LMFDB - Embedded newform 230.4.a.h.1.3

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} - 68x^{2} - 111x + 342 $ x^4 - 68x^2 - 111x + 342
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.58997$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} +0.589969 q^{3} +4.00000 q^{4} -5.00000 q^{5} -1.17994 q^{6} -18.5077 q^{7} -8.00000 q^{8} -26.6519 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +0.589969 q^{3} +4.00000 q^{4} -5.00000 q^{5} -1.17994 q^{6} -18.5077 q^{7} -8.00000 q^{8} -26.6519 q^{9} +10.0000 q^{10} +47.9296 q^{11} +2.35988 q^{12} +42.3717 q^{13} +37.0155 q^{14} -2.94985 q^{15} +16.0000 q^{16} +1.70534 q^{17} +53.3039 q^{18} +21.4208 q^{19} -20.0000 q^{20} -10.9190 q^{21} -95.8592 q^{22} -23.0000 q^{23} -4.71976 q^{24} +25.0000 q^{25} -84.7434 q^{26} -31.6530 q^{27} -74.0310 q^{28} +57.6332 q^{29} +5.89969 q^{30} +295.699 q^{31} -32.0000 q^{32} +28.2770 q^{33} -3.41069 q^{34} +92.5387 q^{35} -106.608 q^{36} -7.85184 q^{37} -42.8416 q^{38} +24.9980 q^{39} +40.0000 q^{40} +465.929 q^{41} +21.8380 q^{42} +182.374 q^{43} +191.718 q^{44} +133.260 q^{45} +46.0000 q^{46} +449.193 q^{47} +9.43951 q^{48} -0.463605 q^{49} -50.0000 q^{50} +1.00610 q^{51} +169.487 q^{52} -368.316 q^{53} +63.3060 q^{54} -239.648 q^{55} +148.062 q^{56} +12.6376 q^{57} -115.266 q^{58} -377.032 q^{59} -11.7994 q^{60} +849.042 q^{61} -591.398 q^{62} +493.267 q^{63} +64.0000 q^{64} -211.858 q^{65} -56.5540 q^{66} +92.3424 q^{67} +6.82138 q^{68} -13.5693 q^{69} -185.077 q^{70} -626.854 q^{71} +213.215 q^{72} +439.227 q^{73} +15.7037 q^{74} +14.7492 q^{75} +85.6831 q^{76} -887.068 q^{77} -49.9960 q^{78} +641.707 q^{79} -80.0000 q^{80} +700.928 q^{81} -931.859 q^{82} -609.932 q^{83} -43.6760 q^{84} -8.52672 q^{85} -364.747 q^{86} +34.0018 q^{87} -383.437 q^{88} +1122.87 q^{89} -266.519 q^{90} -784.204 q^{91} -92.0000 q^{92} +174.453 q^{93} -898.386 q^{94} -107.104 q^{95} -18.8790 q^{96} -1428.80 q^{97} +0.927209 q^{98} -1277.42 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} - 4 q^{3} + 16 q^{4} - 20 q^{5} + 8 q^{6} - q^{7} - 32 q^{8} + 32 q^{9}+O(q^{10}) $ 4 * q - 8 * q^2 - 4 * q^3 + 16 * q^4 - 20 * q^5 + 8 * q^6 - q^7 - 32 * q^8 + 32 * q^9	\( 4 q - 8 q^{2} - 4 q^{3} + 16 q^{4} - 20 q^{5} + 8 q^{6} - q^{7} - 32 q^{8} + 32 q^{9} + 40 q^{10} - 39 q^{11} - 16 q^{12} - 20 q^{13} + 2 q^{14} + 20 q^{15} + 64 q^{16} - 23 q^{17} - 64 q^{18} + 53 q^{19} - 80 q^{20} + 300 q^{21} + 78 q^{22} - 92 q^{23} + 32 q^{24} + 100 q^{25} + 40 q^{26} + 137 q^{27} - 4 q^{28} + 161 q^{29} - 40 q^{30} + 388 q^{31} - 128 q^{32} + 87 q^{33} + 46 q^{34} + 5 q^{35} + 128 q^{36} + 466 q^{37} - 106 q^{38} + 1047 q^{39} + 160 q^{40} + 484 q^{41} - 600 q^{42} + 894 q^{43} - 156 q^{44} - 160 q^{45} + 184 q^{46} - 265 q^{47} - 64 q^{48} + 1643 q^{49} - 200 q^{50} + 1825 q^{51} - 80 q^{52} + 576 q^{53} - 274 q^{54} + 195 q^{55} + 8 q^{56} + 178 q^{57} - 322 q^{58} - 94 q^{59} + 80 q^{60} + 1153 q^{61} - 776 q^{62} + 60 q^{63} + 256 q^{64} + 100 q^{65} - 174 q^{66} - 1472 q^{67} - 92 q^{68} + 92 q^{69} - 10 q^{70} + 200 q^{71} - 256 q^{72} + 1147 q^{73} - 932 q^{74} - 100 q^{75} + 212 q^{76} - 2176 q^{77} - 2094 q^{78} - 908 q^{79} - 320 q^{80} - 1056 q^{81} - 968 q^{82} - 1048 q^{83} + 1200 q^{84} + 115 q^{85} - 1788 q^{86} - 2167 q^{87} + 312 q^{88} - 1784 q^{89} + 320 q^{90} + 2329 q^{91} - 368 q^{92} + 1483 q^{93} + 530 q^{94} - 265 q^{95} + 128 q^{96} - 2047 q^{97} - 3286 q^{98} - 2665 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 4 * q^3 + 16 * q^4 - 20 * q^5 + 8 * q^6 - q^7 - 32 * q^8 + 32 * q^9 + 40 * q^10 - 39 * q^11 - 16 * q^12 - 20 * q^13 + 2 * q^14 + 20 * q^15 + 64 * q^16 - 23 * q^17 - 64 * q^18 + 53 * q^19 - 80 * q^20 + 300 * q^21 + 78 * q^22 - 92 * q^23 + 32 * q^24 + 100 * q^25 + 40 * q^26 + 137 * q^27 - 4 * q^28 + 161 * q^29 - 40 * q^30 + 388 * q^31 - 128 * q^32 + 87 * q^33 + 46 * q^34 + 5 * q^35 + 128 * q^36 + 466 * q^37 - 106 * q^38 + 1047 * q^39 + 160 * q^40 + 484 * q^41 - 600 * q^42 + 894 * q^43 - 156 * q^44 - 160 * q^45 + 184 * q^46 - 265 * q^47 - 64 * q^48 + 1643 * q^49 - 200 * q^50 + 1825 * q^51 - 80 * q^52 + 576 * q^53 - 274 * q^54 + 195 * q^55 + 8 * q^56 + 178 * q^57 - 322 * q^58 - 94 * q^59 + 80 * q^60 + 1153 * q^61 - 776 * q^62 + 60 * q^63 + 256 * q^64 + 100 * q^65 - 174 * q^66 - 1472 * q^67 - 92 * q^68 + 92 * q^69 - 10 * q^70 + 200 * q^71 - 256 * q^72 + 1147 * q^73 - 932 * q^74 - 100 * q^75 + 212 * q^76 - 2176 * q^77 - 2094 * q^78 - 908 * q^79 - 320 * q^80 - 1056 * q^81 - 968 * q^82 - 1048 * q^83 + 1200 * q^84 + 115 * q^85 - 1788 * q^86 - 2167 * q^87 + 312 * q^88 - 1784 * q^89 + 320 * q^90 + 2329 * q^91 - 368 * q^92 + 1483 * q^93 + 530 * q^94 - 265 * q^95 + 128 * q^96 - 2047 * q^97 - 3286 * q^98 - 2665 * 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
$3$	0.589969	0.113540	0.0567698	−	0.998387i	$-0.481920\pi$
$3$	0.589969	0.113540	0.0567698	+	0.998387i	$0.481920\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−1.17994	−0.0802847
$7$	−18.5077	−0.999324	−0.499662	−	0.866220i	$-0.666542\pi$
$7$	−18.5077	−0.999324	−0.499662	+	0.866220i	$0.666542\pi$
$8$	−8.00000	−0.353553
$9$	−26.6519	−0.987109
$10$	10.0000	0.316228
$11$	47.9296	1.31376	0.656878	−	0.753997i	$-0.271877\pi$
$11$	47.9296	1.31376	0.656878	+	0.753997i	$0.271877\pi$
$12$	2.35988	0.0567698
$13$	42.3717	0.903984	0.451992	−	0.892022i	$-0.350714\pi$
$13$	42.3717	0.903984	0.451992	+	0.892022i	$0.350714\pi$
$14$	37.0155	0.706629
$15$	−2.94985	−0.0507765
$16$	16.0000	0.250000
$17$	1.70534	0.0243298	0.0121649	−	0.999926i	$-0.496128\pi$
$17$	1.70534	0.0243298	0.0121649	+	0.999926i	$0.496128\pi$
$18$	53.3039	0.697991
$19$	21.4208	0.258645	0.129323	−	0.991603i	$-0.458720\pi$
$19$	21.4208	0.258645	0.129323	+	0.991603i	$0.458720\pi$
$20$	−20.0000	−0.223607
$21$	−10.9190	−0.113463
$22$	−95.8592	−0.928966
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−4.71976	−0.0401423
$25$	25.0000	0.200000
$26$	−84.7434	−0.639213
$27$	−31.6530	−0.225616
$28$	−74.0310	−0.499662
$29$	57.6332	0.369042	0.184521	−	0.982829i	$-0.440927\pi$
$29$	57.6332	0.369042	0.184521	+	0.982829i	$0.440927\pi$
$30$	5.89969	0.0359044
$31$	295.699	1.71320	0.856599	−	0.515983i	$-0.172573\pi$
$31$	295.699	1.71320	0.856599	+	0.515983i	$0.172573\pi$
$32$	−32.0000	−0.176777
$33$	28.2770	0.149163
$34$	−3.41069	−0.0172038
$35$	92.5387	0.446911
$36$	−106.608	−0.493554
$37$	−7.85184	−0.0348874	−0.0174437	−	0.999848i	$-0.505553\pi$
$37$	−7.85184	−0.0348874	−0.0174437	+	0.999848i	$0.505553\pi$
$38$	−42.8416	−0.182890
$39$	24.9980	0.102638
$40$	40.0000	0.158114
$41$	465.929	1.77478	0.887390	−	0.461020i	$-0.152516\pi$
$41$	465.929	1.77478	0.887390	+	0.461020i	$0.152516\pi$
$42$	21.8380	0.0802304
$43$	182.374	0.646784	0.323392	−	0.946265i	$-0.395177\pi$
$43$	182.374	0.646784	0.323392	+	0.946265i	$0.395177\pi$
$44$	191.718	0.656878
$45$	133.260	0.441448
$46$	46.0000	0.147442
$47$	449.193	1.39408	0.697038	−	0.717035i	$-0.254501\pi$
$47$	449.193	1.39408	0.697038	+	0.717035i	$0.254501\pi$
$48$	9.43951	0.0283849
$49$	−0.463605	−0.00135162
$50$	−50.0000	−0.141421
$51$	1.00610	0.00276240
$52$	169.487	0.451992
$53$	−368.316	−0.954567	−0.477283	−	0.878749i	$-0.658379\pi$
$53$	−368.316	−0.954567	−0.477283	+	0.878749i	$0.658379\pi$
$54$	63.3060	0.159534
$55$	−239.648	−0.587529
$56$	148.062	0.353314
$57$	12.6376	0.0293665
$58$	−115.266	−0.260952
$59$	−377.032	−0.831955	−0.415977	−	0.909375i	$-0.636560\pi$
$59$	−377.032	−0.831955	−0.415977	+	0.909375i	$0.636560\pi$
$60$	−11.7994	−0.0253882
$61$	849.042	1.78211	0.891055	−	0.453896i	$-0.149966\pi$
$61$	849.042	1.78211	0.891055	+	0.453896i	$0.149966\pi$
$62$	−591.398	−1.21141
$63$	493.267	0.986441
$64$	64.0000	0.125000
$65$	−211.858	−0.404274
$66$	−56.5540	−0.105474
$67$	92.3424	0.168379	0.0841897	−	0.996450i	$-0.473170\pi$
$67$	92.3424	0.168379	0.0841897	+	0.996450i	$0.473170\pi$
$68$	6.82138	0.0121649
$69$	−13.5693	−0.0236747
$70$	−185.077	−0.316014
$71$	−626.854	−1.04780	−0.523901	−	0.851779i	$-0.675524\pi$
$71$	−626.854	−1.04780	−0.523901	+	0.851779i	$0.675524\pi$
$72$	213.215	0.348996
$73$	439.227	0.704214	0.352107	−	0.935960i	$-0.385465\pi$
$73$	439.227	0.704214	0.352107	+	0.935960i	$0.385465\pi$
$74$	15.7037	0.0246691
$75$	14.7492	0.0227079
$76$	85.6831	0.129323
$77$	−887.068	−1.31287
$78$	−49.9960	−0.0725761
$79$	641.707	0.913894	0.456947	−	0.889494i	$-0.348943\pi$
$79$	641.707	0.913894	0.456947	+	0.889494i	$0.348943\pi$
$80$	−80.0000	−0.111803
$81$	700.928	0.961492
$82$	−931.859	−1.25496
$83$	−609.932	−0.806611	−0.403306	−	0.915065i	$-0.632139\pi$
$83$	−609.932	−0.806611	−0.403306	+	0.915065i	$0.632139\pi$
$84$	−43.6760	−0.0567315
$85$	−8.52672	−0.0108806
$86$	−364.747	−0.457346
$87$	34.0018	0.0419009
$88$	−383.437	−0.464483
$89$	1122.87	1.33735	0.668673	−	0.743557i	$-0.266863\pi$
$89$	1122.87	1.33735	0.668673	+	0.743557i	$0.266863\pi$
$90$	−266.519	−0.312151
$91$	−784.204	−0.903373
$92$	−92.0000	−0.104257
$93$	174.453	0.194516
$94$	−898.386	−0.985760
$95$	−107.104	−0.115670
$96$	−18.8790	−0.0200712
$97$	−1428.80	−1.49559	−0.747795	−	0.663930i	$-0.768887\pi$
$97$	−1428.80	−1.49559	−0.747795	+	0.663930i	$0.768887\pi$
$98$	0.927209	0.000955737 0
$99$	−1277.42	−1.29682
$100$	100.000	0.100000
$101$	−1512.15	−1.48975	−0.744875	−	0.667204i	$-0.767491\pi$
$101$	−1512.15	−1.48975	−0.744875	+	0.667204i	$0.767491\pi$
$102$	−2.01220	−0.00195331
$103$	957.279	0.915762	0.457881	−	0.889013i	$-0.348609\pi$
$103$	957.279	0.915762	0.457881	+	0.889013i	$0.348609\pi$
$104$	−338.974	−0.319607
$105$	54.5950	0.0507422
$106$	736.631	0.674981
$107$	−1742.16	−1.57403	−0.787013	−	0.616936i	$-0.788374\pi$
$107$	−1742.16	−1.57403	−0.787013	+	0.616936i	$0.788374\pi$
$108$	−126.612	−0.112808
$109$	1166.77	1.02529	0.512644	−	0.858601i	$-0.328666\pi$
$109$	1166.77	1.02529	0.512644	+	0.858601i	$0.328666\pi$
$110$	479.296	0.415446
$111$	−4.63234	−0.00396111
$112$	−296.124	−0.249831
$113$	−393.287	−0.327410	−0.163705	−	0.986509i	$-0.552345\pi$
$113$	−393.287	−0.327410	−0.163705	+	0.986509i	$0.552345\pi$
$114$	−25.2752	−0.0207653
$115$	115.000	0.0932505
$116$	230.533	0.184521
$117$	−1129.29	−0.892331
$118$	754.063	0.588281
$119$	−31.5621	−0.0243134
$120$	23.5988	0.0179522
$121$	966.245	0.725954
$122$	−1698.08	−1.26014
$123$	274.884	0.201508
$124$	1182.80	0.856599
$125$	−125.000	−0.0894427
$126$	−986.534	−0.697519
$127$	−1067.87	−0.746127	−0.373063	−	0.927806i	$-0.621693\pi$
$127$	−1067.87	−0.746127	−0.373063	+	0.927806i	$0.621693\pi$
$128$	−128.000	−0.0883883
$129$	107.595	0.0734357
$130$	423.717	0.285865
$131$	−175.497	−0.117047	−0.0585237	−	0.998286i	$-0.518639\pi$
$131$	−175.497	−0.117047	−0.0585237	+	0.998286i	$0.518639\pi$
$132$	113.108	0.0745817
$133$	−396.450	−0.258471
$134$	−184.685	−0.119062
$135$	158.265	0.100898
$136$	−13.6428	−0.00860189
$137$	475.898	0.296779	0.148389	−	0.988929i	$-0.452591\pi$
$137$	475.898	0.296779	0.148389	+	0.988929i	$0.452591\pi$
$138$	27.1386	0.0167405
$139$	153.167	0.0934638	0.0467319	−	0.998907i	$-0.485119\pi$
$139$	153.167	0.0934638	0.0467319	+	0.998907i	$0.485119\pi$
$140$	370.155	0.223456
$141$	265.010	0.158283
$142$	1253.71	0.740907
$143$	2030.86	1.18761
$144$	−426.431	−0.246777
$145$	−288.166	−0.165041
$146$	−878.454	−0.497954
$147$	−0.273513	−0.000153462 0
$148$	−31.4074	−0.0174437
$149$	506.906	0.278707	0.139353	−	0.990243i	$-0.455498\pi$
$149$	506.906	0.278707	0.139353	+	0.990243i	$0.455498\pi$
$150$	−29.4985	−0.0160569
$151$	2437.84	1.31383	0.656916	−	0.753964i	$-0.271861\pi$
$151$	2437.84	1.31383	0.656916	+	0.753964i	$0.271861\pi$
$152$	−171.366	−0.0914450
$153$	−45.4507	−0.0240162
$154$	1774.14	0.928338
$155$	−1478.50	−0.766166
$156$	99.9920	0.0513190
$157$	255.966	0.130117	0.0650584	−	0.997881i	$-0.479277\pi$
$157$	255.966	0.130117	0.0650584	+	0.997881i	$0.479277\pi$
$158$	−1283.41	−0.646221
$159$	−217.295	−0.108381
$160$	160.000	0.0790569
$161$	425.678	0.208373
$162$	−1401.86	−0.679878
$163$	321.632	0.154553	0.0772767	−	0.997010i	$-0.475378\pi$
$163$	321.632	0.154553	0.0772767	+	0.997010i	$0.475378\pi$
$164$	1863.72	0.887390
$165$	−141.385	−0.0667079
$166$	1219.86	0.570360
$167$	−2926.22	−1.35591	−0.677957	−	0.735102i	$-0.737134\pi$
$167$	−2926.22	−1.35591	−0.677957	+	0.735102i	$0.737134\pi$
$168$	87.3520	0.0401152
$169$	−401.640	−0.182813
$170$	17.0534	0.00769376
$171$	−570.905	−0.255311
$172$	729.495	0.323392
$173$	1811.84	0.796254	0.398127	−	0.917330i	$-0.369660\pi$
$173$	1811.84	0.796254	0.398127	+	0.917330i	$0.369660\pi$
$174$	−68.0037	−0.0296284
$175$	−462.693	−0.199865
$176$	766.873	0.328439
$177$	−222.437	−0.0944599
$178$	−2245.74	−0.945646
$179$	912.664	0.381093	0.190547	−	0.981678i	$-0.438974\pi$
$179$	912.664	0.381093	0.190547	+	0.981678i	$0.438974\pi$
$180$	533.039	0.220724
$181$	3670.55	1.50735	0.753673	−	0.657249i	$-0.228280\pi$
$181$	3670.55	1.50735	0.753673	+	0.657249i	$0.228280\pi$
$182$	1568.41	0.638781
$183$	500.909	0.202340
$184$	184.000	0.0737210
$185$	39.2592	0.0156021
$186$	−348.907	−0.137544
$187$	81.7364	0.0319634
$188$	1796.77	0.697038
$189$	585.826	0.225463
$190$	214.208	0.0817909
$191$	−1840.96	−0.697419	−0.348710	−	0.937231i	$-0.613380\pi$
$191$	−1840.96	−0.697419	−0.348710	+	0.937231i	$0.613380\pi$
$192$	37.7580	0.0141925
$193$	−611.817	−0.228184	−0.114092	−	0.993470i	$-0.536396\pi$
$193$	−611.817	−0.228184	−0.114092	+	0.993470i	$0.536396\pi$
$194$	2857.59	1.05754
$195$	−124.990	−0.0459011
$196$	−1.85442	−0.000675808 0
$197$	2830.26	1.02359	0.511796	−	0.859107i	$-0.328980\pi$
$197$	2830.26	1.02359	0.511796	+	0.859107i	$0.328980\pi$
$198$	2554.83	0.916990
$199$	−1162.74	−0.414195	−0.207097	−	0.978320i	$-0.566402\pi$
$199$	−1162.74	−0.414195	−0.207097	+	0.978320i	$0.566402\pi$
$200$	−200.000	−0.0707107
$201$	54.4792	0.0191177
$202$	3024.31	1.05341
$203$	−1066.66	−0.368792
$204$	4.02440	0.00138120
$205$	−2329.65	−0.793705
$206$	−1914.56	−0.647542
$207$	612.995	0.205826
$208$	677.947	0.225996
$209$	1026.69	0.339797
$210$	−109.190	−0.0358801
$211$	1399.58	0.456641	0.228320	−	0.973586i	$-0.426677\pi$
$211$	1399.58	0.456641	0.228320	+	0.973586i	$0.426677\pi$
$212$	−1473.26	−0.477283
$213$	−369.825	−0.118967
$214$	3484.32	1.11300
$215$	−911.869	−0.289251
$216$	253.224	0.0797672
$217$	−5472.72	−1.71204
$218$	−2333.54	−0.724988
$219$	259.130	0.0799562
$220$	−958.592	−0.293765
$221$	72.2583	0.0219938
$222$	9.26469	0.00280092
$223$	4257.98	1.27863	0.639317	−	0.768943i	$-0.279217\pi$
$223$	4257.98	1.27863	0.639317	+	0.768943i	$0.279217\pi$
$224$	592.248	0.176657
$225$	−666.298	−0.197422
$226$	786.574	0.231514
$227$	−4025.03	−1.17688	−0.588438	−	0.808542i	$-0.700257\pi$
$227$	−4025.03	−1.17688	−0.588438	+	0.808542i	$0.700257\pi$
$228$	50.5504	0.0146833
$229$	3623.04	1.04549	0.522745	−	0.852489i	$-0.324908\pi$
$229$	3623.04	1.04549	0.522745	+	0.852489i	$0.324908\pi$
$230$	−230.000	−0.0659380
$231$	−523.343	−0.149063
$232$	−461.066	−0.130476
$233$	6502.81	1.82838	0.914192	−	0.405282i	$-0.132827\pi$
$233$	6502.81	1.82838	0.914192	+	0.405282i	$0.132827\pi$
$234$	2258.58	0.630973
$235$	−2245.96	−0.623449
$236$	−1508.13	−0.415977
$237$	378.587	0.103763
$238$	63.1241	0.0171921
$239$	−2690.07	−0.728059	−0.364030	−	0.931387i	$-0.618599\pi$
$239$	−2690.07	−0.728059	−0.364030	+	0.931387i	$0.618599\pi$
$240$	−47.1976	−0.0126941
$241$	−44.6958	−0.0119465	−0.00597326	−	0.999982i	$-0.501901\pi$
$241$	−44.6958	−0.0119465	−0.00597326	+	0.999982i	$0.501901\pi$
$242$	−1932.49	−0.513327
$243$	1268.16	0.334783
$244$	3396.17	0.891055
$245$	2.31802	0.000604461 0
$246$	−549.768	−0.142488
$247$	907.635	0.233811
$248$	−2365.59	−0.605707
$249$	−359.841	−0.0915824
$250$	250.000	0.0632456
$251$	−6801.41	−1.71036	−0.855181	−	0.518329i	$-0.826554\pi$
$251$	−6801.41	−1.71036	−0.855181	+	0.518329i	$0.826554\pi$
$252$	1973.07	0.493221
$253$	−1102.38	−0.273937
$254$	2135.74	0.527591
$255$	−5.03050	−0.00123538
$256$	256.000	0.0625000
$257$	5576.00	1.35339	0.676695	−	0.736263i	$-0.263411\pi$
$257$	5576.00	1.35339	0.676695	+	0.736263i	$0.263411\pi$
$258$	−215.190	−0.0519269
$259$	145.320	0.0348638
$260$	−847.434	−0.202137
$261$	−1536.04	−0.364285
$262$	350.993	0.0827651
$263$	−5669.58	−1.32928	−0.664641	−	0.747163i	$-0.731415\pi$
$263$	−5669.58	−1.32928	−0.664641	+	0.747163i	$0.731415\pi$
$264$	−226.216	−0.0527372
$265$	1841.58	0.426895
$266$	792.900	0.182766
$267$	662.458	0.151842
$268$	369.370	0.0841897
$269$	6040.21	1.36906	0.684532	−	0.728983i	$-0.260006\pi$
$269$	6040.21	1.36906	0.684532	+	0.728983i	$0.260006\pi$
$270$	−316.530	−0.0713459
$271$	−6899.26	−1.54650	−0.773248	−	0.634104i	$-0.781369\pi$
$271$	−6899.26	−1.54650	−0.773248	+	0.634104i	$0.781369\pi$
$272$	27.2855	0.00608245
$273$	−462.657	−0.102569
$274$	−951.795	−0.209854
$275$	1198.24	0.262751
$276$	−54.2772	−0.0118373
$277$	5617.68	1.21853	0.609267	−	0.792965i	$-0.291464\pi$
$277$	5617.68	1.21853	0.609267	+	0.792965i	$0.291464\pi$
$278$	−306.334	−0.0660889
$279$	−7880.96	−1.69111
$280$	−740.310	−0.158007
$281$	3069.89	0.651723	0.325861	−	0.945418i	$-0.394346\pi$
$281$	3069.89	0.651723	0.325861	+	0.945418i	$0.394346\pi$
$282$	−530.020	−0.111923
$283$	1404.86	0.295089	0.147544	−	0.989055i	$-0.452863\pi$
$283$	1404.86	0.295089	0.147544	+	0.989055i	$0.452863\pi$
$284$	−2507.42	−0.523901
$285$	−63.1880	−0.0131331
$286$	−4061.72	−0.839770
$287$	−8623.30	−1.77358
$288$	852.862	0.174498
$289$	−4910.09	−0.999408
$290$	576.332	0.116701
$291$	−842.946	−0.169809
$292$	1756.91	0.352107
$293$	−2407.05	−0.479936	−0.239968	−	0.970781i	$-0.577137\pi$
$293$	−2407.05	−0.479936	−0.239968	+	0.970781i	$0.577137\pi$
$294$	0.547025	0.000108514 0
$295$	1885.16	0.372062
$296$	62.8147	0.0123346
$297$	−1517.12	−0.296404
$298$	−1013.81	−0.197076
$299$	−974.549	−0.188494
$300$	58.9969	0.0113540
$301$	−3375.33	−0.646347
$302$	−4875.68	−0.929020
$303$	−892.124	−0.169146
$304$	342.732	0.0646614
$305$	−4245.21	−0.796984
$306$	90.9015	0.0169820
$307$	−459.743	−0.0854689	−0.0427344	−	0.999086i	$-0.513607\pi$
$307$	−459.743	−0.0854689	−0.0427344	+	0.999086i	$0.513607\pi$
$308$	−3548.27	−0.656434
$309$	564.765	0.103975
$310$	2956.99	0.541761
$311$	4119.48	0.751107	0.375553	−	0.926801i	$-0.377453\pi$
$311$	4119.48	0.751107	0.375553	+	0.926801i	$0.377453\pi$
$312$	−199.984	−0.0362880
$313$	1684.15	0.304133	0.152066	−	0.988370i	$-0.451407\pi$
$313$	1684.15	0.304133	0.152066	+	0.988370i	$0.451407\pi$
$314$	−511.933	−0.0920065
$315$	−2466.34	−0.441150
$316$	2566.83	0.456947
$317$	8686.47	1.53906	0.769528	−	0.638613i	$-0.220492\pi$
$317$	8686.47	1.53906	0.769528	+	0.638613i	$0.220492\pi$
$318$	434.590	0.0766371
$319$	2762.34	0.484831
$320$	−320.000	−0.0559017
$321$	−1027.82	−0.178714
$322$	−851.356	−0.147342
$323$	36.5298	0.00629279
$324$	2803.71	0.480746
$325$	1059.29	0.180797
$326$	−643.265	−0.109286
$327$	688.360	0.116411
$328$	−3727.44	−0.627479
$329$	−8313.55	−1.39313
$330$	282.770	0.0471696
$331$	4307.91	0.715359	0.357680	−	0.933844i	$-0.383568\pi$
$331$	4307.91	0.715359	0.357680	+	0.933844i	$0.383568\pi$
$332$	−2439.73	−0.403306
$333$	209.267	0.0344377
$334$	5852.44	0.958776
$335$	−461.712	−0.0753015
$336$	−174.704	−0.0283657
$337$	−290.156	−0.0469015	−0.0234507	−	0.999725i	$-0.507465\pi$
$337$	−290.156	−0.0469015	−0.0234507	+	0.999725i	$0.507465\pi$
$338$	803.280	0.129268
$339$	−232.027	−0.0371740
$340$	−34.1069	−0.00544031
$341$	14172.7	2.25072
$342$	1141.81	0.180532
$343$	6356.73	1.00067
$344$	−1458.99	−0.228673
$345$	67.8465	0.0105876
$346$	−3623.69	−0.563037
$347$	1042.94	0.161349	0.0806743	−	0.996741i	$-0.474293\pi$
$347$	1042.94	0.161349	0.0806743	+	0.996741i	$0.474293\pi$
$348$	136.007	0.0209505
$349$	−1819.56	−0.279080	−0.139540	−	0.990216i	$-0.544562\pi$
$349$	−1819.56	−0.279080	−0.139540	+	0.990216i	$0.544562\pi$
$350$	925.387	0.141326
$351$	−1341.19	−0.203953
$352$	−1533.75	−0.232241
$353$	−4514.29	−0.680656	−0.340328	−	0.940307i	$-0.610538\pi$
$353$	−4514.29	−0.680656	−0.340328	+	0.940307i	$0.610538\pi$
$354$	444.874	0.0667932
$355$	3134.27	0.468591
$356$	4491.47	0.668673
$357$	−18.6207	−0.00276053
$358$	−1825.33	−0.269474
$359$	11527.9	1.69476	0.847379	−	0.530988i	$-0.178179\pi$
$359$	11527.9	1.69476	0.847379	+	0.530988i	$0.178179\pi$
$360$	−1066.08	−0.156076
$361$	−6400.15	−0.933103
$362$	−7341.10	−1.06585
$363$	570.055	0.0824246
$364$	−3136.82	−0.451686
$365$	−2196.13	−0.314934
$366$	−1001.82	−0.143076
$367$	6894.09	0.980568	0.490284	−	0.871563i	$-0.336893\pi$
$367$	6894.09	0.980568	0.490284	+	0.871563i	$0.336893\pi$
$368$	−368.000	−0.0521286
$369$	−12417.9	−1.75190
$370$	−78.5184	−0.0110324
$371$	6816.69	0.953922
$372$	697.814	0.0972580
$373$	7733.25	1.07349	0.536746	−	0.843744i	$-0.319653\pi$
$373$	7733.25	1.07349	0.536746	+	0.843744i	$0.319653\pi$
$374$	−163.473	−0.0226016
$375$	−73.7462	−0.0101553
$376$	−3593.54	−0.492880
$377$	2442.02	0.333608
$378$	−1171.65	−0.159427
$379$	−9495.72	−1.28697	−0.643486	−	0.765458i	$-0.722512\pi$
$379$	−9495.72	−1.28697	−0.643486	+	0.765458i	$0.722512\pi$
$380$	−428.416	−0.0578349
$381$	−630.011	−0.0847150
$382$	3681.92	0.493150
$383$	−12877.0	−1.71797	−0.858987	−	0.511998i	$-0.828906\pi$
$383$	−12877.0	−1.71797	−0.858987	+	0.511998i	$0.828906\pi$
$384$	−75.5161	−0.0100356
$385$	4435.34	0.587132
$386$	1223.63	0.161351
$387$	−4860.61	−0.638447
$388$	−5715.18	−0.747795
$389$	−8200.40	−1.06884	−0.534418	−	0.845221i	$-0.679469\pi$
$389$	−8200.40	−1.06884	−0.534418	+	0.845221i	$0.679469\pi$
$390$	249.980	0.0324570
$391$	−39.2229	−0.00507312
$392$	3.70884	0.000477869 0
$393$	−103.538	−0.0132895
$394$	−5660.52	−0.723789
$395$	−3208.53	−0.408706
$396$	−5109.66	−0.648410
$397$	7842.68	0.991468	0.495734	−	0.868475i	$-0.334899\pi$
$397$	7842.68	0.991468	0.495734	+	0.868475i	$0.334899\pi$
$398$	2325.49	0.292880
$399$	−233.893	−0.0293467
$400$	400.000	0.0500000
$401$	−14534.2	−1.80999	−0.904993	−	0.425427i	$-0.860124\pi$
$401$	−14534.2	−1.80999	−0.904993	+	0.425427i	$0.860124\pi$
$402$	−108.958	−0.0135183
$403$	12529.3	1.54870
$404$	−6048.61	−0.744875
$405$	−3504.64	−0.429992
$406$	2133.32	0.260776
$407$	−376.335	−0.0458335
$408$	−8.04881	−0.000976655 0
$409$	13388.0	1.61857	0.809283	−	0.587419i	$-0.199856\pi$
$409$	13388.0	1.61857	0.809283	+	0.587419i	$0.199856\pi$
$410$	4659.29	0.561234
$411$	280.765	0.0336962
$412$	3829.12	0.457881
$413$	6978.00	0.831393
$414$	−1225.99	−0.145541
$415$	3049.66	0.360727
$416$	−1355.89	−0.159803
$417$	90.3640	0.0106119
$418$	−2053.38	−0.240273
$419$	−3103.10	−0.361805	−0.180903	−	0.983501i	$-0.557902\pi$
$419$	−3103.10	−0.361805	−0.180903	+	0.983501i	$0.557902\pi$
$420$	218.380	0.0253711
$421$	−6075.82	−0.703367	−0.351684	−	0.936119i	$-0.614391\pi$
$421$	−6075.82	−0.703367	−0.351684	+	0.936119i	$0.614391\pi$
$422$	−2799.16	−0.322894
$423$	−11971.9	−1.37610
$424$	2946.53	0.337490
$425$	42.6336	0.00486596
$426$	739.649	0.0841224
$427$	−15713.8	−1.78090
$428$	−6968.63	−0.787013
$429$	1198.14	0.134841
$430$	1823.74	0.204531
$431$	14120.3	1.57808	0.789040	−	0.614341i	$-0.210578\pi$
$431$	14120.3	1.57808	0.789040	+	0.614341i	$0.210578\pi$
$432$	−506.448	−0.0564039
$433$	8555.96	0.949592	0.474796	−	0.880096i	$-0.342522\pi$
$433$	8555.96	0.949592	0.474796	+	0.880096i	$0.342522\pi$
$434$	10945.4	1.21060
$435$	−170.009	−0.0187387
$436$	4667.09	0.512644
$437$	−492.678	−0.0539313
$438$	−518.261	−0.0565376
$439$	−10894.1	−1.18439	−0.592194	−	0.805796i	$-0.701738\pi$
$439$	−10894.1	−1.18439	−0.592194	+	0.805796i	$0.701738\pi$
$440$	1917.18	0.207723
$441$	12.3560	0.00133419
$442$	−144.517	−0.0155519
$443$	16120.5	1.72891	0.864456	−	0.502708i	$-0.167663\pi$
$443$	16120.5	1.72891	0.864456	+	0.502708i	$0.167663\pi$
$444$	−18.5294	−0.00198055
$445$	−5614.34	−0.598079
$446$	−8515.96	−0.904130
$447$	299.059	0.0316443
$448$	−1184.50	−0.124915
$449$	4811.29	0.505699	0.252849	−	0.967506i	$-0.418632\pi$
$449$	4811.29	0.505699	0.252849	+	0.967506i	$0.418632\pi$
$450$	1332.60	0.139598
$451$	22331.8	2.33163
$452$	−1573.15	−0.163705
$453$	1438.25	0.149172
$454$	8050.06	0.832177
$455$	3921.02	0.404001
$456$	−101.101	−0.0103826
$457$	−226.329	−0.0231667	−0.0115834	−	0.999933i	$-0.503687\pi$
$457$	−226.329	−0.0231667	−0.0115834	+	0.999933i	$0.503687\pi$
$458$	−7246.08	−0.739273
$459$	−53.9793	−0.00548919
$460$	460.000	0.0466252
$461$	−4349.17	−0.439395	−0.219697	−	0.975568i	$-0.570507\pi$
$461$	−4349.17	−0.439395	−0.219697	+	0.975568i	$0.570507\pi$
$462$	1046.69	0.105403
$463$	−989.313	−0.0993030	−0.0496515	−	0.998767i	$-0.515811\pi$
$463$	−989.313	−0.0993030	−0.0496515	+	0.998767i	$0.515811\pi$
$464$	922.131	0.0922605
$465$	−872.267	−0.0869902
$466$	−13005.6	−1.29286
$467$	8512.91	0.843535	0.421767	−	0.906704i	$-0.361410\pi$
$467$	8512.91	0.843535	0.421767	+	0.906704i	$0.361410\pi$
$468$	−4517.15	−0.446165
$469$	−1709.05	−0.168266
$470$	4491.93	0.440845
$471$	151.012	0.0147734
$472$	3016.25	0.294140
$473$	8741.10	0.849717
$474$	−757.175	−0.0733717
$475$	535.519	0.0517291
$476$	−126.248	−0.0121567
$477$	9816.33	0.942261
$478$	5380.14	0.514816
$479$	−12058.6	−1.15025	−0.575125	−	0.818065i	$-0.695047\pi$
$479$	−12058.6	−1.15025	−0.575125	+	0.818065i	$0.695047\pi$
$480$	94.3951	0.00897610
$481$	−332.696	−0.0315377
$482$	89.3916	0.00844746
$483$	251.137	0.0236587
$484$	3864.98	0.362977
$485$	7143.98	0.668848
$486$	−2536.31	−0.236727
$487$	11605.3	1.07985	0.539924	−	0.841714i	$-0.318453\pi$
$487$	11605.3	1.07985	0.539924	+	0.841714i	$0.318453\pi$
$488$	−6792.34	−0.630071
$489$	189.753	0.0175479
$490$	−4.63605	−0.000427419 0
$491$	−4651.88	−0.427569	−0.213785	−	0.976881i	$-0.568579\pi$
$491$	−4651.88	−0.427569	−0.213785	+	0.976881i	$0.568579\pi$
$492$	1099.54	0.100754
$493$	98.2845	0.00897872
$494$	−1815.27	−0.165330
$495$	6387.08	0.579955
$496$	4731.19	0.428300
$497$	11601.6	1.04709
$498$	719.682	0.0647585
$499$	−7953.03	−0.713480	−0.356740	−	0.934204i	$-0.616112\pi$
$499$	−7953.03	−0.713480	−0.356740	+	0.934204i	$0.616112\pi$
$500$	−500.000	−0.0447214
$501$	−1726.38	−0.153950
$502$	13602.8	1.20941
$503$	−11805.6	−1.04649	−0.523245	−	0.852182i	$-0.675279\pi$
$503$	−11805.6	−1.04649	−0.523245	+	0.852182i	$0.675279\pi$
$504$	−3946.14	−0.348760
$505$	7560.76	0.666237
$506$	2204.76	0.193703
$507$	−236.955	−0.0207565
$508$	−4271.48	−0.373063
$509$	−2732.89	−0.237983	−0.118991	−	0.992895i	$-0.537966\pi$
$509$	−2732.89	−0.237983	−0.118991	+	0.992895i	$0.537966\pi$
$510$	10.0610	0.000873547 0
$511$	−8129.09	−0.703738
$512$	−512.000	−0.0441942
$513$	−678.032	−0.0583545
$514$	−11152.0	−0.956992
$515$	−4786.40	−0.409541
$516$	430.380	0.0367178
$517$	21529.6	1.83147
$518$	−290.640	−0.0246525
$519$	1068.93	0.0904065
$520$	1694.87	0.142932
$521$	14710.9	1.23704	0.618518	−	0.785771i	$-0.287733\pi$
$521$	14710.9	1.23704	0.618518	+	0.785771i	$0.287733\pi$
$522$	3072.07	0.257588
$523$	−7034.35	−0.588127	−0.294064	−	0.955786i	$-0.595008\pi$
$523$	−7034.35	−0.588127	−0.294064	+	0.955786i	$0.595008\pi$
$524$	−701.987	−0.0585237
$525$	−272.975	−0.0226926
$526$	11339.2	0.939944
$527$	504.269	0.0416818
$528$	452.432	0.0372908
$529$	529.000	0.0434783
$530$	−3683.16	−0.301861
$531$	10048.6	0.821230
$532$	−1585.80	−0.129235
$533$	19742.2	1.60437
$534$	−1324.92	−0.107368
$535$	8710.79	0.703926
$536$	−738.739	−0.0595311
$537$	538.444	0.0432692
$538$	−12080.4	−0.968075
$539$	−22.2204	−0.00177569
$540$	633.060	0.0504492
$541$	1552.90	0.123409	0.0617045	−	0.998094i	$-0.480346\pi$
$541$	1552.90	0.123409	0.0617045	+	0.998094i	$0.480346\pi$
$542$	13798.5	1.09354
$543$	2165.51	0.171144
$544$	−54.5710	−0.00430094
$545$	−5833.86	−0.458523
$546$	925.313	0.0725270
$547$	174.657	0.0136523	0.00682614	−	0.999977i	$-0.497827\pi$
$547$	174.657	0.0136523	0.00682614	+	0.999977i	$0.497827\pi$
$548$	1903.59	0.148389
$549$	−22628.6	−1.75914
$550$	−2396.48	−0.185793
$551$	1234.55	0.0954510
$552$	108.554	0.00837026
$553$	−11876.5	−0.913276
$554$	−11235.4	−0.861633
$555$	23.1617	0.00177146
$556$	612.669	0.0467319
$557$	−1990.63	−0.151429	−0.0757143	−	0.997130i	$-0.524124\pi$
$557$	−1990.63	−0.151429	−0.0757143	+	0.997130i	$0.524124\pi$
$558$	15761.9	1.19580
$559$	7727.48	0.584683
$560$	1480.62	0.111728
$561$	48.2220	0.00362912
$562$	−6139.78	−0.460838
$563$	208.006	0.0155709	0.00778543	−	0.999970i	$-0.497522\pi$
$563$	208.006	0.0155709	0.00778543	+	0.999970i	$0.497522\pi$
$564$	1060.04	0.0791414
$565$	1966.44	0.146422
$566$	−2809.71	−0.208659
$567$	−12972.6	−0.960842
$568$	5014.83	0.370454
$569$	−3003.05	−0.221256	−0.110628	−	0.993862i	$-0.535286\pi$
$569$	−3003.05	−0.221256	−0.110628	+	0.993862i	$0.535286\pi$
$570$	126.376	0.00928651
$571$	−10796.1	−0.791249	−0.395624	−	0.918412i	$-0.629472\pi$
$571$	−10796.1	−0.791249	−0.395624	+	0.918412i	$0.629472\pi$
$572$	8123.43	0.593807
$573$	−1086.11	−0.0791847
$574$	17246.6	1.25411
$575$	−575.000	−0.0417029
$576$	−1705.72	−0.123389
$577$	−26011.3	−1.87671	−0.938357	−	0.345667i	$-0.887653\pi$
$577$	−26011.3	−1.87671	−0.938357	+	0.345667i	$0.887653\pi$
$578$	9820.18	0.706688
$579$	−360.953	−0.0259079
$580$	−1152.66	−0.0825203
$581$	11288.5	0.806066
$582$	1685.89	0.120073
$583$	−17653.2	−1.25407
$584$	−3513.81	−0.248977
$585$	5646.44	0.399062
$586$	4814.09	0.339366
$587$	−2774.97	−0.195120	−0.0975598	−	0.995230i	$-0.531104\pi$
$587$	−2774.97	−0.195120	−0.0975598	+	0.995230i	$0.531104\pi$
$588$	−1.09405	−7.67311e−5 0
$589$	6334.11	0.443111
$590$	−3770.32	−0.263087
$591$	1669.77	0.116218
$592$	−125.629	−0.00872185
$593$	−2384.07	−0.165096	−0.0825481	−	0.996587i	$-0.526306\pi$
$593$	−2384.07	−0.165096	−0.0825481	+	0.996587i	$0.526306\pi$
$594$	3034.23	0.209589
$595$	157.810	0.0108733
$596$	2027.62	0.139353
$597$	−685.984	−0.0470276
$598$	1949.10	0.133285
$599$	−1090.87	−0.0744102	−0.0372051	−	0.999308i	$-0.511845\pi$
$599$	−1090.87	−0.0744102	−0.0372051	+	0.999308i	$0.511845\pi$
$600$	−117.994	−0.00802847
$601$	−5192.37	−0.352414	−0.176207	−	0.984353i	$-0.556383\pi$
$601$	−5192.37	−0.352414	−0.176207	+	0.984353i	$0.556383\pi$
$602$	6750.65	0.457036
$603$	−2461.10	−0.166209
$604$	9751.36	0.656916
$605$	−4831.22	−0.324657
$606$	1784.25	0.119604
$607$	1205.44	0.0806054	0.0403027	−	0.999188i	$-0.487168\pi$
$607$	1205.44	0.0806054	0.0403027	+	0.999188i	$0.487168\pi$
$608$	−685.465	−0.0457225
$609$	−629.297	−0.0418726
$610$	8490.42	0.563553
$611$	19033.1	1.26022
$612$	−181.803	−0.0120081
$613$	−14243.2	−0.938466	−0.469233	−	0.883075i	$-0.655469\pi$
$613$	−14243.2	−0.938466	−0.469233	+	0.883075i	$0.655469\pi$
$614$	919.487	0.0604356
$615$	−1374.42	−0.0901170
$616$	7096.55	0.464169
$617$	−422.492	−0.0275671	−0.0137835	−	0.999905i	$-0.504388\pi$
$617$	−422.492	−0.0275671	−0.0137835	+	0.999905i	$0.504388\pi$
$618$	−1129.53	−0.0735217
$619$	−8826.35	−0.573119	−0.286560	−	0.958062i	$-0.592512\pi$
$619$	−8826.35	−0.573119	−0.286560	+	0.958062i	$0.592512\pi$
$620$	−5913.98	−0.383083
$621$	728.019	0.0470441
$622$	−8238.96	−0.531113
$623$	−20781.7	−1.33644
$624$	399.968	0.0256595
$625$	625.000	0.0400000
$626$	−3368.29	−0.215054
$627$	605.715	0.0385804
$628$	1023.87	0.0650584
$629$	−13.3901	−0.000848804 0
$630$	4932.67	0.311940
$631$	−19684.1	−1.24186	−0.620929	−	0.783867i	$-0.713244\pi$
$631$	−19684.1	−1.24186	−0.620929	+	0.783867i	$0.713244\pi$
$632$	−5133.65	−0.323110
$633$	825.710	0.0518468
$634$	−17372.9	−1.08828
$635$	5339.35	0.333678
$636$	−869.180	−0.0541906
$637$	−19.6437	−0.00122184
$638$	−5524.67	−0.342827
$639$	16706.9	1.03429
$640$	640.000	0.0395285
$641$	15113.1	0.931253	0.465626	−	0.884981i	$-0.345829\pi$
$641$	15113.1	0.931253	0.465626	+	0.884981i	$0.345829\pi$
$642$	2055.64	0.126370
$643$	−16917.8	−1.03760	−0.518798	−	0.854897i	$-0.673620\pi$
$643$	−16917.8	−1.03760	−0.518798	+	0.854897i	$0.673620\pi$
$644$	1702.71	0.104187
$645$	−537.975	−0.0328414
$646$	−73.0596	−0.00444968
$647$	19564.5	1.18881	0.594405	−	0.804166i	$-0.297388\pi$
$647$	19564.5	1.18881	0.594405	+	0.804166i	$0.297388\pi$
$648$	−5607.42	−0.339939
$649$	−18071.0	−1.09299
$650$	−2118.58	−0.127843
$651$	−3228.74	−0.194384
$652$	1286.53	0.0772767
$653$	−22735.0	−1.36247	−0.681233	−	0.732067i	$-0.738556\pi$
$653$	−22735.0	−1.36247	−0.681233	+	0.732067i	$0.738556\pi$
$654$	−1376.72	−0.0823149
$655$	877.483	0.0523452
$656$	7454.87	0.443695
$657$	−11706.2	−0.695136
$658$	16627.1	0.985094
$659$	−30730.7	−1.81654	−0.908269	−	0.418388i	$-0.862595\pi$
$659$	−30730.7	−1.81654	−0.908269	+	0.418388i	$0.862595\pi$
$660$	−565.540	−0.0333539
$661$	−29204.3	−1.71848	−0.859240	−	0.511573i	$-0.829063\pi$
$661$	−29204.3	−1.71848	−0.859240	+	0.511573i	$0.829063\pi$
$662$	−8615.81	−0.505835
$663$	42.6302	0.00249716
$664$	4879.45	0.285180
$665$	1982.25	0.115592
$666$	−418.533	−0.0243511
$667$	−1325.56	−0.0769506
$668$	−11704.9	−0.677957
$669$	2512.08	0.145176
$670$	923.424	0.0532462
$671$	40694.2	2.34126
$672$	349.408	0.0200576
$673$	−17530.1	−1.00406	−0.502032	−	0.864849i	$-0.667414\pi$
$673$	−17530.1	−1.00406	−0.502032	+	0.864849i	$0.667414\pi$
$674$	580.312	0.0331644
$675$	−791.325	−0.0451231
$676$	−1606.56	−0.0914064
$677$	−20553.4	−1.16681	−0.583407	−	0.812180i	$-0.698281\pi$
$677$	−20553.4	−1.16681	−0.583407	+	0.812180i	$0.698281\pi$
$678$	464.055	0.0262860
$679$	26443.8	1.49458
$680$	68.2138	0.00384688
$681$	−2374.65	−0.133622
$682$	−28345.5	−1.59150
$683$	13174.8	0.738098	0.369049	−	0.929410i	$-0.379684\pi$
$683$	13174.8	0.738098	0.369049	+	0.929410i	$0.379684\pi$
$684$	−2283.62	−0.127656
$685$	−2379.49	−0.132723
$686$	−12713.5	−0.707584
$687$	2137.48	0.118705
$688$	2917.98	0.161696
$689$	−15606.2	−0.862913
$690$	−135.693	−0.00748658
$691$	−14800.8	−0.814831	−0.407415	−	0.913243i	$-0.633570\pi$
$691$	−14800.8	−0.814831	−0.407415	+	0.913243i	$0.633570\pi$
$692$	7247.38	0.398127
$693$	23642.1	1.29594
$694$	−2085.88	−0.114091
$695$	−765.836	−0.0417983
$696$	−272.015	−0.0148142
$697$	794.570	0.0431800
$698$	3639.13	0.197339
$699$	3836.46	0.207594
$700$	−1850.77	−0.0999324
$701$	−12311.5	−0.663336	−0.331668	−	0.943396i	$-0.607611\pi$
$701$	−12311.5	−0.663336	−0.331668	+	0.943396i	$0.607611\pi$
$702$	2682.38	0.144217
$703$	−168.192	−0.00902347
$704$	3067.49	0.164219
$705$	−1325.05	−0.0707862
$706$	9028.59	0.481297
$707$	27986.5	1.48874
$708$	−889.749	−0.0472299
$709$	3893.89	0.206260	0.103130	−	0.994668i	$-0.467114\pi$
$709$	3893.89	0.206260	0.103130	+	0.994668i	$0.467114\pi$
$710$	−6268.54	−0.331344
$711$	−17102.7	−0.902113
$712$	−8982.94	−0.472823
$713$	−6801.08	−0.357227
$714$	37.2413	0.00195199
$715$	−10154.3	−0.531117
$716$	3650.65	0.190547
$717$	−1587.06	−0.0826636
$718$	−23055.8	−1.19838
$719$	−19942.5	−1.03440	−0.517198	−	0.855866i	$-0.673025\pi$
$719$	−19942.5	−1.03440	−0.517198	+	0.855866i	$0.673025\pi$
$720$	2132.15	0.110362
$721$	−17717.1	−0.915143
$722$	12800.3	0.659803
$723$	−26.3692	−0.00135640
$724$	14682.2	0.753673
$725$	1440.83	0.0738084
$726$	−1140.11	−0.0582830
$727$	36167.0	1.84506	0.922530	−	0.385926i	$-0.126118\pi$
$727$	36167.0	1.84506	0.922530	+	0.385926i	$0.126118\pi$
$728$	6273.63	0.319391
$729$	−18176.9	−0.923481
$730$	4392.27	0.222692
$731$	311.010	0.0157361
$732$	2003.64	0.101170
$733$	−11669.5	−0.588025	−0.294013	−	0.955802i	$-0.594991\pi$
$733$	−11669.5	−0.588025	−0.294013	+	0.955802i	$0.594991\pi$
$734$	−13788.2	−0.693366
$735$	1.36756	6.86304e−5 0
$736$	736.000	0.0368605
$737$	4425.93	0.221209
$738$	24835.8	1.23878
$739$	75.0536	0.00373598	0.00186799	−	0.999998i	$-0.499405\pi$
$739$	75.0536	0.00373598	0.00186799	+	0.999998i	$0.499405\pi$
$740$	157.037	0.00780106
$741$	535.477	0.0265469
$742$	−13633.4	−0.674524
$743$	28279.8	1.39635	0.698173	−	0.715929i	$-0.253997\pi$
$743$	28279.8	1.39635	0.698173	+	0.715929i	$0.253997\pi$
$744$	−1395.63	−0.0687718
$745$	−2534.53	−0.124641
$746$	−15466.5	−0.759074
$747$	16255.9	0.796213
$748$	326.946	0.0159817
$749$	32243.4	1.57296
$750$	147.492	0.00718088
$751$	−17268.1	−0.839044	−0.419522	−	0.907745i	$-0.637802\pi$
$751$	−17268.1	−0.839044	−0.419522	+	0.907745i	$0.637802\pi$
$752$	7187.09	0.348519
$753$	−4012.62	−0.194194
$754$	−4884.03	−0.235897
$755$	−12189.2	−0.587564
$756$	2343.30	0.112732
$757$	−12525.8	−0.601400	−0.300700	−	0.953719i	$-0.597220\pi$
$757$	−12525.8	−0.601400	−0.300700	+	0.953719i	$0.597220\pi$
$758$	18991.4	0.910026
$759$	−650.371	−0.0311027
$760$	856.831	0.0408954
$761$	−18670.1	−0.889343	−0.444672	−	0.895694i	$-0.646680\pi$
$761$	−18670.1	−0.889343	−0.444672	+	0.895694i	$0.646680\pi$
$762$	1260.02	0.0599026
$763$	−21594.3	−1.02460
$764$	−7363.83	−0.348710
$765$	227.254	0.0107404
$766$	25754.0	1.21479
$767$	−15975.5	−0.752074
$768$	151.032	0.00709623
$769$	−32969.6	−1.54605	−0.773027	−	0.634373i	$-0.781258\pi$
$769$	−32969.6	−1.54605	−0.773027	+	0.634373i	$0.781258\pi$
$770$	−8870.68	−0.415165
$771$	3289.67	0.153664
$772$	−2447.27	−0.114092
$773$	−23251.3	−1.08188	−0.540938	−	0.841062i	$-0.681931\pi$
$773$	−23251.3	−1.08188	−0.540938	+	0.841062i	$0.681931\pi$
$774$	9721.23	0.451450
$775$	7392.48	0.342640
$776$	11430.4	0.528771
$777$	85.7342	0.00395843
$778$	16400.8	0.755781
$779$	9980.57	0.459039
$780$	−499.960	−0.0229506
$781$	−30044.8	−1.37655
$782$	78.4458	0.00358723
$783$	−1824.26	−0.0832617
$784$	−7.41767	−0.000337904 0
$785$	−1279.83	−0.0581900
$786$	207.075	0.00939712
$787$	−29782.8	−1.34897	−0.674486	−	0.738288i	$-0.735635\pi$
$787$	−29782.8	−1.34897	−0.674486	+	0.738288i	$0.735635\pi$
$788$	11321.0	0.511796
$789$	−3344.88	−0.150926
$790$	6417.07	0.288999
$791$	7278.86	0.327189
$792$	10219.3	0.458495
$793$	35975.3	1.61100
$794$	−15685.4	−0.701073
$795$	1086.47	0.0484696
$796$	−4650.98	−0.207097
$797$	35307.2	1.56919	0.784596	−	0.620008i	$-0.212871\pi$
$797$	35307.2	1.56919	0.784596	+	0.620008i	$0.212871\pi$
$798$	467.787	0.0207512
$799$	766.029	0.0339176
$800$	−800.000	−0.0353553
$801$	−29926.6	−1.32011
$802$	29068.4	1.27985
$803$	21052.0	0.925165
$804$	217.917	0.00955887
$805$	−2128.39	−0.0931874
$806$	−25058.5	−1.09510
$807$	3563.54	0.155443
$808$	12097.2	0.526706
$809$	7752.46	0.336912	0.168456	−	0.985709i	$-0.446122\pi$
$809$	7752.46	0.336912	0.168456	+	0.985709i	$0.446122\pi$
$810$	7009.28	0.304051
$811$	23471.6	1.01627	0.508137	−	0.861276i	$-0.330334\pi$
$811$	23471.6	1.01627	0.508137	+	0.861276i	$0.330334\pi$
$812$	−4266.64	−0.184396
$813$	−4070.35	−0.175589
$814$	752.671	0.0324092
$815$	−1608.16	−0.0691184
$816$	16.0976	0.000690600 0
$817$	3906.59	0.167288
$818$	−26776.0	−1.14450
$819$	20900.6	0.891727
$820$	−9318.59	−0.396853
$821$	2467.55	0.104894	0.0524470	−	0.998624i	$-0.483298\pi$
$821$	2467.55	0.104894	0.0524470	+	0.998624i	$0.483298\pi$
$822$	−561.530	−0.0238268
$823$	21984.5	0.931144	0.465572	−	0.885010i	$-0.345849\pi$
$823$	21984.5	0.931144	0.465572	+	0.885010i	$0.345849\pi$
$824$	−7658.23	−0.323771
$825$	706.925	0.0298327
$826$	−13956.0	−0.587883
$827$	−587.293	−0.0246943	−0.0123472	−	0.999924i	$-0.503930\pi$
$827$	−587.293	−0.0246943	−0.0123472	+	0.999924i	$0.503930\pi$
$828$	2451.98	0.102913
$829$	41822.8	1.75219	0.876096	−	0.482137i	$-0.160139\pi$
$829$	41822.8	1.75219	0.876096	+	0.482137i	$0.160139\pi$
$830$	−6099.32	−0.255073
$831$	3314.26	0.138352
$832$	2711.79	0.112998
$833$	−0.790605	−3.28846e−5 0
$834$	−180.728	−0.00750371
$835$	14631.1	0.606383
$836$	4106.76	0.169898
$837$	−9359.77	−0.386524
$838$	6206.20	0.255835
$839$	−10126.5	−0.416693	−0.208346	−	0.978055i	$-0.566808\pi$
$839$	−10126.5	−0.416693	−0.208346	+	0.978055i	$0.566808\pi$
$840$	−436.760	−0.0179401
$841$	−21067.4	−0.863808
$842$	12151.6	0.497356
$843$	1811.14	0.0739964
$844$	5598.33	0.228320
$845$	2008.20	0.0817564
$846$	23943.7	0.973052
$847$	−17883.0	−0.725463
$848$	−5893.05	−0.238642
$849$	828.822	0.0335043
$850$	−85.2672	−0.00344075
$851$	180.592	0.00727453
$852$	−1479.30	−0.0594835
$853$	11584.4	0.464995	0.232498	−	0.972597i	$-0.425310\pi$
$853$	11584.4	0.464995	0.232498	+	0.972597i	$0.425310\pi$
$854$	31427.7	1.25929
$855$	2854.53	0.114179
$856$	13937.3	0.556502
$857$	−9221.47	−0.367561	−0.183780	−	0.982967i	$-0.558834\pi$
$857$	−9221.47	−0.367561	−0.183780	+	0.982967i	$0.558834\pi$
$858$	−2396.29	−0.0953472
$859$	34654.2	1.37647	0.688235	−	0.725488i	$-0.258386\pi$
$859$	34654.2	1.37647	0.688235	+	0.725488i	$0.258386\pi$
$860$	−3647.47	−0.144625
$861$	−5087.48	−0.201372
$862$	−28240.7	−1.11587
$863$	42887.7	1.69167	0.845837	−	0.533441i	$-0.179101\pi$
$863$	42887.7	1.69167	0.845837	+	0.533441i	$0.179101\pi$
$864$	1012.90	0.0398836
$865$	−9059.22	−0.356096
$866$	−17111.9	−0.671463
$867$	−2896.80	−0.113472
$868$	−21890.9	−0.856020
$869$	30756.7	1.20063
$870$	340.018	0.0132502
$871$	3912.70	0.152212
$872$	−9334.17	−0.362494
$873$	38080.2	1.47631
$874$	985.356	0.0381352
$875$	2313.47	0.0893823
$876$	1036.52	0.0399781
$877$	45935.5	1.76868	0.884339	−	0.466846i	$-0.154610\pi$
$877$	45935.5	1.76868	0.884339	+	0.466846i	$0.154610\pi$
$878$	21788.2	0.837488
$879$	−1420.08	−0.0544917
$880$	−3834.37	−0.146882
$881$	−71.9309	−0.00275075	−0.00137538	−	0.999999i	$-0.500438\pi$
$881$	−71.9309	−0.00275075	−0.00137538	+	0.999999i	$0.500438\pi$
$882$	−24.7119	−0.000943417 0
$883$	20003.8	0.762379	0.381189	−	0.924497i	$-0.375515\pi$
$883$	20003.8	0.762379	0.381189	+	0.924497i	$0.375515\pi$
$884$	289.033	0.0109969
$885$	1112.19	0.0422437
$886$	−32241.0	−1.22253
$887$	26357.3	0.997737	0.498869	−	0.866678i	$-0.333749\pi$
$887$	26357.3	0.997737	0.498869	+	0.866678i	$0.333749\pi$
$888$	37.0588	0.00140046
$889$	19763.9	0.745623
$890$	11228.7	0.422906
$891$	33595.2	1.26317
$892$	17031.9	0.639317
$893$	9622.06	0.360571
$894$	−598.118	−0.0223759
$895$	−4563.32	−0.170430
$896$	2368.99	0.0883286
$897$	−574.954	−0.0214015
$898$	−9622.57	−0.357583
$899$	17042.1	0.632242
$900$	−2665.19	−0.0987109
$901$	−628.105	−0.0232244
$902$	−44663.6	−1.64871
$903$	−1991.34	−0.0733860
$904$	3146.30	0.115757
$905$	−18352.7	−0.674106
$906$	−2876.50	−0.105481
$907$	−39300.4	−1.43875	−0.719377	−	0.694620i	$-0.755572\pi$
$907$	−39300.4	−1.43875	−0.719377	+	0.694620i	$0.755572\pi$
$908$	−16100.1	−0.588438
$909$	40301.8	1.47055
$910$	−7842.04	−0.285672
$911$	31099.2	1.13103	0.565513	−	0.824740i	$-0.308678\pi$
$911$	31099.2	1.13103	0.565513	+	0.824740i	$0.308678\pi$
$912$	202.202	0.00734163
$913$	−29233.8	−1.05969
$914$	452.657	0.0163814
$915$	−2504.54	−0.0904893
$916$	14492.2	0.522745
$917$	3248.05	0.116968
$918$	107.959	0.00388144
$919$	18935.8	0.679690	0.339845	−	0.940481i	$-0.389625\pi$
$919$	18935.8	0.679690	0.339845	+	0.940481i	$0.389625\pi$
$920$	−920.000	−0.0329690
$921$	−271.235	−0.00970411
$922$	8698.33	0.310699
$923$	−26560.9	−0.947195
$924$	−2093.37	−0.0745313
$925$	−196.296	−0.00697748
$926$	1978.63	0.0702178
$927$	−25513.3	−0.903957
$928$	−1844.26	−0.0652380
$929$	40156.1	1.41817	0.709085	−	0.705123i	$-0.249108\pi$
$929$	40156.1	1.41817	0.709085	+	0.705123i	$0.249108\pi$
$930$	1744.53	0.0615113
$931$	−9.93077	−0.000349590 0
$932$	26011.2	0.914192
$933$	2430.37	0.0852804
$934$	−17025.8	−0.596469
$935$	−408.682	−0.0142945
$936$	9034.30	0.315486
$937$	126.898	0.00442432	0.00221216	−	0.999998i	$-0.499296\pi$
$937$	126.898	0.00442432	0.00221216	+	0.999998i	$0.499296\pi$
$938$	3418.10	0.118982
$939$	993.594	0.0345311
$940$	−8983.86	−0.311725
$941$	−19266.6	−0.667452	−0.333726	−	0.942670i	$-0.608306\pi$
$941$	−19266.6	−0.667452	−0.333726	+	0.942670i	$0.608306\pi$
$942$	−302.025	−0.0104464
$943$	−10716.4	−0.370067
$944$	−6032.51	−0.207989
$945$	−2929.13	−0.100830
$946$	−17482.2	−0.600840
$947$	−54560.4	−1.87220	−0.936101	−	0.351732i	$-0.885593\pi$
$947$	−54560.4	−1.87220	−0.936101	+	0.351732i	$0.885593\pi$
$948$	1514.35	0.0518816
$949$	18610.8	0.636598
$950$	−1071.04	−0.0365780
$951$	5124.75	0.174744
$952$	252.497	0.00859607
$953$	−44976.2	−1.52877	−0.764387	−	0.644758i	$-0.776958\pi$
$953$	−44976.2	−1.52877	−0.764387	+	0.644758i	$0.776958\pi$
$954$	−19632.7	−0.666279
$955$	9204.79	0.311895
$956$	−10760.3	−0.364030
$957$	1629.69	0.0550476
$958$	24117.1	0.813350
$959$	−8807.79	−0.296578
$960$	−188.790	−0.00634706
$961$	57647.0	1.93505
$962$	665.391	0.0223005
$963$	46431.9	1.55374
$964$	−178.783	−0.00597326
$965$	3059.08	0.102047
$966$	−502.274	−0.0167292
$967$	−39431.7	−1.31131	−0.655656	−	0.755059i	$-0.727608\pi$
$967$	−39431.7	−1.31131	−0.655656	+	0.755059i	$0.727608\pi$
$968$	−7729.96	−0.256664
$969$	21.5515	0.000714482 0
$970$	−14288.0	−0.472947
$971$	20249.9	0.669258	0.334629	−	0.942350i	$-0.391389\pi$
$971$	20249.9	0.669258	0.334629	+	0.942350i	$0.391389\pi$
$972$	5072.63	0.167392
$973$	−2834.78	−0.0934006
$974$	−23210.6	−0.763567
$975$	624.950	0.0205276
$976$	13584.7	0.445527
$977$	−9673.55	−0.316770	−0.158385	−	0.987377i	$-0.550629\pi$
$977$	−9673.55	−0.316770	−0.158385	+	0.987377i	$0.550629\pi$
$978$	−379.507	−0.0124083
$979$	53818.6	1.75695
$980$	9.27209	0.000302231 0
$981$	−31096.7	−1.01207
$982$	9303.77	0.302337
$983$	−17264.3	−0.560168	−0.280084	−	0.959975i	$-0.590362\pi$
$983$	−17264.3	−0.560168	−0.280084	+	0.959975i	$0.590362\pi$
$984$	−2199.07	−0.0712438
$985$	−14151.3	−0.457764
$986$	−196.569	−0.00634891
$987$	−4904.74	−0.158176
$988$	3630.54	0.116906
$989$	−4194.60	−0.134864
$990$	−12774.2	−0.410090
$991$	23892.9	0.765876	0.382938	−	0.923774i	$-0.374912\pi$
$991$	23892.9	0.765876	0.382938	+	0.923774i	$0.374912\pi$
$992$	−9462.37	−0.302854
$993$	2541.53	0.0812217
$994$	−23203.3	−0.740406
$995$	5813.72	0.185234
$996$	−1439.36	−0.0457912
$997$	−35830.2	−1.13817	−0.569083	−	0.822280i	$-0.692702\pi$
$997$	−35830.2	−1.13817	−0.569083	+	0.822280i	$0.692702\pi$
$998$	15906.1	0.504507
$999$	248.534	0.00787115

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.h.1.3	✓	4	1.1	even	1	trivial
1150.4.a.p.1.2		4	5.4	even	2
1150.4.b.n.599.2		8	5.2	odd	4
1150.4.b.n.599.7		8	5.3	odd	4
1840.4.a.m.1.2		4	4.3	odd	2
2070.4.a.bj.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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +0.589969 q^{3} +4.00000 q^{4} -5.00000 q^{5} -1.17994 q^{6} -18.5077 q^{7} -8.00000 q^{8} -26.6519 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +0.589969 q^{3} +4.00000 q^{4} -5.00000 q^{5} -1.17994 q^{6} -18.5077 q^{7} -8.00000 q^{8} -26.6519 q^{9} +10.0000 q^{10} +47.9296 q^{11} +2.35988 q^{12} +42.3717 q^{13} +37.0155 q^{14} -2.94985 q^{15} +16.0000 q^{16} +1.70534 q^{17} +53.3039 q^{18} +21.4208 q^{19} -20.0000 q^{20} -10.9190 q^{21} -95.8592 q^{22} -23.0000 q^{23} -4.71976 q^{24} +25.0000 q^{25} -84.7434 q^{26} -31.6530 q^{27} -74.0310 q^{28} +57.6332 q^{29} +5.89969 q^{30} +295.699 q^{31} -32.0000 q^{32} +28.2770 q^{33} -3.41069 q^{34} +92.5387 q^{35} -106.608 q^{36} -7.85184 q^{37} -42.8416 q^{38} +24.9980 q^{39} +40.0000 q^{40} +465.929 q^{41} +21.8380 q^{42} +182.374 q^{43} +191.718 q^{44} +133.260 q^{45} +46.0000 q^{46} +449.193 q^{47} +9.43951 q^{48} -0.463605 q^{49} -50.0000 q^{50} +1.00610 q^{51} +169.487 q^{52} -368.316 q^{53} +63.3060 q^{54} -239.648 q^{55} +148.062 q^{56} +12.6376 q^{57} -115.266 q^{58} -377.032 q^{59} -11.7994 q^{60} +849.042 q^{61} -591.398 q^{62} +493.267 q^{63} +64.0000 q^{64} -211.858 q^{65} -56.5540 q^{66} +92.3424 q^{67} +6.82138 q^{68} -13.5693 q^{69} -185.077 q^{70} -626.854 q^{71} +213.215 q^{72} +439.227 q^{73} +15.7037 q^{74} +14.7492 q^{75} +85.6831 q^{76} -887.068 q^{77} -49.9960 q^{78} +641.707 q^{79} -80.0000 q^{80} +700.928 q^{81} -931.859 q^{82} -609.932 q^{83} -43.6760 q^{84} -8.52672 q^{85} -364.747 q^{86} +34.0018 q^{87} -383.437 q^{88} +1122.87 q^{89} -266.519 q^{90} -784.204 q^{91} -92.0000 q^{92} +174.453 q^{93} -898.386 q^{94} -107.104 q^{95} -18.8790 q^{96} -1428.80 q^{97} +0.927209 q^{98} -1277.42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} - 4 q^{3} + 16 q^{4} - 20 q^{5} + 8 q^{6} - q^{7} - 32 q^{8} + 32 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 - 4 * q^3 + 16 * q^4 - 20 * q^5 + 8 * q^6 - q^7 - 32 * q^8 + 32 * q^9	\( 4 q - 8 q^{2} - 4 q^{3} + 16 q^{4} - 20 q^{5} + 8 q^{6} - q^{7} - 32 q^{8} + 32 q^{9} + 40 q^{10} - 39 q^{11} - 16 q^{12} - 20 q^{13} + 2 q^{14} + 20 q^{15} + 64 q^{16} - 23 q^{17} - 64 q^{18} + 53 q^{19} - 80 q^{20} + 300 q^{21} + 78 q^{22} - 92 q^{23} + 32 q^{24} + 100 q^{25} + 40 q^{26} + 137 q^{27} - 4 q^{28} + 161 q^{29} - 40 q^{30} + 388 q^{31} - 128 q^{32} + 87 q^{33} + 46 q^{34} + 5 q^{35} + 128 q^{36} + 466 q^{37} - 106 q^{38} + 1047 q^{39} + 160 q^{40} + 484 q^{41} - 600 q^{42} + 894 q^{43} - 156 q^{44} - 160 q^{45} + 184 q^{46} - 265 q^{47} - 64 q^{48} + 1643 q^{49} - 200 q^{50} + 1825 q^{51} - 80 q^{52} + 576 q^{53} - 274 q^{54} + 195 q^{55} + 8 q^{56} + 178 q^{57} - 322 q^{58} - 94 q^{59} + 80 q^{60} + 1153 q^{61} - 776 q^{62} + 60 q^{63} + 256 q^{64} + 100 q^{65} - 174 q^{66} - 1472 q^{67} - 92 q^{68} + 92 q^{69} - 10 q^{70} + 200 q^{71} - 256 q^{72} + 1147 q^{73} - 932 q^{74} - 100 q^{75} + 212 q^{76} - 2176 q^{77} - 2094 q^{78} - 908 q^{79} - 320 q^{80} - 1056 q^{81} - 968 q^{82} - 1048 q^{83} + 1200 q^{84} + 115 q^{85} - 1788 q^{86} - 2167 q^{87} + 312 q^{88} - 1784 q^{89} + 320 q^{90} + 2329 q^{91} - 368 q^{92} + 1483 q^{93} + 530 q^{94} - 265 q^{95} + 128 q^{96} - 2047 q^{97} - 3286 q^{98} - 2665 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 4 * q^3 + 16 * q^4 - 20 * q^5 + 8 * q^6 - q^7 - 32 * q^8 + 32 * q^9 + 40 * q^10 - 39 * q^11 - 16 * q^12 - 20 * q^13 + 2 * q^14 + 20 * q^15 + 64 * q^16 - 23 * q^17 - 64 * q^18 + 53 * q^19 - 80 * q^20 + 300 * q^21 + 78 * q^22 - 92 * q^23 + 32 * q^24 + 100 * q^25 + 40 * q^26 + 137 * q^27 - 4 * q^28 + 161 * q^29 - 40 * q^30 + 388 * q^31 - 128 * q^32 + 87 * q^33 + 46 * q^34 + 5 * q^35 + 128 * q^36 + 466 * q^37 - 106 * q^38 + 1047 * q^39 + 160 * q^40 + 484 * q^41 - 600 * q^42 + 894 * q^43 - 156 * q^44 - 160 * q^45 + 184 * q^46 - 265 * q^47 - 64 * q^48 + 1643 * q^49 - 200 * q^50 + 1825 * q^51 - 80 * q^52 + 576 * q^53 - 274 * q^54 + 195 * q^55 + 8 * q^56 + 178 * q^57 - 322 * q^58 - 94 * q^59 + 80 * q^60 + 1153 * q^61 - 776 * q^62 + 60 * q^63 + 256 * q^64 + 100 * q^65 - 174 * q^66 - 1472 * q^67 - 92 * q^68 + 92 * q^69 - 10 * q^70 + 200 * q^71 - 256 * q^72 + 1147 * q^73 - 932 * q^74 - 100 * q^75 + 212 * q^76 - 2176 * q^77 - 2094 * q^78 - 908 * q^79 - 320 * q^80 - 1056 * q^81 - 968 * q^82 - 1048 * q^83 + 1200 * q^84 + 115 * q^85 - 1788 * q^86 - 2167 * q^87 + 312 * q^88 - 1784 * q^89 + 320 * q^90 + 2329 * q^91 - 368 * q^92 + 1483 * q^93 + 530 * q^94 - 265 * q^95 + 128 * q^96 - 2047 * q^97 - 3286 * q^98 - 2665 * q^99

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