LMFDB - Embedded newform 8022.2.a.ba.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8022,2,Mod(1,8022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8022, 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("8022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8022 = 2 \cdot 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8022.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0559925015$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 39 x^{14} + 165 x^{13} + 711 x^{12} - 1949 x^{11} - 7497 x^{10} + 8238 x^{9} + \cdots + 30 $ x^16 - 5x^15 - 39x^14 + 165x^13 + 711x^12 - 1949x^11 - 7497x^10 + 8238x^9 + 42708x^8 + 7872x^7 - 97852x^6 - 109082x^5 - 6830x^4 + 49478x^3 + 28368x^2 + 4947*x + 30
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-0.811854$ of defining polynomial
Character	$\chi$	$=$	8022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.81185 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.81185 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.81185 q^{10} -2.33076 q^{11} +1.00000 q^{12} +5.12319 q^{13} +1.00000 q^{14} +1.81185 q^{15} +1.00000 q^{16} +1.70675 q^{17} +1.00000 q^{18} +4.09017 q^{19} +1.81185 q^{20} +1.00000 q^{21} -2.33076 q^{22} +1.70062 q^{23} +1.00000 q^{24} -1.71719 q^{25} +5.12319 q^{26} +1.00000 q^{27} +1.00000 q^{28} +7.78507 q^{29} +1.81185 q^{30} +4.50374 q^{31} +1.00000 q^{32} -2.33076 q^{33} +1.70675 q^{34} +1.81185 q^{35} +1.00000 q^{36} -9.45831 q^{37} +4.09017 q^{38} +5.12319 q^{39} +1.81185 q^{40} -9.24349 q^{41} +1.00000 q^{42} +6.37480 q^{43} -2.33076 q^{44} +1.81185 q^{45} +1.70062 q^{46} -4.70925 q^{47} +1.00000 q^{48} +1.00000 q^{49} -1.71719 q^{50} +1.70675 q^{51} +5.12319 q^{52} +0.308609 q^{53} +1.00000 q^{54} -4.22300 q^{55} +1.00000 q^{56} +4.09017 q^{57} +7.78507 q^{58} -2.48380 q^{59} +1.81185 q^{60} -2.90828 q^{61} +4.50374 q^{62} +1.00000 q^{63} +1.00000 q^{64} +9.28246 q^{65} -2.33076 q^{66} -7.19368 q^{67} +1.70675 q^{68} +1.70062 q^{69} +1.81185 q^{70} +4.54384 q^{71} +1.00000 q^{72} +5.25013 q^{73} -9.45831 q^{74} -1.71719 q^{75} +4.09017 q^{76} -2.33076 q^{77} +5.12319 q^{78} -1.92371 q^{79} +1.81185 q^{80} +1.00000 q^{81} -9.24349 q^{82} -12.9363 q^{83} +1.00000 q^{84} +3.09238 q^{85} +6.37480 q^{86} +7.78507 q^{87} -2.33076 q^{88} -1.71038 q^{89} +1.81185 q^{90} +5.12319 q^{91} +1.70062 q^{92} +4.50374 q^{93} -4.70925 q^{94} +7.41079 q^{95} +1.00000 q^{96} +10.7875 q^{97} +1.00000 q^{98} -2.33076 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 11 q^{5} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 11 * q^5 + 16 * q^6 + 16 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 11 q^{5} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 16 q^{12} + 6 q^{13} + 16 q^{14} + 11 q^{15} + 16 q^{16} + 14 q^{17} + 16 q^{18} + 29 q^{19} + 11 q^{20} + 16 q^{21} + 8 q^{22} + 9 q^{23} + 16 q^{24} + 29 q^{25} + 6 q^{26} + 16 q^{27} + 16 q^{28} + 11 q^{30} + 14 q^{31} + 16 q^{32} + 8 q^{33} + 14 q^{34} + 11 q^{35} + 16 q^{36} + 11 q^{37} + 29 q^{38} + 6 q^{39} + 11 q^{40} + 14 q^{41} + 16 q^{42} + 28 q^{43} + 8 q^{44} + 11 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 16 q^{49} + 29 q^{50} + 14 q^{51} + 6 q^{52} - 4 q^{53} + 16 q^{54} + 17 q^{55} + 16 q^{56} + 29 q^{57} + 25 q^{59} + 11 q^{60} + 16 q^{61} + 14 q^{62} + 16 q^{63} + 16 q^{64} + 6 q^{65} + 8 q^{66} + 26 q^{67} + 14 q^{68} + 9 q^{69} + 11 q^{70} + 9 q^{71} + 16 q^{72} + 31 q^{73} + 11 q^{74} + 29 q^{75} + 29 q^{76} + 8 q^{77} + 6 q^{78} + 9 q^{79} + 11 q^{80} + 16 q^{81} + 14 q^{82} + 13 q^{83} + 16 q^{84} + 20 q^{85} + 28 q^{86} + 8 q^{88} + 21 q^{89} + 11 q^{90} + 6 q^{91} + 9 q^{92} + 14 q^{93} - q^{94} - 37 q^{95} + 16 q^{96} + 18 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 11 * q^5 + 16 * q^6 + 16 * q^7 + 16 * q^8 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 16 * q^12 + 6 * q^13 + 16 * q^14 + 11 * q^15 + 16 * q^16 + 14 * q^17 + 16 * q^18 + 29 * q^19 + 11 * q^20 + 16 * q^21 + 8 * q^22 + 9 * q^23 + 16 * q^24 + 29 * q^25 + 6 * q^26 + 16 * q^27 + 16 * q^28 + 11 * q^30 + 14 * q^31 + 16 * q^32 + 8 * q^33 + 14 * q^34 + 11 * q^35 + 16 * q^36 + 11 * q^37 + 29 * q^38 + 6 * q^39 + 11 * q^40 + 14 * q^41 + 16 * q^42 + 28 * q^43 + 8 * q^44 + 11 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 16 * q^49 + 29 * q^50 + 14 * q^51 + 6 * q^52 - 4 * q^53 + 16 * q^54 + 17 * q^55 + 16 * q^56 + 29 * q^57 + 25 * q^59 + 11 * q^60 + 16 * q^61 + 14 * q^62 + 16 * q^63 + 16 * q^64 + 6 * q^65 + 8 * q^66 + 26 * q^67 + 14 * q^68 + 9 * q^69 + 11 * q^70 + 9 * q^71 + 16 * q^72 + 31 * q^73 + 11 * q^74 + 29 * q^75 + 29 * q^76 + 8 * q^77 + 6 * q^78 + 9 * q^79 + 11 * q^80 + 16 * q^81 + 14 * q^82 + 13 * q^83 + 16 * q^84 + 20 * q^85 + 28 * q^86 + 8 * q^88 + 21 * q^89 + 11 * q^90 + 6 * q^91 + 9 * q^92 + 14 * q^93 - q^94 - 37 * q^95 + 16 * q^96 + 18 * q^97 + 16 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.81185	0.810286	0.405143	−	0.914253i	$-0.367222\pi$
$5$	1.81185	0.810286	0.405143	+	0.914253i	$0.367222\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.81185	0.572958
$11$	−2.33076	−0.702752	−0.351376	−	0.936234i	$-0.614286\pi$
$11$	−2.33076	−0.702752	−0.351376	+	0.936234i	$0.614286\pi$
$12$	1.00000	0.288675
$13$	5.12319	1.42092	0.710458	−	0.703740i	$-0.248488\pi$
$13$	5.12319	1.42092	0.710458	+	0.703740i	$0.248488\pi$
$14$	1.00000	0.267261
$15$	1.81185	0.467819
$16$	1.00000	0.250000
$17$	1.70675	0.413947	0.206974	−	0.978347i	$-0.433639\pi$
$17$	1.70675	0.413947	0.206974	+	0.978347i	$0.433639\pi$
$18$	1.00000	0.235702
$19$	4.09017	0.938349	0.469175	−	0.883105i	$-0.344551\pi$
$19$	4.09017	0.938349	0.469175	+	0.883105i	$0.344551\pi$
$20$	1.81185	0.405143
$21$	1.00000	0.218218
$22$	−2.33076	−0.496921
$23$	1.70062	0.354605	0.177302	−	0.984156i	$-0.443263\pi$
$23$	1.70062	0.354605	0.177302	+	0.984156i	$0.443263\pi$
$24$	1.00000	0.204124
$25$	−1.71719	−0.343437
$26$	5.12319	1.00474
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	7.78507	1.44565	0.722826	−	0.691030i	$-0.242843\pi$
$29$	7.78507	1.44565	0.722826	+	0.691030i	$0.242843\pi$
$30$	1.81185	0.330798
$31$	4.50374	0.808896	0.404448	−	0.914561i	$-0.367464\pi$
$31$	4.50374	0.808896	0.404448	+	0.914561i	$0.367464\pi$
$32$	1.00000	0.176777
$33$	−2.33076	−0.405734
$34$	1.70675	0.292705
$35$	1.81185	0.306259
$36$	1.00000	0.166667
$37$	−9.45831	−1.55494	−0.777468	−	0.628923i	$-0.783496\pi$
$37$	−9.45831	−1.55494	−0.777468	+	0.628923i	$0.783496\pi$
$38$	4.09017	0.663513
$39$	5.12319	0.820366
$40$	1.81185	0.286479
$41$	−9.24349	−1.44359	−0.721795	−	0.692107i	$-0.756683\pi$
$41$	−9.24349	−1.44359	−0.721795	+	0.692107i	$0.756683\pi$
$42$	1.00000	0.154303
$43$	6.37480	0.972148	0.486074	−	0.873918i	$-0.338429\pi$
$43$	6.37480	0.972148	0.486074	+	0.873918i	$0.338429\pi$
$44$	−2.33076	−0.351376
$45$	1.81185	0.270095
$46$	1.70062	0.250743
$47$	−4.70925	−0.686915	−0.343457	−	0.939168i	$-0.611598\pi$
$47$	−4.70925	−0.686915	−0.343457	+	0.939168i	$0.611598\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−1.71719	−0.242847
$51$	1.70675	0.238993
$52$	5.12319	0.710458
$53$	0.308609	0.0423907	0.0211954	−	0.999775i	$-0.493253\pi$
$53$	0.308609	0.0423907	0.0211954	+	0.999775i	$0.493253\pi$
$54$	1.00000	0.136083
$55$	−4.22300	−0.569430
$56$	1.00000	0.133631
$57$	4.09017	0.541756
$58$	7.78507	1.02223
$59$	−2.48380	−0.323363	−0.161681	−	0.986843i	$-0.551692\pi$
$59$	−2.48380	−0.323363	−0.161681	+	0.986843i	$0.551692\pi$
$60$	1.81185	0.233909
$61$	−2.90828	−0.372367	−0.186184	−	0.982515i	$-0.559612\pi$
$61$	−2.90828	−0.372367	−0.186184	+	0.982515i	$0.559612\pi$
$62$	4.50374	0.571976
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	9.28246	1.15135
$66$	−2.33076	−0.286897
$67$	−7.19368	−0.878847	−0.439424	−	0.898280i	$-0.644817\pi$
$67$	−7.19368	−0.878847	−0.439424	+	0.898280i	$0.644817\pi$
$68$	1.70675	0.206974
$69$	1.70062	0.204731
$70$	1.81185	0.216558
$71$	4.54384	0.539255	0.269628	−	0.962965i	$-0.413099\pi$
$71$	4.54384	0.539255	0.269628	+	0.962965i	$0.413099\pi$
$72$	1.00000	0.117851
$73$	5.25013	0.614482	0.307241	−	0.951632i	$-0.400594\pi$
$73$	5.25013	0.614482	0.307241	+	0.951632i	$0.400594\pi$
$74$	−9.45831	−1.09951
$75$	−1.71719	−0.198284
$76$	4.09017	0.469175
$77$	−2.33076	−0.265615
$78$	5.12319	0.580086
$79$	−1.92371	−0.216434	−0.108217	−	0.994127i	$-0.534514\pi$
$79$	−1.92371	−0.216434	−0.108217	+	0.994127i	$0.534514\pi$
$80$	1.81185	0.202571
$81$	1.00000	0.111111
$82$	−9.24349	−1.02077
$83$	−12.9363	−1.41995	−0.709973	−	0.704229i	$-0.751293\pi$
$83$	−12.9363	−1.41995	−0.709973	+	0.704229i	$0.751293\pi$
$84$	1.00000	0.109109
$85$	3.09238	0.335415
$86$	6.37480	0.687413
$87$	7.78507	0.834647
$88$	−2.33076	−0.248460
$89$	−1.71038	−0.181300	−0.0906501	−	0.995883i	$-0.528895\pi$
$89$	−1.71038	−0.181300	−0.0906501	+	0.995883i	$0.528895\pi$
$90$	1.81185	0.190986
$91$	5.12319	0.537056
$92$	1.70062	0.177302
$93$	4.50374	0.467016
$94$	−4.70925	−0.485722
$95$	7.41079	0.760331
$96$	1.00000	0.102062
$97$	10.7875	1.09531	0.547654	−	0.836705i	$-0.315521\pi$
$97$	10.7875	1.09531	0.547654	+	0.836705i	$0.315521\pi$
$98$	1.00000	0.101015
$99$	−2.33076	−0.234251
$100$	−1.71719	−0.171719
$101$	−15.0127	−1.49382	−0.746912	−	0.664923i	$-0.768464\pi$
$101$	−15.0127	−1.49382	−0.746912	+	0.664923i	$0.768464\pi$
$102$	1.70675	0.168993
$103$	−4.03171	−0.397257	−0.198628	−	0.980075i	$-0.563649\pi$
$103$	−4.03171	−0.397257	−0.198628	+	0.980075i	$0.563649\pi$
$104$	5.12319	0.502370
$105$	1.81185	0.176819
$106$	0.308609	0.0299748
$107$	4.98264	0.481690	0.240845	−	0.970564i	$-0.422575\pi$
$107$	4.98264	0.481690	0.240845	+	0.970564i	$0.422575\pi$
$108$	1.00000	0.0962250
$109$	−5.90451	−0.565549	−0.282775	−	0.959186i	$-0.591255\pi$
$109$	−5.90451	−0.565549	−0.282775	+	0.959186i	$0.591255\pi$
$110$	−4.22300	−0.402648
$111$	−9.45831	−0.897743
$112$	1.00000	0.0944911
$113$	4.66166	0.438532	0.219266	−	0.975665i	$-0.429634\pi$
$113$	4.66166	0.438532	0.219266	+	0.975665i	$0.429634\pi$
$114$	4.09017	0.383080
$115$	3.08128	0.287331
$116$	7.78507	0.722826
$117$	5.12319	0.473639
$118$	−2.48380	−0.228652
$119$	1.70675	0.156457
$120$	1.81185	0.165399
$121$	−5.56754	−0.506140
$122$	−2.90828	−0.263303
$123$	−9.24349	−0.833457
$124$	4.50374	0.404448
$125$	−12.1706	−1.08857
$126$	1.00000	0.0890871
$127$	9.51608	0.844415	0.422208	−	0.906499i	$-0.361255\pi$
$127$	9.51608	0.844415	0.422208	+	0.906499i	$0.361255\pi$
$128$	1.00000	0.0883883
$129$	6.37480	0.561270
$130$	9.28246	0.814126
$131$	−4.77929	−0.417568	−0.208784	−	0.977962i	$-0.566951\pi$
$131$	−4.77929	−0.417568	−0.208784	+	0.977962i	$0.566951\pi$
$132$	−2.33076	−0.202867
$133$	4.09017	0.354663
$134$	−7.19368	−0.621439
$135$	1.81185	0.155940
$136$	1.70675	0.146352
$137$	9.14096	0.780965	0.390482	−	0.920610i	$-0.372308\pi$
$137$	9.14096	0.780965	0.390482	+	0.920610i	$0.372308\pi$
$138$	1.70062	0.144767
$139$	−8.55659	−0.725761	−0.362880	−	0.931836i	$-0.618207\pi$
$139$	−8.55659	−0.725761	−0.362880	+	0.931836i	$0.618207\pi$
$140$	1.81185	0.153130
$141$	−4.70925	−0.396590
$142$	4.54384	0.381311
$143$	−11.9409	−0.998551
$144$	1.00000	0.0833333
$145$	14.1054	1.17139
$146$	5.25013	0.434504
$147$	1.00000	0.0824786
$148$	−9.45831	−0.777468
$149$	19.2674	1.57845	0.789225	−	0.614104i	$-0.210482\pi$
$149$	19.2674	1.57845	0.789225	+	0.614104i	$0.210482\pi$
$150$	−1.71719	−0.140208
$151$	17.7794	1.44687	0.723433	−	0.690395i	$-0.242563\pi$
$151$	17.7794	1.44687	0.723433	+	0.690395i	$0.242563\pi$
$152$	4.09017	0.331757
$153$	1.70675	0.137982
$154$	−2.33076	−0.187818
$155$	8.16012	0.655436
$156$	5.12319	0.410183
$157$	4.22349	0.337071	0.168536	−	0.985696i	$-0.446096\pi$
$157$	4.22349	0.337071	0.168536	+	0.985696i	$0.446096\pi$
$158$	−1.92371	−0.153042
$159$	0.308609	0.0244743
$160$	1.81185	0.143240
$161$	1.70062	0.134028
$162$	1.00000	0.0785674
$163$	−14.8242	−1.16112	−0.580562	−	0.814216i	$-0.697167\pi$
$163$	−14.8242	−1.16112	−0.580562	+	0.814216i	$0.697167\pi$
$164$	−9.24349	−0.721795
$165$	−4.22300	−0.328760
$166$	−12.9363	−1.00405
$167$	19.0143	1.47137	0.735684	−	0.677325i	$-0.236861\pi$
$167$	19.0143	1.47137	0.735684	+	0.677325i	$0.236861\pi$
$168$	1.00000	0.0771517
$169$	13.2470	1.01900
$170$	3.09238	0.237175
$171$	4.09017	0.312783
$172$	6.37480	0.486074
$173$	−24.7673	−1.88302	−0.941510	−	0.336985i	$-0.890593\pi$
$173$	−24.7673	−1.88302	−0.941510	+	0.336985i	$0.890593\pi$
$174$	7.78507	0.590185
$175$	−1.71719	−0.129807
$176$	−2.33076	−0.175688
$177$	−2.48380	−0.186693
$178$	−1.71038	−0.128199
$179$	−0.403011	−0.0301225	−0.0150612	−	0.999887i	$-0.504794\pi$
$179$	−0.403011	−0.0301225	−0.0150612	+	0.999887i	$0.504794\pi$
$180$	1.81185	0.135048
$181$	23.6960	1.76131	0.880654	−	0.473760i	$-0.157103\pi$
$181$	23.6960	1.76131	0.880654	+	0.473760i	$0.157103\pi$
$182$	5.12319	0.379756
$183$	−2.90828	−0.214986
$184$	1.70062	0.125372
$185$	−17.1371	−1.25994
$186$	4.50374	0.330230
$187$	−3.97803	−0.290902
$188$	−4.70925	−0.343457
$189$	1.00000	0.0727393
$190$	7.41079	0.537635
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	1.00000	0.0721688
$193$	12.4451	0.895818	0.447909	−	0.894079i	$-0.352169\pi$
$193$	12.4451	0.895818	0.447909	+	0.894079i	$0.352169\pi$
$194$	10.7875	0.774500
$195$	9.28246	0.664731
$196$	1.00000	0.0714286
$197$	10.2196	0.728117	0.364058	−	0.931376i	$-0.381391\pi$
$197$	10.2196	0.728117	0.364058	+	0.931376i	$0.381391\pi$
$198$	−2.33076	−0.165640
$199$	5.29285	0.375200	0.187600	−	0.982245i	$-0.439929\pi$
$199$	5.29285	0.375200	0.187600	+	0.982245i	$0.439929\pi$
$200$	−1.71719	−0.121423
$201$	−7.19368	−0.507403
$202$	−15.0127	−1.05629
$203$	7.78507	0.546405
$204$	1.70675	0.119496
$205$	−16.7479	−1.16972
$206$	−4.03171	−0.280903
$207$	1.70062	0.118202
$208$	5.12319	0.355229
$209$	−9.53322	−0.659427
$210$	1.81185	0.125030
$211$	1.54823	0.106585	0.0532924	−	0.998579i	$-0.483028\pi$
$211$	1.54823	0.106585	0.0532924	+	0.998579i	$0.483028\pi$
$212$	0.308609	0.0211954
$213$	4.54384	0.311339
$214$	4.98264	0.340606
$215$	11.5502	0.787718
$216$	1.00000	0.0680414
$217$	4.50374	0.305734
$218$	−5.90451	−0.399904
$219$	5.25013	0.354771
$220$	−4.22300	−0.284715
$221$	8.74399	0.588184
$222$	−9.45831	−0.634800
$223$	2.27194	0.152140	0.0760701	−	0.997102i	$-0.475763\pi$
$223$	2.27194	0.152140	0.0760701	+	0.997102i	$0.475763\pi$
$224$	1.00000	0.0668153
$225$	−1.71719	−0.114479
$226$	4.66166	0.310089
$227$	26.8006	1.77882	0.889411	−	0.457109i	$-0.151115\pi$
$227$	26.8006	1.77882	0.889411	+	0.457109i	$0.151115\pi$
$228$	4.09017	0.270878
$229$	5.11268	0.337856	0.168928	−	0.985628i	$-0.445970\pi$
$229$	5.11268	0.337856	0.168928	+	0.985628i	$0.445970\pi$
$230$	3.08128	0.203174
$231$	−2.33076	−0.153353
$232$	7.78507	0.511115
$233$	−25.2453	−1.65388	−0.826938	−	0.562293i	$-0.809919\pi$
$233$	−25.2453	−1.65388	−0.826938	+	0.562293i	$0.809919\pi$
$234$	5.12319	0.334913
$235$	−8.53247	−0.556597
$236$	−2.48380	−0.161681
$237$	−1.92371	−0.124958
$238$	1.70675	0.110632
$239$	−22.8000	−1.47481	−0.737405	−	0.675451i	$-0.763949\pi$
$239$	−22.8000	−1.47481	−0.737405	+	0.675451i	$0.763949\pi$
$240$	1.81185	0.116955
$241$	12.2156	0.786876	0.393438	−	0.919351i	$-0.371286\pi$
$241$	12.2156	0.786876	0.393438	+	0.919351i	$0.371286\pi$
$242$	−5.56754	−0.357895
$243$	1.00000	0.0641500
$244$	−2.90828	−0.186184
$245$	1.81185	0.115755
$246$	−9.24349	−0.589343
$247$	20.9547	1.33332
$248$	4.50374	0.285988
$249$	−12.9363	−0.819806
$250$	−12.1706	−0.769734
$251$	−3.15970	−0.199439	−0.0997193	−	0.995016i	$-0.531794\pi$
$251$	−3.15970	−0.199439	−0.0997193	+	0.995016i	$0.531794\pi$
$252$	1.00000	0.0629941
$253$	−3.96375	−0.249199
$254$	9.51608	0.597092
$255$	3.09238	0.193652
$256$	1.00000	0.0625000
$257$	−30.4266	−1.89796	−0.948979	−	0.315340i	$-0.897882\pi$
$257$	−30.4266	−1.89796	−0.948979	+	0.315340i	$0.897882\pi$
$258$	6.37480	0.396878
$259$	−9.45831	−0.587711
$260$	9.28246	0.575674
$261$	7.78507	0.481884
$262$	−4.77929	−0.295265
$263$	12.3573	0.761984	0.380992	−	0.924578i	$-0.375582\pi$
$263$	12.3573	0.761984	0.380992	+	0.924578i	$0.375582\pi$
$264$	−2.33076	−0.143449
$265$	0.559155	0.0343486
$266$	4.09017	0.250784
$267$	−1.71038	−0.104674
$268$	−7.19368	−0.439424
$269$	2.87011	0.174994	0.0874969	−	0.996165i	$-0.472113\pi$
$269$	2.87011	0.174994	0.0874969	+	0.996165i	$0.472113\pi$
$270$	1.81185	0.110266
$271$	22.6088	1.37339	0.686694	−	0.726947i	$-0.259061\pi$
$271$	22.6088	1.37339	0.686694	+	0.726947i	$0.259061\pi$
$272$	1.70675	0.103487
$273$	5.12319	0.310069
$274$	9.14096	0.552226
$275$	4.00235	0.241351
$276$	1.70062	0.102366
$277$	16.5300	0.993191	0.496595	−	0.867982i	$-0.334583\pi$
$277$	16.5300	0.993191	0.496595	+	0.867982i	$0.334583\pi$
$278$	−8.55659	−0.513190
$279$	4.50374	0.269632
$280$	1.81185	0.108279
$281$	−10.1510	−0.605557	−0.302778	−	0.953061i	$-0.597914\pi$
$281$	−10.1510	−0.605557	−0.302778	+	0.953061i	$0.597914\pi$
$282$	−4.70925	−0.280432
$283$	−26.5216	−1.57654	−0.788271	−	0.615328i	$-0.789024\pi$
$283$	−26.5216	−1.57654	−0.788271	+	0.615328i	$0.789024\pi$
$284$	4.54384	0.269628
$285$	7.41079	0.438977
$286$	−11.9409	−0.706082
$287$	−9.24349	−0.545626
$288$	1.00000	0.0589256
$289$	−14.0870	−0.828648
$290$	14.1054	0.828298
$291$	10.7875	0.632376
$292$	5.25013	0.307241
$293$	−18.0775	−1.05610	−0.528050	−	0.849213i	$-0.677077\pi$
$293$	−18.0775	−1.05610	−0.528050	+	0.849213i	$0.677077\pi$
$294$	1.00000	0.0583212
$295$	−4.50027	−0.262016
$296$	−9.45831	−0.549753
$297$	−2.33076	−0.135245
$298$	19.2674	1.11613
$299$	8.71261	0.503863
$300$	−1.71719	−0.0991418
$301$	6.37480	0.367437
$302$	17.7794	1.02309
$303$	−15.0127	−0.862460
$304$	4.09017	0.234587
$305$	−5.26938	−0.301724
$306$	1.70675	0.0975683
$307$	4.35420	0.248507	0.124254	−	0.992250i	$-0.460346\pi$
$307$	4.35420	0.248507	0.124254	+	0.992250i	$0.460346\pi$
$308$	−2.33076	−0.132808
$309$	−4.03171	−0.229356
$310$	8.16012	0.463464
$311$	25.2339	1.43088	0.715441	−	0.698673i	$-0.246226\pi$
$311$	25.2339	1.43088	0.715441	+	0.698673i	$0.246226\pi$
$312$	5.12319	0.290043
$313$	−14.2521	−0.805574	−0.402787	−	0.915294i	$-0.631958\pi$
$313$	−14.2521	−0.805574	−0.402787	+	0.915294i	$0.631958\pi$
$314$	4.22349	0.238345
$315$	1.81185	0.102086
$316$	−1.92371	−0.108217
$317$	−28.3883	−1.59444	−0.797222	−	0.603686i	$-0.793698\pi$
$317$	−28.3883	−1.59444	−0.797222	+	0.603686i	$0.793698\pi$
$318$	0.308609	0.0173059
$319$	−18.1452	−1.01593
$320$	1.81185	0.101286
$321$	4.98264	0.278104
$322$	1.70062	0.0947721
$323$	6.98089	0.388427
$324$	1.00000	0.0555556
$325$	−8.79746	−0.487995
$326$	−14.8242	−0.821039
$327$	−5.90451	−0.326520
$328$	−9.24349	−0.510386
$329$	−4.70925	−0.259629
$330$	−4.22300	−0.232469
$331$	2.47156	0.135849	0.0679246	−	0.997690i	$-0.478362\pi$
$331$	2.47156	0.135849	0.0679246	+	0.997690i	$0.478362\pi$
$332$	−12.9363	−0.709973
$333$	−9.45831	−0.518312
$334$	19.0143	1.04041
$335$	−13.0339	−0.712117
$336$	1.00000	0.0545545
$337$	5.39529	0.293900	0.146950	−	0.989144i	$-0.453054\pi$
$337$	5.39529	0.293900	0.146950	+	0.989144i	$0.453054\pi$
$338$	13.2470	0.720543
$339$	4.66166	0.253187
$340$	3.09238	0.167708
$341$	−10.4972	−0.568453
$342$	4.09017	0.221171
$343$	1.00000	0.0539949
$344$	6.37480	0.343706
$345$	3.08128	0.165891
$346$	−24.7673	−1.33150
$347$	25.4142	1.36430	0.682152	−	0.731211i	$-0.261044\pi$
$347$	25.4142	1.36430	0.682152	+	0.731211i	$0.261044\pi$
$348$	7.78507	0.417324
$349$	−28.7420	−1.53853	−0.769263	−	0.638932i	$-0.779376\pi$
$349$	−28.7420	−1.53853	−0.769263	+	0.638932i	$0.779376\pi$
$350$	−1.71719	−0.0917874
$351$	5.12319	0.273455
$352$	−2.33076	−0.124230
$353$	9.74695	0.518778	0.259389	−	0.965773i	$-0.416479\pi$
$353$	9.74695	0.518778	0.259389	+	0.965773i	$0.416479\pi$
$354$	−2.48380	−0.132012
$355$	8.23278	0.436951
$356$	−1.71038	−0.0906501
$357$	1.70675	0.0903307
$358$	−0.403011	−0.0212998
$359$	−17.0779	−0.901340	−0.450670	−	0.892691i	$-0.648815\pi$
$359$	−17.0779	−0.901340	−0.450670	+	0.892691i	$0.648815\pi$
$360$	1.81185	0.0954931
$361$	−2.27051	−0.119500
$362$	23.6960	1.24543
$363$	−5.56754	−0.292220
$364$	5.12319	0.268528
$365$	9.51247	0.497906
$366$	−2.90828	−0.152018
$367$	3.17561	0.165766	0.0828828	−	0.996559i	$-0.473587\pi$
$367$	3.17561	0.165766	0.0828828	+	0.996559i	$0.473587\pi$
$368$	1.70062	0.0886512
$369$	−9.24349	−0.481197
$370$	−17.1371	−0.890914
$371$	0.308609	0.0160222
$372$	4.50374	0.233508
$373$	−20.2693	−1.04950	−0.524752	−	0.851255i	$-0.675842\pi$
$373$	−20.2693	−1.04950	−0.524752	+	0.851255i	$0.675842\pi$
$374$	−3.97803	−0.205699
$375$	−12.1706	−0.628485
$376$	−4.70925	−0.242861
$377$	39.8844	2.05415
$378$	1.00000	0.0514344
$379$	13.1470	0.675318	0.337659	−	0.941269i	$-0.390365\pi$
$379$	13.1470	0.675318	0.337659	+	0.941269i	$0.390365\pi$
$380$	7.41079	0.380166
$381$	9.51608	0.487523
$382$	−1.00000	−0.0511645
$383$	−6.45666	−0.329920	−0.164960	−	0.986300i	$-0.552749\pi$
$383$	−6.45666	−0.329920	−0.164960	+	0.986300i	$0.552749\pi$
$384$	1.00000	0.0510310
$385$	−4.22300	−0.215224
$386$	12.4451	0.633439
$387$	6.37480	0.324049
$388$	10.7875	0.547654
$389$	21.4986	1.09002	0.545011	−	0.838429i	$-0.316525\pi$
$389$	21.4986	1.09002	0.545011	+	0.838429i	$0.316525\pi$
$390$	9.28246	0.470036
$391$	2.90254	0.146788
$392$	1.00000	0.0505076
$393$	−4.77929	−0.241083
$394$	10.2196	0.514856
$395$	−3.48548	−0.175374
$396$	−2.33076	−0.117125
$397$	30.1329	1.51233	0.756163	−	0.654383i	$-0.227072\pi$
$397$	30.1329	1.51233	0.756163	+	0.654383i	$0.227072\pi$
$398$	5.29285	0.265307
$399$	4.09017	0.204765
$400$	−1.71719	−0.0858593
$401$	−3.78266	−0.188897	−0.0944486	−	0.995530i	$-0.530109\pi$
$401$	−3.78266	−0.188897	−0.0944486	+	0.995530i	$0.530109\pi$
$402$	−7.19368	−0.358788
$403$	23.0735	1.14937
$404$	−15.0127	−0.746912
$405$	1.81185	0.0900317
$406$	7.78507	0.386367
$407$	22.0451	1.09273
$408$	1.70675	0.0844966
$409$	−8.74442	−0.432384	−0.216192	−	0.976351i	$-0.569364\pi$
$409$	−8.74442	−0.432384	−0.216192	+	0.976351i	$0.569364\pi$
$410$	−16.7479	−0.827118
$411$	9.14096	0.450890
$412$	−4.03171	−0.198628
$413$	−2.48380	−0.122220
$414$	1.70062	0.0835811
$415$	−23.4387	−1.15056
$416$	5.12319	0.251185
$417$	−8.55659	−0.419018
$418$	−9.53322	−0.466285
$419$	3.53106	0.172503	0.0862517	−	0.996273i	$-0.472511\pi$
$419$	3.53106	0.172503	0.0862517	+	0.996273i	$0.472511\pi$
$420$	1.81185	0.0884094
$421$	−0.639833	−0.0311836	−0.0155918	−	0.999878i	$-0.504963\pi$
$421$	−0.639833	−0.0311836	−0.0155918	+	0.999878i	$0.504963\pi$
$422$	1.54823	0.0753668
$423$	−4.70925	−0.228972
$424$	0.308609	0.0149874
$425$	−2.93080	−0.142165
$426$	4.54384	0.220150
$427$	−2.90828	−0.140742
$428$	4.98264	0.240845
$429$	−11.9409	−0.576514
$430$	11.5502	0.557001
$431$	−33.3402	−1.60594	−0.802971	−	0.596018i	$-0.796749\pi$
$431$	−33.3402	−1.60594	−0.802971	+	0.596018i	$0.796749\pi$
$432$	1.00000	0.0481125
$433$	−13.9925	−0.672436	−0.336218	−	0.941784i	$-0.609148\pi$
$433$	−13.9925	−0.672436	−0.336218	+	0.941784i	$0.609148\pi$
$434$	4.50374	0.216186
$435$	14.1054	0.676303
$436$	−5.90451	−0.282775
$437$	6.95584	0.332743
$438$	5.25013	0.250861
$439$	−35.9488	−1.71574	−0.857871	−	0.513864i	$-0.828213\pi$
$439$	−35.9488	−1.71574	−0.857871	+	0.513864i	$0.828213\pi$
$440$	−4.22300	−0.201324
$441$	1.00000	0.0476190
$442$	8.74399	0.415909
$443$	19.2365	0.913953	0.456977	−	0.889479i	$-0.348932\pi$
$443$	19.2365	0.913953	0.456977	+	0.889479i	$0.348932\pi$
$444$	−9.45831	−0.448871
$445$	−3.09896	−0.146905
$446$	2.27194	0.107579
$447$	19.2674	0.911319
$448$	1.00000	0.0472456
$449$	−8.76655	−0.413719	−0.206859	−	0.978371i	$-0.566324\pi$
$449$	−8.76655	−0.413719	−0.206859	+	0.978371i	$0.566324\pi$
$450$	−1.71719	−0.0809489
$451$	21.5444	1.01449
$452$	4.66166	0.219266
$453$	17.7794	0.835348
$454$	26.8006	1.25782
$455$	9.28246	0.435169
$456$	4.09017	0.191540
$457$	−37.5337	−1.75575	−0.877875	−	0.478889i	$-0.841039\pi$
$457$	−37.5337	−1.75575	−0.877875	+	0.478889i	$0.841039\pi$
$458$	5.11268	0.238900
$459$	1.70675	0.0796642
$460$	3.08128	0.143666
$461$	−16.1415	−0.751784	−0.375892	−	0.926663i	$-0.622664\pi$
$461$	−16.1415	−0.751784	−0.375892	+	0.926663i	$0.622664\pi$
$462$	−2.33076	−0.108437
$463$	21.9643	1.02077	0.510384	−	0.859947i	$-0.329503\pi$
$463$	21.9643	1.02077	0.510384	+	0.859947i	$0.329503\pi$
$464$	7.78507	0.361413
$465$	8.16012	0.378416
$466$	−25.2453	−1.16947
$467$	13.7320	0.635442	0.317721	−	0.948184i	$-0.397082\pi$
$467$	13.7320	0.635442	0.317721	+	0.948184i	$0.397082\pi$
$468$	5.12319	0.236819
$469$	−7.19368	−0.332173
$470$	−8.53247	−0.393574
$471$	4.22349	0.194608
$472$	−2.48380	−0.114326
$473$	−14.8582	−0.683179
$474$	−1.92371	−0.0883589
$475$	−7.02358	−0.322264
$476$	1.70675	0.0782287
$477$	0.308609	0.0141302
$478$	−22.8000	−1.04285
$479$	0.347429	0.0158744	0.00793722	−	0.999968i	$-0.497473\pi$
$479$	0.347429	0.0158744	0.00793722	+	0.999968i	$0.497473\pi$
$480$	1.81185	0.0826994
$481$	−48.4567	−2.20943
$482$	12.2156	0.556405
$483$	1.70062	0.0773811
$484$	−5.56754	−0.253070
$485$	19.5454	0.887513
$486$	1.00000	0.0453609
$487$	−8.39823	−0.380560	−0.190280	−	0.981730i	$-0.560940\pi$
$487$	−8.39823	−0.380560	−0.190280	+	0.981730i	$0.560940\pi$
$488$	−2.90828	−0.131652
$489$	−14.8242	−0.670375
$490$	1.81185	0.0818512
$491$	−4.70800	−0.212469	−0.106234	−	0.994341i	$-0.533879\pi$
$491$	−4.70800	−0.212469	−0.106234	+	0.994341i	$0.533879\pi$
$492$	−9.24349	−0.416729
$493$	13.2872	0.598423
$494$	20.9547	0.942796
$495$	−4.22300	−0.189810
$496$	4.50374	0.202224
$497$	4.54384	0.203819
$498$	−12.9363	−0.579690
$499$	−7.45565	−0.333761	−0.166880	−	0.985977i	$-0.553369\pi$
$499$	−7.45565	−0.333761	−0.166880	+	0.985977i	$0.553369\pi$
$500$	−12.1706	−0.544284
$501$	19.0143	0.849495
$502$	−3.15970	−0.141024
$503$	−3.31472	−0.147796	−0.0738980	−	0.997266i	$-0.523544\pi$
$503$	−3.31472	−0.147796	−0.0738980	+	0.997266i	$0.523544\pi$
$504$	1.00000	0.0445435
$505$	−27.2009	−1.21042
$506$	−3.96375	−0.176210
$507$	13.2470	0.588321
$508$	9.51608	0.422208
$509$	23.3775	1.03619	0.518095	−	0.855323i	$-0.326641\pi$
$509$	23.3775	1.03619	0.518095	+	0.855323i	$0.326641\pi$
$510$	3.09238	0.136933
$511$	5.25013	0.232252
$512$	1.00000	0.0441942
$513$	4.09017	0.180585
$514$	−30.4266	−1.34206
$515$	−7.30487	−0.321891
$516$	6.37480	0.280635
$517$	10.9762	0.482731
$518$	−9.45831	−0.415574
$519$	−24.7673	−1.08716
$520$	9.28246	0.407063
$521$	−25.4327	−1.11423	−0.557113	−	0.830437i	$-0.688091\pi$
$521$	−25.4327	−1.11423	−0.557113	+	0.830437i	$0.688091\pi$
$522$	7.78507	0.340743
$523$	−9.44288	−0.412909	−0.206454	−	0.978456i	$-0.566192\pi$
$523$	−9.44288	−0.412909	−0.206454	+	0.978456i	$0.566192\pi$
$524$	−4.77929	−0.208784
$525$	−1.71719	−0.0749441
$526$	12.3573	0.538804
$527$	7.68675	0.334840
$528$	−2.33076	−0.101433
$529$	−20.1079	−0.874256
$530$	0.559155	0.0242881
$531$	−2.48380	−0.107788
$532$	4.09017	0.177331
$533$	−47.3561	−2.05122
$534$	−1.71038	−0.0740155
$535$	9.02781	0.390306
$536$	−7.19368	−0.310719
$537$	−0.403011	−0.0173912
$538$	2.87011	0.123739
$539$	−2.33076	−0.100393
$540$	1.81185	0.0779698
$541$	−2.33864	−0.100546	−0.0502729	−	0.998736i	$-0.516009\pi$
$541$	−2.33864	−0.100546	−0.0502729	+	0.998736i	$0.516009\pi$
$542$	22.6088	0.971131
$543$	23.6960	1.01689
$544$	1.70675	0.0731762
$545$	−10.6981	−0.458256
$546$	5.12319	0.219252
$547$	−34.3949	−1.47062	−0.735309	−	0.677732i	$-0.762963\pi$
$547$	−34.3949	−1.47062	−0.735309	+	0.677732i	$0.762963\pi$
$548$	9.14096	0.390482
$549$	−2.90828	−0.124122
$550$	4.00235	0.170661
$551$	31.8423	1.35653
$552$	1.70062	0.0723834
$553$	−1.92371	−0.0818044
$554$	16.5300	0.702292
$555$	−17.1371	−0.727428
$556$	−8.55659	−0.362880
$557$	−13.0801	−0.554221	−0.277110	−	0.960838i	$-0.589377\pi$
$557$	−13.0801	−0.554221	−0.277110	+	0.960838i	$0.589377\pi$
$558$	4.50374	0.190659
$559$	32.6593	1.38134
$560$	1.81185	0.0765648
$561$	−3.97803	−0.167952
$562$	−10.1510	−0.428193
$563$	1.51386	0.0638017	0.0319009	−	0.999491i	$-0.489844\pi$
$563$	1.51386	0.0638017	0.0319009	+	0.999491i	$0.489844\pi$
$564$	−4.70925	−0.198295
$565$	8.44625	0.355336
$566$	−26.5216	−1.11478
$567$	1.00000	0.0419961
$568$	4.54384	0.190655
$569$	36.4730	1.52903	0.764514	−	0.644607i	$-0.222979\pi$
$569$	36.4730	1.52903	0.764514	+	0.644607i	$0.222979\pi$
$570$	7.41079	0.310404
$571$	−33.9482	−1.42069	−0.710345	−	0.703854i	$-0.751461\pi$
$571$	−33.9482	−1.42069	−0.710345	+	0.703854i	$0.751461\pi$
$572$	−11.9409	−0.499276
$573$	−1.00000	−0.0417756
$574$	−9.24349	−0.385816
$575$	−2.92029	−0.121784
$576$	1.00000	0.0416667
$577$	−28.5825	−1.18990	−0.594952	−	0.803761i	$-0.702829\pi$
$577$	−28.5825	−1.18990	−0.594952	+	0.803761i	$0.702829\pi$
$578$	−14.0870	−0.585942
$579$	12.4451	0.517201
$580$	14.1054	0.585695
$581$	−12.9363	−0.536689
$582$	10.7875	0.447158
$583$	−0.719295	−0.0297902
$584$	5.25013	0.217252
$585$	9.28246	0.383783
$586$	−18.0775	−0.746776
$587$	−19.5666	−0.807602	−0.403801	−	0.914847i	$-0.632311\pi$
$587$	−19.5666	−0.807602	−0.403801	+	0.914847i	$0.632311\pi$
$588$	1.00000	0.0412393
$589$	18.4211	0.759027
$590$	−4.50027	−0.185273
$591$	10.2196	0.420379
$592$	−9.45831	−0.388734
$593$	18.7510	0.770010	0.385005	−	0.922914i	$-0.374200\pi$
$593$	18.7510	0.770010	0.385005	+	0.922914i	$0.374200\pi$
$594$	−2.33076	−0.0956324
$595$	3.09238	0.126775
$596$	19.2674	0.789225
$597$	5.29285	0.216622
$598$	8.71261	0.356285
$599$	4.75217	0.194168	0.0970842	−	0.995276i	$-0.469048\pi$
$599$	4.75217	0.194168	0.0970842	+	0.995276i	$0.469048\pi$
$600$	−1.71719	−0.0701038
$601$	−6.72834	−0.274455	−0.137227	−	0.990540i	$-0.543819\pi$
$601$	−6.72834	−0.274455	−0.137227	+	0.990540i	$0.543819\pi$
$602$	6.37480	0.259818
$603$	−7.19368	−0.292949
$604$	17.7794	0.723433
$605$	−10.0876	−0.410118
$606$	−15.0127	−0.609851
$607$	15.0113	0.609292	0.304646	−	0.952466i	$-0.401462\pi$
$607$	15.0113	0.609292	0.304646	+	0.952466i	$0.401462\pi$
$608$	4.09017	0.165878
$609$	7.78507	0.315467
$610$	−5.26938	−0.213351
$611$	−24.1264	−0.976048
$612$	1.70675	0.0689912
$613$	6.42220	0.259390	0.129695	−	0.991554i	$-0.458600\pi$
$613$	6.42220	0.259390	0.129695	+	0.991554i	$0.458600\pi$
$614$	4.35420	0.175721
$615$	−16.7479	−0.675339
$616$	−2.33076	−0.0939092
$617$	−27.1884	−1.09457	−0.547283	−	0.836948i	$-0.684338\pi$
$617$	−27.1884	−1.09457	−0.547283	+	0.836948i	$0.684338\pi$
$618$	−4.03171	−0.162179
$619$	15.9885	0.642633	0.321316	−	0.946972i	$-0.395875\pi$
$619$	15.9885	0.642633	0.321316	+	0.946972i	$0.395875\pi$
$620$	8.16012	0.327718
$621$	1.70062	0.0682437
$622$	25.2339	1.01179
$623$	−1.71038	−0.0685251
$624$	5.12319	0.205092
$625$	−13.4653	−0.538614
$626$	−14.2521	−0.569627
$627$	−9.53322	−0.380720
$628$	4.22349	0.168536
$629$	−16.1429	−0.643661
$630$	1.81185	0.0721860
$631$	0.669413	0.0266489	0.0133244	−	0.999911i	$-0.495759\pi$
$631$	0.669413	0.0266489	0.0133244	+	0.999911i	$0.495759\pi$
$632$	−1.92371	−0.0765210
$633$	1.54823	0.0615367
$634$	−28.3883	−1.12744
$635$	17.2417	0.684218
$636$	0.308609	0.0122371
$637$	5.12319	0.202988
$638$	−18.1452	−0.718374
$639$	4.54384	0.179752
$640$	1.81185	0.0716198
$641$	−36.8763	−1.45653	−0.728264	−	0.685297i	$-0.759672\pi$
$641$	−36.8763	−1.45653	−0.728264	+	0.685297i	$0.759672\pi$
$642$	4.98264	0.196649
$643$	0.906667	0.0357555	0.0178777	−	0.999840i	$-0.494309\pi$
$643$	0.906667	0.0357555	0.0178777	+	0.999840i	$0.494309\pi$
$644$	1.70062	0.0670140
$645$	11.5502	0.454789
$646$	6.98089	0.274659
$647$	47.7950	1.87901	0.939507	−	0.342530i	$-0.111284\pi$
$647$	47.7950	1.87901	0.939507	+	0.342530i	$0.111284\pi$
$648$	1.00000	0.0392837
$649$	5.78914	0.227244
$650$	−8.79746	−0.345065
$651$	4.50374	0.176515
$652$	−14.8242	−0.580562
$653$	22.6609	0.886788	0.443394	−	0.896327i	$-0.353774\pi$
$653$	22.6609	0.886788	0.443394	+	0.896327i	$0.353774\pi$
$654$	−5.90451	−0.230884
$655$	−8.65937	−0.338350
$656$	−9.24349	−0.360898
$657$	5.25013	0.204827
$658$	−4.70925	−0.183586
$659$	−20.4792	−0.797755	−0.398878	−	0.917004i	$-0.630600\pi$
$659$	−20.4792	−0.797755	−0.398878	+	0.917004i	$0.630600\pi$
$660$	−4.22300	−0.164380
$661$	32.6459	1.26978	0.634888	−	0.772604i	$-0.281046\pi$
$661$	32.6459	1.26978	0.634888	+	0.772604i	$0.281046\pi$
$662$	2.47156	0.0960598
$663$	8.74399	0.339588
$664$	−12.9363	−0.502027
$665$	7.41079	0.287378
$666$	−9.45831	−0.366502
$667$	13.2395	0.512635
$668$	19.0143	0.735684
$669$	2.27194	0.0878382
$670$	−13.0339	−0.503543
$671$	6.77852	0.261682
$672$	1.00000	0.0385758
$673$	2.99973	0.115631	0.0578156	−	0.998327i	$-0.481586\pi$
$673$	2.99973	0.115631	0.0578156	+	0.998327i	$0.481586\pi$
$674$	5.39529	0.207819
$675$	−1.71719	−0.0660945
$676$	13.2470	0.509501
$677$	−15.1102	−0.580731	−0.290365	−	0.956916i	$-0.593777\pi$
$677$	−15.1102	−0.580731	−0.290365	+	0.956916i	$0.593777\pi$
$678$	4.66166	0.179030
$679$	10.7875	0.413988
$680$	3.09238	0.118587
$681$	26.8006	1.02700
$682$	−10.4972	−0.401957
$683$	17.8303	0.682258	0.341129	−	0.940016i	$-0.389191\pi$
$683$	17.8303	0.682258	0.341129	+	0.940016i	$0.389191\pi$
$684$	4.09017	0.156392
$685$	16.5621	0.632805
$686$	1.00000	0.0381802
$687$	5.11268	0.195061
$688$	6.37480	0.243037
$689$	1.58106	0.0602336
$690$	3.08128	0.117302
$691$	24.1490	0.918671	0.459336	−	0.888263i	$-0.348088\pi$
$691$	24.1490	0.918671	0.459336	+	0.888263i	$0.348088\pi$
$692$	−24.7673	−0.941510
$693$	−2.33076	−0.0885384
$694$	25.4142	0.964708
$695$	−15.5033	−0.588074
$696$	7.78507	0.295092
$697$	−15.7763	−0.597570
$698$	−28.7420	−1.08790
$699$	−25.2453	−0.954866
$700$	−1.71719	−0.0649035
$701$	0.0365188	0.00137929	0.000689647	−	1.00000i	$-0.499780\pi$
$701$	0.0365188	0.00137929	0.000689647		1.00000i	$0.499780\pi$
$702$	5.12319	0.193362
$703$	−38.6861	−1.45907
$704$	−2.33076	−0.0878440
$705$	−8.53247	−0.321352
$706$	9.74695	0.366831
$707$	−15.0127	−0.564612
$708$	−2.48380	−0.0933467
$709$	31.3848	1.17868	0.589340	−	0.807885i	$-0.299388\pi$
$709$	31.3848	1.17868	0.589340	+	0.807885i	$0.299388\pi$
$710$	8.23278	0.308971
$711$	−1.92371	−0.0721447
$712$	−1.71038	−0.0640993
$713$	7.65917	0.286838
$714$	1.70675	0.0638734
$715$	−21.6352	−0.809112
$716$	−0.403011	−0.0150612
$717$	−22.8000	−0.851482
$718$	−17.0779	−0.637343
$719$	25.5929	0.954453	0.477227	−	0.878780i	$-0.341642\pi$
$719$	25.5929	0.954453	0.477227	+	0.878780i	$0.341642\pi$
$720$	1.81185	0.0675238
$721$	−4.03171	−0.150149
$722$	−2.27051	−0.0844995
$723$	12.2156	0.454303
$724$	23.6960	0.880654
$725$	−13.3684	−0.496490
$726$	−5.56754	−0.206631
$727$	−30.5652	−1.13360	−0.566801	−	0.823855i	$-0.691819\pi$
$727$	−30.5652	−1.13360	−0.566801	+	0.823855i	$0.691819\pi$
$728$	5.12319	0.189878
$729$	1.00000	0.0370370
$730$	9.51247	0.352072
$731$	10.8802	0.402418
$732$	−2.90828	−0.107493
$733$	33.3157	1.23054	0.615271	−	0.788316i	$-0.289047\pi$
$733$	33.3157	1.23054	0.615271	+	0.788316i	$0.289047\pi$
$734$	3.17561	0.117214
$735$	1.81185	0.0668312
$736$	1.70062	0.0626858
$737$	16.7668	0.617612
$738$	−9.24349	−0.340258
$739$	4.36686	0.160638	0.0803188	−	0.996769i	$-0.474406\pi$
$739$	4.36686	0.160638	0.0803188	+	0.996769i	$0.474406\pi$
$740$	−17.1371	−0.629971
$741$	20.9547	0.769790
$742$	0.308609	0.0113294
$743$	−6.78119	−0.248778	−0.124389	−	0.992234i	$-0.539697\pi$
$743$	−6.78119	−0.248778	−0.124389	+	0.992234i	$0.539697\pi$
$744$	4.50374	0.165115
$745$	34.9098	1.27900
$746$	−20.2693	−0.742112
$747$	−12.9363	−0.473315
$748$	−3.97803	−0.145451
$749$	4.98264	0.182062
$750$	−12.1706	−0.444406
$751$	32.1632	1.17365	0.586826	−	0.809713i	$-0.300377\pi$
$751$	32.1632	1.17365	0.586826	+	0.809713i	$0.300377\pi$
$752$	−4.70925	−0.171729
$753$	−3.15970	−0.115146
$754$	39.8844	1.45250
$755$	32.2136	1.17237
$756$	1.00000	0.0363696
$757$	−22.2682	−0.809352	−0.404676	−	0.914460i	$-0.632616\pi$
$757$	−22.2682	−0.809352	−0.404676	+	0.914460i	$0.632616\pi$
$758$	13.1470	0.477522
$759$	−3.96375	−0.143875
$760$	7.41079	0.268818
$761$	−53.1824	−1.92786	−0.963931	−	0.266153i	$-0.914247\pi$
$761$	−53.1824	−1.92786	−0.963931	+	0.266153i	$0.914247\pi$
$762$	9.51608	0.344731
$763$	−5.90451	−0.213757
$764$	−1.00000	−0.0361787
$765$	3.09238	0.111805
$766$	−6.45666	−0.233289
$767$	−12.7249	−0.459471
$768$	1.00000	0.0360844
$769$	−16.5363	−0.596314	−0.298157	−	0.954517i	$-0.596372\pi$
$769$	−16.5363	−0.596314	−0.298157	+	0.954517i	$0.596372\pi$
$770$	−4.22300	−0.152186
$771$	−30.4266	−1.09579
$772$	12.4451	0.447909
$773$	−5.82979	−0.209683	−0.104841	−	0.994489i	$-0.533434\pi$
$773$	−5.82979	−0.209683	−0.104841	+	0.994489i	$0.533434\pi$
$774$	6.37480	0.229138
$775$	−7.73376	−0.277805
$776$	10.7875	0.387250
$777$	−9.45831	−0.339315
$778$	21.4986	0.770762
$779$	−37.8074	−1.35459
$780$	9.28246	0.332365
$781$	−10.5906	−0.378963
$782$	2.90254	0.103795
$783$	7.78507	0.278216
$784$	1.00000	0.0357143
$785$	7.65235	0.273124
$786$	−4.77929	−0.170472
$787$	49.0970	1.75012	0.875059	−	0.484015i	$-0.160822\pi$
$787$	49.0970	1.75012	0.875059	+	0.484015i	$0.160822\pi$
$788$	10.2196	0.364058
$789$	12.3573	0.439932
$790$	−3.48548	−0.124008
$791$	4.66166	0.165750
$792$	−2.33076	−0.0828201
$793$	−14.8997	−0.529102
$794$	30.1329	1.06938
$795$	0.559155	0.0198312
$796$	5.29285	0.187600
$797$	2.32882	0.0824910	0.0412455	−	0.999149i	$-0.486867\pi$
$797$	2.32882	0.0824910	0.0412455	+	0.999149i	$0.486867\pi$
$798$	4.09017	0.144790
$799$	−8.03750	−0.284346
$800$	−1.71719	−0.0607117
$801$	−1.71038	−0.0604334
$802$	−3.78266	−0.133570
$803$	−12.2368	−0.431828
$804$	−7.19368	−0.253701
$805$	3.08128	0.108601
$806$	23.0735	0.812729
$807$	2.87011	0.101033
$808$	−15.0127	−0.528146
$809$	−31.3835	−1.10338	−0.551692	−	0.834048i	$-0.686018\pi$
$809$	−31.3835	−1.10338	−0.551692	+	0.834048i	$0.686018\pi$
$810$	1.81185	0.0636621
$811$	23.2944	0.817978	0.408989	−	0.912539i	$-0.365881\pi$
$811$	23.2944	0.817978	0.408989	+	0.912539i	$0.365881\pi$
$812$	7.78507	0.273202
$813$	22.6088	0.792926
$814$	22.0451	0.772680
$815$	−26.8594	−0.940842
$816$	1.70675	0.0597481
$817$	26.0740	0.912215
$818$	−8.74442	−0.305742
$819$	5.12319	0.179019
$820$	−16.7479	−0.584860
$821$	6.74296	0.235331	0.117665	−	0.993053i	$-0.462459\pi$
$821$	6.74296	0.235331	0.117665	+	0.993053i	$0.462459\pi$
$822$	9.14096	0.318828
$823$	35.7589	1.24648	0.623239	−	0.782032i	$-0.285816\pi$
$823$	35.7589	1.24648	0.623239	+	0.782032i	$0.285816\pi$
$824$	−4.03171	−0.140451
$825$	4.00235	0.139344
$826$	−2.48380	−0.0864223
$827$	−44.0419	−1.53149	−0.765743	−	0.643146i	$-0.777629\pi$
$827$	−44.0419	−1.53149	−0.765743	+	0.643146i	$0.777629\pi$
$828$	1.70062	0.0591008
$829$	39.3505	1.36670	0.683349	−	0.730092i	$-0.260523\pi$
$829$	39.3505	1.36670	0.683349	+	0.730092i	$0.260523\pi$
$830$	−23.4387	−0.813570
$831$	16.5300	0.573419
$832$	5.12319	0.177614
$833$	1.70675	0.0591353
$834$	−8.55659	−0.296291
$835$	34.4511	1.19223
$836$	−9.53322	−0.329713
$837$	4.50374	0.155672
$838$	3.53106	0.121978
$839$	−15.5039	−0.535255	−0.267628	−	0.963522i	$-0.586240\pi$
$839$	−15.5039	−0.535255	−0.267628	+	0.963522i	$0.586240\pi$
$840$	1.81185	0.0625149
$841$	31.6073	1.08991
$842$	−0.639833	−0.0220501
$843$	−10.1510	−0.349618
$844$	1.54823	0.0532924
$845$	24.0017	0.825683
$846$	−4.70925	−0.161907
$847$	−5.56754	−0.191303
$848$	0.308609	0.0105977
$849$	−26.5216	−0.910217
$850$	−2.93080	−0.100526
$851$	−16.0850	−0.551388
$852$	4.54384	0.155670
$853$	42.3239	1.44914	0.724572	−	0.689199i	$-0.242038\pi$
$853$	42.3239	1.44914	0.724572	+	0.689199i	$0.242038\pi$
$854$	−2.90828	−0.0995193
$855$	7.41079	0.253444
$856$	4.98264	0.170303
$857$	−18.5894	−0.635002	−0.317501	−	0.948258i	$-0.602844\pi$
$857$	−18.5894	−0.635002	−0.317501	+	0.948258i	$0.602844\pi$
$858$	−11.9409	−0.407657
$859$	−48.3440	−1.64948	−0.824739	−	0.565514i	$-0.808678\pi$
$859$	−48.3440	−1.64948	−0.824739	+	0.565514i	$0.808678\pi$
$860$	11.5502	0.393859
$861$	−9.24349	−0.315017
$862$	−33.3402	−1.13557
$863$	−10.4785	−0.356694	−0.178347	−	0.983968i	$-0.557075\pi$
$863$	−10.4785	−0.356694	−0.178347	+	0.983968i	$0.557075\pi$
$864$	1.00000	0.0340207
$865$	−44.8747	−1.52578
$866$	−13.9925	−0.475484
$867$	−14.0870	−0.478420
$868$	4.50374	0.152867
$869$	4.48371	0.152100
$870$	14.1054	0.478218
$871$	−36.8545	−1.24877
$872$	−5.90451	−0.199952
$873$	10.7875	0.365103
$874$	6.95584	0.235285
$875$	−12.1706	−0.411440
$876$	5.25013	0.177386
$877$	−24.8948	−0.840638	−0.420319	−	0.907376i	$-0.638082\pi$
$877$	−24.8948	−0.840638	−0.420319	+	0.907376i	$0.638082\pi$
$878$	−35.9488	−1.21321
$879$	−18.0775	−0.609740
$880$	−4.22300	−0.142357
$881$	31.6595	1.06664	0.533318	−	0.845915i	$-0.320945\pi$
$881$	31.6595	1.06664	0.533318	+	0.845915i	$0.320945\pi$
$882$	1.00000	0.0336718
$883$	44.3098	1.49114	0.745571	−	0.666426i	$-0.232177\pi$
$883$	44.3098	1.49114	0.745571	+	0.666426i	$0.232177\pi$
$884$	8.74399	0.294092
$885$	−4.50027	−0.151275
$886$	19.2365	0.646262
$887$	−23.3681	−0.784625	−0.392313	−	0.919832i	$-0.628325\pi$
$887$	−23.3681	−0.784625	−0.392313	+	0.919832i	$0.628325\pi$
$888$	−9.45831	−0.317400
$889$	9.51608	0.319159
$890$	−3.09896	−0.103878
$891$	−2.33076	−0.0780835
$892$	2.27194	0.0760701
$893$	−19.2616	−0.644566
$894$	19.2674	0.644400
$895$	−0.730197	−0.0244078
$896$	1.00000	0.0334077
$897$	8.71261	0.290906
$898$	−8.76655	−0.292544
$899$	35.0619	1.16938
$900$	−1.71719	−0.0572395
$901$	0.526718	0.0175475
$902$	21.5444	0.717350
$903$	6.37480	0.212140
$904$	4.66166	0.155045
$905$	42.9337	1.42716
$906$	17.7794	0.590680
$907$	19.0334	0.631993	0.315996	−	0.948760i	$-0.397661\pi$
$907$	19.0334	0.631993	0.315996	+	0.948760i	$0.397661\pi$
$908$	26.8006	0.889411
$909$	−15.0127	−0.497941
$910$	9.28246	0.307711
$911$	−17.5712	−0.582159	−0.291080	−	0.956699i	$-0.594014\pi$
$911$	−17.5712	−0.582159	−0.291080	+	0.956699i	$0.594014\pi$
$912$	4.09017	0.135439
$913$	30.1515	0.997869
$914$	−37.5337	−1.24150
$915$	−5.26938	−0.174200
$916$	5.11268	0.168928
$917$	−4.77929	−0.157826
$918$	1.70675	0.0563311
$919$	−25.2128	−0.831693	−0.415846	−	0.909435i	$-0.636515\pi$
$919$	−25.2128	−0.831693	−0.415846	+	0.909435i	$0.636515\pi$
$920$	3.08128	0.101587
$921$	4.35420	0.143476
$922$	−16.1415	−0.531592
$923$	23.2790	0.766236
$924$	−2.33076	−0.0766765
$925$	16.2417	0.534023
$926$	21.9643	0.721792
$927$	−4.03171	−0.132419
$928$	7.78507	0.255557
$929$	20.0037	0.656300	0.328150	−	0.944626i	$-0.393575\pi$
$929$	20.0037	0.656300	0.328150	+	0.944626i	$0.393575\pi$
$930$	8.16012	0.267581
$931$	4.09017	0.134050
$932$	−25.2453	−0.826938
$933$	25.2339	0.826121
$934$	13.7320	0.449326
$935$	−7.20760	−0.235714
$936$	5.12319	0.167457
$937$	25.1477	0.821539	0.410770	−	0.911739i	$-0.365260\pi$
$937$	25.1477	0.821539	0.410770	+	0.911739i	$0.365260\pi$
$938$	−7.19368	−0.234882
$939$	−14.2521	−0.465098
$940$	−8.53247	−0.278299
$941$	−11.7558	−0.383229	−0.191614	−	0.981470i	$-0.561372\pi$
$941$	−11.7558	−0.383229	−0.191614	+	0.981470i	$0.561372\pi$
$942$	4.22349	0.137609
$943$	−15.7197	−0.511904
$944$	−2.48380	−0.0808407
$945$	1.81185	0.0589396
$946$	−14.8582	−0.483080
$947$	−11.5208	−0.374375	−0.187187	−	0.982324i	$-0.559937\pi$
$947$	−11.5208	−0.374375	−0.187187	+	0.982324i	$0.559937\pi$
$948$	−1.92371	−0.0624792
$949$	26.8974	0.873127
$950$	−7.02358	−0.227875
$951$	−28.3883	−0.920553
$952$	1.70675	0.0553160
$953$	36.0275	1.16704	0.583522	−	0.812097i	$-0.301674\pi$
$953$	36.0275	1.16704	0.583522	+	0.812097i	$0.301674\pi$
$954$	0.308609	0.00999159
$955$	−1.81185	−0.0586302
$956$	−22.8000	−0.737405
$957$	−18.1452	−0.586550
$958$	0.347429	0.0112249
$959$	9.14096	0.295177
$960$	1.81185	0.0584773
$961$	−10.7163	−0.345688
$962$	−48.4567	−1.56231
$963$	4.98264	0.160563
$964$	12.2156	0.393438
$965$	22.5487	0.725868
$966$	1.70062	0.0547167
$967$	50.7989	1.63358	0.816791	−	0.576933i	$-0.195751\pi$
$967$	50.7989	1.63358	0.816791	+	0.576933i	$0.195751\pi$
$968$	−5.56754	−0.178947
$969$	6.98089	0.224258
$970$	19.5454	0.627566
$971$	−27.9856	−0.898101	−0.449051	−	0.893506i	$-0.648238\pi$
$971$	−27.9856	−0.898101	−0.449051	+	0.893506i	$0.648238\pi$
$972$	1.00000	0.0320750
$973$	−8.55659	−0.274312
$974$	−8.39823	−0.269097
$975$	−8.79746	−0.281744
$976$	−2.90828	−0.0930918
$977$	−37.0761	−1.18617	−0.593086	−	0.805139i	$-0.702090\pi$
$977$	−37.0761	−1.18617	−0.593086	+	0.805139i	$0.702090\pi$
$978$	−14.8242	−0.474027
$979$	3.98650	0.127409
$980$	1.81185	0.0578775
$981$	−5.90451	−0.188516
$982$	−4.70800	−0.150238
$983$	−47.2836	−1.50811	−0.754056	−	0.656810i	$-0.771905\pi$
$983$	−47.2836	−1.50811	−0.754056	+	0.656810i	$0.771905\pi$
$984$	−9.24349	−0.294672
$985$	18.5164	0.589983
$986$	13.2872	0.423149
$987$	−4.70925	−0.149897
$988$	20.9547	0.666658
$989$	10.8411	0.344728
$990$	−4.22300	−0.134216
$991$	−4.74821	−0.150832	−0.0754159	−	0.997152i	$-0.524028\pi$
$991$	−4.74821	−0.150832	−0.0754159	+	0.997152i	$0.524028\pi$
$992$	4.50374	0.142994
$993$	2.47156	0.0784325
$994$	4.54384	0.144122
$995$	9.58987	0.304019
$996$	−12.9363	−0.409903
$997$	−2.99270	−0.0947799	−0.0473899	−	0.998876i	$-0.515090\pi$
$997$	−2.99270	−0.0947799	−0.0473899	+	0.998876i	$0.515090\pi$
$998$	−7.45565	−0.236004
$999$	−9.45831	−0.299248

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.ba.1.10	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.ba.1.10	✓	16	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:	\( N \)	\(=\)	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.81185 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.81185 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.81185 q^{10} -2.33076 q^{11} +1.00000 q^{12} +5.12319 q^{13} +1.00000 q^{14} +1.81185 q^{15} +1.00000 q^{16} +1.70675 q^{17} +1.00000 q^{18} +4.09017 q^{19} +1.81185 q^{20} +1.00000 q^{21} -2.33076 q^{22} +1.70062 q^{23} +1.00000 q^{24} -1.71719 q^{25} +5.12319 q^{26} +1.00000 q^{27} +1.00000 q^{28} +7.78507 q^{29} +1.81185 q^{30} +4.50374 q^{31} +1.00000 q^{32} -2.33076 q^{33} +1.70675 q^{34} +1.81185 q^{35} +1.00000 q^{36} -9.45831 q^{37} +4.09017 q^{38} +5.12319 q^{39} +1.81185 q^{40} -9.24349 q^{41} +1.00000 q^{42} +6.37480 q^{43} -2.33076 q^{44} +1.81185 q^{45} +1.70062 q^{46} -4.70925 q^{47} +1.00000 q^{48} +1.00000 q^{49} -1.71719 q^{50} +1.70675 q^{51} +5.12319 q^{52} +0.308609 q^{53} +1.00000 q^{54} -4.22300 q^{55} +1.00000 q^{56} +4.09017 q^{57} +7.78507 q^{58} -2.48380 q^{59} +1.81185 q^{60} -2.90828 q^{61} +4.50374 q^{62} +1.00000 q^{63} +1.00000 q^{64} +9.28246 q^{65} -2.33076 q^{66} -7.19368 q^{67} +1.70675 q^{68} +1.70062 q^{69} +1.81185 q^{70} +4.54384 q^{71} +1.00000 q^{72} +5.25013 q^{73} -9.45831 q^{74} -1.71719 q^{75} +4.09017 q^{76} -2.33076 q^{77} +5.12319 q^{78} -1.92371 q^{79} +1.81185 q^{80} +1.00000 q^{81} -9.24349 q^{82} -12.9363 q^{83} +1.00000 q^{84} +3.09238 q^{85} +6.37480 q^{86} +7.78507 q^{87} -2.33076 q^{88} -1.71038 q^{89} +1.81185 q^{90} +5.12319 q^{91} +1.70062 q^{92} +4.50374 q^{93} -4.70925 q^{94} +7.41079 q^{95} +1.00000 q^{96} +10.7875 q^{97} +1.00000 q^{98} -2.33076 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 11 q^{5} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 11 * q^5 + 16 * q^6 + 16 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 11 q^{5} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 16 q^{12} + 6 q^{13} + 16 q^{14} + 11 q^{15} + 16 q^{16} + 14 q^{17} + 16 q^{18} + 29 q^{19} + 11 q^{20} + 16 q^{21} + 8 q^{22} + 9 q^{23} + 16 q^{24} + 29 q^{25} + 6 q^{26} + 16 q^{27} + 16 q^{28} + 11 q^{30} + 14 q^{31} + 16 q^{32} + 8 q^{33} + 14 q^{34} + 11 q^{35} + 16 q^{36} + 11 q^{37} + 29 q^{38} + 6 q^{39} + 11 q^{40} + 14 q^{41} + 16 q^{42} + 28 q^{43} + 8 q^{44} + 11 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 16 q^{49} + 29 q^{50} + 14 q^{51} + 6 q^{52} - 4 q^{53} + 16 q^{54} + 17 q^{55} + 16 q^{56} + 29 q^{57} + 25 q^{59} + 11 q^{60} + 16 q^{61} + 14 q^{62} + 16 q^{63} + 16 q^{64} + 6 q^{65} + 8 q^{66} + 26 q^{67} + 14 q^{68} + 9 q^{69} + 11 q^{70} + 9 q^{71} + 16 q^{72} + 31 q^{73} + 11 q^{74} + 29 q^{75} + 29 q^{76} + 8 q^{77} + 6 q^{78} + 9 q^{79} + 11 q^{80} + 16 q^{81} + 14 q^{82} + 13 q^{83} + 16 q^{84} + 20 q^{85} + 28 q^{86} + 8 q^{88} + 21 q^{89} + 11 q^{90} + 6 q^{91} + 9 q^{92} + 14 q^{93} - q^{94} - 37 q^{95} + 16 q^{96} + 18 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 11 * q^5 + 16 * q^6 + 16 * q^7 + 16 * q^8 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 16 * q^12 + 6 * q^13 + 16 * q^14 + 11 * q^15 + 16 * q^16 + 14 * q^17 + 16 * q^18 + 29 * q^19 + 11 * q^20 + 16 * q^21 + 8 * q^22 + 9 * q^23 + 16 * q^24 + 29 * q^25 + 6 * q^26 + 16 * q^27 + 16 * q^28 + 11 * q^30 + 14 * q^31 + 16 * q^32 + 8 * q^33 + 14 * q^34 + 11 * q^35 + 16 * q^36 + 11 * q^37 + 29 * q^38 + 6 * q^39 + 11 * q^40 + 14 * q^41 + 16 * q^42 + 28 * q^43 + 8 * q^44 + 11 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 16 * q^49 + 29 * q^50 + 14 * q^51 + 6 * q^52 - 4 * q^53 + 16 * q^54 + 17 * q^55 + 16 * q^56 + 29 * q^57 + 25 * q^59 + 11 * q^60 + 16 * q^61 + 14 * q^62 + 16 * q^63 + 16 * q^64 + 6 * q^65 + 8 * q^66 + 26 * q^67 + 14 * q^68 + 9 * q^69 + 11 * q^70 + 9 * q^71 + 16 * q^72 + 31 * q^73 + 11 * q^74 + 29 * q^75 + 29 * q^76 + 8 * q^77 + 6 * q^78 + 9 * q^79 + 11 * q^80 + 16 * q^81 + 14 * q^82 + 13 * q^83 + 16 * q^84 + 20 * q^85 + 28 * q^86 + 8 * q^88 + 21 * q^89 + 11 * q^90 + 6 * q^91 + 9 * q^92 + 14 * q^93 - q^94 - 37 * q^95 + 16 * q^96 + 18 * q^97 + 16 * q^98 + 8 * q^99

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