LMFDB - Embedded newform 6017.2.a.f.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0459868962$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57735 q^{2} -3.20978 q^{3} +4.64274 q^{4} +2.33292 q^{5} +8.27272 q^{6} +1.38140 q^{7} -6.81126 q^{8} +7.30267 q^{9} +O(q^{10})$	\(q-2.57735 q^{2} -3.20978 q^{3} +4.64274 q^{4} +2.33292 q^{5} +8.27272 q^{6} +1.38140 q^{7} -6.81126 q^{8} +7.30267 q^{9} -6.01276 q^{10} -1.00000 q^{11} -14.9022 q^{12} +0.769601 q^{13} -3.56035 q^{14} -7.48817 q^{15} +8.26953 q^{16} +6.58139 q^{17} -18.8216 q^{18} +5.77216 q^{19} +10.8311 q^{20} -4.43399 q^{21} +2.57735 q^{22} +3.17024 q^{23} +21.8626 q^{24} +0.442533 q^{25} -1.98353 q^{26} -13.8106 q^{27} +6.41348 q^{28} -8.93163 q^{29} +19.2996 q^{30} +1.12347 q^{31} -7.69095 q^{32} +3.20978 q^{33} -16.9626 q^{34} +3.22270 q^{35} +33.9044 q^{36} -1.89906 q^{37} -14.8769 q^{38} -2.47025 q^{39} -15.8901 q^{40} -9.43805 q^{41} +11.4279 q^{42} +9.02537 q^{43} -4.64274 q^{44} +17.0366 q^{45} -8.17081 q^{46} +10.6335 q^{47} -26.5433 q^{48} -5.09173 q^{49} -1.14056 q^{50} -21.1248 q^{51} +3.57306 q^{52} +6.21181 q^{53} +35.5948 q^{54} -2.33292 q^{55} -9.40907 q^{56} -18.5273 q^{57} +23.0199 q^{58} +0.0178386 q^{59} -34.7656 q^{60} -3.23513 q^{61} -2.89559 q^{62} +10.0879 q^{63} +3.28323 q^{64} +1.79542 q^{65} -8.27272 q^{66} -2.98653 q^{67} +30.5557 q^{68} -10.1758 q^{69} -8.30603 q^{70} -0.135869 q^{71} -49.7404 q^{72} +2.06341 q^{73} +4.89454 q^{74} -1.42043 q^{75} +26.7986 q^{76} -1.38140 q^{77} +6.36670 q^{78} +14.0930 q^{79} +19.2922 q^{80} +22.4210 q^{81} +24.3252 q^{82} +0.342920 q^{83} -20.5858 q^{84} +15.3539 q^{85} -23.2615 q^{86} +28.6685 q^{87} +6.81126 q^{88} +11.2035 q^{89} -43.9092 q^{90} +1.06313 q^{91} +14.7186 q^{92} -3.60610 q^{93} -27.4063 q^{94} +13.4660 q^{95} +24.6863 q^{96} +18.0597 q^{97} +13.1232 q^{98} -7.30267 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) $ 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * 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 $

$2$	−2.57735	−1.82246	−0.911231	−	0.411896i	$-0.864867\pi$
$2$	−2.57735	−1.82246	−0.911231	+	0.411896i	$0.864867\pi$
$3$	−3.20978	−1.85317	−0.926583	−	0.376090i	$-0.877268\pi$
$3$	−3.20978	−1.85317	−0.926583	+	0.376090i	$0.877268\pi$
$4$	4.64274	2.32137
$5$	2.33292	1.04332	0.521658	−	0.853155i	$-0.325314\pi$
$5$	2.33292	1.04332	0.521658	+	0.853155i	$0.325314\pi$
$6$	8.27272	3.37733
$7$	1.38140	0.522120	0.261060	−	0.965323i	$-0.415928\pi$
$7$	1.38140	0.522120	0.261060	+	0.965323i	$0.415928\pi$
$8$	−6.81126	−2.40814
$9$	7.30267	2.43422
$10$	−6.01276	−1.90140
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−14.9022	−4.30188
$13$	0.769601	0.213449	0.106725	−	0.994289i	$-0.465964\pi$
$13$	0.769601	0.213449	0.106725	+	0.994289i	$0.465964\pi$
$14$	−3.56035	−0.951544
$15$	−7.48817	−1.93344
$16$	8.26953	2.06738
$17$	6.58139	1.59622	0.798111	−	0.602510i	$-0.205833\pi$
$17$	6.58139	1.59622	0.798111	+	0.602510i	$0.205833\pi$
$18$	−18.8216	−4.43628
$19$	5.77216	1.32422	0.662112	−	0.749405i	$-0.269660\pi$
$19$	5.77216	1.32422	0.662112	+	0.749405i	$0.269660\pi$
$20$	10.8311	2.42192
$21$	−4.43399	−0.967576
$22$	2.57735	0.549493
$23$	3.17024	0.661040	0.330520	−	0.943799i	$-0.392776\pi$
$23$	3.17024	0.661040	0.330520	+	0.943799i	$0.392776\pi$
$24$	21.8626	4.46269
$25$	0.442533	0.0885066
$26$	−1.98353	−0.389003
$27$	−13.8106	−2.65786
$28$	6.41348	1.21203
$29$	−8.93163	−1.65856	−0.829281	−	0.558832i	$-0.811250\pi$
$29$	−8.93163	−1.65856	−0.829281	+	0.558832i	$0.811250\pi$
$30$	19.2996	3.52361
$31$	1.12347	0.201782	0.100891	−	0.994897i	$-0.467831\pi$
$31$	1.12347	0.201782	0.100891	+	0.994897i	$0.467831\pi$
$32$	−7.69095	−1.35958
$33$	3.20978	0.558751
$34$	−16.9626	−2.90905
$35$	3.22270	0.544736
$36$	33.9044	5.65073
$37$	−1.89906	−0.312203	−0.156102	−	0.987741i	$-0.549893\pi$
$37$	−1.89906	−0.312203	−0.156102	+	0.987741i	$0.549893\pi$
$38$	−14.8769	−2.41335
$39$	−2.47025	−0.395557
$40$	−15.8901	−2.51245
$41$	−9.43805	−1.47398	−0.736988	−	0.675906i	$-0.763753\pi$
$41$	−9.43805	−1.47398	−0.736988	+	0.675906i	$0.763753\pi$
$42$	11.4279	1.76337
$43$	9.02537	1.37636	0.688178	−	0.725542i	$-0.258411\pi$
$43$	9.02537	1.37636	0.688178	+	0.725542i	$0.258411\pi$
$44$	−4.64274	−0.699919
$45$	17.0366	2.53966
$46$	−8.17081	−1.20472
$47$	10.6335	1.55106	0.775530	−	0.631311i	$-0.217483\pi$
$47$	10.6335	1.55106	0.775530	+	0.631311i	$0.217483\pi$
$48$	−26.5433	−3.83120
$49$	−5.09173	−0.727390
$50$	−1.14056	−0.161300
$51$	−21.1248	−2.95806
$52$	3.57306	0.495494
$53$	6.21181	0.853258	0.426629	−	0.904427i	$-0.359701\pi$
$53$	6.21181	0.853258	0.426629	+	0.904427i	$0.359701\pi$
$54$	35.5948	4.84384
$55$	−2.33292	−0.314571
$56$	−9.40907	−1.25734
$57$	−18.5273	−2.45401
$58$	23.0199	3.02267
$59$	0.0178386	0.00232238	0.00116119	−	0.999999i	$-0.499630\pi$
$59$	0.0178386	0.00232238	0.00116119	+	0.999999i	$0.499630\pi$
$60$	−34.7656	−4.48822
$61$	−3.23513	−0.414216	−0.207108	−	0.978318i	$-0.566405\pi$
$61$	−3.23513	−0.414216	−0.207108	+	0.978318i	$0.566405\pi$
$62$	−2.89559	−0.367740
$63$	10.0879	1.27096
$64$	3.28323	0.410404
$65$	1.79542	0.222695
$66$	−8.27272	−1.01830
$67$	−2.98653	−0.364862	−0.182431	−	0.983219i	$-0.558397\pi$
$67$	−2.98653	−0.364862	−0.182431	+	0.983219i	$0.558397\pi$
$68$	30.5557	3.70542
$69$	−10.1758	−1.22502
$70$	−8.30603	−0.992761
$71$	−0.135869	−0.0161247	−0.00806234	−	0.999967i	$-0.502566\pi$
$71$	−0.135869	−0.0161247	−0.00806234	+	0.999967i	$0.502566\pi$
$72$	−49.7404	−5.86196
$73$	2.06341	0.241504	0.120752	−	0.992683i	$-0.461469\pi$
$73$	2.06341	0.241504	0.120752	+	0.992683i	$0.461469\pi$
$74$	4.89454	0.568979
$75$	−1.42043	−0.164017
$76$	26.7986	3.07401
$77$	−1.38140	−0.157425
$78$	6.36670	0.720887
$79$	14.0930	1.58559	0.792794	−	0.609490i	$-0.208626\pi$
$79$	14.0930	1.58559	0.792794	+	0.609490i	$0.208626\pi$
$80$	19.2922	2.15693
$81$	22.4210	2.49123
$82$	24.3252	2.68627
$83$	0.342920	0.0376404	0.0188202	−	0.999823i	$-0.494009\pi$
$83$	0.342920	0.0376404	0.0188202	+	0.999823i	$0.494009\pi$
$84$	−20.5858	−2.24610
$85$	15.3539	1.66536
$86$	−23.2615	−2.50836
$87$	28.6685	3.07359
$88$	6.81126	0.726082
$89$	11.2035	1.18756	0.593782	−	0.804626i	$-0.297634\pi$
$89$	11.2035	1.18756	0.593782	+	0.804626i	$0.297634\pi$
$90$	−43.9092	−4.62844
$91$	1.06313	0.111446
$92$	14.7186	1.53452
$93$	−3.60610	−0.373936
$94$	−27.4063	−2.82675
$95$	13.4660	1.38158
$96$	24.6863	2.51953
$97$	18.0597	1.83368	0.916840	−	0.399254i	$-0.130731\pi$
$97$	18.0597	1.83368	0.916840	+	0.399254i	$0.130731\pi$
$98$	13.1232	1.32564
$99$	−7.30267	−0.733946
$100$	2.05456	0.205456
$101$	−6.00007	−0.597029	−0.298514	−	0.954405i	$-0.596491\pi$
$101$	−6.00007	−0.597029	−0.298514	+	0.954405i	$0.596491\pi$
$102$	54.4460	5.39096
$103$	13.0078	1.28170	0.640851	−	0.767666i	$-0.278582\pi$
$103$	13.0078	1.28170	0.640851	+	0.767666i	$0.278582\pi$
$104$	−5.24195	−0.514016
$105$	−10.3442	−1.00949
$106$	−16.0100	−1.55503
$107$	−1.32107	−0.127713	−0.0638564	−	0.997959i	$-0.520340\pi$
$107$	−1.32107	−0.127713	−0.0638564	+	0.997959i	$0.520340\pi$
$108$	−64.1191	−6.16986
$109$	7.22114	0.691660	0.345830	−	0.938297i	$-0.387597\pi$
$109$	7.22114	0.691660	0.345830	+	0.938297i	$0.387597\pi$
$110$	6.01276	0.573294
$111$	6.09555	0.578564
$112$	11.4235	1.07942
$113$	−13.4355	−1.26391	−0.631953	−	0.775007i	$-0.717746\pi$
$113$	−13.4355	−1.26391	−0.631953	+	0.775007i	$0.717746\pi$
$114$	47.7515	4.47233
$115$	7.39592	0.689673
$116$	−41.4672	−3.85013
$117$	5.62015	0.519583
$118$	−0.0459762	−0.00423245
$119$	9.09154	0.833420
$120$	51.0038	4.65599
$121$	1.00000	0.0909091
$122$	8.33807	0.754894
$123$	30.2941	2.73152
$124$	5.21600	0.468410
$125$	−10.6322	−0.950975
$126$	−26.0001	−2.31627
$127$	3.00645	0.266779	0.133389	−	0.991064i	$-0.457414\pi$
$127$	3.00645	0.266779	0.133389	+	0.991064i	$0.457414\pi$
$128$	6.91987	0.611636
$129$	−28.9694	−2.55062
$130$	−4.62743	−0.405853
$131$	−14.8214	−1.29495	−0.647475	−	0.762087i	$-0.724175\pi$
$131$	−14.8214	−1.29495	−0.647475	+	0.762087i	$0.724175\pi$
$132$	14.9022	1.29707
$133$	7.97366	0.691404
$134$	7.69732	0.664947
$135$	−32.2191	−2.77298
$136$	−44.8276	−3.84393
$137$	10.3194	0.881650	0.440825	−	0.897593i	$-0.354686\pi$
$137$	10.3194	0.881650	0.440825	+	0.897593i	$0.354686\pi$
$138$	26.2265	2.23255
$139$	11.9377	1.01254	0.506272	−	0.862374i	$-0.331023\pi$
$139$	11.9377	1.01254	0.506272	+	0.862374i	$0.331023\pi$
$140$	14.9622	1.26453
$141$	−34.1313	−2.87437
$142$	0.350182	0.0293866
$143$	−0.769601	−0.0643573
$144$	60.3897	5.03247
$145$	−20.8368	−1.73040
$146$	−5.31813	−0.440132
$147$	16.3433	1.34798
$148$	−8.81682	−0.724739
$149$	17.1702	1.40664	0.703320	−	0.710873i	$-0.251700\pi$
$149$	17.1702	1.40664	0.703320	+	0.710873i	$0.251700\pi$
$150$	3.66095	0.298916
$151$	8.12230	0.660983	0.330492	−	0.943809i	$-0.392785\pi$
$151$	8.12230	0.660983	0.330492	+	0.943809i	$0.392785\pi$
$152$	−39.3157	−3.18892
$153$	48.0618	3.88556
$154$	3.56035	0.286901
$155$	2.62098	0.210522
$156$	−11.4687	−0.918232
$157$	21.2969	1.69968	0.849839	−	0.527042i	$-0.176699\pi$
$157$	21.2969	1.69968	0.849839	+	0.527042i	$0.176699\pi$
$158$	−36.3226	−2.88967
$159$	−19.9385	−1.58123
$160$	−17.9424	−1.41847
$161$	4.37936	0.345142
$162$	−57.7869	−4.54016
$163$	−6.83850	−0.535632	−0.267816	−	0.963470i	$-0.586302\pi$
$163$	−6.83850	−0.535632	−0.267816	+	0.963470i	$0.586302\pi$
$164$	−43.8184	−3.42164
$165$	7.48817	0.582953
$166$	−0.883825	−0.0685982
$167$	2.08895	0.161648	0.0808241	−	0.996728i	$-0.474245\pi$
$167$	2.08895	0.161648	0.0808241	+	0.996728i	$0.474245\pi$
$168$	30.2010	2.33006
$169$	−12.4077	−0.954440
$170$	−39.5723	−3.03506
$171$	42.1522	3.22346
$172$	41.9024	3.19503
$173$	−13.1599	−1.00053	−0.500265	−	0.865872i	$-0.666764\pi$
$173$	−13.1599	−1.00053	−0.500265	+	0.865872i	$0.666764\pi$
$174$	−73.8889	−5.60150
$175$	0.611315	0.0462111
$176$	−8.26953	−0.623339
$177$	−0.0572578	−0.00430376
$178$	−28.8752	−2.16429
$179$	7.31004	0.546378	0.273189	−	0.961960i	$-0.411922\pi$
$179$	7.31004	0.546378	0.273189	+	0.961960i	$0.411922\pi$
$180$	79.0964	5.89549
$181$	−19.8789	−1.47759	−0.738794	−	0.673931i	$-0.764604\pi$
$181$	−19.8789	−1.47759	−0.738794	+	0.673931i	$0.764604\pi$
$182$	−2.74005	−0.203106
$183$	10.3841	0.767612
$184$	−21.5933	−1.59188
$185$	−4.43036	−0.325726
$186$	9.29419	0.681483
$187$	−6.58139	−0.481279
$188$	49.3687	3.60058
$189$	−19.0780	−1.38772
$190$	−34.7066	−2.51788
$191$	19.0651	1.37950	0.689751	−	0.724046i	$-0.257720\pi$
$191$	19.0651	1.37950	0.689751	+	0.724046i	$0.257720\pi$
$192$	−10.5384	−0.760546
$193$	−0.281245	−0.0202444	−0.0101222	−	0.999949i	$-0.503222\pi$
$193$	−0.281245	−0.0202444	−0.0101222	+	0.999949i	$0.503222\pi$
$194$	−46.5461	−3.34181
$195$	−5.76290	−0.412690
$196$	−23.6396	−1.68854
$197$	−16.5147	−1.17663	−0.588313	−	0.808633i	$-0.700208\pi$
$197$	−16.5147	−1.17663	−0.588313	+	0.808633i	$0.700208\pi$
$198$	18.8216	1.33759
$199$	−5.90149	−0.418345	−0.209173	−	0.977879i	$-0.567077\pi$
$199$	−5.90149	−0.418345	−0.209173	+	0.977879i	$0.567077\pi$
$200$	−3.01421	−0.213137
$201$	9.58608	0.676150
$202$	15.4643	1.08806
$203$	−12.3382	−0.865969
$204$	−98.0769	−6.86676
$205$	−22.0183	−1.53782
$206$	−33.5258	−2.33585
$207$	23.1512	1.60912
$208$	6.36424	0.441281
$209$	−5.77216	−0.399269
$210$	26.6605	1.83975
$211$	14.0450	0.966895	0.483447	−	0.875373i	$-0.339384\pi$
$211$	14.0450	0.966895	0.483447	+	0.875373i	$0.339384\pi$
$212$	28.8398	1.98073
$213$	0.436109	0.0298817
$214$	3.40486	0.232752
$215$	21.0555	1.43597
$216$	94.0678	6.40050
$217$	1.55197	0.105354
$218$	−18.6114	−1.26052
$219$	−6.62309	−0.447547
$220$	−10.8311	−0.730236
$221$	5.06505	0.340712
$222$	−15.7104	−1.05441
$223$	−12.8365	−0.859597	−0.429799	−	0.902925i	$-0.641415\pi$
$223$	−12.8365	−0.859597	−0.429799	+	0.902925i	$0.641415\pi$
$224$	−10.6243	−0.709865
$225$	3.23167	0.215445
$226$	34.6280	2.30342
$227$	−9.41289	−0.624756	−0.312378	−	0.949958i	$-0.601126\pi$
$227$	−9.41289	−0.624756	−0.312378	+	0.949958i	$0.601126\pi$
$228$	−86.0176	−5.69665
$229$	−6.80902	−0.449953	−0.224976	−	0.974364i	$-0.572230\pi$
$229$	−6.80902	−0.449953	−0.224976	+	0.974364i	$0.572230\pi$
$230$	−19.0619	−1.25690
$231$	4.43399	0.291735
$232$	60.8356	3.99405
$233$	8.45611	0.553978	0.276989	−	0.960873i	$-0.410663\pi$
$233$	8.45611	0.553978	0.276989	+	0.960873i	$0.410663\pi$
$234$	−14.4851	−0.946920
$235$	24.8072	1.61824
$236$	0.0828197	0.00539110
$237$	−45.2354	−2.93836
$238$	−23.4321	−1.51888
$239$	−17.5385	−1.13447	−0.567234	−	0.823556i	$-0.691987\pi$
$239$	−17.5385	−1.13447	−0.567234	+	0.823556i	$0.691987\pi$
$240$	−61.9236	−3.99715
$241$	−2.59226	−0.166982	−0.0834911	−	0.996509i	$-0.526607\pi$
$241$	−2.59226	−0.166982	−0.0834911	+	0.996509i	$0.526607\pi$
$242$	−2.57735	−0.165678
$243$	−30.5346	−1.95880
$244$	−15.0199	−0.961549
$245$	−11.8786	−0.758898
$246$	−78.0784	−4.97810
$247$	4.44226	0.282654
$248$	−7.65227	−0.485920
$249$	−1.10070	−0.0697539
$250$	27.4030	1.73312
$251$	−8.47328	−0.534829	−0.267414	−	0.963582i	$-0.586169\pi$
$251$	−8.47328	−0.534829	−0.267414	+	0.963582i	$0.586169\pi$
$252$	46.8355	2.95036
$253$	−3.17024	−0.199311
$254$	−7.74866	−0.486194
$255$	−49.2826	−3.08619
$256$	−24.4014	−1.52509
$257$	−21.4980	−1.34101	−0.670505	−	0.741905i	$-0.733923\pi$
$257$	−21.4980	−1.34101	−0.670505	+	0.741905i	$0.733923\pi$
$258$	74.6644	4.64840
$259$	−2.62336	−0.163008
$260$	8.33567	0.516956
$261$	−65.2248	−4.03731
$262$	38.1999	2.36000
$263$	8.59907	0.530241	0.265121	−	0.964215i	$-0.414588\pi$
$263$	8.59907	0.530241	0.265121	+	0.964215i	$0.414588\pi$
$264$	−21.8626	−1.34555
$265$	14.4917	0.890217
$266$	−20.5509	−1.26006
$267$	−35.9606	−2.20075
$268$	−13.8657	−0.846979
$269$	14.4973	0.883916	0.441958	−	0.897036i	$-0.354284\pi$
$269$	14.4973	0.883916	0.441958	+	0.897036i	$0.354284\pi$
$270$	83.0400	5.05366
$271$	−24.2610	−1.47375	−0.736874	−	0.676030i	$-0.763699\pi$
$271$	−24.2610	−1.47375	−0.736874	+	0.676030i	$0.763699\pi$
$272$	54.4250	3.30000
$273$	−3.41240	−0.206528
$274$	−26.5968	−1.60677
$275$	−0.442533	−0.0266857
$276$	−47.2433	−2.84371
$277$	−12.3393	−0.741399	−0.370699	−	0.928753i	$-0.620882\pi$
$277$	−12.3393	−0.741399	−0.370699	+	0.928753i	$0.620882\pi$
$278$	−30.7677	−1.84532
$279$	8.20437	0.491183
$280$	−21.9506	−1.31180
$281$	−1.43908	−0.0858486	−0.0429243	−	0.999078i	$-0.513667\pi$
$281$	−1.43908	−0.0858486	−0.0429243	+	0.999078i	$0.513667\pi$
$282$	87.9683	5.23843
$283$	20.0728	1.19321	0.596603	−	0.802537i	$-0.296517\pi$
$283$	20.0728	1.19321	0.596603	+	0.802537i	$0.296517\pi$
$284$	−0.630804	−0.0374313
$285$	−43.2229	−2.56030
$286$	1.98353	0.117289
$287$	−13.0377	−0.769593
$288$	−56.1645	−3.30953
$289$	26.3147	1.54793
$290$	53.7038	3.15359
$291$	−57.9675	−3.39811
$292$	9.57987	0.560620
$293$	−28.5544	−1.66817	−0.834084	−	0.551637i	$-0.814003\pi$
$293$	−28.5544	−1.66817	−0.834084	+	0.551637i	$0.814003\pi$
$294$	−42.1225	−2.45663
$295$	0.0416160	0.00242298
$296$	12.9350	0.751830
$297$	13.8106	0.801374
$298$	−44.2537	−2.56355
$299$	2.43982	0.141098
$300$	−6.59469	−0.380745
$301$	12.4676	0.718623
$302$	−20.9340	−1.20462
$303$	19.2589	1.10639
$304$	47.7330	2.73768
$305$	−7.54732	−0.432158
$306$	−123.872	−7.08129
$307$	12.5858	0.718308	0.359154	−	0.933278i	$-0.383065\pi$
$307$	12.5858	0.718308	0.359154	+	0.933278i	$0.383065\pi$
$308$	−6.41348	−0.365442
$309$	−41.7523	−2.37521
$310$	−6.75519	−0.383669
$311$	−21.5978	−1.22470	−0.612350	−	0.790587i	$-0.709776\pi$
$311$	−21.5978	−1.22470	−0.612350	+	0.790587i	$0.709776\pi$
$312$	16.8255	0.952557
$313$	20.0110	1.13109	0.565544	−	0.824718i	$-0.308666\pi$
$313$	20.0110	1.13109	0.565544	+	0.824718i	$0.308666\pi$
$314$	−54.8896	−3.09760
$315$	23.5343	1.32601
$316$	65.4301	3.68073
$317$	−10.0061	−0.561998	−0.280999	−	0.959708i	$-0.590666\pi$
$317$	−10.0061	−0.561998	−0.280999	+	0.959708i	$0.590666\pi$
$318$	51.3886	2.88173
$319$	8.93163	0.500075
$320$	7.65953	0.428181
$321$	4.24034	0.236673
$322$	−11.2872	−0.629009
$323$	37.9888	2.11376
$324$	104.095	5.78305
$325$	0.340574	0.0188916
$326$	17.6252	0.976170
$327$	−23.1783	−1.28176
$328$	64.2850	3.54955
$329$	14.6892	0.809840
$330$	−19.2996	−1.06241
$331$	29.7987	1.63788	0.818942	−	0.573876i	$-0.194561\pi$
$331$	29.7987	1.63788	0.818942	+	0.573876i	$0.194561\pi$
$332$	1.59209	0.0873772
$333$	−13.8682	−0.759973
$334$	−5.38397	−0.294598
$335$	−6.96734	−0.380666
$336$	−36.6670	−2.00035
$337$	−20.0353	−1.09139	−0.545697	−	0.837982i	$-0.683735\pi$
$337$	−20.0353	−1.09139	−0.545697	+	0.837982i	$0.683735\pi$
$338$	31.9790	1.73943
$339$	43.1250	2.34223
$340$	71.2840	3.86592
$341$	−1.12347	−0.0608396
$342$	−108.641	−5.87463
$343$	−16.7035	−0.901905
$344$	−61.4741	−3.31446
$345$	−23.7393	−1.27808
$346$	33.9177	1.82343
$347$	−23.9790	−1.28726	−0.643629	−	0.765337i	$-0.722572\pi$
$347$	−23.9790	−1.28726	−0.643629	+	0.765337i	$0.722572\pi$
$348$	133.100	7.13493
$349$	−6.11350	−0.327248	−0.163624	−	0.986523i	$-0.552318\pi$
$349$	−6.11350	−0.327248	−0.163624	+	0.986523i	$0.552318\pi$
$350$	−1.57557	−0.0842180
$351$	−10.6287	−0.567317
$352$	7.69095	0.409929
$353$	13.1569	0.700269	0.350134	−	0.936699i	$-0.386136\pi$
$353$	13.1569	0.700269	0.350134	+	0.936699i	$0.386136\pi$
$354$	0.147573	0.00784344
$355$	−0.316972	−0.0168231
$356$	52.0147	2.75677
$357$	−29.1818	−1.54447
$358$	−18.8405	−0.995754
$359$	0.957506	0.0505352	0.0252676	−	0.999681i	$-0.491956\pi$
$359$	0.957506	0.0505352	0.0252676	+	0.999681i	$0.491956\pi$
$360$	−116.041	−6.11587
$361$	14.3178	0.753569
$362$	51.2349	2.69285
$363$	−3.20978	−0.168470
$364$	4.93582	0.258707
$365$	4.81378	0.251965
$366$	−26.7634	−1.39894
$367$	26.5373	1.38524	0.692618	−	0.721304i	$-0.256457\pi$
$367$	26.5373	1.38524	0.692618	+	0.721304i	$0.256457\pi$
$368$	26.2163	1.36662
$369$	−68.9230	−3.58799
$370$	11.4186	0.593624
$371$	8.58100	0.445503
$372$	−16.7422	−0.868042
$373$	22.3055	1.15493	0.577467	−	0.816414i	$-0.304041\pi$
$373$	22.3055	1.15493	0.577467	+	0.816414i	$0.304041\pi$
$374$	16.9626	0.877113
$375$	34.1271	1.76231
$376$	−72.4277	−3.73517
$377$	−6.87379	−0.354018
$378$	49.1707	2.52907
$379$	−29.1644	−1.49807	−0.749037	−	0.662528i	$-0.769483\pi$
$379$	−29.1644	−1.49807	−0.749037	+	0.662528i	$0.769483\pi$
$380$	62.5191	3.20716
$381$	−9.65002	−0.494386
$382$	−49.1375	−2.51409
$383$	12.9243	0.660402	0.330201	−	0.943911i	$-0.392883\pi$
$383$	12.9243	0.660402	0.330201	+	0.943911i	$0.392883\pi$
$384$	−22.2112	−1.13346
$385$	−3.22270	−0.164244
$386$	0.724866	0.0368947
$387$	65.9093	3.35036
$388$	83.8462	4.25665
$389$	10.7342	0.544247	0.272123	−	0.962262i	$-0.412274\pi$
$389$	10.7342	0.544247	0.272123	+	0.962262i	$0.412274\pi$
$390$	14.8530	0.752112
$391$	20.8646	1.05517
$392$	34.6811	1.75166
$393$	47.5733	2.39976
$394$	42.5643	2.14436
$395$	32.8779	1.65427
$396$	−33.9044	−1.70376
$397$	10.5470	0.529339	0.264669	−	0.964339i	$-0.414737\pi$
$397$	10.5470	0.529339	0.264669	+	0.964339i	$0.414737\pi$
$398$	15.2102	0.762419
$399$	−25.5937	−1.28129
$400$	3.65954	0.182977
$401$	−5.88750	−0.294008	−0.147004	−	0.989136i	$-0.546963\pi$
$401$	−5.88750	−0.294008	−0.147004	+	0.989136i	$0.546963\pi$
$402$	−24.7067	−1.23226
$403$	0.864628	0.0430702
$404$	−27.8567	−1.38592
$405$	52.3066	2.59913
$406$	31.7997	1.57819
$407$	1.89906	0.0941328
$408$	143.887	7.12344
$409$	−18.4142	−0.910524	−0.455262	−	0.890357i	$-0.650454\pi$
$409$	−18.4142	−0.910524	−0.455262	+	0.890357i	$0.650454\pi$
$410$	56.7488	2.80262
$411$	−33.1231	−1.63384
$412$	60.3920	2.97530
$413$	0.0246422	0.00121256
$414$	−59.6688	−2.93256
$415$	0.800007	0.0392708
$416$	−5.91897	−0.290201
$417$	−38.3174	−1.87641
$418$	14.8769	0.727652
$419$	8.10769	0.396086	0.198043	−	0.980193i	$-0.436541\pi$
$419$	8.10769	0.396086	0.198043	+	0.980193i	$0.436541\pi$
$420$	−48.0252	−2.34339
$421$	28.3488	1.38163	0.690817	−	0.723030i	$-0.257251\pi$
$421$	28.3488	1.38163	0.690817	+	0.723030i	$0.257251\pi$
$422$	−36.1988	−1.76213
$423$	77.6532	3.77563
$424$	−42.3102	−2.05477
$425$	2.91248	0.141276
$426$	−1.12401	−0.0544583
$427$	−4.46901	−0.216271
$428$	−6.13338	−0.296468
$429$	2.47025	0.119265
$430$	−54.2674	−2.61701
$431$	11.6853	0.562859	0.281429	−	0.959582i	$-0.409191\pi$
$431$	11.6853	0.562859	0.281429	+	0.959582i	$0.409191\pi$
$432$	−114.207	−5.49480
$433$	19.4370	0.934082	0.467041	−	0.884236i	$-0.345320\pi$
$433$	19.4370	0.934082	0.467041	+	0.884236i	$0.345320\pi$
$434$	−3.99997	−0.192004
$435$	66.8815	3.20672
$436$	33.5258	1.60560
$437$	18.2991	0.875365
$438$	17.0700	0.815638
$439$	30.4812	1.45479	0.727394	−	0.686220i	$-0.240731\pi$
$439$	30.4812	1.45479	0.727394	+	0.686220i	$0.240731\pi$
$440$	15.8901	0.757533
$441$	−37.1833	−1.77063
$442$	−13.0544	−0.620935
$443$	−16.2171	−0.770496	−0.385248	−	0.922813i	$-0.625884\pi$
$443$	−16.2171	−0.770496	−0.385248	+	0.922813i	$0.625884\pi$
$444$	28.3001	1.34306
$445$	26.1368	1.23900
$446$	33.0842	1.56658
$447$	−55.1127	−2.60674
$448$	4.53546	0.214280
$449$	36.5803	1.72633	0.863167	−	0.504919i	$-0.168478\pi$
$449$	36.5803	1.72633	0.863167	+	0.504919i	$0.168478\pi$
$450$	−8.32916	−0.392640
$451$	9.43805	0.444421
$452$	−62.3775	−2.93399
$453$	−26.0708	−1.22491
$454$	24.2603	1.13859
$455$	2.48020	0.116273
$456$	126.195	5.90960
$457$	−4.51917	−0.211398	−0.105699	−	0.994398i	$-0.533708\pi$
$457$	−4.51917	−0.211398	−0.105699	+	0.994398i	$0.533708\pi$
$458$	17.5492	0.820022
$459$	−90.8932	−4.24253
$460$	34.3373	1.60098
$461$	−18.8411	−0.877517	−0.438758	−	0.898605i	$-0.644582\pi$
$461$	−18.8411	−0.877517	−0.438758	+	0.898605i	$0.644582\pi$
$462$	−11.4279	−0.531676
$463$	−3.54446	−0.164725	−0.0823626	−	0.996602i	$-0.526247\pi$
$463$	−3.54446	−0.164725	−0.0823626	+	0.996602i	$0.526247\pi$
$464$	−73.8603	−3.42888
$465$	−8.41277	−0.390133
$466$	−21.7944	−1.00960
$467$	9.96830	0.461278	0.230639	−	0.973039i	$-0.425918\pi$
$467$	9.96830	0.461278	0.230639	+	0.973039i	$0.425918\pi$
$468$	26.0929	1.20614
$469$	−4.12559	−0.190502
$470$	−63.9369	−2.94919
$471$	−68.3583	−3.14979
$472$	−0.121503	−0.00559263
$473$	−9.02537	−0.414987
$474$	116.588	5.35504
$475$	2.55437	0.117203
$476$	42.2096	1.93467
$477$	45.3628	2.07702
$478$	45.2028	2.06753
$479$	−40.2592	−1.83949	−0.919745	−	0.392515i	$-0.871605\pi$
$479$	−40.2592	−1.83949	−0.919745	+	0.392515i	$0.871605\pi$
$480$	57.5911	2.62866
$481$	−1.46152	−0.0666395
$482$	6.68116	0.304319
$483$	−14.0568	−0.639606
$484$	4.64274	0.211033
$485$	42.1318	1.91311
$486$	78.6985	3.56984
$487$	12.9893	0.588601	0.294301	−	0.955713i	$-0.404913\pi$
$487$	12.9893	0.588601	0.294301	+	0.955713i	$0.404913\pi$
$488$	22.0353	0.997492
$489$	21.9501	0.992616
$490$	30.6154	1.38306
$491$	42.8913	1.93566	0.967829	−	0.251609i	$-0.0809597\pi$
$491$	42.8913	1.93566	0.967829	+	0.251609i	$0.0809597\pi$
$492$	140.647	6.34087
$493$	−58.7825	−2.64743
$494$	−11.4493	−0.515127
$495$	−17.0366	−0.765737
$496$	9.29060	0.417160
$497$	−0.187689	−0.00841902
$498$	2.83688	0.127124
$499$	35.8763	1.60604	0.803021	−	0.595951i	$-0.203225\pi$
$499$	35.8763	1.60604	0.803021	+	0.595951i	$0.203225\pi$
$500$	−49.3626	−2.20756
$501$	−6.70508	−0.299561
$502$	21.8386	0.974705
$503$	5.08196	0.226594	0.113297	−	0.993561i	$-0.463859\pi$
$503$	5.08196	0.226594	0.113297	+	0.993561i	$0.463859\pi$
$504$	−68.7114	−3.06065
$505$	−13.9977	−0.622889
$506$	8.17081	0.363237
$507$	39.8260	1.76874
$508$	13.9581	0.619292
$509$	19.8926	0.881722	0.440861	−	0.897575i	$-0.354673\pi$
$509$	19.8926	0.881722	0.440861	+	0.897575i	$0.354673\pi$
$510$	127.018	5.62447
$511$	2.85040	0.126094
$512$	49.0512	2.16778
$513$	−79.7171	−3.51960
$514$	55.4080	2.44394
$515$	30.3463	1.33722
$516$	−134.497	−5.92092
$517$	−10.6335	−0.467662
$518$	6.76132	0.297075
$519$	42.2404	1.85415
$520$	−12.2291	−0.536281
$521$	−28.8343	−1.26325	−0.631627	−	0.775273i	$-0.717612\pi$
$521$	−28.8343	−1.26325	−0.631627	+	0.775273i	$0.717612\pi$
$522$	168.107	7.35785
$523$	−35.2451	−1.54116	−0.770581	−	0.637342i	$-0.780034\pi$
$523$	−35.2451	−1.54116	−0.770581	+	0.637342i	$0.780034\pi$
$524$	−68.8118	−3.00606
$525$	−1.96219	−0.0856368
$526$	−22.1628	−0.966345
$527$	7.39403	0.322089
$528$	26.5433	1.15515
$529$	−12.9496	−0.563026
$530$	−37.3501	−1.62239
$531$	0.130269	0.00565320
$532$	37.0196	1.60500
$533$	−7.26354	−0.314619
$534$	92.6831	4.01079
$535$	−3.08196	−0.133245
$536$	20.3420	0.878640
$537$	−23.4636	−1.01253
$538$	−37.3646	−1.61090
$539$	5.09173	0.219316
$540$	−149.585	−6.43711
$541$	−9.89636	−0.425478	−0.212739	−	0.977109i	$-0.568238\pi$
$541$	−9.89636	−0.425478	−0.212739	+	0.977109i	$0.568238\pi$
$542$	62.5290	2.68585
$543$	63.8069	2.73822
$544$	−50.6172	−2.17019
$545$	16.8464	0.721619
$546$	8.79496	0.376390
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	47.9105	2.04663
$549$	−23.6251	−1.00830
$550$	1.14056	0.0486338
$551$	−51.5548	−2.19631
$552$	69.3097	2.95002
$553$	19.4681	0.827867
$554$	31.8028	1.35117
$555$	14.2205	0.603625
$556$	55.4236	2.35049
$557$	−18.3965	−0.779485	−0.389743	−	0.920924i	$-0.627436\pi$
$557$	−18.3965	−0.779485	−0.389743	+	0.920924i	$0.627436\pi$
$558$	−21.1455	−0.895162
$559$	6.94594	0.293782
$560$	26.6502	1.12618
$561$	21.1248	0.891890
$562$	3.70902	0.156456
$563$	−45.7526	−1.92824	−0.964121	−	0.265462i	$-0.914476\pi$
$563$	−45.7526	−1.92824	−0.964121	+	0.265462i	$0.914476\pi$
$564$	−158.463	−6.67248
$565$	−31.3440	−1.31865
$566$	−51.7347	−2.17457
$567$	30.9724	1.30072
$568$	0.925439	0.0388305
$569$	−2.85684	−0.119765	−0.0598824	−	0.998205i	$-0.519073\pi$
$569$	−2.85684	−0.119765	−0.0598824	+	0.998205i	$0.519073\pi$
$570$	111.401	4.66605
$571$	−5.83956	−0.244378	−0.122189	−	0.992507i	$-0.538991\pi$
$571$	−5.83956	−0.244378	−0.122189	+	0.992507i	$0.538991\pi$
$572$	−3.57306	−0.149397
$573$	−61.1948	−2.55645
$574$	33.6028	1.40255
$575$	1.40293	0.0585064
$576$	23.9764	0.999015
$577$	18.5549	0.772451	0.386226	−	0.922404i	$-0.373779\pi$
$577$	18.5549	0.772451	0.386226	+	0.922404i	$0.373779\pi$
$578$	−67.8223	−2.82103
$579$	0.902733	0.0375163
$580$	−96.7398	−4.01690
$581$	0.473710	0.0196528
$582$	149.403	6.19293
$583$	−6.21181	−0.257267
$584$	−14.0544	−0.581576
$585$	13.1114	0.542089
$586$	73.5948	3.04017
$587$	19.1370	0.789867	0.394933	−	0.918710i	$-0.370768\pi$
$587$	19.1370	0.789867	0.394933	+	0.918710i	$0.370768\pi$
$588$	75.8778	3.12915
$589$	6.48487	0.267205
$590$	−0.107259	−0.00441578
$591$	53.0087	2.18048
$592$	−15.7043	−0.645443
$593$	30.5384	1.25406	0.627031	−	0.778994i	$-0.284270\pi$
$593$	30.5384	1.25406	0.627031	+	0.778994i	$0.284270\pi$
$594$	−35.5948	−1.46047
$595$	21.2099	0.869520
$596$	79.7169	3.26533
$597$	18.9425	0.775264
$598$	−6.28827	−0.257146
$599$	10.7649	0.439842	0.219921	−	0.975518i	$-0.429420\pi$
$599$	10.7649	0.439842	0.219921	+	0.975518i	$0.429420\pi$
$600$	9.67493	0.394977
$601$	−16.7367	−0.682703	−0.341351	−	0.939936i	$-0.610885\pi$
$601$	−16.7367	−0.682703	−0.341351	+	0.939936i	$0.610885\pi$
$602$	−32.1335	−1.30966
$603$	−21.8096	−0.888157
$604$	37.7097	1.53439
$605$	2.33292	0.0948468
$606$	−49.6369	−2.01636
$607$	−42.9376	−1.74278	−0.871391	−	0.490590i	$-0.836781\pi$
$607$	−42.9376	−1.74278	−0.871391	+	0.490590i	$0.836781\pi$
$608$	−44.3934	−1.80039
$609$	39.6027	1.60478
$610$	19.4521	0.787592
$611$	8.18358	0.331072
$612$	223.138	9.01982
$613$	−21.5216	−0.869251	−0.434625	−	0.900611i	$-0.643119\pi$
$613$	−21.5216	−0.869251	−0.434625	+	0.900611i	$0.643119\pi$
$614$	−32.4380	−1.30909
$615$	70.6737	2.84984
$616$	9.40907	0.379102
$617$	−39.9130	−1.60683	−0.803417	−	0.595416i	$-0.796987\pi$
$617$	−39.9130	−1.60683	−0.803417	+	0.595416i	$0.796987\pi$
$618$	107.610	4.32872
$619$	11.6150	0.466848	0.233424	−	0.972375i	$-0.425007\pi$
$619$	11.6150	0.466848	0.233424	+	0.972375i	$0.425007\pi$
$620$	12.1685	0.488700
$621$	−43.7830	−1.75695
$622$	55.6652	2.23197
$623$	15.4765	0.620051
$624$	−20.4278	−0.817766
$625$	−27.0168	−1.08067
$626$	−51.5754	−2.06137
$627$	18.5273	0.739911
$628$	98.8759	3.94558
$629$	−12.4984	−0.498346
$630$	−60.6562	−2.41660
$631$	−29.6275	−1.17945	−0.589726	−	0.807604i	$-0.700764\pi$
$631$	−29.6275	−1.17945	−0.589726	+	0.807604i	$0.700764\pi$
$632$	−95.9911	−3.81832
$633$	−45.0812	−1.79182
$634$	25.7892	1.02422
$635$	7.01381	0.278335
$636$	−92.5693	−3.67061
$637$	−3.91861	−0.155261
$638$	−23.0199	−0.911368
$639$	−0.992207	−0.0392511
$640$	16.1435	0.638129
$641$	21.7058	0.857329	0.428665	−	0.903464i	$-0.358984\pi$
$641$	21.7058	0.857329	0.428665	+	0.903464i	$0.358984\pi$
$642$	−10.9289	−0.431327
$643$	10.8110	0.426346	0.213173	−	0.977014i	$-0.431620\pi$
$643$	10.8110	0.426346	0.213173	+	0.977014i	$0.431620\pi$
$644$	20.3322	0.801202
$645$	−67.5835	−2.66110
$646$	−97.9106	−3.85224
$647$	−16.1537	−0.635068	−0.317534	−	0.948247i	$-0.602855\pi$
$647$	−16.1537	−0.635068	−0.317534	+	0.948247i	$0.602855\pi$
$648$	−152.715	−5.99923
$649$	−0.0178386	−0.000700225 0
$650$	−0.877779	−0.0344293
$651$	−4.98147	−0.195239
$652$	−31.7493	−1.24340
$653$	34.9183	1.36646	0.683229	−	0.730204i	$-0.260575\pi$
$653$	34.9183	1.36646	0.683229	+	0.730204i	$0.260575\pi$
$654$	59.7385	2.33596
$655$	−34.5771	−1.35104
$656$	−78.0482	−3.04727
$657$	15.0684	0.587875
$658$	−37.8591	−1.47590
$659$	−7.20066	−0.280498	−0.140249	−	0.990116i	$-0.544790\pi$
$659$	−7.20066	−0.280498	−0.140249	+	0.990116i	$0.544790\pi$
$660$	34.7656	1.35325
$661$	13.2807	0.516561	0.258281	−	0.966070i	$-0.416844\pi$
$661$	13.2807	0.516561	0.258281	+	0.966070i	$0.416844\pi$
$662$	−76.8017	−2.98498
$663$	−16.2577	−0.631396
$664$	−2.33572	−0.0906434
$665$	18.6019	0.721352
$666$	35.7432	1.38502
$667$	−28.3154	−1.09638
$668$	9.69846	0.375245
$669$	41.2024	1.59298
$670$	17.9573	0.693750
$671$	3.23513	0.124891
$672$	34.1016	1.31550
$673$	24.7329	0.953383	0.476692	−	0.879071i	$-0.341836\pi$
$673$	24.7329	0.953383	0.476692	+	0.879071i	$0.341836\pi$
$674$	51.6381	1.98903
$675$	−6.11166	−0.235238
$676$	−57.6057	−2.21561
$677$	−29.8588	−1.14757	−0.573783	−	0.819008i	$-0.694525\pi$
$677$	−29.8588	−1.14757	−0.573783	+	0.819008i	$0.694525\pi$
$678$	−111.148	−4.26862
$679$	24.9476	0.957402
$680$	−104.579	−4.01043
$681$	30.2133	1.15778
$682$	2.89559	0.110878
$683$	13.4527	0.514753	0.257376	−	0.966311i	$-0.417142\pi$
$683$	13.4527	0.514753	0.257376	+	0.966311i	$0.417142\pi$
$684$	195.702	7.48283
$685$	24.0745	0.919839
$686$	43.0508	1.64369
$687$	21.8554	0.833837
$688$	74.6355	2.84545
$689$	4.78062	0.182127
$690$	61.1844	2.32925
$691$	−35.2201	−1.33983	−0.669917	−	0.742436i	$-0.733670\pi$
$691$	−35.2201	−1.33983	−0.669917	+	0.742436i	$0.733670\pi$
$692$	−61.0981	−2.32260
$693$	−10.0879	−0.383208
$694$	61.8022	2.34598
$695$	27.8498	1.05640
$696$	−195.269	−7.40165
$697$	−62.1155	−2.35279
$698$	15.7566	0.596397
$699$	−27.1422	−1.02661
$700$	2.83818	0.107273
$701$	−21.2554	−0.802805	−0.401402	−	0.915902i	$-0.631477\pi$
$701$	−21.2554	−0.802805	−0.401402	+	0.915902i	$0.631477\pi$
$702$	27.3938	1.03391
$703$	−10.9617	−0.413427
$704$	−3.28323	−0.123741
$705$	−79.6257	−2.99888
$706$	−33.9098	−1.27621
$707$	−8.28849	−0.311721
$708$	−0.265833	−0.00999061
$709$	−17.9272	−0.673271	−0.336636	−	0.941635i	$-0.609289\pi$
$709$	−17.9272	−0.673271	−0.336636	+	0.941635i	$0.609289\pi$
$710$	0.816948	0.0306595
$711$	102.917	3.85968
$712$	−76.3097	−2.85983
$713$	3.56168	0.133386
$714$	75.2118	2.81473
$715$	−1.79542	−0.0671450
$716$	33.9386	1.26835
$717$	56.2946	2.10236
$718$	−2.46783	−0.0920985
$719$	−31.9946	−1.19320	−0.596599	−	0.802540i	$-0.703482\pi$
$719$	−31.9946	−1.19320	−0.596599	+	0.802540i	$0.703482\pi$
$720$	140.884	5.25045
$721$	17.9690	0.669202
$722$	−36.9020	−1.37335
$723$	8.32058	0.309446
$724$	−92.2926	−3.43003
$725$	−3.95254	−0.146794
$726$	8.27272	0.307030
$727$	34.5436	1.28115	0.640576	−	0.767895i	$-0.278696\pi$
$727$	34.5436	1.28115	0.640576	+	0.767895i	$0.278696\pi$
$728$	−7.24124	−0.268378
$729$	30.7463	1.13875
$730$	−12.4068	−0.459196
$731$	59.3995	2.19697
$732$	48.2104	1.78191
$733$	6.05541	0.223662	0.111831	−	0.993727i	$-0.464329\pi$
$733$	6.05541	0.223662	0.111831	+	0.993727i	$0.464329\pi$
$734$	−68.3960	−2.52454
$735$	38.1278	1.40636
$736$	−24.3821	−0.898737
$737$	2.98653	0.110010
$738$	177.639	6.53897
$739$	36.5162	1.34327	0.671636	−	0.740881i	$-0.265592\pi$
$739$	36.5162	1.34327	0.671636	+	0.740881i	$0.265592\pi$
$740$	−20.5690	−0.756131
$741$	−14.2587	−0.523805
$742$	−22.1162	−0.811913
$743$	46.4323	1.70344	0.851718	−	0.524000i	$-0.175561\pi$
$743$	46.4323	1.70344	0.851718	+	0.524000i	$0.175561\pi$
$744$	24.5621	0.900490
$745$	40.0569	1.46757
$746$	−57.4890	−2.10482
$747$	2.50423	0.0916251
$748$	−30.5557	−1.11723
$749$	−1.82493	−0.0666814
$750$	−87.9574	−3.21175
$751$	32.1893	1.17460	0.587301	−	0.809368i	$-0.300190\pi$
$751$	32.1893	1.17460	0.587301	+	0.809368i	$0.300190\pi$
$752$	87.9343	3.20663
$753$	27.1973	0.991126
$754$	17.7162	0.645185
$755$	18.9487	0.689614
$756$	−88.5742	−3.22141
$757$	40.7272	1.48026	0.740128	−	0.672466i	$-0.234765\pi$
$757$	40.7272	1.48026	0.740128	+	0.672466i	$0.234765\pi$
$758$	75.1668	2.73018
$759$	10.1758	0.369356
$760$	−91.7204	−3.32705
$761$	46.4901	1.68527	0.842633	−	0.538489i	$-0.181005\pi$
$761$	46.4901	1.68527	0.842633	+	0.538489i	$0.181005\pi$
$762$	24.8715	0.900999
$763$	9.97528	0.361129
$764$	88.5143	3.20233
$765$	112.124	4.05387
$766$	−33.3105	−1.20356
$767$	0.0137286	0.000495710 0
$768$	78.3231	2.82624
$769$	21.6810	0.781839	0.390919	−	0.920425i	$-0.372157\pi$
$769$	21.6810	0.781839	0.390919	+	0.920425i	$0.372157\pi$
$770$	8.30603	0.299329
$771$	69.0039	2.48511
$772$	−1.30575	−0.0469948
$773$	−37.0840	−1.33382	−0.666910	−	0.745139i	$-0.732383\pi$
$773$	−37.0840	−1.33382	−0.666910	+	0.745139i	$0.732383\pi$
$774$	−169.871	−6.10590
$775$	0.497175	0.0178590
$776$	−123.009	−4.41576
$777$	8.42040	0.302080
$778$	−27.6659	−0.991869
$779$	−54.4779	−1.95187
$780$	−26.7556	−0.958006
$781$	0.135869	0.00486178
$782$	−53.7753	−1.92300
$783$	123.351	4.40822
$784$	−42.1062	−1.50379
$785$	49.6841	1.77330
$786$	−122.613	−4.37347
$787$	−39.3274	−1.40187	−0.700934	−	0.713226i	$-0.747233\pi$
$787$	−39.3274	−1.40187	−0.700934	+	0.713226i	$0.747233\pi$
$788$	−76.6736	−2.73138
$789$	−27.6011	−0.982625
$790$	−84.7379	−3.01484
$791$	−18.5598	−0.659910
$792$	49.7404	1.76745
$793$	−2.48976	−0.0884141
$794$	−27.1833	−0.964700
$795$	−46.5151	−1.64972
$796$	−27.3991	−0.971134
$797$	−16.2624	−0.576045	−0.288023	−	0.957624i	$-0.592998\pi$
$797$	−16.2624	−0.576045	−0.288023	+	0.957624i	$0.592998\pi$
$798$	65.9639	2.33510
$799$	69.9835	2.47584
$800$	−3.40350	−0.120332
$801$	81.8152	2.89080
$802$	15.1742	0.535818
$803$	−2.06341	−0.0728162
$804$	44.5057	1.56959
$805$	10.2167	0.360092
$806$	−2.22845	−0.0784938
$807$	−46.5331	−1.63804
$808$	40.8680	1.43773
$809$	11.6886	0.410951	0.205476	−	0.978662i	$-0.434126\pi$
$809$	11.6886	0.410951	0.205476	+	0.978662i	$0.434126\pi$
$810$	−134.812	−4.73682
$811$	12.0599	0.423480	0.211740	−	0.977326i	$-0.432087\pi$
$811$	12.0599	0.423480	0.211740	+	0.977326i	$0.432087\pi$
$812$	−57.2828	−2.01023
$813$	77.8723	2.73110
$814$	−4.89454	−0.171553
$815$	−15.9537	−0.558833
$816$	−174.692	−6.11545
$817$	52.0959	1.82260
$818$	47.4599	1.65940
$819$	7.76368	0.271285
$820$	−102.225	−3.56985
$821$	−54.6082	−1.90584	−0.952919	−	0.303224i	$-0.901937\pi$
$821$	−54.6082	−1.90584	−0.952919	+	0.303224i	$0.901937\pi$
$822$	85.3700	2.97762
$823$	23.4957	0.819008	0.409504	−	0.912308i	$-0.365702\pi$
$823$	23.4957	0.819008	0.409504	+	0.912308i	$0.365702\pi$
$824$	−88.5998	−3.08652
$825$	1.42043	0.0494531
$826$	−0.0635116	−0.00220985
$827$	−42.1340	−1.46514	−0.732572	−	0.680690i	$-0.761680\pi$
$827$	−42.1340	−1.46514	−0.732572	+	0.680690i	$0.761680\pi$
$828$	107.485	3.73536
$829$	−9.35412	−0.324882	−0.162441	−	0.986718i	$-0.551937\pi$
$829$	−9.35412	−0.324882	−0.162441	+	0.986718i	$0.551937\pi$
$830$	−2.06190	−0.0715695
$831$	39.6065	1.37394
$832$	2.52678	0.0876003
$833$	−33.5107	−1.16108
$834$	98.7574	3.41969
$835$	4.87337	0.168650
$836$	−26.7986	−0.926849
$837$	−15.5159	−0.536308
$838$	−20.8963	−0.721852
$839$	12.4421	0.429549	0.214774	−	0.976664i	$-0.431098\pi$
$839$	12.4421	0.429549	0.214774	+	0.976664i	$0.431098\pi$
$840$	70.4567	2.43099
$841$	50.7740	1.75083
$842$	−73.0647	−2.51798
$843$	4.61914	0.159092
$844$	65.2070	2.24452
$845$	−28.9462	−0.995781
$846$	−200.140	−6.88094
$847$	1.38140	0.0474655
$848$	51.3687	1.76401
$849$	−64.4293	−2.21121
$850$	−7.50649	−0.257471
$851$	−6.02046	−0.206379
$852$	2.02474	0.0693665
$853$	49.5700	1.69724	0.848622	−	0.529000i	$-0.177433\pi$
$853$	49.5700	1.69724	0.848622	+	0.529000i	$0.177433\pi$
$854$	11.5182	0.394145
$855$	98.3379	3.36308
$856$	8.99815	0.307551
$857$	−0.171008	−0.00584153	−0.00292077	−	0.999996i	$-0.500930\pi$
$857$	−0.171008	−0.00584153	−0.00292077	+	0.999996i	$0.500930\pi$
$858$	−6.36670	−0.217356
$859$	38.3276	1.30772	0.653861	−	0.756615i	$-0.273148\pi$
$859$	38.3276	1.30772	0.653861	+	0.756615i	$0.273148\pi$
$860$	97.7551	3.33342
$861$	41.8482	1.42618
$862$	−30.1170	−1.02579
$863$	−37.5896	−1.27957	−0.639783	−	0.768556i	$-0.720976\pi$
$863$	−37.5896	−1.27957	−0.639783	+	0.768556i	$0.720976\pi$
$864$	106.217	3.61357
$865$	−30.7011	−1.04387
$866$	−50.0959	−1.70233
$867$	−84.4644	−2.86856
$868$	7.20538	0.244566
$869$	−14.0930	−0.478072
$870$	−172.377	−5.84413
$871$	−2.29843	−0.0778795
$872$	−49.1850	−1.66562
$873$	131.884	4.46359
$874$	−47.1632	−1.59532
$875$	−14.6874	−0.496523
$876$	−30.7493	−1.03892
$877$	−33.8154	−1.14186	−0.570932	−	0.820998i	$-0.693418\pi$
$877$	−33.8154	−1.14186	−0.570932	+	0.820998i	$0.693418\pi$
$878$	−78.5607	−2.65130
$879$	91.6534	3.09139
$880$	−19.2922	−0.650339
$881$	−46.6245	−1.57082	−0.785410	−	0.618976i	$-0.787548\pi$
$881$	−46.6245	−1.57082	−0.785410	+	0.618976i	$0.787548\pi$
$882$	95.8343	3.22691
$883$	−18.3579	−0.617793	−0.308896	−	0.951096i	$-0.599960\pi$
$883$	−18.3579	−0.617793	−0.308896	+	0.951096i	$0.599960\pi$
$884$	23.5157	0.790918
$885$	−0.133578	−0.00449018
$886$	41.7971	1.40420
$887$	16.4266	0.551552	0.275776	−	0.961222i	$-0.411065\pi$
$887$	16.4266	0.551552	0.275776	+	0.961222i	$0.411065\pi$
$888$	−41.5184	−1.39327
$889$	4.15310	0.139291
$890$	−67.3638	−2.25804
$891$	−22.4210	−0.751133
$892$	−59.5966	−1.99544
$893$	61.3784	2.05395
$894$	142.045	4.75068
$895$	17.0538	0.570045
$896$	9.55911	0.319347
$897$	−7.83127	−0.261479
$898$	−94.2804	−3.14618
$899$	−10.0345	−0.334668
$900$	15.0038	0.500127
$901$	40.8824	1.36199
$902$	−24.3252	−0.809940
$903$	−40.0184	−1.33173
$904$	91.5126	3.04366
$905$	−46.3760	−1.54159
$906$	67.1935	2.23236
$907$	−23.3796	−0.776308	−0.388154	−	0.921594i	$-0.626887\pi$
$907$	−23.3796	−0.776308	−0.388154	+	0.921594i	$0.626887\pi$
$908$	−43.7016	−1.45029
$909$	−43.8165	−1.45330
$910$	−6.39233	−0.211904
$911$	43.8123	1.45156	0.725782	−	0.687924i	$-0.241478\pi$
$911$	43.8123	1.45156	0.725782	+	0.687924i	$0.241478\pi$
$912$	−153.212	−5.07337
$913$	−0.342920	−0.0113490
$914$	11.6475	0.385265
$915$	24.2252	0.800861
$916$	−31.6125	−1.04451
$917$	−20.4743	−0.676120
$918$	234.264	7.73185
$919$	30.8518	1.01771	0.508853	−	0.860854i	$-0.330070\pi$
$919$	30.8518	1.01771	0.508853	+	0.860854i	$0.330070\pi$
$920$	−50.3755	−1.66083
$921$	−40.3975	−1.33114
$922$	48.5601	1.59924
$923$	−0.104565	−0.00344180
$924$	20.5858	0.677224
$925$	−0.840396	−0.0276320
$926$	9.13533	0.300205
$927$	94.9921	3.11995
$928$	68.6927	2.25495
$929$	−35.4105	−1.16178	−0.580891	−	0.813981i	$-0.697296\pi$
$929$	−35.4105	−1.16178	−0.580891	+	0.813981i	$0.697296\pi$
$930$	21.6826	0.711002
$931$	−29.3903	−0.963228
$932$	39.2595	1.28599
$933$	69.3242	2.26957
$934$	−25.6918	−0.840662
$935$	−15.3539	−0.502126
$936$	−38.2803	−1.25123
$937$	−55.4325	−1.81090	−0.905451	−	0.424450i	$-0.860467\pi$
$937$	−55.4325	−1.81090	−0.905451	+	0.424450i	$0.860467\pi$
$938$	10.6331	0.347183
$939$	−64.2309	−2.09610
$940$	115.173	3.75654
$941$	−20.2243	−0.659292	−0.329646	−	0.944105i	$-0.606929\pi$
$941$	−20.2243	−0.659292	−0.329646	+	0.944105i	$0.606929\pi$
$942$	176.183	5.74037
$943$	−29.9208	−0.974357
$944$	0.147516	0.00480125
$945$	−44.5075	−1.44783
$946$	23.2615	0.756298
$947$	7.88328	0.256172	0.128086	−	0.991763i	$-0.459117\pi$
$947$	7.88328	0.256172	0.128086	+	0.991763i	$0.459117\pi$
$948$	−210.016	−6.82101
$949$	1.58800	0.0515488
$950$	−6.58351	−0.213597
$951$	32.1173	1.04148
$952$	−61.9248	−2.00699
$953$	−2.41705	−0.0782960	−0.0391480	−	0.999233i	$-0.512464\pi$
$953$	−2.41705	−0.0782960	−0.0391480	+	0.999233i	$0.512464\pi$
$954$	−116.916	−3.78529
$955$	44.4774	1.43926
$956$	−81.4264	−2.63352
$957$	−28.6685	−0.926722
$958$	103.762	3.35240
$959$	14.2553	0.460327
$960$	−24.5854	−0.793490
$961$	−29.7378	−0.959284
$962$	3.76684	0.121448
$963$	−9.64735	−0.310881
$964$	−12.0352	−0.387627
$965$	−0.656123	−0.0211213
$966$	36.2293	1.16566
$967$	−35.2845	−1.13467	−0.567336	−	0.823486i	$-0.692026\pi$
$967$	−35.2845	−1.13467	−0.567336	+	0.823486i	$0.692026\pi$
$968$	−6.81126	−0.218922
$969$	−121.936	−3.91714
$970$	−108.588	−3.48656
$971$	0.558831	0.0179337	0.00896687	−	0.999960i	$-0.497146\pi$
$971$	0.558831	0.0179337	0.00896687	+	0.999960i	$0.497146\pi$
$972$	−141.764	−4.54709
$973$	16.4908	0.528669
$974$	−33.4780	−1.07270
$975$	−1.09317	−0.0350094
$976$	−26.7530	−0.856343
$977$	27.5089	0.880088	0.440044	−	0.897976i	$-0.354963\pi$
$977$	27.5089	0.880088	0.440044	+	0.897976i	$0.354963\pi$
$978$	−56.5730	−1.80900
$979$	−11.2035	−0.358064
$980$	−55.1493	−1.76168
$981$	52.7336	1.68366
$982$	−110.546	−3.52766
$983$	49.8167	1.58891	0.794453	−	0.607325i	$-0.207757\pi$
$983$	49.8167	1.58891	0.794453	+	0.607325i	$0.207757\pi$
$984$	−206.341	−6.57790
$985$	−38.5276	−1.22759
$986$	151.503	4.82485
$987$	−47.1490	−1.50077
$988$	20.6242	0.656145
$989$	28.6125	0.909826
$990$	43.9092	1.39553
$991$	−40.5386	−1.28775	−0.643876	−	0.765130i	$-0.722675\pi$
$991$	−40.5386	−1.28775	−0.643876	+	0.765130i	$0.722675\pi$
$992$	−8.64059	−0.274339
$993$	−95.6472	−3.03527
$994$	0.483742	0.0153434
$995$	−13.7677	−0.436466
$996$	−5.11025	−0.161924
$997$	44.8148	1.41930	0.709649	−	0.704555i	$-0.248853\pi$
$997$	44.8148	1.41930	0.709649	+	0.704555i	$0.248853\pi$
$998$	−92.4657	−2.92695
$999$	26.2272	0.829792

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.f.1.9	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.f.1.9	✓	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57735 q^{2} -3.20978 q^{3} +4.64274 q^{4} +2.33292 q^{5} +8.27272 q^{6} +1.38140 q^{7} -6.81126 q^{8} +7.30267 q^{9} +O(q^{10})\)	\(q-2.57735 q^{2} -3.20978 q^{3} +4.64274 q^{4} +2.33292 q^{5} +8.27272 q^{6} +1.38140 q^{7} -6.81126 q^{8} +7.30267 q^{9} -6.01276 q^{10} -1.00000 q^{11} -14.9022 q^{12} +0.769601 q^{13} -3.56035 q^{14} -7.48817 q^{15} +8.26953 q^{16} +6.58139 q^{17} -18.8216 q^{18} +5.77216 q^{19} +10.8311 q^{20} -4.43399 q^{21} +2.57735 q^{22} +3.17024 q^{23} +21.8626 q^{24} +0.442533 q^{25} -1.98353 q^{26} -13.8106 q^{27} +6.41348 q^{28} -8.93163 q^{29} +19.2996 q^{30} +1.12347 q^{31} -7.69095 q^{32} +3.20978 q^{33} -16.9626 q^{34} +3.22270 q^{35} +33.9044 q^{36} -1.89906 q^{37} -14.8769 q^{38} -2.47025 q^{39} -15.8901 q^{40} -9.43805 q^{41} +11.4279 q^{42} +9.02537 q^{43} -4.64274 q^{44} +17.0366 q^{45} -8.17081 q^{46} +10.6335 q^{47} -26.5433 q^{48} -5.09173 q^{49} -1.14056 q^{50} -21.1248 q^{51} +3.57306 q^{52} +6.21181 q^{53} +35.5948 q^{54} -2.33292 q^{55} -9.40907 q^{56} -18.5273 q^{57} +23.0199 q^{58} +0.0178386 q^{59} -34.7656 q^{60} -3.23513 q^{61} -2.89559 q^{62} +10.0879 q^{63} +3.28323 q^{64} +1.79542 q^{65} -8.27272 q^{66} -2.98653 q^{67} +30.5557 q^{68} -10.1758 q^{69} -8.30603 q^{70} -0.135869 q^{71} -49.7404 q^{72} +2.06341 q^{73} +4.89454 q^{74} -1.42043 q^{75} +26.7986 q^{76} -1.38140 q^{77} +6.36670 q^{78} +14.0930 q^{79} +19.2922 q^{80} +22.4210 q^{81} +24.3252 q^{82} +0.342920 q^{83} -20.5858 q^{84} +15.3539 q^{85} -23.2615 q^{86} +28.6685 q^{87} +6.81126 q^{88} +11.2035 q^{89} -43.9092 q^{90} +1.06313 q^{91} +14.7186 q^{92} -3.60610 q^{93} -27.4063 q^{94} +13.4660 q^{95} +24.6863 q^{96} +18.0597 q^{97} +13.1232 q^{98} -7.30267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * q^99

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