LMFDB - Embedded newform 8034.2.a.bc.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - x^{14} - 48 x^{13} + 44 x^{12} + 872 x^{11} - 707 x^{10} - 7580 x^{9} + 5112 x^{8} + \cdots + 2048 $ x^15 - x^14 - 48x^13 + 44x^12 + 872x^11 - 707x^10 - 7580x^9 + 5112x^8 + 33191x^7 - 16428x^6 - 71361x^5 + 21747x^4 + 65434x^3 - 11840x^2 - 17600*x + 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.656329$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.656329 q^{5} -1.00000 q^{6} +2.89208 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.656329 q^{5} -1.00000 q^{6} +2.89208 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.656329 q^{10} +2.55119 q^{11} -1.00000 q^{12} -1.00000 q^{13} +2.89208 q^{14} -0.656329 q^{15} +1.00000 q^{16} -3.68086 q^{17} +1.00000 q^{18} +2.16301 q^{19} +0.656329 q^{20} -2.89208 q^{21} +2.55119 q^{22} +6.84289 q^{23} -1.00000 q^{24} -4.56923 q^{25} -1.00000 q^{26} -1.00000 q^{27} +2.89208 q^{28} -8.30733 q^{29} -0.656329 q^{30} +8.50156 q^{31} +1.00000 q^{32} -2.55119 q^{33} -3.68086 q^{34} +1.89816 q^{35} +1.00000 q^{36} -2.04906 q^{37} +2.16301 q^{38} +1.00000 q^{39} +0.656329 q^{40} +10.0847 q^{41} -2.89208 q^{42} -0.666049 q^{43} +2.55119 q^{44} +0.656329 q^{45} +6.84289 q^{46} -5.56855 q^{47} -1.00000 q^{48} +1.36415 q^{49} -4.56923 q^{50} +3.68086 q^{51} -1.00000 q^{52} +8.88913 q^{53} -1.00000 q^{54} +1.67442 q^{55} +2.89208 q^{56} -2.16301 q^{57} -8.30733 q^{58} +6.49563 q^{59} -0.656329 q^{60} +3.88458 q^{61} +8.50156 q^{62} +2.89208 q^{63} +1.00000 q^{64} -0.656329 q^{65} -2.55119 q^{66} +9.97687 q^{67} -3.68086 q^{68} -6.84289 q^{69} +1.89816 q^{70} +10.0087 q^{71} +1.00000 q^{72} -2.34621 q^{73} -2.04906 q^{74} +4.56923 q^{75} +2.16301 q^{76} +7.37825 q^{77} +1.00000 q^{78} +14.6755 q^{79} +0.656329 q^{80} +1.00000 q^{81} +10.0847 q^{82} -0.205035 q^{83} -2.89208 q^{84} -2.41586 q^{85} -0.666049 q^{86} +8.30733 q^{87} +2.55119 q^{88} -15.8023 q^{89} +0.656329 q^{90} -2.89208 q^{91} +6.84289 q^{92} -8.50156 q^{93} -5.56855 q^{94} +1.41965 q^{95} -1.00000 q^{96} -11.3618 q^{97} +1.36415 q^{98} +2.55119 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} - 15 q^{3} + 15 q^{4} - q^{5} - 15 q^{6} + 5 q^{7} + 15 q^{8} + 15 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 - 15 * q^3 + 15 * q^4 - q^5 - 15 * q^6 + 5 * q^7 + 15 * q^8 + 15 * q^9	\( 15 q + 15 q^{2} - 15 q^{3} + 15 q^{4} - q^{5} - 15 q^{6} + 5 q^{7} + 15 q^{8} + 15 q^{9} - q^{10} + 3 q^{11} - 15 q^{12} - 15 q^{13} + 5 q^{14} + q^{15} + 15 q^{16} - 2 q^{17} + 15 q^{18} + 8 q^{19} - q^{20} - 5 q^{21} + 3 q^{22} + 3 q^{23} - 15 q^{24} + 22 q^{25} - 15 q^{26} - 15 q^{27} + 5 q^{28} + 26 q^{29} + q^{30} + 15 q^{32} - 3 q^{33} - 2 q^{34} - 8 q^{35} + 15 q^{36} + 25 q^{37} + 8 q^{38} + 15 q^{39} - q^{40} - q^{41} - 5 q^{42} + 10 q^{43} + 3 q^{44} - q^{45} + 3 q^{46} - 3 q^{47} - 15 q^{48} + 32 q^{49} + 22 q^{50} + 2 q^{51} - 15 q^{52} + 13 q^{53} - 15 q^{54} - 2 q^{55} + 5 q^{56} - 8 q^{57} + 26 q^{58} + 28 q^{59} + q^{60} + 22 q^{61} + 5 q^{63} + 15 q^{64} + q^{65} - 3 q^{66} + 29 q^{67} - 2 q^{68} - 3 q^{69} - 8 q^{70} + 18 q^{71} + 15 q^{72} + 23 q^{73} + 25 q^{74} - 22 q^{75} + 8 q^{76} + 17 q^{77} + 15 q^{78} + 27 q^{79} - q^{80} + 15 q^{81} - q^{82} + 7 q^{83} - 5 q^{84} + 43 q^{85} + 10 q^{86} - 26 q^{87} + 3 q^{88} + 35 q^{89} - q^{90} - 5 q^{91} + 3 q^{92} - 3 q^{94} + 6 q^{95} - 15 q^{96} + 19 q^{97} + 32 q^{98} + 3 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 15 * q^3 + 15 * q^4 - q^5 - 15 * q^6 + 5 * q^7 + 15 * q^8 + 15 * q^9 - q^10 + 3 * q^11 - 15 * q^12 - 15 * q^13 + 5 * q^14 + q^15 + 15 * q^16 - 2 * q^17 + 15 * q^18 + 8 * q^19 - q^20 - 5 * q^21 + 3 * q^22 + 3 * q^23 - 15 * q^24 + 22 * q^25 - 15 * q^26 - 15 * q^27 + 5 * q^28 + 26 * q^29 + q^30 + 15 * q^32 - 3 * q^33 - 2 * q^34 - 8 * q^35 + 15 * q^36 + 25 * q^37 + 8 * q^38 + 15 * q^39 - q^40 - q^41 - 5 * q^42 + 10 * q^43 + 3 * q^44 - q^45 + 3 * q^46 - 3 * q^47 - 15 * q^48 + 32 * q^49 + 22 * q^50 + 2 * q^51 - 15 * q^52 + 13 * q^53 - 15 * q^54 - 2 * q^55 + 5 * q^56 - 8 * q^57 + 26 * q^58 + 28 * q^59 + q^60 + 22 * q^61 + 5 * q^63 + 15 * q^64 + q^65 - 3 * q^66 + 29 * q^67 - 2 * q^68 - 3 * q^69 - 8 * q^70 + 18 * q^71 + 15 * q^72 + 23 * q^73 + 25 * q^74 - 22 * q^75 + 8 * q^76 + 17 * q^77 + 15 * q^78 + 27 * q^79 - q^80 + 15 * q^81 - q^82 + 7 * q^83 - 5 * q^84 + 43 * q^85 + 10 * q^86 - 26 * q^87 + 3 * q^88 + 35 * q^89 - q^90 - 5 * q^91 + 3 * q^92 - 3 * q^94 + 6 * q^95 - 15 * q^96 + 19 * q^97 + 32 * q^98 + 3 * 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
$5$	0.656329	0.293519	0.146760	−	0.989172i	$-0.453116\pi$
$5$	0.656329	0.293519	0.146760	+	0.989172i	$0.453116\pi$
$6$	−1.00000	−0.408248
$7$	2.89208	1.09310	0.546552	−	0.837425i	$-0.315940\pi$
$7$	2.89208	1.09310	0.546552	+	0.837425i	$0.315940\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.656329	0.207550
$11$	2.55119	0.769212	0.384606	−	0.923081i	$-0.374337\pi$
$11$	2.55119	0.769212	0.384606	+	0.923081i	$0.374337\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.89208	0.772942
$15$	−0.656329	−0.169464
$16$	1.00000	0.250000
$17$	−3.68086	−0.892740	−0.446370	−	0.894848i	$-0.647284\pi$
$17$	−3.68086	−0.892740	−0.446370	+	0.894848i	$0.647284\pi$
$18$	1.00000	0.235702
$19$	2.16301	0.496228	0.248114	−	0.968731i	$-0.420189\pi$
$19$	2.16301	0.496228	0.248114	+	0.968731i	$0.420189\pi$
$20$	0.656329	0.146760
$21$	−2.89208	−0.631104
$22$	2.55119	0.543915
$23$	6.84289	1.42684	0.713421	−	0.700736i	$-0.247145\pi$
$23$	6.84289	1.42684	0.713421	+	0.700736i	$0.247145\pi$
$24$	−1.00000	−0.204124
$25$	−4.56923	−0.913846
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	2.89208	0.546552
$29$	−8.30733	−1.54263	−0.771316	−	0.636452i	$-0.780401\pi$
$29$	−8.30733	−1.54263	−0.771316	+	0.636452i	$0.780401\pi$
$30$	−0.656329	−0.119829
$31$	8.50156	1.52693	0.763463	−	0.645852i	$-0.223498\pi$
$31$	8.50156	1.52693	0.763463	+	0.645852i	$0.223498\pi$
$32$	1.00000	0.176777
$33$	−2.55119	−0.444105
$34$	−3.68086	−0.631263
$35$	1.89816	0.320847
$36$	1.00000	0.166667
$37$	−2.04906	−0.336863	−0.168432	−	0.985713i	$-0.553870\pi$
$37$	−2.04906	−0.336863	−0.168432	+	0.985713i	$0.553870\pi$
$38$	2.16301	0.350886
$39$	1.00000	0.160128
$40$	0.656329	0.103775
$41$	10.0847	1.57497	0.787483	−	0.616336i	$-0.211384\pi$
$41$	10.0847	1.57497	0.787483	+	0.616336i	$0.211384\pi$
$42$	−2.89208	−0.446258
$43$	−0.666049	−0.101571	−0.0507857	−	0.998710i	$-0.516173\pi$
$43$	−0.666049	−0.101571	−0.0507857	+	0.998710i	$0.516173\pi$
$44$	2.55119	0.384606
$45$	0.656329	0.0978398
$46$	6.84289	1.00893
$47$	−5.56855	−0.812256	−0.406128	−	0.913816i	$-0.633121\pi$
$47$	−5.56855	−0.812256	−0.406128	+	0.913816i	$0.633121\pi$
$48$	−1.00000	−0.144338
$49$	1.36415	0.194878
$50$	−4.56923	−0.646187
$51$	3.68086	0.515424
$52$	−1.00000	−0.138675
$53$	8.88913	1.22102	0.610508	−	0.792010i	$-0.290965\pi$
$53$	8.88913	1.22102	0.610508	+	0.792010i	$0.290965\pi$
$54$	−1.00000	−0.136083
$55$	1.67442	0.225779
$56$	2.89208	0.386471
$57$	−2.16301	−0.286497
$58$	−8.30733	−1.09081
$59$	6.49563	0.845659	0.422829	−	0.906209i	$-0.361037\pi$
$59$	6.49563	0.845659	0.422829	+	0.906209i	$0.361037\pi$
$60$	−0.656329	−0.0847318
$61$	3.88458	0.497370	0.248685	−	0.968584i	$-0.420002\pi$
$61$	3.88458	0.497370	0.248685	+	0.968584i	$0.420002\pi$
$62$	8.50156	1.07970
$63$	2.89208	0.364368
$64$	1.00000	0.125000
$65$	−0.656329	−0.0814076
$66$	−2.55119	−0.314030
$67$	9.97687	1.21887	0.609434	−	0.792837i	$-0.291397\pi$
$67$	9.97687	1.21887	0.609434	+	0.792837i	$0.291397\pi$
$68$	−3.68086	−0.446370
$69$	−6.84289	−0.823788
$70$	1.89816	0.226873
$71$	10.0087	1.18781	0.593905	−	0.804535i	$-0.297585\pi$
$71$	10.0087	1.18781	0.593905	+	0.804535i	$0.297585\pi$
$72$	1.00000	0.117851
$73$	−2.34621	−0.274604	−0.137302	−	0.990529i	$-0.543843\pi$
$73$	−2.34621	−0.274604	−0.137302	+	0.990529i	$0.543843\pi$
$74$	−2.04906	−0.238198
$75$	4.56923	0.527609
$76$	2.16301	0.248114
$77$	7.37825	0.840830
$78$	1.00000	0.113228
$79$	14.6755	1.65112	0.825562	−	0.564311i	$-0.190858\pi$
$79$	14.6755	1.65112	0.825562	+	0.564311i	$0.190858\pi$
$80$	0.656329	0.0733799
$81$	1.00000	0.111111
$82$	10.0847	1.11367
$83$	−0.205035	−0.0225056	−0.0112528	−	0.999937i	$-0.503582\pi$
$83$	−0.205035	−0.0225056	−0.0112528	+	0.999937i	$0.503582\pi$
$84$	−2.89208	−0.315552
$85$	−2.41586	−0.262037
$86$	−0.666049	−0.0718219
$87$	8.30733	0.890640
$88$	2.55119	0.271958
$89$	−15.8023	−1.67504	−0.837520	−	0.546407i	$-0.815995\pi$
$89$	−15.8023	−1.67504	−0.837520	+	0.546407i	$0.815995\pi$
$90$	0.656329	0.0691832
$91$	−2.89208	−0.303173
$92$	6.84289	0.713421
$93$	−8.50156	−0.881571
$94$	−5.56855	−0.574352
$95$	1.41965	0.145653
$96$	−1.00000	−0.102062
$97$	−11.3618	−1.15362	−0.576810	−	0.816878i	$-0.695703\pi$
$97$	−11.3618	−1.15362	−0.576810	+	0.816878i	$0.695703\pi$
$98$	1.36415	0.137800
$99$	2.55119	0.256404
$100$	−4.56923	−0.456923
$101$	6.72895	0.669555	0.334778	−	0.942297i	$-0.391339\pi$
$101$	6.72895	0.669555	0.334778	+	0.942297i	$0.391339\pi$
$102$	3.68086	0.364460
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	−1.89816	−0.185241
$106$	8.88913	0.863389
$107$	−7.54576	−0.729476	−0.364738	−	0.931110i	$-0.618841\pi$
$107$	−7.54576	−0.729476	−0.364738	+	0.931110i	$0.618841\pi$
$108$	−1.00000	−0.0962250
$109$	4.71913	0.452010	0.226005	−	0.974126i	$-0.427433\pi$
$109$	4.71913	0.452010	0.226005	+	0.974126i	$0.427433\pi$
$110$	1.67442	0.159650
$111$	2.04906	0.194488
$112$	2.89208	0.273276
$113$	−14.2188	−1.33759	−0.668794	−	0.743447i	$-0.733189\pi$
$113$	−14.2188	−1.33759	−0.668794	+	0.743447i	$0.733189\pi$
$114$	−2.16301	−0.202584
$115$	4.49119	0.418806
$116$	−8.30733	−0.771316
$117$	−1.00000	−0.0924500
$118$	6.49563	0.597971
$119$	−10.6454	−0.975859
$120$	−0.656329	−0.0599144
$121$	−4.49143	−0.408312
$122$	3.88458	0.351694
$123$	−10.0847	−0.909308
$124$	8.50156	0.763463
$125$	−6.28057	−0.561751
$126$	2.89208	0.257647
$127$	3.34533	0.296850	0.148425	−	0.988924i	$-0.452580\pi$
$127$	3.34533	0.296850	0.148425	+	0.988924i	$0.452580\pi$
$128$	1.00000	0.0883883
$129$	0.666049	0.0586423
$130$	−0.656329	−0.0575639
$131$	−14.1498	−1.23627	−0.618136	−	0.786071i	$-0.712112\pi$
$131$	−14.1498	−1.23627	−0.618136	+	0.786071i	$0.712112\pi$
$132$	−2.55119	−0.222052
$133$	6.25560	0.542429
$134$	9.97687	0.861870
$135$	−0.656329	−0.0564878
$136$	−3.68086	−0.315631
$137$	−4.05511	−0.346451	−0.173226	−	0.984882i	$-0.555419\pi$
$137$	−4.05511	−0.346451	−0.173226	+	0.984882i	$0.555419\pi$
$138$	−6.84289	−0.582506
$139$	0.498690	0.0422983	0.0211491	−	0.999776i	$-0.493268\pi$
$139$	0.498690	0.0422983	0.0211491	+	0.999776i	$0.493268\pi$
$140$	1.89816	0.160424
$141$	5.56855	0.468956
$142$	10.0087	0.839909
$143$	−2.55119	−0.213341
$144$	1.00000	0.0833333
$145$	−5.45235	−0.452793
$146$	−2.34621	−0.194174
$147$	−1.36415	−0.112513
$148$	−2.04906	−0.168432
$149$	20.6355	1.69052	0.845262	−	0.534353i	$-0.179445\pi$
$149$	20.6355	1.69052	0.845262	+	0.534353i	$0.179445\pi$
$150$	4.56923	0.373076
$151$	10.7708	0.876516	0.438258	−	0.898849i	$-0.355596\pi$
$151$	10.7708	0.876516	0.438258	+	0.898849i	$0.355596\pi$
$152$	2.16301	0.175443
$153$	−3.68086	−0.297580
$154$	7.37825	0.594556
$155$	5.57983	0.448182
$156$	1.00000	0.0800641
$157$	−11.2398	−0.897030	−0.448515	−	0.893775i	$-0.648047\pi$
$157$	−11.2398	−0.897030	−0.448515	+	0.893775i	$0.648047\pi$
$158$	14.6755	1.16752
$159$	−8.88913	−0.704954
$160$	0.656329	0.0518874
$161$	19.7902	1.55969
$162$	1.00000	0.0785674
$163$	10.5560	0.826808	0.413404	−	0.910548i	$-0.364340\pi$
$163$	10.5560	0.826808	0.413404	+	0.910548i	$0.364340\pi$
$164$	10.0847	0.787483
$165$	−1.67442	−0.130353
$166$	−0.205035	−0.0159138
$167$	−8.41456	−0.651138	−0.325569	−	0.945518i	$-0.605556\pi$
$167$	−8.41456	−0.651138	−0.325569	+	0.945518i	$0.605556\pi$
$168$	−2.89208	−0.223129
$169$	1.00000	0.0769231
$170$	−2.41586	−0.185288
$171$	2.16301	0.165409
$172$	−0.666049	−0.0507857
$173$	−6.31337	−0.479996	−0.239998	−	0.970773i	$-0.577147\pi$
$173$	−6.31337	−0.479996	−0.239998	+	0.970773i	$0.577147\pi$
$174$	8.30733	0.629777
$175$	−13.2146	−0.998930
$176$	2.55119	0.192303
$177$	−6.49563	−0.488241
$178$	−15.8023	−1.18443
$179$	11.2133	0.838122	0.419061	−	0.907958i	$-0.362359\pi$
$179$	11.2133	0.838122	0.419061	+	0.907958i	$0.362359\pi$
$180$	0.656329	0.0489199
$181$	4.89458	0.363811	0.181906	−	0.983316i	$-0.441773\pi$
$181$	4.89458	0.363811	0.181906	+	0.983316i	$0.441773\pi$
$182$	−2.89208	−0.214375
$183$	−3.88458	−0.287157
$184$	6.84289	0.504465
$185$	−1.34486	−0.0988759
$186$	−8.50156	−0.623365
$187$	−9.39058	−0.686707
$188$	−5.56855	−0.406128
$189$	−2.89208	−0.210368
$190$	1.41965	0.102992
$191$	17.2636	1.24915	0.624574	−	0.780966i	$-0.285273\pi$
$191$	17.2636	1.24915	0.624574	+	0.780966i	$0.285273\pi$
$192$	−1.00000	−0.0721688
$193$	−17.8750	−1.28667	−0.643335	−	0.765585i	$-0.722450\pi$
$193$	−17.8750	−1.28667	−0.643335	+	0.765585i	$0.722450\pi$
$194$	−11.3618	−0.815733
$195$	0.656329	0.0470007
$196$	1.36415	0.0974390
$197$	15.6986	1.11848	0.559238	−	0.829007i	$-0.311094\pi$
$197$	15.6986	1.11848	0.559238	+	0.829007i	$0.311094\pi$
$198$	2.55119	0.181305
$199$	10.1854	0.722027	0.361013	−	0.932561i	$-0.382431\pi$
$199$	10.1854	0.722027	0.361013	+	0.932561i	$0.382431\pi$
$200$	−4.56923	−0.323093
$201$	−9.97687	−0.703714
$202$	6.72895	0.473447
$203$	−24.0255	−1.68626
$204$	3.68086	0.257712
$205$	6.61889	0.462283
$206$	−1.00000	−0.0696733
$207$	6.84289	0.475614
$208$	−1.00000	−0.0693375
$209$	5.51824	0.381705
$210$	−1.89816	−0.130985
$211$	−11.2856	−0.776930	−0.388465	−	0.921464i	$-0.626995\pi$
$211$	−11.2856	−0.776930	−0.388465	+	0.921464i	$0.626995\pi$
$212$	8.88913	0.610508
$213$	−10.0087	−0.685782
$214$	−7.54576	−0.515818
$215$	−0.437147	−0.0298132
$216$	−1.00000	−0.0680414
$217$	24.5872	1.66909
$218$	4.71913	0.319620
$219$	2.34621	0.158542
$220$	1.67442	0.112889
$221$	3.68086	0.247602
$222$	2.04906	0.137524
$223$	12.1915	0.816406	0.408203	−	0.912891i	$-0.366156\pi$
$223$	12.1915	0.816406	0.408203	+	0.912891i	$0.366156\pi$
$224$	2.89208	0.193235
$225$	−4.56923	−0.304615
$226$	−14.2188	−0.945818
$227$	2.61611	0.173638	0.0868188	−	0.996224i	$-0.472330\pi$
$227$	2.61611	0.173638	0.0868188	+	0.996224i	$0.472330\pi$
$228$	−2.16301	−0.143249
$229$	−3.08691	−0.203989	−0.101994	−	0.994785i	$-0.532522\pi$
$229$	−3.08691	−0.203989	−0.101994	+	0.994785i	$0.532522\pi$
$230$	4.49119	0.296140
$231$	−7.37825	−0.485453
$232$	−8.30733	−0.545403
$233$	0.417209	0.0273323	0.0136661	−	0.999907i	$-0.495650\pi$
$233$	0.417209	0.0273323	0.0136661	+	0.999907i	$0.495650\pi$
$234$	−1.00000	−0.0653720
$235$	−3.65480	−0.238413
$236$	6.49563	0.422829
$237$	−14.6755	−0.953277
$238$	−10.6454	−0.690036
$239$	−21.8617	−1.41412	−0.707058	−	0.707155i	$-0.749978\pi$
$239$	−21.8617	−1.41412	−0.707058	+	0.707155i	$0.749978\pi$
$240$	−0.656329	−0.0423659
$241$	26.3640	1.69826	0.849128	−	0.528187i	$-0.177128\pi$
$241$	26.3640	1.69826	0.849128	+	0.528187i	$0.177128\pi$
$242$	−4.49143	−0.288720
$243$	−1.00000	−0.0641500
$244$	3.88458	0.248685
$245$	0.895329	0.0572005
$246$	−10.0847	−0.642978
$247$	−2.16301	−0.137629
$248$	8.50156	0.539850
$249$	0.205035	0.0129936
$250$	−6.28057	−0.397218
$251$	21.5806	1.36215	0.681077	−	0.732212i	$-0.261512\pi$
$251$	21.5806	1.36215	0.681077	+	0.732212i	$0.261512\pi$
$252$	2.89208	0.182184
$253$	17.4575	1.09754
$254$	3.34533	0.209905
$255$	2.41586	0.151287
$256$	1.00000	0.0625000
$257$	14.0027	0.873465	0.436733	−	0.899591i	$-0.356136\pi$
$257$	14.0027	0.873465	0.436733	+	0.899591i	$0.356136\pi$
$258$	0.666049	0.0414664
$259$	−5.92605	−0.368227
$260$	−0.656329	−0.0407038
$261$	−8.30733	−0.514211
$262$	−14.1498	−0.874176
$263$	13.3638	0.824049	0.412024	−	0.911173i	$-0.364822\pi$
$263$	13.3638	0.824049	0.412024	+	0.911173i	$0.364822\pi$
$264$	−2.55119	−0.157015
$265$	5.83420	0.358392
$266$	6.25560	0.383556
$267$	15.8023	0.967084
$268$	9.97687	0.609434
$269$	−14.9933	−0.914159	−0.457079	−	0.889426i	$-0.651105\pi$
$269$	−14.9933	−0.914159	−0.457079	+	0.889426i	$0.651105\pi$
$270$	−0.656329	−0.0399429
$271$	−8.95971	−0.544263	−0.272132	−	0.962260i	$-0.587729\pi$
$271$	−8.95971	−0.544263	−0.272132	+	0.962260i	$0.587729\pi$
$272$	−3.68086	−0.223185
$273$	2.89208	0.175037
$274$	−4.05511	−0.244978
$275$	−11.6570	−0.702942
$276$	−6.84289	−0.411894
$277$	15.9036	0.955556	0.477778	−	0.878480i	$-0.341442\pi$
$277$	15.9036	0.955556	0.477778	+	0.878480i	$0.341442\pi$
$278$	0.498690	0.0299094
$279$	8.50156	0.508975
$280$	1.89816	0.113437
$281$	−11.1504	−0.665177	−0.332589	−	0.943072i	$-0.607922\pi$
$281$	−11.1504	−0.665177	−0.332589	+	0.943072i	$0.607922\pi$
$282$	5.56855	0.331602
$283$	27.1978	1.61674	0.808370	−	0.588674i	$-0.200350\pi$
$283$	27.1978	1.61674	0.808370	+	0.588674i	$0.200350\pi$
$284$	10.0087	0.593905
$285$	−1.41965	−0.0840926
$286$	−2.55119	−0.150855
$287$	29.1658	1.72160
$288$	1.00000	0.0589256
$289$	−3.45125	−0.203014
$290$	−5.45235	−0.320173
$291$	11.3618	0.666043
$292$	−2.34621	−0.137302
$293$	−26.2040	−1.53086	−0.765428	−	0.643521i	$-0.777473\pi$
$293$	−26.2040	−1.53086	−0.765428	+	0.643521i	$0.777473\pi$
$294$	−1.36415	−0.0795586
$295$	4.26327	0.248217
$296$	−2.04906	−0.119099
$297$	−2.55119	−0.148035
$298$	20.6355	1.19538
$299$	−6.84289	−0.395735
$300$	4.56923	0.263805
$301$	−1.92627	−0.111028
$302$	10.7708	0.619790
$303$	−6.72895	−0.386568
$304$	2.16301	0.124057
$305$	2.54957	0.145988
$306$	−3.68086	−0.210421
$307$	7.42744	0.423906	0.211953	−	0.977280i	$-0.432018\pi$
$307$	7.42744	0.423906	0.211953	+	0.977280i	$0.432018\pi$
$308$	7.37825	0.420415
$309$	1.00000	0.0568880
$310$	5.57983	0.316913
$311$	−2.89222	−0.164003	−0.0820014	−	0.996632i	$-0.526131\pi$
$311$	−2.89222	−0.164003	−0.0820014	+	0.996632i	$0.526131\pi$
$312$	1.00000	0.0566139
$313$	−0.277979	−0.0157123	−0.00785615	−	0.999969i	$-0.502501\pi$
$313$	−0.277979	−0.0157123	−0.00785615	+	0.999969i	$0.502501\pi$
$314$	−11.2398	−0.634296
$315$	1.89816	0.106949
$316$	14.6755	0.825562
$317$	−8.02479	−0.450717	−0.225359	−	0.974276i	$-0.572355\pi$
$317$	−8.02479	−0.450717	−0.225359	+	0.974276i	$0.572355\pi$
$318$	−8.88913	−0.498478
$319$	−21.1936	−1.18661
$320$	0.656329	0.0366899
$321$	7.54576	0.421163
$322$	19.7902	1.10287
$323$	−7.96174	−0.443003
$324$	1.00000	0.0555556
$325$	4.56923	0.253455
$326$	10.5560	0.584641
$327$	−4.71913	−0.260968
$328$	10.0847	0.556835
$329$	−16.1047	−0.887881
$330$	−1.67442	−0.0921738
$331$	−24.2699	−1.33400	−0.666998	−	0.745059i	$-0.732421\pi$
$331$	−24.2699	−1.33400	−0.666998	+	0.745059i	$0.732421\pi$
$332$	−0.205035	−0.0112528
$333$	−2.04906	−0.112288
$334$	−8.41456	−0.460424
$335$	6.54811	0.357762
$336$	−2.89208	−0.157776
$337$	14.8739	0.810235	0.405118	−	0.914265i	$-0.367231\pi$
$337$	14.8739	0.810235	0.405118	+	0.914265i	$0.367231\pi$
$338$	1.00000	0.0543928
$339$	14.2188	0.772257
$340$	−2.41586	−0.131018
$341$	21.6891	1.17453
$342$	2.16301	0.116962
$343$	−16.2994	−0.880083
$344$	−0.666049	−0.0359109
$345$	−4.49119	−0.241798
$346$	−6.31337	−0.339409
$347$	−14.8380	−0.796548	−0.398274	−	0.917267i	$-0.630391\pi$
$347$	−14.8380	−0.796548	−0.398274	+	0.917267i	$0.630391\pi$
$348$	8.30733	0.445320
$349$	4.95172	0.265059	0.132530	−	0.991179i	$-0.457690\pi$
$349$	4.95172	0.265059	0.132530	+	0.991179i	$0.457690\pi$
$350$	−13.2146	−0.706350
$351$	1.00000	0.0533761
$352$	2.55119	0.135979
$353$	−18.8072	−1.00101	−0.500504	−	0.865734i	$-0.666852\pi$
$353$	−18.8072	−1.00101	−0.500504	+	0.865734i	$0.666852\pi$
$354$	−6.49563	−0.345239
$355$	6.56898	0.348645
$356$	−15.8023	−0.837520
$357$	10.6454	0.563412
$358$	11.2133	0.592641
$359$	23.9366	1.26333	0.631663	−	0.775243i	$-0.282372\pi$
$359$	23.9366	1.26333	0.631663	+	0.775243i	$0.282372\pi$
$360$	0.656329	0.0345916
$361$	−14.3214	−0.753758
$362$	4.89458	0.257254
$363$	4.49143	0.235739
$364$	−2.89208	−0.151586
$365$	−1.53989	−0.0806015
$366$	−3.88458	−0.203050
$367$	37.8746	1.97704	0.988519	−	0.151095i	$-0.0482799\pi$
$367$	37.8746	1.97704	0.988519	+	0.151095i	$0.0482799\pi$
$368$	6.84289	0.356710
$369$	10.0847	0.524989
$370$	−1.34486	−0.0699158
$371$	25.7081	1.33470
$372$	−8.50156	−0.440785
$373$	11.4552	0.593127	0.296563	−	0.955013i	$-0.404159\pi$
$373$	11.4552	0.593127	0.296563	+	0.955013i	$0.404159\pi$
$374$	−9.39058	−0.485575
$375$	6.28057	0.324327
$376$	−5.56855	−0.287176
$377$	8.30733	0.427849
$378$	−2.89208	−0.148753
$379$	27.4077	1.40784	0.703919	−	0.710280i	$-0.251432\pi$
$379$	27.4077	1.40784	0.703919	+	0.710280i	$0.251432\pi$
$380$	1.41965	0.0728263
$381$	−3.34533	−0.171386
$382$	17.2636	0.883281
$383$	−9.69866	−0.495578	−0.247789	−	0.968814i	$-0.579704\pi$
$383$	−9.69866	−0.495578	−0.247789	+	0.968814i	$0.579704\pi$
$384$	−1.00000	−0.0510310
$385$	4.84256	0.246800
$386$	−17.8750	−0.909812
$387$	−0.666049	−0.0338571
$388$	−11.3618	−0.576810
$389$	−13.6955	−0.694390	−0.347195	−	0.937793i	$-0.612866\pi$
$389$	−13.6955	−0.694390	−0.347195	+	0.937793i	$0.612866\pi$
$390$	0.656329	0.0332345
$391$	−25.1878	−1.27380
$392$	1.36415	0.0688998
$393$	14.1498	0.713762
$394$	15.6986	0.790883
$395$	9.63197	0.484637
$396$	2.55119	0.128202
$397$	0.618503	0.0310418	0.0155209	−	0.999880i	$-0.495059\pi$
$397$	0.618503	0.0310418	0.0155209	+	0.999880i	$0.495059\pi$
$398$	10.1854	0.510550
$399$	−6.25560	−0.313172
$400$	−4.56923	−0.228462
$401$	−16.0957	−0.803781	−0.401890	−	0.915688i	$-0.631647\pi$
$401$	−16.0957	−0.803781	−0.401890	+	0.915688i	$0.631647\pi$
$402$	−9.97687	−0.497601
$403$	−8.50156	−0.423493
$404$	6.72895	0.334778
$405$	0.656329	0.0326133
$406$	−24.0255	−1.19237
$407$	−5.22754	−0.259119
$408$	3.68086	0.182230
$409$	−23.0712	−1.14080	−0.570399	−	0.821367i	$-0.693212\pi$
$409$	−23.0712	−1.14080	−0.570399	+	0.821367i	$0.693212\pi$
$410$	6.61889	0.326884
$411$	4.05511	0.200024
$412$	−1.00000	−0.0492665
$413$	18.7859	0.924393
$414$	6.84289	0.336310
$415$	−0.134571	−0.00660582
$416$	−1.00000	−0.0490290
$417$	−0.498690	−0.0244209
$418$	5.51824	0.269906
$419$	21.0454	1.02813	0.514067	−	0.857750i	$-0.328138\pi$
$419$	21.0454	1.02813	0.514067	+	0.857750i	$0.328138\pi$
$420$	−1.89816	−0.0926207
$421$	28.0643	1.36777	0.683884	−	0.729591i	$-0.260289\pi$
$421$	28.0643	1.36777	0.683884	+	0.729591i	$0.260289\pi$
$422$	−11.2856	−0.549372
$423$	−5.56855	−0.270752
$424$	8.88913	0.431694
$425$	16.8187	0.815828
$426$	−10.0087	−0.484921
$427$	11.2345	0.543677
$428$	−7.54576	−0.364738
$429$	2.55119	0.123173
$430$	−0.437147	−0.0210811
$431$	−21.0838	−1.01557	−0.507785	−	0.861484i	$-0.669536\pi$
$431$	−21.0838	−1.01557	−0.507785	+	0.861484i	$0.669536\pi$
$432$	−1.00000	−0.0481125
$433$	16.3609	0.786255	0.393127	−	0.919484i	$-0.371393\pi$
$433$	16.3609	0.786255	0.393127	+	0.919484i	$0.371393\pi$
$434$	24.5872	1.18022
$435$	5.45235	0.261420
$436$	4.71913	0.226005
$437$	14.8012	0.708039
$438$	2.34621	0.112106
$439$	−29.0513	−1.38654	−0.693272	−	0.720676i	$-0.743832\pi$
$439$	−29.0513	−1.38654	−0.693272	+	0.720676i	$0.743832\pi$
$440$	1.67442	0.0798249
$441$	1.36415	0.0649593
$442$	3.68086	0.175081
$443$	−38.5298	−1.83060	−0.915302	−	0.402768i	$-0.868048\pi$
$443$	−38.5298	−1.83060	−0.915302	+	0.402768i	$0.868048\pi$
$444$	2.04906	0.0972441
$445$	−10.3715	−0.491657
$446$	12.1915	0.577286
$447$	−20.6355	−0.976024
$448$	2.89208	0.136638
$449$	0.892366	0.0421134	0.0210567	−	0.999778i	$-0.493297\pi$
$449$	0.892366	0.0421134	0.0210567	+	0.999778i	$0.493297\pi$
$450$	−4.56923	−0.215396
$451$	25.7280	1.21148
$452$	−14.2188	−0.668794
$453$	−10.7708	−0.506057
$454$	2.61611	0.122780
$455$	−1.89816	−0.0889871
$456$	−2.16301	−0.101292
$457$	−22.3844	−1.04710	−0.523549	−	0.851995i	$-0.675392\pi$
$457$	−22.3844	−1.04710	−0.523549	+	0.851995i	$0.675392\pi$
$458$	−3.08691	−0.144242
$459$	3.68086	0.171808
$460$	4.49119	0.209403
$461$	−12.2927	−0.572530	−0.286265	−	0.958150i	$-0.592414\pi$
$461$	−12.2927	−0.572530	−0.286265	+	0.958150i	$0.592414\pi$
$462$	−7.37825	−0.343267
$463$	−22.6408	−1.05221	−0.526103	−	0.850421i	$-0.676347\pi$
$463$	−22.6408	−1.05221	−0.526103	+	0.850421i	$0.676347\pi$
$464$	−8.30733	−0.385658
$465$	−5.57983	−0.258758
$466$	0.417209	0.0193268
$467$	−2.86491	−0.132572	−0.0662861	−	0.997801i	$-0.521115\pi$
$467$	−2.86491	−0.132572	−0.0662861	+	0.997801i	$0.521115\pi$
$468$	−1.00000	−0.0462250
$469$	28.8539	1.33235
$470$	−3.65480	−0.168583
$471$	11.2398	0.517901
$472$	6.49563	0.298985
$473$	−1.69922	−0.0781300
$474$	−14.6755	−0.674069
$475$	−9.88329	−0.453476
$476$	−10.6454	−0.487929
$477$	8.88913	0.407005
$478$	−21.8617	−0.999932
$479$	32.3676	1.47891	0.739456	−	0.673205i	$-0.235083\pi$
$479$	32.3676	1.47891	0.739456	+	0.673205i	$0.235083\pi$
$480$	−0.656329	−0.0299572
$481$	2.04906	0.0934291
$482$	26.3640	1.20085
$483$	−19.7902	−0.900486
$484$	−4.49143	−0.204156
$485$	−7.45711	−0.338610
$486$	−1.00000	−0.0453609
$487$	5.28092	0.239301	0.119651	−	0.992816i	$-0.461823\pi$
$487$	5.28092	0.239301	0.119651	+	0.992816i	$0.461823\pi$
$488$	3.88458	0.175847
$489$	−10.5560	−0.477358
$490$	0.895329	0.0404468
$491$	2.25221	0.101641	0.0508205	−	0.998708i	$-0.483816\pi$
$491$	2.25221	0.101641	0.0508205	+	0.998708i	$0.483816\pi$
$492$	−10.0847	−0.454654
$493$	30.5782	1.37717
$494$	−2.16301	−0.0973184
$495$	1.67442	0.0752596
$496$	8.50156	0.381731
$497$	28.9459	1.29840
$498$	0.205035	0.00918786
$499$	7.45562	0.333759	0.166880	−	0.985977i	$-0.446631\pi$
$499$	7.45562	0.333759	0.166880	+	0.985977i	$0.446631\pi$
$500$	−6.28057	−0.280876
$501$	8.41456	0.375935
$502$	21.5806	0.963188
$503$	23.1612	1.03271	0.516353	−	0.856376i	$-0.327289\pi$
$503$	23.1612	1.03271	0.516353	+	0.856376i	$0.327289\pi$
$504$	2.89208	0.128824
$505$	4.41641	0.196528
$506$	17.4575	0.776081
$507$	−1.00000	−0.0444116
$508$	3.34533	0.148425
$509$	25.8002	1.14358	0.571788	−	0.820402i	$-0.306250\pi$
$509$	25.8002	1.14358	0.571788	+	0.820402i	$0.306250\pi$
$510$	2.41586	0.106976
$511$	−6.78545	−0.300170
$512$	1.00000	0.0441942
$513$	−2.16301	−0.0954992
$514$	14.0027	0.617633
$515$	−0.656329	−0.0289213
$516$	0.666049	0.0293212
$517$	−14.2064	−0.624798
$518$	−5.92605	−0.260376
$519$	6.31337	0.277126
$520$	−0.656329	−0.0287819
$521$	17.1592	0.751758	0.375879	−	0.926669i	$-0.377341\pi$
$521$	17.1592	0.751758	0.375879	+	0.926669i	$0.377341\pi$
$522$	−8.30733	−0.363602
$523$	25.6104	1.11986	0.559932	−	0.828538i	$-0.310827\pi$
$523$	25.6104	1.11986	0.559932	+	0.828538i	$0.310827\pi$
$524$	−14.1498	−0.618136
$525$	13.2146	0.576732
$526$	13.3638	0.582691
$527$	−31.2931	−1.36315
$528$	−2.55119	−0.111026
$529$	23.8252	1.03588
$530$	5.83420	0.253421
$531$	6.49563	0.281886
$532$	6.25560	0.271215
$533$	−10.0847	−0.436817
$534$	15.8023	0.683832
$535$	−4.95251	−0.214115
$536$	9.97687	0.430935
$537$	−11.2133	−0.483890
$538$	−14.9933	−0.646408
$539$	3.48019	0.149903
$540$	−0.656329	−0.0282439
$541$	15.0116	0.645397	0.322698	−	0.946502i	$-0.395410\pi$
$541$	15.0116	0.645397	0.322698	+	0.946502i	$0.395410\pi$
$542$	−8.95971	−0.384852
$543$	−4.89458	−0.210047
$544$	−3.68086	−0.157816
$545$	3.09730	0.132674
$546$	2.89208	0.123770
$547$	27.7252	1.18545	0.592723	−	0.805406i	$-0.298053\pi$
$547$	27.7252	1.18545	0.592723	+	0.805406i	$0.298053\pi$
$548$	−4.05511	−0.173226
$549$	3.88458	0.165790
$550$	−11.6570	−0.497055
$551$	−17.9688	−0.765498
$552$	−6.84289	−0.291253
$553$	42.4428	1.80485
$554$	15.9036	0.675680
$555$	1.34486	0.0570860
$556$	0.498690	0.0211491
$557$	3.21139	0.136071	0.0680354	−	0.997683i	$-0.478327\pi$
$557$	3.21139	0.136071	0.0680354	+	0.997683i	$0.478327\pi$
$558$	8.50156	0.359900
$559$	0.666049	0.0281709
$560$	1.89816	0.0802119
$561$	9.39058	0.396470
$562$	−11.1504	−0.470351
$563$	−39.7260	−1.67425	−0.837125	−	0.547011i	$-0.815765\pi$
$563$	−39.7260	−1.67425	−0.837125	+	0.547011i	$0.815765\pi$
$564$	5.56855	0.234478
$565$	−9.33219	−0.392608
$566$	27.1978	1.14321
$567$	2.89208	0.121456
$568$	10.0087	0.419954
$569$	−7.40803	−0.310561	−0.155280	−	0.987870i	$-0.549628\pi$
$569$	−7.40803	−0.310561	−0.155280	+	0.987870i	$0.549628\pi$
$570$	−1.41965	−0.0594624
$571$	28.8822	1.20868	0.604341	−	0.796726i	$-0.293437\pi$
$571$	28.8822	1.20868	0.604341	+	0.796726i	$0.293437\pi$
$572$	−2.55119	−0.106671
$573$	−17.2636	−0.721196
$574$	29.1658	1.21736
$575$	−31.2668	−1.30391
$576$	1.00000	0.0416667
$577$	−15.8961	−0.661764	−0.330882	−	0.943672i	$-0.607346\pi$
$577$	−15.8961	−0.661764	−0.330882	+	0.943672i	$0.607346\pi$
$578$	−3.45125	−0.143553
$579$	17.8750	0.742859
$580$	−5.45235	−0.226396
$581$	−0.592979	−0.0246009
$582$	11.3618	0.470964
$583$	22.6779	0.939221
$584$	−2.34621	−0.0970870
$585$	−0.656329	−0.0271359
$586$	−26.2040	−1.08248
$587$	10.1734	0.419900	0.209950	−	0.977712i	$-0.432670\pi$
$587$	10.1734	0.419900	0.209950	+	0.977712i	$0.432670\pi$
$588$	−1.36415	−0.0562564
$589$	18.3890	0.757704
$590$	4.26327	0.175516
$591$	−15.6986	−0.645753
$592$	−2.04906	−0.0842158
$593$	34.3987	1.41259	0.706293	−	0.707920i	$-0.250366\pi$
$593$	34.3987	1.41259	0.706293	+	0.707920i	$0.250366\pi$
$594$	−2.55119	−0.104677
$595$	−6.98686	−0.286434
$596$	20.6355	0.845262
$597$	−10.1854	−0.416862
$598$	−6.84289	−0.279827
$599$	−11.9637	−0.488823	−0.244411	−	0.969672i	$-0.578595\pi$
$599$	−11.9637	−0.488823	−0.244411	+	0.969672i	$0.578595\pi$
$600$	4.56923	0.186538
$601$	−5.59948	−0.228408	−0.114204	−	0.993457i	$-0.536432\pi$
$601$	−5.59948	−0.228408	−0.114204	+	0.993457i	$0.536432\pi$
$602$	−1.92627	−0.0785088
$603$	9.97687	0.406289
$604$	10.7708	0.438258
$605$	−2.94786	−0.119848
$606$	−6.72895	−0.273345
$607$	−39.1365	−1.58850	−0.794251	−	0.607590i	$-0.792136\pi$
$607$	−39.1365	−1.58850	−0.794251	+	0.607590i	$0.792136\pi$
$608$	2.16301	0.0877216
$609$	24.0255	0.973562
$610$	2.54957	0.103229
$611$	5.56855	0.225279
$612$	−3.68086	−0.148790
$613$	−10.9031	−0.440372	−0.220186	−	0.975458i	$-0.570666\pi$
$613$	−10.9031	−0.440372	−0.220186	+	0.975458i	$0.570666\pi$
$614$	7.42744	0.299747
$615$	−6.61889	−0.266899
$616$	7.37825	0.297278
$617$	−37.6860	−1.51718	−0.758590	−	0.651569i	$-0.774111\pi$
$617$	−37.6860	−1.51718	−0.758590	+	0.651569i	$0.774111\pi$
$618$	1.00000	0.0402259
$619$	−10.7806	−0.433307	−0.216653	−	0.976249i	$-0.569514\pi$
$619$	−10.7806	−0.433307	−0.216653	+	0.976249i	$0.569514\pi$
$620$	5.57983	0.224091
$621$	−6.84289	−0.274596
$622$	−2.89222	−0.115967
$623$	−45.7015	−1.83099
$624$	1.00000	0.0400320
$625$	18.7240	0.748961
$626$	−0.277979	−0.0111103
$627$	−5.51824	−0.220377
$628$	−11.2398	−0.448515
$629$	7.54231	0.300732
$630$	1.89816	0.0756245
$631$	15.7530	0.627116	0.313558	−	0.949569i	$-0.398479\pi$
$631$	15.7530	0.627116	0.313558	+	0.949569i	$0.398479\pi$
$632$	14.6755	0.583761
$633$	11.2856	0.448561
$634$	−8.02479	−0.318705
$635$	2.19564	0.0871312
$636$	−8.88913	−0.352477
$637$	−1.36415	−0.0540494
$638$	−21.1936	−0.839062
$639$	10.0087	0.395937
$640$	0.656329	0.0259437
$641$	−23.3905	−0.923870	−0.461935	−	0.886914i	$-0.652845\pi$
$641$	−23.3905	−0.923870	−0.461935	+	0.886914i	$0.652845\pi$
$642$	7.54576	0.297807
$643$	23.0205	0.907840	0.453920	−	0.891043i	$-0.350025\pi$
$643$	23.0205	0.907840	0.453920	+	0.891043i	$0.350025\pi$
$644$	19.7902	0.779844
$645$	0.437147	0.0172127
$646$	−7.96174	−0.313250
$647$	12.2922	0.483255	0.241628	−	0.970369i	$-0.422319\pi$
$647$	12.2922	0.483255	0.241628	+	0.970369i	$0.422319\pi$
$648$	1.00000	0.0392837
$649$	16.5716	0.650491
$650$	4.56923	0.179220
$651$	−24.5872	−0.963649
$652$	10.5560	0.413404
$653$	38.7002	1.51446	0.757228	−	0.653151i	$-0.226553\pi$
$653$	38.7002	1.51446	0.757228	+	0.653151i	$0.226553\pi$
$654$	−4.71913	−0.184533
$655$	−9.28691	−0.362870
$656$	10.0847	0.393742
$657$	−2.34621	−0.0915345
$658$	−16.1047	−0.627827
$659$	−40.2741	−1.56886	−0.784429	−	0.620219i	$-0.787044\pi$
$659$	−40.2741	−1.56886	−0.784429	+	0.620219i	$0.787044\pi$
$660$	−1.67442	−0.0651767
$661$	13.5937	0.528732	0.264366	−	0.964422i	$-0.414837\pi$
$661$	13.5937	0.528732	0.264366	+	0.964422i	$0.414837\pi$
$662$	−24.2699	−0.943278
$663$	−3.68086	−0.142953
$664$	−0.205035	−0.00795692
$665$	4.10573	0.159214
$666$	−2.04906	−0.0793994
$667$	−56.8462	−2.20109
$668$	−8.41456	−0.325569
$669$	−12.1915	−0.471352
$670$	6.54811	0.252976
$671$	9.91030	0.382583
$672$	−2.89208	−0.111565
$673$	41.0267	1.58146	0.790732	−	0.612163i	$-0.209700\pi$
$673$	41.0267	1.58146	0.790732	+	0.612163i	$0.209700\pi$
$674$	14.8739	0.572923
$675$	4.56923	0.175870
$676$	1.00000	0.0384615
$677$	−11.2949	−0.434099	−0.217049	−	0.976161i	$-0.569643\pi$
$677$	−11.2949	−0.434099	−0.217049	+	0.976161i	$0.569643\pi$
$678$	14.2188	0.546068
$679$	−32.8594	−1.26103
$680$	−2.41586	−0.0926440
$681$	−2.61611	−0.100250
$682$	21.6891	0.830518
$683$	−8.47663	−0.324349	−0.162175	−	0.986762i	$-0.551851\pi$
$683$	−8.47663	−0.324349	−0.162175	+	0.986762i	$0.551851\pi$
$684$	2.16301	0.0827047
$685$	−2.66149	−0.101690
$686$	−16.2994	−0.622312
$687$	3.08691	0.117773
$688$	−0.666049	−0.0253929
$689$	−8.88913	−0.338649
$690$	−4.49119	−0.170977
$691$	−26.4454	−1.00603	−0.503015	−	0.864277i	$-0.667776\pi$
$691$	−26.4454	−1.00603	−0.503015	+	0.864277i	$0.667776\pi$
$692$	−6.31337	−0.239998
$693$	7.37825	0.280277
$694$	−14.8380	−0.563244
$695$	0.327305	0.0124154
$696$	8.30733	0.314889
$697$	−37.1204	−1.40604
$698$	4.95172	0.187425
$699$	−0.417209	−0.0157803
$700$	−13.2146	−0.499465
$701$	44.4712	1.67965	0.839826	−	0.542855i	$-0.182657\pi$
$701$	44.4712	1.67965	0.839826	+	0.542855i	$0.182657\pi$
$702$	1.00000	0.0377426
$703$	−4.43213	−0.167161
$704$	2.55119	0.0961516
$705$	3.65480	0.137648
$706$	−18.8072	−0.707820
$707$	19.4607	0.731894
$708$	−6.49563	−0.244121
$709$	39.4804	1.48272	0.741360	−	0.671108i	$-0.234181\pi$
$709$	39.4804	1.48272	0.741360	+	0.671108i	$0.234181\pi$
$710$	6.56898	0.246529
$711$	14.6755	0.550375
$712$	−15.8023	−0.592216
$713$	58.1753	2.17868
$714$	10.6454	0.398393
$715$	−1.67442	−0.0626198
$716$	11.2133	0.419061
$717$	21.8617	0.816441
$718$	23.9366	0.893307
$719$	−24.2062	−0.902738	−0.451369	−	0.892337i	$-0.649064\pi$
$719$	−24.2062	−0.902738	−0.451369	+	0.892337i	$0.649064\pi$
$720$	0.656329	0.0244600
$721$	−2.89208	−0.107707
$722$	−14.3214	−0.532987
$723$	−26.3640	−0.980489
$724$	4.89458	0.181906
$725$	37.9581	1.40973
$726$	4.49143	0.166693
$727$	−35.5726	−1.31932	−0.659658	−	0.751566i	$-0.729299\pi$
$727$	−35.5726	−1.31932	−0.659658	+	0.751566i	$0.729299\pi$
$728$	−2.89208	−0.107188
$729$	1.00000	0.0370370
$730$	−1.53989	−0.0569939
$731$	2.45163	0.0906769
$732$	−3.88458	−0.143578
$733$	11.7305	0.433276	0.216638	−	0.976252i	$-0.430491\pi$
$733$	11.7305	0.433276	0.216638	+	0.976252i	$0.430491\pi$
$734$	37.8746	1.39798
$735$	−0.895329	−0.0330247
$736$	6.84289	0.252232
$737$	25.4529	0.937569
$738$	10.0847	0.371223
$739$	18.7704	0.690480	0.345240	−	0.938514i	$-0.387798\pi$
$739$	18.7704	0.690480	0.345240	+	0.938514i	$0.387798\pi$
$740$	−1.34486	−0.0494380
$741$	2.16301	0.0794601
$742$	25.7081	0.943774
$743$	−36.6647	−1.34510	−0.672549	−	0.740053i	$-0.734801\pi$
$743$	−36.6647	−1.34510	−0.672549	+	0.740053i	$0.734801\pi$
$744$	−8.50156	−0.311682
$745$	13.5437	0.496201
$746$	11.4552	0.419404
$747$	−0.205035	−0.00750185
$748$	−9.39058	−0.343354
$749$	−21.8230	−0.797394
$750$	6.28057	0.229334
$751$	−29.2857	−1.06865	−0.534325	−	0.845279i	$-0.679434\pi$
$751$	−29.2857	−1.06865	−0.534325	+	0.845279i	$0.679434\pi$
$752$	−5.56855	−0.203064
$753$	−21.5806	−0.786440
$754$	8.30733	0.302535
$755$	7.06920	0.257274
$756$	−2.89208	−0.105184
$757$	−42.7918	−1.55529	−0.777647	−	0.628702i	$-0.783587\pi$
$757$	−42.7918	−1.55529	−0.777647	+	0.628702i	$0.783587\pi$
$758$	27.4077	0.995492
$759$	−17.4575	−0.633668
$760$	1.41965	0.0514960
$761$	−10.8233	−0.392345	−0.196172	−	0.980569i	$-0.562851\pi$
$761$	−10.8233	−0.392345	−0.196172	+	0.980569i	$0.562851\pi$
$762$	−3.34533	−0.121188
$763$	13.6481	0.494095
$764$	17.2636	0.624574
$765$	−2.41586	−0.0873456
$766$	−9.69866	−0.350427
$767$	−6.49563	−0.234543
$768$	−1.00000	−0.0360844
$769$	−49.8448	−1.79745	−0.898725	−	0.438513i	$-0.855505\pi$
$769$	−49.8448	−1.79745	−0.898725	+	0.438513i	$0.855505\pi$
$770$	4.84256	0.174514
$771$	−14.0027	−0.504295
$772$	−17.8750	−0.643335
$773$	−3.40980	−0.122642	−0.0613211	−	0.998118i	$-0.519531\pi$
$773$	−3.40980	−0.122642	−0.0613211	+	0.998118i	$0.519531\pi$
$774$	−0.666049	−0.0239406
$775$	−38.8456	−1.39538
$776$	−11.3618	−0.407866
$777$	5.92605	0.212596
$778$	−13.6955	−0.491008
$779$	21.8133	0.781543
$780$	0.656329	0.0235004
$781$	25.5340	0.913678
$782$	−25.1878	−0.900712
$783$	8.30733	0.296880
$784$	1.36415	0.0487195
$785$	−7.37698	−0.263296
$786$	14.1498	0.504706
$787$	−10.6139	−0.378345	−0.189173	−	0.981944i	$-0.560581\pi$
$787$	−10.6139	−0.378345	−0.189173	+	0.981944i	$0.560581\pi$
$788$	15.6986	0.559238
$789$	−13.3638	−0.475765
$790$	9.63197	0.342690
$791$	−41.1219	−1.46212
$792$	2.55119	0.0906526
$793$	−3.88458	−0.137946
$794$	0.618503	0.0219498
$795$	−5.83420	−0.206918
$796$	10.1854	0.361013
$797$	12.9337	0.458134	0.229067	−	0.973411i	$-0.426432\pi$
$797$	12.9337	0.458134	0.229067	+	0.973411i	$0.426432\pi$
$798$	−6.25560	−0.221446
$799$	20.4971	0.725134
$800$	−4.56923	−0.161547
$801$	−15.8023	−0.558346
$802$	−16.0957	−0.568359
$803$	−5.98563	−0.211228
$804$	−9.97687	−0.351857
$805$	12.9889	0.457799
$806$	−8.50156	−0.299455
$807$	14.9933	0.527790
$808$	6.72895	0.236724
$809$	−28.4844	−1.00146	−0.500730	−	0.865604i	$-0.666935\pi$
$809$	−28.4844	−1.00146	−0.500730	+	0.865604i	$0.666935\pi$
$810$	0.656329	0.0230611
$811$	−42.7330	−1.50056	−0.750279	−	0.661122i	$-0.770081\pi$
$811$	−42.7330	−1.50056	−0.750279	+	0.661122i	$0.770081\pi$
$812$	−24.0255	−0.843130
$813$	8.95971	0.314231
$814$	−5.22754	−0.183225
$815$	6.92820	0.242684
$816$	3.68086	0.128856
$817$	−1.44067	−0.0504026
$818$	−23.0712	−0.806667
$819$	−2.89208	−0.101058
$820$	6.61889	0.231142
$821$	0.941138	0.0328459	0.0164230	−	0.999865i	$-0.494772\pi$
$821$	0.941138	0.0328459	0.0164230	+	0.999865i	$0.494772\pi$
$822$	4.05511	0.141438
$823$	14.2890	0.498082	0.249041	−	0.968493i	$-0.419885\pi$
$823$	14.2890	0.498082	0.249041	+	0.968493i	$0.419885\pi$
$824$	−1.00000	−0.0348367
$825$	11.6570	0.405844
$826$	18.7859	0.653645
$827$	−5.91860	−0.205810	−0.102905	−	0.994691i	$-0.532814\pi$
$827$	−5.91860	−0.205810	−0.102905	+	0.994691i	$0.532814\pi$
$828$	6.84289	0.237807
$829$	22.6907	0.788080	0.394040	−	0.919093i	$-0.371077\pi$
$829$	22.6907	0.788080	0.394040	+	0.919093i	$0.371077\pi$
$830$	−0.134571	−0.00467102
$831$	−15.9036	−0.551691
$832$	−1.00000	−0.0346688
$833$	−5.02123	−0.173975
$834$	−0.498690	−0.0172682
$835$	−5.52272	−0.191122
$836$	5.51824	0.190852
$837$	−8.50156	−0.293857
$838$	21.0454	0.727001
$839$	−22.8837	−0.790035	−0.395017	−	0.918674i	$-0.629261\pi$
$839$	−22.8837	−0.790035	−0.395017	+	0.918674i	$0.629261\pi$
$840$	−1.89816	−0.0654927
$841$	40.0118	1.37972
$842$	28.0643	0.967158
$843$	11.1504	0.384040
$844$	−11.2856	−0.388465
$845$	0.656329	0.0225784
$846$	−5.56855	−0.191451
$847$	−12.9896	−0.446328
$848$	8.88913	0.305254
$849$	−27.1978	−0.933426
$850$	16.8187	0.576877
$851$	−14.0215	−0.480651
$852$	−10.0087	−0.342891
$853$	0.575726	0.0197125	0.00985625	−	0.999951i	$-0.496863\pi$
$853$	0.575726	0.0197125	0.00985625	+	0.999951i	$0.496863\pi$
$854$	11.2345	0.384438
$855$	1.41965	0.0485509
$856$	−7.54576	−0.257909
$857$	29.1028	0.994133	0.497066	−	0.867713i	$-0.334411\pi$
$857$	29.1028	0.994133	0.497066	+	0.867713i	$0.334411\pi$
$858$	2.55119	0.0870962
$859$	−18.1428	−0.619025	−0.309513	−	0.950895i	$-0.600166\pi$
$859$	−18.1428	−0.619025	−0.309513	+	0.950895i	$0.600166\pi$
$860$	−0.437147	−0.0149066
$861$	−29.1658	−0.993968
$862$	−21.0838	−0.718117
$863$	11.7829	0.401094	0.200547	−	0.979684i	$-0.435728\pi$
$863$	11.7829	0.401094	0.200547	+	0.979684i	$0.435728\pi$
$864$	−1.00000	−0.0340207
$865$	−4.14365	−0.140888
$866$	16.3609	0.555966
$867$	3.45125	0.117210
$868$	24.5872	0.834545
$869$	37.4400	1.27007
$870$	5.45235	0.184852
$871$	−9.97687	−0.338053
$872$	4.71913	0.159810
$873$	−11.3618	−0.384540
$874$	14.8012	0.500659
$875$	−18.1639	−0.614053
$876$	2.34621	0.0792712
$877$	1.75567	0.0592847	0.0296424	−	0.999561i	$-0.490563\pi$
$877$	1.75567	0.0592847	0.0296424	+	0.999561i	$0.490563\pi$
$878$	−29.0513	−0.980435
$879$	26.2040	0.883840
$880$	1.67442	0.0564447
$881$	−26.1340	−0.880477	−0.440239	−	0.897881i	$-0.645106\pi$
$881$	−26.1340	−0.880477	−0.440239	+	0.897881i	$0.645106\pi$
$882$	1.36415	0.0459332
$883$	−3.28660	−0.110603	−0.0553014	−	0.998470i	$-0.517612\pi$
$883$	−3.28660	−0.110603	−0.0553014	+	0.998470i	$0.517612\pi$
$884$	3.68086	0.123801
$885$	−4.26327	−0.143308
$886$	−38.5298	−1.29443
$887$	−25.5225	−0.856960	−0.428480	−	0.903551i	$-0.640951\pi$
$887$	−25.5225	−0.856960	−0.428480	+	0.903551i	$0.640951\pi$
$888$	2.04906	0.0687619
$889$	9.67497	0.324488
$890$	−10.3715	−0.347654
$891$	2.55119	0.0854680
$892$	12.1915	0.408203
$893$	−12.0448	−0.403065
$894$	−20.6355	−0.690153
$895$	7.35962	0.246005
$896$	2.89208	0.0966177
$897$	6.84289	0.228478
$898$	0.892366	0.0297786
$899$	−70.6253	−2.35549
$900$	−4.56923	−0.152308
$901$	−32.7197	−1.09005
$902$	25.7280	0.856649
$903$	1.92627	0.0641022
$904$	−14.2188	−0.472909
$905$	3.21246	0.106786
$906$	−10.7708	−0.357836
$907$	−54.8934	−1.82270	−0.911352	−	0.411628i	$-0.864960\pi$
$907$	−54.8934	−1.82270	−0.911352	+	0.411628i	$0.864960\pi$
$908$	2.61611	0.0868188
$909$	6.72895	0.223185
$910$	−1.89816	−0.0629234
$911$	53.0254	1.75681	0.878404	−	0.477918i	$-0.158609\pi$
$911$	53.0254	1.75681	0.878404	+	0.477918i	$0.158609\pi$
$912$	−2.16301	−0.0716244
$913$	−0.523084	−0.0173116
$914$	−22.3844	−0.740411
$915$	−2.54957	−0.0842861
$916$	−3.08691	−0.101994
$917$	−40.9223	−1.35137
$918$	3.68086	0.121487
$919$	−21.2737	−0.701754	−0.350877	−	0.936422i	$-0.614116\pi$
$919$	−21.2737	−0.701754	−0.350877	+	0.936422i	$0.614116\pi$
$920$	4.49119	0.148070
$921$	−7.42744	−0.244742
$922$	−12.2927	−0.404840
$923$	−10.0087	−0.329439
$924$	−7.37825	−0.242727
$925$	9.36263	0.307841
$926$	−22.6408	−0.744022
$927$	−1.00000	−0.0328443
$928$	−8.30733	−0.272702
$929$	−24.6312	−0.808122	−0.404061	−	0.914732i	$-0.632402\pi$
$929$	−24.6312	−0.808122	−0.404061	+	0.914732i	$0.632402\pi$
$930$	−5.57983	−0.182970
$931$	2.95066	0.0967040
$932$	0.417209	0.0136661
$933$	2.89222	0.0946870
$934$	−2.86491	−0.0937427
$935$	−6.16331	−0.201562
$936$	−1.00000	−0.0326860
$937$	41.3911	1.35219	0.676093	−	0.736816i	$-0.263672\pi$
$937$	41.3911	1.35219	0.676093	+	0.736816i	$0.263672\pi$
$938$	28.8539	0.942114
$939$	0.277979	0.00907150
$940$	−3.65480	−0.119207
$941$	−18.1667	−0.592217	−0.296108	−	0.955154i	$-0.595689\pi$
$941$	−18.1667	−0.592217	−0.296108	+	0.955154i	$0.595689\pi$
$942$	11.2398	0.366211
$943$	69.0086	2.24723
$944$	6.49563	0.211415
$945$	−1.89816	−0.0617471
$946$	−1.69922	−0.0552463
$947$	12.1010	0.393230	0.196615	−	0.980481i	$-0.437005\pi$
$947$	12.1010	0.393230	0.196615	+	0.980481i	$0.437005\pi$
$948$	−14.6755	−0.476638
$949$	2.34621	0.0761613
$950$	−9.88329	−0.320656
$951$	8.02479	0.260222
$952$	−10.6454	−0.345018
$953$	−17.9947	−0.582905	−0.291453	−	0.956585i	$-0.594139\pi$
$953$	−17.9947	−0.582905	−0.291453	+	0.956585i	$0.594139\pi$
$954$	8.88913	0.287796
$955$	11.3306	0.366649
$956$	−21.8617	−0.707058
$957$	21.1936	0.685091
$958$	32.3676	1.04575
$959$	−11.7277	−0.378707
$960$	−0.656329	−0.0211829
$961$	41.2766	1.33150
$962$	2.04906	0.0660643
$963$	−7.54576	−0.243159
$964$	26.3640	0.849128
$965$	−11.7319	−0.377662
$966$	−19.7902	−0.636740
$967$	−11.3422	−0.364741	−0.182371	−	0.983230i	$-0.558377\pi$
$967$	−11.3422	−0.364741	−0.182371	+	0.983230i	$0.558377\pi$
$968$	−4.49143	−0.144360
$969$	7.96174	0.255768
$970$	−7.45711	−0.239433
$971$	−22.8430	−0.733067	−0.366534	−	0.930405i	$-0.619456\pi$
$971$	−22.8430	−0.733067	−0.366534	+	0.930405i	$0.619456\pi$
$972$	−1.00000	−0.0320750
$973$	1.44225	0.0462365
$974$	5.28092	0.169212
$975$	−4.56923	−0.146333
$976$	3.88458	0.124342
$977$	39.8336	1.27439	0.637195	−	0.770703i	$-0.280095\pi$
$977$	39.8336	1.27439	0.637195	+	0.770703i	$0.280095\pi$
$978$	−10.5560	−0.337543
$979$	−40.3146	−1.28846
$980$	0.895329	0.0286002
$981$	4.71913	0.150670
$982$	2.25221	0.0718710
$983$	−27.4531	−0.875617	−0.437809	−	0.899068i	$-0.644245\pi$
$983$	−27.4531	−0.875617	−0.437809	+	0.899068i	$0.644245\pi$
$984$	−10.0847	−0.321489
$985$	10.3034	0.328295
$986$	30.5782	0.973807
$987$	16.1047	0.512619
$988$	−2.16301	−0.0688145
$989$	−4.55770	−0.144926
$990$	1.67442	0.0532166
$991$	4.04537	0.128506	0.0642528	−	0.997934i	$-0.479534\pi$
$991$	4.04537	0.128506	0.0642528	+	0.997934i	$0.479534\pi$
$992$	8.50156	0.269925
$993$	24.2699	0.770183
$994$	28.9459	0.918108
$995$	6.68501	0.211929
$996$	0.205035	0.00649680
$997$	−28.9642	−0.917305	−0.458652	−	0.888616i	$-0.651668\pi$
$997$	−28.9642	−0.917305	−0.458652	+	0.888616i	$0.651668\pi$
$998$	7.45562	0.236004
$999$	2.04906	0.0648294

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bc.1.9	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bc.1.9	✓	15	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.656329 q^{5} -1.00000 q^{6} +2.89208 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.656329 q^{5} -1.00000 q^{6} +2.89208 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.656329 q^{10} +2.55119 q^{11} -1.00000 q^{12} -1.00000 q^{13} +2.89208 q^{14} -0.656329 q^{15} +1.00000 q^{16} -3.68086 q^{17} +1.00000 q^{18} +2.16301 q^{19} +0.656329 q^{20} -2.89208 q^{21} +2.55119 q^{22} +6.84289 q^{23} -1.00000 q^{24} -4.56923 q^{25} -1.00000 q^{26} -1.00000 q^{27} +2.89208 q^{28} -8.30733 q^{29} -0.656329 q^{30} +8.50156 q^{31} +1.00000 q^{32} -2.55119 q^{33} -3.68086 q^{34} +1.89816 q^{35} +1.00000 q^{36} -2.04906 q^{37} +2.16301 q^{38} +1.00000 q^{39} +0.656329 q^{40} +10.0847 q^{41} -2.89208 q^{42} -0.666049 q^{43} +2.55119 q^{44} +0.656329 q^{45} +6.84289 q^{46} -5.56855 q^{47} -1.00000 q^{48} +1.36415 q^{49} -4.56923 q^{50} +3.68086 q^{51} -1.00000 q^{52} +8.88913 q^{53} -1.00000 q^{54} +1.67442 q^{55} +2.89208 q^{56} -2.16301 q^{57} -8.30733 q^{58} +6.49563 q^{59} -0.656329 q^{60} +3.88458 q^{61} +8.50156 q^{62} +2.89208 q^{63} +1.00000 q^{64} -0.656329 q^{65} -2.55119 q^{66} +9.97687 q^{67} -3.68086 q^{68} -6.84289 q^{69} +1.89816 q^{70} +10.0087 q^{71} +1.00000 q^{72} -2.34621 q^{73} -2.04906 q^{74} +4.56923 q^{75} +2.16301 q^{76} +7.37825 q^{77} +1.00000 q^{78} +14.6755 q^{79} +0.656329 q^{80} +1.00000 q^{81} +10.0847 q^{82} -0.205035 q^{83} -2.89208 q^{84} -2.41586 q^{85} -0.666049 q^{86} +8.30733 q^{87} +2.55119 q^{88} -15.8023 q^{89} +0.656329 q^{90} -2.89208 q^{91} +6.84289 q^{92} -8.50156 q^{93} -5.56855 q^{94} +1.41965 q^{95} -1.00000 q^{96} -11.3618 q^{97} +1.36415 q^{98} +2.55119 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} - 15 q^{3} + 15 q^{4} - q^{5} - 15 q^{6} + 5 q^{7} + 15 q^{8} + 15 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 - 15 * q^3 + 15 * q^4 - q^5 - 15 * q^6 + 5 * q^7 + 15 * q^8 + 15 * q^9	\( 15 q + 15 q^{2} - 15 q^{3} + 15 q^{4} - q^{5} - 15 q^{6} + 5 q^{7} + 15 q^{8} + 15 q^{9} - q^{10} + 3 q^{11} - 15 q^{12} - 15 q^{13} + 5 q^{14} + q^{15} + 15 q^{16} - 2 q^{17} + 15 q^{18} + 8 q^{19} - q^{20} - 5 q^{21} + 3 q^{22} + 3 q^{23} - 15 q^{24} + 22 q^{25} - 15 q^{26} - 15 q^{27} + 5 q^{28} + 26 q^{29} + q^{30} + 15 q^{32} - 3 q^{33} - 2 q^{34} - 8 q^{35} + 15 q^{36} + 25 q^{37} + 8 q^{38} + 15 q^{39} - q^{40} - q^{41} - 5 q^{42} + 10 q^{43} + 3 q^{44} - q^{45} + 3 q^{46} - 3 q^{47} - 15 q^{48} + 32 q^{49} + 22 q^{50} + 2 q^{51} - 15 q^{52} + 13 q^{53} - 15 q^{54} - 2 q^{55} + 5 q^{56} - 8 q^{57} + 26 q^{58} + 28 q^{59} + q^{60} + 22 q^{61} + 5 q^{63} + 15 q^{64} + q^{65} - 3 q^{66} + 29 q^{67} - 2 q^{68} - 3 q^{69} - 8 q^{70} + 18 q^{71} + 15 q^{72} + 23 q^{73} + 25 q^{74} - 22 q^{75} + 8 q^{76} + 17 q^{77} + 15 q^{78} + 27 q^{79} - q^{80} + 15 q^{81} - q^{82} + 7 q^{83} - 5 q^{84} + 43 q^{85} + 10 q^{86} - 26 q^{87} + 3 q^{88} + 35 q^{89} - q^{90} - 5 q^{91} + 3 q^{92} - 3 q^{94} + 6 q^{95} - 15 q^{96} + 19 q^{97} + 32 q^{98} + 3 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 15 * q^3 + 15 * q^4 - q^5 - 15 * q^6 + 5 * q^7 + 15 * q^8 + 15 * q^9 - q^10 + 3 * q^11 - 15 * q^12 - 15 * q^13 + 5 * q^14 + q^15 + 15 * q^16 - 2 * q^17 + 15 * q^18 + 8 * q^19 - q^20 - 5 * q^21 + 3 * q^22 + 3 * q^23 - 15 * q^24 + 22 * q^25 - 15 * q^26 - 15 * q^27 + 5 * q^28 + 26 * q^29 + q^30 + 15 * q^32 - 3 * q^33 - 2 * q^34 - 8 * q^35 + 15 * q^36 + 25 * q^37 + 8 * q^38 + 15 * q^39 - q^40 - q^41 - 5 * q^42 + 10 * q^43 + 3 * q^44 - q^45 + 3 * q^46 - 3 * q^47 - 15 * q^48 + 32 * q^49 + 22 * q^50 + 2 * q^51 - 15 * q^52 + 13 * q^53 - 15 * q^54 - 2 * q^55 + 5 * q^56 - 8 * q^57 + 26 * q^58 + 28 * q^59 + q^60 + 22 * q^61 + 5 * q^63 + 15 * q^64 + q^65 - 3 * q^66 + 29 * q^67 - 2 * q^68 - 3 * q^69 - 8 * q^70 + 18 * q^71 + 15 * q^72 + 23 * q^73 + 25 * q^74 - 22 * q^75 + 8 * q^76 + 17 * q^77 + 15 * q^78 + 27 * q^79 - q^80 + 15 * q^81 - q^82 + 7 * q^83 - 5 * q^84 + 43 * q^85 + 10 * q^86 - 26 * q^87 + 3 * q^88 + 35 * q^89 - q^90 - 5 * q^91 + 3 * q^92 - 3 * q^94 + 6 * q^95 - 15 * q^96 + 19 * q^97 + 32 * q^98 + 3 * q^99

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