LMFDB - Embedded newform 8034.2.a.z.1.5

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			1.5
Root			$1.52247$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.52247 q^{5} +1.00000 q^{6} -3.40750 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.52247 q^{5} +1.00000 q^{6} -3.40750 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.52247 q^{10} +2.89222 q^{11} -1.00000 q^{12} +1.00000 q^{13} +3.40750 q^{14} +1.52247 q^{15} +1.00000 q^{16} +3.63214 q^{17} -1.00000 q^{18} +8.33542 q^{19} -1.52247 q^{20} +3.40750 q^{21} -2.89222 q^{22} -8.49258 q^{23} +1.00000 q^{24} -2.68210 q^{25} -1.00000 q^{26} -1.00000 q^{27} -3.40750 q^{28} -1.96589 q^{29} -1.52247 q^{30} +2.49196 q^{31} -1.00000 q^{32} -2.89222 q^{33} -3.63214 q^{34} +5.18780 q^{35} +1.00000 q^{36} +5.76014 q^{37} -8.33542 q^{38} -1.00000 q^{39} +1.52247 q^{40} +1.30953 q^{41} -3.40750 q^{42} -6.49471 q^{43} +2.89222 q^{44} -1.52247 q^{45} +8.49258 q^{46} +4.75831 q^{47} -1.00000 q^{48} +4.61105 q^{49} +2.68210 q^{50} -3.63214 q^{51} +1.00000 q^{52} +7.93365 q^{53} +1.00000 q^{54} -4.40330 q^{55} +3.40750 q^{56} -8.33542 q^{57} +1.96589 q^{58} -7.98118 q^{59} +1.52247 q^{60} +8.78947 q^{61} -2.49196 q^{62} -3.40750 q^{63} +1.00000 q^{64} -1.52247 q^{65} +2.89222 q^{66} +3.78863 q^{67} +3.63214 q^{68} +8.49258 q^{69} -5.18780 q^{70} +12.6153 q^{71} -1.00000 q^{72} -8.45160 q^{73} -5.76014 q^{74} +2.68210 q^{75} +8.33542 q^{76} -9.85523 q^{77} +1.00000 q^{78} +3.93397 q^{79} -1.52247 q^{80} +1.00000 q^{81} -1.30953 q^{82} +11.4679 q^{83} +3.40750 q^{84} -5.52980 q^{85} +6.49471 q^{86} +1.96589 q^{87} -2.89222 q^{88} -15.2946 q^{89} +1.52247 q^{90} -3.40750 q^{91} -8.49258 q^{92} -2.49196 q^{93} -4.75831 q^{94} -12.6904 q^{95} +1.00000 q^{96} -14.2627 q^{97} -4.61105 q^{98} +2.89222 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.52247	−0.680868	−0.340434	−	0.940268i	$-0.610574\pi$
$5$	−1.52247	−0.680868	−0.340434	+	0.940268i	$0.610574\pi$
$6$	1.00000	0.408248
$7$	−3.40750	−1.28791	−0.643957	−	0.765062i	$-0.722708\pi$
$7$	−3.40750	−1.28791	−0.643957	+	0.765062i	$0.722708\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.52247	0.481446
$11$	2.89222	0.872036	0.436018	−	0.899938i	$-0.356388\pi$
$11$	2.89222	0.872036	0.436018	+	0.899938i	$0.356388\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	3.40750	0.910693
$15$	1.52247	0.393099
$16$	1.00000	0.250000
$17$	3.63214	0.880922	0.440461	−	0.897772i	$-0.354815\pi$
$17$	3.63214	0.880922	0.440461	+	0.897772i	$0.354815\pi$
$18$	−1.00000	−0.235702
$19$	8.33542	1.91228	0.956139	−	0.292914i	$-0.0946251\pi$
$19$	8.33542	1.91228	0.956139	+	0.292914i	$0.0946251\pi$
$20$	−1.52247	−0.340434
$21$	3.40750	0.743577
$22$	−2.89222	−0.616623
$23$	−8.49258	−1.77083	−0.885413	−	0.464806i	$-0.846124\pi$
$23$	−8.49258	−1.77083	−0.885413	+	0.464806i	$0.846124\pi$
$24$	1.00000	0.204124
$25$	−2.68210	−0.536419
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	−3.40750	−0.643957
$29$	−1.96589	−0.365057	−0.182528	−	0.983201i	$-0.558428\pi$
$29$	−1.96589	−0.365057	−0.182528	+	0.983201i	$0.558428\pi$
$30$	−1.52247	−0.277963
$31$	2.49196	0.447569	0.223784	−	0.974639i	$-0.428159\pi$
$31$	2.49196	0.447569	0.223784	+	0.974639i	$0.428159\pi$
$32$	−1.00000	−0.176777
$33$	−2.89222	−0.503470
$34$	−3.63214	−0.622906
$35$	5.18780	0.876899
$36$	1.00000	0.166667
$37$	5.76014	0.946962	0.473481	−	0.880804i	$-0.342997\pi$
$37$	5.76014	0.946962	0.473481	+	0.880804i	$0.342997\pi$
$38$	−8.33542	−1.35218
$39$	−1.00000	−0.160128
$40$	1.52247	0.240723
$41$	1.30953	0.204514	0.102257	−	0.994758i	$-0.467394\pi$
$41$	1.30953	0.204514	0.102257	+	0.994758i	$0.467394\pi$
$42$	−3.40750	−0.525789
$43$	−6.49471	−0.990434	−0.495217	−	0.868769i	$-0.664912\pi$
$43$	−6.49471	−0.990434	−0.495217	+	0.868769i	$0.664912\pi$
$44$	2.89222	0.436018
$45$	−1.52247	−0.226956
$46$	8.49258	1.25216
$47$	4.75831	0.694071	0.347035	−	0.937852i	$-0.387188\pi$
$47$	4.75831	0.694071	0.347035	+	0.937852i	$0.387188\pi$
$48$	−1.00000	−0.144338
$49$	4.61105	0.658722
$50$	2.68210	0.379306
$51$	−3.63214	−0.508601
$52$	1.00000	0.138675
$53$	7.93365	1.08977	0.544885	−	0.838511i	$-0.316573\pi$
$53$	7.93365	1.08977	0.544885	+	0.838511i	$0.316573\pi$
$54$	1.00000	0.136083
$55$	−4.40330	−0.593741
$56$	3.40750	0.455346
$57$	−8.33542	−1.10405
$58$	1.96589	0.258134
$59$	−7.98118	−1.03906	−0.519531	−	0.854452i	$-0.673893\pi$
$59$	−7.98118	−1.03906	−0.519531	+	0.854452i	$0.673893\pi$
$60$	1.52247	0.196550
$61$	8.78947	1.12538	0.562688	−	0.826669i	$-0.309767\pi$
$61$	8.78947	1.12538	0.562688	+	0.826669i	$0.309767\pi$
$62$	−2.49196	−0.316479
$63$	−3.40750	−0.429305
$64$	1.00000	0.125000
$65$	−1.52247	−0.188839
$66$	2.89222	0.356007
$67$	3.78863	0.462855	0.231428	−	0.972852i	$-0.425660\pi$
$67$	3.78863	0.462855	0.231428	+	0.972852i	$0.425660\pi$
$68$	3.63214	0.440461
$69$	8.49258	1.02239
$70$	−5.18780	−0.620061
$71$	12.6153	1.49716	0.748581	−	0.663044i	$-0.230736\pi$
$71$	12.6153	1.49716	0.748581	+	0.663044i	$0.230736\pi$
$72$	−1.00000	−0.117851
$73$	−8.45160	−0.989185	−0.494593	−	0.869125i	$-0.664683\pi$
$73$	−8.45160	−0.989185	−0.494593	+	0.869125i	$0.664683\pi$
$74$	−5.76014	−0.669603
$75$	2.68210	0.309702
$76$	8.33542	0.956139
$77$	−9.85523	−1.12311
$78$	1.00000	0.113228
$79$	3.93397	0.442607	0.221303	−	0.975205i	$-0.428969\pi$
$79$	3.93397	0.442607	0.221303	+	0.975205i	$0.428969\pi$
$80$	−1.52247	−0.170217
$81$	1.00000	0.111111
$82$	−1.30953	−0.144613
$83$	11.4679	1.25876	0.629382	−	0.777096i	$-0.283308\pi$
$83$	11.4679	1.25876	0.629382	+	0.777096i	$0.283308\pi$
$84$	3.40750	0.371789
$85$	−5.52980	−0.599791
$86$	6.49471	0.700343
$87$	1.96589	0.210766
$88$	−2.89222	−0.308311
$89$	−15.2946	−1.62122	−0.810611	−	0.585585i	$-0.800865\pi$
$89$	−15.2946	−1.62122	−0.810611	+	0.585585i	$0.800865\pi$
$90$	1.52247	0.160482
$91$	−3.40750	−0.357203
$92$	−8.49258	−0.885413
$93$	−2.49196	−0.258404
$94$	−4.75831	−0.490782
$95$	−12.6904	−1.30201
$96$	1.00000	0.102062
$97$	−14.2627	−1.44816	−0.724080	−	0.689716i	$-0.757735\pi$
$97$	−14.2627	−1.44816	−0.724080	+	0.689716i	$0.757735\pi$
$98$	−4.61105	−0.465787
$99$	2.89222	0.290679
$100$	−2.68210	−0.268210
$101$	−6.08371	−0.605352	−0.302676	−	0.953094i	$-0.597880\pi$
$101$	−6.08371	−0.605352	−0.302676	+	0.953094i	$0.597880\pi$
$102$	3.63214	0.359635
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	−5.18780	−0.506278
$106$	−7.93365	−0.770584
$107$	−0.0118287	−0.00114352	−0.000571760	−	1.00000i	$-0.500182\pi$
$107$	−0.0118287	−0.00114352	−0.000571760		1.00000i	$0.500182\pi$
$108$	−1.00000	−0.0962250
$109$	9.52537	0.912365	0.456182	−	0.889886i	$-0.349216\pi$
$109$	9.52537	0.912365	0.456182	+	0.889886i	$0.349216\pi$
$110$	4.40330	0.419838
$111$	−5.76014	−0.546729
$112$	−3.40750	−0.321978
$113$	−12.3005	−1.15713	−0.578565	−	0.815637i	$-0.696387\pi$
$113$	−12.3005	−1.15713	−0.578565	+	0.815637i	$0.696387\pi$
$114$	8.33542	0.780684
$115$	12.9297	1.20570
$116$	−1.96589	−0.182528
$117$	1.00000	0.0924500
$118$	7.98118	0.734728
$119$	−12.3765	−1.13455
$120$	−1.52247	−0.138982
$121$	−2.63508	−0.239553
$122$	−8.78947	−0.795762
$123$	−1.30953	−0.118076
$124$	2.49196	0.223784
$125$	11.6957	1.04610
$126$	3.40750	0.303564
$127$	9.53346	0.845958	0.422979	−	0.906139i	$-0.360984\pi$
$127$	9.53346	0.845958	0.422979	+	0.906139i	$0.360984\pi$
$128$	−1.00000	−0.0883883
$129$	6.49471	0.571828
$130$	1.52247	0.133529
$131$	4.16630	0.364011	0.182005	−	0.983298i	$-0.441741\pi$
$131$	4.16630	0.364011	0.182005	+	0.983298i	$0.441741\pi$
$132$	−2.89222	−0.251735
$133$	−28.4030	−2.46285
$134$	−3.78863	−0.327288
$135$	1.52247	0.131033
$136$	−3.63214	−0.311453
$137$	−22.5972	−1.93061	−0.965304	−	0.261130i	$-0.915905\pi$
$137$	−22.5972	−1.93061	−0.965304	+	0.261130i	$0.915905\pi$
$138$	−8.49258	−0.722937
$139$	−1.82634	−0.154908	−0.0774541	−	0.996996i	$-0.524679\pi$
$139$	−1.82634	−0.154908	−0.0774541	+	0.996996i	$0.524679\pi$
$140$	5.18780	0.438449
$141$	−4.75831	−0.400722
$142$	−12.6153	−1.05865
$143$	2.89222	0.241859
$144$	1.00000	0.0833333
$145$	2.99300	0.248555
$146$	8.45160	0.699460
$147$	−4.61105	−0.380313
$148$	5.76014	0.473481
$149$	−7.97737	−0.653531	−0.326766	−	0.945105i	$-0.605959\pi$
$149$	−7.97737	−0.653531	−0.326766	+	0.945105i	$0.605959\pi$
$150$	−2.68210	−0.218992
$151$	−24.2779	−1.97570	−0.987852	−	0.155398i	$-0.950334\pi$
$151$	−24.2779	−1.97570	−0.987852	+	0.155398i	$0.950334\pi$
$152$	−8.33542	−0.676092
$153$	3.63214	0.293641
$154$	9.85523	0.794157
$155$	−3.79392	−0.304735
$156$	−1.00000	−0.0800641
$157$	11.7313	0.936260	0.468130	−	0.883660i	$-0.344928\pi$
$157$	11.7313	0.936260	0.468130	+	0.883660i	$0.344928\pi$
$158$	−3.93397	−0.312970
$159$	−7.93365	−0.629179
$160$	1.52247	0.120362
$161$	28.9385	2.28067
$162$	−1.00000	−0.0785674
$163$	−11.2838	−0.883818	−0.441909	−	0.897060i	$-0.645699\pi$
$163$	−11.2838	−0.883818	−0.441909	+	0.897060i	$0.645699\pi$
$164$	1.30953	0.102257
$165$	4.40330	0.342797
$166$	−11.4679	−0.890080
$167$	−21.2258	−1.64250	−0.821249	−	0.570569i	$-0.806723\pi$
$167$	−21.2258	−1.64250	−0.821249	+	0.570569i	$0.806723\pi$
$168$	−3.40750	−0.262894
$169$	1.00000	0.0769231
$170$	5.52980	0.424117
$171$	8.33542	0.637426
$172$	−6.49471	−0.495217
$173$	−10.3787	−0.789081	−0.394541	−	0.918878i	$-0.629096\pi$
$173$	−10.3787	−0.789081	−0.394541	+	0.918878i	$0.629096\pi$
$174$	−1.96589	−0.149034
$175$	9.13924	0.690862
$176$	2.89222	0.218009
$177$	7.98118	0.599903
$178$	15.2946	1.14638
$179$	−5.05976	−0.378184	−0.189092	−	0.981959i	$-0.560554\pi$
$179$	−5.05976	−0.378184	−0.189092	+	0.981959i	$0.560554\pi$
$180$	−1.52247	−0.113478
$181$	−13.1453	−0.977084	−0.488542	−	0.872540i	$-0.662471\pi$
$181$	−13.1453	−0.977084	−0.488542	+	0.872540i	$0.662471\pi$
$182$	3.40750	0.252581
$183$	−8.78947	−0.649737
$184$	8.49258	0.626081
$185$	−8.76962	−0.644756
$186$	2.49196	0.182719
$187$	10.5049	0.768196
$188$	4.75831	0.347035
$189$	3.40750	0.247859
$190$	12.6904	0.920658
$191$	10.6105	0.767750	0.383875	−	0.923385i	$-0.374589\pi$
$191$	10.6105	0.767750	0.383875	+	0.923385i	$0.374589\pi$
$192$	−1.00000	−0.0721688
$193$	−13.6729	−0.984200	−0.492100	−	0.870539i	$-0.663771\pi$
$193$	−13.6729	−0.984200	−0.492100	+	0.870539i	$0.663771\pi$
$194$	14.2627	1.02400
$195$	1.52247	0.109026
$196$	4.61105	0.329361
$197$	13.0622	0.930646	0.465323	−	0.885141i	$-0.345938\pi$
$197$	13.0622	0.930646	0.465323	+	0.885141i	$0.345938\pi$
$198$	−2.89222	−0.205541
$199$	21.9234	1.55411	0.777054	−	0.629434i	$-0.216713\pi$
$199$	21.9234	1.55411	0.777054	+	0.629434i	$0.216713\pi$
$200$	2.68210	0.189653
$201$	−3.78863	−0.267230
$202$	6.08371	0.428048
$203$	6.69877	0.470162
$204$	−3.63214	−0.254300
$205$	−1.99371	−0.139247
$206$	1.00000	0.0696733
$207$	−8.49258	−0.590275
$208$	1.00000	0.0693375
$209$	24.1078	1.66757
$210$	5.18780	0.357992
$211$	15.1150	1.04056	0.520280	−	0.853995i	$-0.325827\pi$
$211$	15.1150	1.04056	0.520280	+	0.853995i	$0.325827\pi$
$212$	7.93365	0.544885
$213$	−12.6153	−0.864386
$214$	0.0118287	0.000808591 0
$215$	9.88798	0.674355
$216$	1.00000	0.0680414
$217$	−8.49135	−0.576430
$218$	−9.52537	−0.645139
$219$	8.45160	0.571107
$220$	−4.40330	−0.296871
$221$	3.63214	0.244324
$222$	5.76014	0.386596
$223$	18.7880	1.25813	0.629067	−	0.777351i	$-0.283437\pi$
$223$	18.7880	1.25813	0.629067	+	0.777351i	$0.283437\pi$
$224$	3.40750	0.227673
$225$	−2.68210	−0.178806
$226$	12.3005	0.818214
$227$	6.60501	0.438390	0.219195	−	0.975681i	$-0.429657\pi$
$227$	6.60501	0.438390	0.219195	+	0.975681i	$0.429657\pi$
$228$	−8.33542	−0.552027
$229$	4.77427	0.315493	0.157746	−	0.987480i	$-0.449577\pi$
$229$	4.77427	0.315493	0.157746	+	0.987480i	$0.449577\pi$
$230$	−12.9297	−0.852557
$231$	9.85523	0.648426
$232$	1.96589	0.129067
$233$	−7.86773	−0.515432	−0.257716	−	0.966221i	$-0.582970\pi$
$233$	−7.86773	−0.515432	−0.257716	+	0.966221i	$0.582970\pi$
$234$	−1.00000	−0.0653720
$235$	−7.24437	−0.472570
$236$	−7.98118	−0.519531
$237$	−3.93397	−0.255539
$238$	12.3765	0.802249
$239$	−12.9810	−0.839673	−0.419837	−	0.907600i	$-0.637913\pi$
$239$	−12.9810	−0.839673	−0.419837	+	0.907600i	$0.637913\pi$
$240$	1.52247	0.0982748
$241$	11.8220	0.761519	0.380760	−	0.924674i	$-0.375663\pi$
$241$	11.8220	0.761519	0.380760	+	0.924674i	$0.375663\pi$
$242$	2.63508	0.169390
$243$	−1.00000	−0.0641500
$244$	8.78947	0.562688
$245$	−7.02017	−0.448502
$246$	1.30953	0.0834923
$247$	8.33542	0.530370
$248$	−2.49196	−0.158240
$249$	−11.4679	−0.726747
$250$	−11.6957	−0.739703
$251$	10.2546	0.647267	0.323634	−	0.946183i	$-0.395096\pi$
$251$	10.2546	0.647267	0.323634	+	0.946183i	$0.395096\pi$
$252$	−3.40750	−0.214652
$253$	−24.5624	−1.54422
$254$	−9.53346	−0.598183
$255$	5.52980	0.346290
$256$	1.00000	0.0625000
$257$	7.88163	0.491643	0.245821	−	0.969315i	$-0.420942\pi$
$257$	7.88163	0.491643	0.245821	+	0.969315i	$0.420942\pi$
$258$	−6.49471	−0.404343
$259$	−19.6277	−1.21961
$260$	−1.52247	−0.0944193
$261$	−1.96589	−0.121686
$262$	−4.16630	−0.257395
$263$	−19.5054	−1.20276	−0.601379	−	0.798964i	$-0.705382\pi$
$263$	−19.5054	−1.20276	−0.601379	+	0.798964i	$0.705382\pi$
$264$	2.89222	0.178004
$265$	−12.0787	−0.741989
$266$	28.4030	1.74150
$267$	15.2946	0.936013
$268$	3.78863	0.231428
$269$	29.6814	1.80971	0.904853	−	0.425724i	$-0.139980\pi$
$269$	29.6814	1.80971	0.904853	+	0.425724i	$0.139980\pi$
$270$	−1.52247	−0.0926543
$271$	1.48750	0.0903590	0.0451795	−	0.998979i	$-0.485614\pi$
$271$	1.48750	0.0903590	0.0451795	+	0.998979i	$0.485614\pi$
$272$	3.63214	0.220231
$273$	3.40750	0.206231
$274$	22.5972	1.36515
$275$	−7.75720	−0.467777
$276$	8.49258	0.511193
$277$	32.2188	1.93584	0.967921	−	0.251255i	$-0.0808432\pi$
$277$	32.2188	1.93584	0.967921	+	0.251255i	$0.0808432\pi$
$278$	1.82634	0.109537
$279$	2.49196	0.149190
$280$	−5.18780	−0.310031
$281$	15.9702	0.952700	0.476350	−	0.879256i	$-0.341960\pi$
$281$	15.9702	0.952700	0.476350	+	0.879256i	$0.341960\pi$
$282$	4.75831	0.283353
$283$	15.5347	0.923440	0.461720	−	0.887026i	$-0.347232\pi$
$283$	15.5347	0.923440	0.461720	+	0.887026i	$0.347232\pi$
$284$	12.6153	0.748581
$285$	12.6904	0.751714
$286$	−2.89222	−0.171020
$287$	−4.46221	−0.263396
$288$	−1.00000	−0.0589256
$289$	−3.80759	−0.223976
$290$	−2.99300	−0.175755
$291$	14.2627	0.836096
$292$	−8.45160	−0.494593
$293$	0.645648	0.0377191	0.0188596	−	0.999822i	$-0.493996\pi$
$293$	0.645648	0.0377191	0.0188596	+	0.999822i	$0.493996\pi$
$294$	4.61105	0.268922
$295$	12.1511	0.707463
$296$	−5.76014	−0.334802
$297$	−2.89222	−0.167823
$298$	7.97737	0.462117
$299$	−8.49258	−0.491139
$300$	2.68210	0.154851
$301$	22.1307	1.27559
$302$	24.2779	1.39703
$303$	6.08371	0.349500
$304$	8.33542	0.478069
$305$	−13.3817	−0.766232
$306$	−3.63214	−0.207635
$307$	17.3345	0.989331	0.494666	−	0.869083i	$-0.335291\pi$
$307$	17.3345	0.989331	0.494666	+	0.869083i	$0.335291\pi$
$308$	−9.85523	−0.561554
$309$	1.00000	0.0568880
$310$	3.79392	0.215480
$311$	1.26256	0.0715933	0.0357966	−	0.999359i	$-0.488603\pi$
$311$	1.26256	0.0715933	0.0357966	+	0.999359i	$0.488603\pi$
$312$	1.00000	0.0566139
$313$	22.2729	1.25894	0.629469	−	0.777026i	$-0.283273\pi$
$313$	22.2729	1.25894	0.629469	+	0.777026i	$0.283273\pi$
$314$	−11.7313	−0.662036
$315$	5.18780	0.292300
$316$	3.93397	0.221303
$317$	−1.98445	−0.111458	−0.0557288	−	0.998446i	$-0.517748\pi$
$317$	−1.98445	−0.111458	−0.0557288	+	0.998446i	$0.517748\pi$
$318$	7.93365	0.444897
$319$	−5.68578	−0.318343
$320$	−1.52247	−0.0851084
$321$	0.0118287	0.000660212 0
$322$	−28.9385	−1.61268
$323$	30.2754	1.68457
$324$	1.00000	0.0555556
$325$	−2.68210	−0.148776
$326$	11.2838	0.624954
$327$	−9.52537	−0.526754
$328$	−1.30953	−0.0723065
$329$	−16.2139	−0.893904
$330$	−4.40330	−0.242394
$331$	7.80176	0.428823	0.214412	−	0.976743i	$-0.431217\pi$
$331$	7.80176	0.428823	0.214412	+	0.976743i	$0.431217\pi$
$332$	11.4679	0.629382
$333$	5.76014	0.315654
$334$	21.2258	1.16142
$335$	−5.76806	−0.315143
$336$	3.40750	0.185894
$337$	12.8629	0.700687	0.350343	−	0.936621i	$-0.386065\pi$
$337$	12.8629	0.700687	0.350343	+	0.936621i	$0.386065\pi$
$338$	−1.00000	−0.0543928
$339$	12.3005	0.668069
$340$	−5.52980	−0.299896
$341$	7.20728	0.390296
$342$	−8.33542	−0.450728
$343$	8.14033	0.439537
$344$	6.49471	0.350171
$345$	−12.9297	−0.696110
$346$	10.3787	0.557965
$347$	−14.1100	−0.757464	−0.378732	−	0.925506i	$-0.623640\pi$
$347$	−14.1100	−0.757464	−0.378732	+	0.925506i	$0.623640\pi$
$348$	1.96589	0.105383
$349$	20.8994	1.11872	0.559361	−	0.828924i	$-0.311047\pi$
$349$	20.8994	1.11872	0.559361	+	0.828924i	$0.311047\pi$
$350$	−9.13924	−0.488513
$351$	−1.00000	−0.0533761
$352$	−2.89222	−0.154156
$353$	−4.18829	−0.222920	−0.111460	−	0.993769i	$-0.535553\pi$
$353$	−4.18829	−0.222920	−0.111460	+	0.993769i	$0.535553\pi$
$354$	−7.98118	−0.424195
$355$	−19.2064	−1.01937
$356$	−15.2946	−0.810611
$357$	12.3765	0.655034
$358$	5.05976	0.267416
$359$	−27.7433	−1.46423	−0.732117	−	0.681179i	$-0.761468\pi$
$359$	−27.7433	−1.46423	−0.732117	+	0.681179i	$0.761468\pi$
$360$	1.52247	0.0802410
$361$	50.4793	2.65680
$362$	13.1453	0.690903
$363$	2.63508	0.138306
$364$	−3.40750	−0.178602
$365$	12.8673	0.673504
$366$	8.78947	0.459433
$367$	5.85048	0.305392	0.152696	−	0.988273i	$-0.451204\pi$
$367$	5.85048	0.305392	0.152696	+	0.988273i	$0.451204\pi$
$368$	−8.49258	−0.442706
$369$	1.30953	0.0681712
$370$	8.76962	0.455911
$371$	−27.0339	−1.40353
$372$	−2.49196	−0.129202
$373$	15.8596	0.821177	0.410588	−	0.911821i	$-0.365323\pi$
$373$	15.8596	0.821177	0.410588	+	0.911821i	$0.365323\pi$
$374$	−10.5049	−0.543197
$375$	−11.6957	−0.603965
$376$	−4.75831	−0.245391
$377$	−1.96589	−0.101249
$378$	−3.40750	−0.175263
$379$	13.7262	0.705070	0.352535	−	0.935799i	$-0.385320\pi$
$379$	13.7262	0.705070	0.352535	+	0.935799i	$0.385320\pi$
$380$	−12.6904	−0.651004
$381$	−9.53346	−0.488414
$382$	−10.6105	−0.542881
$383$	11.4824	0.586721	0.293360	−	0.956002i	$-0.405226\pi$
$383$	11.4824	0.586721	0.293360	+	0.956002i	$0.405226\pi$
$384$	1.00000	0.0510310
$385$	15.0042	0.764687
$386$	13.6729	0.695935
$387$	−6.49471	−0.330145
$388$	−14.2627	−0.724080
$389$	−22.4333	−1.13741	−0.568707	−	0.822540i	$-0.692556\pi$
$389$	−22.4333	−1.13741	−0.568707	+	0.822540i	$0.692556\pi$
$390$	−1.52247	−0.0770931
$391$	−30.8462	−1.55996
$392$	−4.61105	−0.232893
$393$	−4.16630	−0.210162
$394$	−13.0622	−0.658066
$395$	−5.98934	−0.301356
$396$	2.89222	0.145339
$397$	25.1274	1.26111	0.630554	−	0.776145i	$-0.282828\pi$
$397$	25.1274	1.26111	0.630554	+	0.776145i	$0.282828\pi$
$398$	−21.9234	−1.09892
$399$	28.4030	1.42193
$400$	−2.68210	−0.134105
$401$	15.4267	0.770374	0.385187	−	0.922838i	$-0.374137\pi$
$401$	15.4267	0.770374	0.385187	+	0.922838i	$0.374137\pi$
$402$	3.78863	0.188960
$403$	2.49196	0.124133
$404$	−6.08371	−0.302676
$405$	−1.52247	−0.0756519
$406$	−6.69877	−0.332455
$407$	16.6596	0.825785
$408$	3.63214	0.179818
$409$	−33.1984	−1.64156	−0.820778	−	0.571247i	$-0.806460\pi$
$409$	−33.1984	−1.64156	−0.820778	+	0.571247i	$0.806460\pi$
$410$	1.99371	0.0984623
$411$	22.5972	1.11464
$412$	−1.00000	−0.0492665
$413$	27.1959	1.33822
$414$	8.49258	0.417388
$415$	−17.4595	−0.857051
$416$	−1.00000	−0.0490290
$417$	1.82634	0.0894362
$418$	−24.1078	−1.17915
$419$	7.81068	0.381577	0.190788	−	0.981631i	$-0.438896\pi$
$419$	7.81068	0.381577	0.190788	+	0.981631i	$0.438896\pi$
$420$	−5.18780	−0.253139
$421$	−9.14589	−0.445743	−0.222872	−	0.974848i	$-0.571543\pi$
$421$	−9.14589	−0.445743	−0.222872	+	0.974848i	$0.571543\pi$
$422$	−15.1150	−0.735788
$423$	4.75831	0.231357
$424$	−7.93365	−0.385292
$425$	−9.74174	−0.472544
$426$	12.6153	0.611213
$427$	−29.9501	−1.44939
$428$	−0.0118287	−0.000571760 0
$429$	−2.89222	−0.139638
$430$	−9.88798	−0.476841
$431$	14.0382	0.676194	0.338097	−	0.941111i	$-0.390217\pi$
$431$	14.0382	0.676194	0.338097	+	0.941111i	$0.390217\pi$
$432$	−1.00000	−0.0481125
$433$	13.8082	0.663580	0.331790	−	0.943353i	$-0.392347\pi$
$433$	13.8082	0.663580	0.331790	+	0.943353i	$0.392347\pi$
$434$	8.49135	0.407598
$435$	−2.99300	−0.143504
$436$	9.52537	0.456182
$437$	−70.7893	−3.38631
$438$	−8.45160	−0.403833
$439$	−4.89323	−0.233541	−0.116771	−	0.993159i	$-0.537254\pi$
$439$	−4.89323	−0.233541	−0.116771	+	0.993159i	$0.537254\pi$
$440$	4.40330	0.209919
$441$	4.61105	0.219574
$442$	−3.63214	−0.172763
$443$	−6.91668	−0.328621	−0.164311	−	0.986409i	$-0.552540\pi$
$443$	−6.91668	−0.328621	−0.164311	+	0.986409i	$0.552540\pi$
$444$	−5.76014	−0.273364
$445$	23.2855	1.10384
$446$	−18.7880	−0.889636
$447$	7.97737	0.377317
$448$	−3.40750	−0.160989
$449$	−12.9209	−0.609773	−0.304887	−	0.952389i	$-0.598619\pi$
$449$	−12.9209	−0.609773	−0.304887	+	0.952389i	$0.598619\pi$
$450$	2.68210	0.126435
$451$	3.78743	0.178343
$452$	−12.3005	−0.578565
$453$	24.2779	1.14067
$454$	−6.60501	−0.309988
$455$	5.18780	0.243208
$456$	8.33542	0.390342
$457$	−25.8588	−1.20962	−0.604811	−	0.796369i	$-0.706752\pi$
$457$	−25.8588	−1.20962	−0.604811	+	0.796369i	$0.706752\pi$
$458$	−4.77427	−0.223087
$459$	−3.63214	−0.169534
$460$	12.9297	0.602849
$461$	−0.0963236	−0.00448624	−0.00224312	−	0.999997i	$-0.500714\pi$
$461$	−0.0963236	−0.00448624	−0.00224312	+	0.999997i	$0.500714\pi$
$462$	−9.85523	−0.458507
$463$	35.9141	1.66907	0.834534	−	0.550956i	$-0.185737\pi$
$463$	35.9141	1.66907	0.834534	+	0.550956i	$0.185737\pi$
$464$	−1.96589	−0.0912642
$465$	3.79392	0.175939
$466$	7.86773	0.364465
$467$	−24.8147	−1.14829	−0.574143	−	0.818755i	$-0.694665\pi$
$467$	−24.8147	−1.14829	−0.574143	+	0.818755i	$0.694665\pi$
$468$	1.00000	0.0462250
$469$	−12.9098	−0.596117
$470$	7.24437	0.334158
$471$	−11.7313	−0.540550
$472$	7.98118	0.367364
$473$	−18.7841	−0.863694
$474$	3.93397	0.180693
$475$	−22.3564	−1.02578
$476$	−12.3765	−0.567276
$477$	7.93365	0.363257
$478$	12.9810	0.593739
$479$	7.77361	0.355186	0.177593	−	0.984104i	$-0.443169\pi$
$479$	7.77361	0.355186	0.177593	+	0.984104i	$0.443169\pi$
$480$	−1.52247	−0.0694908
$481$	5.76014	0.262640
$482$	−11.8220	−0.538475
$483$	−28.9385	−1.31675
$484$	−2.63508	−0.119777
$485$	21.7145	0.986005
$486$	1.00000	0.0453609
$487$	−2.38601	−0.108120	−0.0540601	−	0.998538i	$-0.517216\pi$
$487$	−2.38601	−0.108120	−0.0540601	+	0.998538i	$0.517216\pi$
$488$	−8.78947	−0.397881
$489$	11.2838	0.510273
$490$	7.02017	0.317139
$491$	39.7482	1.79381	0.896906	−	0.442222i	$-0.145810\pi$
$491$	39.7482	1.79381	0.896906	+	0.442222i	$0.145810\pi$
$492$	−1.30953	−0.0590380
$493$	−7.14038	−0.321587
$494$	−8.33542	−0.375028
$495$	−4.40330	−0.197914
$496$	2.49196	0.111892
$497$	−42.9866	−1.92821
$498$	11.4679	0.513888
$499$	31.1133	1.39282	0.696412	−	0.717643i	$-0.254779\pi$
$499$	31.1133	1.39282	0.696412	+	0.717643i	$0.254779\pi$
$500$	11.6957	0.523049
$501$	21.2258	0.948297
$502$	−10.2546	−0.457687
$503$	−26.4300	−1.17845	−0.589227	−	0.807967i	$-0.700568\pi$
$503$	−26.4300	−1.17845	−0.589227	+	0.807967i	$0.700568\pi$
$504$	3.40750	0.151782
$505$	9.26224	0.412164
$506$	24.5624	1.09193
$507$	−1.00000	−0.0444116
$508$	9.53346	0.422979
$509$	0.544742	0.0241453	0.0120726	−	0.999927i	$-0.496157\pi$
$509$	0.544742	0.0241453	0.0120726	+	0.999927i	$0.496157\pi$
$510$	−5.52980	−0.244864
$511$	28.7988	1.27399
$512$	−1.00000	−0.0441942
$513$	−8.33542	−0.368018
$514$	−7.88163	−0.347644
$515$	1.52247	0.0670879
$516$	6.49471	0.285914
$517$	13.7621	0.605255
$518$	19.6277	0.862391
$519$	10.3787	0.455576
$520$	1.52247	0.0667646
$521$	43.8413	1.92072	0.960360	−	0.278762i	$-0.0899241\pi$
$521$	43.8413	1.92072	0.960360	+	0.278762i	$0.0899241\pi$
$522$	1.96589	0.0860447
$523$	34.7287	1.51858	0.759291	−	0.650752i	$-0.225546\pi$
$523$	34.7287	1.51858	0.759291	+	0.650752i	$0.225546\pi$
$524$	4.16630	0.182005
$525$	−9.13924	−0.398869
$526$	19.5054	0.850478
$527$	9.05113	0.394274
$528$	−2.89222	−0.125868
$529$	49.1239	2.13582
$530$	12.0787	0.524666
$531$	−7.98118	−0.346354
$532$	−28.4030	−1.23142
$533$	1.30953	0.0567219
$534$	−15.2946	−0.661861
$535$	0.0180087	0.000778586 0
$536$	−3.78863	−0.163644
$537$	5.05976	0.218345
$538$	−29.6814	−1.27966
$539$	13.3362	0.574429
$540$	1.52247	0.0655165
$541$	5.48239	0.235706	0.117853	−	0.993031i	$-0.462399\pi$
$541$	5.48239	0.235706	0.117853	+	0.993031i	$0.462399\pi$
$542$	−1.48750	−0.0638935
$543$	13.1453	0.564120
$544$	−3.63214	−0.155727
$545$	−14.5021	−0.621200
$546$	−3.40750	−0.145828
$547$	15.2348	0.651392	0.325696	−	0.945475i	$-0.394401\pi$
$547$	15.2348	0.651392	0.325696	+	0.945475i	$0.394401\pi$
$548$	−22.5972	−0.965304
$549$	8.78947	0.375126
$550$	7.75720	0.330768
$551$	−16.3865	−0.698090
$552$	−8.49258	−0.361468
$553$	−13.4050	−0.570039
$554$	−32.2188	−1.36885
$555$	8.76962	0.372250
$556$	−1.82634	−0.0774541
$557$	−43.2263	−1.83156	−0.915779	−	0.401682i	$-0.868426\pi$
$557$	−43.2263	−1.83156	−0.915779	+	0.401682i	$0.868426\pi$
$558$	−2.49196	−0.105493
$559$	−6.49471	−0.274697
$560$	5.18780	0.219225
$561$	−10.5049	−0.443518
$562$	−15.9702	−0.673661
$563$	−16.1975	−0.682642	−0.341321	−	0.939947i	$-0.610874\pi$
$563$	−16.1975	−0.682642	−0.341321	+	0.939947i	$0.610874\pi$
$564$	−4.75831	−0.200361
$565$	18.7270	0.787852
$566$	−15.5347	−0.652971
$567$	−3.40750	−0.143102
$568$	−12.6153	−0.529326
$569$	21.6497	0.907601	0.453801	−	0.891103i	$-0.350068\pi$
$569$	21.6497	0.907601	0.453801	+	0.891103i	$0.350068\pi$
$570$	−12.6904	−0.531542
$571$	23.3965	0.979112	0.489556	−	0.871972i	$-0.337159\pi$
$571$	23.3965	0.979112	0.489556	+	0.871972i	$0.337159\pi$
$572$	2.89222	0.120930
$573$	−10.6105	−0.443261
$574$	4.46221	0.186249
$575$	22.7779	0.949905
$576$	1.00000	0.0416667
$577$	−12.7028	−0.528823	−0.264412	−	0.964410i	$-0.585178\pi$
$577$	−12.7028	−0.528823	−0.264412	+	0.964410i	$0.585178\pi$
$578$	3.80759	0.158375
$579$	13.6729	0.568228
$580$	2.99300	0.124278
$581$	−39.0768	−1.62118
$582$	−14.2627	−0.591209
$583$	22.9458	0.950319
$584$	8.45160	0.349730
$585$	−1.52247	−0.0629462
$586$	−0.645648	−0.0266715
$587$	5.24679	0.216558	0.108279	−	0.994121i	$-0.465466\pi$
$587$	5.24679	0.216558	0.108279	+	0.994121i	$0.465466\pi$
$588$	−4.61105	−0.190157
$589$	20.7715	0.855876
$590$	−12.1511	−0.500252
$591$	−13.0622	−0.537309
$592$	5.76014	0.236740
$593$	−10.7972	−0.443389	−0.221695	−	0.975116i	$-0.571159\pi$
$593$	−10.7972	−0.443389	−0.221695	+	0.975116i	$0.571159\pi$
$594$	2.89222	0.118669
$595$	18.8428	0.772480
$596$	−7.97737	−0.326766
$597$	−21.9234	−0.897265
$598$	8.49258	0.347287
$599$	42.3898	1.73200	0.866001	−	0.500042i	$-0.166682\pi$
$599$	42.3898	1.73200	0.866001	+	0.500042i	$0.166682\pi$
$600$	−2.68210	−0.109496
$601$	−34.5825	−1.41065	−0.705324	−	0.708885i	$-0.749199\pi$
$601$	−34.5825	−1.41065	−0.705324	+	0.708885i	$0.749199\pi$
$602$	−22.1307	−0.901981
$603$	3.78863	0.154285
$604$	−24.2779	−0.987852
$605$	4.01183	0.163104
$606$	−6.08371	−0.247134
$607$	33.3540	1.35380	0.676899	−	0.736076i	$-0.263324\pi$
$607$	33.3540	1.35380	0.676899	+	0.736076i	$0.263324\pi$
$608$	−8.33542	−0.338046
$609$	−6.69877	−0.271448
$610$	13.3817	0.541808
$611$	4.75831	0.192501
$612$	3.63214	0.146820
$613$	−9.48303	−0.383016	−0.191508	−	0.981491i	$-0.561338\pi$
$613$	−9.48303	−0.383016	−0.191508	+	0.981491i	$0.561338\pi$
$614$	−17.3345	−0.699563
$615$	1.99371	0.0803941
$616$	9.85523	0.397078
$617$	−40.8304	−1.64377	−0.821885	−	0.569653i	$-0.807077\pi$
$617$	−40.8304	−1.64377	−0.821885	+	0.569653i	$0.807077\pi$
$618$	−1.00000	−0.0402259
$619$	39.1180	1.57228	0.786142	−	0.618046i	$-0.212075\pi$
$619$	39.1180	1.57228	0.786142	+	0.618046i	$0.212075\pi$
$620$	−3.79392	−0.152368
$621$	8.49258	0.340796
$622$	−1.26256	−0.0506241
$623$	52.1163	2.08799
$624$	−1.00000	−0.0400320
$625$	−4.39587	−0.175835
$626$	−22.2729	−0.890203
$627$	−24.1078	−0.962775
$628$	11.7313	0.468130
$629$	20.9216	0.834200
$630$	−5.18780	−0.206687
$631$	6.22753	0.247914	0.123957	−	0.992288i	$-0.460442\pi$
$631$	6.22753	0.247914	0.123957	+	0.992288i	$0.460442\pi$
$632$	−3.93397	−0.156485
$633$	−15.1150	−0.600768
$634$	1.98445	0.0788125
$635$	−14.5144	−0.575985
$636$	−7.93365	−0.314590
$637$	4.61105	0.182697
$638$	5.68578	0.225102
$639$	12.6153	0.499054
$640$	1.52247	0.0601808
$641$	0.0610278	0.00241045	0.00120523	−	0.999999i	$-0.499616\pi$
$641$	0.0610278	0.00241045	0.00120523	+	0.999999i	$0.499616\pi$
$642$	−0.0118287	−0.000466840 0
$643$	−24.5399	−0.967757	−0.483879	−	0.875135i	$-0.660772\pi$
$643$	−24.5399	−0.967757	−0.483879	+	0.875135i	$0.660772\pi$
$644$	28.9385	1.14034
$645$	−9.88798	−0.389339
$646$	−30.2754	−1.19117
$647$	27.2088	1.06969	0.534845	−	0.844950i	$-0.320370\pi$
$647$	27.2088	1.06969	0.534845	+	0.844950i	$0.320370\pi$
$648$	−1.00000	−0.0392837
$649$	−23.0833	−0.906099
$650$	2.68210	0.105200
$651$	8.49135	0.332802
$652$	−11.2838	−0.441909
$653$	−14.8510	−0.581166	−0.290583	−	0.956850i	$-0.593849\pi$
$653$	−14.8510	−0.581166	−0.290583	+	0.956850i	$0.593849\pi$
$654$	9.52537	0.372471
$655$	−6.34304	−0.247843
$656$	1.30953	0.0511284
$657$	−8.45160	−0.329728
$658$	16.2139	0.632085
$659$	−4.94968	−0.192812	−0.0964060	−	0.995342i	$-0.530735\pi$
$659$	−4.94968	−0.192812	−0.0964060	+	0.995342i	$0.530735\pi$
$660$	4.40330	0.171398
$661$	34.5141	1.34244	0.671222	−	0.741256i	$-0.265770\pi$
$661$	34.5141	1.34244	0.671222	+	0.741256i	$0.265770\pi$
$662$	−7.80176	−0.303224
$663$	−3.63214	−0.141060
$664$	−11.4679	−0.445040
$665$	43.2425	1.67687
$666$	−5.76014	−0.223201
$667$	16.6955	0.646452
$668$	−21.2258	−0.821249
$669$	−18.7880	−0.726384
$670$	5.76806	0.222840
$671$	25.4211	0.981369
$672$	−3.40750	−0.131447
$673$	−20.6255	−0.795054	−0.397527	−	0.917591i	$-0.630131\pi$
$673$	−20.6255	−0.795054	−0.397527	+	0.917591i	$0.630131\pi$
$674$	−12.8629	−0.495460
$675$	2.68210	0.103234
$676$	1.00000	0.0384615
$677$	2.12877	0.0818155	0.0409077	−	0.999163i	$-0.486975\pi$
$677$	2.12877	0.0818155	0.0409077	+	0.999163i	$0.486975\pi$
$678$	−12.3005	−0.472396
$679$	48.6002	1.86511
$680$	5.52980	0.212058
$681$	−6.60501	−0.253104
$682$	−7.20728	−0.275981
$683$	−13.9481	−0.533708	−0.266854	−	0.963737i	$-0.585984\pi$
$683$	−13.9481	−0.533708	−0.266854	+	0.963737i	$0.585984\pi$
$684$	8.33542	0.318713
$685$	34.4034	1.31449
$686$	−8.14033	−0.310799
$687$	−4.77427	−0.182150
$688$	−6.49471	−0.247609
$689$	7.93365	0.302248
$690$	12.9297	0.492224
$691$	−5.07598	−0.193099	−0.0965497	−	0.995328i	$-0.530781\pi$
$691$	−5.07598	−0.193099	−0.0965497	+	0.995328i	$0.530781\pi$
$692$	−10.3787	−0.394541
$693$	−9.85523	−0.374369
$694$	14.1100	0.535608
$695$	2.78054	0.105472
$696$	−1.96589	−0.0745169
$697$	4.75638	0.180161
$698$	−20.8994	−0.791055
$699$	7.86773	0.297585
$700$	9.13924	0.345431
$701$	19.6370	0.741678	0.370839	−	0.928697i	$-0.379070\pi$
$701$	19.6370	0.741678	0.370839	+	0.928697i	$0.379070\pi$
$702$	1.00000	0.0377426
$703$	48.0132	1.81085
$704$	2.89222	0.109005
$705$	7.24437	0.272839
$706$	4.18829	0.157629
$707$	20.7302	0.779641
$708$	7.98118	0.299951
$709$	12.6875	0.476487	0.238244	−	0.971205i	$-0.423428\pi$
$709$	12.6875	0.476487	0.238244	+	0.971205i	$0.423428\pi$
$710$	19.2064	0.720802
$711$	3.93397	0.147536
$712$	15.2946	0.573188
$713$	−21.1632	−0.792567
$714$	−12.3765	−0.463179
$715$	−4.40330	−0.164674
$716$	−5.05976	−0.189092
$717$	12.9810	0.484786
$718$	27.7433	1.03537
$719$	25.7246	0.959365	0.479683	−	0.877442i	$-0.340752\pi$
$719$	25.7246	0.959365	0.479683	+	0.877442i	$0.340752\pi$
$720$	−1.52247	−0.0567390
$721$	3.40750	0.126902
$722$	−50.4793	−1.87864
$723$	−11.8220	−0.439663
$724$	−13.1453	−0.488542
$725$	5.27271	0.195824
$726$	−2.63508	−0.0977972
$727$	37.9623	1.40794	0.703972	−	0.710228i	$-0.251408\pi$
$727$	37.9623	1.40794	0.703972	+	0.710228i	$0.251408\pi$
$728$	3.40750	0.126290
$729$	1.00000	0.0370370
$730$	−12.8673	−0.476239
$731$	−23.5897	−0.872496
$732$	−8.78947	−0.324868
$733$	15.9783	0.590173	0.295087	−	0.955470i	$-0.404651\pi$
$733$	15.9783	0.590173	0.295087	+	0.955470i	$0.404651\pi$
$734$	−5.85048	−0.215945
$735$	7.02017	0.258943
$736$	8.49258	0.313041
$737$	10.9575	0.403626
$738$	−1.30953	−0.0482043
$739$	−21.1633	−0.778504	−0.389252	−	0.921131i	$-0.627266\pi$
$739$	−21.1633	−0.778504	−0.389252	+	0.921131i	$0.627266\pi$
$740$	−8.76962	−0.322378
$741$	−8.33542	−0.306209
$742$	27.0339	0.992446
$743$	−11.0708	−0.406148	−0.203074	−	0.979163i	$-0.565093\pi$
$743$	−11.0708	−0.406148	−0.203074	+	0.979163i	$0.565093\pi$
$744$	2.49196	0.0913596
$745$	12.1453	0.444968
$746$	−15.8596	−0.580660
$747$	11.4679	0.419588
$748$	10.5049	0.384098
$749$	0.0403062	0.00147276
$750$	11.6957	0.427068
$751$	−34.9978	−1.27709	−0.638545	−	0.769585i	$-0.720463\pi$
$751$	−34.9978	−1.27709	−0.638545	+	0.769585i	$0.720463\pi$
$752$	4.75831	0.173518
$753$	−10.2546	−0.373700
$754$	1.96589	0.0715935
$755$	36.9622	1.34519
$756$	3.40750	0.123930
$757$	17.5111	0.636451	0.318225	−	0.948015i	$-0.396913\pi$
$757$	17.5111	0.636451	0.318225	+	0.948015i	$0.396913\pi$
$758$	−13.7262	−0.498560
$759$	24.5624	0.891558
$760$	12.6904	0.460329
$761$	2.75012	0.0996916	0.0498458	−	0.998757i	$-0.484127\pi$
$761$	2.75012	0.0996916	0.0498458	+	0.998757i	$0.484127\pi$
$762$	9.53346	0.345361
$763$	−32.4577	−1.17505
$764$	10.6105	0.383875
$765$	−5.52980	−0.199930
$766$	−11.4824	−0.414874
$767$	−7.98118	−0.288184
$768$	−1.00000	−0.0360844
$769$	−27.0234	−0.974487	−0.487244	−	0.873266i	$-0.661998\pi$
$769$	−27.0234	−0.974487	−0.487244	+	0.873266i	$0.661998\pi$
$770$	−15.0042	−0.540716
$771$	−7.88163	−0.283850
$772$	−13.6729	−0.492100
$773$	17.7262	0.637568	0.318784	−	0.947827i	$-0.396726\pi$
$773$	17.7262	0.637568	0.318784	+	0.947827i	$0.396726\pi$
$774$	6.49471	0.233448
$775$	−6.68367	−0.240085
$776$	14.2627	0.512002
$777$	19.6277	0.704139
$778$	22.4333	0.804273
$779$	10.9155	0.391087
$780$	1.52247	0.0545130
$781$	36.4862	1.30558
$782$	30.8462	1.10306
$783$	1.96589	0.0702552
$784$	4.61105	0.164681
$785$	−17.8605	−0.637469
$786$	4.16630	0.148607
$787$	22.2536	0.793254	0.396627	−	0.917980i	$-0.370181\pi$
$787$	22.2536	0.793254	0.396627	+	0.917980i	$0.370181\pi$
$788$	13.0622	0.465323
$789$	19.5054	0.694412
$790$	5.98934	0.213091
$791$	41.9138	1.49028
$792$	−2.89222	−0.102770
$793$	8.78947	0.312123
$794$	−25.1274	−0.891739
$795$	12.0787	0.428388
$796$	21.9234	0.777054
$797$	51.2856	1.81663	0.908315	−	0.418287i	$-0.137369\pi$
$797$	51.2856	1.81663	0.908315	+	0.418287i	$0.137369\pi$
$798$	−28.4030	−1.00545
$799$	17.2828	0.611423
$800$	2.68210	0.0948264
$801$	−15.2946	−0.540407
$802$	−15.4267	−0.544737
$803$	−24.4439	−0.862605
$804$	−3.78863	−0.133615
$805$	−44.0578	−1.55283
$806$	−2.49196	−0.0877755
$807$	−29.6814	−1.04483
$808$	6.08371	0.214024
$809$	37.3055	1.31159	0.655795	−	0.754939i	$-0.272334\pi$
$809$	37.3055	1.31159	0.655795	+	0.754939i	$0.272334\pi$
$810$	1.52247	0.0534940
$811$	19.1085	0.670991	0.335495	−	0.942042i	$-0.391096\pi$
$811$	19.1085	0.670991	0.335495	+	0.942042i	$0.391096\pi$
$812$	6.69877	0.235081
$813$	−1.48750	−0.0521688
$814$	−16.6596	−0.583918
$815$	17.1793	0.601763
$816$	−3.63214	−0.127150
$817$	−54.1362	−1.89399
$818$	33.1984	1.16076
$819$	−3.40750	−0.119068
$820$	−1.99371	−0.0696234
$821$	−36.5634	−1.27607	−0.638036	−	0.770007i	$-0.720253\pi$
$821$	−36.5634	−1.27607	−0.638036	+	0.770007i	$0.720253\pi$
$822$	−22.5972	−0.788167
$823$	21.8196	0.760585	0.380293	−	0.924866i	$-0.375823\pi$
$823$	21.8196	0.760585	0.380293	+	0.924866i	$0.375823\pi$
$824$	1.00000	0.0348367
$825$	7.75720	0.270071
$826$	−27.1959	−0.946266
$827$	−15.4165	−0.536085	−0.268043	−	0.963407i	$-0.586377\pi$
$827$	−15.4165	−0.536085	−0.268043	+	0.963407i	$0.586377\pi$
$828$	−8.49258	−0.295138
$829$	−39.4438	−1.36994	−0.684970	−	0.728571i	$-0.740185\pi$
$829$	−39.4438	−1.36994	−0.684970	+	0.728571i	$0.740185\pi$
$830$	17.4595	0.606027
$831$	−32.2188	−1.11766
$832$	1.00000	0.0346688
$833$	16.7480	0.580283
$834$	−1.82634	−0.0632410
$835$	32.3155	1.11832
$836$	24.1078	0.833787
$837$	−2.49196	−0.0861347
$838$	−7.81068	−0.269816
$839$	−37.6597	−1.30016	−0.650079	−	0.759867i	$-0.725264\pi$
$839$	−37.6597	−1.30016	−0.650079	+	0.759867i	$0.725264\pi$
$840$	5.18780	0.178996
$841$	−25.1353	−0.866733
$842$	9.14589	0.315188
$843$	−15.9702	−0.550042
$844$	15.1150	0.520280
$845$	−1.52247	−0.0523744
$846$	−4.75831	−0.163594
$847$	8.97905	0.308524
$848$	7.93365	0.272443
$849$	−15.5347	−0.533149
$850$	9.74174	0.334139
$851$	−48.9185	−1.67690
$852$	−12.6153	−0.432193
$853$	19.8404	0.679322	0.339661	−	0.940548i	$-0.389688\pi$
$853$	19.8404	0.679322	0.339661	+	0.940548i	$0.389688\pi$
$854$	29.9501	1.02487
$855$	−12.6904	−0.434003
$856$	0.0118287	0.000404295 0
$857$	21.3369	0.728855	0.364427	−	0.931232i	$-0.381265\pi$
$857$	21.3369	0.728855	0.364427	+	0.931232i	$0.381265\pi$
$858$	2.89222	0.0987386
$859$	−49.6574	−1.69429	−0.847144	−	0.531363i	$-0.821680\pi$
$859$	−49.6574	−1.69429	−0.847144	+	0.531363i	$0.821680\pi$
$860$	9.88798	0.337177
$861$	4.46221	0.152072
$862$	−14.0382	−0.478141
$863$	56.4664	1.92214	0.961069	−	0.276310i	$-0.0891115\pi$
$863$	56.4664	1.92214	0.961069	+	0.276310i	$0.0891115\pi$
$864$	1.00000	0.0340207
$865$	15.8013	0.537260
$866$	−13.8082	−0.469222
$867$	3.80759	0.129313
$868$	−8.49135	−0.288215
$869$	11.3779	0.385969
$870$	2.99300	0.101472
$871$	3.78863	0.128373
$872$	−9.52537	−0.322570
$873$	−14.2627	−0.482720
$874$	70.7893	2.39448
$875$	−39.8532	−1.34728
$876$	8.45160	0.285553
$877$	−42.8506	−1.44696	−0.723482	−	0.690344i	$-0.757459\pi$
$877$	−42.8506	−1.44696	−0.723482	+	0.690344i	$0.757459\pi$
$878$	4.89323	0.165138
$879$	−0.645648	−0.0217772
$880$	−4.40330	−0.148435
$881$	−28.9109	−0.974033	−0.487017	−	0.873393i	$-0.661915\pi$
$881$	−28.9109	−0.974033	−0.487017	+	0.873393i	$0.661915\pi$
$882$	−4.61105	−0.155262
$883$	−23.6224	−0.794957	−0.397479	−	0.917611i	$-0.630115\pi$
$883$	−23.6224	−0.794957	−0.397479	+	0.917611i	$0.630115\pi$
$884$	3.63214	0.122162
$885$	−12.1511	−0.408454
$886$	6.91668	0.232370
$887$	−17.9173	−0.601605	−0.300803	−	0.953686i	$-0.597255\pi$
$887$	−17.9173	−0.601605	−0.300803	+	0.953686i	$0.597255\pi$
$888$	5.76014	0.193298
$889$	−32.4853	−1.08952
$890$	−23.2855	−0.780531
$891$	2.89222	0.0968929
$892$	18.7880	0.629067
$893$	39.6625	1.32726
$894$	−7.97737	−0.266803
$895$	7.70331	0.257493
$896$	3.40750	0.113837
$897$	8.49258	0.283559
$898$	12.9209	0.431175
$899$	−4.89892	−0.163388
$900$	−2.68210	−0.0894032
$901$	28.8161	0.960003
$902$	−3.78743	−0.126108
$903$	−22.1307	−0.736465
$904$	12.3005	0.409107
$905$	20.0133	0.665265
$906$	−24.2779	−0.806578
$907$	11.3808	0.377894	0.188947	−	0.981987i	$-0.439493\pi$
$907$	11.3808	0.377894	0.188947	+	0.981987i	$0.439493\pi$
$908$	6.60501	0.219195
$909$	−6.08371	−0.201784
$910$	−5.18780	−0.171974
$911$	14.2585	0.472406	0.236203	−	0.971704i	$-0.424097\pi$
$911$	14.2585	0.472406	0.236203	+	0.971704i	$0.424097\pi$
$912$	−8.33542	−0.276013
$913$	33.1676	1.09769
$914$	25.8588	0.855333
$915$	13.3817	0.442385
$916$	4.77427	0.157746
$917$	−14.1967	−0.468815
$918$	3.63214	0.119878
$919$	26.4965	0.874040	0.437020	−	0.899452i	$-0.356034\pi$
$919$	26.4965	0.874040	0.437020	+	0.899452i	$0.356034\pi$
$920$	−12.9297	−0.426279
$921$	−17.3345	−0.571191
$922$	0.0963236	0.00317225
$923$	12.6153	0.415238
$924$	9.85523	0.324213
$925$	−15.4493	−0.507969
$926$	−35.9141	−1.18021
$927$	−1.00000	−0.0328443
$928$	1.96589	0.0645335
$929$	12.1480	0.398562	0.199281	−	0.979942i	$-0.436139\pi$
$929$	12.1480	0.398562	0.199281	+	0.979942i	$0.436139\pi$
$930$	−3.79392	−0.124408
$931$	38.4351	1.25966
$932$	−7.86773	−0.257716
$933$	−1.26256	−0.0413344
$934$	24.8147	0.811961
$935$	−15.9934	−0.523040
$936$	−1.00000	−0.0326860
$937$	6.14465	0.200737	0.100368	−	0.994950i	$-0.467998\pi$
$937$	6.14465	0.200737	0.100368	+	0.994950i	$0.467998\pi$
$938$	12.9098	0.421519
$939$	−22.2729	−0.726848
$940$	−7.24437	−0.236285
$941$	−11.1205	−0.362519	−0.181259	−	0.983435i	$-0.558017\pi$
$941$	−11.1205	−0.362519	−0.181259	+	0.983435i	$0.558017\pi$
$942$	11.7313	0.382227
$943$	−11.1213	−0.362158
$944$	−7.98118	−0.259765
$945$	−5.18780	−0.168759
$946$	18.7841	0.610724
$947$	−33.8107	−1.09870	−0.549349	−	0.835593i	$-0.685124\pi$
$947$	−33.8107	−1.09870	−0.549349	+	0.835593i	$0.685124\pi$
$948$	−3.93397	−0.127770
$949$	−8.45160	−0.274351
$950$	22.3564	0.725338
$951$	1.98445	0.0643501
$952$	12.3765	0.401125
$953$	15.5173	0.502656	0.251328	−	0.967902i	$-0.419133\pi$
$953$	15.5173	0.502656	0.251328	+	0.967902i	$0.419133\pi$
$954$	−7.93365	−0.256861
$955$	−16.1541	−0.522736
$956$	−12.9810	−0.419837
$957$	5.68578	0.183795
$958$	−7.77361	−0.251154
$959$	76.9999	2.48646
$960$	1.52247	0.0491374
$961$	−24.7901	−0.799682
$962$	−5.76014	−0.185714
$963$	−0.0118287	−0.000381173 0
$964$	11.8220	0.380760
$965$	20.8166	0.670110
$966$	28.9385	0.931080
$967$	30.3374	0.975586	0.487793	−	0.872959i	$-0.337802\pi$
$967$	30.3374	0.975586	0.487793	+	0.872959i	$0.337802\pi$
$968$	2.63508	0.0846948
$969$	−30.2754	−0.972586
$970$	−21.7145	−0.697211
$971$	5.26170	0.168856	0.0844280	−	0.996430i	$-0.473094\pi$
$971$	5.26170	0.168856	0.0844280	+	0.996430i	$0.473094\pi$
$972$	−1.00000	−0.0320750
$973$	6.22325	0.199508
$974$	2.38601	0.0764526
$975$	2.68210	0.0858958
$976$	8.78947	0.281344
$977$	−44.4704	−1.42274	−0.711368	−	0.702820i	$-0.751924\pi$
$977$	−44.4704	−1.42274	−0.711368	+	0.702820i	$0.751924\pi$
$978$	−11.2838	−0.360817
$979$	−44.2352	−1.41376
$980$	−7.02017	−0.224251
$981$	9.52537	0.304122
$982$	−39.7482	−1.26842
$983$	−54.8819	−1.75046	−0.875230	−	0.483706i	$-0.839290\pi$
$983$	−54.8819	−1.75046	−0.875230	+	0.483706i	$0.839290\pi$
$984$	1.30953	0.0417462
$985$	−19.8868	−0.633647
$986$	7.14038	0.227396
$987$	16.2139	0.516095
$988$	8.33542	0.265185
$989$	55.1569	1.75389
$990$	4.40330	0.139946
$991$	−32.0269	−1.01737	−0.508683	−	0.860954i	$-0.669868\pi$
$991$	−32.0269	−1.01737	−0.508683	+	0.860954i	$0.669868\pi$
$992$	−2.49196	−0.0791198
$993$	−7.80176	−0.247581
$994$	42.9866	1.36345
$995$	−33.3776	−1.05814
$996$	−11.4679	−0.363374
$997$	51.3065	1.62489	0.812446	−	0.583036i	$-0.198135\pi$
$997$	51.3065	1.62489	0.812446	+	0.583036i	$0.198135\pi$
$998$	−31.1133	−0.984875
$999$	−5.76014	−0.182243

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.z.1.5	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.z.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.52247 q^{5} +1.00000 q^{6} -3.40750 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.52247 q^{5} +1.00000 q^{6} -3.40750 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.52247 q^{10} +2.89222 q^{11} -1.00000 q^{12} +1.00000 q^{13} +3.40750 q^{14} +1.52247 q^{15} +1.00000 q^{16} +3.63214 q^{17} -1.00000 q^{18} +8.33542 q^{19} -1.52247 q^{20} +3.40750 q^{21} -2.89222 q^{22} -8.49258 q^{23} +1.00000 q^{24} -2.68210 q^{25} -1.00000 q^{26} -1.00000 q^{27} -3.40750 q^{28} -1.96589 q^{29} -1.52247 q^{30} +2.49196 q^{31} -1.00000 q^{32} -2.89222 q^{33} -3.63214 q^{34} +5.18780 q^{35} +1.00000 q^{36} +5.76014 q^{37} -8.33542 q^{38} -1.00000 q^{39} +1.52247 q^{40} +1.30953 q^{41} -3.40750 q^{42} -6.49471 q^{43} +2.89222 q^{44} -1.52247 q^{45} +8.49258 q^{46} +4.75831 q^{47} -1.00000 q^{48} +4.61105 q^{49} +2.68210 q^{50} -3.63214 q^{51} +1.00000 q^{52} +7.93365 q^{53} +1.00000 q^{54} -4.40330 q^{55} +3.40750 q^{56} -8.33542 q^{57} +1.96589 q^{58} -7.98118 q^{59} +1.52247 q^{60} +8.78947 q^{61} -2.49196 q^{62} -3.40750 q^{63} +1.00000 q^{64} -1.52247 q^{65} +2.89222 q^{66} +3.78863 q^{67} +3.63214 q^{68} +8.49258 q^{69} -5.18780 q^{70} +12.6153 q^{71} -1.00000 q^{72} -8.45160 q^{73} -5.76014 q^{74} +2.68210 q^{75} +8.33542 q^{76} -9.85523 q^{77} +1.00000 q^{78} +3.93397 q^{79} -1.52247 q^{80} +1.00000 q^{81} -1.30953 q^{82} +11.4679 q^{83} +3.40750 q^{84} -5.52980 q^{85} +6.49471 q^{86} +1.96589 q^{87} -2.89222 q^{88} -15.2946 q^{89} +1.52247 q^{90} -3.40750 q^{91} -8.49258 q^{92} -2.49196 q^{93} -4.75831 q^{94} -12.6904 q^{95} +1.00000 q^{96} -14.2627 q^{97} -4.61105 q^{98} +2.89222 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 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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