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

Embedding invariants

Embedding label			1.2
Root			$-1.47894$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -0.957876 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -0.957876 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +1.91575 q^{10} +42.6751 q^{11} +12.0000 q^{12} +32.1911 q^{13} -14.0000 q^{14} -2.87363 q^{15} +16.0000 q^{16} +10.7868 q^{17} -18.0000 q^{18} -19.0000 q^{19} -3.83151 q^{20} +21.0000 q^{21} -85.3501 q^{22} +190.538 q^{23} -24.0000 q^{24} -124.082 q^{25} -64.3822 q^{26} +27.0000 q^{27} +28.0000 q^{28} -278.767 q^{29} +5.74726 q^{30} +289.158 q^{31} -32.0000 q^{32} +128.025 q^{33} -21.5736 q^{34} -6.70513 q^{35} +36.0000 q^{36} -216.395 q^{37} +38.0000 q^{38} +96.5733 q^{39} +7.66301 q^{40} -62.3473 q^{41} -42.0000 q^{42} +16.0683 q^{43} +170.700 q^{44} -8.62089 q^{45} -381.077 q^{46} +25.3458 q^{47} +48.0000 q^{48} +49.0000 q^{49} +248.165 q^{50} +32.3604 q^{51} +128.764 q^{52} +706.577 q^{53} -54.0000 q^{54} -40.8774 q^{55} -56.0000 q^{56} -57.0000 q^{57} +557.535 q^{58} +655.812 q^{59} -11.4945 q^{60} -291.703 q^{61} -578.317 q^{62} +63.0000 q^{63} +64.0000 q^{64} -30.8351 q^{65} -256.050 q^{66} -688.378 q^{67} +43.1472 q^{68} +571.615 q^{69} +13.4103 q^{70} +768.017 q^{71} -72.0000 q^{72} -446.292 q^{73} +432.790 q^{74} -372.247 q^{75} -76.0000 q^{76} +298.725 q^{77} -193.147 q^{78} +385.573 q^{79} -15.3260 q^{80} +81.0000 q^{81} +124.695 q^{82} -797.673 q^{83} +84.0000 q^{84} -10.3324 q^{85} -32.1365 q^{86} -836.302 q^{87} -341.400 q^{88} +847.360 q^{89} +17.2418 q^{90} +225.338 q^{91} +762.154 q^{92} +867.475 q^{93} -50.6916 q^{94} +18.1997 q^{95} -96.0000 q^{96} +307.957 q^{97} -98.0000 q^{98} +384.076 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} + 10 q^{5} - 24 q^{6} + 28 q^{7} - 32 q^{8} + 36 q^{9}+O(q^{10}) $ 4 * q - 8 * q^2 + 12 * q^3 + 16 * q^4 + 10 * q^5 - 24 * q^6 + 28 * q^7 - 32 * q^8 + 36 * q^9	\( 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} + 10 q^{5} - 24 q^{6} + 28 q^{7} - 32 q^{8} + 36 q^{9} - 20 q^{10} + 48 q^{11} + 48 q^{12} - 30 q^{13} - 56 q^{14} + 30 q^{15} + 64 q^{16} + 128 q^{17} - 72 q^{18} - 76 q^{19} + 40 q^{20} + 84 q^{21} - 96 q^{22} + 98 q^{23} - 96 q^{24} + 312 q^{25} + 60 q^{26} + 108 q^{27} + 112 q^{28} + 144 q^{29} - 60 q^{30} + 10 q^{31} - 128 q^{32} + 144 q^{33} - 256 q^{34} + 70 q^{35} + 144 q^{36} + 222 q^{37} + 152 q^{38} - 90 q^{39} - 80 q^{40} + 256 q^{41} - 168 q^{42} + 188 q^{43} + 192 q^{44} + 90 q^{45} - 196 q^{46} + 522 q^{47} + 192 q^{48} + 196 q^{49} - 624 q^{50} + 384 q^{51} - 120 q^{52} + 1088 q^{53} - 216 q^{54} - 1092 q^{55} - 224 q^{56} - 228 q^{57} - 288 q^{58} + 1456 q^{59} + 120 q^{60} - 108 q^{61} - 20 q^{62} + 252 q^{63} + 256 q^{64} + 836 q^{65} - 288 q^{66} + 296 q^{67} + 512 q^{68} + 294 q^{69} - 140 q^{70} + 808 q^{71} - 288 q^{72} - 1384 q^{73} - 444 q^{74} + 936 q^{75} - 304 q^{76} + 336 q^{77} + 180 q^{78} + 582 q^{79} + 160 q^{80} + 324 q^{81} - 512 q^{82} - 1236 q^{83} + 336 q^{84} - 2216 q^{85} - 376 q^{86} + 432 q^{87} - 384 q^{88} + 2528 q^{89} - 180 q^{90} - 210 q^{91} + 392 q^{92} + 30 q^{93} - 1044 q^{94} - 190 q^{95} - 384 q^{96} - 1028 q^{97} - 392 q^{98} + 432 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 + 12 * q^3 + 16 * q^4 + 10 * q^5 - 24 * q^6 + 28 * q^7 - 32 * q^8 + 36 * q^9 - 20 * q^10 + 48 * q^11 + 48 * q^12 - 30 * q^13 - 56 * q^14 + 30 * q^15 + 64 * q^16 + 128 * q^17 - 72 * q^18 - 76 * q^19 + 40 * q^20 + 84 * q^21 - 96 * q^22 + 98 * q^23 - 96 * q^24 + 312 * q^25 + 60 * q^26 + 108 * q^27 + 112 * q^28 + 144 * q^29 - 60 * q^30 + 10 * q^31 - 128 * q^32 + 144 * q^33 - 256 * q^34 + 70 * q^35 + 144 * q^36 + 222 * q^37 + 152 * q^38 - 90 * q^39 - 80 * q^40 + 256 * q^41 - 168 * q^42 + 188 * q^43 + 192 * q^44 + 90 * q^45 - 196 * q^46 + 522 * q^47 + 192 * q^48 + 196 * q^49 - 624 * q^50 + 384 * q^51 - 120 * q^52 + 1088 * q^53 - 216 * q^54 - 1092 * q^55 - 224 * q^56 - 228 * q^57 - 288 * q^58 + 1456 * q^59 + 120 * q^60 - 108 * q^61 - 20 * q^62 + 252 * q^63 + 256 * q^64 + 836 * q^65 - 288 * q^66 + 296 * q^67 + 512 * q^68 + 294 * q^69 - 140 * q^70 + 808 * q^71 - 288 * q^72 - 1384 * q^73 - 444 * q^74 + 936 * q^75 - 304 * q^76 + 336 * q^77 + 180 * q^78 + 582 * q^79 + 160 * q^80 + 324 * q^81 - 512 * q^82 - 1236 * q^83 + 336 * q^84 - 2216 * q^85 - 376 * q^86 + 432 * q^87 - 384 * q^88 + 2528 * q^89 - 180 * q^90 - 210 * q^91 + 392 * q^92 + 30 * q^93 - 1044 * q^94 - 190 * q^95 - 384 * q^96 - 1028 * q^97 - 392 * q^98 + 432 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	−0.957876	−0.0856751	−0.0428375	−	0.999082i	$-0.513640\pi$
$5$	−0.957876	−0.0856751	−0.0428375	+	0.999082i	$0.513640\pi$
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	1.91575	0.0605814
$11$	42.6751	1.16973	0.584864	−	0.811131i	$-0.301148\pi$
$11$	42.6751	1.16973	0.584864	+	0.811131i	$0.301148\pi$
$12$	12.0000	0.288675
$13$	32.1911	0.686785	0.343393	−	0.939192i	$-0.388424\pi$
$13$	32.1911	0.686785	0.343393	+	0.939192i	$0.388424\pi$
$14$	−14.0000	−0.267261
$15$	−2.87363	−0.0494645
$16$	16.0000	0.250000
$17$	10.7868	0.153893	0.0769467	−	0.997035i	$-0.475483\pi$
$17$	10.7868	0.153893	0.0769467	+	0.997035i	$0.475483\pi$
$18$	−18.0000	−0.235702
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−3.83151	−0.0428375
$21$	21.0000	0.218218
$22$	−85.3501	−0.827123
$23$	190.538	1.72739	0.863696	−	0.504014i	$-0.168144\pi$
$23$	190.538	1.72739	0.863696	+	0.504014i	$0.168144\pi$
$24$	−24.0000	−0.204124
$25$	−124.082	−0.992660
$26$	−64.3822	−0.485630
$27$	27.0000	0.192450
$28$	28.0000	0.188982
$29$	−278.767	−1.78503	−0.892514	−	0.451021i	$-0.851060\pi$
$29$	−278.767	−1.78503	−0.892514	+	0.451021i	$0.851060\pi$
$30$	5.74726	0.0349767
$31$	289.158	1.67530	0.837651	−	0.546205i	$-0.183928\pi$
$31$	289.158	1.67530	0.837651	+	0.546205i	$0.183928\pi$
$32$	−32.0000	−0.176777
$33$	128.025	0.675343
$34$	−21.5736	−0.108819
$35$	−6.70513	−0.0323821
$36$	36.0000	0.166667
$37$	−216.395	−0.961490	−0.480745	−	0.876860i	$-0.659634\pi$
$37$	−216.395	−0.961490	−0.480745	+	0.876860i	$0.659634\pi$
$38$	38.0000	0.162221
$39$	96.5733	0.396516
$40$	7.66301	0.0302907
$41$	−62.3473	−0.237488	−0.118744	−	0.992925i	$-0.537887\pi$
$41$	−62.3473	−0.237488	−0.118744	+	0.992925i	$0.537887\pi$
$42$	−42.0000	−0.154303
$43$	16.0683	0.0569857	0.0284929	−	0.999594i	$-0.490929\pi$
$43$	16.0683	0.0569857	0.0284929	+	0.999594i	$0.490929\pi$
$44$	170.700	0.584864
$45$	−8.62089	−0.0285584
$46$	−381.077	−1.22145
$47$	25.3458	0.0786610	0.0393305	−	0.999226i	$-0.487477\pi$
$47$	25.3458	0.0786610	0.0393305	+	0.999226i	$0.487477\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	248.165	0.701916
$51$	32.3604	0.0888503
$52$	128.764	0.343393
$53$	706.577	1.83124	0.915621	−	0.402043i	$-0.131700\pi$
$53$	706.577	1.83124	0.915621	+	0.402043i	$0.131700\pi$
$54$	−54.0000	−0.136083
$55$	−40.8774	−0.100217
$56$	−56.0000	−0.133631
$57$	−57.0000	−0.132453
$58$	557.535	1.26220
$59$	655.812	1.44711	0.723555	−	0.690267i	$-0.242507\pi$
$59$	655.812	1.44711	0.723555	+	0.690267i	$0.242507\pi$
$60$	−11.4945	−0.0247323
$61$	−291.703	−0.612273	−0.306137	−	0.951988i	$-0.599036\pi$
$61$	−291.703	−0.612273	−0.306137	+	0.951988i	$0.599036\pi$
$62$	−578.317	−1.18462
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	−30.8351	−0.0588404
$66$	−256.050	−0.477540
$67$	−688.378	−1.25521	−0.627603	−	0.778534i	$-0.715964\pi$
$67$	−688.378	−1.25521	−0.627603	+	0.778534i	$0.715964\pi$
$68$	43.1472	0.0769467
$69$	571.615	0.997310
$70$	13.4103	0.0228976
$71$	768.017	1.28376	0.641879	−	0.766806i	$-0.278155\pi$
$71$	768.017	1.28376	0.641879	+	0.766806i	$0.278155\pi$
$72$	−72.0000	−0.117851
$73$	−446.292	−0.715542	−0.357771	−	0.933809i	$-0.616463\pi$
$73$	−446.292	−0.715542	−0.357771	+	0.933809i	$0.616463\pi$
$74$	432.790	0.679876
$75$	−372.247	−0.573112
$76$	−76.0000	−0.114708
$77$	298.725	0.442116
$78$	−193.147	−0.280379
$79$	385.573	0.549118	0.274559	−	0.961570i	$-0.411468\pi$
$79$	385.573	0.549118	0.274559	+	0.961570i	$0.411468\pi$
$80$	−15.3260	−0.0214188
$81$	81.0000	0.111111
$82$	124.695	0.167929
$83$	−797.673	−1.05489	−0.527446	−	0.849589i	$-0.676850\pi$
$83$	−797.673	−1.05489	−0.527446	+	0.849589i	$0.676850\pi$
$84$	84.0000	0.109109
$85$	−10.3324	−0.0131848
$86$	−32.1365	−0.0402950
$87$	−836.302	−1.03059
$88$	−341.400	−0.413562
$89$	847.360	1.00921	0.504607	−	0.863349i	$-0.331637\pi$
$89$	847.360	1.00921	0.504607	+	0.863349i	$0.331637\pi$
$90$	17.2418	0.0201938
$91$	225.338	0.259580
$92$	762.154	0.863696
$93$	867.475	0.967237
$94$	−50.6916	−0.0556217
$95$	18.1997	0.0196552
$96$	−96.0000	−0.102062
$97$	307.957	0.322353	0.161177	−	0.986926i	$-0.448471\pi$
$97$	307.957	0.322353	0.161177	+	0.986926i	$0.448471\pi$
$98$	−98.0000	−0.101015
$99$	384.076	0.389910
$100$	−496.330	−0.496330
$101$	−1287.78	−1.26870	−0.634350	−	0.773046i	$-0.718732\pi$
$101$	−1287.78	−1.26870	−0.634350	+	0.773046i	$0.718732\pi$
$102$	−64.7209	−0.0628267
$103$	1095.06	1.04756	0.523782	−	0.851852i	$-0.324521\pi$
$103$	1095.06	1.04756	0.523782	+	0.851852i	$0.324521\pi$
$104$	−257.529	−0.242815
$105$	−20.1154	−0.0186958
$106$	−1413.15	−1.29488
$107$	−1156.75	−1.04511	−0.522557	−	0.852604i	$-0.675022\pi$
$107$	−1156.75	−1.04511	−0.522557	+	0.852604i	$0.675022\pi$
$108$	108.000	0.0962250
$109$	253.350	0.222629	0.111314	−	0.993785i	$-0.464494\pi$
$109$	253.350	0.222629	0.111314	+	0.993785i	$0.464494\pi$
$110$	81.7549	0.0708638
$111$	−649.185	−0.555117
$112$	112.000	0.0944911
$113$	584.755	0.486806	0.243403	−	0.969925i	$-0.421736\pi$
$113$	584.755	0.486806	0.243403	+	0.969925i	$0.421736\pi$
$114$	114.000	0.0936586
$115$	−182.512	−0.147994
$116$	−1115.07	−0.892514
$117$	289.720	0.228928
$118$	−1311.62	−1.02326
$119$	75.5077	0.0581662
$120$	22.9890	0.0174883
$121$	490.161	0.368265
$122$	583.405	0.432943
$123$	−187.042	−0.137114
$124$	1156.63	0.837651
$125$	238.590	0.170721
$126$	−126.000	−0.0890871
$127$	1164.08	0.813353	0.406676	−	0.913572i	$-0.366688\pi$
$127$	1164.08	0.813353	0.406676	+	0.913572i	$0.366688\pi$
$128$	−128.000	−0.0883883
$129$	48.2048	0.0329007
$130$	61.6702	0.0416064
$131$	2387.11	1.59209	0.796043	−	0.605240i	$-0.206923\pi$
$131$	2387.11	1.59209	0.796043	+	0.605240i	$0.206923\pi$
$132$	512.101	0.337672
$133$	−133.000	−0.0867110
$134$	1376.76	0.887564
$135$	−25.8627	−0.0164882
$136$	−86.2945	−0.0544095
$137$	2338.92	1.45859	0.729297	−	0.684197i	$-0.239847\pi$
$137$	2338.92	1.45859	0.729297	+	0.684197i	$0.239847\pi$
$138$	−1143.23	−0.705205
$139$	697.918	0.425875	0.212938	−	0.977066i	$-0.431697\pi$
$139$	697.918	0.425875	0.212938	+	0.977066i	$0.431697\pi$
$140$	−26.8205	−0.0161911
$141$	76.0374	0.0454149
$142$	−1536.03	−0.907754
$143$	1373.76	0.803352
$144$	144.000	0.0833333
$145$	267.025	0.152932
$146$	892.585	0.505965
$147$	147.000	0.0824786
$148$	−865.580	−0.480745
$149$	2015.68	1.10826	0.554130	−	0.832430i	$-0.313051\pi$
$149$	2015.68	1.10826	0.554130	+	0.832430i	$0.313051\pi$
$150$	744.495	0.405252
$151$	−932.325	−0.502461	−0.251230	−	0.967927i	$-0.580835\pi$
$151$	−932.325	−0.502461	−0.251230	+	0.967927i	$0.580835\pi$
$152$	152.000	0.0811107
$153$	97.0813	0.0512978
$154$	−597.451	−0.312623
$155$	−276.978	−0.143532
$156$	386.293	0.198258
$157$	−1641.26	−0.834309	−0.417155	−	0.908836i	$-0.636973\pi$
$157$	−1641.26	−0.834309	−0.417155	+	0.908836i	$0.636973\pi$
$158$	−771.145	−0.388285
$159$	2119.73	1.05727
$160$	30.6520	0.0151454
$161$	1333.77	0.652893
$162$	−162.000	−0.0785674
$163$	1832.31	0.880476	0.440238	−	0.897881i	$-0.354894\pi$
$163$	1832.31	0.880476	0.440238	+	0.897881i	$0.354894\pi$
$164$	−249.389	−0.118744
$165$	−122.632	−0.0578601
$166$	1595.35	0.745921
$167$	1922.77	0.890950	0.445475	−	0.895294i	$-0.353035\pi$
$167$	1922.77	0.890950	0.445475	+	0.895294i	$0.353035\pi$
$168$	−168.000	−0.0771517
$169$	−1160.73	−0.528326
$170$	20.6649	0.00932307
$171$	−171.000	−0.0764719
$172$	64.2730	0.0284929
$173$	1196.31	0.525746	0.262873	−	0.964830i	$-0.415330\pi$
$173$	1196.31	0.525746	0.262873	+	0.964830i	$0.415330\pi$
$174$	1672.60	0.728734
$175$	−868.577	−0.375190
$176$	682.801	0.292432
$177$	1967.44	0.835489
$178$	−1694.72	−0.713622
$179$	3327.58	1.38947	0.694734	−	0.719266i	$-0.255522\pi$
$179$	3327.58	1.38947	0.694734	+	0.719266i	$0.255522\pi$
$180$	−34.4835	−0.0142792
$181$	−1426.72	−0.585898	−0.292949	−	0.956128i	$-0.594637\pi$
$181$	−1426.72	−0.585898	−0.292949	+	0.956128i	$0.594637\pi$
$182$	−450.676	−0.183551
$183$	−875.108	−0.353496
$184$	−1524.31	−0.610725
$185$	207.280	0.0823757
$186$	−1734.95	−0.683940
$187$	460.328	0.180013
$188$	101.383	0.0393305
$189$	189.000	0.0727393
$190$	−36.3993	−0.0138983
$191$	2325.31	0.880908	0.440454	−	0.897775i	$-0.354818\pi$
$191$	2325.31	0.880908	0.440454	+	0.897775i	$0.354818\pi$
$192$	192.000	0.0721688
$193$	−484.652	−0.180756	−0.0903782	−	0.995908i	$-0.528808\pi$
$193$	−484.652	−0.180756	−0.0903782	+	0.995908i	$0.528808\pi$
$194$	−615.914	−0.227938
$195$	−92.5053	−0.0339715
$196$	196.000	0.0714286
$197$	−4555.04	−1.64738	−0.823689	−	0.567042i	$-0.808088\pi$
$197$	−4555.04	−1.64738	−0.823689	+	0.567042i	$0.808088\pi$
$198$	−768.151	−0.275708
$199$	4013.27	1.42961	0.714806	−	0.699323i	$-0.246515\pi$
$199$	4013.27	1.42961	0.714806	+	0.699323i	$0.246515\pi$
$200$	992.660	0.350958
$201$	−2065.13	−0.724693
$202$	2575.56	0.897107
$203$	−1951.37	−0.674677
$204$	129.442	0.0444252
$205$	59.7210	0.0203468
$206$	−2190.11	−0.740740
$207$	1714.85	0.575797
$208$	515.058	0.171696
$209$	−810.826	−0.268354
$210$	40.2308	0.0132199
$211$	3710.82	1.21073	0.605363	−	0.795949i	$-0.293028\pi$
$211$	3710.82	1.21073	0.605363	+	0.795949i	$0.293028\pi$
$212$	2826.31	0.915621
$213$	2304.05	0.741178
$214$	2313.50	0.739008
$215$	−15.3914	−0.00488226
$216$	−216.000	−0.0680414
$217$	2024.11	0.633205
$218$	−506.700	−0.157422
$219$	−1338.88	−0.413118
$220$	−163.510	−0.0501083
$221$	347.239	0.105692
$222$	1298.37	0.392527
$223$	1869.27	0.561326	0.280663	−	0.959806i	$-0.409446\pi$
$223$	1869.27	0.561326	0.280663	+	0.959806i	$0.409446\pi$
$224$	−224.000	−0.0668153
$225$	−1116.74	−0.330887
$226$	−1169.51	−0.344224
$227$	424.371	0.124082	0.0620408	−	0.998074i	$-0.480239\pi$
$227$	424.371	0.124082	0.0620408	+	0.998074i	$0.480239\pi$
$228$	−228.000	−0.0662266
$229$	−4675.88	−1.34930	−0.674652	−	0.738136i	$-0.735706\pi$
$229$	−4675.88	−1.34930	−0.674652	+	0.738136i	$0.735706\pi$
$230$	365.024	0.104648
$231$	896.176	0.255256
$232$	2230.14	0.631102
$233$	5733.79	1.61216	0.806080	−	0.591806i	$-0.201585\pi$
$233$	5733.79	1.61216	0.806080	+	0.591806i	$0.201585\pi$
$234$	−579.440	−0.161877
$235$	−24.2782	−0.00673929
$236$	2623.25	0.723555
$237$	1156.72	0.317033
$238$	−151.015	−0.0411297
$239$	−5006.21	−1.35492	−0.677458	−	0.735561i	$-0.736919\pi$
$239$	−5006.21	−1.35492	−0.677458	+	0.735561i	$0.736919\pi$
$240$	−45.9781	−0.0123661
$241$	−5780.27	−1.54498	−0.772489	−	0.635028i	$-0.780989\pi$
$241$	−5780.27	−1.54498	−0.772489	+	0.635028i	$0.780989\pi$
$242$	−980.322	−0.260403
$243$	243.000	0.0641500
$244$	−1166.81	−0.306137
$245$	−46.9359	−0.0122393
$246$	374.084	0.0969541
$247$	−611.631	−0.157559
$248$	−2313.27	−0.592309
$249$	−2393.02	−0.609042
$250$	−477.180	−0.120718
$251$	−312.377	−0.0785540	−0.0392770	−	0.999228i	$-0.512505\pi$
$251$	−312.377	−0.0785540	−0.0392770	+	0.999228i	$0.512505\pi$
$252$	252.000	0.0629941
$253$	8131.24	2.02058
$254$	−2328.17	−0.575127
$255$	−30.9973	−0.00761226
$256$	256.000	0.0625000
$257$	659.728	0.160127	0.0800637	−	0.996790i	$-0.474488\pi$
$257$	659.728	0.160127	0.0800637	+	0.996790i	$0.474488\pi$
$258$	−96.4095	−0.0232643
$259$	−1514.77	−0.363409
$260$	−123.340	−0.0294202
$261$	−2508.91	−0.595009
$262$	−4774.23	−1.12577
$263$	2130.34	0.499477	0.249739	−	0.968313i	$-0.419655\pi$
$263$	2130.34	0.499477	0.249739	+	0.968313i	$0.419655\pi$
$264$	−1024.20	−0.238770
$265$	−676.813	−0.156892
$266$	266.000	0.0613139
$267$	2542.08	0.582670
$268$	−2753.51	−0.627603
$269$	694.530	0.157421	0.0787105	−	0.996898i	$-0.474920\pi$
$269$	694.530	0.157421	0.0787105	+	0.996898i	$0.474920\pi$
$270$	51.7253	0.0116589
$271$	−953.784	−0.213794	−0.106897	−	0.994270i	$-0.534092\pi$
$271$	−953.784	−0.213794	−0.106897	+	0.994270i	$0.534092\pi$
$272$	172.589	0.0384733
$273$	676.013	0.149869
$274$	−4677.84	−1.03138
$275$	−5295.23	−1.16114
$276$	2286.46	0.498655
$277$	867.260	0.188118	0.0940588	−	0.995567i	$-0.470016\pi$
$277$	867.260	0.188118	0.0940588	+	0.995567i	$0.470016\pi$
$278$	−1395.84	−0.301139
$279$	2602.43	0.558434
$280$	53.6411	0.0114488
$281$	3713.02	0.788256	0.394128	−	0.919055i	$-0.371047\pi$
$281$	3713.02	0.788256	0.394128	+	0.919055i	$0.371047\pi$
$282$	−152.075	−0.0321132
$283$	−5891.85	−1.23758	−0.618789	−	0.785558i	$-0.712376\pi$
$283$	−5891.85	−1.23758	−0.618789	+	0.785558i	$0.712376\pi$
$284$	3072.07	0.641879
$285$	54.5990	0.0113479
$286$	−2747.52	−0.568056
$287$	−436.431	−0.0897620
$288$	−288.000	−0.0589256
$289$	−4796.64	−0.976317
$290$	−534.049	−0.108139
$291$	923.871	0.186111
$292$	−1785.17	−0.357771
$293$	5808.24	1.15809	0.579046	−	0.815295i	$-0.303425\pi$
$293$	5808.24	1.15809	0.579046	+	0.815295i	$0.303425\pi$
$294$	−294.000	−0.0583212
$295$	−628.187	−0.123981
$296$	1731.16	0.339938
$297$	1152.23	0.225114
$298$	−4031.35	−0.783658
$299$	6133.64	1.18635
$300$	−1488.99	−0.286556
$301$	112.478	0.0215386
$302$	1864.65	0.355293
$303$	−3863.33	−0.732484
$304$	−304.000	−0.0573539
$305$	279.415	0.0524566
$306$	−194.163	−0.0362730
$307$	1013.66	0.188445	0.0942224	−	0.995551i	$-0.469964\pi$
$307$	1013.66	0.188445	0.0942224	+	0.995551i	$0.469964\pi$
$308$	1194.90	0.221058
$309$	3285.17	0.604812
$310$	553.956	0.101492
$311$	−6476.58	−1.18088	−0.590440	−	0.807082i	$-0.701046\pi$
$311$	−6476.58	−1.18088	−0.590440	+	0.807082i	$0.701046\pi$
$312$	−772.587	−0.140189
$313$	5465.04	0.986908	0.493454	−	0.869772i	$-0.335734\pi$
$313$	5465.04	0.986908	0.493454	+	0.869772i	$0.335734\pi$
$314$	3282.51	0.589946
$315$	−60.3462	−0.0107940
$316$	1542.29	0.274559
$317$	−2858.75	−0.506508	−0.253254	−	0.967400i	$-0.581501\pi$
$317$	−2858.75	−0.506508	−0.253254	+	0.967400i	$0.581501\pi$
$318$	−4239.46	−0.747601
$319$	−11896.4	−2.08800
$320$	−61.3041	−0.0107094
$321$	−3470.25	−0.603397
$322$	−2667.54	−0.461665
$323$	−204.949	−0.0353055
$324$	324.000	0.0555556
$325$	−3994.35	−0.681744
$326$	−3664.62	−0.622590
$327$	760.050	0.128535
$328$	498.778	0.0839647
$329$	177.421	0.0297311
$330$	245.265	0.0409132
$331$	−9156.88	−1.52057	−0.760283	−	0.649592i	$-0.774940\pi$
$331$	−9156.88	−1.52057	−0.760283	+	0.649592i	$0.774940\pi$
$332$	−3190.69	−0.527446
$333$	−1947.56	−0.320497
$334$	−3845.54	−0.629997
$335$	659.381	0.107540
$336$	336.000	0.0545545
$337$	−7940.83	−1.28357	−0.641787	−	0.766883i	$-0.721807\pi$
$337$	−7940.83	−1.28357	−0.641787	+	0.766883i	$0.721807\pi$
$338$	2321.46	0.373583
$339$	1754.26	0.281058
$340$	−41.3297	−0.00659241
$341$	12339.9	1.95965
$342$	342.000	0.0540738
$343$	343.000	0.0539949
$344$	−128.546	−0.0201475
$345$	−547.537	−0.0854446
$346$	−2392.63	−0.371759
$347$	−8353.36	−1.29231	−0.646156	−	0.763206i	$-0.723624\pi$
$347$	−8353.36	−1.29231	−0.646156	+	0.763206i	$0.723624\pi$
$348$	−3345.21	−0.515293
$349$	−5608.82	−0.860268	−0.430134	−	0.902765i	$-0.641534\pi$
$349$	−5608.82	−0.860268	−0.430134	+	0.902765i	$0.641534\pi$
$350$	1737.15	0.265299
$351$	869.160	0.132172
$352$	−1365.60	−0.206781
$353$	−11741.6	−1.77038	−0.885189	−	0.465232i	$-0.845971\pi$
$353$	−11741.6	−1.77038	−0.885189	+	0.465232i	$0.845971\pi$
$354$	−3934.87	−0.590780
$355$	−735.665	−0.109986
$356$	3389.44	0.504607
$357$	226.523	0.0335823
$358$	−6655.16	−0.982503
$359$	−10330.6	−1.51874	−0.759370	−	0.650659i	$-0.774493\pi$
$359$	−10330.6	−1.51874	−0.759370	+	0.650659i	$0.774493\pi$
$360$	68.9671	0.0100969
$361$	361.000	0.0526316
$362$	2853.45	0.414292
$363$	1470.48	0.212618
$364$	901.351	0.129790
$365$	427.493	0.0613041
$366$	1750.22	0.249960
$367$	−9002.04	−1.28039	−0.640194	−	0.768213i	$-0.721146\pi$
$367$	−9002.04	−1.28039	−0.640194	+	0.768213i	$0.721146\pi$
$368$	3048.61	0.431848
$369$	−561.125	−0.0791627
$370$	−414.559	−0.0582484
$371$	4946.04	0.692144
$372$	3469.90	0.483618
$373$	−2262.27	−0.314038	−0.157019	−	0.987596i	$-0.550188\pi$
$373$	−2262.27	−0.314038	−0.157019	+	0.987596i	$0.550188\pi$
$374$	−920.656	−0.127289
$375$	715.771	0.0985660
$376$	−202.767	−0.0278109
$377$	−8973.83	−1.22593
$378$	−378.000	−0.0514344
$379$	121.307	0.0164410	0.00822049	−	0.999966i	$-0.497383\pi$
$379$	121.307	0.0164410	0.00822049	+	0.999966i	$0.497383\pi$
$380$	72.7986	0.00982760
$381$	3492.25	0.469589
$382$	−4650.61	−0.622896
$383$	−2196.03	−0.292982	−0.146491	−	0.989212i	$-0.546798\pi$
$383$	−2196.03	−0.292982	−0.146491	+	0.989212i	$0.546798\pi$
$384$	−384.000	−0.0510310
$385$	−286.142	−0.0378783
$386$	969.303	0.127814
$387$	144.614	0.0189952
$388$	1231.83	0.161177
$389$	−12574.0	−1.63889	−0.819443	−	0.573160i	$-0.805717\pi$
$389$	−12574.0	−1.63889	−0.819443	+	0.573160i	$0.805717\pi$
$390$	185.011	0.0240215
$391$	2055.30	0.265834
$392$	−392.000	−0.0505076
$393$	7161.34	0.919191
$394$	9110.09	1.16487
$395$	−369.331	−0.0470457
$396$	1536.30	0.194955
$397$	13714.6	1.73380	0.866899	−	0.498485i	$-0.166110\pi$
$397$	13714.6	1.73380	0.866899	+	0.498485i	$0.166110\pi$
$398$	−8026.53	−1.01089
$399$	−399.000	−0.0500626
$400$	−1985.32	−0.248165
$401$	−1293.45	−0.161076	−0.0805381	−	0.996752i	$-0.525664\pi$
$401$	−1293.45	−0.161076	−0.0805381	+	0.996752i	$0.525664\pi$
$402$	4130.27	0.512436
$403$	9308.33	1.15057
$404$	−5151.11	−0.634350
$405$	−77.5880	−0.00951945
$406$	3902.74	0.477069
$407$	−9234.67	−1.12468
$408$	−258.883	−0.0314133
$409$	−3537.93	−0.427724	−0.213862	−	0.976864i	$-0.568604\pi$
$409$	−3537.93	−0.427724	−0.213862	+	0.976864i	$0.568604\pi$
$410$	−119.442	−0.0143874
$411$	7016.76	0.842120
$412$	4380.23	0.523782
$413$	4590.68	0.546956
$414$	−3429.69	−0.407150
$415$	764.072	0.0903779
$416$	−1030.12	−0.121408
$417$	2093.75	0.245879
$418$	1621.65	0.189755
$419$	13244.5	1.54424	0.772118	−	0.635480i	$-0.219198\pi$
$419$	13244.5	1.54424	0.772118	+	0.635480i	$0.219198\pi$
$420$	−80.4616	−0.00934792
$421$	5406.68	0.625903	0.312952	−	0.949769i	$-0.398682\pi$
$421$	5406.68	0.625903	0.312952	+	0.949769i	$0.398682\pi$
$422$	−7421.64	−0.856113
$423$	228.112	0.0262203
$424$	−5652.62	−0.647442
$425$	−1338.45	−0.152764
$426$	−4608.10	−0.524092
$427$	−2041.92	−0.231418
$428$	−4627.00	−0.522557
$429$	4121.27	0.463816
$430$	30.7828	0.00345228
$431$	−1156.74	−0.129276	−0.0646381	−	0.997909i	$-0.520589\pi$
$431$	−1156.74	−0.129276	−0.0646381	+	0.997909i	$0.520589\pi$
$432$	432.000	0.0481125
$433$	−3942.00	−0.437506	−0.218753	−	0.975780i	$-0.570199\pi$
$433$	−3942.00	−0.437506	−0.218753	+	0.975780i	$0.570199\pi$
$434$	−4048.22	−0.447744
$435$	801.074	0.0882955
$436$	1013.40	0.111314
$437$	−3620.23	−0.396291
$438$	2677.75	0.292119
$439$	−12042.4	−1.30923	−0.654614	−	0.755964i	$-0.727169\pi$
$439$	−12042.4	−1.30923	−0.654614	+	0.755964i	$0.727169\pi$
$440$	327.019	0.0354319
$441$	441.000	0.0476190
$442$	−694.479	−0.0747353
$443$	−7792.48	−0.835738	−0.417869	−	0.908507i	$-0.637223\pi$
$443$	−7792.48	−0.835738	−0.417869	+	0.908507i	$0.637223\pi$
$444$	−2596.74	−0.277558
$445$	−811.666	−0.0864645
$446$	−3738.54	−0.396918
$447$	6047.03	0.639854
$448$	448.000	0.0472456
$449$	16263.4	1.70939	0.854694	−	0.519132i	$-0.173745\pi$
$449$	16263.4	1.70939	0.854694	+	0.519132i	$0.173745\pi$
$450$	2233.48	0.233972
$451$	−2660.67	−0.277797
$452$	2339.02	0.243403
$453$	−2796.98	−0.290096
$454$	−848.743	−0.0877389
$455$	−215.846	−0.0222396
$456$	456.000	0.0468293
$457$	5441.46	0.556982	0.278491	−	0.960439i	$-0.410166\pi$
$457$	5441.46	0.556982	0.278491	+	0.960439i	$0.410166\pi$
$458$	9351.75	0.954102
$459$	291.244	0.0296168
$460$	−730.049	−0.0739972
$461$	−3237.10	−0.327043	−0.163521	−	0.986540i	$-0.552285\pi$
$461$	−3237.10	−0.327043	−0.163521	+	0.986540i	$0.552285\pi$
$462$	−1792.35	−0.180493
$463$	−3099.11	−0.311075	−0.155537	−	0.987830i	$-0.549711\pi$
$463$	−3099.11	−0.311075	−0.155537	+	0.987830i	$0.549711\pi$
$464$	−4460.28	−0.446257
$465$	−830.934	−0.0828681
$466$	−11467.6	−1.13997
$467$	6407.27	0.634889	0.317444	−	0.948277i	$-0.397175\pi$
$467$	6407.27	0.634889	0.317444	+	0.948277i	$0.397175\pi$
$468$	1158.88	0.114464
$469$	−4818.65	−0.474423
$470$	48.5563	0.00476539
$471$	−4923.77	−0.481689
$472$	−5246.50	−0.511630
$473$	685.714	0.0666578
$474$	−2313.44	−0.224176
$475$	2357.57	0.227732
$476$	302.031	0.0290831
$477$	6359.19	0.610414
$478$	10012.4	0.958071
$479$	13646.5	1.30172	0.650859	−	0.759198i	$-0.274409\pi$
$479$	13646.5	1.30172	0.650859	+	0.759198i	$0.274409\pi$
$480$	91.9561	0.00874417
$481$	−6966.00	−0.660337
$482$	11560.5	1.09246
$483$	4001.31	0.376948
$484$	1960.64	0.184133
$485$	−294.985	−0.0276177
$486$	−486.000	−0.0453609
$487$	−6542.48	−0.608764	−0.304382	−	0.952550i	$-0.598450\pi$
$487$	−6542.48	−0.608764	−0.304382	+	0.952550i	$0.598450\pi$
$488$	2333.62	0.216471
$489$	5496.93	0.508343
$490$	93.8719	0.00865449
$491$	16818.8	1.54587	0.772937	−	0.634483i	$-0.218787\pi$
$491$	16818.8	1.54587	0.772937	+	0.634483i	$0.218787\pi$
$492$	−748.167	−0.0685569
$493$	−3007.01	−0.274704
$494$	1223.26	0.111411
$495$	−367.897	−0.0334055
$496$	4626.54	0.418826
$497$	5376.12	0.485215
$498$	4786.04	0.430658
$499$	−10750.8	−0.964468	−0.482234	−	0.876042i	$-0.660175\pi$
$499$	−10750.8	−0.964468	−0.482234	+	0.876042i	$0.660175\pi$
$500$	954.361	0.0853606
$501$	5768.32	0.514390
$502$	624.754	0.0555461
$503$	−15880.7	−1.40772	−0.703861	−	0.710337i	$-0.748542\pi$
$503$	−15880.7	−1.40772	−0.703861	+	0.710337i	$0.748542\pi$
$504$	−504.000	−0.0445435
$505$	1233.53	0.108696
$506$	−16262.5	−1.42877
$507$	−3482.20	−0.305029
$508$	4656.34	0.406676
$509$	−14703.6	−1.28040	−0.640201	−	0.768207i	$-0.721149\pi$
$509$	−14703.6	−1.28040	−0.640201	+	0.768207i	$0.721149\pi$
$510$	61.9946	0.00538268
$511$	−3124.05	−0.270449
$512$	−512.000	−0.0441942
$513$	−513.000	−0.0441511
$514$	−1319.46	−0.113227
$515$	−1048.93	−0.0897502
$516$	192.819	0.0164504
$517$	1081.63	0.0920120
$518$	3029.53	0.256969
$519$	3588.94	0.303540
$520$	246.681	0.0208032
$521$	−22660.3	−1.90550	−0.952750	−	0.303756i	$-0.901759\pi$
$521$	−22660.3	−1.90550	−0.952750	+	0.303756i	$0.901759\pi$
$522$	5017.81	0.420735
$523$	−14888.8	−1.24482	−0.622409	−	0.782692i	$-0.713846\pi$
$523$	−14888.8	−1.24482	−0.622409	+	0.782692i	$0.713846\pi$
$524$	9548.46	0.796043
$525$	−2605.73	−0.216616
$526$	−4260.68	−0.353184
$527$	3119.10	0.257818
$528$	2048.40	0.168836
$529$	24137.9	1.98388
$530$	1353.63	0.110939
$531$	5902.31	0.482370
$532$	−532.000	−0.0433555
$533$	−2007.03	−0.163103
$534$	−5084.16	−0.412010
$535$	1108.02	0.0895403
$536$	5507.02	0.443782
$537$	9982.74	0.802210
$538$	−1389.06	−0.111313
$539$	2091.08	0.167104
$540$	−103.451	−0.00824409
$541$	−12432.5	−0.988015	−0.494007	−	0.869458i	$-0.664468\pi$
$541$	−12432.5	−0.988015	−0.494007	+	0.869458i	$0.664468\pi$
$542$	1907.57	0.151175
$543$	−4280.17	−0.338268
$544$	−345.178	−0.0272047
$545$	−242.678	−0.0190737
$546$	−1352.03	−0.105973
$547$	22525.0	1.76070	0.880349	−	0.474327i	$-0.157309\pi$
$547$	22525.0	1.76070	0.880349	+	0.474327i	$0.157309\pi$
$548$	9355.68	0.729297
$549$	−2625.32	−0.204091
$550$	10590.5	0.821052
$551$	5296.58	0.409513
$552$	−4572.92	−0.352602
$553$	2699.01	0.207547
$554$	−1734.52	−0.133019
$555$	621.839	0.0475596
$556$	2791.67	0.212938
$557$	227.234	0.0172858	0.00864292	−	0.999963i	$-0.497249\pi$
$557$	227.234	0.0172858	0.00864292	+	0.999963i	$0.497249\pi$
$558$	−5204.85	−0.394873
$559$	517.255	0.0391370
$560$	−107.282	−0.00809553
$561$	1380.98	0.103931
$562$	−7426.04	−0.557381
$563$	4284.66	0.320741	0.160370	−	0.987057i	$-0.448731\pi$
$563$	4284.66	0.320741	0.160370	+	0.987057i	$0.448731\pi$
$564$	304.150	0.0227075
$565$	−560.123	−0.0417072
$566$	11783.7	0.875099
$567$	567.000	0.0419961
$568$	−6144.13	−0.453877
$569$	−750.365	−0.0552846	−0.0276423	−	0.999618i	$-0.508800\pi$
$569$	−750.365	−0.0552846	−0.0276423	+	0.999618i	$0.508800\pi$
$570$	−109.198	−0.00802421
$571$	23834.9	1.74687	0.873433	−	0.486945i	$-0.161889\pi$
$571$	23834.9	1.74687	0.873433	+	0.486945i	$0.161889\pi$
$572$	5495.03	0.401676
$573$	6975.92	0.508592
$574$	872.862	0.0634713
$575$	−23642.5	−1.71471
$576$	576.000	0.0416667
$577$	8526.28	0.615171	0.307586	−	0.951520i	$-0.400479\pi$
$577$	8526.28	0.615171	0.307586	+	0.951520i	$0.400479\pi$
$578$	9593.29	0.690360
$579$	−1453.96	−0.104360
$580$	1068.10	0.0764662
$581$	−5583.71	−0.398712
$582$	−1847.74	−0.131600
$583$	30153.2	2.14206
$584$	3570.34	0.252982
$585$	−277.516	−0.0196135
$586$	−11616.5	−0.818894
$587$	−3995.61	−0.280948	−0.140474	−	0.990084i	$-0.544863\pi$
$587$	−3995.61	−0.280948	−0.140474	+	0.990084i	$0.544863\pi$
$588$	588.000	0.0412393
$589$	−5494.01	−0.384341
$590$	1256.37	0.0876679
$591$	−13665.1	−0.951114
$592$	−3462.32	−0.240373
$593$	25494.6	1.76549	0.882747	−	0.469849i	$-0.155692\pi$
$593$	25494.6	1.76549	0.882747	+	0.469849i	$0.155692\pi$
$594$	−2304.45	−0.159180
$595$	−72.3270	−0.00498339
$596$	8062.71	0.554130
$597$	12039.8	0.825387
$598$	−12267.3	−0.838874
$599$	−10081.5	−0.687678	−0.343839	−	0.939029i	$-0.611728\pi$
$599$	−10081.5	−0.687678	−0.343839	+	0.939029i	$0.611728\pi$
$600$	2977.98	0.202626
$601$	−22714.5	−1.54167	−0.770836	−	0.637034i	$-0.780161\pi$
$601$	−22714.5	−1.54167	−0.770836	+	0.637034i	$0.780161\pi$
$602$	−224.956	−0.0152301
$603$	−6195.40	−0.418402
$604$	−3729.30	−0.251230
$605$	−469.514	−0.0315511
$606$	7726.67	0.517945
$607$	27611.5	1.84632	0.923158	−	0.384420i	$-0.125599\pi$
$607$	27611.5	1.84632	0.923158	+	0.384420i	$0.125599\pi$
$608$	608.000	0.0405554
$609$	−5854.11	−0.389525
$610$	−558.830	−0.0370924
$611$	815.910	0.0540232
$612$	388.325	0.0256489
$613$	−1618.61	−0.106648	−0.0533240	−	0.998577i	$-0.516982\pi$
$613$	−1618.61	−0.106648	−0.0533240	+	0.998577i	$0.516982\pi$
$614$	−2027.32	−0.133251
$615$	179.163	0.0117472
$616$	−2389.80	−0.156312
$617$	14155.6	0.923634	0.461817	−	0.886975i	$-0.347198\pi$
$617$	14155.6	0.923634	0.461817	+	0.886975i	$0.347198\pi$
$618$	−6570.34	−0.427666
$619$	−20382.9	−1.32352	−0.661758	−	0.749717i	$-0.730189\pi$
$619$	−20382.9	−1.32352	−0.661758	+	0.749717i	$0.730189\pi$
$620$	−1107.91	−0.0717658
$621$	5144.54	0.332437
$622$	12953.2	0.835008
$623$	5931.52	0.381447
$624$	1545.17	0.0991289
$625$	15281.8	0.978033
$626$	−10930.1	−0.697849
$627$	−2432.48	−0.154934
$628$	−6565.03	−0.417155
$629$	−2334.21	−0.147967
$630$	120.692	0.00763254
$631$	22496.1	1.41926	0.709631	−	0.704573i	$-0.248861\pi$
$631$	22496.1	1.41926	0.709631	+	0.704573i	$0.248861\pi$
$632$	−3084.58	−0.194142
$633$	11132.5	0.699013
$634$	5717.49	0.358156
$635$	−1115.05	−0.0696840
$636$	8478.92	0.528634
$637$	1577.36	0.0981122
$638$	23792.8	1.47644
$639$	6912.15	0.427919
$640$	122.608	0.00757268
$641$	−19327.3	−1.19092	−0.595461	−	0.803384i	$-0.703031\pi$
$641$	−19327.3	−1.19092	−0.595461	+	0.803384i	$0.703031\pi$
$642$	6940.50	0.426666
$643$	5394.52	0.330854	0.165427	−	0.986222i	$-0.447100\pi$
$643$	5394.52	0.330854	0.165427	+	0.986222i	$0.447100\pi$
$644$	5335.07	0.326446
$645$	−46.1742	−0.00281877
$646$	409.899	0.0249648
$647$	−27663.6	−1.68094	−0.840469	−	0.541860i	$-0.817720\pi$
$647$	−27663.6	−1.68094	−0.840469	+	0.541860i	$0.817720\pi$
$648$	−648.000	−0.0392837
$649$	27986.8	1.69273
$650$	7988.71	0.482066
$651$	6072.33	0.365581
$652$	7329.24	0.440238
$653$	−19718.9	−1.18172	−0.590858	−	0.806775i	$-0.701211\pi$
$653$	−19718.9	−1.18172	−0.590858	+	0.806775i	$0.701211\pi$
$654$	−1520.10	−0.0908878
$655$	−2286.56	−0.136402
$656$	−997.556	−0.0593720
$657$	−4016.63	−0.238514
$658$	−354.841	−0.0210230
$659$	11468.0	0.677890	0.338945	−	0.940806i	$-0.389930\pi$
$659$	11468.0	0.677890	0.338945	+	0.940806i	$0.389930\pi$
$660$	−490.529	−0.0289300
$661$	22961.0	1.35110	0.675551	−	0.737313i	$-0.263906\pi$
$661$	22961.0	1.35110	0.675551	+	0.737313i	$0.263906\pi$
$662$	18313.8	1.07520
$663$	1041.72	0.0610211
$664$	6381.39	0.372961
$665$	127.398	0.00742897
$666$	3895.11	0.226625
$667$	−53115.9	−3.08344
$668$	7691.09	0.445475
$669$	5607.82	0.324082
$670$	−1318.76	−0.0760421
$671$	−12448.4	−0.716194
$672$	−672.000	−0.0385758
$673$	−8261.77	−0.473206	−0.236603	−	0.971606i	$-0.576034\pi$
$673$	−8261.77	−0.473206	−0.236603	+	0.971606i	$0.576034\pi$
$674$	15881.7	0.907624
$675$	−3350.23	−0.191037
$676$	−4642.93	−0.264163
$677$	−4792.63	−0.272076	−0.136038	−	0.990704i	$-0.543437\pi$
$677$	−4792.63	−0.272076	−0.136038	+	0.990704i	$0.543437\pi$
$678$	−3508.53	−0.198738
$679$	2155.70	0.121838
$680$	82.6595	0.00466154
$681$	1273.11	0.0716385
$682$	−24679.7	−1.38568
$683$	−1823.02	−0.102132	−0.0510659	−	0.998695i	$-0.516262\pi$
$683$	−1823.02	−0.102132	−0.0510659	+	0.998695i	$0.516262\pi$
$684$	−684.000	−0.0382360
$685$	−2240.40	−0.124965
$686$	−686.000	−0.0381802
$687$	−14027.6	−0.779021
$688$	257.092	0.0142464
$689$	22745.5	1.25767
$690$	1095.07	0.0604184
$691$	−23537.2	−1.29580	−0.647900	−	0.761725i	$-0.724353\pi$
$691$	−23537.2	−1.29580	−0.647900	+	0.761725i	$0.724353\pi$
$692$	4785.26	0.262873
$693$	2688.53	0.147372
$694$	16706.7	0.913802
$695$	−668.519	−0.0364869
$696$	6690.41	0.364367
$697$	−672.528	−0.0365478
$698$	11217.6	0.608301
$699$	17201.4	0.930781
$700$	−3474.31	−0.187595
$701$	−6475.06	−0.348873	−0.174436	−	0.984668i	$-0.555810\pi$
$701$	−6475.06	−0.348873	−0.174436	+	0.984668i	$0.555810\pi$
$702$	−1738.32	−0.0934596
$703$	4111.51	0.220581
$704$	2731.20	0.146216
$705$	−72.8345	−0.00389093
$706$	23483.2	1.25185
$707$	−9014.45	−0.479524
$708$	7869.74	0.417744
$709$	−16594.2	−0.878998	−0.439499	−	0.898243i	$-0.644844\pi$
$709$	−16594.2	−0.878998	−0.439499	+	0.898243i	$0.644844\pi$
$710$	1471.33	0.0777719
$711$	3470.15	0.183039
$712$	−6778.88	−0.356811
$713$	55095.8	2.89390
$714$	−453.046	−0.0237463
$715$	−1315.89	−0.0688273
$716$	13310.3	0.694734
$717$	−15018.6	−0.782261
$718$	20661.2	1.07391
$719$	−28113.3	−1.45820	−0.729102	−	0.684405i	$-0.760062\pi$
$719$	−28113.3	−1.45820	−0.729102	+	0.684405i	$0.760062\pi$
$720$	−137.934	−0.00713959
$721$	7665.40	0.395942
$722$	−722.000	−0.0372161
$723$	−17340.8	−0.891994
$724$	−5706.89	−0.292949
$725$	34590.1	1.77192
$726$	−2940.97	−0.150344
$727$	−5198.50	−0.265202	−0.132601	−	0.991170i	$-0.542333\pi$
$727$	−5198.50	−0.265202	−0.132601	+	0.991170i	$0.542333\pi$
$728$	−1802.70	−0.0917755
$729$	729.000	0.0370370
$730$	−854.986	−0.0433485
$731$	173.325	0.00876972
$732$	−3500.43	−0.176748
$733$	9445.28	0.475947	0.237974	−	0.971272i	$-0.423517\pi$
$733$	9445.28	0.475947	0.237974	+	0.971272i	$0.423517\pi$
$734$	18004.1	0.905371
$735$	−140.808	−0.00706636
$736$	−6097.23	−0.305363
$737$	−29376.6	−1.46825
$738$	1122.25	0.0559765
$739$	2222.26	0.110618	0.0553092	−	0.998469i	$-0.482386\pi$
$739$	2222.26	0.110618	0.0553092	+	0.998469i	$0.482386\pi$
$740$	829.119	0.0411879
$741$	−1834.89	−0.0909669
$742$	−9892.08	−0.489420
$743$	−3015.06	−0.148872	−0.0744360	−	0.997226i	$-0.523716\pi$
$743$	−3015.06	−0.148872	−0.0744360	+	0.997226i	$0.523716\pi$
$744$	−6939.80	−0.341970
$745$	−1930.77	−0.0949502
$746$	4524.54	0.222058
$747$	−7179.06	−0.351631
$748$	1841.31	0.0900067
$749$	−8097.25	−0.395016
$750$	−1431.54	−0.0696967
$751$	24780.4	1.20406	0.602031	−	0.798472i	$-0.294358\pi$
$751$	24780.4	1.20406	0.602031	+	0.798472i	$0.294358\pi$
$752$	405.533	0.0196652
$753$	−937.131	−0.0453532
$754$	17947.7	0.866864
$755$	893.052	0.0430483
$756$	756.000	0.0363696
$757$	−24015.3	−1.15304	−0.576519	−	0.817084i	$-0.695589\pi$
$757$	−24015.3	−1.15304	−0.576519	+	0.817084i	$0.695589\pi$
$758$	−242.614	−0.0116255
$759$	24393.7	1.16658
$760$	−145.597	−0.00694917
$761$	290.631	0.0138441	0.00692204	−	0.999976i	$-0.497797\pi$
$761$	290.631	0.0138441	0.00692204	+	0.999976i	$0.497797\pi$
$762$	−6984.51	−0.332050
$763$	1773.45	0.0841457
$764$	9301.23	0.440454
$765$	−92.9919	−0.00439494
$766$	4392.06	0.207169
$767$	21111.3	0.993853
$768$	768.000	0.0360844
$769$	35788.8	1.67825	0.839126	−	0.543937i	$-0.183067\pi$
$769$	35788.8	1.67825	0.839126	+	0.543937i	$0.183067\pi$
$770$	572.284	0.0267840
$771$	1979.18	0.0924496
$772$	−1938.61	−0.0903782
$773$	−15452.0	−0.718977	−0.359488	−	0.933150i	$-0.617049\pi$
$773$	−15452.0	−0.718977	−0.359488	+	0.933150i	$0.617049\pi$
$774$	−289.229	−0.0134317
$775$	−35879.5	−1.66301
$776$	−2463.66	−0.113969
$777$	−4544.30	−0.209814
$778$	25148.0	1.15887
$779$	1184.60	0.0544835
$780$	−370.021	−0.0169858
$781$	32775.2	1.50165
$782$	−4110.60	−0.187973
$783$	−7526.72	−0.343529
$784$	784.000	0.0357143
$785$	1572.12	0.0714795
$786$	−14322.7	−0.649966
$787$	−33236.4	−1.50540	−0.752700	−	0.658363i	$-0.771249\pi$
$787$	−33236.4	−1.50540	−0.752700	+	0.658363i	$0.771249\pi$
$788$	−18220.2	−0.823689
$789$	6391.02	0.288373
$790$	738.662	0.0332663
$791$	4093.28	0.183995
$792$	−3072.60	−0.137854
$793$	−9390.23	−0.420500
$794$	−27429.3	−1.22598
$795$	−2030.44	−0.0905815
$796$	16053.1	0.714806
$797$	−2087.03	−0.0927557	−0.0463778	−	0.998924i	$-0.514768\pi$
$797$	−2087.03	−0.0927557	−0.0463778	+	0.998924i	$0.514768\pi$
$798$	798.000	0.0353996
$799$	273.401	0.0121054
$800$	3970.64	0.175479
$801$	7626.24	0.336405
$802$	2586.89	0.113898
$803$	−19045.6	−0.836990
$804$	−8260.54	−0.362347
$805$	−1277.59	−0.0559366
$806$	−18616.7	−0.813578
$807$	2083.59	0.0908871
$808$	10302.2	0.448553
$809$	−20630.0	−0.896556	−0.448278	−	0.893894i	$-0.647963\pi$
$809$	−20630.0	−0.896556	−0.448278	+	0.893894i	$0.647963\pi$
$810$	155.176	0.00673127
$811$	−13487.1	−0.583967	−0.291984	−	0.956423i	$-0.594315\pi$
$811$	−13487.1	−0.583967	−0.291984	+	0.956423i	$0.594315\pi$
$812$	−7805.48	−0.337338
$813$	−2861.35	−0.123434
$814$	18469.3	0.795271
$815$	−1755.13	−0.0754348
$816$	517.767	0.0222126
$817$	−305.297	−0.0130734
$818$	7075.86	0.302447
$819$	2028.04	0.0865268
$820$	238.884	0.0101734
$821$	−4755.66	−0.202160	−0.101080	−	0.994878i	$-0.532230\pi$
$821$	−4755.66	−0.202160	−0.101080	+	0.994878i	$0.532230\pi$
$822$	−14033.5	−0.595469
$823$	17095.3	0.724065	0.362033	−	0.932165i	$-0.382083\pi$
$823$	17095.3	0.724065	0.362033	+	0.932165i	$0.382083\pi$
$824$	−8760.45	−0.370370
$825$	−15885.7	−0.670386
$826$	−9181.37	−0.386756
$827$	−25657.9	−1.07885	−0.539426	−	0.842033i	$-0.681359\pi$
$827$	−25657.9	−1.07885	−0.539426	+	0.842033i	$0.681359\pi$
$828$	6859.38	0.287899
$829$	1196.09	0.0501108	0.0250554	−	0.999686i	$-0.492024\pi$
$829$	1196.09	0.0501108	0.0250554	+	0.999686i	$0.492024\pi$
$830$	−1528.14	−0.0639068
$831$	2601.78	0.108610
$832$	2060.23	0.0858482
$833$	528.554	0.0219848
$834$	−4187.51	−0.173863
$835$	−1841.78	−0.0763322
$836$	−3243.30	−0.134177
$837$	7807.28	0.322412
$838$	−26488.9	−1.09194
$839$	−15857.4	−0.652513	−0.326257	−	0.945281i	$-0.605787\pi$
$839$	−15857.4	−0.652513	−0.326257	+	0.945281i	$0.605787\pi$
$840$	160.923	0.00660997
$841$	53322.2	2.18632
$842$	−10813.4	−0.442580
$843$	11139.1	0.455100
$844$	14843.3	0.605363
$845$	1111.84	0.0452644
$846$	−456.225	−0.0185406
$847$	3431.13	0.139191
$848$	11305.2	0.457811
$849$	−17675.6	−0.714515
$850$	2676.91	0.108020
$851$	−41231.6	−1.66087
$852$	9216.20	0.370589
$853$	−4769.97	−0.191466	−0.0957330	−	0.995407i	$-0.530520\pi$
$853$	−4769.97	−0.191466	−0.0957330	+	0.995407i	$0.530520\pi$
$854$	4083.84	0.163637
$855$	163.797	0.00655174
$856$	9254.00	0.369504
$857$	26231.0	1.04555	0.522773	−	0.852472i	$-0.324897\pi$
$857$	26231.0	1.04555	0.522773	+	0.852472i	$0.324897\pi$
$858$	−8242.55	−0.327967
$859$	−11099.5	−0.440873	−0.220437	−	0.975401i	$-0.570748\pi$
$859$	−11099.5	−0.440873	−0.220437	+	0.975401i	$0.570748\pi$
$860$	−61.5656	−0.00244113
$861$	−1309.29	−0.0518241
$862$	2313.47	0.0914121
$863$	6675.79	0.263322	0.131661	−	0.991295i	$-0.457969\pi$
$863$	6675.79	0.263322	0.131661	+	0.991295i	$0.457969\pi$
$864$	−864.000	−0.0340207
$865$	−1145.92	−0.0450433
$866$	7883.99	0.309364
$867$	−14389.9	−0.563677
$868$	8096.44	0.316602
$869$	16454.3	0.642319
$870$	−1602.15	−0.0624344
$871$	−22159.7	−0.862057
$872$	−2026.80	−0.0787111
$873$	2771.61	0.107451
$874$	7240.46	0.280220
$875$	1670.13	0.0645266
$876$	−5355.51	−0.206559
$877$	29534.9	1.13720	0.568600	−	0.822614i	$-0.307485\pi$
$877$	29534.9	1.13720	0.568600	+	0.822614i	$0.307485\pi$
$878$	24084.7	0.925763
$879$	17424.7	0.668624
$880$	−654.039	−0.0250541
$881$	−15594.4	−0.596354	−0.298177	−	0.954511i	$-0.596379\pi$
$881$	−15594.4	−0.596354	−0.298177	+	0.954511i	$0.596379\pi$
$882$	−882.000	−0.0336718
$883$	22338.2	0.851349	0.425675	−	0.904876i	$-0.360037\pi$
$883$	22338.2	0.851349	0.425675	+	0.904876i	$0.360037\pi$
$884$	1388.96	0.0528458
$885$	−1884.56	−0.0715806
$886$	15585.0	0.590956
$887$	−43433.7	−1.64415	−0.822074	−	0.569381i	$-0.807183\pi$
$887$	−43433.7	−1.64415	−0.822074	+	0.569381i	$0.807183\pi$
$888$	5193.48	0.196263
$889$	8148.59	0.307418
$890$	1623.33	0.0611396
$891$	3456.68	0.129970
$892$	7477.09	0.280663
$893$	−481.570	−0.0180461
$894$	−12094.1	−0.452445
$895$	−3187.41	−0.119043
$896$	−896.000	−0.0334077
$897$	18400.9	0.684938
$898$	−32526.7	−1.20872
$899$	−80607.9	−2.99046
$900$	−4466.97	−0.165443
$901$	7621.71	0.281816
$902$	5321.35	0.196432
$903$	337.433	0.0124353
$904$	−4678.04	−0.172112
$905$	1366.62	0.0501968
$906$	5593.95	0.205129
$907$	42112.4	1.54170	0.770849	−	0.637018i	$-0.219832\pi$
$907$	42112.4	1.54170	0.770849	+	0.637018i	$0.219832\pi$
$908$	1697.49	0.0620408
$909$	−11590.0	−0.422900
$910$	431.691	0.0157258
$911$	−1148.33	−0.0417626	−0.0208813	−	0.999782i	$-0.506647\pi$
$911$	−1148.33	−0.0417626	−0.0208813	+	0.999782i	$0.506647\pi$
$912$	−912.000	−0.0331133
$913$	−34040.8	−1.23394
$914$	−10882.9	−0.393845
$915$	838.245	0.0302858
$916$	−18703.5	−0.674652
$917$	16709.8	0.601752
$918$	−582.488	−0.0209422
$919$	−37464.1	−1.34475	−0.672376	−	0.740210i	$-0.734726\pi$
$919$	−37464.1	−1.34475	−0.672376	+	0.740210i	$0.734726\pi$
$920$	1460.10	0.0523239
$921$	3040.98	0.108799
$922$	6474.19	0.231254
$923$	24723.3	0.881666
$924$	3584.71	0.127628
$925$	26850.8	0.954432
$926$	6198.21	0.219963
$927$	9855.51	0.349188
$928$	8920.55	0.315551
$929$	−31397.2	−1.10884	−0.554419	−	0.832238i	$-0.687059\pi$
$929$	−31397.2	−1.10884	−0.554419	+	0.832238i	$0.687059\pi$
$930$	1661.87	0.0585966
$931$	−931.000	−0.0327737
$932$	22935.2	0.806080
$933$	−19429.8	−0.681781
$934$	−12814.5	−0.448934
$935$	−440.937	−0.0154227
$936$	−2317.76	−0.0809384
$937$	−28148.6	−0.981404	−0.490702	−	0.871328i	$-0.663260\pi$
$937$	−28148.6	−0.981404	−0.490702	+	0.871328i	$0.663260\pi$
$938$	9637.29	0.335468
$939$	16395.1	0.569792
$940$	−97.1126	−0.00336964
$941$	−49168.6	−1.70335	−0.851674	−	0.524072i	$-0.824412\pi$
$941$	−49168.6	−1.70335	−0.851674	+	0.524072i	$0.824412\pi$
$942$	9847.54	0.340605
$943$	−11879.5	−0.410235
$944$	10493.0	0.361777
$945$	−181.039	−0.00623194
$946$	−1371.43	−0.0471342
$947$	−10448.2	−0.358521	−0.179261	−	0.983802i	$-0.557371\pi$
$947$	−10448.2	−0.358521	−0.179261	+	0.983802i	$0.557371\pi$
$948$	4626.87	0.158517
$949$	−14366.6	−0.491424
$950$	−4715.13	−0.161031
$951$	−8576.24	−0.292433
$952$	−604.061	−0.0205649
$953$	10037.1	0.341170	0.170585	−	0.985343i	$-0.445434\pi$
$953$	10037.1	0.341170	0.170585	+	0.985343i	$0.445434\pi$
$954$	−12718.4	−0.431628
$955$	−2227.36	−0.0754718
$956$	−20024.9	−0.677458
$957$	−35689.2	−1.20551
$958$	−27292.9	−0.920454
$959$	16372.4	0.551297
$960$	−183.912	−0.00618307
$961$	53821.6	1.80664
$962$	13932.0	0.466929
$963$	−10410.8	−0.348372
$964$	−23121.1	−0.772489
$965$	464.236	0.0154863
$966$	−8002.61	−0.266542
$967$	35883.8	1.19333	0.596663	−	0.802492i	$-0.296493\pi$
$967$	35883.8	1.19333	0.596663	+	0.802492i	$0.296493\pi$
$968$	−3921.29	−0.130201
$969$	−614.848	−0.0203837
$970$	589.969	0.0195286
$971$	19652.9	0.649528	0.324764	−	0.945795i	$-0.394715\pi$
$971$	19652.9	0.649528	0.324764	+	0.945795i	$0.394715\pi$
$972$	972.000	0.0320750
$973$	4885.43	0.160966
$974$	13085.0	0.430461
$975$	−11983.1	−0.393605
$976$	−4667.24	−0.153068
$977$	−26441.8	−0.865862	−0.432931	−	0.901427i	$-0.642521\pi$
$977$	−26441.8	−0.865862	−0.432931	+	0.901427i	$0.642521\pi$
$978$	−10993.9	−0.359453
$979$	36161.2	1.18051
$980$	−187.744	−0.00611965
$981$	2280.15	0.0742096
$982$	−33637.7	−1.09310
$983$	9550.93	0.309896	0.154948	−	0.987923i	$-0.450479\pi$
$983$	9550.93	0.309896	0.154948	+	0.987923i	$0.450479\pi$
$984$	1496.33	0.0484770
$985$	4363.17	0.141139
$986$	6014.02	0.194245
$987$	532.262	0.0171652
$988$	−2446.52	−0.0787797
$989$	3061.62	0.0984366
$990$	735.794	0.0236213
$991$	−1002.40	−0.0321316	−0.0160658	−	0.999871i	$-0.505114\pi$
$991$	−1002.40	−0.0321316	−0.0160658	+	0.999871i	$0.505114\pi$
$992$	−9253.07	−0.296155
$993$	−27470.6	−0.877900
$994$	−10752.2	−0.343099
$995$	−3844.21	−0.122482
$996$	−9572.08	−0.304521
$997$	−10111.1	−0.321186	−0.160593	−	0.987021i	$-0.551341\pi$
$997$	−10111.1	−0.321186	−0.160593	+	0.987021i	$0.551341\pi$
$998$	21501.5	0.681982
$999$	−5842.67	−0.185039

Twists

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

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

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -0.957876 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -0.957876 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +1.91575 q^{10} +42.6751 q^{11} +12.0000 q^{12} +32.1911 q^{13} -14.0000 q^{14} -2.87363 q^{15} +16.0000 q^{16} +10.7868 q^{17} -18.0000 q^{18} -19.0000 q^{19} -3.83151 q^{20} +21.0000 q^{21} -85.3501 q^{22} +190.538 q^{23} -24.0000 q^{24} -124.082 q^{25} -64.3822 q^{26} +27.0000 q^{27} +28.0000 q^{28} -278.767 q^{29} +5.74726 q^{30} +289.158 q^{31} -32.0000 q^{32} +128.025 q^{33} -21.5736 q^{34} -6.70513 q^{35} +36.0000 q^{36} -216.395 q^{37} +38.0000 q^{38} +96.5733 q^{39} +7.66301 q^{40} -62.3473 q^{41} -42.0000 q^{42} +16.0683 q^{43} +170.700 q^{44} -8.62089 q^{45} -381.077 q^{46} +25.3458 q^{47} +48.0000 q^{48} +49.0000 q^{49} +248.165 q^{50} +32.3604 q^{51} +128.764 q^{52} +706.577 q^{53} -54.0000 q^{54} -40.8774 q^{55} -56.0000 q^{56} -57.0000 q^{57} +557.535 q^{58} +655.812 q^{59} -11.4945 q^{60} -291.703 q^{61} -578.317 q^{62} +63.0000 q^{63} +64.0000 q^{64} -30.8351 q^{65} -256.050 q^{66} -688.378 q^{67} +43.1472 q^{68} +571.615 q^{69} +13.4103 q^{70} +768.017 q^{71} -72.0000 q^{72} -446.292 q^{73} +432.790 q^{74} -372.247 q^{75} -76.0000 q^{76} +298.725 q^{77} -193.147 q^{78} +385.573 q^{79} -15.3260 q^{80} +81.0000 q^{81} +124.695 q^{82} -797.673 q^{83} +84.0000 q^{84} -10.3324 q^{85} -32.1365 q^{86} -836.302 q^{87} -341.400 q^{88} +847.360 q^{89} +17.2418 q^{90} +225.338 q^{91} +762.154 q^{92} +867.475 q^{93} -50.6916 q^{94} +18.1997 q^{95} -96.0000 q^{96} +307.957 q^{97} -98.0000 q^{98} +384.076 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} + 10 q^{5} - 24 q^{6} + 28 q^{7} - 32 q^{8} + 36 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 + 12 * q^3 + 16 * q^4 + 10 * q^5 - 24 * q^6 + 28 * q^7 - 32 * q^8 + 36 * q^9	\( 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} + 10 q^{5} - 24 q^{6} + 28 q^{7} - 32 q^{8} + 36 q^{9} - 20 q^{10} + 48 q^{11} + 48 q^{12} - 30 q^{13} - 56 q^{14} + 30 q^{15} + 64 q^{16} + 128 q^{17} - 72 q^{18} - 76 q^{19} + 40 q^{20} + 84 q^{21} - 96 q^{22} + 98 q^{23} - 96 q^{24} + 312 q^{25} + 60 q^{26} + 108 q^{27} + 112 q^{28} + 144 q^{29} - 60 q^{30} + 10 q^{31} - 128 q^{32} + 144 q^{33} - 256 q^{34} + 70 q^{35} + 144 q^{36} + 222 q^{37} + 152 q^{38} - 90 q^{39} - 80 q^{40} + 256 q^{41} - 168 q^{42} + 188 q^{43} + 192 q^{44} + 90 q^{45} - 196 q^{46} + 522 q^{47} + 192 q^{48} + 196 q^{49} - 624 q^{50} + 384 q^{51} - 120 q^{52} + 1088 q^{53} - 216 q^{54} - 1092 q^{55} - 224 q^{56} - 228 q^{57} - 288 q^{58} + 1456 q^{59} + 120 q^{60} - 108 q^{61} - 20 q^{62} + 252 q^{63} + 256 q^{64} + 836 q^{65} - 288 q^{66} + 296 q^{67} + 512 q^{68} + 294 q^{69} - 140 q^{70} + 808 q^{71} - 288 q^{72} - 1384 q^{73} - 444 q^{74} + 936 q^{75} - 304 q^{76} + 336 q^{77} + 180 q^{78} + 582 q^{79} + 160 q^{80} + 324 q^{81} - 512 q^{82} - 1236 q^{83} + 336 q^{84} - 2216 q^{85} - 376 q^{86} + 432 q^{87} - 384 q^{88} + 2528 q^{89} - 180 q^{90} - 210 q^{91} + 392 q^{92} + 30 q^{93} - 1044 q^{94} - 190 q^{95} - 384 q^{96} - 1028 q^{97} - 392 q^{98} + 432 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 + 12 * q^3 + 16 * q^4 + 10 * q^5 - 24 * q^6 + 28 * q^7 - 32 * q^8 + 36 * q^9 - 20 * q^10 + 48 * q^11 + 48 * q^12 - 30 * q^13 - 56 * q^14 + 30 * q^15 + 64 * q^16 + 128 * q^17 - 72 * q^18 - 76 * q^19 + 40 * q^20 + 84 * q^21 - 96 * q^22 + 98 * q^23 - 96 * q^24 + 312 * q^25 + 60 * q^26 + 108 * q^27 + 112 * q^28 + 144 * q^29 - 60 * q^30 + 10 * q^31 - 128 * q^32 + 144 * q^33 - 256 * q^34 + 70 * q^35 + 144 * q^36 + 222 * q^37 + 152 * q^38 - 90 * q^39 - 80 * q^40 + 256 * q^41 - 168 * q^42 + 188 * q^43 + 192 * q^44 + 90 * q^45 - 196 * q^46 + 522 * q^47 + 192 * q^48 + 196 * q^49 - 624 * q^50 + 384 * q^51 - 120 * q^52 + 1088 * q^53 - 216 * q^54 - 1092 * q^55 - 224 * q^56 - 228 * q^57 - 288 * q^58 + 1456 * q^59 + 120 * q^60 - 108 * q^61 - 20 * q^62 + 252 * q^63 + 256 * q^64 + 836 * q^65 - 288 * q^66 + 296 * q^67 + 512 * q^68 + 294 * q^69 - 140 * q^70 + 808 * q^71 - 288 * q^72 - 1384 * q^73 - 444 * q^74 + 936 * q^75 - 304 * q^76 + 336 * q^77 + 180 * q^78 + 582 * q^79 + 160 * q^80 + 324 * q^81 - 512 * q^82 - 1236 * q^83 + 336 * q^84 - 2216 * q^85 - 376 * q^86 + 432 * q^87 - 384 * q^88 + 2528 * q^89 - 180 * q^90 - 210 * q^91 + 392 * q^92 + 30 * q^93 - 1044 * q^94 - 190 * q^95 - 384 * q^96 - 1028 * q^97 - 392 * q^98 + 432 * q^99

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