LMFDB - Embedded newform 8034.2.a.z.1.1

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:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} - 36 x^{12} + 108 x^{11} + 434 x^{10} - 1239 x^{9} - 2404 x^{8} + 6204 x^{7} + \cdots + 1552 $ x^14 - 3x^13 - 36x^12 + 108x^11 + 434x^10 - 1239x^9 - 2404x^8 + 6204x^7 + 6361x^6 - 14618x^5 - 7015x^4 + 15763x^3 + 1118x^2 - 6316*x + 1552
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.68342$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.68342 q^{5} +1.00000 q^{6} +5.03243 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.68342 q^{5} +1.00000 q^{6} +5.03243 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.68342 q^{10} -6.07783 q^{11} -1.00000 q^{12} +1.00000 q^{13} -5.03243 q^{14} +3.68342 q^{15} +1.00000 q^{16} +0.687836 q^{17} -1.00000 q^{18} +4.84475 q^{19} -3.68342 q^{20} -5.03243 q^{21} +6.07783 q^{22} +5.54263 q^{23} +1.00000 q^{24} +8.56755 q^{25} -1.00000 q^{26} -1.00000 q^{27} +5.03243 q^{28} +6.66499 q^{29} -3.68342 q^{30} -3.81844 q^{31} -1.00000 q^{32} +6.07783 q^{33} -0.687836 q^{34} -18.5365 q^{35} +1.00000 q^{36} +0.460154 q^{37} -4.84475 q^{38} -1.00000 q^{39} +3.68342 q^{40} -7.54316 q^{41} +5.03243 q^{42} -8.38067 q^{43} -6.07783 q^{44} -3.68342 q^{45} -5.54263 q^{46} +5.56288 q^{47} -1.00000 q^{48} +18.3254 q^{49} -8.56755 q^{50} -0.687836 q^{51} +1.00000 q^{52} +7.78611 q^{53} +1.00000 q^{54} +22.3872 q^{55} -5.03243 q^{56} -4.84475 q^{57} -6.66499 q^{58} -5.42438 q^{59} +3.68342 q^{60} -6.72933 q^{61} +3.81844 q^{62} +5.03243 q^{63} +1.00000 q^{64} -3.68342 q^{65} -6.07783 q^{66} +10.8290 q^{67} +0.687836 q^{68} -5.54263 q^{69} +18.5365 q^{70} +14.1374 q^{71} -1.00000 q^{72} -11.0586 q^{73} -0.460154 q^{74} -8.56755 q^{75} +4.84475 q^{76} -30.5863 q^{77} +1.00000 q^{78} +1.41867 q^{79} -3.68342 q^{80} +1.00000 q^{81} +7.54316 q^{82} -5.18575 q^{83} -5.03243 q^{84} -2.53359 q^{85} +8.38067 q^{86} -6.66499 q^{87} +6.07783 q^{88} +4.44024 q^{89} +3.68342 q^{90} +5.03243 q^{91} +5.54263 q^{92} +3.81844 q^{93} -5.56288 q^{94} -17.8452 q^{95} +1.00000 q^{96} -14.0901 q^{97} -18.3254 q^{98} -6.07783 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9} + 3 q^{10} + 5 q^{11} - 14 q^{12} + 14 q^{13} - 4 q^{14} + 3 q^{15} + 14 q^{16} - 7 q^{17} - 14 q^{18} + 31 q^{19} - 3 q^{20} - 4 q^{21} - 5 q^{22} + 14 q^{23} + 14 q^{24} + 11 q^{25} - 14 q^{26} - 14 q^{27} + 4 q^{28} + 9 q^{29} - 3 q^{30} + 23 q^{31} - 14 q^{32} - 5 q^{33} + 7 q^{34} - 2 q^{35} + 14 q^{36} + 12 q^{37} - 31 q^{38} - 14 q^{39} + 3 q^{40} - 5 q^{41} + 4 q^{42} - 2 q^{43} + 5 q^{44} - 3 q^{45} - 14 q^{46} - 11 q^{47} - 14 q^{48} + 52 q^{49} - 11 q^{50} + 7 q^{51} + 14 q^{52} + 6 q^{53} + 14 q^{54} + 30 q^{55} - 4 q^{56} - 31 q^{57} - 9 q^{58} - 4 q^{59} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 4 q^{63} + 14 q^{64} - 3 q^{65} + 5 q^{66} + 24 q^{67} - 7 q^{68} - 14 q^{69} + 2 q^{70} + 20 q^{71} - 14 q^{72} + 2 q^{73} - 12 q^{74} - 11 q^{75} + 31 q^{76} - 28 q^{77} + 14 q^{78} + 59 q^{79} - 3 q^{80} + 14 q^{81} + 5 q^{82} + q^{83} - 4 q^{84} - 29 q^{85} + 2 q^{86} - 9 q^{87} - 5 q^{88} + 6 q^{89} + 3 q^{90} + 4 q^{91} + 14 q^{92} - 23 q^{93} + 11 q^{94} - 58 q^{95} + 14 q^{96} - 6 q^{97} - 52 q^{98} + 5 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9 + 3 * q^10 + 5 * q^11 - 14 * q^12 + 14 * q^13 - 4 * q^14 + 3 * q^15 + 14 * q^16 - 7 * q^17 - 14 * q^18 + 31 * q^19 - 3 * q^20 - 4 * q^21 - 5 * q^22 + 14 * q^23 + 14 * q^24 + 11 * q^25 - 14 * q^26 - 14 * q^27 + 4 * q^28 + 9 * q^29 - 3 * q^30 + 23 * q^31 - 14 * q^32 - 5 * q^33 + 7 * q^34 - 2 * q^35 + 14 * q^36 + 12 * q^37 - 31 * q^38 - 14 * q^39 + 3 * q^40 - 5 * q^41 + 4 * q^42 - 2 * q^43 + 5 * q^44 - 3 * q^45 - 14 * q^46 - 11 * q^47 - 14 * q^48 + 52 * q^49 - 11 * q^50 + 7 * q^51 + 14 * q^52 + 6 * q^53 + 14 * q^54 + 30 * q^55 - 4 * q^56 - 31 * q^57 - 9 * q^58 - 4 * q^59 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 4 * q^63 + 14 * q^64 - 3 * q^65 + 5 * q^66 + 24 * q^67 - 7 * q^68 - 14 * q^69 + 2 * q^70 + 20 * q^71 - 14 * q^72 + 2 * q^73 - 12 * q^74 - 11 * q^75 + 31 * q^76 - 28 * q^77 + 14 * q^78 + 59 * q^79 - 3 * q^80 + 14 * q^81 + 5 * q^82 + q^83 - 4 * q^84 - 29 * q^85 + 2 * q^86 - 9 * q^87 - 5 * q^88 + 6 * q^89 + 3 * q^90 + 4 * q^91 + 14 * q^92 - 23 * q^93 + 11 * q^94 - 58 * q^95 + 14 * q^96 - 6 * q^97 - 52 * 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
$5$	−3.68342	−1.64727	−0.823637	−	0.567118i	$-0.808059\pi$
$5$	−3.68342	−1.64727	−0.823637	+	0.567118i	$0.808059\pi$
$6$	1.00000	0.408248
$7$	5.03243	1.90208	0.951040	−	0.309067i	$-0.100017\pi$
$7$	5.03243	1.90208	0.951040	+	0.309067i	$0.100017\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.68342	1.16480
$11$	−6.07783	−1.83254	−0.916268	−	0.400567i	$-0.868813\pi$
$11$	−6.07783	−1.83254	−0.916268	+	0.400567i	$0.868813\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−5.03243	−1.34497
$15$	3.68342	0.951054
$16$	1.00000	0.250000
$17$	0.687836	0.166825	0.0834124	−	0.996515i	$-0.473418\pi$
$17$	0.687836	0.166825	0.0834124	+	0.996515i	$0.473418\pi$
$18$	−1.00000	−0.235702
$19$	4.84475	1.11146	0.555731	−	0.831362i	$-0.312438\pi$
$19$	4.84475	1.11146	0.555731	+	0.831362i	$0.312438\pi$
$20$	−3.68342	−0.823637
$21$	−5.03243	−1.09817
$22$	6.07783	1.29580
$23$	5.54263	1.15572	0.577859	−	0.816136i	$-0.303888\pi$
$23$	5.54263	1.15572	0.577859	+	0.816136i	$0.303888\pi$
$24$	1.00000	0.204124
$25$	8.56755	1.71351
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	5.03243	0.951040
$29$	6.66499	1.23766	0.618829	−	0.785526i	$-0.287607\pi$
$29$	6.66499	1.23766	0.618829	+	0.785526i	$0.287607\pi$
$30$	−3.68342	−0.672497
$31$	−3.81844	−0.685813	−0.342906	−	0.939370i	$-0.611411\pi$
$31$	−3.81844	−0.685813	−0.342906	+	0.939370i	$0.611411\pi$
$32$	−1.00000	−0.176777
$33$	6.07783	1.05801
$34$	−0.687836	−0.117963
$35$	−18.5365	−3.13325
$36$	1.00000	0.166667
$37$	0.460154	0.0756489	0.0378244	−	0.999284i	$-0.487957\pi$
$37$	0.460154	0.0756489	0.0378244	+	0.999284i	$0.487957\pi$
$38$	−4.84475	−0.785923
$39$	−1.00000	−0.160128
$40$	3.68342	0.582399
$41$	−7.54316	−1.17804	−0.589022	−	0.808117i	$-0.700487\pi$
$41$	−7.54316	−1.17804	−0.589022	+	0.808117i	$0.700487\pi$
$42$	5.03243	0.776521
$43$	−8.38067	−1.27804	−0.639020	−	0.769190i	$-0.720660\pi$
$43$	−8.38067	−1.27804	−0.639020	+	0.769190i	$0.720660\pi$
$44$	−6.07783	−0.916268
$45$	−3.68342	−0.549091
$46$	−5.54263	−0.817217
$47$	5.56288	0.811429	0.405714	−	0.914000i	$-0.367023\pi$
$47$	5.56288	0.811429	0.405714	+	0.914000i	$0.367023\pi$
$48$	−1.00000	−0.144338
$49$	18.3254	2.61791
$50$	−8.56755	−1.21163
$51$	−0.687836	−0.0963163
$52$	1.00000	0.138675
$53$	7.78611	1.06950	0.534752	−	0.845009i	$-0.320405\pi$
$53$	7.78611	1.06950	0.534752	+	0.845009i	$0.320405\pi$
$54$	1.00000	0.136083
$55$	22.3872	3.01869
$56$	−5.03243	−0.672487
$57$	−4.84475	−0.641703
$58$	−6.66499	−0.875157
$59$	−5.42438	−0.706194	−0.353097	−	0.935587i	$-0.614871\pi$
$59$	−5.42438	−0.706194	−0.353097	+	0.935587i	$0.614871\pi$
$60$	3.68342	0.475527
$61$	−6.72933	−0.861603	−0.430801	−	0.902447i	$-0.641769\pi$
$61$	−6.72933	−0.861603	−0.430801	+	0.902447i	$0.641769\pi$
$62$	3.81844	0.484943
$63$	5.03243	0.634027
$64$	1.00000	0.125000
$65$	−3.68342	−0.456872
$66$	−6.07783	−0.748129
$67$	10.8290	1.32298	0.661488	−	0.749956i	$-0.269925\pi$
$67$	10.8290	1.32298	0.661488	+	0.749956i	$0.269925\pi$
$68$	0.687836	0.0834124
$69$	−5.54263	−0.667254
$70$	18.5365	2.21554
$71$	14.1374	1.67780	0.838902	−	0.544282i	$-0.183198\pi$
$71$	14.1374	1.67780	0.838902	+	0.544282i	$0.183198\pi$
$72$	−1.00000	−0.117851
$73$	−11.0586	−1.29431	−0.647157	−	0.762357i	$-0.724042\pi$
$73$	−11.0586	−1.29431	−0.647157	+	0.762357i	$0.724042\pi$
$74$	−0.460154	−0.0534918
$75$	−8.56755	−0.989296
$76$	4.84475	0.555731
$77$	−30.5863	−3.48563
$78$	1.00000	0.113228
$79$	1.41867	0.159613	0.0798067	−	0.996810i	$-0.474570\pi$
$79$	1.41867	0.159613	0.0798067	+	0.996810i	$0.474570\pi$
$80$	−3.68342	−0.411818
$81$	1.00000	0.111111
$82$	7.54316	0.833003
$83$	−5.18575	−0.569210	−0.284605	−	0.958645i	$-0.591862\pi$
$83$	−5.18575	−0.569210	−0.284605	+	0.958645i	$0.591862\pi$
$84$	−5.03243	−0.549083
$85$	−2.53359	−0.274806
$86$	8.38067	0.903711
$87$	−6.66499	−0.714562
$88$	6.07783	0.647899
$89$	4.44024	0.470665	0.235332	−	0.971915i	$-0.424382\pi$
$89$	4.44024	0.470665	0.235332	+	0.971915i	$0.424382\pi$
$90$	3.68342	0.388266
$91$	5.03243	0.527542
$92$	5.54263	0.577859
$93$	3.81844	0.395954
$94$	−5.56288	−0.573767
$95$	−17.8452	−1.83088
$96$	1.00000	0.102062
$97$	−14.0901	−1.43063	−0.715315	−	0.698802i	$-0.753717\pi$
$97$	−14.0901	−1.43063	−0.715315	+	0.698802i	$0.753717\pi$
$98$	−18.3254	−1.85114
$99$	−6.07783	−0.610845
$100$	8.56755	0.856755
$101$	−6.16928	−0.613866	−0.306933	−	0.951731i	$-0.599303\pi$
$101$	−6.16928	−0.613866	−0.306933	+	0.951731i	$0.599303\pi$
$102$	0.687836	0.0681059
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	18.5365	1.80898
$106$	−7.78611	−0.756254
$107$	20.0623	1.93950	0.969748	−	0.244108i	$-0.0784951\pi$
$107$	20.0623	1.93950	0.969748	+	0.244108i	$0.0784951\pi$
$108$	−1.00000	−0.0962250
$109$	−10.7098	−1.02581	−0.512907	−	0.858444i	$-0.671431\pi$
$109$	−10.7098	−1.02581	−0.512907	+	0.858444i	$0.671431\pi$
$110$	−22.3872	−2.13453
$111$	−0.460154	−0.0436759
$112$	5.03243	0.475520
$113$	−0.229504	−0.0215899	−0.0107950	−	0.999942i	$-0.503436\pi$
$113$	−0.229504	−0.0215899	−0.0107950	+	0.999942i	$0.503436\pi$
$114$	4.84475	0.453753
$115$	−20.4158	−1.90378
$116$	6.66499	0.618829
$117$	1.00000	0.0924500
$118$	5.42438	0.499355
$119$	3.46149	0.317314
$120$	−3.68342	−0.336248
$121$	25.9400	2.35818
$122$	6.72933	0.609245
$123$	7.54316	0.680144
$124$	−3.81844	−0.342906
$125$	−13.1408	−1.17535
$126$	−5.03243	−0.448325
$127$	−0.988933	−0.0877536	−0.0438768	−	0.999037i	$-0.513971\pi$
$127$	−0.988933	−0.0877536	−0.0438768	+	0.999037i	$0.513971\pi$
$128$	−1.00000	−0.0883883
$129$	8.38067	0.737877
$130$	3.68342	0.323057
$131$	−12.7607	−1.11491	−0.557455	−	0.830207i	$-0.688222\pi$
$131$	−12.7607	−1.11491	−0.557455	+	0.830207i	$0.688222\pi$
$132$	6.07783	0.529007
$133$	24.3809	2.11409
$134$	−10.8290	−0.935485
$135$	3.68342	0.317018
$136$	−0.687836	−0.0589815
$137$	8.89751	0.760166	0.380083	−	0.924952i	$-0.375895\pi$
$137$	8.89751	0.760166	0.380083	+	0.924952i	$0.375895\pi$
$138$	5.54263	0.471820
$139$	−8.11255	−0.688097	−0.344049	−	0.938952i	$-0.611799\pi$
$139$	−8.11255	−0.688097	−0.344049	+	0.938952i	$0.611799\pi$
$140$	−18.5365	−1.56662
$141$	−5.56288	−0.468479
$142$	−14.1374	−1.18639
$143$	−6.07783	−0.508254
$144$	1.00000	0.0833333
$145$	−24.5499	−2.03876
$146$	11.0586	0.915219
$147$	−18.3254	−1.51145
$148$	0.460154	0.0378244
$149$	−15.4097	−1.26241	−0.631204	−	0.775616i	$-0.717439\pi$
$149$	−15.4097	−1.26241	−0.631204	+	0.775616i	$0.717439\pi$
$150$	8.56755	0.699538
$151$	−14.6840	−1.19496	−0.597482	−	0.801882i	$-0.703832\pi$
$151$	−14.6840	−1.19496	−0.597482	+	0.801882i	$0.703832\pi$
$152$	−4.84475	−0.392962
$153$	0.687836	0.0556083
$154$	30.5863	2.46471
$155$	14.0649	1.12972
$156$	−1.00000	−0.0800641
$157$	12.6431	1.00903	0.504515	−	0.863403i	$-0.331671\pi$
$157$	12.6431	1.00903	0.504515	+	0.863403i	$0.331671\pi$
$158$	−1.41867	−0.112864
$159$	−7.78611	−0.617479
$160$	3.68342	0.291200
$161$	27.8929	2.19827
$162$	−1.00000	−0.0785674
$163$	22.7600	1.78270	0.891349	−	0.453319i	$-0.149760\pi$
$163$	22.7600	1.78270	0.891349	+	0.453319i	$0.149760\pi$
$164$	−7.54316	−0.589022
$165$	−22.3872	−1.74284
$166$	5.18575	0.402492
$167$	−9.07055	−0.701900	−0.350950	−	0.936394i	$-0.614141\pi$
$167$	−9.07055	−0.701900	−0.350950	+	0.936394i	$0.614141\pi$
$168$	5.03243	0.388261
$169$	1.00000	0.0769231
$170$	2.53359	0.194317
$171$	4.84475	0.370488
$172$	−8.38067	−0.639020
$173$	20.7522	1.57776	0.788878	−	0.614549i	$-0.210662\pi$
$173$	20.7522	1.57776	0.788878	+	0.614549i	$0.210662\pi$
$174$	6.66499	0.505272
$175$	43.1156	3.25924
$176$	−6.07783	−0.458134
$177$	5.42438	0.407721
$178$	−4.44024	−0.332810
$179$	−14.8788	−1.11209	−0.556046	−	0.831151i	$-0.687682\pi$
$179$	−14.8788	−1.11209	−0.556046	+	0.831151i	$0.687682\pi$
$180$	−3.68342	−0.274546
$181$	1.77972	0.132285	0.0661426	−	0.997810i	$-0.478931\pi$
$181$	1.77972	0.132285	0.0661426	+	0.997810i	$0.478931\pi$
$182$	−5.03243	−0.373029
$183$	6.72933	0.497447
$184$	−5.54263	−0.408608
$185$	−1.69494	−0.124614
$186$	−3.81844	−0.279982
$187$	−4.18055	−0.305712
$188$	5.56288	0.405714
$189$	−5.03243	−0.366056
$190$	17.8452	1.29463
$191$	−27.1288	−1.96297	−0.981485	−	0.191541i	$-0.938651\pi$
$191$	−27.1288	−1.96297	−0.981485	+	0.191541i	$0.938651\pi$
$192$	−1.00000	−0.0721688
$193$	25.0012	1.79963	0.899814	−	0.436274i	$-0.143702\pi$
$193$	25.0012	1.79963	0.899814	+	0.436274i	$0.143702\pi$
$194$	14.0901	1.01161
$195$	3.68342	0.263775
$196$	18.3254	1.30896
$197$	−16.4004	−1.16848	−0.584238	−	0.811582i	$-0.698607\pi$
$197$	−16.4004	−1.16848	−0.584238	+	0.811582i	$0.698607\pi$
$198$	6.07783	0.431933
$199$	−1.59261	−0.112897	−0.0564485	−	0.998406i	$-0.517978\pi$
$199$	−1.59261	−0.112897	−0.0564485	+	0.998406i	$0.517978\pi$
$200$	−8.56755	−0.605817
$201$	−10.8290	−0.763821
$202$	6.16928	0.434069
$203$	33.5411	2.35413
$204$	−0.687836	−0.0481582
$205$	27.7846	1.94056
$206$	1.00000	0.0696733
$207$	5.54263	0.385240
$208$	1.00000	0.0693375
$209$	−29.4456	−2.03679
$210$	−18.5365	−1.27914
$211$	12.4299	0.855709	0.427855	−	0.903848i	$-0.359269\pi$
$211$	12.4299	0.855709	0.427855	+	0.903848i	$0.359269\pi$
$212$	7.78611	0.534752
$213$	−14.1374	−0.968681
$214$	−20.0623	−1.37143
$215$	30.8695	2.10528
$216$	1.00000	0.0680414
$217$	−19.2161	−1.30447
$218$	10.7098	0.725360
$219$	11.0586	0.747273
$220$	22.3872	1.50934
$221$	0.687836	0.0462689
$222$	0.460154	0.0308835
$223$	−12.2201	−0.818317	−0.409159	−	0.912463i	$-0.634178\pi$
$223$	−12.2201	−0.818317	−0.409159	+	0.912463i	$0.634178\pi$
$224$	−5.03243	−0.336244
$225$	8.56755	0.571170
$226$	0.229504	0.0152664
$227$	−6.31622	−0.419222	−0.209611	−	0.977785i	$-0.567220\pi$
$227$	−6.31622	−0.419222	−0.209611	+	0.977785i	$0.567220\pi$
$228$	−4.84475	−0.320852
$229$	9.72002	0.642317	0.321158	−	0.947025i	$-0.395928\pi$
$229$	9.72002	0.642317	0.321158	+	0.947025i	$0.395928\pi$
$230$	20.4158	1.34618
$231$	30.5863	2.01243
$232$	−6.66499	−0.437578
$233$	18.4155	1.20644	0.603220	−	0.797575i	$-0.293884\pi$
$233$	18.4155	1.20644	0.603220	+	0.797575i	$0.293884\pi$
$234$	−1.00000	−0.0653720
$235$	−20.4904	−1.33665
$236$	−5.42438	−0.353097
$237$	−1.41867	−0.0921528
$238$	−3.46149	−0.224375
$239$	20.0784	1.29876	0.649382	−	0.760462i	$-0.275027\pi$
$239$	20.0784	1.29876	0.649382	+	0.760462i	$0.275027\pi$
$240$	3.68342	0.237763
$241$	20.9951	1.35241	0.676207	−	0.736711i	$-0.263622\pi$
$241$	20.9951	1.35241	0.676207	+	0.736711i	$0.263622\pi$
$242$	−25.9400	−1.66749
$243$	−1.00000	−0.0641500
$244$	−6.72933	−0.430801
$245$	−67.5000	−4.31242
$246$	−7.54316	−0.480934
$247$	4.84475	0.308264
$248$	3.81844	0.242471
$249$	5.18575	0.328634
$250$	13.1408	0.831096
$251$	−5.21065	−0.328893	−0.164447	−	0.986386i	$-0.552584\pi$
$251$	−5.21065	−0.328893	−0.164447	+	0.986386i	$0.552584\pi$
$252$	5.03243	0.317013
$253$	−33.6872	−2.11790
$254$	0.988933	0.0620512
$255$	2.53359	0.158659
$256$	1.00000	0.0625000
$257$	0.904912	0.0564468	0.0282234	−	0.999602i	$-0.491015\pi$
$257$	0.904912	0.0564468	0.0282234	+	0.999602i	$0.491015\pi$
$258$	−8.38067	−0.521758
$259$	2.31569	0.143890
$260$	−3.68342	−0.228436
$261$	6.66499	0.412553
$262$	12.7607	0.788361
$263$	8.88779	0.548045	0.274022	−	0.961723i	$-0.411646\pi$
$263$	8.88779	0.548045	0.274022	+	0.961723i	$0.411646\pi$
$264$	−6.07783	−0.374065
$265$	−28.6795	−1.76177
$266$	−24.3809	−1.49489
$267$	−4.44024	−0.271738
$268$	10.8290	0.661488
$269$	−6.00072	−0.365870	−0.182935	−	0.983125i	$-0.558560\pi$
$269$	−6.00072	−0.365870	−0.182935	+	0.983125i	$0.558560\pi$
$270$	−3.68342	−0.224166
$271$	−23.0789	−1.40194	−0.700972	−	0.713188i	$-0.747250\pi$
$271$	−23.0789	−1.40194	−0.700972	+	0.713188i	$0.747250\pi$
$272$	0.687836	0.0417062
$273$	−5.03243	−0.304577
$274$	−8.89751	−0.537518
$275$	−52.0721	−3.14007
$276$	−5.54263	−0.333627
$277$	−2.17618	−0.130754	−0.0653770	−	0.997861i	$-0.520825\pi$
$277$	−2.17618	−0.130754	−0.0653770	+	0.997861i	$0.520825\pi$
$278$	8.11255	0.486558
$279$	−3.81844	−0.228604
$280$	18.5365	1.10777
$281$	1.74352	0.104010	0.0520049	−	0.998647i	$-0.483439\pi$
$281$	1.74352	0.104010	0.0520049	+	0.998647i	$0.483439\pi$
$282$	5.56288	0.331264
$283$	12.7346	0.756991	0.378496	−	0.925603i	$-0.376442\pi$
$283$	12.7346	0.756991	0.378496	+	0.925603i	$0.376442\pi$
$284$	14.1374	0.838902
$285$	17.8452	1.05706
$286$	6.07783	0.359390
$287$	−37.9605	−2.24074
$288$	−1.00000	−0.0589256
$289$	−16.5269	−0.972170
$290$	24.5499	1.44162
$291$	14.0901	0.825975
$292$	−11.0586	−0.647157
$293$	−21.2582	−1.24191	−0.620957	−	0.783844i	$-0.713256\pi$
$293$	−21.2582	−1.24191	−0.620957	+	0.783844i	$0.713256\pi$
$294$	18.3254	1.06876
$295$	19.9802	1.16329
$296$	−0.460154	−0.0267459
$297$	6.07783	0.352672
$298$	15.4097	0.892658
$299$	5.54263	0.320539
$300$	−8.56755	−0.494648
$301$	−42.1752	−2.43094
$302$	14.6840	0.844967
$303$	6.16928	0.354416
$304$	4.84475	0.277866
$305$	24.7869	1.41930
$306$	−0.687836	−0.0393210
$307$	−23.5910	−1.34641	−0.673204	−	0.739457i	$-0.735082\pi$
$307$	−23.5910	−1.34641	−0.673204	+	0.739457i	$0.735082\pi$
$308$	−30.5863	−1.74281
$309$	1.00000	0.0568880
$310$	−14.0649	−0.798834
$311$	12.7248	0.721559	0.360780	−	0.932651i	$-0.382511\pi$
$311$	12.7248	0.721559	0.360780	+	0.932651i	$0.382511\pi$
$312$	1.00000	0.0566139
$313$	30.6522	1.73256	0.866282	−	0.499554i	$-0.166503\pi$
$313$	30.6522	1.73256	0.866282	+	0.499554i	$0.166503\pi$
$314$	−12.6431	−0.713493
$315$	−18.5365	−1.04442
$316$	1.41867	0.0798067
$317$	−19.2824	−1.08301	−0.541503	−	0.840699i	$-0.682144\pi$
$317$	−19.2824	−1.08301	−0.541503	+	0.840699i	$0.682144\pi$
$318$	7.78611	0.436624
$319$	−40.5087	−2.26805
$320$	−3.68342	−0.205909
$321$	−20.0623	−1.11977
$322$	−27.8929	−1.55441
$323$	3.33240	0.185420
$324$	1.00000	0.0555556
$325$	8.56755	0.475242
$326$	−22.7600	−1.26056
$327$	10.7098	0.592254
$328$	7.54316	0.416501
$329$	27.9948	1.54340
$330$	22.3872	1.23237
$331$	−34.7227	−1.90853	−0.954267	−	0.298957i	$-0.903361\pi$
$331$	−34.7227	−1.90853	−0.954267	+	0.298957i	$0.903361\pi$
$332$	−5.18575	−0.284605
$333$	0.460154	0.0252163
$334$	9.07055	0.496319
$335$	−39.8878	−2.17930
$336$	−5.03243	−0.274542
$337$	−2.87112	−0.156400	−0.0782000	−	0.996938i	$-0.524917\pi$
$337$	−2.87112	−0.156400	−0.0782000	+	0.996938i	$0.524917\pi$
$338$	−1.00000	−0.0543928
$339$	0.229504	0.0124650
$340$	−2.53359	−0.137403
$341$	23.2079	1.25678
$342$	−4.84475	−0.261974
$343$	56.9942	3.07740
$344$	8.38067	0.451855
$345$	20.4158	1.09915
$346$	−20.7522	−1.11564
$347$	17.9238	0.962201	0.481101	−	0.876665i	$-0.340237\pi$
$347$	17.9238	0.962201	0.481101	+	0.876665i	$0.340237\pi$
$348$	−6.66499	−0.357281
$349$	−5.68935	−0.304544	−0.152272	−	0.988339i	$-0.548659\pi$
$349$	−5.68935	−0.304544	−0.152272	+	0.988339i	$0.548659\pi$
$350$	−43.1156	−2.30463
$351$	−1.00000	−0.0533761
$352$	6.07783	0.323949
$353$	12.6046	0.670874	0.335437	−	0.942063i	$-0.391116\pi$
$353$	12.6046	0.670874	0.335437	+	0.942063i	$0.391116\pi$
$354$	−5.42438	−0.288302
$355$	−52.0740	−2.76380
$356$	4.44024	0.235332
$357$	−3.46149	−0.183201
$358$	14.8788	0.786368
$359$	32.9331	1.73814	0.869070	−	0.494688i	$-0.164718\pi$
$359$	32.9331	1.73814	0.869070	+	0.494688i	$0.164718\pi$
$360$	3.68342	0.194133
$361$	4.47165	0.235350
$362$	−1.77972	−0.0935398
$363$	−25.9400	−1.36150
$364$	5.03243	0.263771
$365$	40.7335	2.13209
$366$	−6.72933	−0.351748
$367$	−31.8850	−1.66438	−0.832191	−	0.554489i	$-0.812914\pi$
$367$	−31.8850	−1.66438	−0.832191	+	0.554489i	$0.812914\pi$
$368$	5.54263	0.288930
$369$	−7.54316	−0.392681
$370$	1.69494	0.0881157
$371$	39.1831	2.03428
$372$	3.81844	0.197977
$373$	18.7119	0.968867	0.484433	−	0.874828i	$-0.339026\pi$
$373$	18.7119	0.968867	0.484433	+	0.874828i	$0.339026\pi$
$374$	4.18055	0.216171
$375$	13.1408	0.678587
$376$	−5.56288	−0.286883
$377$	6.66499	0.343265
$378$	5.03243	0.258840
$379$	0.754775	0.0387702	0.0193851	−	0.999812i	$-0.493829\pi$
$379$	0.754775	0.0387702	0.0193851	+	0.999812i	$0.493829\pi$
$380$	−17.8452	−0.915442
$381$	0.988933	0.0506646
$382$	27.1288	1.38803
$383$	2.46500	0.125955	0.0629777	−	0.998015i	$-0.479940\pi$
$383$	2.46500	0.125955	0.0629777	+	0.998015i	$0.479940\pi$
$384$	1.00000	0.0510310
$385$	112.662	5.74179
$386$	−25.0012	−1.27253
$387$	−8.38067	−0.426013
$388$	−14.0901	−0.715315
$389$	3.11542	0.157958	0.0789789	−	0.996876i	$-0.474834\pi$
$389$	3.11542	0.157958	0.0789789	+	0.996876i	$0.474834\pi$
$390$	−3.68342	−0.186517
$391$	3.81242	0.192802
$392$	−18.3254	−0.925571
$393$	12.7607	0.643694
$394$	16.4004	0.826238
$395$	−5.22557	−0.262927
$396$	−6.07783	−0.305423
$397$	−1.53453	−0.0770156	−0.0385078	−	0.999258i	$-0.512260\pi$
$397$	−1.53453	−0.0770156	−0.0385078	+	0.999258i	$0.512260\pi$
$398$	1.59261	0.0798302
$399$	−24.3809	−1.22057
$400$	8.56755	0.428378
$401$	34.0311	1.69943	0.849717	−	0.527239i	$-0.176773\pi$
$401$	34.0311	1.69943	0.849717	+	0.527239i	$0.176773\pi$
$402$	10.8290	0.540103
$403$	−3.81844	−0.190210
$404$	−6.16928	−0.306933
$405$	−3.68342	−0.183030
$406$	−33.5411	−1.66462
$407$	−2.79674	−0.138629
$408$	0.687836	0.0340530
$409$	18.5088	0.915200	0.457600	−	0.889158i	$-0.348709\pi$
$409$	18.5088	0.915200	0.457600	+	0.889158i	$0.348709\pi$
$410$	−27.7846	−1.37218
$411$	−8.89751	−0.438882
$412$	−1.00000	−0.0492665
$413$	−27.2978	−1.34324
$414$	−5.54263	−0.272406
$415$	19.1013	0.937645
$416$	−1.00000	−0.0490290
$417$	8.11255	0.397273
$418$	29.4456	1.44023
$419$	9.52179	0.465170	0.232585	−	0.972576i	$-0.425282\pi$
$419$	9.52179	0.465170	0.232585	+	0.972576i	$0.425282\pi$
$420$	18.5365	0.904491
$421$	−40.2831	−1.96328	−0.981639	−	0.190746i	$-0.938909\pi$
$421$	−40.2831	−1.96328	−0.981639	+	0.190746i	$0.938909\pi$
$422$	−12.4299	−0.605078
$423$	5.56288	0.270476
$424$	−7.78611	−0.378127
$425$	5.89307	0.285856
$426$	14.1374	0.684961
$427$	−33.8649	−1.63884
$428$	20.0623	0.969748
$429$	6.07783	0.293440
$430$	−30.8695	−1.48866
$431$	−8.41932	−0.405544	−0.202772	−	0.979226i	$-0.564995\pi$
$431$	−8.41932	−0.405544	−0.202772	+	0.979226i	$0.564995\pi$
$432$	−1.00000	−0.0481125
$433$	26.6609	1.28124	0.640621	−	0.767857i	$-0.278677\pi$
$433$	26.6609	1.28124	0.640621	+	0.767857i	$0.278677\pi$
$434$	19.2161	0.922400
$435$	24.5499	1.17708
$436$	−10.7098	−0.512907
$437$	26.8527	1.28454
$438$	−11.0586	−0.528402
$439$	−0.393637	−0.0187873	−0.00939363	−	0.999956i	$-0.502990\pi$
$439$	−0.393637	−0.0187873	−0.00939363	+	0.999956i	$0.502990\pi$
$440$	−22.3872	−1.06727
$441$	18.3254	0.872637
$442$	−0.687836	−0.0327170
$443$	−12.8404	−0.610065	−0.305033	−	0.952342i	$-0.598667\pi$
$443$	−12.8404	−0.610065	−0.305033	+	0.952342i	$0.598667\pi$
$444$	−0.460154	−0.0218379
$445$	−16.3553	−0.775314
$446$	12.2201	0.578638
$447$	15.4097	0.728852
$448$	5.03243	0.237760
$449$	3.61376	0.170544	0.0852719	−	0.996358i	$-0.472824\pi$
$449$	3.61376	0.170544	0.0852719	+	0.996358i	$0.472824\pi$
$450$	−8.56755	−0.403878
$451$	45.8461	2.15881
$452$	−0.229504	−0.0107950
$453$	14.6840	0.689913
$454$	6.31622	0.296435
$455$	−18.5365	−0.869007
$456$	4.84475	0.226876
$457$	33.7785	1.58009	0.790045	−	0.613048i	$-0.210057\pi$
$457$	33.7785	1.58009	0.790045	+	0.613048i	$0.210057\pi$
$458$	−9.72002	−0.454187
$459$	−0.687836	−0.0321054
$460$	−20.4158	−0.951892
$461$	39.8441	1.85572	0.927862	−	0.372923i	$-0.121644\pi$
$461$	39.8441	1.85572	0.927862	+	0.372923i	$0.121644\pi$
$462$	−30.5863	−1.42300
$463$	15.5460	0.722484	0.361242	−	0.932472i	$-0.382353\pi$
$463$	15.5460	0.722484	0.361242	+	0.932472i	$0.382353\pi$
$464$	6.66499	0.309415
$465$	−14.0649	−0.652245
$466$	−18.4155	−0.853082
$467$	−3.24823	−0.150310	−0.0751550	−	0.997172i	$-0.523945\pi$
$467$	−3.24823	−0.150310	−0.0751550	+	0.997172i	$0.523945\pi$
$468$	1.00000	0.0462250
$469$	54.4963	2.51641
$470$	20.4904	0.945151
$471$	−12.6431	−0.582564
$472$	5.42438	0.249677
$473$	50.9363	2.34205
$474$	1.41867	0.0651619
$475$	41.5077	1.90450
$476$	3.46149	0.158657
$477$	7.78611	0.356502
$478$	−20.0784	−0.918365
$479$	29.4666	1.34636	0.673181	−	0.739478i	$-0.264928\pi$
$479$	29.4666	1.34636	0.673181	+	0.739478i	$0.264928\pi$
$480$	−3.68342	−0.168124
$481$	0.460154	0.0209812
$482$	−20.9951	−0.956302
$483$	−27.8929	−1.26917
$484$	25.9400	1.17909
$485$	51.8996	2.35664
$486$	1.00000	0.0453609
$487$	39.0218	1.76825	0.884123	−	0.467254i	$-0.154757\pi$
$487$	39.0218	1.76825	0.884123	+	0.467254i	$0.154757\pi$
$488$	6.72933	0.304623
$489$	−22.7600	−1.02924
$490$	67.5000	3.04934
$491$	2.37906	0.107365	0.0536827	−	0.998558i	$-0.482904\pi$
$491$	2.37906	0.107365	0.0536827	+	0.998558i	$0.482904\pi$
$492$	7.54316	0.340072
$493$	4.58442	0.206472
$494$	−4.84475	−0.217976
$495$	22.3872	1.00623
$496$	−3.81844	−0.171453
$497$	71.1457	3.19132
$498$	−5.18575	−0.232379
$499$	6.26699	0.280549	0.140275	−	0.990113i	$-0.455201\pi$
$499$	6.26699	0.280549	0.140275	+	0.990113i	$0.455201\pi$
$500$	−13.1408	−0.587674
$501$	9.07055	0.405242
$502$	5.21065	0.232563
$503$	24.3898	1.08749	0.543744	−	0.839251i	$-0.317006\pi$
$503$	24.3898	1.08749	0.543744	+	0.839251i	$0.317006\pi$
$504$	−5.03243	−0.224162
$505$	22.7240	1.01121
$506$	33.6872	1.49758
$507$	−1.00000	−0.0444116
$508$	−0.988933	−0.0438768
$509$	11.5495	0.511924	0.255962	−	0.966687i	$-0.417608\pi$
$509$	11.5495	0.511924	0.255962	+	0.966687i	$0.417608\pi$
$510$	−2.53359	−0.112189
$511$	−55.6518	−2.46189
$512$	−1.00000	−0.0441942
$513$	−4.84475	−0.213901
$514$	−0.904912	−0.0399140
$515$	3.68342	0.162311
$516$	8.38067	0.368938
$517$	−33.8102	−1.48697
$518$	−2.31569	−0.101746
$519$	−20.7522	−0.910918
$520$	3.68342	0.161528
$521$	24.9889	1.09478	0.547391	−	0.836877i	$-0.315621\pi$
$521$	24.9889	1.09478	0.547391	+	0.836877i	$0.315621\pi$
$522$	−6.66499	−0.291719
$523$	2.47928	0.108411	0.0542057	−	0.998530i	$-0.482737\pi$
$523$	2.47928	0.108411	0.0542057	+	0.998530i	$0.482737\pi$
$524$	−12.7607	−0.557455
$525$	−43.1156	−1.88172
$526$	−8.88779	−0.387526
$527$	−2.62646	−0.114411
$528$	6.07783	0.264504
$529$	7.72077	0.335686
$530$	28.6795	1.24576
$531$	−5.42438	−0.235398
$532$	24.3809	1.05705
$533$	−7.54316	−0.326731
$534$	4.44024	0.192148
$535$	−73.8978	−3.19488
$536$	−10.8290	−0.467743
$537$	14.8788	0.642067
$538$	6.00072	0.258709
$539$	−111.379	−4.79741
$540$	3.68342	0.158509
$541$	−20.5295	−0.882632	−0.441316	−	0.897352i	$-0.645488\pi$
$541$	−20.5295	−0.882632	−0.441316	+	0.897352i	$0.645488\pi$
$542$	23.0789	0.991325
$543$	−1.77972	−0.0763749
$544$	−0.687836	−0.0294907
$545$	39.4487	1.68980
$546$	5.03243	0.215368
$547$	35.3566	1.51174	0.755869	−	0.654722i	$-0.227214\pi$
$547$	35.3566	1.51174	0.755869	+	0.654722i	$0.227214\pi$
$548$	8.89751	0.380083
$549$	−6.72933	−0.287201
$550$	52.0721	2.22036
$551$	32.2903	1.37561
$552$	5.54263	0.235910
$553$	7.13939	0.303598
$554$	2.17618	0.0924571
$555$	1.69494	0.0719461
$556$	−8.11255	−0.344049
$557$	25.7429	1.09076	0.545380	−	0.838189i	$-0.316385\pi$
$557$	25.7429	1.09076	0.545380	+	0.838189i	$0.316385\pi$
$558$	3.81844	0.161648
$559$	−8.38067	−0.354465
$560$	−18.5365	−0.783312
$561$	4.18055	0.176503
$562$	−1.74352	−0.0735461
$563$	18.7924	0.792005	0.396003	−	0.918249i	$-0.370397\pi$
$563$	18.7924	0.792005	0.396003	+	0.918249i	$0.370397\pi$
$564$	−5.56288	−0.234239
$565$	0.845360	0.0355646
$566$	−12.7346	−0.535274
$567$	5.03243	0.211342
$568$	−14.1374	−0.593193
$569$	−34.8935	−1.46281	−0.731406	−	0.681942i	$-0.761136\pi$
$569$	−34.8935	−1.46281	−0.731406	+	0.681942i	$0.761136\pi$
$570$	−17.8452	−0.747455
$571$	25.9802	1.08724	0.543619	−	0.839332i	$-0.317054\pi$
$571$	25.9802	1.08724	0.543619	+	0.839332i	$0.317054\pi$
$572$	−6.07783	−0.254127
$573$	27.1288	1.13332
$574$	37.9605	1.58444
$575$	47.4868	1.98034
$576$	1.00000	0.0416667
$577$	−24.0007	−0.999162	−0.499581	−	0.866267i	$-0.666513\pi$
$577$	−24.0007	−0.999162	−0.499581	+	0.866267i	$0.666513\pi$
$578$	16.5269	0.687428
$579$	−25.0012	−1.03902
$580$	−24.5499	−1.01938
$581$	−26.0969	−1.08268
$582$	−14.0901	−0.584053
$583$	−47.3227	−1.95991
$584$	11.0586	0.457609
$585$	−3.68342	−0.152291
$586$	21.2582	0.878166
$587$	26.8579	1.10854	0.554271	−	0.832336i	$-0.312997\pi$
$587$	26.8579	1.10854	0.554271	+	0.832336i	$0.312997\pi$
$588$	−18.3254	−0.755726
$589$	−18.4994	−0.762255
$590$	−19.9802	−0.822574
$591$	16.4004	0.674621
$592$	0.460154	0.0189122
$593$	−5.35277	−0.219812	−0.109906	−	0.993942i	$-0.535055\pi$
$593$	−5.35277	−0.219812	−0.109906	+	0.993942i	$0.535055\pi$
$594$	−6.07783	−0.249376
$595$	−12.7501	−0.522703
$596$	−15.4097	−0.631204
$597$	1.59261	0.0651811
$598$	−5.54263	−0.226655
$599$	−4.91192	−0.200696	−0.100348	−	0.994952i	$-0.531996\pi$
$599$	−4.91192	−0.200696	−0.100348	+	0.994952i	$0.531996\pi$
$600$	8.56755	0.349769
$601$	0.846204	0.0345174	0.0172587	−	0.999851i	$-0.494506\pi$
$601$	0.846204	0.0345174	0.0172587	+	0.999851i	$0.494506\pi$
$602$	42.1752	1.71893
$603$	10.8290	0.440992
$604$	−14.6840	−0.597482
$605$	−95.5479	−3.88458
$606$	−6.16928	−0.250610
$607$	−17.1652	−0.696713	−0.348357	−	0.937362i	$-0.613260\pi$
$607$	−17.1652	−0.696713	−0.348357	+	0.937362i	$0.613260\pi$
$608$	−4.84475	−0.196481
$609$	−33.5411	−1.35916
$610$	−24.7869	−1.00359
$611$	5.56288	0.225050
$612$	0.687836	0.0278041
$613$	29.9714	1.21054	0.605268	−	0.796022i	$-0.293066\pi$
$613$	29.9714	1.21054	0.605268	+	0.796022i	$0.293066\pi$
$614$	23.5910	0.952054
$615$	−27.7846	−1.12038
$616$	30.5863	1.23236
$617$	−34.6639	−1.39552	−0.697758	−	0.716334i	$-0.745819\pi$
$617$	−34.6639	−1.39552	−0.697758	+	0.716334i	$0.745819\pi$
$618$	−1.00000	−0.0402259
$619$	28.2338	1.13481	0.567406	−	0.823438i	$-0.307947\pi$
$619$	28.2338	1.13481	0.567406	+	0.823438i	$0.307947\pi$
$620$	14.0649	0.564861
$621$	−5.54263	−0.222418
$622$	−12.7248	−0.510219
$623$	22.3452	0.895243
$624$	−1.00000	−0.0400320
$625$	5.56520	0.222608
$626$	−30.6522	−1.22511
$627$	29.4456	1.17594
$628$	12.6431	0.504515
$629$	0.316511	0.0126201
$630$	18.5365	0.738514
$631$	−37.9817	−1.51203	−0.756014	−	0.654555i	$-0.772856\pi$
$631$	−37.9817	−1.51203	−0.756014	+	0.654555i	$0.772856\pi$
$632$	−1.41867	−0.0564319
$633$	−12.4299	−0.494044
$634$	19.2824	0.765800
$635$	3.64265	0.144554
$636$	−7.78611	−0.308739
$637$	18.3254	0.726078
$638$	40.5087	1.60376
$639$	14.1374	0.559268
$640$	3.68342	0.145600
$641$	33.2759	1.31432	0.657159	−	0.753752i	$-0.271758\pi$
$641$	33.2759	1.31432	0.657159	+	0.753752i	$0.271758\pi$
$642$	20.0623	0.791796
$643$	31.0624	1.22498	0.612491	−	0.790478i	$-0.290168\pi$
$643$	31.0624	1.22498	0.612491	+	0.790478i	$0.290168\pi$
$644$	27.8929	1.09914
$645$	−30.8695	−1.21549
$646$	−3.33240	−0.131111
$647$	27.9655	1.09944	0.549719	−	0.835350i	$-0.314735\pi$
$647$	27.9655	1.09944	0.549719	+	0.835350i	$0.314735\pi$
$648$	−1.00000	−0.0392837
$649$	32.9685	1.29413
$650$	−8.56755	−0.336047
$651$	19.2161	0.753137
$652$	22.7600	0.891349
$653$	0.814236	0.0318635	0.0159318	−	0.999873i	$-0.494929\pi$
$653$	0.814236	0.0318635	0.0159318	+	0.999873i	$0.494929\pi$
$654$	−10.7098	−0.418787
$655$	47.0031	1.83656
$656$	−7.54316	−0.294511
$657$	−11.0586	−0.431438
$658$	−27.9948	−1.09135
$659$	−18.3533	−0.714943	−0.357472	−	0.933924i	$-0.616361\pi$
$659$	−18.3533	−0.714943	−0.357472	+	0.933924i	$0.616361\pi$
$660$	−22.3872	−0.871420
$661$	48.5449	1.88818	0.944090	−	0.329689i	$-0.106944\pi$
$661$	48.5449	1.88818	0.944090	+	0.329689i	$0.106944\pi$
$662$	34.7227	1.34954
$663$	−0.687836	−0.0267133
$664$	5.18575	0.201246
$665$	−89.8050	−3.48249
$666$	−0.460154	−0.0178306
$667$	36.9416	1.43038
$668$	−9.07055	−0.350950
$669$	12.2201	0.472456
$670$	39.8878	1.54100
$671$	40.8998	1.57892
$672$	5.03243	0.194130
$673$	−2.13932	−0.0824647	−0.0412323	−	0.999150i	$-0.513128\pi$
$673$	−2.13932	−0.0824647	−0.0412323	+	0.999150i	$0.513128\pi$
$674$	2.87112	0.110592
$675$	−8.56755	−0.329765
$676$	1.00000	0.0384615
$677$	−12.4305	−0.477743	−0.238871	−	0.971051i	$-0.576777\pi$
$677$	−12.4305	−0.477743	−0.238871	+	0.971051i	$0.576777\pi$
$678$	−0.229504	−0.00881406
$679$	−70.9074	−2.72118
$680$	2.53359	0.0971586
$681$	6.31622	0.242038
$682$	−23.2079	−0.888675
$683$	11.9972	0.459060	0.229530	−	0.973302i	$-0.426281\pi$
$683$	11.9972	0.459060	0.229530	+	0.973302i	$0.426281\pi$
$684$	4.84475	0.185244
$685$	−32.7732	−1.25220
$686$	−56.9942	−2.17605
$687$	−9.72002	−0.370842
$688$	−8.38067	−0.319510
$689$	7.78611	0.296627
$690$	−20.4158	−0.777217
$691$	−27.0180	−1.02781	−0.513906	−	0.857847i	$-0.671802\pi$
$691$	−27.0180	−1.02781	−0.513906	+	0.857847i	$0.671802\pi$
$692$	20.7522	0.788878
$693$	−30.5863	−1.16188
$694$	−17.9238	−0.680379
$695$	29.8819	1.13348
$696$	6.66499	0.252636
$697$	−5.18846	−0.196527
$698$	5.68935	0.215345
$699$	−18.4155	−0.696538
$700$	43.1156	1.62962
$701$	11.4617	0.432902	0.216451	−	0.976293i	$-0.430552\pi$
$701$	11.4617	0.432902	0.216451	+	0.976293i	$0.430552\pi$
$702$	1.00000	0.0377426
$703$	2.22933	0.0840809
$704$	−6.07783	−0.229067
$705$	20.4904	0.771713
$706$	−12.6046	−0.474380
$707$	−31.0465	−1.16762
$708$	5.42438	0.203861
$709$	−4.22477	−0.158665	−0.0793323	−	0.996848i	$-0.525279\pi$
$709$	−4.22477	−0.158665	−0.0793323	+	0.996848i	$0.525279\pi$
$710$	52.0740	1.95430
$711$	1.41867	0.0532045
$712$	−4.44024	−0.166405
$713$	−21.1642	−0.792607
$714$	3.46149	0.129543
$715$	22.3872	0.837233
$716$	−14.8788	−0.556046
$717$	−20.0784	−0.749842
$718$	−32.9331	−1.22905
$719$	13.9429	0.519983	0.259992	−	0.965611i	$-0.416280\pi$
$719$	13.9429	0.519983	0.259992	+	0.965611i	$0.416280\pi$
$720$	−3.68342	−0.137273
$721$	−5.03243	−0.187418
$722$	−4.47165	−0.166418
$723$	−20.9951	−0.780817
$724$	1.77972	0.0661426
$725$	57.1027	2.12074
$726$	25.9400	0.962725
$727$	33.4359	1.24007	0.620034	−	0.784575i	$-0.287119\pi$
$727$	33.4359	1.24007	0.620034	+	0.784575i	$0.287119\pi$
$728$	−5.03243	−0.186514
$729$	1.00000	0.0370370
$730$	−40.7335	−1.50762
$731$	−5.76453	−0.213209
$732$	6.72933	0.248723
$733$	35.4827	1.31058	0.655292	−	0.755376i	$-0.272546\pi$
$733$	35.4827	1.31058	0.655292	+	0.755376i	$0.272546\pi$
$734$	31.8850	1.17690
$735$	67.5000	2.48977
$736$	−5.54263	−0.204304
$737$	−65.8170	−2.42440
$738$	7.54316	0.277668
$739$	36.8815	1.35671	0.678353	−	0.734736i	$-0.262694\pi$
$739$	36.8815	1.35671	0.678353	+	0.734736i	$0.262694\pi$
$740$	−1.69494	−0.0623072
$741$	−4.84475	−0.177977
$742$	−39.1831	−1.43846
$743$	−25.5306	−0.936628	−0.468314	−	0.883562i	$-0.655138\pi$
$743$	−25.5306	−0.936628	−0.468314	+	0.883562i	$0.655138\pi$
$744$	−3.81844	−0.139991
$745$	56.7602	2.07953
$746$	−18.7119	−0.685092
$747$	−5.18575	−0.189737
$748$	−4.18055	−0.152856
$749$	100.962	3.68908
$750$	−13.1408	−0.479833
$751$	−6.00067	−0.218968	−0.109484	−	0.993989i	$-0.534920\pi$
$751$	−6.00067	−0.218968	−0.109484	+	0.993989i	$0.534920\pi$
$752$	5.56288	0.202857
$753$	5.21065	0.189886
$754$	−6.66499	−0.242725
$755$	54.0872	1.96843
$756$	−5.03243	−0.183028
$757$	−21.3919	−0.777503	−0.388752	−	0.921343i	$-0.627094\pi$
$757$	−21.3919	−0.777503	−0.388752	+	0.921343i	$0.627094\pi$
$758$	−0.754775	−0.0274147
$759$	33.6872	1.22277
$760$	17.8452	0.647315
$761$	18.5331	0.671823	0.335911	−	0.941894i	$-0.390956\pi$
$761$	18.5331	0.671823	0.335911	+	0.941894i	$0.390956\pi$
$762$	−0.988933	−0.0358253
$763$	−53.8964	−1.95118
$764$	−27.1288	−0.981485
$765$	−2.53359	−0.0916020
$766$	−2.46500	−0.0890639
$767$	−5.42438	−0.195863
$768$	−1.00000	−0.0360844
$769$	32.4916	1.17168	0.585838	−	0.810428i	$-0.300766\pi$
$769$	32.4916	1.17168	0.585838	+	0.810428i	$0.300766\pi$
$770$	−112.662	−4.06006
$771$	−0.904912	−0.0325896
$772$	25.0012	0.899814
$773$	44.8293	1.61240	0.806199	−	0.591644i	$-0.201521\pi$
$773$	44.8293	1.61240	0.806199	+	0.591644i	$0.201521\pi$
$774$	8.38067	0.301237
$775$	−32.7147	−1.17515
$776$	14.0901	0.505804
$777$	−2.31569	−0.0830751
$778$	−3.11542	−0.111693
$779$	−36.5448	−1.30935
$780$	3.68342	0.131887
$781$	−85.9249	−3.07463
$782$	−3.81242	−0.136332
$783$	−6.66499	−0.238187
$784$	18.3254	0.654478
$785$	−46.5699	−1.66215
$786$	−12.7607	−0.455160
$787$	−50.2159	−1.79000	−0.895001	−	0.446064i	$-0.852825\pi$
$787$	−50.2159	−1.79000	−0.895001	+	0.446064i	$0.852825\pi$
$788$	−16.4004	−0.584238
$789$	−8.88779	−0.316414
$790$	5.22557	0.185917
$791$	−1.15496	−0.0410658
$792$	6.07783	0.215966
$793$	−6.72933	−0.238966
$794$	1.53453	0.0544583
$795$	28.6795	1.01716
$796$	−1.59261	−0.0564485
$797$	15.1919	0.538124	0.269062	−	0.963123i	$-0.413286\pi$
$797$	15.1919	0.538124	0.269062	+	0.963123i	$0.413286\pi$
$798$	24.3809	0.863075
$799$	3.82635	0.135366
$800$	−8.56755	−0.302909
$801$	4.44024	0.156888
$802$	−34.0311	−1.20168
$803$	67.2125	2.37188
$804$	−10.8290	−0.381910
$805$	−102.741	−3.62115
$806$	3.81844	0.134499
$807$	6.00072	0.211235
$808$	6.16928	0.217034
$809$	−21.1652	−0.744128	−0.372064	−	0.928207i	$-0.621350\pi$
$809$	−21.1652	−0.744128	−0.372064	+	0.928207i	$0.621350\pi$
$810$	3.68342	0.129422
$811$	3.68919	0.129545	0.0647725	−	0.997900i	$-0.479368\pi$
$811$	3.68919	0.129545	0.0647725	+	0.997900i	$0.479368\pi$
$812$	33.5411	1.17706
$813$	23.0789	0.809413
$814$	2.79674	0.0980256
$815$	−83.8344	−2.93659
$816$	−0.687836	−0.0240791
$817$	−40.6023	−1.42049
$818$	−18.5088	−0.647144
$819$	5.03243	0.175847
$820$	27.7846	0.970281
$821$	−25.6266	−0.894374	−0.447187	−	0.894440i	$-0.647574\pi$
$821$	−25.6266	−0.894374	−0.447187	+	0.894440i	$0.647574\pi$
$822$	8.89751	0.310336
$823$	41.7967	1.45694	0.728471	−	0.685077i	$-0.240231\pi$
$823$	41.7967	1.45694	0.728471	+	0.685077i	$0.240231\pi$
$824$	1.00000	0.0348367
$825$	52.0721	1.81292
$826$	27.2978	0.949813
$827$	9.04757	0.314615	0.157307	−	0.987550i	$-0.449719\pi$
$827$	9.04757	0.314615	0.157307	+	0.987550i	$0.449719\pi$
$828$	5.54263	0.192620
$829$	−11.8349	−0.411042	−0.205521	−	0.978653i	$-0.565889\pi$
$829$	−11.8349	−0.411042	−0.205521	+	0.978653i	$0.565889\pi$
$830$	−19.1013	−0.663015
$831$	2.17618	0.0754909
$832$	1.00000	0.0346688
$833$	12.6049	0.436732
$834$	−8.11255	−0.280915
$835$	33.4106	1.15622
$836$	−29.4456	−1.01840
$837$	3.81844	0.131985
$838$	−9.52179	−0.328925
$839$	7.23430	0.249756	0.124878	−	0.992172i	$-0.460146\pi$
$839$	7.23430	0.249756	0.124878	+	0.992172i	$0.460146\pi$
$840$	−18.5365	−0.639572
$841$	15.4221	0.531798
$842$	40.2831	1.38825
$843$	−1.74352	−0.0600501
$844$	12.4299	0.427855
$845$	−3.68342	−0.126713
$846$	−5.56288	−0.191256
$847$	130.541	4.48546
$848$	7.78611	0.267376
$849$	−12.7346	−0.437049
$850$	−5.89307	−0.202131
$851$	2.55046	0.0874288
$852$	−14.1374	−0.484340
$853$	19.9288	0.682348	0.341174	−	0.940000i	$-0.389175\pi$
$853$	19.9288	0.682348	0.341174	+	0.940000i	$0.389175\pi$
$854$	33.8649	1.15883
$855$	−17.8452	−0.610295
$856$	−20.0623	−0.685715
$857$	−37.5409	−1.28237	−0.641187	−	0.767385i	$-0.721558\pi$
$857$	−37.5409	−1.28237	−0.641187	+	0.767385i	$0.721558\pi$
$858$	−6.07783	−0.207494
$859$	41.5544	1.41782	0.708909	−	0.705300i	$-0.249188\pi$
$859$	41.5544	1.41782	0.708909	+	0.705300i	$0.249188\pi$
$860$	30.8695	1.05264
$861$	37.9605	1.29369
$862$	8.41932	0.286763
$863$	1.79748	0.0611869	0.0305935	−	0.999532i	$-0.490260\pi$
$863$	1.79748	0.0611869	0.0305935	+	0.999532i	$0.490260\pi$
$864$	1.00000	0.0340207
$865$	−76.4388	−2.59900
$866$	−26.6609	−0.905975
$867$	16.5269	0.561282
$868$	−19.2161	−0.652236
$869$	−8.62247	−0.292497
$870$	−24.5499	−0.832321
$871$	10.8290	0.366928
$872$	10.7098	0.362680
$873$	−14.0901	−0.476877
$874$	−26.8527	−0.908306
$875$	−66.1301	−2.23561
$876$	11.0586	0.373636
$877$	−3.59307	−0.121329	−0.0606647	−	0.998158i	$-0.519322\pi$
$877$	−3.59307	−0.121329	−0.0606647	+	0.998158i	$0.519322\pi$
$878$	0.393637	0.0132846
$879$	21.2582	0.717020
$880$	22.3872	0.754672
$881$	20.6360	0.695244	0.347622	−	0.937635i	$-0.386989\pi$
$881$	20.6360	0.695244	0.347622	+	0.937635i	$0.386989\pi$
$882$	−18.3254	−0.617048
$883$	12.6857	0.426909	0.213454	−	0.976953i	$-0.431529\pi$
$883$	12.6857	0.426909	0.213454	+	0.976953i	$0.431529\pi$
$884$	0.687836	0.0231344
$885$	−19.9802	−0.671629
$886$	12.8404	0.431381
$887$	48.4068	1.62534	0.812671	−	0.582723i	$-0.198013\pi$
$887$	48.4068	1.62534	0.812671	+	0.582723i	$0.198013\pi$
$888$	0.460154	0.0154418
$889$	−4.97674	−0.166915
$890$	16.3553	0.548230
$891$	−6.07783	−0.203615
$892$	−12.2201	−0.409159
$893$	26.9508	0.901873
$894$	−15.4097	−0.515376
$895$	54.8047	1.83192
$896$	−5.03243	−0.168122
$897$	−5.54263	−0.185063
$898$	−3.61376	−0.120593
$899$	−25.4499	−0.848802
$900$	8.56755	0.285585
$901$	5.35557	0.178420
$902$	−45.8461	−1.52651
$903$	42.1752	1.40350
$904$	0.229504	0.00763320
$905$	−6.55543	−0.217910
$906$	−14.6840	−0.487842
$907$	−8.19429	−0.272087	−0.136044	−	0.990703i	$-0.543439\pi$
$907$	−8.19429	−0.272087	−0.136044	+	0.990703i	$0.543439\pi$
$908$	−6.31622	−0.209611
$909$	−6.16928	−0.204622
$910$	18.5365	0.614480
$911$	54.0981	1.79235	0.896176	−	0.443699i	$-0.146334\pi$
$911$	54.0981	1.79235	0.896176	+	0.443699i	$0.146334\pi$
$912$	−4.84475	−0.160426
$913$	31.5181	1.04310
$914$	−33.7785	−1.11729
$915$	−24.7869	−0.819431
$916$	9.72002	0.321158
$917$	−64.2176	−2.12065
$918$	0.687836	0.0227020
$919$	−5.38044	−0.177484	−0.0887421	−	0.996055i	$-0.528285\pi$
$919$	−5.38044	−0.177484	−0.0887421	+	0.996055i	$0.528285\pi$
$920$	20.4158	0.673090
$921$	23.5910	0.777349
$922$	−39.8441	−1.31220
$923$	14.1374	0.465339
$924$	30.5863	1.00621
$925$	3.94239	0.129625
$926$	−15.5460	−0.510874
$927$	−1.00000	−0.0328443
$928$	−6.66499	−0.218789
$929$	−2.15526	−0.0707117	−0.0353558	−	0.999375i	$-0.511256\pi$
$929$	−2.15526	−0.0707117	−0.0353558	+	0.999375i	$0.511256\pi$
$930$	14.0649	0.461207
$931$	88.7820	2.90971
$932$	18.4155	0.603220
$933$	−12.7248	−0.416592
$934$	3.24823	0.106285
$935$	15.3987	0.503592
$936$	−1.00000	−0.0326860
$937$	3.85420	0.125911	0.0629557	−	0.998016i	$-0.479947\pi$
$937$	3.85420	0.125911	0.0629557	+	0.998016i	$0.479947\pi$
$938$	−54.4963	−1.77937
$939$	−30.6522	−1.00030
$940$	−20.4904	−0.668323
$941$	42.9530	1.40023	0.700114	−	0.714031i	$-0.253133\pi$
$941$	42.9530	1.40023	0.700114	+	0.714031i	$0.253133\pi$
$942$	12.6431	0.411935
$943$	−41.8090	−1.36149
$944$	−5.42438	−0.176548
$945$	18.5365	0.602994
$946$	−50.9363	−1.65608
$947$	−29.8809	−0.970999	−0.485499	−	0.874237i	$-0.661362\pi$
$947$	−29.8809	−0.970999	−0.485499	+	0.874237i	$0.661362\pi$
$948$	−1.41867	−0.0460764
$949$	−11.0586	−0.358978
$950$	−41.5077	−1.34669
$951$	19.2824	0.625273
$952$	−3.46149	−0.112188
$953$	−5.36459	−0.173776	−0.0868880	−	0.996218i	$-0.527692\pi$
$953$	−5.36459	−0.173776	−0.0868880	+	0.996218i	$0.527692\pi$
$954$	−7.78611	−0.252085
$955$	99.9266	3.23355
$956$	20.0784	0.649382
$957$	40.5087	1.30946
$958$	−29.4666	−0.952021
$959$	44.7761	1.44590
$960$	3.68342	0.118882
$961$	−16.4195	−0.529661
$962$	−0.460154	−0.0148360
$963$	20.0623	0.646499
$964$	20.9951	0.676207
$965$	−92.0899	−2.96448
$966$	27.8929	0.897440
$967$	55.0991	1.77187	0.885935	−	0.463810i	$-0.153518\pi$
$967$	55.0991	1.77187	0.885935	+	0.463810i	$0.153518\pi$
$968$	−25.9400	−0.833744
$969$	−3.33240	−0.107052
$970$	−51.8996	−1.66640
$971$	39.5765	1.27007	0.635035	−	0.772484i	$-0.280986\pi$
$971$	39.5765	1.27007	0.635035	+	0.772484i	$0.280986\pi$
$972$	−1.00000	−0.0320750
$973$	−40.8259	−1.30882
$974$	−39.0218	−1.25034
$975$	−8.56755	−0.274381
$976$	−6.72933	−0.215401
$977$	16.4514	0.526327	0.263164	−	0.964751i	$-0.415234\pi$
$977$	16.4514	0.526327	0.263164	+	0.964751i	$0.415234\pi$
$978$	22.7600	0.727783
$979$	−26.9870	−0.862510
$980$	−67.5000	−2.15621
$981$	−10.7098	−0.341938
$982$	−2.37906	−0.0759188
$983$	−20.6326	−0.658076	−0.329038	−	0.944317i	$-0.606725\pi$
$983$	−20.6326	−0.658076	−0.329038	+	0.944317i	$0.606725\pi$
$984$	−7.54316	−0.240467
$985$	60.4093	1.92480
$986$	−4.58442	−0.145998
$987$	−27.9948	−0.891084
$988$	4.84475	0.154132
$989$	−46.4510	−1.47705
$990$	−22.3872	−0.711511
$991$	26.7235	0.848901	0.424451	−	0.905451i	$-0.360467\pi$
$991$	26.7235	0.848901	0.424451	+	0.905451i	$0.360467\pi$
$992$	3.81844	0.121236
$993$	34.7227	1.10189
$994$	−71.1457	−2.25660
$995$	5.86624	0.185972
$996$	5.18575	0.164317
$997$	−32.8776	−1.04124	−0.520622	−	0.853787i	$-0.674300\pi$
$997$	−32.8776	−1.04124	−0.520622	+	0.853787i	$0.674300\pi$
$998$	−6.26699	−0.198378
$999$	−0.460154	−0.0145586

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.z.1.1	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.z.1.1	✓	14	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.68342 q^{5} +1.00000 q^{6} +5.03243 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.68342 q^{5} +1.00000 q^{6} +5.03243 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.68342 q^{10} -6.07783 q^{11} -1.00000 q^{12} +1.00000 q^{13} -5.03243 q^{14} +3.68342 q^{15} +1.00000 q^{16} +0.687836 q^{17} -1.00000 q^{18} +4.84475 q^{19} -3.68342 q^{20} -5.03243 q^{21} +6.07783 q^{22} +5.54263 q^{23} +1.00000 q^{24} +8.56755 q^{25} -1.00000 q^{26} -1.00000 q^{27} +5.03243 q^{28} +6.66499 q^{29} -3.68342 q^{30} -3.81844 q^{31} -1.00000 q^{32} +6.07783 q^{33} -0.687836 q^{34} -18.5365 q^{35} +1.00000 q^{36} +0.460154 q^{37} -4.84475 q^{38} -1.00000 q^{39} +3.68342 q^{40} -7.54316 q^{41} +5.03243 q^{42} -8.38067 q^{43} -6.07783 q^{44} -3.68342 q^{45} -5.54263 q^{46} +5.56288 q^{47} -1.00000 q^{48} +18.3254 q^{49} -8.56755 q^{50} -0.687836 q^{51} +1.00000 q^{52} +7.78611 q^{53} +1.00000 q^{54} +22.3872 q^{55} -5.03243 q^{56} -4.84475 q^{57} -6.66499 q^{58} -5.42438 q^{59} +3.68342 q^{60} -6.72933 q^{61} +3.81844 q^{62} +5.03243 q^{63} +1.00000 q^{64} -3.68342 q^{65} -6.07783 q^{66} +10.8290 q^{67} +0.687836 q^{68} -5.54263 q^{69} +18.5365 q^{70} +14.1374 q^{71} -1.00000 q^{72} -11.0586 q^{73} -0.460154 q^{74} -8.56755 q^{75} +4.84475 q^{76} -30.5863 q^{77} +1.00000 q^{78} +1.41867 q^{79} -3.68342 q^{80} +1.00000 q^{81} +7.54316 q^{82} -5.18575 q^{83} -5.03243 q^{84} -2.53359 q^{85} +8.38067 q^{86} -6.66499 q^{87} +6.07783 q^{88} +4.44024 q^{89} +3.68342 q^{90} +5.03243 q^{91} +5.54263 q^{92} +3.81844 q^{93} -5.56288 q^{94} -17.8452 q^{95} +1.00000 q^{96} -14.0901 q^{97} -18.3254 q^{98} -6.07783 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9} + 3 q^{10} + 5 q^{11} - 14 q^{12} + 14 q^{13} - 4 q^{14} + 3 q^{15} + 14 q^{16} - 7 q^{17} - 14 q^{18} + 31 q^{19} - 3 q^{20} - 4 q^{21} - 5 q^{22} + 14 q^{23} + 14 q^{24} + 11 q^{25} - 14 q^{26} - 14 q^{27} + 4 q^{28} + 9 q^{29} - 3 q^{30} + 23 q^{31} - 14 q^{32} - 5 q^{33} + 7 q^{34} - 2 q^{35} + 14 q^{36} + 12 q^{37} - 31 q^{38} - 14 q^{39} + 3 q^{40} - 5 q^{41} + 4 q^{42} - 2 q^{43} + 5 q^{44} - 3 q^{45} - 14 q^{46} - 11 q^{47} - 14 q^{48} + 52 q^{49} - 11 q^{50} + 7 q^{51} + 14 q^{52} + 6 q^{53} + 14 q^{54} + 30 q^{55} - 4 q^{56} - 31 q^{57} - 9 q^{58} - 4 q^{59} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 4 q^{63} + 14 q^{64} - 3 q^{65} + 5 q^{66} + 24 q^{67} - 7 q^{68} - 14 q^{69} + 2 q^{70} + 20 q^{71} - 14 q^{72} + 2 q^{73} - 12 q^{74} - 11 q^{75} + 31 q^{76} - 28 q^{77} + 14 q^{78} + 59 q^{79} - 3 q^{80} + 14 q^{81} + 5 q^{82} + q^{83} - 4 q^{84} - 29 q^{85} + 2 q^{86} - 9 q^{87} - 5 q^{88} + 6 q^{89} + 3 q^{90} + 4 q^{91} + 14 q^{92} - 23 q^{93} + 11 q^{94} - 58 q^{95} + 14 q^{96} - 6 q^{97} - 52 q^{98} + 5 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9 + 3 * q^10 + 5 * q^11 - 14 * q^12 + 14 * q^13 - 4 * q^14 + 3 * q^15 + 14 * q^16 - 7 * q^17 - 14 * q^18 + 31 * q^19 - 3 * q^20 - 4 * q^21 - 5 * q^22 + 14 * q^23 + 14 * q^24 + 11 * q^25 - 14 * q^26 - 14 * q^27 + 4 * q^28 + 9 * q^29 - 3 * q^30 + 23 * q^31 - 14 * q^32 - 5 * q^33 + 7 * q^34 - 2 * q^35 + 14 * q^36 + 12 * q^37 - 31 * q^38 - 14 * q^39 + 3 * q^40 - 5 * q^41 + 4 * q^42 - 2 * q^43 + 5 * q^44 - 3 * q^45 - 14 * q^46 - 11 * q^47 - 14 * q^48 + 52 * q^49 - 11 * q^50 + 7 * q^51 + 14 * q^52 + 6 * q^53 + 14 * q^54 + 30 * q^55 - 4 * q^56 - 31 * q^57 - 9 * q^58 - 4 * q^59 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 4 * q^63 + 14 * q^64 - 3 * q^65 + 5 * q^66 + 24 * q^67 - 7 * q^68 - 14 * q^69 + 2 * q^70 + 20 * q^71 - 14 * q^72 + 2 * q^73 - 12 * q^74 - 11 * q^75 + 31 * q^76 - 28 * q^77 + 14 * q^78 + 59 * q^79 - 3 * q^80 + 14 * q^81 + 5 * q^82 + q^83 - 4 * q^84 - 29 * q^85 + 2 * q^86 - 9 * q^87 - 5 * q^88 + 6 * q^89 + 3 * q^90 + 4 * q^91 + 14 * q^92 - 23 * q^93 + 11 * q^94 - 58 * q^95 + 14 * q^96 - 6 * q^97 - 52 * q^98 + 5 * q^99

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