LMFDB - Embedded newform 6042.2.a.bg.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.2456129013$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} - 34 x^{10} + 169 x^{9} + 453 x^{8} - 2095 x^{7} - 3056 x^{6} + 11545 x^{5} + \cdots + 7848 $ x^12 - 5x^11 - 34x^10 + 169x^9 + 453x^8 - 2095x^7 - 3056x^6 + 11545x^5 + 11014x^4 - 26766x^3 - 19370x^2 + 18296*x + 7848
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.927745$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.927745 q^{5} +1.00000 q^{6} +1.16139 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.927745 q^{5} +1.00000 q^{6} +1.16139 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.927745 q^{10} +3.50645 q^{11} +1.00000 q^{12} +0.153367 q^{13} +1.16139 q^{14} +0.927745 q^{15} +1.00000 q^{16} +4.78743 q^{17} +1.00000 q^{18} -1.00000 q^{19} +0.927745 q^{20} +1.16139 q^{21} +3.50645 q^{22} +9.11325 q^{23} +1.00000 q^{24} -4.13929 q^{25} +0.153367 q^{26} +1.00000 q^{27} +1.16139 q^{28} -5.43285 q^{29} +0.927745 q^{30} -2.77867 q^{31} +1.00000 q^{32} +3.50645 q^{33} +4.78743 q^{34} +1.07748 q^{35} +1.00000 q^{36} +7.39188 q^{37} -1.00000 q^{38} +0.153367 q^{39} +0.927745 q^{40} +2.71223 q^{41} +1.16139 q^{42} +0.708540 q^{43} +3.50645 q^{44} +0.927745 q^{45} +9.11325 q^{46} -11.3152 q^{47} +1.00000 q^{48} -5.65116 q^{49} -4.13929 q^{50} +4.78743 q^{51} +0.153367 q^{52} +1.00000 q^{53} +1.00000 q^{54} +3.25309 q^{55} +1.16139 q^{56} -1.00000 q^{57} -5.43285 q^{58} -10.9588 q^{59} +0.927745 q^{60} +3.95330 q^{61} -2.77867 q^{62} +1.16139 q^{63} +1.00000 q^{64} +0.142285 q^{65} +3.50645 q^{66} -5.34069 q^{67} +4.78743 q^{68} +9.11325 q^{69} +1.07748 q^{70} +8.92840 q^{71} +1.00000 q^{72} -0.967789 q^{73} +7.39188 q^{74} -4.13929 q^{75} -1.00000 q^{76} +4.07237 q^{77} +0.153367 q^{78} -16.3115 q^{79} +0.927745 q^{80} +1.00000 q^{81} +2.71223 q^{82} +16.3006 q^{83} +1.16139 q^{84} +4.44152 q^{85} +0.708540 q^{86} -5.43285 q^{87} +3.50645 q^{88} -1.57832 q^{89} +0.927745 q^{90} +0.178120 q^{91} +9.11325 q^{92} -2.77867 q^{93} -11.3152 q^{94} -0.927745 q^{95} +1.00000 q^{96} -14.6153 q^{97} -5.65116 q^{98} +3.50645 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 5 q^{5} + 12 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 5 * q^5 + 12 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 5 q^{5} + 12 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9} + 5 q^{10} + 7 q^{11} + 12 q^{12} + 9 q^{13} + 6 q^{14} + 5 q^{15} + 12 q^{16} + 25 q^{17} + 12 q^{18} - 12 q^{19} + 5 q^{20} + 6 q^{21} + 7 q^{22} + 22 q^{23} + 12 q^{24} + 33 q^{25} + 9 q^{26} + 12 q^{27} + 6 q^{28} + q^{29} + 5 q^{30} + 23 q^{31} + 12 q^{32} + 7 q^{33} + 25 q^{34} + 5 q^{35} + 12 q^{36} - q^{37} - 12 q^{38} + 9 q^{39} + 5 q^{40} - 15 q^{41} + 6 q^{42} + 2 q^{43} + 7 q^{44} + 5 q^{45} + 22 q^{46} + 11 q^{47} + 12 q^{48} + 36 q^{49} + 33 q^{50} + 25 q^{51} + 9 q^{52} + 12 q^{53} + 12 q^{54} - 4 q^{55} + 6 q^{56} - 12 q^{57} + q^{58} + 3 q^{59} + 5 q^{60} + 16 q^{61} + 23 q^{62} + 6 q^{63} + 12 q^{64} + 7 q^{65} + 7 q^{66} - 2 q^{67} + 25 q^{68} + 22 q^{69} + 5 q^{70} - 4 q^{71} + 12 q^{72} + 35 q^{73} - q^{74} + 33 q^{75} - 12 q^{76} + 11 q^{77} + 9 q^{78} + 4 q^{79} + 5 q^{80} + 12 q^{81} - 15 q^{82} + 39 q^{83} + 6 q^{84} + 10 q^{85} + 2 q^{86} + q^{87} + 7 q^{88} + 11 q^{89} + 5 q^{90} - 18 q^{91} + 22 q^{92} + 23 q^{93} + 11 q^{94} - 5 q^{95} + 12 q^{96} - 21 q^{97} + 36 q^{98} + 7 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 5 * q^5 + 12 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9 + 5 * q^10 + 7 * q^11 + 12 * q^12 + 9 * q^13 + 6 * q^14 + 5 * q^15 + 12 * q^16 + 25 * q^17 + 12 * q^18 - 12 * q^19 + 5 * q^20 + 6 * q^21 + 7 * q^22 + 22 * q^23 + 12 * q^24 + 33 * q^25 + 9 * q^26 + 12 * q^27 + 6 * q^28 + q^29 + 5 * q^30 + 23 * q^31 + 12 * q^32 + 7 * q^33 + 25 * q^34 + 5 * q^35 + 12 * q^36 - q^37 - 12 * q^38 + 9 * q^39 + 5 * q^40 - 15 * q^41 + 6 * q^42 + 2 * q^43 + 7 * q^44 + 5 * q^45 + 22 * q^46 + 11 * q^47 + 12 * q^48 + 36 * q^49 + 33 * q^50 + 25 * q^51 + 9 * q^52 + 12 * q^53 + 12 * q^54 - 4 * q^55 + 6 * q^56 - 12 * q^57 + q^58 + 3 * q^59 + 5 * q^60 + 16 * q^61 + 23 * q^62 + 6 * q^63 + 12 * q^64 + 7 * q^65 + 7 * q^66 - 2 * q^67 + 25 * q^68 + 22 * q^69 + 5 * q^70 - 4 * q^71 + 12 * q^72 + 35 * q^73 - q^74 + 33 * q^75 - 12 * q^76 + 11 * q^77 + 9 * q^78 + 4 * q^79 + 5 * q^80 + 12 * q^81 - 15 * q^82 + 39 * q^83 + 6 * q^84 + 10 * q^85 + 2 * q^86 + q^87 + 7 * q^88 + 11 * q^89 + 5 * q^90 - 18 * q^91 + 22 * q^92 + 23 * q^93 + 11 * q^94 - 5 * q^95 + 12 * q^96 - 21 * q^97 + 36 * q^98 + 7 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.927745	0.414900	0.207450	−	0.978246i	$-0.433484\pi$
$5$	0.927745	0.414900	0.207450	+	0.978246i	$0.433484\pi$
$6$	1.00000	0.408248
$7$	1.16139	0.438966	0.219483	−	0.975616i	$-0.429563\pi$
$7$	1.16139	0.438966	0.219483	+	0.975616i	$0.429563\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.927745	0.293379
$11$	3.50645	1.05723	0.528617	−	0.848860i	$-0.322711\pi$
$11$	3.50645	1.05723	0.528617	+	0.848860i	$0.322711\pi$
$12$	1.00000	0.288675
$13$	0.153367	0.0425364	0.0212682	−	0.999774i	$-0.493230\pi$
$13$	0.153367	0.0425364	0.0212682	+	0.999774i	$0.493230\pi$
$14$	1.16139	0.310396
$15$	0.927745	0.239543
$16$	1.00000	0.250000
$17$	4.78743	1.16112	0.580562	−	0.814216i	$-0.302833\pi$
$17$	4.78743	1.16112	0.580562	+	0.814216i	$0.302833\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.927745	0.207450
$21$	1.16139	0.253437
$22$	3.50645	0.747578
$23$	9.11325	1.90024	0.950122	−	0.311878i	$-0.100958\pi$
$23$	9.11325	1.90024	0.950122	+	0.311878i	$0.100958\pi$
$24$	1.00000	0.204124
$25$	−4.13929	−0.827858
$26$	0.153367	0.0300777
$27$	1.00000	0.192450
$28$	1.16139	0.219483
$29$	−5.43285	−1.00886	−0.504428	−	0.863454i	$-0.668297\pi$
$29$	−5.43285	−1.00886	−0.504428	+	0.863454i	$0.668297\pi$
$30$	0.927745	0.169382
$31$	−2.77867	−0.499064	−0.249532	−	0.968367i	$-0.580277\pi$
$31$	−2.77867	−0.499064	−0.249532	+	0.968367i	$0.580277\pi$
$32$	1.00000	0.176777
$33$	3.50645	0.610395
$34$	4.78743	0.821038
$35$	1.07748	0.182127
$36$	1.00000	0.166667
$37$	7.39188	1.21522	0.607608	−	0.794237i	$-0.292129\pi$
$37$	7.39188	1.21522	0.607608	+	0.794237i	$0.292129\pi$
$38$	−1.00000	−0.162221
$39$	0.153367	0.0245584
$40$	0.927745	0.146689
$41$	2.71223	0.423579	0.211789	−	0.977315i	$-0.432071\pi$
$41$	2.71223	0.423579	0.211789	+	0.977315i	$0.432071\pi$
$42$	1.16139	0.179207
$43$	0.708540	0.108051	0.0540257	−	0.998540i	$-0.482795\pi$
$43$	0.708540	0.108051	0.0540257	+	0.998540i	$0.482795\pi$
$44$	3.50645	0.528617
$45$	0.927745	0.138300
$46$	9.11325	1.34368
$47$	−11.3152	−1.65050	−0.825249	−	0.564769i	$-0.808965\pi$
$47$	−11.3152	−1.65050	−0.825249	+	0.564769i	$0.808965\pi$
$48$	1.00000	0.144338
$49$	−5.65116	−0.807309
$50$	−4.13929	−0.585384
$51$	4.78743	0.670375
$52$	0.153367	0.0212682
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	1.00000	0.136083
$55$	3.25309	0.438647
$56$	1.16139	0.155198
$57$	−1.00000	−0.132453
$58$	−5.43285	−0.713369
$59$	−10.9588	−1.42672	−0.713359	−	0.700799i	$-0.752827\pi$
$59$	−10.9588	−1.42672	−0.713359	+	0.700799i	$0.752827\pi$
$60$	0.927745	0.119771
$61$	3.95330	0.506168	0.253084	−	0.967444i	$-0.418555\pi$
$61$	3.95330	0.506168	0.253084	+	0.967444i	$0.418555\pi$
$62$	−2.77867	−0.352892
$63$	1.16139	0.146322
$64$	1.00000	0.125000
$65$	0.142285	0.0176483
$66$	3.50645	0.431614
$67$	−5.34069	−0.652470	−0.326235	−	0.945289i	$-0.605780\pi$
$67$	−5.34069	−0.652470	−0.326235	+	0.945289i	$0.605780\pi$
$68$	4.78743	0.580562
$69$	9.11325	1.09711
$70$	1.07748	0.128783
$71$	8.92840	1.05961	0.529803	−	0.848121i	$-0.322266\pi$
$71$	8.92840	1.05961	0.529803	+	0.848121i	$0.322266\pi$
$72$	1.00000	0.117851
$73$	−0.967789	−0.113271	−0.0566356	−	0.998395i	$-0.518037\pi$
$73$	−0.967789	−0.113271	−0.0566356	+	0.998395i	$0.518037\pi$
$74$	7.39188	0.859288
$75$	−4.13929	−0.477964
$76$	−1.00000	−0.114708
$77$	4.07237	0.464090
$78$	0.153367	0.0173654
$79$	−16.3115	−1.83518	−0.917592	−	0.397523i	$-0.869870\pi$
$79$	−16.3115	−1.83518	−0.917592	+	0.397523i	$0.869870\pi$
$80$	0.927745	0.103725
$81$	1.00000	0.111111
$82$	2.71223	0.299515
$83$	16.3006	1.78922	0.894610	−	0.446847i	$-0.147453\pi$
$83$	16.3006	1.78922	0.894610	+	0.446847i	$0.147453\pi$
$84$	1.16139	0.126719
$85$	4.44152	0.481750
$86$	0.708540	0.0764039
$87$	−5.43285	−0.582463
$88$	3.50645	0.373789
$89$	−1.57832	−0.167301	−0.0836505	−	0.996495i	$-0.526658\pi$
$89$	−1.57832	−0.167301	−0.0836505	+	0.996495i	$0.526658\pi$
$90$	0.927745	0.0977929
$91$	0.178120	0.0186720
$92$	9.11325	0.950122
$93$	−2.77867	−0.288135
$94$	−11.3152	−1.16708
$95$	−0.927745	−0.0951846
$96$	1.00000	0.102062
$97$	−14.6153	−1.48396	−0.741979	−	0.670423i	$-0.766113\pi$
$97$	−14.6153	−1.48396	−0.741979	+	0.670423i	$0.766113\pi$
$98$	−5.65116	−0.570854
$99$	3.50645	0.352412
$100$	−4.13929	−0.413929
$101$	7.97455	0.793498	0.396749	−	0.917927i	$-0.370138\pi$
$101$	7.97455	0.793498	0.396749	+	0.917927i	$0.370138\pi$
$102$	4.78743	0.474027
$103$	−15.4228	−1.51965	−0.759826	−	0.650126i	$-0.774716\pi$
$103$	−15.4228	−1.51965	−0.759826	+	0.650126i	$0.774716\pi$
$104$	0.153367	0.0150389
$105$	1.07748	0.105151
$106$	1.00000	0.0971286
$107$	10.1866	0.984778	0.492389	−	0.870375i	$-0.336124\pi$
$107$	10.1866	0.984778	0.492389	+	0.870375i	$0.336124\pi$
$108$	1.00000	0.0962250
$109$	9.35935	0.896463	0.448232	−	0.893917i	$-0.352054\pi$
$109$	9.35935	0.896463	0.448232	+	0.893917i	$0.352054\pi$
$110$	3.25309	0.310170
$111$	7.39188	0.701606
$112$	1.16139	0.109741
$113$	10.5471	0.992191	0.496096	−	0.868268i	$-0.334767\pi$
$113$	10.5471	0.992191	0.496096	+	0.868268i	$0.334767\pi$
$114$	−1.00000	−0.0936586
$115$	8.45477	0.788411
$116$	−5.43285	−0.504428
$117$	0.153367	0.0141788
$118$	−10.9588	−1.00884
$119$	5.56010	0.509694
$120$	0.927745	0.0846911
$121$	1.29520	0.117745
$122$	3.95330	0.357915
$123$	2.71223	0.244553
$124$	−2.77867	−0.249532
$125$	−8.47893	−0.758378
$126$	1.16139	0.103465
$127$	4.74237	0.420818	0.210409	−	0.977613i	$-0.432521\pi$
$127$	4.74237	0.420818	0.210409	+	0.977613i	$0.432521\pi$
$128$	1.00000	0.0883883
$129$	0.708540	0.0623835
$130$	0.142285	0.0124793
$131$	7.60522	0.664471	0.332236	−	0.943196i	$-0.392197\pi$
$131$	7.60522	0.664471	0.332236	+	0.943196i	$0.392197\pi$
$132$	3.50645	0.305197
$133$	−1.16139	−0.100706
$134$	−5.34069	−0.461366
$135$	0.927745	0.0798476
$136$	4.78743	0.410519
$137$	−16.1698	−1.38148	−0.690741	−	0.723102i	$-0.742716\pi$
$137$	−16.1698	−1.38148	−0.690741	+	0.723102i	$0.742716\pi$
$138$	9.11325	0.775771
$139$	21.8298	1.85158	0.925790	−	0.378038i	$-0.123401\pi$
$139$	21.8298	1.85158	0.925790	+	0.378038i	$0.123401\pi$
$140$	1.07748	0.0910635
$141$	−11.3152	−0.952916
$142$	8.92840	0.749255
$143$	0.537774	0.0449709
$144$	1.00000	0.0833333
$145$	−5.04030	−0.418574
$146$	−0.967789	−0.0800948
$147$	−5.65116	−0.466100
$148$	7.39188	0.607608
$149$	−23.4273	−1.91924	−0.959621	−	0.281296i	$-0.909236\pi$
$149$	−23.4273	−1.91924	−0.959621	+	0.281296i	$0.909236\pi$
$150$	−4.13929	−0.337972
$151$	−5.95655	−0.484738	−0.242369	−	0.970184i	$-0.577924\pi$
$151$	−5.95655	−0.484738	−0.242369	+	0.970184i	$0.577924\pi$
$152$	−1.00000	−0.0811107
$153$	4.78743	0.387041
$154$	4.07237	0.328161
$155$	−2.57790	−0.207062
$156$	0.153367	0.0122792
$157$	3.65440	0.291653	0.145826	−	0.989310i	$-0.453416\pi$
$157$	3.65440	0.291653	0.145826	+	0.989310i	$0.453416\pi$
$158$	−16.3115	−1.29767
$159$	1.00000	0.0793052
$160$	0.927745	0.0733447
$161$	10.5841	0.834142
$162$	1.00000	0.0785674
$163$	12.0826	0.946380	0.473190	−	0.880961i	$-0.343102\pi$
$163$	12.0826	0.946380	0.473190	+	0.880961i	$0.343102\pi$
$164$	2.71223	0.211789
$165$	3.25309	0.253253
$166$	16.3006	1.26517
$167$	2.22021	0.171805	0.0859025	−	0.996304i	$-0.472623\pi$
$167$	2.22021	0.171805	0.0859025	+	0.996304i	$0.472623\pi$
$168$	1.16139	0.0896035
$169$	−12.9765	−0.998191
$170$	4.44152	0.340649
$171$	−1.00000	−0.0764719
$172$	0.708540	0.0540257
$173$	1.37698	0.104690	0.0523451	−	0.998629i	$-0.483330\pi$
$173$	1.37698	0.104690	0.0523451	+	0.998629i	$0.483330\pi$
$174$	−5.43285	−0.411864
$175$	−4.80735	−0.363401
$176$	3.50645	0.264309
$177$	−10.9588	−0.823716
$178$	−1.57832	−0.118300
$179$	0.166620	0.0124537	0.00622686	−	0.999981i	$-0.498018\pi$
$179$	0.166620	0.0124537	0.00622686	+	0.999981i	$0.498018\pi$
$180$	0.927745	0.0691500
$181$	16.5026	1.22663	0.613315	−	0.789839i	$-0.289836\pi$
$181$	16.5026	1.22663	0.613315	+	0.789839i	$0.289836\pi$
$182$	0.178120	0.0132031
$183$	3.95330	0.292236
$184$	9.11325	0.671838
$185$	6.85777	0.504194
$186$	−2.77867	−0.203742
$187$	16.7869	1.22758
$188$	−11.3152	−0.825249
$189$	1.16139	0.0844790
$190$	−0.927745	−0.0673057
$191$	15.6020	1.12892	0.564459	−	0.825461i	$-0.309085\pi$
$191$	15.6020	1.12892	0.564459	+	0.825461i	$0.309085\pi$
$192$	1.00000	0.0721688
$193$	−19.8402	−1.42813	−0.714063	−	0.700082i	$-0.753147\pi$
$193$	−19.8402	−1.42813	−0.714063	+	0.700082i	$0.753147\pi$
$194$	−14.6153	−1.04932
$195$	0.142285	0.0101893
$196$	−5.65116	−0.403654
$197$	−21.2007	−1.51049	−0.755243	−	0.655445i	$-0.772481\pi$
$197$	−21.2007	−1.51049	−0.755243	+	0.655445i	$0.772481\pi$
$198$	3.50645	0.249193
$199$	14.0550	0.996331	0.498166	−	0.867082i	$-0.334007\pi$
$199$	14.0550	0.996331	0.498166	+	0.867082i	$0.334007\pi$
$200$	−4.13929	−0.292692
$201$	−5.34069	−0.376704
$202$	7.97455	0.561088
$203$	−6.30969	−0.442853
$204$	4.78743	0.335187
$205$	2.51626	0.175743
$206$	−15.4228	−1.07456
$207$	9.11325	0.633415
$208$	0.153367	0.0106341
$209$	−3.50645	−0.242546
$210$	1.07748	0.0743530
$211$	−7.62576	−0.524979	−0.262490	−	0.964935i	$-0.584544\pi$
$211$	−7.62576	−0.524979	−0.262490	+	0.964935i	$0.584544\pi$
$212$	1.00000	0.0686803
$213$	8.92840	0.611764
$214$	10.1866	0.696343
$215$	0.657345	0.0448305
$216$	1.00000	0.0680414
$217$	−3.22713	−0.219072
$218$	9.35935	0.633895
$219$	−0.967789	−0.0653971
$220$	3.25309	0.219323
$221$	0.734234	0.0493900
$222$	7.39188	0.496110
$223$	27.8011	1.86170	0.930849	−	0.365403i	$-0.119069\pi$
$223$	27.8011	1.86170	0.930849	+	0.365403i	$0.119069\pi$
$224$	1.16139	0.0775989
$225$	−4.13929	−0.275953
$226$	10.5471	0.701585
$227$	−26.5567	−1.76263	−0.881314	−	0.472530i	$-0.843341\pi$
$227$	−26.5567	−1.76263	−0.881314	+	0.472530i	$0.843341\pi$
$228$	−1.00000	−0.0662266
$229$	21.1782	1.39949	0.699746	−	0.714391i	$-0.253296\pi$
$229$	21.1782	1.39949	0.699746	+	0.714391i	$0.253296\pi$
$230$	8.45477	0.557491
$231$	4.07237	0.267943
$232$	−5.43285	−0.356684
$233$	8.53946	0.559439	0.279719	−	0.960082i	$-0.409759\pi$
$233$	8.53946	0.559439	0.279719	+	0.960082i	$0.409759\pi$
$234$	0.153367	0.0100259
$235$	−10.4977	−0.684792
$236$	−10.9588	−0.713359
$237$	−16.3115	−1.05954
$238$	5.56010	0.360408
$239$	−14.6674	−0.948752	−0.474376	−	0.880322i	$-0.657326\pi$
$239$	−14.6674	−0.948752	−0.474376	+	0.880322i	$0.657326\pi$
$240$	0.927745	0.0598857
$241$	20.8129	1.34068	0.670339	−	0.742055i	$-0.266149\pi$
$241$	20.8129	1.34068	0.670339	+	0.742055i	$0.266149\pi$
$242$	1.29520	0.0832585
$243$	1.00000	0.0641500
$244$	3.95330	0.253084
$245$	−5.24284	−0.334953
$246$	2.71223	0.172925
$247$	−0.153367	−0.00975851
$248$	−2.77867	−0.176446
$249$	16.3006	1.03301
$250$	−8.47893	−0.536255
$251$	14.1095	0.890582	0.445291	−	0.895386i	$-0.353100\pi$
$251$	14.1095	0.890582	0.445291	+	0.895386i	$0.353100\pi$
$252$	1.16139	0.0731610
$253$	31.9552	2.00900
$254$	4.74237	0.297563
$255$	4.44152	0.278139
$256$	1.00000	0.0625000
$257$	15.0503	0.938809	0.469404	−	0.882983i	$-0.344469\pi$
$257$	15.0503	0.938809	0.469404	+	0.882983i	$0.344469\pi$
$258$	0.708540	0.0441118
$259$	8.58489	0.533439
$260$	0.142285	0.00882417
$261$	−5.43285	−0.336285
$262$	7.60522	0.469852
$263$	−0.751667	−0.0463498	−0.0231749	−	0.999731i	$-0.507377\pi$
$263$	−0.751667	−0.0463498	−0.0231749	+	0.999731i	$0.507377\pi$
$264$	3.50645	0.215807
$265$	0.927745	0.0569909
$266$	−1.16139	−0.0712097
$267$	−1.57832	−0.0965913
$268$	−5.34069	−0.326235
$269$	14.2126	0.866556	0.433278	−	0.901260i	$-0.357357\pi$
$269$	14.2126	0.866556	0.433278	+	0.901260i	$0.357357\pi$
$270$	0.927745	0.0564608
$271$	−14.0951	−0.856216	−0.428108	−	0.903728i	$-0.640820\pi$
$271$	−14.0951	−0.856216	−0.428108	+	0.903728i	$0.640820\pi$
$272$	4.78743	0.290281
$273$	0.178120	0.0107803
$274$	−16.1698	−0.976856
$275$	−14.5142	−0.875240
$276$	9.11325	0.548553
$277$	−19.5463	−1.17443	−0.587213	−	0.809433i	$-0.699775\pi$
$277$	−19.5463	−1.17443	−0.587213	+	0.809433i	$0.699775\pi$
$278$	21.8298	1.30926
$279$	−2.77867	−0.166355
$280$	1.07748	0.0643916
$281$	16.1610	0.964082	0.482041	−	0.876149i	$-0.339896\pi$
$281$	16.1610	0.964082	0.482041	+	0.876149i	$0.339896\pi$
$282$	−11.3152	−0.673813
$283$	−20.9598	−1.24593	−0.622966	−	0.782249i	$-0.714073\pi$
$283$	−20.9598	−1.24593	−0.622966	+	0.782249i	$0.714073\pi$
$284$	8.92840	0.529803
$285$	−0.927745	−0.0549549
$286$	0.537774	0.0317992
$287$	3.14997	0.185937
$288$	1.00000	0.0589256
$289$	5.91953	0.348208
$290$	−5.04030	−0.295977
$291$	−14.6153	−0.856764
$292$	−0.967789	−0.0566356
$293$	−32.0945	−1.87498	−0.937489	−	0.348014i	$-0.886856\pi$
$293$	−32.0945	−1.87498	−0.937489	+	0.348014i	$0.886856\pi$
$294$	−5.65116	−0.329582
$295$	−10.1670	−0.591945
$296$	7.39188	0.429644
$297$	3.50645	0.203465
$298$	−23.4273	−1.35711
$299$	1.39767	0.0808295
$300$	−4.13929	−0.238982
$301$	0.822895	0.0474309
$302$	−5.95655	−0.342761
$303$	7.97455	0.458126
$304$	−1.00000	−0.0573539
$305$	3.66765	0.210009
$306$	4.78743	0.273679
$307$	10.5823	0.603964	0.301982	−	0.953314i	$-0.402352\pi$
$307$	10.5823	0.603964	0.301982	+	0.953314i	$0.402352\pi$
$308$	4.07237	0.232045
$309$	−15.4228	−0.877372
$310$	−2.57790	−0.146415
$311$	−8.96308	−0.508250	−0.254125	−	0.967171i	$-0.581787\pi$
$311$	−8.96308	−0.508250	−0.254125	+	0.967171i	$0.581787\pi$
$312$	0.153367	0.00868270
$313$	−11.2298	−0.634747	−0.317374	−	0.948301i	$-0.602801\pi$
$313$	−11.2298	−0.634747	−0.317374	+	0.948301i	$0.602801\pi$
$314$	3.65440	0.206230
$315$	1.07748	0.0607090
$316$	−16.3115	−0.917592
$317$	−3.23175	−0.181513	−0.0907565	−	0.995873i	$-0.528928\pi$
$317$	−3.23175	−0.181513	−0.0907565	+	0.995873i	$0.528928\pi$
$318$	1.00000	0.0560772
$319$	−19.0500	−1.06660
$320$	0.927745	0.0518625
$321$	10.1866	0.568562
$322$	10.5841	0.589828
$323$	−4.78743	−0.266380
$324$	1.00000	0.0555556
$325$	−0.634830	−0.0352141
$326$	12.0826	0.669191
$327$	9.35935	0.517573
$328$	2.71223	0.149758
$329$	−13.1415	−0.724513
$330$	3.25309	0.179077
$331$	−25.3546	−1.39361	−0.696807	−	0.717259i	$-0.745397\pi$
$331$	−25.3546	−1.39361	−0.696807	+	0.717259i	$0.745397\pi$
$332$	16.3006	0.894610
$333$	7.39188	0.405072
$334$	2.22021	0.121484
$335$	−4.95480	−0.270710
$336$	1.16139	0.0633593
$337$	−24.5931	−1.33967	−0.669835	−	0.742510i	$-0.733635\pi$
$337$	−24.5931	−1.33967	−0.669835	+	0.742510i	$0.733635\pi$
$338$	−12.9765	−0.705827
$339$	10.5471	0.572842
$340$	4.44152	0.240875
$341$	−9.74327	−0.527628
$342$	−1.00000	−0.0540738
$343$	−14.6930	−0.793347
$344$	0.708540	0.0382019
$345$	8.45477	0.455190
$346$	1.37698	0.0740271
$347$	−8.73316	−0.468820	−0.234410	−	0.972138i	$-0.575316\pi$
$347$	−8.73316	−0.468820	−0.234410	+	0.972138i	$0.575316\pi$
$348$	−5.43285	−0.291232
$349$	16.0533	0.859311	0.429655	−	0.902993i	$-0.358635\pi$
$349$	16.0533	0.859311	0.429655	+	0.902993i	$0.358635\pi$
$350$	−4.80735	−0.256964
$351$	0.153367	0.00818612
$352$	3.50645	0.186894
$353$	−6.59110	−0.350809	−0.175404	−	0.984496i	$-0.556123\pi$
$353$	−6.59110	−0.350809	−0.175404	+	0.984496i	$0.556123\pi$
$354$	−10.9588	−0.582455
$355$	8.28328	0.439631
$356$	−1.57832	−0.0836505
$357$	5.56010	0.294272
$358$	0.166620	0.00880612
$359$	−6.83128	−0.360541	−0.180270	−	0.983617i	$-0.557697\pi$
$359$	−6.83128	−0.360541	−0.180270	+	0.983617i	$0.557697\pi$
$360$	0.927745	0.0488964
$361$	1.00000	0.0526316
$362$	16.5026	0.867358
$363$	1.29520	0.0679803
$364$	0.178120	0.00933600
$365$	−0.897861	−0.0469962
$366$	3.95330	0.206642
$367$	13.2802	0.693220	0.346610	−	0.938009i	$-0.387333\pi$
$367$	13.2802	0.693220	0.346610	+	0.938009i	$0.387333\pi$
$368$	9.11325	0.475061
$369$	2.71223	0.141193
$370$	6.85777	0.356519
$371$	1.16139	0.0602966
$372$	−2.77867	−0.144067
$373$	13.7576	0.712343	0.356171	−	0.934421i	$-0.384082\pi$
$373$	13.7576	0.712343	0.356171	+	0.934421i	$0.384082\pi$
$374$	16.7869	0.868030
$375$	−8.47893	−0.437850
$376$	−11.3152	−0.583539
$377$	−0.833221	−0.0429130
$378$	1.16139	0.0597357
$379$	6.48503	0.333114	0.166557	−	0.986032i	$-0.446735\pi$
$379$	6.48503	0.333114	0.166557	+	0.986032i	$0.446735\pi$
$380$	−0.927745	−0.0475923
$381$	4.74237	0.242959
$382$	15.6020	0.798265
$383$	−36.7299	−1.87681	−0.938405	−	0.345536i	$-0.887697\pi$
$383$	−36.7299	−1.87681	−0.938405	+	0.345536i	$0.887697\pi$
$384$	1.00000	0.0510310
$385$	3.77812	0.192551
$386$	−19.8402	−1.00984
$387$	0.708540	0.0360171
$388$	−14.6153	−0.741979
$389$	15.3419	0.777866	0.388933	−	0.921266i	$-0.372844\pi$
$389$	15.3419	0.777866	0.388933	+	0.921266i	$0.372844\pi$
$390$	0.142285	0.00720490
$391$	43.6291	2.20642
$392$	−5.65116	−0.285427
$393$	7.60522	0.383633
$394$	−21.2007	−1.06807
$395$	−15.1329	−0.761418
$396$	3.50645	0.176206
$397$	1.89265	0.0949895	0.0474947	−	0.998871i	$-0.484876\pi$
$397$	1.89265	0.0949895	0.0474947	+	0.998871i	$0.484876\pi$
$398$	14.0550	0.704513
$399$	−1.16139	−0.0581425
$400$	−4.13929	−0.206964
$401$	29.8981	1.49304	0.746521	−	0.665362i	$-0.231723\pi$
$401$	29.8981	1.49304	0.746521	+	0.665362i	$0.231723\pi$
$402$	−5.34069	−0.266370
$403$	−0.426156	−0.0212284
$404$	7.97455	0.396749
$405$	0.927745	0.0461000
$406$	−6.30969	−0.313145
$407$	25.9192	1.28477
$408$	4.78743	0.237013
$409$	25.2484	1.24845	0.624226	−	0.781244i	$-0.285414\pi$
$409$	25.2484	1.24845	0.624226	+	0.781244i	$0.285414\pi$
$410$	2.51626	0.124269
$411$	−16.1698	−0.797599
$412$	−15.4228	−0.759826
$413$	−12.7275	−0.626281
$414$	9.11325	0.447892
$415$	15.1228	0.742348
$416$	0.153367	0.00751944
$417$	21.8298	1.06901
$418$	−3.50645	−0.171506
$419$	−6.72841	−0.328704	−0.164352	−	0.986402i	$-0.552553\pi$
$419$	−6.72841	−0.328704	−0.164352	+	0.986402i	$0.552553\pi$
$420$	1.07748	0.0525755
$421$	−12.0717	−0.588339	−0.294170	−	0.955753i	$-0.595043\pi$
$421$	−12.0717	−0.588339	−0.294170	+	0.955753i	$0.595043\pi$
$422$	−7.62576	−0.371216
$423$	−11.3152	−0.550166
$424$	1.00000	0.0485643
$425$	−19.8166	−0.961245
$426$	8.92840	0.432582
$427$	4.59134	0.222190
$428$	10.1866	0.492389
$429$	0.537774	0.0259640
$430$	0.657345	0.0317000
$431$	0.259149	0.0124828	0.00624138	−	0.999981i	$-0.498013\pi$
$431$	0.259149	0.0124828	0.00624138	+	0.999981i	$0.498013\pi$
$432$	1.00000	0.0481125
$433$	−0.164921	−0.00792557	−0.00396279	−	0.999992i	$-0.501261\pi$
$433$	−0.164921	−0.00792557	−0.00396279	+	0.999992i	$0.501261\pi$
$434$	−3.22713	−0.154907
$435$	−5.04030	−0.241664
$436$	9.35935	0.448232
$437$	−9.11325	−0.435946
$438$	−0.967789	−0.0462428
$439$	15.3617	0.733174	0.366587	−	0.930384i	$-0.380526\pi$
$439$	15.3617	0.733174	0.366587	+	0.930384i	$0.380526\pi$
$440$	3.25309	0.155085
$441$	−5.65116	−0.269103
$442$	0.734234	0.0349240
$443$	14.0243	0.666313	0.333157	−	0.942871i	$-0.391886\pi$
$443$	14.0243	0.666313	0.333157	+	0.942871i	$0.391886\pi$
$444$	7.39188	0.350803
$445$	−1.46427	−0.0694132
$446$	27.8011	1.31642
$447$	−23.4273	−1.10807
$448$	1.16139	0.0548707
$449$	−12.9789	−0.612510	−0.306255	−	0.951950i	$-0.599076\pi$
$449$	−12.9789	−0.612510	−0.306255	+	0.951950i	$0.599076\pi$
$450$	−4.13929	−0.195128
$451$	9.51030	0.447822
$452$	10.5471	0.496096
$453$	−5.95655	−0.279863
$454$	−26.5567	−1.24637
$455$	0.165250	0.00774702
$456$	−1.00000	−0.0468293
$457$	16.8082	0.786256	0.393128	−	0.919484i	$-0.371393\pi$
$457$	16.8082	0.786256	0.393128	+	0.919484i	$0.371393\pi$
$458$	21.1782	0.989591
$459$	4.78743	0.223458
$460$	8.45477	0.394206
$461$	−10.0120	−0.466304	−0.233152	−	0.972440i	$-0.574904\pi$
$461$	−10.0120	−0.466304	−0.233152	+	0.972440i	$0.574904\pi$
$462$	4.07237	0.189464
$463$	−1.66416	−0.0773399	−0.0386699	−	0.999252i	$-0.512312\pi$
$463$	−1.66416	−0.0773399	−0.0386699	+	0.999252i	$0.512312\pi$
$464$	−5.43285	−0.252214
$465$	−2.57790	−0.119547
$466$	8.53946	0.395583
$467$	−8.41488	−0.389394	−0.194697	−	0.980863i	$-0.562372\pi$
$467$	−8.41488	−0.389394	−0.194697	+	0.980863i	$0.562372\pi$
$468$	0.153367	0.00708939
$469$	−6.20265	−0.286412
$470$	−10.4977	−0.484221
$471$	3.65440	0.168386
$472$	−10.9588	−0.504421
$473$	2.48446	0.114236
$474$	−16.3115	−0.749211
$475$	4.13929	0.189924
$476$	5.56010	0.254847
$477$	1.00000	0.0457869
$478$	−14.6674	−0.670869
$479$	6.48998	0.296535	0.148267	−	0.988947i	$-0.452630\pi$
$479$	6.48998	0.296535	0.148267	+	0.988947i	$0.452630\pi$
$480$	0.927745	0.0423456
$481$	1.13367	0.0516909
$482$	20.8129	0.948002
$483$	10.5841	0.481592
$484$	1.29520	0.0588727
$485$	−13.5593	−0.615694
$486$	1.00000	0.0453609
$487$	−41.2755	−1.87037	−0.935185	−	0.354158i	$-0.884767\pi$
$487$	−41.2755	−1.87037	−0.935185	+	0.354158i	$0.884767\pi$
$488$	3.95330	0.178957
$489$	12.0826	0.546393
$490$	−5.24284	−0.236847
$491$	−15.9618	−0.720346	−0.360173	−	0.932886i	$-0.617282\pi$
$491$	−15.9618	−0.720346	−0.360173	+	0.932886i	$0.617282\pi$
$492$	2.71223	0.122277
$493$	−26.0094	−1.17141
$494$	−0.153367	−0.00690031
$495$	3.25309	0.146216
$496$	−2.77867	−0.124766
$497$	10.3694	0.465131
$498$	16.3006	0.730446
$499$	16.7242	0.748679	0.374340	−	0.927292i	$-0.377869\pi$
$499$	16.7242	0.748679	0.374340	+	0.927292i	$0.377869\pi$
$500$	−8.47893	−0.379189
$501$	2.22021	0.0991916
$502$	14.1095	0.629737
$503$	34.8596	1.55431	0.777156	−	0.629307i	$-0.216661\pi$
$503$	34.8596	1.55431	0.777156	+	0.629307i	$0.216661\pi$
$504$	1.16139	0.0517326
$505$	7.39835	0.329222
$506$	31.9552	1.42058
$507$	−12.9765	−0.576306
$508$	4.74237	0.210409
$509$	−1.40127	−0.0621101	−0.0310550	−	0.999518i	$-0.509887\pi$
$509$	−1.40127	−0.0621101	−0.0310550	+	0.999518i	$0.509887\pi$
$510$	4.44152	0.196674
$511$	−1.12399	−0.0497222
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	15.0503	0.663838
$515$	−14.3084	−0.630504
$516$	0.708540	0.0311918
$517$	−39.6764	−1.74496
$518$	8.58489	0.377198
$519$	1.37698	0.0604429
$520$	0.142285	0.00623963
$521$	−10.3473	−0.453323	−0.226661	−	0.973974i	$-0.572781\pi$
$521$	−10.3473	−0.453323	−0.226661	+	0.973974i	$0.572781\pi$
$522$	−5.43285	−0.237790
$523$	−36.8848	−1.61286	−0.806431	−	0.591328i	$-0.798604\pi$
$523$	−36.8848	−1.61286	−0.806431	+	0.591328i	$0.798604\pi$
$524$	7.60522	0.332236
$525$	−4.80735	−0.209810
$526$	−0.751667	−0.0327742
$527$	−13.3027	−0.579475
$528$	3.50645	0.152599
$529$	60.0513	2.61093
$530$	0.927745	0.0402987
$531$	−10.9588	−0.475573
$532$	−1.16139	−0.0503528
$533$	0.415966	0.0180175
$534$	−1.57832	−0.0683004
$535$	9.45059	0.408584
$536$	−5.34069	−0.230683
$537$	0.166620	0.00719016
$538$	14.2126	0.612748
$539$	−19.8155	−0.853515
$540$	0.927745	0.0399238
$541$	−36.8575	−1.58463	−0.792314	−	0.610114i	$-0.791124\pi$
$541$	−36.8575	−1.58463	−0.792314	+	0.610114i	$0.791124\pi$
$542$	−14.0951	−0.605436
$543$	16.5026	0.708195
$544$	4.78743	0.205260
$545$	8.68309	0.371943
$546$	0.178120	0.00762282
$547$	−30.0787	−1.28607	−0.643037	−	0.765835i	$-0.722326\pi$
$547$	−30.0787	−1.28607	−0.643037	+	0.765835i	$0.722326\pi$
$548$	−16.1698	−0.690741
$549$	3.95330	0.168723
$550$	−14.5142	−0.618888
$551$	5.43285	0.231447
$552$	9.11325	0.387886
$553$	−18.9441	−0.805584
$554$	−19.5463	−0.830444
$555$	6.85777	0.291096
$556$	21.8298	0.925790
$557$	−16.6466	−0.705337	−0.352669	−	0.935748i	$-0.614726\pi$
$557$	−16.6466	−0.705337	−0.352669	+	0.935748i	$0.614726\pi$
$558$	−2.77867	−0.117631
$559$	0.108667	0.00459611
$560$	1.07748	0.0455318
$561$	16.7869	0.708744
$562$	16.1610	0.681709
$563$	26.1981	1.10412	0.552059	−	0.833805i	$-0.313842\pi$
$563$	26.1981	1.10412	0.552059	+	0.833805i	$0.313842\pi$
$564$	−11.3152	−0.476458
$565$	9.78505	0.411660
$566$	−20.9598	−0.881007
$567$	1.16139	0.0487740
$568$	8.92840	0.374627
$569$	−42.6414	−1.78762	−0.893811	−	0.448444i	$-0.851978\pi$
$569$	−42.6414	−1.78762	−0.893811	+	0.448444i	$0.851978\pi$
$570$	−0.927745	−0.0388590
$571$	−5.68978	−0.238110	−0.119055	−	0.992888i	$-0.537986\pi$
$571$	−5.68978	−0.238110	−0.119055	+	0.992888i	$0.537986\pi$
$572$	0.537774	0.0224855
$573$	15.6020	0.651781
$574$	3.14997	0.131477
$575$	−37.7224	−1.57313
$576$	1.00000	0.0416667
$577$	23.3377	0.971561	0.485781	−	0.874081i	$-0.338535\pi$
$577$	23.3377	0.971561	0.485781	+	0.874081i	$0.338535\pi$
$578$	5.91953	0.246220
$579$	−19.8402	−0.824529
$580$	−5.04030	−0.209287
$581$	18.9314	0.785407
$582$	−14.6153	−0.605823
$583$	3.50645	0.145222
$584$	−0.967789	−0.0400474
$585$	0.142285	0.00588278
$586$	−32.0945	−1.32581
$587$	−3.03831	−0.125404	−0.0627022	−	0.998032i	$-0.519972\pi$
$587$	−3.03831	−0.125404	−0.0627022	+	0.998032i	$0.519972\pi$
$588$	−5.65116	−0.233050
$589$	2.77867	0.114493
$590$	−10.1670	−0.418569
$591$	−21.2007	−0.872079
$592$	7.39188	0.303804
$593$	4.08909	0.167919	0.0839594	−	0.996469i	$-0.473243\pi$
$593$	4.08909	0.167919	0.0839594	+	0.996469i	$0.473243\pi$
$594$	3.50645	0.143871
$595$	5.15835	0.211472
$596$	−23.4273	−0.959621
$597$	14.0550	0.575232
$598$	1.39767	0.0571551
$599$	32.0787	1.31070	0.655350	−	0.755326i	$-0.272521\pi$
$599$	32.0787	1.31070	0.655350	+	0.755326i	$0.272521\pi$
$600$	−4.13929	−0.168986
$601$	−20.4217	−0.833017	−0.416509	−	0.909132i	$-0.636746\pi$
$601$	−20.4217	−0.833017	−0.416509	+	0.909132i	$0.636746\pi$
$602$	0.822895	0.0335387
$603$	−5.34069	−0.217490
$604$	−5.95655	−0.242369
$605$	1.20161	0.0488526
$606$	7.97455	0.323944
$607$	−44.2985	−1.79802	−0.899010	−	0.437927i	$-0.855713\pi$
$607$	−44.2985	−1.79802	−0.899010	+	0.437927i	$0.855713\pi$
$608$	−1.00000	−0.0405554
$609$	−6.30969	−0.255681
$610$	3.66765	0.148499
$611$	−1.73539	−0.0702062
$612$	4.78743	0.193521
$613$	38.1347	1.54025	0.770123	−	0.637895i	$-0.220195\pi$
$613$	38.1347	1.54025	0.770123	+	0.637895i	$0.220195\pi$
$614$	10.5823	0.427067
$615$	2.51626	0.101465
$616$	4.07237	0.164081
$617$	−25.1364	−1.01195	−0.505977	−	0.862547i	$-0.668868\pi$
$617$	−25.1364	−1.01195	−0.505977	+	0.862547i	$0.668868\pi$
$618$	−15.4228	−0.620396
$619$	19.4166	0.780417	0.390209	−	0.920726i	$-0.372403\pi$
$619$	19.4166	0.780417	0.390209	+	0.920726i	$0.372403\pi$
$620$	−2.57790	−0.103531
$621$	9.11325	0.365702
$622$	−8.96308	−0.359387
$623$	−1.83305	−0.0734395
$624$	0.153367	0.00613959
$625$	12.8302	0.513207
$626$	−11.2298	−0.448834
$627$	−3.50645	−0.140034
$628$	3.65440	0.145826
$629$	35.3881	1.41102
$630$	1.07748	0.0429277
$631$	46.9241	1.86802	0.934010	−	0.357246i	$-0.116284\pi$
$631$	46.9241	1.86802	0.934010	+	0.357246i	$0.116284\pi$
$632$	−16.3115	−0.648836
$633$	−7.62576	−0.303097
$634$	−3.23175	−0.128349
$635$	4.39971	0.174597
$636$	1.00000	0.0396526
$637$	−0.866702	−0.0343400
$638$	−19.0500	−0.754198
$639$	8.92840	0.353202
$640$	0.927745	0.0366723
$641$	−9.45612	−0.373494	−0.186747	−	0.982408i	$-0.559795\pi$
$641$	−9.45612	−0.373494	−0.186747	+	0.982408i	$0.559795\pi$
$642$	10.1866	0.402034
$643$	−8.02495	−0.316473	−0.158237	−	0.987401i	$-0.550581\pi$
$643$	−8.02495	−0.316473	−0.158237	+	0.987401i	$0.550581\pi$
$644$	10.5841	0.417071
$645$	0.657345	0.0258829
$646$	−4.78743	−0.188359
$647$	−11.7677	−0.462634	−0.231317	−	0.972878i	$-0.574303\pi$
$647$	−11.7677	−0.462634	−0.231317	+	0.972878i	$0.574303\pi$
$648$	1.00000	0.0392837
$649$	−38.4266	−1.50838
$650$	−0.634830	−0.0249001
$651$	−3.22713	−0.126481
$652$	12.0826	0.473190
$653$	17.2695	0.675809	0.337904	−	0.941180i	$-0.390282\pi$
$653$	17.2695	0.675809	0.337904	+	0.941180i	$0.390282\pi$
$654$	9.35935	0.365980
$655$	7.05570	0.275689
$656$	2.71223	0.105895
$657$	−0.967789	−0.0377571
$658$	−13.1415	−0.512308
$659$	−27.5126	−1.07174	−0.535870	−	0.844301i	$-0.680016\pi$
$659$	−27.5126	−1.07174	−0.535870	+	0.844301i	$0.680016\pi$
$660$	3.25309	0.126626
$661$	−25.7341	−1.00094	−0.500470	−	0.865754i	$-0.666839\pi$
$661$	−25.7341	−1.00094	−0.500470	+	0.865754i	$0.666839\pi$
$662$	−25.3546	−0.985434
$663$	0.734234	0.0285153
$664$	16.3006	0.632585
$665$	−1.07748	−0.0417828
$666$	7.39188	0.286429
$667$	−49.5110	−1.91707
$668$	2.22021	0.0859025
$669$	27.8011	1.07485
$670$	−4.95480	−0.191421
$671$	13.8620	0.535138
$672$	1.16139	0.0448018
$673$	27.7622	1.07016	0.535078	−	0.844803i	$-0.320282\pi$
$673$	27.7622	1.07016	0.535078	+	0.844803i	$0.320282\pi$
$674$	−24.5931	−0.947290
$675$	−4.13929	−0.159321
$676$	−12.9765	−0.499095
$677$	−33.2264	−1.27700	−0.638498	−	0.769624i	$-0.720444\pi$
$677$	−33.2264	−1.27700	−0.638498	+	0.769624i	$0.720444\pi$
$678$	10.5471	0.405060
$679$	−16.9741	−0.651407
$680$	4.44152	0.170324
$681$	−26.5567	−1.01765
$682$	−9.74327	−0.373089
$683$	−32.7494	−1.25312	−0.626560	−	0.779373i	$-0.715538\pi$
$683$	−32.7494	−1.25312	−0.626560	+	0.779373i	$0.715538\pi$
$684$	−1.00000	−0.0382360
$685$	−15.0015	−0.573177
$686$	−14.6930	−0.560981
$687$	21.1782	0.807998
$688$	0.708540	0.0270129
$689$	0.153367	0.00584282
$690$	8.45477	0.321868
$691$	1.51337	0.0575712	0.0287856	−	0.999586i	$-0.490836\pi$
$691$	1.51337	0.0575712	0.0287856	+	0.999586i	$0.490836\pi$
$692$	1.37698	0.0523451
$693$	4.07237	0.154697
$694$	−8.73316	−0.331506
$695$	20.2525	0.768221
$696$	−5.43285	−0.205932
$697$	12.9846	0.491827
$698$	16.0533	0.607625
$699$	8.53946	0.322992
$700$	−4.80735	−0.181701
$701$	6.61229	0.249743	0.124871	−	0.992173i	$-0.460148\pi$
$701$	6.61229	0.249743	0.124871	+	0.992173i	$0.460148\pi$
$702$	0.153367	0.00578846
$703$	−7.39188	−0.278790
$704$	3.50645	0.132154
$705$	−10.4977	−0.395365
$706$	−6.59110	−0.248059
$707$	9.26160	0.348318
$708$	−10.9588	−0.411858
$709$	8.44376	0.317112	0.158556	−	0.987350i	$-0.449316\pi$
$709$	8.44376	0.317112	0.158556	+	0.987350i	$0.449316\pi$
$710$	8.28328	0.310866
$711$	−16.3115	−0.611728
$712$	−1.57832	−0.0591499
$713$	−25.3227	−0.948344
$714$	5.56010	0.208082
$715$	0.498917	0.0186584
$716$	0.166620	0.00622686
$717$	−14.6674	−0.547762
$718$	−6.83128	−0.254941
$719$	−11.4746	−0.427931	−0.213966	−	0.976841i	$-0.568638\pi$
$719$	−11.4746	−0.427931	−0.213966	+	0.976841i	$0.568638\pi$
$720$	0.927745	0.0345750
$721$	−17.9119	−0.667076
$722$	1.00000	0.0372161
$723$	20.8129	0.774040
$724$	16.5026	0.613315
$725$	22.4882	0.835189
$726$	1.29520	0.0480693
$727$	25.8761	0.959692	0.479846	−	0.877353i	$-0.340692\pi$
$727$	25.8761	0.959692	0.479846	+	0.877353i	$0.340692\pi$
$728$	0.178120	0.00660155
$729$	1.00000	0.0370370
$730$	−0.897861	−0.0332313
$731$	3.39209	0.125461
$732$	3.95330	0.146118
$733$	−2.43105	−0.0897929	−0.0448964	−	0.998992i	$-0.514296\pi$
$733$	−2.43105	−0.0897929	−0.0448964	+	0.998992i	$0.514296\pi$
$734$	13.2802	0.490181
$735$	−5.24284	−0.193385
$736$	9.11325	0.335919
$737$	−18.7269	−0.689814
$738$	2.71223	0.0998385
$739$	−15.8637	−0.583556	−0.291778	−	0.956486i	$-0.594247\pi$
$739$	−15.8637	−0.583556	−0.291778	+	0.956486i	$0.594247\pi$
$740$	6.85777	0.252097
$741$	−0.153367	−0.00563408
$742$	1.16139	0.0426361
$743$	4.52885	0.166148	0.0830738	−	0.996543i	$-0.473526\pi$
$743$	4.52885	0.166148	0.0830738	+	0.996543i	$0.473526\pi$
$744$	−2.77867	−0.101871
$745$	−21.7346	−0.796294
$746$	13.7576	0.503702
$747$	16.3006	0.596407
$748$	16.7869	0.613790
$749$	11.8307	0.432284
$750$	−8.47893	−0.309607
$751$	44.2143	1.61340	0.806701	−	0.590959i	$-0.201251\pi$
$751$	44.2143	1.61340	0.806701	+	0.590959i	$0.201251\pi$
$752$	−11.3152	−0.412625
$753$	14.1095	0.514178
$754$	−0.833221	−0.0303441
$755$	−5.52616	−0.201118
$756$	1.16139	0.0422395
$757$	36.1056	1.31228	0.656139	−	0.754640i	$-0.272188\pi$
$757$	36.1056	1.31228	0.656139	+	0.754640i	$0.272188\pi$
$758$	6.48503	0.235547
$759$	31.9552	1.15990
$760$	−0.927745	−0.0336528
$761$	−0.745116	−0.0270104	−0.0135052	−	0.999909i	$-0.504299\pi$
$761$	−0.745116	−0.0270104	−0.0135052	+	0.999909i	$0.504299\pi$
$762$	4.74237	0.171798
$763$	10.8699	0.393517
$764$	15.6020	0.564459
$765$	4.44152	0.160583
$766$	−36.7299	−1.32711
$767$	−1.68072	−0.0606874
$768$	1.00000	0.0360844
$769$	−8.91924	−0.321636	−0.160818	−	0.986984i	$-0.551413\pi$
$769$	−8.91924	−0.321636	−0.160818	+	0.986984i	$0.551413\pi$
$770$	3.77812	0.136154
$771$	15.0503	0.542022
$772$	−19.8402	−0.714063
$773$	−44.0205	−1.58331	−0.791654	−	0.610970i	$-0.790780\pi$
$773$	−44.0205	−1.58331	−0.791654	+	0.610970i	$0.790780\pi$
$774$	0.708540	0.0254680
$775$	11.5017	0.413154
$776$	−14.6153	−0.524658
$777$	8.58489	0.307981
$778$	15.3419	0.550035
$779$	−2.71223	−0.0971757
$780$	0.142285	0.00509464
$781$	31.3070	1.12025
$782$	43.6291	1.56017
$783$	−5.43285	−0.194154
$784$	−5.65116	−0.201827
$785$	3.39035	0.121007
$786$	7.60522	0.271269
$787$	−21.8783	−0.779876	−0.389938	−	0.920841i	$-0.627504\pi$
$787$	−21.8783	−0.779876	−0.389938	+	0.920841i	$0.627504\pi$
$788$	−21.2007	−0.755243
$789$	−0.751667	−0.0267600
$790$	−15.1329	−0.538404
$791$	12.2494	0.435538
$792$	3.50645	0.124596
$793$	0.606305	0.0215305
$794$	1.89265	0.0671677
$795$	0.927745	0.0329037
$796$	14.0550	0.498166
$797$	24.0133	0.850593	0.425297	−	0.905054i	$-0.360170\pi$
$797$	24.0133	0.850593	0.425297	+	0.905054i	$0.360170\pi$
$798$	−1.16139	−0.0411129
$799$	−54.1710	−1.91643
$800$	−4.13929	−0.146346
$801$	−1.57832	−0.0557670
$802$	29.8981	1.05574
$803$	−3.39351	−0.119754
$804$	−5.34069	−0.188352
$805$	9.81933	0.346086
$806$	−0.426156	−0.0150107
$807$	14.2126	0.500307
$808$	7.97455	0.280544
$809$	38.6491	1.35883	0.679415	−	0.733754i	$-0.262234\pi$
$809$	38.6491	1.35883	0.679415	+	0.733754i	$0.262234\pi$
$810$	0.927745	0.0325976
$811$	−21.1404	−0.742340	−0.371170	−	0.928565i	$-0.621043\pi$
$811$	−21.1404	−0.742340	−0.371170	+	0.928565i	$0.621043\pi$
$812$	−6.30969	−0.221427
$813$	−14.0951	−0.494336
$814$	25.9192	0.908469
$815$	11.2095	0.392653
$816$	4.78743	0.167594
$817$	−0.708540	−0.0247887
$818$	25.2484	0.882789
$819$	0.178120	0.00622400
$820$	2.51626	0.0878715
$821$	−44.7316	−1.56114	−0.780572	−	0.625066i	$-0.785072\pi$
$821$	−44.7316	−1.56114	−0.780572	+	0.625066i	$0.785072\pi$
$822$	−16.1698	−0.563988
$823$	−19.5505	−0.681487	−0.340744	−	0.940156i	$-0.610679\pi$
$823$	−19.5505	−0.681487	−0.340744	+	0.940156i	$0.610679\pi$
$824$	−15.4228	−0.537278
$825$	−14.5142	−0.505320
$826$	−12.7275	−0.442847
$827$	−22.1042	−0.768639	−0.384319	−	0.923200i	$-0.625564\pi$
$827$	−22.1042	−0.768639	−0.384319	+	0.923200i	$0.625564\pi$
$828$	9.11325	0.316707
$829$	32.5758	1.13140	0.565702	−	0.824609i	$-0.308605\pi$
$829$	32.5758	1.13140	0.565702	+	0.824609i	$0.308605\pi$
$830$	15.1228	0.524919
$831$	−19.5463	−0.678055
$832$	0.153367	0.00531704
$833$	−27.0546	−0.937385
$834$	21.8298	0.755904
$835$	2.05979	0.0712819
$836$	−3.50645	−0.121273
$837$	−2.77867	−0.0960449
$838$	−6.72841	−0.232429
$839$	−3.53401	−0.122007	−0.0610037	−	0.998138i	$-0.519430\pi$
$839$	−3.53401	−0.122007	−0.0610037	+	0.998138i	$0.519430\pi$
$840$	1.07748	0.0371765
$841$	0.515906	0.0177899
$842$	−12.0717	−0.416019
$843$	16.1610	0.556613
$844$	−7.62576	−0.262490
$845$	−12.0389	−0.414149
$846$	−11.3152	−0.389026
$847$	1.50424	0.0516862
$848$	1.00000	0.0343401
$849$	−20.9598	−0.719339
$850$	−19.8166	−0.679703
$851$	67.3640	2.30921
$852$	8.92840	0.305882
$853$	15.8630	0.543140	0.271570	−	0.962419i	$-0.412457\pi$
$853$	15.8630	0.543140	0.271570	+	0.962419i	$0.412457\pi$
$854$	4.59134	0.157112
$855$	−0.927745	−0.0317282
$856$	10.1866	0.348172
$857$	−16.5826	−0.566451	−0.283225	−	0.959053i	$-0.591404\pi$
$857$	−16.5826	−0.566451	−0.283225	+	0.959053i	$0.591404\pi$
$858$	0.537774	0.0183593
$859$	−48.4792	−1.65409	−0.827045	−	0.562136i	$-0.809980\pi$
$859$	−48.4792	−1.65409	−0.827045	+	0.562136i	$0.809980\pi$
$860$	0.657345	0.0224153
$861$	3.14997	0.107351
$862$	0.259149	0.00882665
$863$	−38.8436	−1.32225	−0.661126	−	0.750275i	$-0.729921\pi$
$863$	−38.8436	−1.32225	−0.661126	+	0.750275i	$0.729921\pi$
$864$	1.00000	0.0340207
$865$	1.27749	0.0434360
$866$	−0.164921	−0.00560423
$867$	5.91953	0.201038
$868$	−3.22713	−0.109536
$869$	−57.1954	−1.94022
$870$	−5.04030	−0.170882
$871$	−0.819086	−0.0277537
$872$	9.35935	0.316948
$873$	−14.6153	−0.494653
$874$	−9.11325	−0.308260
$875$	−9.84738	−0.332902
$876$	−0.967789	−0.0326986
$877$	52.5334	1.77393	0.886964	−	0.461839i	$-0.152810\pi$
$877$	52.5334	1.77393	0.886964	+	0.461839i	$0.152810\pi$
$878$	15.3617	0.518433
$879$	−32.0945	−1.08252
$880$	3.25309	0.109662
$881$	20.2004	0.680568	0.340284	−	0.940323i	$-0.389477\pi$
$881$	20.2004	0.680568	0.340284	+	0.940323i	$0.389477\pi$
$882$	−5.65116	−0.190285
$883$	35.6027	1.19812	0.599062	−	0.800702i	$-0.295540\pi$
$883$	35.6027	1.19812	0.599062	+	0.800702i	$0.295540\pi$
$884$	0.734234	0.0246950
$885$	−10.1670	−0.341760
$886$	14.0243	0.471155
$887$	−11.0889	−0.372330	−0.186165	−	0.982519i	$-0.559606\pi$
$887$	−11.0889	−0.372330	−0.186165	+	0.982519i	$0.559606\pi$
$888$	7.39188	0.248055
$889$	5.50777	0.184725
$890$	−1.46427	−0.0490826
$891$	3.50645	0.117471
$892$	27.8011	0.930849
$893$	11.3152	0.378650
$894$	−23.4273	−0.783527
$895$	0.154580	0.00516705
$896$	1.16139	0.0387995
$897$	1.39767	0.0466669
$898$	−12.9789	−0.433110
$899$	15.0961	0.503484
$900$	−4.13929	−0.137976
$901$	4.78743	0.159493
$902$	9.51030	0.316658
$903$	0.822895	0.0273842
$904$	10.5471	0.350793
$905$	15.3102	0.508929
$906$	−5.95655	−0.197893
$907$	−7.47225	−0.248112	−0.124056	−	0.992275i	$-0.539590\pi$
$907$	−7.47225	−0.248112	−0.124056	+	0.992275i	$0.539590\pi$
$908$	−26.5567	−0.881314
$909$	7.97455	0.264499
$910$	0.165250	0.00547797
$911$	−55.2761	−1.83138	−0.915689	−	0.401887i	$-0.868355\pi$
$911$	−55.2761	−1.83138	−0.915689	+	0.401887i	$0.868355\pi$
$912$	−1.00000	−0.0331133
$913$	57.1572	1.89163
$914$	16.8082	0.555967
$915$	3.66765	0.121249
$916$	21.1782	0.699746
$917$	8.83266	0.291680
$918$	4.78743	0.158009
$919$	7.66222	0.252753	0.126377	−	0.991982i	$-0.459665\pi$
$919$	7.66222	0.252753	0.126377	+	0.991982i	$0.459665\pi$
$920$	8.45477	0.278746
$921$	10.5823	0.348699
$922$	−10.0120	−0.329727
$923$	1.36932	0.0450718
$924$	4.07237	0.133971
$925$	−30.5971	−1.00603
$926$	−1.66416	−0.0546876
$927$	−15.4228	−0.506551
$928$	−5.43285	−0.178342
$929$	35.9515	1.17953	0.589765	−	0.807575i	$-0.299220\pi$
$929$	35.9515	1.17953	0.589765	+	0.807575i	$0.299220\pi$
$930$	−2.57790	−0.0845326
$931$	5.65116	0.185209
$932$	8.53946	0.279719
$933$	−8.96308	−0.293438
$934$	−8.41488	−0.275343
$935$	15.5740	0.509323
$936$	0.153367	0.00501296
$937$	−12.7486	−0.416478	−0.208239	−	0.978078i	$-0.566773\pi$
$937$	−12.7486	−0.416478	−0.208239	+	0.978078i	$0.566773\pi$
$938$	−6.20265	−0.202524
$939$	−11.2298	−0.366472
$940$	−10.4977	−0.342396
$941$	22.3205	0.727628	0.363814	−	0.931472i	$-0.381474\pi$
$941$	22.3205	0.727628	0.363814	+	0.931472i	$0.381474\pi$
$942$	3.65440	0.119067
$943$	24.7172	0.804903
$944$	−10.9588	−0.356679
$945$	1.07748	0.0350504
$946$	2.48446	0.0807768
$947$	−21.3950	−0.695244	−0.347622	−	0.937635i	$-0.613011\pi$
$947$	−21.3950	−0.695244	−0.347622	+	0.937635i	$0.613011\pi$
$948$	−16.3115	−0.529772
$949$	−0.148427	−0.00481814
$950$	4.13929	0.134296
$951$	−3.23175	−0.104797
$952$	5.56010	0.180204
$953$	−52.4778	−1.69992	−0.849961	−	0.526846i	$-0.823374\pi$
$953$	−52.4778	−1.69992	−0.849961	+	0.526846i	$0.823374\pi$
$954$	1.00000	0.0323762
$955$	14.4746	0.468388
$956$	−14.6674	−0.474376
$957$	−19.0500	−0.615800
$958$	6.48998	0.209682
$959$	−18.7796	−0.606424
$960$	0.927745	0.0299428
$961$	−23.2790	−0.750935
$962$	1.13367	0.0365510
$963$	10.1866	0.328259
$964$	20.8129	0.670339
$965$	−18.4066	−0.592529
$966$	10.5841	0.340537
$967$	−6.23655	−0.200554	−0.100277	−	0.994960i	$-0.531973\pi$
$967$	−6.23655	−0.200554	−0.100277	+	0.994960i	$0.531973\pi$
$968$	1.29520	0.0416293
$969$	−4.78743	−0.153795
$970$	−13.5593	−0.435362
$971$	0.949161	0.0304600	0.0152300	−	0.999884i	$-0.495152\pi$
$971$	0.949161	0.0304600	0.0152300	+	0.999884i	$0.495152\pi$
$972$	1.00000	0.0320750
$973$	25.3530	0.812781
$974$	−41.2755	−1.32255
$975$	−0.634830	−0.0203308
$976$	3.95330	0.126542
$977$	38.5522	1.23339	0.616696	−	0.787201i	$-0.288471\pi$
$977$	38.5522	1.23339	0.616696	+	0.787201i	$0.288471\pi$
$978$	12.0826	0.386358
$979$	−5.53429	−0.176877
$980$	−5.24284	−0.167476
$981$	9.35935	0.298821
$982$	−15.9618	−0.509361
$983$	1.22258	0.0389942	0.0194971	−	0.999810i	$-0.493793\pi$
$983$	1.22258	0.0389942	0.0194971	+	0.999810i	$0.493793\pi$
$984$	2.71223	0.0864627
$985$	−19.6688	−0.626701
$986$	−26.0094	−0.828309
$987$	−13.1415	−0.418298
$988$	−0.153367	−0.00487925
$989$	6.45711	0.205324
$990$	3.25309	0.103390
$991$	8.55117	0.271637	0.135818	−	0.990734i	$-0.456634\pi$
$991$	8.55117	0.271637	0.135818	+	0.990734i	$0.456634\pi$
$992$	−2.77867	−0.0882229
$993$	−25.3546	−0.804603
$994$	10.3694	0.328897
$995$	13.0394	0.413378
$996$	16.3006	0.516504
$997$	32.0488	1.01500	0.507498	−	0.861653i	$-0.330570\pi$
$997$	32.0488	1.01500	0.507498	+	0.861653i	$0.330570\pi$
$998$	16.7242	0.529396
$999$	7.39188	0.233869

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bg.1.7	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bg.1.7	✓	12	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:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.927745 q^{5} +1.00000 q^{6} +1.16139 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.927745 q^{5} +1.00000 q^{6} +1.16139 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.927745 q^{10} +3.50645 q^{11} +1.00000 q^{12} +0.153367 q^{13} +1.16139 q^{14} +0.927745 q^{15} +1.00000 q^{16} +4.78743 q^{17} +1.00000 q^{18} -1.00000 q^{19} +0.927745 q^{20} +1.16139 q^{21} +3.50645 q^{22} +9.11325 q^{23} +1.00000 q^{24} -4.13929 q^{25} +0.153367 q^{26} +1.00000 q^{27} +1.16139 q^{28} -5.43285 q^{29} +0.927745 q^{30} -2.77867 q^{31} +1.00000 q^{32} +3.50645 q^{33} +4.78743 q^{34} +1.07748 q^{35} +1.00000 q^{36} +7.39188 q^{37} -1.00000 q^{38} +0.153367 q^{39} +0.927745 q^{40} +2.71223 q^{41} +1.16139 q^{42} +0.708540 q^{43} +3.50645 q^{44} +0.927745 q^{45} +9.11325 q^{46} -11.3152 q^{47} +1.00000 q^{48} -5.65116 q^{49} -4.13929 q^{50} +4.78743 q^{51} +0.153367 q^{52} +1.00000 q^{53} +1.00000 q^{54} +3.25309 q^{55} +1.16139 q^{56} -1.00000 q^{57} -5.43285 q^{58} -10.9588 q^{59} +0.927745 q^{60} +3.95330 q^{61} -2.77867 q^{62} +1.16139 q^{63} +1.00000 q^{64} +0.142285 q^{65} +3.50645 q^{66} -5.34069 q^{67} +4.78743 q^{68} +9.11325 q^{69} +1.07748 q^{70} +8.92840 q^{71} +1.00000 q^{72} -0.967789 q^{73} +7.39188 q^{74} -4.13929 q^{75} -1.00000 q^{76} +4.07237 q^{77} +0.153367 q^{78} -16.3115 q^{79} +0.927745 q^{80} +1.00000 q^{81} +2.71223 q^{82} +16.3006 q^{83} +1.16139 q^{84} +4.44152 q^{85} +0.708540 q^{86} -5.43285 q^{87} +3.50645 q^{88} -1.57832 q^{89} +0.927745 q^{90} +0.178120 q^{91} +9.11325 q^{92} -2.77867 q^{93} -11.3152 q^{94} -0.927745 q^{95} +1.00000 q^{96} -14.6153 q^{97} -5.65116 q^{98} +3.50645 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 5 q^{5} + 12 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 5 * q^5 + 12 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 5 q^{5} + 12 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9} + 5 q^{10} + 7 q^{11} + 12 q^{12} + 9 q^{13} + 6 q^{14} + 5 q^{15} + 12 q^{16} + 25 q^{17} + 12 q^{18} - 12 q^{19} + 5 q^{20} + 6 q^{21} + 7 q^{22} + 22 q^{23} + 12 q^{24} + 33 q^{25} + 9 q^{26} + 12 q^{27} + 6 q^{28} + q^{29} + 5 q^{30} + 23 q^{31} + 12 q^{32} + 7 q^{33} + 25 q^{34} + 5 q^{35} + 12 q^{36} - q^{37} - 12 q^{38} + 9 q^{39} + 5 q^{40} - 15 q^{41} + 6 q^{42} + 2 q^{43} + 7 q^{44} + 5 q^{45} + 22 q^{46} + 11 q^{47} + 12 q^{48} + 36 q^{49} + 33 q^{50} + 25 q^{51} + 9 q^{52} + 12 q^{53} + 12 q^{54} - 4 q^{55} + 6 q^{56} - 12 q^{57} + q^{58} + 3 q^{59} + 5 q^{60} + 16 q^{61} + 23 q^{62} + 6 q^{63} + 12 q^{64} + 7 q^{65} + 7 q^{66} - 2 q^{67} + 25 q^{68} + 22 q^{69} + 5 q^{70} - 4 q^{71} + 12 q^{72} + 35 q^{73} - q^{74} + 33 q^{75} - 12 q^{76} + 11 q^{77} + 9 q^{78} + 4 q^{79} + 5 q^{80} + 12 q^{81} - 15 q^{82} + 39 q^{83} + 6 q^{84} + 10 q^{85} + 2 q^{86} + q^{87} + 7 q^{88} + 11 q^{89} + 5 q^{90} - 18 q^{91} + 22 q^{92} + 23 q^{93} + 11 q^{94} - 5 q^{95} + 12 q^{96} - 21 q^{97} + 36 q^{98} + 7 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 5 * q^5 + 12 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9 + 5 * q^10 + 7 * q^11 + 12 * q^12 + 9 * q^13 + 6 * q^14 + 5 * q^15 + 12 * q^16 + 25 * q^17 + 12 * q^18 - 12 * q^19 + 5 * q^20 + 6 * q^21 + 7 * q^22 + 22 * q^23 + 12 * q^24 + 33 * q^25 + 9 * q^26 + 12 * q^27 + 6 * q^28 + q^29 + 5 * q^30 + 23 * q^31 + 12 * q^32 + 7 * q^33 + 25 * q^34 + 5 * q^35 + 12 * q^36 - q^37 - 12 * q^38 + 9 * q^39 + 5 * q^40 - 15 * q^41 + 6 * q^42 + 2 * q^43 + 7 * q^44 + 5 * q^45 + 22 * q^46 + 11 * q^47 + 12 * q^48 + 36 * q^49 + 33 * q^50 + 25 * q^51 + 9 * q^52 + 12 * q^53 + 12 * q^54 - 4 * q^55 + 6 * q^56 - 12 * q^57 + q^58 + 3 * q^59 + 5 * q^60 + 16 * q^61 + 23 * q^62 + 6 * q^63 + 12 * q^64 + 7 * q^65 + 7 * q^66 - 2 * q^67 + 25 * q^68 + 22 * q^69 + 5 * q^70 - 4 * q^71 + 12 * q^72 + 35 * q^73 - q^74 + 33 * q^75 - 12 * q^76 + 11 * q^77 + 9 * q^78 + 4 * q^79 + 5 * q^80 + 12 * q^81 - 15 * q^82 + 39 * q^83 + 6 * q^84 + 10 * q^85 + 2 * q^86 + q^87 + 7 * q^88 + 11 * q^89 + 5 * q^90 - 18 * q^91 + 22 * q^92 + 23 * q^93 + 11 * q^94 - 5 * q^95 + 12 * q^96 - 21 * q^97 + 36 * q^98 + 7 * q^99

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