LMFDB - Embedded newform 8034.2.a.ba.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} - x^{13} - 44 x^{12} + 36 x^{11} + 722 x^{10} - 451 x^{9} - 5438 x^{8} + 2268 x^{7} + 18441 x^{6} + \cdots - 1492 $ x^14 - x^13 - 44x^12 + 36x^11 + 722x^10 - 451x^9 - 5438x^8 + 2268x^7 + 18441x^6 - 4126x^5 - 22759x^4 + 2997x^3 + 10504x^2 - 506x - 1492
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.891518$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.891518 q^{5} +1.00000 q^{6} +4.07845 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.891518 q^{5} +1.00000 q^{6} +4.07845 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.891518 q^{10} -4.41011 q^{11} -1.00000 q^{12} -1.00000 q^{13} -4.07845 q^{14} +0.891518 q^{15} +1.00000 q^{16} -3.83133 q^{17} -1.00000 q^{18} +1.31800 q^{19} -0.891518 q^{20} -4.07845 q^{21} +4.41011 q^{22} -6.87898 q^{23} +1.00000 q^{24} -4.20520 q^{25} +1.00000 q^{26} -1.00000 q^{27} +4.07845 q^{28} -7.06622 q^{29} -0.891518 q^{30} -4.56821 q^{31} -1.00000 q^{32} +4.41011 q^{33} +3.83133 q^{34} -3.63601 q^{35} +1.00000 q^{36} -8.36395 q^{37} -1.31800 q^{38} +1.00000 q^{39} +0.891518 q^{40} -0.436547 q^{41} +4.07845 q^{42} -3.87678 q^{43} -4.41011 q^{44} -0.891518 q^{45} +6.87898 q^{46} +1.61571 q^{47} -1.00000 q^{48} +9.63379 q^{49} +4.20520 q^{50} +3.83133 q^{51} -1.00000 q^{52} +4.54487 q^{53} +1.00000 q^{54} +3.93169 q^{55} -4.07845 q^{56} -1.31800 q^{57} +7.06622 q^{58} +3.89094 q^{59} +0.891518 q^{60} +10.3612 q^{61} +4.56821 q^{62} +4.07845 q^{63} +1.00000 q^{64} +0.891518 q^{65} -4.41011 q^{66} +3.87397 q^{67} -3.83133 q^{68} +6.87898 q^{69} +3.63601 q^{70} -8.92491 q^{71} -1.00000 q^{72} +9.37758 q^{73} +8.36395 q^{74} +4.20520 q^{75} +1.31800 q^{76} -17.9864 q^{77} -1.00000 q^{78} +8.17661 q^{79} -0.891518 q^{80} +1.00000 q^{81} +0.436547 q^{82} +4.84486 q^{83} -4.07845 q^{84} +3.41570 q^{85} +3.87678 q^{86} +7.06622 q^{87} +4.41011 q^{88} +10.7038 q^{89} +0.891518 q^{90} -4.07845 q^{91} -6.87898 q^{92} +4.56821 q^{93} -1.61571 q^{94} -1.17502 q^{95} +1.00000 q^{96} -1.63498 q^{97} -9.63379 q^{98} -4.41011 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - 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
$5$	−0.891518	−0.398699	−0.199349	−	0.979928i	$-0.563883\pi$
$5$	−0.891518	−0.398699	−0.199349	+	0.979928i	$0.563883\pi$
$6$	1.00000	0.408248
$7$	4.07845	1.54151	0.770755	−	0.637131i	$-0.219879\pi$
$7$	4.07845	1.54151	0.770755	+	0.637131i	$0.219879\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.891518	0.281923
$11$	−4.41011	−1.32970	−0.664849	−	0.746978i	$-0.731504\pi$
$11$	−4.41011	−1.32970	−0.664849	+	0.746978i	$0.731504\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−4.07845	−1.09001
$15$	0.891518	0.230189
$16$	1.00000	0.250000
$17$	−3.83133	−0.929235	−0.464617	−	0.885512i	$-0.653808\pi$
$17$	−3.83133	−0.929235	−0.464617	+	0.885512i	$0.653808\pi$
$18$	−1.00000	−0.235702
$19$	1.31800	0.302371	0.151185	−	0.988505i	$-0.451691\pi$
$19$	1.31800	0.302371	0.151185	+	0.988505i	$0.451691\pi$
$20$	−0.891518	−0.199349
$21$	−4.07845	−0.889992
$22$	4.41011	0.940238
$23$	−6.87898	−1.43437	−0.717183	−	0.696885i	$-0.754569\pi$
$23$	−6.87898	−1.43437	−0.717183	+	0.696885i	$0.754569\pi$
$24$	1.00000	0.204124
$25$	−4.20520	−0.841039
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	4.07845	0.770755
$29$	−7.06622	−1.31216	−0.656082	−	0.754690i	$-0.727787\pi$
$29$	−7.06622	−1.31216	−0.656082	+	0.754690i	$0.727787\pi$
$30$	−0.891518	−0.162768
$31$	−4.56821	−0.820475	−0.410238	−	0.911979i	$-0.634554\pi$
$31$	−4.56821	−0.820475	−0.410238	+	0.911979i	$0.634554\pi$
$32$	−1.00000	−0.176777
$33$	4.41011	0.767701
$34$	3.83133	0.657068
$35$	−3.63601	−0.614599
$36$	1.00000	0.166667
$37$	−8.36395	−1.37502	−0.687512	−	0.726173i	$-0.741297\pi$
$37$	−8.36395	−1.37502	−0.687512	+	0.726173i	$0.741297\pi$
$38$	−1.31800	−0.213808
$39$	1.00000	0.160128
$40$	0.891518	0.140961
$41$	−0.436547	−0.0681771	−0.0340886	−	0.999419i	$-0.510853\pi$
$41$	−0.436547	−0.0681771	−0.0340886	+	0.999419i	$0.510853\pi$
$42$	4.07845	0.629319
$43$	−3.87678	−0.591204	−0.295602	−	0.955311i	$-0.595520\pi$
$43$	−3.87678	−0.591204	−0.295602	+	0.955311i	$0.595520\pi$
$44$	−4.41011	−0.664849
$45$	−0.891518	−0.132900
$46$	6.87898	1.01425
$47$	1.61571	0.235675	0.117838	−	0.993033i	$-0.462404\pi$
$47$	1.61571	0.235675	0.117838	+	0.993033i	$0.462404\pi$
$48$	−1.00000	−0.144338
$49$	9.63379	1.37626
$50$	4.20520	0.594704
$51$	3.83133	0.536494
$52$	−1.00000	−0.138675
$53$	4.54487	0.624286	0.312143	−	0.950035i	$-0.398953\pi$
$53$	4.54487	0.624286	0.312143	+	0.950035i	$0.398953\pi$
$54$	1.00000	0.136083
$55$	3.93169	0.530149
$56$	−4.07845	−0.545006
$57$	−1.31800	−0.174574
$58$	7.06622	0.927840
$59$	3.89094	0.506557	0.253279	−	0.967393i	$-0.418491\pi$
$59$	3.89094	0.506557	0.253279	+	0.967393i	$0.418491\pi$
$60$	0.891518	0.115094
$61$	10.3612	1.32662	0.663308	−	0.748346i	$-0.269152\pi$
$61$	10.3612	1.32662	0.663308	+	0.748346i	$0.269152\pi$
$62$	4.56821	0.580164
$63$	4.07845	0.513837
$64$	1.00000	0.125000
$65$	0.891518	0.110579
$66$	−4.41011	−0.542847
$67$	3.87397	0.473281	0.236641	−	0.971597i	$-0.423954\pi$
$67$	3.87397	0.473281	0.236641	+	0.971597i	$0.423954\pi$
$68$	−3.83133	−0.464617
$69$	6.87898	0.828132
$70$	3.63601	0.434587
$71$	−8.92491	−1.05919	−0.529596	−	0.848250i	$-0.677657\pi$
$71$	−8.92491	−1.05919	−0.529596	+	0.848250i	$0.677657\pi$
$72$	−1.00000	−0.117851
$73$	9.37758	1.09756	0.548781	−	0.835966i	$-0.315092\pi$
$73$	9.37758	1.09756	0.548781	+	0.835966i	$0.315092\pi$
$74$	8.36395	0.972289
$75$	4.20520	0.485574
$76$	1.31800	0.151185
$77$	−17.9864	−2.04974
$78$	−1.00000	−0.113228
$79$	8.17661	0.919941	0.459970	−	0.887934i	$-0.347860\pi$
$79$	8.17661	0.919941	0.459970	+	0.887934i	$0.347860\pi$
$80$	−0.891518	−0.0996747
$81$	1.00000	0.111111
$82$	0.436547	0.0482085
$83$	4.84486	0.531793	0.265896	−	0.964002i	$-0.414332\pi$
$83$	4.84486	0.531793	0.265896	+	0.964002i	$0.414332\pi$
$84$	−4.07845	−0.444996
$85$	3.41570	0.370485
$86$	3.87678	0.418044
$87$	7.06622	0.757578
$88$	4.41011	0.470119
$89$	10.7038	1.13460	0.567301	−	0.823511i	$-0.307988\pi$
$89$	10.7038	1.13460	0.567301	+	0.823511i	$0.307988\pi$
$90$	0.891518	0.0939742
$91$	−4.07845	−0.427538
$92$	−6.87898	−0.717183
$93$	4.56821	0.473702
$94$	−1.61571	−0.166647
$95$	−1.17502	−0.120555
$96$	1.00000	0.102062
$97$	−1.63498	−0.166007	−0.0830037	−	0.996549i	$-0.526451\pi$
$97$	−1.63498	−0.166007	−0.0830037	+	0.996549i	$0.526451\pi$
$98$	−9.63379	−0.973160
$99$	−4.41011	−0.443232
$100$	−4.20520	−0.420520
$101$	7.15302	0.711752	0.355876	−	0.934533i	$-0.384182\pi$
$101$	7.15302	0.711752	0.355876	+	0.934533i	$0.384182\pi$
$102$	−3.83133	−0.379358
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	3.63601	0.354839
$106$	−4.54487	−0.441437
$107$	−6.28356	−0.607455	−0.303728	−	0.952759i	$-0.598231\pi$
$107$	−6.28356	−0.607455	−0.303728	+	0.952759i	$0.598231\pi$
$108$	−1.00000	−0.0962250
$109$	−3.77713	−0.361784	−0.180892	−	0.983503i	$-0.557898\pi$
$109$	−3.77713	−0.361784	−0.180892	+	0.983503i	$0.557898\pi$
$110$	−3.93169	−0.374872
$111$	8.36395	0.793871
$112$	4.07845	0.385378
$113$	10.7015	1.00671	0.503355	−	0.864079i	$-0.332099\pi$
$113$	10.7015	1.00671	0.503355	+	0.864079i	$0.332099\pi$
$114$	1.31800	0.123442
$115$	6.13273	0.571880
$116$	−7.06622	−0.656082
$117$	−1.00000	−0.0924500
$118$	−3.89094	−0.358190
$119$	−15.6259	−1.43243
$120$	−0.891518	−0.0813841
$121$	8.44905	0.768095
$122$	−10.3612	−0.938060
$123$	0.436547	0.0393621
$124$	−4.56821	−0.410238
$125$	8.20660	0.734020
$126$	−4.07845	−0.363338
$127$	14.7723	1.31083	0.655417	−	0.755268i	$-0.272493\pi$
$127$	14.7723	1.31083	0.655417	+	0.755268i	$0.272493\pi$
$128$	−1.00000	−0.0883883
$129$	3.87678	0.341332
$130$	−0.891518	−0.0781913
$131$	−0.121373	−0.0106044	−0.00530219	−	0.999986i	$-0.501688\pi$
$131$	−0.121373	−0.0106044	−0.00530219	+	0.999986i	$0.501688\pi$
$132$	4.41011	0.383851
$133$	5.37541	0.466108
$134$	−3.87397	−0.334660
$135$	0.891518	0.0767296
$136$	3.83133	0.328534
$137$	−18.9964	−1.62297	−0.811485	−	0.584373i	$-0.801340\pi$
$137$	−18.9964	−1.62297	−0.811485	+	0.584373i	$0.801340\pi$
$138$	−6.87898	−0.585577
$139$	15.1465	1.28471	0.642354	−	0.766408i	$-0.277958\pi$
$139$	15.1465	1.28471	0.642354	+	0.766408i	$0.277958\pi$
$140$	−3.63601	−0.307299
$141$	−1.61571	−0.136067
$142$	8.92491	0.748962
$143$	4.41011	0.368792
$144$	1.00000	0.0833333
$145$	6.29966	0.523158
$146$	−9.37758	−0.776094
$147$	−9.63379	−0.794582
$148$	−8.36395	−0.687512
$149$	−4.78470	−0.391978	−0.195989	−	0.980606i	$-0.562792\pi$
$149$	−4.78470	−0.391978	−0.195989	+	0.980606i	$0.562792\pi$
$150$	−4.20520	−0.343353
$151$	−21.4491	−1.74550	−0.872751	−	0.488167i	$-0.837666\pi$
$151$	−21.4491	−1.74550	−0.872751	+	0.488167i	$0.837666\pi$
$152$	−1.31800	−0.106904
$153$	−3.83133	−0.309745
$154$	17.9864	1.44939
$155$	4.07264	0.327123
$156$	1.00000	0.0800641
$157$	10.9038	0.870219	0.435110	−	0.900377i	$-0.356710\pi$
$157$	10.9038	0.870219	0.435110	+	0.900377i	$0.356710\pi$
$158$	−8.17661	−0.650496
$159$	−4.54487	−0.360432
$160$	0.891518	0.0704807
$161$	−28.0556	−2.21109
$162$	−1.00000	−0.0785674
$163$	−5.98549	−0.468820	−0.234410	−	0.972138i	$-0.575316\pi$
$163$	−5.98549	−0.468820	−0.234410	+	0.972138i	$0.575316\pi$
$164$	−0.436547	−0.0340886
$165$	−3.93169	−0.306082
$166$	−4.84486	−0.376034
$167$	18.9623	1.46735	0.733674	−	0.679501i	$-0.237804\pi$
$167$	18.9623	1.46735	0.733674	+	0.679501i	$0.237804\pi$
$168$	4.07845	0.314660
$169$	1.00000	0.0769231
$170$	−3.41570	−0.261972
$171$	1.31800	0.100790
$172$	−3.87678	−0.295602
$173$	19.1488	1.45586	0.727928	−	0.685654i	$-0.240483\pi$
$173$	19.1488	1.45586	0.727928	+	0.685654i	$0.240483\pi$
$174$	−7.06622	−0.535689
$175$	−17.1507	−1.29647
$176$	−4.41011	−0.332424
$177$	−3.89094	−0.292461
$178$	−10.7038	−0.802284
$179$	14.7047	1.09908	0.549540	−	0.835467i	$-0.314803\pi$
$179$	14.7047	1.09908	0.549540	+	0.835467i	$0.314803\pi$
$180$	−0.891518	−0.0664498
$181$	5.74905	0.427323	0.213662	−	0.976908i	$-0.431461\pi$
$181$	5.74905	0.427323	0.213662	+	0.976908i	$0.431461\pi$
$182$	4.07845	0.302315
$183$	−10.3612	−0.765923
$184$	6.87898	0.507125
$185$	7.45661	0.548221
$186$	−4.56821	−0.334958
$187$	16.8966	1.23560
$188$	1.61571	0.117838
$189$	−4.07845	−0.296664
$190$	1.17502	0.0852451
$191$	22.7543	1.64644	0.823222	−	0.567719i	$-0.192174\pi$
$191$	22.7543	1.64644	0.823222	+	0.567719i	$0.192174\pi$
$192$	−1.00000	−0.0721688
$193$	12.9628	0.933084	0.466542	−	0.884499i	$-0.345500\pi$
$193$	12.9628	0.933084	0.466542	+	0.884499i	$0.345500\pi$
$194$	1.63498	0.117385
$195$	−0.891518	−0.0638429
$196$	9.63379	0.688128
$197$	13.9660	0.995033	0.497517	−	0.867454i	$-0.334245\pi$
$197$	13.9660	0.995033	0.497517	+	0.867454i	$0.334245\pi$
$198$	4.41011	0.313413
$199$	18.9472	1.34313	0.671567	−	0.740944i	$-0.265622\pi$
$199$	18.9472	1.34313	0.671567	+	0.740944i	$0.265622\pi$
$200$	4.20520	0.297352
$201$	−3.87397	−0.273249
$202$	−7.15302	−0.503285
$203$	−28.8193	−2.02271
$204$	3.83133	0.268247
$205$	0.389189	0.0271822
$206$	−1.00000	−0.0696733
$207$	−6.87898	−0.478122
$208$	−1.00000	−0.0693375
$209$	−5.81253	−0.402061
$210$	−3.63601	−0.250909
$211$	−25.0073	−1.72157	−0.860785	−	0.508968i	$-0.830027\pi$
$211$	−25.0073	−1.72157	−0.860785	+	0.508968i	$0.830027\pi$
$212$	4.54487	0.312143
$213$	8.92491	0.611525
$214$	6.28356	0.429536
$215$	3.45622	0.235712
$216$	1.00000	0.0680414
$217$	−18.6312	−1.26477
$218$	3.77713	0.255820
$219$	−9.37758	−0.633678
$220$	3.93169	0.265074
$221$	3.83133	0.257723
$222$	−8.36395	−0.561351
$223$	12.6477	0.846950	0.423475	−	0.905908i	$-0.360810\pi$
$223$	12.6477	0.846950	0.423475	+	0.905908i	$0.360810\pi$
$224$	−4.07845	−0.272503
$225$	−4.20520	−0.280346
$226$	−10.7015	−0.711852
$227$	6.84365	0.454229	0.227115	−	0.973868i	$-0.427071\pi$
$227$	6.84365	0.454229	0.227115	+	0.973868i	$0.427071\pi$
$228$	−1.31800	−0.0872869
$229$	−1.06504	−0.0703799	−0.0351900	−	0.999381i	$-0.511204\pi$
$229$	−1.06504	−0.0703799	−0.0351900	+	0.999381i	$0.511204\pi$
$230$	−6.13273	−0.404380
$231$	17.9864	1.18342
$232$	7.06622	0.463920
$233$	−4.95796	−0.324807	−0.162403	−	0.986724i	$-0.551925\pi$
$233$	−4.95796	−0.324807	−0.162403	+	0.986724i	$0.551925\pi$
$234$	1.00000	0.0653720
$235$	−1.44043	−0.0939634
$236$	3.89094	0.253279
$237$	−8.17661	−0.531128
$238$	15.6259	1.01288
$239$	−17.9214	−1.15924	−0.579621	−	0.814886i	$-0.696799\pi$
$239$	−17.9214	−1.15924	−0.579621	+	0.814886i	$0.696799\pi$
$240$	0.891518	0.0575472
$241$	22.2265	1.43174	0.715868	−	0.698235i	$-0.246031\pi$
$241$	22.2265	1.43174	0.715868	+	0.698235i	$0.246031\pi$
$242$	−8.44905	−0.543125
$243$	−1.00000	−0.0641500
$244$	10.3612	0.663308
$245$	−8.58870	−0.548712
$246$	−0.436547	−0.0278332
$247$	−1.31800	−0.0838625
$248$	4.56821	0.290082
$249$	−4.84486	−0.307031
$250$	−8.20660	−0.519031
$251$	−19.5551	−1.23431	−0.617153	−	0.786843i	$-0.711714\pi$
$251$	−19.5551	−1.23431	−0.617153	+	0.786843i	$0.711714\pi$
$252$	4.07845	0.256918
$253$	30.3370	1.90727
$254$	−14.7723	−0.926899
$255$	−3.41570	−0.213900
$256$	1.00000	0.0625000
$257$	−6.39342	−0.398810	−0.199405	−	0.979917i	$-0.563901\pi$
$257$	−6.39342	−0.398810	−0.199405	+	0.979917i	$0.563901\pi$
$258$	−3.87678	−0.241358
$259$	−34.1120	−2.11961
$260$	0.891518	0.0552896
$261$	−7.06622	−0.437388
$262$	0.121373	0.00749843
$263$	1.21355	0.0748306	0.0374153	−	0.999300i	$-0.488088\pi$
$263$	1.21355	0.0748306	0.0374153	+	0.999300i	$0.488088\pi$
$264$	−4.41011	−0.271423
$265$	−4.05184	−0.248902
$266$	−5.37541	−0.329588
$267$	−10.7038	−0.655062
$268$	3.87397	0.236641
$269$	15.0912	0.920127	0.460064	−	0.887886i	$-0.347827\pi$
$269$	15.0912	0.920127	0.460064	+	0.887886i	$0.347827\pi$
$270$	−0.891518	−0.0542561
$271$	26.4715	1.60803	0.804015	−	0.594610i	$-0.202693\pi$
$271$	26.4715	1.60803	0.804015	+	0.594610i	$0.202693\pi$
$272$	−3.83133	−0.232309
$273$	4.07845	0.246839
$274$	18.9964	1.14761
$275$	18.5454	1.11833
$276$	6.87898	0.414066
$277$	−22.7248	−1.36540	−0.682699	−	0.730699i	$-0.739194\pi$
$277$	−22.7248	−1.36540	−0.682699	+	0.730699i	$0.739194\pi$
$278$	−15.1465	−0.908426
$279$	−4.56821	−0.273492
$280$	3.63601	0.217293
$281$	9.21995	0.550016	0.275008	−	0.961442i	$-0.411319\pi$
$281$	9.21995	0.550016	0.275008	+	0.961442i	$0.411319\pi$
$282$	1.61571	0.0962139
$283$	−21.5212	−1.27930	−0.639650	−	0.768666i	$-0.720921\pi$
$283$	−21.5212	−1.27930	−0.639650	+	0.768666i	$0.720921\pi$
$284$	−8.92491	−0.529596
$285$	1.17502	0.0696024
$286$	−4.41011	−0.260775
$287$	−1.78044	−0.105096
$288$	−1.00000	−0.0589256
$289$	−2.32089	−0.136523
$290$	−6.29966	−0.369929
$291$	1.63498	0.0958444
$292$	9.37758	0.548781
$293$	−24.1063	−1.40831	−0.704154	−	0.710047i	$-0.748673\pi$
$293$	−24.1063	−1.40831	−0.704154	+	0.710047i	$0.748673\pi$
$294$	9.63379	0.561854
$295$	−3.46884	−0.201964
$296$	8.36395	0.486144
$297$	4.41011	0.255900
$298$	4.78470	0.277170
$299$	6.87898	0.397822
$300$	4.20520	0.242787
$301$	−15.8113	−0.911347
$302$	21.4491	1.23426
$303$	−7.15302	−0.410930
$304$	1.31800	0.0755927
$305$	−9.23720	−0.528921
$306$	3.83133	0.219023
$307$	−28.1373	−1.60588	−0.802941	−	0.596059i	$-0.796733\pi$
$307$	−28.1373	−1.60588	−0.802941	+	0.596059i	$0.796733\pi$
$308$	−17.9864	−1.02487
$309$	−1.00000	−0.0568880
$310$	−4.07264	−0.231311
$311$	22.9358	1.30057	0.650285	−	0.759691i	$-0.274650\pi$
$311$	22.9358	1.30057	0.650285	+	0.759691i	$0.274650\pi$
$312$	−1.00000	−0.0566139
$313$	−21.1390	−1.19485	−0.597424	−	0.801925i	$-0.703809\pi$
$313$	−21.1390	−1.19485	−0.597424	+	0.801925i	$0.703809\pi$
$314$	−10.9038	−0.615338
$315$	−3.63601	−0.204866
$316$	8.17661	0.459970
$317$	−12.2082	−0.685680	−0.342840	−	0.939394i	$-0.611389\pi$
$317$	−12.2082	−0.685680	−0.342840	+	0.939394i	$0.611389\pi$
$318$	4.54487	0.254864
$319$	31.1628	1.74478
$320$	−0.891518	−0.0498374
$321$	6.28356	0.350714
$322$	28.0556	1.56348
$323$	−5.04971	−0.280973
$324$	1.00000	0.0555556
$325$	4.20520	0.233262
$326$	5.98549	0.331506
$327$	3.77713	0.208876
$328$	0.436547	0.0241043
$329$	6.58959	0.363296
$330$	3.93169	0.216432
$331$	−1.90976	−0.104970	−0.0524849	−	0.998622i	$-0.516714\pi$
$331$	−1.90976	−0.104970	−0.0524849	+	0.998622i	$0.516714\pi$
$332$	4.84486	0.265896
$333$	−8.36395	−0.458341
$334$	−18.9623	−1.03757
$335$	−3.45372	−0.188697
$336$	−4.07845	−0.222498
$337$	3.62376	0.197399	0.0986994	−	0.995117i	$-0.468532\pi$
$337$	3.62376	0.197399	0.0986994	+	0.995117i	$0.468532\pi$
$338$	−1.00000	−0.0543928
$339$	−10.7015	−0.581225
$340$	3.41570	0.185242
$341$	20.1463	1.09098
$342$	−1.31800	−0.0712694
$343$	10.7418	0.580002
$344$	3.87678	0.209022
$345$	−6.13273	−0.330175
$346$	−19.1488	−1.02945
$347$	−2.20372	−0.118302	−0.0591509	−	0.998249i	$-0.518839\pi$
$347$	−2.20372	−0.118302	−0.0591509	+	0.998249i	$0.518839\pi$
$348$	7.06622	0.378789
$349$	−4.15341	−0.222327	−0.111164	−	0.993802i	$-0.535458\pi$
$349$	−4.15341	−0.222327	−0.111164	+	0.993802i	$0.535458\pi$
$350$	17.1507	0.916743
$351$	1.00000	0.0533761
$352$	4.41011	0.235060
$353$	15.1988	0.808949	0.404474	−	0.914549i	$-0.367454\pi$
$353$	15.1988	0.808949	0.404474	+	0.914549i	$0.367454\pi$
$354$	3.89094	0.206801
$355$	7.95672	0.422299
$356$	10.7038	0.567301
$357$	15.6259	0.827011
$358$	−14.7047	−0.777167
$359$	−8.81818	−0.465406	−0.232703	−	0.972548i	$-0.574757\pi$
$359$	−8.81818	−0.465406	−0.232703	+	0.972548i	$0.574757\pi$
$360$	0.891518	0.0469871
$361$	−17.2629	−0.908572
$362$	−5.74905	−0.302163
$363$	−8.44905	−0.443460
$364$	−4.07845	−0.213769
$365$	−8.36028	−0.437597
$366$	10.3612	0.541589
$367$	−22.3664	−1.16752	−0.583758	−	0.811928i	$-0.698418\pi$
$367$	−22.3664	−1.16752	−0.583758	+	0.811928i	$0.698418\pi$
$368$	−6.87898	−0.358591
$369$	−0.436547	−0.0227257
$370$	−7.45661	−0.387651
$371$	18.5361	0.962344
$372$	4.56821	0.236851
$373$	−24.7009	−1.27896	−0.639481	−	0.768807i	$-0.720851\pi$
$373$	−24.7009	−1.27896	−0.639481	+	0.768807i	$0.720851\pi$
$374$	−16.8966	−0.873702
$375$	−8.20660	−0.423787
$376$	−1.61571	−0.0833237
$377$	7.06622	0.363929
$378$	4.07845	0.209773
$379$	−24.3122	−1.24884	−0.624418	−	0.781091i	$-0.714664\pi$
$379$	−24.3122	−1.24884	−0.624418	+	0.781091i	$0.714664\pi$
$380$	−1.17502	−0.0602774
$381$	−14.7723	−0.756810
$382$	−22.7543	−1.16421
$383$	5.30660	0.271155	0.135577	−	0.990767i	$-0.456711\pi$
$383$	5.30660	0.271155	0.135577	+	0.990767i	$0.456711\pi$
$384$	1.00000	0.0510310
$385$	16.0352	0.817230
$386$	−12.9628	−0.659790
$387$	−3.87678	−0.197068
$388$	−1.63498	−0.0830037
$389$	−28.2582	−1.43275	−0.716374	−	0.697716i	$-0.754200\pi$
$389$	−28.2582	−1.43275	−0.716374	+	0.697716i	$0.754200\pi$
$390$	0.891518	0.0451438
$391$	26.3557	1.33286
$392$	−9.63379	−0.486580
$393$	0.121373	0.00612244
$394$	−13.9660	−0.703595
$395$	−7.28959	−0.366779
$396$	−4.41011	−0.221616
$397$	5.52509	0.277296	0.138648	−	0.990342i	$-0.455724\pi$
$397$	5.52509	0.277296	0.138648	+	0.990342i	$0.455724\pi$
$398$	−18.9472	−0.949739
$399$	−5.37541	−0.269107
$400$	−4.20520	−0.210260
$401$	20.3794	1.01770	0.508850	−	0.860855i	$-0.330071\pi$
$401$	20.3794	1.01770	0.508850	+	0.860855i	$0.330071\pi$
$402$	3.87397	0.193216
$403$	4.56821	0.227559
$404$	7.15302	0.355876
$405$	−0.891518	−0.0442999
$406$	28.8193	1.43028
$407$	36.8859	1.82837
$408$	−3.83133	−0.189679
$409$	12.8602	0.635896	0.317948	−	0.948108i	$-0.397006\pi$
$409$	12.8602	0.635896	0.317948	+	0.948108i	$0.397006\pi$
$410$	−0.389189	−0.0192207
$411$	18.9964	0.937022
$412$	1.00000	0.0492665
$413$	15.8690	0.780864
$414$	6.87898	0.338083
$415$	−4.31928	−0.212025
$416$	1.00000	0.0490290
$417$	−15.1465	−0.741727
$418$	5.81253	0.284300
$419$	17.2438	0.842413	0.421207	−	0.906965i	$-0.361607\pi$
$419$	17.2438	0.842413	0.421207	+	0.906965i	$0.361607\pi$
$420$	3.63601	0.177419
$421$	−8.60431	−0.419348	−0.209674	−	0.977771i	$-0.567240\pi$
$421$	−8.60431	−0.419348	−0.209674	+	0.977771i	$0.567240\pi$
$422$	25.0073	1.21733
$423$	1.61571	0.0785584
$424$	−4.54487	−0.220719
$425$	16.1115	0.781523
$426$	−8.92491	−0.432413
$427$	42.2577	2.04499
$428$	−6.28356	−0.303728
$429$	−4.41011	−0.212922
$430$	−3.45622	−0.166674
$431$	29.0333	1.39848	0.699241	−	0.714886i	$-0.253521\pi$
$431$	29.0333	1.39848	0.699241	+	0.714886i	$0.253521\pi$
$432$	−1.00000	−0.0481125
$433$	13.7831	0.662373	0.331186	−	0.943565i	$-0.392551\pi$
$433$	13.7831	0.662373	0.331186	+	0.943565i	$0.392551\pi$
$434$	18.6312	0.894328
$435$	−6.29966	−0.302046
$436$	−3.77713	−0.180892
$437$	−9.06651	−0.433710
$438$	9.37758	0.448078
$439$	−14.3736	−0.686013	−0.343007	−	0.939333i	$-0.611445\pi$
$439$	−14.3736	−0.686013	−0.343007	+	0.939333i	$0.611445\pi$
$440$	−3.93169	−0.187436
$441$	9.63379	0.458752
$442$	−3.83133	−0.182238
$443$	−4.89352	−0.232498	−0.116249	−	0.993220i	$-0.537087\pi$
$443$	−4.89352	−0.232498	−0.116249	+	0.993220i	$0.537087\pi$
$444$	8.36395	0.396935
$445$	−9.54264	−0.452364
$446$	−12.6477	−0.598884
$447$	4.78470	0.226309
$448$	4.07845	0.192689
$449$	15.7086	0.741337	0.370668	−	0.928765i	$-0.379129\pi$
$449$	15.7086	0.741337	0.370668	+	0.928765i	$0.379129\pi$
$450$	4.20520	0.198235
$451$	1.92522	0.0906550
$452$	10.7015	0.503355
$453$	21.4491	1.00777
$454$	−6.84365	−0.321188
$455$	3.63601	0.170459
$456$	1.31800	0.0617211
$457$	39.5699	1.85100	0.925500	−	0.378747i	$-0.123645\pi$
$457$	39.5699	1.85100	0.925500	+	0.378747i	$0.123645\pi$
$458$	1.06504	0.0497661
$459$	3.83133	0.178831
$460$	6.13273	0.285940
$461$	−26.8050	−1.24843	−0.624216	−	0.781252i	$-0.714582\pi$
$461$	−26.8050	−1.24843	−0.624216	+	0.781252i	$0.714582\pi$
$462$	−17.9864	−0.836804
$463$	21.2693	0.988470	0.494235	−	0.869328i	$-0.335448\pi$
$463$	21.2693	0.988470	0.494235	+	0.869328i	$0.335448\pi$
$464$	−7.06622	−0.328041
$465$	−4.07264	−0.188864
$466$	4.95796	0.229673
$467$	−0.247842	−0.0114688	−0.00573438	−	0.999984i	$-0.501825\pi$
$467$	−0.247842	−0.0114688	−0.00573438	+	0.999984i	$0.501825\pi$
$468$	−1.00000	−0.0462250
$469$	15.7998	0.729568
$470$	1.44043	0.0664422
$471$	−10.9038	−0.502421
$472$	−3.89094	−0.179095
$473$	17.0970	0.786122
$474$	8.17661	0.375564
$475$	−5.54246	−0.254306
$476$	−15.6259	−0.716213
$477$	4.54487	0.208095
$478$	17.9214	0.819708
$479$	−6.39802	−0.292333	−0.146167	−	0.989260i	$-0.546694\pi$
$479$	−6.39802	−0.292333	−0.146167	+	0.989260i	$0.546694\pi$
$480$	−0.891518	−0.0406920
$481$	8.36395	0.381363
$482$	−22.2265	−1.01239
$483$	28.0556	1.27657
$484$	8.44905	0.384048
$485$	1.45762	0.0661869
$486$	1.00000	0.0453609
$487$	−13.1572	−0.596208	−0.298104	−	0.954533i	$-0.596354\pi$
$487$	−13.1572	−0.596208	−0.298104	+	0.954533i	$0.596354\pi$
$488$	−10.3612	−0.469030
$489$	5.98549	0.270673
$490$	8.58870	0.387998
$491$	17.1405	0.773538	0.386769	−	0.922177i	$-0.373591\pi$
$491$	17.1405	0.773538	0.386769	+	0.922177i	$0.373591\pi$
$492$	0.436547	0.0196810
$493$	27.0730	1.21931
$494$	1.31800	0.0592998
$495$	3.93169	0.176716
$496$	−4.56821	−0.205119
$497$	−36.3999	−1.63276
$498$	4.84486	0.217103
$499$	−6.32801	−0.283281	−0.141640	−	0.989918i	$-0.545238\pi$
$499$	−6.32801	−0.283281	−0.141640	+	0.989918i	$0.545238\pi$
$500$	8.20660	0.367010
$501$	−18.9623	−0.847174
$502$	19.5551	0.872786
$503$	−9.22271	−0.411220	−0.205610	−	0.978634i	$-0.565918\pi$
$503$	−9.22271	−0.411220	−0.205610	+	0.978634i	$0.565918\pi$
$504$	−4.07845	−0.181669
$505$	−6.37705	−0.283775
$506$	−30.3370	−1.34865
$507$	−1.00000	−0.0444116
$508$	14.7723	0.655417
$509$	−4.34576	−0.192622	−0.0963111	−	0.995351i	$-0.530704\pi$
$509$	−4.34576	−0.192622	−0.0963111	+	0.995351i	$0.530704\pi$
$510$	3.41570	0.151250
$511$	38.2460	1.69190
$512$	−1.00000	−0.0441942
$513$	−1.31800	−0.0581913
$514$	6.39342	0.282002
$515$	−0.891518	−0.0392850
$516$	3.87678	0.170666
$517$	−7.12544	−0.313377
$518$	34.1120	1.49879
$519$	−19.1488	−0.840539
$520$	−0.891518	−0.0390956
$521$	−19.0186	−0.833220	−0.416610	−	0.909085i	$-0.636782\pi$
$521$	−19.0186	−0.833220	−0.416610	+	0.909085i	$0.636782\pi$
$522$	7.06622	0.309280
$523$	29.5410	1.29174	0.645868	−	0.763449i	$-0.276496\pi$
$523$	29.5410	1.29174	0.645868	+	0.763449i	$0.276496\pi$
$524$	−0.121373	−0.00530219
$525$	17.1507	0.748518
$526$	−1.21355	−0.0529132
$527$	17.5023	0.762414
$528$	4.41011	0.191925
$529$	24.3203	1.05741
$530$	4.05184	0.176001
$531$	3.89094	0.168852
$532$	5.37541	0.233054
$533$	0.436547	0.0189089
$534$	10.7038	0.463199
$535$	5.60191	0.242192
$536$	−3.87397	−0.167330
$537$	−14.7047	−0.634554
$538$	−15.0912	−0.650628
$539$	−42.4860	−1.83000
$540$	0.891518	0.0383648
$541$	21.7968	0.937117	0.468559	−	0.883432i	$-0.344773\pi$
$541$	21.7968	0.937117	0.468559	+	0.883432i	$0.344773\pi$
$542$	−26.4715	−1.13705
$543$	−5.74905	−0.246715
$544$	3.83133	0.164267
$545$	3.36738	0.144243
$546$	−4.07845	−0.174542
$547$	−4.43820	−0.189764	−0.0948819	−	0.995489i	$-0.530247\pi$
$547$	−4.43820	−0.189764	−0.0948819	+	0.995489i	$0.530247\pi$
$548$	−18.9964	−0.811485
$549$	10.3612	0.442206
$550$	−18.5454	−0.790777
$551$	−9.31330	−0.396760
$552$	−6.87898	−0.292789
$553$	33.3479	1.41810
$554$	22.7248	0.965483
$555$	−7.45661	−0.316515
$556$	15.1465	0.642354
$557$	−0.959232	−0.0406439	−0.0203220	−	0.999793i	$-0.506469\pi$
$557$	−0.959232	−0.0406439	−0.0203220	+	0.999793i	$0.506469\pi$
$558$	4.56821	0.193388
$559$	3.87678	0.163970
$560$	−3.63601	−0.153650
$561$	−16.8966	−0.713375
$562$	−9.21995	−0.388920
$563$	−7.04973	−0.297111	−0.148555	−	0.988904i	$-0.547462\pi$
$563$	−7.04973	−0.297111	−0.148555	+	0.988904i	$0.547462\pi$
$564$	−1.61571	−0.0680335
$565$	−9.54056	−0.401375
$566$	21.5212	0.904602
$567$	4.07845	0.171279
$568$	8.92491	0.374481
$569$	26.5564	1.11330	0.556651	−	0.830746i	$-0.312086\pi$
$569$	26.5564	1.11330	0.556651	+	0.830746i	$0.312086\pi$
$570$	−1.17502	−0.0492163
$571$	−2.11440	−0.0884849	−0.0442424	−	0.999021i	$-0.514087\pi$
$571$	−2.11440	−0.0884849	−0.0442424	+	0.999021i	$0.514087\pi$
$572$	4.41011	0.184396
$573$	−22.7543	−0.950575
$574$	1.78044	0.0743140
$575$	28.9274	1.20636
$576$	1.00000	0.0416667
$577$	5.24850	0.218498	0.109249	−	0.994014i	$-0.465155\pi$
$577$	5.24850	0.218498	0.109249	+	0.994014i	$0.465155\pi$
$578$	2.32089	0.0965362
$579$	−12.9628	−0.538716
$580$	6.29966	0.261579
$581$	19.7595	0.819764
$582$	−1.63498	−0.0677722
$583$	−20.0434	−0.830112
$584$	−9.37758	−0.388047
$585$	0.891518	0.0368597
$586$	24.1063	0.995824
$587$	14.6107	0.603049	0.301524	−	0.953458i	$-0.402505\pi$
$587$	14.6107	0.603049	0.301524	+	0.953458i	$0.402505\pi$
$588$	−9.63379	−0.397291
$589$	−6.02092	−0.248088
$590$	3.46884	0.142810
$591$	−13.9660	−0.574483
$592$	−8.36395	−0.343756
$593$	1.63231	0.0670308	0.0335154	−	0.999438i	$-0.489330\pi$
$593$	1.63231	0.0670308	0.0335154	+	0.999438i	$0.489330\pi$
$594$	−4.41011	−0.180949
$595$	13.9308	0.571106
$596$	−4.78470	−0.195989
$597$	−18.9472	−0.775459
$598$	−6.87898	−0.281302
$599$	1.16804	0.0477249	0.0238625	−	0.999715i	$-0.492404\pi$
$599$	1.16804	0.0477249	0.0238625	+	0.999715i	$0.492404\pi$
$600$	−4.20520	−0.171676
$601$	−12.9978	−0.530192	−0.265096	−	0.964222i	$-0.585404\pi$
$601$	−12.9978	−0.530192	−0.265096	+	0.964222i	$0.585404\pi$
$602$	15.8113	0.644420
$603$	3.87397	0.157760
$604$	−21.4491	−0.872751
$605$	−7.53248	−0.306239
$606$	7.15302	0.290572
$607$	24.9606	1.01312	0.506560	−	0.862205i	$-0.330917\pi$
$607$	24.9606	1.01312	0.506560	+	0.862205i	$0.330917\pi$
$608$	−1.31800	−0.0534521
$609$	28.8193	1.16781
$610$	9.23720	0.374003
$611$	−1.61571	−0.0653645
$612$	−3.83133	−0.154872
$613$	10.9244	0.441232	0.220616	−	0.975361i	$-0.429193\pi$
$613$	10.9244	0.441232	0.220616	+	0.975361i	$0.429193\pi$
$614$	28.1373	1.13553
$615$	−0.389189	−0.0156936
$616$	17.9864	0.724694
$617$	9.26005	0.372796	0.186398	−	0.982474i	$-0.440319\pi$
$617$	9.26005	0.372796	0.186398	+	0.982474i	$0.440319\pi$
$618$	1.00000	0.0402259
$619$	−3.74311	−0.150448	−0.0752242	−	0.997167i	$-0.523967\pi$
$619$	−3.74311	−0.150448	−0.0752242	+	0.997167i	$0.523967\pi$
$620$	4.07264	0.163561
$621$	6.87898	0.276044
$622$	−22.9358	−0.919641
$623$	43.6550	1.74900
$624$	1.00000	0.0400320
$625$	13.7097	0.548386
$626$	21.1390	0.844885
$627$	5.81253	0.232130
$628$	10.9038	0.435110
$629$	32.0451	1.27772
$630$	3.63601	0.144862
$631$	20.5453	0.817894	0.408947	−	0.912558i	$-0.365896\pi$
$631$	20.5453	0.817894	0.408947	+	0.912558i	$0.365896\pi$
$632$	−8.17661	−0.325248
$633$	25.0073	0.993949
$634$	12.2082	0.484849
$635$	−13.1698	−0.522628
$636$	−4.54487	−0.180216
$637$	−9.63379	−0.381705
$638$	−31.1628	−1.23375
$639$	−8.92491	−0.353064
$640$	0.891518	0.0352403
$641$	−4.29432	−0.169616	−0.0848078	−	0.996397i	$-0.527028\pi$
$641$	−4.29432	−0.169616	−0.0848078	+	0.996397i	$0.527028\pi$
$642$	−6.28356	−0.247992
$643$	31.3180	1.23506	0.617530	−	0.786547i	$-0.288133\pi$
$643$	31.3180	1.23506	0.617530	+	0.786547i	$0.288133\pi$
$644$	−28.0556	−1.10555
$645$	−3.45622	−0.136089
$646$	5.04971	0.198678
$647$	19.3978	0.762606	0.381303	−	0.924450i	$-0.375475\pi$
$647$	19.3978	0.762606	0.381303	+	0.924450i	$0.375475\pi$
$648$	−1.00000	−0.0392837
$649$	−17.1595	−0.673568
$650$	−4.20520	−0.164941
$651$	18.6312	0.730216
$652$	−5.98549	−0.234410
$653$	12.7751	0.499927	0.249964	−	0.968255i	$-0.419581\pi$
$653$	12.7751	0.499927	0.249964	+	0.968255i	$0.419581\pi$
$654$	−3.77713	−0.147698
$655$	0.108206	0.00422796
$656$	−0.436547	−0.0170443
$657$	9.37758	0.365854
$658$	−6.58959	−0.256889
$659$	5.95057	0.231801	0.115901	−	0.993261i	$-0.463025\pi$
$659$	5.95057	0.231801	0.115901	+	0.993261i	$0.463025\pi$
$660$	−3.93169	−0.153041
$661$	−21.1806	−0.823831	−0.411915	−	0.911222i	$-0.635140\pi$
$661$	−21.1806	−0.823831	−0.411915	+	0.911222i	$0.635140\pi$
$662$	1.90976	0.0742248
$663$	−3.83133	−0.148797
$664$	−4.84486	−0.188017
$665$	−4.79228	−0.185837
$666$	8.36395	0.324096
$667$	48.6084	1.88212
$668$	18.9623	0.733674
$669$	−12.6477	−0.488987
$670$	3.45372	0.133429
$671$	−45.6940	−1.76400
$672$	4.07845	0.157330
$673$	23.9055	0.921489	0.460744	−	0.887533i	$-0.347583\pi$
$673$	23.9055	0.921489	0.460744	+	0.887533i	$0.347583\pi$
$674$	−3.62376	−0.139582
$675$	4.20520	0.161858
$676$	1.00000	0.0384615
$677$	−4.68892	−0.180210	−0.0901049	−	0.995932i	$-0.528720\pi$
$677$	−4.68892	−0.180210	−0.0901049	+	0.995932i	$0.528720\pi$
$678$	10.7015	0.410988
$679$	−6.66820	−0.255902
$680$	−3.41570	−0.130986
$681$	−6.84365	−0.262249
$682$	−20.1463	−0.771442
$683$	29.1205	1.11426	0.557132	−	0.830424i	$-0.311902\pi$
$683$	29.1205	1.11426	0.557132	+	0.830424i	$0.311902\pi$
$684$	1.31800	0.0503951
$685$	16.9356	0.647076
$686$	−10.7418	−0.410123
$687$	1.06504	0.0406339
$688$	−3.87678	−0.147801
$689$	−4.54487	−0.173146
$690$	6.13273	0.233469
$691$	36.7897	1.39955	0.699773	−	0.714365i	$-0.253285\pi$
$691$	36.7897	1.39955	0.699773	+	0.714365i	$0.253285\pi$
$692$	19.1488	0.727928
$693$	−17.9864	−0.683248
$694$	2.20372	0.0836520
$695$	−13.5034	−0.512212
$696$	−7.06622	−0.267844
$697$	1.67256	0.0633526
$698$	4.15341	0.157209
$699$	4.95796	0.187527
$700$	−17.1507	−0.648235
$701$	−23.1946	−0.876049	−0.438025	−	0.898963i	$-0.644322\pi$
$701$	−23.1946	−0.876049	−0.438025	+	0.898963i	$0.644322\pi$
$702$	−1.00000	−0.0377426
$703$	−11.0237	−0.415767
$704$	−4.41011	−0.166212
$705$	1.44043	0.0542498
$706$	−15.1988	−0.572013
$707$	29.1733	1.09717
$708$	−3.89094	−0.146231
$709$	−10.0809	−0.378596	−0.189298	−	0.981920i	$-0.560621\pi$
$709$	−10.0809	−0.378596	−0.189298	+	0.981920i	$0.560621\pi$
$710$	−7.95672	−0.298610
$711$	8.17661	0.306647
$712$	−10.7038	−0.401142
$713$	31.4246	1.17686
$714$	−15.6259	−0.584785
$715$	−3.93169	−0.147037
$716$	14.7047	0.549540
$717$	17.9214	0.669289
$718$	8.81818	0.329092
$719$	−15.2349	−0.568168	−0.284084	−	0.958799i	$-0.591689\pi$
$719$	−15.2349	−0.568168	−0.284084	+	0.958799i	$0.591689\pi$
$720$	−0.891518	−0.0332249
$721$	4.07845	0.151890
$722$	17.2629	0.642457
$723$	−22.2265	−0.826614
$724$	5.74905	0.213662
$725$	29.7148	1.10358
$726$	8.44905	0.313574
$727$	−20.5445	−0.761953	−0.380976	−	0.924585i	$-0.624412\pi$
$727$	−20.5445	−0.761953	−0.380976	+	0.924585i	$0.624412\pi$
$728$	4.07845	0.151158
$729$	1.00000	0.0370370
$730$	8.36028	0.309428
$731$	14.8532	0.549367
$732$	−10.3612	−0.382961
$733$	−11.0053	−0.406489	−0.203244	−	0.979128i	$-0.565149\pi$
$733$	−11.0053	−0.406489	−0.203244	+	0.979128i	$0.565149\pi$
$734$	22.3664	0.825558
$735$	8.58870	0.316799
$736$	6.87898	0.253562
$737$	−17.0846	−0.629321
$738$	0.436547	0.0160695
$739$	10.7796	0.396532	0.198266	−	0.980148i	$-0.436469\pi$
$739$	10.7796	0.396532	0.198266	+	0.980148i	$0.436469\pi$
$740$	7.45661	0.274110
$741$	1.31800	0.0484180
$742$	−18.5361	−0.680480
$743$	21.4755	0.787860	0.393930	−	0.919140i	$-0.371115\pi$
$743$	21.4755	0.787860	0.393930	+	0.919140i	$0.371115\pi$
$744$	−4.56821	−0.167479
$745$	4.26565	0.156281
$746$	24.7009	0.904363
$747$	4.84486	0.177264
$748$	16.8966	0.617801
$749$	−25.6272	−0.936399
$750$	8.20660	0.299663
$751$	−44.2278	−1.61389	−0.806947	−	0.590623i	$-0.798882\pi$
$751$	−44.2278	−1.61389	−0.806947	+	0.590623i	$0.798882\pi$
$752$	1.61571	0.0589188
$753$	19.5551	0.712626
$754$	−7.06622	−0.257337
$755$	19.1222	0.695929
$756$	−4.07845	−0.148332
$757$	23.2092	0.843551	0.421776	−	0.906700i	$-0.361407\pi$
$757$	23.2092	0.843551	0.421776	+	0.906700i	$0.361407\pi$
$758$	24.3122	0.883060
$759$	−30.3370	−1.10116
$760$	1.17502	0.0426226
$761$	28.0527	1.01691	0.508455	−	0.861088i	$-0.330217\pi$
$761$	28.0527	1.01691	0.508455	+	0.861088i	$0.330217\pi$
$762$	14.7723	0.535145
$763$	−15.4049	−0.557694
$764$	22.7543	0.823222
$765$	3.41570	0.123495
$766$	−5.30660	−0.191735
$767$	−3.89094	−0.140494
$768$	−1.00000	−0.0360844
$769$	−43.5951	−1.57208	−0.786040	−	0.618176i	$-0.787872\pi$
$769$	−43.5951	−1.57208	−0.786040	+	0.618176i	$0.787872\pi$
$770$	−16.0352	−0.577869
$771$	6.39342	0.230253
$772$	12.9628	0.466542
$773$	−4.86642	−0.175033	−0.0875165	−	0.996163i	$-0.527893\pi$
$773$	−4.86642	−0.175033	−0.0875165	+	0.996163i	$0.527893\pi$
$774$	3.87678	0.139348
$775$	19.2102	0.690052
$776$	1.63498	0.0586924
$777$	34.1120	1.22376
$778$	28.2582	1.01311
$779$	−0.575370	−0.0206148
$780$	−0.891518	−0.0319215
$781$	39.3598	1.40841
$782$	−26.3557	−0.942476
$783$	7.06622	0.252526
$784$	9.63379	0.344064
$785$	−9.72095	−0.346956
$786$	−0.121373	−0.00432922
$787$	46.0753	1.64241	0.821203	−	0.570636i	$-0.193303\pi$
$787$	46.0753	1.64241	0.821203	+	0.570636i	$0.193303\pi$
$788$	13.9660	0.497517
$789$	−1.21355	−0.0432035
$790$	7.28959	0.259352
$791$	43.6455	1.55186
$792$	4.41011	0.156706
$793$	−10.3612	−0.367937
$794$	−5.52509	−0.196078
$795$	4.05184	0.143704
$796$	18.9472	0.671567
$797$	−41.4859	−1.46951	−0.734753	−	0.678335i	$-0.762702\pi$
$797$	−41.4859	−1.46951	−0.734753	+	0.678335i	$0.762702\pi$
$798$	5.37541	0.190288
$799$	−6.19031	−0.218997
$800$	4.20520	0.148676
$801$	10.7038	0.378200
$802$	−20.3794	−0.719622
$803$	−41.3561	−1.45943
$804$	−3.87397	−0.136625
$805$	25.0121	0.881559
$806$	−4.56821	−0.160908
$807$	−15.0912	−0.531236
$808$	−7.15302	−0.251642
$809$	−40.9959	−1.44134	−0.720670	−	0.693279i	$-0.756166\pi$
$809$	−40.9959	−1.44134	−0.720670	+	0.693279i	$0.756166\pi$
$810$	0.891518	0.0313247
$811$	3.82293	0.134241	0.0671207	−	0.997745i	$-0.478619\pi$
$811$	3.82293	0.134241	0.0671207	+	0.997745i	$0.478619\pi$
$812$	−28.8193	−1.01136
$813$	−26.4715	−0.928396
$814$	−36.8859	−1.29285
$815$	5.33617	0.186918
$816$	3.83133	0.134123
$817$	−5.10961	−0.178763
$818$	−12.8602	−0.449646
$819$	−4.07845	−0.142513
$820$	0.389189	0.0135911
$821$	−13.3049	−0.464344	−0.232172	−	0.972675i	$-0.574583\pi$
$821$	−13.3049	−0.464344	−0.232172	+	0.972675i	$0.574583\pi$
$822$	−18.9964	−0.662575
$823$	42.6312	1.48603	0.743016	−	0.669274i	$-0.233395\pi$
$823$	42.6312	1.48603	0.743016	+	0.669274i	$0.233395\pi$
$824$	−1.00000	−0.0348367
$825$	−18.5454	−0.645667
$826$	−15.8690	−0.552154
$827$	−36.4742	−1.26833	−0.634166	−	0.773197i	$-0.718656\pi$
$827$	−36.4742	−1.26833	−0.634166	+	0.773197i	$0.718656\pi$
$828$	−6.87898	−0.239061
$829$	28.4917	0.989556	0.494778	−	0.869019i	$-0.335249\pi$
$829$	28.4917	0.989556	0.494778	+	0.869019i	$0.335249\pi$
$830$	4.31928	0.149924
$831$	22.7248	0.788313
$832$	−1.00000	−0.0346688
$833$	−36.9103	−1.27886
$834$	15.1465	0.524480
$835$	−16.9053	−0.585030
$836$	−5.81253	−0.201031
$837$	4.56821	0.157901
$838$	−17.2438	−0.595676
$839$	−28.5577	−0.985921	−0.492961	−	0.870052i	$-0.664085\pi$
$839$	−28.5577	−0.985921	−0.492961	+	0.870052i	$0.664085\pi$
$840$	−3.63601	−0.125454
$841$	20.9314	0.721774
$842$	8.60431	0.296524
$843$	−9.21995	−0.317552
$844$	−25.0073	−0.860785
$845$	−0.891518	−0.0306691
$846$	−1.61571	−0.0555491
$847$	34.4591	1.18403
$848$	4.54487	0.156072
$849$	21.5212	0.738604
$850$	−16.1115	−0.552620
$851$	57.5354	1.97229
$852$	8.92491	0.305762
$853$	2.56693	0.0878902	0.0439451	−	0.999034i	$-0.486007\pi$
$853$	2.56693	0.0878902	0.0439451	+	0.999034i	$0.486007\pi$
$854$	−42.2577	−1.44603
$855$	−1.17502	−0.0401849
$856$	6.28356	0.214768
$857$	−21.7233	−0.742055	−0.371027	−	0.928622i	$-0.620994\pi$
$857$	−21.7233	−0.742055	−0.371027	+	0.928622i	$0.620994\pi$
$858$	4.41011	0.150559
$859$	−5.66069	−0.193140	−0.0965701	−	0.995326i	$-0.530787\pi$
$859$	−5.66069	−0.193140	−0.0965701	+	0.995326i	$0.530787\pi$
$860$	3.45622	0.117856
$861$	1.78044	0.0606771
$862$	−29.0333	−0.988877
$863$	48.7380	1.65906	0.829531	−	0.558461i	$-0.188608\pi$
$863$	48.7380	1.65906	0.829531	+	0.558461i	$0.188608\pi$
$864$	1.00000	0.0340207
$865$	−17.0715	−0.580448
$866$	−13.7831	−0.468368
$867$	2.32089	0.0788215
$868$	−18.6312	−0.632386
$869$	−36.0597	−1.22324
$870$	6.29966	0.213578
$871$	−3.87397	−0.131265
$872$	3.77713	0.127910
$873$	−1.63498	−0.0553358
$874$	9.06651	0.306679
$875$	33.4702	1.13150
$876$	−9.37758	−0.316839
$877$	−34.9677	−1.18077	−0.590387	−	0.807120i	$-0.701025\pi$
$877$	−34.9677	−1.18077	−0.590387	+	0.807120i	$0.701025\pi$
$878$	14.3736	0.485085
$879$	24.1063	0.813087
$880$	3.93169	0.132537
$881$	−41.9907	−1.41470	−0.707351	−	0.706863i	$-0.750110\pi$
$881$	−41.9907	−1.41470	−0.707351	+	0.706863i	$0.750110\pi$
$882$	−9.63379	−0.324387
$883$	−55.5234	−1.86851	−0.934256	−	0.356604i	$-0.883935\pi$
$883$	−55.5234	−1.86851	−0.934256	+	0.356604i	$0.883935\pi$
$884$	3.83133	0.128862
$885$	3.46884	0.116604
$886$	4.89352	0.164401
$887$	17.4782	0.586862	0.293431	−	0.955980i	$-0.405203\pi$
$887$	17.4782	0.586862	0.293431	+	0.955980i	$0.405203\pi$
$888$	−8.36395	−0.280676
$889$	60.2483	2.02066
$890$	9.54264	0.319870
$891$	−4.41011	−0.147744
$892$	12.6477	0.423475
$893$	2.12951	0.0712612
$894$	−4.78470	−0.160024
$895$	−13.1095	−0.438202
$896$	−4.07845	−0.136252
$897$	−6.87898	−0.229682
$898$	−15.7086	−0.524204
$899$	32.2800	1.07660
$900$	−4.20520	−0.140173
$901$	−17.4129	−0.580109
$902$	−1.92522	−0.0641027
$903$	15.8113	0.526166
$904$	−10.7015	−0.355926
$905$	−5.12538	−0.170373
$906$	−21.4491	−0.712598
$907$	−5.52710	−0.183524	−0.0917622	−	0.995781i	$-0.529250\pi$
$907$	−5.52710	−0.183524	−0.0917622	+	0.995781i	$0.529250\pi$
$908$	6.84365	0.227115
$909$	7.15302	0.237251
$910$	−3.63601	−0.120533
$911$	33.9205	1.12384	0.561918	−	0.827193i	$-0.310064\pi$
$911$	33.9205	1.12384	0.561918	+	0.827193i	$0.310064\pi$
$912$	−1.31800	−0.0436434
$913$	−21.3664	−0.707123
$914$	−39.5699	−1.30885
$915$	9.23720	0.305373
$916$	−1.06504	−0.0351900
$917$	−0.495013	−0.0163468
$918$	−3.83133	−0.126453
$919$	−10.8130	−0.356689	−0.178344	−	0.983968i	$-0.557074\pi$
$919$	−10.8130	−0.356689	−0.178344	+	0.983968i	$0.557074\pi$
$920$	−6.13273	−0.202190
$921$	28.1373	0.927156
$922$	26.8050	0.882775
$923$	8.92491	0.293767
$924$	17.9864	0.591710
$925$	35.1720	1.15645
$926$	−21.2693	−0.698954
$927$	1.00000	0.0328443
$928$	7.06622	0.231960
$929$	8.27943	0.271639	0.135820	−	0.990734i	$-0.456633\pi$
$929$	8.27943	0.271639	0.135820	+	0.990734i	$0.456633\pi$
$930$	4.07264	0.133547
$931$	12.6974	0.416139
$932$	−4.95796	−0.162403
$933$	−22.9358	−0.750884
$934$	0.247842	0.00810964
$935$	−15.0636	−0.492633
$936$	1.00000	0.0326860
$937$	23.5881	0.770591	0.385295	−	0.922793i	$-0.374100\pi$
$937$	23.5881	0.770591	0.385295	+	0.922793i	$0.374100\pi$
$938$	−15.7998	−0.515883
$939$	21.1390	0.689846
$940$	−1.44043	−0.0469817
$941$	21.6294	0.705097	0.352548	−	0.935794i	$-0.385315\pi$
$941$	21.6294	0.705097	0.352548	+	0.935794i	$0.385315\pi$
$942$	10.9038	0.355266
$943$	3.00299	0.0977910
$944$	3.89094	0.126639
$945$	3.63601	0.118280
$946$	−17.0970	−0.555872
$947$	40.0713	1.30214	0.651071	−	0.759016i	$-0.274320\pi$
$947$	40.0713	1.30214	0.651071	+	0.759016i	$0.274320\pi$
$948$	−8.17661	−0.265564
$949$	−9.37758	−0.304409
$950$	5.54246	0.179821
$951$	12.2082	0.395878
$952$	15.6259	0.506439
$953$	−38.4990	−1.24710	−0.623552	−	0.781782i	$-0.714311\pi$
$953$	−38.4990	−1.24710	−0.623552	+	0.781782i	$0.714311\pi$
$954$	−4.54487	−0.147146
$955$	−20.2859	−0.656436
$956$	−17.9214	−0.579621
$957$	−31.1628	−1.00735
$958$	6.39802	0.206711
$959$	−77.4759	−2.50183
$960$	0.891518	0.0287736
$961$	−10.1314	−0.326820
$962$	−8.36395	−0.269664
$963$	−6.28356	−0.202485
$964$	22.2265	0.715868
$965$	−11.5566	−0.372020
$966$	−28.0556	−0.902674
$967$	−44.5554	−1.43280	−0.716402	−	0.697687i	$-0.754212\pi$
$967$	−44.5554	−1.43280	−0.716402	+	0.697687i	$0.754212\pi$
$968$	−8.44905	−0.271563
$969$	5.04971	0.162220
$970$	−1.45762	−0.0468012
$971$	49.9507	1.60299	0.801497	−	0.597999i	$-0.204037\pi$
$971$	49.9507	1.60299	0.801497	+	0.597999i	$0.204037\pi$
$972$	−1.00000	−0.0320750
$973$	61.7743	1.98039
$974$	13.1572	0.421583
$975$	−4.20520	−0.134674
$976$	10.3612	0.331654
$977$	−8.48621	−0.271498	−0.135749	−	0.990743i	$-0.543344\pi$
$977$	−8.48621	−0.271498	−0.135749	+	0.990743i	$0.543344\pi$
$978$	−5.98549	−0.191395
$979$	−47.2049	−1.50868
$980$	−8.58870	−0.274356
$981$	−3.77713	−0.120595
$982$	−17.1405	−0.546974
$983$	−3.73281	−0.119058	−0.0595291	−	0.998227i	$-0.518960\pi$
$983$	−3.73281	−0.119058	−0.0595291	+	0.998227i	$0.518960\pi$
$984$	−0.436547	−0.0139166
$985$	−12.4509	−0.396719
$986$	−27.0730	−0.862181
$987$	−6.58959	−0.209749
$988$	−1.31800	−0.0419313
$989$	26.6683	0.848002
$990$	−3.93169	−0.124957
$991$	43.0792	1.36846	0.684228	−	0.729268i	$-0.260139\pi$
$991$	43.0792	1.36846	0.684228	+	0.729268i	$0.260139\pi$
$992$	4.56821	0.145041
$993$	1.90976	0.0606043
$994$	36.3999	1.15453
$995$	−16.8918	−0.535506
$996$	−4.84486	−0.153515
$997$	−11.8723	−0.376000	−0.188000	−	0.982169i	$-0.560200\pi$
$997$	−11.8723	−0.376000	−0.188000	+	0.982169i	$0.560200\pi$
$998$	6.32801	0.200310
$999$	8.36395	0.264624

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.ba.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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.891518 q^{5} +1.00000 q^{6} +4.07845 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.891518 q^{5} +1.00000 q^{6} +4.07845 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.891518 q^{10} -4.41011 q^{11} -1.00000 q^{12} -1.00000 q^{13} -4.07845 q^{14} +0.891518 q^{15} +1.00000 q^{16} -3.83133 q^{17} -1.00000 q^{18} +1.31800 q^{19} -0.891518 q^{20} -4.07845 q^{21} +4.41011 q^{22} -6.87898 q^{23} +1.00000 q^{24} -4.20520 q^{25} +1.00000 q^{26} -1.00000 q^{27} +4.07845 q^{28} -7.06622 q^{29} -0.891518 q^{30} -4.56821 q^{31} -1.00000 q^{32} +4.41011 q^{33} +3.83133 q^{34} -3.63601 q^{35} +1.00000 q^{36} -8.36395 q^{37} -1.31800 q^{38} +1.00000 q^{39} +0.891518 q^{40} -0.436547 q^{41} +4.07845 q^{42} -3.87678 q^{43} -4.41011 q^{44} -0.891518 q^{45} +6.87898 q^{46} +1.61571 q^{47} -1.00000 q^{48} +9.63379 q^{49} +4.20520 q^{50} +3.83133 q^{51} -1.00000 q^{52} +4.54487 q^{53} +1.00000 q^{54} +3.93169 q^{55} -4.07845 q^{56} -1.31800 q^{57} +7.06622 q^{58} +3.89094 q^{59} +0.891518 q^{60} +10.3612 q^{61} +4.56821 q^{62} +4.07845 q^{63} +1.00000 q^{64} +0.891518 q^{65} -4.41011 q^{66} +3.87397 q^{67} -3.83133 q^{68} +6.87898 q^{69} +3.63601 q^{70} -8.92491 q^{71} -1.00000 q^{72} +9.37758 q^{73} +8.36395 q^{74} +4.20520 q^{75} +1.31800 q^{76} -17.9864 q^{77} -1.00000 q^{78} +8.17661 q^{79} -0.891518 q^{80} +1.00000 q^{81} +0.436547 q^{82} +4.84486 q^{83} -4.07845 q^{84} +3.41570 q^{85} +3.87678 q^{86} +7.06622 q^{87} +4.41011 q^{88} +10.7038 q^{89} +0.891518 q^{90} -4.07845 q^{91} -6.87898 q^{92} +4.56821 q^{93} -1.61571 q^{94} -1.17502 q^{95} +1.00000 q^{96} -1.63498 q^{97} -9.63379 q^{98} -4.41011 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - q^99

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