LMFDB - Embedded newform 8022.2.a.v.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:	$1$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 5 x^{12} - 30 x^{11} + 172 x^{10} + 262 x^{9} - 2086 x^{8} - 264 x^{7} + 10549 x^{6} + \cdots - 3574 $ x^13 - 5x^12 - 30x^11 + 172x^10 + 262x^9 - 2086x^8 - 264x^7 + 10549x^6 - 4222x^5 - 20661x^4 + 6628x^3 + 18042x^2 - 56x - 3574
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-0.913967$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.913967 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.913967 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.913967 q^{10} +6.52458 q^{11} -1.00000 q^{12} -1.89717 q^{13} +1.00000 q^{14} -0.913967 q^{15} +1.00000 q^{16} -0.494433 q^{17} -1.00000 q^{18} -1.63700 q^{19} +0.913967 q^{20} +1.00000 q^{21} -6.52458 q^{22} -5.83868 q^{23} +1.00000 q^{24} -4.16466 q^{25} +1.89717 q^{26} -1.00000 q^{27} -1.00000 q^{28} +7.22157 q^{29} +0.913967 q^{30} +1.28580 q^{31} -1.00000 q^{32} -6.52458 q^{33} +0.494433 q^{34} -0.913967 q^{35} +1.00000 q^{36} +4.17912 q^{37} +1.63700 q^{38} +1.89717 q^{39} -0.913967 q^{40} -3.26106 q^{41} -1.00000 q^{42} -3.04847 q^{43} +6.52458 q^{44} +0.913967 q^{45} +5.83868 q^{46} +4.83330 q^{47} -1.00000 q^{48} +1.00000 q^{49} +4.16466 q^{50} +0.494433 q^{51} -1.89717 q^{52} -11.4473 q^{53} +1.00000 q^{54} +5.96325 q^{55} +1.00000 q^{56} +1.63700 q^{57} -7.22157 q^{58} +9.31761 q^{59} -0.913967 q^{60} -3.24910 q^{61} -1.28580 q^{62} -1.00000 q^{63} +1.00000 q^{64} -1.73395 q^{65} +6.52458 q^{66} -7.93586 q^{67} -0.494433 q^{68} +5.83868 q^{69} +0.913967 q^{70} -6.81250 q^{71} -1.00000 q^{72} -12.1767 q^{73} -4.17912 q^{74} +4.16466 q^{75} -1.63700 q^{76} -6.52458 q^{77} -1.89717 q^{78} -11.9229 q^{79} +0.913967 q^{80} +1.00000 q^{81} +3.26106 q^{82} -11.9214 q^{83} +1.00000 q^{84} -0.451895 q^{85} +3.04847 q^{86} -7.22157 q^{87} -6.52458 q^{88} +9.90618 q^{89} -0.913967 q^{90} +1.89717 q^{91} -5.83868 q^{92} -1.28580 q^{93} -4.83330 q^{94} -1.49617 q^{95} +1.00000 q^{96} +11.0572 q^{97} -1.00000 q^{98} +6.52458 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 13 q^{2} - 13 q^{3} + 13 q^{4} - 5 q^{5} + 13 q^{6} - 13 q^{7} - 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q - 13 * q^2 - 13 * q^3 + 13 * q^4 - 5 * q^5 + 13 * q^6 - 13 * q^7 - 13 * q^8 + 13 * q^9	\( 13 q - 13 q^{2} - 13 q^{3} + 13 q^{4} - 5 q^{5} + 13 q^{6} - 13 q^{7} - 13 q^{8} + 13 q^{9} + 5 q^{10} + 2 q^{11} - 13 q^{12} - 9 q^{13} + 13 q^{14} + 5 q^{15} + 13 q^{16} - 15 q^{17} - 13 q^{18} + 7 q^{19} - 5 q^{20} + 13 q^{21} - 2 q^{22} - 5 q^{23} + 13 q^{24} + 20 q^{25} + 9 q^{26} - 13 q^{27} - 13 q^{28} - 10 q^{29} - 5 q^{30} + 23 q^{31} - 13 q^{32} - 2 q^{33} + 15 q^{34} + 5 q^{35} + 13 q^{36} - 8 q^{37} - 7 q^{38} + 9 q^{39} + 5 q^{40} - 2 q^{41} - 13 q^{42} - 14 q^{43} + 2 q^{44} - 5 q^{45} + 5 q^{46} + q^{47} - 13 q^{48} + 13 q^{49} - 20 q^{50} + 15 q^{51} - 9 q^{52} - 20 q^{53} + 13 q^{54} + 27 q^{55} + 13 q^{56} - 7 q^{57} + 10 q^{58} + 11 q^{59} + 5 q^{60} + 32 q^{61} - 23 q^{62} - 13 q^{63} + 13 q^{64} - 20 q^{65} + 2 q^{66} - 8 q^{67} - 15 q^{68} + 5 q^{69} - 5 q^{70} + 10 q^{71} - 13 q^{72} + 10 q^{73} + 8 q^{74} - 20 q^{75} + 7 q^{76} - 2 q^{77} - 9 q^{78} + 20 q^{79} - 5 q^{80} + 13 q^{81} + 2 q^{82} + 4 q^{83} + 13 q^{84} - 4 q^{85} + 14 q^{86} + 10 q^{87} - 2 q^{88} + 19 q^{89} + 5 q^{90} + 9 q^{91} - 5 q^{92} - 23 q^{93} - q^{94} - 3 q^{95} + 13 q^{96} + 16 q^{97} - 13 q^{98} + 2 q^{99}+O(q^{100}) \) 13 * q - 13 * q^2 - 13 * q^3 + 13 * q^4 - 5 * q^5 + 13 * q^6 - 13 * q^7 - 13 * q^8 + 13 * q^9 + 5 * q^10 + 2 * q^11 - 13 * q^12 - 9 * q^13 + 13 * q^14 + 5 * q^15 + 13 * q^16 - 15 * q^17 - 13 * q^18 + 7 * q^19 - 5 * q^20 + 13 * q^21 - 2 * q^22 - 5 * q^23 + 13 * q^24 + 20 * q^25 + 9 * q^26 - 13 * q^27 - 13 * q^28 - 10 * q^29 - 5 * q^30 + 23 * q^31 - 13 * q^32 - 2 * q^33 + 15 * q^34 + 5 * q^35 + 13 * q^36 - 8 * q^37 - 7 * q^38 + 9 * q^39 + 5 * q^40 - 2 * q^41 - 13 * q^42 - 14 * q^43 + 2 * q^44 - 5 * q^45 + 5 * q^46 + q^47 - 13 * q^48 + 13 * q^49 - 20 * q^50 + 15 * q^51 - 9 * q^52 - 20 * q^53 + 13 * q^54 + 27 * q^55 + 13 * q^56 - 7 * q^57 + 10 * q^58 + 11 * q^59 + 5 * q^60 + 32 * q^61 - 23 * q^62 - 13 * q^63 + 13 * q^64 - 20 * q^65 + 2 * q^66 - 8 * q^67 - 15 * q^68 + 5 * q^69 - 5 * q^70 + 10 * q^71 - 13 * q^72 + 10 * q^73 + 8 * q^74 - 20 * q^75 + 7 * q^76 - 2 * q^77 - 9 * q^78 + 20 * q^79 - 5 * q^80 + 13 * q^81 + 2 * q^82 + 4 * q^83 + 13 * q^84 - 4 * q^85 + 14 * q^86 + 10 * q^87 - 2 * q^88 + 19 * q^89 + 5 * q^90 + 9 * q^91 - 5 * q^92 - 23 * q^93 - q^94 - 3 * q^95 + 13 * q^96 + 16 * q^97 - 13 * q^98 + 2 * 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
$5$	0.913967	0.408738	0.204369	−	0.978894i	$-0.434486\pi$
$5$	0.913967	0.408738	0.204369	+	0.978894i	$0.434486\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.913967	−0.289022
$11$	6.52458	1.96724	0.983618	−	0.180265i	$-0.0576954\pi$
$11$	6.52458	1.96724	0.983618	+	0.180265i	$0.0576954\pi$
$12$	−1.00000	−0.288675
$13$	−1.89717	−0.526181	−0.263090	−	0.964771i	$-0.584742\pi$
$13$	−1.89717	−0.526181	−0.263090	+	0.964771i	$0.584742\pi$
$14$	1.00000	0.267261
$15$	−0.913967	−0.235985
$16$	1.00000	0.250000
$17$	−0.494433	−0.119918	−0.0599588	−	0.998201i	$-0.519097\pi$
$17$	−0.494433	−0.119918	−0.0599588	+	0.998201i	$0.519097\pi$
$18$	−1.00000	−0.235702
$19$	−1.63700	−0.375554	−0.187777	−	0.982212i	$-0.560128\pi$
$19$	−1.63700	−0.375554	−0.187777	+	0.982212i	$0.560128\pi$
$20$	0.913967	0.204369
$21$	1.00000	0.218218
$22$	−6.52458	−1.39105
$23$	−5.83868	−1.21745	−0.608725	−	0.793382i	$-0.708319\pi$
$23$	−5.83868	−1.21745	−0.608725	+	0.793382i	$0.708319\pi$
$24$	1.00000	0.204124
$25$	−4.16466	−0.832933
$26$	1.89717	0.372066
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	7.22157	1.34101	0.670506	−	0.741904i	$-0.266077\pi$
$29$	7.22157	1.34101	0.670506	+	0.741904i	$0.266077\pi$
$30$	0.913967	0.166867
$31$	1.28580	0.230937	0.115468	−	0.993311i	$-0.463163\pi$
$31$	1.28580	0.230937	0.115468	+	0.993311i	$0.463163\pi$
$32$	−1.00000	−0.176777
$33$	−6.52458	−1.13578
$34$	0.494433	0.0847945
$35$	−0.913967	−0.154489
$36$	1.00000	0.166667
$37$	4.17912	0.687043	0.343522	−	0.939145i	$-0.388380\pi$
$37$	4.17912	0.687043	0.343522	+	0.939145i	$0.388380\pi$
$38$	1.63700	0.265557
$39$	1.89717	0.303791
$40$	−0.913967	−0.144511
$41$	−3.26106	−0.509292	−0.254646	−	0.967034i	$-0.581959\pi$
$41$	−3.26106	−0.509292	−0.254646	+	0.967034i	$0.581959\pi$
$42$	−1.00000	−0.154303
$43$	−3.04847	−0.464887	−0.232443	−	0.972610i	$-0.574672\pi$
$43$	−3.04847	−0.464887	−0.232443	+	0.972610i	$0.574672\pi$
$44$	6.52458	0.983618
$45$	0.913967	0.136246
$46$	5.83868	0.860867
$47$	4.83330	0.705009	0.352504	−	0.935810i	$-0.385330\pi$
$47$	4.83330	0.705009	0.352504	+	0.935810i	$0.385330\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	4.16466	0.588973
$51$	0.494433	0.0692344
$52$	−1.89717	−0.263090
$53$	−11.4473	−1.57241	−0.786206	−	0.617965i	$-0.787957\pi$
$53$	−11.4473	−1.57241	−0.786206	+	0.617965i	$0.787957\pi$
$54$	1.00000	0.136083
$55$	5.96325	0.804085
$56$	1.00000	0.133631
$57$	1.63700	0.216826
$58$	−7.22157	−0.948238
$59$	9.31761	1.21305	0.606525	−	0.795065i	$-0.292563\pi$
$59$	9.31761	1.21305	0.606525	+	0.795065i	$0.292563\pi$
$60$	−0.913967	−0.117993
$61$	−3.24910	−0.416005	−0.208002	−	0.978128i	$-0.566696\pi$
$61$	−3.24910	−0.416005	−0.208002	+	0.978128i	$0.566696\pi$
$62$	−1.28580	−0.163297
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	−1.73395	−0.215070
$66$	6.52458	0.803121
$67$	−7.93586	−0.969519	−0.484760	−	0.874647i	$-0.661093\pi$
$67$	−7.93586	−0.969519	−0.484760	+	0.874647i	$0.661093\pi$
$68$	−0.494433	−0.0599588
$69$	5.83868	0.702895
$70$	0.913967	0.109240
$71$	−6.81250	−0.808495	−0.404247	−	0.914650i	$-0.632467\pi$
$71$	−6.81250	−0.808495	−0.404247	+	0.914650i	$0.632467\pi$
$72$	−1.00000	−0.117851
$73$	−12.1767	−1.42518	−0.712588	−	0.701583i	$-0.752477\pi$
$73$	−12.1767	−1.42518	−0.712588	+	0.701583i	$0.752477\pi$
$74$	−4.17912	−0.485813
$75$	4.16466	0.480894
$76$	−1.63700	−0.187777
$77$	−6.52458	−0.743545
$78$	−1.89717	−0.214812
$79$	−11.9229	−1.34143	−0.670715	−	0.741715i	$-0.734013\pi$
$79$	−11.9229	−1.34143	−0.670715	+	0.741715i	$0.734013\pi$
$80$	0.913967	0.102185
$81$	1.00000	0.111111
$82$	3.26106	0.360124
$83$	−11.9214	−1.30854	−0.654271	−	0.756260i	$-0.727024\pi$
$83$	−11.9214	−1.30854	−0.654271	+	0.756260i	$0.727024\pi$
$84$	1.00000	0.109109
$85$	−0.451895	−0.0490149
$86$	3.04847	0.328724
$87$	−7.22157	−0.774233
$88$	−6.52458	−0.695523
$89$	9.90618	1.05005	0.525027	−	0.851086i	$-0.324055\pi$
$89$	9.90618	1.05005	0.525027	+	0.851086i	$0.324055\pi$
$90$	−0.913967	−0.0963406
$91$	1.89717	0.198878
$92$	−5.83868	−0.608725
$93$	−1.28580	−0.133331
$94$	−4.83330	−0.498516
$95$	−1.49617	−0.153503
$96$	1.00000	0.102062
$97$	11.0572	1.12269	0.561345	−	0.827582i	$-0.310284\pi$
$97$	11.0572	1.12269	0.561345	+	0.827582i	$0.310284\pi$
$98$	−1.00000	−0.101015
$99$	6.52458	0.655745
$100$	−4.16466	−0.416466
$101$	−11.0065	−1.09519	−0.547595	−	0.836744i	$-0.684456\pi$
$101$	−11.0065	−1.09519	−0.547595	+	0.836744i	$0.684456\pi$
$102$	−0.494433	−0.0489561
$103$	−11.3154	−1.11494	−0.557471	−	0.830197i	$-0.688228\pi$
$103$	−11.3154	−1.11494	−0.557471	+	0.830197i	$0.688228\pi$
$104$	1.89717	0.186033
$105$	0.913967	0.0891940
$106$	11.4473	1.11186
$107$	8.21611	0.794281	0.397141	−	0.917758i	$-0.370003\pi$
$107$	8.21611	0.794281	0.397141	+	0.917758i	$0.370003\pi$
$108$	−1.00000	−0.0962250
$109$	−3.58806	−0.343674	−0.171837	−	0.985125i	$-0.554970\pi$
$109$	−3.58806	−0.343674	−0.171837	+	0.985125i	$0.554970\pi$
$110$	−5.96325	−0.568574
$111$	−4.17912	−0.396665
$112$	−1.00000	−0.0944911
$113$	−13.0273	−1.22551	−0.612753	−	0.790275i	$-0.709938\pi$
$113$	−13.0273	−1.22551	−0.612753	+	0.790275i	$0.709938\pi$
$114$	−1.63700	−0.153319
$115$	−5.33636	−0.497618
$116$	7.22157	0.670506
$117$	−1.89717	−0.175394
$118$	−9.31761	−0.857755
$119$	0.494433	0.0453246
$120$	0.913967	0.0834334
$121$	31.5702	2.87002
$122$	3.24910	0.294160
$123$	3.26106	0.294040
$124$	1.28580	0.115468
$125$	−8.37620	−0.749190
$126$	1.00000	0.0890871
$127$	−17.0045	−1.50891	−0.754453	−	0.656354i	$-0.772098\pi$
$127$	−17.0045	−1.50891	−0.754453	+	0.656354i	$0.772098\pi$
$128$	−1.00000	−0.0883883
$129$	3.04847	0.268402
$130$	1.73395	0.152078
$131$	18.9593	1.65648	0.828240	−	0.560373i	$-0.189342\pi$
$131$	18.9593	1.65648	0.828240	+	0.560373i	$0.189342\pi$
$132$	−6.52458	−0.567892
$133$	1.63700	0.141946
$134$	7.93586	0.685554
$135$	−0.913967	−0.0786617
$136$	0.494433	0.0423973
$137$	19.6646	1.68006	0.840031	−	0.542539i	$-0.182537\pi$
$137$	19.6646	1.68006	0.840031	+	0.542539i	$0.182537\pi$
$138$	−5.83868	−0.497022
$139$	13.7297	1.16454	0.582270	−	0.812996i	$-0.302165\pi$
$139$	13.7297	1.16454	0.582270	+	0.812996i	$0.302165\pi$
$140$	−0.913967	−0.0772443
$141$	−4.83330	−0.407037
$142$	6.81250	0.571692
$143$	−12.3783	−1.03512
$144$	1.00000	0.0833333
$145$	6.60027	0.548123
$146$	12.1767	1.00775
$147$	−1.00000	−0.0824786
$148$	4.17912	0.343522
$149$	−10.7604	−0.881526	−0.440763	−	0.897624i	$-0.645292\pi$
$149$	−10.7604	−0.881526	−0.440763	+	0.897624i	$0.645292\pi$
$150$	−4.16466	−0.340043
$151$	−2.00141	−0.162873	−0.0814363	−	0.996679i	$-0.525951\pi$
$151$	−2.00141	−0.162873	−0.0814363	+	0.996679i	$0.525951\pi$
$152$	1.63700	0.132778
$153$	−0.494433	−0.0399725
$154$	6.52458	0.525766
$155$	1.17518	0.0943927
$156$	1.89717	0.151895
$157$	6.06325	0.483900	0.241950	−	0.970289i	$-0.422213\pi$
$157$	6.06325	0.483900	0.241950	+	0.970289i	$0.422213\pi$
$158$	11.9229	0.948534
$159$	11.4473	0.907832
$160$	−0.913967	−0.0722554
$161$	5.83868	0.460153
$162$	−1.00000	−0.0785674
$163$	−0.829014	−0.0649334	−0.0324667	−	0.999473i	$-0.510336\pi$
$163$	−0.829014	−0.0649334	−0.0324667	+	0.999473i	$0.510336\pi$
$164$	−3.26106	−0.254646
$165$	−5.96325	−0.464239
$166$	11.9214	0.925279
$167$	5.76775	0.446322	0.223161	−	0.974782i	$-0.428362\pi$
$167$	5.76775	0.446322	0.223161	+	0.974782i	$0.428362\pi$
$168$	−1.00000	−0.0771517
$169$	−9.40074	−0.723134
$170$	0.451895	0.0346588
$171$	−1.63700	−0.125185
$172$	−3.04847	−0.232443
$173$	−8.60658	−0.654346	−0.327173	−	0.944964i	$-0.606096\pi$
$173$	−8.60658	−0.654346	−0.327173	+	0.944964i	$0.606096\pi$
$174$	7.22157	0.547466
$175$	4.16466	0.314819
$176$	6.52458	0.491809
$177$	−9.31761	−0.700354
$178$	−9.90618	−0.742500
$179$	−12.2846	−0.918192	−0.459096	−	0.888387i	$-0.651827\pi$
$179$	−12.2846	−0.918192	−0.459096	+	0.888387i	$0.651827\pi$
$180$	0.913967	0.0681231
$181$	7.31418	0.543659	0.271829	−	0.962345i	$-0.412371\pi$
$181$	7.31418	0.543659	0.271829	+	0.962345i	$0.412371\pi$
$182$	−1.89717	−0.140628
$183$	3.24910	0.240181
$184$	5.83868	0.430433
$185$	3.81958	0.280821
$186$	1.28580	0.0942795
$187$	−3.22597	−0.235906
$188$	4.83330	0.352504
$189$	1.00000	0.0727393
$190$	1.49617	0.108543
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	−1.00000	−0.0721688
$193$	−1.55348	−0.111822	−0.0559108	−	0.998436i	$-0.517806\pi$
$193$	−1.55348	−0.111822	−0.0559108	+	0.998436i	$0.517806\pi$
$194$	−11.0572	−0.793861
$195$	1.73395	0.124171
$196$	1.00000	0.0714286
$197$	−9.40127	−0.669813	−0.334906	−	0.942251i	$-0.608705\pi$
$197$	−9.40127	−0.669813	−0.334906	+	0.942251i	$0.608705\pi$
$198$	−6.52458	−0.463682
$199$	16.8642	1.19547	0.597735	−	0.801694i	$-0.296067\pi$
$199$	16.8642	1.19547	0.597735	+	0.801694i	$0.296067\pi$
$200$	4.16466	0.294486
$201$	7.93586	0.559752
$202$	11.0065	0.774416
$203$	−7.22157	−0.506855
$204$	0.494433	0.0346172
$205$	−2.98050	−0.208167
$206$	11.3154	0.788383
$207$	−5.83868	−0.405816
$208$	−1.89717	−0.131545
$209$	−10.6808	−0.738804
$210$	−0.913967	−0.0630697
$211$	−4.52445	−0.311476	−0.155738	−	0.987798i	$-0.549776\pi$
$211$	−4.52445	−0.311476	−0.155738	+	0.987798i	$0.549776\pi$
$212$	−11.4473	−0.786206
$213$	6.81250	0.466785
$214$	−8.21611	−0.561642
$215$	−2.78620	−0.190017
$216$	1.00000	0.0680414
$217$	−1.28580	−0.0872858
$218$	3.58806	0.243014
$219$	12.1767	0.822825
$220$	5.96325	0.402043
$221$	0.938024	0.0630983
$222$	4.17912	0.280484
$223$	15.1315	1.01328	0.506639	−	0.862158i	$-0.330888\pi$
$223$	15.1315	1.01328	0.506639	+	0.862158i	$0.330888\pi$
$224$	1.00000	0.0668153
$225$	−4.16466	−0.277644
$226$	13.0273	0.866564
$227$	7.50713	0.498266	0.249133	−	0.968469i	$-0.419854\pi$
$227$	7.50713	0.498266	0.249133	+	0.968469i	$0.419854\pi$
$228$	1.63700	0.108413
$229$	20.3584	1.34532	0.672661	−	0.739951i	$-0.265151\pi$
$229$	20.3584	1.34532	0.672661	+	0.739951i	$0.265151\pi$
$230$	5.33636	0.351869
$231$	6.52458	0.429286
$232$	−7.22157	−0.474119
$233$	−5.93663	−0.388921	−0.194461	−	0.980910i	$-0.562296\pi$
$233$	−5.93663	−0.388921	−0.194461	+	0.980910i	$0.562296\pi$
$234$	1.89717	0.124022
$235$	4.41747	0.288164
$236$	9.31761	0.606525
$237$	11.9229	0.774475
$238$	−0.494433	−0.0320493
$239$	−26.2961	−1.70095	−0.850476	−	0.526013i	$-0.823686\pi$
$239$	−26.2961	−1.70095	−0.850476	+	0.526013i	$0.823686\pi$
$240$	−0.913967	−0.0589963
$241$	−14.4774	−0.932572	−0.466286	−	0.884634i	$-0.654408\pi$
$241$	−14.4774	−0.932572	−0.466286	+	0.884634i	$0.654408\pi$
$242$	−31.5702	−2.02941
$243$	−1.00000	−0.0641500
$244$	−3.24910	−0.208002
$245$	0.913967	0.0583912
$246$	−3.26106	−0.207918
$247$	3.10567	0.197609
$248$	−1.28580	−0.0816484
$249$	11.9214	0.755487
$250$	8.37620	0.529757
$251$	17.8010	1.12359	0.561795	−	0.827276i	$-0.310111\pi$
$251$	17.8010	1.12359	0.561795	+	0.827276i	$0.310111\pi$
$252$	−1.00000	−0.0629941
$253$	−38.0950	−2.39501
$254$	17.0045	1.06696
$255$	0.451895	0.0282988
$256$	1.00000	0.0625000
$257$	−7.71954	−0.481532	−0.240766	−	0.970583i	$-0.577399\pi$
$257$	−7.71954	−0.481532	−0.240766	+	0.970583i	$0.577399\pi$
$258$	−3.04847	−0.189789
$259$	−4.17912	−0.259678
$260$	−1.73395	−0.107535
$261$	7.22157	0.447004
$262$	−18.9593	−1.17131
$263$	8.79817	0.542518	0.271259	−	0.962506i	$-0.412560\pi$
$263$	8.79817	0.542518	0.271259	+	0.962506i	$0.412560\pi$
$264$	6.52458	0.401560
$265$	−10.4625	−0.642705
$266$	−1.63700	−0.100371
$267$	−9.90618	−0.606248
$268$	−7.93586	−0.484760
$269$	−25.8700	−1.57732	−0.788660	−	0.614830i	$-0.789225\pi$
$269$	−25.8700	−1.57732	−0.788660	+	0.614830i	$0.789225\pi$
$270$	0.913967	0.0556223
$271$	−14.2975	−0.868510	−0.434255	−	0.900790i	$-0.642988\pi$
$271$	−14.2975	−0.868510	−0.434255	+	0.900790i	$0.642988\pi$
$272$	−0.494433	−0.0299794
$273$	−1.89717	−0.114822
$274$	−19.6646	−1.18798
$275$	−27.1727	−1.63858
$276$	5.83868	0.351447
$277$	24.1474	1.45088	0.725439	−	0.688286i	$-0.241637\pi$
$277$	24.1474	1.45088	0.725439	+	0.688286i	$0.241637\pi$
$278$	−13.7297	−0.823454
$279$	1.28580	0.0769789
$280$	0.913967	0.0546200
$281$	−13.2987	−0.793331	−0.396666	−	0.917963i	$-0.629833\pi$
$281$	−13.2987	−0.793331	−0.396666	+	0.917963i	$0.629833\pi$
$282$	4.83330	0.287819
$283$	32.0622	1.90590	0.952949	−	0.303131i	$-0.0980318\pi$
$283$	32.0622	1.90590	0.952949	+	0.303131i	$0.0980318\pi$
$284$	−6.81250	−0.404247
$285$	1.49617	0.0886252
$286$	12.3783	0.731941
$287$	3.26106	0.192494
$288$	−1.00000	−0.0589256
$289$	−16.7555	−0.985620
$290$	−6.60027	−0.387581
$291$	−11.0572	−0.648185
$292$	−12.1767	−0.712588
$293$	10.7568	0.628418	0.314209	−	0.949354i	$-0.398261\pi$
$293$	10.7568	0.628418	0.314209	+	0.949354i	$0.398261\pi$
$294$	1.00000	0.0583212
$295$	8.51599	0.495820
$296$	−4.17912	−0.242906
$297$	−6.52458	−0.378595
$298$	10.7604	0.623333
$299$	11.0770	0.640598
$300$	4.16466	0.240447
$301$	3.04847	0.175711
$302$	2.00141	0.115168
$303$	11.0065	0.632308
$304$	−1.63700	−0.0938885
$305$	−2.96957	−0.170037
$306$	0.494433	0.0282648
$307$	23.0373	1.31481	0.657404	−	0.753538i	$-0.271654\pi$
$307$	23.0373	1.31481	0.657404	+	0.753538i	$0.271654\pi$
$308$	−6.52458	−0.371773
$309$	11.3154	0.643712
$310$	−1.17518	−0.0667457
$311$	−20.5875	−1.16741	−0.583706	−	0.811965i	$-0.698398\pi$
$311$	−20.5875	−1.16741	−0.583706	+	0.811965i	$0.698398\pi$
$312$	−1.89717	−0.107406
$313$	−3.18770	−0.180179	−0.0900897	−	0.995934i	$-0.528715\pi$
$313$	−3.18770	−0.180179	−0.0900897	+	0.995934i	$0.528715\pi$
$314$	−6.06325	−0.342169
$315$	−0.913967	−0.0514962
$316$	−11.9229	−0.670715
$317$	16.0819	0.903248	0.451624	−	0.892208i	$-0.350845\pi$
$317$	16.0819	0.903248	0.451624	+	0.892208i	$0.350845\pi$
$318$	−11.4473	−0.641934
$319$	47.1177	2.63809
$320$	0.913967	0.0510923
$321$	−8.21611	−0.458578
$322$	−5.83868	−0.325377
$323$	0.809388	0.0450355
$324$	1.00000	0.0555556
$325$	7.90108	0.438273
$326$	0.829014	0.0459149
$327$	3.58806	0.198420
$328$	3.26106	0.180062
$329$	−4.83330	−0.266468
$330$	5.96325	0.328266
$331$	−0.381922	−0.0209923	−0.0104962	−	0.999945i	$-0.503341\pi$
$331$	−0.381922	−0.0209923	−0.0104962	+	0.999945i	$0.503341\pi$
$332$	−11.9214	−0.654271
$333$	4.17912	0.229014
$334$	−5.76775	−0.315597
$335$	−7.25311	−0.396280
$336$	1.00000	0.0545545
$337$	−23.3934	−1.27432	−0.637160	−	0.770731i	$-0.719891\pi$
$337$	−23.3934	−1.27432	−0.637160	+	0.770731i	$0.719891\pi$
$338$	9.40074	0.511333
$339$	13.0273	0.707546
$340$	−0.451895	−0.0245075
$341$	8.38931	0.454307
$342$	1.63700	0.0885189
$343$	−1.00000	−0.0539949
$344$	3.04847	0.164362
$345$	5.33636	0.287300
$346$	8.60658	0.462692
$347$	−31.0843	−1.66869	−0.834345	−	0.551242i	$-0.814154\pi$
$347$	−31.0843	−1.66869	−0.834345	+	0.551242i	$0.814154\pi$
$348$	−7.22157	−0.387117
$349$	5.81155	0.311085	0.155543	−	0.987829i	$-0.450287\pi$
$349$	5.81155	0.311085	0.155543	+	0.987829i	$0.450287\pi$
$350$	−4.16466	−0.222611
$351$	1.89717	0.101264
$352$	−6.52458	−0.347762
$353$	−31.3856	−1.67049	−0.835243	−	0.549881i	$-0.814673\pi$
$353$	−31.3856	−1.67049	−0.835243	+	0.549881i	$0.814673\pi$
$354$	9.31761	0.495225
$355$	−6.22640	−0.330463
$356$	9.90618	0.525027
$357$	−0.494433	−0.0261682
$358$	12.2846	0.649259
$359$	−37.3490	−1.97121	−0.985603	−	0.169075i	$-0.945922\pi$
$359$	−37.3490	−1.97121	−0.985603	+	0.169075i	$0.945922\pi$
$360$	−0.913967	−0.0481703
$361$	−16.3202	−0.858959
$362$	−7.31418	−0.384425
$363$	−31.5702	−1.65701
$364$	1.89717	0.0994388
$365$	−11.1291	−0.582524
$366$	−3.24910	−0.169833
$367$	−0.214310	−0.0111869	−0.00559345	−	0.999984i	$-0.501780\pi$
$367$	−0.214310	−0.0111869	−0.00559345	+	0.999984i	$0.501780\pi$
$368$	−5.83868	−0.304362
$369$	−3.26106	−0.169764
$370$	−3.81958	−0.198570
$371$	11.4473	0.594316
$372$	−1.28580	−0.0666657
$373$	26.2018	1.35668	0.678338	−	0.734750i	$-0.262701\pi$
$373$	26.2018	1.35668	0.678338	+	0.734750i	$0.262701\pi$
$374$	3.22597	0.166811
$375$	8.37620	0.432545
$376$	−4.83330	−0.249258
$377$	−13.7005	−0.705614
$378$	−1.00000	−0.0514344
$379$	31.7256	1.62963	0.814817	−	0.579718i	$-0.196837\pi$
$379$	31.7256	1.62963	0.814817	+	0.579718i	$0.196837\pi$
$380$	−1.49617	−0.0767517
$381$	17.0045	0.871168
$382$	1.00000	0.0511645
$383$	−15.2381	−0.778632	−0.389316	−	0.921104i	$-0.627289\pi$
$383$	−15.2381	−0.778632	−0.389316	+	0.921104i	$0.627289\pi$
$384$	1.00000	0.0510310
$385$	−5.96325	−0.303916
$386$	1.55348	0.0790698
$387$	−3.04847	−0.154962
$388$	11.0572	0.561345
$389$	−1.97726	−0.100251	−0.0501256	−	0.998743i	$-0.515962\pi$
$389$	−1.97726	−0.100251	−0.0501256	+	0.998743i	$0.515962\pi$
$390$	−1.73395	−0.0878020
$391$	2.88684	0.145994
$392$	−1.00000	−0.0505076
$393$	−18.9593	−0.956370
$394$	9.40127	0.473629
$395$	−10.8971	−0.548294
$396$	6.52458	0.327873
$397$	−31.9761	−1.60483	−0.802417	−	0.596763i	$-0.796453\pi$
$397$	−31.9761	−1.60483	−0.802417	+	0.596763i	$0.796453\pi$
$398$	−16.8642	−0.845325
$399$	−1.63700	−0.0819526
$400$	−4.16466	−0.208233
$401$	18.2924	0.913480	0.456740	−	0.889600i	$-0.349017\pi$
$401$	18.2924	0.913480	0.456740	+	0.889600i	$0.349017\pi$
$402$	−7.93586	−0.395805
$403$	−2.43938	−0.121514
$404$	−11.0065	−0.547595
$405$	0.913967	0.0454154
$406$	7.22157	0.358400
$407$	27.2670	1.35158
$408$	−0.494433	−0.0244781
$409$	−21.5325	−1.06471	−0.532357	−	0.846520i	$-0.678694\pi$
$409$	−21.5325	−1.06471	−0.532357	+	0.846520i	$0.678694\pi$
$410$	2.98050	0.147197
$411$	−19.6646	−0.969984
$412$	−11.3154	−0.557471
$413$	−9.31761	−0.458490
$414$	5.83868	0.286956
$415$	−10.8958	−0.534851
$416$	1.89717	0.0930165
$417$	−13.7297	−0.672347
$418$	10.6808	0.522413
$419$	18.1275	0.885589	0.442794	−	0.896623i	$-0.353987\pi$
$419$	18.1275	0.885589	0.442794	+	0.896623i	$0.353987\pi$
$420$	0.913967	0.0445970
$421$	7.96959	0.388414	0.194207	−	0.980961i	$-0.437787\pi$
$421$	7.96959	0.388414	0.194207	+	0.980961i	$0.437787\pi$
$422$	4.52445	0.220247
$423$	4.83330	0.235003
$424$	11.4473	0.555931
$425$	2.05915	0.0998833
$426$	−6.81250	−0.330067
$427$	3.24910	0.157235
$428$	8.21611	0.397141
$429$	12.3783	0.597628
$430$	2.78620	0.134362
$431$	−28.1085	−1.35394	−0.676969	−	0.736011i	$-0.736707\pi$
$431$	−28.1085	−1.35394	−0.676969	+	0.736011i	$0.736707\pi$
$432$	−1.00000	−0.0481125
$433$	40.6629	1.95413	0.977066	−	0.212936i	$-0.0683025\pi$
$433$	40.6629	1.95413	0.977066	+	0.212936i	$0.0683025\pi$
$434$	1.28580	0.0617204
$435$	−6.60027	−0.316459
$436$	−3.58806	−0.171837
$437$	9.55793	0.457218
$438$	−12.1767	−0.581825
$439$	−11.7699	−0.561744	−0.280872	−	0.959745i	$-0.590624\pi$
$439$	−11.7699	−0.561744	−0.280872	+	0.959745i	$0.590624\pi$
$440$	−5.96325	−0.284287
$441$	1.00000	0.0476190
$442$	−0.938024	−0.0446172
$443$	−7.00709	−0.332917	−0.166459	−	0.986048i	$-0.553233\pi$
$443$	−7.00709	−0.332917	−0.166459	+	0.986048i	$0.553233\pi$
$444$	−4.17912	−0.198332
$445$	9.05392	0.429197
$446$	−15.1315	−0.716496
$447$	10.7604	0.508949
$448$	−1.00000	−0.0472456
$449$	−18.0204	−0.850436	−0.425218	−	0.905091i	$-0.639803\pi$
$449$	−18.0204	−0.850436	−0.425218	+	0.905091i	$0.639803\pi$
$450$	4.16466	0.196324
$451$	−21.2771	−1.00190
$452$	−13.0273	−0.612753
$453$	2.00141	0.0940345
$454$	−7.50713	−0.352327
$455$	1.73395	0.0812889
$456$	−1.63700	−0.0766597
$457$	−31.3765	−1.46773	−0.733866	−	0.679294i	$-0.762286\pi$
$457$	−31.3765	−1.46773	−0.733866	+	0.679294i	$0.762286\pi$
$458$	−20.3584	−0.951286
$459$	0.494433	0.0230781
$460$	−5.33636	−0.248809
$461$	6.91279	0.321961	0.160980	−	0.986958i	$-0.448534\pi$
$461$	6.91279	0.321961	0.160980	+	0.986958i	$0.448534\pi$
$462$	−6.52458	−0.303551
$463$	24.7648	1.15092	0.575458	−	0.817831i	$-0.304824\pi$
$463$	24.7648	1.15092	0.575458	+	0.817831i	$0.304824\pi$
$464$	7.22157	0.335253
$465$	−1.17518	−0.0544976
$466$	5.93663	0.275009
$467$	20.1636	0.933058	0.466529	−	0.884506i	$-0.345504\pi$
$467$	20.1636	0.933058	0.466529	+	0.884506i	$0.345504\pi$
$468$	−1.89717	−0.0876968
$469$	7.93586	0.366444
$470$	−4.41747	−0.203763
$471$	−6.06325	−0.279380
$472$	−9.31761	−0.428878
$473$	−19.8900	−0.914542
$474$	−11.9229	−0.547637
$475$	6.81757	0.312811
$476$	0.494433	0.0226623
$477$	−11.4473	−0.524137
$478$	26.2961	1.20276
$479$	37.5365	1.71509	0.857543	−	0.514412i	$-0.171990\pi$
$479$	37.5365	1.71509	0.857543	+	0.514412i	$0.171990\pi$
$480$	0.913967	0.0417167
$481$	−7.92851	−0.361509
$482$	14.4774	0.659428
$483$	−5.83868	−0.265669
$484$	31.5702	1.43501
$485$	10.1059	0.458886
$486$	1.00000	0.0453609
$487$	−4.01405	−0.181894	−0.0909470	−	0.995856i	$-0.528989\pi$
$487$	−4.01405	−0.181894	−0.0909470	+	0.995856i	$0.528989\pi$
$488$	3.24910	0.147080
$489$	0.829014	0.0374893
$490$	−0.913967	−0.0412888
$491$	−20.5387	−0.926897	−0.463449	−	0.886124i	$-0.653388\pi$
$491$	−20.5387	−0.926897	−0.463449	+	0.886124i	$0.653388\pi$
$492$	3.26106	0.147020
$493$	−3.57058	−0.160811
$494$	−3.10567	−0.139731
$495$	5.96325	0.268028
$496$	1.28580	0.0577341
$497$	6.81250	0.305582
$498$	−11.9214	−0.534210
$499$	−35.7466	−1.60024	−0.800120	−	0.599841i	$-0.795231\pi$
$499$	−35.7466	−1.60024	−0.800120	+	0.599841i	$0.795231\pi$
$500$	−8.37620	−0.374595
$501$	−5.76775	−0.257684
$502$	−17.8010	−0.794499
$503$	−34.1432	−1.52237	−0.761185	−	0.648534i	$-0.775382\pi$
$503$	−34.1432	−1.52237	−0.761185	+	0.648534i	$0.775382\pi$
$504$	1.00000	0.0445435
$505$	−10.0596	−0.447646
$506$	38.0950	1.69353
$507$	9.40074	0.417502
$508$	−17.0045	−0.754453
$509$	−7.23589	−0.320725	−0.160363	−	0.987058i	$-0.551266\pi$
$509$	−7.23589	−0.320725	−0.160363	+	0.987058i	$0.551266\pi$
$510$	−0.451895	−0.0200103
$511$	12.1767	0.538666
$512$	−1.00000	−0.0441942
$513$	1.63700	0.0722754
$514$	7.71954	0.340494
$515$	−10.3419	−0.455719
$516$	3.04847	0.134201
$517$	31.5352	1.38692
$518$	4.17912	0.183620
$519$	8.60658	0.377787
$520$	1.73395	0.0760388
$521$	−22.3277	−0.978195	−0.489098	−	0.872229i	$-0.662674\pi$
$521$	−22.3277	−0.978195	−0.489098	+	0.872229i	$0.662674\pi$
$522$	−7.22157	−0.316079
$523$	7.13492	0.311988	0.155994	−	0.987758i	$-0.450142\pi$
$523$	7.13492	0.311988	0.155994	+	0.987758i	$0.450142\pi$
$524$	18.9593	0.828240
$525$	−4.16466	−0.181761
$526$	−8.79817	−0.383618
$527$	−0.635742	−0.0276934
$528$	−6.52458	−0.283946
$529$	11.0902	0.482182
$530$	10.4625	0.454461
$531$	9.31761	0.404350
$532$	1.63700	0.0709730
$533$	6.18679	0.267980
$534$	9.90618	0.428682
$535$	7.50925	0.324653
$536$	7.93586	0.342777
$537$	12.2846	0.530118
$538$	25.8700	1.11533
$539$	6.52458	0.281034
$540$	−0.913967	−0.0393309
$541$	11.3022	0.485918	0.242959	−	0.970037i	$-0.421882\pi$
$541$	11.3022	0.485918	0.242959	+	0.970037i	$0.421882\pi$
$542$	14.2975	0.614130
$543$	−7.31418	−0.313881
$544$	0.494433	0.0211986
$545$	−3.27937	−0.140473
$546$	1.89717	0.0811914
$547$	−6.97871	−0.298388	−0.149194	−	0.988808i	$-0.547668\pi$
$547$	−6.97871	−0.298388	−0.149194	+	0.988808i	$0.547668\pi$
$548$	19.6646	0.840031
$549$	−3.24910	−0.138668
$550$	27.1727	1.15865
$551$	−11.8217	−0.503622
$552$	−5.83868	−0.248511
$553$	11.9229	0.507013
$554$	−24.1474	−1.02593
$555$	−3.81958	−0.162132
$556$	13.7297	0.582270
$557$	−31.2583	−1.32446	−0.662228	−	0.749302i	$-0.730389\pi$
$557$	−31.2583	−1.32446	−0.662228	+	0.749302i	$0.730389\pi$
$558$	−1.28580	−0.0544323
$559$	5.78346	0.244614
$560$	−0.913967	−0.0386221
$561$	3.22597	0.136201
$562$	13.2987	0.560970
$563$	−22.7139	−0.957276	−0.478638	−	0.878012i	$-0.658869\pi$
$563$	−22.7139	−0.957276	−0.478638	+	0.878012i	$0.658869\pi$
$564$	−4.83330	−0.203518
$565$	−11.9065	−0.500911
$566$	−32.0622	−1.34767
$567$	−1.00000	−0.0419961
$568$	6.81250	0.285846
$569$	3.26965	0.137071	0.0685354	−	0.997649i	$-0.478167\pi$
$569$	3.26965	0.137071	0.0685354	+	0.997649i	$0.478167\pi$
$570$	−1.49617	−0.0626675
$571$	21.7962	0.912141	0.456071	−	0.889944i	$-0.349256\pi$
$571$	21.7962	0.912141	0.456071	+	0.889944i	$0.349256\pi$
$572$	−12.3783	−0.517561
$573$	1.00000	0.0417756
$574$	−3.26106	−0.136114
$575$	24.3161	1.01405
$576$	1.00000	0.0416667
$577$	−32.3422	−1.34642	−0.673211	−	0.739450i	$-0.735085\pi$
$577$	−32.3422	−1.34642	−0.673211	+	0.739450i	$0.735085\pi$
$578$	16.7555	0.696938
$579$	1.55348	0.0645602
$580$	6.60027	0.274061
$581$	11.9214	0.494582
$582$	11.0572	0.458336
$583$	−74.6890	−3.09330
$584$	12.1767	0.503875
$585$	−1.73395	−0.0716901
$586$	−10.7568	−0.444358
$587$	−1.46556	−0.0604900	−0.0302450	−	0.999543i	$-0.509629\pi$
$587$	−1.46556	−0.0604900	−0.0302450	+	0.999543i	$0.509629\pi$
$588$	−1.00000	−0.0412393
$589$	−2.10486	−0.0867292
$590$	−8.51599	−0.350598
$591$	9.40127	0.386717
$592$	4.17912	0.171761
$593$	−14.2326	−0.584463	−0.292231	−	0.956348i	$-0.594398\pi$
$593$	−14.2326	−0.584463	−0.292231	+	0.956348i	$0.594398\pi$
$594$	6.52458	0.267707
$595$	0.451895	0.0185259
$596$	−10.7604	−0.440763
$597$	−16.8642	−0.690205
$598$	−11.0770	−0.452971
$599$	−0.275719	−0.0112656	−0.00563278	−	0.999984i	$-0.501793\pi$
$599$	−0.275719	−0.0112656	−0.00563278	+	0.999984i	$0.501793\pi$
$600$	−4.16466	−0.170022
$601$	−15.1237	−0.616908	−0.308454	−	0.951239i	$-0.599812\pi$
$601$	−15.1237	−0.616908	−0.308454	+	0.951239i	$0.599812\pi$
$602$	−3.04847	−0.124246
$603$	−7.93586	−0.323173
$604$	−2.00141	−0.0814363
$605$	28.8541	1.17309
$606$	−11.0065	−0.447109
$607$	25.7178	1.04385	0.521927	−	0.852990i	$-0.325213\pi$
$607$	25.7178	1.04385	0.521927	+	0.852990i	$0.325213\pi$
$608$	1.63700	0.0663892
$609$	7.22157	0.292633
$610$	2.96957	0.120234
$611$	−9.16959	−0.370962
$612$	−0.494433	−0.0199863
$613$	44.2862	1.78870	0.894352	−	0.447364i	$-0.147637\pi$
$613$	44.2862	1.78870	0.894352	+	0.447364i	$0.147637\pi$
$614$	−23.0373	−0.929710
$615$	2.98050	0.120185
$616$	6.52458	0.262883
$617$	−6.75164	−0.271811	−0.135905	−	0.990722i	$-0.543394\pi$
$617$	−6.75164	−0.271811	−0.135905	+	0.990722i	$0.543394\pi$
$618$	−11.3154	−0.455173
$619$	6.20057	0.249222	0.124611	−	0.992206i	$-0.460232\pi$
$619$	6.20057	0.249222	0.124611	+	0.992206i	$0.460232\pi$
$620$	1.17518	0.0471963
$621$	5.83868	0.234298
$622$	20.5875	0.825484
$623$	−9.90618	−0.396883
$624$	1.89717	0.0759476
$625$	13.1678	0.526710
$626$	3.18770	0.127406
$627$	10.6808	0.426548
$628$	6.06325	0.241950
$629$	−2.06629	−0.0823886
$630$	0.913967	0.0364133
$631$	−42.9105	−1.70824	−0.854119	−	0.520077i	$-0.825903\pi$
$631$	−42.9105	−1.70824	−0.854119	+	0.520077i	$0.825903\pi$
$632$	11.9229	0.474267
$633$	4.52445	0.179831
$634$	−16.0819	−0.638693
$635$	−15.5416	−0.616748
$636$	11.4473	0.453916
$637$	−1.89717	−0.0751687
$638$	−47.1177	−1.86541
$639$	−6.81250	−0.269498
$640$	−0.913967	−0.0361277
$641$	−31.5285	−1.24530	−0.622651	−	0.782500i	$-0.713944\pi$
$641$	−31.5285	−1.24530	−0.622651	+	0.782500i	$0.713944\pi$
$642$	8.21611	0.324264
$643$	14.7311	0.580940	0.290470	−	0.956884i	$-0.406188\pi$
$643$	14.7311	0.580940	0.290470	+	0.956884i	$0.406188\pi$
$644$	5.83868	0.230076
$645$	2.78620	0.109706
$646$	−0.809388	−0.0318449
$647$	0.306569	0.0120525	0.00602623	−	0.999982i	$-0.498082\pi$
$647$	0.306569	0.0120525	0.00602623	+	0.999982i	$0.498082\pi$
$648$	−1.00000	−0.0392837
$649$	60.7935	2.38635
$650$	−7.90108	−0.309906
$651$	1.28580	0.0503945
$652$	−0.829014	−0.0324667
$653$	16.9120	0.661816	0.330908	−	0.943663i	$-0.392645\pi$
$653$	16.9120	0.661816	0.330908	+	0.943663i	$0.392645\pi$
$654$	−3.58806	−0.140304
$655$	17.3282	0.677067
$656$	−3.26106	−0.127323
$657$	−12.1767	−0.475058
$658$	4.83330	0.188421
$659$	30.0308	1.16984	0.584918	−	0.811093i	$-0.301127\pi$
$659$	30.0308	1.16984	0.584918	+	0.811093i	$0.301127\pi$
$660$	−5.96325	−0.232119
$661$	−46.7199	−1.81719	−0.908596	−	0.417676i	$-0.862845\pi$
$661$	−46.7199	−1.81719	−0.908596	+	0.417676i	$0.862845\pi$
$662$	0.381922	0.0148438
$663$	−0.938024	−0.0364298
$664$	11.9214	0.462639
$665$	1.49617	0.0580188
$666$	−4.17912	−0.161938
$667$	−42.1644	−1.63261
$668$	5.76775	0.223161
$669$	−15.1315	−0.585017
$670$	7.25311	0.280212
$671$	−21.1990	−0.818380
$672$	−1.00000	−0.0385758
$673$	−29.5201	−1.13792	−0.568958	−	0.822366i	$-0.692653\pi$
$673$	−29.5201	−1.13792	−0.568958	+	0.822366i	$0.692653\pi$
$674$	23.3934	0.901081
$675$	4.16466	0.160298
$676$	−9.40074	−0.361567
$677$	−9.04365	−0.347576	−0.173788	−	0.984783i	$-0.555601\pi$
$677$	−9.04365	−0.347576	−0.173788	+	0.984783i	$0.555601\pi$
$678$	−13.0273	−0.500311
$679$	−11.0572	−0.424337
$680$	0.451895	0.0173294
$681$	−7.50713	−0.287674
$682$	−8.38931	−0.321243
$683$	−35.3412	−1.35229	−0.676147	−	0.736767i	$-0.736352\pi$
$683$	−35.3412	−1.35229	−0.676147	+	0.736767i	$0.736352\pi$
$684$	−1.63700	−0.0625923
$685$	17.9728	0.686706
$686$	1.00000	0.0381802
$687$	−20.3584	−0.776722
$688$	−3.04847	−0.116222
$689$	21.7175	0.827372
$690$	−5.33636	−0.203152
$691$	−12.2104	−0.464506	−0.232253	−	0.972655i	$-0.574610\pi$
$691$	−12.2104	−0.464506	−0.232253	+	0.972655i	$0.574610\pi$
$692$	−8.60658	−0.327173
$693$	−6.52458	−0.247848
$694$	31.0843	1.17994
$695$	12.5485	0.475992
$696$	7.22157	0.273733
$697$	1.61238	0.0610731
$698$	−5.81155	−0.219971
$699$	5.93663	0.224544
$700$	4.16466	0.157410
$701$	1.31662	0.0497279	0.0248640	−	0.999691i	$-0.492085\pi$
$701$	1.31662	0.0497279	0.0248640	+	0.999691i	$0.492085\pi$
$702$	−1.89717	−0.0716041
$703$	−6.84123	−0.258022
$704$	6.52458	0.245905
$705$	−4.41747	−0.166372
$706$	31.3856	1.18121
$707$	11.0065	0.413943
$708$	−9.31761	−0.350177
$709$	5.05676	0.189911	0.0949554	−	0.995482i	$-0.469729\pi$
$709$	5.05676	0.189911	0.0949554	+	0.995482i	$0.469729\pi$
$710$	6.22640	0.233673
$711$	−11.9229	−0.447143
$712$	−9.90618	−0.371250
$713$	−7.50738	−0.281154
$714$	0.494433	0.0185037
$715$	−11.3133	−0.423094
$716$	−12.2846	−0.459096
$717$	26.2961	0.982045
$718$	37.3490	1.39385
$719$	34.2198	1.27618	0.638091	−	0.769961i	$-0.279724\pi$
$719$	34.2198	1.27618	0.638091	+	0.769961i	$0.279724\pi$
$720$	0.913967	0.0340615
$721$	11.3154	0.421408
$722$	16.3202	0.607376
$723$	14.4774	0.538420
$724$	7.31418	0.271829
$725$	−30.0754	−1.11697
$726$	31.5702	1.17168
$727$	−2.67863	−0.0993447	−0.0496724	−	0.998766i	$-0.515818\pi$
$727$	−2.67863	−0.0993447	−0.0496724	+	0.998766i	$0.515818\pi$
$728$	−1.89717	−0.0703138
$729$	1.00000	0.0370370
$730$	11.1291	0.411907
$731$	1.50726	0.0557481
$732$	3.24910	0.120090
$733$	−16.8727	−0.623208	−0.311604	−	0.950212i	$-0.600866\pi$
$733$	−16.8727	−0.623208	−0.311604	+	0.950212i	$0.600866\pi$
$734$	0.214310	0.00791034
$735$	−0.913967	−0.0337122
$736$	5.83868	0.215217
$737$	−51.7782	−1.90727
$738$	3.26106	0.120041
$739$	0.383350	0.0141018	0.00705088	−	0.999975i	$-0.497756\pi$
$739$	0.383350	0.0141018	0.00705088	+	0.999975i	$0.497756\pi$
$740$	3.81958	0.140410
$741$	−3.10567	−0.114090
$742$	−11.4473	−0.420245
$743$	5.25272	0.192703	0.0963517	−	0.995347i	$-0.469283\pi$
$743$	5.25272	0.192703	0.0963517	+	0.995347i	$0.469283\pi$
$744$	1.28580	0.0471397
$745$	−9.83464	−0.360313
$746$	−26.2018	−0.959315
$747$	−11.9214	−0.436181
$748$	−3.22597	−0.117953
$749$	−8.21611	−0.300210
$750$	−8.37620	−0.305856
$751$	−19.1985	−0.700563	−0.350281	−	0.936644i	$-0.613914\pi$
$751$	−19.1985	−0.700563	−0.350281	+	0.936644i	$0.613914\pi$
$752$	4.83330	0.176252
$753$	−17.8010	−0.648705
$754$	13.7005	0.498944
$755$	−1.82922	−0.0665723
$756$	1.00000	0.0363696
$757$	4.65339	0.169130	0.0845651	−	0.996418i	$-0.473050\pi$
$757$	4.65339	0.169130	0.0845651	+	0.996418i	$0.473050\pi$
$758$	−31.7256	−1.15233
$759$	38.0950	1.38276
$760$	1.49617	0.0542716
$761$	20.7886	0.753585	0.376793	−	0.926298i	$-0.377027\pi$
$761$	20.7886	0.753585	0.376793	+	0.926298i	$0.377027\pi$
$762$	−17.0045	−0.616009
$763$	3.58806	0.129897
$764$	−1.00000	−0.0361787
$765$	−0.451895	−0.0163383
$766$	15.2381	0.550576
$767$	−17.6771	−0.638283
$768$	−1.00000	−0.0360844
$769$	−42.2552	−1.52376	−0.761881	−	0.647717i	$-0.775724\pi$
$769$	−42.2552	−1.52376	−0.761881	+	0.647717i	$0.775724\pi$
$770$	5.96325	0.214901
$771$	7.71954	0.278012
$772$	−1.55348	−0.0559108
$773$	−29.0790	−1.04590	−0.522949	−	0.852364i	$-0.675168\pi$
$773$	−29.0790	−1.04590	−0.522949	+	0.852364i	$0.675168\pi$
$774$	3.04847	0.109575
$775$	−5.35493	−0.192355
$776$	−11.0572	−0.396931
$777$	4.17912	0.149925
$778$	1.97726	0.0708883
$779$	5.33837	0.191267
$780$	1.73395	0.0620854
$781$	−44.4487	−1.59050
$782$	−2.88684	−0.103233
$783$	−7.22157	−0.258078
$784$	1.00000	0.0357143
$785$	5.54161	0.197788
$786$	18.9593	0.676255
$787$	13.3519	0.475942	0.237971	−	0.971272i	$-0.423518\pi$
$787$	13.3519	0.475942	0.237971	+	0.971272i	$0.423518\pi$
$788$	−9.40127	−0.334906
$789$	−8.79817	−0.313223
$790$	10.8971	0.387702
$791$	13.0273	0.463198
$792$	−6.52458	−0.231841
$793$	6.16410	0.218894
$794$	31.9761	1.13479
$795$	10.4625	0.371066
$796$	16.8642	0.597735
$797$	−32.0365	−1.13479	−0.567396	−	0.823445i	$-0.692049\pi$
$797$	−32.0365	−1.13479	−0.567396	+	0.823445i	$0.692049\pi$
$798$	1.63700	0.0579493
$799$	−2.38974	−0.0845429
$800$	4.16466	0.147243
$801$	9.90618	0.350018
$802$	−18.2924	−0.645928
$803$	−79.4479	−2.80366
$804$	7.93586	0.279876
$805$	5.33636	0.188082
$806$	2.43938	0.0859236
$807$	25.8700	0.910666
$808$	11.0065	0.387208
$809$	28.3115	0.995381	0.497690	−	0.867355i	$-0.334182\pi$
$809$	28.3115	0.995381	0.497690	+	0.867355i	$0.334182\pi$
$810$	−0.913967	−0.0321135
$811$	14.8584	0.521747	0.260874	−	0.965373i	$-0.415989\pi$
$811$	14.8584	0.521747	0.260874	+	0.965373i	$0.415989\pi$
$812$	−7.22157	−0.253427
$813$	14.2975	0.501435
$814$	−27.2670	−0.955709
$815$	−0.757692	−0.0265408
$816$	0.494433	0.0173086
$817$	4.99034	0.174590
$818$	21.5325	0.752866
$819$	1.89717	0.0662925
$820$	−2.98050	−0.104084
$821$	−44.4801	−1.55236	−0.776182	−	0.630508i	$-0.782846\pi$
$821$	−44.4801	−1.55236	−0.776182	+	0.630508i	$0.782846\pi$
$822$	19.6646	0.685882
$823$	−20.1014	−0.700691	−0.350345	−	0.936621i	$-0.613936\pi$
$823$	−20.1014	−0.700691	−0.350345	+	0.936621i	$0.613936\pi$
$824$	11.3154	0.394191
$825$	27.1727	0.946032
$826$	9.31761	0.324201
$827$	4.76809	0.165803	0.0829014	−	0.996558i	$-0.473581\pi$
$827$	4.76809	0.165803	0.0829014	+	0.996558i	$0.473581\pi$
$828$	−5.83868	−0.202908
$829$	−19.5310	−0.678340	−0.339170	−	0.940725i	$-0.610146\pi$
$829$	−19.5310	−0.678340	−0.339170	+	0.940725i	$0.610146\pi$
$830$	10.8958	0.378197
$831$	−24.1474	−0.837665
$832$	−1.89717	−0.0657726
$833$	−0.494433	−0.0171311
$834$	13.7297	0.475421
$835$	5.27154	0.182429
$836$	−10.6808	−0.369402
$837$	−1.28580	−0.0444438
$838$	−18.1275	−0.626206
$839$	−5.76428	−0.199005	−0.0995026	−	0.995037i	$-0.531725\pi$
$839$	−5.76428	−0.199005	−0.0995026	+	0.995037i	$0.531725\pi$
$840$	−0.913967	−0.0315349
$841$	23.1510	0.798311
$842$	−7.96959	−0.274650
$843$	13.2987	0.458030
$844$	−4.52445	−0.155738
$845$	−8.59197	−0.295573
$846$	−4.83330	−0.166172
$847$	−31.5702	−1.08477
$848$	−11.4473	−0.393103
$849$	−32.0622	−1.10037
$850$	−2.05915	−0.0706282
$851$	−24.4006	−0.836440
$852$	6.81250	0.233392
$853$	−3.05645	−0.104651	−0.0523255	−	0.998630i	$-0.516663\pi$
$853$	−3.05645	−0.104651	−0.0523255	+	0.998630i	$0.516663\pi$
$854$	−3.24910	−0.111182
$855$	−1.49617	−0.0511678
$856$	−8.21611	−0.280821
$857$	−47.6233	−1.62678	−0.813390	−	0.581718i	$-0.802381\pi$
$857$	−47.6233	−1.62678	−0.813390	+	0.581718i	$0.802381\pi$
$858$	−12.3783	−0.422587
$859$	−12.0382	−0.410737	−0.205369	−	0.978685i	$-0.565839\pi$
$859$	−12.0382	−0.410737	−0.205369	+	0.978685i	$0.565839\pi$
$860$	−2.78620	−0.0950085
$861$	−3.26106	−0.111137
$862$	28.1085	0.957379
$863$	10.2315	0.348283	0.174142	−	0.984721i	$-0.444285\pi$
$863$	10.2315	0.348283	0.174142	+	0.984721i	$0.444285\pi$
$864$	1.00000	0.0340207
$865$	−7.86612	−0.267456
$866$	−40.6629	−1.38178
$867$	16.7555	0.569048
$868$	−1.28580	−0.0436429
$869$	−77.7919	−2.63891
$870$	6.60027	0.223770
$871$	15.0557	0.510142
$872$	3.58806	0.121507
$873$	11.0572	0.374230
$874$	−9.55793	−0.323302
$875$	8.37620	0.283167
$876$	12.1767	0.411413
$877$	−9.86283	−0.333044	−0.166522	−	0.986038i	$-0.553254\pi$
$877$	−9.86283	−0.333044	−0.166522	+	0.986038i	$0.553254\pi$
$878$	11.7699	0.397213
$879$	−10.7568	−0.362817
$880$	5.96325	0.201021
$881$	41.4226	1.39556	0.697781	−	0.716311i	$-0.254171\pi$
$881$	41.4226	1.39556	0.697781	+	0.716311i	$0.254171\pi$
$882$	−1.00000	−0.0336718
$883$	18.3062	0.616053	0.308027	−	0.951378i	$-0.400331\pi$
$883$	18.3062	0.616053	0.308027	+	0.951378i	$0.400331\pi$
$884$	0.938024	0.0315492
$885$	−8.51599	−0.286262
$886$	7.00709	0.235408
$887$	−57.1877	−1.92017	−0.960087	−	0.279702i	$-0.909764\pi$
$887$	−57.1877	−1.92017	−0.960087	+	0.279702i	$0.909764\pi$
$888$	4.17912	0.140242
$889$	17.0045	0.570313
$890$	−9.05392	−0.303488
$891$	6.52458	0.218582
$892$	15.1315	0.506639
$893$	−7.91211	−0.264769
$894$	−10.7604	−0.359881
$895$	−11.2277	−0.375300
$896$	1.00000	0.0334077
$897$	−11.0770	−0.369849
$898$	18.0204	0.601349
$899$	9.28549	0.309689
$900$	−4.16466	−0.138822
$901$	5.65993	0.188560
$902$	21.2771	0.708449
$903$	−3.04847	−0.101447
$904$	13.0273	0.433282
$905$	6.68492	0.222214
$906$	−2.00141	−0.0664924
$907$	−41.8513	−1.38965	−0.694824	−	0.719180i	$-0.744518\pi$
$907$	−41.8513	−1.38965	−0.694824	+	0.719180i	$0.744518\pi$
$908$	7.50713	0.249133
$909$	−11.0065	−0.365063
$910$	−1.73395	−0.0574799
$911$	50.1808	1.66256	0.831282	−	0.555850i	$-0.187607\pi$
$911$	50.1808	1.66256	0.831282	+	0.555850i	$0.187607\pi$
$912$	1.63700	0.0542066
$913$	−77.7821	−2.57421
$914$	31.3765	1.03784
$915$	2.96957	0.0981710
$916$	20.3584	0.672661
$917$	−18.9593	−0.626091
$918$	−0.494433	−0.0163187
$919$	−28.9635	−0.955416	−0.477708	−	0.878519i	$-0.658532\pi$
$919$	−28.9635	−0.955416	−0.477708	+	0.878519i	$0.658532\pi$
$920$	5.33636	0.175935
$921$	−23.0373	−0.759105
$922$	−6.91279	−0.227661
$923$	12.9245	0.425414
$924$	6.52458	0.214643
$925$	−17.4046	−0.572261
$926$	−24.7648	−0.813820
$927$	−11.3154	−0.371647
$928$	−7.22157	−0.237060
$929$	−17.6276	−0.578342	−0.289171	−	0.957277i	$-0.593380\pi$
$929$	−17.6276	−0.578342	−0.289171	+	0.957277i	$0.593380\pi$
$930$	1.17518	0.0385356
$931$	−1.63700	−0.0536506
$932$	−5.93663	−0.194461
$933$	20.5875	0.674005
$934$	−20.1636	−0.659772
$935$	−2.94843	−0.0964239
$936$	1.89717	0.0620110
$937$	35.7571	1.16813	0.584067	−	0.811705i	$-0.301460\pi$
$937$	35.7571	1.16813	0.584067	+	0.811705i	$0.301460\pi$
$938$	−7.93586	−0.259115
$939$	3.18770	0.104027
$940$	4.41747	0.144082
$941$	−14.2522	−0.464608	−0.232304	−	0.972643i	$-0.574626\pi$
$941$	−14.2522	−0.464608	−0.232304	+	0.972643i	$0.574626\pi$
$942$	6.06325	0.197551
$943$	19.0403	0.620038
$944$	9.31761	0.303262
$945$	0.913967	0.0297313
$946$	19.8900	0.646679
$947$	35.4728	1.15271	0.576356	−	0.817199i	$-0.304474\pi$
$947$	35.4728	1.15271	0.576356	+	0.817199i	$0.304474\pi$
$948$	11.9229	0.387238
$949$	23.1013	0.749899
$950$	−6.81757	−0.221191
$951$	−16.0819	−0.521490
$952$	−0.494433	−0.0160247
$953$	10.4214	0.337582	0.168791	−	0.985652i	$-0.446014\pi$
$953$	10.4214	0.337582	0.168791	+	0.985652i	$0.446014\pi$
$954$	11.4473	0.370621
$955$	−0.913967	−0.0295753
$956$	−26.2961	−0.850476
$957$	−47.1177	−1.52310
$958$	−37.5365	−1.21275
$959$	−19.6646	−0.635004
$960$	−0.913967	−0.0294982
$961$	−29.3467	−0.946668
$962$	7.92851	0.255625
$963$	8.21611	0.264760
$964$	−14.4774	−0.466286
$965$	−1.41982	−0.0457058
$966$	5.83868	0.187856
$967$	38.1395	1.22648	0.613242	−	0.789895i	$-0.289865\pi$
$967$	38.1395	1.22648	0.613242	+	0.789895i	$0.289865\pi$
$968$	−31.5702	−1.01470
$969$	−0.809388	−0.0260013
$970$	−10.1059	−0.324482
$971$	−10.2438	−0.328740	−0.164370	−	0.986399i	$-0.552559\pi$
$971$	−10.2438	−0.328740	−0.164370	+	0.986399i	$0.552559\pi$
$972$	−1.00000	−0.0320750
$973$	−13.7297	−0.440155
$974$	4.01405	0.128619
$975$	−7.90108	−0.253037
$976$	−3.24910	−0.104001
$977$	−3.86077	−0.123517	−0.0617585	−	0.998091i	$-0.519671\pi$
$977$	−3.86077	−0.123517	−0.0617585	+	0.998091i	$0.519671\pi$
$978$	−0.829014	−0.0265090
$979$	64.6337	2.06570
$980$	0.913967	0.0291956
$981$	−3.58806	−0.114558
$982$	20.5387	0.655415
$983$	−16.5955	−0.529314	−0.264657	−	0.964343i	$-0.585259\pi$
$983$	−16.5955	−0.529314	−0.264657	+	0.964343i	$0.585259\pi$
$984$	−3.26106	−0.103959
$985$	−8.59245	−0.273778
$986$	3.57058	0.113710
$987$	4.83330	0.153845
$988$	3.10567	0.0988046
$989$	17.7990	0.565976
$990$	−5.96325	−0.189525
$991$	−31.8051	−1.01032	−0.505162	−	0.863025i	$-0.668567\pi$
$991$	−31.8051	−1.01032	−0.505162	+	0.863025i	$0.668567\pi$
$992$	−1.28580	−0.0408242
$993$	0.381922	0.0121199
$994$	−6.81250	−0.216079
$995$	15.4133	0.488635
$996$	11.9214	0.377744
$997$	−2.14001	−0.0677748	−0.0338874	−	0.999426i	$-0.510789\pi$
$997$	−2.14001	−0.0677748	−0.0338874	+	0.999426i	$0.510789\pi$
$998$	35.7466	1.13154
$999$	−4.17912	−0.132222

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.v.1.10	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.v.1.10	✓	13	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.913967 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.913967 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.913967 q^{10} +6.52458 q^{11} -1.00000 q^{12} -1.89717 q^{13} +1.00000 q^{14} -0.913967 q^{15} +1.00000 q^{16} -0.494433 q^{17} -1.00000 q^{18} -1.63700 q^{19} +0.913967 q^{20} +1.00000 q^{21} -6.52458 q^{22} -5.83868 q^{23} +1.00000 q^{24} -4.16466 q^{25} +1.89717 q^{26} -1.00000 q^{27} -1.00000 q^{28} +7.22157 q^{29} +0.913967 q^{30} +1.28580 q^{31} -1.00000 q^{32} -6.52458 q^{33} +0.494433 q^{34} -0.913967 q^{35} +1.00000 q^{36} +4.17912 q^{37} +1.63700 q^{38} +1.89717 q^{39} -0.913967 q^{40} -3.26106 q^{41} -1.00000 q^{42} -3.04847 q^{43} +6.52458 q^{44} +0.913967 q^{45} +5.83868 q^{46} +4.83330 q^{47} -1.00000 q^{48} +1.00000 q^{49} +4.16466 q^{50} +0.494433 q^{51} -1.89717 q^{52} -11.4473 q^{53} +1.00000 q^{54} +5.96325 q^{55} +1.00000 q^{56} +1.63700 q^{57} -7.22157 q^{58} +9.31761 q^{59} -0.913967 q^{60} -3.24910 q^{61} -1.28580 q^{62} -1.00000 q^{63} +1.00000 q^{64} -1.73395 q^{65} +6.52458 q^{66} -7.93586 q^{67} -0.494433 q^{68} +5.83868 q^{69} +0.913967 q^{70} -6.81250 q^{71} -1.00000 q^{72} -12.1767 q^{73} -4.17912 q^{74} +4.16466 q^{75} -1.63700 q^{76} -6.52458 q^{77} -1.89717 q^{78} -11.9229 q^{79} +0.913967 q^{80} +1.00000 q^{81} +3.26106 q^{82} -11.9214 q^{83} +1.00000 q^{84} -0.451895 q^{85} +3.04847 q^{86} -7.22157 q^{87} -6.52458 q^{88} +9.90618 q^{89} -0.913967 q^{90} +1.89717 q^{91} -5.83868 q^{92} -1.28580 q^{93} -4.83330 q^{94} -1.49617 q^{95} +1.00000 q^{96} +11.0572 q^{97} -1.00000 q^{98} +6.52458 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 13 q^{2} - 13 q^{3} + 13 q^{4} - 5 q^{5} + 13 q^{6} - 13 q^{7} - 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q - 13 * q^2 - 13 * q^3 + 13 * q^4 - 5 * q^5 + 13 * q^6 - 13 * q^7 - 13 * q^8 + 13 * q^9	\( 13 q - 13 q^{2} - 13 q^{3} + 13 q^{4} - 5 q^{5} + 13 q^{6} - 13 q^{7} - 13 q^{8} + 13 q^{9} + 5 q^{10} + 2 q^{11} - 13 q^{12} - 9 q^{13} + 13 q^{14} + 5 q^{15} + 13 q^{16} - 15 q^{17} - 13 q^{18} + 7 q^{19} - 5 q^{20} + 13 q^{21} - 2 q^{22} - 5 q^{23} + 13 q^{24} + 20 q^{25} + 9 q^{26} - 13 q^{27} - 13 q^{28} - 10 q^{29} - 5 q^{30} + 23 q^{31} - 13 q^{32} - 2 q^{33} + 15 q^{34} + 5 q^{35} + 13 q^{36} - 8 q^{37} - 7 q^{38} + 9 q^{39} + 5 q^{40} - 2 q^{41} - 13 q^{42} - 14 q^{43} + 2 q^{44} - 5 q^{45} + 5 q^{46} + q^{47} - 13 q^{48} + 13 q^{49} - 20 q^{50} + 15 q^{51} - 9 q^{52} - 20 q^{53} + 13 q^{54} + 27 q^{55} + 13 q^{56} - 7 q^{57} + 10 q^{58} + 11 q^{59} + 5 q^{60} + 32 q^{61} - 23 q^{62} - 13 q^{63} + 13 q^{64} - 20 q^{65} + 2 q^{66} - 8 q^{67} - 15 q^{68} + 5 q^{69} - 5 q^{70} + 10 q^{71} - 13 q^{72} + 10 q^{73} + 8 q^{74} - 20 q^{75} + 7 q^{76} - 2 q^{77} - 9 q^{78} + 20 q^{79} - 5 q^{80} + 13 q^{81} + 2 q^{82} + 4 q^{83} + 13 q^{84} - 4 q^{85} + 14 q^{86} + 10 q^{87} - 2 q^{88} + 19 q^{89} + 5 q^{90} + 9 q^{91} - 5 q^{92} - 23 q^{93} - q^{94} - 3 q^{95} + 13 q^{96} + 16 q^{97} - 13 q^{98} + 2 q^{99}+O(q^{100}) \) 13 * q - 13 * q^2 - 13 * q^3 + 13 * q^4 - 5 * q^5 + 13 * q^6 - 13 * q^7 - 13 * q^8 + 13 * q^9 + 5 * q^10 + 2 * q^11 - 13 * q^12 - 9 * q^13 + 13 * q^14 + 5 * q^15 + 13 * q^16 - 15 * q^17 - 13 * q^18 + 7 * q^19 - 5 * q^20 + 13 * q^21 - 2 * q^22 - 5 * q^23 + 13 * q^24 + 20 * q^25 + 9 * q^26 - 13 * q^27 - 13 * q^28 - 10 * q^29 - 5 * q^30 + 23 * q^31 - 13 * q^32 - 2 * q^33 + 15 * q^34 + 5 * q^35 + 13 * q^36 - 8 * q^37 - 7 * q^38 + 9 * q^39 + 5 * q^40 - 2 * q^41 - 13 * q^42 - 14 * q^43 + 2 * q^44 - 5 * q^45 + 5 * q^46 + q^47 - 13 * q^48 + 13 * q^49 - 20 * q^50 + 15 * q^51 - 9 * q^52 - 20 * q^53 + 13 * q^54 + 27 * q^55 + 13 * q^56 - 7 * q^57 + 10 * q^58 + 11 * q^59 + 5 * q^60 + 32 * q^61 - 23 * q^62 - 13 * q^63 + 13 * q^64 - 20 * q^65 + 2 * q^66 - 8 * q^67 - 15 * q^68 + 5 * q^69 - 5 * q^70 + 10 * q^71 - 13 * q^72 + 10 * q^73 + 8 * q^74 - 20 * q^75 + 7 * q^76 - 2 * q^77 - 9 * q^78 + 20 * q^79 - 5 * q^80 + 13 * q^81 + 2 * q^82 + 4 * q^83 + 13 * q^84 - 4 * q^85 + 14 * q^86 + 10 * q^87 - 2 * q^88 + 19 * q^89 + 5 * q^90 + 9 * q^91 - 5 * q^92 - 23 * q^93 - q^94 - 3 * q^95 + 13 * q^96 + 16 * q^97 - 13 * q^98 + 2 * q^99

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