LMFDB - Embedded newform 8007.2.a.c.1.10

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:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-1.63095 q^{2} -1.00000 q^{3} +0.660014 q^{4} +1.38859 q^{5} +1.63095 q^{6} +2.37558 q^{7} +2.18546 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.63095 q^{2} -1.00000 q^{3} +0.660014 q^{4} +1.38859 q^{5} +1.63095 q^{6} +2.37558 q^{7} +2.18546 q^{8} +1.00000 q^{9} -2.26473 q^{10} -1.95226 q^{11} -0.660014 q^{12} -2.02534 q^{13} -3.87446 q^{14} -1.38859 q^{15} -4.88441 q^{16} +1.00000 q^{17} -1.63095 q^{18} +2.21429 q^{19} +0.916488 q^{20} -2.37558 q^{21} +3.18404 q^{22} +3.80128 q^{23} -2.18546 q^{24} -3.07182 q^{25} +3.30323 q^{26} -1.00000 q^{27} +1.56792 q^{28} -7.93340 q^{29} +2.26473 q^{30} -3.32374 q^{31} +3.59534 q^{32} +1.95226 q^{33} -1.63095 q^{34} +3.29871 q^{35} +0.660014 q^{36} +11.1954 q^{37} -3.61141 q^{38} +2.02534 q^{39} +3.03470 q^{40} +4.09779 q^{41} +3.87446 q^{42} +3.60885 q^{43} -1.28852 q^{44} +1.38859 q^{45} -6.19971 q^{46} -0.0414365 q^{47} +4.88441 q^{48} -1.35662 q^{49} +5.01000 q^{50} -1.00000 q^{51} -1.33675 q^{52} +2.03991 q^{53} +1.63095 q^{54} -2.71088 q^{55} +5.19173 q^{56} -2.21429 q^{57} +12.9390 q^{58} -0.596046 q^{59} -0.916488 q^{60} -5.88020 q^{61} +5.42087 q^{62} +2.37558 q^{63} +3.90499 q^{64} -2.81236 q^{65} -3.18404 q^{66} -4.79611 q^{67} +0.660014 q^{68} -3.80128 q^{69} -5.38004 q^{70} -4.60483 q^{71} +2.18546 q^{72} -10.9519 q^{73} -18.2592 q^{74} +3.07182 q^{75} +1.46146 q^{76} -4.63774 q^{77} -3.30323 q^{78} -1.83474 q^{79} -6.78244 q^{80} +1.00000 q^{81} -6.68331 q^{82} -12.4574 q^{83} -1.56792 q^{84} +1.38859 q^{85} -5.88586 q^{86} +7.93340 q^{87} -4.26657 q^{88} -9.18735 q^{89} -2.26473 q^{90} -4.81135 q^{91} +2.50889 q^{92} +3.32374 q^{93} +0.0675811 q^{94} +3.07475 q^{95} -3.59534 q^{96} +3.30682 q^{97} +2.21258 q^{98} -1.95226 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + 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 $

$2$	−1.63095	−1.15326	−0.576630	−	0.817006i	$-0.695632\pi$
$2$	−1.63095	−1.15326	−0.576630	+	0.817006i	$0.695632\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.660014	0.330007
$5$	1.38859	0.620996	0.310498	−	0.950574i	$-0.399504\pi$
$5$	1.38859	0.620996	0.310498	+	0.950574i	$0.399504\pi$
$6$	1.63095	0.665835
$7$	2.37558	0.897885	0.448942	−	0.893561i	$-0.351801\pi$
$7$	2.37558	0.897885	0.448942	+	0.893561i	$0.351801\pi$
$8$	2.18546	0.772676
$9$	1.00000	0.333333
$10$	−2.26473	−0.716169
$11$	−1.95226	−0.588628	−0.294314	−	0.955709i	$-0.595091\pi$
$11$	−1.95226	−0.588628	−0.294314	+	0.955709i	$0.595091\pi$
$12$	−0.660014	−0.190530
$13$	−2.02534	−0.561728	−0.280864	−	0.959748i	$-0.590621\pi$
$13$	−2.02534	−0.561728	−0.280864	+	0.959748i	$0.590621\pi$
$14$	−3.87446	−1.03549
$15$	−1.38859	−0.358532
$16$	−4.88441	−1.22110
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.63095	−0.384420
$19$	2.21429	0.507994	0.253997	−	0.967205i	$-0.418255\pi$
$19$	2.21429	0.507994	0.253997	+	0.967205i	$0.418255\pi$
$20$	0.916488	0.204933
$21$	−2.37558	−0.518394
$22$	3.18404	0.678840
$23$	3.80128	0.792621	0.396310	−	0.918117i	$-0.370290\pi$
$23$	3.80128	0.792621	0.396310	+	0.918117i	$0.370290\pi$
$24$	−2.18546	−0.446105
$25$	−3.07182	−0.614364
$26$	3.30323	0.647817
$27$	−1.00000	−0.192450
$28$	1.56792	0.296308
$29$	−7.93340	−1.47320	−0.736598	−	0.676331i	$-0.763569\pi$
$29$	−7.93340	−1.47320	−0.736598	+	0.676331i	$0.763569\pi$
$30$	2.26473	0.413481
$31$	−3.32374	−0.596961	−0.298480	−	0.954416i	$-0.596480\pi$
$31$	−3.32374	−0.596961	−0.298480	+	0.954416i	$0.596480\pi$
$32$	3.59534	0.635572
$33$	1.95226	0.339844
$34$	−1.63095	−0.279706
$35$	3.29871	0.557583
$36$	0.660014	0.110002
$37$	11.1954	1.84052	0.920258	−	0.391311i	$-0.127978\pi$
$37$	11.1954	1.84052	0.920258	+	0.391311i	$0.127978\pi$
$38$	−3.61141	−0.585849
$39$	2.02534	0.324314
$40$	3.03470	0.479829
$41$	4.09779	0.639967	0.319983	−	0.947423i	$-0.396323\pi$
$41$	4.09779	0.639967	0.319983	+	0.947423i	$0.396323\pi$
$42$	3.87446	0.597843
$43$	3.60885	0.550344	0.275172	−	0.961395i	$-0.411265\pi$
$43$	3.60885	0.550344	0.275172	+	0.961395i	$0.411265\pi$
$44$	−1.28852	−0.194251
$45$	1.38859	0.206999
$46$	−6.19971	−0.914097
$47$	−0.0414365	−0.00604414	−0.00302207	−	0.999995i	$-0.500962\pi$
$47$	−0.0414365	−0.00604414	−0.00302207	+	0.999995i	$0.500962\pi$
$48$	4.88441	0.705004
$49$	−1.35662	−0.193803
$50$	5.01000	0.708521
$51$	−1.00000	−0.140028
$52$	−1.33675	−0.185374
$53$	2.03991	0.280203	0.140102	−	0.990137i	$-0.455257\pi$
$53$	2.03991	0.280203	0.140102	+	0.990137i	$0.455257\pi$
$54$	1.63095	0.221945
$55$	−2.71088	−0.365535
$56$	5.19173	0.693774
$57$	−2.21429	−0.293290
$58$	12.9390	1.69898
$59$	−0.596046	−0.0775986	−0.0387993	−	0.999247i	$-0.512353\pi$
$59$	−0.596046	−0.0775986	−0.0387993	+	0.999247i	$0.512353\pi$
$60$	−0.916488	−0.118318
$61$	−5.88020	−0.752882	−0.376441	−	0.926441i	$-0.622852\pi$
$61$	−5.88020	−0.752882	−0.376441	+	0.926441i	$0.622852\pi$
$62$	5.42087	0.688451
$63$	2.37558	0.299295
$64$	3.90499	0.488123
$65$	−2.81236	−0.348831
$66$	−3.18404	−0.391929
$67$	−4.79611	−0.585939	−0.292969	−	0.956122i	$-0.594643\pi$
$67$	−4.79611	−0.585939	−0.292969	+	0.956122i	$0.594643\pi$
$68$	0.660014	0.0800384
$69$	−3.80128	−0.457620
$70$	−5.38004	−0.643038
$71$	−4.60483	−0.546493	−0.273247	−	0.961944i	$-0.588097\pi$
$71$	−4.60483	−0.546493	−0.273247	+	0.961944i	$0.588097\pi$
$72$	2.18546	0.257559
$73$	−10.9519	−1.28182	−0.640909	−	0.767616i	$-0.721443\pi$
$73$	−10.9519	−1.28182	−0.640909	+	0.767616i	$0.721443\pi$
$74$	−18.2592	−2.12259
$75$	3.07182	0.354703
$76$	1.46146	0.167641
$77$	−4.63774	−0.528520
$78$	−3.30323	−0.374018
$79$	−1.83474	−0.206425	−0.103212	−	0.994659i	$-0.532912\pi$
$79$	−1.83474	−0.206425	−0.103212	+	0.994659i	$0.532912\pi$
$80$	−6.78244	−0.758300
$81$	1.00000	0.111111
$82$	−6.68331	−0.738048
$83$	−12.4574	−1.36738	−0.683689	−	0.729773i	$-0.739626\pi$
$83$	−12.4574	−1.36738	−0.683689	+	0.729773i	$0.739626\pi$
$84$	−1.56792	−0.171074
$85$	1.38859	0.150614
$86$	−5.88586	−0.634689
$87$	7.93340	0.850550
$88$	−4.26657	−0.454818
$89$	−9.18735	−0.973858	−0.486929	−	0.873442i	$-0.661883\pi$
$89$	−9.18735	−0.973858	−0.486929	+	0.873442i	$0.661883\pi$
$90$	−2.26473	−0.238723
$91$	−4.81135	−0.504367
$92$	2.50889	0.261570
$93$	3.32374	0.344656
$94$	0.0675811	0.00697046
$95$	3.07475	0.315462
$96$	−3.59534	−0.366948
$97$	3.30682	0.335756	0.167878	−	0.985808i	$-0.446308\pi$
$97$	3.30682	0.335756	0.167878	+	0.985808i	$0.446308\pi$
$98$	2.21258	0.223505
$99$	−1.95226	−0.196209
$100$	−2.02744	−0.202744
$101$	−1.74442	−0.173577	−0.0867884	−	0.996227i	$-0.527660\pi$
$101$	−1.74442	−0.173577	−0.0867884	+	0.996227i	$0.527660\pi$
$102$	1.63095	0.161489
$103$	10.1173	0.996885	0.498443	−	0.866923i	$-0.333905\pi$
$103$	10.1173	0.996885	0.498443	+	0.866923i	$0.333905\pi$
$104$	−4.42629	−0.434033
$105$	−3.29871	−0.321921
$106$	−3.32700	−0.323147
$107$	−10.6795	−1.03242	−0.516212	−	0.856461i	$-0.672658\pi$
$107$	−10.6795	−1.03242	−0.516212	+	0.856461i	$0.672658\pi$
$108$	−0.660014	−0.0635098
$109$	−5.11875	−0.490287	−0.245144	−	0.969487i	$-0.578835\pi$
$109$	−5.11875	−0.490287	−0.245144	+	0.969487i	$0.578835\pi$
$110$	4.42133	0.421557
$111$	−11.1954	−1.06262
$112$	−11.6033	−1.09641
$113$	7.96643	0.749419	0.374709	−	0.927142i	$-0.377742\pi$
$113$	7.96643	0.749419	0.374709	+	0.927142i	$0.377742\pi$
$114$	3.61141	0.338240
$115$	5.27841	0.492214
$116$	−5.23615	−0.486165
$117$	−2.02534	−0.187243
$118$	0.972124	0.0894912
$119$	2.37558	0.217769
$120$	−3.03470	−0.277029
$121$	−7.18869	−0.653518
$122$	9.59034	0.868268
$123$	−4.09779	−0.369485
$124$	−2.19371	−0.197001
$125$	−11.2084	−1.00251
$126$	−3.87446	−0.345165
$127$	−6.54251	−0.580554	−0.290277	−	0.956943i	$-0.593747\pi$
$127$	−6.54251	−0.580554	−0.290277	+	0.956943i	$0.593747\pi$
$128$	−13.5595	−1.19850
$129$	−3.60885	−0.317741
$130$	4.58684	0.402292
$131$	8.63455	0.754404	0.377202	−	0.926131i	$-0.376886\pi$
$131$	8.63455	0.754404	0.377202	+	0.926131i	$0.376886\pi$
$132$	1.28852	0.112151
$133$	5.26023	0.456120
$134$	7.82225	0.675739
$135$	−1.38859	−0.119511
$136$	2.18546	0.187401
$137$	21.8727	1.86872	0.934358	−	0.356337i	$-0.115974\pi$
$137$	21.8727	1.86872	0.934358	+	0.356337i	$0.115974\pi$
$138$	6.19971	0.527754
$139$	−3.71694	−0.315267	−0.157633	−	0.987498i	$-0.550386\pi$
$139$	−3.71694	−0.315267	−0.157633	+	0.987498i	$0.550386\pi$
$140$	2.17719	0.184006
$141$	0.0414365	0.00348959
$142$	7.51028	0.630248
$143$	3.95398	0.330648
$144$	−4.88441	−0.407034
$145$	−11.0162	−0.914849
$146$	17.8620	1.47827
$147$	1.35662	0.111892
$148$	7.38913	0.607383
$149$	14.7784	1.21069	0.605347	−	0.795962i	$-0.293034\pi$
$149$	14.7784	1.21069	0.605347	+	0.795962i	$0.293034\pi$
$150$	−5.01000	−0.409065
$151$	−23.1761	−1.88604	−0.943021	−	0.332732i	$-0.892030\pi$
$151$	−23.1761	−1.88604	−0.943021	+	0.332732i	$0.892030\pi$
$152$	4.83925	0.392515
$153$	1.00000	0.0808452
$154$	7.56395	0.609520
$155$	−4.61531	−0.370710
$156$	1.33675	0.107026
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	2.99238	0.238061
$159$	−2.03991	−0.161775
$160$	4.99245	0.394688
$161$	9.03024	0.711682
$162$	−1.63095	−0.128140
$163$	−16.5974	−1.30001	−0.650005	−	0.759930i	$-0.725233\pi$
$163$	−16.5974	−1.30001	−0.650005	+	0.759930i	$0.725233\pi$
$164$	2.70460	0.211193
$165$	2.71088	0.211042
$166$	20.3175	1.57694
$167$	−7.95155	−0.615309	−0.307655	−	0.951498i	$-0.599544\pi$
$167$	−7.95155	−0.615309	−0.307655	+	0.951498i	$0.599544\pi$
$168$	−5.19173	−0.400551
$169$	−8.89801	−0.684462
$170$	−2.26473	−0.173697
$171$	2.21429	0.169331
$172$	2.38189	0.181617
$173$	16.8262	1.27927	0.639636	−	0.768678i	$-0.279085\pi$
$173$	16.8262	1.27927	0.639636	+	0.768678i	$0.279085\pi$
$174$	−12.9390	−0.980905
$175$	−7.29735	−0.551628
$176$	9.53562	0.718775
$177$	0.596046	0.0448015
$178$	14.9842	1.12311
$179$	1.12061	0.0837585	0.0418792	−	0.999123i	$-0.486666\pi$
$179$	1.12061	0.0837585	0.0418792	+	0.999123i	$0.486666\pi$
$180$	0.916488	0.0683110
$181$	−23.7229	−1.76331	−0.881655	−	0.471894i	$-0.843571\pi$
$181$	−23.7229	−1.76331	−0.881655	+	0.471894i	$0.843571\pi$
$182$	7.84710	0.581666
$183$	5.88020	0.434677
$184$	8.30753	0.612439
$185$	15.5459	1.14295
$186$	−5.42087	−0.397477
$187$	−1.95226	−0.142763
$188$	−0.0273487	−0.00199461
$189$	−2.37558	−0.172798
$190$	−5.01477	−0.363810
$191$	−1.08853	−0.0787636	−0.0393818	−	0.999224i	$-0.512539\pi$
$191$	−1.08853	−0.0787636	−0.0393818	+	0.999224i	$0.512539\pi$
$192$	−3.90499	−0.281818
$193$	24.2440	1.74512	0.872560	−	0.488507i	$-0.162458\pi$
$193$	24.2440	1.74512	0.872560	+	0.488507i	$0.162458\pi$
$194$	−5.39327	−0.387214
$195$	2.81236	0.201397
$196$	−0.895387	−0.0639562
$197$	4.48344	0.319432	0.159716	−	0.987163i	$-0.448942\pi$
$197$	4.48344	0.319432	0.159716	+	0.987163i	$0.448942\pi$
$198$	3.18404	0.226280
$199$	−6.77236	−0.480080	−0.240040	−	0.970763i	$-0.577161\pi$
$199$	−6.77236	−0.480080	−0.240040	+	0.970763i	$0.577161\pi$
$200$	−6.71333	−0.474704
$201$	4.79611	0.338292
$202$	2.84508	0.200179
$203$	−18.8464	−1.32276
$204$	−0.660014	−0.0462102
$205$	5.69014	0.397417
$206$	−16.5008	−1.14967
$207$	3.80128	0.264207
$208$	9.89258	0.685927
$209$	−4.32287	−0.299019
$210$	5.38004	0.371258
$211$	2.52702	0.173967	0.0869836	−	0.996210i	$-0.472277\pi$
$211$	2.52702	0.173967	0.0869836	+	0.996210i	$0.472277\pi$
$212$	1.34637	0.0924690
$213$	4.60483	0.315518
$214$	17.4178	1.19065
$215$	5.01120	0.341761
$216$	−2.18546	−0.148702
$217$	−7.89580	−0.536002
$218$	8.34845	0.565428
$219$	10.9519	0.740059
$220$	−1.78922	−0.120629
$221$	−2.02534	−0.136239
$222$	18.2592	1.22548
$223$	−5.56077	−0.372377	−0.186188	−	0.982514i	$-0.559613\pi$
$223$	−5.56077	−0.372377	−0.186188	+	0.982514i	$0.559613\pi$
$224$	8.54101	0.570670
$225$	−3.07182	−0.204788
$226$	−12.9929	−0.864274
$227$	27.1183	1.79990	0.899952	−	0.435989i	$-0.143601\pi$
$227$	27.1183	1.79990	0.899952	+	0.435989i	$0.143601\pi$
$228$	−1.46146	−0.0967879
$229$	10.3903	0.686611	0.343305	−	0.939224i	$-0.388453\pi$
$229$	10.3903	0.686611	0.343305	+	0.939224i	$0.388453\pi$
$230$	−8.60885	−0.567651
$231$	4.63774	0.305141
$232$	−17.3381	−1.13830
$233$	−19.5398	−1.28009	−0.640047	−	0.768336i	$-0.721085\pi$
$233$	−19.5398	−1.28009	−0.640047	+	0.768336i	$0.721085\pi$
$234$	3.30323	0.215939
$235$	−0.0575383	−0.00375339
$236$	−0.393398	−0.0256081
$237$	1.83474	0.119179
$238$	−3.87446	−0.251144
$239$	−12.5770	−0.813541	−0.406770	−	0.913530i	$-0.633345\pi$
$239$	−12.5770	−0.813541	−0.406770	+	0.913530i	$0.633345\pi$
$240$	6.78244	0.437805
$241$	−2.92636	−0.188503	−0.0942517	−	0.995548i	$-0.530046\pi$
$241$	−2.92636	−0.188503	−0.0942517	+	0.995548i	$0.530046\pi$
$242$	11.7244	0.753675
$243$	−1.00000	−0.0641500
$244$	−3.88101	−0.248456
$245$	−1.88379	−0.120351
$246$	6.68331	0.426112
$247$	−4.48469	−0.285354
$248$	−7.26389	−0.461257
$249$	12.4574	0.789456
$250$	18.2805	1.15616
$251$	−19.3774	−1.22309	−0.611546	−	0.791209i	$-0.709452\pi$
$251$	−19.3774	−1.22309	−0.611546	+	0.791209i	$0.709452\pi$
$252$	1.56792	0.0987694
$253$	−7.42107	−0.466558
$254$	10.6705	0.669529
$255$	−1.38859	−0.0869568
$256$	14.3050	0.894063
$257$	0.665979	0.0415426	0.0207713	−	0.999784i	$-0.493388\pi$
$257$	0.665979	0.0415426	0.0207713	+	0.999784i	$0.493388\pi$
$258$	5.88586	0.366438
$259$	26.5956	1.65257
$260$	−1.85620	−0.115116
$261$	−7.93340	−0.491065
$262$	−14.0826	−0.870024
$263$	0.249822	0.0154047	0.00770235	−	0.999970i	$-0.497548\pi$
$263$	0.249822	0.0154047	0.00770235	+	0.999970i	$0.497548\pi$
$264$	4.26657	0.262589
$265$	2.83260	0.174005
$266$	−8.57920	−0.526025
$267$	9.18735	0.562257
$268$	−3.16550	−0.193364
$269$	−21.3703	−1.30297	−0.651485	−	0.758661i	$-0.725854\pi$
$269$	−21.3703	−1.30297	−0.651485	+	0.758661i	$0.725854\pi$
$270$	2.26473	0.137827
$271$	−11.1217	−0.675597	−0.337798	−	0.941219i	$-0.609682\pi$
$271$	−11.1217	−0.675597	−0.337798	+	0.941219i	$0.609682\pi$
$272$	−4.88441	−0.296161
$273$	4.81135	0.291196
$274$	−35.6735	−2.15511
$275$	5.99698	0.361632
$276$	−2.50889	−0.151018
$277$	25.3139	1.52097	0.760483	−	0.649358i	$-0.224962\pi$
$277$	25.3139	1.52097	0.760483	+	0.649358i	$0.224962\pi$
$278$	6.06217	0.363585
$279$	−3.32374	−0.198987
$280$	7.20918	0.430831
$281$	1.34523	0.0802494	0.0401247	−	0.999195i	$-0.487224\pi$
$281$	1.34523	0.0802494	0.0401247	+	0.999195i	$0.487224\pi$
$282$	−0.0675811	−0.00402440
$283$	20.3342	1.20875	0.604373	−	0.796702i	$-0.293424\pi$
$283$	20.3342	1.20875	0.604373	+	0.796702i	$0.293424\pi$
$284$	−3.03925	−0.180346
$285$	−3.07475	−0.182132
$286$	−6.44876	−0.381323
$287$	9.73462	0.574617
$288$	3.59534	0.211857
$289$	1.00000	0.0588235
$290$	17.9670	1.05506
$291$	−3.30682	−0.193849
$292$	−7.22838	−0.423009
$293$	18.2670	1.06717	0.533586	−	0.845746i	$-0.320844\pi$
$293$	18.2670	1.06717	0.533586	+	0.845746i	$0.320844\pi$
$294$	−2.21258	−0.129041
$295$	−0.827663	−0.0481884
$296$	24.4671	1.42212
$297$	1.95226	0.113281
$298$	−24.1029	−1.39624
$299$	−7.69887	−0.445237
$300$	2.02744	0.117054
$301$	8.57310	0.494145
$302$	37.7991	2.17510
$303$	1.74442	0.100215
$304$	−10.8155	−0.620313
$305$	−8.16518	−0.467537
$306$	−1.63095	−0.0932355
$307$	20.9522	1.19581	0.597904	−	0.801568i	$-0.296000\pi$
$307$	20.9522	1.19581	0.597904	+	0.801568i	$0.296000\pi$
$308$	−3.06097	−0.174415
$309$	−10.1173	−0.575552
$310$	7.52736	0.427525
$311$	32.3282	1.83316	0.916582	−	0.399848i	$-0.130937\pi$
$311$	32.3282	1.83316	0.916582	+	0.399848i	$0.130937\pi$
$312$	4.42629	0.250589
$313$	−34.3294	−1.94041	−0.970205	−	0.242284i	$-0.922103\pi$
$313$	−34.3294	−1.94041	−0.970205	+	0.242284i	$0.922103\pi$
$314$	−1.63095	−0.0920401
$315$	3.29871	0.185861
$316$	−1.21095	−0.0681215
$317$	−1.91871	−0.107766	−0.0538829	−	0.998547i	$-0.517160\pi$
$317$	−1.91871	−0.107766	−0.0538829	+	0.998547i	$0.517160\pi$
$318$	3.32700	0.186569
$319$	15.4880	0.867164
$320$	5.42242	0.303123
$321$	10.6795	0.596071
$322$	−14.7279	−0.820754
$323$	2.21429	0.123207
$324$	0.660014	0.0366674
$325$	6.22147	0.345105
$326$	27.0696	1.49925
$327$	5.11875	0.283068
$328$	8.95554	0.494487
$329$	−0.0984358	−0.00542694
$330$	−4.42133	−0.243386
$331$	23.8782	1.31246	0.656231	−	0.754560i	$-0.272150\pi$
$331$	23.8782	1.31246	0.656231	+	0.754560i	$0.272150\pi$
$332$	−8.22206	−0.451244
$333$	11.1954	0.613506
$334$	12.9686	0.709611
$335$	−6.65983	−0.363866
$336$	11.6033	0.633012
$337$	−13.3733	−0.728489	−0.364245	−	0.931303i	$-0.618673\pi$
$337$	−13.3733	−0.728489	−0.364245	+	0.931303i	$0.618673\pi$
$338$	14.5122	0.789362
$339$	−7.96643	−0.432677
$340$	0.916488	0.0497035
$341$	6.48879	0.351388
$342$	−3.61141	−0.195283
$343$	−19.8518	−1.07190
$344$	7.88698	0.425237
$345$	−5.27841	−0.284180
$346$	−27.4428	−1.47533
$347$	−16.4594	−0.883588	−0.441794	−	0.897117i	$-0.645658\pi$
$347$	−16.4594	−0.883588	−0.441794	+	0.897117i	$0.645658\pi$
$348$	5.23615	0.280687
$349$	30.3631	1.62530	0.812650	−	0.582753i	$-0.198024\pi$
$349$	30.3631	1.62530	0.812650	+	0.582753i	$0.198024\pi$
$350$	11.9017	0.636170
$351$	2.02534	0.108105
$352$	−7.01902	−0.374115
$353$	12.7752	0.679956	0.339978	−	0.940433i	$-0.389580\pi$
$353$	12.7752	0.679956	0.339978	+	0.940433i	$0.389580\pi$
$354$	−0.972124	−0.0516678
$355$	−6.39422	−0.339370
$356$	−6.06378	−0.321380
$357$	−2.37558	−0.125729
$358$	−1.82767	−0.0965953
$359$	20.4202	1.07774	0.538868	−	0.842390i	$-0.318852\pi$
$359$	20.4202	1.07774	0.538868	+	0.842390i	$0.318852\pi$
$360$	3.03470	0.159943
$361$	−14.0969	−0.741942
$362$	38.6910	2.03355
$363$	7.18869	0.377309
$364$	−3.17556	−0.166444
$365$	−15.2076	−0.796004
$366$	−9.59034	−0.501295
$367$	−8.00192	−0.417697	−0.208848	−	0.977948i	$-0.566972\pi$
$367$	−8.00192	−0.417697	−0.208848	+	0.977948i	$0.566972\pi$
$368$	−18.5670	−0.967871
$369$	4.09779	0.213322
$370$	−25.3546	−1.31812
$371$	4.84597	0.251590
$372$	2.19371	0.113739
$373$	−7.08890	−0.367050	−0.183525	−	0.983015i	$-0.558751\pi$
$373$	−7.08890	−0.367050	−0.183525	+	0.983015i	$0.558751\pi$
$374$	3.18404	0.164643
$375$	11.2084	0.578801
$376$	−0.0905578	−0.00467016
$377$	16.0678	0.827535
$378$	3.87446	0.199281
$379$	−22.1308	−1.13678	−0.568391	−	0.822759i	$-0.692434\pi$
$379$	−22.1308	−1.13678	−0.568391	+	0.822759i	$0.692434\pi$
$380$	2.02937	0.104105
$381$	6.54251	0.335183
$382$	1.77535	0.0908349
$383$	2.60313	0.133013	0.0665067	−	0.997786i	$-0.478815\pi$
$383$	2.60313	0.133013	0.0665067	+	0.997786i	$0.478815\pi$
$384$	13.5595	0.691957
$385$	−6.43992	−0.328209
$386$	−39.5408	−2.01258
$387$	3.60885	0.183448
$388$	2.18254	0.110802
$389$	−23.4684	−1.18989	−0.594946	−	0.803765i	$-0.702827\pi$
$389$	−23.4684	−1.18989	−0.594946	+	0.803765i	$0.702827\pi$
$390$	−4.58684	−0.232263
$391$	3.80128	0.192239
$392$	−2.96483	−0.149747
$393$	−8.63455	−0.435555
$394$	−7.31229	−0.368388
$395$	−2.54770	−0.128189
$396$	−1.28852	−0.0647504
$397$	−13.0697	−0.655947	−0.327974	−	0.944687i	$-0.606366\pi$
$397$	−13.0697	−0.655947	−0.327974	+	0.944687i	$0.606366\pi$
$398$	11.0454	0.553657
$399$	−5.26023	−0.263341
$400$	15.0040	0.750201
$401$	5.58643	0.278973	0.139486	−	0.990224i	$-0.455455\pi$
$401$	5.58643	0.278973	0.139486	+	0.990224i	$0.455455\pi$
$402$	−7.82225	−0.390138
$403$	6.73169	0.335329
$404$	−1.15134	−0.0572815
$405$	1.38859	0.0689996
$406$	30.7377	1.52549
$407$	−21.8563	−1.08338
$408$	−2.18546	−0.108196
$409$	9.45533	0.467536	0.233768	−	0.972292i	$-0.424894\pi$
$409$	9.45533	0.467536	0.233768	+	0.972292i	$0.424894\pi$
$410$	−9.28037	−0.458325
$411$	−21.8727	−1.07890
$412$	6.67754	0.328979
$413$	−1.41595	−0.0696746
$414$	−6.19971	−0.304699
$415$	−17.2982	−0.849136
$416$	−7.28177	−0.357018
$417$	3.71694	0.182019
$418$	7.05041	0.344847
$419$	2.38129	0.116333	0.0581667	−	0.998307i	$-0.481475\pi$
$419$	2.38129	0.116333	0.0581667	+	0.998307i	$0.481475\pi$
$420$	−2.17719	−0.106236
$421$	−17.7632	−0.865724	−0.432862	−	0.901460i	$-0.642496\pi$
$421$	−17.7632	−0.865724	−0.432862	+	0.901460i	$0.642496\pi$
$422$	−4.12146	−0.200629
$423$	−0.0414365	−0.00201471
$424$	4.45814	0.216506
$425$	−3.07182	−0.149005
$426$	−7.51028	−0.363874
$427$	−13.9689	−0.676002
$428$	−7.04861	−0.340707
$429$	−3.95398	−0.190900
$430$	−8.17305	−0.394139
$431$	36.7215	1.76881	0.884407	−	0.466717i	$-0.154563\pi$
$431$	36.7215	1.76881	0.884407	+	0.466717i	$0.154563\pi$
$432$	4.88441	0.235001
$433$	−35.2394	−1.69350	−0.846749	−	0.531992i	$-0.821444\pi$
$433$	−35.2394	−1.69350	−0.846749	+	0.531992i	$0.821444\pi$
$434$	12.8777	0.618149
$435$	11.0162	0.528188
$436$	−3.37845	−0.161798
$437$	8.41714	0.402647
$438$	−17.8620	−0.853479
$439$	−24.3683	−1.16304	−0.581518	−	0.813534i	$-0.697541\pi$
$439$	−24.3683	−1.16304	−0.581518	+	0.813534i	$0.697541\pi$
$440$	−5.92452	−0.282440
$441$	−1.35662	−0.0646009
$442$	3.30323	0.157119
$443$	14.5156	0.689658	0.344829	−	0.938665i	$-0.387937\pi$
$443$	14.5156	0.689658	0.344829	+	0.938665i	$0.387937\pi$
$444$	−7.38913	−0.350673
$445$	−12.7575	−0.604762
$446$	9.06937	0.429447
$447$	−14.7784	−0.698995
$448$	9.27661	0.438279
$449$	−14.6717	−0.692399	−0.346200	−	0.938161i	$-0.612528\pi$
$449$	−14.6717	−0.692399	−0.346200	+	0.938161i	$0.612528\pi$
$450$	5.01000	0.236174
$451$	−7.99993	−0.376702
$452$	5.25795	0.247313
$453$	23.1761	1.08891
$454$	−44.2287	−2.07576
$455$	−6.68099	−0.313210
$456$	−4.83925	−0.226618
$457$	−23.4238	−1.09572	−0.547859	−	0.836571i	$-0.684557\pi$
$457$	−23.4238	−1.09572	−0.547859	+	0.836571i	$0.684557\pi$
$458$	−16.9461	−0.791840
$459$	−1.00000	−0.0466760
$460$	3.48382	0.162434
$461$	−35.8457	−1.66950	−0.834752	−	0.550627i	$-0.814389\pi$
$461$	−35.8457	−1.66950	−0.834752	+	0.550627i	$0.814389\pi$
$462$	−7.56395	−0.351907
$463$	0.0315112	0.00146445	0.000732225	−	1.00000i	$-0.499767\pi$
$463$	0.0315112	0.00146445	0.000732225		1.00000i	$0.499767\pi$
$464$	38.7500	1.79892
$465$	4.61531	0.214030
$466$	31.8685	1.47628
$467$	29.6850	1.37366	0.686829	−	0.726819i	$-0.259002\pi$
$467$	29.6850	1.37366	0.686829	+	0.726819i	$0.259002\pi$
$468$	−1.33675	−0.0617913
$469$	−11.3936	−0.526105
$470$	0.0938424	0.00432863
$471$	−1.00000	−0.0460776
$472$	−1.30263	−0.0599585
$473$	−7.04539	−0.323948
$474$	−2.99238	−0.137445
$475$	−6.80191	−0.312093
$476$	1.56792	0.0718653
$477$	2.03991	0.0934011
$478$	20.5126	0.938224
$479$	30.6535	1.40059	0.700296	−	0.713852i	$-0.253051\pi$
$479$	30.6535	1.40059	0.700296	+	0.713852i	$0.253051\pi$
$480$	−4.99245	−0.227873
$481$	−22.6745	−1.03387
$482$	4.77276	0.217393
$483$	−9.03024	−0.410890
$484$	−4.74464	−0.215665
$485$	4.59181	0.208503
$486$	1.63095	0.0739816
$487$	−21.6657	−0.981766	−0.490883	−	0.871226i	$-0.663326\pi$
$487$	−21.6657	−0.981766	−0.490883	+	0.871226i	$0.663326\pi$
$488$	−12.8509	−0.581734
$489$	16.5974	0.750561
$490$	3.07237	0.138796
$491$	10.2333	0.461820	0.230910	−	0.972975i	$-0.425830\pi$
$491$	10.2333	0.461820	0.230910	+	0.972975i	$0.425830\pi$
$492$	−2.70460	−0.121933
$493$	−7.93340	−0.357302
$494$	7.31433	0.329087
$495$	−2.71088	−0.121845
$496$	16.2345	0.728950
$497$	−10.9392	−0.490688
$498$	−20.3175	−0.910448
$499$	9.67331	0.433037	0.216518	−	0.976279i	$-0.430530\pi$
$499$	9.67331	0.433037	0.216518	+	0.976279i	$0.430530\pi$
$500$	−7.39773	−0.330836
$501$	7.95155	0.355249
$502$	31.6037	1.41054
$503$	−24.0496	−1.07232	−0.536159	−	0.844117i	$-0.680125\pi$
$503$	−24.0496	−1.07232	−0.536159	+	0.844117i	$0.680125\pi$
$504$	5.19173	0.231258
$505$	−2.42229	−0.107790
$506$	12.1034	0.538063
$507$	8.89801	0.395174
$508$	−4.31814	−0.191587
$509$	−23.5613	−1.04433	−0.522167	−	0.852843i	$-0.674876\pi$
$509$	−23.5613	−1.04433	−0.522167	+	0.852843i	$0.674876\pi$
$510$	2.26473	0.100284
$511$	−26.0170	−1.15093
$512$	3.78824	0.167418
$513$	−2.21429	−0.0977635
$514$	−1.08618	−0.0479094
$515$	14.0487	0.619062
$516$	−2.38189	−0.104857
$517$	0.0808948	0.00355775
$518$	−43.3763	−1.90584
$519$	−16.8262	−0.738588
$520$	−6.14630	−0.269533
$521$	2.46091	0.107815	0.0539073	−	0.998546i	$-0.482832\pi$
$521$	2.46091	0.107815	0.0539073	+	0.998546i	$0.482832\pi$
$522$	12.9390	0.566326
$523$	11.1734	0.488579	0.244290	−	0.969702i	$-0.421445\pi$
$523$	11.1734	0.488579	0.244290	+	0.969702i	$0.421445\pi$
$524$	5.69892	0.248959
$525$	7.29735	0.318483
$526$	−0.407449	−0.0177656
$527$	−3.32374	−0.144784
$528$	−9.53562	−0.414985
$529$	−8.55030	−0.371752
$530$	−4.61984	−0.200673
$531$	−0.596046	−0.0258662
$532$	3.47183	0.150523
$533$	−8.29940	−0.359487
$534$	−14.9842	−0.648428
$535$	−14.8294	−0.641132
$536$	−10.4817	−0.452741
$537$	−1.12061	−0.0483580
$538$	34.8540	1.50266
$539$	2.64847	0.114078
$540$	−0.916488	−0.0394394
$541$	−27.8397	−1.19692	−0.598462	−	0.801151i	$-0.704221\pi$
$541$	−27.8397	−1.19692	−0.598462	+	0.801151i	$0.704221\pi$
$542$	18.1390	0.779138
$543$	23.7229	1.01805
$544$	3.59534	0.154149
$545$	−7.10784	−0.304467
$546$	−7.84710	−0.335825
$547$	18.4066	0.787007	0.393504	−	0.919323i	$-0.371263\pi$
$547$	18.4066	0.787007	0.393504	+	0.919323i	$0.371263\pi$
$548$	14.4363	0.616689
$549$	−5.88020	−0.250961
$550$	−9.78081	−0.417055
$551$	−17.5669	−0.748375
$552$	−8.30753	−0.353592
$553$	−4.35858	−0.185346
$554$	−41.2858	−1.75407
$555$	−15.5459	−0.659885
$556$	−2.45323	−0.104040
$557$	−4.57492	−0.193846	−0.0969229	−	0.995292i	$-0.530900\pi$
$557$	−4.57492	−0.193846	−0.0969229	+	0.995292i	$0.530900\pi$
$558$	5.42087	0.229484
$559$	−7.30913	−0.309143
$560$	−16.1122	−0.680866
$561$	1.95226	0.0824243
$562$	−2.19400	−0.0925484
$563$	28.4996	1.20112	0.600558	−	0.799581i	$-0.294945\pi$
$563$	28.4996	1.20112	0.600558	+	0.799581i	$0.294945\pi$
$564$	0.0273487	0.00115159
$565$	11.0621	0.465386
$566$	−33.1642	−1.39400
$567$	2.37558	0.0997650
$568$	−10.0637	−0.422262
$569$	1.71526	0.0719073	0.0359536	−	0.999353i	$-0.488553\pi$
$569$	1.71526	0.0719073	0.0359536	+	0.999353i	$0.488553\pi$
$570$	5.01477	0.210046
$571$	−14.4910	−0.606432	−0.303216	−	0.952922i	$-0.598060\pi$
$571$	−14.4910	−0.606432	−0.303216	+	0.952922i	$0.598060\pi$
$572$	2.60968	0.109116
$573$	1.08853	0.0454742
$574$	−15.8767	−0.662682
$575$	−11.6768	−0.486958
$576$	3.90499	0.162708
$577$	−12.1257	−0.504799	−0.252399	−	0.967623i	$-0.581220\pi$
$577$	−12.1257	−0.504799	−0.252399	+	0.967623i	$0.581220\pi$
$578$	−1.63095	−0.0678388
$579$	−24.2440	−1.00755
$580$	−7.27087	−0.301906
$581$	−29.5936	−1.22775
$582$	5.39327	0.223558
$583$	−3.98243	−0.164935
$584$	−23.9348	−0.990430
$585$	−2.81236	−0.116277
$586$	−29.7927	−1.23073
$587$	−15.1958	−0.627198	−0.313599	−	0.949555i	$-0.601535\pi$
$587$	−15.1958	−0.627198	−0.313599	+	0.949555i	$0.601535\pi$
$588$	0.895387	0.0369251
$589$	−7.35973	−0.303253
$590$	1.34988	0.0555737
$591$	−4.48344	−0.184424
$592$	−54.6830	−2.24746
$593$	17.5232	0.719592	0.359796	−	0.933031i	$-0.382846\pi$
$593$	17.5232	0.719592	0.359796	+	0.933031i	$0.382846\pi$
$594$	−3.18404	−0.130643
$595$	3.29871	0.135234
$596$	9.75395	0.399537
$597$	6.77236	0.277174
$598$	12.5565	0.513474
$599$	−10.7969	−0.441148	−0.220574	−	0.975370i	$-0.570793\pi$
$599$	−10.7969	−0.441148	−0.220574	+	0.975370i	$0.570793\pi$
$600$	6.71333	0.274071
$601$	7.82972	0.319381	0.159690	−	0.987167i	$-0.448950\pi$
$601$	7.82972	0.319381	0.159690	+	0.987167i	$0.448950\pi$
$602$	−13.9823	−0.569878
$603$	−4.79611	−0.195313
$604$	−15.2965	−0.622407
$605$	−9.98214	−0.405832
$606$	−2.84508	−0.115573
$607$	−29.6897	−1.20507	−0.602534	−	0.798093i	$-0.705842\pi$
$607$	−29.6897	−1.20507	−0.602534	+	0.798093i	$0.705842\pi$
$608$	7.96113	0.322867
$609$	18.8464	0.763696
$610$	13.3170	0.539191
$611$	0.0839230	0.00339516
$612$	0.660014	0.0266795
$613$	−41.2587	−1.66642	−0.833212	−	0.552954i	$-0.813500\pi$
$613$	−41.2587	−1.66642	−0.833212	+	0.552954i	$0.813500\pi$
$614$	−34.1722	−1.37908
$615$	−5.69014	−0.229449
$616$	−10.1356	−0.408374
$617$	−9.63876	−0.388042	−0.194021	−	0.980997i	$-0.562153\pi$
$617$	−9.63876	−0.388042	−0.194021	+	0.980997i	$0.562153\pi$
$618$	16.5008	0.663761
$619$	−21.6398	−0.869777	−0.434888	−	0.900484i	$-0.643212\pi$
$619$	−21.6398	−0.869777	−0.434888	+	0.900484i	$0.643212\pi$
$620$	−3.04617	−0.122337
$621$	−3.80128	−0.152540
$622$	−52.7258	−2.11411
$623$	−21.8253	−0.874412
$624$	−9.89258	−0.396020
$625$	−0.204825	−0.00819300
$626$	55.9897	2.23780
$627$	4.32287	0.172639
$628$	0.660014	0.0263374
$629$	11.1954	0.446391
$630$	−5.38004	−0.214346
$631$	23.0891	0.919164	0.459582	−	0.888135i	$-0.347999\pi$
$631$	23.0891	0.919164	0.459582	+	0.888135i	$0.347999\pi$
$632$	−4.00975	−0.159499
$633$	−2.52702	−0.100440
$634$	3.12934	0.124282
$635$	−9.08486	−0.360522
$636$	−1.34637	−0.0533870
$637$	2.74761	0.108864
$638$	−25.2603	−1.00006
$639$	−4.60483	−0.182164
$640$	−18.8286	−0.744267
$641$	−21.2261	−0.838381	−0.419191	−	0.907898i	$-0.637686\pi$
$641$	−21.2261	−0.838381	−0.419191	+	0.907898i	$0.637686\pi$
$642$	−17.4178	−0.687424
$643$	−28.8546	−1.13791	−0.568957	−	0.822367i	$-0.692653\pi$
$643$	−28.8546	−1.13791	−0.568957	+	0.822367i	$0.692653\pi$
$644$	5.96008	0.234860
$645$	−5.01120	−0.197316
$646$	−3.61141	−0.142089
$647$	14.0367	0.551841	0.275921	−	0.961180i	$-0.411017\pi$
$647$	14.0367	0.551841	0.275921	+	0.961180i	$0.411017\pi$
$648$	2.18546	0.0858529
$649$	1.16363	0.0456766
$650$	−10.1469	−0.397996
$651$	7.89580	0.309461
$652$	−10.9545	−0.429012
$653$	29.8587	1.16846	0.584230	−	0.811588i	$-0.301397\pi$
$653$	29.8587	1.16846	0.584230	+	0.811588i	$0.301397\pi$
$654$	−8.34845	−0.326450
$655$	11.9898	0.468482
$656$	−20.0153	−0.781465
$657$	−10.9519	−0.427273
$658$	0.160544	0.00625867
$659$	−44.9933	−1.75269	−0.876345	−	0.481685i	$-0.840025\pi$
$659$	−44.9933	−1.75269	−0.876345	+	0.481685i	$0.840025\pi$
$660$	1.78922	0.0696453
$661$	−5.28863	−0.205704	−0.102852	−	0.994697i	$-0.532797\pi$
$661$	−5.28863	−0.205704	−0.102852	+	0.994697i	$0.532797\pi$
$662$	−38.9442	−1.51361
$663$	2.02534	0.0786576
$664$	−27.2251	−1.05654
$665$	7.30430	0.283249
$666$	−18.2592	−0.707531
$667$	−30.1571	−1.16769
$668$	−5.24813	−0.203056
$669$	5.56077	0.214992
$670$	10.8619	0.419631
$671$	11.4797	0.443167
$672$	−8.54101	−0.329477
$673$	−18.5041	−0.713282	−0.356641	−	0.934242i	$-0.616078\pi$
$673$	−18.5041	−0.713282	−0.356641	+	0.934242i	$0.616078\pi$
$674$	21.8112	0.840137
$675$	3.07182	0.118234
$676$	−5.87281	−0.225877
$677$	31.7699	1.22102	0.610509	−	0.792009i	$-0.290965\pi$
$677$	31.7699	1.22102	0.610509	+	0.792009i	$0.290965\pi$
$678$	12.9929	0.498989
$679$	7.85561	0.301471
$680$	3.03470	0.116376
$681$	−27.1183	−1.03918
$682$	−10.5829	−0.405241
$683$	−32.0534	−1.22649	−0.613245	−	0.789893i	$-0.710136\pi$
$683$	−32.0534	−1.22649	−0.613245	+	0.789893i	$0.710136\pi$
$684$	1.46146	0.0558805
$685$	30.3723	1.16046
$686$	32.3774	1.23618
$687$	−10.3903	−0.396415
$688$	−17.6271	−0.672026
$689$	−4.13151	−0.157398
$690$	8.60885	0.327733
$691$	17.7689	0.675959	0.337979	−	0.941153i	$-0.390257\pi$
$691$	17.7689	0.675959	0.337979	+	0.941153i	$0.390257\pi$
$692$	11.1055	0.422168
$693$	−4.63774	−0.176173
$694$	26.8446	1.01901
$695$	−5.16131	−0.195780
$696$	17.3381	0.657199
$697$	4.09779	0.155215
$698$	−49.5208	−1.87439
$699$	19.5398	0.739062
$700$	−4.81635	−0.182041
$701$	−25.8698	−0.977087	−0.488544	−	0.872539i	$-0.662472\pi$
$701$	−25.8698	−0.977087	−0.488544	+	0.872539i	$0.662472\pi$
$702$	−3.30323	−0.124673
$703$	24.7900	0.934972
$704$	−7.62354	−0.287323
$705$	0.0575383	0.00216702
$706$	−20.8358	−0.784165
$707$	−4.14402	−0.155852
$708$	0.393398	0.0147848
$709$	24.5893	0.923469	0.461734	−	0.887018i	$-0.347227\pi$
$709$	24.5893	0.923469	0.461734	+	0.887018i	$0.347227\pi$
$710$	10.4287	0.391382
$711$	−1.83474	−0.0688082
$712$	−20.0786	−0.752476
$713$	−12.6344	−0.473164
$714$	3.87446	0.144998
$715$	5.49045	0.205331
$716$	0.739619	0.0276409
$717$	12.5770	0.469698
$718$	−33.3044	−1.24291
$719$	34.7811	1.29712	0.648558	−	0.761165i	$-0.275372\pi$
$719$	34.7811	1.29712	0.648558	+	0.761165i	$0.275372\pi$
$720$	−6.78244	−0.252767
$721$	24.0344	0.895088
$722$	22.9914	0.855652
$723$	2.92636	0.108833
$724$	−15.6575	−0.581905
$725$	24.3700	0.905078
$726$	−11.7244	−0.435135
$727$	32.5468	1.20709	0.603546	−	0.797328i	$-0.293754\pi$
$727$	32.5468	1.20709	0.603546	+	0.797328i	$0.293754\pi$
$728$	−10.5150	−0.389712
$729$	1.00000	0.0370370
$730$	24.8030	0.917999
$731$	3.60885	0.133478
$732$	3.88101	0.143446
$733$	−18.8236	−0.695266	−0.347633	−	0.937631i	$-0.613014\pi$
$733$	−18.8236	−0.695266	−0.347633	+	0.937631i	$0.613014\pi$
$734$	13.0508	0.481713
$735$	1.88379	0.0694845
$736$	13.6669	0.503767
$737$	9.36325	0.344900
$738$	−6.68331	−0.246016
$739$	−17.0080	−0.625648	−0.312824	−	0.949811i	$-0.601275\pi$
$739$	−17.0080	−0.625648	−0.312824	+	0.949811i	$0.601275\pi$
$740$	10.2605	0.377183
$741$	4.48469	0.164749
$742$	−7.90356	−0.290149
$743$	−39.8288	−1.46118	−0.730589	−	0.682818i	$-0.760754\pi$
$743$	−39.8288	−1.46118	−0.730589	+	0.682818i	$0.760754\pi$
$744$	7.26389	0.266307
$745$	20.5211	0.751836
$746$	11.5617	0.423303
$747$	−12.4574	−0.455793
$748$	−1.28852	−0.0471128
$749$	−25.3700	−0.926999
$750$	−18.2805	−0.667508
$751$	8.36466	0.305231	0.152615	−	0.988286i	$-0.451230\pi$
$751$	8.36466	0.305231	0.152615	+	0.988286i	$0.451230\pi$
$752$	0.202393	0.00738052
$753$	19.3774	0.706153
$754$	−26.2059	−0.954362
$755$	−32.1821	−1.17123
$756$	−1.56792	−0.0570245
$757$	−12.6034	−0.458077	−0.229039	−	0.973417i	$-0.573558\pi$
$757$	−12.6034	−0.458077	−0.229039	+	0.973417i	$0.573558\pi$
$758$	36.0943	1.31100
$759$	7.42107	0.269368
$760$	6.71973	0.243750
$761$	−4.11791	−0.149274	−0.0746371	−	0.997211i	$-0.523780\pi$
$761$	−4.11791	−0.149274	−0.0746371	+	0.997211i	$0.523780\pi$
$762$	−10.6705	−0.386553
$763$	−12.1600	−0.440222
$764$	−0.718448	−0.0259925
$765$	1.38859	0.0502046
$766$	−4.24558	−0.153399
$767$	1.20719	0.0435892
$768$	−14.3050	−0.516188
$769$	−10.1725	−0.366829	−0.183415	−	0.983036i	$-0.558715\pi$
$769$	−10.1725	−0.366829	−0.183415	+	0.983036i	$0.558715\pi$
$770$	10.5032	0.378510
$771$	−0.665979	−0.0239846
$772$	16.0014	0.575902
$773$	0.364381	0.0131059	0.00655293	−	0.999979i	$-0.497914\pi$
$773$	0.364381	0.0131059	0.00655293	+	0.999979i	$0.497914\pi$
$774$	−5.88586	−0.211563
$775$	10.2099	0.366751
$776$	7.22691	0.259431
$777$	−26.5956	−0.954113
$778$	38.2758	1.37225
$779$	9.07371	0.325099
$780$	1.85620	0.0664625
$781$	8.98982	0.321681
$782$	−6.19971	−0.221701
$783$	7.93340	0.283517
$784$	6.62628	0.236653
$785$	1.38859	0.0495609
$786$	14.0826	0.502308
$787$	−49.0372	−1.74799	−0.873994	−	0.485937i	$-0.838479\pi$
$787$	−49.0372	−1.74799	−0.873994	+	0.485937i	$0.838479\pi$
$788$	2.95913	0.105415
$789$	−0.249822	−0.00889391
$790$	4.15519	0.147835
$791$	18.9249	0.672892
$792$	−4.26657	−0.151606
$793$	11.9094	0.422915
$794$	21.3160	0.756477
$795$	−2.83260	−0.100462
$796$	−4.46985	−0.158430
$797$	14.1931	0.502744	0.251372	−	0.967890i	$-0.419118\pi$
$797$	14.1931	0.502744	0.251372	+	0.967890i	$0.419118\pi$
$798$	8.57920	0.303701
$799$	−0.0414365	−0.00146592
$800$	−11.0442	−0.390472
$801$	−9.18735	−0.324619
$802$	−9.11121	−0.321728
$803$	21.3809	0.754514
$804$	3.16550	0.111639
$805$	12.5393	0.441952
$806$	−10.9791	−0.386722
$807$	21.3703	0.752270
$808$	−3.81237	−0.134119
$809$	7.88086	0.277076	0.138538	−	0.990357i	$-0.455760\pi$
$809$	7.88086	0.277076	0.138538	+	0.990357i	$0.455760\pi$
$810$	−2.26473	−0.0795744
$811$	−4.67120	−0.164028	−0.0820141	−	0.996631i	$-0.526135\pi$
$811$	−4.67120	−0.164028	−0.0820141	+	0.996631i	$0.526135\pi$
$812$	−12.4389	−0.436520
$813$	11.1217	0.390056
$814$	35.6467	1.24942
$815$	−23.0470	−0.807301
$816$	4.88441	0.170989
$817$	7.99105	0.279571
$818$	−15.4212	−0.539190
$819$	−4.81135	−0.168122
$820$	3.75557	0.131150
$821$	−7.64967	−0.266975	−0.133488	−	0.991050i	$-0.542618\pi$
$821$	−7.64967	−0.266975	−0.133488	+	0.991050i	$0.542618\pi$
$822$	35.6735	1.24425
$823$	−21.3014	−0.742519	−0.371259	−	0.928529i	$-0.621074\pi$
$823$	−21.3014	−0.742519	−0.371259	+	0.928529i	$0.621074\pi$
$824$	22.1109	0.770269
$825$	−5.99698	−0.208788
$826$	2.30936	0.0803528
$827$	27.0958	0.942214	0.471107	−	0.882076i	$-0.343855\pi$
$827$	27.0958	0.942214	0.471107	+	0.882076i	$0.343855\pi$
$828$	2.50889	0.0871901
$829$	−12.0102	−0.417132	−0.208566	−	0.978008i	$-0.566880\pi$
$829$	−12.0102	−0.417132	−0.208566	+	0.978008i	$0.566880\pi$
$830$	28.2126	0.979274
$831$	−25.3139	−0.878130
$832$	−7.90892	−0.274192
$833$	−1.35662	−0.0470041
$834$	−6.06217	−0.209916
$835$	−11.0414	−0.382105
$836$	−2.85315	−0.0986784
$837$	3.32374	0.114885
$838$	−3.88377	−0.134163
$839$	40.8771	1.41123	0.705617	−	0.708593i	$-0.250670\pi$
$839$	40.8771	1.41123	0.705617	+	0.708593i	$0.250670\pi$
$840$	−7.20918	−0.248740
$841$	33.9389	1.17031
$842$	28.9709	0.998404
$843$	−1.34523	−0.0463320
$844$	1.66787	0.0574104
$845$	−12.3557	−0.425048
$846$	0.0675811	0.00232349
$847$	−17.0773	−0.586784
$848$	−9.96376	−0.342157
$849$	−20.3342	−0.697869
$850$	5.01000	0.171842
$851$	42.5569	1.45883
$852$	3.03925	0.104123
$853$	−23.6549	−0.809927	−0.404964	−	0.914333i	$-0.632716\pi$
$853$	−23.6549	−0.809927	−0.404964	+	0.914333i	$0.632716\pi$
$854$	22.7826	0.779605
$855$	3.07475	0.105154
$856$	−23.3396	−0.797730
$857$	1.84214	0.0629264	0.0314632	−	0.999505i	$-0.489983\pi$
$857$	1.84214	0.0629264	0.0314632	+	0.999505i	$0.489983\pi$
$858$	6.44876	0.220157
$859$	−1.64608	−0.0561635	−0.0280818	−	0.999606i	$-0.508940\pi$
$859$	−1.64608	−0.0561635	−0.0280818	+	0.999606i	$0.508940\pi$
$860$	3.30746	0.112784
$861$	−9.73462	−0.331755
$862$	−59.8911	−2.03990
$863$	−43.2392	−1.47188	−0.735939	−	0.677048i	$-0.763259\pi$
$863$	−43.2392	−1.47188	−0.735939	+	0.677048i	$0.763259\pi$
$864$	−3.59534	−0.122316
$865$	23.3647	0.794423
$866$	57.4739	1.95304
$867$	−1.00000	−0.0339618
$868$	−5.21134	−0.176884
$869$	3.58189	0.121507
$870$	−17.9670	−0.609138
$871$	9.71375	0.329138
$872$	−11.1868	−0.378833
$873$	3.30682	0.111919
$874$	−13.7280	−0.464356
$875$	−26.6266	−0.900142
$876$	7.22838	0.244224
$877$	−2.39618	−0.0809131	−0.0404566	−	0.999181i	$-0.512881\pi$
$877$	−2.39618	−0.0809131	−0.0404566	+	0.999181i	$0.512881\pi$
$878$	39.7436	1.34128
$879$	−18.2670	−0.616132
$880$	13.2411	0.446356
$881$	51.5181	1.73569	0.867845	−	0.496835i	$-0.165505\pi$
$881$	51.5181	1.73569	0.867845	+	0.496835i	$0.165505\pi$
$882$	2.21258	0.0745016
$883$	47.6457	1.60341	0.801703	−	0.597722i	$-0.203927\pi$
$883$	47.6457	1.60341	0.801703	+	0.597722i	$0.203927\pi$
$884$	−1.33675	−0.0449598
$885$	0.827663	0.0278216
$886$	−23.6743	−0.795355
$887$	−20.0028	−0.671627	−0.335814	−	0.941928i	$-0.609011\pi$
$887$	−20.0028	−0.671627	−0.335814	+	0.941928i	$0.609011\pi$
$888$	−24.4671	−0.821063
$889$	−15.5423	−0.521270
$890$	20.8068	0.697447
$891$	−1.95226	−0.0654031
$892$	−3.67018	−0.122887
$893$	−0.0917527	−0.00307039
$894$	24.1029	0.806122
$895$	1.55607	0.0520137
$896$	−32.2118	−1.07612
$897$	7.69887	0.257058
$898$	23.9288	0.798516
$899$	26.3685	0.879440
$900$	−2.02744	−0.0675814
$901$	2.03991	0.0679593
$902$	13.0475	0.434435
$903$	−8.57310	−0.285295
$904$	17.4103	0.579058
$905$	−32.9414	−1.09501
$906$	−37.7991	−1.25579
$907$	32.8164	1.08965	0.544826	−	0.838549i	$-0.316596\pi$
$907$	32.8164	1.08965	0.544826	+	0.838549i	$0.316596\pi$
$908$	17.8984	0.593981
$909$	−1.74442	−0.0578589
$910$	10.8964	0.361212
$911$	−25.0836	−0.831056	−0.415528	−	0.909580i	$-0.636403\pi$
$911$	−25.0836	−0.831056	−0.415528	+	0.909580i	$0.636403\pi$
$912$	10.8155	0.358138
$913$	24.3201	0.804876
$914$	38.2031	1.26365
$915$	8.16518	0.269933
$916$	6.85774	0.226586
$917$	20.5121	0.677368
$918$	1.63095	0.0538295
$919$	7.87486	0.259768	0.129884	−	0.991529i	$-0.458540\pi$
$919$	7.87486	0.259768	0.129884	+	0.991529i	$0.458540\pi$
$920$	11.5357	0.380322
$921$	−20.9522	−0.690400
$922$	58.4628	1.92537
$923$	9.32634	0.306980
$924$	3.06097	0.100699
$925$	−34.3903	−1.13075
$926$	−0.0513933	−0.00168889
$927$	10.1173	0.332295
$928$	−28.5233	−0.936322
$929$	18.8542	0.618586	0.309293	−	0.950967i	$-0.399908\pi$
$929$	18.8542	0.618586	0.309293	+	0.950967i	$0.399908\pi$
$930$	−7.52736	−0.246832
$931$	−3.00395	−0.0984506
$932$	−12.8965	−0.422440
$933$	−32.3282	−1.05838
$934$	−48.4149	−1.58418
$935$	−2.71088	−0.0886554
$936$	−4.42629	−0.144678
$937$	−32.9832	−1.07751	−0.538757	−	0.842461i	$-0.681106\pi$
$937$	−32.9832	−1.07751	−0.538757	+	0.842461i	$0.681106\pi$
$938$	18.5824	0.606736
$939$	34.3294	1.12030
$940$	−0.0379761	−0.00123864
$941$	−24.9724	−0.814078	−0.407039	−	0.913411i	$-0.633439\pi$
$941$	−24.9724	−0.814078	−0.407039	+	0.913411i	$0.633439\pi$
$942$	1.63095	0.0531394
$943$	15.5768	0.507251
$944$	2.91133	0.0947558
$945$	−3.29871	−0.107307
$946$	11.4907	0.373595
$947$	−24.6507	−0.801040	−0.400520	−	0.916288i	$-0.631170\pi$
$947$	−24.6507	−0.801040	−0.400520	+	0.916288i	$0.631170\pi$
$948$	1.21095	0.0393300
$949$	22.1812	0.720033
$950$	11.0936	0.359924
$951$	1.91871	0.0622186
$952$	5.19173	0.168265
$953$	36.6746	1.18801	0.594003	−	0.804463i	$-0.297547\pi$
$953$	36.6746	1.18801	0.594003	+	0.804463i	$0.297547\pi$
$954$	−3.32700	−0.107716
$955$	−1.51153	−0.0489119
$956$	−8.30102	−0.268474
$957$	−15.4880	−0.500657
$958$	−49.9944	−1.61525
$959$	51.9605	1.67789
$960$	−5.42242	−0.175008
$961$	−19.9528	−0.643638
$962$	36.9811	1.19232
$963$	−10.6795	−0.344142
$964$	−1.93144	−0.0622074
$965$	33.6649	1.08371
$966$	14.7279	0.473863
$967$	25.6067	0.823456	0.411728	−	0.911307i	$-0.364925\pi$
$967$	25.6067	0.823456	0.411728	+	0.911307i	$0.364925\pi$
$968$	−15.7106	−0.504957
$969$	−2.21429	−0.0711334
$970$	−7.48904	−0.240458
$971$	−37.4406	−1.20153	−0.600763	−	0.799427i	$-0.705137\pi$
$971$	−37.4406	−1.20153	−0.600763	+	0.799427i	$0.705137\pi$
$972$	−0.660014	−0.0211699
$973$	−8.82990	−0.283073
$974$	35.3358	1.13223
$975$	−6.22147	−0.199247
$976$	28.7213	0.919346
$977$	−55.0383	−1.76083	−0.880415	−	0.474203i	$-0.842736\pi$
$977$	−55.0383	−1.76083	−0.880415	+	0.474203i	$0.842736\pi$
$978$	−27.0696	−0.865592
$979$	17.9361	0.573239
$980$	−1.24333	−0.0397166
$981$	−5.11875	−0.163429
$982$	−16.6900	−0.532598
$983$	15.0668	0.480555	0.240277	−	0.970704i	$-0.422762\pi$
$983$	15.0668	0.480555	0.240277	+	0.970704i	$0.422762\pi$
$984$	−8.95554	−0.285492
$985$	6.22565	0.198366
$986$	12.9390	0.412062
$987$	0.0984358	0.00313325
$988$	−2.95996	−0.0941688
$989$	13.7182	0.436214
$990$	4.42133	0.140519
$991$	−55.8925	−1.77548	−0.887741	−	0.460342i	$-0.847727\pi$
$991$	−55.8925	−1.77548	−0.887741	+	0.460342i	$0.847727\pi$
$992$	−11.9500	−0.379411
$993$	−23.8782	−0.757751
$994$	17.8413	0.565890
$995$	−9.40403	−0.298128
$996$	8.22206	0.260526
$997$	−53.8993	−1.70701	−0.853505	−	0.521085i	$-0.825527\pi$
$997$	−53.8993	−1.70701	−0.853505	+	0.521085i	$0.825527\pi$
$998$	−15.7767	−0.499404
$999$	−11.1954	−0.354208

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.c.1.10	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.c.1.10	✓	39	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)

\(f(q)\)	\(=\)	\(q-1.63095 q^{2} -1.00000 q^{3} +0.660014 q^{4} +1.38859 q^{5} +1.63095 q^{6} +2.37558 q^{7} +2.18546 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.63095 q^{2} -1.00000 q^{3} +0.660014 q^{4} +1.38859 q^{5} +1.63095 q^{6} +2.37558 q^{7} +2.18546 q^{8} +1.00000 q^{9} -2.26473 q^{10} -1.95226 q^{11} -0.660014 q^{12} -2.02534 q^{13} -3.87446 q^{14} -1.38859 q^{15} -4.88441 q^{16} +1.00000 q^{17} -1.63095 q^{18} +2.21429 q^{19} +0.916488 q^{20} -2.37558 q^{21} +3.18404 q^{22} +3.80128 q^{23} -2.18546 q^{24} -3.07182 q^{25} +3.30323 q^{26} -1.00000 q^{27} +1.56792 q^{28} -7.93340 q^{29} +2.26473 q^{30} -3.32374 q^{31} +3.59534 q^{32} +1.95226 q^{33} -1.63095 q^{34} +3.29871 q^{35} +0.660014 q^{36} +11.1954 q^{37} -3.61141 q^{38} +2.02534 q^{39} +3.03470 q^{40} +4.09779 q^{41} +3.87446 q^{42} +3.60885 q^{43} -1.28852 q^{44} +1.38859 q^{45} -6.19971 q^{46} -0.0414365 q^{47} +4.88441 q^{48} -1.35662 q^{49} +5.01000 q^{50} -1.00000 q^{51} -1.33675 q^{52} +2.03991 q^{53} +1.63095 q^{54} -2.71088 q^{55} +5.19173 q^{56} -2.21429 q^{57} +12.9390 q^{58} -0.596046 q^{59} -0.916488 q^{60} -5.88020 q^{61} +5.42087 q^{62} +2.37558 q^{63} +3.90499 q^{64} -2.81236 q^{65} -3.18404 q^{66} -4.79611 q^{67} +0.660014 q^{68} -3.80128 q^{69} -5.38004 q^{70} -4.60483 q^{71} +2.18546 q^{72} -10.9519 q^{73} -18.2592 q^{74} +3.07182 q^{75} +1.46146 q^{76} -4.63774 q^{77} -3.30323 q^{78} -1.83474 q^{79} -6.78244 q^{80} +1.00000 q^{81} -6.68331 q^{82} -12.4574 q^{83} -1.56792 q^{84} +1.38859 q^{85} -5.88586 q^{86} +7.93340 q^{87} -4.26657 q^{88} -9.18735 q^{89} -2.26473 q^{90} -4.81135 q^{91} +2.50889 q^{92} +3.32374 q^{93} +0.0675811 q^{94} +3.07475 q^{95} -3.59534 q^{96} +3.30682 q^{97} +2.21258 q^{98} -1.95226 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + q^99

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