LMFDB - Embedded newform 6046.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$0$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.14488 q^{3} +1.00000 q^{4} -1.06232 q^{5} -3.14488 q^{6} -3.74953 q^{7} +1.00000 q^{8} +6.89025 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.14488 q^{3} +1.00000 q^{4} -1.06232 q^{5} -3.14488 q^{6} -3.74953 q^{7} +1.00000 q^{8} +6.89025 q^{9} -1.06232 q^{10} +3.52800 q^{11} -3.14488 q^{12} -4.39795 q^{13} -3.74953 q^{14} +3.34088 q^{15} +1.00000 q^{16} -4.10143 q^{17} +6.89025 q^{18} -1.53240 q^{19} -1.06232 q^{20} +11.7918 q^{21} +3.52800 q^{22} +1.71182 q^{23} -3.14488 q^{24} -3.87147 q^{25} -4.39795 q^{26} -12.2343 q^{27} -3.74953 q^{28} -2.11444 q^{29} +3.34088 q^{30} -2.50881 q^{31} +1.00000 q^{32} -11.0951 q^{33} -4.10143 q^{34} +3.98321 q^{35} +6.89025 q^{36} +0.817764 q^{37} -1.53240 q^{38} +13.8310 q^{39} -1.06232 q^{40} +4.45238 q^{41} +11.7918 q^{42} -4.40622 q^{43} +3.52800 q^{44} -7.31967 q^{45} +1.71182 q^{46} -0.673654 q^{47} -3.14488 q^{48} +7.05897 q^{49} -3.87147 q^{50} +12.8985 q^{51} -4.39795 q^{52} -1.80235 q^{53} -12.2343 q^{54} -3.74788 q^{55} -3.74953 q^{56} +4.81920 q^{57} -2.11444 q^{58} +0.673101 q^{59} +3.34088 q^{60} -4.24458 q^{61} -2.50881 q^{62} -25.8352 q^{63} +1.00000 q^{64} +4.67204 q^{65} -11.0951 q^{66} +5.94494 q^{67} -4.10143 q^{68} -5.38345 q^{69} +3.98321 q^{70} -9.36892 q^{71} +6.89025 q^{72} -8.89430 q^{73} +0.817764 q^{74} +12.1753 q^{75} -1.53240 q^{76} -13.2284 q^{77} +13.8310 q^{78} -2.67137 q^{79} -1.06232 q^{80} +17.8048 q^{81} +4.45238 q^{82} -9.13444 q^{83} +11.7918 q^{84} +4.35704 q^{85} -4.40622 q^{86} +6.64966 q^{87} +3.52800 q^{88} -6.33337 q^{89} -7.31967 q^{90} +16.4902 q^{91} +1.71182 q^{92} +7.88989 q^{93} -0.673654 q^{94} +1.62790 q^{95} -3.14488 q^{96} -4.11251 q^{97} +7.05897 q^{98} +24.3088 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 67 q^{2} + 21 q^{3} + 67 q^{4} + 21 q^{5} + 21 q^{6} + 38 q^{7} + 67 q^{8} + 90 q^{9}+O(q^{10}) $ 67 * q + 67 * q^2 + 21 * q^3 + 67 * q^4 + 21 * q^5 + 21 * q^6 + 38 * q^7 + 67 * q^8 + 90 * q^9	\( 67 q + 67 q^{2} + 21 q^{3} + 67 q^{4} + 21 q^{5} + 21 q^{6} + 38 q^{7} + 67 q^{8} + 90 q^{9} + 21 q^{10} + 56 q^{11} + 21 q^{12} + 33 q^{13} + 38 q^{14} + 25 q^{15} + 67 q^{16} + 30 q^{17} + 90 q^{18} + 36 q^{19} + 21 q^{20} + 20 q^{21} + 56 q^{22} + 65 q^{23} + 21 q^{24} + 72 q^{25} + 33 q^{26} + 57 q^{27} + 38 q^{28} + 84 q^{29} + 25 q^{30} + 52 q^{31} + 67 q^{32} - 9 q^{33} + 30 q^{34} + 30 q^{35} + 90 q^{36} + 52 q^{37} + 36 q^{38} + 41 q^{39} + 21 q^{40} + 46 q^{41} + 20 q^{42} + 61 q^{43} + 56 q^{44} + 23 q^{45} + 65 q^{46} + 51 q^{47} + 21 q^{48} + 81 q^{49} + 72 q^{50} + 33 q^{51} + 33 q^{52} + 72 q^{53} + 57 q^{54} + 14 q^{55} + 38 q^{56} - 26 q^{57} + 84 q^{58} + 71 q^{59} + 25 q^{60} + 42 q^{61} + 52 q^{62} + 63 q^{63} + 67 q^{64} - 2 q^{65} - 9 q^{66} + 70 q^{67} + 30 q^{68} + 21 q^{69} + 30 q^{70} + 104 q^{71} + 90 q^{72} - 31 q^{73} + 52 q^{74} + 69 q^{75} + 36 q^{76} + 48 q^{77} + 41 q^{78} + 79 q^{79} + 21 q^{80} + 123 q^{81} + 46 q^{82} + 41 q^{83} + 20 q^{84} + 6 q^{85} + 61 q^{86} + 19 q^{87} + 56 q^{88} + 58 q^{89} + 23 q^{90} + 31 q^{91} + 65 q^{92} + 13 q^{93} + 51 q^{94} + 77 q^{95} + 21 q^{96} - 8 q^{97} + 81 q^{98} + 129 q^{99}+O(q^{100}) \) 67 * q + 67 * q^2 + 21 * q^3 + 67 * q^4 + 21 * q^5 + 21 * q^6 + 38 * q^7 + 67 * q^8 + 90 * q^9 + 21 * q^10 + 56 * q^11 + 21 * q^12 + 33 * q^13 + 38 * q^14 + 25 * q^15 + 67 * q^16 + 30 * q^17 + 90 * q^18 + 36 * q^19 + 21 * q^20 + 20 * q^21 + 56 * q^22 + 65 * q^23 + 21 * q^24 + 72 * q^25 + 33 * q^26 + 57 * q^27 + 38 * q^28 + 84 * q^29 + 25 * q^30 + 52 * q^31 + 67 * q^32 - 9 * q^33 + 30 * q^34 + 30 * q^35 + 90 * q^36 + 52 * q^37 + 36 * q^38 + 41 * q^39 + 21 * q^40 + 46 * q^41 + 20 * q^42 + 61 * q^43 + 56 * q^44 + 23 * q^45 + 65 * q^46 + 51 * q^47 + 21 * q^48 + 81 * q^49 + 72 * q^50 + 33 * q^51 + 33 * q^52 + 72 * q^53 + 57 * q^54 + 14 * q^55 + 38 * q^56 - 26 * q^57 + 84 * q^58 + 71 * q^59 + 25 * q^60 + 42 * q^61 + 52 * q^62 + 63 * q^63 + 67 * q^64 - 2 * q^65 - 9 * q^66 + 70 * q^67 + 30 * q^68 + 21 * q^69 + 30 * q^70 + 104 * q^71 + 90 * q^72 - 31 * q^73 + 52 * q^74 + 69 * q^75 + 36 * q^76 + 48 * q^77 + 41 * q^78 + 79 * q^79 + 21 * q^80 + 123 * q^81 + 46 * q^82 + 41 * q^83 + 20 * q^84 + 6 * q^85 + 61 * q^86 + 19 * q^87 + 56 * q^88 + 58 * q^89 + 23 * q^90 + 31 * q^91 + 65 * q^92 + 13 * q^93 + 51 * q^94 + 77 * q^95 + 21 * q^96 - 8 * q^97 + 81 * q^98 + 129 * 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
$3$	−3.14488	−1.81570	−0.907848	−	0.419300i	$-0.862275\pi$
$3$	−3.14488	−1.81570	−0.907848	+	0.419300i	$0.862275\pi$
$4$	1.00000	0.500000
$5$	−1.06232	−0.475085	−0.237543	−	0.971377i	$-0.576342\pi$
$5$	−1.06232	−0.475085	−0.237543	+	0.971377i	$0.576342\pi$
$6$	−3.14488	−1.28389
$7$	−3.74953	−1.41719	−0.708595	−	0.705616i	$-0.750670\pi$
$7$	−3.74953	−1.41719	−0.708595	+	0.705616i	$0.750670\pi$
$8$	1.00000	0.353553
$9$	6.89025	2.29675
$10$	−1.06232	−0.335936
$11$	3.52800	1.06373	0.531867	−	0.846828i	$-0.321491\pi$
$11$	3.52800	1.06373	0.531867	+	0.846828i	$0.321491\pi$
$12$	−3.14488	−0.907848
$13$	−4.39795	−1.21977	−0.609885	−	0.792490i	$-0.708785\pi$
$13$	−4.39795	−1.21977	−0.609885	+	0.792490i	$0.708785\pi$
$14$	−3.74953	−1.00210
$15$	3.34088	0.862610
$16$	1.00000	0.250000
$17$	−4.10143	−0.994742	−0.497371	−	0.867538i	$-0.665701\pi$
$17$	−4.10143	−0.994742	−0.497371	+	0.867538i	$0.665701\pi$
$18$	6.89025	1.62405
$19$	−1.53240	−0.351556	−0.175778	−	0.984430i	$-0.556244\pi$
$19$	−1.53240	−0.351556	−0.175778	+	0.984430i	$0.556244\pi$
$20$	−1.06232	−0.237543
$21$	11.7918	2.57318
$22$	3.52800	0.752173
$23$	1.71182	0.356938	0.178469	−	0.983945i	$-0.442886\pi$
$23$	1.71182	0.356938	0.178469	+	0.983945i	$0.442886\pi$
$24$	−3.14488	−0.641945
$25$	−3.87147	−0.774294
$26$	−4.39795	−0.862508
$27$	−12.2343	−2.35450
$28$	−3.74953	−0.708595
$29$	−2.11444	−0.392642	−0.196321	−	0.980540i	$-0.562899\pi$
$29$	−2.11444	−0.392642	−0.196321	+	0.980540i	$0.562899\pi$
$30$	3.34088	0.609958
$31$	−2.50881	−0.450595	−0.225298	−	0.974290i	$-0.572335\pi$
$31$	−2.50881	−0.450595	−0.225298	+	0.974290i	$0.572335\pi$
$32$	1.00000	0.176777
$33$	−11.0951	−1.93141
$34$	−4.10143	−0.703389
$35$	3.98321	0.673286
$36$	6.89025	1.14837
$37$	0.817764	0.134440	0.0672198	−	0.997738i	$-0.478587\pi$
$37$	0.817764	0.134440	0.0672198	+	0.997738i	$0.478587\pi$
$38$	−1.53240	−0.248588
$39$	13.8310	2.21473
$40$	−1.06232	−0.167968
$41$	4.45238	0.695345	0.347672	−	0.937616i	$-0.386972\pi$
$41$	4.45238	0.695345	0.347672	+	0.937616i	$0.386972\pi$
$42$	11.7918	1.81952
$43$	−4.40622	−0.671942	−0.335971	−	0.941872i	$-0.609064\pi$
$43$	−4.40622	−0.671942	−0.335971	+	0.941872i	$0.609064\pi$
$44$	3.52800	0.531867
$45$	−7.31967	−1.09115
$46$	1.71182	0.252394
$47$	−0.673654	−0.0982626	−0.0491313	−	0.998792i	$-0.515645\pi$
$47$	−0.673654	−0.0982626	−0.0491313	+	0.998792i	$0.515645\pi$
$48$	−3.14488	−0.453924
$49$	7.05897	1.00842
$50$	−3.87147	−0.547508
$51$	12.8985	1.80615
$52$	−4.39795	−0.609885
$53$	−1.80235	−0.247572	−0.123786	−	0.992309i	$-0.539504\pi$
$53$	−1.80235	−0.247572	−0.123786	+	0.992309i	$0.539504\pi$
$54$	−12.2343	−1.66488
$55$	−3.74788	−0.505364
$56$	−3.74953	−0.501052
$57$	4.81920	0.638319
$58$	−2.11444	−0.277640
$59$	0.673101	0.0876303	0.0438152	−	0.999040i	$-0.486049\pi$
$59$	0.673101	0.0876303	0.0438152	+	0.999040i	$0.486049\pi$
$60$	3.34088	0.431305
$61$	−4.24458	−0.543463	−0.271732	−	0.962373i	$-0.587596\pi$
$61$	−4.24458	−0.543463	−0.271732	+	0.962373i	$0.587596\pi$
$62$	−2.50881	−0.318619
$63$	−25.8352	−3.25493
$64$	1.00000	0.125000
$65$	4.67204	0.579495
$66$	−11.0951	−1.36572
$67$	5.94494	0.726291	0.363145	−	0.931733i	$-0.381703\pi$
$67$	5.94494	0.726291	0.363145	+	0.931733i	$0.381703\pi$
$68$	−4.10143	−0.497371
$69$	−5.38345	−0.648091
$70$	3.98321	0.476085
$71$	−9.36892	−1.11189	−0.555943	−	0.831220i	$-0.687643\pi$
$71$	−9.36892	−1.11189	−0.555943	+	0.831220i	$0.687643\pi$
$72$	6.89025	0.812023
$73$	−8.89430	−1.04100	−0.520500	−	0.853862i	$-0.674254\pi$
$73$	−8.89430	−1.04100	−0.520500	+	0.853862i	$0.674254\pi$
$74$	0.817764	0.0950631
$75$	12.1753	1.40588
$76$	−1.53240	−0.175778
$77$	−13.2284	−1.50751
$78$	13.8310	1.56605
$79$	−2.67137	−0.300553	−0.150276	−	0.988644i	$-0.548016\pi$
$79$	−2.67137	−0.300553	−0.150276	+	0.988644i	$0.548016\pi$
$80$	−1.06232	−0.118771
$81$	17.8048	1.97831
$82$	4.45238	0.491683
$83$	−9.13444	−1.00263	−0.501317	−	0.865263i	$-0.667151\pi$
$83$	−9.13444	−1.00263	−0.501317	+	0.865263i	$0.667151\pi$
$84$	11.7918	1.28659
$85$	4.35704	0.472587
$86$	−4.40622	−0.475135
$87$	6.64966	0.712918
$88$	3.52800	0.376086
$89$	−6.33337	−0.671335	−0.335668	−	0.941980i	$-0.608962\pi$
$89$	−6.33337	−0.671335	−0.335668	+	0.941980i	$0.608962\pi$
$90$	−7.31967	−0.771561
$91$	16.4902	1.72865
$92$	1.71182	0.178469
$93$	7.88989	0.818143
$94$	−0.673654	−0.0694821
$95$	1.62790	0.167019
$96$	−3.14488	−0.320973
$97$	−4.11251	−0.417562	−0.208781	−	0.977962i	$-0.566950\pi$
$97$	−4.11251	−0.417562	−0.208781	+	0.977962i	$0.566950\pi$
$98$	7.05897	0.713064
$99$	24.3088	2.44313
$100$	−3.87147	−0.387147
$101$	−3.46383	−0.344664	−0.172332	−	0.985039i	$-0.555130\pi$
$101$	−3.46383	−0.344664	−0.172332	+	0.985039i	$0.555130\pi$
$102$	12.8985	1.27714
$103$	5.31050	0.523259	0.261630	−	0.965168i	$-0.415740\pi$
$103$	5.31050	0.523259	0.261630	+	0.965168i	$0.415740\pi$
$104$	−4.39795	−0.431254
$105$	−12.5267	−1.22248
$106$	−1.80235	−0.175060
$107$	−13.5477	−1.30971	−0.654854	−	0.755756i	$-0.727270\pi$
$107$	−13.5477	−1.30971	−0.654854	+	0.755756i	$0.727270\pi$
$108$	−12.2343	−1.17725
$109$	8.14460	0.780112	0.390056	−	0.920791i	$-0.372456\pi$
$109$	8.14460	0.780112	0.390056	+	0.920791i	$0.372456\pi$
$110$	−3.74788	−0.357346
$111$	−2.57177	−0.244101
$112$	−3.74953	−0.354297
$113$	−5.33633	−0.502000	−0.251000	−	0.967987i	$-0.580759\pi$
$113$	−5.33633	−0.502000	−0.251000	+	0.967987i	$0.580759\pi$
$114$	4.81920	0.451360
$115$	−1.81850	−0.169576
$116$	−2.11444	−0.196321
$117$	−30.3029	−2.80151
$118$	0.673101	0.0619640
$119$	15.3784	1.40974
$120$	3.34088	0.304979
$121$	1.44681	0.131528
$122$	−4.24458	−0.384286
$123$	−14.0022	−1.26253
$124$	−2.50881	−0.225298
$125$	9.42437	0.842941
$126$	−25.8352	−2.30158
$127$	16.0267	1.42214	0.711071	−	0.703120i	$-0.248210\pi$
$127$	16.0267	1.42214	0.711071	+	0.703120i	$0.248210\pi$
$128$	1.00000	0.0883883
$129$	13.8570	1.22004
$130$	4.67204	0.409765
$131$	3.00342	0.262410	0.131205	−	0.991355i	$-0.458115\pi$
$131$	3.00342	0.262410	0.131205	+	0.991355i	$0.458115\pi$
$132$	−11.0951	−0.965707
$133$	5.74577	0.498222
$134$	5.94494	0.513565
$135$	12.9968	1.11859
$136$	−4.10143	−0.351694
$137$	−9.25512	−0.790718	−0.395359	−	0.918527i	$-0.629380\pi$
$137$	−9.25512	−0.790718	−0.395359	+	0.918527i	$0.629380\pi$
$138$	−5.38345	−0.458270
$139$	12.7964	1.08537	0.542686	−	0.839936i	$-0.317407\pi$
$139$	12.7964	1.08537	0.542686	+	0.839936i	$0.317407\pi$
$140$	3.98321	0.336643
$141$	2.11856	0.178415
$142$	−9.36892	−0.786223
$143$	−15.5160	−1.29751
$144$	6.89025	0.574187
$145$	2.24622	0.186539
$146$	−8.89430	−0.736098
$147$	−22.1996	−1.83099
$148$	0.817764	0.0672198
$149$	−14.2376	−1.16639	−0.583195	−	0.812332i	$-0.698198\pi$
$149$	−14.2376	−1.16639	−0.583195	+	0.812332i	$0.698198\pi$
$150$	12.1753	0.994108
$151$	11.4737	0.933716	0.466858	−	0.884332i	$-0.345386\pi$
$151$	11.4737	0.933716	0.466858	+	0.884332i	$0.345386\pi$
$152$	−1.53240	−0.124294
$153$	−28.2598	−2.28467
$154$	−13.2284	−1.06597
$155$	2.66516	0.214071
$156$	13.8310	1.10737
$157$	−3.11695	−0.248759	−0.124380	−	0.992235i	$-0.539694\pi$
$157$	−3.11695	−0.248759	−0.124380	+	0.992235i	$0.539694\pi$
$158$	−2.67137	−0.212523
$159$	5.66818	0.449516
$160$	−1.06232	−0.0839840
$161$	−6.41851	−0.505849
$162$	17.8048	1.39887
$163$	4.26998	0.334451	0.167225	−	0.985919i	$-0.446519\pi$
$163$	4.26998	0.334451	0.167225	+	0.985919i	$0.446519\pi$
$164$	4.45238	0.347672
$165$	11.7866	0.917587
$166$	−9.13444	−0.708970
$167$	−1.50116	−0.116163	−0.0580816	−	0.998312i	$-0.518498\pi$
$167$	−1.50116	−0.116163	−0.0580816	+	0.998312i	$0.518498\pi$
$168$	11.7918	0.909758
$169$	6.34193	0.487841
$170$	4.35704	0.334170
$171$	−10.5586	−0.807437
$172$	−4.40622	−0.335971
$173$	5.60906	0.426449	0.213225	−	0.977003i	$-0.431603\pi$
$173$	5.60906	0.426449	0.213225	+	0.977003i	$0.431603\pi$
$174$	6.64966	0.504109
$175$	14.5162	1.09732
$176$	3.52800	0.265933
$177$	−2.11682	−0.159110
$178$	−6.33337	−0.474706
$179$	8.78995	0.656991	0.328496	−	0.944505i	$-0.393458\pi$
$179$	8.78995	0.656991	0.328496	+	0.944505i	$0.393458\pi$
$180$	−7.31967	−0.545576
$181$	11.4279	0.849433	0.424716	−	0.905327i	$-0.360374\pi$
$181$	11.4279	0.849433	0.424716	+	0.905327i	$0.360374\pi$
$182$	16.4902	1.22234
$183$	13.3487	0.986763
$184$	1.71182	0.126197
$185$	−0.868729	−0.0638703
$186$	7.88989	0.578515
$187$	−14.4698	−1.05814
$188$	−0.673654	−0.0491313
$189$	45.8730	3.33677
$190$	1.62790	0.118100
$191$	9.27936	0.671431	0.335716	−	0.941963i	$-0.391022\pi$
$191$	9.27936	0.671431	0.335716	+	0.941963i	$0.391022\pi$
$192$	−3.14488	−0.226962
$193$	22.1510	1.59447	0.797233	−	0.603672i	$-0.206296\pi$
$193$	22.1510	1.59447	0.797233	+	0.603672i	$0.206296\pi$
$194$	−4.11251	−0.295261
$195$	−14.6930	−1.05219
$196$	7.05897	0.504212
$197$	22.9495	1.63508	0.817541	−	0.575870i	$-0.195337\pi$
$197$	22.9495	1.63508	0.817541	+	0.575870i	$0.195337\pi$
$198$	24.3088	1.72755
$199$	17.0105	1.20585	0.602923	−	0.797800i	$-0.294003\pi$
$199$	17.0105	1.20585	0.602923	+	0.797800i	$0.294003\pi$
$200$	−3.87147	−0.273754
$201$	−18.6961	−1.31872
$202$	−3.46383	−0.243714
$203$	7.92817	0.556448
$204$	12.8985	0.903074
$205$	−4.72987	−0.330348
$206$	5.31050	0.370000
$207$	11.7948	0.819798
$208$	−4.39795	−0.304943
$209$	−5.40631	−0.373962
$210$	−12.5267	−0.864425
$211$	14.3343	0.986811	0.493405	−	0.869799i	$-0.335752\pi$
$211$	14.3343	0.986811	0.493405	+	0.869799i	$0.335752\pi$
$212$	−1.80235	−0.123786
$213$	29.4641	2.01885
$214$	−13.5477	−0.926103
$215$	4.68083	0.319230
$216$	−12.2343	−0.832442
$217$	9.40685	0.638578
$218$	8.14460	0.551622
$219$	27.9715	1.89014
$220$	−3.74788	−0.252682
$221$	18.0379	1.21336
$222$	−2.57177	−0.172606
$223$	14.6970	0.984187	0.492094	−	0.870542i	$-0.336232\pi$
$223$	14.6970	0.984187	0.492094	+	0.870542i	$0.336232\pi$
$224$	−3.74953	−0.250526
$225$	−26.6754	−1.77836
$226$	−5.33633	−0.354967
$227$	−4.45867	−0.295932	−0.147966	−	0.988992i	$-0.547273\pi$
$227$	−4.45867	−0.295932	−0.147966	+	0.988992i	$0.547273\pi$
$228$	4.81920	0.319160
$229$	14.9375	0.987100	0.493550	−	0.869717i	$-0.335699\pi$
$229$	14.9375	0.987100	0.493550	+	0.869717i	$0.335699\pi$
$230$	−1.81850	−0.119909
$231$	41.6015	2.73718
$232$	−2.11444	−0.138820
$233$	5.00340	0.327784	0.163892	−	0.986478i	$-0.447595\pi$
$233$	5.00340	0.327784	0.163892	+	0.986478i	$0.447595\pi$
$234$	−30.3029	−1.98096
$235$	0.715639	0.0466831
$236$	0.673101	0.0438152
$237$	8.40113	0.545712
$238$	15.3784	0.996835
$239$	28.0040	1.81143	0.905715	−	0.423888i	$-0.139335\pi$
$239$	28.0040	1.81143	0.905715	+	0.423888i	$0.139335\pi$
$240$	3.34088	0.215653
$241$	−3.02056	−0.194571	−0.0972856	−	0.995257i	$-0.531016\pi$
$241$	−3.02056	−0.194571	−0.0972856	+	0.995257i	$0.531016\pi$
$242$	1.44681	0.0930043
$243$	−19.2907	−1.23750
$244$	−4.24458	−0.271732
$245$	−7.49891	−0.479088
$246$	−14.0022	−0.892746
$247$	6.73941	0.428818
$248$	−2.50881	−0.159309
$249$	28.7267	1.82048
$250$	9.42437	0.596049
$251$	9.59314	0.605514	0.302757	−	0.953068i	$-0.402093\pi$
$251$	9.59314	0.605514	0.302757	+	0.953068i	$0.402093\pi$
$252$	−25.8352	−1.62746
$253$	6.03929	0.379687
$254$	16.0267	1.00561
$255$	−13.7024	−0.858075
$256$	1.00000	0.0625000
$257$	16.8757	1.05268	0.526338	−	0.850276i	$-0.323565\pi$
$257$	16.8757	1.05268	0.526338	+	0.850276i	$0.323565\pi$
$258$	13.8570	0.862700
$259$	−3.06623	−0.190526
$260$	4.67204	0.289748
$261$	−14.5690	−0.901800
$262$	3.00342	0.185552
$263$	−0.711113	−0.0438491	−0.0219246	−	0.999760i	$-0.506979\pi$
$263$	−0.711113	−0.0438491	−0.0219246	+	0.999760i	$0.506979\pi$
$264$	−11.0951	−0.682858
$265$	1.91468	0.117618
$266$	5.74577	0.352296
$267$	19.9177	1.21894
$268$	5.94494	0.363145
$269$	−15.3668	−0.936933	−0.468466	−	0.883481i	$-0.655193\pi$
$269$	−15.3668	−0.936933	−0.468466	+	0.883481i	$0.655193\pi$
$270$	12.9968	0.790962
$271$	−21.9634	−1.33418	−0.667092	−	0.744976i	$-0.732461\pi$
$271$	−21.9634	−1.33418	−0.667092	+	0.744976i	$0.732461\pi$
$272$	−4.10143	−0.248685
$273$	−51.8597	−3.13869
$274$	−9.25512	−0.559122
$275$	−13.6586	−0.823642
$276$	−5.38345	−0.324046
$277$	−25.2586	−1.51764	−0.758821	−	0.651299i	$-0.774224\pi$
$277$	−25.2586	−1.51764	−0.758821	+	0.651299i	$0.774224\pi$
$278$	12.7964	0.767474
$279$	−17.2863	−1.03490
$280$	3.98321	0.238043
$281$	2.74593	0.163808	0.0819042	−	0.996640i	$-0.473900\pi$
$281$	2.74593	0.163808	0.0819042	+	0.996640i	$0.473900\pi$
$282$	2.11856	0.126158
$283$	19.2346	1.14338	0.571688	−	0.820471i	$-0.306289\pi$
$283$	19.2346	1.14338	0.571688	+	0.820471i	$0.306289\pi$
$284$	−9.36892	−0.555943
$285$	−5.11955	−0.303256
$286$	−15.5160	−0.917478
$287$	−16.6943	−0.985435
$288$	6.89025	0.406012
$289$	−0.178307	−0.0104886
$290$	2.24622	0.131903
$291$	12.9333	0.758165
$292$	−8.89430	−0.520500
$293$	−11.1717	−0.652658	−0.326329	−	0.945256i	$-0.605812\pi$
$293$	−11.1717	−0.652658	−0.326329	+	0.945256i	$0.605812\pi$
$294$	−22.1996	−1.29471
$295$	−0.715051	−0.0416319
$296$	0.817764	0.0475315
$297$	−43.1628	−2.50456
$298$	−14.2376	−0.824762
$299$	−7.52848	−0.435383
$300$	12.1753	0.702941
$301$	16.5213	0.952270
$302$	11.4737	0.660237
$303$	10.8933	0.625805
$304$	−1.53240	−0.0878891
$305$	4.50912	0.258191
$306$	−28.2598	−1.61551
$307$	−2.82947	−0.161487	−0.0807433	−	0.996735i	$-0.525729\pi$
$307$	−2.82947	−0.161487	−0.0807433	+	0.996735i	$0.525729\pi$
$308$	−13.2284	−0.753755
$309$	−16.7009	−0.950079
$310$	2.66516	0.151371
$311$	3.87546	0.219757	0.109879	−	0.993945i	$-0.464954\pi$
$311$	3.87546	0.219757	0.109879	+	0.993945i	$0.464954\pi$
$312$	13.8310	0.783026
$313$	−17.4681	−0.987355	−0.493678	−	0.869645i	$-0.664348\pi$
$313$	−17.4681	−0.987355	−0.493678	+	0.869645i	$0.664348\pi$
$314$	−3.11695	−0.175900
$315$	27.4453	1.54637
$316$	−2.67137	−0.150276
$317$	25.5938	1.43749	0.718745	−	0.695274i	$-0.244717\pi$
$317$	25.5938	1.43749	0.718745	+	0.695274i	$0.244717\pi$
$318$	5.66818	0.317856
$319$	−7.45976	−0.417666
$320$	−1.06232	−0.0593857
$321$	42.6059	2.37803
$322$	−6.41851	−0.357689
$323$	6.28502	0.349708
$324$	17.8048	0.989153
$325$	17.0265	0.944461
$326$	4.26998	0.236492
$327$	−25.6138	−1.41644
$328$	4.45238	0.245841
$329$	2.52589	0.139257
$330$	11.7866	0.648832
$331$	3.99721	0.219707	0.109853	−	0.993948i	$-0.464962\pi$
$331$	3.99721	0.219707	0.109853	+	0.993948i	$0.464962\pi$
$332$	−9.13444	−0.501317
$333$	5.63459	0.308774
$334$	−1.50116	−0.0821398
$335$	−6.31545	−0.345050
$336$	11.7918	0.643296
$337$	5.58884	0.304443	0.152222	−	0.988346i	$-0.451357\pi$
$337$	5.58884	0.304443	0.152222	+	0.988346i	$0.451357\pi$
$338$	6.34193	0.344956
$339$	16.7821	0.911478
$340$	4.35704	0.236294
$341$	−8.85108	−0.479313
$342$	−10.5586	−0.570944
$343$	−0.221126	−0.0119397
$344$	−4.40622	−0.237568
$345$	5.71897	0.307899
$346$	5.60906	0.301545
$347$	−11.3771	−0.610754	−0.305377	−	0.952232i	$-0.598782\pi$
$347$	−11.3771	−0.610754	−0.305377	+	0.952232i	$0.598782\pi$
$348$	6.64966	0.356459
$349$	−21.8206	−1.16803	−0.584014	−	0.811743i	$-0.698519\pi$
$349$	−21.8206	−1.16803	−0.584014	+	0.811743i	$0.698519\pi$
$350$	14.5162	0.775923
$351$	53.8060	2.87195
$352$	3.52800	0.188043
$353$	14.8509	0.790436	0.395218	−	0.918587i	$-0.370669\pi$
$353$	14.8509	0.790436	0.395218	+	0.918587i	$0.370669\pi$
$354$	−2.11682	−0.112508
$355$	9.95283	0.528241
$356$	−6.33337	−0.335668
$357$	−48.3632	−2.55965
$358$	8.78995	0.464563
$359$	5.88712	0.310710	0.155355	−	0.987859i	$-0.450348\pi$
$359$	5.88712	0.310710	0.155355	+	0.987859i	$0.450348\pi$
$360$	−7.31967	−0.385780
$361$	−16.6518	−0.876408
$362$	11.4279	0.600640
$363$	−4.55003	−0.238815
$364$	16.4902	0.864323
$365$	9.44863	0.494564
$366$	13.3487	0.697747
$367$	23.7964	1.24216	0.621081	−	0.783747i	$-0.286694\pi$
$367$	23.7964	1.24216	0.621081	+	0.783747i	$0.286694\pi$
$368$	1.71182	0.0892346
$369$	30.6780	1.59703
$370$	−0.868729	−0.0451631
$371$	6.75798	0.350857
$372$	7.88989	0.409072
$373$	−22.4457	−1.16220	−0.581098	−	0.813833i	$-0.697377\pi$
$373$	−22.4457	−1.16220	−0.581098	+	0.813833i	$0.697377\pi$
$374$	−14.4698	−0.748218
$375$	−29.6385	−1.53052
$376$	−0.673654	−0.0347411
$377$	9.29921	0.478933
$378$	45.8730	2.35945
$379$	13.2234	0.679240	0.339620	−	0.940563i	$-0.389702\pi$
$379$	13.2234	0.679240	0.339620	+	0.940563i	$0.389702\pi$
$380$	1.62790	0.0835097
$381$	−50.4021	−2.58218
$382$	9.27936	0.474773
$383$	27.5835	1.40945	0.704725	−	0.709481i	$-0.251071\pi$
$383$	27.5835	1.40945	0.704725	+	0.709481i	$0.251071\pi$
$384$	−3.14488	−0.160486
$385$	14.0528	0.716196
$386$	22.1510	1.12746
$387$	−30.3600	−1.54328
$388$	−4.11251	−0.208781
$389$	−5.13735	−0.260474	−0.130237	−	0.991483i	$-0.541574\pi$
$389$	−5.13735	−0.260474	−0.130237	+	0.991483i	$0.541574\pi$
$390$	−14.6930	−0.744009
$391$	−7.02089	−0.355062
$392$	7.05897	0.356532
$393$	−9.44540	−0.476457
$394$	22.9495	1.15618
$395$	2.83786	0.142788
$396$	24.3088	1.22156
$397$	26.5501	1.33251	0.666257	−	0.745723i	$-0.267896\pi$
$397$	26.5501	1.33251	0.666257	+	0.745723i	$0.267896\pi$
$398$	17.0105	0.852661
$399$	−18.0697	−0.904619
$400$	−3.87147	−0.193573
$401$	−33.1339	−1.65463	−0.827315	−	0.561738i	$-0.810133\pi$
$401$	−33.1339	−1.65463	−0.827315	+	0.561738i	$0.810133\pi$
$402$	−18.6961	−0.932477
$403$	11.0336	0.549623
$404$	−3.46383	−0.172332
$405$	−18.9144	−0.939865
$406$	7.92817	0.393468
$407$	2.88507	0.143008
$408$	12.8985	0.638570
$409$	−22.7975	−1.12727	−0.563633	−	0.826025i	$-0.690597\pi$
$409$	−22.7975	−1.12727	−0.563633	+	0.826025i	$0.690597\pi$
$410$	−4.72987	−0.233591
$411$	29.1062	1.43570
$412$	5.31050	0.261630
$413$	−2.52381	−0.124189
$414$	11.7948	0.579685
$415$	9.70373	0.476337
$416$	−4.39795	−0.215627
$417$	−40.2429	−1.97071
$418$	−5.40631	−0.264431
$419$	34.2869	1.67502	0.837512	−	0.546418i	$-0.184009\pi$
$419$	34.2869	1.67502	0.837512	+	0.546418i	$0.184009\pi$
$420$	−12.5267	−0.611241
$421$	1.08939	0.0530935	0.0265468	−	0.999648i	$-0.491549\pi$
$421$	1.08939	0.0530935	0.0265468	+	0.999648i	$0.491549\pi$
$422$	14.3343	0.697781
$423$	−4.64164	−0.225684
$424$	−1.80235	−0.0875300
$425$	15.8785	0.770222
$426$	29.4641	1.42754
$427$	15.9152	0.770190
$428$	−13.5477	−0.654854
$429$	48.7958	2.35588
$430$	4.68083	0.225730
$431$	−21.3598	−1.02886	−0.514432	−	0.857531i	$-0.671997\pi$
$431$	−21.3598	−1.02886	−0.514432	+	0.857531i	$0.671997\pi$
$432$	−12.2343	−0.588625
$433$	−23.3565	−1.12244	−0.561221	−	0.827666i	$-0.689668\pi$
$433$	−23.3565	−1.12244	−0.561221	+	0.827666i	$0.689668\pi$
$434$	9.40685	0.451543
$435$	−7.06409	−0.338697
$436$	8.14460	0.390056
$437$	−2.62319	−0.125484
$438$	27.9715	1.33653
$439$	12.0997	0.577489	0.288745	−	0.957406i	$-0.406762\pi$
$439$	12.0997	0.577489	0.288745	+	0.957406i	$0.406762\pi$
$440$	−3.74788	−0.178673
$441$	48.6381	2.31610
$442$	18.0379	0.857973
$443$	22.1695	1.05331	0.526653	−	0.850080i	$-0.323447\pi$
$443$	22.1695	1.05331	0.526653	+	0.850080i	$0.323447\pi$
$444$	−2.57177	−0.122051
$445$	6.72808	0.318942
$446$	14.6970	0.695925
$447$	44.7755	2.11781
$448$	−3.74953	−0.177149
$449$	−11.2379	−0.530348	−0.265174	−	0.964201i	$-0.585429\pi$
$449$	−11.2379	−0.530348	−0.265174	+	0.964201i	$0.585429\pi$
$450$	−26.6754	−1.25749
$451$	15.7080	0.739661
$452$	−5.33633	−0.251000
$453$	−36.0834	−1.69534
$454$	−4.45867	−0.209256
$455$	−17.5180	−0.821255
$456$	4.81920	0.225680
$457$	16.2640	0.760796	0.380398	−	0.924823i	$-0.375787\pi$
$457$	16.2640	0.760796	0.380398	+	0.924823i	$0.375787\pi$
$458$	14.9375	0.697985
$459$	50.1783	2.34212
$460$	−1.81850	−0.0847881
$461$	0.541067	0.0252000	0.0126000	−	0.999921i	$-0.495989\pi$
$461$	0.541067	0.0252000	0.0126000	+	0.999921i	$0.495989\pi$
$462$	41.6015	1.93548
$463$	−20.8915	−0.970909	−0.485454	−	0.874262i	$-0.661346\pi$
$463$	−20.8915	−0.970909	−0.485454	+	0.874262i	$0.661346\pi$
$464$	−2.11444	−0.0981605
$465$	−8.38161	−0.388688
$466$	5.00340	0.231778
$467$	−14.0327	−0.649355	−0.324678	−	0.945825i	$-0.605256\pi$
$467$	−14.0327	−0.649355	−0.324678	+	0.945825i	$0.605256\pi$
$468$	−30.3029	−1.40075
$469$	−22.2907	−1.02929
$470$	0.715639	0.0330100
$471$	9.80241	0.451671
$472$	0.673101	0.0309820
$473$	−15.5452	−0.714767
$474$	8.40113	0.385877
$475$	5.93263	0.272208
$476$	15.3784	0.704869
$477$	−12.4187	−0.568611
$478$	28.0040	1.28087
$479$	11.2604	0.514502	0.257251	−	0.966345i	$-0.417183\pi$
$479$	11.2604	0.514502	0.257251	+	0.966345i	$0.417183\pi$
$480$	3.34088	0.152489
$481$	−3.59648	−0.163985
$482$	−3.02056	−0.137583
$483$	20.1854	0.918468
$484$	1.44681	0.0657640
$485$	4.36881	0.198378
$486$	−19.2907	−0.875045
$487$	−9.58949	−0.434541	−0.217271	−	0.976111i	$-0.569715\pi$
$487$	−9.58949	−0.434541	−0.217271	+	0.976111i	$0.569715\pi$
$488$	−4.24458	−0.192143
$489$	−13.4286	−0.607260
$490$	−7.49891	−0.338766
$491$	39.6145	1.78778	0.893889	−	0.448289i	$-0.147966\pi$
$491$	39.6145	1.78778	0.893889	+	0.448289i	$0.147966\pi$
$492$	−14.0022	−0.631267
$493$	8.67223	0.390578
$494$	6.73941	0.303220
$495$	−25.8238	−1.16069
$496$	−2.50881	−0.112649
$497$	35.1291	1.57575
$498$	28.7267	1.28727
$499$	6.28827	0.281501	0.140751	−	0.990045i	$-0.455048\pi$
$499$	6.28827	0.281501	0.140751	+	0.990045i	$0.455048\pi$
$500$	9.42437	0.421471
$501$	4.72096	0.210917
$502$	9.59314	0.428163
$503$	−44.4492	−1.98189	−0.990946	−	0.134263i	$-0.957133\pi$
$503$	−44.4492	−1.98189	−0.990946	+	0.134263i	$0.957133\pi$
$504$	−25.8352	−1.15079
$505$	3.67971	0.163745
$506$	6.03929	0.268479
$507$	−19.9446	−0.885770
$508$	16.0267	0.711071
$509$	7.12542	0.315829	0.157914	−	0.987453i	$-0.449523\pi$
$509$	7.12542	0.315829	0.157914	+	0.987453i	$0.449523\pi$
$510$	−13.7024	−0.606750
$511$	33.3495	1.47529
$512$	1.00000	0.0441942
$513$	18.7479	0.827740
$514$	16.8757	0.744354
$515$	−5.64147	−0.248593
$516$	13.8570	0.610021
$517$	−2.37665	−0.104525
$518$	−3.06623	−0.134722
$519$	−17.6398	−0.774302
$520$	4.67204	0.204883
$521$	14.2238	0.623157	0.311579	−	0.950220i	$-0.399142\pi$
$521$	14.2238	0.623157	0.311579	+	0.950220i	$0.399142\pi$
$522$	−14.5690	−0.637669
$523$	−37.4602	−1.63802	−0.819009	−	0.573780i	$-0.805476\pi$
$523$	−37.4602	−1.63802	−0.819009	+	0.573780i	$0.805476\pi$
$524$	3.00342	0.131205
$525$	−45.6516	−1.99240
$526$	−0.711113	−0.0310060
$527$	10.2897	0.448226
$528$	−11.0951	−0.482854
$529$	−20.0697	−0.872595
$530$	1.91468	0.0831685
$531$	4.63783	0.201265
$532$	5.74577	0.249111
$533$	−19.5813	−0.848161
$534$	19.9177	0.861921
$535$	14.3921	0.622223
$536$	5.94494	0.256782
$537$	−27.6433	−1.19290
$538$	−15.3668	−0.662511
$539$	24.9041	1.07269
$540$	12.9968	0.559295
$541$	30.0896	1.29365	0.646827	−	0.762637i	$-0.276096\pi$
$541$	30.0896	1.29365	0.646827	+	0.762637i	$0.276096\pi$
$542$	−21.9634	−0.943410
$543$	−35.9395	−1.54231
$544$	−4.10143	−0.175847
$545$	−8.65220	−0.370620
$546$	−51.8597	−2.21939
$547$	1.66045	0.0709959	0.0354980	−	0.999370i	$-0.488698\pi$
$547$	1.66045	0.0709959	0.0354980	+	0.999370i	$0.488698\pi$
$548$	−9.25512	−0.395359
$549$	−29.2462	−1.24820
$550$	−13.6586	−0.582403
$551$	3.24017	0.138036
$552$	−5.38345	−0.229135
$553$	10.0164	0.425940
$554$	−25.2586	−1.07313
$555$	2.73205	0.115969
$556$	12.7964	0.542686
$557$	11.9504	0.506355	0.253177	−	0.967420i	$-0.418524\pi$
$557$	11.9504	0.506355	0.253177	+	0.967420i	$0.418524\pi$
$558$	−17.2863	−0.731787
$559$	19.3783	0.819616
$560$	3.98321	0.168321
$561$	45.5059	1.92126
$562$	2.74593	0.115830
$563$	−12.6146	−0.531640	−0.265820	−	0.964023i	$-0.585643\pi$
$563$	−12.6146	−0.531640	−0.265820	+	0.964023i	$0.585643\pi$
$564$	2.11856	0.0892074
$565$	5.66891	0.238493
$566$	19.2346	0.808489
$567$	−66.7595	−2.80363
$568$	−9.36892	−0.393111
$569$	−43.6872	−1.83146	−0.915732	−	0.401790i	$-0.868388\pi$
$569$	−43.6872	−1.83146	−0.915732	+	0.401790i	$0.868388\pi$
$570$	−5.11955	−0.214434
$571$	−1.76287	−0.0737740	−0.0368870	−	0.999319i	$-0.511744\pi$
$571$	−1.76287	−0.0737740	−0.0368870	+	0.999319i	$0.511744\pi$
$572$	−15.5160	−0.648755
$573$	−29.1824	−1.21911
$574$	−16.6943	−0.696808
$575$	−6.62725	−0.276375
$576$	6.89025	0.287094
$577$	2.73520	0.113868	0.0569339	−	0.998378i	$-0.481868\pi$
$577$	2.73520	0.113868	0.0569339	+	0.998378i	$0.481868\pi$
$578$	−0.178307	−0.00741658
$579$	−69.6622	−2.89506
$580$	2.24622	0.0932693
$581$	34.2499	1.42092
$582$	12.9333	0.536104
$583$	−6.35871	−0.263351
$584$	−8.89430	−0.368049
$585$	32.1915	1.33096
$586$	−11.1717	−0.461499
$587$	7.31761	0.302030	0.151015	−	0.988531i	$-0.451746\pi$
$587$	7.31761	0.302030	0.151015	+	0.988531i	$0.451746\pi$
$588$	−22.1996	−0.915496
$589$	3.84449	0.158410
$590$	−0.715051	−0.0294382
$591$	−72.1733	−2.96881
$592$	0.817764	0.0336099
$593$	−31.4686	−1.29226	−0.646130	−	0.763228i	$-0.723614\pi$
$593$	−31.4686	−1.29226	−0.646130	+	0.763228i	$0.723614\pi$
$594$	−43.1628	−1.77099
$595$	−16.3369	−0.669746
$596$	−14.2376	−0.583195
$597$	−53.4961	−2.18945
$598$	−7.52848	−0.307862
$599$	−25.6700	−1.04885	−0.524425	−	0.851457i	$-0.675720\pi$
$599$	−25.6700	−1.04885	−0.524425	+	0.851457i	$0.675720\pi$
$600$	12.1753	0.497054
$601$	17.6583	0.720299	0.360149	−	0.932895i	$-0.382726\pi$
$601$	17.6583	0.720299	0.360149	+	0.932895i	$0.382726\pi$
$602$	16.5213	0.673356
$603$	40.9621	1.66811
$604$	11.4737	0.466858
$605$	−1.53698	−0.0624870
$606$	10.8933	0.442511
$607$	−15.9938	−0.649169	−0.324585	−	0.945857i	$-0.605225\pi$
$607$	−15.9938	−0.649169	−0.324585	+	0.945857i	$0.605225\pi$
$608$	−1.53240	−0.0621470
$609$	−24.9331	−1.01034
$610$	4.50912	0.182569
$611$	2.96270	0.119858
$612$	−28.2598	−1.14234
$613$	9.84297	0.397554	0.198777	−	0.980045i	$-0.436303\pi$
$613$	9.84297	0.397554	0.198777	+	0.980045i	$0.436303\pi$
$614$	−2.82947	−0.114188
$615$	14.8748	0.599812
$616$	−13.2284	−0.532986
$617$	2.93039	0.117973	0.0589865	−	0.998259i	$-0.481213\pi$
$617$	2.93039	0.117973	0.0589865	+	0.998259i	$0.481213\pi$
$618$	−16.7009	−0.671808
$619$	36.7972	1.47900	0.739502	−	0.673155i	$-0.235061\pi$
$619$	36.7972	1.47900	0.739502	+	0.673155i	$0.235061\pi$
$620$	2.66516	0.107036
$621$	−20.9430	−0.840412
$622$	3.87546	0.155392
$623$	23.7471	0.951409
$624$	13.8310	0.553683
$625$	9.34562	0.373825
$626$	−17.4681	−0.698166
$627$	17.0022	0.679001
$628$	−3.11695	−0.124380
$629$	−3.35400	−0.133733
$630$	27.4453	1.09345
$631$	−22.1222	−0.880672	−0.440336	−	0.897833i	$-0.645141\pi$
$631$	−22.1222	−0.880672	−0.440336	+	0.897833i	$0.645141\pi$
$632$	−2.67137	−0.106261
$633$	−45.0795	−1.79175
$634$	25.5938	1.01646
$635$	−17.0256	−0.675639
$636$	5.66818	0.224758
$637$	−31.0450	−1.23005
$638$	−7.45976	−0.295335
$639$	−64.5542	−2.55372
$640$	−1.06232	−0.0419920
$641$	31.1936	1.23207	0.616036	−	0.787718i	$-0.288738\pi$
$641$	31.1936	1.23207	0.616036	+	0.787718i	$0.288738\pi$
$642$	42.6059	1.68152
$643$	20.4397	0.806065	0.403032	−	0.915186i	$-0.367956\pi$
$643$	20.4397	0.806065	0.403032	+	0.915186i	$0.367956\pi$
$644$	−6.41851	−0.252925
$645$	−14.7206	−0.579625
$646$	6.28502	0.247281
$647$	15.3058	0.601734	0.300867	−	0.953666i	$-0.402724\pi$
$647$	15.3058	0.601734	0.300867	+	0.953666i	$0.402724\pi$
$648$	17.8048	0.699437
$649$	2.37470	0.0932153
$650$	17.0265	0.667835
$651$	−29.5834	−1.15946
$652$	4.26998	0.167225
$653$	6.89232	0.269717	0.134859	−	0.990865i	$-0.456942\pi$
$653$	6.89232	0.269717	0.134859	+	0.990865i	$0.456942\pi$
$654$	−25.6138	−1.00158
$655$	−3.19061	−0.124667
$656$	4.45238	0.173836
$657$	−61.2839	−2.39091
$658$	2.52589	0.0984693
$659$	−10.5291	−0.410155	−0.205078	−	0.978746i	$-0.565745\pi$
$659$	−10.5291	−0.410155	−0.205078	+	0.978746i	$0.565745\pi$
$660$	11.7866	0.458794
$661$	−44.6384	−1.73623	−0.868116	−	0.496361i	$-0.834669\pi$
$661$	−44.6384	−1.73623	−0.868116	+	0.496361i	$0.834669\pi$
$662$	3.99721	0.155356
$663$	−56.7268	−2.20309
$664$	−9.13444	−0.354485
$665$	−6.10387	−0.236698
$666$	5.63459	0.218336
$667$	−3.61954	−0.140149
$668$	−1.50116	−0.0580816
$669$	−46.2204	−1.78698
$670$	−6.31545	−0.243987
$671$	−14.9749	−0.578100
$672$	11.7918	0.454879
$673$	6.55654	0.252736	0.126368	−	0.991983i	$-0.459668\pi$
$673$	6.55654	0.252736	0.126368	+	0.991983i	$0.459668\pi$
$674$	5.58884	0.215274
$675$	47.3649	1.82308
$676$	6.34193	0.243920
$677$	−41.3225	−1.58815	−0.794076	−	0.607818i	$-0.792045\pi$
$677$	−41.3225	−1.58815	−0.794076	+	0.607818i	$0.792045\pi$
$678$	16.7821	0.644513
$679$	15.4200	0.591764
$680$	4.35704	0.167085
$681$	14.0220	0.537323
$682$	−8.85108	−0.338925
$683$	−11.1355	−0.426087	−0.213043	−	0.977043i	$-0.568338\pi$
$683$	−11.1355	−0.426087	−0.213043	+	0.977043i	$0.568338\pi$
$684$	−10.5586	−0.403718
$685$	9.83193	0.375659
$686$	−0.221126	−0.00844262
$687$	−46.9767	−1.79227
$688$	−4.40622	−0.167986
$689$	7.92665	0.301981
$690$	5.71897	0.217717
$691$	18.3339	0.697454	0.348727	−	0.937224i	$-0.386614\pi$
$691$	18.3339	0.697454	0.348727	+	0.937224i	$0.386614\pi$
$692$	5.60906	0.213225
$693$	−91.1466	−3.46237
$694$	−11.3771	−0.431868
$695$	−13.5939	−0.515645
$696$	6.64966	0.252055
$697$	−18.2611	−0.691689
$698$	−21.8206	−0.825921
$699$	−15.7351	−0.595156
$700$	14.5162	0.548660
$701$	47.1095	1.77930	0.889650	−	0.456643i	$-0.150948\pi$
$701$	47.1095	1.77930	0.889650	+	0.456643i	$0.150948\pi$
$702$	53.8060	2.03078
$703$	−1.25314	−0.0472631
$704$	3.52800	0.132967
$705$	−2.25060	−0.0847623
$706$	14.8509	0.558923
$707$	12.9877	0.488454
$708$	−2.11682	−0.0795550
$709$	−28.3261	−1.06381	−0.531905	−	0.846804i	$-0.678524\pi$
$709$	−28.3261	−1.06381	−0.531905	+	0.846804i	$0.678524\pi$
$710$	9.95283	0.373523
$711$	−18.4064	−0.690294
$712$	−6.33337	−0.237353
$713$	−4.29462	−0.160835
$714$	−48.3632	−1.80995
$715$	16.4830	0.616428
$716$	8.78995	0.328496
$717$	−88.0692	−3.28900
$718$	5.88712	0.219705
$719$	−14.0687	−0.524674	−0.262337	−	0.964976i	$-0.584493\pi$
$719$	−14.0687	−0.524674	−0.262337	+	0.964976i	$0.584493\pi$
$720$	−7.31967	−0.272788
$721$	−19.9119	−0.741557
$722$	−16.6518	−0.619714
$723$	9.49928	0.353282
$724$	11.4279	0.424716
$725$	8.18600	0.304020
$726$	−4.55003	−0.168867
$727$	−23.0546	−0.855049	−0.427525	−	0.904004i	$-0.640614\pi$
$727$	−23.0546	−0.855049	−0.427525	+	0.904004i	$0.640614\pi$
$728$	16.4902	0.611169
$729$	7.25267	0.268618
$730$	9.44863	0.349709
$731$	18.0718	0.668409
$732$	13.3487	0.493382
$733$	−6.22030	−0.229752	−0.114876	−	0.993380i	$-0.536647\pi$
$733$	−6.22030	−0.229752	−0.114876	+	0.993380i	$0.536647\pi$
$734$	23.7964	0.878341
$735$	23.5832	0.869878
$736$	1.71182	0.0630984
$737$	20.9738	0.772579
$738$	30.6780	1.12927
$739$	51.2258	1.88437	0.942186	−	0.335090i	$-0.108767\pi$
$739$	51.2258	1.88437	0.942186	+	0.335090i	$0.108767\pi$
$740$	−0.868729	−0.0319351
$741$	−21.1946	−0.778603
$742$	6.75798	0.248093
$743$	−44.3849	−1.62833	−0.814163	−	0.580637i	$-0.802804\pi$
$743$	−44.3849	−1.62833	−0.814163	+	0.580637i	$0.802804\pi$
$744$	7.88989	0.289257
$745$	15.1249	0.554135
$746$	−22.4457	−0.821797
$747$	−62.9385	−2.30280
$748$	−14.4698	−0.529070
$749$	50.7976	1.85610
$750$	−29.6385	−1.08224
$751$	31.0708	1.13379	0.566894	−	0.823791i	$-0.308145\pi$
$751$	31.0708	1.13379	0.566894	+	0.823791i	$0.308145\pi$
$752$	−0.673654	−0.0245656
$753$	−30.1693	−1.09943
$754$	9.29921	0.338657
$755$	−12.1888	−0.443595
$756$	45.8730	1.66839
$757$	46.0001	1.67190	0.835950	−	0.548805i	$-0.184917\pi$
$757$	46.0001	1.67190	0.835950	+	0.548805i	$0.184917\pi$
$758$	13.2234	0.480295
$759$	−18.9928	−0.689396
$760$	1.62790	0.0590502
$761$	−26.9898	−0.978380	−0.489190	−	0.872177i	$-0.662708\pi$
$761$	−26.9898	−0.978380	−0.489190	+	0.872177i	$0.662708\pi$
$762$	−50.4021	−1.82588
$763$	−30.5384	−1.10557
$764$	9.27936	0.335716
$765$	30.0211	1.08541
$766$	27.5835	0.996631
$767$	−2.96026	−0.106889
$768$	−3.14488	−0.113481
$769$	−18.8971	−0.681448	−0.340724	−	0.940163i	$-0.610672\pi$
$769$	−18.8971	−0.681448	−0.340724	+	0.940163i	$0.610672\pi$
$770$	14.0528	0.506427
$771$	−53.0719	−1.91134
$772$	22.1510	0.797233
$773$	52.2557	1.87951	0.939753	−	0.341854i	$-0.111055\pi$
$773$	52.2557	1.87951	0.939753	+	0.341854i	$0.111055\pi$
$774$	−30.3600	−1.09127
$775$	9.71277	0.348893
$776$	−4.11251	−0.147630
$777$	9.64291	0.345938
$778$	−5.13735	−0.184183
$779$	−6.82282	−0.244453
$780$	−14.6930	−0.526094
$781$	−33.0536	−1.18275
$782$	−7.02089	−0.251066
$783$	25.8688	0.924476
$784$	7.05897	0.252106
$785$	3.31121	0.118182
$786$	−9.44540	−0.336906
$787$	6.37499	0.227244	0.113622	−	0.993524i	$-0.463755\pi$
$787$	6.37499	0.227244	0.113622	+	0.993524i	$0.463755\pi$
$788$	22.9495	0.817541
$789$	2.23636	0.0796166
$790$	2.83786	0.100967
$791$	20.0087	0.711428
$792$	24.3088	0.863776
$793$	18.6674	0.662900
$794$	26.5501	0.942229
$795$	−6.02144	−0.213558
$796$	17.0105	0.602923
$797$	15.5062	0.549258	0.274629	−	0.961550i	$-0.411445\pi$
$797$	15.5062	0.549258	0.274629	+	0.961550i	$0.411445\pi$
$798$	−18.0697	−0.639662
$799$	2.76294	0.0977459
$800$	−3.87147	−0.136877
$801$	−43.6384	−1.54189
$802$	−33.1339	−1.17000
$803$	−31.3791	−1.10735
$804$	−18.6961	−0.659361
$805$	6.81853	0.240322
$806$	11.0336	0.388642
$807$	48.3268	1.70118
$808$	−3.46383	−0.121857
$809$	−12.9528	−0.455398	−0.227699	−	0.973732i	$-0.573120\pi$
$809$	−12.9528	−0.455398	−0.227699	+	0.973732i	$0.573120\pi$
$810$	−18.9144	−0.664585
$811$	−7.35643	−0.258319	−0.129160	−	0.991624i	$-0.541228\pi$
$811$	−7.35643	−0.258319	−0.129160	+	0.991624i	$0.541228\pi$
$812$	7.92817	0.278224
$813$	69.0723	2.42247
$814$	2.88507	0.101122
$815$	−4.53610	−0.158893
$816$	12.8985	0.451537
$817$	6.75209	0.236226
$818$	−22.7975	−0.797097
$819$	113.622	3.97027
$820$	−4.72987	−0.165174
$821$	19.4759	0.679713	0.339857	−	0.940477i	$-0.389621\pi$
$821$	19.4759	0.679713	0.339857	+	0.940477i	$0.389621\pi$
$822$	29.1062	1.01520
$823$	44.6747	1.55726	0.778631	−	0.627482i	$-0.215915\pi$
$823$	44.6747	1.55726	0.778631	+	0.627482i	$0.215915\pi$
$824$	5.31050	0.185000
$825$	42.9545	1.49548
$826$	−2.52381	−0.0878147
$827$	13.4807	0.468769	0.234385	−	0.972144i	$-0.424692\pi$
$827$	13.4807	0.468769	0.234385	+	0.972144i	$0.424692\pi$
$828$	11.7948	0.409899
$829$	8.43868	0.293087	0.146544	−	0.989204i	$-0.453185\pi$
$829$	8.43868	0.293087	0.146544	+	0.989204i	$0.453185\pi$
$830$	9.70373	0.336821
$831$	79.4352	2.75558
$832$	−4.39795	−0.152471
$833$	−28.9519	−1.00312
$834$	−40.2429	−1.39350
$835$	1.59472	0.0551875
$836$	−5.40631	−0.186981
$837$	30.6936	1.06093
$838$	34.2869	1.18442
$839$	5.31502	0.183495	0.0917475	−	0.995782i	$-0.470755\pi$
$839$	5.31502	0.183495	0.0917475	+	0.995782i	$0.470755\pi$
$840$	−12.5267	−0.432213
$841$	−24.5291	−0.845832
$842$	1.08939	0.0375428
$843$	−8.63561	−0.297426
$844$	14.3343	0.493405
$845$	−6.73718	−0.231766
$846$	−4.64164	−0.159583
$847$	−5.42485	−0.186400
$848$	−1.80235	−0.0618930
$849$	−60.4903	−2.07602
$850$	15.8785	0.544630
$851$	1.39986	0.0479866
$852$	29.4641	1.00942
$853$	39.7447	1.36083	0.680417	−	0.732825i	$-0.261799\pi$
$853$	39.7447	1.36083	0.680417	+	0.732825i	$0.261799\pi$
$854$	15.9152	0.544606
$855$	11.2167	0.383601
$856$	−13.5477	−0.463051
$857$	−41.9924	−1.43443	−0.717216	−	0.696851i	$-0.754584\pi$
$857$	−41.9924	−1.43443	−0.717216	+	0.696851i	$0.754584\pi$
$858$	48.7958	1.66586
$859$	18.6387	0.635945	0.317973	−	0.948100i	$-0.396998\pi$
$859$	18.6387	0.635945	0.317973	+	0.948100i	$0.396998\pi$
$860$	4.68083	0.159615
$861$	52.5016	1.78925
$862$	−21.3598	−0.727517
$863$	28.3306	0.964386	0.482193	−	0.876065i	$-0.339840\pi$
$863$	28.3306	0.964386	0.482193	+	0.876065i	$0.339840\pi$
$864$	−12.2343	−0.416221
$865$	−5.95864	−0.202600
$866$	−23.3565	−0.793686
$867$	0.560752	0.0190441
$868$	9.40685	0.319289
$869$	−9.42461	−0.319708
$870$	−7.06409	−0.239495
$871$	−26.1455	−0.885908
$872$	8.14460	0.275811
$873$	−28.3362	−0.959035
$874$	−2.62319	−0.0887306
$875$	−35.3370	−1.19461
$876$	27.9715	0.945069
$877$	−11.5031	−0.388431	−0.194216	−	0.980959i	$-0.562216\pi$
$877$	−11.5031	−0.388431	−0.194216	+	0.980959i	$0.562216\pi$
$878$	12.0997	0.408347
$879$	35.1336	1.18503
$880$	−3.74788	−0.126341
$881$	−34.9857	−1.17870	−0.589348	−	0.807879i	$-0.700615\pi$
$881$	−34.9857	−1.17870	−0.589348	+	0.807879i	$0.700615\pi$
$882$	48.6381	1.63773
$883$	−26.5501	−0.893483	−0.446742	−	0.894663i	$-0.647416\pi$
$883$	−26.5501	−0.893483	−0.446742	+	0.894663i	$0.647416\pi$
$884$	18.0379	0.606679
$885$	2.24875	0.0755908
$886$	22.1695	0.744800
$887$	−9.65829	−0.324294	−0.162147	−	0.986767i	$-0.551842\pi$
$887$	−9.65829	−0.324294	−0.162147	+	0.986767i	$0.551842\pi$
$888$	−2.57177	−0.0863028
$889$	−60.0927	−2.01545
$890$	6.72808	0.225526
$891$	62.8152	2.10439
$892$	14.6970	0.492094
$893$	1.03231	0.0345448
$894$	44.7755	1.49752
$895$	−9.33777	−0.312127
$896$	−3.74953	−0.125263
$897$	23.6761	0.790523
$898$	−11.2379	−0.375012
$899$	5.30473	0.176923
$900$	−26.6754	−0.889179
$901$	7.39222	0.246270
$902$	15.7080	0.523019
$903$	−51.9573	−1.72903
$904$	−5.33633	−0.177484
$905$	−12.1402	−0.403553
$906$	−36.0834	−1.19879
$907$	−23.8536	−0.792045	−0.396022	−	0.918241i	$-0.629610\pi$
$907$	−23.8536	−0.792045	−0.396022	+	0.918241i	$0.629610\pi$
$908$	−4.45867	−0.147966
$909$	−23.8667	−0.791607
$910$	−17.5180	−0.580715
$911$	39.0856	1.29496	0.647482	−	0.762081i	$-0.275822\pi$
$911$	39.0856	1.29496	0.647482	+	0.762081i	$0.275822\pi$
$912$	4.81920	0.159580
$913$	−32.2263	−1.06654
$914$	16.2640	0.537964
$915$	−14.1806	−0.468797
$916$	14.9375	0.493550
$917$	−11.2614	−0.371885
$918$	50.1783	1.65613
$919$	−14.4738	−0.477448	−0.238724	−	0.971088i	$-0.576729\pi$
$919$	−14.4738	−0.477448	−0.238724	+	0.971088i	$0.576729\pi$
$920$	−1.81850	−0.0599543
$921$	8.89834	0.293210
$922$	0.541067	0.0178191
$923$	41.2040	1.35625
$924$	41.6015	1.36859
$925$	−3.16595	−0.104096
$926$	−20.8915	−0.686536
$927$	36.5907	1.20180
$928$	−2.11444	−0.0694100
$929$	0.390842	0.0128231	0.00641155	−	0.999979i	$-0.497959\pi$
$929$	0.390842	0.0128231	0.00641155	+	0.999979i	$0.497959\pi$
$930$	−8.38161	−0.274844
$931$	−10.8172	−0.354518
$932$	5.00340	0.163892
$933$	−12.1878	−0.399012
$934$	−14.0327	−0.459163
$935$	15.3717	0.502707
$936$	−30.3029	−0.990482
$937$	8.84865	0.289073	0.144536	−	0.989499i	$-0.453831\pi$
$937$	8.84865	0.289073	0.144536	+	0.989499i	$0.453831\pi$
$938$	−22.2907	−0.727819
$939$	54.9350	1.79274
$940$	0.715639	0.0233416
$941$	−1.51618	−0.0494261	−0.0247131	−	0.999695i	$-0.507867\pi$
$941$	−1.51618	−0.0494261	−0.0247131	+	0.999695i	$0.507867\pi$
$942$	9.80241	0.319380
$943$	7.62166	0.248195
$944$	0.673101	0.0219076
$945$	−48.7320	−1.58525
$946$	−15.5452	−0.505417
$947$	0.872965	0.0283675	0.0141838	−	0.999899i	$-0.495485\pi$
$947$	0.872965	0.0283675	0.0141838	+	0.999899i	$0.495485\pi$
$948$	8.40113	0.272856
$949$	39.1167	1.26978
$950$	5.93263	0.192480
$951$	−80.4893	−2.61004
$952$	15.3784	0.498417
$953$	−9.17998	−0.297369	−0.148684	−	0.988885i	$-0.547504\pi$
$953$	−9.17998	−0.297369	−0.148684	+	0.988885i	$0.547504\pi$
$954$	−12.4187	−0.402069
$955$	−9.85768	−0.318987
$956$	28.0040	0.905715
$957$	23.4600	0.758355
$958$	11.2604	0.363808
$959$	34.7023	1.12060
$960$	3.34088	0.107826
$961$	−24.7059	−0.796964
$962$	−3.59648	−0.115955
$963$	−93.3471	−3.00807
$964$	−3.02056	−0.0972856
$965$	−23.5315	−0.757507
$966$	20.1854	0.649455
$967$	16.3135	0.524607	0.262304	−	0.964985i	$-0.415518\pi$
$967$	16.3135	0.524607	0.262304	+	0.964985i	$0.415518\pi$
$968$	1.44681	0.0465021
$969$	−19.7656	−0.634963
$970$	4.36881	0.140274
$971$	17.1033	0.548872	0.274436	−	0.961605i	$-0.411509\pi$
$971$	17.1033	0.548872	0.274436	+	0.961605i	$0.411509\pi$
$972$	−19.2907	−0.618750
$973$	−47.9803	−1.53818
$974$	−9.58949	−0.307267
$975$	−53.5463	−1.71485
$976$	−4.24458	−0.135866
$977$	34.5454	1.10521	0.552603	−	0.833445i	$-0.313635\pi$
$977$	34.5454	1.10521	0.552603	+	0.833445i	$0.313635\pi$
$978$	−13.4286	−0.429398
$979$	−22.3441	−0.714122
$980$	−7.49891	−0.239544
$981$	56.1183	1.79172
$982$	39.6145	1.26415
$983$	−5.31671	−0.169577	−0.0847883	−	0.996399i	$-0.527021\pi$
$983$	−5.31671	−0.169577	−0.0847883	+	0.996399i	$0.527021\pi$
$984$	−14.0022	−0.446373
$985$	−24.3798	−0.776804
$986$	8.67223	0.276180
$987$	−7.94360	−0.252848
$988$	6.73941	0.214409
$989$	−7.54264	−0.239842
$990$	−25.8238	−0.820735
$991$	13.5934	0.431809	0.215904	−	0.976415i	$-0.430730\pi$
$991$	13.5934	0.431809	0.215904	+	0.976415i	$0.430730\pi$
$992$	−2.50881	−0.0796547
$993$	−12.5707	−0.398920
$994$	35.1291	1.11423
$995$	−18.0707	−0.572880
$996$	28.7267	0.910240
$997$	−18.4574	−0.584552	−0.292276	−	0.956334i	$-0.594413\pi$
$997$	−18.4574	−0.584552	−0.292276	+	0.956334i	$0.594413\pi$
$998$	6.28827	0.199052
$999$	−10.0048	−0.316538

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.f.1.2	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.f.1.2	✓	67	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:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.14488 q^{3} +1.00000 q^{4} -1.06232 q^{5} -3.14488 q^{6} -3.74953 q^{7} +1.00000 q^{8} +6.89025 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.14488 q^{3} +1.00000 q^{4} -1.06232 q^{5} -3.14488 q^{6} -3.74953 q^{7} +1.00000 q^{8} +6.89025 q^{9} -1.06232 q^{10} +3.52800 q^{11} -3.14488 q^{12} -4.39795 q^{13} -3.74953 q^{14} +3.34088 q^{15} +1.00000 q^{16} -4.10143 q^{17} +6.89025 q^{18} -1.53240 q^{19} -1.06232 q^{20} +11.7918 q^{21} +3.52800 q^{22} +1.71182 q^{23} -3.14488 q^{24} -3.87147 q^{25} -4.39795 q^{26} -12.2343 q^{27} -3.74953 q^{28} -2.11444 q^{29} +3.34088 q^{30} -2.50881 q^{31} +1.00000 q^{32} -11.0951 q^{33} -4.10143 q^{34} +3.98321 q^{35} +6.89025 q^{36} +0.817764 q^{37} -1.53240 q^{38} +13.8310 q^{39} -1.06232 q^{40} +4.45238 q^{41} +11.7918 q^{42} -4.40622 q^{43} +3.52800 q^{44} -7.31967 q^{45} +1.71182 q^{46} -0.673654 q^{47} -3.14488 q^{48} +7.05897 q^{49} -3.87147 q^{50} +12.8985 q^{51} -4.39795 q^{52} -1.80235 q^{53} -12.2343 q^{54} -3.74788 q^{55} -3.74953 q^{56} +4.81920 q^{57} -2.11444 q^{58} +0.673101 q^{59} +3.34088 q^{60} -4.24458 q^{61} -2.50881 q^{62} -25.8352 q^{63} +1.00000 q^{64} +4.67204 q^{65} -11.0951 q^{66} +5.94494 q^{67} -4.10143 q^{68} -5.38345 q^{69} +3.98321 q^{70} -9.36892 q^{71} +6.89025 q^{72} -8.89430 q^{73} +0.817764 q^{74} +12.1753 q^{75} -1.53240 q^{76} -13.2284 q^{77} +13.8310 q^{78} -2.67137 q^{79} -1.06232 q^{80} +17.8048 q^{81} +4.45238 q^{82} -9.13444 q^{83} +11.7918 q^{84} +4.35704 q^{85} -4.40622 q^{86} +6.64966 q^{87} +3.52800 q^{88} -6.33337 q^{89} -7.31967 q^{90} +16.4902 q^{91} +1.71182 q^{92} +7.88989 q^{93} -0.673654 q^{94} +1.62790 q^{95} -3.14488 q^{96} -4.11251 q^{97} +7.05897 q^{98} +24.3088 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 67 q^{2} + 21 q^{3} + 67 q^{4} + 21 q^{5} + 21 q^{6} + 38 q^{7} + 67 q^{8} + 90 q^{9}+O(q^{10}) \) 67 * q + 67 * q^2 + 21 * q^3 + 67 * q^4 + 21 * q^5 + 21 * q^6 + 38 * q^7 + 67 * q^8 + 90 * q^9	\( 67 q + 67 q^{2} + 21 q^{3} + 67 q^{4} + 21 q^{5} + 21 q^{6} + 38 q^{7} + 67 q^{8} + 90 q^{9} + 21 q^{10} + 56 q^{11} + 21 q^{12} + 33 q^{13} + 38 q^{14} + 25 q^{15} + 67 q^{16} + 30 q^{17} + 90 q^{18} + 36 q^{19} + 21 q^{20} + 20 q^{21} + 56 q^{22} + 65 q^{23} + 21 q^{24} + 72 q^{25} + 33 q^{26} + 57 q^{27} + 38 q^{28} + 84 q^{29} + 25 q^{30} + 52 q^{31} + 67 q^{32} - 9 q^{33} + 30 q^{34} + 30 q^{35} + 90 q^{36} + 52 q^{37} + 36 q^{38} + 41 q^{39} + 21 q^{40} + 46 q^{41} + 20 q^{42} + 61 q^{43} + 56 q^{44} + 23 q^{45} + 65 q^{46} + 51 q^{47} + 21 q^{48} + 81 q^{49} + 72 q^{50} + 33 q^{51} + 33 q^{52} + 72 q^{53} + 57 q^{54} + 14 q^{55} + 38 q^{56} - 26 q^{57} + 84 q^{58} + 71 q^{59} + 25 q^{60} + 42 q^{61} + 52 q^{62} + 63 q^{63} + 67 q^{64} - 2 q^{65} - 9 q^{66} + 70 q^{67} + 30 q^{68} + 21 q^{69} + 30 q^{70} + 104 q^{71} + 90 q^{72} - 31 q^{73} + 52 q^{74} + 69 q^{75} + 36 q^{76} + 48 q^{77} + 41 q^{78} + 79 q^{79} + 21 q^{80} + 123 q^{81} + 46 q^{82} + 41 q^{83} + 20 q^{84} + 6 q^{85} + 61 q^{86} + 19 q^{87} + 56 q^{88} + 58 q^{89} + 23 q^{90} + 31 q^{91} + 65 q^{92} + 13 q^{93} + 51 q^{94} + 77 q^{95} + 21 q^{96} - 8 q^{97} + 81 q^{98} + 129 q^{99}+O(q^{100}) \) 67 * q + 67 * q^2 + 21 * q^3 + 67 * q^4 + 21 * q^5 + 21 * q^6 + 38 * q^7 + 67 * q^8 + 90 * q^9 + 21 * q^10 + 56 * q^11 + 21 * q^12 + 33 * q^13 + 38 * q^14 + 25 * q^15 + 67 * q^16 + 30 * q^17 + 90 * q^18 + 36 * q^19 + 21 * q^20 + 20 * q^21 + 56 * q^22 + 65 * q^23 + 21 * q^24 + 72 * q^25 + 33 * q^26 + 57 * q^27 + 38 * q^28 + 84 * q^29 + 25 * q^30 + 52 * q^31 + 67 * q^32 - 9 * q^33 + 30 * q^34 + 30 * q^35 + 90 * q^36 + 52 * q^37 + 36 * q^38 + 41 * q^39 + 21 * q^40 + 46 * q^41 + 20 * q^42 + 61 * q^43 + 56 * q^44 + 23 * q^45 + 65 * q^46 + 51 * q^47 + 21 * q^48 + 81 * q^49 + 72 * q^50 + 33 * q^51 + 33 * q^52 + 72 * q^53 + 57 * q^54 + 14 * q^55 + 38 * q^56 - 26 * q^57 + 84 * q^58 + 71 * q^59 + 25 * q^60 + 42 * q^61 + 52 * q^62 + 63 * q^63 + 67 * q^64 - 2 * q^65 - 9 * q^66 + 70 * q^67 + 30 * q^68 + 21 * q^69 + 30 * q^70 + 104 * q^71 + 90 * q^72 - 31 * q^73 + 52 * q^74 + 69 * q^75 + 36 * q^76 + 48 * q^77 + 41 * q^78 + 79 * q^79 + 21 * q^80 + 123 * q^81 + 46 * q^82 + 41 * q^83 + 20 * q^84 + 6 * q^85 + 61 * q^86 + 19 * q^87 + 56 * q^88 + 58 * q^89 + 23 * q^90 + 31 * q^91 + 65 * q^92 + 13 * q^93 + 51 * q^94 + 77 * q^95 + 21 * q^96 - 8 * q^97 + 81 * q^98 + 129 * q^99

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