LMFDB - Embedded newform 6005.2.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$0$
Dimension:	$111$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41916 q^{2} +1.95905 q^{3} +3.85233 q^{4} +1.00000 q^{5} -4.73925 q^{6} -1.88529 q^{7} -4.48108 q^{8} +0.837875 q^{9} +O(q^{10})$	\(q-2.41916 q^{2} +1.95905 q^{3} +3.85233 q^{4} +1.00000 q^{5} -4.73925 q^{6} -1.88529 q^{7} -4.48108 q^{8} +0.837875 q^{9} -2.41916 q^{10} -1.48547 q^{11} +7.54690 q^{12} -3.96488 q^{13} +4.56082 q^{14} +1.95905 q^{15} +3.13578 q^{16} +5.11302 q^{17} -2.02695 q^{18} +6.65636 q^{19} +3.85233 q^{20} -3.69338 q^{21} +3.59359 q^{22} -8.02164 q^{23} -8.77865 q^{24} +1.00000 q^{25} +9.59168 q^{26} -4.23571 q^{27} -7.26276 q^{28} -9.91839 q^{29} -4.73925 q^{30} +0.778558 q^{31} +1.37621 q^{32} -2.91011 q^{33} -12.3692 q^{34} -1.88529 q^{35} +3.22777 q^{36} +7.75089 q^{37} -16.1028 q^{38} -7.76741 q^{39} -4.48108 q^{40} +10.5601 q^{41} +8.93487 q^{42} +11.2957 q^{43} -5.72253 q^{44} +0.837875 q^{45} +19.4056 q^{46} +8.48509 q^{47} +6.14314 q^{48} -3.44568 q^{49} -2.41916 q^{50} +10.0166 q^{51} -15.2740 q^{52} +12.2979 q^{53} +10.2469 q^{54} -1.48547 q^{55} +8.44813 q^{56} +13.0401 q^{57} +23.9942 q^{58} -9.72136 q^{59} +7.54690 q^{60} -12.4661 q^{61} -1.88346 q^{62} -1.57964 q^{63} -9.60082 q^{64} -3.96488 q^{65} +7.04003 q^{66} -6.27143 q^{67} +19.6970 q^{68} -15.7148 q^{69} +4.56082 q^{70} -0.477598 q^{71} -3.75458 q^{72} -9.25598 q^{73} -18.7506 q^{74} +1.95905 q^{75} +25.6425 q^{76} +2.80055 q^{77} +18.7906 q^{78} +7.51295 q^{79} +3.13578 q^{80} -10.8116 q^{81} -25.5467 q^{82} +1.34313 q^{83} -14.2281 q^{84} +5.11302 q^{85} -27.3261 q^{86} -19.4306 q^{87} +6.65652 q^{88} +10.8711 q^{89} -2.02695 q^{90} +7.47496 q^{91} -30.9020 q^{92} +1.52523 q^{93} -20.5268 q^{94} +6.65636 q^{95} +2.69606 q^{96} +9.46655 q^{97} +8.33564 q^{98} -1.24464 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) $ 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9} + 20 q^{10} + 36 q^{11} + 80 q^{12} + 36 q^{13} + 7 q^{14} + 40 q^{15} + 190 q^{16} + 38 q^{17} + 48 q^{18} + 77 q^{19} + 136 q^{20} + 11 q^{21} + 39 q^{22} + 82 q^{23} - 3 q^{24} + 111 q^{25} - 3 q^{26} + 130 q^{27} + 87 q^{28} + 20 q^{29} + 3 q^{30} + 41 q^{31} + 85 q^{32} + 33 q^{33} + 7 q^{34} + 39 q^{35} + 191 q^{36} + 80 q^{37} + 42 q^{38} + 21 q^{39} + 45 q^{40} + 16 q^{41} + 33 q^{42} + 164 q^{43} + 37 q^{44} + 139 q^{45} + 32 q^{46} + 148 q^{47} + 149 q^{48} + 160 q^{49} + 20 q^{50} + 51 q^{51} + 87 q^{52} + 83 q^{53} - 6 q^{54} + 36 q^{55} - 10 q^{56} + 28 q^{57} + 47 q^{58} + 14 q^{59} + 80 q^{60} + 20 q^{61} + 14 q^{62} + 120 q^{63} + 231 q^{64} + 36 q^{65} - 4 q^{66} + 253 q^{67} + 80 q^{68} + 6 q^{69} + 7 q^{70} + 5 q^{71} + 124 q^{72} + 64 q^{73} - 37 q^{74} + 40 q^{75} + 92 q^{76} + 63 q^{77} + 29 q^{78} + 91 q^{79} + 190 q^{80} + 187 q^{81} - 7 q^{82} + 63 q^{83} - 69 q^{84} + 38 q^{85} - 22 q^{86} + 57 q^{87} + 121 q^{88} - 6 q^{89} + 48 q^{90} + 119 q^{91} + 104 q^{92} + 14 q^{93} - q^{94} + 77 q^{95} - 38 q^{96} + 96 q^{97} + 81 q^{98} + 106 q^{99}+O(q^{100}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9 + 20 * q^10 + 36 * q^11 + 80 * q^12 + 36 * q^13 + 7 * q^14 + 40 * q^15 + 190 * q^16 + 38 * q^17 + 48 * q^18 + 77 * q^19 + 136 * q^20 + 11 * q^21 + 39 * q^22 + 82 * q^23 - 3 * q^24 + 111 * q^25 - 3 * q^26 + 130 * q^27 + 87 * q^28 + 20 * q^29 + 3 * q^30 + 41 * q^31 + 85 * q^32 + 33 * q^33 + 7 * q^34 + 39 * q^35 + 191 * q^36 + 80 * q^37 + 42 * q^38 + 21 * q^39 + 45 * q^40 + 16 * q^41 + 33 * q^42 + 164 * q^43 + 37 * q^44 + 139 * q^45 + 32 * q^46 + 148 * q^47 + 149 * q^48 + 160 * q^49 + 20 * q^50 + 51 * q^51 + 87 * q^52 + 83 * q^53 - 6 * q^54 + 36 * q^55 - 10 * q^56 + 28 * q^57 + 47 * q^58 + 14 * q^59 + 80 * q^60 + 20 * q^61 + 14 * q^62 + 120 * q^63 + 231 * q^64 + 36 * q^65 - 4 * q^66 + 253 * q^67 + 80 * q^68 + 6 * q^69 + 7 * q^70 + 5 * q^71 + 124 * q^72 + 64 * q^73 - 37 * q^74 + 40 * q^75 + 92 * q^76 + 63 * q^77 + 29 * q^78 + 91 * q^79 + 190 * q^80 + 187 * q^81 - 7 * q^82 + 63 * q^83 - 69 * q^84 + 38 * q^85 - 22 * q^86 + 57 * q^87 + 121 * q^88 - 6 * q^89 + 48 * q^90 + 119 * q^91 + 104 * q^92 + 14 * q^93 - q^94 + 77 * q^95 - 38 * q^96 + 96 * q^97 + 81 * q^98 + 106 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.41916	−1.71060	−0.855302	−	0.518130i	$-0.826628\pi$
$2$	−2.41916	−1.71060	−0.855302	+	0.518130i	$0.826628\pi$
$3$	1.95905	1.13106	0.565529	−	0.824729i	$-0.308672\pi$
$3$	1.95905	1.13106	0.565529	+	0.824729i	$0.308672\pi$
$4$	3.85233	1.92616
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−4.73925	−1.93479
$7$	−1.88529	−0.712573	−0.356287	−	0.934377i	$-0.615957\pi$
$7$	−1.88529	−0.712573	−0.356287	+	0.934377i	$0.615957\pi$
$8$	−4.48108	−1.58430
$9$	0.837875	0.279292
$10$	−2.41916	−0.765005
$11$	−1.48547	−0.447887	−0.223943	−	0.974602i	$-0.571893\pi$
$11$	−1.48547	−0.447887	−0.223943	+	0.974602i	$0.571893\pi$
$12$	7.54690	2.17860
$13$	−3.96488	−1.09966	−0.549831	−	0.835276i	$-0.685308\pi$
$13$	−3.96488	−1.09966	−0.549831	+	0.835276i	$0.685308\pi$
$14$	4.56082	1.21893
$15$	1.95905	0.505824
$16$	3.13578	0.783944
$17$	5.11302	1.24009	0.620044	−	0.784567i	$-0.287115\pi$
$17$	5.11302	1.24009	0.620044	+	0.784567i	$0.287115\pi$
$18$	−2.02695	−0.477757
$19$	6.65636	1.52707	0.763537	−	0.645764i	$-0.223461\pi$
$19$	6.65636	1.52707	0.763537	+	0.645764i	$0.223461\pi$
$20$	3.85233	0.861407
$21$	−3.69338	−0.805961
$22$	3.59359	0.766157
$23$	−8.02164	−1.67263	−0.836314	−	0.548250i	$-0.815294\pi$
$23$	−8.02164	−1.67263	−0.836314	+	0.548250i	$0.815294\pi$
$24$	−8.77865	−1.79193
$25$	1.00000	0.200000
$26$	9.59168	1.88108
$27$	−4.23571	−0.815163
$28$	−7.26276	−1.37253
$29$	−9.91839	−1.84180	−0.920900	−	0.389800i	$-0.872544\pi$
$29$	−9.91839	−1.84180	−0.920900	+	0.389800i	$0.872544\pi$
$30$	−4.73925	−0.865265
$31$	0.778558	0.139833	0.0699166	−	0.997553i	$-0.477727\pi$
$31$	0.778558	0.139833	0.0699166	+	0.997553i	$0.477727\pi$
$32$	1.37621	0.243282
$33$	−2.91011	−0.506586
$34$	−12.3692	−2.12130
$35$	−1.88529	−0.318672
$36$	3.22777	0.537961
$37$	7.75089	1.27424	0.637120	−	0.770765i	$-0.280126\pi$
$37$	7.75089	1.27424	0.637120	+	0.770765i	$0.280126\pi$
$38$	−16.1028	−2.61222
$39$	−7.76741	−1.24378
$40$	−4.48108	−0.708520
$41$	10.5601	1.64922	0.824609	−	0.565703i	$-0.191395\pi$
$41$	10.5601	1.64922	0.824609	+	0.565703i	$0.191395\pi$
$42$	8.93487	1.37868
$43$	11.2957	1.72258	0.861288	−	0.508117i	$-0.169658\pi$
$43$	11.2957	1.72258	0.861288	+	0.508117i	$0.169658\pi$
$44$	−5.72253	−0.862704
$45$	0.837875	0.124903
$46$	19.4056	2.86120
$47$	8.48509	1.23768	0.618839	−	0.785518i	$-0.287603\pi$
$47$	8.48509	1.23768	0.618839	+	0.785518i	$0.287603\pi$
$48$	6.14314	0.886686
$49$	−3.44568	−0.492240
$50$	−2.41916	−0.342121
$51$	10.0166	1.40261
$52$	−15.2740	−2.11813
$53$	12.2979	1.68924	0.844620	−	0.535366i	$-0.179826\pi$
$53$	12.2979	1.68924	0.844620	+	0.535366i	$0.179826\pi$
$54$	10.2469	1.39442
$55$	−1.48547	−0.200301
$56$	8.44813	1.12893
$57$	13.0401	1.72721
$58$	23.9942	3.15059
$59$	−9.72136	−1.26561	−0.632807	−	0.774310i	$-0.718097\pi$
$59$	−9.72136	−1.26561	−0.632807	+	0.774310i	$0.718097\pi$
$60$	7.54690	0.974301
$61$	−12.4661	−1.59612	−0.798061	−	0.602577i	$-0.794141\pi$
$61$	−12.4661	−1.59612	−0.798061	+	0.602577i	$0.794141\pi$
$62$	−1.88346	−0.239199
$63$	−1.57964	−0.199016
$64$	−9.60082	−1.20010
$65$	−3.96488	−0.491783
$66$	7.04003	0.866568
$67$	−6.27143	−0.766177	−0.383088	−	0.923712i	$-0.625140\pi$
$67$	−6.27143	−0.766177	−0.383088	+	0.923712i	$0.625140\pi$
$68$	19.6970	2.38861
$69$	−15.7148	−1.89184
$70$	4.56082	0.545122
$71$	−0.477598	−0.0566804	−0.0283402	−	0.999598i	$-0.509022\pi$
$71$	−0.477598	−0.0566804	−0.0283402	+	0.999598i	$0.509022\pi$
$72$	−3.75458	−0.442482
$73$	−9.25598	−1.08333	−0.541665	−	0.840594i	$-0.682206\pi$
$73$	−9.25598	−1.08333	−0.541665	+	0.840594i	$0.682206\pi$
$74$	−18.7506	−2.17972
$75$	1.95905	0.226212
$76$	25.6425	2.94139
$77$	2.80055	0.319152
$78$	18.7906	2.12761
$79$	7.51295	0.845273	0.422636	−	0.906299i	$-0.361105\pi$
$79$	7.51295	0.845273	0.422636	+	0.906299i	$0.361105\pi$
$80$	3.13578	0.350591
$81$	−10.8116	−1.20129
$82$	−25.5467	−2.82116
$83$	1.34313	0.147428	0.0737140	−	0.997279i	$-0.476515\pi$
$83$	1.34313	0.147428	0.0737140	+	0.997279i	$0.476515\pi$
$84$	−14.2281	−1.55241
$85$	5.11302	0.554584
$86$	−27.3261	−2.94664
$87$	−19.4306	−2.08318
$88$	6.65652	0.709587
$89$	10.8711	1.15233	0.576165	−	0.817333i	$-0.304548\pi$
$89$	10.8711	1.15233	0.576165	+	0.817333i	$0.304548\pi$
$90$	−2.02695	−0.213660
$91$	7.47496	0.783589
$92$	−30.9020	−3.22176
$93$	1.52523	0.158159
$94$	−20.5268	−2.11718
$95$	6.65636	0.682928
$96$	2.69606	0.275166
$97$	9.46655	0.961183	0.480591	−	0.876945i	$-0.340422\pi$
$97$	9.46655	0.961183	0.480591	+	0.876945i	$0.340422\pi$
$98$	8.33564	0.842027
$99$	−1.24464	−0.125091
$100$	3.85233	0.385233
$101$	−19.3589	−1.92628	−0.963139	−	0.269005i	$-0.913305\pi$
$101$	−19.3589	−1.92628	−0.963139	+	0.269005i	$0.913305\pi$
$102$	−24.2319	−2.39931
$103$	0.867506	0.0854779	0.0427390	−	0.999086i	$-0.486392\pi$
$103$	0.867506	0.0854779	0.0427390	+	0.999086i	$0.486392\pi$
$104$	17.7670	1.74219
$105$	−3.69338	−0.360437
$106$	−29.7505	−2.88962
$107$	−10.3355	−0.999175	−0.499587	−	0.866263i	$-0.666515\pi$
$107$	−10.3355	−0.999175	−0.499587	+	0.866263i	$0.666515\pi$
$108$	−16.3173	−1.57014
$109$	12.7333	1.21963	0.609815	−	0.792544i	$-0.291244\pi$
$109$	12.7333	1.21963	0.609815	+	0.792544i	$0.291244\pi$
$110$	3.59359	0.342636
$111$	15.1844	1.44124
$112$	−5.91185	−0.558618
$113$	13.3032	1.25146	0.625729	−	0.780041i	$-0.284802\pi$
$113$	13.3032	1.25146	0.625729	+	0.780041i	$0.284802\pi$
$114$	−31.5462	−2.95457
$115$	−8.02164	−0.748022
$116$	−38.2089	−3.54761
$117$	−3.32208	−0.307126
$118$	23.5175	2.16496
$119$	−9.63952	−0.883654
$120$	−8.77865	−0.801377
$121$	−8.79337	−0.799397
$122$	30.1575	2.73033
$123$	20.6879	1.86536
$124$	2.99926	0.269342
$125$	1.00000	0.0894427
$126$	3.82139	0.340437
$127$	15.4690	1.37265	0.686325	−	0.727295i	$-0.259223\pi$
$127$	15.4690	1.37265	0.686325	+	0.727295i	$0.259223\pi$
$128$	20.4735	1.80962
$129$	22.1288	1.94833
$130$	9.59168	0.841246
$131$	5.93288	0.518358	0.259179	−	0.965829i	$-0.416548\pi$
$131$	5.93288	0.518358	0.259179	+	0.965829i	$0.416548\pi$
$132$	−11.2107	−0.975768
$133$	−12.5492	−1.08815
$134$	15.1716	1.31062
$135$	−4.23571	−0.364552
$136$	−22.9118	−1.96467
$137$	1.98800	0.169846	0.0849231	−	0.996388i	$-0.472936\pi$
$137$	1.98800	0.169846	0.0849231	+	0.996388i	$0.472936\pi$
$138$	38.0166	3.23619
$139$	8.31308	0.705106	0.352553	−	0.935792i	$-0.385314\pi$
$139$	8.31308	0.705106	0.352553	+	0.935792i	$0.385314\pi$
$140$	−7.26276	−0.613815
$141$	16.6227	1.39989
$142$	1.15538	0.0969577
$143$	5.88973	0.492524
$144$	2.62739	0.218949
$145$	−9.91839	−0.823678
$146$	22.3917	1.85315
$147$	−6.75025	−0.556751
$148$	29.8590	2.45439
$149$	7.23484	0.592701	0.296351	−	0.955079i	$-0.404230\pi$
$149$	7.23484	0.592701	0.296351	+	0.955079i	$0.404230\pi$
$150$	−4.73925	−0.386958
$151$	0.283478	0.0230691	0.0115345	−	0.999933i	$-0.496328\pi$
$151$	0.283478	0.0230691	0.0115345	+	0.999933i	$0.496328\pi$
$152$	−29.8277	−2.41934
$153$	4.28407	0.346346
$154$	−6.77497	−0.545943
$155$	0.778558	0.0625353
$156$	−29.9226	−2.39573
$157$	14.9682	1.19459	0.597294	−	0.802022i	$-0.296242\pi$
$157$	14.9682	1.19459	0.597294	+	0.802022i	$0.296242\pi$
$158$	−18.1750	−1.44593
$159$	24.0921	1.91063
$160$	1.37621	0.108799
$161$	15.1231	1.19187
$162$	26.1550	2.05493
$163$	9.48292	0.742759	0.371380	−	0.928481i	$-0.378885\pi$
$163$	9.48292	0.742759	0.371380	+	0.928481i	$0.378885\pi$
$164$	40.6812	3.17666
$165$	−2.91011	−0.226552
$166$	−3.24925	−0.252191
$167$	−22.4545	−1.73758	−0.868790	−	0.495180i	$-0.835102\pi$
$167$	−22.4545	−1.73758	−0.868790	+	0.495180i	$0.835102\pi$
$168$	16.5503	1.27688
$169$	2.72031	0.209255
$170$	−12.3692	−0.948674
$171$	5.57720	0.426499
$172$	43.5147	3.31796
$173$	−6.82736	−0.519074	−0.259537	−	0.965733i	$-0.583570\pi$
$173$	−6.82736	−0.519074	−0.259537	+	0.965733i	$0.583570\pi$
$174$	47.0058	3.56350
$175$	−1.88529	−0.142515
$176$	−4.65811	−0.351118
$177$	−19.0446	−1.43148
$178$	−26.2988	−1.97118
$179$	21.8762	1.63510	0.817551	−	0.575856i	$-0.195331\pi$
$179$	21.8762	1.63510	0.817551	+	0.575856i	$0.195331\pi$
$180$	3.22777	0.240584
$181$	13.1754	0.979323	0.489661	−	0.871913i	$-0.337120\pi$
$181$	13.1754	0.979323	0.489661	+	0.871913i	$0.337120\pi$
$182$	−18.0831	−1.34041
$183$	−24.4217	−1.80531
$184$	35.9456	2.64995
$185$	7.75089	0.569857
$186$	−3.68978	−0.270548
$187$	−7.59525	−0.555419
$188$	32.6874	2.38397
$189$	7.98555	0.580863
$190$	−16.1028	−1.16822
$191$	15.2000	1.09984	0.549918	−	0.835219i	$-0.314659\pi$
$191$	15.2000	1.09984	0.549918	+	0.835219i	$0.314659\pi$
$192$	−18.8085	−1.35739
$193$	8.48863	0.611025	0.305512	−	0.952188i	$-0.401172\pi$
$193$	8.48863	0.611025	0.305512	+	0.952188i	$0.401172\pi$
$194$	−22.9011	−1.64420
$195$	−7.76741	−0.556235
$196$	−13.2739	−0.948134
$197$	2.08345	0.148440	0.0742198	−	0.997242i	$-0.476353\pi$
$197$	2.08345	0.148440	0.0742198	+	0.997242i	$0.476353\pi$
$198$	3.01098	0.213981
$199$	19.9287	1.41271	0.706355	−	0.707858i	$-0.250338\pi$
$199$	19.9287	1.41271	0.706355	+	0.707858i	$0.250338\pi$
$200$	−4.48108	−0.316860
$201$	−12.2860	−0.866590
$202$	46.8321	3.29510
$203$	18.6991	1.31242
$204$	38.5874	2.70166
$205$	10.5601	0.737553
$206$	−2.09864	−0.146219
$207$	−6.72113	−0.467151
$208$	−12.4330	−0.862073
$209$	−9.88784	−0.683956
$210$	8.93487	0.616565
$211$	1.91803	0.132043	0.0660213	−	0.997818i	$-0.478969\pi$
$211$	1.91803	0.132043	0.0660213	+	0.997818i	$0.478969\pi$
$212$	47.3754	3.25375
$213$	−0.935638	−0.0641088
$214$	25.0033	1.70919
$215$	11.2957	0.770359
$216$	18.9805	1.29146
$217$	−1.46781	−0.0996414
$218$	−30.8039	−2.08630
$219$	−18.1329	−1.22531
$220$	−5.72253	−0.385813
$221$	−20.2725	−1.36368
$222$	−36.7334	−2.46539
$223$	3.73842	0.250343	0.125171	−	0.992135i	$-0.460052\pi$
$223$	3.73842	0.250343	0.125171	+	0.992135i	$0.460052\pi$
$224$	−2.59455	−0.173356
$225$	0.837875	0.0558583
$226$	−32.1825	−2.14075
$227$	−11.5461	−0.766341	−0.383170	−	0.923678i	$-0.625168\pi$
$227$	−11.5461	−0.766341	−0.383170	+	0.923678i	$0.625168\pi$
$228$	50.2349	3.32689
$229$	12.9294	0.854400	0.427200	−	0.904157i	$-0.359500\pi$
$229$	12.9294	0.854400	0.427200	+	0.904157i	$0.359500\pi$
$230$	19.4056	1.27957
$231$	5.48641	0.360980
$232$	44.4451	2.91796
$233$	13.7606	0.901490	0.450745	−	0.892653i	$-0.351158\pi$
$233$	13.7606	0.901490	0.450745	+	0.892653i	$0.351158\pi$
$234$	8.03663	0.525371
$235$	8.48509	0.553507
$236$	−37.4499	−2.43778
$237$	14.7182	0.956052
$238$	23.3195	1.51158
$239$	−6.26810	−0.405450	−0.202725	−	0.979236i	$-0.564980\pi$
$239$	−6.26810	−0.405450	−0.202725	+	0.979236i	$0.564980\pi$
$240$	6.14314	0.396538
$241$	−1.51322	−0.0974748	−0.0487374	−	0.998812i	$-0.515520\pi$
$241$	−1.51322	−0.0974748	−0.0487374	+	0.998812i	$0.515520\pi$
$242$	21.2726	1.36745
$243$	−8.47331	−0.543563
$244$	−48.0236	−3.07439
$245$	−3.44568	−0.220136
$246$	−50.0472	−3.19089
$247$	−26.3917	−1.67926
$248$	−3.48878	−0.221538
$249$	2.63126	0.166750
$250$	−2.41916	−0.153001
$251$	31.0841	1.96201	0.981004	−	0.193986i	$-0.0621417\pi$
$251$	31.0841	1.96201	0.981004	+	0.193986i	$0.0621417\pi$
$252$	−6.08528	−0.383337
$253$	11.9159	0.749149
$254$	−37.4219	−2.34806
$255$	10.0166	0.627267
$256$	−30.3270	−1.89544
$257$	−2.39006	−0.149088	−0.0745438	−	0.997218i	$-0.523750\pi$
$257$	−2.39006	−0.149088	−0.0745438	+	0.997218i	$0.523750\pi$
$258$	−53.5331	−3.33282
$259$	−14.6127	−0.907988
$260$	−15.2740	−0.947256
$261$	−8.31037	−0.514399
$262$	−14.3526	−0.886705
$263$	20.2837	1.25075	0.625373	−	0.780326i	$-0.284947\pi$
$263$	20.2837	1.25075	0.625373	+	0.780326i	$0.284947\pi$
$264$	13.0404	0.802584
$265$	12.2979	0.755451
$266$	30.3584	1.86140
$267$	21.2970	1.30335
$268$	−24.1596	−1.47578
$269$	−28.5461	−1.74049	−0.870244	−	0.492621i	$-0.836039\pi$
$269$	−28.5461	−1.74049	−0.870244	+	0.492621i	$0.836039\pi$
$270$	10.2469	0.623604
$271$	−13.2740	−0.806340	−0.403170	−	0.915125i	$-0.632092\pi$
$271$	−13.2740	−0.806340	−0.403170	+	0.915125i	$0.632092\pi$
$272$	16.0333	0.972160
$273$	14.6438	0.886284
$274$	−4.80929	−0.290540
$275$	−1.48547	−0.0895774
$276$	−60.5386	−3.64399
$277$	28.2487	1.69730	0.848651	−	0.528953i	$-0.177415\pi$
$277$	28.2487	1.69730	0.848651	+	0.528953i	$0.177415\pi$
$278$	−20.1107	−1.20616
$279$	0.652335	0.0390542
$280$	8.44813	0.504873
$281$	−21.9405	−1.30886	−0.654430	−	0.756122i	$-0.727091\pi$
$281$	−21.9405	−1.30886	−0.654430	+	0.756122i	$0.727091\pi$
$282$	−40.2130	−2.39465
$283$	4.06416	0.241589	0.120795	−	0.992678i	$-0.461456\pi$
$283$	4.06416	0.241589	0.120795	+	0.992678i	$0.461456\pi$
$284$	−1.83986	−0.109176
$285$	13.0401	0.772431
$286$	−14.2482	−0.842513
$287$	−19.9090	−1.17519
$288$	1.15309	0.0679465
$289$	9.14292	0.537819
$290$	23.9942	1.40899
$291$	18.5454	1.08715
$292$	−35.6571	−2.08667
$293$	7.44838	0.435139	0.217569	−	0.976045i	$-0.430187\pi$
$293$	7.44838	0.435139	0.217569	+	0.976045i	$0.430187\pi$
$294$	16.3299	0.952381
$295$	−9.72136	−0.566000
$296$	−34.7323	−2.01878
$297$	6.29203	0.365101
$298$	−17.5022	−1.01388
$299$	31.8049	1.83932
$300$	7.54690	0.435721
$301$	−21.2957	−1.22746
$302$	−0.685778	−0.0394621
$303$	−37.9249	−2.17873
$304$	20.8729	1.19714
$305$	−12.4661	−0.713807
$306$	−10.3638	−0.592461
$307$	2.17730	0.124265	0.0621326	−	0.998068i	$-0.480210\pi$
$307$	2.17730	0.124265	0.0621326	+	0.998068i	$0.480210\pi$
$308$	10.7886	0.614740
$309$	1.69949	0.0966805
$310$	−1.88346	−0.106973
$311$	−7.49175	−0.424818	−0.212409	−	0.977181i	$-0.568131\pi$
$311$	−7.49175	−0.424818	−0.212409	+	0.977181i	$0.568131\pi$
$312$	34.8063	1.97052
$313$	−1.48880	−0.0841520	−0.0420760	−	0.999114i	$-0.513397\pi$
$313$	−1.48880	−0.0841520	−0.0420760	+	0.999114i	$0.513397\pi$
$314$	−36.2103	−2.04347
$315$	−1.57964	−0.0890025
$316$	28.9423	1.62813
$317$	−15.6707	−0.880154	−0.440077	−	0.897960i	$-0.645049\pi$
$317$	−15.6707	−0.880154	−0.440077	+	0.897960i	$0.645049\pi$
$318$	−58.2826	−3.26833
$319$	14.7335	0.824918
$320$	−9.60082	−0.536702
$321$	−20.2478	−1.13012
$322$	−36.5853	−2.03882
$323$	34.0341	1.89371
$324$	−41.6498	−2.31388
$325$	−3.96488	−0.219932
$326$	−22.9407	−1.27057
$327$	24.9452	1.37947
$328$	−47.3208	−2.61286
$329$	−15.9969	−0.881936
$330$	7.04003	0.387541
$331$	22.1196	1.21580	0.607902	−	0.794012i	$-0.292011\pi$
$331$	22.1196	1.21580	0.607902	+	0.794012i	$0.292011\pi$
$332$	5.17419	0.283970
$333$	6.49428	0.355884
$334$	54.3210	2.97231
$335$	−6.27143	−0.342645
$336$	−11.5816	−0.631829
$337$	7.70252	0.419583	0.209792	−	0.977746i	$-0.432721\pi$
$337$	7.70252	0.419583	0.209792	+	0.977746i	$0.432721\pi$
$338$	−6.58086	−0.357952
$339$	26.0616	1.41547
$340$	19.6970	1.06822
$341$	−1.15653	−0.0626295
$342$	−13.4921	−0.729570
$343$	19.6931	1.06333
$344$	−50.6168	−2.72908
$345$	−15.7148	−0.846056
$346$	16.5165	0.887931
$347$	3.05317	0.163903	0.0819513	−	0.996636i	$-0.473885\pi$
$347$	3.05317	0.163903	0.0819513	+	0.996636i	$0.473885\pi$
$348$	−74.8531	−4.01255
$349$	0.697123	0.0373161	0.0186581	−	0.999826i	$-0.494061\pi$
$349$	0.697123	0.0373161	0.0186581	+	0.999826i	$0.494061\pi$
$350$	4.56082	0.243786
$351$	16.7941	0.896403
$352$	−2.04432	−0.108963
$353$	23.8935	1.27172	0.635860	−	0.771804i	$-0.280645\pi$
$353$	23.8935	1.27172	0.635860	+	0.771804i	$0.280645\pi$
$354$	46.0720	2.44870
$355$	−0.477598	−0.0253483
$356$	41.8789	2.21958
$357$	−18.8843	−0.999463
$358$	−52.9220	−2.79701
$359$	−8.59265	−0.453503	−0.226751	−	0.973953i	$-0.572810\pi$
$359$	−8.59265	−0.453503	−0.226751	+	0.973953i	$0.572810\pi$
$360$	−3.75458	−0.197884
$361$	25.3071	1.33195
$362$	−31.8735	−1.67523
$363$	−17.2266	−0.904164
$364$	28.7960	1.50932
$365$	−9.25598	−0.484480
$366$	59.0800	3.08816
$367$	2.44406	0.127579	0.0637895	−	0.997963i	$-0.479681\pi$
$367$	2.44406	0.127579	0.0637895	+	0.997963i	$0.479681\pi$
$368$	−25.1541	−1.31125
$369$	8.84808	0.460613
$370$	−18.7506	−0.974799
$371$	−23.1850	−1.20371
$372$	5.87570	0.304641
$373$	21.5387	1.11523	0.557617	−	0.830099i	$-0.311716\pi$
$373$	21.5387	1.11523	0.557617	+	0.830099i	$0.311716\pi$
$374$	18.3741	0.950102
$375$	1.95905	0.101165
$376$	−38.0224	−1.96085
$377$	39.3253	2.02536
$378$	−19.3183	−0.993626
$379$	−0.255901	−0.0131447	−0.00657237	−	0.999978i	$-0.502092\pi$
$379$	−0.255901	−0.0131447	−0.00657237	+	0.999978i	$0.502092\pi$
$380$	25.6425	1.31543
$381$	30.3045	1.55255
$382$	−36.7713	−1.88138
$383$	25.9836	1.32770	0.663850	−	0.747866i	$-0.268921\pi$
$383$	25.9836	1.32770	0.663850	+	0.747866i	$0.268921\pi$
$384$	40.1086	2.04678
$385$	2.80055	0.142729
$386$	−20.5353	−1.04522
$387$	9.46437	0.481101
$388$	36.4683	1.85140
$389$	−3.39584	−0.172176	−0.0860879	−	0.996288i	$-0.527437\pi$
$389$	−3.39584	−0.172176	−0.0860879	+	0.996288i	$0.527437\pi$
$390$	18.7906	0.951498
$391$	−41.0148	−2.07421
$392$	15.4403	0.779855
$393$	11.6228	0.586293
$394$	−5.04019	−0.253921
$395$	7.51295	0.378017
$396$	−4.79476	−0.240946
$397$	−16.5369	−0.829965	−0.414982	−	0.909829i	$-0.636212\pi$
$397$	−16.5369	−0.829965	−0.414982	+	0.909829i	$0.636212\pi$
$398$	−48.2107	−2.41659
$399$	−24.5845	−1.23076
$400$	3.13578	0.156789
$401$	−28.1813	−1.40731	−0.703655	−	0.710542i	$-0.748450\pi$
$401$	−28.1813	−1.40731	−0.703655	+	0.710542i	$0.748450\pi$
$402$	29.7219	1.48239
$403$	−3.08689	−0.153769
$404$	−74.5767	−3.71033
$405$	−10.8116	−0.537232
$406$	−45.2360	−2.24502
$407$	−11.5137	−0.570715
$408$	−44.8854	−2.22216
$409$	23.8288	1.17826	0.589129	−	0.808039i	$-0.299471\pi$
$409$	23.8288	1.17826	0.589129	+	0.808039i	$0.299471\pi$
$410$	−25.5467	−1.26166
$411$	3.89459	0.192106
$412$	3.34192	0.164645
$413$	18.3276	0.901842
$414$	16.2595	0.799110
$415$	1.34313	0.0659318
$416$	−5.45651	−0.267527
$417$	16.2857	0.797516
$418$	23.9203	1.16998
$419$	−23.6707	−1.15639	−0.578194	−	0.815900i	$-0.696242\pi$
$419$	−23.6707	−1.15639	−0.578194	+	0.815900i	$0.696242\pi$
$420$	−14.2281	−0.694261
$421$	13.4294	0.654508	0.327254	−	0.944936i	$-0.393877\pi$
$421$	13.4294	0.654508	0.327254	+	0.944936i	$0.393877\pi$
$422$	−4.64002	−0.225873
$423$	7.10945	0.345673
$424$	−55.1076	−2.67626
$425$	5.11302	0.248018
$426$	2.26346	0.109665
$427$	23.5023	1.13735
$428$	−39.8159	−1.92457
$429$	11.5383	0.557073
$430$	−27.3261	−1.31778
$431$	−22.6485	−1.09094	−0.545469	−	0.838131i	$-0.683648\pi$
$431$	−22.6485	−1.09094	−0.545469	+	0.838131i	$0.683648\pi$
$432$	−13.2822	−0.639042
$433$	6.78374	0.326006	0.163003	−	0.986626i	$-0.447882\pi$
$433$	6.78374	0.326006	0.163003	+	0.986626i	$0.447882\pi$
$434$	3.55086	0.170447
$435$	−19.4306	−0.931627
$436$	49.0529	2.34921
$437$	−53.3949	−2.55423
$438$	43.8664	2.09602
$439$	−32.7710	−1.56408	−0.782038	−	0.623231i	$-0.785820\pi$
$439$	−32.7710	−1.56408	−0.782038	+	0.623231i	$0.785820\pi$
$440$	6.65652	0.317337
$441$	−2.88705	−0.137478
$442$	49.0424	2.33271
$443$	24.2379	1.15158	0.575790	−	0.817598i	$-0.304695\pi$
$443$	24.2379	1.15158	0.575790	+	0.817598i	$0.304695\pi$
$444$	58.4952	2.77606
$445$	10.8711	0.515338
$446$	−9.04382	−0.428237
$447$	14.1734	0.670379
$448$	18.1003	0.855161
$449$	−4.49704	−0.212228	−0.106114	−	0.994354i	$-0.533841\pi$
$449$	−4.49704	−0.212228	−0.106114	+	0.994354i	$0.533841\pi$
$450$	−2.02695	−0.0955514
$451$	−15.6868	−0.738663
$452$	51.2482	2.41051
$453$	0.555347	0.0260925
$454$	27.9318	1.31091
$455$	7.47496	0.350432
$456$	−58.4339	−2.73642
$457$	38.1559	1.78486	0.892429	−	0.451188i	$-0.149000\pi$
$457$	38.1559	1.78486	0.892429	+	0.451188i	$0.149000\pi$
$458$	−31.2783	−1.46154
$459$	−21.6573	−1.01087
$460$	−30.9020	−1.44081
$461$	10.1249	0.471566	0.235783	−	0.971806i	$-0.424235\pi$
$461$	10.1249	0.471566	0.235783	+	0.971806i	$0.424235\pi$
$462$	−13.2725	−0.617493
$463$	26.1869	1.21701	0.608505	−	0.793550i	$-0.291770\pi$
$463$	26.1869	1.21701	0.608505	+	0.793550i	$0.291770\pi$
$464$	−31.1019	−1.44387
$465$	1.52523	0.0707311
$466$	−33.2892	−1.54209
$467$	−8.16898	−0.378015	−0.189008	−	0.981976i	$-0.560527\pi$
$467$	−8.16898	−0.378015	−0.189008	+	0.981976i	$0.560527\pi$
$468$	−12.7977	−0.591575
$469$	11.8235	0.545957
$470$	−20.5268	−0.946830
$471$	29.3233	1.35115
$472$	43.5622	2.00511
$473$	−16.7794	−0.771519
$474$	−35.6057	−1.63543
$475$	6.65636	0.305415
$476$	−37.1346	−1.70206
$477$	10.3041	0.471791
$478$	15.1635	0.693564
$479$	−35.9924	−1.64453	−0.822267	−	0.569101i	$-0.807291\pi$
$479$	−35.9924	−1.64453	−0.822267	+	0.569101i	$0.807291\pi$
$480$	2.69606	0.123058
$481$	−30.7314	−1.40123
$482$	3.66071	0.166741
$483$	29.6270	1.34807
$484$	−33.8750	−1.53977
$485$	9.46655	0.429854
$486$	20.4983	0.929821
$487$	−23.7251	−1.07509	−0.537543	−	0.843237i	$-0.680647\pi$
$487$	−23.7251	−1.07509	−0.537543	+	0.843237i	$0.680647\pi$
$488$	55.8616	2.52874
$489$	18.5775	0.840104
$490$	8.33564	0.376566
$491$	22.7813	1.02811	0.514053	−	0.857759i	$-0.328144\pi$
$491$	22.7813	1.02811	0.514053	+	0.857759i	$0.328144\pi$
$492$	79.6964	3.59299
$493$	−50.7129	−2.28399
$494$	63.8457	2.87255
$495$	−1.24464	−0.0559424
$496$	2.44139	0.109621
$497$	0.900411	0.0403890
$498$	−6.36544	−0.285242
$499$	43.2603	1.93660	0.968298	−	0.249799i	$-0.0803647\pi$
$499$	43.2603	1.93660	0.968298	+	0.249799i	$0.0803647\pi$
$500$	3.85233	0.172281
$501$	−43.9895	−1.96530
$502$	−75.1973	−3.35622
$503$	0.930822	0.0415033	0.0207516	−	0.999785i	$-0.493394\pi$
$503$	0.930822	0.0415033	0.0207516	+	0.999785i	$0.493394\pi$
$504$	7.07848	0.315300
$505$	−19.3589	−0.861458
$506$	−28.8265	−1.28150
$507$	5.32922	0.236679
$508$	59.5916	2.64395
$509$	−36.9957	−1.63981	−0.819904	−	0.572501i	$-0.805973\pi$
$509$	−36.9957	−1.63981	−0.819904	+	0.572501i	$0.805973\pi$
$510$	−24.2319	−1.07300
$511$	17.4502	0.771952
$512$	32.4188	1.43272
$513$	−28.1944	−1.24481
$514$	5.78193	0.255030
$515$	0.867506	0.0382269
$516$	85.2474	3.75281
$517$	−12.6044	−0.554340
$518$	35.3504	1.55321
$519$	−13.3751	−0.587103
$520$	17.7670	0.779132
$521$	−9.68365	−0.424248	−0.212124	−	0.977243i	$-0.568038\pi$
$521$	−9.68365	−0.424248	−0.212124	+	0.977243i	$0.568038\pi$
$522$	20.1041	0.879933
$523$	−40.2395	−1.75955	−0.879776	−	0.475388i	$-0.842308\pi$
$523$	−40.2395	−1.75955	−0.879776	+	0.475388i	$0.842308\pi$
$524$	22.8554	0.998442
$525$	−3.69338	−0.161192
$526$	−49.0695	−2.13953
$527$	3.98078	0.173406
$528$	−9.12547	−0.397135
$529$	41.3468	1.79769
$530$	−29.7505	−1.29228
$531$	−8.14528	−0.353475
$532$	−48.3435	−2.09596
$533$	−41.8698	−1.81358
$534$	−51.5207	−2.22952
$535$	−10.3355	−0.446845
$536$	28.1027	1.21385
$537$	42.8565	1.84940
$538$	69.0576	2.97728
$539$	5.11846	0.220468
$540$	−16.3173	−0.702187
$541$	0.159618	0.00686253	0.00343127	−	0.999994i	$-0.498908\pi$
$541$	0.159618	0.00686253	0.00343127	+	0.999994i	$0.498908\pi$
$542$	32.1120	1.37933
$543$	25.8113	1.10767
$544$	7.03658	0.301691
$545$	12.7333	0.545435
$546$	−35.4257	−1.51608
$547$	−28.6866	−1.22655	−0.613274	−	0.789870i	$-0.710148\pi$
$547$	−28.6866	−1.22655	−0.613274	+	0.789870i	$0.710148\pi$
$548$	7.65843	0.327152
$549$	−10.4450	−0.445783
$550$	3.59359	0.153231
$551$	−66.0204	−2.81256
$552$	70.4192	2.99724
$553$	−14.1641	−0.602319
$554$	−68.3382	−2.90341
$555$	15.1844	0.644541
$556$	32.0247	1.35815
$557$	−14.8851	−0.630701	−0.315350	−	0.948975i	$-0.602122\pi$
$557$	−14.8851	−0.630701	−0.315350	+	0.948975i	$0.602122\pi$
$558$	−1.57810	−0.0668063
$559$	−44.7861	−1.89425
$560$	−5.91185	−0.249821
$561$	−14.8795	−0.628211
$562$	53.0776	2.23894
$563$	2.61162	0.110067	0.0550334	−	0.998485i	$-0.482473\pi$
$563$	2.61162	0.110067	0.0550334	+	0.998485i	$0.482473\pi$
$564$	64.0362	2.69641
$565$	13.3032	0.559669
$566$	−9.83185	−0.413264
$567$	20.3830	0.856005
$568$	2.14015	0.0897988
$569$	1.14662	0.0480690	0.0240345	−	0.999711i	$-0.492349\pi$
$569$	1.14662	0.0480690	0.0240345	+	0.999711i	$0.492349\pi$
$570$	−31.5462	−1.32132
$571$	0.575875	0.0240996	0.0120498	−	0.999927i	$-0.496164\pi$
$571$	0.575875	0.0240996	0.0120498	+	0.999927i	$0.496164\pi$
$572$	22.6892	0.948682
$573$	29.7776	1.24398
$574$	48.1629	2.01028
$575$	−8.02164	−0.334526
$576$	−8.04429	−0.335179
$577$	25.1386	1.04653	0.523266	−	0.852169i	$-0.324713\pi$
$577$	25.1386	1.04653	0.523266	+	0.852169i	$0.324713\pi$
$578$	−22.1182	−0.919995
$579$	16.6296	0.691104
$580$	−38.2089	−1.58654
$581$	−2.53220	−0.105053
$582$	−44.8644	−1.85969
$583$	−18.2681	−0.756589
$584$	41.4767	1.71632
$585$	−3.32208	−0.137351
$586$	−18.0188	−0.744350
$587$	22.6591	0.935240	0.467620	−	0.883930i	$-0.345112\pi$
$587$	22.6591	0.935240	0.467620	+	0.883930i	$0.345112\pi$
$588$	−26.0042	−1.07239
$589$	5.18236	0.213536
$590$	23.5175	0.968201
$591$	4.08158	0.167894
$592$	24.3051	0.998933
$593$	−34.9838	−1.43661	−0.718307	−	0.695727i	$-0.755082\pi$
$593$	−34.9838	−1.43661	−0.718307	+	0.695727i	$0.755082\pi$
$594$	−15.2214	−0.624543
$595$	−9.63952	−0.395182
$596$	27.8710	1.14164
$597$	39.0414	1.59786
$598$	−76.9411	−3.14636
$599$	18.0897	0.739123	0.369562	−	0.929206i	$-0.379508\pi$
$599$	18.0897	0.739123	0.369562	+	0.929206i	$0.379508\pi$
$600$	−8.77865	−0.358387
$601$	−4.32226	−0.176309	−0.0881543	−	0.996107i	$-0.528097\pi$
$601$	−4.32226	−0.176309	−0.0881543	+	0.996107i	$0.528097\pi$
$602$	51.5176	2.09970
$603$	−5.25467	−0.213987
$604$	1.09205	0.0444349
$605$	−8.79337	−0.357501
$606$	91.7465	3.72695
$607$	−7.50387	−0.304573	−0.152286	−	0.988336i	$-0.548664\pi$
$607$	−7.50387	−0.304573	−0.152286	+	0.988336i	$0.548664\pi$
$608$	9.16054	0.371509
$609$	36.6324	1.48442
$610$	30.1575	1.22104
$611$	−33.6424	−1.36103
$612$	16.5036	0.667120
$613$	29.5020	1.19157	0.595787	−	0.803143i	$-0.296840\pi$
$613$	29.5020	1.19157	0.595787	+	0.803143i	$0.296840\pi$
$614$	−5.26724	−0.212569
$615$	20.6879	0.834215
$616$	−12.5495	−0.505633
$617$	−0.801683	−0.0322745	−0.0161373	−	0.999870i	$-0.505137\pi$
$617$	−0.801683	−0.0322745	−0.0161373	+	0.999870i	$0.505137\pi$
$618$	−4.11133	−0.165382
$619$	−0.117255	−0.00471288	−0.00235644	−	0.999997i	$-0.500750\pi$
$619$	−0.117255	−0.00471288	−0.00235644	+	0.999997i	$0.500750\pi$
$620$	2.99926	0.120453
$621$	33.9774	1.36346
$622$	18.1237	0.726695
$623$	−20.4951	−0.821120
$624$	−24.3569	−0.975055
$625$	1.00000	0.0400000
$626$	3.60165	0.143951
$627$	−19.3708	−0.773594
$628$	57.6622	2.30097
$629$	39.6304	1.58017
$630$	3.82139	0.152248
$631$	2.69024	0.107097	0.0535485	−	0.998565i	$-0.482947\pi$
$631$	2.69024	0.107097	0.0535485	+	0.998565i	$0.482947\pi$
$632$	−33.6661	−1.33917
$633$	3.75752	0.149348
$634$	37.9099	1.50559
$635$	15.4690	0.613868
$636$	92.8107	3.68018
$637$	13.6617	0.541297
$638$	−35.6427	−1.41111
$639$	−0.400167	−0.0158304
$640$	20.4735	0.809286
$641$	8.74103	0.345250	0.172625	−	0.984988i	$-0.444775\pi$
$641$	8.74103	0.345250	0.172625	+	0.984988i	$0.444775\pi$
$642$	48.9827	1.93319
$643$	−29.1684	−1.15029	−0.575144	−	0.818052i	$-0.695054\pi$
$643$	−29.1684	−1.15029	−0.575144	+	0.818052i	$0.695054\pi$
$644$	58.2593	2.29574
$645$	22.1288	0.871321
$646$	−82.3338	−3.23938
$647$	29.7857	1.17100	0.585499	−	0.810673i	$-0.300899\pi$
$647$	29.7857	1.17100	0.585499	+	0.810673i	$0.300899\pi$
$648$	48.4476	1.90320
$649$	14.4408	0.566852
$650$	9.59168	0.376217
$651$	−2.87551	−0.112700
$652$	36.5313	1.43068
$653$	−6.24033	−0.244203	−0.122102	−	0.992518i	$-0.538963\pi$
$653$	−6.24033	−0.244203	−0.122102	+	0.992518i	$0.538963\pi$
$654$	−60.3464	−2.35973
$655$	5.93288	0.231817
$656$	33.1143	1.29290
$657$	−7.75535	−0.302565
$658$	38.6990	1.50864
$659$	37.6647	1.46721	0.733605	−	0.679576i	$-0.237836\pi$
$659$	37.6647	1.46721	0.733605	+	0.679576i	$0.237836\pi$
$660$	−11.2107	−0.436377
$661$	−46.5735	−1.81150	−0.905749	−	0.423815i	$-0.860691\pi$
$661$	−46.5735	−1.81150	−0.905749	+	0.423815i	$0.860691\pi$
$662$	−53.5109	−2.07976
$663$	−39.7149	−1.54240
$664$	−6.01868	−0.233570
$665$	−12.5492	−0.486636
$666$	−15.7107	−0.608777
$667$	79.5618	3.08065
$668$	−86.5021	−3.34687
$669$	7.32374	0.283152
$670$	15.1716	0.586129
$671$	18.5181	0.714882
$672$	−5.08286	−0.196076
$673$	49.5380	1.90955	0.954775	−	0.297329i	$-0.0960957\pi$
$673$	49.5380	1.90955	0.954775	+	0.297329i	$0.0960957\pi$
$674$	−18.6336	−0.717740
$675$	−4.23571	−0.163033
$676$	10.4795	0.403059
$677$	−9.11129	−0.350175	−0.175088	−	0.984553i	$-0.556021\pi$
$677$	−9.11129	−0.350175	−0.175088	+	0.984553i	$0.556021\pi$
$678$	−63.0471	−2.42131
$679$	−17.8472	−0.684913
$680$	−22.9118	−0.878628
$681$	−22.6194	−0.866776
$682$	2.79782	0.107134
$683$	24.8460	0.950708	0.475354	−	0.879795i	$-0.342320\pi$
$683$	24.8460	0.950708	0.475354	+	0.879795i	$0.342320\pi$
$684$	21.4852	0.821507
$685$	1.98800	0.0759576
$686$	−47.6408	−1.81894
$687$	25.3294	0.966376
$688$	35.4208	1.35040
$689$	−48.7596	−1.85759
$690$	38.0166	1.44727
$691$	−4.28127	−0.162867	−0.0814336	−	0.996679i	$-0.525950\pi$
$691$	−4.28127	−0.162867	−0.0814336	+	0.996679i	$0.525950\pi$
$692$	−26.3012	−0.999823
$693$	2.34651	0.0891365
$694$	−7.38609	−0.280372
$695$	8.31308	0.315333
$696$	87.0701	3.30038
$697$	53.9942	2.04518
$698$	−1.68645	−0.0638331
$699$	26.9578	1.01964
$700$	−7.26276	−0.274507
$701$	−2.24993	−0.0849788	−0.0424894	−	0.999097i	$-0.513529\pi$
$701$	−2.24993	−0.0849788	−0.0424894	+	0.999097i	$0.513529\pi$
$702$	−40.6276	−1.53339
$703$	51.5927	1.94586
$704$	14.2618	0.537510
$705$	16.6227	0.626048
$706$	−57.8021	−2.17541
$707$	36.4971	1.37261
$708$	−73.3662	−2.75727
$709$	−1.20855	−0.0453880	−0.0226940	−	0.999742i	$-0.507224\pi$
$709$	−1.20855	−0.0453880	−0.0226940	+	0.999742i	$0.507224\pi$
$710$	1.15538	0.0433608
$711$	6.29491	0.236078
$712$	−48.7141	−1.82564
$713$	−6.24532	−0.233889
$714$	45.6841	1.70969
$715$	5.88973	0.220263
$716$	84.2743	3.14948
$717$	−12.2795	−0.458587
$718$	20.7870	0.775764
$719$	−20.4261	−0.761764	−0.380882	−	0.924624i	$-0.624380\pi$
$719$	−20.4261	−0.761764	−0.380882	+	0.924624i	$0.624380\pi$
$720$	2.62739	0.0979170
$721$	−1.63550	−0.0609093
$722$	−61.2219	−2.27844
$723$	−2.96446	−0.110250
$724$	50.7561	1.88634
$725$	−9.91839	−0.368360
$726$	41.6740	1.54667
$727$	13.7301	0.509220	0.254610	−	0.967044i	$-0.418053\pi$
$727$	13.7301	0.509220	0.254610	+	0.967044i	$0.418053\pi$
$728$	−33.4959	−1.24144
$729$	15.8351	0.586487
$730$	22.3917	0.828753
$731$	57.7550	2.13615
$732$	−94.0805	−3.47732
$733$	21.8552	0.807242	0.403621	−	0.914926i	$-0.367751\pi$
$733$	21.8552	0.807242	0.403621	+	0.914926i	$0.367751\pi$
$734$	−5.91257	−0.218237
$735$	−6.75025	−0.248987
$736$	−11.0395	−0.406920
$737$	9.31603	0.343161
$738$	−21.4049	−0.787926
$739$	8.95980	0.329592	0.164796	−	0.986328i	$-0.447303\pi$
$739$	8.95980	0.329592	0.164796	+	0.986328i	$0.447303\pi$
$740$	29.8590	1.09764
$741$	−51.7026	−1.89934
$742$	56.0883	2.05907
$743$	−36.2896	−1.33134	−0.665668	−	0.746248i	$-0.731853\pi$
$743$	−36.2896	−1.33134	−0.665668	+	0.746248i	$0.731853\pi$
$744$	−6.83469	−0.250572
$745$	7.23484	0.265064
$746$	−52.1056	−1.90772
$747$	1.12538	0.0411754
$748$	−29.2594	−1.06983
$749$	19.4855	0.711985
$750$	−4.73925	−0.173053
$751$	14.3672	0.524267	0.262134	−	0.965032i	$-0.415574\pi$
$751$	14.3672	0.524267	0.262134	+	0.965032i	$0.415574\pi$
$752$	26.6074	0.970271
$753$	60.8952	2.21914
$754$	−95.1341	−3.46458
$755$	0.283478	0.0103168
$756$	30.7630	1.11884
$757$	−44.9826	−1.63492	−0.817460	−	0.575986i	$-0.804618\pi$
$757$	−44.9826	−1.63492	−0.817460	+	0.575986i	$0.804618\pi$
$758$	0.619064	0.0224854
$759$	23.3439	0.847330
$760$	−29.8277	−1.08196
$761$	−47.7332	−1.73033	−0.865163	−	0.501490i	$-0.832785\pi$
$761$	−47.7332	−1.73033	−0.865163	+	0.501490i	$0.832785\pi$
$762$	−73.3114	−2.65579
$763$	−24.0060	−0.869075
$764$	58.5555	2.11847
$765$	4.28407	0.154891
$766$	−62.8584	−2.27117
$767$	38.5441	1.39175
$768$	−59.4121	−2.14385
$769$	−11.0473	−0.398376	−0.199188	−	0.979961i	$-0.563830\pi$
$769$	−11.0473	−0.398376	−0.199188	+	0.979961i	$0.563830\pi$
$770$	−6.77497	−0.244153
$771$	−4.68224	−0.168627
$772$	32.7010	1.17693
$773$	40.9552	1.47305	0.736527	−	0.676408i	$-0.236464\pi$
$773$	40.9552	1.47305	0.736527	+	0.676408i	$0.236464\pi$
$774$	−22.8958	−0.822973
$775$	0.778558	0.0279666
$776$	−42.4203	−1.52280
$777$	−28.6270	−1.02699
$778$	8.21507	0.294524
$779$	70.2921	2.51848
$780$	−29.9226	−1.07140
$781$	0.709459	0.0253864
$782$	99.2213	3.54815
$783$	42.0114	1.50137
$784$	−10.8049	−0.385889
$785$	14.9682	0.534236
$786$	−28.1174	−1.00291
$787$	−27.2828	−0.972528	−0.486264	−	0.873812i	$-0.661641\pi$
$787$	−27.2828	−0.972528	−0.486264	+	0.873812i	$0.661641\pi$
$788$	8.02613	0.285919
$789$	39.7368	1.41467
$790$	−18.1750	−0.646638
$791$	−25.0804	−0.891755
$792$	5.57733	0.198182
$793$	49.4267	1.75519
$794$	40.0054	1.41974
$795$	24.0921	0.854459
$796$	76.7720	2.72111
$797$	−26.2545	−0.929981	−0.464991	−	0.885316i	$-0.653942\pi$
$797$	−26.2545	−0.929981	−0.464991	+	0.885316i	$0.653942\pi$
$798$	59.4737	2.10535
$799$	43.3844	1.53483
$800$	1.37621	0.0486563
$801$	9.10859	0.321836
$802$	68.1751	2.40735
$803$	13.7495	0.485209
$804$	−47.3298	−1.66919
$805$	15.1231	0.533021
$806$	7.46769	0.263038
$807$	−55.9233	−1.96859
$808$	86.7485	3.05180
$809$	5.83604	0.205184	0.102592	−	0.994724i	$-0.467286\pi$
$809$	5.83604	0.205184	0.102592	+	0.994724i	$0.467286\pi$
$810$	26.1550	0.918991
$811$	7.92132	0.278155	0.139078	−	0.990281i	$-0.455586\pi$
$811$	7.92132	0.278155	0.139078	+	0.990281i	$0.455586\pi$
$812$	72.0349	2.52793
$813$	−26.0045	−0.912017
$814$	27.8536	0.976267
$815$	9.48292	0.332172
$816$	31.4100	1.09957
$817$	75.1881	2.63050
$818$	−57.6456	−2.01553
$819$	6.26308	0.218850
$820$	40.6812	1.42065
$821$	−26.1455	−0.912486	−0.456243	−	0.889855i	$-0.650805\pi$
$821$	−26.1455	−0.912486	−0.456243	+	0.889855i	$0.650805\pi$
$822$	−9.42163	−0.328617
$823$	54.6378	1.90455	0.952277	−	0.305235i	$-0.0987351\pi$
$823$	54.6378	1.90455	0.952277	+	0.305235i	$0.0987351\pi$
$824$	−3.88736	−0.135423
$825$	−2.91011	−0.101317
$826$	−44.3374	−1.54269
$827$	−1.99631	−0.0694187	−0.0347093	−	0.999397i	$-0.511051\pi$
$827$	−1.99631	−0.0694187	−0.0347093	+	0.999397i	$0.511051\pi$
$828$	−25.8920	−0.899810
$829$	−20.9946	−0.729173	−0.364587	−	0.931170i	$-0.618790\pi$
$829$	−20.9946	−0.729173	−0.364587	+	0.931170i	$0.618790\pi$
$830$	−3.24925	−0.112783
$831$	55.3407	1.91975
$832$	38.0662	1.31971
$833$	−17.6178	−0.610421
$834$	−39.3978	−1.36423
$835$	−22.4545	−0.777070
$836$	−38.0912	−1.31741
$837$	−3.29775	−0.113987
$838$	57.2631	1.97812
$839$	−15.4034	−0.531786	−0.265893	−	0.964003i	$-0.585667\pi$
$839$	−15.4034	−0.531786	−0.265893	+	0.964003i	$0.585667\pi$
$840$	16.5503	0.571040
$841$	69.3745	2.39222
$842$	−32.4878	−1.11960
$843$	−42.9825	−1.48040
$844$	7.38888	0.254336
$845$	2.72031	0.0935815
$846$	−17.1989	−0.591310
$847$	16.5781	0.569629
$848$	38.5633	1.32427
$849$	7.96189	0.273252
$850$	−12.3692	−0.424260
$851$	−62.1749	−2.13133
$852$	−3.60438	−0.123484
$853$	40.9606	1.40247	0.701233	−	0.712932i	$-0.252633\pi$
$853$	40.9606	1.40247	0.701233	+	0.712932i	$0.252633\pi$
$854$	−56.8557	−1.94556
$855$	5.57720	0.190736
$856$	46.3144	1.58299
$857$	−41.2950	−1.41061	−0.705306	−	0.708903i	$-0.749190\pi$
$857$	−41.2950	−1.41061	−0.705306	+	0.708903i	$0.749190\pi$
$858$	−27.9129	−0.952931
$859$	28.1699	0.961146	0.480573	−	0.876955i	$-0.340429\pi$
$859$	28.1699	0.961146	0.480573	+	0.876955i	$0.340429\pi$
$860$	43.5147	1.48384
$861$	−39.0026	−1.32921
$862$	54.7902	1.86616
$863$	−0.932769	−0.0317518	−0.0158759	−	0.999874i	$-0.505054\pi$
$863$	−0.932769	−0.0317518	−0.0158759	+	0.999874i	$0.505054\pi$
$864$	−5.82922	−0.198314
$865$	−6.82736	−0.232137
$866$	−16.4109	−0.557666
$867$	17.9114	0.608304
$868$	−5.65448	−0.191926
$869$	−11.1603	−0.378587
$870$	47.0058	1.59364
$871$	24.8655	0.842535
$872$	−57.0589	−1.93226
$873$	7.93178	0.268450
$874$	129.171	4.36927
$875$	−1.88529	−0.0637345
$876$	−69.8539	−2.36015
$877$	−28.0999	−0.948867	−0.474433	−	0.880291i	$-0.657347\pi$
$877$	−28.0999	−0.948867	−0.474433	+	0.880291i	$0.657347\pi$
$878$	79.2783	2.67551
$879$	14.5917	0.492167
$880$	−4.65811	−0.157025
$881$	−9.38743	−0.316271	−0.158135	−	0.987417i	$-0.550548\pi$
$881$	−9.38743	−0.316271	−0.158135	+	0.987417i	$0.550548\pi$
$882$	6.98422	0.235171
$883$	−9.85827	−0.331757	−0.165879	−	0.986146i	$-0.553046\pi$
$883$	−9.85827	−0.331757	−0.165879	+	0.986146i	$0.553046\pi$
$884$	−78.0964	−2.62667
$885$	−19.0446	−0.640178
$886$	−58.6354	−1.96990
$887$	−29.4202	−0.987834	−0.493917	−	0.869509i	$-0.664435\pi$
$887$	−29.4202	−0.987834	−0.493917	+	0.869509i	$0.664435\pi$
$888$	−68.0424	−2.28335
$889$	−29.1636	−0.978114
$890$	−26.2988	−0.881539
$891$	16.0603	0.538041
$892$	14.4016	0.482201
$893$	56.4798	1.89003
$894$	−34.2877	−1.14675
$895$	21.8762	0.731240
$896$	−38.5985	−1.28949
$897$	62.3074	2.08038
$898$	10.8790	0.363038
$899$	−7.72205	−0.257545
$900$	3.22777	0.107592
$901$	62.8791	2.09481
$902$	37.9489	1.26356
$903$	−41.7192	−1.38833
$904$	−59.6126	−1.98268
$905$	13.1754	0.437967
$906$	−1.34347	−0.0446339
$907$	−2.32744	−0.0772814	−0.0386407	−	0.999253i	$-0.512303\pi$
$907$	−2.32744	−0.0772814	−0.0386407	+	0.999253i	$0.512303\pi$
$908$	−44.4793	−1.47610
$909$	−16.2203	−0.537993
$910$	−18.0831	−0.599450
$911$	−24.7094	−0.818660	−0.409330	−	0.912386i	$-0.634237\pi$
$911$	−24.7094	−0.818660	−0.409330	+	0.912386i	$0.634237\pi$
$912$	40.8910	1.35404
$913$	−1.99519	−0.0660311
$914$	−92.3052	−3.05318
$915$	−24.4217	−0.807357
$916$	49.8084	1.64572
$917$	−11.1852	−0.369368
$918$	52.3923	1.72920
$919$	20.2976	0.669557	0.334779	−	0.942297i	$-0.391338\pi$
$919$	20.2976	0.669557	0.334779	+	0.942297i	$0.391338\pi$
$920$	35.9456	1.18509
$921$	4.26544	0.140551
$922$	−24.4938	−0.806662
$923$	1.89362	0.0623293
$924$	21.1355	0.695306
$925$	7.75089	0.254848
$926$	−63.3503	−2.08182
$927$	0.726862	0.0238733
$928$	−13.6498	−0.448076
$929$	33.7846	1.10844	0.554218	−	0.832371i	$-0.313017\pi$
$929$	33.7846	1.10844	0.554218	+	0.832371i	$0.313017\pi$
$930$	−3.68978	−0.120993
$931$	−22.9357	−0.751686
$932$	53.0105	1.73642
$933$	−14.6767	−0.480494
$934$	19.7621	0.646635
$935$	−7.59525	−0.248391
$936$	14.8865	0.486580
$937$	−6.39850	−0.209030	−0.104515	−	0.994523i	$-0.533329\pi$
$937$	−6.39850	−0.209030	−0.104515	+	0.994523i	$0.533329\pi$
$938$	−28.6028	−0.933916
$939$	−2.91664	−0.0951808
$940$	32.6874	1.06614
$941$	13.2486	0.431892	0.215946	−	0.976405i	$-0.430717\pi$
$941$	13.2486	0.431892	0.215946	+	0.976405i	$0.430717\pi$
$942$	−70.9378	−2.31128
$943$	−84.7098	−2.75853
$944$	−30.4840	−0.992171
$945$	7.98555	0.259770
$946$	40.5921	1.31976
$947$	−20.5511	−0.667821	−0.333910	−	0.942605i	$-0.608368\pi$
$947$	−20.5511	−0.667821	−0.333910	+	0.942605i	$0.608368\pi$
$948$	56.6995	1.84151
$949$	36.6989	1.19130
$950$	−16.1028	−0.522443
$951$	−30.6997	−0.995505
$952$	43.1954	1.39997
$953$	33.1735	1.07460	0.537298	−	0.843392i	$-0.319445\pi$
$953$	33.1735	1.07460	0.537298	+	0.843392i	$0.319445\pi$
$954$	−24.9272	−0.807046
$955$	15.2000	0.491862
$956$	−24.1468	−0.780963
$957$	28.8637	0.933030
$958$	87.0713	2.81315
$959$	−3.74796	−0.121028
$960$	−18.8085	−0.607041
$961$	−30.3938	−0.980447
$962$	74.3441	2.39695
$963$	−8.65989	−0.279061
$964$	−5.82940	−0.187752
$965$	8.48863	0.273259
$966$	−71.6723	−2.30602
$967$	21.8605	0.702986	0.351493	−	0.936191i	$-0.385674\pi$
$967$	21.8605	0.702986	0.351493	+	0.936191i	$0.385674\pi$
$968$	39.4038	1.26648
$969$	66.6744	2.14189
$970$	−22.9011	−0.735310
$971$	23.6089	0.757647	0.378823	−	0.925469i	$-0.376329\pi$
$971$	23.6089	0.757647	0.378823	+	0.925469i	$0.376329\pi$
$972$	−32.6420	−1.04699
$973$	−15.6726	−0.502440
$974$	57.3947	1.83904
$975$	−7.76741	−0.248756
$976$	−39.0910	−1.25127
$977$	−12.1227	−0.387841	−0.193921	−	0.981017i	$-0.562120\pi$
$977$	−12.1227	−0.387841	−0.193921	+	0.981017i	$0.562120\pi$
$978$	−44.9419	−1.43708
$979$	−16.1487	−0.516114
$980$	−13.2739	−0.424019
$981$	10.6689	0.340632
$982$	−55.1116	−1.75868
$983$	−4.24432	−0.135373	−0.0676863	−	0.997707i	$-0.521562\pi$
$983$	−4.24432	−0.135373	−0.0676863	+	0.997707i	$0.521562\pi$
$984$	−92.7038	−2.95529
$985$	2.08345	0.0663842
$986$	122.683	3.90701
$987$	−31.3387	−0.997521
$988$	−101.669	−3.23454
$989$	−90.6100	−2.88123
$990$	3.01098	0.0956953
$991$	6.96509	0.221254	0.110627	−	0.993862i	$-0.464714\pi$
$991$	6.96509	0.221254	0.110627	+	0.993862i	$0.464714\pi$
$992$	1.07146	0.0340189
$993$	43.3334	1.37515
$994$	−2.17824	−0.0690895
$995$	19.9287	0.631783
$996$	10.1365	0.321187
$997$	−14.5356	−0.460346	−0.230173	−	0.973150i	$-0.573929\pi$
$997$	−14.5356	−0.460346	−0.230173	+	0.973150i	$0.573929\pi$
$998$	−104.653	−3.31275
$999$	−32.8305	−1.03871

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.f.1.10	✓	111

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.f.1.10	✓	111	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41916 q^{2} +1.95905 q^{3} +3.85233 q^{4} +1.00000 q^{5} -4.73925 q^{6} -1.88529 q^{7} -4.48108 q^{8} +0.837875 q^{9} +O(q^{10})\)	\(q-2.41916 q^{2} +1.95905 q^{3} +3.85233 q^{4} +1.00000 q^{5} -4.73925 q^{6} -1.88529 q^{7} -4.48108 q^{8} +0.837875 q^{9} -2.41916 q^{10} -1.48547 q^{11} +7.54690 q^{12} -3.96488 q^{13} +4.56082 q^{14} +1.95905 q^{15} +3.13578 q^{16} +5.11302 q^{17} -2.02695 q^{18} +6.65636 q^{19} +3.85233 q^{20} -3.69338 q^{21} +3.59359 q^{22} -8.02164 q^{23} -8.77865 q^{24} +1.00000 q^{25} +9.59168 q^{26} -4.23571 q^{27} -7.26276 q^{28} -9.91839 q^{29} -4.73925 q^{30} +0.778558 q^{31} +1.37621 q^{32} -2.91011 q^{33} -12.3692 q^{34} -1.88529 q^{35} +3.22777 q^{36} +7.75089 q^{37} -16.1028 q^{38} -7.76741 q^{39} -4.48108 q^{40} +10.5601 q^{41} +8.93487 q^{42} +11.2957 q^{43} -5.72253 q^{44} +0.837875 q^{45} +19.4056 q^{46} +8.48509 q^{47} +6.14314 q^{48} -3.44568 q^{49} -2.41916 q^{50} +10.0166 q^{51} -15.2740 q^{52} +12.2979 q^{53} +10.2469 q^{54} -1.48547 q^{55} +8.44813 q^{56} +13.0401 q^{57} +23.9942 q^{58} -9.72136 q^{59} +7.54690 q^{60} -12.4661 q^{61} -1.88346 q^{62} -1.57964 q^{63} -9.60082 q^{64} -3.96488 q^{65} +7.04003 q^{66} -6.27143 q^{67} +19.6970 q^{68} -15.7148 q^{69} +4.56082 q^{70} -0.477598 q^{71} -3.75458 q^{72} -9.25598 q^{73} -18.7506 q^{74} +1.95905 q^{75} +25.6425 q^{76} +2.80055 q^{77} +18.7906 q^{78} +7.51295 q^{79} +3.13578 q^{80} -10.8116 q^{81} -25.5467 q^{82} +1.34313 q^{83} -14.2281 q^{84} +5.11302 q^{85} -27.3261 q^{86} -19.4306 q^{87} +6.65652 q^{88} +10.8711 q^{89} -2.02695 q^{90} +7.47496 q^{91} -30.9020 q^{92} +1.52523 q^{93} -20.5268 q^{94} +6.65636 q^{95} +2.69606 q^{96} +9.46655 q^{97} +8.33564 q^{98} -1.24464 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9} + 20 q^{10} + 36 q^{11} + 80 q^{12} + 36 q^{13} + 7 q^{14} + 40 q^{15} + 190 q^{16} + 38 q^{17} + 48 q^{18} + 77 q^{19} + 136 q^{20} + 11 q^{21} + 39 q^{22} + 82 q^{23} - 3 q^{24} + 111 q^{25} - 3 q^{26} + 130 q^{27} + 87 q^{28} + 20 q^{29} + 3 q^{30} + 41 q^{31} + 85 q^{32} + 33 q^{33} + 7 q^{34} + 39 q^{35} + 191 q^{36} + 80 q^{37} + 42 q^{38} + 21 q^{39} + 45 q^{40} + 16 q^{41} + 33 q^{42} + 164 q^{43} + 37 q^{44} + 139 q^{45} + 32 q^{46} + 148 q^{47} + 149 q^{48} + 160 q^{49} + 20 q^{50} + 51 q^{51} + 87 q^{52} + 83 q^{53} - 6 q^{54} + 36 q^{55} - 10 q^{56} + 28 q^{57} + 47 q^{58} + 14 q^{59} + 80 q^{60} + 20 q^{61} + 14 q^{62} + 120 q^{63} + 231 q^{64} + 36 q^{65} - 4 q^{66} + 253 q^{67} + 80 q^{68} + 6 q^{69} + 7 q^{70} + 5 q^{71} + 124 q^{72} + 64 q^{73} - 37 q^{74} + 40 q^{75} + 92 q^{76} + 63 q^{77} + 29 q^{78} + 91 q^{79} + 190 q^{80} + 187 q^{81} - 7 q^{82} + 63 q^{83} - 69 q^{84} + 38 q^{85} - 22 q^{86} + 57 q^{87} + 121 q^{88} - 6 q^{89} + 48 q^{90} + 119 q^{91} + 104 q^{92} + 14 q^{93} - q^{94} + 77 q^{95} - 38 q^{96} + 96 q^{97} + 81 q^{98} + 106 q^{99}+O(q^{100}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9 + 20 * q^10 + 36 * q^11 + 80 * q^12 + 36 * q^13 + 7 * q^14 + 40 * q^15 + 190 * q^16 + 38 * q^17 + 48 * q^18 + 77 * q^19 + 136 * q^20 + 11 * q^21 + 39 * q^22 + 82 * q^23 - 3 * q^24 + 111 * q^25 - 3 * q^26 + 130 * q^27 + 87 * q^28 + 20 * q^29 + 3 * q^30 + 41 * q^31 + 85 * q^32 + 33 * q^33 + 7 * q^34 + 39 * q^35 + 191 * q^36 + 80 * q^37 + 42 * q^38 + 21 * q^39 + 45 * q^40 + 16 * q^41 + 33 * q^42 + 164 * q^43 + 37 * q^44 + 139 * q^45 + 32 * q^46 + 148 * q^47 + 149 * q^48 + 160 * q^49 + 20 * q^50 + 51 * q^51 + 87 * q^52 + 83 * q^53 - 6 * q^54 + 36 * q^55 - 10 * q^56 + 28 * q^57 + 47 * q^58 + 14 * q^59 + 80 * q^60 + 20 * q^61 + 14 * q^62 + 120 * q^63 + 231 * q^64 + 36 * q^65 - 4 * q^66 + 253 * q^67 + 80 * q^68 + 6 * q^69 + 7 * q^70 + 5 * q^71 + 124 * q^72 + 64 * q^73 - 37 * q^74 + 40 * q^75 + 92 * q^76 + 63 * q^77 + 29 * q^78 + 91 * q^79 + 190 * q^80 + 187 * q^81 - 7 * q^82 + 63 * q^83 - 69 * q^84 + 38 * q^85 - 22 * q^86 + 57 * q^87 + 121 * q^88 - 6 * q^89 + 48 * q^90 + 119 * q^91 + 104 * q^92 + 14 * q^93 - q^94 + 77 * q^95 - 38 * q^96 + 96 * q^97 + 81 * q^98 + 106 * q^99

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