	−0.361120
$437$	−393.597	−0.0430854
$438$	−488.896	−0.0533341
$439$	−6859.93	−0.745801	−0.372900	−	0.927871i	$-0.621637\pi$
$439$	−6859.93	−0.745801	−0.372900	+	0.927871i	$0.621637\pi$
$440$	−10834.0	−1.17384
$441$	441.000	0.0476190
$442$	7766.71	0.835803
$443$	−13227.0	−1.41858	−0.709292	−	0.704915i	$-0.750985\pi$
$443$	−13227.0	−1.41858	−0.709292	+	0.704915i	$0.750985\pi$
$444$	1910.28	0.204184
$445$	24695.3	2.63071
$446$	−585.046	−0.0621138
$447$	4870.30	0.515341
$448$	−448.000	−0.0472456
$449$	−12489.4	−1.31272	−0.656358	−	0.754449i	$-0.727904\pi$
$449$	−12489.4	−1.31272	−0.656358	+	0.754449i	$0.727904\pi$
$450$	−6619.62	−0.693448
$451$	11044.0	1.15308
$452$	5187.10	0.539780
$453$	−7841.04	−0.813254
$454$	9224.67	0.953602
$455$	−7292.98	−0.751429
$456$	−456.000	−0.0468293
$457$	−15241.2	−1.56008	−0.780038	−	0.625733i	$-0.784800\pi$
$457$	−15241.2	−1.56008	−0.780038	+	0.625733i	$0.784800\pi$
$458$	4499.43	0.459049
$459$	−2233.98	−0.227175
$460$	−1839.39	−0.186440
$461$	−8556.48	−0.864458	−0.432229	−	0.901764i	$-0.642273\pi$
$461$	−8556.48	−0.864458	−0.432229	+	0.901764i	$0.642273\pi$
$462$	2562.31	0.258029
$463$	3879.82	0.389439	0.194720	−	0.980859i	$-0.437620\pi$
$463$	3879.82	0.389439	0.194720	+	0.980859i	$0.437620\pi$
$464$	−2328.18	−0.232938
$465$	5771.85	0.575619
$466$	−12728.0	−1.26527
$467$	−9778.53	−0.968943	−0.484472	−	0.874807i	$-0.660988\pi$
$467$	−9778.53	−0.968943	−0.484472	+	0.874807i	$0.660988\pi$
$468$	1689.64	0.166888
$469$	4656.07	0.458417
$470$	−19826.9	−1.94585
$471$	4961.25	0.485355
$472$	4781.78	0.466312
$473$	−3770.54	−0.366531
$474$	7243.61	0.701920
$475$	6987.37	0.674953
$476$	2316.72	0.223082
$477$	−2831.50	−0.271794
$478$	4885.82	0.467515
$479$	−7934.42	−0.756854	−0.378427	−	0.925631i	$-0.623535\pi$
$479$	−7934.42	−0.756854	−0.378427	+	0.925631i	$0.623535\pi$
$480$	−2131.02	−0.202640
$481$	7471.47	0.708253
$482$	4122.02	0.389529
$483$	435.029	0.0409824
$484$	9563.55	0.898154
$485$	−24816.4	−2.32341
$486$	−486.000	−0.0453609
$487$	−15053.3	−1.40068	−0.700338	−	0.713811i	$-0.746968\pi$
$487$	−15053.3	−1.40068	−0.700338	+	0.713811i	$0.746968\pi$
$488$	6075.93	0.563616
$489$	304.465	0.0281562
$490$	−2175.42	−0.200562
$491$	−132.952	−0.0122201	−0.00611003	−	0.999981i	$-0.501945\pi$
$491$	−132.952	−0.0122201	−0.00611003	+	0.999981i	$0.501945\pi$
$492$	2172.33	0.199057
$493$	12039.6	1.09988
$494$	−1783.51	−0.162437
$495$	12188.2	1.10671
$496$	1386.75	0.125538
$497$	−539.440	−0.0486865
$498$	1358.85	0.122272
$499$	−2913.57	−0.261381	−0.130691	−	0.991423i	$-0.541719\pi$
$499$	−2913.57	−0.261381	−0.130691	+	0.991423i	$0.541719\pi$
$500$	21554.9	1.92793
$501$	−7074.38	−0.630858
$502$	746.564	0.0663761
$503$	13537.9	1.20005	0.600026	−	0.799980i	$-0.295157\pi$
$503$	13537.9	1.20005	0.600026	+	0.799980i	$0.295157\pi$
$504$	504.000	0.0445435
$505$	−10592.8	−0.933411
$506$	2527.61	0.222067
$507$	17.5037	0.00153327
$508$	8068.58	0.704695
$509$	15766.9	1.37300	0.686498	−	0.727132i	$-0.259147\pi$
$509$	15766.9	1.37300	0.686498	+	0.727132i	$0.259147\pi$
$510$	11020.1	0.956816
$511$	−570.378	−0.0493778
$512$	−512.000	−0.0441942
$513$	513.000	0.0441511
$514$	−1065.96	−0.0914733
$515$	22727.8	1.94467
$516$	−741.656	−0.0632744
$517$	27245.2	2.31769
$518$	2228.66	0.189038
$519$	4158.81	0.351737
$520$	−8334.84	−0.702898
$521$	802.373	0.0674714	0.0337357	−	0.999431i	$-0.489260\pi$
$521$	802.373	0.0674714	0.0337357	+	0.999431i	$0.489260\pi$
$522$	2619.21	0.219616
$523$	5338.51	0.446342	0.223171	−	0.974779i	$-0.428359\pi$
$523$	5338.51	0.446342	0.223171	+	0.974779i	$0.428359\pi$
$524$	−9669.42	−0.806127
$525$	−7722.89	−0.642008
$526$	−7948.38	−0.658871
$527$	−7171.23	−0.592758
$528$	2928.35	0.241364
$529$	−11737.9	−0.964729
$530$	13967.6	1.14474
$531$	−5379.50	−0.439643
$532$	−532.000	−0.0433555
$533$	8496.40	0.690469
$534$	−6674.96	−0.540925
$535$	5139.94	0.415362
$536$	5321.23	0.428810
$537$	−3191.32	−0.256454
$538$	−7918.26	−0.634536
$539$	2989.36	0.238888
$540$	2397.40	0.191051
$541$	−13018.1	−1.03455	−0.517274	−	0.855820i	$-0.673053\pi$
$541$	−13018.1	−1.03455	−0.517274	+	0.855820i	$0.673053\pi$
$542$	−4537.91	−0.359631
$543$	−3438.60	−0.271758
$544$	2647.69	0.208674
$545$	−18244.7	−1.43398
$546$	1971.24	0.154508
$547$	−23796.9	−1.86011	−0.930057	−	0.367416i	$-0.880242\pi$
$547$	−23796.9	−1.86011	−0.930057	+	0.367416i	$0.880242\pi$
$548$	7539.69	0.587737
$549$	−6835.43	−0.531382
$550$	−44871.6	−3.47879
$551$	−2764.72	−0.213759
$552$	497.176	0.0383355
$553$	8450.88	0.649851
$554$	−8329.03	−0.638748
$555$	10601.1	0.810799
$556$	8227.21	0.627539
$557$	20187.4	1.53567	0.767833	−	0.640650i	$-0.221335\pi$
$557$	20187.4	1.53567	0.767833	+	0.640650i	$0.221335\pi$
$558$	−1560.09	−0.118358
$559$	−2900.76	−0.219480
$560$	−2486.19	−0.187608
$561$	−15143.3	−1.13966
$562$	−14572.9	−1.09381
$563$	−16830.4	−1.25989	−0.629944	−	0.776641i	$-0.716922\pi$
$563$	−16830.4	−1.25989	−0.629944	+	0.776641i	$0.716922\pi$
$564$	5359.08	0.400103
$565$	28786.0	2.14342
$566$	11710.0	0.869625
$567$	−567.000	−0.0419961
$568$	−616.503	−0.0455420
$569$	11520.5	0.848795	0.424397	−	0.905476i	$-0.360486\pi$
$569$	11520.5	0.848795	0.424397	+	0.905476i	$0.360486\pi$
$570$	−2530.59	−0.185955
$571$	20007.9	1.46638	0.733191	−	0.680023i	$-0.238030\pi$
$571$	20007.9	1.46638	0.733191	+	0.680023i	$0.238030\pi$
$572$	11453.3	0.837218
$573$	−11974.9	−0.873052
$574$	2534.38	0.184291
$575$	−7618.32	−0.552532
$576$	576.000	0.0416667
$577$	−4624.17	−0.333634	−0.166817	−	0.985988i	$-0.553349\pi$
$577$	−4624.17	−0.333634	−0.166817	+	0.985988i	$0.553349\pi$
$578$	−3865.87	−0.278199
$579$	11602.1	0.832761
$580$	−12920.3	−0.924978
$581$	1585.32	0.113202
$582$	6707.70	0.477737
$583$	−19193.6	−1.36349
$584$	−651.861	−0.0461887
$585$	9376.69	0.662698
$586$	11027.7	0.777388
$587$	−2205.85	−0.155102	−0.0775512	−	0.996988i	$-0.524710\pi$
$587$	−2205.85	−0.155102	−0.0775512	+	0.996988i	$0.524710\pi$
$588$	588.000	0.0412393
$589$	1646.76	0.115201
$590$	26536.6	1.85169
$591$	12858.5	0.894971
$592$	2547.04	0.176829
$593$	19928.2	1.38002	0.690012	−	0.723798i	$-0.257605\pi$
$593$	19928.2	1.38002	0.690012	+	0.723798i	$0.257605\pi$
$594$	−3294.39	−0.227560
$595$	12856.7	0.885840
$596$	6493.73	0.446298
$597$	220.305	0.0151030
$598$	1944.55	0.132974
$599$	7606.55	0.518856	0.259428	−	0.965762i	$-0.416466\pi$
$599$	7606.55	0.518856	0.259428	+	0.965762i	$0.416466\pi$
$600$	−8826.16	−0.600544
$601$	10032.5	0.680921	0.340461	−	0.940259i	$-0.389417\pi$
$601$	10032.5	0.680921	0.340461	+	0.940259i	$0.389417\pi$
$602$	−865.266	−0.0585807
$603$	−5986.38	−0.404286
$604$	−10454.7	−0.704299
$605$	53073.2	3.56650
$606$	2863.16	0.191927
$607$	−29039.4	−1.94180	−0.970899	−	0.239491i	$-0.923019\pi$
$607$	−29039.4	−1.94180	−0.970899	+	0.239491i	$0.923019\pi$
$608$	−608.000	−0.0405554
$609$	3055.74	0.203325
$610$	33718.6	2.23807
$611$	20960.4	1.38784
$612$	−2978.65	−0.196740
$613$	18243.5	1.20204	0.601019	−	0.799235i	$-0.294762\pi$
$613$	18243.5	1.20204	0.601019	+	0.799235i	$0.294762\pi$
$614$	6043.42	0.397219
$615$	12055.4	0.790440
$616$	3416.41	0.223459
$617$	12943.9	0.844573	0.422287	−	0.906462i	$-0.361228\pi$
$617$	12943.9	0.844573	0.422287	+	0.906462i	$0.361228\pi$
$618$	−6143.17	−0.399862
$619$	14894.5	0.967144	0.483572	−	0.875305i	$-0.339339\pi$
$619$	14894.5	0.967144	0.483572	+	0.875305i	$0.339339\pi$
$620$	7695.79	0.498501
$621$	−559.323	−0.0361431
$622$	−2768.39	−0.178460
$623$	−7787.46	−0.500799
$624$	2252.85	0.144529
$625$	73650.3	4.71362
$626$	−12132.9	−0.774644
$627$	3477.41	0.221491
$628$	6615.00	0.420330
$629$	−13171.4	−0.834940
$630$	2796.96	0.176879
$631$	−2155.74	−0.136004	−0.0680022	−	0.997685i	$-0.521662\pi$
$631$	−2155.74	−0.136004	−0.0680022	+	0.997685i	$0.521662\pi$
$632$	9658.15	0.607880
$633$	−4138.27	−0.259844
$634$	12033.1	0.753780
$635$	44776.8	2.79829
$636$	−3775.34	−0.235380
$637$	2299.78	0.143047
$638$	17754.5	1.10174
$639$	693.565	0.0429374
$640$	−2841.36	−0.175492
$641$	4904.02	0.302180	0.151090	−	0.988520i	$-0.451722\pi$
$641$	4904.02	0.302180	0.151090	+	0.988520i	$0.451722\pi$
$642$	−1389.29	−0.0854064
$643$	−11771.7	−0.721976	−0.360988	−	0.932570i	$-0.617560\pi$
$643$	−11771.7	−0.721976	−0.360988	+	0.932570i	$0.617560\pi$
$644$	580.038	0.0354918
$645$	−4115.84	−0.251258
$646$	3144.13	0.191492
$647$	23164.9	1.40758	0.703791	−	0.710407i	$-0.251489\pi$
$647$	23164.9	1.40758	0.703791	+	0.710407i	$0.251489\pi$
$648$	−648.000	−0.0392837
$649$	−36465.4	−2.20553
$650$	−34520.8	−2.08311
$651$	−1820.11	−0.109578
$652$	405.954	0.0243840
$653$	24353.7	1.45947	0.729736	−	0.683729i	$-0.239643\pi$
$653$	24353.7	1.45947	0.729736	+	0.683729i	$0.239643\pi$
$654$	4931.42	0.294853
$655$	−53660.7	−3.20106
$656$	2896.44	0.172389
$657$	733.344	0.0435471
$658$	6252.26	0.370423
$659$	3783.51	0.223649	0.111824	−	0.993728i	$-0.464331\pi$
$659$	3783.51	0.223649	0.111824	+	0.993728i	$0.464331\pi$
$660$	16251.0	0.958436
$661$	−2641.84	−0.155455	−0.0777275	−	0.996975i	$-0.524766\pi$
$661$	−2641.84	−0.155455	−0.0777275	+	0.996975i	$0.524766\pi$
$662$	−13779.5	−0.808998
$663$	−11650.1	−0.682430
$664$	1811.80	0.105891
$665$	−2952.35	−0.172161
$666$	−2865.42	−0.166716
$667$	3014.37	0.174988
$668$	−9432.51	−0.546339
$669$	877.570	0.0507157
$670$	29530.3	1.70277
$671$	−46334.5	−2.66576
$672$	672.000	0.0385758
$673$	−5580.48	−0.319631	−0.159816	−	0.987147i	$-0.551090\pi$
$673$	−5580.48	−0.319631	−0.159816	+	0.987147i	$0.551090\pi$
$674$	24387.0	1.39370
$675$	9929.42	0.566198
$676$	23.3383	0.00132785
$677$	−34366.8	−1.95100	−0.975499	−	0.220006i	$-0.929392\pi$
$677$	−34366.8	−1.95100	−0.975499	+	0.220006i	$0.929392\pi$
$678$	−7780.65	−0.440729
$679$	7825.65	0.442299
$680$	14693.4	0.828627
$681$	−13837.0	−0.778613
$682$	−10575.2	−0.593762
$683$	−6093.36	−0.341370	−0.170685	−	0.985326i	$-0.554598\pi$
$683$	−6093.36	−0.341370	−0.170685	+	0.985326i	$0.554598\pi$
$684$	684.000	0.0382360
$685$	41841.7	2.33385
$686$	686.000	0.0381802
$687$	−6749.14	−0.374812
$688$	−988.875	−0.0547972
$689$	−14766.1	−0.816463
$690$	2759.09	0.152227
$691$	−5808.73	−0.319790	−0.159895	−	0.987134i	$-0.551116\pi$
$691$	−5808.73	−0.319790	−0.159895	+	0.987134i	$0.551116\pi$
$692$	5545.07	0.304613
$693$	−3843.46	−0.210679
$694$	−14294.6	−0.781869
$695$	45657.2	2.49191
$696$	3492.28	0.190193
$697$	−14978.2	−0.813976
$698$	4493.54	0.243672
$699$	19092.0	1.03309
$700$	−10297.2	−0.555996
$701$	−19570.2	−1.05443	−0.527217	−	0.849731i	$-0.676764\pi$
$701$	−19570.2	−1.05443	−0.527217	+	0.849731i	$0.676764\pi$
$702$	−2534.46	−0.136263
$703$	3024.61	0.162269
$704$	3904.47	0.209027
$705$	29740.4	1.58878
$706$	−1472.76	−0.0785102
$707$	3340.35	0.177690
$708$	−7172.67	−0.380742
$709$	−18382.3	−0.973711	−0.486856	−	0.873483i	$-0.661856\pi$
$709$	−18382.3	−0.973711	−0.486856	+	0.873483i	$0.661856\pi$
$710$	−3421.30	−0.180844
$711$	−10865.4	−0.573115
$712$	−8899.95	−0.468455
$713$	−1795.46	−0.0943065
$714$	−3475.09	−0.182145
$715$	63560.7	3.32453
$716$	−4255.10	−0.222096
$717$	−7328.73	−0.381724
$718$	−15599.2	−0.810803
$719$	362.212	0.0187875	0.00939375	−	0.999956i	$-0.497010\pi$
$719$	362.212	0.0187875	0.00939375	+	0.999956i	$0.497010\pi$
$720$	3196.53	0.165455
$721$	−7167.03	−0.370200
$722$	−722.000	−0.0372161
$723$	−6183.03	−0.318049
$724$	−4584.81	−0.235349
$725$	−53512.8	−2.74126
$726$	−14345.3	−0.733340
$727$	−26286.7	−1.34102	−0.670509	−	0.741901i	$-0.733924\pi$
$727$	−26286.7	−1.34102	−0.670509	+	0.741901i	$0.733924\pi$
$728$	2628.32	0.133808
$729$	729.000	0.0370370
$730$	−3617.52	−0.183412
$731$	5113.73	0.258739
$732$	−9113.90	−0.460191
$733$	−19480.3	−0.981612	−0.490806	−	0.871269i	$-0.663298\pi$
$733$	−19480.3	−0.981612	−0.490806	+	0.871269i	$0.663298\pi$
$734$	−12436.6	−0.625401
$735$	3263.12	0.163758
$736$	662.901	0.0331995
$737$	−40579.2	−2.02816
$738$	−3258.49	−0.162529
$739$	−32472.0	−1.61638	−0.808188	−	0.588924i	$-0.799552\pi$
$739$	−32472.0	−1.61638	−0.808188	+	0.588924i	$0.799552\pi$
$740$	14134.9	0.702172
$741$	2675.26	0.132629
$742$	−4404.56	−0.217920
$743$	22886.7	1.13006	0.565028	−	0.825072i	$-0.308865\pi$
$743$	22886.7	1.13006	0.565028	+	0.825072i	$0.308865\pi$
$744$	−2080.12	−0.102501
$745$	36037.2	1.77221
$746$	8861.24	0.434897
$747$	−2038.27	−0.0998345
$748$	−20191.0	−0.986974
$749$	−1620.84	−0.0790709
$750$	−32332.4	−1.57415
$751$	32111.8	1.56029	0.780144	−	0.625601i	$-0.215146\pi$
$751$	32111.8	1.56029	0.780144	+	0.625601i	$0.215146\pi$
$752$	7145.44	0.346499
$753$	−1119.85	−0.0541959
$754$	13659.0	0.659723
$755$	−58018.8	−2.79671
$756$	−756.000	−0.0363696
$757$	−29087.9	−1.39659	−0.698294	−	0.715811i	$-0.746057\pi$
$757$	−29087.9	−1.39659	−0.698294	+	0.715811i	$0.746057\pi$
$758$	29350.7	1.40642
$759$	−3791.42	−0.181317
$760$	−3374.11	−0.161042
$761$	−29455.0	−1.40308	−0.701539	−	0.712631i	$-0.747503\pi$
$761$	−29455.0	−1.40308	−0.701539	+	0.712631i	$0.747503\pi$
$762$	−12102.9	−0.575381
$763$	5753.33	0.272981
$764$	−15966.5	−0.756085
$765$	−16530.1	−0.781237
$766$	−8884.67	−0.419081
$767$	−28053.7	−1.32068
$768$	768.000	0.0360844
$769$	18804.2	0.881791	0.440895	−	0.897558i	$-0.354661\pi$
$769$	18804.2	0.881791	0.440895	+	0.897558i	$0.354661\pi$
$770$	18959.5	0.887339
$771$	1598.93	0.0746876
$772$	15469.5	0.721192
$773$	33012.2	1.53605	0.768025	−	0.640420i	$-0.221240\pi$
$773$	33012.2	1.53605	0.768025	+	0.640420i	$0.221240\pi$
$774$	1112.48	0.0516633
$775$	31874.1	1.47736
$776$	8943.60	0.413733
$777$	−3342.98	−0.154349
$778$	2817.48	0.129835
$779$	3439.52	0.158195
$780$	12502.3	0.573914
$781$	4701.39	0.215402
$782$	−3428.03	−0.156760
$783$	−3928.81	−0.179316
$784$	784.000	0.0357143
$785$	36710.1	1.66910
$786$	14504.1	0.658200
$787$	−6483.94	−0.293682	−0.146841	−	0.989160i	$-0.546911\pi$
$787$	−6483.94	−0.293682	−0.146841	+	0.989160i	$0.546911\pi$
$788$	17144.7	0.775068
$789$	11922.6	0.537966
$790$	53598.2	2.41384
$791$	−9077.42	−0.408035
$792$	−4392.52	−0.197073
$793$	−35646.3	−1.59626
$794$	23579.2	1.05390
$795$	−20951.3	−0.934676
$796$	293.740	0.0130796
$797$	−7587.59	−0.337222	−0.168611	−	0.985683i	$-0.553928\pi$
$797$	−7587.59	−0.337222	−0.168611	+	0.985683i	$0.553928\pi$
$798$	798.000	0.0353996
$799$	−36950.9	−1.63608
$800$	−11768.2	−0.520086
$801$	10012.4	0.441663
$802$	6217.39	0.273745
$803$	4971.03	0.218461
$804$	−7981.84	−0.350122
$805$	3218.94	0.140935
$806$	−8135.76	−0.355546
$807$	11877.4	0.518096
$808$	3817.54	0.166214
$809$	33129.1	1.43975	0.719874	−	0.694105i	$-0.244200\pi$
$809$	33129.1	1.43975	0.719874	+	0.694105i	$0.244200\pi$
$810$	−3596.10	−0.155992
$811$	23249.3	1.00665	0.503325	−	0.864097i	$-0.332110\pi$
$811$	23249.3	1.00665	0.503325	+	0.864097i	$0.332110\pi$
$812$	4074.32	0.176085
$813$	6806.87	0.293638
$814$	−19423.5	−0.836354
$815$	2252.85	0.0968270
$816$	−3971.53	−0.170381
$817$	−1174.29	−0.0502854
$818$	−6829.32	−0.291909
$819$	−2956.86	−0.126155
$820$	16073.9	0.684541
$821$	−18272.4	−0.776748	−0.388374	−	0.921502i	$-0.626963\pi$
$821$	−18272.4	−0.776748	−0.388374	+	0.921502i	$0.626963\pi$
$822$	−11309.5	−0.479885
$823$	−32132.5	−1.36096	−0.680478	−	0.732768i	$-0.738228\pi$
$823$	−32132.5	−1.36096	−0.680478	+	0.732768i	$0.738228\pi$
$824$	−8190.89	−0.346290
$825$	67307.5	2.84042
$826$	−8368.11	−0.352499
$827$	−22406.3	−0.942133	−0.471067	−	0.882098i	$-0.656131\pi$
$827$	−22406.3	−0.942133	−0.471067	+	0.882098i	$0.656131\pi$
$828$	−745.764	−0.0313008
$829$	15805.9	0.662195	0.331098	−	0.943596i	$-0.392581\pi$
$829$	15805.9	0.662195	0.331098	+	0.943596i	$0.392581\pi$
$830$	10054.6	0.420483
$831$	12493.5	0.521536
$832$	3003.80	0.125166
$833$	−4054.27	−0.168634
$834$	−12340.8	−0.512383
$835$	−52346.0	−2.16947
$836$	4636.55	0.191816
$837$	2340.14	0.0966391
$838$	25514.6	1.05178
$839$	−16180.0	−0.665788	−0.332894	−	0.942964i	$-0.608025\pi$
$839$	−16180.0	−0.665788	−0.332894	+	0.942964i	$0.608025\pi$
$840$	3729.28	0.153182
$841$	−3215.39	−0.131838
$842$	25642.3	1.04952
$843$	21859.4	0.893093
$844$	−5517.69	−0.225032
$845$	129.516	0.00527278
$846$	−8038.62	−0.326683
$847$	−16736.2	−0.678941
$848$	−5033.78	−0.203845
$849$	−17565.0	−0.710046
$850$	60856.5	2.45572
$851$	−3297.72	−0.132837
$852$	924.754	0.0371849
$853$	−29515.8	−1.18476	−0.592382	−	0.805658i	$-0.701812\pi$
$853$	−29515.8	−1.18476	−0.592382	+	0.805658i	$0.701812\pi$
$854$	−10632.9	−0.426054
$855$	3795.88	0.151832
$856$	−1852.39	−0.0739641
$857$	28789.3	1.14752	0.573759	−	0.819024i	$-0.305485\pi$
$857$	28789.3	1.14752	0.573759	+	0.819024i	$0.305485\pi$
$858$	−17180.0	−0.683585
$859$	−30155.1	−1.19776	−0.598881	−	0.800838i	$-0.704388\pi$
$859$	−30155.1	−1.19776	−0.598881	+	0.800838i	$0.704388\pi$
$860$	−5487.79	−0.217596
$861$	−3801.57	−0.150473
$862$	−4031.99	−0.159316
$863$	45592.5	1.79836	0.899181	−	0.437577i	$-0.144163\pi$
$863$	45592.5	1.79836	0.899181	+	0.437577i	$0.144163\pi$
$864$	−864.000	−0.0340207
$865$	30772.6	1.20959
$866$	3486.01	0.136789
$867$	5798.80	0.227148
$868$	−2426.81	−0.0948977
$869$	−73652.1	−2.87512
$870$	19380.5	0.755242
$871$	−31218.6	−1.21447
$872$	6575.23	0.255350
$873$	−10061.5	−0.390071
$874$	787.195	0.0304660
$875$	−37721.2	−1.45738
$876$	977.791	0.0377129
$877$	46456.3	1.78873	0.894365	−	0.447338i	$-0.147628\pi$
$877$	46456.3	1.78873	0.894365	+	0.447338i	$0.147628\pi$
$878$	13719.9	0.527361
$879$	−16541.5	−0.634735
$880$	21667.9	0.830030
$881$	48505.8	1.85494	0.927470	−	0.373898i	$-0.121979\pi$
$881$	48505.8	1.85494	0.927470	+	0.373898i	$0.121979\pi$
$882$	−882.000	−0.0336718
$883$	−4472.54	−0.170456	−0.0852281	−	0.996361i	$-0.527162\pi$
$883$	−4472.54	−0.170456	−0.0852281	+	0.996361i	$0.527162\pi$
$884$	−15533.4	−0.591002
$885$	−39804.9	−1.51190
$886$	26454.0	1.00309
$887$	−28815.9	−1.09081	−0.545403	−	0.838174i	$-0.683623\pi$
$887$	−28815.9	−1.09081	−0.545403	+	0.838174i	$0.683623\pi$
$888$	−3820.55	−0.144380
$889$	−14120.0	−0.532700
$890$	−49390.5	−1.86020
$891$	4941.59	0.185802
$892$	1170.09	0.0439211
$893$	8485.21	0.317969
$894$	−9740.60	−0.364401
$895$	−23613.8	−0.881924
$896$	896.000	0.0334077
$897$	−2916.83	−0.108573
$898$	24978.7	0.928231
$899$	−12611.7	−0.467881
$900$	13239.2	0.490342
$901$	26031.0	0.962506
$902$	−22088.0	−0.815353
$903$	1297.90	0.0478310
$904$	−10374.2	−0.381682
$905$	−25443.5	−0.934554
$906$	15682.1	0.575057
$907$	21142.3	0.774000	0.387000	−	0.922080i	$-0.373511\pi$
$907$	21142.3	0.774000	0.387000	+	0.922080i	$0.373511\pi$
$908$	−18449.3	−0.674298
$909$	−4294.73	−0.156708
$910$	14586.0	0.531341
$911$	−9257.10	−0.336664	−0.168332	−	0.985730i	$-0.553838\pi$
$911$	−9257.10	−0.336664	−0.168332	+	0.985730i	$0.553838\pi$
$912$	912.000	0.0331133
$913$	−13816.6	−0.500835
$914$	30482.4	1.10314
$915$	−50577.9	−1.82738
$916$	−8998.85	−0.324597
$917$	16921.5	0.609374
$918$	4467.97	0.160637
$919$	41492.0	1.48933	0.744665	−	0.667438i	$-0.232609\pi$
$919$	41492.0	1.48933	0.744665	+	0.667438i	$0.232609\pi$
$920$	3678.79	0.131833
$921$	−9065.14	−0.324328
$922$	17113.0	0.611264
$923$	3616.89	0.128983
$924$	−5124.61	−0.182454
$925$	58543.1	2.08096
$926$	−7759.64	−0.275375
$927$	9214.75	0.326486
$928$	4656.37	0.164712
$929$	21777.2	0.769093	0.384547	−	0.923106i	$-0.374358\pi$
$929$	21777.2	0.769093	0.384547	+	0.923106i	$0.374358\pi$
$930$	−11543.7	−0.407024
$931$	931.000	0.0327737
$932$	25456.1	0.894679
$933$	4152.59	0.145712
$934$	19557.1	0.685146
$935$	−112051.	−3.91919
$936$	−3379.27	−0.118008
$937$	2414.32	0.0841754	0.0420877	−	0.999114i	$-0.486599\pi$
$937$	2414.32	0.0841754	0.0420877	+	0.999114i	$0.486599\pi$
$938$	−9312.15	−0.324150
$939$	18199.3	0.632494
$940$	39653.8	1.37592
$941$	−33958.1	−1.17641	−0.588205	−	0.808712i	$-0.700165\pi$
$941$	−33958.1	−1.17641	−0.588205	+	0.808712i	$0.700165\pi$
$942$	−9922.49	−0.343198
$943$	−3750.10	−0.129502
$944$	−9563.56	−0.329732
$945$	−4195.44	−0.144421
$946$	7541.07	0.259177
$947$	−4492.29	−0.154150	−0.0770749	−	0.997025i	$-0.524558\pi$
$947$	−4492.29	−0.154150	−0.0770749	+	0.997025i	$0.524558\pi$
$948$	−14487.2	−0.496332
$949$	3824.34	0.130815
$950$	−13974.7	−0.477264
$951$	−18049.7	−0.615459
$952$	−4633.45	−0.157743
$953$	−6844.32	−0.232644	−0.116322	−	0.993212i	$-0.537110\pi$
$953$	−6844.32	−0.232644	−0.116322	+	0.993212i	$0.537110\pi$
$954$	5663.00	0.192187
$955$	−88606.7	−3.00235
$956$	−9771.64	−0.330583
$957$	−26631.8	−0.899565
$958$	15868.8	0.535176
$959$	−13194.5	−0.444287
$960$	4262.04	0.143288
$961$	−22279.0	−0.747844
$962$	−14942.9	−0.500810
$963$	2083.93	0.0697340
$964$	−8244.05	−0.275439
$965$	85848.6	2.86380
$966$	−870.058	−0.0289789
$967$	−21291.0	−0.708038	−0.354019	−	0.935238i	$-0.615185\pi$
$967$	−21291.0	−0.708038	−0.354019	+	0.935238i	$0.615185\pi$
$968$	−19127.1	−0.635091
$969$	−4716.19	−0.156353
$970$	49632.8	1.64290
$971$	2658.56	0.0878652	0.0439326	−	0.999034i	$-0.486011\pi$
$971$	2658.56	0.0878652	0.0439326	+	0.999034i	$0.486011\pi$
$972$	972.000	0.0320750
$973$	−14397.6	−0.474375
$974$	30106.6	0.990428
$975$	51781.2	1.70085
$976$	−12151.9	−0.398537
$977$	−24206.1	−0.792652	−0.396326	−	0.918110i	$-0.629715\pi$
$977$	−24206.1	−0.792652	−0.396326	+	0.918110i	$0.629715\pi$
$978$	−608.931	−0.0199095
$979$	67870.2	2.21567
$980$	4350.83	0.141819
$981$	−7397.13	−0.240746
$982$	265.904	0.00864089
$983$	37035.3	1.20167	0.600835	−	0.799373i	$-0.294835\pi$
$983$	37035.3	1.20167	0.600835	+	0.799373i	$0.294835\pi$
$984$	−4344.66	−0.140755
$985$	95144.8	3.07773
$986$	−24079.3	−0.777729
$987$	−9378.39	−0.302449
$988$	3567.01	0.114860
$989$	1280.32	0.0411648
$990$	−24376.4	−0.782560
$991$	23052.7	0.738945	0.369472	−	0.929242i	$-0.379538\pi$
$991$	23052.7	0.738945	0.369472	+	0.929242i	$0.379538\pi$
$992$	−2773.49	−0.0887687
$993$	20669.3	0.660544
$994$	1078.88	0.0344265
$995$	1630.12	0.0519378
$996$	−2717.69	−0.0864592
$997$	53912.8	1.71257	0.856286	−	0.516502i	$-0.172766\pi$
$997$	53912.8	1.71257	0.856286	+	0.516502i	$0.172766\pi$
$998$	5827.14	0.184825
$999$	4298.12	0.136123

Twists

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

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

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +22.1981 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +22.1981 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -44.3962 q^{10} +61.0073 q^{11} +12.0000 q^{12} +46.9344 q^{13} +14.0000 q^{14} +66.5944 q^{15} +16.0000 q^{16} -82.7402 q^{17} -18.0000 q^{18} +19.0000 q^{19} +88.7925 q^{20} -21.0000 q^{21} -122.015 q^{22} -20.7157 q^{23} -24.0000 q^{24} +367.756 q^{25} -93.8687 q^{26} +27.0000 q^{27} -28.0000 q^{28} -145.512 q^{29} -133.189 q^{30} +86.6717 q^{31} -32.0000 q^{32} +183.022 q^{33} +165.480 q^{34} -155.387 q^{35} +36.0000 q^{36} +159.190 q^{37} -38.0000 q^{38} +140.803 q^{39} -177.585 q^{40} +181.027 q^{41} +42.0000 q^{42} -61.8047 q^{43} +244.029 q^{44} +199.783 q^{45} +41.4313 q^{46} +446.590 q^{47} +48.0000 q^{48} +49.0000 q^{49} -735.513 q^{50} -248.220 q^{51} +187.737 q^{52} -314.611 q^{53} -54.0000 q^{54} +1354.25 q^{55} +56.0000 q^{56} +57.0000 q^{57} +291.023 q^{58} -597.722 q^{59} +266.377 q^{60} -759.492 q^{61} -173.343 q^{62} -63.0000 q^{63} +64.0000 q^{64} +1041.85 q^{65} -366.044 q^{66} -665.153 q^{67} -330.961 q^{68} -62.1470 q^{69} +310.774 q^{70} +77.0628 q^{71} -72.0000 q^{72} +81.4826 q^{73} -318.379 q^{74} +1103.27 q^{75} +76.0000 q^{76} -427.051 q^{77} -281.606 q^{78} -1207.27 q^{79} +355.170 q^{80} +81.0000 q^{81} -362.055 q^{82} -226.474 q^{83} -84.0000 q^{84} -1836.68 q^{85} +123.609 q^{86} -436.535 q^{87} -488.058 q^{88} +1112.49 q^{89} -399.566 q^{90} -328.541 q^{91} -82.8626 q^{92} +260.015 q^{93} -893.180 q^{94} +421.764 q^{95} -96.0000 q^{96} -1117.95 q^{97} -98.0000 q^{98} +549.065 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} + 10 q^{5} - 24 q^{6} - 28 q^{7} - 32 q^{8} + 36 q^{9}+O(q^{10}) \) 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	\( 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} + 10 q^{5} - 24 q^{6} - 28 q^{7} - 32 q^{8} + 36 q^{9} - 20 q^{10} + 64 q^{11} + 48 q^{12} + 16 q^{13} + 56 q^{14} + 30 q^{15} + 64 q^{16} - 78 q^{17} - 72 q^{18} + 76 q^{19} + 40 q^{20} - 84 q^{21} - 128 q^{22} + 64 q^{23} - 96 q^{24} + 124 q^{25} - 32 q^{26} + 108 q^{27} - 112 q^{28} + 70 q^{29} - 60 q^{30} - 28 q^{31} - 128 q^{32} + 192 q^{33} + 156 q^{34} - 70 q^{35} + 144 q^{36} + 224 q^{37} - 152 q^{38} + 48 q^{39} - 80 q^{40} + 568 q^{41} + 168 q^{42} + 348 q^{43} + 256 q^{44} + 90 q^{45} - 128 q^{46} + 886 q^{47} + 192 q^{48} + 196 q^{49} - 248 q^{50} - 234 q^{51} + 64 q^{52} + 382 q^{53} - 216 q^{54} + 1232 q^{55} + 224 q^{56} + 228 q^{57} - 140 q^{58} + 552 q^{59} + 120 q^{60} - 744 q^{61} + 56 q^{62} - 252 q^{63} + 256 q^{64} + 1288 q^{65} - 384 q^{66} + 92 q^{67} - 312 q^{68} + 192 q^{69} + 140 q^{70} + 1154 q^{71} - 288 q^{72} + 508 q^{73} - 448 q^{74} + 372 q^{75} + 304 q^{76} - 448 q^{77} - 96 q^{78} - 2320 q^{79} + 160 q^{80} + 324 q^{81} - 1136 q^{82} + 1318 q^{83} - 336 q^{84} - 1640 q^{85} - 696 q^{86} + 210 q^{87} - 512 q^{88} - 56 q^{89} - 180 q^{90} - 112 q^{91} + 256 q^{92} - 84 q^{93} - 1772 q^{94} + 190 q^{95} - 384 q^{96} - 504 q^{97} - 392 q^{98} + 576 q^{99}+O(q^{100}) \) 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 + 64 * q^11 + 48 * q^12 + 16 * q^13 + 56 * q^14 + 30 * q^15 + 64 * q^16 - 78 * q^17 - 72 * q^18 + 76 * q^19 + 40 * q^20 - 84 * q^21 - 128 * q^22 + 64 * q^23 - 96 * q^24 + 124 * q^25 - 32 * q^26 + 108 * q^27 - 112 * q^28 + 70 * q^29 - 60 * q^30 - 28 * q^31 - 128 * q^32 + 192 * q^33 + 156 * q^34 - 70 * q^35 + 144 * q^36 + 224 * q^37 - 152 * q^38 + 48 * q^39 - 80 * q^40 + 568 * q^41 + 168 * q^42 + 348 * q^43 + 256 * q^44 + 90 * q^45 - 128 * q^46 + 886 * q^47 + 192 * q^48 + 196 * q^49 - 248 * q^50 - 234 * q^51 + 64 * q^52 + 382 * q^53 - 216 * q^54 + 1232 * q^55 + 224 * q^56 + 228 * q^57 - 140 * q^58 + 552 * q^59 + 120 * q^60 - 744 * q^61 + 56 * q^62 - 252 * q^63 + 256 * q^64 + 1288 * q^65 - 384 * q^66 + 92 * q^67 - 312 * q^68 + 192 * q^69 + 140 * q^70 + 1154 * q^71 - 288 * q^72 + 508 * q^73 - 448 * q^74 + 372 * q^75 + 304 * q^76 - 448 * q^77 - 96 * q^78 - 2320 * q^79 + 160 * q^80 + 324 * q^81 - 1136 * q^82 + 1318 * q^83 - 336 * q^84 - 1640 * q^85 - 696 * q^86 + 210 * q^87 - 512 * q^88 - 56 * q^89 - 180 * q^90 - 112 * q^91 + 256 * q^92 - 84 * q^93 - 1772 * q^94 + 190 * q^95 - 384 * q^96 - 504 * q^97 - 392 * q^98 + 576 * q^99

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