LMFDB - Embedded newform 798.4.a.m.1.2

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:	$1$
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} - 84x^{2} - 9x + 1321 $ x^4 - x^3 - 84x^2 - 9x + 1321
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$4.28191$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -10.5638 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -10.5638 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +21.1276 q^{10} +68.6581 q^{11} +12.0000 q^{12} -43.1667 q^{13} +14.0000 q^{14} -31.6914 q^{15} +16.0000 q^{16} -47.5963 q^{17} -18.0000 q^{18} -19.0000 q^{19} -42.2553 q^{20} -21.0000 q^{21} -137.316 q^{22} -25.5800 q^{23} -24.0000 q^{24} -13.4058 q^{25} +86.3333 q^{26} +27.0000 q^{27} -28.0000 q^{28} +123.651 q^{29} +63.3829 q^{30} +336.793 q^{31} -32.0000 q^{32} +205.974 q^{33} +95.1925 q^{34} +73.9467 q^{35} +36.0000 q^{36} +144.040 q^{37} +38.0000 q^{38} -129.500 q^{39} +84.5105 q^{40} -150.126 q^{41} +42.0000 q^{42} -411.242 q^{43} +274.633 q^{44} -95.0743 q^{45} +51.1600 q^{46} -493.245 q^{47} +48.0000 q^{48} +49.0000 q^{49} +26.8116 q^{50} -142.789 q^{51} -172.667 q^{52} -335.887 q^{53} -54.0000 q^{54} -725.292 q^{55} +56.0000 q^{56} -57.0000 q^{57} -247.301 q^{58} -848.785 q^{59} -126.766 q^{60} +811.045 q^{61} -673.585 q^{62} -63.0000 q^{63} +64.0000 q^{64} +456.005 q^{65} -411.949 q^{66} +540.594 q^{67} -190.385 q^{68} -76.7401 q^{69} -147.893 q^{70} -102.658 q^{71} -72.0000 q^{72} +245.807 q^{73} -288.080 q^{74} -40.2174 q^{75} -76.0000 q^{76} -480.607 q^{77} +259.000 q^{78} +288.231 q^{79} -169.021 q^{80} +81.0000 q^{81} +300.251 q^{82} -1018.71 q^{83} -84.0000 q^{84} +502.798 q^{85} +822.484 q^{86} +370.952 q^{87} -549.265 q^{88} -281.138 q^{89} +190.149 q^{90} +302.167 q^{91} -102.320 q^{92} +1010.38 q^{93} +986.490 q^{94} +200.712 q^{95} -96.0000 q^{96} -1412.72 q^{97} -98.0000 q^{98} +617.923 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} - 10 q^{5} - 24 q^{6} - 28 q^{7} - 32 q^{8} + 36 q^{9} + 20 q^{10} + 4 q^{11} + 48 q^{12} + 16 q^{13} + 56 q^{14} - 30 q^{15} + 64 q^{16} - 66 q^{17} - 72 q^{18} - 76 q^{19} - 40 q^{20} - 84 q^{21} - 8 q^{22} + 32 q^{23} - 96 q^{24} + 200 q^{25} - 32 q^{26} + 108 q^{27} - 112 q^{28} - 10 q^{29} + 60 q^{30} + 108 q^{31} - 128 q^{32} + 12 q^{33} + 132 q^{34} + 70 q^{35} + 144 q^{36} - 116 q^{37} + 152 q^{38} + 48 q^{39} + 80 q^{40} - 988 q^{41} + 168 q^{42} - 448 q^{43} + 16 q^{44} - 90 q^{45} - 64 q^{46} - 850 q^{47} + 192 q^{48} + 196 q^{49} - 400 q^{50} - 198 q^{51} + 64 q^{52} - 998 q^{53} - 216 q^{54} - 904 q^{55} + 224 q^{56} - 228 q^{57} + 20 q^{58} - 680 q^{59} - 120 q^{60} - 208 q^{61} - 216 q^{62} - 252 q^{63} + 256 q^{64} - 676 q^{65} - 24 q^{66} + 108 q^{67} - 264 q^{68} + 96 q^{69} - 140 q^{70} - 1050 q^{71} - 288 q^{72} + 100 q^{73} + 232 q^{74} + 600 q^{75} - 304 q^{76} - 28 q^{77} - 96 q^{78} + 1540 q^{79} - 160 q^{80} + 324 q^{81} + 1976 q^{82} + 94 q^{83} - 336 q^{84} - 844 q^{85} + 896 q^{86} - 30 q^{87} - 32 q^{88} - 2284 q^{89} + 180 q^{90} - 112 q^{91} + 128 q^{92} + 324 q^{93} + 1700 q^{94} + 190 q^{95} - 384 q^{96} - 136 q^{97} - 392 q^{98} + 36 q^{99}+O(q^{100}) \) 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 + 4 * q^11 + 48 * q^12 + 16 * q^13 + 56 * q^14 - 30 * q^15 + 64 * q^16 - 66 * q^17 - 72 * q^18 - 76 * q^19 - 40 * q^20 - 84 * q^21 - 8 * q^22 + 32 * q^23 - 96 * q^24 + 200 * q^25 - 32 * q^26 + 108 * q^27 - 112 * q^28 - 10 * q^29 + 60 * q^30 + 108 * q^31 - 128 * q^32 + 12 * q^33 + 132 * q^34 + 70 * q^35 + 144 * q^36 - 116 * q^37 + 152 * q^38 + 48 * q^39 + 80 * q^40 - 988 * q^41 + 168 * q^42 - 448 * q^43 + 16 * q^44 - 90 * q^45 - 64 * q^46 - 850 * q^47 + 192 * q^48 + 196 * q^49 - 400 * q^50 - 198 * q^51 + 64 * q^52 - 998 * q^53 - 216 * q^54 - 904 * q^55 + 224 * q^56 - 228 * q^57 + 20 * q^58 - 680 * q^59 - 120 * q^60 - 208 * q^61 - 216 * q^62 - 252 * q^63 + 256 * q^64 - 676 * q^65 - 24 * q^66 + 108 * q^67 - 264 * q^68 + 96 * q^69 - 140 * q^70 - 1050 * q^71 - 288 * q^72 + 100 * q^73 + 232 * q^74 + 600 * q^75 - 304 * q^76 - 28 * q^77 - 96 * q^78 + 1540 * q^79 - 160 * q^80 + 324 * q^81 + 1976 * q^82 + 94 * q^83 - 336 * q^84 - 844 * q^85 + 896 * q^86 - 30 * q^87 - 32 * q^88 - 2284 * q^89 + 180 * q^90 - 112 * q^91 + 128 * q^92 + 324 * q^93 + 1700 * q^94 + 190 * q^95 - 384 * q^96 - 136 * q^97 - 392 * q^98 + 36 * 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
$5$	−10.5638	−0.944856	−0.472428	−	0.881369i	$-0.656622\pi$
$5$	−10.5638	−0.944856	−0.472428	+	0.881369i	$0.656622\pi$
$6$	−6.00000	−0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	21.1276	0.668114
$11$	68.6581	1.88193	0.940964	−	0.338507i	$-0.109922\pi$
$11$	68.6581	1.88193	0.940964	+	0.338507i	$0.109922\pi$
$12$	12.0000	0.288675
$13$	−43.1667	−0.920945	−0.460472	−	0.887674i	$-0.652320\pi$
$13$	−43.1667	−0.920945	−0.460472	+	0.887674i	$0.652320\pi$
$14$	14.0000	0.267261
$15$	−31.6914	−0.545513
$16$	16.0000	0.250000
$17$	−47.5963	−0.679047	−0.339523	−	0.940598i	$-0.610266\pi$
$17$	−47.5963	−0.679047	−0.339523	+	0.940598i	$0.610266\pi$
$18$	−18.0000	−0.235702
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−42.2553	−0.472428
$21$	−21.0000	−0.218218
$22$	−137.316	−1.33072
$23$	−25.5800	−0.231905	−0.115952	−	0.993255i	$-0.536992\pi$
$23$	−25.5800	−0.231905	−0.115952	+	0.993255i	$0.536992\pi$
$24$	−24.0000	−0.204124
$25$	−13.4058	−0.107246
$26$	86.3333	0.651206
$27$	27.0000	0.192450
$28$	−28.0000	−0.188982
$29$	123.651	0.791771	0.395886	−	0.918300i	$-0.370438\pi$
$29$	123.651	0.791771	0.395886	+	0.918300i	$0.370438\pi$
$30$	63.3829	0.385736
$31$	336.793	1.95128	0.975641	−	0.219373i	$-0.0704012\pi$
$31$	336.793	1.95128	0.975641	+	0.219373i	$0.0704012\pi$
$32$	−32.0000	−0.176777
$33$	205.974	1.08653
$34$	95.1925	0.480158
$35$	73.9467	0.357122
$36$	36.0000	0.166667
$37$	144.040	0.640001	0.320001	−	0.947417i	$-0.396317\pi$
$37$	144.040	0.640001	0.320001	+	0.947417i	$0.396317\pi$
$38$	38.0000	0.162221
$39$	−129.500	−0.531708
$40$	84.5105	0.334057
$41$	−150.126	−0.571846	−0.285923	−	0.958253i	$-0.592300\pi$
$41$	−150.126	−0.571846	−0.285923	+	0.958253i	$0.592300\pi$
$42$	42.0000	0.154303
$43$	−411.242	−1.45846	−0.729231	−	0.684268i	$-0.760122\pi$
$43$	−411.242	−1.45846	−0.729231	+	0.684268i	$0.760122\pi$
$44$	274.633	0.940964
$45$	−95.0743	−0.314952
$46$	51.1600	0.163981
$47$	−493.245	−1.53079	−0.765396	−	0.643560i	$-0.777457\pi$
$47$	−493.245	−1.53079	−0.765396	+	0.643560i	$0.777457\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	26.8116	0.0758347
$51$	−142.789	−0.392048
$52$	−172.667	−0.460472
$53$	−335.887	−0.870521	−0.435261	−	0.900305i	$-0.643344\pi$
$53$	−335.887	−0.870521	−0.435261	+	0.900305i	$0.643344\pi$
$54$	−54.0000	−0.136083
$55$	−725.292	−1.77815
$56$	56.0000	0.133631
$57$	−57.0000	−0.132453
$58$	−247.301	−0.559867
$59$	−848.785	−1.87292	−0.936461	−	0.350772i	$-0.885919\pi$
$59$	−848.785	−1.87292	−0.936461	+	0.350772i	$0.885919\pi$
$60$	−126.766	−0.272757
$61$	811.045	1.70235	0.851177	−	0.524878i	$-0.175889\pi$
$61$	811.045	1.70235	0.851177	+	0.524878i	$0.175889\pi$
$62$	−673.585	−1.37976
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	456.005	0.870160
$66$	−411.949	−0.768294
$67$	540.594	0.985732	0.492866	−	0.870105i	$-0.335949\pi$
$67$	540.594	0.985732	0.492866	+	0.870105i	$0.335949\pi$
$68$	−190.385	−0.339523
$69$	−76.7401	−0.133890
$70$	−147.893	−0.252523
$71$	−102.658	−0.171595	−0.0857974	−	0.996313i	$-0.527344\pi$
$71$	−102.658	−0.171595	−0.0857974	+	0.996313i	$0.527344\pi$
$72$	−72.0000	−0.117851
$73$	245.807	0.394104	0.197052	−	0.980393i	$-0.436863\pi$
$73$	245.807	0.394104	0.197052	+	0.980393i	$0.436863\pi$
$74$	−288.080	−0.452549
$75$	−40.2174	−0.0619187
$76$	−76.0000	−0.114708
$77$	−480.607	−0.711302
$78$	259.000	0.375974
$79$	288.231	0.410488	0.205244	−	0.978711i	$-0.434201\pi$
$79$	288.231	0.410488	0.205244	+	0.978711i	$0.434201\pi$
$80$	−169.021	−0.236214
$81$	81.0000	0.111111
$82$	300.251	0.404356
$83$	−1018.71	−1.34720	−0.673601	−	0.739095i	$-0.735253\pi$
$83$	−1018.71	−1.34720	−0.673601	+	0.739095i	$0.735253\pi$
$84$	−84.0000	−0.109109
$85$	502.798	0.641601
$86$	822.484	1.03129
$87$	370.952	0.457129
$88$	−549.265	−0.665362
$89$	−281.138	−0.334838	−0.167419	−	0.985886i	$-0.553543\pi$
$89$	−281.138	−0.334838	−0.167419	+	0.985886i	$0.553543\pi$
$90$	190.149	0.222705
$91$	302.167	0.348084
$92$	−102.320	−0.115952
$93$	1010.38	1.12657
$94$	986.490	1.08243
$95$	200.712	0.216765
$96$	−96.0000	−0.102062
$97$	−1412.72	−1.47876	−0.739382	−	0.673286i	$-0.764882\pi$
$97$	−1412.72	−1.47876	−0.739382	+	0.673286i	$0.764882\pi$
$98$	−98.0000	−0.101015
$99$	617.923	0.627309
$100$	−53.6232	−0.0536232
$101$	−1715.83	−1.69041	−0.845206	−	0.534441i	$-0.820522\pi$
$101$	−1715.83	−1.69041	−0.845206	+	0.534441i	$0.820522\pi$
$102$	285.578	0.277220
$103$	−853.744	−0.816718	−0.408359	−	0.912822i	$-0.633899\pi$
$103$	−853.744	−0.816718	−0.408359	+	0.912822i	$0.633899\pi$
$104$	345.333	0.325603
$105$	221.840	0.206185
$106$	671.774	0.615551
$107$	−790.192	−0.713932	−0.356966	−	0.934117i	$-0.616189\pi$
$107$	−790.192	−0.713932	−0.356966	+	0.934117i	$0.616189\pi$
$108$	108.000	0.0962250
$109$	−643.308	−0.565301	−0.282650	−	0.959223i	$-0.591214\pi$
$109$	−643.308	−0.565301	−0.282650	+	0.959223i	$0.591214\pi$
$110$	1450.58	1.25734
$111$	432.120	0.369505
$112$	−112.000	−0.0944911
$113$	−1177.14	−0.979965	−0.489983	−	0.871732i	$-0.662997\pi$
$113$	−1177.14	−0.979965	−0.489983	+	0.871732i	$0.662997\pi$
$114$	114.000	0.0936586
$115$	270.223	0.219116
$116$	494.603	0.395886
$117$	−388.500	−0.306982
$118$	1697.57	1.32436
$119$	333.174	0.256655
$120$	253.532	0.192868
$121$	3382.94	2.54165
$122$	−1622.09	−1.20375
$123$	−450.377	−0.330156
$124$	1347.17	0.975641
$125$	1462.09	1.04619
$126$	126.000	0.0890871
$127$	−396.557	−0.277077	−0.138538	−	0.990357i	$-0.544240\pi$
$127$	−396.557	−0.277077	−0.138538	+	0.990357i	$0.544240\pi$
$128$	−128.000	−0.0883883
$129$	−1233.73	−0.842043
$130$	−912.009	−0.615296
$131$	−338.343	−0.225658	−0.112829	−	0.993614i	$-0.535991\pi$
$131$	−338.343	−0.225658	−0.112829	+	0.993614i	$0.535991\pi$
$132$	823.898	0.543266
$133$	133.000	0.0867110
$134$	−1081.19	−0.697018
$135$	−285.223	−0.181838
$136$	380.770	0.240079
$137$	−176.073	−0.109803	−0.0549014	−	0.998492i	$-0.517484\pi$
$137$	−176.073	−0.109803	−0.0549014	+	0.998492i	$0.517484\pi$
$138$	153.480	0.0946746
$139$	−1527.59	−0.932146	−0.466073	−	0.884746i	$-0.654332\pi$
$139$	−1527.59	−0.932146	−0.466073	+	0.884746i	$0.654332\pi$
$140$	295.787	0.178561
$141$	−1479.74	−0.883803
$142$	205.316	0.121336
$143$	−2963.74	−1.73315
$144$	144.000	0.0833333
$145$	−1306.22	−0.748110
$146$	−491.615	−0.278674
$147$	147.000	0.0824786
$148$	576.160	0.320001
$149$	620.478	0.341152	0.170576	−	0.985345i	$-0.445437\pi$
$149$	620.478	0.341152	0.170576	+	0.985345i	$0.445437\pi$
$150$	80.4348	0.0437832
$151$	−572.814	−0.308708	−0.154354	−	0.988016i	$-0.549330\pi$
$151$	−572.814	−0.308708	−0.154354	+	0.988016i	$0.549330\pi$
$152$	152.000	0.0811107
$153$	−428.366	−0.226349
$154$	961.214	0.502966
$155$	−3557.82	−1.84368
$156$	−518.000	−0.265854
$157$	−622.463	−0.316420	−0.158210	−	0.987405i	$-0.550572\pi$
$157$	−622.463	−0.316420	−0.158210	+	0.987405i	$0.550572\pi$
$158$	−576.462	−0.290259
$159$	−1007.66	−0.502596
$160$	338.042	0.167029
$161$	179.060	0.0876517
$162$	−162.000	−0.0785674
$163$	−3101.57	−1.49039	−0.745197	−	0.666845i	$-0.767644\pi$
$163$	−3101.57	−1.49039	−0.745197	+	0.666845i	$0.767644\pi$
$164$	−600.503	−0.285923
$165$	−2175.88	−1.02662
$166$	2037.42	0.952616
$167$	1314.57	0.609128	0.304564	−	0.952492i	$-0.401489\pi$
$167$	1314.57	0.609128	0.304564	+	0.952492i	$0.401489\pi$
$168$	168.000	0.0771517
$169$	−333.639	−0.151861
$170$	−1005.60	−0.453681
$171$	−171.000	−0.0764719
$172$	−1644.97	−0.729231
$173$	−1390.14	−0.610927	−0.305463	−	0.952204i	$-0.598811\pi$
$173$	−1390.14	−0.610927	−0.305463	+	0.952204i	$0.598811\pi$
$174$	−741.904	−0.323239
$175$	93.8406	0.0405353
$176$	1098.53	0.470482
$177$	−2546.35	−1.08133
$178$	562.277	0.236766
$179$	2436.64	1.01745	0.508723	−	0.860930i	$-0.330118\pi$
$179$	2436.64	1.01745	0.508723	+	0.860930i	$0.330118\pi$
$180$	−380.297	−0.157476
$181$	440.466	0.180882	0.0904408	−	0.995902i	$-0.471172\pi$
$181$	440.466	0.180882	0.0904408	+	0.995902i	$0.471172\pi$
$182$	−604.333	−0.246133
$183$	2433.13	0.982855
$184$	204.640	0.0819906
$185$	−1521.61	−0.604709
$186$	−2020.76	−0.796608
$187$	−3267.87	−1.27792
$188$	−1972.98	−0.765396
$189$	−189.000	−0.0727393
$190$	−401.425	−0.153276
$191$	−1888.25	−0.715335	−0.357667	−	0.933849i	$-0.616428\pi$
$191$	−1888.25	−0.715335	−0.357667	+	0.933849i	$0.616428\pi$
$192$	192.000	0.0721688
$193$	−2515.24	−0.938087	−0.469044	−	0.883175i	$-0.655401\pi$
$193$	−2515.24	−0.938087	−0.469044	+	0.883175i	$0.655401\pi$
$194$	2825.44	1.04564
$195$	1368.01	0.502387
$196$	196.000	0.0714286
$197$	1653.60	0.598040	0.299020	−	0.954247i	$-0.403340\pi$
$197$	1653.60	0.598040	0.299020	+	0.954247i	$0.403340\pi$
$198$	−1235.85	−0.443575
$199$	−5207.20	−1.85492	−0.927459	−	0.373925i	$-0.878012\pi$
$199$	−5207.20	−1.85492	−0.927459	+	0.373925i	$0.878012\pi$
$200$	107.246	0.0379173
$201$	1621.78	0.569113
$202$	3431.66	1.19530
$203$	−865.555	−0.299261
$204$	−571.155	−0.196024
$205$	1585.90	0.540312
$206$	1707.49	0.577507
$207$	−230.220	−0.0773015
$208$	−690.667	−0.230236
$209$	−1304.50	−0.431744
$210$	−443.680	−0.145795
$211$	−414.238	−0.135153	−0.0675766	−	0.997714i	$-0.521527\pi$
$211$	−414.238	−0.135153	−0.0675766	+	0.997714i	$0.521527\pi$
$212$	−1343.55	−0.435261
$213$	−307.973	−0.0990703
$214$	1580.38	0.504826
$215$	4344.29	1.37804
$216$	−216.000	−0.0680414
$217$	−2357.55	−0.737515
$218$	1286.62	0.399728
$219$	737.422	0.227536
$220$	−2901.17	−0.889076
$221$	2054.57	0.625364
$222$	−864.241	−0.261279
$223$	2063.07	0.619522	0.309761	−	0.950815i	$-0.399751\pi$
$223$	2063.07	0.619522	0.309761	+	0.950815i	$0.399751\pi$
$224$	224.000	0.0668153
$225$	−120.652	−0.0357488
$226$	2354.28	0.692940
$227$	−1145.64	−0.334973	−0.167486	−	0.985874i	$-0.553565\pi$
$227$	−1145.64	−0.334973	−0.167486	+	0.985874i	$0.553565\pi$
$228$	−228.000	−0.0662266
$229$	602.161	0.173764	0.0868820	−	0.996219i	$-0.472310\pi$
$229$	602.161	0.173764	0.0868820	+	0.996219i	$0.472310\pi$
$230$	−540.445	−0.154939
$231$	−1441.82	−0.410670
$232$	−989.206	−0.279933
$233$	1501.50	0.422173	0.211087	−	0.977467i	$-0.432300\pi$
$233$	1501.50	0.422173	0.211087	+	0.977467i	$0.432300\pi$
$234$	777.000	0.217069
$235$	5210.55	1.44638
$236$	−3395.14	−0.936461
$237$	864.694	0.236995
$238$	−666.348	−0.181483
$239$	4219.35	1.14195	0.570977	−	0.820966i	$-0.306565\pi$
$239$	4219.35	1.14195	0.570977	+	0.820966i	$0.306565\pi$
$240$	−507.063	−0.136378
$241$	5888.36	1.57387	0.786935	−	0.617036i	$-0.211667\pi$
$241$	5888.36	1.57387	0.786935	+	0.617036i	$0.211667\pi$
$242$	−6765.88	−1.79722
$243$	243.000	0.0641500
$244$	3244.18	0.851177
$245$	−517.627	−0.134979
$246$	900.754	0.233455
$247$	820.167	0.211279
$248$	−2694.34	−0.689882
$249$	−3056.12	−0.777807
$250$	−2924.19	−0.739767
$251$	−4526.66	−1.13833	−0.569164	−	0.822224i	$-0.692733\pi$
$251$	−4526.66	−1.13833	−0.569164	+	0.822224i	$0.692733\pi$
$252$	−252.000	−0.0629941
$253$	−1756.28	−0.436428
$254$	793.114	0.195923
$255$	1508.39	0.370429
$256$	256.000	0.0625000
$257$	−819.690	−0.198953	−0.0994763	−	0.995040i	$-0.531717\pi$
$257$	−819.690	−0.198953	−0.0994763	+	0.995040i	$0.531717\pi$
$258$	2467.45	0.595414
$259$	−1008.28	−0.241898
$260$	1824.02	0.435080
$261$	1112.86	0.263924
$262$	676.686	0.159564
$263$	2929.57	0.686864	0.343432	−	0.939178i	$-0.388411\pi$
$263$	2929.57	0.686864	0.343432	+	0.939178i	$0.388411\pi$
$264$	−1647.80	−0.384147
$265$	3548.25	0.822517
$266$	−266.000	−0.0613139
$267$	−843.415	−0.193319
$268$	2162.37	0.492866
$269$	−7646.10	−1.73305	−0.866526	−	0.499131i	$-0.833652\pi$
$269$	−7646.10	−1.73305	−0.866526	+	0.499131i	$0.833652\pi$
$270$	570.446	0.128579
$271$	−2665.78	−0.597545	−0.298772	−	0.954324i	$-0.596577\pi$
$271$	−2665.78	−0.597545	−0.298772	+	0.954324i	$0.596577\pi$
$272$	−761.540	−0.169762
$273$	906.500	0.200967
$274$	352.147	0.0776422
$275$	−920.417	−0.201830
$276$	−306.960	−0.0669451
$277$	1474.23	0.319776	0.159888	−	0.987135i	$-0.448887\pi$
$277$	1474.23	0.319776	0.159888	+	0.987135i	$0.448887\pi$
$278$	3055.17	0.659127
$279$	3031.13	0.650427
$280$	−591.574	−0.126262
$281$	−5307.92	−1.12685	−0.563424	−	0.826168i	$-0.690516\pi$
$281$	−5307.92	−1.12685	−0.563424	+	0.826168i	$0.690516\pi$
$282$	2959.47	0.624943
$283$	240.645	0.0505473	0.0252736	−	0.999681i	$-0.491954\pi$
$283$	240.645	0.0505473	0.0252736	+	0.999681i	$0.491954\pi$
$284$	−410.631	−0.0857974
$285$	602.137	0.125149
$286$	5927.49	1.22552
$287$	1050.88	0.216138
$288$	−288.000	−0.0589256
$289$	−2647.59	−0.538896
$290$	2612.45	0.528994
$291$	−4238.16	−0.853765
$292$	983.230	0.197052
$293$	779.511	0.155425	0.0777125	−	0.996976i	$-0.475238\pi$
$293$	779.511	0.155425	0.0777125	+	0.996976i	$0.475238\pi$
$294$	−294.000	−0.0583212
$295$	8966.41	1.76964
$296$	−1152.32	−0.226275
$297$	1853.77	0.362177
$298$	−1240.96	−0.241231
$299$	1104.20	0.213571
$300$	−160.870	−0.0309594
$301$	2878.69	0.551247
$302$	1145.63	0.218290
$303$	−5147.49	−0.975959
$304$	−304.000	−0.0573539
$305$	−8567.73	−1.60848
$306$	856.733	0.160053
$307$	−4808.10	−0.893853	−0.446926	−	0.894571i	$-0.647481\pi$
$307$	−4808.10	−0.893853	−0.446926	+	0.894571i	$0.647481\pi$
$308$	−1922.43	−0.355651
$309$	−2561.23	−0.471532
$310$	7115.63	1.30368
$311$	5843.82	1.06551	0.532754	−	0.846270i	$-0.321157\pi$
$311$	5843.82	1.06551	0.532754	+	0.846270i	$0.321157\pi$
$312$	1036.00	0.187987
$313$	7258.67	1.31081	0.655407	−	0.755276i	$-0.272497\pi$
$313$	7258.67	1.31081	0.655407	+	0.755276i	$0.272497\pi$
$314$	1244.93	0.223743
$315$	665.520	0.119041
$316$	1152.92	0.205244
$317$	−3623.96	−0.642089	−0.321044	−	0.947064i	$-0.604034\pi$
$317$	−3623.96	−0.642089	−0.321044	+	0.947064i	$0.604034\pi$
$318$	2015.32	0.355389
$319$	8489.63	1.49006
$320$	−676.084	−0.118107
$321$	−2370.58	−0.412189
$322$	−358.120	−0.0619791
$323$	904.329	0.155784
$324$	324.000	0.0555556
$325$	578.684	0.0987680
$326$	6203.15	1.05387
$327$	−1929.93	−0.326376
$328$	1201.01	0.202178
$329$	3452.72	0.578585
$330$	4351.75	0.725927
$331$	−2655.79	−0.441013	−0.220506	−	0.975386i	$-0.570771\pi$
$331$	−2655.79	−0.441013	−0.220506	+	0.975386i	$0.570771\pi$
$332$	−4074.83	−0.673601
$333$	1296.36	0.213334
$334$	−2629.14	−0.430719
$335$	−5710.73	−0.931375
$336$	−336.000	−0.0545545
$337$	11609.4	1.87658	0.938288	−	0.345856i	$-0.112411\pi$
$337$	11609.4	1.87658	0.938288	+	0.345856i	$0.112411\pi$
$338$	667.277	0.107382
$339$	−3531.42	−0.565783
$340$	2011.19	0.320801
$341$	23123.6	3.67217
$342$	342.000	0.0540738
$343$	−343.000	−0.0539949
$344$	3289.94	0.515644
$345$	810.668	0.126507
$346$	2780.28	0.431990
$347$	8183.51	1.26603	0.633017	−	0.774138i	$-0.281816\pi$
$347$	8183.51	1.26603	0.633017	+	0.774138i	$0.281816\pi$
$348$	1483.81	0.228565
$349$	8457.96	1.29726	0.648630	−	0.761103i	$-0.275342\pi$
$349$	8457.96	1.29726	0.648630	+	0.761103i	$0.275342\pi$
$350$	−187.681	−0.0286628
$351$	−1165.50	−0.177236
$352$	−2197.06	−0.332681
$353$	−12882.0	−1.94232	−0.971158	−	0.238438i	$-0.923365\pi$
$353$	−12882.0	−1.94232	−0.971158	+	0.238438i	$0.923365\pi$
$354$	5092.71	0.764617
$355$	1084.46	0.162133
$356$	−1124.55	−0.167419
$357$	999.522	0.148180
$358$	−4873.27	−0.719443
$359$	6728.55	0.989190	0.494595	−	0.869123i	$-0.335316\pi$
$359$	6728.55	0.989190	0.494595	+	0.869123i	$0.335316\pi$
$360$	760.595	0.111352
$361$	361.000	0.0526316
$362$	−880.932	−0.127903
$363$	10148.8	1.46742
$364$	1208.67	0.174042
$365$	−2596.66	−0.372372
$366$	−4866.27	−0.694983
$367$	−5872.63	−0.835282	−0.417641	−	0.908612i	$-0.637143\pi$
$367$	−5872.63	−0.835282	−0.417641	+	0.908612i	$0.637143\pi$
$368$	−409.280	−0.0579761
$369$	−1351.13	−0.190615
$370$	3043.23	0.427594
$371$	2351.21	0.329026
$372$	4041.51	0.563287
$373$	−2328.50	−0.323231	−0.161615	−	0.986854i	$-0.551670\pi$
$373$	−2328.50	−0.323231	−0.161615	+	0.986854i	$0.551670\pi$
$374$	6535.74	0.903624
$375$	4386.28	0.604017
$376$	3945.96	0.541217
$377$	−5337.59	−0.729177
$378$	378.000	0.0514344
$379$	−1351.84	−0.183217	−0.0916086	−	0.995795i	$-0.529201\pi$
$379$	−1351.84	−0.183217	−0.0916086	+	0.995795i	$0.529201\pi$
$380$	802.850	0.108382
$381$	−1189.67	−0.159970
$382$	3776.50	0.505818
$383$	9710.53	1.29552	0.647761	−	0.761844i	$-0.275706\pi$
$383$	9710.53	1.29552	0.647761	+	0.761844i	$0.275706\pi$
$384$	−384.000	−0.0510310
$385$	5077.04	0.672078
$386$	5030.48	0.663328
$387$	−3701.18	−0.486154
$388$	−5650.89	−0.739382
$389$	7061.39	0.920377	0.460189	−	0.887821i	$-0.347782\pi$
$389$	7061.39	0.920377	0.460189	+	0.887821i	$0.347782\pi$
$390$	−2736.03	−0.355241
$391$	1217.51	0.157474
$392$	−392.000	−0.0505076
$393$	−1015.03	−0.130284
$394$	−3307.19	−0.422878
$395$	−3044.82	−0.387852
$396$	2471.69	0.313655
$397$	12975.7	1.64038	0.820191	−	0.572089i	$-0.193867\pi$
$397$	12975.7	1.64038	0.820191	+	0.572089i	$0.193867\pi$
$398$	10414.4	1.31162
$399$	399.000	0.0500626
$400$	−214.493	−0.0268116
$401$	−10622.7	−1.32287	−0.661434	−	0.750003i	$-0.730052\pi$
$401$	−10622.7	−1.32287	−0.661434	+	0.750003i	$0.730052\pi$
$402$	−3243.56	−0.402423
$403$	−14538.2	−1.79702
$404$	−6863.32	−0.845206
$405$	−855.669	−0.104984
$406$	1731.11	0.211610
$407$	9889.53	1.20444
$408$	1142.31	0.138610
$409$	7692.57	0.930007	0.465004	−	0.885309i	$-0.346053\pi$
$409$	7692.57	0.930007	0.465004	+	0.885309i	$0.346053\pi$
$410$	−3171.80	−0.382059
$411$	−528.220	−0.0633946
$412$	−3414.98	−0.408359
$413$	5941.49	0.707898
$414$	460.440	0.0546604
$415$	10761.4	1.27291
$416$	1381.33	0.162802
$417$	−4582.76	−0.538175
$418$	2609.01	0.305289
$419$	−8487.75	−0.989627	−0.494814	−	0.868999i	$-0.664764\pi$
$419$	−8487.75	−0.989627	−0.494814	+	0.868999i	$0.664764\pi$
$420$	887.361	0.103092
$421$	−3370.98	−0.390241	−0.195120	−	0.980779i	$-0.562510\pi$
$421$	−3370.98	−0.390241	−0.195120	+	0.980779i	$0.562510\pi$
$422$	828.476	0.0955677
$423$	−4439.21	−0.510264
$424$	2687.10	0.307776
$425$	638.066	0.0728253
$426$	615.947	0.0700533
$427$	−5677.31	−0.643429
$428$	−3160.77	−0.356966
$429$	−8891.23	−1.00064
$430$	−8688.57	−0.974419
$431$	−3601.99	−0.402557	−0.201278	−	0.979534i	$-0.564510\pi$
$431$	−3601.99	−0.402557	−0.201278	+	0.979534i	$0.564510\pi$
$432$	432.000	0.0481125
$433$	4971.47	0.551763	0.275882	−	0.961192i	$-0.411030\pi$
$433$	4971.47	0.551763	0.275882	+	0.961192i	$0.411030\pi$
$434$	4715.10	0.521502
$435$	−3918.67	−0.431921
$436$	−2573.23	−0.282650
$437$	486.020	0.0532025
$438$	−1474.84	−0.160892
$439$	12827.5	1.39459	0.697294	−	0.716785i	$-0.254387\pi$
$439$	12827.5	1.39459	0.697294	+	0.716785i	$0.254387\pi$
$440$	5802.34	0.628672
$441$	441.000	0.0476190
$442$	−4109.14	−0.442199
$443$	−3768.26	−0.404143	−0.202072	−	0.979371i	$-0.564767\pi$
$443$	−3768.26	−0.404143	−0.202072	+	0.979371i	$0.564767\pi$
$444$	1728.48	0.184752
$445$	2969.89	0.316374
$446$	−4126.14	−0.438068
$447$	1861.44	0.196964
$448$	−448.000	−0.0472456
$449$	8995.36	0.945473	0.472736	−	0.881204i	$-0.343266\pi$
$449$	8995.36	0.945473	0.472736	+	0.881204i	$0.343266\pi$
$450$	241.304	0.0252782
$451$	−10307.3	−1.07617
$452$	−4708.56	−0.489983
$453$	−1718.44	−0.178233
$454$	2291.28	0.236861
$455$	−3192.03	−0.328890
$456$	456.000	0.0468293
$457$	6950.72	0.711468	0.355734	−	0.934587i	$-0.384231\pi$
$457$	6950.72	0.711468	0.355734	+	0.934587i	$0.384231\pi$
$458$	−1204.32	−0.122870
$459$	−1285.10	−0.130683
$460$	1080.89	0.109558
$461$	−2643.94	−0.267116	−0.133558	−	0.991041i	$-0.542640\pi$
$461$	−2643.94	−0.267116	−0.133558	+	0.991041i	$0.542640\pi$
$462$	2883.64	0.290388
$463$	10534.3	1.05739	0.528695	−	0.848812i	$-0.322682\pi$
$463$	10534.3	1.05739	0.528695	+	0.848812i	$0.322682\pi$
$464$	1978.41	0.197943
$465$	−10673.4	−1.06445
$466$	−3002.99	−0.298522
$467$	10665.6	1.05684	0.528419	−	0.848984i	$-0.322785\pi$
$467$	10665.6	1.05684	0.528419	+	0.848984i	$0.322785\pi$
$468$	−1554.00	−0.153491
$469$	−3784.16	−0.372572
$470$	−10421.1	−1.02274
$471$	−1867.39	−0.182685
$472$	6790.28	0.662178
$473$	−28235.1	−2.74472
$474$	−1729.39	−0.167581
$475$	254.710	0.0246040
$476$	1332.70	0.128328
$477$	−3022.98	−0.290174
$478$	−8438.70	−0.807483
$479$	−12408.9	−1.18367	−0.591834	−	0.806060i	$-0.701596\pi$
$479$	−12408.9	−1.18367	−0.591834	+	0.806060i	$0.701596\pi$
$480$	1014.13	0.0964340
$481$	−6217.73	−0.589406
$482$	−11776.7	−1.11289
$483$	537.180	0.0506057
$484$	13531.8	1.27083
$485$	14923.7	1.39722
$486$	−486.000	−0.0453609
$487$	10137.6	0.943280	0.471640	−	0.881791i	$-0.343662\pi$
$487$	10137.6	0.943280	0.471640	+	0.881791i	$0.343662\pi$
$488$	−6488.36	−0.601873
$489$	−9304.72	−0.860479
$490$	1035.25	0.0954449
$491$	−13578.6	−1.24805	−0.624026	−	0.781404i	$-0.714504\pi$
$491$	−13578.6	−1.24805	−0.624026	+	0.781404i	$0.714504\pi$
$492$	−1801.51	−0.165078
$493$	−5885.31	−0.537649
$494$	−1640.33	−0.149397
$495$	−6527.63	−0.592717
$496$	5388.68	0.487821
$497$	718.604	0.0648568
$498$	6112.25	0.549993
$499$	−6677.46	−0.599047	−0.299523	−	0.954089i	$-0.596828\pi$
$499$	−6677.46	−0.599047	−0.299523	+	0.954089i	$0.596828\pi$
$500$	5848.37	0.523094
$501$	3943.71	0.351680
$502$	9053.32	0.804919
$503$	8795.39	0.779656	0.389828	−	0.920888i	$-0.372534\pi$
$503$	8795.39	0.779656	0.389828	+	0.920888i	$0.372534\pi$
$504$	504.000	0.0445435
$505$	18125.7	1.59720
$506$	3512.55	0.308601
$507$	−1000.92	−0.0876770
$508$	−1586.23	−0.138538
$509$	11450.3	0.997100	0.498550	−	0.866861i	$-0.333866\pi$
$509$	11450.3	0.997100	0.498550	+	0.866861i	$0.333866\pi$
$510$	−3016.79	−0.261933
$511$	−1720.65	−0.148957
$512$	−512.000	−0.0441942
$513$	−513.000	−0.0441511
$514$	1639.38	0.140681
$515$	9018.80	0.771681
$516$	−4934.91	−0.421021
$517$	−33865.3	−2.88084
$518$	2016.56	0.171048
$519$	−4170.42	−0.352719
$520$	−3648.04	−0.307648
$521$	4258.15	0.358067	0.179033	−	0.983843i	$-0.442703\pi$
$521$	4258.15	0.358067	0.179033	+	0.983843i	$0.442703\pi$
$522$	−2225.71	−0.186622
$523$	−1702.02	−0.142302	−0.0711512	−	0.997466i	$-0.522667\pi$
$523$	−1702.02	−0.142302	−0.0711512	+	0.997466i	$0.522667\pi$
$524$	−1353.37	−0.112829
$525$	281.522	0.0234031
$526$	−5859.15	−0.485686
$527$	−16030.1	−1.32501
$528$	3295.59	0.271633
$529$	−11512.7	−0.946220
$530$	−7096.50	−0.581608
$531$	−7639.06	−0.624307
$532$	532.000	0.0433555
$533$	6480.43	0.526639
$534$	1686.83	0.136697
$535$	8347.44	0.674563
$536$	−4324.75	−0.348509
$537$	7309.91	0.587423
$538$	15292.2	1.22545
$539$	3364.25	0.268847
$540$	−1140.89	−0.0909188
$541$	1825.18	0.145047	0.0725236	−	0.997367i	$-0.476895\pi$
$541$	1825.18	0.145047	0.0725236	+	0.997367i	$0.476895\pi$
$542$	5331.56	0.422528
$543$	1321.40	0.104432
$544$	1523.08	0.120040
$545$	6795.79	0.534128
$546$	−1813.00	−0.142105
$547$	−11896.9	−0.929938	−0.464969	−	0.885327i	$-0.653934\pi$
$547$	−11896.9	−0.929938	−0.464969	+	0.885327i	$0.653934\pi$
$548$	−704.294	−0.0549014
$549$	7299.40	0.567451
$550$	1840.83	0.142715
$551$	−2349.36	−0.181645
$552$	613.921	0.0473373
$553$	−2017.62	−0.155150
$554$	−2948.46	−0.226115
$555$	−4564.84	−0.349129
$556$	−6110.35	−0.466073
$557$	20907.4	1.59044	0.795221	−	0.606320i	$-0.207355\pi$
$557$	20907.4	1.59044	0.795221	+	0.606320i	$0.207355\pi$
$558$	−6062.27	−0.459922
$559$	17752.0	1.34316
$560$	1183.15	0.0892805
$561$	−9803.61	−0.737806
$562$	10615.8	0.796801
$563$	5961.23	0.446245	0.223122	−	0.974790i	$-0.428375\pi$
$563$	5961.23	0.446245	0.223122	+	0.974790i	$0.428375\pi$
$564$	−5918.94	−0.441901
$565$	12435.1	0.925926
$566$	−481.291	−0.0357423
$567$	−567.000	−0.0419961
$568$	821.262	0.0606679
$569$	−21805.6	−1.60657	−0.803283	−	0.595597i	$-0.796915\pi$
$569$	−21805.6	−1.60657	−0.803283	+	0.595597i	$0.796915\pi$
$570$	−1204.27	−0.0884939
$571$	25334.5	1.85677	0.928385	−	0.371621i	$-0.121198\pi$
$571$	25334.5	1.85677	0.928385	+	0.371621i	$0.121198\pi$
$572$	−11855.0	−0.866576
$573$	−5664.75	−0.412999
$574$	−2101.76	−0.152832
$575$	342.921	0.0248709
$576$	576.000	0.0416667
$577$	16032.7	1.15676	0.578380	−	0.815768i	$-0.303685\pi$
$577$	16032.7	1.15676	0.578380	+	0.815768i	$0.303685\pi$
$578$	5295.19	0.381057
$579$	−7545.72	−0.541605
$580$	−5224.89	−0.374055
$581$	7130.96	0.509194
$582$	8476.33	0.603703
$583$	−23061.4	−1.63826
$584$	−1966.46	−0.139337
$585$	4104.04	0.290053
$586$	−1559.02	−0.109902
$587$	19842.2	1.39519	0.697593	−	0.716494i	$-0.254254\pi$
$587$	19842.2	1.39519	0.697593	+	0.716494i	$0.254254\pi$
$588$	588.000	0.0412393
$589$	−6399.06	−0.447655
$590$	−17932.8	−1.25133
$591$	4960.79	0.345279
$592$	2304.64	0.160000
$593$	−11811.7	−0.817958	−0.408979	−	0.912544i	$-0.634115\pi$
$593$	−11811.7	−0.817958	−0.408979	+	0.912544i	$0.634115\pi$
$594$	−3707.54	−0.256098
$595$	−3519.59	−0.242503
$596$	2481.91	0.170576
$597$	−15621.6	−1.07094
$598$	−2208.41	−0.151018
$599$	−22275.5	−1.51945	−0.759727	−	0.650242i	$-0.774668\pi$
$599$	−22275.5	−1.51945	−0.759727	+	0.650242i	$0.774668\pi$
$600$	321.739	0.0218916
$601$	−7473.17	−0.507216	−0.253608	−	0.967307i	$-0.581617\pi$
$601$	−7473.17	−0.507216	−0.253608	+	0.967307i	$0.581617\pi$
$602$	−5757.39	−0.389790
$603$	4865.34	0.328577
$604$	−2291.26	−0.154354
$605$	−35736.8	−2.40150
$606$	10295.0	0.690107
$607$	20047.3	1.34052	0.670259	−	0.742127i	$-0.266183\pi$
$607$	20047.3	1.34052	0.670259	+	0.742127i	$0.266183\pi$
$608$	608.000	0.0405554
$609$	−2596.66	−0.172779
$610$	17135.5	1.13737
$611$	21291.8	1.40977
$612$	−1713.47	−0.113174
$613$	9223.16	0.607700	0.303850	−	0.952720i	$-0.401728\pi$
$613$	9223.16	0.607700	0.303850	+	0.952720i	$0.401728\pi$
$614$	9616.20	0.632049
$615$	4757.70	0.311950
$616$	3844.86	0.251483
$617$	8403.06	0.548289	0.274145	−	0.961688i	$-0.411605\pi$
$617$	8403.06	0.548289	0.274145	+	0.961688i	$0.411605\pi$
$618$	5122.46	0.333424
$619$	−22489.3	−1.46029	−0.730147	−	0.683290i	$-0.760548\pi$
$619$	−22489.3	−1.46029	−0.730147	+	0.683290i	$0.760548\pi$
$620$	−14231.3	−0.921841
$621$	−690.661	−0.0446300
$622$	−11687.6	−0.753427
$623$	1967.97	0.126557
$624$	−2072.00	−0.132927
$625$	−13769.6	−0.881252
$626$	−14517.3	−0.926885
$627$	−3913.51	−0.249267
$628$	−2489.85	−0.158210
$629$	−6855.77	−0.434591
$630$	−1331.04	−0.0841745
$631$	−15801.9	−0.996930	−0.498465	−	0.866910i	$-0.666103\pi$
$631$	−15801.9	−0.996930	−0.498465	+	0.866910i	$0.666103\pi$
$632$	−2305.85	−0.145129
$633$	−1242.71	−0.0780307
$634$	7247.93	0.454025
$635$	4189.15	0.261798
$636$	−4030.64	−0.251298
$637$	−2115.17	−0.131564
$638$	−16979.3	−1.05363
$639$	−923.920	−0.0571983
$640$	1352.17	0.0835143
$641$	−10489.7	−0.646360	−0.323180	−	0.946338i	$-0.604752\pi$
$641$	−10489.7	−0.646360	−0.323180	+	0.946338i	$0.604752\pi$
$642$	4741.15	0.291462
$643$	26148.5	1.60373	0.801863	−	0.597508i	$-0.203843\pi$
$643$	26148.5	1.60373	0.801863	+	0.597508i	$0.203843\pi$
$644$	716.241	0.0438258
$645$	13032.9	0.795610
$646$	−1808.66	−0.110156
$647$	8939.59	0.543201	0.271601	−	0.962410i	$-0.412447\pi$
$647$	8939.59	0.543201	0.271601	+	0.962410i	$0.412447\pi$
$648$	−648.000	−0.0392837
$649$	−58276.0	−3.52470
$650$	−1157.37	−0.0698395
$651$	−7072.65	−0.425805
$652$	−12406.3	−0.745197
$653$	−32038.1	−1.91998	−0.959992	−	0.280029i	$-0.909656\pi$
$653$	−32038.1	−1.91998	−0.959992	+	0.280029i	$0.909656\pi$
$654$	3859.85	0.230783
$655$	3574.19	0.213214
$656$	−2402.01	−0.142962
$657$	2212.27	0.131368
$658$	−6905.43	−0.409121
$659$	29168.9	1.72422	0.862109	−	0.506723i	$-0.169143\pi$
$659$	29168.9	1.72422	0.862109	+	0.506723i	$0.169143\pi$
$660$	−8703.50	−0.513308
$661$	−26990.0	−1.58819	−0.794093	−	0.607796i	$-0.792054\pi$
$661$	−26990.0	−1.58819	−0.794093	+	0.607796i	$0.792054\pi$
$662$	5311.57	0.311843
$663$	6163.72	0.361054
$664$	8149.67	0.476308
$665$	−1404.99	−0.0819294
$666$	−2592.72	−0.150850
$667$	−3162.99	−0.183615
$668$	5258.28	0.304564
$669$	6189.21	0.357681
$670$	11421.5	0.658582
$671$	55684.8	3.20371
$672$	672.000	0.0385758
$673$	−12629.5	−0.723374	−0.361687	−	0.932300i	$-0.617799\pi$
$673$	−12629.5	−0.723374	−0.361687	+	0.932300i	$0.617799\pi$
$674$	−23218.9	−1.32694
$675$	−361.957	−0.0206396
$676$	−1334.55	−0.0759305
$677$	9822.53	0.557623	0.278811	−	0.960346i	$-0.410060\pi$
$677$	9822.53	0.557623	0.278811	+	0.960346i	$0.410060\pi$
$678$	7062.84	0.400069
$679$	9889.05	0.558920
$680$	−4022.39	−0.226840
$681$	−3436.92	−0.193396
$682$	−46247.1	−2.59662
$683$	−19889.6	−1.11428	−0.557142	−	0.830418i	$-0.688102\pi$
$683$	−19889.6	−1.11428	−0.557142	+	0.830418i	$0.688102\pi$
$684$	−684.000	−0.0382360
$685$	1860.01	0.103748
$686$	686.000	0.0381802
$687$	1806.48	0.100323
$688$	−6579.87	−0.364615
$689$	14499.1	0.801702
$690$	−1621.34	−0.0894539
$691$	−25258.2	−1.39055	−0.695273	−	0.718746i	$-0.744716\pi$
$691$	−25258.2	−1.39055	−0.695273	+	0.718746i	$0.744716\pi$
$692$	−5560.56	−0.305463
$693$	−4325.46	−0.237101
$694$	−16367.0	−0.895222
$695$	16137.1	0.880744
$696$	−2967.62	−0.161620
$697$	7145.42	0.388310
$698$	−16915.9	−0.917302
$699$	4504.49	0.243742
$700$	375.362	0.0202677
$701$	34965.2	1.88390	0.941952	−	0.335746i	$-0.108988\pi$
$701$	34965.2	1.88390	0.941952	+	0.335746i	$0.108988\pi$
$702$	2331.00	0.125325
$703$	−2736.76	−0.146826
$704$	4394.12	0.235241
$705$	15631.7	0.835067
$706$	25763.9	1.37342
$707$	12010.8	0.638915
$708$	−10185.4	−0.540666
$709$	−2287.22	−0.121154	−0.0605770	−	0.998164i	$-0.519294\pi$
$709$	−2287.22	−0.121154	−0.0605770	+	0.998164i	$0.519294\pi$
$710$	−2168.92	−0.114645
$711$	2594.08	0.136829
$712$	2249.11	0.118383
$713$	−8615.16	−0.452511
$714$	−1999.04	−0.104779
$715$	31308.4	1.63758
$716$	9746.55	0.508723
$717$	12658.0	0.659307
$718$	−13457.1	−0.699463
$719$	−23394.2	−1.21343	−0.606715	−	0.794919i	$-0.707513\pi$
$719$	−23394.2	−1.21343	−0.606715	+	0.794919i	$0.707513\pi$
$720$	−1521.19	−0.0787380
$721$	5976.21	0.308690
$722$	−722.000	−0.0372161
$723$	17665.1	0.908674
$724$	1761.86	0.0904408
$725$	−1657.64	−0.0849146
$726$	−20297.6	−1.03763
$727$	−21562.7	−1.10002	−0.550012	−	0.835156i	$-0.685377\pi$
$727$	−21562.7	−1.10002	−0.550012	+	0.835156i	$0.685377\pi$
$728$	−2417.33	−0.123066
$729$	729.000	0.0370370
$730$	5193.33	0.263307
$731$	19573.6	0.990363
$732$	9732.53	0.491427
$733$	−27075.8	−1.36435	−0.682173	−	0.731191i	$-0.738965\pi$
$733$	−27075.8	−1.36435	−0.682173	+	0.731191i	$0.738965\pi$
$734$	11745.3	0.590634
$735$	−1552.88	−0.0779304
$736$	818.561	0.0409953
$737$	37116.2	1.85508
$738$	2702.26	0.134785
$739$	27290.9	1.35847	0.679236	−	0.733920i	$-0.262311\pi$
$739$	27290.9	1.35847	0.679236	+	0.733920i	$0.262311\pi$
$740$	−6086.45	−0.302355
$741$	2460.50	0.121982
$742$	−4702.42	−0.232657
$743$	−32536.6	−1.60653	−0.803265	−	0.595621i	$-0.796906\pi$
$743$	−32536.6	−1.60653	−0.803265	+	0.595621i	$0.796906\pi$
$744$	−8083.02	−0.398304
$745$	−6554.62	−0.322339
$746$	4656.99	0.228559
$747$	−9168.37	−0.449067
$748$	−13071.5	−0.638958
$749$	5531.34	0.269841
$750$	−8772.56	−0.427105
$751$	−20517.8	−0.996946	−0.498473	−	0.866905i	$-0.666106\pi$
$751$	−20517.8	−0.996946	−0.498473	+	0.866905i	$0.666106\pi$
$752$	−7891.92	−0.382698
$753$	−13580.0	−0.657214
$754$	10675.2	0.515606
$755$	6051.11	0.291685
$756$	−756.000	−0.0363696
$757$	35131.7	1.68677	0.843383	−	0.537313i	$-0.180561\pi$
$757$	35131.7	1.68677	0.843383	+	0.537313i	$0.180561\pi$
$758$	2703.68	0.129554
$759$	−5268.83	−0.251972
$760$	−1605.70	−0.0766380
$761$	−13875.9	−0.660975	−0.330488	−	0.943810i	$-0.607213\pi$
$761$	−13875.9	−0.660975	−0.330488	+	0.943810i	$0.607213\pi$
$762$	2379.34	0.113116
$763$	4503.16	0.213664
$764$	−7553.00	−0.357667
$765$	4525.18	0.213867
$766$	−19421.1	−0.916072
$767$	36639.2	1.72486
$768$	768.000	0.0360844
$769$	−17072.6	−0.800590	−0.400295	−	0.916386i	$-0.631092\pi$
$769$	−17072.6	−0.800590	−0.400295	+	0.916386i	$0.631092\pi$
$770$	−10154.1	−0.475231
$771$	−2459.07	−0.114865
$772$	−10061.0	−0.469044
$773$	−12584.6	−0.585556	−0.292778	−	0.956180i	$-0.594580\pi$
$773$	−12584.6	−0.585556	−0.292778	+	0.956180i	$0.594580\pi$
$774$	7402.36	0.343763
$775$	−4514.98	−0.209268
$776$	11301.8	0.522822
$777$	−3024.84	−0.139660
$778$	−14122.8	−0.650805
$779$	2852.39	0.131191
$780$	5472.06	0.251194
$781$	−7048.29	−0.322929
$782$	−2435.03	−0.111351
$783$	3338.57	0.152376
$784$	784.000	0.0357143
$785$	6575.58	0.298971
$786$	2030.06	0.0921244
$787$	176.226	0.00798194	0.00399097	−	0.999992i	$-0.498730\pi$
$787$	176.226	0.00798194	0.00399097	+	0.999992i	$0.498730\pi$
$788$	6614.39	0.299020
$789$	8788.72	0.396561
$790$	6089.64	0.274253
$791$	8239.98	0.370392
$792$	−4943.39	−0.221787
$793$	−35010.1	−1.56777
$794$	−25951.4	−1.15993
$795$	10644.7	0.474881
$796$	−20828.8	−0.927459
$797$	−27516.3	−1.22293	−0.611466	−	0.791271i	$-0.709420\pi$
$797$	−27516.3	−1.22293	−0.611466	+	0.791271i	$0.709420\pi$
$798$	−798.000	−0.0353996
$799$	23476.6	1.03948
$800$	428.986	0.0189587
$801$	−2530.25	−0.111613
$802$	21245.3	0.935410
$803$	16876.7	0.741675
$804$	6487.12	0.284556
$805$	−1891.56	−0.0828182
$806$	29076.4	1.27069
$807$	−22938.3	−1.00058
$808$	13726.6	0.597651
$809$	−7554.35	−0.328302	−0.164151	−	0.986435i	$-0.552489\pi$
$809$	−7554.35	−0.328302	−0.164151	+	0.986435i	$0.552489\pi$
$810$	1711.34	0.0742349
$811$	−6594.21	−0.285517	−0.142758	−	0.989758i	$-0.545597\pi$
$811$	−6594.21	−0.285517	−0.142758	+	0.989758i	$0.545597\pi$
$812$	−3462.22	−0.149631
$813$	−7997.34	−0.344992
$814$	−19779.1	−0.851665
$815$	32764.5	1.40821
$816$	−2284.62	−0.0980119
$817$	7813.60	0.334594
$818$	−15385.1	−0.657615
$819$	2719.50	0.116028
$820$	6343.60	0.270156
$821$	−23861.0	−1.01432	−0.507158	−	0.861853i	$-0.669304\pi$
$821$	−23861.0	−1.01432	−0.507158	+	0.861853i	$0.669304\pi$
$822$	1056.44	0.0448268
$823$	42234.5	1.78882	0.894411	−	0.447246i	$-0.147595\pi$
$823$	42234.5	1.78882	0.894411	+	0.447246i	$0.147595\pi$
$824$	6829.95	0.288753
$825$	−2761.25	−0.116527
$826$	−11883.0	−0.500559
$827$	8967.69	0.377070	0.188535	−	0.982066i	$-0.439626\pi$
$827$	8967.69	0.377070	0.188535	+	0.982066i	$0.439626\pi$
$828$	−920.881	−0.0386508
$829$	−13330.5	−0.558489	−0.279244	−	0.960220i	$-0.590084\pi$
$829$	−13330.5	−0.558489	−0.279244	+	0.960220i	$0.590084\pi$
$830$	−21522.9	−0.900085
$831$	4422.69	0.184622
$832$	−2762.67	−0.115118
$833$	−2332.22	−0.0970067
$834$	9165.52	0.380547
$835$	−13886.9	−0.575539
$836$	−5218.02	−0.215872
$837$	9093.40	0.375524
$838$	16975.5	0.699772
$839$	7760.86	0.319350	0.159675	−	0.987170i	$-0.448955\pi$
$839$	7760.86	0.319350	0.159675	+	0.987170i	$0.448955\pi$
$840$	−1774.72	−0.0728973
$841$	−9099.50	−0.373099
$842$	6741.96	0.275942
$843$	−15923.8	−0.650586
$844$	−1656.95	−0.0675766
$845$	3524.50	0.143487
$846$	8878.41	0.360811
$847$	−23680.6	−0.960655
$848$	−5374.19	−0.217630
$849$	721.936	0.0291835
$850$	−1276.13	−0.0514953
$851$	−3684.55	−0.148419
$852$	−1231.89	−0.0495352
$853$	10347.4	0.415345	0.207673	−	0.978198i	$-0.433411\pi$
$853$	10347.4	0.415345	0.207673	+	0.978198i	$0.433411\pi$
$854$	11354.6	0.454973
$855$	1806.41	0.0722550
$856$	6321.54	0.252413
$857$	19499.5	0.777236	0.388618	−	0.921399i	$-0.372953\pi$
$857$	19499.5	0.777236	0.388618	+	0.921399i	$0.372953\pi$
$858$	17782.5	0.707556
$859$	−30814.0	−1.22393	−0.611967	−	0.790883i	$-0.709622\pi$
$859$	−30814.0	−1.22393	−0.611967	+	0.790883i	$0.709622\pi$
$860$	17377.1	0.689018
$861$	3152.64	0.124787
$862$	7203.98	0.284650
$863$	11919.7	0.470166	0.235083	−	0.971975i	$-0.424464\pi$
$863$	11919.7	0.470166	0.235083	+	0.971975i	$0.424464\pi$
$864$	−864.000	−0.0340207
$865$	14685.2	0.577238
$866$	−9942.93	−0.390155
$867$	−7942.78	−0.311132
$868$	−9430.19	−0.368758
$869$	19789.4	0.772509
$870$	7837.34	0.305415
$871$	−23335.6	−0.907804
$872$	5146.47	0.199864
$873$	−12714.5	−0.492921
$874$	−972.041	−0.0376199
$875$	−10234.7	−0.395422
$876$	2949.69	0.113768
$877$	−38627.1	−1.48728	−0.743639	−	0.668581i	$-0.766902\pi$
$877$	−38627.1	−1.48728	−0.743639	+	0.668581i	$0.766902\pi$
$878$	−25655.0	−0.986122
$879$	2338.53	0.0897347
$880$	−11604.7	−0.444538
$881$	−40286.6	−1.54063	−0.770313	−	0.637666i	$-0.779900\pi$
$881$	−40286.6	−1.54063	−0.770313	+	0.637666i	$0.779900\pi$
$882$	−882.000	−0.0336718
$883$	48756.4	1.85819	0.929095	−	0.369840i	$-0.120588\pi$
$883$	48756.4	1.85819	0.929095	+	0.369840i	$0.120588\pi$
$884$	8218.29	0.312682
$885$	26899.2	1.02170
$886$	7536.52	0.285772
$887$	30581.9	1.15766	0.578828	−	0.815450i	$-0.303510\pi$
$887$	30581.9	1.15766	0.578828	+	0.815450i	$0.303510\pi$
$888$	−3456.96	−0.130640
$889$	2775.90	0.104725
$890$	−5939.79	−0.223710
$891$	5561.31	0.209103
$892$	8252.28	0.309761
$893$	9371.66	0.351188
$894$	−3722.87	−0.139275
$895$	−25740.2	−0.961340
$896$	896.000	0.0334077
$897$	3312.61	0.123305
$898$	−17990.7	−0.668550
$899$	41644.6	1.54497
$900$	−482.609	−0.0178744
$901$	15987.0	0.591124
$902$	20614.7	0.760969
$903$	8636.08	0.318262
$904$	9417.12	0.346470
$905$	−4653.00	−0.170907
$906$	3436.89	0.126030
$907$	25484.7	0.932973	0.466486	−	0.884528i	$-0.345520\pi$
$907$	25484.7	0.932973	0.466486	+	0.884528i	$0.345520\pi$
$908$	−4582.56	−0.167486
$909$	−15442.5	−0.563470
$910$	6384.07	0.232560
$911$	−7771.58	−0.282639	−0.141319	−	0.989964i	$-0.545134\pi$
$911$	−7771.58	−0.282639	−0.141319	+	0.989964i	$0.545134\pi$
$912$	−912.000	−0.0331133
$913$	−69942.6	−2.53534
$914$	−13901.4	−0.503084
$915$	−25703.2	−0.928657
$916$	2408.65	0.0868820
$917$	2368.40	0.0852906
$918$	2570.20	0.0924065
$919$	46116.7	1.65533	0.827666	−	0.561221i	$-0.189668\pi$
$919$	46116.7	1.65533	0.827666	+	0.561221i	$0.189668\pi$
$920$	−2161.78	−0.0774694
$921$	−14424.3	−0.516066
$922$	5287.88	0.188880
$923$	4431.39	0.158029
$924$	−5767.28	−0.205335
$925$	−1930.97	−0.0686378
$926$	−21068.6	−0.747687
$927$	−7683.70	−0.272239
$928$	−3956.82	−0.139967
$929$	−20828.1	−0.735573	−0.367786	−	0.929910i	$-0.619884\pi$
$929$	−20828.1	−0.735573	−0.367786	+	0.929910i	$0.619884\pi$
$930$	21346.9	0.752680
$931$	−931.000	−0.0327737
$932$	6005.99	0.211087
$933$	17531.5	0.615171
$934$	−21331.1	−0.747298
$935$	34521.2	1.20745
$936$	3108.00	0.108534
$937$	26349.1	0.918663	0.459331	−	0.888265i	$-0.348089\pi$
$937$	26349.1	0.918663	0.459331	+	0.888265i	$0.348089\pi$
$938$	7568.31	0.263448
$939$	21776.0	0.756798
$940$	20842.2	0.723189
$941$	−48724.6	−1.68797	−0.843983	−	0.536370i	$-0.819795\pi$
$941$	−48724.6	−1.68797	−0.843983	+	0.536370i	$0.819795\pi$
$942$	3734.78	0.129178
$943$	3840.22	0.132614
$944$	−13580.6	−0.468230
$945$	1996.56	0.0687282
$946$	56470.2	1.94081
$947$	20644.6	0.708404	0.354202	−	0.935169i	$-0.384753\pi$
$947$	20644.6	0.708404	0.354202	+	0.935169i	$0.384753\pi$
$948$	3458.77	0.118498
$949$	−10610.7	−0.362948
$950$	−509.420	−0.0173977
$951$	−10871.9	−0.370710
$952$	−2665.39	−0.0907414
$953$	−52008.0	−1.76779	−0.883895	−	0.467686i	$-0.845088\pi$
$953$	−52008.0	−1.76779	−0.883895	+	0.467686i	$0.845088\pi$
$954$	6045.97	0.205184
$955$	19947.1	0.675889
$956$	16877.4	0.570977
$957$	25468.9	0.860284
$958$	24817.8	0.836980
$959$	1232.51	0.0415015
$960$	−2028.25	−0.0681891
$961$	83638.3	2.80750
$962$	12435.5	0.416773
$963$	−7111.73	−0.237977
$964$	23553.4	0.786935
$965$	26570.5	0.886358
$966$	−1074.36	−0.0357836
$967$	−32070.9	−1.06652	−0.533262	−	0.845950i	$-0.679034\pi$
$967$	−32070.9	−1.06652	−0.533262	+	0.845950i	$0.679034\pi$
$968$	−27063.5	−0.898610
$969$	2712.99	0.0899419
$970$	−29847.5	−0.987984
$971$	7700.21	0.254492	0.127246	−	0.991871i	$-0.459386\pi$
$971$	7700.21	0.254492	0.127246	+	0.991871i	$0.459386\pi$
$972$	972.000	0.0320750
$973$	10693.1	0.352318
$974$	−20275.1	−0.667000
$975$	1736.05	0.0570237
$976$	12976.7	0.425589
$977$	−6175.10	−0.202210	−0.101105	−	0.994876i	$-0.532238\pi$
$977$	−6175.10	−0.202210	−0.101105	+	0.994876i	$0.532238\pi$
$978$	18609.4	0.608450
$979$	−19302.4	−0.630142
$980$	−2070.51	−0.0674897
$981$	−5789.78	−0.188434
$982$	27157.2	0.882506
$983$	−55187.2	−1.79064	−0.895320	−	0.445424i	$-0.853053\pi$
$983$	−55187.2	−1.79064	−0.895320	+	0.445424i	$0.853053\pi$
$984$	3603.02	0.116728
$985$	−17468.3	−0.565062
$986$	11770.6	0.380176
$987$	10358.1	0.334046
$988$	3280.67	0.105640
$989$	10519.6	0.338224
$990$	13055.3	0.419114
$991$	−4295.10	−0.137677	−0.0688386	−	0.997628i	$-0.521929\pi$
$991$	−4295.10	−0.137677	−0.0688386	+	0.997628i	$0.521929\pi$
$992$	−10777.4	−0.344941
$993$	−7967.36	−0.254619
$994$	−1437.21	−0.0458607
$995$	55007.9	1.75263
$996$	−12224.5	−0.388904
$997$	17207.7	0.546613	0.273306	−	0.961927i	$-0.411883\pi$
$997$	17207.7	0.546613	0.273306	+	0.961927i	$0.411883\pi$
$998$	13354.9	0.423590
$999$	3889.08	0.123168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.4.a.m.1.2	✓	4
3.2	odd	2		2394.4.a.y.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.4.a.m.1.2	✓	4	1.1	even	1	trivial
2394.4.a.y.1.3		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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -10.5638 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -10.5638 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +21.1276 q^{10} +68.6581 q^{11} +12.0000 q^{12} -43.1667 q^{13} +14.0000 q^{14} -31.6914 q^{15} +16.0000 q^{16} -47.5963 q^{17} -18.0000 q^{18} -19.0000 q^{19} -42.2553 q^{20} -21.0000 q^{21} -137.316 q^{22} -25.5800 q^{23} -24.0000 q^{24} -13.4058 q^{25} +86.3333 q^{26} +27.0000 q^{27} -28.0000 q^{28} +123.651 q^{29} +63.3829 q^{30} +336.793 q^{31} -32.0000 q^{32} +205.974 q^{33} +95.1925 q^{34} +73.9467 q^{35} +36.0000 q^{36} +144.040 q^{37} +38.0000 q^{38} -129.500 q^{39} +84.5105 q^{40} -150.126 q^{41} +42.0000 q^{42} -411.242 q^{43} +274.633 q^{44} -95.0743 q^{45} +51.1600 q^{46} -493.245 q^{47} +48.0000 q^{48} +49.0000 q^{49} +26.8116 q^{50} -142.789 q^{51} -172.667 q^{52} -335.887 q^{53} -54.0000 q^{54} -725.292 q^{55} +56.0000 q^{56} -57.0000 q^{57} -247.301 q^{58} -848.785 q^{59} -126.766 q^{60} +811.045 q^{61} -673.585 q^{62} -63.0000 q^{63} +64.0000 q^{64} +456.005 q^{65} -411.949 q^{66} +540.594 q^{67} -190.385 q^{68} -76.7401 q^{69} -147.893 q^{70} -102.658 q^{71} -72.0000 q^{72} +245.807 q^{73} -288.080 q^{74} -40.2174 q^{75} -76.0000 q^{76} -480.607 q^{77} +259.000 q^{78} +288.231 q^{79} -169.021 q^{80} +81.0000 q^{81} +300.251 q^{82} -1018.71 q^{83} -84.0000 q^{84} +502.798 q^{85} +822.484 q^{86} +370.952 q^{87} -549.265 q^{88} -281.138 q^{89} +190.149 q^{90} +302.167 q^{91} -102.320 q^{92} +1010.38 q^{93} +986.490 q^{94} +200.712 q^{95} -96.0000 q^{96} -1412.72 q^{97} -98.0000 q^{98} +617.923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} - 10 q^{5} - 24 q^{6} - 28 q^{7} - 32 q^{8} + 36 q^{9}+O(q^{10}) \) 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	\( 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} - 10 q^{5} - 24 q^{6} - 28 q^{7} - 32 q^{8} + 36 q^{9} + 20 q^{10} + 4 q^{11} + 48 q^{12} + 16 q^{13} + 56 q^{14} - 30 q^{15} + 64 q^{16} - 66 q^{17} - 72 q^{18} - 76 q^{19} - 40 q^{20} - 84 q^{21} - 8 q^{22} + 32 q^{23} - 96 q^{24} + 200 q^{25} - 32 q^{26} + 108 q^{27} - 112 q^{28} - 10 q^{29} + 60 q^{30} + 108 q^{31} - 128 q^{32} + 12 q^{33} + 132 q^{34} + 70 q^{35} + 144 q^{36} - 116 q^{37} + 152 q^{38} + 48 q^{39} + 80 q^{40} - 988 q^{41} + 168 q^{42} - 448 q^{43} + 16 q^{44} - 90 q^{45} - 64 q^{46} - 850 q^{47} + 192 q^{48} + 196 q^{49} - 400 q^{50} - 198 q^{51} + 64 q^{52} - 998 q^{53} - 216 q^{54} - 904 q^{55} + 224 q^{56} - 228 q^{57} + 20 q^{58} - 680 q^{59} - 120 q^{60} - 208 q^{61} - 216 q^{62} - 252 q^{63} + 256 q^{64} - 676 q^{65} - 24 q^{66} + 108 q^{67} - 264 q^{68} + 96 q^{69} - 140 q^{70} - 1050 q^{71} - 288 q^{72} + 100 q^{73} + 232 q^{74} + 600 q^{75} - 304 q^{76} - 28 q^{77} - 96 q^{78} + 1540 q^{79} - 160 q^{80} + 324 q^{81} + 1976 q^{82} + 94 q^{83} - 336 q^{84} - 844 q^{85} + 896 q^{86} - 30 q^{87} - 32 q^{88} - 2284 q^{89} + 180 q^{90} - 112 q^{91} + 128 q^{92} + 324 q^{93} + 1700 q^{94} + 190 q^{95} - 384 q^{96} - 136 q^{97} - 392 q^{98} + 36 q^{99}+O(q^{100}) \) 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 + 4 * q^11 + 48 * q^12 + 16 * q^13 + 56 * q^14 - 30 * q^15 + 64 * q^16 - 66 * q^17 - 72 * q^18 - 76 * q^19 - 40 * q^20 - 84 * q^21 - 8 * q^22 + 32 * q^23 - 96 * q^24 + 200 * q^25 - 32 * q^26 + 108 * q^27 - 112 * q^28 - 10 * q^29 + 60 * q^30 + 108 * q^31 - 128 * q^32 + 12 * q^33 + 132 * q^34 + 70 * q^35 + 144 * q^36 - 116 * q^37 + 152 * q^38 + 48 * q^39 + 80 * q^40 - 988 * q^41 + 168 * q^42 - 448 * q^43 + 16 * q^44 - 90 * q^45 - 64 * q^46 - 850 * q^47 + 192 * q^48 + 196 * q^49 - 400 * q^50 - 198 * q^51 + 64 * q^52 - 998 * q^53 - 216 * q^54 - 904 * q^55 + 224 * q^56 - 228 * q^57 + 20 * q^58 - 680 * q^59 - 120 * q^60 - 208 * q^61 - 216 * q^62 - 252 * q^63 + 256 * q^64 - 676 * q^65 - 24 * q^66 + 108 * q^67 - 264 * q^68 + 96 * q^69 - 140 * q^70 - 1050 * q^71 - 288 * q^72 + 100 * q^73 + 232 * q^74 + 600 * q^75 - 304 * q^76 - 28 * q^77 - 96 * q^78 + 1540 * q^79 - 160 * q^80 + 324 * q^81 + 1976 * q^82 + 94 * q^83 - 336 * q^84 - 844 * q^85 + 896 * q^86 - 30 * q^87 - 32 * q^88 - 2284 * q^89 + 180 * q^90 - 112 * q^91 + 128 * q^92 + 324 * q^93 + 1700 * q^94 + 190 * q^95 - 384 * q^96 - 136 * q^97 - 392 * q^98 + 36 * q^99

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