LMFDB - Embedded newform 798.4.a.l.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:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 94x^{2} + 2x + 1632 $ x^4 - 2x^3 - 94x^2 + 2*x + 1632
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$4.44228$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -4.88456 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -4.88456 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +9.76913 q^{10} +63.9398 q^{11} -12.0000 q^{12} +61.9693 q^{13} -14.0000 q^{14} +14.6537 q^{15} +16.0000 q^{16} +22.0400 q^{17} -18.0000 q^{18} +19.0000 q^{19} -19.5383 q^{20} -21.0000 q^{21} -127.880 q^{22} +22.9847 q^{23} +24.0000 q^{24} -101.141 q^{25} -123.939 q^{26} -27.0000 q^{27} +28.0000 q^{28} -110.484 q^{29} -29.3074 q^{30} -54.7242 q^{31} -32.0000 q^{32} -191.819 q^{33} -44.0800 q^{34} -34.1919 q^{35} +36.0000 q^{36} +286.413 q^{37} -38.0000 q^{38} -185.908 q^{39} +39.0765 q^{40} -56.8360 q^{41} +42.0000 q^{42} +299.456 q^{43} +255.759 q^{44} -43.9611 q^{45} -45.9695 q^{46} -54.7423 q^{47} -48.0000 q^{48} +49.0000 q^{49} +202.282 q^{50} -66.1199 q^{51} +247.877 q^{52} -620.715 q^{53} +54.0000 q^{54} -312.318 q^{55} -56.0000 q^{56} -57.0000 q^{57} +220.968 q^{58} +100.478 q^{59} +58.6148 q^{60} +560.411 q^{61} +109.448 q^{62} +63.0000 q^{63} +64.0000 q^{64} -302.693 q^{65} +383.639 q^{66} -208.034 q^{67} +88.1599 q^{68} -68.9542 q^{69} +68.3839 q^{70} -228.579 q^{71} -72.0000 q^{72} -259.831 q^{73} -572.825 q^{74} +303.423 q^{75} +76.0000 q^{76} +447.579 q^{77} +371.816 q^{78} +747.655 q^{79} -78.1530 q^{80} +81.0000 q^{81} +113.672 q^{82} +407.337 q^{83} -84.0000 q^{84} -107.656 q^{85} -598.912 q^{86} +331.452 q^{87} -511.519 q^{88} -442.968 q^{89} +87.9221 q^{90} +433.785 q^{91} +91.9389 q^{92} +164.173 q^{93} +109.485 q^{94} -92.8067 q^{95} +96.0000 q^{96} -591.250 q^{97} -98.0000 q^{98} +575.458 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} - 12 q^{3} + 16 q^{4} + 12 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 + 12 * q^5 + 24 * q^6 + 28 * q^7 - 32 * q^8 + 36 * q^9	\( 4 q - 8 q^{2} - 12 q^{3} + 16 q^{4} + 12 q^{5} + 24 q^{6} + 28 q^{7} - 32 q^{8} + 36 q^{9} - 24 q^{10} + 54 q^{11} - 48 q^{12} - 46 q^{13} - 56 q^{14} - 36 q^{15} + 64 q^{16} + 100 q^{17} - 72 q^{18} + 76 q^{19} + 48 q^{20} - 84 q^{21} - 108 q^{22} + 274 q^{23} + 96 q^{24} + 300 q^{25} + 92 q^{26} - 108 q^{27} + 112 q^{28} - 214 q^{29} + 72 q^{30} + 228 q^{31} - 128 q^{32} - 162 q^{33} - 200 q^{34} + 84 q^{35} + 144 q^{36} - 124 q^{37} - 152 q^{38} + 138 q^{39} - 96 q^{40} - 484 q^{41} + 168 q^{42} + 276 q^{43} + 216 q^{44} + 108 q^{45} - 548 q^{46} - 506 q^{47} - 192 q^{48} + 196 q^{49} - 600 q^{50} - 300 q^{51} - 184 q^{52} - 1002 q^{53} + 216 q^{54} + 8 q^{55} - 224 q^{56} - 228 q^{57} + 428 q^{58} - 808 q^{59} - 144 q^{60} - 72 q^{61} - 456 q^{62} + 252 q^{63} + 256 q^{64} + 616 q^{65} + 324 q^{66} + 138 q^{67} + 400 q^{68} - 822 q^{69} - 168 q^{70} - 654 q^{71} - 288 q^{72} + 2348 q^{73} + 248 q^{74} - 900 q^{75} + 304 q^{76} + 378 q^{77} - 276 q^{78} + 234 q^{79} + 192 q^{80} + 324 q^{81} + 968 q^{82} - 258 q^{83} - 336 q^{84} + 2696 q^{85} - 552 q^{86} + 642 q^{87} - 432 q^{88} - 1316 q^{89} - 216 q^{90} - 322 q^{91} + 1096 q^{92} - 684 q^{93} + 1012 q^{94} + 228 q^{95} + 384 q^{96} + 1166 q^{97} - 392 q^{98} + 486 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 12 * q^3 + 16 * q^4 + 12 * q^5 + 24 * q^6 + 28 * q^7 - 32 * q^8 + 36 * q^9 - 24 * q^10 + 54 * q^11 - 48 * q^12 - 46 * q^13 - 56 * q^14 - 36 * q^15 + 64 * q^16 + 100 * q^17 - 72 * q^18 + 76 * q^19 + 48 * q^20 - 84 * q^21 - 108 * q^22 + 274 * q^23 + 96 * q^24 + 300 * q^25 + 92 * q^26 - 108 * q^27 + 112 * q^28 - 214 * q^29 + 72 * q^30 + 228 * q^31 - 128 * q^32 - 162 * q^33 - 200 * q^34 + 84 * q^35 + 144 * q^36 - 124 * q^37 - 152 * q^38 + 138 * q^39 - 96 * q^40 - 484 * q^41 + 168 * q^42 + 276 * q^43 + 216 * q^44 + 108 * q^45 - 548 * q^46 - 506 * q^47 - 192 * q^48 + 196 * q^49 - 600 * q^50 - 300 * q^51 - 184 * q^52 - 1002 * q^53 + 216 * q^54 + 8 * q^55 - 224 * q^56 - 228 * q^57 + 428 * q^58 - 808 * q^59 - 144 * q^60 - 72 * q^61 - 456 * q^62 + 252 * q^63 + 256 * q^64 + 616 * q^65 + 324 * q^66 + 138 * q^67 + 400 * q^68 - 822 * q^69 - 168 * q^70 - 654 * q^71 - 288 * q^72 + 2348 * q^73 + 248 * q^74 - 900 * q^75 + 304 * q^76 + 378 * q^77 - 276 * q^78 + 234 * q^79 + 192 * q^80 + 324 * q^81 + 968 * q^82 - 258 * q^83 - 336 * q^84 + 2696 * q^85 - 552 * q^86 + 642 * q^87 - 432 * q^88 - 1316 * q^89 - 216 * q^90 - 322 * q^91 + 1096 * q^92 - 684 * q^93 + 1012 * q^94 + 228 * q^95 + 384 * q^96 + 1166 * q^97 - 392 * q^98 + 486 * 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
$5$	−4.88456	−0.436889	−0.218444	−	0.975849i	$-0.570098\pi$
$5$	−4.88456	−0.436889	−0.218444	+	0.975849i	$0.570098\pi$
$6$	6.00000	0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	9.76913	0.308927
$11$	63.9398	1.75260	0.876299	−	0.481768i	$-0.160005\pi$
$11$	63.9398	1.75260	0.876299	+	0.481768i	$0.160005\pi$
$12$	−12.0000	−0.288675
$13$	61.9693	1.32209	0.661046	−	0.750345i	$-0.270113\pi$
$13$	61.9693	1.32209	0.661046	+	0.750345i	$0.270113\pi$
$14$	−14.0000	−0.267261
$15$	14.6537	0.252238
$16$	16.0000	0.250000
$17$	22.0400	0.314440	0.157220	−	0.987564i	$-0.449747\pi$
$17$	22.0400	0.314440	0.157220	+	0.987564i	$0.449747\pi$
$18$	−18.0000	−0.235702
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	−19.5383	−0.218444
$21$	−21.0000	−0.218218
$22$	−127.880	−1.23927
$23$	22.9847	0.208376	0.104188	−	0.994558i	$-0.466776\pi$
$23$	22.9847	0.208376	0.104188	+	0.994558i	$0.466776\pi$
$24$	24.0000	0.204124
$25$	−101.141	−0.809128
$26$	−123.939	−0.934860
$27$	−27.0000	−0.192450
$28$	28.0000	0.188982
$29$	−110.484	−0.707461	−0.353731	−	0.935347i	$-0.615087\pi$
$29$	−110.484	−0.707461	−0.353731	+	0.935347i	$0.615087\pi$
$30$	−29.3074	−0.178359
$31$	−54.7242	−0.317057	−0.158528	−	0.987354i	$-0.550675\pi$
$31$	−54.7242	−0.317057	−0.158528	+	0.987354i	$0.550675\pi$
$32$	−32.0000	−0.176777
$33$	−191.819	−1.01186
$34$	−44.0800	−0.222343
$35$	−34.1919	−0.165128
$36$	36.0000	0.166667
$37$	286.413	1.27259	0.636296	−	0.771445i	$-0.280466\pi$
$37$	286.413	1.27259	0.636296	+	0.771445i	$0.280466\pi$
$38$	−38.0000	−0.162221
$39$	−185.908	−0.763310
$40$	39.0765	0.154463
$41$	−56.8360	−0.216495	−0.108248	−	0.994124i	$-0.534524\pi$
$41$	−56.8360	−0.216495	−0.108248	+	0.994124i	$0.534524\pi$
$42$	42.0000	0.154303
$43$	299.456	1.06201	0.531007	−	0.847367i	$-0.321814\pi$
$43$	299.456	1.06201	0.531007	+	0.847367i	$0.321814\pi$
$44$	255.759	0.876299
$45$	−43.9611	−0.145630
$46$	−45.9695	−0.147344
$47$	−54.7423	−0.169893	−0.0849467	−	0.996385i	$-0.527072\pi$
$47$	−54.7423	−0.169893	−0.0849467	+	0.996385i	$0.527072\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	202.282	0.572140
$51$	−66.1199	−0.181542
$52$	247.877	0.661046
$53$	−620.715	−1.60871	−0.804356	−	0.594148i	$-0.797489\pi$
$53$	−620.715	−1.60871	−0.804356	+	0.594148i	$0.797489\pi$
$54$	54.0000	0.136083
$55$	−312.318	−0.765690
$56$	−56.0000	−0.133631
$57$	−57.0000	−0.132453
$58$	220.968	0.500251
$59$	100.478	0.221714	0.110857	−	0.993836i	$-0.464640\pi$
$59$	100.478	0.221714	0.110857	+	0.993836i	$0.464640\pi$
$60$	58.6148	0.126119
$61$	560.411	1.17628	0.588142	−	0.808758i	$-0.299860\pi$
$61$	560.411	1.17628	0.588142	+	0.808758i	$0.299860\pi$
$62$	109.448	0.224193
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	−302.693	−0.577607
$66$	383.639	0.715495
$67$	−208.034	−0.379334	−0.189667	−	0.981848i	$-0.560741\pi$
$67$	−208.034	−0.379334	−0.189667	+	0.981848i	$0.560741\pi$
$68$	88.1599	0.157220
$69$	−68.9542	−0.120306
$70$	68.3839	0.116763
$71$	−228.579	−0.382075	−0.191038	−	0.981583i	$-0.561185\pi$
$71$	−228.579	−0.382075	−0.191038	+	0.981583i	$0.561185\pi$
$72$	−72.0000	−0.117851
$73$	−259.831	−0.416588	−0.208294	−	0.978066i	$-0.566791\pi$
$73$	−259.831	−0.416588	−0.208294	+	0.978066i	$0.566791\pi$
$74$	−572.825	−0.899859
$75$	303.423	0.467150
$76$	76.0000	0.114708
$77$	447.579	0.662420
$78$	371.816	0.539742
$79$	747.655	1.06478	0.532391	−	0.846499i	$-0.321294\pi$
$79$	747.655	1.06478	0.532391	+	0.846499i	$0.321294\pi$
$80$	−78.1530	−0.109222
$81$	81.0000	0.111111
$82$	113.672	0.153085
$83$	407.337	0.538687	0.269344	−	0.963044i	$-0.413193\pi$
$83$	407.337	0.538687	0.269344	+	0.963044i	$0.413193\pi$
$84$	−84.0000	−0.109109
$85$	−107.656	−0.137375
$86$	−598.912	−0.750957
$87$	331.452	0.408453
$88$	−511.519	−0.619637
$89$	−442.968	−0.527579	−0.263789	−	0.964580i	$-0.584972\pi$
$89$	−442.968	−0.527579	−0.263789	+	0.964580i	$0.584972\pi$
$90$	87.9221	0.102976
$91$	433.785	0.499704
$92$	91.9389	0.104188
$93$	164.173	0.183053
$94$	109.485	0.120133
$95$	−92.8067	−0.100229
$96$	96.0000	0.102062
$97$	−591.250	−0.618890	−0.309445	−	0.950917i	$-0.600143\pi$
$97$	−591.250	−0.618890	−0.309445	+	0.950917i	$0.600143\pi$
$98$	−98.0000	−0.101015
$99$	575.458	0.584199
$100$	−404.564	−0.404564
$101$	−766.264	−0.754912	−0.377456	−	0.926027i	$-0.623201\pi$
$101$	−766.264	−0.754912	−0.377456	+	0.926027i	$0.623201\pi$
$102$	132.240	0.128370
$103$	−816.233	−0.780833	−0.390417	−	0.920638i	$-0.627669\pi$
$103$	−816.233	−0.780833	−0.390417	+	0.920638i	$0.627669\pi$
$104$	−495.755	−0.467430
$105$	102.576	0.0953369
$106$	1241.43	1.13753
$107$	417.701	0.377389	0.188695	−	0.982036i	$-0.439574\pi$
$107$	417.701	0.377389	0.188695	+	0.982036i	$0.439574\pi$
$108$	−108.000	−0.0962250
$109$	2142.87	1.88303	0.941514	−	0.336974i	$-0.109403\pi$
$109$	2142.87	1.88303	0.941514	+	0.336974i	$0.109403\pi$
$110$	624.636	0.541425
$111$	−859.238	−0.734732
$112$	112.000	0.0944911
$113$	2092.09	1.74166	0.870830	−	0.491585i	$-0.163582\pi$
$113$	2092.09	1.74166	0.870830	+	0.491585i	$0.163582\pi$
$114$	114.000	0.0936586
$115$	−112.270	−0.0910371
$116$	−441.936	−0.353731
$117$	557.724	0.440697
$118$	−200.956	−0.156775
$119$	154.280	0.118847
$120$	−117.230	−0.0891795
$121$	2757.30	2.07160
$122$	−1120.82	−0.831758
$123$	170.508	0.124994
$124$	−218.897	−0.158528
$125$	1104.60	0.790388
$126$	−126.000	−0.0890871
$127$	285.917	0.199772	0.0998861	−	0.994999i	$-0.468152\pi$
$127$	285.917	0.199772	0.0998861	+	0.994999i	$0.468152\pi$
$128$	−128.000	−0.0883883
$129$	−898.368	−0.613154
$130$	605.386	0.408430
$131$	−1191.86	−0.794909	−0.397455	−	0.917622i	$-0.630106\pi$
$131$	−1191.86	−0.794909	−0.397455	+	0.917622i	$0.630106\pi$
$132$	−767.278	−0.505932
$133$	133.000	0.0867110
$134$	416.068	0.268230
$135$	131.883	0.0840792
$136$	−176.320	−0.111171
$137$	−1605.87	−1.00145	−0.500726	−	0.865606i	$-0.666933\pi$
$137$	−1605.87	−1.00145	−0.500726	+	0.865606i	$0.666933\pi$
$138$	137.908	0.0850691
$139$	2799.05	1.70800	0.854000	−	0.520273i	$-0.174170\pi$
$139$	2799.05	1.70800	0.854000	+	0.520273i	$0.174170\pi$
$140$	−136.768	−0.0825642
$141$	164.227	0.0980880
$142$	457.158	0.270168
$143$	3962.31	2.31710
$144$	144.000	0.0833333
$145$	539.666	0.309082
$146$	519.662	0.294572
$147$	−147.000	−0.0824786
$148$	1145.65	0.636296
$149$	−579.465	−0.318602	−0.159301	−	0.987230i	$-0.550924\pi$
$149$	−579.465	−0.318602	−0.159301	+	0.987230i	$0.550924\pi$
$150$	−606.846	−0.330325
$151$	276.397	0.148959	0.0744796	−	0.997223i	$-0.476270\pi$
$151$	276.397	0.148959	0.0744796	+	0.997223i	$0.476270\pi$
$152$	−152.000	−0.0811107
$153$	198.360	0.104813
$154$	−895.157	−0.468402
$155$	267.304	0.138518
$156$	−743.632	−0.381655
$157$	2308.17	1.17332	0.586662	−	0.809832i	$-0.300442\pi$
$157$	2308.17	1.17332	0.586662	+	0.809832i	$0.300442\pi$
$158$	−1495.31	−0.752914
$159$	1862.14	0.928790
$160$	156.306	0.0772317
$161$	160.893	0.0787587
$162$	−162.000	−0.0785674
$163$	3279.10	1.57570	0.787850	−	0.615867i	$-0.211194\pi$
$163$	3279.10	1.57570	0.787850	+	0.615867i	$0.211194\pi$
$164$	−227.344	−0.108248
$165$	936.954	0.442071
$166$	−814.674	−0.380909
$167$	1047.89	0.485556	0.242778	−	0.970082i	$-0.421941\pi$
$167$	1047.89	0.485556	0.242778	+	0.970082i	$0.421941\pi$
$168$	168.000	0.0771517
$169$	1643.20	0.747927
$170$	215.311	0.0971390
$171$	171.000	0.0764719
$172$	1197.82	0.531007
$173$	349.546	0.153616	0.0768078	−	0.997046i	$-0.475527\pi$
$173$	349.546	0.153616	0.0768078	+	0.997046i	$0.475527\pi$
$174$	−662.904	−0.288820
$175$	−707.987	−0.305822
$176$	1023.04	0.438150
$177$	−301.434	−0.128007
$178$	885.936	0.373055
$179$	−808.408	−0.337560	−0.168780	−	0.985654i	$-0.553983\pi$
$179$	−808.408	−0.337560	−0.168780	+	0.985654i	$0.553983\pi$
$180$	−175.844	−0.0728148
$181$	−4185.72	−1.71891	−0.859454	−	0.511212i	$-0.829197\pi$
$181$	−4185.72	−1.71891	−0.859454	+	0.511212i	$0.829197\pi$
$182$	−867.570	−0.353344
$183$	−1681.23	−0.679128
$184$	−183.878	−0.0736720
$185$	−1399.00	−0.555981
$186$	−328.345	−0.129438
$187$	1409.23	0.551087
$188$	−218.969	−0.0849467
$189$	−189.000	−0.0727393
$190$	185.613	0.0708727
$191$	−78.9476	−0.0299081	−0.0149541	−	0.999888i	$-0.504760\pi$
$191$	−78.9476	−0.0299081	−0.0149541	+	0.999888i	$0.504760\pi$
$192$	−192.000	−0.0721688
$193$	2618.12	0.976460	0.488230	−	0.872715i	$-0.337643\pi$
$193$	2618.12	0.976460	0.488230	+	0.872715i	$0.337643\pi$
$194$	1182.50	0.437622
$195$	908.079	0.333481
$196$	196.000	0.0714286
$197$	4155.03	1.50271	0.751355	−	0.659898i	$-0.229401\pi$
$197$	4155.03	1.50271	0.751355	+	0.659898i	$0.229401\pi$
$198$	−1150.92	−0.413091
$199$	−2913.91	−1.03800	−0.518999	−	0.854775i	$-0.673695\pi$
$199$	−2913.91	−1.03800	−0.518999	+	0.854775i	$0.673695\pi$
$200$	809.128	0.286070
$201$	624.102	0.219009
$202$	1532.53	0.533804
$203$	−773.388	−0.267395
$204$	−264.480	−0.0907710
$205$	277.619	0.0945842
$206$	1632.47	0.552133
$207$	206.863	0.0694587
$208$	991.509	0.330523
$209$	1214.86	0.402074
$210$	−205.152	−0.0674134
$211$	−2946.90	−0.961485	−0.480742	−	0.876862i	$-0.659633\pi$
$211$	−2946.90	−0.961485	−0.480742	+	0.876862i	$0.659633\pi$
$212$	−2482.86	−0.804356
$213$	685.737	0.220591
$214$	−835.401	−0.266854
$215$	−1462.71	−0.463982
$216$	216.000	0.0680414
$217$	−383.069	−0.119836
$218$	−4285.75	−1.33150
$219$	779.493	0.240517
$220$	−1249.27	−0.382845
$221$	1365.80	0.415719
$222$	1718.48	0.519534
$223$	679.626	0.204086	0.102043	−	0.994780i	$-0.467462\pi$
$223$	679.626	0.204086	0.102043	+	0.994780i	$0.467462\pi$
$224$	−224.000	−0.0668153
$225$	−910.269	−0.269709
$226$	−4184.19	−1.23154
$227$	−1341.85	−0.392343	−0.196172	−	0.980570i	$-0.562851\pi$
$227$	−1341.85	−0.392343	−0.196172	+	0.980570i	$0.562851\pi$
$228$	−228.000	−0.0662266
$229$	2626.56	0.757939	0.378969	−	0.925409i	$-0.376279\pi$
$229$	2626.56	0.757939	0.378969	+	0.925409i	$0.376279\pi$
$230$	224.541	0.0643729
$231$	−1342.74	−0.382448
$232$	883.872	0.250125
$233$	−1118.87	−0.314591	−0.157295	−	0.987552i	$-0.550277\pi$
$233$	−1118.87	−0.314591	−0.157295	+	0.987552i	$0.550277\pi$
$234$	−1115.45	−0.311620
$235$	267.392	0.0742245
$236$	401.912	0.110857
$237$	−2242.96	−0.614752
$238$	−308.560	−0.0840376
$239$	4083.58	1.10521	0.552604	−	0.833444i	$-0.313634\pi$
$239$	4083.58	1.10521	0.552604	+	0.833444i	$0.313634\pi$
$240$	234.459	0.0630594
$241$	−843.407	−0.225430	−0.112715	−	0.993627i	$-0.535955\pi$
$241$	−843.407	−0.225430	−0.112715	+	0.993627i	$0.535955\pi$
$242$	−5514.60	−1.46484
$243$	−243.000	−0.0641500
$244$	2241.64	0.588142
$245$	−239.344	−0.0624127
$246$	−341.016	−0.0883838
$247$	1177.42	0.303309
$248$	437.794	0.112096
$249$	−1222.01	−0.311011
$250$	−2209.20	−0.558888
$251$	2701.04	0.679235	0.339617	−	0.940564i	$-0.389702\pi$
$251$	2701.04	0.679235	0.339617	+	0.940564i	$0.389702\pi$
$252$	252.000	0.0629941
$253$	1469.64	0.365199
$254$	−571.835	−0.141260
$255$	322.967	0.0793136
$256$	256.000	0.0625000
$257$	−263.604	−0.0639812	−0.0319906	−	0.999488i	$-0.510185\pi$
$257$	−263.604	−0.0639812	−0.0319906	+	0.999488i	$0.510185\pi$
$258$	1796.74	0.433565
$259$	2004.89	0.480995
$260$	−1210.77	−0.288803
$261$	−994.356	−0.235820
$262$	2383.72	0.562086
$263$	6378.28	1.49544	0.747721	−	0.664013i	$-0.231148\pi$
$263$	6378.28	1.49544	0.747721	+	0.664013i	$0.231148\pi$
$264$	1534.56	0.357748
$265$	3031.92	0.702828
$266$	−266.000	−0.0613139
$267$	1328.90	0.304598
$268$	−832.136	−0.189667
$269$	−4629.74	−1.04937	−0.524685	−	0.851297i	$-0.675817\pi$
$269$	−4629.74	−1.04937	−0.524685	+	0.851297i	$0.675817\pi$
$270$	−263.766	−0.0594530
$271$	−7105.60	−1.59275	−0.796374	−	0.604805i	$-0.793251\pi$
$271$	−7105.60	−1.59275	−0.796374	+	0.604805i	$0.793251\pi$
$272$	352.640	0.0786100
$273$	−1301.36	−0.288504
$274$	3211.74	0.708133
$275$	−6466.94	−1.41808
$276$	−275.817	−0.0601530
$277$	6641.48	1.44061	0.720303	−	0.693660i	$-0.244003\pi$
$277$	6641.48	1.44061	0.720303	+	0.693660i	$0.244003\pi$
$278$	−5598.09	−1.20774
$279$	−492.518	−0.105686
$280$	273.536	0.0583817
$281$	2721.22	0.577703	0.288851	−	0.957374i	$-0.406727\pi$
$281$	2721.22	0.577703	0.288851	+	0.957374i	$0.406727\pi$
$282$	−328.454	−0.0693587
$283$	2208.57	0.463907	0.231953	−	0.972727i	$-0.425488\pi$
$283$	2208.57	0.463907	0.231953	+	0.972727i	$0.425488\pi$
$284$	−914.316	−0.191038
$285$	278.420	0.0578673
$286$	−7924.61	−1.63843
$287$	−397.852	−0.0818275
$288$	−288.000	−0.0589256
$289$	−4427.24	−0.901127
$290$	−1079.33	−0.218554
$291$	1773.75	0.357317
$292$	−1039.32	−0.208294
$293$	−5479.70	−1.09258	−0.546292	−	0.837595i	$-0.683961\pi$
$293$	−5479.70	−1.09258	−0.546292	+	0.837595i	$0.683961\pi$
$294$	294.000	0.0583212
$295$	−490.791	−0.0968642
$296$	−2291.30	−0.449929
$297$	−1726.37	−0.337288
$298$	1158.93	0.225285
$299$	1424.35	0.275492
$300$	1213.69	0.233575
$301$	2096.19	0.401404
$302$	−552.794	−0.105330
$303$	2298.79	0.435849
$304$	304.000	0.0573539
$305$	−2737.36	−0.513905
$306$	−396.720	−0.0741142
$307$	1651.24	0.306974	0.153487	−	0.988151i	$-0.450950\pi$
$307$	1651.24	0.306974	0.153487	+	0.988151i	$0.450950\pi$
$308$	1790.31	0.331210
$309$	2448.70	0.450814
$310$	−534.608	−0.0979473
$311$	−6004.18	−1.09474	−0.547372	−	0.836889i	$-0.684372\pi$
$311$	−6004.18	−1.09474	−0.547372	+	0.836889i	$0.684372\pi$
$312$	1487.26	0.269871
$313$	9821.06	1.77354	0.886772	−	0.462207i	$-0.152942\pi$
$313$	9821.06	1.77354	0.886772	+	0.462207i	$0.152942\pi$
$314$	−4616.33	−0.829665
$315$	−307.727	−0.0550428
$316$	2990.62	0.532391
$317$	312.554	0.0553778	0.0276889	−	0.999617i	$-0.491185\pi$
$317$	312.554	0.0553778	0.0276889	+	0.999617i	$0.491185\pi$
$318$	−3724.29	−0.656754
$319$	−7064.33	−1.23990
$320$	−312.612	−0.0546111
$321$	−1253.10	−0.217886
$322$	−321.786	−0.0556908
$323$	418.760	0.0721375
$324$	324.000	0.0555556
$325$	−6267.64	−1.06974
$326$	−6558.21	−1.11419
$327$	−6428.62	−1.08717
$328$	454.688	0.0765426
$329$	−383.196	−0.0642137
$330$	−1873.91	−0.312592
$331$	−10078.0	−1.67352	−0.836759	−	0.547572i	$-0.815552\pi$
$331$	−10078.0	−1.67352	−0.836759	+	0.547572i	$0.815552\pi$
$332$	1629.35	0.269344
$333$	2577.71	0.424198
$334$	−2095.77	−0.343340
$335$	1016.15	0.165727
$336$	−336.000	−0.0545545
$337$	11838.6	1.91363	0.956813	−	0.290705i	$-0.0938898\pi$
$337$	11838.6	1.91363	0.956813	+	0.290705i	$0.0938898\pi$
$338$	−3286.39	−0.528864
$339$	−6276.28	−1.00555
$340$	−430.623	−0.0686876
$341$	−3499.06	−0.555673
$342$	−342.000	−0.0540738
$343$	343.000	0.0539949
$344$	−2395.65	−0.375479
$345$	336.811	0.0525603
$346$	−699.092	−0.108623
$347$	−8872.60	−1.37264	−0.686320	−	0.727300i	$-0.740775\pi$
$347$	−8872.60	−1.37264	−0.686320	+	0.727300i	$0.740775\pi$
$348$	1325.81	0.204226
$349$	7675.51	1.17725	0.588626	−	0.808406i	$-0.299669\pi$
$349$	7675.51	1.17725	0.588626	+	0.808406i	$0.299669\pi$
$350$	1415.97	0.216249
$351$	−1673.17	−0.254437
$352$	−2046.07	−0.309819
$353$	−2583.59	−0.389549	−0.194774	−	0.980848i	$-0.562398\pi$
$353$	−2583.59	−0.389549	−0.194774	+	0.980848i	$0.562398\pi$
$354$	602.868	0.0905143
$355$	1116.51	0.166924
$356$	−1771.87	−0.263789
$357$	−462.840	−0.0686164
$358$	1616.82	0.238691
$359$	−3548.78	−0.521721	−0.260860	−	0.965377i	$-0.584006\pi$
$359$	−3548.78	−0.521721	−0.260860	+	0.965377i	$0.584006\pi$
$360$	351.689	0.0514878
$361$	361.000	0.0526316
$362$	8371.45	1.21545
$363$	−8271.90	−1.19604
$364$	1735.14	0.249852
$365$	1269.16	0.182003
$366$	3362.47	0.480216
$367$	−871.475	−0.123953	−0.0619763	−	0.998078i	$-0.519740\pi$
$367$	−871.475	−0.123953	−0.0619763	+	0.998078i	$0.519740\pi$
$368$	367.756	0.0520940
$369$	−511.524	−0.0721650
$370$	2798.00	0.393138
$371$	−4345.00	−0.608036
$372$	656.691	0.0915264
$373$	−2596.47	−0.360429	−0.180215	−	0.983627i	$-0.557679\pi$
$373$	−2596.47	−0.360429	−0.180215	+	0.983627i	$0.557679\pi$
$374$	−2818.46	−0.389677
$375$	−3313.80	−0.456330
$376$	437.939	0.0600664
$377$	−6846.62	−0.935329
$378$	378.000	0.0514344
$379$	−1268.21	−0.171883	−0.0859413	−	0.996300i	$-0.527390\pi$
$379$	−1268.21	−0.171883	−0.0859413	+	0.996300i	$0.527390\pi$
$380$	−371.227	−0.0501146
$381$	−857.752	−0.115339
$382$	157.895	0.0211482
$383$	−11924.6	−1.59090	−0.795452	−	0.606016i	$-0.792767\pi$
$383$	−11924.6	−1.59090	−0.795452	+	0.606016i	$0.792767\pi$
$384$	384.000	0.0510310
$385$	−2186.23	−0.289404
$386$	−5236.25	−0.690461
$387$	2695.10	0.354005
$388$	−2365.00	−0.309445
$389$	−4194.27	−0.546678	−0.273339	−	0.961918i	$-0.588128\pi$
$389$	−4194.27	−0.546678	−0.273339	+	0.961918i	$0.588128\pi$
$390$	−1816.16	−0.235807
$391$	506.583	0.0655217
$392$	−392.000	−0.0505076
$393$	3575.57	0.458941
$394$	−8310.07	−1.06258
$395$	−3651.97	−0.465191
$396$	2301.83	0.292100
$397$	9842.49	1.24428	0.622142	−	0.782905i	$-0.286263\pi$
$397$	9842.49	1.24428	0.622142	+	0.782905i	$0.286263\pi$
$398$	5827.82	0.733975
$399$	−399.000	−0.0500626
$400$	−1618.26	−0.202282
$401$	10796.0	1.34446	0.672228	−	0.740344i	$-0.265337\pi$
$401$	10796.0	1.34446	0.672228	+	0.740344i	$0.265337\pi$
$402$	−1248.20	−0.154863
$403$	−3391.22	−0.419178
$404$	−3065.06	−0.377456
$405$	−395.650	−0.0485432
$406$	1546.78	0.189077
$407$	18313.2	2.23034
$408$	528.960	0.0641848
$409$	−417.538	−0.0504791	−0.0252395	−	0.999681i	$-0.508035\pi$
$409$	−417.538	−0.0504791	−0.0252395	+	0.999681i	$0.508035\pi$
$410$	−555.238	−0.0668812
$411$	4817.61	0.578188
$412$	−3264.93	−0.390417
$413$	703.346	0.0837999
$414$	−413.725	−0.0491147
$415$	−1989.66	−0.235346
$416$	−1983.02	−0.233715
$417$	−8397.14	−0.986114
$418$	−2429.71	−0.284309
$419$	8057.15	0.939421	0.469710	−	0.882821i	$-0.344358\pi$
$419$	8057.15	0.939421	0.469710	+	0.882821i	$0.344358\pi$
$420$	410.303	0.0476685
$421$	3663.30	0.424081	0.212041	−	0.977261i	$-0.431989\pi$
$421$	3663.30	0.424081	0.212041	+	0.977261i	$0.431989\pi$
$422$	5893.81	0.679872
$423$	−492.681	−0.0566311
$424$	4965.72	0.568765
$425$	−2229.15	−0.254422
$426$	−1371.47	−0.155982
$427$	3922.88	0.444593
$428$	1670.80	0.188695
$429$	−11886.9	−1.33778
$430$	2925.42	0.328085
$431$	−2870.69	−0.320827	−0.160413	−	0.987050i	$-0.551283\pi$
$431$	−2870.69	−0.320827	−0.160413	+	0.987050i	$0.551283\pi$
$432$	−432.000	−0.0481125
$433$	−8472.29	−0.940306	−0.470153	−	0.882585i	$-0.655801\pi$
$433$	−8472.29	−0.940306	−0.470153	+	0.882585i	$0.655801\pi$
$434$	766.139	0.0847370
$435$	−1619.00	−0.178448
$436$	8571.49	0.941514
$437$	436.710	0.0478047
$438$	−1558.99	−0.170071
$439$	3955.11	0.429993	0.214997	−	0.976615i	$-0.431026\pi$
$439$	3955.11	0.429993	0.214997	+	0.976615i	$0.431026\pi$
$440$	2498.54	0.270712
$441$	441.000	0.0476190
$442$	−2731.60	−0.293957
$443$	−9342.81	−1.00201	−0.501005	−	0.865445i	$-0.667036\pi$
$443$	−9342.81	−1.00201	−0.501005	+	0.865445i	$0.667036\pi$
$444$	−3436.95	−0.367366
$445$	2163.71	0.230493
$446$	−1359.25	−0.144310
$447$	1738.40	0.183945
$448$	448.000	0.0472456
$449$	15120.4	1.58925	0.794626	−	0.607099i	$-0.207667\pi$
$449$	15120.4	1.58925	0.794626	+	0.607099i	$0.207667\pi$
$450$	1820.54	0.190713
$451$	−3634.09	−0.379429
$452$	8368.37	0.870830
$453$	−829.190	−0.0860017
$454$	2683.71	0.277429
$455$	−2118.85	−0.218315
$456$	456.000	0.0468293
$457$	4582.06	0.469014	0.234507	−	0.972114i	$-0.424652\pi$
$457$	4582.06	0.469014	0.234507	+	0.972114i	$0.424652\pi$
$458$	−5253.12	−0.535944
$459$	−595.079	−0.0605140
$460$	−449.081	−0.0455185
$461$	1938.29	0.195824	0.0979122	−	0.995195i	$-0.468784\pi$
$461$	1938.29	0.195824	0.0979122	+	0.995195i	$0.468784\pi$
$462$	2685.47	0.270432
$463$	−2641.05	−0.265097	−0.132549	−	0.991176i	$-0.542316\pi$
$463$	−2641.05	−0.265097	−0.132549	+	0.991176i	$0.542316\pi$
$464$	−1767.74	−0.176865
$465$	−801.912	−0.0799737
$466$	2237.74	0.222449
$467$	12632.8	1.25177	0.625884	−	0.779916i	$-0.284738\pi$
$467$	12632.8	1.25177	0.625884	+	0.779916i	$0.284738\pi$
$468$	2230.90	0.220349
$469$	−1456.24	−0.143375
$470$	−534.785	−0.0524846
$471$	−6924.50	−0.677419
$472$	−803.824	−0.0783877
$473$	19147.2	1.86128
$474$	4485.93	0.434695
$475$	−1921.68	−0.185627
$476$	617.119	0.0594236
$477$	−5586.43	−0.536237
$478$	−8167.16	−0.781500
$479$	−14093.1	−1.34432	−0.672162	−	0.740404i	$-0.734634\pi$
$479$	−14093.1	−1.34432	−0.672162	+	0.740404i	$0.734634\pi$
$480$	−468.918	−0.0445898
$481$	17748.8	1.68248
$482$	1686.81	0.159403
$483$	−482.679	−0.0454714
$484$	11029.2	1.03580
$485$	2888.00	0.270386
$486$	486.000	0.0453609
$487$	−17229.4	−1.60316	−0.801579	−	0.597889i	$-0.796006\pi$
$487$	−17229.4	−1.60316	−0.801579	+	0.597889i	$0.796006\pi$
$488$	−4483.29	−0.415879
$489$	−9837.31	−0.909731
$490$	478.687	0.0441324
$491$	2224.49	0.204460	0.102230	−	0.994761i	$-0.467402\pi$
$491$	2224.49	0.204460	0.102230	+	0.994761i	$0.467402\pi$
$492$	682.033	0.0624968
$493$	−2435.07	−0.222454
$494$	−2354.83	−0.214472
$495$	−2810.86	−0.255230
$496$	−875.587	−0.0792642
$497$	−1600.05	−0.144411
$498$	2444.02	0.219918
$499$	11583.0	1.03913	0.519565	−	0.854431i	$-0.326094\pi$
$499$	11583.0	1.03913	0.519565	+	0.854431i	$0.326094\pi$
$500$	4418.40	0.395194
$501$	−3143.66	−0.280336
$502$	−5402.08	−0.480292
$503$	6476.25	0.574079	0.287040	−	0.957919i	$-0.407329\pi$
$503$	6476.25	0.574079	0.287040	+	0.957919i	$0.407329\pi$
$504$	−504.000	−0.0445435
$505$	3742.87	0.329813
$506$	−2939.28	−0.258235
$507$	−4929.59	−0.431816
$508$	1143.67	0.0998861
$509$	−5642.06	−0.491316	−0.245658	−	0.969357i	$-0.579004\pi$
$509$	−5642.06	−0.491316	−0.245658	+	0.969357i	$0.579004\pi$
$510$	−645.934	−0.0560832
$511$	−1818.82	−0.157456
$512$	−512.000	−0.0441942
$513$	−513.000	−0.0441511
$514$	527.208	0.0452415
$515$	3986.94	0.341137
$516$	−3593.47	−0.306577
$517$	−3500.21	−0.297755
$518$	−4009.78	−0.340115
$519$	−1048.64	−0.0886900
$520$	2421.54	0.204215
$521$	9431.46	0.793090	0.396545	−	0.918015i	$-0.370209\pi$
$521$	9431.46	0.793090	0.396545	+	0.918015i	$0.370209\pi$
$522$	1988.71	0.166750
$523$	18098.5	1.51318	0.756591	−	0.653888i	$-0.226863\pi$
$523$	18098.5	1.51318	0.756591	+	0.653888i	$0.226863\pi$
$524$	−4767.43	−0.397455
$525$	2123.96	0.176566
$526$	−12756.6	−1.05744
$527$	−1206.12	−0.0996953
$528$	−3069.11	−0.252966
$529$	−11638.7	−0.956579
$530$	−6063.84	−0.496974
$531$	904.302	0.0739046
$532$	532.000	0.0433555
$533$	−3522.09	−0.286226
$534$	−2657.81	−0.215383
$535$	−2040.29	−0.164877
$536$	1664.27	0.134115
$537$	2425.22	0.194890
$538$	9259.48	0.742016
$539$	3133.05	0.250371
$540$	527.533	0.0420396
$541$	1688.32	0.134171	0.0670857	−	0.997747i	$-0.478630\pi$
$541$	1688.32	0.134171	0.0670857	+	0.997747i	$0.478630\pi$
$542$	14211.2	1.12624
$543$	12557.2	0.992412
$544$	−705.279	−0.0555857
$545$	−10467.0	−0.822674
$546$	2602.71	0.204003
$547$	10458.0	0.817460	0.408730	−	0.912655i	$-0.365972\pi$
$547$	10458.0	0.817460	0.408730	+	0.912655i	$0.365972\pi$
$548$	−6423.48	−0.500726
$549$	5043.70	0.392095
$550$	12933.9	1.00273
$551$	−2099.20	−0.162303
$552$	551.633	0.0425346
$553$	5233.58	0.402450
$554$	−13283.0	−1.01866
$555$	4197.00	0.320996
$556$	11196.2	0.854000
$557$	11488.5	0.873940	0.436970	−	0.899476i	$-0.356052\pi$
$557$	11488.5	0.873940	0.436970	+	0.899476i	$0.356052\pi$
$558$	985.036	0.0747310
$559$	18557.1	1.40408
$560$	−547.071	−0.0412821
$561$	−4227.70	−0.318170
$562$	−5442.44	−0.408497
$563$	−10535.2	−0.788645	−0.394323	−	0.918972i	$-0.629021\pi$
$563$	−10535.2	−0.788645	−0.394323	+	0.918972i	$0.629021\pi$
$564$	656.908	0.0490440
$565$	−10219.0	−0.760911
$566$	−4417.13	−0.328032
$567$	567.000	0.0419961
$568$	1828.63	0.135084
$569$	1568.10	0.115533	0.0577666	−	0.998330i	$-0.481602\pi$
$569$	1568.10	0.115533	0.0577666	+	0.998330i	$0.481602\pi$
$570$	−556.840	−0.0409184
$571$	−3488.17	−0.255649	−0.127824	−	0.991797i	$-0.540799\pi$
$571$	−3488.17	−0.255649	−0.127824	+	0.991797i	$0.540799\pi$
$572$	15849.2	1.15855
$573$	236.843	0.0172674
$574$	795.705	0.0578608
$575$	−2324.70	−0.168603
$576$	576.000	0.0416667
$577$	−11275.8	−0.813549	−0.406774	−	0.913529i	$-0.633347\pi$
$577$	−11275.8	−0.813549	−0.406774	+	0.913529i	$0.633347\pi$
$578$	8854.48	0.637193
$579$	−7854.37	−0.563759
$580$	2158.66	0.154541
$581$	2851.36	0.203605
$582$	−3547.50	−0.252661
$583$	−39688.4	−2.81942
$584$	2078.65	0.147286
$585$	−2724.24	−0.192536
$586$	10959.4	0.772574
$587$	−12921.6	−0.908570	−0.454285	−	0.890856i	$-0.650105\pi$
$587$	−12921.6	−0.908570	−0.454285	+	0.890856i	$0.650105\pi$
$588$	−588.000	−0.0412393
$589$	−1039.76	−0.0727378
$590$	981.582	0.0684934
$591$	−12465.1	−0.867590
$592$	4582.60	0.318148
$593$	6603.65	0.457301	0.228650	−	0.973509i	$-0.426569\pi$
$593$	6603.65	0.457301	0.228650	+	0.973509i	$0.426569\pi$
$594$	3452.75	0.238498
$595$	−753.590	−0.0519230
$596$	−2317.86	−0.159301
$597$	8741.72	0.599288
$598$	−2848.70	−0.194802
$599$	17066.8	1.16416	0.582081	−	0.813131i	$-0.302239\pi$
$599$	17066.8	1.16416	0.582081	+	0.813131i	$0.302239\pi$
$600$	−2427.39	−0.165163
$601$	−9574.65	−0.649847	−0.324924	−	0.945740i	$-0.605339\pi$
$601$	−9574.65	−0.649847	−0.324924	+	0.945740i	$0.605339\pi$
$602$	−4192.38	−0.283835
$603$	−1872.31	−0.126445
$604$	1105.59	0.0744796
$605$	−13468.2	−0.905058
$606$	−4597.59	−0.308192
$607$	−1334.47	−0.0892330	−0.0446165	−	0.999004i	$-0.514207\pi$
$607$	−1334.47	−0.0892330	−0.0446165	+	0.999004i	$0.514207\pi$
$608$	−608.000	−0.0405554
$609$	2320.16	0.154381
$610$	5474.73	0.363386
$611$	−3392.34	−0.224615
$612$	793.439	0.0524067
$613$	−4724.66	−0.311301	−0.155650	−	0.987812i	$-0.549747\pi$
$613$	−4724.66	−0.311301	−0.155650	+	0.987812i	$0.549747\pi$
$614$	−3302.48	−0.217064
$615$	−832.858	−0.0546082
$616$	−3580.63	−0.234201
$617$	−15170.7	−0.989867	−0.494934	−	0.868931i	$-0.664808\pi$
$617$	−15170.7	−0.989867	−0.494934	+	0.868931i	$0.664808\pi$
$618$	−4897.40	−0.318774
$619$	−4760.34	−0.309102	−0.154551	−	0.987985i	$-0.549393\pi$
$619$	−4760.34	−0.309102	−0.154551	+	0.987985i	$0.549393\pi$
$620$	1069.22	0.0692592
$621$	−620.588	−0.0401020
$622$	12008.4	0.774101
$623$	−3100.78	−0.199406
$624$	−2974.53	−0.190828
$625$	7247.14	0.463817
$626$	−19642.1	−1.25408
$627$	−3644.57	−0.232137
$628$	9232.67	0.586662
$629$	6312.53	0.400154
$630$	615.455	0.0389211
$631$	−4803.98	−0.303080	−0.151540	−	0.988451i	$-0.548423\pi$
$631$	−4803.98	−0.303080	−0.151540	+	0.988451i	$0.548423\pi$
$632$	−5981.24	−0.376457
$633$	8840.71	0.555113
$634$	−625.108	−0.0391580
$635$	−1396.58	−0.0872782
$636$	7448.58	0.464395
$637$	3036.50	0.188870
$638$	14128.7	0.876738
$639$	−2057.21	−0.127358
$640$	625.224	0.0386159
$641$	30918.3	1.90515	0.952574	−	0.304308i	$-0.0984251\pi$
$641$	30918.3	1.90515	0.952574	+	0.304308i	$0.0984251\pi$
$642$	2506.20	0.154069
$643$	1504.80	0.0922918	0.0461459	−	0.998935i	$-0.485306\pi$
$643$	1504.80	0.0922918	0.0461459	+	0.998935i	$0.485306\pi$
$644$	643.572	0.0393794
$645$	4388.13	0.267880
$646$	−837.519	−0.0510089
$647$	21511.4	1.30711	0.653556	−	0.756878i	$-0.273276\pi$
$647$	21511.4	1.30711	0.653556	+	0.756878i	$0.273276\pi$
$648$	−648.000	−0.0392837
$649$	6424.54	0.388575
$650$	12535.3	0.756422
$651$	1149.21	0.0691875
$652$	13116.4	0.787850
$653$	18578.8	1.11339	0.556694	−	0.830717i	$-0.312069\pi$
$653$	18578.8	1.11339	0.556694	+	0.830717i	$0.312069\pi$
$654$	12857.2	0.768743
$655$	5821.71	0.347287
$656$	−909.377	−0.0541238
$657$	−2338.48	−0.138863
$658$	766.393	0.0454059
$659$	−21920.0	−1.29573	−0.647863	−	0.761757i	$-0.724337\pi$
$659$	−21920.0	−1.29573	−0.647863	+	0.761757i	$0.724337\pi$
$660$	3747.82	0.221036
$661$	−12659.8	−0.744947	−0.372473	−	0.928043i	$-0.621490\pi$
$661$	−12659.8	−0.744947	−0.372473	+	0.928043i	$0.621490\pi$
$662$	20155.9	1.18336
$663$	−4097.41	−0.240015
$664$	−3258.69	−0.190455
$665$	−649.647	−0.0378830
$666$	−5155.43	−0.299953
$667$	−2539.45	−0.147418
$668$	4191.54	0.242778
$669$	−2038.88	−0.117829
$670$	−2032.31	−0.117186
$671$	35832.6	2.06155
$672$	672.000	0.0385758
$673$	29909.1	1.71309	0.856545	−	0.516073i	$-0.172607\pi$
$673$	29909.1	1.71309	0.856545	+	0.516073i	$0.172607\pi$
$674$	−23677.3	−1.35314
$675$	2730.81	0.155717
$676$	6572.78	0.373964
$677$	22975.1	1.30429	0.652144	−	0.758095i	$-0.273870\pi$
$677$	22975.1	1.30429	0.652144	+	0.758095i	$0.273870\pi$
$678$	12552.6	0.711030
$679$	−4138.75	−0.233919
$680$	861.245	0.0485695
$681$	4025.56	0.226519
$682$	6998.11	0.392920
$683$	−6579.51	−0.368606	−0.184303	−	0.982869i	$-0.559003\pi$
$683$	−6579.51	−0.368606	−0.184303	+	0.982869i	$0.559003\pi$
$684$	684.000	0.0382360
$685$	7843.98	0.437523
$686$	−686.000	−0.0381802
$687$	−7879.68	−0.437596
$688$	4791.29	0.265503
$689$	−38465.3	−2.12686
$690$	−673.622	−0.0371657
$691$	−25029.4	−1.37795	−0.688974	−	0.724786i	$-0.741938\pi$
$691$	−25029.4	−1.37795	−0.688974	+	0.724786i	$0.741938\pi$
$692$	1398.18	0.0768078
$693$	4028.21	0.220807
$694$	17745.2	0.970603
$695$	−13672.1	−0.746206
$696$	−2651.62	−0.144410
$697$	−1252.67	−0.0680747
$698$	−15351.0	−0.832442
$699$	3356.61	0.181629
$700$	−2831.95	−0.152911
$701$	21265.8	1.14579	0.572894	−	0.819629i	$-0.305821\pi$
$701$	21265.8	1.14579	0.572894	+	0.819629i	$0.305821\pi$
$702$	3346.34	0.179914
$703$	5441.84	0.291953
$704$	4092.15	0.219075
$705$	−802.177	−0.0428535
$706$	5167.19	0.275453
$707$	−5363.85	−0.285330
$708$	−1205.74	−0.0640033
$709$	4115.38	0.217992	0.108996	−	0.994042i	$-0.465236\pi$
$709$	4115.38	0.217992	0.108996	+	0.994042i	$0.465236\pi$
$710$	−2233.02	−0.118033
$711$	6728.89	0.354927
$712$	3543.74	0.186527
$713$	−1257.82	−0.0660670
$714$	925.679	0.0485191
$715$	−19354.1	−1.01231
$716$	−3233.63	−0.168780
$717$	−12250.7	−0.638092
$718$	7097.57	0.368912
$719$	1137.57	0.0590045	0.0295022	−	0.999565i	$-0.490608\pi$
$719$	1137.57	0.0590045	0.0295022	+	0.999565i	$0.490608\pi$
$720$	−703.377	−0.0364074
$721$	−5713.63	−0.295127
$722$	−722.000	−0.0372161
$723$	2530.22	0.130152
$724$	−16742.9	−0.859454
$725$	11174.5	0.572427
$726$	16543.8	0.845727
$727$	35669.5	1.81968	0.909840	−	0.414960i	$-0.136204\pi$
$727$	35669.5	1.81968	0.909840	+	0.414960i	$0.136204\pi$
$728$	−3470.28	−0.176672
$729$	729.000	0.0370370
$730$	−2538.32	−0.128695
$731$	6600.00	0.333940
$732$	−6724.93	−0.339564
$733$	5522.64	0.278286	0.139143	−	0.990272i	$-0.455565\pi$
$733$	5522.64	0.278286	0.139143	+	0.990272i	$0.455565\pi$
$734$	1742.95	0.0876477
$735$	718.031	0.0360340
$736$	−735.511	−0.0368360
$737$	−13301.6	−0.664820
$738$	1023.05	0.0510284
$739$	3917.66	0.195011	0.0975056	−	0.995235i	$-0.468914\pi$
$739$	3917.66	0.195011	0.0975056	+	0.995235i	$0.468914\pi$
$740$	−5596.00	−0.277991
$741$	−3532.25	−0.175115
$742$	8690.00	0.429946
$743$	25380.0	1.25316	0.626582	−	0.779356i	$-0.284454\pi$
$743$	25380.0	1.25316	0.626582	+	0.779356i	$0.284454\pi$
$744$	−1313.38	−0.0647189
$745$	2830.44	0.139193
$746$	5192.94	0.254862
$747$	3666.03	0.179562
$748$	5636.93	0.275544
$749$	2923.90	0.142640
$750$	6627.60	0.322674
$751$	−29922.8	−1.45393	−0.726964	−	0.686675i	$-0.759069\pi$
$751$	−29922.8	−1.45393	−0.726964	+	0.686675i	$0.759069\pi$
$752$	−875.877	−0.0424733
$753$	−8103.11	−0.392157
$754$	13693.2	0.661377
$755$	−1350.08	−0.0650786
$756$	−756.000	−0.0363696
$757$	−14545.4	−0.698366	−0.349183	−	0.937055i	$-0.613541\pi$
$757$	−14545.4	−0.698366	−0.349183	+	0.937055i	$0.613541\pi$
$758$	2536.42	0.121539
$759$	−4408.92	−0.210848
$760$	742.454	0.0354363
$761$	22377.4	1.06594	0.532970	−	0.846134i	$-0.321076\pi$
$761$	22377.4	1.06594	0.532970	+	0.846134i	$0.321076\pi$
$762$	1715.50	0.0815567
$763$	15000.1	0.711718
$764$	−315.790	−0.0149541
$765$	−968.901	−0.0457918
$766$	23849.1	1.12494
$767$	6226.55	0.293126
$768$	−768.000	−0.0360844
$769$	14349.4	0.672891	0.336446	−	0.941703i	$-0.390775\pi$
$769$	14349.4	0.672891	0.336446	+	0.941703i	$0.390775\pi$
$770$	4372.45	0.204639
$771$	790.812	0.0369395
$772$	10472.5	0.488230
$773$	8056.20	0.374853	0.187427	−	0.982279i	$-0.439985\pi$
$773$	8056.20	0.374853	0.187427	+	0.982279i	$0.439985\pi$
$774$	−5390.21	−0.250319
$775$	5534.86	0.256540
$776$	4730.00	0.218811
$777$	−6014.66	−0.277702
$778$	8388.53	0.386560
$779$	−1079.88	−0.0496674
$780$	3632.32	0.166741
$781$	−14615.3	−0.669624
$782$	−1013.17	−0.0463309
$783$	2983.07	0.136151
$784$	784.000	0.0357143
$785$	−11274.4	−0.512612
$786$	−7151.15	−0.324520
$787$	−22754.3	−1.03063	−0.515313	−	0.857002i	$-0.672324\pi$
$787$	−22754.3	−1.03063	−0.515313	+	0.857002i	$0.672324\pi$
$788$	16620.1	0.751355
$789$	−19134.8	−0.863394
$790$	7303.93	0.328940
$791$	14644.6	0.658285
$792$	−4603.67	−0.206546
$793$	34728.3	1.55516
$794$	−19685.0	−0.879841
$795$	−9095.76	−0.405778
$796$	−11655.6	−0.518999
$797$	41078.2	1.82568	0.912839	−	0.408320i	$-0.133885\pi$
$797$	41078.2	1.82568	0.912839	+	0.408320i	$0.133885\pi$
$798$	798.000	0.0353996
$799$	−1206.52	−0.0534213
$800$	3236.51	0.143035
$801$	−3986.71	−0.175860
$802$	−21592.0	−0.950674
$803$	−16613.6	−0.730112
$804$	2496.41	0.109504
$805$	−785.892	−0.0344088
$806$	6782.44	0.296404
$807$	13889.2	0.605854
$808$	6130.11	0.266902
$809$	24859.6	1.08037	0.540184	−	0.841547i	$-0.318354\pi$
$809$	24859.6	1.08037	0.540184	+	0.841547i	$0.318354\pi$
$810$	791.299	0.0343252
$811$	17690.8	0.765976	0.382988	−	0.923753i	$-0.374895\pi$
$811$	17690.8	0.765976	0.382988	+	0.923753i	$0.374895\pi$
$812$	−3093.55	−0.133698
$813$	21316.8	0.919573
$814$	−36626.3	−1.57709
$815$	−16017.0	−0.688406
$816$	−1057.92	−0.0453855
$817$	5689.66	0.243643
$818$	835.077	0.0356941
$819$	3904.07	0.166568
$820$	1110.48	0.0472921
$821$	−4055.67	−0.172404	−0.0862021	−	0.996278i	$-0.527473\pi$
$821$	−4055.67	−0.172404	−0.0862021	+	0.996278i	$0.527473\pi$
$822$	−9635.23	−0.408841
$823$	5806.37	0.245926	0.122963	−	0.992411i	$-0.460760\pi$
$823$	5806.37	0.245926	0.122963	+	0.992411i	$0.460760\pi$
$824$	6529.87	0.276066
$825$	19400.8	0.818727
$826$	−1406.69	−0.0592555
$827$	12894.9	0.542202	0.271101	−	0.962551i	$-0.412612\pi$
$827$	12894.9	0.542202	0.271101	+	0.962551i	$0.412612\pi$
$828$	827.450	0.0347293
$829$	−40177.1	−1.68324	−0.841621	−	0.540069i	$-0.818398\pi$
$829$	−40177.1	−1.68324	−0.841621	+	0.540069i	$0.818398\pi$
$830$	3979.33	0.166415
$831$	−19924.4	−0.831734
$832$	3966.04	0.165261
$833$	1079.96	0.0449200
$834$	16794.3	0.697288
$835$	−5118.47	−0.212134
$836$	4859.43	0.201037
$837$	1477.55	0.0610176
$838$	−16114.3	−0.664271
$839$	−26024.6	−1.07088	−0.535440	−	0.844573i	$-0.679854\pi$
$839$	−26024.6	−1.07088	−0.535440	+	0.844573i	$0.679854\pi$
$840$	−820.607	−0.0337067
$841$	−12182.3	−0.499499
$842$	−7326.60	−0.299871
$843$	−8163.66	−0.333537
$844$	−11787.6	−0.480742
$845$	−8026.29	−0.326761
$846$	985.362	0.0400443
$847$	19301.1	0.782991
$848$	−9931.43	−0.402178
$849$	−6625.70	−0.267837
$850$	4458.29	0.179904
$851$	6583.11	0.265178
$852$	2742.95	0.110296
$853$	−28631.6	−1.14927	−0.574635	−	0.818410i	$-0.694856\pi$
$853$	−28631.6	−1.14927	−0.574635	+	0.818410i	$0.694856\pi$
$854$	−7845.76	−0.314375
$855$	−835.260	−0.0334097
$856$	−3341.61	−0.133427
$857$	33652.5	1.34136	0.670681	−	0.741746i	$-0.266002\pi$
$857$	33652.5	1.34136	0.670681	+	0.741746i	$0.266002\pi$
$858$	23773.8	0.945950
$859$	−43974.1	−1.74666	−0.873328	−	0.487133i	$-0.838043\pi$
$859$	−43974.1	−1.74666	−0.873328	+	0.487133i	$0.838043\pi$
$860$	−5850.84	−0.231991
$861$	1193.56	0.0472431
$862$	5741.39	0.226859
$863$	23940.9	0.944332	0.472166	−	0.881510i	$-0.343472\pi$
$863$	23940.9	0.944332	0.472166	+	0.881510i	$0.343472\pi$
$864$	864.000	0.0340207
$865$	−1707.38	−0.0671129
$866$	16944.6	0.664897
$867$	13281.7	0.520266
$868$	−1532.28	−0.0599181
$869$	47804.9	1.86613
$870$	3238.00	0.126182
$871$	−12891.7	−0.501515
$872$	−17143.0	−0.665751
$873$	−5321.25	−0.206297
$874$	−873.420	−0.0338030
$875$	7732.20	0.298738
$876$	3117.97	0.120259
$877$	−45157.8	−1.73873	−0.869367	−	0.494167i	$-0.835473\pi$
$877$	−45157.8	−1.73873	−0.869367	+	0.494167i	$0.835473\pi$
$878$	−7910.21	−0.304051
$879$	16439.1	0.630804
$880$	−4997.09	−0.191423
$881$	8170.97	0.312471	0.156236	−	0.987720i	$-0.450064\pi$
$881$	8170.97	0.312471	0.156236	+	0.987720i	$0.450064\pi$
$882$	−882.000	−0.0336718
$883$	−26587.9	−1.01331	−0.506655	−	0.862149i	$-0.669118\pi$
$883$	−26587.9	−1.01331	−0.506655	+	0.862149i	$0.669118\pi$
$884$	5463.21	0.207859
$885$	1472.37	0.0559246
$886$	18685.6	0.708528
$887$	−27728.7	−1.04965	−0.524825	−	0.851210i	$-0.675869\pi$
$887$	−27728.7	−1.04965	−0.524825	+	0.851210i	$0.675869\pi$
$888$	6873.90	0.259767
$889$	2001.42	0.0755068
$890$	−4327.41	−0.162983
$891$	5179.12	0.194733
$892$	2718.50	0.102043
$893$	−1040.10	−0.0389762
$894$	−3476.79	−0.130069
$895$	3948.72	0.147476
$896$	−896.000	−0.0334077
$897$	−4273.04	−0.159055
$898$	−30240.7	−1.12377
$899$	6046.15	0.224305
$900$	−3641.08	−0.134855
$901$	−13680.5	−0.505843
$902$	7268.17	0.268297
$903$	−6288.57	−0.231750
$904$	−16736.7	−0.615770
$905$	20445.4	0.750972
$906$	1658.38	0.0608124
$907$	−39581.9	−1.44906	−0.724529	−	0.689244i	$-0.757943\pi$
$907$	−39581.9	−1.44906	−0.724529	+	0.689244i	$0.757943\pi$
$908$	−5367.41	−0.196172
$909$	−6896.38	−0.251637
$910$	4237.70	0.154372
$911$	16063.6	0.584204	0.292102	−	0.956387i	$-0.405645\pi$
$911$	16063.6	0.584204	0.292102	+	0.956387i	$0.405645\pi$
$912$	−912.000	−0.0331133
$913$	26045.0	0.944102
$914$	−9164.11	−0.331643
$915$	8212.09	0.296703
$916$	10506.2	0.378969
$917$	−8343.01	−0.300447
$918$	1190.16	0.0427899
$919$	40427.9	1.45114	0.725568	−	0.688151i	$-0.241577\pi$
$919$	40427.9	1.45114	0.725568	+	0.688151i	$0.241577\pi$
$920$	898.163	0.0321865
$921$	−4953.71	−0.177232
$922$	−3876.57	−0.138469
$923$	−14164.9	−0.505138
$924$	−5370.94	−0.191224
$925$	−28968.1	−1.02969
$926$	5282.11	0.187452
$927$	−7346.10	−0.260278
$928$	3535.49	0.125063
$929$	−3876.52	−0.136905	−0.0684523	−	0.997654i	$-0.521806\pi$
$929$	−3876.52	−0.136905	−0.0684523	+	0.997654i	$0.521806\pi$
$930$	1603.82	0.0565499
$931$	931.000	0.0327737
$932$	−4475.48	−0.157295
$933$	18012.5	0.632051
$934$	−25265.6	−0.885133
$935$	−6883.48	−0.240764
$936$	−4461.79	−0.155810
$937$	19054.0	0.664320	0.332160	−	0.943223i	$-0.392223\pi$
$937$	19054.0	0.664320	0.332160	+	0.943223i	$0.392223\pi$
$938$	2912.47	0.101381
$939$	−29463.2	−1.02396
$940$	1069.57	0.0371122
$941$	−32421.0	−1.12316	−0.561581	−	0.827422i	$-0.689807\pi$
$941$	−32421.0	−1.12316	−0.561581	+	0.827422i	$0.689807\pi$
$942$	13849.0	0.479007
$943$	−1306.36	−0.0451124
$944$	1607.65	0.0554285
$945$	923.182	0.0317790
$946$	−38294.3	−1.31613
$947$	−23686.0	−0.812770	−0.406385	−	0.913702i	$-0.633211\pi$
$947$	−23686.0	−0.812770	−0.406385	+	0.913702i	$0.633211\pi$
$948$	−8971.86	−0.307376
$949$	−16101.6	−0.550768
$950$	3843.36	0.131258
$951$	−937.661	−0.0319724
$952$	−1234.24	−0.0420188
$953$	3442.30	0.117006	0.0585032	−	0.998287i	$-0.481367\pi$
$953$	3442.30	0.117006	0.0585032	+	0.998287i	$0.481367\pi$
$954$	11172.9	0.379177
$955$	385.624	0.0130665
$956$	16334.3	0.552604
$957$	21193.0	0.715854
$958$	28186.3	0.950581
$959$	−11241.1	−0.378513
$960$	937.836	0.0315297
$961$	−26796.3	−0.899475
$962$	−35497.6	−1.18970
$963$	3759.31	0.125796
$964$	−3373.63	−0.112715
$965$	−12788.4	−0.426604
$966$	965.359	0.0321531
$967$	−17525.3	−0.582807	−0.291403	−	0.956600i	$-0.594122\pi$
$967$	−17525.3	−0.582807	−0.291403	+	0.956600i	$0.594122\pi$
$968$	−22058.4	−0.732421
$969$	−1256.28	−0.0416486
$970$	−5776.00	−0.191192
$971$	−32048.6	−1.05920	−0.529602	−	0.848246i	$-0.677659\pi$
$971$	−32048.6	−1.05920	−0.529602	+	0.848246i	$0.677659\pi$
$972$	−972.000	−0.0320750
$973$	19593.3	0.645563
$974$	34458.8	1.13360
$975$	18802.9	0.617616
$976$	8966.58	0.294071
$977$	−41556.6	−1.36081	−0.680406	−	0.732835i	$-0.738197\pi$
$977$	−41556.6	−1.36081	−0.680406	+	0.732835i	$0.738197\pi$
$978$	19674.6	0.643277
$979$	−28323.3	−0.924634
$980$	−957.374	−0.0312063
$981$	19285.9	0.627676
$982$	−4448.98	−0.144575
$983$	−48446.3	−1.57192	−0.785961	−	0.618277i	$-0.787831\pi$
$983$	−48446.3	−1.57192	−0.785961	+	0.618277i	$0.787831\pi$
$984$	−1364.07	−0.0441919
$985$	−20295.5	−0.656517
$986$	4870.13	0.157299
$987$	1149.59	0.0370738
$988$	4709.67	0.151654
$989$	6882.91	0.221298
$990$	5621.72	0.180475
$991$	−10866.8	−0.348331	−0.174165	−	0.984716i	$-0.555723\pi$
$991$	−10866.8	−0.348331	−0.174165	+	0.984716i	$0.555723\pi$
$992$	1751.17	0.0560482
$993$	30233.9	0.966206
$994$	3200.11	0.102114
$995$	14233.2	0.453489
$996$	−4888.04	−0.155506
$997$	−26654.7	−0.846703	−0.423351	−	0.905966i	$-0.639146\pi$
$997$	−26654.7	−0.846703	−0.423351	+	0.905966i	$0.639146\pi$
$998$	−23166.0	−0.734776
$999$	−7733.14	−0.244911

Twists

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

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

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -4.88456 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -4.88456 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +9.76913 q^{10} +63.9398 q^{11} -12.0000 q^{12} +61.9693 q^{13} -14.0000 q^{14} +14.6537 q^{15} +16.0000 q^{16} +22.0400 q^{17} -18.0000 q^{18} +19.0000 q^{19} -19.5383 q^{20} -21.0000 q^{21} -127.880 q^{22} +22.9847 q^{23} +24.0000 q^{24} -101.141 q^{25} -123.939 q^{26} -27.0000 q^{27} +28.0000 q^{28} -110.484 q^{29} -29.3074 q^{30} -54.7242 q^{31} -32.0000 q^{32} -191.819 q^{33} -44.0800 q^{34} -34.1919 q^{35} +36.0000 q^{36} +286.413 q^{37} -38.0000 q^{38} -185.908 q^{39} +39.0765 q^{40} -56.8360 q^{41} +42.0000 q^{42} +299.456 q^{43} +255.759 q^{44} -43.9611 q^{45} -45.9695 q^{46} -54.7423 q^{47} -48.0000 q^{48} +49.0000 q^{49} +202.282 q^{50} -66.1199 q^{51} +247.877 q^{52} -620.715 q^{53} +54.0000 q^{54} -312.318 q^{55} -56.0000 q^{56} -57.0000 q^{57} +220.968 q^{58} +100.478 q^{59} +58.6148 q^{60} +560.411 q^{61} +109.448 q^{62} +63.0000 q^{63} +64.0000 q^{64} -302.693 q^{65} +383.639 q^{66} -208.034 q^{67} +88.1599 q^{68} -68.9542 q^{69} +68.3839 q^{70} -228.579 q^{71} -72.0000 q^{72} -259.831 q^{73} -572.825 q^{74} +303.423 q^{75} +76.0000 q^{76} +447.579 q^{77} +371.816 q^{78} +747.655 q^{79} -78.1530 q^{80} +81.0000 q^{81} +113.672 q^{82} +407.337 q^{83} -84.0000 q^{84} -107.656 q^{85} -598.912 q^{86} +331.452 q^{87} -511.519 q^{88} -442.968 q^{89} +87.9221 q^{90} +433.785 q^{91} +91.9389 q^{92} +164.173 q^{93} +109.485 q^{94} -92.8067 q^{95} +96.0000 q^{96} -591.250 q^{97} -98.0000 q^{98} +575.458 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} - 12 q^{3} + 16 q^{4} + 12 q^{5} + 24 q^{6} + 28 q^{7} - 32 q^{8} + 36 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 - 12 * q^3 + 16 * q^4 + 12 * q^5 + 24 * q^6 + 28 * q^7 - 32 * q^8 + 36 * q^9	\( 4 q - 8 q^{2} - 12 q^{3} + 16 q^{4} + 12 q^{5} + 24 q^{6} + 28 q^{7} - 32 q^{8} + 36 q^{9} - 24 q^{10} + 54 q^{11} - 48 q^{12} - 46 q^{13} - 56 q^{14} - 36 q^{15} + 64 q^{16} + 100 q^{17} - 72 q^{18} + 76 q^{19} + 48 q^{20} - 84 q^{21} - 108 q^{22} + 274 q^{23} + 96 q^{24} + 300 q^{25} + 92 q^{26} - 108 q^{27} + 112 q^{28} - 214 q^{29} + 72 q^{30} + 228 q^{31} - 128 q^{32} - 162 q^{33} - 200 q^{34} + 84 q^{35} + 144 q^{36} - 124 q^{37} - 152 q^{38} + 138 q^{39} - 96 q^{40} - 484 q^{41} + 168 q^{42} + 276 q^{43} + 216 q^{44} + 108 q^{45} - 548 q^{46} - 506 q^{47} - 192 q^{48} + 196 q^{49} - 600 q^{50} - 300 q^{51} - 184 q^{52} - 1002 q^{53} + 216 q^{54} + 8 q^{55} - 224 q^{56} - 228 q^{57} + 428 q^{58} - 808 q^{59} - 144 q^{60} - 72 q^{61} - 456 q^{62} + 252 q^{63} + 256 q^{64} + 616 q^{65} + 324 q^{66} + 138 q^{67} + 400 q^{68} - 822 q^{69} - 168 q^{70} - 654 q^{71} - 288 q^{72} + 2348 q^{73} + 248 q^{74} - 900 q^{75} + 304 q^{76} + 378 q^{77} - 276 q^{78} + 234 q^{79} + 192 q^{80} + 324 q^{81} + 968 q^{82} - 258 q^{83} - 336 q^{84} + 2696 q^{85} - 552 q^{86} + 642 q^{87} - 432 q^{88} - 1316 q^{89} - 216 q^{90} - 322 q^{91} + 1096 q^{92} - 684 q^{93} + 1012 q^{94} + 228 q^{95} + 384 q^{96} + 1166 q^{97} - 392 q^{98} + 486 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 12 * q^3 + 16 * q^4 + 12 * q^5 + 24 * q^6 + 28 * q^7 - 32 * q^8 + 36 * q^9 - 24 * q^10 + 54 * q^11 - 48 * q^12 - 46 * q^13 - 56 * q^14 - 36 * q^15 + 64 * q^16 + 100 * q^17 - 72 * q^18 + 76 * q^19 + 48 * q^20 - 84 * q^21 - 108 * q^22 + 274 * q^23 + 96 * q^24 + 300 * q^25 + 92 * q^26 - 108 * q^27 + 112 * q^28 - 214 * q^29 + 72 * q^30 + 228 * q^31 - 128 * q^32 - 162 * q^33 - 200 * q^34 + 84 * q^35 + 144 * q^36 - 124 * q^37 - 152 * q^38 + 138 * q^39 - 96 * q^40 - 484 * q^41 + 168 * q^42 + 276 * q^43 + 216 * q^44 + 108 * q^45 - 548 * q^46 - 506 * q^47 - 192 * q^48 + 196 * q^49 - 600 * q^50 - 300 * q^51 - 184 * q^52 - 1002 * q^53 + 216 * q^54 + 8 * q^55 - 224 * q^56 - 228 * q^57 + 428 * q^58 - 808 * q^59 - 144 * q^60 - 72 * q^61 - 456 * q^62 + 252 * q^63 + 256 * q^64 + 616 * q^65 + 324 * q^66 + 138 * q^67 + 400 * q^68 - 822 * q^69 - 168 * q^70 - 654 * q^71 - 288 * q^72 + 2348 * q^73 + 248 * q^74 - 900 * q^75 + 304 * q^76 + 378 * q^77 - 276 * q^78 + 234 * q^79 + 192 * q^80 + 324 * q^81 + 968 * q^82 - 258 * q^83 - 336 * q^84 + 2696 * q^85 - 552 * q^86 + 642 * q^87 - 432 * q^88 - 1316 * q^89 - 216 * q^90 - 322 * q^91 + 1096 * q^92 - 684 * q^93 + 1012 * q^94 + 228 * q^95 + 384 * q^96 + 1166 * q^97 - 392 * q^98 + 486 * q^99

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