LMFDB - Embedded newform 6017.2.a.c.1.19

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:	$1$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-2.01004 q^{2} -2.26087 q^{3} +2.04024 q^{4} -3.50443 q^{5} +4.54443 q^{6} +2.31355 q^{7} -0.0808885 q^{8} +2.11154 q^{9} +O(q^{10})$	\(q-2.01004 q^{2} -2.26087 q^{3} +2.04024 q^{4} -3.50443 q^{5} +4.54443 q^{6} +2.31355 q^{7} -0.0808885 q^{8} +2.11154 q^{9} +7.04404 q^{10} +1.00000 q^{11} -4.61272 q^{12} +0.932710 q^{13} -4.65032 q^{14} +7.92307 q^{15} -3.91790 q^{16} +2.24975 q^{17} -4.24426 q^{18} -1.81538 q^{19} -7.14989 q^{20} -5.23064 q^{21} -2.01004 q^{22} +7.60522 q^{23} +0.182878 q^{24} +7.28105 q^{25} -1.87478 q^{26} +2.00870 q^{27} +4.72020 q^{28} -0.260714 q^{29} -15.9257 q^{30} -8.81982 q^{31} +8.03689 q^{32} -2.26087 q^{33} -4.52207 q^{34} -8.10768 q^{35} +4.30805 q^{36} -0.763248 q^{37} +3.64897 q^{38} -2.10874 q^{39} +0.283468 q^{40} -9.05116 q^{41} +10.5138 q^{42} -5.33038 q^{43} +2.04024 q^{44} -7.39974 q^{45} -15.2868 q^{46} -7.77051 q^{47} +8.85786 q^{48} -1.64749 q^{49} -14.6352 q^{50} -5.08639 q^{51} +1.90295 q^{52} +6.46060 q^{53} -4.03756 q^{54} -3.50443 q^{55} -0.187140 q^{56} +4.10433 q^{57} +0.524043 q^{58} +14.8158 q^{59} +16.1650 q^{60} +9.18233 q^{61} +17.7282 q^{62} +4.88514 q^{63} -8.31863 q^{64} -3.26862 q^{65} +4.54443 q^{66} -4.86067 q^{67} +4.59003 q^{68} -17.1944 q^{69} +16.2967 q^{70} +1.33641 q^{71} -0.170799 q^{72} -3.28867 q^{73} +1.53416 q^{74} -16.4615 q^{75} -3.70381 q^{76} +2.31355 q^{77} +4.23863 q^{78} -11.5544 q^{79} +13.7300 q^{80} -10.8760 q^{81} +18.1932 q^{82} -3.21228 q^{83} -10.6718 q^{84} -7.88409 q^{85} +10.7143 q^{86} +0.589440 q^{87} -0.0808885 q^{88} -9.75901 q^{89} +14.8737 q^{90} +2.15787 q^{91} +15.5165 q^{92} +19.9405 q^{93} +15.6190 q^{94} +6.36187 q^{95} -18.1704 q^{96} +3.45493 q^{97} +3.31151 q^{98} +2.11154 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) $ 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * 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 $

$2$	−2.01004	−1.42131	−0.710655	−	0.703541i	$-0.751601\pi$
$2$	−2.01004	−1.42131	−0.710655	+	0.703541i	$0.751601\pi$
$3$	−2.26087	−1.30531	−0.652657	−	0.757653i	$-0.726346\pi$
$3$	−2.26087	−1.30531	−0.652657	+	0.757653i	$0.726346\pi$
$4$	2.04024	1.02012
$5$	−3.50443	−1.56723	−0.783615	−	0.621247i	$-0.786627\pi$
$5$	−3.50443	−1.56723	−0.783615	+	0.621247i	$0.786627\pi$
$6$	4.54443	1.85526
$7$	2.31355	0.874439	0.437220	−	0.899355i	$-0.355963\pi$
$7$	2.31355	0.874439	0.437220	+	0.899355i	$0.355963\pi$
$8$	−0.0808885	−0.0285984
$9$	2.11154	0.703845
$10$	7.04404	2.22752
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.61272	−1.33158
$13$	0.932710	0.258687	0.129344	−	0.991600i	$-0.458713\pi$
$13$	0.932710	0.258687	0.129344	+	0.991600i	$0.458713\pi$
$14$	−4.65032	−1.24285
$15$	7.92307	2.04573
$16$	−3.91790	−0.979474
$17$	2.24975	0.545644	0.272822	−	0.962065i	$-0.412043\pi$
$17$	2.24975	0.545644	0.272822	+	0.962065i	$0.412043\pi$
$18$	−4.24426	−1.00038
$19$	−1.81538	−0.416476	−0.208238	−	0.978078i	$-0.566773\pi$
$19$	−1.81538	−0.416476	−0.208238	+	0.978078i	$0.566773\pi$
$20$	−7.14989	−1.59876
$21$	−5.23064	−1.14142
$22$	−2.01004	−0.428541
$23$	7.60522	1.58580	0.792899	−	0.609353i	$-0.208571\pi$
$23$	7.60522	1.58580	0.792899	+	0.609353i	$0.208571\pi$
$24$	0.182878	0.0373299
$25$	7.28105	1.45621
$26$	−1.87478	−0.367674
$27$	2.00870	0.386575
$28$	4.72020	0.892034
$29$	−0.260714	−0.0484133	−0.0242066	−	0.999707i	$-0.507706\pi$
$29$	−0.260714	−0.0484133	−0.0242066	+	0.999707i	$0.507706\pi$
$30$	−15.9257	−2.90761
$31$	−8.81982	−1.58409	−0.792043	−	0.610465i	$-0.790983\pi$
$31$	−8.81982	−1.58409	−0.792043	+	0.610465i	$0.790983\pi$
$32$	8.03689	1.42073
$33$	−2.26087	−0.393567
$34$	−4.52207	−0.775529
$35$	−8.10768	−1.37045
$36$	4.30805	0.718008
$37$	−0.763248	−0.125477	−0.0627386	−	0.998030i	$-0.519983\pi$
$37$	−0.763248	−0.125477	−0.0627386	+	0.998030i	$0.519983\pi$
$38$	3.64897	0.591941
$39$	−2.10874	−0.337668
$40$	0.283468	0.0448203
$41$	−9.05116	−1.41355	−0.706777	−	0.707437i	$-0.749852\pi$
$41$	−9.05116	−1.41355	−0.706777	+	0.707437i	$0.749852\pi$
$42$	10.5138	1.62231
$43$	−5.33038	−0.812876	−0.406438	−	0.913678i	$-0.633229\pi$
$43$	−5.33038	−0.812876	−0.406438	+	0.913678i	$0.633229\pi$
$44$	2.04024	0.307578
$45$	−7.39974	−1.10309
$46$	−15.2868	−2.25391
$47$	−7.77051	−1.13344	−0.566722	−	0.823909i	$-0.691789\pi$
$47$	−7.77051	−1.13344	−0.566722	+	0.823909i	$0.691789\pi$
$48$	8.85786	1.27852
$49$	−1.64749	−0.235356
$50$	−14.6352	−2.06973
$51$	−5.08639	−0.712237
$52$	1.90295	0.263892
$53$	6.46060	0.887432	0.443716	−	0.896167i	$-0.353660\pi$
$53$	6.46060	0.887432	0.443716	+	0.896167i	$0.353660\pi$
$54$	−4.03756	−0.549443
$55$	−3.50443	−0.472538
$56$	−0.187140	−0.0250076
$57$	4.10433	0.543632
$58$	0.524043	0.0688103
$59$	14.8158	1.92886	0.964428	−	0.264344i	$-0.0851555\pi$
$59$	14.8158	1.92886	0.964428	+	0.264344i	$0.0851555\pi$
$60$	16.1650	2.08689
$61$	9.18233	1.17568	0.587838	−	0.808978i	$-0.299979\pi$
$61$	9.18233	1.17568	0.587838	+	0.808978i	$0.299979\pi$
$62$	17.7282	2.25148
$63$	4.88514	0.615470
$64$	−8.31863	−1.03983
$65$	−3.26862	−0.405422
$66$	4.54443	0.559381
$67$	−4.86067	−0.593826	−0.296913	−	0.954905i	$-0.595957\pi$
$67$	−4.86067	−0.593826	−0.296913	+	0.954905i	$0.595957\pi$
$68$	4.59003	0.556623
$69$	−17.1944	−2.06996
$70$	16.2967	1.94783
$71$	1.33641	0.158602	0.0793011	−	0.996851i	$-0.474731\pi$
$71$	1.33641	0.158602	0.0793011	+	0.996851i	$0.474731\pi$
$72$	−0.170799	−0.0201289
$73$	−3.28867	−0.384909	−0.192455	−	0.981306i	$-0.561645\pi$
$73$	−3.28867	−0.384909	−0.192455	+	0.981306i	$0.561645\pi$
$74$	1.53416	0.178342
$75$	−16.4615	−1.90081
$76$	−3.70381	−0.424856
$77$	2.31355	0.263653
$78$	4.23863	0.479931
$79$	−11.5544	−1.29997	−0.649985	−	0.759947i	$-0.725225\pi$
$79$	−11.5544	−1.29997	−0.649985	+	0.759947i	$0.725225\pi$
$80$	13.7300	1.53506
$81$	−10.8760	−1.20845
$82$	18.1932	2.00910
$83$	−3.21228	−0.352593	−0.176297	−	0.984337i	$-0.556412\pi$
$83$	−3.21228	−0.352593	−0.176297	+	0.984337i	$0.556412\pi$
$84$	−10.6718	−1.16438
$85$	−7.88409	−0.855150
$86$	10.7143	1.15535
$87$	0.589440	0.0631946
$88$	−0.0808885	−0.00862274
$89$	−9.75901	−1.03445	−0.517226	−	0.855849i	$-0.673035\pi$
$89$	−9.75901	−1.03445	−0.517226	+	0.855849i	$0.673035\pi$
$90$	14.8737	1.56783
$91$	2.15787	0.226206
$92$	15.5165	1.61771
$93$	19.9405	2.06773
$94$	15.6190	1.61098
$95$	6.36187	0.652714
$96$	−18.1704	−1.85450
$97$	3.45493	0.350795	0.175397	−	0.984498i	$-0.443879\pi$
$97$	3.45493	0.350795	0.175397	+	0.984498i	$0.443879\pi$
$98$	3.31151	0.334513
$99$	2.11154	0.212217
$100$	14.8551	1.48551
$101$	−2.21590	−0.220490	−0.110245	−	0.993904i	$-0.535164\pi$
$101$	−2.21590	−0.220490	−0.110245	+	0.993904i	$0.535164\pi$
$102$	10.2238	1.01231
$103$	3.92284	0.386529	0.193265	−	0.981147i	$-0.438092\pi$
$103$	3.92284	0.386529	0.193265	+	0.981147i	$0.438092\pi$
$104$	−0.0754455	−0.00739804
$105$	18.3304	1.78887
$106$	−12.9860	−1.26132
$107$	1.77673	0.171763	0.0858816	−	0.996305i	$-0.472629\pi$
$107$	1.77673	0.171763	0.0858816	+	0.996305i	$0.472629\pi$
$108$	4.09824	0.394353
$109$	9.06939	0.868690	0.434345	−	0.900747i	$-0.356980\pi$
$109$	9.06939	0.868690	0.434345	+	0.900747i	$0.356980\pi$
$110$	7.04404	0.671622
$111$	1.72561	0.163787
$112$	−9.06425	−0.856491
$113$	−10.4686	−0.984803	−0.492402	−	0.870368i	$-0.663881\pi$
$113$	−10.4686	−0.984803	−0.492402	+	0.870368i	$0.663881\pi$
$114$	−8.24985	−0.772670
$115$	−26.6520	−2.48531
$116$	−0.531919	−0.0493874
$117$	1.96945	0.182076
$118$	−29.7803	−2.74150
$119$	5.20490	0.477132
$120$	−0.640885	−0.0585046
$121$	1.00000	0.0909091
$122$	−18.4568	−1.67100
$123$	20.4635	1.84513
$124$	−17.9946	−1.61596
$125$	−7.99380	−0.714987
$126$	−9.81931	−0.874774
$127$	4.28096	0.379874	0.189937	−	0.981796i	$-0.439172\pi$
$127$	4.28096	0.379874	0.189937	+	0.981796i	$0.439172\pi$
$128$	0.646977	0.0571852
$129$	12.0513	1.06106
$130$	6.57004	0.576231
$131$	22.8795	1.99899	0.999495	−	0.0317873i	$-0.0101199\pi$
$131$	22.8795	1.99899	0.999495	+	0.0317873i	$0.0101199\pi$
$132$	−4.61272	−0.401486
$133$	−4.19996	−0.364183
$134$	9.77013	0.844010
$135$	−7.03936	−0.605852
$136$	−0.181979	−0.0156045
$137$	−11.5420	−0.986099	−0.493050	−	0.870001i	$-0.664118\pi$
$137$	−11.5420	−0.986099	−0.493050	+	0.870001i	$0.664118\pi$
$138$	34.5614	2.94206
$139$	−16.1738	−1.37184	−0.685922	−	0.727675i	$-0.740601\pi$
$139$	−16.1738	−1.37184	−0.685922	+	0.727675i	$0.740601\pi$
$140$	−16.5416	−1.39802
$141$	17.5681	1.47950
$142$	−2.68622	−0.225423
$143$	0.932710	0.0779971
$144$	−8.27278	−0.689398
$145$	0.913653	0.0758748
$146$	6.61034	0.547075
$147$	3.72476	0.307213
$148$	−1.55721	−0.128002
$149$	17.5665	1.43910	0.719552	−	0.694438i	$-0.244347\pi$
$149$	17.5665	1.43910	0.719552	+	0.694438i	$0.244347\pi$
$150$	33.0882	2.70164
$151$	21.1298	1.71952	0.859759	−	0.510699i	$-0.170614\pi$
$151$	21.1298	1.71952	0.859759	+	0.510699i	$0.170614\pi$
$152$	0.146843	0.0119106
$153$	4.75042	0.384049
$154$	−4.65032	−0.374733
$155$	30.9085	2.48263
$156$	−4.30233	−0.344462
$157$	20.4171	1.62946	0.814730	−	0.579841i	$-0.196885\pi$
$157$	20.4171	1.62946	0.814730	+	0.579841i	$0.196885\pi$
$158$	23.2247	1.84766
$159$	−14.6066	−1.15838
$160$	−28.1647	−2.22662
$161$	17.5951	1.38668
$162$	21.8612	1.71758
$163$	−19.6856	−1.54189	−0.770947	−	0.636900i	$-0.780217\pi$
$163$	−19.6856	−1.54189	−0.770947	+	0.636900i	$0.780217\pi$
$164$	−18.4666	−1.44200
$165$	7.92307	0.616810
$166$	6.45679	0.501144
$167$	13.7573	1.06457	0.532284	−	0.846566i	$-0.321334\pi$
$167$	13.7573	1.06457	0.532284	+	0.846566i	$0.321334\pi$
$168$	0.423098	0.0326427
$169$	−12.1301	−0.933081
$170$	15.8473	1.21543
$171$	−3.83323	−0.293135
$172$	−10.8753	−0.829232
$173$	−0.793270	−0.0603112	−0.0301556	−	0.999545i	$-0.509600\pi$
$173$	−0.793270	−0.0603112	−0.0301556	+	0.999545i	$0.509600\pi$
$174$	−1.18479	−0.0898190
$175$	16.8451	1.27337
$176$	−3.91790	−0.295323
$177$	−33.4967	−2.51776
$178$	19.6160	1.47028
$179$	−0.814349	−0.0608673	−0.0304336	−	0.999537i	$-0.509689\pi$
$179$	−0.814349	−0.0608673	−0.0304336	+	0.999537i	$0.509689\pi$
$180$	−15.0973	−1.12528
$181$	−12.8153	−0.952551	−0.476276	−	0.879296i	$-0.658014\pi$
$181$	−12.8153	−0.952551	−0.476276	+	0.879296i	$0.658014\pi$
$182$	−4.33739	−0.321509
$183$	−20.7601	−1.53463
$184$	−0.615175	−0.0453513
$185$	2.67475	0.196652
$186$	−40.0811	−2.93889
$187$	2.24975	0.164518
$188$	−15.8537	−1.15625
$189$	4.64723	0.338036
$190$	−12.7876	−0.927708
$191$	24.8604	1.79884	0.899418	−	0.437089i	$-0.143990\pi$
$191$	24.8604	1.79884	0.899418	+	0.437089i	$0.143990\pi$
$192$	18.8074	1.35730
$193$	8.20499	0.590608	0.295304	−	0.955403i	$-0.404579\pi$
$193$	8.20499	0.590608	0.295304	+	0.955403i	$0.404579\pi$
$194$	−6.94453	−0.498588
$195$	7.38992	0.529203
$196$	−3.36128	−0.240091
$197$	9.64035	0.686847	0.343423	−	0.939181i	$-0.388413\pi$
$197$	9.64035	0.686847	0.343423	+	0.939181i	$0.388413\pi$
$198$	−4.24426	−0.301627
$199$	9.92421	0.703509	0.351754	−	0.936092i	$-0.385585\pi$
$199$	9.92421	0.703509	0.351754	+	0.936092i	$0.385585\pi$
$200$	−0.588954	−0.0416453
$201$	10.9894	0.775129
$202$	4.45404	0.313385
$203$	−0.603174	−0.0423345
$204$	−10.3775	−0.726568
$205$	31.7192	2.21536
$206$	−7.88505	−0.549378
$207$	16.0587	1.11616
$208$	−3.65426	−0.253377
$209$	−1.81538	−0.125572
$210$	−36.8448	−2.54253
$211$	4.75228	0.327161	0.163580	−	0.986530i	$-0.447696\pi$
$211$	4.75228	0.327161	0.163580	+	0.986530i	$0.447696\pi$
$212$	13.1812	0.905288
$213$	−3.02144	−0.207026
$214$	−3.57130	−0.244129
$215$	18.6800	1.27396
$216$	−0.162481	−0.0110554
$217$	−20.4051	−1.38519
$218$	−18.2298	−1.23468
$219$	7.43525	0.502428
$220$	−7.14989	−0.482046
$221$	2.09836	0.141151
$222$	−3.46853	−0.232792
$223$	24.7024	1.65420	0.827098	−	0.562058i	$-0.189990\pi$
$223$	24.7024	1.65420	0.827098	+	0.562058i	$0.189990\pi$
$224$	18.5937	1.24235
$225$	15.3742	1.02495
$226$	21.0423	1.39971
$227$	8.42187	0.558979	0.279490	−	0.960149i	$-0.409835\pi$
$227$	8.42187	0.558979	0.279490	+	0.960149i	$0.409835\pi$
$228$	8.37383	0.554571
$229$	−21.9274	−1.44900	−0.724502	−	0.689273i	$-0.757930\pi$
$229$	−21.9274	−1.44900	−0.724502	+	0.689273i	$0.757930\pi$
$230$	53.5714	3.53240
$231$	−5.23064	−0.344151
$232$	0.0210887	0.00138454
$233$	5.82125	0.381363	0.190681	−	0.981652i	$-0.438930\pi$
$233$	5.82125	0.381363	0.190681	+	0.981652i	$0.438930\pi$
$234$	−3.95866	−0.258786
$235$	27.2312	1.77637
$236$	30.2279	1.96767
$237$	26.1230	1.69687
$238$	−10.4620	−0.678153
$239$	3.33427	0.215676	0.107838	−	0.994168i	$-0.465607\pi$
$239$	3.33427	0.215676	0.107838	+	0.994168i	$0.465607\pi$
$240$	−31.0418	−2.00374
$241$	−25.7942	−1.66155	−0.830775	−	0.556609i	$-0.812102\pi$
$241$	−25.7942	−1.66155	−0.830775	+	0.556609i	$0.812102\pi$
$242$	−2.01004	−0.129210
$243$	18.5632	1.19083
$244$	18.7342	1.19933
$245$	5.77352	0.368857
$246$	−41.1324	−2.62250
$247$	−1.69322	−0.107737
$248$	0.713422	0.0453023
$249$	7.26254	0.460245
$250$	16.0678	1.01622
$251$	−17.4887	−1.10388	−0.551939	−	0.833884i	$-0.686112\pi$
$251$	−17.4887	−1.10388	−0.551939	+	0.833884i	$0.686112\pi$
$252$	9.96688	0.627854
$253$	7.60522	0.478136
$254$	−8.60489	−0.539919
$255$	17.8249	1.11624
$256$	15.3368	0.958551
$257$	−15.2016	−0.948249	−0.474124	−	0.880458i	$-0.657235\pi$
$257$	−15.2016	−0.948249	−0.474124	+	0.880458i	$0.657235\pi$
$258$	−24.2236	−1.50809
$259$	−1.76581	−0.109722
$260$	−6.66877	−0.413580
$261$	−0.550506	−0.0340755
$262$	−45.9886	−2.84118
$263$	−7.62342	−0.470080	−0.235040	−	0.971986i	$-0.575522\pi$
$263$	−7.62342	−0.470080	−0.235040	+	0.971986i	$0.575522\pi$
$264$	0.182878	0.0112554
$265$	−22.6407	−1.39081
$266$	8.44208	0.517617
$267$	22.0639	1.35029
$268$	−9.91695	−0.605774
$269$	17.1807	1.04753	0.523764	−	0.851864i	$-0.324527\pi$
$269$	17.1807	1.04753	0.523764	+	0.851864i	$0.324527\pi$
$270$	14.1494	0.861103
$271$	−17.1951	−1.04453	−0.522265	−	0.852783i	$-0.674913\pi$
$271$	−17.1951	−1.04453	−0.522265	+	0.852783i	$0.674913\pi$
$272$	−8.81428	−0.534444
$273$	−4.87866	−0.295270
$274$	23.1998	1.40155
$275$	7.28105	0.439064
$276$	−35.0808	−2.11161
$277$	7.27007	0.436816	0.218408	−	0.975858i	$-0.429914\pi$
$277$	7.27007	0.436816	0.218408	+	0.975858i	$0.429914\pi$
$278$	32.5099	1.94982
$279$	−18.6234	−1.11495
$280$	0.655818	0.0391926
$281$	28.0082	1.67083	0.835415	−	0.549619i	$-0.185227\pi$
$281$	28.0082	1.67083	0.835415	+	0.549619i	$0.185227\pi$
$282$	−35.3125	−2.10283
$283$	−4.00734	−0.238212	−0.119106	−	0.992882i	$-0.538003\pi$
$283$	−4.00734	−0.238212	−0.119106	+	0.992882i	$0.538003\pi$
$284$	2.72659	0.161794
$285$	−14.3834	−0.851997
$286$	−1.87478	−0.110858
$287$	−20.9403	−1.23607
$288$	16.9702	0.999977
$289$	−11.9386	−0.702273
$290$	−1.83648	−0.107842
$291$	−7.81114	−0.457897
$292$	−6.70968	−0.392654
$293$	−25.1586	−1.46978	−0.734892	−	0.678184i	$-0.762767\pi$
$293$	−25.1586	−1.46978	−0.734892	+	0.678184i	$0.762767\pi$
$294$	−7.48690	−0.436645
$295$	−51.9211	−3.02296
$296$	0.0617380	0.00358845
$297$	2.00870	0.116557
$298$	−35.3093	−2.04541
$299$	7.09346	0.410225
$300$	−33.5855	−1.93906
$301$	−12.3321	−0.710811
$302$	−42.4716	−2.44397
$303$	5.00987	0.287809
$304$	7.11246	0.407927
$305$	−32.1789	−1.84256
$306$	−9.54852	−0.545852
$307$	−32.2330	−1.83963	−0.919817	−	0.392347i	$-0.871663\pi$
$307$	−32.2330	−1.83963	−0.919817	+	0.392347i	$0.871663\pi$
$308$	4.72020	0.268958
$309$	−8.86904	−0.504542
$310$	−62.1271	−3.52858
$311$	1.34046	0.0760105	0.0380053	−	0.999278i	$-0.487900\pi$
$311$	1.34046	0.0760105	0.0380053	+	0.999278i	$0.487900\pi$
$312$	0.170572	0.00965677
$313$	27.2252	1.53886	0.769430	−	0.638731i	$-0.220540\pi$
$313$	27.2252	1.53886	0.769430	+	0.638731i	$0.220540\pi$
$314$	−41.0390	−2.31597
$315$	−17.1197	−0.964583
$316$	−23.5738	−1.32613
$317$	−28.6058	−1.60666	−0.803332	−	0.595532i	$-0.796941\pi$
$317$	−28.6058	−1.60666	−0.803332	+	0.595532i	$0.796941\pi$
$318$	29.3598	1.64641
$319$	−0.260714	−0.0145972
$320$	29.1521	1.62965
$321$	−4.01696	−0.224205
$322$	−35.3667	−1.97091
$323$	−4.08414	−0.227248
$324$	−22.1897	−1.23276
$325$	6.79111	0.376703
$326$	39.5687	2.19151
$327$	−20.5047	−1.13391
$328$	0.732135	0.0404254
$329$	−17.9775	−0.991129
$330$	−15.9257	−0.876678
$331$	14.1311	0.776717	0.388358	−	0.921508i	$-0.373042\pi$
$331$	14.1311	0.776717	0.388358	+	0.921508i	$0.373042\pi$
$332$	−6.55383	−0.359688
$333$	−1.61163	−0.0883166
$334$	−27.6526	−1.51308
$335$	17.0339	0.930662
$336$	20.4931	1.11799
$337$	13.2250	0.720413	0.360207	−	0.932873i	$-0.382706\pi$
$337$	13.2250	0.720413	0.360207	+	0.932873i	$0.382706\pi$
$338$	24.3818	1.32620
$339$	23.6682	1.28548
$340$	−16.0855	−0.872356
$341$	−8.81982	−0.477620
$342$	7.70494	0.416635
$343$	−20.0064	−1.08024
$344$	0.431167	0.0232470
$345$	60.2567	3.24411
$346$	1.59450	0.0857209
$347$	23.3255	1.25218	0.626089	−	0.779752i	$-0.284655\pi$
$347$	23.3255	1.25218	0.626089	+	0.779752i	$0.284655\pi$
$348$	1.20260	0.0644661
$349$	25.7753	1.37972	0.689860	−	0.723943i	$-0.257672\pi$
$349$	25.7753	1.37972	0.689860	+	0.723943i	$0.257672\pi$
$350$	−33.8592	−1.80985
$351$	1.87354	0.100002
$352$	8.03689	0.428367
$353$	−12.2977	−0.654542	−0.327271	−	0.944930i	$-0.606129\pi$
$353$	−12.2977	−0.654542	−0.327271	+	0.944930i	$0.606129\pi$
$354$	67.3295	3.57852
$355$	−4.68335	−0.248566
$356$	−19.9107	−1.05527
$357$	−11.7676	−0.622808
$358$	1.63687	0.0865113
$359$	21.5225	1.13592	0.567958	−	0.823058i	$-0.307734\pi$
$359$	21.5225	1.13592	0.567958	+	0.823058i	$0.307734\pi$
$360$	0.598554	0.0315466
$361$	−15.7044	−0.826548
$362$	25.7591	1.35387
$363$	−2.26087	−0.118665
$364$	4.40258	0.230758
$365$	11.5249	0.603242
$366$	41.7285	2.18118
$367$	−4.55110	−0.237566	−0.118783	−	0.992920i	$-0.537899\pi$
$367$	−4.55110	−0.237566	−0.118783	+	0.992920i	$0.537899\pi$
$368$	−29.7965	−1.55325
$369$	−19.1119	−0.994923
$370$	−5.37635	−0.279503
$371$	14.9469	0.776005
$372$	40.6834	2.10934
$373$	−3.18621	−0.164976	−0.0824879	−	0.996592i	$-0.526287\pi$
$373$	−3.18621	−0.164976	−0.0824879	+	0.996592i	$0.526287\pi$
$374$	−4.52207	−0.233831
$375$	18.0729	0.933283
$376$	0.628545	0.0324147
$377$	−0.243170	−0.0125239
$378$	−9.34110	−0.480454
$379$	−33.1587	−1.70325	−0.851624	−	0.524152i	$-0.824382\pi$
$379$	−33.1587	−1.70325	−0.851624	+	0.524152i	$0.824382\pi$
$380$	12.9798	0.665847
$381$	−9.67871	−0.495855
$382$	−49.9703	−2.55670
$383$	−8.23616	−0.420848	−0.210424	−	0.977610i	$-0.567484\pi$
$383$	−8.23616	−0.420848	−0.210424	+	0.977610i	$0.567484\pi$
$384$	−1.46273	−0.0746447
$385$	−8.10768	−0.413206
$386$	−16.4923	−0.839436
$387$	−11.2553	−0.572139
$388$	7.04889	0.357853
$389$	−5.75199	−0.291638	−0.145819	−	0.989311i	$-0.546582\pi$
$389$	−5.75199	−0.291638	−0.145819	+	0.989311i	$0.546582\pi$
$390$	−14.8540	−0.752162
$391$	17.1098	0.865281
$392$	0.133263	0.00673080
$393$	−51.7275	−2.60931
$394$	−19.3774	−0.976222
$395$	40.4916	2.03735
$396$	4.30805	0.216487
$397$	−16.7872	−0.842525	−0.421263	−	0.906939i	$-0.638413\pi$
$397$	−16.7872	−0.842525	−0.421263	+	0.906939i	$0.638413\pi$
$398$	−19.9480	−0.999903
$399$	9.49557	0.475373
$400$	−28.5264	−1.42632
$401$	32.7393	1.63492	0.817461	−	0.575983i	$-0.195381\pi$
$401$	32.7393	1.63492	0.817461	+	0.575983i	$0.195381\pi$
$402$	−22.0890	−1.10170
$403$	−8.22633	−0.409783
$404$	−4.52097	−0.224927
$405$	38.1143	1.89391
$406$	1.21240	0.0601704
$407$	−0.763248	−0.0378328
$408$	0.411430	0.0203688
$409$	−32.1549	−1.58996	−0.794978	−	0.606638i	$-0.792518\pi$
$409$	−32.1549	−1.58996	−0.794978	+	0.606638i	$0.792518\pi$
$410$	−63.7567	−3.14872
$411$	26.0950	1.28717
$412$	8.00355	0.394307
$413$	34.2772	1.68667
$414$	−32.2785	−1.58640
$415$	11.2572	0.552595
$416$	7.49608	0.367526
$417$	36.5669	1.79069
$418$	3.64897	0.178477
$419$	0.0347615	0.00169821	0.000849106	−	1.00000i	$-0.499730\pi$
$419$	0.0347615	0.00169821	0.000849106		1.00000i	$0.499730\pi$
$420$	37.3985	1.82486
$421$	−7.23701	−0.352710	−0.176355	−	0.984327i	$-0.556431\pi$
$421$	−7.23701	−0.352710	−0.176355	+	0.984327i	$0.556431\pi$
$422$	−9.55225	−0.464996
$423$	−16.4077	−0.797770
$424$	−0.522588	−0.0253791
$425$	16.3805	0.794572
$426$	6.07321	0.294248
$427$	21.2438	1.02806
$428$	3.62496	0.175219
$429$	−2.10874	−0.101811
$430$	−37.5474	−1.81070
$431$	0.508803	0.0245082	0.0122541	−	0.999925i	$-0.496099\pi$
$431$	0.508803	0.0245082	0.0122541	+	0.999925i	$0.496099\pi$
$432$	−7.86988	−0.378640
$433$	−3.32438	−0.159760	−0.0798798	−	0.996805i	$-0.525454\pi$
$433$	−3.32438	−0.159760	−0.0798798	+	0.996805i	$0.525454\pi$
$434$	41.0149	1.96878
$435$	−2.06565	−0.0990404
$436$	18.5037	0.886169
$437$	−13.8063	−0.660447
$438$	−14.9451	−0.714105
$439$	20.1137	0.959975	0.479988	−	0.877275i	$-0.340641\pi$
$439$	20.1137	0.959975	0.479988	+	0.877275i	$0.340641\pi$
$440$	0.283468	0.0135138
$441$	−3.47873	−0.165654
$442$	−4.21778	−0.200619
$443$	18.4878	0.878380	0.439190	−	0.898394i	$-0.355265\pi$
$443$	18.4878	0.878380	0.439190	+	0.898394i	$0.355265\pi$
$444$	3.52065	0.167083
$445$	34.1998	1.62123
$446$	−49.6527	−2.35113
$447$	−39.7156	−1.87848
$448$	−19.2456	−0.909268
$449$	6.95664	0.328304	0.164152	−	0.986435i	$-0.447511\pi$
$449$	6.95664	0.328304	0.164152	+	0.986435i	$0.447511\pi$
$450$	−30.9027	−1.45677
$451$	−9.05116	−0.426202
$452$	−21.3585	−1.00462
$453$	−47.7717	−2.24451
$454$	−16.9283	−0.794482
$455$	−7.56211	−0.354517
$456$	−0.331993	−0.0155470
$457$	12.3110	0.575885	0.287943	−	0.957648i	$-0.407029\pi$
$457$	12.3110	0.575885	0.287943	+	0.957648i	$0.407029\pi$
$458$	44.0748	2.05948
$459$	4.51907	0.210932
$460$	−54.3765	−2.53532
$461$	4.99936	0.232843	0.116422	−	0.993200i	$-0.462858\pi$
$461$	4.99936	0.232843	0.116422	+	0.993200i	$0.462858\pi$
$462$	10.5138	0.489145
$463$	−24.0374	−1.11711	−0.558557	−	0.829466i	$-0.688645\pi$
$463$	−24.0374	−1.11711	−0.558557	+	0.829466i	$0.688645\pi$
$464$	1.02145	0.0474196
$465$	−69.8801	−3.24061
$466$	−11.7009	−0.542034
$467$	8.20936	0.379884	0.189942	−	0.981795i	$-0.439170\pi$
$467$	8.20936	0.379884	0.189942	+	0.981795i	$0.439170\pi$
$468$	4.01816	0.185739
$469$	−11.2454	−0.519265
$470$	−54.7357	−2.52477
$471$	−46.1604	−2.12696
$472$	−1.19843	−0.0551622
$473$	−5.33038	−0.245091
$474$	−52.5081	−2.41178
$475$	−13.2179	−0.606477
$476$	10.6193	0.486733
$477$	13.6418	0.624615
$478$	−6.70200	−0.306542
$479$	−18.6176	−0.850660	−0.425330	−	0.905038i	$-0.639842\pi$
$479$	−18.6176	−0.850660	−0.425330	+	0.905038i	$0.639842\pi$
$480$	63.6768	2.90644
$481$	−0.711889	−0.0324593
$482$	51.8472	2.36158
$483$	−39.7801	−1.81006
$484$	2.04024	0.0927383
$485$	−12.1076	−0.549776
$486$	−37.3126	−1.69254
$487$	−4.37826	−0.198398	−0.0991990	−	0.995068i	$-0.531628\pi$
$487$	−4.37826	−0.198398	−0.0991990	+	0.995068i	$0.531628\pi$
$488$	−0.742745	−0.0336225
$489$	44.5065	2.01266
$490$	−11.6050	−0.524259
$491$	−1.71768	−0.0775178	−0.0387589	−	0.999249i	$-0.512340\pi$
$491$	−1.71768	−0.0775178	−0.0387589	+	0.999249i	$0.512340\pi$
$492$	41.7505	1.88226
$493$	−0.586540	−0.0264164
$494$	3.40343	0.153128
$495$	−7.39974	−0.332593
$496$	34.5551	1.55157
$497$	3.09184	0.138688
$498$	−14.5980	−0.654151
$499$	23.6332	1.05797	0.528983	−	0.848633i	$-0.322574\pi$
$499$	23.6332	1.05797	0.528983	+	0.848633i	$0.322574\pi$
$500$	−16.3093	−0.729373
$501$	−31.1034	−1.38960
$502$	35.1530	1.56895
$503$	−40.5158	−1.80651	−0.903256	−	0.429102i	$-0.858830\pi$
$503$	−40.5158	−1.80651	−0.903256	+	0.429102i	$0.858830\pi$
$504$	−0.395152	−0.0176015
$505$	7.76548	0.345559
$506$	−15.2868	−0.679579
$507$	27.4245	1.21796
$508$	8.73420	0.387518
$509$	16.3939	0.726647	0.363324	−	0.931663i	$-0.381642\pi$
$509$	16.3939	0.726647	0.363324	+	0.931663i	$0.381642\pi$
$510$	−35.8287	−1.58652
$511$	−7.60849	−0.336580
$512$	−32.1215	−1.41958
$513$	−3.64655	−0.160999
$514$	30.5557	1.34775
$515$	−13.7473	−0.605780
$516$	24.5876	1.08241
$517$	−7.77051	−0.341747
$518$	3.54934	0.155949
$519$	1.79348	0.0787251
$520$	0.264394	0.0115944
$521$	30.5139	1.33684	0.668420	−	0.743784i	$-0.266971\pi$
$521$	30.5139	1.33684	0.668420	+	0.743784i	$0.266971\pi$
$522$	1.10654	0.0484318
$523$	19.4440	0.850225	0.425113	−	0.905140i	$-0.360234\pi$
$523$	19.4440	0.850225	0.425113	+	0.905140i	$0.360234\pi$
$524$	46.6797	2.03921
$525$	−38.0845	−1.66215
$526$	15.3233	0.668130
$527$	−19.8424	−0.864347
$528$	8.85786	0.385489
$529$	34.8394	1.51476
$530$	45.5087	1.97677
$531$	31.2842	1.35762
$532$	−8.56894	−0.371511
$533$	−8.44210	−0.365668
$534$	−44.3491	−1.91917
$535$	−6.22644	−0.269192
$536$	0.393173	0.0169825
$537$	1.84114	0.0794510
$538$	−34.5339	−1.48886
$539$	−1.64749	−0.0709624
$540$	−14.3620	−0.618042
$541$	−7.86025	−0.337939	−0.168969	−	0.985621i	$-0.554044\pi$
$541$	−7.86025	−0.337939	−0.168969	+	0.985621i	$0.554044\pi$
$542$	34.5628	1.48460
$543$	28.9737	1.24338
$544$	18.0810	0.775215
$545$	−31.7831	−1.36144
$546$	9.80629	0.419670
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	−23.5485	−1.00594
$549$	19.3888	0.827495
$550$	−14.6352	−0.624046
$551$	0.473293	0.0201630
$552$	1.39083	0.0591977
$553$	−26.7316	−1.13675
$554$	−14.6131	−0.620851
$555$	−6.04727	−0.256692
$556$	−32.9985	−1.39945
$557$	20.2622	0.858535	0.429268	−	0.903177i	$-0.358772\pi$
$557$	20.2622	0.858535	0.429268	+	0.903177i	$0.358772\pi$
$558$	37.4336	1.58469
$559$	−4.97170	−0.210281
$560$	31.7650	1.34232
$561$	−5.08639	−0.214747
$562$	−56.2975	−2.37477
$563$	28.9996	1.22219	0.611093	−	0.791559i	$-0.290730\pi$
$563$	28.9996	1.22219	0.611093	+	0.791559i	$0.290730\pi$
$564$	35.8432	1.50927
$565$	36.6865	1.54341
$566$	8.05490	0.338573
$567$	−25.1622	−1.05671
$568$	−0.108100	−0.00453577
$569$	−19.8095	−0.830458	−0.415229	−	0.909717i	$-0.636299\pi$
$569$	−19.8095	−0.830458	−0.415229	+	0.909717i	$0.636299\pi$
$570$	28.9111	1.21095
$571$	−20.9861	−0.878240	−0.439120	−	0.898428i	$-0.644710\pi$
$571$	−20.9861	−0.878240	−0.439120	+	0.898428i	$0.644710\pi$
$572$	1.90295	0.0795665
$573$	−56.2062	−2.34805
$574$	42.0908	1.75683
$575$	55.3740	2.30926
$576$	−17.5651	−0.731879
$577$	−37.8828	−1.57708	−0.788541	−	0.614982i	$-0.789163\pi$
$577$	−37.8828	−1.57708	−0.788541	+	0.614982i	$0.789163\pi$
$578$	23.9971	0.998147
$579$	−18.5504	−0.770929
$580$	1.86407	0.0774015
$581$	−7.43176	−0.308321
$582$	15.7007	0.650814
$583$	6.46060	0.267571
$584$	0.266015	0.0110078
$585$	−6.90181	−0.285355
$586$	50.5698	2.08902
$587$	−29.8032	−1.23011	−0.615055	−	0.788484i	$-0.710866\pi$
$587$	−29.8032	−1.23011	−0.615055	+	0.788484i	$0.710866\pi$
$588$	7.59942	0.313395
$589$	16.0113	0.659734
$590$	104.363	4.29657
$591$	−21.7956	−0.896551
$592$	2.99033	0.122902
$593$	−37.2265	−1.52871	−0.764355	−	0.644796i	$-0.776942\pi$
$593$	−37.2265	−1.52871	−0.764355	+	0.644796i	$0.776942\pi$
$594$	−4.03756	−0.165663
$595$	−18.2402	−0.747776
$596$	35.8399	1.46806
$597$	−22.4374	−0.918300
$598$	−14.2581	−0.583057
$599$	28.4562	1.16269	0.581345	−	0.813657i	$-0.302527\pi$
$599$	28.4562	1.16269	0.581345	+	0.813657i	$0.302527\pi$
$600$	1.33155	0.0543602
$601$	−10.1810	−0.415291	−0.207646	−	0.978204i	$-0.566580\pi$
$601$	−10.1810	−0.415291	−0.207646	+	0.978204i	$0.566580\pi$
$602$	24.7880	1.01028
$603$	−10.2635	−0.417962
$604$	43.1099	1.75412
$605$	−3.50443	−0.142475
$606$	−10.0700	−0.409066
$607$	−18.1655	−0.737316	−0.368658	−	0.929565i	$-0.620183\pi$
$607$	−18.1655	−0.737316	−0.368658	+	0.929565i	$0.620183\pi$
$608$	−14.5900	−0.591702
$609$	1.36370	0.0552598
$610$	64.6807	2.61884
$611$	−7.24763	−0.293208
$612$	9.69201	0.391776
$613$	10.9672	0.442961	0.221480	−	0.975165i	$-0.428911\pi$
$613$	10.9672	0.442961	0.221480	+	0.975165i	$0.428911\pi$
$614$	64.7895	2.61469
$615$	−71.7130	−2.89175
$616$	−0.187140	−0.00754007
$617$	−33.4979	−1.34858	−0.674288	−	0.738469i	$-0.735549\pi$
$617$	−33.4979	−1.34858	−0.674288	+	0.738469i	$0.735549\pi$
$618$	17.8271	0.717111
$619$	−26.8222	−1.07808	−0.539038	−	0.842282i	$-0.681212\pi$
$619$	−26.8222	−1.07808	−0.539038	+	0.842282i	$0.681212\pi$
$620$	63.0608	2.53258
$621$	15.2766	0.613030
$622$	−2.69437	−0.108035
$623$	−22.5779	−0.904566
$624$	8.26181	0.330737
$625$	−8.39153	−0.335661
$626$	−54.7237	−2.18720
$627$	4.10433	0.163911
$628$	41.6558	1.66225
$629$	−1.71712	−0.0684659
$630$	34.4111	1.37097
$631$	−37.7397	−1.50239	−0.751196	−	0.660079i	$-0.770523\pi$
$631$	−37.7397	−1.50239	−0.751196	+	0.660079i	$0.770523\pi$
$632$	0.934617	0.0371771
$633$	−10.7443	−0.427047
$634$	57.4987	2.28357
$635$	−15.0024	−0.595350
$636$	−29.8010	−1.18169
$637$	−1.53663	−0.0608835
$638$	0.524043	0.0207471
$639$	2.82187	0.111631
$640$	−2.26729	−0.0896224
$641$	−15.7515	−0.622146	−0.311073	−	0.950386i	$-0.600688\pi$
$641$	−15.7515	−0.622146	−0.311073	+	0.950386i	$0.600688\pi$
$642$	8.07424	0.318665
$643$	13.4623	0.530903	0.265451	−	0.964124i	$-0.414479\pi$
$643$	13.4623	0.530903	0.265451	+	0.964124i	$0.414479\pi$
$644$	35.8982	1.41459
$645$	−42.2330	−1.66292
$646$	8.20926	0.322989
$647$	−39.5673	−1.55555	−0.777776	−	0.628541i	$-0.783652\pi$
$647$	−39.5673	−1.55555	−0.777776	+	0.628541i	$0.783652\pi$
$648$	0.879745	0.0345597
$649$	14.8158	0.581572
$650$	−13.6504	−0.535411
$651$	46.1333	1.80811
$652$	−40.1633	−1.57292
$653$	−33.8280	−1.32379	−0.661895	−	0.749596i	$-0.730248\pi$
$653$	−33.8280	−1.32379	−0.661895	+	0.749596i	$0.730248\pi$
$654$	41.2152	1.61164
$655$	−80.1796	−3.13288
$656$	35.4615	1.38454
$657$	−6.94414	−0.270917
$658$	36.1353	1.40870
$659$	29.7582	1.15922	0.579608	−	0.814896i	$-0.303206\pi$
$659$	29.7582	1.15922	0.579608	+	0.814896i	$0.303206\pi$
$660$	16.1650	0.629221
$661$	33.7638	1.31326	0.656630	−	0.754213i	$-0.271981\pi$
$661$	33.7638	1.31326	0.656630	+	0.754213i	$0.271981\pi$
$662$	−28.4041	−1.10395
$663$	−4.74412	−0.184246
$664$	0.259836	0.0100836
$665$	14.7185	0.570759
$666$	3.23942	0.125525
$667$	−1.98278	−0.0767737
$668$	28.0681	1.08599
$669$	−55.8490	−2.15925
$670$	−34.2388	−1.32276
$671$	9.18233	0.354480
$672$	−42.0380	−1.62165
$673$	−5.13330	−0.197874	−0.0989372	−	0.995094i	$-0.531544\pi$
$673$	−5.13330	−0.197874	−0.0989372	+	0.995094i	$0.531544\pi$
$674$	−26.5828	−1.02393
$675$	14.6255	0.562934
$676$	−24.7482	−0.951856
$677$	−22.0451	−0.847260	−0.423630	−	0.905835i	$-0.639244\pi$
$677$	−22.0451	−0.847260	−0.423630	+	0.905835i	$0.639244\pi$
$678$	−47.5738	−1.82706
$679$	7.99314	0.306749
$680$	0.637732	0.0244559
$681$	−19.0408	−0.729643
$682$	17.7282	0.678846
$683$	−26.6671	−1.02039	−0.510194	−	0.860060i	$-0.670426\pi$
$683$	−26.6671	−1.02039	−0.510194	+	0.860060i	$0.670426\pi$
$684$	−7.82073	−0.299033
$685$	40.4482	1.54544
$686$	40.2136	1.53536
$687$	49.5750	1.89140
$688$	20.8839	0.796191
$689$	6.02587	0.229567
$690$	−121.118	−4.61089
$691$	−0.838822	−0.0319103	−0.0159551	−	0.999873i	$-0.505079\pi$
$691$	−0.838822	−0.0319103	−0.0159551	+	0.999873i	$0.505079\pi$
$692$	−1.61846	−0.0615247
$693$	4.88514	0.185571
$694$	−46.8851	−1.77973
$695$	56.6800	2.15000
$696$	−0.0476789	−0.00180726
$697$	−20.3628	−0.771297
$698$	−51.8092	−1.96101
$699$	−13.1611	−0.497798
$700$	34.3680	1.29899
$701$	7.29645	0.275583	0.137792	−	0.990461i	$-0.456000\pi$
$701$	7.29645	0.275583	0.137792	+	0.990461i	$0.456000\pi$
$702$	−3.76587	−0.142134
$703$	1.38558	0.0522582
$704$	−8.31863	−0.313520
$705$	−61.5663	−2.31872
$706$	24.7189	0.930307
$707$	−5.12660	−0.192805
$708$	−68.3413	−2.56842
$709$	−1.90352	−0.0714881	−0.0357441	−	0.999361i	$-0.511380\pi$
$709$	−1.90352	−0.0714881	−0.0357441	+	0.999361i	$0.511380\pi$
$710$	9.41370	0.353290
$711$	−24.3975	−0.914978
$712$	0.789392	0.0295837
$713$	−67.0767	−2.51204
$714$	23.6533	0.885203
$715$	−3.26862	−0.122239
$716$	−1.66147	−0.0620920
$717$	−7.53836	−0.281525
$718$	−43.2610	−1.61449
$719$	38.5890	1.43913	0.719564	−	0.694426i	$-0.244342\pi$
$719$	38.5890	1.43913	0.719564	+	0.694426i	$0.244342\pi$
$720$	28.9914	1.08045
$721$	9.07569	0.337996
$722$	31.5664	1.17478
$723$	58.3173	2.16884
$724$	−26.1462	−0.971718
$725$	−1.89827	−0.0704999
$726$	4.54443	0.168660
$727$	−13.8078	−0.512104	−0.256052	−	0.966663i	$-0.582422\pi$
$727$	−13.8078	−0.512104	−0.256052	+	0.966663i	$0.582422\pi$
$728$	−0.174547	−0.00646914
$729$	−9.34087	−0.345958
$730$	−23.1655	−0.857393
$731$	−11.9920	−0.443541
$732$	−42.3556	−1.56551
$733$	1.29045	0.0476640	0.0238320	−	0.999716i	$-0.492413\pi$
$733$	1.29045	0.0476640	0.0238320	+	0.999716i	$0.492413\pi$
$734$	9.14788	0.337654
$735$	−13.0532	−0.481474
$736$	61.1223	2.25300
$737$	−4.86067	−0.179045
$738$	38.4155	1.41409
$739$	−23.9818	−0.882184	−0.441092	−	0.897462i	$-0.645409\pi$
$739$	−23.9818	−0.882184	−0.441092	+	0.897462i	$0.645409\pi$
$740$	5.45714	0.200609
$741$	3.82815	0.140631
$742$	−30.0438	−1.10294
$743$	−11.1566	−0.409297	−0.204648	−	0.978836i	$-0.565605\pi$
$743$	−11.1566	−0.409297	−0.204648	+	0.978836i	$0.565605\pi$
$744$	−1.61296	−0.0591338
$745$	−61.5607	−2.25541
$746$	6.40440	0.234482
$747$	−6.78284	−0.248171
$748$	4.59003	0.167828
$749$	4.11056	0.150197
$750$	−36.3273	−1.32648
$751$	−44.7928	−1.63451	−0.817257	−	0.576274i	$-0.804506\pi$
$751$	−44.7928	−1.63451	−0.817257	+	0.576274i	$0.804506\pi$
$752$	30.4440	1.11018
$753$	39.5397	1.44091
$754$	0.488780	0.0178003
$755$	−74.0480	−2.69488
$756$	9.48148	0.344838
$757$	4.87549	0.177203	0.0886013	−	0.996067i	$-0.471760\pi$
$757$	4.87549	0.177203	0.0886013	+	0.996067i	$0.471760\pi$
$758$	66.6502	2.42084
$759$	−17.1944	−0.624118
$760$	−0.514602	−0.0186666
$761$	19.3458	0.701283	0.350642	−	0.936510i	$-0.385964\pi$
$761$	19.3458	0.701283	0.350642	+	0.936510i	$0.385964\pi$
$762$	19.4545	0.704764
$763$	20.9825	0.759617
$764$	50.7213	1.83503
$765$	−16.6475	−0.601893
$766$	16.5550	0.598155
$767$	13.8189	0.498970
$768$	−34.6746	−1.25121
$769$	33.5037	1.20817	0.604087	−	0.796918i	$-0.293538\pi$
$769$	33.5037	1.20817	0.604087	+	0.796918i	$0.293538\pi$
$770$	16.2967	0.587293
$771$	34.3688	1.23776
$772$	16.7402	0.602491
$773$	−16.0251	−0.576384	−0.288192	−	0.957573i	$-0.593054\pi$
$773$	−16.0251	−0.576384	−0.288192	+	0.957573i	$0.593054\pi$
$774$	22.6235	0.813187
$775$	−64.2176	−2.30676
$776$	−0.279464	−0.0100322
$777$	3.99227	0.143222
$778$	11.5617	0.414508
$779$	16.4313	0.588711
$780$	15.0772	0.539852
$781$	1.33641	0.0478204
$782$	−34.3913	−1.22983
$783$	−0.523696	−0.0187154
$784$	6.45469	0.230525
$785$	−71.5503	−2.55374
$786$	103.974	3.70864
$787$	36.8159	1.31235	0.656173	−	0.754610i	$-0.272174\pi$
$787$	36.8159	1.31235	0.656173	+	0.754610i	$0.272174\pi$
$788$	19.6687	0.700667
$789$	17.2356	0.613603
$790$	−81.3895	−2.89571
$791$	−24.2196	−0.861151
$792$	−0.170799	−0.00606908
$793$	8.56445	0.304132
$794$	33.7429	1.19749
$795$	51.1878	1.81544
$796$	20.2478	0.717664
$797$	−48.2904	−1.71053	−0.855266	−	0.518189i	$-0.826606\pi$
$797$	−48.2904	−1.71053	−0.855266	+	0.518189i	$0.826606\pi$
$798$	−19.0864	−0.675653
$799$	−17.4817	−0.618457
$800$	58.5170	2.06889
$801$	−20.6065	−0.728095
$802$	−65.8072	−2.32373
$803$	−3.28867	−0.116055
$804$	22.4209	0.790726
$805$	−61.6607	−2.17325
$806$	16.5352	0.582428
$807$	−38.8434	−1.36735
$808$	0.179241	0.00630567
$809$	34.5397	1.21435	0.607175	−	0.794568i	$-0.292303\pi$
$809$	34.5397	1.21435	0.607175	+	0.794568i	$0.292303\pi$
$810$	−76.6111	−2.69184
$811$	−50.5894	−1.77643	−0.888217	−	0.459424i	$-0.848056\pi$
$811$	−50.5894	−1.77643	−0.888217	+	0.459424i	$0.848056\pi$
$812$	−1.23062	−0.0431863
$813$	38.8759	1.36344
$814$	1.53416	0.0537721
$815$	68.9868	2.41650
$816$	19.9279	0.697617
$817$	9.67666	0.338543
$818$	64.6324	2.25982
$819$	4.55642	0.159214
$820$	64.7148	2.25994
$821$	−41.1509	−1.43618	−0.718088	−	0.695952i	$-0.754982\pi$
$821$	−41.1509	−1.43618	−0.718088	+	0.695952i	$0.754982\pi$
$822$	−52.4518	−1.82947
$823$	22.8544	0.796653	0.398326	−	0.917244i	$-0.369591\pi$
$823$	22.8544	0.796653	0.398326	+	0.917244i	$0.369591\pi$
$824$	−0.317313	−0.0110541
$825$	−16.4615	−0.573117
$826$	−68.8983	−2.39728
$827$	31.1659	1.08374	0.541872	−	0.840461i	$-0.317716\pi$
$827$	31.1659	1.08374	0.541872	+	0.840461i	$0.317716\pi$
$828$	32.7636	1.13861
$829$	33.9754	1.18001	0.590006	−	0.807399i	$-0.299125\pi$
$829$	33.9754	1.18001	0.590006	+	0.807399i	$0.299125\pi$
$830$	−22.6274	−0.785408
$831$	−16.4367	−0.570182
$832$	−7.75887	−0.268990
$833$	−3.70644	−0.128420
$834$	−73.5007	−2.54512
$835$	−48.2114	−1.66842
$836$	−3.70381	−0.128099
$837$	−17.7164	−0.612368
$838$	−0.0698719	−0.00241368
$839$	−35.8235	−1.23677	−0.618383	−	0.785877i	$-0.712212\pi$
$839$	−35.8235	−1.23677	−0.618383	+	0.785877i	$0.712212\pi$
$840$	−1.48272	−0.0511587
$841$	−28.9320	−0.997656
$842$	14.5467	0.501311
$843$	−63.3230	−2.18096
$844$	9.69580	0.333743
$845$	42.5090	1.46235
$846$	32.9801	1.13388
$847$	2.31355	0.0794945
$848$	−25.3120	−0.869217
$849$	9.06008	0.310941
$850$	−32.9254	−1.12933
$851$	−5.80467	−0.198981
$852$	−6.16448	−0.211191
$853$	33.4260	1.14448	0.572242	−	0.820085i	$-0.306074\pi$
$853$	33.4260	1.14448	0.572242	+	0.820085i	$0.306074\pi$
$854$	−42.7007	−1.46119
$855$	13.4333	0.459410
$856$	−0.143717	−0.00491215
$857$	30.5860	1.04480	0.522400	−	0.852701i	$-0.325037\pi$
$857$	30.5860	1.04480	0.522400	+	0.852701i	$0.325037\pi$
$858$	4.23863	0.144705
$859$	49.5233	1.68971	0.844856	−	0.534994i	$-0.179686\pi$
$859$	49.5233	1.68971	0.844856	+	0.534994i	$0.179686\pi$
$860$	38.1117	1.29960
$861$	47.3433	1.61346
$862$	−1.02271	−0.0348337
$863$	18.0332	0.613856	0.306928	−	0.951733i	$-0.400699\pi$
$863$	18.0332	0.613856	0.306928	+	0.951733i	$0.400699\pi$
$864$	16.1437	0.549220
$865$	2.77996	0.0945215
$866$	6.68212	0.227068
$867$	26.9917	0.916687
$868$	−41.6313	−1.41306
$869$	−11.5544	−0.391956
$870$	4.15203	0.140767
$871$	−4.53360	−0.153615
$872$	−0.733609	−0.0248431
$873$	7.29520	0.246905
$874$	27.7512	0.938699
$875$	−18.4940	−0.625213
$876$	15.1697	0.512537
$877$	43.1678	1.45767	0.728836	−	0.684689i	$-0.240062\pi$
$877$	43.1678	1.45767	0.728836	+	0.684689i	$0.240062\pi$
$878$	−40.4293	−1.36442
$879$	56.8804	1.91853
$880$	13.7300	0.462838
$881$	−4.14944	−0.139798	−0.0698991	−	0.997554i	$-0.522268\pi$
$881$	−4.14944	−0.139798	−0.0698991	+	0.997554i	$0.522268\pi$
$882$	6.99238	0.235446
$883$	−36.2827	−1.22101	−0.610505	−	0.792013i	$-0.709033\pi$
$883$	−36.2827	−1.22101	−0.610505	+	0.792013i	$0.709033\pi$
$884$	4.28116	0.143991
$885$	117.387	3.94592
$886$	−37.1611	−1.24845
$887$	−31.6444	−1.06252	−0.531258	−	0.847210i	$-0.678280\pi$
$887$	−31.6444	−1.06252	−0.531258	+	0.847210i	$0.678280\pi$
$888$	−0.139582	−0.00468405
$889$	9.90422	0.332177
$890$	−68.7428	−2.30426
$891$	−10.8760	−0.364360
$892$	50.3989	1.68748
$893$	14.1064	0.472053
$894$	79.8298	2.66991
$895$	2.85383	0.0953931
$896$	1.49681	0.0500050
$897$	−16.0374	−0.535473
$898$	−13.9831	−0.466622
$899$	2.29945	0.0766908
$900$	31.3671	1.04557
$901$	14.5347	0.484222
$902$	18.1932	0.605766
$903$	27.8813	0.927831
$904$	0.846789	0.0281638
$905$	44.9102	1.49287
$906$	96.0229	3.19015
$907$	27.4863	0.912667	0.456333	−	0.889809i	$-0.349162\pi$
$907$	27.4863	0.912667	0.456333	+	0.889809i	$0.349162\pi$
$908$	17.1827	0.570226
$909$	−4.67895	−0.155191
$910$	15.2001	0.503879
$911$	16.3125	0.540456	0.270228	−	0.962796i	$-0.412901\pi$
$911$	16.3125	0.540456	0.270228	+	0.962796i	$0.412901\pi$
$912$	−16.0803	−0.532473
$913$	−3.21228	−0.106311
$914$	−24.7456	−0.818512
$915$	72.7523	2.40512
$916$	−44.7372	−1.47816
$917$	52.9328	1.74800
$918$	−9.08349	−0.299800
$919$	19.2632	0.635434	0.317717	−	0.948186i	$-0.397084\pi$
$919$	19.2632	0.635434	0.317717	+	0.948186i	$0.397084\pi$
$920$	2.15584	0.0710759
$921$	72.8746	2.40130
$922$	−10.0489	−0.330942
$923$	1.24648	0.0410284
$924$	−10.6718	−0.351075
$925$	−5.55725	−0.182721
$926$	48.3161	1.58777
$927$	8.28323	0.272057
$928$	−2.09533	−0.0687824
$929$	41.7821	1.37083	0.685413	−	0.728155i	$-0.259622\pi$
$929$	41.7821	1.37083	0.685413	+	0.728155i	$0.259622\pi$
$930$	140.461	4.60591
$931$	2.99082	0.0980200
$932$	11.8768	0.389036
$933$	−3.03061	−0.0992177
$934$	−16.5011	−0.539933
$935$	−7.88409	−0.257837
$936$	−0.159306	−0.00520708
$937$	−13.3650	−0.436615	−0.218307	−	0.975880i	$-0.570054\pi$
$937$	−13.3650	−0.436615	−0.218307	+	0.975880i	$0.570054\pi$
$938$	22.6037	0.738036
$939$	−61.5527	−2.00870
$940$	55.5583	1.81211
$941$	−46.6373	−1.52033	−0.760166	−	0.649728i	$-0.774883\pi$
$941$	−46.6373	−1.52033	−0.760166	+	0.649728i	$0.774883\pi$
$942$	92.7839	3.02306
$943$	−68.8361	−2.24161
$944$	−58.0469	−1.88927
$945$	−16.2859	−0.529781
$946$	10.7143	0.348351
$947$	−17.9205	−0.582337	−0.291168	−	0.956672i	$-0.594044\pi$
$947$	−17.9205	−0.582337	−0.291168	+	0.956672i	$0.594044\pi$
$948$	53.2972	1.73101
$949$	−3.06737	−0.0995711
$950$	26.5684	0.861991
$951$	64.6741	2.09720
$952$	−0.421017	−0.0136452
$953$	5.00763	0.162213	0.0811066	−	0.996705i	$-0.474155\pi$
$953$	5.00763	0.162213	0.0811066	+	0.996705i	$0.474155\pi$
$954$	−27.4205	−0.887771
$955$	−87.1217	−2.81919
$956$	6.80272	0.220016
$957$	0.589440	0.0190539
$958$	37.4220	1.20905
$959$	−26.7030	−0.862284
$960$	−65.9091	−2.12721
$961$	46.7892	1.50933
$962$	1.43092	0.0461348
$963$	3.75163	0.120895
$964$	−52.6264	−1.69498
$965$	−28.7538	−0.925618
$966$	79.9595	2.57265
$967$	42.0730	1.35298	0.676489	−	0.736453i	$-0.263501\pi$
$967$	42.0730	1.35298	0.676489	+	0.736453i	$0.263501\pi$
$968$	−0.0808885	−0.00259986
$969$	9.23371	0.296630
$970$	24.3366	0.781402
$971$	23.2678	0.746699	0.373350	−	0.927691i	$-0.378209\pi$
$971$	23.2678	0.746699	0.373350	+	0.927691i	$0.378209\pi$
$972$	37.8734	1.21479
$973$	−37.4189	−1.19959
$974$	8.80046	0.281985
$975$	−15.3538	−0.491716
$976$	−35.9754	−1.15154
$977$	11.3184	0.362106	0.181053	−	0.983473i	$-0.442049\pi$
$977$	11.3184	0.362106	0.181053	+	0.983473i	$0.442049\pi$
$978$	−89.4597	−2.86061
$979$	−9.75901	−0.311899
$980$	11.7794	0.376278
$981$	19.1503	0.611423
$982$	3.45260	0.110177
$983$	8.38506	0.267442	0.133721	−	0.991019i	$-0.457307\pi$
$983$	8.38506	0.267442	0.133721	+	0.991019i	$0.457307\pi$
$984$	−1.65526	−0.0527678
$985$	−33.7840	−1.07645
$986$	1.17897	0.0375459
$987$	40.6447	1.29373
$988$	−3.45458	−0.109905
$989$	−40.5387	−1.28906
$990$	14.8737	0.472718
$991$	8.82781	0.280425	0.140212	−	0.990121i	$-0.455221\pi$
$991$	8.82781	0.280425	0.140212	+	0.990121i	$0.455221\pi$
$992$	−70.8839	−2.25057
$993$	−31.9486	−1.01386
$994$	−6.21471	−0.197119
$995$	−34.7787	−1.10256
$996$	14.8174	0.469506
$997$	−6.93005	−0.219477	−0.109738	−	0.993961i	$-0.535001\pi$
$997$	−6.93005	−0.219477	−0.109738	+	0.993961i	$0.535001\pi$
$998$	−47.5035	−1.50370
$999$	−1.53314	−0.0485063

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.c.1.19	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.c.1.19	✓	106	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)

\(f(q)\)	\(=\)	\(q-2.01004 q^{2} -2.26087 q^{3} +2.04024 q^{4} -3.50443 q^{5} +4.54443 q^{6} +2.31355 q^{7} -0.0808885 q^{8} +2.11154 q^{9} +O(q^{10})\)	\(q-2.01004 q^{2} -2.26087 q^{3} +2.04024 q^{4} -3.50443 q^{5} +4.54443 q^{6} +2.31355 q^{7} -0.0808885 q^{8} +2.11154 q^{9} +7.04404 q^{10} +1.00000 q^{11} -4.61272 q^{12} +0.932710 q^{13} -4.65032 q^{14} +7.92307 q^{15} -3.91790 q^{16} +2.24975 q^{17} -4.24426 q^{18} -1.81538 q^{19} -7.14989 q^{20} -5.23064 q^{21} -2.01004 q^{22} +7.60522 q^{23} +0.182878 q^{24} +7.28105 q^{25} -1.87478 q^{26} +2.00870 q^{27} +4.72020 q^{28} -0.260714 q^{29} -15.9257 q^{30} -8.81982 q^{31} +8.03689 q^{32} -2.26087 q^{33} -4.52207 q^{34} -8.10768 q^{35} +4.30805 q^{36} -0.763248 q^{37} +3.64897 q^{38} -2.10874 q^{39} +0.283468 q^{40} -9.05116 q^{41} +10.5138 q^{42} -5.33038 q^{43} +2.04024 q^{44} -7.39974 q^{45} -15.2868 q^{46} -7.77051 q^{47} +8.85786 q^{48} -1.64749 q^{49} -14.6352 q^{50} -5.08639 q^{51} +1.90295 q^{52} +6.46060 q^{53} -4.03756 q^{54} -3.50443 q^{55} -0.187140 q^{56} +4.10433 q^{57} +0.524043 q^{58} +14.8158 q^{59} +16.1650 q^{60} +9.18233 q^{61} +17.7282 q^{62} +4.88514 q^{63} -8.31863 q^{64} -3.26862 q^{65} +4.54443 q^{66} -4.86067 q^{67} +4.59003 q^{68} -17.1944 q^{69} +16.2967 q^{70} +1.33641 q^{71} -0.170799 q^{72} -3.28867 q^{73} +1.53416 q^{74} -16.4615 q^{75} -3.70381 q^{76} +2.31355 q^{77} +4.23863 q^{78} -11.5544 q^{79} +13.7300 q^{80} -10.8760 q^{81} +18.1932 q^{82} -3.21228 q^{83} -10.6718 q^{84} -7.88409 q^{85} +10.7143 q^{86} +0.589440 q^{87} -0.0808885 q^{88} -9.75901 q^{89} +14.8737 q^{90} +2.15787 q^{91} +15.5165 q^{92} +19.9405 q^{93} +15.6190 q^{94} +6.36187 q^{95} -18.1704 q^{96} +3.45493 q^{97} +3.31151 q^{98} +2.11154 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * q^99

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