LMFDB - Embedded newform 8034.2.a.r.1.4

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:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 9x^{7} + 45x^{6} + 7x^{5} - 123x^{4} + 37x^{3} + 87x^{2} - 54x + 8 $ x^9 - 4x^8 - 9x^7 + 45x^6 + 7x^5 - 123x^4 + 37x^3 + 87x^2 - 54x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.840786$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.840786 q^{5} -1.00000 q^{6} +2.87036 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.840786 q^{5} -1.00000 q^{6} +2.87036 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.840786 q^{10} +0.959226 q^{11} -1.00000 q^{12} +1.00000 q^{13} +2.87036 q^{14} +0.840786 q^{15} +1.00000 q^{16} -0.635045 q^{17} +1.00000 q^{18} +1.12227 q^{19} -0.840786 q^{20} -2.87036 q^{21} +0.959226 q^{22} -4.87791 q^{23} -1.00000 q^{24} -4.29308 q^{25} +1.00000 q^{26} -1.00000 q^{27} +2.87036 q^{28} -2.53276 q^{29} +0.840786 q^{30} -8.86299 q^{31} +1.00000 q^{32} -0.959226 q^{33} -0.635045 q^{34} -2.41336 q^{35} +1.00000 q^{36} -4.33725 q^{37} +1.12227 q^{38} -1.00000 q^{39} -0.840786 q^{40} -1.67958 q^{41} -2.87036 q^{42} -9.46454 q^{43} +0.959226 q^{44} -0.840786 q^{45} -4.87791 q^{46} -13.0759 q^{47} -1.00000 q^{48} +1.23897 q^{49} -4.29308 q^{50} +0.635045 q^{51} +1.00000 q^{52} -4.83984 q^{53} -1.00000 q^{54} -0.806503 q^{55} +2.87036 q^{56} -1.12227 q^{57} -2.53276 q^{58} +7.29208 q^{59} +0.840786 q^{60} -3.53114 q^{61} -8.86299 q^{62} +2.87036 q^{63} +1.00000 q^{64} -0.840786 q^{65} -0.959226 q^{66} +2.91288 q^{67} -0.635045 q^{68} +4.87791 q^{69} -2.41336 q^{70} +16.3127 q^{71} +1.00000 q^{72} -4.24258 q^{73} -4.33725 q^{74} +4.29308 q^{75} +1.12227 q^{76} +2.75332 q^{77} -1.00000 q^{78} -3.54035 q^{79} -0.840786 q^{80} +1.00000 q^{81} -1.67958 q^{82} +4.91365 q^{83} -2.87036 q^{84} +0.533937 q^{85} -9.46454 q^{86} +2.53276 q^{87} +0.959226 q^{88} -5.72071 q^{89} -0.840786 q^{90} +2.87036 q^{91} -4.87791 q^{92} +8.86299 q^{93} -13.0759 q^{94} -0.943588 q^{95} -1.00000 q^{96} +4.07411 q^{97} +1.23897 q^{98} +0.959226 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} - 4 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 - 4 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} - 4 q^{7} + 9 q^{8} + 9 q^{9} - 4 q^{10} - 5 q^{11} - 9 q^{12} + 9 q^{13} - 4 q^{14} + 4 q^{15} + 9 q^{16} - 6 q^{17} + 9 q^{18} - 4 q^{19} - 4 q^{20} + 4 q^{21} - 5 q^{22} - 6 q^{23} - 9 q^{24} - 11 q^{25} + 9 q^{26} - 9 q^{27} - 4 q^{28} - 19 q^{29} + 4 q^{30} - 6 q^{31} + 9 q^{32} + 5 q^{33} - 6 q^{34} + 10 q^{35} + 9 q^{36} - 13 q^{37} - 4 q^{38} - 9 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} - 20 q^{43} - 5 q^{44} - 4 q^{45} - 6 q^{46} + 14 q^{47} - 9 q^{48} - 3 q^{49} - 11 q^{50} + 6 q^{51} + 9 q^{52} - 3 q^{53} - 9 q^{54} - 4 q^{55} - 4 q^{56} + 4 q^{57} - 19 q^{58} - 9 q^{59} + 4 q^{60} - 24 q^{61} - 6 q^{62} - 4 q^{63} + 9 q^{64} - 4 q^{65} + 5 q^{66} - 4 q^{67} - 6 q^{68} + 6 q^{69} + 10 q^{70} - 9 q^{71} + 9 q^{72} - 24 q^{73} - 13 q^{74} + 11 q^{75} - 4 q^{76} + 3 q^{77} - 9 q^{78} - 15 q^{79} - 4 q^{80} + 9 q^{81} - 18 q^{82} + 20 q^{83} + 4 q^{84} - 31 q^{85} - 20 q^{86} + 19 q^{87} - 5 q^{88} + 3 q^{89} - 4 q^{90} - 4 q^{91} - 6 q^{92} + 6 q^{93} + 14 q^{94} - 4 q^{95} - 9 q^{96} - 19 q^{97} - 3 q^{98} - 5 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 - 4 * q^7 + 9 * q^8 + 9 * q^9 - 4 * q^10 - 5 * q^11 - 9 * q^12 + 9 * q^13 - 4 * q^14 + 4 * q^15 + 9 * q^16 - 6 * q^17 + 9 * q^18 - 4 * q^19 - 4 * q^20 + 4 * q^21 - 5 * q^22 - 6 * q^23 - 9 * q^24 - 11 * q^25 + 9 * q^26 - 9 * q^27 - 4 * q^28 - 19 * q^29 + 4 * q^30 - 6 * q^31 + 9 * q^32 + 5 * q^33 - 6 * q^34 + 10 * q^35 + 9 * q^36 - 13 * q^37 - 4 * q^38 - 9 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 - 20 * q^43 - 5 * q^44 - 4 * q^45 - 6 * q^46 + 14 * q^47 - 9 * q^48 - 3 * q^49 - 11 * q^50 + 6 * q^51 + 9 * q^52 - 3 * q^53 - 9 * q^54 - 4 * q^55 - 4 * q^56 + 4 * q^57 - 19 * q^58 - 9 * q^59 + 4 * q^60 - 24 * q^61 - 6 * q^62 - 4 * q^63 + 9 * q^64 - 4 * q^65 + 5 * q^66 - 4 * q^67 - 6 * q^68 + 6 * q^69 + 10 * q^70 - 9 * q^71 + 9 * q^72 - 24 * q^73 - 13 * q^74 + 11 * q^75 - 4 * q^76 + 3 * q^77 - 9 * q^78 - 15 * q^79 - 4 * q^80 + 9 * q^81 - 18 * q^82 + 20 * q^83 + 4 * q^84 - 31 * q^85 - 20 * q^86 + 19 * q^87 - 5 * q^88 + 3 * q^89 - 4 * q^90 - 4 * q^91 - 6 * q^92 + 6 * q^93 + 14 * q^94 - 4 * q^95 - 9 * q^96 - 19 * q^97 - 3 * q^98 - 5 * 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
$5$	−0.840786	−0.376011	−0.188005	−	0.982168i	$-0.560202\pi$
$5$	−0.840786	−0.376011	−0.188005	+	0.982168i	$0.560202\pi$
$6$	−1.00000	−0.408248
$7$	2.87036	1.08489	0.542447	−	0.840090i	$-0.317498\pi$
$7$	2.87036	1.08489	0.542447	+	0.840090i	$0.317498\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.840786	−0.265880
$11$	0.959226	0.289217	0.144609	−	0.989489i	$-0.453808\pi$
$11$	0.959226	0.289217	0.144609	+	0.989489i	$0.453808\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.87036	0.767136
$15$	0.840786	0.217090
$16$	1.00000	0.250000
$17$	−0.635045	−0.154021	−0.0770106	−	0.997030i	$-0.524538\pi$
$17$	−0.635045	−0.154021	−0.0770106	+	0.997030i	$0.524538\pi$
$18$	1.00000	0.235702
$19$	1.12227	0.257466	0.128733	−	0.991679i	$-0.458909\pi$
$19$	1.12227	0.257466	0.128733	+	0.991679i	$0.458909\pi$
$20$	−0.840786	−0.188005
$21$	−2.87036	−0.626364
$22$	0.959226	0.204508
$23$	−4.87791	−1.01711	−0.508557	−	0.861028i	$-0.669821\pi$
$23$	−4.87791	−1.01711	−0.508557	+	0.861028i	$0.669821\pi$
$24$	−1.00000	−0.204124
$25$	−4.29308	−0.858616
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	2.87036	0.542447
$29$	−2.53276	−0.470321	−0.235161	−	0.971957i	$-0.575562\pi$
$29$	−2.53276	−0.470321	−0.235161	+	0.971957i	$0.575562\pi$
$30$	0.840786	0.153506
$31$	−8.86299	−1.59184	−0.795920	−	0.605402i	$-0.793012\pi$
$31$	−8.86299	−1.59184	−0.795920	+	0.605402i	$0.793012\pi$
$32$	1.00000	0.176777
$33$	−0.959226	−0.166980
$34$	−0.635045	−0.108909
$35$	−2.41336	−0.407932
$36$	1.00000	0.166667
$37$	−4.33725	−0.713039	−0.356519	−	0.934288i	$-0.616037\pi$
$37$	−4.33725	−0.713039	−0.356519	+	0.934288i	$0.616037\pi$
$38$	1.12227	0.182056
$39$	−1.00000	−0.160128
$40$	−0.840786	−0.132940
$41$	−1.67958	−0.262307	−0.131153	−	0.991362i	$-0.541868\pi$
$41$	−1.67958	−0.262307	−0.131153	+	0.991362i	$0.541868\pi$
$42$	−2.87036	−0.442906
$43$	−9.46454	−1.44333	−0.721664	−	0.692243i	$-0.756623\pi$
$43$	−9.46454	−1.44333	−0.721664	+	0.692243i	$0.756623\pi$
$44$	0.959226	0.144609
$45$	−0.840786	−0.125337
$46$	−4.87791	−0.719208
$47$	−13.0759	−1.90731	−0.953655	−	0.300902i	$-0.902712\pi$
$47$	−13.0759	−1.90731	−0.953655	+	0.300902i	$0.902712\pi$
$48$	−1.00000	−0.144338
$49$	1.23897	0.176995
$50$	−4.29308	−0.607133
$51$	0.635045	0.0889241
$52$	1.00000	0.138675
$53$	−4.83984	−0.664803	−0.332402	−	0.943138i	$-0.607859\pi$
$53$	−4.83984	−0.664803	−0.332402	+	0.943138i	$0.607859\pi$
$54$	−1.00000	−0.136083
$55$	−0.806503	−0.108749
$56$	2.87036	0.383568
$57$	−1.12227	−0.148648
$58$	−2.53276	−0.332567
$59$	7.29208	0.949349	0.474674	−	0.880162i	$-0.342566\pi$
$59$	7.29208	0.949349	0.474674	+	0.880162i	$0.342566\pi$
$60$	0.840786	0.108545
$61$	−3.53114	−0.452116	−0.226058	−	0.974114i	$-0.572584\pi$
$61$	−3.53114	−0.452116	−0.226058	+	0.974114i	$0.572584\pi$
$62$	−8.86299	−1.12560
$63$	2.87036	0.361631
$64$	1.00000	0.125000
$65$	−0.840786	−0.104287
$66$	−0.959226	−0.118073
$67$	2.91288	0.355865	0.177932	−	0.984043i	$-0.443059\pi$
$67$	2.91288	0.355865	0.177932	+	0.984043i	$0.443059\pi$
$68$	−0.635045	−0.0770106
$69$	4.87791	0.587231
$70$	−2.41336	−0.288451
$71$	16.3127	1.93596	0.967981	−	0.251024i	$-0.0807675\pi$
$71$	16.3127	1.93596	0.967981	+	0.251024i	$0.0807675\pi$
$72$	1.00000	0.117851
$73$	−4.24258	−0.496557	−0.248278	−	0.968689i	$-0.579865\pi$
$73$	−4.24258	−0.496557	−0.248278	+	0.968689i	$0.579865\pi$
$74$	−4.33725	−0.504195
$75$	4.29308	0.495722
$76$	1.12227	0.128733
$77$	2.75332	0.313770
$78$	−1.00000	−0.113228
$79$	−3.54035	−0.398321	−0.199161	−	0.979967i	$-0.563822\pi$
$79$	−3.54035	−0.398321	−0.199161	+	0.979967i	$0.563822\pi$
$80$	−0.840786	−0.0940027
$81$	1.00000	0.111111
$82$	−1.67958	−0.185479
$83$	4.91365	0.539343	0.269671	−	0.962952i	$-0.413085\pi$
$83$	4.91365	0.539343	0.269671	+	0.962952i	$0.413085\pi$
$84$	−2.87036	−0.313182
$85$	0.533937	0.0579136
$86$	−9.46454	−1.02059
$87$	2.53276	0.271540
$88$	0.959226	0.102254
$89$	−5.72071	−0.606394	−0.303197	−	0.952928i	$-0.598054\pi$
$89$	−5.72071	−0.606394	−0.303197	+	0.952928i	$0.598054\pi$
$90$	−0.840786	−0.0886266
$91$	2.87036	0.300895
$92$	−4.87791	−0.508557
$93$	8.86299	0.919049
$94$	−13.0759	−1.34867
$95$	−0.943588	−0.0968100
$96$	−1.00000	−0.102062
$97$	4.07411	0.413663	0.206832	−	0.978377i	$-0.433685\pi$
$97$	4.07411	0.413663	0.206832	+	0.978377i	$0.433685\pi$
$98$	1.23897	0.125154
$99$	0.959226	0.0964058
$100$	−4.29308	−0.429308
$101$	17.3660	1.72798	0.863992	−	0.503505i	$-0.167957\pi$
$101$	17.3660	1.72798	0.863992	+	0.503505i	$0.167957\pi$
$102$	0.635045	0.0628789
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	2.41336	0.235520
$106$	−4.83984	−0.470087
$107$	−2.19333	−0.212038	−0.106019	−	0.994364i	$-0.533810\pi$
$107$	−2.19333	−0.212038	−0.106019	+	0.994364i	$0.533810\pi$
$108$	−1.00000	−0.0962250
$109$	−8.20488	−0.785885	−0.392942	−	0.919563i	$-0.628543\pi$
$109$	−8.20488	−0.785885	−0.392942	+	0.919563i	$0.628543\pi$
$110$	−0.806503	−0.0768971
$111$	4.33725	0.411673
$112$	2.87036	0.271224
$113$	16.8074	1.58111	0.790554	−	0.612393i	$-0.209793\pi$
$113$	16.8074	1.58111	0.790554	+	0.612393i	$0.209793\pi$
$114$	−1.12227	−0.105110
$115$	4.10128	0.382446
$116$	−2.53276	−0.235161
$117$	1.00000	0.0924500
$118$	7.29208	0.671291
$119$	−1.82281	−0.167097
$120$	0.840786	0.0767529
$121$	−10.0799	−0.916353
$122$	−3.53114	−0.319694
$123$	1.67958	0.151443
$124$	−8.86299	−0.795920
$125$	7.81349	0.698860
$126$	2.87036	0.255712
$127$	17.3802	1.54224	0.771122	−	0.636688i	$-0.219696\pi$
$127$	17.3802	1.54224	0.771122	+	0.636688i	$0.219696\pi$
$128$	1.00000	0.0883883
$129$	9.46454	0.833306
$130$	−0.840786	−0.0737418
$131$	−14.4680	−1.26407	−0.632036	−	0.774939i	$-0.717780\pi$
$131$	−14.4680	−1.26407	−0.632036	+	0.774939i	$0.717780\pi$
$132$	−0.959226	−0.0834899
$133$	3.22131	0.279323
$134$	2.91288	0.251634
$135$	0.840786	0.0723633
$136$	−0.635045	−0.0544547
$137$	−11.1154	−0.949649	−0.474824	−	0.880081i	$-0.657488\pi$
$137$	−11.1154	−0.949649	−0.474824	+	0.880081i	$0.657488\pi$
$138$	4.87791	0.415235
$139$	−10.0601	−0.853285	−0.426642	−	0.904420i	$-0.640304\pi$
$139$	−10.0601	−0.853285	−0.426642	+	0.904420i	$0.640304\pi$
$140$	−2.41336	−0.203966
$141$	13.0759	1.10119
$142$	16.3127	1.36893
$143$	0.959226	0.0802145
$144$	1.00000	0.0833333
$145$	2.12951	0.176846
$146$	−4.24258	−0.351119
$147$	−1.23897	−0.102188
$148$	−4.33725	−0.356519
$149$	−11.1732	−0.915346	−0.457673	−	0.889121i	$-0.651317\pi$
$149$	−11.1732	−0.915346	−0.457673	+	0.889121i	$0.651317\pi$
$150$	4.29308	0.350528
$151$	−12.2427	−0.996300	−0.498150	−	0.867091i	$-0.665987\pi$
$151$	−12.2427	−0.996300	−0.498150	+	0.867091i	$0.665987\pi$
$152$	1.12227	0.0910280
$153$	−0.635045	−0.0513404
$154$	2.75332	0.221869
$155$	7.45188	0.598549
$156$	−1.00000	−0.0800641
$157$	5.33403	0.425702	0.212851	−	0.977085i	$-0.431725\pi$
$157$	5.33403	0.425702	0.212851	+	0.977085i	$0.431725\pi$
$158$	−3.54035	−0.281655
$159$	4.83984	0.383824
$160$	−0.840786	−0.0664700
$161$	−14.0014	−1.10346
$162$	1.00000	0.0785674
$163$	−21.7156	−1.70089	−0.850447	−	0.526061i	$-0.823668\pi$
$163$	−21.7156	−1.70089	−0.850447	+	0.526061i	$0.823668\pi$
$164$	−1.67958	−0.131153
$165$	0.806503	0.0627862
$166$	4.91365	0.381373
$167$	4.21632	0.326269	0.163134	−	0.986604i	$-0.447840\pi$
$167$	4.21632	0.326269	0.163134	+	0.986604i	$0.447840\pi$
$168$	−2.87036	−0.221453
$169$	1.00000	0.0769231
$170$	0.533937	0.0409511
$171$	1.12227	0.0858220
$172$	−9.46454	−0.721664
$173$	11.2346	0.854149	0.427074	−	0.904216i	$-0.359544\pi$
$173$	11.2346	0.854149	0.427074	+	0.904216i	$0.359544\pi$
$174$	2.53276	0.192008
$175$	−12.3227	−0.931507
$176$	0.959226	0.0723044
$177$	−7.29208	−0.548107
$178$	−5.72071	−0.428785
$179$	−3.59429	−0.268650	−0.134325	−	0.990937i	$-0.542887\pi$
$179$	−3.59429	−0.268650	−0.134325	+	0.990937i	$0.542887\pi$
$180$	−0.840786	−0.0626685
$181$	−21.2458	−1.57919	−0.789593	−	0.613631i	$-0.789708\pi$
$181$	−21.2458	−1.57919	−0.789593	+	0.613631i	$0.789708\pi$
$182$	2.87036	0.212765
$183$	3.53114	0.261029
$184$	−4.87791	−0.359604
$185$	3.64669	0.268110
$186$	8.86299	0.649866
$187$	−0.609152	−0.0445456
$188$	−13.0759	−0.953655
$189$	−2.87036	−0.208788
$190$	−0.943588	−0.0684550
$191$	6.37313	0.461144	0.230572	−	0.973055i	$-0.425940\pi$
$191$	6.37313	0.461144	0.230572	+	0.973055i	$0.425940\pi$
$192$	−1.00000	−0.0721688
$193$	9.98167	0.718497	0.359248	−	0.933242i	$-0.383033\pi$
$193$	9.98167	0.718497	0.359248	+	0.933242i	$0.383033\pi$
$194$	4.07411	0.292504
$195$	0.840786	0.0602099
$196$	1.23897	0.0884976
$197$	−12.7608	−0.909170	−0.454585	−	0.890703i	$-0.650212\pi$
$197$	−12.7608	−0.909170	−0.454585	+	0.890703i	$0.650212\pi$
$198$	0.959226	0.0681692
$199$	−4.71634	−0.334332	−0.167166	−	0.985929i	$-0.553462\pi$
$199$	−4.71634	−0.334332	−0.167166	+	0.985929i	$0.553462\pi$
$200$	−4.29308	−0.303567
$201$	−2.91288	−0.205459
$202$	17.3660	1.22187
$203$	−7.26993	−0.510249
$204$	0.635045	0.0444621
$205$	1.41217	0.0986302
$206$	−1.00000	−0.0696733
$207$	−4.87791	−0.339038
$208$	1.00000	0.0693375
$209$	1.07651	0.0744637
$210$	2.41336	0.166538
$211$	12.6353	0.869852	0.434926	−	0.900466i	$-0.356775\pi$
$211$	12.6353	0.869852	0.434926	+	0.900466i	$0.356775\pi$
$212$	−4.83984	−0.332402
$213$	−16.3127	−1.11773
$214$	−2.19333	−0.149933
$215$	7.95765	0.542707
$216$	−1.00000	−0.0680414
$217$	−25.4400	−1.72698
$218$	−8.20488	−0.555705
$219$	4.24258	0.286687
$220$	−0.806503	−0.0543745
$221$	−0.635045	−0.0427178
$222$	4.33725	0.291097
$223$	−20.1062	−1.34641	−0.673205	−	0.739456i	$-0.735083\pi$
$223$	−20.1062	−1.34641	−0.673205	+	0.739456i	$0.735083\pi$
$224$	2.87036	0.191784
$225$	−4.29308	−0.286205
$226$	16.8074	1.11801
$227$	13.4638	0.893623	0.446812	−	0.894628i	$-0.352559\pi$
$227$	13.4638	0.893623	0.446812	+	0.894628i	$0.352559\pi$
$228$	−1.12227	−0.0743240
$229$	−18.3441	−1.21221	−0.606107	−	0.795383i	$-0.707270\pi$
$229$	−18.3441	−1.21221	−0.606107	+	0.795383i	$0.707270\pi$
$230$	4.10128	0.270430
$231$	−2.75332	−0.181155
$232$	−2.53276	−0.166284
$233$	9.05183	0.593005	0.296503	−	0.955032i	$-0.404180\pi$
$233$	9.05183	0.593005	0.296503	+	0.955032i	$0.404180\pi$
$234$	1.00000	0.0653720
$235$	10.9940	0.717169
$236$	7.29208	0.474674
$237$	3.54035	0.229971
$238$	−1.82281	−0.118155
$239$	7.00588	0.453173	0.226586	−	0.973991i	$-0.427243\pi$
$239$	7.00588	0.453173	0.226586	+	0.973991i	$0.427243\pi$
$240$	0.840786	0.0542725
$241$	15.9310	1.02621	0.513104	−	0.858327i	$-0.328496\pi$
$241$	15.9310	1.02621	0.513104	+	0.858327i	$0.328496\pi$
$242$	−10.0799	−0.647960
$243$	−1.00000	−0.0641500
$244$	−3.53114	−0.226058
$245$	−1.04170	−0.0665521
$246$	1.67958	0.107086
$247$	1.12227	0.0714082
$248$	−8.86299	−0.562800
$249$	−4.91365	−0.311390
$250$	7.81349	0.494169
$251$	−6.70993	−0.423527	−0.211763	−	0.977321i	$-0.567921\pi$
$251$	−6.70993	−0.423527	−0.211763	+	0.977321i	$0.567921\pi$
$252$	2.87036	0.180816
$253$	−4.67902	−0.294167
$254$	17.3802	1.09053
$255$	−0.533937	−0.0334364
$256$	1.00000	0.0625000
$257$	19.0171	1.18625	0.593127	−	0.805109i	$-0.297893\pi$
$257$	19.0171	1.18625	0.593127	+	0.805109i	$0.297893\pi$
$258$	9.46454	0.589236
$259$	−12.4495	−0.773571
$260$	−0.840786	−0.0521433
$261$	−2.53276	−0.156774
$262$	−14.4680	−0.893834
$263$	−11.2845	−0.695835	−0.347918	−	0.937525i	$-0.613111\pi$
$263$	−11.2845	−0.695835	−0.347918	+	0.937525i	$0.613111\pi$
$264$	−0.959226	−0.0590363
$265$	4.06927	0.249973
$266$	3.22131	0.197511
$267$	5.72071	0.350102
$268$	2.91288	0.177932
$269$	−13.1807	−0.803641	−0.401821	−	0.915718i	$-0.631622\pi$
$269$	−13.1807	−0.803641	−0.401821	+	0.915718i	$0.631622\pi$
$270$	0.840786	0.0511686
$271$	2.75257	0.167206	0.0836032	−	0.996499i	$-0.473357\pi$
$271$	2.75257	0.167206	0.0836032	+	0.996499i	$0.473357\pi$
$272$	−0.635045	−0.0385053
$273$	−2.87036	−0.173722
$274$	−11.1154	−0.671503
$275$	−4.11803	−0.248327
$276$	4.87791	0.293616
$277$	9.40705	0.565215	0.282607	−	0.959236i	$-0.408801\pi$
$277$	9.40705	0.565215	0.282607	+	0.959236i	$0.408801\pi$
$278$	−10.0601	−0.603363
$279$	−8.86299	−0.530613
$280$	−2.41336	−0.144226
$281$	−10.9480	−0.653103	−0.326551	−	0.945179i	$-0.605887\pi$
$281$	−10.9480	−0.653103	−0.326551	+	0.945179i	$0.605887\pi$
$282$	13.0759	0.778656
$283$	0.947236	0.0563073	0.0281537	−	0.999604i	$-0.491037\pi$
$283$	0.947236	0.0563073	0.0281537	+	0.999604i	$0.491037\pi$
$284$	16.3127	0.967981
$285$	0.943588	0.0558933
$286$	0.959226	0.0567202
$287$	−4.82101	−0.284575
$288$	1.00000	0.0589256
$289$	−16.5967	−0.976277
$290$	2.12951	0.125049
$291$	−4.07411	−0.238829
$292$	−4.24258	−0.248278
$293$	20.0668	1.17231	0.586157	−	0.810198i	$-0.300640\pi$
$293$	20.0668	1.17231	0.586157	+	0.810198i	$0.300640\pi$
$294$	−1.23897	−0.0722579
$295$	−6.13108	−0.356965
$296$	−4.33725	−0.252097
$297$	−0.959226	−0.0556599
$298$	−11.1732	−0.647247
$299$	−4.87791	−0.282097
$300$	4.29308	0.247861
$301$	−27.1666	−1.56586
$302$	−12.2427	−0.704491
$303$	−17.3660	−0.997652
$304$	1.12227	0.0643665
$305$	2.96893	0.170000
$306$	−0.635045	−0.0363031
$307$	19.8775	1.13447	0.567235	−	0.823556i	$-0.308013\pi$
$307$	19.8775	1.13447	0.567235	+	0.823556i	$0.308013\pi$
$308$	2.75332	0.156885
$309$	1.00000	0.0568880
$310$	7.45188	0.423238
$311$	6.41925	0.364002	0.182001	−	0.983298i	$-0.441743\pi$
$311$	6.41925	0.364002	0.182001	+	0.983298i	$0.441743\pi$
$312$	−1.00000	−0.0566139
$313$	−3.93875	−0.222631	−0.111316	−	0.993785i	$-0.535506\pi$
$313$	−3.93875	−0.222631	−0.111316	+	0.993785i	$0.535506\pi$
$314$	5.33403	0.301017
$315$	−2.41336	−0.135977
$316$	−3.54035	−0.199161
$317$	13.2964	0.746799	0.373400	−	0.927671i	$-0.378192\pi$
$317$	13.2964	0.746799	0.373400	+	0.927671i	$0.378192\pi$
$318$	4.83984	0.271405
$319$	−2.42949	−0.136025
$320$	−0.840786	−0.0470014
$321$	2.19333	0.122420
$322$	−14.0014	−0.780265
$323$	−0.712691	−0.0396552
$324$	1.00000	0.0555556
$325$	−4.29308	−0.238137
$326$	−21.7156	−1.20271
$327$	8.20488	0.453731
$328$	−1.67958	−0.0927394
$329$	−37.5324	−2.06923
$330$	0.806503	0.0443966
$331$	8.93355	0.491032	0.245516	−	0.969393i	$-0.421043\pi$
$331$	8.93355	0.491032	0.245516	+	0.969393i	$0.421043\pi$
$332$	4.91365	0.269671
$333$	−4.33725	−0.237680
$334$	4.21632	0.230707
$335$	−2.44911	−0.133809
$336$	−2.87036	−0.156591
$337$	15.6846	0.854394	0.427197	−	0.904158i	$-0.359501\pi$
$337$	15.6846	0.854394	0.427197	+	0.904158i	$0.359501\pi$
$338$	1.00000	0.0543928
$339$	−16.8074	−0.912853
$340$	0.533937	0.0289568
$341$	−8.50161	−0.460388
$342$	1.12227	0.0606853
$343$	−16.5362	−0.892873
$344$	−9.46454	−0.510294
$345$	−4.10128	−0.220805
$346$	11.2346	0.603974
$347$	−26.2990	−1.41180	−0.705901	−	0.708311i	$-0.749458\pi$
$347$	−26.2990	−1.41180	−0.705901	+	0.708311i	$0.749458\pi$
$348$	2.53276	0.135770
$349$	−0.469947	−0.0251557	−0.0125778	−	0.999921i	$-0.504004\pi$
$349$	−0.469947	−0.0251557	−0.0125778	+	0.999921i	$0.504004\pi$
$350$	−12.3227	−0.658675
$351$	−1.00000	−0.0533761
$352$	0.959226	0.0511269
$353$	−10.3377	−0.550220	−0.275110	−	0.961413i	$-0.588714\pi$
$353$	−10.3377	−0.550220	−0.275110	+	0.961413i	$0.588714\pi$
$354$	−7.29208	−0.387570
$355$	−13.7155	−0.727943
$356$	−5.72071	−0.303197
$357$	1.82281	0.0964733
$358$	−3.59429	−0.189964
$359$	29.8282	1.57427	0.787135	−	0.616780i	$-0.211563\pi$
$359$	29.8282	1.57427	0.787135	+	0.616780i	$0.211563\pi$
$360$	−0.840786	−0.0443133
$361$	−17.7405	−0.933711
$362$	−21.2458	−1.11665
$363$	10.0799	0.529057
$364$	2.87036	0.150448
$365$	3.56710	0.186711
$366$	3.53114	0.184575
$367$	−4.61094	−0.240689	−0.120345	−	0.992732i	$-0.538400\pi$
$367$	−4.61094	−0.240689	−0.120345	+	0.992732i	$0.538400\pi$
$368$	−4.87791	−0.254279
$369$	−1.67958	−0.0874356
$370$	3.64669	0.189583
$371$	−13.8921	−0.721241
$372$	8.86299	0.459525
$373$	12.9389	0.669950	0.334975	−	0.942227i	$-0.391272\pi$
$373$	12.9389	0.669950	0.334975	+	0.942227i	$0.391272\pi$
$374$	−0.609152	−0.0314985
$375$	−7.81349	−0.403487
$376$	−13.0759	−0.674336
$377$	−2.53276	−0.130444
$378$	−2.87036	−0.147635
$379$	−25.7972	−1.32511	−0.662555	−	0.749013i	$-0.730528\pi$
$379$	−25.7972	−1.32511	−0.662555	+	0.749013i	$0.730528\pi$
$380$	−0.943588	−0.0484050
$381$	−17.3802	−0.890414
$382$	6.37313	0.326078
$383$	−9.23126	−0.471695	−0.235848	−	0.971790i	$-0.575787\pi$
$383$	−9.23126	−0.471695	−0.235848	+	0.971790i	$0.575787\pi$
$384$	−1.00000	−0.0510310
$385$	−2.31496	−0.117981
$386$	9.98167	0.508054
$387$	−9.46454	−0.481110
$388$	4.07411	0.206832
$389$	32.5797	1.65185	0.825927	−	0.563777i	$-0.190652\pi$
$389$	32.5797	1.65185	0.825927	+	0.563777i	$0.190652\pi$
$390$	0.840786	0.0425749
$391$	3.09769	0.156657
$392$	1.23897	0.0625772
$393$	14.4680	0.729812
$394$	−12.7608	−0.642880
$395$	2.97668	0.149773
$396$	0.959226	0.0482029
$397$	38.9182	1.95325	0.976625	−	0.214949i	$-0.0689586\pi$
$397$	38.9182	1.95325	0.976625	+	0.214949i	$0.0689586\pi$
$398$	−4.71634	−0.236409
$399$	−3.22131	−0.161267
$400$	−4.29308	−0.214654
$401$	−19.2889	−0.963244	−0.481622	−	0.876379i	$-0.659952\pi$
$401$	−19.2889	−0.963244	−0.481622	+	0.876379i	$0.659952\pi$
$402$	−2.91288	−0.145281
$403$	−8.86299	−0.441497
$404$	17.3660	0.863992
$405$	−0.840786	−0.0417790
$406$	−7.26993	−0.360800
$407$	−4.16040	−0.206223
$408$	0.635045	0.0314394
$409$	−33.3527	−1.64919	−0.824594	−	0.565726i	$-0.808596\pi$
$409$	−33.3527	−1.64919	−0.824594	+	0.565726i	$0.808596\pi$
$410$	1.41217	0.0697421
$411$	11.1154	0.548280
$412$	−1.00000	−0.0492665
$413$	20.9309	1.02994
$414$	−4.87791	−0.239736
$415$	−4.13132	−0.202799
$416$	1.00000	0.0490290
$417$	10.0601	0.492644
$418$	1.07651	0.0526538
$419$	34.4802	1.68447	0.842235	−	0.539111i	$-0.181240\pi$
$419$	34.4802	1.68447	0.842235	+	0.539111i	$0.181240\pi$
$420$	2.41336	0.117760
$421$	11.2000	0.545855	0.272927	−	0.962035i	$-0.412008\pi$
$421$	11.2000	0.545855	0.272927	+	0.962035i	$0.412008\pi$
$422$	12.6353	0.615078
$423$	−13.0759	−0.635770
$424$	−4.83984	−0.235043
$425$	2.72630	0.132245
$426$	−16.3127	−0.790353
$427$	−10.1356	−0.490497
$428$	−2.19333	−0.106019
$429$	−0.959226	−0.0463119
$430$	7.95765	0.383752
$431$	−24.4670	−1.17854	−0.589268	−	0.807938i	$-0.700584\pi$
$431$	−24.4670	−1.17854	−0.589268	+	0.807938i	$0.700584\pi$
$432$	−1.00000	−0.0481125
$433$	3.45321	0.165950	0.0829752	−	0.996552i	$-0.473558\pi$
$433$	3.45321	0.165950	0.0829752	+	0.996552i	$0.473558\pi$
$434$	−25.4400	−1.22116
$435$	−2.12951	−0.102102
$436$	−8.20488	−0.392942
$437$	−5.47432	−0.261872
$438$	4.24258	0.202718
$439$	19.9667	0.952957	0.476478	−	0.879186i	$-0.341913\pi$
$439$	19.9667	0.952957	0.476478	+	0.879186i	$0.341913\pi$
$440$	−0.806503	−0.0384485
$441$	1.23897	0.0589984
$442$	−0.635045	−0.0302060
$443$	−23.4942	−1.11624	−0.558122	−	0.829759i	$-0.688478\pi$
$443$	−23.4942	−1.11624	−0.558122	+	0.829759i	$0.688478\pi$
$444$	4.33725	0.205837
$445$	4.80989	0.228011
$446$	−20.1062	−0.952055
$447$	11.1732	0.528475
$448$	2.87036	0.135612
$449$	−4.18988	−0.197732	−0.0988662	−	0.995101i	$-0.531522\pi$
$449$	−4.18988	−0.197732	−0.0988662	+	0.995101i	$0.531522\pi$
$450$	−4.29308	−0.202378
$451$	−1.61110	−0.0758637
$452$	16.8074	0.790554
$453$	12.2427	0.575214
$454$	13.4638	0.631887
$455$	−2.41336	−0.113140
$456$	−1.12227	−0.0525550
$457$	4.12176	0.192808	0.0964040	−	0.995342i	$-0.469266\pi$
$457$	4.12176	0.192808	0.0964040	+	0.995342i	$0.469266\pi$
$458$	−18.3441	−0.857165
$459$	0.635045	0.0296414
$460$	4.10128	0.191223
$461$	−11.6031	−0.540411	−0.270206	−	0.962803i	$-0.587092\pi$
$461$	−11.6031	−0.540411	−0.270206	+	0.962803i	$0.587092\pi$
$462$	−2.75332	−0.128096
$463$	12.5438	0.582962	0.291481	−	0.956577i	$-0.405852\pi$
$463$	12.5438	0.582962	0.291481	+	0.956577i	$0.405852\pi$
$464$	−2.53276	−0.117580
$465$	−7.45188	−0.345572
$466$	9.05183	0.419318
$467$	−25.9896	−1.20266	−0.601328	−	0.799002i	$-0.705362\pi$
$467$	−25.9896	−1.20266	−0.601328	+	0.799002i	$0.705362\pi$
$468$	1.00000	0.0462250
$469$	8.36101	0.386076
$470$	10.9940	0.507115
$471$	−5.33403	−0.245779
$472$	7.29208	0.335645
$473$	−9.07863	−0.417436
$474$	3.54035	0.162614
$475$	−4.81799	−0.221064
$476$	−1.82281	−0.0835483
$477$	−4.83984	−0.221601
$478$	7.00588	0.320442
$479$	−4.32007	−0.197389	−0.0986945	−	0.995118i	$-0.531467\pi$
$479$	−4.32007	−0.197389	−0.0986945	+	0.995118i	$0.531467\pi$
$480$	0.840786	0.0383765
$481$	−4.33725	−0.197761
$482$	15.9310	0.725638
$483$	14.0014	0.637084
$484$	−10.0799	−0.458177
$485$	−3.42546	−0.155542
$486$	−1.00000	−0.0453609
$487$	18.2070	0.825036	0.412518	−	0.910949i	$-0.364649\pi$
$487$	18.2070	0.825036	0.412518	+	0.910949i	$0.364649\pi$
$488$	−3.53114	−0.159847
$489$	21.7156	0.982011
$490$	−1.04170	−0.0470594
$491$	37.8351	1.70747	0.853736	−	0.520706i	$-0.174331\pi$
$491$	37.8351	1.70747	0.853736	+	0.520706i	$0.174331\pi$
$492$	1.67958	0.0757214
$493$	1.60842	0.0724394
$494$	1.12227	0.0504932
$495$	−0.806503	−0.0362496
$496$	−8.86299	−0.397960
$497$	46.8233	2.10031
$498$	−4.91365	−0.220186
$499$	−36.4658	−1.63243	−0.816216	−	0.577746i	$-0.803932\pi$
$499$	−36.4658	−1.63243	−0.816216	+	0.577746i	$0.803932\pi$
$500$	7.81349	0.349430
$501$	−4.21632	−0.188371
$502$	−6.70993	−0.299479
$503$	13.5070	0.602249	0.301125	−	0.953585i	$-0.402638\pi$
$503$	13.5070	0.602249	0.301125	+	0.953585i	$0.402638\pi$
$504$	2.87036	0.127856
$505$	−14.6011	−0.649741
$506$	−4.67902	−0.208008
$507$	−1.00000	−0.0444116
$508$	17.3802	0.771122
$509$	21.1100	0.935685	0.467843	−	0.883812i	$-0.345031\pi$
$509$	21.1100	0.935685	0.467843	+	0.883812i	$0.345031\pi$
$510$	−0.533937	−0.0236431
$511$	−12.1777	−0.538711
$512$	1.00000	0.0441942
$513$	−1.12227	−0.0495494
$514$	19.0171	0.838809
$515$	0.840786	0.0370495
$516$	9.46454	0.416653
$517$	−12.5427	−0.551627
$518$	−12.4495	−0.546998
$519$	−11.2346	−0.493143
$520$	−0.840786	−0.0368709
$521$	18.5104	0.810955	0.405478	−	0.914105i	$-0.367105\pi$
$521$	18.5104	0.810955	0.405478	+	0.914105i	$0.367105\pi$
$522$	−2.53276	−0.110856
$523$	−14.4697	−0.632718	−0.316359	−	0.948640i	$-0.602460\pi$
$523$	−14.4697	−0.632718	−0.316359	+	0.948640i	$0.602460\pi$
$524$	−14.4680	−0.632036
$525$	12.3227	0.537806
$526$	−11.2845	−0.492030
$527$	5.62840	0.245177
$528$	−0.959226	−0.0417449
$529$	0.793992	0.0345214
$530$	4.06927	0.176758
$531$	7.29208	0.316450
$532$	3.22131	0.139662
$533$	−1.67958	−0.0727508
$534$	5.72071	0.247559
$535$	1.84412	0.0797285
$536$	2.91288	0.125817
$537$	3.59429	0.155105
$538$	−13.1807	−0.568260
$539$	1.18845	0.0511901
$540$	0.840786	0.0361817
$541$	−34.6722	−1.49068	−0.745338	−	0.666687i	$-0.767712\pi$
$541$	−34.6722	−1.49068	−0.745338	+	0.666687i	$0.767712\pi$
$542$	2.75257	0.118233
$543$	21.2458	0.911743
$544$	−0.635045	−0.0272273
$545$	6.89855	0.295501
$546$	−2.87036	−0.122840
$547$	−30.9403	−1.32291	−0.661456	−	0.749984i	$-0.730061\pi$
$547$	−30.9403	−1.32291	−0.661456	+	0.749984i	$0.730061\pi$
$548$	−11.1154	−0.474824
$549$	−3.53114	−0.150705
$550$	−4.11803	−0.175593
$551$	−2.84243	−0.121092
$552$	4.87791	0.207618
$553$	−10.1621	−0.432136
$554$	9.40705	0.399667
$555$	−3.64669	−0.154794
$556$	−10.0601	−0.426642
$557$	8.17623	0.346438	0.173219	−	0.984883i	$-0.444583\pi$
$557$	8.17623	0.346438	0.173219	+	0.984883i	$0.444583\pi$
$558$	−8.86299	−0.375200
$559$	−9.46454	−0.400307
$560$	−2.41336	−0.101983
$561$	0.609152	0.0257184
$562$	−10.9480	−0.461813
$563$	24.2383	1.02152	0.510762	−	0.859722i	$-0.329363\pi$
$563$	24.2383	1.02152	0.510762	+	0.859722i	$0.329363\pi$
$564$	13.0759	0.550593
$565$	−14.1314	−0.594514
$566$	0.947236	0.0398153
$567$	2.87036	0.120544
$568$	16.3127	0.684466
$569$	2.73985	0.114860	0.0574301	−	0.998350i	$-0.481709\pi$
$569$	2.73985	0.114860	0.0574301	+	0.998350i	$0.481709\pi$
$570$	0.943588	0.0395225
$571$	−13.7388	−0.574949	−0.287474	−	0.957788i	$-0.592816\pi$
$571$	−13.7388	−0.574949	−0.287474	+	0.957788i	$0.592816\pi$
$572$	0.959226	0.0401072
$573$	−6.37313	−0.266241
$574$	−4.82101	−0.201225
$575$	20.9412	0.873310
$576$	1.00000	0.0416667
$577$	3.15137	0.131193	0.0655965	−	0.997846i	$-0.479105\pi$
$577$	3.15137	0.131193	0.0655965	+	0.997846i	$0.479105\pi$
$578$	−16.5967	−0.690332
$579$	−9.98167	−0.414824
$580$	2.12951	0.0884230
$581$	14.1039	0.585130
$582$	−4.07411	−0.168877
$583$	−4.64250	−0.192273
$584$	−4.24258	−0.175559
$585$	−0.840786	−0.0347622
$586$	20.0668	0.828951
$587$	−3.59798	−0.148505	−0.0742523	−	0.997239i	$-0.523657\pi$
$587$	−3.59798	−0.148505	−0.0742523	+	0.997239i	$0.523657\pi$
$588$	−1.23897	−0.0510941
$589$	−9.94665	−0.409845
$590$	−6.13108	−0.252413
$591$	12.7608	0.524910
$592$	−4.33725	−0.178260
$593$	−26.8743	−1.10359	−0.551797	−	0.833979i	$-0.686058\pi$
$593$	−26.8743	−1.10359	−0.551797	+	0.833979i	$0.686058\pi$
$594$	−0.959226	−0.0393575
$595$	1.53259	0.0628301
$596$	−11.1732	−0.457673
$597$	4.71634	0.193027
$598$	−4.87791	−0.199473
$599$	−24.5483	−1.00301	−0.501507	−	0.865153i	$-0.667221\pi$
$599$	−24.5483	−1.00301	−0.501507	+	0.865153i	$0.667221\pi$
$600$	4.29308	0.175264
$601$	−12.8884	−0.525729	−0.262864	−	0.964833i	$-0.584667\pi$
$601$	−12.8884	−0.525729	−0.262864	+	0.964833i	$0.584667\pi$
$602$	−27.1666	−1.10723
$603$	2.91288	0.118622
$604$	−12.2427	−0.498150
$605$	8.47503	0.344559
$606$	−17.3660	−0.705447
$607$	31.3913	1.27413	0.637066	−	0.770809i	$-0.280148\pi$
$607$	31.3913	1.27413	0.637066	+	0.770809i	$0.280148\pi$
$608$	1.12227	0.0455140
$609$	7.26993	0.294592
$610$	2.96893	0.120208
$611$	−13.0759	−0.528993
$612$	−0.635045	−0.0256702
$613$	22.5065	0.909029	0.454514	−	0.890739i	$-0.349813\pi$
$613$	22.5065	0.909029	0.454514	+	0.890739i	$0.349813\pi$
$614$	19.8775	0.802191
$615$	−1.41217	−0.0569442
$616$	2.75332	0.110935
$617$	−23.4723	−0.944961	−0.472481	−	0.881341i	$-0.656641\pi$
$617$	−23.4723	−0.944961	−0.472481	+	0.881341i	$0.656641\pi$
$618$	1.00000	0.0402259
$619$	−15.1948	−0.610733	−0.305366	−	0.952235i	$-0.598779\pi$
$619$	−15.1948	−0.610733	−0.305366	+	0.952235i	$0.598779\pi$
$620$	7.45188	0.299275
$621$	4.87791	0.195744
$622$	6.41925	0.257389
$623$	−16.4205	−0.657873
$624$	−1.00000	−0.0400320
$625$	14.8959	0.595837
$626$	−3.93875	−0.157424
$627$	−1.07651	−0.0429916
$628$	5.33403	0.212851
$629$	2.75435	0.109823
$630$	−2.41336	−0.0961505
$631$	49.8506	1.98452	0.992261	−	0.124170i	$-0.0396267\pi$
$631$	49.8506	1.98452	0.992261	+	0.124170i	$0.0396267\pi$
$632$	−3.54035	−0.140828
$633$	−12.6353	−0.502209
$634$	13.2964	0.528067
$635$	−14.6130	−0.579900
$636$	4.83984	0.191912
$637$	1.23897	0.0490896
$638$	−2.42949	−0.0961843
$639$	16.3127	0.645320
$640$	−0.840786	−0.0332350
$641$	33.9141	1.33953	0.669764	−	0.742574i	$-0.266395\pi$
$641$	33.9141	1.33953	0.669764	+	0.742574i	$0.266395\pi$
$642$	2.19333	0.0865640
$643$	−37.6032	−1.48292	−0.741462	−	0.670995i	$-0.765867\pi$
$643$	−37.6032	−1.48292	−0.741462	+	0.670995i	$0.765867\pi$
$644$	−14.0014	−0.551731
$645$	−7.95765	−0.313332
$646$	−0.712691	−0.0280405
$647$	21.5299	0.846428	0.423214	−	0.906030i	$-0.360902\pi$
$647$	21.5299	0.846428	0.423214	+	0.906030i	$0.360902\pi$
$648$	1.00000	0.0392837
$649$	6.99475	0.274568
$650$	−4.29308	−0.168388
$651$	25.4400	0.997071
$652$	−21.7156	−0.850447
$653$	−46.4226	−1.81666	−0.908329	−	0.418257i	$-0.862641\pi$
$653$	−46.4226	−1.81666	−0.908329	+	0.418257i	$0.862641\pi$
$654$	8.20488	0.320836
$655$	12.1645	0.475305
$656$	−1.67958	−0.0655767
$657$	−4.24258	−0.165519
$658$	−37.5324	−1.46317
$659$	−8.08772	−0.315053	−0.157526	−	0.987515i	$-0.550352\pi$
$659$	−8.08772	−0.315053	−0.157526	+	0.987515i	$0.550352\pi$
$660$	0.806503	0.0313931
$661$	18.8441	0.732952	0.366476	−	0.930428i	$-0.380564\pi$
$661$	18.8441	0.732952	0.366476	+	0.930428i	$0.380564\pi$
$662$	8.93355	0.347212
$663$	0.635045	0.0246631
$664$	4.91365	0.190686
$665$	−2.70844	−0.105029
$666$	−4.33725	−0.168065
$667$	12.3546	0.478371
$668$	4.21632	0.163134
$669$	20.1062	0.777350
$670$	−2.44911	−0.0946173
$671$	−3.38716	−0.130760
$672$	−2.87036	−0.110727
$673$	−25.9224	−0.999235	−0.499617	−	0.866246i	$-0.666526\pi$
$673$	−25.9224	−0.999235	−0.499617	+	0.866246i	$0.666526\pi$
$674$	15.6846	0.604148
$675$	4.29308	0.165241
$676$	1.00000	0.0384615
$677$	−19.9238	−0.765732	−0.382866	−	0.923804i	$-0.625063\pi$
$677$	−19.9238	−0.765732	−0.382866	+	0.923804i	$0.625063\pi$
$678$	−16.8074	−0.645484
$679$	11.6942	0.448781
$680$	0.533937	0.0204756
$681$	−13.4638	−0.515934
$682$	−8.50161	−0.325543
$683$	13.0916	0.500934	0.250467	−	0.968125i	$-0.419416\pi$
$683$	13.0916	0.500934	0.250467	+	0.968125i	$0.419416\pi$
$684$	1.12227	0.0429110
$685$	9.34563	0.357078
$686$	−16.5362	−0.631357
$687$	18.3441	0.699873
$688$	−9.46454	−0.360832
$689$	−4.83984	−0.184383
$690$	−4.10128	−0.156133
$691$	19.9999	0.760834	0.380417	−	0.924815i	$-0.375781\pi$
$691$	19.9999	0.760834	0.380417	+	0.924815i	$0.375781\pi$
$692$	11.2346	0.427074
$693$	2.75332	0.104590
$694$	−26.2990	−0.998295
$695$	8.45837	0.320844
$696$	2.53276	0.0960039
$697$	1.06661	0.0404008
$698$	−0.469947	−0.0177877
$699$	−9.05183	−0.342372
$700$	−12.3227	−0.465754
$701$	−14.2446	−0.538012	−0.269006	−	0.963138i	$-0.586695\pi$
$701$	−14.2446	−0.538012	−0.269006	+	0.963138i	$0.586695\pi$
$702$	−1.00000	−0.0377426
$703$	−4.86755	−0.183583
$704$	0.959226	0.0361522
$705$	−10.9940	−0.414058
$706$	−10.3377	−0.389064
$707$	49.8468	1.87468
$708$	−7.29208	−0.274053
$709$	−2.56981	−0.0965113	−0.0482556	−	0.998835i	$-0.515366\pi$
$709$	−2.56981	−0.0965113	−0.0482556	+	0.998835i	$0.515366\pi$
$710$	−13.7155	−0.514733
$711$	−3.54035	−0.132774
$712$	−5.72071	−0.214393
$713$	43.2328	1.61908
$714$	1.82281	0.0682169
$715$	−0.806503	−0.0301615
$716$	−3.59429	−0.134325
$717$	−7.00588	−0.261640
$718$	29.8282	1.11318
$719$	14.9190	0.556385	0.278193	−	0.960525i	$-0.410265\pi$
$719$	14.9190	0.556385	0.278193	+	0.960525i	$0.410265\pi$
$720$	−0.840786	−0.0313342
$721$	−2.87036	−0.106898
$722$	−17.7405	−0.660234
$723$	−15.9310	−0.592481
$724$	−21.2458	−0.789593
$725$	10.8733	0.403825
$726$	10.0799	0.374100
$727$	20.1508	0.747352	0.373676	−	0.927559i	$-0.378097\pi$
$727$	20.1508	0.747352	0.373676	+	0.927559i	$0.378097\pi$
$728$	2.87036	0.106383
$729$	1.00000	0.0370370
$730$	3.56710	0.132024
$731$	6.01041	0.222303
$732$	3.53114	0.130515
$733$	−27.0536	−0.999246	−0.499623	−	0.866243i	$-0.666528\pi$
$733$	−27.0536	−0.999246	−0.499623	+	0.866243i	$0.666528\pi$
$734$	−4.61094	−0.170193
$735$	1.04170	0.0384239
$736$	−4.87791	−0.179802
$737$	2.79411	0.102922
$738$	−1.67958	−0.0618263
$739$	−3.29221	−0.121106	−0.0605530	−	0.998165i	$-0.519286\pi$
$739$	−3.29221	−0.121106	−0.0605530	+	0.998165i	$0.519286\pi$
$740$	3.64669	0.134055
$741$	−1.12227	−0.0412276
$742$	−13.8921	−0.509994
$743$	−23.3367	−0.856140	−0.428070	−	0.903746i	$-0.640806\pi$
$743$	−23.3367	−0.856140	−0.428070	+	0.903746i	$0.640806\pi$
$744$	8.86299	0.324933
$745$	9.39429	0.344180
$746$	12.9389	0.473726
$747$	4.91365	0.179781
$748$	−0.609152	−0.0222728
$749$	−6.29566	−0.230038
$750$	−7.81349	−0.285308
$751$	−3.01694	−0.110090	−0.0550448	−	0.998484i	$-0.517530\pi$
$751$	−3.01694	−0.110090	−0.0550448	+	0.998484i	$0.517530\pi$
$752$	−13.0759	−0.476827
$753$	6.70993	0.244523
$754$	−2.53276	−0.0922376
$755$	10.2935	0.374620
$756$	−2.87036	−0.104394
$757$	−38.7473	−1.40830	−0.704148	−	0.710054i	$-0.748671\pi$
$757$	−38.7473	−1.40830	−0.704148	+	0.710054i	$0.748671\pi$
$758$	−25.7972	−0.936995
$759$	4.67902	0.169837
$760$	−0.943588	−0.0342275
$761$	−15.0828	−0.546753	−0.273376	−	0.961907i	$-0.588140\pi$
$761$	−15.0828	−0.546753	−0.273376	+	0.961907i	$0.588140\pi$
$762$	−17.3802	−0.629618
$763$	−23.5510	−0.852602
$764$	6.37313	0.230572
$765$	0.533937	0.0193045
$766$	−9.23126	−0.333539
$767$	7.29208	0.263302
$768$	−1.00000	−0.0360844
$769$	−21.2712	−0.767059	−0.383529	−	0.923529i	$-0.625292\pi$
$769$	−21.2712	−0.767059	−0.383529	+	0.923529i	$0.625292\pi$
$770$	−2.31496	−0.0834252
$771$	−19.0171	−0.684884
$772$	9.98167	0.359248
$773$	−20.9555	−0.753718	−0.376859	−	0.926271i	$-0.622996\pi$
$773$	−20.9555	−0.753718	−0.376859	+	0.926271i	$0.622996\pi$
$774$	−9.46454	−0.340196
$775$	38.0495	1.36678
$776$	4.07411	0.146252
$777$	12.4495	0.446622
$778$	32.5797	1.16804
$779$	−1.88494	−0.0675351
$780$	0.840786	0.0301050
$781$	15.6476	0.559914
$782$	3.09769	0.110773
$783$	2.53276	0.0905134
$784$	1.23897	0.0442488
$785$	−4.48478	−0.160069
$786$	14.4680	0.516055
$787$	0.715717	0.0255125	0.0127563	−	0.999919i	$-0.495939\pi$
$787$	0.715717	0.0255125	0.0127563	+	0.999919i	$0.495939\pi$
$788$	−12.7608	−0.454585
$789$	11.2845	0.401741
$790$	2.97668	0.105906
$791$	48.2433	1.71533
$792$	0.959226	0.0340846
$793$	−3.53114	−0.125394
$794$	38.9182	1.38116
$795$	−4.06927	−0.144322
$796$	−4.71634	−0.167166
$797$	−38.1159	−1.35013	−0.675067	−	0.737757i	$-0.735885\pi$
$797$	−38.1159	−1.35013	−0.675067	+	0.737757i	$0.735885\pi$
$798$	−3.22131	−0.114033
$799$	8.30376	0.293766
$800$	−4.29308	−0.151783
$801$	−5.72071	−0.202131
$802$	−19.2889	−0.681116
$803$	−4.06959	−0.143613
$804$	−2.91288	−0.102729
$805$	11.7721	0.414913
$806$	−8.86299	−0.312185
$807$	13.1807	0.463983
$808$	17.3660	0.610935
$809$	31.1047	1.09358	0.546791	−	0.837269i	$-0.315849\pi$
$809$	31.1047	1.09358	0.546791	+	0.837269i	$0.315849\pi$
$810$	−0.840786	−0.0295422
$811$	36.5722	1.28422	0.642111	−	0.766612i	$-0.278059\pi$
$811$	36.5722	1.28422	0.642111	+	0.766612i	$0.278059\pi$
$812$	−7.26993	−0.255124
$813$	−2.75257	−0.0965367
$814$	−4.16040	−0.145822
$815$	18.2581	0.639554
$816$	0.635045	0.0222310
$817$	−10.6218	−0.371608
$818$	−33.3527	−1.16615
$819$	2.87036	0.100298
$820$	1.41217	0.0493151
$821$	−17.1087	−0.597097	−0.298548	−	0.954394i	$-0.596502\pi$
$821$	−17.1087	−0.597097	−0.298548	+	0.954394i	$0.596502\pi$
$822$	11.1154	0.387693
$823$	−8.11106	−0.282734	−0.141367	−	0.989957i	$-0.545150\pi$
$823$	−8.11106	−0.282734	−0.141367	+	0.989957i	$0.545150\pi$
$824$	−1.00000	−0.0348367
$825$	4.11803	0.143371
$826$	20.9309	0.728279
$827$	−8.29080	−0.288299	−0.144150	−	0.989556i	$-0.546045\pi$
$827$	−8.29080	−0.288299	−0.144150	+	0.989556i	$0.546045\pi$
$828$	−4.87791	−0.169519
$829$	−5.82808	−0.202417	−0.101209	−	0.994865i	$-0.532271\pi$
$829$	−5.82808	−0.202417	−0.101209	+	0.994865i	$0.532271\pi$
$830$	−4.13132	−0.143400
$831$	−9.40705	−0.326327
$832$	1.00000	0.0346688
$833$	−0.786799	−0.0272610
$834$	10.0601	0.348352
$835$	−3.54503	−0.122681
$836$	1.07651	0.0372318
$837$	8.86299	0.306350
$838$	34.4802	1.19110
$839$	26.2119	0.904935	0.452468	−	0.891781i	$-0.350544\pi$
$839$	26.2119	0.904935	0.452468	+	0.891781i	$0.350544\pi$
$840$	2.41336	0.0832688
$841$	−22.5851	−0.778798
$842$	11.2000	0.385978
$843$	10.9480	0.377069
$844$	12.6353	0.434926
$845$	−0.840786	−0.0289239
$846$	−13.0759	−0.449557
$847$	−28.9329	−0.994146
$848$	−4.83984	−0.166201
$849$	−0.947236	−0.0325091
$850$	2.72630	0.0935113
$851$	21.1567	0.725242
$852$	−16.3127	−0.558864
$853$	−3.60158	−0.123316	−0.0616578	−	0.998097i	$-0.519639\pi$
$853$	−3.60158	−0.123316	−0.0616578	+	0.998097i	$0.519639\pi$
$854$	−10.1356	−0.346834
$855$	−0.943588	−0.0322700
$856$	−2.19333	−0.0749666
$857$	−22.2768	−0.760962	−0.380481	−	0.924789i	$-0.624242\pi$
$857$	−22.2768	−0.760962	−0.380481	+	0.924789i	$0.624242\pi$
$858$	−0.959226	−0.0327474
$859$	27.4258	0.935757	0.467879	−	0.883793i	$-0.345018\pi$
$859$	27.4258	0.935757	0.467879	+	0.883793i	$0.345018\pi$
$860$	7.95765	0.271354
$861$	4.82101	0.164299
$862$	−24.4670	−0.833351
$863$	−25.7496	−0.876527	−0.438264	−	0.898846i	$-0.644406\pi$
$863$	−25.7496	−0.876527	−0.438264	+	0.898846i	$0.644406\pi$
$864$	−1.00000	−0.0340207
$865$	−9.44587	−0.321169
$866$	3.45321	0.117345
$867$	16.5967	0.563654
$868$	−25.4400	−0.863489
$869$	−3.39600	−0.115201
$870$	−2.12951	−0.0721971
$871$	2.91288	0.0986992
$872$	−8.20488	−0.277852
$873$	4.07411	0.137888
$874$	−5.47432	−0.185172
$875$	22.4275	0.758189
$876$	4.24258	0.143344
$877$	3.11144	0.105066	0.0525329	−	0.998619i	$-0.483271\pi$
$877$	3.11144	0.105066	0.0525329	+	0.998619i	$0.483271\pi$
$878$	19.9667	0.673842
$879$	−20.0668	−0.676835
$880$	−0.806503	−0.0271872
$881$	44.6220	1.50335	0.751677	−	0.659531i	$-0.229245\pi$
$881$	44.6220	1.50335	0.751677	+	0.659531i	$0.229245\pi$
$882$	1.23897	0.0417181
$883$	−6.71113	−0.225848	−0.112924	−	0.993604i	$-0.536022\pi$
$883$	−6.71113	−0.225848	−0.112924	+	0.993604i	$0.536022\pi$
$884$	−0.635045	−0.0213589
$885$	6.13108	0.206094
$886$	−23.4942	−0.789303
$887$	1.16264	0.0390375	0.0195187	−	0.999809i	$-0.493787\pi$
$887$	1.16264	0.0390375	0.0195187	+	0.999809i	$0.493787\pi$
$888$	4.33725	0.145548
$889$	49.8874	1.67317
$890$	4.80989	0.161228
$891$	0.959226	0.0321353
$892$	−20.1062	−0.673205
$893$	−14.6746	−0.491068
$894$	11.1732	0.373688
$895$	3.02203	0.101015
$896$	2.87036	0.0958920
$897$	4.87791	0.162869
$898$	−4.18988	−0.139818
$899$	22.4478	0.748676
$900$	−4.29308	−0.143103
$901$	3.07352	0.102394
$902$	−1.61110	−0.0536437
$903$	27.1666	0.904049
$904$	16.8074	0.559006
$905$	17.8631	0.593791
$906$	12.2427	0.406738
$907$	55.2315	1.83393	0.916966	−	0.398966i	$-0.130631\pi$
$907$	55.2315	1.83393	0.916966	+	0.398966i	$0.130631\pi$
$908$	13.4638	0.446812
$909$	17.3660	0.575995
$910$	−2.41336	−0.0800020
$911$	−13.4307	−0.444979	−0.222489	−	0.974935i	$-0.571418\pi$
$911$	−13.4307	−0.444979	−0.222489	+	0.974935i	$0.571418\pi$
$912$	−1.12227	−0.0371620
$913$	4.71329	0.155987
$914$	4.12176	0.136336
$915$	−2.96893	−0.0981498
$916$	−18.3441	−0.606107
$917$	−41.5283	−1.37138
$918$	0.635045	0.0209596
$919$	−4.06308	−0.134029	−0.0670143	−	0.997752i	$-0.521347\pi$
$919$	−4.06308	−0.134029	−0.0670143	+	0.997752i	$0.521347\pi$
$920$	4.10128	0.135215
$921$	−19.8775	−0.654986
$922$	−11.6031	−0.382128
$923$	16.3127	0.536939
$924$	−2.75332	−0.0905777
$925$	18.6201	0.612226
$926$	12.5438	0.412216
$927$	−1.00000	−0.0328443
$928$	−2.53276	−0.0831418
$929$	−23.5782	−0.773576	−0.386788	−	0.922169i	$-0.626416\pi$
$929$	−23.5782	−0.773576	−0.386788	+	0.922169i	$0.626416\pi$
$930$	−7.45188	−0.244357
$931$	1.39045	0.0455702
$932$	9.05183	0.296503
$933$	−6.41925	−0.210157
$934$	−25.9896	−0.850406
$935$	0.512166	0.0167496
$936$	1.00000	0.0326860
$937$	15.2804	0.499190	0.249595	−	0.968350i	$-0.419702\pi$
$937$	15.2804	0.499190	0.249595	+	0.968350i	$0.419702\pi$
$938$	8.36101	0.272997
$939$	3.93875	0.128536
$940$	10.9940	0.358585
$941$	16.7263	0.545263	0.272632	−	0.962118i	$-0.412106\pi$
$941$	16.7263	0.545263	0.272632	+	0.962118i	$0.412106\pi$
$942$	−5.33403	−0.173792
$943$	8.19285	0.266796
$944$	7.29208	0.237337
$945$	2.41336	0.0785065
$946$	−9.07863	−0.295172
$947$	45.8657	1.49043	0.745217	−	0.666822i	$-0.232346\pi$
$947$	45.8657	1.49043	0.745217	+	0.666822i	$0.232346\pi$
$948$	3.54035	0.114985
$949$	−4.24258	−0.137720
$950$	−4.81799	−0.156316
$951$	−13.2964	−0.431165
$952$	−1.82281	−0.0590776
$953$	−10.9743	−0.355492	−0.177746	−	0.984076i	$-0.556881\pi$
$953$	−10.9743	−0.355492	−0.177746	+	0.984076i	$0.556881\pi$
$954$	−4.83984	−0.156696
$955$	−5.35844	−0.173395
$956$	7.00588	0.226586
$957$	2.42949	0.0785341
$958$	−4.32007	−0.139575
$959$	−31.9051	−1.03027
$960$	0.840786	0.0271362
$961$	47.5526	1.53395
$962$	−4.33725	−0.139838
$963$	−2.19333	−0.0706792
$964$	15.9310	0.513104
$965$	−8.39245	−0.270163
$966$	14.0014	0.450486
$967$	−55.8854	−1.79715	−0.898576	−	0.438818i	$-0.855397\pi$
$967$	−55.8854	−1.79715	−0.898576	+	0.438818i	$0.855397\pi$
$968$	−10.0799	−0.323980
$969$	0.712691	0.0228949
$970$	−3.42546	−0.109985
$971$	18.0694	0.579876	0.289938	−	0.957045i	$-0.406365\pi$
$971$	18.0694	0.579876	0.289938	+	0.957045i	$0.406365\pi$
$972$	−1.00000	−0.0320750
$973$	−28.8760	−0.925723
$974$	18.2070	0.583388
$975$	4.29308	0.137489
$976$	−3.53114	−0.113029
$977$	−51.7591	−1.65592	−0.827959	−	0.560788i	$-0.810498\pi$
$977$	−51.7591	−1.65592	−0.827959	+	0.560788i	$0.810498\pi$
$978$	21.7156	0.694387
$979$	−5.48745	−0.175380
$980$	−1.04170	−0.0332760
$981$	−8.20488	−0.261962
$982$	37.8351	1.20737
$983$	53.5655	1.70848	0.854238	−	0.519883i	$-0.174024\pi$
$983$	53.5655	1.70848	0.854238	+	0.519883i	$0.174024\pi$
$984$	1.67958	0.0535431
$985$	10.7291	0.341858
$986$	1.60842	0.0512224
$987$	37.5324	1.19467
$988$	1.12227	0.0357041
$989$	46.1672	1.46803
$990$	−0.806503	−0.0256324
$991$	42.8796	1.36212	0.681058	−	0.732230i	$-0.261520\pi$
$991$	42.8796	1.36212	0.681058	+	0.732230i	$0.261520\pi$
$992$	−8.86299	−0.281400
$993$	−8.93355	−0.283498
$994$	46.8233	1.48515
$995$	3.96543	0.125713
$996$	−4.91365	−0.155695
$997$	25.3855	0.803965	0.401983	−	0.915647i	$-0.368321\pi$
$997$	25.3855	0.803965	0.401983	+	0.915647i	$0.368321\pi$
$998$	−36.4658	−1.15430
$999$	4.33725	0.137224

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.r.1.4	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.r.1.4	✓	9	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.840786 q^{5} -1.00000 q^{6} +2.87036 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.840786 q^{5} -1.00000 q^{6} +2.87036 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.840786 q^{10} +0.959226 q^{11} -1.00000 q^{12} +1.00000 q^{13} +2.87036 q^{14} +0.840786 q^{15} +1.00000 q^{16} -0.635045 q^{17} +1.00000 q^{18} +1.12227 q^{19} -0.840786 q^{20} -2.87036 q^{21} +0.959226 q^{22} -4.87791 q^{23} -1.00000 q^{24} -4.29308 q^{25} +1.00000 q^{26} -1.00000 q^{27} +2.87036 q^{28} -2.53276 q^{29} +0.840786 q^{30} -8.86299 q^{31} +1.00000 q^{32} -0.959226 q^{33} -0.635045 q^{34} -2.41336 q^{35} +1.00000 q^{36} -4.33725 q^{37} +1.12227 q^{38} -1.00000 q^{39} -0.840786 q^{40} -1.67958 q^{41} -2.87036 q^{42} -9.46454 q^{43} +0.959226 q^{44} -0.840786 q^{45} -4.87791 q^{46} -13.0759 q^{47} -1.00000 q^{48} +1.23897 q^{49} -4.29308 q^{50} +0.635045 q^{51} +1.00000 q^{52} -4.83984 q^{53} -1.00000 q^{54} -0.806503 q^{55} +2.87036 q^{56} -1.12227 q^{57} -2.53276 q^{58} +7.29208 q^{59} +0.840786 q^{60} -3.53114 q^{61} -8.86299 q^{62} +2.87036 q^{63} +1.00000 q^{64} -0.840786 q^{65} -0.959226 q^{66} +2.91288 q^{67} -0.635045 q^{68} +4.87791 q^{69} -2.41336 q^{70} +16.3127 q^{71} +1.00000 q^{72} -4.24258 q^{73} -4.33725 q^{74} +4.29308 q^{75} +1.12227 q^{76} +2.75332 q^{77} -1.00000 q^{78} -3.54035 q^{79} -0.840786 q^{80} +1.00000 q^{81} -1.67958 q^{82} +4.91365 q^{83} -2.87036 q^{84} +0.533937 q^{85} -9.46454 q^{86} +2.53276 q^{87} +0.959226 q^{88} -5.72071 q^{89} -0.840786 q^{90} +2.87036 q^{91} -4.87791 q^{92} +8.86299 q^{93} -13.0759 q^{94} -0.943588 q^{95} -1.00000 q^{96} +4.07411 q^{97} +1.23897 q^{98} +0.959226 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} - 4 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 - 4 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} - 4 q^{7} + 9 q^{8} + 9 q^{9} - 4 q^{10} - 5 q^{11} - 9 q^{12} + 9 q^{13} - 4 q^{14} + 4 q^{15} + 9 q^{16} - 6 q^{17} + 9 q^{18} - 4 q^{19} - 4 q^{20} + 4 q^{21} - 5 q^{22} - 6 q^{23} - 9 q^{24} - 11 q^{25} + 9 q^{26} - 9 q^{27} - 4 q^{28} - 19 q^{29} + 4 q^{30} - 6 q^{31} + 9 q^{32} + 5 q^{33} - 6 q^{34} + 10 q^{35} + 9 q^{36} - 13 q^{37} - 4 q^{38} - 9 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} - 20 q^{43} - 5 q^{44} - 4 q^{45} - 6 q^{46} + 14 q^{47} - 9 q^{48} - 3 q^{49} - 11 q^{50} + 6 q^{51} + 9 q^{52} - 3 q^{53} - 9 q^{54} - 4 q^{55} - 4 q^{56} + 4 q^{57} - 19 q^{58} - 9 q^{59} + 4 q^{60} - 24 q^{61} - 6 q^{62} - 4 q^{63} + 9 q^{64} - 4 q^{65} + 5 q^{66} - 4 q^{67} - 6 q^{68} + 6 q^{69} + 10 q^{70} - 9 q^{71} + 9 q^{72} - 24 q^{73} - 13 q^{74} + 11 q^{75} - 4 q^{76} + 3 q^{77} - 9 q^{78} - 15 q^{79} - 4 q^{80} + 9 q^{81} - 18 q^{82} + 20 q^{83} + 4 q^{84} - 31 q^{85} - 20 q^{86} + 19 q^{87} - 5 q^{88} + 3 q^{89} - 4 q^{90} - 4 q^{91} - 6 q^{92} + 6 q^{93} + 14 q^{94} - 4 q^{95} - 9 q^{96} - 19 q^{97} - 3 q^{98} - 5 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 - 4 * q^7 + 9 * q^8 + 9 * q^9 - 4 * q^10 - 5 * q^11 - 9 * q^12 + 9 * q^13 - 4 * q^14 + 4 * q^15 + 9 * q^16 - 6 * q^17 + 9 * q^18 - 4 * q^19 - 4 * q^20 + 4 * q^21 - 5 * q^22 - 6 * q^23 - 9 * q^24 - 11 * q^25 + 9 * q^26 - 9 * q^27 - 4 * q^28 - 19 * q^29 + 4 * q^30 - 6 * q^31 + 9 * q^32 + 5 * q^33 - 6 * q^34 + 10 * q^35 + 9 * q^36 - 13 * q^37 - 4 * q^38 - 9 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 - 20 * q^43 - 5 * q^44 - 4 * q^45 - 6 * q^46 + 14 * q^47 - 9 * q^48 - 3 * q^49 - 11 * q^50 + 6 * q^51 + 9 * q^52 - 3 * q^53 - 9 * q^54 - 4 * q^55 - 4 * q^56 + 4 * q^57 - 19 * q^58 - 9 * q^59 + 4 * q^60 - 24 * q^61 - 6 * q^62 - 4 * q^63 + 9 * q^64 - 4 * q^65 + 5 * q^66 - 4 * q^67 - 6 * q^68 + 6 * q^69 + 10 * q^70 - 9 * q^71 + 9 * q^72 - 24 * q^73 - 13 * q^74 + 11 * q^75 - 4 * q^76 + 3 * q^77 - 9 * q^78 - 15 * q^79 - 4 * q^80 + 9 * q^81 - 18 * q^82 + 20 * q^83 + 4 * q^84 - 31 * q^85 - 20 * q^86 + 19 * q^87 - 5 * q^88 + 3 * q^89 - 4 * q^90 - 4 * q^91 - 6 * q^92 + 6 * q^93 + 14 * q^94 - 4 * q^95 - 9 * q^96 - 19 * q^97 - 3 * q^98 - 5 * q^99

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