LMFDB - Embedded newform 8007.2.a.e.1.11

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:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-1.59838 q^{2} +1.00000 q^{3} +0.554812 q^{4} +1.16995 q^{5} -1.59838 q^{6} +1.82514 q^{7} +2.30996 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.59838 q^{2} +1.00000 q^{3} +0.554812 q^{4} +1.16995 q^{5} -1.59838 q^{6} +1.82514 q^{7} +2.30996 q^{8} +1.00000 q^{9} -1.87002 q^{10} -1.19165 q^{11} +0.554812 q^{12} +0.914789 q^{13} -2.91726 q^{14} +1.16995 q^{15} -4.80181 q^{16} -1.00000 q^{17} -1.59838 q^{18} +7.92558 q^{19} +0.649103 q^{20} +1.82514 q^{21} +1.90471 q^{22} -4.14054 q^{23} +2.30996 q^{24} -3.63121 q^{25} -1.46218 q^{26} +1.00000 q^{27} +1.01261 q^{28} -3.17393 q^{29} -1.87002 q^{30} -6.18408 q^{31} +3.05519 q^{32} -1.19165 q^{33} +1.59838 q^{34} +2.13532 q^{35} +0.554812 q^{36} +4.92235 q^{37} -12.6681 q^{38} +0.914789 q^{39} +2.70254 q^{40} -6.06804 q^{41} -2.91726 q^{42} +2.66271 q^{43} -0.661141 q^{44} +1.16995 q^{45} +6.61815 q^{46} -11.4831 q^{47} -4.80181 q^{48} -3.66888 q^{49} +5.80405 q^{50} -1.00000 q^{51} +0.507536 q^{52} -11.2579 q^{53} -1.59838 q^{54} -1.39417 q^{55} +4.21598 q^{56} +7.92558 q^{57} +5.07315 q^{58} +3.73292 q^{59} +0.649103 q^{60} -7.41983 q^{61} +9.88449 q^{62} +1.82514 q^{63} +4.72027 q^{64} +1.07026 q^{65} +1.90471 q^{66} -6.67305 q^{67} -0.554812 q^{68} -4.14054 q^{69} -3.41305 q^{70} -0.615000 q^{71} +2.30996 q^{72} -10.3127 q^{73} -7.86778 q^{74} -3.63121 q^{75} +4.39720 q^{76} -2.17492 q^{77} -1.46218 q^{78} -11.3799 q^{79} -5.61788 q^{80} +1.00000 q^{81} +9.69903 q^{82} +4.29496 q^{83} +1.01261 q^{84} -1.16995 q^{85} -4.25601 q^{86} -3.17393 q^{87} -2.75266 q^{88} -1.40908 q^{89} -1.87002 q^{90} +1.66961 q^{91} -2.29722 q^{92} -6.18408 q^{93} +18.3544 q^{94} +9.27254 q^{95} +3.05519 q^{96} +7.58902 q^{97} +5.86426 q^{98} -1.19165 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * 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 $

$2$	−1.59838	−1.13022	−0.565112	−	0.825014i	$-0.691167\pi$
$2$	−1.59838	−1.13022	−0.565112	+	0.825014i	$0.691167\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.554812	0.277406
$5$	1.16995	0.523218	0.261609	−	0.965174i	$-0.415747\pi$
$5$	1.16995	0.523218	0.261609	+	0.965174i	$0.415747\pi$
$6$	−1.59838	−0.652535
$7$	1.82514	0.689836	0.344918	−	0.938633i	$-0.387907\pi$
$7$	1.82514	0.689836	0.344918	+	0.938633i	$0.387907\pi$
$8$	2.30996	0.816693
$9$	1.00000	0.333333
$10$	−1.87002	−0.591354
$11$	−1.19165	−0.359296	−0.179648	−	0.983731i	$-0.557496\pi$
$11$	−1.19165	−0.359296	−0.179648	+	0.983731i	$0.557496\pi$
$12$	0.554812	0.160160
$13$	0.914789	0.253717	0.126858	−	0.991921i	$-0.459511\pi$
$13$	0.914789	0.253717	0.126858	+	0.991921i	$0.459511\pi$
$14$	−2.91726	−0.779670
$15$	1.16995	0.302080
$16$	−4.80181	−1.20045
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.59838	−0.376741
$19$	7.92558	1.81825	0.909126	−	0.416521i	$-0.136751\pi$
$19$	7.92558	1.81825	0.909126	+	0.416521i	$0.136751\pi$
$20$	0.649103	0.145144
$21$	1.82514	0.398277
$22$	1.90471	0.406085
$23$	−4.14054	−0.863363	−0.431681	−	0.902026i	$-0.642079\pi$
$23$	−4.14054	−0.863363	−0.431681	+	0.902026i	$0.642079\pi$
$24$	2.30996	0.471518
$25$	−3.63121	−0.726243
$26$	−1.46218	−0.286757
$27$	1.00000	0.192450
$28$	1.01261	0.191365
$29$	−3.17393	−0.589385	−0.294692	−	0.955592i	$-0.595217\pi$
$29$	−3.17393	−0.589385	−0.294692	+	0.955592i	$0.595217\pi$
$30$	−1.87002	−0.341418
$31$	−6.18408	−1.11069	−0.555346	−	0.831619i	$-0.687414\pi$
$31$	−6.18408	−1.11069	−0.555346	+	0.831619i	$0.687414\pi$
$32$	3.05519	0.540086
$33$	−1.19165	−0.207440
$34$	1.59838	0.274120
$35$	2.13532	0.360935
$36$	0.554812	0.0924687
$37$	4.92235	0.809230	0.404615	−	0.914487i	$-0.367406\pi$
$37$	4.92235	0.809230	0.404615	+	0.914487i	$0.367406\pi$
$38$	−12.6681	−2.05503
$39$	0.914789	0.146483
$40$	2.70254	0.427309
$41$	−6.06804	−0.947669	−0.473835	−	0.880614i	$-0.657131\pi$
$41$	−6.06804	−0.947669	−0.473835	+	0.880614i	$0.657131\pi$
$42$	−2.91726	−0.450142
$43$	2.66271	0.406059	0.203030	−	0.979173i	$-0.434921\pi$
$43$	2.66271	0.406059	0.203030	+	0.979173i	$0.434921\pi$
$44$	−0.661141	−0.0996708
$45$	1.16995	0.174406
$46$	6.61815	0.975793
$47$	−11.4831	−1.67499	−0.837493	−	0.546448i	$-0.815980\pi$
$47$	−11.4831	−1.67499	−0.837493	+	0.546448i	$0.815980\pi$
$48$	−4.80181	−0.693081
$49$	−3.66888	−0.524126
$50$	5.80405	0.820817
$51$	−1.00000	−0.140028
$52$	0.507536	0.0703825
$53$	−11.2579	−1.54639	−0.773194	−	0.634170i	$-0.781342\pi$
$53$	−11.2579	−1.54639	−0.773194	+	0.634170i	$0.781342\pi$
$54$	−1.59838	−0.217512
$55$	−1.39417	−0.187990
$56$	4.21598	0.563385
$57$	7.92558	1.04977
$58$	5.07315	0.666137
$59$	3.73292	0.485985	0.242993	−	0.970028i	$-0.421871\pi$
$59$	3.73292	0.485985	0.242993	+	0.970028i	$0.421871\pi$
$60$	0.649103	0.0837988
$61$	−7.41983	−0.950012	−0.475006	−	0.879983i	$-0.657554\pi$
$61$	−7.41983	−0.950012	−0.475006	+	0.879983i	$0.657554\pi$
$62$	9.88449	1.25533
$63$	1.82514	0.229945
$64$	4.72027	0.590033
$65$	1.07026	0.132749
$66$	1.90471	0.234453
$67$	−6.67305	−0.815243	−0.407621	−	0.913151i	$-0.633642\pi$
$67$	−6.67305	−0.815243	−0.407621	+	0.913151i	$0.633642\pi$
$68$	−0.554812	−0.0672808
$69$	−4.14054	−0.498463
$70$	−3.41305	−0.407937
$71$	−0.615000	−0.0729871	−0.0364935	−	0.999334i	$-0.511619\pi$
$71$	−0.615000	−0.0729871	−0.0364935	+	0.999334i	$0.511619\pi$
$72$	2.30996	0.272231
$73$	−10.3127	−1.20701	−0.603504	−	0.797360i	$-0.706229\pi$
$73$	−10.3127	−1.20701	−0.603504	+	0.797360i	$0.706229\pi$
$74$	−7.86778	−0.914611
$75$	−3.63121	−0.419296
$76$	4.39720	0.504394
$77$	−2.17492	−0.247855
$78$	−1.46218	−0.165559
$79$	−11.3799	−1.28034	−0.640171	−	0.768232i	$-0.721137\pi$
$79$	−11.3799	−1.28034	−0.640171	+	0.768232i	$0.721137\pi$
$80$	−5.61788	−0.628098
$81$	1.00000	0.111111
$82$	9.69903	1.07108
$83$	4.29496	0.471433	0.235717	−	0.971822i	$-0.424256\pi$
$83$	4.29496	0.471433	0.235717	+	0.971822i	$0.424256\pi$
$84$	1.01261	0.110484
$85$	−1.16995	−0.126899
$86$	−4.25601	−0.458938
$87$	−3.17393	−0.340281
$88$	−2.75266	−0.293434
$89$	−1.40908	−0.149363	−0.0746813	−	0.997207i	$-0.523794\pi$
$89$	−1.40908	−0.149363	−0.0746813	+	0.997207i	$0.523794\pi$
$90$	−1.87002	−0.197118
$91$	1.66961	0.175023
$92$	−2.29722	−0.239502
$93$	−6.18408	−0.641259
$94$	18.3544	1.89311
$95$	9.27254	0.951343
$96$	3.05519	0.311819
$97$	7.58902	0.770549	0.385274	−	0.922802i	$-0.374107\pi$
$97$	7.58902	0.770549	0.385274	+	0.922802i	$0.374107\pi$
$98$	5.86426	0.592379
$99$	−1.19165	−0.119765
$100$	−2.01464	−0.201464
$101$	9.91608	0.986687	0.493343	−	0.869835i	$-0.335775\pi$
$101$	9.91608	0.986687	0.493343	+	0.869835i	$0.335775\pi$
$102$	1.59838	0.158263
$103$	−12.2113	−1.20322	−0.601608	−	0.798792i	$-0.705473\pi$
$103$	−12.2113	−1.20322	−0.601608	+	0.798792i	$0.705473\pi$
$104$	2.11312	0.207209
$105$	2.13532	0.208386
$106$	17.9943	1.74776
$107$	−7.73584	−0.747852	−0.373926	−	0.927459i	$-0.621989\pi$
$107$	−7.73584	−0.747852	−0.373926	+	0.927459i	$0.621989\pi$
$108$	0.554812	0.0533868
$109$	0.144579	0.0138481	0.00692405	−	0.999976i	$-0.497796\pi$
$109$	0.144579	0.0138481	0.00692405	+	0.999976i	$0.497796\pi$
$110$	2.22841	0.212471
$111$	4.92235	0.467209
$112$	−8.76395	−0.828116
$113$	4.24017	0.398882	0.199441	−	0.979910i	$-0.436087\pi$
$113$	4.24017	0.398882	0.199441	+	0.979910i	$0.436087\pi$
$114$	−12.6681	−1.18647
$115$	−4.84423	−0.451727
$116$	−1.76094	−0.163499
$117$	0.914789	0.0845722
$118$	−5.96662	−0.549272
$119$	−1.82514	−0.167310
$120$	2.70254	0.246707
$121$	−9.57997	−0.870907
$122$	11.8597	1.07373
$123$	−6.06804	−0.547137
$124$	−3.43100	−0.308113
$125$	−10.0981	−0.903202
$126$	−2.91726	−0.259890
$127$	0.134297	0.0119169	0.00595846	−	0.999982i	$-0.498103\pi$
$127$	0.134297	0.0119169	0.00595846	+	0.999982i	$0.498103\pi$
$128$	−13.6552	−1.20696
$129$	2.66271	0.234438
$130$	−1.71068	−0.150036
$131$	−13.1459	−1.14856	−0.574280	−	0.818659i	$-0.694718\pi$
$131$	−13.1459	−1.14856	−0.574280	+	0.818659i	$0.694718\pi$
$132$	−0.661141	−0.0575450
$133$	14.4653	1.25430
$134$	10.6661	0.921407
$135$	1.16995	0.100693
$136$	−2.30996	−0.198077
$137$	1.00302	0.0856937	0.0428469	−	0.999082i	$-0.486357\pi$
$137$	1.00302	0.0856937	0.0428469	+	0.999082i	$0.486357\pi$
$138$	6.61815	0.563374
$139$	−19.0468	−1.61553	−0.807765	−	0.589505i	$-0.799323\pi$
$139$	−19.0468	−1.61553	−0.807765	+	0.589505i	$0.799323\pi$
$140$	1.18470	0.100126
$141$	−11.4831	−0.967054
$142$	0.983003	0.0824917
$143$	−1.09011	−0.0911594
$144$	−4.80181	−0.400151
$145$	−3.71335	−0.308377
$146$	16.4836	1.36419
$147$	−3.66888	−0.302604
$148$	2.73098	0.224485
$149$	−9.48443	−0.776995	−0.388497	−	0.921450i	$-0.627006\pi$
$149$	−9.48443	−0.776995	−0.388497	+	0.921450i	$0.627006\pi$
$150$	5.80405	0.473899
$151$	16.3026	1.32669	0.663343	−	0.748316i	$-0.269137\pi$
$151$	16.3026	1.32669	0.663343	+	0.748316i	$0.269137\pi$
$152$	18.3077	1.48495
$153$	−1.00000	−0.0808452
$154$	3.47635	0.280132
$155$	−7.23507	−0.581135
$156$	0.507536	0.0406354
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	18.1894	1.44707
$159$	−11.2579	−0.892807
$160$	3.57442	0.282583
$161$	−7.55705	−0.595579
$162$	−1.59838	−0.125580
$163$	1.59418	0.124866	0.0624330	−	0.998049i	$-0.480114\pi$
$163$	1.59418	0.124866	0.0624330	+	0.998049i	$0.480114\pi$
$164$	−3.36662	−0.262889
$165$	−1.39417	−0.108536
$166$	−6.86497	−0.532825
$167$	−3.59270	−0.278011	−0.139006	−	0.990292i	$-0.544391\pi$
$167$	−3.59270	−0.278011	−0.139006	+	0.990292i	$0.544391\pi$
$168$	4.21598	0.325270
$169$	−12.1632	−0.935628
$170$	1.87002	0.143424
$171$	7.92558	0.606084
$172$	1.47730	0.112643
$173$	−13.3136	−1.01222	−0.506108	−	0.862470i	$-0.668916\pi$
$173$	−13.3136	−1.01222	−0.506108	+	0.862470i	$0.668916\pi$
$174$	5.07315	0.384594
$175$	−6.62746	−0.500989
$176$	5.72207	0.431317
$177$	3.73292	0.280584
$178$	2.25225	0.168813
$179$	2.11734	0.158257	0.0791286	−	0.996864i	$-0.474786\pi$
$179$	2.11734	0.158257	0.0791286	+	0.996864i	$0.474786\pi$
$180$	0.649103	0.0483813
$181$	25.3083	1.88115	0.940577	−	0.339581i	$-0.110285\pi$
$181$	25.3083	1.88115	0.940577	+	0.339581i	$0.110285\pi$
$182$	−2.66867	−0.197815
$183$	−7.41983	−0.548490
$184$	−9.56447	−0.705102
$185$	5.75891	0.423404
$186$	9.88449	0.724766
$187$	1.19165	0.0871420
$188$	−6.37098	−0.464651
$189$	1.82514	0.132759
$190$	−14.8210	−1.07523
$191$	−1.16316	−0.0841636	−0.0420818	−	0.999114i	$-0.513399\pi$
$191$	−1.16316	−0.0841636	−0.0420818	+	0.999114i	$0.513399\pi$
$192$	4.72027	0.340656
$193$	12.5277	0.901766	0.450883	−	0.892583i	$-0.351109\pi$
$193$	12.5277	0.901766	0.450883	+	0.892583i	$0.351109\pi$
$194$	−12.1301	−0.870892
$195$	1.07026	0.0766428
$196$	−2.03554	−0.145396
$197$	20.1117	1.43290	0.716449	−	0.697639i	$-0.245766\pi$
$197$	20.1117	1.43290	0.716449	+	0.697639i	$0.245766\pi$
$198$	1.90471	0.135362
$199$	26.5047	1.87887	0.939436	−	0.342725i	$-0.111350\pi$
$199$	26.5047	1.87887	0.939436	+	0.342725i	$0.111350\pi$
$200$	−8.38795	−0.593117
$201$	−6.67305	−0.470681
$202$	−15.8496	−1.11518
$203$	−5.79286	−0.406579
$204$	−0.554812	−0.0388446
$205$	−7.09932	−0.495838
$206$	19.5183	1.35990
$207$	−4.14054	−0.287788
$208$	−4.39264	−0.304575
$209$	−9.44451	−0.653290
$210$	−3.41305	−0.235523
$211$	1.51443	0.104257	0.0521287	−	0.998640i	$-0.483399\pi$
$211$	1.51443	0.104257	0.0521287	+	0.998640i	$0.483399\pi$
$212$	−6.24600	−0.428977
$213$	−0.615000	−0.0421391
$214$	12.3648	0.845240
$215$	3.11524	0.212457
$216$	2.30996	0.157173
$217$	−11.2868	−0.766196
$218$	−0.231091	−0.0156515
$219$	−10.3127	−0.696867
$220$	−0.773503	−0.0521496
$221$	−0.914789	−0.0615354
$222$	−7.86778	−0.528051
$223$	−8.21582	−0.550172	−0.275086	−	0.961420i	$-0.588706\pi$
$223$	−8.21582	−0.550172	−0.275086	+	0.961420i	$0.588706\pi$
$224$	5.57614	0.372571
$225$	−3.63121	−0.242081
$226$	−6.77739	−0.450826
$227$	−19.5546	−1.29789	−0.648943	−	0.760837i	$-0.724789\pi$
$227$	−19.5546	−1.29789	−0.648943	+	0.760837i	$0.724789\pi$
$228$	4.39720	0.291212
$229$	3.90448	0.258015	0.129008	−	0.991644i	$-0.458821\pi$
$229$	3.90448	0.258015	0.129008	+	0.991644i	$0.458821\pi$
$230$	7.74292	0.510553
$231$	−2.17492	−0.143099
$232$	−7.33165	−0.481346
$233$	5.54967	0.363571	0.181786	−	0.983338i	$-0.441812\pi$
$233$	5.54967	0.363571	0.181786	+	0.983338i	$0.441812\pi$
$234$	−1.46218	−0.0955856
$235$	−13.4347	−0.876383
$236$	2.07107	0.134815
$237$	−11.3799	−0.739206
$238$	2.91726	0.189098
$239$	−27.0026	−1.74665	−0.873326	−	0.487136i	$-0.838041\pi$
$239$	−27.0026	−1.74665	−0.873326	+	0.487136i	$0.838041\pi$
$240$	−5.61788	−0.362633
$241$	1.79439	0.115587	0.0577934	−	0.998329i	$-0.481594\pi$
$241$	1.79439	0.115587	0.0577934	+	0.998329i	$0.481594\pi$
$242$	15.3124	0.984319
$243$	1.00000	0.0641500
$244$	−4.11661	−0.263539
$245$	−4.29241	−0.274232
$246$	9.69903	0.618387
$247$	7.25023	0.461321
$248$	−14.2849	−0.907095
$249$	4.29496	0.272182
$250$	16.1406	1.02082
$251$	−23.6353	−1.49185	−0.745923	−	0.666032i	$-0.767991\pi$
$251$	−23.6353	−1.49185	−0.745923	+	0.666032i	$0.767991\pi$
$252$	1.01261	0.0637883
$253$	4.93407	0.310203
$254$	−0.214657	−0.0134688
$255$	−1.16995	−0.0732652
$256$	12.3856	0.774097
$257$	−2.53190	−0.157936	−0.0789678	−	0.996877i	$-0.525162\pi$
$257$	−2.53190	−0.157936	−0.0789678	+	0.996877i	$0.525162\pi$
$258$	−4.25601	−0.264968
$259$	8.98396	0.558236
$260$	0.593792	0.0368254
$261$	−3.17393	−0.196462
$262$	21.0121	1.29813
$263$	10.9297	0.673954	0.336977	−	0.941513i	$-0.390596\pi$
$263$	10.9297	0.673954	0.336977	+	0.941513i	$0.390596\pi$
$264$	−2.75266	−0.169414
$265$	−13.1712	−0.809098
$266$	−23.1209	−1.41764
$267$	−1.40908	−0.0862346
$268$	−3.70229	−0.226153
$269$	21.8703	1.33346	0.666729	−	0.745300i	$-0.267694\pi$
$269$	21.8703	1.33346	0.666729	+	0.745300i	$0.267694\pi$
$270$	−1.87002	−0.113806
$271$	24.6482	1.49727	0.748635	−	0.662982i	$-0.230710\pi$
$271$	24.6482	1.49727	0.748635	+	0.662982i	$0.230710\pi$
$272$	4.80181	0.291152
$273$	1.66961	0.101050
$274$	−1.60320	−0.0968531
$275$	4.32713	0.260936
$276$	−2.29722	−0.138277
$277$	5.04804	0.303307	0.151654	−	0.988434i	$-0.451540\pi$
$277$	5.04804	0.303307	0.151654	+	0.988434i	$0.451540\pi$
$278$	30.4440	1.82591
$279$	−6.18408	−0.370231
$280$	4.93250	0.294773
$281$	14.4208	0.860275	0.430138	−	0.902763i	$-0.358465\pi$
$281$	14.4208	0.860275	0.430138	+	0.902763i	$0.358465\pi$
$282$	18.3544	1.09299
$283$	−7.62556	−0.453293	−0.226646	−	0.973977i	$-0.572776\pi$
$283$	−7.62556	−0.453293	−0.226646	+	0.973977i	$0.572776\pi$
$284$	−0.341209	−0.0202471
$285$	9.27254	0.549258
$286$	1.74240	0.103030
$287$	−11.0750	−0.653737
$288$	3.05519	0.180029
$289$	1.00000	0.0588235
$290$	5.93533	0.348535
$291$	7.58902	0.444876
$292$	−5.72160	−0.334831
$293$	−31.3261	−1.83009	−0.915046	−	0.403350i	$-0.867846\pi$
$293$	−31.3261	−1.83009	−0.915046	+	0.403350i	$0.867846\pi$
$294$	5.86426	0.342010
$295$	4.36734	0.254276
$296$	11.3704	0.660892
$297$	−1.19165	−0.0691465
$298$	15.1597	0.878178
$299$	−3.78772	−0.219050
$300$	−2.01464	−0.116315
$301$	4.85980	0.280114
$302$	−26.0577	−1.49945
$303$	9.91608	0.569664
$304$	−38.0571	−2.18272
$305$	−8.68084	−0.497064
$306$	1.59838	0.0913732
$307$	15.6359	0.892387	0.446193	−	0.894937i	$-0.352779\pi$
$307$	15.6359	0.892387	0.446193	+	0.894937i	$0.352779\pi$
$308$	−1.20667	−0.0687566
$309$	−12.2113	−0.694677
$310$	11.5644	0.656812
$311$	26.3713	1.49538	0.747689	−	0.664049i	$-0.231164\pi$
$311$	26.3713	1.49538	0.747689	+	0.664049i	$0.231164\pi$
$312$	2.11312	0.119632
$313$	14.8269	0.838066	0.419033	−	0.907971i	$-0.362369\pi$
$313$	14.8269	0.838066	0.419033	+	0.907971i	$0.362369\pi$
$314$	−1.59838	−0.0902017
$315$	2.13532	0.120312
$316$	−6.31372	−0.355175
$317$	2.03310	0.114190	0.0570952	−	0.998369i	$-0.481816\pi$
$317$	2.03310	0.114190	0.0570952	+	0.998369i	$0.481816\pi$
$318$	17.9943	1.00907
$319$	3.78222	0.211763
$320$	5.52248	0.308716
$321$	−7.73584	−0.431772
$322$	12.0790	0.673138
$323$	−7.92558	−0.440991
$324$	0.554812	0.0308229
$325$	−3.32179	−0.184260
$326$	−2.54811	−0.141127
$327$	0.144579	0.00799521
$328$	−14.0169	−0.773955
$329$	−20.9583	−1.15547
$330$	2.22841	0.122670
$331$	30.1357	1.65641	0.828203	−	0.560428i	$-0.189364\pi$
$331$	30.1357	1.65641	0.828203	+	0.560428i	$0.189364\pi$
$332$	2.38290	0.130778
$333$	4.92235	0.269743
$334$	5.74249	0.314215
$335$	−7.80714	−0.426550
$336$	−8.76395	−0.478113
$337$	34.2672	1.86665	0.933326	−	0.359029i	$-0.116892\pi$
$337$	34.2672	1.86665	0.933326	+	0.359029i	$0.116892\pi$
$338$	19.4413	1.05747
$339$	4.24017	0.230294
$340$	−0.649103	−0.0352026
$341$	7.36925	0.399067
$342$	−12.6681	−0.685011
$343$	−19.4722	−1.05140
$344$	6.15074	0.331626
$345$	−4.84423	−0.260805
$346$	21.2802	1.14403
$347$	5.34595	0.286986	0.143493	−	0.989651i	$-0.454167\pi$
$347$	5.34595	0.286986	0.143493	+	0.989651i	$0.454167\pi$
$348$	−1.76094	−0.0943961
$349$	8.97988	0.480682	0.240341	−	0.970689i	$-0.422741\pi$
$349$	8.97988	0.480682	0.240341	+	0.970689i	$0.422741\pi$
$350$	10.5932	0.566229
$351$	0.914789	0.0488278
$352$	−3.64072	−0.194051
$353$	18.4935	0.984310	0.492155	−	0.870508i	$-0.336209\pi$
$353$	18.4935	0.984310	0.492155	+	0.870508i	$0.336209\pi$
$354$	−5.96662	−0.317122
$355$	−0.719520	−0.0381882
$356$	−0.781777	−0.0414341
$357$	−1.82514	−0.0965964
$358$	−3.38430	−0.178866
$359$	−11.3864	−0.600949	−0.300475	−	0.953790i	$-0.597145\pi$
$359$	−11.3864	−0.600949	−0.300475	+	0.953790i	$0.597145\pi$
$360$	2.70254	0.142436
$361$	43.8148	2.30604
$362$	−40.4523	−2.12612
$363$	−9.57997	−0.502818
$364$	0.926322	0.0485524
$365$	−12.0653	−0.631529
$366$	11.8597	0.619916
$367$	36.8049	1.92120	0.960600	−	0.277934i	$-0.0896496\pi$
$367$	36.8049	1.92120	0.960600	+	0.277934i	$0.0896496\pi$
$368$	19.8821	1.03643
$369$	−6.06804	−0.315890
$370$	−9.20492	−0.478541
$371$	−20.5471	−1.06675
$372$	−3.43100	−0.177889
$373$	−20.4161	−1.05710	−0.528552	−	0.848901i	$-0.677265\pi$
$373$	−20.4161	−1.05710	−0.528552	+	0.848901i	$0.677265\pi$
$374$	−1.90471	−0.0984900
$375$	−10.0981	−0.521464
$376$	−26.5255	−1.36795
$377$	−2.90348	−0.149537
$378$	−2.91726	−0.150047
$379$	−1.68452	−0.0865282	−0.0432641	−	0.999064i	$-0.513776\pi$
$379$	−1.68452	−0.0865282	−0.0432641	+	0.999064i	$0.513776\pi$
$380$	5.14452	0.263908
$381$	0.134297	0.00688024
$382$	1.85918	0.0951237
$383$	11.8427	0.605136	0.302568	−	0.953128i	$-0.402156\pi$
$383$	11.8427	0.605136	0.302568	+	0.953128i	$0.402156\pi$
$384$	−13.6552	−0.696836
$385$	−2.54455	−0.129682
$386$	−20.0240	−1.01920
$387$	2.66271	0.135353
$388$	4.21048	0.213755
$389$	8.79280	0.445813	0.222906	−	0.974840i	$-0.428446\pi$
$389$	8.79280	0.445813	0.222906	+	0.974840i	$0.428446\pi$
$390$	−1.71068	−0.0866235
$391$	4.14054	0.209396
$392$	−8.47495	−0.428050
$393$	−13.1459	−0.663122
$394$	−32.1461	−1.61950
$395$	−13.3140	−0.669898
$396$	−0.661141	−0.0332236
$397$	−20.7022	−1.03901	−0.519507	−	0.854466i	$-0.673884\pi$
$397$	−20.7022	−1.03901	−0.519507	+	0.854466i	$0.673884\pi$
$398$	−42.3646	−2.12355
$399$	14.4653	0.724168
$400$	17.4364	0.871819
$401$	−21.1791	−1.05763	−0.528817	−	0.848736i	$-0.677364\pi$
$401$	−21.1791	−1.05763	−0.528817	+	0.848736i	$0.677364\pi$
$402$	10.6661	0.531975
$403$	−5.65712	−0.281801
$404$	5.50156	0.273713
$405$	1.16995	0.0581354
$406$	9.25918	0.459525
$407$	−5.86572	−0.290753
$408$	−2.30996	−0.114360
$409$	19.0501	0.941965	0.470982	−	0.882143i	$-0.343900\pi$
$409$	19.0501	0.941965	0.470982	+	0.882143i	$0.343900\pi$
$410$	11.3474	0.560408
$411$	1.00302	0.0494753
$412$	−6.77498	−0.333779
$413$	6.81309	0.335250
$414$	6.61815	0.325264
$415$	5.02490	0.246663
$416$	2.79485	0.137029
$417$	−19.0468	−0.932727
$418$	15.0959	0.738364
$419$	1.31693	0.0643362	0.0321681	−	0.999482i	$-0.489759\pi$
$419$	1.31693	0.0643362	0.0321681	+	0.999482i	$0.489759\pi$
$420$	1.18470	0.0578075
$421$	−27.9279	−1.36112	−0.680561	−	0.732692i	$-0.738264\pi$
$421$	−27.9279	−1.36112	−0.680561	+	0.732692i	$0.738264\pi$
$422$	−2.42062	−0.117834
$423$	−11.4831	−0.558329
$424$	−26.0052	−1.26292
$425$	3.63121	0.176140
$426$	0.983003	0.0476266
$427$	−13.5422	−0.655353
$428$	−4.29194	−0.207459
$429$	−1.09011	−0.0526309
$430$	−4.97933	−0.240125
$431$	−39.6960	−1.91209	−0.956043	−	0.293225i	$-0.905272\pi$
$431$	−39.6960	−1.91209	−0.956043	+	0.293225i	$0.905272\pi$
$432$	−4.80181	−0.231027
$433$	−0.168206	−0.00808346	−0.00404173	−	0.999992i	$-0.501287\pi$
$433$	−0.168206	−0.00808346	−0.00404173	+	0.999992i	$0.501287\pi$
$434$	18.0405	0.865973
$435$	−3.71335	−0.178041
$436$	0.0802139	0.00384155
$437$	−32.8162	−1.56981
$438$	16.4836	0.787615
$439$	−17.2389	−0.822766	−0.411383	−	0.911463i	$-0.634954\pi$
$439$	−17.2389	−0.822766	−0.411383	+	0.911463i	$0.634954\pi$
$440$	−3.22048	−0.153530
$441$	−3.66888	−0.174709
$442$	1.46218	0.0695487
$443$	−1.01157	−0.0480612	−0.0240306	−	0.999711i	$-0.507650\pi$
$443$	−1.01157	−0.0480612	−0.0240306	+	0.999711i	$0.507650\pi$
$444$	2.73098	0.129607
$445$	−1.64856	−0.0781493
$446$	13.1320	0.621817
$447$	−9.48443	−0.448598
$448$	8.61513	0.407027
$449$	−18.9364	−0.893666	−0.446833	−	0.894617i	$-0.647448\pi$
$449$	−18.9364	−0.893666	−0.446833	+	0.894617i	$0.647448\pi$
$450$	5.80405	0.273606
$451$	7.23098	0.340494
$452$	2.35250	0.110652
$453$	16.3026	0.765962
$454$	31.2557	1.46690
$455$	1.95337	0.0915753
$456$	18.3077	0.857338
$457$	−14.5817	−0.682102	−0.341051	−	0.940045i	$-0.610783\pi$
$457$	−14.5817	−0.682102	−0.341051	+	0.940045i	$0.610783\pi$
$458$	−6.24083	−0.291615
$459$	−1.00000	−0.0466760
$460$	−2.68764	−0.125312
$461$	0.893761	0.0416266	0.0208133	−	0.999783i	$-0.493374\pi$
$461$	0.893761	0.0416266	0.0208133	+	0.999783i	$0.493374\pi$
$462$	3.47635	0.161734
$463$	32.8412	1.52626	0.763130	−	0.646245i	$-0.223662\pi$
$463$	32.8412	1.52626	0.763130	+	0.646245i	$0.223662\pi$
$464$	15.2406	0.707528
$465$	−7.23507	−0.335518
$466$	−8.87047	−0.410917
$467$	9.67004	0.447476	0.223738	−	0.974649i	$-0.428174\pi$
$467$	9.67004	0.447476	0.223738	+	0.974649i	$0.428174\pi$
$468$	0.507536	0.0234608
$469$	−12.1792	−0.562384
$470$	21.4737	0.990510
$471$	1.00000	0.0460776
$472$	8.62289	0.396901
$473$	−3.17301	−0.145895
$474$	18.1894	0.835468
$475$	−28.7795	−1.32049
$476$	−1.01261	−0.0464128
$477$	−11.2579	−0.515463
$478$	43.1603	1.97411
$479$	22.3165	1.01966	0.509832	−	0.860274i	$-0.329707\pi$
$479$	22.3165	1.01966	0.509832	+	0.860274i	$0.329707\pi$
$480$	3.57442	0.163149
$481$	4.50291	0.205315
$482$	−2.86811	−0.130639
$483$	−7.55705	−0.343858
$484$	−5.31508	−0.241595
$485$	8.87879	0.403165
$486$	−1.59838	−0.0725039
$487$	26.3789	1.19534	0.597670	−	0.801742i	$-0.296093\pi$
$487$	26.3789	1.19534	0.597670	+	0.801742i	$0.296093\pi$
$488$	−17.1395	−0.775868
$489$	1.59418	0.0720915
$490$	6.86089	0.309944
$491$	3.04590	0.137460	0.0687299	−	0.997635i	$-0.478105\pi$
$491$	3.04590	0.137460	0.0687299	+	0.997635i	$0.478105\pi$
$492$	−3.36662	−0.151779
$493$	3.17393	0.142947
$494$	−11.5886	−0.521396
$495$	−1.39417	−0.0626634
$496$	29.6947	1.33333
$497$	−1.12246	−0.0503492
$498$	−6.86497	−0.307627
$499$	−41.8886	−1.87519	−0.937596	−	0.347727i	$-0.886954\pi$
$499$	−41.8886	−1.87519	−0.937596	+	0.347727i	$0.886954\pi$
$500$	−5.60255	−0.250554
$501$	−3.59270	−0.160510
$502$	37.7781	1.68612
$503$	9.70741	0.432832	0.216416	−	0.976301i	$-0.430563\pi$
$503$	9.70741	0.432832	0.216416	+	0.976301i	$0.430563\pi$
$504$	4.21598	0.187795
$505$	11.6013	0.516253
$506$	−7.88652	−0.350598
$507$	−12.1632	−0.540185
$508$	0.0745095	0.00330583
$509$	24.3865	1.08091	0.540457	−	0.841372i	$-0.318252\pi$
$509$	24.3865	1.08091	0.540457	+	0.841372i	$0.318252\pi$
$510$	1.87002	0.0828061
$511$	−18.8221	−0.832639
$512$	7.51350	0.332053
$513$	7.92558	0.349923
$514$	4.04693	0.178502
$515$	−14.2866	−0.629544
$516$	1.47730	0.0650346
$517$	13.6839	0.601816
$518$	−14.3598	−0.630932
$519$	−13.3136	−0.584404
$520$	2.47225	0.108415
$521$	17.5420	0.768529	0.384264	−	0.923223i	$-0.374455\pi$
$521$	17.5420	0.768529	0.384264	+	0.923223i	$0.374455\pi$
$522$	5.07315	0.222046
$523$	6.44271	0.281720	0.140860	−	0.990030i	$-0.455013\pi$
$523$	6.44271	0.281720	0.140860	+	0.990030i	$0.455013\pi$
$524$	−7.29349	−0.318618
$525$	−6.62746	−0.289246
$526$	−17.4698	−0.761719
$527$	6.18408	0.269383
$528$	5.72207	0.249021
$529$	−5.85591	−0.254605
$530$	21.0525	0.914462
$531$	3.73292	0.161995
$532$	8.02550	0.347949
$533$	−5.55098	−0.240440
$534$	2.25225	0.0974644
$535$	−9.05055	−0.391290
$536$	−15.4145	−0.665803
$537$	2.11734	0.0913698
$538$	−34.9570	−1.50711
$539$	4.37202	0.188316
$540$	0.649103	0.0279329
$541$	−16.9721	−0.729686	−0.364843	−	0.931069i	$-0.618877\pi$
$541$	−16.9721	−0.729686	−0.364843	+	0.931069i	$0.618877\pi$
$542$	−39.3971	−1.69225
$543$	25.3083	1.08608
$544$	−3.05519	−0.130990
$545$	0.169150	0.00724558
$546$	−2.66867	−0.114209
$547$	−34.2583	−1.46478	−0.732390	−	0.680885i	$-0.761595\pi$
$547$	−34.2583	−1.46478	−0.732390	+	0.680885i	$0.761595\pi$
$548$	0.556487	0.0237719
$549$	−7.41983	−0.316671
$550$	−6.91639	−0.294916
$551$	−25.1553	−1.07165
$552$	−9.56447	−0.407091
$553$	−20.7699	−0.883227
$554$	−8.06868	−0.342805
$555$	5.75891	0.244452
$556$	−10.5674	−0.448158
$557$	11.8770	0.503244	0.251622	−	0.967826i	$-0.419036\pi$
$557$	11.8770	0.503244	0.251622	+	0.967826i	$0.419036\pi$
$558$	9.88449	0.418444
$559$	2.43581	0.103024
$560$	−10.2534	−0.433285
$561$	1.19165	0.0503115
$562$	−23.0500	−0.972304
$563$	15.9768	0.673342	0.336671	−	0.941622i	$-0.390699\pi$
$563$	15.9768	0.673342	0.336671	+	0.941622i	$0.390699\pi$
$564$	−6.37098	−0.268267
$565$	4.96079	0.208702
$566$	12.1885	0.512322
$567$	1.82514	0.0766485
$568$	−1.42062	−0.0596080
$569$	−43.1045	−1.80703	−0.903517	−	0.428552i	$-0.859024\pi$
$569$	−43.1045	−1.80703	−0.903517	+	0.428552i	$0.859024\pi$
$570$	−14.8210	−0.620784
$571$	−19.2958	−0.807506	−0.403753	−	0.914868i	$-0.632295\pi$
$571$	−19.2958	−0.807506	−0.403753	+	0.914868i	$0.632295\pi$
$572$	−0.604805	−0.0252882
$573$	−1.16316	−0.0485919
$574$	17.7020	0.738869
$575$	15.0352	0.627011
$576$	4.72027	0.196678
$577$	27.6731	1.15205	0.576023	−	0.817433i	$-0.304604\pi$
$577$	27.6731	1.15205	0.576023	+	0.817433i	$0.304604\pi$
$578$	−1.59838	−0.0664838
$579$	12.5277	0.520635
$580$	−2.06021	−0.0855456
$581$	7.83889	0.325212
$582$	−12.1301	−0.502810
$583$	13.4154	0.555611
$584$	−23.8219	−0.985756
$585$	1.07026	0.0442497
$586$	50.0710	2.06841
$587$	9.11122	0.376060	0.188030	−	0.982163i	$-0.439790\pi$
$587$	9.11122	0.376060	0.188030	+	0.982163i	$0.439790\pi$
$588$	−2.03554	−0.0839442
$589$	−49.0124	−2.01952
$590$	−6.98066	−0.287389
$591$	20.1117	0.827284
$592$	−23.6362	−0.971442
$593$	−25.5826	−1.05055	−0.525276	−	0.850932i	$-0.676038\pi$
$593$	−25.5826	−1.05055	−0.525276	+	0.850932i	$0.676038\pi$
$594$	1.90471	0.0781510
$595$	−2.13532	−0.0875396
$596$	−5.26208	−0.215543
$597$	26.5047	1.08477
$598$	6.05421	0.247575
$599$	17.1300	0.699912	0.349956	−	0.936766i	$-0.386196\pi$
$599$	17.1300	0.699912	0.349956	+	0.936766i	$0.386196\pi$
$600$	−8.38795	−0.342436
$601$	−13.6416	−0.556452	−0.278226	−	0.960516i	$-0.589746\pi$
$601$	−13.6416	−0.556452	−0.278226	+	0.960516i	$0.589746\pi$
$602$	−7.76780	−0.316592
$603$	−6.67305	−0.271748
$604$	9.04487	0.368030
$605$	−11.2081	−0.455674
$606$	−15.8496	−0.643848
$607$	0.842494	0.0341958	0.0170979	−	0.999854i	$-0.494557\pi$
$607$	0.842494	0.0341958	0.0170979	+	0.999854i	$0.494557\pi$
$608$	24.2141	0.982013
$609$	−5.79286	−0.234739
$610$	13.8753	0.561793
$611$	−10.5046	−0.424972
$612$	−0.554812	−0.0224269
$613$	−8.18001	−0.330388	−0.165194	−	0.986261i	$-0.552825\pi$
$613$	−8.18001	−0.330388	−0.165194	+	0.986261i	$0.552825\pi$
$614$	−24.9920	−1.00860
$615$	−7.09932	−0.286272
$616$	−5.02398	−0.202422
$617$	−10.3775	−0.417784	−0.208892	−	0.977939i	$-0.566986\pi$
$617$	−10.3775	−0.417784	−0.208892	+	0.977939i	$0.566986\pi$
$618$	19.5183	0.785140
$619$	−43.5241	−1.74938	−0.874690	−	0.484683i	$-0.838935\pi$
$619$	−43.5241	−1.74938	−0.874690	+	0.484683i	$0.838935\pi$
$620$	−4.01410	−0.161210
$621$	−4.14054	−0.166154
$622$	−42.1513	−1.69011
$623$	−2.57177	−0.103036
$624$	−4.39264	−0.175846
$625$	6.34178	0.253671
$626$	−23.6990	−0.947202
$627$	−9.44451	−0.377177
$628$	0.554812	0.0221394
$629$	−4.92235	−0.196267
$630$	−3.41305	−0.135979
$631$	−8.72146	−0.347196	−0.173598	−	0.984817i	$-0.555539\pi$
$631$	−8.72146	−0.347196	−0.173598	+	0.984817i	$0.555539\pi$
$632$	−26.2871	−1.04565
$633$	1.51443	0.0601930
$634$	−3.24967	−0.129061
$635$	0.157121	0.00623515
$636$	−6.24600	−0.247670
$637$	−3.35625	−0.132979
$638$	−6.04541	−0.239340
$639$	−0.615000	−0.0243290
$640$	−15.9759	−0.631501
$641$	−44.9265	−1.77449	−0.887246	−	0.461297i	$-0.847384\pi$
$641$	−44.9265	−1.77449	−0.887246	+	0.461297i	$0.847384\pi$
$642$	12.3648	0.487999
$643$	−37.1690	−1.46580	−0.732901	−	0.680335i	$-0.761834\pi$
$643$	−37.1690	−1.46580	−0.732901	+	0.680335i	$0.761834\pi$
$644$	−4.19274	−0.165217
$645$	3.11524	0.122662
$646$	12.6681	0.498418
$647$	−6.18672	−0.243225	−0.121613	−	0.992578i	$-0.538807\pi$
$647$	−6.18672	−0.243225	−0.121613	+	0.992578i	$0.538807\pi$
$648$	2.30996	0.0907437
$649$	−4.44834	−0.174612
$650$	5.30948	0.208255
$651$	−11.2868	−0.442364
$652$	0.884472	0.0346386
$653$	9.26678	0.362637	0.181319	−	0.983424i	$-0.441964\pi$
$653$	9.26678	0.362637	0.181319	+	0.983424i	$0.441964\pi$
$654$	−0.231091	−0.00903638
$655$	−15.3800	−0.600948
$656$	29.1376	1.13763
$657$	−10.3127	−0.402336
$658$	33.4992	1.30594
$659$	48.6158	1.89380	0.946901	−	0.321526i	$-0.104196\pi$
$659$	48.6158	1.89380	0.946901	+	0.321526i	$0.104196\pi$
$660$	−0.773503	−0.0301086
$661$	44.4602	1.72930	0.864650	−	0.502375i	$-0.167540\pi$
$661$	44.4602	1.72930	0.864650	+	0.502375i	$0.167540\pi$
$662$	−48.1682	−1.87211
$663$	−0.914789	−0.0355275
$664$	9.92118	0.385016
$665$	16.9236	0.656271
$666$	−7.86778	−0.304870
$667$	13.1418	0.508853
$668$	−1.99327	−0.0771220
$669$	−8.21582	−0.317642
$670$	12.4788	0.482097
$671$	8.84184	0.341335
$672$	5.57614	0.215104
$673$	40.5655	1.56369	0.781843	−	0.623475i	$-0.214280\pi$
$673$	40.5655	1.56369	0.781843	+	0.623475i	$0.214280\pi$
$674$	−54.7719	−2.10974
$675$	−3.63121	−0.139765
$676$	−6.74827	−0.259549
$677$	−11.3379	−0.435749	−0.217875	−	0.975977i	$-0.569912\pi$
$677$	−11.3379	−0.435749	−0.217875	+	0.975977i	$0.569912\pi$
$678$	−6.77739	−0.260284
$679$	13.8510	0.531552
$680$	−2.70254	−0.103638
$681$	−19.5546	−0.749335
$682$	−11.7788	−0.451035
$683$	−32.6132	−1.24791	−0.623954	−	0.781461i	$-0.714475\pi$
$683$	−32.6132	−1.24791	−0.623954	+	0.781461i	$0.714475\pi$
$684$	4.39720	0.168131
$685$	1.17348	0.0448365
$686$	31.1239	1.18831
$687$	3.90448	0.148965
$688$	−12.7858	−0.487454
$689$	−10.2986	−0.392345
$690$	7.74292	0.294768
$691$	18.2254	0.693327	0.346663	−	0.937990i	$-0.387315\pi$
$691$	18.2254	0.693327	0.346663	+	0.937990i	$0.387315\pi$
$692$	−7.38656	−0.280795
$693$	−2.17492	−0.0826185
$694$	−8.54485	−0.324358
$695$	−22.2838	−0.845275
$696$	−7.33165	−0.277905
$697$	6.06804	0.229844
$698$	−14.3532	−0.543278
$699$	5.54967	0.209908
$700$	−3.67699	−0.138977
$701$	10.6258	0.401332	0.200666	−	0.979660i	$-0.435689\pi$
$701$	10.6258	0.401332	0.200666	+	0.979660i	$0.435689\pi$
$702$	−1.46218	−0.0551864
$703$	39.0125	1.47138
$704$	−5.62490	−0.211997
$705$	−13.4347	−0.505980
$706$	−29.5596	−1.11249
$707$	18.0982	0.680653
$708$	2.07107	0.0778356
$709$	27.2324	1.02273	0.511366	−	0.859363i	$-0.329140\pi$
$709$	27.2324	1.02273	0.511366	+	0.859363i	$0.329140\pi$
$710$	1.15007	0.0431612
$711$	−11.3799	−0.426781
$712$	−3.25492	−0.121983
$713$	25.6054	0.958931
$714$	2.91726	0.109176
$715$	−1.27537	−0.0476962
$716$	1.17472	0.0439015
$717$	−27.0026	−1.00843
$718$	18.1997	0.679207
$719$	−13.6791	−0.510144	−0.255072	−	0.966922i	$-0.582099\pi$
$719$	−13.6791	−0.510144	−0.255072	+	0.966922i	$0.582099\pi$
$720$	−5.61788	−0.209366
$721$	−22.2873	−0.830022
$722$	−70.0326	−2.60634
$723$	1.79439	0.0667341
$724$	14.0414	0.521843
$725$	11.5252	0.428036
$726$	15.3124	0.568297
$727$	22.4776	0.833648	0.416824	−	0.908987i	$-0.363143\pi$
$727$	22.4776	0.833648	0.416824	+	0.908987i	$0.363143\pi$
$728$	3.85674	0.142940
$729$	1.00000	0.0370370
$730$	19.2850	0.713769
$731$	−2.66271	−0.0984838
$732$	−4.11661	−0.152154
$733$	34.1131	1.26000	0.629998	−	0.776597i	$-0.283056\pi$
$733$	34.1131	1.26000	0.629998	+	0.776597i	$0.283056\pi$
$734$	−58.8281	−2.17139
$735$	−4.29241	−0.158328
$736$	−12.6501	−0.466290
$737$	7.95194	0.292913
$738$	9.69903	0.357026
$739$	11.7842	0.433490	0.216745	−	0.976228i	$-0.430456\pi$
$739$	11.7842	0.433490	0.216745	+	0.976228i	$0.430456\pi$
$740$	3.19511	0.117455
$741$	7.25023	0.266344
$742$	32.8421	1.20567
$743$	−22.1508	−0.812633	−0.406316	−	0.913732i	$-0.633187\pi$
$743$	−22.1508	−0.812633	−0.406316	+	0.913732i	$0.633187\pi$
$744$	−14.2849	−0.523712
$745$	−11.0963	−0.406538
$746$	32.6326	1.19476
$747$	4.29496	0.157144
$748$	0.661141	0.0241737
$749$	−14.1190	−0.515895
$750$	16.1406	0.589371
$751$	13.0798	0.477288	0.238644	−	0.971107i	$-0.423297\pi$
$751$	13.0798	0.477288	0.238644	+	0.971107i	$0.423297\pi$
$752$	55.1398	2.01074
$753$	−23.6353	−0.861318
$754$	4.64086	0.169010
$755$	19.0732	0.694146
$756$	1.01261	0.0368282
$757$	−13.1165	−0.476728	−0.238364	−	0.971176i	$-0.576611\pi$
$757$	−13.1165	−0.476728	−0.238364	+	0.971176i	$0.576611\pi$
$758$	2.69251	0.0977963
$759$	4.93407	0.179096
$760$	21.4192	0.776955
$761$	−22.0185	−0.798169	−0.399085	−	0.916914i	$-0.630672\pi$
$761$	−22.0185	−0.798169	−0.399085	+	0.916914i	$0.630672\pi$
$762$	−0.214657	−0.00777621
$763$	0.263875	0.00955293
$764$	−0.645337	−0.0233475
$765$	−1.16995	−0.0422997
$766$	−18.9292	−0.683939
$767$	3.41484	0.123303
$768$	12.3856	0.446925
$769$	7.28707	0.262779	0.131389	−	0.991331i	$-0.458056\pi$
$769$	7.28707	0.262779	0.131389	+	0.991331i	$0.458056\pi$
$770$	4.06716	0.146570
$771$	−2.53190	−0.0911841
$772$	6.95053	0.250155
$773$	−38.1396	−1.37179	−0.685894	−	0.727702i	$-0.740589\pi$
$773$	−38.1396	−1.37179	−0.685894	+	0.727702i	$0.740589\pi$
$774$	−4.25601	−0.152979
$775$	22.4557	0.806633
$776$	17.5303	0.629302
$777$	8.98396	0.322298
$778$	−14.0542	−0.503868
$779$	−48.0928	−1.72310
$780$	0.593792	0.0212612
$781$	0.732864	0.0262240
$782$	−6.61815	−0.236665
$783$	−3.17393	−0.113427
$784$	17.6173	0.629188
$785$	1.16995	0.0417574
$786$	21.0121	0.749476
$787$	−11.3590	−0.404906	−0.202453	−	0.979292i	$-0.564891\pi$
$787$	−11.3590	−0.404906	−0.202453	+	0.979292i	$0.564891\pi$
$788$	11.1582	0.397495
$789$	10.9297	0.389108
$790$	21.2808	0.757135
$791$	7.73889	0.275163
$792$	−2.75266	−0.0978115
$793$	−6.78758	−0.241034
$794$	33.0900	1.17432
$795$	−13.1712	−0.467133
$796$	14.7052	0.521210
$797$	−46.1330	−1.63411	−0.817057	−	0.576556i	$-0.804396\pi$
$797$	−46.1330	−1.63411	−0.817057	+	0.576556i	$0.804396\pi$
$798$	−23.1209	−0.818472
$799$	11.4831	0.406244
$800$	−11.0940	−0.392234
$801$	−1.40908	−0.0497875
$802$	33.8522	1.19536
$803$	12.2891	0.433673
$804$	−3.70229	−0.130570
$805$	−8.84138	−0.311618
$806$	9.04222	0.318499
$807$	21.8703	0.769872
$808$	22.9057	0.805820
$809$	−39.2273	−1.37916	−0.689579	−	0.724211i	$-0.742204\pi$
$809$	−39.2273	−1.37916	−0.689579	+	0.724211i	$0.742204\pi$
$810$	−1.87002	−0.0657060
$811$	−50.5614	−1.77545	−0.887725	−	0.460374i	$-0.847715\pi$
$811$	−50.5614	−1.77545	−0.887725	+	0.460374i	$0.847715\pi$
$812$	−3.21395	−0.112787
$813$	24.6482	0.864449
$814$	9.37564	0.328616
$815$	1.86512	0.0653322
$816$	4.80181	0.168097
$817$	21.1035	0.738318
$818$	−30.4492	−1.06463
$819$	1.66961	0.0583410
$820$	−3.93879	−0.137548
$821$	31.8923	1.11305	0.556525	−	0.830831i	$-0.312134\pi$
$821$	31.8923	1.11305	0.556525	+	0.830831i	$0.312134\pi$
$822$	−1.60320	−0.0559182
$823$	35.3608	1.23260	0.616299	−	0.787512i	$-0.288631\pi$
$823$	35.3608	1.23260	0.616299	+	0.787512i	$0.288631\pi$
$824$	−28.2076	−0.982657
$825$	4.32713	0.150651
$826$	−10.8899	−0.378908
$827$	−30.8392	−1.07238	−0.536192	−	0.844096i	$-0.680138\pi$
$827$	−30.8392	−1.07238	−0.536192	+	0.844096i	$0.680138\pi$
$828$	−2.29722	−0.0798340
$829$	6.47862	0.225012	0.112506	−	0.993651i	$-0.464112\pi$
$829$	6.47862	0.225012	0.112506	+	0.993651i	$0.464112\pi$
$830$	−8.03169	−0.278784
$831$	5.04804	0.175115
$832$	4.31805	0.149701
$833$	3.66888	0.127119
$834$	30.4440	1.05419
$835$	−4.20328	−0.145460
$836$	−5.23993	−0.181227
$837$	−6.18408	−0.213753
$838$	−2.10495	−0.0727143
$839$	47.1502	1.62781	0.813903	−	0.581000i	$-0.197338\pi$
$839$	47.1502	1.62781	0.813903	+	0.581000i	$0.197338\pi$
$840$	4.93250	0.170187
$841$	−18.9261	−0.652626
$842$	44.6393	1.53837
$843$	14.4208	0.496680
$844$	0.840222	0.0289216
$845$	−14.2303	−0.489538
$846$	18.3544	0.631037
$847$	−17.4847	−0.600783
$848$	54.0581	1.85636
$849$	−7.62556	−0.261709
$850$	−5.80405	−0.199077
$851$	−20.3812	−0.698659
$852$	−0.341209	−0.0116896
$853$	25.2125	0.863261	0.431631	−	0.902050i	$-0.357938\pi$
$853$	25.2125	0.863261	0.431631	+	0.902050i	$0.357938\pi$
$854$	21.6456	0.740696
$855$	9.27254	0.317114
$856$	−17.8694	−0.610765
$857$	10.6982	0.365444	0.182722	−	0.983165i	$-0.441509\pi$
$857$	10.6982	0.365444	0.182722	+	0.983165i	$0.441509\pi$
$858$	1.74240	0.0594847
$859$	2.37214	0.0809363	0.0404681	−	0.999181i	$-0.487115\pi$
$859$	2.37214	0.0809363	0.0404681	+	0.999181i	$0.487115\pi$
$860$	1.72837	0.0589370
$861$	−11.0750	−0.377435
$862$	63.4491	2.16109
$863$	−28.4664	−0.969007	−0.484504	−	0.874789i	$-0.661000\pi$
$863$	−28.4664	−0.969007	−0.484504	+	0.874789i	$0.661000\pi$
$864$	3.05519	0.103940
$865$	−15.5763	−0.529610
$866$	0.268857	0.00913612
$867$	1.00000	0.0339618
$868$	−6.26204	−0.212547
$869$	13.5609	0.460022
$870$	5.93533	0.201227
$871$	−6.10443	−0.206841
$872$	0.333970	0.0113097
$873$	7.58902	0.256850
$874$	52.4527	1.77424
$875$	−18.4304	−0.623061
$876$	−5.72160	−0.193315
$877$	51.4641	1.73782	0.868910	−	0.494971i	$-0.164821\pi$
$877$	51.4641	1.73782	0.868910	+	0.494971i	$0.164821\pi$
$878$	27.5542	0.929910
$879$	−31.3261	−1.05660
$880$	6.69455	0.225673
$881$	−34.6633	−1.16784	−0.583919	−	0.811812i	$-0.698481\pi$
$881$	−34.6633	−1.16784	−0.583919	+	0.811812i	$0.698481\pi$
$882$	5.86426	0.197460
$883$	−19.2797	−0.648813	−0.324406	−	0.945918i	$-0.605165\pi$
$883$	−19.2797	−0.648813	−0.324406	+	0.945918i	$0.605165\pi$
$884$	−0.507536	−0.0170703
$885$	4.36734	0.146807
$886$	1.61687	0.0543200
$887$	−20.4113	−0.685343	−0.342672	−	0.939455i	$-0.611332\pi$
$887$	−20.4113	−0.685343	−0.342672	+	0.939455i	$0.611332\pi$
$888$	11.3704	0.381566
$889$	0.245110	0.00822073
$890$	2.63502	0.0883261
$891$	−1.19165	−0.0399218
$892$	−4.55823	−0.152621
$893$	−91.0104	−3.04555
$894$	15.1597	0.507016
$895$	2.47718	0.0828030
$896$	−24.9225	−0.832602
$897$	−3.78772	−0.126468
$898$	30.2676	1.01004
$899$	19.6278	0.654625
$900$	−2.01464	−0.0671547
$901$	11.2579	0.375054
$902$	−11.5578	−0.384834
$903$	4.85980	0.161724
$904$	9.79461	0.325764
$905$	29.6095	0.984254
$906$	−26.0577	−0.865709
$907$	−42.2351	−1.40239	−0.701196	−	0.712968i	$-0.747350\pi$
$907$	−42.2351	−1.40239	−0.701196	+	0.712968i	$0.747350\pi$
$908$	−10.8491	−0.360041
$909$	9.91608	0.328896
$910$	−3.12222	−0.103501
$911$	20.6857	0.685349	0.342675	−	0.939454i	$-0.388667\pi$
$911$	20.6857	0.685349	0.342675	+	0.939454i	$0.388667\pi$
$912$	−38.0571	−1.26020
$913$	−5.11809	−0.169384
$914$	23.3070	0.770927
$915$	−8.68084	−0.286980
$916$	2.16625	0.0715750
$917$	−23.9930	−0.792319
$918$	1.59838	0.0527543
$919$	51.3814	1.69492	0.847458	−	0.530862i	$-0.178132\pi$
$919$	51.3814	1.69492	0.847458	+	0.530862i	$0.178132\pi$
$920$	−11.1900	−0.368922
$921$	15.6359	0.515220
$922$	−1.42857	−0.0470474
$923$	−0.562595	−0.0185180
$924$	−1.20667	−0.0396966
$925$	−17.8741	−0.587697
$926$	−52.4927	−1.72502
$927$	−12.2113	−0.401072
$928$	−9.69697	−0.318319
$929$	−40.6243	−1.33284	−0.666420	−	0.745577i	$-0.732174\pi$
$929$	−40.6243	−1.33284	−0.666420	+	0.745577i	$0.732174\pi$
$930$	11.5644	0.379211
$931$	−29.0780	−0.952992
$932$	3.07902	0.100857
$933$	26.3713	0.863357
$934$	−15.4564	−0.505748
$935$	1.39417	0.0455943
$936$	2.11312	0.0690696
$937$	−3.48615	−0.113888	−0.0569439	−	0.998377i	$-0.518136\pi$
$937$	−3.48615	−0.113888	−0.0569439	+	0.998377i	$0.518136\pi$
$938$	19.4670	0.635620
$939$	14.8269	0.483857
$940$	−7.45373	−0.243114
$941$	−49.5379	−1.61489	−0.807444	−	0.589944i	$-0.799150\pi$
$941$	−49.5379	−1.61489	−0.807444	+	0.589944i	$0.799150\pi$
$942$	−1.59838	−0.0520780
$943$	25.1250	0.818182
$944$	−17.9248	−0.583402
$945$	2.13532	0.0694620
$946$	5.07167	0.164894
$947$	27.1935	0.883668	0.441834	−	0.897097i	$-0.354328\pi$
$947$	27.1935	0.883668	0.441834	+	0.897097i	$0.354328\pi$
$948$	−6.31372	−0.205060
$949$	−9.43393	−0.306238
$950$	46.0005	1.49245
$951$	2.03310	0.0659278
$952$	−4.21598	−0.136641
$953$	44.9531	1.45617	0.728086	−	0.685486i	$-0.240410\pi$
$953$	44.9531	1.45617	0.728086	+	0.685486i	$0.240410\pi$
$954$	17.9943	0.582588
$955$	−1.36085	−0.0440359
$956$	−14.9814	−0.484532
$957$	3.78222	0.122262
$958$	−35.6701	−1.15245
$959$	1.83065	0.0591146
$960$	5.52248	0.178237
$961$	7.24279	0.233638
$962$	−7.19736	−0.232052
$963$	−7.73584	−0.249284
$964$	0.995549	0.0320645
$965$	14.6568	0.471820
$966$	12.0790	0.388636
$967$	22.0804	0.710056	0.355028	−	0.934856i	$-0.384471\pi$
$967$	22.0804	0.710056	0.355028	+	0.934856i	$0.384471\pi$
$968$	−22.1293	−0.711263
$969$	−7.92558	−0.254606
$970$	−14.1917	−0.455667
$971$	12.1338	0.389392	0.194696	−	0.980864i	$-0.437628\pi$
$971$	12.1338	0.389392	0.194696	+	0.980864i	$0.437628\pi$
$972$	0.554812	0.0177956
$973$	−34.7630	−1.11445
$974$	−42.1634	−1.35100
$975$	−3.32179	−0.106383
$976$	35.6286	1.14044
$977$	15.4070	0.492914	0.246457	−	0.969154i	$-0.420734\pi$
$977$	15.4070	0.492914	0.246457	+	0.969154i	$0.420734\pi$
$978$	−2.54811	−0.0814795
$979$	1.67913	0.0536654
$980$	−2.38148	−0.0760736
$981$	0.144579	0.00461604
$982$	−4.86851	−0.155360
$983$	1.17533	0.0374873	0.0187437	−	0.999824i	$-0.494033\pi$
$983$	1.17533	0.0374873	0.0187437	+	0.999824i	$0.494033\pi$
$984$	−14.0169	−0.446843
$985$	23.5297	0.749719
$986$	−5.07315	−0.161562
$987$	−20.9583	−0.667109
$988$	4.02251	0.127973
$989$	−11.0251	−0.350576
$990$	2.22841	0.0708236
$991$	27.9081	0.886531	0.443265	−	0.896390i	$-0.353820\pi$
$991$	27.9081	0.886531	0.443265	+	0.896390i	$0.353820\pi$
$992$	−18.8935	−0.599870
$993$	30.1357	0.956326
$994$	1.79411	0.0569058
$995$	31.0093	0.983060
$996$	2.38290	0.0755050
$997$	26.8151	0.849243	0.424622	−	0.905371i	$-0.360407\pi$
$997$	26.8151	0.849243	0.424622	+	0.905371i	$0.360407\pi$
$998$	66.9538	2.11939
$999$	4.92235	0.155736

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.11	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.11	✓	46	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)

\(f(q)\)	\(=\)	\(q-1.59838 q^{2} +1.00000 q^{3} +0.554812 q^{4} +1.16995 q^{5} -1.59838 q^{6} +1.82514 q^{7} +2.30996 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.59838 q^{2} +1.00000 q^{3} +0.554812 q^{4} +1.16995 q^{5} -1.59838 q^{6} +1.82514 q^{7} +2.30996 q^{8} +1.00000 q^{9} -1.87002 q^{10} -1.19165 q^{11} +0.554812 q^{12} +0.914789 q^{13} -2.91726 q^{14} +1.16995 q^{15} -4.80181 q^{16} -1.00000 q^{17} -1.59838 q^{18} +7.92558 q^{19} +0.649103 q^{20} +1.82514 q^{21} +1.90471 q^{22} -4.14054 q^{23} +2.30996 q^{24} -3.63121 q^{25} -1.46218 q^{26} +1.00000 q^{27} +1.01261 q^{28} -3.17393 q^{29} -1.87002 q^{30} -6.18408 q^{31} +3.05519 q^{32} -1.19165 q^{33} +1.59838 q^{34} +2.13532 q^{35} +0.554812 q^{36} +4.92235 q^{37} -12.6681 q^{38} +0.914789 q^{39} +2.70254 q^{40} -6.06804 q^{41} -2.91726 q^{42} +2.66271 q^{43} -0.661141 q^{44} +1.16995 q^{45} +6.61815 q^{46} -11.4831 q^{47} -4.80181 q^{48} -3.66888 q^{49} +5.80405 q^{50} -1.00000 q^{51} +0.507536 q^{52} -11.2579 q^{53} -1.59838 q^{54} -1.39417 q^{55} +4.21598 q^{56} +7.92558 q^{57} +5.07315 q^{58} +3.73292 q^{59} +0.649103 q^{60} -7.41983 q^{61} +9.88449 q^{62} +1.82514 q^{63} +4.72027 q^{64} +1.07026 q^{65} +1.90471 q^{66} -6.67305 q^{67} -0.554812 q^{68} -4.14054 q^{69} -3.41305 q^{70} -0.615000 q^{71} +2.30996 q^{72} -10.3127 q^{73} -7.86778 q^{74} -3.63121 q^{75} +4.39720 q^{76} -2.17492 q^{77} -1.46218 q^{78} -11.3799 q^{79} -5.61788 q^{80} +1.00000 q^{81} +9.69903 q^{82} +4.29496 q^{83} +1.01261 q^{84} -1.16995 q^{85} -4.25601 q^{86} -3.17393 q^{87} -2.75266 q^{88} -1.40908 q^{89} -1.87002 q^{90} +1.66961 q^{91} -2.29722 q^{92} -6.18408 q^{93} +18.3544 q^{94} +9.27254 q^{95} +3.05519 q^{96} +7.58902 q^{97} +5.86426 q^{98} -1.19165 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

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