LMFDB - Embedded newform 6422.2.a.bm.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6422,2,Mod(1,6422)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6422, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6422.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6422 = 2 \cdot 13^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6422.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:	$51.2799281781$
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} - 4 x^{13} - 22 x^{12} + 98 x^{11} + 164 x^{10} - 912 x^{9} - 374 x^{8} + 3996 x^{7} - 817 x^{6} + \cdots + 358 $ x^14 - 4x^13 - 22x^12 + 98x^11 + 164x^10 - 912x^9 - 374x^8 + 3996x^7 - 817x^6 - 8194x^5 + 4418x^4 + 6430x^3 - 4327x^2 - 922*x + 358
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 494)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.343703$ of defining polynomial
Character	$\chi$	$=$	6422.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.343703 q^{3} +1.00000 q^{4} +2.06376 q^{5} +0.343703 q^{6} -1.08834 q^{7} -1.00000 q^{8} -2.88187 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.343703 q^{3} +1.00000 q^{4} +2.06376 q^{5} +0.343703 q^{6} -1.08834 q^{7} -1.00000 q^{8} -2.88187 q^{9} -2.06376 q^{10} -6.18132 q^{11} -0.343703 q^{12} +1.08834 q^{14} -0.709321 q^{15} +1.00000 q^{16} -6.94860 q^{17} +2.88187 q^{18} -1.00000 q^{19} +2.06376 q^{20} +0.374065 q^{21} +6.18132 q^{22} +7.55632 q^{23} +0.343703 q^{24} -0.740893 q^{25} +2.02162 q^{27} -1.08834 q^{28} +4.02284 q^{29} +0.709321 q^{30} +2.17241 q^{31} -1.00000 q^{32} +2.12454 q^{33} +6.94860 q^{34} -2.24607 q^{35} -2.88187 q^{36} -7.24464 q^{37} +1.00000 q^{38} -2.06376 q^{40} +3.92476 q^{41} -0.374065 q^{42} -11.4843 q^{43} -6.18132 q^{44} -5.94748 q^{45} -7.55632 q^{46} -1.67300 q^{47} -0.343703 q^{48} -5.81552 q^{49} +0.740893 q^{50} +2.38826 q^{51} +11.9342 q^{53} -2.02162 q^{54} -12.7568 q^{55} +1.08834 q^{56} +0.343703 q^{57} -4.02284 q^{58} -4.82403 q^{59} -0.709321 q^{60} +7.45330 q^{61} -2.17241 q^{62} +3.13644 q^{63} +1.00000 q^{64} -2.12454 q^{66} +5.83809 q^{67} -6.94860 q^{68} -2.59713 q^{69} +2.24607 q^{70} -5.90186 q^{71} +2.88187 q^{72} +2.20839 q^{73} +7.24464 q^{74} +0.254648 q^{75} -1.00000 q^{76} +6.72736 q^{77} -12.6207 q^{79} +2.06376 q^{80} +7.95077 q^{81} -3.92476 q^{82} -10.6791 q^{83} +0.374065 q^{84} -14.3402 q^{85} +11.4843 q^{86} -1.38267 q^{87} +6.18132 q^{88} -6.19799 q^{89} +5.94748 q^{90} +7.55632 q^{92} -0.746664 q^{93} +1.67300 q^{94} -2.06376 q^{95} +0.343703 q^{96} +13.1047 q^{97} +5.81552 q^{98} +17.8138 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} + 4 q^{3} + 14 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 14 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 + 4 * q^3 + 14 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 14 * q^8 + 18 * q^9	\( 14 q - 14 q^{2} + 4 q^{3} + 14 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 14 q^{8} + 18 q^{9} - 2 q^{10} - 10 q^{11} + 4 q^{12} + 2 q^{14} + 4 q^{15} + 14 q^{16} + 2 q^{17} - 18 q^{18} - 14 q^{19} + 2 q^{20} + 18 q^{21} + 10 q^{22} + 12 q^{23} - 4 q^{24} + 44 q^{25} + 10 q^{27} - 2 q^{28} + 4 q^{29} - 4 q^{30} - 4 q^{31} - 14 q^{32} - 12 q^{33} - 2 q^{34} + 14 q^{35} + 18 q^{36} - 18 q^{37} + 14 q^{38} - 2 q^{40} - 6 q^{41} - 18 q^{42} + 28 q^{43} - 10 q^{44} - 8 q^{45} - 12 q^{46} + 20 q^{47} + 4 q^{48} + 28 q^{49} - 44 q^{50} + 10 q^{51} + 12 q^{53} - 10 q^{54} - 2 q^{55} + 2 q^{56} - 4 q^{57} - 4 q^{58} - 16 q^{59} + 4 q^{60} + 30 q^{61} + 4 q^{62} - 28 q^{63} + 14 q^{64} + 12 q^{66} - 2 q^{67} + 2 q^{68} - 42 q^{69} - 14 q^{70} - 44 q^{71} - 18 q^{72} + 36 q^{73} + 18 q^{74} + 46 q^{75} - 14 q^{76} + 68 q^{77} + 34 q^{79} + 2 q^{80} - 6 q^{81} + 6 q^{82} - 2 q^{83} + 18 q^{84} + 30 q^{85} - 28 q^{86} + 52 q^{87} + 10 q^{88} - 42 q^{89} + 8 q^{90} + 12 q^{92} + 12 q^{93} - 20 q^{94} - 2 q^{95} - 4 q^{96} - 40 q^{97} - 28 q^{98} - 12 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 4 * q^3 + 14 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 14 * q^8 + 18 * q^9 - 2 * q^10 - 10 * q^11 + 4 * q^12 + 2 * q^14 + 4 * q^15 + 14 * q^16 + 2 * q^17 - 18 * q^18 - 14 * q^19 + 2 * q^20 + 18 * q^21 + 10 * q^22 + 12 * q^23 - 4 * q^24 + 44 * q^25 + 10 * q^27 - 2 * q^28 + 4 * q^29 - 4 * q^30 - 4 * q^31 - 14 * q^32 - 12 * q^33 - 2 * q^34 + 14 * q^35 + 18 * q^36 - 18 * q^37 + 14 * q^38 - 2 * q^40 - 6 * q^41 - 18 * q^42 + 28 * q^43 - 10 * q^44 - 8 * q^45 - 12 * q^46 + 20 * q^47 + 4 * q^48 + 28 * q^49 - 44 * q^50 + 10 * q^51 + 12 * q^53 - 10 * q^54 - 2 * q^55 + 2 * q^56 - 4 * q^57 - 4 * q^58 - 16 * q^59 + 4 * q^60 + 30 * q^61 + 4 * q^62 - 28 * q^63 + 14 * q^64 + 12 * q^66 - 2 * q^67 + 2 * q^68 - 42 * q^69 - 14 * q^70 - 44 * q^71 - 18 * q^72 + 36 * q^73 + 18 * q^74 + 46 * q^75 - 14 * q^76 + 68 * q^77 + 34 * q^79 + 2 * q^80 - 6 * q^81 + 6 * q^82 - 2 * q^83 + 18 * q^84 + 30 * q^85 - 28 * q^86 + 52 * q^87 + 10 * q^88 - 42 * q^89 + 8 * q^90 + 12 * q^92 + 12 * q^93 - 20 * q^94 - 2 * q^95 - 4 * q^96 - 40 * q^97 - 28 * q^98 - 12 * 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
$3$	−0.343703	−0.198437	−0.0992186	−	0.995066i	$-0.531634\pi$
$3$	−0.343703	−0.198437	−0.0992186	+	0.995066i	$0.531634\pi$
$4$	1.00000	0.500000
$5$	2.06376	0.922942	0.461471	−	0.887155i	$-0.347322\pi$
$5$	2.06376	0.922942	0.461471	+	0.887155i	$0.347322\pi$
$6$	0.343703	0.140316
$7$	−1.08834	−0.411353	−0.205676	−	0.978620i	$-0.565939\pi$
$7$	−1.08834	−0.411353	−0.205676	+	0.978620i	$0.565939\pi$
$8$	−1.00000	−0.353553
$9$	−2.88187	−0.960623
$10$	−2.06376	−0.652618
$11$	−6.18132	−1.86374	−0.931869	−	0.362794i	$-0.881823\pi$
$11$	−6.18132	−1.86374	−0.931869	+	0.362794i	$0.881823\pi$
$12$	−0.343703	−0.0992186
$13$	0	0
$13$	0	0
$14$	1.08834	0.290870
$15$	−0.709321	−0.183146
$16$	1.00000	0.250000
$17$	−6.94860	−1.68528	−0.842641	−	0.538476i	$-0.819000\pi$
$17$	−6.94860	−1.68528	−0.842641	+	0.538476i	$0.819000\pi$
$18$	2.88187	0.679263
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	2.06376	0.461471
$21$	0.374065	0.0816277
$22$	6.18132	1.31786
$23$	7.55632	1.57560	0.787800	−	0.615931i	$-0.211220\pi$
$23$	7.55632	1.57560	0.787800	+	0.615931i	$0.211220\pi$
$24$	0.343703	0.0701582
$25$	−0.740893	−0.148179
$26$	0	0
$27$	2.02162	0.389061
$28$	−1.08834	−0.205676
$29$	4.02284	0.747024	0.373512	−	0.927625i	$-0.378154\pi$
$29$	4.02284	0.747024	0.373512	+	0.927625i	$0.378154\pi$
$30$	0.709321	0.129504
$31$	2.17241	0.390176	0.195088	−	0.980786i	$-0.437501\pi$
$31$	2.17241	0.390176	0.195088	+	0.980786i	$0.437501\pi$
$32$	−1.00000	−0.176777
$33$	2.12454	0.369835
$34$	6.94860	1.19167
$35$	−2.24607	−0.379655
$36$	−2.88187	−0.480311
$37$	−7.24464	−1.19101	−0.595506	−	0.803351i	$-0.703048\pi$
$37$	−7.24464	−1.19101	−0.595506	+	0.803351i	$0.703048\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	−2.06376	−0.326309
$41$	3.92476	0.612944	0.306472	−	0.951880i	$-0.400851\pi$
$41$	3.92476	0.612944	0.306472	+	0.951880i	$0.400851\pi$
$42$	−0.374065	−0.0577195
$43$	−11.4843	−1.75134	−0.875672	−	0.482907i	$-0.839581\pi$
$43$	−11.4843	−1.75134	−0.875672	+	0.482907i	$0.839581\pi$
$44$	−6.18132	−0.931869
$45$	−5.94748	−0.886599
$46$	−7.55632	−1.11412
$47$	−1.67300	−0.244032	−0.122016	−	0.992528i	$-0.538936\pi$
$47$	−1.67300	−0.244032	−0.122016	+	0.992528i	$0.538936\pi$
$48$	−0.343703	−0.0496093
$49$	−5.81552	−0.830789
$50$	0.740893	0.104778
$51$	2.38826	0.334423
$52$	0	0
$53$	11.9342	1.63928	0.819641	−	0.572878i	$-0.194173\pi$
$53$	11.9342	1.63928	0.819641	+	0.572878i	$0.194173\pi$
$54$	−2.02162	−0.275107
$55$	−12.7568	−1.72012
$56$	1.08834	0.145435
$57$	0.343703	0.0455246
$58$	−4.02284	−0.528225
$59$	−4.82403	−0.628036	−0.314018	−	0.949417i	$-0.601675\pi$
$59$	−4.82403	−0.628036	−0.314018	+	0.949417i	$0.601675\pi$
$60$	−0.709321	−0.0915730
$61$	7.45330	0.954298	0.477149	−	0.878822i	$-0.341670\pi$
$61$	7.45330	0.954298	0.477149	+	0.878822i	$0.341670\pi$
$62$	−2.17241	−0.275896
$63$	3.13644	0.395155
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.12454	−0.261513
$67$	5.83809	0.713236	0.356618	−	0.934250i	$-0.383930\pi$
$67$	5.83809	0.713236	0.356618	+	0.934250i	$0.383930\pi$
$68$	−6.94860	−0.842641
$69$	−2.59713	−0.312658
$70$	2.24607	0.268456
$71$	−5.90186	−0.700422	−0.350211	−	0.936671i	$-0.613890\pi$
$71$	−5.90186	−0.700422	−0.350211	+	0.936671i	$0.613890\pi$
$72$	2.88187	0.339631
$73$	2.20839	0.258473	0.129237	−	0.991614i	$-0.458747\pi$
$73$	2.20839	0.258473	0.129237	+	0.991614i	$0.458747\pi$
$74$	7.24464	0.842172
$75$	0.254648	0.0294042
$76$	−1.00000	−0.114708
$77$	6.72736	0.766654
$78$	0	0
$79$	−12.6207	−1.41994	−0.709969	−	0.704233i	$-0.751291\pi$
$79$	−12.6207	−1.41994	−0.709969	+	0.704233i	$0.751291\pi$
$80$	2.06376	0.230735
$81$	7.95077	0.883419
$82$	−3.92476	−0.433417
$83$	−10.6791	−1.17218	−0.586089	−	0.810246i	$-0.699333\pi$
$83$	−10.6791	−1.17218	−0.586089	+	0.810246i	$0.699333\pi$
$84$	0.374065	0.0408139
$85$	−14.3402	−1.55542
$86$	11.4843	1.23839
$87$	−1.38267	−0.148237
$88$	6.18132	0.658931
$89$	−6.19799	−0.656986	−0.328493	−	0.944506i	$-0.606541\pi$
$89$	−6.19799	−0.656986	−0.328493	+	0.944506i	$0.606541\pi$
$90$	5.94748	0.626920
$91$	0	0
$92$	7.55632	0.787800
$93$	−0.746664	−0.0774254
$94$	1.67300	0.172557
$95$	−2.06376	−0.211737
$96$	0.343703	0.0350791
$97$	13.1047	1.33058	0.665291	−	0.746584i	$-0.268307\pi$
$97$	13.1047	1.33058	0.665291	+	0.746584i	$0.268307\pi$
$98$	5.81552	0.587456
$99$	17.8138	1.79035
$100$	−0.740893	−0.0740893
$101$	8.05630	0.801632	0.400816	−	0.916159i	$-0.368727\pi$
$101$	8.05630	0.801632	0.400816	+	0.916159i	$0.368727\pi$
$102$	−2.38826	−0.236473
$103$	11.8144	1.16411	0.582054	−	0.813150i	$-0.302249\pi$
$103$	11.8144	1.16411	0.582054	+	0.813150i	$0.302249\pi$
$104$	0	0
$105$	0.771981	0.0753376
$106$	−11.9342	−1.15915
$107$	6.03533	0.583457	0.291729	−	0.956501i	$-0.405770\pi$
$107$	6.03533	0.583457	0.291729	+	0.956501i	$0.405770\pi$
$108$	2.02162	0.194530
$109$	1.19012	0.113993	0.0569964	−	0.998374i	$-0.481848\pi$
$109$	1.19012	0.113993	0.0569964	+	0.998374i	$0.481848\pi$
$110$	12.7568	1.21631
$111$	2.49001	0.236341
$112$	−1.08834	−0.102838
$113$	−5.63553	−0.530146	−0.265073	−	0.964228i	$-0.585396\pi$
$113$	−5.63553	−0.530146	−0.265073	+	0.964228i	$0.585396\pi$
$114$	−0.343703	−0.0321908
$115$	15.5944	1.45419
$116$	4.02284	0.373512
$117$	0	0
$118$	4.82403	0.444088
$119$	7.56242	0.693246
$120$	0.709321	0.0647519
$121$	27.2087	2.47352
$122$	−7.45330	−0.674790
$123$	−1.34895	−0.121631
$124$	2.17241	0.195088
$125$	−11.8478	−1.05970
$126$	−3.13644	−0.279417
$127$	14.5804	1.29380	0.646900	−	0.762575i	$-0.276065\pi$
$127$	14.5804	1.29380	0.646900	+	0.762575i	$0.276065\pi$
$128$	−1.00000	−0.0883883
$129$	3.94720	0.347532
$130$	0	0
$131$	−0.559347	−0.0488704	−0.0244352	−	0.999701i	$-0.507779\pi$
$131$	−0.559347	−0.0488704	−0.0244352	+	0.999701i	$0.507779\pi$
$132$	2.12454	0.184918
$133$	1.08834	0.0943708
$134$	−5.83809	−0.504334
$135$	4.17214	0.359080
$136$	6.94860	0.595837
$137$	−4.40035	−0.375948	−0.187974	−	0.982174i	$-0.560192\pi$
$137$	−4.40035	−0.375948	−0.187974	+	0.982174i	$0.560192\pi$
$138$	2.59713	0.221083
$139$	13.4207	1.13833	0.569163	−	0.822225i	$-0.307267\pi$
$139$	13.4207	1.13833	0.569163	+	0.822225i	$0.307267\pi$
$140$	−2.24607	−0.189827
$141$	0.575017	0.0484251
$142$	5.90186	0.495273
$143$	0	0
$144$	−2.88187	−0.240156
$145$	8.30219	0.689459
$146$	−2.20839	−0.182768
$147$	1.99881	0.164859
$148$	−7.24464	−0.595506
$149$	2.56792	0.210372	0.105186	−	0.994453i	$-0.466456\pi$
$149$	2.56792	0.210372	0.105186	+	0.994453i	$0.466456\pi$
$150$	−0.254648	−0.0207919
$151$	9.08459	0.739293	0.369647	−	0.929172i	$-0.379479\pi$
$151$	9.08459	0.739293	0.369647	+	0.929172i	$0.379479\pi$
$152$	1.00000	0.0811107
$153$	20.0249	1.61892
$154$	−6.72736	−0.542106
$155$	4.48333	0.360110
$156$	0	0
$157$	2.02540	0.161645	0.0808224	−	0.996729i	$-0.474245\pi$
$157$	2.02540	0.161645	0.0808224	+	0.996729i	$0.474245\pi$
$158$	12.6207	1.00405
$159$	−4.10181	−0.325295
$160$	−2.06376	−0.163155
$161$	−8.22382	−0.648128
$162$	−7.95077	−0.624671
$163$	−15.5321	−1.21657	−0.608283	−	0.793720i	$-0.708142\pi$
$163$	−15.5321	−1.21657	−0.608283	+	0.793720i	$0.708142\pi$
$164$	3.92476	0.306472
$165$	4.38454	0.341336
$166$	10.6791	0.828855
$167$	17.0948	1.32283	0.661416	−	0.750019i	$-0.269956\pi$
$167$	17.0948	1.32283	0.661416	+	0.750019i	$0.269956\pi$
$168$	−0.374065	−0.0288598
$169$	0	0
$170$	14.3402	1.09985
$171$	2.88187	0.220382
$172$	−11.4843	−0.875672
$173$	6.83216	0.519440	0.259720	−	0.965684i	$-0.416370\pi$
$173$	6.83216	0.519440	0.259720	+	0.965684i	$0.416370\pi$
$174$	1.38267	0.104820
$175$	0.806342	0.0609537
$176$	−6.18132	−0.465935
$177$	1.65804	0.124626
$178$	6.19799	0.464559
$179$	5.99659	0.448206	0.224103	−	0.974565i	$-0.428055\pi$
$179$	5.99659	0.448206	0.224103	+	0.974565i	$0.428055\pi$
$180$	−5.94748	−0.443299
$181$	21.0552	1.56502	0.782512	−	0.622635i	$-0.213938\pi$
$181$	21.0552	1.56502	0.782512	+	0.622635i	$0.213938\pi$
$182$	0	0
$183$	−2.56173	−0.189368
$184$	−7.55632	−0.557059
$185$	−14.9512	−1.09923
$186$	0.746664	0.0547481
$187$	42.9515	3.14093
$188$	−1.67300	−0.122016
$189$	−2.20020	−0.160041
$190$	2.06376	0.149721
$191$	−1.31552	−0.0951874	−0.0475937	−	0.998867i	$-0.515155\pi$
$191$	−1.31552	−0.0951874	−0.0475937	+	0.998867i	$0.515155\pi$
$192$	−0.343703	−0.0248047
$193$	−20.4269	−1.47036	−0.735179	−	0.677873i	$-0.762902\pi$
$193$	−20.4269	−1.47036	−0.735179	+	0.677873i	$0.762902\pi$
$194$	−13.1047	−0.940864
$195$	0	0
$196$	−5.81552	−0.415394
$197$	−17.6032	−1.25418	−0.627088	−	0.778949i	$-0.715753\pi$
$197$	−17.6032	−1.25418	−0.627088	+	0.778949i	$0.715753\pi$
$198$	−17.8138	−1.26597
$199$	14.1150	1.00059	0.500293	−	0.865856i	$-0.333226\pi$
$199$	14.1150	1.00059	0.500293	+	0.865856i	$0.333226\pi$
$200$	0.740893	0.0523891
$201$	−2.00657	−0.141533
$202$	−8.05630	−0.566839
$203$	−4.37821	−0.307290
$204$	2.38826	0.167211
$205$	8.09976	0.565711
$206$	−11.8144	−0.823149
$207$	−21.7763	−1.51356
$208$	0	0
$209$	6.18132	0.427571
$210$	−0.771981	−0.0532718
$211$	−0.991337	−0.0682465	−0.0341232	−	0.999418i	$-0.510864\pi$
$211$	−0.991337	−0.0682465	−0.0341232	+	0.999418i	$0.510864\pi$
$212$	11.9342	0.819641
$213$	2.02849	0.138990
$214$	−6.03533	−0.412567
$215$	−23.7009	−1.61639
$216$	−2.02162	−0.137554
$217$	−2.36431	−0.160500
$218$	−1.19012	−0.0806051
$219$	−0.759033	−0.0512907
$220$	−12.7568	−0.860061
$221$	0	0
$222$	−2.49001	−0.167118
$223$	−15.6032	−1.04487	−0.522433	−	0.852680i	$-0.674976\pi$
$223$	−15.6032	−1.04487	−0.522433	+	0.852680i	$0.674976\pi$
$224$	1.08834	0.0727176
$225$	2.13516	0.142344
$226$	5.63553	0.374870
$227$	19.2538	1.27792	0.638959	−	0.769241i	$-0.279365\pi$
$227$	19.2538	1.27792	0.638959	+	0.769241i	$0.279365\pi$
$228$	0.343703	0.0227623
$229$	−10.1986	−0.673941	−0.336970	−	0.941515i	$-0.609402\pi$
$229$	−10.1986	−0.673941	−0.336970	+	0.941515i	$0.609402\pi$
$230$	−15.5944	−1.02827
$231$	−2.31222	−0.152133
$232$	−4.02284	−0.264113
$233$	5.49002	0.359663	0.179832	−	0.983697i	$-0.442445\pi$
$233$	5.49002	0.359663	0.179832	+	0.983697i	$0.442445\pi$
$234$	0	0
$235$	−3.45268	−0.225228
$236$	−4.82403	−0.314018
$237$	4.33777	0.281769
$238$	−7.56242	−0.490199
$239$	12.3377	0.798061	0.399031	−	0.916938i	$-0.369347\pi$
$239$	12.3377	0.798061	0.399031	+	0.916938i	$0.369347\pi$
$240$	−0.709321	−0.0457865
$241$	16.0413	1.03331	0.516655	−	0.856194i	$-0.327177\pi$
$241$	16.0413	1.03331	0.516655	+	0.856194i	$0.327177\pi$
$242$	−27.2087	−1.74904
$243$	−8.79756	−0.564364
$244$	7.45330	0.477149
$245$	−12.0018	−0.766770
$246$	1.34895	0.0860060
$247$	0	0
$248$	−2.17241	−0.137948
$249$	3.67043	0.232604
$250$	11.8478	0.749322
$251$	−20.9424	−1.32188	−0.660938	−	0.750441i	$-0.729841\pi$
$251$	−20.9424	−1.32188	−0.660938	+	0.750441i	$0.729841\pi$
$252$	3.13644	0.197577
$253$	−46.7080	−2.93651
$254$	−14.5804	−0.914855
$255$	4.92879	0.308653
$256$	1.00000	0.0625000
$257$	−26.7317	−1.66748	−0.833740	−	0.552157i	$-0.813805\pi$
$257$	−26.7317	−1.66748	−0.833740	+	0.552157i	$0.813805\pi$
$258$	−3.94720	−0.245742
$259$	7.88461	0.489926
$260$	0	0
$261$	−11.5933	−0.717608
$262$	0.559347	0.0345566
$263$	−28.4672	−1.75536	−0.877681	−	0.479246i	$-0.840910\pi$
$263$	−28.4672	−1.75536	−0.877681	+	0.479246i	$0.840910\pi$
$264$	−2.12454	−0.130757
$265$	24.6292	1.51296
$266$	−1.08834	−0.0667302
$267$	2.13027	0.130370
$268$	5.83809	0.356618
$269$	12.5621	0.765926	0.382963	−	0.923764i	$-0.374904\pi$
$269$	12.5621	0.765926	0.382963	+	0.923764i	$0.374904\pi$
$270$	−4.17214	−0.253908
$271$	−1.52953	−0.0929123	−0.0464561	−	0.998920i	$-0.514793\pi$
$271$	−1.52953	−0.0929123	−0.0464561	+	0.998920i	$0.514793\pi$
$272$	−6.94860	−0.421321
$273$	0	0
$274$	4.40035	0.265835
$275$	4.57970	0.276166
$276$	−2.59713	−0.156329
$277$	31.6025	1.89881	0.949404	−	0.314058i	$-0.101689\pi$
$277$	31.6025	1.89881	0.949404	+	0.314058i	$0.101689\pi$
$278$	−13.4207	−0.804918
$279$	−6.26059	−0.374812
$280$	2.24607	0.134228
$281$	26.3388	1.57124	0.785621	−	0.618708i	$-0.212344\pi$
$281$	26.3388	1.57124	0.785621	+	0.618708i	$0.212344\pi$
$282$	−0.575017	−0.0342417
$283$	17.7602	1.05574	0.527868	−	0.849326i	$-0.322991\pi$
$283$	17.7602	1.05574	0.527868	+	0.849326i	$0.322991\pi$
$284$	−5.90186	−0.350211
$285$	0.709321	0.0420166
$286$	0	0
$287$	−4.27146	−0.252136
$288$	2.88187	0.169816
$289$	31.2830	1.84018
$290$	−8.30219	−0.487521
$291$	−4.50414	−0.264037
$292$	2.20839	0.129237
$293$	3.67595	0.214751	0.107376	−	0.994219i	$-0.465755\pi$
$293$	3.67595	0.214751	0.107376	+	0.994219i	$0.465755\pi$
$294$	−1.99881	−0.116573
$295$	−9.95565	−0.579640
$296$	7.24464	0.421086
$297$	−12.4963	−0.725107
$298$	−2.56792	−0.148756
$299$	0	0
$300$	0.254648	0.0147021
$301$	12.4988	0.720420
$302$	−9.08459	−0.522759
$303$	−2.76898	−0.159074
$304$	−1.00000	−0.0573539
$305$	15.3818	0.880761
$306$	−20.0249	−1.14475
$307$	14.2456	0.813039	0.406519	−	0.913642i	$-0.366742\pi$
$307$	14.2456	0.813039	0.406519	+	0.913642i	$0.366742\pi$
$308$	6.72736	0.383327
$309$	−4.06065	−0.231002
$310$	−4.48333	−0.254636
$311$	−2.30578	−0.130749	−0.0653743	−	0.997861i	$-0.520824\pi$
$311$	−2.30578	−0.130749	−0.0653743	+	0.997861i	$0.520824\pi$
$312$	0	0
$313$	2.28518	0.129166	0.0645831	−	0.997912i	$-0.479428\pi$
$313$	2.28518	0.129166	0.0645831	+	0.997912i	$0.479428\pi$
$314$	−2.02540	−0.114300
$315$	6.47287	0.364705
$316$	−12.6207	−0.709969
$317$	5.84456	0.328263	0.164132	−	0.986438i	$-0.447518\pi$
$317$	5.84456	0.328263	0.164132	+	0.986438i	$0.447518\pi$
$318$	4.10181	0.230018
$319$	−24.8665	−1.39226
$320$	2.06376	0.115368
$321$	−2.07436	−0.115780
$322$	8.22382	0.458296
$323$	6.94860	0.386630
$324$	7.95077	0.441709
$325$	0	0
$326$	15.5321	0.860242
$327$	−0.409048	−0.0226204
$328$	−3.92476	−0.216708
$329$	1.82079	0.100383
$330$	−4.38454	−0.241361
$331$	−27.4737	−1.51009	−0.755045	−	0.655673i	$-0.772385\pi$
$331$	−27.4737	−1.51009	−0.755045	+	0.655673i	$0.772385\pi$
$332$	−10.6791	−0.586089
$333$	20.8781	1.14411
$334$	−17.0948	−0.935384
$335$	12.0484	0.658275
$336$	0.374065	0.0204069
$337$	28.2054	1.53645	0.768224	−	0.640181i	$-0.221141\pi$
$337$	28.2054	1.53645	0.768224	+	0.640181i	$0.221141\pi$
$338$	0	0
$339$	1.93695	0.105201
$340$	−14.3402	−0.777709
$341$	−13.4284	−0.727186
$342$	−2.88187	−0.155834
$343$	13.9476	0.753100
$344$	11.4843	0.619193
$345$	−5.35986	−0.288565
$346$	−6.83216	−0.367299
$347$	30.4046	1.63221	0.816103	−	0.577906i	$-0.196130\pi$
$347$	30.4046	1.63221	0.816103	+	0.577906i	$0.196130\pi$
$348$	−1.38267	−0.0741187
$349$	−0.180030	−0.00963680	−0.00481840	−	0.999988i	$-0.501534\pi$
$349$	−0.180030	−0.00963680	−0.00481840	+	0.999988i	$0.501534\pi$
$350$	−0.806342	−0.0431008
$351$	0	0
$352$	6.18132	0.329466
$353$	−11.5112	−0.612680	−0.306340	−	0.951922i	$-0.599104\pi$
$353$	−11.5112	−0.612680	−0.306340	+	0.951922i	$0.599104\pi$
$354$	−1.65804	−0.0881237
$355$	−12.1800	−0.646448
$356$	−6.19799	−0.328493
$357$	−2.59923	−0.137566
$358$	−5.99659	−0.316930
$359$	−12.4440	−0.656768	−0.328384	−	0.944544i	$-0.606504\pi$
$359$	−12.4440	−0.656768	−0.328384	+	0.944544i	$0.606504\pi$
$360$	5.94748	0.313460
$361$	1.00000	0.0526316
$362$	−21.0552	−1.10664
$363$	−9.35174	−0.490839
$364$	0	0
$365$	4.55760	0.238556
$366$	2.56173	0.133904
$367$	18.0907	0.944329	0.472164	−	0.881510i	$-0.343473\pi$
$367$	18.0907	0.944329	0.472164	+	0.881510i	$0.343473\pi$
$368$	7.55632	0.393900
$369$	−11.3106	−0.588808
$370$	14.9512	0.777276
$371$	−12.9884	−0.674323
$372$	−0.746664	−0.0387127
$373$	34.9139	1.80777	0.903887	−	0.427771i	$-0.140701\pi$
$373$	34.9139	1.80777	0.903887	+	0.427771i	$0.140701\pi$
$374$	−42.9515	−2.22097
$375$	4.07214	0.210284
$376$	1.67300	0.0862785
$377$	0	0
$378$	2.20020	0.113166
$379$	−9.05428	−0.465087	−0.232544	−	0.972586i	$-0.574705\pi$
$379$	−9.05428	−0.465087	−0.232544	+	0.972586i	$0.574705\pi$
$380$	−2.06376	−0.105869
$381$	−5.01133	−0.256738
$382$	1.31552	0.0673076
$383$	−22.2814	−1.13853	−0.569264	−	0.822155i	$-0.692772\pi$
$383$	−22.2814	−1.13853	−0.569264	+	0.822155i	$0.692772\pi$
$384$	0.343703	0.0175395
$385$	13.8837	0.707577
$386$	20.4269	1.03970
$387$	33.0963	1.68238
$388$	13.1047	0.665291
$389$	5.51389	0.279565	0.139783	−	0.990182i	$-0.455360\pi$
$389$	5.51389	0.279565	0.139783	+	0.990182i	$0.455360\pi$
$390$	0	0
$391$	−52.5058	−2.65533
$392$	5.81552	0.293728
$393$	0.192250	0.00969771
$394$	17.6032	0.886836
$395$	−26.0461	−1.31052
$396$	17.8138	0.895175
$397$	−22.1371	−1.11103	−0.555514	−	0.831507i	$-0.687478\pi$
$397$	−22.1371	−1.11103	−0.555514	+	0.831507i	$0.687478\pi$
$398$	−14.1150	−0.707521
$399$	−0.374065	−0.0187267
$400$	−0.740893	−0.0370447
$401$	−10.0446	−0.501603	−0.250802	−	0.968039i	$-0.580694\pi$
$401$	−10.0446	−0.501603	−0.250802	+	0.968039i	$0.580694\pi$
$402$	2.00657	0.100079
$403$	0	0
$404$	8.05630	0.400816
$405$	16.4085	0.815344
$406$	4.37821	0.217287
$407$	44.7814	2.21973
$408$	−2.38826	−0.118236
$409$	22.5601	1.11553	0.557763	−	0.830001i	$-0.311660\pi$
$409$	22.5601	1.11553	0.557763	+	0.830001i	$0.311660\pi$
$410$	−8.09976	−0.400018
$411$	1.51242	0.0746020
$412$	11.8144	0.582054
$413$	5.25018	0.258344
$414$	21.7763	1.07025
$415$	−22.0390	−1.08185
$416$	0	0
$417$	−4.61273	−0.225886
$418$	−6.18132	−0.302338
$419$	−9.56888	−0.467470	−0.233735	−	0.972300i	$-0.575095\pi$
$419$	−9.56888	−0.467470	−0.233735	+	0.972300i	$0.575095\pi$
$420$	0.771981	0.0376688
$421$	−21.9026	−1.06747	−0.533734	−	0.845653i	$-0.679212\pi$
$421$	−21.9026	−1.06747	−0.533734	+	0.845653i	$0.679212\pi$
$422$	0.991337	0.0482575
$423$	4.82137	0.234423
$424$	−11.9342	−0.579574
$425$	5.14817	0.249723
$426$	−2.02849	−0.0982806
$427$	−8.11171	−0.392553
$428$	6.03533	0.291729
$429$	0	0
$430$	23.7009	1.14296
$431$	−21.1703	−1.01974	−0.509868	−	0.860253i	$-0.670306\pi$
$431$	−21.1703	−1.01974	−0.509868	+	0.860253i	$0.670306\pi$
$432$	2.02162	0.0972651
$433$	−14.1212	−0.678623	−0.339311	−	0.940674i	$-0.610194\pi$
$433$	−14.1212	−0.678623	−0.339311	+	0.940674i	$0.610194\pi$
$434$	2.36431	0.113491
$435$	−2.85349	−0.136814
$436$	1.19012	0.0569964
$437$	−7.55632	−0.361468
$438$	0.759033	0.0362680
$439$	−29.3753	−1.40200	−0.701002	−	0.713159i	$-0.747264\pi$
$439$	−29.3753	−1.40200	−0.701002	+	0.713159i	$0.747264\pi$
$440$	12.7568	0.608155
$441$	16.7596	0.798075
$442$	0	0
$443$	−10.8465	−0.515333	−0.257666	−	0.966234i	$-0.582954\pi$
$443$	−10.8465	−0.515333	−0.257666	+	0.966234i	$0.582954\pi$
$444$	2.49001	0.118170
$445$	−12.7912	−0.606360
$446$	15.6032	0.738832
$447$	−0.882603	−0.0417457
$448$	−1.08834	−0.0514191
$449$	36.1004	1.70368	0.851841	−	0.523800i	$-0.175486\pi$
$449$	36.1004	1.70368	0.851841	+	0.523800i	$0.175486\pi$
$450$	−2.13516	−0.100652
$451$	−24.2602	−1.14237
$452$	−5.63553	−0.265073
$453$	−3.12240	−0.146703
$454$	−19.2538	−0.903624
$455$	0	0
$456$	−0.343703	−0.0160954
$457$	17.8993	0.837294	0.418647	−	0.908149i	$-0.362505\pi$
$457$	17.8993	0.837294	0.418647	+	0.908149i	$0.362505\pi$
$458$	10.1986	0.476548
$459$	−14.0474	−0.655677
$460$	15.5944	0.727094
$461$	19.4425	0.905527	0.452764	−	0.891631i	$-0.350438\pi$
$461$	19.4425	0.905527	0.452764	+	0.891631i	$0.350438\pi$
$462$	2.31222	0.107574
$463$	−5.76923	−0.268119	−0.134059	−	0.990973i	$-0.542801\pi$
$463$	−5.76923	−0.268119	−0.134059	+	0.990973i	$0.542801\pi$
$464$	4.02284	0.186756
$465$	−1.54094	−0.0714592
$466$	−5.49002	−0.254320
$467$	−26.7574	−1.23819	−0.619093	−	0.785317i	$-0.712500\pi$
$467$	−26.7574	−1.23819	−0.619093	+	0.785317i	$0.712500\pi$
$468$	0	0
$469$	−6.35381	−0.293392
$470$	3.45268	0.159260
$471$	−0.696138	−0.0320763
$472$	4.82403	0.222044
$473$	70.9883	3.26405
$474$	−4.33777	−0.199241
$475$	0.740893	0.0339945
$476$	7.56242	0.346623
$477$	−34.3926	−1.57473
$478$	−12.3377	−0.564314
$479$	−11.7216	−0.535574	−0.267787	−	0.963478i	$-0.586292\pi$
$479$	−11.7216	−0.535574	−0.267787	+	0.963478i	$0.586292\pi$
$480$	0.709321	0.0323759
$481$	0	0
$482$	−16.0413	−0.730660
$483$	2.82656	0.128613
$484$	27.2087	1.23676
$485$	27.0450	1.22805
$486$	8.79756	0.399065
$487$	29.7172	1.34661	0.673307	−	0.739363i	$-0.264873\pi$
$487$	29.7172	1.34661	0.673307	+	0.739363i	$0.264873\pi$
$488$	−7.45330	−0.337395
$489$	5.33843	0.241412
$490$	12.0018	0.542188
$491$	4.42307	0.199611	0.0998053	−	0.995007i	$-0.468178\pi$
$491$	4.42307	0.199611	0.0998053	+	0.995007i	$0.468178\pi$
$492$	−1.34895	−0.0608155
$493$	−27.9531	−1.25895
$494$	0	0
$495$	36.7633	1.65239
$496$	2.17241	0.0975440
$497$	6.42321	0.288120
$498$	−3.67043	−0.164476
$499$	−28.6830	−1.28403	−0.642015	−	0.766692i	$-0.721901\pi$
$499$	−28.6830	−1.28403	−0.642015	+	0.766692i	$0.721901\pi$
$500$	−11.8478	−0.529851
$501$	−5.87553	−0.262499
$502$	20.9424	0.934707
$503$	6.76474	0.301625	0.150813	−	0.988562i	$-0.451811\pi$
$503$	6.76474	0.301625	0.150813	+	0.988562i	$0.451811\pi$
$504$	−3.13644	−0.139708
$505$	16.6263	0.739859
$506$	46.7080	2.07643
$507$	0	0
$508$	14.5804	0.646900
$509$	−2.48903	−0.110324	−0.0551622	−	0.998477i	$-0.517568\pi$
$509$	−2.48903	−0.110324	−0.0551622	+	0.998477i	$0.517568\pi$
$510$	−4.92879	−0.218250
$511$	−2.40348	−0.106324
$512$	−1.00000	−0.0441942
$513$	−2.02162	−0.0892566
$514$	26.7317	1.17909
$515$	24.3821	1.07440
$516$	3.94720	0.173766
$517$	10.3414	0.454813
$518$	−7.88461	−0.346430
$519$	−2.34824	−0.103076
$520$	0	0
$521$	−10.7042	−0.468958	−0.234479	−	0.972121i	$-0.575338\pi$
$521$	−10.7042	−0.468958	−0.234479	+	0.972121i	$0.575338\pi$
$522$	11.5933	0.507425
$523$	−21.0134	−0.918852	−0.459426	−	0.888216i	$-0.651945\pi$
$523$	−21.0134	−0.918852	−0.459426	+	0.888216i	$0.651945\pi$
$524$	−0.559347	−0.0244352
$525$	−0.277143	−0.0120955
$526$	28.4672	1.24123
$527$	−15.0952	−0.657557
$528$	2.12454	0.0924588
$529$	34.0979	1.48252
$530$	−24.6292	−1.06983
$531$	13.9022	0.603305
$532$	1.08834	0.0471854
$533$	0	0
$534$	−2.13027	−0.0921859
$535$	12.4555	0.538497
$536$	−5.83809	−0.252167
$537$	−2.06105	−0.0889408
$538$	−12.5621	−0.541591
$539$	35.9476	1.54837
$540$	4.17214	0.179540
$541$	−10.4885	−0.450938	−0.225469	−	0.974250i	$-0.572391\pi$
$541$	−10.4885	−0.450938	−0.225469	+	0.974250i	$0.572391\pi$
$542$	1.52953	0.0656989
$543$	−7.23676	−0.310559
$544$	6.94860	0.297919
$545$	2.45612	0.105209
$546$	0	0
$547$	3.21744	0.137568	0.0687840	−	0.997632i	$-0.478088\pi$
$547$	3.21744	0.137568	0.0687840	+	0.997632i	$0.478088\pi$
$548$	−4.40035	−0.187974
$549$	−21.4794	−0.916720
$550$	−4.57970	−0.195279
$551$	−4.02284	−0.171379
$552$	2.59713	0.110541
$553$	13.7356	0.584096
$554$	−31.6025	−1.34266
$555$	5.13878	0.218129
$556$	13.4207	0.569163
$557$	41.1486	1.74352	0.871762	−	0.489930i	$-0.162978\pi$
$557$	41.1486	1.74352	0.871762	+	0.489930i	$0.162978\pi$
$558$	6.26059	0.265032
$559$	0	0
$560$	−2.24607	−0.0949137
$561$	−14.7626	−0.623277
$562$	−26.3388	−1.11104
$563$	−5.76418	−0.242931	−0.121466	−	0.992596i	$-0.538759\pi$
$563$	−5.76418	−0.242931	−0.121466	+	0.992596i	$0.538759\pi$
$564$	0.575017	0.0242126
$565$	−11.6304	−0.489294
$566$	−17.7602	−0.746518
$567$	−8.65312	−0.363397
$568$	5.90186	0.247636
$569$	−19.1835	−0.804214	−0.402107	−	0.915593i	$-0.631722\pi$
$569$	−19.1835	−0.804214	−0.402107	+	0.915593i	$0.631722\pi$
$570$	−0.709321	−0.0297102
$571$	28.6524	1.19907	0.599533	−	0.800350i	$-0.295353\pi$
$571$	28.6524	1.19907	0.599533	+	0.800350i	$0.295353\pi$
$572$	0	0
$573$	0.452147	0.0188887
$574$	4.27146	0.178287
$575$	−5.59842	−0.233470
$576$	−2.88187	−0.120078
$577$	44.8182	1.86581	0.932904	−	0.360126i	$-0.117266\pi$
$577$	44.8182	1.86581	0.932904	+	0.360126i	$0.117266\pi$
$578$	−31.2830	−1.30120
$579$	7.02078	0.291774
$580$	8.30219	0.344730
$581$	11.6224	0.482179
$582$	4.50414	0.186702
$583$	−73.7688	−3.05519
$584$	−2.20839	−0.0913840
$585$	0	0
$586$	−3.67595	−0.151852
$587$	16.5113	0.681496	0.340748	−	0.940155i	$-0.389320\pi$
$587$	16.5113	0.681496	0.340748	+	0.940155i	$0.389320\pi$
$588$	1.99881	0.0824297
$589$	−2.17241	−0.0895125
$590$	9.95565	0.409868
$591$	6.05027	0.248875
$592$	−7.24464	−0.297753
$593$	15.5703	0.639397	0.319698	−	0.947519i	$-0.396418\pi$
$593$	15.5703	0.639397	0.319698	+	0.947519i	$0.396418\pi$
$594$	12.4963	0.512728
$595$	15.6070	0.639825
$596$	2.56792	0.105186
$597$	−4.85138	−0.198554
$598$	0	0
$599$	−3.77618	−0.154290	−0.0771452	−	0.997020i	$-0.524581\pi$
$599$	−3.77618	−0.154290	−0.0771452	+	0.997020i	$0.524581\pi$
$600$	−0.254648	−0.0103959
$601$	33.2655	1.35693	0.678465	−	0.734633i	$-0.262646\pi$
$601$	33.2655	1.35693	0.678465	+	0.734633i	$0.262646\pi$
$602$	−12.4988	−0.509414
$603$	−16.8246	−0.685150
$604$	9.08459	0.369647
$605$	56.1523	2.28292
$606$	2.76898	0.112482
$607$	−16.1074	−0.653780	−0.326890	−	0.945062i	$-0.606001\pi$
$607$	−16.1074	−0.653780	−0.326890	+	0.945062i	$0.606001\pi$
$608$	1.00000	0.0405554
$609$	1.50481	0.0609778
$610$	−15.3818	−0.622792
$611$	0	0
$612$	20.0249	0.809460
$613$	40.5410	1.63744	0.818718	−	0.574195i	$-0.194685\pi$
$613$	40.5410	1.63744	0.818718	+	0.574195i	$0.194685\pi$
$614$	−14.2456	−0.574905
$615$	−2.78391	−0.112258
$616$	−6.72736	−0.271053
$617$	9.42421	0.379404	0.189702	−	0.981842i	$-0.439248\pi$
$617$	9.42421	0.379404	0.189702	+	0.981842i	$0.439248\pi$
$618$	4.06065	0.163343
$619$	22.5851	0.907773	0.453887	−	0.891059i	$-0.350037\pi$
$619$	22.5851	0.907773	0.453887	+	0.891059i	$0.350037\pi$
$620$	4.48333	0.180055
$621$	15.2760	0.613004
$622$	2.30578	0.0924532
$623$	6.74551	0.270253
$624$	0	0
$625$	−20.7466	−0.829864
$626$	−2.28518	−0.0913343
$627$	−2.12454	−0.0848460
$628$	2.02540	0.0808224
$629$	50.3401	2.00719
$630$	−6.47287	−0.257885
$631$	25.9440	1.03282	0.516408	−	0.856343i	$-0.327269\pi$
$631$	25.9440	1.03282	0.516408	+	0.856343i	$0.327269\pi$
$632$	12.6207	0.502024
$633$	0.340726	0.0135426
$634$	−5.84456	−0.232117
$635$	30.0904	1.19410
$636$	−4.10181	−0.162647
$637$	0	0
$638$	24.8665	0.984474
$639$	17.0084	0.672841
$640$	−2.06376	−0.0815773
$641$	−15.9405	−0.629611	−0.314805	−	0.949156i	$-0.601939\pi$
$641$	−15.9405	−0.629611	−0.314805	+	0.949156i	$0.601939\pi$
$642$	2.07436	0.0818686
$643$	−9.15968	−0.361223	−0.180611	−	0.983555i	$-0.557808\pi$
$643$	−9.15968	−0.361223	−0.180611	+	0.983555i	$0.557808\pi$
$644$	−8.22382	−0.324064
$645$	8.14608	0.320752
$646$	−6.94860	−0.273389
$647$	−17.3786	−0.683223	−0.341611	−	0.939841i	$-0.610973\pi$
$647$	−17.3786	−0.683223	−0.341611	+	0.939841i	$0.610973\pi$
$648$	−7.95077	−0.312336
$649$	29.8189	1.17049
$650$	0	0
$651$	0.812622	0.0318492
$652$	−15.5321	−0.608283
$653$	0.290149	0.0113544	0.00567720	−	0.999984i	$-0.498193\pi$
$653$	0.290149	0.0113544	0.00567720	+	0.999984i	$0.498193\pi$
$654$	0.409048	0.0159951
$655$	−1.15436	−0.0451045
$656$	3.92476	0.153236
$657$	−6.36430	−0.248295
$658$	−1.82079	−0.0709818
$659$	18.4565	0.718963	0.359482	−	0.933152i	$-0.382954\pi$
$659$	18.4565	0.718963	0.359482	+	0.933152i	$0.382954\pi$
$660$	4.38454	0.170668
$661$	−4.18652	−0.162837	−0.0814183	−	0.996680i	$-0.525945\pi$
$661$	−4.18652	−0.162837	−0.0814183	+	0.996680i	$0.525945\pi$
$662$	27.4737	1.06780
$663$	0	0
$664$	10.6791	0.414428
$665$	2.24607	0.0870988
$666$	−20.8781	−0.809009
$667$	30.3979	1.17701
$668$	17.0948	0.661416
$669$	5.36287	0.207341
$670$	−12.0484	−0.465471
$671$	−46.0713	−1.77856
$672$	−0.374065	−0.0144299
$673$	3.56241	0.137321	0.0686605	−	0.997640i	$-0.478127\pi$
$673$	3.56241	0.137321	0.0686605	+	0.997640i	$0.478127\pi$
$674$	−28.2054	−1.08643
$675$	−1.49780	−0.0576505
$676$	0	0
$677$	−8.93634	−0.343451	−0.171726	−	0.985145i	$-0.554934\pi$
$677$	−8.93634	−0.343451	−0.171726	+	0.985145i	$0.554934\pi$
$678$	−1.93695	−0.0743881
$679$	−14.2624	−0.547339
$680$	14.3402	0.549923
$681$	−6.61759	−0.253587
$682$	13.4284	0.514198
$683$	−11.7173	−0.448351	−0.224175	−	0.974549i	$-0.571969\pi$
$683$	−11.7173	−0.448351	−0.224175	+	0.974549i	$0.571969\pi$
$684$	2.88187	0.110191
$685$	−9.08127	−0.346978
$686$	−13.9476	−0.532522
$687$	3.50528	0.133735
$688$	−11.4843	−0.437836
$689$	0	0
$690$	5.35986	0.204046
$691$	43.8379	1.66767	0.833836	−	0.552013i	$-0.186140\pi$
$691$	43.8379	1.66767	0.833836	+	0.552013i	$0.186140\pi$
$692$	6.83216	0.259720
$693$	−19.3874	−0.736466
$694$	−30.4046	−1.15414
$695$	27.6970	1.05061
$696$	1.38267	0.0524098
$697$	−27.2715	−1.03298
$698$	0.180030	0.00681425
$699$	−1.88694	−0.0713706
$700$	0.806342	0.0304769
$701$	−45.7788	−1.72904	−0.864522	−	0.502596i	$-0.832378\pi$
$701$	−45.7788	−1.72904	−0.864522	+	0.502596i	$0.832378\pi$
$702$	0	0
$703$	7.24464	0.273237
$704$	−6.18132	−0.232967
$705$	1.18670	0.0446936
$706$	11.5112	0.433230
$707$	−8.76797	−0.329754
$708$	1.65804	0.0623129
$709$	15.7482	0.591436	0.295718	−	0.955275i	$-0.404441\pi$
$709$	15.7482	0.591436	0.295718	+	0.955275i	$0.404441\pi$
$710$	12.1800	0.457108
$711$	36.3712	1.36402
$712$	6.19799	0.232280
$713$	16.4154	0.614762
$714$	2.59923	0.0972737
$715$	0	0
$716$	5.99659	0.224103
$717$	−4.24052	−0.158365
$718$	12.4440	0.464405
$719$	9.33636	0.348187	0.174094	−	0.984729i	$-0.444300\pi$
$719$	9.33636	0.348187	0.174094	+	0.984729i	$0.444300\pi$
$720$	−5.94748	−0.221650
$721$	−12.8581	−0.478859
$722$	−1.00000	−0.0372161
$723$	−5.51344	−0.205047
$724$	21.0552	0.782512
$725$	−2.98050	−0.110693
$726$	9.35174	0.347076
$727$	−11.9950	−0.444870	−0.222435	−	0.974948i	$-0.571401\pi$
$727$	−11.9950	−0.444870	−0.222435	+	0.974948i	$0.571401\pi$
$728$	0	0
$729$	−20.8285	−0.771428
$730$	−4.55760	−0.168684
$731$	79.7999	2.95151
$732$	−2.56173	−0.0946841
$733$	−7.72140	−0.285196	−0.142598	−	0.989781i	$-0.545546\pi$
$733$	−7.72140	−0.285196	−0.142598	+	0.989781i	$0.545546\pi$
$734$	−18.0907	−0.667741
$735$	4.12507	0.152156
$736$	−7.55632	−0.278530
$737$	−36.0871	−1.32929
$738$	11.3106	0.416350
$739$	−3.62268	−0.133262	−0.0666312	−	0.997778i	$-0.521225\pi$
$739$	−3.62268	−0.133262	−0.0666312	+	0.997778i	$0.521225\pi$
$740$	−14.9512	−0.549617
$741$	0	0
$742$	12.9884	0.476819
$743$	−37.8661	−1.38917	−0.694586	−	0.719410i	$-0.744412\pi$
$743$	−37.8661	−1.38917	−0.694586	+	0.719410i	$0.744412\pi$
$744$	0.746664	0.0273740
$745$	5.29957	0.194161
$746$	−34.9139	−1.27829
$747$	30.7756	1.12602
$748$	42.9515	1.57046
$749$	−6.56847	−0.240007
$750$	−4.07214	−0.148693
$751$	−19.5455	−0.713225	−0.356612	−	0.934252i	$-0.616068\pi$
$751$	−19.5455	−0.713225	−0.356612	+	0.934252i	$0.616068\pi$
$752$	−1.67300	−0.0610081
$753$	7.19799	0.262309
$754$	0	0
$755$	18.7484	0.682324
$756$	−2.20020	−0.0800206
$757$	−13.5298	−0.491749	−0.245875	−	0.969302i	$-0.579075\pi$
$757$	−13.5298	−0.491749	−0.245875	+	0.969302i	$0.579075\pi$
$758$	9.05428	0.328866
$759$	16.0537	0.582713
$760$	2.06376	0.0748605
$761$	−0.109610	−0.00397335	−0.00198667	−	0.999998i	$-0.500632\pi$
$761$	−0.109610	−0.00397335	−0.00198667	+	0.999998i	$0.500632\pi$
$762$	5.01133	0.181541
$763$	−1.29525	−0.0468913
$764$	−1.31552	−0.0475937
$765$	41.3267	1.49417
$766$	22.2814	0.805061
$767$	0	0
$768$	−0.343703	−0.0124023
$769$	7.55757	0.272533	0.136267	−	0.990672i	$-0.456490\pi$
$769$	7.55757	0.272533	0.136267	+	0.990672i	$0.456490\pi$
$770$	−13.8837	−0.500333
$771$	9.18779	0.330890
$772$	−20.4269	−0.735179
$773$	−46.7535	−1.68161	−0.840803	−	0.541341i	$-0.817917\pi$
$773$	−46.7535	−1.68161	−0.840803	+	0.541341i	$0.817917\pi$
$774$	−33.0963	−1.18962
$775$	−1.60952	−0.0578158
$776$	−13.1047	−0.470432
$777$	−2.70997	−0.0972195
$778$	−5.51389	−0.197683
$779$	−3.92476	−0.140619
$780$	0	0
$781$	36.4813	1.30540
$782$	52.5058	1.87760
$783$	8.13266	0.290637
$784$	−5.81552	−0.207697
$785$	4.17995	0.149189
$786$	−0.192250	−0.00685731
$787$	8.92346	0.318087	0.159043	−	0.987272i	$-0.449159\pi$
$787$	8.92346	0.318087	0.159043	+	0.987272i	$0.449159\pi$
$788$	−17.6032	−0.627088
$789$	9.78426	0.348329
$790$	26.0461	0.926678
$791$	6.13336	0.218077
$792$	−17.8138	−0.632984
$793$	0	0
$794$	22.1371	0.785615
$795$	−8.46515	−0.300228
$796$	14.1150	0.500293
$797$	−33.0477	−1.17061	−0.585304	−	0.810814i	$-0.699025\pi$
$797$	−33.0477	−1.17061	−0.585304	+	0.810814i	$0.699025\pi$
$798$	0.374065	0.0132418
$799$	11.6250	0.411264
$800$	0.740893	0.0261945
$801$	17.8618	0.631116
$802$	10.0446	0.354687
$803$	−13.6508	−0.481726
$804$	−2.00657	−0.0707663
$805$	−16.9720	−0.598184
$806$	0	0
$807$	−4.31764	−0.151988
$808$	−8.05630	−0.283420
$809$	3.68593	0.129590	0.0647951	−	0.997899i	$-0.479361\pi$
$809$	3.68593	0.129590	0.0647951	+	0.997899i	$0.479361\pi$
$810$	−16.4085	−0.576535
$811$	11.0617	0.388430	0.194215	−	0.980959i	$-0.437784\pi$
$811$	11.0617	0.388430	0.194215	+	0.980959i	$0.437784\pi$
$812$	−4.37821	−0.153645
$813$	0.525704	0.0184373
$814$	−44.7814	−1.56959
$815$	−32.0545	−1.12282
$816$	2.38826	0.0836057
$817$	11.4843	0.401786
$818$	−22.5601	−0.788795
$819$	0	0
$820$	8.09976	0.282856
$821$	6.27438	0.218977	0.109489	−	0.993988i	$-0.465079\pi$
$821$	6.27438	0.218977	0.109489	+	0.993988i	$0.465079\pi$
$822$	−1.51242	−0.0527516
$823$	−15.8794	−0.553522	−0.276761	−	0.960939i	$-0.589261\pi$
$823$	−15.8794	−0.553522	−0.276761	+	0.960939i	$0.589261\pi$
$824$	−11.8144	−0.411574
$825$	−1.57406	−0.0548017
$826$	−5.25018	−0.182677
$827$	−39.4637	−1.37229	−0.686144	−	0.727466i	$-0.740698\pi$
$827$	−39.4637	−1.37229	−0.686144	+	0.727466i	$0.740698\pi$
$828$	−21.7763	−0.756779
$829$	−12.0240	−0.417609	−0.208805	−	0.977957i	$-0.566957\pi$
$829$	−12.0240	−0.417609	−0.208805	+	0.977957i	$0.566957\pi$
$830$	22.0390	0.764985
$831$	−10.8619	−0.376794
$832$	0	0
$833$	40.4097	1.40011
$834$	4.61273	0.159726
$835$	35.2795	1.22090
$836$	6.18132	0.213786
$837$	4.39178	0.151802
$838$	9.56888	0.330552
$839$	14.8596	0.513010	0.256505	−	0.966543i	$-0.417429\pi$
$839$	14.8596	0.513010	0.256505	+	0.966543i	$0.417429\pi$
$840$	−0.771981	−0.0266359
$841$	−12.8167	−0.441956
$842$	21.9026	0.754814
$843$	−9.05274	−0.311793
$844$	−0.991337	−0.0341232
$845$	0	0
$846$	−4.82137	−0.165762
$847$	−29.6123	−1.01749
$848$	11.9342	0.409820
$849$	−6.10425	−0.209497
$850$	−5.14817	−0.176581
$851$	−54.7428	−1.87656
$852$	2.02849	0.0694949
$853$	18.3290	0.627574	0.313787	−	0.949493i	$-0.398402\pi$
$853$	18.3290	0.627574	0.313787	+	0.949493i	$0.398402\pi$
$854$	8.11171	0.277577
$855$	5.94748	0.203400
$856$	−6.03533	−0.206283
$857$	57.0425	1.94853	0.974267	−	0.225398i	$-0.0723682\pi$
$857$	57.0425	1.94853	0.974267	+	0.225398i	$0.0723682\pi$
$858$	0	0
$859$	−20.1190	−0.686453	−0.343226	−	0.939253i	$-0.611520\pi$
$859$	−20.1190	−0.686453	−0.343226	+	0.939253i	$0.611520\pi$
$860$	−23.7009	−0.808194
$861$	1.46811	0.0500332
$862$	21.1703	0.721062
$863$	14.2086	0.483667	0.241833	−	0.970318i	$-0.422251\pi$
$863$	14.2086	0.483667	0.241833	+	0.970318i	$0.422251\pi$
$864$	−2.02162	−0.0687768
$865$	14.0999	0.479412
$866$	14.1212	0.479859
$867$	−10.7521	−0.365160
$868$	−2.36431	−0.0802500
$869$	78.0125	2.64639
$870$	2.85349	0.0967424
$871$	0	0
$872$	−1.19012	−0.0403026
$873$	−37.7661	−1.27819
$874$	7.55632	0.255596
$875$	12.8944	0.435911
$876$	−0.759033	−0.0256453
$877$	−12.3271	−0.416255	−0.208127	−	0.978102i	$-0.566737\pi$
$877$	−12.3271	−0.416255	−0.208127	+	0.978102i	$0.566737\pi$
$878$	29.3753	0.991367
$879$	−1.26343	−0.0426146
$880$	−12.7568	−0.430031
$881$	8.81144	0.296865	0.148433	−	0.988923i	$-0.452577\pi$
$881$	8.81144	0.296865	0.148433	+	0.988923i	$0.452577\pi$
$882$	−16.7596	−0.564324
$883$	15.8887	0.534696	0.267348	−	0.963600i	$-0.413853\pi$
$883$	15.8887	0.534696	0.267348	+	0.963600i	$0.413853\pi$
$884$	0	0
$885$	3.42179	0.115022
$886$	10.8465	0.364395
$887$	10.8059	0.362827	0.181413	−	0.983407i	$-0.441933\pi$
$887$	10.8059	0.362827	0.181413	+	0.983407i	$0.441933\pi$
$888$	−2.49001	−0.0835592
$889$	−15.8684	−0.532209
$890$	12.7912	0.428761
$891$	−49.1463	−1.64646
$892$	−15.6032	−0.522433
$893$	1.67300	0.0559849
$894$	0.882603	0.0295187
$895$	12.3755	0.413668
$896$	1.08834	0.0363588
$897$	0	0
$898$	−36.1004	−1.20469
$899$	8.73926	0.291471
$900$	2.13516	0.0711719
$901$	−82.9256	−2.76265
$902$	24.2602	0.807776
$903$	−4.29589	−0.142958
$904$	5.63553	0.187435
$905$	43.4530	1.44443
$906$	3.12240	0.103735
$907$	25.1694	0.835738	0.417869	−	0.908507i	$-0.362777\pi$
$907$	25.1694	0.835738	0.417869	+	0.908507i	$0.362777\pi$
$908$	19.2538	0.638959
$909$	−23.2172	−0.770066
$910$	0	0
$911$	1.68478	0.0558194	0.0279097	−	0.999610i	$-0.491115\pi$
$911$	1.68478	0.0558194	0.0279097	+	0.999610i	$0.491115\pi$
$912$	0.343703	0.0113812
$913$	66.0107	2.18463
$914$	−17.8993	−0.592056
$915$	−5.28679	−0.174776
$916$	−10.1986	−0.336970
$917$	0.608758	0.0201030
$918$	14.0474	0.463634
$919$	−38.3955	−1.26655	−0.633275	−	0.773927i	$-0.718290\pi$
$919$	−38.3955	−1.26655	−0.633275	+	0.773927i	$0.718290\pi$
$920$	−15.5944	−0.514133
$921$	−4.89626	−0.161337
$922$	−19.4425	−0.640304
$923$	0	0
$924$	−2.31222	−0.0760664
$925$	5.36750	0.176482
$926$	5.76923	0.189589
$927$	−34.0476	−1.11827
$928$	−4.02284	−0.132056
$929$	−17.5982	−0.577379	−0.288690	−	0.957423i	$-0.593220\pi$
$929$	−17.5982	−0.577379	−0.288690	+	0.957423i	$0.593220\pi$
$930$	1.54094	0.0505293
$931$	5.81552	0.190596
$932$	5.49002	0.179832
$933$	0.792503	0.0259454
$934$	26.7574	0.875530
$935$	88.6416	2.89889
$936$	0	0
$937$	57.5547	1.88023	0.940115	−	0.340859i	$-0.110718\pi$
$937$	57.5547	1.88023	0.940115	+	0.340859i	$0.110718\pi$
$938$	6.35381	0.207459
$939$	−0.785425	−0.0256314
$940$	−3.45268	−0.112614
$941$	28.6348	0.933466	0.466733	−	0.884398i	$-0.345431\pi$
$941$	28.6348	0.933466	0.466733	+	0.884398i	$0.345431\pi$
$942$	0.696138	0.0226814
$943$	29.6567	0.965755
$944$	−4.82403	−0.157009
$945$	−4.54069	−0.147709
$946$	−70.9883	−2.30803
$947$	20.5615	0.668160	0.334080	−	0.942545i	$-0.391574\pi$
$947$	20.5615	0.668160	0.334080	+	0.942545i	$0.391574\pi$
$948$	4.33777	0.140884
$949$	0	0
$950$	−0.740893	−0.0240378
$951$	−2.00880	−0.0651397
$952$	−7.56242	−0.245099
$953$	−2.10288	−0.0681190	−0.0340595	−	0.999420i	$-0.510844\pi$
$953$	−2.10288	−0.0681190	−0.0340595	+	0.999420i	$0.510844\pi$
$954$	34.3926	1.11350
$955$	−2.71491	−0.0878524
$956$	12.3377	0.399031
$957$	8.54670	0.276276
$958$	11.7216	0.378708
$959$	4.78907	0.154647
$960$	−0.709321	−0.0228933
$961$	−26.2806	−0.847763
$962$	0	0
$963$	−17.3930	−0.560482
$964$	16.0413	0.516655
$965$	−42.1561	−1.35705
$966$	−2.82656	−0.0909429
$967$	−34.5025	−1.10953	−0.554763	−	0.832008i	$-0.687191\pi$
$967$	−34.5025	−1.10953	−0.554763	+	0.832008i	$0.687191\pi$
$968$	−27.2087	−0.874522
$969$	−2.38826	−0.0767219
$970$	−27.0450	−0.868363
$971$	−41.3747	−1.32778	−0.663889	−	0.747831i	$-0.731095\pi$
$971$	−41.3747	−1.32778	−0.663889	+	0.747831i	$0.731095\pi$
$972$	−8.79756	−0.282182
$973$	−14.6062	−0.468254
$974$	−29.7172	−0.952200
$975$	0	0
$976$	7.45330	0.238574
$977$	4.77337	0.152714	0.0763569	−	0.997081i	$-0.475671\pi$
$977$	4.77337	0.152714	0.0763569	+	0.997081i	$0.475671\pi$
$978$	−5.33843	−0.170704
$979$	38.3118	1.22445
$980$	−12.0018	−0.383385
$981$	−3.42977	−0.109504
$982$	−4.42307	−0.141146
$983$	26.5491	0.846786	0.423393	−	0.905946i	$-0.360839\pi$
$983$	26.5491	0.846786	0.423393	+	0.905946i	$0.360839\pi$
$984$	1.34895	0.0430030
$985$	−36.3288	−1.15753
$986$	27.9531	0.890209
$987$	−0.625812	−0.0199198
$988$	0	0
$989$	−86.7792	−2.75942
$990$	−36.7633	−1.16842
$991$	−5.63432	−0.178980	−0.0894901	−	0.995988i	$-0.528524\pi$
$991$	−5.63432	−0.178980	−0.0894901	+	0.995988i	$0.528524\pi$
$992$	−2.17241	−0.0689740
$993$	9.44280	0.299658
$994$	−6.42321	−0.203732
$995$	29.1300	0.923483
$996$	3.67043	0.116302
$997$	48.7600	1.54424	0.772122	−	0.635474i	$-0.219195\pi$
$997$	48.7600	1.54424	0.772122	+	0.635474i	$0.219195\pi$
$998$	28.6830	0.907946
$999$	−14.6459	−0.463375

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6422.2.a.bm.1.6		14
13.2	odd	12		494.2.m.b.381.5	yes	28
13.7	odd	12		494.2.m.b.153.5	✓	28
13.12	even	2		6422.2.a.bn.1.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.m.b.153.5	✓	28	13.7	odd	12
494.2.m.b.381.5	yes	28	13.2	odd	12
6422.2.a.bm.1.6		14	1.1	even	1	trivial
6422.2.a.bn.1.6		14	13.12	even	2

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:	\( N \)	\(=\)	\( 6422 = 2 \cdot 13^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6422.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.343703 q^{3} +1.00000 q^{4} +2.06376 q^{5} +0.343703 q^{6} -1.08834 q^{7} -1.00000 q^{8} -2.88187 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.343703 q^{3} +1.00000 q^{4} +2.06376 q^{5} +0.343703 q^{6} -1.08834 q^{7} -1.00000 q^{8} -2.88187 q^{9} -2.06376 q^{10} -6.18132 q^{11} -0.343703 q^{12} +1.08834 q^{14} -0.709321 q^{15} +1.00000 q^{16} -6.94860 q^{17} +2.88187 q^{18} -1.00000 q^{19} +2.06376 q^{20} +0.374065 q^{21} +6.18132 q^{22} +7.55632 q^{23} +0.343703 q^{24} -0.740893 q^{25} +2.02162 q^{27} -1.08834 q^{28} +4.02284 q^{29} +0.709321 q^{30} +2.17241 q^{31} -1.00000 q^{32} +2.12454 q^{33} +6.94860 q^{34} -2.24607 q^{35} -2.88187 q^{36} -7.24464 q^{37} +1.00000 q^{38} -2.06376 q^{40} +3.92476 q^{41} -0.374065 q^{42} -11.4843 q^{43} -6.18132 q^{44} -5.94748 q^{45} -7.55632 q^{46} -1.67300 q^{47} -0.343703 q^{48} -5.81552 q^{49} +0.740893 q^{50} +2.38826 q^{51} +11.9342 q^{53} -2.02162 q^{54} -12.7568 q^{55} +1.08834 q^{56} +0.343703 q^{57} -4.02284 q^{58} -4.82403 q^{59} -0.709321 q^{60} +7.45330 q^{61} -2.17241 q^{62} +3.13644 q^{63} +1.00000 q^{64} -2.12454 q^{66} +5.83809 q^{67} -6.94860 q^{68} -2.59713 q^{69} +2.24607 q^{70} -5.90186 q^{71} +2.88187 q^{72} +2.20839 q^{73} +7.24464 q^{74} +0.254648 q^{75} -1.00000 q^{76} +6.72736 q^{77} -12.6207 q^{79} +2.06376 q^{80} +7.95077 q^{81} -3.92476 q^{82} -10.6791 q^{83} +0.374065 q^{84} -14.3402 q^{85} +11.4843 q^{86} -1.38267 q^{87} +6.18132 q^{88} -6.19799 q^{89} +5.94748 q^{90} +7.55632 q^{92} -0.746664 q^{93} +1.67300 q^{94} -2.06376 q^{95} +0.343703 q^{96} +13.1047 q^{97} +5.81552 q^{98} +17.8138 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} + 4 q^{3} + 14 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 14 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 + 4 * q^3 + 14 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 14 * q^8 + 18 * q^9	\( 14 q - 14 q^{2} + 4 q^{3} + 14 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 14 q^{8} + 18 q^{9} - 2 q^{10} - 10 q^{11} + 4 q^{12} + 2 q^{14} + 4 q^{15} + 14 q^{16} + 2 q^{17} - 18 q^{18} - 14 q^{19} + 2 q^{20} + 18 q^{21} + 10 q^{22} + 12 q^{23} - 4 q^{24} + 44 q^{25} + 10 q^{27} - 2 q^{28} + 4 q^{29} - 4 q^{30} - 4 q^{31} - 14 q^{32} - 12 q^{33} - 2 q^{34} + 14 q^{35} + 18 q^{36} - 18 q^{37} + 14 q^{38} - 2 q^{40} - 6 q^{41} - 18 q^{42} + 28 q^{43} - 10 q^{44} - 8 q^{45} - 12 q^{46} + 20 q^{47} + 4 q^{48} + 28 q^{49} - 44 q^{50} + 10 q^{51} + 12 q^{53} - 10 q^{54} - 2 q^{55} + 2 q^{56} - 4 q^{57} - 4 q^{58} - 16 q^{59} + 4 q^{60} + 30 q^{61} + 4 q^{62} - 28 q^{63} + 14 q^{64} + 12 q^{66} - 2 q^{67} + 2 q^{68} - 42 q^{69} - 14 q^{70} - 44 q^{71} - 18 q^{72} + 36 q^{73} + 18 q^{74} + 46 q^{75} - 14 q^{76} + 68 q^{77} + 34 q^{79} + 2 q^{80} - 6 q^{81} + 6 q^{82} - 2 q^{83} + 18 q^{84} + 30 q^{85} - 28 q^{86} + 52 q^{87} + 10 q^{88} - 42 q^{89} + 8 q^{90} + 12 q^{92} + 12 q^{93} - 20 q^{94} - 2 q^{95} - 4 q^{96} - 40 q^{97} - 28 q^{98} - 12 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 4 * q^3 + 14 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 14 * q^8 + 18 * q^9 - 2 * q^10 - 10 * q^11 + 4 * q^12 + 2 * q^14 + 4 * q^15 + 14 * q^16 + 2 * q^17 - 18 * q^18 - 14 * q^19 + 2 * q^20 + 18 * q^21 + 10 * q^22 + 12 * q^23 - 4 * q^24 + 44 * q^25 + 10 * q^27 - 2 * q^28 + 4 * q^29 - 4 * q^30 - 4 * q^31 - 14 * q^32 - 12 * q^33 - 2 * q^34 + 14 * q^35 + 18 * q^36 - 18 * q^37 + 14 * q^38 - 2 * q^40 - 6 * q^41 - 18 * q^42 + 28 * q^43 - 10 * q^44 - 8 * q^45 - 12 * q^46 + 20 * q^47 + 4 * q^48 + 28 * q^49 - 44 * q^50 + 10 * q^51 + 12 * q^53 - 10 * q^54 - 2 * q^55 + 2 * q^56 - 4 * q^57 - 4 * q^58 - 16 * q^59 + 4 * q^60 + 30 * q^61 + 4 * q^62 - 28 * q^63 + 14 * q^64 + 12 * q^66 - 2 * q^67 + 2 * q^68 - 42 * q^69 - 14 * q^70 - 44 * q^71 - 18 * q^72 + 36 * q^73 + 18 * q^74 + 46 * q^75 - 14 * q^76 + 68 * q^77 + 34 * q^79 + 2 * q^80 - 6 * q^81 + 6 * q^82 - 2 * q^83 + 18 * q^84 + 30 * q^85 - 28 * q^86 + 52 * q^87 + 10 * q^88 - 42 * q^89 + 8 * q^90 + 12 * q^92 + 12 * q^93 - 20 * q^94 - 2 * q^95 - 4 * q^96 - 40 * q^97 - 28 * q^98 - 12 * q^99

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