LMFDB - Embedded newform 6017.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0459868962$
Analytic rank:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-2.72367 q^{2} -2.85757 q^{3} +5.41840 q^{4} -2.70389 q^{5} +7.78308 q^{6} +4.38831 q^{7} -9.31062 q^{8} +5.16569 q^{9} +O(q^{10})$	\(q-2.72367 q^{2} -2.85757 q^{3} +5.41840 q^{4} -2.70389 q^{5} +7.78308 q^{6} +4.38831 q^{7} -9.31062 q^{8} +5.16569 q^{9} +7.36452 q^{10} +1.00000 q^{11} -15.4835 q^{12} +0.972201 q^{13} -11.9523 q^{14} +7.72655 q^{15} +14.5223 q^{16} +3.62938 q^{17} -14.0697 q^{18} -7.61438 q^{19} -14.6508 q^{20} -12.5399 q^{21} -2.72367 q^{22} -1.26309 q^{23} +26.6057 q^{24} +2.31103 q^{25} -2.64796 q^{26} -6.18860 q^{27} +23.7777 q^{28} -0.828679 q^{29} -21.0446 q^{30} +2.43847 q^{31} -20.9328 q^{32} -2.85757 q^{33} -9.88525 q^{34} -11.8655 q^{35} +27.9898 q^{36} -3.60471 q^{37} +20.7391 q^{38} -2.77813 q^{39} +25.1749 q^{40} -4.50166 q^{41} +34.1546 q^{42} +5.42155 q^{43} +5.41840 q^{44} -13.9675 q^{45} +3.44026 q^{46} +2.25795 q^{47} -41.4984 q^{48} +12.2573 q^{49} -6.29449 q^{50} -10.3712 q^{51} +5.26778 q^{52} -7.76521 q^{53} +16.8557 q^{54} -2.70389 q^{55} -40.8579 q^{56} +21.7586 q^{57} +2.25705 q^{58} -13.6287 q^{59} +41.8656 q^{60} +5.54857 q^{61} -6.64161 q^{62} +22.6687 q^{63} +27.9695 q^{64} -2.62872 q^{65} +7.78308 q^{66} +5.80300 q^{67} +19.6655 q^{68} +3.60937 q^{69} +32.3178 q^{70} +6.67499 q^{71} -48.0958 q^{72} +13.1635 q^{73} +9.81805 q^{74} -6.60392 q^{75} -41.2578 q^{76} +4.38831 q^{77} +7.56672 q^{78} +11.2562 q^{79} -39.2667 q^{80} +2.18728 q^{81} +12.2611 q^{82} +6.40149 q^{83} -67.9462 q^{84} -9.81345 q^{85} -14.7665 q^{86} +2.36801 q^{87} -9.31062 q^{88} +12.4591 q^{89} +38.0428 q^{90} +4.26632 q^{91} -6.84395 q^{92} -6.96810 q^{93} -6.14993 q^{94} +20.5885 q^{95} +59.8168 q^{96} -1.93701 q^{97} -33.3849 q^{98} +5.16569 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) $ 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * 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 $

$2$	−2.72367	−1.92593	−0.962964	−	0.269628i	$-0.913099\pi$
$2$	−2.72367	−1.92593	−0.962964	+	0.269628i	$0.913099\pi$
$3$	−2.85757	−1.64982	−0.824909	−	0.565266i	$-0.808773\pi$
$3$	−2.85757	−1.64982	−0.824909	+	0.565266i	$0.808773\pi$
$4$	5.41840	2.70920
$5$	−2.70389	−1.20922	−0.604608	−	0.796523i	$-0.706670\pi$
$5$	−2.70389	−1.20922	−0.604608	+	0.796523i	$0.706670\pi$
$6$	7.78308	3.17743
$7$	4.38831	1.65863	0.829313	−	0.558784i	$-0.188732\pi$
$7$	4.38831	1.65863	0.829313	+	0.558784i	$0.188732\pi$
$8$	−9.31062	−3.29180
$9$	5.16569	1.72190
$10$	7.36452	2.32887
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−15.4835	−4.46969
$13$	0.972201	0.269640	0.134820	−	0.990870i	$-0.456954\pi$
$13$	0.972201	0.269640	0.134820	+	0.990870i	$0.456954\pi$
$14$	−11.9523	−3.19440
$15$	7.72655	1.99499
$16$	14.5223	3.63057
$17$	3.62938	0.880254	0.440127	−	0.897936i	$-0.354933\pi$
$17$	3.62938	0.880254	0.440127	+	0.897936i	$0.354933\pi$
$18$	−14.0697	−3.31625
$19$	−7.61438	−1.74686	−0.873429	−	0.486951i	$-0.838109\pi$
$19$	−7.61438	−1.74686	−0.873429	+	0.486951i	$0.838109\pi$
$20$	−14.6508	−3.27601
$21$	−12.5399	−2.73643
$22$	−2.72367	−0.580689
$23$	−1.26309	−0.263373	−0.131687	−	0.991291i	$-0.542039\pi$
$23$	−1.26309	−0.263373	−0.131687	+	0.991291i	$0.542039\pi$
$24$	26.6057	5.43087
$25$	2.31103	0.462206
$26$	−2.64796	−0.519307
$27$	−6.18860	−1.19100
$28$	23.7777	4.49355
$29$	−0.828679	−0.153882	−0.0769409	−	0.997036i	$-0.524515\pi$
$29$	−0.828679	−0.153882	−0.0769409	+	0.997036i	$0.524515\pi$
$30$	−21.0446	−3.84220
$31$	2.43847	0.437963	0.218981	−	0.975729i	$-0.429727\pi$
$31$	2.43847	0.437963	0.218981	+	0.975729i	$0.429727\pi$
$32$	−20.9328	−3.70043
$33$	−2.85757	−0.497439
$34$	−9.88525	−1.69531
$35$	−11.8655	−2.00564
$36$	27.9898	4.66497
$37$	−3.60471	−0.592610	−0.296305	−	0.955093i	$-0.595755\pi$
$37$	−3.60471	−0.592610	−0.296305	+	0.955093i	$0.595755\pi$
$38$	20.7391	3.36432
$39$	−2.77813	−0.444857
$40$	25.1749	3.98050
$41$	−4.50166	−0.703041	−0.351520	−	0.936180i	$-0.614335\pi$
$41$	−4.50166	−0.703041	−0.351520	+	0.936180i	$0.614335\pi$
$42$	34.1546	5.27017
$43$	5.42155	0.826779	0.413389	−	0.910554i	$-0.364345\pi$
$43$	5.42155	0.826779	0.413389	+	0.910554i	$0.364345\pi$
$44$	5.41840	0.816855
$45$	−13.9675	−2.08215
$46$	3.44026	0.507238
$47$	2.25795	0.329356	0.164678	−	0.986347i	$-0.447341\pi$
$47$	2.25795	0.329356	0.164678	+	0.986347i	$0.447341\pi$
$48$	−41.4984	−5.98978
$49$	12.2573	1.75104
$50$	−6.29449	−0.890175
$51$	−10.3712	−1.45226
$52$	5.26778	0.730509
$53$	−7.76521	−1.06663	−0.533317	−	0.845916i	$-0.679055\pi$
$53$	−7.76521	−1.06663	−0.533317	+	0.845916i	$0.679055\pi$
$54$	16.8557	2.29378
$55$	−2.70389	−0.364593
$56$	−40.8579	−5.45987
$57$	21.7586	2.88200
$58$	2.25705	0.296365
$59$	−13.6287	−1.77430	−0.887152	−	0.461478i	$-0.847319\pi$
$59$	−13.6287	−1.77430	−0.887152	+	0.461478i	$0.847319\pi$
$60$	41.8656	5.40482
$61$	5.54857	0.710421	0.355211	−	0.934786i	$-0.384409\pi$
$61$	5.54857	0.710421	0.355211	+	0.934786i	$0.384409\pi$
$62$	−6.64161	−0.843486
$63$	22.6687	2.85598
$64$	27.9695	3.49618
$65$	−2.62872	−0.326053
$66$	7.78308	0.958031
$67$	5.80300	0.708949	0.354474	−	0.935066i	$-0.384660\pi$
$67$	5.80300	0.708949	0.354474	+	0.935066i	$0.384660\pi$
$68$	19.6655	2.38479
$69$	3.60937	0.434518
$70$	32.3178	3.86272
$71$	6.67499	0.792176	0.396088	−	0.918213i	$-0.370368\pi$
$71$	6.67499	0.792176	0.396088	+	0.918213i	$0.370368\pi$
$72$	−48.0958	−5.66814
$73$	13.1635	1.54067	0.770334	−	0.637641i	$-0.220090\pi$
$73$	13.1635	1.54067	0.770334	+	0.637641i	$0.220090\pi$
$74$	9.81805	1.14133
$75$	−6.60392	−0.762555
$76$	−41.2578	−4.73259
$77$	4.38831	0.500095
$78$	7.56672	0.856762
$79$	11.2562	1.26642	0.633209	−	0.773981i	$-0.281738\pi$
$79$	11.2562	1.26642	0.633209	+	0.773981i	$0.281738\pi$
$80$	−39.2667	−4.39015
$81$	2.18728	0.243031
$82$	12.2611	1.35401
$83$	6.40149	0.702654	0.351327	−	0.936253i	$-0.385730\pi$
$83$	6.40149	0.702654	0.351327	+	0.936253i	$0.385730\pi$
$84$	−67.9462	−7.41354
$85$	−9.81345	−1.06442
$86$	−14.7665	−1.59232
$87$	2.36801	0.253877
$88$	−9.31062	−0.992516
$89$	12.4591	1.32067	0.660334	−	0.750972i	$-0.270415\pi$
$89$	12.4591	1.32067	0.660334	+	0.750972i	$0.270415\pi$
$90$	38.0428	4.01007
$91$	4.26632	0.447232
$92$	−6.84395	−0.713531
$93$	−6.96810	−0.722559
$94$	−6.14993	−0.634317
$95$	20.5885	2.11233
$96$	59.8168	6.10503
$97$	−1.93701	−0.196673	−0.0983367	−	0.995153i	$-0.531352\pi$
$97$	−1.93701	−0.196673	−0.0983367	+	0.995153i	$0.531352\pi$
$98$	−33.3849	−3.37238
$99$	5.16569	0.519171
$100$	12.5221	1.25221
$101$	−18.2046	−1.81143	−0.905714	−	0.423889i	$-0.860665\pi$
$101$	−18.2046	−1.81143	−0.905714	+	0.423889i	$0.860665\pi$
$102$	28.2478	2.79695
$103$	−0.410321	−0.0404301	−0.0202151	−	0.999796i	$-0.506435\pi$
$103$	−0.410321	−0.0404301	−0.0202151	+	0.999796i	$0.506435\pi$
$104$	−9.05179	−0.887601
$105$	33.9065	3.30894
$106$	21.1499	2.05426
$107$	−8.92853	−0.863154	−0.431577	−	0.902076i	$-0.642043\pi$
$107$	−8.92853	−0.863154	−0.431577	+	0.902076i	$0.642043\pi$
$108$	−33.5323	−3.22665
$109$	−3.40288	−0.325937	−0.162969	−	0.986631i	$-0.552107\pi$
$109$	−3.40288	−0.325937	−0.162969	+	0.986631i	$0.552107\pi$
$110$	7.36452	0.702179
$111$	10.3007	0.977699
$112$	63.7284	6.02177
$113$	18.9793	1.78543	0.892713	−	0.450627i	$-0.148799\pi$
$113$	18.9793	1.78543	0.892713	+	0.450627i	$0.148799\pi$
$114$	−59.2633	−5.55052
$115$	3.41527	0.318475
$116$	−4.49012	−0.416897
$117$	5.02209	0.464292
$118$	37.1201	3.41718
$119$	15.9269	1.46001
$120$	−71.9390	−6.56710
$121$	1.00000	0.0909091
$122$	−15.1125	−1.36822
$123$	12.8638	1.15989
$124$	13.2126	1.18653
$125$	7.27069	0.650310
$126$	−61.7421	−5.50042
$127$	−19.1631	−1.70045	−0.850223	−	0.526422i	$-0.823533\pi$
$127$	−19.1631	−1.70045	−0.850223	+	0.526422i	$0.823533\pi$
$128$	−34.3142	−3.03298
$129$	−15.4924	−1.36403
$130$	7.15979	0.627955
$131$	12.6763	1.10754	0.553768	−	0.832671i	$-0.313190\pi$
$131$	12.6763	1.10754	0.553768	+	0.832671i	$0.313190\pi$
$132$	−15.4835	−1.34766
$133$	−33.4143	−2.89739
$134$	−15.8055	−1.36539
$135$	16.7333	1.44017
$136$	−33.7918	−2.89762
$137$	−9.74715	−0.832755	−0.416377	−	0.909192i	$-0.636701\pi$
$137$	−9.74715	−0.832755	−0.416377	+	0.909192i	$0.636701\pi$
$138$	−9.83076	−0.836850
$139$	−1.91712	−0.162608	−0.0813042	−	0.996689i	$-0.525909\pi$
$139$	−1.91712	−0.162608	−0.0813042	+	0.996689i	$0.525909\pi$
$140$	−64.2922	−5.43368
$141$	−6.45225	−0.543377
$142$	−18.1805	−1.52567
$143$	0.972201	0.0812995
$144$	75.0177	6.25147
$145$	2.24066	0.186077
$146$	−35.8530	−2.96722
$147$	−35.0260	−2.88890
$148$	−19.5318	−1.60550
$149$	2.56198	0.209886	0.104943	−	0.994478i	$-0.466534\pi$
$149$	2.56198	0.209886	0.104943	+	0.994478i	$0.466534\pi$
$150$	17.9869	1.46863
$151$	−19.4100	−1.57957	−0.789784	−	0.613385i	$-0.789807\pi$
$151$	−19.4100	−1.57957	−0.789784	+	0.613385i	$0.789807\pi$
$152$	70.8946	5.75031
$153$	18.7483	1.51571
$154$	−11.9523	−0.963147
$155$	−6.59337	−0.529592
$156$	−15.0530	−1.20521
$157$	8.13275	0.649064	0.324532	−	0.945875i	$-0.394793\pi$
$157$	8.13275	0.649064	0.324532	+	0.945875i	$0.394793\pi$
$158$	−30.6581	−2.43903
$159$	22.1896	1.75975
$160$	56.5999	4.47462
$161$	−5.54285	−0.436838
$162$	−5.95743	−0.468060
$163$	23.1832	1.81585	0.907924	−	0.419136i	$-0.137667\pi$
$163$	23.1832	1.81585	0.907924	+	0.419136i	$0.137667\pi$
$164$	−24.3918	−1.90468
$165$	7.72655	0.601511
$166$	−17.4356	−1.35326
$167$	9.24475	0.715380	0.357690	−	0.933840i	$-0.383564\pi$
$167$	9.24475	0.715380	0.357690	+	0.933840i	$0.383564\pi$
$168$	116.754	9.00779
$169$	−12.0548	−0.927294
$170$	26.7286	2.04999
$171$	−39.3335	−3.00791
$172$	29.3762	2.23991
$173$	4.73112	0.359700	0.179850	−	0.983694i	$-0.442439\pi$
$173$	4.73112	0.359700	0.179850	+	0.983694i	$0.442439\pi$
$174$	−6.44968	−0.488949
$175$	10.1415	0.766626
$176$	14.5223	1.09466
$177$	38.9449	2.92728
$178$	−33.9347	−2.54351
$179$	−17.3500	−1.29680	−0.648399	−	0.761300i	$-0.724561\pi$
$179$	−17.3500	−1.29680	−0.648399	+	0.761300i	$0.724561\pi$
$180$	−75.6814	−5.64096
$181$	12.1820	0.905481	0.452740	−	0.891642i	$-0.350446\pi$
$181$	12.1820	0.905481	0.452740	+	0.891642i	$0.350446\pi$
$182$	−11.6201	−0.861337
$183$	−15.8554	−1.17206
$184$	11.7602	0.866973
$185$	9.74674	0.716595
$186$	18.9789	1.39160
$187$	3.62938	0.265407
$188$	12.2345	0.892293
$189$	−27.1575	−1.97542
$190$	−56.0762	−4.06820
$191$	22.2206	1.60783	0.803913	−	0.594747i	$-0.202748\pi$
$191$	22.2206	1.60783	0.803913	+	0.594747i	$0.202748\pi$
$192$	−79.9246	−5.76806
$193$	−20.6837	−1.48885	−0.744423	−	0.667708i	$-0.767276\pi$
$193$	−20.6837	−1.48885	−0.744423	+	0.667708i	$0.767276\pi$
$194$	5.27578	0.378779
$195$	7.51176	0.537928
$196$	66.4150	4.74393
$197$	15.1354	1.07835	0.539175	−	0.842194i	$-0.318736\pi$
$197$	15.1354	1.07835	0.539175	+	0.842194i	$0.318736\pi$
$198$	−14.0697	−0.999887
$199$	−21.9766	−1.55788	−0.778938	−	0.627101i	$-0.784241\pi$
$199$	−21.9766	−1.55788	−0.778938	+	0.627101i	$0.784241\pi$
$200$	−21.5171	−1.52149
$201$	−16.5825	−1.16964
$202$	49.5835	3.48868
$203$	−3.63650	−0.255232
$204$	−56.1953	−3.93446
$205$	12.1720	0.850129
$206$	1.11758	0.0778655
$207$	−6.52475	−0.453501
$208$	14.1186	0.978948
$209$	−7.61438	−0.526698
$210$	−92.3503	−6.37278
$211$	−15.4828	−1.06588	−0.532940	−	0.846153i	$-0.678913\pi$
$211$	−15.4828	−1.06588	−0.532940	+	0.846153i	$0.678913\pi$
$212$	−42.0751	−2.88973
$213$	−19.0742	−1.30695
$214$	24.3184	1.66237
$215$	−14.6593	−0.999755
$216$	57.6197	3.92053
$217$	10.7008	0.726417
$218$	9.26835	0.627732
$219$	−37.6155	−2.54182
$220$	−14.6508	−0.987755
$221$	3.52849	0.237352
$222$	−28.0557	−1.88298
$223$	23.1258	1.54862	0.774308	−	0.632809i	$-0.218098\pi$
$223$	23.1258	1.54862	0.774308	+	0.632809i	$0.218098\pi$
$224$	−91.8596	−6.13763
$225$	11.9381	0.795870
$226$	−51.6935	−3.43860
$227$	17.6225	1.16965	0.584823	−	0.811161i	$-0.301164\pi$
$227$	17.6225	1.16965	0.584823	+	0.811161i	$0.301164\pi$
$228$	117.897	7.80791
$229$	0.0483466	0.00319483	0.00159742	−	0.999999i	$-0.499492\pi$
$229$	0.0483466	0.00319483	0.00159742	+	0.999999i	$0.499492\pi$
$230$	−9.30208	−0.613361
$231$	−12.5399	−0.825065
$232$	7.71552	0.506549
$233$	−5.22133	−0.342061	−0.171030	−	0.985266i	$-0.554710\pi$
$233$	−5.22133	−0.342061	−0.171030	+	0.985266i	$0.554710\pi$
$234$	−13.6785	−0.894193
$235$	−6.10526	−0.398263
$236$	−73.8457	−4.80695
$237$	−32.1652	−2.08936
$238$	−43.3796	−2.81188
$239$	−12.3439	−0.798459	−0.399229	−	0.916851i	$-0.630722\pi$
$239$	−12.3439	−0.798459	−0.399229	+	0.916851i	$0.630722\pi$
$240$	112.207	7.24295
$241$	−25.4626	−1.64019	−0.820094	−	0.572229i	$-0.806079\pi$
$241$	−25.4626	−1.64019	−0.820094	+	0.572229i	$0.806079\pi$
$242$	−2.72367	−0.175084
$243$	12.3155	0.790041
$244$	30.0644	1.92467
$245$	−33.1424	−2.11739
$246$	−35.0368	−2.23386
$247$	−7.40270	−0.471023
$248$	−22.7037	−1.44169
$249$	−18.2927	−1.15925
$250$	−19.8030	−1.25245
$251$	−8.16771	−0.515542	−0.257771	−	0.966206i	$-0.582988\pi$
$251$	−8.16771	−0.515542	−0.257771	+	0.966206i	$0.582988\pi$
$252$	122.828	7.73743
$253$	−1.26309	−0.0794100
$254$	52.1939	3.27494
$255$	28.0426	1.75610
$256$	37.5218	2.34511
$257$	3.98005	0.248268	0.124134	−	0.992265i	$-0.460385\pi$
$257$	3.98005	0.248268	0.124134	+	0.992265i	$0.460385\pi$
$258$	42.1964	2.62703
$259$	−15.8186	−0.982919
$260$	−14.2435	−0.883344
$261$	−4.28070	−0.264969
$262$	−34.5262	−2.13303
$263$	−9.51209	−0.586541	−0.293270	−	0.956030i	$-0.594744\pi$
$263$	−9.51209	−0.586541	−0.293270	+	0.956030i	$0.594744\pi$
$264$	26.6057	1.63747
$265$	20.9963	1.28979
$266$	91.0096	5.58016
$267$	−35.6029	−2.17886
$268$	31.4430	1.92069
$269$	−8.72031	−0.531687	−0.265843	−	0.964016i	$-0.585650\pi$
$269$	−8.72031	−0.531687	−0.265843	+	0.964016i	$0.585650\pi$
$270$	−45.5761	−2.77367
$271$	15.7107	0.954355	0.477177	−	0.878807i	$-0.341660\pi$
$271$	15.7107	0.954355	0.477177	+	0.878807i	$0.341660\pi$
$272$	52.7069	3.19583
$273$	−12.1913	−0.737851
$274$	26.5481	1.60383
$275$	2.31103	0.139360
$276$	19.5571	1.17720
$277$	−2.28145	−0.137079	−0.0685395	−	0.997648i	$-0.521834\pi$
$277$	−2.28145	−0.137079	−0.0685395	+	0.997648i	$0.521834\pi$
$278$	5.22162	0.313172
$279$	12.5964	0.754127
$280$	110.475	6.60217
$281$	−29.1592	−1.73949	−0.869747	−	0.493498i	$-0.835718\pi$
$281$	−29.1592	−1.73949	−0.869747	+	0.493498i	$0.835718\pi$
$282$	17.5738	1.04651
$283$	10.1217	0.601675	0.300837	−	0.953675i	$-0.402734\pi$
$283$	10.1217	0.601675	0.300837	+	0.953675i	$0.402734\pi$
$284$	36.1678	2.14617
$285$	−58.8329	−3.48496
$286$	−2.64796	−0.156577
$287$	−19.7547	−1.16608
$288$	−108.132	−6.37175
$289$	−3.82760	−0.225153
$290$	−6.10282	−0.358370
$291$	5.53513	0.324475
$292$	71.3250	4.17398
$293$	28.3489	1.65616	0.828080	−	0.560610i	$-0.189433\pi$
$293$	28.3489	1.65616	0.828080	+	0.560610i	$0.189433\pi$
$294$	95.3995	5.56381
$295$	36.8505	2.14552
$296$	33.5621	1.95076
$297$	−6.18860	−0.359099
$298$	−6.97800	−0.404225
$299$	−1.22798	−0.0710159
$300$	−35.7827	−2.06592
$301$	23.7915	1.37132
$302$	52.8667	3.04213
$303$	52.0210	2.98853
$304$	−110.578	−6.34210
$305$	−15.0027	−0.859053
$306$	−51.0641	−2.91914
$307$	16.3986	0.935918	0.467959	−	0.883750i	$-0.344989\pi$
$307$	16.3986	0.935918	0.467959	+	0.883750i	$0.344989\pi$
$308$	23.7777	1.35486
$309$	1.17252	0.0667023
$310$	17.9582	1.01996
$311$	−11.8689	−0.673023	−0.336511	−	0.941679i	$-0.609247\pi$
$311$	−11.8689	−0.673023	−0.336511	+	0.941679i	$0.609247\pi$
$312$	25.8661	1.46438
$313$	−1.27772	−0.0722212	−0.0361106	−	0.999348i	$-0.511497\pi$
$313$	−1.27772	−0.0722212	−0.0361106	+	0.999348i	$0.511497\pi$
$314$	−22.1510	−1.25005
$315$	−61.2936	−3.45350
$316$	60.9904	3.43098
$317$	−32.9150	−1.84869	−0.924346	−	0.381555i	$-0.875389\pi$
$317$	−32.9150	−1.84869	−0.924346	+	0.381555i	$0.875389\pi$
$318$	−60.4373	−3.38915
$319$	−0.828679	−0.0463971
$320$	−75.6264	−4.22765
$321$	25.5139	1.42405
$322$	15.0969	0.841319
$323$	−27.6355	−1.53768
$324$	11.8515	0.658419
$325$	2.24678	0.124629
$326$	−63.1435	−3.49719
$327$	9.72397	0.537737
$328$	41.9132	2.31427
$329$	9.90860	0.546279
$330$	−21.0446	−1.15847
$331$	−0.127505	−0.00700830	−0.00350415	−	0.999994i	$-0.501115\pi$
$331$	−0.127505	−0.00700830	−0.00350415	+	0.999994i	$0.501115\pi$
$332$	34.6858	1.90363
$333$	−18.6208	−1.02041
$334$	−25.1797	−1.37777
$335$	−15.6907	−0.857273
$336$	−182.108	−9.93481
$337$	14.7512	0.803549	0.401775	−	0.915739i	$-0.368393\pi$
$337$	14.7512	0.803549	0.401775	+	0.915739i	$0.368393\pi$
$338$	32.8334	1.78590
$339$	−54.2347	−2.94562
$340$	−53.1732	−2.88372
$341$	2.43847	0.132051
$342$	107.132	5.79302
$343$	23.0706	1.24570
$344$	−50.4780	−2.72159
$345$	−9.75936	−0.525426
$346$	−12.8860	−0.692757
$347$	−15.2190	−0.816999	−0.408500	−	0.912759i	$-0.633948\pi$
$347$	−15.2190	−0.816999	−0.408500	+	0.912759i	$0.633948\pi$
$348$	12.8308	0.687804
$349$	6.77772	0.362803	0.181401	−	0.983409i	$-0.441937\pi$
$349$	6.77772	0.362803	0.181401	+	0.983409i	$0.441937\pi$
$350$	−27.6222	−1.47647
$351$	−6.01656	−0.321140
$352$	−20.9328	−1.11572
$353$	−12.7620	−0.679255	−0.339627	−	0.940560i	$-0.610301\pi$
$353$	−12.7620	−0.679255	−0.339627	+	0.940560i	$0.610301\pi$
$354$	−106.073	−5.63773
$355$	−18.0485	−0.957913
$356$	67.5087	3.57795
$357$	−45.5121	−2.40875
$358$	47.2557	2.49754
$359$	−7.75735	−0.409417	−0.204709	−	0.978823i	$-0.565625\pi$
$359$	−7.75735	−0.409417	−0.204709	+	0.978823i	$0.565625\pi$
$360$	130.046	6.85401
$361$	38.9788	2.05151
$362$	−33.1798	−1.74389
$363$	−2.85757	−0.149983
$364$	23.1167	1.21164
$365$	−35.5926	−1.86300
$366$	43.1850	2.25731
$367$	−18.9443	−0.988885	−0.494442	−	0.869210i	$-0.664628\pi$
$367$	−18.9443	−0.988885	−0.494442	+	0.869210i	$0.664628\pi$
$368$	−18.3430	−0.956196
$369$	−23.2542	−1.21056
$370$	−26.5469	−1.38011
$371$	−34.0762	−1.76915
$372$	−37.7560	−1.95756
$373$	−31.0134	−1.60582	−0.802908	−	0.596103i	$-0.796715\pi$
$373$	−31.0134	−1.60582	−0.802908	+	0.596103i	$0.796715\pi$
$374$	−9.88525	−0.511154
$375$	−20.7765	−1.07289
$376$	−21.0229	−1.08418
$377$	−0.805642	−0.0414927
$378$	73.9683	3.80452
$379$	−22.5784	−1.15977	−0.579886	−	0.814697i	$-0.696903\pi$
$379$	−22.5784	−1.15977	−0.579886	+	0.814697i	$0.696903\pi$
$380$	111.557	5.72273
$381$	54.7597	2.80543
$382$	−60.5217	−3.09656
$383$	20.2710	1.03580	0.517900	−	0.855441i	$-0.326714\pi$
$383$	20.2710	1.03580	0.517900	+	0.855441i	$0.326714\pi$
$384$	98.0551	5.00385
$385$	−11.8655	−0.604723
$386$	56.3357	2.86741
$387$	28.0061	1.42363
$388$	−10.4955	−0.532828
$389$	26.9522	1.36653	0.683266	−	0.730169i	$-0.260559\pi$
$389$	26.9522	1.36653	0.683266	+	0.730169i	$0.260559\pi$
$390$	−20.4596	−1.03601
$391$	−4.58425	−0.231835
$392$	−114.123	−5.76408
$393$	−36.2234	−1.82723
$394$	−41.2238	−2.07682
$395$	−30.4354	−1.53137
$396$	27.9898	1.40654
$397$	25.8659	1.29817	0.649086	−	0.760715i	$-0.275152\pi$
$397$	25.8659	1.29817	0.649086	+	0.760715i	$0.275152\pi$
$398$	59.8570	3.00036
$399$	95.4835	4.78016
$400$	33.5614	1.67807
$401$	28.8931	1.44285	0.721425	−	0.692492i	$-0.243487\pi$
$401$	28.8931	1.44285	0.721425	+	0.692492i	$0.243487\pi$
$402$	45.1652	2.25264
$403$	2.37069	0.118092
$404$	−98.6401	−4.90753
$405$	−5.91416	−0.293877
$406$	9.90465	0.491560
$407$	−3.60471	−0.178679
$408$	96.5623	4.78055
$409$	9.18174	0.454008	0.227004	−	0.973894i	$-0.427107\pi$
$409$	9.18174	0.454008	0.227004	+	0.973894i	$0.427107\pi$
$410$	−33.1525	−1.63729
$411$	27.8531	1.37389
$412$	−2.22328	−0.109533
$413$	−59.8069	−2.94291
$414$	17.7713	0.873412
$415$	−17.3089	−0.849661
$416$	−20.3509	−0.997783
$417$	5.47831	0.268274
$418$	20.7391	1.01438
$419$	−19.0296	−0.929659	−0.464829	−	0.885400i	$-0.653884\pi$
$419$	−19.0296	−0.929659	−0.464829	+	0.885400i	$0.653884\pi$
$420$	183.719	8.96458
$421$	31.4204	1.53134	0.765668	−	0.643236i	$-0.222409\pi$
$421$	31.4204	1.53134	0.765668	+	0.643236i	$0.222409\pi$
$422$	42.1701	2.05281
$423$	11.6639	0.567117
$424$	72.2989	3.51115
$425$	8.38760	0.406858
$426$	51.9520	2.51708
$427$	24.3488	1.17832
$428$	−48.3784	−2.33846
$429$	−2.77813	−0.134129
$430$	39.9271	1.92546
$431$	12.6346	0.608589	0.304294	−	0.952578i	$-0.401579\pi$
$431$	12.6346	0.608589	0.304294	+	0.952578i	$0.401579\pi$
$432$	−89.8727	−4.32400
$433$	−2.55424	−0.122749	−0.0613744	−	0.998115i	$-0.519548\pi$
$433$	−2.55424	−0.122749	−0.0613744	+	0.998115i	$0.519548\pi$
$434$	−29.1455	−1.39903
$435$	−6.40283	−0.306992
$436$	−18.4382	−0.883030
$437$	9.61767	0.460076
$438$	102.452	4.89536
$439$	−12.9654	−0.618806	−0.309403	−	0.950931i	$-0.600129\pi$
$439$	−12.9654	−0.618806	−0.309403	+	0.950931i	$0.600129\pi$
$440$	25.1749	1.20017
$441$	63.3174	3.01511
$442$	−9.61045	−0.457122
$443$	−18.8049	−0.893448	−0.446724	−	0.894672i	$-0.647409\pi$
$443$	−18.8049	−0.893448	−0.446724	+	0.894672i	$0.647409\pi$
$444$	55.8133	2.64878
$445$	−33.6882	−1.59697
$446$	−62.9871	−2.98252
$447$	−7.32103	−0.346273
$448$	122.739	5.79886
$449$	21.0568	0.993734	0.496867	−	0.867827i	$-0.334484\pi$
$449$	21.0568	0.993734	0.496867	+	0.867827i	$0.334484\pi$
$450$	−32.5154	−1.53279
$451$	−4.50166	−0.211975
$452$	102.838	4.83708
$453$	55.4655	2.60600
$454$	−47.9980	−2.25266
$455$	−11.5357	−0.540800
$456$	−202.586	−9.48696
$457$	−14.8336	−0.693888	−0.346944	−	0.937886i	$-0.612781\pi$
$457$	−14.8336	−0.693888	−0.346944	+	0.937886i	$0.612781\pi$
$458$	−0.131680	−0.00615302
$459$	−22.4608	−1.04838
$460$	18.5053	0.862814
$461$	−6.80607	−0.316990	−0.158495	−	0.987360i	$-0.550664\pi$
$461$	−6.80607	−0.316990	−0.158495	+	0.987360i	$0.550664\pi$
$462$	34.1546	1.58902
$463$	−10.0139	−0.465386	−0.232693	−	0.972550i	$-0.574754\pi$
$463$	−10.0139	−0.465386	−0.232693	+	0.972550i	$0.574754\pi$
$464$	−12.0343	−0.558679
$465$	18.8410	0.873730
$466$	14.2212	0.658784
$467$	25.1647	1.16448	0.582241	−	0.813016i	$-0.302176\pi$
$467$	25.1647	1.16448	0.582241	+	0.813016i	$0.302176\pi$
$468$	27.2117	1.25786
$469$	25.4654	1.17588
$470$	16.6287	0.767026
$471$	−23.2399	−1.07084
$472$	126.892	5.84066
$473$	5.42155	0.249283
$474$	87.6076	4.02395
$475$	−17.5970	−0.807408
$476$	86.2982	3.95547
$477$	−40.1127	−1.83663
$478$	33.6207	1.53778
$479$	15.3669	0.702130	0.351065	−	0.936351i	$-0.385820\pi$
$479$	15.3669	0.702130	0.351065	+	0.936351i	$0.385820\pi$
$480$	−161.738	−7.38230
$481$	−3.50450	−0.159791
$482$	69.3518	3.15889
$483$	15.8391	0.720702
$484$	5.41840	0.246291
$485$	5.23746	0.237821
$486$	−33.5435	−1.52156
$487$	−12.7673	−0.578544	−0.289272	−	0.957247i	$-0.593413\pi$
$487$	−12.7673	−0.578544	−0.289272	+	0.957247i	$0.593413\pi$
$488$	−51.6606	−2.33857
$489$	−66.2475	−2.99582
$490$	90.2691	4.07794
$491$	−5.08947	−0.229684	−0.114842	−	0.993384i	$-0.536636\pi$
$491$	−5.08947	−0.229684	−0.114842	+	0.993384i	$0.536636\pi$
$492$	69.7012	3.14237
$493$	−3.00759	−0.135455
$494$	20.1626	0.907156
$495$	−13.9675	−0.627791
$496$	35.4123	1.59006
$497$	29.2920	1.31392
$498$	49.8233	2.23264
$499$	7.32666	0.327986	0.163993	−	0.986461i	$-0.447562\pi$
$499$	7.32666	0.327986	0.163993	+	0.986461i	$0.447562\pi$
$500$	39.3955	1.76182
$501$	−26.4175	−1.18025
$502$	22.2462	0.992896
$503$	43.0257	1.91842	0.959210	−	0.282693i	$-0.0912278\pi$
$503$	43.0257	1.91842	0.959210	+	0.282693i	$0.0912278\pi$
$504$	−211.059	−9.40133
$505$	49.2233	2.19041
$506$	3.44026	0.152938
$507$	34.4475	1.52987
$508$	−103.833	−4.60685
$509$	5.34243	0.236799	0.118400	−	0.992966i	$-0.462224\pi$
$509$	5.34243	0.236799	0.118400	+	0.992966i	$0.462224\pi$
$510$	−76.3789	−3.38211
$511$	57.7654	2.55539
$512$	−33.5687	−1.48354
$513$	47.1224	2.08050
$514$	−10.8404	−0.478147
$515$	1.10946	0.0488888
$516$	−83.9444	−3.69544
$517$	2.25795	0.0993046
$518$	43.0847	1.89303
$519$	−13.5195	−0.593440
$520$	24.4751	1.07330
$521$	35.9579	1.57534	0.787672	−	0.616094i	$-0.211286\pi$
$521$	35.9579	1.57534	0.787672	+	0.616094i	$0.211286\pi$
$522$	11.6592	0.510311
$523$	1.22771	0.0536840	0.0268420	−	0.999640i	$-0.491455\pi$
$523$	1.22771	0.0536840	0.0268420	+	0.999640i	$0.491455\pi$
$524$	68.6854	3.00054
$525$	−28.9801	−1.26479
$526$	25.9078	1.12964
$527$	8.85015	0.385519
$528$	−41.4984	−1.80599
$529$	−21.4046	−0.930635
$530$	−57.1871	−2.48405
$531$	−70.4015	−3.05517
$532$	−181.052	−7.84960
$533$	−4.37651	−0.189568
$534$	96.9706	4.19633
$535$	24.1418	1.04374
$536$	−54.0295	−2.33372
$537$	49.5787	2.13948
$538$	23.7513	1.02399
$539$	12.2573	0.527959
$540$	90.6678	3.90172
$541$	33.2004	1.42740	0.713699	−	0.700453i	$-0.247019\pi$
$541$	33.2004	1.42740	0.713699	+	0.700453i	$0.247019\pi$
$542$	−42.7907	−1.83802
$543$	−34.8109	−1.49388
$544$	−75.9730	−3.25732
$545$	9.20103	0.394129
$546$	33.2051	1.42105
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−52.8140	−2.25610
$549$	28.6622	1.22327
$550$	−6.29449	−0.268398
$551$	6.30988	0.268810
$552$	−33.6055	−1.43035
$553$	49.3956	2.10051
$554$	6.21393	0.264005
$555$	−27.8520	−1.18225
$556$	−10.3878	−0.440539
$557$	8.44220	0.357708	0.178854	−	0.983876i	$-0.442761\pi$
$557$	8.44220	0.357708	0.178854	+	0.983876i	$0.442761\pi$
$558$	−34.3085	−1.45239
$559$	5.27084	0.222933
$560$	−172.315	−7.28162
$561$	−10.3712	−0.437872
$562$	79.4203	3.35014
$563$	9.22171	0.388649	0.194324	−	0.980937i	$-0.437749\pi$
$563$	9.22171	0.388649	0.194324	+	0.980937i	$0.437749\pi$
$564$	−34.9609	−1.47212
$565$	−51.3180	−2.15897
$566$	−27.5683	−1.15878
$567$	9.59845	0.403097
$568$	−62.1483	−2.60769
$569$	0.490672	0.0205701	0.0102850	−	0.999947i	$-0.496726\pi$
$569$	0.490672	0.0205701	0.0102850	+	0.999947i	$0.496726\pi$
$570$	160.242	6.71178
$571$	9.81011	0.410540	0.205270	−	0.978705i	$-0.434193\pi$
$571$	9.81011	0.410540	0.205270	+	0.978705i	$0.434193\pi$
$572$	5.26778	0.220257
$573$	−63.4969	−2.65262
$574$	53.8053	2.24579
$575$	−2.91905	−0.121733
$576$	144.482	6.02007
$577$	−9.20533	−0.383223	−0.191611	−	0.981471i	$-0.561371\pi$
$577$	−9.20533	−0.383223	−0.191611	+	0.981471i	$0.561371\pi$
$578$	10.4251	0.433628
$579$	59.1051	2.45632
$580$	12.1408	0.504119
$581$	28.0917	1.16544
$582$	−15.0759	−0.624916
$583$	−7.76521	−0.321602
$584$	−122.560	−5.07157
$585$	−13.5792	−0.561430
$586$	−77.2131	−3.18965
$587$	−22.6768	−0.935973	−0.467987	−	0.883736i	$-0.655020\pi$
$587$	−22.6768	−0.935973	−0.467987	+	0.883736i	$0.655020\pi$
$588$	−189.785	−7.82661
$589$	−18.5675	−0.765059
$590$	−100.369	−4.13211
$591$	−43.2503	−1.77908
$592$	−52.3486	−2.15152
$593$	44.4662	1.82601	0.913003	−	0.407952i	$-0.133757\pi$
$593$	44.4662	1.82601	0.913003	+	0.407952i	$0.133757\pi$
$594$	16.8557	0.691599
$595$	−43.0645	−1.76547
$596$	13.8819	0.568623
$597$	62.7995	2.57021
$598$	3.34462	0.136772
$599$	−22.5707	−0.922215	−0.461107	−	0.887344i	$-0.652548\pi$
$599$	−22.5707	−0.922215	−0.461107	+	0.887344i	$0.652548\pi$
$600$	61.4866	2.51018
$601$	18.6949	0.762582	0.381291	−	0.924455i	$-0.375480\pi$
$601$	18.6949	0.762582	0.381291	+	0.924455i	$0.375480\pi$
$602$	−64.8002	−2.64106
$603$	29.9765	1.22074
$604$	−105.172	−4.27937
$605$	−2.70389	−0.109929
$606$	−141.688	−5.75569
$607$	37.3827	1.51732	0.758659	−	0.651488i	$-0.225855\pi$
$607$	37.3827	1.51732	0.758659	+	0.651488i	$0.225855\pi$
$608$	159.390	6.46412
$609$	10.3916	0.421087
$610$	40.8625	1.65448
$611$	2.19518	0.0888076
$612$	101.586	4.10635
$613$	−32.8805	−1.32803	−0.664015	−	0.747719i	$-0.731149\pi$
$613$	−32.8805	−1.32803	−0.664015	+	0.747719i	$0.731149\pi$
$614$	−44.6645	−1.80251
$615$	−34.7823	−1.40256
$616$	−40.8579	−1.64621
$617$	−17.8757	−0.719648	−0.359824	−	0.933020i	$-0.617163\pi$
$617$	−17.8757	−0.719648	−0.359824	+	0.933020i	$0.617163\pi$
$618$	−3.19356	−0.128464
$619$	−2.04745	−0.0822938	−0.0411469	−	0.999153i	$-0.513101\pi$
$619$	−2.04745	−0.0822938	−0.0411469	+	0.999153i	$0.513101\pi$
$620$	−35.7255	−1.43477
$621$	7.81678	0.313677
$622$	32.3270	1.29619
$623$	54.6746	2.19049
$624$	−40.3448	−1.61509
$625$	−31.2143	−1.24857
$626$	3.48011	0.139093
$627$	21.7586	0.868955
$628$	44.0665	1.75845
$629$	−13.0829	−0.521648
$630$	166.944	6.65120
$631$	19.9231	0.793125	0.396563	−	0.918008i	$-0.370203\pi$
$631$	19.9231	0.793125	0.396563	+	0.918008i	$0.370203\pi$
$632$	−104.802	−4.16879
$633$	44.2431	1.75851
$634$	89.6499	3.56045
$635$	51.8148	2.05621
$636$	120.232	4.76752
$637$	11.9165	0.472151
$638$	2.25705	0.0893576
$639$	34.4809	1.36405
$640$	92.7819	3.66753
$641$	34.6619	1.36906	0.684531	−	0.728984i	$-0.260007\pi$
$641$	34.6619	1.36906	0.684531	+	0.728984i	$0.260007\pi$
$642$	−69.4915	−2.74261
$643$	22.8479	0.901032	0.450516	−	0.892768i	$-0.351240\pi$
$643$	22.8479	0.901032	0.450516	+	0.892768i	$0.351240\pi$
$644$	−30.0334	−1.18348
$645$	41.8899	1.64941
$646$	75.2701	2.96146
$647$	−0.290591	−0.0114243	−0.00571216	−	0.999984i	$-0.501818\pi$
$647$	−0.290591	−0.0114243	−0.00571216	+	0.999984i	$0.501818\pi$
$648$	−20.3649	−0.800009
$649$	−13.6287	−0.534973
$650$	−6.11951	−0.240027
$651$	−30.5782	−1.19846
$652$	125.616	4.91950
$653$	−40.5393	−1.58643	−0.793213	−	0.608945i	$-0.791593\pi$
$653$	−40.5393	−1.58643	−0.793213	+	0.608945i	$0.791593\pi$
$654$	−26.4849	−1.03564
$655$	−34.2754	−1.33925
$656$	−65.3744	−2.55244
$657$	67.9984	2.65287
$658$	−26.9878	−1.05209
$659$	−2.66212	−0.103702	−0.0518508	−	0.998655i	$-0.516512\pi$
$659$	−2.66212	−0.103702	−0.0518508	+	0.998655i	$0.516512\pi$
$660$	41.8656	1.62962
$661$	2.25027	0.0875253	0.0437626	−	0.999042i	$-0.486065\pi$
$661$	2.25027	0.0875253	0.0437626	+	0.999042i	$0.486065\pi$
$662$	0.347282	0.0134975
$663$	−10.0829	−0.391587
$664$	−59.6018	−2.31300
$665$	90.3486	3.50357
$666$	50.7170	1.96524
$667$	1.04670	0.0405284
$668$	50.0918	1.93811
$669$	−66.0834	−2.55493
$670$	42.7363	1.65105
$671$	5.54857	0.214200
$672$	262.495	10.1260
$673$	12.4433	0.479655	0.239827	−	0.970816i	$-0.422909\pi$
$673$	12.4433	0.479655	0.239827	+	0.970816i	$0.422909\pi$
$674$	−40.1775	−1.54758
$675$	−14.3020	−0.550485
$676$	−65.3179	−2.51223
$677$	32.7071	1.25704	0.628518	−	0.777795i	$-0.283662\pi$
$677$	32.7071	1.25704	0.628518	+	0.777795i	$0.283662\pi$
$678$	147.718	5.67306
$679$	−8.50020	−0.326208
$680$	91.3693	3.50385
$681$	−50.3575	−1.92970
$682$	−6.64161	−0.254320
$683$	47.6195	1.82211	0.911054	−	0.412286i	$-0.135270\pi$
$683$	47.6195	1.82211	0.911054	+	0.412286i	$0.135270\pi$
$684$	−213.125	−8.14903
$685$	26.3552	1.00698
$686$	−62.8369	−2.39912
$687$	−0.138154	−0.00527089
$688$	78.7334	3.00168
$689$	−7.54934	−0.287607
$690$	26.5813	1.01193
$691$	26.5143	1.00865	0.504327	−	0.863513i	$-0.331741\pi$
$691$	26.5143	1.00865	0.504327	+	0.863513i	$0.331741\pi$
$692$	25.6351	0.974501
$693$	22.6687	0.861111
$694$	41.4516	1.57348
$695$	5.18370	0.196629
$696$	−22.0476	−0.835712
$697$	−16.3382	−0.618854
$698$	−18.4603	−0.698732
$699$	14.9203	0.564337
$700$	54.9508	2.07695
$701$	−34.5820	−1.30614	−0.653072	−	0.757296i	$-0.726520\pi$
$701$	−34.5820	−1.30614	−0.653072	+	0.757296i	$0.726520\pi$
$702$	16.3872	0.618493
$703$	27.4476	1.03521
$704$	27.9695	1.05414
$705$	17.4462	0.657061
$706$	34.7596	1.30820
$707$	−79.8876	−3.00448
$708$	211.019	7.93058
$709$	−43.8404	−1.64646	−0.823230	−	0.567708i	$-0.807830\pi$
$709$	−43.8404	−1.64646	−0.823230	+	0.567708i	$0.807830\pi$
$710$	49.1581	1.84487
$711$	58.1458	2.18064
$712$	−116.002	−4.34737
$713$	−3.08002	−0.115348
$714$	123.960	4.63909
$715$	−2.62872	−0.0983087
$716$	−94.0092	−3.51329
$717$	35.2735	1.31731
$718$	21.1285	0.788509
$719$	19.0731	0.711308	0.355654	−	0.934618i	$-0.384258\pi$
$719$	19.0731	0.711308	0.355654	+	0.934618i	$0.384258\pi$
$720$	−202.840	−7.55939
$721$	−1.80062	−0.0670585
$722$	−106.165	−3.95107
$723$	72.7610	2.70601
$724$	66.0070	2.45313
$725$	−1.91510	−0.0711251
$726$	7.78308	0.288857
$727$	−36.5966	−1.35729	−0.678647	−	0.734465i	$-0.737433\pi$
$727$	−36.5966	−1.35729	−0.678647	+	0.734465i	$0.737433\pi$
$728$	−39.7221	−1.47220
$729$	−41.7542	−1.54645
$730$	96.9426	3.58801
$731$	19.6769	0.727775
$732$	−85.9110	−3.17536
$733$	32.1425	1.18721	0.593606	−	0.804756i	$-0.297704\pi$
$733$	32.1425	1.18721	0.593606	+	0.804756i	$0.297704\pi$
$734$	51.5981	1.90452
$735$	94.7066	3.49330
$736$	26.4401	0.974593
$737$	5.80300	0.213756
$738$	63.3368	2.33146
$739$	15.1124	0.555919	0.277959	−	0.960593i	$-0.410342\pi$
$739$	15.1124	0.555919	0.277959	+	0.960593i	$0.410342\pi$
$740$	52.8118	1.94140
$741$	21.1537	0.777101
$742$	92.8124	3.40725
$743$	21.6219	0.793231	0.396616	−	0.917985i	$-0.370185\pi$
$743$	21.6219	0.793231	0.396616	+	0.917985i	$0.370185\pi$
$744$	64.8774	2.37852
$745$	−6.92732	−0.253797
$746$	84.4705	3.09269
$747$	33.0681	1.20990
$748$	19.6655	0.719040
$749$	−39.1812	−1.43165
$750$	56.5884	2.06631
$751$	−14.8735	−0.542741	−0.271370	−	0.962475i	$-0.587477\pi$
$751$	−14.8735	−0.542741	−0.271370	+	0.962475i	$0.587477\pi$
$752$	32.7907	1.19575
$753$	23.3398	0.850549
$754$	2.19431	0.0799120
$755$	52.4827	1.91004
$756$	−147.150	−5.35181
$757$	−53.9591	−1.96118	−0.980588	−	0.196080i	$-0.937179\pi$
$757$	−53.9591	−1.96118	−0.980588	+	0.196080i	$0.937179\pi$
$758$	61.4961	2.23364
$759$	3.60937	0.131012
$760$	−191.691	−6.95337
$761$	−30.0532	−1.08943	−0.544714	−	0.838622i	$-0.683362\pi$
$761$	−30.0532	−1.08943	−0.544714	+	0.838622i	$0.683362\pi$
$762$	−149.148	−5.40305
$763$	−14.9329	−0.540608
$764$	120.400	4.35593
$765$	−50.6932	−1.83282
$766$	−55.2116	−1.99488
$767$	−13.2498	−0.478423
$768$	−107.221	−3.86900
$769$	35.9329	1.29577	0.647887	−	0.761737i	$-0.275653\pi$
$769$	35.9329	1.29577	0.647887	+	0.761737i	$0.275653\pi$
$770$	32.3178	1.16465
$771$	−11.3733	−0.409598
$772$	−112.073	−4.03359
$773$	13.4688	0.484440	0.242220	−	0.970221i	$-0.422124\pi$
$773$	13.4688	0.484440	0.242220	+	0.970221i	$0.422124\pi$
$774$	−76.2794	−2.74181
$775$	5.63538	0.202429
$776$	18.0347	0.647410
$777$	45.2027	1.62164
$778$	−73.4091	−2.63184
$779$	34.2773	1.22811
$780$	40.7017	1.45736
$781$	6.67499	0.238850
$782$	12.4860	0.446498
$783$	5.12836	0.183273
$784$	178.004	6.35729
$785$	−21.9901	−0.784860
$786$	98.6608	3.51912
$787$	18.9535	0.675621	0.337810	−	0.941214i	$-0.390314\pi$
$787$	18.9535	0.675621	0.337810	+	0.941214i	$0.390314\pi$
$788$	82.0095	2.92147
$789$	27.1814	0.967685
$790$	82.8962	2.94932
$791$	83.2872	2.96135
$792$	−48.0958	−1.70901
$793$	5.39432	0.191558
$794$	−70.4503	−2.50019
$795$	−59.9983	−2.12792
$796$	−119.078	−4.22060
$797$	−51.7597	−1.83342	−0.916712	−	0.399549i	$-0.869167\pi$
$797$	−51.7597	−1.83342	−0.916712	+	0.399549i	$0.869167\pi$
$798$	−260.066	−9.20624
$799$	8.19497	0.289917
$800$	−48.3762	−1.71036
$801$	64.3601	2.27405
$802$	−78.6953	−2.77883
$803$	13.1635	0.464529
$804$	−89.8504	−3.16878
$805$	14.9873	0.528232
$806$	−6.45698	−0.227437
$807$	24.9189	0.877186
$808$	169.496	5.96286
$809$	11.8954	0.418220	0.209110	−	0.977892i	$-0.432943\pi$
$809$	11.8954	0.418220	0.209110	+	0.977892i	$0.432943\pi$
$810$	16.1082	0.565986
$811$	−54.0016	−1.89625	−0.948127	−	0.317893i	$-0.897025\pi$
$811$	−54.0016	−1.89625	−0.948127	+	0.317893i	$0.897025\pi$
$812$	−19.7040	−0.691476
$813$	−44.8943	−1.57451
$814$	9.81805	0.344123
$815$	−62.6848	−2.19575
$816$	−150.614	−5.27253
$817$	−41.2817	−1.44427
$818$	−25.0081	−0.874386
$819$	22.0385	0.770087
$820$	65.9528	2.30317
$821$	24.3597	0.850160	0.425080	−	0.905156i	$-0.360246\pi$
$821$	24.3597	0.850160	0.425080	+	0.905156i	$0.360246\pi$
$822$	−75.8628	−2.64602
$823$	−7.42322	−0.258757	−0.129379	−	0.991595i	$-0.541298\pi$
$823$	−7.42322	−0.258757	−0.129379	+	0.991595i	$0.541298\pi$
$824$	3.82034	0.133088
$825$	−6.60392	−0.229919
$826$	162.895	5.66783
$827$	24.9580	0.867875	0.433937	−	0.900943i	$-0.357124\pi$
$827$	24.9580	0.867875	0.433937	+	0.900943i	$0.357124\pi$
$828$	−35.3537	−1.22863
$829$	−13.9202	−0.483469	−0.241734	−	0.970342i	$-0.577716\pi$
$829$	−13.9202	−0.483469	−0.241734	+	0.970342i	$0.577716\pi$
$830$	47.1439	1.63639
$831$	6.51940	0.226155
$832$	27.1919	0.942711
$833$	44.4864	1.54136
$834$	−14.9211	−0.516677
$835$	−24.9968	−0.865050
$836$	−41.2578	−1.42693
$837$	−15.0907	−0.521613
$838$	51.8306	1.79046
$839$	−42.6344	−1.47190	−0.735951	−	0.677035i	$-0.763265\pi$
$839$	−42.6344	−1.47190	−0.735951	+	0.677035i	$0.763265\pi$
$840$	−315.691	−10.8924
$841$	−28.3133	−0.976320
$842$	−85.5789	−2.94924
$843$	83.3245	2.86985
$844$	−83.8921	−2.88768
$845$	32.5949	1.12130
$846$	−31.7686	−1.09223
$847$	4.38831	0.150784
$848$	−112.769	−3.87249
$849$	−28.9235	−0.992653
$850$	−22.8451	−0.783580
$851$	4.55308	0.156078
$852$	−103.352	−3.54078
$853$	8.16362	0.279517	0.139759	−	0.990186i	$-0.455367\pi$
$853$	8.16362	0.279517	0.139759	+	0.990186i	$0.455367\pi$
$854$	−66.3183	−2.26937
$855$	106.354	3.63721
$856$	83.1302	2.84133
$857$	−24.6334	−0.841460	−0.420730	−	0.907186i	$-0.638226\pi$
$857$	−24.6334	−0.841460	−0.420730	+	0.907186i	$0.638226\pi$
$858$	7.56672	0.258324
$859$	−2.15728	−0.0736054	−0.0368027	−	0.999323i	$-0.511717\pi$
$859$	−2.15728	−0.0736054	−0.0368027	+	0.999323i	$0.511717\pi$
$860$	−79.4299	−2.70854
$861$	56.4503	1.92382
$862$	−34.4126	−1.17210
$863$	15.5351	0.528821	0.264410	−	0.964410i	$-0.414823\pi$
$863$	15.5351	0.528821	0.264410	+	0.964410i	$0.414823\pi$
$864$	129.545	4.40720
$865$	−12.7924	−0.434956
$866$	6.95691	0.236406
$867$	10.9376	0.371461
$868$	57.9812	1.96801
$869$	11.2562	0.381839
$870$	17.4392	0.591245
$871$	5.64168	0.191161
$872$	31.6830	1.07292
$873$	−10.0060	−0.338651
$874$	−26.1954	−0.886073
$875$	31.9061	1.07862
$876$	−203.816	−6.88630
$877$	50.4322	1.70297	0.851487	−	0.524376i	$-0.175701\pi$
$877$	50.4322	1.70297	0.851487	+	0.524376i	$0.175701\pi$
$878$	35.3136	1.19178
$879$	−81.0088	−2.73236
$880$	−39.2667	−1.32368
$881$	−8.91634	−0.300399	−0.150200	−	0.988656i	$-0.547992\pi$
$881$	−8.91634	−0.300399	−0.150200	+	0.988656i	$0.547992\pi$
$882$	−172.456	−5.80689
$883$	3.13290	0.105431	0.0527153	−	0.998610i	$-0.483212\pi$
$883$	3.13290	0.105431	0.0527153	+	0.998610i	$0.483212\pi$
$884$	19.1188	0.643034
$885$	−105.303	−3.53971
$886$	51.2184	1.72072
$887$	−49.7806	−1.67147	−0.835734	−	0.549135i	$-0.814957\pi$
$887$	−49.7806	−1.67147	−0.835734	+	0.549135i	$0.814957\pi$
$888$	−95.9059	−3.21839
$889$	−84.0935	−2.82041
$890$	91.7557	3.07566
$891$	2.18728	0.0732765
$892$	125.305	4.19551
$893$	−17.1929	−0.575339
$894$	19.9401	0.666897
$895$	46.9125	1.56811
$896$	−150.581	−5.03057
$897$	3.50904	0.117163
$898$	−57.3520	−1.91386
$899$	−2.02071	−0.0673945
$900$	64.6852	2.15617
$901$	−28.1829	−0.938909
$902$	12.2611	0.408248
$903$	−67.9857	−2.26242
$904$	−176.709	−5.87727
$905$	−32.9388	−1.09492
$906$	−151.070	−5.01897
$907$	−21.0609	−0.699316	−0.349658	−	0.936877i	$-0.613702\pi$
$907$	−21.0609	−0.699316	−0.349658	+	0.936877i	$0.613702\pi$
$908$	95.4859	3.16881
$909$	−94.0395	−3.11909
$910$	31.4194	1.04154
$911$	−1.12643	−0.0373203	−0.0186602	−	0.999826i	$-0.505940\pi$
$911$	−1.12643	−0.0373203	−0.0186602	+	0.999826i	$0.505940\pi$
$912$	315.985	10.4633
$913$	6.40149	0.211858
$914$	40.4020	1.33638
$915$	42.8713	1.41728
$916$	0.261961	0.00865544
$917$	55.6277	1.83699
$918$	61.1759	2.01911
$919$	37.8077	1.24716	0.623580	−	0.781760i	$-0.285678\pi$
$919$	37.8077	1.24716	0.623580	+	0.781760i	$0.285678\pi$
$920$	−31.7983	−1.04836
$921$	−46.8601	−1.54409
$922$	18.5375	0.610501
$923$	6.48943	0.213602
$924$	−67.9462	−2.23527
$925$	−8.33058	−0.273908
$926$	27.2747	0.896301
$927$	−2.11959	−0.0696165
$928$	17.3466	0.569428
$929$	−7.37929	−0.242107	−0.121053	−	0.992646i	$-0.538627\pi$
$929$	−7.37929	−0.242107	−0.121053	+	0.992646i	$0.538627\pi$
$930$	−51.3168	−1.68274
$931$	−93.3317	−3.05882
$932$	−28.2913	−0.926711
$933$	33.9161	1.11036
$934$	−68.5404	−2.24271
$935$	−9.81345	−0.320934
$936$	−46.7587	−1.52836
$937$	−7.30951	−0.238791	−0.119396	−	0.992847i	$-0.538096\pi$
$937$	−7.30951	−0.238791	−0.119396	+	0.992847i	$0.538096\pi$
$938$	−69.3594	−2.26466
$939$	3.65118	0.119152
$940$	−33.0808	−1.07898
$941$	42.0431	1.37057	0.685283	−	0.728277i	$-0.259678\pi$
$941$	42.0431	1.37057	0.685283	+	0.728277i	$0.259678\pi$
$942$	63.2979	2.06236
$943$	5.68602	0.185162
$944$	−197.920	−6.44174
$945$	73.4310	2.38871
$946$	−14.7665	−0.480102
$947$	49.0225	1.59302	0.796509	−	0.604626i	$-0.206678\pi$
$947$	49.0225	1.59302	0.796509	+	0.604626i	$0.206678\pi$
$948$	−174.284	−5.66049
$949$	12.7975	0.415425
$950$	47.9286	1.55501
$951$	94.0569	3.05000
$952$	−148.289	−4.80607
$953$	27.9016	0.903820	0.451910	−	0.892064i	$-0.350743\pi$
$953$	27.9016	0.903820	0.451910	+	0.892064i	$0.350743\pi$
$954$	109.254	3.53722
$955$	−60.0821	−1.94421
$956$	−66.8841	−2.16319
$957$	2.36801	0.0765468
$958$	−41.8543	−1.35225
$959$	−42.7735	−1.38123
$960$	216.108	6.97484
$961$	−25.0538	−0.808188
$962$	9.54512	0.307747
$963$	−46.1220	−1.48626
$964$	−137.966	−4.44360
$965$	55.9265	1.80034
$966$	−43.1405	−1.38802
$967$	34.5274	1.11033	0.555163	−	0.831742i	$-0.312656\pi$
$967$	34.5274	1.11033	0.555163	+	0.831742i	$0.312656\pi$
$968$	−9.31062	−0.299255
$969$	78.9702	2.53689
$970$	−14.2651	−0.458026
$971$	−1.79068	−0.0574657	−0.0287328	−	0.999587i	$-0.509147\pi$
$971$	−1.79068	−0.0574657	−0.0287328	+	0.999587i	$0.509147\pi$
$972$	66.7305	2.14038
$973$	−8.41294	−0.269707
$974$	34.7741	1.11423
$975$	−6.42033	−0.205615
$976$	80.5779	2.57924
$977$	−1.49358	−0.0477838	−0.0238919	−	0.999715i	$-0.507606\pi$
$977$	−1.49358	−0.0477838	−0.0238919	+	0.999715i	$0.507606\pi$
$978$	180.437	5.76973
$979$	12.4591	0.398196
$980$	−179.579	−5.73644
$981$	−17.5782	−0.561230
$982$	13.8621	0.442356
$983$	−4.32489	−0.137942	−0.0689712	−	0.997619i	$-0.521972\pi$
$983$	−4.32489	−0.137942	−0.0689712	+	0.997619i	$0.521972\pi$
$984$	−119.770	−3.81812
$985$	−40.9244	−1.30396
$986$	8.19170	0.260877
$987$	−28.3145	−0.901260
$988$	−40.1108	−1.27610
$989$	−6.84793	−0.217751
$990$	38.0428	1.20908
$991$	−5.58733	−0.177487	−0.0887437	−	0.996054i	$-0.528285\pi$
$991$	−5.58733	−0.177487	−0.0887437	+	0.996054i	$0.528285\pi$
$992$	−51.0440	−1.62065
$993$	0.364353	0.0115624
$994$	−79.7818	−2.53052
$995$	59.4222	1.88381
$996$	−99.1171	−3.14065
$997$	−14.0382	−0.444594	−0.222297	−	0.974979i	$-0.571356\pi$
$997$	−14.0382	−0.444594	−0.222297	+	0.974979i	$0.571356\pi$
$998$	−19.9554	−0.631679
$999$	22.3081	0.705797

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.e.1.2	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.e.1.2	✓	119	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)

\(f(q)\)	\(=\)	\(q-2.72367 q^{2} -2.85757 q^{3} +5.41840 q^{4} -2.70389 q^{5} +7.78308 q^{6} +4.38831 q^{7} -9.31062 q^{8} +5.16569 q^{9} +O(q^{10})\)	\(q-2.72367 q^{2} -2.85757 q^{3} +5.41840 q^{4} -2.70389 q^{5} +7.78308 q^{6} +4.38831 q^{7} -9.31062 q^{8} +5.16569 q^{9} +7.36452 q^{10} +1.00000 q^{11} -15.4835 q^{12} +0.972201 q^{13} -11.9523 q^{14} +7.72655 q^{15} +14.5223 q^{16} +3.62938 q^{17} -14.0697 q^{18} -7.61438 q^{19} -14.6508 q^{20} -12.5399 q^{21} -2.72367 q^{22} -1.26309 q^{23} +26.6057 q^{24} +2.31103 q^{25} -2.64796 q^{26} -6.18860 q^{27} +23.7777 q^{28} -0.828679 q^{29} -21.0446 q^{30} +2.43847 q^{31} -20.9328 q^{32} -2.85757 q^{33} -9.88525 q^{34} -11.8655 q^{35} +27.9898 q^{36} -3.60471 q^{37} +20.7391 q^{38} -2.77813 q^{39} +25.1749 q^{40} -4.50166 q^{41} +34.1546 q^{42} +5.42155 q^{43} +5.41840 q^{44} -13.9675 q^{45} +3.44026 q^{46} +2.25795 q^{47} -41.4984 q^{48} +12.2573 q^{49} -6.29449 q^{50} -10.3712 q^{51} +5.26778 q^{52} -7.76521 q^{53} +16.8557 q^{54} -2.70389 q^{55} -40.8579 q^{56} +21.7586 q^{57} +2.25705 q^{58} -13.6287 q^{59} +41.8656 q^{60} +5.54857 q^{61} -6.64161 q^{62} +22.6687 q^{63} +27.9695 q^{64} -2.62872 q^{65} +7.78308 q^{66} +5.80300 q^{67} +19.6655 q^{68} +3.60937 q^{69} +32.3178 q^{70} +6.67499 q^{71} -48.0958 q^{72} +13.1635 q^{73} +9.81805 q^{74} -6.60392 q^{75} -41.2578 q^{76} +4.38831 q^{77} +7.56672 q^{78} +11.2562 q^{79} -39.2667 q^{80} +2.18728 q^{81} +12.2611 q^{82} +6.40149 q^{83} -67.9462 q^{84} -9.81345 q^{85} -14.7665 q^{86} +2.36801 q^{87} -9.31062 q^{88} +12.4591 q^{89} +38.0428 q^{90} +4.26632 q^{91} -6.84395 q^{92} -6.96810 q^{93} -6.14993 q^{94} +20.5885 q^{95} +59.8168 q^{96} -1.93701 q^{97} -33.3849 q^{98} +5.16569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * q^99

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