LMFDB - Embedded newform 6026.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.27057 q^{3} +1.00000 q^{4} -0.103796 q^{5} +3.27057 q^{6} +0.553111 q^{7} -1.00000 q^{8} +7.69663 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.27057 q^{3} +1.00000 q^{4} -0.103796 q^{5} +3.27057 q^{6} +0.553111 q^{7} -1.00000 q^{8} +7.69663 q^{9} +0.103796 q^{10} +0.813628 q^{11} -3.27057 q^{12} +6.58692 q^{13} -0.553111 q^{14} +0.339471 q^{15} +1.00000 q^{16} +5.83144 q^{17} -7.69663 q^{18} +3.59717 q^{19} -0.103796 q^{20} -1.80899 q^{21} -0.813628 q^{22} -1.00000 q^{23} +3.27057 q^{24} -4.98923 q^{25} -6.58692 q^{26} -15.3607 q^{27} +0.553111 q^{28} -5.37661 q^{29} -0.339471 q^{30} -7.85678 q^{31} -1.00000 q^{32} -2.66103 q^{33} -5.83144 q^{34} -0.0574106 q^{35} +7.69663 q^{36} +0.849438 q^{37} -3.59717 q^{38} -21.5430 q^{39} +0.103796 q^{40} +2.88800 q^{41} +1.80899 q^{42} -6.56175 q^{43} +0.813628 q^{44} -0.798877 q^{45} +1.00000 q^{46} -4.80920 q^{47} -3.27057 q^{48} -6.69407 q^{49} +4.98923 q^{50} -19.0721 q^{51} +6.58692 q^{52} +3.40640 q^{53} +15.3607 q^{54} -0.0844511 q^{55} -0.553111 q^{56} -11.7648 q^{57} +5.37661 q^{58} -3.93780 q^{59} +0.339471 q^{60} +3.68508 q^{61} +7.85678 q^{62} +4.25709 q^{63} +1.00000 q^{64} -0.683695 q^{65} +2.66103 q^{66} +0.873340 q^{67} +5.83144 q^{68} +3.27057 q^{69} +0.0574106 q^{70} +6.26870 q^{71} -7.69663 q^{72} -10.8758 q^{73} -0.849438 q^{74} +16.3176 q^{75} +3.59717 q^{76} +0.450027 q^{77} +21.5430 q^{78} +5.08034 q^{79} -0.103796 q^{80} +27.1482 q^{81} -2.88800 q^{82} -14.7386 q^{83} -1.80899 q^{84} -0.605278 q^{85} +6.56175 q^{86} +17.5846 q^{87} -0.813628 q^{88} -1.29826 q^{89} +0.798877 q^{90} +3.64330 q^{91} -1.00000 q^{92} +25.6962 q^{93} +4.80920 q^{94} -0.373371 q^{95} +3.27057 q^{96} -5.53397 q^{97} +6.69407 q^{98} +6.26219 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * 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
$3$	−3.27057	−1.88826	−0.944132	−	0.329567i	$-0.893097\pi$
$3$	−3.27057	−1.88826	−0.944132	+	0.329567i	$0.893097\pi$
$4$	1.00000	0.500000
$5$	−0.103796	−0.0464189	−0.0232094	−	0.999731i	$-0.507388\pi$
$5$	−0.103796	−0.0464189	−0.0232094	+	0.999731i	$0.507388\pi$
$6$	3.27057	1.33520
$7$	0.553111	0.209056	0.104528	−	0.994522i	$-0.466667\pi$
$7$	0.553111	0.209056	0.104528	+	0.994522i	$0.466667\pi$
$8$	−1.00000	−0.353553
$9$	7.69663	2.56554
$10$	0.103796	0.0328231
$11$	0.813628	0.245318	0.122659	−	0.992449i	$-0.460858\pi$
$11$	0.813628	0.245318	0.122659	+	0.992449i	$0.460858\pi$
$12$	−3.27057	−0.944132
$13$	6.58692	1.82688	0.913442	−	0.406969i	$-0.133414\pi$
$13$	6.58692	1.82688	0.913442	+	0.406969i	$0.133414\pi$
$14$	−0.553111	−0.147825
$15$	0.339471	0.0876511
$16$	1.00000	0.250000
$17$	5.83144	1.41433	0.707166	−	0.707048i	$-0.249974\pi$
$17$	5.83144	1.41433	0.707166	+	0.707048i	$0.249974\pi$
$18$	−7.69663	−1.81411
$19$	3.59717	0.825247	0.412623	−	0.910902i	$-0.364613\pi$
$19$	3.59717	0.825247	0.412623	+	0.910902i	$0.364613\pi$
$20$	−0.103796	−0.0232094
$21$	−1.80899	−0.394754
$22$	−0.813628	−0.173466
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	3.27057	0.667602
$25$	−4.98923	−0.997845
$26$	−6.58692	−1.29180
$27$	−15.3607	−2.95616
$28$	0.553111	0.104528
$29$	−5.37661	−0.998411	−0.499205	−	0.866484i	$-0.666375\pi$
$29$	−5.37661	−0.998411	−0.499205	+	0.866484i	$0.666375\pi$
$30$	−0.339471	−0.0619787
$31$	−7.85678	−1.41112	−0.705560	−	0.708650i	$-0.749304\pi$
$31$	−7.85678	−1.41112	−0.705560	+	0.708650i	$0.749304\pi$
$32$	−1.00000	−0.176777
$33$	−2.66103	−0.463225
$34$	−5.83144	−1.00008
$35$	−0.0574106	−0.00970416
$36$	7.69663	1.28277
$37$	0.849438	0.139647	0.0698233	−	0.997559i	$-0.477756\pi$
$37$	0.849438	0.139647	0.0698233	+	0.997559i	$0.477756\pi$
$38$	−3.59717	−0.583538
$39$	−21.5430	−3.44964
$40$	0.103796	0.0164115
$41$	2.88800	0.451030	0.225515	−	0.974240i	$-0.427593\pi$
$41$	2.88800	0.451030	0.225515	+	0.974240i	$0.427593\pi$
$42$	1.80899	0.279133
$43$	−6.56175	−1.00066	−0.500329	−	0.865835i	$-0.666788\pi$
$43$	−6.56175	−1.00066	−0.500329	+	0.865835i	$0.666788\pi$
$44$	0.813628	0.122659
$45$	−0.798877	−0.119090
$46$	1.00000	0.147442
$47$	−4.80920	−0.701493	−0.350747	−	0.936470i	$-0.614072\pi$
$47$	−4.80920	−0.701493	−0.350747	+	0.936470i	$0.614072\pi$
$48$	−3.27057	−0.472066
$49$	−6.69407	−0.956295
$50$	4.98923	0.705583
$51$	−19.0721	−2.67063
$52$	6.58692	0.913442
$53$	3.40640	0.467905	0.233952	−	0.972248i	$-0.424834\pi$
$53$	3.40640	0.467905	0.233952	+	0.972248i	$0.424834\pi$
$54$	15.3607	2.09032
$55$	−0.0844511	−0.0113874
$56$	−0.553111	−0.0739126
$57$	−11.7648	−1.55828
$58$	5.37661	0.705983
$59$	−3.93780	−0.512658	−0.256329	−	0.966590i	$-0.582513\pi$
$59$	−3.93780	−0.512658	−0.256329	+	0.966590i	$0.582513\pi$
$60$	0.339471	0.0438255
$61$	3.68508	0.471826	0.235913	−	0.971774i	$-0.424192\pi$
$61$	3.68508	0.471826	0.235913	+	0.971774i	$0.424192\pi$
$62$	7.85678	0.997813
$63$	4.25709	0.536343
$64$	1.00000	0.125000
$65$	−0.683695	−0.0848019
$66$	2.66103	0.327550
$67$	0.873340	0.106695	0.0533477	−	0.998576i	$-0.483011\pi$
$67$	0.873340	0.106695	0.0533477	+	0.998576i	$0.483011\pi$
$68$	5.83144	0.707166
$69$	3.27057	0.393730
$70$	0.0574106	0.00686188
$71$	6.26870	0.743957	0.371979	−	0.928241i	$-0.378679\pi$
$71$	6.26870	0.743957	0.371979	+	0.928241i	$0.378679\pi$
$72$	−7.69663	−0.907056
$73$	−10.8758	−1.27291	−0.636455	−	0.771314i	$-0.719600\pi$
$73$	−10.8758	−1.27291	−0.636455	+	0.771314i	$0.719600\pi$
$74$	−0.849438	−0.0987451
$75$	16.3176	1.88420
$76$	3.59717	0.412623
$77$	0.450027	0.0512853
$78$	21.5430	2.43926
$79$	5.08034	0.571583	0.285792	−	0.958292i	$-0.407743\pi$
$79$	5.08034	0.571583	0.285792	+	0.958292i	$0.407743\pi$
$80$	−0.103796	−0.0116047
$81$	27.1482	3.01647
$82$	−2.88800	−0.318927
$83$	−14.7386	−1.61777	−0.808886	−	0.587965i	$-0.799929\pi$
$83$	−14.7386	−1.61777	−0.808886	+	0.587965i	$0.799929\pi$
$84$	−1.80899	−0.197377
$85$	−0.605278	−0.0656516
$86$	6.56175	0.707572
$87$	17.5846	1.88526
$88$	−0.813628	−0.0867330
$89$	−1.29826	−0.137616	−0.0688078	−	0.997630i	$-0.521920\pi$
$89$	−1.29826	−0.137616	−0.0688078	+	0.997630i	$0.521920\pi$
$90$	0.798877	0.0842090
$91$	3.64330	0.381922
$92$	−1.00000	−0.104257
$93$	25.6962	2.66457
$94$	4.80920	0.496031
$95$	−0.373371	−0.0383070
$96$	3.27057	0.333801
$97$	−5.53397	−0.561890	−0.280945	−	0.959724i	$-0.590648\pi$
$97$	−5.53397	−0.561890	−0.280945	+	0.959724i	$0.590648\pi$
$98$	6.69407	0.676203
$99$	6.26219	0.629374
$100$	−4.98923	−0.498923
$101$	−6.54370	−0.651122	−0.325561	−	0.945521i	$-0.605553\pi$
$101$	−6.54370	−0.651122	−0.325561	+	0.945521i	$0.605553\pi$
$102$	19.0721	1.88842
$103$	−15.6836	−1.54535	−0.772674	−	0.634803i	$-0.781081\pi$
$103$	−15.6836	−1.54535	−0.772674	+	0.634803i	$0.781081\pi$
$104$	−6.58692	−0.645901
$105$	0.187765	0.0183240
$106$	−3.40640	−0.330859
$107$	12.2966	1.18875	0.594377	−	0.804187i	$-0.297399\pi$
$107$	12.2966	1.18875	0.594377	+	0.804187i	$0.297399\pi$
$108$	−15.3607	−1.47808
$109$	−17.0299	−1.63117	−0.815587	−	0.578635i	$-0.803586\pi$
$109$	−17.0299	−1.63117	−0.815587	+	0.578635i	$0.803586\pi$
$110$	0.0844511	0.00805210
$111$	−2.77815	−0.263690
$112$	0.553111	0.0522641
$113$	10.7077	1.00730	0.503650	−	0.863908i	$-0.331990\pi$
$113$	10.7077	1.00730	0.503650	+	0.863908i	$0.331990\pi$
$114$	11.7648	1.10187
$115$	0.103796	0.00967900
$116$	−5.37661	−0.499205
$117$	50.6971	4.68695
$118$	3.93780	0.362504
$119$	3.22543	0.295675
$120$	−0.339471	−0.0309893
$121$	−10.3380	−0.939819
$122$	−3.68508	−0.333631
$123$	−9.44542	−0.851665
$124$	−7.85678	−0.705560
$125$	1.03684	0.0927377
$126$	−4.25709	−0.379252
$127$	−11.4513	−1.01614	−0.508070	−	0.861315i	$-0.669641\pi$
$127$	−11.4513	−1.01614	−0.508070	+	0.861315i	$0.669641\pi$
$128$	−1.00000	−0.0883883
$129$	21.4607	1.88951
$130$	0.683695	0.0599640
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−2.66103	−0.231613
$133$	1.98963	0.172523
$134$	−0.873340	−0.0754451
$135$	1.59437	0.137222
$136$	−5.83144	−0.500042
$137$	5.16549	0.441317	0.220659	−	0.975351i	$-0.429179\pi$
$137$	5.16549	0.441317	0.220659	+	0.975351i	$0.429179\pi$
$138$	−3.27057	−0.278409
$139$	−8.99810	−0.763209	−0.381605	−	0.924326i	$-0.624628\pi$
$139$	−8.99810	−0.763209	−0.381605	+	0.924326i	$0.624628\pi$
$140$	−0.0574106	−0.00485208
$141$	15.7288	1.32460
$142$	−6.26870	−0.526057
$143$	5.35930	0.448168
$144$	7.69663	0.641386
$145$	0.558069	0.0463451
$146$	10.8758	0.900084
$147$	21.8934	1.80574
$148$	0.849438	0.0698233
$149$	−9.32690	−0.764090	−0.382045	−	0.924144i	$-0.624780\pi$
$149$	−9.32690	−0.764090	−0.382045	+	0.924144i	$0.624780\pi$
$150$	−16.3176	−1.33233
$151$	0.997646	0.0811873	0.0405936	−	0.999176i	$-0.487075\pi$
$151$	0.997646	0.0811873	0.0405936	+	0.999176i	$0.487075\pi$
$152$	−3.59717	−0.291769
$153$	44.8824	3.62853
$154$	−0.450027	−0.0362642
$155$	0.815501	0.0655026
$156$	−21.5430	−1.72482
$157$	8.07137	0.644165	0.322083	−	0.946712i	$-0.395617\pi$
$157$	8.07137	0.644165	0.322083	+	0.946712i	$0.395617\pi$
$158$	−5.08034	−0.404170
$159$	−11.1409	−0.883528
$160$	0.103796	0.00820577
$161$	−0.553111	−0.0435913
$162$	−27.1482	−2.13296
$163$	−12.8186	−1.00403	−0.502016	−	0.864858i	$-0.667408\pi$
$163$	−12.8186	−1.00403	−0.502016	+	0.864858i	$0.667408\pi$
$164$	2.88800	0.225515
$165$	0.276203	0.0215024
$166$	14.7386	1.14394
$167$	4.11370	0.318328	0.159164	−	0.987252i	$-0.449120\pi$
$167$	4.11370	0.318328	0.159164	+	0.987252i	$0.449120\pi$
$168$	1.80899	0.139567
$169$	30.3876	2.33750
$170$	0.605278	0.0464227
$171$	27.6861	2.11721
$172$	−6.56175	−0.500329
$173$	19.5085	1.48320	0.741601	−	0.670841i	$-0.234067\pi$
$173$	19.5085	1.48320	0.741601	+	0.670841i	$0.234067\pi$
$174$	−17.5846	−1.33308
$175$	−2.75960	−0.208606
$176$	0.813628	0.0613295
$177$	12.8788	0.968033
$178$	1.29826	0.0973090
$179$	−4.98903	−0.372897	−0.186449	−	0.982465i	$-0.559698\pi$
$179$	−4.98903	−0.372897	−0.186449	+	0.982465i	$0.559698\pi$
$180$	−0.798877	−0.0595448
$181$	−16.2634	−1.20885	−0.604424	−	0.796663i	$-0.706597\pi$
$181$	−16.2634	−1.20885	−0.604424	+	0.796663i	$0.706597\pi$
$182$	−3.64330	−0.270060
$183$	−12.0523	−0.890932
$184$	1.00000	0.0737210
$185$	−0.0881680	−0.00648224
$186$	−25.6962	−1.88413
$187$	4.74462	0.346961
$188$	−4.80920	−0.350747
$189$	−8.49615	−0.618004
$190$	0.373371	0.0270871
$191$	−25.3888	−1.83707	−0.918534	−	0.395341i	$-0.870626\pi$
$191$	−25.3888	−1.83707	−0.918534	+	0.395341i	$0.870626\pi$
$192$	−3.27057	−0.236033
$193$	23.8491	1.71670	0.858348	−	0.513069i	$-0.171491\pi$
$193$	23.8491	1.71670	0.858348	+	0.513069i	$0.171491\pi$
$194$	5.53397	0.397316
$195$	2.23607	0.160128
$196$	−6.69407	−0.478148
$197$	−21.3368	−1.52018	−0.760092	−	0.649815i	$-0.774846\pi$
$197$	−21.3368	−1.52018	−0.760092	+	0.649815i	$0.774846\pi$
$198$	−6.26219	−0.445035
$199$	−1.55914	−0.110525	−0.0552624	−	0.998472i	$-0.517600\pi$
$199$	−1.55914	−0.110525	−0.0552624	+	0.998472i	$0.517600\pi$
$200$	4.98923	0.352792
$201$	−2.85632	−0.201469
$202$	6.54370	0.460413
$203$	−2.97386	−0.208724
$204$	−19.0721	−1.33532
$205$	−0.299762	−0.0209363
$206$	15.6836	1.09273
$207$	−7.69663	−0.534953
$208$	6.58692	0.456721
$209$	2.92676	0.202448
$210$	−0.187765	−0.0129570
$211$	−10.6739	−0.734822	−0.367411	−	0.930059i	$-0.619756\pi$
$211$	−10.6739	−0.734822	−0.367411	+	0.930059i	$0.619756\pi$
$212$	3.40640	0.233952
$213$	−20.5022	−1.40479
$214$	−12.2966	−0.840576
$215$	0.681082	0.0464494
$216$	15.3607	1.04516
$217$	−4.34568	−0.295004
$218$	17.0299	1.15341
$219$	35.5699	2.40359
$220$	−0.0844511	−0.00569369
$221$	38.4112	2.58382
$222$	2.77815	0.186457
$223$	−18.7321	−1.25439	−0.627196	−	0.778861i	$-0.715798\pi$
$223$	−18.7321	−1.25439	−0.627196	+	0.778861i	$0.715798\pi$
$224$	−0.553111	−0.0369563
$225$	−38.4002	−2.56001
$226$	−10.7077	−0.712269
$227$	−15.9561	−1.05904	−0.529521	−	0.848297i	$-0.677628\pi$
$227$	−15.9561	−1.05904	−0.529521	+	0.848297i	$0.677628\pi$
$228$	−11.7648	−0.779142
$229$	−4.97330	−0.328645	−0.164323	−	0.986407i	$-0.552544\pi$
$229$	−4.97330	−0.328645	−0.164323	+	0.986407i	$0.552544\pi$
$230$	−0.103796	−0.00684409
$231$	−1.47184	−0.0968403
$232$	5.37661	0.352992
$233$	17.6289	1.15491	0.577455	−	0.816422i	$-0.304046\pi$
$233$	17.6289	1.15491	0.577455	+	0.816422i	$0.304046\pi$
$234$	−50.6971	−3.31417
$235$	0.499174	0.0325625
$236$	−3.93780	−0.256329
$237$	−16.6156	−1.07930
$238$	−3.22543	−0.209074
$239$	17.1659	1.11037	0.555184	−	0.831728i	$-0.312648\pi$
$239$	17.1659	1.11037	0.555184	+	0.831728i	$0.312648\pi$
$240$	0.339471	0.0219128
$241$	−2.77248	−0.178591	−0.0892955	−	0.996005i	$-0.528462\pi$
$241$	−2.77248	−0.178591	−0.0892955	+	0.996005i	$0.528462\pi$
$242$	10.3380	0.664552
$243$	−42.7082	−2.73973
$244$	3.68508	0.235913
$245$	0.694816	0.0443901
$246$	9.44542	0.602218
$247$	23.6943	1.50763
$248$	7.85678	0.498906
$249$	48.2036	3.05478
$250$	−1.03684	−0.0655755
$251$	10.5438	0.665520	0.332760	−	0.943011i	$-0.392020\pi$
$251$	10.5438	0.665520	0.332760	+	0.943011i	$0.392020\pi$
$252$	4.25709	0.268172
$253$	−0.813628	−0.0511523
$254$	11.4513	0.718520
$255$	1.97960	0.123968
$256$	1.00000	0.0625000
$257$	−12.9752	−0.809372	−0.404686	−	0.914456i	$-0.632619\pi$
$257$	−12.9752	−0.809372	−0.404686	+	0.914456i	$0.632619\pi$
$258$	−21.4607	−1.33608
$259$	0.469834	0.0291940
$260$	−0.683695	−0.0424009
$261$	−41.3817	−2.56147
$262$	1.00000	0.0617802
$263$	26.6163	1.64123	0.820617	−	0.571479i	$-0.193630\pi$
$263$	26.6163	1.64123	0.820617	+	0.571479i	$0.193630\pi$
$264$	2.66103	0.163775
$265$	−0.353569	−0.0217196
$266$	−1.98963	−0.121992
$267$	4.24606	0.259855
$268$	0.873340	0.0533477
$269$	−23.2985	−1.42054	−0.710269	−	0.703931i	$-0.751426\pi$
$269$	−23.2985	−1.42054	−0.710269	+	0.703931i	$0.751426\pi$
$270$	−1.59437	−0.0970303
$271$	−6.30180	−0.382807	−0.191404	−	0.981511i	$-0.561304\pi$
$271$	−6.30180	−0.382807	−0.191404	+	0.981511i	$0.561304\pi$
$272$	5.83144	0.353583
$273$	−11.9157	−0.721170
$274$	−5.16549	−0.312059
$275$	−4.05937	−0.244789
$276$	3.27057	0.196865
$277$	17.7476	1.06635	0.533176	−	0.846005i	$-0.320998\pi$
$277$	17.7476	1.06635	0.533176	+	0.846005i	$0.320998\pi$
$278$	8.99810	0.539670
$279$	−60.4708	−3.62029
$280$	0.0574106	0.00343094
$281$	−23.4346	−1.39799	−0.698996	−	0.715126i	$-0.746369\pi$
$281$	−23.4346	−1.39799	−0.698996	+	0.715126i	$0.746369\pi$
$282$	−15.7288	−0.936637
$283$	31.8897	1.89565	0.947823	−	0.318797i	$-0.103279\pi$
$283$	31.8897	1.89565	0.947823	+	0.318797i	$0.103279\pi$
$284$	6.26870	0.371979
$285$	1.22113	0.0723338
$286$	−5.35930	−0.316902
$287$	1.59739	0.0942908
$288$	−7.69663	−0.453528
$289$	17.0056	1.00033
$290$	−0.558069	−0.0327709
$291$	18.0993	1.06100
$292$	−10.8758	−0.636455
$293$	−2.58226	−0.150857	−0.0754286	−	0.997151i	$-0.524032\pi$
$293$	−2.58226	−0.150857	−0.0754286	+	0.997151i	$0.524032\pi$
$294$	−21.8934	−1.27685
$295$	0.408727	0.0237970
$296$	−0.849438	−0.0493726
$297$	−12.4979	−0.725199
$298$	9.32690	0.540293
$299$	−6.58692	−0.380932
$300$	16.3176	0.942098
$301$	−3.62938	−0.209194
$302$	−0.997646	−0.0574081
$303$	21.4016	1.22949
$304$	3.59717	0.206312
$305$	−0.382495	−0.0219016
$306$	−44.8824	−2.56576
$307$	−21.7822	−1.24318	−0.621588	−	0.783345i	$-0.713512\pi$
$307$	−21.7822	−1.24318	−0.621588	+	0.783345i	$0.713512\pi$
$308$	0.450027	0.0256427
$309$	51.2942	2.91803
$310$	−0.815501	−0.0463173
$311$	1.83548	0.104080	0.0520402	−	0.998645i	$-0.483428\pi$
$311$	1.83548	0.104080	0.0520402	+	0.998645i	$0.483428\pi$
$312$	21.5430	1.21963
$313$	21.1874	1.19758	0.598792	−	0.800905i	$-0.295648\pi$
$313$	21.1874	1.19758	0.598792	+	0.800905i	$0.295648\pi$
$314$	−8.07137	−0.455494
$315$	−0.441868	−0.0248965
$316$	5.08034	0.285792
$317$	21.2260	1.19217	0.596085	−	0.802921i	$-0.296722\pi$
$317$	21.2260	1.19217	0.596085	+	0.802921i	$0.296722\pi$
$318$	11.1409	0.624748
$319$	−4.37456	−0.244928
$320$	−0.103796	−0.00580236
$321$	−40.2168	−2.24468
$322$	0.553111	0.0308237
$323$	20.9766	1.16717
$324$	27.1482	1.50823
$325$	−32.8637	−1.82295
$326$	12.8186	0.709958
$327$	55.6976	3.08009
$328$	−2.88800	−0.159463
$329$	−2.66002	−0.146652
$330$	−0.276203	−0.0152045
$331$	−0.479692	−0.0263662	−0.0131831	−	0.999913i	$-0.504196\pi$
$331$	−0.479692	−0.0263662	−0.0131831	+	0.999913i	$0.504196\pi$
$332$	−14.7386	−0.808886
$333$	6.53781	0.358270
$334$	−4.11370	−0.225092
$335$	−0.0906490	−0.00495268
$336$	−1.80899	−0.0986885
$337$	−6.87190	−0.374336	−0.187168	−	0.982328i	$-0.559931\pi$
$337$	−6.87190	−0.374336	−0.187168	+	0.982328i	$0.559931\pi$
$338$	−30.3876	−1.65287
$339$	−35.0204	−1.90205
$340$	−0.605278	−0.0328258
$341$	−6.39250	−0.346173
$342$	−27.6861	−1.49709
$343$	−7.57435	−0.408976
$344$	6.56175	0.353786
$345$	−0.339471	−0.0182765
$346$	−19.5085	−1.04878
$347$	−22.5168	−1.20876	−0.604382	−	0.796695i	$-0.706580\pi$
$347$	−22.5168	−1.20876	−0.604382	+	0.796695i	$0.706580\pi$
$348$	17.5846	0.942632
$349$	−33.9857	−1.81921	−0.909607	−	0.415470i	$-0.863617\pi$
$349$	−33.9857	−1.81921	−0.909607	+	0.415470i	$0.863617\pi$
$350$	2.75960	0.147507
$351$	−101.179	−5.40056
$352$	−0.813628	−0.0433665
$353$	8.70927	0.463548	0.231774	−	0.972770i	$-0.425547\pi$
$353$	8.70927	0.463548	0.231774	+	0.972770i	$0.425547\pi$
$354$	−12.8788	−0.684503
$355$	−0.650664	−0.0345337
$356$	−1.29826	−0.0688078
$357$	−10.5490	−0.558313
$358$	4.98903	0.263678
$359$	25.6573	1.35414	0.677069	−	0.735920i	$-0.263250\pi$
$359$	25.6573	1.35414	0.677069	+	0.735920i	$0.263250\pi$
$360$	0.798877	0.0421045
$361$	−6.06039	−0.318968
$362$	16.2634	0.854785
$363$	33.8112	1.77463
$364$	3.64330	0.190961
$365$	1.12886	0.0590871
$366$	12.0523	0.629984
$367$	31.5144	1.64504	0.822518	−	0.568739i	$-0.192568\pi$
$367$	31.5144	1.64504	0.822518	+	0.568739i	$0.192568\pi$
$368$	−1.00000	−0.0521286
$369$	22.2279	1.15714
$370$	0.0881680	0.00458364
$371$	1.88412	0.0978185
$372$	25.6962	1.33228
$373$	−13.1965	−0.683291	−0.341645	−	0.939829i	$-0.610984\pi$
$373$	−13.1965	−0.683291	−0.341645	+	0.939829i	$0.610984\pi$
$374$	−4.74462	−0.245338
$375$	−3.39105	−0.175113
$376$	4.80920	0.248015
$377$	−35.4153	−1.82398
$378$	8.49615	0.436995
$379$	−29.7503	−1.52817	−0.764085	−	0.645116i	$-0.776809\pi$
$379$	−29.7503	−1.52817	−0.764085	+	0.645116i	$0.776809\pi$
$380$	−0.373371	−0.0191535
$381$	37.4524	1.91874
$382$	25.3888	1.29900
$383$	17.7377	0.906354	0.453177	−	0.891421i	$-0.350291\pi$
$383$	17.7377	0.906354	0.453177	+	0.891421i	$0.350291\pi$
$384$	3.27057	0.166901
$385$	−0.0467109	−0.00238061
$386$	−23.8491	−1.21389
$387$	−50.5034	−2.56723
$388$	−5.53397	−0.280945
$389$	−23.4052	−1.18669	−0.593346	−	0.804948i	$-0.702193\pi$
$389$	−23.4052	−1.18669	−0.593346	+	0.804948i	$0.702193\pi$
$390$	−2.23607	−0.113228
$391$	−5.83144	−0.294908
$392$	6.69407	0.338101
$393$	3.27057	0.164978
$394$	21.3368	1.07493
$395$	−0.527318	−0.0265322
$396$	6.26219	0.314687
$397$	−28.6307	−1.43693	−0.718467	−	0.695561i	$-0.755156\pi$
$397$	−28.6307	−1.43693	−0.718467	+	0.695561i	$0.755156\pi$
$398$	1.55914	0.0781528
$399$	−6.50724	−0.325769
$400$	−4.98923	−0.249461
$401$	25.6823	1.28251	0.641256	−	0.767327i	$-0.278414\pi$
$401$	25.6823	1.28251	0.641256	+	0.767327i	$0.278414\pi$
$402$	2.85632	0.142460
$403$	−51.7520	−2.57795
$404$	−6.54370	−0.325561
$405$	−2.81787	−0.140021
$406$	2.97386	0.147590
$407$	0.691126	0.0342578
$408$	19.0721	0.944211
$409$	−22.7718	−1.12599	−0.562997	−	0.826459i	$-0.690352\pi$
$409$	−22.7718	−1.12599	−0.562997	+	0.826459i	$0.690352\pi$
$410$	0.299762	0.0148042
$411$	−16.8941	−0.833324
$412$	−15.6836	−0.772674
$413$	−2.17804	−0.107174
$414$	7.69663	0.378269
$415$	1.52980	0.0750951
$416$	−6.58692	−0.322950
$417$	29.4289	1.44114
$418$	−2.92676	−0.143152
$419$	13.6945	0.669021	0.334510	−	0.942392i	$-0.391429\pi$
$419$	13.6945	0.669021	0.334510	+	0.942392i	$0.391429\pi$
$420$	0.187765	0.00916201
$421$	23.7960	1.15974	0.579872	−	0.814708i	$-0.303103\pi$
$421$	23.7960	1.15974	0.579872	+	0.814708i	$0.303103\pi$
$422$	10.6739	0.519597
$423$	−37.0146	−1.79971
$424$	−3.40640	−0.165429
$425$	−29.0944	−1.41128
$426$	20.5022	0.993335
$427$	2.03826	0.0986383
$428$	12.2966	0.594377
$429$	−17.5280	−0.846259
$430$	−0.681082	−0.0328447
$431$	−8.00088	−0.385389	−0.192694	−	0.981259i	$-0.561723\pi$
$431$	−8.00088	−0.385389	−0.192694	+	0.981259i	$0.561723\pi$
$432$	−15.3607	−0.739040
$433$	15.5345	0.746539	0.373269	−	0.927723i	$-0.378237\pi$
$433$	15.5345	0.746539	0.373269	+	0.927723i	$0.378237\pi$
$434$	4.34568	0.208599
$435$	−1.82520	−0.0875118
$436$	−17.0299	−0.815587
$437$	−3.59717	−0.172076
$438$	−35.5699	−1.69960
$439$	5.52337	0.263616	0.131808	−	0.991275i	$-0.457922\pi$
$439$	5.52337	0.263616	0.131808	+	0.991275i	$0.457922\pi$
$440$	0.0844511	0.00402605
$441$	−51.5218	−2.45342
$442$	−38.4112	−1.82704
$443$	−30.6957	−1.45840	−0.729198	−	0.684303i	$-0.760107\pi$
$443$	−30.6957	−1.45840	−0.729198	+	0.684303i	$0.760107\pi$
$444$	−2.77815	−0.131845
$445$	0.134754	0.00638796
$446$	18.7321	0.886989
$447$	30.5043	1.44280
$448$	0.553111	0.0261321
$449$	−23.6906	−1.11803	−0.559015	−	0.829158i	$-0.688820\pi$
$449$	−23.6906	−1.11803	−0.559015	+	0.829158i	$0.688820\pi$
$450$	38.4002	1.81020
$451$	2.34976	0.110646
$452$	10.7077	0.503650
$453$	−3.26287	−0.153303
$454$	15.9561	0.748856
$455$	−0.378159	−0.0177284
$456$	11.7648	0.550937
$457$	−16.5657	−0.774909	−0.387454	−	0.921889i	$-0.626645\pi$
$457$	−16.5657	−0.774909	−0.387454	+	0.921889i	$0.626645\pi$
$458$	4.97330	0.232387
$459$	−89.5747	−4.18099
$460$	0.103796	0.00483950
$461$	31.5062	1.46739	0.733695	−	0.679479i	$-0.237794\pi$
$461$	31.5062	1.46739	0.733695	+	0.679479i	$0.237794\pi$
$462$	1.47184	0.0684764
$463$	−6.79440	−0.315762	−0.157881	−	0.987458i	$-0.550466\pi$
$463$	−6.79440	−0.315762	−0.157881	+	0.987458i	$0.550466\pi$
$464$	−5.37661	−0.249603
$465$	−2.66715	−0.123686
$466$	−17.6289	−0.816645
$467$	30.2173	1.39829	0.699145	−	0.714980i	$-0.253564\pi$
$467$	30.2173	1.39829	0.699145	+	0.714980i	$0.253564\pi$
$468$	50.6971	2.34347
$469$	0.483054	0.0223054
$470$	−0.499174	−0.0230252
$471$	−26.3980	−1.21635
$472$	3.93780	0.181252
$473$	−5.33882	−0.245479
$474$	16.6156	0.763181
$475$	−17.9471	−0.823469
$476$	3.22543	0.147838
$477$	26.2178	1.20043
$478$	−17.1659	−0.785149
$479$	7.26895	0.332127	0.166063	−	0.986115i	$-0.446894\pi$
$479$	7.26895	0.332127	0.166063	+	0.986115i	$0.446894\pi$
$480$	−0.339471	−0.0154947
$481$	5.59518	0.255118
$482$	2.77248	0.126283
$483$	1.80899	0.0823119
$484$	−10.3380	−0.469910
$485$	0.574403	0.0260823
$486$	42.7082	1.93728
$487$	4.39003	0.198931	0.0994657	−	0.995041i	$-0.468287\pi$
$487$	4.39003	0.198931	0.0994657	+	0.995041i	$0.468287\pi$
$488$	−3.68508	−0.166816
$489$	41.9242	1.89588
$490$	−0.694816	−0.0313886
$491$	−17.8862	−0.807193	−0.403597	−	0.914937i	$-0.632240\pi$
$491$	−17.8862	−0.807193	−0.403597	+	0.914937i	$0.632240\pi$
$492$	−9.44542	−0.425832
$493$	−31.3533	−1.41208
$494$	−23.6943	−1.06606
$495$	−0.649989	−0.0292148
$496$	−7.85678	−0.352780
$497$	3.46729	0.155529
$498$	−48.2036	−2.16006
$499$	−21.4420	−0.959874	−0.479937	−	0.877303i	$-0.659341\pi$
$499$	−21.4420	−0.959874	−0.479937	+	0.877303i	$0.659341\pi$
$500$	1.03684	0.0463689
$501$	−13.4541	−0.601087
$502$	−10.5438	−0.470594
$503$	25.5554	1.13946	0.569730	−	0.821832i	$-0.307048\pi$
$503$	25.5554	1.13946	0.569730	+	0.821832i	$0.307048\pi$
$504$	−4.25709	−0.189626
$505$	0.679208	0.0302244
$506$	0.813628	0.0361702
$507$	−99.3846	−4.41383
$508$	−11.4513	−0.508070
$509$	−3.25761	−0.144391	−0.0721955	−	0.997391i	$-0.523001\pi$
$509$	−3.25761	−0.144391	−0.0721955	+	0.997391i	$0.523001\pi$
$510$	−1.97960	−0.0876584
$511$	−6.01550	−0.266110
$512$	−1.00000	−0.0441942
$513$	−55.2548	−2.43956
$514$	12.9752	0.572312
$515$	1.62789	0.0717333
$516$	21.4607	0.944753
$517$	−3.91290	−0.172089
$518$	−0.469834	−0.0206433
$519$	−63.8039	−2.80068
$520$	0.683695	0.0299820
$521$	−33.1407	−1.45192	−0.725959	−	0.687738i	$-0.758604\pi$
$521$	−33.1407	−1.45192	−0.725959	+	0.687738i	$0.758604\pi$
$522$	41.3817	1.81123
$523$	−15.3236	−0.670054	−0.335027	−	0.942209i	$-0.608745\pi$
$523$	−15.3236	−0.670054	−0.335027	+	0.942209i	$0.608745\pi$
$524$	−1.00000	−0.0436852
$525$	9.02546	0.393903
$526$	−26.6163	−1.16053
$527$	−45.8163	−1.99579
$528$	−2.66103	−0.115806
$529$	1.00000	0.0434783
$530$	0.353569	0.0153581
$531$	−30.3078	−1.31525
$532$	1.98963	0.0862616
$533$	19.0231	0.823980
$534$	−4.24606	−0.183745
$535$	−1.27633	−0.0551806
$536$	−0.873340	−0.0377225
$537$	16.3170	0.704129
$538$	23.2985	1.00447
$539$	−5.44648	−0.234597
$540$	1.59437	0.0686108
$541$	−38.0860	−1.63744	−0.818722	−	0.574190i	$-0.805317\pi$
$541$	−38.0860	−1.63744	−0.818722	+	0.574190i	$0.805317\pi$
$542$	6.30180	0.270686
$543$	53.1906	2.28263
$544$	−5.83144	−0.250021
$545$	1.76764	0.0757172
$546$	11.9157	0.509944
$547$	15.3913	0.658083	0.329042	−	0.944315i	$-0.393274\pi$
$547$	15.3913	0.658083	0.329042	+	0.944315i	$0.393274\pi$
$548$	5.16549	0.220659
$549$	28.3627	1.21049
$550$	4.05937	0.173092
$551$	−19.3406	−0.823935
$552$	−3.27057	−0.139205
$553$	2.81000	0.119493
$554$	−17.7476	−0.754024
$555$	0.288360	0.0122402
$556$	−8.99810	−0.381605
$557$	−34.6386	−1.46769	−0.733843	−	0.679319i	$-0.762275\pi$
$557$	−34.6386	−1.46769	−0.733843	+	0.679319i	$0.762275\pi$
$558$	60.4708	2.55993
$559$	−43.2218	−1.82809
$560$	−0.0574106	−0.00242604
$561$	−15.5176	−0.655154
$562$	23.4346	0.988529
$563$	41.5326	1.75039	0.875196	−	0.483768i	$-0.160732\pi$
$563$	41.5326	1.75039	0.875196	+	0.483768i	$0.160732\pi$
$564$	15.7288	0.662302
$565$	−1.11142	−0.0467577
$566$	−31.8897	−1.34042
$567$	15.0160	0.630612
$568$	−6.26870	−0.263029
$569$	33.9059	1.42141	0.710704	−	0.703491i	$-0.248377\pi$
$569$	33.9059	1.42141	0.710704	+	0.703491i	$0.248377\pi$
$570$	−1.22113	−0.0511477
$571$	−14.4246	−0.603650	−0.301825	−	0.953363i	$-0.597596\pi$
$571$	−14.4246	−0.603650	−0.301825	+	0.953363i	$0.597596\pi$
$572$	5.35930	0.224084
$573$	83.0358	3.46887
$574$	−1.59739	−0.0666737
$575$	4.98923	0.208065
$576$	7.69663	0.320693
$577$	−41.7768	−1.73919	−0.869596	−	0.493764i	$-0.835621\pi$
$577$	−41.7768	−1.73919	−0.869596	+	0.493764i	$0.835621\pi$
$578$	−17.0056	−0.707342
$579$	−78.0001	−3.24157
$580$	0.558069	0.0231725
$581$	−8.15209	−0.338206
$582$	−18.0993	−0.750238
$583$	2.77154	0.114785
$584$	10.8758	0.450042
$585$	−5.26214	−0.217563
$586$	2.58226	0.106672
$587$	−9.54667	−0.394033	−0.197017	−	0.980400i	$-0.563125\pi$
$587$	−9.54667	−0.394033	−0.197017	+	0.980400i	$0.563125\pi$
$588$	21.8934	0.902869
$589$	−28.2622	−1.16452
$590$	−0.408727	−0.0168270
$591$	69.7835	2.87051
$592$	0.849438	0.0349117
$593$	29.2963	1.20306	0.601528	−	0.798852i	$-0.294559\pi$
$593$	29.2963	1.20306	0.601528	+	0.798852i	$0.294559\pi$
$594$	12.4979	0.512793
$595$	−0.334786	−0.0137249
$596$	−9.32690	−0.382045
$597$	5.09929	0.208700
$598$	6.58692	0.269359
$599$	−1.37298	−0.0560983	−0.0280491	−	0.999607i	$-0.508929\pi$
$599$	−1.37298	−0.0560983	−0.0280491	+	0.999607i	$0.508929\pi$
$600$	−16.3176	−0.666164
$601$	45.4304	1.85314	0.926571	−	0.376119i	$-0.122742\pi$
$601$	45.4304	1.85314	0.926571	+	0.376119i	$0.122742\pi$
$602$	3.62938	0.147923
$603$	6.72177	0.273732
$604$	0.997646	0.0405936
$605$	1.07304	0.0436253
$606$	−21.4016	−0.869381
$607$	24.2017	0.982316	0.491158	−	0.871070i	$-0.336574\pi$
$607$	24.2017	0.982316	0.491158	+	0.871070i	$0.336574\pi$
$608$	−3.59717	−0.145884
$609$	9.72623	0.394127
$610$	0.382495	0.0154868
$611$	−31.6778	−1.28155
$612$	44.8824	1.81426
$613$	48.2556	1.94903	0.974513	−	0.224332i	$-0.0720200\pi$
$613$	48.2556	1.94903	0.974513	+	0.224332i	$0.0720200\pi$
$614$	21.7822	0.879058
$615$	0.980394	0.0395333
$616$	−0.450027	−0.0181321
$617$	−26.6222	−1.07177	−0.535885	−	0.844291i	$-0.680022\pi$
$617$	−26.6222	−1.07177	−0.535885	+	0.844291i	$0.680022\pi$
$618$	−51.2942	−2.06336
$619$	−13.4359	−0.540034	−0.270017	−	0.962856i	$-0.587029\pi$
$619$	−13.4359	−0.540034	−0.270017	+	0.962856i	$0.587029\pi$
$620$	0.815501	0.0327513
$621$	15.3607	0.616402
$622$	−1.83548	−0.0735959
$623$	−0.718084	−0.0287694
$624$	−21.5430	−0.862410
$625$	24.8385	0.993541
$626$	−21.1874	−0.846819
$627$	−9.57216	−0.382275
$628$	8.07137	0.322083
$629$	4.95344	0.197507
$630$	0.441868	0.0176044
$631$	16.3866	0.652341	0.326170	−	0.945311i	$-0.394242\pi$
$631$	16.3866	0.652341	0.326170	+	0.945311i	$0.394242\pi$
$632$	−5.08034	−0.202085
$633$	34.9097	1.38754
$634$	−21.2260	−0.842991
$635$	1.18860	0.0471681
$636$	−11.1409	−0.441764
$637$	−44.0933	−1.74704
$638$	4.37456	0.173190
$639$	48.2478	1.90865
$640$	0.103796	0.00410289
$641$	23.5328	0.929491	0.464745	−	0.885444i	$-0.346146\pi$
$641$	23.5328	0.929491	0.464745	+	0.885444i	$0.346146\pi$
$642$	40.2168	1.58723
$643$	43.1590	1.70203	0.851013	−	0.525145i	$-0.175989\pi$
$643$	43.1590	1.70203	0.851013	+	0.525145i	$0.175989\pi$
$644$	−0.553111	−0.0217956
$645$	−2.22753	−0.0877087
$646$	−20.9766	−0.825315
$647$	−34.4748	−1.35534	−0.677672	−	0.735364i	$-0.737011\pi$
$647$	−34.4748	−1.35534	−0.677672	+	0.735364i	$0.737011\pi$
$648$	−27.1482	−1.06648
$649$	−3.20390	−0.125764
$650$	32.8637	1.28902
$651$	14.2128	0.557045
$652$	−12.8186	−0.502016
$653$	−42.5702	−1.66590	−0.832950	−	0.553348i	$-0.813350\pi$
$653$	−42.5702	−1.66590	−0.832950	+	0.553348i	$0.813350\pi$
$654$	−55.6976	−2.17795
$655$	0.103796	0.00405563
$656$	2.88800	0.112758
$657$	−83.7066	−3.26571
$658$	2.66002	0.103698
$659$	−16.7309	−0.651745	−0.325873	−	0.945414i	$-0.605658\pi$
$659$	−16.7309	−0.651745	−0.325873	+	0.945414i	$0.605658\pi$
$660$	0.276203	0.0107512
$661$	14.6001	0.567879	0.283940	−	0.958842i	$-0.408358\pi$
$661$	14.6001	0.567879	0.283940	+	0.958842i	$0.408358\pi$
$662$	0.479692	0.0186438
$663$	−125.627	−4.87893
$664$	14.7386	0.571969
$665$	−0.206516	−0.00800833
$666$	−6.53781	−0.253335
$667$	5.37661	0.208183
$668$	4.11370	0.159164
$669$	61.2646	2.36862
$670$	0.0906490	0.00350207
$671$	2.99828	0.115747
$672$	1.80899	0.0697833
$673$	−17.7531	−0.684331	−0.342165	−	0.939640i	$-0.611160\pi$
$673$	−17.7531	−0.684331	−0.342165	+	0.939640i	$0.611160\pi$
$674$	6.87190	0.264696
$675$	76.6378	2.94979
$676$	30.3876	1.16875
$677$	19.3630	0.744182	0.372091	−	0.928196i	$-0.378641\pi$
$677$	19.3630	0.744182	0.372091	+	0.928196i	$0.378641\pi$
$678$	35.0204	1.34495
$679$	−3.06090	−0.117467
$680$	0.605278	0.0232114
$681$	52.1855	1.99975
$682$	6.39250	0.244781
$683$	−15.2627	−0.584009	−0.292005	−	0.956417i	$-0.594322\pi$
$683$	−15.2627	−0.584009	−0.292005	+	0.956417i	$0.594322\pi$
$684$	27.6861	1.05860
$685$	−0.536156	−0.0204855
$686$	7.57435	0.289190
$687$	16.2655	0.620569
$688$	−6.56175	−0.250164
$689$	22.4377	0.854807
$690$	0.339471	0.0129234
$691$	27.2884	1.03810	0.519049	−	0.854745i	$-0.326286\pi$
$691$	27.2884	1.03810	0.519049	+	0.854745i	$0.326286\pi$
$692$	19.5085	0.741601
$693$	3.46369	0.131575
$694$	22.5168	0.854725
$695$	0.933965	0.0354273
$696$	−17.5846	−0.666541
$697$	16.8412	0.637906
$698$	33.9857	1.28638
$699$	−57.6567	−2.18078
$700$	−2.75960	−0.104303
$701$	4.11493	0.155419	0.0777094	−	0.996976i	$-0.475239\pi$
$701$	4.11493	0.155419	0.0777094	+	0.996976i	$0.475239\pi$
$702$	101.179	3.81877
$703$	3.05557	0.115243
$704$	0.813628	0.0306648
$705$	−1.63258	−0.0614866
$706$	−8.70927	−0.327778
$707$	−3.61939	−0.136121
$708$	12.8788	0.484017
$709$	20.3696	0.764997	0.382498	−	0.923956i	$-0.375064\pi$
$709$	20.3696	0.764997	0.382498	+	0.923956i	$0.375064\pi$
$710$	0.650664	0.0244190
$711$	39.1015	1.46642
$712$	1.29826	0.0486545
$713$	7.85678	0.294239
$714$	10.5490	0.394787
$715$	−0.556273	−0.0208034
$716$	−4.98903	−0.186449
$717$	−56.1422	−2.09667
$718$	−25.6573	−0.957520
$719$	−45.0007	−1.67824	−0.839121	−	0.543944i	$-0.816930\pi$
$719$	−45.0007	−1.67824	−0.839121	+	0.543944i	$0.816930\pi$
$720$	−0.798877	−0.0297724
$721$	−8.67476	−0.323065
$722$	6.06039	0.225544
$723$	9.06759	0.337227
$724$	−16.2634	−0.604424
$725$	26.8251	0.996260
$726$	−33.8112	−1.25485
$727$	13.5284	0.501742	0.250871	−	0.968021i	$-0.419283\pi$
$727$	13.5284	0.501742	0.250871	+	0.968021i	$0.419283\pi$
$728$	−3.64330	−0.135030
$729$	58.2354	2.15687
$730$	−1.12886	−0.0417809
$731$	−38.2644	−1.41526
$732$	−12.0523	−0.445466
$733$	29.7436	1.09861	0.549303	−	0.835623i	$-0.314893\pi$
$733$	29.7436	1.09861	0.549303	+	0.835623i	$0.314893\pi$
$734$	−31.5144	−1.16322
$735$	−2.27244	−0.0838203
$736$	1.00000	0.0368605
$737$	0.710574	0.0261743
$738$	−22.2279	−0.818220
$739$	−8.97532	−0.330163	−0.165081	−	0.986280i	$-0.552789\pi$
$739$	−8.97532	−0.330163	−0.165081	+	0.986280i	$0.552789\pi$
$740$	−0.0881680	−0.00324112
$741$	−77.4937	−2.84680
$742$	−1.88412	−0.0691681
$743$	−3.75835	−0.137881	−0.0689403	−	0.997621i	$-0.521962\pi$
$743$	−3.75835	−0.137881	−0.0689403	+	0.997621i	$0.521962\pi$
$744$	−25.6962	−0.942067
$745$	0.968093	0.0354682
$746$	13.1965	0.483160
$747$	−113.438	−4.15046
$748$	4.74462	0.173480
$749$	6.80137	0.248517
$750$	3.39105	0.123824
$751$	−22.8451	−0.833628	−0.416814	−	0.908992i	$-0.636853\pi$
$751$	−22.8451	−0.833628	−0.416814	+	0.908992i	$0.636853\pi$
$752$	−4.80920	−0.175373
$753$	−34.4843	−1.25668
$754$	35.4153	1.28975
$755$	−0.103551	−0.00376862
$756$	−8.49615	−0.309002
$757$	−5.22591	−0.189939	−0.0949695	−	0.995480i	$-0.530275\pi$
$757$	−5.22591	−0.189939	−0.0949695	+	0.995480i	$0.530275\pi$
$758$	29.7503	1.08058
$759$	2.66103	0.0965892
$760$	0.373371	0.0135436
$761$	5.93105	0.215000	0.107500	−	0.994205i	$-0.465715\pi$
$761$	5.93105	0.215000	0.107500	+	0.994205i	$0.465715\pi$
$762$	−37.4524	−1.35676
$763$	−9.41946	−0.341007
$764$	−25.3888	−0.918534
$765$	−4.65860	−0.168432
$766$	−17.7377	−0.640889
$767$	−25.9380	−0.936566
$768$	−3.27057	−0.118017
$769$	36.7969	1.32693	0.663465	−	0.748207i	$-0.269085\pi$
$769$	36.7969	1.32693	0.663465	+	0.748207i	$0.269085\pi$
$770$	0.0467109	0.00168334
$771$	42.4363	1.52831
$772$	23.8491	0.858348
$773$	−39.0025	−1.40282	−0.701412	−	0.712756i	$-0.747447\pi$
$773$	−39.0025	−1.40282	−0.701412	+	0.712756i	$0.747447\pi$
$774$	50.5034	1.81531
$775$	39.1993	1.40808
$776$	5.53397	0.198658
$777$	−1.53662	−0.0551261
$778$	23.4052	0.839118
$779$	10.3886	0.372211
$780$	2.23607	0.0800642
$781$	5.10039	0.182506
$782$	5.83144	0.208532
$783$	82.5882	2.95146
$784$	−6.69407	−0.239074
$785$	−0.837774	−0.0299014
$786$	−3.27057	−0.116657
$787$	−9.82088	−0.350077	−0.175038	−	0.984562i	$-0.556005\pi$
$787$	−9.82088	−0.350077	−0.175038	+	0.984562i	$0.556005\pi$
$788$	−21.3368	−0.760092
$789$	−87.0506	−3.09908
$790$	0.527318	0.0187611
$791$	5.92258	0.210583
$792$	−6.26219	−0.222517
$793$	24.2733	0.861971
$794$	28.6307	1.01607
$795$	1.15637	0.0410123
$796$	−1.55914	−0.0552624
$797$	34.6833	1.22855	0.614273	−	0.789093i	$-0.289449\pi$
$797$	34.6833	1.22855	0.614273	+	0.789093i	$0.289449\pi$
$798$	6.50724	0.230354
$799$	−28.0445	−0.992144
$800$	4.98923	0.176396
$801$	−9.99225	−0.353059
$802$	−25.6823	−0.906873
$803$	−8.84882	−0.312268
$804$	−2.85632	−0.100735
$805$	0.0574106	0.00202346
$806$	51.7520	1.82289
$807$	76.1995	2.68235
$808$	6.54370	0.230206
$809$	9.11147	0.320342	0.160171	−	0.987089i	$-0.448795\pi$
$809$	9.11147	0.320342	0.160171	+	0.987089i	$0.448795\pi$
$810$	2.81787	0.0990098
$811$	−26.3495	−0.925255	−0.462627	−	0.886553i	$-0.653093\pi$
$811$	−26.3495	−0.925255	−0.462627	+	0.886553i	$0.653093\pi$
$812$	−2.97386	−0.104362
$813$	20.6105	0.722842
$814$	−0.691126	−0.0242240
$815$	1.33052	0.0466060
$816$	−19.0721	−0.667658
$817$	−23.6037	−0.825790
$818$	22.7718	0.796198
$819$	28.0412	0.979837
$820$	−0.299762	−0.0104682
$821$	−35.1236	−1.22582	−0.612911	−	0.790152i	$-0.710001\pi$
$821$	−35.1236	−1.22582	−0.612911	+	0.790152i	$0.710001\pi$
$822$	16.8941	0.589249
$823$	35.7993	1.24789	0.623943	−	0.781470i	$-0.285530\pi$
$823$	35.7993	1.24789	0.623943	+	0.781470i	$0.285530\pi$
$824$	15.6836	0.546363
$825$	13.2765	0.462227
$826$	2.17804	0.0757837
$827$	−22.1728	−0.771025	−0.385513	−	0.922703i	$-0.625975\pi$
$827$	−22.1728	−0.771025	−0.385513	+	0.922703i	$0.625975\pi$
$828$	−7.69663	−0.267476
$829$	−6.75868	−0.234739	−0.117369	−	0.993088i	$-0.537446\pi$
$829$	−6.75868	−0.234739	−0.117369	+	0.993088i	$0.537446\pi$
$830$	−1.52980	−0.0531003
$831$	−58.0448	−2.01355
$832$	6.58692	0.228360
$833$	−39.0360	−1.35252
$834$	−29.4289	−1.01904
$835$	−0.426985	−0.0147764
$836$	2.92676	0.101224
$837$	120.685	4.17150
$838$	−13.6945	−0.473069
$839$	10.3264	0.356505	0.178253	−	0.983985i	$-0.442956\pi$
$839$	10.3264	0.356505	0.178253	+	0.983985i	$0.442956\pi$
$840$	−0.187765	−0.00647852
$841$	−0.0920959	−0.00317572
$842$	−23.7960	−0.820063
$843$	76.6445	2.63978
$844$	−10.6739	−0.367411
$845$	−3.15410	−0.108504
$846$	37.0146	1.27259
$847$	−5.71807	−0.196475
$848$	3.40640	0.116976
$849$	−104.297	−3.57948
$850$	29.0944	0.997928
$851$	−0.849438	−0.0291183
$852$	−20.5022	−0.702394
$853$	−4.96506	−0.170000	−0.0850002	−	0.996381i	$-0.527089\pi$
$853$	−4.96506	−0.170000	−0.0850002	+	0.996381i	$0.527089\pi$
$854$	−2.03826	−0.0697478
$855$	−2.87369	−0.0982783
$856$	−12.2966	−0.420288
$857$	29.0834	0.993471	0.496735	−	0.867902i	$-0.334532\pi$
$857$	29.0834	0.993471	0.496735	+	0.867902i	$0.334532\pi$
$858$	17.5280	0.598395
$859$	−36.5035	−1.24548	−0.622742	−	0.782427i	$-0.713981\pi$
$859$	−36.5035	−1.24548	−0.622742	+	0.782427i	$0.713981\pi$
$860$	0.681082	0.0232247
$861$	−5.22437	−0.178046
$862$	8.00088	0.272511
$863$	15.4104	0.524577	0.262289	−	0.964989i	$-0.415523\pi$
$863$	15.4104	0.524577	0.262289	+	0.964989i	$0.415523\pi$
$864$	15.3607	0.522580
$865$	−2.02490	−0.0688486
$866$	−15.5345	−0.527883
$867$	−55.6182	−1.88889
$868$	−4.34568	−0.147502
$869$	4.13351	0.140220
$870$	1.82520	0.0618802
$871$	5.75262	0.194920
$872$	17.0299	0.576707
$873$	−42.5929	−1.44155
$874$	3.59717	0.121676
$875$	0.573488	0.0193874
$876$	35.5699	1.20180
$877$	44.0940	1.48895	0.744475	−	0.667650i	$-0.232700\pi$
$877$	44.0940	1.48895	0.744475	+	0.667650i	$0.232700\pi$
$878$	−5.52337	−0.186405
$879$	8.44546	0.284858
$880$	−0.0844511	−0.00284685
$881$	8.08071	0.272246	0.136123	−	0.990692i	$-0.456536\pi$
$881$	8.08071	0.272246	0.136123	+	0.990692i	$0.456536\pi$
$882$	51.5218	1.73483
$883$	−43.6298	−1.46826	−0.734129	−	0.679010i	$-0.762409\pi$
$883$	−43.6298	−1.46826	−0.734129	+	0.679010i	$0.762409\pi$
$884$	38.4112	1.29191
$885$	−1.33677	−0.0449350
$886$	30.6957	1.03124
$887$	49.4212	1.65940	0.829701	−	0.558209i	$-0.188511\pi$
$887$	49.4212	1.65940	0.829701	+	0.558209i	$0.188511\pi$
$888$	2.77815	0.0932284
$889$	−6.33386	−0.212431
$890$	−0.134754	−0.00451697
$891$	22.0885	0.739994
$892$	−18.7321	−0.627196
$893$	−17.2995	−0.578905
$894$	−30.5043	−1.02022
$895$	0.517840	0.0173095
$896$	−0.553111	−0.0184782
$897$	21.5430	0.719300
$898$	23.6906	0.790566
$899$	42.2428	1.40888
$900$	−38.4002	−1.28001
$901$	19.8642	0.661772
$902$	−2.34976	−0.0782385
$903$	11.8701	0.395014
$904$	−10.7077	−0.356134
$905$	1.68807	0.0561134
$906$	3.26287	0.108402
$907$	−27.0440	−0.897981	−0.448991	−	0.893536i	$-0.648216\pi$
$907$	−27.0440	−0.897981	−0.448991	+	0.893536i	$0.648216\pi$
$908$	−15.9561	−0.529521
$909$	−50.3644	−1.67048
$910$	0.378159	0.0125359
$911$	−44.4434	−1.47248	−0.736238	−	0.676723i	$-0.763400\pi$
$911$	−44.4434	−1.47248	−0.736238	+	0.676723i	$0.763400\pi$
$912$	−11.7648	−0.389571
$913$	−11.9917	−0.396869
$914$	16.5657	0.547943
$915$	1.25098	0.0413560
$916$	−4.97330	−0.164323
$917$	−0.553111	−0.0182654
$918$	89.5747	2.95640
$919$	37.1601	1.22580	0.612899	−	0.790161i	$-0.290003\pi$
$919$	37.1601	1.22580	0.612899	+	0.790161i	$0.290003\pi$
$920$	−0.103796	−0.00342204
$921$	71.2402	2.34744
$922$	−31.5062	−1.03760
$923$	41.2914	1.35912
$924$	−1.47184	−0.0484201
$925$	−4.23804	−0.139346
$926$	6.79440	0.223278
$927$	−120.711	−3.96466
$928$	5.37661	0.176496
$929$	13.8557	0.454589	0.227295	−	0.973826i	$-0.427012\pi$
$929$	13.8557	0.454589	0.227295	+	0.973826i	$0.427012\pi$
$930$	2.66715	0.0874594
$931$	−24.0797	−0.789180
$932$	17.6289	0.577455
$933$	−6.00306	−0.196531
$934$	−30.2173	−0.988740
$935$	−0.492471	−0.0161055
$936$	−50.6971	−1.65709
$937$	−28.9854	−0.946912	−0.473456	−	0.880818i	$-0.656994\pi$
$937$	−28.9854	−0.946912	−0.473456	+	0.880818i	$0.656994\pi$
$938$	−0.483054	−0.0157723
$939$	−69.2949	−2.26135
$940$	0.499174	0.0162813
$941$	37.8281	1.23316	0.616581	−	0.787292i	$-0.288517\pi$
$941$	37.8281	1.23316	0.616581	+	0.787292i	$0.288517\pi$
$942$	26.3980	0.860093
$943$	−2.88800	−0.0940463
$944$	−3.93780	−0.128164
$945$	0.881864	0.0286871
$946$	5.33882	0.173580
$947$	46.4610	1.50978	0.754889	−	0.655852i	$-0.227691\pi$
$947$	46.4610	1.50978	0.754889	+	0.655852i	$0.227691\pi$
$948$	−16.6156	−0.539650
$949$	−71.6377	−2.32546
$950$	17.9471	0.582280
$951$	−69.4211	−2.25113
$952$	−3.22543	−0.104537
$953$	−9.99306	−0.323707	−0.161853	−	0.986815i	$-0.551747\pi$
$953$	−9.99306	−0.323707	−0.161853	+	0.986815i	$0.551747\pi$
$954$	−26.2178	−0.848832
$955$	2.63525	0.0852746
$956$	17.1659	0.555184
$957$	14.3073	0.462489
$958$	−7.26895	−0.234849
$959$	2.85709	0.0922603
$960$	0.339471	0.0109564
$961$	30.7291	0.991260
$962$	−5.59518	−0.180396
$963$	94.6421	3.04980
$964$	−2.77248	−0.0892955
$965$	−2.47543	−0.0796870
$966$	−1.80899	−0.0582033
$967$	12.0629	0.387916	0.193958	−	0.981010i	$-0.437868\pi$
$967$	12.0629	0.387916	0.193958	+	0.981010i	$0.437868\pi$
$968$	10.3380	0.332276
$969$	−68.6056	−2.20393
$970$	−0.574403	−0.0184430
$971$	31.4224	1.00839	0.504196	−	0.863589i	$-0.331789\pi$
$971$	31.4224	1.00839	0.504196	+	0.863589i	$0.331789\pi$
$972$	−42.7082	−1.36986
$973$	−4.97695	−0.159554
$974$	−4.39003	−0.140666
$975$	107.483	3.44221
$976$	3.68508	0.117956
$977$	58.7991	1.88115	0.940575	−	0.339586i	$-0.110287\pi$
$977$	58.7991	1.88115	0.940575	+	0.339586i	$0.110287\pi$
$978$	−41.9242	−1.34059
$979$	−1.05630	−0.0337596
$980$	0.694816	0.0221951
$981$	−131.073	−4.18484
$982$	17.8862	0.570772
$983$	−47.1483	−1.50380	−0.751898	−	0.659279i	$-0.770862\pi$
$983$	−47.1483	−1.50380	−0.751898	+	0.659279i	$0.770862\pi$
$984$	9.44542	0.301109
$985$	2.21467	0.0705652
$986$	31.3533	0.998494
$987$	8.69979	0.276917
$988$	23.6943	0.753815
$989$	6.56175	0.208652
$990$	0.649989	0.0206580
$991$	−3.21762	−0.102211	−0.0511055	−	0.998693i	$-0.516274\pi$
$991$	−3.21762	−0.102211	−0.0511055	+	0.998693i	$0.516274\pi$
$992$	7.85678	0.249453
$993$	1.56887	0.0497864
$994$	−3.46729	−0.109976
$995$	0.161832	0.00513043
$996$	48.2036	1.52739
$997$	37.6316	1.19180	0.595902	−	0.803057i	$-0.296794\pi$
$997$	37.6316	1.19180	0.595902	+	0.803057i	$0.296794\pi$
$998$	21.4420	0.678734
$999$	−13.0479	−0.412818

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.h.1.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.h.1.1	✓	24	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.27057 q^{3} +1.00000 q^{4} -0.103796 q^{5} +3.27057 q^{6} +0.553111 q^{7} -1.00000 q^{8} +7.69663 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.27057 q^{3} +1.00000 q^{4} -0.103796 q^{5} +3.27057 q^{6} +0.553111 q^{7} -1.00000 q^{8} +7.69663 q^{9} +0.103796 q^{10} +0.813628 q^{11} -3.27057 q^{12} +6.58692 q^{13} -0.553111 q^{14} +0.339471 q^{15} +1.00000 q^{16} +5.83144 q^{17} -7.69663 q^{18} +3.59717 q^{19} -0.103796 q^{20} -1.80899 q^{21} -0.813628 q^{22} -1.00000 q^{23} +3.27057 q^{24} -4.98923 q^{25} -6.58692 q^{26} -15.3607 q^{27} +0.553111 q^{28} -5.37661 q^{29} -0.339471 q^{30} -7.85678 q^{31} -1.00000 q^{32} -2.66103 q^{33} -5.83144 q^{34} -0.0574106 q^{35} +7.69663 q^{36} +0.849438 q^{37} -3.59717 q^{38} -21.5430 q^{39} +0.103796 q^{40} +2.88800 q^{41} +1.80899 q^{42} -6.56175 q^{43} +0.813628 q^{44} -0.798877 q^{45} +1.00000 q^{46} -4.80920 q^{47} -3.27057 q^{48} -6.69407 q^{49} +4.98923 q^{50} -19.0721 q^{51} +6.58692 q^{52} +3.40640 q^{53} +15.3607 q^{54} -0.0844511 q^{55} -0.553111 q^{56} -11.7648 q^{57} +5.37661 q^{58} -3.93780 q^{59} +0.339471 q^{60} +3.68508 q^{61} +7.85678 q^{62} +4.25709 q^{63} +1.00000 q^{64} -0.683695 q^{65} +2.66103 q^{66} +0.873340 q^{67} +5.83144 q^{68} +3.27057 q^{69} +0.0574106 q^{70} +6.26870 q^{71} -7.69663 q^{72} -10.8758 q^{73} -0.849438 q^{74} +16.3176 q^{75} +3.59717 q^{76} +0.450027 q^{77} +21.5430 q^{78} +5.08034 q^{79} -0.103796 q^{80} +27.1482 q^{81} -2.88800 q^{82} -14.7386 q^{83} -1.80899 q^{84} -0.605278 q^{85} +6.56175 q^{86} +17.5846 q^{87} -0.813628 q^{88} -1.29826 q^{89} +0.798877 q^{90} +3.64330 q^{91} -1.00000 q^{92} +25.6962 q^{93} +4.80920 q^{94} -0.373371 q^{95} +3.27057 q^{96} -5.53397 q^{97} +6.69407 q^{98} +6.26219 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * q^99

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