LMFDB - Embedded newform 6010.2.a.j.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$47.9900916148$
Analytic rank:	$0$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.97405 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.97405 q^{6} -4.80622 q^{7} +1.00000 q^{8} +5.84500 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.97405 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.97405 q^{6} -4.80622 q^{7} +1.00000 q^{8} +5.84500 q^{9} +1.00000 q^{10} +2.59234 q^{11} -2.97405 q^{12} -6.28465 q^{13} -4.80622 q^{14} -2.97405 q^{15} +1.00000 q^{16} +0.918471 q^{17} +5.84500 q^{18} -4.09117 q^{19} +1.00000 q^{20} +14.2940 q^{21} +2.59234 q^{22} -4.33889 q^{23} -2.97405 q^{24} +1.00000 q^{25} -6.28465 q^{26} -8.46119 q^{27} -4.80622 q^{28} -2.12393 q^{29} -2.97405 q^{30} +2.92057 q^{31} +1.00000 q^{32} -7.70976 q^{33} +0.918471 q^{34} -4.80622 q^{35} +5.84500 q^{36} -7.54264 q^{37} -4.09117 q^{38} +18.6909 q^{39} +1.00000 q^{40} +9.52239 q^{41} +14.2940 q^{42} -11.9820 q^{43} +2.59234 q^{44} +5.84500 q^{45} -4.33889 q^{46} +11.0942 q^{47} -2.97405 q^{48} +16.0997 q^{49} +1.00000 q^{50} -2.73158 q^{51} -6.28465 q^{52} -2.61334 q^{53} -8.46119 q^{54} +2.59234 q^{55} -4.80622 q^{56} +12.1674 q^{57} -2.12393 q^{58} -10.8165 q^{59} -2.97405 q^{60} -7.21313 q^{61} +2.92057 q^{62} -28.0923 q^{63} +1.00000 q^{64} -6.28465 q^{65} -7.70976 q^{66} -4.99497 q^{67} +0.918471 q^{68} +12.9041 q^{69} -4.80622 q^{70} +4.43429 q^{71} +5.84500 q^{72} +15.0396 q^{73} -7.54264 q^{74} -2.97405 q^{75} -4.09117 q^{76} -12.4593 q^{77} +18.6909 q^{78} -10.0460 q^{79} +1.00000 q^{80} +7.62904 q^{81} +9.52239 q^{82} +6.13982 q^{83} +14.2940 q^{84} +0.918471 q^{85} -11.9820 q^{86} +6.31668 q^{87} +2.59234 q^{88} -11.0480 q^{89} +5.84500 q^{90} +30.2054 q^{91} -4.33889 q^{92} -8.68593 q^{93} +11.0942 q^{94} -4.09117 q^{95} -2.97405 q^{96} -0.761486 q^{97} +16.0997 q^{98} +15.1522 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9}+O(q^{10}) $ 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9	\( 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9} + 33 q^{10} + 12 q^{11} + 6 q^{12} + 20 q^{13} + 4 q^{14} + 6 q^{15} + 33 q^{16} + 33 q^{17} + 49 q^{18} + 17 q^{19} + 33 q^{20} + 26 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 33 q^{25} + 20 q^{26} + 21 q^{27} + 4 q^{28} + 33 q^{29} + 6 q^{30} + 35 q^{31} + 33 q^{32} + 25 q^{33} + 33 q^{34} + 4 q^{35} + 49 q^{36} + 16 q^{37} + 17 q^{38} + 22 q^{39} + 33 q^{40} + 39 q^{41} + 26 q^{42} - 3 q^{43} + 12 q^{44} + 49 q^{45} + 7 q^{46} + 19 q^{47} + 6 q^{48} + 69 q^{49} + 33 q^{50} + 21 q^{51} + 20 q^{52} + 41 q^{53} + 21 q^{54} + 12 q^{55} + 4 q^{56} + 33 q^{58} + 18 q^{59} + 6 q^{60} + 30 q^{61} + 35 q^{62} - 15 q^{63} + 33 q^{64} + 20 q^{65} + 25 q^{66} - 9 q^{67} + 33 q^{68} + 23 q^{69} + 4 q^{70} + 36 q^{71} + 49 q^{72} + 35 q^{73} + 16 q^{74} + 6 q^{75} + 17 q^{76} + 26 q^{77} + 22 q^{78} + 32 q^{79} + 33 q^{80} + 53 q^{81} + 39 q^{82} + 24 q^{83} + 26 q^{84} + 33 q^{85} - 3 q^{86} + 12 q^{87} + 12 q^{88} + 40 q^{89} + 49 q^{90} + 5 q^{91} + 7 q^{92} + 18 q^{93} + 19 q^{94} + 17 q^{95} + 6 q^{96} + 39 q^{97} + 69 q^{98} + 3 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9 + 33 * q^10 + 12 * q^11 + 6 * q^12 + 20 * q^13 + 4 * q^14 + 6 * q^15 + 33 * q^16 + 33 * q^17 + 49 * q^18 + 17 * q^19 + 33 * q^20 + 26 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 33 * q^25 + 20 * q^26 + 21 * q^27 + 4 * q^28 + 33 * q^29 + 6 * q^30 + 35 * q^31 + 33 * q^32 + 25 * q^33 + 33 * q^34 + 4 * q^35 + 49 * q^36 + 16 * q^37 + 17 * q^38 + 22 * q^39 + 33 * q^40 + 39 * q^41 + 26 * q^42 - 3 * q^43 + 12 * q^44 + 49 * q^45 + 7 * q^46 + 19 * q^47 + 6 * q^48 + 69 * q^49 + 33 * q^50 + 21 * q^51 + 20 * q^52 + 41 * q^53 + 21 * q^54 + 12 * q^55 + 4 * q^56 + 33 * q^58 + 18 * q^59 + 6 * q^60 + 30 * q^61 + 35 * q^62 - 15 * q^63 + 33 * q^64 + 20 * q^65 + 25 * q^66 - 9 * q^67 + 33 * q^68 + 23 * q^69 + 4 * q^70 + 36 * q^71 + 49 * q^72 + 35 * q^73 + 16 * q^74 + 6 * q^75 + 17 * q^76 + 26 * q^77 + 22 * q^78 + 32 * q^79 + 33 * q^80 + 53 * q^81 + 39 * q^82 + 24 * q^83 + 26 * q^84 + 33 * q^85 - 3 * q^86 + 12 * q^87 + 12 * q^88 + 40 * q^89 + 49 * q^90 + 5 * q^91 + 7 * q^92 + 18 * q^93 + 19 * q^94 + 17 * q^95 + 6 * q^96 + 39 * q^97 + 69 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.97405	−1.71707	−0.858536	−	0.512754i	$-0.828625\pi$
$3$	−2.97405	−1.71707	−0.858536	+	0.512754i	$0.828625\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.97405	−1.21415
$7$	−4.80622	−1.81658	−0.908290	−	0.418342i	$-0.862611\pi$
$7$	−4.80622	−1.81658	−0.908290	+	0.418342i	$0.862611\pi$
$8$	1.00000	0.353553
$9$	5.84500	1.94833
$10$	1.00000	0.316228
$11$	2.59234	0.781620	0.390810	−	0.920471i	$-0.372195\pi$
$11$	2.59234	0.781620	0.390810	+	0.920471i	$0.372195\pi$
$12$	−2.97405	−0.858536
$13$	−6.28465	−1.74305	−0.871524	−	0.490353i	$-0.836868\pi$
$13$	−6.28465	−1.74305	−0.871524	+	0.490353i	$0.836868\pi$
$14$	−4.80622	−1.28452
$15$	−2.97405	−0.767898
$16$	1.00000	0.250000
$17$	0.918471	0.222762	0.111381	−	0.993778i	$-0.464473\pi$
$17$	0.918471	0.222762	0.111381	+	0.993778i	$0.464473\pi$
$18$	5.84500	1.37768
$19$	−4.09117	−0.938580	−0.469290	−	0.883044i	$-0.655490\pi$
$19$	−4.09117	−0.938580	−0.469290	+	0.883044i	$0.655490\pi$
$20$	1.00000	0.223607
$21$	14.2940	3.11920
$22$	2.59234	0.552689
$23$	−4.33889	−0.904721	−0.452360	−	0.891835i	$-0.649418\pi$
$23$	−4.33889	−0.904721	−0.452360	+	0.891835i	$0.649418\pi$
$24$	−2.97405	−0.607076
$25$	1.00000	0.200000
$26$	−6.28465	−1.23252
$27$	−8.46119	−1.62836
$28$	−4.80622	−0.908290
$29$	−2.12393	−0.394404	−0.197202	−	0.980363i	$-0.563185\pi$
$29$	−2.12393	−0.394404	−0.197202	+	0.980363i	$0.563185\pi$
$30$	−2.97405	−0.542986
$31$	2.92057	0.524550	0.262275	−	0.964993i	$-0.415527\pi$
$31$	2.92057	0.524550	0.262275	+	0.964993i	$0.415527\pi$
$32$	1.00000	0.176777
$33$	−7.70976	−1.34210
$34$	0.918471	0.157516
$35$	−4.80622	−0.812399
$36$	5.84500	0.974167
$37$	−7.54264	−1.24000	−0.620001	−	0.784601i	$-0.712868\pi$
$37$	−7.54264	−1.24000	−0.620001	+	0.784601i	$0.712868\pi$
$38$	−4.09117	−0.663676
$39$	18.6909	2.99294
$40$	1.00000	0.158114
$41$	9.52239	1.48715	0.743574	−	0.668654i	$-0.233129\pi$
$41$	9.52239	1.48715	0.743574	+	0.668654i	$0.233129\pi$
$42$	14.2940	2.20560
$43$	−11.9820	−1.82723	−0.913615	−	0.406580i	$-0.866721\pi$
$43$	−11.9820	−1.82723	−0.913615	+	0.406580i	$0.866721\pi$
$44$	2.59234	0.390810
$45$	5.84500	0.871321
$46$	−4.33889	−0.639734
$47$	11.0942	1.61825	0.809126	−	0.587635i	$-0.199941\pi$
$47$	11.0942	1.61825	0.809126	+	0.587635i	$0.199941\pi$
$48$	−2.97405	−0.429268
$49$	16.0997	2.29996
$50$	1.00000	0.141421
$51$	−2.73158	−0.382498
$52$	−6.28465	−0.871524
$53$	−2.61334	−0.358969	−0.179485	−	0.983761i	$-0.557443\pi$
$53$	−2.61334	−0.358969	−0.179485	+	0.983761i	$0.557443\pi$
$54$	−8.46119	−1.15142
$55$	2.59234	0.349551
$56$	−4.80622	−0.642258
$57$	12.1674	1.61161
$58$	−2.12393	−0.278886
$59$	−10.8165	−1.40819	−0.704095	−	0.710106i	$-0.748647\pi$
$59$	−10.8165	−1.40819	−0.704095	+	0.710106i	$0.748647\pi$
$60$	−2.97405	−0.383949
$61$	−7.21313	−0.923547	−0.461773	−	0.886998i	$-0.652787\pi$
$61$	−7.21313	−0.923547	−0.461773	+	0.886998i	$0.652787\pi$
$62$	2.92057	0.370913
$63$	−28.0923	−3.53930
$64$	1.00000	0.125000
$65$	−6.28465	−0.779515
$66$	−7.70976	−0.949006
$67$	−4.99497	−0.610232	−0.305116	−	0.952315i	$-0.598695\pi$
$67$	−4.99497	−0.610232	−0.305116	+	0.952315i	$0.598695\pi$
$68$	0.918471	0.111381
$69$	12.9041	1.55347
$70$	−4.80622	−0.574453
$71$	4.43429	0.526253	0.263127	−	0.964761i	$-0.415246\pi$
$71$	4.43429	0.526253	0.263127	+	0.964761i	$0.415246\pi$
$72$	5.84500	0.688840
$73$	15.0396	1.76025	0.880123	−	0.474745i	$-0.157460\pi$
$73$	15.0396	1.76025	0.880123	+	0.474745i	$0.157460\pi$
$74$	−7.54264	−0.876814
$75$	−2.97405	−0.343414
$76$	−4.09117	−0.469290
$77$	−12.4593	−1.41987
$78$	18.6909	2.11633
$79$	−10.0460	−1.13027	−0.565134	−	0.824999i	$-0.691175\pi$
$79$	−10.0460	−1.13027	−0.565134	+	0.824999i	$0.691175\pi$
$80$	1.00000	0.111803
$81$	7.62904	0.847671
$82$	9.52239	1.05157
$83$	6.13982	0.673933	0.336967	−	0.941517i	$-0.390599\pi$
$83$	6.13982	0.673933	0.336967	+	0.941517i	$0.390599\pi$
$84$	14.2940	1.55960
$85$	0.918471	0.0996222
$86$	−11.9820	−1.29205
$87$	6.31668	0.677219
$88$	2.59234	0.276344
$89$	−11.0480	−1.17109	−0.585544	−	0.810641i	$-0.699119\pi$
$89$	−11.0480	−1.17109	−0.585544	+	0.810641i	$0.699119\pi$
$90$	5.84500	0.616117
$91$	30.2054	3.16638
$92$	−4.33889	−0.452360
$93$	−8.68593	−0.900689
$94$	11.0942	1.14428
$95$	−4.09117	−0.419746
$96$	−2.97405	−0.303538
$97$	−0.761486	−0.0773172	−0.0386586	−	0.999252i	$-0.512308\pi$
$97$	−0.761486	−0.0773172	−0.0386586	+	0.999252i	$0.512308\pi$
$98$	16.0997	1.62632
$99$	15.1522	1.52286
$100$	1.00000	0.100000
$101$	18.5339	1.84419	0.922095	−	0.386965i	$-0.126476\pi$
$101$	18.5339	1.84419	0.922095	+	0.386965i	$0.126476\pi$
$102$	−2.73158	−0.270467
$103$	8.28906	0.816746	0.408373	−	0.912815i	$-0.366096\pi$
$103$	8.28906	0.816746	0.408373	+	0.912815i	$0.366096\pi$
$104$	−6.28465	−0.616261
$105$	14.2940	1.39495
$106$	−2.61334	−0.253830
$107$	−18.1625	−1.75583	−0.877915	−	0.478816i	$-0.841066\pi$
$107$	−18.1625	−1.75583	−0.877915	+	0.478816i	$0.841066\pi$
$108$	−8.46119	−0.814178
$109$	10.7061	1.02546	0.512728	−	0.858551i	$-0.328635\pi$
$109$	10.7061	1.02546	0.512728	+	0.858551i	$0.328635\pi$
$110$	2.59234	0.247170
$111$	22.4322	2.12917
$112$	−4.80622	−0.454145
$113$	4.86185	0.457365	0.228682	−	0.973501i	$-0.426558\pi$
$113$	4.86185	0.457365	0.228682	+	0.973501i	$0.426558\pi$
$114$	12.1674	1.13958
$115$	−4.33889	−0.404603
$116$	−2.12393	−0.197202
$117$	−36.7338	−3.39604
$118$	−10.8165	−0.995741
$119$	−4.41437	−0.404665
$120$	−2.97405	−0.271493
$121$	−4.27977	−0.389070
$122$	−7.21313	−0.653046
$123$	−28.3201	−2.55354
$124$	2.92057	0.262275
$125$	1.00000	0.0894427
$126$	−28.0923	−2.50266
$127$	6.61628	0.587100	0.293550	−	0.955944i	$-0.405163\pi$
$127$	6.61628	0.587100	0.293550	+	0.955944i	$0.405163\pi$
$128$	1.00000	0.0883883
$129$	35.6350	3.13749
$130$	−6.28465	−0.551200
$131$	−14.7236	−1.28641	−0.643204	−	0.765695i	$-0.722395\pi$
$131$	−14.7236	−1.28641	−0.643204	+	0.765695i	$0.722395\pi$
$132$	−7.70976	−0.671049
$133$	19.6631	1.70500
$134$	−4.99497	−0.431499
$135$	−8.46119	−0.728223
$136$	0.918471	0.0787582
$137$	−8.67137	−0.740845	−0.370422	−	0.928863i	$-0.620787\pi$
$137$	−8.67137	−0.740845	−0.370422	+	0.928863i	$0.620787\pi$
$138$	12.9041	1.09847
$139$	−15.5993	−1.32311	−0.661556	−	0.749896i	$-0.730104\pi$
$139$	−15.5993	−1.32311	−0.661556	+	0.749896i	$0.730104\pi$
$140$	−4.80622	−0.406199
$141$	−32.9947	−2.77865
$142$	4.43429	0.372117
$143$	−16.2919	−1.36240
$144$	5.84500	0.487083
$145$	−2.12393	−0.176383
$146$	15.0396	1.24468
$147$	−47.8814	−3.94919
$148$	−7.54264	−0.620001
$149$	−10.7333	−0.879309	−0.439655	−	0.898167i	$-0.644899\pi$
$149$	−10.7333	−0.879309	−0.439655	+	0.898167i	$0.644899\pi$
$150$	−2.97405	−0.242831
$151$	16.5185	1.34426	0.672130	−	0.740434i	$-0.265380\pi$
$151$	16.5185	1.34426	0.672130	+	0.740434i	$0.265380\pi$
$152$	−4.09117	−0.331838
$153$	5.36846	0.434015
$154$	−12.4593	−1.00400
$155$	2.92057	0.234586
$156$	18.6909	1.49647
$157$	22.4898	1.79488	0.897440	−	0.441137i	$-0.145425\pi$
$157$	22.4898	1.79488	0.897440	+	0.441137i	$0.145425\pi$
$158$	−10.0460	−0.799220
$159$	7.77221	0.616376
$160$	1.00000	0.0790569
$161$	20.8536	1.64350
$162$	7.62904	0.599394
$163$	15.7805	1.23602	0.618011	−	0.786169i	$-0.287939\pi$
$163$	15.7805	1.23602	0.618011	+	0.786169i	$0.287939\pi$
$164$	9.52239	0.743574
$165$	−7.70976	−0.600204
$166$	6.13982	0.476543
$167$	9.03064	0.698812	0.349406	−	0.936971i	$-0.386383\pi$
$167$	9.03064	0.698812	0.349406	+	0.936971i	$0.386383\pi$
$168$	14.2940	1.10280
$169$	26.4968	2.03822
$170$	0.918471	0.0704435
$171$	−23.9129	−1.82867
$172$	−11.9820	−0.913615
$173$	7.99723	0.608018	0.304009	−	0.952669i	$-0.401675\pi$
$173$	7.99723	0.608018	0.304009	+	0.952669i	$0.401675\pi$
$174$	6.31668	0.478866
$175$	−4.80622	−0.363316
$176$	2.59234	0.195405
$177$	32.1689	2.41796
$178$	−11.0480	−0.828084
$179$	12.8073	0.957260	0.478630	−	0.878017i	$-0.341134\pi$
$179$	12.8073	0.957260	0.478630	+	0.878017i	$0.341134\pi$
$180$	5.84500	0.435661
$181$	1.92779	0.143292	0.0716459	−	0.997430i	$-0.477175\pi$
$181$	1.92779	0.143292	0.0716459	+	0.997430i	$0.477175\pi$
$182$	30.2054	2.23897
$183$	21.4522	1.58580
$184$	−4.33889	−0.319867
$185$	−7.54264	−0.554546
$186$	−8.68593	−0.636883
$187$	2.38099	0.174115
$188$	11.0942	0.809126
$189$	40.6663	2.95804
$190$	−4.09117	−0.296805
$191$	−6.06367	−0.438752	−0.219376	−	0.975640i	$-0.570402\pi$
$191$	−6.06367	−0.438752	−0.219376	+	0.975640i	$0.570402\pi$
$192$	−2.97405	−0.214634
$193$	6.63846	0.477847	0.238924	−	0.971038i	$-0.423205\pi$
$193$	6.63846	0.477847	0.238924	+	0.971038i	$0.423205\pi$
$194$	−0.761486	−0.0546715
$195$	18.6909	1.33848
$196$	16.0997	1.14998
$197$	6.68908	0.476577	0.238289	−	0.971194i	$-0.423414\pi$
$197$	6.68908	0.476577	0.238289	+	0.971194i	$0.423414\pi$
$198$	15.1522	1.07682
$199$	1.32428	0.0938757	0.0469378	−	0.998898i	$-0.485054\pi$
$199$	1.32428	0.0938757	0.0469378	+	0.998898i	$0.485054\pi$
$200$	1.00000	0.0707107
$201$	14.8553	1.04781
$202$	18.5339	1.30404
$203$	10.2081	0.716465
$204$	−2.73158	−0.191249
$205$	9.52239	0.665073
$206$	8.28906	0.577526
$207$	−25.3608	−1.76270
$208$	−6.28465	−0.435762
$209$	−10.6057	−0.733613
$210$	14.2940	0.986376
$211$	−17.8274	−1.22729	−0.613645	−	0.789582i	$-0.710297\pi$
$211$	−17.8274	−1.22729	−0.613645	+	0.789582i	$0.710297\pi$
$212$	−2.61334	−0.179485
$213$	−13.1878	−0.903614
$214$	−18.1625	−1.24156
$215$	−11.9820	−0.817162
$216$	−8.46119	−0.575711
$217$	−14.0369	−0.952886
$218$	10.7061	0.725107
$219$	−44.7285	−3.02247
$220$	2.59234	0.174776
$221$	−5.77227	−0.388285
$222$	22.4322	1.50555
$223$	17.3987	1.16510	0.582551	−	0.812794i	$-0.302055\pi$
$223$	17.3987	1.16510	0.582551	+	0.812794i	$0.302055\pi$
$224$	−4.80622	−0.321129
$225$	5.84500	0.389667
$226$	4.86185	0.323406
$227$	22.6748	1.50498	0.752489	−	0.658605i	$-0.228853\pi$
$227$	22.6748	1.50498	0.752489	+	0.658605i	$0.228853\pi$
$228$	12.1674	0.805804
$229$	5.55136	0.366844	0.183422	−	0.983034i	$-0.441283\pi$
$229$	5.55136	0.366844	0.183422	+	0.983034i	$0.441283\pi$
$230$	−4.33889	−0.286098
$231$	37.0548	2.43803
$232$	−2.12393	−0.139443
$233$	15.9688	1.04615	0.523077	−	0.852286i	$-0.324784\pi$
$233$	15.9688	1.04615	0.523077	+	0.852286i	$0.324784\pi$
$234$	−36.7338	−2.40136
$235$	11.0942	0.723705
$236$	−10.8165	−0.704095
$237$	29.8775	1.94075
$238$	−4.41437	−0.286141
$239$	−24.5663	−1.58906	−0.794531	−	0.607224i	$-0.792283\pi$
$239$	−24.5663	−1.58906	−0.794531	+	0.607224i	$0.792283\pi$
$240$	−2.97405	−0.191974
$241$	22.7039	1.46249	0.731243	−	0.682117i	$-0.238941\pi$
$241$	22.7039	1.46249	0.731243	+	0.682117i	$0.238941\pi$
$242$	−4.27977	−0.275114
$243$	2.69439	0.172845
$244$	−7.21313	−0.461773
$245$	16.0997	1.02857
$246$	−28.3201	−1.80562
$247$	25.7116	1.63599
$248$	2.92057	0.185456
$249$	−18.2602	−1.15719
$250$	1.00000	0.0632456
$251$	−0.0797102	−0.00503126	−0.00251563	−	0.999997i	$-0.500801\pi$
$251$	−0.0797102	−0.00503126	−0.00251563	+	0.999997i	$0.500801\pi$
$252$	−28.0923	−1.76965
$253$	−11.2479	−0.707148
$254$	6.61628	0.415142
$255$	−2.73158	−0.171058
$256$	1.00000	0.0625000
$257$	0.528422	0.0329620	0.0164810	−	0.999864i	$-0.494754\pi$
$257$	0.528422	0.0329620	0.0164810	+	0.999864i	$0.494754\pi$
$258$	35.6350	2.21854
$259$	36.2516	2.25256
$260$	−6.28465	−0.389757
$261$	−12.4144	−0.768430
$262$	−14.7236	−0.909628
$263$	19.1327	1.17977	0.589886	−	0.807486i	$-0.299173\pi$
$263$	19.1327	1.17977	0.589886	+	0.807486i	$0.299173\pi$
$264$	−7.70976	−0.474503
$265$	−2.61334	−0.160536
$266$	19.6631	1.20562
$267$	32.8574	2.01084
$268$	−4.99497	−0.305116
$269$	−20.9013	−1.27438	−0.637188	−	0.770708i	$-0.719903\pi$
$269$	−20.9013	−1.27438	−0.637188	+	0.770708i	$0.719903\pi$
$270$	−8.46119	−0.514932
$271$	24.9655	1.51655	0.758273	−	0.651937i	$-0.226043\pi$
$271$	24.9655	1.51655	0.758273	+	0.651937i	$0.226043\pi$
$272$	0.918471	0.0556905
$273$	−89.8325	−5.43691
$274$	−8.67137	−0.523856
$275$	2.59234	0.156324
$276$	12.9041	0.776735
$277$	−17.3975	−1.04532	−0.522658	−	0.852542i	$-0.675060\pi$
$277$	−17.3975	−1.04532	−0.522658	+	0.852542i	$0.675060\pi$
$278$	−15.5993	−0.935582
$279$	17.0707	1.02200
$280$	−4.80622	−0.287226
$281$	23.1892	1.38335	0.691675	−	0.722209i	$-0.256873\pi$
$281$	23.1892	1.38335	0.691675	+	0.722209i	$0.256873\pi$
$282$	−32.9947	−1.96481
$283$	−30.6479	−1.82183	−0.910915	−	0.412594i	$-0.864623\pi$
$283$	−30.6479	−1.82183	−0.910915	+	0.412594i	$0.864623\pi$
$284$	4.43429	0.263127
$285$	12.1674	0.720733
$286$	−16.2919	−0.963363
$287$	−45.7667	−2.70152
$288$	5.84500	0.344420
$289$	−16.1564	−0.950377
$290$	−2.12393	−0.124721
$291$	2.26470	0.132759
$292$	15.0396	0.880123
$293$	27.2270	1.59062	0.795309	−	0.606204i	$-0.207308\pi$
$293$	27.2270	1.59062	0.795309	+	0.606204i	$0.207308\pi$
$294$	−47.8814	−2.79250
$295$	−10.8165	−0.629762
$296$	−7.54264	−0.438407
$297$	−21.9343	−1.27276
$298$	−10.7333	−0.621765
$299$	27.2684	1.57697
$300$	−2.97405	−0.171707
$301$	57.5879	3.31931
$302$	16.5185	0.950535
$303$	−55.1207	−3.16660
$304$	−4.09117	−0.234645
$305$	−7.21313	−0.413023
$306$	5.36846	0.306895
$307$	11.9012	0.679240	0.339620	−	0.940563i	$-0.389702\pi$
$307$	11.9012	0.679240	0.339620	+	0.940563i	$0.389702\pi$
$308$	−12.4593	−0.709937
$309$	−24.6521	−1.40241
$310$	2.92057	0.165877
$311$	19.5101	1.10632	0.553159	−	0.833076i	$-0.313422\pi$
$311$	19.5101	1.10632	0.553159	+	0.833076i	$0.313422\pi$
$312$	18.6909	1.05816
$313$	−5.13610	−0.290309	−0.145155	−	0.989409i	$-0.546368\pi$
$313$	−5.13610	−0.290309	−0.145155	+	0.989409i	$0.546368\pi$
$314$	22.4898	1.26917
$315$	−28.0923	−1.58282
$316$	−10.0460	−0.565134
$317$	19.7462	1.10906	0.554530	−	0.832164i	$-0.312898\pi$
$317$	19.7462	1.10906	0.554530	+	0.832164i	$0.312898\pi$
$318$	7.77221	0.435844
$319$	−5.50595	−0.308274
$320$	1.00000	0.0559017
$321$	54.0161	3.01489
$322$	20.8536	1.16213
$323$	−3.75763	−0.209080
$324$	7.62904	0.423836
$325$	−6.28465	−0.348610
$326$	15.7805	0.874000
$327$	−31.8405	−1.76078
$328$	9.52239	0.525786
$329$	−53.3210	−2.93968
$330$	−7.70976	−0.424408
$331$	−5.55711	−0.305446	−0.152723	−	0.988269i	$-0.548804\pi$
$331$	−5.55711	−0.305446	−0.152723	+	0.988269i	$0.548804\pi$
$332$	6.13982	0.336967
$333$	−44.0868	−2.41594
$334$	9.03064	0.494135
$335$	−4.99497	−0.272904
$336$	14.2940	0.779799
$337$	14.5339	0.791710	0.395855	−	0.918313i	$-0.370448\pi$
$337$	14.5339	0.791710	0.395855	+	0.918313i	$0.370448\pi$
$338$	26.4968	1.44124
$339$	−14.4594	−0.785328
$340$	0.918471	0.0498111
$341$	7.57111	0.409998
$342$	−23.9129	−1.29306
$343$	−43.7352	−2.36148
$344$	−11.9820	−0.646024
$345$	12.9041	0.694733
$346$	7.99723	0.429934
$347$	23.6795	1.27118	0.635592	−	0.772025i	$-0.280756\pi$
$347$	23.6795	1.27118	0.635592	+	0.772025i	$0.280756\pi$
$348$	6.31668	0.338610
$349$	3.53162	0.189043	0.0945216	−	0.995523i	$-0.469868\pi$
$349$	3.53162	0.189043	0.0945216	+	0.995523i	$0.469868\pi$
$350$	−4.80622	−0.256903
$351$	53.1756	2.83830
$352$	2.59234	0.138172
$353$	−1.42814	−0.0760122	−0.0380061	−	0.999278i	$-0.512101\pi$
$353$	−1.42814	−0.0760122	−0.0380061	+	0.999278i	$0.512101\pi$
$354$	32.1689	1.70976
$355$	4.43429	0.235348
$356$	−11.0480	−0.585544
$357$	13.1286	0.694838
$358$	12.8073	0.676885
$359$	−16.7562	−0.884359	−0.442179	−	0.896927i	$-0.645795\pi$
$359$	−16.7562	−0.884359	−0.442179	+	0.896927i	$0.645795\pi$
$360$	5.84500	0.308059
$361$	−2.26229	−0.119068
$362$	1.92779	0.101323
$363$	12.7283	0.668062
$364$	30.2054	1.58319
$365$	15.0396	0.787206
$366$	21.4522	1.12133
$367$	−23.5028	−1.22684	−0.613418	−	0.789758i	$-0.710206\pi$
$367$	−23.5028	−1.22684	−0.613418	+	0.789758i	$0.710206\pi$
$368$	−4.33889	−0.226180
$369$	55.6584	2.89746
$370$	−7.54264	−0.392123
$371$	12.5603	0.652096
$372$	−8.68593	−0.450345
$373$	26.6001	1.37730	0.688651	−	0.725093i	$-0.258203\pi$
$373$	26.6001	1.37730	0.688651	+	0.725093i	$0.258203\pi$
$374$	2.38099	0.123118
$375$	−2.97405	−0.153580
$376$	11.0942	0.572139
$377$	13.3481	0.687465
$378$	40.6663	2.09165
$379$	7.12869	0.366176	0.183088	−	0.983097i	$-0.441391\pi$
$379$	7.12869	0.366176	0.183088	+	0.983097i	$0.441391\pi$
$380$	−4.09117	−0.209873
$381$	−19.6772	−1.00809
$382$	−6.06367	−0.310244
$383$	−13.2508	−0.677085	−0.338543	−	0.940951i	$-0.609934\pi$
$383$	−13.2508	−0.677085	−0.338543	+	0.940951i	$0.609934\pi$
$384$	−2.97405	−0.151769
$385$	−12.4593	−0.634987
$386$	6.63846	0.337889
$387$	−70.0345	−3.56006
$388$	−0.761486	−0.0386586
$389$	1.05689	0.0535862	0.0267931	−	0.999641i	$-0.491470\pi$
$389$	1.05689	0.0535862	0.0267931	+	0.999641i	$0.491470\pi$
$390$	18.6909	0.946450
$391$	−3.98514	−0.201537
$392$	16.0997	0.813158
$393$	43.7888	2.20885
$394$	6.68908	0.336991
$395$	−10.0460	−0.505471
$396$	15.1522	0.761428
$397$	13.9564	0.700451	0.350226	−	0.936665i	$-0.386105\pi$
$397$	13.9564	0.700451	0.350226	+	0.936665i	$0.386105\pi$
$398$	1.32428	0.0663801
$399$	−58.4791	−2.92761
$400$	1.00000	0.0500000
$401$	−18.4617	−0.921934	−0.460967	−	0.887417i	$-0.652497\pi$
$401$	−18.4617	−0.921934	−0.460967	+	0.887417i	$0.652497\pi$
$402$	14.8553	0.740915
$403$	−18.3548	−0.914315
$404$	18.5339	0.922095
$405$	7.62904	0.379090
$406$	10.2081	0.506618
$407$	−19.5531	−0.969211
$408$	−2.73158	−0.135234
$409$	34.0913	1.68571	0.842853	−	0.538145i	$-0.180875\pi$
$409$	34.0913	1.68571	0.842853	+	0.538145i	$0.180875\pi$
$410$	9.52239	0.470277
$411$	25.7891	1.27208
$412$	8.28906	0.408373
$413$	51.9865	2.55809
$414$	−25.3608	−1.24642
$415$	6.13982	0.301392
$416$	−6.28465	−0.308130
$417$	46.3931	2.27188
$418$	−10.6057	−0.518743
$419$	1.33118	0.0650322	0.0325161	−	0.999471i	$-0.489648\pi$
$419$	1.33118	0.0650322	0.0325161	+	0.999471i	$0.489648\pi$
$420$	14.2940	0.697473
$421$	10.1548	0.494912	0.247456	−	0.968899i	$-0.420405\pi$
$421$	10.1548	0.494912	0.247456	+	0.968899i	$0.420405\pi$
$422$	−17.8274	−0.867825
$423$	64.8455	3.15290
$424$	−2.61334	−0.126915
$425$	0.918471	0.0445524
$426$	−13.1878	−0.638952
$427$	34.6679	1.67770
$428$	−18.1625	−0.877915
$429$	48.4531	2.33934
$430$	−11.9820	−0.577821
$431$	−24.8500	−1.19698	−0.598491	−	0.801130i	$-0.704233\pi$
$431$	−24.8500	−1.19698	−0.598491	+	0.801130i	$0.704233\pi$
$432$	−8.46119	−0.407089
$433$	7.59337	0.364914	0.182457	−	0.983214i	$-0.441595\pi$
$433$	7.59337	0.364914	0.182457	+	0.983214i	$0.441595\pi$
$434$	−14.0369	−0.673792
$435$	6.31668	0.302862
$436$	10.7061	0.512728
$437$	17.7512	0.849153
$438$	−44.7285	−2.13721
$439$	21.7794	1.03947	0.519736	−	0.854327i	$-0.326030\pi$
$439$	21.7794	1.03947	0.519736	+	0.854327i	$0.326030\pi$
$440$	2.59234	0.123585
$441$	94.1029	4.48109
$442$	−5.77227	−0.274559
$443$	−20.3095	−0.964933	−0.482467	−	0.875914i	$-0.660259\pi$
$443$	−20.3095	−0.964933	−0.482467	+	0.875914i	$0.660259\pi$
$444$	22.4322	1.06459
$445$	−11.0480	−0.523726
$446$	17.3987	0.823851
$447$	31.9215	1.50984
$448$	−4.80622	−0.227072
$449$	−15.3541	−0.724605	−0.362303	−	0.932060i	$-0.618009\pi$
$449$	−15.3541	−0.724605	−0.362303	+	0.932060i	$0.618009\pi$
$450$	5.84500	0.275536
$451$	24.6853	1.16238
$452$	4.86185	0.228682
$453$	−49.1270	−2.30819
$454$	22.6748	1.06418
$455$	30.2054	1.41605
$456$	12.1674	0.569790
$457$	−27.4280	−1.28303	−0.641514	−	0.767111i	$-0.721693\pi$
$457$	−27.4280	−1.28303	−0.641514	+	0.767111i	$0.721693\pi$
$458$	5.55136	0.259398
$459$	−7.77136	−0.362736
$460$	−4.33889	−0.202302
$461$	−28.7604	−1.33950	−0.669752	−	0.742585i	$-0.733599\pi$
$461$	−28.7604	−1.33950	−0.669752	+	0.742585i	$0.733599\pi$
$462$	37.0548	1.72394
$463$	15.7435	0.731662	0.365831	−	0.930681i	$-0.380785\pi$
$463$	15.7435	0.731662	0.365831	+	0.930681i	$0.380785\pi$
$464$	−2.12393	−0.0986009
$465$	−8.68593	−0.402800
$466$	15.9688	0.739742
$467$	8.00627	0.370486	0.185243	−	0.982693i	$-0.440693\pi$
$467$	8.00627	0.370486	0.185243	+	0.982693i	$0.440693\pi$
$468$	−36.7338	−1.69802
$469$	24.0069	1.10854
$470$	11.0942	0.511736
$471$	−66.8858	−3.08194
$472$	−10.8165	−0.497870
$473$	−31.0613	−1.42820
$474$	29.8775	1.37232
$475$	−4.09117	−0.187716
$476$	−4.41437	−0.202332
$477$	−15.2750	−0.699392
$478$	−24.5663	−1.12364
$479$	18.8910	0.863150	0.431575	−	0.902077i	$-0.357958\pi$
$479$	18.8910	0.863150	0.431575	+	0.902077i	$0.357958\pi$
$480$	−2.97405	−0.135746
$481$	47.4029	2.16138
$482$	22.7039	1.03413
$483$	−62.0199	−2.82200
$484$	−4.27977	−0.194535
$485$	−0.761486	−0.0345773
$486$	2.69439	0.122220
$487$	13.8868	0.629273	0.314637	−	0.949212i	$-0.398117\pi$
$487$	13.8868	0.629273	0.314637	+	0.949212i	$0.398117\pi$
$488$	−7.21313	−0.326523
$489$	−46.9320	−2.12234
$490$	16.0997	0.727311
$491$	30.4482	1.37411	0.687054	−	0.726606i	$-0.258904\pi$
$491$	30.4482	1.37411	0.687054	+	0.726606i	$0.258904\pi$
$492$	−28.3201	−1.27677
$493$	−1.95077	−0.0878581
$494$	25.7116	1.15682
$495$	15.1522	0.681042
$496$	2.92057	0.131137
$497$	−21.3121	−0.955980
$498$	−18.2602	−0.818258
$499$	35.0187	1.56765	0.783826	−	0.620980i	$-0.213265\pi$
$499$	35.0187	1.56765	0.783826	+	0.620980i	$0.213265\pi$
$500$	1.00000	0.0447214
$501$	−26.8576	−1.19991
$502$	−0.0797102	−0.00355764
$503$	−6.41353	−0.285965	−0.142983	−	0.989725i	$-0.545669\pi$
$503$	−6.41353	−0.285965	−0.142983	+	0.989725i	$0.545669\pi$
$504$	−28.0923	−1.25133
$505$	18.5339	0.824746
$506$	−11.2479	−0.500029
$507$	−78.8030	−3.49976
$508$	6.61628	0.293550
$509$	−12.5622	−0.556809	−0.278404	−	0.960464i	$-0.589806\pi$
$509$	−12.5622	−0.556809	−0.278404	+	0.960464i	$0.589806\pi$
$510$	−2.73158	−0.120957
$511$	−72.2834	−3.19763
$512$	1.00000	0.0441942
$513$	34.6162	1.52834
$514$	0.528422	0.0233077
$515$	8.28906	0.365260
$516$	35.6350	1.56874
$517$	28.7599	1.26486
$518$	36.2516	1.59280
$519$	−23.7842	−1.04401
$520$	−6.28465	−0.275600
$521$	8.76158	0.383852	0.191926	−	0.981409i	$-0.438527\pi$
$521$	8.76158	0.383852	0.191926	+	0.981409i	$0.438527\pi$
$522$	−12.4144	−0.543362
$523$	−6.92753	−0.302920	−0.151460	−	0.988463i	$-0.548397\pi$
$523$	−6.92753	−0.302920	−0.151460	+	0.988463i	$0.548397\pi$
$524$	−14.7236	−0.643204
$525$	14.2940	0.623839
$526$	19.1327	0.834225
$527$	2.68246	0.116850
$528$	−7.70976	−0.335524
$529$	−4.17404	−0.181480
$530$	−2.61334	−0.113516
$531$	−63.2225	−2.74362
$532$	19.6631	0.852502
$533$	−59.8449	−2.59217
$534$	32.8574	1.42188
$535$	−18.1625	−0.785231
$536$	−4.99497	−0.215750
$537$	−38.0895	−1.64368
$538$	−20.9013	−0.901120
$539$	41.7359	1.79769
$540$	−8.46119	−0.364112
$541$	32.0490	1.37790	0.688948	−	0.724811i	$-0.258073\pi$
$541$	32.0490	1.37790	0.688948	+	0.724811i	$0.258073\pi$
$542$	24.9655	1.07236
$543$	−5.73336	−0.246042
$544$	0.918471	0.0393791
$545$	10.7061	0.458598
$546$	−89.8325	−3.84448
$547$	22.3759	0.956724	0.478362	−	0.878163i	$-0.341231\pi$
$547$	22.3759	0.956724	0.478362	+	0.878163i	$0.341231\pi$
$548$	−8.67137	−0.370422
$549$	−42.1608	−1.79938
$550$	2.59234	0.110538
$551$	8.68936	0.370179
$552$	12.9041	0.549235
$553$	48.2834	2.05322
$554$	−17.3975	−0.739151
$555$	22.4322	0.952195
$556$	−15.5993	−0.661556
$557$	26.0274	1.10282	0.551408	−	0.834236i	$-0.314091\pi$
$557$	26.0274	1.10282	0.551408	+	0.834236i	$0.314091\pi$
$558$	17.0707	0.722662
$559$	75.3024	3.18495
$560$	−4.80622	−0.203100
$561$	−7.08119	−0.298968
$562$	23.1892	0.978176
$563$	29.2859	1.23426	0.617128	−	0.786863i	$-0.288296\pi$
$563$	29.2859	1.23426	0.617128	+	0.786863i	$0.288296\pi$
$564$	−32.9947	−1.38933
$565$	4.86185	0.204540
$566$	−30.6479	−1.28823
$567$	−36.6668	−1.53986
$568$	4.43429	0.186059
$569$	−43.5116	−1.82410	−0.912050	−	0.410078i	$-0.865501\pi$
$569$	−43.5116	−1.82410	−0.912050	+	0.410078i	$0.865501\pi$
$570$	12.1674	0.509635
$571$	−19.1525	−0.801506	−0.400753	−	0.916186i	$-0.631252\pi$
$571$	−19.1525	−0.801506	−0.400753	+	0.916186i	$0.631252\pi$
$572$	−16.2919	−0.681201
$573$	18.0337	0.753368
$574$	−45.7667	−1.91026
$575$	−4.33889	−0.180944
$576$	5.84500	0.243542
$577$	−21.2710	−0.885521	−0.442761	−	0.896640i	$-0.646001\pi$
$577$	−21.2710	−0.885521	−0.442761	+	0.896640i	$0.646001\pi$
$578$	−16.1564	−0.672018
$579$	−19.7432	−0.820498
$580$	−2.12393	−0.0881913
$581$	−29.5093	−1.22425
$582$	2.26470	0.0938748
$583$	−6.77466	−0.280578
$584$	15.0396	0.622341
$585$	−36.7338	−1.51876
$586$	27.2270	1.12474
$587$	−23.3947	−0.965601	−0.482800	−	0.875730i	$-0.660380\pi$
$587$	−23.3947	−0.965601	−0.482800	+	0.875730i	$0.660380\pi$
$588$	−47.8814	−1.97460
$589$	−11.9486	−0.492332
$590$	−10.8165	−0.445309
$591$	−19.8937	−0.818317
$592$	−7.54264	−0.310001
$593$	−3.02765	−0.124331	−0.0621653	−	0.998066i	$-0.519801\pi$
$593$	−3.02765	−0.124331	−0.0621653	+	0.998066i	$0.519801\pi$
$594$	−21.9343	−0.899974
$595$	−4.41437	−0.180972
$596$	−10.7333	−0.439655
$597$	−3.93848	−0.161191
$598$	27.2684	1.11509
$599$	39.6125	1.61852	0.809262	−	0.587448i	$-0.199867\pi$
$599$	39.6125	1.61852	0.809262	+	0.587448i	$0.199867\pi$
$600$	−2.97405	−0.121415
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	57.5879	2.34711
$603$	−29.1956	−1.18894
$604$	16.5185	0.672130
$605$	−4.27977	−0.173998
$606$	−55.1207	−2.23913
$607$	−1.96728	−0.0798494	−0.0399247	−	0.999203i	$-0.512712\pi$
$607$	−1.96728	−0.0798494	−0.0399247	+	0.999203i	$0.512712\pi$
$608$	−4.09117	−0.165919
$609$	−30.3593	−1.23022
$610$	−7.21313	−0.292051
$611$	−69.7230	−2.82069
$612$	5.36846	0.217007
$613$	2.62750	0.106124	0.0530618	−	0.998591i	$-0.483102\pi$
$613$	2.62750	0.106124	0.0530618	+	0.998591i	$0.483102\pi$
$614$	11.9012	0.480295
$615$	−28.3201	−1.14198
$616$	−12.4593	−0.502001
$617$	6.27999	0.252823	0.126411	−	0.991978i	$-0.459654\pi$
$617$	6.27999	0.252823	0.126411	+	0.991978i	$0.459654\pi$
$618$	−24.6521	−0.991654
$619$	4.79722	0.192817	0.0964083	−	0.995342i	$-0.469265\pi$
$619$	4.79722	0.192817	0.0964083	+	0.995342i	$0.469265\pi$
$620$	2.92057	0.117293
$621$	36.7122	1.47321
$622$	19.5101	0.782284
$623$	53.0991	2.12737
$624$	18.6909	0.748235
$625$	1.00000	0.0400000
$626$	−5.13610	−0.205280
$627$	31.5420	1.25967
$628$	22.4898	0.897440
$629$	−6.92770	−0.276225
$630$	−28.0923	−1.11923
$631$	−22.1999	−0.883762	−0.441881	−	0.897074i	$-0.645689\pi$
$631$	−22.1999	−0.883762	−0.441881	+	0.897074i	$0.645689\pi$
$632$	−10.0460	−0.399610
$633$	53.0197	2.10734
$634$	19.7462	0.784224
$635$	6.61628	0.262559
$636$	7.77221	0.308188
$637$	−101.181	−4.00894
$638$	−5.50595	−0.217982
$639$	25.9184	1.02532
$640$	1.00000	0.0395285
$641$	−33.9948	−1.34271	−0.671357	−	0.741134i	$-0.734288\pi$
$641$	−33.9948	−1.34271	−0.671357	+	0.741134i	$0.734288\pi$
$642$	54.0161	2.13185
$643$	−43.7587	−1.72567	−0.862837	−	0.505482i	$-0.831315\pi$
$643$	−43.7587	−1.72567	−0.862837	+	0.505482i	$0.831315\pi$
$644$	20.8536	0.821749
$645$	35.6350	1.40313
$646$	−3.75763	−0.147842
$647$	−25.6504	−1.00842	−0.504210	−	0.863581i	$-0.668216\pi$
$647$	−25.6504	−1.00842	−0.504210	+	0.863581i	$0.668216\pi$
$648$	7.62904	0.299697
$649$	−28.0401	−1.10067
$650$	−6.28465	−0.246504
$651$	41.7465	1.63617
$652$	15.7805	0.618011
$653$	−36.6173	−1.43295	−0.716473	−	0.697614i	$-0.754245\pi$
$653$	−36.6173	−1.43295	−0.716473	+	0.697614i	$0.754245\pi$
$654$	−31.8405	−1.24506
$655$	−14.7236	−0.575299
$656$	9.52239	0.371787
$657$	87.9062	3.42955
$658$	−53.3210	−2.07867
$659$	9.39938	0.366148	0.183074	−	0.983099i	$-0.441395\pi$
$659$	9.39938	0.366148	0.183074	+	0.983099i	$0.441395\pi$
$660$	−7.70976	−0.300102
$661$	−26.3758	−1.02590	−0.512950	−	0.858419i	$-0.671447\pi$
$661$	−26.3758	−1.02590	−0.512950	+	0.858419i	$0.671447\pi$
$662$	−5.55711	−0.215983
$663$	17.1670	0.666713
$664$	6.13982	0.238271
$665$	19.6631	0.762501
$666$	−44.0868	−1.70833
$667$	9.21549	0.356825
$668$	9.03064	0.349406
$669$	−51.7446	−2.00056
$670$	−4.99497	−0.192972
$671$	−18.6989	−0.721863
$672$	14.2940	0.551401
$673$	−12.0566	−0.464749	−0.232374	−	0.972626i	$-0.574649\pi$
$673$	−12.0566	−0.464749	−0.232374	+	0.972626i	$0.574649\pi$
$674$	14.5339	0.559823
$675$	−8.46119	−0.325671
$676$	26.4968	1.01911
$677$	18.7980	0.722467	0.361233	−	0.932475i	$-0.382356\pi$
$677$	18.7980	0.722467	0.361233	+	0.932475i	$0.382356\pi$
$678$	−14.4594	−0.555311
$679$	3.65987	0.140453
$680$	0.918471	0.0352218
$681$	−67.4360	−2.58415
$682$	7.57111	0.289913
$683$	−36.2540	−1.38722	−0.693610	−	0.720350i	$-0.743981\pi$
$683$	−36.2540	−1.38722	−0.693610	+	0.720350i	$0.743981\pi$
$684$	−23.9129	−0.914334
$685$	−8.67137	−0.331316
$686$	−43.7352	−1.66982
$687$	−16.5100	−0.629897
$688$	−11.9820	−0.456808
$689$	16.4239	0.625701
$690$	12.9041	0.491250
$691$	33.2962	1.26665	0.633324	−	0.773887i	$-0.281690\pi$
$691$	33.2962	1.26665	0.633324	+	0.773887i	$0.281690\pi$
$692$	7.99723	0.304009
$693$	−72.8249	−2.76639
$694$	23.6795	0.898863
$695$	−15.5993	−0.591714
$696$	6.31668	0.239433
$697$	8.74604	0.331280
$698$	3.53162	0.133674
$699$	−47.4922	−1.79632
$700$	−4.80622	−0.181658
$701$	23.5199	0.888333	0.444167	−	0.895944i	$-0.353500\pi$
$701$	23.5199	0.888333	0.444167	+	0.895944i	$0.353500\pi$
$702$	53.1756	2.00698
$703$	30.8583	1.16384
$704$	2.59234	0.0977025
$705$	−32.9947	−1.24265
$706$	−1.42814	−0.0537488
$707$	−89.0778	−3.35012
$708$	32.1689	1.20898
$709$	0.401918	0.0150943	0.00754717	−	0.999972i	$-0.497598\pi$
$709$	0.401918	0.0150943	0.00754717	+	0.999972i	$0.497598\pi$
$710$	4.43429	0.166416
$711$	−58.7191	−2.20214
$712$	−11.0480	−0.414042
$713$	−12.6720	−0.474571
$714$	13.1286	0.491325
$715$	−16.2919	−0.609284
$716$	12.8073	0.478630
$717$	73.0615	2.72853
$718$	−16.7562	−0.625336
$719$	−3.09013	−0.115242	−0.0576212	−	0.998339i	$-0.518352\pi$
$719$	−3.09013	−0.115242	−0.0576212	+	0.998339i	$0.518352\pi$
$720$	5.84500	0.217830
$721$	−39.8390	−1.48368
$722$	−2.26229	−0.0841936
$723$	−67.5226	−2.51119
$724$	1.92779	0.0716459
$725$	−2.12393	−0.0788807
$726$	12.7283	0.472391
$727$	17.2809	0.640912	0.320456	−	0.947263i	$-0.396164\pi$
$727$	17.2809	0.640912	0.320456	+	0.947263i	$0.396164\pi$
$728$	30.2054	1.11949
$729$	−30.9004	−1.14446
$730$	15.0396	0.556639
$731$	−11.0051	−0.407037
$732$	21.4522	0.792898
$733$	−5.80158	−0.214286	−0.107143	−	0.994244i	$-0.534170\pi$
$733$	−5.80158	−0.214286	−0.107143	+	0.994244i	$0.534170\pi$
$734$	−23.5028	−0.867505
$735$	−47.8814	−1.76613
$736$	−4.33889	−0.159934
$737$	−12.9487	−0.476970
$738$	55.6584	2.04881
$739$	−9.52194	−0.350270	−0.175135	−	0.984544i	$-0.556036\pi$
$739$	−9.52194	−0.350270	−0.175135	+	0.984544i	$0.556036\pi$
$740$	−7.54264	−0.277273
$741$	−76.4677	−2.80911
$742$	12.5603	0.461102
$743$	−9.55265	−0.350453	−0.175226	−	0.984528i	$-0.556066\pi$
$743$	−9.55265	−0.350453	−0.175226	+	0.984528i	$0.556066\pi$
$744$	−8.68593	−0.318442
$745$	−10.7333	−0.393239
$746$	26.6001	0.973900
$747$	35.8873	1.31305
$748$	2.38099	0.0870576
$749$	87.2927	3.18961
$750$	−2.97405	−0.108597
$751$	16.3795	0.597696	0.298848	−	0.954301i	$-0.403398\pi$
$751$	16.3795	0.597696	0.298848	+	0.954301i	$0.403398\pi$
$752$	11.0942	0.404563
$753$	0.237062	0.00863904
$754$	13.3481	0.486111
$755$	16.5185	0.601171
$756$	40.6663	1.47902
$757$	17.0358	0.619176	0.309588	−	0.950871i	$-0.399809\pi$
$757$	17.0358	0.619176	0.309588	+	0.950871i	$0.399809\pi$
$758$	7.12869	0.258926
$759$	33.4518	1.21422
$760$	−4.09117	−0.148403
$761$	48.5904	1.76140	0.880701	−	0.473673i	$-0.157072\pi$
$761$	48.5904	1.76140	0.880701	+	0.473673i	$0.157072\pi$
$762$	−19.6772	−0.712829
$763$	−51.4557	−1.86282
$764$	−6.06367	−0.219376
$765$	5.36846	0.194097
$766$	−13.2508	−0.478772
$767$	67.9780	2.45454
$768$	−2.97405	−0.107317
$769$	−28.4010	−1.02417	−0.512083	−	0.858936i	$-0.671126\pi$
$769$	−28.4010	−1.02417	−0.512083	+	0.858936i	$0.671126\pi$
$770$	−12.4593	−0.449004
$771$	−1.57156	−0.0565982
$772$	6.63846	0.238924
$773$	−25.4916	−0.916868	−0.458434	−	0.888728i	$-0.651589\pi$
$773$	−25.4916	−0.916868	−0.458434	+	0.888728i	$0.651589\pi$
$774$	−70.0345	−2.51734
$775$	2.92057	0.104910
$776$	−0.761486	−0.0273357
$777$	−107.814	−3.86781
$778$	1.05689	0.0378912
$779$	−38.9578	−1.39581
$780$	18.6909	0.669241
$781$	11.4952	0.411330
$782$	−3.98514	−0.142508
$783$	17.9710	0.642230
$784$	16.0997	0.574990
$785$	22.4898	0.802695
$786$	43.7888	1.56190
$787$	−11.5121	−0.410362	−0.205181	−	0.978724i	$-0.565778\pi$
$787$	−11.5121	−0.410362	−0.205181	+	0.978724i	$0.565778\pi$
$788$	6.68908	0.238289
$789$	−56.9017	−2.02575
$790$	−10.0460	−0.357422
$791$	−23.3671	−0.830839
$792$	15.1522	0.538411
$793$	45.3320	1.60979
$794$	13.9564	0.495294
$795$	7.77221	0.275652
$796$	1.32428	0.0469378
$797$	−18.0009	−0.637625	−0.318812	−	0.947818i	$-0.603284\pi$
$797$	−18.0009	−0.637625	−0.318812	+	0.947818i	$0.603284\pi$
$798$	−58.4791	−2.07014
$799$	10.1897	0.360485
$800$	1.00000	0.0353553
$801$	−64.5757	−2.28167
$802$	−18.4617	−0.651906
$803$	38.9876	1.37584
$804$	14.8553	0.523906
$805$	20.8536	0.734994
$806$	−18.3548	−0.646519
$807$	62.1617	2.18820
$808$	18.5339	0.652019
$809$	7.76100	0.272862	0.136431	−	0.990650i	$-0.456437\pi$
$809$	7.76100	0.272862	0.136431	+	0.990650i	$0.456437\pi$
$810$	7.62904	0.268057
$811$	36.5415	1.28314	0.641572	−	0.767063i	$-0.278283\pi$
$811$	36.5415	1.28314	0.641572	+	0.767063i	$0.278283\pi$
$812$	10.2081	0.358233
$813$	−74.2488	−2.60402
$814$	−19.5531	−0.685336
$815$	15.7805	0.552766
$816$	−2.73158	−0.0956245
$817$	49.0203	1.71500
$818$	34.0913	1.19197
$819$	176.551	6.16918
$820$	9.52239	0.332536
$821$	−17.6749	−0.616859	−0.308430	−	0.951247i	$-0.599803\pi$
$821$	−17.6749	−0.616859	−0.308430	+	0.951247i	$0.599803\pi$
$822$	25.7891	0.899499
$823$	13.5668	0.472908	0.236454	−	0.971643i	$-0.424015\pi$
$823$	13.5668	0.472908	0.236454	+	0.971643i	$0.424015\pi$
$824$	8.28906	0.288763
$825$	−7.70976	−0.268419
$826$	51.9865	1.80884
$827$	−43.3958	−1.50902	−0.754511	−	0.656288i	$-0.772126\pi$
$827$	−43.3958	−1.50902	−0.754511	+	0.656288i	$0.772126\pi$
$828$	−25.3608	−0.881349
$829$	14.0842	0.489166	0.244583	−	0.969628i	$-0.421349\pi$
$829$	14.0842	0.489166	0.244583	+	0.969628i	$0.421349\pi$
$830$	6.13982	0.213116
$831$	51.7412	1.79488
$832$	−6.28465	−0.217881
$833$	14.7871	0.512343
$834$	46.3931	1.60646
$835$	9.03064	0.312518
$836$	−10.6057	−0.366806
$837$	−24.7115	−0.854154
$838$	1.33118	0.0459847
$839$	−49.4827	−1.70833	−0.854167	−	0.519999i	$-0.825932\pi$
$839$	−49.4827	−1.70833	−0.854167	+	0.519999i	$0.825932\pi$
$840$	14.2940	0.493188
$841$	−24.4889	−0.844446
$842$	10.1548	0.349956
$843$	−68.9658	−2.37531
$844$	−17.8274	−0.613645
$845$	26.4968	0.911518
$846$	64.8455	2.22943
$847$	20.5695	0.706777
$848$	−2.61334	−0.0897423
$849$	91.1486	3.12821
$850$	0.918471	0.0315033
$851$	32.7267	1.12186
$852$	−13.1878	−0.451807
$853$	36.8028	1.26011	0.630053	−	0.776553i	$-0.283033\pi$
$853$	36.8028	1.26011	0.630053	+	0.776553i	$0.283033\pi$
$854$	34.6679	1.18631
$855$	−23.9129	−0.817805
$856$	−18.1625	−0.620780
$857$	−12.2273	−0.417675	−0.208838	−	0.977950i	$-0.566968\pi$
$857$	−12.2273	−0.417675	−0.208838	+	0.977950i	$0.566968\pi$
$858$	48.4531	1.65416
$859$	−24.7399	−0.844116	−0.422058	−	0.906569i	$-0.638692\pi$
$859$	−24.7399	−0.844116	−0.422058	+	0.906569i	$0.638692\pi$
$860$	−11.9820	−0.408581
$861$	136.113	4.63870
$862$	−24.8500	−0.846394
$863$	42.1605	1.43516	0.717580	−	0.696476i	$-0.245250\pi$
$863$	42.1605	1.43516	0.717580	+	0.696476i	$0.245250\pi$
$864$	−8.46119	−0.287856
$865$	7.99723	0.271914
$866$	7.59337	0.258033
$867$	48.0501	1.63187
$868$	−14.0369	−0.476443
$869$	−26.0427	−0.883440
$870$	6.31668	0.214156
$871$	31.3916	1.06366
$872$	10.7061	0.362553
$873$	−4.45089	−0.150640
$874$	17.7512	0.600442
$875$	−4.80622	−0.162480
$876$	−44.7285	−1.51123
$877$	33.7470	1.13955	0.569777	−	0.821799i	$-0.307030\pi$
$877$	33.7470	1.13955	0.569777	+	0.821799i	$0.307030\pi$
$878$	21.7794	0.735018
$879$	−80.9746	−2.73121
$880$	2.59234	0.0873878
$881$	−50.7878	−1.71108	−0.855542	−	0.517733i	$-0.826776\pi$
$881$	−50.7878	−1.71108	−0.855542	+	0.517733i	$0.826776\pi$
$882$	94.1029	3.16861
$883$	−52.5784	−1.76941	−0.884703	−	0.466156i	$-0.845639\pi$
$883$	−52.5784	−1.76941	−0.884703	+	0.466156i	$0.845639\pi$
$884$	−5.77227	−0.194142
$885$	32.1689	1.08135
$886$	−20.3095	−0.682311
$887$	46.4600	1.55997	0.779987	−	0.625796i	$-0.215226\pi$
$887$	46.4600	1.55997	0.779987	+	0.625796i	$0.215226\pi$
$888$	22.4322	0.752776
$889$	−31.7993	−1.06651
$890$	−11.0480	−0.370330
$891$	19.7771	0.662557
$892$	17.3987	0.582551
$893$	−45.3882	−1.51886
$894$	31.9215	1.06762
$895$	12.8073	0.428100
$896$	−4.80622	−0.160564
$897$	−81.0977	−2.70777
$898$	−15.3541	−0.512373
$899$	−6.20308	−0.206884
$900$	5.84500	0.194833
$901$	−2.40027	−0.0799647
$902$	24.6853	0.821930
$903$	−171.269	−5.69949
$904$	4.86185	0.161703
$905$	1.92779	0.0640820
$906$	−49.1270	−1.63214
$907$	30.1922	1.00251	0.501257	−	0.865298i	$-0.332871\pi$
$907$	30.1922	1.00251	0.501257	+	0.865298i	$0.332871\pi$
$908$	22.6748	0.752489
$909$	108.331	3.59310
$910$	30.2054	1.00130
$911$	−43.0139	−1.42512	−0.712558	−	0.701613i	$-0.752463\pi$
$911$	−43.0139	−1.42512	−0.712558	+	0.701613i	$0.752463\pi$
$912$	12.1674	0.402902
$913$	15.9165	0.526760
$914$	−27.4280	−0.907238
$915$	21.4522	0.709189
$916$	5.55136	0.183422
$917$	70.7649	2.33686
$918$	−7.77136	−0.256493
$919$	6.57745	0.216970	0.108485	−	0.994098i	$-0.465400\pi$
$919$	6.57745	0.216970	0.108485	+	0.994098i	$0.465400\pi$
$920$	−4.33889	−0.143049
$921$	−35.3950	−1.16630
$922$	−28.7604	−0.947172
$923$	−27.8679	−0.917285
$924$	37.0548	1.21901
$925$	−7.54264	−0.248001
$926$	15.7435	0.517363
$927$	48.4496	1.59129
$928$	−2.12393	−0.0697214
$929$	2.10826	0.0691698	0.0345849	−	0.999402i	$-0.488989\pi$
$929$	2.10826	0.0691698	0.0345849	+	0.999402i	$0.488989\pi$
$930$	−8.68593	−0.284823
$931$	−65.8668	−2.15870
$932$	15.9688	0.523077
$933$	−58.0242	−1.89963
$934$	8.00627	0.261973
$935$	2.38099	0.0778667
$936$	−36.7338	−1.20068
$937$	−47.5830	−1.55447	−0.777235	−	0.629210i	$-0.783378\pi$
$937$	−47.5830	−1.55447	−0.777235	+	0.629210i	$0.783378\pi$
$938$	24.0069	0.783853
$939$	15.2750	0.498482
$940$	11.0942	0.361852
$941$	25.3732	0.827144	0.413572	−	0.910471i	$-0.364281\pi$
$941$	25.3732	0.827144	0.413572	+	0.910471i	$0.364281\pi$
$942$	−66.8858	−2.17926
$943$	−41.3166	−1.34545
$944$	−10.8165	−0.352047
$945$	40.6663	1.32288
$946$	−31.0613	−1.00989
$947$	18.8159	0.611435	0.305718	−	0.952122i	$-0.401104\pi$
$947$	18.8159	0.611435	0.305718	+	0.952122i	$0.401104\pi$
$948$	29.8775	0.970375
$949$	−94.5183	−3.06820
$950$	−4.09117	−0.132735
$951$	−58.7264	−1.90433
$952$	−4.41437	−0.143071
$953$	−0.988895	−0.0320335	−0.0160167	−	0.999872i	$-0.505099\pi$
$953$	−0.988895	−0.0320335	−0.0160167	+	0.999872i	$0.505099\pi$
$954$	−15.2750	−0.494545
$955$	−6.06367	−0.196216
$956$	−24.5663	−0.794531
$957$	16.3750	0.529328
$958$	18.8910	0.610340
$959$	41.6765	1.34580
$960$	−2.97405	−0.0959872
$961$	−22.4703	−0.724848
$962$	47.4029	1.52833
$963$	−106.160	−3.42094
$964$	22.7039	0.731243
$965$	6.63846	0.213700
$966$	−62.0199	−1.99546
$967$	5.85910	0.188416	0.0942079	−	0.995553i	$-0.469968\pi$
$967$	5.85910	0.188416	0.0942079	+	0.995553i	$0.469968\pi$
$968$	−4.27977	−0.137557
$969$	11.1754	0.359005
$970$	−0.761486	−0.0244498
$971$	−11.4039	−0.365967	−0.182984	−	0.983116i	$-0.558575\pi$
$971$	−11.4039	−0.365967	−0.182984	+	0.983116i	$0.558575\pi$
$972$	2.69439	0.0864226
$973$	74.9734	2.40354
$974$	13.8868	0.444963
$975$	18.6909	0.598588
$976$	−7.21313	−0.230887
$977$	18.2483	0.583816	0.291908	−	0.956446i	$-0.405710\pi$
$977$	18.2483	0.583816	0.291908	+	0.956446i	$0.405710\pi$
$978$	−46.9320	−1.50072
$979$	−28.6402	−0.915345
$980$	16.0997	0.514287
$981$	62.5770	1.99793
$982$	30.4482	0.971641
$983$	18.5779	0.592542	0.296271	−	0.955104i	$-0.404257\pi$
$983$	18.5779	0.592542	0.296271	+	0.955104i	$0.404257\pi$
$984$	−28.3201	−0.902812
$985$	6.68908	0.213132
$986$	−1.95077	−0.0621251
$987$	158.580	5.04765
$988$	25.7116	0.817995
$989$	51.9884	1.65313
$990$	15.1522	0.481570
$991$	−10.6883	−0.339526	−0.169763	−	0.985485i	$-0.554300\pi$
$991$	−10.6883	−0.339526	−0.169763	+	0.985485i	$0.554300\pi$
$992$	2.92057	0.0927282
$993$	16.5271	0.524473
$994$	−21.3121	−0.675980
$995$	1.32428	0.0419825
$996$	−18.2602	−0.578596
$997$	19.0897	0.604577	0.302288	−	0.953217i	$-0.402249\pi$
$997$	19.0897	0.604577	0.302288	+	0.953217i	$0.402249\pi$
$998$	35.0187	1.10850
$999$	63.8197	2.01917

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.j.1.3	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.j.1.3	✓	33	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.97405 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.97405 q^{6} -4.80622 q^{7} +1.00000 q^{8} +5.84500 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.97405 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.97405 q^{6} -4.80622 q^{7} +1.00000 q^{8} +5.84500 q^{9} +1.00000 q^{10} +2.59234 q^{11} -2.97405 q^{12} -6.28465 q^{13} -4.80622 q^{14} -2.97405 q^{15} +1.00000 q^{16} +0.918471 q^{17} +5.84500 q^{18} -4.09117 q^{19} +1.00000 q^{20} +14.2940 q^{21} +2.59234 q^{22} -4.33889 q^{23} -2.97405 q^{24} +1.00000 q^{25} -6.28465 q^{26} -8.46119 q^{27} -4.80622 q^{28} -2.12393 q^{29} -2.97405 q^{30} +2.92057 q^{31} +1.00000 q^{32} -7.70976 q^{33} +0.918471 q^{34} -4.80622 q^{35} +5.84500 q^{36} -7.54264 q^{37} -4.09117 q^{38} +18.6909 q^{39} +1.00000 q^{40} +9.52239 q^{41} +14.2940 q^{42} -11.9820 q^{43} +2.59234 q^{44} +5.84500 q^{45} -4.33889 q^{46} +11.0942 q^{47} -2.97405 q^{48} +16.0997 q^{49} +1.00000 q^{50} -2.73158 q^{51} -6.28465 q^{52} -2.61334 q^{53} -8.46119 q^{54} +2.59234 q^{55} -4.80622 q^{56} +12.1674 q^{57} -2.12393 q^{58} -10.8165 q^{59} -2.97405 q^{60} -7.21313 q^{61} +2.92057 q^{62} -28.0923 q^{63} +1.00000 q^{64} -6.28465 q^{65} -7.70976 q^{66} -4.99497 q^{67} +0.918471 q^{68} +12.9041 q^{69} -4.80622 q^{70} +4.43429 q^{71} +5.84500 q^{72} +15.0396 q^{73} -7.54264 q^{74} -2.97405 q^{75} -4.09117 q^{76} -12.4593 q^{77} +18.6909 q^{78} -10.0460 q^{79} +1.00000 q^{80} +7.62904 q^{81} +9.52239 q^{82} +6.13982 q^{83} +14.2940 q^{84} +0.918471 q^{85} -11.9820 q^{86} +6.31668 q^{87} +2.59234 q^{88} -11.0480 q^{89} +5.84500 q^{90} +30.2054 q^{91} -4.33889 q^{92} -8.68593 q^{93} +11.0942 q^{94} -4.09117 q^{95} -2.97405 q^{96} -0.761486 q^{97} +16.0997 q^{98} +15.1522 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9}+O(q^{10}) \) 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9	\( 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9} + 33 q^{10} + 12 q^{11} + 6 q^{12} + 20 q^{13} + 4 q^{14} + 6 q^{15} + 33 q^{16} + 33 q^{17} + 49 q^{18} + 17 q^{19} + 33 q^{20} + 26 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 33 q^{25} + 20 q^{26} + 21 q^{27} + 4 q^{28} + 33 q^{29} + 6 q^{30} + 35 q^{31} + 33 q^{32} + 25 q^{33} + 33 q^{34} + 4 q^{35} + 49 q^{36} + 16 q^{37} + 17 q^{38} + 22 q^{39} + 33 q^{40} + 39 q^{41} + 26 q^{42} - 3 q^{43} + 12 q^{44} + 49 q^{45} + 7 q^{46} + 19 q^{47} + 6 q^{48} + 69 q^{49} + 33 q^{50} + 21 q^{51} + 20 q^{52} + 41 q^{53} + 21 q^{54} + 12 q^{55} + 4 q^{56} + 33 q^{58} + 18 q^{59} + 6 q^{60} + 30 q^{61} + 35 q^{62} - 15 q^{63} + 33 q^{64} + 20 q^{65} + 25 q^{66} - 9 q^{67} + 33 q^{68} + 23 q^{69} + 4 q^{70} + 36 q^{71} + 49 q^{72} + 35 q^{73} + 16 q^{74} + 6 q^{75} + 17 q^{76} + 26 q^{77} + 22 q^{78} + 32 q^{79} + 33 q^{80} + 53 q^{81} + 39 q^{82} + 24 q^{83} + 26 q^{84} + 33 q^{85} - 3 q^{86} + 12 q^{87} + 12 q^{88} + 40 q^{89} + 49 q^{90} + 5 q^{91} + 7 q^{92} + 18 q^{93} + 19 q^{94} + 17 q^{95} + 6 q^{96} + 39 q^{97} + 69 q^{98} + 3 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9 + 33 * q^10 + 12 * q^11 + 6 * q^12 + 20 * q^13 + 4 * q^14 + 6 * q^15 + 33 * q^16 + 33 * q^17 + 49 * q^18 + 17 * q^19 + 33 * q^20 + 26 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 33 * q^25 + 20 * q^26 + 21 * q^27 + 4 * q^28 + 33 * q^29 + 6 * q^30 + 35 * q^31 + 33 * q^32 + 25 * q^33 + 33 * q^34 + 4 * q^35 + 49 * q^36 + 16 * q^37 + 17 * q^38 + 22 * q^39 + 33 * q^40 + 39 * q^41 + 26 * q^42 - 3 * q^43 + 12 * q^44 + 49 * q^45 + 7 * q^46 + 19 * q^47 + 6 * q^48 + 69 * q^49 + 33 * q^50 + 21 * q^51 + 20 * q^52 + 41 * q^53 + 21 * q^54 + 12 * q^55 + 4 * q^56 + 33 * q^58 + 18 * q^59 + 6 * q^60 + 30 * q^61 + 35 * q^62 - 15 * q^63 + 33 * q^64 + 20 * q^65 + 25 * q^66 - 9 * q^67 + 33 * q^68 + 23 * q^69 + 4 * q^70 + 36 * q^71 + 49 * q^72 + 35 * q^73 + 16 * q^74 + 6 * q^75 + 17 * q^76 + 26 * q^77 + 22 * q^78 + 32 * q^79 + 33 * q^80 + 53 * q^81 + 39 * q^82 + 24 * q^83 + 26 * q^84 + 33 * q^85 - 3 * q^86 + 12 * q^87 + 12 * q^88 + 40 * q^89 + 49 * q^90 + 5 * q^91 + 7 * q^92 + 18 * q^93 + 19 * q^94 + 17 * q^95 + 6 * q^96 + 39 * q^97 + 69 * q^98 + 3 * q^99

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