LMFDB - Embedded newform 6010.2.a.i.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.49423 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.49423 q^{6} -3.71754 q^{7} -1.00000 q^{8} +3.22119 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.49423 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.49423 q^{6} -3.71754 q^{7} -1.00000 q^{8} +3.22119 q^{9} +1.00000 q^{10} +4.76328 q^{11} -2.49423 q^{12} -5.80528 q^{13} +3.71754 q^{14} +2.49423 q^{15} +1.00000 q^{16} -7.30705 q^{17} -3.22119 q^{18} -5.76760 q^{19} -1.00000 q^{20} +9.27241 q^{21} -4.76328 q^{22} +8.18397 q^{23} +2.49423 q^{24} +1.00000 q^{25} +5.80528 q^{26} -0.551697 q^{27} -3.71754 q^{28} +6.33367 q^{29} -2.49423 q^{30} -9.57684 q^{31} -1.00000 q^{32} -11.8807 q^{33} +7.30705 q^{34} +3.71754 q^{35} +3.22119 q^{36} +6.43345 q^{37} +5.76760 q^{38} +14.4797 q^{39} +1.00000 q^{40} +4.48913 q^{41} -9.27241 q^{42} +2.43339 q^{43} +4.76328 q^{44} -3.22119 q^{45} -8.18397 q^{46} +8.19569 q^{47} -2.49423 q^{48} +6.82013 q^{49} -1.00000 q^{50} +18.2255 q^{51} -5.80528 q^{52} -5.07535 q^{53} +0.551697 q^{54} -4.76328 q^{55} +3.71754 q^{56} +14.3857 q^{57} -6.33367 q^{58} +4.76454 q^{59} +2.49423 q^{60} -11.4925 q^{61} +9.57684 q^{62} -11.9749 q^{63} +1.00000 q^{64} +5.80528 q^{65} +11.8807 q^{66} -11.5251 q^{67} -7.30705 q^{68} -20.4127 q^{69} -3.71754 q^{70} +2.20778 q^{71} -3.22119 q^{72} -4.03153 q^{73} -6.43345 q^{74} -2.49423 q^{75} -5.76760 q^{76} -17.7077 q^{77} -14.4797 q^{78} -1.52617 q^{79} -1.00000 q^{80} -8.28751 q^{81} -4.48913 q^{82} -0.382022 q^{83} +9.27241 q^{84} +7.30705 q^{85} -2.43339 q^{86} -15.7976 q^{87} -4.76328 q^{88} +15.0075 q^{89} +3.22119 q^{90} +21.5814 q^{91} +8.18397 q^{92} +23.8869 q^{93} -8.19569 q^{94} +5.76760 q^{95} +2.49423 q^{96} +2.46648 q^{97} -6.82013 q^{98} +15.3434 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9} + 29 q^{10} - 10 q^{12} - 4 q^{13} + 10 q^{15} + 29 q^{16} - 23 q^{17} - 29 q^{18} + q^{19} - 29 q^{20} + 2 q^{21} - 9 q^{23} + 10 q^{24} + 29 q^{25} + 4 q^{26} - 43 q^{27} - 5 q^{29} - 10 q^{30} + 21 q^{31} - 29 q^{32} - 19 q^{33} + 23 q^{34} + 29 q^{36} - 6 q^{37} - q^{38} + 18 q^{39} + 29 q^{40} - 17 q^{41} - 2 q^{42} - 19 q^{43} - 29 q^{45} + 9 q^{46} - 21 q^{47} - 10 q^{48} + 45 q^{49} - 29 q^{50} + 11 q^{51} - 4 q^{52} - 53 q^{53} + 43 q^{54} - 16 q^{57} + 5 q^{58} - 30 q^{59} + 10 q^{60} + 16 q^{61} - 21 q^{62} - 17 q^{63} + 29 q^{64} + 4 q^{65} + 19 q^{66} - 35 q^{67} - 23 q^{68} + 13 q^{69} + 2 q^{71} - 29 q^{72} - q^{73} + 6 q^{74} - 10 q^{75} + q^{76} - 50 q^{77} - 18 q^{78} + 26 q^{79} - 29 q^{80} + 33 q^{81} + 17 q^{82} - 54 q^{83} + 2 q^{84} + 23 q^{85} + 19 q^{86} - 56 q^{87} - 2 q^{89} + 29 q^{90} + 27 q^{91} - 9 q^{92} - 26 q^{93} + 21 q^{94} - q^{95} + 10 q^{96} + 15 q^{97} - 45 q^{98} + 27 q^{99}+O(q^{100}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9 + 29 * q^10 - 10 * q^12 - 4 * q^13 + 10 * q^15 + 29 * q^16 - 23 * q^17 - 29 * q^18 + q^19 - 29 * q^20 + 2 * q^21 - 9 * q^23 + 10 * q^24 + 29 * q^25 + 4 * q^26 - 43 * q^27 - 5 * q^29 - 10 * q^30 + 21 * q^31 - 29 * q^32 - 19 * q^33 + 23 * q^34 + 29 * q^36 - 6 * q^37 - q^38 + 18 * q^39 + 29 * q^40 - 17 * q^41 - 2 * q^42 - 19 * q^43 - 29 * q^45 + 9 * q^46 - 21 * q^47 - 10 * q^48 + 45 * q^49 - 29 * q^50 + 11 * q^51 - 4 * q^52 - 53 * q^53 + 43 * q^54 - 16 * q^57 + 5 * q^58 - 30 * q^59 + 10 * q^60 + 16 * q^61 - 21 * q^62 - 17 * q^63 + 29 * q^64 + 4 * q^65 + 19 * q^66 - 35 * q^67 - 23 * q^68 + 13 * q^69 + 2 * q^71 - 29 * q^72 - q^73 + 6 * q^74 - 10 * q^75 + q^76 - 50 * q^77 - 18 * q^78 + 26 * q^79 - 29 * q^80 + 33 * q^81 + 17 * q^82 - 54 * q^83 + 2 * q^84 + 23 * q^85 + 19 * q^86 - 56 * q^87 - 2 * q^89 + 29 * q^90 + 27 * q^91 - 9 * q^92 - 26 * q^93 + 21 * q^94 - q^95 + 10 * q^96 + 15 * q^97 - 45 * q^98 + 27 * 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
$3$	−2.49423	−1.44005	−0.720023	−	0.693951i	$-0.755869\pi$
$3$	−2.49423	−1.44005	−0.720023	+	0.693951i	$0.755869\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.49423	1.01827
$7$	−3.71754	−1.40510	−0.702550	−	0.711635i	$-0.747955\pi$
$7$	−3.71754	−1.40510	−0.702550	+	0.711635i	$0.747955\pi$
$8$	−1.00000	−0.353553
$9$	3.22119	1.07373
$10$	1.00000	0.316228
$11$	4.76328	1.43618	0.718091	−	0.695949i	$-0.245016\pi$
$11$	4.76328	1.43618	0.718091	+	0.695949i	$0.245016\pi$
$12$	−2.49423	−0.720023
$13$	−5.80528	−1.61009	−0.805047	−	0.593211i	$-0.797860\pi$
$13$	−5.80528	−1.61009	−0.805047	+	0.593211i	$0.797860\pi$
$14$	3.71754	0.993555
$15$	2.49423	0.644008
$16$	1.00000	0.250000
$17$	−7.30705	−1.77222	−0.886110	−	0.463475i	$-0.846602\pi$
$17$	−7.30705	−1.77222	−0.886110	+	0.463475i	$0.846602\pi$
$18$	−3.22119	−0.759242
$19$	−5.76760	−1.32318	−0.661589	−	0.749867i	$-0.730118\pi$
$19$	−5.76760	−1.32318	−0.661589	+	0.749867i	$0.730118\pi$
$20$	−1.00000	−0.223607
$21$	9.27241	2.02341
$22$	−4.76328	−1.01553
$23$	8.18397	1.70648	0.853238	−	0.521521i	$-0.174635\pi$
$23$	8.18397	1.70648	0.853238	+	0.521521i	$0.174635\pi$
$24$	2.49423	0.509133
$25$	1.00000	0.200000
$26$	5.80528	1.13851
$27$	−0.551697	−0.106174
$28$	−3.71754	−0.702550
$29$	6.33367	1.17613	0.588066	−	0.808813i	$-0.299889\pi$
$29$	6.33367	1.17613	0.588066	+	0.808813i	$0.299889\pi$
$30$	−2.49423	−0.455382
$31$	−9.57684	−1.72005	−0.860026	−	0.510250i	$-0.829553\pi$
$31$	−9.57684	−1.72005	−0.860026	+	0.510250i	$0.829553\pi$
$32$	−1.00000	−0.176777
$33$	−11.8807	−2.06817
$34$	7.30705	1.25315
$35$	3.71754	0.628380
$36$	3.22119	0.536865
$37$	6.43345	1.05765	0.528826	−	0.848730i	$-0.322632\pi$
$37$	6.43345	1.05765	0.528826	+	0.848730i	$0.322632\pi$
$38$	5.76760	0.935628
$39$	14.4797	2.31861
$40$	1.00000	0.158114
$41$	4.48913	0.701084	0.350542	−	0.936547i	$-0.385997\pi$
$41$	4.48913	0.701084	0.350542	+	0.936547i	$0.385997\pi$
$42$	−9.27241	−1.43076
$43$	2.43339	0.371088	0.185544	−	0.982636i	$-0.440595\pi$
$43$	2.43339	0.371088	0.185544	+	0.982636i	$0.440595\pi$
$44$	4.76328	0.718091
$45$	−3.22119	−0.480187
$46$	−8.18397	−1.20666
$47$	8.19569	1.19546	0.597732	−	0.801696i	$-0.296069\pi$
$47$	8.19569	1.19546	0.597732	+	0.801696i	$0.296069\pi$
$48$	−2.49423	−0.360011
$49$	6.82013	0.974304
$50$	−1.00000	−0.141421
$51$	18.2255	2.55208
$52$	−5.80528	−0.805047
$53$	−5.07535	−0.697153	−0.348577	−	0.937280i	$-0.613335\pi$
$53$	−5.07535	−0.697153	−0.348577	+	0.937280i	$0.613335\pi$
$54$	0.551697	0.0750765
$55$	−4.76328	−0.642280
$56$	3.71754	0.496778
$57$	14.3857	1.90544
$58$	−6.33367	−0.831651
$59$	4.76454	0.620291	0.310145	−	0.950689i	$-0.399622\pi$
$59$	4.76454	0.620291	0.310145	+	0.950689i	$0.399622\pi$
$60$	2.49423	0.322004
$61$	−11.4925	−1.47146	−0.735731	−	0.677274i	$-0.763161\pi$
$61$	−11.4925	−1.47146	−0.735731	+	0.677274i	$0.763161\pi$
$62$	9.57684	1.21626
$63$	−11.9749	−1.50870
$64$	1.00000	0.125000
$65$	5.80528	0.720056
$66$	11.8807	1.46241
$67$	−11.5251	−1.40802	−0.704008	−	0.710192i	$-0.748608\pi$
$67$	−11.5251	−1.40802	−0.704008	+	0.710192i	$0.748608\pi$
$68$	−7.30705	−0.886110
$69$	−20.4127	−2.45740
$70$	−3.71754	−0.444331
$71$	2.20778	0.262015	0.131008	−	0.991381i	$-0.458179\pi$
$71$	2.20778	0.262015	0.131008	+	0.991381i	$0.458179\pi$
$72$	−3.22119	−0.379621
$73$	−4.03153	−0.471855	−0.235928	−	0.971771i	$-0.575813\pi$
$73$	−4.03153	−0.471855	−0.235928	+	0.971771i	$0.575813\pi$
$74$	−6.43345	−0.747873
$75$	−2.49423	−0.288009
$76$	−5.76760	−0.661589
$77$	−17.7077	−2.01798
$78$	−14.4797	−1.63950
$79$	−1.52617	−0.171708	−0.0858538	−	0.996308i	$-0.527362\pi$
$79$	−1.52617	−0.171708	−0.0858538	+	0.996308i	$0.527362\pi$
$80$	−1.00000	−0.111803
$81$	−8.28751	−0.920834
$82$	−4.48913	−0.495741
$83$	−0.382022	−0.0419324	−0.0209662	−	0.999780i	$-0.506674\pi$
$83$	−0.382022	−0.0419324	−0.0209662	+	0.999780i	$0.506674\pi$
$84$	9.27241	1.01170
$85$	7.30705	0.792561
$86$	−2.43339	−0.262399
$87$	−15.7976	−1.69368
$88$	−4.76328	−0.507767
$89$	15.0075	1.59079	0.795396	−	0.606091i	$-0.207263\pi$
$89$	15.0075	1.59079	0.795396	+	0.606091i	$0.207263\pi$
$90$	3.22119	0.339543
$91$	21.5814	2.26234
$92$	8.18397	0.853238
$93$	23.8869	2.47695
$94$	−8.19569	−0.845321
$95$	5.76760	0.591743
$96$	2.49423	0.254566
$97$	2.46648	0.250433	0.125216	−	0.992129i	$-0.460037\pi$
$97$	2.46648	0.250433	0.125216	+	0.992129i	$0.460037\pi$
$98$	−6.82013	−0.688937
$99$	15.3434	1.54207
$100$	1.00000	0.100000
$101$	−0.763870	−0.0760079	−0.0380039	−	0.999278i	$-0.512100\pi$
$101$	−0.763870	−0.0760079	−0.0380039	+	0.999278i	$0.512100\pi$
$102$	−18.2255	−1.80459
$103$	10.8505	1.06913	0.534567	−	0.845126i	$-0.320475\pi$
$103$	10.8505	1.06913	0.534567	+	0.845126i	$0.320475\pi$
$104$	5.80528	0.569254
$105$	−9.27241	−0.904895
$106$	5.07535	0.492962
$107$	−9.60142	−0.928204	−0.464102	−	0.885782i	$-0.653623\pi$
$107$	−9.60142	−0.928204	−0.464102	+	0.885782i	$0.653623\pi$
$108$	−0.551697	−0.0530871
$109$	19.2682	1.84556	0.922778	−	0.385332i	$-0.125913\pi$
$109$	19.2682	1.84556	0.922778	+	0.385332i	$0.125913\pi$
$110$	4.76328	0.454161
$111$	−16.0465	−1.52307
$112$	−3.71754	−0.351275
$113$	17.4460	1.64118	0.820589	−	0.571519i	$-0.193646\pi$
$113$	17.4460	1.64118	0.820589	+	0.571519i	$0.193646\pi$
$114$	−14.3857	−1.34735
$115$	−8.18397	−0.763159
$116$	6.33367	0.588066
$117$	−18.6999	−1.72881
$118$	−4.76454	−0.438612
$119$	27.1643	2.49015
$120$	−2.49423	−0.227691
$121$	11.6888	1.06262
$122$	11.4925	1.04048
$123$	−11.1969	−1.00959
$124$	−9.57684	−0.860026
$125$	−1.00000	−0.0894427
$126$	11.9749	1.06681
$127$	6.37569	0.565751	0.282875	−	0.959157i	$-0.408712\pi$
$127$	6.37569	0.565751	0.282875	+	0.959157i	$0.408712\pi$
$128$	−1.00000	−0.0883883
$129$	−6.06943	−0.534384
$130$	−5.80528	−0.509156
$131$	13.2659	1.15905	0.579523	−	0.814956i	$-0.303239\pi$
$131$	13.2659	1.15905	0.579523	+	0.814956i	$0.303239\pi$
$132$	−11.8807	−1.03408
$133$	21.4413	1.85920
$134$	11.5251	0.995618
$135$	0.551697	0.0474826
$136$	7.30705	0.626574
$137$	5.48480	0.468598	0.234299	−	0.972165i	$-0.424720\pi$
$137$	5.48480	0.468598	0.234299	+	0.972165i	$0.424720\pi$
$138$	20.4127	1.73765
$139$	5.09400	0.432068	0.216034	−	0.976386i	$-0.430688\pi$
$139$	5.09400	0.432068	0.216034	+	0.976386i	$0.430688\pi$
$140$	3.71754	0.314190
$141$	−20.4420	−1.72152
$142$	−2.20778	−0.185273
$143$	−27.6521	−2.31239
$144$	3.22119	0.268432
$145$	−6.33367	−0.525982
$146$	4.03153	0.333652
$147$	−17.0110	−1.40304
$148$	6.43345	0.528826
$149$	20.6186	1.68915	0.844573	−	0.535441i	$-0.179855\pi$
$149$	20.6186	1.68915	0.844573	+	0.535441i	$0.179855\pi$
$150$	2.49423	0.203653
$151$	−7.83803	−0.637850	−0.318925	−	0.947780i	$-0.603322\pi$
$151$	−7.83803	−0.637850	−0.318925	+	0.947780i	$0.603322\pi$
$152$	5.76760	0.467814
$153$	−23.5374	−1.90289
$154$	17.7077	1.42693
$155$	9.57684	0.769231
$156$	14.4797	1.15930
$157$	15.4093	1.22979	0.614897	−	0.788608i	$-0.289198\pi$
$157$	15.4093	1.22979	0.614897	+	0.788608i	$0.289198\pi$
$158$	1.52617	0.121416
$159$	12.6591	1.00393
$160$	1.00000	0.0790569
$161$	−30.4243	−2.39777
$162$	8.28751	0.651128
$163$	−12.7913	−1.00189	−0.500946	−	0.865479i	$-0.667014\pi$
$163$	−12.7913	−1.00189	−0.500946	+	0.865479i	$0.667014\pi$
$164$	4.48913	0.350542
$165$	11.8807	0.924912
$166$	0.382022	0.0296507
$167$	13.1409	1.01687	0.508437	−	0.861099i	$-0.330223\pi$
$167$	13.1409	1.01687	0.508437	+	0.861099i	$0.330223\pi$
$168$	−9.27241	−0.715382
$169$	20.7012	1.59240
$170$	−7.30705	−0.560425
$171$	−18.5785	−1.42074
$172$	2.43339	0.185544
$173$	10.9753	0.834439	0.417219	−	0.908806i	$-0.363005\pi$
$173$	10.9753	0.834439	0.417219	+	0.908806i	$0.363005\pi$
$174$	15.7976	1.19762
$175$	−3.71754	−0.281020
$176$	4.76328	0.359045
$177$	−11.8839	−0.893246
$178$	−15.0075	−1.12486
$179$	−6.23908	−0.466330	−0.233165	−	0.972437i	$-0.574908\pi$
$179$	−6.23908	−0.466330	−0.233165	+	0.972437i	$0.574908\pi$
$180$	−3.22119	−0.240093
$181$	−6.71439	−0.499077	−0.249538	−	0.968365i	$-0.580279\pi$
$181$	−6.71439	−0.499077	−0.249538	+	0.968365i	$0.580279\pi$
$182$	−21.5814	−1.59972
$183$	28.6649	2.11897
$184$	−8.18397	−0.603330
$185$	−6.43345	−0.472997
$186$	−23.8869	−1.75147
$187$	−34.8055	−2.54523
$188$	8.19569	0.597732
$189$	2.05096	0.149185
$190$	−5.76760	−0.418426
$191$	−23.3903	−1.69246	−0.846232	−	0.532814i	$-0.821134\pi$
$191$	−23.3903	−1.69246	−0.846232	+	0.532814i	$0.821134\pi$
$192$	−2.49423	−0.180006
$193$	−24.2217	−1.74352	−0.871758	−	0.489936i	$-0.837020\pi$
$193$	−24.2217	−1.74352	−0.871758	+	0.489936i	$0.837020\pi$
$194$	−2.46648	−0.177083
$195$	−14.4797	−1.03691
$196$	6.82013	0.487152
$197$	−13.9779	−0.995886	−0.497943	−	0.867210i	$-0.665911\pi$
$197$	−13.9779	−0.995886	−0.497943	+	0.867210i	$0.665911\pi$
$198$	−15.3434	−1.09041
$199$	−10.6632	−0.755891	−0.377946	−	0.925828i	$-0.623369\pi$
$199$	−10.6632	−0.755891	−0.377946	+	0.925828i	$0.623369\pi$
$200$	−1.00000	−0.0707107
$201$	28.7463	2.02761
$202$	0.763870	0.0537457
$203$	−23.5457	−1.65258
$204$	18.2255	1.27604
$205$	−4.48913	−0.313534
$206$	−10.8505	−0.755992
$207$	26.3621	1.83229
$208$	−5.80528	−0.402523
$209$	−27.4727	−1.90032
$210$	9.27241	0.639857
$211$	−4.91830	−0.338589	−0.169295	−	0.985565i	$-0.554149\pi$
$211$	−4.91830	−0.338589	−0.169295	+	0.985565i	$0.554149\pi$
$212$	−5.07535	−0.348577
$213$	−5.50671	−0.377314
$214$	9.60142	0.656340
$215$	−2.43339	−0.165956
$216$	0.551697	0.0375383
$217$	35.6023	2.41684
$218$	−19.2682	−1.30501
$219$	10.0556	0.679493
$220$	−4.76328	−0.321140
$221$	42.4195	2.85344
$222$	16.0465	1.07697
$223$	7.62879	0.510862	0.255431	−	0.966827i	$-0.417783\pi$
$223$	7.62879	0.510862	0.255431	+	0.966827i	$0.417783\pi$
$224$	3.71754	0.248389
$225$	3.22119	0.214746
$226$	−17.4460	−1.16049
$227$	15.9477	1.05849	0.529244	−	0.848470i	$-0.322476\pi$
$227$	15.9477	1.05849	0.529244	+	0.848470i	$0.322476\pi$
$228$	14.3857	0.952718
$229$	7.44033	0.491671	0.245836	−	0.969312i	$-0.420938\pi$
$229$	7.44033	0.491671	0.245836	+	0.969312i	$0.420938\pi$
$230$	8.18397	0.539635
$231$	44.1671	2.90598
$232$	−6.33367	−0.415826
$233$	−20.4502	−1.33974	−0.669869	−	0.742479i	$-0.733650\pi$
$233$	−20.4502	−1.33974	−0.669869	+	0.742479i	$0.733650\pi$
$234$	18.6999	1.22245
$235$	−8.19569	−0.534628
$236$	4.76454	0.310145
$237$	3.80662	0.247267
$238$	−27.1643	−1.76080
$239$	−7.66521	−0.495821	−0.247911	−	0.968783i	$-0.579744\pi$
$239$	−7.66521	−0.495821	−0.247911	+	0.968783i	$0.579744\pi$
$240$	2.49423	0.161002
$241$	−5.72880	−0.369024	−0.184512	−	0.982830i	$-0.559070\pi$
$241$	−5.72880	−0.369024	−0.184512	+	0.982830i	$0.559070\pi$
$242$	−11.6888	−0.751385
$243$	22.3261	1.43222
$244$	−11.4925	−0.735731
$245$	−6.82013	−0.435722
$246$	11.1969	0.713890
$247$	33.4825	2.13044
$248$	9.57684	0.608130
$249$	0.952851	0.0603845
$250$	1.00000	0.0632456
$251$	18.9875	1.19848	0.599240	−	0.800570i	$-0.295470\pi$
$251$	18.9875	1.19848	0.599240	+	0.800570i	$0.295470\pi$
$252$	−11.9749	−0.754348
$253$	38.9825	2.45081
$254$	−6.37569	−0.400046
$255$	−18.2255	−1.14132
$256$	1.00000	0.0625000
$257$	25.3380	1.58054	0.790269	−	0.612760i	$-0.209941\pi$
$257$	25.3380	1.58054	0.790269	+	0.612760i	$0.209941\pi$
$258$	6.06943	0.377866
$259$	−23.9166	−1.48611
$260$	5.80528	0.360028
$261$	20.4019	1.26285
$262$	−13.2659	−0.819570
$263$	−20.7240	−1.27790	−0.638948	−	0.769250i	$-0.720630\pi$
$263$	−20.7240	−1.27790	−0.638948	+	0.769250i	$0.720630\pi$
$264$	11.8807	0.731207
$265$	5.07535	0.311776
$266$	−21.4413	−1.31465
$267$	−37.4322	−2.29081
$268$	−11.5251	−0.704008
$269$	−2.80224	−0.170855	−0.0854277	−	0.996344i	$-0.527226\pi$
$269$	−2.80224	−0.170855	−0.0854277	+	0.996344i	$0.527226\pi$
$270$	−0.551697	−0.0335752
$271$	−6.02355	−0.365905	−0.182952	−	0.983122i	$-0.558565\pi$
$271$	−6.02355	−0.365905	−0.182952	+	0.983122i	$0.558565\pi$
$272$	−7.30705	−0.443055
$273$	−53.8289	−3.25787
$274$	−5.48480	−0.331349
$275$	4.76328	0.287236
$276$	−20.4127	−1.22870
$277$	12.9449	0.777782	0.388891	−	0.921284i	$-0.372858\pi$
$277$	12.9449	0.777782	0.388891	+	0.921284i	$0.372858\pi$
$278$	−5.09400	−0.305518
$279$	−30.8488	−1.84687
$280$	−3.71754	−0.222166
$281$	−2.62463	−0.156572	−0.0782860	−	0.996931i	$-0.524945\pi$
$281$	−2.62463	−0.156572	−0.0782860	+	0.996931i	$0.524945\pi$
$282$	20.4420	1.21730
$283$	8.47788	0.503958	0.251979	−	0.967733i	$-0.418919\pi$
$283$	8.47788	0.503958	0.251979	+	0.967733i	$0.418919\pi$
$284$	2.20778	0.131008
$285$	−14.3857	−0.852137
$286$	27.6521	1.63511
$287$	−16.6885	−0.985093
$288$	−3.22119	−0.189810
$289$	36.3930	2.14076
$290$	6.33367	0.371926
$291$	−6.15197	−0.360635
$292$	−4.03153	−0.235928
$293$	0.440886	0.0257568	0.0128784	−	0.999917i	$-0.495901\pi$
$293$	0.440886	0.0257568	0.0128784	+	0.999917i	$0.495901\pi$
$294$	17.0110	0.992100
$295$	−4.76454	−0.277402
$296$	−6.43345	−0.373937
$297$	−2.62789	−0.152485
$298$	−20.6186	−1.19441
$299$	−47.5102	−2.74759
$300$	−2.49423	−0.144005
$301$	−9.04623	−0.521416
$302$	7.83803	0.451028
$303$	1.90527	0.109455
$304$	−5.76760	−0.330794
$305$	11.4925	0.658058
$306$	23.5374	1.34554
$307$	13.5623	0.774043	0.387021	−	0.922071i	$-0.373504\pi$
$307$	13.5623	0.774043	0.387021	+	0.922071i	$0.373504\pi$
$308$	−17.7077	−1.00899
$309$	−27.0637	−1.53960
$310$	−9.57684	−0.543928
$311$	−22.3001	−1.26452	−0.632262	−	0.774755i	$-0.717873\pi$
$311$	−22.3001	−1.26452	−0.632262	+	0.774755i	$0.717873\pi$
$312$	−14.4797	−0.819752
$313$	−14.0082	−0.791789	−0.395895	−	0.918296i	$-0.629565\pi$
$313$	−14.0082	−0.791789	−0.395895	+	0.918296i	$0.629565\pi$
$314$	−15.4093	−0.869596
$315$	11.9749	0.674710
$316$	−1.52617	−0.0858538
$317$	2.51601	0.141313	0.0706567	−	0.997501i	$-0.477491\pi$
$317$	2.51601	0.141313	0.0706567	+	0.997501i	$0.477491\pi$
$318$	−12.6591	−0.709887
$319$	30.1690	1.68914
$320$	−1.00000	−0.0559017
$321$	23.9482	1.33666
$322$	30.4243	1.69548
$323$	42.1441	2.34496
$324$	−8.28751	−0.460417
$325$	−5.80528	−0.322019
$326$	12.7913	0.708445
$327$	−48.0593	−2.65768
$328$	−4.48913	−0.247871
$329$	−30.4678	−1.67975
$330$	−11.8807	−0.654012
$331$	−5.99424	−0.329473	−0.164736	−	0.986338i	$-0.552677\pi$
$331$	−5.99424	−0.329473	−0.164736	+	0.986338i	$0.552677\pi$
$332$	−0.382022	−0.0209662
$333$	20.7234	1.13563
$334$	−13.1409	−0.719039
$335$	11.5251	0.629684
$336$	9.27241	0.505852
$337$	−14.2382	−0.775602	−0.387801	−	0.921743i	$-0.626765\pi$
$337$	−14.2382	−0.775602	−0.387801	+	0.921743i	$0.626765\pi$
$338$	−20.7012	−1.12600
$339$	−43.5143	−2.36337
$340$	7.30705	0.396281
$341$	−45.6172	−2.47031
$342$	18.5785	1.00461
$343$	0.668679	0.0361053
$344$	−2.43339	−0.131200
$345$	20.4127	1.09898
$346$	−10.9753	−0.590037
$347$	−1.01558	−0.0545192	−0.0272596	−	0.999628i	$-0.508678\pi$
$347$	−1.01558	−0.0545192	−0.0272596	+	0.999628i	$0.508678\pi$
$348$	−15.7976	−0.846842
$349$	−16.1305	−0.863445	−0.431723	−	0.902006i	$-0.642094\pi$
$349$	−16.1305	−0.863445	−0.431723	+	0.902006i	$0.642094\pi$
$350$	3.71754	0.198711
$351$	3.20276	0.170950
$352$	−4.76328	−0.253884
$353$	−25.2692	−1.34494	−0.672471	−	0.740124i	$-0.734767\pi$
$353$	−25.2692	−1.34494	−0.672471	+	0.740124i	$0.734767\pi$
$354$	11.8839	0.631621
$355$	−2.20778	−0.117177
$356$	15.0075	0.795396
$357$	−67.7540	−3.58592
$358$	6.23908	0.329745
$359$	11.4668	0.605197	0.302598	−	0.953118i	$-0.402146\pi$
$359$	11.4668	0.605197	0.302598	+	0.953118i	$0.402146\pi$
$360$	3.22119	0.169772
$361$	14.2652	0.750799
$362$	6.71439	0.352900
$363$	−29.1546	−1.53022
$364$	21.5814	1.13117
$365$	4.03153	0.211020
$366$	−28.6649	−1.49834
$367$	−25.4074	−1.32625	−0.663127	−	0.748507i	$-0.730771\pi$
$367$	−25.4074	−1.32625	−0.663127	+	0.748507i	$0.730771\pi$
$368$	8.18397	0.426619
$369$	14.4603	0.752775
$370$	6.43345	0.334459
$371$	18.8678	0.979570
$372$	23.8869	1.23848
$373$	−25.0351	−1.29627	−0.648135	−	0.761525i	$-0.724451\pi$
$373$	−25.0351	−1.29627	−0.648135	+	0.761525i	$0.724451\pi$
$374$	34.8055	1.79975
$375$	2.49423	0.128802
$376$	−8.19569	−0.422661
$377$	−36.7687	−1.89368
$378$	−2.05096	−0.105490
$379$	−30.8141	−1.58281	−0.791406	−	0.611291i	$-0.790651\pi$
$379$	−30.8141	−1.58281	−0.791406	+	0.611291i	$0.790651\pi$
$380$	5.76760	0.295872
$381$	−15.9024	−0.814706
$382$	23.3903	1.19675
$383$	−23.9338	−1.22296	−0.611479	−	0.791260i	$-0.709425\pi$
$383$	−23.9338	−1.22296	−0.611479	+	0.791260i	$0.709425\pi$
$384$	2.49423	0.127283
$385$	17.7077	0.902467
$386$	24.2217	1.23285
$387$	7.83841	0.398449
$388$	2.46648	0.125216
$389$	10.7474	0.544914	0.272457	−	0.962168i	$-0.412164\pi$
$389$	10.7474	0.544914	0.272457	+	0.962168i	$0.412164\pi$
$390$	14.4797	0.733208
$391$	−59.8007	−3.02425
$392$	−6.82013	−0.344469
$393$	−33.0882	−1.66908
$394$	13.9779	0.704198
$395$	1.52617	0.0767899
$396$	15.3434	0.771036
$397$	30.5034	1.53092	0.765460	−	0.643483i	$-0.222511\pi$
$397$	30.5034	1.53092	0.765460	+	0.643483i	$0.222511\pi$
$398$	10.6632	0.534496
$399$	−53.4795	−2.67733
$400$	1.00000	0.0500000
$401$	24.6517	1.23105	0.615524	−	0.788118i	$-0.288945\pi$
$401$	24.6517	1.23105	0.615524	+	0.788118i	$0.288945\pi$
$402$	−28.7463	−1.43373
$403$	55.5962	2.76944
$404$	−0.763870	−0.0380039
$405$	8.28751	0.411810
$406$	23.5457	1.16855
$407$	30.6443	1.51898
$408$	−18.2255	−0.902296
$409$	20.7576	1.02640	0.513198	−	0.858270i	$-0.328461\pi$
$409$	20.7576	1.02640	0.513198	+	0.858270i	$0.328461\pi$
$410$	4.48913	0.221702
$411$	−13.6804	−0.674803
$412$	10.8505	0.534567
$413$	−17.7124	−0.871570
$414$	−26.3621	−1.29563
$415$	0.382022	0.0187527
$416$	5.80528	0.284627
$417$	−12.7056	−0.622197
$418$	27.4727	1.34373
$419$	−34.7099	−1.69569	−0.847845	−	0.530244i	$-0.822100\pi$
$419$	−34.7099	−1.69569	−0.847845	+	0.530244i	$0.822100\pi$
$420$	−9.27241	−0.452447
$421$	−34.9813	−1.70488	−0.852442	−	0.522822i	$-0.824879\pi$
$421$	−34.9813	−1.70488	−0.852442	+	0.522822i	$0.824879\pi$
$422$	4.91830	0.239419
$423$	26.3999	1.28361
$424$	5.07535	0.246481
$425$	−7.30705	−0.354444
$426$	5.50671	0.266801
$427$	42.7238	2.06755
$428$	−9.60142	−0.464102
$429$	68.9708	3.32994
$430$	2.43339	0.117348
$431$	14.2655	0.687144	0.343572	−	0.939126i	$-0.388363\pi$
$431$	14.2655	0.687144	0.343572	+	0.939126i	$0.388363\pi$
$432$	−0.551697	−0.0265436
$433$	30.2302	1.45277	0.726386	−	0.687287i	$-0.241198\pi$
$433$	30.2302	1.45277	0.726386	+	0.687287i	$0.241198\pi$
$434$	−35.6023	−1.70897
$435$	15.7976	0.757438
$436$	19.2682	0.922778
$437$	−47.2019	−2.25797
$438$	−10.0556	−0.480474
$439$	−5.82087	−0.277815	−0.138907	−	0.990305i	$-0.544359\pi$
$439$	−5.82087	−0.277815	−0.138907	+	0.990305i	$0.544359\pi$
$440$	4.76328	0.227080
$441$	21.9689	1.04614
$442$	−42.4195	−2.01769
$443$	−19.7495	−0.938328	−0.469164	−	0.883111i	$-0.655445\pi$
$443$	−19.7495	−0.938328	−0.469164	+	0.883111i	$0.655445\pi$
$444$	−16.0465	−0.761534
$445$	−15.0075	−0.711423
$446$	−7.62879	−0.361234
$447$	−51.4277	−2.43245
$448$	−3.71754	−0.175637
$449$	0.493409	0.0232854	0.0116427	−	0.999932i	$-0.496294\pi$
$449$	0.493409	0.0232854	0.0116427	+	0.999932i	$0.496294\pi$
$450$	−3.22119	−0.151848
$451$	21.3830	1.00688
$452$	17.4460	0.820589
$453$	19.5499	0.918533
$454$	−15.9477	−0.748464
$455$	−21.5814	−1.01175
$456$	−14.3857	−0.673673
$457$	2.73681	0.128023	0.0640113	−	0.997949i	$-0.479611\pi$
$457$	2.73681	0.128023	0.0640113	+	0.997949i	$0.479611\pi$
$458$	−7.44033	−0.347664
$459$	4.03128	0.188164
$460$	−8.18397	−0.381580
$461$	8.74063	0.407092	0.203546	−	0.979065i	$-0.434753\pi$
$461$	8.74063	0.407092	0.203546	+	0.979065i	$0.434753\pi$
$462$	−44.1671	−2.05484
$463$	−10.1123	−0.469957	−0.234978	−	0.972001i	$-0.575502\pi$
$463$	−10.1123	−0.469957	−0.234978	+	0.972001i	$0.575502\pi$
$464$	6.33367	0.294033
$465$	−23.8869	−1.10773
$466$	20.4502	0.947338
$467$	7.61428	0.352347	0.176173	−	0.984359i	$-0.443628\pi$
$467$	7.61428	0.352347	0.176173	+	0.984359i	$0.443628\pi$
$468$	−18.6999	−0.864403
$469$	42.8451	1.97840
$470$	8.19569	0.378039
$471$	−38.4343	−1.77096
$472$	−4.76454	−0.219306
$473$	11.5909	0.532950
$474$	−3.80662	−0.174844
$475$	−5.76760	−0.264636
$476$	27.1643	1.24507
$477$	−16.3487	−0.748554
$478$	7.66521	0.350599
$479$	−21.7987	−0.996009	−0.498005	−	0.867174i	$-0.665934\pi$
$479$	−21.7987	−0.996009	−0.498005	+	0.867174i	$0.665934\pi$
$480$	−2.49423	−0.113846
$481$	−37.3479	−1.70292
$482$	5.72880	0.260940
$483$	75.8852	3.45290
$484$	11.6888	0.531309
$485$	−2.46648	−0.111997
$486$	−22.3261	−1.01273
$487$	−18.0188	−0.816509	−0.408255	−	0.912868i	$-0.633862\pi$
$487$	−18.0188	−0.816509	−0.408255	+	0.912868i	$0.633862\pi$
$488$	11.4925	0.520241
$489$	31.9045	1.44277
$490$	6.82013	0.308102
$491$	18.5708	0.838090	0.419045	−	0.907966i	$-0.362365\pi$
$491$	18.5708	0.838090	0.419045	+	0.907966i	$0.362365\pi$
$492$	−11.1969	−0.504796
$493$	−46.2804	−2.08437
$494$	−33.4825	−1.50645
$495$	−15.3434	−0.689635
$496$	−9.57684	−0.430013
$497$	−8.20751	−0.368157
$498$	−0.952851	−0.0426983
$499$	−43.9047	−1.96545	−0.982723	−	0.185082i	$-0.940745\pi$
$499$	−43.9047	−1.96545	−0.982723	+	0.185082i	$0.940745\pi$
$500$	−1.00000	−0.0447214
$501$	−32.7765	−1.46434
$502$	−18.9875	−0.847453
$503$	0.433518	0.0193296	0.00966480	−	0.999953i	$-0.496924\pi$
$503$	0.433518	0.0193296	0.00966480	+	0.999953i	$0.496924\pi$
$504$	11.9749	0.533405
$505$	0.763870	0.0339918
$506$	−38.9825	−1.73298
$507$	−51.6337	−2.29313
$508$	6.37569	0.282875
$509$	−40.4042	−1.79088	−0.895442	−	0.445178i	$-0.853140\pi$
$509$	−40.4042	−1.79088	−0.895442	+	0.445178i	$0.853140\pi$
$510$	18.2255	0.807038
$511$	14.9874	0.663003
$512$	−1.00000	−0.0441942
$513$	3.18197	0.140487
$514$	−25.3380	−1.11761
$515$	−10.8505	−0.478132
$516$	−6.06943	−0.267192
$517$	39.0383	1.71690
$518$	23.9166	1.05084
$519$	−27.3750	−1.20163
$520$	−5.80528	−0.254578
$521$	26.0035	1.13923	0.569617	−	0.821910i	$-0.307091\pi$
$521$	26.0035	1.13923	0.569617	+	0.821910i	$0.307091\pi$
$522$	−20.4019	−0.892969
$523$	7.63080	0.333672	0.166836	−	0.985985i	$-0.446645\pi$
$523$	7.63080	0.333672	0.166836	+	0.985985i	$0.446645\pi$
$524$	13.2659	0.579523
$525$	9.27241	0.404681
$526$	20.7240	0.903609
$527$	69.9785	3.04831
$528$	−11.8807	−0.517042
$529$	43.9774	1.91206
$530$	−5.07535	−0.220459
$531$	15.3475	0.666025
$532$	21.4413	0.929598
$533$	−26.0606	−1.12881
$534$	37.4322	1.61985
$535$	9.60142	0.415106
$536$	11.5251	0.497809
$537$	15.5617	0.671537
$538$	2.80224	0.120813
$539$	32.4862	1.39928
$540$	0.551697	0.0237413
$541$	−28.0668	−1.20668	−0.603342	−	0.797482i	$-0.706165\pi$
$541$	−28.0668	−1.20668	−0.603342	+	0.797482i	$0.706165\pi$
$542$	6.02355	0.258734
$543$	16.7472	0.718693
$544$	7.30705	0.313287
$545$	−19.2682	−0.825358
$546$	53.8289	2.30366
$547$	−31.1863	−1.33343	−0.666716	−	0.745312i	$-0.732300\pi$
$547$	−31.1863	−1.33343	−0.666716	+	0.745312i	$0.732300\pi$
$548$	5.48480	0.234299
$549$	−37.0195	−1.57995
$550$	−4.76328	−0.203107
$551$	−36.5300	−1.55623
$552$	20.4127	0.868823
$553$	5.67360	0.241266
$554$	−12.9449	−0.549975
$555$	16.0465	0.681136
$556$	5.09400	0.216034
$557$	29.8391	1.26432	0.632161	−	0.774837i	$-0.282168\pi$
$557$	29.8391	1.26432	0.632161	+	0.774837i	$0.282168\pi$
$558$	30.8488	1.30593
$559$	−14.1265	−0.597487
$560$	3.71754	0.157095
$561$	86.8130	3.66525
$562$	2.62463	0.110713
$563$	−14.4335	−0.608301	−0.304151	−	0.952624i	$-0.598373\pi$
$563$	−14.4335	−0.608301	−0.304151	+	0.952624i	$0.598373\pi$
$564$	−20.4420	−0.860761
$565$	−17.4460	−0.733957
$566$	−8.47788	−0.356352
$567$	30.8092	1.29386
$568$	−2.20778	−0.0926363
$569$	−9.96509	−0.417758	−0.208879	−	0.977941i	$-0.566982\pi$
$569$	−9.96509	−0.417758	−0.208879	+	0.977941i	$0.566982\pi$
$570$	14.3857	0.602552
$571$	1.85665	0.0776985	0.0388493	−	0.999245i	$-0.487631\pi$
$571$	1.85665	0.0776985	0.0388493	+	0.999245i	$0.487631\pi$
$572$	−27.6521	−1.15619
$573$	58.3409	2.43723
$574$	16.6885	0.696566
$575$	8.18397	0.341295
$576$	3.22119	0.134216
$577$	21.1780	0.881652	0.440826	−	0.897593i	$-0.354686\pi$
$577$	21.1780	0.881652	0.440826	+	0.897593i	$0.354686\pi$
$578$	−36.3930	−1.51375
$579$	60.4145	2.51074
$580$	−6.33367	−0.262991
$581$	1.42018	0.0589191
$582$	6.15197	0.255007
$583$	−24.1753	−1.00124
$584$	4.03153	0.166826
$585$	18.6999	0.773145
$586$	−0.440886	−0.0182128
$587$	−11.1817	−0.461518	−0.230759	−	0.973011i	$-0.574121\pi$
$587$	−11.1817	−0.461518	−0.230759	+	0.973011i	$0.574121\pi$
$588$	−17.0110	−0.701521
$589$	55.2354	2.27593
$590$	4.76454	0.196153
$591$	34.8642	1.43412
$592$	6.43345	0.264413
$593$	−3.56951	−0.146582	−0.0732910	−	0.997311i	$-0.523350\pi$
$593$	−3.56951	−0.146582	−0.0732910	+	0.997311i	$0.523350\pi$
$594$	2.62789	0.107824
$595$	−27.1643	−1.11363
$596$	20.6186	0.844573
$597$	26.5964	1.08852
$598$	47.5102	1.94284
$599$	10.8883	0.444882	0.222441	−	0.974946i	$-0.428598\pi$
$599$	10.8883	0.444882	0.222441	+	0.974946i	$0.428598\pi$
$600$	2.49423	0.101827
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	9.04623	0.368697
$603$	−37.1246	−1.51183
$604$	−7.83803	−0.318925
$605$	−11.6888	−0.475218
$606$	−1.90527	−0.0773962
$607$	−7.32433	−0.297285	−0.148643	−	0.988891i	$-0.547490\pi$
$607$	−7.32433	−0.297285	−0.148643	+	0.988891i	$0.547490\pi$
$608$	5.76760	0.233907
$609$	58.7284	2.37979
$610$	−11.4925	−0.465317
$611$	−47.5783	−1.92481
$612$	−23.5374	−0.951443
$613$	−17.9930	−0.726732	−0.363366	−	0.931646i	$-0.618373\pi$
$613$	−17.9930	−0.726732	−0.363366	+	0.931646i	$0.618373\pi$
$614$	−13.5623	−0.547331
$615$	11.1969	0.451504
$616$	17.7077	0.713463
$617$	21.1837	0.852825	0.426413	−	0.904529i	$-0.359777\pi$
$617$	21.1837	0.852825	0.426413	+	0.904529i	$0.359777\pi$
$618$	27.0637	1.08866
$619$	−16.2237	−0.652085	−0.326043	−	0.945355i	$-0.605715\pi$
$619$	−16.2237	−0.652085	−0.326043	+	0.945355i	$0.605715\pi$
$620$	9.57684	0.384615
$621$	−4.51508	−0.181184
$622$	22.3001	0.894153
$623$	−55.7910	−2.23522
$624$	14.4797	0.579652
$625$	1.00000	0.0400000
$626$	14.0082	0.559879
$627$	68.5232	2.73655
$628$	15.4093	0.614897
$629$	−47.0095	−1.87439
$630$	−11.9749	−0.477092
$631$	−18.6785	−0.743578	−0.371789	−	0.928317i	$-0.621256\pi$
$631$	−18.6785	−0.743578	−0.371789	+	0.928317i	$0.621256\pi$
$632$	1.52617	0.0607078
$633$	12.2674	0.487584
$634$	−2.51601	−0.0999237
$635$	−6.37569	−0.253011
$636$	12.6591	0.501966
$637$	−39.5927	−1.56872
$638$	−30.1690	−1.19440
$639$	7.11167	0.281333
$640$	1.00000	0.0395285
$641$	−13.4724	−0.532128	−0.266064	−	0.963955i	$-0.585723\pi$
$641$	−13.4724	−0.532128	−0.266064	+	0.963955i	$0.585723\pi$
$642$	−23.9482	−0.945159
$643$	19.8496	0.782794	0.391397	−	0.920222i	$-0.371992\pi$
$643$	19.8496	0.782794	0.391397	+	0.920222i	$0.371992\pi$
$644$	−30.4243	−1.19888
$645$	6.06943	0.238984
$646$	−42.1441	−1.65814
$647$	24.4785	0.962350	0.481175	−	0.876624i	$-0.340210\pi$
$647$	24.4785	0.962350	0.481175	+	0.876624i	$0.340210\pi$
$648$	8.28751	0.325564
$649$	22.6948	0.890850
$650$	5.80528	0.227702
$651$	−88.8004	−3.48036
$652$	−12.7913	−0.500946
$653$	15.2681	0.597488	0.298744	−	0.954333i	$-0.403432\pi$
$653$	15.2681	0.597488	0.298744	+	0.954333i	$0.403432\pi$
$654$	48.0593	1.87927
$655$	−13.2659	−0.518342
$656$	4.48913	0.175271
$657$	−12.9863	−0.506645
$658$	30.4678	1.18776
$659$	−33.8427	−1.31832	−0.659162	−	0.752001i	$-0.729089\pi$
$659$	−33.8427	−1.31832	−0.659162	+	0.752001i	$0.729089\pi$
$660$	11.8807	0.462456
$661$	−14.5493	−0.565901	−0.282950	−	0.959135i	$-0.591313\pi$
$661$	−14.5493	−0.565901	−0.282950	+	0.959135i	$0.591313\pi$
$662$	5.99424	0.232973
$663$	−105.804	−4.10908
$664$	0.382022	0.0148253
$665$	−21.4413	−0.831458
$666$	−20.7234	−0.803014
$667$	51.8346	2.00704
$668$	13.1409	0.508437
$669$	−19.0280	−0.735664
$670$	−11.5251	−0.445254
$671$	−54.7419	−2.11329
$672$	−9.27241	−0.357691
$673$	−42.7204	−1.64675	−0.823375	−	0.567498i	$-0.807911\pi$
$673$	−42.7204	−1.64675	−0.823375	+	0.567498i	$0.807911\pi$
$674$	14.2382	0.548434
$675$	−0.551697	−0.0212348
$676$	20.7012	0.796201
$677$	0.134023	0.00515092	0.00257546	−	0.999997i	$-0.499180\pi$
$677$	0.134023	0.00515092	0.00257546	+	0.999997i	$0.499180\pi$
$678$	43.5143	1.67115
$679$	−9.16924	−0.351883
$680$	−7.30705	−0.280213
$681$	−39.7773	−1.52427
$682$	45.6172	1.74677
$683$	15.2499	0.583522	0.291761	−	0.956491i	$-0.405759\pi$
$683$	15.2499	0.583522	0.291761	+	0.956491i	$0.405759\pi$
$684$	−18.5785	−0.710368
$685$	−5.48480	−0.209564
$686$	−0.668679	−0.0255303
$687$	−18.5579	−0.708028
$688$	2.43339	0.0927721
$689$	29.4638	1.12248
$690$	−20.4127	−0.777099
$691$	−10.9693	−0.417290	−0.208645	−	0.977991i	$-0.566905\pi$
$691$	−10.9693	−0.417290	−0.208645	+	0.977991i	$0.566905\pi$
$692$	10.9753	0.417219
$693$	−57.0398	−2.16676
$694$	1.01558	0.0385509
$695$	−5.09400	−0.193227
$696$	15.7976	0.598808
$697$	−32.8023	−1.24248
$698$	16.1305	0.610548
$699$	51.0076	1.92928
$700$	−3.71754	−0.140510
$701$	−18.6844	−0.705699	−0.352850	−	0.935680i	$-0.614787\pi$
$701$	−18.6844	−0.705699	−0.352850	+	0.935680i	$0.614787\pi$
$702$	−3.20276	−0.120880
$703$	−37.1055	−1.39946
$704$	4.76328	0.179523
$705$	20.4420	0.769888
$706$	25.2692	0.951017
$707$	2.83972	0.106799
$708$	−11.8839	−0.446623
$709$	7.07256	0.265616	0.132808	−	0.991142i	$-0.457601\pi$
$709$	7.07256	0.265616	0.132808	+	0.991142i	$0.457601\pi$
$710$	2.20778	0.0828564
$711$	−4.91608	−0.184367
$712$	−15.0075	−0.562430
$713$	−78.3766	−2.93523
$714$	67.7540	2.53563
$715$	27.6521	1.03413
$716$	−6.23908	−0.233165
$717$	19.1188	0.714005
$718$	−11.4668	−0.427939
$719$	23.8456	0.889289	0.444645	−	0.895707i	$-0.353330\pi$
$719$	23.8456	0.889289	0.444645	+	0.895707i	$0.353330\pi$
$720$	−3.22119	−0.120047
$721$	−40.3373	−1.50224
$722$	−14.2652	−0.530895
$723$	14.2889	0.531411
$724$	−6.71439	−0.249538
$725$	6.33367	0.235226
$726$	29.1546	1.08203
$727$	16.6598	0.617877	0.308938	−	0.951082i	$-0.400026\pi$
$727$	16.6598	0.617877	0.308938	+	0.951082i	$0.400026\pi$
$728$	−21.5814	−0.799859
$729$	−30.8238	−1.14162
$730$	−4.03153	−0.149214
$731$	−17.7809	−0.657650
$732$	28.6649	1.05949
$733$	15.2150	0.561978	0.280989	−	0.959711i	$-0.409338\pi$
$733$	15.2150	0.561978	0.280989	+	0.959711i	$0.409338\pi$
$734$	25.4074	0.937803
$735$	17.0110	0.627459
$736$	−8.18397	−0.301665
$737$	−54.8973	−2.02217
$738$	−14.4603	−0.532292
$739$	−9.78131	−0.359811	−0.179906	−	0.983684i	$-0.557579\pi$
$739$	−9.78131	−0.359811	−0.179906	+	0.983684i	$0.557579\pi$
$740$	−6.43345	−0.236498
$741$	−83.5131	−3.06793
$742$	−18.8678	−0.692660
$743$	45.3948	1.66537	0.832687	−	0.553744i	$-0.186801\pi$
$743$	45.3948	1.66537	0.832687	+	0.553744i	$0.186801\pi$
$744$	−23.8869	−0.875735
$745$	−20.6186	−0.755409
$746$	25.0351	0.916602
$747$	−1.23057	−0.0450240
$748$	−34.8055	−1.27262
$749$	35.6937	1.30422
$750$	−2.49423	−0.0910764
$751$	−23.7277	−0.865834	−0.432917	−	0.901434i	$-0.642516\pi$
$751$	−23.7277	−0.865834	−0.432917	+	0.901434i	$0.642516\pi$
$752$	8.19569	0.298866
$753$	−47.3592	−1.72586
$754$	36.7687	1.33904
$755$	7.83803	0.285255
$756$	2.05096	0.0745927
$757$	46.4180	1.68709	0.843546	−	0.537057i	$-0.180464\pi$
$757$	46.4180	1.68709	0.843546	+	0.537057i	$0.180464\pi$
$758$	30.8141	1.11922
$759$	−97.2314	−3.52928
$760$	−5.76760	−0.209213
$761$	−17.6542	−0.639964	−0.319982	−	0.947424i	$-0.603677\pi$
$761$	−17.6542	−0.639964	−0.319982	+	0.947424i	$0.603677\pi$
$762$	15.9024	0.576084
$763$	−71.6303	−2.59319
$764$	−23.3903	−0.846232
$765$	23.5374	0.850996
$766$	23.9338	0.864763
$767$	−27.6595	−0.998726
$768$	−2.49423	−0.0900028
$769$	34.9205	1.25927	0.629633	−	0.776893i	$-0.283205\pi$
$769$	34.9205	1.25927	0.629633	+	0.776893i	$0.283205\pi$
$770$	−17.7077	−0.638141
$771$	−63.1987	−2.27605
$772$	−24.2217	−0.871758
$773$	−1.64269	−0.0590835	−0.0295418	−	0.999564i	$-0.509405\pi$
$773$	−1.64269	−0.0590835	−0.0295418	+	0.999564i	$0.509405\pi$
$774$	−7.83841	−0.281746
$775$	−9.57684	−0.344010
$776$	−2.46648	−0.0885414
$777$	59.6536	2.14006
$778$	−10.7474	−0.385313
$779$	−25.8915	−0.927659
$780$	−14.4797	−0.518456
$781$	10.5163	0.376301
$782$	59.8007	2.13847
$783$	−3.49427	−0.124875
$784$	6.82013	0.243576
$785$	−15.4093	−0.549980
$786$	33.0882	1.18022
$787$	−16.2227	−0.578276	−0.289138	−	0.957287i	$-0.593369\pi$
$787$	−16.2227	−0.578276	−0.289138	+	0.957287i	$0.593369\pi$
$788$	−13.9779	−0.497943
$789$	51.6905	1.84023
$790$	−1.52617	−0.0542987
$791$	−64.8561	−2.30602
$792$	−15.3434	−0.545205
$793$	66.7171	2.36919
$794$	−30.5034	−1.08252
$795$	−12.6591	−0.448972
$796$	−10.6632	−0.377946
$797$	−23.9009	−0.846614	−0.423307	−	0.905986i	$-0.639131\pi$
$797$	−23.9009	−0.846614	−0.423307	+	0.905986i	$0.639131\pi$
$798$	53.4795	1.89316
$799$	−59.8863	−2.11863
$800$	−1.00000	−0.0353553
$801$	48.3420	1.70808
$802$	−24.6517	−0.870482
$803$	−19.2033	−0.677670
$804$	28.7463	1.01380
$805$	30.4243	1.07231
$806$	−55.5962	−1.95829
$807$	6.98943	0.246040
$808$	0.763870	0.0268728
$809$	41.4896	1.45870	0.729348	−	0.684143i	$-0.239824\pi$
$809$	41.4896	1.45870	0.729348	+	0.684143i	$0.239824\pi$
$810$	−8.28751	−0.291193
$811$	−55.6983	−1.95583	−0.977916	−	0.208998i	$-0.932980\pi$
$811$	−55.6983	−1.95583	−0.977916	+	0.208998i	$0.932980\pi$
$812$	−23.5457	−0.826291
$813$	15.0241	0.526920
$814$	−30.6443	−1.07408
$815$	12.7913	0.448060
$816$	18.2255	0.638019
$817$	−14.0348	−0.491016
$818$	−20.7576	−0.725772
$819$	69.5177	2.42914
$820$	−4.48913	−0.156767
$821$	42.1155	1.46984	0.734920	−	0.678154i	$-0.237220\pi$
$821$	42.1155	1.46984	0.734920	+	0.678154i	$0.237220\pi$
$822$	13.6804	0.477158
$823$	31.2305	1.08863	0.544313	−	0.838882i	$-0.316790\pi$
$823$	31.2305	1.08863	0.544313	+	0.838882i	$0.316790\pi$
$824$	−10.8505	−0.377996
$825$	−11.8807	−0.413633
$826$	17.7124	0.616293
$827$	−4.86811	−0.169281	−0.0846403	−	0.996412i	$-0.526974\pi$
$827$	−4.86811	−0.169281	−0.0846403	+	0.996412i	$0.526974\pi$
$828$	26.3621	0.916147
$829$	7.76882	0.269822	0.134911	−	0.990858i	$-0.456925\pi$
$829$	7.76882	0.269822	0.134911	+	0.990858i	$0.456925\pi$
$830$	−0.382022	−0.0132602
$831$	−32.2875	−1.12004
$832$	−5.80528	−0.201262
$833$	−49.8350	−1.72668
$834$	12.7056	0.439960
$835$	−13.1409	−0.454760
$836$	−27.4727	−0.950162
$837$	5.28352	0.182625
$838$	34.7099	1.19903
$839$	−38.3767	−1.32491	−0.662455	−	0.749102i	$-0.730485\pi$
$839$	−38.3767	−1.32491	−0.662455	+	0.749102i	$0.730485\pi$
$840$	9.27241	0.319929
$841$	11.1153	0.383287
$842$	34.9813	1.20554
$843$	6.54642	0.225471
$844$	−4.91830	−0.169295
$845$	−20.7012	−0.712144
$846$	−26.3999	−0.907646
$847$	−43.4536	−1.49308
$848$	−5.07535	−0.174288
$849$	−21.1458	−0.725722
$850$	7.30705	0.250630
$851$	52.6512	1.80486
$852$	−5.50671	−0.188657
$853$	36.0557	1.23452	0.617262	−	0.786758i	$-0.288242\pi$
$853$	36.0557	1.23452	0.617262	+	0.786758i	$0.288242\pi$
$854$	−42.7238	−1.46198
$855$	18.5785	0.635372
$856$	9.60142	0.328170
$857$	−0.950887	−0.0324817	−0.0162408	−	0.999868i	$-0.505170\pi$
$857$	−0.950887	−0.0324817	−0.0162408	+	0.999868i	$0.505170\pi$
$858$	−68.9708	−2.35462
$859$	19.6192	0.669400	0.334700	−	0.942325i	$-0.391365\pi$
$859$	19.6192	0.669400	0.334700	+	0.942325i	$0.391365\pi$
$860$	−2.43339	−0.0829779
$861$	41.6250	1.41858
$862$	−14.2655	−0.485884
$863$	50.8124	1.72967	0.864837	−	0.502052i	$-0.167421\pi$
$863$	50.8124	1.72967	0.864837	+	0.502052i	$0.167421\pi$
$864$	0.551697	0.0187691
$865$	−10.9753	−0.373172
$866$	−30.2302	−1.02727
$867$	−90.7726	−3.08280
$868$	35.6023	1.20842
$869$	−7.26957	−0.246603
$870$	−15.7976	−0.535590
$871$	66.9064	2.26704
$872$	−19.2682	−0.652503
$873$	7.94499	0.268897
$874$	47.2019	1.59663
$875$	3.71754	0.125676
$876$	10.0556	0.339746
$877$	38.0804	1.28588	0.642942	−	0.765915i	$-0.277714\pi$
$877$	38.0804	1.28588	0.642942	+	0.765915i	$0.277714\pi$
$878$	5.82087	0.196445
$879$	−1.09967	−0.0370910
$880$	−4.76328	−0.160570
$881$	20.0959	0.677048	0.338524	−	0.940958i	$-0.390072\pi$
$881$	20.0959	0.677048	0.338524	+	0.940958i	$0.390072\pi$
$882$	−21.9689	−0.739732
$883$	5.13610	0.172844	0.0864218	−	0.996259i	$-0.472457\pi$
$883$	5.13610	0.172844	0.0864218	+	0.996259i	$0.472457\pi$
$884$	42.4195	1.42672
$885$	11.8839	0.399472
$886$	19.7495	0.663498
$887$	−48.6727	−1.63427	−0.817135	−	0.576446i	$-0.804439\pi$
$887$	−48.6727	−1.63427	−0.817135	+	0.576446i	$0.804439\pi$
$888$	16.0465	0.538486
$889$	−23.7019	−0.794936
$890$	15.0075	0.503052
$891$	−39.4757	−1.32249
$892$	7.62879	0.255431
$893$	−47.2695	−1.58181
$894$	51.4277	1.72000
$895$	6.23908	0.208549
$896$	3.71754	0.124194
$897$	118.501	3.95665
$898$	−0.493409	−0.0164653
$899$	−60.6565	−2.02301
$900$	3.22119	0.107373
$901$	37.0859	1.23551
$902$	−21.3830	−0.711975
$903$	22.5634	0.750862
$904$	−17.4460	−0.580244
$905$	6.71439	0.223194
$906$	−19.5499	−0.649501
$907$	−3.71753	−0.123439	−0.0617194	−	0.998094i	$-0.519658\pi$
$907$	−3.71753	−0.123439	−0.0617194	+	0.998094i	$0.519658\pi$
$908$	15.9477	0.529244
$909$	−2.46057	−0.0816119
$910$	21.5814	0.715415
$911$	44.8861	1.48714	0.743572	−	0.668656i	$-0.233130\pi$
$911$	44.8861	1.48714	0.743572	+	0.668656i	$0.233130\pi$
$912$	14.3857	0.476359
$913$	−1.81968	−0.0602225
$914$	−2.73681	−0.0905256
$915$	−28.6649	−0.947633
$916$	7.44033	0.245836
$917$	−49.3166	−1.62858
$918$	−4.03128	−0.133052
$919$	60.4335	1.99352	0.996759	−	0.0804410i	$-0.0256329\pi$
$919$	60.4335	1.99352	0.996759	+	0.0804410i	$0.0256329\pi$
$920$	8.18397	0.269818
$921$	−33.8276	−1.11466
$922$	−8.74063	−0.287857
$923$	−12.8168	−0.421869
$924$	44.1671	1.45299
$925$	6.43345	0.211530
$926$	10.1123	0.332310
$927$	34.9516	1.14796
$928$	−6.33367	−0.207913
$929$	45.6453	1.49757	0.748787	−	0.662810i	$-0.230636\pi$
$929$	45.6453	1.49757	0.748787	+	0.662810i	$0.230636\pi$
$930$	23.8869	0.783281
$931$	−39.3358	−1.28918
$932$	−20.4502	−0.669869
$933$	55.6216	1.82097
$934$	−7.61428	−0.249147
$935$	34.8055	1.13826
$936$	18.6999	0.611225
$937$	39.3939	1.28694	0.643471	−	0.765470i	$-0.277494\pi$
$937$	39.3939	1.28694	0.643471	+	0.765470i	$0.277494\pi$
$938$	−42.8451	−1.39894
$939$	34.9396	1.14021
$940$	−8.19569	−0.267314
$941$	−9.82711	−0.320355	−0.160177	−	0.987088i	$-0.551207\pi$
$941$	−9.82711	−0.320355	−0.160177	+	0.987088i	$0.551207\pi$
$942$	38.4343	1.25226
$943$	36.7389	1.19638
$944$	4.76454	0.155073
$945$	−2.05096	−0.0667177
$946$	−11.5909	−0.376853
$947$	−30.1508	−0.979770	−0.489885	−	0.871787i	$-0.662961\pi$
$947$	−30.1508	−0.979770	−0.489885	+	0.871787i	$0.662961\pi$
$948$	3.80662	0.123633
$949$	23.4042	0.759731
$950$	5.76760	0.187126
$951$	−6.27552	−0.203498
$952$	−27.1643	−0.880399
$953$	−38.7029	−1.25371	−0.626855	−	0.779136i	$-0.715658\pi$
$953$	−38.7029	−1.25371	−0.626855	+	0.779136i	$0.715658\pi$
$954$	16.3487	0.529308
$955$	23.3903	0.756893
$956$	−7.66521	−0.247911
$957$	−75.2485	−2.43244
$958$	21.7987	0.704285
$959$	−20.3900	−0.658427
$960$	2.49423	0.0805010
$961$	60.7159	1.95858
$962$	37.3479	1.20415
$963$	−30.9280	−0.996641
$964$	−5.72880	−0.184512
$965$	24.2217	0.779724
$966$	−75.8852	−2.44157
$967$	38.7140	1.24496	0.622480	−	0.782636i	$-0.286125\pi$
$967$	38.7140	1.24496	0.622480	+	0.782636i	$0.286125\pi$
$968$	−11.6888	−0.375692
$969$	−105.117	−3.37685
$970$	2.46648	0.0791938
$971$	−57.1600	−1.83435	−0.917175	−	0.398484i	$-0.869536\pi$
$971$	−57.1600	−1.83435	−0.917175	+	0.398484i	$0.869536\pi$
$972$	22.3261	0.716108
$973$	−18.9372	−0.607098
$974$	18.0188	0.577359
$975$	14.4797	0.463722
$976$	−11.4925	−0.367866
$977$	−58.5503	−1.87319	−0.936594	−	0.350416i	$-0.886040\pi$
$977$	−58.5503	−1.87319	−0.936594	+	0.350416i	$0.886040\pi$
$978$	−31.9045	−1.02019
$979$	71.4848	2.28467
$980$	−6.82013	−0.217861
$981$	62.0664	1.98163
$982$	−18.5708	−0.592619
$983$	−24.3081	−0.775307	−0.387653	−	0.921805i	$-0.626714\pi$
$983$	−24.3081	−0.775307	−0.387653	+	0.921805i	$0.626714\pi$
$984$	11.1969	0.356945
$985$	13.9779	0.445374
$986$	46.2804	1.47387
$987$	75.9938	2.41891
$988$	33.4825	1.06522
$989$	19.9148	0.633253
$990$	15.3434	0.487646
$991$	19.5272	0.620301	0.310150	−	0.950687i	$-0.399621\pi$
$991$	19.5272	0.620301	0.310150	+	0.950687i	$0.399621\pi$
$992$	9.57684	0.304065
$993$	14.9510	0.474456
$994$	8.20751	0.260326
$995$	10.6632	0.338045
$996$	0.952851	0.0301922
$997$	−16.0332	−0.507777	−0.253889	−	0.967233i	$-0.581710\pi$
$997$	−16.0332	−0.507777	−0.253889	+	0.967233i	$0.581710\pi$
$998$	43.9047	1.38978
$999$	−3.54932	−0.112295

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.i.1.6	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.i.1.6	✓	29	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.49423 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.49423 q^{6} -3.71754 q^{7} -1.00000 q^{8} +3.22119 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.49423 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.49423 q^{6} -3.71754 q^{7} -1.00000 q^{8} +3.22119 q^{9} +1.00000 q^{10} +4.76328 q^{11} -2.49423 q^{12} -5.80528 q^{13} +3.71754 q^{14} +2.49423 q^{15} +1.00000 q^{16} -7.30705 q^{17} -3.22119 q^{18} -5.76760 q^{19} -1.00000 q^{20} +9.27241 q^{21} -4.76328 q^{22} +8.18397 q^{23} +2.49423 q^{24} +1.00000 q^{25} +5.80528 q^{26} -0.551697 q^{27} -3.71754 q^{28} +6.33367 q^{29} -2.49423 q^{30} -9.57684 q^{31} -1.00000 q^{32} -11.8807 q^{33} +7.30705 q^{34} +3.71754 q^{35} +3.22119 q^{36} +6.43345 q^{37} +5.76760 q^{38} +14.4797 q^{39} +1.00000 q^{40} +4.48913 q^{41} -9.27241 q^{42} +2.43339 q^{43} +4.76328 q^{44} -3.22119 q^{45} -8.18397 q^{46} +8.19569 q^{47} -2.49423 q^{48} +6.82013 q^{49} -1.00000 q^{50} +18.2255 q^{51} -5.80528 q^{52} -5.07535 q^{53} +0.551697 q^{54} -4.76328 q^{55} +3.71754 q^{56} +14.3857 q^{57} -6.33367 q^{58} +4.76454 q^{59} +2.49423 q^{60} -11.4925 q^{61} +9.57684 q^{62} -11.9749 q^{63} +1.00000 q^{64} +5.80528 q^{65} +11.8807 q^{66} -11.5251 q^{67} -7.30705 q^{68} -20.4127 q^{69} -3.71754 q^{70} +2.20778 q^{71} -3.22119 q^{72} -4.03153 q^{73} -6.43345 q^{74} -2.49423 q^{75} -5.76760 q^{76} -17.7077 q^{77} -14.4797 q^{78} -1.52617 q^{79} -1.00000 q^{80} -8.28751 q^{81} -4.48913 q^{82} -0.382022 q^{83} +9.27241 q^{84} +7.30705 q^{85} -2.43339 q^{86} -15.7976 q^{87} -4.76328 q^{88} +15.0075 q^{89} +3.22119 q^{90} +21.5814 q^{91} +8.18397 q^{92} +23.8869 q^{93} -8.19569 q^{94} +5.76760 q^{95} +2.49423 q^{96} +2.46648 q^{97} -6.82013 q^{98} +15.3434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9} + 29 q^{10} - 10 q^{12} - 4 q^{13} + 10 q^{15} + 29 q^{16} - 23 q^{17} - 29 q^{18} + q^{19} - 29 q^{20} + 2 q^{21} - 9 q^{23} + 10 q^{24} + 29 q^{25} + 4 q^{26} - 43 q^{27} - 5 q^{29} - 10 q^{30} + 21 q^{31} - 29 q^{32} - 19 q^{33} + 23 q^{34} + 29 q^{36} - 6 q^{37} - q^{38} + 18 q^{39} + 29 q^{40} - 17 q^{41} - 2 q^{42} - 19 q^{43} - 29 q^{45} + 9 q^{46} - 21 q^{47} - 10 q^{48} + 45 q^{49} - 29 q^{50} + 11 q^{51} - 4 q^{52} - 53 q^{53} + 43 q^{54} - 16 q^{57} + 5 q^{58} - 30 q^{59} + 10 q^{60} + 16 q^{61} - 21 q^{62} - 17 q^{63} + 29 q^{64} + 4 q^{65} + 19 q^{66} - 35 q^{67} - 23 q^{68} + 13 q^{69} + 2 q^{71} - 29 q^{72} - q^{73} + 6 q^{74} - 10 q^{75} + q^{76} - 50 q^{77} - 18 q^{78} + 26 q^{79} - 29 q^{80} + 33 q^{81} + 17 q^{82} - 54 q^{83} + 2 q^{84} + 23 q^{85} + 19 q^{86} - 56 q^{87} - 2 q^{89} + 29 q^{90} + 27 q^{91} - 9 q^{92} - 26 q^{93} + 21 q^{94} - q^{95} + 10 q^{96} + 15 q^{97} - 45 q^{98} + 27 q^{99}+O(q^{100}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9 + 29 * q^10 - 10 * q^12 - 4 * q^13 + 10 * q^15 + 29 * q^16 - 23 * q^17 - 29 * q^18 + q^19 - 29 * q^20 + 2 * q^21 - 9 * q^23 + 10 * q^24 + 29 * q^25 + 4 * q^26 - 43 * q^27 - 5 * q^29 - 10 * q^30 + 21 * q^31 - 29 * q^32 - 19 * q^33 + 23 * q^34 + 29 * q^36 - 6 * q^37 - q^38 + 18 * q^39 + 29 * q^40 - 17 * q^41 - 2 * q^42 - 19 * q^43 - 29 * q^45 + 9 * q^46 - 21 * q^47 - 10 * q^48 + 45 * q^49 - 29 * q^50 + 11 * q^51 - 4 * q^52 - 53 * q^53 + 43 * q^54 - 16 * q^57 + 5 * q^58 - 30 * q^59 + 10 * q^60 + 16 * q^61 - 21 * q^62 - 17 * q^63 + 29 * q^64 + 4 * q^65 + 19 * q^66 - 35 * q^67 - 23 * q^68 + 13 * q^69 + 2 * q^71 - 29 * q^72 - q^73 + 6 * q^74 - 10 * q^75 + q^76 - 50 * q^77 - 18 * q^78 + 26 * q^79 - 29 * q^80 + 33 * q^81 + 17 * q^82 - 54 * q^83 + 2 * q^84 + 23 * q^85 + 19 * q^86 - 56 * q^87 - 2 * q^89 + 29 * q^90 + 27 * q^91 - 9 * q^92 - 26 * q^93 + 21 * q^94 - q^95 + 10 * q^96 + 15 * q^97 - 45 * q^98 + 27 * q^99

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