LMFDB - Embedded newform 8007.2.a.j.1.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.33
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.121956 q^{2} -1.00000 q^{3} -1.98513 q^{4} -1.88580 q^{5} -0.121956 q^{6} -2.22779 q^{7} -0.486009 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.121956 q^{2} -1.00000 q^{3} -1.98513 q^{4} -1.88580 q^{5} -0.121956 q^{6} -2.22779 q^{7} -0.486009 q^{8} +1.00000 q^{9} -0.229984 q^{10} +5.24222 q^{11} +1.98513 q^{12} +4.19462 q^{13} -0.271692 q^{14} +1.88580 q^{15} +3.91098 q^{16} +1.00000 q^{17} +0.121956 q^{18} -2.59487 q^{19} +3.74354 q^{20} +2.22779 q^{21} +0.639320 q^{22} +1.63093 q^{23} +0.486009 q^{24} -1.44377 q^{25} +0.511558 q^{26} -1.00000 q^{27} +4.42244 q^{28} +10.1714 q^{29} +0.229984 q^{30} +10.3508 q^{31} +1.44899 q^{32} -5.24222 q^{33} +0.121956 q^{34} +4.20116 q^{35} -1.98513 q^{36} -3.19418 q^{37} -0.316460 q^{38} -4.19462 q^{39} +0.916514 q^{40} -6.17225 q^{41} +0.271692 q^{42} +4.97844 q^{43} -10.4065 q^{44} -1.88580 q^{45} +0.198902 q^{46} -3.26912 q^{47} -3.91098 q^{48} -2.03695 q^{49} -0.176077 q^{50} -1.00000 q^{51} -8.32685 q^{52} -2.35459 q^{53} -0.121956 q^{54} -9.88576 q^{55} +1.08273 q^{56} +2.59487 q^{57} +1.24046 q^{58} -5.50612 q^{59} -3.74354 q^{60} +8.86828 q^{61} +1.26234 q^{62} -2.22779 q^{63} -7.64525 q^{64} -7.91019 q^{65} -0.639320 q^{66} +1.66460 q^{67} -1.98513 q^{68} -1.63093 q^{69} +0.512355 q^{70} +10.7503 q^{71} -0.486009 q^{72} -11.0327 q^{73} -0.389549 q^{74} +1.44377 q^{75} +5.15115 q^{76} -11.6786 q^{77} -0.511558 q^{78} -7.94714 q^{79} -7.37531 q^{80} +1.00000 q^{81} -0.752741 q^{82} +15.1896 q^{83} -4.42244 q^{84} -1.88580 q^{85} +0.607150 q^{86} -10.1714 q^{87} -2.54777 q^{88} -15.0118 q^{89} -0.229984 q^{90} -9.34473 q^{91} -3.23761 q^{92} -10.3508 q^{93} -0.398688 q^{94} +4.89340 q^{95} -1.44899 q^{96} -14.5973 q^{97} -0.248418 q^{98} +5.24222 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * 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 $

$2$	0.121956	0.0862358	0.0431179	−	0.999070i	$-0.486271\pi$
$2$	0.121956	0.0862358	0.0431179	+	0.999070i	$0.486271\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.98513	−0.992563
$5$	−1.88580	−0.843353	−0.421677	−	0.906746i	$-0.638558\pi$
$5$	−1.88580	−0.843353	−0.421677	+	0.906746i	$0.638558\pi$
$6$	−0.121956	−0.0497882
$7$	−2.22779	−0.842025	−0.421013	−	0.907055i	$-0.638325\pi$
$7$	−2.22779	−0.842025	−0.421013	+	0.907055i	$0.638325\pi$
$8$	−0.486009	−0.171830
$9$	1.00000	0.333333
$10$	−0.229984	−0.0727272
$11$	5.24222	1.58059	0.790295	−	0.612726i	$-0.209927\pi$
$11$	5.24222	1.58059	0.790295	+	0.612726i	$0.209927\pi$
$12$	1.98513	0.573057
$13$	4.19462	1.16338	0.581689	−	0.813411i	$-0.302392\pi$
$13$	4.19462	1.16338	0.581689	+	0.813411i	$0.302392\pi$
$14$	−0.271692	−0.0726127
$15$	1.88580	0.486910
$16$	3.91098	0.977745
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.121956	0.0287453
$19$	−2.59487	−0.595305	−0.297652	−	0.954674i	$-0.596204\pi$
$19$	−2.59487	−0.595305	−0.297652	+	0.954674i	$0.596204\pi$
$20$	3.74354	0.837082
$21$	2.22779	0.486143
$22$	0.639320	0.136303
$23$	1.63093	0.340073	0.170037	−	0.985438i	$-0.445611\pi$
$23$	1.63093	0.340073	0.170037	+	0.985438i	$0.445611\pi$
$24$	0.486009	0.0992062
$25$	−1.44377	−0.288755
$26$	0.511558	0.100325
$27$	−1.00000	−0.192450
$28$	4.42244	0.835763
$29$	10.1714	1.88878	0.944391	−	0.328825i	$-0.106653\pi$
$29$	10.1714	1.88878	0.944391	+	0.328825i	$0.106653\pi$
$30$	0.229984	0.0419891
$31$	10.3508	1.85906	0.929529	−	0.368748i	$-0.120213\pi$
$31$	10.3508	1.85906	0.929529	+	0.368748i	$0.120213\pi$
$32$	1.44899	0.256147
$33$	−5.24222	−0.912554
$34$	0.121956	0.0209152
$35$	4.20116	0.710125
$36$	−1.98513	−0.330854
$37$	−3.19418	−0.525121	−0.262560	−	0.964916i	$-0.584567\pi$
$37$	−3.19418	−0.525121	−0.262560	+	0.964916i	$0.584567\pi$
$38$	−0.316460	−0.0513366
$39$	−4.19462	−0.671677
$40$	0.916514	0.144914
$41$	−6.17225	−0.963943	−0.481971	−	0.876187i	$-0.660079\pi$
$41$	−6.17225	−0.963943	−0.481971	+	0.876187i	$0.660079\pi$
$42$	0.271692	0.0419230
$43$	4.97844	0.759205	0.379602	−	0.925150i	$-0.376061\pi$
$43$	4.97844	0.759205	0.379602	+	0.925150i	$0.376061\pi$
$44$	−10.4065	−1.56884
$45$	−1.88580	−0.281118
$46$	0.198902	0.0293265
$47$	−3.26912	−0.476851	−0.238425	−	0.971161i	$-0.576631\pi$
$47$	−3.26912	−0.476851	−0.238425	+	0.971161i	$0.576631\pi$
$48$	−3.91098	−0.564502
$49$	−2.03695	−0.290994
$50$	−0.176077	−0.0249010
$51$	−1.00000	−0.140028
$52$	−8.32685	−1.15473
$53$	−2.35459	−0.323428	−0.161714	−	0.986838i	$-0.551702\pi$
$53$	−2.35459	−0.323428	−0.161714	+	0.986838i	$0.551702\pi$
$54$	−0.121956	−0.0165961
$55$	−9.88576	−1.33300
$56$	1.08273	0.144685
$57$	2.59487	0.343699
$58$	1.24046	0.162881
$59$	−5.50612	−0.716836	−0.358418	−	0.933561i	$-0.616684\pi$
$59$	−5.50612	−0.716836	−0.358418	+	0.933561i	$0.616684\pi$
$60$	−3.74354	−0.483289
$61$	8.86828	1.13547	0.567734	−	0.823212i	$-0.307820\pi$
$61$	8.86828	1.13547	0.567734	+	0.823212i	$0.307820\pi$
$62$	1.26234	0.160317
$63$	−2.22779	−0.280675
$64$	−7.64525	−0.955656
$65$	−7.91019	−0.981139
$66$	−0.639320	−0.0786948
$67$	1.66460	0.203363	0.101682	−	0.994817i	$-0.467578\pi$
$67$	1.66460	0.203363	0.101682	+	0.994817i	$0.467578\pi$
$68$	−1.98513	−0.240732
$69$	−1.63093	−0.196341
$70$	0.512355	0.0612382
$71$	10.7503	1.27582	0.637912	−	0.770110i	$-0.279799\pi$
$71$	10.7503	1.27582	0.637912	+	0.770110i	$0.279799\pi$
$72$	−0.486009	−0.0572767
$73$	−11.0327	−1.29128	−0.645640	−	0.763642i	$-0.723409\pi$
$73$	−11.0327	−1.29128	−0.645640	+	0.763642i	$0.723409\pi$
$74$	−0.389549	−0.0452842
$75$	1.44377	0.166713
$76$	5.15115	0.590878
$77$	−11.6786	−1.33090
$78$	−0.511558	−0.0579225
$79$	−7.94714	−0.894123	−0.447062	−	0.894503i	$-0.647530\pi$
$79$	−7.94714	−0.894123	−0.447062	+	0.894503i	$0.647530\pi$
$80$	−7.37531	−0.824585
$81$	1.00000	0.111111
$82$	−0.752741	−0.0831264
$83$	15.1896	1.66728	0.833638	−	0.552312i	$-0.186254\pi$
$83$	15.1896	1.66728	0.833638	+	0.552312i	$0.186254\pi$
$84$	−4.42244	−0.482528
$85$	−1.88580	−0.204543
$86$	0.607150	0.0654706
$87$	−10.1714	−1.09049
$88$	−2.54777	−0.271593
$89$	−15.0118	−1.59125	−0.795625	−	0.605790i	$-0.792857\pi$
$89$	−15.0118	−1.59125	−0.795625	+	0.605790i	$0.792857\pi$
$90$	−0.229984	−0.0242424
$91$	−9.34473	−0.979593
$92$	−3.23761	−0.337544
$93$	−10.3508	−1.07333
$94$	−0.398688	−0.0411216
$95$	4.89340	0.502052
$96$	−1.44899	−0.147886
$97$	−14.5973	−1.48213	−0.741065	−	0.671434i	$-0.765679\pi$
$97$	−14.5973	−1.48213	−0.741065	+	0.671434i	$0.765679\pi$
$98$	−0.248418	−0.0250941
$99$	5.24222	0.526863
$100$	2.86608	0.286608
$101$	15.2202	1.51447	0.757235	−	0.653143i	$-0.226550\pi$
$101$	15.2202	1.51447	0.757235	+	0.653143i	$0.226550\pi$
$102$	−0.121956	−0.0120754
$103$	3.74759	0.369261	0.184630	−	0.982808i	$-0.440891\pi$
$103$	3.74759	0.369261	0.184630	+	0.982808i	$0.440891\pi$
$104$	−2.03862	−0.199903
$105$	−4.20116	−0.409991
$106$	−0.287156	−0.0278911
$107$	16.3660	1.58216	0.791080	−	0.611712i	$-0.209519\pi$
$107$	16.3660	1.58216	0.791080	+	0.611712i	$0.209519\pi$
$108$	1.98513	0.191019
$109$	−13.7884	−1.32069	−0.660343	−	0.750964i	$-0.729589\pi$
$109$	−13.7884	−1.32069	−0.660343	+	0.750964i	$0.729589\pi$
$110$	−1.20563	−0.114952
$111$	3.19418	0.303179
$112$	−8.71284	−0.823286
$113$	−6.52188	−0.613527	−0.306763	−	0.951786i	$-0.599246\pi$
$113$	−6.52188	−0.613527	−0.306763	+	0.951786i	$0.599246\pi$
$114$	0.316460	0.0296392
$115$	−3.07561	−0.286802
$116$	−20.1915	−1.87474
$117$	4.19462	0.387793
$118$	−0.671503	−0.0618169
$119$	−2.22779	−0.204221
$120$	−0.916514	−0.0836659
$121$	16.4809	1.49827
$122$	1.08154	0.0979179
$123$	6.17225	0.556533
$124$	−20.5477	−1.84523
$125$	12.1516	1.08688
$126$	−0.271692	−0.0242042
$127$	13.8352	1.22768	0.613839	−	0.789431i	$-0.289624\pi$
$127$	13.8352	1.22768	0.613839	+	0.789431i	$0.289624\pi$
$128$	−3.83035	−0.338559
$129$	−4.97844	−0.438327
$130$	−0.964694	−0.0846093
$131$	−17.6555	−1.54256	−0.771282	−	0.636493i	$-0.780384\pi$
$131$	−17.6555	−1.54256	−0.771282	+	0.636493i	$0.780384\pi$
$132$	10.4065	0.905768
$133$	5.78083	0.501262
$134$	0.203007	0.0175372
$135$	1.88580	0.162303
$136$	−0.486009	−0.0416750
$137$	2.05488	0.175561	0.0877803	−	0.996140i	$-0.472023\pi$
$137$	2.05488	0.175561	0.0877803	+	0.996140i	$0.472023\pi$
$138$	−0.198902	−0.0169316
$139$	2.92773	0.248327	0.124164	−	0.992262i	$-0.460375\pi$
$139$	2.92773	0.248327	0.124164	+	0.992262i	$0.460375\pi$
$140$	−8.33983	−0.704844
$141$	3.26912	0.275310
$142$	1.31106	0.110022
$143$	21.9891	1.83882
$144$	3.91098	0.325915
$145$	−19.1812	−1.59291
$146$	−1.34550	−0.111355
$147$	2.03695	0.168005
$148$	6.34086	0.521216
$149$	3.44130	0.281922	0.140961	−	0.990015i	$-0.454981\pi$
$149$	3.44130	0.281922	0.140961	+	0.990015i	$0.454981\pi$
$150$	0.176077	0.0143766
$151$	−7.13847	−0.580921	−0.290460	−	0.956887i	$-0.593808\pi$
$151$	−7.13847	−0.580921	−0.290460	+	0.956887i	$0.593808\pi$
$152$	1.26113	0.102291
$153$	1.00000	0.0808452
$154$	−1.42427	−0.114771
$155$	−19.5195	−1.56784
$156$	8.32685	0.666682
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−0.969200	−0.0771054
$159$	2.35459	0.186731
$160$	−2.73249	−0.216022
$161$	−3.63338	−0.286350
$162$	0.121956	0.00958175
$163$	16.1321	1.26356	0.631781	−	0.775147i	$-0.282324\pi$
$163$	16.1321	1.26356	0.631781	+	0.775147i	$0.282324\pi$
$164$	12.2527	0.956774
$165$	9.88576	0.769606
$166$	1.85246	0.143779
$167$	−0.253883	−0.0196461	−0.00982303	−	0.999952i	$-0.503127\pi$
$167$	−0.253883	−0.0196461	−0.00982303	+	0.999952i	$0.503127\pi$
$168$	−1.08273	−0.0835342
$169$	4.59482	0.353448
$170$	−0.229984	−0.0176389
$171$	−2.59487	−0.198435
$172$	−9.88283	−0.753559
$173$	24.1574	1.83666	0.918328	−	0.395819i	$-0.129539\pi$
$173$	24.1574	1.83666	0.918328	+	0.395819i	$0.129539\pi$
$174$	−1.24046	−0.0940391
$175$	3.21643	0.243139
$176$	20.5022	1.54541
$177$	5.50612	0.413865
$178$	−1.83078	−0.137223
$179$	−20.0610	−1.49943	−0.749713	−	0.661763i	$-0.769809\pi$
$179$	−20.0610	−1.49943	−0.749713	+	0.661763i	$0.769809\pi$
$180$	3.74354	0.279027
$181$	19.7737	1.46977	0.734885	−	0.678192i	$-0.237236\pi$
$181$	19.7737	1.46977	0.734885	+	0.678192i	$0.237236\pi$
$182$	−1.13964	−0.0844760
$183$	−8.86828	−0.655562
$184$	−0.792649	−0.0584348
$185$	6.02358	0.442862
$186$	−1.26234	−0.0925593
$187$	5.24222	0.383349
$188$	6.48962	0.473304
$189$	2.22779	0.162048
$190$	0.596779	0.0432949
$191$	0.175992	0.0127344	0.00636718	−	0.999980i	$-0.497973\pi$
$191$	0.175992	0.0127344	0.00636718	+	0.999980i	$0.497973\pi$
$192$	7.64525	0.551749
$193$	−26.8338	−1.93154	−0.965768	−	0.259408i	$-0.916473\pi$
$193$	−26.8338	−1.93154	−0.965768	+	0.259408i	$0.916473\pi$
$194$	−1.78022	−0.127813
$195$	7.91019	0.566461
$196$	4.04361	0.288830
$197$	7.61173	0.542313	0.271157	−	0.962535i	$-0.412594\pi$
$197$	7.61173	0.542313	0.271157	+	0.962535i	$0.412594\pi$
$198$	0.639320	0.0454345
$199$	−8.18004	−0.579868	−0.289934	−	0.957047i	$-0.593633\pi$
$199$	−8.18004	−0.579868	−0.289934	+	0.957047i	$0.593633\pi$
$200$	0.701688	0.0496168
$201$	−1.66460	−0.117412
$202$	1.85619	0.130601
$203$	−22.6597	−1.59040
$204$	1.98513	0.138987
$205$	11.6396	0.812945
$206$	0.457040	0.0318435
$207$	1.63093	0.113358
$208$	16.4051	1.13749
$209$	−13.6029	−0.940933
$210$	−0.512355	−0.0353559
$211$	−8.21823	−0.565766	−0.282883	−	0.959154i	$-0.591291\pi$
$211$	−8.21823	−0.565766	−0.282883	+	0.959154i	$0.591291\pi$
$212$	4.67417	0.321023
$213$	−10.7503	−0.736597
$214$	1.99593	0.136439
$215$	−9.38832	−0.640278
$216$	0.486009	0.0330687
$217$	−23.0594	−1.56537
$218$	−1.68157	−0.113890
$219$	11.0327	0.745521
$220$	19.6245	1.32308
$221$	4.19462	0.282161
$222$	0.389549	0.0261448
$223$	3.85440	0.258110	0.129055	−	0.991637i	$-0.458806\pi$
$223$	3.85440	0.258110	0.129055	+	0.991637i	$0.458806\pi$
$224$	−3.22803	−0.215682
$225$	−1.44377	−0.0962517
$226$	−0.795381	−0.0529080
$227$	5.54675	0.368151	0.184076	−	0.982912i	$-0.441071\pi$
$227$	5.54675	0.368151	0.184076	+	0.982912i	$0.441071\pi$
$228$	−5.15115	−0.341143
$229$	27.5762	1.82229	0.911143	−	0.412089i	$-0.135201\pi$
$229$	27.5762	1.82229	0.911143	+	0.412089i	$0.135201\pi$
$230$	−0.375088	−0.0247326
$231$	11.6786	0.768394
$232$	−4.94340	−0.324550
$233$	16.0748	1.05310	0.526548	−	0.850145i	$-0.323486\pi$
$233$	16.0748	1.05310	0.526548	+	0.850145i	$0.323486\pi$
$234$	0.511558	0.0334416
$235$	6.16490	0.402154
$236$	10.9303	0.711505
$237$	7.94714	0.516222
$238$	−0.271692	−0.0176112
$239$	1.92800	0.124712	0.0623559	−	0.998054i	$-0.480139\pi$
$239$	1.92800	0.124712	0.0623559	+	0.998054i	$0.480139\pi$
$240$	7.37531	0.476074
$241$	13.7618	0.886477	0.443239	−	0.896404i	$-0.353829\pi$
$241$	13.7618	0.886477	0.443239	+	0.896404i	$0.353829\pi$
$242$	2.00994	0.129204
$243$	−1.00000	−0.0641500
$244$	−17.6047	−1.12702
$245$	3.84128	0.245410
$246$	0.752741	0.0479930
$247$	−10.8845	−0.692565
$248$	−5.03059	−0.319443
$249$	−15.1896	−0.962602
$250$	1.48196	0.0937276
$251$	−27.6545	−1.74553	−0.872767	−	0.488137i	$-0.837677\pi$
$251$	−27.6545	−1.74553	−0.872767	+	0.488137i	$0.837677\pi$
$252$	4.42244	0.278588
$253$	8.54972	0.537516
$254$	1.68729	0.105870
$255$	1.88580	0.118093
$256$	14.8234	0.926461
$257$	−14.9157	−0.930415	−0.465207	−	0.885202i	$-0.654020\pi$
$257$	−14.9157	−0.930415	−0.465207	+	0.885202i	$0.654020\pi$
$258$	−0.607150	−0.0377995
$259$	7.11597	0.442165
$260$	15.7027	0.973842
$261$	10.1714	0.629594
$262$	−2.15318	−0.133024
$263$	−16.6888	−1.02907	−0.514537	−	0.857468i	$-0.672036\pi$
$263$	−16.6888	−1.02907	−0.514537	+	0.857468i	$0.672036\pi$
$264$	2.54777	0.156804
$265$	4.44028	0.272764
$266$	0.705006	0.0432267
$267$	15.0118	0.918708
$268$	−3.30444	−0.201851
$269$	−30.2729	−1.84577	−0.922885	−	0.385075i	$-0.874176\pi$
$269$	−30.2729	−1.84577	−0.922885	+	0.385075i	$0.874176\pi$
$270$	0.229984	0.0139964
$271$	−14.6471	−0.889745	−0.444873	−	0.895594i	$-0.646751\pi$
$271$	−14.6471	−0.889745	−0.444873	+	0.895594i	$0.646751\pi$
$272$	3.91098	0.237138
$273$	9.34473	0.565569
$274$	0.250605	0.0151396
$275$	−7.56859	−0.456403
$276$	3.23761	0.194881
$277$	8.47048	0.508942	0.254471	−	0.967080i	$-0.418099\pi$
$277$	8.47048	0.508942	0.254471	+	0.967080i	$0.418099\pi$
$278$	0.357054	0.0214147
$279$	10.3508	0.619686
$280$	−2.04180	−0.122021
$281$	19.9187	1.18825	0.594125	−	0.804372i	$-0.297498\pi$
$281$	19.9187	1.18825	0.594125	+	0.804372i	$0.297498\pi$
$282$	0.398688	0.0237416
$283$	−5.44697	−0.323789	−0.161894	−	0.986808i	$-0.551760\pi$
$283$	−5.44697	−0.323789	−0.161894	+	0.986808i	$0.551760\pi$
$284$	−21.3407	−1.26634
$285$	−4.89340	−0.289860
$286$	2.68170	0.158572
$287$	13.7505	0.811664
$288$	1.44899	0.0853823
$289$	1.00000	0.0588235
$290$	−2.33926	−0.137366
$291$	14.5973	0.855708
$292$	21.9013	1.28168
$293$	5.58322	0.326175	0.163088	−	0.986612i	$-0.447855\pi$
$293$	5.58322	0.326175	0.163088	+	0.986612i	$0.447855\pi$
$294$	0.248418	0.0144881
$295$	10.3834	0.604546
$296$	1.55240	0.0902316
$297$	−5.24222	−0.304185
$298$	0.419686	0.0243118
$299$	6.84114	0.395633
$300$	−2.86608	−0.165473
$301$	−11.0909	−0.639270
$302$	−0.870578	−0.0500962
$303$	−15.2202	−0.874379
$304$	−10.1485	−0.582057
$305$	−16.7238	−0.957600
$306$	0.121956	0.00697175
$307$	0.379767	0.0216744	0.0108372	−	0.999941i	$-0.496550\pi$
$307$	0.379767	0.0216744	0.0108372	+	0.999941i	$0.496550\pi$
$308$	23.1834	1.32100
$309$	−3.74759	−0.213193
$310$	−2.38052	−0.135204
$311$	−20.3654	−1.15482	−0.577408	−	0.816456i	$-0.695936\pi$
$311$	−20.3654	−1.15482	−0.577408	+	0.816456i	$0.695936\pi$
$312$	2.03862	0.115414
$313$	31.2318	1.76533	0.882663	−	0.470006i	$-0.155748\pi$
$313$	31.2318	1.76533	0.882663	+	0.470006i	$0.155748\pi$
$314$	−0.121956	−0.00688236
$315$	4.20116	0.236708
$316$	15.7761	0.887474
$317$	31.5386	1.77138	0.885691	−	0.464275i	$-0.153685\pi$
$317$	31.5386	1.77138	0.885691	+	0.464275i	$0.153685\pi$
$318$	0.287156	0.0161029
$319$	53.3208	2.98539
$320$	14.4174	0.805956
$321$	−16.3660	−0.913461
$322$	−0.443111	−0.0246936
$323$	−2.59487	−0.144383
$324$	−1.98513	−0.110285
$325$	−6.05609	−0.335931
$326$	1.96740	0.108964
$327$	13.7884	0.762499
$328$	2.99977	0.165635
$329$	7.28292	0.401520
$330$	1.20563	0.0663675
$331$	4.05336	0.222793	0.111396	−	0.993776i	$-0.464468\pi$
$331$	4.05336	0.222793	0.111396	+	0.993776i	$0.464468\pi$
$332$	−30.1533	−1.65488
$333$	−3.19418	−0.175040
$334$	−0.0309625	−0.00169419
$335$	−3.13909	−0.171507
$336$	8.71284	0.475325
$337$	−1.27984	−0.0697174	−0.0348587	−	0.999392i	$-0.511098\pi$
$337$	−1.27984	−0.0697174	−0.0348587	+	0.999392i	$0.511098\pi$
$338$	0.560365	0.0304799
$339$	6.52188	0.354220
$340$	3.74354	0.203022
$341$	54.2612	2.93841
$342$	−0.316460	−0.0171122
$343$	20.1324	1.08705
$344$	−2.41957	−0.130454
$345$	3.07561	0.165585
$346$	2.94614	0.158386
$347$	25.8958	1.39016	0.695080	−	0.718932i	$-0.255369\pi$
$347$	25.8958	1.39016	0.695080	+	0.718932i	$0.255369\pi$
$348$	20.1915	1.08238
$349$	−11.4063	−0.610567	−0.305283	−	0.952262i	$-0.598751\pi$
$349$	−11.4063	−0.610567	−0.305283	+	0.952262i	$0.598751\pi$
$350$	0.392262	0.0209673
$351$	−4.19462	−0.223892
$352$	7.59591	0.404863
$353$	12.5955	0.670391	0.335195	−	0.942149i	$-0.391198\pi$
$353$	12.5955	0.670391	0.335195	+	0.942149i	$0.391198\pi$
$354$	0.671503	0.0356900
$355$	−20.2728	−1.07597
$356$	29.8004	1.57942
$357$	2.22779	0.117907
$358$	−2.44655	−0.129304
$359$	−3.34860	−0.176732	−0.0883662	−	0.996088i	$-0.528165\pi$
$359$	−3.34860	−0.176732	−0.0883662	+	0.996088i	$0.528165\pi$
$360$	0.916514	0.0483045
$361$	−12.2666	−0.645612
$362$	2.41152	0.126747
$363$	−16.4809	−0.865024
$364$	18.5505	0.972309
$365$	20.8054	1.08901
$366$	−1.08154	−0.0565329
$367$	5.95281	0.310734	0.155367	−	0.987857i	$-0.450344\pi$
$367$	5.95281	0.310734	0.155367	+	0.987857i	$0.450344\pi$
$368$	6.37855	0.332505
$369$	−6.17225	−0.321314
$370$	0.734610	0.0381906
$371$	5.24554	0.272335
$372$	20.5477	1.06535
$373$	27.7033	1.43442	0.717212	−	0.696855i	$-0.245418\pi$
$373$	27.7033	1.43442	0.717212	+	0.696855i	$0.245418\pi$
$374$	0.639320	0.0330584
$375$	−12.1516	−0.627508
$376$	1.58882	0.0819373
$377$	42.6652	2.19737
$378$	0.271692	0.0139743
$379$	−7.80175	−0.400749	−0.200375	−	0.979719i	$-0.564216\pi$
$379$	−7.80175	−0.400749	−0.200375	+	0.979719i	$0.564216\pi$
$380$	−9.71402	−0.498319
$381$	−13.8352	−0.708801
$382$	0.0214633	0.00109816
$383$	−1.29704	−0.0662755	−0.0331377	−	0.999451i	$-0.510550\pi$
$383$	−1.29704	−0.0662755	−0.0331377	+	0.999451i	$0.510550\pi$
$384$	3.83035	0.195467
$385$	22.0234	1.12242
$386$	−3.27253	−0.166567
$387$	4.97844	0.253068
$388$	28.9774	1.47111
$389$	31.8439	1.61455	0.807276	−	0.590174i	$-0.200941\pi$
$389$	31.8439	1.61455	0.807276	+	0.590174i	$0.200941\pi$
$390$	0.964694	0.0488492
$391$	1.63093	0.0824798
$392$	0.989979	0.0500015
$393$	17.6555	0.890600
$394$	0.928295	0.0467668
$395$	14.9867	0.754062
$396$	−10.4065	−0.522945
$397$	−9.13128	−0.458286	−0.229143	−	0.973393i	$-0.573592\pi$
$397$	−9.13128	−0.458286	−0.229143	+	0.973393i	$0.573592\pi$
$398$	−0.997604	−0.0500053
$399$	−5.78083	−0.289404
$400$	−5.64658	−0.282329
$401$	11.4043	0.569506	0.284753	−	0.958601i	$-0.408088\pi$
$401$	11.4043	0.569506	0.284753	+	0.958601i	$0.408088\pi$
$402$	−0.203007	−0.0101251
$403$	43.4177	2.16279
$404$	−30.2141	−1.50321
$405$	−1.88580	−0.0937059
$406$	−2.76349	−0.137150
$407$	−16.7446	−0.830001
$408$	0.486009	0.0240610
$409$	30.4084	1.50360	0.751800	−	0.659392i	$-0.229186\pi$
$409$	30.4084	1.50360	0.751800	+	0.659392i	$0.229186\pi$
$410$	1.41952	0.0701049
$411$	−2.05488	−0.101360
$412$	−7.43943	−0.366515
$413$	12.2665	0.603594
$414$	0.198902	0.00977549
$415$	−28.6445	−1.40610
$416$	6.07794	0.297996
$417$	−2.92773	−0.143372
$418$	−1.65895	−0.0811421
$419$	1.77450	0.0866899	0.0433449	−	0.999060i	$-0.486199\pi$
$419$	1.77450	0.0866899	0.0433449	+	0.999060i	$0.486199\pi$
$420$	8.33983	0.406942
$421$	−17.9498	−0.874822	−0.437411	−	0.899262i	$-0.644105\pi$
$421$	−17.9498	−0.874822	−0.437411	+	0.899262i	$0.644105\pi$
$422$	−1.00226	−0.0487893
$423$	−3.26912	−0.158950
$424$	1.14435	0.0555748
$425$	−1.44377	−0.0700334
$426$	−1.31106	−0.0635210
$427$	−19.7567	−0.956092
$428$	−32.4886	−1.57039
$429$	−21.9891	−1.06165
$430$	−1.14496	−0.0552149
$431$	−10.7065	−0.515712	−0.257856	−	0.966183i	$-0.583016\pi$
$431$	−10.7065	−0.515712	−0.257856	+	0.966183i	$0.583016\pi$
$432$	−3.91098	−0.188167
$433$	10.7071	0.514552	0.257276	−	0.966338i	$-0.417175\pi$
$433$	10.7071	0.514552	0.257276	+	0.966338i	$0.417175\pi$
$434$	−2.81223	−0.134991
$435$	19.1812	0.919667
$436$	27.3717	1.31087
$437$	−4.23207	−0.202447
$438$	1.34550	0.0642906
$439$	−14.4161	−0.688045	−0.344022	−	0.938961i	$-0.611790\pi$
$439$	−14.4161	−0.688045	−0.344022	+	0.938961i	$0.611790\pi$
$440$	4.80457	0.229049
$441$	−2.03695	−0.0969978
$442$	0.511558	0.0243323
$443$	5.53768	0.263103	0.131551	−	0.991309i	$-0.458004\pi$
$443$	5.53768	0.263103	0.131551	+	0.991309i	$0.458004\pi$
$444$	−6.34086	−0.300924
$445$	28.3092	1.34199
$446$	0.470066	0.0222583
$447$	−3.44130	−0.162768
$448$	17.0320	0.804687
$449$	−6.33801	−0.299109	−0.149555	−	0.988753i	$-0.547784\pi$
$449$	−6.33801	−0.299109	−0.149555	+	0.988753i	$0.547784\pi$
$450$	−0.176077	−0.00830034
$451$	−32.3563	−1.52360
$452$	12.9468	0.608964
$453$	7.13847	0.335395
$454$	0.676459	0.0317478
$455$	17.6222	0.826144
$456$	−1.26113	−0.0590580
$457$	26.4189	1.23583	0.617913	−	0.786247i	$-0.287978\pi$
$457$	26.4189	1.23583	0.617913	+	0.786247i	$0.287978\pi$
$458$	3.36308	0.157146
$459$	−1.00000	−0.0466760
$460$	6.10547	0.284669
$461$	−27.9131	−1.30004	−0.650020	−	0.759917i	$-0.725240\pi$
$461$	−27.9131	−1.30004	−0.650020	+	0.759917i	$0.725240\pi$
$462$	1.42427	0.0662630
$463$	23.2706	1.08148	0.540739	−	0.841191i	$-0.318145\pi$
$463$	23.2706	1.08148	0.540739	+	0.841191i	$0.318145\pi$
$464$	39.7802	1.84675
$465$	19.5195	0.905195
$466$	1.96042	0.0908146
$467$	−1.65319	−0.0765003	−0.0382502	−	0.999268i	$-0.512178\pi$
$467$	−1.65319	−0.0765003	−0.0382502	+	0.999268i	$0.512178\pi$
$468$	−8.32685	−0.384909
$469$	−3.70838	−0.171237
$470$	0.751845	0.0346800
$471$	1.00000	0.0460776
$472$	2.67602	0.123174
$473$	26.0981	1.19999
$474$	0.969200	0.0445168
$475$	3.74641	0.171897
$476$	4.42244	0.202702
$477$	−2.35459	−0.107809
$478$	0.235130	0.0107546
$479$	−8.70019	−0.397522	−0.198761	−	0.980048i	$-0.563692\pi$
$479$	−8.70019	−0.397522	−0.198761	+	0.980048i	$0.563692\pi$
$480$	2.73249	0.124721
$481$	−13.3984	−0.610914
$482$	1.67833	0.0764460
$483$	3.63338	0.165324
$484$	−32.7167	−1.48712
$485$	27.5275	1.24996
$486$	−0.121956	−0.00553203
$487$	−24.6387	−1.11649	−0.558243	−	0.829677i	$-0.688524\pi$
$487$	−24.6387	−1.11649	−0.558243	+	0.829677i	$0.688524\pi$
$488$	−4.31007	−0.195108
$489$	−16.1321	−0.729517
$490$	0.468466	0.0211632
$491$	32.1551	1.45114	0.725569	−	0.688149i	$-0.241577\pi$
$491$	32.1551	1.45114	0.725569	+	0.688149i	$0.241577\pi$
$492$	−12.2527	−0.552394
$493$	10.1714	0.458097
$494$	−1.32743	−0.0597238
$495$	−9.88576	−0.444332
$496$	40.4818	1.81769
$497$	−23.9494	−1.07428
$498$	−1.85246	−0.0830107
$499$	16.3248	0.730798	0.365399	−	0.930851i	$-0.380932\pi$
$499$	16.3248	0.730798	0.365399	+	0.930851i	$0.380932\pi$
$500$	−24.1226	−1.07879
$501$	0.253883	0.0113427
$502$	−3.37262	−0.150527
$503$	−24.0205	−1.07102	−0.535511	−	0.844528i	$-0.679881\pi$
$503$	−24.0205	−1.07102	−0.535511	+	0.844528i	$0.679881\pi$
$504$	1.08273	0.0482285
$505$	−28.7022	−1.27723
$506$	1.04269	0.0463531
$507$	−4.59482	−0.204063
$508$	−27.4647	−1.21855
$509$	−4.18972	−0.185706	−0.0928531	−	0.995680i	$-0.529599\pi$
$509$	−4.18972	−0.185706	−0.0928531	+	0.995680i	$0.529599\pi$
$510$	0.229984	0.0101838
$511$	24.5785	1.08729
$512$	9.46850	0.418453
$513$	2.59487	0.114566
$514$	−1.81905	−0.0802350
$515$	−7.06718	−0.311417
$516$	9.88283	0.435068
$517$	−17.1375	−0.753705
$518$	0.867834	0.0381304
$519$	−24.1574	−1.06039
$520$	3.84443	0.168589
$521$	−36.0616	−1.57989	−0.789944	−	0.613179i	$-0.789890\pi$
$521$	−36.0616	−1.57989	−0.789944	+	0.613179i	$0.789890\pi$
$522$	1.24046	0.0542935
$523$	15.7040	0.686686	0.343343	−	0.939210i	$-0.388441\pi$
$523$	15.7040	0.686686	0.343343	+	0.939210i	$0.388441\pi$
$524$	35.0483	1.53109
$525$	−3.21643	−0.140376
$526$	−2.03529	−0.0887430
$527$	10.3508	0.450888
$528$	−20.5022	−0.892246
$529$	−20.3401	−0.884350
$530$	0.541518	0.0235221
$531$	−5.50612	−0.238945
$532$	−11.4757	−0.497534
$533$	−25.8902	−1.12143
$534$	1.83078	0.0792255
$535$	−30.8629	−1.33432
$536$	−0.809011	−0.0349439
$537$	20.0610	0.865694
$538$	−3.69195	−0.159171
$539$	−10.6782	−0.459942
$540$	−3.74354	−0.161096
$541$	−15.5382	−0.668041	−0.334020	−	0.942566i	$-0.608405\pi$
$541$	−15.5382	−0.668041	−0.334020	+	0.942566i	$0.608405\pi$
$542$	−1.78629	−0.0767279
$543$	−19.7737	−0.848572
$544$	1.44899	0.0621247
$545$	26.0021	1.11381
$546$	1.13964	0.0487722
$547$	9.72621	0.415863	0.207931	−	0.978143i	$-0.433327\pi$
$547$	9.72621	0.415863	0.207931	+	0.978143i	$0.433327\pi$
$548$	−4.07920	−0.174255
$549$	8.86828	0.378489
$550$	−0.923034	−0.0393583
$551$	−26.3935	−1.12440
$552$	0.792649	0.0337374
$553$	17.7046	0.752874
$554$	1.03302	0.0438890
$555$	−6.02358	−0.255687
$556$	−5.81192	−0.246480
$557$	34.5824	1.46530	0.732652	−	0.680603i	$-0.238282\pi$
$557$	34.5824	1.46530	0.732652	+	0.680603i	$0.238282\pi$
$558$	1.26234	0.0534391
$559$	20.8827	0.883242
$560$	16.4306	0.694321
$561$	−5.24222	−0.221327
$562$	2.42920	0.102470
$563$	−20.4837	−0.863286	−0.431643	−	0.902045i	$-0.642066\pi$
$563$	−20.4837	−0.863286	−0.431643	+	0.902045i	$0.642066\pi$
$564$	−6.48962	−0.273262
$565$	12.2989	0.517420
$566$	−0.664289	−0.0279222
$567$	−2.22779	−0.0935584
$568$	−5.22473	−0.219225
$569$	−21.4950	−0.901116	−0.450558	−	0.892747i	$-0.648775\pi$
$569$	−21.4950	−0.901116	−0.450558	+	0.892747i	$0.648775\pi$
$570$	−0.596779	−0.0249963
$571$	37.2981	1.56088	0.780439	−	0.625232i	$-0.214996\pi$
$571$	37.2981	1.56088	0.780439	+	0.625232i	$0.214996\pi$
$572$	−43.6512	−1.82515
$573$	−0.175992	−0.00735219
$574$	1.67695	0.0699945
$575$	−2.35470	−0.0981978
$576$	−7.64525	−0.318552
$577$	25.6256	1.06681	0.533403	−	0.845861i	$-0.320913\pi$
$577$	25.6256	1.06681	0.533403	+	0.845861i	$0.320913\pi$
$578$	0.121956	0.00507269
$579$	26.8338	1.11517
$580$	38.0771	1.58106
$581$	−33.8392	−1.40389
$582$	1.78022	0.0737926
$583$	−12.3433	−0.511208
$584$	5.36200	0.221881
$585$	−7.91019	−0.327046
$586$	0.680906	0.0281280
$587$	−35.3314	−1.45828	−0.729141	−	0.684363i	$-0.760080\pi$
$587$	−35.3314	−1.45828	−0.729141	+	0.684363i	$0.760080\pi$
$588$	−4.04361	−0.166756
$589$	−26.8590	−1.10671
$590$	1.26632	0.0521335
$591$	−7.61173	−0.313105
$592$	−12.4924	−0.513434
$593$	10.1375	0.416299	0.208150	−	0.978097i	$-0.433256\pi$
$593$	10.1375	0.416299	0.208150	+	0.978097i	$0.433256\pi$
$594$	−0.639320	−0.0262316
$595$	4.20116	0.172231
$596$	−6.83142	−0.279826
$597$	8.18004	0.334787
$598$	0.834317	0.0341178
$599$	−11.5136	−0.470432	−0.235216	−	0.971943i	$-0.575580\pi$
$599$	−11.5136	−0.470432	−0.235216	+	0.971943i	$0.575580\pi$
$600$	−0.701688	−0.0286463
$601$	−0.158839	−0.00647916	−0.00323958	−	0.999995i	$-0.501031\pi$
$601$	−0.158839	−0.00647916	−0.00323958	+	0.999995i	$0.501031\pi$
$602$	−1.35260	−0.0551279
$603$	1.66460	0.0677877
$604$	14.1708	0.576601
$605$	−31.0796	−1.26357
$606$	−1.85619	−0.0754028
$607$	27.1854	1.10342	0.551711	−	0.834035i	$-0.313975\pi$
$607$	27.1854	1.10342	0.551711	+	0.834035i	$0.313975\pi$
$608$	−3.75993	−0.152485
$609$	22.6597	0.918219
$610$	−2.03956	−0.0825794
$611$	−13.7127	−0.554757
$612$	−1.98513	−0.0802440
$613$	−27.1947	−1.09839	−0.549193	−	0.835696i	$-0.685065\pi$
$613$	−27.1947	−1.09839	−0.549193	+	0.835696i	$0.685065\pi$
$614$	0.0463148	0.00186911
$615$	−11.6396	−0.469354
$616$	5.67589	0.228688
$617$	10.4372	0.420187	0.210093	−	0.977681i	$-0.432623\pi$
$617$	10.4372	0.420187	0.210093	+	0.977681i	$0.432623\pi$
$618$	−0.457040	−0.0183848
$619$	−18.4200	−0.740361	−0.370181	−	0.928960i	$-0.620704\pi$
$619$	−18.4200	−0.740361	−0.370181	+	0.928960i	$0.620704\pi$
$620$	38.7487	1.55618
$621$	−1.63093	−0.0654471
$622$	−2.48368	−0.0995865
$623$	33.4432	1.33987
$624$	−16.4051	−0.656729
$625$	−15.6966	−0.627866
$626$	3.80890	0.152234
$627$	13.6029	0.543248
$628$	1.98513	0.0792152
$629$	−3.19418	−0.127360
$630$	0.512355	0.0204127
$631$	−20.3870	−0.811594	−0.405797	−	0.913963i	$-0.633006\pi$
$631$	−20.3870	−0.811594	−0.405797	+	0.913963i	$0.633006\pi$
$632$	3.86239	0.153637
$633$	8.21823	0.326645
$634$	3.84631	0.152757
$635$	−26.0904	−1.03537
$636$	−4.67417	−0.185343
$637$	−8.54425	−0.338535
$638$	6.50278	0.257447
$639$	10.7503	0.425274
$640$	7.22326	0.285525
$641$	−23.9791	−0.947117	−0.473558	−	0.880762i	$-0.657031\pi$
$641$	−23.9791	−0.947117	−0.473558	+	0.880762i	$0.657031\pi$
$642$	−1.99593	−0.0787730
$643$	6.29559	0.248274	0.124137	−	0.992265i	$-0.460384\pi$
$643$	6.29559	0.248274	0.124137	+	0.992265i	$0.460384\pi$
$644$	7.21271	0.284221
$645$	9.38832	0.369665
$646$	−0.316460	−0.0124509
$647$	47.7035	1.87542	0.937709	−	0.347421i	$-0.112943\pi$
$647$	47.7035	1.87542	0.937709	+	0.347421i	$0.112943\pi$
$648$	−0.486009	−0.0190922
$649$	−28.8643	−1.13302
$650$	−0.738575	−0.0289693
$651$	23.0594	0.903769
$652$	−32.0242	−1.25416
$653$	−43.0050	−1.68292	−0.841458	−	0.540323i	$-0.818302\pi$
$653$	−43.0050	−1.68292	−0.841458	+	0.540323i	$0.818302\pi$
$654$	1.68157	0.0657547
$655$	33.2946	1.30093
$656$	−24.1395	−0.942491
$657$	−11.0327	−0.430427
$658$	0.888194	0.0346254
$659$	44.7707	1.74402	0.872009	−	0.489491i	$-0.162817\pi$
$659$	44.7707	1.74402	0.872009	+	0.489491i	$0.162817\pi$
$660$	−19.6245	−0.763882
$661$	−17.8406	−0.693920	−0.346960	−	0.937880i	$-0.612786\pi$
$661$	−17.8406	−0.693920	−0.346960	+	0.937880i	$0.612786\pi$
$662$	0.494330	0.0192127
$663$	−4.19462	−0.162905
$664$	−7.38229	−0.286488
$665$	−10.9015	−0.422741
$666$	−0.389549	−0.0150947
$667$	16.5889	0.642324
$668$	0.503990	0.0195000
$669$	−3.85440	−0.149020
$670$	−0.382831	−0.0147900
$671$	46.4895	1.79471
$672$	3.22803	0.124524
$673$	−21.7779	−0.839476	−0.419738	−	0.907645i	$-0.637878\pi$
$673$	−21.7779	−0.839476	−0.419738	+	0.907645i	$0.637878\pi$
$674$	−0.156084	−0.00601213
$675$	1.44377	0.0555709
$676$	−9.12131	−0.350820
$677$	16.0856	0.618219	0.309109	−	0.951027i	$-0.399969\pi$
$677$	16.0856	0.618219	0.309109	+	0.951027i	$0.399969\pi$
$678$	0.795381	0.0305464
$679$	32.5197	1.24799
$680$	0.916514	0.0351467
$681$	−5.54675	−0.212552
$682$	6.61747	0.253396
$683$	−27.8933	−1.06731	−0.533654	−	0.845703i	$-0.679182\pi$
$683$	−27.8933	−1.06731	−0.533654	+	0.845703i	$0.679182\pi$
$684$	5.15115	0.196959
$685$	−3.87509	−0.148060
$686$	2.45527	0.0937425
$687$	−27.5762	−1.05210
$688$	19.4706	0.742309
$689$	−9.87663	−0.376269
$690$	0.375088	0.0142794
$691$	−5.90846	−0.224768	−0.112384	−	0.993665i	$-0.535849\pi$
$691$	−5.90846	−0.224768	−0.112384	+	0.993665i	$0.535849\pi$
$692$	−47.9556	−1.82300
$693$	−11.6786	−0.443632
$694$	3.15815	0.119882
$695$	−5.52111	−0.209427
$696$	4.94340	0.187379
$697$	−6.17225	−0.233790
$698$	−1.39107	−0.0526527
$699$	−16.0748	−0.608006
$700$	−6.38501	−0.241331
$701$	28.6450	1.08191	0.540954	−	0.841052i	$-0.318063\pi$
$701$	28.6450	1.08191	0.540954	+	0.841052i	$0.318063\pi$
$702$	−0.511558	−0.0193075
$703$	8.28851	0.312607
$704$	−40.0781	−1.51050
$705$	−6.16490	−0.232183
$706$	1.53609	0.0578117
$707$	−33.9075	−1.27522
$708$	−10.9303	−0.410787
$709$	−18.4802	−0.694039	−0.347020	−	0.937858i	$-0.612806\pi$
$709$	−18.4802	−0.694039	−0.347020	+	0.937858i	$0.612806\pi$
$710$	−2.47239	−0.0927871
$711$	−7.94714	−0.298041
$712$	7.29588	0.273425
$713$	16.8815	0.632216
$714$	0.271692	0.0101678
$715$	−41.4670	−1.55078
$716$	39.8235	1.48828
$717$	−1.92800	−0.0720024
$718$	−0.408381	−0.0152407
$719$	−8.62927	−0.321817	−0.160909	−	0.986969i	$-0.551442\pi$
$719$	−8.62927	−0.321817	−0.160909	+	0.986969i	$0.551442\pi$
$720$	−7.37531	−0.274862
$721$	−8.34883	−0.310927
$722$	−1.49599	−0.0556749
$723$	−13.7618	−0.511808
$724$	−39.2534	−1.45884
$725$	−14.6852	−0.545395
$726$	−2.00994	−0.0745960
$727$	−24.4308	−0.906088	−0.453044	−	0.891488i	$-0.649662\pi$
$727$	−24.4308	−0.906088	−0.453044	+	0.891488i	$0.649662\pi$
$728$	4.54162	0.168324
$729$	1.00000	0.0370370
$730$	2.53734	0.0939113
$731$	4.97844	0.184134
$732$	17.6047	0.650687
$733$	−5.30346	−0.195888	−0.0979439	−	0.995192i	$-0.531227\pi$
$733$	−5.30346	−0.195888	−0.0979439	+	0.995192i	$0.531227\pi$
$734$	0.725980	0.0267964
$735$	−3.84128	−0.141688
$736$	2.36320	0.0871087
$737$	8.72620	0.321434
$738$	−0.752741	−0.0277088
$739$	48.3391	1.77818	0.889092	−	0.457729i	$-0.151337\pi$
$739$	48.3391	1.77818	0.889092	+	0.457729i	$0.151337\pi$
$740$	−11.9576	−0.439569
$741$	10.8845	0.399852
$742$	0.639724	0.0234850
$743$	32.1292	1.17871	0.589353	−	0.807876i	$-0.299383\pi$
$743$	32.1292	1.17871	0.589353	+	0.807876i	$0.299383\pi$
$744$	5.03059	0.184430
$745$	−6.48959	−0.237760
$746$	3.37858	0.123699
$747$	15.1896	0.555758
$748$	−10.4065	−0.380499
$749$	−36.4600	−1.33222
$750$	−1.48196	−0.0541136
$751$	0.100705	0.00367478	0.00183739	−	0.999998i	$-0.499415\pi$
$751$	0.100705	0.00367478	0.00183739	+	0.999998i	$0.499415\pi$
$752$	−12.7855	−0.466238
$753$	27.6545	1.00778
$754$	5.20326	0.189492
$755$	13.4617	0.489922
$756$	−4.42244	−0.160843
$757$	45.0735	1.63823	0.819113	−	0.573632i	$-0.194466\pi$
$757$	45.0735	1.63823	0.819113	+	0.573632i	$0.194466\pi$
$758$	−0.951469	−0.0345589
$759$	−8.54972	−0.310335
$760$	−2.37824	−0.0862678
$761$	18.5490	0.672400	0.336200	−	0.941791i	$-0.390858\pi$
$761$	18.5490	0.672400	0.336200	+	0.941791i	$0.390858\pi$
$762$	−1.68729	−0.0611240
$763$	30.7176	1.11205
$764$	−0.349367	−0.0126397
$765$	−1.88580	−0.0681811
$766$	−0.158181	−0.00571532
$767$	−23.0961	−0.833951
$768$	−14.8234	−0.534892
$769$	11.6538	0.420249	0.210124	−	0.977675i	$-0.432613\pi$
$769$	11.6538	0.420249	0.210124	+	0.977675i	$0.432613\pi$
$770$	2.68588	0.0967924
$771$	14.9157	0.537175
$772$	53.2684	1.91717
$773$	−44.3933	−1.59672	−0.798359	−	0.602182i	$-0.794298\pi$
$773$	−44.3933	−1.59672	−0.798359	+	0.602182i	$0.794298\pi$
$774$	0.607150	0.0218235
$775$	−14.9442	−0.536813
$776$	7.09441	0.254675
$777$	−7.11597	−0.255284
$778$	3.88355	0.139232
$779$	16.0162	0.573840
$780$	−15.7027	−0.562248
$781$	56.3554	2.01655
$782$	0.198902	0.00711271
$783$	−10.1714	−0.363496
$784$	−7.96649	−0.284518
$785$	1.88580	0.0673069
$786$	2.15318	0.0768016
$787$	−8.68359	−0.309537	−0.154768	−	0.987951i	$-0.549463\pi$
$787$	−8.68359	−0.309537	−0.154768	+	0.987951i	$0.549463\pi$
$788$	−15.1103	−0.538280
$789$	16.6888	0.594136
$790$	1.82771	0.0650271
$791$	14.5294	0.516605
$792$	−2.54777	−0.0905311
$793$	37.1991	1.32098
$794$	−1.11361	−0.0395206
$795$	−4.44028	−0.157481
$796$	16.2384	0.575556
$797$	27.9551	0.990222	0.495111	−	0.868830i	$-0.335127\pi$
$797$	27.9551	0.990222	0.495111	+	0.868830i	$0.335127\pi$
$798$	−0.705006	−0.0249569
$799$	−3.26912	−0.115653
$800$	−2.09201	−0.0739637
$801$	−15.0118	−0.530417
$802$	1.39083	0.0491118
$803$	−57.8359	−2.04099
$804$	3.30444	0.116539
$805$	6.85180	0.241494
$806$	5.29504	0.186510
$807$	30.2729	1.06566
$808$	−7.39717	−0.260232
$809$	38.2841	1.34600	0.672999	−	0.739644i	$-0.265006\pi$
$809$	38.2841	1.34600	0.672999	+	0.739644i	$0.265006\pi$
$810$	−0.229984	−0.00808080
$811$	15.2822	0.536632	0.268316	−	0.963331i	$-0.413533\pi$
$811$	15.2822	0.536632	0.268316	+	0.963331i	$0.413533\pi$
$812$	44.9825	1.57857
$813$	14.6471	0.513695
$814$	−2.04211	−0.0715758
$815$	−30.4218	−1.06563
$816$	−3.91098	−0.136912
$817$	−12.9184	−0.451958
$818$	3.70848	0.129664
$819$	−9.34473	−0.326531
$820$	−23.1061	−0.806899
$821$	16.7478	0.584501	0.292251	−	0.956342i	$-0.405596\pi$
$821$	16.7478	0.584501	0.292251	+	0.956342i	$0.405596\pi$
$822$	−0.250605	−0.00874085
$823$	−11.2535	−0.392272	−0.196136	−	0.980577i	$-0.562839\pi$
$823$	−11.2535	−0.392272	−0.196136	+	0.980577i	$0.562839\pi$
$824$	−1.82136	−0.0634501
$825$	7.56859	0.263505
$826$	1.49597	0.0520514
$827$	39.8561	1.38593	0.692966	−	0.720970i	$-0.256304\pi$
$827$	39.8561	1.38593	0.692966	+	0.720970i	$0.256304\pi$
$828$	−3.23761	−0.112515
$829$	56.7957	1.97260	0.986299	−	0.164969i	$-0.0527525\pi$
$829$	56.7957	1.97260	0.986299	+	0.164969i	$0.0527525\pi$
$830$	−3.49336	−0.121256
$831$	−8.47048	−0.293838
$832$	−32.0689	−1.11179
$833$	−2.03695	−0.0705763
$834$	−0.357054	−0.0123638
$835$	0.478772	0.0165686
$836$	27.0035	0.933936
$837$	−10.3508	−0.357776
$838$	0.216410	0.00747577
$839$	−20.3334	−0.701986	−0.350993	−	0.936378i	$-0.614156\pi$
$839$	−20.3334	−0.701986	−0.350993	+	0.936378i	$0.614156\pi$
$840$	2.04180	0.0704488
$841$	74.4574	2.56750
$842$	−2.18909	−0.0754410
$843$	−19.9187	−0.686037
$844$	16.3142	0.561559
$845$	−8.66490	−0.298082
$846$	−0.398688	−0.0137072
$847$	−36.7160	−1.26158
$848$	−9.20878	−0.316231
$849$	5.44697	0.186939
$850$	−0.176077	−0.00603938
$851$	−5.20950	−0.178579
$852$	21.3407	0.731119
$853$	30.3234	1.03825	0.519126	−	0.854698i	$-0.326257\pi$
$853$	30.3234	1.03825	0.519126	+	0.854698i	$0.326257\pi$
$854$	−2.40944	−0.0824493
$855$	4.89340	0.167351
$856$	−7.95403	−0.271863
$857$	−49.5256	−1.69176	−0.845881	−	0.533372i	$-0.820925\pi$
$857$	−49.5256	−1.69176	−0.845881	+	0.533372i	$0.820925\pi$
$858$	−2.68170	−0.0915518
$859$	40.1950	1.37143	0.685717	−	0.727868i	$-0.259489\pi$
$859$	40.1950	1.37143	0.685717	+	0.727868i	$0.259489\pi$
$860$	18.6370	0.635517
$861$	−13.7505	−0.468615
$862$	−1.30571	−0.0444728
$863$	−54.7332	−1.86314	−0.931569	−	0.363564i	$-0.881560\pi$
$863$	−54.7332	−1.86314	−0.931569	+	0.363564i	$0.881560\pi$
$864$	−1.44899	−0.0492955
$865$	−45.5560	−1.54895
$866$	1.30580	0.0443728
$867$	−1.00000	−0.0339618
$868$	45.7758	1.55373
$869$	−41.6607	−1.41324
$870$	2.33926	0.0793082
$871$	6.98236	0.236588
$872$	6.70128	0.226934
$873$	−14.5973	−0.494043
$874$	−0.516125	−0.0174582
$875$	−27.0713	−0.915177
$876$	−21.9013	−0.739977
$877$	−46.5523	−1.57196	−0.785980	−	0.618252i	$-0.787841\pi$
$877$	−46.5523	−1.57196	−0.785980	+	0.618252i	$0.787841\pi$
$878$	−1.75813	−0.0593341
$879$	−5.58322	−0.188317
$880$	−38.6630	−1.30333
$881$	−6.46301	−0.217744	−0.108872	−	0.994056i	$-0.534724\pi$
$881$	−6.46301	−0.217744	−0.108872	+	0.994056i	$0.534724\pi$
$882$	−0.248418	−0.00836468
$883$	−8.07960	−0.271900	−0.135950	−	0.990716i	$-0.543409\pi$
$883$	−8.07960	−0.271900	−0.135950	+	0.990716i	$0.543409\pi$
$884$	−8.32685	−0.280062
$885$	−10.3834	−0.349035
$886$	0.675352	0.0226889
$887$	−45.2698	−1.52001	−0.760005	−	0.649917i	$-0.774804\pi$
$887$	−45.2698	−1.52001	−0.760005	+	0.649917i	$0.774804\pi$
$888$	−1.55240	−0.0520953
$889$	−30.8220	−1.03374
$890$	3.45247	0.115727
$891$	5.24222	0.175621
$892$	−7.65147	−0.256190
$893$	8.48296	0.283871
$894$	−0.419686	−0.0140364
$895$	37.8309	1.26455
$896$	8.53322	0.285075
$897$	−6.84114	−0.228419
$898$	−0.772957	−0.0257939
$899$	105.282	3.51136
$900$	2.86608	0.0955359
$901$	−2.35459	−0.0784429
$902$	−3.94604	−0.131389
$903$	11.0909	0.369083
$904$	3.16969	0.105422
$905$	−37.2892	−1.23954
$906$	0.870578	0.0289230
$907$	36.9402	1.22658	0.613289	−	0.789858i	$-0.289846\pi$
$907$	36.9402	1.22658	0.613289	+	0.789858i	$0.289846\pi$
$908$	−11.0110	−0.365413
$909$	15.2202	0.504823
$910$	2.14913	0.0712431
$911$	−28.5158	−0.944770	−0.472385	−	0.881392i	$-0.656607\pi$
$911$	−28.5158	−0.944770	−0.472385	+	0.881392i	$0.656607\pi$
$912$	10.1485	0.336051
$913$	79.6273	2.63528
$914$	3.22194	0.106572
$915$	16.7238	0.552871
$916$	−54.7423	−1.80874
$917$	39.3326	1.29888
$918$	−0.121956	−0.00402514
$919$	29.7798	0.982346	0.491173	−	0.871062i	$-0.336568\pi$
$919$	29.7798	0.982346	0.491173	+	0.871062i	$0.336568\pi$
$920$	1.49477	0.0492812
$921$	−0.379767	−0.0125137
$922$	−3.40416	−0.112110
$923$	45.0933	1.48426
$924$	−23.1834	−0.762679
$925$	4.61168	0.151631
$926$	2.83799	0.0932621
$927$	3.74759	0.123087
$928$	14.7382	0.483806
$929$	9.77570	0.320730	0.160365	−	0.987058i	$-0.448733\pi$
$929$	9.77570	0.320730	0.160365	+	0.987058i	$0.448733\pi$
$930$	2.38052	0.0780602
$931$	5.28564	0.173230
$932$	−31.9106	−1.04527
$933$	20.3654	0.666734
$934$	−0.201616	−0.00659707
$935$	−9.88576	−0.323299
$936$	−2.03862	−0.0666345
$937$	21.0914	0.689025	0.344513	−	0.938782i	$-0.388044\pi$
$937$	21.0914	0.689025	0.344513	+	0.938782i	$0.388044\pi$
$938$	−0.452258	−0.0147667
$939$	−31.2318	−1.01921
$940$	−12.2381	−0.399163
$941$	−36.8326	−1.20071	−0.600354	−	0.799735i	$-0.704974\pi$
$941$	−36.8326	−1.20071	−0.600354	+	0.799735i	$0.704974\pi$
$942$	0.121956	0.00397353
$943$	−10.0665	−0.327811
$944$	−21.5343	−0.700883
$945$	−4.20116	−0.136664
$946$	3.18281	0.103482
$947$	−58.0801	−1.88735	−0.943675	−	0.330874i	$-0.892656\pi$
$947$	−58.0801	−1.88735	−0.943675	+	0.330874i	$0.892656\pi$
$948$	−15.7761	−0.512383
$949$	−46.2780	−1.50225
$950$	0.456897	0.0148237
$951$	−31.5386	−1.02271
$952$	1.08273	0.0350914
$953$	−18.4044	−0.596176	−0.298088	−	0.954538i	$-0.596349\pi$
$953$	−18.4044	−0.596176	−0.298088	+	0.954538i	$0.596349\pi$
$954$	−0.287156	−0.00929703
$955$	−0.331886	−0.0107396
$956$	−3.82732	−0.123784
$957$	−53.3208	−1.72362
$958$	−1.06104	−0.0342806
$959$	−4.57785	−0.147826
$960$	−14.4174	−0.465319
$961$	76.1391	2.45610
$962$	−1.63401	−0.0526826
$963$	16.3660	0.527387
$964$	−27.3190	−0.879885
$965$	50.6030	1.62897
$966$	0.443111	0.0142569
$967$	35.9422	1.15582	0.577912	−	0.816099i	$-0.303868\pi$
$967$	35.9422	1.15582	0.577912	+	0.816099i	$0.303868\pi$
$968$	−8.00988	−0.257447
$969$	2.59487	0.0833594
$970$	3.35714	0.107791
$971$	−48.3779	−1.55252	−0.776260	−	0.630413i	$-0.782886\pi$
$971$	−48.3779	−1.55252	−0.776260	+	0.630413i	$0.782886\pi$
$972$	1.98513	0.0636730
$973$	−6.52237	−0.209098
$974$	−3.00483	−0.0962811
$975$	6.05609	0.193950
$976$	34.6837	1.11020
$977$	−32.8198	−1.05000	−0.524999	−	0.851103i	$-0.675934\pi$
$977$	−32.8198	−1.05000	−0.524999	+	0.851103i	$0.675934\pi$
$978$	−1.96740	−0.0629105
$979$	−78.6953	−2.51511
$980$	−7.62543	−0.243585
$981$	−13.7884	−0.440229
$982$	3.92150	0.125140
$983$	18.0034	0.574218	0.287109	−	0.957898i	$-0.407306\pi$
$983$	18.0034	0.574218	0.287109	+	0.957898i	$0.407306\pi$
$984$	−2.99977	−0.0956291
$985$	−14.3542	−0.457362
$986$	1.24046	0.0395043
$987$	−7.28292	−0.231818
$988$	21.6071	0.687414
$989$	8.11950	0.258185
$990$	−1.20563	−0.0383173
$991$	−5.81870	−0.184837	−0.0924186	−	0.995720i	$-0.529460\pi$
$991$	−5.81870	−0.184837	−0.0924186	+	0.995720i	$0.529460\pi$
$992$	14.9982	0.476192
$993$	−4.05336	−0.128629
$994$	−2.92076	−0.0926410
$995$	15.4259	0.489033
$996$	30.1533	0.955443
$997$	29.6147	0.937908	0.468954	−	0.883223i	$-0.344631\pi$
$997$	29.6147	0.937908	0.468954	+	0.883223i	$0.344631\pi$
$998$	1.99090	0.0630210
$999$	3.19418	0.101060

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.33	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.33	✓	64	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+0.121956 q^{2} -1.00000 q^{3} -1.98513 q^{4} -1.88580 q^{5} -0.121956 q^{6} -2.22779 q^{7} -0.486009 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.121956 q^{2} -1.00000 q^{3} -1.98513 q^{4} -1.88580 q^{5} -0.121956 q^{6} -2.22779 q^{7} -0.486009 q^{8} +1.00000 q^{9} -0.229984 q^{10} +5.24222 q^{11} +1.98513 q^{12} +4.19462 q^{13} -0.271692 q^{14} +1.88580 q^{15} +3.91098 q^{16} +1.00000 q^{17} +0.121956 q^{18} -2.59487 q^{19} +3.74354 q^{20} +2.22779 q^{21} +0.639320 q^{22} +1.63093 q^{23} +0.486009 q^{24} -1.44377 q^{25} +0.511558 q^{26} -1.00000 q^{27} +4.42244 q^{28} +10.1714 q^{29} +0.229984 q^{30} +10.3508 q^{31} +1.44899 q^{32} -5.24222 q^{33} +0.121956 q^{34} +4.20116 q^{35} -1.98513 q^{36} -3.19418 q^{37} -0.316460 q^{38} -4.19462 q^{39} +0.916514 q^{40} -6.17225 q^{41} +0.271692 q^{42} +4.97844 q^{43} -10.4065 q^{44} -1.88580 q^{45} +0.198902 q^{46} -3.26912 q^{47} -3.91098 q^{48} -2.03695 q^{49} -0.176077 q^{50} -1.00000 q^{51} -8.32685 q^{52} -2.35459 q^{53} -0.121956 q^{54} -9.88576 q^{55} +1.08273 q^{56} +2.59487 q^{57} +1.24046 q^{58} -5.50612 q^{59} -3.74354 q^{60} +8.86828 q^{61} +1.26234 q^{62} -2.22779 q^{63} -7.64525 q^{64} -7.91019 q^{65} -0.639320 q^{66} +1.66460 q^{67} -1.98513 q^{68} -1.63093 q^{69} +0.512355 q^{70} +10.7503 q^{71} -0.486009 q^{72} -11.0327 q^{73} -0.389549 q^{74} +1.44377 q^{75} +5.15115 q^{76} -11.6786 q^{77} -0.511558 q^{78} -7.94714 q^{79} -7.37531 q^{80} +1.00000 q^{81} -0.752741 q^{82} +15.1896 q^{83} -4.42244 q^{84} -1.88580 q^{85} +0.607150 q^{86} -10.1714 q^{87} -2.54777 q^{88} -15.0118 q^{89} -0.229984 q^{90} -9.34473 q^{91} -3.23761 q^{92} -10.3508 q^{93} -0.398688 q^{94} +4.89340 q^{95} -1.44899 q^{96} -14.5973 q^{97} -0.248418 q^{98} +5.24222 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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