LMFDB - Embedded newform 6001.2.a.d.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48199 q^{2} +1.43528 q^{3} +4.16025 q^{4} +0.277666 q^{5} -3.56234 q^{6} +3.77920 q^{7} -5.36171 q^{8} -0.939973 q^{9} +O(q^{10})$	\(q-2.48199 q^{2} +1.43528 q^{3} +4.16025 q^{4} +0.277666 q^{5} -3.56234 q^{6} +3.77920 q^{7} -5.36171 q^{8} -0.939973 q^{9} -0.689164 q^{10} +4.20622 q^{11} +5.97112 q^{12} +2.72188 q^{13} -9.37991 q^{14} +0.398529 q^{15} +4.98718 q^{16} +1.00000 q^{17} +2.33300 q^{18} -0.978299 q^{19} +1.15516 q^{20} +5.42421 q^{21} -10.4398 q^{22} -3.17903 q^{23} -7.69555 q^{24} -4.92290 q^{25} -6.75566 q^{26} -5.65496 q^{27} +15.7224 q^{28} +0.536296 q^{29} -0.989142 q^{30} -9.10459 q^{31} -1.65469 q^{32} +6.03709 q^{33} -2.48199 q^{34} +1.04936 q^{35} -3.91052 q^{36} -6.86711 q^{37} +2.42812 q^{38} +3.90665 q^{39} -1.48877 q^{40} +1.77455 q^{41} -13.4628 q^{42} +3.97589 q^{43} +17.4989 q^{44} -0.260999 q^{45} +7.89031 q^{46} +11.0202 q^{47} +7.15799 q^{48} +7.28234 q^{49} +12.2186 q^{50} +1.43528 q^{51} +11.3237 q^{52} +7.99396 q^{53} +14.0355 q^{54} +1.16792 q^{55} -20.2630 q^{56} -1.40413 q^{57} -1.33108 q^{58} -0.301193 q^{59} +1.65798 q^{60} +6.23491 q^{61} +22.5974 q^{62} -3.55235 q^{63} -5.86745 q^{64} +0.755773 q^{65} -14.9840 q^{66} +10.4834 q^{67} +4.16025 q^{68} -4.56280 q^{69} -2.60449 q^{70} -3.80575 q^{71} +5.03986 q^{72} -10.0591 q^{73} +17.0441 q^{74} -7.06574 q^{75} -4.06997 q^{76} +15.8961 q^{77} -9.69625 q^{78} +11.4349 q^{79} +1.38477 q^{80} -5.29653 q^{81} -4.40441 q^{82} +12.0659 q^{83} +22.5660 q^{84} +0.277666 q^{85} -9.86809 q^{86} +0.769734 q^{87} -22.5525 q^{88} +5.72993 q^{89} +0.647796 q^{90} +10.2865 q^{91} -13.2256 q^{92} -13.0676 q^{93} -27.3519 q^{94} -0.271641 q^{95} -2.37494 q^{96} +6.42228 q^{97} -18.0747 q^{98} -3.95373 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * 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 $

$2$	−2.48199	−1.75503	−0.877514	−	0.479551i	$-0.840800\pi$
$2$	−2.48199	−1.75503	−0.877514	+	0.479551i	$0.840800\pi$
$3$	1.43528	0.828659	0.414329	−	0.910127i	$-0.364016\pi$
$3$	1.43528	0.828659	0.414329	+	0.910127i	$0.364016\pi$
$4$	4.16025	2.08012
$5$	0.277666	0.124176	0.0620881	−	0.998071i	$-0.480224\pi$
$5$	0.277666	0.124176	0.0620881	+	0.998071i	$0.480224\pi$
$6$	−3.56234	−1.45432
$7$	3.77920	1.42840	0.714201	−	0.699940i	$-0.246790\pi$
$7$	3.77920	1.42840	0.714201	+	0.699940i	$0.246790\pi$
$8$	−5.36171	−1.89565
$9$	−0.939973	−0.313324
$10$	−0.689164	−0.217933
$11$	4.20622	1.26822	0.634111	−	0.773242i	$-0.281366\pi$
$11$	4.20622	1.26822	0.634111	+	0.773242i	$0.281366\pi$
$12$	5.97112	1.72371
$13$	2.72188	0.754913	0.377456	−	0.926027i	$-0.376799\pi$
$13$	2.72188	0.754913	0.377456	+	0.926027i	$0.376799\pi$
$14$	−9.37991	−2.50689
$15$	0.398529	0.102900
$16$	4.98718	1.24679
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.33300	0.549893
$19$	−0.978299	−0.224437	−0.112219	−	0.993684i	$-0.535796\pi$
$19$	−0.978299	−0.224437	−0.112219	+	0.993684i	$0.535796\pi$
$20$	1.15516	0.258302
$21$	5.42421	1.18366
$22$	−10.4398	−2.22577
$23$	−3.17903	−0.662874	−0.331437	−	0.943477i	$-0.607533\pi$
$23$	−3.17903	−0.662874	−0.331437	+	0.943477i	$0.607533\pi$
$24$	−7.69555	−1.57085
$25$	−4.92290	−0.984580
$26$	−6.75566	−1.32489
$27$	−5.65496	−1.08830
$28$	15.7224	2.97126
$29$	0.536296	0.0995876	0.0497938	−	0.998760i	$-0.484144\pi$
$29$	0.536296	0.0995876	0.0497938	+	0.998760i	$0.484144\pi$
$30$	−0.989142	−0.180592
$31$	−9.10459	−1.63523	−0.817616	−	0.575764i	$-0.804705\pi$
$31$	−9.10459	−1.63523	−0.817616	+	0.575764i	$0.804705\pi$
$32$	−1.65469	−0.292510
$33$	6.03709	1.05092
$34$	−2.48199	−0.425657
$35$	1.04936	0.177374
$36$	−3.91052	−0.651754
$37$	−6.86711	−1.12895	−0.564473	−	0.825452i	$-0.690920\pi$
$37$	−6.86711	−1.12895	−0.564473	+	0.825452i	$0.690920\pi$
$38$	2.42812	0.393893
$39$	3.90665	0.625565
$40$	−1.48877	−0.235395
$41$	1.77455	0.277139	0.138569	−	0.990353i	$-0.455750\pi$
$41$	1.77455	0.277139	0.138569	+	0.990353i	$0.455750\pi$
$42$	−13.4628	−2.07735
$43$	3.97589	0.606317	0.303158	−	0.952940i	$-0.401959\pi$
$43$	3.97589	0.606317	0.303158	+	0.952940i	$0.401959\pi$
$44$	17.4989	2.63806
$45$	−0.260999	−0.0389074
$46$	7.89031	1.16336
$47$	11.0202	1.60746	0.803728	−	0.594997i	$-0.202847\pi$
$47$	11.0202	1.60746	0.803728	+	0.594997i	$0.202847\pi$
$48$	7.15799	1.03317
$49$	7.28234	1.04033
$50$	12.2186	1.72797
$51$	1.43528	0.200979
$52$	11.3237	1.57031
$53$	7.99396	1.09805	0.549027	−	0.835804i	$-0.314998\pi$
$53$	7.99396	1.09805	0.549027	+	0.835804i	$0.314998\pi$
$54$	14.0355	1.90999
$55$	1.16792	0.157483
$56$	−20.2630	−2.70775
$57$	−1.40413	−0.185982
$58$	−1.33108	−0.174779
$59$	−0.301193	−0.0392120	−0.0196060	−	0.999808i	$-0.506241\pi$
$59$	−0.301193	−0.0392120	−0.0196060	+	0.999808i	$0.506241\pi$
$60$	1.65798	0.214044
$61$	6.23491	0.798299	0.399149	−	0.916886i	$-0.369305\pi$
$61$	6.23491	0.798299	0.399149	+	0.916886i	$0.369305\pi$
$62$	22.5974	2.86988
$63$	−3.55235	−0.447554
$64$	−5.86745	−0.733431
$65$	0.755773	0.0937421
$66$	−14.9840	−1.84440
$67$	10.4834	1.28075	0.640374	−	0.768064i	$-0.278780\pi$
$67$	10.4834	1.28075	0.640374	+	0.768064i	$0.278780\pi$
$68$	4.16025	0.504504
$69$	−4.56280	−0.549297
$70$	−2.60449	−0.311296
$71$	−3.80575	−0.451659	−0.225829	−	0.974167i	$-0.572509\pi$
$71$	−3.80575	−0.451659	−0.225829	+	0.974167i	$0.572509\pi$
$72$	5.03986	0.593953
$73$	−10.0591	−1.17733	−0.588664	−	0.808378i	$-0.700346\pi$
$73$	−10.0591	−1.17733	−0.588664	+	0.808378i	$0.700346\pi$
$74$	17.0441	1.98133
$75$	−7.06574	−0.815881
$76$	−4.06997	−0.466857
$77$	15.8961	1.81153
$78$	−9.69625	−1.09788
$79$	11.4349	1.28652	0.643261	−	0.765647i	$-0.277581\pi$
$79$	11.4349	1.28652	0.643261	+	0.765647i	$0.277581\pi$
$80$	1.38477	0.154822
$81$	−5.29653	−0.588503
$82$	−4.40441	−0.486386
$83$	12.0659	1.32440	0.662200	−	0.749327i	$-0.269623\pi$
$83$	12.0659	1.32440	0.662200	+	0.749327i	$0.269623\pi$
$84$	22.5660	2.46216
$85$	0.277666	0.0301171
$86$	−9.86809	−1.06410
$87$	0.769734	0.0825241
$88$	−22.5525	−2.40410
$89$	5.72993	0.607372	0.303686	−	0.952772i	$-0.401783\pi$
$89$	5.72993	0.607372	0.303686	+	0.952772i	$0.401783\pi$
$90$	0.647796	0.0682837
$91$	10.2865	1.07832
$92$	−13.2256	−1.37886
$93$	−13.0676	−1.35505
$94$	−27.3519	−2.82113
$95$	−0.271641	−0.0278697
$96$	−2.37494	−0.242391
$97$	6.42228	0.652084	0.326042	−	0.945355i	$-0.394285\pi$
$97$	6.42228	0.652084	0.326042	+	0.945355i	$0.394285\pi$
$98$	−18.0747	−1.82582
$99$	−3.95373	−0.397365
$100$	−20.4805	−2.04805
$101$	0.450826	0.0448588	0.0224294	−	0.999748i	$-0.492860\pi$
$101$	0.450826	0.0448588	0.0224294	+	0.999748i	$0.492860\pi$
$102$	−3.56234	−0.352724
$103$	−5.08324	−0.500866	−0.250433	−	0.968134i	$-0.580573\pi$
$103$	−5.08324	−0.500866	−0.250433	+	0.968134i	$0.580573\pi$
$104$	−14.5939	−1.43105
$105$	1.50612	0.146982
$106$	−19.8409	−1.92712
$107$	−4.14499	−0.400711	−0.200356	−	0.979723i	$-0.564210\pi$
$107$	−4.14499	−0.400711	−0.200356	+	0.979723i	$0.564210\pi$
$108$	−23.5261	−2.26380
$109$	7.54018	0.722218	0.361109	−	0.932524i	$-0.382398\pi$
$109$	7.54018	0.722218	0.361109	+	0.932524i	$0.382398\pi$
$110$	−2.89877	−0.276387
$111$	−9.85622	−0.935511
$112$	18.8475	1.78092
$113$	14.6290	1.37618	0.688090	−	0.725625i	$-0.258449\pi$
$113$	14.6290	1.37618	0.688090	+	0.725625i	$0.258449\pi$
$114$	3.48503	0.326403
$115$	−0.882711	−0.0823132
$116$	2.23112	0.207155
$117$	−2.55849	−0.236533
$118$	0.747558	0.0688183
$119$	3.77920	0.346439
$120$	−2.13679	−0.195062
$121$	6.69226	0.608387
$122$	−15.4750	−1.40104
$123$	2.54698	0.229653
$124$	−37.8774	−3.40149
$125$	−2.75526	−0.246438
$126$	8.81687	0.785469
$127$	20.5742	1.82566	0.912831	−	0.408337i	$-0.133891\pi$
$127$	20.5742	1.82566	0.912831	+	0.408337i	$0.133891\pi$
$128$	17.8723	1.57970
$129$	5.70651	0.502430
$130$	−1.87582	−0.164520
$131$	21.9445	1.91730	0.958651	−	0.284584i	$-0.0918554\pi$
$131$	21.9445	1.91730	0.958651	+	0.284584i	$0.0918554\pi$
$132$	25.1158	2.18605
$133$	−3.69718	−0.320587
$134$	−26.0196	−2.24775
$135$	−1.57019	−0.135141
$136$	−5.36171	−0.459763
$137$	8.31489	0.710389	0.355194	−	0.934792i	$-0.384415\pi$
$137$	8.31489	0.710389	0.355194	+	0.934792i	$0.384415\pi$
$138$	11.3248	0.964031
$139$	2.69931	0.228952	0.114476	−	0.993426i	$-0.463481\pi$
$139$	2.69931	0.228952	0.114476	+	0.993426i	$0.463481\pi$
$140$	4.36558	0.368959
$141$	15.8170	1.33203
$142$	9.44581	0.792674
$143$	11.4488	0.957397
$144$	−4.68781	−0.390651
$145$	0.148911	0.0123664
$146$	24.9665	2.06624
$147$	10.4522	0.862083
$148$	−28.5689	−2.34835
$149$	9.53406	0.781060	0.390530	−	0.920590i	$-0.372292\pi$
$149$	9.53406	0.781060	0.390530	+	0.920590i	$0.372292\pi$
$150$	17.5371	1.43189
$151$	10.5658	0.859836	0.429918	−	0.902868i	$-0.358542\pi$
$151$	10.5658	0.859836	0.429918	+	0.902868i	$0.358542\pi$
$152$	5.24535	0.425454
$153$	−0.939973	−0.0759924
$154$	−39.4539	−3.17929
$155$	−2.52804	−0.203057
$156$	16.2526	1.30125
$157$	−18.2513	−1.45661	−0.728306	−	0.685252i	$-0.759692\pi$
$157$	−18.2513	−1.45661	−0.728306	+	0.685252i	$0.759692\pi$
$158$	−28.3812	−2.25788
$159$	11.4736	0.909913
$160$	−0.459450	−0.0363227
$161$	−12.0142	−0.946852
$162$	13.1459	1.03284
$163$	−9.02054	−0.706543	−0.353272	−	0.935521i	$-0.614931\pi$
$163$	−9.02054	−0.706543	−0.353272	+	0.935521i	$0.614931\pi$
$164$	7.38258	0.576483
$165$	1.67630	0.130500
$166$	−29.9473	−2.32436
$167$	8.77481	0.679016	0.339508	−	0.940603i	$-0.389740\pi$
$167$	8.77481	0.679016	0.339508	+	0.940603i	$0.389740\pi$
$168$	−29.0830	−2.24380
$169$	−5.59139	−0.430107
$170$	−0.689164	−0.0528564
$171$	0.919575	0.0703216
$172$	16.5407	1.26121
$173$	21.7882	1.65653	0.828265	−	0.560337i	$-0.189328\pi$
$173$	21.7882	1.65653	0.828265	+	0.560337i	$0.189328\pi$
$174$	−1.91047	−0.144832
$175$	−18.6046	−1.40638
$176$	20.9771	1.58121
$177$	−0.432297	−0.0324934
$178$	−14.2216	−1.06595
$179$	−20.7976	−1.55449	−0.777245	−	0.629199i	$-0.783383\pi$
$179$	−20.7976	−1.55449	−0.777245	+	0.629199i	$0.783383\pi$
$180$	−1.08582	−0.0809323
$181$	0.360374	0.0267864	0.0133932	−	0.999910i	$-0.495737\pi$
$181$	0.360374	0.0267864	0.0133932	+	0.999910i	$0.495737\pi$
$182$	−25.5310	−1.89248
$183$	8.94884	0.661517
$184$	17.0450	1.25658
$185$	−1.90676	−0.140188
$186$	32.4336	2.37815
$187$	4.20622	0.307589
$188$	45.8466	3.34371
$189$	−21.3712	−1.55453
$190$	0.674208	0.0489122
$191$	−4.50425	−0.325916	−0.162958	−	0.986633i	$-0.552104\pi$
$191$	−4.50425	−0.325916	−0.162958	+	0.986633i	$0.552104\pi$
$192$	−8.42143	−0.607764
$193$	−2.15128	−0.154853	−0.0774264	−	0.996998i	$-0.524670\pi$
$193$	−2.15128	−0.154853	−0.0774264	+	0.996998i	$0.524670\pi$
$194$	−15.9400	−1.14443
$195$	1.08475	0.0776803
$196$	30.2964	2.16403
$197$	4.53559	0.323148	0.161574	−	0.986861i	$-0.448343\pi$
$197$	4.53559	0.323148	0.161574	+	0.986861i	$0.448343\pi$
$198$	9.81310	0.697387
$199$	−9.71419	−0.688621	−0.344310	−	0.938856i	$-0.611887\pi$
$199$	−9.71419	−0.688621	−0.344310	+	0.938856i	$0.611887\pi$
$200$	26.3952	1.86642
$201$	15.0466	1.06130
$202$	−1.11894	−0.0787285
$203$	2.02677	0.142251
$204$	5.97112	0.418062
$205$	0.492734	0.0344140
$206$	12.6165	0.879035
$207$	2.98821	0.207695
$208$	13.5745	0.941221
$209$	−4.11494	−0.284636
$210$	−3.73817	−0.257958
$211$	15.7249	1.08254	0.541272	−	0.840847i	$-0.317943\pi$
$211$	15.7249	1.08254	0.541272	+	0.840847i	$0.317943\pi$
$212$	33.2569	2.28409
$213$	−5.46231	−0.374271
$214$	10.2878	0.703260
$215$	1.10397	0.0752901
$216$	30.3203	2.06303
$217$	−34.4080	−2.33577
$218$	−18.7146	−1.26751
$219$	−14.4376	−0.975603
$220$	4.85886	0.327584
$221$	2.72188	0.183093
$222$	24.4630	1.64185
$223$	0.194992	0.0130576	0.00652882	−	0.999979i	$-0.497922\pi$
$223$	0.194992	0.0130576	0.00652882	+	0.999979i	$0.497922\pi$
$224$	−6.25338	−0.417822
$225$	4.62740	0.308493
$226$	−36.3089	−2.41523
$227$	3.56514	0.236627	0.118313	−	0.992976i	$-0.462251\pi$
$227$	3.56514	0.236627	0.118313	+	0.992976i	$0.462251\pi$
$228$	−5.84154	−0.386865
$229$	9.58050	0.633097	0.316549	−	0.948576i	$-0.397476\pi$
$229$	9.58050	0.633097	0.316549	+	0.948576i	$0.397476\pi$
$230$	2.19087	0.144462
$231$	22.8154	1.50114
$232$	−2.87546	−0.188783
$233$	17.2692	1.13134	0.565671	−	0.824631i	$-0.308617\pi$
$233$	17.2692	1.13134	0.565671	+	0.824631i	$0.308617\pi$
$234$	6.35014	0.415121
$235$	3.05993	0.199608
$236$	−1.25304	−0.0815659
$237$	16.4122	1.06609
$238$	−9.37991	−0.608010
$239$	3.04681	0.197081	0.0985407	−	0.995133i	$-0.468583\pi$
$239$	3.04681	0.197081	0.0985407	+	0.995133i	$0.468583\pi$
$240$	1.98753	0.128295
$241$	5.71679	0.368251	0.184125	−	0.982903i	$-0.441055\pi$
$241$	5.71679	0.368251	0.184125	+	0.982903i	$0.441055\pi$
$242$	−16.6101	−1.06774
$243$	9.36289	0.600630
$244$	25.9388	1.66056
$245$	2.02206	0.129185
$246$	−6.32156	−0.403048
$247$	−2.66281	−0.169430
$248$	48.8161	3.09983
$249$	17.3179	1.09748
$250$	6.83850	0.432505
$251$	5.18002	0.326960	0.163480	−	0.986547i	$-0.447728\pi$
$251$	5.18002	0.326960	0.163480	+	0.986547i	$0.447728\pi$
$252$	−14.7786	−0.930967
$253$	−13.3717	−0.840672
$254$	−51.0648	−3.20409
$255$	0.398529	0.0249568
$256$	−32.6239	−2.03899
$257$	12.1992	0.760968	0.380484	−	0.924788i	$-0.375757\pi$
$257$	12.1992	0.760968	0.380484	+	0.924788i	$0.375757\pi$
$258$	−14.1635	−0.881779
$259$	−25.9522	−1.61259
$260$	3.14421	0.194995
$261$	−0.504104	−0.0312032
$262$	−54.4660	−3.36492
$263$	−15.4227	−0.951005	−0.475502	−	0.879714i	$-0.657734\pi$
$263$	−15.4227	−0.951005	−0.475502	+	0.879714i	$0.657734\pi$
$264$	−32.3691	−1.99218
$265$	2.21965	0.136352
$266$	9.17636	0.562639
$267$	8.22406	0.503304
$268$	43.6134	2.66411
$269$	−11.3387	−0.691333	−0.345667	−	0.938357i	$-0.612347\pi$
$269$	−11.3387	−0.691333	−0.345667	+	0.938357i	$0.612347\pi$
$270$	3.89719	0.237176
$271$	−8.83877	−0.536917	−0.268459	−	0.963291i	$-0.586514\pi$
$271$	−8.83877	−0.536917	−0.268459	+	0.963291i	$0.586514\pi$
$272$	4.98718	0.302392
$273$	14.7640	0.893559
$274$	−20.6374	−1.24675
$275$	−20.7068	−1.24867
$276$	−18.9824	−1.14261
$277$	17.9184	1.07661	0.538306	−	0.842749i	$-0.319064\pi$
$277$	17.9184	1.07661	0.538306	+	0.842749i	$0.319064\pi$
$278$	−6.69965	−0.401818
$279$	8.55807	0.512358
$280$	−5.62634	−0.336238
$281$	−0.602333	−0.0359321	−0.0179661	−	0.999839i	$-0.505719\pi$
$281$	−0.602333	−0.0359321	−0.0179661	+	0.999839i	$0.505719\pi$
$282$	−39.2576	−2.33775
$283$	24.1768	1.43716	0.718580	−	0.695445i	$-0.244793\pi$
$283$	24.1768	1.43716	0.718580	+	0.695445i	$0.244793\pi$
$284$	−15.8329	−0.939507
$285$	−0.389880	−0.0230945
$286$	−28.4157	−1.68026
$287$	6.70639	0.395866
$288$	1.55536	0.0916505
$289$	1.00000	0.0588235
$290$	−0.369595	−0.0217034
$291$	9.21777	0.540355
$292$	−41.8483	−2.44899
$293$	−5.78422	−0.337918	−0.168959	−	0.985623i	$-0.554040\pi$
$293$	−5.78422	−0.337918	−0.168959	+	0.985623i	$0.554040\pi$
$294$	−25.9422	−1.51298
$295$	−0.0836313	−0.00486920
$296$	36.8194	2.14009
$297$	−23.7860	−1.38020
$298$	−23.6634	−1.37078
$299$	−8.65294	−0.500412
$300$	−29.3952	−1.69713
$301$	15.0257	0.866065
$302$	−26.2243	−1.50904
$303$	0.647061	0.0371727
$304$	−4.87895	−0.279827
$305$	1.73123	0.0991297
$306$	2.33300	0.133369
$307$	−23.9252	−1.36548	−0.682742	−	0.730659i	$-0.739213\pi$
$307$	−23.9252	−1.36548	−0.682742	+	0.730659i	$0.739213\pi$
$308$	66.1319	3.76821
$309$	−7.29587	−0.415047
$310$	6.27455	0.356371
$311$	3.12328	0.177105	0.0885524	−	0.996072i	$-0.471776\pi$
$311$	3.12328	0.177105	0.0885524	+	0.996072i	$0.471776\pi$
$312$	−20.9463	−1.18585
$313$	−29.9803	−1.69459	−0.847295	−	0.531123i	$-0.821770\pi$
$313$	−29.9803	−1.69459	−0.847295	+	0.531123i	$0.821770\pi$
$314$	45.2994	2.55640
$315$	−0.986367	−0.0555755
$316$	47.5719	2.67613
$317$	−0.216064	−0.0121354	−0.00606770	−	0.999982i	$-0.501931\pi$
$317$	−0.216064	−0.0121354	−0.00606770	+	0.999982i	$0.501931\pi$
$318$	−28.4772	−1.59692
$319$	2.25578	0.126299
$320$	−1.62919	−0.0910747
$321$	−5.94922	−0.332053
$322$	29.8191	1.66175
$323$	−0.978299	−0.0544340
$324$	−22.0349	−1.22416
$325$	−13.3995	−0.743272
$326$	22.3888	1.24000
$327$	10.8223	0.598472
$328$	−9.51463	−0.525358
$329$	41.6474	2.29609
$330$	−4.16055	−0.229031
$331$	4.90634	0.269677	0.134839	−	0.990868i	$-0.456948\pi$
$331$	4.90634	0.269677	0.134839	+	0.990868i	$0.456948\pi$
$332$	50.1970	2.75492
$333$	6.45490	0.353726
$334$	−21.7790	−1.19169
$335$	2.91088	0.159038
$336$	27.0515	1.47578
$337$	−8.78664	−0.478639	−0.239319	−	0.970941i	$-0.576924\pi$
$337$	−8.78664	−0.478639	−0.239319	+	0.970941i	$0.576924\pi$
$338$	13.8778	0.754850
$339$	20.9967	1.14038
$340$	1.15516	0.0626474
$341$	−38.2959	−2.07384
$342$	−2.28237	−0.123416
$343$	1.06703	0.0576143
$344$	−21.3175	−1.14936
$345$	−1.26694	−0.0682096
$346$	−54.0781	−2.90726
$347$	−20.1876	−1.08373	−0.541865	−	0.840466i	$-0.682282\pi$
$347$	−20.1876	−1.08373	−0.541865	+	0.840466i	$0.682282\pi$
$348$	3.20229	0.171661
$349$	2.76017	0.147749	0.0738743	−	0.997268i	$-0.476464\pi$
$349$	2.76017	0.147749	0.0738743	+	0.997268i	$0.476464\pi$
$350$	46.1764	2.46823
$351$	−15.3921	−0.821570
$352$	−6.95996	−0.370967
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	1.07295	0.0570269
$355$	−1.05673	−0.0560853
$356$	23.8380	1.26341
$357$	5.42421	0.287079
$358$	51.6194	2.72817
$359$	−21.4938	−1.13440	−0.567200	−	0.823580i	$-0.691973\pi$
$359$	−21.4938	−1.13440	−0.567200	+	0.823580i	$0.691973\pi$
$360$	1.39940	0.0737549
$361$	−18.0429	−0.949628
$362$	−0.894444	−0.0470109
$363$	9.60525	0.504145
$364$	42.7944	2.24304
$365$	−2.79307	−0.146196
$366$	−22.2109	−1.16098
$367$	−6.79233	−0.354557	−0.177278	−	0.984161i	$-0.556729\pi$
$367$	−6.79233	−0.354557	−0.177278	+	0.984161i	$0.556729\pi$
$368$	−15.8544	−0.826468
$369$	−1.66803	−0.0868343
$370$	4.73256	0.246034
$371$	30.2108	1.56846
$372$	−54.3646	−2.81867
$373$	7.58283	0.392624	0.196312	−	0.980541i	$-0.437103\pi$
$373$	7.58283	0.392624	0.196312	+	0.980541i	$0.437103\pi$
$374$	−10.4398	−0.539827
$375$	−3.95456	−0.204213
$376$	−59.0869	−3.04717
$377$	1.45973	0.0751799
$378$	53.0431	2.72824
$379$	−22.9866	−1.18074	−0.590372	−	0.807131i	$-0.701019\pi$
$379$	−22.9866	−1.18074	−0.590372	+	0.807131i	$0.701019\pi$
$380$	−1.13009	−0.0579725
$381$	29.5297	1.51285
$382$	11.1795	0.571992
$383$	−8.64576	−0.441778	−0.220889	−	0.975299i	$-0.570896\pi$
$383$	−8.64576	−0.441778	−0.220889	+	0.975299i	$0.570896\pi$
$384$	25.6517	1.30903
$385$	4.41382	0.224949
$386$	5.33946	0.271771
$387$	−3.73723	−0.189974
$388$	26.7183	1.35642
$389$	23.6530	1.19926	0.599628	−	0.800279i	$-0.295315\pi$
$389$	23.6530	1.19926	0.599628	+	0.800279i	$0.295315\pi$
$390$	−2.69232	−0.136331
$391$	−3.17903	−0.160771
$392$	−39.0458	−1.97211
$393$	31.4965	1.58879
$394$	−11.2573	−0.567133
$395$	3.17508	0.159755
$396$	−16.4485	−0.826569
$397$	10.2887	0.516374	0.258187	−	0.966095i	$-0.416875\pi$
$397$	10.2887	0.516374	0.258187	+	0.966095i	$0.416875\pi$
$398$	24.1105	1.20855
$399$	−5.30649	−0.265657
$400$	−24.5514	−1.22757
$401$	−6.94438	−0.346786	−0.173393	−	0.984853i	$-0.555473\pi$
$401$	−6.94438	−0.346786	−0.173393	+	0.984853i	$0.555473\pi$
$402$	−37.3453	−1.86262
$403$	−24.7816	−1.23446
$404$	1.87555	0.0933120
$405$	−1.47067	−0.0730781
$406$	−5.03041	−0.249655
$407$	−28.8845	−1.43175
$408$	−7.69555	−0.380986
$409$	−10.8554	−0.536767	−0.268383	−	0.963312i	$-0.586489\pi$
$409$	−10.8554	−0.536767	−0.268383	+	0.963312i	$0.586489\pi$
$410$	−1.22296	−0.0603976
$411$	11.9342	0.588670
$412$	−21.1475	−1.04186
$413$	−1.13827	−0.0560106
$414$	−7.41669	−0.364510
$415$	3.35028	0.164459
$416$	−4.50385	−0.220819
$417$	3.87426	0.189723
$418$	10.2132	0.499544
$419$	5.20241	0.254154	0.127077	−	0.991893i	$-0.459440\pi$
$419$	5.20241	0.254154	0.127077	+	0.991893i	$0.459440\pi$
$420$	6.26583	0.305741
$421$	−11.5056	−0.560750	−0.280375	−	0.959891i	$-0.590459\pi$
$421$	−11.5056	−0.560750	−0.280375	+	0.959891i	$0.590459\pi$
$422$	−39.0289	−1.89990
$423$	−10.3587	−0.503655
$424$	−42.8613	−2.08153
$425$	−4.92290	−0.238796
$426$	13.5574	0.656857
$427$	23.5630	1.14029
$428$	−17.2442	−0.833530
$429$	16.4322	0.793355
$430$	−2.74004	−0.132136
$431$	−17.2942	−0.833033	−0.416517	−	0.909128i	$-0.636749\pi$
$431$	−17.2942	−0.833033	−0.416517	+	0.909128i	$0.636749\pi$
$432$	−28.2023	−1.35688
$433$	−0.921727	−0.0442954	−0.0221477	−	0.999755i	$-0.507050\pi$
$433$	−0.921727	−0.0442954	−0.0221477	+	0.999755i	$0.507050\pi$
$434$	85.4002	4.09934
$435$	0.213729	0.0102475
$436$	31.3690	1.50230
$437$	3.11004	0.148774
$438$	35.8339	1.71221
$439$	29.2974	1.39829	0.699144	−	0.714981i	$-0.253565\pi$
$439$	29.2974	1.39829	0.699144	+	0.714981i	$0.253565\pi$
$440$	−6.26207	−0.298532
$441$	−6.84521	−0.325962
$442$	−6.75566	−0.321334
$443$	1.35637	0.0644433	0.0322216	−	0.999481i	$-0.489742\pi$
$443$	1.35637	0.0644433	0.0322216	+	0.999481i	$0.489742\pi$
$444$	−41.0043	−1.94598
$445$	1.59101	0.0754211
$446$	−0.483968	−0.0229165
$447$	13.6840	0.647233
$448$	−22.1743	−1.04764
$449$	−16.5590	−0.781468	−0.390734	−	0.920504i	$-0.627779\pi$
$449$	−16.5590	−0.781468	−0.390734	+	0.920504i	$0.627779\pi$
$450$	−11.4851	−0.541414
$451$	7.46415	0.351473
$452$	60.8603	2.86263
$453$	15.1649	0.712511
$454$	−8.84862	−0.415286
$455$	2.85622	0.133902
$456$	7.52854	0.352556
$457$	−25.7376	−1.20395	−0.601976	−	0.798514i	$-0.705620\pi$
$457$	−25.7376	−1.20395	−0.601976	+	0.798514i	$0.705620\pi$
$458$	−23.7787	−1.11110
$459$	−5.65496	−0.263951
$460$	−3.67230	−0.171222
$461$	−22.1859	−1.03330	−0.516650	−	0.856197i	$-0.672821\pi$
$461$	−22.1859	−1.03330	−0.516650	+	0.856197i	$0.672821\pi$
$462$	−56.6274	−2.63455
$463$	11.8476	0.550604	0.275302	−	0.961358i	$-0.411222\pi$
$463$	11.8476	0.550604	0.275302	+	0.961358i	$0.411222\pi$
$464$	2.67460	0.124165
$465$	−3.62844	−0.168265
$466$	−42.8619	−1.98554
$467$	0.404557	0.0187206	0.00936032	−	0.999956i	$-0.497020\pi$
$467$	0.404557	0.0187206	0.00936032	+	0.999956i	$0.497020\pi$
$468$	−10.6440	−0.492017
$469$	39.6187	1.82942
$470$	−7.59469	−0.350317
$471$	−26.1957	−1.20703
$472$	1.61491	0.0743323
$473$	16.7234	0.768944
$474$	−40.7349	−1.87102
$475$	4.81607	0.220976
$476$	15.7224	0.720635
$477$	−7.51411	−0.344047
$478$	−7.56213	−0.345884
$479$	1.71129	0.0781910	0.0390955	−	0.999235i	$-0.487552\pi$
$479$	1.71129	0.0781910	0.0390955	+	0.999235i	$0.487552\pi$
$480$	−0.659440	−0.0300992
$481$	−18.6914	−0.852255
$482$	−14.1890	−0.646290
$483$	−17.2437	−0.784617
$484$	27.8415	1.26552
$485$	1.78325	0.0809733
$486$	−23.2385	−1.05412
$487$	−17.1105	−0.775352	−0.387676	−	0.921796i	$-0.626722\pi$
$487$	−17.1105	−0.775352	−0.387676	+	0.921796i	$0.626722\pi$
$488$	−33.4298	−1.51329
$489$	−12.9470	−0.585483
$490$	−5.01873	−0.226723
$491$	27.1408	1.22485	0.612424	−	0.790530i	$-0.290195\pi$
$491$	27.1408	1.22485	0.612424	+	0.790530i	$0.290195\pi$
$492$	10.5961	0.477708
$493$	0.536296	0.0241535
$494$	6.60905	0.297355
$495$	−1.09782	−0.0493433
$496$	−45.4062	−2.03880
$497$	−14.3827	−0.645151
$498$	−42.9827	−1.92610
$499$	−18.6038	−0.832820	−0.416410	−	0.909177i	$-0.636712\pi$
$499$	−18.6038	−0.832820	−0.416410	+	0.909177i	$0.636712\pi$
$500$	−11.4626	−0.512621
$501$	12.5943	0.562672
$502$	−12.8567	−0.573824
$503$	−35.2784	−1.57298	−0.786492	−	0.617600i	$-0.788105\pi$
$503$	−35.2784	−1.57298	−0.786492	+	0.617600i	$0.788105\pi$
$504$	19.0466	0.848405
$505$	0.125179	0.00557040
$506$	33.1884	1.47540
$507$	−8.02521	−0.356412
$508$	85.5937	3.79761
$509$	32.0007	1.41841	0.709203	−	0.705004i	$-0.249055\pi$
$509$	32.0007	1.41841	0.709203	+	0.705004i	$0.249055\pi$
$510$	−0.989142	−0.0438000
$511$	−38.0153	−1.68170
$512$	45.2274	1.99879
$513$	5.53224	0.244254
$514$	−30.2783	−1.33552
$515$	−1.41144	−0.0621957
$516$	23.7405	1.04512
$517$	46.3532	2.03861
$518$	64.4129	2.83014
$519$	31.2722	1.37270
$520$	−4.05224	−0.177702
$521$	−22.9815	−1.00684	−0.503419	−	0.864042i	$-0.667925\pi$
$521$	−22.9815	−1.00684	−0.503419	+	0.864042i	$0.667925\pi$
$522$	1.25118	0.0547626
$523$	15.3861	0.672789	0.336394	−	0.941721i	$-0.390793\pi$
$523$	15.3861	0.672789	0.336394	+	0.941721i	$0.390793\pi$
$524$	91.2947	3.98823
$525$	−26.7028	−1.16541
$526$	38.2789	1.66904
$527$	−9.10459	−0.396602
$528$	30.1081	1.31029
$529$	−12.8937	−0.560598
$530$	−5.50915	−0.239302
$531$	0.283114	0.0122861
$532$	−15.3812	−0.666860
$533$	4.83011	0.209215
$534$	−20.4120	−0.883313
$535$	−1.15092	−0.0497588
$536$	−56.2087	−2.42785
$537$	−29.8504	−1.28814
$538$	28.1425	1.21331
$539$	30.6311	1.31938
$540$	−6.53239	−0.281109
$541$	−2.04470	−0.0879083	−0.0439542	−	0.999034i	$-0.513996\pi$
$541$	−2.04470	−0.0879083	−0.0439542	+	0.999034i	$0.513996\pi$
$542$	21.9377	0.942305
$543$	0.517238	0.0221968
$544$	−1.65469	−0.0709440
$545$	2.09365	0.0896823
$546$	−36.6441	−1.56822
$547$	25.2900	1.08132	0.540661	−	0.841240i	$-0.318174\pi$
$547$	25.2900	1.08132	0.540661	+	0.841240i	$0.318174\pi$
$548$	34.5920	1.47770
$549$	−5.86065	−0.250127
$550$	51.3939	2.19144
$551$	−0.524657	−0.0223511
$552$	24.4644	1.04127
$553$	43.2146	1.83767
$554$	−44.4732	−1.88948
$555$	−2.73674	−0.116168
$556$	11.2298	0.476250
$557$	9.66350	0.409456	0.204728	−	0.978819i	$-0.434369\pi$
$557$	9.66350	0.409456	0.204728	+	0.978819i	$0.434369\pi$
$558$	−21.2410	−0.899203
$559$	10.8219	0.457716
$560$	5.23333	0.221148
$561$	6.03709	0.254886
$562$	1.49498	0.0630619
$563$	−25.0397	−1.05530	−0.527649	−	0.849462i	$-0.676926\pi$
$563$	−25.0397	−1.05530	−0.527649	+	0.849462i	$0.676926\pi$
$564$	65.8027	2.77079
$565$	4.06198	0.170889
$566$	−60.0063	−2.52226
$567$	−20.0166	−0.840620
$568$	20.4053	0.856187
$569$	−31.1976	−1.30787	−0.653935	−	0.756551i	$-0.726883\pi$
$569$	−31.1976	−1.30787	−0.653935	+	0.756551i	$0.726883\pi$
$570$	0.967677	0.0405315
$571$	6.95777	0.291173	0.145587	−	0.989345i	$-0.453493\pi$
$571$	6.95777	0.291173	0.145587	+	0.989345i	$0.453493\pi$
$572$	47.6299	1.99150
$573$	−6.46486	−0.270073
$574$	−16.6452	−0.694755
$575$	15.6501	0.652653
$576$	5.51525	0.229802
$577$	43.7403	1.82093	0.910467	−	0.413581i	$-0.135722\pi$
$577$	43.7403	1.82093	0.910467	+	0.413581i	$0.135722\pi$
$578$	−2.48199	−0.103237
$579$	−3.08769	−0.128320
$580$	0.619508	0.0257237
$581$	45.5993	1.89178
$582$	−22.8784	−0.948339
$583$	33.6243	1.39258
$584$	53.9339	2.23180
$585$	−0.710407	−0.0293717
$586$	14.3563	0.593055
$587$	−10.7018	−0.441709	−0.220855	−	0.975307i	$-0.570885\pi$
$587$	−10.7018	−0.441709	−0.220855	+	0.975307i	$0.570885\pi$
$588$	43.4837	1.79324
$589$	8.90700	0.367007
$590$	0.207572	0.00854559
$591$	6.50984	0.267779
$592$	−34.2475	−1.40756
$593$	−22.4523	−0.922007	−0.461003	−	0.887398i	$-0.652510\pi$
$593$	−22.4523	−0.922007	−0.461003	+	0.887398i	$0.652510\pi$
$594$	59.0365	2.42230
$595$	1.04936	0.0430194
$596$	39.6641	1.62470
$597$	−13.9426	−0.570632
$598$	21.4765	0.878238
$599$	−34.9068	−1.42625	−0.713126	−	0.701036i	$-0.752721\pi$
$599$	−34.9068	−1.42625	−0.713126	+	0.701036i	$0.752721\pi$
$600$	37.8844	1.54662
$601$	16.6039	0.677287	0.338644	−	0.940915i	$-0.390032\pi$
$601$	16.6039	0.677287	0.338644	+	0.940915i	$0.390032\pi$
$602$	−37.2935	−1.51997
$603$	−9.85409	−0.401289
$604$	43.9566	1.78857
$605$	1.85821	0.0755471
$606$	−1.60599	−0.0652391
$607$	−22.9755	−0.932545	−0.466272	−	0.884641i	$-0.654403\pi$
$607$	−22.9755	−0.932545	−0.466272	+	0.884641i	$0.654403\pi$
$608$	1.61878	0.0656500
$609$	2.90898	0.117878
$610$	−4.29688	−0.173975
$611$	29.9955	1.21349
$612$	−3.91052	−0.158074
$613$	−18.9947	−0.767187	−0.383594	−	0.923502i	$-0.625314\pi$
$613$	−18.9947	−0.767187	−0.383594	+	0.923502i	$0.625314\pi$
$614$	59.3821	2.39646
$615$	0.707210	0.0285175
$616$	−85.2304	−3.43403
$617$	16.4094	0.660617	0.330309	−	0.943873i	$-0.392847\pi$
$617$	16.4094	0.660617	0.330309	+	0.943873i	$0.392847\pi$
$618$	18.1082	0.728420
$619$	31.2186	1.25478	0.627391	−	0.778704i	$-0.284123\pi$
$619$	31.2186	1.25478	0.627391	+	0.778704i	$0.284123\pi$
$620$	−10.5173	−0.422384
$621$	17.9773	0.721405
$622$	−7.75193	−0.310824
$623$	21.6546	0.867572
$624$	19.4832	0.779951
$625$	23.8495	0.953979
$626$	74.4108	2.97405
$627$	−5.90608	−0.235866
$628$	−75.9299	−3.02993
$629$	−6.86711	−0.273809
$630$	2.44815	0.0975366
$631$	−5.63100	−0.224166	−0.112083	−	0.993699i	$-0.535752\pi$
$631$	−5.63100	−0.224166	−0.112083	+	0.993699i	$0.535752\pi$
$632$	−61.3104	−2.43880
$633$	22.5696	0.897060
$634$	0.536269	0.0212980
$635$	5.71275	0.226704
$636$	47.7329	1.89273
$637$	19.8216	0.785362
$638$	−5.59880	−0.221659
$639$	3.57730	0.141516
$640$	4.96253	0.196161
$641$	28.7972	1.13742	0.568711	−	0.822538i	$-0.307442\pi$
$641$	28.7972	1.13742	0.568711	+	0.822538i	$0.307442\pi$
$642$	14.7659	0.582762
$643$	−32.1411	−1.26752	−0.633760	−	0.773530i	$-0.718489\pi$
$643$	−32.1411	−1.26752	−0.633760	+	0.773530i	$0.718489\pi$
$644$	−49.9821	−1.96957
$645$	1.58450	0.0623898
$646$	2.42812	0.0955332
$647$	−46.0957	−1.81221	−0.906105	−	0.423053i	$-0.860958\pi$
$647$	−46.0957	−1.81221	−0.906105	+	0.423053i	$0.860958\pi$
$648$	28.3984	1.11560
$649$	−1.26688	−0.0497296
$650$	33.2574	1.30446
$651$	−49.3851	−1.93556
$652$	−37.5277	−1.46970
$653$	−3.99520	−0.156344	−0.0781722	−	0.996940i	$-0.524908\pi$
$653$	−3.99520	−0.156344	−0.0781722	+	0.996940i	$0.524908\pi$
$654$	−26.8607	−1.05034
$655$	6.09326	0.238083
$656$	8.85001	0.345535
$657$	9.45528	0.368886
$658$	−103.368	−4.02971
$659$	21.8916	0.852776	0.426388	−	0.904540i	$-0.359786\pi$
$659$	21.8916	0.852776	0.426388	+	0.904540i	$0.359786\pi$
$660$	6.97382	0.271456
$661$	−43.9859	−1.71085	−0.855426	−	0.517925i	$-0.826705\pi$
$661$	−43.9859	−1.71085	−0.855426	+	0.517925i	$0.826705\pi$
$662$	−12.1775	−0.473291
$663$	3.90665	0.151722
$664$	−64.6936	−2.51060
$665$	−1.02658	−0.0398092
$666$	−16.0210	−0.620800
$667$	−1.70490	−0.0660141
$668$	36.5054	1.41244
$669$	0.279868	0.0108203
$670$	−7.22476	−0.279117
$671$	26.2254	1.01242
$672$	−8.97535	−0.346232
$673$	49.5184	1.90879	0.954397	−	0.298540i	$-0.0964997\pi$
$673$	49.5184	1.90879	0.954397	+	0.298540i	$0.0964997\pi$
$674$	21.8083	0.840024
$675$	27.8388	1.07152
$676$	−23.2616	−0.894676
$677$	−15.6046	−0.599733	−0.299867	−	0.953981i	$-0.596942\pi$
$677$	−15.6046	−0.599733	−0.299867	+	0.953981i	$0.596942\pi$
$678$	−52.1135	−2.00141
$679$	24.2711	0.931439
$680$	−1.48877	−0.0570916
$681$	5.11697	0.196083
$682$	95.0498	3.63964
$683$	11.4695	0.438869	0.219435	−	0.975627i	$-0.429579\pi$
$683$	11.4695	0.438869	0.219435	+	0.975627i	$0.429579\pi$
$684$	3.82566	0.146278
$685$	2.30876	0.0882134
$686$	−2.64835	−0.101115
$687$	13.7507	0.524622
$688$	19.8284	0.755953
$689$	21.7586	0.828935
$690$	3.14452	0.119710
$691$	12.3650	0.470387	0.235194	−	0.971949i	$-0.424428\pi$
$691$	12.3650	0.470387	0.235194	+	0.971949i	$0.424428\pi$
$692$	90.6445	3.44579
$693$	−14.9419	−0.567597
$694$	50.1054	1.90198
$695$	0.749507	0.0284304
$696$	−4.12709	−0.156437
$697$	1.77455	0.0672160
$698$	−6.85071	−0.259303
$699$	24.7861	0.937497
$700$	−77.3999	−2.92544
$701$	30.2062	1.14087	0.570435	−	0.821342i	$-0.306774\pi$
$701$	30.2062	1.14087	0.570435	+	0.821342i	$0.306774\pi$
$702$	38.2030	1.44188
$703$	6.71808	0.253377
$704$	−24.6798	−0.930154
$705$	4.39185	0.165407
$706$	2.48199	0.0934107
$707$	1.70376	0.0640765
$708$	−1.79846	−0.0675903
$709$	−43.5355	−1.63501	−0.817505	−	0.575921i	$-0.804644\pi$
$709$	−43.5355	−1.63501	−0.817505	+	0.575921i	$0.804644\pi$
$710$	2.62278	0.0984313
$711$	−10.7485	−0.403099
$712$	−30.7222	−1.15136
$713$	28.9438	1.08395
$714$	−13.4628	−0.503833
$715$	3.17895	0.118886
$716$	−86.5234	−3.23353
$717$	4.37302	0.163313
$718$	53.3473	1.99090
$719$	28.2991	1.05538	0.527688	−	0.849438i	$-0.323059\pi$
$719$	28.2991	1.05538	0.527688	+	0.849438i	$0.323059\pi$
$720$	−1.30165	−0.0485096
$721$	−19.2106	−0.715439
$722$	44.7823	1.66662
$723$	8.20518	0.305154
$724$	1.49925	0.0557191
$725$	−2.64013	−0.0980520
$726$	−23.8401	−0.884789
$727$	−5.72859	−0.212461	−0.106231	−	0.994342i	$-0.533878\pi$
$727$	−5.72859	−0.212461	−0.106231	+	0.994342i	$0.533878\pi$
$728$	−55.1533	−2.04412
$729$	29.3279	1.08622
$730$	6.93236	0.256578
$731$	3.97589	0.147053
$732$	37.2294	1.37604
$733$	22.7946	0.841938	0.420969	−	0.907075i	$-0.361690\pi$
$733$	22.7946	0.841938	0.420969	+	0.907075i	$0.361690\pi$
$734$	16.8585	0.622257
$735$	2.90222	0.107050
$736$	5.26030	0.193897
$737$	44.0953	1.62427
$738$	4.14003	0.152397
$739$	−33.8244	−1.24425	−0.622125	−	0.782918i	$-0.713731\pi$
$739$	−33.8244	−1.24425	−0.622125	+	0.782918i	$0.713731\pi$
$740$	−7.93262	−0.291609
$741$	−3.82187	−0.140400
$742$	−74.9827	−2.75270
$743$	−31.5709	−1.15823	−0.579113	−	0.815248i	$-0.696601\pi$
$743$	−31.5709	−1.15823	−0.579113	+	0.815248i	$0.696601\pi$
$744$	70.0648	2.56870
$745$	2.64729	0.0969891
$746$	−18.8205	−0.689066
$747$	−11.3416	−0.414967
$748$	17.4989	0.639823
$749$	−15.6647	−0.572377
$750$	9.81516	0.358399
$751$	−19.3264	−0.705230	−0.352615	−	0.935769i	$-0.614707\pi$
$751$	−19.3264	−0.705230	−0.352615	+	0.935769i	$0.614707\pi$
$752$	54.9595	2.00417
$753$	7.43477	0.270938
$754$	−3.62303	−0.131943
$755$	2.93378	0.106771
$756$	−88.9096	−3.23361
$757$	30.8417	1.12096	0.560480	−	0.828168i	$-0.310617\pi$
$757$	30.8417	1.12096	0.560480	+	0.828168i	$0.310617\pi$
$758$	57.0525	2.07224
$759$	−19.1921	−0.696630
$760$	1.45646	0.0528313
$761$	46.7865	1.69601	0.848005	−	0.529989i	$-0.177804\pi$
$761$	46.7865	1.69601	0.848005	+	0.529989i	$0.177804\pi$
$762$	−73.2922	−2.65510
$763$	28.4958	1.03162
$764$	−18.7388	−0.677946
$765$	−0.260999	−0.00943644
$766$	21.4587	0.775333
$767$	−0.819811	−0.0296017
$768$	−46.8244	−1.68963
$769$	51.8980	1.87149	0.935746	−	0.352676i	$-0.114728\pi$
$769$	51.8980	1.87149	0.935746	+	0.352676i	$0.114728\pi$
$770$	−10.9550	−0.394792
$771$	17.5093	0.630583
$772$	−8.94988	−0.322113
$773$	−1.32053	−0.0474960	−0.0237480	−	0.999718i	$-0.507560\pi$
$773$	−1.32053	−0.0474960	−0.0237480	+	0.999718i	$0.507560\pi$
$774$	9.27574	0.333410
$775$	44.8210	1.61002
$776$	−34.4344	−1.23612
$777$	−37.2486	−1.33629
$778$	−58.7064	−2.10473
$779$	−1.73604	−0.0622002
$780$	4.51281	0.161585
$781$	−16.0078	−0.572804
$782$	7.89031	0.282157
$783$	−3.03273	−0.108381
$784$	36.3183	1.29708
$785$	−5.06777	−0.180876
$786$	−78.1739	−2.78837
$787$	−44.9079	−1.60079	−0.800397	−	0.599471i	$-0.795378\pi$
$787$	−44.9079	−1.60079	−0.800397	+	0.599471i	$0.795378\pi$
$788$	18.8692	0.672187
$789$	−22.1359	−0.788059
$790$	−7.88049	−0.280375
$791$	55.2859	1.96574
$792$	21.1988	0.753265
$793$	16.9707	0.602646
$794$	−25.5364	−0.906252
$795$	3.18582	0.112989
$796$	−40.4134	−1.43242
$797$	40.6535	1.44002	0.720011	−	0.693963i	$-0.244137\pi$
$797$	40.6535	1.44002	0.720011	+	0.693963i	$0.244137\pi$
$798$	13.1706	0.466235
$799$	11.0202	0.389865
$800$	8.14585	0.287999
$801$	−5.38599	−0.190304
$802$	17.2358	0.608619
$803$	−42.3107	−1.49311
$804$	62.5974	2.20764
$805$	−3.33594	−0.117576
$806$	61.5074	2.16651
$807$	−16.2742	−0.572880
$808$	−2.41719	−0.0850366
$809$	−9.72545	−0.341929	−0.170964	−	0.985277i	$-0.554688\pi$
$809$	−9.72545	−0.341929	−0.170964	+	0.985277i	$0.554688\pi$
$810$	3.65018	0.128254
$811$	16.6905	0.586081	0.293041	−	0.956100i	$-0.405333\pi$
$811$	16.6905	0.586081	0.293041	+	0.956100i	$0.405333\pi$
$812$	8.43186	0.295900
$813$	−12.6861	−0.444921
$814$	71.6910	2.51277
$815$	−2.50470	−0.0877358
$816$	7.15799	0.250580
$817$	−3.88960	−0.136080
$818$	26.9430	0.942041
$819$	−9.66905	−0.337864
$820$	2.04989	0.0715854
$821$	1.16610	0.0406972	0.0203486	−	0.999793i	$-0.493522\pi$
$821$	1.16610	0.0406972	0.0203486	+	0.999793i	$0.493522\pi$
$822$	−29.6205	−1.03313
$823$	26.1427	0.911276	0.455638	−	0.890165i	$-0.349411\pi$
$823$	26.1427	0.911276	0.455638	+	0.890165i	$0.349411\pi$
$824$	27.2548	0.949467
$825$	−29.7200	−1.03472
$826$	2.82517	0.0983002
$827$	−42.5667	−1.48019	−0.740094	−	0.672503i	$-0.765219\pi$
$827$	−42.5667	−1.48019	−0.740094	+	0.672503i	$0.765219\pi$
$828$	12.4317	0.432031
$829$	−9.98421	−0.346766	−0.173383	−	0.984854i	$-0.555470\pi$
$829$	−9.98421	−0.346766	−0.173383	+	0.984854i	$0.555470\pi$
$830$	−8.31535	−0.288630
$831$	25.7179	0.892144
$832$	−15.9705	−0.553676
$833$	7.28234	0.252318
$834$	−9.61586	−0.332970
$835$	2.43647	0.0843175
$836$	−17.1192	−0.592078
$837$	51.4861	1.77962
$838$	−12.9123	−0.446048
$839$	−9.33042	−0.322122	−0.161061	−	0.986944i	$-0.551492\pi$
$839$	−9.33042	−0.322122	−0.161061	+	0.986944i	$0.551492\pi$
$840$	−8.07537	−0.278627
$841$	−28.7124	−0.990082
$842$	28.5568	0.984132
$843$	−0.864515	−0.0297755
$844$	65.4194	2.25183
$845$	−1.55254	−0.0534090
$846$	25.7100	0.883929
$847$	25.2914	0.869021
$848$	39.8673	1.36905
$849$	34.7004	1.19091
$850$	12.2186	0.419093
$851$	21.8308	0.748349
$852$	−22.7246	−0.778531
$853$	−13.9332	−0.477063	−0.238532	−	0.971135i	$-0.576666\pi$
$853$	−13.9332	−0.477063	−0.238532	+	0.971135i	$0.576666\pi$
$854$	−58.4829	−2.00125
$855$	0.255335	0.00873227
$856$	22.2242	0.759608
$857$	−23.3276	−0.796854	−0.398427	−	0.917200i	$-0.630444\pi$
$857$	−23.3276	−0.796854	−0.398427	+	0.917200i	$0.630444\pi$
$858$	−40.7845	−1.39236
$859$	−40.8289	−1.39306	−0.696532	−	0.717525i	$-0.745275\pi$
$859$	−40.8289	−1.39306	−0.696532	+	0.717525i	$0.745275\pi$
$860$	4.59279	0.156613
$861$	9.62554	0.328038
$862$	42.9240	1.46200
$863$	−33.7882	−1.15016	−0.575082	−	0.818096i	$-0.695030\pi$
$863$	−33.7882	−1.15016	−0.575082	+	0.818096i	$0.695030\pi$
$864$	9.35718	0.318338
$865$	6.04986	0.205702
$866$	2.28771	0.0777397
$867$	1.43528	0.0487446
$868$	−143.146	−4.85869
$869$	48.0975	1.63160
$870$	−0.530473	−0.0179847
$871$	28.5344	0.966852
$872$	−40.4282	−1.36907
$873$	−6.03678	−0.204314
$874$	−7.71908	−0.261102
$875$	−10.4127	−0.352012
$876$	−60.0640	−2.02938
$877$	50.6075	1.70890	0.854448	−	0.519538i	$-0.173896\pi$
$877$	50.6075	1.70890	0.854448	+	0.519538i	$0.173896\pi$
$878$	−72.7157	−2.45403
$879$	−8.30197	−0.280018
$880$	5.82465	0.196349
$881$	−1.32320	−0.0445796	−0.0222898	−	0.999752i	$-0.507096\pi$
$881$	−1.32320	−0.0445796	−0.0222898	+	0.999752i	$0.507096\pi$
$882$	16.9897	0.572073
$883$	−20.2995	−0.683134	−0.341567	−	0.939857i	$-0.610958\pi$
$883$	−20.2995	−0.683134	−0.341567	+	0.939857i	$0.610958\pi$
$884$	11.3237	0.380857
$885$	−0.120034	−0.00403491
$886$	−3.36650	−0.113100
$887$	1.96713	0.0660497	0.0330249	−	0.999455i	$-0.489486\pi$
$887$	1.96713	0.0660497	0.0330249	+	0.999455i	$0.489486\pi$
$888$	52.8461	1.77340
$889$	77.7539	2.60778
$890$	−3.94886	−0.132366
$891$	−22.2783	−0.746353
$892$	0.811216	0.0271615
$893$	−10.7810	−0.360773
$894$	−33.9636	−1.13591
$895$	−5.77481	−0.193030
$896$	67.5430	2.25645
$897$	−12.4194	−0.414671
$898$	41.0992	1.37150
$899$	−4.88275	−0.162849
$900$	19.2511	0.641704
$901$	7.99396	0.266317
$902$	−18.5259	−0.616846
$903$	21.5660	0.717672
$904$	−78.4364	−2.60875
$905$	0.100064	0.00332623
$906$	−37.6391	−1.25048
$907$	16.8794	0.560472	0.280236	−	0.959931i	$-0.409587\pi$
$907$	16.8794	0.560472	0.280236	+	0.959931i	$0.409587\pi$
$908$	14.8319	0.492213
$909$	−0.423764	−0.0140554
$910$	−7.08909	−0.235001
$911$	49.7681	1.64889	0.824446	−	0.565941i	$-0.191487\pi$
$911$	49.7681	1.64889	0.824446	+	0.565941i	$0.191487\pi$
$912$	−7.00265	−0.231881
$913$	50.7516	1.67963
$914$	63.8802	2.11297
$915$	2.48479	0.0821447
$916$	39.8573	1.31692
$917$	82.9327	2.73868
$918$	14.0355	0.463242
$919$	−28.6267	−0.944308	−0.472154	−	0.881516i	$-0.656523\pi$
$919$	−28.6267	−0.944308	−0.472154	+	0.881516i	$0.656523\pi$
$920$	4.73284	0.156037
$921$	−34.3394	−1.13152
$922$	55.0651	1.81347
$923$	−10.3588	−0.340963
$924$	94.9177	3.12256
$925$	33.8061	1.11154
$926$	−29.4055	−0.966326
$927$	4.77811	0.156934
$928$	−0.887401	−0.0291303
$929$	−22.7823	−0.747463	−0.373731	−	0.927537i	$-0.621922\pi$
$929$	−22.7823	−0.747463	−0.373731	+	0.927537i	$0.621922\pi$
$930$	9.00573	0.295310
$931$	−7.12431	−0.233490
$932$	71.8441	2.35333
$933$	4.48277	0.146759
$934$	−1.00410	−0.0328553
$935$	1.16792	0.0381952
$936$	13.7179	0.448383
$937$	16.7379	0.546804	0.273402	−	0.961900i	$-0.411851\pi$
$937$	16.7379	0.546804	0.273402	+	0.961900i	$0.411851\pi$
$938$	−98.3331	−3.21069
$939$	−43.0302	−1.40424
$940$	12.7301	0.415209
$941$	−1.11472	−0.0363389	−0.0181695	−	0.999835i	$-0.505784\pi$
$941$	−1.11472	−0.0363389	−0.0181695	+	0.999835i	$0.505784\pi$
$942$	65.0173	2.11838
$943$	−5.64136	−0.183708
$944$	−1.50211	−0.0488894
$945$	−5.93407	−0.193035
$946$	−41.5073	−1.34952
$947$	−32.9839	−1.07183	−0.535916	−	0.844271i	$-0.680034\pi$
$947$	−32.9839	−1.07183	−0.535916	+	0.844271i	$0.680034\pi$
$948$	68.2789	2.21760
$949$	−27.3796	−0.888779
$950$	−11.9534	−0.387820
$951$	−0.310113	−0.0100561
$952$	−20.2630	−0.656726
$953$	4.22634	0.136904	0.0684522	−	0.997654i	$-0.478194\pi$
$953$	4.22634	0.136904	0.0684522	+	0.997654i	$0.478194\pi$
$954$	18.6499	0.603813
$955$	−1.25068	−0.0404710
$956$	12.6755	0.409954
$957$	3.23767	0.104659
$958$	−4.24741	−0.137227
$959$	31.4236	1.01472
$960$	−2.33835	−0.0754698
$961$	51.8935	1.67398
$962$	46.3918	1.49573
$963$	3.89618	0.125553
$964$	23.7833	0.766007
$965$	−0.597339	−0.0192290
$966$	42.7987	1.37703
$967$	14.6524	0.471190	0.235595	−	0.971851i	$-0.424296\pi$
$967$	14.6524	0.471190	0.235595	+	0.971851i	$0.424296\pi$
$968$	−35.8819	−1.15329
$969$	−1.40413	−0.0451072
$970$	−4.42600	−0.142110
$971$	33.4018	1.07192	0.535958	−	0.844245i	$-0.319951\pi$
$971$	33.4018	1.07192	0.535958	+	0.844245i	$0.319951\pi$
$972$	38.9520	1.24938
$973$	10.2012	0.327036
$974$	42.4681	1.36076
$975$	−19.2321	−0.615919
$976$	31.0946	0.995314
$977$	−18.5838	−0.594547	−0.297274	−	0.954792i	$-0.596077\pi$
$977$	−18.5838	−0.594547	−0.297274	+	0.954792i	$0.596077\pi$
$978$	32.1342	1.02754
$979$	24.1013	0.770282
$980$	8.41228	0.268720
$981$	−7.08757	−0.226289
$982$	−67.3631	−2.14964
$983$	−33.6536	−1.07338	−0.536691	−	0.843779i	$-0.680326\pi$
$983$	−33.6536	−1.07338	−0.536691	+	0.843779i	$0.680326\pi$
$984$	−13.6562	−0.435342
$985$	1.25938	0.0401272
$986$	−1.33108	−0.0423901
$987$	59.7756	1.90268
$988$	−11.0779	−0.352436
$989$	−12.6395	−0.401912
$990$	2.72477	0.0865988
$991$	−8.79455	−0.279368	−0.139684	−	0.990196i	$-0.544609\pi$
$991$	−8.79455	−0.279368	−0.139684	+	0.990196i	$0.544609\pi$
$992$	15.0652	0.478321
$993$	7.04198	0.223470
$994$	35.6976	1.13226
$995$	−2.69730	−0.0855103
$996$	72.0467	2.28289
$997$	3.58996	0.113695	0.0568476	−	0.998383i	$-0.481895\pi$
$997$	3.58996	0.113695	0.0568476	+	0.998383i	$0.481895\pi$
$998$	46.1743	1.46162
$999$	38.8332	1.22863

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.d.1.10	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.d.1.10	✓	121	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48199 q^{2} +1.43528 q^{3} +4.16025 q^{4} +0.277666 q^{5} -3.56234 q^{6} +3.77920 q^{7} -5.36171 q^{8} -0.939973 q^{9} +O(q^{10})\)	\(q-2.48199 q^{2} +1.43528 q^{3} +4.16025 q^{4} +0.277666 q^{5} -3.56234 q^{6} +3.77920 q^{7} -5.36171 q^{8} -0.939973 q^{9} -0.689164 q^{10} +4.20622 q^{11} +5.97112 q^{12} +2.72188 q^{13} -9.37991 q^{14} +0.398529 q^{15} +4.98718 q^{16} +1.00000 q^{17} +2.33300 q^{18} -0.978299 q^{19} +1.15516 q^{20} +5.42421 q^{21} -10.4398 q^{22} -3.17903 q^{23} -7.69555 q^{24} -4.92290 q^{25} -6.75566 q^{26} -5.65496 q^{27} +15.7224 q^{28} +0.536296 q^{29} -0.989142 q^{30} -9.10459 q^{31} -1.65469 q^{32} +6.03709 q^{33} -2.48199 q^{34} +1.04936 q^{35} -3.91052 q^{36} -6.86711 q^{37} +2.42812 q^{38} +3.90665 q^{39} -1.48877 q^{40} +1.77455 q^{41} -13.4628 q^{42} +3.97589 q^{43} +17.4989 q^{44} -0.260999 q^{45} +7.89031 q^{46} +11.0202 q^{47} +7.15799 q^{48} +7.28234 q^{49} +12.2186 q^{50} +1.43528 q^{51} +11.3237 q^{52} +7.99396 q^{53} +14.0355 q^{54} +1.16792 q^{55} -20.2630 q^{56} -1.40413 q^{57} -1.33108 q^{58} -0.301193 q^{59} +1.65798 q^{60} +6.23491 q^{61} +22.5974 q^{62} -3.55235 q^{63} -5.86745 q^{64} +0.755773 q^{65} -14.9840 q^{66} +10.4834 q^{67} +4.16025 q^{68} -4.56280 q^{69} -2.60449 q^{70} -3.80575 q^{71} +5.03986 q^{72} -10.0591 q^{73} +17.0441 q^{74} -7.06574 q^{75} -4.06997 q^{76} +15.8961 q^{77} -9.69625 q^{78} +11.4349 q^{79} +1.38477 q^{80} -5.29653 q^{81} -4.40441 q^{82} +12.0659 q^{83} +22.5660 q^{84} +0.277666 q^{85} -9.86809 q^{86} +0.769734 q^{87} -22.5525 q^{88} +5.72993 q^{89} +0.647796 q^{90} +10.2865 q^{91} -13.2256 q^{92} -13.0676 q^{93} -27.3519 q^{94} -0.271641 q^{95} -2.37494 q^{96} +6.42228 q^{97} -18.0747 q^{98} -3.95373 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * q^99

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