LMFDB - Embedded newform 6010.2.a.f.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.17759 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.17759 q^{6} +1.86080 q^{7} +1.00000 q^{8} -1.61328 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.17759 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.17759 q^{6} +1.86080 q^{7} +1.00000 q^{8} -1.61328 q^{9} -1.00000 q^{10} -1.45944 q^{11} +1.17759 q^{12} -2.35293 q^{13} +1.86080 q^{14} -1.17759 q^{15} +1.00000 q^{16} +0.777421 q^{17} -1.61328 q^{18} -7.57200 q^{19} -1.00000 q^{20} +2.19127 q^{21} -1.45944 q^{22} -1.98127 q^{23} +1.17759 q^{24} +1.00000 q^{25} -2.35293 q^{26} -5.43256 q^{27} +1.86080 q^{28} +8.14923 q^{29} -1.17759 q^{30} -0.725455 q^{31} +1.00000 q^{32} -1.71863 q^{33} +0.777421 q^{34} -1.86080 q^{35} -1.61328 q^{36} -5.70722 q^{37} -7.57200 q^{38} -2.77079 q^{39} -1.00000 q^{40} -8.44881 q^{41} +2.19127 q^{42} +3.91559 q^{43} -1.45944 q^{44} +1.61328 q^{45} -1.98127 q^{46} -1.60325 q^{47} +1.17759 q^{48} -3.53741 q^{49} +1.00000 q^{50} +0.915484 q^{51} -2.35293 q^{52} -0.320258 q^{53} -5.43256 q^{54} +1.45944 q^{55} +1.86080 q^{56} -8.91673 q^{57} +8.14923 q^{58} -9.73150 q^{59} -1.17759 q^{60} -5.49216 q^{61} -0.725455 q^{62} -3.00199 q^{63} +1.00000 q^{64} +2.35293 q^{65} -1.71863 q^{66} +7.96878 q^{67} +0.777421 q^{68} -2.33313 q^{69} -1.86080 q^{70} -1.16082 q^{71} -1.61328 q^{72} +1.72913 q^{73} -5.70722 q^{74} +1.17759 q^{75} -7.57200 q^{76} -2.71574 q^{77} -2.77079 q^{78} +13.4069 q^{79} -1.00000 q^{80} -1.55751 q^{81} -8.44881 q^{82} -9.39662 q^{83} +2.19127 q^{84} -0.777421 q^{85} +3.91559 q^{86} +9.59647 q^{87} -1.45944 q^{88} -10.4359 q^{89} +1.61328 q^{90} -4.37834 q^{91} -1.98127 q^{92} -0.854290 q^{93} -1.60325 q^{94} +7.57200 q^{95} +1.17759 q^{96} -5.98729 q^{97} -3.53741 q^{98} +2.35449 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * 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
$3$	1.17759	0.679883	0.339942	−	0.940447i	$-0.389593\pi$
$3$	1.17759	0.679883	0.339942	+	0.940447i	$0.389593\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.17759	0.480750
$7$	1.86080	0.703317	0.351659	−	0.936128i	$-0.385618\pi$
$7$	1.86080	0.703317	0.351659	+	0.936128i	$0.385618\pi$
$8$	1.00000	0.353553
$9$	−1.61328	−0.537759
$10$	−1.00000	−0.316228
$11$	−1.45944	−0.440039	−0.220019	−	0.975495i	$-0.570612\pi$
$11$	−1.45944	−0.440039	−0.220019	+	0.975495i	$0.570612\pi$
$12$	1.17759	0.339942
$13$	−2.35293	−0.652585	−0.326292	−	0.945269i	$-0.605799\pi$
$13$	−2.35293	−0.652585	−0.326292	+	0.945269i	$0.605799\pi$
$14$	1.86080	0.497320
$15$	−1.17759	−0.304053
$16$	1.00000	0.250000
$17$	0.777421	0.188552	0.0942761	−	0.995546i	$-0.469946\pi$
$17$	0.777421	0.188552	0.0942761	+	0.995546i	$0.469946\pi$
$18$	−1.61328	−0.380253
$19$	−7.57200	−1.73714	−0.868568	−	0.495570i	$-0.834959\pi$
$19$	−7.57200	−1.73714	−0.868568	+	0.495570i	$0.834959\pi$
$20$	−1.00000	−0.223607
$21$	2.19127	0.478174
$22$	−1.45944	−0.311154
$23$	−1.98127	−0.413124	−0.206562	−	0.978434i	$-0.566228\pi$
$23$	−1.98127	−0.413124	−0.206562	+	0.978434i	$0.566228\pi$
$24$	1.17759	0.240375
$25$	1.00000	0.200000
$26$	−2.35293	−0.461447
$27$	−5.43256	−1.04550
$28$	1.86080	0.351659
$29$	8.14923	1.51327	0.756637	−	0.653835i	$-0.226841\pi$
$29$	8.14923	1.51327	0.756637	+	0.653835i	$0.226841\pi$
$30$	−1.17759	−0.214998
$31$	−0.725455	−0.130296	−0.0651478	−	0.997876i	$-0.520752\pi$
$31$	−0.725455	−0.130296	−0.0651478	+	0.997876i	$0.520752\pi$
$32$	1.00000	0.176777
$33$	−1.71863	−0.299175
$34$	0.777421	0.133327
$35$	−1.86080	−0.314533
$36$	−1.61328	−0.268879
$37$	−5.70722	−0.938261	−0.469130	−	0.883129i	$-0.655433\pi$
$37$	−5.70722	−0.938261	−0.469130	+	0.883129i	$0.655433\pi$
$38$	−7.57200	−1.22834
$39$	−2.77079	−0.443682
$40$	−1.00000	−0.158114
$41$	−8.44881	−1.31948	−0.659741	−	0.751493i	$-0.729334\pi$
$41$	−8.44881	−1.31948	−0.659741	+	0.751493i	$0.729334\pi$
$42$	2.19127	0.338120
$43$	3.91559	0.597121	0.298561	−	0.954391i	$-0.403494\pi$
$43$	3.91559	0.597121	0.298561	+	0.954391i	$0.403494\pi$
$44$	−1.45944	−0.220019
$45$	1.61328	0.240493
$46$	−1.98127	−0.292123
$47$	−1.60325	−0.233858	−0.116929	−	0.993140i	$-0.537305\pi$
$47$	−1.60325	−0.233858	−0.116929	+	0.993140i	$0.537305\pi$
$48$	1.17759	0.169971
$49$	−3.53741	−0.505345
$50$	1.00000	0.141421
$51$	0.915484	0.128193
$52$	−2.35293	−0.326292
$53$	−0.320258	−0.0439908	−0.0219954	−	0.999758i	$-0.507002\pi$
$53$	−0.320258	−0.0439908	−0.0219954	+	0.999758i	$0.507002\pi$
$54$	−5.43256	−0.739278
$55$	1.45944	0.196791
$56$	1.86080	0.248660
$57$	−8.91673	−1.18105
$58$	8.14923	1.07005
$59$	−9.73150	−1.26693	−0.633466	−	0.773770i	$-0.718369\pi$
$59$	−9.73150	−1.26693	−0.633466	+	0.773770i	$0.718369\pi$
$60$	−1.17759	−0.152027
$61$	−5.49216	−0.703199	−0.351600	−	0.936150i	$-0.614362\pi$
$61$	−5.49216	−0.703199	−0.351600	+	0.936150i	$0.614362\pi$
$62$	−0.725455	−0.0921329
$63$	−3.00199	−0.378215
$64$	1.00000	0.125000
$65$	2.35293	0.291845
$66$	−1.71863	−0.211549
$67$	7.96878	0.973541	0.486771	−	0.873530i	$-0.338175\pi$
$67$	7.96878	0.973541	0.486771	+	0.873530i	$0.338175\pi$
$68$	0.777421	0.0942761
$69$	−2.33313	−0.280876
$70$	−1.86080	−0.222408
$71$	−1.16082	−0.137764	−0.0688819	−	0.997625i	$-0.521943\pi$
$71$	−1.16082	−0.137764	−0.0688819	+	0.997625i	$0.521943\pi$
$72$	−1.61328	−0.190126
$73$	1.72913	0.202379	0.101190	−	0.994867i	$-0.467735\pi$
$73$	1.72913	0.202379	0.101190	+	0.994867i	$0.467735\pi$
$74$	−5.70722	−0.663451
$75$	1.17759	0.135977
$76$	−7.57200	−0.868568
$77$	−2.71574	−0.309487
$78$	−2.77079	−0.313730
$79$	13.4069	1.50840	0.754199	−	0.656646i	$-0.228026\pi$
$79$	13.4069	1.50840	0.754199	+	0.656646i	$0.228026\pi$
$80$	−1.00000	−0.111803
$81$	−1.55751	−0.173057
$82$	−8.44881	−0.933015
$83$	−9.39662	−1.03141	−0.515707	−	0.856765i	$-0.672471\pi$
$83$	−9.39662	−1.03141	−0.515707	+	0.856765i	$0.672471\pi$
$84$	2.19127	0.239087
$85$	−0.777421	−0.0843231
$86$	3.91559	0.422228
$87$	9.59647	1.02885
$88$	−1.45944	−0.155577
$89$	−10.4359	−1.10621	−0.553103	−	0.833113i	$-0.686556\pi$
$89$	−10.4359	−1.10621	−0.553103	+	0.833113i	$0.686556\pi$
$90$	1.61328	0.170054
$91$	−4.37834	−0.458974
$92$	−1.98127	−0.206562
$93$	−0.854290	−0.0885857
$94$	−1.60325	−0.165362
$95$	7.57200	0.776871
$96$	1.17759	0.120188
$97$	−5.98729	−0.607918	−0.303959	−	0.952685i	$-0.598309\pi$
$97$	−5.98729	−0.607918	−0.303959	+	0.952685i	$0.598309\pi$
$98$	−3.53741	−0.357333
$99$	2.35449	0.236635
$100$	1.00000	0.100000
$101$	−6.31468	−0.628334	−0.314167	−	0.949368i	$-0.601725\pi$
$101$	−6.31468	−0.628334	−0.314167	+	0.949368i	$0.601725\pi$
$102$	0.915484	0.0906465
$103$	−12.9815	−1.27911	−0.639555	−	0.768746i	$-0.720881\pi$
$103$	−12.9815	−1.27911	−0.639555	+	0.768746i	$0.720881\pi$
$104$	−2.35293	−0.230724
$105$	−2.19127	−0.213846
$106$	−0.320258	−0.0311062
$107$	5.69990	0.551030	0.275515	−	0.961297i	$-0.411152\pi$
$107$	5.69990	0.551030	0.275515	+	0.961297i	$0.411152\pi$
$108$	−5.43256	−0.522748
$109$	9.06008	0.867798	0.433899	−	0.900961i	$-0.357137\pi$
$109$	9.06008	0.867798	0.433899	+	0.900961i	$0.357137\pi$
$110$	1.45944	0.139153
$111$	−6.72078	−0.637908
$112$	1.86080	0.175829
$113$	−13.6007	−1.27945	−0.639725	−	0.768604i	$-0.720952\pi$
$113$	−13.6007	−1.27945	−0.639725	+	0.768604i	$0.720952\pi$
$114$	−8.91673	−0.835128
$115$	1.98127	0.184755
$116$	8.14923	0.756637
$117$	3.79592	0.350933
$118$	−9.73150	−0.895857
$119$	1.44663	0.132612
$120$	−1.17759	−0.107499
$121$	−8.87002	−0.806366
$122$	−5.49216	−0.497237
$123$	−9.94926	−0.897094
$124$	−0.725455	−0.0651478
$125$	−1.00000	−0.0894427
$126$	−3.00199	−0.267438
$127$	4.26561	0.378512	0.189256	−	0.981928i	$-0.439392\pi$
$127$	4.26561	0.378512	0.189256	+	0.981928i	$0.439392\pi$
$128$	1.00000	0.0883883
$129$	4.61096	0.405973
$130$	2.35293	0.206365
$131$	6.29276	0.549801	0.274900	−	0.961473i	$-0.411355\pi$
$131$	6.29276	0.549801	0.274900	+	0.961473i	$0.411355\pi$
$132$	−1.71863	−0.149588
$133$	−14.0900	−1.22176
$134$	7.96878	0.688398
$135$	5.43256	0.467560
$136$	0.777421	0.0666633
$137$	6.70671	0.572993	0.286497	−	0.958081i	$-0.407509\pi$
$137$	6.70671	0.572993	0.286497	+	0.958081i	$0.407509\pi$
$138$	−2.33313	−0.198609
$139$	−13.3305	−1.13068	−0.565341	−	0.824857i	$-0.691255\pi$
$139$	−13.3305	−1.13068	−0.565341	+	0.824857i	$0.691255\pi$
$140$	−1.86080	−0.157267
$141$	−1.88797	−0.158996
$142$	−1.16082	−0.0974137
$143$	3.43397	0.287163
$144$	−1.61328	−0.134440
$145$	−8.14923	−0.676757
$146$	1.72913	0.143104
$147$	−4.16563	−0.343575
$148$	−5.70722	−0.469130
$149$	−8.48748	−0.695321	−0.347661	−	0.937620i	$-0.613024\pi$
$149$	−8.48748	−0.695321	−0.347661	+	0.937620i	$0.613024\pi$
$150$	1.17759	0.0961500
$151$	16.7160	1.36033	0.680166	−	0.733058i	$-0.261908\pi$
$151$	16.7160	1.36033	0.680166	+	0.733058i	$0.261908\pi$
$152$	−7.57200	−0.614170
$153$	−1.25419	−0.101396
$154$	−2.71574	−0.218840
$155$	0.725455	0.0582699
$156$	−2.77079	−0.221841
$157$	23.9219	1.90917	0.954586	−	0.297935i	$-0.0962977\pi$
$157$	23.9219	1.90917	0.954586	+	0.297935i	$0.0962977\pi$
$158$	13.4069	1.06660
$159$	−0.377133	−0.0299086
$160$	−1.00000	−0.0790569
$161$	−3.68676	−0.290557
$162$	−1.55751	−0.122370
$163$	−13.4668	−1.05480	−0.527400	−	0.849617i	$-0.676833\pi$
$163$	−13.4668	−1.05480	−0.527400	+	0.849617i	$0.676833\pi$
$164$	−8.44881	−0.659741
$165$	1.71863	0.133795
$166$	−9.39662	−0.729319
$167$	5.69994	0.441075	0.220537	−	0.975379i	$-0.429219\pi$
$167$	5.69994	0.441075	0.220537	+	0.975379i	$0.429219\pi$
$168$	2.19127	0.169060
$169$	−7.46373	−0.574133
$170$	−0.777421	−0.0596254
$171$	12.2157	0.934160
$172$	3.91559	0.298561
$173$	10.4757	0.796452	0.398226	−	0.917287i	$-0.369626\pi$
$173$	10.4757	0.796452	0.398226	+	0.917287i	$0.369626\pi$
$174$	9.59647	0.727506
$175$	1.86080	0.140663
$176$	−1.45944	−0.110010
$177$	−11.4597	−0.861366
$178$	−10.4359	−0.782206
$179$	6.85050	0.512031	0.256015	−	0.966673i	$-0.417590\pi$
$179$	6.85050	0.512031	0.256015	+	0.966673i	$0.417590\pi$
$180$	1.61328	0.120247
$181$	−23.3960	−1.73901	−0.869507	−	0.493921i	$-0.835563\pi$
$181$	−23.3960	−1.73901	−0.869507	+	0.493921i	$0.835563\pi$
$182$	−4.37834	−0.324544
$183$	−6.46753	−0.478093
$184$	−1.98127	−0.146061
$185$	5.70722	0.419603
$186$	−0.854290	−0.0626396
$187$	−1.13460	−0.0829703
$188$	−1.60325	−0.116929
$189$	−10.1089	−0.735316
$190$	7.57200	0.549331
$191$	9.28310	0.671702	0.335851	−	0.941915i	$-0.390976\pi$
$191$	9.28310	0.671702	0.335851	+	0.941915i	$0.390976\pi$
$192$	1.17759	0.0849854
$193$	24.7215	1.77949	0.889747	−	0.456453i	$-0.150880\pi$
$193$	24.7215	1.77949	0.889747	+	0.456453i	$0.150880\pi$
$194$	−5.98729	−0.429863
$195$	2.77079	0.198420
$196$	−3.53741	−0.252672
$197$	11.6091	0.827117	0.413558	−	0.910478i	$-0.364286\pi$
$197$	11.6091	0.827117	0.413558	+	0.910478i	$0.364286\pi$
$198$	2.35449	0.167326
$199$	−28.0473	−1.98822	−0.994109	−	0.108381i	$-0.965433\pi$
$199$	−28.0473	−1.98822	−0.994109	+	0.108381i	$0.965433\pi$
$200$	1.00000	0.0707107
$201$	9.38397	0.661894
$202$	−6.31468	−0.444299
$203$	15.1641	1.06431
$204$	0.915484	0.0640967
$205$	8.44881	0.590091
$206$	−12.9815	−0.904467
$207$	3.19634	0.222161
$208$	−2.35293	−0.163146
$209$	11.0509	0.764408
$210$	−2.19127	−0.151212
$211$	3.32979	0.229232	0.114616	−	0.993410i	$-0.463436\pi$
$211$	3.32979	0.229232	0.114616	+	0.993410i	$0.463436\pi$
$212$	−0.320258	−0.0219954
$213$	−1.36697	−0.0936633
$214$	5.69990	0.389637
$215$	−3.91559	−0.267041
$216$	−5.43256	−0.369639
$217$	−1.34993	−0.0916391
$218$	9.06008	0.613626
$219$	2.03621	0.137594
$220$	1.45944	0.0983957
$221$	−1.82921	−0.123046
$222$	−6.72078	−0.451069
$223$	−25.5533	−1.71117	−0.855586	−	0.517660i	$-0.826803\pi$
$223$	−25.5533	−1.71117	−0.855586	+	0.517660i	$0.826803\pi$
$224$	1.86080	0.124330
$225$	−1.61328	−0.107552
$226$	−13.6007	−0.904708
$227$	−20.2693	−1.34532	−0.672660	−	0.739952i	$-0.734848\pi$
$227$	−20.2693	−1.34532	−0.672660	+	0.739952i	$0.734848\pi$
$228$	−8.91673	−0.590525
$229$	25.6694	1.69628	0.848140	−	0.529773i	$-0.177723\pi$
$229$	25.6694	1.69628	0.848140	+	0.529773i	$0.177723\pi$
$230$	1.98127	0.130641
$231$	−3.19803	−0.210415
$232$	8.14923	0.535023
$233$	1.57501	0.103182	0.0515912	−	0.998668i	$-0.483571\pi$
$233$	1.57501	0.103182	0.0515912	+	0.998668i	$0.483571\pi$
$234$	3.79592	0.248147
$235$	1.60325	0.104584
$236$	−9.73150	−0.633466
$237$	15.7879	1.02553
$238$	1.44663	0.0937709
$239$	15.7700	1.02008	0.510039	−	0.860151i	$-0.329631\pi$
$239$	15.7700	1.02008	0.510039	+	0.860151i	$0.329631\pi$
$240$	−1.17759	−0.0760133
$241$	−1.74793	−0.112594	−0.0562970	−	0.998414i	$-0.517929\pi$
$241$	−1.74793	−0.112594	−0.0562970	+	0.998414i	$0.517929\pi$
$242$	−8.87002	−0.570187
$243$	14.4636	0.927838
$244$	−5.49216	−0.351600
$245$	3.53741	0.225997
$246$	−9.94926	−0.634341
$247$	17.8164	1.13363
$248$	−0.725455	−0.0460664
$249$	−11.0654	−0.701240
$250$	−1.00000	−0.0632456
$251$	0.950129	0.0599716	0.0299858	−	0.999550i	$-0.490454\pi$
$251$	0.950129	0.0599716	0.0299858	+	0.999550i	$0.490454\pi$
$252$	−3.00199	−0.189108
$253$	2.89156	0.181791
$254$	4.26561	0.267648
$255$	−0.915484	−0.0573299
$256$	1.00000	0.0625000
$257$	4.77629	0.297937	0.148968	−	0.988842i	$-0.452405\pi$
$257$	4.77629	0.297937	0.148968	+	0.988842i	$0.452405\pi$
$258$	4.61096	0.287066
$259$	−10.6200	−0.659895
$260$	2.35293	0.145922
$261$	−13.1470	−0.813776
$262$	6.29276	0.388768
$263$	10.0994	0.622758	0.311379	−	0.950286i	$-0.399209\pi$
$263$	10.0994	0.622758	0.311379	+	0.950286i	$0.399209\pi$
$264$	−1.71863	−0.105774
$265$	0.320258	0.0196733
$266$	−14.0900	−0.863914
$267$	−12.2893	−0.752091
$268$	7.96878	0.486771
$269$	0.806053	0.0491459	0.0245729	−	0.999698i	$-0.492177\pi$
$269$	0.806053	0.0491459	0.0245729	+	0.999698i	$0.492177\pi$
$270$	5.43256	0.330615
$271$	0.0942066	0.00572265	0.00286132	−	0.999996i	$-0.499089\pi$
$271$	0.0942066	0.00572265	0.00286132	+	0.999996i	$0.499089\pi$
$272$	0.777421	0.0471380
$273$	−5.15589	−0.312049
$274$	6.70671	0.405167
$275$	−1.45944	−0.0880078
$276$	−2.33313	−0.140438
$277$	7.38090	0.443475	0.221738	−	0.975106i	$-0.428827\pi$
$277$	7.38090	0.443475	0.221738	+	0.975106i	$0.428827\pi$
$278$	−13.3305	−0.799513
$279$	1.17036	0.0700676
$280$	−1.86080	−0.111204
$281$	−19.0279	−1.13511	−0.567555	−	0.823335i	$-0.692111\pi$
$281$	−19.0279	−1.13511	−0.567555	+	0.823335i	$0.692111\pi$
$282$	−1.88797	−0.112427
$283$	22.7452	1.35206	0.676032	−	0.736872i	$-0.263698\pi$
$283$	22.7452	1.35206	0.676032	+	0.736872i	$0.263698\pi$
$284$	−1.16082	−0.0688819
$285$	8.91673	0.528182
$286$	3.43397	0.203055
$287$	−15.7216	−0.928015
$288$	−1.61328	−0.0950632
$289$	−16.3956	−0.964448
$290$	−8.14923	−0.478539
$291$	−7.05059	−0.413313
$292$	1.72913	0.101190
$293$	13.8938	0.811687	0.405843	−	0.913943i	$-0.366978\pi$
$293$	13.8938	0.811687	0.405843	+	0.913943i	$0.366978\pi$
$294$	−4.16563	−0.242944
$295$	9.73150	0.566590
$296$	−5.70722	−0.331725
$297$	7.92851	0.460059
$298$	−8.48748	−0.491666
$299$	4.66179	0.269598
$300$	1.17759	0.0679883
$301$	7.28613	0.419966
$302$	16.7160	0.961900
$303$	−7.43612	−0.427194
$304$	−7.57200	−0.434284
$305$	5.49216	0.314480
$306$	−1.25419	−0.0716975
$307$	−6.59192	−0.376221	−0.188110	−	0.982148i	$-0.560236\pi$
$307$	−6.59192	−0.376221	−0.188110	+	0.982148i	$0.560236\pi$
$308$	−2.71574	−0.154743
$309$	−15.2870	−0.869645
$310$	0.725455	0.0412031
$311$	−35.1510	−1.99323	−0.996615	−	0.0822067i	$-0.973803\pi$
$311$	−35.1510	−1.99323	−0.996615	+	0.0822067i	$0.973803\pi$
$312$	−2.77079	−0.156865
$313$	2.80140	0.158345	0.0791724	−	0.996861i	$-0.474772\pi$
$313$	2.80140	0.158345	0.0791724	+	0.996861i	$0.474772\pi$
$314$	23.9219	1.34999
$315$	3.00199	0.169143
$316$	13.4069	0.754199
$317$	5.76763	0.323942	0.161971	−	0.986795i	$-0.448215\pi$
$317$	5.76763	0.323942	0.161971	+	0.986795i	$0.448215\pi$
$318$	−0.377133	−0.0211486
$319$	−11.8933	−0.665899
$320$	−1.00000	−0.0559017
$321$	6.71216	0.374636
$322$	−3.68676	−0.205455
$323$	−5.88663	−0.327541
$324$	−1.55751	−0.0865283
$325$	−2.35293	−0.130517
$326$	−13.4668	−0.745856
$327$	10.6691	0.590001
$328$	−8.44881	−0.466508
$329$	−2.98333	−0.164476
$330$	1.71863	0.0946074
$331$	−21.3642	−1.17428	−0.587141	−	0.809484i	$-0.699747\pi$
$331$	−21.3642	−1.17428	−0.587141	+	0.809484i	$0.699747\pi$
$332$	−9.39662	−0.515707
$333$	9.20732	0.504558
$334$	5.69994	0.311887
$335$	−7.96878	−0.435381
$336$	2.19127	0.119543
$337$	6.87747	0.374640	0.187320	−	0.982299i	$-0.440020\pi$
$337$	6.87747	0.374640	0.187320	+	0.982299i	$0.440020\pi$
$338$	−7.46373	−0.405973
$339$	−16.0161	−0.869877
$340$	−0.777421	−0.0421615
$341$	1.05876	0.0573351
$342$	12.2157	0.660551
$343$	−19.6080	−1.05874
$344$	3.91559	0.211114
$345$	2.33313	0.125612
$346$	10.4757	0.563177
$347$	−4.35294	−0.233678	−0.116839	−	0.993151i	$-0.537276\pi$
$347$	−4.35294	−0.233678	−0.116839	+	0.993151i	$0.537276\pi$
$348$	9.59647	0.514425
$349$	−11.2588	−0.602670	−0.301335	−	0.953518i	$-0.597432\pi$
$349$	−11.2588	−0.602670	−0.301335	+	0.953518i	$0.597432\pi$
$350$	1.86080	0.0994641
$351$	12.7824	0.682275
$352$	−1.45944	−0.0777886
$353$	10.4390	0.555612	0.277806	−	0.960637i	$-0.410393\pi$
$353$	10.4390	0.555612	0.277806	+	0.960637i	$0.410393\pi$
$354$	−11.4597	−0.609078
$355$	1.16082	0.0616098
$356$	−10.4359	−0.553103
$357$	1.70354	0.0901607
$358$	6.85050	0.362060
$359$	19.4408	1.02605	0.513024	−	0.858374i	$-0.328525\pi$
$359$	19.4408	1.02605	0.513024	+	0.858374i	$0.328525\pi$
$360$	1.61328	0.0850271
$361$	38.3352	2.01764
$362$	−23.3960	−1.22967
$363$	−10.4453	−0.548235
$364$	−4.37834	−0.229487
$365$	−1.72913	−0.0905066
$366$	−6.46753	−0.338063
$367$	−28.8298	−1.50490	−0.752451	−	0.658648i	$-0.771129\pi$
$367$	−28.8298	−1.50490	−0.752451	+	0.658648i	$0.771129\pi$
$368$	−1.98127	−0.103281
$369$	13.6303	0.709563
$370$	5.70722	0.296704
$371$	−0.595937	−0.0309395
$372$	−0.854290	−0.0442929
$373$	−4.73603	−0.245223	−0.122611	−	0.992455i	$-0.539127\pi$
$373$	−4.73603	−0.245223	−0.122611	+	0.992455i	$0.539127\pi$
$374$	−1.13460	−0.0586689
$375$	−1.17759	−0.0608106
$376$	−1.60325	−0.0826811
$377$	−19.1746	−0.987540
$378$	−10.1089	−0.519947
$379$	25.4732	1.30847	0.654235	−	0.756291i	$-0.272991\pi$
$379$	25.4732	1.30847	0.654235	+	0.756291i	$0.272991\pi$
$380$	7.57200	0.388436
$381$	5.02315	0.257344
$382$	9.28310	0.474965
$383$	9.30468	0.475447	0.237723	−	0.971333i	$-0.423599\pi$
$383$	9.30468	0.475447	0.237723	+	0.971333i	$0.423599\pi$
$384$	1.17759	0.0600938
$385$	2.71574	0.138407
$386$	24.7215	1.25829
$387$	−6.31692	−0.321107
$388$	−5.98729	−0.303959
$389$	−27.8924	−1.41420	−0.707101	−	0.707112i	$-0.749997\pi$
$389$	−27.8924	−1.41420	−0.707101	+	0.707112i	$0.749997\pi$
$390$	2.77079	0.140304
$391$	−1.54028	−0.0778954
$392$	−3.53741	−0.178666
$393$	7.41030	0.373800
$394$	11.6091	0.584860
$395$	−13.4069	−0.674576
$396$	2.35449	0.118317
$397$	18.4448	0.925717	0.462859	−	0.886432i	$-0.346824\pi$
$397$	18.4448	0.925717	0.462859	+	0.886432i	$0.346824\pi$
$398$	−28.0473	−1.40588
$399$	−16.5923	−0.830653
$400$	1.00000	0.0500000
$401$	16.4245	0.820199	0.410100	−	0.912041i	$-0.365494\pi$
$401$	16.4245	0.820199	0.410100	+	0.912041i	$0.365494\pi$
$402$	9.38397	0.468030
$403$	1.70694	0.0850289
$404$	−6.31468	−0.314167
$405$	1.55751	0.0773933
$406$	15.1641	0.752582
$407$	8.32936	0.412871
$408$	0.915484	0.0453232
$409$	−3.65073	−0.180517	−0.0902586	−	0.995918i	$-0.528769\pi$
$409$	−3.65073	−0.180517	−0.0902586	+	0.995918i	$0.528769\pi$
$410$	8.44881	0.417257
$411$	7.89778	0.389569
$412$	−12.9815	−0.639555
$413$	−18.1084	−0.891056
$414$	3.19634	0.157092
$415$	9.39662	0.461262
$416$	−2.35293	−0.115362
$417$	−15.6979	−0.768731
$418$	11.0509	0.540518
$419$	22.1740	1.08327	0.541636	−	0.840613i	$-0.317805\pi$
$419$	22.1740	1.08327	0.541636	+	0.840613i	$0.317805\pi$
$420$	−2.19127	−0.106923
$421$	−14.0066	−0.682639	−0.341320	−	0.939947i	$-0.610874\pi$
$421$	−14.0066	−0.682639	−0.341320	+	0.939947i	$0.610874\pi$
$422$	3.32979	0.162092
$423$	2.58648	0.125759
$424$	−0.320258	−0.0155531
$425$	0.777421	0.0377104
$426$	−1.36697	−0.0662299
$427$	−10.2198	−0.494572
$428$	5.69990	0.275515
$429$	4.04381	0.195237
$430$	−3.91559	−0.188826
$431$	8.15538	0.392831	0.196415	−	0.980521i	$-0.437070\pi$
$431$	8.15538	0.392831	0.196415	+	0.980521i	$0.437070\pi$
$432$	−5.43256	−0.261374
$433$	12.1347	0.583159	0.291579	−	0.956547i	$-0.405819\pi$
$433$	12.1347	0.583159	0.291579	+	0.956547i	$0.405819\pi$
$434$	−1.34993	−0.0647986
$435$	−9.59647	−0.460115
$436$	9.06008	0.433899
$437$	15.0022	0.717653
$438$	2.03621	0.0972937
$439$	0.753967	0.0359849	0.0179925	−	0.999838i	$-0.494273\pi$
$439$	0.753967	0.0359849	0.0179925	+	0.999838i	$0.494273\pi$
$440$	1.45944	0.0695763
$441$	5.70682	0.271754
$442$	−1.82921	−0.0870069
$443$	−28.7028	−1.36371	−0.681855	−	0.731487i	$-0.738827\pi$
$443$	−28.7028	−1.36371	−0.681855	+	0.731487i	$0.738827\pi$
$444$	−6.72078	−0.318954
$445$	10.4359	0.494711
$446$	−25.5533	−1.20998
$447$	−9.99479	−0.472737
$448$	1.86080	0.0879147
$449$	12.0697	0.569605	0.284802	−	0.958586i	$-0.408072\pi$
$449$	12.0697	0.569605	0.284802	+	0.958586i	$0.408072\pi$
$450$	−1.61328	−0.0760506
$451$	12.3306	0.580624
$452$	−13.6007	−0.639725
$453$	19.6847	0.924867
$454$	−20.2693	−0.951284
$455$	4.37834	0.205260
$456$	−8.91673	−0.417564
$457$	23.2310	1.08670	0.543349	−	0.839507i	$-0.317156\pi$
$457$	23.2310	1.08670	0.543349	+	0.839507i	$0.317156\pi$
$458$	25.6694	1.19945
$459$	−4.22338	−0.197131
$460$	1.98127	0.0923773
$461$	1.65421	0.0770440	0.0385220	−	0.999258i	$-0.487735\pi$
$461$	1.65421	0.0770440	0.0385220	+	0.999258i	$0.487735\pi$
$462$	−3.19803	−0.148786
$463$	−14.5988	−0.678466	−0.339233	−	0.940702i	$-0.610167\pi$
$463$	−14.5988	−0.678466	−0.339233	+	0.940702i	$0.610167\pi$
$464$	8.14923	0.378318
$465$	0.854290	0.0396167
$466$	1.57501	0.0729610
$467$	15.8867	0.735150	0.367575	−	0.929994i	$-0.380188\pi$
$467$	15.8867	0.735150	0.367575	+	0.929994i	$0.380188\pi$
$468$	3.79592	0.175467
$469$	14.8283	0.684709
$470$	1.60325	0.0739523
$471$	28.1702	1.29801
$472$	−9.73150	−0.447928
$473$	−5.71458	−0.262757
$474$	15.7879	0.725162
$475$	−7.57200	−0.347427
$476$	1.44663	0.0663060
$477$	0.516665	0.0236564
$478$	15.7700	0.721305
$479$	7.80178	0.356473	0.178236	−	0.983988i	$-0.442961\pi$
$479$	7.80178	0.356473	0.178236	+	0.983988i	$0.442961\pi$
$480$	−1.17759	−0.0537495
$481$	13.4287	0.612295
$482$	−1.74793	−0.0796160
$483$	−4.34150	−0.197545
$484$	−8.87002	−0.403183
$485$	5.98729	0.271869
$486$	14.4636	0.656081
$487$	19.5321	0.885085	0.442542	−	0.896748i	$-0.354077\pi$
$487$	19.5321	0.885085	0.442542	+	0.896748i	$0.354077\pi$
$488$	−5.49216	−0.248619
$489$	−15.8584	−0.717141
$490$	3.53741	0.159804
$491$	−26.9058	−1.21424	−0.607122	−	0.794609i	$-0.707676\pi$
$491$	−26.9058	−1.21424	−0.607122	+	0.794609i	$0.707676\pi$
$492$	−9.94926	−0.448547
$493$	6.33538	0.285331
$494$	17.8164	0.801597
$495$	−2.35449	−0.105826
$496$	−0.725455	−0.0325739
$497$	−2.16005	−0.0968916
$498$	−11.0654	−0.495852
$499$	−13.9532	−0.624629	−0.312315	−	0.949979i	$-0.601104\pi$
$499$	−13.9532	−0.624629	−0.312315	+	0.949979i	$0.601104\pi$
$500$	−1.00000	−0.0447214
$501$	6.71220	0.299879
$502$	0.950129	0.0424063
$503$	−17.7107	−0.789681	−0.394841	−	0.918750i	$-0.629200\pi$
$503$	−17.7107	−0.789681	−0.394841	+	0.918750i	$0.629200\pi$
$504$	−3.00199	−0.133719
$505$	6.31468	0.281000
$506$	2.89156	0.128545
$507$	−8.78923	−0.390343
$508$	4.26561	0.189256
$509$	−4.84363	−0.214690	−0.107345	−	0.994222i	$-0.534235\pi$
$509$	−4.84363	−0.214690	−0.107345	+	0.994222i	$0.534235\pi$
$510$	−0.915484	−0.0405383
$511$	3.21756	0.142337
$512$	1.00000	0.0441942
$513$	41.1353	1.81617
$514$	4.77629	0.210673
$515$	12.9815	0.572035
$516$	4.61096	0.202986
$517$	2.33985	0.102906
$518$	−10.6200	−0.466616
$519$	12.3361	0.541494
$520$	2.35293	0.103183
$521$	−32.2443	−1.41265	−0.706325	−	0.707888i	$-0.749648\pi$
$521$	−32.2443	−1.41265	−0.706325	+	0.707888i	$0.749648\pi$
$522$	−13.1470	−0.575427
$523$	−12.2854	−0.537204	−0.268602	−	0.963251i	$-0.586562\pi$
$523$	−12.2854	−0.537204	−0.268602	+	0.963251i	$0.586562\pi$
$524$	6.29276	0.274900
$525$	2.19127	0.0956347
$526$	10.0994	0.440357
$527$	−0.563983	−0.0245675
$528$	−1.71863	−0.0747938
$529$	−19.0746	−0.829329
$530$	0.320258	0.0139111
$531$	15.6996	0.681304
$532$	−14.0900	−0.610879
$533$	19.8794	0.861074
$534$	−12.2893	−0.531809
$535$	−5.69990	−0.246428
$536$	7.96878	0.344199
$537$	8.06710	0.348121
$538$	0.806053	0.0347514
$539$	5.16265	0.222371
$540$	5.43256	0.233780
$541$	33.6315	1.44593	0.722965	−	0.690885i	$-0.242779\pi$
$541$	33.6315	1.44593	0.722965	+	0.690885i	$0.242779\pi$
$542$	0.0942066	0.00404652
$543$	−27.5510	−1.18233
$544$	0.777421	0.0333316
$545$	−9.06008	−0.388091
$546$	−5.15589	−0.220652
$547$	2.20372	0.0942241	0.0471121	−	0.998890i	$-0.484998\pi$
$547$	2.20372	0.0942241	0.0471121	+	0.998890i	$0.484998\pi$
$548$	6.70671	0.286497
$549$	8.86038	0.378152
$550$	−1.45944	−0.0622309
$551$	−61.7060	−2.62876
$552$	−2.33313	−0.0993047
$553$	24.9477	1.06088
$554$	7.38090	0.313584
$555$	6.72078	0.285281
$556$	−13.3305	−0.565341
$557$	−11.5966	−0.491362	−0.245681	−	0.969351i	$-0.579012\pi$
$557$	−11.5966	−0.491362	−0.245681	+	0.969351i	$0.579012\pi$
$558$	1.17036	0.0495453
$559$	−9.21309	−0.389672
$560$	−1.86080	−0.0786333
$561$	−1.33610	−0.0564101
$562$	−19.0279	−0.802645
$563$	−22.8950	−0.964911	−0.482455	−	0.875921i	$-0.660255\pi$
$563$	−22.8950	−0.964911	−0.482455	+	0.875921i	$0.660255\pi$
$564$	−1.88797	−0.0794979
$565$	13.6007	0.572188
$566$	22.7452	0.956054
$567$	−2.89822	−0.121714
$568$	−1.16082	−0.0487068
$569$	3.07255	0.128808	0.0644039	−	0.997924i	$-0.479485\pi$
$569$	3.07255	0.128808	0.0644039	+	0.997924i	$0.479485\pi$
$570$	8.91673	0.373481
$571$	−7.08107	−0.296334	−0.148167	−	0.988962i	$-0.547337\pi$
$571$	−7.08107	−0.296334	−0.148167	+	0.988962i	$0.547337\pi$
$572$	3.43397	0.143581
$573$	10.9317	0.456679
$574$	−15.7216	−0.656206
$575$	−1.98127	−0.0826248
$576$	−1.61328	−0.0672199
$577$	−1.59578	−0.0664331	−0.0332165	−	0.999448i	$-0.510575\pi$
$577$	−1.59578	−0.0664331	−0.0332165	+	0.999448i	$0.510575\pi$
$578$	−16.3956	−0.681968
$579$	29.1119	1.20985
$580$	−8.14923	−0.338378
$581$	−17.4853	−0.725411
$582$	−7.05059	−0.292256
$583$	0.467398	0.0193577
$584$	1.72913	0.0715518
$585$	−3.79592	−0.156942
$586$	13.8938	0.573949
$587$	26.1192	1.07806	0.539028	−	0.842288i	$-0.318792\pi$
$587$	26.1192	1.07806	0.539028	+	0.842288i	$0.318792\pi$
$588$	−4.16563	−0.171788
$589$	5.49315	0.226341
$590$	9.73150	0.400639
$591$	13.6708	0.562343
$592$	−5.70722	−0.234565
$593$	−6.91028	−0.283771	−0.141886	−	0.989883i	$-0.545317\pi$
$593$	−6.91028	−0.283771	−0.141886	+	0.989883i	$0.545317\pi$
$594$	7.92851	0.325311
$595$	−1.44663	−0.0593059
$596$	−8.48748	−0.347661
$597$	−33.0283	−1.35176
$598$	4.66179	0.190635
$599$	−11.2027	−0.457729	−0.228865	−	0.973458i	$-0.573501\pi$
$599$	−11.2027	−0.457729	−0.228865	+	0.973458i	$0.573501\pi$
$600$	1.17759	0.0480750
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	7.28613	0.296961
$603$	−12.8558	−0.523530
$604$	16.7160	0.680166
$605$	8.87002	0.360618
$606$	−7.43612	−0.302072
$607$	19.3855	0.786833	0.393417	−	0.919360i	$-0.371293\pi$
$607$	19.3855	0.786833	0.393417	+	0.919360i	$0.371293\pi$
$608$	−7.57200	−0.307085
$609$	17.8571	0.723608
$610$	5.49216	0.222371
$611$	3.77232	0.152612
$612$	−1.25419	−0.0506978
$613$	−4.14338	−0.167349	−0.0836747	−	0.996493i	$-0.526666\pi$
$613$	−4.14338	−0.167349	−0.0836747	+	0.996493i	$0.526666\pi$
$614$	−6.59192	−0.266028
$615$	9.94926	0.401193
$616$	−2.71574	−0.109420
$617$	−26.7145	−1.07548	−0.537742	−	0.843109i	$-0.680723\pi$
$617$	−26.7145	−1.07548	−0.537742	+	0.843109i	$0.680723\pi$
$618$	−15.2870	−0.614932
$619$	−11.0516	−0.444203	−0.222101	−	0.975024i	$-0.571292\pi$
$619$	−11.0516	−0.444203	−0.222101	+	0.975024i	$0.571292\pi$
$620$	0.725455	0.0291350
$621$	10.7634	0.431920
$622$	−35.1510	−1.40943
$623$	−19.4192	−0.778014
$624$	−2.77079	−0.110920
$625$	1.00000	0.0400000
$626$	2.80140	0.111967
$627$	13.0135	0.519708
$628$	23.9219	0.954586
$629$	−4.43691	−0.176911
$630$	3.00199	0.119602
$631$	−16.1841	−0.644280	−0.322140	−	0.946692i	$-0.604402\pi$
$631$	−16.1841	−0.644280	−0.322140	+	0.946692i	$0.604402\pi$
$632$	13.4069	0.533299
$633$	3.92113	0.155851
$634$	5.76763	0.229062
$635$	−4.26561	−0.169276
$636$	−0.377133	−0.0149543
$637$	8.32328	0.329780
$638$	−11.8933	−0.470862
$639$	1.87272	0.0740837
$640$	−1.00000	−0.0395285
$641$	−16.9266	−0.668559	−0.334280	−	0.942474i	$-0.608493\pi$
$641$	−16.9266	−0.668559	−0.334280	+	0.942474i	$0.608493\pi$
$642$	6.71216	0.264908
$643$	36.0748	1.42265	0.711325	−	0.702863i	$-0.248095\pi$
$643$	36.0748	1.42265	0.711325	+	0.702863i	$0.248095\pi$
$644$	−3.68676	−0.145279
$645$	−4.61096	−0.181557
$646$	−5.88663	−0.231606
$647$	−41.1650	−1.61836	−0.809181	−	0.587560i	$-0.800089\pi$
$647$	−41.1650	−1.61836	−0.809181	+	0.587560i	$0.800089\pi$
$648$	−1.55751	−0.0611848
$649$	14.2026	0.557500
$650$	−2.35293	−0.0922894
$651$	−1.58967	−0.0623039
$652$	−13.4668	−0.527400
$653$	−43.6388	−1.70772	−0.853860	−	0.520503i	$-0.825744\pi$
$653$	−43.6388	−1.70772	−0.853860	+	0.520503i	$0.825744\pi$
$654$	10.6691	0.417194
$655$	−6.29276	−0.245878
$656$	−8.44881	−0.329871
$657$	−2.78956	−0.108831
$658$	−2.98333	−0.116302
$659$	20.6103	0.802862	0.401431	−	0.915889i	$-0.368513\pi$
$659$	20.6103	0.802862	0.401431	+	0.915889i	$0.368513\pi$
$660$	1.71863	0.0668976
$661$	11.3568	0.441728	0.220864	−	0.975305i	$-0.429112\pi$
$661$	11.3568	0.441728	0.220864	+	0.975305i	$0.429112\pi$
$662$	−21.3642	−0.830343
$663$	−2.15407	−0.0836571
$664$	−9.39662	−0.364660
$665$	14.0900	0.546387
$666$	9.20732	0.356776
$667$	−16.1458	−0.625170
$668$	5.69994	0.220537
$669$	−30.0913	−1.16340
$670$	−7.96878	−0.307861
$671$	8.01550	0.309435
$672$	2.19127	0.0845300
$673$	−41.6781	−1.60657	−0.803286	−	0.595593i	$-0.796917\pi$
$673$	−41.6781	−1.60657	−0.803286	+	0.595593i	$0.796917\pi$
$674$	6.87747	0.264910
$675$	−5.43256	−0.209099
$676$	−7.46373	−0.287066
$677$	16.1636	0.621217	0.310608	−	0.950538i	$-0.399467\pi$
$677$	16.1636	0.621217	0.310608	+	0.950538i	$0.399467\pi$
$678$	−16.0161	−0.615096
$679$	−11.1412	−0.427559
$680$	−0.777421	−0.0298127
$681$	−23.8689	−0.914660
$682$	1.05876	0.0405420
$683$	−25.8749	−0.990075	−0.495037	−	0.868872i	$-0.664846\pi$
$683$	−25.8749	−0.990075	−0.495037	+	0.868872i	$0.664846\pi$
$684$	12.2157	0.467080
$685$	−6.70671	−0.256250
$686$	−19.6080	−0.748639
$687$	30.2280	1.15327
$688$	3.91559	0.149280
$689$	0.753544	0.0287077
$690$	2.33313	0.0888208
$691$	51.2561	1.94987	0.974937	−	0.222480i	$-0.0714151\pi$
$691$	51.2561	1.94987	0.974937	+	0.222480i	$0.0714151\pi$
$692$	10.4757	0.398226
$693$	4.38123	0.166429
$694$	−4.35294	−0.165235
$695$	13.3305	0.505656
$696$	9.59647	0.363753
$697$	−6.56828	−0.248791
$698$	−11.2588	−0.426152
$699$	1.85472	0.0701520
$700$	1.86080	0.0703317
$701$	7.94384	0.300035	0.150017	−	0.988683i	$-0.452067\pi$
$701$	7.94384	0.300035	0.150017	+	0.988683i	$0.452067\pi$
$702$	12.7824	0.482441
$703$	43.2151	1.62989
$704$	−1.45944	−0.0550049
$705$	1.88797	0.0711051
$706$	10.4390	0.392877
$707$	−11.7504	−0.441918
$708$	−11.4597	−0.430683
$709$	26.7179	1.00341	0.501705	−	0.865039i	$-0.332706\pi$
$709$	26.7179	1.00341	0.501705	+	0.865039i	$0.332706\pi$
$710$	1.16082	0.0435647
$711$	−21.6291	−0.811154
$712$	−10.4359	−0.391103
$713$	1.43732	0.0538282
$714$	1.70354	0.0637532
$715$	−3.43397	−0.128423
$716$	6.85050	0.256015
$717$	18.5707	0.693534
$718$	19.4408	0.725525
$719$	30.2058	1.12649	0.563243	−	0.826291i	$-0.309554\pi$
$719$	30.2058	1.12649	0.563243	+	0.826291i	$0.309554\pi$
$720$	1.61328	0.0601233
$721$	−24.1561	−0.899620
$722$	38.3352	1.42669
$723$	−2.05835	−0.0765508
$724$	−23.3960	−0.869507
$725$	8.14923	0.302655
$726$	−10.4453	−0.387660
$727$	11.4208	0.423575	0.211788	−	0.977316i	$-0.432071\pi$
$727$	11.4208	0.423575	0.211788	+	0.977316i	$0.432071\pi$
$728$	−4.37834	−0.162272
$729$	21.7047	0.803878
$730$	−1.72913	−0.0639979
$731$	3.04406	0.112589
$732$	−6.46753	−0.239047
$733$	27.3941	1.01183	0.505913	−	0.862585i	$-0.331156\pi$
$733$	27.3941	1.01183	0.505913	+	0.862585i	$0.331156\pi$
$734$	−28.8298	−1.06413
$735$	4.16563	0.153652
$736$	−1.98127	−0.0730307
$737$	−11.6300	−0.428396
$738$	13.6303	0.501737
$739$	29.8772	1.09905	0.549525	−	0.835477i	$-0.314809\pi$
$739$	29.8772	1.09905	0.549525	+	0.835477i	$0.314809\pi$
$740$	5.70722	0.209801
$741$	20.9804	0.770735
$742$	−0.595937	−0.0218775
$743$	41.9235	1.53802	0.769012	−	0.639235i	$-0.220749\pi$
$743$	41.9235	1.53802	0.769012	+	0.639235i	$0.220749\pi$
$744$	−0.854290	−0.0313198
$745$	8.48748	0.310957
$746$	−4.73603	−0.173399
$747$	15.1593	0.554651
$748$	−1.13460	−0.0414851
$749$	10.6064	0.387549
$750$	−1.17759	−0.0429996
$751$	−6.58259	−0.240202	−0.120101	−	0.992762i	$-0.538322\pi$
$751$	−6.58259	−0.240202	−0.120101	+	0.992762i	$0.538322\pi$
$752$	−1.60325	−0.0584644
$753$	1.11886	0.0407737
$754$	−19.1746	−0.698296
$755$	−16.7160	−0.608359
$756$	−10.1089	−0.367658
$757$	1.77402	0.0644780	0.0322390	−	0.999480i	$-0.489736\pi$
$757$	1.77402	0.0644780	0.0322390	+	0.999480i	$0.489736\pi$
$758$	25.4732	0.925228
$759$	3.40507	0.123596
$760$	7.57200	0.274665
$761$	−22.7063	−0.823103	−0.411551	−	0.911387i	$-0.635013\pi$
$761$	−22.7063	−0.823103	−0.411551	+	0.911387i	$0.635013\pi$
$762$	5.02315	0.181970
$763$	16.8590	0.610338
$764$	9.28310	0.335851
$765$	1.25419	0.0453455
$766$	9.30468	0.336192
$767$	22.8975	0.826781
$768$	1.17759	0.0424927
$769$	24.4810	0.882807	0.441403	−	0.897309i	$-0.354481\pi$
$769$	24.4810	0.882807	0.441403	+	0.897309i	$0.354481\pi$
$770$	2.71574	0.0978684
$771$	5.62452	0.202562
$772$	24.7215	0.889747
$773$	−8.78645	−0.316027	−0.158013	−	0.987437i	$-0.550509\pi$
$773$	−8.78645	−0.316027	−0.158013	+	0.987437i	$0.550509\pi$
$774$	−6.31692	−0.227057
$775$	−0.725455	−0.0260591
$776$	−5.98729	−0.214931
$777$	−12.5060	−0.448652
$778$	−27.8924	−0.999992
$779$	63.9744	2.29212
$780$	2.77079	0.0992102
$781$	1.69415	0.0606214
$782$	−1.54028	−0.0550804
$783$	−44.2712	−1.58212
$784$	−3.53741	−0.126336
$785$	−23.9219	−0.853808
$786$	7.41030	0.264317
$787$	24.9000	0.887590	0.443795	−	0.896128i	$-0.353632\pi$
$787$	24.9000	0.887590	0.443795	+	0.896128i	$0.353632\pi$
$788$	11.6091	0.413558
$789$	11.8930	0.423403
$790$	−13.4069	−0.476997
$791$	−25.3083	−0.899860
$792$	2.35449	0.0836630
$793$	12.9227	0.458897
$794$	18.4448	0.654581
$795$	0.377133	0.0133755
$796$	−28.0473	−0.994109
$797$	18.1021	0.641209	0.320605	−	0.947213i	$-0.396114\pi$
$797$	18.1021	0.641209	0.320605	+	0.947213i	$0.396114\pi$
$798$	−16.5923	−0.587360
$799$	−1.24640	−0.0440944
$800$	1.00000	0.0353553
$801$	16.8360	0.594872
$802$	16.4245	0.579969
$803$	−2.52356	−0.0890546
$804$	9.38397	0.330947
$805$	3.68676	0.129941
$806$	1.70694	0.0601245
$807$	0.949201	0.0334135
$808$	−6.31468	−0.222150
$809$	40.0761	1.40900	0.704500	−	0.709704i	$-0.251171\pi$
$809$	40.0761	1.40900	0.704500	+	0.709704i	$0.251171\pi$
$810$	1.55751	0.0547253
$811$	−3.92383	−0.137784	−0.0688921	−	0.997624i	$-0.521946\pi$
$811$	−3.92383	−0.137784	−0.0688921	+	0.997624i	$0.521946\pi$
$812$	15.1641	0.532156
$813$	0.110937	0.00389073
$814$	8.32936	0.291944
$815$	13.4668	0.471721
$816$	0.915484	0.0320484
$817$	−29.6488	−1.03728
$818$	−3.65073	−0.127645
$819$	7.06347	0.246817
$820$	8.44881	0.295045
$821$	−21.9120	−0.764733	−0.382366	−	0.924011i	$-0.624891\pi$
$821$	−21.9120	−0.764733	−0.382366	+	0.924011i	$0.624891\pi$
$822$	7.89778	0.275467
$823$	11.6769	0.407031	0.203516	−	0.979072i	$-0.434763\pi$
$823$	11.6769	0.407031	0.203516	+	0.979072i	$0.434763\pi$
$824$	−12.9815	−0.452233
$825$	−1.71863	−0.0598350
$826$	−18.1084	−0.630072
$827$	26.9358	0.936651	0.468326	−	0.883556i	$-0.344857\pi$
$827$	26.9358	0.936651	0.468326	+	0.883556i	$0.344857\pi$
$828$	3.19634	0.111081
$829$	11.3971	0.395837	0.197918	−	0.980218i	$-0.436582\pi$
$829$	11.3971	0.395837	0.197918	+	0.980218i	$0.436582\pi$
$830$	9.39662	0.326161
$831$	8.69169	0.301511
$832$	−2.35293	−0.0815731
$833$	−2.75006	−0.0952838
$834$	−15.6979	−0.543575
$835$	−5.69994	−0.197255
$836$	11.0509	0.382204
$837$	3.94108	0.136224
$838$	22.1740	0.765988
$839$	−25.3860	−0.876421	−0.438210	−	0.898872i	$-0.644388\pi$
$839$	−25.3860	−0.876421	−0.438210	+	0.898872i	$0.644388\pi$
$840$	−2.19127	−0.0756059
$841$	37.4099	1.29000
$842$	−14.0066	−0.482699
$843$	−22.4071	−0.771743
$844$	3.32979	0.114616
$845$	7.46373	0.256760
$846$	2.58648	0.0889250
$847$	−16.5054	−0.567131
$848$	−0.320258	−0.0109977
$849$	26.7846	0.919246
$850$	0.777421	0.0266653
$851$	11.3076	0.387618
$852$	−1.36697	−0.0468316
$853$	14.6841	0.502775	0.251387	−	0.967887i	$-0.419113\pi$
$853$	14.6841	0.502775	0.251387	+	0.967887i	$0.419113\pi$
$854$	−10.2198	−0.349715
$855$	−12.2157	−0.417769
$856$	5.69990	0.194819
$857$	2.56753	0.0877051	0.0438526	−	0.999038i	$-0.486037\pi$
$857$	2.56753	0.0877051	0.0438526	+	0.999038i	$0.486037\pi$
$858$	4.04381	0.138053
$859$	56.2711	1.91994	0.959972	−	0.280096i	$-0.0903662\pi$
$859$	56.2711	1.91994	0.959972	+	0.280096i	$0.0903662\pi$
$860$	−3.91559	−0.133520
$861$	−18.5136	−0.630942
$862$	8.15538	0.277773
$863$	13.4681	0.458459	0.229229	−	0.973372i	$-0.426379\pi$
$863$	13.4681	0.458459	0.229229	+	0.973372i	$0.426379\pi$
$864$	−5.43256	−0.184819
$865$	−10.4757	−0.356184
$866$	12.1347	0.412355
$867$	−19.3074	−0.655712
$868$	−1.34993	−0.0458196
$869$	−19.5667	−0.663753
$870$	−9.59647	−0.325351
$871$	−18.7500	−0.635318
$872$	9.06008	0.306813
$873$	9.65916	0.326913
$874$	15.0022	0.507457
$875$	−1.86080	−0.0629066
$876$	2.03621	0.0687970
$877$	29.5498	0.997825	0.498912	−	0.866652i	$-0.333733\pi$
$877$	29.5498	0.997825	0.498912	+	0.866652i	$0.333733\pi$
$878$	0.753967	0.0254452
$879$	16.3613	0.551852
$880$	1.45944	0.0491978
$881$	−32.1836	−1.08429	−0.542146	−	0.840284i	$-0.682388\pi$
$881$	−32.1836	−1.08429	−0.542146	+	0.840284i	$0.682388\pi$
$882$	5.70682	0.192159
$883$	−31.0199	−1.04390	−0.521952	−	0.852975i	$-0.674796\pi$
$883$	−31.0199	−1.04390	−0.521952	+	0.852975i	$0.674796\pi$
$884$	−1.82921	−0.0615232
$885$	11.4597	0.385215
$886$	−28.7028	−0.964289
$887$	34.3255	1.15254	0.576269	−	0.817260i	$-0.304508\pi$
$887$	34.3255	1.15254	0.576269	+	0.817260i	$0.304508\pi$
$888$	−6.72078	−0.225534
$889$	7.93746	0.266214
$890$	10.4359	0.349813
$891$	2.27310	0.0761516
$892$	−25.5533	−0.855586
$893$	12.1398	0.406242
$894$	−9.99479	−0.334276
$895$	−6.85050	−0.228987
$896$	1.86080	0.0621651
$897$	5.48969	0.183295
$898$	12.0697	0.402771
$899$	−5.91190	−0.197173
$900$	−1.61328	−0.0537759
$901$	−0.248975	−0.00829456
$902$	12.3306	0.410563
$903$	8.58009	0.285528
$904$	−13.6007	−0.452354
$905$	23.3960	0.777710
$906$	19.6847	0.653980
$907$	20.2626	0.672809	0.336405	−	0.941718i	$-0.390789\pi$
$907$	20.2626	0.672809	0.336405	+	0.941718i	$0.390789\pi$
$908$	−20.2693	−0.672660
$909$	10.1873	0.337892
$910$	4.37834	0.145140
$911$	−37.9869	−1.25856	−0.629281	−	0.777178i	$-0.716650\pi$
$911$	−37.9869	−1.25856	−0.629281	+	0.777178i	$0.716650\pi$
$912$	−8.91673	−0.295262
$913$	13.7138	0.453862
$914$	23.2310	0.768412
$915$	6.46753	0.213810
$916$	25.6694	0.848140
$917$	11.7096	0.386684
$918$	−4.22338	−0.139392
$919$	−14.9291	−0.492466	−0.246233	−	0.969211i	$-0.579193\pi$
$919$	−14.9291	−0.492466	−0.246233	+	0.969211i	$0.579193\pi$
$920$	1.98127	0.0653206
$921$	−7.76260	−0.255786
$922$	1.65421	0.0544784
$923$	2.73132	0.0899025
$924$	−3.19803	−0.105207
$925$	−5.70722	−0.187652
$926$	−14.5988	−0.479748
$927$	20.9428	0.687852
$928$	8.14923	0.267512
$929$	−45.0720	−1.47877	−0.739383	−	0.673286i	$-0.764882\pi$
$929$	−45.0720	−1.47877	−0.739383	+	0.673286i	$0.764882\pi$
$930$	0.854290	0.0280133
$931$	26.7853	0.877853
$932$	1.57501	0.0515912
$933$	−41.3936	−1.35516
$934$	15.8867	0.519829
$935$	1.13460	0.0371054
$936$	3.79592	0.124074
$937$	−3.81367	−0.124587	−0.0622936	−	0.998058i	$-0.519842\pi$
$937$	−3.81367	−0.124587	−0.0622936	+	0.998058i	$0.519842\pi$
$938$	14.8283	0.484162
$939$	3.29891	0.107656
$940$	1.60325	0.0522921
$941$	21.1632	0.689901	0.344951	−	0.938621i	$-0.387896\pi$
$941$	21.1632	0.689901	0.344951	+	0.938621i	$0.387896\pi$
$942$	28.1702	0.917835
$943$	16.7394	0.545110
$944$	−9.73150	−0.316733
$945$	10.1089	0.328843
$946$	−5.71458	−0.185797
$947$	−26.4976	−0.861057	−0.430529	−	0.902577i	$-0.641673\pi$
$947$	−26.4976	−0.861057	−0.430529	+	0.902577i	$0.641673\pi$
$948$	15.7879	0.512767
$949$	−4.06851	−0.132069
$950$	−7.57200	−0.245668
$951$	6.79192	0.220243
$952$	1.44663	0.0468854
$953$	−39.7293	−1.28696	−0.643480	−	0.765463i	$-0.722510\pi$
$953$	−39.7293	−1.28696	−0.643480	+	0.765463i	$0.722510\pi$
$954$	0.516665	0.0167276
$955$	−9.28310	−0.300394
$956$	15.7700	0.510039
$957$	−14.0055	−0.452734
$958$	7.80178	0.252064
$959$	12.4799	0.402996
$960$	−1.17759	−0.0380066
$961$	−30.4737	−0.983023
$962$	13.4287	0.432958
$963$	−9.19551	−0.296321
$964$	−1.74793	−0.0562970
$965$	−24.7215	−0.795814
$966$	−4.34150	−0.139685
$967$	−14.0488	−0.451778	−0.225889	−	0.974153i	$-0.572529\pi$
$967$	−14.0488	−0.451778	−0.225889	+	0.974153i	$0.572529\pi$
$968$	−8.87002	−0.285093
$969$	−6.93205	−0.222690
$970$	5.98729	0.192240
$971$	−54.4067	−1.74599	−0.872997	−	0.487726i	$-0.837826\pi$
$971$	−54.4067	−1.74599	−0.872997	+	0.487726i	$0.837826\pi$
$972$	14.4636	0.463919
$973$	−24.8055	−0.795228
$974$	19.5321	0.625850
$975$	−2.77079	−0.0887363
$976$	−5.49216	−0.175800
$977$	4.53537	0.145099	0.0725497	−	0.997365i	$-0.476886\pi$
$977$	4.53537	0.145099	0.0725497	+	0.997365i	$0.476886\pi$
$978$	−15.8584	−0.507095
$979$	15.2307	0.486774
$980$	3.53741	0.112999
$981$	−14.6164	−0.466666
$982$	−26.9058	−0.858600
$983$	−16.3215	−0.520575	−0.260288	−	0.965531i	$-0.583817\pi$
$983$	−16.3215	−0.520575	−0.260288	+	0.965531i	$0.583817\pi$
$984$	−9.94926	−0.317171
$985$	−11.6091	−0.369898
$986$	6.33538	0.201760
$987$	−3.51314	−0.111825
$988$	17.8164	0.566814
$989$	−7.75784	−0.246685
$990$	−2.35449	−0.0748305
$991$	5.80639	0.184446	0.0922230	−	0.995738i	$-0.470603\pi$
$991$	5.80639	0.184446	0.0922230	+	0.995738i	$0.470603\pi$
$992$	−0.725455	−0.0230332
$993$	−25.1583	−0.798375
$994$	−2.16005	−0.0685127
$995$	28.0473	0.889159
$996$	−11.0654	−0.350620
$997$	18.3277	0.580446	0.290223	−	0.956959i	$-0.406271\pi$
$997$	18.3277	0.580446	0.290223	+	0.956959i	$0.406271\pi$
$998$	−13.9532	−0.441680
$999$	31.0048	0.980948

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.f.1.16	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.f.1.16	✓	22	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.17759 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.17759 q^{6} +1.86080 q^{7} +1.00000 q^{8} -1.61328 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.17759 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.17759 q^{6} +1.86080 q^{7} +1.00000 q^{8} -1.61328 q^{9} -1.00000 q^{10} -1.45944 q^{11} +1.17759 q^{12} -2.35293 q^{13} +1.86080 q^{14} -1.17759 q^{15} +1.00000 q^{16} +0.777421 q^{17} -1.61328 q^{18} -7.57200 q^{19} -1.00000 q^{20} +2.19127 q^{21} -1.45944 q^{22} -1.98127 q^{23} +1.17759 q^{24} +1.00000 q^{25} -2.35293 q^{26} -5.43256 q^{27} +1.86080 q^{28} +8.14923 q^{29} -1.17759 q^{30} -0.725455 q^{31} +1.00000 q^{32} -1.71863 q^{33} +0.777421 q^{34} -1.86080 q^{35} -1.61328 q^{36} -5.70722 q^{37} -7.57200 q^{38} -2.77079 q^{39} -1.00000 q^{40} -8.44881 q^{41} +2.19127 q^{42} +3.91559 q^{43} -1.45944 q^{44} +1.61328 q^{45} -1.98127 q^{46} -1.60325 q^{47} +1.17759 q^{48} -3.53741 q^{49} +1.00000 q^{50} +0.915484 q^{51} -2.35293 q^{52} -0.320258 q^{53} -5.43256 q^{54} +1.45944 q^{55} +1.86080 q^{56} -8.91673 q^{57} +8.14923 q^{58} -9.73150 q^{59} -1.17759 q^{60} -5.49216 q^{61} -0.725455 q^{62} -3.00199 q^{63} +1.00000 q^{64} +2.35293 q^{65} -1.71863 q^{66} +7.96878 q^{67} +0.777421 q^{68} -2.33313 q^{69} -1.86080 q^{70} -1.16082 q^{71} -1.61328 q^{72} +1.72913 q^{73} -5.70722 q^{74} +1.17759 q^{75} -7.57200 q^{76} -2.71574 q^{77} -2.77079 q^{78} +13.4069 q^{79} -1.00000 q^{80} -1.55751 q^{81} -8.44881 q^{82} -9.39662 q^{83} +2.19127 q^{84} -0.777421 q^{85} +3.91559 q^{86} +9.59647 q^{87} -1.45944 q^{88} -10.4359 q^{89} +1.61328 q^{90} -4.37834 q^{91} -1.98127 q^{92} -0.854290 q^{93} -1.60325 q^{94} +7.57200 q^{95} +1.17759 q^{96} -5.98729 q^{97} -3.53741 q^{98} +2.35449 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * q^99

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