LMFDB - Embedded newform 6017.2.a.d.1.20

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:	$107$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q-1.94021 q^{2} -0.488619 q^{3} +1.76440 q^{4} -3.27450 q^{5} +0.948022 q^{6} -5.11134 q^{7} +0.457109 q^{8} -2.76125 q^{9} +O(q^{10})$	\(q-1.94021 q^{2} -0.488619 q^{3} +1.76440 q^{4} -3.27450 q^{5} +0.948022 q^{6} -5.11134 q^{7} +0.457109 q^{8} -2.76125 q^{9} +6.35321 q^{10} -1.00000 q^{11} -0.862121 q^{12} -1.65002 q^{13} +9.91706 q^{14} +1.59999 q^{15} -4.41569 q^{16} -0.361675 q^{17} +5.35740 q^{18} -6.51406 q^{19} -5.77754 q^{20} +2.49750 q^{21} +1.94021 q^{22} -3.28334 q^{23} -0.223352 q^{24} +5.72237 q^{25} +3.20137 q^{26} +2.81506 q^{27} -9.01846 q^{28} -3.07969 q^{29} -3.10430 q^{30} -0.108979 q^{31} +7.65313 q^{32} +0.488619 q^{33} +0.701725 q^{34} +16.7371 q^{35} -4.87196 q^{36} +6.91812 q^{37} +12.6386 q^{38} +0.806230 q^{39} -1.49680 q^{40} +2.36210 q^{41} -4.84567 q^{42} +10.3157 q^{43} -1.76440 q^{44} +9.04172 q^{45} +6.37035 q^{46} -9.06923 q^{47} +2.15759 q^{48} +19.1258 q^{49} -11.1026 q^{50} +0.176722 q^{51} -2.91129 q^{52} -7.86751 q^{53} -5.46180 q^{54} +3.27450 q^{55} -2.33644 q^{56} +3.18290 q^{57} +5.97523 q^{58} +2.89724 q^{59} +2.82302 q^{60} -4.56108 q^{61} +0.211442 q^{62} +14.1137 q^{63} -6.01728 q^{64} +5.40298 q^{65} -0.948022 q^{66} -6.48900 q^{67} -0.638141 q^{68} +1.60430 q^{69} -32.4734 q^{70} -7.54573 q^{71} -1.26219 q^{72} +9.77411 q^{73} -13.4226 q^{74} -2.79606 q^{75} -11.4934 q^{76} +5.11134 q^{77} -1.56425 q^{78} -9.18891 q^{79} +14.4592 q^{80} +6.90826 q^{81} -4.58297 q^{82} -5.65099 q^{83} +4.40660 q^{84} +1.18431 q^{85} -20.0146 q^{86} +1.50480 q^{87} -0.457109 q^{88} +7.82643 q^{89} -17.5428 q^{90} +8.43380 q^{91} -5.79313 q^{92} +0.0532493 q^{93} +17.5962 q^{94} +21.3303 q^{95} -3.73947 q^{96} +1.34946 q^{97} -37.1081 q^{98} +2.76125 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) $ 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9 - 14 * q^10 - 107 * q^11 - 50 * q^12 - 24 * q^13 - 17 * q^14 - 47 * q^15 + 63 * q^16 + 25 * q^17 - 37 * q^18 - 55 * q^19 - 31 * q^20 + 15 * q^21 + 3 * q^22 - 38 * q^23 + 4 * q^24 + 62 * q^25 - 16 * q^26 - 57 * q^27 - 101 * q^28 + 27 * q^29 - 14 * q^30 - 112 * q^31 - 4 * q^32 + 18 * q^33 - 66 * q^34 + 8 * q^35 + 35 * q^36 - 60 * q^37 - 45 * q^38 - 58 * q^39 - 50 * q^40 - 14 * q^41 - 36 * q^42 - 78 * q^43 - 91 * q^44 - 68 * q^45 - 18 * q^46 - 109 * q^47 - 99 * q^48 + 61 * q^49 - 32 * q^50 - 10 * q^51 - 111 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 44 * q^56 + q^57 - 98 * q^58 - 48 * q^59 - 119 * q^60 - 30 * q^61 + 32 * q^62 - 126 * q^63 + 3 * q^64 + 43 * q^65 - 77 * q^67 + 53 * q^68 - 51 * q^69 - 87 * q^70 - 40 * q^71 - 82 * q^72 - 83 * q^73 + 11 * q^74 - 69 * q^75 - 108 * q^76 + 54 * q^77 - 53 * q^78 - 66 * q^79 - 96 * q^80 + 51 * q^81 - 133 * q^82 - 32 * q^83 + 27 * q^84 - 66 * q^85 - 46 * q^86 - 136 * q^87 + 3 * q^88 - 56 * q^89 + 9 * q^90 - 86 * q^91 - 94 * q^92 - 33 * q^93 - 93 * q^94 - 25 * q^95 - 4 * q^96 - 109 * q^97 - 38 * q^98 - 95 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.94021	−1.37193	−0.685967	−	0.727633i	$-0.740620\pi$
$2$	−1.94021	−1.37193	−0.685967	+	0.727633i	$0.740620\pi$
$3$	−0.488619	−0.282104	−0.141052	−	0.990002i	$-0.545049\pi$
$3$	−0.488619	−0.282104	−0.141052	+	0.990002i	$0.545049\pi$
$4$	1.76440	0.882201
$5$	−3.27450	−1.46440	−0.732201	−	0.681089i	$-0.761507\pi$
$5$	−3.27450	−1.46440	−0.732201	+	0.681089i	$0.761507\pi$
$6$	0.948022	0.387029
$7$	−5.11134	−1.93191	−0.965953	−	0.258717i	$-0.916700\pi$
$7$	−5.11134	−1.93191	−0.965953	+	0.258717i	$0.916700\pi$
$8$	0.457109	0.161612
$9$	−2.76125	−0.920417
$10$	6.35321	2.00906
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.862121	−0.248873
$13$	−1.65002	−0.457632	−0.228816	−	0.973470i	$-0.573485\pi$
$13$	−1.65002	−0.457632	−0.228816	+	0.973470i	$0.573485\pi$
$14$	9.91706	2.65045
$15$	1.59999	0.413114
$16$	−4.41569	−1.10392
$17$	−0.361675	−0.0877191	−0.0438596	−	0.999038i	$-0.513965\pi$
$17$	−0.361675	−0.0877191	−0.0438596	+	0.999038i	$0.513965\pi$
$18$	5.35740	1.26275
$19$	−6.51406	−1.49443	−0.747214	−	0.664584i	$-0.768609\pi$
$19$	−6.51406	−1.49443	−0.747214	+	0.664584i	$0.768609\pi$
$20$	−5.77754	−1.29190
$21$	2.49750	0.544999
$22$	1.94021	0.413653
$23$	−3.28334	−0.684623	−0.342312	−	0.939586i	$-0.611210\pi$
$23$	−3.28334	−0.684623	−0.342312	+	0.939586i	$0.611210\pi$
$24$	−0.223352	−0.0455916
$25$	5.72237	1.14447
$26$	3.20137	0.627841
$27$	2.81506	0.541758
$28$	−9.01846	−1.70433
$29$	−3.07969	−0.571884	−0.285942	−	0.958247i	$-0.592306\pi$
$29$	−3.07969	−0.571884	−0.285942	+	0.958247i	$0.592306\pi$
$30$	−3.10430	−0.566765
$31$	−0.108979	−0.0195732	−0.00978661	−	0.999952i	$-0.503115\pi$
$31$	−0.108979	−0.0195732	−0.00978661	+	0.999952i	$0.503115\pi$
$32$	7.65313	1.35290
$33$	0.488619	0.0850577
$34$	0.701725	0.120345
$35$	16.7371	2.82909
$36$	−4.87196	−0.811993
$37$	6.91812	1.13733	0.568666	−	0.822568i	$-0.307460\pi$
$37$	6.91812	1.13733	0.568666	+	0.822568i	$0.307460\pi$
$38$	12.6386	2.05026
$39$	0.806230	0.129100
$40$	−1.49680	−0.236666
$41$	2.36210	0.368898	0.184449	−	0.982842i	$-0.440950\pi$
$41$	2.36210	0.368898	0.184449	+	0.982842i	$0.440950\pi$
$42$	−4.84567	−0.747703
$43$	10.3157	1.57313	0.786565	−	0.617508i	$-0.211858\pi$
$43$	10.3157	1.57313	0.786565	+	0.617508i	$0.211858\pi$
$44$	−1.76440	−0.265994
$45$	9.04172	1.34786
$46$	6.37035	0.939258
$47$	−9.06923	−1.32288	−0.661442	−	0.749997i	$-0.730055\pi$
$47$	−9.06923	−1.32288	−0.661442	+	0.749997i	$0.730055\pi$
$48$	2.15759	0.311421
$49$	19.1258	2.73226
$50$	−11.1026	−1.57014
$51$	0.176722	0.0247460
$52$	−2.91129	−0.403723
$53$	−7.86751	−1.08069	−0.540343	−	0.841445i	$-0.681705\pi$
$53$	−7.86751	−1.08069	−0.540343	+	0.841445i	$0.681705\pi$
$54$	−5.46180	−0.743256
$55$	3.27450	0.441534
$56$	−2.33644	−0.312220
$57$	3.18290	0.421585
$58$	5.97523	0.784586
$59$	2.89724	0.377189	0.188594	−	0.982055i	$-0.439607\pi$
$59$	2.89724	0.377189	0.188594	+	0.982055i	$0.439607\pi$
$60$	2.82302	0.364450
$61$	−4.56108	−0.583987	−0.291993	−	0.956420i	$-0.594319\pi$
$61$	−4.56108	−0.583987	−0.291993	+	0.956420i	$0.594319\pi$
$62$	0.211442	0.0268532
$63$	14.1137	1.77816
$64$	−6.01728	−0.752160
$65$	5.40298	0.670157
$66$	−0.948022	−0.116693
$67$	−6.48900	−0.792758	−0.396379	−	0.918087i	$-0.629733\pi$
$67$	−6.48900	−0.792758	−0.396379	+	0.918087i	$0.629733\pi$
$68$	−0.638141	−0.0773859
$69$	1.60430	0.193135
$70$	−32.4734	−3.88132
$71$	−7.54573	−0.895514	−0.447757	−	0.894155i	$-0.647777\pi$
$71$	−7.54573	−0.895514	−0.447757	+	0.894155i	$0.647777\pi$
$72$	−1.26219	−0.148751
$73$	9.77411	1.14397	0.571986	−	0.820263i	$-0.306173\pi$
$73$	9.77411	1.14397	0.571986	+	0.820263i	$0.306173\pi$
$74$	−13.4226	−1.56034
$75$	−2.79606	−0.322861
$76$	−11.4934	−1.31839
$77$	5.11134	0.582492
$78$	−1.56425	−0.177117
$79$	−9.18891	−1.03383	−0.516916	−	0.856036i	$-0.672920\pi$
$79$	−9.18891	−1.03383	−0.516916	+	0.856036i	$0.672920\pi$
$80$	14.4592	1.61659
$81$	6.90826	0.767585
$82$	−4.58297	−0.506104
$83$	−5.65099	−0.620277	−0.310138	−	0.950691i	$-0.600375\pi$
$83$	−5.65099	−0.620277	−0.310138	+	0.950691i	$0.600375\pi$
$84$	4.40660	0.480799
$85$	1.18431	0.128456
$86$	−20.0146	−2.15823
$87$	1.50480	0.161331
$88$	−0.457109	−0.0487280
$89$	7.82643	0.829600	0.414800	−	0.909913i	$-0.363852\pi$
$89$	7.82643	0.829600	0.414800	+	0.909913i	$0.363852\pi$
$90$	−17.5428	−1.84917
$91$	8.43380	0.884102
$92$	−5.79313	−0.603975
$93$	0.0532493	0.00552169
$94$	17.5962	1.81491
$95$	21.3303	2.18844
$96$	−3.73947	−0.381658
$97$	1.34946	0.137017	0.0685085	−	0.997651i	$-0.478176\pi$
$97$	1.34946	0.137017	0.0685085	+	0.997651i	$0.478176\pi$
$98$	−37.1081	−3.74848
$99$	2.76125	0.277516
$100$	10.0966	1.00966
$101$	16.2351	1.61546	0.807728	−	0.589555i	$-0.200697\pi$
$101$	16.2351	1.61546	0.807728	+	0.589555i	$0.200697\pi$
$102$	−0.342876	−0.0339498
$103$	6.17465	0.608406	0.304203	−	0.952607i	$-0.401610\pi$
$103$	6.17465	0.608406	0.304203	+	0.952607i	$0.401610\pi$
$104$	−0.754237	−0.0739590
$105$	−8.17807	−0.798098
$106$	15.2646	1.48263
$107$	19.8620	1.92013	0.960065	−	0.279776i	$-0.0902603\pi$
$107$	19.8620	1.92013	0.960065	+	0.279776i	$0.0902603\pi$
$108$	4.96689	0.477940
$109$	−7.68956	−0.736526	−0.368263	−	0.929722i	$-0.620047\pi$
$109$	−7.68956	−0.736526	−0.368263	+	0.929722i	$0.620047\pi$
$110$	−6.35321	−0.605755
$111$	−3.38033	−0.320847
$112$	22.5701	2.13267
$113$	13.9204	1.30952	0.654762	−	0.755835i	$-0.272769\pi$
$113$	13.9204	1.30952	0.654762	+	0.755835i	$0.272769\pi$
$114$	−6.17548	−0.578386
$115$	10.7513	1.00256
$116$	−5.43381	−0.504516
$117$	4.55611	0.421212
$118$	−5.62124	−0.517478
$119$	1.84865	0.169465
$120$	0.731368	0.0667644
$121$	1.00000	0.0909091
$122$	8.84944	0.801191
$123$	−1.15417	−0.104068
$124$	−0.192283	−0.0172675
$125$	−2.36539	−0.211567
$126$	−27.3835	−2.43952
$127$	−17.7158	−1.57202	−0.786010	−	0.618213i	$-0.787857\pi$
$127$	−17.7158	−1.57202	−0.786010	+	0.618213i	$0.787857\pi$
$128$	−3.63150	−0.320982
$129$	−5.04045	−0.443787
$130$	−10.4829	−0.919411
$131$	20.3593	1.77880	0.889399	−	0.457132i	$-0.151123\pi$
$131$	20.3593	1.77880	0.889399	+	0.457132i	$0.151123\pi$
$132$	0.862121	0.0750380
$133$	33.2956	2.88709
$134$	12.5900	1.08761
$135$	−9.21792	−0.793352
$136$	−0.165325	−0.0141765
$137$	−5.39588	−0.461001	−0.230501	−	0.973072i	$-0.574036\pi$
$137$	−5.39588	−0.461001	−0.230501	+	0.973072i	$0.574036\pi$
$138$	−3.11268	−0.264969
$139$	−8.52650	−0.723208	−0.361604	−	0.932332i	$-0.617771\pi$
$139$	−8.52650	−0.723208	−0.361604	+	0.932332i	$0.617771\pi$
$140$	29.5310	2.49582
$141$	4.43140	0.373191
$142$	14.6403	1.22859
$143$	1.65002	0.137981
$144$	12.1928	1.01607
$145$	10.0844	0.837468
$146$	−18.9638	−1.56945
$147$	−9.34525	−0.770783
$148$	12.2063	1.00336
$149$	−9.43989	−0.773346	−0.386673	−	0.922217i	$-0.626376\pi$
$149$	−9.43989	−0.773346	−0.386673	+	0.922217i	$0.626376\pi$
$150$	5.42493	0.442944
$151$	13.0255	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$151$	13.0255	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$152$	−2.97763	−0.241518
$153$	0.998676	0.0807382
$154$	−9.91706	−0.799140
$155$	0.356852	0.0286631
$156$	1.42251	0.113892
$157$	−10.3279	−0.824253	−0.412126	−	0.911127i	$-0.635214\pi$
$157$	−10.3279	−0.824253	−0.412126	+	0.911127i	$0.635214\pi$
$158$	17.8284	1.41835
$159$	3.84422	0.304866
$160$	−25.0602	−1.98118
$161$	16.7823	1.32263
$162$	−13.4035	−1.05307
$163$	−23.3460	−1.82860	−0.914299	−	0.405039i	$-0.867258\pi$
$163$	−23.3460	−1.82860	−0.914299	+	0.405039i	$0.867258\pi$
$164$	4.16770	0.325443
$165$	−1.59999	−0.124559
$166$	10.9641	0.850978
$167$	−13.6832	−1.05884	−0.529418	−	0.848361i	$-0.677590\pi$
$167$	−13.6832	−1.05884	−0.529418	+	0.848361i	$0.677590\pi$
$168$	1.14163	0.0880787
$169$	−10.2774	−0.790573
$170$	−2.29780	−0.176233
$171$	17.9870	1.37550
$172$	18.2010	1.38782
$173$	−9.32965	−0.709320	−0.354660	−	0.934995i	$-0.615403\pi$
$173$	−9.32965	−0.709320	−0.354660	+	0.934995i	$0.615403\pi$
$174$	−2.91961	−0.221335
$175$	−29.2490	−2.21102
$176$	4.41569	0.332845
$177$	−1.41565	−0.106407
$178$	−15.1849	−1.13816
$179$	13.5365	1.01176	0.505882	−	0.862603i	$-0.331167\pi$
$179$	13.5365	1.01176	0.505882	+	0.862603i	$0.331167\pi$
$180$	15.9532	1.18908
$181$	1.52476	0.113335	0.0566674	−	0.998393i	$-0.481953\pi$
$181$	1.52476	0.113335	0.0566674	+	0.998393i	$0.481953\pi$
$182$	−16.3633	−1.21293
$183$	2.22863	0.164745
$184$	−1.50084	−0.110644
$185$	−22.6534	−1.66551
$186$	−0.103315	−0.00757540
$187$	0.361675	0.0264483
$188$	−16.0018	−1.16705
$189$	−14.3887	−1.04663
$190$	−41.3852	−3.00240
$191$	−10.1873	−0.737128	−0.368564	−	0.929602i	$-0.620150\pi$
$191$	−10.1873	−0.737128	−0.368564	+	0.929602i	$0.620150\pi$
$192$	2.94016	0.212188
$193$	14.6455	1.05420	0.527102	−	0.849802i	$-0.323279\pi$
$193$	14.6455	1.05420	0.527102	+	0.849802i	$0.323279\pi$
$194$	−2.61823	−0.187978
$195$	−2.64000	−0.189054
$196$	33.7457	2.41040
$197$	−2.51361	−0.179088	−0.0895438	−	0.995983i	$-0.528541\pi$
$197$	−2.51361	−0.179088	−0.0895438	+	0.995983i	$0.528541\pi$
$198$	−5.35740	−0.380734
$199$	−2.59262	−0.183786	−0.0918930	−	0.995769i	$-0.529292\pi$
$199$	−2.59262	−0.183786	−0.0918930	+	0.995769i	$0.529292\pi$
$200$	2.61575	0.184961
$201$	3.17065	0.223640
$202$	−31.4995	−2.21630
$203$	15.7413	1.10483
$204$	0.311808	0.0218309
$205$	−7.73471	−0.540216
$206$	−11.9801	−0.834693
$207$	9.06612	0.630139
$208$	7.28596	0.505190
$209$	6.51406	0.450587
$210$	15.8672	1.09494
$211$	17.3270	1.19284	0.596418	−	0.802674i	$-0.296590\pi$
$211$	17.3270	1.19284	0.596418	+	0.802674i	$0.296590\pi$
$212$	−13.8815	−0.953382
$213$	3.68699	0.252628
$214$	−38.5364	−2.63429
$215$	−33.7788	−2.30369
$216$	1.28679	0.0875549
$217$	0.557030	0.0378136
$218$	14.9193	1.01046
$219$	−4.77582	−0.322720
$220$	5.77754	0.389522
$221$	0.596770	0.0401431
$222$	6.55854	0.440180
$223$	21.6868	1.45225	0.726126	−	0.687561i	$-0.241319\pi$
$223$	21.6868	1.45225	0.726126	+	0.687561i	$0.241319\pi$
$224$	−39.1178	−2.61367
$225$	−15.8009	−1.05339
$226$	−27.0085	−1.79658
$227$	13.0956	0.869188	0.434594	−	0.900626i	$-0.356892\pi$
$227$	13.0956	0.869188	0.434594	+	0.900626i	$0.356892\pi$
$228$	5.61591	0.371923
$229$	19.7395	1.30442	0.652212	−	0.758036i	$-0.273841\pi$
$229$	19.7395	1.30442	0.652212	+	0.758036i	$0.273841\pi$
$230$	−20.8597	−1.37545
$231$	−2.49750	−0.164324
$232$	−1.40775	−0.0924235
$233$	−14.1692	−0.928253	−0.464126	−	0.885769i	$-0.653632\pi$
$233$	−14.1692	−0.928253	−0.464126	+	0.885769i	$0.653632\pi$
$234$	−8.83979	−0.577875
$235$	29.6972	1.93723
$236$	5.11190	0.332756
$237$	4.48988	0.291649
$238$	−3.58676	−0.232495
$239$	12.4553	0.805664	0.402832	−	0.915274i	$-0.368026\pi$
$239$	12.4553	0.805664	0.402832	+	0.915274i	$0.368026\pi$
$240$	−7.06504	−0.456046
$241$	13.8102	0.889593	0.444796	−	0.895632i	$-0.353276\pi$
$241$	13.8102	0.889593	0.444796	+	0.895632i	$0.353276\pi$
$242$	−1.94021	−0.124721
$243$	−11.8207	−0.758297
$244$	−8.04758	−0.515194
$245$	−62.6276	−4.00113
$246$	2.23933	0.142774
$247$	10.7483	0.683898
$248$	−0.0498153	−0.00316328
$249$	2.76118	0.174983
$250$	4.58935	0.290256
$251$	−19.7467	−1.24640	−0.623199	−	0.782063i	$-0.714167\pi$
$251$	−19.7467	−1.24640	−0.623199	+	0.782063i	$0.714167\pi$
$252$	24.9022	1.56869
$253$	3.28334	0.206422
$254$	34.3723	2.15671
$255$	−0.578675	−0.0362380
$256$	19.0804	1.19253
$257$	15.5863	0.972244	0.486122	−	0.873891i	$-0.338411\pi$
$257$	15.5863	0.972244	0.486122	+	0.873891i	$0.338411\pi$
$258$	9.77952	0.608846
$259$	−35.3609	−2.19722
$260$	9.53303	0.591213
$261$	8.50379	0.526372
$262$	−39.5012	−2.44039
$263$	−2.31352	−0.142657	−0.0713287	−	0.997453i	$-0.522724\pi$
$263$	−2.31352	−0.142657	−0.0713287	+	0.997453i	$0.522724\pi$
$264$	0.223352	0.0137464
$265$	25.7622	1.58256
$266$	−64.6003	−3.96090
$267$	−3.82414	−0.234034
$268$	−11.4492	−0.699372
$269$	1.62022	0.0987867	0.0493933	−	0.998779i	$-0.484271\pi$
$269$	1.62022	0.0987867	0.0493933	+	0.998779i	$0.484271\pi$
$270$	17.8847	1.08843
$271$	−3.68946	−0.224119	−0.112059	−	0.993702i	$-0.535745\pi$
$271$	−3.68946	−0.224119	−0.112059	+	0.993702i	$0.535745\pi$
$272$	1.59705	0.0968351
$273$	−4.12092	−0.249409
$274$	10.4691	0.632463
$275$	−5.72237	−0.345072
$276$	2.83063	0.170384
$277$	−25.2818	−1.51904	−0.759519	−	0.650485i	$-0.774566\pi$
$277$	−25.2818	−1.51904	−0.759519	+	0.650485i	$0.774566\pi$
$278$	16.5432	0.992193
$279$	0.300919	0.0180155
$280$	7.65068	0.457216
$281$	13.8071	0.823661	0.411830	−	0.911261i	$-0.364890\pi$
$281$	13.8071	0.823661	0.411830	+	0.911261i	$0.364890\pi$
$282$	−8.59783	−0.511994
$283$	−17.0626	−1.01427	−0.507134	−	0.861867i	$-0.669295\pi$
$283$	−17.0626	−1.01427	−0.507134	+	0.861867i	$0.669295\pi$
$284$	−13.3137	−0.790023
$285$	−10.4224	−0.617370
$286$	−3.20137	−0.189301
$287$	−12.0735	−0.712677
$288$	−21.1322	−1.24523
$289$	−16.8692	−0.992305
$290$	−19.5659	−1.14895
$291$	−0.659373	−0.0386531
$292$	17.2455	1.00921
$293$	9.73080	0.568479	0.284240	−	0.958753i	$-0.408259\pi$
$293$	9.73080	0.568479	0.284240	+	0.958753i	$0.408259\pi$
$294$	18.1317	1.05746
$295$	−9.48702	−0.552356
$296$	3.16234	0.183807
$297$	−2.81506	−0.163346
$298$	18.3153	1.06098
$299$	5.41756	0.313306
$300$	−4.93337	−0.284828
$301$	−52.7271	−3.03914
$302$	−25.2721	−1.45425
$303$	−7.93280	−0.455727
$304$	28.7641	1.64973
$305$	14.9353	0.855191
$306$	−1.93764	−0.110767
$307$	−15.7531	−0.899075	−0.449537	−	0.893262i	$-0.648411\pi$
$307$	−15.7531	−0.899075	−0.449537	+	0.893262i	$0.648411\pi$
$308$	9.01846	0.513875
$309$	−3.01705	−0.171634
$310$	−0.692367	−0.0393238
$311$	31.5579	1.78948	0.894742	−	0.446583i	$-0.147359\pi$
$311$	31.5579	1.78948	0.894742	+	0.446583i	$0.147359\pi$
$312$	0.368535	0.0208642
$313$	3.90631	0.220798	0.110399	−	0.993887i	$-0.464787\pi$
$313$	3.90631	0.220798	0.110399	+	0.993887i	$0.464787\pi$
$314$	20.0382	1.13082
$315$	−46.2154	−2.60394
$316$	−16.2129	−0.912048
$317$	8.87227	0.498316	0.249158	−	0.968463i	$-0.419846\pi$
$317$	8.87227	0.498316	0.249158	+	0.968463i	$0.419846\pi$
$318$	−7.45858	−0.418256
$319$	3.07969	0.172429
$320$	19.7036	1.10146
$321$	−9.70495	−0.541677
$322$	−32.5611	−1.81456
$323$	2.35597	0.131090
$324$	12.1889	0.677164
$325$	−9.44200	−0.523748
$326$	45.2960	2.50872
$327$	3.75727	0.207777
$328$	1.07974	0.0596186
$329$	46.3560	2.55569
$330$	3.10430	0.170886
$331$	−12.7756	−0.702209	−0.351104	−	0.936336i	$-0.614194\pi$
$331$	−12.7756	−0.702209	−0.351104	+	0.936336i	$0.614194\pi$
$332$	−9.97062	−0.547209
$333$	−19.1027	−1.04682
$334$	26.5482	1.45265
$335$	21.2483	1.16092
$336$	−11.0282	−0.601637
$337$	−9.02825	−0.491800	−0.245900	−	0.969295i	$-0.579083\pi$
$337$	−9.02825	−0.491800	−0.245900	+	0.969295i	$0.579083\pi$
$338$	19.9404	1.08461
$339$	−6.80179	−0.369423
$340$	2.08959	0.113324
$341$	0.108979	0.00590155
$342$	−34.8984	−1.88709
$343$	−61.9793	−3.34657
$344$	4.71540	0.254237
$345$	−5.25329	−0.282828
$346$	18.1015	0.973140
$347$	0.317896	0.0170655	0.00853276	−	0.999964i	$-0.497284\pi$
$347$	0.317896	0.0170655	0.00853276	+	0.999964i	$0.497284\pi$
$348$	2.65506	0.142326
$349$	1.72771	0.0924819	0.0462410	−	0.998930i	$-0.485276\pi$
$349$	1.72771	0.0924819	0.0462410	+	0.998930i	$0.485276\pi$
$350$	56.7491	3.03337
$351$	−4.64489	−0.247926
$352$	−7.65313	−0.407913
$353$	−30.3094	−1.61321	−0.806604	−	0.591092i	$-0.798697\pi$
$353$	−30.3094	−1.61321	−0.806604	+	0.591092i	$0.798697\pi$
$354$	2.74665	0.145983
$355$	24.7085	1.31139
$356$	13.8090	0.731874
$357$	−0.903285	−0.0478069
$358$	−26.2636	−1.38807
$359$	23.7197	1.25188	0.625939	−	0.779872i	$-0.284716\pi$
$359$	23.7197	1.25188	0.625939	+	0.779872i	$0.284716\pi$
$360$	4.13305	0.217831
$361$	23.4330	1.23331
$362$	−2.95836	−0.155488
$363$	−0.488619	−0.0256459
$364$	14.8806	0.779956
$365$	−32.0053	−1.67524
$366$	−4.32401	−0.226020
$367$	8.06560	0.421021	0.210511	−	0.977592i	$-0.432487\pi$
$367$	8.06560	0.421021	0.210511	+	0.977592i	$0.432487\pi$
$368$	14.4982	0.755771
$369$	−6.52236	−0.339540
$370$	43.9523	2.28497
$371$	40.2136	2.08778
$372$	0.0939531	0.00487124
$373$	19.4001	1.00450	0.502248	−	0.864723i	$-0.332506\pi$
$373$	19.4001	1.00450	0.502248	+	0.864723i	$0.332506\pi$
$374$	−0.701725	−0.0362853
$375$	1.15578	0.0596841
$376$	−4.14563	−0.213794
$377$	5.08153	0.261712
$378$	27.9171	1.43590
$379$	−32.1355	−1.65069	−0.825344	−	0.564630i	$-0.809019\pi$
$379$	−32.1355	−1.65069	−0.825344	+	0.564630i	$0.809019\pi$
$380$	37.6352	1.93065
$381$	8.65627	0.443474
$382$	19.7655	1.01129
$383$	−0.920470	−0.0470338	−0.0235169	−	0.999723i	$-0.507486\pi$
$383$	−0.920470	−0.0470338	−0.0235169	+	0.999723i	$0.507486\pi$
$384$	1.77442	0.0905505
$385$	−16.7371	−0.853002
$386$	−28.4152	−1.44630
$387$	−28.4842	−1.44794
$388$	2.38099	0.120877
$389$	27.2608	1.38218	0.691090	−	0.722769i	$-0.257131\pi$
$389$	27.2608	1.38218	0.691090	+	0.722769i	$0.257131\pi$
$390$	5.12215	0.259370
$391$	1.18750	0.0600546
$392$	8.74259	0.441567
$393$	−9.94793	−0.501807
$394$	4.87693	0.245696
$395$	30.0891	1.51395
$396$	4.87196	0.244825
$397$	−9.11001	−0.457218	−0.228609	−	0.973518i	$-0.573418\pi$
$397$	−9.11001	−0.457218	−0.228609	+	0.973518i	$0.573418\pi$
$398$	5.03022	0.252142
$399$	−16.2689	−0.814462
$400$	−25.2682	−1.26341
$401$	9.00268	0.449572	0.224786	−	0.974408i	$-0.427832\pi$
$401$	9.00268	0.449572	0.224786	+	0.974408i	$0.427832\pi$
$402$	−6.15172	−0.306820
$403$	0.179817	0.00895733
$404$	28.6453	1.42516
$405$	−22.6211	−1.12405
$406$	−30.5415	−1.51575
$407$	−6.91812	−0.342919
$408$	0.0807810	0.00399926
$409$	−15.1035	−0.746818	−0.373409	−	0.927667i	$-0.621811\pi$
$409$	−15.1035	−0.746818	−0.373409	+	0.927667i	$0.621811\pi$
$410$	15.0069	0.741140
$411$	2.63653	0.130051
$412$	10.8946	0.536736
$413$	−14.8088	−0.728693
$414$	−17.5901	−0.864509
$415$	18.5042	0.908334
$416$	−12.6278	−0.619128
$417$	4.16621	0.204020
$418$	−12.6386	−0.618175
$419$	−5.76354	−0.281568	−0.140784	−	0.990040i	$-0.544962\pi$
$419$	−5.76354	−0.281568	−0.140784	+	0.990040i	$0.544962\pi$
$420$	−14.4294	−0.704083
$421$	8.39019	0.408913	0.204457	−	0.978876i	$-0.434457\pi$
$421$	8.39019	0.408913	0.204457	+	0.978876i	$0.434457\pi$
$422$	−33.6179	−1.63649
$423$	25.0424	1.21760
$424$	−3.59631	−0.174652
$425$	−2.06964	−0.100392
$426$	−7.15352	−0.346589
$427$	23.3133	1.12821
$428$	35.0445	1.69394
$429$	−0.806230	−0.0389251
$430$	65.5378	3.16051
$431$	−32.9025	−1.58486	−0.792430	−	0.609963i	$-0.791184\pi$
$431$	−32.9025	−1.58486	−0.792430	+	0.609963i	$0.791184\pi$
$432$	−12.4304	−0.598059
$433$	−38.2281	−1.83712	−0.918562	−	0.395276i	$-0.870649\pi$
$433$	−38.2281	−1.83712	−0.918562	+	0.395276i	$0.870649\pi$
$434$	−1.08075	−0.0518778
$435$	−4.92746	−0.236253
$436$	−13.5675	−0.649764
$437$	21.3879	1.02312
$438$	9.26608	0.442750
$439$	−8.85289	−0.422525	−0.211263	−	0.977429i	$-0.567758\pi$
$439$	−8.85289	−0.422525	−0.211263	+	0.977429i	$0.567758\pi$
$440$	1.49680	0.0713573
$441$	−52.8112	−2.51482
$442$	−1.15786	−0.0550736
$443$	7.31931	0.347751	0.173876	−	0.984768i	$-0.444371\pi$
$443$	7.31931	0.347751	0.173876	+	0.984768i	$0.444371\pi$
$444$	−5.96426	−0.283051
$445$	−25.6277	−1.21487
$446$	−42.0768	−1.99239
$447$	4.61251	0.218164
$448$	30.7564	1.45310
$449$	18.9455	0.894093	0.447046	−	0.894511i	$-0.352476\pi$
$449$	18.9455	0.894093	0.447046	+	0.894511i	$0.352476\pi$
$450$	30.6570	1.44518
$451$	−2.36210	−0.111227
$452$	24.5612	1.15526
$453$	−6.36450	−0.299030
$454$	−25.4082	−1.19247
$455$	−27.6165	−1.29468
$456$	1.45493	0.0681333
$457$	35.2067	1.64690	0.823450	−	0.567389i	$-0.192046\pi$
$457$	35.2067	1.64690	0.823450	+	0.567389i	$0.192046\pi$
$458$	−38.2988	−1.78958
$459$	−1.01814	−0.0475226
$460$	18.9696	0.884463
$461$	−23.0972	−1.07574	−0.537871	−	0.843027i	$-0.680771\pi$
$461$	−23.0972	−1.07574	−0.537871	+	0.843027i	$0.680771\pi$
$462$	4.84567	0.225441
$463$	−4.85058	−0.225426	−0.112713	−	0.993628i	$-0.535954\pi$
$463$	−4.85058	−0.225426	−0.112713	+	0.993628i	$0.535954\pi$
$464$	13.5989	0.631315
$465$	−0.174365	−0.00808598
$466$	27.4911	1.27350
$467$	15.4737	0.716038	0.358019	−	0.933714i	$-0.383452\pi$
$467$	15.4737	0.716038	0.358019	+	0.933714i	$0.383452\pi$
$468$	8.03881	0.371594
$469$	33.1675	1.53153
$470$	−57.6187	−2.65775
$471$	5.04639	0.232525
$472$	1.32435	0.0609583
$473$	−10.3157	−0.474316
$474$	−8.71129	−0.400123
$475$	−37.2758	−1.71033
$476$	3.26176	0.149502
$477$	21.7242	0.994682
$478$	−24.1658	−1.10532
$479$	9.88432	0.451626	0.225813	−	0.974171i	$-0.427496\pi$
$479$	9.88432	0.451626	0.225813	+	0.974171i	$0.427496\pi$
$480$	12.2449	0.558901
$481$	−11.4150	−0.520480
$482$	−26.7946	−1.22046
$483$	−8.20014	−0.373119
$484$	1.76440	0.0802001
$485$	−4.41881	−0.200648
$486$	22.9346	1.04033
$487$	1.77137	0.0802684	0.0401342	−	0.999194i	$-0.487221\pi$
$487$	1.77137	0.0802684	0.0401342	+	0.999194i	$0.487221\pi$
$488$	−2.08491	−0.0943795
$489$	11.4073	0.515856
$490$	121.510	5.48928
$491$	34.8247	1.57162	0.785808	−	0.618471i	$-0.212248\pi$
$491$	34.8247	1.57162	0.785808	+	0.618471i	$0.212248\pi$
$492$	−2.03642	−0.0918088
$493$	1.11385	0.0501651
$494$	−20.8539	−0.938262
$495$	−9.04172	−0.406395
$496$	0.481218	0.0216073
$497$	38.5688	1.73005
$498$	−5.35726	−0.240065
$499$	−40.9804	−1.83453	−0.917267	−	0.398273i	$-0.869610\pi$
$499$	−40.9804	−1.83453	−0.917267	+	0.398273i	$0.869610\pi$
$500$	−4.17351	−0.186645
$501$	6.68586	0.298702
$502$	38.3126	1.70997
$503$	16.2627	0.725117	0.362559	−	0.931961i	$-0.381903\pi$
$503$	16.2627	0.725117	0.362559	+	0.931961i	$0.381903\pi$
$504$	6.45150	0.287373
$505$	−53.1620	−2.36568
$506$	−6.37035	−0.283197
$507$	5.02176	0.223024
$508$	−31.2577	−1.38684
$509$	−8.85673	−0.392568	−0.196284	−	0.980547i	$-0.562887\pi$
$509$	−8.85673	−0.392568	−0.196284	+	0.980547i	$0.562887\pi$
$510$	1.12275	0.0497162
$511$	−49.9588	−2.21005
$512$	−29.7570	−1.31508
$513$	−18.3375	−0.809619
$514$	−30.2406	−1.33385
$515$	−20.2189	−0.890951
$516$	−8.89338	−0.391509
$517$	9.06923	0.398864
$518$	68.6075	3.01444
$519$	4.55865	0.200102
$520$	2.46975	0.108306
$521$	22.0038	0.964004	0.482002	−	0.876170i	$-0.339910\pi$
$521$	22.0038	0.964004	0.482002	+	0.876170i	$0.339910\pi$
$522$	−16.4991	−0.722147
$523$	−16.6957	−0.730053	−0.365026	−	0.930997i	$-0.618940\pi$
$523$	−16.6957	−0.730053	−0.365026	+	0.930997i	$0.618940\pi$
$524$	35.9219	1.56926
$525$	14.2916	0.623737
$526$	4.48870	0.195717
$527$	0.0394150	0.00171695
$528$	−2.15759	−0.0938971
$529$	−12.2197	−0.531291
$530$	−49.9840	−2.17116
$531$	−8.00001	−0.347171
$532$	58.7468	2.54700
$533$	−3.89751	−0.168820
$534$	7.41963	0.321079
$535$	−65.0381	−2.81184
$536$	−2.96618	−0.128119
$537$	−6.61419	−0.285423
$538$	−3.14357	−0.135529
$539$	−19.1258	−0.823808
$540$	−16.2641	−0.699896
$541$	12.8557	0.552710	0.276355	−	0.961056i	$-0.410874\pi$
$541$	12.8557	0.552710	0.276355	+	0.961056i	$0.410874\pi$
$542$	7.15832	0.307476
$543$	−0.745029	−0.0319723
$544$	−2.76795	−0.118675
$545$	25.1795	1.07857
$546$	7.99543	0.342173
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−9.52050	−0.406696
$549$	12.5943	0.537511
$550$	11.1026	0.473415
$551$	20.0613	0.854639
$552$	0.733341	0.0312131
$553$	46.9677	1.99727
$554$	49.0520	2.08402
$555$	11.0689	0.469848
$556$	−15.0442	−0.638015
$557$	−20.6132	−0.873410	−0.436705	−	0.899605i	$-0.643855\pi$
$557$	−20.6132	−0.873410	−0.436705	+	0.899605i	$0.643855\pi$
$558$	−0.583844	−0.0247161
$559$	−17.0211	−0.719914
$560$	−73.9059	−3.12309
$561$	−0.176722	−0.00746119
$562$	−26.7886	−1.13001
$563$	17.7405	0.747671	0.373836	−	0.927495i	$-0.378042\pi$
$563$	17.7405	0.747671	0.373836	+	0.927495i	$0.378042\pi$
$564$	7.81877	0.329230
$565$	−45.5825	−1.91767
$566$	33.1050	1.39151
$567$	−35.3105	−1.48290
$568$	−3.44922	−0.144726
$569$	11.2057	0.469769	0.234884	−	0.972023i	$-0.424529\pi$
$569$	11.2057	0.469769	0.234884	+	0.972023i	$0.424529\pi$
$570$	20.2216	0.846990
$571$	18.9788	0.794240	0.397120	−	0.917767i	$-0.370010\pi$
$571$	18.9788	0.794240	0.397120	+	0.917767i	$0.370010\pi$
$572$	2.91129	0.121727
$573$	4.97772	0.207947
$574$	23.4251	0.977746
$575$	−18.7885	−0.783533
$576$	16.6152	0.692301
$577$	−39.7154	−1.65337	−0.826687	−	0.562662i	$-0.809777\pi$
$577$	−39.7154	−1.65337	−0.826687	+	0.562662i	$0.809777\pi$
$578$	32.7297	1.36138
$579$	−7.15605	−0.297395
$580$	17.7930	0.738815
$581$	28.8841	1.19832
$582$	1.27932	0.0530295
$583$	7.86751	0.325839
$584$	4.46783	0.184880
$585$	−14.9190	−0.616824
$586$	−18.8798	−0.779915
$587$	−24.4578	−1.00948	−0.504740	−	0.863271i	$-0.668412\pi$
$587$	−24.4578	−1.00948	−0.504740	+	0.863271i	$0.668412\pi$
$588$	−16.4888	−0.679986
$589$	0.709896	0.0292508
$590$	18.4068	0.757795
$591$	1.22820	0.0505214
$592$	−30.5483	−1.25553
$593$	−2.76514	−0.113551	−0.0567753	−	0.998387i	$-0.518082\pi$
$593$	−2.76514	−0.113551	−0.0567753	+	0.998387i	$0.518082\pi$
$594$	5.46180	0.224100
$595$	−6.05340	−0.248165
$596$	−16.6558	−0.682247
$597$	1.26680	0.0518468
$598$	−10.5112	−0.429834
$599$	15.8915	0.649310	0.324655	−	0.945832i	$-0.394752\pi$
$599$	15.8915	0.649310	0.324655	+	0.945832i	$0.394752\pi$
$600$	−1.27810	−0.0521784
$601$	11.9971	0.489373	0.244686	−	0.969602i	$-0.421315\pi$
$601$	11.9971	0.489373	0.244686	+	0.969602i	$0.421315\pi$
$602$	102.301	4.16950
$603$	17.9178	0.729668
$604$	22.9822	0.935131
$605$	−3.27450	−0.133127
$606$	15.3913	0.625228
$607$	−22.2404	−0.902710	−0.451355	−	0.892345i	$-0.649059\pi$
$607$	−22.2404	−0.902710	−0.451355	+	0.892345i	$0.649059\pi$
$608$	−49.8530	−2.02180
$609$	−7.69152	−0.311676
$610$	−28.9775	−1.17327
$611$	14.9644	0.605394
$612$	1.76207	0.0712273
$613$	5.48896	0.221697	0.110848	−	0.993837i	$-0.464643\pi$
$613$	5.48896	0.221697	0.110848	+	0.993837i	$0.464643\pi$
$614$	30.5642	1.23347
$615$	3.77933	0.152397
$616$	2.33644	0.0941379
$617$	−35.2720	−1.42000	−0.709998	−	0.704203i	$-0.751304\pi$
$617$	−35.2720	−1.42000	−0.709998	+	0.704203i	$0.751304\pi$
$618$	5.85370	0.235471
$619$	−13.1948	−0.530344	−0.265172	−	0.964201i	$-0.585429\pi$
$619$	−13.1948	−0.530344	−0.265172	+	0.964201i	$0.585429\pi$
$620$	0.629631	0.0252866
$621$	−9.24279	−0.370900
$622$	−61.2289	−2.45505
$623$	−40.0036	−1.60271
$624$	−3.56006	−0.142516
$625$	−20.8663	−0.834654
$626$	−7.57906	−0.302920
$627$	−3.18290	−0.127113
$628$	−18.2225	−0.727156
$629$	−2.50211	−0.0997658
$630$	89.6673	3.57243
$631$	−9.09116	−0.361913	−0.180957	−	0.983491i	$-0.557919\pi$
$631$	−9.09116	−0.361913	−0.180957	+	0.983491i	$0.557919\pi$
$632$	−4.20033	−0.167080
$633$	−8.46629	−0.336505
$634$	−17.2140	−0.683656
$635$	58.0104	2.30207
$636$	6.78275	0.268953
$637$	−31.5579	−1.25037
$638$	−5.97523	−0.236562
$639$	20.8357	0.824246
$640$	11.8914	0.470047
$641$	6.75915	0.266970	0.133485	−	0.991051i	$-0.457383\pi$
$641$	6.75915	0.266970	0.133485	+	0.991051i	$0.457383\pi$
$642$	18.8296	0.743145
$643$	19.9750	0.787739	0.393869	−	0.919166i	$-0.371136\pi$
$643$	19.9750	0.787739	0.393869	+	0.919166i	$0.371136\pi$
$644$	29.6107	1.16682
$645$	16.5050	0.649882
$646$	−4.57108	−0.179847
$647$	20.2495	0.796091	0.398046	−	0.917366i	$-0.369689\pi$
$647$	20.2495	0.796091	0.398046	+	0.917366i	$0.369689\pi$
$648$	3.15783	0.124051
$649$	−2.89724	−0.113727
$650$	18.3194	0.718547
$651$	−0.272175	−0.0106674
$652$	−41.1917	−1.61319
$653$	27.4286	1.07337	0.536683	−	0.843784i	$-0.319677\pi$
$653$	27.4286	1.07337	0.536683	+	0.843784i	$0.319677\pi$
$654$	−7.28987	−0.285057
$655$	−66.6665	−2.60488
$656$	−10.4303	−0.407235
$657$	−26.9888	−1.05293
$658$	−89.9401	−3.50623
$659$	34.9071	1.35979	0.679894	−	0.733311i	$-0.262026\pi$
$659$	34.9071	1.35979	0.679894	+	0.733311i	$0.262026\pi$
$660$	−2.82302	−0.109886
$661$	26.4739	1.02972	0.514858	−	0.857275i	$-0.327845\pi$
$661$	26.4739	1.02972	0.514858	+	0.857275i	$0.327845\pi$
$662$	24.7872	0.963383
$663$	−0.291593	−0.0113245
$664$	−2.58312	−0.100244
$665$	−109.027	−4.22787
$666$	37.0631	1.43617
$667$	10.1117	0.391525
$668$	−24.1426	−0.934106
$669$	−10.5966	−0.409687
$670$	−41.2260	−1.59270
$671$	4.56108	0.176079
$672$	19.1137	0.737327
$673$	20.0735	0.773775	0.386888	−	0.922127i	$-0.373550\pi$
$673$	20.0735	0.773775	0.386888	+	0.922127i	$0.373550\pi$
$674$	17.5167	0.674717
$675$	16.1088	0.620028
$676$	−18.1336	−0.697444
$677$	−10.1734	−0.390995	−0.195497	−	0.980704i	$-0.562632\pi$
$677$	−10.1734	−0.390995	−0.195497	+	0.980704i	$0.562632\pi$
$678$	13.1969	0.506823
$679$	−6.89756	−0.264704
$680$	0.541357	0.0207601
$681$	−6.39878	−0.245202
$682$	−0.211442	−0.00809653
$683$	20.2889	0.776334	0.388167	−	0.921589i	$-0.373108\pi$
$683$	20.2889	0.776334	0.388167	+	0.921589i	$0.373108\pi$
$684$	31.7362	1.21346
$685$	17.6688	0.675091
$686$	120.253	4.59127
$687$	−9.64511	−0.367984
$688$	−45.5509	−1.73661
$689$	12.9815	0.494556
$690$	10.1925	0.388021
$691$	43.0784	1.63878	0.819389	−	0.573237i	$-0.194313\pi$
$691$	43.0784	1.63878	0.819389	+	0.573237i	$0.194313\pi$
$692$	−16.4613	−0.625763
$693$	−14.1137	−0.536135
$694$	−0.616783	−0.0234128
$695$	27.9200	1.05907
$696$	0.687855	0.0260731
$697$	−0.854314	−0.0323595
$698$	−3.35211	−0.126879
$699$	6.92333	0.261864
$700$	−51.6070	−1.95056
$701$	30.4733	1.15096	0.575480	−	0.817816i	$-0.304815\pi$
$701$	30.4733	1.15096	0.575480	+	0.817816i	$0.304815\pi$
$702$	9.01205	0.340138
$703$	−45.0651	−1.69966
$704$	6.01728	0.226785
$705$	−14.5106	−0.546502
$706$	58.8066	2.21321
$707$	−82.9833	−3.12091
$708$	−2.49777	−0.0938720
$709$	32.2468	1.21105	0.605526	−	0.795825i	$-0.292963\pi$
$709$	32.2468	1.21105	0.605526	+	0.795825i	$0.292963\pi$
$710$	−47.9396	−1.79914
$711$	25.3729	0.951557
$712$	3.57753	0.134074
$713$	0.357815	0.0134003
$714$	1.75256	0.0655879
$715$	−5.40298	−0.202060
$716$	23.8838	0.892580
$717$	−6.08588	−0.227282
$718$	−46.0211	−1.71749
$719$	−33.2211	−1.23894	−0.619469	−	0.785021i	$-0.712652\pi$
$719$	−33.2211	−1.23894	−0.619469	+	0.785021i	$0.712652\pi$
$720$	−39.9254	−1.48793
$721$	−31.5607	−1.17538
$722$	−45.4648	−1.69203
$723$	−6.74793	−0.250958
$724$	2.69030	0.0999841
$725$	−17.6231	−0.654506
$726$	0.948022	0.0351844
$727$	−21.2412	−0.787793	−0.393897	−	0.919155i	$-0.628873\pi$
$727$	−21.2412	−0.787793	−0.393897	+	0.919155i	$0.628873\pi$
$728$	3.85516	0.142882
$729$	−14.9490	−0.553666
$730$	62.0970	2.29831
$731$	−3.73093	−0.137994
$732$	3.93220	0.145338
$733$	−45.5654	−1.68300	−0.841498	−	0.540261i	$-0.818326\pi$
$733$	−45.5654	−1.68300	−0.841498	+	0.540261i	$0.818326\pi$
$734$	−15.6489	−0.577613
$735$	30.6011	1.12874
$736$	−25.1278	−0.926224
$737$	6.48900	0.239025
$738$	12.6547	0.465827
$739$	−10.4760	−0.385367	−0.192684	−	0.981261i	$-0.561719\pi$
$739$	−10.4760	−0.385367	−0.192684	+	0.981261i	$0.561719\pi$
$740$	−39.9697	−1.46932
$741$	−5.25183	−0.192931
$742$	−78.0226	−2.86430
$743$	−38.7806	−1.42272	−0.711360	−	0.702828i	$-0.751921\pi$
$743$	−38.7806	−1.42272	−0.711360	+	0.702828i	$0.751921\pi$
$744$	0.0243407	0.000892374 0
$745$	30.9110	1.13249
$746$	−37.6401	−1.37810
$747$	15.6038	0.570913
$748$	0.638141	0.0233327
$749$	−101.521	−3.70951
$750$	−2.24245	−0.0818826
$751$	20.5384	0.749456	0.374728	−	0.927135i	$-0.377736\pi$
$751$	20.5384	0.749456	0.374728	+	0.927135i	$0.377736\pi$
$752$	40.0469	1.46036
$753$	9.64860	0.351614
$754$	−9.85922	−0.359052
$755$	−42.6520	−1.55226
$756$	−25.3875	−0.923335
$757$	−49.1282	−1.78560	−0.892798	−	0.450457i	$-0.851261\pi$
$757$	−49.1282	−1.78560	−0.892798	+	0.450457i	$0.851261\pi$
$758$	62.3494	2.26463
$759$	−1.60430	−0.0582325
$760$	9.75027	0.353680
$761$	−15.0139	−0.544254	−0.272127	−	0.962261i	$-0.587727\pi$
$761$	−15.0139	−0.544254	−0.272127	+	0.962261i	$0.587727\pi$
$762$	−16.7950	−0.608417
$763$	39.3040	1.42290
$764$	−17.9745	−0.650295
$765$	−3.27017	−0.118233
$766$	1.78590	0.0645272
$767$	−4.78049	−0.172614
$768$	−9.32306	−0.336417
$769$	−2.01229	−0.0725649	−0.0362825	−	0.999342i	$-0.511552\pi$
$769$	−2.01229	−0.0725649	−0.0362825	+	0.999342i	$0.511552\pi$
$770$	32.4734	1.17026
$771$	−7.61575	−0.274274
$772$	25.8405	0.930019
$773$	25.0292	0.900237	0.450119	−	0.892969i	$-0.351382\pi$
$773$	25.0292	0.900237	0.450119	+	0.892969i	$0.351382\pi$
$774$	55.2653	1.98647
$775$	−0.623618	−0.0224010
$776$	0.616851	0.0221437
$777$	17.2780	0.619846
$778$	−52.8917	−1.89626
$779$	−15.3869	−0.551292
$780$	−4.65802	−0.166784
$781$	7.54573	0.270008
$782$	−2.30400	−0.0823909
$783$	−8.66950	−0.309823
$784$	−84.4537	−3.01621
$785$	33.8186	1.20704
$786$	19.3010	0.688446
$787$	−26.9062	−0.959104	−0.479552	−	0.877514i	$-0.659201\pi$
$787$	−26.9062	−0.959104	−0.479552	+	0.877514i	$0.659201\pi$
$788$	−4.43503	−0.157991
$789$	1.13043	0.0402443
$790$	−58.3791	−2.07703
$791$	−71.1521	−2.52988
$792$	1.26219	0.0448501
$793$	7.52586	0.267251
$794$	17.6753	0.627273
$795$	−12.5879	−0.446447
$796$	−4.57442	−0.162136
$797$	−33.8435	−1.19880	−0.599399	−	0.800450i	$-0.704594\pi$
$797$	−33.8435	−1.19880	−0.599399	+	0.800450i	$0.704594\pi$
$798$	31.5650	1.11739
$799$	3.28012	0.116042
$800$	43.7940	1.54835
$801$	−21.6107	−0.763578
$802$	−17.4671	−0.616783
$803$	−9.77411	−0.344921
$804$	5.59430	0.197296
$805$	−54.9536	−1.93686
$806$	−0.348883	−0.0122889
$807$	−0.791672	−0.0278682
$808$	7.42122	0.261078
$809$	55.3092	1.94457	0.972283	−	0.233806i	$-0.0751181\pi$
$809$	55.3092	1.94457	0.972283	+	0.233806i	$0.0751181\pi$
$810$	43.8896	1.54213
$811$	−36.4249	−1.27905	−0.639526	−	0.768770i	$-0.720869\pi$
$811$	−36.4249	−1.27905	−0.639526	+	0.768770i	$0.720869\pi$
$812$	27.7741	0.974678
$813$	1.80274	0.0632249
$814$	13.4226	0.470461
$815$	76.4465	2.67780
$816$	−0.780347	−0.0273176
$817$	−67.1971	−2.35093
$818$	29.3038	1.02458
$819$	−23.2878	−0.813743
$820$	−13.6471	−0.476579
$821$	−4.81530	−0.168055	−0.0840276	−	0.996463i	$-0.526778\pi$
$821$	−4.81530	−0.168055	−0.0840276	+	0.996463i	$0.526778\pi$
$822$	−5.11542	−0.178421
$823$	−41.8330	−1.45821	−0.729103	−	0.684404i	$-0.760062\pi$
$823$	−41.8330	−1.45821	−0.729103	+	0.684404i	$0.760062\pi$
$824$	2.82249	0.0983260
$825$	2.79606	0.0973463
$826$	28.7321	0.999718
$827$	37.8199	1.31513	0.657564	−	0.753399i	$-0.271587\pi$
$827$	37.8199	1.31513	0.657564	+	0.753399i	$0.271587\pi$
$828$	15.9963	0.555909
$829$	−24.9835	−0.867713	−0.433857	−	0.900982i	$-0.642848\pi$
$829$	−24.9835	−0.867713	−0.433857	+	0.900982i	$0.642848\pi$
$830$	−35.9019	−1.24617
$831$	12.3532	0.428528
$832$	9.92861	0.344212
$833$	−6.91734	−0.239672
$834$	−8.08331	−0.279902
$835$	44.8056	1.55056
$836$	11.4934	0.397508
$837$	−0.306783	−0.0106040
$838$	11.1825	0.386292
$839$	−26.0845	−0.900537	−0.450269	−	0.892893i	$-0.648672\pi$
$839$	−26.0845	−0.900537	−0.450269	+	0.892893i	$0.648672\pi$
$840$	−3.73827	−0.128983
$841$	−19.5155	−0.672949
$842$	−16.2787	−0.561001
$843$	−6.74640	−0.232358
$844$	30.5717	1.05232
$845$	33.6535	1.15772
$846$	−48.5875	−1.67047
$847$	−5.11134	−0.175628
$848$	34.7405	1.19299
$849$	8.33713	0.286129
$850$	4.01553	0.137731
$851$	−22.7145	−0.778644
$852$	6.50533	0.222869
$853$	46.4101	1.58905	0.794526	−	0.607230i	$-0.207719\pi$
$853$	46.4101	1.58905	0.794526	+	0.607230i	$0.207719\pi$
$854$	−45.2325	−1.54783
$855$	−58.8983	−2.01428
$856$	9.07909	0.310317
$857$	12.5345	0.428171	0.214086	−	0.976815i	$-0.431323\pi$
$857$	12.5345	0.428171	0.214086	+	0.976815i	$0.431323\pi$
$858$	1.56425	0.0534027
$859$	10.1386	0.345926	0.172963	−	0.984928i	$-0.444666\pi$
$859$	10.1386	0.345926	0.172963	+	0.984928i	$0.444666\pi$
$860$	−59.5994	−2.03232
$861$	5.89935	0.201049
$862$	63.8377	2.17432
$863$	−24.6810	−0.840151	−0.420075	−	0.907489i	$-0.637996\pi$
$863$	−24.6810	−0.840151	−0.420075	+	0.907489i	$0.637996\pi$
$864$	21.5440	0.732942
$865$	30.5500	1.03873
$866$	74.1704	2.52041
$867$	8.24261	0.279934
$868$	0.982824	0.0333592
$869$	9.18891	0.311712
$870$	9.56028	0.324124
$871$	10.7070	0.362791
$872$	−3.51497	−0.119032
$873$	−3.72620	−0.126113
$874$	−41.4969	−1.40365
$875$	12.0903	0.408728
$876$	−8.42646	−0.284704
$877$	33.0435	1.11580	0.557900	−	0.829908i	$-0.311607\pi$
$877$	33.0435	1.11580	0.557900	+	0.829908i	$0.311607\pi$
$878$	17.1764	0.579676
$879$	−4.75465	−0.160371
$880$	−14.4592	−0.487419
$881$	−2.12325	−0.0715341	−0.0357671	−	0.999360i	$-0.511387\pi$
$881$	−2.12325	−0.0715341	−0.0357671	+	0.999360i	$0.511387\pi$
$882$	102.465	3.45017
$883$	32.2644	1.08578	0.542891	−	0.839803i	$-0.317330\pi$
$883$	32.2644	1.08578	0.542891	+	0.839803i	$0.317330\pi$
$884$	1.05294	0.0354143
$885$	4.63554	0.155822
$886$	−14.2010	−0.477091
$887$	0.265292	0.00890763	0.00445381	−	0.999990i	$-0.498582\pi$
$887$	0.265292	0.00890763	0.00445381	+	0.999990i	$0.498582\pi$
$888$	−1.54518	−0.0518528
$889$	90.5514	3.03700
$890$	49.7230	1.66672
$891$	−6.90826	−0.231435
$892$	38.2642	1.28118
$893$	59.0775	1.97695
$894$	−8.94923	−0.299307
$895$	−44.3253	−1.48163
$896$	18.5618	0.620108
$897$	−2.64712	−0.0883849
$898$	−36.7582	−1.22664
$899$	0.335622	0.0111936
$900$	−27.8791	−0.929304
$901$	2.84548	0.0947968
$902$	4.58297	0.152596
$903$	25.7635	0.857355
$904$	6.36315	0.211635
$905$	−4.99285	−0.165968
$906$	12.3484	0.410250
$907$	11.4845	0.381338	0.190669	−	0.981654i	$-0.438934\pi$
$907$	11.4845	0.381338	0.190669	+	0.981654i	$0.438934\pi$
$908$	23.1060	0.766798
$909$	−44.8293	−1.48689
$910$	53.5817	1.77622
$911$	−33.6860	−1.11607	−0.558034	−	0.829818i	$-0.688444\pi$
$911$	−33.6860	−1.11607	−0.558034	+	0.829818i	$0.688444\pi$
$912$	−14.0547	−0.465397
$913$	5.65099	0.187020
$914$	−68.3083	−2.25944
$915$	−7.29766	−0.241253
$916$	34.8285	1.15076
$917$	−104.063	−3.43647
$918$	1.97540	0.0651978
$919$	28.5969	0.943325	0.471662	−	0.881779i	$-0.343654\pi$
$919$	28.5969	0.943325	0.471662	+	0.881779i	$0.343654\pi$
$920$	4.91451	0.162027
$921$	7.69725	0.253633
$922$	44.8133	1.47585
$923$	12.4506	0.409816
$924$	−4.40660	−0.144966
$925$	39.5880	1.30165
$926$	9.41113	0.309269
$927$	−17.0498	−0.559987
$928$	−23.5693	−0.773699
$929$	−23.1997	−0.761157	−0.380579	−	0.924749i	$-0.624275\pi$
$929$	−23.1997	−0.761157	−0.380579	+	0.924749i	$0.624275\pi$
$930$	0.338304	0.0110934
$931$	−124.587	−4.08317
$932$	−25.0001	−0.818905
$933$	−15.4198	−0.504822
$934$	−30.0222	−0.982357
$935$	−1.18431	−0.0387310
$936$	2.08264	0.0680731
$937$	54.4489	1.77877	0.889384	−	0.457160i	$-0.151133\pi$
$937$	54.4489	1.77877	0.889384	+	0.457160i	$0.151133\pi$
$938$	−64.3518	−2.10116
$939$	−1.90870	−0.0622881
$940$	52.3978	1.70903
$941$	52.6826	1.71740	0.858701	−	0.512476i	$-0.171272\pi$
$941$	52.6826	1.71740	0.858701	+	0.512476i	$0.171272\pi$
$942$	−9.79104	−0.319009
$943$	−7.75558	−0.252557
$944$	−12.7933	−0.416387
$945$	47.1159	1.53268
$946$	20.0146	0.650730
$947$	−35.7126	−1.16050	−0.580251	−	0.814437i	$-0.697046\pi$
$947$	−35.7126	−1.16050	−0.580251	+	0.814437i	$0.697046\pi$
$948$	7.92195	0.257293
$949$	−16.1274	−0.523519
$950$	72.3228	2.34646
$951$	−4.33516	−0.140577
$952$	0.845033	0.0273877
$953$	12.8011	0.414667	0.207334	−	0.978270i	$-0.433521\pi$
$953$	12.8011	0.414667	0.207334	+	0.978270i	$0.433521\pi$
$954$	−42.1494	−1.36464
$955$	33.3584	1.07945
$956$	21.9761	0.710758
$957$	−1.50480	−0.0486431
$958$	−19.1776	−0.619601
$959$	27.5802	0.890611
$960$	−9.62756	−0.310728
$961$	−30.9881	−0.999617
$962$	22.1475	0.714063
$963$	−54.8439	−1.76732
$964$	24.3667	0.784799
$965$	−47.9566	−1.54378
$966$	15.9100	0.511895
$967$	−5.76620	−0.185429	−0.0927143	−	0.995693i	$-0.529554\pi$
$967$	−5.76620	−0.185429	−0.0927143	+	0.995693i	$0.529554\pi$
$968$	0.457109	0.0146920
$969$	−1.15117	−0.0369811
$970$	8.57341	0.275276
$971$	−36.5647	−1.17342	−0.586709	−	0.809798i	$-0.699577\pi$
$971$	−36.5647	−1.17342	−0.586709	+	0.809798i	$0.699577\pi$
$972$	−20.8564	−0.668971
$973$	43.5819	1.39717
$974$	−3.43682	−0.110123
$975$	4.61354	0.147752
$976$	20.1403	0.644676
$977$	21.1331	0.676108	0.338054	−	0.941127i	$-0.390231\pi$
$977$	21.1331	0.676108	0.338054	+	0.941127i	$0.390231\pi$
$978$	−22.1325	−0.707720
$979$	−7.82643	−0.250134
$980$	−110.500	−3.52980
$981$	21.2328	0.677911
$982$	−67.5671	−2.15615
$983$	−3.79218	−0.120952	−0.0604758	−	0.998170i	$-0.519262\pi$
$983$	−3.79218	−0.120952	−0.0604758	+	0.998170i	$0.519262\pi$
$984$	−0.527581	−0.0168187
$985$	8.23084	0.262256
$986$	−2.16109	−0.0688232
$987$	−22.6504	−0.720971
$988$	18.9643	0.603335
$989$	−33.8699	−1.07700
$990$	17.5428	0.557547
$991$	53.1928	1.68972	0.844862	−	0.534985i	$-0.179683\pi$
$991$	53.1928	1.68972	0.844862	+	0.534985i	$0.179683\pi$
$992$	−0.834031	−0.0264805
$993$	6.24239	0.198096
$994$	−74.8315	−2.37351
$995$	8.48954	0.269136
$996$	4.87184	0.154370
$997$	0.472238	0.0149559	0.00747796	−	0.999972i	$-0.497620\pi$
$997$	0.472238	0.0149559	0.00747796	+	0.999972i	$0.497620\pi$
$998$	79.5104	2.51686
$999$	19.4749	0.616159

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.d.1.20	✓	107

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.d.1.20	✓	107	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)

\(f(q)\)	\(=\)	\(q-1.94021 q^{2} -0.488619 q^{3} +1.76440 q^{4} -3.27450 q^{5} +0.948022 q^{6} -5.11134 q^{7} +0.457109 q^{8} -2.76125 q^{9} +O(q^{10})\)	\(q-1.94021 q^{2} -0.488619 q^{3} +1.76440 q^{4} -3.27450 q^{5} +0.948022 q^{6} -5.11134 q^{7} +0.457109 q^{8} -2.76125 q^{9} +6.35321 q^{10} -1.00000 q^{11} -0.862121 q^{12} -1.65002 q^{13} +9.91706 q^{14} +1.59999 q^{15} -4.41569 q^{16} -0.361675 q^{17} +5.35740 q^{18} -6.51406 q^{19} -5.77754 q^{20} +2.49750 q^{21} +1.94021 q^{22} -3.28334 q^{23} -0.223352 q^{24} +5.72237 q^{25} +3.20137 q^{26} +2.81506 q^{27} -9.01846 q^{28} -3.07969 q^{29} -3.10430 q^{30} -0.108979 q^{31} +7.65313 q^{32} +0.488619 q^{33} +0.701725 q^{34} +16.7371 q^{35} -4.87196 q^{36} +6.91812 q^{37} +12.6386 q^{38} +0.806230 q^{39} -1.49680 q^{40} +2.36210 q^{41} -4.84567 q^{42} +10.3157 q^{43} -1.76440 q^{44} +9.04172 q^{45} +6.37035 q^{46} -9.06923 q^{47} +2.15759 q^{48} +19.1258 q^{49} -11.1026 q^{50} +0.176722 q^{51} -2.91129 q^{52} -7.86751 q^{53} -5.46180 q^{54} +3.27450 q^{55} -2.33644 q^{56} +3.18290 q^{57} +5.97523 q^{58} +2.89724 q^{59} +2.82302 q^{60} -4.56108 q^{61} +0.211442 q^{62} +14.1137 q^{63} -6.01728 q^{64} +5.40298 q^{65} -0.948022 q^{66} -6.48900 q^{67} -0.638141 q^{68} +1.60430 q^{69} -32.4734 q^{70} -7.54573 q^{71} -1.26219 q^{72} +9.77411 q^{73} -13.4226 q^{74} -2.79606 q^{75} -11.4934 q^{76} +5.11134 q^{77} -1.56425 q^{78} -9.18891 q^{79} +14.4592 q^{80} +6.90826 q^{81} -4.58297 q^{82} -5.65099 q^{83} +4.40660 q^{84} +1.18431 q^{85} -20.0146 q^{86} +1.50480 q^{87} -0.457109 q^{88} +7.82643 q^{89} -17.5428 q^{90} +8.43380 q^{91} -5.79313 q^{92} +0.0532493 q^{93} +17.5962 q^{94} +21.3303 q^{95} -3.73947 q^{96} +1.34946 q^{97} -37.1081 q^{98} +2.76125 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9 - 14 * q^10 - 107 * q^11 - 50 * q^12 - 24 * q^13 - 17 * q^14 - 47 * q^15 + 63 * q^16 + 25 * q^17 - 37 * q^18 - 55 * q^19 - 31 * q^20 + 15 * q^21 + 3 * q^22 - 38 * q^23 + 4 * q^24 + 62 * q^25 - 16 * q^26 - 57 * q^27 - 101 * q^28 + 27 * q^29 - 14 * q^30 - 112 * q^31 - 4 * q^32 + 18 * q^33 - 66 * q^34 + 8 * q^35 + 35 * q^36 - 60 * q^37 - 45 * q^38 - 58 * q^39 - 50 * q^40 - 14 * q^41 - 36 * q^42 - 78 * q^43 - 91 * q^44 - 68 * q^45 - 18 * q^46 - 109 * q^47 - 99 * q^48 + 61 * q^49 - 32 * q^50 - 10 * q^51 - 111 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 44 * q^56 + q^57 - 98 * q^58 - 48 * q^59 - 119 * q^60 - 30 * q^61 + 32 * q^62 - 126 * q^63 + 3 * q^64 + 43 * q^65 - 77 * q^67 + 53 * q^68 - 51 * q^69 - 87 * q^70 - 40 * q^71 - 82 * q^72 - 83 * q^73 + 11 * q^74 - 69 * q^75 - 108 * q^76 + 54 * q^77 - 53 * q^78 - 66 * q^79 - 96 * q^80 + 51 * q^81 - 133 * q^82 - 32 * q^83 + 27 * q^84 - 66 * q^85 - 46 * q^86 - 136 * q^87 + 3 * q^88 - 56 * q^89 + 9 * q^90 - 86 * q^91 - 94 * q^92 - 33 * q^93 - 93 * q^94 - 25 * q^95 - 4 * q^96 - 109 * q^97 - 38 * q^98 - 95 * q^99

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