LMFDB - Embedded newform 6010.2.a.h.1.9

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:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.14577 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.14577 q^{6} +0.345550 q^{7} +1.00000 q^{8} -1.68722 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.14577 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.14577 q^{6} +0.345550 q^{7} +1.00000 q^{8} -1.68722 q^{9} -1.00000 q^{10} -2.94303 q^{11} -1.14577 q^{12} -5.44236 q^{13} +0.345550 q^{14} +1.14577 q^{15} +1.00000 q^{16} -4.68942 q^{17} -1.68722 q^{18} -3.29241 q^{19} -1.00000 q^{20} -0.395919 q^{21} -2.94303 q^{22} +4.16600 q^{23} -1.14577 q^{24} +1.00000 q^{25} -5.44236 q^{26} +5.37046 q^{27} +0.345550 q^{28} -2.64769 q^{29} +1.14577 q^{30} +1.97604 q^{31} +1.00000 q^{32} +3.37203 q^{33} -4.68942 q^{34} -0.345550 q^{35} -1.68722 q^{36} -8.30644 q^{37} -3.29241 q^{38} +6.23568 q^{39} -1.00000 q^{40} +5.85967 q^{41} -0.395919 q^{42} +2.54426 q^{43} -2.94303 q^{44} +1.68722 q^{45} +4.16600 q^{46} +5.46084 q^{47} -1.14577 q^{48} -6.88060 q^{49} +1.00000 q^{50} +5.37298 q^{51} -5.44236 q^{52} +8.94020 q^{53} +5.37046 q^{54} +2.94303 q^{55} +0.345550 q^{56} +3.77234 q^{57} -2.64769 q^{58} +3.69888 q^{59} +1.14577 q^{60} +4.01040 q^{61} +1.97604 q^{62} -0.583017 q^{63} +1.00000 q^{64} +5.44236 q^{65} +3.37203 q^{66} +3.34207 q^{67} -4.68942 q^{68} -4.77327 q^{69} -0.345550 q^{70} +0.666494 q^{71} -1.68722 q^{72} +7.11379 q^{73} -8.30644 q^{74} -1.14577 q^{75} -3.29241 q^{76} -1.01696 q^{77} +6.23568 q^{78} +10.0928 q^{79} -1.00000 q^{80} -1.09164 q^{81} +5.85967 q^{82} -10.9935 q^{83} -0.395919 q^{84} +4.68942 q^{85} +2.54426 q^{86} +3.03363 q^{87} -2.94303 q^{88} +17.8773 q^{89} +1.68722 q^{90} -1.88061 q^{91} +4.16600 q^{92} -2.26409 q^{93} +5.46084 q^{94} +3.29241 q^{95} -1.14577 q^{96} +4.74512 q^{97} -6.88060 q^{98} +4.96554 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9}+O(q^{10}) $ 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9} - 28 q^{10} + 4 q^{11} + 4 q^{12} + 22 q^{13} + 10 q^{14} - 4 q^{15} + 28 q^{16} + 15 q^{17} + 40 q^{18} - 11 q^{19} - 28 q^{20} + 18 q^{21} + 4 q^{22} + 23 q^{23} + 4 q^{24} + 28 q^{25} + 22 q^{26} + 19 q^{27} + 10 q^{28} + 19 q^{29} - 4 q^{30} + 7 q^{31} + 28 q^{32} + 33 q^{33} + 15 q^{34} - 10 q^{35} + 40 q^{36} + 22 q^{37} - 11 q^{38} + 8 q^{39} - 28 q^{40} + 41 q^{41} + 18 q^{42} + 7 q^{43} + 4 q^{44} - 40 q^{45} + 23 q^{46} + 51 q^{47} + 4 q^{48} + 60 q^{49} + 28 q^{50} - 5 q^{51} + 22 q^{52} + 25 q^{53} + 19 q^{54} - 4 q^{55} + 10 q^{56} + 8 q^{57} + 19 q^{58} + 32 q^{59} - 4 q^{60} + 24 q^{61} + 7 q^{62} + 33 q^{63} + 28 q^{64} - 22 q^{65} + 33 q^{66} + 3 q^{67} + 15 q^{68} + 43 q^{69} - 10 q^{70} + 8 q^{71} + 40 q^{72} + 47 q^{73} + 22 q^{74} + 4 q^{75} - 11 q^{76} + 46 q^{77} + 8 q^{78} - 22 q^{79} - 28 q^{80} + 76 q^{81} + 41 q^{82} + 36 q^{83} + 18 q^{84} - 15 q^{85} + 7 q^{86} + 72 q^{87} + 4 q^{88} + 70 q^{89} - 40 q^{90} - 21 q^{91} + 23 q^{92} + 24 q^{93} + 51 q^{94} + 11 q^{95} + 4 q^{96} + 43 q^{97} + 60 q^{98} - 9 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9 - 28 * q^10 + 4 * q^11 + 4 * q^12 + 22 * q^13 + 10 * q^14 - 4 * q^15 + 28 * q^16 + 15 * q^17 + 40 * q^18 - 11 * q^19 - 28 * q^20 + 18 * q^21 + 4 * q^22 + 23 * q^23 + 4 * q^24 + 28 * q^25 + 22 * q^26 + 19 * q^27 + 10 * q^28 + 19 * q^29 - 4 * q^30 + 7 * q^31 + 28 * q^32 + 33 * q^33 + 15 * q^34 - 10 * q^35 + 40 * q^36 + 22 * q^37 - 11 * q^38 + 8 * q^39 - 28 * q^40 + 41 * q^41 + 18 * q^42 + 7 * q^43 + 4 * q^44 - 40 * q^45 + 23 * q^46 + 51 * q^47 + 4 * q^48 + 60 * q^49 + 28 * q^50 - 5 * q^51 + 22 * q^52 + 25 * q^53 + 19 * q^54 - 4 * q^55 + 10 * q^56 + 8 * q^57 + 19 * q^58 + 32 * q^59 - 4 * q^60 + 24 * q^61 + 7 * q^62 + 33 * q^63 + 28 * q^64 - 22 * q^65 + 33 * q^66 + 3 * q^67 + 15 * q^68 + 43 * q^69 - 10 * q^70 + 8 * q^71 + 40 * q^72 + 47 * q^73 + 22 * q^74 + 4 * q^75 - 11 * q^76 + 46 * q^77 + 8 * q^78 - 22 * q^79 - 28 * q^80 + 76 * q^81 + 41 * q^82 + 36 * q^83 + 18 * q^84 - 15 * q^85 + 7 * q^86 + 72 * q^87 + 4 * q^88 + 70 * q^89 - 40 * q^90 - 21 * q^91 + 23 * q^92 + 24 * q^93 + 51 * q^94 + 11 * q^95 + 4 * q^96 + 43 * q^97 + 60 * q^98 - 9 * 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
$3$	−1.14577	−0.661509	−0.330754	−	0.943717i	$-0.607303\pi$
$3$	−1.14577	−0.661509	−0.330754	+	0.943717i	$0.607303\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.14577	−0.467757
$7$	0.345550	0.130605	0.0653027	−	0.997865i	$-0.479199\pi$
$7$	0.345550	0.130605	0.0653027	+	0.997865i	$0.479199\pi$
$8$	1.00000	0.353553
$9$	−1.68722	−0.562406
$10$	−1.00000	−0.316228
$11$	−2.94303	−0.887358	−0.443679	−	0.896186i	$-0.646327\pi$
$11$	−2.94303	−0.887358	−0.443679	+	0.896186i	$0.646327\pi$
$12$	−1.14577	−0.330754
$13$	−5.44236	−1.50944	−0.754720	−	0.656047i	$-0.772227\pi$
$13$	−5.44236	−1.50944	−0.754720	+	0.656047i	$0.772227\pi$
$14$	0.345550	0.0923520
$15$	1.14577	0.295836
$16$	1.00000	0.250000
$17$	−4.68942	−1.13735	−0.568675	−	0.822562i	$-0.692544\pi$
$17$	−4.68942	−1.13735	−0.568675	+	0.822562i	$0.692544\pi$
$18$	−1.68722	−0.397681
$19$	−3.29241	−0.755331	−0.377665	−	0.925942i	$-0.623273\pi$
$19$	−3.29241	−0.755331	−0.377665	+	0.925942i	$0.623273\pi$
$20$	−1.00000	−0.223607
$21$	−0.395919	−0.0863967
$22$	−2.94303	−0.627457
$23$	4.16600	0.868672	0.434336	−	0.900751i	$-0.356983\pi$
$23$	4.16600	0.868672	0.434336	+	0.900751i	$0.356983\pi$
$24$	−1.14577	−0.233879
$25$	1.00000	0.200000
$26$	−5.44236	−1.06733
$27$	5.37046	1.03355
$28$	0.345550	0.0653027
$29$	−2.64769	−0.491663	−0.245831	−	0.969313i	$-0.579061\pi$
$29$	−2.64769	−0.491663	−0.245831	+	0.969313i	$0.579061\pi$
$30$	1.14577	0.209187
$31$	1.97604	0.354908	0.177454	−	0.984129i	$-0.443214\pi$
$31$	1.97604	0.354908	0.177454	+	0.984129i	$0.443214\pi$
$32$	1.00000	0.176777
$33$	3.37203	0.586995
$34$	−4.68942	−0.804228
$35$	−0.345550	−0.0584085
$36$	−1.68722	−0.281203
$37$	−8.30644	−1.36557	−0.682785	−	0.730619i	$-0.739231\pi$
$37$	−8.30644	−1.36557	−0.682785	+	0.730619i	$0.739231\pi$
$38$	−3.29241	−0.534100
$39$	6.23568	0.998508
$40$	−1.00000	−0.158114
$41$	5.85967	0.915126	0.457563	−	0.889177i	$-0.348722\pi$
$41$	5.85967	0.915126	0.457563	+	0.889177i	$0.348722\pi$
$42$	−0.395919	−0.0610917
$43$	2.54426	0.387997	0.193998	−	0.981002i	$-0.437854\pi$
$43$	2.54426	0.387997	0.193998	+	0.981002i	$0.437854\pi$
$44$	−2.94303	−0.443679
$45$	1.68722	0.251516
$46$	4.16600	0.614244
$47$	5.46084	0.796545	0.398273	−	0.917267i	$-0.369610\pi$
$47$	5.46084	0.796545	0.398273	+	0.917267i	$0.369610\pi$
$48$	−1.14577	−0.165377
$49$	−6.88060	−0.982942
$50$	1.00000	0.141421
$51$	5.37298	0.752368
$52$	−5.44236	−0.754720
$53$	8.94020	1.22803	0.614016	−	0.789294i	$-0.289553\pi$
$53$	8.94020	1.22803	0.614016	+	0.789294i	$0.289553\pi$
$54$	5.37046	0.730827
$55$	2.94303	0.396839
$56$	0.345550	0.0461760
$57$	3.77234	0.499658
$58$	−2.64769	−0.347658
$59$	3.69888	0.481554	0.240777	−	0.970581i	$-0.422598\pi$
$59$	3.69888	0.481554	0.240777	+	0.970581i	$0.422598\pi$
$60$	1.14577	0.147918
$61$	4.01040	0.513480	0.256740	−	0.966481i	$-0.417352\pi$
$61$	4.01040	0.513480	0.256740	+	0.966481i	$0.417352\pi$
$62$	1.97604	0.250958
$63$	−0.583017	−0.0734533
$64$	1.00000	0.125000
$65$	5.44236	0.675042
$66$	3.37203	0.415068
$67$	3.34207	0.408299	0.204149	−	0.978940i	$-0.434557\pi$
$67$	3.34207	0.408299	0.204149	+	0.978940i	$0.434557\pi$
$68$	−4.68942	−0.568675
$69$	−4.77327	−0.574634
$70$	−0.345550	−0.0413011
$71$	0.666494	0.0790982	0.0395491	−	0.999218i	$-0.487408\pi$
$71$	0.666494	0.0790982	0.0395491	+	0.999218i	$0.487408\pi$
$72$	−1.68722	−0.198841
$73$	7.11379	0.832606	0.416303	−	0.909226i	$-0.363326\pi$
$73$	7.11379	0.832606	0.416303	+	0.909226i	$0.363326\pi$
$74$	−8.30644	−0.965604
$75$	−1.14577	−0.132302
$76$	−3.29241	−0.377665
$77$	−1.01696	−0.115894
$78$	6.23568	0.706051
$79$	10.0928	1.13553	0.567763	−	0.823192i	$-0.307809\pi$
$79$	10.0928	1.13553	0.567763	+	0.823192i	$0.307809\pi$
$80$	−1.00000	−0.111803
$81$	−1.09164	−0.121294
$82$	5.85967	0.647092
$83$	−10.9935	−1.20670	−0.603349	−	0.797477i	$-0.706167\pi$
$83$	−10.9935	−1.20670	−0.603349	+	0.797477i	$0.706167\pi$
$84$	−0.395919	−0.0431983
$85$	4.68942	0.508639
$86$	2.54426	0.274355
$87$	3.03363	0.325239
$88$	−2.94303	−0.313728
$89$	17.8773	1.89499	0.947495	−	0.319769i	$-0.103605\pi$
$89$	17.8773	1.89499	0.947495	+	0.319769i	$0.103605\pi$
$90$	1.68722	0.177848
$91$	−1.88061	−0.197141
$92$	4.16600	0.434336
$93$	−2.26409	−0.234775
$94$	5.46084	0.563243
$95$	3.29241	0.337794
$96$	−1.14577	−0.116939
$97$	4.74512	0.481794	0.240897	−	0.970551i	$-0.422558\pi$
$97$	4.74512	0.481794	0.240897	+	0.970551i	$0.422558\pi$
$98$	−6.88060	−0.695045
$99$	4.96554	0.499055
$100$	1.00000	0.100000
$101$	−9.47745	−0.943041	−0.471521	−	0.881855i	$-0.656295\pi$
$101$	−9.47745	−0.943041	−0.471521	+	0.881855i	$0.656295\pi$
$102$	5.37298	0.532004
$103$	19.4574	1.91719	0.958595	−	0.284771i	$-0.0919177\pi$
$103$	19.4574	1.91719	0.958595	+	0.284771i	$0.0919177\pi$
$104$	−5.44236	−0.533667
$105$	0.395919	0.0386378
$106$	8.94020	0.868349
$107$	−17.8094	−1.72170	−0.860848	−	0.508863i	$-0.830066\pi$
$107$	−17.8094	−1.72170	−0.860848	+	0.508863i	$0.830066\pi$
$108$	5.37046	0.516773
$109$	6.47669	0.620354	0.310177	−	0.950679i	$-0.399612\pi$
$109$	6.47669	0.620354	0.310177	+	0.950679i	$0.399612\pi$
$110$	2.94303	0.280607
$111$	9.51724	0.903337
$112$	0.345550	0.0326514
$113$	−10.2749	−0.966586	−0.483293	−	0.875459i	$-0.660559\pi$
$113$	−10.2749	−0.966586	−0.483293	+	0.875459i	$0.660559\pi$
$114$	3.77234	0.353312
$115$	−4.16600	−0.388482
$116$	−2.64769	−0.245831
$117$	9.18245	0.848918
$118$	3.69888	0.340510
$119$	−1.62043	−0.148544
$120$	1.14577	0.104594
$121$	−2.33855	−0.212595
$122$	4.01040	0.363085
$123$	−6.71382	−0.605364
$124$	1.97604	0.177454
$125$	−1.00000	−0.0894427
$126$	−0.583017	−0.0519393
$127$	4.32859	0.384100	0.192050	−	0.981385i	$-0.438486\pi$
$127$	4.32859	0.384100	0.192050	+	0.981385i	$0.438486\pi$
$128$	1.00000	0.0883883
$129$	−2.91513	−0.256663
$130$	5.44236	0.477327
$131$	−4.13086	−0.360915	−0.180457	−	0.983583i	$-0.557758\pi$
$131$	−4.13086	−0.360915	−0.180457	+	0.983583i	$0.557758\pi$
$132$	3.37203	0.293498
$133$	−1.13769	−0.0986503
$134$	3.34207	0.288711
$135$	−5.37046	−0.462216
$136$	−4.68942	−0.402114
$137$	−10.6482	−0.909739	−0.454870	−	0.890558i	$-0.650314\pi$
$137$	−10.6482	−0.909739	−0.454870	+	0.890558i	$0.650314\pi$
$138$	−4.77327	−0.406328
$139$	21.5601	1.82870	0.914351	−	0.404922i	$-0.132701\pi$
$139$	21.5601	1.82870	0.914351	+	0.404922i	$0.132701\pi$
$140$	−0.345550	−0.0292043
$141$	−6.25685	−0.526922
$142$	0.666494	0.0559309
$143$	16.0171	1.33941
$144$	−1.68722	−0.140601
$145$	2.64769	0.219878
$146$	7.11379	0.588741
$147$	7.88356	0.650225
$148$	−8.30644	−0.682785
$149$	−17.3963	−1.42516	−0.712580	−	0.701590i	$-0.752474\pi$
$149$	−17.3963	−1.42516	−0.712580	+	0.701590i	$0.752474\pi$
$150$	−1.14577	−0.0935515
$151$	2.87530	0.233988	0.116994	−	0.993133i	$-0.462674\pi$
$151$	2.87530	0.233988	0.116994	+	0.993133i	$0.462674\pi$
$152$	−3.29241	−0.267050
$153$	7.91207	0.639653
$154$	−1.01696	−0.0819493
$155$	−1.97604	−0.158720
$156$	6.23568	0.499254
$157$	−19.8999	−1.58819	−0.794094	−	0.607796i	$-0.792054\pi$
$157$	−19.8999	−1.58819	−0.794094	+	0.607796i	$0.792054\pi$
$158$	10.0928	0.802937
$159$	−10.2434	−0.812354
$160$	−1.00000	−0.0790569
$161$	1.43956	0.113453
$162$	−1.09164	−0.0857676
$163$	25.0275	1.96031	0.980153	−	0.198240i	$-0.0635226\pi$
$163$	25.0275	1.96031	0.980153	+	0.198240i	$0.0635226\pi$
$164$	5.85967	0.457563
$165$	−3.37203	−0.262512
$166$	−10.9935	−0.853264
$167$	20.4350	1.58131	0.790654	−	0.612263i	$-0.209741\pi$
$167$	20.4350	1.58131	0.790654	+	0.612263i	$0.209741\pi$
$168$	−0.395919	−0.0305458
$169$	16.6193	1.27841
$170$	4.68942	0.359662
$171$	5.55501	0.424803
$172$	2.54426	0.193998
$173$	8.69676	0.661202	0.330601	−	0.943771i	$-0.392748\pi$
$173$	8.69676	0.661202	0.330601	+	0.943771i	$0.392748\pi$
$174$	3.03363	0.229979
$175$	0.345550	0.0261211
$176$	−2.94303	−0.221840
$177$	−4.23806	−0.318552
$178$	17.8773	1.33996
$179$	14.9832	1.11990	0.559949	−	0.828527i	$-0.310821\pi$
$179$	14.9832	1.11990	0.559949	+	0.828527i	$0.310821\pi$
$180$	1.68722	0.125758
$181$	−22.0825	−1.64138	−0.820690	−	0.571374i	$-0.806411\pi$
$181$	−22.0825	−1.64138	−0.820690	+	0.571374i	$0.806411\pi$
$182$	−1.88061	−0.139400
$183$	−4.59499	−0.339671
$184$	4.16600	0.307122
$185$	8.30644	0.610702
$186$	−2.26409	−0.166011
$187$	13.8011	1.00924
$188$	5.46084	0.398273
$189$	1.85576	0.134987
$190$	3.29241	0.238857
$191$	−22.8968	−1.65675	−0.828377	−	0.560172i	$-0.810735\pi$
$191$	−22.8968	−1.65675	−0.828377	+	0.560172i	$0.810735\pi$
$192$	−1.14577	−0.0826886
$193$	13.1396	0.945810	0.472905	−	0.881114i	$-0.343205\pi$
$193$	13.1396	0.945810	0.472905	+	0.881114i	$0.343205\pi$
$194$	4.74512	0.340680
$195$	−6.23568	−0.446546
$196$	−6.88060	−0.491471
$197$	−14.1330	−1.00694	−0.503469	−	0.864013i	$-0.667943\pi$
$197$	−14.1330	−1.00694	−0.503469	+	0.864013i	$0.667943\pi$
$198$	4.96554	0.352886
$199$	−15.9514	−1.13076	−0.565381	−	0.824830i	$-0.691271\pi$
$199$	−15.9514	−1.13076	−0.565381	+	0.824830i	$0.691271\pi$
$200$	1.00000	0.0707107
$201$	−3.82923	−0.270093
$202$	−9.47745	−0.666831
$203$	−0.914906	−0.0642138
$204$	5.37298	0.376184
$205$	−5.85967	−0.409257
$206$	19.4574	1.35566
$207$	−7.02895	−0.488546
$208$	−5.44236	−0.377360
$209$	9.68968	0.670249
$210$	0.395919	0.0273210
$211$	−17.2960	−1.19071	−0.595354	−	0.803464i	$-0.702988\pi$
$211$	−17.2960	−1.19071	−0.595354	+	0.803464i	$0.702988\pi$
$212$	8.94020	0.614016
$213$	−0.763646	−0.0523242
$214$	−17.8094	−1.21742
$215$	−2.54426	−0.173517
$216$	5.37046	0.365414
$217$	0.682821	0.0463529
$218$	6.47669	0.438656
$219$	−8.15074	−0.550776
$220$	2.94303	0.198419
$221$	25.5215	1.71676
$222$	9.51724	0.638756
$223$	−16.2423	−1.08767	−0.543833	−	0.839193i	$-0.683028\pi$
$223$	−16.2423	−1.08767	−0.543833	+	0.839193i	$0.683028\pi$
$224$	0.345550	0.0230880
$225$	−1.68722	−0.112481
$226$	−10.2749	−0.683479
$227$	−15.1362	−1.00463	−0.502313	−	0.864686i	$-0.667518\pi$
$227$	−15.1362	−1.00463	−0.502313	+	0.864686i	$0.667518\pi$
$228$	3.77234	0.249829
$229$	−8.90349	−0.588359	−0.294180	−	0.955750i	$-0.595046\pi$
$229$	−8.90349	−0.588359	−0.294180	+	0.955750i	$0.595046\pi$
$230$	−4.16600	−0.274698
$231$	1.16520	0.0766648
$232$	−2.64769	−0.173829
$233$	4.30517	0.282041	0.141021	−	0.990007i	$-0.454962\pi$
$233$	4.30517	0.282041	0.141021	+	0.990007i	$0.454962\pi$
$234$	9.18245	0.600275
$235$	−5.46084	−0.356226
$236$	3.69888	0.240777
$237$	−11.5640	−0.751160
$238$	−1.62043	−0.105037
$239$	13.7120	0.886952	0.443476	−	0.896286i	$-0.353745\pi$
$239$	13.7120	0.886952	0.443476	+	0.896286i	$0.353745\pi$
$240$	1.14577	0.0739589
$241$	−19.9414	−1.28454	−0.642268	−	0.766480i	$-0.722007\pi$
$241$	−19.9414	−1.28454	−0.642268	+	0.766480i	$0.722007\pi$
$242$	−2.33855	−0.150328
$243$	−14.8606	−0.953309
$244$	4.01040	0.256740
$245$	6.88060	0.439585
$246$	−6.71382	−0.428057
$247$	17.9185	1.14013
$248$	1.97604	0.125479
$249$	12.5960	0.798242
$250$	−1.00000	−0.0632456
$251$	20.5416	1.29657	0.648286	−	0.761397i	$-0.275486\pi$
$251$	20.5416	1.29657	0.648286	+	0.761397i	$0.275486\pi$
$252$	−0.583017	−0.0367266
$253$	−12.2607	−0.770823
$254$	4.32859	0.271600
$255$	−5.37298	−0.336469
$256$	1.00000	0.0625000
$257$	17.6681	1.10211	0.551053	−	0.834470i	$-0.314226\pi$
$257$	17.6681	1.10211	0.551053	+	0.834470i	$0.314226\pi$
$258$	−2.91513	−0.181488
$259$	−2.87029	−0.178351
$260$	5.44236	0.337521
$261$	4.46722	0.276514
$262$	−4.13086	−0.255205
$263$	−18.6087	−1.14746	−0.573730	−	0.819044i	$-0.694504\pi$
$263$	−18.6087	−1.14746	−0.573730	+	0.819044i	$0.694504\pi$
$264$	3.37203	0.207534
$265$	−8.94020	−0.549192
$266$	−1.13769	−0.0697563
$267$	−20.4832	−1.25355
$268$	3.34207	0.204149
$269$	3.23898	0.197484	0.0987422	−	0.995113i	$-0.468518\pi$
$269$	3.23898	0.197484	0.0987422	+	0.995113i	$0.468518\pi$
$270$	−5.37046	−0.326836
$271$	0.190381	0.0115648	0.00578240	−	0.999983i	$-0.498159\pi$
$271$	0.190381	0.0115648	0.00578240	+	0.999983i	$0.498159\pi$
$272$	−4.68942	−0.284338
$273$	2.15474	0.130411
$274$	−10.6482	−0.643283
$275$	−2.94303	−0.177472
$276$	−4.77327	−0.287317
$277$	28.5478	1.71527	0.857636	−	0.514257i	$-0.171932\pi$
$277$	28.5478	1.71527	0.857636	+	0.514257i	$0.171932\pi$
$278$	21.5601	1.29309
$279$	−3.33402	−0.199602
$280$	−0.345550	−0.0206505
$281$	23.8544	1.42304	0.711518	−	0.702668i	$-0.248008\pi$
$281$	23.8544	1.42304	0.711518	+	0.702668i	$0.248008\pi$
$282$	−6.25685	−0.372590
$283$	13.5078	0.802957	0.401478	−	0.915869i	$-0.368497\pi$
$283$	13.5078	0.802957	0.401478	+	0.915869i	$0.368497\pi$
$284$	0.666494	0.0395491
$285$	−3.77234	−0.223454
$286$	16.0171	0.947108
$287$	2.02481	0.119520
$288$	−1.68722	−0.0994203
$289$	4.99063	0.293567
$290$	2.64769	0.155477
$291$	−5.43680	−0.318711
$292$	7.11379	0.416303
$293$	13.5190	0.789789	0.394894	−	0.918726i	$-0.370781\pi$
$293$	13.5190	0.789789	0.394894	+	0.918726i	$0.370781\pi$
$294$	7.88356	0.459779
$295$	−3.69888	−0.215357
$296$	−8.30644	−0.482802
$297$	−15.8054	−0.917125
$298$	−17.3963	−1.00774
$299$	−22.6729	−1.31121
$300$	−1.14577	−0.0661509
$301$	0.879169	0.0506745
$302$	2.87530	0.165455
$303$	10.8589	0.623830
$304$	−3.29241	−0.188833
$305$	−4.01040	−0.229635
$306$	7.91207	0.452303
$307$	13.0933	0.747274	0.373637	−	0.927575i	$-0.378111\pi$
$307$	13.0933	0.747274	0.373637	+	0.927575i	$0.378111\pi$
$308$	−1.01696	−0.0579469
$309$	−22.2936	−1.26824
$310$	−1.97604	−0.112232
$311$	14.5138	0.823004	0.411502	−	0.911409i	$-0.365004\pi$
$311$	14.5138	0.823004	0.411502	+	0.911409i	$0.365004\pi$
$312$	6.23568	0.353026
$313$	15.7820	0.892050	0.446025	−	0.895020i	$-0.352839\pi$
$313$	15.7820	0.892050	0.446025	+	0.895020i	$0.352839\pi$
$314$	−19.8999	−1.12302
$315$	0.583017	0.0328493
$316$	10.0928	0.567763
$317$	10.2629	0.576420	0.288210	−	0.957567i	$-0.406940\pi$
$317$	10.2629	0.576420	0.288210	+	0.957567i	$0.406940\pi$
$318$	−10.2434	−0.574421
$319$	7.79223	0.436281
$320$	−1.00000	−0.0559017
$321$	20.4054	1.13892
$322$	1.43956	0.0802236
$323$	15.4395	0.859076
$324$	−1.09164	−0.0606468
$325$	−5.44236	−0.301888
$326$	25.0275	1.38615
$327$	−7.42077	−0.410370
$328$	5.85967	0.323546
$329$	1.88699	0.104033
$330$	−3.37203	−0.185624
$331$	−34.1565	−1.87741	−0.938706	−	0.344718i	$-0.887974\pi$
$331$	−34.1565	−1.87741	−0.938706	+	0.344718i	$0.887974\pi$
$332$	−10.9935	−0.603349
$333$	14.0148	0.768005
$334$	20.4350	1.11815
$335$	−3.34207	−0.182597
$336$	−0.395919	−0.0215992
$337$	−23.6293	−1.28717	−0.643584	−	0.765376i	$-0.722553\pi$
$337$	−23.6293	−1.28717	−0.643584	+	0.765376i	$0.722553\pi$
$338$	16.6193	0.903970
$339$	11.7727	0.639405
$340$	4.68942	0.254319
$341$	−5.81557	−0.314931
$342$	5.55501	0.300381
$343$	−4.79643	−0.258983
$344$	2.54426	0.137177
$345$	4.77327	0.256984
$346$	8.69676	0.467541
$347$	15.4466	0.829216	0.414608	−	0.910000i	$-0.363919\pi$
$347$	15.4466	0.829216	0.414608	+	0.910000i	$0.363919\pi$
$348$	3.03363	0.162620
$349$	26.5492	1.42115	0.710573	−	0.703624i	$-0.248436\pi$
$349$	26.5492	1.42115	0.710573	+	0.703624i	$0.248436\pi$
$350$	0.345550	0.0184704
$351$	−29.2280	−1.56007
$352$	−2.94303	−0.156864
$353$	34.5192	1.83727	0.918636	−	0.395105i	$-0.129292\pi$
$353$	34.5192	1.83727	0.918636	+	0.395105i	$0.129292\pi$
$354$	−4.23806	−0.225250
$355$	−0.666494	−0.0353738
$356$	17.8773	0.947495
$357$	1.85663	0.0982633
$358$	14.9832	0.791887
$359$	−13.4973	−0.712360	−0.356180	−	0.934417i	$-0.615921\pi$
$359$	−13.4973	−0.712360	−0.356180	+	0.934417i	$0.615921\pi$
$360$	1.68722	0.0889242
$361$	−8.16003	−0.429475
$362$	−22.0825	−1.16063
$363$	2.67943	0.140634
$364$	−1.88061	−0.0985705
$365$	−7.11379	−0.372353
$366$	−4.59499	−0.240184
$367$	1.72683	0.0901398	0.0450699	−	0.998984i	$-0.485649\pi$
$367$	1.72683	0.0901398	0.0450699	+	0.998984i	$0.485649\pi$
$368$	4.16600	0.217168
$369$	−9.88654	−0.514673
$370$	8.30644	0.431831
$371$	3.08928	0.160388
$372$	−2.26409	−0.117387
$373$	35.5781	1.84217	0.921083	−	0.389365i	$-0.127306\pi$
$373$	35.5781	1.84217	0.921083	+	0.389365i	$0.127306\pi$
$374$	13.8011	0.713639
$375$	1.14577	0.0591672
$376$	5.46084	0.281621
$377$	14.4097	0.742135
$378$	1.85576	0.0954500
$379$	−19.6326	−1.00846	−0.504230	−	0.863570i	$-0.668223\pi$
$379$	−19.6326	−1.00846	−0.504230	+	0.863570i	$0.668223\pi$
$380$	3.29241	0.168897
$381$	−4.95955	−0.254086
$382$	−22.8968	−1.17150
$383$	−17.0507	−0.871252	−0.435626	−	0.900128i	$-0.643473\pi$
$383$	−17.0507	−0.871252	−0.435626	+	0.900128i	$0.643473\pi$
$384$	−1.14577	−0.0584697
$385$	1.01696	0.0518293
$386$	13.1396	0.668788
$387$	−4.29273	−0.218212
$388$	4.74512	0.240897
$389$	16.5258	0.837894	0.418947	−	0.908011i	$-0.362399\pi$
$389$	16.5258	0.837894	0.418947	+	0.908011i	$0.362399\pi$
$390$	−6.23568	−0.315756
$391$	−19.5361	−0.987984
$392$	−6.88060	−0.347523
$393$	4.73300	0.238748
$394$	−14.1330	−0.712013
$395$	−10.0928	−0.507822
$396$	4.96554	0.249528
$397$	35.9502	1.80429	0.902144	−	0.431434i	$-0.141992\pi$
$397$	35.9502	1.80429	0.902144	+	0.431434i	$0.141992\pi$
$398$	−15.9514	−0.799570
$399$	1.30353	0.0652581
$400$	1.00000	0.0500000
$401$	−16.4555	−0.821750	−0.410875	−	0.911692i	$-0.634777\pi$
$401$	−16.4555	−0.821750	−0.410875	+	0.911692i	$0.634777\pi$
$402$	−3.82923	−0.190985
$403$	−10.7543	−0.535712
$404$	−9.47745	−0.471521
$405$	1.09164	0.0542442
$406$	−0.914906	−0.0454060
$407$	24.4461	1.21175
$408$	5.37298	0.266002
$409$	21.3965	1.05799	0.528994	−	0.848625i	$-0.322569\pi$
$409$	21.3965	1.05799	0.528994	+	0.848625i	$0.322569\pi$
$410$	−5.85967	−0.289388
$411$	12.2004	0.601801
$412$	19.4574	0.958595
$413$	1.27815	0.0628935
$414$	−7.02895	−0.345454
$415$	10.9935	0.539652
$416$	−5.44236	−0.266834
$417$	−24.7028	−1.20970
$418$	9.68968	0.473938
$419$	2.96844	0.145018	0.0725090	−	0.997368i	$-0.476899\pi$
$419$	2.96844	0.145018	0.0725090	+	0.997368i	$0.476899\pi$
$420$	0.395919	0.0193189
$421$	5.97765	0.291333	0.145666	−	0.989334i	$-0.453467\pi$
$421$	5.97765	0.291333	0.145666	+	0.989334i	$0.453467\pi$
$422$	−17.2960	−0.841958
$423$	−9.21363	−0.447982
$424$	8.94020	0.434175
$425$	−4.68942	−0.227470
$426$	−0.763646	−0.0369988
$427$	1.38579	0.0670632
$428$	−17.8094	−0.860848
$429$	−18.3518	−0.886034
$430$	−2.54426	−0.122695
$431$	−9.44746	−0.455068	−0.227534	−	0.973770i	$-0.573066\pi$
$431$	−9.44746	−0.455068	−0.227534	+	0.973770i	$0.573066\pi$
$432$	5.37046	0.258386
$433$	−40.1216	−1.92812	−0.964061	−	0.265681i	$-0.914403\pi$
$433$	−40.1216	−1.92812	−0.964061	+	0.265681i	$0.914403\pi$
$434$	0.682821	0.0327765
$435$	−3.03363	−0.145451
$436$	6.47669	0.310177
$437$	−13.7162	−0.656135
$438$	−8.15074	−0.389458
$439$	12.7114	0.606682	0.303341	−	0.952882i	$-0.401898\pi$
$439$	12.7114	0.606682	0.303341	+	0.952882i	$0.401898\pi$
$440$	2.94303	0.140304
$441$	11.6091	0.552813
$442$	25.5215	1.21393
$443$	11.1537	0.529926	0.264963	−	0.964259i	$-0.414640\pi$
$443$	11.1537	0.529926	0.264963	+	0.964259i	$0.414640\pi$
$444$	9.51724	0.451668
$445$	−17.8773	−0.847466
$446$	−16.2423	−0.769096
$447$	19.9321	0.942757
$448$	0.345550	0.0163257
$449$	18.6910	0.882082	0.441041	−	0.897487i	$-0.354609\pi$
$449$	18.6910	0.882082	0.441041	+	0.897487i	$0.354609\pi$
$450$	−1.68722	−0.0795362
$451$	−17.2452	−0.812045
$452$	−10.2749	−0.483293
$453$	−3.29442	−0.154785
$454$	−15.1362	−0.710378
$455$	1.88061	0.0881641
$456$	3.77234	0.176656
$457$	−12.2430	−0.572705	−0.286352	−	0.958124i	$-0.592443\pi$
$457$	−12.2430	−0.572705	−0.286352	+	0.958124i	$0.592443\pi$
$458$	−8.90349	−0.416033
$459$	−25.1843	−1.17550
$460$	−4.16600	−0.194241
$461$	14.9946	0.698369	0.349184	−	0.937054i	$-0.386459\pi$
$461$	14.9946	0.698369	0.349184	+	0.937054i	$0.386459\pi$
$462$	1.16520	0.0542102
$463$	25.4255	1.18162	0.590811	−	0.806810i	$-0.298808\pi$
$463$	25.4255	1.18162	0.590811	+	0.806810i	$0.298808\pi$
$464$	−2.64769	−0.122916
$465$	2.26409	0.104995
$466$	4.30517	0.199433
$467$	28.0434	1.29769	0.648847	−	0.760919i	$-0.275252\pi$
$467$	28.0434	1.29769	0.648847	+	0.760919i	$0.275252\pi$
$468$	9.18245	0.424459
$469$	1.15485	0.0533260
$470$	−5.46084	−0.251890
$471$	22.8007	1.05060
$472$	3.69888	0.170255
$473$	−7.48785	−0.344292
$474$	−11.5640	−0.531150
$475$	−3.29241	−0.151066
$476$	−1.62043	−0.0742721
$477$	−15.0841	−0.690652
$478$	13.7120	0.627170
$479$	38.4752	1.75798	0.878989	−	0.476842i	$-0.158219\pi$
$479$	38.4752	1.75798	0.878989	+	0.476842i	$0.158219\pi$
$480$	1.14577	0.0522969
$481$	45.2066	2.06125
$482$	−19.9414	−0.908305
$483$	−1.64940	−0.0750503
$484$	−2.33855	−0.106298
$485$	−4.74512	−0.215465
$486$	−14.8606	−0.674091
$487$	−4.74878	−0.215188	−0.107594	−	0.994195i	$-0.534315\pi$
$487$	−4.74878	−0.215188	−0.107594	+	0.994195i	$0.534315\pi$
$488$	4.01040	0.181542
$489$	−28.6757	−1.29676
$490$	6.88060	0.310834
$491$	1.07914	0.0487010	0.0243505	−	0.999703i	$-0.492248\pi$
$491$	1.07914	0.0487010	0.0243505	+	0.999703i	$0.492248\pi$
$492$	−6.71382	−0.302682
$493$	12.4161	0.559193
$494$	17.9185	0.806191
$495$	−4.96554	−0.223184
$496$	1.97604	0.0887270
$497$	0.230307	0.0103307
$498$	12.5960	0.564442
$499$	25.5861	1.14539	0.572695	−	0.819768i	$-0.305898\pi$
$499$	25.5861	1.14539	0.572695	+	0.819768i	$0.305898\pi$
$500$	−1.00000	−0.0447214
$501$	−23.4138	−1.04605
$502$	20.5416	0.916815
$503$	9.89151	0.441041	0.220520	−	0.975382i	$-0.429224\pi$
$503$	9.89151	0.441041	0.220520	+	0.975382i	$0.429224\pi$
$504$	−0.583017	−0.0259697
$505$	9.47745	0.421741
$506$	−12.2607	−0.545054
$507$	−19.0418	−0.845678
$508$	4.32859	0.192050
$509$	34.1853	1.51524	0.757618	−	0.652698i	$-0.226363\pi$
$509$	34.1853	1.51524	0.757618	+	0.652698i	$0.226363\pi$
$510$	−5.37298	−0.237920
$511$	2.45817	0.108743
$512$	1.00000	0.0441942
$513$	−17.6818	−0.780669
$514$	17.6681	0.779307
$515$	−19.4574	−0.857394
$516$	−2.91513	−0.128332
$517$	−16.0714	−0.706821
$518$	−2.87029	−0.126113
$519$	−9.96446	−0.437391
$520$	5.44236	0.238663
$521$	22.7476	0.996592	0.498296	−	0.867007i	$-0.333959\pi$
$521$	22.7476	0.996592	0.498296	+	0.867007i	$0.333959\pi$
$522$	4.46722	0.195525
$523$	−32.0937	−1.40336	−0.701679	−	0.712493i	$-0.747566\pi$
$523$	−32.0937	−1.40336	−0.701679	+	0.712493i	$0.747566\pi$
$524$	−4.13086	−0.180457
$525$	−0.395919	−0.0172793
$526$	−18.6087	−0.811377
$527$	−9.26650	−0.403655
$528$	3.37203	0.146749
$529$	−5.64442	−0.245410
$530$	−8.94020	−0.388338
$531$	−6.24082	−0.270829
$532$	−1.13769	−0.0493252
$533$	−31.8904	−1.38133
$534$	−20.4832	−0.886396
$535$	17.8094	0.769965
$536$	3.34207	0.144355
$537$	−17.1673	−0.740822
$538$	3.23898	0.139643
$539$	20.2498	0.872222
$540$	−5.37046	−0.231108
$541$	−11.2120	−0.482039	−0.241020	−	0.970520i	$-0.577482\pi$
$541$	−11.2120	−0.482039	−0.241020	+	0.970520i	$0.577482\pi$
$542$	0.190381	0.00817756
$543$	25.3014	1.08579
$544$	−4.68942	−0.201057
$545$	−6.47669	−0.277431
$546$	2.15474	0.0922142
$547$	8.51225	0.363958	0.181979	−	0.983302i	$-0.441750\pi$
$547$	8.51225	0.363958	0.181979	+	0.983302i	$0.441750\pi$
$548$	−10.6482	−0.454870
$549$	−6.76643	−0.288784
$550$	−2.94303	−0.125491
$551$	8.71727	0.371368
$552$	−4.77327	−0.203164
$553$	3.48755	0.148306
$554$	28.5478	1.21288
$555$	−9.51724	−0.403985
$556$	21.5601	0.914351
$557$	−33.8711	−1.43517	−0.717583	−	0.696473i	$-0.754751\pi$
$557$	−33.8711	−1.43517	−0.717583	+	0.696473i	$0.754751\pi$
$558$	−3.33402	−0.141140
$559$	−13.8468	−0.585657
$560$	−0.345550	−0.0146021
$561$	−15.8129	−0.667620
$562$	23.8544	1.00624
$563$	30.1386	1.27019	0.635096	−	0.772433i	$-0.280960\pi$
$563$	30.1386	1.27019	0.635096	+	0.772433i	$0.280960\pi$
$564$	−6.25685	−0.263461
$565$	10.2749	0.432270
$566$	13.5078	0.567776
$567$	−0.377217	−0.0158416
$568$	0.666494	0.0279654
$569$	13.4055	0.561987	0.280994	−	0.959710i	$-0.409336\pi$
$569$	13.4055	0.561987	0.280994	+	0.959710i	$0.409336\pi$
$570$	−3.77234	−0.158006
$571$	−24.4997	−1.02528	−0.512639	−	0.858604i	$-0.671332\pi$
$571$	−24.4997	−1.02528	−0.512639	+	0.858604i	$0.671332\pi$
$572$	16.0171	0.669707
$573$	26.2344	1.09596
$574$	2.02481	0.0845138
$575$	4.16600	0.173734
$576$	−1.68722	−0.0703007
$577$	10.0912	0.420103	0.210051	−	0.977690i	$-0.432637\pi$
$577$	10.0912	0.420103	0.210051	+	0.977690i	$0.432637\pi$
$578$	4.99063	0.207583
$579$	−15.0549	−0.625661
$580$	2.64769	0.109939
$581$	−3.79881	−0.157601
$582$	−5.43680	−0.225363
$583$	−26.3113	−1.08970
$584$	7.11379	0.294371
$585$	−9.18245	−0.379647
$586$	13.5190	0.558465
$587$	−12.6250	−0.521091	−0.260546	−	0.965462i	$-0.583902\pi$
$587$	−12.6250	−0.521091	−0.260546	+	0.965462i	$0.583902\pi$
$588$	7.88356	0.325113
$589$	−6.50595	−0.268073
$590$	−3.69888	−0.152281
$591$	16.1932	0.666098
$592$	−8.30644	−0.341393
$593$	36.8706	1.51409	0.757047	−	0.653360i	$-0.226641\pi$
$593$	36.8706	1.51409	0.757047	+	0.653360i	$0.226641\pi$
$594$	−15.8054	−0.648505
$595$	1.62043	0.0664310
$596$	−17.3963	−0.712580
$597$	18.2766	0.748010
$598$	−22.6729	−0.927163
$599$	−39.0843	−1.59694	−0.798470	−	0.602035i	$-0.794357\pi$
$599$	−39.0843	−1.59694	−0.798470	+	0.602035i	$0.794357\pi$
$600$	−1.14577	−0.0467757
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	0.879169	0.0358323
$603$	−5.63880	−0.229630
$604$	2.87530	0.116994
$605$	2.33855	0.0950756
$606$	10.8589	0.441114
$607$	−39.5369	−1.60475	−0.802377	−	0.596817i	$-0.796432\pi$
$607$	−39.5369	−1.60475	−0.802377	+	0.596817i	$0.796432\pi$
$608$	−3.29241	−0.133525
$609$	1.04827	0.0424780
$610$	−4.01040	−0.162377
$611$	−29.7199	−1.20234
$612$	7.91207	0.319826
$613$	7.72421	0.311978	0.155989	−	0.987759i	$-0.450144\pi$
$613$	7.72421	0.311978	0.155989	+	0.987759i	$0.450144\pi$
$614$	13.0933	0.528403
$615$	6.71382	0.270727
$616$	−1.01696	−0.0409746
$617$	−19.8679	−0.799852	−0.399926	−	0.916547i	$-0.630964\pi$
$617$	−19.8679	−0.799852	−0.399926	+	0.916547i	$0.630964\pi$
$618$	−22.2936	−0.896780
$619$	1.57320	0.0632324	0.0316162	−	0.999500i	$-0.489935\pi$
$619$	1.57320	0.0632324	0.0316162	+	0.999500i	$0.489935\pi$
$620$	−1.97604	−0.0793599
$621$	22.3734	0.897812
$622$	14.5138	0.581951
$623$	6.17750	0.247496
$624$	6.23568	0.249627
$625$	1.00000	0.0400000
$626$	15.7820	0.630775
$627$	−11.1021	−0.443376
$628$	−19.8999	−0.794094
$629$	38.9524	1.55313
$630$	0.583017	0.0232280
$631$	−19.7331	−0.785564	−0.392782	−	0.919632i	$-0.628487\pi$
$631$	−19.7331	−0.785564	−0.392782	+	0.919632i	$0.628487\pi$
$632$	10.0928	0.401469
$633$	19.8172	0.787664
$634$	10.2629	0.407591
$635$	−4.32859	−0.171775
$636$	−10.2434	−0.406177
$637$	37.4467	1.48369
$638$	7.79223	0.308497
$639$	−1.12452	−0.0444853
$640$	−1.00000	−0.0395285
$641$	20.7095	0.817976	0.408988	−	0.912540i	$-0.365882\pi$
$641$	20.7095	0.817976	0.408988	+	0.912540i	$0.365882\pi$
$642$	20.4054	0.805336
$643$	−0.863391	−0.0340488	−0.0170244	−	0.999855i	$-0.505419\pi$
$643$	−0.863391	−0.0340488	−0.0170244	+	0.999855i	$0.505419\pi$
$644$	1.43956	0.0567266
$645$	2.91513	0.114783
$646$	15.4395	0.607459
$647$	0.738834	0.0290466	0.0145233	−	0.999895i	$-0.495377\pi$
$647$	0.738834	0.0290466	0.0145233	+	0.999895i	$0.495377\pi$
$648$	−1.09164	−0.0428838
$649$	−10.8859	−0.427310
$650$	−5.44236	−0.213467
$651$	−0.782354	−0.0306629
$652$	25.0275	0.980153
$653$	−16.4756	−0.644740	−0.322370	−	0.946614i	$-0.604479\pi$
$653$	−16.4756	−0.644740	−0.322370	+	0.946614i	$0.604479\pi$
$654$	−7.42077	−0.290175
$655$	4.13086	0.161406
$656$	5.85967	0.228782
$657$	−12.0025	−0.468262
$658$	1.88699	0.0735626
$659$	−41.1611	−1.60341	−0.801705	−	0.597720i	$-0.796073\pi$
$659$	−41.1611	−1.60341	−0.801705	+	0.597720i	$0.796073\pi$
$660$	−3.37203	−0.131256
$661$	−44.2288	−1.72030	−0.860151	−	0.510039i	$-0.829631\pi$
$661$	−44.2288	−1.72030	−0.860151	+	0.510039i	$0.829631\pi$
$662$	−34.1565	−1.32753
$663$	−29.2417	−1.13565
$664$	−10.9935	−0.426632
$665$	1.13769	0.0441178
$666$	14.0148	0.543061
$667$	−11.0303	−0.427094
$668$	20.4350	0.790654
$669$	18.6099	0.719501
$670$	−3.34207	−0.129115
$671$	−11.8028	−0.455640
$672$	−0.395919	−0.0152729
$673$	9.56297	0.368626	0.184313	−	0.982868i	$-0.440994\pi$
$673$	9.56297	0.368626	0.184313	+	0.982868i	$0.440994\pi$
$674$	−23.6293	−0.910165
$675$	5.37046	0.206709
$676$	16.6193	0.639203
$677$	−31.3514	−1.20493	−0.602467	−	0.798144i	$-0.705815\pi$
$677$	−31.3514	−1.20493	−0.602467	+	0.798144i	$0.705815\pi$
$678$	11.7727	0.452128
$679$	1.63967	0.0629249
$680$	4.68942	0.179831
$681$	17.3426	0.664570
$682$	−5.81557	−0.222690
$683$	23.8948	0.914308	0.457154	−	0.889388i	$-0.348869\pi$
$683$	23.8948	0.914308	0.457154	+	0.889388i	$0.348869\pi$
$684$	5.55501	0.212401
$685$	10.6482	0.406848
$686$	−4.79643	−0.183129
$687$	10.2013	0.389205
$688$	2.54426	0.0969991
$689$	−48.6558	−1.85364
$690$	4.77327	0.181715
$691$	−13.0174	−0.495207	−0.247603	−	0.968861i	$-0.579643\pi$
$691$	−13.0174	−0.495207	−0.247603	+	0.968861i	$0.579643\pi$
$692$	8.69676	0.330601
$693$	1.71584	0.0651794
$694$	15.4466	0.586344
$695$	−21.5601	−0.817821
$696$	3.03363	0.114989
$697$	−27.4784	−1.04082
$698$	26.5492	1.00490
$699$	−4.93272	−0.186573
$700$	0.345550	0.0130605
$701$	2.82024	0.106519	0.0532595	−	0.998581i	$-0.483039\pi$
$701$	2.82024	0.106519	0.0532595	+	0.998581i	$0.483039\pi$
$702$	−29.2280	−1.10314
$703$	27.3482	1.03146
$704$	−2.94303	−0.110920
$705$	6.25685	0.235647
$706$	34.5192	1.29915
$707$	−3.27493	−0.123166
$708$	−4.23806	−0.159276
$709$	−9.17136	−0.344438	−0.172219	−	0.985059i	$-0.555094\pi$
$709$	−9.17136	−0.344438	−0.172219	+	0.985059i	$0.555094\pi$
$710$	−0.666494	−0.0250131
$711$	−17.0287	−0.638626
$712$	17.8773	0.669980
$713$	8.23221	0.308299
$714$	1.85663	0.0694827
$715$	−16.0171	−0.599004
$716$	14.9832	0.559949
$717$	−15.7107	−0.586727
$718$	−13.4973	−0.503715
$719$	−9.96054	−0.371465	−0.185733	−	0.982600i	$-0.559466\pi$
$719$	−9.96054	−0.371465	−0.185733	+	0.982600i	$0.559466\pi$
$720$	1.68722	0.0628789
$721$	6.72348	0.250396
$722$	−8.16003	−0.303685
$723$	22.8482	0.849733
$724$	−22.0825	−0.820690
$725$	−2.64769	−0.0983326
$726$	2.67943	0.0994431
$727$	−6.02817	−0.223572	−0.111786	−	0.993732i	$-0.535657\pi$
$727$	−6.02817	−0.223572	−0.111786	+	0.993732i	$0.535657\pi$
$728$	−1.88061	−0.0696999
$729$	20.3017	0.751916
$730$	−7.11379	−0.263293
$731$	−11.9311	−0.441288
$732$	−4.59499	−0.169836
$733$	−17.8445	−0.659101	−0.329551	−	0.944138i	$-0.606897\pi$
$733$	−17.8445	−0.659101	−0.329551	+	0.944138i	$0.606897\pi$
$734$	1.72683	0.0637384
$735$	−7.88356	−0.290789
$736$	4.16600	0.153561
$737$	−9.83582	−0.362307
$738$	−9.88654	−0.363928
$739$	−43.2126	−1.58960	−0.794801	−	0.606870i	$-0.792425\pi$
$739$	−43.2126	−1.58960	−0.794801	+	0.606870i	$0.792425\pi$
$740$	8.30644	0.305351
$741$	−20.5304	−0.754204
$742$	3.08928	0.113411
$743$	37.8247	1.38765	0.693827	−	0.720142i	$-0.255923\pi$
$743$	37.8247	1.38765	0.693827	+	0.720142i	$0.255923\pi$
$744$	−2.26409	−0.0830054
$745$	17.3963	0.637351
$746$	35.5781	1.30261
$747$	18.5485	0.678654
$748$	13.8011	0.504619
$749$	−6.15401	−0.224863
$750$	1.14577	0.0418375
$751$	−0.976260	−0.0356242	−0.0178121	−	0.999841i	$-0.505670\pi$
$751$	−0.976260	−0.0356242	−0.0178121	+	0.999841i	$0.505670\pi$
$752$	5.46084	0.199136
$753$	−23.5359	−0.857694
$754$	14.4097	0.524769
$755$	−2.87530	−0.104643
$756$	1.85576	0.0674933
$757$	1.23333	0.0448263	0.0224132	−	0.999749i	$-0.492865\pi$
$757$	1.23333	0.0448263	0.0224132	+	0.999749i	$0.492865\pi$
$758$	−19.6326	−0.713088
$759$	14.0479	0.509906
$760$	3.29241	0.119428
$761$	17.2729	0.626140	0.313070	−	0.949730i	$-0.398642\pi$
$761$	17.2729	0.626140	0.313070	+	0.949730i	$0.398642\pi$
$762$	−4.95955	−0.179666
$763$	2.23802	0.0810216
$764$	−22.8968	−0.828377
$765$	−7.91207	−0.286061
$766$	−17.0507	−0.616068
$767$	−20.1307	−0.726876
$768$	−1.14577	−0.0413443
$769$	13.9443	0.502846	0.251423	−	0.967877i	$-0.419102\pi$
$769$	13.9443	0.502846	0.251423	+	0.967877i	$0.419102\pi$
$770$	1.01696	0.0366488
$771$	−20.2435	−0.729053
$772$	13.1396	0.472905
$773$	13.9661	0.502324	0.251162	−	0.967945i	$-0.419187\pi$
$773$	13.9661	0.502324	0.251162	+	0.967945i	$0.419187\pi$
$774$	−4.29273	−0.154299
$775$	1.97604	0.0709816
$776$	4.74512	0.170340
$777$	3.28868	0.117981
$778$	16.5258	0.592480
$779$	−19.2924	−0.691223
$780$	−6.23568	−0.223273
$781$	−1.96151	−0.0701885
$782$	−19.5361	−0.698610
$783$	−14.2193	−0.508156
$784$	−6.88060	−0.245736
$785$	19.8999	0.710259
$786$	4.73300	0.168820
$787$	6.99580	0.249373	0.124687	−	0.992196i	$-0.460207\pi$
$787$	6.99580	0.249373	0.124687	+	0.992196i	$0.460207\pi$
$788$	−14.1330	−0.503469
$789$	21.3212	0.759056
$790$	−10.0928	−0.359085
$791$	−3.55050	−0.126241
$792$	4.96554	0.176443
$793$	−21.8261	−0.775066
$794$	35.9502	1.27582
$795$	10.2434	0.363296
$796$	−15.9514	−0.565381
$797$	−26.8488	−0.951032	−0.475516	−	0.879707i	$-0.657739\pi$
$797$	−26.8488	−0.951032	−0.475516	+	0.879707i	$0.657739\pi$
$798$	1.30353	0.0461444
$799$	−25.6082	−0.905952
$800$	1.00000	0.0353553
$801$	−30.1629	−1.06575
$802$	−16.4555	−0.581065
$803$	−20.9361	−0.738820
$804$	−3.82923	−0.135047
$805$	−1.43956	−0.0507378
$806$	−10.7543	−0.378806
$807$	−3.71112	−0.130638
$808$	−9.47745	−0.333415
$809$	−10.1653	−0.357393	−0.178696	−	0.983904i	$-0.557188\pi$
$809$	−10.1653	−0.357393	−0.178696	+	0.983904i	$0.557188\pi$
$810$	1.09164	0.0383564
$811$	31.6257	1.11053	0.555264	−	0.831674i	$-0.312617\pi$
$811$	31.6257	1.11053	0.555264	+	0.831674i	$0.312617\pi$
$812$	−0.914906	−0.0321069
$813$	−0.218132	−0.00765023
$814$	24.4461	0.856837
$815$	−25.0275	−0.876676
$816$	5.37298	0.188092
$817$	−8.37676	−0.293066
$818$	21.3965	0.748111
$819$	3.17299	0.110873
$820$	−5.85967	−0.204628
$821$	42.5490	1.48497	0.742484	−	0.669863i	$-0.233647\pi$
$821$	42.5490	1.48497	0.742484	+	0.669863i	$0.233647\pi$
$822$	12.2004	0.425537
$823$	2.87637	0.100264	0.0501320	−	0.998743i	$-0.484036\pi$
$823$	2.87637	0.100264	0.0501320	+	0.998743i	$0.484036\pi$
$824$	19.4574	0.677829
$825$	3.37203	0.117399
$826$	1.27815	0.0444724
$827$	36.9027	1.28323	0.641617	−	0.767025i	$-0.278264\pi$
$827$	36.9027	1.28323	0.641617	+	0.767025i	$0.278264\pi$
$828$	−7.02895	−0.244273
$829$	−31.6447	−1.09907	−0.549533	−	0.835472i	$-0.685194\pi$
$829$	−31.6447	−1.09907	−0.549533	+	0.835472i	$0.685194\pi$
$830$	10.9935	0.381591
$831$	−32.7092	−1.13467
$832$	−5.44236	−0.188680
$833$	32.2660	1.11795
$834$	−24.7028	−0.855389
$835$	−20.4350	−0.707183
$836$	9.68968	0.335125
$837$	10.6123	0.366814
$838$	2.96844	0.102543
$839$	−47.0713	−1.62508	−0.812542	−	0.582903i	$-0.801917\pi$
$839$	−47.0713	−1.62508	−0.812542	+	0.582903i	$0.801917\pi$
$840$	0.395919	0.0136605
$841$	−21.9898	−0.758268
$842$	5.97765	0.206003
$843$	−27.3316	−0.941351
$844$	−17.2960	−0.595354
$845$	−16.6193	−0.571721
$846$	−9.21363	−0.316771
$847$	−0.808085	−0.0277661
$848$	8.94020	0.307008
$849$	−15.4768	−0.531163
$850$	−4.68942	−0.160846
$851$	−34.6047	−1.18623
$852$	−0.763646	−0.0261621
$853$	−36.7471	−1.25820	−0.629099	−	0.777325i	$-0.716576\pi$
$853$	−36.7471	−1.25820	−0.629099	+	0.777325i	$0.716576\pi$
$854$	1.38579	0.0474209
$855$	−5.55501	−0.189977
$856$	−17.8094	−0.608711
$857$	18.3688	0.627467	0.313734	−	0.949511i	$-0.398420\pi$
$857$	18.3688	0.627467	0.313734	+	0.949511i	$0.398420\pi$
$858$	−18.3518	−0.626521
$859$	−38.8888	−1.32687	−0.663434	−	0.748235i	$-0.730902\pi$
$859$	−38.8888	−1.32687	−0.663434	+	0.748235i	$0.730902\pi$
$860$	−2.54426	−0.0867587
$861$	−2.31996	−0.0790639
$862$	−9.44746	−0.321782
$863$	36.0625	1.22758	0.613790	−	0.789469i	$-0.289644\pi$
$863$	36.0625	1.22758	0.613790	+	0.789469i	$0.289644\pi$
$864$	5.37046	0.182707
$865$	−8.69676	−0.295699
$866$	−40.1216	−1.36339
$867$	−5.71810	−0.194197
$868$	0.682821	0.0231765
$869$	−29.7034	−1.00762
$870$	−3.03363	−0.102850
$871$	−18.1887	−0.616302
$872$	6.47669	0.219328
$873$	−8.00605	−0.270964
$874$	−13.7162	−0.463957
$875$	−0.345550	−0.0116817
$876$	−8.15074	−0.275388
$877$	−52.4237	−1.77022	−0.885111	−	0.465381i	$-0.845917\pi$
$877$	−52.4237	−1.77022	−0.885111	+	0.465381i	$0.845917\pi$
$878$	12.7114	0.428989
$879$	−15.4896	−0.522452
$880$	2.94303	0.0992097
$881$	54.3405	1.83078	0.915389	−	0.402571i	$-0.131883\pi$
$881$	54.3405	1.83078	0.915389	+	0.402571i	$0.131883\pi$
$882$	11.6091	0.390897
$883$	8.38695	0.282243	0.141122	−	0.989992i	$-0.454929\pi$
$883$	8.38695	0.282243	0.141122	+	0.989992i	$0.454929\pi$
$884$	25.5215	0.858381
$885$	4.23806	0.142461
$886$	11.1537	0.374714
$887$	15.3828	0.516505	0.258253	−	0.966077i	$-0.416853\pi$
$887$	15.3828	0.516505	0.258253	+	0.966077i	$0.416853\pi$
$888$	9.51724	0.319378
$889$	1.49574	0.0501656
$890$	−17.8773	−0.599249
$891$	3.21274	0.107631
$892$	−16.2423	−0.543833
$893$	−17.9793	−0.601655
$894$	19.9321	0.666630
$895$	−14.9832	−0.500833
$896$	0.345550	0.0115440
$897$	25.9779	0.867375
$898$	18.6910	0.623726
$899$	−5.23194	−0.174495
$900$	−1.68722	−0.0562406
$901$	−41.9243	−1.39670
$902$	−17.2452	−0.574202
$903$	−1.00732	−0.0335216
$904$	−10.2749	−0.341740
$905$	22.0825	0.734048
$906$	−3.29442	−0.109450
$907$	42.3168	1.40511	0.702553	−	0.711631i	$-0.252043\pi$
$907$	42.3168	1.40511	0.702553	+	0.711631i	$0.252043\pi$
$908$	−15.1362	−0.502313
$909$	15.9905	0.530372
$910$	1.88061	0.0623415
$911$	−35.8644	−1.18824	−0.594119	−	0.804377i	$-0.702499\pi$
$911$	−35.8644	−1.18824	−0.594119	+	0.804377i	$0.702499\pi$
$912$	3.77234	0.124915
$913$	32.3544	1.07077
$914$	−12.2430	−0.404964
$915$	4.59499	0.151906
$916$	−8.90349	−0.294180
$917$	−1.42742	−0.0471374
$918$	−25.1843	−0.831207
$919$	35.9377	1.18548	0.592738	−	0.805395i	$-0.298047\pi$
$919$	35.9377	1.18548	0.592738	+	0.805395i	$0.298047\pi$
$920$	−4.16600	−0.137349
$921$	−15.0019	−0.494329
$922$	14.9946	0.493821
$923$	−3.62730	−0.119394
$924$	1.16520	0.0383324
$925$	−8.30644	−0.273114
$926$	25.4255	0.835533
$927$	−32.8288	−1.07824
$928$	−2.64769	−0.0869145
$929$	−26.2278	−0.860506	−0.430253	−	0.902708i	$-0.641576\pi$
$929$	−26.2278	−0.860506	−0.430253	+	0.902708i	$0.641576\pi$
$930$	2.26409	0.0742423
$931$	22.6537	0.742447
$932$	4.30517	0.141021
$933$	−16.6295	−0.544424
$934$	28.0434	0.917608
$935$	−13.8011	−0.451345
$936$	9.18245	0.300138
$937$	−0.0453267	−0.00148076	−0.000740379	−	1.00000i	$-0.500236\pi$
$937$	−0.0453267	−0.00148076	−0.000740379		1.00000i	$0.500236\pi$
$938$	1.15485	0.0377072
$939$	−18.0825	−0.590099
$940$	−5.46084	−0.178113
$941$	15.9255	0.519157	0.259579	−	0.965722i	$-0.416416\pi$
$941$	15.9255	0.519157	0.259579	+	0.965722i	$0.416416\pi$
$942$	22.8007	0.742886
$943$	24.4114	0.794944
$944$	3.69888	0.120388
$945$	−1.85576	−0.0603679
$946$	−7.48785	−0.243451
$947$	5.00662	0.162693	0.0813467	−	0.996686i	$-0.474078\pi$
$947$	5.00662	0.162693	0.0813467	+	0.996686i	$0.474078\pi$
$948$	−11.5640	−0.375580
$949$	−38.7158	−1.25677
$950$	−3.29241	−0.106820
$951$	−11.7589	−0.381307
$952$	−1.62043	−0.0525183
$953$	−6.95125	−0.225173	−0.112586	−	0.993642i	$-0.535914\pi$
$953$	−6.95125	−0.225173	−0.112586	+	0.993642i	$0.535914\pi$
$954$	−15.0841	−0.488365
$955$	22.8968	0.740923
$956$	13.7120	0.443476
$957$	−8.92808	−0.288604
$958$	38.4752	1.24308
$959$	−3.67949	−0.118817
$960$	1.14577	0.0369795
$961$	−27.0952	−0.874040
$962$	45.2066	1.45752
$963$	30.0483	0.968292
$964$	−19.9414	−0.642268
$965$	−13.1396	−0.422979
$966$	−1.64940	−0.0530686
$967$	−3.54960	−0.114147	−0.0570737	−	0.998370i	$-0.518177\pi$
$967$	−3.54960	−0.114147	−0.0570737	+	0.998370i	$0.518177\pi$
$968$	−2.33855	−0.0751639
$969$	−17.6901	−0.568287
$970$	−4.74512	−0.152357
$971$	43.4765	1.39523	0.697614	−	0.716474i	$-0.254245\pi$
$971$	43.4765	1.39523	0.697614	+	0.716474i	$0.254245\pi$
$972$	−14.8606	−0.476654
$973$	7.45008	0.238839
$974$	−4.74878	−0.152161
$975$	6.23568	0.199702
$976$	4.01040	0.128370
$977$	11.3651	0.363602	0.181801	−	0.983335i	$-0.441807\pi$
$977$	11.3651	0.363602	0.181801	+	0.983335i	$0.441807\pi$
$978$	−28.6757	−0.916948
$979$	−52.6135	−1.68154
$980$	6.88060	0.219793
$981$	−10.9276	−0.348891
$982$	1.07914	0.0344368
$983$	45.9110	1.46433	0.732166	−	0.681126i	$-0.238510\pi$
$983$	45.9110	1.46433	0.732166	+	0.681126i	$0.238510\pi$
$984$	−6.71382	−0.214029
$985$	14.1330	0.450316
$986$	12.4161	0.395409
$987$	−2.16205	−0.0688189
$988$	17.9185	0.570063
$989$	10.5994	0.337042
$990$	−4.96554	−0.157815
$991$	−12.5594	−0.398964	−0.199482	−	0.979902i	$-0.563926\pi$
$991$	−12.5594	−0.398964	−0.199482	+	0.979902i	$0.563926\pi$
$992$	1.97604	0.0627395
$993$	39.1354	1.24193
$994$	0.230307	0.00730488
$995$	15.9514	0.505693
$996$	12.5960	0.399121
$997$	39.1890	1.24113	0.620564	−	0.784156i	$-0.286904\pi$
$997$	39.1890	1.24113	0.620564	+	0.784156i	$0.286904\pi$
$998$	25.5861	0.809914
$999$	−44.6094	−1.41138

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.h.1.9	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.h.1.9	✓	28	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.14577 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.14577 q^{6} +0.345550 q^{7} +1.00000 q^{8} -1.68722 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.14577 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.14577 q^{6} +0.345550 q^{7} +1.00000 q^{8} -1.68722 q^{9} -1.00000 q^{10} -2.94303 q^{11} -1.14577 q^{12} -5.44236 q^{13} +0.345550 q^{14} +1.14577 q^{15} +1.00000 q^{16} -4.68942 q^{17} -1.68722 q^{18} -3.29241 q^{19} -1.00000 q^{20} -0.395919 q^{21} -2.94303 q^{22} +4.16600 q^{23} -1.14577 q^{24} +1.00000 q^{25} -5.44236 q^{26} +5.37046 q^{27} +0.345550 q^{28} -2.64769 q^{29} +1.14577 q^{30} +1.97604 q^{31} +1.00000 q^{32} +3.37203 q^{33} -4.68942 q^{34} -0.345550 q^{35} -1.68722 q^{36} -8.30644 q^{37} -3.29241 q^{38} +6.23568 q^{39} -1.00000 q^{40} +5.85967 q^{41} -0.395919 q^{42} +2.54426 q^{43} -2.94303 q^{44} +1.68722 q^{45} +4.16600 q^{46} +5.46084 q^{47} -1.14577 q^{48} -6.88060 q^{49} +1.00000 q^{50} +5.37298 q^{51} -5.44236 q^{52} +8.94020 q^{53} +5.37046 q^{54} +2.94303 q^{55} +0.345550 q^{56} +3.77234 q^{57} -2.64769 q^{58} +3.69888 q^{59} +1.14577 q^{60} +4.01040 q^{61} +1.97604 q^{62} -0.583017 q^{63} +1.00000 q^{64} +5.44236 q^{65} +3.37203 q^{66} +3.34207 q^{67} -4.68942 q^{68} -4.77327 q^{69} -0.345550 q^{70} +0.666494 q^{71} -1.68722 q^{72} +7.11379 q^{73} -8.30644 q^{74} -1.14577 q^{75} -3.29241 q^{76} -1.01696 q^{77} +6.23568 q^{78} +10.0928 q^{79} -1.00000 q^{80} -1.09164 q^{81} +5.85967 q^{82} -10.9935 q^{83} -0.395919 q^{84} +4.68942 q^{85} +2.54426 q^{86} +3.03363 q^{87} -2.94303 q^{88} +17.8773 q^{89} +1.68722 q^{90} -1.88061 q^{91} +4.16600 q^{92} -2.26409 q^{93} +5.46084 q^{94} +3.29241 q^{95} -1.14577 q^{96} +4.74512 q^{97} -6.88060 q^{98} +4.96554 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9}+O(q^{10}) \) 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9} - 28 q^{10} + 4 q^{11} + 4 q^{12} + 22 q^{13} + 10 q^{14} - 4 q^{15} + 28 q^{16} + 15 q^{17} + 40 q^{18} - 11 q^{19} - 28 q^{20} + 18 q^{21} + 4 q^{22} + 23 q^{23} + 4 q^{24} + 28 q^{25} + 22 q^{26} + 19 q^{27} + 10 q^{28} + 19 q^{29} - 4 q^{30} + 7 q^{31} + 28 q^{32} + 33 q^{33} + 15 q^{34} - 10 q^{35} + 40 q^{36} + 22 q^{37} - 11 q^{38} + 8 q^{39} - 28 q^{40} + 41 q^{41} + 18 q^{42} + 7 q^{43} + 4 q^{44} - 40 q^{45} + 23 q^{46} + 51 q^{47} + 4 q^{48} + 60 q^{49} + 28 q^{50} - 5 q^{51} + 22 q^{52} + 25 q^{53} + 19 q^{54} - 4 q^{55} + 10 q^{56} + 8 q^{57} + 19 q^{58} + 32 q^{59} - 4 q^{60} + 24 q^{61} + 7 q^{62} + 33 q^{63} + 28 q^{64} - 22 q^{65} + 33 q^{66} + 3 q^{67} + 15 q^{68} + 43 q^{69} - 10 q^{70} + 8 q^{71} + 40 q^{72} + 47 q^{73} + 22 q^{74} + 4 q^{75} - 11 q^{76} + 46 q^{77} + 8 q^{78} - 22 q^{79} - 28 q^{80} + 76 q^{81} + 41 q^{82} + 36 q^{83} + 18 q^{84} - 15 q^{85} + 7 q^{86} + 72 q^{87} + 4 q^{88} + 70 q^{89} - 40 q^{90} - 21 q^{91} + 23 q^{92} + 24 q^{93} + 51 q^{94} + 11 q^{95} + 4 q^{96} + 43 q^{97} + 60 q^{98} - 9 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9 - 28 * q^10 + 4 * q^11 + 4 * q^12 + 22 * q^13 + 10 * q^14 - 4 * q^15 + 28 * q^16 + 15 * q^17 + 40 * q^18 - 11 * q^19 - 28 * q^20 + 18 * q^21 + 4 * q^22 + 23 * q^23 + 4 * q^24 + 28 * q^25 + 22 * q^26 + 19 * q^27 + 10 * q^28 + 19 * q^29 - 4 * q^30 + 7 * q^31 + 28 * q^32 + 33 * q^33 + 15 * q^34 - 10 * q^35 + 40 * q^36 + 22 * q^37 - 11 * q^38 + 8 * q^39 - 28 * q^40 + 41 * q^41 + 18 * q^42 + 7 * q^43 + 4 * q^44 - 40 * q^45 + 23 * q^46 + 51 * q^47 + 4 * q^48 + 60 * q^49 + 28 * q^50 - 5 * q^51 + 22 * q^52 + 25 * q^53 + 19 * q^54 - 4 * q^55 + 10 * q^56 + 8 * q^57 + 19 * q^58 + 32 * q^59 - 4 * q^60 + 24 * q^61 + 7 * q^62 + 33 * q^63 + 28 * q^64 - 22 * q^65 + 33 * q^66 + 3 * q^67 + 15 * q^68 + 43 * q^69 - 10 * q^70 + 8 * q^71 + 40 * q^72 + 47 * q^73 + 22 * q^74 + 4 * q^75 - 11 * q^76 + 46 * q^77 + 8 * q^78 - 22 * q^79 - 28 * q^80 + 76 * q^81 + 41 * q^82 + 36 * q^83 + 18 * q^84 - 15 * q^85 + 7 * q^86 + 72 * q^87 + 4 * q^88 + 70 * q^89 - 40 * q^90 - 21 * q^91 + 23 * q^92 + 24 * q^93 + 51 * q^94 + 11 * q^95 + 4 * q^96 + 43 * q^97 + 60 * q^98 - 9 * q^99

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