LMFDB - Embedded newform 4334.2.a.g.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.88207 q^{3} +1.00000 q^{4} -1.63726 q^{5} -1.88207 q^{6} +4.48475 q^{7} +1.00000 q^{8} +0.542179 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.88207 q^{3} +1.00000 q^{4} -1.63726 q^{5} -1.88207 q^{6} +4.48475 q^{7} +1.00000 q^{8} +0.542179 q^{9} -1.63726 q^{10} +1.00000 q^{11} -1.88207 q^{12} +6.11826 q^{13} +4.48475 q^{14} +3.08144 q^{15} +1.00000 q^{16} +2.15479 q^{17} +0.542179 q^{18} -2.30422 q^{19} -1.63726 q^{20} -8.44061 q^{21} +1.00000 q^{22} +0.0928639 q^{23} -1.88207 q^{24} -2.31937 q^{25} +6.11826 q^{26} +4.62579 q^{27} +4.48475 q^{28} +2.13117 q^{29} +3.08144 q^{30} +5.15501 q^{31} +1.00000 q^{32} -1.88207 q^{33} +2.15479 q^{34} -7.34272 q^{35} +0.542179 q^{36} +3.37246 q^{37} -2.30422 q^{38} -11.5150 q^{39} -1.63726 q^{40} -8.75411 q^{41} -8.44061 q^{42} +4.08530 q^{43} +1.00000 q^{44} -0.887690 q^{45} +0.0928639 q^{46} -3.36119 q^{47} -1.88207 q^{48} +13.1130 q^{49} -2.31937 q^{50} -4.05545 q^{51} +6.11826 q^{52} -0.399288 q^{53} +4.62579 q^{54} -1.63726 q^{55} +4.48475 q^{56} +4.33669 q^{57} +2.13117 q^{58} -3.40033 q^{59} +3.08144 q^{60} +7.70576 q^{61} +5.15501 q^{62} +2.43154 q^{63} +1.00000 q^{64} -10.0172 q^{65} -1.88207 q^{66} -14.0518 q^{67} +2.15479 q^{68} -0.174776 q^{69} -7.34272 q^{70} +0.404031 q^{71} +0.542179 q^{72} +3.36481 q^{73} +3.37246 q^{74} +4.36522 q^{75} -2.30422 q^{76} +4.48475 q^{77} -11.5150 q^{78} +2.01261 q^{79} -1.63726 q^{80} -10.3326 q^{81} -8.75411 q^{82} -3.54345 q^{83} -8.44061 q^{84} -3.52795 q^{85} +4.08530 q^{86} -4.01100 q^{87} +1.00000 q^{88} -17.5347 q^{89} -0.887690 q^{90} +27.4389 q^{91} +0.0928639 q^{92} -9.70207 q^{93} -3.36119 q^{94} +3.77261 q^{95} -1.88207 q^{96} +7.45722 q^{97} +13.1130 q^{98} +0.542179 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) $ 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9 + 13 * q^10 + 26 * q^11 + 12 * q^12 + 24 * q^13 + 13 * q^14 + 12 * q^15 + 26 * q^16 + q^17 + 38 * q^18 + 24 * q^19 + 13 * q^20 + 5 * q^21 + 26 * q^22 + 19 * q^23 + 12 * q^24 + 35 * q^25 + 24 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 12 * q^30 + 34 * q^31 + 26 * q^32 + 12 * q^33 + q^34 + 14 * q^35 + 38 * q^36 + 15 * q^37 + 24 * q^38 + 3 * q^39 + 13 * q^40 - 9 * q^41 + 5 * q^42 + 6 * q^43 + 26 * q^44 + 22 * q^45 + 19 * q^46 + 34 * q^47 + 12 * q^48 + 53 * q^49 + 35 * q^50 - 2 * q^51 + 24 * q^52 + 6 * q^53 + 39 * q^54 + 13 * q^55 + 13 * q^56 - 16 * q^57 + 5 * q^58 + 50 * q^59 + 12 * q^60 + 26 * q^61 + 34 * q^62 + 2 * q^63 + 26 * q^64 - 5 * q^65 + 12 * q^66 + 18 * q^67 + q^68 + 15 * q^69 + 14 * q^70 + 23 * q^71 + 38 * q^72 + 37 * q^73 + 15 * q^74 + 18 * q^75 + 24 * q^76 + 13 * q^77 + 3 * q^78 + 10 * q^79 + 13 * q^80 + 50 * q^81 - 9 * q^82 + 7 * q^83 + 5 * q^84 - 7 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^88 + 3 * q^89 + 22 * q^90 + 31 * q^91 + 19 * q^92 + 52 * q^93 + 34 * q^94 + 9 * q^95 + 12 * q^96 - 9 * q^97 + 53 * q^98 + 38 * 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
$3$	−1.88207	−1.08661	−0.543306	−	0.839535i	$-0.682828\pi$
$3$	−1.88207	−1.08661	−0.543306	+	0.839535i	$0.682828\pi$
$4$	1.00000	0.500000
$5$	−1.63726	−0.732206	−0.366103	−	0.930574i	$-0.619308\pi$
$5$	−1.63726	−0.732206	−0.366103	+	0.930574i	$0.619308\pi$
$6$	−1.88207	−0.768351
$7$	4.48475	1.69508	0.847539	−	0.530733i	$-0.178083\pi$
$7$	4.48475	1.69508	0.847539	+	0.530733i	$0.178083\pi$
$8$	1.00000	0.353553
$9$	0.542179	0.180726
$10$	−1.63726	−0.517748
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.88207	−0.543306
$13$	6.11826	1.69690	0.848451	−	0.529275i	$-0.177536\pi$
$13$	6.11826	1.69690	0.848451	+	0.529275i	$0.177536\pi$
$14$	4.48475	1.19860
$15$	3.08144	0.795624
$16$	1.00000	0.250000
$17$	2.15479	0.522612	0.261306	−	0.965256i	$-0.415847\pi$
$17$	2.15479	0.522612	0.261306	+	0.965256i	$0.415847\pi$
$18$	0.542179	0.127793
$19$	−2.30422	−0.528624	−0.264312	−	0.964437i	$-0.585145\pi$
$19$	−2.30422	−0.528624	−0.264312	+	0.964437i	$0.585145\pi$
$20$	−1.63726	−0.366103
$21$	−8.44061	−1.84189
$22$	1.00000	0.213201
$23$	0.0928639	0.0193635	0.00968173	−	0.999953i	$-0.496918\pi$
$23$	0.0928639	0.0193635	0.00968173	+	0.999953i	$0.496918\pi$
$24$	−1.88207	−0.384175
$25$	−2.31937	−0.463875
$26$	6.11826	1.19989
$27$	4.62579	0.890233
$28$	4.48475	0.847539
$29$	2.13117	0.395748	0.197874	−	0.980228i	$-0.436596\pi$
$29$	2.13117	0.395748	0.197874	+	0.980228i	$0.436596\pi$
$30$	3.08144	0.562591
$31$	5.15501	0.925866	0.462933	−	0.886393i	$-0.346797\pi$
$31$	5.15501	0.925866	0.462933	+	0.886393i	$0.346797\pi$
$32$	1.00000	0.176777
$33$	−1.88207	−0.327626
$34$	2.15479	0.369543
$35$	−7.34272	−1.24115
$36$	0.542179	0.0903632
$37$	3.37246	0.554429	0.277215	−	0.960808i	$-0.410589\pi$
$37$	3.37246	0.554429	0.277215	+	0.960808i	$0.410589\pi$
$38$	−2.30422	−0.373793
$39$	−11.5150	−1.84387
$40$	−1.63726	−0.258874
$41$	−8.75411	−1.36716	−0.683581	−	0.729875i	$-0.739578\pi$
$41$	−8.75411	−1.36716	−0.683581	+	0.729875i	$0.739578\pi$
$42$	−8.44061	−1.30241
$43$	4.08530	0.623003	0.311501	−	0.950246i	$-0.399168\pi$
$43$	4.08530	0.623003	0.311501	+	0.950246i	$0.399168\pi$
$44$	1.00000	0.150756
$45$	−0.887690	−0.132329
$46$	0.0928639	0.0136920
$47$	−3.36119	−0.490280	−0.245140	−	0.969488i	$-0.578834\pi$
$47$	−3.36119	−0.490280	−0.245140	+	0.969488i	$0.578834\pi$
$48$	−1.88207	−0.271653
$49$	13.1130	1.87329
$50$	−2.31937	−0.328009
$51$	−4.05545	−0.567877
$52$	6.11826	0.848451
$53$	−0.399288	−0.0548464	−0.0274232	−	0.999624i	$-0.508730\pi$
$53$	−0.399288	−0.0548464	−0.0274232	+	0.999624i	$0.508730\pi$
$54$	4.62579	0.629490
$55$	−1.63726	−0.220768
$56$	4.48475	0.599300
$57$	4.33669	0.574409
$58$	2.13117	0.279836
$59$	−3.40033	−0.442685	−0.221342	−	0.975196i	$-0.571044\pi$
$59$	−3.40033	−0.442685	−0.221342	+	0.975196i	$0.571044\pi$
$60$	3.08144	0.397812
$61$	7.70576	0.986622	0.493311	−	0.869853i	$-0.335786\pi$
$61$	7.70576	0.986622	0.493311	+	0.869853i	$0.335786\pi$
$62$	5.15501	0.654686
$63$	2.43154	0.306345
$64$	1.00000	0.125000
$65$	−10.0172	−1.24248
$66$	−1.88207	−0.231667
$67$	−14.0518	−1.71670	−0.858349	−	0.513067i	$-0.828509\pi$
$67$	−14.0518	−1.71670	−0.858349	+	0.513067i	$0.828509\pi$
$68$	2.15479	0.261306
$69$	−0.174776	−0.0210406
$70$	−7.34272	−0.877622
$71$	0.404031	0.0479497	0.0239748	−	0.999713i	$-0.492368\pi$
$71$	0.404031	0.0479497	0.0239748	+	0.999713i	$0.492368\pi$
$72$	0.542179	0.0638965
$73$	3.36481	0.393821	0.196911	−	0.980421i	$-0.436909\pi$
$73$	3.36481	0.393821	0.196911	+	0.980421i	$0.436909\pi$
$74$	3.37246	0.392041
$75$	4.36522	0.504052
$76$	−2.30422	−0.264312
$77$	4.48475	0.511085
$78$	−11.5150	−1.30382
$79$	2.01261	0.226437	0.113218	−	0.993570i	$-0.463884\pi$
$79$	2.01261	0.226437	0.113218	+	0.993570i	$0.463884\pi$
$80$	−1.63726	−0.183051
$81$	−10.3326	−1.14806
$82$	−8.75411	−0.966729
$83$	−3.54345	−0.388944	−0.194472	−	0.980908i	$-0.562299\pi$
$83$	−3.54345	−0.388944	−0.194472	+	0.980908i	$0.562299\pi$
$84$	−8.44061	−0.920946
$85$	−3.52795	−0.382660
$86$	4.08530	0.440530
$87$	−4.01100	−0.430024
$88$	1.00000	0.106600
$89$	−17.5347	−1.85868	−0.929338	−	0.369230i	$-0.879621\pi$
$89$	−17.5347	−1.85868	−0.929338	+	0.369230i	$0.879621\pi$
$90$	−0.887690	−0.0935707
$91$	27.4389	2.87638
$92$	0.0928639	0.00968173
$93$	−9.70207	−1.00606
$94$	−3.36119	−0.346680
$95$	3.77261	0.387061
$96$	−1.88207	−0.192088
$97$	7.45722	0.757166	0.378583	−	0.925567i	$-0.376411\pi$
$97$	7.45722	0.757166	0.378583	+	0.925567i	$0.376411\pi$
$98$	13.1130	1.32461
$99$	0.542179	0.0544911
$100$	−2.31937	−0.231937
$101$	−12.0344	−1.19747	−0.598736	−	0.800947i	$-0.704330\pi$
$101$	−12.0344	−1.19747	−0.598736	+	0.800947i	$0.704330\pi$
$102$	−4.05545	−0.401550
$103$	11.3548	1.11883	0.559413	−	0.828889i	$-0.311027\pi$
$103$	11.3548	1.11883	0.559413	+	0.828889i	$0.311027\pi$
$104$	6.11826	0.599945
$105$	13.8195	1.34864
$106$	−0.399288	−0.0387823
$107$	12.1504	1.17462	0.587310	−	0.809362i	$-0.300187\pi$
$107$	12.1504	1.17462	0.587310	+	0.809362i	$0.300187\pi$
$108$	4.62579	0.445116
$109$	5.06410	0.485053	0.242526	−	0.970145i	$-0.422024\pi$
$109$	5.06410	0.485053	0.242526	+	0.970145i	$0.422024\pi$
$110$	−1.63726	−0.156107
$111$	−6.34720	−0.602449
$112$	4.48475	0.423769
$113$	14.5735	1.37096	0.685481	−	0.728090i	$-0.259592\pi$
$113$	14.5735	1.37096	0.685481	+	0.728090i	$0.259592\pi$
$114$	4.33669	0.406168
$115$	−0.152042	−0.0141780
$116$	2.13117	0.197874
$117$	3.31720	0.306675
$118$	−3.40033	−0.313025
$119$	9.66368	0.885868
$120$	3.08144	0.281295
$121$	1.00000	0.0909091
$122$	7.70576	0.697647
$123$	16.4758	1.48557
$124$	5.15501	0.462933
$125$	11.9837	1.07186
$126$	2.43154	0.216619
$127$	−6.22322	−0.552222	−0.276111	−	0.961126i	$-0.589046\pi$
$127$	−6.22322	−0.552222	−0.276111	+	0.961126i	$0.589046\pi$
$128$	1.00000	0.0883883
$129$	−7.68882	−0.676963
$130$	−10.0172	−0.878566
$131$	−4.02557	−0.351716	−0.175858	−	0.984416i	$-0.556270\pi$
$131$	−4.02557	−0.351716	−0.175858	+	0.984416i	$0.556270\pi$
$132$	−1.88207	−0.163813
$133$	−10.3338	−0.896058
$134$	−14.0518	−1.21389
$135$	−7.57362	−0.651833
$136$	2.15479	0.184771
$137$	11.7296	1.00213	0.501063	−	0.865411i	$-0.332943\pi$
$137$	11.7296	1.00213	0.501063	+	0.865411i	$0.332943\pi$
$138$	−0.174776	−0.0148779
$139$	4.75055	0.402936	0.201468	−	0.979495i	$-0.435429\pi$
$139$	4.75055	0.402936	0.201468	+	0.979495i	$0.435429\pi$
$140$	−7.34272	−0.620573
$141$	6.32598	0.532744
$142$	0.404031	0.0339056
$143$	6.11826	0.511635
$144$	0.542179	0.0451816
$145$	−3.48928	−0.289769
$146$	3.36481	0.278474
$147$	−24.6796	−2.03554
$148$	3.37246	0.277215
$149$	−12.3142	−1.00882	−0.504410	−	0.863465i	$-0.668290\pi$
$149$	−12.3142	−1.00882	−0.504410	+	0.863465i	$0.668290\pi$
$150$	4.36522	0.356419
$151$	−14.7569	−1.20090	−0.600449	−	0.799663i	$-0.705012\pi$
$151$	−14.7569	−1.20090	−0.600449	+	0.799663i	$0.705012\pi$
$152$	−2.30422	−0.186897
$153$	1.16828	0.0944499
$154$	4.48475	0.361392
$155$	−8.44009	−0.677925
$156$	−11.5150	−0.921937
$157$	11.7765	0.939868	0.469934	−	0.882701i	$-0.344278\pi$
$157$	11.7765	0.939868	0.469934	+	0.882701i	$0.344278\pi$
$158$	2.01261	0.160115
$159$	0.751487	0.0595968
$160$	−1.63726	−0.129437
$161$	0.416472	0.0328226
$162$	−10.3326	−0.811804
$163$	5.38552	0.421826	0.210913	−	0.977505i	$-0.432356\pi$
$163$	5.38552	0.421826	0.210913	+	0.977505i	$0.432356\pi$
$164$	−8.75411	−0.683581
$165$	3.08144	0.239890
$166$	−3.54345	−0.275025
$167$	11.0835	0.857667	0.428834	−	0.903384i	$-0.358925\pi$
$167$	11.0835	0.857667	0.428834	+	0.903384i	$0.358925\pi$
$168$	−8.44061	−0.651207
$169$	24.4332	1.87947
$170$	−3.52795	−0.270581
$171$	−1.24930	−0.0955363
$172$	4.08530	0.311501
$173$	17.5850	1.33696	0.668480	−	0.743730i	$-0.266945\pi$
$173$	17.5850	1.33696	0.668480	+	0.743730i	$0.266945\pi$
$174$	−4.01100	−0.304073
$175$	−10.4018	−0.786304
$176$	1.00000	0.0753778
$177$	6.39964	0.481027
$178$	−17.5347	−1.31428
$179$	23.2553	1.73819	0.869093	−	0.494648i	$-0.164703\pi$
$179$	23.2553	1.73819	0.869093	+	0.494648i	$0.164703\pi$
$180$	−0.887690	−0.0661645
$181$	23.0417	1.71268	0.856340	−	0.516413i	$-0.172733\pi$
$181$	23.0417	1.71268	0.856340	+	0.516413i	$0.172733\pi$
$182$	27.4389	2.03391
$183$	−14.5028	−1.07208
$184$	0.0928639	0.00684601
$185$	−5.52160	−0.405956
$186$	−9.70207	−0.711390
$187$	2.15479	0.157574
$188$	−3.36119	−0.245140
$189$	20.7455	1.50901
$190$	3.77261	0.273694
$191$	−9.60999	−0.695355	−0.347677	−	0.937614i	$-0.613030\pi$
$191$	−9.60999	−0.695355	−0.347677	+	0.937614i	$0.613030\pi$
$192$	−1.88207	−0.135827
$193$	20.8235	1.49891	0.749454	−	0.662057i	$-0.230316\pi$
$193$	20.8235	1.49891	0.749454	+	0.662057i	$0.230316\pi$
$194$	7.45722	0.535397
$195$	18.8530	1.35009
$196$	13.1130	0.936644
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	0.542179	0.0385310
$199$	−10.5678	−0.749133	−0.374566	−	0.927200i	$-0.622208\pi$
$199$	−10.5678	−0.749133	−0.374566	+	0.927200i	$0.622208\pi$
$200$	−2.31937	−0.164005
$201$	26.4464	1.86538
$202$	−12.0344	−0.846740
$203$	9.55775	0.670823
$204$	−4.05545	−0.283938
$205$	14.3328	1.00104
$206$	11.3548	0.791129
$207$	0.0503489	0.00349949
$208$	6.11826	0.424225
$209$	−2.30422	−0.159386
$210$	13.8195	0.953635
$211$	−7.60340	−0.523439	−0.261720	−	0.965144i	$-0.584290\pi$
$211$	−7.60340	−0.523439	−0.261720	+	0.965144i	$0.584290\pi$
$212$	−0.399288	−0.0274232
$213$	−0.760414	−0.0521027
$214$	12.1504	0.830582
$215$	−6.68871	−0.456166
$216$	4.62579	0.314745
$217$	23.1189	1.56942
$218$	5.06410	0.342984
$219$	−6.33280	−0.427931
$220$	−1.63726	−0.110384
$221$	13.1835	0.886821
$222$	−6.34720	−0.425996
$223$	−2.46578	−0.165121	−0.0825603	−	0.996586i	$-0.526310\pi$
$223$	−2.46578	−0.165121	−0.0825603	+	0.996586i	$0.526310\pi$
$224$	4.48475	0.299650
$225$	−1.25752	−0.0838345
$226$	14.5735	0.969417
$227$	21.5432	1.42987	0.714935	−	0.699191i	$-0.246456\pi$
$227$	21.5432	1.42987	0.714935	+	0.699191i	$0.246456\pi$
$228$	4.33669	0.287204
$229$	−20.9565	−1.38484	−0.692421	−	0.721494i	$-0.743456\pi$
$229$	−20.9565	−1.38484	−0.692421	+	0.721494i	$0.743456\pi$
$230$	−0.152042	−0.0100254
$231$	−8.44061	−0.555351
$232$	2.13117	0.139918
$233$	15.0098	0.983323	0.491662	−	0.870786i	$-0.336390\pi$
$233$	15.0098	0.983323	0.491662	+	0.870786i	$0.336390\pi$
$234$	3.31720	0.216852
$235$	5.50314	0.358985
$236$	−3.40033	−0.221342
$237$	−3.78787	−0.246049
$238$	9.66368	0.626403
$239$	15.9482	1.03160	0.515800	−	0.856709i	$-0.327495\pi$
$239$	15.9482	1.03160	0.515800	+	0.856709i	$0.327495\pi$
$240$	3.08144	0.198906
$241$	−23.5615	−1.51773	−0.758863	−	0.651250i	$-0.774245\pi$
$241$	−23.5615	−1.51773	−0.758863	+	0.651250i	$0.774245\pi$
$242$	1.00000	0.0642824
$243$	5.56926	0.357268
$244$	7.70576	0.493311
$245$	−21.4694	−1.37163
$246$	16.4758	1.05046
$247$	−14.0978	−0.897022
$248$	5.15501	0.327343
$249$	6.66901	0.422631
$250$	11.9837	0.757918
$251$	8.76719	0.553380	0.276690	−	0.960959i	$-0.410762\pi$
$251$	8.76719	0.553380	0.276690	+	0.960959i	$0.410762\pi$
$252$	2.43154	0.153173
$253$	0.0928639	0.00583830
$254$	−6.22322	−0.390480
$255$	6.63984	0.415803
$256$	1.00000	0.0625000
$257$	−3.34900	−0.208905	−0.104452	−	0.994530i	$-0.533309\pi$
$257$	−3.34900	−0.208905	−0.104452	+	0.994530i	$0.533309\pi$
$258$	−7.68882	−0.478685
$259$	15.1247	0.939800
$260$	−10.0172	−0.621240
$261$	1.15547	0.0715221
$262$	−4.02557	−0.248700
$263$	20.4658	1.26198	0.630988	−	0.775793i	$-0.282650\pi$
$263$	20.4658	1.26198	0.630988	+	0.775793i	$0.282650\pi$
$264$	−1.88207	−0.115833
$265$	0.653739	0.0401589
$266$	−10.3338	−0.633609
$267$	33.0015	2.01966
$268$	−14.0518	−0.858349
$269$	−24.5024	−1.49394	−0.746970	−	0.664858i	$-0.768492\pi$
$269$	−24.5024	−1.49394	−0.746970	+	0.664858i	$0.768492\pi$
$270$	−7.57362	−0.460916
$271$	28.7064	1.74379	0.871896	−	0.489692i	$-0.162891\pi$
$271$	28.7064	1.74379	0.871896	+	0.489692i	$0.162891\pi$
$272$	2.15479	0.130653
$273$	−51.6419	−3.12551
$274$	11.7296	0.708610
$275$	−2.31937	−0.139864
$276$	−0.174776	−0.0105203
$277$	−26.0067	−1.56259	−0.781297	−	0.624160i	$-0.785441\pi$
$277$	−26.0067	−1.56259	−0.781297	+	0.624160i	$0.785441\pi$
$278$	4.75055	0.284919
$279$	2.79494	0.167329
$280$	−7.34272	−0.438811
$281$	−2.06677	−0.123293	−0.0616467	−	0.998098i	$-0.519635\pi$
$281$	−2.06677	−0.123293	−0.0616467	+	0.998098i	$0.519635\pi$
$282$	6.32598	0.376707
$283$	12.3639	0.734957	0.367479	−	0.930032i	$-0.380221\pi$
$283$	12.3639	0.734957	0.367479	+	0.930032i	$0.380221\pi$
$284$	0.404031	0.0239748
$285$	−7.10030	−0.420585
$286$	6.11826	0.361781
$287$	−39.2600	−2.31745
$288$	0.542179	0.0319482
$289$	−12.3569	−0.726876
$290$	−3.48928	−0.204897
$291$	−14.0350	−0.822746
$292$	3.36481	0.196911
$293$	22.9858	1.34284	0.671421	−	0.741076i	$-0.265684\pi$
$293$	22.9858	1.34284	0.671421	+	0.741076i	$0.265684\pi$
$294$	−24.6796	−1.43934
$295$	5.56722	0.324136
$296$	3.37246	0.196020
$297$	4.62579	0.268415
$298$	−12.3142	−0.713343
$299$	0.568166	0.0328579
$300$	4.36522	0.252026
$301$	18.3216	1.05604
$302$	−14.7569	−0.849164
$303$	22.6496	1.30119
$304$	−2.30422	−0.132156
$305$	−12.6164	−0.722410
$306$	1.16828	0.0667861
$307$	12.5610	0.716895	0.358448	−	0.933550i	$-0.383306\pi$
$307$	12.5610	0.716895	0.358448	+	0.933550i	$0.383306\pi$
$308$	4.48475	0.255543
$309$	−21.3706	−1.21573
$310$	−8.44009	−0.479365
$311$	−25.8453	−1.46556	−0.732778	−	0.680468i	$-0.761776\pi$
$311$	−25.8453	−1.46556	−0.732778	+	0.680468i	$0.761776\pi$
$312$	−11.5150	−0.651908
$313$	−3.58407	−0.202584	−0.101292	−	0.994857i	$-0.532298\pi$
$313$	−3.58407	−0.202584	−0.101292	+	0.994857i	$0.532298\pi$
$314$	11.7765	0.664587
$315$	−3.98107	−0.224308
$316$	2.01261	0.113218
$317$	−16.2971	−0.915337	−0.457669	−	0.889123i	$-0.651315\pi$
$317$	−16.2971	−0.915337	−0.457669	+	0.889123i	$0.651315\pi$
$318$	0.751487	0.0421413
$319$	2.13117	0.119322
$320$	−1.63726	−0.0915257
$321$	−22.8678	−1.27636
$322$	0.416472	0.0232091
$323$	−4.96509	−0.276265
$324$	−10.3326	−0.574032
$325$	−14.1905	−0.787150
$326$	5.38552	0.298276
$327$	−9.53098	−0.527064
$328$	−8.75411	−0.483365
$329$	−15.0741	−0.831062
$330$	3.08144	0.169628
$331$	−11.9211	−0.655243	−0.327621	−	0.944809i	$-0.606247\pi$
$331$	−11.9211	−0.655243	−0.327621	+	0.944809i	$0.606247\pi$
$332$	−3.54345	−0.194472
$333$	1.82848	0.100200
$334$	11.0835	0.606462
$335$	23.0064	1.25698
$336$	−8.44061	−0.460473
$337$	−13.5551	−0.738392	−0.369196	−	0.929352i	$-0.620367\pi$
$337$	−13.5551	−0.738392	−0.369196	+	0.929352i	$0.620367\pi$
$338$	24.4332	1.32899
$339$	−27.4284	−1.48971
$340$	−3.52795	−0.191330
$341$	5.15501	0.279159
$342$	−1.24930	−0.0675544
$343$	27.4154	1.48029
$344$	4.08530	0.220265
$345$	0.286154	0.0154060
$346$	17.5850	0.945373
$347$	−18.3761	−0.986480	−0.493240	−	0.869893i	$-0.664188\pi$
$347$	−18.3761	−0.986480	−0.493240	+	0.869893i	$0.664188\pi$
$348$	−4.01100	−0.215012
$349$	−14.7319	−0.788578	−0.394289	−	0.918986i	$-0.629009\pi$
$349$	−14.7319	−0.788578	−0.394289	+	0.918986i	$0.629009\pi$
$350$	−10.4018	−0.556001
$351$	28.3018	1.51064
$352$	1.00000	0.0533002
$353$	−7.31924	−0.389564	−0.194782	−	0.980847i	$-0.562400\pi$
$353$	−7.31924	−0.389564	−0.194782	+	0.980847i	$0.562400\pi$
$354$	6.39964	0.340137
$355$	−0.661505	−0.0351090
$356$	−17.5347	−0.929338
$357$	−18.1877	−0.962595
$358$	23.2553	1.22908
$359$	−34.6731	−1.82998	−0.914988	−	0.403482i	$-0.867800\pi$
$359$	−34.6731	−1.82998	−0.914988	+	0.403482i	$0.867800\pi$
$360$	−0.887690	−0.0467854
$361$	−13.6906	−0.720557
$362$	23.0417	1.21105
$363$	−1.88207	−0.0987829
$364$	27.4389	1.43819
$365$	−5.50908	−0.288358
$366$	−14.5028	−0.758072
$367$	10.2339	0.534203	0.267101	−	0.963668i	$-0.413934\pi$
$367$	10.2339	0.534203	0.267101	+	0.963668i	$0.413934\pi$
$368$	0.0928639	0.00484086
$369$	−4.74630	−0.247082
$370$	−5.52160	−0.287054
$371$	−1.79071	−0.0929690
$372$	−9.70207	−0.503029
$373$	25.4963	1.32015	0.660074	−	0.751200i	$-0.270525\pi$
$373$	25.4963	1.32015	0.660074	+	0.751200i	$0.270525\pi$
$374$	2.15479	0.111421
$375$	−22.5542	−1.16469
$376$	−3.36119	−0.173340
$377$	13.0390	0.671544
$378$	20.7455	1.06703
$379$	5.02046	0.257884	0.128942	−	0.991652i	$-0.458842\pi$
$379$	5.02046	0.257884	0.128942	+	0.991652i	$0.458842\pi$
$380$	3.77261	0.193531
$381$	11.7125	0.600051
$382$	−9.60999	−0.491690
$383$	1.38308	0.0706720	0.0353360	−	0.999375i	$-0.488750\pi$
$383$	1.38308	0.0706720	0.0353360	+	0.999375i	$0.488750\pi$
$384$	−1.88207	−0.0960439
$385$	−7.34272	−0.374219
$386$	20.8235	1.05989
$387$	2.21497	0.112593
$388$	7.45722	0.378583
$389$	14.9766	0.759344	0.379672	−	0.925121i	$-0.376037\pi$
$389$	14.9766	0.759344	0.379672	+	0.925121i	$0.376037\pi$
$390$	18.8530	0.954661
$391$	0.200102	0.0101196
$392$	13.1130	0.662307
$393$	7.57639	0.382178
$394$	1.00000	0.0503793
$395$	−3.29517	−0.165798
$396$	0.542179	0.0272455
$397$	4.27518	0.214565	0.107283	−	0.994229i	$-0.465785\pi$
$397$	4.27518	0.214565	0.107283	+	0.994229i	$0.465785\pi$
$398$	−10.5678	−0.529717
$399$	19.4490	0.973668
$400$	−2.31937	−0.115969
$401$	−30.2593	−1.51108	−0.755539	−	0.655104i	$-0.772625\pi$
$401$	−30.2593	−1.51108	−0.755539	+	0.655104i	$0.772625\pi$
$402$	26.4464	1.31903
$403$	31.5397	1.57110
$404$	−12.0344	−0.598736
$405$	16.9171	0.840619
$406$	9.55775	0.474343
$407$	3.37246	0.167167
$408$	−4.05545	−0.200775
$409$	12.3362	0.609984	0.304992	−	0.952355i	$-0.401346\pi$
$409$	12.3362	0.609984	0.304992	+	0.952355i	$0.401346\pi$
$410$	14.3328	0.707845
$411$	−22.0759	−1.08892
$412$	11.3548	0.559413
$413$	−15.2496	−0.750385
$414$	0.0503489	0.00247451
$415$	5.80155	0.284787
$416$	6.11826	0.299973
$417$	−8.94085	−0.437835
$418$	−2.30422	−0.112703
$419$	12.8114	0.625877	0.312939	−	0.949773i	$-0.398687\pi$
$419$	12.8114	0.625877	0.312939	+	0.949773i	$0.398687\pi$
$420$	13.8195	0.674322
$421$	−6.11634	−0.298092	−0.149046	−	0.988830i	$-0.547620\pi$
$421$	−6.11634	−0.298092	−0.149046	+	0.988830i	$0.547620\pi$
$422$	−7.60340	−0.370127
$423$	−1.82237	−0.0886065
$424$	−0.399288	−0.0193911
$425$	−4.99775	−0.242427
$426$	−0.760414	−0.0368422
$427$	34.5585	1.67240
$428$	12.1504	0.587310
$429$	−11.5150	−0.555949
$430$	−6.68871	−0.322558
$431$	−9.65479	−0.465055	−0.232527	−	0.972590i	$-0.574700\pi$
$431$	−9.65479	−0.465055	−0.232527	+	0.972590i	$0.574700\pi$
$432$	4.62579	0.222558
$433$	3.29335	0.158268	0.0791341	−	0.996864i	$-0.474784\pi$
$433$	3.29335	0.158268	0.0791341	+	0.996864i	$0.474784\pi$
$434$	23.1189	1.10974
$435$	6.56705	0.314866
$436$	5.06410	0.242526
$437$	−0.213978	−0.0102360
$438$	−6.33280	−0.302593
$439$	20.2420	0.966100	0.483050	−	0.875593i	$-0.339529\pi$
$439$	20.2420	0.966100	0.483050	+	0.875593i	$0.339529\pi$
$440$	−1.63726	−0.0780534
$441$	7.10961	0.338553
$442$	13.1835	0.627077
$443$	−11.5791	−0.550138	−0.275069	−	0.961424i	$-0.588701\pi$
$443$	−11.5791	−0.550138	−0.275069	+	0.961424i	$0.588701\pi$
$444$	−6.34720	−0.301225
$445$	28.7089	1.36093
$446$	−2.46578	−0.116758
$447$	23.1762	1.09620
$448$	4.48475	0.211885
$449$	−10.6927	−0.504619	−0.252309	−	0.967647i	$-0.581190\pi$
$449$	−10.6927	−0.504619	−0.252309	+	0.967647i	$0.581190\pi$
$450$	−1.25752	−0.0592799
$451$	−8.75411	−0.412215
$452$	14.5735	0.685481
$453$	27.7735	1.30491
$454$	21.5432	1.01107
$455$	−44.9247	−2.10610
$456$	4.33669	0.203084
$457$	2.48493	0.116240	0.0581201	−	0.998310i	$-0.481489\pi$
$457$	2.48493	0.116240	0.0581201	+	0.998310i	$0.481489\pi$
$458$	−20.9565	−0.979231
$459$	9.96757	0.465246
$460$	−0.152042	−0.00708902
$461$	32.3886	1.50849	0.754244	−	0.656595i	$-0.228004\pi$
$461$	32.3886	1.50849	0.754244	+	0.656595i	$0.228004\pi$
$462$	−8.44061	−0.392693
$463$	−36.1502	−1.68004	−0.840022	−	0.542553i	$-0.817458\pi$
$463$	−36.1502	−1.68004	−0.840022	+	0.542553i	$0.817458\pi$
$464$	2.13117	0.0989369
$465$	15.8848	0.736641
$466$	15.0098	0.695315
$467$	26.0821	1.20693	0.603467	−	0.797388i	$-0.293786\pi$
$467$	26.0821	1.20693	0.603467	+	0.797388i	$0.293786\pi$
$468$	3.31720	0.153337
$469$	−63.0187	−2.90994
$470$	5.50314	0.253841
$471$	−22.1642	−1.02127
$472$	−3.40033	−0.156513
$473$	4.08530	0.187842
$474$	−3.78787	−0.173983
$475$	5.34434	0.245215
$476$	9.66368	0.442934
$477$	−0.216486	−0.00991221
$478$	15.9482	0.729452
$479$	24.0006	1.09661	0.548307	−	0.836277i	$-0.315272\pi$
$479$	24.0006	1.09661	0.548307	+	0.836277i	$0.315272\pi$
$480$	3.08144	0.140648
$481$	20.6336	0.940811
$482$	−23.5615	−1.07319
$483$	−0.783828	−0.0356654
$484$	1.00000	0.0454545
$485$	−12.2094	−0.554401
$486$	5.56926	0.252627
$487$	−26.6842	−1.20918	−0.604589	−	0.796538i	$-0.706662\pi$
$487$	−26.6842	−1.20918	−0.604589	+	0.796538i	$0.706662\pi$
$488$	7.70576	0.348824
$489$	−10.1359	−0.458361
$490$	−21.4694	−0.969891
$491$	−39.3498	−1.77583	−0.887916	−	0.460006i	$-0.847847\pi$
$491$	−39.3498	−1.77583	−0.887916	+	0.460006i	$0.847847\pi$
$492$	16.4758	0.742787
$493$	4.59220	0.206822
$494$	−14.0978	−0.634290
$495$	−0.887690	−0.0398987
$496$	5.15501	0.231467
$497$	1.81198	0.0812785
$498$	6.66901	0.298845
$499$	23.4405	1.04934	0.524671	−	0.851305i	$-0.324188\pi$
$499$	23.4405	1.04934	0.524671	+	0.851305i	$0.324188\pi$
$500$	11.9837	0.535929
$501$	−20.8599	−0.931952
$502$	8.76719	0.391299
$503$	14.8603	0.662587	0.331294	−	0.943528i	$-0.392515\pi$
$503$	14.8603	0.662587	0.331294	+	0.943528i	$0.392515\pi$
$504$	2.43154	0.108309
$505$	19.7035	0.876795
$506$	0.0928639	0.00412830
$507$	−45.9849	−2.04226
$508$	−6.22322	−0.276111
$509$	−21.0569	−0.933331	−0.466665	−	0.884434i	$-0.654545\pi$
$509$	−21.0569	−0.933331	−0.466665	+	0.884434i	$0.654545\pi$
$510$	6.63984	0.294017
$511$	15.0904	0.667558
$512$	1.00000	0.0441942
$513$	−10.6588	−0.470598
$514$	−3.34900	−0.147718
$515$	−18.5908	−0.819210
$516$	−7.68882	−0.338481
$517$	−3.36119	−0.147825
$518$	15.1247	0.664539
$519$	−33.0961	−1.45276
$520$	−10.0172	−0.439283
$521$	−44.1962	−1.93627	−0.968136	−	0.250424i	$-0.919430\pi$
$521$	−44.1962	−1.93627	−0.968136	+	0.250424i	$0.919430\pi$
$522$	1.15547	0.0505737
$523$	7.73832	0.338373	0.169187	−	0.985584i	$-0.445886\pi$
$523$	7.73832	0.338373	0.169187	+	0.985584i	$0.445886\pi$
$524$	−4.02557	−0.175858
$525$	19.5769	0.854408
$526$	20.4658	0.892352
$527$	11.1079	0.483869
$528$	−1.88207	−0.0819065
$529$	−22.9914	−0.999625
$530$	0.653739	0.0283966
$531$	−1.84359	−0.0800048
$532$	−10.3338	−0.448029
$533$	−53.5599	−2.31994
$534$	33.0015	1.42812
$535$	−19.8933	−0.860064
$536$	−14.0518	−0.606944
$537$	−43.7681	−1.88873
$538$	−24.5024	−1.05637
$539$	13.1130	0.564818
$540$	−7.57362	−0.325917
$541$	12.5490	0.539524	0.269762	−	0.962927i	$-0.413055\pi$
$541$	12.5490	0.539524	0.269762	+	0.962927i	$0.413055\pi$
$542$	28.7064	1.23305
$543$	−43.3661	−1.86102
$544$	2.15479	0.0923857
$545$	−8.29125	−0.355158
$546$	−51.6419	−2.21007
$547$	10.9154	0.466711	0.233355	−	0.972392i	$-0.425029\pi$
$547$	10.9154	0.466711	0.233355	+	0.972392i	$0.425029\pi$
$548$	11.7296	0.501063
$549$	4.17791	0.178309
$550$	−2.31937	−0.0988984
$551$	−4.91067	−0.209201
$552$	−0.174776	−0.00743896
$553$	9.02607	0.383828
$554$	−26.0067	−1.10492
$555$	10.3920	0.441117
$556$	4.75055	0.201468
$557$	−13.9969	−0.593069	−0.296534	−	0.955022i	$-0.595831\pi$
$557$	−13.9969	−0.593069	−0.296534	+	0.955022i	$0.595831\pi$
$558$	2.79494	0.118319
$559$	24.9950	1.05717
$560$	−7.34272	−0.310286
$561$	−4.05545	−0.171221
$562$	−2.06677	−0.0871815
$563$	39.0531	1.64589	0.822947	−	0.568118i	$-0.192328\pi$
$563$	39.0531	1.64589	0.822947	+	0.568118i	$0.192328\pi$
$564$	6.32598	0.266372
$565$	−23.8607	−1.00383
$566$	12.3639	0.519693
$567$	−46.3391	−1.94606
$568$	0.404031	0.0169528
$569$	−16.4874	−0.691190	−0.345595	−	0.938384i	$-0.612323\pi$
$569$	−16.4874	−0.691190	−0.345595	+	0.938384i	$0.612323\pi$
$570$	−7.10030	−0.297399
$571$	16.9401	0.708923	0.354462	−	0.935071i	$-0.384664\pi$
$571$	16.9401	0.708923	0.354462	+	0.935071i	$0.384664\pi$
$572$	6.11826	0.255817
$573$	18.0867	0.755581
$574$	−39.2600	−1.63868
$575$	−0.215386	−0.00898222
$576$	0.542179	0.0225908
$577$	15.1849	0.632156	0.316078	−	0.948733i	$-0.397634\pi$
$577$	15.1849	0.632156	0.316078	+	0.948733i	$0.397634\pi$
$578$	−12.3569	−0.513979
$579$	−39.1912	−1.62873
$580$	−3.48928	−0.144884
$581$	−15.8915	−0.659290
$582$	−14.0350	−0.581769
$583$	−0.399288	−0.0165368
$584$	3.36481	0.139237
$585$	−5.43112	−0.224549
$586$	22.9858	0.949533
$587$	1.45881	0.0602114	0.0301057	−	0.999547i	$-0.490416\pi$
$587$	1.45881	0.0602114	0.0301057	+	0.999547i	$0.490416\pi$
$588$	−24.6796	−1.01777
$589$	−11.8782	−0.489435
$590$	5.56722	0.229199
$591$	−1.88207	−0.0774179
$592$	3.37246	0.138607
$593$	7.79478	0.320093	0.160047	−	0.987109i	$-0.448836\pi$
$593$	7.79478	0.320093	0.160047	+	0.987109i	$0.448836\pi$
$594$	4.62579	0.189798
$595$	−15.8220	−0.648638
$596$	−12.3142	−0.504410
$597$	19.8893	0.814017
$598$	0.568166	0.0232340
$599$	−34.8057	−1.42212	−0.711061	−	0.703130i	$-0.751785\pi$
$599$	−34.8057	−1.42212	−0.711061	+	0.703130i	$0.751785\pi$
$600$	4.36522	0.178209
$601$	−22.3429	−0.911387	−0.455694	−	0.890137i	$-0.650609\pi$
$601$	−22.3429	−0.911387	−0.455694	+	0.890137i	$0.650609\pi$
$602$	18.3216	0.746732
$603$	−7.61858	−0.310253
$604$	−14.7569	−0.600449
$605$	−1.63726	−0.0665642
$606$	22.6496	0.920078
$607$	−22.8211	−0.926278	−0.463139	−	0.886286i	$-0.653277\pi$
$607$	−22.8211	−0.926278	−0.463139	+	0.886286i	$0.653277\pi$
$608$	−2.30422	−0.0934483
$609$	−17.9883	−0.728924
$610$	−12.6164	−0.510821
$611$	−20.5646	−0.831956
$612$	1.16828	0.0472249
$613$	10.5636	0.426661	0.213331	−	0.976980i	$-0.431569\pi$
$613$	10.5636	0.426661	0.213331	+	0.976980i	$0.431569\pi$
$614$	12.5610	0.506921
$615$	−26.9752	−1.08775
$616$	4.48475	0.180696
$617$	−19.1997	−0.772952	−0.386476	−	0.922300i	$-0.626308\pi$
$617$	−19.1997	−0.772952	−0.386476	+	0.922300i	$0.626308\pi$
$618$	−21.3706	−0.859651
$619$	33.0927	1.33011	0.665055	−	0.746795i	$-0.268408\pi$
$619$	33.0927	1.33011	0.665055	+	0.746795i	$0.268408\pi$
$620$	−8.44009	−0.338962
$621$	0.429568	0.0172380
$622$	−25.8453	−1.03630
$623$	−78.6389	−3.15060
$624$	−11.5150	−0.460968
$625$	−8.02363	−0.320945
$626$	−3.58407	−0.143248
$627$	4.33669	0.173191
$628$	11.7765	0.469934
$629$	7.26693	0.289751
$630$	−3.98107	−0.158610
$631$	−11.8185	−0.470489	−0.235244	−	0.971936i	$-0.575589\pi$
$631$	−11.8185	−0.470489	−0.235244	+	0.971936i	$0.575589\pi$
$632$	2.01261	0.0800574
$633$	14.3101	0.568776
$634$	−16.2971	−0.647241
$635$	10.1890	0.404340
$636$	0.751487	0.0297984
$637$	80.2289	3.17879
$638$	2.13117	0.0843737
$639$	0.219057	0.00866578
$640$	−1.63726	−0.0647185
$641$	24.9251	0.984481	0.492241	−	0.870459i	$-0.336178\pi$
$641$	24.9251	0.984481	0.492241	+	0.870459i	$0.336178\pi$
$642$	−22.8678	−0.902521
$643$	1.73987	0.0686138	0.0343069	−	0.999411i	$-0.489078\pi$
$643$	1.73987	0.0686138	0.0343069	+	0.999411i	$0.489078\pi$
$644$	0.416472	0.0164113
$645$	12.5886	0.495676
$646$	−4.96509	−0.195349
$647$	−15.5354	−0.610761	−0.305380	−	0.952230i	$-0.598784\pi$
$647$	−15.5354	−0.610761	−0.305380	+	0.952230i	$0.598784\pi$
$648$	−10.3326	−0.405902
$649$	−3.40033	−0.133474
$650$	−14.1905	−0.556599
$651$	−43.5114	−1.70535
$652$	5.38552	0.210913
$653$	20.1805	0.789722	0.394861	−	0.918741i	$-0.370793\pi$
$653$	20.1805	0.789722	0.394861	+	0.918741i	$0.370793\pi$
$654$	−9.53098	−0.372691
$655$	6.59091	0.257528
$656$	−8.75411	−0.341790
$657$	1.82433	0.0711740
$658$	−15.0741	−0.587650
$659$	45.2358	1.76214	0.881069	−	0.472988i	$-0.156825\pi$
$659$	45.2358	1.76214	0.881069	+	0.472988i	$0.156825\pi$
$660$	3.08144	0.119945
$661$	−4.26810	−0.166010	−0.0830049	−	0.996549i	$-0.526452\pi$
$661$	−4.26810	−0.166010	−0.0830049	+	0.996549i	$0.526452\pi$
$662$	−11.9211	−0.463326
$663$	−24.8123	−0.963631
$664$	−3.54345	−0.137512
$665$	16.9192	0.656099
$666$	1.82848	0.0708521
$667$	0.197908	0.00766304
$668$	11.0835	0.428834
$669$	4.64076	0.179422
$670$	23.0064	0.888816
$671$	7.70576	0.297478
$672$	−8.44061	−0.325604
$673$	6.87296	0.264933	0.132467	−	0.991187i	$-0.457710\pi$
$673$	6.87296	0.264933	0.132467	+	0.991187i	$0.457710\pi$
$674$	−13.5551	−0.522122
$675$	−10.7289	−0.412957
$676$	24.4332	0.939737
$677$	−12.5778	−0.483405	−0.241703	−	0.970350i	$-0.577706\pi$
$677$	−12.5778	−0.483405	−0.241703	+	0.970350i	$0.577706\pi$
$678$	−27.4284	−1.05338
$679$	33.4438	1.28346
$680$	−3.52795	−0.135291
$681$	−40.5457	−1.55372
$682$	5.15501	0.197395
$683$	−27.6723	−1.05885	−0.529426	−	0.848356i	$-0.677593\pi$
$683$	−27.6723	−1.05885	−0.529426	+	0.848356i	$0.677593\pi$
$684$	−1.24930	−0.0477681
$685$	−19.2044	−0.733762
$686$	27.4154	1.04672
$687$	39.4415	1.50479
$688$	4.08530	0.155751
$689$	−2.44295	−0.0930690
$690$	0.286154	0.0108937
$691$	33.7087	1.28234	0.641169	−	0.767400i	$-0.278450\pi$
$691$	33.7087	1.28234	0.641169	+	0.767400i	$0.278450\pi$
$692$	17.5850	0.668480
$693$	2.43154	0.0923666
$694$	−18.3761	−0.697547
$695$	−7.77789	−0.295032
$696$	−4.01100	−0.152037
$697$	−18.8632	−0.714495
$698$	−14.7319	−0.557609
$699$	−28.2494	−1.06849
$700$	−10.4018	−0.393152
$701$	−26.8678	−1.01478	−0.507391	−	0.861716i	$-0.669390\pi$
$701$	−26.8678	−1.01478	−0.507391	+	0.861716i	$0.669390\pi$
$702$	28.3018	1.06818
$703$	−7.77088	−0.293084
$704$	1.00000	0.0376889
$705$	−10.3573	−0.390078
$706$	−7.31924	−0.275463
$707$	−53.9715	−2.02981
$708$	6.39964	0.240513
$709$	−44.1551	−1.65828	−0.829139	−	0.559042i	$-0.811169\pi$
$709$	−44.1551	−1.65828	−0.829139	+	0.559042i	$0.811169\pi$
$710$	−0.661505	−0.0248258
$711$	1.09120	0.0409231
$712$	−17.5347	−0.657141
$713$	0.478714	0.0179280
$714$	−18.1877	−0.680658
$715$	−10.0172	−0.374622
$716$	23.2553	0.869093
$717$	−30.0155	−1.12095
$718$	−34.6731	−1.29399
$719$	−14.4825	−0.540107	−0.270053	−	0.962845i	$-0.587041\pi$
$719$	−14.4825	−0.540107	−0.270053	+	0.962845i	$0.587041\pi$
$720$	−0.887690	−0.0330822
$721$	50.9237	1.89650
$722$	−13.6906	−0.509511
$723$	44.3443	1.64918
$724$	23.0417	0.856340
$725$	−4.94297	−0.183577
$726$	−1.88207	−0.0698501
$727$	−10.6111	−0.393543	−0.196771	−	0.980449i	$-0.563046\pi$
$727$	−10.6111	−0.393543	−0.196771	+	0.980449i	$0.563046\pi$
$728$	27.4389	1.01695
$729$	20.5160	0.759852
$730$	−5.50908	−0.203900
$731$	8.80295	0.325589
$732$	−14.5028	−0.536038
$733$	6.14048	0.226804	0.113402	−	0.993549i	$-0.463825\pi$
$733$	6.14048	0.226804	0.113402	+	0.993549i	$0.463825\pi$
$734$	10.2339	0.377738
$735$	40.4070	1.49043
$736$	0.0928639	0.00342301
$737$	−14.0518	−0.517604
$738$	−4.74630	−0.174714
$739$	2.48586	0.0914437	0.0457219	−	0.998954i	$-0.485441\pi$
$739$	2.48586	0.0914437	0.0457219	+	0.998954i	$0.485441\pi$
$740$	−5.52160	−0.202978
$741$	26.5330	0.974715
$742$	−1.79071	−0.0657390
$743$	−5.18482	−0.190213	−0.0951064	−	0.995467i	$-0.530319\pi$
$743$	−5.18482	−0.190213	−0.0951064	+	0.995467i	$0.530319\pi$
$744$	−9.70207	−0.355695
$745$	20.1616	0.738663
$746$	25.4963	0.933486
$747$	−1.92118	−0.0702925
$748$	2.15479	0.0787868
$749$	54.4914	1.99107
$750$	−22.5542	−0.823563
$751$	−22.9872	−0.838816	−0.419408	−	0.907798i	$-0.637762\pi$
$751$	−22.9872	−0.838816	−0.419408	+	0.907798i	$0.637762\pi$
$752$	−3.36119	−0.122570
$753$	−16.5004	−0.601310
$754$	13.0390	0.474854
$755$	24.1609	0.879305
$756$	20.7455	0.754507
$757$	−37.0413	−1.34629	−0.673145	−	0.739510i	$-0.735057\pi$
$757$	−37.0413	−1.34629	−0.673145	+	0.739510i	$0.735057\pi$
$758$	5.02046	0.182351
$759$	−0.174776	−0.00634397
$760$	3.77261	0.136847
$761$	19.4707	0.705811	0.352906	−	0.935659i	$-0.385194\pi$
$761$	19.4707	0.705811	0.352906	+	0.935659i	$0.385194\pi$
$762$	11.7125	0.424300
$763$	22.7112	0.822202
$764$	−9.60999	−0.347677
$765$	−1.91278	−0.0691567
$766$	1.38308	0.0499727
$767$	−20.8041	−0.751192
$768$	−1.88207	−0.0679133
$769$	−41.7500	−1.50554	−0.752772	−	0.658282i	$-0.771284\pi$
$769$	−41.7500	−1.50554	−0.752772	+	0.658282i	$0.771284\pi$
$770$	−7.34272	−0.264613
$771$	6.30304	0.226998
$772$	20.8235	0.749454
$773$	−8.08792	−0.290902	−0.145451	−	0.989365i	$-0.546463\pi$
$773$	−8.08792	−0.290902	−0.145451	+	0.989365i	$0.546463\pi$
$774$	2.21497	0.0796154
$775$	−11.9564	−0.429486
$776$	7.45722	0.267699
$777$	−28.4656	−1.02120
$778$	14.9766	0.536938
$779$	20.1714	0.722714
$780$	18.8530	0.675047
$781$	0.404031	0.0144574
$782$	0.200102	0.00715562
$783$	9.85832	0.352307
$784$	13.1130	0.468322
$785$	−19.2812	−0.688177
$786$	7.57639	0.270241
$787$	−8.72846	−0.311136	−0.155568	−	0.987825i	$-0.549721\pi$
$787$	−8.72846	−0.311136	−0.155568	+	0.987825i	$0.549721\pi$
$788$	1.00000	0.0356235
$789$	−38.5180	−1.37128
$790$	−3.29517	−0.117237
$791$	65.3587	2.32389
$792$	0.542179	0.0192655
$793$	47.1459	1.67420
$794$	4.27518	0.151720
$795$	−1.23038	−0.0436371
$796$	−10.5678	−0.374566
$797$	2.56969	0.0910231	0.0455115	−	0.998964i	$-0.485508\pi$
$797$	2.56969	0.0910231	0.0455115	+	0.998964i	$0.485508\pi$
$798$	19.4490	0.688487
$799$	−7.24264	−0.256226
$800$	−2.31937	−0.0820023
$801$	−9.50696	−0.335912
$802$	−30.2593	−1.06849
$803$	3.36481	0.118742
$804$	26.4464	0.932692
$805$	−0.681873	−0.0240329
$806$	31.5397	1.11094
$807$	46.1152	1.62333
$808$	−12.0344	−0.423370
$809$	−45.2303	−1.59021	−0.795105	−	0.606471i	$-0.792585\pi$
$809$	−45.2303	−1.59021	−0.795105	+	0.606471i	$0.792585\pi$
$810$	16.9171	0.594408
$811$	40.9910	1.43939	0.719695	−	0.694291i	$-0.244282\pi$
$811$	40.9910	1.43939	0.719695	+	0.694291i	$0.244282\pi$
$812$	9.55775	0.335411
$813$	−54.0274	−1.89482
$814$	3.37246	0.118205
$815$	−8.81750	−0.308863
$816$	−4.05545	−0.141969
$817$	−9.41342	−0.329334
$818$	12.3362	0.431324
$819$	14.8768	0.519838
$820$	14.3328	0.500522
$821$	−1.46821	−0.0512409	−0.0256205	−	0.999672i	$-0.508156\pi$
$821$	−1.46821	−0.0512409	−0.0256205	+	0.999672i	$0.508156\pi$
$822$	−22.0759	−0.769984
$823$	12.9638	0.451890	0.225945	−	0.974140i	$-0.427453\pi$
$823$	12.9638	0.451890	0.225945	+	0.974140i	$0.427453\pi$
$824$	11.3548	0.395565
$825$	4.36522	0.151977
$826$	−15.2496	−0.530602
$827$	0.401117	0.0139482	0.00697410	−	0.999976i	$-0.497780\pi$
$827$	0.401117	0.0139482	0.00697410	+	0.999976i	$0.497780\pi$
$828$	0.0503489	0.00174974
$829$	−19.6948	−0.684028	−0.342014	−	0.939695i	$-0.611109\pi$
$829$	−19.6948	−0.684028	−0.342014	+	0.939695i	$0.611109\pi$
$830$	5.80155	0.201375
$831$	48.9464	1.69793
$832$	6.11826	0.212113
$833$	28.2557	0.979003
$834$	−8.94085	−0.309596
$835$	−18.1466	−0.627989
$836$	−2.30422	−0.0796930
$837$	23.8459	0.824237
$838$	12.8114	0.442562
$839$	54.0223	1.86506	0.932528	−	0.361098i	$-0.117598\pi$
$839$	54.0223	1.86506	0.932528	+	0.361098i	$0.117598\pi$
$840$	13.8195	0.476818
$841$	−24.4581	−0.843384
$842$	−6.11634	−0.210783
$843$	3.88981	0.133972
$844$	−7.60340	−0.261720
$845$	−40.0035	−1.37616
$846$	−1.82237	−0.0626543
$847$	4.48475	0.154098
$848$	−0.399288	−0.0137116
$849$	−23.2697	−0.798614
$850$	−4.99775	−0.171422
$851$	0.313180	0.0107357
$852$	−0.760414	−0.0260514
$853$	28.4294	0.973405	0.486702	−	0.873568i	$-0.338200\pi$
$853$	28.4294	0.973405	0.486702	+	0.873568i	$0.338200\pi$
$854$	34.5585	1.18257
$855$	2.04543	0.0699522
$856$	12.1504	0.415291
$857$	−2.97678	−0.101685	−0.0508425	−	0.998707i	$-0.516191\pi$
$857$	−2.97678	−0.101685	−0.0508425	+	0.998707i	$0.516191\pi$
$858$	−11.5150	−0.393115
$859$	−11.6904	−0.398870	−0.199435	−	0.979911i	$-0.563911\pi$
$859$	−11.6904	−0.398870	−0.199435	+	0.979911i	$0.563911\pi$
$860$	−6.68871	−0.228083
$861$	73.8900	2.51816
$862$	−9.65479	−0.328843
$863$	3.03927	0.103458	0.0517290	−	0.998661i	$-0.483527\pi$
$863$	3.03927	0.103458	0.0517290	+	0.998661i	$0.483527\pi$
$864$	4.62579	0.157372
$865$	−28.7912	−0.978929
$866$	3.29335	0.111913
$867$	23.2565	0.789833
$868$	23.1189	0.784708
$869$	2.01261	0.0682732
$870$	6.56705	0.222644
$871$	−85.9724	−2.91307
$872$	5.06410	0.171492
$873$	4.04315	0.136840
$874$	−0.213978	−0.00723793
$875$	53.7441	1.81688
$876$	−6.33280	−0.213966
$877$	0.522008	0.0176269	0.00881347	−	0.999961i	$-0.497195\pi$
$877$	0.522008	0.0176269	0.00881347	+	0.999961i	$0.497195\pi$
$878$	20.2420	0.683136
$879$	−43.2608	−1.45915
$880$	−1.63726	−0.0551921
$881$	−30.4830	−1.02700	−0.513499	−	0.858090i	$-0.671651\pi$
$881$	−30.4830	−1.02700	−0.513499	+	0.858090i	$0.671651\pi$
$882$	7.10961	0.239393
$883$	−0.465843	−0.0156769	−0.00783843	−	0.999969i	$-0.502495\pi$
$883$	−0.465843	−0.0156769	−0.00783843	+	0.999969i	$0.502495\pi$
$884$	13.1835	0.443411
$885$	−10.4779	−0.352210
$886$	−11.5791	−0.389007
$887$	20.0270	0.672442	0.336221	−	0.941783i	$-0.390851\pi$
$887$	20.0270	0.672442	0.336221	+	0.941783i	$0.390851\pi$
$888$	−6.34720	−0.212998
$889$	−27.9096	−0.936059
$890$	28.7089	0.962325
$891$	−10.3326	−0.346154
$892$	−2.46578	−0.0825603
$893$	7.74490	0.259173
$894$	23.1762	0.775127
$895$	−38.0751	−1.27271
$896$	4.48475	0.149825
$897$	−1.06933	−0.0357038
$898$	−10.6927	−0.356819
$899$	10.9862	0.366409
$900$	−1.25752	−0.0419172
$901$	−0.860380	−0.0286634
$902$	−8.75411	−0.291480
$903$	−34.4825	−1.14750
$904$	14.5735	0.484709
$905$	−37.7254	−1.25403
$906$	27.7735	0.922712
$907$	−50.0233	−1.66100	−0.830498	−	0.557021i	$-0.811944\pi$
$907$	−50.0233	−1.66100	−0.830498	+	0.557021i	$0.811944\pi$
$908$	21.5432	0.714935
$909$	−6.52483	−0.216415
$910$	−44.9247	−1.48924
$911$	−27.9726	−0.926772	−0.463386	−	0.886157i	$-0.653366\pi$
$911$	−27.9726	−0.926772	−0.463386	+	0.886157i	$0.653366\pi$
$912$	4.33669	0.143602
$913$	−3.54345	−0.117271
$914$	2.48493	0.0821943
$915$	23.7448	0.784980
$916$	−20.9565	−0.692421
$917$	−18.0537	−0.596185
$918$	9.96757	0.328979
$919$	18.7950	0.619991	0.309996	−	0.950738i	$-0.399672\pi$
$919$	18.7950	0.619991	0.309996	+	0.950738i	$0.399672\pi$
$920$	−0.152042	−0.00501269
$921$	−23.6407	−0.778987
$922$	32.3886	1.06666
$923$	2.47197	0.0813659
$924$	−8.44061	−0.277676
$925$	−7.82200	−0.257186
$926$	−36.1502	−1.18797
$927$	6.15636	0.202201
$928$	2.13117	0.0699589
$929$	−33.2130	−1.08968	−0.544841	−	0.838539i	$-0.683410\pi$
$929$	−33.2130	−1.08968	−0.544841	+	0.838539i	$0.683410\pi$
$930$	15.8848	0.520884
$931$	−30.2152	−0.990264
$932$	15.0098	0.491662
$933$	48.6427	1.59249
$934$	26.0821	0.853431
$935$	−3.52795	−0.115376
$936$	3.31720	0.108426
$937$	−43.1196	−1.40866	−0.704328	−	0.709875i	$-0.748751\pi$
$937$	−43.1196	−1.40866	−0.704328	+	0.709875i	$0.748751\pi$
$938$	−63.0187	−2.05763
$939$	6.74546	0.220130
$940$	5.50314	0.179493
$941$	47.6131	1.55214	0.776072	−	0.630645i	$-0.217210\pi$
$941$	47.6131	1.55214	0.776072	+	0.630645i	$0.217210\pi$
$942$	−22.1642	−0.722149
$943$	−0.812940	−0.0264730
$944$	−3.40033	−0.110671
$945$	−33.9658	−1.10491
$946$	4.08530	0.132825
$947$	−9.28462	−0.301710	−0.150855	−	0.988556i	$-0.548203\pi$
$947$	−9.28462	−0.301710	−0.150855	+	0.988556i	$0.548203\pi$
$948$	−3.78787	−0.123024
$949$	20.5868	0.668276
$950$	5.34434	0.173393
$951$	30.6723	0.994617
$952$	9.66368	0.313202
$953$	−11.4282	−0.370195	−0.185097	−	0.982720i	$-0.559260\pi$
$953$	−11.4282	−0.370195	−0.185097	+	0.982720i	$0.559260\pi$
$954$	−0.216486	−0.00700899
$955$	15.7341	0.509143
$956$	15.9482	0.515800
$957$	−4.01100	−0.129657
$958$	24.0006	0.775423
$959$	52.6043	1.69868
$960$	3.08144	0.0994530
$961$	−4.42592	−0.142772
$962$	20.6336	0.665254
$963$	6.58768	0.212285
$964$	−23.5615	−0.758863
$965$	−34.0935	−1.09751
$966$	−0.783828	−0.0252192
$967$	19.7888	0.636365	0.318183	−	0.948029i	$-0.396927\pi$
$967$	19.7888	0.636365	0.318183	+	0.948029i	$0.396927\pi$
$968$	1.00000	0.0321412
$969$	9.34464	0.300193
$970$	−12.2094	−0.392021
$971$	44.6251	1.43209	0.716043	−	0.698056i	$-0.245951\pi$
$971$	44.6251	1.43209	0.716043	+	0.698056i	$0.245951\pi$
$972$	5.56926	0.178634
$973$	21.3050	0.683008
$974$	−26.6842	−0.855017
$975$	26.7076	0.855327
$976$	7.70576	0.246655
$977$	−14.8991	−0.476664	−0.238332	−	0.971184i	$-0.576601\pi$
$977$	−14.8991	−0.476664	−0.238332	+	0.971184i	$0.576601\pi$
$978$	−10.1359	−0.324111
$979$	−17.5347	−0.560412
$980$	−21.4694	−0.685816
$981$	2.74565	0.0876619
$982$	−39.3498	−1.25570
$983$	21.5618	0.687714	0.343857	−	0.939022i	$-0.388266\pi$
$983$	21.5618	0.687714	0.343857	+	0.939022i	$0.388266\pi$
$984$	16.4758	0.525230
$985$	−1.63726	−0.0521675
$986$	4.59220	0.146246
$987$	28.3705	0.903042
$988$	−14.0978	−0.448511
$989$	0.379377	0.0120635
$990$	−0.887690	−0.0282126
$991$	−42.6982	−1.35635	−0.678176	−	0.734899i	$-0.737230\pi$
$991$	−42.6982	−1.35635	−0.678176	+	0.734899i	$0.737230\pi$
$992$	5.15501	0.163672
$993$	22.4363	0.711995
$994$	1.81198	0.0574725
$995$	17.3023	0.548519
$996$	6.66901	0.211316
$997$	−23.7654	−0.752657	−0.376329	−	0.926486i	$-0.622814\pi$
$997$	−23.7654	−0.752657	−0.376329	+	0.926486i	$0.622814\pi$
$998$	23.4405	0.741996
$999$	15.6003	0.493571

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.g.1.5	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.g.1.5	✓	26	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.88207 q^{3} +1.00000 q^{4} -1.63726 q^{5} -1.88207 q^{6} +4.48475 q^{7} +1.00000 q^{8} +0.542179 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.88207 q^{3} +1.00000 q^{4} -1.63726 q^{5} -1.88207 q^{6} +4.48475 q^{7} +1.00000 q^{8} +0.542179 q^{9} -1.63726 q^{10} +1.00000 q^{11} -1.88207 q^{12} +6.11826 q^{13} +4.48475 q^{14} +3.08144 q^{15} +1.00000 q^{16} +2.15479 q^{17} +0.542179 q^{18} -2.30422 q^{19} -1.63726 q^{20} -8.44061 q^{21} +1.00000 q^{22} +0.0928639 q^{23} -1.88207 q^{24} -2.31937 q^{25} +6.11826 q^{26} +4.62579 q^{27} +4.48475 q^{28} +2.13117 q^{29} +3.08144 q^{30} +5.15501 q^{31} +1.00000 q^{32} -1.88207 q^{33} +2.15479 q^{34} -7.34272 q^{35} +0.542179 q^{36} +3.37246 q^{37} -2.30422 q^{38} -11.5150 q^{39} -1.63726 q^{40} -8.75411 q^{41} -8.44061 q^{42} +4.08530 q^{43} +1.00000 q^{44} -0.887690 q^{45} +0.0928639 q^{46} -3.36119 q^{47} -1.88207 q^{48} +13.1130 q^{49} -2.31937 q^{50} -4.05545 q^{51} +6.11826 q^{52} -0.399288 q^{53} +4.62579 q^{54} -1.63726 q^{55} +4.48475 q^{56} +4.33669 q^{57} +2.13117 q^{58} -3.40033 q^{59} +3.08144 q^{60} +7.70576 q^{61} +5.15501 q^{62} +2.43154 q^{63} +1.00000 q^{64} -10.0172 q^{65} -1.88207 q^{66} -14.0518 q^{67} +2.15479 q^{68} -0.174776 q^{69} -7.34272 q^{70} +0.404031 q^{71} +0.542179 q^{72} +3.36481 q^{73} +3.37246 q^{74} +4.36522 q^{75} -2.30422 q^{76} +4.48475 q^{77} -11.5150 q^{78} +2.01261 q^{79} -1.63726 q^{80} -10.3326 q^{81} -8.75411 q^{82} -3.54345 q^{83} -8.44061 q^{84} -3.52795 q^{85} +4.08530 q^{86} -4.01100 q^{87} +1.00000 q^{88} -17.5347 q^{89} -0.887690 q^{90} +27.4389 q^{91} +0.0928639 q^{92} -9.70207 q^{93} -3.36119 q^{94} +3.77261 q^{95} -1.88207 q^{96} +7.45722 q^{97} +13.1130 q^{98} +0.542179 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9 + 13 * q^10 + 26 * q^11 + 12 * q^12 + 24 * q^13 + 13 * q^14 + 12 * q^15 + 26 * q^16 + q^17 + 38 * q^18 + 24 * q^19 + 13 * q^20 + 5 * q^21 + 26 * q^22 + 19 * q^23 + 12 * q^24 + 35 * q^25 + 24 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 12 * q^30 + 34 * q^31 + 26 * q^32 + 12 * q^33 + q^34 + 14 * q^35 + 38 * q^36 + 15 * q^37 + 24 * q^38 + 3 * q^39 + 13 * q^40 - 9 * q^41 + 5 * q^42 + 6 * q^43 + 26 * q^44 + 22 * q^45 + 19 * q^46 + 34 * q^47 + 12 * q^48 + 53 * q^49 + 35 * q^50 - 2 * q^51 + 24 * q^52 + 6 * q^53 + 39 * q^54 + 13 * q^55 + 13 * q^56 - 16 * q^57 + 5 * q^58 + 50 * q^59 + 12 * q^60 + 26 * q^61 + 34 * q^62 + 2 * q^63 + 26 * q^64 - 5 * q^65 + 12 * q^66 + 18 * q^67 + q^68 + 15 * q^69 + 14 * q^70 + 23 * q^71 + 38 * q^72 + 37 * q^73 + 15 * q^74 + 18 * q^75 + 24 * q^76 + 13 * q^77 + 3 * q^78 + 10 * q^79 + 13 * q^80 + 50 * q^81 - 9 * q^82 + 7 * q^83 + 5 * q^84 - 7 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^88 + 3 * q^89 + 22 * q^90 + 31 * q^91 + 19 * q^92 + 52 * q^93 + 34 * q^94 + 9 * q^95 + 12 * q^96 - 9 * q^97 + 53 * q^98 + 38 * q^99

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