LMFDB - Embedded newform 6002.2.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$47.9262112932$
Analytic rank:	$1$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.53853 q^{3} +1.00000 q^{4} +3.20594 q^{5} +2.53853 q^{6} +2.08261 q^{7} -1.00000 q^{8} +3.44415 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.53853 q^{3} +1.00000 q^{4} +3.20594 q^{5} +2.53853 q^{6} +2.08261 q^{7} -1.00000 q^{8} +3.44415 q^{9} -3.20594 q^{10} -3.18904 q^{11} -2.53853 q^{12} -2.89866 q^{13} -2.08261 q^{14} -8.13838 q^{15} +1.00000 q^{16} -6.73430 q^{17} -3.44415 q^{18} +2.60546 q^{19} +3.20594 q^{20} -5.28678 q^{21} +3.18904 q^{22} -3.47603 q^{23} +2.53853 q^{24} +5.27803 q^{25} +2.89866 q^{26} -1.12748 q^{27} +2.08261 q^{28} +5.76337 q^{29} +8.13838 q^{30} +8.67232 q^{31} -1.00000 q^{32} +8.09548 q^{33} +6.73430 q^{34} +6.67673 q^{35} +3.44415 q^{36} +2.53440 q^{37} -2.60546 q^{38} +7.35835 q^{39} -3.20594 q^{40} +11.2196 q^{41} +5.28678 q^{42} -9.37850 q^{43} -3.18904 q^{44} +11.0417 q^{45} +3.47603 q^{46} -7.29692 q^{47} -2.53853 q^{48} -2.66272 q^{49} -5.27803 q^{50} +17.0952 q^{51} -2.89866 q^{52} -0.676103 q^{53} +1.12748 q^{54} -10.2239 q^{55} -2.08261 q^{56} -6.61404 q^{57} -5.76337 q^{58} -0.0334189 q^{59} -8.13838 q^{60} -11.4942 q^{61} -8.67232 q^{62} +7.17283 q^{63} +1.00000 q^{64} -9.29293 q^{65} -8.09548 q^{66} -5.56872 q^{67} -6.73430 q^{68} +8.82403 q^{69} -6.67673 q^{70} +7.00465 q^{71} -3.44415 q^{72} +3.29046 q^{73} -2.53440 q^{74} -13.3985 q^{75} +2.60546 q^{76} -6.64154 q^{77} -7.35835 q^{78} -5.20920 q^{79} +3.20594 q^{80} -7.47029 q^{81} -11.2196 q^{82} +15.9201 q^{83} -5.28678 q^{84} -21.5897 q^{85} +9.37850 q^{86} -14.6305 q^{87} +3.18904 q^{88} +3.39080 q^{89} -11.0417 q^{90} -6.03679 q^{91} -3.47603 q^{92} -22.0150 q^{93} +7.29692 q^{94} +8.35294 q^{95} +2.53853 q^{96} -3.04429 q^{97} +2.66272 q^{98} -10.9835 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) $ 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.53853	−1.46562	−0.732811	−	0.680432i	$-0.761792\pi$
$3$	−2.53853	−1.46562	−0.732811	+	0.680432i	$0.761792\pi$
$4$	1.00000	0.500000
$5$	3.20594	1.43374	0.716869	−	0.697208i	$-0.245574\pi$
$5$	3.20594	1.43374	0.716869	+	0.697208i	$0.245574\pi$
$6$	2.53853	1.03635
$7$	2.08261	0.787154	0.393577	−	0.919292i	$-0.371237\pi$
$7$	2.08261	0.787154	0.393577	+	0.919292i	$0.371237\pi$
$8$	−1.00000	−0.353553
$9$	3.44415	1.14805
$10$	−3.20594	−1.01381
$11$	−3.18904	−0.961531	−0.480766	−	0.876849i	$-0.659641\pi$
$11$	−3.18904	−0.961531	−0.480766	+	0.876849i	$0.659641\pi$
$12$	−2.53853	−0.732811
$13$	−2.89866	−0.803944	−0.401972	−	0.915652i	$-0.631675\pi$
$13$	−2.89866	−0.803944	−0.401972	+	0.915652i	$0.631675\pi$
$14$	−2.08261	−0.556602
$15$	−8.13838	−2.10132
$16$	1.00000	0.250000
$17$	−6.73430	−1.63331	−0.816654	−	0.577128i	$-0.804173\pi$
$17$	−6.73430	−1.63331	−0.816654	+	0.577128i	$0.804173\pi$
$18$	−3.44415	−0.811793
$19$	2.60546	0.597733	0.298867	−	0.954295i	$-0.403391\pi$
$19$	2.60546	0.597733	0.298867	+	0.954295i	$0.403391\pi$
$20$	3.20594	0.716869
$21$	−5.28678	−1.15367
$22$	3.18904	0.679905
$23$	−3.47603	−0.724803	−0.362402	−	0.932022i	$-0.618043\pi$
$23$	−3.47603	−0.724803	−0.362402	+	0.932022i	$0.618043\pi$
$24$	2.53853	0.518176
$25$	5.27803	1.05561
$26$	2.89866	0.568474
$27$	−1.12748	−0.216984
$28$	2.08261	0.393577
$29$	5.76337	1.07023	0.535115	−	0.844779i	$-0.320268\pi$
$29$	5.76337	1.07023	0.535115	+	0.844779i	$0.320268\pi$
$30$	8.13838	1.48586
$31$	8.67232	1.55759	0.778797	−	0.627276i	$-0.215830\pi$
$31$	8.67232	1.55759	0.778797	+	0.627276i	$0.215830\pi$
$32$	−1.00000	−0.176777
$33$	8.09548	1.40924
$34$	6.73430	1.15492
$35$	6.67673	1.12857
$36$	3.44415	0.574024
$37$	2.53440	0.416653	0.208327	−	0.978059i	$-0.433198\pi$
$37$	2.53440	0.416653	0.208327	+	0.978059i	$0.433198\pi$
$38$	−2.60546	−0.422661
$39$	7.35835	1.17828
$40$	−3.20594	−0.506903
$41$	11.2196	1.75221	0.876105	−	0.482120i	$-0.160133\pi$
$41$	11.2196	1.75221	0.876105	+	0.482120i	$0.160133\pi$
$42$	5.28678	0.815769
$43$	−9.37850	−1.43021	−0.715104	−	0.699018i	$-0.753621\pi$
$43$	−9.37850	−1.43021	−0.715104	+	0.699018i	$0.753621\pi$
$44$	−3.18904	−0.480766
$45$	11.0417	1.64600
$46$	3.47603	0.512513
$47$	−7.29692	−1.06437	−0.532183	−	0.846629i	$-0.678628\pi$
$47$	−7.29692	−1.06437	−0.532183	+	0.846629i	$0.678628\pi$
$48$	−2.53853	−0.366406
$49$	−2.66272	−0.380388
$50$	−5.27803	−0.746427
$51$	17.0952	2.39381
$52$	−2.89866	−0.401972
$53$	−0.676103	−0.0928699	−0.0464350	−	0.998921i	$-0.514786\pi$
$53$	−0.676103	−0.0928699	−0.0464350	+	0.998921i	$0.514786\pi$
$54$	1.12748	0.153431
$55$	−10.2239	−1.37858
$56$	−2.08261	−0.278301
$57$	−6.61404	−0.876051
$58$	−5.76337	−0.756768
$59$	−0.0334189	−0.00435077	−0.00217539	−	0.999998i	$-0.500692\pi$
$59$	−0.0334189	−0.00435077	−0.00217539	+	0.999998i	$0.500692\pi$
$60$	−8.13838	−1.05066
$61$	−11.4942	−1.47168	−0.735842	−	0.677153i	$-0.763213\pi$
$61$	−11.4942	−1.47168	−0.735842	+	0.677153i	$0.763213\pi$
$62$	−8.67232	−1.10139
$63$	7.17283	0.903692
$64$	1.00000	0.125000
$65$	−9.29293	−1.15265
$66$	−8.09548	−0.996484
$67$	−5.56872	−0.680327	−0.340163	−	0.940366i	$-0.610482\pi$
$67$	−5.56872	−0.680327	−0.340163	+	0.940366i	$0.610482\pi$
$68$	−6.73430	−0.816654
$69$	8.82403	1.06229
$70$	−6.67673	−0.798022
$71$	7.00465	0.831299	0.415650	−	0.909525i	$-0.363554\pi$
$71$	7.00465	0.831299	0.415650	+	0.909525i	$0.363554\pi$
$72$	−3.44415	−0.405897
$73$	3.29046	0.385119	0.192559	−	0.981285i	$-0.438321\pi$
$73$	3.29046	0.385119	0.192559	+	0.981285i	$0.438321\pi$
$74$	−2.53440	−0.294618
$75$	−13.3985	−1.54712
$76$	2.60546	0.298867
$77$	−6.64154	−0.756873
$78$	−7.35835	−0.833169
$79$	−5.20920	−0.586081	−0.293040	−	0.956100i	$-0.594667\pi$
$79$	−5.20920	−0.586081	−0.293040	+	0.956100i	$0.594667\pi$
$80$	3.20594	0.358435
$81$	−7.47029	−0.830033
$82$	−11.2196	−1.23900
$83$	15.9201	1.74745	0.873727	−	0.486416i	$-0.161696\pi$
$83$	15.9201	1.74745	0.873727	+	0.486416i	$0.161696\pi$
$84$	−5.28678	−0.576835
$85$	−21.5897	−2.34174
$86$	9.37850	1.01131
$87$	−14.6305	−1.56855
$88$	3.18904	0.339953
$89$	3.39080	0.359424	0.179712	−	0.983719i	$-0.442483\pi$
$89$	3.39080	0.359424	0.179712	+	0.983719i	$0.442483\pi$
$90$	−11.0417	−1.16390
$91$	−6.03679	−0.632828
$92$	−3.47603	−0.362402
$93$	−22.0150	−2.28284
$94$	7.29692	0.752620
$95$	8.35294	0.856993
$96$	2.53853	0.259088
$97$	−3.04429	−0.309101	−0.154550	−	0.987985i	$-0.549393\pi$
$97$	−3.04429	−0.309101	−0.154550	+	0.987985i	$0.549393\pi$
$98$	2.66272	0.268975
$99$	−10.9835	−1.10388
$100$	5.27803	0.527803
$101$	13.3838	1.33174	0.665871	−	0.746067i	$-0.268060\pi$
$101$	13.3838	1.33174	0.665871	+	0.746067i	$0.268060\pi$
$102$	−17.0952	−1.69268
$103$	−16.1643	−1.59272	−0.796358	−	0.604826i	$-0.793243\pi$
$103$	−16.1643	−1.59272	−0.796358	+	0.604826i	$0.793243\pi$
$104$	2.89866	0.284237
$105$	−16.9491	−1.65406
$106$	0.676103	0.0656690
$107$	−8.17366	−0.790178	−0.395089	−	0.918643i	$-0.629286\pi$
$107$	−8.17366	−0.790178	−0.395089	+	0.918643i	$0.629286\pi$
$108$	−1.12748	−0.108492
$109$	0.503019	0.0481805	0.0240903	−	0.999710i	$-0.492331\pi$
$109$	0.503019	0.0481805	0.0240903	+	0.999710i	$0.492331\pi$
$110$	10.2239	0.974806
$111$	−6.43366	−0.610656
$112$	2.08261	0.196789
$113$	3.62379	0.340897	0.170449	−	0.985367i	$-0.445478\pi$
$113$	3.62379	0.340897	0.170449	+	0.985367i	$0.445478\pi$
$114$	6.61404	0.619462
$115$	−11.1439	−1.03918
$116$	5.76337	0.535115
$117$	−9.98342	−0.922967
$118$	0.0334189	0.00307646
$119$	−14.0250	−1.28567
$120$	8.13838	0.742929
$121$	−0.830037	−0.0754579
$122$	11.4942	1.04064
$123$	−28.4814	−2.56808
$124$	8.67232	0.778797
$125$	0.891356	0.0797253
$126$	−7.17283	−0.639007
$127$	−8.72326	−0.774065	−0.387032	−	0.922066i	$-0.626500\pi$
$127$	−8.72326	−0.774065	−0.387032	+	0.922066i	$0.626500\pi$
$128$	−1.00000	−0.0883883
$129$	23.8076	2.09614
$130$	9.29293	0.815044
$131$	−15.5356	−1.35735	−0.678676	−	0.734438i	$-0.737446\pi$
$131$	−15.5356	−1.35735	−0.678676	+	0.734438i	$0.737446\pi$
$132$	8.09548	0.704621
$133$	5.42617	0.470508
$134$	5.56872	0.481064
$135$	−3.61463	−0.311098
$136$	6.73430	0.577461
$137$	15.5703	1.33026	0.665130	−	0.746727i	$-0.268376\pi$
$137$	15.5703	1.33026	0.665130	+	0.746727i	$0.268376\pi$
$138$	−8.82403	−0.751151
$139$	−1.30096	−0.110346	−0.0551728	−	0.998477i	$-0.517571\pi$
$139$	−1.30096	−0.110346	−0.0551728	+	0.998477i	$0.517571\pi$
$140$	6.67673	0.564287
$141$	18.5235	1.55996
$142$	−7.00465	−0.587818
$143$	9.24394	0.773017
$144$	3.44415	0.287012
$145$	18.4770	1.53443
$146$	−3.29046	−0.272320
$147$	6.75939	0.557505
$148$	2.53440	0.208327
$149$	21.1195	1.73018	0.865090	−	0.501617i	$-0.167261\pi$
$149$	21.1195	1.73018	0.865090	+	0.501617i	$0.167261\pi$
$150$	13.3985	1.09398
$151$	8.63478	0.702689	0.351344	−	0.936246i	$-0.385725\pi$
$151$	8.63478	0.702689	0.351344	+	0.936246i	$0.385725\pi$
$152$	−2.60546	−0.211331
$153$	−23.1939	−1.87512
$154$	6.64154	0.535190
$155$	27.8029	2.23318
$156$	7.35835	0.589139
$157$	0.964200	0.0769515	0.0384758	−	0.999260i	$-0.487750\pi$
$157$	0.964200	0.0769515	0.0384758	+	0.999260i	$0.487750\pi$
$158$	5.20920	0.414422
$159$	1.71631	0.136112
$160$	−3.20594	−0.253452
$161$	−7.23924	−0.570532
$162$	7.47029	0.586922
$163$	1.54555	0.121057	0.0605283	−	0.998166i	$-0.480721\pi$
$163$	1.54555	0.121057	0.0605283	+	0.998166i	$0.480721\pi$
$164$	11.2196	0.876105
$165$	25.9536	2.02048
$166$	−15.9201	−1.23564
$167$	−24.8238	−1.92093	−0.960463	−	0.278406i	$-0.910194\pi$
$167$	−24.8238	−1.92093	−0.960463	+	0.278406i	$0.910194\pi$
$168$	5.28678	0.407884
$169$	−4.59776	−0.353674
$170$	21.5897	1.65586
$171$	8.97359	0.686227
$172$	−9.37850	−0.715104
$173$	3.45824	0.262925	0.131462	−	0.991321i	$-0.458033\pi$
$173$	3.45824	0.262925	0.131462	+	0.991321i	$0.458033\pi$
$174$	14.6305	1.10914
$175$	10.9921	0.830925
$176$	−3.18904	−0.240383
$177$	0.0848350	0.00637659
$178$	−3.39080	−0.254151
$179$	−9.70147	−0.725122	−0.362561	−	0.931960i	$-0.618097\pi$
$179$	−9.70147	−0.725122	−0.362561	+	0.931960i	$0.618097\pi$
$180$	11.0417	0.823001
$181$	−12.9295	−0.961044	−0.480522	−	0.876983i	$-0.659553\pi$
$181$	−12.9295	−0.961044	−0.480522	+	0.876983i	$0.659553\pi$
$182$	6.03679	0.447477
$183$	29.1784	2.15693
$184$	3.47603	0.256257
$185$	8.12513	0.597372
$186$	22.0150	1.61422
$187$	21.4759	1.57048
$188$	−7.29692	−0.532183
$189$	−2.34811	−0.170800
$190$	−8.35294	−0.605986
$191$	−7.75599	−0.561203	−0.280602	−	0.959824i	$-0.590534\pi$
$191$	−7.75599	−0.561203	−0.280602	+	0.959824i	$0.590534\pi$
$192$	−2.53853	−0.183203
$193$	16.2567	1.17018	0.585092	−	0.810967i	$-0.301059\pi$
$193$	16.2567	1.17018	0.585092	+	0.810967i	$0.301059\pi$
$194$	3.04429	0.218567
$195$	23.5904	1.68934
$196$	−2.66272	−0.190194
$197$	8.94741	0.637476	0.318738	−	0.947843i	$-0.396741\pi$
$197$	8.94741	0.637476	0.318738	+	0.947843i	$0.396741\pi$
$198$	10.9835	0.780564
$199$	−25.1709	−1.78431	−0.892157	−	0.451725i	$-0.850809\pi$
$199$	−25.1709	−1.78431	−0.892157	+	0.451725i	$0.850809\pi$
$200$	−5.27803	−0.373213
$201$	14.1364	0.997102
$202$	−13.3838	−0.941684
$203$	12.0029	0.842437
$204$	17.0952	1.19691
$205$	35.9694	2.51221
$206$	16.1643	1.12622
$207$	−11.9720	−0.832110
$208$	−2.89866	−0.200986
$209$	−8.30891	−0.574739
$210$	16.9491	1.16960
$211$	−22.0701	−1.51937	−0.759683	−	0.650294i	$-0.774646\pi$
$211$	−22.0701	−1.51937	−0.759683	+	0.650294i	$0.774646\pi$
$212$	−0.676103	−0.0464350
$213$	−17.7815	−1.21837
$214$	8.17366	0.558740
$215$	−30.0669	−2.05054
$216$	1.12748	0.0767154
$217$	18.0611	1.22607
$218$	−0.503019	−0.0340688
$219$	−8.35293	−0.564439
$220$	−10.2239	−0.689292
$221$	19.5205	1.31309
$222$	6.43366	0.431799
$223$	−23.2649	−1.55793	−0.778966	−	0.627067i	$-0.784255\pi$
$223$	−23.2649	−1.55793	−0.778966	+	0.627067i	$0.784255\pi$
$224$	−2.08261	−0.139151
$225$	18.1783	1.21189
$226$	−3.62379	−0.241051
$227$	−17.4009	−1.15494	−0.577469	−	0.816412i	$-0.695960\pi$
$227$	−17.4009	−1.15494	−0.577469	+	0.816412i	$0.695960\pi$
$228$	−6.61404	−0.438026
$229$	−2.85336	−0.188555	−0.0942777	−	0.995546i	$-0.530054\pi$
$229$	−2.85336	−0.188555	−0.0942777	+	0.995546i	$0.530054\pi$
$230$	11.1439	0.734810
$231$	16.8598	1.10929
$232$	−5.76337	−0.378384
$233$	−11.6320	−0.762037	−0.381019	−	0.924567i	$-0.624427\pi$
$233$	−11.6320	−0.762037	−0.381019	+	0.924567i	$0.624427\pi$
$234$	9.98342	0.652636
$235$	−23.3935	−1.52602
$236$	−0.0334189	−0.00217539
$237$	13.2237	0.858973
$238$	14.0250	0.909103
$239$	−4.90254	−0.317119	−0.158559	−	0.987349i	$-0.550685\pi$
$239$	−4.90254	−0.317119	−0.158559	+	0.987349i	$0.550685\pi$
$240$	−8.13838	−0.525330
$241$	−7.58819	−0.488798	−0.244399	−	0.969675i	$-0.578591\pi$
$241$	−7.58819	−0.488798	−0.244399	+	0.969675i	$0.578591\pi$
$242$	0.830037	0.0533568
$243$	22.3460	1.43350
$244$	−11.4942	−0.735842
$245$	−8.53650	−0.545377
$246$	28.4814	1.81591
$247$	−7.55234	−0.480544
$248$	−8.67232	−0.550693
$249$	−40.4136	−2.56111
$250$	−0.891356	−0.0563743
$251$	14.2175	0.897400	0.448700	−	0.893682i	$-0.351887\pi$
$251$	14.2175	0.897400	0.448700	+	0.893682i	$0.351887\pi$
$252$	7.17283	0.451846
$253$	11.0852	0.696921
$254$	8.72326	0.547346
$255$	54.8063	3.43210
$256$	1.00000	0.0625000
$257$	2.94251	0.183549	0.0917743	−	0.995780i	$-0.470746\pi$
$257$	2.94251	0.183549	0.0917743	+	0.995780i	$0.470746\pi$
$258$	−23.8076	−1.48220
$259$	5.27818	0.327970
$260$	−9.29293	−0.576323
$261$	19.8499	1.22868
$262$	15.5356	0.959793
$263$	−24.0038	−1.48014	−0.740069	−	0.672531i	$-0.765207\pi$
$263$	−24.0038	−1.48014	−0.740069	+	0.672531i	$0.765207\pi$
$264$	−8.09548	−0.498242
$265$	−2.16754	−0.133151
$266$	−5.42617	−0.332700
$267$	−8.60766	−0.526780
$268$	−5.56872	−0.340163
$269$	−3.16034	−0.192689	−0.0963446	−	0.995348i	$-0.530715\pi$
$269$	−3.16034	−0.192689	−0.0963446	+	0.995348i	$0.530715\pi$
$270$	3.61463	0.219980
$271$	10.0643	0.611364	0.305682	−	0.952134i	$-0.401116\pi$
$271$	10.0643	0.611364	0.305682	+	0.952134i	$0.401116\pi$
$272$	−6.73430	−0.408327
$273$	15.3246	0.927487
$274$	−15.5703	−0.940636
$275$	−16.8318	−1.01500
$276$	8.82403	0.531144
$277$	−9.25315	−0.555968	−0.277984	−	0.960586i	$-0.589666\pi$
$277$	−9.25315	−0.555968	−0.277984	+	0.960586i	$0.589666\pi$
$278$	1.30096	0.0780261
$279$	29.8687	1.78819
$280$	−6.67673	−0.399011
$281$	8.18271	0.488139	0.244070	−	0.969758i	$-0.421517\pi$
$281$	8.18271	0.488139	0.244070	+	0.969758i	$0.421517\pi$
$282$	−18.5235	−1.10306
$283$	24.1637	1.43638	0.718191	−	0.695846i	$-0.244970\pi$
$283$	24.1637	1.43638	0.718191	+	0.695846i	$0.244970\pi$
$284$	7.00465	0.415650
$285$	−21.2042	−1.25603
$286$	−9.24394	−0.546606
$287$	23.3661	1.37926
$288$	−3.44415	−0.202948
$289$	28.3508	1.66769
$290$	−18.4770	−1.08501
$291$	7.72802	0.453025
$292$	3.29046	0.192559
$293$	−28.4192	−1.66027	−0.830133	−	0.557565i	$-0.811736\pi$
$293$	−28.4192	−1.66027	−0.830133	+	0.557565i	$0.811736\pi$
$294$	−6.75939	−0.394216
$295$	−0.107139	−0.00623787
$296$	−2.53440	−0.147309
$297$	3.59558	0.208637
$298$	−21.1195	−1.22342
$299$	10.0758	0.582701
$300$	−13.3985	−0.773560
$301$	−19.5318	−1.12579
$302$	−8.63478	−0.496876
$303$	−33.9753	−1.95183
$304$	2.60546	0.149433
$305$	−36.8497	−2.11001
$306$	23.1939	1.32591
$307$	3.92738	0.224147	0.112074	−	0.993700i	$-0.464251\pi$
$307$	3.92738	0.224147	0.112074	+	0.993700i	$0.464251\pi$
$308$	−6.64154	−0.378437
$309$	41.0336	2.33432
$310$	−27.8029	−1.57910
$311$	−3.87896	−0.219955	−0.109978	−	0.993934i	$-0.535078\pi$
$311$	−3.87896	−0.219955	−0.109978	+	0.993934i	$0.535078\pi$
$312$	−7.35835	−0.416584
$313$	−1.93937	−0.109620	−0.0548098	−	0.998497i	$-0.517455\pi$
$313$	−1.93937	−0.109620	−0.0548098	+	0.998497i	$0.517455\pi$
$314$	−0.964200	−0.0544130
$315$	22.9956	1.29566
$316$	−5.20920	−0.293040
$317$	19.6915	1.10599	0.552994	−	0.833186i	$-0.313485\pi$
$317$	19.6915	1.10599	0.552994	+	0.833186i	$0.313485\pi$
$318$	−1.71631	−0.0962459
$319$	−18.3796	−1.02906
$320$	3.20594	0.179217
$321$	20.7491	1.15810
$322$	7.23924	0.403427
$323$	−17.5459	−0.976283
$324$	−7.47029	−0.415016
$325$	−15.2992	−0.848649
$326$	−1.54555	−0.0855999
$327$	−1.27693	−0.0706144
$328$	−11.2196	−0.619500
$329$	−15.1967	−0.837820
$330$	−25.9536	−1.42870
$331$	−20.0451	−1.10178	−0.550889	−	0.834578i	$-0.685711\pi$
$331$	−20.0451	−1.10178	−0.550889	+	0.834578i	$0.685711\pi$
$332$	15.9201	0.873727
$333$	8.72885	0.478338
$334$	24.8238	1.35830
$335$	−17.8530	−0.975411
$336$	−5.28678	−0.288418
$337$	17.2605	0.940237	0.470119	−	0.882603i	$-0.344211\pi$
$337$	17.2605	0.940237	0.470119	+	0.882603i	$0.344211\pi$
$338$	4.59776	0.250085
$339$	−9.19910	−0.499627
$340$	−21.5897	−1.17087
$341$	−27.6563	−1.49768
$342$	−8.97359	−0.485236
$343$	−20.1237	−1.08658
$344$	9.37850	0.505655
$345$	28.2893	1.52304
$346$	−3.45824	−0.185916
$347$	22.4044	1.20273	0.601365	−	0.798974i	$-0.294624\pi$
$347$	22.4044	1.20273	0.601365	+	0.798974i	$0.294624\pi$
$348$	−14.6305	−0.784277
$349$	−28.3268	−1.51630	−0.758150	−	0.652080i	$-0.773897\pi$
$349$	−28.3268	−1.51630	−0.758150	+	0.652080i	$0.773897\pi$
$350$	−10.9921	−0.587553
$351$	3.26819	0.174443
$352$	3.18904	0.169976
$353$	−26.1323	−1.39088	−0.695442	−	0.718582i	$-0.744791\pi$
$353$	−26.1323	−1.39088	−0.695442	+	0.718582i	$0.744791\pi$
$354$	−0.0848350	−0.00450893
$355$	22.4565	1.19187
$356$	3.39080	0.179712
$357$	35.6028	1.88430
$358$	9.70147	0.512738
$359$	−26.5231	−1.39983	−0.699917	−	0.714225i	$-0.746780\pi$
$359$	−26.5231	−1.39983	−0.699917	+	0.714225i	$0.746780\pi$
$360$	−11.0417	−0.581950
$361$	−12.2116	−0.642715
$362$	12.9295	0.679561
$363$	2.10708	0.110593
$364$	−6.03679	−0.316414
$365$	10.5490	0.552160
$366$	−29.1784	−1.52518
$367$	19.1470	0.999466	0.499733	−	0.866180i	$-0.333431\pi$
$367$	19.1470	0.999466	0.499733	+	0.866180i	$0.333431\pi$
$368$	−3.47603	−0.181201
$369$	38.6420	2.01162
$370$	−8.12513	−0.422406
$371$	−1.40806	−0.0731030
$372$	−22.0150	−1.14142
$373$	−5.28395	−0.273592	−0.136796	−	0.990599i	$-0.543681\pi$
$373$	−5.28395	−0.273592	−0.136796	+	0.990599i	$0.543681\pi$
$374$	−21.4759	−1.11049
$375$	−2.26274	−0.116847
$376$	7.29692	0.376310
$377$	−16.7061	−0.860406
$378$	2.34811	0.120774
$379$	37.1038	1.90590	0.952948	−	0.303133i	$-0.0980326\pi$
$379$	37.1038	1.90590	0.952948	+	0.303133i	$0.0980326\pi$
$380$	8.35294	0.428497
$381$	22.1443	1.13449
$382$	7.75599	0.396831
$383$	4.66717	0.238481	0.119241	−	0.992865i	$-0.461954\pi$
$383$	4.66717	0.238481	0.119241	+	0.992865i	$0.461954\pi$
$384$	2.53853	0.129544
$385$	−21.2923	−1.08516
$386$	−16.2567	−0.827445
$387$	−32.3009	−1.64195
$388$	−3.04429	−0.154550
$389$	−15.4239	−0.782024	−0.391012	−	0.920386i	$-0.627875\pi$
$389$	−15.4239	−0.782024	−0.391012	+	0.920386i	$0.627875\pi$
$390$	−23.5904	−1.19455
$391$	23.4087	1.18383
$392$	2.66272	0.134487
$393$	39.4376	1.98937
$394$	−8.94741	−0.450764
$395$	−16.7004	−0.840287
$396$	−10.9835	−0.551942
$397$	−15.9787	−0.801948	−0.400974	−	0.916089i	$-0.631328\pi$
$397$	−15.9787	−0.801948	−0.400974	+	0.916089i	$0.631328\pi$
$398$	25.1709	1.26170
$399$	−13.7745	−0.689588
$400$	5.27803	0.263902
$401$	1.30054	0.0649461	0.0324730	−	0.999473i	$-0.489662\pi$
$401$	1.30054	0.0649461	0.0324730	+	0.999473i	$0.489662\pi$
$402$	−14.1364	−0.705058
$403$	−25.1381	−1.25222
$404$	13.3838	0.665871
$405$	−23.9493	−1.19005
$406$	−12.0029	−0.595693
$407$	−8.08230	−0.400625
$408$	−17.0952	−0.846340
$409$	−15.9592	−0.789130	−0.394565	−	0.918868i	$-0.629105\pi$
$409$	−15.9592	−0.789130	−0.394565	+	0.918868i	$0.629105\pi$
$410$	−35.9694	−1.77640
$411$	−39.5257	−1.94966
$412$	−16.1643	−0.796358
$413$	−0.0695987	−0.00342473
$414$	11.9720	0.588390
$415$	51.0387	2.50539
$416$	2.89866	0.142119
$417$	3.30252	0.161725
$418$	8.30891	0.406402
$419$	3.52193	0.172058	0.0860288	−	0.996293i	$-0.472582\pi$
$419$	3.52193	0.172058	0.0860288	+	0.996293i	$0.472582\pi$
$420$	−16.9491	−0.827031
$421$	16.0418	0.781828	0.390914	−	0.920427i	$-0.372159\pi$
$421$	16.0418	0.781828	0.390914	+	0.920427i	$0.372159\pi$
$422$	22.0701	1.07435
$423$	−25.1317	−1.22194
$424$	0.676103	0.0328345
$425$	−35.5439	−1.72413
$426$	17.7815	0.861518
$427$	−23.9380	−1.15844
$428$	−8.17366	−0.395089
$429$	−23.4660	−1.13295
$430$	30.0669	1.44995
$431$	5.94149	0.286191	0.143096	−	0.989709i	$-0.454294\pi$
$431$	5.94149	0.286191	0.143096	+	0.989709i	$0.454294\pi$
$432$	−1.12748	−0.0542460
$433$	−2.47593	−0.118986	−0.0594929	−	0.998229i	$-0.518948\pi$
$433$	−2.47593	−0.118986	−0.0594929	+	0.998229i	$0.518948\pi$
$434$	−18.0611	−0.866960
$435$	−46.9045	−2.24890
$436$	0.503019	0.0240903
$437$	−9.05667	−0.433239
$438$	8.35293	0.399118
$439$	−19.9922	−0.954174	−0.477087	−	0.878856i	$-0.658307\pi$
$439$	−19.9922	−0.954174	−0.477087	+	0.878856i	$0.658307\pi$
$440$	10.2239	0.487403
$441$	−9.17079	−0.436704
$442$	−19.5205	−0.928493
$443$	15.1569	0.720126	0.360063	−	0.932928i	$-0.382755\pi$
$443$	15.1569	0.720126	0.360063	+	0.932928i	$0.382755\pi$
$444$	−6.43366	−0.305328
$445$	10.8707	0.515321
$446$	23.2649	1.10162
$447$	−53.6126	−2.53579
$448$	2.08261	0.0983943
$449$	4.76164	0.224716	0.112358	−	0.993668i	$-0.464160\pi$
$449$	4.76164	0.224716	0.112358	+	0.993668i	$0.464160\pi$
$450$	−18.1783	−0.856934
$451$	−35.7798	−1.68480
$452$	3.62379	0.170449
$453$	−21.9197	−1.02988
$454$	17.4009	0.816665
$455$	−19.3536	−0.907310
$456$	6.61404	0.309731
$457$	36.2187	1.69424	0.847119	−	0.531402i	$-0.178335\pi$
$457$	36.2187	1.69424	0.847119	+	0.531402i	$0.178335\pi$
$458$	2.85336	0.133329
$459$	7.59280	0.354401
$460$	−11.1439	−0.519589
$461$	−7.99677	−0.372447	−0.186223	−	0.982507i	$-0.559625\pi$
$461$	−7.99677	−0.372447	−0.186223	+	0.982507i	$0.559625\pi$
$462$	−16.8598	−0.784387
$463$	31.4475	1.46149	0.730744	−	0.682651i	$-0.239173\pi$
$463$	31.4475	1.46149	0.730744	+	0.682651i	$0.239173\pi$
$464$	5.76337	0.267558
$465$	−70.5786	−3.27300
$466$	11.6320	0.538842
$467$	28.6239	1.32455	0.662277	−	0.749259i	$-0.269590\pi$
$467$	28.6239	1.32455	0.662277	+	0.749259i	$0.269590\pi$
$468$	−9.98342	−0.461484
$469$	−11.5975	−0.535522
$470$	23.3935	1.07906
$471$	−2.44765	−0.112782
$472$	0.0334189	0.00153823
$473$	29.9084	1.37519
$474$	−13.2237	−0.607386
$475$	13.7517	0.630971
$476$	−14.0250	−0.642833
$477$	−2.32860	−0.106619
$478$	4.90254	0.224237
$479$	12.0863	0.552237	0.276119	−	0.961124i	$-0.410952\pi$
$479$	12.0863	0.552237	0.276119	+	0.961124i	$0.410952\pi$
$480$	8.13838	0.371464
$481$	−7.34637	−0.334966
$482$	7.58819	0.345632
$483$	18.3770	0.836184
$484$	−0.830037	−0.0377290
$485$	−9.75979	−0.443169
$486$	−22.3460	−1.01364
$487$	−3.63117	−0.164544	−0.0822721	−	0.996610i	$-0.526218\pi$
$487$	−3.63117	−0.164544	−0.0822721	+	0.996610i	$0.526218\pi$
$488$	11.4942	0.520319
$489$	−3.92342	−0.177423
$490$	8.53650	0.385640
$491$	1.69766	0.0766145	0.0383072	−	0.999266i	$-0.487803\pi$
$491$	1.69766	0.0766145	0.0383072	+	0.999266i	$0.487803\pi$
$492$	−28.4814	−1.28404
$493$	−38.8123	−1.74802
$494$	7.55234	0.339796
$495$	−35.2125	−1.58268
$496$	8.67232	0.389399
$497$	14.5880	0.654361
$498$	40.4136	1.81098
$499$	−35.0558	−1.56931	−0.784656	−	0.619931i	$-0.787161\pi$
$499$	−35.0558	−1.56931	−0.784656	+	0.619931i	$0.787161\pi$
$500$	0.891356	0.0398626
$501$	63.0161	2.81535
$502$	−14.2175	−0.634557
$503$	34.6286	1.54401	0.772007	−	0.635614i	$-0.219253\pi$
$503$	34.6286	1.54401	0.772007	+	0.635614i	$0.219253\pi$
$504$	−7.17283	−0.319503
$505$	42.9077	1.90937
$506$	−11.0852	−0.492797
$507$	11.6716	0.518353
$508$	−8.72326	−0.387032
$509$	−13.8096	−0.612101	−0.306050	−	0.952015i	$-0.599008\pi$
$509$	−13.8096	−0.612101	−0.306050	+	0.952015i	$0.599008\pi$
$510$	−54.8063	−2.42686
$511$	6.85275	0.303148
$512$	−1.00000	−0.0441942
$513$	−2.93761	−0.129699
$514$	−2.94251	−0.129788
$515$	−51.8217	−2.28354
$516$	23.8076	1.04807
$517$	23.2702	1.02342
$518$	−5.27818	−0.231910
$519$	−8.77885	−0.385349
$520$	9.29293	0.407522
$521$	43.6817	1.91373	0.956865	−	0.290534i	$-0.0938331\pi$
$521$	43.6817	1.91373	0.956865	+	0.290534i	$0.0938331\pi$
$522$	−19.8499	−0.868806
$523$	−37.3086	−1.63139	−0.815696	−	0.578481i	$-0.803646\pi$
$523$	−37.3086	−1.63139	−0.815696	+	0.578481i	$0.803646\pi$
$524$	−15.5356	−0.678676
$525$	−27.9038	−1.21782
$526$	24.0038	1.04662
$527$	−58.4020	−2.54403
$528$	8.09548	0.352310
$529$	−10.9172	−0.474660
$530$	2.16754	0.0941521
$531$	−0.115100	−0.00499490
$532$	5.42617	0.235254
$533$	−32.5219	−1.40868
$534$	8.60766	0.372490
$535$	−26.2043	−1.13291
$536$	5.56872	0.240532
$537$	24.6275	1.06275
$538$	3.16034	0.136252
$539$	8.49150	0.365755
$540$	−3.61463	−0.155549
$541$	31.7366	1.36446	0.682231	−	0.731136i	$-0.261010\pi$
$541$	31.7366	1.36446	0.682231	+	0.731136i	$0.261010\pi$
$542$	−10.0643	−0.432300
$543$	32.8220	1.40853
$544$	6.73430	0.288731
$545$	1.61265	0.0690783
$546$	−15.3246	−0.655832
$547$	−26.9670	−1.15303	−0.576513	−	0.817088i	$-0.695587\pi$
$547$	−26.9670	−1.15303	−0.576513	+	0.817088i	$0.695587\pi$
$548$	15.5703	0.665130
$549$	−39.5878	−1.68957
$550$	16.8318	0.717712
$551$	15.0162	0.639713
$552$	−8.82403	−0.375575
$553$	−10.8488	−0.461336
$554$	9.25315	0.393129
$555$	−20.6259	−0.875521
$556$	−1.30096	−0.0551728
$557$	5.40420	0.228983	0.114492	−	0.993424i	$-0.463476\pi$
$557$	5.40420	0.228983	0.114492	+	0.993424i	$0.463476\pi$
$558$	−29.8687	−1.26444
$559$	27.1851	1.14981
$560$	6.67673	0.282143
$561$	−54.5174	−2.30172
$562$	−8.18271	−0.345167
$563$	−21.9812	−0.926397	−0.463199	−	0.886255i	$-0.653298\pi$
$563$	−21.9812	−0.926397	−0.463199	+	0.886255i	$0.653298\pi$
$564$	18.5235	0.779979
$565$	11.6176	0.488758
$566$	−24.1637	−1.01568
$567$	−15.5577	−0.653364
$568$	−7.00465	−0.293909
$569$	10.4913	0.439818	0.219909	−	0.975520i	$-0.429424\pi$
$569$	10.4913	0.439818	0.219909	+	0.975520i	$0.429424\pi$
$570$	21.2042	0.888147
$571$	−35.3614	−1.47983	−0.739915	−	0.672700i	$-0.765134\pi$
$571$	−35.3614	−1.47983	−0.739915	+	0.672700i	$0.765134\pi$
$572$	9.24394	0.386509
$573$	19.6888	0.822512
$574$	−23.3661	−0.975284
$575$	−18.3466	−0.765107
$576$	3.44415	0.143506
$577$	−40.6064	−1.69046	−0.845232	−	0.534399i	$-0.820538\pi$
$577$	−40.6064	−1.69046	−0.845232	+	0.534399i	$0.820538\pi$
$578$	−28.3508	−1.17924
$579$	−41.2682	−1.71505
$580$	18.4770	0.767216
$581$	33.1554	1.37552
$582$	−7.72802	−0.320337
$583$	2.15612	0.0892973
$584$	−3.29046	−0.136160
$585$	−32.0062	−1.32329
$586$	28.4192	1.17399
$587$	24.5617	1.01377	0.506885	−	0.862013i	$-0.330797\pi$
$587$	24.5617	1.01377	0.506885	+	0.862013i	$0.330797\pi$
$588$	6.75939	0.278753
$589$	22.5954	0.931026
$590$	0.107139	0.00441084
$591$	−22.7133	−0.934300
$592$	2.53440	0.104163
$593$	−1.67154	−0.0686418	−0.0343209	−	0.999411i	$-0.510927\pi$
$593$	−1.67154	−0.0686418	−0.0343209	+	0.999411i	$0.510927\pi$
$594$	−3.59558	−0.147528
$595$	−44.9631	−1.84331
$596$	21.1195	0.865090
$597$	63.8970	2.61513
$598$	−10.0758	−0.412032
$599$	−26.7568	−1.09325	−0.546626	−	0.837377i	$-0.684088\pi$
$599$	−26.7568	−1.09325	−0.546626	+	0.837377i	$0.684088\pi$
$600$	13.3985	0.546990
$601$	16.5178	0.673776	0.336888	−	0.941545i	$-0.390626\pi$
$601$	16.5178	0.673776	0.336888	+	0.941545i	$0.390626\pi$
$602$	19.5318	0.796057
$603$	−19.1795	−0.781049
$604$	8.63478	0.351344
$605$	−2.66105	−0.108187
$606$	33.9753	1.38015
$607$	12.6327	0.512744	0.256372	−	0.966578i	$-0.417473\pi$
$607$	12.6327	0.512744	0.256372	+	0.966578i	$0.417473\pi$
$608$	−2.60546	−0.105665
$609$	−30.4697	−1.23469
$610$	36.8497	1.49200
$611$	21.1513	0.855691
$612$	−23.1939	−0.937559
$613$	−31.5075	−1.27257	−0.636287	−	0.771452i	$-0.719531\pi$
$613$	−31.5075	−1.27257	−0.636287	+	0.771452i	$0.719531\pi$
$614$	−3.92738	−0.158496
$615$	−91.3095	−3.68195
$616$	6.64154	0.267595
$617$	11.1508	0.448913	0.224456	−	0.974484i	$-0.427939\pi$
$617$	11.1508	0.448913	0.224456	+	0.974484i	$0.427939\pi$
$618$	−41.0336	−1.65061
$619$	−22.3405	−0.897940	−0.448970	−	0.893547i	$-0.648209\pi$
$619$	−22.3405	−0.897940	−0.448970	+	0.893547i	$0.648209\pi$
$620$	27.8029	1.11659
$621$	3.91916	0.157271
$622$	3.87896	0.155532
$623$	7.06174	0.282922
$624$	7.35835	0.294570
$625$	−23.5325	−0.941301
$626$	1.93937	0.0775127
$627$	21.0924	0.842351
$628$	0.964200	0.0384758
$629$	−17.0674	−0.680523
$630$	−22.9956	−0.916168
$631$	−22.6577	−0.901988	−0.450994	−	0.892527i	$-0.648930\pi$
$631$	−22.6577	−0.901988	−0.450994	+	0.892527i	$0.648930\pi$
$632$	5.20920	0.207211
$633$	56.0256	2.22682
$634$	−19.6915	−0.782051
$635$	−27.9662	−1.10981
$636$	1.71631	0.0680561
$637$	7.71831	0.305811
$638$	18.3796	0.727656
$639$	24.1251	0.954373
$640$	−3.20594	−0.126726
$641$	−1.33756	−0.0528303	−0.0264151	−	0.999651i	$-0.508409\pi$
$641$	−1.33756	−0.0528303	−0.0264151	+	0.999651i	$0.508409\pi$
$642$	−20.7491	−0.818902
$643$	41.5631	1.63909	0.819544	−	0.573016i	$-0.194227\pi$
$643$	41.5631	1.63909	0.819544	+	0.573016i	$0.194227\pi$
$644$	−7.23924	−0.285266
$645$	76.3258	3.00532
$646$	17.5459	0.690336
$647$	−43.4388	−1.70775	−0.853877	−	0.520474i	$-0.825755\pi$
$647$	−43.4388	−1.70775	−0.853877	+	0.520474i	$0.825755\pi$
$648$	7.47029	0.293461
$649$	0.106574	0.00418340
$650$	15.2992	0.600085
$651$	−45.8487	−1.79695
$652$	1.54555	0.0605283
$653$	−41.6228	−1.62883	−0.814413	−	0.580286i	$-0.802941\pi$
$653$	−41.6228	−1.62883	−0.814413	+	0.580286i	$0.802941\pi$
$654$	1.27693	0.0499319
$655$	−49.8062	−1.94609
$656$	11.2196	0.438053
$657$	11.3328	0.442135
$658$	15.1967	0.592428
$659$	2.28015	0.0888222	0.0444111	−	0.999013i	$-0.485859\pi$
$659$	2.28015	0.0888222	0.0444111	+	0.999013i	$0.485859\pi$
$660$	25.9536	1.01024
$661$	32.9028	1.27977	0.639885	−	0.768471i	$-0.278982\pi$
$661$	32.9028	1.27977	0.639885	+	0.768471i	$0.278982\pi$
$662$	20.0451	0.779075
$663$	−49.5533	−1.92449
$664$	−15.9201	−0.617818
$665$	17.3960	0.674586
$666$	−8.72885	−0.338236
$667$	−20.0337	−0.775707
$668$	−24.8238	−0.960463
$669$	59.0586	2.28334
$670$	17.8530	0.689720
$671$	36.6555	1.41507
$672$	5.28678	0.203942
$673$	−20.6621	−0.796465	−0.398233	−	0.917284i	$-0.630376\pi$
$673$	−20.6621	−0.796465	−0.398233	+	0.917284i	$0.630376\pi$
$674$	−17.2605	−0.664848
$675$	−5.95088	−0.229050
$676$	−4.59776	−0.176837
$677$	−5.69968	−0.219057	−0.109528	−	0.993984i	$-0.534934\pi$
$677$	−5.69968	−0.219057	−0.109528	+	0.993984i	$0.534934\pi$
$678$	9.19910	0.353289
$679$	−6.34008	−0.243310
$680$	21.5897	0.827929
$681$	44.1728	1.69270
$682$	27.6563	1.05902
$683$	−28.7176	−1.09885	−0.549424	−	0.835544i	$-0.685153\pi$
$683$	−28.7176	−1.09885	−0.549424	+	0.835544i	$0.685153\pi$
$684$	8.97359	0.343114
$685$	49.9174	1.90725
$686$	20.1237	0.768327
$687$	7.24335	0.276351
$688$	−9.37850	−0.357552
$689$	1.95979	0.0746622
$690$	−28.2893	−1.07695
$691$	−39.2726	−1.49400	−0.747000	−	0.664824i	$-0.768506\pi$
$691$	−39.2726	−1.49400	−0.747000	+	0.664824i	$0.768506\pi$
$692$	3.45824	0.131462
$693$	−22.8744	−0.868928
$694$	−22.4044	−0.850459
$695$	−4.17078	−0.158207
$696$	14.6305	0.554568
$697$	−75.5563	−2.86190
$698$	28.3268	1.07219
$699$	29.5282	1.11686
$700$	10.9921	0.415463
$701$	13.2235	0.499445	0.249723	−	0.968317i	$-0.419661\pi$
$701$	13.2235	0.499445	0.249723	+	0.968317i	$0.419661\pi$
$702$	−3.26819	−0.123350
$703$	6.60328	0.249047
$704$	−3.18904	−0.120191
$705$	59.3851	2.23657
$706$	26.1323	0.983503
$707$	27.8734	1.04829
$708$	0.0848350	0.00318830
$709$	−31.0046	−1.16440	−0.582201	−	0.813045i	$-0.697808\pi$
$709$	−31.0046	−1.16440	−0.582201	+	0.813045i	$0.697808\pi$
$710$	−22.4565	−0.842777
$711$	−17.9412	−0.672849
$712$	−3.39080	−0.127076
$713$	−30.1453	−1.12895
$714$	−35.6028	−1.33240
$715$	29.6355	1.10830
$716$	−9.70147	−0.362561
$717$	12.4453	0.464777
$718$	26.5231	0.989831
$719$	−27.2148	−1.01494	−0.507470	−	0.861669i	$-0.669419\pi$
$719$	−27.2148	−1.01494	−0.507470	+	0.861669i	$0.669419\pi$
$720$	11.0417	0.411501
$721$	−33.6640	−1.25371
$722$	12.2116	0.454468
$723$	19.2629	0.716393
$724$	−12.9295	−0.480522
$725$	30.4193	1.12974
$726$	−2.10708	−0.0782009
$727$	24.6962	0.915930	0.457965	−	0.888970i	$-0.348578\pi$
$727$	24.6962	0.915930	0.457965	+	0.888970i	$0.348578\pi$
$728$	6.03679	0.223738
$729$	−34.3152	−1.27093
$730$	−10.5490	−0.390436
$731$	63.1576	2.33597
$732$	29.1784	1.07847
$733$	1.79787	0.0664057	0.0332028	−	0.999449i	$-0.489429\pi$
$733$	1.79787	0.0664057	0.0332028	+	0.999449i	$0.489429\pi$
$734$	−19.1470	−0.706729
$735$	21.6702	0.799317
$736$	3.47603	0.128128
$737$	17.7588	0.654155
$738$	−38.6420	−1.42243
$739$	−12.6872	−0.466707	−0.233354	−	0.972392i	$-0.574970\pi$
$739$	−12.6872	−0.466707	−0.233354	+	0.972392i	$0.574970\pi$
$740$	8.12513	0.298686
$741$	19.1719	0.704296
$742$	1.40806	0.0516916
$743$	−32.5122	−1.19276	−0.596379	−	0.802703i	$-0.703394\pi$
$743$	−32.5122	−1.19276	−0.596379	+	0.802703i	$0.703394\pi$
$744$	22.0150	0.807108
$745$	67.7079	2.48062
$746$	5.28395	0.193459
$747$	54.8311	2.00616
$748$	21.4759	0.785238
$749$	−17.0226	−0.621992
$750$	2.26274	0.0826234
$751$	−36.8790	−1.34573	−0.672867	−	0.739763i	$-0.734937\pi$
$751$	−36.8790	−1.34573	−0.672867	+	0.739763i	$0.734937\pi$
$752$	−7.29692	−0.266091
$753$	−36.0916	−1.31525
$754$	16.7061	0.608399
$755$	27.6826	1.00747
$756$	−2.34811	−0.0853999
$757$	17.2314	0.626284	0.313142	−	0.949706i	$-0.398618\pi$
$757$	17.2314	0.626284	0.313142	+	0.949706i	$0.398618\pi$
$758$	−37.1038	−1.34767
$759$	−28.1402	−1.02142
$760$	−8.35294	−0.302993
$761$	28.0509	1.01684	0.508421	−	0.861108i	$-0.330229\pi$
$761$	28.0509	1.01684	0.508421	+	0.861108i	$0.330229\pi$
$762$	−22.1443	−0.802203
$763$	1.04760	0.0379255
$764$	−7.75599	−0.280602
$765$	−74.3582	−2.68843
$766$	−4.66717	−0.168632
$767$	0.0968701	0.00349778
$768$	−2.53853	−0.0916014
$769$	33.9937	1.22584	0.612921	−	0.790144i	$-0.289994\pi$
$769$	33.9937	1.22584	0.612921	+	0.790144i	$0.289994\pi$
$770$	21.2923	0.767323
$771$	−7.46965	−0.269013
$772$	16.2567	0.585092
$773$	−9.46422	−0.340404	−0.170202	−	0.985409i	$-0.554442\pi$
$773$	−9.46422	−0.340404	−0.170202	+	0.985409i	$0.554442\pi$
$774$	32.3009	1.16103
$775$	45.7728	1.64421
$776$	3.04429	0.109284
$777$	−13.3988	−0.480681
$778$	15.4239	0.552974
$779$	29.2323	1.04735
$780$	23.5904	0.844672
$781$	−22.3381	−0.799320
$782$	−23.4087	−0.837092
$783$	−6.49809	−0.232223
$784$	−2.66272	−0.0950970
$785$	3.09116	0.110328
$786$	−39.4376	−1.40669
$787$	−44.0511	−1.57025	−0.785127	−	0.619335i	$-0.787402\pi$
$787$	−44.0511	−1.57025	−0.785127	+	0.619335i	$0.787402\pi$
$788$	8.94741	0.318738
$789$	60.9344	2.16932
$790$	16.7004	0.594172
$791$	7.54695	0.268339
$792$	10.9835	0.390282
$793$	33.3178	1.18315
$794$	15.9787	0.567063
$795$	5.50238	0.195149
$796$	−25.1709	−0.892157
$797$	−38.2685	−1.35554	−0.677771	−	0.735274i	$-0.737054\pi$
$797$	−38.2685	−1.35554	−0.677771	+	0.735274i	$0.737054\pi$
$798$	13.7745	0.487612
$799$	49.1397	1.73844
$800$	−5.27803	−0.186607
$801$	11.6784	0.412637
$802$	−1.30054	−0.0459238
$803$	−10.4934	−0.370304
$804$	14.1364	0.498551
$805$	−23.2085	−0.817994
$806$	25.1381	0.885452
$807$	8.02262	0.282410
$808$	−13.3838	−0.470842
$809$	−18.4191	−0.647582	−0.323791	−	0.946129i	$-0.604957\pi$
$809$	−18.4191	−0.647582	−0.323791	+	0.946129i	$0.604957\pi$
$810$	23.9493	0.841492
$811$	34.0567	1.19589	0.597946	−	0.801536i	$-0.295984\pi$
$811$	34.0567	1.19589	0.597946	+	0.801536i	$0.295984\pi$
$812$	12.0029	0.421218
$813$	−25.5486	−0.896029
$814$	8.08230	0.283285
$815$	4.95492	0.173563
$816$	17.0952	0.598453
$817$	−24.4353	−0.854883
$818$	15.9592	0.557999
$819$	−20.7916	−0.726518
$820$	35.9694	1.25611
$821$	6.13648	0.214165	0.107082	−	0.994250i	$-0.465849\pi$
$821$	6.13648	0.214165	0.107082	+	0.994250i	$0.465849\pi$
$822$	39.5257	1.37862
$823$	−32.4724	−1.13192	−0.565958	−	0.824434i	$-0.691493\pi$
$823$	−32.4724	−1.13192	−0.565958	+	0.824434i	$0.691493\pi$
$824$	16.1643	0.563110
$825$	42.7282	1.48760
$826$	0.0695987	0.00242165
$827$	−1.35550	−0.0471352	−0.0235676	−	0.999722i	$-0.507503\pi$
$827$	−1.35550	−0.0471352	−0.0235676	+	0.999722i	$0.507503\pi$
$828$	−11.9720	−0.416055
$829$	−15.0118	−0.521382	−0.260691	−	0.965422i	$-0.583950\pi$
$829$	−15.0118	−0.521382	−0.260691	+	0.965422i	$0.583950\pi$
$830$	−51.0387	−1.77158
$831$	23.4894	0.814839
$832$	−2.89866	−0.100493
$833$	17.9315	0.621291
$834$	−3.30252	−0.114357
$835$	−79.5837	−2.75411
$836$	−8.30891	−0.287370
$837$	−9.77787	−0.337973
$838$	−3.52193	−0.121663
$839$	−33.9559	−1.17229	−0.586145	−	0.810206i	$-0.699355\pi$
$839$	−33.9559	−1.17229	−0.586145	+	0.810206i	$0.699355\pi$
$840$	16.9491	0.584799
$841$	4.21643	0.145394
$842$	−16.0418	−0.552836
$843$	−20.7721	−0.715428
$844$	−22.0701	−0.759683
$845$	−14.7401	−0.507076
$846$	25.1317	0.864045
$847$	−1.72865	−0.0593970
$848$	−0.676103	−0.0232175
$849$	−61.3403	−2.10519
$850$	35.5439	1.21914
$851$	−8.80967	−0.301992
$852$	−17.7815	−0.609186
$853$	15.4879	0.530297	0.265149	−	0.964208i	$-0.414579\pi$
$853$	15.4879	0.530297	0.265149	+	0.964208i	$0.414579\pi$
$854$	23.9380	0.819142
$855$	28.7687	0.983870
$856$	8.17366	0.279370
$857$	4.12226	0.140814	0.0704069	−	0.997518i	$-0.477570\pi$
$857$	4.12226	0.140814	0.0704069	+	0.997518i	$0.477570\pi$
$858$	23.4660	0.801118
$859$	50.5497	1.72473	0.862366	−	0.506285i	$-0.168981\pi$
$859$	50.5497	1.72473	0.862366	+	0.506285i	$0.168981\pi$
$860$	−30.0669	−1.02527
$861$	−59.3157	−2.02147
$862$	−5.94149	−0.202368
$863$	−44.1052	−1.50136	−0.750680	−	0.660666i	$-0.770274\pi$
$863$	−44.1052	−1.50136	−0.750680	+	0.660666i	$0.770274\pi$
$864$	1.12748	0.0383577
$865$	11.0869	0.376966
$866$	2.47593	0.0841357
$867$	−71.9694	−2.44421
$868$	18.0611	0.613033
$869$	16.6123	0.563535
$870$	46.9045	1.59021
$871$	16.1418	0.546945
$872$	−0.503019	−0.0170344
$873$	−10.4850	−0.354863
$874$	9.05667	0.306346
$875$	1.85635	0.0627561
$876$	−8.35293	−0.282219
$877$	−52.6835	−1.77900	−0.889498	−	0.456938i	$-0.848946\pi$
$877$	−52.6835	−1.77900	−0.889498	+	0.456938i	$0.848946\pi$
$878$	19.9922	0.674703
$879$	72.1430	2.43332
$880$	−10.2239	−0.344646
$881$	−44.3335	−1.49363	−0.746817	−	0.665029i	$-0.768419\pi$
$881$	−44.3335	−1.49363	−0.746817	+	0.665029i	$0.768419\pi$
$882$	9.17079	0.308796
$883$	37.6203	1.26602	0.633012	−	0.774142i	$-0.281818\pi$
$883$	37.6203	1.26602	0.633012	+	0.774142i	$0.281818\pi$
$884$	19.5205	0.656544
$885$	0.271976	0.00914237
$886$	−15.1569	−0.509206
$887$	3.04643	0.102289	0.0511445	−	0.998691i	$-0.483713\pi$
$887$	3.04643	0.102289	0.0511445	+	0.998691i	$0.483713\pi$
$888$	6.43366	0.215900
$889$	−18.1672	−0.609308
$890$	−10.8707	−0.364387
$891$	23.8230	0.798102
$892$	−23.2649	−0.778966
$893$	−19.0118	−0.636207
$894$	53.6126	1.79307
$895$	−31.1023	−1.03963
$896$	−2.08261	−0.0695753
$897$	−25.5779	−0.854020
$898$	−4.76164	−0.158898
$899$	49.9818	1.66699
$900$	18.1783	0.605944
$901$	4.55308	0.151685
$902$	35.7798	1.19134
$903$	49.5821	1.64999
$904$	−3.62379	−0.120525
$905$	−41.4512	−1.37789
$906$	21.9197	0.728233
$907$	8.44968	0.280567	0.140284	−	0.990111i	$-0.455199\pi$
$907$	8.44968	0.280567	0.140284	+	0.990111i	$0.455199\pi$
$908$	−17.4009	−0.577469
$909$	46.0959	1.52890
$910$	19.3536	0.641565
$911$	24.3917	0.808134	0.404067	−	0.914729i	$-0.367596\pi$
$911$	24.3917	0.808134	0.404067	+	0.914729i	$0.367596\pi$
$912$	−6.61404	−0.219013
$913$	−50.7697	−1.68023
$914$	−36.2187	−1.19801
$915$	93.5443	3.09248
$916$	−2.85336	−0.0942777
$917$	−32.3547	−1.06845
$918$	−7.59280	−0.250600
$919$	12.2838	0.405205	0.202602	−	0.979261i	$-0.435060\pi$
$919$	12.2838	0.405205	0.202602	+	0.979261i	$0.435060\pi$
$920$	11.1439	0.367405
$921$	−9.96978	−0.328515
$922$	7.99677	0.263359
$923$	−20.3041	−0.668318
$924$	16.8598	0.554645
$925$	13.3767	0.439822
$926$	−31.4475	−1.03343
$927$	−55.6722	−1.82852
$928$	−5.76337	−0.189192
$929$	−38.8038	−1.27311	−0.636555	−	0.771231i	$-0.719641\pi$
$929$	−38.8038	−1.27311	−0.636555	+	0.771231i	$0.719641\pi$
$930$	70.5786	2.31436
$931$	−6.93760	−0.227371
$932$	−11.6320	−0.381019
$933$	9.84686	0.322372
$934$	−28.6239	−0.936601
$935$	68.8505	2.25165
$936$	9.98342	0.326318
$937$	2.63323	0.0860240	0.0430120	−	0.999075i	$-0.486305\pi$
$937$	2.63323	0.0860240	0.0430120	+	0.999075i	$0.486305\pi$
$938$	11.5975	0.378671
$939$	4.92315	0.160661
$940$	−23.3935	−0.763011
$941$	−39.5974	−1.29084	−0.645419	−	0.763828i	$-0.723317\pi$
$941$	−39.5974	−1.29084	−0.645419	+	0.763828i	$0.723317\pi$
$942$	2.44765	0.0797488
$943$	−38.9998	−1.27001
$944$	−0.0334189	−0.00108769
$945$	−7.52789	−0.244882
$946$	−29.9084	−0.972406
$947$	−16.1216	−0.523880	−0.261940	−	0.965084i	$-0.584362\pi$
$947$	−16.1216	−0.523880	−0.261940	+	0.965084i	$0.584362\pi$
$948$	13.2237	0.429486
$949$	−9.53792	−0.309614
$950$	−13.7517	−0.446164
$951$	−49.9876	−1.62096
$952$	14.0250	0.454551
$953$	−43.9020	−1.42213	−0.711063	−	0.703128i	$-0.751786\pi$
$953$	−43.9020	−1.42213	−0.711063	+	0.703128i	$0.751786\pi$
$954$	2.32860	0.0753912
$955$	−24.8652	−0.804619
$956$	−4.90254	−0.158559
$957$	46.6572	1.50821
$958$	−12.0863	−0.390491
$959$	32.4269	1.04712
$960$	−8.13838	−0.262665
$961$	44.2091	1.42610
$962$	7.34637	0.236857
$963$	−28.1513	−0.907163
$964$	−7.58819	−0.244399
$965$	52.1180	1.67774
$966$	−18.3770	−0.591272
$967$	14.4895	0.465951	0.232975	−	0.972483i	$-0.425154\pi$
$967$	14.4895	0.465951	0.232975	+	0.972483i	$0.425154\pi$
$968$	0.830037	0.0266784
$969$	44.5410	1.43086
$970$	9.75979	0.313368
$971$	33.0699	1.06126	0.530631	−	0.847603i	$-0.321955\pi$
$971$	33.0699	1.06126	0.530631	+	0.847603i	$0.321955\pi$
$972$	22.3460	0.716749
$973$	−2.70939	−0.0868590
$974$	3.63117	0.116350
$975$	38.8376	1.24380
$976$	−11.4942	−0.367921
$977$	−17.9454	−0.574123	−0.287062	−	0.957912i	$-0.592678\pi$
$977$	−17.9454	−0.574123	−0.287062	+	0.957912i	$0.592678\pi$
$978$	3.92342	0.125457
$979$	−10.8134	−0.345598
$980$	−8.53650	−0.272689
$981$	1.73247	0.0553136
$982$	−1.69766	−0.0541746
$983$	22.3770	0.713716	0.356858	−	0.934159i	$-0.383848\pi$
$983$	22.3770	0.713716	0.356858	+	0.934159i	$0.383848\pi$
$984$	28.4814	0.907953
$985$	28.6848	0.913974
$986$	38.8123	1.23603
$987$	38.5773	1.22793
$988$	−7.55234	−0.240272
$989$	32.6000	1.03662
$990$	35.2125	1.11913
$991$	−43.1424	−1.37046	−0.685231	−	0.728325i	$-0.740299\pi$
$991$	−43.1424	−1.37046	−0.685231	+	0.728325i	$0.740299\pi$
$992$	−8.67232	−0.275346
$993$	50.8851	1.61479
$994$	−14.5880	−0.462703
$995$	−80.6962	−2.55824
$996$	−40.4136	−1.28055
$997$	26.3942	0.835914	0.417957	−	0.908467i	$-0.362746\pi$
$997$	26.3942	0.835914	0.417957	+	0.908467i	$0.362746\pi$
$998$	35.0558	1.10967
$999$	−2.85749	−0.0904070

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.b.1.9	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.b.1.9	✓	56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.53853 q^{3} +1.00000 q^{4} +3.20594 q^{5} +2.53853 q^{6} +2.08261 q^{7} -1.00000 q^{8} +3.44415 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.53853 q^{3} +1.00000 q^{4} +3.20594 q^{5} +2.53853 q^{6} +2.08261 q^{7} -1.00000 q^{8} +3.44415 q^{9} -3.20594 q^{10} -3.18904 q^{11} -2.53853 q^{12} -2.89866 q^{13} -2.08261 q^{14} -8.13838 q^{15} +1.00000 q^{16} -6.73430 q^{17} -3.44415 q^{18} +2.60546 q^{19} +3.20594 q^{20} -5.28678 q^{21} +3.18904 q^{22} -3.47603 q^{23} +2.53853 q^{24} +5.27803 q^{25} +2.89866 q^{26} -1.12748 q^{27} +2.08261 q^{28} +5.76337 q^{29} +8.13838 q^{30} +8.67232 q^{31} -1.00000 q^{32} +8.09548 q^{33} +6.73430 q^{34} +6.67673 q^{35} +3.44415 q^{36} +2.53440 q^{37} -2.60546 q^{38} +7.35835 q^{39} -3.20594 q^{40} +11.2196 q^{41} +5.28678 q^{42} -9.37850 q^{43} -3.18904 q^{44} +11.0417 q^{45} +3.47603 q^{46} -7.29692 q^{47} -2.53853 q^{48} -2.66272 q^{49} -5.27803 q^{50} +17.0952 q^{51} -2.89866 q^{52} -0.676103 q^{53} +1.12748 q^{54} -10.2239 q^{55} -2.08261 q^{56} -6.61404 q^{57} -5.76337 q^{58} -0.0334189 q^{59} -8.13838 q^{60} -11.4942 q^{61} -8.67232 q^{62} +7.17283 q^{63} +1.00000 q^{64} -9.29293 q^{65} -8.09548 q^{66} -5.56872 q^{67} -6.73430 q^{68} +8.82403 q^{69} -6.67673 q^{70} +7.00465 q^{71} -3.44415 q^{72} +3.29046 q^{73} -2.53440 q^{74} -13.3985 q^{75} +2.60546 q^{76} -6.64154 q^{77} -7.35835 q^{78} -5.20920 q^{79} +3.20594 q^{80} -7.47029 q^{81} -11.2196 q^{82} +15.9201 q^{83} -5.28678 q^{84} -21.5897 q^{85} +9.37850 q^{86} -14.6305 q^{87} +3.18904 q^{88} +3.39080 q^{89} -11.0417 q^{90} -6.03679 q^{91} -3.47603 q^{92} -22.0150 q^{93} +7.29692 q^{94} +8.35294 q^{95} +2.53853 q^{96} -3.04429 q^{97} +2.66272 q^{98} -10.9835 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * q^99

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