LMFDB - Embedded newform 8015.2.a.l.1.45

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.45
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.36075 q^{2} -0.257132 q^{3} -0.148369 q^{4} -1.00000 q^{5} -0.349892 q^{6} -1.00000 q^{7} -2.92339 q^{8} -2.93388 q^{9} +O(q^{10})$	\(q+1.36075 q^{2} -0.257132 q^{3} -0.148369 q^{4} -1.00000 q^{5} -0.349892 q^{6} -1.00000 q^{7} -2.92339 q^{8} -2.93388 q^{9} -1.36075 q^{10} +2.45315 q^{11} +0.0381503 q^{12} -6.54712 q^{13} -1.36075 q^{14} +0.257132 q^{15} -3.68125 q^{16} +2.41213 q^{17} -3.99227 q^{18} -1.82799 q^{19} +0.148369 q^{20} +0.257132 q^{21} +3.33812 q^{22} -3.40426 q^{23} +0.751696 q^{24} +1.00000 q^{25} -8.90897 q^{26} +1.52579 q^{27} +0.148369 q^{28} -6.44943 q^{29} +0.349892 q^{30} -5.10199 q^{31} +0.837522 q^{32} -0.630784 q^{33} +3.28230 q^{34} +1.00000 q^{35} +0.435296 q^{36} -4.22793 q^{37} -2.48743 q^{38} +1.68347 q^{39} +2.92339 q^{40} +2.29311 q^{41} +0.349892 q^{42} +3.23324 q^{43} -0.363970 q^{44} +2.93388 q^{45} -4.63233 q^{46} -5.65402 q^{47} +0.946567 q^{48} +1.00000 q^{49} +1.36075 q^{50} -0.620236 q^{51} +0.971386 q^{52} +2.83506 q^{53} +2.07622 q^{54} -2.45315 q^{55} +2.92339 q^{56} +0.470034 q^{57} -8.77605 q^{58} -2.81329 q^{59} -0.0381503 q^{60} +13.5670 q^{61} -6.94252 q^{62} +2.93388 q^{63} +8.50216 q^{64} +6.54712 q^{65} -0.858337 q^{66} -6.06202 q^{67} -0.357884 q^{68} +0.875344 q^{69} +1.36075 q^{70} +5.47026 q^{71} +8.57687 q^{72} +4.63235 q^{73} -5.75315 q^{74} -0.257132 q^{75} +0.271216 q^{76} -2.45315 q^{77} +2.29078 q^{78} -0.283484 q^{79} +3.68125 q^{80} +8.40932 q^{81} +3.12034 q^{82} +16.5586 q^{83} -0.0381503 q^{84} -2.41213 q^{85} +4.39963 q^{86} +1.65836 q^{87} -7.17150 q^{88} -15.1817 q^{89} +3.99227 q^{90} +6.54712 q^{91} +0.505085 q^{92} +1.31189 q^{93} -7.69369 q^{94} +1.82799 q^{95} -0.215354 q^{96} +18.0448 q^{97} +1.36075 q^{98} -7.19726 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	1.36075	0.962193	0.481097	−	0.876668i	$-0.340239\pi$
$2$	1.36075	0.962193	0.481097	+	0.876668i	$0.340239\pi$
$3$	−0.257132	−0.148455	−0.0742276	−	0.997241i	$-0.523649\pi$
$3$	−0.257132	−0.148455	−0.0742276	+	0.997241i	$0.523649\pi$
$4$	−0.148369	−0.0741843
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.349892	−0.142843
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.92339	−1.03357
$9$	−2.93388	−0.977961
$10$	−1.36075	−0.430306
$11$	2.45315	0.739653	0.369826	−	0.929101i	$-0.379417\pi$
$11$	2.45315	0.739653	0.369826	+	0.929101i	$0.379417\pi$
$12$	0.0381503	0.0110130
$13$	−6.54712	−1.81584	−0.907922	−	0.419139i	$-0.862332\pi$
$13$	−6.54712	−1.81584	−0.907922	+	0.419139i	$0.862332\pi$
$14$	−1.36075	−0.363675
$15$	0.257132	0.0663912
$16$	−3.68125	−0.920312
$17$	2.41213	0.585027	0.292514	−	0.956261i	$-0.405508\pi$
$17$	2.41213	0.585027	0.292514	+	0.956261i	$0.405508\pi$
$18$	−3.99227	−0.940987
$19$	−1.82799	−0.419369	−0.209685	−	0.977769i	$-0.567244\pi$
$19$	−1.82799	−0.419369	−0.209685	+	0.977769i	$0.567244\pi$
$20$	0.148369	0.0331762
$21$	0.257132	0.0561108
$22$	3.33812	0.711689
$23$	−3.40426	−0.709837	−0.354918	−	0.934897i	$-0.615491\pi$
$23$	−3.40426	−0.709837	−0.354918	+	0.934897i	$0.615491\pi$
$24$	0.751696	0.153439
$25$	1.00000	0.200000
$26$	−8.90897	−1.74719
$27$	1.52579	0.293639
$28$	0.148369	0.0280390
$29$	−6.44943	−1.19763	−0.598815	−	0.800887i	$-0.704362\pi$
$29$	−6.44943	−1.19763	−0.598815	+	0.800887i	$0.704362\pi$
$30$	0.349892	0.0638812
$31$	−5.10199	−0.916344	−0.458172	−	0.888863i	$-0.651496\pi$
$31$	−5.10199	−0.916344	−0.458172	+	0.888863i	$0.651496\pi$
$32$	0.837522	0.148054
$33$	−0.630784	−0.109805
$34$	3.28230	0.562909
$35$	1.00000	0.169031
$36$	0.435296	0.0725493
$37$	−4.22793	−0.695068	−0.347534	−	0.937667i	$-0.612981\pi$
$37$	−4.22793	−0.695068	−0.347534	+	0.937667i	$0.612981\pi$
$38$	−2.48743	−0.403514
$39$	1.68347	0.269572
$40$	2.92339	0.462228
$41$	2.29311	0.358124	0.179062	−	0.983838i	$-0.442694\pi$
$41$	2.29311	0.358124	0.179062	+	0.983838i	$0.442694\pi$
$42$	0.349892	0.0539894
$43$	3.23324	0.493065	0.246533	−	0.969135i	$-0.420709\pi$
$43$	3.23324	0.493065	0.246533	+	0.969135i	$0.420709\pi$
$44$	−0.363970	−0.0548706
$45$	2.93388	0.437357
$46$	−4.63233	−0.683000
$47$	−5.65402	−0.824723	−0.412362	−	0.911020i	$-0.635296\pi$
$47$	−5.65402	−0.824723	−0.412362	+	0.911020i	$0.635296\pi$
$48$	0.946567	0.136625
$49$	1.00000	0.142857
$50$	1.36075	0.192439
$51$	−0.620236	−0.0868504
$52$	0.971386	0.134707
$53$	2.83506	0.389426	0.194713	−	0.980860i	$-0.437622\pi$
$53$	2.83506	0.389426	0.194713	+	0.980860i	$0.437622\pi$
$54$	2.07622	0.282537
$55$	−2.45315	−0.330783
$56$	2.92339	0.390654
$57$	0.470034	0.0622576
$58$	−8.77605	−1.15235
$59$	−2.81329	−0.366260	−0.183130	−	0.983089i	$-0.558623\pi$
$59$	−2.81329	−0.366260	−0.183130	+	0.983089i	$0.558623\pi$
$60$	−0.0381503	−0.00492518
$61$	13.5670	1.73708	0.868540	−	0.495619i	$-0.165059\pi$
$61$	13.5670	1.73708	0.868540	+	0.495619i	$0.165059\pi$
$62$	−6.94252	−0.881700
$63$	2.93388	0.369635
$64$	8.50216	1.06277
$65$	6.54712	0.812070
$66$	−0.858337	−0.105654
$67$	−6.06202	−0.740593	−0.370297	−	0.928914i	$-0.620744\pi$
$67$	−6.06202	−0.740593	−0.370297	+	0.928914i	$0.620744\pi$
$68$	−0.357884	−0.0433998
$69$	0.875344	0.105379
$70$	1.36075	0.162640
$71$	5.47026	0.649201	0.324600	−	0.945851i	$-0.394770\pi$
$71$	5.47026	0.649201	0.324600	+	0.945851i	$0.394770\pi$
$72$	8.57687	1.01079
$73$	4.63235	0.542176	0.271088	−	0.962555i	$-0.412617\pi$
$73$	4.63235	0.542176	0.271088	+	0.962555i	$0.412617\pi$
$74$	−5.75315	−0.668790
$75$	−0.257132	−0.0296911
$76$	0.271216	0.0311106
$77$	−2.45315	−0.279562
$78$	2.29078	0.259380
$79$	−0.283484	−0.0318944	−0.0159472	−	0.999873i	$-0.505076\pi$
$79$	−0.283484	−0.0318944	−0.0159472	+	0.999873i	$0.505076\pi$
$80$	3.68125	0.411576
$81$	8.40932	0.934369
$82$	3.12034	0.344584
$83$	16.5586	1.81754	0.908772	−	0.417293i	$-0.137021\pi$
$83$	16.5586	1.81754	0.908772	+	0.417293i	$0.137021\pi$
$84$	−0.0381503	−0.00416254
$85$	−2.41213	−0.261632
$86$	4.39963	0.474424
$87$	1.65836	0.177794
$88$	−7.17150	−0.764485
$89$	−15.1817	−1.60925	−0.804627	−	0.593781i	$-0.797635\pi$
$89$	−15.1817	−1.60925	−0.804627	+	0.593781i	$0.797635\pi$
$90$	3.99227	0.420822
$91$	6.54712	0.686325
$92$	0.505085	0.0526587
$93$	1.31189	0.136036
$94$	−7.69369	−0.793543
$95$	1.82799	0.187548
$96$	−0.215354	−0.0219795
$97$	18.0448	1.83217	0.916085	−	0.400984i	$-0.131332\pi$
$97$	18.0448	1.83217	0.916085	+	0.400984i	$0.131332\pi$
$98$	1.36075	0.137456
$99$	−7.19726	−0.723352
$100$	−0.148369	−0.0148369
$101$	−13.1455	−1.30803	−0.654014	−	0.756482i	$-0.726916\pi$
$101$	−13.1455	−1.30803	−0.654014	+	0.756482i	$0.726916\pi$
$102$	−0.843984	−0.0835668
$103$	−15.2547	−1.50309	−0.751545	−	0.659681i	$-0.770691\pi$
$103$	−15.2547	−1.50309	−0.751545	+	0.659681i	$0.770691\pi$
$104$	19.1397	1.87681
$105$	−0.257132	−0.0250935
$106$	3.85780	0.374703
$107$	1.60109	0.154783	0.0773914	−	0.997001i	$-0.475341\pi$
$107$	1.60109	0.154783	0.0773914	+	0.997001i	$0.475341\pi$
$108$	−0.226379	−0.0217834
$109$	−6.34412	−0.607656	−0.303828	−	0.952727i	$-0.598265\pi$
$109$	−6.34412	−0.607656	−0.303828	+	0.952727i	$0.598265\pi$
$110$	−3.33812	−0.318277
$111$	1.08714	0.103186
$112$	3.68125	0.347845
$113$	−12.8340	−1.20732	−0.603660	−	0.797242i	$-0.706292\pi$
$113$	−12.8340	−1.20732	−0.603660	+	0.797242i	$0.706292\pi$
$114$	0.639598	0.0599038
$115$	3.40426	0.317449
$116$	0.956893	0.0888453
$117$	19.2085	1.77582
$118$	−3.82818	−0.352413
$119$	−2.41213	−0.221120
$120$	−0.751696	−0.0686201
$121$	−4.98205	−0.452914
$122$	18.4613	1.67141
$123$	−0.589632	−0.0531654
$124$	0.756975	0.0679783
$125$	−1.00000	−0.0894427
$126$	3.99227	0.355660
$127$	5.69003	0.504908	0.252454	−	0.967609i	$-0.418762\pi$
$127$	5.69003	0.504908	0.252454	+	0.967609i	$0.418762\pi$
$128$	9.89423	0.874535
$129$	−0.831371	−0.0731981
$130$	8.90897	0.781368
$131$	10.0008	0.873772	0.436886	−	0.899517i	$-0.356081\pi$
$131$	10.0008	0.873772	0.436886	+	0.899517i	$0.356081\pi$
$132$	0.0935884	0.00814583
$133$	1.82799	0.158507
$134$	−8.24887	−0.712594
$135$	−1.52579	−0.131319
$136$	−7.05158	−0.604668
$137$	−1.29589	−0.110715	−0.0553575	−	0.998467i	$-0.517630\pi$
$137$	−1.29589	−0.110715	−0.0553575	+	0.998467i	$0.517630\pi$
$138$	1.19112	0.101395
$139$	−15.5953	−1.32278	−0.661389	−	0.750043i	$-0.730033\pi$
$139$	−15.5953	−1.32278	−0.661389	+	0.750043i	$0.730033\pi$
$140$	−0.148369	−0.0125394
$141$	1.45383	0.122435
$142$	7.44364	0.624656
$143$	−16.0611	−1.34309
$144$	10.8004	0.900030
$145$	6.44943	0.535596
$146$	6.30346	0.521678
$147$	−0.257132	−0.0212079
$148$	0.627292	0.0515631
$149$	4.95261	0.405733	0.202867	−	0.979206i	$-0.434974\pi$
$149$	4.95261	0.405733	0.202867	+	0.979206i	$0.434974\pi$
$150$	−0.349892	−0.0285685
$151$	9.06032	0.737319	0.368659	−	0.929565i	$-0.379817\pi$
$151$	9.06032	0.737319	0.368659	+	0.929565i	$0.379817\pi$
$152$	5.34392	0.433449
$153$	−7.07691	−0.572134
$154$	−3.33812	−0.268993
$155$	5.10199	0.409802
$156$	−0.249775	−0.0199980
$157$	13.0286	1.03980	0.519899	−	0.854228i	$-0.325970\pi$
$157$	13.0286	1.03980	0.519899	+	0.854228i	$0.325970\pi$
$158$	−0.385750	−0.0306886
$159$	−0.728986	−0.0578123
$160$	−0.837522	−0.0662120
$161$	3.40426	0.268293
$162$	11.4430	0.899043
$163$	−14.8154	−1.16043	−0.580216	−	0.814463i	$-0.697032\pi$
$163$	−14.8154	−1.16043	−0.580216	+	0.814463i	$0.697032\pi$
$164$	−0.340226	−0.0265672
$165$	0.630784	0.0491064
$166$	22.5321	1.74883
$167$	21.1167	1.63406	0.817030	−	0.576595i	$-0.195619\pi$
$167$	21.1167	1.63406	0.817030	+	0.576595i	$0.195619\pi$
$168$	−0.751696	−0.0579946
$169$	29.8648	2.29729
$170$	−3.28230	−0.251741
$171$	5.36310	0.410127
$172$	−0.479712	−0.0365777
$173$	−1.60426	−0.121969	−0.0609847	−	0.998139i	$-0.519424\pi$
$173$	−1.60426	−0.121969	−0.0609847	+	0.998139i	$0.519424\pi$
$174$	2.25660	0.171073
$175$	−1.00000	−0.0755929
$176$	−9.03066	−0.680712
$177$	0.723388	0.0543732
$178$	−20.6584	−1.54841
$179$	21.2800	1.59054	0.795271	−	0.606254i	$-0.207329\pi$
$179$	21.2800	1.59054	0.795271	+	0.606254i	$0.207329\pi$
$180$	−0.435296	−0.0324450
$181$	17.7462	1.31906	0.659532	−	0.751677i	$-0.270755\pi$
$181$	17.7462	1.31906	0.659532	+	0.751677i	$0.270755\pi$
$182$	8.90897	0.660377
$183$	−3.48852	−0.257879
$184$	9.95196	0.733668
$185$	4.22793	0.310844
$186$	1.78514	0.130893
$187$	5.91732	0.432717
$188$	0.838878	0.0611815
$189$	−1.52579	−0.110985
$190$	2.48743	0.180457
$191$	−0.375150	−0.0271449	−0.0135724	−	0.999908i	$-0.504320\pi$
$191$	−0.375150	−0.0271449	−0.0135724	+	0.999908i	$0.504320\pi$
$192$	−2.18618	−0.157774
$193$	−25.4886	−1.83471	−0.917355	−	0.398070i	$-0.869680\pi$
$193$	−25.4886	−1.83471	−0.917355	+	0.398070i	$0.869680\pi$
$194$	24.5544	1.76290
$195$	−1.68347	−0.120556
$196$	−0.148369	−0.0105978
$197$	−15.4933	−1.10385	−0.551925	−	0.833894i	$-0.686106\pi$
$197$	−15.4933	−1.10385	−0.551925	+	0.833894i	$0.686106\pi$
$198$	−9.79364	−0.696004
$199$	−23.6269	−1.67486	−0.837432	−	0.546542i	$-0.815944\pi$
$199$	−23.6269	−1.67486	−0.837432	+	0.546542i	$0.815944\pi$
$200$	−2.92339	−0.206715
$201$	1.55874	0.109945
$202$	−17.8877	−1.25858
$203$	6.44943	0.452662
$204$	0.0920235	0.00644293
$205$	−2.29311	−0.160158
$206$	−20.7578	−1.44626
$207$	9.98770	0.694193
$208$	24.1016	1.67114
$209$	−4.48433	−0.310188
$210$	−0.349892	−0.0241448
$211$	10.2622	0.706479	0.353239	−	0.935533i	$-0.385080\pi$
$211$	10.2622	0.706479	0.353239	+	0.935533i	$0.385080\pi$
$212$	−0.420634	−0.0288893
$213$	−1.40658	−0.0963773
$214$	2.17867	0.148931
$215$	−3.23324	−0.220505
$216$	−4.46048	−0.303497
$217$	5.10199	0.346346
$218$	−8.63274	−0.584683
$219$	−1.19113	−0.0804889
$220$	0.363970	0.0245389
$221$	−15.7925	−1.06232
$222$	1.47932	0.0992853
$223$	25.3651	1.69857	0.849285	−	0.527935i	$-0.177034\pi$
$223$	25.3651	1.69857	0.849285	+	0.527935i	$0.177034\pi$
$224$	−0.837522	−0.0559593
$225$	−2.93388	−0.195592
$226$	−17.4638	−1.16168
$227$	18.0852	1.20035	0.600177	−	0.799867i	$-0.295097\pi$
$227$	18.0852	1.20035	0.600177	+	0.799867i	$0.295097\pi$
$228$	−0.0697383	−0.00461853
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	4.63233	0.305447
$231$	0.630784	0.0415025
$232$	18.8542	1.23784
$233$	22.2252	1.45602	0.728011	−	0.685566i	$-0.240445\pi$
$233$	22.2252	1.45602	0.728011	+	0.685566i	$0.240445\pi$
$234$	26.1379	1.70869
$235$	5.65402	0.368827
$236$	0.417404	0.0271707
$237$	0.0728928	0.00473489
$238$	−3.28230	−0.212760
$239$	18.8965	1.22231	0.611156	−	0.791510i	$-0.290705\pi$
$239$	18.8965	1.22231	0.611156	+	0.791510i	$0.290705\pi$
$240$	−0.946567	−0.0611007
$241$	17.0858	1.10059	0.550297	−	0.834969i	$-0.314514\pi$
$241$	17.0858	1.10059	0.550297	+	0.834969i	$0.314514\pi$
$242$	−6.77931	−0.435791
$243$	−6.73968	−0.432351
$244$	−2.01292	−0.128864
$245$	−1.00000	−0.0638877
$246$	−0.802340	−0.0511553
$247$	11.9681	0.761509
$248$	14.9151	0.947109
$249$	−4.25775	−0.269824
$250$	−1.36075	−0.0860612
$251$	−3.38783	−0.213838	−0.106919	−	0.994268i	$-0.534099\pi$
$251$	−3.38783	−0.213838	−0.106919	+	0.994268i	$0.534099\pi$
$252$	−0.435296	−0.0274211
$253$	−8.35116	−0.525033
$254$	7.74269	0.485819
$255$	0.620236	0.0388407
$256$	−3.54076	−0.221298
$257$	5.98187	0.373139	0.186569	−	0.982442i	$-0.440263\pi$
$257$	5.98187	0.373139	0.186569	+	0.982442i	$0.440263\pi$
$258$	−1.13129	−0.0704307
$259$	4.22793	0.262711
$260$	−0.971386	−0.0602428
$261$	18.9219	1.17124
$262$	13.6085	0.840738
$263$	14.6794	0.905171	0.452586	−	0.891721i	$-0.350502\pi$
$263$	14.6794	0.905171	0.452586	+	0.891721i	$0.350502\pi$
$264$	1.84402	0.113492
$265$	−2.83506	−0.174157
$266$	2.48743	0.152514
$267$	3.90369	0.238902
$268$	0.899413	0.0549404
$269$	−19.5727	−1.19337	−0.596683	−	0.802477i	$-0.703515\pi$
$269$	−19.5727	−1.19337	−0.596683	+	0.802477i	$0.703515\pi$
$270$	−2.07622	−0.126354
$271$	−30.3199	−1.84180	−0.920900	−	0.389798i	$-0.872545\pi$
$271$	−30.3199	−1.84180	−0.920900	+	0.389798i	$0.872545\pi$
$272$	−8.87965	−0.538408
$273$	−1.68347	−0.101888
$274$	−1.76337	−0.106529
$275$	2.45315	0.147931
$276$	−0.129873	−0.00781747
$277$	−10.3698	−0.623063	−0.311531	−	0.950236i	$-0.600842\pi$
$277$	−10.3698	−0.623063	−0.311531	+	0.950236i	$0.600842\pi$
$278$	−21.2213	−1.27277
$279$	14.9686	0.896149
$280$	−2.92339	−0.174706
$281$	−5.60689	−0.334479	−0.167240	−	0.985916i	$-0.553485\pi$
$281$	−5.60689	−0.334479	−0.167240	+	0.985916i	$0.553485\pi$
$282$	1.97829	0.117806
$283$	16.9436	1.00719	0.503597	−	0.863939i	$-0.332010\pi$
$283$	16.9436	1.00719	0.503597	+	0.863939i	$0.332010\pi$
$284$	−0.811615	−0.0481605
$285$	−0.470034	−0.0278424
$286$	−21.8550	−1.29232
$287$	−2.29311	−0.135358
$288$	−2.45719	−0.144791
$289$	−11.1816	−0.657743
$290$	8.77605	0.515347
$291$	−4.63989	−0.271995
$292$	−0.687296	−0.0402209
$293$	20.8585	1.21856	0.609282	−	0.792953i	$-0.291458\pi$
$293$	20.8585	1.21856	0.609282	+	0.792953i	$0.291458\pi$
$294$	−0.349892	−0.0204061
$295$	2.81329	0.163796
$296$	12.3599	0.718403
$297$	3.74300	0.217191
$298$	6.73924	0.390394
$299$	22.2881	1.28895
$300$	0.0381503	0.00220261
$301$	−3.23324	−0.186361
$302$	12.3288	0.709443
$303$	3.38013	0.194184
$304$	6.72928	0.385951
$305$	−13.5670	−0.776846
$306$	−9.62987	−0.550503
$307$	−7.05883	−0.402868	−0.201434	−	0.979502i	$-0.564560\pi$
$307$	−7.05883	−0.402868	−0.201434	+	0.979502i	$0.564560\pi$
$308$	0.363970	0.0207391
$309$	3.92247	0.223142
$310$	6.94252	0.394308
$311$	29.2429	1.65821	0.829107	−	0.559089i	$-0.188849\pi$
$311$	29.2429	1.65821	0.829107	+	0.559089i	$0.188849\pi$
$312$	−4.92144	−0.278622
$313$	−4.35508	−0.246164	−0.123082	−	0.992397i	$-0.539278\pi$
$313$	−4.35508	−0.246164	−0.123082	+	0.992397i	$0.539278\pi$
$314$	17.7287	1.00049
$315$	−2.93388	−0.165306
$316$	0.0420601	0.00236606
$317$	8.45347	0.474794	0.237397	−	0.971413i	$-0.423706\pi$
$317$	8.45347	0.474794	0.237397	+	0.971413i	$0.423706\pi$
$318$	−0.991965	−0.0556266
$319$	−15.8214	−0.885830
$320$	−8.50216	−0.475285
$321$	−0.411691	−0.0229783
$322$	4.63233	0.258150
$323$	−4.40934	−0.245343
$324$	−1.24768	−0.0693155
$325$	−6.54712	−0.363169
$326$	−20.1600	−1.11656
$327$	1.63128	0.0902098
$328$	−6.70365	−0.370147
$329$	5.65402	0.311716
$330$	0.858337	0.0472499
$331$	3.24624	0.178429	0.0892146	−	0.996012i	$-0.471564\pi$
$331$	3.24624	0.178429	0.0892146	+	0.996012i	$0.471564\pi$
$332$	−2.45678	−0.134833
$333$	12.4043	0.679749
$334$	28.7345	1.57228
$335$	6.06202	0.331203
$336$	−0.946567	−0.0516395
$337$	11.9661	0.651833	0.325916	−	0.945399i	$-0.394327\pi$
$337$	11.9661	0.651833	0.325916	+	0.945399i	$0.394327\pi$
$338$	40.6384	2.21044
$339$	3.30003	0.179233
$340$	0.357884	0.0194090
$341$	−12.5159	−0.677777
$342$	7.29783	0.394621
$343$	−1.00000	−0.0539949
$344$	−9.45202	−0.509619
$345$	−0.875344	−0.0471269
$346$	−2.18299	−0.117358
$347$	22.7992	1.22393	0.611963	−	0.790887i	$-0.290380\pi$
$347$	22.7992	1.22393	0.611963	+	0.790887i	$0.290380\pi$
$348$	−0.246048	−0.0131896
$349$	1.06720	0.0571260	0.0285630	−	0.999592i	$-0.490907\pi$
$349$	1.06720	0.0571260	0.0285630	+	0.999592i	$0.490907\pi$
$350$	−1.36075	−0.0727350
$351$	−9.98954	−0.533202
$352$	2.05457	0.109509
$353$	−1.72208	−0.0916573	−0.0458286	−	0.998949i	$-0.514593\pi$
$353$	−1.72208	−0.0916573	−0.0458286	+	0.998949i	$0.514593\pi$
$354$	0.984348	0.0523175
$355$	−5.47026	−0.290331
$356$	2.25248	0.119381
$357$	0.620236	0.0328264
$358$	28.9567	1.53041
$359$	−6.23114	−0.328867	−0.164433	−	0.986388i	$-0.552580\pi$
$359$	−6.23114	−0.328867	−0.164433	+	0.986388i	$0.552580\pi$
$360$	−8.57687	−0.452041
$361$	−15.6585	−0.824129
$362$	24.1481	1.26919
$363$	1.28105	0.0672374
$364$	−0.971386	−0.0509145
$365$	−4.63235	−0.242469
$366$	−4.74699	−0.248129
$367$	−15.1775	−0.792257	−0.396128	−	0.918195i	$-0.629646\pi$
$367$	−15.1775	−0.792257	−0.396128	+	0.918195i	$0.629646\pi$
$368$	12.5319	0.653272
$369$	−6.72772	−0.350231
$370$	5.75315	0.299092
$371$	−2.83506	−0.147189
$372$	−0.194642	−0.0100917
$373$	9.06530	0.469384	0.234692	−	0.972070i	$-0.424592\pi$
$373$	9.06530	0.469384	0.234692	+	0.972070i	$0.424592\pi$
$374$	8.05197	0.416357
$375$	0.257132	0.0132782
$376$	16.5289	0.852412
$377$	42.2252	2.17471
$378$	−2.07622	−0.106789
$379$	−10.3267	−0.530448	−0.265224	−	0.964187i	$-0.585446\pi$
$379$	−10.3267	−0.530448	−0.265224	+	0.964187i	$0.585446\pi$
$380$	−0.271216	−0.0139131
$381$	−1.46309	−0.0749563
$382$	−0.510484	−0.0261186
$383$	−1.14557	−0.0585360	−0.0292680	−	0.999572i	$-0.509318\pi$
$383$	−1.14557	−0.0585360	−0.0292680	+	0.999572i	$0.509318\pi$
$384$	−2.54412	−0.129829
$385$	2.45315	0.125024
$386$	−34.6835	−1.76535
$387$	−9.48596	−0.482199
$388$	−2.67728	−0.135918
$389$	−12.6708	−0.642435	−0.321218	−	0.947005i	$-0.604092\pi$
$389$	−12.6708	−0.642435	−0.321218	+	0.947005i	$0.604092\pi$
$390$	−2.29078	−0.115998
$391$	−8.21151	−0.415274
$392$	−2.92339	−0.147653
$393$	−2.57152	−0.129716
$394$	−21.0824	−1.06212
$395$	0.283484	0.0142636
$396$	1.06785	0.0536613
$397$	−15.7512	−0.790529	−0.395264	−	0.918567i	$-0.629347\pi$
$397$	−15.7512	−0.790529	−0.395264	+	0.918567i	$0.629347\pi$
$398$	−32.1502	−1.61154
$399$	−0.470034	−0.0235312
$400$	−3.68125	−0.184062
$401$	−30.5113	−1.52366	−0.761832	−	0.647775i	$-0.775700\pi$
$401$	−30.5113	−1.52366	−0.761832	+	0.647775i	$0.775700\pi$
$402$	2.12105	0.105788
$403$	33.4033	1.66394
$404$	1.95038	0.0970351
$405$	−8.40932	−0.417862
$406$	8.77605	0.435548
$407$	−10.3718	−0.514109
$408$	1.81319	0.0897662
$409$	−9.50078	−0.469783	−0.234892	−	0.972022i	$-0.575474\pi$
$409$	−9.50078	−0.469783	−0.234892	+	0.972022i	$0.575474\pi$
$410$	−3.12034	−0.154103
$411$	0.333214	0.0164362
$412$	2.26332	0.111506
$413$	2.81329	0.138433
$414$	13.5907	0.667948
$415$	−16.5586	−0.812830
$416$	−5.48336	−0.268844
$417$	4.01006	0.196373
$418$	−6.10204	−0.298460
$419$	−37.1451	−1.81466	−0.907329	−	0.420421i	$-0.861882\pi$
$419$	−37.1451	−1.81466	−0.907329	+	0.420421i	$0.861882\pi$
$420$	0.0381503	0.00186154
$421$	−29.8844	−1.45648	−0.728239	−	0.685324i	$-0.759661\pi$
$421$	−29.8844	−1.45648	−0.728239	+	0.685324i	$0.759661\pi$
$422$	13.9643	0.679769
$423$	16.5882	0.806547
$424$	−8.28799	−0.402500
$425$	2.41213	0.117005
$426$	−1.91400	−0.0927335
$427$	−13.5670	−0.656554
$428$	−0.237551	−0.0114825
$429$	4.12982	0.199389
$430$	−4.39963	−0.212169
$431$	10.6556	0.513262	0.256631	−	0.966509i	$-0.417387\pi$
$431$	10.6556	0.513262	0.256631	+	0.966509i	$0.417387\pi$
$432$	−5.61682	−0.270239
$433$	−13.5004	−0.648789	−0.324395	−	0.945922i	$-0.605161\pi$
$433$	−13.5004	−0.648789	−0.324395	+	0.945922i	$0.605161\pi$
$434$	6.94252	0.333251
$435$	−1.65836	−0.0795121
$436$	0.941268	0.0450785
$437$	6.22295	0.297684
$438$	−1.62082	−0.0774459
$439$	−23.5744	−1.12514	−0.562571	−	0.826749i	$-0.690188\pi$
$439$	−23.5744	−1.12514	−0.562571	+	0.826749i	$0.690188\pi$
$440$	7.17150	0.341888
$441$	−2.93388	−0.139709
$442$	−21.4896	−1.02216
$443$	−3.22835	−0.153383	−0.0766917	−	0.997055i	$-0.524436\pi$
$443$	−3.22835	−0.153383	−0.0766917	+	0.997055i	$0.524436\pi$
$444$	−0.161297	−0.00765481
$445$	15.1817	0.719680
$446$	34.5154	1.63435
$447$	−1.27347	−0.0602333
$448$	−8.50216	−0.401689
$449$	0.148445	0.00700554	0.00350277	−	0.999994i	$-0.498885\pi$
$449$	0.148445	0.00700554	0.00350277	+	0.999994i	$0.498885\pi$
$450$	−3.99227	−0.188197
$451$	5.62535	0.264887
$452$	1.90416	0.0895642
$453$	−2.32970	−0.109459
$454$	24.6093	1.15497
$455$	−6.54712	−0.306934
$456$	−1.37409	−0.0643477
$457$	−29.1669	−1.36437	−0.682184	−	0.731180i	$-0.738970\pi$
$457$	−29.1669	−1.36437	−0.682184	+	0.731180i	$0.738970\pi$
$458$	1.36075	0.0635835
$459$	3.68041	0.171787
$460$	−0.505085	−0.0235497
$461$	−1.40469	−0.0654230	−0.0327115	−	0.999465i	$-0.510414\pi$
$461$	−1.40469	−0.0654230	−0.0327115	+	0.999465i	$0.510414\pi$
$462$	0.858337	0.0399334
$463$	11.1139	0.516505	0.258253	−	0.966077i	$-0.416853\pi$
$463$	11.1139	0.516505	0.258253	+	0.966077i	$0.416853\pi$
$464$	23.7420	1.10219
$465$	−1.31189	−0.0608372
$466$	30.2429	1.40097
$467$	27.1339	1.25561	0.627804	−	0.778372i	$-0.283954\pi$
$467$	27.1339	1.25561	0.627804	+	0.778372i	$0.283954\pi$
$468$	−2.84993	−0.131738
$469$	6.06202	0.279918
$470$	7.69369	0.354883
$471$	−3.35008	−0.154363
$472$	8.22434	0.378556
$473$	7.93164	0.364697
$474$	0.0991886	0.00455588
$475$	−1.82799	−0.0838739
$476$	0.357884	0.0164036
$477$	−8.31775	−0.380844
$478$	25.7133	1.17610
$479$	19.9724	0.912563	0.456282	−	0.889835i	$-0.349181\pi$
$479$	19.9724	0.912563	0.456282	+	0.889835i	$0.349181\pi$
$480$	0.215354	0.00982951
$481$	27.6808	1.26213
$482$	23.2495	1.05898
$483$	−0.875344	−0.0398295
$484$	0.739180	0.0335991
$485$	−18.0448	−0.819371
$486$	−9.17100	−0.416005
$487$	1.33355	0.0604289	0.0302145	−	0.999543i	$-0.490381\pi$
$487$	1.33355	0.0604289	0.0302145	+	0.999543i	$0.490381\pi$
$488$	−39.6616	−1.79540
$489$	3.80952	0.172272
$490$	−1.36075	−0.0614723
$491$	−28.1494	−1.27036	−0.635182	−	0.772362i	$-0.719075\pi$
$491$	−28.1494	−1.27036	−0.635182	+	0.772362i	$0.719075\pi$
$492$	0.0874829	0.00394403
$493$	−15.5569	−0.700646
$494$	16.2855	0.732719
$495$	7.19726	0.323493
$496$	18.7817	0.843323
$497$	−5.47026	−0.245375
$498$	−5.79372	−0.259623
$499$	37.6786	1.68672	0.843362	−	0.537346i	$-0.180573\pi$
$499$	37.6786	1.68672	0.843362	+	0.537346i	$0.180573\pi$
$500$	0.148369	0.00663524
$501$	−5.42978	−0.242585
$502$	−4.60998	−0.205754
$503$	−2.49071	−0.111055	−0.0555276	−	0.998457i	$-0.517684\pi$
$503$	−2.49071	−0.111055	−0.0555276	+	0.998457i	$0.517684\pi$
$504$	−8.57687	−0.382044
$505$	13.1455	0.584968
$506$	−11.3638	−0.505183
$507$	−7.67919	−0.341045
$508$	−0.844221	−0.0374562
$509$	22.4737	0.996131	0.498065	−	0.867139i	$-0.334044\pi$
$509$	22.4737	0.996131	0.498065	+	0.867139i	$0.334044\pi$
$510$	0.843984	0.0373722
$511$	−4.63235	−0.204923
$512$	−24.6066	−1.08747
$513$	−2.78913	−0.123143
$514$	8.13981	0.359032
$515$	15.2547	0.672203
$516$	0.123349	0.00543015
$517$	−13.8702	−0.610009
$518$	5.75315	0.252779
$519$	0.412506	0.0181070
$520$	−19.1397	−0.839334
$521$	29.9008	1.30998	0.654988	−	0.755639i	$-0.272674\pi$
$521$	29.9008	1.30998	0.654988	+	0.755639i	$0.272674\pi$
$522$	25.7479	1.12695
$523$	26.3058	1.15027	0.575137	−	0.818057i	$-0.304949\pi$
$523$	26.3058	1.15027	0.575137	+	0.818057i	$0.304949\pi$
$524$	−1.48380	−0.0648202
$525$	0.257132	0.0112222
$526$	19.9750	0.870950
$527$	−12.3067	−0.536086
$528$	2.32207	0.101055
$529$	−11.4110	−0.496132
$530$	−3.85780	−0.167572
$531$	8.25388	0.358188
$532$	−0.271216	−0.0117587
$533$	−15.0133	−0.650297
$534$	5.31194	0.229870
$535$	−1.60109	−0.0692210
$536$	17.7216	0.765457
$537$	−5.47177	−0.236124
$538$	−26.6334	−1.14825
$539$	2.45315	0.105665
$540$	0.226379	0.00974182
$541$	−6.39561	−0.274969	−0.137484	−	0.990504i	$-0.543902\pi$
$541$	−6.39561	−0.274969	−0.137484	+	0.990504i	$0.543902\pi$
$542$	−41.2577	−1.77217
$543$	−4.56311	−0.195822
$544$	2.02021	0.0866159
$545$	6.34412	0.271752
$546$	−2.29078	−0.0980364
$547$	−41.1075	−1.75763	−0.878815	−	0.477163i	$-0.841665\pi$
$547$	−41.1075	−1.75763	−0.878815	+	0.477163i	$0.841665\pi$
$548$	0.192269	0.00821331
$549$	−39.8041	−1.69880
$550$	3.33812	0.142338
$551$	11.7895	0.502249
$552$	−2.55897	−0.108917
$553$	0.283484	0.0120550
$554$	−14.1107	−0.599507
$555$	−1.08714	−0.0461464
$556$	2.31386	0.0981294
$557$	−5.28448	−0.223911	−0.111955	−	0.993713i	$-0.535711\pi$
$557$	−5.28448	−0.223911	−0.111955	+	0.993713i	$0.535711\pi$
$558$	20.3685	0.862269
$559$	−21.1684	−0.895329
$560$	−3.68125	−0.155561
$561$	−1.52153	−0.0642391
$562$	−7.62956	−0.321834
$563$	−0.231516	−0.00975723	−0.00487861	−	0.999988i	$-0.501553\pi$
$563$	−0.231516	−0.00975723	−0.00487861	+	0.999988i	$0.501553\pi$
$564$	−0.215703	−0.00908271
$565$	12.8340	0.539930
$566$	23.0560	0.969115
$567$	−8.40932	−0.353158
$568$	−15.9917	−0.670996
$569$	36.9119	1.54743	0.773714	−	0.633535i	$-0.218397\pi$
$569$	36.9119	1.54743	0.773714	+	0.633535i	$0.218397\pi$
$570$	−0.639598	−0.0267898
$571$	−14.4711	−0.605598	−0.302799	−	0.953055i	$-0.597921\pi$
$571$	−14.4711	−0.605598	−0.302799	+	0.953055i	$0.597921\pi$
$572$	2.38296	0.0996364
$573$	0.0964631	0.00402980
$574$	−3.12034	−0.130241
$575$	−3.40426	−0.141967
$576$	−24.9443	−1.03935
$577$	29.7407	1.23812	0.619060	−	0.785344i	$-0.287514\pi$
$577$	29.7407	1.23812	0.619060	+	0.785344i	$0.287514\pi$
$578$	−15.2154	−0.632876
$579$	6.55394	0.272372
$580$	−0.956893	−0.0397328
$581$	−16.5586	−0.686967
$582$	−6.31372	−0.261712
$583$	6.95484	0.288040
$584$	−13.5422	−0.560378
$585$	−19.2085	−0.794173
$586$	28.3831	1.17249
$587$	9.11988	0.376418	0.188209	−	0.982129i	$-0.439732\pi$
$587$	9.11988	0.376418	0.188209	+	0.982129i	$0.439732\pi$
$588$	0.0381503	0.00157329
$589$	9.32638	0.384287
$590$	3.82818	0.157604
$591$	3.98381	0.163872
$592$	15.5641	0.639680
$593$	18.8927	0.775830	0.387915	−	0.921695i	$-0.373195\pi$
$593$	18.8927	0.775830	0.387915	+	0.921695i	$0.373195\pi$
$594$	5.09327	0.208979
$595$	2.41213	0.0988877
$596$	−0.734811	−0.0300990
$597$	6.07522	0.248642
$598$	30.3284	1.24022
$599$	−21.2020	−0.866291	−0.433146	−	0.901324i	$-0.642596\pi$
$599$	−21.2020	−0.866291	−0.433146	+	0.901324i	$0.642596\pi$
$600$	0.751696	0.0306879
$601$	27.7285	1.13107	0.565535	−	0.824724i	$-0.308670\pi$
$601$	27.7285	1.13107	0.565535	+	0.824724i	$0.308670\pi$
$602$	−4.39963	−0.179315
$603$	17.7853	0.724272
$604$	−1.34427	−0.0546974
$605$	4.98205	0.202549
$606$	4.59951	0.186842
$607$	−42.6469	−1.73098	−0.865492	−	0.500922i	$-0.832994\pi$
$607$	−42.6469	−1.73098	−0.865492	+	0.500922i	$0.832994\pi$
$608$	−1.53098	−0.0620895
$609$	−1.65836	−0.0672000
$610$	−18.4613	−0.747476
$611$	37.0175	1.49757
$612$	1.04999	0.0424433
$613$	−26.4348	−1.06769	−0.533845	−	0.845582i	$-0.679254\pi$
$613$	−26.4348	−1.06769	−0.533845	+	0.845582i	$0.679254\pi$
$614$	−9.60527	−0.387637
$615$	0.589632	0.0237763
$616$	7.17150	0.288948
$617$	12.3532	0.497323	0.248661	−	0.968591i	$-0.420009\pi$
$617$	12.3532	0.497323	0.248661	+	0.968591i	$0.420009\pi$
$618$	5.33749	0.214705
$619$	24.8927	1.00052	0.500260	−	0.865875i	$-0.333238\pi$
$619$	24.8927	1.00052	0.500260	+	0.865875i	$0.333238\pi$
$620$	−0.756975	−0.0304008
$621$	−5.19419	−0.208436
$622$	39.7922	1.59552
$623$	15.1817	0.608241
$624$	−6.19729	−0.248090
$625$	1.00000	0.0400000
$626$	−5.92616	−0.236857
$627$	1.15307	0.0460490
$628$	−1.93304	−0.0771366
$629$	−10.1983	−0.406634
$630$	−3.99227	−0.159056
$631$	−18.4029	−0.732609	−0.366305	−	0.930495i	$-0.619377\pi$
$631$	−18.4029	−0.732609	−0.366305	+	0.930495i	$0.619377\pi$
$632$	0.828732	0.0329652
$633$	−2.63874	−0.104881
$634$	11.5030	0.456844
$635$	−5.69003	−0.225802
$636$	0.108159	0.00428877
$637$	−6.54712	−0.259406
$638$	−21.5290	−0.852340
$639$	−16.0491	−0.634893
$640$	−9.89423	−0.391104
$641$	1.32388	0.0522902	0.0261451	−	0.999658i	$-0.491677\pi$
$641$	1.32388	0.0522902	0.0261451	+	0.999658i	$0.491677\pi$
$642$	−0.560207	−0.0221096
$643$	27.0779	1.06785	0.533924	−	0.845533i	$-0.320717\pi$
$643$	27.0779	1.06785	0.533924	+	0.845533i	$0.320717\pi$
$644$	−0.505085	−0.0199031
$645$	0.831371	0.0327352
$646$	−6.00000	−0.236067
$647$	39.3873	1.54848	0.774238	−	0.632895i	$-0.218133\pi$
$647$	39.3873	1.54848	0.774238	+	0.632895i	$0.218133\pi$
$648$	−24.5837	−0.965738
$649$	−6.90144	−0.270905
$650$	−8.90897	−0.349439
$651$	−1.31189	−0.0514168
$652$	2.19814	0.0860858
$653$	−22.4220	−0.877441	−0.438721	−	0.898624i	$-0.644568\pi$
$653$	−22.4220	−0.877441	−0.438721	+	0.898624i	$0.644568\pi$
$654$	2.21975	0.0867992
$655$	−10.0008	−0.390763
$656$	−8.44151	−0.329586
$657$	−13.5908	−0.530227
$658$	7.69369	0.299931
$659$	36.2517	1.41216	0.706082	−	0.708130i	$-0.250461\pi$
$659$	36.2517	1.41216	0.706082	+	0.708130i	$0.250461\pi$
$660$	−0.0935884	−0.00364293
$661$	−5.98017	−0.232602	−0.116301	−	0.993214i	$-0.537104\pi$
$661$	−5.98017	−0.232602	−0.116301	+	0.993214i	$0.537104\pi$
$662$	4.41731	0.171683
$663$	4.06076	0.157707
$664$	−48.4072	−1.87856
$665$	−1.82799	−0.0708864
$666$	16.8791	0.654050
$667$	21.9555	0.850122
$668$	−3.13306	−0.121222
$669$	−6.52217	−0.252162
$670$	8.24887	0.318682
$671$	33.2820	1.28484
$672$	0.215354	0.00830745
$673$	15.4410	0.595207	0.297604	−	0.954690i	$-0.403813\pi$
$673$	15.4410	0.595207	0.297604	+	0.954690i	$0.403813\pi$
$674$	16.2828	0.627189
$675$	1.52579	0.0587277
$676$	−4.43099	−0.170423
$677$	−17.4510	−0.670698	−0.335349	−	0.942094i	$-0.608854\pi$
$677$	−17.4510	−0.670698	−0.335349	+	0.942094i	$0.608854\pi$
$678$	4.49051	0.172457
$679$	−18.0448	−0.692495
$680$	7.05158	0.270416
$681$	−4.65027	−0.178199
$682$	−17.0310	−0.652152
$683$	−22.4917	−0.860619	−0.430310	−	0.902681i	$-0.641596\pi$
$683$	−22.4917	−0.860619	−0.430310	+	0.902681i	$0.641596\pi$
$684$	−0.795716	−0.0304250
$685$	1.29589	0.0495132
$686$	−1.36075	−0.0519535
$687$	−0.257132	−0.00981020
$688$	−11.9024	−0.453774
$689$	−18.5615	−0.707137
$690$	−1.19112	−0.0453452
$691$	−27.9142	−1.06191	−0.530953	−	0.847401i	$-0.678166\pi$
$691$	−27.9142	−1.06191	−0.530953	+	0.847401i	$0.678166\pi$
$692$	0.238021	0.00904821
$693$	7.19726	0.273401
$694$	31.0239	1.17765
$695$	15.5953	0.591565
$696$	−4.84801	−0.183764
$697$	5.53128	0.209512
$698$	1.45219	0.0549663
$699$	−5.71481	−0.216154
$700$	0.148369	0.00560780
$701$	−30.2996	−1.14440	−0.572199	−	0.820114i	$-0.693910\pi$
$701$	−30.2996	−1.14440	−0.572199	+	0.820114i	$0.693910\pi$
$702$	−13.5932	−0.513043
$703$	7.72861	0.291490
$704$	20.8571	0.786080
$705$	−1.45383	−0.0547544
$706$	−2.34332	−0.0881920
$707$	13.1455	0.494388
$708$	−0.107328	−0.00403363
$709$	40.9315	1.53721	0.768607	−	0.639721i	$-0.220950\pi$
$709$	40.9315	1.53721	0.768607	+	0.639721i	$0.220950\pi$
$710$	−7.44364	−0.279355
$711$	0.831708	0.0311915
$712$	44.3819	1.66328
$713$	17.3685	0.650455
$714$	0.843984	0.0315853
$715$	16.0611	0.600650
$716$	−3.15728	−0.117993
$717$	−4.85889	−0.181459
$718$	−8.47900	−0.316434
$719$	47.0285	1.75387	0.876934	−	0.480610i	$-0.159585\pi$
$719$	47.0285	1.75387	0.876934	+	0.480610i	$0.159585\pi$
$720$	−10.8004	−0.402506
$721$	15.2547	0.568115
$722$	−21.3072	−0.792972
$723$	−4.39331	−0.163389
$724$	−2.63298	−0.0978537
$725$	−6.44943	−0.239526
$726$	1.74318	0.0646954
$727$	−45.5396	−1.68897	−0.844485	−	0.535579i	$-0.820094\pi$
$727$	−45.5396	−1.68897	−0.844485	+	0.535579i	$0.820094\pi$
$728$	−19.1397	−0.709366
$729$	−23.4950	−0.870184
$730$	−6.30346	−0.233302
$731$	7.79900	0.288457
$732$	0.517586	0.0191305
$733$	−43.7539	−1.61609	−0.808044	−	0.589123i	$-0.799473\pi$
$733$	−43.7539	−1.61609	−0.808044	+	0.589123i	$0.799473\pi$
$734$	−20.6527	−0.762304
$735$	0.257132	0.00948446
$736$	−2.85114	−0.105094
$737$	−14.8710	−0.547782
$738$	−9.15472	−0.336990
$739$	−22.6412	−0.832872	−0.416436	−	0.909165i	$-0.636721\pi$
$739$	−22.6412	−0.832872	−0.416436	+	0.909165i	$0.636721\pi$
$740$	−0.627292	−0.0230597
$741$	−3.07737	−0.113050
$742$	−3.85780	−0.141624
$743$	3.15496	0.115744	0.0578721	−	0.998324i	$-0.481568\pi$
$743$	3.15496	0.115744	0.0578721	+	0.998324i	$0.481568\pi$
$744$	−3.83515	−0.140603
$745$	−4.95261	−0.181449
$746$	12.3356	0.451638
$747$	−48.5810	−1.77749
$748$	−0.877944	−0.0321008
$749$	−1.60109	−0.0585024
$750$	0.349892	0.0127762
$751$	3.29089	0.120086	0.0600432	−	0.998196i	$-0.480876\pi$
$751$	3.29089	0.120086	0.0600432	+	0.998196i	$0.480876\pi$
$752$	20.8139	0.759003
$753$	0.871120	0.0317454
$754$	57.4578	2.09249
$755$	−9.06032	−0.329739
$756$	0.226379	0.00823334
$757$	30.0841	1.09343	0.546713	−	0.837320i	$-0.315879\pi$
$757$	30.0841	1.09343	0.546713	+	0.837320i	$0.315879\pi$
$758$	−14.0520	−0.510393
$759$	2.14735	0.0779439
$760$	−5.34392	−0.193844
$761$	−44.6296	−1.61782	−0.808911	−	0.587931i	$-0.799943\pi$
$761$	−44.6296	−1.61782	−0.808911	+	0.587931i	$0.799943\pi$
$762$	−1.99089	−0.0721224
$763$	6.34412	0.229673
$764$	0.0556604	0.00201372
$765$	7.07691	0.255866
$766$	−1.55883	−0.0563229
$767$	18.4190	0.665071
$768$	0.910444	0.0328528
$769$	11.3535	0.409418	0.204709	−	0.978823i	$-0.434375\pi$
$769$	11.3535	0.409418	0.204709	+	0.978823i	$0.434375\pi$
$770$	3.33812	0.120297
$771$	−1.53813	−0.0553944
$772$	3.78171	0.136107
$773$	24.6584	0.886903	0.443451	−	0.896298i	$-0.353754\pi$
$773$	24.6584	0.886903	0.443451	+	0.896298i	$0.353754\pi$
$774$	−12.9080	−0.463968
$775$	−5.10199	−0.183269
$776$	−52.7519	−1.89368
$777$	−1.08714	−0.0390008
$778$	−17.2418	−0.618147
$779$	−4.19178	−0.150186
$780$	0.249775	0.00894336
$781$	13.4194	0.480183
$782$	−11.1738	−0.399574
$783$	−9.84049	−0.351671
$784$	−3.68125	−0.131473
$785$	−13.0286	−0.465011
$786$	−3.49919	−0.124812
$787$	32.2771	1.15055	0.575277	−	0.817959i	$-0.304894\pi$
$787$	32.2771	1.15055	0.575277	+	0.817959i	$0.304894\pi$
$788$	2.29871	0.0818883
$789$	−3.77455	−0.134377
$790$	0.385750	0.0137244
$791$	12.8340	0.456324
$792$	21.0404	0.747637
$793$	−88.8249	−3.15427
$794$	−21.4334	−0.760641
$795$	0.728986	0.0258545
$796$	3.50548	0.124248
$797$	−34.2727	−1.21400	−0.607000	−	0.794701i	$-0.707627\pi$
$797$	−34.2727	−1.21400	−0.607000	+	0.794701i	$0.707627\pi$
$798$	−0.639598	−0.0226415
$799$	−13.6382	−0.482486
$800$	0.837522	0.0296109
$801$	44.5412	1.57379
$802$	−41.5182	−1.46606
$803$	11.3639	0.401022
$804$	−0.231268	−0.00815619
$805$	−3.40426	−0.119984
$806$	45.4535	1.60103
$807$	5.03276	0.177161
$808$	38.4294	1.35194
$809$	21.5274	0.756863	0.378432	−	0.925629i	$-0.376464\pi$
$809$	21.5274	0.756863	0.378432	+	0.925629i	$0.376464\pi$
$810$	−11.4430	−0.402064
$811$	−41.4583	−1.45580	−0.727900	−	0.685684i	$-0.759503\pi$
$811$	−41.4583	−1.45580	−0.727900	+	0.685684i	$0.759503\pi$
$812$	−0.956893	−0.0335804
$813$	7.79621	0.273425
$814$	−14.1133	−0.494672
$815$	14.8154	0.518961
$816$	2.28324	0.0799295
$817$	−5.91033	−0.206776
$818$	−12.9282	−0.452022
$819$	−19.2085	−0.671199
$820$	0.340226	0.0118812
$821$	−20.0560	−0.699958	−0.349979	−	0.936758i	$-0.613811\pi$
$821$	−20.0560	−0.699958	−0.349979	+	0.936758i	$0.613811\pi$
$822$	0.453419	0.0158148
$823$	11.9200	0.415505	0.207753	−	0.978181i	$-0.433385\pi$
$823$	11.9200	0.415505	0.207753	+	0.978181i	$0.433385\pi$
$824$	44.5954	1.55355
$825$	−0.630784	−0.0219611
$826$	3.82818	0.133199
$827$	−9.97425	−0.346839	−0.173419	−	0.984848i	$-0.555482\pi$
$827$	−9.97425	−0.346839	−0.173419	+	0.984848i	$0.555482\pi$
$828$	−1.48186	−0.0514982
$829$	−2.21474	−0.0769211	−0.0384605	−	0.999260i	$-0.512245\pi$
$829$	−2.21474	−0.0769211	−0.0384605	+	0.999260i	$0.512245\pi$
$830$	−22.5321	−0.782100
$831$	2.66642	0.0924970
$832$	−55.6646	−1.92982
$833$	2.41213	0.0835753
$834$	5.45667	0.188949
$835$	−21.1167	−0.730774
$836$	0.665334	0.0230110
$837$	−7.78457	−0.269074
$838$	−50.5451	−1.74605
$839$	−2.20808	−0.0762312	−0.0381156	−	0.999273i	$-0.512136\pi$
$839$	−2.20808	−0.0762312	−0.0381156	+	0.999273i	$0.512136\pi$
$840$	0.751696	0.0259360
$841$	12.5952	0.434318
$842$	−40.6651	−1.40141
$843$	1.44171	0.0496552
$844$	−1.52259	−0.0524096
$845$	−29.8648	−1.02738
$846$	22.5724	0.776054
$847$	4.98205	0.171185
$848$	−10.4366	−0.358394
$849$	−4.35675	−0.149523
$850$	3.28230	0.112582
$851$	14.3930	0.493385
$852$	0.208692	0.00714968
$853$	25.8071	0.883618	0.441809	−	0.897109i	$-0.354337\pi$
$853$	25.8071	0.883618	0.441809	+	0.897109i	$0.354337\pi$
$854$	−18.4613	−0.631732
$855$	−5.36310	−0.183414
$856$	−4.68059	−0.159979
$857$	52.6781	1.79945	0.899724	−	0.436459i	$-0.143768\pi$
$857$	52.6781	1.79945	0.899724	+	0.436459i	$0.143768\pi$
$858$	5.61963	0.191851
$859$	21.4872	0.733133	0.366566	−	0.930392i	$-0.380533\pi$
$859$	21.4872	0.733133	0.366566	+	0.930392i	$0.380533\pi$
$860$	0.479712	0.0163580
$861$	0.589632	0.0200946
$862$	14.4996	0.493857
$863$	−5.13712	−0.174870	−0.0874348	−	0.996170i	$-0.527867\pi$
$863$	−5.13712	−0.174870	−0.0874348	+	0.996170i	$0.527867\pi$
$864$	1.27788	0.0434745
$865$	1.60426	0.0545464
$866$	−18.3707	−0.624261
$867$	2.87516	0.0976454
$868$	−0.756975	−0.0256934
$869$	−0.695429	−0.0235908
$870$	−2.25660	−0.0765060
$871$	39.6888	1.34480
$872$	18.5463	0.628057
$873$	−52.9413	−1.79179
$874$	8.46785	0.286429
$875$	1.00000	0.0338062
$876$	0.176726	0.00597101
$877$	16.7997	0.567284	0.283642	−	0.958930i	$-0.408457\pi$
$877$	16.7997	0.567284	0.283642	+	0.958930i	$0.408457\pi$
$878$	−32.0787	−1.08260
$879$	−5.36338	−0.180902
$880$	9.03066	0.304423
$881$	−21.0577	−0.709453	−0.354727	−	0.934970i	$-0.615426\pi$
$881$	−21.0577	−0.709453	−0.354727	+	0.934970i	$0.615426\pi$
$882$	−3.99227	−0.134427
$883$	40.5920	1.36603	0.683014	−	0.730405i	$-0.260669\pi$
$883$	40.5920	1.36603	0.683014	+	0.730405i	$0.260669\pi$
$884$	2.34311	0.0788073
$885$	−0.723388	−0.0243164
$886$	−4.39296	−0.147584
$887$	−35.0020	−1.17525	−0.587627	−	0.809132i	$-0.699938\pi$
$887$	−35.0020	−1.17525	−0.587627	+	0.809132i	$0.699938\pi$
$888$	−3.17812	−0.106651
$889$	−5.69003	−0.190837
$890$	20.6584	0.692471
$891$	20.6293	0.691108
$892$	−3.76338	−0.126007
$893$	10.3355	0.345864
$894$	−1.73288	−0.0579560
$895$	−21.2800	−0.711312
$896$	−9.89423	−0.330543
$897$	−5.73098	−0.191352
$898$	0.201996	0.00674068
$899$	32.9050	1.09744
$900$	0.435296	0.0145099
$901$	6.83854	0.227825
$902$	7.65467	0.254873
$903$	0.831371	0.0276663
$904$	37.5187	1.24785
$905$	−17.7462	−0.589903
$906$	−3.17013	−0.105321
$907$	−16.8302	−0.558838	−0.279419	−	0.960169i	$-0.590142\pi$
$907$	−16.8302	−0.558838	−0.279419	+	0.960169i	$0.590142\pi$
$908$	−2.68327	−0.0890474
$909$	38.5674	1.27920
$910$	−8.90897	−0.295329
$911$	−15.2405	−0.504939	−0.252469	−	0.967605i	$-0.581243\pi$
$911$	−15.2405	−0.504939	−0.252469	+	0.967605i	$0.581243\pi$
$912$	−1.73031	−0.0572964
$913$	40.6208	1.34435
$914$	−39.6887	−1.31279
$915$	3.48852	0.115327
$916$	−0.148369	−0.00490223
$917$	−10.0008	−0.330255
$918$	5.00810	0.165292
$919$	4.84045	0.159672	0.0798358	−	0.996808i	$-0.474560\pi$
$919$	4.84045	0.159672	0.0798358	+	0.996808i	$0.474560\pi$
$920$	−9.95196	−0.328106
$921$	1.81505	0.0598079
$922$	−1.91143	−0.0629495
$923$	−35.8145	−1.17885
$924$	−0.0935884	−0.00307883
$925$	−4.22793	−0.139014
$926$	15.1232	0.496978
$927$	44.7555	1.46996
$928$	−5.40155	−0.177314
$929$	−29.0077	−0.951712	−0.475856	−	0.879523i	$-0.657862\pi$
$929$	−29.0077	−0.951712	−0.475856	+	0.879523i	$0.657862\pi$
$930$	−1.78514	−0.0585372
$931$	−1.82799	−0.0599099
$932$	−3.29752	−0.108014
$933$	−7.51930	−0.246171
$934$	36.9224	1.20814
$935$	−5.91732	−0.193517
$936$	−56.1538	−1.83544
$937$	30.7586	1.00484	0.502420	−	0.864624i	$-0.332443\pi$
$937$	30.7586	1.00484	0.502420	+	0.864624i	$0.332443\pi$
$938$	8.24887	0.269335
$939$	1.11983	0.0365443
$940$	−0.838878	−0.0273612
$941$	31.7351	1.03453	0.517267	−	0.855824i	$-0.326949\pi$
$941$	31.7351	1.03453	0.517267	+	0.855824i	$0.326949\pi$
$942$	−4.55860	−0.148527
$943$	−7.80634	−0.254209
$944$	10.3564	0.337073
$945$	1.52579	0.0496340
$946$	10.7929	0.350909
$947$	−44.6632	−1.45136	−0.725679	−	0.688033i	$-0.758474\pi$
$947$	−44.6632	−1.45136	−0.725679	+	0.688033i	$0.758474\pi$
$948$	−0.0108150	−0.000351255 0
$949$	−30.3286	−0.984507
$950$	−2.48743	−0.0807029
$951$	−2.17366	−0.0704857
$952$	7.05158	0.228543
$953$	−44.8784	−1.45375	−0.726877	−	0.686768i	$-0.759029\pi$
$953$	−44.8784	−1.45375	−0.726877	+	0.686768i	$0.759029\pi$
$954$	−11.3183	−0.366445
$955$	0.375150	0.0121396
$956$	−2.80364	−0.0906763
$957$	4.06820	0.131506
$958$	27.1774	0.878062
$959$	1.29589	0.0418463
$960$	2.18618	0.0705585
$961$	−4.96970	−0.160313
$962$	37.6665	1.21442
$963$	−4.69740	−0.151372
$964$	−2.53500	−0.0816468
$965$	25.4886	0.820507
$966$	−1.19112	−0.0383237
$967$	35.3280	1.13607	0.568036	−	0.823004i	$-0.307703\pi$
$967$	35.3280	1.13607	0.568036	+	0.823004i	$0.307703\pi$
$968$	14.5645	0.468119
$969$	1.13378	0.0364224
$970$	−24.5544	−0.788394
$971$	22.2768	0.714897	0.357448	−	0.933933i	$-0.383647\pi$
$971$	22.2768	0.714897	0.357448	+	0.933933i	$0.383647\pi$
$972$	0.999956	0.0320736
$973$	15.5953	0.499963
$974$	1.81462	0.0581443
$975$	1.68347	0.0539143
$976$	−49.9436	−1.59866
$977$	−44.8479	−1.43481	−0.717405	−	0.696656i	$-0.754670\pi$
$977$	−44.8479	−1.43481	−0.717405	+	0.696656i	$0.754670\pi$
$978$	5.18379	0.165759
$979$	−37.2429	−1.19029
$980$	0.148369	0.00473946
$981$	18.6129	0.594264
$982$	−38.3042	−1.22234
$983$	−9.23765	−0.294635	−0.147318	−	0.989089i	$-0.547064\pi$
$983$	−9.23765	−0.294635	−0.147318	+	0.989089i	$0.547064\pi$
$984$	1.72372	0.0549503
$985$	15.4933	0.493656
$986$	−21.1690	−0.674157
$987$	−1.45383	−0.0462759
$988$	−1.77568	−0.0564920
$989$	−11.0068	−0.349996
$990$	9.79364	0.311262
$991$	40.7308	1.29386	0.646928	−	0.762551i	$-0.276053\pi$
$991$	40.7308	1.29386	0.646928	+	0.762551i	$0.276053\pi$
$992$	−4.27303	−0.135669
$993$	−0.834711	−0.0264888
$994$	−7.44364	−0.236098
$995$	23.6269	0.749022
$996$	0.631716	0.0200167
$997$	−15.6236	−0.494805	−0.247402	−	0.968913i	$-0.579577\pi$
$997$	−15.6236	−0.494805	−0.247402	+	0.968913i	$0.579577\pi$
$998$	51.2710	1.62295
$999$	−6.45094	−0.204099

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.45	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.45	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q+1.36075 q^{2} -0.257132 q^{3} -0.148369 q^{4} -1.00000 q^{5} -0.349892 q^{6} -1.00000 q^{7} -2.92339 q^{8} -2.93388 q^{9} +O(q^{10})\)	\(q+1.36075 q^{2} -0.257132 q^{3} -0.148369 q^{4} -1.00000 q^{5} -0.349892 q^{6} -1.00000 q^{7} -2.92339 q^{8} -2.93388 q^{9} -1.36075 q^{10} +2.45315 q^{11} +0.0381503 q^{12} -6.54712 q^{13} -1.36075 q^{14} +0.257132 q^{15} -3.68125 q^{16} +2.41213 q^{17} -3.99227 q^{18} -1.82799 q^{19} +0.148369 q^{20} +0.257132 q^{21} +3.33812 q^{22} -3.40426 q^{23} +0.751696 q^{24} +1.00000 q^{25} -8.90897 q^{26} +1.52579 q^{27} +0.148369 q^{28} -6.44943 q^{29} +0.349892 q^{30} -5.10199 q^{31} +0.837522 q^{32} -0.630784 q^{33} +3.28230 q^{34} +1.00000 q^{35} +0.435296 q^{36} -4.22793 q^{37} -2.48743 q^{38} +1.68347 q^{39} +2.92339 q^{40} +2.29311 q^{41} +0.349892 q^{42} +3.23324 q^{43} -0.363970 q^{44} +2.93388 q^{45} -4.63233 q^{46} -5.65402 q^{47} +0.946567 q^{48} +1.00000 q^{49} +1.36075 q^{50} -0.620236 q^{51} +0.971386 q^{52} +2.83506 q^{53} +2.07622 q^{54} -2.45315 q^{55} +2.92339 q^{56} +0.470034 q^{57} -8.77605 q^{58} -2.81329 q^{59} -0.0381503 q^{60} +13.5670 q^{61} -6.94252 q^{62} +2.93388 q^{63} +8.50216 q^{64} +6.54712 q^{65} -0.858337 q^{66} -6.06202 q^{67} -0.357884 q^{68} +0.875344 q^{69} +1.36075 q^{70} +5.47026 q^{71} +8.57687 q^{72} +4.63235 q^{73} -5.75315 q^{74} -0.257132 q^{75} +0.271216 q^{76} -2.45315 q^{77} +2.29078 q^{78} -0.283484 q^{79} +3.68125 q^{80} +8.40932 q^{81} +3.12034 q^{82} +16.5586 q^{83} -0.0381503 q^{84} -2.41213 q^{85} +4.39963 q^{86} +1.65836 q^{87} -7.17150 q^{88} -15.1817 q^{89} +3.99227 q^{90} +6.54712 q^{91} +0.505085 q^{92} +1.31189 q^{93} -7.69369 q^{94} +1.82799 q^{95} -0.215354 q^{96} +18.0448 q^{97} +1.36075 q^{98} -7.19726 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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