LMFDB - Embedded newform 6022.2.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$0$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.39055 q^{3} +1.00000 q^{4} +1.34087 q^{5} +1.39055 q^{6} -2.43238 q^{7} -1.00000 q^{8} -1.06637 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.39055 q^{3} +1.00000 q^{4} +1.34087 q^{5} +1.39055 q^{6} -2.43238 q^{7} -1.00000 q^{8} -1.06637 q^{9} -1.34087 q^{10} +6.55242 q^{11} -1.39055 q^{12} +5.32706 q^{13} +2.43238 q^{14} -1.86454 q^{15} +1.00000 q^{16} +2.23928 q^{17} +1.06637 q^{18} -4.38982 q^{19} +1.34087 q^{20} +3.38235 q^{21} -6.55242 q^{22} -2.33146 q^{23} +1.39055 q^{24} -3.20208 q^{25} -5.32706 q^{26} +5.65449 q^{27} -2.43238 q^{28} -2.34106 q^{29} +1.86454 q^{30} +6.04400 q^{31} -1.00000 q^{32} -9.11148 q^{33} -2.23928 q^{34} -3.26149 q^{35} -1.06637 q^{36} +6.28779 q^{37} +4.38982 q^{38} -7.40755 q^{39} -1.34087 q^{40} +3.03964 q^{41} -3.38235 q^{42} +9.54720 q^{43} +6.55242 q^{44} -1.42986 q^{45} +2.33146 q^{46} -0.726106 q^{47} -1.39055 q^{48} -1.08354 q^{49} +3.20208 q^{50} -3.11383 q^{51} +5.32706 q^{52} +8.59802 q^{53} -5.65449 q^{54} +8.78593 q^{55} +2.43238 q^{56} +6.10428 q^{57} +2.34106 q^{58} +4.76256 q^{59} -1.86454 q^{60} -0.237591 q^{61} -6.04400 q^{62} +2.59381 q^{63} +1.00000 q^{64} +7.14288 q^{65} +9.11148 q^{66} -3.19260 q^{67} +2.23928 q^{68} +3.24202 q^{69} +3.26149 q^{70} +0.738274 q^{71} +1.06637 q^{72} -4.72756 q^{73} -6.28779 q^{74} +4.45265 q^{75} -4.38982 q^{76} -15.9380 q^{77} +7.40755 q^{78} -6.83970 q^{79} +1.34087 q^{80} -4.66376 q^{81} -3.03964 q^{82} -15.0810 q^{83} +3.38235 q^{84} +3.00257 q^{85} -9.54720 q^{86} +3.25536 q^{87} -6.55242 q^{88} +1.39078 q^{89} +1.42986 q^{90} -12.9574 q^{91} -2.33146 q^{92} -8.40450 q^{93} +0.726106 q^{94} -5.88617 q^{95} +1.39055 q^{96} +10.3562 q^{97} +1.08354 q^{98} -6.98728 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) $ 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9 - 16 * q^10 + 14 * q^11 + 8 * q^12 + 27 * q^13 - 2 * q^14 + 61 * q^16 + 60 * q^17 - 67 * q^18 - 29 * q^19 + 16 * q^20 + 30 * q^21 - 14 * q^22 + 39 * q^23 - 8 * q^24 + 61 * q^25 - 27 * q^26 + 32 * q^27 + 2 * q^28 + 36 * q^29 - 40 * q^31 - 61 * q^32 + 28 * q^33 - 60 * q^34 + 55 * q^35 + 67 * q^36 + 20 * q^37 + 29 * q^38 + 17 * q^39 - 16 * q^40 + 44 * q^41 - 30 * q^42 + 22 * q^43 + 14 * q^44 + 52 * q^45 - 39 * q^46 + 64 * q^47 + 8 * q^48 + 49 * q^49 - 61 * q^50 + 15 * q^51 + 27 * q^52 + 65 * q^53 - 32 * q^54 + 5 * q^55 - 2 * q^56 + 9 * q^57 - 36 * q^58 + 2 * q^59 + 45 * q^61 + 40 * q^62 + 28 * q^63 + 61 * q^64 + 41 * q^65 - 28 * q^66 - 20 * q^67 + 60 * q^68 + 21 * q^69 - 55 * q^70 - q^71 - 67 * q^72 + 25 * q^73 - 20 * q^74 + 27 * q^75 - 29 * q^76 + 131 * q^77 - 17 * q^78 - 17 * q^79 + 16 * q^80 + 85 * q^81 - 44 * q^82 + 104 * q^83 + 30 * q^84 + 44 * q^85 - 22 * q^86 + 86 * q^87 - 14 * q^88 + 32 * q^89 - 52 * q^90 - 68 * q^91 + 39 * q^92 + 52 * q^93 - 64 * q^94 + 58 * q^95 - 8 * q^96 + 5 * q^97 - 49 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.39055	−0.802835	−0.401418	−	0.915895i	$-0.631482\pi$
$3$	−1.39055	−0.802835	−0.401418	+	0.915895i	$0.631482\pi$
$4$	1.00000	0.500000
$5$	1.34087	0.599654	0.299827	−	0.953994i	$-0.403071\pi$
$5$	1.34087	0.599654	0.299827	+	0.953994i	$0.403071\pi$
$6$	1.39055	0.567690
$7$	−2.43238	−0.919352	−0.459676	−	0.888087i	$-0.652034\pi$
$7$	−2.43238	−0.919352	−0.459676	+	0.888087i	$0.652034\pi$
$8$	−1.00000	−0.353553
$9$	−1.06637	−0.355456
$10$	−1.34087	−0.424019
$11$	6.55242	1.97563	0.987815	−	0.155634i	$-0.0497421\pi$
$11$	6.55242	1.97563	0.987815	+	0.155634i	$0.0497421\pi$
$12$	−1.39055	−0.401418
$13$	5.32706	1.47746	0.738730	−	0.674001i	$-0.235426\pi$
$13$	5.32706	1.47746	0.738730	+	0.674001i	$0.235426\pi$
$14$	2.43238	0.650080
$15$	−1.86454	−0.481423
$16$	1.00000	0.250000
$17$	2.23928	0.543104	0.271552	−	0.962424i	$-0.412463\pi$
$17$	2.23928	0.543104	0.271552	+	0.962424i	$0.412463\pi$
$18$	1.06637	0.251345
$19$	−4.38982	−1.00709	−0.503547	−	0.863968i	$-0.667972\pi$
$19$	−4.38982	−1.00709	−0.503547	+	0.863968i	$0.667972\pi$
$20$	1.34087	0.299827
$21$	3.38235	0.738088
$22$	−6.55242	−1.39698
$23$	−2.33146	−0.486143	−0.243072	−	0.970008i	$-0.578155\pi$
$23$	−2.33146	−0.486143	−0.243072	+	0.970008i	$0.578155\pi$
$24$	1.39055	0.283845
$25$	−3.20208	−0.640415
$26$	−5.32706	−1.04472
$27$	5.65449	1.08821
$28$	−2.43238	−0.459676
$29$	−2.34106	−0.434723	−0.217362	−	0.976091i	$-0.569745\pi$
$29$	−2.34106	−0.434723	−0.217362	+	0.976091i	$0.569745\pi$
$30$	1.86454	0.340418
$31$	6.04400	1.08554	0.542768	−	0.839883i	$-0.317376\pi$
$31$	6.04400	1.08554	0.542768	+	0.839883i	$0.317376\pi$
$32$	−1.00000	−0.176777
$33$	−9.11148	−1.58611
$34$	−2.23928	−0.384033
$35$	−3.26149	−0.551293
$36$	−1.06637	−0.177728
$37$	6.28779	1.03371	0.516853	−	0.856074i	$-0.327103\pi$
$37$	6.28779	1.03371	0.516853	+	0.856074i	$0.327103\pi$
$38$	4.38982	0.712123
$39$	−7.40755	−1.18616
$40$	−1.34087	−0.212010
$41$	3.03964	0.474713	0.237356	−	0.971423i	$-0.423719\pi$
$41$	3.03964	0.474713	0.237356	+	0.971423i	$0.423719\pi$
$42$	−3.38235	−0.521907
$43$	9.54720	1.45593	0.727967	−	0.685612i	$-0.240465\pi$
$43$	9.54720	1.45593	0.727967	+	0.685612i	$0.240465\pi$
$44$	6.55242	0.987815
$45$	−1.42986	−0.213150
$46$	2.33146	0.343755
$47$	−0.726106	−0.105913	−0.0529567	−	0.998597i	$-0.516865\pi$
$47$	−0.726106	−0.105913	−0.0529567	+	0.998597i	$0.516865\pi$
$48$	−1.39055	−0.200709
$49$	−1.08354	−0.154792
$50$	3.20208	0.452842
$51$	−3.11383	−0.436023
$52$	5.32706	0.738730
$53$	8.59802	1.18103	0.590515	−	0.807027i	$-0.298925\pi$
$53$	8.59802	1.18103	0.590515	+	0.807027i	$0.298925\pi$
$54$	−5.65449	−0.769479
$55$	8.78593	1.18469
$56$	2.43238	0.325040
$57$	6.10428	0.808531
$58$	2.34106	0.307396
$59$	4.76256	0.620033	0.310016	−	0.950731i	$-0.399665\pi$
$59$	4.76256	0.620033	0.310016	+	0.950731i	$0.399665\pi$
$60$	−1.86454	−0.240712
$61$	−0.237591	−0.0304204	−0.0152102	−	0.999884i	$-0.504842\pi$
$61$	−0.237591	−0.0304204	−0.0152102	+	0.999884i	$0.504842\pi$
$62$	−6.04400	−0.767589
$63$	2.59381	0.326789
$64$	1.00000	0.125000
$65$	7.14288	0.885965
$66$	9.11148	1.12155
$67$	−3.19260	−0.390039	−0.195019	−	0.980799i	$-0.562477\pi$
$67$	−3.19260	−0.390039	−0.195019	+	0.980799i	$0.562477\pi$
$68$	2.23928	0.271552
$69$	3.24202	0.390293
$70$	3.26149	0.389823
$71$	0.738274	0.0876170	0.0438085	−	0.999040i	$-0.486051\pi$
$71$	0.738274	0.0876170	0.0438085	+	0.999040i	$0.486051\pi$
$72$	1.06637	0.125673
$73$	−4.72756	−0.553319	−0.276660	−	0.960968i	$-0.589227\pi$
$73$	−4.72756	−0.553319	−0.276660	+	0.960968i	$0.589227\pi$
$74$	−6.28779	−0.730940
$75$	4.45265	0.514148
$76$	−4.38982	−0.503547
$77$	−15.9380	−1.81630
$78$	7.40755	0.838740
$79$	−6.83970	−0.769527	−0.384763	−	0.923015i	$-0.625717\pi$
$79$	−6.83970	−0.769527	−0.384763	+	0.923015i	$0.625717\pi$
$80$	1.34087	0.149913
$81$	−4.66376	−0.518196
$82$	−3.03964	−0.335673
$83$	−15.0810	−1.65535	−0.827676	−	0.561207i	$-0.810337\pi$
$83$	−15.0810	−1.65535	−0.827676	+	0.561207i	$0.810337\pi$
$84$	3.38235	0.369044
$85$	3.00257	0.325675
$86$	−9.54720	−1.02950
$87$	3.25536	0.349011
$88$	−6.55242	−0.698491
$89$	1.39078	0.147422	0.0737110	−	0.997280i	$-0.476516\pi$
$89$	1.39078	0.147422	0.0737110	+	0.997280i	$0.476516\pi$
$90$	1.42986	0.150720
$91$	−12.9574	−1.35831
$92$	−2.33146	−0.243072
$93$	−8.40450	−0.871506
$94$	0.726106	0.0748921
$95$	−5.88617	−0.603908
$96$	1.39055	0.141923
$97$	10.3562	1.05152	0.525758	−	0.850634i	$-0.323782\pi$
$97$	10.3562	1.05152	0.525758	+	0.850634i	$0.323782\pi$
$98$	1.08354	0.109454
$99$	−6.98728	−0.702248
$100$	−3.20208	−0.320208
$101$	−4.09374	−0.407342	−0.203671	−	0.979039i	$-0.565287\pi$
$101$	−4.09374	−0.407342	−0.203671	+	0.979039i	$0.565287\pi$
$102$	3.11383	0.308315
$103$	−2.79894	−0.275788	−0.137894	−	0.990447i	$-0.544033\pi$
$103$	−2.79894	−0.275788	−0.137894	+	0.990447i	$0.544033\pi$
$104$	−5.32706	−0.522361
$105$	4.53527	0.442598
$106$	−8.59802	−0.835114
$107$	−3.73346	−0.360928	−0.180464	−	0.983582i	$-0.557760\pi$
$107$	−3.73346	−0.360928	−0.180464	+	0.983582i	$0.557760\pi$
$108$	5.65449	0.544104
$109$	13.2354	1.26772	0.633860	−	0.773448i	$-0.281469\pi$
$109$	13.2354	1.26772	0.633860	+	0.773448i	$0.281469\pi$
$110$	−8.78593	−0.837705
$111$	−8.74349	−0.829895
$112$	−2.43238	−0.229838
$113$	−15.7022	−1.47713	−0.738567	−	0.674180i	$-0.764497\pi$
$113$	−15.7022	−1.47713	−0.738567	+	0.674180i	$0.764497\pi$
$114$	−6.10428	−0.571718
$115$	−3.12618	−0.291518
$116$	−2.34106	−0.217362
$117$	−5.68060	−0.525172
$118$	−4.76256	−0.438429
$119$	−5.44676	−0.499304
$120$	1.86454	0.170209
$121$	31.9342	2.90311
$122$	0.237591	0.0215104
$123$	−4.22678	−0.381116
$124$	6.04400	0.542768
$125$	−10.9979	−0.983681
$126$	−2.59381	−0.231075
$127$	13.3081	1.18091	0.590454	−	0.807072i	$-0.298949\pi$
$127$	13.3081	1.18091	0.590454	+	0.807072i	$0.298949\pi$
$128$	−1.00000	−0.0883883
$129$	−13.2759	−1.16888
$130$	−7.14288	−0.626472
$131$	0.662124	0.0578501	0.0289250	−	0.999582i	$-0.490792\pi$
$131$	0.662124	0.0578501	0.0289250	+	0.999582i	$0.490792\pi$
$132$	−9.11148	−0.793053
$133$	10.6777	0.925874
$134$	3.19260	0.275799
$135$	7.58192	0.652548
$136$	−2.23928	−0.192016
$137$	16.8490	1.43950	0.719752	−	0.694231i	$-0.244255\pi$
$137$	16.8490	1.43950	0.719752	+	0.694231i	$0.244255\pi$
$138$	−3.24202	−0.275979
$139$	5.45297	0.462515	0.231257	−	0.972893i	$-0.425716\pi$
$139$	5.45297	0.462515	0.231257	+	0.972893i	$0.425716\pi$
$140$	−3.26149	−0.275647
$141$	1.00969	0.0850311
$142$	−0.738274	−0.0619546
$143$	34.9051	2.91891
$144$	−1.06637	−0.0888639
$145$	−3.13904	−0.260683
$146$	4.72756	0.391256
$147$	1.50672	0.124272
$148$	6.28779	0.516853
$149$	−23.9256	−1.96006	−0.980030	−	0.198849i	$-0.936280\pi$
$149$	−23.9256	−1.96006	−0.980030	+	0.198849i	$0.936280\pi$
$150$	−4.45265	−0.363557
$151$	0.366762	0.0298467	0.0149233	−	0.999889i	$-0.495250\pi$
$151$	0.366762	0.0298467	0.0149233	+	0.999889i	$0.495250\pi$
$152$	4.38982	0.356062
$153$	−2.38789	−0.193049
$154$	15.9380	1.28432
$155$	8.10420	0.650945
$156$	−7.40755	−0.593079
$157$	−20.3319	−1.62267	−0.811333	−	0.584584i	$-0.801258\pi$
$157$	−20.3319	−1.62267	−0.811333	+	0.584584i	$0.801258\pi$
$158$	6.83970	0.544138
$159$	−11.9560	−0.948172
$160$	−1.34087	−0.106005
$161$	5.67099	0.446937
$162$	4.66376	0.366420
$163$	−14.8443	−1.16269	−0.581346	−	0.813656i	$-0.697474\pi$
$163$	−14.8443	−1.16269	−0.581346	+	0.813656i	$0.697474\pi$
$164$	3.03964	0.237356
$165$	−12.2173	−0.951114
$166$	15.0810	1.17051
$167$	−12.0819	−0.934923	−0.467462	−	0.884013i	$-0.654831\pi$
$167$	−12.0819	−0.934923	−0.467462	+	0.884013i	$0.654831\pi$
$168$	−3.38235	−0.260954
$169$	15.3776	1.18289
$170$	−3.00257	−0.230287
$171$	4.68116	0.357977
$172$	9.54720	0.727967
$173$	25.8355	1.96423	0.982117	−	0.188269i	$-0.0602877\pi$
$173$	25.8355	1.96423	0.982117	+	0.188269i	$0.0602877\pi$
$174$	−3.25536	−0.246788
$175$	7.78866	0.588767
$176$	6.55242	0.493907
$177$	−6.62259	−0.497784
$178$	−1.39078	−0.104243
$179$	7.55735	0.564863	0.282432	−	0.959287i	$-0.408859\pi$
$179$	7.55735	0.564863	0.282432	+	0.959287i	$0.408859\pi$
$180$	−1.42986	−0.106575
$181$	16.5038	1.22672	0.613359	−	0.789804i	$-0.289818\pi$
$181$	16.5038	1.22672	0.613359	+	0.789804i	$0.289818\pi$
$182$	12.9574	0.960468
$183$	0.330382	0.0244225
$184$	2.33146	0.171878
$185$	8.43108	0.619866
$186$	8.40450	0.616248
$187$	14.6727	1.07297
$188$	−0.726106	−0.0529567
$189$	−13.7539	−1.00045
$190$	5.88617	0.427028
$191$	−20.3462	−1.47220	−0.736098	−	0.676875i	$-0.763334\pi$
$191$	−20.3462	−1.47220	−0.736098	+	0.676875i	$0.763334\pi$
$192$	−1.39055	−0.100354
$193$	7.88357	0.567472	0.283736	−	0.958902i	$-0.408426\pi$
$193$	7.88357	0.567472	0.283736	+	0.958902i	$0.408426\pi$
$194$	−10.3562	−0.743534
$195$	−9.93254	−0.711284
$196$	−1.08354	−0.0773959
$197$	9.08218	0.647079	0.323539	−	0.946215i	$-0.395127\pi$
$197$	9.08218	0.647079	0.323539	+	0.946215i	$0.395127\pi$
$198$	6.98728	0.496565
$199$	−19.5584	−1.38646	−0.693230	−	0.720716i	$-0.743813\pi$
$199$	−19.5584	−1.38646	−0.693230	+	0.720716i	$0.743813\pi$
$200$	3.20208	0.226421
$201$	4.43948	0.313137
$202$	4.09374	0.288034
$203$	5.69433	0.399664
$204$	−3.11383	−0.218012
$205$	4.07576	0.284663
$206$	2.79894	0.195012
$207$	2.48619	0.172802
$208$	5.32706	0.369365
$209$	−28.7640	−1.98965
$210$	−4.53527	−0.312964
$211$	−26.0308	−1.79203	−0.896016	−	0.444021i	$-0.853552\pi$
$211$	−26.0308	−1.79203	−0.896016	+	0.444021i	$0.853552\pi$
$212$	8.59802	0.590515
$213$	−1.02661	−0.0703420
$214$	3.73346	0.255214
$215$	12.8015	0.873056
$216$	−5.65449	−0.384739
$217$	−14.7013	−0.997989
$218$	−13.2354	−0.896414
$219$	6.57392	0.444224
$220$	8.78593	0.592347
$221$	11.9288	0.802415
$222$	8.74349	0.586825
$223$	−22.7191	−1.52139	−0.760693	−	0.649112i	$-0.775141\pi$
$223$	−22.7191	−1.52139	−0.760693	+	0.649112i	$0.775141\pi$
$224$	2.43238	0.162520
$225$	3.41459	0.227639
$226$	15.7022	1.04449
$227$	10.2201	0.678334	0.339167	−	0.940726i	$-0.389855\pi$
$227$	10.2201	0.678334	0.339167	+	0.940726i	$0.389855\pi$
$228$	6.10428	0.404266
$229$	23.4186	1.54755	0.773773	−	0.633463i	$-0.218367\pi$
$229$	23.4186	1.54755	0.773773	+	0.633463i	$0.218367\pi$
$230$	3.12618	0.206134
$231$	22.1626	1.45819
$232$	2.34106	0.153698
$233$	−0.955048	−0.0625672	−0.0312836	−	0.999511i	$-0.509960\pi$
$233$	−0.955048	−0.0625672	−0.0312836	+	0.999511i	$0.509960\pi$
$234$	5.68060	0.371352
$235$	−0.973611	−0.0635114
$236$	4.76256	0.310016
$237$	9.51096	0.617803
$238$	5.44676	0.353061
$239$	−2.34502	−0.151687	−0.0758435	−	0.997120i	$-0.524165\pi$
$239$	−2.34502	−0.151687	−0.0758435	+	0.997120i	$0.524165\pi$
$240$	−1.86454	−0.120356
$241$	−5.44477	−0.350728	−0.175364	−	0.984504i	$-0.556110\pi$
$241$	−5.44477	−0.350728	−0.175364	+	0.984504i	$0.556110\pi$
$242$	−31.9342	−2.05281
$243$	−10.4783	−0.672182
$244$	−0.237591	−0.0152102
$245$	−1.45289	−0.0928215
$246$	4.22678	0.269490
$247$	−23.3849	−1.48794
$248$	−6.04400	−0.383795
$249$	20.9709	1.32897
$250$	10.9979	0.695568
$251$	19.4649	1.22861	0.614307	−	0.789067i	$-0.289436\pi$
$251$	19.4649	1.22861	0.614307	+	0.789067i	$0.289436\pi$
$252$	2.59381	0.163394
$253$	−15.2767	−0.960439
$254$	−13.3081	−0.835027
$255$	−4.17523	−0.261463
$256$	1.00000	0.0625000
$257$	18.1700	1.13341	0.566706	−	0.823920i	$-0.308218\pi$
$257$	18.1700	1.13341	0.566706	+	0.823920i	$0.308218\pi$
$258$	13.2759	0.826520
$259$	−15.2943	−0.950339
$260$	7.14288	0.442983
$261$	2.49642	0.154525
$262$	−0.662124	−0.0409062
$263$	14.7442	0.909167	0.454584	−	0.890704i	$-0.349788\pi$
$263$	14.7442	0.909167	0.454584	+	0.890704i	$0.349788\pi$
$264$	9.11148	0.560773
$265$	11.5288	0.708209
$266$	−10.6777	−0.654692
$267$	−1.93395	−0.118356
$268$	−3.19260	−0.195019
$269$	11.0500	0.673733	0.336867	−	0.941552i	$-0.390633\pi$
$269$	11.0500	0.673733	0.336867	+	0.941552i	$0.390633\pi$
$270$	−7.58192	−0.461421
$271$	15.2418	0.925874	0.462937	−	0.886391i	$-0.346796\pi$
$271$	15.2418	0.925874	0.462937	+	0.886391i	$0.346796\pi$
$272$	2.23928	0.135776
$273$	18.0180	1.09050
$274$	−16.8490	−1.01788
$275$	−20.9814	−1.26522
$276$	3.24202	0.195146
$277$	22.2687	1.33799	0.668997	−	0.743265i	$-0.266724\pi$
$277$	22.2687	1.33799	0.668997	+	0.743265i	$0.266724\pi$
$278$	−5.45297	−0.327047
$279$	−6.44512	−0.385859
$280$	3.26149	0.194912
$281$	18.1100	1.08035	0.540175	−	0.841552i	$-0.318358\pi$
$281$	18.1100	1.08035	0.540175	+	0.841552i	$0.318358\pi$
$282$	−1.00969	−0.0601260
$283$	13.0123	0.773500	0.386750	−	0.922185i	$-0.373598\pi$
$283$	13.0123	0.773500	0.386750	+	0.922185i	$0.373598\pi$
$284$	0.738274	0.0438085
$285$	8.18502	0.484839
$286$	−34.9051	−2.06398
$287$	−7.39356	−0.436428
$288$	1.06637	0.0628363
$289$	−11.9856	−0.705038
$290$	3.13904	0.184331
$291$	−14.4009	−0.844194
$292$	−4.72756	−0.276660
$293$	−10.7110	−0.625744	−0.312872	−	0.949795i	$-0.601291\pi$
$293$	−10.7110	−0.625744	−0.312872	+	0.949795i	$0.601291\pi$
$294$	−1.50672	−0.0878738
$295$	6.38596	0.371805
$296$	−6.28779	−0.365470
$297$	37.0506	2.14989
$298$	23.9256	1.38597
$299$	−12.4198	−0.718258
$300$	4.45265	0.257074
$301$	−23.2224	−1.33852
$302$	−0.366762	−0.0211048
$303$	5.69255	0.327029
$304$	−4.38982	−0.251774
$305$	−0.318577	−0.0182417
$306$	2.38789	0.136507
$307$	4.03369	0.230215	0.115108	−	0.993353i	$-0.463279\pi$
$307$	4.03369	0.230215	0.115108	+	0.993353i	$0.463279\pi$
$308$	−15.9380	−0.908150
$309$	3.89208	0.221412
$310$	−8.10420	−0.460288
$311$	4.98177	0.282490	0.141245	−	0.989975i	$-0.454889\pi$
$311$	4.98177	0.282490	0.141245	+	0.989975i	$0.454889\pi$
$312$	7.40755	0.419370
$313$	15.6403	0.884040	0.442020	−	0.897005i	$-0.354262\pi$
$313$	15.6403	0.884040	0.442020	+	0.897005i	$0.354262\pi$
$314$	20.3319	1.14740
$315$	3.47795	0.195960
$316$	−6.83970	−0.384763
$317$	−8.33376	−0.468071	−0.234035	−	0.972228i	$-0.575193\pi$
$317$	−8.33376	−0.468071	−0.234035	+	0.972228i	$0.575193\pi$
$318$	11.9560	0.670459
$319$	−15.3396	−0.858852
$320$	1.34087	0.0749567
$321$	5.19157	0.289765
$322$	−5.67099	−0.316032
$323$	−9.83003	−0.546957
$324$	−4.66376	−0.259098
$325$	−17.0577	−0.946188
$326$	14.8443	0.822148
$327$	−18.4045	−1.01777
$328$	−3.03964	−0.167836
$329$	1.76616	0.0973717
$330$	12.2173	0.672539
$331$	8.91070	0.489776	0.244888	−	0.969551i	$-0.421249\pi$
$331$	8.91070	0.489776	0.244888	+	0.969551i	$0.421249\pi$
$332$	−15.0810	−0.827676
$333$	−6.70508	−0.367436
$334$	12.0819	0.661090
$335$	−4.28086	−0.233888
$336$	3.38235	0.184522
$337$	24.3496	1.32641	0.663203	−	0.748440i	$-0.269197\pi$
$337$	24.3496	1.32641	0.663203	+	0.748440i	$0.269197\pi$
$338$	−15.3776	−0.836429
$339$	21.8347	1.18590
$340$	3.00257	0.162837
$341$	39.6029	2.14462
$342$	−4.68116	−0.253128
$343$	19.6622	1.06166
$344$	−9.54720	−0.514750
$345$	4.34711	0.234041
$346$	−25.8355	−1.38892
$347$	4.20153	0.225550	0.112775	−	0.993621i	$-0.464026\pi$
$347$	4.20153	0.225550	0.112775	+	0.993621i	$0.464026\pi$
$348$	3.25536	0.174506
$349$	−5.58442	−0.298927	−0.149464	−	0.988767i	$-0.547755\pi$
$349$	−5.58442	−0.298927	−0.149464	+	0.988767i	$0.547755\pi$
$350$	−7.78866	−0.416321
$351$	30.1218	1.60778
$352$	−6.55242	−0.349245
$353$	21.0962	1.12284	0.561418	−	0.827532i	$-0.310256\pi$
$353$	21.0962	1.12284	0.561418	+	0.827532i	$0.310256\pi$
$354$	6.62259	0.351987
$355$	0.989927	0.0525399
$356$	1.39078	0.0737110
$357$	7.57401	0.400859
$358$	−7.55735	−0.399419
$359$	−17.0284	−0.898724	−0.449362	−	0.893350i	$-0.648349\pi$
$359$	−17.0284	−0.898724	−0.449362	+	0.893350i	$0.648349\pi$
$360$	1.42986	0.0753600
$361$	0.270551	0.0142395
$362$	−16.5038	−0.867421
$363$	−44.4062	−2.33072
$364$	−12.9574	−0.679153
$365$	−6.33903	−0.331800
$366$	−0.330382	−0.0172693
$367$	14.9231	0.778978	0.389489	−	0.921031i	$-0.372652\pi$
$367$	14.9231	0.778978	0.389489	+	0.921031i	$0.372652\pi$
$368$	−2.33146	−0.121536
$369$	−3.24137	−0.168739
$370$	−8.43108	−0.438311
$371$	−20.9136	−1.08578
$372$	−8.40450	−0.435753
$373$	5.26202	0.272457	0.136229	−	0.990677i	$-0.456502\pi$
$373$	5.26202	0.272457	0.136229	+	0.990677i	$0.456502\pi$
$374$	−14.6727	−0.758706
$375$	15.2931	0.789734
$376$	0.726106	0.0374461
$377$	−12.4709	−0.642286
$378$	13.7539	0.707422
$379$	−25.4602	−1.30780	−0.653902	−	0.756579i	$-0.726869\pi$
$379$	−25.4602	−1.30780	−0.653902	+	0.756579i	$0.726869\pi$
$380$	−5.88617	−0.301954
$381$	−18.5057	−0.948074
$382$	20.3462	1.04100
$383$	23.4133	1.19636	0.598181	−	0.801361i	$-0.295890\pi$
$383$	23.4133	1.19636	0.598181	+	0.801361i	$0.295890\pi$
$384$	1.39055	0.0709613
$385$	−21.3707	−1.08915
$386$	−7.88357	−0.401263
$387$	−10.1808	−0.517520
$388$	10.3562	0.525758
$389$	−12.9167	−0.654904	−0.327452	−	0.944868i	$-0.606190\pi$
$389$	−12.9167	−0.654904	−0.327452	+	0.944868i	$0.606190\pi$
$390$	9.93254	0.502954
$391$	−5.22079	−0.264026
$392$	1.08354	0.0547272
$393$	−0.920718	−0.0464441
$394$	−9.08218	−0.457554
$395$	−9.17113	−0.461450
$396$	−6.98728	−0.351124
$397$	−16.4182	−0.824006	−0.412003	−	0.911182i	$-0.635171\pi$
$397$	−16.4182	−0.824006	−0.412003	+	0.911182i	$0.635171\pi$
$398$	19.5584	0.980375
$399$	−14.8479	−0.743325
$400$	−3.20208	−0.160104
$401$	15.7410	0.786069	0.393034	−	0.919524i	$-0.371425\pi$
$401$	15.7410	0.786069	0.393034	+	0.919524i	$0.371425\pi$
$402$	−4.43948	−0.221421
$403$	32.1968	1.60384
$404$	−4.09374	−0.203671
$405$	−6.25349	−0.310738
$406$	−5.69433	−0.282605
$407$	41.2002	2.04222
$408$	3.11383	0.154158
$409$	26.8665	1.32846	0.664231	−	0.747527i	$-0.268759\pi$
$409$	26.8665	1.32846	0.664231	+	0.747527i	$0.268759\pi$
$410$	−4.07576	−0.201287
$411$	−23.4294	−1.15569
$412$	−2.79894	−0.137894
$413$	−11.5843	−0.570028
$414$	−2.48619	−0.122190
$415$	−20.2216	−0.992638
$416$	−5.32706	−0.261181
$417$	−7.58263	−0.371323
$418$	28.7640	1.40689
$419$	−33.1814	−1.62102	−0.810509	−	0.585726i	$-0.800809\pi$
$419$	−33.1814	−1.62102	−0.810509	+	0.585726i	$0.800809\pi$
$420$	4.53527	0.221299
$421$	0.722267	0.0352012	0.0176006	−	0.999845i	$-0.494397\pi$
$421$	0.722267	0.0352012	0.0176006	+	0.999845i	$0.494397\pi$
$422$	26.0308	1.26716
$423$	0.774295	0.0376475
$424$	−8.59802	−0.417557
$425$	−7.17033	−0.347812
$426$	1.02661	0.0497393
$427$	0.577910	0.0279670
$428$	−3.73346	−0.180464
$429$	−48.5374	−2.34341
$430$	−12.8015	−0.617344
$431$	20.9525	1.00925	0.504623	−	0.863340i	$-0.331632\pi$
$431$	20.9525	1.00925	0.504623	+	0.863340i	$0.331632\pi$
$432$	5.65449	0.272052
$433$	13.2396	0.636256	0.318128	−	0.948048i	$-0.396946\pi$
$433$	13.2396	0.636256	0.318128	+	0.948048i	$0.396946\pi$
$434$	14.7013	0.705685
$435$	4.36500	0.209286
$436$	13.2354	0.633860
$437$	10.2347	0.489592
$438$	−6.57392	−0.314114
$439$	−12.4337	−0.593430	−0.296715	−	0.954966i	$-0.595891\pi$
$439$	−12.4337	−0.593430	−0.296715	+	0.954966i	$0.595891\pi$
$440$	−8.78593	−0.418853
$441$	1.15545	0.0550216
$442$	−11.9288	−0.567393
$443$	−11.5095	−0.546831	−0.273415	−	0.961896i	$-0.588153\pi$
$443$	−11.5095	−0.546831	−0.273415	+	0.961896i	$0.588153\pi$
$444$	−8.74349	−0.414948
$445$	1.86485	0.0884022
$446$	22.7191	1.07578
$447$	33.2698	1.57361
$448$	−2.43238	−0.114919
$449$	14.6630	0.691989	0.345994	−	0.938237i	$-0.387542\pi$
$449$	14.6630	0.691989	0.345994	+	0.938237i	$0.387542\pi$
$450$	−3.41459	−0.160965
$451$	19.9170	0.937856
$452$	−15.7022	−0.738567
$453$	−0.510002	−0.0239620
$454$	−10.2201	−0.479654
$455$	−17.3742	−0.814514
$456$	−6.10428	−0.285859
$457$	21.2396	0.993547	0.496773	−	0.867880i	$-0.334518\pi$
$457$	21.2396	0.993547	0.496773	+	0.867880i	$0.334518\pi$
$458$	−23.4186	−1.09428
$459$	12.6620	0.591010
$460$	−3.12618	−0.145759
$461$	−10.0735	−0.469170	−0.234585	−	0.972096i	$-0.575373\pi$
$461$	−10.0735	−0.469170	−0.234585	+	0.972096i	$0.575373\pi$
$462$	−22.1626	−1.03110
$463$	36.5052	1.69654	0.848269	−	0.529565i	$-0.177645\pi$
$463$	36.5052	1.69654	0.848269	+	0.529565i	$0.177645\pi$
$464$	−2.34106	−0.108681
$465$	−11.2693	−0.522602
$466$	0.955048	0.0442417
$467$	5.39078	0.249456	0.124728	−	0.992191i	$-0.460194\pi$
$467$	5.39078	0.249456	0.124728	+	0.992191i	$0.460194\pi$
$468$	−5.68060	−0.262586
$469$	7.76562	0.358583
$470$	0.973611	0.0449093
$471$	28.2726	1.30273
$472$	−4.76256	−0.219215
$473$	62.5573	2.87639
$474$	−9.51096	−0.436853
$475$	14.0565	0.644959
$476$	−5.44676	−0.249652
$477$	−9.16864	−0.419803
$478$	2.34502	0.107259
$479$	11.7148	0.535264	0.267632	−	0.963521i	$-0.413759\pi$
$479$	11.7148	0.535264	0.267632	+	0.963521i	$0.413759\pi$
$480$	1.86454	0.0851044
$481$	33.4954	1.52726
$482$	5.44477	0.248002
$483$	−7.88581	−0.358817
$484$	31.9342	1.45156
$485$	13.8863	0.630545
$486$	10.4783	0.475304
$487$	17.6255	0.798686	0.399343	−	0.916802i	$-0.369238\pi$
$487$	17.6255	0.798686	0.399343	+	0.916802i	$0.369238\pi$
$488$	0.237591	0.0107552
$489$	20.6417	0.933451
$490$	1.45289	0.0656347
$491$	24.0198	1.08400	0.542000	−	0.840379i	$-0.317667\pi$
$491$	24.0198	1.08400	0.542000	+	0.840379i	$0.317667\pi$
$492$	−4.22678	−0.190558
$493$	−5.24227	−0.236100
$494$	23.3849	1.05213
$495$	−9.36902	−0.421106
$496$	6.04400	0.271384
$497$	−1.79576	−0.0805509
$498$	−20.9709	−0.939727
$499$	−20.7852	−0.930472	−0.465236	−	0.885187i	$-0.654031\pi$
$499$	−20.7852	−0.930472	−0.465236	+	0.885187i	$0.654031\pi$
$500$	−10.9979	−0.491841
$501$	16.8005	0.750589
$502$	−19.4649	−0.868761
$503$	−23.9078	−1.06600	−0.532998	−	0.846117i	$-0.678935\pi$
$503$	−23.9078	−1.06600	−0.532998	+	0.846117i	$0.678935\pi$
$504$	−2.59381	−0.115537
$505$	−5.48916	−0.244264
$506$	15.2767	0.679133
$507$	−21.3833	−0.949666
$508$	13.3081	0.590454
$509$	12.2557	0.543225	0.271612	−	0.962407i	$-0.412443\pi$
$509$	12.2557	0.543225	0.271612	+	0.962407i	$0.412443\pi$
$510$	4.17523	0.184882
$511$	11.4992	0.508695
$512$	−1.00000	−0.0441942
$513$	−24.8222	−1.09593
$514$	−18.1700	−0.801443
$515$	−3.75301	−0.165377
$516$	−13.2759	−0.584438
$517$	−4.75775	−0.209246
$518$	15.2943	0.671991
$519$	−35.9256	−1.57696
$520$	−7.14288	−0.313236
$521$	−19.3736	−0.848771	−0.424386	−	0.905482i	$-0.639510\pi$
$521$	−19.3736	−0.848771	−0.424386	+	0.905482i	$0.639510\pi$
$522$	−2.49642	−0.109266
$523$	−42.5036	−1.85855	−0.929276	−	0.369385i	$-0.879568\pi$
$523$	−42.5036	−1.85855	−0.929276	+	0.369385i	$0.879568\pi$
$524$	0.662124	0.0289250
$525$	−10.8305	−0.472683
$526$	−14.7442	−0.642878
$527$	13.5342	0.589559
$528$	−9.11148	−0.396526
$529$	−17.5643	−0.763665
$530$	−11.5288	−0.500779
$531$	−5.07864	−0.220394
$532$	10.6777	0.462937
$533$	16.1924	0.701369
$534$	1.93395	0.0836900
$535$	−5.00608	−0.216432
$536$	3.19260	0.137900
$537$	−10.5089	−0.453492
$538$	−11.0500	−0.476401
$539$	−7.09983	−0.305811
$540$	7.58192	0.326274
$541$	6.05262	0.260222	0.130111	−	0.991499i	$-0.458467\pi$
$541$	6.05262	0.260222	0.130111	+	0.991499i	$0.458467\pi$
$542$	−15.2418	−0.654691
$543$	−22.9494	−0.984853
$544$	−2.23928	−0.0960082
$545$	17.7469	0.760193
$546$	−18.0180	−0.771097
$547$	31.9021	1.36404	0.682018	−	0.731336i	$-0.261103\pi$
$547$	31.9021	1.36404	0.682018	+	0.731336i	$0.261103\pi$
$548$	16.8490	0.719752
$549$	0.253359	0.0108131
$550$	20.9814	0.894648
$551$	10.2768	0.437807
$552$	−3.24202	−0.137989
$553$	16.6367	0.707466
$554$	−22.2687	−0.946105
$555$	−11.7239	−0.497650
$556$	5.45297	0.231257
$557$	−6.38347	−0.270476	−0.135238	−	0.990813i	$-0.543180\pi$
$557$	−6.38347	−0.270476	−0.135238	+	0.990813i	$0.543180\pi$
$558$	6.44512	0.272844
$559$	50.8585	2.15108
$560$	−3.26149	−0.137823
$561$	−20.4031	−0.861420
$562$	−18.1100	−0.763923
$563$	23.9742	1.01039	0.505196	−	0.863005i	$-0.331420\pi$
$563$	23.9742	1.01039	0.505196	+	0.863005i	$0.331420\pi$
$564$	1.00969	0.0425155
$565$	−21.0545	−0.885769
$566$	−13.0123	−0.546947
$567$	11.3440	0.476404
$568$	−0.738274	−0.0309773
$569$	−3.97663	−0.166709	−0.0833546	−	0.996520i	$-0.526563\pi$
$569$	−3.97663	−0.166709	−0.0833546	+	0.996520i	$0.526563\pi$
$570$	−8.18502	−0.342833
$571$	29.4151	1.23098	0.615491	−	0.788144i	$-0.288958\pi$
$571$	29.4151	1.23098	0.615491	+	0.788144i	$0.288958\pi$
$572$	34.9051	1.45946
$573$	28.2924	1.18193
$574$	7.39356	0.308601
$575$	7.46552	0.311334
$576$	−1.06637	−0.0444319
$577$	13.6611	0.568720	0.284360	−	0.958718i	$-0.408219\pi$
$577$	13.6611	0.568720	0.284360	+	0.958718i	$0.408219\pi$
$578$	11.9856	0.498537
$579$	−10.9625	−0.455587
$580$	−3.13904	−0.130342
$581$	36.6826	1.52185
$582$	14.4009	0.596935
$583$	56.3379	2.33328
$584$	4.72756	0.195628
$585$	−7.61693	−0.314921
$586$	10.7110	0.442468
$587$	4.39606	0.181445	0.0907224	−	0.995876i	$-0.471082\pi$
$587$	4.39606	0.181445	0.0907224	+	0.995876i	$0.471082\pi$
$588$	1.50672	0.0621362
$589$	−26.5321	−1.09324
$590$	−6.38596	−0.262906
$591$	−12.6292	−0.519498
$592$	6.28779	0.258426
$593$	1.66090	0.0682051	0.0341026	−	0.999418i	$-0.489143\pi$
$593$	1.66090	0.0682051	0.0341026	+	0.999418i	$0.489143\pi$
$594$	−37.0506	−1.52021
$595$	−7.30339	−0.299410
$596$	−23.9256	−0.980030
$597$	27.1970	1.11310
$598$	12.4198	0.507885
$599$	30.1877	1.23344	0.616718	−	0.787184i	$-0.288462\pi$
$599$	30.1877	1.23344	0.616718	+	0.787184i	$0.288462\pi$
$600$	−4.45265	−0.181779
$601$	26.2785	1.07192	0.535960	−	0.844243i	$-0.319950\pi$
$601$	26.2785	1.07192	0.535960	+	0.844243i	$0.319950\pi$
$602$	23.2224	0.946474
$603$	3.40449	0.138641
$604$	0.366762	0.0149233
$605$	42.8196	1.74086
$606$	−5.69255	−0.231244
$607$	13.0472	0.529569	0.264784	−	0.964308i	$-0.414699\pi$
$607$	13.0472	0.529569	0.264784	+	0.964308i	$0.414699\pi$
$608$	4.38982	0.178031
$609$	−7.91826	−0.320864
$610$	0.318577	0.0128988
$611$	−3.86801	−0.156483
$612$	−2.38789	−0.0965247
$613$	−32.8605	−1.32722	−0.663612	−	0.748077i	$-0.730977\pi$
$613$	−32.8605	−1.32722	−0.663612	+	0.748077i	$0.730977\pi$
$614$	−4.03369	−0.162787
$615$	−5.66755	−0.228538
$616$	15.9380	0.642159
$617$	37.8931	1.52552	0.762760	−	0.646682i	$-0.223844\pi$
$617$	37.8931	1.52552	0.762760	+	0.646682i	$0.223844\pi$
$618$	−3.89208	−0.156562
$619$	−9.46606	−0.380473	−0.190237	−	0.981738i	$-0.560926\pi$
$619$	−9.46606	−0.380473	−0.190237	+	0.981738i	$0.560926\pi$
$620$	8.10420	0.325473
$621$	−13.1832	−0.529025
$622$	−4.98177	−0.199751
$623$	−3.38289	−0.135533
$624$	−7.40755	−0.296539
$625$	1.26367	0.0505468
$626$	−15.6403	−0.625110
$627$	39.9978	1.59736
$628$	−20.3319	−0.811333
$629$	14.0801	0.561410
$630$	−3.47795	−0.138565
$631$	7.82859	0.311651	0.155826	−	0.987785i	$-0.450196\pi$
$631$	7.82859	0.311651	0.155826	+	0.987785i	$0.450196\pi$
$632$	6.83970	0.272069
$633$	36.1971	1.43871
$634$	8.33376	0.330976
$635$	17.8445	0.708136
$636$	−11.9560	−0.474086
$637$	−5.77210	−0.228699
$638$	15.3396	0.607300
$639$	−0.787271	−0.0311439
$640$	−1.34087	−0.0530024
$641$	14.3300	0.566000	0.283000	−	0.959120i	$-0.408670\pi$
$641$	14.3300	0.566000	0.283000	+	0.959120i	$0.408670\pi$
$642$	−5.19157	−0.204895
$643$	−1.51594	−0.0597827	−0.0298913	−	0.999553i	$-0.509516\pi$
$643$	−1.51594	−0.0597827	−0.0298913	+	0.999553i	$0.509516\pi$
$644$	5.67099	0.223468
$645$	−17.8012	−0.700921
$646$	9.83003	0.386757
$647$	19.6948	0.774283	0.387141	−	0.922020i	$-0.373463\pi$
$647$	19.6948	0.774283	0.387141	+	0.922020i	$0.373463\pi$
$648$	4.66376	0.183210
$649$	31.2063	1.22496
$650$	17.0577	0.669056
$651$	20.4429	0.801221
$652$	−14.8443	−0.581346
$653$	10.0416	0.392958	0.196479	−	0.980508i	$-0.437049\pi$
$653$	10.0416	0.392958	0.196479	+	0.980508i	$0.437049\pi$
$654$	18.4045	0.719672
$655$	0.887821	0.0346900
$656$	3.03964	0.118678
$657$	5.04132	0.196680
$658$	−1.76616	−0.0688522
$659$	−26.5768	−1.03528	−0.517642	−	0.855597i	$-0.673190\pi$
$659$	−26.5768	−1.03528	−0.517642	+	0.855597i	$0.673190\pi$
$660$	−12.2173	−0.475557
$661$	−40.1582	−1.56197	−0.780986	−	0.624548i	$-0.785283\pi$
$661$	−40.1582	−1.56197	−0.780986	+	0.624548i	$0.785283\pi$
$662$	−8.91070	−0.346324
$663$	−16.5876	−0.644207
$664$	15.0810	0.585255
$665$	14.3174	0.555204
$666$	6.70508	0.259817
$667$	5.45808	0.211338
$668$	−12.0819	−0.467462
$669$	31.5921	1.22142
$670$	4.28086	0.165384
$671$	−1.55679	−0.0600993
$672$	−3.38235	−0.130477
$673$	1.98712	0.0765977	0.0382988	−	0.999266i	$-0.487806\pi$
$673$	1.98712	0.0765977	0.0382988	+	0.999266i	$0.487806\pi$
$674$	−24.3496	−0.937911
$675$	−18.1061	−0.696905
$676$	15.3776	0.591445
$677$	30.9198	1.18835	0.594173	−	0.804338i	$-0.297480\pi$
$677$	30.9198	1.18835	0.594173	+	0.804338i	$0.297480\pi$
$678$	−21.8347	−0.838555
$679$	−25.1902	−0.966713
$680$	−3.00257	−0.115143
$681$	−14.2116	−0.544590
$682$	−39.6029	−1.51647
$683$	34.6653	1.32643	0.663215	−	0.748429i	$-0.269191\pi$
$683$	34.6653	1.32643	0.663215	+	0.748429i	$0.269191\pi$
$684$	4.68116	0.178989
$685$	22.5922	0.863205
$686$	−19.6622	−0.750707
$687$	−32.5648	−1.24243
$688$	9.54720	0.363983
$689$	45.8022	1.74492
$690$	−4.34711	−0.165492
$691$	−18.6232	−0.708460	−0.354230	−	0.935158i	$-0.615257\pi$
$691$	−18.6232	−0.708460	−0.354230	+	0.935158i	$0.615257\pi$
$692$	25.8355	0.982117
$693$	16.9957	0.645613
$694$	−4.20153	−0.159488
$695$	7.31170	0.277349
$696$	−3.25536	−0.123394
$697$	6.80660	0.257818
$698$	5.58442	0.211373
$699$	1.32804	0.0502312
$700$	7.78866	0.294384
$701$	24.9981	0.944163	0.472082	−	0.881555i	$-0.343503\pi$
$701$	24.9981	0.944163	0.472082	+	0.881555i	$0.343503\pi$
$702$	−30.1218	−1.13687
$703$	−27.6023	−1.04104
$704$	6.55242	0.246954
$705$	1.35386	0.0509892
$706$	−21.0962	−0.793965
$707$	9.95752	0.374491
$708$	−6.62259	−0.248892
$709$	−1.75067	−0.0657479	−0.0328739	−	0.999460i	$-0.510466\pi$
$709$	−1.75067	−0.0657479	−0.0328739	+	0.999460i	$0.510466\pi$
$710$	−0.989927	−0.0371513
$711$	7.29363	0.273533
$712$	−1.39078	−0.0521215
$713$	−14.0914	−0.527726
$714$	−7.57401	−0.283450
$715$	46.8032	1.75034
$716$	7.55735	0.282432
$717$	3.26087	0.121780
$718$	17.0284	0.635494
$719$	−6.26472	−0.233635	−0.116817	−	0.993153i	$-0.537269\pi$
$719$	−6.26472	−0.233635	−0.116817	+	0.993153i	$0.537269\pi$
$720$	−1.42986	−0.0532876
$721$	6.80809	0.253546
$722$	−0.270551	−0.0100689
$723$	7.57123	0.281577
$724$	16.5038	0.613359
$725$	7.49624	0.278403
$726$	44.4062	1.64807
$727$	−26.1703	−0.970603	−0.485301	−	0.874347i	$-0.661290\pi$
$727$	−26.1703	−0.970603	−0.485301	+	0.874347i	$0.661290\pi$
$728$	12.9574	0.480234
$729$	28.5619	1.05785
$730$	6.33903	0.234618
$731$	21.3788	0.790724
$732$	0.330382	0.0122113
$733$	9.75069	0.360150	0.180075	−	0.983653i	$-0.442366\pi$
$733$	9.75069	0.360150	0.180075	+	0.983653i	$0.442366\pi$
$734$	−14.9231	−0.550821
$735$	2.02031	0.0745204
$736$	2.33146	0.0859388
$737$	−20.9193	−0.770572
$738$	3.24137	0.119317
$739$	−24.7104	−0.908986	−0.454493	−	0.890750i	$-0.650180\pi$
$739$	−24.7104	−0.908986	−0.454493	+	0.890750i	$0.650180\pi$
$740$	8.43108	0.309933
$741$	32.5178	1.19457
$742$	20.9136	0.767763
$743$	22.0400	0.808570	0.404285	−	0.914633i	$-0.367520\pi$
$743$	22.0400	0.808570	0.404285	+	0.914633i	$0.367520\pi$
$744$	8.40450	0.308124
$745$	−32.0810	−1.17536
$746$	−5.26202	−0.192656
$747$	16.0818	0.588404
$748$	14.6727	0.536486
$749$	9.08119	0.331819
$750$	−15.2931	−0.558426
$751$	−47.3795	−1.72890	−0.864452	−	0.502716i	$-0.832334\pi$
$751$	−47.3795	−1.72890	−0.864452	+	0.502716i	$0.832334\pi$
$752$	−0.726106	−0.0264784
$753$	−27.0670	−0.986375
$754$	12.4709	0.454165
$755$	0.491779	0.0178977
$756$	−13.7539	−0.500223
$757$	−12.0990	−0.439745	−0.219873	−	0.975529i	$-0.570564\pi$
$757$	−12.0990	−0.439745	−0.219873	+	0.975529i	$0.570564\pi$
$758$	25.4602	0.924757
$759$	21.2431	0.771074
$760$	5.88617	0.213514
$761$	−3.28101	−0.118936	−0.0594682	−	0.998230i	$-0.518940\pi$
$761$	−3.28101	−0.118936	−0.0594682	+	0.998230i	$0.518940\pi$
$762$	18.5057	0.670389
$763$	−32.1935	−1.16548
$764$	−20.3462	−0.736098
$765$	−3.20184	−0.115763
$766$	−23.4133	−0.845956
$767$	25.3705	0.916074
$768$	−1.39055	−0.0501772
$769$	−0.622128	−0.0224345	−0.0112172	−	0.999937i	$-0.503571\pi$
$769$	−0.622128	−0.0224345	−0.0112172	+	0.999937i	$0.503571\pi$
$770$	21.3707	0.770146
$771$	−25.2663	−0.909943
$772$	7.88357	0.283736
$773$	14.7866	0.531838	0.265919	−	0.963995i	$-0.414325\pi$
$773$	14.7866	0.531838	0.265919	+	0.963995i	$0.414325\pi$
$774$	10.1808	0.365942
$775$	−19.3534	−0.695193
$776$	−10.3562	−0.371767
$777$	21.2675	0.762966
$778$	12.9167	0.463087
$779$	−13.3435	−0.478081
$780$	−9.93254	−0.355642
$781$	4.83748	0.173099
$782$	5.22079	0.186695
$783$	−13.2375	−0.473069
$784$	−1.08354	−0.0386980
$785$	−27.2624	−0.973038
$786$	0.920718	0.0328409
$787$	18.3883	0.655473	0.327737	−	0.944769i	$-0.393714\pi$
$787$	18.3883	0.655473	0.327737	+	0.944769i	$0.393714\pi$
$788$	9.08218	0.323539
$789$	−20.5026	−0.729912
$790$	9.17113	0.326294
$791$	38.1936	1.35801
$792$	6.98728	0.248282
$793$	−1.26566	−0.0449449
$794$	16.4182	0.582661
$795$	−16.0314	−0.568575
$796$	−19.5584	−0.693230
$797$	52.1204	1.84620	0.923100	−	0.384560i	$-0.125647\pi$
$797$	52.1204	1.84620	0.923100	+	0.384560i	$0.125647\pi$
$798$	14.8479	0.525610
$799$	−1.62595	−0.0575220
$800$	3.20208	0.113210
$801$	−1.48308	−0.0524020
$802$	−15.7410	−0.555835
$803$	−30.9770	−1.09315
$804$	4.43948	0.156568
$805$	7.60405	0.268007
$806$	−32.1968	−1.13408
$807$	−15.3657	−0.540897
$808$	4.09374	0.144017
$809$	−3.11456	−0.109502	−0.0547510	−	0.998500i	$-0.517436\pi$
$809$	−3.11456	−0.109502	−0.0547510	+	0.998500i	$0.517436\pi$
$810$	6.25349	0.219725
$811$	−34.1452	−1.19900	−0.599500	−	0.800374i	$-0.704634\pi$
$811$	−34.1452	−1.19900	−0.599500	+	0.800374i	$0.704634\pi$
$812$	5.69433	0.199832
$813$	−21.1945	−0.743324
$814$	−41.2002	−1.44407
$815$	−19.9042	−0.697213
$816$	−3.11383	−0.109006
$817$	−41.9105	−1.46626
$818$	−26.8665	−0.939364
$819$	13.8174	0.482818
$820$	4.07576	0.142332
$821$	−28.5993	−0.998122	−0.499061	−	0.866567i	$-0.666322\pi$
$821$	−28.5993	−0.998122	−0.499061	+	0.866567i	$0.666322\pi$
$822$	23.4294	0.817193
$823$	5.13434	0.178972	0.0894860	−	0.995988i	$-0.471478\pi$
$823$	5.13434	0.178972	0.0894860	+	0.995988i	$0.471478\pi$
$824$	2.79894	0.0975058
$825$	29.1757	1.01577
$826$	11.5843	0.403071
$827$	39.2610	1.36524	0.682620	−	0.730773i	$-0.260840\pi$
$827$	39.2610	1.36524	0.682620	+	0.730773i	$0.260840\pi$
$828$	2.48619	0.0864011
$829$	−32.8732	−1.14173	−0.570866	−	0.821043i	$-0.693392\pi$
$829$	−32.8732	−1.14173	−0.570866	+	0.821043i	$0.693392\pi$
$830$	20.2216	0.701901
$831$	−30.9657	−1.07419
$832$	5.32706	0.184683
$833$	−2.42635	−0.0840681
$834$	7.58263	0.262565
$835$	−16.2002	−0.560630
$836$	−28.7640	−0.994823
$837$	34.1758	1.18129
$838$	33.1814	1.14623
$839$	3.59068	0.123964	0.0619819	−	0.998077i	$-0.480258\pi$
$839$	3.59068	0.123964	0.0619819	+	0.998077i	$0.480258\pi$
$840$	−4.53527	−0.156482
$841$	−23.5195	−0.811016
$842$	−0.722267	−0.0248910
$843$	−25.1829	−0.867344
$844$	−26.0308	−0.896016
$845$	20.6193	0.709325
$846$	−0.774295	−0.0266208
$847$	−77.6761	−2.66898
$848$	8.59802	0.295257
$849$	−18.0943	−0.620993
$850$	7.17033	0.245940
$851$	−14.6597	−0.502529
$852$	−1.02661	−0.0351710
$853$	26.7640	0.916381	0.458190	−	0.888854i	$-0.348498\pi$
$853$	26.7640	0.916381	0.458190	+	0.888854i	$0.348498\pi$
$854$	−0.577910	−0.0197757
$855$	6.27681	0.214663
$856$	3.73346	0.127607
$857$	−31.9732	−1.09218	−0.546091	−	0.837726i	$-0.683885\pi$
$857$	−31.9732	−1.09218	−0.546091	+	0.837726i	$0.683885\pi$
$858$	48.5374	1.65704
$859$	−22.5066	−0.767916	−0.383958	−	0.923351i	$-0.625439\pi$
$859$	−22.5066	−0.767916	−0.383958	+	0.923351i	$0.625439\pi$
$860$	12.8015	0.436528
$861$	10.2811	0.350380
$862$	−20.9525	−0.713644
$863$	50.7399	1.72721	0.863603	−	0.504173i	$-0.168202\pi$
$863$	50.7399	1.72721	0.863603	+	0.504173i	$0.168202\pi$
$864$	−5.65449	−0.192370
$865$	34.6419	1.17786
$866$	−13.2396	−0.449901
$867$	16.6667	0.566029
$868$	−14.7013	−0.498994
$869$	−44.8166	−1.52030
$870$	−4.36500	−0.147987
$871$	−17.0072	−0.576267
$872$	−13.2354	−0.448207
$873$	−11.0435	−0.373767
$874$	−10.2347	−0.346194
$875$	26.7510	0.904349
$876$	6.57392	0.222112
$877$	14.9408	0.504514	0.252257	−	0.967660i	$-0.418827\pi$
$877$	14.9408	0.504514	0.252257	+	0.967660i	$0.418827\pi$
$878$	12.4337	0.419618
$879$	14.8942	0.502369
$880$	8.78593	0.296173
$881$	−35.7332	−1.20388	−0.601941	−	0.798540i	$-0.705606\pi$
$881$	−35.7332	−1.20388	−0.601941	+	0.798540i	$0.705606\pi$
$882$	−1.15545	−0.0389061
$883$	39.0941	1.31562	0.657811	−	0.753183i	$-0.271483\pi$
$883$	39.0941	1.31562	0.657811	+	0.753183i	$0.271483\pi$
$884$	11.9288	0.401208
$885$	−8.88001	−0.298498
$886$	11.5095	0.386668
$887$	43.0593	1.44579	0.722895	−	0.690958i	$-0.242811\pi$
$887$	43.0593	1.44579	0.722895	+	0.690958i	$0.242811\pi$
$888$	8.74349	0.293412
$889$	−32.3704	−1.08567
$890$	−1.86485	−0.0625098
$891$	−30.5589	−1.02376
$892$	−22.7191	−0.760693
$893$	3.18748	0.106665
$894$	−33.2698	−1.11271
$895$	10.1334	0.338722
$896$	2.43238	0.0812600
$897$	17.2704	0.576642
$898$	−14.6630	−0.489310
$899$	−14.1494	−0.471907
$900$	3.41459	0.113820
$901$	19.2533	0.641422
$902$	−19.9170	−0.663165
$903$	32.2919	1.07461
$904$	15.7022	0.522246
$905$	22.1294	0.735607
$906$	0.510002	0.0169437
$907$	−0.928588	−0.0308333	−0.0154166	−	0.999881i	$-0.504907\pi$
$907$	−0.928588	−0.0308333	−0.0154166	+	0.999881i	$0.504907\pi$
$908$	10.2201	0.339167
$909$	4.36543	0.144792
$910$	17.3742	0.575948
$911$	−18.6152	−0.616748	−0.308374	−	0.951265i	$-0.599785\pi$
$911$	−18.6152	−0.616748	−0.308374	+	0.951265i	$0.599785\pi$
$912$	6.10428	0.202133
$913$	−98.8169	−3.27036
$914$	−21.2396	−0.702544
$915$	0.442998	0.0146451
$916$	23.4186	0.773773
$917$	−1.61054	−0.0531846
$918$	−12.6620	−0.417907
$919$	−2.00725	−0.0662130	−0.0331065	−	0.999452i	$-0.510540\pi$
$919$	−2.00725	−0.0662130	−0.0331065	+	0.999452i	$0.510540\pi$
$920$	3.12618	0.103067
$921$	−5.60906	−0.184825
$922$	10.0735	0.331753
$923$	3.93283	0.129451
$924$	22.1626	0.729094
$925$	−20.1340	−0.662001
$926$	−36.5052	−1.19963
$927$	2.98470	0.0980304
$928$	2.34106	0.0768489
$929$	30.5738	1.00310	0.501548	−	0.865130i	$-0.332764\pi$
$929$	30.5738	1.00310	0.501548	+	0.865130i	$0.332764\pi$
$930$	11.2693	0.369535
$931$	4.75656	0.155890
$932$	−0.955048	−0.0312836
$933$	−6.92741	−0.226793
$934$	−5.39078	−0.176392
$935$	19.6741	0.643412
$936$	5.68060	0.185676
$937$	30.0198	0.980704	0.490352	−	0.871525i	$-0.336868\pi$
$937$	30.0198	0.980704	0.490352	+	0.871525i	$0.336868\pi$
$938$	−7.76562	−0.253556
$939$	−21.7486	−0.709738
$940$	−0.973611	−0.0317557
$941$	24.4407	0.796744	0.398372	−	0.917224i	$-0.369575\pi$
$941$	24.4407	0.796744	0.398372	+	0.917224i	$0.369575\pi$
$942$	−28.2726	−0.921172
$943$	−7.08681	−0.230778
$944$	4.76256	0.155008
$945$	−18.4421	−0.599921
$946$	−62.5573	−2.03391
$947$	28.0160	0.910398	0.455199	−	0.890390i	$-0.349568\pi$
$947$	28.0160	0.910398	0.455199	+	0.890390i	$0.349568\pi$
$948$	9.51096	0.308902
$949$	−25.1840	−0.817508
$950$	−14.0565	−0.456055
$951$	11.5885	0.375784
$952$	5.44676	0.176531
$953$	−14.7147	−0.476656	−0.238328	−	0.971185i	$-0.576599\pi$
$953$	−14.7147	−0.476656	−0.238328	+	0.971185i	$0.576599\pi$
$954$	9.16864	0.296846
$955$	−27.2815	−0.882808
$956$	−2.34502	−0.0758435
$957$	21.3305	0.689517
$958$	−11.7148	−0.378489
$959$	−40.9830	−1.32341
$960$	−1.86454	−0.0601779
$961$	5.52998	0.178387
$962$	−33.4954	−1.07994
$963$	3.98124	0.128294
$964$	−5.44477	−0.175364
$965$	10.5708	0.340287
$966$	7.88581	0.253722
$967$	−12.3110	−0.395895	−0.197948	−	0.980213i	$-0.563428\pi$
$967$	−12.3110	−0.395895	−0.197948	+	0.980213i	$0.563428\pi$
$968$	−31.9342	−1.02641
$969$	13.6692	0.439117
$970$	−13.8863	−0.445863
$971$	9.60711	0.308307	0.154153	−	0.988047i	$-0.450735\pi$
$971$	9.60711	0.308307	0.154153	+	0.988047i	$0.450735\pi$
$972$	−10.4783	−0.336091
$973$	−13.2637	−0.425214
$974$	−17.6255	−0.564756
$975$	23.7195	0.759633
$976$	−0.237591	−0.00760509
$977$	10.5063	0.336128	0.168064	−	0.985776i	$-0.446249\pi$
$977$	10.5063	0.336128	0.168064	+	0.985776i	$0.446249\pi$
$978$	−20.6417	−0.660049
$979$	9.11295	0.291251
$980$	−1.45289	−0.0464108
$981$	−14.1138	−0.450618
$982$	−24.0198	−0.766504
$983$	−7.86859	−0.250969	−0.125485	−	0.992096i	$-0.540049\pi$
$983$	−7.86859	−0.250969	−0.125485	+	0.992096i	$0.540049\pi$
$984$	4.22678	0.134745
$985$	12.1780	0.388023
$986$	5.24227	0.166948
$987$	−2.45594	−0.0781735
$988$	−23.3849	−0.743971
$989$	−22.2589	−0.707792
$990$	9.36902	0.297767
$991$	−3.84560	−0.122159	−0.0610797	−	0.998133i	$-0.519454\pi$
$991$	−3.84560	−0.122159	−0.0610797	+	0.998133i	$0.519454\pi$
$992$	−6.04400	−0.191897
$993$	−12.3908	−0.393210
$994$	1.79576	0.0569581
$995$	−26.2252	−0.831396
$996$	20.9709	0.664487
$997$	28.1266	0.890778	0.445389	−	0.895337i	$-0.353065\pi$
$997$	28.1266	0.890778	0.445389	+	0.895337i	$0.353065\pi$
$998$	20.7852	0.657943
$999$	35.5542	1.12489

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.c.1.17	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.c.1.17	✓	61	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.39055 q^{3} +1.00000 q^{4} +1.34087 q^{5} +1.39055 q^{6} -2.43238 q^{7} -1.00000 q^{8} -1.06637 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.39055 q^{3} +1.00000 q^{4} +1.34087 q^{5} +1.39055 q^{6} -2.43238 q^{7} -1.00000 q^{8} -1.06637 q^{9} -1.34087 q^{10} +6.55242 q^{11} -1.39055 q^{12} +5.32706 q^{13} +2.43238 q^{14} -1.86454 q^{15} +1.00000 q^{16} +2.23928 q^{17} +1.06637 q^{18} -4.38982 q^{19} +1.34087 q^{20} +3.38235 q^{21} -6.55242 q^{22} -2.33146 q^{23} +1.39055 q^{24} -3.20208 q^{25} -5.32706 q^{26} +5.65449 q^{27} -2.43238 q^{28} -2.34106 q^{29} +1.86454 q^{30} +6.04400 q^{31} -1.00000 q^{32} -9.11148 q^{33} -2.23928 q^{34} -3.26149 q^{35} -1.06637 q^{36} +6.28779 q^{37} +4.38982 q^{38} -7.40755 q^{39} -1.34087 q^{40} +3.03964 q^{41} -3.38235 q^{42} +9.54720 q^{43} +6.55242 q^{44} -1.42986 q^{45} +2.33146 q^{46} -0.726106 q^{47} -1.39055 q^{48} -1.08354 q^{49} +3.20208 q^{50} -3.11383 q^{51} +5.32706 q^{52} +8.59802 q^{53} -5.65449 q^{54} +8.78593 q^{55} +2.43238 q^{56} +6.10428 q^{57} +2.34106 q^{58} +4.76256 q^{59} -1.86454 q^{60} -0.237591 q^{61} -6.04400 q^{62} +2.59381 q^{63} +1.00000 q^{64} +7.14288 q^{65} +9.11148 q^{66} -3.19260 q^{67} +2.23928 q^{68} +3.24202 q^{69} +3.26149 q^{70} +0.738274 q^{71} +1.06637 q^{72} -4.72756 q^{73} -6.28779 q^{74} +4.45265 q^{75} -4.38982 q^{76} -15.9380 q^{77} +7.40755 q^{78} -6.83970 q^{79} +1.34087 q^{80} -4.66376 q^{81} -3.03964 q^{82} -15.0810 q^{83} +3.38235 q^{84} +3.00257 q^{85} -9.54720 q^{86} +3.25536 q^{87} -6.55242 q^{88} +1.39078 q^{89} +1.42986 q^{90} -12.9574 q^{91} -2.33146 q^{92} -8.40450 q^{93} +0.726106 q^{94} -5.88617 q^{95} +1.39055 q^{96} +10.3562 q^{97} +1.08354 q^{98} -6.98728 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9 - 16 * q^10 + 14 * q^11 + 8 * q^12 + 27 * q^13 - 2 * q^14 + 61 * q^16 + 60 * q^17 - 67 * q^18 - 29 * q^19 + 16 * q^20 + 30 * q^21 - 14 * q^22 + 39 * q^23 - 8 * q^24 + 61 * q^25 - 27 * q^26 + 32 * q^27 + 2 * q^28 + 36 * q^29 - 40 * q^31 - 61 * q^32 + 28 * q^33 - 60 * q^34 + 55 * q^35 + 67 * q^36 + 20 * q^37 + 29 * q^38 + 17 * q^39 - 16 * q^40 + 44 * q^41 - 30 * q^42 + 22 * q^43 + 14 * q^44 + 52 * q^45 - 39 * q^46 + 64 * q^47 + 8 * q^48 + 49 * q^49 - 61 * q^50 + 15 * q^51 + 27 * q^52 + 65 * q^53 - 32 * q^54 + 5 * q^55 - 2 * q^56 + 9 * q^57 - 36 * q^58 + 2 * q^59 + 45 * q^61 + 40 * q^62 + 28 * q^63 + 61 * q^64 + 41 * q^65 - 28 * q^66 - 20 * q^67 + 60 * q^68 + 21 * q^69 - 55 * q^70 - q^71 - 67 * q^72 + 25 * q^73 - 20 * q^74 + 27 * q^75 - 29 * q^76 + 131 * q^77 - 17 * q^78 - 17 * q^79 + 16 * q^80 + 85 * q^81 - 44 * q^82 + 104 * q^83 + 30 * q^84 + 44 * q^85 - 22 * q^86 + 86 * q^87 - 14 * q^88 + 32 * q^89 - 52 * q^90 - 68 * q^91 + 39 * q^92 + 52 * q^93 - 64 * q^94 + 58 * q^95 - 8 * q^96 + 5 * q^97 - 49 * q^98 + 15 * q^99

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