LMFDB - Embedded newform 6001.2.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$47.9182262530$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48167 q^{2} +1.61831 q^{3} +4.15867 q^{4} -3.04222 q^{5} -4.01610 q^{6} +0.428830 q^{7} -5.35710 q^{8} -0.381079 q^{9} +O(q^{10})$	\(q-2.48167 q^{2} +1.61831 q^{3} +4.15867 q^{4} -3.04222 q^{5} -4.01610 q^{6} +0.428830 q^{7} -5.35710 q^{8} -0.381079 q^{9} +7.54977 q^{10} +4.36208 q^{11} +6.73001 q^{12} -3.80622 q^{13} -1.06421 q^{14} -4.92324 q^{15} +4.97719 q^{16} -1.00000 q^{17} +0.945710 q^{18} +3.99583 q^{19} -12.6516 q^{20} +0.693979 q^{21} -10.8252 q^{22} +4.55705 q^{23} -8.66943 q^{24} +4.25508 q^{25} +9.44578 q^{26} -5.47163 q^{27} +1.78336 q^{28} +9.82781 q^{29} +12.2178 q^{30} +3.22567 q^{31} -1.63753 q^{32} +7.05919 q^{33} +2.48167 q^{34} -1.30459 q^{35} -1.58478 q^{36} -3.81223 q^{37} -9.91632 q^{38} -6.15964 q^{39} +16.2974 q^{40} -10.8893 q^{41} -1.72222 q^{42} +1.75666 q^{43} +18.1405 q^{44} +1.15932 q^{45} -11.3091 q^{46} +0.449942 q^{47} +8.05462 q^{48} -6.81610 q^{49} -10.5597 q^{50} -1.61831 q^{51} -15.8288 q^{52} -1.26973 q^{53} +13.5788 q^{54} -13.2704 q^{55} -2.29728 q^{56} +6.46649 q^{57} -24.3894 q^{58} +13.3647 q^{59} -20.4741 q^{60} +3.54702 q^{61} -8.00503 q^{62} -0.163418 q^{63} -5.89057 q^{64} +11.5794 q^{65} -17.5186 q^{66} +4.54766 q^{67} -4.15867 q^{68} +7.37472 q^{69} +3.23757 q^{70} -8.92724 q^{71} +2.04148 q^{72} -12.7559 q^{73} +9.46069 q^{74} +6.88603 q^{75} +16.6173 q^{76} +1.87059 q^{77} +15.2862 q^{78} -2.58695 q^{79} -15.1417 q^{80} -7.71154 q^{81} +27.0235 q^{82} +14.5052 q^{83} +2.88603 q^{84} +3.04222 q^{85} -4.35943 q^{86} +15.9044 q^{87} -23.3681 q^{88} +10.6168 q^{89} -2.87706 q^{90} -1.63222 q^{91} +18.9513 q^{92} +5.22012 q^{93} -1.11661 q^{94} -12.1562 q^{95} -2.65003 q^{96} -0.593647 q^{97} +16.9153 q^{98} -1.66230 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * 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 $

$2$	−2.48167	−1.75480	−0.877402	−	0.479757i	$-0.840725\pi$
$2$	−2.48167	−1.75480	−0.877402	+	0.479757i	$0.840725\pi$
$3$	1.61831	0.934331	0.467165	−	0.884170i	$-0.345275\pi$
$3$	1.61831	0.934331	0.467165	+	0.884170i	$0.345275\pi$
$4$	4.15867	2.07933
$5$	−3.04222	−1.36052	−0.680260	−	0.732971i	$-0.738133\pi$
$5$	−3.04222	−1.36052	−0.680260	+	0.732971i	$0.738133\pi$
$6$	−4.01610	−1.63957
$7$	0.428830	0.162082	0.0810412	−	0.996711i	$-0.474175\pi$
$7$	0.428830	0.162082	0.0810412	+	0.996711i	$0.474175\pi$
$8$	−5.35710	−1.89402
$9$	−0.381079	−0.127026
$10$	7.54977	2.38745
$11$	4.36208	1.31522	0.657609	−	0.753360i	$-0.271568\pi$
$11$	4.36208	1.31522	0.657609	+	0.753360i	$0.271568\pi$
$12$	6.73001	1.94279
$13$	−3.80622	−1.05566	−0.527828	−	0.849351i	$-0.676994\pi$
$13$	−3.80622	−1.05566	−0.527828	+	0.849351i	$0.676994\pi$
$14$	−1.06421	−0.284423
$15$	−4.92324	−1.27118
$16$	4.97719	1.24430
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.945710	0.222906
$19$	3.99583	0.916706	0.458353	−	0.888770i	$-0.348439\pi$
$19$	3.99583	0.916706	0.458353	+	0.888770i	$0.348439\pi$
$20$	−12.6516	−2.82898
$21$	0.693979	0.151439
$22$	−10.8252	−2.30795
$23$	4.55705	0.950211	0.475106	−	0.879929i	$-0.342410\pi$
$23$	4.55705	0.950211	0.475106	+	0.879929i	$0.342410\pi$
$24$	−8.66943	−1.76964
$25$	4.25508	0.851016
$26$	9.44578	1.85247
$27$	−5.47163	−1.05302
$28$	1.78336	0.337024
$29$	9.82781	1.82498	0.912490	−	0.409100i	$-0.134157\pi$
$29$	9.82781	1.82498	0.912490	+	0.409100i	$0.134157\pi$
$30$	12.2178	2.23066
$31$	3.22567	0.579347	0.289673	−	0.957126i	$-0.406453\pi$
$31$	3.22567	0.579347	0.289673	+	0.957126i	$0.406453\pi$
$32$	−1.63753	−0.289477
$33$	7.05919	1.22885
$34$	2.48167	0.425602
$35$	−1.30459	−0.220517
$36$	−1.58478	−0.264130
$37$	−3.81223	−0.626727	−0.313364	−	0.949633i	$-0.601456\pi$
$37$	−3.81223	−0.626727	−0.313364	+	0.949633i	$0.601456\pi$
$38$	−9.91632	−1.60864
$39$	−6.15964	−0.986332
$40$	16.2974	2.57685
$41$	−10.8893	−1.70062	−0.850308	−	0.526285i	$-0.823585\pi$
$41$	−10.8893	−1.70062	−0.850308	+	0.526285i	$0.823585\pi$
$42$	−1.72222	−0.265745
$43$	1.75666	0.267887	0.133944	−	0.990989i	$-0.457236\pi$
$43$	1.75666	0.267887	0.133944	+	0.990989i	$0.457236\pi$
$44$	18.1405	2.73478
$45$	1.15932	0.172822
$46$	−11.3091	−1.66743
$47$	0.449942	0.0656308	0.0328154	−	0.999461i	$-0.489553\pi$
$47$	0.449942	0.0656308	0.0328154	+	0.999461i	$0.489553\pi$
$48$	8.05462	1.16258
$49$	−6.81610	−0.973729
$50$	−10.5597	−1.49337
$51$	−1.61831	−0.226608
$52$	−15.8288	−2.19506
$53$	−1.26973	−0.174410	−0.0872051	−	0.996190i	$-0.527794\pi$
$53$	−1.26973	−0.174410	−0.0872051	+	0.996190i	$0.527794\pi$
$54$	13.5788	1.84783
$55$	−13.2704	−1.78938
$56$	−2.29728	−0.306987
$57$	6.46649	0.856507
$58$	−24.3894	−3.20248
$59$	13.3647	1.73994	0.869968	−	0.493108i	$-0.164139\pi$
$59$	13.3647	1.73994	0.869968	+	0.493108i	$0.164139\pi$
$60$	−20.4741	−2.64320
$61$	3.54702	0.454149	0.227074	−	0.973877i	$-0.427084\pi$
$61$	3.54702	0.454149	0.227074	+	0.973877i	$0.427084\pi$
$62$	−8.00503	−1.01664
$63$	−0.163418	−0.0205887
$64$	−5.89057	−0.736322
$65$	11.5794	1.43624
$66$	−17.5186	−2.15639
$67$	4.54766	0.555585	0.277793	−	0.960641i	$-0.410397\pi$
$67$	4.54766	0.555585	0.277793	+	0.960641i	$0.410397\pi$
$68$	−4.15867	−0.504313
$69$	7.37472	0.887811
$70$	3.23757	0.386963
$71$	−8.92724	−1.05947	−0.529734	−	0.848164i	$-0.677708\pi$
$71$	−8.92724	−1.05947	−0.529734	+	0.848164i	$0.677708\pi$
$72$	2.04148	0.240590
$73$	−12.7559	−1.49297	−0.746484	−	0.665404i	$-0.768259\pi$
$73$	−12.7559	−1.49297	−0.746484	+	0.665404i	$0.768259\pi$
$74$	9.46069	1.09978
$75$	6.88603	0.795131
$76$	16.6173	1.90614
$77$	1.87059	0.213174
$78$	15.2862	1.73082
$79$	−2.58695	−0.291055	−0.145527	−	0.989354i	$-0.546488\pi$
$79$	−2.58695	−0.291055	−0.145527	+	0.989354i	$0.546488\pi$
$80$	−15.1417	−1.69289
$81$	−7.71154	−0.856838
$82$	27.0235	2.98425
$83$	14.5052	1.59215	0.796075	−	0.605197i	$-0.206906\pi$
$83$	14.5052	1.59215	0.796075	+	0.605197i	$0.206906\pi$
$84$	2.88603	0.314892
$85$	3.04222	0.329975
$86$	−4.35943	−0.470090
$87$	15.9044	1.70513
$88$	−23.3681	−2.49105
$89$	10.6168	1.12538	0.562690	−	0.826668i	$-0.309766\pi$
$89$	10.6168	1.12538	0.562690	+	0.826668i	$0.309766\pi$
$90$	−2.87706	−0.303268
$91$	−1.63222	−0.171103
$92$	18.9513	1.97581
$93$	5.22012	0.541302
$94$	−1.11661	−0.115169
$95$	−12.1562	−1.24720
$96$	−2.65003	−0.270467
$97$	−0.593647	−0.0602757	−0.0301378	−	0.999546i	$-0.509595\pi$
$97$	−0.593647	−0.0602757	−0.0301378	+	0.999546i	$0.509595\pi$
$98$	16.9153	1.70870
$99$	−1.66230	−0.167067
$100$	17.6955	1.76955
$101$	−1.26281	−0.125655	−0.0628273	−	0.998024i	$-0.520012\pi$
$101$	−1.26281	−0.125655	−0.0628273	+	0.998024i	$0.520012\pi$
$102$	4.01610	0.397653
$103$	−9.08588	−0.895258	−0.447629	−	0.894219i	$-0.647732\pi$
$103$	−9.08588	−0.895258	−0.447629	+	0.894219i	$0.647732\pi$
$104$	20.3903	1.99943
$105$	−2.11123	−0.206035
$106$	3.15104	0.306056
$107$	10.1685	0.983029	0.491514	−	0.870869i	$-0.336443\pi$
$107$	10.1685	0.983029	0.491514	+	0.870869i	$0.336443\pi$
$108$	−22.7547	−2.18957
$109$	−16.0542	−1.53771	−0.768856	−	0.639422i	$-0.779174\pi$
$109$	−16.0542	−1.53771	−0.768856	+	0.639422i	$0.779174\pi$
$110$	32.9327	3.14001
$111$	−6.16937	−0.585570
$112$	2.13437	0.201679
$113$	−20.0427	−1.88546	−0.942729	−	0.333560i	$-0.891750\pi$
$113$	−20.0427	−1.88546	−0.942729	+	0.333560i	$0.891750\pi$
$114$	−16.0477	−1.50300
$115$	−13.8635	−1.29278
$116$	40.8706	3.79474
$117$	1.45047	0.134096
$118$	−33.1667	−3.05325
$119$	−0.428830	−0.0393108
$120$	26.3743	2.40763
$121$	8.02777	0.729797
$122$	−8.80251	−0.796942
$123$	−17.6222	−1.58894
$124$	13.4145	1.20466
$125$	2.26620	0.202695
$126$	0.405549	0.0361292
$127$	−21.2652	−1.88698	−0.943489	−	0.331405i	$-0.892477\pi$
$127$	−21.2652	−1.88698	−0.943489	+	0.331405i	$0.892477\pi$
$128$	17.8935	1.58158
$129$	2.84281	0.250295
$130$	−28.7361	−2.52032
$131$	−4.29823	−0.375538	−0.187769	−	0.982213i	$-0.560126\pi$
$131$	−4.29823	−0.375538	−0.187769	+	0.982213i	$0.560126\pi$
$132$	29.3569	2.55519
$133$	1.71353	0.148582
$134$	−11.2858	−0.974942
$135$	16.6459	1.43265
$136$	5.35710	0.459367
$137$	−16.6445	−1.42204	−0.711018	−	0.703174i	$-0.751765\pi$
$137$	−16.6445	−1.42204	−0.711018	+	0.703174i	$0.751765\pi$
$138$	−18.3016	−1.55793
$139$	12.3913	1.05101	0.525507	−	0.850789i	$-0.323876\pi$
$139$	12.3913	1.05101	0.525507	+	0.850789i	$0.323876\pi$
$140$	−5.42537	−0.458528
$141$	0.728145	0.0613209
$142$	22.1544	1.85916
$143$	−16.6031	−1.38842
$144$	−1.89670	−0.158058
$145$	−29.8983	−2.48292
$146$	31.6559	2.61986
$147$	−11.0306	−0.909785
$148$	−15.8538	−1.30318
$149$	14.6305	1.19858	0.599290	−	0.800532i	$-0.295450\pi$
$149$	14.6305	1.19858	0.599290	+	0.800532i	$0.295450\pi$
$150$	−17.0888	−1.39530
$151$	12.4140	1.01023	0.505117	−	0.863051i	$-0.331449\pi$
$151$	12.4140	1.01023	0.505117	+	0.863051i	$0.331449\pi$
$152$	−21.4060	−1.73626
$153$	0.381079	0.0308084
$154$	−4.64218	−0.374078
$155$	−9.81318	−0.788213
$156$	−25.6159	−2.05091
$157$	17.0582	1.36139	0.680697	−	0.732565i	$-0.261677\pi$
$157$	17.0582	1.36139	0.680697	+	0.732565i	$0.261677\pi$
$158$	6.41995	0.510744
$159$	−2.05481	−0.162957
$160$	4.98172	0.393839
$161$	1.95420	0.154013
$162$	19.1375	1.50358
$163$	−8.67586	−0.679545	−0.339773	−	0.940508i	$-0.610350\pi$
$163$	−8.67586	−0.679545	−0.339773	+	0.940508i	$0.610350\pi$
$164$	−45.2848	−3.53615
$165$	−21.4756	−1.67187
$166$	−35.9970	−2.79391
$167$	22.0526	1.70648	0.853240	−	0.521519i	$-0.174634\pi$
$167$	22.0526	1.70648	0.853240	+	0.521519i	$0.174634\pi$
$168$	−3.71771	−0.286828
$169$	1.48734	0.114411
$170$	−7.54977	−0.579041
$171$	−1.52273	−0.116446
$172$	7.30535	0.557028
$173$	15.8706	1.20662	0.603311	−	0.797506i	$-0.293848\pi$
$173$	15.8706	1.20662	0.603311	+	0.797506i	$0.293848\pi$
$174$	−39.4695	−2.99217
$175$	1.82471	0.137935
$176$	21.7109	1.63652
$177$	21.6282	1.62568
$178$	−26.3474	−1.97482
$179$	8.79288	0.657211	0.328605	−	0.944467i	$-0.393421\pi$
$179$	8.79288	0.657211	0.328605	+	0.944467i	$0.393421\pi$
$180$	4.82124	0.359354
$181$	18.6771	1.38826	0.694128	−	0.719851i	$-0.255790\pi$
$181$	18.6771	1.38826	0.694128	+	0.719851i	$0.255790\pi$
$182$	4.05063	0.300253
$183$	5.74017	0.424325
$184$	−24.4126	−1.79972
$185$	11.5976	0.852675
$186$	−12.9546	−0.949878
$187$	−4.36208	−0.318987
$188$	1.87116	0.136468
$189$	−2.34640	−0.170675
$190$	30.1676	2.18859
$191$	26.3272	1.90497	0.952484	−	0.304588i	$-0.0985189\pi$
$191$	26.3272	1.90497	0.952484	+	0.304588i	$0.0985189\pi$
$192$	−9.53276	−0.687968
$193$	0.829707	0.0597236	0.0298618	−	0.999554i	$-0.490493\pi$
$193$	0.829707	0.0597236	0.0298618	+	0.999554i	$0.490493\pi$
$194$	1.47323	0.105772
$195$	18.7390	1.34193
$196$	−28.3459	−2.02471
$197$	−13.2560	−0.944453	−0.472227	−	0.881477i	$-0.656550\pi$
$197$	−13.2560	−0.944453	−0.472227	+	0.881477i	$0.656550\pi$
$198$	4.12527	0.293170
$199$	12.2339	0.867235	0.433618	−	0.901097i	$-0.357237\pi$
$199$	12.2339	0.867235	0.433618	+	0.901097i	$0.357237\pi$
$200$	−22.7949	−1.61184
$201$	7.35951	0.519100
$202$	3.13388	0.220499
$203$	4.21446	0.295797
$204$	−6.73001	−0.471195
$205$	33.1275	2.31372
$206$	22.5481	1.57100
$207$	−1.73660	−0.120702
$208$	−18.9443	−1.31355
$209$	17.4301	1.20567
$210$	5.23938	0.361551
$211$	10.0179	0.689660	0.344830	−	0.938665i	$-0.387937\pi$
$211$	10.0179	0.689660	0.344830	+	0.938665i	$0.387937\pi$
$212$	−5.28037	−0.362657
$213$	−14.4470	−0.989894
$214$	−25.2349	−1.72502
$215$	−5.34413	−0.364466
$216$	29.3120	1.99443
$217$	1.38326	0.0939020
$218$	39.8412	2.69838
$219$	−20.6430	−1.39492
$220$	−55.1872	−3.72072
$221$	3.80622	0.256034
$222$	15.3103	1.02756
$223$	18.2064	1.21919	0.609595	−	0.792713i	$-0.291332\pi$
$223$	18.2064	1.21919	0.609595	+	0.792713i	$0.291332\pi$
$224$	−0.702222	−0.0469192
$225$	−1.62152	−0.108101
$226$	49.7393	3.30861
$227$	−14.1108	−0.936565	−0.468282	−	0.883579i	$-0.655127\pi$
$227$	−14.1108	−0.936565	−0.468282	+	0.883579i	$0.655127\pi$
$228$	26.8920	1.78096
$229$	20.6832	1.36678	0.683392	−	0.730051i	$-0.260504\pi$
$229$	20.6832	1.36678	0.683392	+	0.730051i	$0.260504\pi$
$230$	34.4047	2.26858
$231$	3.02719	0.199175
$232$	−52.6485	−3.45655
$233$	17.9511	1.17601	0.588006	−	0.808856i	$-0.299913\pi$
$233$	17.9511	1.17601	0.588006	+	0.808856i	$0.299913\pi$
$234$	−3.59959	−0.235312
$235$	−1.36882	−0.0892921
$236$	55.5794	3.61791
$237$	−4.18649	−0.271942
$238$	1.06421	0.0689827
$239$	−2.97189	−0.192235	−0.0961177	−	0.995370i	$-0.530643\pi$
$239$	−2.97189	−0.192235	−0.0961177	+	0.995370i	$0.530643\pi$
$240$	−24.5039	−1.58172
$241$	−1.54640	−0.0996126	−0.0498063	−	0.998759i	$-0.515860\pi$
$241$	−1.54640	−0.0996126	−0.0498063	+	0.998759i	$0.515860\pi$
$242$	−19.9222	−1.28065
$243$	3.93523	0.252445
$244$	14.7509	0.944327
$245$	20.7361	1.32478
$246$	43.7324	2.78827
$247$	−15.2090	−0.967727
$248$	−17.2802	−1.09729
$249$	23.4739	1.48760
$250$	−5.62396	−0.355691
$251$	−13.6343	−0.860590	−0.430295	−	0.902688i	$-0.641591\pi$
$251$	−13.6343	−0.860590	−0.430295	+	0.902688i	$0.641591\pi$
$252$	−0.679601	−0.0428108
$253$	19.8782	1.24973
$254$	52.7730	3.31127
$255$	4.92324	0.308305
$256$	−32.6246	−2.03903
$257$	−23.8827	−1.48976	−0.744881	−	0.667197i	$-0.767494\pi$
$257$	−23.8827	−1.48976	−0.744881	+	0.667197i	$0.767494\pi$
$258$	−7.05491	−0.439219
$259$	−1.63480	−0.101581
$260$	48.1547	2.98643
$261$	−3.74517	−0.231820
$262$	10.6668	0.658995
$263$	15.9084	0.980951	0.490476	−	0.871455i	$-0.336823\pi$
$263$	15.9084	0.980951	0.490476	+	0.871455i	$0.336823\pi$
$264$	−37.8168	−2.32746
$265$	3.86278	0.237289
$266$	−4.25241	−0.260732
$267$	17.1813	1.05148
$268$	18.9122	1.15525
$269$	6.26787	0.382159	0.191079	−	0.981575i	$-0.438801\pi$
$269$	6.26787	0.382159	0.191079	+	0.981575i	$0.438801\pi$
$270$	−41.3095	−2.51402
$271$	−19.8588	−1.20634	−0.603168	−	0.797614i	$-0.706095\pi$
$271$	−19.8588	−1.20634	−0.603168	+	0.797614i	$0.706095\pi$
$272$	−4.97719	−0.301786
$273$	−2.64144	−0.159867
$274$	41.3061	2.49539
$275$	18.5610	1.11927
$276$	30.6690	1.84606
$277$	−13.0990	−0.787044	−0.393522	−	0.919315i	$-0.628743\pi$
$277$	−13.0990	−0.787044	−0.393522	+	0.919315i	$0.628743\pi$
$278$	−30.7510	−1.84432
$279$	−1.22923	−0.0735922
$280$	6.98883	0.417663
$281$	−19.2923	−1.15088	−0.575442	−	0.817843i	$-0.695170\pi$
$281$	−19.2923	−1.15088	−0.575442	+	0.817843i	$0.695170\pi$
$282$	−1.80701	−0.107606
$283$	24.2210	1.43979	0.719894	−	0.694084i	$-0.244191\pi$
$283$	24.2210	1.43979	0.719894	+	0.694084i	$0.244191\pi$
$284$	−37.1254	−2.20299
$285$	−19.6724	−1.16530
$286$	41.2033	2.43640
$287$	−4.66964	−0.275640
$288$	0.624028	0.0367712
$289$	1.00000	0.0588235
$290$	74.1977	4.35704
$291$	−0.960703	−0.0563174
$292$	−53.0476	−3.10438
$293$	15.4309	0.901485	0.450743	−	0.892654i	$-0.351159\pi$
$293$	15.4309	0.901485	0.450743	+	0.892654i	$0.351159\pi$
$294$	27.3742	1.59649
$295$	−40.6583	−2.36722
$296$	20.4225	1.18703
$297$	−23.8677	−1.38494
$298$	−36.3081	−2.10327
$299$	−17.3452	−1.00310
$300$	28.6367	1.65334
$301$	0.753306	0.0434199
$302$	−30.8073	−1.77276
$303$	−2.04362	−0.117403
$304$	19.8880	1.14066
$305$	−10.7908	−0.617879
$306$	−0.945710	−0.0540627
$307$	16.6126	0.948132	0.474066	−	0.880489i	$-0.342786\pi$
$307$	16.6126	0.948132	0.474066	+	0.880489i	$0.342786\pi$
$308$	7.77917	0.443259
$309$	−14.7038	−0.836467
$310$	24.3530	1.38316
$311$	7.67400	0.435153	0.217576	−	0.976043i	$-0.430185\pi$
$311$	7.67400	0.435153	0.217576	+	0.976043i	$0.430185\pi$
$312$	32.9978	1.86813
$313$	−21.2208	−1.19947	−0.599736	−	0.800198i	$-0.704728\pi$
$313$	−21.2208	−1.19947	−0.599736	+	0.800198i	$0.704728\pi$
$314$	−42.3328	−2.38898
$315$	0.497153	0.0280114
$316$	−10.7583	−0.605201
$317$	17.0171	0.955774	0.477887	−	0.878421i	$-0.341403\pi$
$317$	17.0171	0.955774	0.477887	+	0.878421i	$0.341403\pi$
$318$	5.09935	0.285957
$319$	42.8697	2.40024
$320$	17.9204	1.00178
$321$	16.4558	0.918474
$322$	−4.84967	−0.270262
$323$	−3.99583	−0.222334
$324$	−32.0698	−1.78165
$325$	−16.1958	−0.898381
$326$	21.5306	1.19247
$327$	−25.9806	−1.43673
$328$	58.3348	3.22100
$329$	0.192949	0.0106376
$330$	53.2953	2.93381
$331$	7.78518	0.427912	0.213956	−	0.976843i	$-0.431365\pi$
$331$	7.78518	0.427912	0.213956	+	0.976843i	$0.431365\pi$
$332$	60.3223	3.31061
$333$	1.45276	0.0796108
$334$	−54.7271	−2.99454
$335$	−13.8350	−0.755885
$336$	3.45406	0.188435
$337$	12.0920	0.658696	0.329348	−	0.944209i	$-0.393171\pi$
$337$	12.0920	0.658696	0.329348	+	0.944209i	$0.393171\pi$
$338$	−3.69109	−0.200769
$339$	−32.4352	−1.76164
$340$	12.6516	0.686128
$341$	14.0706	0.761967
$342$	3.77890	0.204339
$343$	−5.92476	−0.319907
$344$	−9.41057	−0.507384
$345$	−22.4355	−1.20789
$346$	−39.3856	−2.11738
$347$	−6.56949	−0.352669	−0.176334	−	0.984330i	$-0.556424\pi$
$347$	−6.56949	−0.352669	−0.176334	+	0.984330i	$0.556424\pi$
$348$	66.1413	3.54554
$349$	−20.8670	−1.11698	−0.558492	−	0.829510i	$-0.688620\pi$
$349$	−20.8670	−1.11698	−0.558492	+	0.829510i	$0.688620\pi$
$350$	−4.52831	−0.242048
$351$	20.8262	1.11162
$352$	−7.14304	−0.380725
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	−53.6740	−2.85274
$355$	27.1586	1.44143
$356$	44.1518	2.34004
$357$	−0.693979	−0.0367293
$358$	−21.8210	−1.15328
$359$	9.56403	0.504770	0.252385	−	0.967627i	$-0.418785\pi$
$359$	9.56403	0.504770	0.252385	+	0.967627i	$0.418785\pi$
$360$	−6.21061	−0.327328
$361$	−3.03334	−0.159649
$362$	−46.3503	−2.43612
$363$	12.9914	0.681872
$364$	−6.78787	−0.355781
$365$	38.8063	2.03121
$366$	−14.2452	−0.744607
$367$	−26.4549	−1.38094	−0.690468	−	0.723363i	$-0.742595\pi$
$367$	−26.4549	−1.38094	−0.690468	+	0.723363i	$0.742595\pi$
$368$	22.6813	1.18234
$369$	4.14967	0.216023
$370$	−28.7815	−1.49628
$371$	−0.544496	−0.0282688
$372$	21.7088	1.12555
$373$	29.0479	1.50404	0.752021	−	0.659139i	$-0.229079\pi$
$373$	29.0479	1.50404	0.752021	+	0.659139i	$0.229079\pi$
$374$	10.8252	0.559760
$375$	3.66742	0.189385
$376$	−2.41038	−0.124306
$377$	−37.4069	−1.92655
$378$	5.82298	0.299502
$379$	3.46411	0.177939	0.0889697	−	0.996034i	$-0.471643\pi$
$379$	3.46411	0.177939	0.0889697	+	0.996034i	$0.471643\pi$
$380$	−50.5535	−2.59334
$381$	−34.4136	−1.76306
$382$	−65.3353	−3.34284
$383$	−14.3078	−0.731095	−0.365547	−	0.930793i	$-0.619118\pi$
$383$	−14.3078	−0.731095	−0.365547	+	0.930793i	$0.619118\pi$
$384$	28.9572	1.47772
$385$	−5.69074	−0.290027
$386$	−2.05906	−0.104803
$387$	−0.669424	−0.0340287
$388$	−2.46878	−0.125333
$389$	24.1137	1.22261	0.611307	−	0.791393i	$-0.290644\pi$
$389$	24.1137	1.22261	0.611307	+	0.791393i	$0.290644\pi$
$390$	−46.5039	−2.35482
$391$	−4.55705	−0.230460
$392$	36.5145	1.84426
$393$	−6.95586	−0.350877
$394$	32.8971	1.65733
$395$	7.87007	0.395986
$396$	−6.91294	−0.347388
$397$	39.2175	1.96827	0.984136	−	0.177417i	$-0.0567740\pi$
$397$	39.2175	1.96827	0.984136	+	0.177417i	$0.0567740\pi$
$398$	−30.3604	−1.52183
$399$	2.77302	0.138825
$400$	21.1783	1.05892
$401$	13.3260	0.665471	0.332736	−	0.943020i	$-0.392028\pi$
$401$	13.3260	0.665471	0.332736	+	0.943020i	$0.392028\pi$
$402$	−18.2639	−0.910919
$403$	−12.2776	−0.611591
$404$	−5.25162	−0.261278
$405$	23.4602	1.16575
$406$	−10.4589	−0.519066
$407$	−16.6293	−0.824283
$408$	8.66943	0.429201
$409$	30.7946	1.52270	0.761349	−	0.648343i	$-0.224538\pi$
$409$	30.7946	1.52270	0.761349	+	0.648343i	$0.224538\pi$
$410$	−82.2114	−4.06013
$411$	−26.9359	−1.32865
$412$	−37.7852	−1.86154
$413$	5.73118	0.282013
$414$	4.30965	0.211808
$415$	−44.1279	−2.16615
$416$	6.23280	0.305588
$417$	20.0529	0.981995
$418$	−43.2558	−2.11571
$419$	−12.8655	−0.628520	−0.314260	−	0.949337i	$-0.601756\pi$
$419$	−12.8655	−0.628520	−0.314260	+	0.949337i	$0.601756\pi$
$420$	−8.77992	−0.428416
$421$	29.7678	1.45080	0.725398	−	0.688330i	$-0.241656\pi$
$421$	29.7678	1.45080	0.725398	+	0.688330i	$0.241656\pi$
$422$	−24.8611	−1.21022
$423$	−0.171463	−0.00833684
$424$	6.80204	0.330336
$425$	−4.25508	−0.206402
$426$	35.8527	1.73707
$427$	1.52107	0.0736096
$428$	42.2876	2.04405
$429$	−26.8689	−1.29724
$430$	13.2623	0.639567
$431$	37.6861	1.81528	0.907638	−	0.419755i	$-0.137884\pi$
$431$	37.6861	1.81528	0.907638	+	0.419755i	$0.137884\pi$
$432$	−27.2333	−1.31026
$433$	−10.5677	−0.507851	−0.253925	−	0.967224i	$-0.581722\pi$
$433$	−10.5677	−0.507851	−0.253925	+	0.967224i	$0.581722\pi$
$434$	−3.43280	−0.164779
$435$	−48.3847	−2.31987
$436$	−66.7641	−3.19742
$437$	18.2092	0.871065
$438$	51.2291	2.44782
$439$	5.93220	0.283128	0.141564	−	0.989929i	$-0.454787\pi$
$439$	5.93220	0.283128	0.141564	+	0.989929i	$0.454787\pi$
$440$	71.0908	3.38912
$441$	2.59747	0.123689
$442$	−9.44578	−0.449290
$443$	−2.75292	−0.130795	−0.0653976	−	0.997859i	$-0.520832\pi$
$443$	−2.75292	−0.130795	−0.0653976	+	0.997859i	$0.520832\pi$
$444$	−25.6564	−1.21760
$445$	−32.2987	−1.53110
$446$	−45.1822	−2.13944
$447$	23.6767	1.11987
$448$	−2.52605	−0.119345
$449$	28.0099	1.32187	0.660935	−	0.750443i	$-0.270160\pi$
$449$	28.0099	1.32187	0.660935	+	0.750443i	$0.270160\pi$
$450$	4.02407	0.189697
$451$	−47.4999	−2.23668
$452$	−83.3509	−3.92050
$453$	20.0896	0.943893
$454$	35.0182	1.64349
$455$	4.96558	0.232790
$456$	−34.6416	−1.62224
$457$	2.18226	0.102082	0.0510410	−	0.998697i	$-0.483746\pi$
$457$	2.18226	0.102082	0.0510410	+	0.998697i	$0.483746\pi$
$458$	−51.3288	−2.39844
$459$	5.47163	0.255394
$460$	−57.6539	−2.68813
$461$	23.0385	1.07301	0.536506	−	0.843897i	$-0.319744\pi$
$461$	23.0385	1.07301	0.536506	+	0.843897i	$0.319744\pi$
$462$	−7.51249	−0.349512
$463$	−27.7353	−1.28897	−0.644485	−	0.764617i	$-0.722928\pi$
$463$	−27.7353	−1.28897	−0.644485	+	0.764617i	$0.722928\pi$
$464$	48.9149	2.27082
$465$	−15.8807	−0.736452
$466$	−44.5485	−2.06367
$467$	28.7866	1.33208	0.666041	−	0.745915i	$-0.267987\pi$
$467$	28.7866	1.33208	0.666041	+	0.745915i	$0.267987\pi$
$468$	6.03203	0.278831
$469$	1.95017	0.0900506
$470$	3.39696	0.156690
$471$	27.6055	1.27199
$472$	−71.5960	−3.29547
$473$	7.66268	0.352330
$474$	10.3895	0.477204
$475$	17.0026	0.780132
$476$	−1.78336	−0.0817402
$477$	0.483865	0.0221547
$478$	7.37523	0.337335
$479$	−1.58939	−0.0726210	−0.0363105	−	0.999341i	$-0.511561\pi$
$479$	−1.58939	−0.0726210	−0.0363105	+	0.999341i	$0.511561\pi$
$480$	8.06196	0.367976
$481$	14.5102	0.661609
$482$	3.83766	0.174801
$483$	3.16250	0.143899
$484$	33.3848	1.51749
$485$	1.80600	0.0820063
$486$	−9.76593	−0.442991
$487$	7.90752	0.358324	0.179162	−	0.983820i	$-0.442661\pi$
$487$	7.90752	0.358324	0.179162	+	0.983820i	$0.442661\pi$
$488$	−19.0017	−0.860167
$489$	−14.0402	−0.634920
$490$	−51.4600	−2.32473
$491$	−9.35655	−0.422255	−0.211128	−	0.977459i	$-0.567714\pi$
$491$	−9.35655	−0.422255	−0.211128	+	0.977459i	$0.567714\pi$
$492$	−73.2848	−3.30393
$493$	−9.82781	−0.442623
$494$	37.7437	1.69817
$495$	5.05707	0.227298
$496$	16.0548	0.720880
$497$	−3.82827	−0.171721
$498$	−58.2543	−2.61044
$499$	16.0847	0.720051	0.360025	−	0.932943i	$-0.382768\pi$
$499$	16.0847	0.720051	0.360025	+	0.932943i	$0.382768\pi$
$500$	9.42439	0.421472
$501$	35.6879	1.59442
$502$	33.8358	1.51017
$503$	−31.2460	−1.39319	−0.696594	−	0.717465i	$-0.745302\pi$
$503$	−31.2460	−1.39319	−0.696594	+	0.717465i	$0.745302\pi$
$504$	0.875446	0.0389954
$505$	3.84175	0.170956
$506$	−49.3312	−2.19304
$507$	2.40698	0.106898
$508$	−88.4347	−3.92366
$509$	−24.6661	−1.09331	−0.546653	−	0.837359i	$-0.684098\pi$
$509$	−24.6661	−1.09331	−0.546653	+	0.837359i	$0.684098\pi$
$510$	−12.2178	−0.541015
$511$	−5.47012	−0.241984
$512$	45.1763	1.99653
$513$	−21.8637	−0.965306
$514$	59.2689	2.61424
$515$	27.6412	1.21802
$516$	11.8223	0.520448
$517$	1.96269	0.0863188
$518$	4.05703	0.178255
$519$	25.6836	1.12738
$520$	−62.0317	−2.72027
$521$	−29.1940	−1.27901	−0.639507	−	0.768785i	$-0.720861\pi$
$521$	−29.1940	−1.27901	−0.639507	+	0.768785i	$0.720861\pi$
$522$	9.29426	0.406799
$523$	−22.6449	−0.990192	−0.495096	−	0.868838i	$-0.664867\pi$
$523$	−22.6449	−0.990192	−0.495096	+	0.868838i	$0.664867\pi$
$524$	−17.8749	−0.780869
$525$	2.95294	0.128877
$526$	−39.4792	−1.72138
$527$	−3.22567	−0.140512
$528$	35.1349	1.52905
$529$	−2.23327	−0.0970987
$530$	−9.58614	−0.416395
$531$	−5.09300	−0.221018
$532$	7.12601	0.308952
$533$	41.4470	1.79527
$534$	−42.6382	−1.84514
$535$	−30.9349	−1.33743
$536$	−24.3622	−1.05229
$537$	14.2296	0.614052
$538$	−15.5548	−0.670614
$539$	−29.7324	−1.28067
$540$	69.2247	2.97896
$541$	−29.4295	−1.26527	−0.632636	−	0.774450i	$-0.718027\pi$
$541$	−29.4295	−1.26527	−0.632636	+	0.774450i	$0.718027\pi$
$542$	49.2829	2.11688
$543$	30.2253	1.29709
$544$	1.63753	0.0702085
$545$	48.8403	2.09209
$546$	6.55517	0.280535
$547$	−25.4580	−1.08851	−0.544253	−	0.838921i	$-0.683187\pi$
$547$	−25.4580	−1.08851	−0.544253	+	0.838921i	$0.683187\pi$
$548$	−69.2190	−2.95689
$549$	−1.35169	−0.0576888
$550$	−46.0623	−1.96410
$551$	39.2703	1.67297
$552$	−39.5071	−1.68153
$553$	−1.10936	−0.0471749
$554$	32.5074	1.38111
$555$	18.7685	0.796681
$556$	51.5312	2.18541
$557$	34.2503	1.45123	0.725616	−	0.688100i	$-0.241555\pi$
$557$	34.2503	1.45123	0.725616	+	0.688100i	$0.241555\pi$
$558$	3.05055	0.129140
$559$	−6.68623	−0.282797
$560$	−6.49321	−0.274388
$561$	−7.05919	−0.298039
$562$	47.8771	2.01958
$563$	−14.8105	−0.624188	−0.312094	−	0.950051i	$-0.601030\pi$
$563$	−14.8105	−0.624188	−0.312094	+	0.950051i	$0.601030\pi$
$564$	3.02811	0.127507
$565$	60.9742	2.56520
$566$	−60.1084	−2.52654
$567$	−3.30694	−0.138878
$568$	47.8241	2.00665
$569$	−35.9391	−1.50665	−0.753323	−	0.657651i	$-0.771550\pi$
$569$	−35.9391	−1.50665	−0.753323	+	0.657651i	$0.771550\pi$
$570$	48.8205	2.04486
$571$	−7.81328	−0.326975	−0.163488	−	0.986545i	$-0.552274\pi$
$571$	−7.81328	−0.326975	−0.163488	+	0.986545i	$0.552274\pi$
$572$	−69.0467	−2.88699
$573$	42.6055	1.77987
$574$	11.5885	0.483694
$575$	19.3906	0.808645
$576$	2.24477	0.0935322
$577$	27.3146	1.13712	0.568562	−	0.822641i	$-0.307500\pi$
$577$	27.3146	1.13712	0.568562	+	0.822641i	$0.307500\pi$
$578$	−2.48167	−0.103224
$579$	1.34272	0.0558016
$580$	−124.337	−5.16283
$581$	6.22026	0.258060
$582$	2.38415	0.0988260
$583$	−5.53865	−0.229387
$584$	68.3347	2.82771
$585$	−4.41265	−0.182440
$586$	−38.2945	−1.58193
$587$	40.2666	1.66198	0.830990	−	0.556288i	$-0.187775\pi$
$587$	40.2666	1.66198	0.830990	+	0.556288i	$0.187775\pi$
$588$	−45.8724	−1.89175
$589$	12.8892	0.531091
$590$	100.900	4.15400
$591$	−21.4524	−0.882432
$592$	−18.9742	−0.779835
$593$	−7.61962	−0.312900	−0.156450	−	0.987686i	$-0.550005\pi$
$593$	−7.61962	−0.312900	−0.156450	+	0.987686i	$0.550005\pi$
$594$	59.2317	2.43030
$595$	1.30459	0.0534831
$596$	60.8436	2.49225
$597$	19.7982	0.810284
$598$	43.0449	1.76024
$599$	−8.97816	−0.366837	−0.183419	−	0.983035i	$-0.558716\pi$
$599$	−8.97816	−0.366837	−0.183419	+	0.983035i	$0.558716\pi$
$600$	−36.8891	−1.50599
$601$	21.6677	0.883843	0.441922	−	0.897054i	$-0.354297\pi$
$601$	21.6677	0.883843	0.441922	+	0.897054i	$0.354297\pi$
$602$	−1.86946	−0.0761933
$603$	−1.73302	−0.0705739
$604$	51.6256	2.10061
$605$	−24.4222	−0.992904
$606$	5.07159	0.206019
$607$	12.8737	0.522528	0.261264	−	0.965267i	$-0.415861\pi$
$607$	12.8737	0.522528	0.261264	+	0.965267i	$0.415861\pi$
$608$	−6.54329	−0.265365
$609$	6.82030	0.276372
$610$	26.7791	1.08426
$611$	−1.71258	−0.0692836
$612$	1.58478	0.0640609
$613$	32.7130	1.32127	0.660633	−	0.750709i	$-0.270288\pi$
$613$	32.7130	1.32127	0.660633	+	0.750709i	$0.270288\pi$
$614$	−41.2270	−1.66379
$615$	53.6105	2.16178
$616$	−10.0209	−0.403755
$617$	34.7272	1.39807	0.699033	−	0.715089i	$-0.253614\pi$
$617$	34.7272	1.39807	0.699033	+	0.715089i	$0.253614\pi$
$618$	36.4898	1.46784
$619$	−15.6980	−0.630955	−0.315477	−	0.948933i	$-0.602165\pi$
$619$	−15.6980	−0.630955	−0.315477	+	0.948933i	$0.602165\pi$
$620$	−40.8098	−1.63896
$621$	−24.9345	−1.00059
$622$	−19.0443	−0.763607
$623$	4.55281	0.182404
$624$	−30.6577	−1.22729
$625$	−28.1697	−1.12679
$626$	52.6630	2.10484
$627$	28.2073	1.12649
$628$	70.9395	2.83079
$629$	3.81223	0.152004
$630$	−1.23377	−0.0491545
$631$	12.1453	0.483496	0.241748	−	0.970339i	$-0.422279\pi$
$631$	12.1453	0.483496	0.241748	+	0.970339i	$0.422279\pi$
$632$	13.8586	0.551264
$633$	16.2120	0.644371
$634$	−42.2307	−1.67720
$635$	64.6932	2.56727
$636$	−8.54527	−0.338842
$637$	25.9436	1.02792
$638$	−106.388	−4.21196
$639$	3.40198	0.134580
$640$	−54.4359	−2.15177
$641$	41.6549	1.64527	0.822634	−	0.568571i	$-0.192503\pi$
$641$	41.6549	1.64527	0.822634	+	0.568571i	$0.192503\pi$
$642$	−40.8378	−1.61174
$643$	19.9965	0.788584	0.394292	−	0.918985i	$-0.370990\pi$
$643$	19.9965	0.788584	0.394292	+	0.918985i	$0.370990\pi$
$644$	8.12687	0.320244
$645$	−8.64844	−0.340532
$646$	9.91632	0.390152
$647$	−41.6356	−1.63687	−0.818433	−	0.574602i	$-0.805157\pi$
$647$	−41.6356	−1.63687	−0.818433	+	0.574602i	$0.805157\pi$
$648$	41.3115	1.62287
$649$	58.2979	2.28839
$650$	40.1926	1.57648
$651$	2.23854	0.0877355
$652$	−36.0800	−1.41300
$653$	34.2125	1.33884	0.669419	−	0.742885i	$-0.266543\pi$
$653$	34.2125	1.33884	0.669419	+	0.742885i	$0.266543\pi$
$654$	64.4753	2.52118
$655$	13.0761	0.510927
$656$	−54.1979	−2.11607
$657$	4.86101	0.189646
$658$	−0.478834	−0.0186669
$659$	−3.55475	−0.138473	−0.0692366	−	0.997600i	$-0.522056\pi$
$659$	−3.55475	−0.138473	−0.0692366	+	0.997600i	$0.522056\pi$
$660$	−89.3099	−3.47638
$661$	1.93999	0.0754570	0.0377285	−	0.999288i	$-0.487988\pi$
$661$	1.93999	0.0754570	0.0377285	+	0.999288i	$0.487988\pi$
$662$	−19.3202	−0.750902
$663$	6.15964	0.239221
$664$	−77.7057	−3.01556
$665$	−5.21293	−0.202149
$666$	−3.60527	−0.139701
$667$	44.7859	1.73412
$668$	91.7094	3.54834
$669$	29.4635	1.13913
$670$	34.3338	1.32643
$671$	15.4724	0.597305
$672$	−1.13641	−0.0438380
$673$	12.0182	0.463267	0.231634	−	0.972803i	$-0.425593\pi$
$673$	12.0182	0.463267	0.231634	+	0.972803i	$0.425593\pi$
$674$	−30.0084	−1.15588
$675$	−23.2822	−0.896133
$676$	6.18538	0.237899
$677$	−40.9644	−1.57439	−0.787195	−	0.616705i	$-0.788467\pi$
$677$	−40.9644	−1.57439	−0.787195	+	0.616705i	$0.788467\pi$
$678$	80.4935	3.09133
$679$	−0.254573	−0.00976963
$680$	−16.2974	−0.624979
$681$	−22.8356	−0.875061
$682$	−34.9186	−1.33710
$683$	−18.1529	−0.694600	−0.347300	−	0.937754i	$-0.612901\pi$
$683$	−18.1529	−0.694600	−0.347300	+	0.937754i	$0.612901\pi$
$684$	−6.33251	−0.242130
$685$	50.6362	1.93471
$686$	14.7033	0.561374
$687$	33.4718	1.27703
$688$	8.74321	0.333332
$689$	4.83286	0.184117
$690$	55.6774	2.11960
$691$	−3.56142	−0.135483	−0.0677414	−	0.997703i	$-0.521579\pi$
$691$	−3.56142	−0.135483	−0.0677414	+	0.997703i	$0.521579\pi$
$692$	66.0007	2.50897
$693$	−0.712843	−0.0270787
$694$	16.3033	0.618864
$695$	−37.6969	−1.42993
$696$	−85.2016	−3.22956
$697$	10.8893	0.412460
$698$	51.7849	1.96009
$699$	29.0503	1.09878
$700$	7.58835	0.286813
$701$	−2.72014	−0.102738	−0.0513692	−	0.998680i	$-0.516359\pi$
$701$	−2.72014	−0.102738	−0.0513692	+	0.998680i	$0.516359\pi$
$702$	−51.6838	−1.95068
$703$	−15.2330	−0.574525
$704$	−25.6952	−0.968423
$705$	−2.21518	−0.0834283
$706$	−2.48167	−0.0933988
$707$	−0.541532	−0.0203664
$708$	89.9445	3.38032
$709$	−42.2268	−1.58586	−0.792930	−	0.609312i	$-0.791446\pi$
$709$	−42.2268	−1.58586	−0.792930	+	0.609312i	$0.791446\pi$
$710$	−67.3986	−2.52942
$711$	0.985833	0.0369716
$712$	−56.8753	−2.13149
$713$	14.6995	0.550502
$714$	1.72222	0.0644526
$715$	50.5101	1.88897
$716$	36.5667	1.36656
$717$	−4.80943	−0.179611
$718$	−23.7347	−0.885773
$719$	7.94134	0.296162	0.148081	−	0.988975i	$-0.452690\pi$
$719$	7.94134	0.296162	0.148081	+	0.988975i	$0.452690\pi$
$720$	5.77017	0.215042
$721$	−3.89630	−0.145106
$722$	7.52773	0.280153
$723$	−2.50256	−0.0930711
$724$	77.6718	2.88665
$725$	41.8182	1.55309
$726$	−32.2403	−1.19655
$727$	24.6624	0.914678	0.457339	−	0.889292i	$-0.348803\pi$
$727$	24.6624	0.914678	0.457339	+	0.889292i	$0.348803\pi$
$728$	8.74397	0.324073
$729$	29.5030	1.09271
$730$	−96.3042	−3.56438
$731$	−1.75666	−0.0649723
$732$	23.8714	0.882314
$733$	−41.0647	−1.51676	−0.758379	−	0.651813i	$-0.774009\pi$
$733$	−41.0647	−1.51676	−0.758379	+	0.651813i	$0.774009\pi$
$734$	65.6523	2.42327
$735$	33.5573	1.23778
$736$	−7.46231	−0.275064
$737$	19.8373	0.730715
$738$	−10.2981	−0.379078
$739$	−26.3991	−0.971107	−0.485554	−	0.874207i	$-0.661382\pi$
$739$	−26.3991	−0.971107	−0.485554	+	0.874207i	$0.661382\pi$
$740$	48.2307	1.77300
$741$	−24.6129	−0.904177
$742$	1.35126	0.0496063
$743$	8.33998	0.305964	0.152982	−	0.988229i	$-0.451112\pi$
$743$	8.33998	0.305964	0.152982	+	0.988229i	$0.451112\pi$
$744$	−27.9647	−1.02524
$745$	−44.5093	−1.63069
$746$	−72.0871	−2.63930
$747$	−5.52762	−0.202245
$748$	−18.1405	−0.663281
$749$	4.36057	0.159332
$750$	−9.10130	−0.332333
$751$	39.4885	1.44096	0.720478	−	0.693478i	$-0.243922\pi$
$751$	39.4885	1.44096	0.720478	+	0.693478i	$0.243922\pi$
$752$	2.23945	0.0816642
$753$	−22.0645	−0.804076
$754$	92.8314	3.38072
$755$	−37.7660	−1.37444
$756$	−9.75789	−0.354891
$757$	9.69560	0.352392	0.176196	−	0.984355i	$-0.443621\pi$
$757$	9.69560	0.352392	0.176196	+	0.984355i	$0.443621\pi$
$758$	−8.59676	−0.312249
$759$	32.1691	1.16767
$760$	65.1218	2.36222
$761$	4.68910	0.169980	0.0849898	−	0.996382i	$-0.472914\pi$
$761$	4.68910	0.169980	0.0849898	+	0.996382i	$0.472914\pi$
$762$	85.4030	3.09382
$763$	−6.88452	−0.249236
$764$	109.486	3.96107
$765$	−1.15932	−0.0419154
$766$	35.5072	1.28293
$767$	−50.8691	−1.83678
$768$	−52.7966	−1.90513
$769$	4.91782	0.177341	0.0886705	−	0.996061i	$-0.471738\pi$
$769$	4.91782	0.177341	0.0886705	+	0.996061i	$0.471738\pi$
$770$	14.1225	0.508941
$771$	−38.6496	−1.39193
$772$	3.45048	0.124185
$773$	51.1072	1.83820	0.919099	−	0.394027i	$-0.128918\pi$
$773$	51.1072	1.83820	0.919099	+	0.394027i	$0.128918\pi$
$774$	1.66129	0.0597137
$775$	13.7255	0.493034
$776$	3.18022	0.114163
$777$	−2.64561	−0.0949107
$778$	−59.8422	−2.14545
$779$	−43.5116	−1.55897
$780$	77.9292	2.79031
$781$	−38.9414	−1.39343
$782$	11.3091	0.404412
$783$	−53.7741	−1.92173
$784$	−33.9250	−1.21161
$785$	−51.8948	−1.85221
$786$	17.2621	0.615719
$787$	8.96878	0.319703	0.159851	−	0.987141i	$-0.448899\pi$
$787$	8.96878	0.319703	0.159851	+	0.987141i	$0.448899\pi$
$788$	−55.1275	−1.96383
$789$	25.7446	0.916533
$790$	−19.5309	−0.694878
$791$	−8.59490	−0.305600
$792$	8.90508	0.316428
$793$	−13.5007	−0.479425
$794$	−97.3248	−3.45393
$795$	6.25117	0.221706
$796$	50.8766	1.80327
$797$	−7.47487	−0.264774	−0.132387	−	0.991198i	$-0.542264\pi$
$797$	−7.47487	−0.264774	−0.132387	+	0.991198i	$0.542264\pi$
$798$	−6.88172	−0.243610
$799$	−0.449942	−0.0159178
$800$	−6.96782	−0.246350
$801$	−4.04584	−0.142953
$802$	−33.0708	−1.16777
$803$	−55.6424	−1.96358
$804$	30.6058	1.07938
$805$	−5.94510	−0.209537
$806$	30.4689	1.07322
$807$	10.1433	0.357063
$808$	6.76501	0.237992
$809$	−32.5441	−1.14419	−0.572095	−	0.820187i	$-0.693869\pi$
$809$	−32.5441	−1.14419	−0.572095	+	0.820187i	$0.693869\pi$
$810$	−58.2204	−2.04565
$811$	25.1276	0.882349	0.441175	−	0.897421i	$-0.354562\pi$
$811$	25.1276	0.882349	0.441175	+	0.897421i	$0.354562\pi$
$812$	17.5265	0.615061
$813$	−32.1377	−1.12712
$814$	41.2683	1.44645
$815$	26.3938	0.924536
$816$	−8.05462	−0.281968
$817$	7.01930	0.245574
$818$	−76.4220	−2.67203
$819$	0.622005	0.0217346
$820$	137.766	4.81101
$821$	49.9774	1.74422	0.872111	−	0.489308i	$-0.162751\pi$
$821$	49.9774	1.74422	0.872111	+	0.489308i	$0.162751\pi$
$822$	66.8460	2.33152
$823$	25.4376	0.886698	0.443349	−	0.896349i	$-0.353790\pi$
$823$	25.4376	0.886698	0.443349	+	0.896349i	$0.353790\pi$
$824$	48.6739	1.69564
$825$	30.0374	1.04577
$826$	−14.2229	−0.494878
$827$	49.5039	1.72142	0.860709	−	0.509096i	$-0.170020\pi$
$827$	49.5039	1.72142	0.860709	+	0.509096i	$0.170020\pi$
$828$	−7.22193	−0.250979
$829$	−7.14551	−0.248174	−0.124087	−	0.992271i	$-0.539600\pi$
$829$	−7.14551	−0.248174	−0.124087	+	0.992271i	$0.539600\pi$
$830$	109.511	3.80117
$831$	−21.1983	−0.735359
$832$	22.4208	0.777303
$833$	6.81610	0.236164
$834$	−49.7646	−1.72321
$835$	−67.0887	−2.32170
$836$	72.4862	2.50699
$837$	−17.6496	−0.610061
$838$	31.9278	1.10293
$839$	−2.45979	−0.0849214	−0.0424607	−	0.999098i	$-0.513520\pi$
$839$	−2.45979	−0.0849214	−0.0424607	+	0.999098i	$0.513520\pi$
$840$	11.3101	0.390235
$841$	67.5859	2.33055
$842$	−73.8738	−2.54586
$843$	−31.2209	−1.07531
$844$	41.6611	1.43403
$845$	−4.52483	−0.155659
$846$	0.425515	0.0146295
$847$	3.44255	0.118287
$848$	−6.31967	−0.217018
$849$	39.1970	1.34524
$850$	10.5597	0.362194
$851$	−17.3725	−0.595523
$852$	−60.0804	−2.05832
$853$	33.4480	1.14524	0.572619	−	0.819821i	$-0.305927\pi$
$853$	33.4480	1.14524	0.572619	+	0.819821i	$0.305927\pi$
$854$	−3.77478	−0.129170
$855$	4.63246	0.158427
$856$	−54.4738	−1.86188
$857$	0.849261	0.0290102	0.0145051	−	0.999895i	$-0.495383\pi$
$857$	0.849261	0.0290102	0.0145051	+	0.999895i	$0.495383\pi$
$858$	66.6796	2.27640
$859$	4.88534	0.166686	0.0833429	−	0.996521i	$-0.473440\pi$
$859$	4.88534	0.166686	0.0833429	+	0.996521i	$0.473440\pi$
$860$	−22.2245	−0.757848
$861$	−7.55692	−0.257539
$862$	−93.5243	−3.18545
$863$	−14.2902	−0.486444	−0.243222	−	0.969971i	$-0.578204\pi$
$863$	−14.2902	−0.486444	−0.243222	+	0.969971i	$0.578204\pi$
$864$	8.95995	0.304824
$865$	−48.2819	−1.64163
$866$	26.2255	0.891178
$867$	1.61831	0.0549606
$868$	5.75253	0.195254
$869$	−11.2845	−0.382801
$870$	120.075	4.07092
$871$	−17.3094	−0.586507
$872$	86.0039	2.91246
$873$	0.226226	0.00765659
$874$	−45.1892	−1.52855
$875$	0.971816	0.0328534
$876$	−85.8474	−2.90052
$877$	28.8699	0.974866	0.487433	−	0.873160i	$-0.337933\pi$
$877$	28.8699	0.974866	0.487433	+	0.873160i	$0.337933\pi$
$878$	−14.7217	−0.496835
$879$	24.9720	0.842285
$880$	−66.0493	−2.22652
$881$	55.1914	1.85945	0.929723	−	0.368261i	$-0.120047\pi$
$881$	55.1914	1.85945	0.929723	+	0.368261i	$0.120047\pi$
$882$	−6.44606	−0.217050
$883$	−29.3225	−0.986780	−0.493390	−	0.869808i	$-0.664243\pi$
$883$	−29.3225	−0.986780	−0.493390	+	0.869808i	$0.664243\pi$
$884$	15.8288	0.532381
$885$	−65.7977	−2.21177
$886$	6.83183	0.229520
$887$	26.3527	0.884836	0.442418	−	0.896809i	$-0.354121\pi$
$887$	26.3527	0.884836	0.442418	+	0.896809i	$0.354121\pi$
$888$	33.0499	1.10908
$889$	−9.11913	−0.305846
$890$	80.1545	2.68679
$891$	−33.6384	−1.12693
$892$	75.7143	2.53510
$893$	1.79789	0.0601642
$894$	−58.7577	−1.96515
$895$	−26.7498	−0.894149
$896$	7.67327	0.256346
$897$	−28.0698	−0.937224
$898$	−69.5113	−2.31962
$899$	31.7013	1.05730
$900$	−6.74337	−0.224779
$901$	1.26973	0.0423007
$902$	117.879	3.92494
$903$	1.21908	0.0405685
$904$	107.371	3.57109
$905$	−56.8197	−1.88875
$906$	−49.8557	−1.65635
$907$	−49.0769	−1.62957	−0.814785	−	0.579763i	$-0.803145\pi$
$907$	−49.0769	−1.62957	−0.814785	+	0.579763i	$0.803145\pi$
$908$	−58.6820	−1.94743
$909$	0.481231	0.0159614
$910$	−12.3229	−0.408500
$911$	−14.6116	−0.484104	−0.242052	−	0.970263i	$-0.577820\pi$
$911$	−14.6116	−0.484104	−0.242052	+	0.970263i	$0.577820\pi$
$912$	32.1849	1.06575
$913$	63.2728	2.09402
$914$	−5.41565	−0.179134
$915$	−17.4628	−0.577303
$916$	86.0146	2.84200
$917$	−1.84321	−0.0608681
$918$	−13.5788	−0.448166
$919$	34.7991	1.14792	0.573958	−	0.818885i	$-0.305407\pi$
$919$	34.7991	1.14792	0.573958	+	0.818885i	$0.305407\pi$
$920$	74.2683	2.44855
$921$	26.8843	0.885869
$922$	−57.1740	−1.88292
$923$	33.9791	1.11844
$924$	12.5891	0.414151
$925$	−16.2214	−0.533355
$926$	68.8299	2.26189
$927$	3.46243	0.113721
$928$	−16.0933	−0.528290
$929$	26.4347	0.867294	0.433647	−	0.901083i	$-0.357226\pi$
$929$	26.4347	0.867294	0.433647	+	0.901083i	$0.357226\pi$
$930$	39.4107	1.29233
$931$	−27.2360	−0.892624
$932$	74.6525	2.44532
$933$	12.4189	0.406577
$934$	−71.4386	−2.33754
$935$	13.2704	0.433989
$936$	−7.77031	−0.253981
$937$	19.7680	0.645793	0.322897	−	0.946434i	$-0.395343\pi$
$937$	19.7680	0.645793	0.322897	+	0.946434i	$0.395343\pi$
$938$	−4.83968	−0.158021
$939$	−34.3418	−1.12070
$940$	−5.69248	−0.185668
$941$	28.4800	0.928421	0.464211	−	0.885725i	$-0.346338\pi$
$941$	28.4800	0.928421	0.464211	+	0.885725i	$0.346338\pi$
$942$	−68.5076	−2.23210
$943$	−49.6229	−1.61595
$944$	66.5186	2.16500
$945$	7.13825	0.232207
$946$	−19.0162	−0.618270
$947$	50.8815	1.65343	0.826713	−	0.562624i	$-0.190208\pi$
$947$	50.8815	1.65343	0.826713	+	0.562624i	$0.190208\pi$
$948$	−17.4102	−0.565457
$949$	48.5519	1.57606
$950$	−42.1947	−1.36898
$951$	27.5389	0.893009
$952$	2.29728	0.0744554
$953$	−33.4205	−1.08260	−0.541298	−	0.840831i	$-0.682067\pi$
$953$	−33.4205	−1.08260	−0.541298	+	0.840831i	$0.682067\pi$
$954$	−1.20079	−0.0388771
$955$	−80.0930	−2.59175
$956$	−12.3591	−0.399722
$957$	69.3765	2.24262
$958$	3.94433	0.127436
$959$	−7.13766	−0.230487
$960$	29.0007	0.935995
$961$	−20.5951	−0.664357
$962$	−36.0095	−1.16099
$963$	−3.87501	−0.124870
$964$	−6.43098	−0.207128
$965$	−2.52415	−0.0812552
$966$	−7.84827	−0.252514
$967$	−8.02033	−0.257917	−0.128958	−	0.991650i	$-0.541163\pi$
$967$	−8.02033	−0.257917	−0.128958	+	0.991650i	$0.541163\pi$
$968$	−43.0055	−1.38225
$969$	−6.46649	−0.207733
$970$	−4.48189	−0.143905
$971$	−1.29672	−0.0416137	−0.0208069	−	0.999784i	$-0.506624\pi$
$971$	−1.29672	−0.0416137	−0.0208069	+	0.999784i	$0.506624\pi$
$972$	16.3653	0.524918
$973$	5.31375	0.170351
$974$	−19.6238	−0.628788
$975$	−26.2098	−0.839385
$976$	17.6542	0.565096
$977$	36.7247	1.17493	0.587463	−	0.809251i	$-0.300127\pi$
$977$	36.7247	1.17493	0.587463	+	0.809251i	$0.300127\pi$
$978$	34.8431	1.11416
$979$	46.3115	1.48012
$980$	86.2344	2.75466
$981$	6.11791	0.195330
$982$	23.2198	0.740975
$983$	55.1867	1.76018	0.880091	−	0.474804i	$-0.157481\pi$
$983$	55.1867	1.76018	0.880091	+	0.474804i	$0.157481\pi$
$984$	94.4037	3.00948
$985$	40.3277	1.28495
$986$	24.3894	0.776715
$987$	0.312250	0.00993904
$988$	−63.2493	−2.01223
$989$	8.00517	0.254550
$990$	−12.5500	−0.398864
$991$	−3.72659	−0.118379	−0.0591896	−	0.998247i	$-0.518852\pi$
$991$	−3.72659	−0.118379	−0.0591896	+	0.998247i	$0.518852\pi$
$992$	−5.28212	−0.167708
$993$	12.5988	0.399811
$994$	9.50048	0.301337
$995$	−37.2180	−1.17989
$996$	97.6200	3.09321
$997$	−4.46765	−0.141492	−0.0707459	−	0.997494i	$-0.522538\pi$
$997$	−4.46765	−0.141492	−0.0707459	+	0.997494i	$0.522538\pi$
$998$	−39.9169	−1.26355
$999$	20.8591	0.659953

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.c.1.10	✓	121	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48167 q^{2} +1.61831 q^{3} +4.15867 q^{4} -3.04222 q^{5} -4.01610 q^{6} +0.428830 q^{7} -5.35710 q^{8} -0.381079 q^{9} +O(q^{10})\)	\(q-2.48167 q^{2} +1.61831 q^{3} +4.15867 q^{4} -3.04222 q^{5} -4.01610 q^{6} +0.428830 q^{7} -5.35710 q^{8} -0.381079 q^{9} +7.54977 q^{10} +4.36208 q^{11} +6.73001 q^{12} -3.80622 q^{13} -1.06421 q^{14} -4.92324 q^{15} +4.97719 q^{16} -1.00000 q^{17} +0.945710 q^{18} +3.99583 q^{19} -12.6516 q^{20} +0.693979 q^{21} -10.8252 q^{22} +4.55705 q^{23} -8.66943 q^{24} +4.25508 q^{25} +9.44578 q^{26} -5.47163 q^{27} +1.78336 q^{28} +9.82781 q^{29} +12.2178 q^{30} +3.22567 q^{31} -1.63753 q^{32} +7.05919 q^{33} +2.48167 q^{34} -1.30459 q^{35} -1.58478 q^{36} -3.81223 q^{37} -9.91632 q^{38} -6.15964 q^{39} +16.2974 q^{40} -10.8893 q^{41} -1.72222 q^{42} +1.75666 q^{43} +18.1405 q^{44} +1.15932 q^{45} -11.3091 q^{46} +0.449942 q^{47} +8.05462 q^{48} -6.81610 q^{49} -10.5597 q^{50} -1.61831 q^{51} -15.8288 q^{52} -1.26973 q^{53} +13.5788 q^{54} -13.2704 q^{55} -2.29728 q^{56} +6.46649 q^{57} -24.3894 q^{58} +13.3647 q^{59} -20.4741 q^{60} +3.54702 q^{61} -8.00503 q^{62} -0.163418 q^{63} -5.89057 q^{64} +11.5794 q^{65} -17.5186 q^{66} +4.54766 q^{67} -4.15867 q^{68} +7.37472 q^{69} +3.23757 q^{70} -8.92724 q^{71} +2.04148 q^{72} -12.7559 q^{73} +9.46069 q^{74} +6.88603 q^{75} +16.6173 q^{76} +1.87059 q^{77} +15.2862 q^{78} -2.58695 q^{79} -15.1417 q^{80} -7.71154 q^{81} +27.0235 q^{82} +14.5052 q^{83} +2.88603 q^{84} +3.04222 q^{85} -4.35943 q^{86} +15.9044 q^{87} -23.3681 q^{88} +10.6168 q^{89} -2.87706 q^{90} -1.63222 q^{91} +18.9513 q^{92} +5.22012 q^{93} -1.11661 q^{94} -12.1562 q^{95} -2.65003 q^{96} -0.593647 q^{97} +16.9153 q^{98} -1.66230 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * q^99

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