LMFDB - Embedded newform 8034.2.a.z.1.12

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			1.12
Root			$-2.28948$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.28948 q^{5} +1.00000 q^{6} -1.19378 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.28948 q^{5} +1.00000 q^{6} -1.19378 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.28948 q^{10} +4.27905 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.19378 q^{14} -2.28948 q^{15} +1.00000 q^{16} -3.59570 q^{17} -1.00000 q^{18} -1.35770 q^{19} +2.28948 q^{20} +1.19378 q^{21} -4.27905 q^{22} -6.42459 q^{23} +1.00000 q^{24} +0.241736 q^{25} -1.00000 q^{26} -1.00000 q^{27} -1.19378 q^{28} -6.53525 q^{29} +2.28948 q^{30} -1.25937 q^{31} -1.00000 q^{32} -4.27905 q^{33} +3.59570 q^{34} -2.73314 q^{35} +1.00000 q^{36} -6.96050 q^{37} +1.35770 q^{38} -1.00000 q^{39} -2.28948 q^{40} +7.36952 q^{41} -1.19378 q^{42} +1.70506 q^{43} +4.27905 q^{44} +2.28948 q^{45} +6.42459 q^{46} +1.19672 q^{47} -1.00000 q^{48} -5.57489 q^{49} -0.241736 q^{50} +3.59570 q^{51} +1.00000 q^{52} +2.84069 q^{53} +1.00000 q^{54} +9.79682 q^{55} +1.19378 q^{56} +1.35770 q^{57} +6.53525 q^{58} +14.3018 q^{59} -2.28948 q^{60} +3.12763 q^{61} +1.25937 q^{62} -1.19378 q^{63} +1.00000 q^{64} +2.28948 q^{65} +4.27905 q^{66} +10.3747 q^{67} -3.59570 q^{68} +6.42459 q^{69} +2.73314 q^{70} +1.20531 q^{71} -1.00000 q^{72} +10.1318 q^{73} +6.96050 q^{74} -0.241736 q^{75} -1.35770 q^{76} -5.10824 q^{77} +1.00000 q^{78} -2.00621 q^{79} +2.28948 q^{80} +1.00000 q^{81} -7.36952 q^{82} +4.49374 q^{83} +1.19378 q^{84} -8.23231 q^{85} -1.70506 q^{86} +6.53525 q^{87} -4.27905 q^{88} +5.55082 q^{89} -2.28948 q^{90} -1.19378 q^{91} -6.42459 q^{92} +1.25937 q^{93} -1.19672 q^{94} -3.10843 q^{95} +1.00000 q^{96} +7.35332 q^{97} +5.57489 q^{98} +4.27905 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.28948	1.02389	0.511944	−	0.859019i	$-0.328925\pi$
$5$	2.28948	1.02389	0.511944	+	0.859019i	$0.328925\pi$
$6$	1.00000	0.408248
$7$	−1.19378	−0.451206	−0.225603	−	0.974219i	$-0.572435\pi$
$7$	−1.19378	−0.451206	−0.225603	+	0.974219i	$0.572435\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.28948	−0.723998
$11$	4.27905	1.29018	0.645091	−	0.764106i	$-0.276819\pi$
$11$	4.27905	1.29018	0.645091	+	0.764106i	$0.276819\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.19378	0.319051
$15$	−2.28948	−0.591142
$16$	1.00000	0.250000
$17$	−3.59570	−0.872086	−0.436043	−	0.899926i	$-0.643621\pi$
$17$	−3.59570	−0.872086	−0.436043	+	0.899926i	$0.643621\pi$
$18$	−1.00000	−0.235702
$19$	−1.35770	−0.311478	−0.155739	−	0.987798i	$-0.549776\pi$
$19$	−1.35770	−0.311478	−0.155739	+	0.987798i	$0.549776\pi$
$20$	2.28948	0.511944
$21$	1.19378	0.260504
$22$	−4.27905	−0.912297
$23$	−6.42459	−1.33962	−0.669810	−	0.742532i	$-0.733625\pi$
$23$	−6.42459	−1.33962	−0.669810	+	0.742532i	$0.733625\pi$
$24$	1.00000	0.204124
$25$	0.241736	0.0483473
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	−1.19378	−0.225603
$29$	−6.53525	−1.21357	−0.606783	−	0.794867i	$-0.707540\pi$
$29$	−6.53525	−1.21357	−0.606783	+	0.794867i	$0.707540\pi$
$30$	2.28948	0.418001
$31$	−1.25937	−0.226189	−0.113095	−	0.993584i	$-0.536076\pi$
$31$	−1.25937	−0.226189	−0.113095	+	0.993584i	$0.536076\pi$
$32$	−1.00000	−0.176777
$33$	−4.27905	−0.744887
$34$	3.59570	0.616658
$35$	−2.73314	−0.461985
$36$	1.00000	0.166667
$37$	−6.96050	−1.14430	−0.572149	−	0.820150i	$-0.693890\pi$
$37$	−6.96050	−1.14430	−0.572149	+	0.820150i	$0.693890\pi$
$38$	1.35770	0.220248
$39$	−1.00000	−0.160128
$40$	−2.28948	−0.361999
$41$	7.36952	1.15093	0.575463	−	0.817828i	$-0.304822\pi$
$41$	7.36952	1.15093	0.575463	+	0.817828i	$0.304822\pi$
$42$	−1.19378	−0.184204
$43$	1.70506	0.260020	0.130010	−	0.991513i	$-0.458499\pi$
$43$	1.70506	0.260020	0.130010	+	0.991513i	$0.458499\pi$
$44$	4.27905	0.645091
$45$	2.28948	0.341296
$46$	6.42459	0.947255
$47$	1.19672	0.174560	0.0872800	−	0.996184i	$-0.472183\pi$
$47$	1.19672	0.174560	0.0872800	+	0.996184i	$0.472183\pi$
$48$	−1.00000	−0.144338
$49$	−5.57489	−0.796413
$50$	−0.241736	−0.0341867
$51$	3.59570	0.503499
$52$	1.00000	0.138675
$53$	2.84069	0.390199	0.195100	−	0.980783i	$-0.437497\pi$
$53$	2.84069	0.390199	0.195100	+	0.980783i	$0.437497\pi$
$54$	1.00000	0.136083
$55$	9.79682	1.32100
$56$	1.19378	0.159525
$57$	1.35770	0.179832
$58$	6.53525	0.858121
$59$	14.3018	1.86194	0.930971	−	0.365093i	$-0.118963\pi$
$59$	14.3018	1.86194	0.930971	+	0.365093i	$0.118963\pi$
$60$	−2.28948	−0.295571
$61$	3.12763	0.400453	0.200226	−	0.979750i	$-0.435832\pi$
$61$	3.12763	0.400453	0.200226	+	0.979750i	$0.435832\pi$
$62$	1.25937	0.159940
$63$	−1.19378	−0.150402
$64$	1.00000	0.125000
$65$	2.28948	0.283976
$66$	4.27905	0.526715
$67$	10.3747	1.26748	0.633738	−	0.773548i	$-0.281520\pi$
$67$	10.3747	1.26748	0.633738	+	0.773548i	$0.281520\pi$
$68$	−3.59570	−0.436043
$69$	6.42459	0.773430
$70$	2.73314	0.326672
$71$	1.20531	0.143044	0.0715222	−	0.997439i	$-0.477214\pi$
$71$	1.20531	0.143044	0.0715222	+	0.997439i	$0.477214\pi$
$72$	−1.00000	−0.117851
$73$	10.1318	1.18584	0.592919	−	0.805262i	$-0.297975\pi$
$73$	10.1318	1.18584	0.592919	+	0.805262i	$0.297975\pi$
$74$	6.96050	0.809141
$75$	−0.241736	−0.0279133
$76$	−1.35770	−0.155739
$77$	−5.10824	−0.582138
$78$	1.00000	0.113228
$79$	−2.00621	−0.225716	−0.112858	−	0.993611i	$-0.536000\pi$
$79$	−2.00621	−0.225716	−0.112858	+	0.993611i	$0.536000\pi$
$80$	2.28948	0.255972
$81$	1.00000	0.111111
$82$	−7.36952	−0.813828
$83$	4.49374	0.493252	0.246626	−	0.969111i	$-0.420678\pi$
$83$	4.49374	0.493252	0.246626	+	0.969111i	$0.420678\pi$
$84$	1.19378	0.130252
$85$	−8.23231	−0.892919
$86$	−1.70506	−0.183862
$87$	6.53525	0.700653
$88$	−4.27905	−0.456148
$89$	5.55082	0.588386	0.294193	−	0.955746i	$-0.404949\pi$
$89$	5.55082	0.588386	0.294193	+	0.955746i	$0.404949\pi$
$90$	−2.28948	−0.241333
$91$	−1.19378	−0.125142
$92$	−6.42459	−0.669810
$93$	1.25937	0.130590
$94$	−1.19672	−0.123433
$95$	−3.10843	−0.318919
$96$	1.00000	0.102062
$97$	7.35332	0.746616	0.373308	−	0.927707i	$-0.378223\pi$
$97$	7.35332	0.746616	0.373308	+	0.927707i	$0.378223\pi$
$98$	5.57489	0.563149
$99$	4.27905	0.430061
$100$	0.241736	0.0241736
$101$	11.1470	1.10917	0.554584	−	0.832128i	$-0.312878\pi$
$101$	11.1470	1.10917	0.554584	+	0.832128i	$0.312878\pi$
$102$	−3.59570	−0.356028
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	2.73314	0.266727
$106$	−2.84069	−0.275912
$107$	−4.78496	−0.462580	−0.231290	−	0.972885i	$-0.574295\pi$
$107$	−4.78496	−0.462580	−0.231290	+	0.972885i	$0.574295\pi$
$108$	−1.00000	−0.0962250
$109$	2.92640	0.280298	0.140149	−	0.990130i	$-0.455242\pi$
$109$	2.92640	0.280298	0.140149	+	0.990130i	$0.455242\pi$
$110$	−9.79682	−0.934090
$111$	6.96050	0.660661
$112$	−1.19378	−0.112801
$113$	2.55170	0.240044	0.120022	−	0.992771i	$-0.461704\pi$
$113$	2.55170	0.240044	0.120022	+	0.992771i	$0.461704\pi$
$114$	−1.35770	−0.127160
$115$	−14.7090	−1.37162
$116$	−6.53525	−0.606783
$117$	1.00000	0.0924500
$118$	−14.3018	−1.31659
$119$	4.29248	0.393491
$120$	2.28948	0.209000
$121$	7.31027	0.664570
$122$	−3.12763	−0.283163
$123$	−7.36952	−0.664487
$124$	−1.25937	−0.113095
$125$	−10.8940	−0.974386
$126$	1.19378	0.106350
$127$	−3.49577	−0.310200	−0.155100	−	0.987899i	$-0.549570\pi$
$127$	−3.49577	−0.310200	−0.155100	+	0.987899i	$0.549570\pi$
$128$	−1.00000	−0.0883883
$129$	−1.70506	−0.150123
$130$	−2.28948	−0.200801
$131$	−18.1097	−1.58226	−0.791128	−	0.611651i	$-0.790506\pi$
$131$	−18.1097	−1.58226	−0.791128	+	0.611651i	$0.790506\pi$
$132$	−4.27905	−0.372444
$133$	1.62079	0.140541
$134$	−10.3747	−0.896241
$135$	−2.28948	−0.197047
$136$	3.59570	0.308329
$137$	0.772432	0.0659933	0.0329967	−	0.999455i	$-0.489495\pi$
$137$	0.772432	0.0659933	0.0329967	+	0.999455i	$0.489495\pi$
$138$	−6.42459	−0.546898
$139$	14.3030	1.21317	0.606583	−	0.795020i	$-0.292540\pi$
$139$	14.3030	1.21317	0.606583	+	0.795020i	$0.292540\pi$
$140$	−2.73314	−0.230992
$141$	−1.19672	−0.100782
$142$	−1.20531	−0.101148
$143$	4.27905	0.357832
$144$	1.00000	0.0833333
$145$	−14.9624	−1.24256
$146$	−10.1318	−0.838515
$147$	5.57489	0.459809
$148$	−6.96050	−0.572149
$149$	17.3427	1.42077	0.710385	−	0.703813i	$-0.248521\pi$
$149$	17.3427	1.42077	0.710385	+	0.703813i	$0.248521\pi$
$150$	0.241736	0.0197377
$151$	14.7147	1.19746	0.598731	−	0.800950i	$-0.295672\pi$
$151$	14.7147	1.19746	0.598731	+	0.800950i	$0.295672\pi$
$152$	1.35770	0.110124
$153$	−3.59570	−0.290695
$154$	5.10824	0.411634
$155$	−2.88331	−0.231593
$156$	−1.00000	−0.0800641
$157$	22.0695	1.76134	0.880671	−	0.473729i	$-0.157092\pi$
$157$	22.0695	1.76134	0.880671	+	0.473729i	$0.157092\pi$
$158$	2.00621	0.159605
$159$	−2.84069	−0.225282
$160$	−2.28948	−0.181000
$161$	7.66954	0.604445
$162$	−1.00000	−0.0785674
$163$	−5.41189	−0.423892	−0.211946	−	0.977281i	$-0.567980\pi$
$163$	−5.41189	−0.423892	−0.211946	+	0.977281i	$0.567980\pi$
$164$	7.36952	0.575463
$165$	−9.79682	−0.762681
$166$	−4.49374	−0.348782
$167$	24.2697	1.87805	0.939025	−	0.343850i	$-0.111731\pi$
$167$	24.2697	1.87805	0.939025	+	0.343850i	$0.111731\pi$
$168$	−1.19378	−0.0921020
$169$	1.00000	0.0769231
$170$	8.23231	0.631389
$171$	−1.35770	−0.103826
$172$	1.70506	0.130010
$173$	−9.74264	−0.740720	−0.370360	−	0.928888i	$-0.620766\pi$
$173$	−9.74264	−0.740720	−0.370360	+	0.928888i	$0.620766\pi$
$174$	−6.53525	−0.495436
$175$	−0.288580	−0.0218146
$176$	4.27905	0.322546
$177$	−14.3018	−1.07499
$178$	−5.55082	−0.416052
$179$	5.63260	0.421000	0.210500	−	0.977594i	$-0.432491\pi$
$179$	5.63260	0.421000	0.210500	+	0.977594i	$0.432491\pi$
$180$	2.28948	0.170648
$181$	−6.35214	−0.472151	−0.236075	−	0.971735i	$-0.575861\pi$
$181$	−6.35214	−0.472151	−0.236075	+	0.971735i	$0.575861\pi$
$182$	1.19378	0.0884888
$183$	−3.12763	−0.231201
$184$	6.42459	0.473627
$185$	−15.9359	−1.17163
$186$	−1.25937	−0.0923414
$187$	−15.3862	−1.12515
$188$	1.19672	0.0872800
$189$	1.19378	0.0868346
$190$	3.10843	0.225509
$191$	0.0280475	0.00202944	0.00101472	−	0.999999i	$-0.499677\pi$
$191$	0.0280475	0.00202944	0.00101472	+	0.999999i	$0.499677\pi$
$192$	−1.00000	−0.0721688
$193$	−16.8861	−1.21549	−0.607743	−	0.794134i	$-0.707925\pi$
$193$	−16.8861	−1.21549	−0.607743	+	0.794134i	$0.707925\pi$
$194$	−7.35332	−0.527937
$195$	−2.28948	−0.163953
$196$	−5.57489	−0.398207
$197$	11.9854	0.853928	0.426964	−	0.904269i	$-0.359583\pi$
$197$	11.9854	0.853928	0.426964	+	0.904269i	$0.359583\pi$
$198$	−4.27905	−0.304099
$199$	16.7843	1.18980	0.594902	−	0.803798i	$-0.297191\pi$
$199$	16.7843	1.18980	0.594902	+	0.803798i	$0.297191\pi$
$200$	−0.241736	−0.0170933
$201$	−10.3747	−0.731778
$202$	−11.1470	−0.784300
$203$	7.80165	0.547568
$204$	3.59570	0.251750
$205$	16.8724	1.17842
$206$	1.00000	0.0696733
$207$	−6.42459	−0.446540
$208$	1.00000	0.0693375
$209$	−5.80967	−0.401863
$210$	−2.73314	−0.188604
$211$	−5.85650	−0.403178	−0.201589	−	0.979470i	$-0.564611\pi$
$211$	−5.85650	−0.403178	−0.201589	+	0.979470i	$0.564611\pi$
$212$	2.84069	0.195100
$213$	−1.20531	−0.0825867
$214$	4.78496	0.327093
$215$	3.90372	0.266231
$216$	1.00000	0.0680414
$217$	1.50341	0.102058
$218$	−2.92640	−0.198201
$219$	−10.1318	−0.684644
$220$	9.79682	0.660501
$221$	−3.59570	−0.241873
$222$	−6.96050	−0.467158
$223$	2.27388	0.152270	0.0761351	−	0.997098i	$-0.475742\pi$
$223$	2.27388	0.152270	0.0761351	+	0.997098i	$0.475742\pi$
$224$	1.19378	0.0797627
$225$	0.241736	0.0161158
$226$	−2.55170	−0.169736
$227$	24.4840	1.62506	0.812530	−	0.582919i	$-0.198090\pi$
$227$	24.4840	1.62506	0.812530	+	0.582919i	$0.198090\pi$
$228$	1.35770	0.0899159
$229$	18.1528	1.19957	0.599786	−	0.800161i	$-0.295252\pi$
$229$	18.1528	1.19957	0.599786	+	0.800161i	$0.295252\pi$
$230$	14.7090	0.969883
$231$	5.10824	0.336097
$232$	6.53525	0.429060
$233$	−12.6906	−0.831392	−0.415696	−	0.909504i	$-0.636462\pi$
$233$	−12.6906	−0.831392	−0.415696	+	0.909504i	$0.636462\pi$
$234$	−1.00000	−0.0653720
$235$	2.73988	0.178730
$236$	14.3018	0.930971
$237$	2.00621	0.130317
$238$	−4.29248	−0.278240
$239$	17.9914	1.16377	0.581883	−	0.813273i	$-0.302316\pi$
$239$	17.9914	1.16377	0.581883	+	0.813273i	$0.302316\pi$
$240$	−2.28948	−0.147786
$241$	3.62121	0.233262	0.116631	−	0.993175i	$-0.462790\pi$
$241$	3.62121	0.233262	0.116631	+	0.993175i	$0.462790\pi$
$242$	−7.31027	−0.469922
$243$	−1.00000	−0.0641500
$244$	3.12763	0.200226
$245$	−12.7636	−0.815438
$246$	7.36952	0.469864
$247$	−1.35770	−0.0863884
$248$	1.25937	0.0799700
$249$	−4.49374	−0.284779
$250$	10.8940	0.688995
$251$	9.61212	0.606712	0.303356	−	0.952877i	$-0.401893\pi$
$251$	9.61212	0.606712	0.303356	+	0.952877i	$0.401893\pi$
$252$	−1.19378	−0.0752010
$253$	−27.4912	−1.72835
$254$	3.49577	0.219344
$255$	8.23231	0.515527
$256$	1.00000	0.0625000
$257$	−4.38700	−0.273654	−0.136827	−	0.990595i	$-0.543690\pi$
$257$	−4.38700	−0.273654	−0.136827	+	0.990595i	$0.543690\pi$
$258$	1.70506	0.106153
$259$	8.30929	0.516314
$260$	2.28948	0.141988
$261$	−6.53525	−0.404522
$262$	18.1097	1.11882
$263$	−28.0116	−1.72727	−0.863635	−	0.504118i	$-0.831818\pi$
$263$	−28.0116	−1.72727	−0.863635	+	0.504118i	$0.831818\pi$
$264$	4.27905	0.263357
$265$	6.50372	0.399520
$266$	−1.62079	−0.0993773
$267$	−5.55082	−0.339705
$268$	10.3747	0.633738
$269$	−7.77286	−0.473920	−0.236960	−	0.971519i	$-0.576151\pi$
$269$	−7.77286	−0.473920	−0.236960	+	0.971519i	$0.576151\pi$
$270$	2.28948	0.139334
$271$	11.6289	0.706406	0.353203	−	0.935547i	$-0.385093\pi$
$271$	11.6289	0.706406	0.353203	+	0.935547i	$0.385093\pi$
$272$	−3.59570	−0.218022
$273$	1.19378	0.0722508
$274$	−0.772432	−0.0466643
$275$	1.03440	0.0623768
$276$	6.42459	0.386715
$277$	15.6095	0.937883	0.468941	−	0.883229i	$-0.344636\pi$
$277$	15.6095	0.937883	0.468941	+	0.883229i	$0.344636\pi$
$278$	−14.3030	−0.857837
$279$	−1.25937	−0.0753965
$280$	2.73314	0.163336
$281$	−14.6040	−0.871199	−0.435599	−	0.900141i	$-0.643464\pi$
$281$	−14.6040	−0.871199	−0.435599	+	0.900141i	$0.643464\pi$
$282$	1.19672	0.0712638
$283$	14.0678	0.836245	0.418122	−	0.908391i	$-0.362688\pi$
$283$	14.0678	0.836245	0.418122	+	0.908391i	$0.362688\pi$
$284$	1.20531	0.0715222
$285$	3.10843	0.184128
$286$	−4.27905	−0.253026
$287$	−8.79758	−0.519305
$288$	−1.00000	−0.0589256
$289$	−4.07091	−0.239465
$290$	14.9624	0.878620
$291$	−7.35332	−0.431059
$292$	10.1318	0.592919
$293$	−24.4565	−1.42876	−0.714381	−	0.699757i	$-0.753292\pi$
$293$	−24.4565	−1.42876	−0.714381	+	0.699757i	$0.753292\pi$
$294$	−5.57489	−0.325134
$295$	32.7438	1.90642
$296$	6.96050	0.404571
$297$	−4.27905	−0.248296
$298$	−17.3427	−1.00464
$299$	−6.42459	−0.371544
$300$	−0.241736	−0.0139566
$301$	−2.03547	−0.117323
$302$	−14.7147	−0.846733
$303$	−11.1470	−0.640378
$304$	−1.35770	−0.0778695
$305$	7.16067	0.410019
$306$	3.59570	0.205553
$307$	−4.95540	−0.282820	−0.141410	−	0.989951i	$-0.545164\pi$
$307$	−4.95540	−0.282820	−0.141410	+	0.989951i	$0.545164\pi$
$308$	−5.10824	−0.291069
$309$	1.00000	0.0568880
$310$	2.88331	0.163761
$311$	0.541516	0.0307066	0.0153533	−	0.999882i	$-0.495113\pi$
$311$	0.541516	0.0307066	0.0153533	+	0.999882i	$0.495113\pi$
$312$	1.00000	0.0566139
$313$	−21.4984	−1.21516	−0.607580	−	0.794258i	$-0.707860\pi$
$313$	−21.4984	−1.21516	−0.607580	+	0.794258i	$0.707860\pi$
$314$	−22.0695	−1.24546
$315$	−2.73314	−0.153995
$316$	−2.00621	−0.112858
$317$	1.44767	0.0813094	0.0406547	−	0.999173i	$-0.487056\pi$
$317$	1.44767	0.0813094	0.0406547	+	0.999173i	$0.487056\pi$
$318$	2.84069	0.159298
$319$	−27.9647	−1.56572
$320$	2.28948	0.127986
$321$	4.78496	0.267070
$322$	−7.66954	−0.427407
$323$	4.88189	0.271636
$324$	1.00000	0.0555556
$325$	0.241736	0.0134091
$326$	5.41189	0.299737
$327$	−2.92640	−0.161830
$328$	−7.36952	−0.406914
$329$	−1.42862	−0.0787625
$330$	9.79682	0.539297
$331$	28.5941	1.57167	0.785836	−	0.618435i	$-0.212233\pi$
$331$	28.5941	1.57167	0.785836	+	0.618435i	$0.212233\pi$
$332$	4.49374	0.246626
$333$	−6.96050	−0.381433
$334$	−24.2697	−1.32798
$335$	23.7528	1.29775
$336$	1.19378	0.0651260
$337$	−32.2295	−1.75565	−0.877827	−	0.478978i	$-0.841007\pi$
$337$	−32.2295	−1.75565	−0.877827	+	0.478978i	$0.841007\pi$
$338$	−1.00000	−0.0543928
$339$	−2.55170	−0.138589
$340$	−8.23231	−0.446460
$341$	−5.38890	−0.291825
$342$	1.35770	0.0734160
$343$	15.0116	0.810552
$344$	−1.70506	−0.0919309
$345$	14.7090	0.791906
$346$	9.74264	0.523768
$347$	22.3484	1.19973	0.599863	−	0.800103i	$-0.295222\pi$
$347$	22.3484	1.19973	0.599863	+	0.800103i	$0.295222\pi$
$348$	6.53525	0.350326
$349$	9.93972	0.532061	0.266030	−	0.963965i	$-0.414288\pi$
$349$	9.93972	0.532061	0.266030	+	0.963965i	$0.414288\pi$
$350$	0.288580	0.0154252
$351$	−1.00000	−0.0533761
$352$	−4.27905	−0.228074
$353$	−17.0214	−0.905958	−0.452979	−	0.891521i	$-0.649639\pi$
$353$	−17.0214	−0.905958	−0.452979	+	0.891521i	$0.649639\pi$
$354$	14.3018	0.760135
$355$	2.75955	0.146462
$356$	5.55082	0.294193
$357$	−4.29248	−0.227182
$358$	−5.63260	−0.297692
$359$	0.00561075	0.000296124 0	0.000148062	−	1.00000i	$-0.499953\pi$
$359$	0.00561075	0.000296124 0	0.000148062		1.00000i	$0.499953\pi$
$360$	−2.28948	−0.120666
$361$	−17.1566	−0.902982
$362$	6.35214	0.333861
$363$	−7.31027	−0.383690
$364$	−1.19378	−0.0625710
$365$	23.1966	1.21417
$366$	3.12763	0.163484
$367$	−4.96085	−0.258954	−0.129477	−	0.991582i	$-0.541330\pi$
$367$	−4.96085	−0.258954	−0.129477	+	0.991582i	$0.541330\pi$
$368$	−6.42459	−0.334905
$369$	7.36952	0.383642
$370$	15.9359	0.828470
$371$	−3.39116	−0.176060
$372$	1.25937	0.0652952
$373$	11.5261	0.596801	0.298400	−	0.954441i	$-0.403547\pi$
$373$	11.5261	0.596801	0.298400	+	0.954441i	$0.403547\pi$
$374$	15.3862	0.795601
$375$	10.8940	0.562562
$376$	−1.19672	−0.0617163
$377$	−6.53525	−0.336583
$378$	−1.19378	−0.0614014
$379$	19.0110	0.976532	0.488266	−	0.872695i	$-0.337630\pi$
$379$	19.0110	0.976532	0.488266	+	0.872695i	$0.337630\pi$
$380$	−3.10843	−0.159459
$381$	3.49577	0.179094
$382$	−0.0280475	−0.00143503
$383$	8.99836	0.459795	0.229897	−	0.973215i	$-0.426161\pi$
$383$	8.99836	0.459795	0.229897	+	0.973215i	$0.426161\pi$
$384$	1.00000	0.0510310
$385$	−11.6952	−0.596044
$386$	16.8861	0.859478
$387$	1.70506	0.0866733
$388$	7.35332	0.373308
$389$	34.9429	1.77168	0.885838	−	0.463995i	$-0.153584\pi$
$389$	34.9429	1.77168	0.885838	+	0.463995i	$0.153584\pi$
$390$	2.28948	0.115933
$391$	23.1009	1.16826
$392$	5.57489	0.281575
$393$	18.1097	0.913516
$394$	−11.9854	−0.603818
$395$	−4.59318	−0.231108
$396$	4.27905	0.215030
$397$	7.48202	0.375512	0.187756	−	0.982216i	$-0.439879\pi$
$397$	7.48202	0.375512	0.187756	+	0.982216i	$0.439879\pi$
$398$	−16.7843	−0.841319
$399$	−1.62079	−0.0811412
$400$	0.241736	0.0120868
$401$	−13.7786	−0.688071	−0.344036	−	0.938957i	$-0.611794\pi$
$401$	−13.7786	−0.688071	−0.344036	+	0.938957i	$0.611794\pi$
$402$	10.3747	0.517445
$403$	−1.25937	−0.0627336
$404$	11.1470	0.554584
$405$	2.28948	0.113765
$406$	−7.80165	−0.387189
$407$	−29.7843	−1.47635
$408$	−3.59570	−0.178014
$409$	18.5833	0.918885	0.459443	−	0.888207i	$-0.348049\pi$
$409$	18.5833	0.918885	0.459443	+	0.888207i	$0.348049\pi$
$410$	−16.8724	−0.833269
$411$	−0.772432	−0.0381013
$412$	−1.00000	−0.0492665
$413$	−17.0732	−0.840119
$414$	6.42459	0.315752
$415$	10.2883	0.505035
$416$	−1.00000	−0.0490290
$417$	−14.3030	−0.700421
$418$	5.80967	0.284160
$419$	−16.9895	−0.829991	−0.414996	−	0.909823i	$-0.636217\pi$
$419$	−16.9895	−0.829991	−0.414996	+	0.909823i	$0.636217\pi$
$420$	2.73314	0.133363
$421$	26.6550	1.29908	0.649542	−	0.760326i	$-0.274961\pi$
$421$	26.6550	1.29908	0.649542	+	0.760326i	$0.274961\pi$
$422$	5.85650	0.285090
$423$	1.19672	0.0581867
$424$	−2.84069	−0.137956
$425$	−0.869212	−0.0421630
$426$	1.20531	0.0583977
$427$	−3.73370	−0.180687
$428$	−4.78496	−0.231290
$429$	−4.27905	−0.206594
$430$	−3.90372	−0.188254
$431$	−31.1412	−1.50002	−0.750011	−	0.661426i	$-0.769952\pi$
$431$	−31.1412	−1.50002	−0.750011	+	0.661426i	$0.769952\pi$
$432$	−1.00000	−0.0481125
$433$	−4.81223	−0.231261	−0.115631	−	0.993292i	$-0.536889\pi$
$433$	−4.81223	−0.231261	−0.115631	+	0.993292i	$0.536889\pi$
$434$	−1.50341	−0.0721659
$435$	14.9624	0.717390
$436$	2.92640	0.140149
$437$	8.72268	0.417262
$438$	10.1318	0.484117
$439$	40.6140	1.93840	0.969200	−	0.246275i	$-0.0792067\pi$
$439$	40.6140	1.93840	0.969200	+	0.246275i	$0.0792067\pi$
$440$	−9.79682	−0.467045
$441$	−5.57489	−0.265471
$442$	3.59570	0.171030
$443$	−12.7887	−0.607611	−0.303806	−	0.952734i	$-0.598257\pi$
$443$	−12.7887	−0.607611	−0.303806	+	0.952734i	$0.598257\pi$
$444$	6.96050	0.330331
$445$	12.7085	0.602442
$446$	−2.27388	−0.107671
$447$	−17.3427	−0.820282
$448$	−1.19378	−0.0564007
$449$	−41.2330	−1.94591	−0.972953	−	0.231002i	$-0.925800\pi$
$449$	−41.2330	−1.94591	−0.972953	+	0.231002i	$0.925800\pi$
$450$	−0.241736	−0.0113956
$451$	31.5346	1.48490
$452$	2.55170	0.120022
$453$	−14.7147	−0.691355
$454$	−24.4840	−1.14909
$455$	−2.73314	−0.128131
$456$	−1.35770	−0.0635802
$457$	−13.7388	−0.642675	−0.321338	−	0.946965i	$-0.604132\pi$
$457$	−13.7388	−0.642675	−0.321338	+	0.946965i	$0.604132\pi$
$458$	−18.1528	−0.848225
$459$	3.59570	0.167833
$460$	−14.7090	−0.685811
$461$	−10.4692	−0.487601	−0.243801	−	0.969825i	$-0.578394\pi$
$461$	−10.4692	−0.487601	−0.243801	+	0.969825i	$0.578394\pi$
$462$	−5.10824	−0.237657
$463$	19.0331	0.884545	0.442272	−	0.896881i	$-0.354172\pi$
$463$	19.0331	0.884545	0.442272	+	0.896881i	$0.354172\pi$
$464$	−6.53525	−0.303392
$465$	2.88331	0.133710
$466$	12.6906	0.587883
$467$	−4.60131	−0.212923	−0.106462	−	0.994317i	$-0.533952\pi$
$467$	−4.60131	−0.212923	−0.106462	+	0.994317i	$0.533952\pi$
$468$	1.00000	0.0462250
$469$	−12.3851	−0.571893
$470$	−2.73988	−0.126381
$471$	−22.0695	−1.01691
$472$	−14.3018	−0.658296
$473$	7.29606	0.335473
$474$	−2.00621	−0.0921481
$475$	−0.328206	−0.0150591
$476$	4.29248	0.196745
$477$	2.84069	0.130066
$478$	−17.9914	−0.822907
$479$	8.25442	0.377154	0.188577	−	0.982058i	$-0.439613\pi$
$479$	8.25442	0.377154	0.188577	+	0.982058i	$0.439613\pi$
$480$	2.28948	0.104500
$481$	−6.96050	−0.317371
$482$	−3.62121	−0.164941
$483$	−7.66954	−0.348976
$484$	7.31027	0.332285
$485$	16.8353	0.764451
$486$	1.00000	0.0453609
$487$	30.9469	1.40234	0.701169	−	0.712996i	$-0.252662\pi$
$487$	30.9469	1.40234	0.701169	+	0.712996i	$0.252662\pi$
$488$	−3.12763	−0.141581
$489$	5.41189	0.244734
$490$	12.7636	0.576602
$491$	2.62104	0.118286	0.0591429	−	0.998250i	$-0.481163\pi$
$491$	2.62104	0.118286	0.0591429	+	0.998250i	$0.481163\pi$
$492$	−7.36952	−0.332244
$493$	23.4988	1.05833
$494$	1.35770	0.0610858
$495$	9.79682	0.440334
$496$	−1.25937	−0.0565473
$497$	−1.43888	−0.0645425
$498$	4.49374	0.201369
$499$	−10.9828	−0.491657	−0.245829	−	0.969313i	$-0.579060\pi$
$499$	−10.9828	−0.491657	−0.245829	+	0.969313i	$0.579060\pi$
$500$	−10.8940	−0.487193
$501$	−24.2697	−1.08429
$502$	−9.61212	−0.429010
$503$	−2.99356	−0.133476	−0.0667382	−	0.997771i	$-0.521259\pi$
$503$	−2.99356	−0.133476	−0.0667382	+	0.997771i	$0.521259\pi$
$504$	1.19378	0.0531751
$505$	25.5209	1.13566
$506$	27.4912	1.22213
$507$	−1.00000	−0.0444116
$508$	−3.49577	−0.155100
$509$	19.6098	0.869188	0.434594	−	0.900626i	$-0.356892\pi$
$509$	19.6098	0.869188	0.434594	+	0.900626i	$0.356892\pi$
$510$	−8.23231	−0.364533
$511$	−12.0951	−0.535058
$512$	−1.00000	−0.0441942
$513$	1.35770	0.0599440
$514$	4.38700	0.193502
$515$	−2.28948	−0.100887
$516$	−1.70506	−0.0750613
$517$	5.12084	0.225214
$518$	−8.30929	−0.365089
$519$	9.74264	0.427655
$520$	−2.28948	−0.100401
$521$	22.8030	0.999017	0.499509	−	0.866309i	$-0.333514\pi$
$521$	22.8030	0.999017	0.499509	+	0.866309i	$0.333514\pi$
$522$	6.53525	0.286040
$523$	−25.2714	−1.10504	−0.552522	−	0.833499i	$-0.686334\pi$
$523$	−25.2714	−1.10504	−0.552522	+	0.833499i	$0.686334\pi$
$524$	−18.1097	−0.791128
$525$	0.288580	0.0125946
$526$	28.0116	1.22136
$527$	4.52832	0.197257
$528$	−4.27905	−0.186222
$529$	18.2754	0.794583
$530$	−6.50372	−0.282504
$531$	14.3018	0.620647
$532$	1.62079	0.0702703
$533$	7.36952	0.319209
$534$	5.55082	0.240208
$535$	−10.9551	−0.473630
$536$	−10.3747	−0.448121
$537$	−5.63260	−0.243065
$538$	7.77286	0.335112
$539$	−23.8552	−1.02752
$540$	−2.28948	−0.0985237
$541$	4.86481	0.209154	0.104577	−	0.994517i	$-0.466651\pi$
$541$	4.86481	0.209154	0.104577	+	0.994517i	$0.466651\pi$
$542$	−11.6289	−0.499504
$543$	6.35214	0.272596
$544$	3.59570	0.154165
$545$	6.69995	0.286994
$546$	−1.19378	−0.0510890
$547$	25.2611	1.08009	0.540043	−	0.841638i	$-0.318408\pi$
$547$	25.2611	1.08009	0.540043	+	0.841638i	$0.318408\pi$
$548$	0.772432	0.0329967
$549$	3.12763	0.133484
$550$	−1.03440	−0.0441070
$551$	8.87292	0.377999
$552$	−6.42459	−0.273449
$553$	2.39497	0.101844
$554$	−15.6095	−0.663183
$555$	15.9359	0.676443
$556$	14.3030	0.606583
$557$	10.1532	0.430205	0.215102	−	0.976591i	$-0.430991\pi$
$557$	10.1532	0.430205	0.215102	+	0.976591i	$0.430991\pi$
$558$	1.25937	0.0533133
$559$	1.70506	0.0721166
$560$	−2.73314	−0.115496
$561$	15.3862	0.649606
$562$	14.6040	0.616031
$563$	−5.09473	−0.214717	−0.107359	−	0.994220i	$-0.534239\pi$
$563$	−5.09473	−0.214717	−0.107359	+	0.994220i	$0.534239\pi$
$564$	−1.19672	−0.0503911
$565$	5.84207	0.245778
$566$	−14.0678	−0.591314
$567$	−1.19378	−0.0501340
$568$	−1.20531	−0.0505738
$569$	−42.8195	−1.79509	−0.897543	−	0.440926i	$-0.854650\pi$
$569$	−42.8195	−1.79509	−0.897543	+	0.440926i	$0.854650\pi$
$570$	−3.10843	−0.130198
$571$	32.0885	1.34286	0.671430	−	0.741068i	$-0.265680\pi$
$571$	32.0885	1.34286	0.671430	+	0.741068i	$0.265680\pi$
$572$	4.27905	0.178916
$573$	−0.0280475	−0.00117170
$574$	8.79758	0.367204
$575$	−1.55306	−0.0647670
$576$	1.00000	0.0416667
$577$	13.9671	0.581458	0.290729	−	0.956805i	$-0.406102\pi$
$577$	13.9671	0.581458	0.290729	+	0.956805i	$0.406102\pi$
$578$	4.07091	0.169327
$579$	16.8861	0.701761
$580$	−14.9624	−0.621278
$581$	−5.36453	−0.222558
$582$	7.35332	0.304805
$583$	12.1555	0.503428
$584$	−10.1318	−0.419257
$585$	2.28948	0.0946585
$586$	24.4565	1.01029
$587$	−13.4259	−0.554147	−0.277073	−	0.960849i	$-0.589365\pi$
$587$	−13.4259	−0.554147	−0.277073	+	0.960849i	$0.589365\pi$
$588$	5.57489	0.229905
$589$	1.70985	0.0704530
$590$	−32.7438	−1.34804
$591$	−11.9854	−0.493016
$592$	−6.96050	−0.286075
$593$	−31.2213	−1.28210	−0.641052	−	0.767497i	$-0.721502\pi$
$593$	−31.2213	−1.28210	−0.641052	+	0.767497i	$0.721502\pi$
$594$	4.27905	0.175572
$595$	9.82755	0.402890
$596$	17.3427	0.710385
$597$	−16.7843	−0.686934
$598$	6.42459	0.262721
$599$	−30.1210	−1.23071	−0.615356	−	0.788250i	$-0.710988\pi$
$599$	−30.1210	−1.23071	−0.615356	+	0.788250i	$0.710988\pi$
$600$	0.241736	0.00986884
$601$	32.1632	1.31197	0.655983	−	0.754776i	$-0.272254\pi$
$601$	32.1632	1.31197	0.655983	+	0.754776i	$0.272254\pi$
$602$	2.03547	0.0829596
$603$	10.3747	0.422492
$604$	14.7147	0.598731
$605$	16.7367	0.680445
$606$	11.1470	0.452816
$607$	26.2385	1.06499	0.532494	−	0.846434i	$-0.321255\pi$
$607$	26.2385	1.06499	0.532494	+	0.846434i	$0.321255\pi$
$608$	1.35770	0.0550620
$609$	−7.80165	−0.316139
$610$	−7.16067	−0.289927
$611$	1.19672	0.0484142
$612$	−3.59570	−0.145348
$613$	−15.6293	−0.631262	−0.315631	−	0.948882i	$-0.602216\pi$
$613$	−15.6293	−0.631262	−0.315631	+	0.948882i	$0.602216\pi$
$614$	4.95540	0.199984
$615$	−16.8724	−0.680361
$616$	5.10824	0.205817
$617$	−1.25068	−0.0503505	−0.0251753	−	0.999683i	$-0.508014\pi$
$617$	−1.25068	−0.0503505	−0.0251753	+	0.999683i	$0.508014\pi$
$618$	−1.00000	−0.0402259
$619$	31.7077	1.27444	0.637221	−	0.770681i	$-0.280084\pi$
$619$	31.7077	1.27444	0.637221	+	0.770681i	$0.280084\pi$
$620$	−2.88331	−0.115796
$621$	6.42459	0.257810
$622$	−0.541516	−0.0217128
$623$	−6.62646	−0.265483
$624$	−1.00000	−0.0400320
$625$	−26.1502	−1.04601
$626$	21.4984	0.859248
$627$	5.80967	0.232016
$628$	22.0695	0.880671
$629$	25.0279	0.997927
$630$	2.73314	0.108891
$631$	−15.6313	−0.622273	−0.311137	−	0.950365i	$-0.600710\pi$
$631$	−15.6313	−0.622273	−0.311137	+	0.950365i	$0.600710\pi$
$632$	2.00621	0.0798026
$633$	5.85650	0.232775
$634$	−1.44767	−0.0574944
$635$	−8.00352	−0.317610
$636$	−2.84069	−0.112641
$637$	−5.57489	−0.220885
$638$	27.9647	1.10713
$639$	1.20531	0.0476815
$640$	−2.28948	−0.0904998
$641$	−33.4222	−1.32010	−0.660048	−	0.751223i	$-0.729464\pi$
$641$	−33.4222	−1.32010	−0.660048	+	0.751223i	$0.729464\pi$
$642$	−4.78496	−0.188847
$643$	−8.92919	−0.352133	−0.176067	−	0.984378i	$-0.556337\pi$
$643$	−8.92919	−0.352133	−0.176067	+	0.984378i	$0.556337\pi$
$644$	7.66954	0.302222
$645$	−3.90372	−0.153709
$646$	−4.88189	−0.192075
$647$	−42.6542	−1.67691	−0.838455	−	0.544970i	$-0.816541\pi$
$647$	−42.6542	−1.67691	−0.838455	+	0.544970i	$0.816541\pi$
$648$	−1.00000	−0.0392837
$649$	61.1983	2.40224
$650$	−0.241736	−0.00948168
$651$	−1.50341	−0.0589232
$652$	−5.41189	−0.211946
$653$	15.3018	0.598806	0.299403	−	0.954127i	$-0.403213\pi$
$653$	15.3018	0.598806	0.299403	+	0.954127i	$0.403213\pi$
$654$	2.92640	0.114431
$655$	−41.4620	−1.62005
$656$	7.36952	0.287732
$657$	10.1318	0.395280
$658$	1.42862	0.0556935
$659$	4.82352	0.187898	0.0939489	−	0.995577i	$-0.470051\pi$
$659$	4.82352	0.187898	0.0939489	+	0.995577i	$0.470051\pi$
$660$	−9.79682	−0.381341
$661$	24.6784	0.959880	0.479940	−	0.877301i	$-0.340658\pi$
$661$	24.6784	0.959880	0.479940	+	0.877301i	$0.340658\pi$
$662$	−28.5941	−1.11134
$663$	3.59570	0.139646
$664$	−4.49374	−0.174391
$665$	3.71078	0.143898
$666$	6.96050	0.269714
$667$	41.9864	1.62572
$668$	24.2697	0.939025
$669$	−2.27388	−0.0879133
$670$	−23.7528	−0.917651
$671$	13.3833	0.516657
$672$	−1.19378	−0.0460510
$673$	−7.82552	−0.301652	−0.150826	−	0.988560i	$-0.548193\pi$
$673$	−7.82552	−0.301652	−0.150826	+	0.988560i	$0.548193\pi$
$674$	32.2295	1.24143
$675$	−0.241736	−0.00930443
$676$	1.00000	0.0384615
$677$	20.1050	0.772699	0.386350	−	0.922352i	$-0.373736\pi$
$677$	20.1050	0.772699	0.386350	+	0.922352i	$0.373736\pi$
$678$	2.55170	0.0979974
$679$	−8.77823	−0.336878
$680$	8.23231	0.315695
$681$	−24.4840	−0.938229
$682$	5.38890	0.206352
$683$	4.60842	0.176336	0.0881681	−	0.996106i	$-0.471899\pi$
$683$	4.60842	0.176336	0.0881681	+	0.996106i	$0.471899\pi$
$684$	−1.35770	−0.0519130
$685$	1.76847	0.0675698
$686$	−15.0116	−0.573147
$687$	−18.1528	−0.692573
$688$	1.70506	0.0650050
$689$	2.84069	0.108222
$690$	−14.7090	−0.559962
$691$	−2.68257	−0.102050	−0.0510249	−	0.998697i	$-0.516249\pi$
$691$	−2.68257	−0.102050	−0.0510249	+	0.998697i	$0.516249\pi$
$692$	−9.74264	−0.370360
$693$	−5.10824	−0.194046
$694$	−22.3484	−0.848335
$695$	32.7465	1.24215
$696$	−6.53525	−0.247718
$697$	−26.4986	−1.00371
$698$	−9.93972	−0.376224
$699$	12.6906	0.480004
$700$	−0.288580	−0.0109073
$701$	−35.8678	−1.35471	−0.677354	−	0.735657i	$-0.736873\pi$
$701$	−35.8678	−1.35471	−0.677354	+	0.735657i	$0.736873\pi$
$702$	1.00000	0.0377426
$703$	9.45027	0.356424
$704$	4.27905	0.161273
$705$	−2.73988	−0.103190
$706$	17.0214	0.640609
$707$	−13.3070	−0.500463
$708$	−14.3018	−0.537496
$709$	4.94712	0.185793	0.0928965	−	0.995676i	$-0.470387\pi$
$709$	4.94712	0.185793	0.0928965	+	0.995676i	$0.470387\pi$
$710$	−2.75955	−0.103564
$711$	−2.00621	−0.0752386
$712$	−5.55082	−0.208026
$713$	8.09093	0.303008
$714$	4.29248	0.160642
$715$	9.79682	0.366380
$716$	5.63260	0.210500
$717$	−17.9914	−0.671900
$718$	−0.00561075	−0.000209391 0
$719$	11.8733	0.442800	0.221400	−	0.975183i	$-0.428937\pi$
$719$	11.8733	0.442800	0.221400	+	0.975183i	$0.428937\pi$
$720$	2.28948	0.0853240
$721$	1.19378	0.0444586
$722$	17.1566	0.638504
$723$	−3.62121	−0.134674
$724$	−6.35214	−0.236075
$725$	−1.57981	−0.0586726
$726$	7.31027	0.271310
$727$	30.5078	1.13147	0.565736	−	0.824587i	$-0.308592\pi$
$727$	30.5078	1.13147	0.565736	+	0.824587i	$0.308592\pi$
$728$	1.19378	0.0442444
$729$	1.00000	0.0370370
$730$	−23.1966	−0.858545
$731$	−6.13091	−0.226760
$732$	−3.12763	−0.115601
$733$	−4.82880	−0.178356	−0.0891779	−	0.996016i	$-0.528424\pi$
$733$	−4.82880	−0.178356	−0.0891779	+	0.996016i	$0.528424\pi$
$734$	4.96085	0.183108
$735$	12.7636	0.470793
$736$	6.42459	0.236814
$737$	44.3940	1.63528
$738$	−7.36952	−0.271276
$739$	−3.09730	−0.113936	−0.0569681	−	0.998376i	$-0.518143\pi$
$739$	−3.09730	−0.113936	−0.0569681	+	0.998376i	$0.518143\pi$
$740$	−15.9359	−0.585817
$741$	1.35770	0.0498764
$742$	3.39116	0.124493
$743$	16.3166	0.598597	0.299299	−	0.954159i	$-0.403247\pi$
$743$	16.3166	0.598597	0.299299	+	0.954159i	$0.403247\pi$
$744$	−1.25937	−0.0461707
$745$	39.7059	1.45471
$746$	−11.5261	−0.422002
$747$	4.49374	0.164417
$748$	−15.3862	−0.562575
$749$	5.71218	0.208719
$750$	−10.8940	−0.397791
$751$	39.3121	1.43452	0.717259	−	0.696807i	$-0.245396\pi$
$751$	39.3121	1.43452	0.717259	+	0.696807i	$0.245396\pi$
$752$	1.19672	0.0436400
$753$	−9.61212	−0.350285
$754$	6.53525	0.238000
$755$	33.6890	1.22607
$756$	1.19378	0.0434173
$757$	−41.8503	−1.52107	−0.760537	−	0.649294i	$-0.775064\pi$
$757$	−41.8503	−1.52107	−0.760537	+	0.649294i	$0.775064\pi$
$758$	−19.0110	−0.690512
$759$	27.4912	0.997866
$760$	3.10843	0.112755
$761$	−34.0486	−1.23426	−0.617131	−	0.786861i	$-0.711705\pi$
$761$	−34.0486	−1.23426	−0.617131	+	0.786861i	$0.711705\pi$
$762$	−3.49577	−0.126639
$763$	−3.49348	−0.126472
$764$	0.0280475	0.00101472
$765$	−8.23231	−0.297640
$766$	−8.99836	−0.325124
$767$	14.3018	0.516410
$768$	−1.00000	−0.0360844
$769$	10.7045	0.386014	0.193007	−	0.981197i	$-0.438176\pi$
$769$	10.7045	0.386014	0.193007	+	0.981197i	$0.438176\pi$
$770$	11.6952	0.421467
$771$	4.38700	0.157994
$772$	−16.8861	−0.607743
$773$	23.6267	0.849793	0.424896	−	0.905242i	$-0.360311\pi$
$773$	23.6267	0.849793	0.424896	+	0.905242i	$0.360311\pi$
$774$	−1.70506	−0.0612873
$775$	−0.304435	−0.0109356
$776$	−7.35332	−0.263969
$777$	−8.30929	−0.298094
$778$	−34.9429	−1.25276
$779$	−10.0056	−0.358488
$780$	−2.28948	−0.0819767
$781$	5.15760	0.184553
$782$	−23.1009	−0.826088
$783$	6.53525	0.233551
$784$	−5.57489	−0.199103
$785$	50.5279	1.80342
$786$	−18.1097	−0.645953
$787$	19.1971	0.684304	0.342152	−	0.939645i	$-0.388844\pi$
$787$	19.1971	0.684304	0.342152	+	0.939645i	$0.388844\pi$
$788$	11.9854	0.426964
$789$	28.0116	0.997240
$790$	4.59318	0.163418
$791$	−3.04616	−0.108309
$792$	−4.27905	−0.152049
$793$	3.12763	0.111066
$794$	−7.48202	−0.265527
$795$	−6.50372	−0.230663
$796$	16.7843	0.594902
$797$	−42.4158	−1.50245	−0.751223	−	0.660049i	$-0.770536\pi$
$797$	−42.4158	−1.50245	−0.751223	+	0.660049i	$0.770536\pi$
$798$	1.62079	0.0573755
$799$	−4.30306	−0.152231
$800$	−0.241736	−0.00854667
$801$	5.55082	0.196129
$802$	13.7786	0.486540
$803$	43.3545	1.52995
$804$	−10.3747	−0.365889
$805$	17.5593	0.618884
$806$	1.25937	0.0443594
$807$	7.77286	0.273618
$808$	−11.1470	−0.392150
$809$	−5.02509	−0.176673	−0.0883363	−	0.996091i	$-0.528155\pi$
$809$	−5.02509	−0.176673	−0.0883363	+	0.996091i	$0.528155\pi$
$810$	−2.28948	−0.0804443
$811$	22.9949	0.807462	0.403731	−	0.914878i	$-0.367713\pi$
$811$	22.9949	0.807462	0.403731	+	0.914878i	$0.367713\pi$
$812$	7.80165	0.273784
$813$	−11.6289	−0.407844
$814$	29.7843	1.04394
$815$	−12.3904	−0.434018
$816$	3.59570	0.125875
$817$	−2.31497	−0.0809905
$818$	−18.5833	−0.649750
$819$	−1.19378	−0.0417140
$820$	16.8724	0.589210
$821$	21.0749	0.735519	0.367760	−	0.929921i	$-0.380125\pi$
$821$	21.0749	0.735519	0.367760	+	0.929921i	$0.380125\pi$
$822$	0.772432	0.0269417
$823$	−42.8530	−1.49376	−0.746881	−	0.664958i	$-0.768449\pi$
$823$	−42.8530	−1.49376	−0.746881	+	0.664958i	$0.768449\pi$
$824$	1.00000	0.0348367
$825$	−1.03440	−0.0360132
$826$	17.0732	0.594054
$827$	35.1982	1.22396	0.611980	−	0.790873i	$-0.290373\pi$
$827$	35.1982	1.22396	0.611980	+	0.790873i	$0.290373\pi$
$828$	−6.42459	−0.223270
$829$	−16.5382	−0.574395	−0.287197	−	0.957871i	$-0.592724\pi$
$829$	−16.5382	−0.574395	−0.287197	+	0.957871i	$0.592724\pi$
$830$	−10.2883	−0.357113
$831$	−15.6095	−0.541487
$832$	1.00000	0.0346688
$833$	20.0457	0.694541
$834$	14.3030	0.495273
$835$	55.5652	1.92291
$836$	−5.80967	−0.200932
$837$	1.25937	0.0435302
$838$	16.9895	0.586892
$839$	1.93922	0.0669493	0.0334747	−	0.999440i	$-0.489343\pi$
$839$	1.93922	0.0669493	0.0334747	+	0.999440i	$0.489343\pi$
$840$	−2.73314	−0.0943022
$841$	13.7095	0.472743
$842$	−26.6550	−0.918591
$843$	14.6040	0.502987
$844$	−5.85650	−0.201589
$845$	2.28948	0.0787606
$846$	−1.19672	−0.0411442
$847$	−8.72685	−0.299858
$848$	2.84069	0.0975498
$849$	−14.0678	−0.482806
$850$	0.869212	0.0298137
$851$	44.7184	1.53293
$852$	−1.20531	−0.0412934
$853$	−18.4017	−0.630064	−0.315032	−	0.949081i	$-0.602015\pi$
$853$	−18.4017	−0.630064	−0.315032	+	0.949081i	$0.602015\pi$
$854$	3.73370	0.127765
$855$	−3.10843	−0.106306
$856$	4.78496	0.163547
$857$	22.7555	0.777314	0.388657	−	0.921383i	$-0.372939\pi$
$857$	22.7555	0.777314	0.388657	+	0.921383i	$0.372939\pi$
$858$	4.27905	0.146084
$859$	−35.4905	−1.21092	−0.605461	−	0.795875i	$-0.707011\pi$
$859$	−35.4905	−1.21092	−0.605461	+	0.795875i	$0.707011\pi$
$860$	3.90372	0.133116
$861$	8.79758	0.299821
$862$	31.1412	1.06068
$863$	16.4055	0.558449	0.279224	−	0.960226i	$-0.409923\pi$
$863$	16.4055	0.558449	0.279224	+	0.960226i	$0.409923\pi$
$864$	1.00000	0.0340207
$865$	−22.3056	−0.758414
$866$	4.81223	0.163526
$867$	4.07091	0.138255
$868$	1.50341	0.0510290
$869$	−8.58466	−0.291215
$870$	−14.9624	−0.507271
$871$	10.3747	0.351535
$872$	−2.92640	−0.0991005
$873$	7.35332	0.248872
$874$	−8.72268	−0.295049
$875$	13.0050	0.439649
$876$	−10.1318	−0.342322
$877$	4.73131	0.159765	0.0798825	−	0.996804i	$-0.474545\pi$
$877$	4.73131	0.159765	0.0798825	+	0.996804i	$0.474545\pi$
$878$	−40.6140	−1.37066
$879$	24.4565	0.824896
$880$	9.79682	0.330251
$881$	−23.2448	−0.783138	−0.391569	−	0.920149i	$-0.628067\pi$
$881$	−23.2448	−0.783138	−0.391569	+	0.920149i	$0.628067\pi$
$882$	5.57489	0.187716
$883$	−11.6759	−0.392925	−0.196462	−	0.980511i	$-0.562945\pi$
$883$	−11.6759	−0.392925	−0.196462	+	0.980511i	$0.562945\pi$
$884$	−3.59570	−0.120937
$885$	−32.7438	−1.10067
$886$	12.7887	0.429646
$887$	−18.4731	−0.620268	−0.310134	−	0.950693i	$-0.600374\pi$
$887$	−18.4731	−0.620268	−0.310134	+	0.950693i	$0.600374\pi$
$888$	−6.96050	−0.233579
$889$	4.17318	0.139964
$890$	−12.7085	−0.425991
$891$	4.27905	0.143354
$892$	2.27388	0.0761351
$893$	−1.62479	−0.0543716
$894$	17.3427	0.580027
$895$	12.8957	0.431057
$896$	1.19378	0.0398813
$897$	6.42459	0.214511
$898$	41.2330	1.37596
$899$	8.23030	0.274496
$900$	0.241736	0.00805788
$901$	−10.2143	−0.340287
$902$	−31.5346	−1.04999
$903$	2.03547	0.0677362
$904$	−2.55170	−0.0848682
$905$	−14.5431	−0.483430
$906$	14.7147	0.488862
$907$	11.3470	0.376770	0.188385	−	0.982095i	$-0.439675\pi$
$907$	11.3470	0.376770	0.188385	+	0.982095i	$0.439675\pi$
$908$	24.4840	0.812530
$909$	11.1470	0.369723
$910$	2.73314	0.0906026
$911$	0.347605	0.0115167	0.00575834	−	0.999983i	$-0.498167\pi$
$911$	0.347605	0.0115167	0.00575834	+	0.999983i	$0.498167\pi$
$912$	1.35770	0.0449580
$913$	19.2289	0.636385
$914$	13.7388	0.454440
$915$	−7.16067	−0.236724
$916$	18.1528	0.599786
$917$	21.6190	0.713923
$918$	−3.59570	−0.118676
$919$	56.7382	1.87162	0.935810	−	0.352505i	$-0.114670\pi$
$919$	56.7382	1.87162	0.935810	+	0.352505i	$0.114670\pi$
$920$	14.7090	0.484941
$921$	4.95540	0.163286
$922$	10.4692	0.344786
$923$	1.20531	0.0396734
$924$	5.10824	0.168049
$925$	−1.68260	−0.0553237
$926$	−19.0331	−0.625468
$927$	−1.00000	−0.0328443
$928$	6.53525	0.214530
$929$	29.7076	0.974675	0.487337	−	0.873214i	$-0.337968\pi$
$929$	29.7076	0.974675	0.487337	+	0.873214i	$0.337968\pi$
$930$	−2.88331	−0.0945473
$931$	7.56904	0.248065
$932$	−12.6906	−0.415696
$933$	−0.541516	−0.0177284
$934$	4.60131	0.150560
$935$	−35.2265	−1.15203
$936$	−1.00000	−0.0326860
$937$	0.370005	0.0120875	0.00604377	−	0.999982i	$-0.498076\pi$
$937$	0.370005	0.0120875	0.00604377	+	0.999982i	$0.498076\pi$
$938$	12.3851	0.404389
$939$	21.4984	0.701573
$940$	2.73988	0.0893650
$941$	−10.8330	−0.353146	−0.176573	−	0.984288i	$-0.556501\pi$
$941$	−10.8330	−0.353146	−0.176573	+	0.984288i	$0.556501\pi$
$942$	22.0695	0.719065
$943$	−47.3462	−1.54180
$944$	14.3018	0.465486
$945$	2.73314	0.0889090
$946$	−7.29606	−0.237215
$947$	6.65466	0.216247	0.108124	−	0.994137i	$-0.465516\pi$
$947$	6.65466	0.216247	0.108124	+	0.994137i	$0.465516\pi$
$948$	2.00621	0.0651585
$949$	10.1318	0.328893
$950$	0.328206	0.0106484
$951$	−1.44767	−0.0469440
$952$	−4.29248	−0.139120
$953$	24.0843	0.780168	0.390084	−	0.920779i	$-0.372446\pi$
$953$	24.0843	0.780168	0.390084	+	0.920779i	$0.372446\pi$
$954$	−2.84069	−0.0919708
$955$	0.0642142	0.00207792
$956$	17.9914	0.581883
$957$	27.9647	0.903970
$958$	−8.25442	−0.266688
$959$	−0.922113	−0.0297766
$960$	−2.28948	−0.0738928
$961$	−29.4140	−0.948838
$962$	6.96050	0.224415
$963$	−4.78496	−0.154193
$964$	3.62121	0.116631
$965$	−38.6604	−1.24452
$966$	7.66954	0.246764
$967$	41.6001	1.33777	0.668885	−	0.743366i	$-0.266772\pi$
$967$	41.6001	1.33777	0.668885	+	0.743366i	$0.266772\pi$
$968$	−7.31027	−0.234961
$969$	−4.88189	−0.156829
$970$	−16.8353	−0.540549
$971$	28.7867	0.923808	0.461904	−	0.886930i	$-0.347166\pi$
$971$	28.7867	0.923808	0.461904	+	0.886930i	$0.347166\pi$
$972$	−1.00000	−0.0320750
$973$	−17.0746	−0.547387
$974$	−30.9469	−0.991602
$975$	−0.241736	−0.00774176
$976$	3.12763	0.100113
$977$	−17.8877	−0.572277	−0.286138	−	0.958188i	$-0.592372\pi$
$977$	−17.8877	−0.572277	−0.286138	+	0.958188i	$0.592372\pi$
$978$	−5.41189	−0.173053
$979$	23.7523	0.759125
$980$	−12.7636	−0.407719
$981$	2.92640	0.0934328
$982$	−2.62104	−0.0836407
$983$	7.03181	0.224280	0.112140	−	0.993692i	$-0.464229\pi$
$983$	7.03181	0.224280	0.112140	+	0.993692i	$0.464229\pi$
$984$	7.36952	0.234932
$985$	27.4405	0.874327
$986$	−23.4988	−0.748356
$987$	1.42862	0.0454736
$988$	−1.35770	−0.0431942
$989$	−10.9543	−0.348328
$990$	−9.79682	−0.311363
$991$	1.50489	0.0478044	0.0239022	−	0.999714i	$-0.492391\pi$
$991$	1.50489	0.0478044	0.0239022	+	0.999714i	$0.492391\pi$
$992$	1.25937	0.0399850
$993$	−28.5941	−0.907405
$994$	1.43888	0.0456384
$995$	38.4273	1.21823
$996$	−4.49374	−0.142390
$997$	26.0217	0.824116	0.412058	−	0.911158i	$-0.364810\pi$
$997$	26.0217	0.824116	0.412058	+	0.911158i	$0.364810\pi$
$998$	10.9828	0.347654
$999$	6.96050	0.220220

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.z.1.12	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.z.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.28948 q^{5} +1.00000 q^{6} -1.19378 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.28948 q^{5} +1.00000 q^{6} -1.19378 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.28948 q^{10} +4.27905 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.19378 q^{14} -2.28948 q^{15} +1.00000 q^{16} -3.59570 q^{17} -1.00000 q^{18} -1.35770 q^{19} +2.28948 q^{20} +1.19378 q^{21} -4.27905 q^{22} -6.42459 q^{23} +1.00000 q^{24} +0.241736 q^{25} -1.00000 q^{26} -1.00000 q^{27} -1.19378 q^{28} -6.53525 q^{29} +2.28948 q^{30} -1.25937 q^{31} -1.00000 q^{32} -4.27905 q^{33} +3.59570 q^{34} -2.73314 q^{35} +1.00000 q^{36} -6.96050 q^{37} +1.35770 q^{38} -1.00000 q^{39} -2.28948 q^{40} +7.36952 q^{41} -1.19378 q^{42} +1.70506 q^{43} +4.27905 q^{44} +2.28948 q^{45} +6.42459 q^{46} +1.19672 q^{47} -1.00000 q^{48} -5.57489 q^{49} -0.241736 q^{50} +3.59570 q^{51} +1.00000 q^{52} +2.84069 q^{53} +1.00000 q^{54} +9.79682 q^{55} +1.19378 q^{56} +1.35770 q^{57} +6.53525 q^{58} +14.3018 q^{59} -2.28948 q^{60} +3.12763 q^{61} +1.25937 q^{62} -1.19378 q^{63} +1.00000 q^{64} +2.28948 q^{65} +4.27905 q^{66} +10.3747 q^{67} -3.59570 q^{68} +6.42459 q^{69} +2.73314 q^{70} +1.20531 q^{71} -1.00000 q^{72} +10.1318 q^{73} +6.96050 q^{74} -0.241736 q^{75} -1.35770 q^{76} -5.10824 q^{77} +1.00000 q^{78} -2.00621 q^{79} +2.28948 q^{80} +1.00000 q^{81} -7.36952 q^{82} +4.49374 q^{83} +1.19378 q^{84} -8.23231 q^{85} -1.70506 q^{86} +6.53525 q^{87} -4.27905 q^{88} +5.55082 q^{89} -2.28948 q^{90} -1.19378 q^{91} -6.42459 q^{92} +1.25937 q^{93} -1.19672 q^{94} -3.10843 q^{95} +1.00000 q^{96} +7.35332 q^{97} +5.57489 q^{98} +4.27905 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 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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