LMFDB - Embedded newform 8034.2.a.bd.1.10

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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 36 x^{14} + 196 x^{13} + 498 x^{12} - 3101 x^{11} - 3150 x^{10} + 25368 x^{9} + \cdots - 66432 $ x^16 - 5x^15 - 36x^14 + 196x^13 + 498x^12 - 3101x^11 - 3150x^10 + 25368x^9 + 6763x^8 - 113788x^7 + 19731x^6 + 270913x^5 - 122680x^4 - 296326x^3 + 185524x^2 + 94528*x - 66432
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$1.64745$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.64745 q^{5} +1.00000 q^{6} +3.14335 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.64745 q^{5} +1.00000 q^{6} +3.14335 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.64745 q^{10} -0.445224 q^{11} +1.00000 q^{12} -1.00000 q^{13} +3.14335 q^{14} +1.64745 q^{15} +1.00000 q^{16} +2.45663 q^{17} +1.00000 q^{18} +5.11019 q^{19} +1.64745 q^{20} +3.14335 q^{21} -0.445224 q^{22} +5.71435 q^{23} +1.00000 q^{24} -2.28591 q^{25} -1.00000 q^{26} +1.00000 q^{27} +3.14335 q^{28} -0.516530 q^{29} +1.64745 q^{30} +4.19628 q^{31} +1.00000 q^{32} -0.445224 q^{33} +2.45663 q^{34} +5.17850 q^{35} +1.00000 q^{36} -4.57485 q^{37} +5.11019 q^{38} -1.00000 q^{39} +1.64745 q^{40} -8.86335 q^{41} +3.14335 q^{42} -0.324343 q^{43} -0.445224 q^{44} +1.64745 q^{45} +5.71435 q^{46} -1.57233 q^{47} +1.00000 q^{48} +2.88064 q^{49} -2.28591 q^{50} +2.45663 q^{51} -1.00000 q^{52} +3.81066 q^{53} +1.00000 q^{54} -0.733484 q^{55} +3.14335 q^{56} +5.11019 q^{57} -0.516530 q^{58} +3.45384 q^{59} +1.64745 q^{60} -0.127249 q^{61} +4.19628 q^{62} +3.14335 q^{63} +1.00000 q^{64} -1.64745 q^{65} -0.445224 q^{66} +8.34136 q^{67} +2.45663 q^{68} +5.71435 q^{69} +5.17850 q^{70} -13.1492 q^{71} +1.00000 q^{72} -10.4075 q^{73} -4.57485 q^{74} -2.28591 q^{75} +5.11019 q^{76} -1.39950 q^{77} -1.00000 q^{78} -12.2671 q^{79} +1.64745 q^{80} +1.00000 q^{81} -8.86335 q^{82} +8.54090 q^{83} +3.14335 q^{84} +4.04717 q^{85} -0.324343 q^{86} -0.516530 q^{87} -0.445224 q^{88} +13.2135 q^{89} +1.64745 q^{90} -3.14335 q^{91} +5.71435 q^{92} +4.19628 q^{93} -1.57233 q^{94} +8.41878 q^{95} +1.00000 q^{96} +4.87022 q^{97} +2.88064 q^{98} -0.445224 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9} + 5 q^{10} + 18 q^{11} + 16 q^{12} - 16 q^{13} + 4 q^{14} + 5 q^{15} + 16 q^{16} + 17 q^{17} + 16 q^{18} + 8 q^{19} + 5 q^{20} + 4 q^{21} + 18 q^{22} + 9 q^{23} + 16 q^{24} + 17 q^{25} - 16 q^{26} + 16 q^{27} + 4 q^{28} + 14 q^{29} + 5 q^{30} + 12 q^{31} + 16 q^{32} + 18 q^{33} + 17 q^{34} + 16 q^{35} + 16 q^{36} + 31 q^{37} + 8 q^{38} - 16 q^{39} + 5 q^{40} + 29 q^{41} + 4 q^{42} + 30 q^{43} + 18 q^{44} + 5 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 36 q^{49} + 17 q^{50} + 17 q^{51} - 16 q^{52} + 12 q^{53} + 16 q^{54} + 30 q^{55} + 4 q^{56} + 8 q^{57} + 14 q^{58} + 38 q^{59} + 5 q^{60} + 12 q^{62} + 4 q^{63} + 16 q^{64} - 5 q^{65} + 18 q^{66} + 28 q^{67} + 17 q^{68} + 9 q^{69} + 16 q^{70} + 32 q^{71} + 16 q^{72} + 20 q^{73} + 31 q^{74} + 17 q^{75} + 8 q^{76} + 26 q^{77} - 16 q^{78} + 13 q^{79} + 5 q^{80} + 16 q^{81} + 29 q^{82} + 39 q^{83} + 4 q^{84} + 31 q^{85} + 30 q^{86} + 14 q^{87} + 18 q^{88} + 9 q^{89} + 5 q^{90} - 4 q^{91} + 9 q^{92} + 12 q^{93} - q^{94} - 20 q^{95} + 16 q^{96} + 35 q^{97} + 36 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9 + 5 * q^10 + 18 * q^11 + 16 * q^12 - 16 * q^13 + 4 * q^14 + 5 * q^15 + 16 * q^16 + 17 * q^17 + 16 * q^18 + 8 * q^19 + 5 * q^20 + 4 * q^21 + 18 * q^22 + 9 * q^23 + 16 * q^24 + 17 * q^25 - 16 * q^26 + 16 * q^27 + 4 * q^28 + 14 * q^29 + 5 * q^30 + 12 * q^31 + 16 * q^32 + 18 * q^33 + 17 * q^34 + 16 * q^35 + 16 * q^36 + 31 * q^37 + 8 * q^38 - 16 * q^39 + 5 * q^40 + 29 * q^41 + 4 * q^42 + 30 * q^43 + 18 * q^44 + 5 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 36 * q^49 + 17 * q^50 + 17 * q^51 - 16 * q^52 + 12 * q^53 + 16 * q^54 + 30 * q^55 + 4 * q^56 + 8 * q^57 + 14 * q^58 + 38 * q^59 + 5 * q^60 + 12 * q^62 + 4 * q^63 + 16 * q^64 - 5 * q^65 + 18 * q^66 + 28 * q^67 + 17 * q^68 + 9 * q^69 + 16 * q^70 + 32 * q^71 + 16 * q^72 + 20 * q^73 + 31 * q^74 + 17 * q^75 + 8 * q^76 + 26 * q^77 - 16 * q^78 + 13 * q^79 + 5 * q^80 + 16 * q^81 + 29 * q^82 + 39 * q^83 + 4 * q^84 + 31 * q^85 + 30 * q^86 + 14 * q^87 + 18 * q^88 + 9 * q^89 + 5 * q^90 - 4 * q^91 + 9 * q^92 + 12 * q^93 - q^94 - 20 * q^95 + 16 * q^96 + 35 * q^97 + 36 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.64745	0.736761	0.368381	−	0.929675i	$-0.379912\pi$
$5$	1.64745	0.736761	0.368381	+	0.929675i	$0.379912\pi$
$6$	1.00000	0.408248
$7$	3.14335	1.18807	0.594037	−	0.804438i	$-0.297533\pi$
$7$	3.14335	1.18807	0.594037	+	0.804438i	$0.297533\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.64745	0.520969
$11$	−0.445224	−0.134240	−0.0671201	−	0.997745i	$-0.521381\pi$
$11$	−0.445224	−0.134240	−0.0671201	+	0.997745i	$0.521381\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	3.14335	0.840095
$15$	1.64745	0.425369
$16$	1.00000	0.250000
$17$	2.45663	0.595819	0.297910	−	0.954594i	$-0.403711\pi$
$17$	2.45663	0.595819	0.297910	+	0.954594i	$0.403711\pi$
$18$	1.00000	0.235702
$19$	5.11019	1.17236	0.586179	−	0.810181i	$-0.300631\pi$
$19$	5.11019	1.17236	0.586179	+	0.810181i	$0.300631\pi$
$20$	1.64745	0.368381
$21$	3.14335	0.685935
$22$	−0.445224	−0.0949221
$23$	5.71435	1.19152	0.595762	−	0.803161i	$-0.296850\pi$
$23$	5.71435	1.19152	0.595762	+	0.803161i	$0.296850\pi$
$24$	1.00000	0.204124
$25$	−2.28591	−0.457183
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	3.14335	0.594037
$29$	−0.516530	−0.0959172	−0.0479586	−	0.998849i	$-0.515272\pi$
$29$	−0.516530	−0.0959172	−0.0479586	+	0.998849i	$0.515272\pi$
$30$	1.64745	0.300782
$31$	4.19628	0.753674	0.376837	−	0.926280i	$-0.377012\pi$
$31$	4.19628	0.753674	0.376837	+	0.926280i	$0.377012\pi$
$32$	1.00000	0.176777
$33$	−0.445224	−0.0775036
$34$	2.45663	0.421308
$35$	5.17850	0.875327
$36$	1.00000	0.166667
$37$	−4.57485	−0.752100	−0.376050	−	0.926599i	$-0.622718\pi$
$37$	−4.57485	−0.752100	−0.376050	+	0.926599i	$0.622718\pi$
$38$	5.11019	0.828983
$39$	−1.00000	−0.160128
$40$	1.64745	0.260484
$41$	−8.86335	−1.38422	−0.692111	−	0.721791i	$-0.743319\pi$
$41$	−8.86335	−1.38422	−0.692111	+	0.721791i	$0.743319\pi$
$42$	3.14335	0.485029
$43$	−0.324343	−0.0494619	−0.0247310	−	0.999694i	$-0.507873\pi$
$43$	−0.324343	−0.0494619	−0.0247310	+	0.999694i	$0.507873\pi$
$44$	−0.445224	−0.0671201
$45$	1.64745	0.245587
$46$	5.71435	0.842535
$47$	−1.57233	−0.229348	−0.114674	−	0.993403i	$-0.536582\pi$
$47$	−1.57233	−0.229348	−0.114674	+	0.993403i	$0.536582\pi$
$48$	1.00000	0.144338
$49$	2.88064	0.411520
$50$	−2.28591	−0.323277
$51$	2.45663	0.343997
$52$	−1.00000	−0.138675
$53$	3.81066	0.523434	0.261717	−	0.965145i	$-0.415711\pi$
$53$	3.81066	0.523434	0.261717	+	0.965145i	$0.415711\pi$
$54$	1.00000	0.136083
$55$	−0.733484	−0.0989029
$56$	3.14335	0.420048
$57$	5.11019	0.676862
$58$	−0.516530	−0.0678237
$59$	3.45384	0.449651	0.224826	−	0.974399i	$-0.427819\pi$
$59$	3.45384	0.449651	0.224826	+	0.974399i	$0.427819\pi$
$60$	1.64745	0.212685
$61$	−0.127249	−0.0162925	−0.00814626	−	0.999967i	$-0.502593\pi$
$61$	−0.127249	−0.0162925	−0.00814626	+	0.999967i	$0.502593\pi$
$62$	4.19628	0.532928
$63$	3.14335	0.396025
$64$	1.00000	0.125000
$65$	−1.64745	−0.204341
$66$	−0.445224	−0.0548033
$67$	8.34136	1.01906	0.509530	−	0.860453i	$-0.329819\pi$
$67$	8.34136	1.01906	0.509530	+	0.860453i	$0.329819\pi$
$68$	2.45663	0.297910
$69$	5.71435	0.687927
$70$	5.17850	0.618950
$71$	−13.1492	−1.56052	−0.780262	−	0.625453i	$-0.784914\pi$
$71$	−13.1492	−1.56052	−0.780262	+	0.625453i	$0.784914\pi$
$72$	1.00000	0.117851
$73$	−10.4075	−1.21811	−0.609055	−	0.793128i	$-0.708451\pi$
$73$	−10.4075	−1.21811	−0.609055	+	0.793128i	$0.708451\pi$
$74$	−4.57485	−0.531815
$75$	−2.28591	−0.263955
$76$	5.11019	0.586179
$77$	−1.39950	−0.159487
$78$	−1.00000	−0.113228
$79$	−12.2671	−1.38016	−0.690079	−	0.723734i	$-0.742424\pi$
$79$	−12.2671	−1.38016	−0.690079	+	0.723734i	$0.742424\pi$
$80$	1.64745	0.184190
$81$	1.00000	0.111111
$82$	−8.86335	−0.978793
$83$	8.54090	0.937486	0.468743	−	0.883335i	$-0.344707\pi$
$83$	8.54090	0.937486	0.468743	+	0.883335i	$0.344707\pi$
$84$	3.14335	0.342967
$85$	4.04717	0.438977
$86$	−0.324343	−0.0349749
$87$	−0.516530	−0.0553778
$88$	−0.445224	−0.0474611
$89$	13.2135	1.40063	0.700314	−	0.713834i	$-0.253043\pi$
$89$	13.2135	1.40063	0.700314	+	0.713834i	$0.253043\pi$
$90$	1.64745	0.173656
$91$	−3.14335	−0.329513
$92$	5.71435	0.595762
$93$	4.19628	0.435134
$94$	−1.57233	−0.162173
$95$	8.41878	0.863748
$96$	1.00000	0.102062
$97$	4.87022	0.494496	0.247248	−	0.968952i	$-0.420474\pi$
$97$	4.87022	0.494496	0.247248	+	0.968952i	$0.420474\pi$
$98$	2.88064	0.290989
$99$	−0.445224	−0.0447467
$100$	−2.28591	−0.228591
$101$	−11.3727	−1.13162	−0.565811	−	0.824535i	$-0.691437\pi$
$101$	−11.3727	−1.13162	−0.565811	+	0.824535i	$0.691437\pi$
$102$	2.45663	0.243242
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	5.17850	0.505370
$106$	3.81066	0.370124
$107$	−8.95681	−0.865888	−0.432944	−	0.901421i	$-0.642525\pi$
$107$	−8.95681	−0.865888	−0.432944	+	0.901421i	$0.642525\pi$
$108$	1.00000	0.0962250
$109$	0.559598	0.0535998	0.0267999	−	0.999641i	$-0.491468\pi$
$109$	0.559598	0.0535998	0.0267999	+	0.999641i	$0.491468\pi$
$110$	−0.733484	−0.0699349
$111$	−4.57485	−0.434225
$112$	3.14335	0.297019
$113$	−0.00733242	−0.000689776 0	−0.000344888	−	1.00000i	$-0.500110\pi$
$113$	−0.00733242	−0.000689776 0	−0.000344888		1.00000i	$0.500110\pi$
$114$	5.11019	0.478613
$115$	9.41410	0.877869
$116$	−0.516530	−0.0479586
$117$	−1.00000	−0.0924500
$118$	3.45384	0.317952
$119$	7.72203	0.707878
$120$	1.64745	0.150391
$121$	−10.8018	−0.981980
$122$	−0.127249	−0.0115205
$123$	−8.86335	−0.799181
$124$	4.19628	0.376837
$125$	−12.0032	−1.07360
$126$	3.14335	0.280032
$127$	3.33349	0.295800	0.147900	−	0.989002i	$-0.452749\pi$
$127$	3.33349	0.295800	0.147900	+	0.989002i	$0.452749\pi$
$128$	1.00000	0.0883883
$129$	−0.324343	−0.0285569
$130$	−1.64745	−0.144491
$131$	17.0779	1.49210	0.746051	−	0.665889i	$-0.231948\pi$
$131$	17.0779	1.49210	0.746051	+	0.665889i	$0.231948\pi$
$132$	−0.445224	−0.0387518
$133$	16.0631	1.39285
$134$	8.34136	0.720584
$135$	1.64745	0.141790
$136$	2.45663	0.210654
$137$	−18.7771	−1.60424	−0.802119	−	0.597164i	$-0.796294\pi$
$137$	−18.7771	−1.60424	−0.802119	+	0.597164i	$0.796294\pi$
$138$	5.71435	0.486438
$139$	9.58702	0.813161	0.406580	−	0.913615i	$-0.366721\pi$
$139$	9.58702	0.813161	0.406580	+	0.913615i	$0.366721\pi$
$140$	5.17850	0.437664
$141$	−1.57233	−0.132414
$142$	−13.1492	−1.10346
$143$	0.445224	0.0372315
$144$	1.00000	0.0833333
$145$	−0.850956	−0.0706681
$146$	−10.4075	−0.861333
$147$	2.88064	0.237591
$148$	−4.57485	−0.376050
$149$	−7.91964	−0.648802	−0.324401	−	0.945920i	$-0.605163\pi$
$149$	−7.91964	−0.648802	−0.324401	+	0.945920i	$0.605163\pi$
$150$	−2.28591	−0.186644
$151$	7.26797	0.591459	0.295729	−	0.955272i	$-0.404437\pi$
$151$	7.26797	0.591459	0.295729	+	0.955272i	$0.404437\pi$
$152$	5.11019	0.414491
$153$	2.45663	0.198606
$154$	−1.39950	−0.112775
$155$	6.91315	0.555278
$156$	−1.00000	−0.0800641
$157$	−14.8068	−1.18171	−0.590857	−	0.806776i	$-0.701210\pi$
$157$	−14.8068	−1.18171	−0.590857	+	0.806776i	$0.701210\pi$
$158$	−12.2671	−0.975919
$159$	3.81066	0.302205
$160$	1.64745	0.130242
$161$	17.9622	1.41562
$162$	1.00000	0.0785674
$163$	−15.2991	−1.19831	−0.599157	−	0.800631i	$-0.704498\pi$
$163$	−15.2991	−1.19831	−0.599157	+	0.800631i	$0.704498\pi$
$164$	−8.86335	−0.692111
$165$	−0.733484	−0.0571016
$166$	8.54090	0.662902
$167$	8.10539	0.627214	0.313607	−	0.949553i	$-0.398463\pi$
$167$	8.10539	0.627214	0.313607	+	0.949553i	$0.398463\pi$
$168$	3.14335	0.242515
$169$	1.00000	0.0769231
$170$	4.04717	0.310403
$171$	5.11019	0.390786
$172$	−0.324343	−0.0247310
$173$	−5.47187	−0.416018	−0.208009	−	0.978127i	$-0.566698\pi$
$173$	−5.47187	−0.416018	−0.208009	+	0.978127i	$0.566698\pi$
$174$	−0.516530	−0.0391580
$175$	−7.18543	−0.543167
$176$	−0.445224	−0.0335600
$177$	3.45384	0.259606
$178$	13.2135	0.990394
$179$	6.59751	0.493121	0.246560	−	0.969127i	$-0.420700\pi$
$179$	6.59751	0.493121	0.246560	+	0.969127i	$0.420700\pi$
$180$	1.64745	0.122794
$181$	−13.5270	−1.00545	−0.502726	−	0.864446i	$-0.667670\pi$
$181$	−13.5270	−1.00545	−0.502726	+	0.864446i	$0.667670\pi$
$182$	−3.14335	−0.233001
$183$	−0.127249	−0.00940649
$184$	5.71435	0.421268
$185$	−7.53682	−0.554118
$186$	4.19628	0.307686
$187$	−1.09375	−0.0799829
$188$	−1.57233	−0.114674
$189$	3.14335	0.228645
$190$	8.41878	0.610762
$191$	14.2788	1.03318	0.516590	−	0.856233i	$-0.327201\pi$
$191$	14.2788	1.03318	0.516590	+	0.856233i	$0.327201\pi$
$192$	1.00000	0.0721688
$193$	12.8990	0.928492	0.464246	−	0.885706i	$-0.346325\pi$
$193$	12.8990	0.928492	0.464246	+	0.885706i	$0.346325\pi$
$194$	4.87022	0.349662
$195$	−1.64745	−0.117976
$196$	2.88064	0.205760
$197$	12.9914	0.925602	0.462801	−	0.886462i	$-0.346844\pi$
$197$	12.9914	0.925602	0.462801	+	0.886462i	$0.346844\pi$
$198$	−0.445224	−0.0316407
$199$	26.0852	1.84913	0.924566	−	0.381022i	$-0.124428\pi$
$199$	26.0852	1.84913	0.924566	+	0.381022i	$0.124428\pi$
$200$	−2.28591	−0.161639
$201$	8.34136	0.588354
$202$	−11.3727	−0.800177
$203$	−1.62363	−0.113957
$204$	2.45663	0.171998
$205$	−14.6019	−1.01984
$206$	1.00000	0.0696733
$207$	5.71435	0.397175
$208$	−1.00000	−0.0693375
$209$	−2.27518	−0.157378
$210$	5.17850	0.357351
$211$	−5.80689	−0.399763	−0.199881	−	0.979820i	$-0.564056\pi$
$211$	−5.80689	−0.399763	−0.199881	+	0.979820i	$0.564056\pi$
$212$	3.81066	0.261717
$213$	−13.1492	−0.900969
$214$	−8.95681	−0.612275
$215$	−0.534339	−0.0364416
$216$	1.00000	0.0680414
$217$	13.1904	0.895421
$218$	0.559598	0.0379008
$219$	−10.4075	−0.703276
$220$	−0.733484	−0.0494515
$221$	−2.45663	−0.165251
$222$	−4.57485	−0.307044
$223$	11.7297	0.785479	0.392739	−	0.919650i	$-0.371527\pi$
$223$	11.7297	0.785479	0.392739	+	0.919650i	$0.371527\pi$
$224$	3.14335	0.210024
$225$	−2.28591	−0.152394
$226$	−0.00733242	−0.000487745 0
$227$	15.7177	1.04322	0.521610	−	0.853184i	$-0.325332\pi$
$227$	15.7177	1.04322	0.521610	+	0.853184i	$0.325332\pi$
$228$	5.11019	0.338431
$229$	13.4224	0.886977	0.443489	−	0.896280i	$-0.353741\pi$
$229$	13.4224	0.886977	0.443489	+	0.896280i	$0.353741\pi$
$230$	9.41410	0.620747
$231$	−1.39950	−0.0920800
$232$	−0.516530	−0.0339118
$233$	25.7551	1.68727	0.843636	−	0.536915i	$-0.180411\pi$
$233$	25.7551	1.68727	0.843636	+	0.536915i	$0.180411\pi$
$234$	−1.00000	−0.0653720
$235$	−2.59033	−0.168974
$236$	3.45384	0.224826
$237$	−12.2671	−0.796835
$238$	7.72203	0.500545
$239$	−15.5419	−1.00532	−0.502661	−	0.864484i	$-0.667646\pi$
$239$	−15.5419	−1.00532	−0.502661	+	0.864484i	$0.667646\pi$
$240$	1.64745	0.106342
$241$	−16.6473	−1.07235	−0.536173	−	0.844108i	$-0.680130\pi$
$241$	−16.6473	−1.07235	−0.536173	+	0.844108i	$0.680130\pi$
$242$	−10.8018	−0.694364
$243$	1.00000	0.0641500
$244$	−0.127249	−0.00814626
$245$	4.74571	0.303192
$246$	−8.86335	−0.565106
$247$	−5.11019	−0.325154
$248$	4.19628	0.266464
$249$	8.54090	0.541258
$250$	−12.0032	−0.759147
$251$	−28.7325	−1.81358	−0.906790	−	0.421583i	$-0.861475\pi$
$251$	−28.7325	−1.81358	−0.906790	+	0.421583i	$0.861475\pi$
$252$	3.14335	0.198012
$253$	−2.54417	−0.159950
$254$	3.33349	0.209162
$255$	4.04717	0.253443
$256$	1.00000	0.0625000
$257$	25.6373	1.59921	0.799605	−	0.600527i	$-0.205042\pi$
$257$	25.6373	1.59921	0.799605	+	0.600527i	$0.205042\pi$
$258$	−0.324343	−0.0201927
$259$	−14.3803	−0.893551
$260$	−1.64745	−0.102170
$261$	−0.516530	−0.0319724
$262$	17.0779	1.05508
$263$	26.4960	1.63381	0.816907	−	0.576769i	$-0.195687\pi$
$263$	26.4960	1.63381	0.816907	+	0.576769i	$0.195687\pi$
$264$	−0.445224	−0.0274017
$265$	6.27786	0.385646
$266$	16.0631	0.984893
$267$	13.2135	0.808653
$268$	8.34136	0.509530
$269$	−26.2684	−1.60162	−0.800808	−	0.598922i	$-0.795596\pi$
$269$	−26.2684	−1.60162	−0.800808	+	0.598922i	$0.795596\pi$
$270$	1.64745	0.100261
$271$	−3.18614	−0.193545	−0.0967723	−	0.995307i	$-0.530852\pi$
$271$	−3.18614	−0.193545	−0.0967723	+	0.995307i	$0.530852\pi$
$272$	2.45663	0.148955
$273$	−3.14335	−0.190244
$274$	−18.7771	−1.13437
$275$	1.01774	0.0613723
$276$	5.71435	0.343964
$277$	−22.3622	−1.34361	−0.671806	−	0.740727i	$-0.734481\pi$
$277$	−22.3622	−1.34361	−0.671806	+	0.740727i	$0.734481\pi$
$278$	9.58702	0.574991
$279$	4.19628	0.251225
$280$	5.17850	0.309475
$281$	−6.10222	−0.364028	−0.182014	−	0.983296i	$-0.558262\pi$
$281$	−6.10222	−0.364028	−0.182014	+	0.983296i	$0.558262\pi$
$282$	−1.57233	−0.0936308
$283$	−9.77475	−0.581049	−0.290524	−	0.956868i	$-0.593830\pi$
$283$	−9.77475	−0.581049	−0.290524	+	0.956868i	$0.593830\pi$
$284$	−13.1492	−0.780262
$285$	8.41878	0.498685
$286$	0.445224	0.0263267
$287$	−27.8606	−1.64456
$288$	1.00000	0.0589256
$289$	−10.9650	−0.644999
$290$	−0.850956	−0.0499699
$291$	4.87022	0.285497
$292$	−10.4075	−0.609055
$293$	0.290205	0.0169540	0.00847698	−	0.999964i	$-0.497302\pi$
$293$	0.290205	0.0169540	0.00847698	+	0.999964i	$0.497302\pi$
$294$	2.88064	0.168002
$295$	5.69002	0.331286
$296$	−4.57485	−0.265908
$297$	−0.445224	−0.0258345
$298$	−7.91964	−0.458772
$299$	−5.71435	−0.330470
$300$	−2.28591	−0.131977
$301$	−1.01952	−0.0587644
$302$	7.26797	0.418225
$303$	−11.3727	−0.653342
$304$	5.11019	0.293090
$305$	−0.209636	−0.0120037
$306$	2.45663	0.140436
$307$	−0.267331	−0.0152574	−0.00762869	−	0.999971i	$-0.502428\pi$
$307$	−0.267331	−0.0152574	−0.00762869	+	0.999971i	$0.502428\pi$
$308$	−1.39950	−0.0797436
$309$	1.00000	0.0568880
$310$	6.91315	0.392641
$311$	34.5132	1.95707	0.978533	−	0.206090i	$-0.0660740\pi$
$311$	34.5132	1.95707	0.978533	+	0.206090i	$0.0660740\pi$
$312$	−1.00000	−0.0566139
$313$	−20.3089	−1.14792	−0.573962	−	0.818882i	$-0.694594\pi$
$313$	−20.3089	−1.14792	−0.573962	+	0.818882i	$0.694594\pi$
$314$	−14.8068	−0.835599
$315$	5.17850	0.291776
$316$	−12.2671	−0.690079
$317$	9.65700	0.542391	0.271195	−	0.962524i	$-0.412581\pi$
$317$	9.65700	0.542391	0.271195	+	0.962524i	$0.412581\pi$
$318$	3.81066	0.213691
$319$	0.229972	0.0128759
$320$	1.64745	0.0920952
$321$	−8.95681	−0.499920
$322$	17.9622	1.00099
$323$	12.5538	0.698514
$324$	1.00000	0.0555556
$325$	2.28591	0.126800
$326$	−15.2991	−0.847336
$327$	0.559598	0.0309459
$328$	−8.86335	−0.489396
$329$	−4.94238	−0.272482
$330$	−0.733484	−0.0403770
$331$	−24.6225	−1.35337	−0.676687	−	0.736270i	$-0.736585\pi$
$331$	−24.6225	−1.35337	−0.676687	+	0.736270i	$0.736585\pi$
$332$	8.54090	0.468743
$333$	−4.57485	−0.250700
$334$	8.10539	0.443507
$335$	13.7420	0.750804
$336$	3.14335	0.171484
$337$	8.50500	0.463297	0.231648	−	0.972800i	$-0.425588\pi$
$337$	8.50500	0.463297	0.231648	+	0.972800i	$0.425588\pi$
$338$	1.00000	0.0543928
$339$	−0.00733242	−0.000398242 0
$340$	4.04717	0.219488
$341$	−1.86829	−0.101173
$342$	5.11019	0.276328
$343$	−12.9486	−0.699157
$344$	−0.324343	−0.0174874
$345$	9.41410	0.506838
$346$	−5.47187	−0.294169
$347$	−14.0818	−0.755953	−0.377976	−	0.925815i	$-0.623380\pi$
$347$	−14.0818	−0.755953	−0.377976	+	0.925815i	$0.623380\pi$
$348$	−0.516530	−0.0276889
$349$	30.5453	1.63505	0.817526	−	0.575891i	$-0.195345\pi$
$349$	30.5453	1.63505	0.817526	+	0.575891i	$0.195345\pi$
$350$	−7.18543	−0.384077
$351$	−1.00000	−0.0533761
$352$	−0.445224	−0.0237305
$353$	−20.7707	−1.10552	−0.552758	−	0.833342i	$-0.686424\pi$
$353$	−20.7707	−1.10552	−0.552758	+	0.833342i	$0.686424\pi$
$354$	3.45384	0.183569
$355$	−21.6626	−1.14973
$356$	13.2135	0.700314
$357$	7.72203	0.408693
$358$	6.59751	0.348689
$359$	−10.1146	−0.533830	−0.266915	−	0.963720i	$-0.586004\pi$
$359$	−10.1146	−0.533830	−0.266915	+	0.963720i	$0.586004\pi$
$360$	1.64745	0.0868281
$361$	7.11407	0.374425
$362$	−13.5270	−0.710962
$363$	−10.8018	−0.566946
$364$	−3.14335	−0.164756
$365$	−17.1459	−0.897456
$366$	−0.127249	−0.00665139
$367$	−18.4861	−0.964968	−0.482484	−	0.875905i	$-0.660265\pi$
$367$	−18.4861	−0.964968	−0.482484	+	0.875905i	$0.660265\pi$
$368$	5.71435	0.297881
$369$	−8.86335	−0.461407
$370$	−7.53682	−0.391821
$371$	11.9782	0.621879
$372$	4.19628	0.217567
$373$	−4.84903	−0.251073	−0.125537	−	0.992089i	$-0.540065\pi$
$373$	−4.84903	−0.251073	−0.125537	+	0.992089i	$0.540065\pi$
$374$	−1.09375	−0.0565564
$375$	−12.0032	−0.619841
$376$	−1.57233	−0.0810866
$377$	0.516530	0.0266026
$378$	3.14335	0.161676
$379$	−24.8791	−1.27795	−0.638976	−	0.769226i	$-0.720642\pi$
$379$	−24.8791	−1.27795	−0.638976	+	0.769226i	$0.720642\pi$
$380$	8.41878	0.431874
$381$	3.33349	0.170780
$382$	14.2788	0.730568
$383$	−16.2501	−0.830340	−0.415170	−	0.909744i	$-0.636278\pi$
$383$	−16.2501	−0.830340	−0.415170	+	0.909744i	$0.636278\pi$
$384$	1.00000	0.0510310
$385$	−2.30560	−0.117504
$386$	12.8990	0.656543
$387$	−0.324343	−0.0164873
$388$	4.87022	0.247248
$389$	6.53625	0.331401	0.165700	−	0.986176i	$-0.447012\pi$
$389$	6.53625	0.331401	0.165700	+	0.986176i	$0.447012\pi$
$390$	−1.64745	−0.0834218
$391$	14.0380	0.709934
$392$	2.88064	0.145494
$393$	17.0779	0.861465
$394$	12.9914	0.654500
$395$	−20.2094	−1.01685
$396$	−0.445224	−0.0223734
$397$	16.4399	0.825094	0.412547	−	0.910936i	$-0.364639\pi$
$397$	16.4399	0.825094	0.412547	+	0.910936i	$0.364639\pi$
$398$	26.0852	1.30753
$399$	16.0631	0.804162
$400$	−2.28591	−0.114296
$401$	−19.2395	−0.960773	−0.480386	−	0.877057i	$-0.659504\pi$
$401$	−19.2395	−0.960773	−0.480386	+	0.877057i	$0.659504\pi$
$402$	8.34136	0.416029
$403$	−4.19628	−0.209032
$404$	−11.3727	−0.565811
$405$	1.64745	0.0818624
$406$	−1.62363	−0.0805796
$407$	2.03683	0.100962
$408$	2.45663	0.121621
$409$	3.94273	0.194956	0.0974778	−	0.995238i	$-0.468922\pi$
$409$	3.94273	0.194956	0.0974778	+	0.995238i	$0.468922\pi$
$410$	−14.6019	−0.721137
$411$	−18.7771	−0.926207
$412$	1.00000	0.0492665
$413$	10.8566	0.534219
$414$	5.71435	0.280845
$415$	14.0707	0.690703
$416$	−1.00000	−0.0490290
$417$	9.58702	0.469479
$418$	−2.27518	−0.111283
$419$	−6.52311	−0.318675	−0.159337	−	0.987224i	$-0.550936\pi$
$419$	−6.52311	−0.318675	−0.159337	+	0.987224i	$0.550936\pi$
$420$	5.17850	0.252685
$421$	14.1139	0.687869	0.343934	−	0.938994i	$-0.388240\pi$
$421$	14.1139	0.687869	0.343934	+	0.938994i	$0.388240\pi$
$422$	−5.80689	−0.282675
$423$	−1.57233	−0.0764492
$424$	3.81066	0.185062
$425$	−5.61564	−0.272398
$426$	−13.1492	−0.637081
$427$	−0.399987	−0.0193567
$428$	−8.95681	−0.432944
$429$	0.445224	0.0214956
$430$	−0.534339	−0.0257681
$431$	3.44380	0.165882	0.0829410	−	0.996554i	$-0.473569\pi$
$431$	3.44380	0.165882	0.0829410	+	0.996554i	$0.473569\pi$
$432$	1.00000	0.0481125
$433$	13.4340	0.645597	0.322798	−	0.946468i	$-0.395376\pi$
$433$	13.4340	0.645597	0.322798	+	0.946468i	$0.395376\pi$
$434$	13.1904	0.633158
$435$	−0.850956	−0.0408002
$436$	0.559598	0.0267999
$437$	29.2014	1.39689
$438$	−10.4075	−0.497291
$439$	−29.9480	−1.42934	−0.714669	−	0.699463i	$-0.753423\pi$
$439$	−29.9480	−1.42934	−0.714669	+	0.699463i	$0.753423\pi$
$440$	−0.733484	−0.0349675
$441$	2.88064	0.137173
$442$	−2.45663	−0.116850
$443$	31.0441	1.47495	0.737475	−	0.675375i	$-0.236018\pi$
$443$	31.0441	1.47495	0.737475	+	0.675375i	$0.236018\pi$
$444$	−4.57485	−0.217113
$445$	21.7686	1.03193
$446$	11.7297	0.555418
$447$	−7.91964	−0.374586
$448$	3.14335	0.148509
$449$	−8.58538	−0.405169	−0.202584	−	0.979265i	$-0.564934\pi$
$449$	−8.58538	−0.405169	−0.202584	+	0.979265i	$0.564934\pi$
$450$	−2.28591	−0.107759
$451$	3.94618	0.185818
$452$	−0.00733242	−0.000344888 0
$453$	7.26797	0.341479
$454$	15.7177	0.737668
$455$	−5.17850	−0.242772
$456$	5.11019	0.239307
$457$	15.1935	0.710720	0.355360	−	0.934730i	$-0.384358\pi$
$457$	15.1935	0.710720	0.355360	+	0.934730i	$0.384358\pi$
$458$	13.4224	0.627188
$459$	2.45663	0.114666
$460$	9.41410	0.438935
$461$	−3.98360	−0.185535	−0.0927674	−	0.995688i	$-0.529571\pi$
$461$	−3.98360	−0.185535	−0.0927674	+	0.995688i	$0.529571\pi$
$462$	−1.39950	−0.0651104
$463$	−11.7513	−0.546130	−0.273065	−	0.961996i	$-0.588037\pi$
$463$	−11.7513	−0.546130	−0.273065	+	0.961996i	$0.588037\pi$
$464$	−0.516530	−0.0239793
$465$	6.91315	0.320590
$466$	25.7551	1.19308
$467$	−27.0368	−1.25111	−0.625556	−	0.780179i	$-0.715128\pi$
$467$	−27.0368	−1.25111	−0.625556	+	0.780179i	$0.715128\pi$
$468$	−1.00000	−0.0462250
$469$	26.2198	1.21072
$470$	−2.59033	−0.119483
$471$	−14.8068	−0.682263
$472$	3.45384	0.158976
$473$	0.144406	0.00663978
$474$	−12.2671	−0.563447
$475$	−11.6815	−0.535982
$476$	7.72203	0.353939
$477$	3.81066	0.174478
$478$	−15.5419	−0.710870
$479$	1.88050	0.0859221	0.0429611	−	0.999077i	$-0.486321\pi$
$479$	1.88050	0.0859221	0.0429611	+	0.999077i	$0.486321\pi$
$480$	1.64745	0.0751954
$481$	4.57485	0.208595
$482$	−16.6473	−0.758263
$483$	17.9622	0.817309
$484$	−10.8018	−0.490990
$485$	8.02344	0.364326
$486$	1.00000	0.0453609
$487$	−10.5508	−0.478100	−0.239050	−	0.971007i	$-0.576836\pi$
$487$	−10.5508	−0.478100	−0.239050	+	0.971007i	$0.576836\pi$
$488$	−0.127249	−0.00576027
$489$	−15.2991	−0.691847
$490$	4.74571	0.214389
$491$	−26.9165	−1.21473	−0.607363	−	0.794425i	$-0.707773\pi$
$491$	−26.9165	−1.21473	−0.607363	+	0.794425i	$0.707773\pi$
$492$	−8.86335	−0.399590
$493$	−1.26892	−0.0571493
$494$	−5.11019	−0.229918
$495$	−0.733484	−0.0329676
$496$	4.19628	0.188418
$497$	−41.3326	−1.85402
$498$	8.54090	0.382727
$499$	−4.14628	−0.185613	−0.0928066	−	0.995684i	$-0.529584\pi$
$499$	−4.14628	−0.185613	−0.0928066	+	0.995684i	$0.529584\pi$
$500$	−12.0032	−0.536798
$501$	8.10539	0.362122
$502$	−28.7325	−1.28239
$503$	13.9286	0.621046	0.310523	−	0.950566i	$-0.399496\pi$
$503$	13.9286	0.621046	0.310523	+	0.950566i	$0.399496\pi$
$504$	3.14335	0.140016
$505$	−18.7359	−0.833735
$506$	−2.54417	−0.113102
$507$	1.00000	0.0444116
$508$	3.33349	0.147900
$509$	−8.26518	−0.366348	−0.183174	−	0.983081i	$-0.558637\pi$
$509$	−8.26518	−0.366348	−0.183174	+	0.983081i	$0.558637\pi$
$510$	4.04717	0.179211
$511$	−32.7145	−1.44720
$512$	1.00000	0.0441942
$513$	5.11019	0.225621
$514$	25.6373	1.13081
$515$	1.64745	0.0725952
$516$	−0.324343	−0.0142784
$517$	0.700039	0.0307877
$518$	−14.3803	−0.631836
$519$	−5.47187	−0.240188
$520$	−1.64745	−0.0722454
$521$	5.15752	0.225955	0.112977	−	0.993598i	$-0.463961\pi$
$521$	5.15752	0.225955	0.112977	+	0.993598i	$0.463961\pi$
$522$	−0.516530	−0.0226079
$523$	−11.8046	−0.516178	−0.258089	−	0.966121i	$-0.583093\pi$
$523$	−11.8046	−0.516178	−0.258089	+	0.966121i	$0.583093\pi$
$524$	17.0779	0.746051
$525$	−7.18543	−0.313598
$526$	26.4960	1.15528
$527$	10.3087	0.449054
$528$	−0.445224	−0.0193759
$529$	9.65383	0.419732
$530$	6.27786	0.272693
$531$	3.45384	0.149884
$532$	16.0631	0.696424
$533$	8.86335	0.383914
$534$	13.2135	0.571804
$535$	−14.7559	−0.637952
$536$	8.34136	0.360292
$537$	6.59751	0.284703
$538$	−26.2684	−1.13251
$539$	−1.28253	−0.0552426
$540$	1.64745	0.0708949
$541$	−29.8845	−1.28484	−0.642419	−	0.766354i	$-0.722069\pi$
$541$	−29.8845	−1.28484	−0.642419	+	0.766354i	$0.722069\pi$
$542$	−3.18614	−0.136857
$543$	−13.5270	−0.580498
$544$	2.45663	0.105327
$545$	0.921909	0.0394903
$546$	−3.14335	−0.134523
$547$	7.01732	0.300039	0.150020	−	0.988683i	$-0.452066\pi$
$547$	7.01732	0.300039	0.150020	+	0.988683i	$0.452066\pi$
$548$	−18.7771	−0.802119
$549$	−0.127249	−0.00543084
$550$	1.01774	0.0433968
$551$	−2.63957	−0.112449
$552$	5.71435	0.243219
$553$	−38.5598	−1.63973
$554$	−22.3622	−0.950077
$555$	−7.53682	−0.319920
$556$	9.58702	0.406580
$557$	−6.12787	−0.259646	−0.129823	−	0.991537i	$-0.541441\pi$
$557$	−6.12787	−0.259646	−0.129823	+	0.991537i	$0.541441\pi$
$558$	4.19628	0.177643
$559$	0.324343	0.0137183
$560$	5.17850	0.218832
$561$	−1.09375	−0.0461781
$562$	−6.10222	−0.257407
$563$	28.1376	1.18586	0.592929	−	0.805255i	$-0.297972\pi$
$563$	28.1376	1.18586	0.592929	+	0.805255i	$0.297972\pi$
$564$	−1.57233	−0.0662070
$565$	−0.0120798	−0.000508200 0
$566$	−9.77475	−0.410864
$567$	3.14335	0.132008
$568$	−13.1492	−0.551729
$569$	35.7312	1.49793	0.748966	−	0.662609i	$-0.230551\pi$
$569$	35.7312	1.49793	0.748966	+	0.662609i	$0.230551\pi$
$570$	8.41878	0.352624
$571$	21.4875	0.899225	0.449612	−	0.893224i	$-0.351562\pi$
$571$	21.4875	0.899225	0.449612	+	0.893224i	$0.351562\pi$
$572$	0.445224	0.0186158
$573$	14.2788	0.596507
$574$	−27.8606	−1.16288
$575$	−13.0625	−0.544745
$576$	1.00000	0.0416667
$577$	−1.77066	−0.0737134	−0.0368567	−	0.999321i	$-0.511735\pi$
$577$	−1.77066	−0.0737134	−0.0368567	+	0.999321i	$0.511735\pi$
$578$	−10.9650	−0.456083
$579$	12.8990	0.536065
$580$	−0.850956	−0.0353340
$581$	26.8470	1.11380
$582$	4.87022	0.201877
$583$	−1.69660	−0.0702659
$584$	−10.4075	−0.430667
$585$	−1.64745	−0.0681136
$586$	0.290205	0.0119883
$587$	43.3359	1.78866	0.894332	−	0.447403i	$-0.147651\pi$
$587$	43.3359	1.78866	0.894332	+	0.447403i	$0.147651\pi$
$588$	2.88064	0.118796
$589$	21.4438	0.883576
$590$	5.69002	0.234254
$591$	12.9914	0.534397
$592$	−4.57485	−0.188025
$593$	−26.5623	−1.09078	−0.545391	−	0.838182i	$-0.683619\pi$
$593$	−26.5623	−1.09078	−0.545391	+	0.838182i	$0.683619\pi$
$594$	−0.445224	−0.0182678
$595$	12.7217	0.521537
$596$	−7.91964	−0.324401
$597$	26.0852	1.06760
$598$	−5.71435	−0.233677
$599$	−0.352724	−0.0144119	−0.00720596	−	0.999974i	$-0.502294\pi$
$599$	−0.352724	−0.0144119	−0.00720596	+	0.999974i	$0.502294\pi$
$600$	−2.28591	−0.0933221
$601$	19.4837	0.794757	0.397378	−	0.917655i	$-0.369920\pi$
$601$	19.4837	0.794757	0.397378	+	0.917655i	$0.369920\pi$
$602$	−1.01952	−0.0415527
$603$	8.34136	0.339687
$604$	7.26797	0.295729
$605$	−17.7954	−0.723484
$606$	−11.3727	−0.461983
$607$	−14.9704	−0.607628	−0.303814	−	0.952731i	$-0.598260\pi$
$607$	−14.9704	−0.607628	−0.303814	+	0.952731i	$0.598260\pi$
$608$	5.11019	0.207246
$609$	−1.62363	−0.0657930
$610$	−0.209636	−0.00848789
$611$	1.57233	0.0636096
$612$	2.45663	0.0993032
$613$	−38.5682	−1.55776	−0.778878	−	0.627175i	$-0.784211\pi$
$613$	−38.5682	−1.55776	−0.778878	+	0.627175i	$0.784211\pi$
$614$	−0.267331	−0.0107886
$615$	−14.6019	−0.588806
$616$	−1.39950	−0.0563873
$617$	−4.81454	−0.193826	−0.0969130	−	0.995293i	$-0.530897\pi$
$617$	−4.81454	−0.193826	−0.0969130	+	0.995293i	$0.530897\pi$
$618$	1.00000	0.0402259
$619$	36.6968	1.47497	0.737484	−	0.675364i	$-0.236014\pi$
$619$	36.6968	1.47497	0.737484	+	0.675364i	$0.236014\pi$
$620$	6.91315	0.277639
$621$	5.71435	0.229309
$622$	34.5132	1.38385
$623$	41.5347	1.66405
$624$	−1.00000	−0.0400320
$625$	−8.34502	−0.333801
$626$	−20.3089	−0.811705
$627$	−2.27518	−0.0908620
$628$	−14.8068	−0.590857
$629$	−11.2387	−0.448116
$630$	5.17850	0.206317
$631$	−8.08135	−0.321713	−0.160857	−	0.986978i	$-0.551426\pi$
$631$	−8.08135	−0.321713	−0.160857	+	0.986978i	$0.551426\pi$
$632$	−12.2671	−0.487960
$633$	−5.80689	−0.230803
$634$	9.65700	0.383528
$635$	5.49176	0.217934
$636$	3.81066	0.151102
$637$	−2.88064	−0.114135
$638$	0.229972	0.00910466
$639$	−13.1492	−0.520175
$640$	1.64745	0.0651211
$641$	42.1291	1.66400	0.832000	−	0.554776i	$-0.187196\pi$
$641$	42.1291	1.66400	0.832000	+	0.554776i	$0.187196\pi$
$642$	−8.95681	−0.353497
$643$	32.4845	1.28107	0.640533	−	0.767931i	$-0.278714\pi$
$643$	32.4845	1.28107	0.640533	+	0.767931i	$0.278714\pi$
$644$	17.9622	0.707810
$645$	−0.534339	−0.0210396
$646$	12.5538	0.493924
$647$	−3.54343	−0.139307	−0.0696534	−	0.997571i	$-0.522189\pi$
$647$	−3.54343	−0.139307	−0.0696534	+	0.997571i	$0.522189\pi$
$648$	1.00000	0.0392837
$649$	−1.53773	−0.0603613
$650$	2.28591	0.0896609
$651$	13.1904	0.516971
$652$	−15.2991	−0.599157
$653$	18.8552	0.737860	0.368930	−	0.929457i	$-0.379724\pi$
$653$	18.8552	0.737860	0.368930	+	0.929457i	$0.379724\pi$
$654$	0.559598	0.0218820
$655$	28.1349	1.09932
$656$	−8.86335	−0.346055
$657$	−10.4075	−0.406036
$658$	−4.94238	−0.192674
$659$	8.47619	0.330185	0.165093	−	0.986278i	$-0.447208\pi$
$659$	8.47619	0.330185	0.165093	+	0.986278i	$0.447208\pi$
$660$	−0.733484	−0.0285508
$661$	8.28247	0.322151	0.161075	−	0.986942i	$-0.448504\pi$
$661$	8.28247	0.322151	0.161075	+	0.986942i	$0.448504\pi$
$662$	−24.6225	−0.956981
$663$	−2.45663	−0.0954075
$664$	8.54090	0.331451
$665$	26.4632	1.02620
$666$	−4.57485	−0.177272
$667$	−2.95163	−0.114288
$668$	8.10539	0.313607
$669$	11.7297	0.453497
$670$	13.7420	0.530898
$671$	0.0566542	0.00218711
$672$	3.14335	0.121257
$673$	29.1909	1.12523	0.562613	−	0.826720i	$-0.309796\pi$
$673$	29.1909	1.12523	0.562613	+	0.826720i	$0.309796\pi$
$674$	8.50500	0.327600
$675$	−2.28591	−0.0879849
$676$	1.00000	0.0384615
$677$	16.6056	0.638207	0.319103	−	0.947720i	$-0.396618\pi$
$677$	16.6056	0.638207	0.319103	+	0.947720i	$0.396618\pi$
$678$	−0.00733242	−0.000281600 0
$679$	15.3088	0.587498
$680$	4.04717	0.155202
$681$	15.7177	0.602303
$682$	−1.86829	−0.0715403
$683$	6.20637	0.237480	0.118740	−	0.992925i	$-0.462114\pi$
$683$	6.20637	0.237480	0.118740	+	0.992925i	$0.462114\pi$
$684$	5.11019	0.195393
$685$	−30.9343	−1.18194
$686$	−12.9486	−0.494379
$687$	13.4224	0.512097
$688$	−0.324343	−0.0123655
$689$	−3.81066	−0.145175
$690$	9.41410	0.358389
$691$	8.36372	0.318171	0.159085	−	0.987265i	$-0.449145\pi$
$691$	8.36372	0.318171	0.159085	+	0.987265i	$0.449145\pi$
$692$	−5.47187	−0.208009
$693$	−1.39950	−0.0531624
$694$	−14.0818	−0.534539
$695$	15.7941	0.599105
$696$	−0.516530	−0.0195790
$697$	−21.7739	−0.824746
$698$	30.5453	1.15616
$699$	25.7551	0.974147
$700$	−7.18543	−0.271584
$701$	39.0871	1.47630	0.738149	−	0.674637i	$-0.235700\pi$
$701$	39.0871	1.47630	0.738149	+	0.674637i	$0.235700\pi$
$702$	−1.00000	−0.0377426
$703$	−23.3783	−0.881731
$704$	−0.445224	−0.0167800
$705$	−2.59033	−0.0975575
$706$	−20.7707	−0.781717
$707$	−35.7482	−1.34445
$708$	3.45384	0.129803
$709$	33.2737	1.24962	0.624809	−	0.780777i	$-0.285177\pi$
$709$	33.2737	1.24962	0.624809	+	0.780777i	$0.285177\pi$
$710$	−21.6626	−0.812985
$711$	−12.2671	−0.460053
$712$	13.2135	0.495197
$713$	23.9790	0.898021
$714$	7.72203	0.288990
$715$	0.733484	0.0274307
$716$	6.59751	0.246560
$717$	−15.5419	−0.580423
$718$	−10.1146	−0.377475
$719$	−16.5427	−0.616938	−0.308469	−	0.951234i	$-0.599817\pi$
$719$	−16.5427	−0.616938	−0.308469	+	0.951234i	$0.599817\pi$
$720$	1.64745	0.0613968
$721$	3.14335	0.117064
$722$	7.11407	0.264758
$723$	−16.6473	−0.619119
$724$	−13.5270	−0.502726
$725$	1.18074	0.0438517
$726$	−10.8018	−0.400891
$727$	37.2965	1.38325	0.691625	−	0.722256i	$-0.256895\pi$
$727$	37.2965	1.38325	0.691625	+	0.722256i	$0.256895\pi$
$728$	−3.14335	−0.116500
$729$	1.00000	0.0370370
$730$	−17.1459	−0.634597
$731$	−0.796791	−0.0294704
$732$	−0.127249	−0.00470324
$733$	5.75170	0.212444	0.106222	−	0.994342i	$-0.466125\pi$
$733$	5.75170	0.212444	0.106222	+	0.994342i	$0.466125\pi$
$734$	−18.4861	−0.682336
$735$	4.74571	0.175048
$736$	5.71435	0.210634
$737$	−3.71378	−0.136799
$738$	−8.86335	−0.326264
$739$	−3.61943	−0.133143	−0.0665714	−	0.997782i	$-0.521206\pi$
$739$	−3.61943	−0.133143	−0.0665714	+	0.997782i	$0.521206\pi$
$740$	−7.53682	−0.277059
$741$	−5.11019	−0.187728
$742$	11.9782	0.439735
$743$	−43.8380	−1.60826	−0.804130	−	0.594454i	$-0.797368\pi$
$743$	−43.8380	−1.60826	−0.804130	+	0.594454i	$0.797368\pi$
$744$	4.19628	0.153843
$745$	−13.0472	−0.478012
$746$	−4.84903	−0.177536
$747$	8.54090	0.312495
$748$	−1.09375	−0.0399914
$749$	−28.1544	−1.02874
$750$	−12.0032	−0.438294
$751$	−2.73128	−0.0996657	−0.0498328	−	0.998758i	$-0.515869\pi$
$751$	−2.73128	−0.0996657	−0.0498328	+	0.998758i	$0.515869\pi$
$752$	−1.57233	−0.0573369
$753$	−28.7325	−1.04707
$754$	0.516530	0.0188109
$755$	11.9736	0.435764
$756$	3.14335	0.114322
$757$	15.2811	0.555402	0.277701	−	0.960668i	$-0.410428\pi$
$757$	15.2811	0.555402	0.277701	+	0.960668i	$0.410428\pi$
$758$	−24.8791	−0.903649
$759$	−2.54417	−0.0923475
$760$	8.41878	0.305381
$761$	−19.1358	−0.693673	−0.346836	−	0.937926i	$-0.612744\pi$
$761$	−19.1358	−0.693673	−0.346836	+	0.937926i	$0.612744\pi$
$762$	3.33349	0.120760
$763$	1.75901	0.0636806
$764$	14.2788	0.516590
$765$	4.04717	0.146326
$766$	−16.2501	−0.587139
$767$	−3.45384	−0.124711
$768$	1.00000	0.0360844
$769$	13.4521	0.485097	0.242548	−	0.970139i	$-0.422017\pi$
$769$	13.4521	0.485097	0.242548	+	0.970139i	$0.422017\pi$
$770$	−2.30560	−0.0830879
$771$	25.6373	0.923304
$772$	12.8990	0.464246
$773$	4.18243	0.150431	0.0752157	−	0.997167i	$-0.476035\pi$
$773$	4.18243	0.150431	0.0752157	+	0.997167i	$0.476035\pi$
$774$	−0.324343	−0.0116583
$775$	−9.59233	−0.344567
$776$	4.87022	0.174831
$777$	−14.3803	−0.515892
$778$	6.53625	0.234336
$779$	−45.2934	−1.62280
$780$	−1.64745	−0.0589881
$781$	5.85435	0.209485
$782$	14.0380	0.501999
$783$	−0.516530	−0.0184593
$784$	2.88064	0.102880
$785$	−24.3935	−0.870642
$786$	17.0779	0.609148
$787$	−25.0725	−0.893739	−0.446870	−	0.894599i	$-0.647461\pi$
$787$	−25.0725	−0.893739	−0.446870	+	0.894599i	$0.647461\pi$
$788$	12.9914	0.462801
$789$	26.4960	0.943283
$790$	−20.2094	−0.719019
$791$	−0.0230483	−0.000819505 0
$792$	−0.445224	−0.0158204
$793$	0.127249	0.00451873
$794$	16.4399	0.583430
$795$	6.27786	0.222653
$796$	26.0852	0.924566
$797$	−26.0475	−0.922650	−0.461325	−	0.887231i	$-0.652626\pi$
$797$	−26.0475	−0.922650	−0.461325	+	0.887231i	$0.652626\pi$
$798$	16.0631	0.568628
$799$	−3.86262	−0.136650
$800$	−2.28591	−0.0808193
$801$	13.2135	0.466876
$802$	−19.2395	−0.679369
$803$	4.63368	0.163519
$804$	8.34136	0.294177
$805$	29.5918	1.04297
$806$	−4.19628	−0.147808
$807$	−26.2684	−0.924693
$808$	−11.3727	−0.400089
$809$	−22.1520	−0.778824	−0.389412	−	0.921064i	$-0.627322\pi$
$809$	−22.1520	−0.778824	−0.389412	+	0.921064i	$0.627322\pi$
$810$	1.64745	0.0578854
$811$	30.2671	1.06282	0.531410	−	0.847115i	$-0.321662\pi$
$811$	30.2671	1.06282	0.531410	+	0.847115i	$0.321662\pi$
$812$	−1.62363	−0.0569784
$813$	−3.18614	−0.111743
$814$	2.03683	0.0713909
$815$	−25.2044	−0.882872
$816$	2.45663	0.0859991
$817$	−1.65746	−0.0579871
$818$	3.94273	0.137854
$819$	−3.14335	−0.109838
$820$	−14.6019	−0.509921
$821$	−14.2756	−0.498220	−0.249110	−	0.968475i	$-0.580138\pi$
$821$	−14.2756	−0.498220	−0.249110	+	0.968475i	$0.580138\pi$
$822$	−18.7771	−0.654927
$823$	49.8647	1.73817	0.869086	−	0.494661i	$-0.164708\pi$
$823$	49.8647	1.73817	0.869086	+	0.494661i	$0.164708\pi$
$824$	1.00000	0.0348367
$825$	1.01774	0.0354333
$826$	10.8566	0.377750
$827$	27.8009	0.966731	0.483365	−	0.875419i	$-0.339414\pi$
$827$	27.8009	0.966731	0.483365	+	0.875419i	$0.339414\pi$
$828$	5.71435	0.198587
$829$	−18.7029	−0.649580	−0.324790	−	0.945786i	$-0.605294\pi$
$829$	−18.7029	−0.649580	−0.324790	+	0.945786i	$0.605294\pi$
$830$	14.0707	0.488401
$831$	−22.3622	−0.775734
$832$	−1.00000	−0.0346688
$833$	7.07666	0.245192
$834$	9.58702	0.331971
$835$	13.3532	0.462107
$836$	−2.27518	−0.0786888
$837$	4.19628	0.145045
$838$	−6.52311	−0.225337
$839$	49.6121	1.71280	0.856400	−	0.516313i	$-0.172696\pi$
$839$	49.6121	1.71280	0.856400	+	0.516313i	$0.172696\pi$
$840$	5.17850	0.178675
$841$	−28.7332	−0.990800
$842$	14.1139	0.486397
$843$	−6.10222	−0.210172
$844$	−5.80689	−0.199881
$845$	1.64745	0.0566739
$846$	−1.57233	−0.0540578
$847$	−33.9537	−1.16666
$848$	3.81066	0.130859
$849$	−9.77475	−0.335469
$850$	−5.61564	−0.192615
$851$	−26.1423	−0.896146
$852$	−13.1492	−0.450485
$853$	−43.3523	−1.48436	−0.742178	−	0.670203i	$-0.766207\pi$
$853$	−43.3523	−1.48436	−0.742178	+	0.670203i	$0.766207\pi$
$854$	−0.399987	−0.0136873
$855$	8.41878	0.287916
$856$	−8.95681	−0.306137
$857$	−47.8711	−1.63524	−0.817622	−	0.575755i	$-0.804708\pi$
$857$	−47.8711	−1.63524	−0.817622	+	0.575755i	$0.804708\pi$
$858$	0.445224	0.0151997
$859$	−25.4289	−0.867623	−0.433812	−	0.901004i	$-0.642832\pi$
$859$	−25.4289	−0.867623	−0.433812	+	0.901004i	$0.642832\pi$
$860$	−0.534339	−0.0182208
$861$	−27.8606	−0.949486
$862$	3.44380	0.117296
$863$	37.4799	1.27583	0.637915	−	0.770107i	$-0.279797\pi$
$863$	37.4799	1.27583	0.637915	+	0.770107i	$0.279797\pi$
$864$	1.00000	0.0340207
$865$	−9.01462	−0.306506
$866$	13.4340	0.456506
$867$	−10.9650	−0.372390
$868$	13.1904	0.447710
$869$	5.46162	0.185273
$870$	−0.850956	−0.0288501
$871$	−8.34136	−0.282636
$872$	0.559598	0.0189504
$873$	4.87022	0.164832
$874$	29.2014	0.987754
$875$	−37.7301	−1.27551
$876$	−10.4075	−0.351638
$877$	−5.27695	−0.178190	−0.0890949	−	0.996023i	$-0.528397\pi$
$877$	−5.27695	−0.178190	−0.0890949	+	0.996023i	$0.528397\pi$
$878$	−29.9480	−1.01070
$879$	0.290205	0.00978837
$880$	−0.733484	−0.0247257
$881$	−6.10892	−0.205815	−0.102907	−	0.994691i	$-0.532815\pi$
$881$	−6.10892	−0.205815	−0.102907	+	0.994691i	$0.532815\pi$
$882$	2.88064	0.0969963
$883$	−53.2744	−1.79283	−0.896413	−	0.443220i	$-0.853836\pi$
$883$	−53.2744	−1.79283	−0.896413	+	0.443220i	$0.853836\pi$
$884$	−2.45663	−0.0826253
$885$	5.69002	0.191268
$886$	31.0441	1.04295
$887$	10.4657	0.351403	0.175702	−	0.984443i	$-0.443781\pi$
$887$	10.4657	0.351403	0.175702	+	0.984443i	$0.443781\pi$
$888$	−4.57485	−0.153522
$889$	10.4783	0.351432
$890$	21.7686	0.729684
$891$	−0.445224	−0.0149156
$892$	11.7297	0.392739
$893$	−8.03490	−0.268878
$894$	−7.91964	−0.264872
$895$	10.8690	0.363312
$896$	3.14335	0.105012
$897$	−5.71435	−0.190797
$898$	−8.58538	−0.286498
$899$	−2.16750	−0.0722903
$900$	−2.28591	−0.0761971
$901$	9.36137	0.311872
$902$	3.94618	0.131393
$903$	−1.01952	−0.0339277
$904$	−0.00733242	−0.000243873 0
$905$	−22.2850	−0.740778
$906$	7.26797	0.241462
$907$	−46.8364	−1.55518	−0.777588	−	0.628774i	$-0.783557\pi$
$907$	−46.8364	−1.55518	−0.777588	+	0.628774i	$0.783557\pi$
$908$	15.7177	0.521610
$909$	−11.3727	−0.377207
$910$	−5.17850	−0.171666
$911$	3.96041	0.131214	0.0656072	−	0.997846i	$-0.479102\pi$
$911$	3.96041	0.131214	0.0656072	+	0.997846i	$0.479102\pi$
$912$	5.11019	0.169215
$913$	−3.80262	−0.125848
$914$	15.1935	0.502555
$915$	−0.209636	−0.00693034
$916$	13.4224	0.443489
$917$	53.6817	1.77273
$918$	2.45663	0.0810808
$919$	16.6325	0.548655	0.274328	−	0.961636i	$-0.411545\pi$
$919$	16.6325	0.548655	0.274328	+	0.961636i	$0.411545\pi$
$920$	9.41410	0.310374
$921$	−0.267331	−0.00880885
$922$	−3.98360	−0.131193
$923$	13.1492	0.432812
$924$	−1.39950	−0.0460400
$925$	10.4577	0.343847
$926$	−11.7513	−0.386172
$927$	1.00000	0.0328443
$928$	−0.516530	−0.0169559
$929$	−20.6639	−0.677961	−0.338980	−	0.940793i	$-0.610082\pi$
$929$	−20.6639	−0.677961	−0.338980	+	0.940793i	$0.610082\pi$
$930$	6.91315	0.226691
$931$	14.7206	0.482449
$932$	25.7551	0.843636
$933$	34.5132	1.12991
$934$	−27.0368	−0.884670
$935$	−1.80190	−0.0589283
$936$	−1.00000	−0.0326860
$937$	42.2327	1.37968	0.689841	−	0.723961i	$-0.257680\pi$
$937$	42.2327	1.37968	0.689841	+	0.723961i	$0.257680\pi$
$938$	26.2198	0.856107
$939$	−20.3089	−0.662754
$940$	−2.59033	−0.0844872
$941$	18.9977	0.619306	0.309653	−	0.950850i	$-0.399787\pi$
$941$	18.9977	0.619306	0.309653	+	0.950850i	$0.399787\pi$
$942$	−14.8068	−0.482433
$943$	−50.6483	−1.64933
$944$	3.45384	0.112413
$945$	5.17850	0.168457
$946$	0.144406	0.00469503
$947$	−43.7171	−1.42062	−0.710308	−	0.703891i	$-0.751444\pi$
$947$	−43.7171	−1.42062	−0.710308	+	0.703891i	$0.751444\pi$
$948$	−12.2671	−0.398417
$949$	10.4075	0.337843
$950$	−11.6815	−0.378997
$951$	9.65700	0.313150
$952$	7.72203	0.250273
$953$	5.21437	0.168910	0.0844550	−	0.996427i	$-0.473085\pi$
$953$	5.21437	0.168910	0.0844550	+	0.996427i	$0.473085\pi$
$954$	3.81066	0.123375
$955$	23.5236	0.761207
$956$	−15.5419	−0.502661
$957$	0.229972	0.00743393
$958$	1.88050	0.0607561
$959$	−59.0231	−1.90595
$960$	1.64745	0.0531712
$961$	−13.3912	−0.431976
$962$	4.57485	0.147499
$963$	−8.95681	−0.288629
$964$	−16.6473	−0.536173
$965$	21.2505	0.684077
$966$	17.9622	0.577924
$967$	−30.3857	−0.977137	−0.488568	−	0.872526i	$-0.662481\pi$
$967$	−30.3857	−0.977137	−0.488568	+	0.872526i	$0.662481\pi$
$968$	−10.8018	−0.347182
$969$	12.5538	0.403287
$970$	8.02344	0.257617
$971$	−8.94712	−0.287127	−0.143563	−	0.989641i	$-0.545856\pi$
$971$	−8.94712	−0.287127	−0.143563	+	0.989641i	$0.545856\pi$
$972$	1.00000	0.0320750
$973$	30.1354	0.966095
$974$	−10.5508	−0.338068
$975$	2.28591	0.0732079
$976$	−0.127249	−0.00407313
$977$	−54.8758	−1.75563	−0.877817	−	0.478997i	$-0.841001\pi$
$977$	−54.8758	−1.75563	−0.877817	+	0.478997i	$0.841001\pi$
$978$	−15.2991	−0.489210
$979$	−5.88297	−0.188021
$980$	4.74571	0.151596
$981$	0.559598	0.0178666
$982$	−26.9165	−0.858941
$983$	25.6730	0.818841	0.409421	−	0.912346i	$-0.365731\pi$
$983$	25.6730	0.818841	0.409421	+	0.912346i	$0.365731\pi$
$984$	−8.86335	−0.282553
$985$	21.4027	0.681948
$986$	−1.26892	−0.0404107
$987$	−4.94238	−0.157318
$988$	−5.11019	−0.162577
$989$	−1.85341	−0.0589351
$990$	−0.733484	−0.0233116
$991$	−9.24193	−0.293580	−0.146790	−	0.989168i	$-0.546894\pi$
$991$	−9.24193	−0.293580	−0.146790	+	0.989168i	$0.546894\pi$
$992$	4.19628	0.133232
$993$	−24.6225	−0.781371
$994$	−41.3326	−1.31099
$995$	42.9740	1.36237
$996$	8.54090	0.270629
$997$	−21.4718	−0.680019	−0.340010	−	0.940422i	$-0.610430\pi$
$997$	−21.4718	−0.680019	−0.340010	+	0.940422i	$0.610430\pi$
$998$	−4.14628	−0.131248
$999$	−4.57485	−0.144742

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bd.1.10	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bd.1.10	✓	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.64745 q^{5} +1.00000 q^{6} +3.14335 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.64745 q^{5} +1.00000 q^{6} +3.14335 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.64745 q^{10} -0.445224 q^{11} +1.00000 q^{12} -1.00000 q^{13} +3.14335 q^{14} +1.64745 q^{15} +1.00000 q^{16} +2.45663 q^{17} +1.00000 q^{18} +5.11019 q^{19} +1.64745 q^{20} +3.14335 q^{21} -0.445224 q^{22} +5.71435 q^{23} +1.00000 q^{24} -2.28591 q^{25} -1.00000 q^{26} +1.00000 q^{27} +3.14335 q^{28} -0.516530 q^{29} +1.64745 q^{30} +4.19628 q^{31} +1.00000 q^{32} -0.445224 q^{33} +2.45663 q^{34} +5.17850 q^{35} +1.00000 q^{36} -4.57485 q^{37} +5.11019 q^{38} -1.00000 q^{39} +1.64745 q^{40} -8.86335 q^{41} +3.14335 q^{42} -0.324343 q^{43} -0.445224 q^{44} +1.64745 q^{45} +5.71435 q^{46} -1.57233 q^{47} +1.00000 q^{48} +2.88064 q^{49} -2.28591 q^{50} +2.45663 q^{51} -1.00000 q^{52} +3.81066 q^{53} +1.00000 q^{54} -0.733484 q^{55} +3.14335 q^{56} +5.11019 q^{57} -0.516530 q^{58} +3.45384 q^{59} +1.64745 q^{60} -0.127249 q^{61} +4.19628 q^{62} +3.14335 q^{63} +1.00000 q^{64} -1.64745 q^{65} -0.445224 q^{66} +8.34136 q^{67} +2.45663 q^{68} +5.71435 q^{69} +5.17850 q^{70} -13.1492 q^{71} +1.00000 q^{72} -10.4075 q^{73} -4.57485 q^{74} -2.28591 q^{75} +5.11019 q^{76} -1.39950 q^{77} -1.00000 q^{78} -12.2671 q^{79} +1.64745 q^{80} +1.00000 q^{81} -8.86335 q^{82} +8.54090 q^{83} +3.14335 q^{84} +4.04717 q^{85} -0.324343 q^{86} -0.516530 q^{87} -0.445224 q^{88} +13.2135 q^{89} +1.64745 q^{90} -3.14335 q^{91} +5.71435 q^{92} +4.19628 q^{93} -1.57233 q^{94} +8.41878 q^{95} +1.00000 q^{96} +4.87022 q^{97} +2.88064 q^{98} -0.445224 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9} + 5 q^{10} + 18 q^{11} + 16 q^{12} - 16 q^{13} + 4 q^{14} + 5 q^{15} + 16 q^{16} + 17 q^{17} + 16 q^{18} + 8 q^{19} + 5 q^{20} + 4 q^{21} + 18 q^{22} + 9 q^{23} + 16 q^{24} + 17 q^{25} - 16 q^{26} + 16 q^{27} + 4 q^{28} + 14 q^{29} + 5 q^{30} + 12 q^{31} + 16 q^{32} + 18 q^{33} + 17 q^{34} + 16 q^{35} + 16 q^{36} + 31 q^{37} + 8 q^{38} - 16 q^{39} + 5 q^{40} + 29 q^{41} + 4 q^{42} + 30 q^{43} + 18 q^{44} + 5 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 36 q^{49} + 17 q^{50} + 17 q^{51} - 16 q^{52} + 12 q^{53} + 16 q^{54} + 30 q^{55} + 4 q^{56} + 8 q^{57} + 14 q^{58} + 38 q^{59} + 5 q^{60} + 12 q^{62} + 4 q^{63} + 16 q^{64} - 5 q^{65} + 18 q^{66} + 28 q^{67} + 17 q^{68} + 9 q^{69} + 16 q^{70} + 32 q^{71} + 16 q^{72} + 20 q^{73} + 31 q^{74} + 17 q^{75} + 8 q^{76} + 26 q^{77} - 16 q^{78} + 13 q^{79} + 5 q^{80} + 16 q^{81} + 29 q^{82} + 39 q^{83} + 4 q^{84} + 31 q^{85} + 30 q^{86} + 14 q^{87} + 18 q^{88} + 9 q^{89} + 5 q^{90} - 4 q^{91} + 9 q^{92} + 12 q^{93} - q^{94} - 20 q^{95} + 16 q^{96} + 35 q^{97} + 36 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9 + 5 * q^10 + 18 * q^11 + 16 * q^12 - 16 * q^13 + 4 * q^14 + 5 * q^15 + 16 * q^16 + 17 * q^17 + 16 * q^18 + 8 * q^19 + 5 * q^20 + 4 * q^21 + 18 * q^22 + 9 * q^23 + 16 * q^24 + 17 * q^25 - 16 * q^26 + 16 * q^27 + 4 * q^28 + 14 * q^29 + 5 * q^30 + 12 * q^31 + 16 * q^32 + 18 * q^33 + 17 * q^34 + 16 * q^35 + 16 * q^36 + 31 * q^37 + 8 * q^38 - 16 * q^39 + 5 * q^40 + 29 * q^41 + 4 * q^42 + 30 * q^43 + 18 * q^44 + 5 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 36 * q^49 + 17 * q^50 + 17 * q^51 - 16 * q^52 + 12 * q^53 + 16 * q^54 + 30 * q^55 + 4 * q^56 + 8 * q^57 + 14 * q^58 + 38 * q^59 + 5 * q^60 + 12 * q^62 + 4 * q^63 + 16 * q^64 - 5 * q^65 + 18 * q^66 + 28 * q^67 + 17 * q^68 + 9 * q^69 + 16 * q^70 + 32 * q^71 + 16 * q^72 + 20 * q^73 + 31 * q^74 + 17 * q^75 + 8 * q^76 + 26 * q^77 - 16 * q^78 + 13 * q^79 + 5 * q^80 + 16 * q^81 + 29 * q^82 + 39 * q^83 + 4 * q^84 + 31 * q^85 + 30 * q^86 + 14 * q^87 + 18 * q^88 + 9 * q^89 + 5 * q^90 - 4 * q^91 + 9 * q^92 + 12 * q^93 - q^94 - 20 * q^95 + 16 * q^96 + 35 * q^97 + 36 * q^98 + 18 * q^99

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