LMFDB - Embedded newform 230.4.a.h.1.4

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			1.4
Root			$8.73081$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} +7.73081 q^{3} +4.00000 q^{4} -5.00000 q^{5} -15.4616 q^{6} +23.5622 q^{7} -8.00000 q^{8} +32.7654 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +7.73081 q^{3} +4.00000 q^{4} -5.00000 q^{5} -15.4616 q^{6} +23.5622 q^{7} -8.00000 q^{8} +32.7654 q^{9} +10.0000 q^{10} -32.1352 q^{11} +30.9232 q^{12} +40.0811 q^{13} -47.1245 q^{14} -38.6540 q^{15} +16.0000 q^{16} +126.165 q^{17} -65.5308 q^{18} +0.232742 q^{19} -20.0000 q^{20} +182.155 q^{21} +64.2704 q^{22} -23.0000 q^{23} -61.8465 q^{24} +25.0000 q^{25} -80.1621 q^{26} +44.5711 q^{27} +94.2490 q^{28} -137.226 q^{29} +77.3081 q^{30} +112.866 q^{31} -32.0000 q^{32} -248.431 q^{33} -252.331 q^{34} -117.811 q^{35} +131.062 q^{36} +45.7057 q^{37} -0.465483 q^{38} +309.859 q^{39} +40.0000 q^{40} -135.385 q^{41} -364.310 q^{42} +543.528 q^{43} -128.541 q^{44} -163.827 q^{45} +46.0000 q^{46} +26.4344 q^{47} +123.693 q^{48} +212.180 q^{49} -50.0000 q^{50} +975.359 q^{51} +160.324 q^{52} +43.6958 q^{53} -89.1422 q^{54} +160.676 q^{55} -188.498 q^{56} +1.79928 q^{57} +274.451 q^{58} +202.248 q^{59} -154.616 q^{60} +150.279 q^{61} -225.732 q^{62} +772.026 q^{63} +64.0000 q^{64} -200.405 q^{65} +496.862 q^{66} -420.722 q^{67} +504.661 q^{68} -177.809 q^{69} +235.622 q^{70} +667.381 q^{71} -262.123 q^{72} +602.960 q^{73} -91.4115 q^{74} +193.270 q^{75} +0.930966 q^{76} -757.178 q^{77} -619.718 q^{78} -1378.88 q^{79} -80.0000 q^{80} -540.095 q^{81} +270.769 q^{82} -485.178 q^{83} +728.621 q^{84} -630.826 q^{85} -1087.06 q^{86} -1060.86 q^{87} +257.082 q^{88} -1127.71 q^{89} +327.654 q^{90} +944.400 q^{91} -92.0000 q^{92} +872.545 q^{93} -52.8688 q^{94} -1.16371 q^{95} -247.386 q^{96} -1486.24 q^{97} -424.359 q^{98} -1052.92 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	7.73081	1.48779	0.743897	−	0.668294i	$-0.232975\pi$
$3$	7.73081	1.48779	0.743897	+	0.668294i	$0.232975\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−15.4616	−1.05203
$7$	23.5622	1.27224	0.636121	−	0.771589i	$-0.280538\pi$
$7$	23.5622	1.27224	0.636121	+	0.771589i	$0.280538\pi$
$8$	−8.00000	−0.353553
$9$	32.7654	1.21353
$10$	10.0000	0.316228
$11$	−32.1352	−0.880830	−0.440415	−	0.897794i	$-0.645169\pi$
$11$	−32.1352	−0.880830	−0.440415	+	0.897794i	$0.645169\pi$
$12$	30.9232	0.743897
$13$	40.0811	0.855115	0.427557	−	0.903988i	$-0.359374\pi$
$13$	40.0811	0.855115	0.427557	+	0.903988i	$0.359374\pi$
$14$	−47.1245	−0.899611
$15$	−38.6540	−0.665362
$16$	16.0000	0.250000
$17$	126.165	1.79997	0.899987	−	0.435916i	$-0.143576\pi$
$17$	126.165	1.79997	0.899987	+	0.435916i	$0.143576\pi$
$18$	−65.5308	−0.858097
$19$	0.232742	0.00281024	0.00140512	−	0.999999i	$-0.499553\pi$
$19$	0.232742	0.00281024	0.00140512	+	0.999999i	$0.499553\pi$
$20$	−20.0000	−0.223607
$21$	182.155	1.89283
$22$	64.2704	0.622841
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−61.8465	−0.526015
$25$	25.0000	0.200000
$26$	−80.1621	−0.604657
$27$	44.5711	0.317693
$28$	94.2490	0.636121
$29$	−137.226	−0.878695	−0.439347	−	0.898317i	$-0.644790\pi$
$29$	−137.226	−0.878695	−0.439347	+	0.898317i	$0.644790\pi$
$30$	77.3081	0.470482
$31$	112.866	0.653914	0.326957	−	0.945039i	$-0.393977\pi$
$31$	112.866	0.653914	0.326957	+	0.945039i	$0.393977\pi$
$32$	−32.0000	−0.176777
$33$	−248.431	−1.31049
$34$	−252.331	−1.27277
$35$	−117.811	−0.568964
$36$	131.062	0.606766
$37$	45.7057	0.203080	0.101540	−	0.994831i	$-0.467623\pi$
$37$	45.7057	0.203080	0.101540	+	0.994831i	$0.467623\pi$
$38$	−0.465483	−0.00198714
$39$	309.859	1.27223
$40$	40.0000	0.158114
$41$	−135.385	−0.515696	−0.257848	−	0.966186i	$-0.583013\pi$
$41$	−135.385	−0.515696	−0.257848	+	0.966186i	$0.583013\pi$
$42$	−364.310	−1.33844
$43$	543.528	1.92761	0.963805	−	0.266608i	$-0.0859030\pi$
$43$	543.528	1.92761	0.963805	+	0.266608i	$0.0859030\pi$
$44$	−128.541	−0.440415
$45$	−163.827	−0.542708
$46$	46.0000	0.147442
$47$	26.4344	0.0820394	0.0410197	−	0.999158i	$-0.486939\pi$
$47$	26.4344	0.0820394	0.0410197	+	0.999158i	$0.486939\pi$
$48$	123.693	0.371949
$49$	212.180	0.618599
$50$	−50.0000	−0.141421
$51$	975.359	2.67799
$52$	160.324	0.427557
$53$	43.6958	0.113247	0.0566235	−	0.998396i	$-0.481967\pi$
$53$	43.6958	0.113247	0.0566235	+	0.998396i	$0.481967\pi$
$54$	−89.1422	−0.224643
$55$	160.676	0.393919
$56$	−188.498	−0.449805
$57$	1.79928	0.00418106
$58$	274.451	0.621331
$59$	202.248	0.446278	0.223139	−	0.974787i	$-0.428370\pi$
$59$	202.248	0.446278	0.223139	+	0.974787i	$0.428370\pi$
$60$	−154.616	−0.332681
$61$	150.279	0.315430	0.157715	−	0.987485i	$-0.449587\pi$
$61$	150.279	0.315430	0.157715	+	0.987485i	$0.449587\pi$
$62$	−225.732	−0.462387
$63$	772.026	1.54391
$64$	64.0000	0.125000
$65$	−200.405	−0.382419
$66$	496.862	0.926659
$67$	−420.722	−0.767155	−0.383577	−	0.923509i	$-0.625308\pi$
$67$	−420.722	−0.767155	−0.383577	+	0.923509i	$0.625308\pi$
$68$	504.661	0.899987
$69$	−177.809	−0.310227
$70$	235.622	0.402318
$71$	667.381	1.11554	0.557771	−	0.829995i	$-0.311657\pi$
$71$	667.381	1.11554	0.557771	+	0.829995i	$0.311657\pi$
$72$	−262.123	−0.429049
$73$	602.960	0.966728	0.483364	−	0.875420i	$-0.339415\pi$
$73$	602.960	0.966728	0.483364	+	0.875420i	$0.339415\pi$
$74$	−91.4115	−0.143600
$75$	193.270	0.297559
$76$	0.930966	0.00140512
$77$	−757.178	−1.12063
$78$	−619.718	−0.899606
$79$	−1378.88	−1.96374	−0.981872	−	0.189545i	$-0.939299\pi$
$79$	−1378.88	−1.96374	−0.981872	+	0.189545i	$0.939299\pi$
$80$	−80.0000	−0.111803
$81$	−540.095	−0.740871
$82$	270.769	0.364652
$83$	−485.178	−0.641629	−0.320815	−	0.947142i	$-0.603957\pi$
$83$	−485.178	−0.641629	−0.320815	+	0.947142i	$0.603957\pi$
$84$	728.621	0.946417
$85$	−630.826	−0.804973
$86$	−1087.06	−1.36303
$87$	−1060.86	−1.30732
$88$	257.082	0.311420
$89$	−1127.71	−1.34311	−0.671556	−	0.740954i	$-0.734374\pi$
$89$	−1127.71	−1.34311	−0.671556	+	0.740954i	$0.734374\pi$
$90$	327.654	0.383753
$91$	944.400	1.08791
$92$	−92.0000	−0.104257
$93$	872.545	0.972890
$94$	−52.8688	−0.0580106
$95$	−1.16371	−0.00125678
$96$	−247.386	−0.263007
$97$	−1486.24	−1.55572	−0.777858	−	0.628441i	$-0.783694\pi$
$97$	−1486.24	−1.55572	−0.777858	+	0.628441i	$0.783694\pi$
$98$	−424.359	−0.437416
$99$	−1052.92	−1.06892
$100$	100.000	0.100000
$101$	1888.86	1.86087	0.930437	−	0.366451i	$-0.119427\pi$
$101$	1888.86	1.86087	0.930437	+	0.366451i	$0.119427\pi$
$102$	−1950.72	−1.89363
$103$	−1497.17	−1.43224	−0.716118	−	0.697979i	$-0.754083\pi$
$103$	−1497.17	−1.43224	−0.716118	+	0.697979i	$0.754083\pi$
$104$	−320.649	−0.302329
$105$	−910.776	−0.846501
$106$	−87.3917	−0.0800777
$107$	−585.150	−0.528678	−0.264339	−	0.964430i	$-0.585154\pi$
$107$	−585.150	−0.528678	−0.264339	+	0.964430i	$0.585154\pi$
$108$	178.284	0.158846
$109$	−139.166	−0.122290	−0.0611452	−	0.998129i	$-0.519475\pi$
$109$	−139.166	−0.122290	−0.0611452	+	0.998129i	$0.519475\pi$
$110$	−321.352	−0.278543
$111$	353.342	0.302142
$112$	376.996	0.318060
$113$	−1293.18	−1.07656	−0.538282	−	0.842765i	$-0.680927\pi$
$113$	−1293.18	−1.07656	−0.538282	+	0.842765i	$0.680927\pi$
$114$	−3.59856	−0.00295646
$115$	115.000	0.0932505
$116$	−548.902	−0.439347
$117$	1313.27	1.03771
$118$	−404.495	−0.315566
$119$	2972.74	2.29000
$120$	309.232	0.235241
$121$	−298.328	−0.224138
$122$	−300.557	−0.223043
$123$	−1046.63	−0.767250
$124$	451.464	0.326957
$125$	−125.000	−0.0894427
$126$	−1544.05	−1.09171
$127$	−1298.43	−0.907221	−0.453610	−	0.891200i	$-0.649864\pi$
$127$	−1298.43	−0.907221	−0.453610	+	0.891200i	$0.649864\pi$
$128$	−128.000	−0.0883883
$129$	4201.91	2.86789
$130$	400.811	0.270411
$131$	−525.247	−0.350313	−0.175157	−	0.984541i	$-0.556043\pi$
$131$	−525.247	−0.350313	−0.175157	+	0.984541i	$0.556043\pi$
$132$	−993.725	−0.655247
$133$	5.48392	0.00357531
$134$	841.444	0.542460
$135$	−222.855	−0.142077
$136$	−1009.32	−0.636387
$137$	−2428.12	−1.51422	−0.757109	−	0.653288i	$-0.773389\pi$
$137$	−2428.12	−1.51422	−0.757109	+	0.653288i	$0.773389\pi$
$138$	355.617	0.219363
$139$	2456.46	1.49895	0.749476	−	0.662031i	$-0.230305\pi$
$139$	2456.46	1.49895	0.749476	+	0.662031i	$0.230305\pi$
$140$	−471.245	−0.284482
$141$	204.359	0.122058
$142$	−1334.76	−0.788808
$143$	−1288.01	−0.753211
$144$	524.246	0.303383
$145$	686.128	0.392964
$146$	−1205.92	−0.683580
$147$	1640.32	0.920349
$148$	182.823	0.101540
$149$	−2405.39	−1.32253	−0.661266	−	0.750151i	$-0.729981\pi$
$149$	−2405.39	−1.32253	−0.661266	+	0.750151i	$0.729981\pi$
$150$	−386.540	−0.210406
$151$	−649.276	−0.349916	−0.174958	−	0.984576i	$-0.555979\pi$
$151$	−649.276	−0.349916	−0.174958	+	0.984576i	$0.555979\pi$
$152$	−1.86193	−0.000993570 0
$153$	4133.85	2.18433
$154$	1514.36	0.792404
$155$	−564.330	−0.292439
$156$	1239.44	0.636117
$157$	3665.04	1.86307	0.931536	−	0.363650i	$-0.118470\pi$
$157$	3665.04	1.86307	0.931536	+	0.363650i	$0.118470\pi$
$158$	2757.75	1.38858
$159$	337.804	0.168488
$160$	160.000	0.0790569
$161$	−541.932	−0.265281
$162$	1080.19	0.523875
$163$	−1055.27	−0.507088	−0.253544	−	0.967324i	$-0.581596\pi$
$163$	−1055.27	−0.507088	−0.253544	+	0.967324i	$0.581596\pi$
$164$	−541.539	−0.257848
$165$	1242.16	0.586071
$166$	970.356	0.453700
$167$	−731.805	−0.339095	−0.169547	−	0.985522i	$-0.554231\pi$
$167$	−731.805	−0.339095	−0.169547	+	0.985522i	$0.554231\pi$
$168$	−1457.24	−0.669218
$169$	−590.507	−0.268779
$170$	1261.65	0.569202
$171$	7.62587	0.00341032
$172$	2174.11	0.963805
$173$	−521.773	−0.229304	−0.114652	−	0.993406i	$-0.536575\pi$
$173$	−521.773	−0.229304	−0.114652	+	0.993406i	$0.536575\pi$
$174$	2121.73	0.924413
$175$	589.056	0.254448
$176$	−514.163	−0.220208
$177$	1563.54	0.663970
$178$	2255.42	0.949723
$179$	−1183.07	−0.494005	−0.247002	−	0.969015i	$-0.579446\pi$
$179$	−1183.07	−0.494005	−0.247002	+	0.969015i	$0.579446\pi$
$180$	−655.308	−0.271354
$181$	1723.92	0.707946	0.353973	−	0.935256i	$-0.384830\pi$
$181$	1723.92	0.707946	0.353973	+	0.935256i	$0.384830\pi$
$182$	−1888.80	−0.769270
$183$	1161.78	0.469295
$184$	184.000	0.0737210
$185$	−228.529	−0.0908204
$186$	−1745.09	−0.687937
$187$	−4054.35	−1.58547
$188$	105.738	0.0410197
$189$	1050.20	0.404182
$190$	2.32742	0.000888676 0
$191$	−2798.12	−1.06002	−0.530012	−	0.847990i	$-0.677813\pi$
$191$	−2798.12	−1.06002	−0.530012	+	0.847990i	$0.677813\pi$
$192$	494.772	0.185974
$193$	−497.686	−0.185618	−0.0928089	−	0.995684i	$-0.529585\pi$
$193$	−497.686	−0.185618	−0.0928089	+	0.995684i	$0.529585\pi$
$194$	2972.47	1.10006
$195$	−1549.30	−0.568961
$196$	848.718	0.309300
$197$	296.489	0.107228	0.0536141	−	0.998562i	$-0.482926\pi$
$197$	296.489	0.107228	0.0536141	+	0.998562i	$0.482926\pi$
$198$	2105.85	0.755838
$199$	2347.43	0.836207	0.418103	−	0.908399i	$-0.362695\pi$
$199$	2347.43	0.836207	0.418103	+	0.908399i	$0.362695\pi$
$200$	−200.000	−0.0707107
$201$	−3252.52	−1.14137
$202$	−3777.71	−1.31584
$203$	−3233.34	−1.11791
$204$	3901.44	1.33900
$205$	676.923	0.230626
$206$	2994.34	1.01274
$207$	−753.604	−0.253039
$208$	641.297	0.213779
$209$	−7.47920	−0.00247535
$210$	1821.55	0.598567
$211$	2838.61	0.926153	0.463076	−	0.886318i	$-0.346746\pi$
$211$	2838.61	0.926153	0.463076	+	0.886318i	$0.346746\pi$
$212$	174.783	0.0566235
$213$	5159.39	1.65970
$214$	1170.30	0.373832
$215$	−2717.64	−0.862053
$216$	−356.569	−0.112321
$217$	2659.38	0.831937
$218$	278.331	0.0864723
$219$	4661.37	1.43829
$220$	642.704	0.196960
$221$	5056.84	1.53918
$222$	−706.685	−0.213647
$223$	−2124.68	−0.638024	−0.319012	−	0.947751i	$-0.603351\pi$
$223$	−2124.68	−0.638024	−0.319012	+	0.947751i	$0.603351\pi$
$224$	−753.992	−0.224903
$225$	819.135	0.242707
$226$	2586.35	0.761246
$227$	1551.97	0.453780	0.226890	−	0.973920i	$-0.427144\pi$
$227$	1551.97	0.453780	0.226890	+	0.973920i	$0.427144\pi$
$228$	7.19712	0.00209053
$229$	−158.531	−0.0457469	−0.0228735	−	0.999738i	$-0.507281\pi$
$229$	−158.531	−0.0457469	−0.0228735	+	0.999738i	$0.507281\pi$
$230$	−230.000	−0.0659380
$231$	−5853.60	−1.66727
$232$	1097.80	0.310666
$233$	−728.999	−0.204971	−0.102486	−	0.994734i	$-0.532680\pi$
$233$	−728.999	−0.204971	−0.102486	+	0.994734i	$0.532680\pi$
$234$	−2626.54	−0.733772
$235$	−132.172	−0.0366891
$236$	808.991	0.223139
$237$	−10659.8	−2.92165
$238$	−5945.47	−1.61928
$239$	−6201.60	−1.67844	−0.839222	−	0.543789i	$-0.816989\pi$
$239$	−6201.60	−1.67844	−0.839222	+	0.543789i	$0.816989\pi$
$240$	−618.465	−0.166340
$241$	−7223.04	−1.93061	−0.965305	−	0.261126i	$-0.915906\pi$
$241$	−7223.04	−1.93061	−0.965305	+	0.261126i	$0.915906\pi$
$242$	596.656	0.158490
$243$	−5378.79	−1.41996
$244$	601.115	0.157715
$245$	−1060.90	−0.276646
$246$	2093.27	0.542527
$247$	9.32853	0.00240308
$248$	−902.928	−0.231193
$249$	−3750.82	−0.954612
$250$	250.000	0.0632456
$251$	5042.78	1.26812	0.634059	−	0.773285i	$-0.281388\pi$
$251$	5042.78	1.26812	0.634059	+	0.773285i	$0.281388\pi$
$252$	3088.10	0.771954
$253$	739.110	0.183666
$254$	2596.86	0.641502
$255$	−4876.80	−1.19763
$256$	256.000	0.0625000
$257$	2981.15	0.723577	0.361788	−	0.932260i	$-0.382166\pi$
$257$	2981.15	0.723577	0.361788	+	0.932260i	$0.382166\pi$
$258$	−8403.82	−2.02790
$259$	1076.93	0.258367
$260$	−801.621	−0.191209
$261$	−4496.25	−1.06632
$262$	1050.49	0.247709
$263$	7242.86	1.69815	0.849076	−	0.528271i	$-0.177159\pi$
$263$	7242.86	1.69815	0.849076	+	0.528271i	$0.177159\pi$
$264$	1987.45	0.463330
$265$	−218.479	−0.0506456
$266$	−10.9678	−0.00252812
$267$	−8718.10	−1.99827
$268$	−1682.89	−0.383577
$269$	−2567.58	−0.581962	−0.290981	−	0.956729i	$-0.593982\pi$
$269$	−2567.58	−0.581962	−0.290981	+	0.956729i	$0.593982\pi$
$270$	445.711	0.100463
$271$	8066.27	1.80808	0.904042	−	0.427443i	$-0.140586\pi$
$271$	8066.27	1.80808	0.904042	+	0.427443i	$0.140586\pi$
$272$	2018.64	0.449994
$273$	7300.98	1.61859
$274$	4856.23	1.07071
$275$	−803.380	−0.176166
$276$	−711.234	−0.155113
$277$	8991.54	1.95036	0.975179	−	0.221418i	$-0.0710684\pi$
$277$	8991.54	1.95036	0.975179	+	0.221418i	$0.0710684\pi$
$278$	−4912.92	−1.05992
$279$	3698.10	0.793546
$280$	942.490	0.201159
$281$	968.130	0.205529	0.102765	−	0.994706i	$-0.467231\pi$
$281$	968.130	0.205529	0.102765	+	0.994706i	$0.467231\pi$
$282$	−408.718	−0.0863079
$283$	−2252.65	−0.473167	−0.236583	−	0.971611i	$-0.576028\pi$
$283$	−2252.65	−0.473167	−0.236583	+	0.971611i	$0.576028\pi$
$284$	2669.52	0.557771
$285$	−8.99640	−0.00186983
$286$	2576.03	0.532600
$287$	−3189.97	−0.656090
$288$	−1048.49	−0.214524
$289$	11004.7	2.23991
$290$	−1372.26	−0.277868
$291$	−11489.8	−2.31458
$292$	2411.84	0.483364
$293$	2734.35	0.545196	0.272598	−	0.962128i	$-0.412117\pi$
$293$	2734.35	0.545196	0.272598	+	0.962128i	$0.412117\pi$
$294$	−3280.64	−0.650785
$295$	−1011.24	−0.199582
$296$	−365.646	−0.0717998
$297$	−1432.30	−0.279834
$298$	4810.78	0.935172
$299$	−921.865	−0.178304
$300$	773.081	0.148779
$301$	12806.7	2.45239
$302$	1298.55	0.247428
$303$	14602.4	2.76860
$304$	3.72387	0.000702560 0
$305$	−751.394	−0.141065
$306$	−8267.71	−1.54455
$307$	−7977.09	−1.48299	−0.741493	−	0.670961i	$-0.765882\pi$
$307$	−7977.09	−1.48299	−0.741493	+	0.670961i	$0.765882\pi$
$308$	−3028.71	−0.560314
$309$	−11574.3	−2.13087
$310$	1128.66	0.206786
$311$	7729.43	1.40931	0.704655	−	0.709550i	$-0.251102\pi$
$311$	7729.43	1.40931	0.704655	+	0.709550i	$0.251102\pi$
$312$	−2478.87	−0.449803
$313$	5506.25	0.994350	0.497175	−	0.867650i	$-0.334371\pi$
$313$	5506.25	0.994350	0.497175	+	0.867650i	$0.334371\pi$
$314$	−7330.08	−1.31739
$315$	−3860.13	−0.690456
$316$	−5515.51	−0.981872
$317$	5231.37	0.926887	0.463443	−	0.886126i	$-0.346614\pi$
$317$	5231.37	0.926887	0.463443	+	0.886126i	$0.346614\pi$
$318$	−675.608	−0.119139
$319$	4409.77	0.773981
$320$	−320.000	−0.0559017
$321$	−4523.68	−0.786565
$322$	1083.86	0.187582
$323$	29.3639	0.00505836
$324$	−2160.38	−0.370435
$325$	1002.03	0.171023
$326$	2110.55	0.358566
$327$	−1075.86	−0.181943
$328$	1083.08	0.182326
$329$	622.854	0.104374
$330$	−2484.31	−0.414415
$331$	−3551.61	−0.589771	−0.294885	−	0.955533i	$-0.595281\pi$
$331$	−3551.61	−0.589771	−0.294885	+	0.955533i	$0.595281\pi$
$332$	−1940.71	−0.320815
$333$	1497.57	0.246445
$334$	1463.61	0.239776
$335$	2103.61	0.343082
$336$	2914.48	0.473209
$337$	−7002.99	−1.13198	−0.565990	−	0.824412i	$-0.691506\pi$
$337$	−7002.99	−1.13198	−0.565990	+	0.824412i	$0.691506\pi$
$338$	1181.01	0.190055
$339$	−9997.29	−1.60171
$340$	−2523.31	−0.402487
$341$	−3626.97	−0.575987
$342$	−15.2517	−0.00241146
$343$	−3082.42	−0.485234
$344$	−4348.22	−0.681513
$345$	889.043	0.138738
$346$	1043.55	0.162143
$347$	−10268.2	−1.58854	−0.794272	−	0.607562i	$-0.792148\pi$
$347$	−10268.2	−1.58854	−0.794272	+	0.607562i	$0.792148\pi$
$348$	−4243.46	−0.653659
$349$	4515.58	0.692588	0.346294	−	0.938126i	$-0.387440\pi$
$349$	4515.58	0.692588	0.346294	+	0.938126i	$0.387440\pi$
$350$	−1178.11	−0.179922
$351$	1786.46	0.271664
$352$	1028.33	0.155710
$353$	7838.63	1.18189	0.590947	−	0.806711i	$-0.298754\pi$
$353$	7838.63	1.18189	0.590947	+	0.806711i	$0.298754\pi$
$354$	−3127.08	−0.469498
$355$	−3336.90	−0.498886
$356$	−4510.84	−0.671556
$357$	22981.7	3.40705
$358$	2366.14	0.349314
$359$	−12464.8	−1.83250	−0.916250	−	0.400606i	$-0.868799\pi$
$359$	−12464.8	−1.83250	−0.916250	+	0.400606i	$0.868799\pi$
$360$	1310.62	0.191876
$361$	−6858.95	−0.999992
$362$	−3447.85	−0.500594
$363$	−2306.32	−0.333472
$364$	3777.60	0.543956
$365$	−3014.80	−0.432334
$366$	−2323.55	−0.331842
$367$	3936.14	0.559850	0.279925	−	0.960022i	$-0.409690\pi$
$367$	3936.14	0.559850	0.279925	+	0.960022i	$0.409690\pi$
$368$	−368.000	−0.0521286
$369$	−4435.93	−0.625814
$370$	457.057	0.0642197
$371$	1029.57	0.144077
$372$	3490.18	0.486445
$373$	1920.72	0.266625	0.133313	−	0.991074i	$-0.457439\pi$
$373$	1920.72	0.266625	0.133313	+	0.991074i	$0.457439\pi$
$374$	8108.69	1.12110
$375$	−966.351	−0.133072
$376$	−211.475	−0.0290053
$377$	−5500.15	−0.751385
$378$	−2100.39	−0.285800
$379$	−13074.5	−1.77201	−0.886004	−	0.463678i	$-0.846530\pi$
$379$	−13074.5	−1.77201	−0.886004	+	0.463678i	$0.846530\pi$
$380$	−4.65483	−0.000628389 0
$381$	−10037.9	−1.34976
$382$	5596.23	0.749550
$383$	8838.22	1.17914	0.589571	−	0.807716i	$-0.299297\pi$
$383$	8838.22	1.17914	0.589571	+	0.807716i	$0.299297\pi$
$384$	−989.543	−0.131504
$385$	3785.89	0.501160
$386$	995.372	0.131252
$387$	17808.9	2.33922
$388$	−5944.94	−0.777858
$389$	−12687.3	−1.65365	−0.826827	−	0.562456i	$-0.809856\pi$
$389$	−12687.3	−1.65365	−0.826827	+	0.562456i	$0.809856\pi$
$390$	3098.59	0.402316
$391$	−2901.80	−0.375321
$392$	−1697.44	−0.218708
$393$	−4060.58	−0.521194
$394$	−592.977	−0.0758218
$395$	6894.38	0.878213
$396$	−4211.69	−0.534458
$397$	8060.49	1.01900	0.509501	−	0.860470i	$-0.329830\pi$
$397$	8060.49	1.01900	0.509501	+	0.860470i	$0.329830\pi$
$398$	−4694.87	−0.591287
$399$	42.3951	0.00531932
$400$	400.000	0.0500000
$401$	12325.1	1.53488	0.767440	−	0.641121i	$-0.221530\pi$
$401$	12325.1	1.53488	0.767440	+	0.641121i	$0.221530\pi$
$402$	6505.04	0.807070
$403$	4523.79	0.559171
$404$	7555.43	0.930437
$405$	2700.47	0.331328
$406$	6466.69	0.790483
$407$	−1468.76	−0.178879
$408$	−7802.87	−0.946813
$409$	−10806.7	−1.30650	−0.653250	−	0.757143i	$-0.726595\pi$
$409$	−10806.7	−1.30650	−0.653250	+	0.757143i	$0.726595\pi$
$410$	−1353.85	−0.163077
$411$	−18771.3	−2.25285
$412$	−5988.67	−0.716118
$413$	4765.41	0.567774
$414$	1507.21	0.178926
$415$	2425.89	0.286945
$416$	−1282.59	−0.151164
$417$	18990.4	2.23013
$418$	14.9584	0.00175033
$419$	−1823.74	−0.212639	−0.106319	−	0.994332i	$-0.533907\pi$
$419$	−1823.74	−0.212639	−0.106319	+	0.994332i	$0.533907\pi$
$420$	−3643.10	−0.423251
$421$	5995.43	0.694060	0.347030	−	0.937854i	$-0.387190\pi$
$421$	5995.43	0.694060	0.347030	+	0.937854i	$0.387190\pi$
$422$	−5677.23	−0.654889
$423$	866.133	0.0995575
$424$	−349.567	−0.0400388
$425$	3154.13	0.359995
$426$	−10318.8	−1.17358
$427$	3540.91	0.401303
$428$	−2340.60	−0.264339
$429$	−9957.39	−1.12062
$430$	5435.28	0.609564
$431$	3887.80	0.434499	0.217249	−	0.976116i	$-0.430292\pi$
$431$	3887.80	0.434499	0.217249	+	0.976116i	$0.430292\pi$
$432$	713.137	0.0794232
$433$	−4422.93	−0.490884	−0.245442	−	0.969411i	$-0.578933\pi$
$433$	−4422.93	−0.490884	−0.245442	+	0.969411i	$0.578933\pi$
$434$	−5318.75	−0.588268
$435$	5304.32	0.584650
$436$	−556.662	−0.0611452
$437$	−5.35306	−0.000585976 0
$438$	−9322.74	−1.01703
$439$	−1748.08	−0.190048	−0.0950242	−	0.995475i	$-0.530293\pi$
$439$	−1748.08	−0.190048	−0.0950242	+	0.995475i	$0.530293\pi$
$440$	−1285.41	−0.139271
$441$	6952.14	0.750690
$442$	−10113.7	−1.08837
$443$	3371.31	0.361571	0.180785	−	0.983523i	$-0.442136\pi$
$443$	3371.31	0.361571	0.180785	+	0.983523i	$0.442136\pi$
$444$	1413.37	0.151071
$445$	5638.55	0.600658
$446$	4249.37	0.451151
$447$	−18595.6	−1.96766
$448$	1507.98	0.159030
$449$	13314.7	1.39947	0.699734	−	0.714404i	$-0.253302\pi$
$449$	13314.7	1.39947	0.699734	+	0.714404i	$0.253302\pi$
$450$	−1638.27	−0.171619
$451$	4350.61	0.454240
$452$	−5172.70	−0.538282
$453$	−5019.43	−0.520603
$454$	−3103.94	−0.320871
$455$	−4722.00	−0.486529
$456$	−14.3942	−0.00147823
$457$	3767.20	0.385607	0.192803	−	0.981237i	$-0.438242\pi$
$457$	3767.20	0.385607	0.192803	+	0.981237i	$0.438242\pi$
$458$	317.063	0.0323480
$459$	5623.32	0.571839
$460$	460.000	0.0466252
$461$	9674.06	0.977366	0.488683	−	0.872461i	$-0.337477\pi$
$461$	9674.06	0.977366	0.488683	+	0.872461i	$0.337477\pi$
$462$	11707.2	1.17893
$463$	2977.73	0.298892	0.149446	−	0.988770i	$-0.452251\pi$
$463$	2977.73	0.298892	0.149446	+	0.988770i	$0.452251\pi$
$464$	−2195.61	−0.219674
$465$	−4362.73	−0.435089
$466$	1458.00	0.144937
$467$	−10701.0	−1.06035	−0.530176	−	0.847888i	$-0.677874\pi$
$467$	−10701.0	−1.06035	−0.530176	+	0.847888i	$0.677874\pi$
$468$	5253.09	0.518855
$469$	−9913.16	−0.976006
$470$	264.344	0.0259431
$471$	28333.7	2.77187
$472$	−1617.98	−0.157783
$473$	−17466.4	−1.69790
$474$	21319.7	2.06592
$475$	5.81854	0.000562048 0
$476$	11890.9	1.14500
$477$	1431.71	0.137429
$478$	12403.2	1.18684
$479$	2337.15	0.222937	0.111469	−	0.993768i	$-0.464445\pi$
$479$	2337.15	0.222937	0.111469	+	0.993768i	$0.464445\pi$
$480$	1236.93	0.117620
$481$	1831.94	0.173657
$482$	14446.1	1.36515
$483$	−4189.57	−0.394683
$484$	−1193.31	−0.112069
$485$	7431.18	0.695737
$486$	10757.6	1.00406
$487$	−7183.85	−0.668442	−0.334221	−	0.942495i	$-0.608473\pi$
$487$	−7183.85	−0.668442	−0.334221	+	0.942495i	$0.608473\pi$
$488$	−1202.23	−0.111521
$489$	−8158.12	−0.754443
$490$	2121.80	0.195618
$491$	−12084.2	−1.11070	−0.555350	−	0.831617i	$-0.687416\pi$
$491$	−12084.2	−1.11070	−0.555350	+	0.831617i	$0.687416\pi$
$492$	−4186.53	−0.383625
$493$	−17313.1	−1.58163
$494$	−18.6571	−0.00169923
$495$	5264.61	0.478034
$496$	1805.86	0.163478
$497$	15725.0	1.41924
$498$	7501.64	0.675013
$499$	7145.78	0.641060	0.320530	−	0.947238i	$-0.396139\pi$
$499$	7145.78	0.641060	0.320530	+	0.947238i	$0.396139\pi$
$500$	−500.000	−0.0447214
$501$	−5657.45	−0.504503
$502$	−10085.6	−0.896695
$503$	20436.2	1.81154	0.905770	−	0.423771i	$-0.139294\pi$
$503$	20436.2	1.81154	0.905770	+	0.423771i	$0.139294\pi$
$504$	−6176.21	−0.545854
$505$	−9444.29	−0.832208
$506$	−1478.22	−0.129871
$507$	−4565.10	−0.399888
$508$	−5193.72	−0.453610
$509$	19721.7	1.71738	0.858690	−	0.512495i	$-0.171279\pi$
$509$	19721.7	1.71738	0.858690	+	0.512495i	$0.171279\pi$
$510$	9753.59	0.846856
$511$	14207.1	1.22991
$512$	−512.000	−0.0441942
$513$	10.3735	0.000892794 0
$514$	−5962.30	−0.511646
$515$	7485.84	0.640516
$516$	16807.6	1.43394
$517$	−849.475	−0.0722628
$518$	−2153.86	−0.182693
$519$	−4033.73	−0.341158
$520$	1603.24	0.135205
$521$	3483.23	0.292904	0.146452	−	0.989218i	$-0.453215\pi$
$521$	3483.23	0.292904	0.146452	+	0.989218i	$0.453215\pi$
$522$	8992.50	0.754006
$523$	15689.0	1.31172	0.655862	−	0.754881i	$-0.272305\pi$
$523$	15689.0	1.31172	0.655862	+	0.754881i	$0.272305\pi$
$524$	−2100.99	−0.175157
$525$	4553.88	0.378567
$526$	−14485.7	−1.20077
$527$	14239.8	1.17703
$528$	−3974.90	−0.327624
$529$	529.000	0.0434783
$530$	436.958	0.0358118
$531$	6626.72	0.541573
$532$	21.9357	0.00178765
$533$	−5426.36	−0.440979
$534$	17436.2	1.41299
$535$	2925.75	0.236432
$536$	3365.78	0.271230
$537$	−9146.09	−0.734977
$538$	5135.15	0.411510
$539$	−6818.43	−0.544881
$540$	−891.422	−0.0710383
$541$	7620.73	0.605621	0.302810	−	0.953051i	$-0.402075\pi$
$541$	7620.73	0.605621	0.302810	+	0.953051i	$0.402075\pi$
$542$	−16132.5	−1.27851
$543$	13327.3	1.05328
$544$	−4037.29	−0.318194
$545$	695.828	0.0546899
$546$	−14602.0	−1.14452
$547$	5925.62	0.463183	0.231592	−	0.972813i	$-0.425607\pi$
$547$	5925.62	0.463183	0.231592	+	0.972813i	$0.425607\pi$
$548$	−9712.47	−0.757109
$549$	4923.94	0.382784
$550$	1606.76	0.124568
$551$	−31.9381	−0.00246934
$552$	1422.47	0.109682
$553$	−32489.4	−2.49836
$554$	−17983.1	−1.37911
$555$	−1766.71	−0.135122
$556$	9825.85	0.749476
$557$	−5456.16	−0.415054	−0.207527	−	0.978229i	$-0.566541\pi$
$557$	−5456.16	−0.415054	−0.207527	+	0.978229i	$0.566541\pi$
$558$	−7396.20	−0.561122
$559$	21785.2	1.64833
$560$	−1884.98	−0.142241
$561$	−31343.4	−2.35886
$562$	−1936.26	−0.145331
$563$	−9194.29	−0.688265	−0.344132	−	0.938921i	$-0.611827\pi$
$563$	−9194.29	−0.688265	−0.344132	+	0.938921i	$0.611827\pi$
$564$	817.437	0.0610289
$565$	6465.88	0.481454
$566$	4505.30	0.334580
$567$	−12725.8	−0.942567
$568$	−5339.05	−0.394404
$569$	338.831	0.0249640	0.0124820	−	0.999922i	$-0.496027\pi$
$569$	338.831	0.0249640	0.0124820	+	0.999922i	$0.496027\pi$
$570$	17.9928	0.00132217
$571$	−1725.34	−0.126451	−0.0632254	−	0.997999i	$-0.520139\pi$
$571$	−1725.34	−0.126451	−0.0632254	+	0.997999i	$0.520139\pi$
$572$	−5152.06	−0.376605
$573$	−21631.7	−1.57710
$574$	6379.93	0.463926
$575$	−575.000	−0.0417029
$576$	2096.98	0.151692
$577$	23300.0	1.68109	0.840547	−	0.541738i	$-0.182234\pi$
$577$	23300.0	1.68109	0.840547	+	0.541738i	$0.182234\pi$
$578$	−22009.3	−1.58385
$579$	−3847.52	−0.276161
$580$	2744.51	0.196482
$581$	−11431.9	−0.816307
$582$	22979.6	1.63666
$583$	−1404.18	−0.0997513
$584$	−4823.68	−0.341790
$585$	−6566.36	−0.464078
$586$	−5468.70	−0.385512
$587$	15653.3	1.10065	0.550325	−	0.834950i	$-0.314504\pi$
$587$	15653.3	1.10065	0.550325	+	0.834950i	$0.314504\pi$
$588$	6561.28	0.460174
$589$	26.2686	0.00183766
$590$	2022.48	0.141126
$591$	2292.10	0.159533
$592$	731.292	0.0507701
$593$	−2658.08	−0.184072	−0.0920358	−	0.995756i	$-0.529337\pi$
$593$	−2658.08	−0.184072	−0.0920358	+	0.995756i	$0.529337\pi$
$594$	2864.60	0.197872
$595$	−14863.7	−1.02412
$596$	−9621.57	−0.661266
$597$	18147.6	1.24410
$598$	1843.73	0.126080
$599$	19417.6	1.32451	0.662256	−	0.749278i	$-0.269599\pi$
$599$	19417.6	1.32451	0.662256	+	0.749278i	$0.269599\pi$
$600$	−1546.16	−0.105203
$601$	−18469.0	−1.25352	−0.626760	−	0.779213i	$-0.715619\pi$
$601$	−18469.0	−1.25352	−0.626760	+	0.779213i	$0.715619\pi$
$602$	−25613.5	−1.73410
$603$	−13785.1	−0.930968
$604$	−2597.10	−0.174958
$605$	1491.64	0.100238
$606$	−29204.8	−1.95770
$607$	3968.56	0.265369	0.132684	−	0.991158i	$-0.457640\pi$
$607$	3968.56	0.265369	0.132684	+	0.991158i	$0.457640\pi$
$608$	−7.44773	−0.000496785 0
$609$	−24996.4	−1.66322
$610$	1502.79	0.0997477
$611$	1059.52	0.0701531
$612$	16535.4	1.09216
$613$	−11478.7	−0.756311	−0.378156	−	0.925742i	$-0.623442\pi$
$613$	−11478.7	−0.756311	−0.378156	+	0.925742i	$0.623442\pi$
$614$	15954.2	1.04863
$615$	5233.16	0.343124
$616$	6057.42	0.396202
$617$	−15691.1	−1.02382	−0.511911	−	0.859039i	$-0.671062\pi$
$617$	−15691.1	−1.02382	−0.511911	+	0.859039i	$0.671062\pi$
$618$	23148.6	1.50676
$619$	−18249.4	−1.18499	−0.592494	−	0.805575i	$-0.701856\pi$
$619$	−18249.4	−1.18499	−0.592494	+	0.805575i	$0.701856\pi$
$620$	−2257.32	−0.146220
$621$	−1025.14	−0.0662436
$622$	−15458.9	−0.996533
$623$	−26571.4	−1.70876
$624$	4957.75	0.318059
$625$	625.000	0.0400000
$626$	−11012.5	−0.703111
$627$	−57.8203	−0.00368281
$628$	14660.2	0.931536
$629$	5766.48	0.365540
$630$	7720.26	0.488226
$631$	−23528.8	−1.48442	−0.742208	−	0.670169i	$-0.766222\pi$
$631$	−23528.8	−1.48442	−0.742208	+	0.670169i	$0.766222\pi$
$632$	11031.0	0.694288
$633$	21944.8	1.37793
$634$	−10462.7	−0.655408
$635$	6492.15	0.405722
$636$	1351.22	0.0842441
$637$	8504.38	0.528973
$638$	−8819.55	−0.547287
$639$	21867.0	1.35375
$640$	640.000	0.0395285
$641$	3748.79	0.230996	0.115498	−	0.993308i	$-0.463154\pi$
$641$	3748.79	0.230996	0.115498	+	0.993308i	$0.463154\pi$
$642$	9047.36	0.556185
$643$	15924.3	0.976660	0.488330	−	0.872659i	$-0.337606\pi$
$643$	15924.3	0.976660	0.488330	+	0.872659i	$0.337606\pi$
$644$	−2167.73	−0.132640
$645$	−21009.5	−1.28256
$646$	−58.7278	−0.00357680
$647$	−2854.11	−0.173426	−0.0867129	−	0.996233i	$-0.527636\pi$
$647$	−2854.11	−0.173426	−0.0867129	+	0.996233i	$0.527636\pi$
$648$	4320.76	0.261937
$649$	−6499.27	−0.393095
$650$	−2004.05	−0.120931
$651$	20559.1	1.23775
$652$	−4221.09	−0.253544
$653$	7925.97	0.474988	0.237494	−	0.971389i	$-0.423674\pi$
$653$	7925.97	0.474988	0.237494	+	0.971389i	$0.423674\pi$
$654$	2151.72	0.128653
$655$	2626.24	0.156665
$656$	−2166.15	−0.128924
$657$	19756.2	1.17316
$658$	−1245.71	−0.0738035
$659$	−5799.43	−0.342813	−0.171406	−	0.985200i	$-0.554831\pi$
$659$	−5799.43	−0.342813	−0.171406	+	0.985200i	$0.554831\pi$
$660$	4968.62	0.293035
$661$	22324.8	1.31367	0.656833	−	0.754036i	$-0.271896\pi$
$661$	22324.8	1.31367	0.656833	+	0.754036i	$0.271896\pi$
$662$	7103.22	0.417031
$663$	39093.4	2.28999
$664$	3881.42	0.226850
$665$	−27.4196	−0.00159893
$666$	−2995.13	−0.174263
$667$	3156.19	0.183221
$668$	−2927.22	−0.169547
$669$	−16425.5	−0.949249
$670$	−4207.22	−0.242596
$671$	−4829.24	−0.277840
$672$	−5828.97	−0.334609
$673$	−23253.5	−1.33188	−0.665940	−	0.746005i	$-0.731969\pi$
$673$	−23253.5	−1.33188	−0.665940	+	0.746005i	$0.731969\pi$
$674$	14006.0	0.800430
$675$	1114.28	0.0635386
$676$	−2362.03	−0.134389
$677$	−19003.7	−1.07884	−0.539419	−	0.842038i	$-0.681356\pi$
$677$	−19003.7	−1.07884	−0.539419	+	0.842038i	$0.681356\pi$
$678$	19994.6	1.13258
$679$	−35019.1	−1.97925
$680$	5046.61	0.284601
$681$	11998.0	0.675131
$682$	7253.94	0.407284
$683$	−11222.5	−0.628722	−0.314361	−	0.949304i	$-0.601790\pi$
$683$	−11222.5	−0.628722	−0.314361	+	0.949304i	$0.601790\pi$
$684$	30.5035	0.00170516
$685$	12140.6	0.677179
$686$	6164.85	0.343112
$687$	−1225.58	−0.0680620
$688$	8696.45	0.481902
$689$	1751.38	0.0968391
$690$	−1778.09	−0.0981023
$691$	4297.68	0.236601	0.118301	−	0.992978i	$-0.462255\pi$
$691$	4297.68	0.236601	0.118301	+	0.992978i	$0.462255\pi$
$692$	−2087.09	−0.114652
$693$	−24809.2	−1.35992
$694$	20536.4	1.12327
$695$	−12282.3	−0.670352
$696$	8486.92	0.462206
$697$	−17080.8	−0.928240
$698$	−9031.15	−0.489734
$699$	−5635.75	−0.304955
$700$	2356.22	0.127224
$701$	25769.6	1.38845	0.694225	−	0.719758i	$-0.255747\pi$
$701$	25769.6	1.38845	0.694225	+	0.719758i	$0.255747\pi$
$702$	−3572.91	−0.192095
$703$	10.6376	0.000570705 0
$704$	−2056.65	−0.110104
$705$	−1021.80	−0.0545859
$706$	−15677.3	−0.835725
$707$	44505.7	2.36748
$708$	6254.15	0.331985
$709$	−4900.01	−0.259554	−0.129777	−	0.991543i	$-0.541426\pi$
$709$	−4900.01	−0.259554	−0.129777	+	0.991543i	$0.541426\pi$
$710$	6673.81	0.352766
$711$	−45179.4	−2.38307
$712$	9021.67	0.474862
$713$	−2595.92	−0.136350
$714$	−45963.3	−2.40915
$715$	6440.07	0.336846
$716$	−4732.28	−0.247002
$717$	−47943.4	−2.49718
$718$	24929.6	1.29577
$719$	7631.85	0.395855	0.197928	−	0.980217i	$-0.436579\pi$
$719$	7631.85	0.395855	0.197928	+	0.980217i	$0.436579\pi$
$720$	−2621.23	−0.135677
$721$	−35276.6	−1.82215
$722$	13717.9	0.707101
$723$	−55839.9	−2.87235
$724$	6895.70	0.353973
$725$	−3430.64	−0.175739
$726$	4612.64	0.235800
$727$	−36985.6	−1.88682	−0.943410	−	0.331628i	$-0.892402\pi$
$727$	−36985.6	−1.88682	−0.943410	+	0.331628i	$0.892402\pi$
$728$	−7555.20	−0.384635
$729$	−26999.8	−1.37173
$730$	6029.60	0.305706
$731$	68574.3	3.46965
$732$	4647.10	0.234647
$733$	−22227.3	−1.12003	−0.560015	−	0.828482i	$-0.689205\pi$
$733$	−22227.3	−1.12003	−0.560015	+	0.828482i	$0.689205\pi$
$734$	−7872.29	−0.395874
$735$	−8201.60	−0.411592
$736$	736.000	0.0368605
$737$	13520.0	0.675733
$738$	8871.86	0.442517
$739$	−17899.1	−0.890974	−0.445487	−	0.895288i	$-0.646970\pi$
$739$	−17899.1	−0.890974	−0.445487	+	0.895288i	$0.646970\pi$
$740$	−914.115	−0.0454102
$741$	72.1171	0.00357529
$742$	−2059.14	−0.101878
$743$	−29843.4	−1.47355	−0.736776	−	0.676137i	$-0.763653\pi$
$743$	−29843.4	−1.47355	−0.736776	+	0.676137i	$0.763653\pi$
$744$	−6980.36	−0.343968
$745$	12027.0	0.591455
$746$	−3841.44	−0.188532
$747$	−15897.0	−0.778638
$748$	−16217.4	−0.792736
$749$	−13787.4	−0.672606
$750$	1932.70	0.0940964
$751$	−9399.65	−0.456722	−0.228361	−	0.973577i	$-0.573337\pi$
$751$	−9399.65	−0.456722	−0.228361	+	0.973577i	$0.573337\pi$
$752$	422.950	0.0205098
$753$	38984.8	1.88670
$754$	11000.3	0.531309
$755$	3246.38	0.156487
$756$	4200.78	0.202091
$757$	29871.6	1.43422	0.717109	−	0.696961i	$-0.245465\pi$
$757$	29871.6	1.43422	0.717109	+	0.696961i	$0.245465\pi$
$758$	26149.0	1.25300
$759$	5713.92	0.273257
$760$	9.30966	0.000444338 0
$761$	−273.955	−0.0130497	−0.00652487	−	0.999979i	$-0.502077\pi$
$761$	−273.955	−0.0130497	−0.00652487	+	0.999979i	$0.502077\pi$
$762$	20075.8	0.954423
$763$	−3279.05	−0.155583
$764$	−11192.5	−0.530012
$765$	−20669.3	−0.976861
$766$	−17676.4	−0.833780
$767$	8106.31	0.381619
$768$	1979.09	0.0929872
$769$	−13273.8	−0.622450	−0.311225	−	0.950336i	$-0.600739\pi$
$769$	−13273.8	−0.622450	−0.311225	+	0.950336i	$0.600739\pi$
$770$	−7571.78	−0.354374
$771$	23046.7	1.07653
$772$	−1990.74	−0.0928089
$773$	34161.1	1.58951	0.794753	−	0.606933i	$-0.207600\pi$
$773$	34161.1	1.58951	0.794753	+	0.606933i	$0.207600\pi$
$774$	−35617.8	−1.65408
$775$	2821.65	0.130783
$776$	11889.9	0.550028
$777$	8325.54	0.384398
$778$	25374.6	1.16931
$779$	−31.5096	−0.00144923
$780$	−6197.18	−0.284480
$781$	−21446.4	−0.982603
$782$	5803.60	0.265392
$783$	−6116.29	−0.279155
$784$	3394.87	0.154650
$785$	−18325.2	−0.833191
$786$	8121.17	0.368540
$787$	−38489.6	−1.74334	−0.871669	−	0.490095i	$-0.836962\pi$
$787$	−38489.6	−1.74334	−0.871669	+	0.490095i	$0.836962\pi$
$788$	1185.95	0.0536141
$789$	55993.2	2.52650
$790$	−13788.8	−0.620990
$791$	−30470.1	−1.36965
$792$	8423.38	0.377919
$793$	6023.33	0.269729
$794$	−16121.0	−0.720544
$795$	−1689.02	−0.0753502
$796$	9389.73	0.418103
$797$	17176.8	0.763405	0.381702	−	0.924285i	$-0.375338\pi$
$797$	17176.8	0.763405	0.381702	+	0.924285i	$0.375338\pi$
$798$	−84.7902	−0.00376133
$799$	3335.10	0.147669
$800$	−800.000	−0.0353553
$801$	−36949.8	−1.62991
$802$	−24650.2	−1.08532
$803$	−19376.2	−0.851523
$804$	−13010.1	−0.570684
$805$	2709.66	0.118637
$806$	−9047.58	−0.395394
$807$	−19849.4	−0.865841
$808$	−15110.9	−0.657918
$809$	8226.61	0.357518	0.178759	−	0.983893i	$-0.442792\pi$
$809$	8226.61	0.357518	0.178759	+	0.983893i	$0.442792\pi$
$810$	−5400.95	−0.234284
$811$	27867.9	1.20662	0.603312	−	0.797505i	$-0.293847\pi$
$811$	27867.9	1.20662	0.603312	+	0.797505i	$0.293847\pi$
$812$	−12933.4	−0.558956
$813$	62358.8	2.69006
$814$	2937.53	0.126487
$815$	5276.37	0.226777
$816$	15605.7	0.669498
$817$	126.502	0.00541705
$818$	21613.5	0.923835
$819$	30943.6	1.32022
$820$	2707.69	0.115313
$821$	−17637.5	−0.749761	−0.374880	−	0.927073i	$-0.622316\pi$
$821$	−17637.5	−0.749761	−0.374880	+	0.927073i	$0.622316\pi$
$822$	37542.6	1.59300
$823$	28048.6	1.18799	0.593993	−	0.804470i	$-0.297551\pi$
$823$	28048.6	1.18799	0.593993	+	0.804470i	$0.297551\pi$
$824$	11977.3	0.506372
$825$	−6210.78	−0.262099
$826$	−9530.82	−0.401477
$827$	−32592.9	−1.37046	−0.685228	−	0.728329i	$-0.740297\pi$
$827$	−32592.9	−1.37046	−0.685228	+	0.728329i	$0.740297\pi$
$828$	−3014.42	−0.126520
$829$	18815.9	0.788303	0.394152	−	0.919045i	$-0.371038\pi$
$829$	18815.9	0.788303	0.394152	+	0.919045i	$0.371038\pi$
$830$	−4851.78	−0.202901
$831$	69511.9	2.90173
$832$	2565.19	0.106889
$833$	26769.7	1.11346
$834$	−37980.9	−1.57694
$835$	3659.03	0.151648
$836$	−29.9168	−0.00123767
$837$	5030.56	0.207744
$838$	3647.48	0.150358
$839$	7612.72	0.313254	0.156627	−	0.987658i	$-0.449938\pi$
$839$	7612.72	0.313254	0.156627	+	0.987658i	$0.449938\pi$
$840$	7286.21	0.299283
$841$	−5558.14	−0.227896
$842$	−11990.9	−0.490775
$843$	7484.43	0.305786
$844$	11354.5	0.463076
$845$	2952.54	0.120202
$846$	−1732.27	−0.0703978
$847$	−7029.28	−0.285158
$848$	699.134	0.0283117
$849$	−17414.8	−0.703975
$850$	−6308.26	−0.254555
$851$	−1051.23	−0.0423452
$852$	20637.6	0.829849
$853$	−31421.4	−1.26125	−0.630627	−	0.776086i	$-0.717202\pi$
$853$	−31421.4	−1.26125	−0.630627	+	0.776086i	$0.717202\pi$
$854$	−7081.81	−0.283764
$855$	−38.1293	−0.00152514
$856$	4681.20	0.186916
$857$	20909.5	0.833435	0.416718	−	0.909036i	$-0.363180\pi$
$857$	20909.5	0.833435	0.416718	+	0.909036i	$0.363180\pi$
$858$	19914.8	0.792400
$859$	23304.5	0.925655	0.462828	−	0.886448i	$-0.346835\pi$
$859$	23304.5	0.925655	0.462828	+	0.886448i	$0.346835\pi$
$860$	−10870.6	−0.431027
$861$	−24661.0	−0.976127
$862$	−7775.61	−0.307237
$863$	−19146.3	−0.755211	−0.377606	−	0.925966i	$-0.623253\pi$
$863$	−19146.3	−0.755211	−0.377606	+	0.925966i	$0.623253\pi$
$864$	−1426.27	−0.0561607
$865$	2608.86	0.102548
$866$	8845.87	0.347107
$867$	85075.0	3.33252
$868$	10637.5	0.415968
$869$	44310.5	1.72972
$870$	−10608.6	−0.413410
$871$	−16863.0	−0.656005
$872$	1113.32	0.0432362
$873$	−48697.1	−1.88791
$874$	10.7061	0.000414347 0
$875$	−2945.28	−0.113793
$876$	18645.5	0.719146
$877$	31389.0	1.20859	0.604293	−	0.796762i	$-0.293456\pi$
$877$	31389.0	1.20859	0.604293	+	0.796762i	$0.293456\pi$
$878$	3496.16	0.134384
$879$	21138.7	0.811139
$880$	2570.82	0.0984798
$881$	44496.3	1.70161	0.850806	−	0.525480i	$-0.176114\pi$
$881$	44496.3	1.70161	0.850806	+	0.525480i	$0.176114\pi$
$882$	−13904.3	−0.530818
$883$	8906.65	0.339448	0.169724	−	0.985492i	$-0.445712\pi$
$883$	8906.65	0.339448	0.169724	+	0.985492i	$0.445712\pi$
$884$	20227.4	0.769592
$885$	−7817.69	−0.296936
$886$	−6742.62	−0.255669
$887$	−36584.7	−1.38489	−0.692444	−	0.721472i	$-0.743466\pi$
$887$	−36584.7	−1.38489	−0.692444	+	0.721472i	$0.743466\pi$
$888$	−2826.74	−0.106823
$889$	−30593.9	−1.15420
$890$	−11277.1	−0.424729
$891$	17356.1	0.652581
$892$	−8498.74	−0.319012
$893$	6.15238	0.000230551 0
$894$	37191.2	1.39134
$895$	5915.35	0.220926
$896$	−3015.97	−0.112451
$897$	−7126.76	−0.265279
$898$	−26629.5	−0.989573
$899$	−15488.1	−0.574591
$900$	3276.54	0.121353
$901$	5512.90	0.203842
$902$	−8701.23	−0.321197
$903$	99006.4	3.64865
$904$	10345.4	0.380623
$905$	−8619.62	−0.316603
$906$	10038.9	0.368122
$907$	−21346.1	−0.781463	−0.390731	−	0.920505i	$-0.627778\pi$
$907$	−21346.1	−0.781463	−0.390731	+	0.920505i	$0.627778\pi$
$908$	6207.89	0.226890
$909$	61889.1	2.25823
$910$	9444.00	0.344028
$911$	−10208.0	−0.371246	−0.185623	−	0.982621i	$-0.559430\pi$
$911$	−10208.0	−0.371246	−0.185623	+	0.982621i	$0.559430\pi$
$912$	28.7885	0.00104527
$913$	15591.3	0.565166
$914$	−7534.40	−0.272665
$915$	−5808.88	−0.209875
$916$	−634.125	−0.0228735
$917$	−12376.0	−0.445683
$918$	−11246.6	−0.404351
$919$	1758.00	0.0631025	0.0315513	−	0.999502i	$-0.489955\pi$
$919$	1758.00	0.0631025	0.0315513	+	0.999502i	$0.489955\pi$
$920$	−920.000	−0.0329690
$921$	−61669.3	−2.20638
$922$	−19348.1	−0.691102
$923$	26749.3	0.953917
$924$	−23414.4	−0.833633
$925$	1142.64	0.0406161
$926$	−5955.46	−0.211348
$927$	−49055.3	−1.73807
$928$	4391.22	0.155333
$929$	−845.008	−0.0298426	−0.0149213	−	0.999889i	$-0.504750\pi$
$929$	−845.008	−0.0298426	−0.0149213	+	0.999889i	$0.504750\pi$
$930$	8725.45	0.307655
$931$	49.3830	0.00173841
$932$	−2915.99	−0.102486
$933$	59754.7	2.09676
$934$	21402.0	0.749782
$935$	20271.7	0.709045
$936$	−10506.2	−0.366886
$937$	3851.61	0.134287	0.0671433	−	0.997743i	$-0.478612\pi$
$937$	3851.61	0.134287	0.0671433	+	0.997743i	$0.478612\pi$
$938$	19826.3	0.690141
$939$	42567.7	1.47939
$940$	−528.688	−0.0183446
$941$	−4379.36	−0.151714	−0.0758571	−	0.997119i	$-0.524169\pi$
$941$	−4379.36	−0.151714	−0.0758571	+	0.997119i	$0.524169\pi$
$942$	−56667.5	−1.96001
$943$	3113.85	0.107530
$944$	3235.96	0.111570
$945$	−5250.98	−0.180756
$946$	34932.8	1.20059
$947$	29746.9	1.02074	0.510371	−	0.859954i	$-0.329508\pi$
$947$	29746.9	1.02074	0.510371	+	0.859954i	$0.329508\pi$
$948$	−42639.3	−1.46082
$949$	24167.3	0.826663
$950$	−11.6371	−0.000397428 0
$951$	40442.7	1.37902
$952$	−23781.9	−0.809638
$953$	4306.61	0.146385	0.0731924	−	0.997318i	$-0.476681\pi$
$953$	4306.61	0.146385	0.0731924	+	0.997318i	$0.476681\pi$
$954$	−2863.42	−0.0971769
$955$	13990.6	0.474057
$956$	−24806.4	−0.839222
$957$	34091.1	1.15152
$958$	−4674.29	−0.157640
$959$	−57211.9	−1.92645
$960$	−2473.86	−0.0831702
$961$	−17052.3	−0.572397
$962$	−3663.87	−0.122794
$963$	−19172.7	−0.641568
$964$	−28892.2	−0.965305
$965$	2488.43	0.0830108
$966$	8379.14	0.279083
$967$	−12233.4	−0.406824	−0.203412	−	0.979093i	$-0.565203\pi$
$967$	−12233.4	−0.406824	−0.203412	+	0.979093i	$0.565203\pi$
$968$	2386.63	0.0792449
$969$	227.007	0.00752581
$970$	−14862.4	−0.491960
$971$	48207.7	1.59326	0.796631	−	0.604465i	$-0.206613\pi$
$971$	48207.7	1.59326	0.796631	+	0.604465i	$0.206613\pi$
$972$	−21515.2	−0.709978
$973$	57879.8	1.90703
$974$	14367.7	0.472660
$975$	7746.48	0.254447
$976$	2404.46	0.0788575
$977$	28662.9	0.938595	0.469298	−	0.883040i	$-0.344507\pi$
$977$	28662.9	0.938595	0.469298	+	0.883040i	$0.344507\pi$
$978$	16316.2	0.533472
$979$	36239.2	1.18305
$980$	−4243.59	−0.138323
$981$	−4559.81	−0.148403
$982$	24168.4	0.785383
$983$	−20944.1	−0.679567	−0.339783	−	0.940504i	$-0.610354\pi$
$983$	−20944.1	−0.679567	−0.339783	+	0.940504i	$0.610354\pi$
$984$	8373.06	0.271264
$985$	−1482.44	−0.0479539
$986$	34626.2	1.11838
$987$	4815.16	0.155287
$988$	37.3141	0.00120154
$989$	−12501.1	−0.401934
$990$	−10529.2	−0.338021
$991$	−36440.2	−1.16808	−0.584038	−	0.811727i	$-0.698528\pi$
$991$	−36440.2	−1.16808	−0.584038	+	0.811727i	$0.698528\pi$
$992$	−3611.71	−0.115597
$993$	−27456.8	−0.877458
$994$	−31450.0	−1.00355
$995$	−11737.2	−0.373963
$996$	−15003.3	−0.477306
$997$	−11945.0	−0.379439	−0.189720	−	0.981838i	$-0.560758\pi$
$997$	−11945.0	−0.379439	−0.189720	+	0.981838i	$0.560758\pi$
$998$	−14291.6	−0.453298
$999$	2037.15	0.0645172

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.a.h.1.4	✓	4
3.2	odd	2		2070.4.a.bj.1.3		4
4.3	odd	2		1840.4.a.m.1.1		4
5.2	odd	4		1150.4.b.n.599.1		8
5.3	odd	4		1150.4.b.n.599.8		8
5.4	even	2		1150.4.a.p.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.h.1.4	✓	4	1.1	even	1	trivial
1150.4.a.p.1.1		4	5.4	even	2
1150.4.b.n.599.1		8	5.2	odd	4
1150.4.b.n.599.8		8	5.3	odd	4
1840.4.a.m.1.1		4	4.3	odd	2
2070.4.a.bj.1.3		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +7.73081 q^{3} +4.00000 q^{4} -5.00000 q^{5} -15.4616 q^{6} +23.5622 q^{7} -8.00000 q^{8} +32.7654 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +7.73081 q^{3} +4.00000 q^{4} -5.00000 q^{5} -15.4616 q^{6} +23.5622 q^{7} -8.00000 q^{8} +32.7654 q^{9} +10.0000 q^{10} -32.1352 q^{11} +30.9232 q^{12} +40.0811 q^{13} -47.1245 q^{14} -38.6540 q^{15} +16.0000 q^{16} +126.165 q^{17} -65.5308 q^{18} +0.232742 q^{19} -20.0000 q^{20} +182.155 q^{21} +64.2704 q^{22} -23.0000 q^{23} -61.8465 q^{24} +25.0000 q^{25} -80.1621 q^{26} +44.5711 q^{27} +94.2490 q^{28} -137.226 q^{29} +77.3081 q^{30} +112.866 q^{31} -32.0000 q^{32} -248.431 q^{33} -252.331 q^{34} -117.811 q^{35} +131.062 q^{36} +45.7057 q^{37} -0.465483 q^{38} +309.859 q^{39} +40.0000 q^{40} -135.385 q^{41} -364.310 q^{42} +543.528 q^{43} -128.541 q^{44} -163.827 q^{45} +46.0000 q^{46} +26.4344 q^{47} +123.693 q^{48} +212.180 q^{49} -50.0000 q^{50} +975.359 q^{51} +160.324 q^{52} +43.6958 q^{53} -89.1422 q^{54} +160.676 q^{55} -188.498 q^{56} +1.79928 q^{57} +274.451 q^{58} +202.248 q^{59} -154.616 q^{60} +150.279 q^{61} -225.732 q^{62} +772.026 q^{63} +64.0000 q^{64} -200.405 q^{65} +496.862 q^{66} -420.722 q^{67} +504.661 q^{68} -177.809 q^{69} +235.622 q^{70} +667.381 q^{71} -262.123 q^{72} +602.960 q^{73} -91.4115 q^{74} +193.270 q^{75} +0.930966 q^{76} -757.178 q^{77} -619.718 q^{78} -1378.88 q^{79} -80.0000 q^{80} -540.095 q^{81} +270.769 q^{82} -485.178 q^{83} +728.621 q^{84} -630.826 q^{85} -1087.06 q^{86} -1060.86 q^{87} +257.082 q^{88} -1127.71 q^{89} +327.654 q^{90} +944.400 q^{91} -92.0000 q^{92} +872.545 q^{93} -52.8688 q^{94} -1.16371 q^{95} -247.386 q^{96} -1486.24 q^{97} -424.359 q^{98} -1052.92 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} - 4 q^{3} + 16 q^{4} - 20 q^{5} + 8 q^{6} - q^{7} - 32 q^{8} + 32 q^{9}+O(q^{10}) \) 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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