LMFDB - Embedded newform 230.4.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,4,Mod(1,230)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("230.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.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:	$13.5704393013$
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} - 60x^{2} - 45x + 108 $ x^4 - 2x^3 - 60x^2 - 45*x + 108
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.01192$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +2.98808 q^{3} +4.00000 q^{4} +5.00000 q^{5} +5.97615 q^{6} +2.98517 q^{7} +8.00000 q^{8} -18.0714 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +2.98808 q^{3} +4.00000 q^{4} +5.00000 q^{5} +5.97615 q^{6} +2.98517 q^{7} +8.00000 q^{8} -18.0714 q^{9} +10.0000 q^{10} +68.6262 q^{11} +11.9523 q^{12} -12.0028 q^{13} +5.97035 q^{14} +14.9404 q^{15} +16.0000 q^{16} +106.208 q^{17} -36.1428 q^{18} -48.4891 q^{19} +20.0000 q^{20} +8.91992 q^{21} +137.252 q^{22} -23.0000 q^{23} +23.9046 q^{24} +25.0000 q^{25} -24.0055 q^{26} -134.677 q^{27} +11.9407 q^{28} +135.226 q^{29} +29.8808 q^{30} -230.782 q^{31} +32.0000 q^{32} +205.060 q^{33} +212.416 q^{34} +14.9259 q^{35} -72.2856 q^{36} -107.956 q^{37} -96.9782 q^{38} -35.8651 q^{39} +40.0000 q^{40} +394.637 q^{41} +17.8398 q^{42} +136.063 q^{43} +274.505 q^{44} -90.3570 q^{45} -46.0000 q^{46} -50.4512 q^{47} +47.8092 q^{48} -334.089 q^{49} +50.0000 q^{50} +317.357 q^{51} -48.0110 q^{52} -414.707 q^{53} -269.353 q^{54} +343.131 q^{55} +23.8814 q^{56} -144.889 q^{57} +270.452 q^{58} -183.586 q^{59} +59.7615 q^{60} -98.4751 q^{61} -461.565 q^{62} -53.9463 q^{63} +64.0000 q^{64} -60.0138 q^{65} +410.121 q^{66} +136.925 q^{67} +424.831 q^{68} -68.7257 q^{69} +29.8517 q^{70} -708.800 q^{71} -144.571 q^{72} -689.605 q^{73} -215.912 q^{74} +74.7019 q^{75} -193.956 q^{76} +204.861 q^{77} -71.7303 q^{78} +546.583 q^{79} +80.0000 q^{80} +85.5038 q^{81} +789.275 q^{82} -20.2622 q^{83} +35.6797 q^{84} +531.039 q^{85} +272.125 q^{86} +404.065 q^{87} +549.010 q^{88} -1087.31 q^{89} -180.714 q^{90} -35.8303 q^{91} -92.0000 q^{92} -689.595 q^{93} -100.902 q^{94} -242.445 q^{95} +95.6184 q^{96} -1115.90 q^{97} -668.177 q^{98} -1240.17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} + 14 q^{3} + 16 q^{4} + 20 q^{5} + 28 q^{6} + 8 q^{7} + 32 q^{8} + 64 q^{9}+O(q^{10}) $ 4 * q + 8 * q^2 + 14 * q^3 + 16 * q^4 + 20 * q^5 + 28 * q^6 + 8 * q^7 + 32 * q^8 + 64 * q^9	\( 4 q + 8 q^{2} + 14 q^{3} + 16 q^{4} + 20 q^{5} + 28 q^{6} + 8 q^{7} + 32 q^{8} + 64 q^{9} + 40 q^{10} + 21 q^{11} + 56 q^{12} + 70 q^{13} + 16 q^{14} + 70 q^{15} + 64 q^{16} + 56 q^{17} + 128 q^{18} + 173 q^{19} + 80 q^{20} - 120 q^{21} + 42 q^{22} - 92 q^{23} + 112 q^{24} + 100 q^{25} + 140 q^{26} + 389 q^{27} + 32 q^{28} - 118 q^{29} + 140 q^{30} + 17 q^{31} + 128 q^{32} - 89 q^{33} + 112 q^{34} + 40 q^{35} + 256 q^{36} - 343 q^{37} + 346 q^{38} - 221 q^{39} + 160 q^{40} + 139 q^{41} - 240 q^{42} - 50 q^{43} + 84 q^{44} + 320 q^{45} - 184 q^{46} + 367 q^{47} + 224 q^{48} - 124 q^{49} + 200 q^{50} + 439 q^{51} + 280 q^{52} - 353 q^{53} + 778 q^{54} + 105 q^{55} + 64 q^{56} - 238 q^{57} - 236 q^{58} - 453 q^{59} + 280 q^{60} - 327 q^{61} + 34 q^{62} - 1723 q^{63} + 256 q^{64} + 350 q^{65} - 178 q^{66} - 455 q^{67} + 224 q^{68} - 322 q^{69} + 80 q^{70} + 195 q^{71} + 512 q^{72} - 633 q^{73} - 686 q^{74} + 350 q^{75} + 692 q^{76} - 2 q^{77} - 442 q^{78} - 1140 q^{79} + 320 q^{80} + 1456 q^{81} + 278 q^{82} - 1199 q^{83} - 480 q^{84} + 280 q^{85} - 100 q^{86} - 1775 q^{87} + 168 q^{88} - 2170 q^{89} + 640 q^{90} + 557 q^{91} - 368 q^{92} - 3241 q^{93} + 734 q^{94} + 865 q^{95} + 448 q^{96} - 703 q^{97} - 248 q^{98} - 2745 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 + 14 * q^3 + 16 * q^4 + 20 * q^5 + 28 * q^6 + 8 * q^7 + 32 * q^8 + 64 * q^9 + 40 * q^10 + 21 * q^11 + 56 * q^12 + 70 * q^13 + 16 * q^14 + 70 * q^15 + 64 * q^16 + 56 * q^17 + 128 * q^18 + 173 * q^19 + 80 * q^20 - 120 * q^21 + 42 * q^22 - 92 * q^23 + 112 * q^24 + 100 * q^25 + 140 * q^26 + 389 * q^27 + 32 * q^28 - 118 * q^29 + 140 * q^30 + 17 * q^31 + 128 * q^32 - 89 * q^33 + 112 * q^34 + 40 * q^35 + 256 * q^36 - 343 * q^37 + 346 * q^38 - 221 * q^39 + 160 * q^40 + 139 * q^41 - 240 * q^42 - 50 * q^43 + 84 * q^44 + 320 * q^45 - 184 * q^46 + 367 * q^47 + 224 * q^48 - 124 * q^49 + 200 * q^50 + 439 * q^51 + 280 * q^52 - 353 * q^53 + 778 * q^54 + 105 * q^55 + 64 * q^56 - 238 * q^57 - 236 * q^58 - 453 * q^59 + 280 * q^60 - 327 * q^61 + 34 * q^62 - 1723 * q^63 + 256 * q^64 + 350 * q^65 - 178 * q^66 - 455 * q^67 + 224 * q^68 - 322 * q^69 + 80 * q^70 + 195 * q^71 + 512 * q^72 - 633 * q^73 - 686 * q^74 + 350 * q^75 + 692 * q^76 - 2 * q^77 - 442 * q^78 - 1140 * q^79 + 320 * q^80 + 1456 * q^81 + 278 * q^82 - 1199 * q^83 - 480 * q^84 + 280 * q^85 - 100 * q^86 - 1775 * q^87 + 168 * q^88 - 2170 * q^89 + 640 * q^90 + 557 * q^91 - 368 * q^92 - 3241 * q^93 + 734 * q^94 + 865 * q^95 + 448 * q^96 - 703 * q^97 - 248 * q^98 - 2745 * 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
$3$	2.98808	0.575055	0.287528	−	0.957772i	$-0.407167\pi$
$3$	2.98808	0.575055	0.287528	+	0.957772i	$0.407167\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	5.97615	0.406626
$7$	2.98517	0.161184	0.0805921	−	0.996747i	$-0.474319\pi$
$7$	2.98517	0.161184	0.0805921	+	0.996747i	$0.474319\pi$
$8$	8.00000	0.353553
$9$	−18.0714	−0.669311
$10$	10.0000	0.316228
$11$	68.6262	1.88105	0.940527	−	0.339720i	$-0.110332\pi$
$11$	68.6262	1.88105	0.940527	+	0.339720i	$0.110332\pi$
$12$	11.9523	0.287528
$13$	−12.0028	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$13$	−12.0028	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$14$	5.97035	0.113974
$15$	14.9404	0.257173
$16$	16.0000	0.250000
$17$	106.208	1.51525	0.757623	−	0.652693i	$-0.226361\pi$
$17$	106.208	1.51525	0.757623	+	0.652693i	$0.226361\pi$
$18$	−36.1428	−0.473275
$19$	−48.4891	−0.585482	−0.292741	−	0.956192i	$-0.594567\pi$
$19$	−48.4891	−0.585482	−0.292741	+	0.956192i	$0.594567\pi$
$20$	20.0000	0.223607
$21$	8.91992	0.0926898
$22$	137.252	1.33011
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	23.9046	0.203313
$25$	25.0000	0.200000
$26$	−24.0055	−0.181072
$27$	−134.677	−0.959946
$28$	11.9407	0.0805921
$29$	135.226	0.865890	0.432945	−	0.901420i	$-0.357474\pi$
$29$	135.226	0.865890	0.432945	+	0.901420i	$0.357474\pi$
$30$	29.8808	0.181848
$31$	−230.782	−1.33709	−0.668544	−	0.743673i	$-0.733082\pi$
$31$	−230.782	−1.33709	−0.668544	+	0.743673i	$0.733082\pi$
$32$	32.0000	0.176777
$33$	205.060	1.08171
$34$	212.416	1.07144
$35$	14.9259	0.0720838
$36$	−72.2856	−0.334656
$37$	−107.956	−0.479672	−0.239836	−	0.970813i	$-0.577094\pi$
$37$	−107.956	−0.479672	−0.239836	+	0.970813i	$0.577094\pi$
$38$	−96.9782	−0.413998
$39$	−35.8651	−0.147257
$40$	40.0000	0.158114
$41$	394.637	1.50322	0.751610	−	0.659608i	$-0.229278\pi$
$41$	394.637	1.50322	0.751610	+	0.659608i	$0.229278\pi$
$42$	17.8398	0.0655416
$43$	136.063	0.482543	0.241272	−	0.970458i	$-0.422436\pi$
$43$	136.063	0.482543	0.241272	+	0.970458i	$0.422436\pi$
$44$	274.505	0.940527
$45$	−90.3570	−0.299325
$46$	−46.0000	−0.147442
$47$	−50.4512	−0.156576	−0.0782880	−	0.996931i	$-0.524945\pi$
$47$	−50.4512	−0.156576	−0.0782880	+	0.996931i	$0.524945\pi$
$48$	47.8092	0.143764
$49$	−334.089	−0.974020
$50$	50.0000	0.141421
$51$	317.357	0.871350
$52$	−48.0110	−0.128037
$53$	−414.707	−1.07480	−0.537400	−	0.843327i	$-0.680594\pi$
$53$	−414.707	−1.07480	−0.537400	+	0.843327i	$0.680594\pi$
$54$	−269.353	−0.678785
$55$	343.131	0.841232
$56$	23.8814	0.0569872
$57$	−144.889	−0.336685
$58$	270.452	0.612277
$59$	−183.586	−0.405100	−0.202550	−	0.979272i	$-0.564923\pi$
$59$	−183.586	−0.405100	−0.202550	+	0.979272i	$0.564923\pi$
$60$	59.7615	0.128586
$61$	−98.4751	−0.206696	−0.103348	−	0.994645i	$-0.532956\pi$
$61$	−98.4751	−0.206696	−0.103348	+	0.994645i	$0.532956\pi$
$62$	−461.565	−0.945464
$63$	−53.9463	−0.107882
$64$	64.0000	0.125000
$65$	−60.0138	−0.114520
$66$	410.121	0.764884
$67$	136.925	0.249672	0.124836	−	0.992177i	$-0.460160\pi$
$67$	136.925	0.249672	0.124836	+	0.992177i	$0.460160\pi$
$68$	424.831	0.757623
$69$	−68.7257	−0.119907
$70$	29.8517	0.0509709
$71$	−708.800	−1.18478	−0.592388	−	0.805653i	$-0.701815\pi$
$71$	−708.800	−1.18478	−0.592388	+	0.805653i	$0.701815\pi$
$72$	−144.571	−0.236637
$73$	−689.605	−1.10565	−0.552823	−	0.833299i	$-0.686449\pi$
$73$	−689.605	−1.10565	−0.552823	+	0.833299i	$0.686449\pi$
$74$	−215.912	−0.339179
$75$	74.7019	0.115011
$76$	−193.956	−0.292741
$77$	204.861	0.303196
$78$	−71.7303	−0.104126
$79$	546.583	0.778423	0.389212	−	0.921148i	$-0.372748\pi$
$79$	546.583	0.778423	0.389212	+	0.921148i	$0.372748\pi$
$80$	80.0000	0.111803
$81$	85.5038	0.117289
$82$	789.275	1.06294
$83$	−20.2622	−0.0267959	−0.0133980	−	0.999910i	$-0.504265\pi$
$83$	−20.2622	−0.0267959	−0.0133980	+	0.999910i	$0.504265\pi$
$84$	35.6797	0.0463449
$85$	531.039	0.677638
$86$	272.125	0.341210
$87$	404.065	0.497935
$88$	549.010	0.665053
$89$	−1087.31	−1.29499	−0.647495	−	0.762069i	$-0.724183\pi$
$89$	−1087.31	−1.29499	−0.647495	+	0.762069i	$0.724183\pi$
$90$	−180.714	−0.211655
$91$	−35.8303	−0.0412751
$92$	−92.0000	−0.104257
$93$	−689.595	−0.768900
$94$	−100.902	−0.110716
$95$	−242.445	−0.261836
$96$	95.6184	0.101656
$97$	−1115.90	−1.16807	−0.584036	−	0.811728i	$-0.698527\pi$
$97$	−1115.90	−1.16807	−0.584036	+	0.811728i	$0.698527\pi$
$98$	−668.177	−0.688736
$99$	−1240.17	−1.25901
$100$	100.000	0.100000
$101$	−134.565	−0.132572	−0.0662859	−	0.997801i	$-0.521115\pi$
$101$	−134.565	−0.132572	−0.0662859	+	0.997801i	$0.521115\pi$
$102$	634.714	0.616137
$103$	−925.953	−0.885795	−0.442898	−	0.896572i	$-0.646049\pi$
$103$	−925.953	−0.885795	−0.442898	+	0.896572i	$0.646049\pi$
$104$	−96.0221	−0.0905360
$105$	44.5996	0.0414522
$106$	−829.415	−0.759999
$107$	1871.13	1.69055	0.845273	−	0.534334i	$-0.179438\pi$
$107$	1871.13	1.69055	0.845273	+	0.534334i	$0.179438\pi$
$108$	−538.707	−0.479973
$109$	−978.242	−0.859620	−0.429810	−	0.902919i	$-0.641419\pi$
$109$	−978.242	−0.859620	−0.429810	+	0.902919i	$0.641419\pi$
$110$	686.262	0.594841
$111$	−322.581	−0.275838
$112$	47.7628	0.0402961
$113$	−1760.45	−1.46557	−0.732786	−	0.680459i	$-0.761780\pi$
$113$	−1760.45	−1.46557	−0.732786	+	0.680459i	$0.761780\pi$
$114$	−289.778	−0.238072
$115$	−115.000	−0.0932505
$116$	540.903	0.432945
$117$	216.907	0.171393
$118$	−367.172	−0.286449
$119$	317.049	0.244234
$120$	119.523	0.0909242
$121$	3378.56	2.53836
$122$	−196.950	−0.146156
$123$	1179.21	0.864434
$124$	−923.129	−0.668544
$125$	125.000	0.0894427
$126$	−107.893	−0.0762844
$127$	−1260.87	−0.880980	−0.440490	−	0.897758i	$-0.645195\pi$
$127$	−1260.87	−0.880980	−0.440490	+	0.897758i	$0.645195\pi$
$128$	128.000	0.0883883
$129$	406.566	0.277489
$130$	−120.028	−0.0809778
$131$	444.283	0.296314	0.148157	−	0.988964i	$-0.452666\pi$
$131$	444.283	0.296314	0.148157	+	0.988964i	$0.452666\pi$
$132$	820.241	0.540855
$133$	−144.748	−0.0943705
$134$	273.849	0.176545
$135$	−673.384	−0.429301
$136$	849.662	0.535720
$137$	429.072	0.267577	0.133789	−	0.991010i	$-0.457286\pi$
$137$	429.072	0.267577	0.133789	+	0.991010i	$0.457286\pi$
$138$	−137.451	−0.0847873
$139$	−249.755	−0.152402	−0.0762012	−	0.997092i	$-0.524279\pi$
$139$	−249.755	−0.152402	−0.0762012	+	0.997092i	$0.524279\pi$
$140$	59.7035	0.0360419
$141$	−150.752	−0.0900398
$142$	−1417.60	−0.837763
$143$	−823.704	−0.481689
$144$	−289.143	−0.167328
$145$	676.129	0.387238
$146$	−1379.21	−0.781809
$147$	−998.282	−0.560115
$148$	−431.824	−0.239836
$149$	−1564.18	−0.860020	−0.430010	−	0.902824i	$-0.641490\pi$
$149$	−1564.18	−0.860020	−0.430010	+	0.902824i	$0.641490\pi$
$150$	149.404	0.0813251
$151$	−1860.04	−1.00244	−0.501219	−	0.865321i	$-0.667115\pi$
$151$	−1860.04	−1.00244	−0.501219	+	0.865321i	$0.667115\pi$
$152$	−387.913	−0.206999
$153$	−1919.32	−1.01417
$154$	409.722	0.214392
$155$	−1153.91	−0.597964
$156$	−143.461	−0.0736285
$157$	2834.52	1.44089	0.720445	−	0.693512i	$-0.243938\pi$
$157$	2834.52	1.44089	0.720445	+	0.693512i	$0.243938\pi$
$158$	1093.17	0.550428
$159$	−1239.18	−0.618070
$160$	160.000	0.0790569
$161$	−68.6590	−0.0336092
$162$	171.008	0.0829359
$163$	2114.51	1.01608	0.508041	−	0.861333i	$-0.330370\pi$
$163$	2114.51	1.01608	0.508041	+	0.861333i	$0.330370\pi$
$164$	1578.55	0.751610
$165$	1025.30	0.483755
$166$	−40.5244	−0.0189476
$167$	2487.41	1.15258	0.576291	−	0.817244i	$-0.304499\pi$
$167$	2487.41	1.15258	0.576291	+	0.817244i	$0.304499\pi$
$168$	71.3594	0.0327708
$169$	−2052.93	−0.934426
$170$	1062.08	0.479163
$171$	876.266	0.391870
$172$	544.251	0.241272
$173$	3672.32	1.61388	0.806939	−	0.590634i	$-0.201122\pi$
$173$	3672.32	1.61388	0.806939	+	0.590634i	$0.201122\pi$
$174$	808.130	0.352093
$175$	74.6293	0.0322368
$176$	1098.02	0.470263
$177$	−548.569	−0.232955
$178$	−2174.61	−0.915697
$179$	−3224.63	−1.34648	−0.673240	−	0.739424i	$-0.735098\pi$
$179$	−3224.63	−1.34648	−0.673240	+	0.739424i	$0.735098\pi$
$180$	−361.428	−0.149663
$181$	−2224.23	−0.913401	−0.456700	−	0.889621i	$-0.650969\pi$
$181$	−2224.23	−0.913401	−0.456700	+	0.889621i	$0.650969\pi$
$182$	−71.6606	−0.0291859
$183$	−294.251	−0.118862
$184$	−184.000	−0.0737210
$185$	−539.780	−0.214516
$186$	−1379.19	−0.543694
$187$	7288.64	2.85026
$188$	−201.805	−0.0782880
$189$	−402.033	−0.154728
$190$	−484.891	−0.185146
$191$	3273.53	1.24013	0.620063	−	0.784552i	$-0.287107\pi$
$191$	3273.53	1.24013	0.620063	+	0.784552i	$0.287107\pi$
$192$	191.237	0.0718819
$193$	5126.86	1.91212	0.956062	−	0.293166i	$-0.0947089\pi$
$193$	5126.86	1.91212	0.956062	+	0.293166i	$0.0947089\pi$
$194$	−2231.81	−0.825951
$195$	−179.326	−0.0658553
$196$	−1336.35	−0.487010
$197$	3262.57	1.17994	0.589971	−	0.807425i	$-0.299139\pi$
$197$	3262.57	1.17994	0.589971	+	0.807425i	$0.299139\pi$
$198$	−2480.34	−0.890255
$199$	−168.282	−0.0599457	−0.0299728	−	0.999551i	$-0.509542\pi$
$199$	−168.282	−0.0599457	−0.0299728	+	0.999551i	$0.509542\pi$
$200$	200.000	0.0707107
$201$	409.141	0.143575
$202$	−269.131	−0.0937424
$203$	403.673	0.139568
$204$	1269.43	0.435675
$205$	1973.19	0.672260
$206$	−1851.91	−0.626352
$207$	415.642	0.139561
$208$	−192.044	−0.0640186
$209$	−3327.62	−1.10132
$210$	89.1992	0.0293111
$211$	4197.01	1.36936	0.684678	−	0.728846i	$-0.259943\pi$
$211$	4197.01	1.36936	0.684678	+	0.728846i	$0.259943\pi$
$212$	−1658.83	−0.537400
$213$	−2117.95	−0.681312
$214$	3742.25	1.19540
$215$	680.313	0.215800
$216$	−1077.41	−0.339392
$217$	−688.925	−0.215518
$218$	−1956.48	−0.607843
$219$	−2060.59	−0.635807
$220$	1372.52	0.420616
$221$	−1274.79	−0.388015
$222$	−645.162	−0.195047
$223$	5192.66	1.55931	0.779656	−	0.626208i	$-0.215394\pi$
$223$	5192.66	1.55931	0.779656	+	0.626208i	$0.215394\pi$
$224$	95.5256	0.0284936
$225$	−451.785	−0.133862
$226$	−3520.91	−1.03632
$227$	4701.24	1.37459	0.687295	−	0.726378i	$-0.258798\pi$
$227$	4701.24	1.37459	0.687295	+	0.726378i	$0.258798\pi$
$228$	−579.556	−0.168342
$229$	−2125.17	−0.613255	−0.306628	−	0.951830i	$-0.599201\pi$
$229$	−2125.17	−0.613255	−0.306628	+	0.951830i	$0.599201\pi$
$230$	−230.000	−0.0659380
$231$	612.141	0.174355
$232$	1081.81	0.306138
$233$	−1646.67	−0.462992	−0.231496	−	0.972836i	$-0.574362\pi$
$233$	−1646.67	−0.462992	−0.231496	+	0.972836i	$0.574362\pi$
$234$	433.814	0.121193
$235$	−252.256	−0.0700229
$236$	−734.345	−0.202550
$237$	1633.23	0.447636
$238$	634.097	0.172699
$239$	2877.88	0.778888	0.389444	−	0.921050i	$-0.372667\pi$
$239$	2877.88	0.778888	0.389444	+	0.921050i	$0.372667\pi$
$240$	239.046	0.0642931
$241$	−4244.54	−1.13450	−0.567251	−	0.823545i	$-0.691993\pi$
$241$	−4244.54	−1.13450	−0.567251	+	0.823545i	$0.691993\pi$
$242$	6757.12	1.79489
$243$	3891.76	1.02739
$244$	−393.900	−0.103348
$245$	−1670.44	−0.435595
$246$	2358.41	0.611247
$247$	582.003	0.149927
$248$	−1846.26	−0.472732
$249$	−60.5449	−0.0154092
$250$	250.000	0.0632456
$251$	4401.99	1.10698	0.553488	−	0.832857i	$-0.313296\pi$
$251$	4401.99	1.10698	0.553488	+	0.832857i	$0.313296\pi$
$252$	−215.785	−0.0539412
$253$	−1578.40	−0.392227
$254$	−2521.75	−0.622947
$255$	1586.78	0.389680
$256$	256.000	0.0625000
$257$	1694.78	0.411352	0.205676	−	0.978620i	$-0.434061\pi$
$257$	1694.78	0.411352	0.205676	+	0.978620i	$0.434061\pi$
$258$	813.131	0.196214
$259$	−322.268	−0.0773156
$260$	−240.055	−0.0572600
$261$	−2443.72	−0.579550
$262$	888.566	0.209526
$263$	−727.462	−0.170560	−0.0852799	−	0.996357i	$-0.527178\pi$
$263$	−727.462	−0.170560	−0.0852799	+	0.996357i	$0.527178\pi$
$264$	1640.48	0.382442
$265$	−2073.54	−0.480666
$266$	−289.497	−0.0667300
$267$	−3248.95	−0.744691
$268$	547.698	0.124836
$269$	94.9937	0.0215311	0.0107656	−	0.999942i	$-0.496573\pi$
$269$	94.9937	0.0215311	0.0107656	+	0.999942i	$0.496573\pi$
$270$	−1346.77	−0.303562
$271$	5321.54	1.19284	0.596422	−	0.802671i	$-0.296589\pi$
$271$	5321.54	1.19284	0.596422	+	0.802671i	$0.296589\pi$
$272$	1699.32	0.378811
$273$	−107.064	−0.0237355
$274$	858.143	0.189206
$275$	1715.66	0.376211
$276$	−274.903	−0.0599537
$277$	2561.25	0.555562	0.277781	−	0.960644i	$-0.410401\pi$
$277$	2561.25	0.555562	0.277781	+	0.960644i	$0.410401\pi$
$278$	−499.510	−0.107765
$279$	4170.56	0.894928
$280$	119.407	0.0254855
$281$	−8753.73	−1.85838	−0.929188	−	0.369606i	$-0.879493\pi$
$281$	−8753.73	−1.85838	−0.929188	+	0.369606i	$0.879493\pi$
$282$	−301.504	−0.0636678
$283$	−2400.14	−0.504147	−0.252073	−	0.967708i	$-0.581112\pi$
$283$	−2400.14	−0.504147	−0.252073	+	0.967708i	$0.581112\pi$
$284$	−2835.20	−0.592388
$285$	−724.445	−0.150570
$286$	−1647.41	−0.340606
$287$	1178.06	0.242295
$288$	−578.285	−0.118319
$289$	6367.09	1.29597
$290$	1352.26	0.273818
$291$	−3334.41	−0.671706
$292$	−2758.42	−0.552823
$293$	1045.56	0.208472	0.104236	−	0.994553i	$-0.466760\pi$
$293$	1045.56	0.208472	0.104236	+	0.994553i	$0.466760\pi$
$294$	−1996.56	−0.396061
$295$	−917.931	−0.181166
$296$	−863.649	−0.169590
$297$	−9242.36	−1.80571
$298$	−3128.37	−0.608126
$299$	276.063	0.0533952
$300$	298.808	0.0575055
$301$	406.171	0.0777784
$302$	−3720.08	−0.708830
$303$	−402.091	−0.0762361
$304$	−775.826	−0.146371
$305$	−492.376	−0.0924372
$306$	−3838.65	−0.717127
$307$	−7905.84	−1.46974	−0.734870	−	0.678208i	$-0.762757\pi$
$307$	−7905.84	−1.46974	−0.734870	+	0.678208i	$0.762757\pi$
$308$	819.445	0.151598
$309$	−2766.82	−0.509381
$310$	−2307.82	−0.422824
$311$	−9227.63	−1.68248	−0.841240	−	0.540662i	$-0.818174\pi$
$311$	−9227.63	−1.68248	−0.841240	+	0.540662i	$0.818174\pi$
$312$	−286.921	−0.0520632
$313$	2712.57	0.489852	0.244926	−	0.969542i	$-0.421236\pi$
$313$	2712.57	0.489852	0.244926	+	0.969542i	$0.421236\pi$
$314$	5669.05	1.01886
$315$	−269.731	−0.0482465
$316$	2186.33	0.389212
$317$	−3440.29	−0.609546	−0.304773	−	0.952425i	$-0.598581\pi$
$317$	−3440.29	−0.609546	−0.304773	+	0.952425i	$0.598581\pi$
$318$	−2478.35	−0.437041
$319$	9280.04	1.62879
$320$	320.000	0.0559017
$321$	5591.06	0.972158
$322$	−137.318	−0.0237653
$323$	−5149.92	−0.887149
$324$	342.015	0.0586446
$325$	−300.069	−0.0512149
$326$	4229.03	0.718479
$327$	−2923.06	−0.494329
$328$	3157.10	0.531468
$329$	−150.606	−0.0252376
$330$	2050.60	0.342067
$331$	3259.75	0.541305	0.270652	−	0.962677i	$-0.412761\pi$
$331$	3259.75	0.541305	0.270652	+	0.962677i	$0.412761\pi$
$332$	−81.0487	−0.0133980
$333$	1950.92	0.321050
$334$	4974.81	0.814999
$335$	684.623	0.111657
$336$	142.719	0.0231725
$337$	7163.38	1.15790	0.578952	−	0.815361i	$-0.303462\pi$
$337$	7163.38	1.15790	0.578952	+	0.815361i	$0.303462\pi$
$338$	−4105.87	−0.660739
$339$	−5260.37	−0.842785
$340$	2124.16	0.338819
$341$	−15837.7	−2.51513
$342$	1752.53	0.277094
$343$	−2021.23	−0.318181
$344$	1088.50	0.170605
$345$	−343.629	−0.0536242
$346$	7344.63	1.14118
$347$	−1833.45	−0.283645	−0.141822	−	0.989892i	$-0.545296\pi$
$347$	−1833.45	−0.283645	−0.141822	+	0.989892i	$0.545296\pi$
$348$	1616.26	0.248967
$349$	−10400.3	−1.59517	−0.797583	−	0.603209i	$-0.793888\pi$
$349$	−10400.3	−1.59517	−0.797583	+	0.603209i	$0.793888\pi$
$350$	149.259	0.0227949
$351$	1616.49	0.245818
$352$	2196.04	0.332526
$353$	−3156.48	−0.475928	−0.237964	−	0.971274i	$-0.576480\pi$
$353$	−3156.48	−0.475928	−0.237964	+	0.971274i	$0.576480\pi$
$354$	−1097.14	−0.164724
$355$	−3544.00	−0.529848
$356$	−4349.22	−0.647495
$357$	947.365	0.140448
$358$	−6449.25	−0.952105
$359$	−9324.16	−1.37078	−0.685390	−	0.728176i	$-0.740368\pi$
$359$	−9324.16	−1.37078	−0.685390	+	0.728176i	$0.740368\pi$
$360$	−722.856	−0.105827
$361$	−4507.81	−0.657211
$362$	−4448.45	−0.645872
$363$	10095.4	1.45970
$364$	−143.321	−0.0206376
$365$	−3448.02	−0.494460
$366$	−588.502	−0.0840478
$367$	3802.68	0.540867	0.270434	−	0.962739i	$-0.412833\pi$
$367$	3802.68	0.540867	0.270434	+	0.962739i	$0.412833\pi$
$368$	−368.000	−0.0521286
$369$	−7131.65	−1.00612
$370$	−1079.56	−0.151686
$371$	−1237.97	−0.173241
$372$	−2758.38	−0.384450
$373$	−8928.03	−1.23935	−0.619673	−	0.784860i	$-0.712735\pi$
$373$	−8928.03	−1.23935	−0.619673	+	0.784860i	$0.712735\pi$
$374$	14577.3	2.01544
$375$	373.509	0.0514345
$376$	−403.610	−0.0553580
$377$	−1623.08	−0.221732
$378$	−804.067	−0.109409
$379$	3798.13	0.514768	0.257384	−	0.966309i	$-0.417140\pi$
$379$	3798.13	0.514768	0.257384	+	0.966309i	$0.417140\pi$
$380$	−969.782	−0.130918
$381$	−3767.58	−0.506612
$382$	6547.05	0.876901
$383$	1456.41	0.194306	0.0971530	−	0.995269i	$-0.469026\pi$
$383$	1456.41	0.194306	0.0971530	+	0.995269i	$0.469026\pi$
$384$	382.474	0.0508282
$385$	1024.31	0.135593
$386$	10253.7	1.35208
$387$	−2458.84	−0.322972
$388$	−4463.62	−0.584036
$389$	−8211.34	−1.07026	−0.535130	−	0.844769i	$-0.679738\pi$
$389$	−8211.34	−1.07026	−0.535130	+	0.844769i	$0.679738\pi$
$390$	−358.651	−0.0465667
$391$	−2442.78	−0.315950
$392$	−2672.71	−0.344368
$393$	1327.55	0.170397
$394$	6525.14	0.834345
$395$	2732.92	0.348121
$396$	−4960.69	−0.629505
$397$	914.365	0.115594	0.0577968	−	0.998328i	$-0.481592\pi$
$397$	914.365	0.115594	0.0577968	+	0.998328i	$0.481592\pi$
$398$	−336.564	−0.0423880
$399$	−432.519	−0.0542683
$400$	400.000	0.0500000
$401$	9414.97	1.17247	0.586236	−	0.810140i	$-0.300609\pi$
$401$	9414.97	1.17247	0.586236	+	0.810140i	$0.300609\pi$
$402$	818.282	0.101523
$403$	2770.02	0.342394
$404$	−538.261	−0.0662859
$405$	427.519	0.0524533
$406$	807.345	0.0986894
$407$	−7408.62	−0.902289
$408$	2538.85	0.308069
$409$	3299.41	0.398889	0.199444	−	0.979909i	$-0.436086\pi$
$409$	3299.41	0.398889	0.199444	+	0.979909i	$0.436086\pi$
$410$	3946.37	0.475360
$411$	1282.10	0.153872
$412$	−3703.81	−0.442898
$413$	−548.037	−0.0652957
$414$	831.285	0.0986846
$415$	−101.311	−0.0119835
$416$	−384.088	−0.0452680
$417$	−746.286	−0.0876398
$418$	−6655.25	−0.778753
$419$	−3554.64	−0.414452	−0.207226	−	0.978293i	$-0.566444\pi$
$419$	−3554.64	−0.414452	−0.207226	+	0.978293i	$0.566444\pi$
$420$	178.398	0.0207261
$421$	11655.5	1.34930	0.674649	−	0.738139i	$-0.264295\pi$
$421$	11655.5	1.34930	0.674649	+	0.738139i	$0.264295\pi$
$422$	8394.02	0.968281
$423$	911.725	0.104798
$424$	−3317.66	−0.380000
$425$	2655.19	0.303049
$426$	−4235.90	−0.481760
$427$	−293.965	−0.0333161
$428$	7484.50	0.845273
$429$	−2461.29	−0.276998
$430$	1360.63	0.152594
$431$	4727.38	0.528330	0.264165	−	0.964478i	$-0.414904\pi$
$431$	4727.38	0.528330	0.264165	+	0.964478i	$0.414904\pi$
$432$	−2154.83	−0.239987
$433$	3936.24	0.436868	0.218434	−	0.975852i	$-0.429905\pi$
$433$	3936.24	0.436868	0.218434	+	0.975852i	$0.429905\pi$
$434$	−1377.85	−0.152394
$435$	2020.33	0.222683
$436$	−3912.97	−0.429810
$437$	1115.25	0.122081
$438$	−4121.18	−0.449584
$439$	6859.77	0.745784	0.372892	−	0.927875i	$-0.378366\pi$
$439$	6859.77	0.745784	0.372892	+	0.927875i	$0.378366\pi$
$440$	2745.05	0.297421
$441$	6037.45	0.651922
$442$	−2549.57	−0.274368
$443$	16814.4	1.80334	0.901668	−	0.432430i	$-0.142344\pi$
$443$	16814.4	1.80334	0.901668	+	0.432430i	$0.142344\pi$
$444$	−1290.32	−0.137919
$445$	−5436.53	−0.579137
$446$	10385.3	1.10260
$447$	−4673.90	−0.494559
$448$	191.051	0.0201480
$449$	10673.8	1.12189	0.560943	−	0.827855i	$-0.310439\pi$
$449$	10673.8	1.12189	0.560943	+	0.827855i	$0.310439\pi$
$450$	−903.570	−0.0946549
$451$	27082.5	2.82764
$452$	−7041.82	−0.732786
$453$	−5557.94	−0.576457
$454$	9402.47	0.971982
$455$	−179.152	−0.0184588
$456$	−1159.11	−0.119036
$457$	15493.0	1.58585	0.792926	−	0.609318i	$-0.208557\pi$
$457$	15493.0	1.58585	0.792926	+	0.609318i	$0.208557\pi$
$458$	−4250.35	−0.433637
$459$	−14303.7	−1.45455
$460$	−460.000	−0.0466252
$461$	−10793.0	−1.09041	−0.545207	−	0.838302i	$-0.683549\pi$
$461$	−10793.0	−1.09041	−0.545207	+	0.838302i	$0.683549\pi$
$462$	1224.28	0.123287
$463$	−6165.87	−0.618904	−0.309452	−	0.950915i	$-0.600146\pi$
$463$	−6165.87	−0.618904	−0.309452	+	0.950915i	$0.600146\pi$
$464$	2163.61	0.216473
$465$	−3447.97	−0.343862
$466$	−3293.34	−0.327385
$467$	−10736.4	−1.06386	−0.531929	−	0.846789i	$-0.678533\pi$
$467$	−10736.4	−1.06386	−0.531929	+	0.846789i	$0.678533\pi$
$468$	867.627	0.0856967
$469$	408.744	0.0402431
$470$	−504.512	−0.0495137
$471$	8469.77	0.828591
$472$	−1468.69	−0.143224
$473$	9337.47	0.907690
$474$	3266.46	0.316527
$475$	−1212.23	−0.117096
$476$	1268.19	0.122117
$477$	7494.35	0.719377
$478$	5755.75	0.550757
$479$	6333.30	0.604125	0.302062	−	0.953288i	$-0.402325\pi$
$479$	6333.30	0.604125	0.302062	+	0.953288i	$0.402325\pi$
$480$	478.092	0.0454621
$481$	1295.77	0.122832
$482$	−8489.08	−0.802213
$483$	−205.158	−0.0193272
$484$	13514.2	1.26918
$485$	−5579.52	−0.522377
$486$	7783.53	0.726477
$487$	−16833.3	−1.56630	−0.783149	−	0.621834i	$-0.786388\pi$
$487$	−16833.3	−1.56630	−0.783149	+	0.621834i	$0.786388\pi$
$488$	−787.801	−0.0730780
$489$	6318.33	0.584304
$490$	−3340.89	−0.308012
$491$	−4.80428	−0.000441577 0	−0.000220788	−	1.00000i	$-0.500070\pi$
$491$	−4.80428	−0.000441577 0	−0.000220788		1.00000i	$0.500070\pi$
$492$	4716.82	0.432217
$493$	14362.0	1.31204
$494$	1164.01	0.106014
$495$	−6200.86	−0.563046
$496$	−3692.52	−0.334272
$497$	−2115.89	−0.190967
$498$	−121.090	−0.0108959
$499$	21206.9	1.90251	0.951253	−	0.308412i	$-0.0997975\pi$
$499$	21206.9	1.90251	0.951253	+	0.308412i	$0.0997975\pi$
$500$	500.000	0.0447214
$501$	7432.56	0.662799
$502$	8803.98	0.782750
$503$	14513.7	1.28655	0.643275	−	0.765635i	$-0.277575\pi$
$503$	14513.7	1.28655	0.643275	+	0.765635i	$0.277575\pi$
$504$	−431.570	−0.0381422
$505$	−672.827	−0.0592879
$506$	−3156.81	−0.277346
$507$	−6134.32	−0.537347
$508$	−5043.49	−0.440490
$509$	−2545.77	−0.221689	−0.110844	−	0.993838i	$-0.535355\pi$
$509$	−2545.77	−0.221689	−0.110844	+	0.993838i	$0.535355\pi$
$510$	3173.57	0.275545
$511$	−2058.59	−0.178213
$512$	512.000	0.0441942
$513$	6530.35	0.562032
$514$	3389.56	0.290870
$515$	−4629.77	−0.396140
$516$	1626.26	0.138745
$517$	−3462.28	−0.294528
$518$	−644.535	−0.0546704
$519$	10973.2	0.928070
$520$	−480.110	−0.0404889
$521$	−21343.1	−1.79473	−0.897367	−	0.441285i	$-0.854523\pi$
$521$	−21343.1	−1.79473	−0.897367	+	0.441285i	$0.854523\pi$
$522$	−4887.44	−0.409804
$523$	−789.191	−0.0659827	−0.0329913	−	0.999456i	$-0.510503\pi$
$523$	−789.191	−0.0659827	−0.0329913	+	0.999456i	$0.510503\pi$
$524$	1777.13	0.148157
$525$	222.998	0.0185380
$526$	−1454.92	−0.120604
$527$	−24510.9	−2.02602
$528$	3280.96	0.270427
$529$	529.000	0.0434783
$530$	−4147.07	−0.339882
$531$	3317.66	0.271138
$532$	−578.994	−0.0471852
$533$	−4736.74	−0.384936
$534$	−6497.90	−0.526576
$535$	9355.63	0.756036
$536$	1095.40	0.0882723
$537$	−9635.42	−0.774300
$538$	189.987	0.0152248
$539$	−22927.2	−1.83218
$540$	−2693.53	−0.214651
$541$	13405.1	1.06531	0.532653	−	0.846334i	$-0.321195\pi$
$541$	13405.1	1.06531	0.532653	+	0.846334i	$0.321195\pi$
$542$	10643.1	0.843468
$543$	−6646.16	−0.525256
$544$	3398.65	0.267860
$545$	−4891.21	−0.384434
$546$	−214.127	−0.0167835
$547$	10088.8	0.788605	0.394303	−	0.918981i	$-0.370986\pi$
$547$	10088.8	0.788605	0.394303	+	0.918981i	$0.370986\pi$
$548$	1716.29	0.133789
$549$	1779.58	0.138344
$550$	3431.31	0.266021
$551$	−6556.98	−0.506963
$552$	−549.806	−0.0423936
$553$	1631.65	0.125470
$554$	5122.50	0.392842
$555$	−1612.90	−0.123359
$556$	−999.019	−0.0762012
$557$	−11657.7	−0.886809	−0.443405	−	0.896322i	$-0.646230\pi$
$557$	−11657.7	−0.886809	−0.443405	+	0.896322i	$0.646230\pi$
$558$	8341.12	0.632810
$559$	−1633.13	−0.123567
$560$	238.814	0.0180209
$561$	21779.0	1.63906
$562$	−17507.5	−1.31407
$563$	4839.43	0.362270	0.181135	−	0.983458i	$-0.442023\pi$
$563$	4839.43	0.362270	0.181135	+	0.983458i	$0.442023\pi$
$564$	−603.008	−0.0450199
$565$	−8802.27	−0.655424
$566$	−4800.28	−0.356486
$567$	255.244	0.0189052
$568$	−5670.40	−0.418882
$569$	−646.680	−0.0476454	−0.0238227	−	0.999716i	$-0.507584\pi$
$569$	−646.680	−0.0476454	−0.0238227	+	0.999716i	$0.507584\pi$
$570$	−1448.89	−0.106469
$571$	3263.66	0.239194	0.119597	−	0.992822i	$-0.461840\pi$
$571$	3263.66	0.239194	0.119597	+	0.992822i	$0.461840\pi$
$572$	−3294.82	−0.240845
$573$	9781.54	0.713141
$574$	2356.12	0.171329
$575$	−575.000	−0.0417029
$576$	−1156.57	−0.0836639
$577$	−8980.46	−0.647940	−0.323970	−	0.946067i	$-0.605018\pi$
$577$	−8980.46	−0.647940	−0.323970	+	0.946067i	$0.605018\pi$
$578$	12734.2	0.916388
$579$	15319.5	1.09958
$580$	2704.52	0.193619
$581$	−60.4861	−0.00431908
$582$	−6668.81	−0.474968
$583$	−28459.8	−2.02176
$584$	−5516.84	−0.390905
$585$	1084.53	0.0766495
$586$	2091.12	0.147412
$587$	−6538.05	−0.459718	−0.229859	−	0.973224i	$-0.573826\pi$
$587$	−6538.05	−0.459718	−0.229859	+	0.973224i	$0.573826\pi$
$588$	−3993.13	−0.280058
$589$	11190.4	0.782841
$590$	−1835.86	−0.128104
$591$	9748.80	0.678532
$592$	−1727.30	−0.119918
$593$	7803.41	0.540384	0.270192	−	0.962806i	$-0.412913\pi$
$593$	7803.41	0.540384	0.270192	+	0.962806i	$0.412913\pi$
$594$	−18484.7	−1.27683
$595$	1585.24	0.109225
$596$	−6256.73	−0.430010
$597$	−502.839	−0.0344721
$598$	552.127	0.0377561
$599$	−27812.0	−1.89711	−0.948555	−	0.316613i	$-0.897454\pi$
$599$	−27812.0	−1.89711	−0.948555	+	0.316613i	$0.897454\pi$
$600$	597.615	0.0406626
$601$	483.216	0.0327966	0.0163983	−	0.999866i	$-0.494780\pi$
$601$	483.216	0.0327966	0.0163983	+	0.999866i	$0.494780\pi$
$602$	812.342	0.0549976
$603$	−2474.42	−0.167108
$604$	−7440.17	−0.501219
$605$	16892.8	1.13519
$606$	−804.183	−0.0539071
$607$	−18104.0	−1.21058	−0.605289	−	0.796006i	$-0.706942\pi$
$607$	−18104.0	−1.21058	−0.605289	+	0.796006i	$0.706942\pi$
$608$	−1551.65	−0.103500
$609$	1206.20	0.0802592
$610$	−984.751	−0.0653630
$611$	605.554	0.0400951
$612$	−7677.30	−0.507085
$613$	2191.19	0.144374	0.0721870	−	0.997391i	$-0.477002\pi$
$613$	2191.19	0.144374	0.0721870	+	0.997391i	$0.477002\pi$
$614$	−15811.7	−1.03926
$615$	5896.03	0.386587
$616$	1638.89	0.107196
$617$	−8243.06	−0.537849	−0.268925	−	0.963161i	$-0.586668\pi$
$617$	−8243.06	−0.537849	−0.268925	+	0.963161i	$0.586668\pi$
$618$	−5533.64	−0.360187
$619$	18298.0	1.18814	0.594069	−	0.804414i	$-0.297521\pi$
$619$	18298.0	1.18814	0.594069	+	0.804414i	$0.297521\pi$
$620$	−4615.65	−0.298982
$621$	3097.57	0.200163
$622$	−18455.3	−1.18969
$623$	−3245.80	−0.208732
$624$	−573.842	−0.0368142
$625$	625.000	0.0400000
$626$	5425.15	0.346378
$627$	−9943.19	−0.633322
$628$	11338.1	0.720445
$629$	−11465.8	−0.726821
$630$	−539.463	−0.0341154
$631$	−26472.0	−1.67010	−0.835051	−	0.550172i	$-0.814562\pi$
$631$	−26472.0	−1.67010	−0.835051	+	0.550172i	$0.814562\pi$
$632$	4372.67	0.275214
$633$	12541.0	0.787455
$634$	−6880.58	−0.431014
$635$	−6304.37	−0.393986
$636$	−4956.71	−0.309035
$637$	4009.99	0.249421
$638$	18560.1	1.15173
$639$	12809.0	0.792984
$640$	640.000	0.0395285
$641$	7411.93	0.456714	0.228357	−	0.973577i	$-0.426665\pi$
$641$	7411.93	0.456714	0.228357	+	0.973577i	$0.426665\pi$
$642$	11182.1	0.687419
$643$	8405.96	0.515550	0.257775	−	0.966205i	$-0.417011\pi$
$643$	8405.96	0.515550	0.257775	+	0.966205i	$0.417011\pi$
$644$	−274.636	−0.0168046
$645$	2032.83	0.124097
$646$	−10299.8	−0.627309
$647$	27878.3	1.69398	0.846992	−	0.531605i	$-0.178411\pi$
$647$	27878.3	1.69398	0.846992	+	0.531605i	$0.178411\pi$
$648$	684.030	0.0414680
$649$	−12598.8	−0.762014
$650$	−600.138	−0.0362144
$651$	−2058.56	−0.123934
$652$	8458.06	0.508041
$653$	−18871.1	−1.13091	−0.565455	−	0.824779i	$-0.691299\pi$
$653$	−18871.1	−1.13091	−0.565455	+	0.824779i	$0.691299\pi$
$654$	−5846.12	−0.349543
$655$	2221.42	0.132516
$656$	6314.20	0.375805
$657$	12462.1	0.740021
$658$	−301.211	−0.0178457
$659$	−12144.4	−0.717872	−0.358936	−	0.933362i	$-0.616860\pi$
$659$	−12144.4	−0.717872	−0.358936	+	0.933362i	$0.616860\pi$
$660$	4101.21	0.241878
$661$	−32504.2	−1.91266	−0.956328	−	0.292295i	$-0.905581\pi$
$661$	−32504.2	−1.91266	−0.956328	+	0.292295i	$0.905581\pi$
$662$	6519.49	0.382760
$663$	−3809.16	−0.223130
$664$	−162.097	−0.00947380
$665$	−723.742	−0.0422038
$666$	3901.84	0.227017
$667$	−3110.19	−0.180551
$668$	9949.62	0.576291
$669$	15516.1	0.896690
$670$	1369.25	0.0789531
$671$	−6757.98	−0.388806
$672$	285.438	0.0163854
$673$	−21387.8	−1.22502	−0.612511	−	0.790462i	$-0.709840\pi$
$673$	−21387.8	−1.22502	−0.612511	+	0.790462i	$0.709840\pi$
$674$	14326.8	0.818762
$675$	−3366.92	−0.191989
$676$	−8211.74	−0.467213
$677$	10494.6	0.595776	0.297888	−	0.954601i	$-0.403718\pi$
$677$	10494.6	0.595776	0.297888	+	0.954601i	$0.403718\pi$
$678$	−10520.7	−0.595939
$679$	−3331.17	−0.188275
$680$	4248.31	0.239581
$681$	14047.6	0.790466
$682$	−31675.4	−1.77847
$683$	24014.2	1.34535	0.672677	−	0.739937i	$-0.265145\pi$
$683$	24014.2	1.34535	0.672677	+	0.739937i	$0.265145\pi$
$684$	3505.07	0.195935
$685$	2145.36	0.119664
$686$	−4042.45	−0.224988
$687$	−6350.18	−0.352656
$688$	2177.00	0.120636
$689$	4977.63	0.275229
$690$	−687.257	−0.0379180
$691$	−10825.8	−0.595995	−0.297997	−	0.954567i	$-0.596319\pi$
$691$	−10825.8	−0.595995	−0.297997	+	0.954567i	$0.596319\pi$
$692$	14689.3	0.806939
$693$	−3702.13	−0.202933
$694$	−3666.90	−0.200567
$695$	−1248.77	−0.0681564
$696$	3232.52	0.176046
$697$	41913.6	2.27775
$698$	−20800.5	−1.12795
$699$	−4920.38	−0.266246
$700$	298.517	0.0161184
$701$	−171.021	−0.00921451	−0.00460726	−	0.999989i	$-0.501467\pi$
$701$	−171.021	−0.00921451	−0.00460726	+	0.999989i	$0.501467\pi$
$702$	3232.99	0.173819
$703$	5234.69	0.280840
$704$	4392.08	0.235132
$705$	−753.760	−0.0402670
$706$	−6312.96	−0.336532
$707$	−401.701	−0.0213685
$708$	−2194.28	−0.116477
$709$	28732.7	1.52197	0.760987	−	0.648767i	$-0.224715\pi$
$709$	28732.7	1.52197	0.760987	+	0.648767i	$0.224715\pi$
$710$	−7088.00	−0.374659
$711$	−9877.53	−0.521007
$712$	−8698.45	−0.457848
$713$	5307.99	0.278802
$714$	1894.73	0.0993116
$715$	−4118.52	−0.215418
$716$	−12898.5	−0.673240
$717$	8599.31	0.447904
$718$	−18648.3	−0.969288
$719$	6976.22	0.361849	0.180924	−	0.983497i	$-0.442091\pi$
$719$	6976.22	0.361849	0.180924	+	0.983497i	$0.442091\pi$
$720$	−1445.71	−0.0748313
$721$	−2764.13	−0.142776
$722$	−9015.61	−0.464718
$723$	−12683.0	−0.652401
$724$	−8896.91	−0.456700
$725$	3380.65	0.173178
$726$	20190.8	1.03216
$727$	13114.6	0.669042	0.334521	−	0.942388i	$-0.391426\pi$
$727$	13114.6	0.669042	0.334521	+	0.942388i	$0.391426\pi$
$728$	−286.643	−0.0145930
$729$	9320.28	0.473519
$730$	−6896.05	−0.349636
$731$	14450.9	0.731172
$732$	−1177.00	−0.0594308
$733$	−22681.7	−1.14293	−0.571466	−	0.820626i	$-0.693625\pi$
$733$	−22681.7	−1.14293	−0.571466	+	0.820626i	$0.693625\pi$
$734$	7605.36	0.382451
$735$	−4991.41	−0.250491
$736$	−736.000	−0.0368605
$737$	9396.62	0.469646
$738$	−14263.3	−0.711436
$739$	24237.8	1.20650	0.603249	−	0.797553i	$-0.293873\pi$
$739$	24237.8	1.20650	0.603249	+	0.797553i	$0.293873\pi$
$740$	−2159.12	−0.107258
$741$	1739.07	0.0862163
$742$	−2475.95	−0.122500
$743$	27356.7	1.35077	0.675384	−	0.737466i	$-0.263978\pi$
$743$	27356.7	1.35077	0.675384	+	0.737466i	$0.263978\pi$
$744$	−5516.76	−0.271847
$745$	−7820.92	−0.384612
$746$	−17856.1	−0.876350
$747$	366.166	0.0179348
$748$	29154.6	1.42513
$749$	5585.63	0.272489
$750$	747.019	0.0363697
$751$	22297.8	1.08343	0.541716	−	0.840561i	$-0.317775\pi$
$751$	22297.8	1.08343	0.541716	+	0.840561i	$0.317775\pi$
$752$	−807.220	−0.0391440
$753$	13153.5	0.636573
$754$	−3246.17	−0.156788
$755$	−9300.21	−0.448304
$756$	−1608.13	−0.0773641
$757$	−16088.4	−0.772447	−0.386224	−	0.922405i	$-0.626221\pi$
$757$	−16088.4	−0.772447	−0.386224	+	0.922405i	$0.626221\pi$
$758$	7596.26	0.363996
$759$	−4716.39	−0.225552
$760$	−1939.56	−0.0925729
$761$	22500.2	1.07179	0.535894	−	0.844285i	$-0.319975\pi$
$761$	22500.2	1.07179	0.535894	+	0.844285i	$0.319975\pi$
$762$	−7535.17	−0.358229
$763$	−2920.22	−0.138557
$764$	13094.1	0.620063
$765$	−9596.62	−0.453551
$766$	2912.82	0.137395
$767$	2203.54	0.103736
$768$	764.947	0.0359410
$769$	−22677.7	−1.06343	−0.531716	−	0.846923i	$-0.678453\pi$
$769$	−22677.7	−1.06343	−0.531716	+	0.846923i	$0.678453\pi$
$770$	2048.61	0.0958790
$771$	5064.13	0.236550
$772$	20507.5	0.956062
$773$	20465.1	0.952235	0.476118	−	0.879382i	$-0.342044\pi$
$773$	20465.1	0.952235	0.476118	+	0.879382i	$0.342044\pi$
$774$	−4917.69	−0.228376
$775$	−5769.56	−0.267418
$776$	−8927.24	−0.412976
$777$	−962.960	−0.0444607
$778$	−16422.7	−0.756789
$779$	−19135.6	−0.880108
$780$	−717.303	−0.0329276
$781$	−48642.3	−2.22863
$782$	−4885.56	−0.223411
$783$	−18211.8	−0.831208
$784$	−5345.42	−0.243505
$785$	14172.6	0.644386
$786$	2655.10	0.120489
$787$	−28850.8	−1.30676	−0.653379	−	0.757031i	$-0.726649\pi$
$787$	−28850.8	−1.30676	−0.653379	+	0.757031i	$0.726649\pi$
$788$	13050.3	0.589971
$789$	−2173.71	−0.0980813
$790$	5465.83	0.246159
$791$	−5255.26	−0.236227
$792$	−9921.38	−0.445127
$793$	1181.97	0.0529295
$794$	1828.73	0.0817370
$795$	−6195.88	−0.276409
$796$	−673.128	−0.0299728
$797$	−39332.9	−1.74811	−0.874054	−	0.485828i	$-0.838518\pi$
$797$	−39332.9	−1.74811	−0.874054	+	0.485828i	$0.838518\pi$
$798$	−865.038	−0.0383735
$799$	−5358.31	−0.237251
$800$	800.000	0.0353553
$801$	19649.1	0.866752
$802$	18829.9	0.829063
$803$	−47325.0	−2.07978
$804$	1636.56	0.0717875
$805$	−343.295	−0.0150305
$806$	5540.05	0.242109
$807$	283.848	0.0123816
$808$	−1076.52	−0.0468712
$809$	33946.5	1.47527	0.737637	−	0.675198i	$-0.235942\pi$
$809$	33946.5	1.47527	0.737637	+	0.675198i	$0.235942\pi$
$810$	855.038	0.0370901
$811$	−20772.2	−0.899398	−0.449699	−	0.893180i	$-0.648469\pi$
$811$	−20772.2	−0.899398	−0.449699	+	0.893180i	$0.648469\pi$
$812$	1614.69	0.0697839
$813$	15901.2	0.685951
$814$	−14817.2	−0.638015
$815$	10572.6	0.454406
$816$	5077.71	0.217837
$817$	−6597.56	−0.282521
$818$	6598.83	0.282057
$819$	647.504	0.0276259
$820$	7892.75	0.336130
$821$	6466.37	0.274882	0.137441	−	0.990510i	$-0.456112\pi$
$821$	6466.37	0.274882	0.137441	+	0.990510i	$0.456112\pi$
$822$	2564.20	0.108804
$823$	−16503.7	−0.699008	−0.349504	−	0.936935i	$-0.613650\pi$
$823$	−16503.7	−0.699008	−0.349504	+	0.936935i	$0.613650\pi$
$824$	−7407.63	−0.313176
$825$	5126.51	0.216342
$826$	−1096.07	−0.0461710
$827$	36540.8	1.53645	0.768227	−	0.640177i	$-0.221139\pi$
$827$	36540.8	1.53645	0.768227	+	0.640177i	$0.221139\pi$
$828$	1662.57	0.0697805
$829$	−24874.5	−1.04213	−0.521066	−	0.853516i	$-0.674465\pi$
$829$	−24874.5	−1.04213	−0.521066	+	0.853516i	$0.674465\pi$
$830$	−202.622	−0.00847362
$831$	7653.21	0.319479
$832$	−768.177	−0.0320093
$833$	−35482.8	−1.47588
$834$	−1492.57	−0.0619707
$835$	12437.0	0.515450
$836$	−13310.5	−0.550662
$837$	31081.0	1.28353
$838$	−7109.28	−0.293062
$839$	15814.3	0.650741	0.325370	−	0.945587i	$-0.394511\pi$
$839$	15814.3	0.650741	0.325370	+	0.945587i	$0.394511\pi$
$840$	356.797	0.0146556
$841$	−6102.97	−0.250234
$842$	23311.0	0.954097
$843$	−26156.8	−1.06867
$844$	16788.0	0.684678
$845$	−10264.7	−0.417888
$846$	1823.45	0.0741034
$847$	10085.6	0.409144
$848$	−6635.32	−0.268700
$849$	−7171.80	−0.289912
$850$	5310.39	0.214288
$851$	2482.99	0.100019
$852$	−8471.79	−0.340656
$853$	−31093.2	−1.24808	−0.624039	−	0.781394i	$-0.714509\pi$
$853$	−31093.2	−1.24808	−0.624039	+	0.781394i	$0.714509\pi$
$854$	−587.931	−0.0235580
$855$	4381.33	0.175250
$856$	14969.0	0.597699
$857$	34212.4	1.36368	0.681840	−	0.731501i	$-0.261180\pi$
$857$	34212.4	1.36368	0.681840	+	0.731501i	$0.261180\pi$
$858$	−4922.58	−0.195867
$859$	4821.57	0.191513	0.0957567	−	0.995405i	$-0.469473\pi$
$859$	4821.57	0.191513	0.0957567	+	0.995405i	$0.469473\pi$
$860$	2721.25	0.107900
$861$	3520.13	0.139333
$862$	9454.77	0.373585
$863$	19145.6	0.755185	0.377593	−	0.925972i	$-0.376752\pi$
$863$	19145.6	0.755185	0.377593	+	0.925972i	$0.376752\pi$
$864$	−4309.66	−0.169696
$865$	18361.6	0.721748
$866$	7872.49	0.308912
$867$	19025.4	0.745254
$868$	−2755.70	−0.107759
$869$	37509.9	1.46426
$870$	4040.65	0.157461
$871$	−1643.47	−0.0639345
$872$	−7825.93	−0.303921
$873$	20166.0	0.781804
$874$	2230.50	0.0863246
$875$	373.147	0.0144168
$876$	−8242.36	−0.317904
$877$	16890.8	0.650354	0.325177	−	0.945653i	$-0.394576\pi$
$877$	16890.8	0.650354	0.325177	+	0.945653i	$0.394576\pi$
$878$	13719.5	0.527349
$879$	3124.21	0.119883
$880$	5490.10	0.210308
$881$	−27802.3	−1.06321	−0.531603	−	0.846994i	$-0.678410\pi$
$881$	−27802.3	−1.06321	−0.531603	+	0.846994i	$0.678410\pi$
$882$	12074.9	0.460979
$883$	9794.15	0.373272	0.186636	−	0.982429i	$-0.440241\pi$
$883$	9794.15	0.373272	0.186636	+	0.982429i	$0.440241\pi$
$884$	−5099.15	−0.194008
$885$	−2742.85	−0.104181
$886$	33628.9	1.27515
$887$	−41652.4	−1.57672	−0.788360	−	0.615214i	$-0.789070\pi$
$887$	−41652.4	−1.57672	−0.788360	+	0.615214i	$0.789070\pi$
$888$	−2580.65	−0.0975235
$889$	−3763.93	−0.142000
$890$	−10873.1	−0.409512
$891$	5867.80	0.220627
$892$	20770.7	0.779656
$893$	2446.34	0.0916724
$894$	−9347.80	−0.349706
$895$	−16123.1	−0.602164
$896$	382.102	0.0142468
$897$	824.898	0.0307052
$898$	21347.5	0.793293
$899$	−31207.7	−1.15777
$900$	−1807.14	−0.0669311
$901$	−44045.2	−1.62859
$902$	54164.9	1.99944
$903$	1213.67	0.0447269
$904$	−14083.6	−0.518158
$905$	−11121.1	−0.408485
$906$	−11115.9	−0.407617
$907$	5467.21	0.200150	0.100075	−	0.994980i	$-0.468092\pi$
$907$	5467.21	0.200150	0.100075	+	0.994980i	$0.468092\pi$
$908$	18804.9	0.687295
$909$	2431.79	0.0887318
$910$	−358.303	−0.0130523
$911$	33520.9	1.21910	0.609549	−	0.792749i	$-0.291351\pi$
$911$	33520.9	1.21910	0.609549	+	0.792749i	$0.291351\pi$
$912$	−2318.23	−0.0841712
$913$	−1390.52	−0.0504046
$914$	30986.1	1.12137
$915$	−1471.26	−0.0531565
$916$	−8500.70	−0.306628
$917$	1326.26	0.0477612
$918$	−28607.4	−1.02853
$919$	21423.9	0.768996	0.384498	−	0.923126i	$-0.374375\pi$
$919$	21423.9	0.768996	0.384498	+	0.923126i	$0.374375\pi$
$920$	−920.000	−0.0329690
$921$	−23623.2	−0.845182
$922$	−21586.0	−0.771039
$923$	8507.56	0.303391
$924$	2448.56	0.0871773
$925$	−2698.90	−0.0959344
$926$	−12331.7	−0.437631
$927$	16733.3	0.592873
$928$	4327.23	0.153069
$929$	25838.9	0.912538	0.456269	−	0.889842i	$-0.349186\pi$
$929$	25838.9	0.912538	0.456269	+	0.889842i	$0.349186\pi$
$930$	−6895.95	−0.243147
$931$	16199.7	0.570271
$932$	−6586.69	−0.231496
$933$	−27572.9	−0.967519
$934$	−21472.8	−0.752261
$935$	36443.2	1.27467
$936$	1735.25	0.0605967
$937$	48095.9	1.67687	0.838434	−	0.545003i	$-0.183472\pi$
$937$	48095.9	1.67687	0.838434	+	0.545003i	$0.183472\pi$
$938$	817.487	0.0284562
$939$	8105.38	0.281692
$940$	−1009.02	−0.0350114
$941$	−32450.4	−1.12418	−0.562089	−	0.827077i	$-0.690002\pi$
$941$	−32450.4	−1.12418	−0.562089	+	0.827077i	$0.690002\pi$
$942$	16939.5	0.585903
$943$	−9076.66	−0.313443
$944$	−2937.38	−0.101275
$945$	−2010.17	−0.0691966
$946$	18674.9	0.641834
$947$	39067.9	1.34059	0.670294	−	0.742096i	$-0.266168\pi$
$947$	39067.9	1.34059	0.670294	+	0.742096i	$0.266168\pi$
$948$	6532.93	0.223818
$949$	8277.16	0.283127
$950$	−2424.45	−0.0827997
$951$	−10279.8	−0.350522
$952$	2536.39	0.0863496
$953$	17756.2	0.603546	0.301773	−	0.953380i	$-0.402422\pi$
$953$	17756.2	0.603546	0.301773	+	0.953380i	$0.402422\pi$
$954$	14988.7	0.508676
$955$	16367.6	0.554601
$956$	11511.5	0.389444
$957$	27729.5	0.936642
$958$	12666.6	0.427181
$959$	1280.85	0.0431292
$960$	956.184	0.0321466
$961$	23469.5	0.787805
$962$	2591.54	0.0868552
$963$	−33813.9	−1.13150
$964$	−16978.2	−0.567251
$965$	25634.3	0.855127
$966$	−410.316	−0.0136664
$967$	−10696.2	−0.355705	−0.177853	−	0.984057i	$-0.556915\pi$
$967$	−10696.2	−0.355705	−0.177853	+	0.984057i	$0.556915\pi$
$968$	27028.5	0.897446
$969$	−15388.3	−0.510160
$970$	−11159.0	−0.369377
$971$	−53635.1	−1.77264	−0.886320	−	0.463074i	$-0.846746\pi$
$971$	−53635.1	−1.77264	−0.886320	+	0.463074i	$0.846746\pi$
$972$	15567.1	0.513697
$973$	−745.561	−0.0245649
$974$	−33666.5	−1.10754
$975$	−896.629	−0.0294514
$976$	−1575.60	−0.0516740
$977$	−21627.7	−0.708220	−0.354110	−	0.935204i	$-0.615216\pi$
$977$	−21627.7	−0.708220	−0.354110	+	0.935204i	$0.615216\pi$
$978$	12636.7	0.413165
$979$	−74617.7	−2.43595
$980$	−6681.77	−0.217797
$981$	17678.2	0.575353
$982$	−9.60856	−0.000312242 0
$983$	12031.4	0.390378	0.195189	−	0.980766i	$-0.437468\pi$
$983$	12031.4	0.390378	0.195189	+	0.980766i	$0.437468\pi$
$984$	9433.65	0.305624
$985$	16312.8	0.527686
$986$	28724.1	0.927749
$987$	−450.021	−0.0145130
$988$	2328.01	0.0749635
$989$	−3129.44	−0.100617
$990$	−12401.7	−0.398134
$991$	−24573.0	−0.787675	−0.393838	−	0.919180i	$-0.628853\pi$
$991$	−24573.0	−0.787675	−0.393838	+	0.919180i	$0.628853\pi$
$992$	−7385.03	−0.236366
$993$	9740.36	0.311280
$994$	−4231.78	−0.135034
$995$	−841.410	−0.0268085
$996$	−242.180	−0.00770458
$997$	−14209.7	−0.451379	−0.225690	−	0.974199i	$-0.572464\pi$
$997$	−14209.7	−0.451379	−0.225690	+	0.974199i	$0.572464\pi$
$998$	42413.8	1.34527
$999$	14539.2	0.460460

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.a.j.1.2	✓	4
3.2	odd	2		2070.4.a.bg.1.2		4
4.3	odd	2		1840.4.a.k.1.3		4
5.2	odd	4		1150.4.b.o.599.7		8
5.3	odd	4		1150.4.b.o.599.2		8
5.4	even	2		1150.4.a.n.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.j.1.2	✓	4	1.1	even	1	trivial
1150.4.a.n.1.3		4	5.4	even	2
1150.4.b.o.599.2		8	5.3	odd	4
1150.4.b.o.599.7		8	5.2	odd	4
1840.4.a.k.1.3		4	4.3	odd	2
2070.4.a.bg.1.2		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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +2.98808 q^{3} +4.00000 q^{4} +5.00000 q^{5} +5.97615 q^{6} +2.98517 q^{7} +8.00000 q^{8} -18.0714 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +2.98808 q^{3} +4.00000 q^{4} +5.00000 q^{5} +5.97615 q^{6} +2.98517 q^{7} +8.00000 q^{8} -18.0714 q^{9} +10.0000 q^{10} +68.6262 q^{11} +11.9523 q^{12} -12.0028 q^{13} +5.97035 q^{14} +14.9404 q^{15} +16.0000 q^{16} +106.208 q^{17} -36.1428 q^{18} -48.4891 q^{19} +20.0000 q^{20} +8.91992 q^{21} +137.252 q^{22} -23.0000 q^{23} +23.9046 q^{24} +25.0000 q^{25} -24.0055 q^{26} -134.677 q^{27} +11.9407 q^{28} +135.226 q^{29} +29.8808 q^{30} -230.782 q^{31} +32.0000 q^{32} +205.060 q^{33} +212.416 q^{34} +14.9259 q^{35} -72.2856 q^{36} -107.956 q^{37} -96.9782 q^{38} -35.8651 q^{39} +40.0000 q^{40} +394.637 q^{41} +17.8398 q^{42} +136.063 q^{43} +274.505 q^{44} -90.3570 q^{45} -46.0000 q^{46} -50.4512 q^{47} +47.8092 q^{48} -334.089 q^{49} +50.0000 q^{50} +317.357 q^{51} -48.0110 q^{52} -414.707 q^{53} -269.353 q^{54} +343.131 q^{55} +23.8814 q^{56} -144.889 q^{57} +270.452 q^{58} -183.586 q^{59} +59.7615 q^{60} -98.4751 q^{61} -461.565 q^{62} -53.9463 q^{63} +64.0000 q^{64} -60.0138 q^{65} +410.121 q^{66} +136.925 q^{67} +424.831 q^{68} -68.7257 q^{69} +29.8517 q^{70} -708.800 q^{71} -144.571 q^{72} -689.605 q^{73} -215.912 q^{74} +74.7019 q^{75} -193.956 q^{76} +204.861 q^{77} -71.7303 q^{78} +546.583 q^{79} +80.0000 q^{80} +85.5038 q^{81} +789.275 q^{82} -20.2622 q^{83} +35.6797 q^{84} +531.039 q^{85} +272.125 q^{86} +404.065 q^{87} +549.010 q^{88} -1087.31 q^{89} -180.714 q^{90} -35.8303 q^{91} -92.0000 q^{92} -689.595 q^{93} -100.902 q^{94} -242.445 q^{95} +95.6184 q^{96} -1115.90 q^{97} -668.177 q^{98} -1240.17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} + 14 q^{3} + 16 q^{4} + 20 q^{5} + 28 q^{6} + 8 q^{7} + 32 q^{8} + 64 q^{9}+O(q^{10}) \) 4 * q + 8 * q^2 + 14 * q^3 + 16 * q^4 + 20 * q^5 + 28 * q^6 + 8 * q^7 + 32 * q^8 + 64 * q^9	\( 4 q + 8 q^{2} + 14 q^{3} + 16 q^{4} + 20 q^{5} + 28 q^{6} + 8 q^{7} + 32 q^{8} + 64 q^{9} + 40 q^{10} + 21 q^{11} + 56 q^{12} + 70 q^{13} + 16 q^{14} + 70 q^{15} + 64 q^{16} + 56 q^{17} + 128 q^{18} + 173 q^{19} + 80 q^{20} - 120 q^{21} + 42 q^{22} - 92 q^{23} + 112 q^{24} + 100 q^{25} + 140 q^{26} + 389 q^{27} + 32 q^{28} - 118 q^{29} + 140 q^{30} + 17 q^{31} + 128 q^{32} - 89 q^{33} + 112 q^{34} + 40 q^{35} + 256 q^{36} - 343 q^{37} + 346 q^{38} - 221 q^{39} + 160 q^{40} + 139 q^{41} - 240 q^{42} - 50 q^{43} + 84 q^{44} + 320 q^{45} - 184 q^{46} + 367 q^{47} + 224 q^{48} - 124 q^{49} + 200 q^{50} + 439 q^{51} + 280 q^{52} - 353 q^{53} + 778 q^{54} + 105 q^{55} + 64 q^{56} - 238 q^{57} - 236 q^{58} - 453 q^{59} + 280 q^{60} - 327 q^{61} + 34 q^{62} - 1723 q^{63} + 256 q^{64} + 350 q^{65} - 178 q^{66} - 455 q^{67} + 224 q^{68} - 322 q^{69} + 80 q^{70} + 195 q^{71} + 512 q^{72} - 633 q^{73} - 686 q^{74} + 350 q^{75} + 692 q^{76} - 2 q^{77} - 442 q^{78} - 1140 q^{79} + 320 q^{80} + 1456 q^{81} + 278 q^{82} - 1199 q^{83} - 480 q^{84} + 280 q^{85} - 100 q^{86} - 1775 q^{87} + 168 q^{88} - 2170 q^{89} + 640 q^{90} + 557 q^{91} - 368 q^{92} - 3241 q^{93} + 734 q^{94} + 865 q^{95} + 448 q^{96} - 703 q^{97} - 248 q^{98} - 2745 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 + 14 * q^3 + 16 * q^4 + 20 * q^5 + 28 * q^6 + 8 * q^7 + 32 * q^8 + 64 * q^9 + 40 * q^10 + 21 * q^11 + 56 * q^12 + 70 * q^13 + 16 * q^14 + 70 * q^15 + 64 * q^16 + 56 * q^17 + 128 * q^18 + 173 * q^19 + 80 * q^20 - 120 * q^21 + 42 * q^22 - 92 * q^23 + 112 * q^24 + 100 * q^25 + 140 * q^26 + 389 * q^27 + 32 * q^28 - 118 * q^29 + 140 * q^30 + 17 * q^31 + 128 * q^32 - 89 * q^33 + 112 * q^34 + 40 * q^35 + 256 * q^36 - 343 * q^37 + 346 * q^38 - 221 * q^39 + 160 * q^40 + 139 * q^41 - 240 * q^42 - 50 * q^43 + 84 * q^44 + 320 * q^45 - 184 * q^46 + 367 * q^47 + 224 * q^48 - 124 * q^49 + 200 * q^50 + 439 * q^51 + 280 * q^52 - 353 * q^53 + 778 * q^54 + 105 * q^55 + 64 * q^56 - 238 * q^57 - 236 * q^58 - 453 * q^59 + 280 * q^60 - 327 * q^61 + 34 * q^62 - 1723 * q^63 + 256 * q^64 + 350 * q^65 - 178 * q^66 - 455 * q^67 + 224 * q^68 - 322 * q^69 + 80 * q^70 + 195 * q^71 + 512 * q^72 - 633 * q^73 - 686 * q^74 + 350 * q^75 + 692 * q^76 - 2 * q^77 - 442 * q^78 - 1140 * q^79 + 320 * q^80 + 1456 * q^81 + 278 * q^82 - 1199 * q^83 - 480 * q^84 + 280 * q^85 - 100 * q^86 - 1775 * q^87 + 168 * q^88 - 2170 * q^89 + 640 * q^90 + 557 * q^91 - 368 * q^92 - 3241 * q^93 + 734 * q^94 + 865 * q^95 + 448 * q^96 - 703 * q^97 - 248 * q^98 - 2745 * q^99

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