LMFDB - Embedded newform 6010.2.a.c.1.1

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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + \cdots - 10 $ x^16 - 8x^15 + 9x^14 + 75x^13 - 178x^12 - 232x^11 + 872x^10 + 228x^9 - 1986x^8 + 164x^7 + 2332x^6 - 440x^5 - 1344x^4 + 244x^3 + 295x^2 - 41*x - 10
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.06059$ of defining polynomial
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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.06059 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.06059 q^{6} +0.302669 q^{7} +1.00000 q^{8} +6.36721 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.06059 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.06059 q^{6} +0.302669 q^{7} +1.00000 q^{8} +6.36721 q^{9} +1.00000 q^{10} +0.393686 q^{11} -3.06059 q^{12} -2.37935 q^{13} +0.302669 q^{14} -3.06059 q^{15} +1.00000 q^{16} -0.379772 q^{17} +6.36721 q^{18} +0.653758 q^{19} +1.00000 q^{20} -0.926345 q^{21} +0.393686 q^{22} +0.240229 q^{23} -3.06059 q^{24} +1.00000 q^{25} -2.37935 q^{26} -10.3056 q^{27} +0.302669 q^{28} -10.4861 q^{29} -3.06059 q^{30} +1.32728 q^{31} +1.00000 q^{32} -1.20491 q^{33} -0.379772 q^{34} +0.302669 q^{35} +6.36721 q^{36} +8.99410 q^{37} +0.653758 q^{38} +7.28221 q^{39} +1.00000 q^{40} -8.36579 q^{41} -0.926345 q^{42} -0.545077 q^{43} +0.393686 q^{44} +6.36721 q^{45} +0.240229 q^{46} -4.02658 q^{47} -3.06059 q^{48} -6.90839 q^{49} +1.00000 q^{50} +1.16233 q^{51} -2.37935 q^{52} -5.16043 q^{53} -10.3056 q^{54} +0.393686 q^{55} +0.302669 q^{56} -2.00089 q^{57} -10.4861 q^{58} -5.74265 q^{59} -3.06059 q^{60} +2.10133 q^{61} +1.32728 q^{62} +1.92715 q^{63} +1.00000 q^{64} -2.37935 q^{65} -1.20491 q^{66} +16.1213 q^{67} -0.379772 q^{68} -0.735243 q^{69} +0.302669 q^{70} -9.79169 q^{71} +6.36721 q^{72} +13.1760 q^{73} +8.99410 q^{74} -3.06059 q^{75} +0.653758 q^{76} +0.119157 q^{77} +7.28221 q^{78} +6.29968 q^{79} +1.00000 q^{80} +12.4397 q^{81} -8.36579 q^{82} +0.717328 q^{83} -0.926345 q^{84} -0.379772 q^{85} -0.545077 q^{86} +32.0937 q^{87} +0.393686 q^{88} -9.68315 q^{89} +6.36721 q^{90} -0.720154 q^{91} +0.240229 q^{92} -4.06226 q^{93} -4.02658 q^{94} +0.653758 q^{95} -3.06059 q^{96} -14.8895 q^{97} -6.90839 q^{98} +2.50668 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.06059	−1.76703	−0.883516	−	0.468401i	$-0.844830\pi$
$3$	−3.06059	−1.76703	−0.883516	+	0.468401i	$0.844830\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.06059	−1.24948
$7$	0.302669	0.114398	0.0571990	−	0.998363i	$-0.481783\pi$
$7$	0.302669	0.114398	0.0571990	+	0.998363i	$0.481783\pi$
$8$	1.00000	0.353553
$9$	6.36721	2.12240
$10$	1.00000	0.316228
$11$	0.393686	0.118701	0.0593505	−	0.998237i	$-0.481097\pi$
$11$	0.393686	0.118701	0.0593505	+	0.998237i	$0.481097\pi$
$12$	−3.06059	−0.883516
$13$	−2.37935	−0.659913	−0.329956	−	0.943996i	$-0.607034\pi$
$13$	−2.37935	−0.659913	−0.329956	+	0.943996i	$0.607034\pi$
$14$	0.302669	0.0808916
$15$	−3.06059	−0.790241
$16$	1.00000	0.250000
$17$	−0.379772	−0.0921082	−0.0460541	−	0.998939i	$-0.514665\pi$
$17$	−0.379772	−0.0921082	−0.0460541	+	0.998939i	$0.514665\pi$
$18$	6.36721	1.50077
$19$	0.653758	0.149982	0.0749912	−	0.997184i	$-0.476107\pi$
$19$	0.653758	0.149982	0.0749912	+	0.997184i	$0.476107\pi$
$20$	1.00000	0.223607
$21$	−0.926345	−0.202145
$22$	0.393686	0.0839342
$23$	0.240229	0.0500912	0.0250456	−	0.999686i	$-0.492027\pi$
$23$	0.240229	0.0500912	0.0250456	+	0.999686i	$0.492027\pi$
$24$	−3.06059	−0.624740
$25$	1.00000	0.200000
$26$	−2.37935	−0.466629
$27$	−10.3056	−1.98332
$28$	0.302669	0.0571990
$29$	−10.4861	−1.94723	−0.973613	−	0.228207i	$-0.926714\pi$
$29$	−10.4861	−1.94723	−0.973613	+	0.228207i	$0.926714\pi$
$30$	−3.06059	−0.558785
$31$	1.32728	0.238387	0.119193	−	0.992871i	$-0.461969\pi$
$31$	1.32728	0.238387	0.119193	+	0.992871i	$0.461969\pi$
$32$	1.00000	0.176777
$33$	−1.20491	−0.209748
$34$	−0.379772	−0.0651303
$35$	0.302669	0.0511604
$36$	6.36721	1.06120
$37$	8.99410	1.47862	0.739311	−	0.673365i	$-0.235152\pi$
$37$	8.99410	1.47862	0.739311	+	0.673365i	$0.235152\pi$
$38$	0.653758	0.106054
$39$	7.28221	1.16609
$40$	1.00000	0.158114
$41$	−8.36579	−1.30652	−0.653259	−	0.757135i	$-0.726599\pi$
$41$	−8.36579	−1.30652	−0.653259	+	0.757135i	$0.726599\pi$
$42$	−0.926345	−0.142938
$43$	−0.545077	−0.0831234	−0.0415617	−	0.999136i	$-0.513233\pi$
$43$	−0.545077	−0.0831234	−0.0415617	+	0.999136i	$0.513233\pi$
$44$	0.393686	0.0593505
$45$	6.36721	0.949167
$46$	0.240229	0.0354199
$47$	−4.02658	−0.587337	−0.293668	−	0.955907i	$-0.594876\pi$
$47$	−4.02658	−0.587337	−0.293668	+	0.955907i	$0.594876\pi$
$48$	−3.06059	−0.441758
$49$	−6.90839	−0.986913
$50$	1.00000	0.141421
$51$	1.16233	0.162758
$52$	−2.37935	−0.329956
$53$	−5.16043	−0.708839	−0.354420	−	0.935087i	$-0.615322\pi$
$53$	−5.16043	−0.708839	−0.354420	+	0.935087i	$0.615322\pi$
$54$	−10.3056	−1.40242
$55$	0.393686	0.0530847
$56$	0.302669	0.0404458
$57$	−2.00089	−0.265024
$58$	−10.4861	−1.37690
$59$	−5.74265	−0.747629	−0.373815	−	0.927503i	$-0.621950\pi$
$59$	−5.74265	−0.747629	−0.373815	+	0.927503i	$0.621950\pi$
$60$	−3.06059	−0.395120
$61$	2.10133	0.269048	0.134524	−	0.990910i	$-0.457050\pi$
$61$	2.10133	0.269048	0.134524	+	0.990910i	$0.457050\pi$
$62$	1.32728	0.168565
$63$	1.92715	0.242799
$64$	1.00000	0.125000
$65$	−2.37935	−0.295122
$66$	−1.20491	−0.148314
$67$	16.1213	1.96953	0.984766	−	0.173882i	$-0.0556313\pi$
$67$	16.1213	1.96953	0.984766	+	0.173882i	$0.0556313\pi$
$68$	−0.379772	−0.0460541
$69$	−0.735243	−0.0885128
$70$	0.302669	0.0361758
$71$	−9.79169	−1.16206	−0.581030	−	0.813882i	$-0.697350\pi$
$71$	−9.79169	−1.16206	−0.581030	+	0.813882i	$0.697350\pi$
$72$	6.36721	0.750383
$73$	13.1760	1.54213	0.771067	−	0.636754i	$-0.219723\pi$
$73$	13.1760	1.54213	0.771067	+	0.636754i	$0.219723\pi$
$74$	8.99410	1.04554
$75$	−3.06059	−0.353406
$76$	0.653758	0.0749912
$77$	0.119157	0.0135791
$78$	7.28221	0.824548
$79$	6.29968	0.708770	0.354385	−	0.935100i	$-0.384690\pi$
$79$	6.29968	0.708770	0.354385	+	0.935100i	$0.384690\pi$
$80$	1.00000	0.111803
$81$	12.4397	1.38219
$82$	−8.36579	−0.923847
$83$	0.717328	0.0787370	0.0393685	−	0.999225i	$-0.487465\pi$
$83$	0.717328	0.0787370	0.0393685	+	0.999225i	$0.487465\pi$
$84$	−0.926345	−0.101072
$85$	−0.379772	−0.0411920
$86$	−0.545077	−0.0587771
$87$	32.0937	3.44081
$88$	0.393686	0.0419671
$89$	−9.68315	−1.02641	−0.513206	−	0.858266i	$-0.671542\pi$
$89$	−9.68315	−1.02641	−0.513206	+	0.858266i	$0.671542\pi$
$90$	6.36721	0.671163
$91$	−0.720154	−0.0754927
$92$	0.240229	0.0250456
$93$	−4.06226	−0.421237
$94$	−4.02658	−0.415310
$95$	0.653758	0.0670742
$96$	−3.06059	−0.312370
$97$	−14.8895	−1.51180	−0.755898	−	0.654690i	$-0.772799\pi$
$97$	−14.8895	−1.51180	−0.755898	+	0.654690i	$0.772799\pi$
$98$	−6.90839	−0.697853
$99$	2.50668	0.251931
$100$	1.00000	0.100000
$101$	−18.4852	−1.83935	−0.919675	−	0.392680i	$-0.871548\pi$
$101$	−18.4852	−1.83935	−0.919675	+	0.392680i	$0.871548\pi$
$102$	1.16233	0.115087
$103$	5.65667	0.557368	0.278684	−	0.960383i	$-0.410102\pi$
$103$	5.65667	0.557368	0.278684	+	0.960383i	$0.410102\pi$
$104$	−2.37935	−0.233314
$105$	−0.926345	−0.0904020
$106$	−5.16043	−0.501225
$107$	9.97666	0.964480	0.482240	−	0.876039i	$-0.339823\pi$
$107$	9.97666	0.964480	0.482240	+	0.876039i	$0.339823\pi$
$108$	−10.3056	−0.991661
$109$	16.0324	1.53563	0.767814	−	0.640673i	$-0.221344\pi$
$109$	16.0324	1.53563	0.767814	+	0.640673i	$0.221344\pi$
$110$	0.393686	0.0375365
$111$	−27.5272	−2.61277
$112$	0.302669	0.0285995
$113$	−10.2264	−0.962015	−0.481008	−	0.876716i	$-0.659729\pi$
$113$	−10.2264	−0.962015	−0.481008	+	0.876716i	$0.659729\pi$
$114$	−2.00089	−0.187400
$115$	0.240229	0.0224015
$116$	−10.4861	−0.973613
$117$	−15.1498	−1.40060
$118$	−5.74265	−0.528654
$119$	−0.114945	−0.0105370
$120$	−3.06059	−0.279392
$121$	−10.8450	−0.985910
$122$	2.10133	0.190245
$123$	25.6043	2.30866
$124$	1.32728	0.119193
$125$	1.00000	0.0894427
$126$	1.92715	0.171685
$127$	19.9875	1.77361	0.886803	−	0.462148i	$-0.152921\pi$
$127$	19.9875	1.77361	0.886803	+	0.462148i	$0.152921\pi$
$128$	1.00000	0.0883883
$129$	1.66826	0.146882
$130$	−2.37935	−0.208683
$131$	9.27593	0.810441	0.405221	−	0.914219i	$-0.367195\pi$
$131$	9.27593	0.810441	0.405221	+	0.914219i	$0.367195\pi$
$132$	−1.20491	−0.104874
$133$	0.197872	0.0171577
$134$	16.1213	1.39267
$135$	−10.3056	−0.886968
$136$	−0.379772	−0.0325652
$137$	0.364833	0.0311698	0.0155849	−	0.999879i	$-0.495039\pi$
$137$	0.364833	0.0311698	0.0155849	+	0.999879i	$0.495039\pi$
$138$	−0.735243	−0.0625880
$139$	−8.30581	−0.704489	−0.352245	−	0.935908i	$-0.614581\pi$
$139$	−8.30581	−0.704489	−0.352245	+	0.935908i	$0.614581\pi$
$140$	0.302669	0.0255802
$141$	12.3237	1.03784
$142$	−9.79169	−0.821701
$143$	−0.936717	−0.0783322
$144$	6.36721	0.530601
$145$	−10.4861	−0.870826
$146$	13.1760	1.09045
$147$	21.1438	1.74391
$148$	8.99410	0.739311
$149$	12.1058	0.991743	0.495872	−	0.868396i	$-0.334849\pi$
$149$	12.1058	0.991743	0.495872	+	0.868396i	$0.334849\pi$
$150$	−3.06059	−0.249896
$151$	−20.5589	−1.67306	−0.836531	−	0.547920i	$-0.815420\pi$
$151$	−20.5589	−1.67306	−0.836531	+	0.547920i	$0.815420\pi$
$152$	0.653758	0.0530268
$153$	−2.41809	−0.195491
$154$	0.119157	0.00960191
$155$	1.32728	0.106610
$156$	7.28221	0.583043
$157$	−7.47357	−0.596456	−0.298228	−	0.954495i	$-0.596395\pi$
$157$	−7.47357	−0.596456	−0.298228	+	0.954495i	$0.596395\pi$
$158$	6.29968	0.501176
$159$	15.7939	1.25254
$160$	1.00000	0.0790569
$161$	0.0727099	0.00573034
$162$	12.4397	0.977356
$163$	−2.21871	−0.173782	−0.0868912	−	0.996218i	$-0.527693\pi$
$163$	−2.21871	−0.173782	−0.0868912	+	0.996218i	$0.527693\pi$
$164$	−8.36579	−0.653259
$165$	−1.20491	−0.0938023
$166$	0.717328	0.0556755
$167$	−12.5368	−0.970129	−0.485064	−	0.874479i	$-0.661204\pi$
$167$	−12.5368	−0.970129	−0.485064	+	0.874479i	$0.661204\pi$
$168$	−0.926345	−0.0714690
$169$	−7.33870	−0.564515
$170$	−0.379772	−0.0291272
$171$	4.16261	0.318323
$172$	−0.545077	−0.0415617
$173$	7.28234	0.553666	0.276833	−	0.960918i	$-0.410715\pi$
$173$	7.28234	0.553666	0.276833	+	0.960918i	$0.410715\pi$
$174$	32.0937	2.43302
$175$	0.302669	0.0228796
$176$	0.393686	0.0296752
$177$	17.5759	1.32108
$178$	−9.68315	−0.725783
$179$	11.8959	0.889144	0.444572	−	0.895743i	$-0.353356\pi$
$179$	11.8959	0.889144	0.444572	+	0.895743i	$0.353356\pi$
$180$	6.36721	0.474584
$181$	−20.4579	−1.52062	−0.760310	−	0.649560i	$-0.774953\pi$
$181$	−20.4579	−1.52062	−0.760310	+	0.649560i	$0.774953\pi$
$182$	−0.720154	−0.0533814
$183$	−6.43131	−0.475416
$184$	0.240229	0.0177099
$185$	8.99410	0.661259
$186$	−4.06226	−0.297859
$187$	−0.149511	−0.0109333
$188$	−4.02658	−0.293668
$189$	−3.11919	−0.226888
$190$	0.653758	0.0474286
$191$	9.68976	0.701127	0.350563	−	0.936539i	$-0.385990\pi$
$191$	9.68976	0.701127	0.350563	+	0.936539i	$0.385990\pi$
$192$	−3.06059	−0.220879
$193$	−3.47297	−0.249990	−0.124995	−	0.992157i	$-0.539891\pi$
$193$	−3.47297	−0.249990	−0.124995	+	0.992157i	$0.539891\pi$
$194$	−14.8895	−1.06900
$195$	7.28221	0.521490
$196$	−6.90839	−0.493457
$197$	−7.43346	−0.529612	−0.264806	−	0.964302i	$-0.585308\pi$
$197$	−7.43346	−0.529612	−0.264806	+	0.964302i	$0.585308\pi$
$198$	2.50668	0.178142
$199$	3.67524	0.260531	0.130265	−	0.991479i	$-0.458417\pi$
$199$	3.67524	0.260531	0.130265	+	0.991479i	$0.458417\pi$
$200$	1.00000	0.0707107
$201$	−49.3407	−3.48023
$202$	−18.4852	−1.30062
$203$	−3.17382	−0.222759
$204$	1.16233	0.0813791
$205$	−8.36579	−0.584292
$206$	5.65667	0.394119
$207$	1.52959	0.106314
$208$	−2.37935	−0.164978
$209$	0.257376	0.0178030
$210$	−0.926345	−0.0639239
$211$	−20.2472	−1.39387	−0.696936	−	0.717134i	$-0.745454\pi$
$211$	−20.2472	−1.39387	−0.696936	+	0.717134i	$0.745454\pi$
$212$	−5.16043	−0.354420
$213$	29.9684	2.05340
$214$	9.97666	0.681990
$215$	−0.545077	−0.0371739
$216$	−10.3056	−0.701210
$217$	0.401726	0.0272710
$218$	16.0324	1.08585
$219$	−40.3263	−2.72500
$220$	0.393686	0.0265423
$221$	0.903609	0.0607833
$222$	−27.5272	−1.84751
$223$	10.8134	0.724117	0.362058	−	0.932155i	$-0.382074\pi$
$223$	10.8134	0.724117	0.362058	+	0.932155i	$0.382074\pi$
$224$	0.302669	0.0202229
$225$	6.36721	0.424480
$226$	−10.2264	−0.680247
$227$	−27.9968	−1.85822	−0.929108	−	0.369808i	$-0.879423\pi$
$227$	−27.9968	−1.85822	−0.929108	+	0.369808i	$0.879423\pi$
$228$	−2.00089	−0.132512
$229$	−21.2086	−1.40151	−0.700753	−	0.713404i	$-0.747152\pi$
$229$	−21.2086	−1.40151	−0.700753	+	0.713404i	$0.747152\pi$
$230$	0.240229	0.0158402
$231$	−0.364689	−0.0239948
$232$	−10.4861	−0.688448
$233$	−29.8509	−1.95559	−0.977797	−	0.209553i	$-0.932799\pi$
$233$	−29.8509	−1.95559	−0.977797	+	0.209553i	$0.932799\pi$
$234$	−15.1498	−0.990374
$235$	−4.02658	−0.262665
$236$	−5.74265	−0.373815
$237$	−19.2807	−1.25242
$238$	−0.114945	−0.00745078
$239$	−9.17427	−0.593434	−0.296717	−	0.954965i	$-0.595892\pi$
$239$	−9.17427	−0.593434	−0.296717	+	0.954965i	$0.595892\pi$
$240$	−3.06059	−0.197560
$241$	14.5645	0.938183	0.469092	−	0.883149i	$-0.344581\pi$
$241$	14.5645	0.938183	0.469092	+	0.883149i	$0.344581\pi$
$242$	−10.8450	−0.697144
$243$	−7.15592	−0.459052
$244$	2.10133	0.134524
$245$	−6.90839	−0.441361
$246$	25.6043	1.63247
$247$	−1.55552	−0.0989753
$248$	1.32728	0.0842824
$249$	−2.19545	−0.139131
$250$	1.00000	0.0632456
$251$	−15.5634	−0.982352	−0.491176	−	0.871060i	$-0.663433\pi$
$251$	−15.5634	−0.982352	−0.491176	+	0.871060i	$0.663433\pi$
$252$	1.92715	0.121399
$253$	0.0945750	0.00594588
$254$	19.9875	1.25413
$255$	1.16233	0.0727876
$256$	1.00000	0.0625000
$257$	16.5130	1.03005	0.515026	−	0.857174i	$-0.327782\pi$
$257$	16.5130	1.03005	0.515026	+	0.857174i	$0.327782\pi$
$258$	1.66826	0.103861
$259$	2.72223	0.169151
$260$	−2.37935	−0.147561
$261$	−66.7674	−4.13280
$262$	9.27593	0.573069
$263$	−4.57687	−0.282222	−0.141111	−	0.989994i	$-0.545067\pi$
$263$	−4.57687	−0.282222	−0.141111	+	0.989994i	$0.545067\pi$
$264$	−1.20491	−0.0741572
$265$	−5.16043	−0.317002
$266$	0.197872	0.0121323
$267$	29.6361	1.81370
$268$	16.1213	0.984766
$269$	28.5382	1.74001	0.870003	−	0.493046i	$-0.164117\pi$
$269$	28.5382	1.74001	0.870003	+	0.493046i	$0.164117\pi$
$270$	−10.3056	−0.627181
$271$	−5.55300	−0.337320	−0.168660	−	0.985674i	$-0.553944\pi$
$271$	−5.55300	−0.337320	−0.168660	+	0.985674i	$0.553944\pi$
$272$	−0.379772	−0.0230270
$273$	2.20410	0.133398
$274$	0.364833	0.0220404
$275$	0.393686	0.0237402
$276$	−0.735243	−0.0442564
$277$	15.4924	0.930846	0.465423	−	0.885088i	$-0.345902\pi$
$277$	15.4924	0.930846	0.465423	+	0.885088i	$0.345902\pi$
$278$	−8.30581	−0.498149
$279$	8.45107	0.505952
$280$	0.302669	0.0180879
$281$	−7.89919	−0.471226	−0.235613	−	0.971847i	$-0.575710\pi$
$281$	−7.89919	−0.471226	−0.235613	+	0.971847i	$0.575710\pi$
$282$	12.3237	0.733866
$283$	−21.8084	−1.29637	−0.648187	−	0.761481i	$-0.724472\pi$
$283$	−21.8084	−1.29637	−0.648187	+	0.761481i	$0.724472\pi$
$284$	−9.79169	−0.581030
$285$	−2.00089	−0.118522
$286$	−0.936717	−0.0553892
$287$	−2.53206	−0.149463
$288$	6.36721	0.375191
$289$	−16.8558	−0.991516
$290$	−10.4861	−0.615767
$291$	45.5705	2.67139
$292$	13.1760	0.771067
$293$	22.3147	1.30364	0.651821	−	0.758373i	$-0.274005\pi$
$293$	22.3147	1.30364	0.651821	+	0.758373i	$0.274005\pi$
$294$	21.1438	1.23313
$295$	−5.74265	−0.334350
$296$	8.99410	0.522771
$297$	−4.05719	−0.235422
$298$	12.1058	0.701268
$299$	−0.571589	−0.0330558
$300$	−3.06059	−0.176703
$301$	−0.164978	−0.00950915
$302$	−20.5589	−1.18303
$303$	56.5757	3.25019
$304$	0.653758	0.0374956
$305$	2.10133	0.120322
$306$	−2.41809	−0.138233
$307$	11.9437	0.681661	0.340830	−	0.940125i	$-0.389292\pi$
$307$	11.9437	0.681661	0.340830	+	0.940125i	$0.389292\pi$
$308$	0.119157	0.00678957
$309$	−17.3127	−0.984887
$310$	1.32728	0.0753845
$311$	−16.4766	−0.934303	−0.467151	−	0.884177i	$-0.654720\pi$
$311$	−16.4766	−0.934303	−0.467151	+	0.884177i	$0.654720\pi$
$312$	7.28221	0.412274
$313$	2.42399	0.137012	0.0685060	−	0.997651i	$-0.478177\pi$
$313$	2.42399	0.137012	0.0685060	+	0.997651i	$0.478177\pi$
$314$	−7.47357	−0.421758
$315$	1.92715	0.108583
$316$	6.29968	0.354385
$317$	−29.9367	−1.68141	−0.840707	−	0.541490i	$-0.817860\pi$
$317$	−29.9367	−1.68141	−0.840707	+	0.541490i	$0.817860\pi$
$318$	15.7939	0.885680
$319$	−4.12825	−0.231137
$320$	1.00000	0.0559017
$321$	−30.5344	−1.70427
$322$	0.0727099	0.00405196
$323$	−0.248279	−0.0138146
$324$	12.4397	0.691095
$325$	−2.37935	−0.131983
$326$	−2.21871	−0.122883
$327$	−49.0687	−2.71350
$328$	−8.36579	−0.461924
$329$	−1.21872	−0.0671902
$330$	−1.20491	−0.0663282
$331$	−10.5453	−0.579622	−0.289811	−	0.957084i	$-0.593592\pi$
$331$	−10.5453	−0.579622	−0.289811	+	0.957084i	$0.593592\pi$
$332$	0.717328	0.0393685
$333$	57.2673	3.13823
$334$	−12.5368	−0.685984
$335$	16.1213	0.880802
$336$	−0.926345	−0.0505362
$337$	−21.1632	−1.15283	−0.576415	−	0.817157i	$-0.695549\pi$
$337$	−21.1632	−1.15283	−0.576415	+	0.817157i	$0.695549\pi$
$338$	−7.33870	−0.399173
$339$	31.2987	1.69991
$340$	−0.379772	−0.0205960
$341$	0.522532	0.0282967
$342$	4.16261	0.225088
$343$	−4.20964	−0.227299
$344$	−0.545077	−0.0293886
$345$	−0.735243	−0.0395841
$346$	7.28234	0.391501
$347$	−7.28255	−0.390948	−0.195474	−	0.980709i	$-0.562625\pi$
$347$	−7.28255	−0.390948	−0.195474	+	0.980709i	$0.562625\pi$
$348$	32.0937	1.72040
$349$	1.21409	0.0649887	0.0324944	−	0.999472i	$-0.489655\pi$
$349$	1.21409	0.0649887	0.0324944	+	0.999472i	$0.489655\pi$
$350$	0.302669	0.0161783
$351$	24.5207	1.30882
$352$	0.393686	0.0209836
$353$	−19.5750	−1.04187	−0.520936	−	0.853596i	$-0.674417\pi$
$353$	−19.5750	−1.04187	−0.520936	+	0.853596i	$0.674417\pi$
$354$	17.5759	0.934148
$355$	−9.79169	−0.519689
$356$	−9.68315	−0.513206
$357$	0.351800	0.0186192
$358$	11.8959	0.628720
$359$	−0.360464	−0.0190245	−0.00951227	−	0.999955i	$-0.503028\pi$
$359$	−0.360464	−0.0190245	−0.00951227	+	0.999955i	$0.503028\pi$
$360$	6.36721	0.335581
$361$	−18.5726	−0.977505
$362$	−20.4579	−1.07524
$363$	33.1921	1.74213
$364$	−0.720154	−0.0377463
$365$	13.1760	0.689664
$366$	−6.43131	−0.336170
$367$	−25.9109	−1.35254	−0.676268	−	0.736656i	$-0.736404\pi$
$367$	−25.9109	−1.35254	−0.676268	+	0.736656i	$0.736404\pi$
$368$	0.240229	0.0125228
$369$	−53.2667	−2.77296
$370$	8.99410	0.467581
$371$	−1.56190	−0.0810898
$372$	−4.06226	−0.210618
$373$	−28.1904	−1.45964	−0.729821	−	0.683638i	$-0.760397\pi$
$373$	−28.1904	−1.45964	−0.729821	+	0.683638i	$0.760397\pi$
$374$	−0.149511	−0.00773103
$375$	−3.06059	−0.158048
$376$	−4.02658	−0.207655
$377$	24.9502	1.28500
$378$	−3.11919	−0.160434
$379$	8.83096	0.453616	0.226808	−	0.973940i	$-0.427171\pi$
$379$	8.83096	0.453616	0.226808	+	0.973940i	$0.427171\pi$
$380$	0.653758	0.0335371
$381$	−61.1736	−3.13402
$382$	9.68976	0.495771
$383$	−23.8392	−1.21813	−0.609064	−	0.793121i	$-0.708455\pi$
$383$	−23.8392	−1.21813	−0.609064	+	0.793121i	$0.708455\pi$
$384$	−3.06059	−0.156185
$385$	0.119157	0.00607278
$386$	−3.47297	−0.176769
$387$	−3.47062	−0.176421
$388$	−14.8895	−0.755898
$389$	7.53468	0.382023	0.191012	−	0.981588i	$-0.438823\pi$
$389$	7.53468	0.382023	0.191012	+	0.981588i	$0.438823\pi$
$390$	7.28221	0.368749
$391$	−0.0912323	−0.00461381
$392$	−6.90839	−0.348926
$393$	−28.3898	−1.43208
$394$	−7.43346	−0.374492
$395$	6.29968	0.316971
$396$	2.50668	0.125966
$397$	32.0835	1.61022	0.805112	−	0.593123i	$-0.202105\pi$
$397$	32.0835	1.61022	0.805112	+	0.593123i	$0.202105\pi$
$398$	3.67524	0.184223
$399$	−0.605605	−0.0303182
$400$	1.00000	0.0500000
$401$	−10.4304	−0.520871	−0.260436	−	0.965491i	$-0.583866\pi$
$401$	−10.4304	−0.520871	−0.260436	+	0.965491i	$0.583866\pi$
$402$	−49.3407	−2.46089
$403$	−3.15806	−0.157314
$404$	−18.4852	−0.919675
$405$	12.4397	0.618134
$406$	−3.17382	−0.157514
$407$	3.54085	0.175514
$408$	1.16233	0.0575437
$409$	1.01459	0.0501684	0.0250842	−	0.999685i	$-0.492015\pi$
$409$	1.01459	0.0501684	0.0250842	+	0.999685i	$0.492015\pi$
$410$	−8.36579	−0.413157
$411$	−1.11660	−0.0550781
$412$	5.65667	0.278684
$413$	−1.73812	−0.0855273
$414$	1.52959	0.0751752
$415$	0.717328	0.0352123
$416$	−2.37935	−0.116657
$417$	25.4207	1.24486
$418$	0.257376	0.0125887
$419$	22.6659	1.10730	0.553651	−	0.832749i	$-0.313234\pi$
$419$	22.6659	1.10730	0.553651	+	0.832749i	$0.313234\pi$
$420$	−0.926345	−0.0452010
$421$	−20.7214	−1.00990	−0.504950	−	0.863149i	$-0.668489\pi$
$421$	−20.7214	−1.00990	−0.504950	+	0.863149i	$0.668489\pi$
$422$	−20.2472	−0.985616
$423$	−25.6381	−1.24656
$424$	−5.16043	−0.250612
$425$	−0.379772	−0.0184216
$426$	29.9684	1.45197
$427$	0.636007	0.0307785
$428$	9.97666	0.482240
$429$	2.86691	0.138416
$430$	−0.545077	−0.0262859
$431$	9.10219	0.438437	0.219219	−	0.975676i	$-0.429649\pi$
$431$	9.10219	0.438437	0.219219	+	0.975676i	$0.429649\pi$
$432$	−10.3056	−0.495830
$433$	−31.4151	−1.50971	−0.754856	−	0.655890i	$-0.772293\pi$
$433$	−31.4151	−1.50971	−0.754856	+	0.655890i	$0.772293\pi$
$434$	0.401726	0.0192835
$435$	32.0937	1.53878
$436$	16.0324	0.767814
$437$	0.157052	0.00751281
$438$	−40.3263	−1.92687
$439$	−0.429760	−0.0205113	−0.0102557	−	0.999947i	$-0.503265\pi$
$439$	−0.429760	−0.0205113	−0.0102557	+	0.999947i	$0.503265\pi$
$440$	0.393686	0.0187683
$441$	−43.9872	−2.09463
$442$	0.903609	0.0429803
$443$	33.5818	1.59552	0.797760	−	0.602975i	$-0.206018\pi$
$443$	33.5818	1.59552	0.797760	+	0.602975i	$0.206018\pi$
$444$	−27.5272	−1.30639
$445$	−9.68315	−0.459025
$446$	10.8134	0.512028
$447$	−37.0508	−1.75244
$448$	0.302669	0.0142998
$449$	−20.7822	−0.980772	−0.490386	−	0.871505i	$-0.663144\pi$
$449$	−20.7822	−0.980772	−0.490386	+	0.871505i	$0.663144\pi$
$450$	6.36721	0.300153
$451$	−3.29350	−0.155085
$452$	−10.2264	−0.481008
$453$	62.9224	2.95635
$454$	−27.9968	−1.31396
$455$	−0.720154	−0.0337614
$456$	−2.00089	−0.0937000
$457$	−1.56659	−0.0732822	−0.0366411	−	0.999328i	$-0.511666\pi$
$457$	−1.56659	−0.0732822	−0.0366411	+	0.999328i	$0.511666\pi$
$458$	−21.2086	−0.991014
$459$	3.91379	0.182680
$460$	0.240229	0.0112007
$461$	−7.95973	−0.370722	−0.185361	−	0.982671i	$-0.559345\pi$
$461$	−7.95973	−0.370722	−0.185361	+	0.982671i	$0.559345\pi$
$462$	−0.364689	−0.0169669
$463$	−40.2680	−1.87141	−0.935705	−	0.352782i	$-0.885236\pi$
$463$	−40.2680	−1.87141	−0.935705	+	0.352782i	$0.885236\pi$
$464$	−10.4861	−0.486806
$465$	−4.06226	−0.188383
$466$	−29.8509	−1.38281
$467$	−34.5397	−1.59831	−0.799154	−	0.601126i	$-0.794719\pi$
$467$	−34.5397	−1.59831	−0.799154	+	0.601126i	$0.794719\pi$
$468$	−15.1498	−0.700300
$469$	4.87942	0.225311
$470$	−4.02658	−0.185732
$471$	22.8735	1.05396
$472$	−5.74265	−0.264327
$473$	−0.214589	−0.00986682
$474$	−19.2807	−0.885594
$475$	0.653758	0.0299965
$476$	−0.114945	−0.00526850
$477$	−32.8575	−1.50444
$478$	−9.17427	−0.419621
$479$	2.87871	0.131532	0.0657659	−	0.997835i	$-0.479051\pi$
$479$	2.87871	0.131532	0.0657659	+	0.997835i	$0.479051\pi$
$480$	−3.06059	−0.139696
$481$	−21.4001	−0.975761
$482$	14.5645	0.663396
$483$	−0.222535	−0.0101257
$484$	−10.8450	−0.492955
$485$	−14.8895	−0.676096
$486$	−7.15592	−0.324599
$487$	−4.69576	−0.212785	−0.106393	−	0.994324i	$-0.533930\pi$
$487$	−4.69576	−0.212785	−0.106393	+	0.994324i	$0.533930\pi$
$488$	2.10133	0.0951227
$489$	6.79055	0.307079
$490$	−6.90839	−0.312089
$491$	4.22768	0.190793	0.0953964	−	0.995439i	$-0.469588\pi$
$491$	4.22768	0.190793	0.0953964	+	0.995439i	$0.469588\pi$
$492$	25.6043	1.15433
$493$	3.98234	0.179355
$494$	−1.55552	−0.0699861
$495$	2.50668	0.112667
$496$	1.32728	0.0595967
$497$	−2.96364	−0.132937
$498$	−2.19545	−0.0983803
$499$	33.4020	1.49528	0.747639	−	0.664105i	$-0.231187\pi$
$499$	33.4020	1.49528	0.747639	+	0.664105i	$0.231187\pi$
$500$	1.00000	0.0447214
$501$	38.3701	1.71425
$502$	−15.5634	−0.694628
$503$	20.2165	0.901408	0.450704	−	0.892673i	$-0.351173\pi$
$503$	20.2165	0.901408	0.450704	+	0.892673i	$0.351173\pi$
$504$	1.92715	0.0858423
$505$	−18.4852	−0.822582
$506$	0.0945750	0.00420437
$507$	22.4608	0.997517
$508$	19.9875	0.886803
$509$	−30.5279	−1.35313	−0.676563	−	0.736384i	$-0.736532\pi$
$509$	−30.5279	−1.35313	−0.676563	+	0.736384i	$0.736532\pi$
$510$	1.16233	0.0514686
$511$	3.98796	0.176417
$512$	1.00000	0.0441942
$513$	−6.73739	−0.297463
$514$	16.5130	0.728357
$515$	5.65667	0.249263
$516$	1.66826	0.0734409
$517$	−1.58521	−0.0697174
$518$	2.72223	0.119608
$519$	−22.2882	−0.978345
$520$	−2.37935	−0.104341
$521$	24.1994	1.06019	0.530096	−	0.847937i	$-0.322156\pi$
$521$	24.1994	1.06019	0.530096	+	0.847937i	$0.322156\pi$
$522$	−66.7674	−2.92233
$523$	12.2653	0.536325	0.268162	−	0.963374i	$-0.413584\pi$
$523$	12.2653	0.536325	0.268162	+	0.963374i	$0.413584\pi$
$524$	9.27593	0.405221
$525$	−0.926345	−0.0404290
$526$	−4.57687	−0.199561
$527$	−0.504064	−0.0219574
$528$	−1.20491	−0.0524371
$529$	−22.9423	−0.997491
$530$	−5.16043	−0.224155
$531$	−36.5646	−1.58677
$532$	0.197872	0.00857885
$533$	19.9051	0.862187
$534$	29.6361	1.28248
$535$	9.97666	0.431328
$536$	16.1213	0.696335
$537$	−36.4086	−1.57115
$538$	28.5382	1.23037
$539$	−2.71974	−0.117147
$540$	−10.3056	−0.443484
$541$	−2.98187	−0.128200	−0.0641002	−	0.997943i	$-0.520418\pi$
$541$	−2.98187	−0.128200	−0.0641002	+	0.997943i	$0.520418\pi$
$542$	−5.55300	−0.238522
$543$	62.6131	2.68698
$544$	−0.379772	−0.0162826
$545$	16.0324	0.686754
$546$	2.20410	0.0943266
$547$	0.380513	0.0162696	0.00813478	−	0.999967i	$-0.497411\pi$
$547$	0.380513	0.0162696	0.00813478	+	0.999967i	$0.497411\pi$
$548$	0.364833	0.0155849
$549$	13.3796	0.571028
$550$	0.393686	0.0167868
$551$	−6.85539	−0.292050
$552$	−0.735243	−0.0312940
$553$	1.90672	0.0810819
$554$	15.4924	0.658208
$555$	−27.5272	−1.16847
$556$	−8.30581	−0.352245
$557$	37.7655	1.60018	0.800088	−	0.599882i	$-0.204786\pi$
$557$	37.7655	1.60018	0.800088	+	0.599882i	$0.204786\pi$
$558$	8.45107	0.357762
$559$	1.29693	0.0548542
$560$	0.302669	0.0127901
$561$	0.457592	0.0193195
$562$	−7.89919	−0.333207
$563$	24.6905	1.04058	0.520291	−	0.853989i	$-0.325824\pi$
$563$	24.6905	1.04058	0.520291	+	0.853989i	$0.325824\pi$
$564$	12.3237	0.518921
$565$	−10.2264	−0.430226
$566$	−21.8084	−0.916675
$567$	3.76511	0.158120
$568$	−9.79169	−0.410850
$569$	39.8520	1.67068	0.835341	−	0.549732i	$-0.185270\pi$
$569$	39.8520	1.67068	0.835341	+	0.549732i	$0.185270\pi$
$570$	−2.00089	−0.0838079
$571$	37.8580	1.58431	0.792154	−	0.610322i	$-0.208960\pi$
$571$	37.8580	1.58431	0.792154	+	0.610322i	$0.208960\pi$
$572$	−0.936717	−0.0391661
$573$	−29.6564	−1.23891
$574$	−2.53206	−0.105686
$575$	0.240229	0.0100182
$576$	6.36721	0.265300
$577$	26.4122	1.09955	0.549777	−	0.835312i	$-0.314713\pi$
$577$	26.4122	1.09955	0.549777	+	0.835312i	$0.314713\pi$
$578$	−16.8558	−0.701108
$579$	10.6293	0.441740
$580$	−10.4861	−0.435413
$581$	0.217113	0.00900736
$582$	45.5705	1.88896
$583$	−2.03159	−0.0841398
$584$	13.1760	0.545227
$585$	−15.1498	−0.626367
$586$	22.3147	0.921814
$587$	−42.1756	−1.74077	−0.870387	−	0.492368i	$-0.836132\pi$
$587$	−42.1756	−1.74077	−0.870387	+	0.492368i	$0.836132\pi$
$588$	21.1438	0.871954
$589$	0.867721	0.0357538
$590$	−5.74265	−0.236421
$591$	22.7508	0.935841
$592$	8.99410	0.369655
$593$	20.6911	0.849683	0.424841	−	0.905268i	$-0.360330\pi$
$593$	20.6911	0.849683	0.424841	+	0.905268i	$0.360330\pi$
$594$	−4.05719	−0.166468
$595$	−0.114945	−0.00471229
$596$	12.1058	0.495872
$597$	−11.2484	−0.460366
$598$	−0.571589	−0.0233740
$599$	−32.8420	−1.34189	−0.670943	−	0.741509i	$-0.734111\pi$
$599$	−32.8420	−1.34189	−0.670943	+	0.741509i	$0.734111\pi$
$600$	−3.06059	−0.124948
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	−0.164978	−0.00672399
$603$	102.648	4.18014
$604$	−20.5589	−0.836531
$605$	−10.8450	−0.440912
$606$	56.5757	2.29823
$607$	−4.05152	−0.164446	−0.0822231	−	0.996614i	$-0.526202\pi$
$607$	−4.05152	−0.164446	−0.0822231	+	0.996614i	$0.526202\pi$
$608$	0.653758	0.0265134
$609$	9.71377	0.393622
$610$	2.10133	0.0850804
$611$	9.58063	0.387591
$612$	−2.41809	−0.0977453
$613$	30.3621	1.22631	0.613157	−	0.789961i	$-0.289899\pi$
$613$	30.3621	1.22631	0.613157	+	0.789961i	$0.289899\pi$
$614$	11.9437	0.482007
$615$	25.6043	1.03246
$616$	0.119157	0.00480095
$617$	−18.9474	−0.762792	−0.381396	−	0.924412i	$-0.624556\pi$
$617$	−18.9474	−0.762792	−0.381396	+	0.924412i	$0.624556\pi$
$618$	−17.3127	−0.696420
$619$	26.6354	1.07057	0.535283	−	0.844673i	$-0.320205\pi$
$619$	26.6354	1.07057	0.535283	+	0.844673i	$0.320205\pi$
$620$	1.32728	0.0533049
$621$	−2.47572	−0.0993470
$622$	−16.4766	−0.660652
$623$	−2.93079	−0.117419
$624$	7.28221	0.291522
$625$	1.00000	0.0400000
$626$	2.42399	0.0968820
$627$	−0.787721	−0.0314586
$628$	−7.47357	−0.298228
$629$	−3.41571	−0.136193
$630$	1.92715	0.0767797
$631$	50.1155	1.99507	0.997533	−	0.0701957i	$-0.0223624\pi$
$631$	50.1155	1.99507	0.997533	+	0.0701957i	$0.0223624\pi$
$632$	6.29968	0.250588
$633$	61.9682	2.46302
$634$	−29.9367	−1.18894
$635$	19.9875	0.793181
$636$	15.7939	0.626271
$637$	16.4375	0.651276
$638$	−4.12825	−0.163439
$639$	−62.3457	−2.46636
$640$	1.00000	0.0395285
$641$	3.86427	0.152630	0.0763148	−	0.997084i	$-0.475685\pi$
$641$	3.86427	0.152630	0.0763148	+	0.997084i	$0.475685\pi$
$642$	−30.5344	−1.20510
$643$	−21.3635	−0.842496	−0.421248	−	0.906946i	$-0.638408\pi$
$643$	−21.3635	−0.842496	−0.421248	+	0.906946i	$0.638408\pi$
$644$	0.0727099	0.00286517
$645$	1.66826	0.0656875
$646$	−0.248279	−0.00976840
$647$	19.5335	0.767941	0.383971	−	0.923345i	$-0.374556\pi$
$647$	19.5335	0.767941	0.383971	+	0.923345i	$0.374556\pi$
$648$	12.4397	0.488678
$649$	−2.26080	−0.0887442
$650$	−2.37935	−0.0933257
$651$	−1.22952	−0.0481887
$652$	−2.21871	−0.0868912
$653$	−42.5938	−1.66682	−0.833411	−	0.552653i	$-0.813615\pi$
$653$	−42.5938	−1.66682	−0.833411	+	0.552653i	$0.813615\pi$
$654$	−49.0687	−1.91874
$655$	9.27593	0.362440
$656$	−8.36579	−0.326629
$657$	83.8943	3.27303
$658$	−1.21872	−0.0475106
$659$	3.46889	0.135129	0.0675644	−	0.997715i	$-0.478477\pi$
$659$	3.46889	0.135129	0.0675644	+	0.997715i	$0.478477\pi$
$660$	−1.20491	−0.0469011
$661$	10.5580	0.410659	0.205329	−	0.978693i	$-0.434173\pi$
$661$	10.5580	0.410659	0.205329	+	0.978693i	$0.434173\pi$
$662$	−10.5453	−0.409855
$663$	−2.76558	−0.107406
$664$	0.717328	0.0278377
$665$	0.197872	0.00767315
$666$	57.2673	2.21906
$667$	−2.51907	−0.0975390
$668$	−12.5368	−0.485064
$669$	−33.0953	−1.27954
$670$	16.1213	0.622821
$671$	0.827265	0.0319362
$672$	−0.926345	−0.0357345
$673$	−28.4403	−1.09629	−0.548147	−	0.836382i	$-0.684667\pi$
$673$	−28.4403	−1.09629	−0.548147	+	0.836382i	$0.684667\pi$
$674$	−21.1632	−0.815174
$675$	−10.3056	−0.396664
$676$	−7.33870	−0.282258
$677$	−0.161383	−0.00620246	−0.00310123	−	0.999995i	$-0.500987\pi$
$677$	−0.161383	−0.00620246	−0.00310123	+	0.999995i	$0.500987\pi$
$678$	31.2987	1.20202
$679$	−4.50657	−0.172946
$680$	−0.379772	−0.0145636
$681$	85.6869	3.28353
$682$	0.522532	0.0200088
$683$	−20.8736	−0.798707	−0.399353	−	0.916797i	$-0.630765\pi$
$683$	−20.8736	−0.798707	−0.399353	+	0.916797i	$0.630765\pi$
$684$	4.16261	0.159162
$685$	0.364833	0.0139396
$686$	−4.20964	−0.160725
$687$	64.9109	2.47651
$688$	−0.545077	−0.0207808
$689$	12.2785	0.467772
$690$	−0.735243	−0.0279902
$691$	12.3797	0.470946	0.235473	−	0.971881i	$-0.424336\pi$
$691$	12.3797	0.470946	0.235473	+	0.971881i	$0.424336\pi$
$692$	7.28234	0.276833
$693$	0.758694	0.0288204
$694$	−7.28255	−0.276442
$695$	−8.30581	−0.315057
$696$	32.0937	1.21651
$697$	3.17709	0.120341
$698$	1.21409	0.0459540
$699$	91.3612	3.45560
$700$	0.302669	0.0114398
$701$	−9.45537	−0.357124	−0.178562	−	0.983929i	$-0.557145\pi$
$701$	−9.45537	−0.357124	−0.178562	+	0.983929i	$0.557145\pi$
$702$	24.5207	0.925474
$703$	5.87997	0.221767
$704$	0.393686	0.0148376
$705$	12.3237	0.464137
$706$	−19.5750	−0.736714
$707$	−5.59490	−0.210418
$708$	17.5759	0.660542
$709$	25.5181	0.958354	0.479177	−	0.877718i	$-0.340935\pi$
$709$	25.5181	0.958354	0.479177	+	0.877718i	$0.340935\pi$
$710$	−9.79169	−0.367476
$711$	40.1114	1.50429
$712$	−9.68315	−0.362891
$713$	0.318852	0.0119411
$714$	0.351800	0.0131658
$715$	−0.936717	−0.0350312
$716$	11.8959	0.444572
$717$	28.0787	1.04862
$718$	−0.360464	−0.0134524
$719$	−6.07987	−0.226741	−0.113370	−	0.993553i	$-0.536165\pi$
$719$	−6.07987	−0.226741	−0.113370	+	0.993553i	$0.536165\pi$
$720$	6.36721	0.237292
$721$	1.71210	0.0637618
$722$	−18.5726	−0.691201
$723$	−44.5760	−1.65780
$724$	−20.4579	−0.760310
$725$	−10.4861	−0.389445
$726$	33.1921	1.23188
$727$	−42.1326	−1.56261	−0.781305	−	0.624149i	$-0.785446\pi$
$727$	−42.1326	−1.56261	−0.781305	+	0.624149i	$0.785446\pi$
$728$	−0.720154	−0.0266907
$729$	−15.4178	−0.571029
$730$	13.1760	0.487666
$731$	0.207005	0.00765635
$732$	−6.43131	−0.237708
$733$	39.4881	1.45852	0.729262	−	0.684234i	$-0.239863\pi$
$733$	39.4881	1.45852	0.729262	+	0.684234i	$0.239863\pi$
$734$	−25.9109	−0.956387
$735$	21.1438	0.779899
$736$	0.240229	0.00885497
$737$	6.34674	0.233785
$738$	−53.2667	−1.96078
$739$	9.43579	0.347101	0.173551	−	0.984825i	$-0.444476\pi$
$739$	9.43579	0.347101	0.173551	+	0.984825i	$0.444476\pi$
$740$	8.99410	0.330630
$741$	4.76080	0.174892
$742$	−1.56190	−0.0573391
$743$	9.27233	0.340169	0.170084	−	0.985429i	$-0.445596\pi$
$743$	9.27233	0.340169	0.170084	+	0.985429i	$0.445596\pi$
$744$	−4.06226	−0.148930
$745$	12.1058	0.443521
$746$	−28.1904	−1.03212
$747$	4.56738	0.167112
$748$	−0.149511	−0.00546666
$749$	3.01962	0.110335
$750$	−3.06059	−0.111757
$751$	30.1938	1.10179	0.550894	−	0.834575i	$-0.314287\pi$
$751$	30.1938	1.10179	0.550894	+	0.834575i	$0.314287\pi$
$752$	−4.02658	−0.146834
$753$	47.6331	1.73585
$754$	24.9502	0.908631
$755$	−20.5589	−0.748216
$756$	−3.11919	−0.113444
$757$	−8.16053	−0.296600	−0.148300	−	0.988942i	$-0.547380\pi$
$757$	−8.16053	−0.296600	−0.148300	+	0.988942i	$0.547380\pi$
$758$	8.83096	0.320755
$759$	−0.289455	−0.0105066
$760$	0.653758	0.0237143
$761$	−6.29743	−0.228282	−0.114141	−	0.993465i	$-0.536411\pi$
$761$	−6.29743	−0.228282	−0.114141	+	0.993465i	$0.536411\pi$
$762$	−61.1736	−2.21609
$763$	4.85252	0.175673
$764$	9.68976	0.350563
$765$	−2.41809	−0.0874261
$766$	−23.8392	−0.861346
$767$	13.6638	0.493370
$768$	−3.06059	−0.110440
$769$	−14.2318	−0.513213	−0.256606	−	0.966516i	$-0.582604\pi$
$769$	−14.2318	−0.513213	−0.256606	+	0.966516i	$0.582604\pi$
$770$	0.119157	0.00429410
$771$	−50.5395	−1.82014
$772$	−3.47297	−0.124995
$773$	−31.3779	−1.12858	−0.564291	−	0.825576i	$-0.690851\pi$
$773$	−31.3779	−1.12858	−0.564291	+	0.825576i	$0.690851\pi$
$774$	−3.47062	−0.124749
$775$	1.32728	0.0476773
$776$	−14.8895	−0.534500
$777$	−8.33164	−0.298896
$778$	7.53468	0.270131
$779$	−5.46921	−0.195955
$780$	7.28221	0.260745
$781$	−3.85486	−0.137938
$782$	−0.0912323	−0.00326246
$783$	108.066	3.86197
$784$	−6.90839	−0.246728
$785$	−7.47357	−0.266743
$786$	−28.3898	−1.01263
$787$	16.1594	0.576019	0.288009	−	0.957628i	$-0.407007\pi$
$787$	16.1594	0.576019	0.288009	+	0.957628i	$0.407007\pi$
$788$	−7.43346	−0.264806
$789$	14.0079	0.498695
$790$	6.29968	0.224133
$791$	−3.09520	−0.110053
$792$	2.50668	0.0890711
$793$	−4.99980	−0.177548
$794$	32.0835	1.13860
$795$	15.7939	0.560154
$796$	3.67524	0.130265
$797$	−25.9997	−0.920957	−0.460478	−	0.887671i	$-0.652322\pi$
$797$	−25.9997	−0.920957	−0.460478	+	0.887671i	$0.652322\pi$
$798$	−0.605605	−0.0214382
$799$	1.52918	0.0540985
$800$	1.00000	0.0353553
$801$	−61.6546	−2.17846
$802$	−10.4304	−0.368311
$803$	5.18721	0.183053
$804$	−49.3407	−1.74011
$805$	0.0727099	0.00256269
$806$	−3.15806	−0.111238
$807$	−87.3438	−3.07465
$808$	−18.4852	−0.650309
$809$	34.8638	1.22575	0.612873	−	0.790181i	$-0.290014\pi$
$809$	34.8638	1.22575	0.612873	+	0.790181i	$0.290014\pi$
$810$	12.4397	0.437087
$811$	17.2743	0.606582	0.303291	−	0.952898i	$-0.401915\pi$
$811$	17.2743	0.606582	0.303291	+	0.952898i	$0.401915\pi$
$812$	−3.17382	−0.111379
$813$	16.9954	0.596056
$814$	3.54085	0.124107
$815$	−2.21871	−0.0777179
$816$	1.16233	0.0406895
$817$	−0.356348	−0.0124670
$818$	1.01459	0.0354744
$819$	−4.58537	−0.160226
$820$	−8.36579	−0.292146
$821$	34.9707	1.22049	0.610243	−	0.792214i	$-0.291072\pi$
$821$	34.9707	1.22049	0.610243	+	0.792214i	$0.291072\pi$
$822$	−1.11660	−0.0389461
$823$	−24.5645	−0.856265	−0.428133	−	0.903716i	$-0.640828\pi$
$823$	−24.5645	−0.856265	−0.428133	+	0.903716i	$0.640828\pi$
$824$	5.65667	0.197059
$825$	−1.20491	−0.0419497
$826$	−1.73812	−0.0604769
$827$	21.7667	0.756901	0.378451	−	0.925621i	$-0.376457\pi$
$827$	21.7667	0.756901	0.378451	+	0.925621i	$0.376457\pi$
$828$	1.52959	0.0531569
$829$	−41.9351	−1.45647	−0.728233	−	0.685330i	$-0.759658\pi$
$829$	−41.9351	−1.45647	−0.728233	+	0.685330i	$0.759658\pi$
$830$	0.717328	0.0248988
$831$	−47.4158	−1.64484
$832$	−2.37935	−0.0824891
$833$	2.62361	0.0909028
$834$	25.4207	0.880245
$835$	−12.5368	−0.433855
$836$	0.257376	0.00890152
$837$	−13.6785	−0.472797
$838$	22.6659	0.782981
$839$	1.34936	0.0465851	0.0232926	−	0.999729i	$-0.492585\pi$
$839$	1.34936	0.0465851	0.0232926	+	0.999729i	$0.492585\pi$
$840$	−0.926345	−0.0319619
$841$	80.9589	2.79169
$842$	−20.7214	−0.714107
$843$	24.1762	0.832672
$844$	−20.2472	−0.696936
$845$	−7.33870	−0.252459
$846$	−25.6381	−0.881454
$847$	−3.28245	−0.112786
$848$	−5.16043	−0.177210
$849$	66.7465	2.29073
$850$	−0.379772	−0.0130261
$851$	2.16065	0.0740660
$852$	29.9684	1.02670
$853$	38.6294	1.32265	0.661323	−	0.750101i	$-0.269995\pi$
$853$	38.6294	1.32265	0.661323	+	0.750101i	$0.269995\pi$
$854$	0.636007	0.0217637
$855$	4.16261	0.142358
$856$	9.97666	0.340995
$857$	−50.7150	−1.73239	−0.866196	−	0.499704i	$-0.833442\pi$
$857$	−50.7150	−1.73239	−0.866196	+	0.499704i	$0.833442\pi$
$858$	2.86691	0.0978746
$859$	42.3999	1.44667	0.723333	−	0.690499i	$-0.242609\pi$
$859$	42.3999	1.44667	0.723333	+	0.690499i	$0.242609\pi$
$860$	−0.545077	−0.0185870
$861$	7.74961	0.264106
$862$	9.10219	0.310022
$863$	40.2068	1.36866	0.684328	−	0.729174i	$-0.260096\pi$
$863$	40.2068	1.36866	0.684328	+	0.729174i	$0.260096\pi$
$864$	−10.3056	−0.350605
$865$	7.28234	0.247607
$866$	−31.4151	−1.06753
$867$	51.5886	1.75204
$868$	0.401726	0.0136355
$869$	2.48010	0.0841316
$870$	32.0937	1.08808
$871$	−38.3582	−1.29972
$872$	16.0324	0.542927
$873$	−94.8043	−3.20864
$874$	0.157052	0.00531236
$875$	0.302669	0.0102321
$876$	−40.3263	−1.36250
$877$	2.34974	0.0793450	0.0396725	−	0.999213i	$-0.487369\pi$
$877$	2.34974	0.0793450	0.0396725	+	0.999213i	$0.487369\pi$
$878$	−0.429760	−0.0145037
$879$	−68.2963	−2.30358
$880$	0.393686	0.0132712
$881$	7.06575	0.238051	0.119026	−	0.992891i	$-0.462023\pi$
$881$	7.06575	0.238051	0.119026	+	0.992891i	$0.462023\pi$
$882$	−43.9872	−1.48112
$883$	53.2309	1.79136	0.895681	−	0.444696i	$-0.146688\pi$
$883$	53.2309	1.79136	0.895681	+	0.444696i	$0.146688\pi$
$884$	0.903609	0.0303917
$885$	17.5759	0.590807
$886$	33.5818	1.12820
$887$	−29.9113	−1.00432	−0.502162	−	0.864774i	$-0.667462\pi$
$887$	−29.9113	−1.00432	−0.502162	+	0.864774i	$0.667462\pi$
$888$	−27.5272	−0.923754
$889$	6.04960	0.202897
$890$	−9.68315	−0.324580
$891$	4.89734	0.164067
$892$	10.8134	0.362058
$893$	−2.63241	−0.0880902
$894$	−37.0508	−1.23916
$895$	11.8959	0.397637
$896$	0.302669	0.0101115
$897$	1.74940	0.0584107
$898$	−20.7822	−0.693510
$899$	−13.9180	−0.464193
$900$	6.36721	0.212240
$901$	1.95978	0.0652899
$902$	−3.29350	−0.109662
$903$	0.504929	0.0168030
$904$	−10.2264	−0.340124
$905$	−20.4579	−0.680042
$906$	62.9224	2.09046
$907$	−5.96352	−0.198015	−0.0990077	−	0.995087i	$-0.531567\pi$
$907$	−5.96352	−0.198015	−0.0990077	+	0.995087i	$0.531567\pi$
$908$	−27.9968	−0.929108
$909$	−117.699	−3.90384
$910$	−0.720154	−0.0238729
$911$	−29.5363	−0.978581	−0.489290	−	0.872121i	$-0.662744\pi$
$911$	−29.5363	−0.978581	−0.489290	+	0.872121i	$0.662744\pi$
$912$	−2.00089	−0.0662559
$913$	0.282402	0.00934615
$914$	−1.56659	−0.0518183
$915$	−6.43131	−0.212612
$916$	−21.2086	−0.700753
$917$	2.80753	0.0927129
$918$	3.91379	0.129174
$919$	2.98568	0.0984886	0.0492443	−	0.998787i	$-0.484319\pi$
$919$	2.98568	0.0984886	0.0492443	+	0.998787i	$0.484319\pi$
$920$	0.240229	0.00792012
$921$	−36.5547	−1.20452
$922$	−7.95973	−0.262140
$923$	23.2978	0.766858
$924$	−0.364689	−0.0119974
$925$	8.99410	0.295724
$926$	−40.2680	−1.32329
$927$	36.0172	1.18296
$928$	−10.4861	−0.344224
$929$	18.5062	0.607170	0.303585	−	0.952804i	$-0.401816\pi$
$929$	18.5062	0.607170	0.303585	+	0.952804i	$0.401816\pi$
$930$	−4.06226	−0.133207
$931$	−4.51642	−0.148020
$932$	−29.8509	−0.977797
$933$	50.4281	1.65094
$934$	−34.5397	−1.13017
$935$	−0.149511	−0.00488953
$936$	−15.1498	−0.495187
$937$	−24.6054	−0.803822	−0.401911	−	0.915679i	$-0.631654\pi$
$937$	−24.6054	−0.803822	−0.401911	+	0.915679i	$0.631654\pi$
$938$	4.87942	0.159319
$939$	−7.41883	−0.242104
$940$	−4.02658	−0.131332
$941$	−21.6435	−0.705558	−0.352779	−	0.935707i	$-0.614763\pi$
$941$	−21.6435	−0.705558	−0.352779	+	0.935707i	$0.614763\pi$
$942$	22.8735	0.745259
$943$	−2.00971	−0.0654451
$944$	−5.74265	−0.186907
$945$	−3.11919	−0.101467
$946$	−0.214589	−0.00697690
$947$	43.9424	1.42794	0.713968	−	0.700178i	$-0.246896\pi$
$947$	43.9424	1.42794	0.713968	+	0.700178i	$0.246896\pi$
$948$	−19.2807	−0.626209
$949$	−31.3503	−1.01767
$950$	0.653758	0.0212107
$951$	91.6240	2.97111
$952$	−0.114945	−0.00372539
$953$	52.7051	1.70728	0.853642	−	0.520860i	$-0.174389\pi$
$953$	52.7051	1.70728	0.853642	+	0.520860i	$0.174389\pi$
$954$	−32.8575	−1.06380
$955$	9.68976	0.313553
$956$	−9.17427	−0.296717
$957$	12.6349	0.408427
$958$	2.87871	0.0930071
$959$	0.110424	0.00356576
$960$	−3.06059	−0.0987801
$961$	−29.2383	−0.943172
$962$	−21.4001	−0.689967
$963$	63.5234	2.04701
$964$	14.5645	0.469092
$965$	−3.47297	−0.111799
$966$	−0.222535	−0.00715995
$967$	30.6050	0.984190	0.492095	−	0.870542i	$-0.336231\pi$
$967$	30.6050	0.984190	0.492095	+	0.870542i	$0.336231\pi$
$968$	−10.8450	−0.348572
$969$	0.759880	0.0244109
$970$	−14.8895	−0.478072
$971$	0.654697	0.0210102	0.0105051	−	0.999945i	$-0.496656\pi$
$971$	0.654697	0.0210102	0.0105051	+	0.999945i	$0.496656\pi$
$972$	−7.15592	−0.229526
$973$	−2.51391	−0.0805922
$974$	−4.69576	−0.150462
$975$	7.28221	0.233217
$976$	2.10133	0.0672619
$977$	50.6299	1.61979	0.809896	−	0.586573i	$-0.199523\pi$
$977$	50.6299	1.61979	0.809896	+	0.586573i	$0.199523\pi$
$978$	6.79055	0.217138
$979$	−3.81212	−0.121836
$980$	−6.90839	−0.220680
$981$	102.082	3.25922
$982$	4.22768	0.134911
$983$	−30.6793	−0.978516	−0.489258	−	0.872139i	$-0.662732\pi$
$983$	−30.6793	−0.978516	−0.489258	+	0.872139i	$0.662732\pi$
$984$	25.6043	0.816234
$985$	−7.43346	−0.236850
$986$	3.98234	0.126823
$987$	3.73000	0.118727
$988$	−1.55552	−0.0494876
$989$	−0.130943	−0.00416375
$990$	2.50668	0.0796676
$991$	28.0894	0.892288	0.446144	−	0.894961i	$-0.352797\pi$
$991$	28.0894	0.892288	0.446144	+	0.894961i	$0.352797\pi$
$992$	1.32728	0.0421412
$993$	32.2748	1.02421
$994$	−2.96364	−0.0940009
$995$	3.67524	0.116513
$996$	−2.19545	−0.0695654
$997$	14.8062	0.468916	0.234458	−	0.972126i	$-0.424669\pi$
$997$	14.8062	0.468916	0.234458	+	0.972126i	$0.424669\pi$
$998$	33.4020	1.05732
$999$	−92.6900	−2.93258

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.c.1.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.c.1.1	✓	16	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.06059 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.06059 q^{6} +0.302669 q^{7} +1.00000 q^{8} +6.36721 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.06059 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.06059 q^{6} +0.302669 q^{7} +1.00000 q^{8} +6.36721 q^{9} +1.00000 q^{10} +0.393686 q^{11} -3.06059 q^{12} -2.37935 q^{13} +0.302669 q^{14} -3.06059 q^{15} +1.00000 q^{16} -0.379772 q^{17} +6.36721 q^{18} +0.653758 q^{19} +1.00000 q^{20} -0.926345 q^{21} +0.393686 q^{22} +0.240229 q^{23} -3.06059 q^{24} +1.00000 q^{25} -2.37935 q^{26} -10.3056 q^{27} +0.302669 q^{28} -10.4861 q^{29} -3.06059 q^{30} +1.32728 q^{31} +1.00000 q^{32} -1.20491 q^{33} -0.379772 q^{34} +0.302669 q^{35} +6.36721 q^{36} +8.99410 q^{37} +0.653758 q^{38} +7.28221 q^{39} +1.00000 q^{40} -8.36579 q^{41} -0.926345 q^{42} -0.545077 q^{43} +0.393686 q^{44} +6.36721 q^{45} +0.240229 q^{46} -4.02658 q^{47} -3.06059 q^{48} -6.90839 q^{49} +1.00000 q^{50} +1.16233 q^{51} -2.37935 q^{52} -5.16043 q^{53} -10.3056 q^{54} +0.393686 q^{55} +0.302669 q^{56} -2.00089 q^{57} -10.4861 q^{58} -5.74265 q^{59} -3.06059 q^{60} +2.10133 q^{61} +1.32728 q^{62} +1.92715 q^{63} +1.00000 q^{64} -2.37935 q^{65} -1.20491 q^{66} +16.1213 q^{67} -0.379772 q^{68} -0.735243 q^{69} +0.302669 q^{70} -9.79169 q^{71} +6.36721 q^{72} +13.1760 q^{73} +8.99410 q^{74} -3.06059 q^{75} +0.653758 q^{76} +0.119157 q^{77} +7.28221 q^{78} +6.29968 q^{79} +1.00000 q^{80} +12.4397 q^{81} -8.36579 q^{82} +0.717328 q^{83} -0.926345 q^{84} -0.379772 q^{85} -0.545077 q^{86} +32.0937 q^{87} +0.393686 q^{88} -9.68315 q^{89} +6.36721 q^{90} -0.720154 q^{91} +0.240229 q^{92} -4.06226 q^{93} -4.02658 q^{94} +0.653758 q^{95} -3.06059 q^{96} -14.8895 q^{97} -6.90839 q^{98} +2.50668 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * q^99

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