LMFDB - Embedded newform 6046.2.a.e.1.17

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:	$1$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.73760 q^{3} +1.00000 q^{4} -0.720137 q^{5} -1.73760 q^{6} -3.09490 q^{7} +1.00000 q^{8} +0.0192639 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.73760 q^{3} +1.00000 q^{4} -0.720137 q^{5} -1.73760 q^{6} -3.09490 q^{7} +1.00000 q^{8} +0.0192639 q^{9} -0.720137 q^{10} +2.74845 q^{11} -1.73760 q^{12} +2.17813 q^{13} -3.09490 q^{14} +1.25131 q^{15} +1.00000 q^{16} +0.644430 q^{17} +0.0192639 q^{18} -5.27810 q^{19} -0.720137 q^{20} +5.37772 q^{21} +2.74845 q^{22} +8.00323 q^{23} -1.73760 q^{24} -4.48140 q^{25} +2.17813 q^{26} +5.17934 q^{27} -3.09490 q^{28} -3.61066 q^{29} +1.25131 q^{30} -2.50706 q^{31} +1.00000 q^{32} -4.77572 q^{33} +0.644430 q^{34} +2.22876 q^{35} +0.0192639 q^{36} +4.18929 q^{37} -5.27810 q^{38} -3.78472 q^{39} -0.720137 q^{40} +5.73358 q^{41} +5.37772 q^{42} +0.454282 q^{43} +2.74845 q^{44} -0.0138726 q^{45} +8.00323 q^{46} -1.31501 q^{47} -1.73760 q^{48} +2.57844 q^{49} -4.48140 q^{50} -1.11976 q^{51} +2.17813 q^{52} -5.39563 q^{53} +5.17934 q^{54} -1.97926 q^{55} -3.09490 q^{56} +9.17125 q^{57} -3.61066 q^{58} +3.31116 q^{59} +1.25131 q^{60} +6.45971 q^{61} -2.50706 q^{62} -0.0596198 q^{63} +1.00000 q^{64} -1.56855 q^{65} -4.77572 q^{66} -14.9554 q^{67} +0.644430 q^{68} -13.9064 q^{69} +2.22876 q^{70} +13.7064 q^{71} +0.0192639 q^{72} +5.78281 q^{73} +4.18929 q^{74} +7.78690 q^{75} -5.27810 q^{76} -8.50620 q^{77} -3.78472 q^{78} -2.08018 q^{79} -0.720137 q^{80} -9.05742 q^{81} +5.73358 q^{82} -14.2001 q^{83} +5.37772 q^{84} -0.464078 q^{85} +0.454282 q^{86} +6.27389 q^{87} +2.74845 q^{88} -2.86584 q^{89} -0.0138726 q^{90} -6.74110 q^{91} +8.00323 q^{92} +4.35628 q^{93} -1.31501 q^{94} +3.80096 q^{95} -1.73760 q^{96} -13.5031 q^{97} +2.57844 q^{98} +0.0529458 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) $ 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9 - 17 * q^10 - 53 * q^11 - 18 * q^12 - 21 * q^13 - 35 * q^14 - 36 * q^15 + 56 * q^16 - 22 * q^17 + 34 * q^18 - 31 * q^19 - 17 * q^20 - 23 * q^21 - 53 * q^22 - 59 * q^23 - 18 * q^24 + 41 * q^25 - 21 * q^26 - 63 * q^27 - 35 * q^28 - 88 * q^29 - 36 * q^30 - 44 * q^31 + 56 * q^32 + 4 * q^33 - 22 * q^34 - 51 * q^35 + 34 * q^36 - 60 * q^37 - 31 * q^38 - 62 * q^39 - 17 * q^40 - 39 * q^41 - 23 * q^42 - 66 * q^43 - 53 * q^44 - 34 * q^45 - 59 * q^46 - 51 * q^47 - 18 * q^48 + 41 * q^49 + 41 * q^50 - 48 * q^51 - 21 * q^52 - 75 * q^53 - 63 * q^54 - 41 * q^55 - 35 * q^56 - 12 * q^57 - 88 * q^58 - 77 * q^59 - 36 * q^60 - 43 * q^61 - 44 * q^62 - 88 * q^63 + 56 * q^64 - 54 * q^65 + 4 * q^66 - 62 * q^67 - 22 * q^68 - 48 * q^69 - 51 * q^70 - 122 * q^71 + 34 * q^72 - 7 * q^73 - 60 * q^74 - 63 * q^75 - 31 * q^76 - 39 * q^77 - 62 * q^78 - 91 * q^79 - 17 * q^80 + 8 * q^81 - 39 * q^82 - 51 * q^83 - 23 * q^84 - 72 * q^85 - 66 * q^86 - 19 * q^87 - 53 * q^88 - 62 * q^89 - 34 * q^90 - 48 * q^91 - 59 * q^92 - 41 * q^93 - 51 * q^94 - 120 * q^95 - 18 * q^96 + 6 * q^97 + 41 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.73760	−1.00321	−0.501603	−	0.865098i	$-0.667256\pi$
$3$	−1.73760	−1.00321	−0.501603	+	0.865098i	$0.667256\pi$
$4$	1.00000	0.500000
$5$	−0.720137	−0.322055	−0.161028	−	0.986950i	$-0.551481\pi$
$5$	−0.720137	−0.322055	−0.161028	+	0.986950i	$0.551481\pi$
$6$	−1.73760	−0.709373
$7$	−3.09490	−1.16976	−0.584882	−	0.811118i	$-0.698859\pi$
$7$	−3.09490	−1.16976	−0.584882	+	0.811118i	$0.698859\pi$
$8$	1.00000	0.353553
$9$	0.0192639	0.00642128
$10$	−0.720137	−0.227727
$11$	2.74845	0.828690	0.414345	−	0.910120i	$-0.364011\pi$
$11$	2.74845	0.828690	0.414345	+	0.910120i	$0.364011\pi$
$12$	−1.73760	−0.501603
$13$	2.17813	0.604104	0.302052	−	0.953291i	$-0.402328\pi$
$13$	2.17813	0.604104	0.302052	+	0.953291i	$0.402328\pi$
$14$	−3.09490	−0.827148
$15$	1.25131	0.323088
$16$	1.00000	0.250000
$17$	0.644430	0.156297	0.0781486	−	0.996942i	$-0.475099\pi$
$17$	0.644430	0.156297	0.0781486	+	0.996942i	$0.475099\pi$
$18$	0.0192639	0.00454053
$19$	−5.27810	−1.21088	−0.605440	−	0.795891i	$-0.707003\pi$
$19$	−5.27810	−1.21088	−0.605440	+	0.795891i	$0.707003\pi$
$20$	−0.720137	−0.161028
$21$	5.37772	1.17351
$22$	2.74845	0.585972
$23$	8.00323	1.66879	0.834395	−	0.551167i	$-0.185817\pi$
$23$	8.00323	1.66879	0.834395	+	0.551167i	$0.185817\pi$
$24$	−1.73760	−0.354687
$25$	−4.48140	−0.896280
$26$	2.17813	0.427166
$27$	5.17934	0.996764
$28$	−3.09490	−0.584882
$29$	−3.61066	−0.670482	−0.335241	−	0.942132i	$-0.608818\pi$
$29$	−3.61066	−0.670482	−0.335241	+	0.942132i	$0.608818\pi$
$30$	1.25131	0.228457
$31$	−2.50706	−0.450281	−0.225141	−	0.974326i	$-0.572284\pi$
$31$	−2.50706	−0.450281	−0.225141	+	0.974326i	$0.572284\pi$
$32$	1.00000	0.176777
$33$	−4.77572	−0.831346
$34$	0.644430	0.110519
$35$	2.22876	0.376729
$36$	0.0192639	0.00321064
$37$	4.18929	0.688716	0.344358	−	0.938839i	$-0.388097\pi$
$37$	4.18929	0.688716	0.344358	+	0.938839i	$0.388097\pi$
$38$	−5.27810	−0.856221
$39$	−3.78472	−0.606041
$40$	−0.720137	−0.113864
$41$	5.73358	0.895434	0.447717	−	0.894175i	$-0.352237\pi$
$41$	5.73358	0.895434	0.447717	+	0.894175i	$0.352237\pi$
$42$	5.37772	0.829800
$43$	0.454282	0.0692773	0.0346387	−	0.999400i	$-0.488972\pi$
$43$	0.454282	0.0692773	0.0346387	+	0.999400i	$0.488972\pi$
$44$	2.74845	0.414345
$45$	−0.0138726	−0.00206801
$46$	8.00323	1.18001
$47$	−1.31501	−0.191814	−0.0959071	−	0.995390i	$-0.530575\pi$
$47$	−1.31501	−0.191814	−0.0959071	+	0.995390i	$0.530575\pi$
$48$	−1.73760	−0.250801
$49$	2.57844	0.368348
$50$	−4.48140	−0.633766
$51$	−1.11976	−0.156798
$52$	2.17813	0.302052
$53$	−5.39563	−0.741147	−0.370573	−	0.928803i	$-0.620839\pi$
$53$	−5.39563	−0.741147	−0.370573	+	0.928803i	$0.620839\pi$
$54$	5.17934	0.704818
$55$	−1.97926	−0.266884
$56$	−3.09490	−0.413574
$57$	9.17125	1.21476
$58$	−3.61066	−0.474103
$59$	3.31116	0.431076	0.215538	−	0.976495i	$-0.430850\pi$
$59$	3.31116	0.431076	0.215538	+	0.976495i	$0.430850\pi$
$60$	1.25131	0.161544
$61$	6.45971	0.827081	0.413540	−	0.910486i	$-0.364292\pi$
$61$	6.45971	0.827081	0.413540	+	0.910486i	$0.364292\pi$
$62$	−2.50706	−0.318397
$63$	−0.0596198	−0.00751139
$64$	1.00000	0.125000
$65$	−1.56855	−0.194555
$66$	−4.77572	−0.587850
$67$	−14.9554	−1.82709	−0.913544	−	0.406739i	$-0.866666\pi$
$67$	−14.9554	−1.82709	−0.913544	+	0.406739i	$0.866666\pi$
$68$	0.644430	0.0781486
$69$	−13.9064	−1.67414
$70$	2.22876	0.266387
$71$	13.7064	1.62664	0.813322	−	0.581813i	$-0.197657\pi$
$71$	13.7064	1.62664	0.813322	+	0.581813i	$0.197657\pi$
$72$	0.0192639	0.00227027
$73$	5.78281	0.676826	0.338413	−	0.940998i	$-0.390110\pi$
$73$	5.78281	0.676826	0.338413	+	0.940998i	$0.390110\pi$
$74$	4.18929	0.486995
$75$	7.78690	0.899153
$76$	−5.27810	−0.605440
$77$	−8.50620	−0.969371
$78$	−3.78472	−0.428535
$79$	−2.08018	−0.234038	−0.117019	−	0.993130i	$-0.537334\pi$
$79$	−2.08018	−0.234038	−0.117019	+	0.993130i	$0.537334\pi$
$80$	−0.720137	−0.0805138
$81$	−9.05742	−1.00638
$82$	5.73358	0.633167
$83$	−14.2001	−1.55867	−0.779333	−	0.626610i	$-0.784442\pi$
$83$	−14.2001	−1.55867	−0.779333	+	0.626610i	$0.784442\pi$
$84$	5.37772	0.586757
$85$	−0.464078	−0.0503363
$86$	0.454282	0.0489865
$87$	6.27389	0.672632
$88$	2.74845	0.292986
$89$	−2.86584	−0.303779	−0.151889	−	0.988397i	$-0.548536\pi$
$89$	−2.86584	−0.303779	−0.151889	+	0.988397i	$0.548536\pi$
$90$	−0.0138726	−0.00146230
$91$	−6.74110	−0.706659
$92$	8.00323	0.834395
$93$	4.35628	0.451725
$94$	−1.31501	−0.135633
$95$	3.80096	0.389970
$96$	−1.73760	−0.177343
$97$	−13.5031	−1.37103	−0.685516	−	0.728058i	$-0.740423\pi$
$97$	−13.5031	−1.37103	−0.685516	+	0.728058i	$0.740423\pi$
$98$	2.57844	0.260461
$99$	0.0529458	0.00532125
$100$	−4.48140	−0.448140
$101$	15.6249	1.55474	0.777369	−	0.629045i	$-0.216554\pi$
$101$	15.6249	1.55474	0.777369	+	0.629045i	$0.216554\pi$
$102$	−1.11976	−0.110873
$103$	8.25776	0.813661	0.406830	−	0.913504i	$-0.366634\pi$
$103$	8.25776	0.813661	0.406830	+	0.913504i	$0.366634\pi$
$104$	2.17813	0.213583
$105$	−3.87269	−0.377936
$106$	−5.39563	−0.524070
$107$	0.170356	0.0164689	0.00823446	−	0.999966i	$-0.497379\pi$
$107$	0.170356	0.0164689	0.00823446	+	0.999966i	$0.497379\pi$
$108$	5.17934	0.498382
$109$	2.45094	0.234758	0.117379	−	0.993087i	$-0.462551\pi$
$109$	2.45094	0.234758	0.117379	+	0.993087i	$0.462551\pi$
$110$	−1.97926	−0.188715
$111$	−7.27933	−0.690923
$112$	−3.09490	−0.292441
$113$	−13.6346	−1.28263	−0.641316	−	0.767277i	$-0.721611\pi$
$113$	−13.6346	−1.28263	−0.641316	+	0.767277i	$0.721611\pi$
$114$	9.17125	0.858966
$115$	−5.76343	−0.537442
$116$	−3.61066	−0.335241
$117$	0.0419591	0.00387912
$118$	3.31116	0.304817
$119$	−1.99445	−0.182831
$120$	1.25131	0.114229
$121$	−3.44601	−0.313273
$122$	6.45971	0.584835
$123$	−9.96268	−0.898304
$124$	−2.50706	−0.225141
$125$	6.82791	0.610707
$126$	−0.0596198	−0.00531135
$127$	−15.4814	−1.37375	−0.686876	−	0.726775i	$-0.741018\pi$
$127$	−15.4814	−1.37375	−0.686876	+	0.726775i	$0.741018\pi$
$128$	1.00000	0.0883883
$129$	−0.789362	−0.0694994
$130$	−1.56855	−0.137571
$131$	9.82176	0.858131	0.429065	−	0.903273i	$-0.358843\pi$
$131$	9.82176	0.858131	0.429065	+	0.903273i	$0.358843\pi$
$132$	−4.77572	−0.415673
$133$	16.3352	1.41644
$134$	−14.9554	−1.29195
$135$	−3.72983	−0.321013
$136$	0.644430	0.0552594
$137$	1.90768	0.162984	0.0814922	−	0.996674i	$-0.474031\pi$
$137$	1.90768	0.162984	0.0814922	+	0.996674i	$0.474031\pi$
$138$	−13.9064	−1.18379
$139$	−11.6557	−0.988625	−0.494313	−	0.869284i	$-0.664580\pi$
$139$	−11.6557	−0.988625	−0.494313	+	0.869284i	$0.664580\pi$
$140$	2.22876	0.188364
$141$	2.28497	0.192429
$142$	13.7064	1.15021
$143$	5.98648	0.500615
$144$	0.0192639	0.00160532
$145$	2.60017	0.215932
$146$	5.78281	0.478589
$147$	−4.48030	−0.369529
$148$	4.18929	0.344358
$149$	−2.01971	−0.165461	−0.0827307	−	0.996572i	$-0.526364\pi$
$149$	−2.01971	−0.165461	−0.0827307	+	0.996572i	$0.526364\pi$
$150$	7.78690	0.635798
$151$	−14.0023	−1.13949	−0.569745	−	0.821821i	$-0.692958\pi$
$151$	−14.0023	−1.13949	−0.569745	+	0.821821i	$0.692958\pi$
$152$	−5.27810	−0.428111
$153$	0.0124142	0.00100363
$154$	−8.50620	−0.685449
$155$	1.80543	0.145015
$156$	−3.78472	−0.303020
$157$	13.6842	1.09212	0.546058	−	0.837747i	$-0.316128\pi$
$157$	13.6842	1.09212	0.546058	+	0.837747i	$0.316128\pi$
$158$	−2.08018	−0.165490
$159$	9.37546	0.743522
$160$	−0.720137	−0.0569319
$161$	−24.7692	−1.95209
$162$	−9.05742	−0.711618
$163$	−24.0889	−1.88679	−0.943394	−	0.331673i	$-0.892387\pi$
$163$	−24.0889	−1.88679	−0.943394	+	0.331673i	$0.892387\pi$
$164$	5.73358	0.447717
$165$	3.43917	0.267739
$166$	−14.2001	−1.10214
$167$	−9.55779	−0.739604	−0.369802	−	0.929111i	$-0.620574\pi$
$167$	−9.55779	−0.739604	−0.369802	+	0.929111i	$0.620574\pi$
$168$	5.37772	0.414900
$169$	−8.25576	−0.635058
$170$	−0.464078	−0.0355931
$171$	−0.101677	−0.00777540
$172$	0.454282	0.0346387
$173$	−13.3876	−1.01784	−0.508919	−	0.860814i	$-0.669955\pi$
$173$	−13.3876	−1.01784	−0.508919	+	0.860814i	$0.669955\pi$
$174$	6.27389	0.475622
$175$	13.8695	1.04844
$176$	2.74845	0.207172
$177$	−5.75348	−0.432458
$178$	−2.86584	−0.214804
$179$	−16.6942	−1.24778	−0.623892	−	0.781510i	$-0.714450\pi$
$179$	−16.6942	−1.24778	−0.623892	+	0.781510i	$0.714450\pi$
$180$	−0.0138726	−0.00103400
$181$	−8.71262	−0.647604	−0.323802	−	0.946125i	$-0.604961\pi$
$181$	−8.71262	−0.647604	−0.323802	+	0.946125i	$0.604961\pi$
$182$	−6.74110	−0.499684
$183$	−11.2244	−0.829732
$184$	8.00323	0.590006
$185$	−3.01687	−0.221804
$186$	4.35628	0.319418
$187$	1.77118	0.129522
$188$	−1.31501	−0.0959071
$189$	−16.0296	−1.16598
$190$	3.80096	0.275751
$191$	−0.558163	−0.0403872	−0.0201936	−	0.999796i	$-0.506428\pi$
$191$	−0.558163	−0.0403872	−0.0201936	+	0.999796i	$0.506428\pi$
$192$	−1.73760	−0.125401
$193$	8.68010	0.624807	0.312404	−	0.949949i	$-0.398866\pi$
$193$	8.68010	0.624807	0.312404	+	0.949949i	$0.398866\pi$
$194$	−13.5031	−0.969466
$195$	2.72552	0.195179
$196$	2.57844	0.184174
$197$	13.7554	0.980033	0.490017	−	0.871713i	$-0.336991\pi$
$197$	13.7554	0.980033	0.490017	+	0.871713i	$0.336991\pi$
$198$	0.0529458	0.00376269
$199$	−25.4245	−1.80230	−0.901148	−	0.433511i	$-0.857274\pi$
$199$	−25.4245	−1.80230	−0.901148	+	0.433511i	$0.857274\pi$
$200$	−4.48140	−0.316883
$201$	25.9865	1.83295
$202$	15.6249	1.09937
$203$	11.1746	0.784306
$204$	−1.11976	−0.0783991
$205$	−4.12896	−0.288379
$206$	8.25776	0.575345
$207$	0.154173	0.0107158
$208$	2.17813	0.151026
$209$	−14.5066	−1.00344
$210$	−3.87269	−0.267241
$211$	−23.7611	−1.63578	−0.817890	−	0.575375i	$-0.804856\pi$
$211$	−23.7611	−1.63578	−0.817890	+	0.575375i	$0.804856\pi$
$212$	−5.39563	−0.370573
$213$	−23.8162	−1.63186
$214$	0.170356	0.0116453
$215$	−0.327145	−0.0223111
$216$	5.17934	0.352409
$217$	7.75911	0.526723
$218$	2.45094	0.165999
$219$	−10.0482	−0.678996
$220$	−1.97926	−0.133442
$221$	1.40365	0.0944197
$222$	−7.27933	−0.488556
$223$	−2.67801	−0.179333	−0.0896664	−	0.995972i	$-0.528580\pi$
$223$	−2.67801	−0.179333	−0.0896664	+	0.995972i	$0.528580\pi$
$224$	−3.09490	−0.206787
$225$	−0.0863291	−0.00575527
$226$	−13.6346	−0.906958
$227$	23.4729	1.55795	0.778976	−	0.627053i	$-0.215739\pi$
$227$	23.4729	1.55795	0.778976	+	0.627053i	$0.215739\pi$
$228$	9.17125	0.607381
$229$	−28.1362	−1.85929	−0.929646	−	0.368455i	$-0.879887\pi$
$229$	−28.1362	−1.85929	−0.929646	+	0.368455i	$0.879887\pi$
$230$	−5.76343	−0.380029
$231$	14.7804	0.972479
$232$	−3.61066	−0.237051
$233$	−21.3509	−1.39874	−0.699370	−	0.714759i	$-0.746536\pi$
$233$	−21.3509	−1.39874	−0.699370	+	0.714759i	$0.746536\pi$
$234$	0.0419591	0.00274295
$235$	0.946989	0.0617747
$236$	3.31116	0.215538
$237$	3.61452	0.234789
$238$	−1.99445	−0.129281
$239$	−12.4516	−0.805426	−0.402713	−	0.915326i	$-0.631933\pi$
$239$	−12.4516	−0.805426	−0.402713	+	0.915326i	$0.631933\pi$
$240$	1.25131	0.0807719
$241$	−9.49982	−0.611937	−0.305969	−	0.952042i	$-0.598980\pi$
$241$	−9.49982	−0.611937	−0.305969	+	0.952042i	$0.598980\pi$
$242$	−3.44601	−0.221518
$243$	0.200193	0.0128424
$244$	6.45971	0.413540
$245$	−1.85683	−0.118628
$246$	−9.96268	−0.635197
$247$	−11.4964	−0.731498
$248$	−2.50706	−0.159198
$249$	24.6742	1.56366
$250$	6.82791	0.431835
$251$	9.28379	0.585987	0.292994	−	0.956114i	$-0.405349\pi$
$251$	9.28379	0.585987	0.292994	+	0.956114i	$0.405349\pi$
$252$	−0.0596198	−0.00375569
$253$	21.9965	1.38291
$254$	−15.4814	−0.971389
$255$	0.806383	0.0504977
$256$	1.00000	0.0625000
$257$	23.2511	1.45036	0.725181	−	0.688558i	$-0.241756\pi$
$257$	23.2511	1.45036	0.725181	+	0.688558i	$0.241756\pi$
$258$	−0.789362	−0.0491435
$259$	−12.9655	−0.805635
$260$	−1.56855	−0.0972774
$261$	−0.0695552	−0.00430536
$262$	9.82176	0.606790
$263$	12.3281	0.760183	0.380092	−	0.924949i	$-0.375892\pi$
$263$	12.3281	0.760183	0.380092	+	0.924949i	$0.375892\pi$
$264$	−4.77572	−0.293925
$265$	3.88559	0.238690
$266$	16.3352	1.00158
$267$	4.97970	0.304753
$268$	−14.9554	−0.913544
$269$	28.7038	1.75010	0.875052	−	0.484028i	$-0.160827\pi$
$269$	28.7038	1.75010	0.875052	+	0.484028i	$0.160827\pi$
$270$	−3.72983	−0.226990
$271$	−15.3986	−0.935401	−0.467700	−	0.883887i	$-0.654917\pi$
$271$	−15.3986	−0.935401	−0.467700	+	0.883887i	$0.654917\pi$
$272$	0.644430	0.0390743
$273$	11.7134	0.708924
$274$	1.90768	0.115247
$275$	−12.3169	−0.742738
$276$	−13.9064	−0.837069
$277$	−1.30832	−0.0786091	−0.0393045	−	0.999227i	$-0.512514\pi$
$277$	−1.30832	−0.0786091	−0.0393045	+	0.999227i	$0.512514\pi$
$278$	−11.6557	−0.699064
$279$	−0.0482956	−0.00289138
$280$	2.22876	0.133194
$281$	24.3435	1.45221	0.726104	−	0.687585i	$-0.241329\pi$
$281$	24.3435	1.45221	0.726104	+	0.687585i	$0.241329\pi$
$282$	2.28497	0.136068
$283$	−6.54757	−0.389213	−0.194606	−	0.980881i	$-0.562343\pi$
$283$	−6.54757	−0.389213	−0.194606	+	0.980881i	$0.562343\pi$
$284$	13.7064	0.813322
$285$	−6.60456	−0.391220
$286$	5.98648	0.353988
$287$	−17.7449	−1.04745
$288$	0.0192639	0.00113513
$289$	−16.5847	−0.975571
$290$	2.60017	0.152687
$291$	23.4630	1.37543
$292$	5.78281	0.338413
$293$	−31.9374	−1.86580	−0.932901	−	0.360132i	$-0.882732\pi$
$293$	−31.9374	−1.86580	−0.932901	+	0.360132i	$0.882732\pi$
$294$	−4.48030	−0.261296
$295$	−2.38449	−0.138830
$296$	4.18929	0.243498
$297$	14.2352	0.826008
$298$	−2.01971	−0.116999
$299$	17.4321	1.00812
$300$	7.78690	0.449577
$301$	−1.40596	−0.0810381
$302$	−14.0023	−0.805742
$303$	−27.1499	−1.55972
$304$	−5.27810	−0.302720
$305$	−4.65188	−0.266366
$306$	0.0124142	0.000709672 0
$307$	−20.0400	−1.14374	−0.571872	−	0.820343i	$-0.693783\pi$
$307$	−20.0400	−1.14374	−0.571872	+	0.820343i	$0.693783\pi$
$308$	−8.50620	−0.484686
$309$	−14.3487	−0.816269
$310$	1.80543	0.102541
$311$	19.8933	1.12805	0.564023	−	0.825759i	$-0.309253\pi$
$311$	19.8933	1.12805	0.564023	+	0.825759i	$0.309253\pi$
$312$	−3.78472	−0.214268
$313$	−17.4305	−0.985232	−0.492616	−	0.870247i	$-0.663959\pi$
$313$	−17.4305	−0.985232	−0.492616	+	0.870247i	$0.663959\pi$
$314$	13.6842	0.772243
$315$	0.0429344	0.00241908
$316$	−2.08018	−0.117019
$317$	−0.791420	−0.0444506	−0.0222253	−	0.999753i	$-0.507075\pi$
$317$	−0.791420	−0.0444506	−0.0222253	+	0.999753i	$0.507075\pi$
$318$	9.37546	0.525750
$319$	−9.92372	−0.555622
$320$	−0.720137	−0.0402569
$321$	−0.296011	−0.0165217
$322$	−24.7692	−1.38034
$323$	−3.40137	−0.189257
$324$	−9.05742	−0.503190
$325$	−9.76107	−0.541447
$326$	−24.0889	−1.33416
$327$	−4.25877	−0.235510
$328$	5.73358	0.316584
$329$	4.06984	0.224377
$330$	3.43917	0.189320
$331$	−5.47143	−0.300737	−0.150369	−	0.988630i	$-0.548046\pi$
$331$	−5.47143	−0.300737	−0.150369	+	0.988630i	$0.548046\pi$
$332$	−14.2001	−0.779333
$333$	0.0807019	0.00442244
$334$	−9.55779	−0.522979
$335$	10.7699	0.588423
$336$	5.37772	0.293378
$337$	18.7068	1.01903	0.509513	−	0.860463i	$-0.329826\pi$
$337$	18.7068	1.01903	0.509513	+	0.860463i	$0.329826\pi$
$338$	−8.25576	−0.449054
$339$	23.6915	1.28674
$340$	−0.464078	−0.0251682
$341$	−6.89054	−0.373143
$342$	−0.101677	−0.00549804
$343$	13.6843	0.738884
$344$	0.454282	0.0244932
$345$	10.0145	0.539165
$346$	−13.3876	−0.719720
$347$	−8.85984	−0.475621	−0.237810	−	0.971312i	$-0.576430\pi$
$347$	−8.85984	−0.475621	−0.237810	+	0.971312i	$0.576430\pi$
$348$	6.27389	0.336316
$349$	−0.119183	−0.00637974	−0.00318987	−	0.999995i	$-0.501015\pi$
$349$	−0.119183	−0.00637974	−0.00318987	+	0.999995i	$0.501015\pi$
$350$	13.8695	0.741357
$351$	11.2813	0.602149
$352$	2.74845	0.146493
$353$	4.24152	0.225753	0.112877	−	0.993609i	$-0.463994\pi$
$353$	4.24152	0.225753	0.112877	+	0.993609i	$0.463994\pi$
$354$	−5.75348	−0.305794
$355$	−9.87046	−0.523869
$356$	−2.86584	−0.151889
$357$	3.46556	0.183417
$358$	−16.6942	−0.882317
$359$	−12.8780	−0.679676	−0.339838	−	0.940484i	$-0.610372\pi$
$359$	−12.8780	−0.679676	−0.339838	+	0.940484i	$0.610372\pi$
$360$	−0.0138726	−0.000731151 0
$361$	8.85838	0.466230
$362$	−8.71262	−0.457925
$363$	5.98779	0.314278
$364$	−6.74110	−0.353330
$365$	−4.16442	−0.217975
$366$	−11.2244	−0.586709
$367$	32.5367	1.69840	0.849200	−	0.528072i	$-0.177085\pi$
$367$	32.5367	1.69840	0.849200	+	0.528072i	$0.177085\pi$
$368$	8.00323	0.417197
$369$	0.110451	0.00574984
$370$	−3.01687	−0.156839
$371$	16.6990	0.866967
$372$	4.35628	0.225862
$373$	13.2899	0.688126	0.344063	−	0.938947i	$-0.388197\pi$
$373$	13.2899	0.688126	0.344063	+	0.938947i	$0.388197\pi$
$374$	1.77118	0.0915858
$375$	−11.8642	−0.612665
$376$	−1.31501	−0.0678165
$377$	−7.86448	−0.405041
$378$	−16.0296	−0.824471
$379$	11.4635	0.588839	0.294419	−	0.955676i	$-0.404874\pi$
$379$	11.4635	0.588839	0.294419	+	0.955676i	$0.404874\pi$
$380$	3.80096	0.194985
$381$	26.9005	1.37816
$382$	−0.558163	−0.0285581
$383$	−33.8098	−1.72760	−0.863800	−	0.503834i	$-0.831922\pi$
$383$	−33.8098	−1.72760	−0.863800	+	0.503834i	$0.831922\pi$
$384$	−1.73760	−0.0886717
$385$	6.12563	0.312191
$386$	8.68010	0.441805
$387$	0.00875122	0.000444849 0
$388$	−13.5031	−0.685516
$389$	−33.3950	−1.69320	−0.846598	−	0.532233i	$-0.821353\pi$
$389$	−33.3950	−1.69320	−0.846598	+	0.532233i	$0.821353\pi$
$390$	2.72552	0.138012
$391$	5.15752	0.260827
$392$	2.57844	0.130231
$393$	−17.0663	−0.860882
$394$	13.7554	0.692988
$395$	1.49801	0.0753733
$396$	0.0529458	0.00266063
$397$	3.61471	0.181417	0.0907084	−	0.995877i	$-0.471087\pi$
$397$	3.61471	0.181417	0.0907084	+	0.995877i	$0.471087\pi$
$398$	−25.4245	−1.27442
$399$	−28.3841	−1.42098
$400$	−4.48140	−0.224070
$401$	10.4578	0.522237	0.261118	−	0.965307i	$-0.415909\pi$
$401$	10.4578	0.522237	0.261118	+	0.965307i	$0.415909\pi$
$402$	25.9865	1.29609
$403$	−5.46070	−0.272017
$404$	15.6249	0.777369
$405$	6.52259	0.324110
$406$	11.1746	0.554588
$407$	11.5141	0.570731
$408$	−1.11976	−0.0554365
$409$	11.3062	0.559056	0.279528	−	0.960138i	$-0.409822\pi$
$409$	11.3062	0.559056	0.279528	+	0.960138i	$0.409822\pi$
$410$	−4.12896	−0.203915
$411$	−3.31480	−0.163507
$412$	8.25776	0.406830
$413$	−10.2477	−0.504257
$414$	0.154173	0.00757719
$415$	10.2260	0.501977
$416$	2.17813	0.106792
$417$	20.2530	0.991794
$418$	−14.5066	−0.709542
$419$	−26.1405	−1.27705	−0.638524	−	0.769602i	$-0.720455\pi$
$419$	−26.1405	−1.27705	−0.638524	+	0.769602i	$0.720455\pi$
$420$	−3.87269	−0.188968
$421$	3.26146	0.158954	0.0794770	−	0.996837i	$-0.474675\pi$
$421$	3.26146	0.158954	0.0794770	+	0.996837i	$0.474675\pi$
$422$	−23.7611	−1.15667
$423$	−0.0253322	−0.00123169
$424$	−5.39563	−0.262035
$425$	−2.88795	−0.140086
$426$	−23.8162	−1.15390
$427$	−19.9922	−0.967490
$428$	0.170356	0.00823446
$429$	−10.4021	−0.502220
$430$	−0.327145	−0.0157763
$431$	−20.5167	−0.988254	−0.494127	−	0.869390i	$-0.664512\pi$
$431$	−20.5167	−0.988254	−0.494127	+	0.869390i	$0.664512\pi$
$432$	5.17934	0.249191
$433$	16.1248	0.774906	0.387453	−	0.921889i	$-0.373355\pi$
$433$	16.1248	0.774906	0.387453	+	0.921889i	$0.373355\pi$
$434$	7.75911	0.372449
$435$	−4.51806	−0.216625
$436$	2.45094	0.117379
$437$	−42.2419	−2.02070
$438$	−10.0482	−0.480123
$439$	−1.68662	−0.0804981	−0.0402491	−	0.999190i	$-0.512815\pi$
$439$	−1.68662	−0.0804981	−0.0402491	+	0.999190i	$0.512815\pi$
$440$	−1.97926	−0.0943577
$441$	0.0496706	0.00236527
$442$	1.40365	0.0667648
$443$	−19.6445	−0.933340	−0.466670	−	0.884431i	$-0.654546\pi$
$443$	−19.6445	−0.933340	−0.466670	+	0.884431i	$0.654546\pi$
$444$	−7.27933	−0.345462
$445$	2.06380	0.0978336
$446$	−2.67801	−0.126807
$447$	3.50946	0.165992
$448$	−3.09490	−0.146221
$449$	30.3207	1.43092	0.715461	−	0.698653i	$-0.246217\pi$
$449$	30.3207	1.43092	0.715461	+	0.698653i	$0.246217\pi$
$450$	−0.0863291	−0.00406959
$451$	15.7585	0.742037
$452$	−13.6346	−0.641316
$453$	24.3304	1.14314
$454$	23.4729	1.10164
$455$	4.85452	0.227583
$456$	9.17125	0.429483
$457$	−1.00271	−0.0469046	−0.0234523	−	0.999725i	$-0.507466\pi$
$457$	−1.00271	−0.0469046	−0.0234523	+	0.999725i	$0.507466\pi$
$458$	−28.1362	−1.31472
$459$	3.33772	0.155791
$460$	−5.76343	−0.268721
$461$	38.8841	1.81101	0.905507	−	0.424331i	$-0.139491\pi$
$461$	38.8841	1.81101	0.905507	+	0.424331i	$0.139491\pi$
$462$	14.7804	0.687646
$463$	−30.2319	−1.40499	−0.702497	−	0.711686i	$-0.747932\pi$
$463$	−30.2319	−1.40499	−0.702497	+	0.711686i	$0.747932\pi$
$464$	−3.61066	−0.167621
$465$	−3.13712	−0.145480
$466$	−21.3509	−0.989059
$467$	37.4755	1.73416	0.867079	−	0.498170i	$-0.165994\pi$
$467$	37.4755	1.73416	0.867079	+	0.498170i	$0.165994\pi$
$468$	0.0419591	0.00193956
$469$	46.2854	2.13726
$470$	0.946989	0.0436813
$471$	−23.7777	−1.09562
$472$	3.31116	0.152408
$473$	1.24857	0.0574094
$474$	3.61452	0.166021
$475$	23.6533	1.08529
$476$	−1.99445	−0.0914154
$477$	−0.103941	−0.00475911
$478$	−12.4516	−0.569522
$479$	−14.8811	−0.679934	−0.339967	−	0.940437i	$-0.610416\pi$
$479$	−14.8811	−0.679934	−0.339967	+	0.940437i	$0.610416\pi$
$480$	1.25131	0.0571143
$481$	9.12482	0.416056
$482$	−9.49982	−0.432705
$483$	43.0391	1.95835
$484$	−3.44601	−0.156637
$485$	9.72409	0.441548
$486$	0.200193	0.00908093
$487$	−3.60515	−0.163365	−0.0816826	−	0.996658i	$-0.526029\pi$
$487$	−3.60515	−0.163365	−0.0816826	+	0.996658i	$0.526029\pi$
$488$	6.45971	0.292417
$489$	41.8570	1.89284
$490$	−1.85683	−0.0838829
$491$	−38.2223	−1.72495	−0.862474	−	0.506101i	$-0.831086\pi$
$491$	−38.2223	−1.72495	−0.862474	+	0.506101i	$0.831086\pi$
$492$	−9.96268	−0.449152
$493$	−2.32682	−0.104794
$494$	−11.4964	−0.517247
$495$	−0.0381282	−0.00171374
$496$	−2.50706	−0.112570
$497$	−42.4199	−1.90279
$498$	24.6742	1.10568
$499$	−32.2835	−1.44521	−0.722605	−	0.691261i	$-0.757055\pi$
$499$	−32.2835	−1.44521	−0.722605	+	0.691261i	$0.757055\pi$
$500$	6.82791	0.305353
$501$	16.6076	0.741975
$502$	9.28379	0.414356
$503$	33.6392	1.49990	0.749950	−	0.661495i	$-0.230078\pi$
$503$	33.6392	1.49990	0.749950	+	0.661495i	$0.230078\pi$
$504$	−0.0596198	−0.00265568
$505$	−11.2521	−0.500712
$506$	21.9965	0.977864
$507$	14.3452	0.637094
$508$	−15.4814	−0.686876
$509$	23.7856	1.05428	0.527140	−	0.849778i	$-0.323264\pi$
$509$	23.7856	1.05428	0.527140	+	0.849778i	$0.323264\pi$
$510$	0.806383	0.0357072
$511$	−17.8972	−0.791727
$512$	1.00000	0.0441942
$513$	−27.3371	−1.20696
$514$	23.2511	1.02556
$515$	−5.94672	−0.262044
$516$	−0.789362	−0.0347497
$517$	−3.61425	−0.158954
$518$	−12.9655	−0.569670
$519$	23.2623	1.02110
$520$	−1.56855	−0.0687855
$521$	−27.8252	−1.21904	−0.609521	−	0.792770i	$-0.708638\pi$
$521$	−27.8252	−1.21904	−0.609521	+	0.792770i	$0.708638\pi$
$522$	−0.0695552	−0.00304435
$523$	22.8953	1.00114	0.500571	−	0.865695i	$-0.333123\pi$
$523$	22.8953	1.00114	0.500571	+	0.865695i	$0.333123\pi$
$524$	9.82176	0.429065
$525$	−24.0997	−1.05180
$526$	12.3281	0.537531
$527$	−1.61562	−0.0703777
$528$	−4.77572	−0.207837
$529$	41.0517	1.78486
$530$	3.88559	0.168779
$531$	0.0637856	0.00276806
$532$	16.3352	0.708222
$533$	12.4885	0.540935
$534$	4.97970	0.215493
$535$	−0.122680	−0.00530390
$536$	−14.9554	−0.645973
$537$	29.0079	1.25178
$538$	28.7038	1.23751
$539$	7.08671	0.305246
$540$	−3.72983	−0.160506
$541$	27.4657	1.18084	0.590422	−	0.807095i	$-0.298961\pi$
$541$	27.4657	1.18084	0.590422	+	0.807095i	$0.298961\pi$
$542$	−15.3986	−0.661428
$543$	15.1391	0.649680
$544$	0.644430	0.0276297
$545$	−1.76502	−0.0756050
$546$	11.7134	0.501285
$547$	−31.1085	−1.33010	−0.665052	−	0.746797i	$-0.731591\pi$
$547$	−31.1085	−1.33010	−0.665052	+	0.746797i	$0.731591\pi$
$548$	1.90768	0.0814922
$549$	0.124439	0.00531092
$550$	−12.3169	−0.525195
$551$	19.0574	0.811874
$552$	−13.9064	−0.591897
$553$	6.43796	0.273770
$554$	−1.30832	−0.0555850
$555$	5.24212	0.222515
$556$	−11.6557	−0.494313
$557$	35.1316	1.48857	0.744287	−	0.667860i	$-0.232790\pi$
$557$	35.1316	1.48857	0.744287	+	0.667860i	$0.232790\pi$
$558$	−0.0482956	−0.00204452
$559$	0.989484	0.0418507
$560$	2.22876	0.0941821
$561$	−3.07761	−0.129937
$562$	24.3435	1.02687
$563$	−25.3956	−1.07030	−0.535149	−	0.844758i	$-0.679744\pi$
$563$	−25.3956	−1.07030	−0.535149	+	0.844758i	$0.679744\pi$
$564$	2.28497	0.0962145
$565$	9.81876	0.413078
$566$	−6.54757	−0.275215
$567$	28.0319	1.17723
$568$	13.7064	0.575106
$569$	−4.88780	−0.204907	−0.102454	−	0.994738i	$-0.532669\pi$
$569$	−4.88780	−0.204907	−0.102454	+	0.994738i	$0.532669\pi$
$570$	−6.60456	−0.276634
$571$	−7.90440	−0.330789	−0.165395	−	0.986227i	$-0.552890\pi$
$571$	−7.90440	−0.330789	−0.165395	+	0.986227i	$0.552890\pi$
$572$	5.98648	0.250307
$573$	0.969865	0.0405167
$574$	−17.7449	−0.740657
$575$	−35.8657	−1.49570
$576$	0.0192639	0.000802660 0
$577$	−42.4161	−1.76581	−0.882903	−	0.469555i	$-0.844414\pi$
$577$	−42.4161	−1.76581	−0.882903	+	0.469555i	$0.844414\pi$
$578$	−16.5847	−0.689833
$579$	−15.0826	−0.626810
$580$	2.60017	0.107966
$581$	43.9480	1.82327
$582$	23.4630	0.972574
$583$	−14.8296	−0.614181
$584$	5.78281	0.239294
$585$	−0.0302163	−0.00124929
$586$	−31.9374	−1.31932
$587$	11.8974	0.491057	0.245528	−	0.969389i	$-0.421039\pi$
$587$	11.8974	0.491057	0.245528	+	0.969389i	$0.421039\pi$
$588$	−4.48030	−0.184764
$589$	13.2325	0.545237
$590$	−2.38449	−0.0981678
$591$	−23.9015	−0.983175
$592$	4.18929	0.172179
$593$	39.3368	1.61537	0.807685	−	0.589614i	$-0.200720\pi$
$593$	39.3368	1.61537	0.807685	+	0.589614i	$0.200720\pi$
$594$	14.2352	0.584076
$595$	1.43628	0.0588816
$596$	−2.01971	−0.0827307
$597$	44.1777	1.80807
$598$	17.4321	0.712850
$599$	−30.5240	−1.24718	−0.623588	−	0.781753i	$-0.714326\pi$
$599$	−30.5240	−1.24718	−0.623588	+	0.781753i	$0.714326\pi$
$600$	7.78690	0.317899
$601$	33.9849	1.38627	0.693136	−	0.720807i	$-0.256229\pi$
$601$	33.9849	1.38627	0.693136	+	0.720807i	$0.256229\pi$
$602$	−1.40596	−0.0573026
$603$	−0.288098	−0.0117323
$604$	−14.0023	−0.569745
$605$	2.48160	0.100891
$606$	−27.1499	−1.10289
$607$	−41.4776	−1.68352	−0.841762	−	0.539848i	$-0.818482\pi$
$607$	−41.4776	−1.68352	−0.841762	+	0.539848i	$0.818482\pi$
$608$	−5.27810	−0.214055
$609$	−19.4171	−0.786820
$610$	−4.65188	−0.188349
$611$	−2.86426	−0.115876
$612$	0.0124142	0.000501814 0
$613$	15.3183	0.618699	0.309349	−	0.950948i	$-0.399889\pi$
$613$	15.3183	0.618699	0.309349	+	0.950948i	$0.399889\pi$
$614$	−20.0400	−0.808749
$615$	7.17450	0.289304
$616$	−8.50620	−0.342725
$617$	40.0101	1.61075	0.805374	−	0.592767i	$-0.201965\pi$
$617$	40.0101	1.61075	0.805374	+	0.592767i	$0.201965\pi$
$618$	−14.3487	−0.577189
$619$	17.7705	0.714256	0.357128	−	0.934055i	$-0.383756\pi$
$619$	17.7705	0.714256	0.357128	+	0.934055i	$0.383756\pi$
$620$	1.80543	0.0725077
$621$	41.4514	1.66339
$622$	19.8933	0.797649
$623$	8.86952	0.355350
$624$	−3.78472	−0.151510
$625$	17.4900	0.699599
$626$	−17.4305	−0.696664
$627$	25.2067	1.00666
$628$	13.6842	0.546058
$629$	2.69970	0.107644
$630$	0.0429344	0.00171055
$631$	31.4827	1.25331	0.626653	−	0.779298i	$-0.284424\pi$
$631$	31.4827	1.25331	0.626653	+	0.779298i	$0.284424\pi$
$632$	−2.08018	−0.0827451
$633$	41.2873	1.64102
$634$	−0.791420	−0.0314313
$635$	11.1487	0.442424
$636$	9.37546	0.371761
$637$	5.61616	0.222521
$638$	−9.92372	−0.392884
$639$	0.264037	0.0104451
$640$	−0.720137	−0.0284659
$641$	−13.8901	−0.548627	−0.274313	−	0.961640i	$-0.588451\pi$
$641$	−13.8901	−0.548627	−0.274313	+	0.961640i	$0.588451\pi$
$642$	−0.296011	−0.0116826
$643$	22.3728	0.882299	0.441149	−	0.897434i	$-0.354571\pi$
$643$	22.3728	0.882299	0.441149	+	0.897434i	$0.354571\pi$
$644$	−24.7692	−0.976045
$645$	0.568449	0.0223826
$646$	−3.40137	−0.133825
$647$	−20.6928	−0.813519	−0.406759	−	0.913535i	$-0.633341\pi$
$647$	−20.6928	−0.813519	−0.406759	+	0.913535i	$0.633341\pi$
$648$	−9.05742	−0.355809
$649$	9.10056	0.357228
$650$	−9.76107	−0.382861
$651$	−13.4823	−0.528411
$652$	−24.0889	−0.943394
$653$	−37.8981	−1.48307	−0.741534	−	0.670915i	$-0.765902\pi$
$653$	−37.8981	−1.48307	−0.741534	+	0.670915i	$0.765902\pi$
$654$	−4.25877	−0.166531
$655$	−7.07301	−0.276365
$656$	5.73358	0.223858
$657$	0.111399	0.00434609
$658$	4.06984	0.158659
$659$	−4.50852	−0.175627	−0.0878135	−	0.996137i	$-0.527988\pi$
$659$	−4.50852	−0.175627	−0.0878135	+	0.996137i	$0.527988\pi$
$660$	3.43917	0.133870
$661$	−15.3699	−0.597820	−0.298910	−	0.954281i	$-0.596623\pi$
$661$	−15.3699	−0.597820	−0.298910	+	0.954281i	$0.596623\pi$
$662$	−5.47143	−0.212653
$663$	−2.43899	−0.0947224
$664$	−14.2001	−0.551072
$665$	−11.7636	−0.456173
$666$	0.0807019	0.00312714
$667$	−28.8969	−1.11889
$668$	−9.55779	−0.369802
$669$	4.65332	0.179908
$670$	10.7699	0.416078
$671$	17.7542	0.685393
$672$	5.37772	0.207450
$673$	−50.2775	−1.93805	−0.969027	−	0.246956i	$-0.920570\pi$
$673$	−50.2775	−1.93805	−0.969027	+	0.246956i	$0.920570\pi$
$674$	18.7068	0.720560
$675$	−23.2107	−0.893380
$676$	−8.25576	−0.317529
$677$	−11.2912	−0.433955	−0.216978	−	0.976177i	$-0.569620\pi$
$677$	−11.2912	−0.433955	−0.216978	+	0.976177i	$0.569620\pi$
$678$	23.6915	0.909865
$679$	41.7908	1.60378
$680$	−0.464078	−0.0177966
$681$	−40.7866	−1.56295
$682$	−6.89054	−0.263852
$683$	38.7018	1.48088	0.740442	−	0.672120i	$-0.234616\pi$
$683$	38.7018	1.48088	0.740442	+	0.672120i	$0.234616\pi$
$684$	−0.101677	−0.00388770
$685$	−1.37379	−0.0524900
$686$	13.6843	0.522470
$687$	48.8895	1.86525
$688$	0.454282	0.0173193
$689$	−11.7524	−0.447730
$690$	10.0145	0.381247
$691$	8.14819	0.309972	0.154986	−	0.987917i	$-0.450467\pi$
$691$	8.14819	0.309972	0.154986	+	0.987917i	$0.450467\pi$
$692$	−13.3876	−0.508919
$693$	−0.163862	−0.00622461
$694$	−8.85984	−0.336315
$695$	8.39372	0.318392
$696$	6.27389	0.237811
$697$	3.69489	0.139954
$698$	−0.119183	−0.00451116
$699$	37.0993	1.40322
$700$	13.8695	0.524218
$701$	−45.8938	−1.73338	−0.866692	−	0.498844i	$-0.833758\pi$
$701$	−45.8938	−1.73338	−0.866692	+	0.498844i	$0.833758\pi$
$702$	11.2813	0.425784
$703$	−22.1115	−0.833952
$704$	2.74845	0.103586
$705$	−1.64549	−0.0619728
$706$	4.24152	0.159632
$707$	−48.3577	−1.81868
$708$	−5.75348	−0.216229
$709$	−17.3449	−0.651402	−0.325701	−	0.945473i	$-0.605600\pi$
$709$	−17.3449	−0.651402	−0.325701	+	0.945473i	$0.605600\pi$
$710$	−9.87046	−0.370432
$711$	−0.0400723	−0.00150283
$712$	−2.86584	−0.107402
$713$	−20.0646	−0.751425
$714$	3.46556	0.129695
$715$	−4.31109	−0.161226
$716$	−16.6942	−0.623892
$717$	21.6359	0.808008
$718$	−12.8780	−0.480603
$719$	36.6437	1.36658	0.683290	−	0.730147i	$-0.260548\pi$
$719$	36.6437	1.36658	0.683290	+	0.730147i	$0.260548\pi$
$720$	−0.0138726	−0.000517002 0
$721$	−25.5570	−0.951791
$722$	8.85838	0.329675
$723$	16.5069	0.613899
$724$	−8.71262	−0.323802
$725$	16.1808	0.600940
$726$	5.98779	0.222228
$727$	22.7421	0.843459	0.421730	−	0.906722i	$-0.361423\pi$
$727$	22.7421	0.843459	0.421730	+	0.906722i	$0.361423\pi$
$728$	−6.74110	−0.249842
$729$	26.8244	0.993497
$730$	−4.16442	−0.154132
$731$	0.292753	0.0108278
$732$	−11.2244	−0.414866
$733$	−32.5944	−1.20390	−0.601951	−	0.798533i	$-0.705610\pi$
$733$	−32.5944	−1.20390	−0.601951	+	0.798533i	$0.705610\pi$
$734$	32.5367	1.20095
$735$	3.22643	0.119009
$736$	8.00323	0.295003
$737$	−41.1041	−1.51409
$738$	0.110451	0.00406575
$739$	39.4372	1.45072	0.725361	−	0.688368i	$-0.241673\pi$
$739$	39.4372	1.45072	0.725361	+	0.688368i	$0.241673\pi$
$740$	−3.01687	−0.110902
$741$	19.9762	0.733842
$742$	16.6990	0.613038
$743$	4.86838	0.178603	0.0893017	−	0.996005i	$-0.471536\pi$
$743$	4.86838	0.178603	0.0893017	+	0.996005i	$0.471536\pi$
$744$	4.35628	0.159709
$745$	1.45447	0.0532877
$746$	13.2899	0.486579
$747$	−0.273549	−0.0100086
$748$	1.77118	0.0647609
$749$	−0.527235	−0.0192648
$750$	−11.8642	−0.433219
$751$	−26.4962	−0.966859	−0.483430	−	0.875383i	$-0.660609\pi$
$751$	−26.4962	−0.966859	−0.483430	+	0.875383i	$0.660609\pi$
$752$	−1.31501	−0.0479535
$753$	−16.1315	−0.587866
$754$	−7.86448	−0.286407
$755$	10.0836	0.366979
$756$	−16.0296	−0.582989
$757$	5.06537	0.184104	0.0920520	−	0.995754i	$-0.470657\pi$
$757$	5.06537	0.184104	0.0920520	+	0.995754i	$0.470657\pi$
$758$	11.4635	0.416372
$759$	−38.2212	−1.38734
$760$	3.80096	0.137875
$761$	−38.2166	−1.38535	−0.692676	−	0.721249i	$-0.743568\pi$
$761$	−38.2166	−1.38535	−0.692676	+	0.721249i	$0.743568\pi$
$762$	26.9005	0.974503
$763$	−7.58544	−0.274611
$764$	−0.558163	−0.0201936
$765$	−0.00893993	−0.000323224 0
$766$	−33.8098	−1.22160
$767$	7.21212	0.260415
$768$	−1.73760	−0.0627003
$769$	−29.2285	−1.05401	−0.527004	−	0.849863i	$-0.676685\pi$
$769$	−29.2285	−1.05401	−0.527004	+	0.849863i	$0.676685\pi$
$770$	6.12563	0.220752
$771$	−40.4011	−1.45501
$772$	8.68010	0.312404
$773$	3.98507	0.143333	0.0716665	−	0.997429i	$-0.477168\pi$
$773$	3.98507	0.143333	0.0716665	+	0.997429i	$0.477168\pi$
$774$	0.00875122	0.000314556 0
$775$	11.2351	0.403578
$776$	−13.5031	−0.484733
$777$	22.5288	0.808217
$778$	−33.3950	−1.19727
$779$	−30.2624	−1.08426
$780$	2.72552	0.0975893
$781$	37.6713	1.34798
$782$	5.15752	0.184433
$783$	−18.7008	−0.668313
$784$	2.57844	0.0920870
$785$	−9.85449	−0.351722
$786$	−17.0663	−0.608735
$787$	4.06242	0.144809	0.0724047	−	0.997375i	$-0.476933\pi$
$787$	4.06242	0.144809	0.0724047	+	0.997375i	$0.476933\pi$
$788$	13.7554	0.490017
$789$	−21.4213	−0.762620
$790$	1.49801	0.0532970
$791$	42.1977	1.50038
$792$	0.0529458	0.00188135
$793$	14.0701	0.499643
$794$	3.61471	0.128281
$795$	−6.75162	−0.239455
$796$	−25.4245	−0.901148
$797$	25.0110	0.885935	0.442967	−	0.896538i	$-0.353926\pi$
$797$	25.0110	0.885935	0.442967	+	0.896538i	$0.353926\pi$
$798$	−28.3841	−1.00479
$799$	−0.847432	−0.0299800
$800$	−4.48140	−0.158441
$801$	−0.0552072	−0.00195065
$802$	10.4578	0.369277
$803$	15.8938	0.560879
$804$	25.9865	0.916473
$805$	17.8373	0.628681
$806$	−5.46070	−0.192345
$807$	−49.8759	−1.75571
$808$	15.6249	0.549683
$809$	−23.3640	−0.821435	−0.410717	−	0.911763i	$-0.634722\pi$
$809$	−23.3640	−0.821435	−0.410717	+	0.911763i	$0.634722\pi$
$810$	6.52259	0.229180
$811$	−32.3487	−1.13592	−0.567958	−	0.823057i	$-0.692266\pi$
$811$	−32.3487	−1.13592	−0.567958	+	0.823057i	$0.692266\pi$
$812$	11.1746	0.392153
$813$	26.7567	0.938399
$814$	11.5141	0.403568
$815$	17.3473	0.607650
$816$	−1.11976	−0.0391995
$817$	−2.39775	−0.0838865
$818$	11.3062	0.395312
$819$	−0.129860	−0.00453766
$820$	−4.12896	−0.144190
$821$	−43.4381	−1.51600	−0.758000	−	0.652255i	$-0.773823\pi$
$821$	−43.4381	−1.51600	−0.758000	+	0.652255i	$0.773823\pi$
$822$	−3.31480	−0.115617
$823$	12.4550	0.434153	0.217076	−	0.976155i	$-0.430348\pi$
$823$	12.4550	0.434153	0.217076	+	0.976155i	$0.430348\pi$
$824$	8.25776	0.287673
$825$	21.4019	0.745119
$826$	−10.2477	−0.356564
$827$	−7.68854	−0.267357	−0.133678	−	0.991025i	$-0.542679\pi$
$827$	−7.68854	−0.267357	−0.133678	+	0.991025i	$0.542679\pi$
$828$	0.154173	0.00535789
$829$	47.3491	1.64450	0.822251	−	0.569125i	$-0.192718\pi$
$829$	47.3491	1.64450	0.822251	+	0.569125i	$0.192718\pi$
$830$	10.2260	0.354951
$831$	2.27333	0.0788610
$832$	2.17813	0.0755130
$833$	1.66162	0.0575717
$834$	20.2530	0.701304
$835$	6.88292	0.238193
$836$	−14.5066	−0.501722
$837$	−12.9849	−0.448824
$838$	−26.1405	−0.903009
$839$	−13.9466	−0.481491	−0.240745	−	0.970588i	$-0.577392\pi$
$839$	−13.9466	−0.481491	−0.240745	+	0.970588i	$0.577392\pi$
$840$	−3.87269	−0.133621
$841$	−15.9631	−0.550453
$842$	3.26146	0.112397
$843$	−42.2993	−1.45686
$844$	−23.7611	−0.817890
$845$	5.94528	0.204524
$846$	−0.0253322	−0.000870939 0
$847$	10.6651	0.366456
$848$	−5.39563	−0.185287
$849$	11.3771	0.390460
$850$	−2.88795	−0.0990558
$851$	33.5279	1.14932
$852$	−23.8162	−0.815930
$853$	54.1563	1.85428	0.927139	−	0.374718i	$-0.122260\pi$
$853$	54.1563	1.85428	0.927139	+	0.374718i	$0.122260\pi$
$854$	−19.9922	−0.684118
$855$	0.0732211	0.00250411
$856$	0.170356	0.00582264
$857$	56.1038	1.91647	0.958235	−	0.285981i	$-0.0923194\pi$
$857$	56.1038	1.91647	0.958235	+	0.285981i	$0.0923194\pi$
$858$	−10.4021	−0.355123
$859$	7.86717	0.268424	0.134212	−	0.990953i	$-0.457150\pi$
$859$	7.86717	0.268424	0.134212	+	0.990953i	$0.457150\pi$
$860$	−0.327145	−0.0111556
$861$	30.8335	1.05080
$862$	−20.5167	−0.698801
$863$	−18.3619	−0.625048	−0.312524	−	0.949910i	$-0.601174\pi$
$863$	−18.3619	−0.625048	−0.312524	+	0.949910i	$0.601174\pi$
$864$	5.17934	0.176205
$865$	9.64089	0.327800
$866$	16.1248	0.547941
$867$	28.8176	0.978698
$868$	7.75911	0.263361
$869$	−5.71727	−0.193945
$870$	−4.51806	−0.153177
$871$	−32.5747	−1.10375
$872$	2.45094	0.0829994
$873$	−0.260122	−0.00880379
$874$	−42.2419	−1.42885
$875$	−21.1317	−0.714383
$876$	−10.0482	−0.339498
$877$	−22.1046	−0.746418	−0.373209	−	0.927747i	$-0.621743\pi$
$877$	−22.1046	−0.746418	−0.373209	+	0.927747i	$0.621743\pi$
$878$	−1.68662	−0.0569208
$879$	55.4945	1.87178
$880$	−1.97926	−0.0667210
$881$	−14.9202	−0.502675	−0.251337	−	0.967900i	$-0.580870\pi$
$881$	−14.9202	−0.502675	−0.251337	+	0.967900i	$0.580870\pi$
$882$	0.0496706	0.00167250
$883$	40.9462	1.37795	0.688975	−	0.724785i	$-0.258061\pi$
$883$	40.9462	1.37795	0.688975	+	0.724785i	$0.258061\pi$
$884$	1.40365	0.0472099
$885$	4.14329	0.139275
$886$	−19.6445	−0.659971
$887$	−42.2774	−1.41954	−0.709769	−	0.704435i	$-0.751201\pi$
$887$	−42.2774	−1.41954	−0.709769	+	0.704435i	$0.751201\pi$
$888$	−7.27933	−0.244278
$889$	47.9135	1.60697
$890$	2.06380	0.0691788
$891$	−24.8939	−0.833977
$892$	−2.67801	−0.0896664
$893$	6.94077	0.232264
$894$	3.50946	0.117374
$895$	12.0221	0.401856
$896$	−3.09490	−0.103394
$897$	−30.2900	−1.01135
$898$	30.3207	1.01181
$899$	9.05214	0.301906
$900$	−0.0863291	−0.00287764
$901$	−3.47710	−0.115839
$902$	15.7585	0.524699
$903$	2.44300	0.0812979
$904$	−13.6346	−0.453479
$905$	6.27428	0.208564
$906$	24.3304	0.808324
$907$	−30.6048	−1.01622	−0.508109	−	0.861293i	$-0.669655\pi$
$907$	−30.6048	−1.01622	−0.508109	+	0.861293i	$0.669655\pi$
$908$	23.4729	0.778976
$909$	0.300996	0.00998342
$910$	4.85452	0.160926
$911$	38.6087	1.27916	0.639581	−	0.768723i	$-0.279108\pi$
$911$	38.6087	1.27916	0.639581	+	0.768723i	$0.279108\pi$
$912$	9.17125	0.303690
$913$	−39.0284	−1.29165
$914$	−1.00271	−0.0331666
$915$	8.08312	0.267220
$916$	−28.1362	−0.929646
$917$	−30.3974	−1.00381
$918$	3.33772	0.110161
$919$	8.69661	0.286875	0.143437	−	0.989659i	$-0.454184\pi$
$919$	8.69661	0.286875	0.143437	+	0.989659i	$0.454184\pi$
$920$	−5.76343	−0.190015
$921$	34.8216	1.14741
$922$	38.8841	1.28058
$923$	29.8542	0.982663
$924$	14.7804	0.486239
$925$	−18.7739	−0.617282
$926$	−30.2319	−0.993481
$927$	0.159076	0.00522475
$928$	−3.61066	−0.118526
$929$	−36.6922	−1.20383	−0.601917	−	0.798559i	$-0.705596\pi$
$929$	−36.6922	−1.20383	−0.601917	+	0.798559i	$0.705596\pi$
$930$	−3.13712	−0.102870
$931$	−13.6093	−0.446025
$932$	−21.3509	−0.699370
$933$	−34.5667	−1.13166
$934$	37.4755	1.22624
$935$	−1.27550	−0.0417132
$936$	0.0419591	0.00137148
$937$	−21.5431	−0.703781	−0.351891	−	0.936041i	$-0.614461\pi$
$937$	−21.5431	−0.703781	−0.351891	+	0.936041i	$0.614461\pi$
$938$	46.2854	1.51127
$939$	30.2873	0.988390
$940$	0.946989	0.0308874
$941$	−30.5927	−0.997294	−0.498647	−	0.866805i	$-0.666170\pi$
$941$	−30.5927	−0.997294	−0.498647	+	0.866805i	$0.666170\pi$
$942$	−23.7777	−0.774718
$943$	45.8871	1.49429
$944$	3.31116	0.107769
$945$	11.5435	0.375509
$946$	1.24857	0.0405946
$947$	44.3493	1.44116	0.720580	−	0.693372i	$-0.243876\pi$
$947$	44.3493	1.44116	0.720580	+	0.693372i	$0.243876\pi$
$948$	3.61452	0.117394
$949$	12.5957	0.408874
$950$	23.6533	0.767415
$951$	1.37517	0.0445931
$952$	−1.99445	−0.0646404
$953$	7.10430	0.230131	0.115065	−	0.993358i	$-0.463292\pi$
$953$	7.10430	0.230131	0.115065	+	0.993358i	$0.463292\pi$
$954$	−0.103941	−0.00336520
$955$	0.401954	0.0130069
$956$	−12.4516	−0.402713
$957$	17.2435	0.557403
$958$	−14.8811	−0.480786
$959$	−5.90410	−0.190653
$960$	1.25131	0.0403859
$961$	−24.7146	−0.797247
$962$	9.12482	0.294196
$963$	0.00328171	0.000105752 0
$964$	−9.49982	−0.305969
$965$	−6.25086	−0.201222
$966$	43.0391	1.38476
$967$	13.9073	0.447227	0.223614	−	0.974678i	$-0.428215\pi$
$967$	13.9073	0.447227	0.223614	+	0.974678i	$0.428215\pi$
$968$	−3.44601	−0.110759
$969$	5.91022	0.189864
$970$	9.72409	0.312222
$971$	5.97896	0.191874	0.0959369	−	0.995387i	$-0.469415\pi$
$971$	5.97896	0.191874	0.0959369	+	0.995387i	$0.469415\pi$
$972$	0.200193	0.00642118
$973$	36.0733	1.15646
$974$	−3.60515	−0.115517
$975$	16.9609	0.543182
$976$	6.45971	0.206770
$977$	39.1211	1.25160	0.625798	−	0.779985i	$-0.284773\pi$
$977$	39.1211	1.25160	0.625798	+	0.779985i	$0.284773\pi$
$978$	41.8570	1.33844
$979$	−7.87664	−0.251738
$980$	−1.85683	−0.0593142
$981$	0.0472146	0.00150745
$982$	−38.2223	−1.21972
$983$	−43.3804	−1.38362	−0.691809	−	0.722080i	$-0.743186\pi$
$983$	−43.3804	−1.38362	−0.691809	+	0.722080i	$0.743186\pi$
$984$	−9.96268	−0.317599
$985$	−9.90579	−0.315625
$986$	−2.32682	−0.0741009
$987$	−7.07176	−0.225097
$988$	−11.4964	−0.365749
$989$	3.63572	0.115609
$990$	−0.0381282	−0.00121179
$991$	34.1373	1.08441	0.542203	−	0.840248i	$-0.317590\pi$
$991$	34.1373	1.08441	0.542203	+	0.840248i	$0.317590\pi$
$992$	−2.50706	−0.0795992
$993$	9.50717	0.301701
$994$	−42.4199	−1.34548
$995$	18.3091	0.580439
$996$	24.6742	0.781831
$997$	52.0006	1.64687	0.823437	−	0.567407i	$-0.192054\pi$
$997$	52.0006	1.64687	0.823437	+	0.567407i	$0.192054\pi$
$998$	−32.2835	−1.02192
$999$	21.6978	0.686487

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.e.1.17	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.e.1.17	✓	56	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.73760 q^{3} +1.00000 q^{4} -0.720137 q^{5} -1.73760 q^{6} -3.09490 q^{7} +1.00000 q^{8} +0.0192639 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.73760 q^{3} +1.00000 q^{4} -0.720137 q^{5} -1.73760 q^{6} -3.09490 q^{7} +1.00000 q^{8} +0.0192639 q^{9} -0.720137 q^{10} +2.74845 q^{11} -1.73760 q^{12} +2.17813 q^{13} -3.09490 q^{14} +1.25131 q^{15} +1.00000 q^{16} +0.644430 q^{17} +0.0192639 q^{18} -5.27810 q^{19} -0.720137 q^{20} +5.37772 q^{21} +2.74845 q^{22} +8.00323 q^{23} -1.73760 q^{24} -4.48140 q^{25} +2.17813 q^{26} +5.17934 q^{27} -3.09490 q^{28} -3.61066 q^{29} +1.25131 q^{30} -2.50706 q^{31} +1.00000 q^{32} -4.77572 q^{33} +0.644430 q^{34} +2.22876 q^{35} +0.0192639 q^{36} +4.18929 q^{37} -5.27810 q^{38} -3.78472 q^{39} -0.720137 q^{40} +5.73358 q^{41} +5.37772 q^{42} +0.454282 q^{43} +2.74845 q^{44} -0.0138726 q^{45} +8.00323 q^{46} -1.31501 q^{47} -1.73760 q^{48} +2.57844 q^{49} -4.48140 q^{50} -1.11976 q^{51} +2.17813 q^{52} -5.39563 q^{53} +5.17934 q^{54} -1.97926 q^{55} -3.09490 q^{56} +9.17125 q^{57} -3.61066 q^{58} +3.31116 q^{59} +1.25131 q^{60} +6.45971 q^{61} -2.50706 q^{62} -0.0596198 q^{63} +1.00000 q^{64} -1.56855 q^{65} -4.77572 q^{66} -14.9554 q^{67} +0.644430 q^{68} -13.9064 q^{69} +2.22876 q^{70} +13.7064 q^{71} +0.0192639 q^{72} +5.78281 q^{73} +4.18929 q^{74} +7.78690 q^{75} -5.27810 q^{76} -8.50620 q^{77} -3.78472 q^{78} -2.08018 q^{79} -0.720137 q^{80} -9.05742 q^{81} +5.73358 q^{82} -14.2001 q^{83} +5.37772 q^{84} -0.464078 q^{85} +0.454282 q^{86} +6.27389 q^{87} +2.74845 q^{88} -2.86584 q^{89} -0.0138726 q^{90} -6.74110 q^{91} +8.00323 q^{92} +4.35628 q^{93} -1.31501 q^{94} +3.80096 q^{95} -1.73760 q^{96} -13.5031 q^{97} +2.57844 q^{98} +0.0529458 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9 - 17 * q^10 - 53 * q^11 - 18 * q^12 - 21 * q^13 - 35 * q^14 - 36 * q^15 + 56 * q^16 - 22 * q^17 + 34 * q^18 - 31 * q^19 - 17 * q^20 - 23 * q^21 - 53 * q^22 - 59 * q^23 - 18 * q^24 + 41 * q^25 - 21 * q^26 - 63 * q^27 - 35 * q^28 - 88 * q^29 - 36 * q^30 - 44 * q^31 + 56 * q^32 + 4 * q^33 - 22 * q^34 - 51 * q^35 + 34 * q^36 - 60 * q^37 - 31 * q^38 - 62 * q^39 - 17 * q^40 - 39 * q^41 - 23 * q^42 - 66 * q^43 - 53 * q^44 - 34 * q^45 - 59 * q^46 - 51 * q^47 - 18 * q^48 + 41 * q^49 + 41 * q^50 - 48 * q^51 - 21 * q^52 - 75 * q^53 - 63 * q^54 - 41 * q^55 - 35 * q^56 - 12 * q^57 - 88 * q^58 - 77 * q^59 - 36 * q^60 - 43 * q^61 - 44 * q^62 - 88 * q^63 + 56 * q^64 - 54 * q^65 + 4 * q^66 - 62 * q^67 - 22 * q^68 - 48 * q^69 - 51 * q^70 - 122 * q^71 + 34 * q^72 - 7 * q^73 - 60 * q^74 - 63 * q^75 - 31 * q^76 - 39 * q^77 - 62 * q^78 - 91 * q^79 - 17 * q^80 + 8 * q^81 - 39 * q^82 - 51 * q^83 - 23 * q^84 - 72 * q^85 - 66 * q^86 - 19 * q^87 - 53 * q^88 - 62 * q^89 - 34 * q^90 - 48 * q^91 - 59 * q^92 - 41 * q^93 - 51 * q^94 - 120 * q^95 - 18 * q^96 + 6 * q^97 + 41 * q^98 - 128 * q^99

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