LMFDB - Embedded newform 8034.2.a.z.1.6

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			1.6
Root			$0.937159$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.937159 q^{5} +1.00000 q^{6} -0.792704 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.937159 q^{5} +1.00000 q^{6} -0.792704 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.937159 q^{10} -4.70314 q^{11} -1.00000 q^{12} +1.00000 q^{13} +0.792704 q^{14} +0.937159 q^{15} +1.00000 q^{16} -3.60442 q^{17} -1.00000 q^{18} -0.803399 q^{19} -0.937159 q^{20} +0.792704 q^{21} +4.70314 q^{22} -4.68922 q^{23} +1.00000 q^{24} -4.12173 q^{25} -1.00000 q^{26} -1.00000 q^{27} -0.792704 q^{28} -3.11482 q^{29} -0.937159 q^{30} -3.57843 q^{31} -1.00000 q^{32} +4.70314 q^{33} +3.60442 q^{34} +0.742890 q^{35} +1.00000 q^{36} +1.63083 q^{37} +0.803399 q^{38} -1.00000 q^{39} +0.937159 q^{40} -7.48219 q^{41} -0.792704 q^{42} +3.98449 q^{43} -4.70314 q^{44} -0.937159 q^{45} +4.68922 q^{46} +0.579710 q^{47} -1.00000 q^{48} -6.37162 q^{49} +4.12173 q^{50} +3.60442 q^{51} +1.00000 q^{52} +5.61866 q^{53} +1.00000 q^{54} +4.40759 q^{55} +0.792704 q^{56} +0.803399 q^{57} +3.11482 q^{58} -1.93187 q^{59} +0.937159 q^{60} -14.8337 q^{61} +3.57843 q^{62} -0.792704 q^{63} +1.00000 q^{64} -0.937159 q^{65} -4.70314 q^{66} +5.77582 q^{67} -3.60442 q^{68} +4.68922 q^{69} -0.742890 q^{70} -5.96557 q^{71} -1.00000 q^{72} +0.810762 q^{73} -1.63083 q^{74} +4.12173 q^{75} -0.803399 q^{76} +3.72820 q^{77} +1.00000 q^{78} +6.43093 q^{79} -0.937159 q^{80} +1.00000 q^{81} +7.48219 q^{82} -5.41646 q^{83} +0.792704 q^{84} +3.37791 q^{85} -3.98449 q^{86} +3.11482 q^{87} +4.70314 q^{88} -18.2668 q^{89} +0.937159 q^{90} -0.792704 q^{91} -4.68922 q^{92} +3.57843 q^{93} -0.579710 q^{94} +0.752913 q^{95} +1.00000 q^{96} +10.4350 q^{97} +6.37162 q^{98} -4.70314 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.937159	−0.419110	−0.209555	−	0.977797i	$-0.567202\pi$
$5$	−0.937159	−0.419110	−0.209555	+	0.977797i	$0.567202\pi$
$6$	1.00000	0.408248
$7$	−0.792704	−0.299614	−0.149807	−	0.988715i	$-0.547865\pi$
$7$	−0.792704	−0.299614	−0.149807	+	0.988715i	$0.547865\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.937159	0.296356
$11$	−4.70314	−1.41805	−0.709025	−	0.705183i	$-0.750865\pi$
$11$	−4.70314	−1.41805	−0.709025	+	0.705183i	$0.750865\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.792704	0.211859
$15$	0.937159	0.241973
$16$	1.00000	0.250000
$17$	−3.60442	−0.874199	−0.437100	−	0.899413i	$-0.643994\pi$
$17$	−3.60442	−0.874199	−0.437100	+	0.899413i	$0.643994\pi$
$18$	−1.00000	−0.235702
$19$	−0.803399	−0.184312	−0.0921562	−	0.995745i	$-0.529376\pi$
$19$	−0.803399	−0.184312	−0.0921562	+	0.995745i	$0.529376\pi$
$20$	−0.937159	−0.209555
$21$	0.792704	0.172982
$22$	4.70314	1.00271
$23$	−4.68922	−0.977770	−0.488885	−	0.872348i	$-0.662596\pi$
$23$	−4.68922	−0.977770	−0.488885	+	0.872348i	$0.662596\pi$
$24$	1.00000	0.204124
$25$	−4.12173	−0.824347
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	−0.792704	−0.149807
$29$	−3.11482	−0.578408	−0.289204	−	0.957268i	$-0.593391\pi$
$29$	−3.11482	−0.578408	−0.289204	+	0.957268i	$0.593391\pi$
$30$	−0.937159	−0.171101
$31$	−3.57843	−0.642704	−0.321352	−	0.946960i	$-0.604137\pi$
$31$	−3.57843	−0.642704	−0.321352	+	0.946960i	$0.604137\pi$
$32$	−1.00000	−0.176777
$33$	4.70314	0.818712
$34$	3.60442	0.618152
$35$	0.742890	0.125571
$36$	1.00000	0.166667
$37$	1.63083	0.268107	0.134054	−	0.990974i	$-0.457201\pi$
$37$	1.63083	0.268107	0.134054	+	0.990974i	$0.457201\pi$
$38$	0.803399	0.130329
$39$	−1.00000	−0.160128
$40$	0.937159	0.148178
$41$	−7.48219	−1.16852	−0.584261	−	0.811566i	$-0.698616\pi$
$41$	−7.48219	−1.16852	−0.584261	+	0.811566i	$0.698616\pi$
$42$	−0.792704	−0.122317
$43$	3.98449	0.607629	0.303815	−	0.952731i	$-0.401740\pi$
$43$	3.98449	0.607629	0.303815	+	0.952731i	$0.401740\pi$
$44$	−4.70314	−0.709025
$45$	−0.937159	−0.139703
$46$	4.68922	0.691387
$47$	0.579710	0.0845593	0.0422797	−	0.999106i	$-0.486538\pi$
$47$	0.579710	0.0845593	0.0422797	+	0.999106i	$0.486538\pi$
$48$	−1.00000	−0.144338
$49$	−6.37162	−0.910231
$50$	4.12173	0.582901
$51$	3.60442	0.504719
$52$	1.00000	0.138675
$53$	5.61866	0.771782	0.385891	−	0.922544i	$-0.373894\pi$
$53$	5.61866	0.771782	0.385891	+	0.922544i	$0.373894\pi$
$54$	1.00000	0.136083
$55$	4.40759	0.594320
$56$	0.792704	0.105930
$57$	0.803399	0.106413
$58$	3.11482	0.408996
$59$	−1.93187	−0.251508	−0.125754	−	0.992061i	$-0.540135\pi$
$59$	−1.93187	−0.251508	−0.125754	+	0.992061i	$0.540135\pi$
$60$	0.937159	0.120987
$61$	−14.8337	−1.89926	−0.949628	−	0.313380i	$-0.898539\pi$
$61$	−14.8337	−1.89926	−0.949628	+	0.313380i	$0.898539\pi$
$62$	3.57843	0.454461
$63$	−0.792704	−0.0998713
$64$	1.00000	0.125000
$65$	−0.937159	−0.116240
$66$	−4.70314	−0.578917
$67$	5.77582	0.705629	0.352815	−	0.935693i	$-0.385225\pi$
$67$	5.77582	0.705629	0.352815	+	0.935693i	$0.385225\pi$
$68$	−3.60442	−0.437100
$69$	4.68922	0.564516
$70$	−0.742890	−0.0887923
$71$	−5.96557	−0.707983	−0.353991	−	0.935249i	$-0.615176\pi$
$71$	−5.96557	−0.707983	−0.353991	+	0.935249i	$0.615176\pi$
$72$	−1.00000	−0.117851
$73$	0.810762	0.0948925	0.0474462	−	0.998874i	$-0.484892\pi$
$73$	0.810762	0.0948925	0.0474462	+	0.998874i	$0.484892\pi$
$74$	−1.63083	−0.189580
$75$	4.12173	0.475937
$76$	−0.803399	−0.0921562
$77$	3.72820	0.424868
$78$	1.00000	0.113228
$79$	6.43093	0.723536	0.361768	−	0.932268i	$-0.382173\pi$
$79$	6.43093	0.723536	0.361768	+	0.932268i	$0.382173\pi$
$80$	−0.937159	−0.104778
$81$	1.00000	0.111111
$82$	7.48219	0.826270
$83$	−5.41646	−0.594534	−0.297267	−	0.954794i	$-0.596075\pi$
$83$	−5.41646	−0.594534	−0.297267	+	0.954794i	$0.596075\pi$
$84$	0.792704	0.0864911
$85$	3.37791	0.366386
$86$	−3.98449	−0.429659
$87$	3.11482	0.333944
$88$	4.70314	0.501357
$89$	−18.2668	−1.93628	−0.968141	−	0.250406i	$-0.919436\pi$
$89$	−18.2668	−1.93628	−0.968141	+	0.250406i	$0.919436\pi$
$90$	0.937159	0.0987852
$91$	−0.792704	−0.0830979
$92$	−4.68922	−0.488885
$93$	3.57843	0.371066
$94$	−0.579710	−0.0597925
$95$	0.752913	0.0772472
$96$	1.00000	0.102062
$97$	10.4350	1.05951	0.529755	−	0.848151i	$-0.322284\pi$
$97$	10.4350	1.05951	0.529755	+	0.848151i	$0.322284\pi$
$98$	6.37162	0.643631
$99$	−4.70314	−0.472684
$100$	−4.12173	−0.412173
$101$	−1.41189	−0.140488	−0.0702441	−	0.997530i	$-0.522378\pi$
$101$	−1.41189	−0.140488	−0.0702441	+	0.997530i	$0.522378\pi$
$102$	−3.60442	−0.356890
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	−0.742890	−0.0724986
$106$	−5.61866	−0.545732
$107$	0.502970	0.0486240	0.0243120	−	0.999704i	$-0.492260\pi$
$107$	0.502970	0.0486240	0.0243120	+	0.999704i	$0.492260\pi$
$108$	−1.00000	−0.0962250
$109$	17.7539	1.70052	0.850259	−	0.526365i	$-0.176445\pi$
$109$	17.7539	1.70052	0.850259	+	0.526365i	$0.176445\pi$
$110$	−4.40759	−0.420247
$111$	−1.63083	−0.154792
$112$	−0.792704	−0.0749035
$113$	8.02786	0.755198	0.377599	−	0.925969i	$-0.376750\pi$
$113$	8.02786	0.755198	0.377599	+	0.925969i	$0.376750\pi$
$114$	−0.803399	−0.0752453
$115$	4.39454	0.409793
$116$	−3.11482	−0.289204
$117$	1.00000	0.0924500
$118$	1.93187	0.177843
$119$	2.85724	0.261922
$120$	−0.937159	−0.0855505
$121$	11.1196	1.01087
$122$	14.8337	1.34298
$123$	7.48219	0.674646
$124$	−3.57843	−0.321352
$125$	8.54851	0.764602
$126$	0.792704	0.0706197
$127$	−8.03716	−0.713183	−0.356591	−	0.934260i	$-0.616061\pi$
$127$	−8.03716	−0.713183	−0.356591	+	0.934260i	$0.616061\pi$
$128$	−1.00000	−0.0883883
$129$	−3.98449	−0.350815
$130$	0.937159	0.0821943
$131$	4.13397	0.361186	0.180593	−	0.983558i	$-0.442198\pi$
$131$	4.13397	0.361186	0.180593	+	0.983558i	$0.442198\pi$
$132$	4.70314	0.409356
$133$	0.636858	0.0552226
$134$	−5.77582	−0.498955
$135$	0.937159	0.0806578
$136$	3.60442	0.309076
$137$	−17.8896	−1.52842	−0.764208	−	0.644970i	$-0.776870\pi$
$137$	−17.8896	−1.52842	−0.764208	+	0.644970i	$0.776870\pi$
$138$	−4.68922	−0.399173
$139$	−17.3454	−1.47122	−0.735608	−	0.677407i	$-0.763104\pi$
$139$	−17.3454	−1.47122	−0.735608	+	0.677407i	$0.763104\pi$
$140$	0.742890	0.0627856
$141$	−0.579710	−0.0488204
$142$	5.96557	0.500619
$143$	−4.70314	−0.393297
$144$	1.00000	0.0833333
$145$	2.91908	0.242417
$146$	−0.810762	−0.0670991
$147$	6.37162	0.525522
$148$	1.63083	0.134054
$149$	−9.59017	−0.785657	−0.392829	−	0.919612i	$-0.628503\pi$
$149$	−9.59017	−0.785657	−0.392829	+	0.919612i	$0.628503\pi$
$150$	−4.12173	−0.336538
$151$	8.93579	0.727184	0.363592	−	0.931558i	$-0.381550\pi$
$151$	8.93579	0.727184	0.363592	+	0.931558i	$0.381550\pi$
$152$	0.803399	0.0651643
$153$	−3.60442	−0.291400
$154$	−3.72820	−0.300427
$155$	3.35355	0.269364
$156$	−1.00000	−0.0800641
$157$	−18.9333	−1.51104	−0.755521	−	0.655125i	$-0.772616\pi$
$157$	−18.9333	−1.51104	−0.755521	+	0.655125i	$0.772616\pi$
$158$	−6.43093	−0.511617
$159$	−5.61866	−0.445588
$160$	0.937159	0.0740889
$161$	3.71716	0.292953
$162$	−1.00000	−0.0785674
$163$	−9.61838	−0.753370	−0.376685	−	0.926341i	$-0.622936\pi$
$163$	−9.61838	−0.753370	−0.376685	+	0.926341i	$0.622936\pi$
$164$	−7.48219	−0.584261
$165$	−4.40759	−0.343131
$166$	5.41646	0.420399
$167$	−25.2414	−1.95324	−0.976621	−	0.214970i	$-0.931035\pi$
$167$	−25.2414	−1.95324	−0.976621	+	0.214970i	$0.931035\pi$
$168$	−0.792704	−0.0611584
$169$	1.00000	0.0769231
$170$	−3.37791	−0.259074
$171$	−0.803399	−0.0614375
$172$	3.98449	0.303815
$173$	0.222644	0.0169273	0.00846364	−	0.999964i	$-0.497306\pi$
$173$	0.222644	0.0169273	0.00846364	+	0.999964i	$0.497306\pi$
$174$	−3.11482	−0.236134
$175$	3.26731	0.246986
$176$	−4.70314	−0.354513
$177$	1.93187	0.145208
$178$	18.2668	1.36916
$179$	25.3993	1.89843	0.949217	−	0.314623i	$-0.101878\pi$
$179$	25.3993	1.89843	0.949217	+	0.314623i	$0.101878\pi$
$180$	−0.937159	−0.0698517
$181$	−6.58007	−0.489093	−0.244546	−	0.969638i	$-0.578639\pi$
$181$	−6.58007	−0.489093	−0.244546	+	0.969638i	$0.578639\pi$
$182$	0.792704	0.0587591
$183$	14.8337	1.09654
$184$	4.68922	0.345694
$185$	−1.52835	−0.112366
$186$	−3.57843	−0.262383
$187$	16.9521	1.23966
$188$	0.579710	0.0422797
$189$	0.792704	0.0576607
$190$	−0.752913	−0.0546220
$191$	11.0853	0.802105	0.401052	−	0.916055i	$-0.368644\pi$
$191$	11.0853	0.802105	0.401052	+	0.916055i	$0.368644\pi$
$192$	−1.00000	−0.0721688
$193$	6.80068	0.489524	0.244762	−	0.969583i	$-0.421290\pi$
$193$	6.80068	0.489524	0.244762	+	0.969583i	$0.421290\pi$
$194$	−10.4350	−0.749186
$195$	0.937159	0.0671113
$196$	−6.37162	−0.455116
$197$	−5.08227	−0.362096	−0.181048	−	0.983474i	$-0.557949\pi$
$197$	−5.08227	−0.362096	−0.181048	+	0.983474i	$0.557949\pi$
$198$	4.70314	0.334238
$199$	15.9413	1.13005	0.565024	−	0.825074i	$-0.308867\pi$
$199$	15.9413	1.13005	0.565024	+	0.825074i	$0.308867\pi$
$200$	4.12173	0.291451
$201$	−5.77582	−0.407395
$202$	1.41189	0.0993401
$203$	2.46913	0.173299
$204$	3.60442	0.252360
$205$	7.01200	0.489740
$206$	1.00000	0.0696733
$207$	−4.68922	−0.325923
$208$	1.00000	0.0693375
$209$	3.77850	0.261364
$210$	0.742890	0.0512643
$211$	10.7284	0.738571	0.369285	−	0.929316i	$-0.379603\pi$
$211$	10.7284	0.738571	0.369285	+	0.929316i	$0.379603\pi$
$212$	5.61866	0.385891
$213$	5.96557	0.408754
$214$	−0.502970	−0.0343824
$215$	−3.73410	−0.254664
$216$	1.00000	0.0680414
$217$	2.83663	0.192563
$218$	−17.7539	−1.20245
$219$	−0.810762	−0.0547862
$220$	4.40759	0.297160
$221$	−3.60442	−0.242459
$222$	1.63083	0.109454
$223$	−19.7800	−1.32457	−0.662284	−	0.749253i	$-0.730413\pi$
$223$	−19.7800	−1.32457	−0.662284	+	0.749253i	$0.730413\pi$
$224$	0.792704	0.0529648
$225$	−4.12173	−0.274782
$226$	−8.02786	−0.534006
$227$	13.3566	0.886507	0.443254	−	0.896396i	$-0.353824\pi$
$227$	13.3566	0.886507	0.443254	+	0.896396i	$0.353824\pi$
$228$	0.803399	0.0532064
$229$	−1.87870	−0.124148	−0.0620741	−	0.998072i	$-0.519772\pi$
$229$	−1.87870	−0.124148	−0.0620741	+	0.998072i	$0.519772\pi$
$230$	−4.39454	−0.289768
$231$	−3.72820	−0.245298
$232$	3.11482	0.204498
$233$	16.0079	1.04871	0.524356	−	0.851499i	$-0.324306\pi$
$233$	16.0079	1.04871	0.524356	+	0.851499i	$0.324306\pi$
$234$	−1.00000	−0.0653720
$235$	−0.543280	−0.0354397
$236$	−1.93187	−0.125754
$237$	−6.43093	−0.417734
$238$	−2.85724	−0.185207
$239$	17.4394	1.12806	0.564031	−	0.825754i	$-0.309250\pi$
$239$	17.4394	1.12806	0.564031	+	0.825754i	$0.309250\pi$
$240$	0.937159	0.0604933
$241$	−6.56601	−0.422954	−0.211477	−	0.977383i	$-0.567827\pi$
$241$	−6.56601	−0.422954	−0.211477	+	0.977383i	$0.567827\pi$
$242$	−11.1196	−0.714792
$243$	−1.00000	−0.0641500
$244$	−14.8337	−0.949628
$245$	5.97122	0.381487
$246$	−7.48219	−0.477047
$247$	−0.803399	−0.0511191
$248$	3.57843	0.227230
$249$	5.41646	0.343254
$250$	−8.54851	−0.540655
$251$	18.8493	1.18976	0.594878	−	0.803816i	$-0.297200\pi$
$251$	18.8493	1.18976	0.594878	+	0.803816i	$0.297200\pi$
$252$	−0.792704	−0.0499357
$253$	22.0541	1.38653
$254$	8.03716	0.504296
$255$	−3.37791	−0.211533
$256$	1.00000	0.0625000
$257$	−15.0916	−0.941389	−0.470694	−	0.882296i	$-0.655997\pi$
$257$	−15.0916	−0.941389	−0.470694	+	0.882296i	$0.655997\pi$
$258$	3.98449	0.248064
$259$	−1.29277	−0.0803287
$260$	−0.937159	−0.0581201
$261$	−3.11482	−0.192803
$262$	−4.13397	−0.255397
$263$	2.51843	0.155293	0.0776465	−	0.996981i	$-0.475259\pi$
$263$	2.51843	0.155293	0.0776465	+	0.996981i	$0.475259\pi$
$264$	−4.70314	−0.289458
$265$	−5.26557	−0.323462
$266$	−0.636858	−0.0390483
$267$	18.2668	1.11791
$268$	5.77582	0.352815
$269$	−26.3178	−1.60462	−0.802312	−	0.596905i	$-0.796397\pi$
$269$	−26.3178	−1.60462	−0.802312	+	0.596905i	$0.796397\pi$
$270$	−0.937159	−0.0570337
$271$	6.11955	0.371736	0.185868	−	0.982575i	$-0.440490\pi$
$271$	6.11955	0.371736	0.185868	+	0.982575i	$0.440490\pi$
$272$	−3.60442	−0.218550
$273$	0.792704	0.0479766
$274$	17.8896	1.08075
$275$	19.3851	1.16897
$276$	4.68922	0.282258
$277$	−31.2379	−1.87690	−0.938451	−	0.345413i	$-0.887739\pi$
$277$	−31.2379	−1.87690	−0.938451	+	0.345413i	$0.887739\pi$
$278$	17.3454	1.04031
$279$	−3.57843	−0.214235
$280$	−0.742890	−0.0443961
$281$	−18.1874	−1.08497	−0.542484	−	0.840066i	$-0.682516\pi$
$281$	−18.1874	−1.08497	−0.542484	+	0.840066i	$0.682516\pi$
$282$	0.579710	0.0345212
$283$	1.52975	0.0909343	0.0454671	−	0.998966i	$-0.485522\pi$
$283$	1.52975	0.0909343	0.0454671	+	0.998966i	$0.485522\pi$
$284$	−5.96557	−0.353991
$285$	−0.752913	−0.0445987
$286$	4.70314	0.278103
$287$	5.93116	0.350105
$288$	−1.00000	−0.0589256
$289$	−4.00818	−0.235775
$290$	−2.91908	−0.171414
$291$	−10.4350	−0.611708
$292$	0.810762	0.0474462
$293$	−9.77976	−0.571340	−0.285670	−	0.958328i	$-0.592216\pi$
$293$	−9.77976	−0.571340	−0.285670	+	0.958328i	$0.592216\pi$
$294$	−6.37162	−0.371600
$295$	1.81047	0.105409
$296$	−1.63083	−0.0947902
$297$	4.70314	0.272904
$298$	9.59017	0.555543
$299$	−4.68922	−0.271184
$300$	4.12173	0.237968
$301$	−3.15852	−0.182054
$302$	−8.93579	−0.514197
$303$	1.41189	0.0811108
$304$	−0.803399	−0.0460781
$305$	13.9015	0.795997
$306$	3.60442	0.206051
$307$	−17.1789	−0.980451	−0.490225	−	0.871596i	$-0.663086\pi$
$307$	−17.1789	−0.980451	−0.490225	+	0.871596i	$0.663086\pi$
$308$	3.72820	0.212434
$309$	1.00000	0.0568880
$310$	−3.35355	−0.190469
$311$	28.7706	1.63143	0.815715	−	0.578454i	$-0.196344\pi$
$311$	28.7706	1.63143	0.815715	+	0.578454i	$0.196344\pi$
$312$	1.00000	0.0566139
$313$	26.0073	1.47002	0.735010	−	0.678057i	$-0.237178\pi$
$313$	26.0073	1.47002	0.735010	+	0.678057i	$0.237178\pi$
$314$	18.9333	1.06847
$315$	0.742890	0.0418571
$316$	6.43093	0.361768
$317$	−0.494041	−0.0277481	−0.0138741	−	0.999904i	$-0.504416\pi$
$317$	−0.494041	−0.0277481	−0.0138741	+	0.999904i	$0.504416\pi$
$318$	5.61866	0.315079
$319$	14.6494	0.820212
$320$	−0.937159	−0.0523888
$321$	−0.502970	−0.0280731
$322$	−3.71716	−0.207149
$323$	2.89579	0.161126
$324$	1.00000	0.0555556
$325$	−4.12173	−0.228633
$326$	9.61838	0.532713
$327$	−17.7539	−0.981794
$328$	7.48219	0.413135
$329$	−0.459538	−0.0253352
$330$	4.40759	0.242630
$331$	13.2952	0.730768	0.365384	−	0.930857i	$-0.380938\pi$
$331$	13.2952	0.730768	0.365384	+	0.930857i	$0.380938\pi$
$332$	−5.41646	−0.297267
$333$	1.63083	0.0893691
$334$	25.2414	1.38115
$335$	−5.41287	−0.295736
$336$	0.792704	0.0432455
$337$	−1.04274	−0.0568015	−0.0284007	−	0.999597i	$-0.509041\pi$
$337$	−1.04274	−0.0568015	−0.0284007	+	0.999597i	$0.509041\pi$
$338$	−1.00000	−0.0543928
$339$	−8.02786	−0.436014
$340$	3.37791	0.183193
$341$	16.8299	0.911388
$342$	0.803399	0.0434429
$343$	10.5997	0.572332
$344$	−3.98449	−0.214829
$345$	−4.39454	−0.236594
$346$	−0.222644	−0.0119694
$347$	25.2951	1.35791	0.678956	−	0.734179i	$-0.262433\pi$
$347$	25.2951	1.35791	0.678956	+	0.734179i	$0.262433\pi$
$348$	3.11482	0.166972
$349$	17.3267	0.927475	0.463737	−	0.885973i	$-0.346508\pi$
$349$	17.3267	0.927475	0.463737	+	0.885973i	$0.346508\pi$
$350$	−3.26731	−0.174645
$351$	−1.00000	−0.0533761
$352$	4.70314	0.250678
$353$	−16.7368	−0.890811	−0.445406	−	0.895329i	$-0.646941\pi$
$353$	−16.7368	−0.890811	−0.445406	+	0.895329i	$0.646941\pi$
$354$	−1.93187	−0.102678
$355$	5.59068	0.296723
$356$	−18.2668	−0.968141
$357$	−2.85724	−0.151221
$358$	−25.3993	−1.34240
$359$	6.34619	0.334939	0.167470	−	0.985877i	$-0.446440\pi$
$359$	6.34619	0.334939	0.167470	+	0.985877i	$0.446440\pi$
$360$	0.937159	0.0493926
$361$	−18.3545	−0.966029
$362$	6.58007	0.345841
$363$	−11.1196	−0.583625
$364$	−0.792704	−0.0415490
$365$	−0.759812	−0.0397704
$366$	−14.8337	−0.775368
$367$	30.8119	1.60837	0.804185	−	0.594379i	$-0.202602\pi$
$367$	30.8119	1.60837	0.804185	+	0.594379i	$0.202602\pi$
$368$	−4.68922	−0.244442
$369$	−7.48219	−0.389507
$370$	1.52835	0.0794551
$371$	−4.45393	−0.231237
$372$	3.57843	0.185533
$373$	−26.3688	−1.36533	−0.682663	−	0.730734i	$-0.739178\pi$
$373$	−26.3688	−1.36533	−0.682663	+	0.730734i	$0.739178\pi$
$374$	−16.9521	−0.876571
$375$	−8.54851	−0.441443
$376$	−0.579710	−0.0298962
$377$	−3.11482	−0.160421
$378$	−0.792704	−0.0407723
$379$	9.77930	0.502329	0.251165	−	0.967944i	$-0.419186\pi$
$379$	9.77930	0.502329	0.251165	+	0.967944i	$0.419186\pi$
$380$	0.752913	0.0386236
$381$	8.03716	0.411756
$382$	−11.0853	−0.567174
$383$	−32.4570	−1.65847	−0.829237	−	0.558897i	$-0.811225\pi$
$383$	−32.4570	−1.65847	−0.829237	+	0.558897i	$0.811225\pi$
$384$	1.00000	0.0510310
$385$	−3.49392	−0.178066
$386$	−6.80068	−0.346146
$387$	3.98449	0.202543
$388$	10.4350	0.529755
$389$	7.67508	0.389142	0.194571	−	0.980888i	$-0.437669\pi$
$389$	7.67508	0.389142	0.194571	+	0.980888i	$0.437669\pi$
$390$	−0.937159	−0.0474549
$391$	16.9019	0.854766
$392$	6.37162	0.321815
$393$	−4.13397	−0.208531
$394$	5.08227	0.256041
$395$	−6.02680	−0.303241
$396$	−4.70314	−0.236342
$397$	−7.64131	−0.383506	−0.191753	−	0.981443i	$-0.561417\pi$
$397$	−7.64131	−0.383506	−0.191753	+	0.981443i	$0.561417\pi$
$398$	−15.9413	−0.799065
$399$	−0.636858	−0.0318828
$400$	−4.12173	−0.206087
$401$	−12.6513	−0.631777	−0.315888	−	0.948796i	$-0.602303\pi$
$401$	−12.6513	−0.631777	−0.315888	+	0.948796i	$0.602303\pi$
$402$	5.77582	0.288072
$403$	−3.57843	−0.178254
$404$	−1.41189	−0.0702441
$405$	−0.937159	−0.0465678
$406$	−2.46913	−0.122541
$407$	−7.67004	−0.380190
$408$	−3.60442	−0.178445
$409$	24.4350	1.20823	0.604115	−	0.796897i	$-0.293527\pi$
$409$	24.4350	1.20823	0.604115	+	0.796897i	$0.293527\pi$
$410$	−7.01200	−0.346298
$411$	17.8896	0.882431
$412$	−1.00000	−0.0492665
$413$	1.53140	0.0753552
$414$	4.68922	0.230462
$415$	5.07609	0.249175
$416$	−1.00000	−0.0490290
$417$	17.3454	0.849407
$418$	−3.77850	−0.184813
$419$	−23.6809	−1.15689	−0.578444	−	0.815722i	$-0.696340\pi$
$419$	−23.6809	−1.15689	−0.578444	+	0.815722i	$0.696340\pi$
$420$	−0.742890	−0.0362493
$421$	−12.5451	−0.611411	−0.305705	−	0.952126i	$-0.598892\pi$
$421$	−12.5451	−0.611411	−0.305705	+	0.952126i	$0.598892\pi$
$422$	−10.7284	−0.522248
$423$	0.579710	0.0281864
$424$	−5.61866	−0.272866
$425$	14.8564	0.720643
$426$	−5.96557	−0.289033
$427$	11.7587	0.569043
$428$	0.502970	0.0243120
$429$	4.70314	0.227070
$430$	3.73410	0.180074
$431$	−18.7049	−0.900984	−0.450492	−	0.892780i	$-0.648751\pi$
$431$	−18.7049	−0.900984	−0.450492	+	0.892780i	$0.648751\pi$
$432$	−1.00000	−0.0481125
$433$	32.1566	1.54535	0.772673	−	0.634805i	$-0.218919\pi$
$433$	32.1566	1.54535	0.772673	+	0.634805i	$0.218919\pi$
$434$	−2.83663	−0.136163
$435$	−2.91908	−0.139959
$436$	17.7539	0.850259
$437$	3.76732	0.180215
$438$	0.810762	0.0387397
$439$	31.5854	1.50749	0.753745	−	0.657167i	$-0.228245\pi$
$439$	31.5854	1.50749	0.753745	+	0.657167i	$0.228245\pi$
$440$	−4.40759	−0.210124
$441$	−6.37162	−0.303410
$442$	3.60442	0.171445
$443$	26.8464	1.27551	0.637756	−	0.770238i	$-0.279863\pi$
$443$	26.8464	1.27551	0.637756	+	0.770238i	$0.279863\pi$
$444$	−1.63083	−0.0773959
$445$	17.1189	0.811515
$446$	19.7800	0.936611
$447$	9.59017	0.453599
$448$	−0.792704	−0.0374517
$449$	−1.58098	−0.0746108	−0.0373054	−	0.999304i	$-0.511877\pi$
$449$	−1.58098	−0.0746108	−0.0373054	+	0.999304i	$0.511877\pi$
$450$	4.12173	0.194300
$451$	35.1898	1.65702
$452$	8.02786	0.377599
$453$	−8.93579	−0.419840
$454$	−13.3566	−0.626855
$455$	0.742890	0.0348272
$456$	−0.803399	−0.0376226
$457$	−13.8693	−0.648777	−0.324389	−	0.945924i	$-0.605159\pi$
$457$	−13.8693	−0.648777	−0.324389	+	0.945924i	$0.605159\pi$
$458$	1.87870	0.0877861
$459$	3.60442	0.168240
$460$	4.39454	0.204897
$461$	2.70162	0.125827	0.0629136	−	0.998019i	$-0.479961\pi$
$461$	2.70162	0.125827	0.0629136	+	0.998019i	$0.479961\pi$
$462$	3.72820	0.173452
$463$	−30.6401	−1.42396	−0.711982	−	0.702198i	$-0.752202\pi$
$463$	−30.6401	−1.42396	−0.711982	+	0.702198i	$0.752202\pi$
$464$	−3.11482	−0.144602
$465$	−3.35355	−0.155517
$466$	−16.0079	−0.741551
$467$	−20.2536	−0.937223	−0.468612	−	0.883404i	$-0.655246\pi$
$467$	−20.2536	−0.937223	−0.468612	+	0.883404i	$0.655246\pi$
$468$	1.00000	0.0462250
$469$	−4.57852	−0.211416
$470$	0.543280	0.0250596
$471$	18.9333	0.872400
$472$	1.93187	0.0889214
$473$	−18.7396	−0.861649
$474$	6.43093	0.295382
$475$	3.31140	0.151937
$476$	2.85724	0.130961
$477$	5.61866	0.257261
$478$	−17.4394	−0.797660
$479$	20.6640	0.944162	0.472081	−	0.881555i	$-0.343503\pi$
$479$	20.6640	0.944162	0.472081	+	0.881555i	$0.343503\pi$
$480$	−0.937159	−0.0427753
$481$	1.63083	0.0743596
$482$	6.56601	0.299074
$483$	−3.71716	−0.169137
$484$	11.1196	0.505434
$485$	−9.77921	−0.444051
$486$	1.00000	0.0453609
$487$	−21.3896	−0.969257	−0.484628	−	0.874720i	$-0.661045\pi$
$487$	−21.3896	−0.969257	−0.484628	+	0.874720i	$0.661045\pi$
$488$	14.8337	0.671488
$489$	9.61838	0.434958
$490$	−5.97122	−0.269752
$491$	−42.5182	−1.91882	−0.959409	−	0.282017i	$-0.908996\pi$
$491$	−42.5182	−1.91882	−0.959409	+	0.282017i	$0.908996\pi$
$492$	7.48219	0.337323
$493$	11.2271	0.505644
$494$	0.803399	0.0361466
$495$	4.40759	0.198107
$496$	−3.57843	−0.160676
$497$	4.72893	0.212121
$498$	−5.41646	−0.242718
$499$	10.6374	0.476196	0.238098	−	0.971241i	$-0.423476\pi$
$499$	10.6374	0.476196	0.238098	+	0.971241i	$0.423476\pi$
$500$	8.54851	0.382301
$501$	25.2414	1.12770
$502$	−18.8493	−0.841285
$503$	5.29457	0.236073	0.118037	−	0.993009i	$-0.462340\pi$
$503$	5.29457	0.236073	0.118037	+	0.993009i	$0.462340\pi$
$504$	0.792704	0.0353098
$505$	1.32316	0.0588800
$506$	−22.0541	−0.980423
$507$	−1.00000	−0.0444116
$508$	−8.03716	−0.356591
$509$	26.7767	1.18686	0.593428	−	0.804887i	$-0.297774\pi$
$509$	26.7767	1.18686	0.593428	+	0.804887i	$0.297774\pi$
$510$	3.37791	0.149576
$511$	−0.642694	−0.0284311
$512$	−1.00000	−0.0441942
$513$	0.803399	0.0354710
$514$	15.0916	0.665662
$515$	0.937159	0.0412962
$516$	−3.98449	−0.175407
$517$	−2.72646	−0.119909
$518$	1.29277	0.0568009
$519$	−0.222644	−0.00977297
$520$	0.937159	0.0410971
$521$	29.6848	1.30052	0.650258	−	0.759714i	$-0.274661\pi$
$521$	29.6848	1.30052	0.650258	+	0.759714i	$0.274661\pi$
$522$	3.11482	0.136332
$523$	−1.23849	−0.0541553	−0.0270777	−	0.999633i	$-0.508620\pi$
$523$	−1.23849	−0.0541553	−0.0270777	+	0.999633i	$0.508620\pi$
$524$	4.13397	0.180593
$525$	−3.26731	−0.142597
$526$	−2.51843	−0.109809
$527$	12.8981	0.561852
$528$	4.70314	0.204678
$529$	−1.01123	−0.0439667
$530$	5.26557	0.228722
$531$	−1.93187	−0.0838359
$532$	0.636858	0.0276113
$533$	−7.48219	−0.324090
$534$	−18.2668	−0.790484
$535$	−0.471363	−0.0203788
$536$	−5.77582	−0.249478
$537$	−25.3993	−1.09606
$538$	26.3178	1.13464
$539$	29.9666	1.29075
$540$	0.937159	0.0403289
$541$	24.2953	1.04454	0.522268	−	0.852781i	$-0.325086\pi$
$541$	24.2953	1.04454	0.522268	+	0.852781i	$0.325086\pi$
$542$	−6.11955	−0.262857
$543$	6.58007	0.282378
$544$	3.60442	0.154538
$545$	−16.6383	−0.712704
$546$	−0.792704	−0.0339246
$547$	−21.1912	−0.906069	−0.453035	−	0.891493i	$-0.649659\pi$
$547$	−21.1912	−0.906069	−0.453035	+	0.891493i	$0.649659\pi$
$548$	−17.8896	−0.764208
$549$	−14.8337	−0.633085
$550$	−19.3851	−0.826583
$551$	2.50244	0.106608
$552$	−4.68922	−0.199586
$553$	−5.09782	−0.216781
$554$	31.2379	1.32717
$555$	1.52835	0.0648748
$556$	−17.3454	−0.735608
$557$	21.2459	0.900217	0.450108	−	0.892974i	$-0.351385\pi$
$557$	21.2459	0.900217	0.450108	+	0.892974i	$0.351385\pi$
$558$	3.57843	0.151487
$559$	3.98449	0.168526
$560$	0.742890	0.0313928
$561$	−16.9521	−0.715718
$562$	18.1874	0.767188
$563$	−29.5654	−1.24603	−0.623017	−	0.782209i	$-0.714093\pi$
$563$	−29.5654	−1.24603	−0.623017	+	0.782209i	$0.714093\pi$
$564$	−0.579710	−0.0244102
$565$	−7.52339	−0.316511
$566$	−1.52975	−0.0643002
$567$	−0.792704	−0.0332904
$568$	5.96557	0.250310
$569$	24.0452	1.00803	0.504013	−	0.863696i	$-0.331856\pi$
$569$	24.0452	1.00803	0.504013	+	0.863696i	$0.331856\pi$
$570$	0.752913	0.0315361
$571$	20.1068	0.841443	0.420721	−	0.907190i	$-0.361777\pi$
$571$	20.1068	0.841443	0.420721	+	0.907190i	$0.361777\pi$
$572$	−4.70314	−0.196648
$573$	−11.0853	−0.463096
$574$	−5.93116	−0.247562
$575$	19.3277	0.806021
$576$	1.00000	0.0416667
$577$	9.84511	0.409857	0.204929	−	0.978777i	$-0.434304\pi$
$577$	9.84511	0.409857	0.204929	+	0.978777i	$0.434304\pi$
$578$	4.00818	0.166718
$579$	−6.80068	−0.282627
$580$	2.91908	0.121208
$581$	4.29365	0.178131
$582$	10.4350	0.432543
$583$	−26.4253	−1.09443
$584$	−0.810762	−0.0335496
$585$	−0.937159	−0.0387468
$586$	9.77976	0.403998
$587$	−31.2144	−1.28836	−0.644179	−	0.764875i	$-0.722801\pi$
$587$	−31.2144	−1.28836	−0.644179	+	0.764875i	$0.722801\pi$
$588$	6.37162	0.262761
$589$	2.87491	0.118458
$590$	−1.81047	−0.0745358
$591$	5.08227	0.209056
$592$	1.63083	0.0670268
$593$	31.3049	1.28554	0.642769	−	0.766060i	$-0.277785\pi$
$593$	31.3049	1.28554	0.642769	+	0.766060i	$0.277785\pi$
$594$	−4.70314	−0.192972
$595$	−2.67768	−0.109774
$596$	−9.59017	−0.392829
$597$	−15.9413	−0.652434
$598$	4.68922	0.191756
$599$	8.02028	0.327700	0.163850	−	0.986485i	$-0.447609\pi$
$599$	8.02028	0.327700	0.163850	+	0.986485i	$0.447609\pi$
$600$	−4.12173	−0.168269
$601$	24.6819	1.00680	0.503398	−	0.864055i	$-0.332083\pi$
$601$	24.6819	1.00680	0.503398	+	0.864055i	$0.332083\pi$
$602$	3.15852	0.128732
$603$	5.77582	0.235210
$604$	8.93579	0.363592
$605$	−10.4208	−0.423665
$606$	−1.41189	−0.0573540
$607$	35.6610	1.44744	0.723718	−	0.690095i	$-0.242431\pi$
$607$	35.6610	1.44744	0.723718	+	0.690095i	$0.242431\pi$
$608$	0.803399	0.0325821
$609$	−2.46913	−0.100054
$610$	−13.9015	−0.562855
$611$	0.579710	0.0234525
$612$	−3.60442	−0.145700
$613$	26.1783	1.05733	0.528665	−	0.848830i	$-0.322693\pi$
$613$	26.1783	1.05733	0.528665	+	0.848830i	$0.322693\pi$
$614$	17.1789	0.693283
$615$	−7.01200	−0.282751
$616$	−3.72820	−0.150213
$617$	−11.4978	−0.462884	−0.231442	−	0.972849i	$-0.574344\pi$
$617$	−11.4978	−0.462884	−0.231442	+	0.972849i	$0.574344\pi$
$618$	−1.00000	−0.0402259
$619$	2.45533	0.0986879	0.0493440	−	0.998782i	$-0.484287\pi$
$619$	2.45533	0.0986879	0.0493440	+	0.998782i	$0.484287\pi$
$620$	3.35355	0.134682
$621$	4.68922	0.188172
$622$	−28.7706	−1.15360
$623$	14.4802	0.580137
$624$	−1.00000	−0.0400320
$625$	12.5973	0.503894
$626$	−26.0073	−1.03946
$627$	−3.77850	−0.150899
$628$	−18.9333	−0.755521
$629$	−5.87820	−0.234379
$630$	−0.742890	−0.0295974
$631$	−18.3325	−0.729807	−0.364904	−	0.931045i	$-0.618898\pi$
$631$	−18.3325	−0.729807	−0.364904	+	0.931045i	$0.618898\pi$
$632$	−6.43093	−0.255809
$633$	−10.7284	−0.426414
$634$	0.494041	0.0196209
$635$	7.53210	0.298902
$636$	−5.61866	−0.222794
$637$	−6.37162	−0.252453
$638$	−14.6494	−0.579977
$639$	−5.96557	−0.235994
$640$	0.937159	0.0370445
$641$	42.7020	1.68663	0.843313	−	0.537423i	$-0.180602\pi$
$641$	42.7020	1.68663	0.843313	+	0.537423i	$0.180602\pi$
$642$	0.502970	0.0198507
$643$	32.3813	1.27699	0.638496	−	0.769625i	$-0.279557\pi$
$643$	32.3813	1.27699	0.638496	+	0.769625i	$0.279557\pi$
$644$	3.71716	0.146477
$645$	3.73410	0.147030
$646$	−2.89579	−0.113933
$647$	−33.6185	−1.32168	−0.660839	−	0.750527i	$-0.729800\pi$
$647$	−33.6185	−1.32168	−0.660839	+	0.750527i	$0.729800\pi$
$648$	−1.00000	−0.0392837
$649$	9.08585	0.356651
$650$	4.12173	0.161668
$651$	−2.83663	−0.111176
$652$	−9.61838	−0.376685
$653$	7.01542	0.274535	0.137267	−	0.990534i	$-0.456168\pi$
$653$	7.01542	0.274535	0.137267	+	0.990534i	$0.456168\pi$
$654$	17.7539	0.694233
$655$	−3.87418	−0.151377
$656$	−7.48219	−0.292131
$657$	0.810762	0.0316308
$658$	0.459538	0.0179147
$659$	19.1360	0.745433	0.372716	−	0.927945i	$-0.378426\pi$
$659$	19.1360	0.745433	0.372716	+	0.927945i	$0.378426\pi$
$660$	−4.40759	−0.171565
$661$	−24.9601	−0.970836	−0.485418	−	0.874282i	$-0.661333\pi$
$661$	−24.9601	−0.970836	−0.485418	+	0.874282i	$0.661333\pi$
$662$	−13.2952	−0.516731
$663$	3.60442	0.139984
$664$	5.41646	0.210200
$665$	−0.596837	−0.0231443
$666$	−1.63083	−0.0631935
$667$	14.6061	0.565549
$668$	−25.2414	−0.976621
$669$	19.7800	0.764739
$670$	5.41287	0.209117
$671$	69.7648	2.69324
$672$	−0.792704	−0.0305792
$673$	30.0790	1.15946	0.579731	−	0.814808i	$-0.303158\pi$
$673$	30.0790	1.15946	0.579731	+	0.814808i	$0.303158\pi$
$674$	1.04274	0.0401647
$675$	4.12173	0.158646
$676$	1.00000	0.0384615
$677$	15.5954	0.599378	0.299689	−	0.954037i	$-0.403117\pi$
$677$	15.5954	0.599378	0.299689	+	0.954037i	$0.403117\pi$
$678$	8.02786	0.308308
$679$	−8.27183	−0.317444
$680$	−3.37791	−0.129537
$681$	−13.3566	−0.511825
$682$	−16.8299	−0.644448
$683$	−29.5061	−1.12902	−0.564509	−	0.825427i	$-0.690935\pi$
$683$	−29.5061	−1.12902	−0.564509	+	0.825427i	$0.690935\pi$
$684$	−0.803399	−0.0307187
$685$	16.7654	0.640575
$686$	−10.5997	−0.404700
$687$	1.87870	0.0716770
$688$	3.98449	0.151907
$689$	5.61866	0.214054
$690$	4.39454	0.167297
$691$	40.5561	1.54283	0.771414	−	0.636333i	$-0.219550\pi$
$691$	40.5561	1.54283	0.771414	+	0.636333i	$0.219550\pi$
$692$	0.222644	0.00846364
$693$	3.72820	0.141623
$694$	−25.2951	−0.960189
$695$	16.2554	0.616602
$696$	−3.11482	−0.118067
$697$	26.9689	1.02152
$698$	−17.3267	−0.655824
$699$	−16.0079	−0.605474
$700$	3.26731	0.123493
$701$	24.4791	0.924564	0.462282	−	0.886733i	$-0.347031\pi$
$701$	24.4791	0.924564	0.462282	+	0.886733i	$0.347031\pi$
$702$	1.00000	0.0377426
$703$	−1.31021	−0.0494155
$704$	−4.70314	−0.177256
$705$	0.543280	0.0204611
$706$	16.7368	0.629899
$707$	1.11921	0.0420922
$708$	1.93187	0.0726041
$709$	29.0564	1.09124	0.545618	−	0.838034i	$-0.316295\pi$
$709$	29.0564	1.09124	0.545618	+	0.838034i	$0.316295\pi$
$710$	−5.59068	−0.209815
$711$	6.43093	0.241179
$712$	18.2668	0.684579
$713$	16.7800	0.628417
$714$	2.85724	0.106929
$715$	4.40759	0.164835
$716$	25.3993	0.949217
$717$	−17.4394	−0.651286
$718$	−6.34619	−0.236838
$719$	38.6846	1.44269	0.721347	−	0.692574i	$-0.243523\pi$
$719$	38.6846	1.44269	0.721347	+	0.692574i	$0.243523\pi$
$720$	−0.937159	−0.0349259
$721$	0.792704	0.0295218
$722$	18.3545	0.683086
$723$	6.56601	0.244193
$724$	−6.58007	−0.244546
$725$	12.8385	0.476808
$726$	11.1196	0.412685
$727$	21.4901	0.797024	0.398512	−	0.917163i	$-0.369527\pi$
$727$	21.4901	0.797024	0.398512	+	0.917163i	$0.369527\pi$
$728$	0.792704	0.0293796
$729$	1.00000	0.0370370
$730$	0.759812	0.0281219
$731$	−14.3618	−0.531189
$732$	14.8337	0.548268
$733$	−33.9224	−1.25295	−0.626475	−	0.779441i	$-0.715503\pi$
$733$	−33.9224	−1.25295	−0.626475	+	0.779441i	$0.715503\pi$
$734$	−30.8119	−1.13729
$735$	−5.97122	−0.220252
$736$	4.68922	0.172847
$737$	−27.1645	−1.00062
$738$	7.48219	0.275423
$739$	3.01425	0.110881	0.0554406	−	0.998462i	$-0.482344\pi$
$739$	3.01425	0.110881	0.0554406	+	0.998462i	$0.482344\pi$
$740$	−1.52835	−0.0561832
$741$	0.803399	0.0295136
$742$	4.45393	0.163509
$743$	−6.72363	−0.246666	−0.123333	−	0.992365i	$-0.539358\pi$
$743$	−6.72363	−0.246666	−0.123333	+	0.992365i	$0.539358\pi$
$744$	−3.57843	−0.131191
$745$	8.98751	0.329277
$746$	26.3688	0.965431
$747$	−5.41646	−0.198178
$748$	16.9521	0.619830
$749$	−0.398707	−0.0145684
$750$	8.54851	0.312148
$751$	45.2545	1.65136	0.825679	−	0.564140i	$-0.190792\pi$
$751$	45.2545	1.65136	0.825679	+	0.564140i	$0.190792\pi$
$752$	0.579710	0.0211398
$753$	−18.8493	−0.686906
$754$	3.11482	0.113435
$755$	−8.37425	−0.304770
$756$	0.792704	0.0288304
$757$	8.39311	0.305053	0.152526	−	0.988299i	$-0.451259\pi$
$757$	8.39311	0.305053	0.152526	+	0.988299i	$0.451259\pi$
$758$	−9.77930	−0.355200
$759$	−22.0541	−0.800512
$760$	−0.752913	−0.0273110
$761$	14.2758	0.517496	0.258748	−	0.965945i	$-0.416690\pi$
$761$	14.2758	0.517496	0.258748	+	0.965945i	$0.416690\pi$
$762$	−8.03716	−0.291156
$763$	−14.0736	−0.509499
$764$	11.0853	0.401052
$765$	3.37791	0.122129
$766$	32.4570	1.17272
$767$	−1.93187	−0.0697557
$768$	−1.00000	−0.0360844
$769$	−29.7150	−1.07155	−0.535776	−	0.844360i	$-0.679981\pi$
$769$	−29.7150	−1.07155	−0.535776	+	0.844360i	$0.679981\pi$
$770$	3.49392	0.125912
$771$	15.0916	0.543511
$772$	6.80068	0.244762
$773$	−32.4335	−1.16655	−0.583277	−	0.812274i	$-0.698230\pi$
$773$	−32.4335	−1.16655	−0.583277	+	0.812274i	$0.698230\pi$
$774$	−3.98449	−0.143220
$775$	14.7493	0.529811
$776$	−10.4350	−0.374593
$777$	1.29277	0.0463778
$778$	−7.67508	−0.275165
$779$	6.01119	0.215373
$780$	0.937159	0.0335557
$781$	28.0569	1.00396
$782$	−16.9019	−0.604411
$783$	3.11482	0.111315
$784$	−6.37162	−0.227558
$785$	17.7435	0.633293
$786$	4.13397	0.147454
$787$	7.44005	0.265209	0.132605	−	0.991169i	$-0.457666\pi$
$787$	7.44005	0.265209	0.132605	+	0.991169i	$0.457666\pi$
$788$	−5.08227	−0.181048
$789$	−2.51843	−0.0896584
$790$	6.02680	0.214424
$791$	−6.36372	−0.226268
$792$	4.70314	0.167119
$793$	−14.8337	−0.526759
$794$	7.64131	0.271180
$795$	5.26557	0.186751
$796$	15.9413	0.565024
$797$	23.0552	0.816658	0.408329	−	0.912835i	$-0.366112\pi$
$797$	23.0552	0.816658	0.408329	+	0.912835i	$0.366112\pi$
$798$	0.636858	0.0225445
$799$	−2.08951	−0.0739217
$800$	4.12173	0.145725
$801$	−18.2668	−0.645427
$802$	12.6513	0.446734
$803$	−3.81313	−0.134562
$804$	−5.77582	−0.203698
$805$	−3.48357	−0.122780
$806$	3.57843	0.126045
$807$	26.3178	0.926430
$808$	1.41189	0.0496700
$809$	−24.4161	−0.858423	−0.429211	−	0.903204i	$-0.641208\pi$
$809$	−24.4161	−0.858423	−0.429211	+	0.903204i	$0.641208\pi$
$810$	0.937159	0.0329284
$811$	1.52704	0.0536217	0.0268108	−	0.999641i	$-0.491465\pi$
$811$	1.52704	0.0536217	0.0268108	+	0.999641i	$0.491465\pi$
$812$	2.46913	0.0866495
$813$	−6.11955	−0.214622
$814$	7.67004	0.268835
$815$	9.01395	0.315745
$816$	3.60442	0.126180
$817$	−3.20114	−0.111994
$818$	−24.4350	−0.854348
$819$	−0.792704	−0.0276993
$820$	7.01200	0.244870
$821$	8.57849	0.299392	0.149696	−	0.988732i	$-0.452171\pi$
$821$	8.57849	0.299392	0.149696	+	0.988732i	$0.452171\pi$
$822$	−17.8896	−0.623973
$823$	−2.61365	−0.0911059	−0.0455530	−	0.998962i	$-0.514505\pi$
$823$	−2.61365	−0.0911059	−0.0455530	+	0.998962i	$0.514505\pi$
$824$	1.00000	0.0348367
$825$	−19.3851	−0.674903
$826$	−1.53140	−0.0532842
$827$	−17.7252	−0.616366	−0.308183	−	0.951327i	$-0.599721\pi$
$827$	−17.7252	−0.616366	−0.308183	+	0.951327i	$0.599721\pi$
$828$	−4.68922	−0.162962
$829$	45.1815	1.56922	0.784610	−	0.619990i	$-0.212863\pi$
$829$	45.1815	1.56922	0.784610	+	0.619990i	$0.212863\pi$
$830$	−5.07609	−0.176194
$831$	31.2379	1.08363
$832$	1.00000	0.0346688
$833$	22.9660	0.795724
$834$	−17.3454	−0.600622
$835$	23.6552	0.818623
$836$	3.77850	0.130682
$837$	3.57843	0.123689
$838$	23.6809	0.818043
$839$	−52.4895	−1.81214	−0.906069	−	0.423129i	$-0.860932\pi$
$839$	−52.4895	−1.81214	−0.906069	+	0.423129i	$0.860932\pi$
$840$	0.742890	0.0256321
$841$	−19.2979	−0.665445
$842$	12.5451	0.432333
$843$	18.1874	0.626406
$844$	10.7284	0.369285
$845$	−0.937159	−0.0322392
$846$	−0.579710	−0.0199308
$847$	−8.81451	−0.302870
$848$	5.61866	0.192945
$849$	−1.52975	−0.0525009
$850$	−14.8564	−0.509572
$851$	−7.64733	−0.262147
$852$	5.96557	0.204377
$853$	−41.2017	−1.41072	−0.705359	−	0.708850i	$-0.749214\pi$
$853$	−41.2017	−1.41072	−0.705359	+	0.708850i	$0.749214\pi$
$854$	−11.7587	−0.402374
$855$	0.752913	0.0257491
$856$	−0.502970	−0.0171912
$857$	−35.6191	−1.21673	−0.608363	−	0.793659i	$-0.708173\pi$
$857$	−35.6191	−1.21673	−0.608363	+	0.793659i	$0.708173\pi$
$858$	−4.70314	−0.160563
$859$	7.62712	0.260234	0.130117	−	0.991499i	$-0.458465\pi$
$859$	7.62712	0.260234	0.130117	+	0.991499i	$0.458465\pi$
$860$	−3.73410	−0.127332
$861$	−5.93116	−0.202133
$862$	18.7049	0.637092
$863$	−4.07478	−0.138707	−0.0693536	−	0.997592i	$-0.522094\pi$
$863$	−4.07478	−0.138707	−0.0693536	+	0.997592i	$0.522094\pi$
$864$	1.00000	0.0340207
$865$	−0.208653	−0.00709440
$866$	−32.1566	−1.09272
$867$	4.00818	0.136125
$868$	2.83663	0.0962816
$869$	−30.2456	−1.02601
$870$	2.91908	0.0989661
$871$	5.77582	0.195706
$872$	−17.7539	−0.601224
$873$	10.4350	0.353170
$874$	−3.76732	−0.127431
$875$	−6.77644	−0.229085
$876$	−0.810762	−0.0273931
$877$	−1.87904	−0.0634506	−0.0317253	−	0.999497i	$-0.510100\pi$
$877$	−1.87904	−0.0634506	−0.0317253	+	0.999497i	$0.510100\pi$
$878$	−31.5854	−1.06596
$879$	9.77976	0.329863
$880$	4.40759	0.148580
$881$	−14.0026	−0.471759	−0.235879	−	0.971782i	$-0.575797\pi$
$881$	−14.0026	−0.471759	−0.235879	+	0.971782i	$0.575797\pi$
$882$	6.37162	0.214544
$883$	−17.2474	−0.580422	−0.290211	−	0.956963i	$-0.593726\pi$
$883$	−17.2474	−0.580422	−0.290211	+	0.956963i	$0.593726\pi$
$884$	−3.60442	−0.121230
$885$	−1.81047	−0.0608582
$886$	−26.8464	−0.901923
$887$	1.85975	0.0624443	0.0312222	−	0.999512i	$-0.490060\pi$
$887$	1.85975	0.0624443	0.0312222	+	0.999512i	$0.490060\pi$
$888$	1.63083	0.0547272
$889$	6.37109	0.213679
$890$	−17.1189	−0.573828
$891$	−4.70314	−0.157561
$892$	−19.7800	−0.662284
$893$	−0.465738	−0.0155853
$894$	−9.59017	−0.320743
$895$	−23.8032	−0.795653
$896$	0.792704	0.0264824
$897$	4.68922	0.156568
$898$	1.58098	0.0527578
$899$	11.1462	0.371745
$900$	−4.12173	−0.137391
$901$	−20.2520	−0.674691
$902$	−35.1898	−1.17169
$903$	3.15852	0.105109
$904$	−8.02786	−0.267003
$905$	6.16657	0.204984
$906$	8.93579	0.296872
$907$	31.3348	1.04046	0.520228	−	0.854028i	$-0.325847\pi$
$907$	31.3348	1.04046	0.520228	+	0.854028i	$0.325847\pi$
$908$	13.3566	0.443254
$909$	−1.41189	−0.0468294
$910$	−0.742890	−0.0246265
$911$	−5.22797	−0.173210	−0.0866051	−	0.996243i	$-0.527602\pi$
$911$	−5.22797	−0.173210	−0.0866051	+	0.996243i	$0.527602\pi$
$912$	0.803399	0.0266032
$913$	25.4744	0.843080
$914$	13.8693	0.458755
$915$	−13.9015	−0.459569
$916$	−1.87870	−0.0620741
$917$	−3.27701	−0.108216
$918$	−3.60442	−0.118963
$919$	39.1606	1.29179	0.645894	−	0.763427i	$-0.276485\pi$
$919$	39.1606	1.29179	0.645894	+	0.763427i	$0.276485\pi$
$920$	−4.39454	−0.144884
$921$	17.1789	0.566064
$922$	−2.70162	−0.0889732
$923$	−5.96557	−0.196359
$924$	−3.72820	−0.122649
$925$	−6.72186	−0.221013
$926$	30.6401	1.00689
$927$	−1.00000	−0.0328443
$928$	3.11482	0.102249
$929$	27.1936	0.892194	0.446097	−	0.894985i	$-0.352814\pi$
$929$	27.1936	0.892194	0.446097	+	0.894985i	$0.352814\pi$
$930$	3.35355	0.109967
$931$	5.11896	0.167767
$932$	16.0079	0.524356
$933$	−28.7706	−0.941907
$934$	20.2536	0.662717
$935$	−15.8868	−0.519554
$936$	−1.00000	−0.0326860
$937$	30.3989	0.993089	0.496545	−	0.868011i	$-0.334602\pi$
$937$	30.3989	0.993089	0.496545	+	0.868011i	$0.334602\pi$
$938$	4.57852	0.149494
$939$	−26.0073	−0.848716
$940$	−0.543280	−0.0177198
$941$	−38.1436	−1.24345	−0.621723	−	0.783237i	$-0.713567\pi$
$941$	−38.1436	−1.24345	−0.621723	+	0.783237i	$0.713567\pi$
$942$	−18.9333	−0.616880
$943$	35.0856	1.14255
$944$	−1.93187	−0.0628770
$945$	−0.742890	−0.0241662
$946$	18.7396	0.609278
$947$	−18.8645	−0.613014	−0.306507	−	0.951868i	$-0.599160\pi$
$947$	−18.8645	−0.613014	−0.306507	+	0.951868i	$0.599160\pi$
$948$	−6.43093	−0.208867
$949$	0.810762	0.0263184
$950$	−3.31140	−0.107436
$951$	0.494041	0.0160204
$952$	−2.85724	−0.0926035
$953$	−22.5227	−0.729582	−0.364791	−	0.931089i	$-0.618860\pi$
$953$	−22.5227	−0.729582	−0.364791	+	0.931089i	$0.618860\pi$
$954$	−5.61866	−0.181911
$955$	−10.3887	−0.336170
$956$	17.4394	0.564031
$957$	−14.6494	−0.473549
$958$	−20.6640	−0.667623
$959$	14.1812	0.457935
$960$	0.937159	0.0302467
$961$	−18.1949	−0.586931
$962$	−1.63083	−0.0525801
$963$	0.502970	0.0162080
$964$	−6.56601	−0.211477
$965$	−6.37332	−0.205164
$966$	3.71716	0.119598
$967$	−38.8121	−1.24811	−0.624057	−	0.781379i	$-0.714517\pi$
$967$	−38.8121	−1.24811	−0.624057	+	0.781379i	$0.714517\pi$
$968$	−11.1196	−0.357396
$969$	−2.89579	−0.0930261
$970$	9.77921	0.313992
$971$	30.7021	0.985276	0.492638	−	0.870234i	$-0.336033\pi$
$971$	30.7021	0.985276	0.492638	+	0.870234i	$0.336033\pi$
$972$	−1.00000	−0.0320750
$973$	13.7498	0.440797
$974$	21.3896	0.685368
$975$	4.12173	0.132001
$976$	−14.8337	−0.474814
$977$	−28.5714	−0.914081	−0.457040	−	0.889446i	$-0.651091\pi$
$977$	−28.5714	−0.914081	−0.457040	+	0.889446i	$0.651091\pi$
$978$	−9.61838	−0.307562
$979$	85.9116	2.74575
$980$	5.97122	0.190744
$981$	17.7539	0.566839
$982$	42.5182	1.35681
$983$	32.6252	1.04058	0.520291	−	0.853989i	$-0.325823\pi$
$983$	32.6252	1.04058	0.520291	+	0.853989i	$0.325823\pi$
$984$	−7.48219	−0.238524
$985$	4.76289	0.151758
$986$	−11.2271	−0.357544
$987$	0.459538	0.0146273
$988$	−0.803399	−0.0255595
$989$	−18.6842	−0.594121
$990$	−4.40759	−0.140082
$991$	−13.3840	−0.425156	−0.212578	−	0.977144i	$-0.568186\pi$
$991$	−13.3840	−0.425156	−0.212578	+	0.977144i	$0.568186\pi$
$992$	3.57843	0.113615
$993$	−13.2952	−0.421909
$994$	−4.72893	−0.149993
$995$	−14.9395	−0.473615
$996$	5.41646	0.171627
$997$	−47.8225	−1.51455	−0.757276	−	0.653094i	$-0.773470\pi$
$997$	−47.8225	−1.51455	−0.757276	+	0.653094i	$0.773470\pi$
$998$	−10.6374	−0.336722
$999$	−1.63083	−0.0515973

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.z.1.6	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.z.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.937159 q^{5} +1.00000 q^{6} -0.792704 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.937159 q^{5} +1.00000 q^{6} -0.792704 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.937159 q^{10} -4.70314 q^{11} -1.00000 q^{12} +1.00000 q^{13} +0.792704 q^{14} +0.937159 q^{15} +1.00000 q^{16} -3.60442 q^{17} -1.00000 q^{18} -0.803399 q^{19} -0.937159 q^{20} +0.792704 q^{21} +4.70314 q^{22} -4.68922 q^{23} +1.00000 q^{24} -4.12173 q^{25} -1.00000 q^{26} -1.00000 q^{27} -0.792704 q^{28} -3.11482 q^{29} -0.937159 q^{30} -3.57843 q^{31} -1.00000 q^{32} +4.70314 q^{33} +3.60442 q^{34} +0.742890 q^{35} +1.00000 q^{36} +1.63083 q^{37} +0.803399 q^{38} -1.00000 q^{39} +0.937159 q^{40} -7.48219 q^{41} -0.792704 q^{42} +3.98449 q^{43} -4.70314 q^{44} -0.937159 q^{45} +4.68922 q^{46} +0.579710 q^{47} -1.00000 q^{48} -6.37162 q^{49} +4.12173 q^{50} +3.60442 q^{51} +1.00000 q^{52} +5.61866 q^{53} +1.00000 q^{54} +4.40759 q^{55} +0.792704 q^{56} +0.803399 q^{57} +3.11482 q^{58} -1.93187 q^{59} +0.937159 q^{60} -14.8337 q^{61} +3.57843 q^{62} -0.792704 q^{63} +1.00000 q^{64} -0.937159 q^{65} -4.70314 q^{66} +5.77582 q^{67} -3.60442 q^{68} +4.68922 q^{69} -0.742890 q^{70} -5.96557 q^{71} -1.00000 q^{72} +0.810762 q^{73} -1.63083 q^{74} +4.12173 q^{75} -0.803399 q^{76} +3.72820 q^{77} +1.00000 q^{78} +6.43093 q^{79} -0.937159 q^{80} +1.00000 q^{81} +7.48219 q^{82} -5.41646 q^{83} +0.792704 q^{84} +3.37791 q^{85} -3.98449 q^{86} +3.11482 q^{87} +4.70314 q^{88} -18.2668 q^{89} +0.937159 q^{90} -0.792704 q^{91} -4.68922 q^{92} +3.57843 q^{93} -0.579710 q^{94} +0.752913 q^{95} +1.00000 q^{96} +10.4350 q^{97} +6.37162 q^{98} -4.70314 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 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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