LMFDB - Embedded newform 1502.2.a.e.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4x^{10} - 9x^{9} + 58x^{8} - 40x^{7} - 146x^{6} + 237x^{5} - 47x^{4} - 89x^{3} + 39x^{2} - 1 $ x^11 - 4x^10 - 9x^9 + 58x^8 - 40x^7 - 146x^6 + 237x^5 - 47x^4 - 89x^3 + 39*x^2 - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.90813$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.785790 q^{3} +1.00000 q^{4} +1.57015 q^{5} -0.785790 q^{6} -1.48223 q^{7} -1.00000 q^{8} -2.38253 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.785790 q^{3} +1.00000 q^{4} +1.57015 q^{5} -0.785790 q^{6} -1.48223 q^{7} -1.00000 q^{8} -2.38253 q^{9} -1.57015 q^{10} +1.12323 q^{11} +0.785790 q^{12} -1.20114 q^{13} +1.48223 q^{14} +1.23381 q^{15} +1.00000 q^{16} -4.99848 q^{17} +2.38253 q^{18} -0.148967 q^{19} +1.57015 q^{20} -1.16472 q^{21} -1.12323 q^{22} -4.44505 q^{23} -0.785790 q^{24} -2.53463 q^{25} +1.20114 q^{26} -4.22954 q^{27} -1.48223 q^{28} +1.85331 q^{29} -1.23381 q^{30} +1.46107 q^{31} -1.00000 q^{32} +0.882623 q^{33} +4.99848 q^{34} -2.32732 q^{35} -2.38253 q^{36} +0.802290 q^{37} +0.148967 q^{38} -0.943844 q^{39} -1.57015 q^{40} +3.17134 q^{41} +1.16472 q^{42} -8.91837 q^{43} +1.12323 q^{44} -3.74093 q^{45} +4.44505 q^{46} -8.64624 q^{47} +0.785790 q^{48} -4.80299 q^{49} +2.53463 q^{50} -3.92776 q^{51} -1.20114 q^{52} -7.34095 q^{53} +4.22954 q^{54} +1.76364 q^{55} +1.48223 q^{56} -0.117057 q^{57} -1.85331 q^{58} +14.6115 q^{59} +1.23381 q^{60} +0.497909 q^{61} -1.46107 q^{62} +3.53146 q^{63} +1.00000 q^{64} -1.88597 q^{65} -0.882623 q^{66} -11.0619 q^{67} -4.99848 q^{68} -3.49287 q^{69} +2.32732 q^{70} -9.04210 q^{71} +2.38253 q^{72} +9.34359 q^{73} -0.802290 q^{74} -1.99169 q^{75} -0.148967 q^{76} -1.66489 q^{77} +0.943844 q^{78} +0.787071 q^{79} +1.57015 q^{80} +3.82407 q^{81} -3.17134 q^{82} +5.96427 q^{83} -1.16472 q^{84} -7.84836 q^{85} +8.91837 q^{86} +1.45631 q^{87} -1.12323 q^{88} +6.02962 q^{89} +3.74093 q^{90} +1.78037 q^{91} -4.44505 q^{92} +1.14809 q^{93} +8.64624 q^{94} -0.233900 q^{95} -0.785790 q^{96} +12.8889 q^{97} +4.80299 q^{98} -2.67614 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 19 q^{13} + 6 q^{14} + q^{15} + 11 q^{16} - 8 q^{17} - 3 q^{18} - 9 q^{19} + q^{20} - 6 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 2 q^{25} + 19 q^{26} - 16 q^{27} - 6 q^{28} + 13 q^{29} - q^{30} - 19 q^{31} - 11 q^{32} - 37 q^{33} + 8 q^{34} + 3 q^{35} + 3 q^{36} - 29 q^{37} + 9 q^{38} + 8 q^{39} - q^{40} - 23 q^{41} + 6 q^{42} - 13 q^{43} + 4 q^{44} - 6 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 5 q^{49} + 2 q^{50} + 33 q^{51} - 19 q^{52} - 25 q^{53} + 16 q^{54} - 14 q^{55} + 6 q^{56} + 4 q^{57} - 13 q^{58} + 6 q^{59} + q^{60} + 10 q^{61} + 19 q^{62} - 7 q^{63} + 11 q^{64} - 19 q^{65} + 37 q^{66} - 16 q^{67} - 8 q^{68} - 25 q^{69} - 3 q^{70} + 8 q^{71} - 3 q^{72} - 56 q^{73} + 29 q^{74} - 50 q^{75} - 9 q^{76} - 7 q^{77} - 8 q^{78} + 2 q^{79} + q^{80} - 5 q^{81} + 23 q^{82} + 21 q^{83} - 6 q^{84} - 55 q^{85} + 13 q^{86} - 11 q^{87} - 4 q^{88} - 24 q^{89} + 6 q^{90} - 43 q^{91} + 2 q^{92} + 10 q^{93} + 16 q^{94} + 25 q^{95} + 4 q^{96} - 84 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9 - q^10 + 4 * q^11 - 4 * q^12 - 19 * q^13 + 6 * q^14 + q^15 + 11 * q^16 - 8 * q^17 - 3 * q^18 - 9 * q^19 + q^20 - 6 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 2 * q^25 + 19 * q^26 - 16 * q^27 - 6 * q^28 + 13 * q^29 - q^30 - 19 * q^31 - 11 * q^32 - 37 * q^33 + 8 * q^34 + 3 * q^35 + 3 * q^36 - 29 * q^37 + 9 * q^38 + 8 * q^39 - q^40 - 23 * q^41 + 6 * q^42 - 13 * q^43 + 4 * q^44 - 6 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 5 * q^49 + 2 * q^50 + 33 * q^51 - 19 * q^52 - 25 * q^53 + 16 * q^54 - 14 * q^55 + 6 * q^56 + 4 * q^57 - 13 * q^58 + 6 * q^59 + q^60 + 10 * q^61 + 19 * q^62 - 7 * q^63 + 11 * q^64 - 19 * q^65 + 37 * q^66 - 16 * q^67 - 8 * q^68 - 25 * q^69 - 3 * q^70 + 8 * q^71 - 3 * q^72 - 56 * q^73 + 29 * q^74 - 50 * q^75 - 9 * q^76 - 7 * q^77 - 8 * q^78 + 2 * q^79 + q^80 - 5 * q^81 + 23 * q^82 + 21 * q^83 - 6 * q^84 - 55 * q^85 + 13 * q^86 - 11 * q^87 - 4 * q^88 - 24 * q^89 + 6 * q^90 - 43 * q^91 + 2 * q^92 + 10 * q^93 + 16 * q^94 + 25 * q^95 + 4 * q^96 - 84 * q^97 + 5 * q^98 + 14 * 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
$3$	0.785790	0.453676	0.226838	−	0.973933i	$-0.427161\pi$
$3$	0.785790	0.453676	0.226838	+	0.973933i	$0.427161\pi$
$4$	1.00000	0.500000
$5$	1.57015	0.702192	0.351096	−	0.936339i	$-0.385809\pi$
$5$	1.57015	0.702192	0.351096	+	0.936339i	$0.385809\pi$
$6$	−0.785790	−0.320797
$7$	−1.48223	−0.560230	−0.280115	−	0.959966i	$-0.590373\pi$
$7$	−1.48223	−0.560230	−0.280115	+	0.959966i	$0.590373\pi$
$8$	−1.00000	−0.353553
$9$	−2.38253	−0.794178
$10$	−1.57015	−0.496525
$11$	1.12323	0.338667	0.169333	−	0.985559i	$-0.445839\pi$
$11$	1.12323	0.338667	0.169333	+	0.985559i	$0.445839\pi$
$12$	0.785790	0.226838
$13$	−1.20114	−0.333137	−0.166568	−	0.986030i	$-0.553269\pi$
$13$	−1.20114	−0.333137	−0.166568	+	0.986030i	$0.553269\pi$
$14$	1.48223	0.396143
$15$	1.23381	0.318568
$16$	1.00000	0.250000
$17$	−4.99848	−1.21231	−0.606155	−	0.795347i	$-0.707289\pi$
$17$	−4.99848	−1.21231	−0.606155	+	0.795347i	$0.707289\pi$
$18$	2.38253	0.561569
$19$	−0.148967	−0.0341753	−0.0170877	−	0.999854i	$-0.505439\pi$
$19$	−0.148967	−0.0341753	−0.0170877	+	0.999854i	$0.505439\pi$
$20$	1.57015	0.351096
$21$	−1.16472	−0.254163
$22$	−1.12323	−0.239474
$23$	−4.44505	−0.926856	−0.463428	−	0.886134i	$-0.653381\pi$
$23$	−4.44505	−0.926856	−0.463428	+	0.886134i	$0.653381\pi$
$24$	−0.785790	−0.160399
$25$	−2.53463	−0.506926
$26$	1.20114	0.235563
$27$	−4.22954	−0.813975
$28$	−1.48223	−0.280115
$29$	1.85331	0.344151	0.172076	−	0.985084i	$-0.444953\pi$
$29$	1.85331	0.344151	0.172076	+	0.985084i	$0.444953\pi$
$30$	−1.23381	−0.225261
$31$	1.46107	0.262416	0.131208	−	0.991355i	$-0.458114\pi$
$31$	1.46107	0.262416	0.131208	+	0.991355i	$0.458114\pi$
$32$	−1.00000	−0.176777
$33$	0.882623	0.153645
$34$	4.99848	0.857233
$35$	−2.32732	−0.393389
$36$	−2.38253	−0.397089
$37$	0.802290	0.131896	0.0659479	−	0.997823i	$-0.478993\pi$
$37$	0.802290	0.131896	0.0659479	+	0.997823i	$0.478993\pi$
$38$	0.148967	0.0241656
$39$	−0.943844	−0.151136
$40$	−1.57015	−0.248262
$41$	3.17134	0.495280	0.247640	−	0.968852i	$-0.420345\pi$
$41$	3.17134	0.495280	0.247640	+	0.968852i	$0.420345\pi$
$42$	1.16472	0.179720
$43$	−8.91837	−1.36004	−0.680020	−	0.733194i	$-0.738029\pi$
$43$	−8.91837	−1.36004	−0.680020	+	0.733194i	$0.738029\pi$
$44$	1.12323	0.169333
$45$	−3.74093	−0.557665
$46$	4.44505	0.655386
$47$	−8.64624	−1.26118	−0.630592	−	0.776114i	$-0.717188\pi$
$47$	−8.64624	−1.26118	−0.630592	+	0.776114i	$0.717188\pi$
$48$	0.785790	0.113419
$49$	−4.80299	−0.686142
$50$	2.53463	0.358451
$51$	−3.92776	−0.549996
$52$	−1.20114	−0.166568
$53$	−7.34095	−1.00836	−0.504179	−	0.863599i	$-0.668205\pi$
$53$	−7.34095	−1.00836	−0.504179	+	0.863599i	$0.668205\pi$
$54$	4.22954	0.575568
$55$	1.76364	0.237809
$56$	1.48223	0.198071
$57$	−0.117057	−0.0155045
$58$	−1.85331	−0.243352
$59$	14.6115	1.90226	0.951128	−	0.308798i	$-0.0999268\pi$
$59$	14.6115	1.90226	0.951128	+	0.308798i	$0.0999268\pi$
$60$	1.23381	0.159284
$61$	0.497909	0.0637507	0.0318754	−	0.999492i	$-0.489852\pi$
$61$	0.497909	0.0637507	0.0318754	+	0.999492i	$0.489852\pi$
$62$	−1.46107	−0.185556
$63$	3.53146	0.444923
$64$	1.00000	0.125000
$65$	−1.88597	−0.233926
$66$	−0.882623	−0.108643
$67$	−11.0619	−1.35143	−0.675715	−	0.737163i	$-0.736165\pi$
$67$	−11.0619	−1.35143	−0.675715	+	0.737163i	$0.736165\pi$
$68$	−4.99848	−0.606155
$69$	−3.49287	−0.420492
$70$	2.32732	0.278168
$71$	−9.04210	−1.07310	−0.536550	−	0.843869i	$-0.680273\pi$
$71$	−9.04210	−1.07310	−0.536550	+	0.843869i	$0.680273\pi$
$72$	2.38253	0.280784
$73$	9.34359	1.09358	0.546792	−	0.837268i	$-0.315849\pi$
$73$	9.34359	1.09358	0.546792	+	0.837268i	$0.315849\pi$
$74$	−0.802290	−0.0932644
$75$	−1.99169	−0.229980
$76$	−0.148967	−0.0170877
$77$	−1.66489	−0.189731
$78$	0.943844	0.106869
$79$	0.787071	0.0885524	0.0442762	−	0.999019i	$-0.485902\pi$
$79$	0.787071	0.0885524	0.0442762	+	0.999019i	$0.485902\pi$
$80$	1.57015	0.175548
$81$	3.82407	0.424897
$82$	−3.17134	−0.350216
$83$	5.96427	0.654664	0.327332	−	0.944909i	$-0.393851\pi$
$83$	5.96427	0.654664	0.327332	+	0.944909i	$0.393851\pi$
$84$	−1.16472	−0.127081
$85$	−7.84836	−0.851274
$86$	8.91837	0.961693
$87$	1.45631	0.156133
$88$	−1.12323	−0.119737
$89$	6.02962	0.639139	0.319569	−	0.947563i	$-0.396462\pi$
$89$	6.02962	0.639139	0.319569	+	0.947563i	$0.396462\pi$
$90$	3.74093	0.394329
$91$	1.78037	0.186633
$92$	−4.44505	−0.463428
$93$	1.14809	0.119052
$94$	8.64624	0.891792
$95$	−0.233900	−0.0239977
$96$	−0.785790	−0.0801993
$97$	12.8889	1.30867	0.654335	−	0.756204i	$-0.272948\pi$
$97$	12.8889	1.30867	0.654335	+	0.756204i	$0.272948\pi$
$98$	4.80299	0.485176
$99$	−2.67614	−0.268962
$100$	−2.53463	−0.253463
$101$	7.26692	0.723085	0.361543	−	0.932356i	$-0.382250\pi$
$101$	7.26692	0.723085	0.361543	+	0.932356i	$0.382250\pi$
$102$	3.92776	0.388906
$103$	13.4787	1.32810	0.664048	−	0.747690i	$-0.268837\pi$
$103$	13.4787	1.32810	0.664048	+	0.747690i	$0.268837\pi$
$104$	1.20114	0.117782
$105$	−1.82879	−0.178471
$106$	7.34095	0.713016
$107$	3.25270	0.314450	0.157225	−	0.987563i	$-0.449745\pi$
$107$	3.25270	0.314450	0.157225	+	0.987563i	$0.449745\pi$
$108$	−4.22954	−0.406988
$109$	−13.2735	−1.27138	−0.635688	−	0.771946i	$-0.719283\pi$
$109$	−13.2735	−1.27138	−0.635688	+	0.771946i	$0.719283\pi$
$110$	−1.76364	−0.168156
$111$	0.630432	0.0598379
$112$	−1.48223	−0.140058
$113$	−12.1726	−1.14510	−0.572549	−	0.819870i	$-0.694045\pi$
$113$	−12.1726	−1.14510	−0.572549	+	0.819870i	$0.694045\pi$
$114$	0.117057	0.0109634
$115$	−6.97939	−0.650831
$116$	1.85331	0.172076
$117$	2.86176	0.264570
$118$	−14.6115	−1.34510
$119$	7.40890	0.679173
$120$	−1.23381	−0.112631
$121$	−9.73835	−0.885305
$122$	−0.497909	−0.0450786
$123$	2.49201	0.224697
$124$	1.46107	0.131208
$125$	−11.8305	−1.05815
$126$	−3.53146	−0.314608
$127$	6.81461	0.604699	0.302350	−	0.953197i	$-0.402229\pi$
$127$	6.81461	0.604699	0.302350	+	0.953197i	$0.402229\pi$
$128$	−1.00000	−0.0883883
$129$	−7.00797	−0.617017
$130$	1.88597	0.165411
$131$	−6.88715	−0.601733	−0.300867	−	0.953666i	$-0.597276\pi$
$131$	−6.88715	−0.601733	−0.300867	+	0.953666i	$0.597276\pi$
$132$	0.882623	0.0768225
$133$	0.220803	0.0191461
$134$	11.0619	0.955605
$135$	−6.64101	−0.571567
$136$	4.99848	0.428616
$137$	−15.8789	−1.35663	−0.678313	−	0.734773i	$-0.737289\pi$
$137$	−15.8789	−1.35663	−0.678313	+	0.734773i	$0.737289\pi$
$138$	3.49287	0.297333
$139$	−16.8630	−1.43030	−0.715152	−	0.698969i	$-0.753642\pi$
$139$	−16.8630	−1.43030	−0.715152	+	0.698969i	$0.753642\pi$
$140$	−2.32732	−0.196695
$141$	−6.79413	−0.572169
$142$	9.04210	0.758796
$143$	−1.34916	−0.112822
$144$	−2.38253	−0.198545
$145$	2.90998	0.241660
$146$	−9.34359	−0.773281
$147$	−3.77414	−0.311286
$148$	0.802290	0.0659479
$149$	10.4664	0.857444	0.428722	−	0.903437i	$-0.358964\pi$
$149$	10.4664	0.857444	0.428722	+	0.903437i	$0.358964\pi$
$150$	1.99169	0.162621
$151$	−11.6911	−0.951410	−0.475705	−	0.879605i	$-0.657807\pi$
$151$	−11.6911	−0.951410	−0.475705	+	0.879605i	$0.657807\pi$
$152$	0.148967	0.0120828
$153$	11.9091	0.962790
$154$	1.66489	0.134160
$155$	2.29410	0.184266
$156$	−0.943844	−0.0755680
$157$	−21.5212	−1.71758	−0.858791	−	0.512326i	$-0.828784\pi$
$157$	−21.5212	−1.71758	−0.858791	+	0.512326i	$0.828784\pi$
$158$	−0.787071	−0.0626160
$159$	−5.76844	−0.457467
$160$	−1.57015	−0.124131
$161$	6.58858	0.519253
$162$	−3.82407	−0.300448
$163$	19.6349	1.53793	0.768963	−	0.639293i	$-0.220773\pi$
$163$	19.6349	1.53793	0.768963	+	0.639293i	$0.220773\pi$
$164$	3.17134	0.247640
$165$	1.38585	0.107888
$166$	−5.96427	−0.462917
$167$	2.68307	0.207622	0.103811	−	0.994597i	$-0.466896\pi$
$167$	2.68307	0.207622	0.103811	+	0.994597i	$0.466896\pi$
$168$	1.16472	0.0898602
$169$	−11.5573	−0.889020
$170$	7.84836	0.601942
$171$	0.354919	0.0271413
$172$	−8.91837	−0.680020
$173$	−25.7024	−1.95412	−0.977060	−	0.212963i	$-0.931689\pi$
$173$	−25.7024	−1.95412	−0.977060	+	0.212963i	$0.931689\pi$
$174$	−1.45631	−0.110403
$175$	3.75691	0.283996
$176$	1.12323	0.0846667
$177$	11.4816	0.863007
$178$	−6.02962	−0.451939
$179$	20.2662	1.51477	0.757384	−	0.652970i	$-0.226477\pi$
$179$	20.2662	1.51477	0.757384	+	0.652970i	$0.226477\pi$
$180$	−3.74093	−0.278833
$181$	−17.2363	−1.28116	−0.640582	−	0.767890i	$-0.721307\pi$
$181$	−17.2363	−1.28116	−0.640582	+	0.767890i	$0.721307\pi$
$182$	−1.78037	−0.131970
$183$	0.391252	0.0289222
$184$	4.44505	0.327693
$185$	1.25972	0.0926161
$186$	−1.14809	−0.0841824
$187$	−5.61445	−0.410569
$188$	−8.64624	−0.630592
$189$	6.26915	0.456014
$190$	0.233900	0.0169689
$191$	4.91472	0.355617	0.177809	−	0.984065i	$-0.443099\pi$
$191$	4.91472	0.355617	0.177809	+	0.984065i	$0.443099\pi$
$192$	0.785790	0.0567095
$193$	−8.26154	−0.594678	−0.297339	−	0.954772i	$-0.596099\pi$
$193$	−8.26154	−0.594678	−0.297339	+	0.954772i	$0.596099\pi$
$194$	−12.8889	−0.925370
$195$	−1.48198	−0.106127
$196$	−4.80299	−0.343071
$197$	2.47513	0.176346	0.0881729	−	0.996105i	$-0.471897\pi$
$197$	2.47513	0.176346	0.0881729	+	0.996105i	$0.471897\pi$
$198$	2.67614	0.190185
$199$	14.8076	1.04968	0.524841	−	0.851200i	$-0.324125\pi$
$199$	14.8076	1.04968	0.524841	+	0.851200i	$0.324125\pi$
$200$	2.53463	0.179226
$201$	−8.69235	−0.613111
$202$	−7.26692	−0.511298
$203$	−2.74703	−0.192804
$204$	−3.92776	−0.274998
$205$	4.97948	0.347782
$206$	−13.4787	−0.939106
$207$	10.5905	0.736089
$208$	−1.20114	−0.0832842
$209$	−0.167324	−0.0115741
$210$	1.82879	0.126198
$211$	−16.7938	−1.15613	−0.578067	−	0.815989i	$-0.696193\pi$
$211$	−16.7938	−1.15613	−0.578067	+	0.815989i	$0.696193\pi$
$212$	−7.34095	−0.504179
$213$	−7.10519	−0.486840
$214$	−3.25270	−0.222350
$215$	−14.0032	−0.955008
$216$	4.22954	0.287784
$217$	−2.16564	−0.147013
$218$	13.2735	0.898998
$219$	7.34209	0.496133
$220$	1.76364	0.118905
$221$	6.00388	0.403865
$222$	−0.630432	−0.0423118
$223$	23.4951	1.57335	0.786675	−	0.617368i	$-0.211801\pi$
$223$	23.4951	1.57335	0.786675	+	0.617368i	$0.211801\pi$
$224$	1.48223	0.0990357
$225$	6.03885	0.402590
$226$	12.1726	0.809707
$227$	21.8781	1.45210	0.726049	−	0.687643i	$-0.241355\pi$
$227$	21.8781	1.45210	0.726049	+	0.687643i	$0.241355\pi$
$228$	−0.117057	−0.00775227
$229$	−26.4789	−1.74978	−0.874888	−	0.484325i	$-0.839065\pi$
$229$	−26.4789	−1.74978	−0.874888	+	0.484325i	$0.839065\pi$
$230$	6.97939	0.460207
$231$	−1.30825	−0.0860766
$232$	−1.85331	−0.121676
$233$	3.58171	0.234645	0.117323	−	0.993094i	$-0.462569\pi$
$233$	3.58171	0.234645	0.117323	+	0.993094i	$0.462569\pi$
$234$	−2.86176	−0.187079
$235$	−13.5759	−0.885594
$236$	14.6115	0.951128
$237$	0.618472	0.0401741
$238$	−7.40890	−0.480248
$239$	20.3035	1.31332	0.656661	−	0.754186i	$-0.271968\pi$
$239$	20.3035	1.31332	0.656661	+	0.754186i	$0.271968\pi$
$240$	1.23381	0.0796419
$241$	6.95275	0.447866	0.223933	−	0.974605i	$-0.428110\pi$
$241$	6.95275	0.447866	0.223933	+	0.974605i	$0.428110\pi$
$242$	9.73835	0.626005
$243$	15.6935	1.00674
$244$	0.497909	0.0318754
$245$	−7.54142	−0.481803
$246$	−2.49201	−0.158885
$247$	0.178930	0.0113851
$248$	−1.46107	−0.0927781
$249$	4.68666	0.297005
$250$	11.8305	0.748226
$251$	−1.48232	−0.0935633	−0.0467816	−	0.998905i	$-0.514896\pi$
$251$	−1.48232	−0.0935633	−0.0467816	+	0.998905i	$0.514896\pi$
$252$	3.53146	0.222461
$253$	−4.99281	−0.313895
$254$	−6.81461	−0.427587
$255$	−6.16716	−0.386203
$256$	1.00000	0.0625000
$257$	−17.8974	−1.11641	−0.558204	−	0.829703i	$-0.688510\pi$
$257$	−17.8974	−1.11641	−0.558204	+	0.829703i	$0.688510\pi$
$258$	7.00797	0.436297
$259$	−1.18918	−0.0738920
$260$	−1.88597	−0.116963
$261$	−4.41558	−0.273318
$262$	6.88715	0.425490
$263$	0.192075	0.0118439	0.00592193	−	0.999982i	$-0.498115\pi$
$263$	0.192075	0.0118439	0.00592193	+	0.999982i	$0.498115\pi$
$264$	−0.882623	−0.0543217
$265$	−11.5264	−0.708060
$266$	−0.220803	−0.0135383
$267$	4.73801	0.289962
$268$	−11.0619	−0.675715
$269$	19.7300	1.20296	0.601480	−	0.798888i	$-0.294578\pi$
$269$	19.7300	1.20296	0.601480	+	0.798888i	$0.294578\pi$
$270$	6.64101	0.404159
$271$	−13.0350	−0.791823	−0.395911	−	0.918289i	$-0.629571\pi$
$271$	−13.0350	−0.791823	−0.395911	+	0.918289i	$0.629571\pi$
$272$	−4.99848	−0.303077
$273$	1.39899	0.0846710
$274$	15.8789	0.959280
$275$	−2.84698	−0.171679
$276$	−3.49287	−0.210246
$277$	−2.94260	−0.176804	−0.0884018	−	0.996085i	$-0.528176\pi$
$277$	−2.94260	−0.176804	−0.0884018	+	0.996085i	$0.528176\pi$
$278$	16.8630	1.01138
$279$	−3.48105	−0.208405
$280$	2.32732	0.139084
$281$	30.2505	1.80459	0.902296	−	0.431117i	$-0.141880\pi$
$281$	30.2505	1.80459	0.902296	+	0.431117i	$0.141880\pi$
$282$	6.79413	0.404585
$283$	−5.98578	−0.355818	−0.177909	−	0.984047i	$-0.556933\pi$
$283$	−5.98578	−0.355818	−0.177909	+	0.984047i	$0.556933\pi$
$284$	−9.04210	−0.536550
$285$	−0.183796	−0.0108872
$286$	1.34916	0.0797774
$287$	−4.70066	−0.277471
$288$	2.38253	0.140392
$289$	7.98482	0.469695
$290$	−2.90998	−0.170880
$291$	10.1280	0.593712
$292$	9.34359	0.546792
$293$	33.6330	1.96486	0.982432	−	0.186622i	$-0.0597540\pi$
$293$	33.6330	1.96486	0.982432	+	0.186622i	$0.0597540\pi$
$294$	3.77414	0.220113
$295$	22.9422	1.33575
$296$	−0.802290	−0.0466322
$297$	−4.75075	−0.275666
$298$	−10.4664	−0.606304
$299$	5.33913	0.308770
$300$	−1.99169	−0.114990
$301$	13.2191	0.761935
$302$	11.6911	0.672749
$303$	5.71027	0.328046
$304$	−0.148967	−0.00854384
$305$	0.781791	0.0447652
$306$	−11.9091	−0.680795
$307$	−20.1738	−1.15138	−0.575691	−	0.817667i	$-0.695267\pi$
$307$	−20.1738	−1.15138	−0.575691	+	0.817667i	$0.695267\pi$
$308$	−1.66489	−0.0948657
$309$	10.5914	0.602525
$310$	−2.29410	−0.130296
$311$	26.8279	1.52127	0.760635	−	0.649179i	$-0.224888\pi$
$311$	26.8279	1.52127	0.760635	+	0.649179i	$0.224888\pi$
$312$	0.943844	0.0534347
$313$	6.99439	0.395346	0.197673	−	0.980268i	$-0.436662\pi$
$313$	6.99439	0.395346	0.197673	+	0.980268i	$0.436662\pi$
$314$	21.5212	1.21451
$315$	5.54492	0.312421
$316$	0.787071	0.0442762
$317$	9.55367	0.536588	0.268294	−	0.963337i	$-0.413540\pi$
$317$	9.55367	0.536588	0.268294	+	0.963337i	$0.413540\pi$
$318$	5.76844	0.323478
$319$	2.08170	0.116553
$320$	1.57015	0.0877740
$321$	2.55594	0.142659
$322$	−6.58858	−0.367167
$323$	0.744608	0.0414311
$324$	3.82407	0.212449
$325$	3.04445	0.168876
$326$	−19.6349	−1.08748
$327$	−10.4302	−0.576792
$328$	−3.17134	−0.175108
$329$	12.8157	0.706554
$330$	−1.38585	−0.0762885
$331$	0.274676	0.0150976	0.00754878	−	0.999972i	$-0.497597\pi$
$331$	0.274676	0.0150976	0.00754878	+	0.999972i	$0.497597\pi$
$332$	5.96427	0.327332
$333$	−1.91148	−0.104749
$334$	−2.68307	−0.146811
$335$	−17.3689	−0.948963
$336$	−1.16472	−0.0635407
$337$	−11.7834	−0.641883	−0.320942	−	0.947099i	$-0.603999\pi$
$337$	−11.7834	−0.641883	−0.320942	+	0.947099i	$0.603999\pi$
$338$	11.5573	0.628632
$339$	−9.56508	−0.519504
$340$	−7.84836	−0.425637
$341$	1.64112	0.0888716
$342$	−0.354919	−0.0191918
$343$	17.4948	0.944628
$344$	8.91837	0.480846
$345$	−5.48433	−0.295266
$346$	25.7024	1.38177
$347$	−5.55057	−0.297970	−0.148985	−	0.988839i	$-0.547601\pi$
$347$	−5.55057	−0.297970	−0.148985	+	0.988839i	$0.547601\pi$
$348$	1.45631	0.0780666
$349$	8.41635	0.450517	0.225259	−	0.974299i	$-0.427677\pi$
$349$	8.41635	0.450517	0.225259	+	0.974299i	$0.427677\pi$
$350$	−3.75691	−0.200815
$351$	5.08028	0.271165
$352$	−1.12323	−0.0598684
$353$	3.26567	0.173814	0.0869069	−	0.996216i	$-0.472302\pi$
$353$	3.26567	0.173814	0.0869069	+	0.996216i	$0.472302\pi$
$354$	−11.4816	−0.610238
$355$	−14.1974	−0.753522
$356$	6.02962	0.319569
$357$	5.82184	0.308124
$358$	−20.2662	−1.07110
$359$	−1.47094	−0.0776331	−0.0388165	−	0.999246i	$-0.512359\pi$
$359$	−1.47094	−0.0776331	−0.0388165	+	0.999246i	$0.512359\pi$
$360$	3.74093	0.197165
$361$	−18.9778	−0.998832
$362$	17.2363	0.905920
$363$	−7.65230	−0.401641
$364$	1.78037	0.0933166
$365$	14.6708	0.767906
$366$	−0.391252	−0.0204511
$367$	−23.2050	−1.21129	−0.605645	−	0.795735i	$-0.707085\pi$
$367$	−23.2050	−1.21129	−0.605645	+	0.795735i	$0.707085\pi$
$368$	−4.44505	−0.231714
$369$	−7.55583	−0.393341
$370$	−1.25972	−0.0654895
$371$	10.8810	0.564912
$372$	1.14809	0.0595259
$373$	32.6930	1.69278	0.846390	−	0.532564i	$-0.178771\pi$
$373$	32.6930	1.69278	0.846390	+	0.532564i	$0.178771\pi$
$374$	5.61445	0.290316
$375$	−9.29628	−0.480058
$376$	8.64624	0.445896
$377$	−2.22609	−0.114649
$378$	−6.26915	−0.322450
$379$	−10.4963	−0.539157	−0.269578	−	0.962978i	$-0.586884\pi$
$379$	−10.4963	−0.539157	−0.269578	+	0.962978i	$0.586884\pi$
$380$	−0.233900	−0.0119988
$381$	5.35485	0.274337
$382$	−4.91472	−0.251459
$383$	23.9917	1.22592	0.612958	−	0.790115i	$-0.289979\pi$
$383$	23.9917	1.22592	0.612958	+	0.790115i	$0.289979\pi$
$384$	−0.785790	−0.0400997
$385$	−2.61412	−0.133228
$386$	8.26154	0.420501
$387$	21.2483	1.08011
$388$	12.8889	0.654335
$389$	−10.1775	−0.516019	−0.258010	−	0.966142i	$-0.583067\pi$
$389$	−10.1775	−0.516019	−0.258010	+	0.966142i	$0.583067\pi$
$390$	1.48198	0.0750428
$391$	22.2185	1.12364
$392$	4.80299	0.242588
$393$	−5.41185	−0.272992
$394$	−2.47513	−0.124695
$395$	1.23582	0.0621808
$396$	−2.67614	−0.134481
$397$	−25.6974	−1.28972	−0.644858	−	0.764303i	$-0.723083\pi$
$397$	−25.6974	−1.28972	−0.644858	+	0.764303i	$0.723083\pi$
$398$	−14.8076	−0.742237
$399$	0.173505	0.00868611
$400$	−2.53463	−0.126732
$401$	−6.43327	−0.321262	−0.160631	−	0.987015i	$-0.551353\pi$
$401$	−6.43327	−0.321262	−0.160631	+	0.987015i	$0.551353\pi$
$402$	8.69235	0.433535
$403$	−1.75495	−0.0874204
$404$	7.26692	0.361543
$405$	6.00436	0.298359
$406$	2.74703	0.136333
$407$	0.901157	0.0446687
$408$	3.92776	0.194453
$409$	35.9996	1.78007	0.890034	−	0.455895i	$-0.150681\pi$
$409$	35.9996	1.78007	0.890034	+	0.455895i	$0.150681\pi$
$410$	−4.97948	−0.245919
$411$	−12.4775	−0.615469
$412$	13.4787	0.664048
$413$	−21.6576	−1.06570
$414$	−10.5905	−0.520494
$415$	9.36479	0.459700
$416$	1.20114	0.0588908
$417$	−13.2508	−0.648894
$418$	0.167324	0.00818409
$419$	−6.88795	−0.336499	−0.168249	−	0.985744i	$-0.553811\pi$
$419$	−6.88795	−0.336499	−0.168249	+	0.985744i	$0.553811\pi$
$420$	−1.82879	−0.0892356
$421$	−3.65448	−0.178109	−0.0890543	−	0.996027i	$-0.528384\pi$
$421$	−3.65448	−0.178109	−0.0890543	+	0.996027i	$0.528384\pi$
$422$	16.7938	0.817511
$423$	20.6000	1.00161
$424$	7.34095	0.356508
$425$	12.6693	0.614552
$426$	7.10519	0.344248
$427$	−0.738016	−0.0357151
$428$	3.25270	0.157225
$429$	−1.06015	−0.0511848
$430$	14.0032	0.675293
$431$	33.2769	1.60289	0.801445	−	0.598068i	$-0.204065\pi$
$431$	33.2769	1.60289	0.801445	+	0.598068i	$0.204065\pi$
$432$	−4.22954	−0.203494
$433$	−28.7825	−1.38320	−0.691599	−	0.722281i	$-0.743094\pi$
$433$	−28.7825	−1.38320	−0.691599	+	0.722281i	$0.743094\pi$
$434$	2.16564	0.103954
$435$	2.28663	0.109635
$436$	−13.2735	−0.635688
$437$	0.662165	0.0316756
$438$	−7.34209	−0.350819
$439$	16.3681	0.781208	0.390604	−	0.920559i	$-0.372266\pi$
$439$	16.3681	0.781208	0.390604	+	0.920559i	$0.372266\pi$
$440$	−1.76364	−0.0840782
$441$	11.4433	0.544919
$442$	−6.00388	−0.285576
$443$	−1.62213	−0.0770699	−0.0385350	−	0.999257i	$-0.512269\pi$
$443$	−1.62213	−0.0770699	−0.0385350	+	0.999257i	$0.512269\pi$
$444$	0.630432	0.0299190
$445$	9.46740	0.448798
$446$	−23.4951	−1.11253
$447$	8.22442	0.389002
$448$	−1.48223	−0.0700288
$449$	−4.57903	−0.216098	−0.108049	−	0.994146i	$-0.534460\pi$
$449$	−4.57903	−0.216098	−0.108049	+	0.994146i	$0.534460\pi$
$450$	−6.03885	−0.284674
$451$	3.56215	0.167735
$452$	−12.1726	−0.572549
$453$	−9.18677	−0.431632
$454$	−21.8781	−1.02679
$455$	2.79544	0.131052
$456$	0.117057	0.00548168
$457$	−8.95623	−0.418955	−0.209477	−	0.977813i	$-0.567176\pi$
$457$	−8.95623	−0.418955	−0.209477	+	0.977813i	$0.567176\pi$
$458$	26.4789	1.23728
$459$	21.1413	0.986791
$460$	−6.97939	−0.325416
$461$	2.61266	0.121684	0.0608418	−	0.998147i	$-0.480621\pi$
$461$	2.61266	0.121684	0.0608418	+	0.998147i	$0.480621\pi$
$462$	1.30825	0.0608653
$463$	−39.3068	−1.82674	−0.913370	−	0.407130i	$-0.866530\pi$
$463$	−39.3068	−1.82674	−0.913370	+	0.407130i	$0.866530\pi$
$464$	1.85331	0.0860378
$465$	1.80268	0.0835973
$466$	−3.58171	−0.165919
$467$	15.6584	0.724586	0.362293	−	0.932064i	$-0.381994\pi$
$467$	15.6584	0.724586	0.362293	+	0.932064i	$0.381994\pi$
$468$	2.86176	0.132285
$469$	16.3963	0.757112
$470$	13.5759	0.626209
$471$	−16.9112	−0.779226
$472$	−14.6115	−0.672549
$473$	−10.0174	−0.460600
$474$	−0.618472	−0.0284074
$475$	0.377576	0.0173244
$476$	7.40890	0.339586
$477$	17.4901	0.800815
$478$	−20.3035	−0.928659
$479$	20.5117	0.937204	0.468602	−	0.883409i	$-0.344758\pi$
$479$	20.5117	0.937204	0.468602	+	0.883409i	$0.344758\pi$
$480$	−1.23381	−0.0563153
$481$	−0.963664	−0.0439393
$482$	−6.95275	−0.316689
$483$	5.17724	0.235573
$484$	−9.73835	−0.442652
$485$	20.2375	0.918938
$486$	−15.6935	−0.711873
$487$	38.7408	1.75551	0.877757	−	0.479105i	$-0.159039\pi$
$487$	38.7408	1.75551	0.877757	+	0.479105i	$0.159039\pi$
$488$	−0.497909	−0.0225393
$489$	15.4289	0.697720
$490$	7.54142	0.340686
$491$	−18.7683	−0.847000	−0.423500	−	0.905896i	$-0.639199\pi$
$491$	−18.7683	−0.847000	−0.423500	+	0.905896i	$0.639199\pi$
$492$	2.49201	0.112348
$493$	−9.26375	−0.417218
$494$	−0.178930	−0.00805045
$495$	−4.20193	−0.188863
$496$	1.46107	0.0656040
$497$	13.4025	0.601183
$498$	−4.68666	−0.210014
$499$	−24.8176	−1.11099	−0.555495	−	0.831520i	$-0.687471\pi$
$499$	−24.8176	−1.11099	−0.555495	+	0.831520i	$0.687471\pi$
$500$	−11.8305	−0.529076
$501$	2.10833	0.0941931
$502$	1.48232	0.0661592
$503$	1.03716	0.0462445	0.0231223	−	0.999733i	$-0.492639\pi$
$503$	1.03716	0.0462445	0.0231223	+	0.999733i	$0.492639\pi$
$504$	−3.53146	−0.157304
$505$	11.4101	0.507745
$506$	4.99281	0.221958
$507$	−9.08158	−0.403327
$508$	6.81461	0.302350
$509$	−1.80453	−0.0799843	−0.0399922	−	0.999200i	$-0.512733\pi$
$509$	−1.80453	−0.0799843	−0.0399922	+	0.999200i	$0.512733\pi$
$510$	6.16716	0.273087
$511$	−13.8493	−0.612659
$512$	−1.00000	−0.0441942
$513$	0.630061	0.0278179
$514$	17.8974	0.789420
$515$	21.1636	0.932578
$516$	−7.00797	−0.308509
$517$	−9.71173	−0.427121
$518$	1.18918	0.0522495
$519$	−20.1967	−0.886537
$520$	1.88597	0.0827053
$521$	8.13398	0.356356	0.178178	−	0.983998i	$-0.442980\pi$
$521$	8.13398	0.356356	0.178178	+	0.983998i	$0.442980\pi$
$522$	4.41558	0.193265
$523$	16.3135	0.713339	0.356670	−	0.934231i	$-0.383912\pi$
$523$	16.3135	0.713339	0.356670	+	0.934231i	$0.383912\pi$
$524$	−6.88715	−0.300867
$525$	2.95214	0.128842
$526$	−0.192075	−0.00837488
$527$	−7.30314	−0.318130
$528$	0.882623	0.0384112
$529$	−3.24155	−0.140937
$530$	11.5264	0.500674
$531$	−34.8124	−1.51073
$532$	0.220803	0.00957303
$533$	−3.80923	−0.164996
$534$	−4.73801	−0.205034
$535$	5.10722	0.220805
$536$	11.0619	0.477802
$537$	15.9250	0.687214
$538$	−19.7300	−0.850621
$539$	−5.39487	−0.232374
$540$	−6.64101	−0.285784
$541$	5.25232	0.225815	0.112907	−	0.993606i	$-0.463984\pi$
$541$	5.25232	0.225815	0.112907	+	0.993606i	$0.463984\pi$
$542$	13.0350	0.559903
$543$	−13.5441	−0.581233
$544$	4.99848	0.214308
$545$	−20.8414	−0.892750
$546$	−1.39899	−0.0598714
$547$	−19.9484	−0.852932	−0.426466	−	0.904503i	$-0.640242\pi$
$547$	−19.9484	−0.852932	−0.426466	+	0.904503i	$0.640242\pi$
$548$	−15.8789	−0.678313
$549$	−1.18629	−0.0506294
$550$	2.84698	0.121395
$551$	−0.276082	−0.0117615
$552$	3.49287	0.148667
$553$	−1.16662	−0.0496097
$554$	2.94260	0.125019
$555$	0.989872	0.0420177
$556$	−16.8630	−0.715152
$557$	7.44153	0.315308	0.157654	−	0.987494i	$-0.449607\pi$
$557$	7.44153	0.315308	0.157654	+	0.987494i	$0.449607\pi$
$558$	3.48105	0.147365
$559$	10.7122	0.453079
$560$	−2.32732	−0.0983473
$561$	−4.41178	−0.186265
$562$	−30.2505	−1.27604
$563$	−2.74939	−0.115873	−0.0579364	−	0.998320i	$-0.518452\pi$
$563$	−2.74939	−0.115873	−0.0579364	+	0.998320i	$0.518452\pi$
$564$	−6.79413	−0.286085
$565$	−19.1127	−0.804079
$566$	5.98578	0.251601
$567$	−5.66816	−0.238040
$568$	9.04210	0.379398
$569$	−0.292119	−0.0122463	−0.00612313	−	0.999981i	$-0.501949\pi$
$569$	−0.292119	−0.0122463	−0.00612313	+	0.999981i	$0.501949\pi$
$570$	0.183796	0.00769838
$571$	29.0098	1.21402	0.607011	−	0.794693i	$-0.292368\pi$
$571$	29.0098	1.21402	0.607011	+	0.794693i	$0.292368\pi$
$572$	−1.34916	−0.0564111
$573$	3.86194	0.161335
$574$	4.70066	0.196202
$575$	11.2666	0.469848
$576$	−2.38253	−0.0992723
$577$	−46.4267	−1.93277	−0.966384	−	0.257103i	$-0.917232\pi$
$577$	−46.4267	−1.93277	−0.966384	+	0.257103i	$0.917232\pi$
$578$	−7.98482	−0.332125
$579$	−6.49183	−0.269791
$580$	2.90998	0.120830
$581$	−8.84042	−0.366762
$582$	−10.1280	−0.419818
$583$	−8.24558	−0.341497
$584$	−9.34359	−0.386640
$585$	4.49339	0.185779
$586$	−33.6330	−1.38937
$587$	23.7548	0.980466	0.490233	−	0.871591i	$-0.336912\pi$
$587$	23.7548	0.980466	0.490233	+	0.871591i	$0.336912\pi$
$588$	−3.77414	−0.155643
$589$	−0.217651	−0.00896816
$590$	−22.9422	−0.944517
$591$	1.94493	0.0800039
$592$	0.802290	0.0329739
$593$	2.17984	0.0895153	0.0447577	−	0.998998i	$-0.485748\pi$
$593$	2.17984	0.0895153	0.0447577	+	0.998998i	$0.485748\pi$
$594$	4.75075	0.194926
$595$	11.6331	0.476910
$596$	10.4664	0.428722
$597$	11.6356	0.476215
$598$	−5.33913	−0.218333
$599$	−16.8553	−0.688689	−0.344345	−	0.938843i	$-0.611899\pi$
$599$	−16.8553	−0.688689	−0.344345	+	0.938843i	$0.611899\pi$
$600$	1.99169	0.0813103
$601$	40.1943	1.63956	0.819780	−	0.572678i	$-0.194096\pi$
$601$	40.1943	1.63956	0.819780	+	0.572678i	$0.194096\pi$
$602$	−13.2191	−0.538769
$603$	26.3554	1.07328
$604$	−11.6911	−0.475705
$605$	−15.2907	−0.621654
$606$	−5.71027	−0.231964
$607$	11.3885	0.462245	0.231122	−	0.972925i	$-0.425760\pi$
$607$	11.3885	0.462245	0.231122	+	0.972925i	$0.425760\pi$
$608$	0.148967	0.00604140
$609$	−2.15859	−0.0874705
$610$	−0.781791	−0.0316538
$611$	10.3854	0.420147
$612$	11.9091	0.481395
$613$	3.87769	0.156618	0.0783092	−	0.996929i	$-0.475048\pi$
$613$	3.87769	0.156618	0.0783092	+	0.996929i	$0.475048\pi$
$614$	20.1738	0.814150
$615$	3.91282	0.157780
$616$	1.66489	0.0670802
$617$	−24.4375	−0.983817	−0.491909	−	0.870647i	$-0.663701\pi$
$617$	−24.4375	−0.983817	−0.491909	+	0.870647i	$0.663701\pi$
$618$	−10.5914	−0.426050
$619$	32.0429	1.28791	0.643956	−	0.765062i	$-0.277292\pi$
$619$	32.0429	1.28791	0.643956	+	0.765062i	$0.277292\pi$
$620$	2.29410	0.0921332
$621$	18.8005	0.754438
$622$	−26.8279	−1.07570
$623$	−8.93728	−0.358065
$624$	−0.943844	−0.0377840
$625$	−5.90248	−0.236099
$626$	−6.99439	−0.279552
$627$	−0.131482	−0.00525087
$628$	−21.5212	−0.858791
$629$	−4.01023	−0.159899
$630$	−5.54492	−0.220915
$631$	10.0949	0.401873	0.200937	−	0.979604i	$-0.435601\pi$
$631$	10.0949	0.401873	0.200937	+	0.979604i	$0.435601\pi$
$632$	−0.787071	−0.0313080
$633$	−13.1964	−0.524510
$634$	−9.55367	−0.379425
$635$	10.7000	0.424615
$636$	−5.76844	−0.228734
$637$	5.76907	0.228579
$638$	−2.08170	−0.0824152
$639$	21.5431	0.852232
$640$	−1.57015	−0.0620656
$641$	−3.55134	−0.140269	−0.0701347	−	0.997538i	$-0.522343\pi$
$641$	−3.55134	−0.140269	−0.0701347	+	0.997538i	$0.522343\pi$
$642$	−2.55594	−0.100875
$643$	−13.4316	−0.529689	−0.264844	−	0.964291i	$-0.585321\pi$
$643$	−13.4316	−0.529689	−0.264844	+	0.964291i	$0.585321\pi$
$644$	6.58858	0.259627
$645$	−11.0036	−0.433264
$646$	−0.744608	−0.0292962
$647$	−30.0156	−1.18003	−0.590017	−	0.807391i	$-0.700879\pi$
$647$	−30.0156	−1.18003	−0.590017	+	0.807391i	$0.700879\pi$
$648$	−3.82407	−0.150224
$649$	16.4121	0.644231
$650$	−3.04445	−0.119413
$651$	−1.70174	−0.0666965
$652$	19.6349	0.768963
$653$	−15.8159	−0.618922	−0.309461	−	0.950912i	$-0.600149\pi$
$653$	−15.8159	−0.618922	−0.309461	+	0.950912i	$0.600149\pi$
$654$	10.4302	0.407854
$655$	−10.8139	−0.422532
$656$	3.17134	0.123820
$657$	−22.2614	−0.868500
$658$	−12.8157	−0.499609
$659$	−39.3464	−1.53272	−0.766359	−	0.642412i	$-0.777934\pi$
$659$	−39.3464	−1.53272	−0.766359	+	0.642412i	$0.777934\pi$
$660$	1.38585	0.0539441
$661$	−30.4640	−1.18491	−0.592456	−	0.805603i	$-0.701841\pi$
$661$	−30.4640	−1.18491	−0.592456	+	0.805603i	$0.701841\pi$
$662$	−0.274676	−0.0106756
$663$	4.71779	0.183224
$664$	−5.96427	−0.231459
$665$	0.346694	0.0134442
$666$	1.91148	0.0740685
$667$	−8.23806	−0.318979
$668$	2.68307	0.103811
$669$	18.4622	0.713791
$670$	17.3689	0.671018
$671$	0.559267	0.0215902
$672$	1.16472	0.0449301
$673$	36.3713	1.40201	0.701005	−	0.713156i	$-0.252735\pi$
$673$	36.3713	1.40201	0.701005	+	0.713156i	$0.252735\pi$
$674$	11.7834	0.453880
$675$	10.7203	0.412626
$676$	−11.5573	−0.444510
$677$	3.81303	0.146547	0.0732733	−	0.997312i	$-0.476655\pi$
$677$	3.81303	0.146547	0.0732733	+	0.997312i	$0.476655\pi$
$678$	9.56508	0.367345
$679$	−19.1043	−0.733157
$680$	7.84836	0.300971
$681$	17.1916	0.658782
$682$	−1.64112	−0.0628417
$683$	40.6149	1.55408	0.777042	−	0.629448i	$-0.216719\pi$
$683$	40.6149	1.55408	0.777042	+	0.629448i	$0.216719\pi$
$684$	0.354919	0.0135707
$685$	−24.9322	−0.952612
$686$	−17.4948	−0.667953
$687$	−20.8069	−0.793831
$688$	−8.91837	−0.340010
$689$	8.81752	0.335921
$690$	5.48433	0.208785
$691$	−48.7181	−1.85332	−0.926662	−	0.375895i	$-0.877335\pi$
$691$	−48.7181	−1.85332	−0.926662	+	0.375895i	$0.877335\pi$
$692$	−25.7024	−0.977060
$693$	3.96665	0.150681
$694$	5.55057	0.210697
$695$	−26.4775	−1.00435
$696$	−1.45631	−0.0552014
$697$	−15.8519	−0.600433
$698$	−8.41635	−0.318564
$699$	2.81447	0.106453
$700$	3.75691	0.141998
$701$	−30.7570	−1.16168	−0.580838	−	0.814019i	$-0.697275\pi$
$701$	−30.7570	−1.16168	−0.580838	+	0.814019i	$0.697275\pi$
$702$	−5.08028	−0.191743
$703$	−0.119515	−0.00450758
$704$	1.12323	0.0423333
$705$	−10.6678	−0.401772
$706$	−3.26567	−0.122905
$707$	−10.7712	−0.405094
$708$	11.4816	0.431504
$709$	8.06076	0.302728	0.151364	−	0.988478i	$-0.451633\pi$
$709$	8.06076	0.302728	0.151364	+	0.988478i	$0.451633\pi$
$710$	14.1974	0.532821
$711$	−1.87522	−0.0703264
$712$	−6.02962	−0.225970
$713$	−6.49453	−0.243222
$714$	−5.82184	−0.217877
$715$	−2.11838	−0.0792229
$716$	20.2662	0.757384
$717$	15.9543	0.595823
$718$	1.47094	0.0548949
$719$	16.1017	0.600491	0.300245	−	0.953862i	$-0.402931\pi$
$719$	16.1017	0.600491	0.300245	+	0.953862i	$0.402931\pi$
$720$	−3.74093	−0.139416
$721$	−19.9785	−0.744039
$722$	18.9778	0.706281
$723$	5.46340	0.203186
$724$	−17.2363	−0.640582
$725$	−4.69746	−0.174459
$726$	7.65230	0.284003
$727$	−19.9152	−0.738615	−0.369307	−	0.929307i	$-0.620405\pi$
$727$	−19.9152	−0.738615	−0.369307	+	0.929307i	$0.620405\pi$
$728$	−1.78037	−0.0659848
$729$	0.859603	0.0318371
$730$	−14.6708	−0.542991
$731$	44.5783	1.64879
$732$	0.391252	0.0144611
$733$	34.8344	1.28664	0.643320	−	0.765598i	$-0.277557\pi$
$733$	34.8344	1.28664	0.643320	+	0.765598i	$0.277557\pi$
$734$	23.2050	0.856511
$735$	−5.92597	−0.218583
$736$	4.44505	0.163847
$737$	−12.4251	−0.457684
$738$	7.55583	0.278134
$739$	11.6653	0.429115	0.214557	−	0.976711i	$-0.431169\pi$
$739$	11.6653	0.429115	0.214557	+	0.976711i	$0.431169\pi$
$740$	1.25972	0.0463081
$741$	0.140602	0.00516513
$742$	−10.8810	−0.399453
$743$	18.5705	0.681287	0.340644	−	0.940193i	$-0.389355\pi$
$743$	18.5705	0.681287	0.340644	+	0.940193i	$0.389355\pi$
$744$	−1.14809	−0.0420912
$745$	16.4339	0.602090
$746$	−32.6930	−1.19698
$747$	−14.2101	−0.519920
$748$	−5.61445	−0.205285
$749$	−4.82125	−0.176165
$750$	9.29628	0.339452
$751$	−1.00000	−0.0364905
$751$	−1.00000	−0.0364905
$752$	−8.64624	−0.315296
$753$	−1.16479	−0.0424474
$754$	2.22609	0.0810694
$755$	−18.3568	−0.668073
$756$	6.26915	0.228007
$757$	10.5801	0.384540	0.192270	−	0.981342i	$-0.438415\pi$
$757$	10.5801	0.384540	0.192270	+	0.981342i	$0.438415\pi$
$758$	10.4963	0.381242
$759$	−3.92330	−0.142407
$760$	0.233900	0.00848445
$761$	−46.0458	−1.66916	−0.834580	−	0.550887i	$-0.814289\pi$
$761$	−46.0458	−1.66916	−0.834580	+	0.550887i	$0.814289\pi$
$762$	−5.35485	−0.193986
$763$	19.6745	0.712263
$764$	4.91472	0.177809
$765$	18.6990	0.676063
$766$	−23.9917	−0.866854
$767$	−17.5505	−0.633711
$768$	0.785790	0.0283547
$769$	−48.8308	−1.76088	−0.880442	−	0.474154i	$-0.842754\pi$
$769$	−48.8308	−1.76088	−0.880442	+	0.474154i	$0.842754\pi$
$770$	2.61412	0.0942063
$771$	−14.0636	−0.506488
$772$	−8.26154	−0.297339
$773$	−29.0119	−1.04349	−0.521743	−	0.853103i	$-0.674718\pi$
$773$	−29.0119	−1.04349	−0.521743	+	0.853103i	$0.674718\pi$
$774$	−21.2483	−0.763755
$775$	−3.70328	−0.133026
$776$	−12.8889	−0.462685
$777$	−0.934445	−0.0335230
$778$	10.1775	0.364881
$779$	−0.472425	−0.0169264
$780$	−1.48198	−0.0530633
$781$	−10.1564	−0.363423
$782$	−22.2185	−0.794532
$783$	−7.83866	−0.280131
$784$	−4.80299	−0.171536
$785$	−33.7916	−1.20607
$786$	5.41185	0.193034
$787$	−5.14685	−0.183465	−0.0917327	−	0.995784i	$-0.529241\pi$
$787$	−5.14685	−0.183465	−0.0917327	+	0.995784i	$0.529241\pi$
$788$	2.47513	0.0881729
$789$	0.150931	0.00537328
$790$	−1.23582	−0.0439685
$791$	18.0425	0.641519
$792$	2.67614	0.0950923
$793$	−0.598059	−0.0212377
$794$	25.6974	0.911966
$795$	−9.05732	−0.321230
$796$	14.8076	0.524841
$797$	−11.2392	−0.398112	−0.199056	−	0.979988i	$-0.563788\pi$
$797$	−11.2392	−0.398112	−0.199056	+	0.979988i	$0.563788\pi$
$798$	−0.173505	−0.00614201
$799$	43.2181	1.52895
$800$	2.53463	0.0896128
$801$	−14.3658	−0.507590
$802$	6.43327	0.227167
$803$	10.4950	0.370361
$804$	−8.69235	−0.306555
$805$	10.3451	0.364615
$806$	1.75495	0.0618156
$807$	15.5036	0.545754
$808$	−7.26692	−0.255649
$809$	−44.4379	−1.56235	−0.781176	−	0.624310i	$-0.785380\pi$
$809$	−44.4379	−1.56235	−0.781176	+	0.624310i	$0.785380\pi$
$810$	−6.00436	−0.210972
$811$	36.2901	1.27432	0.637159	−	0.770732i	$-0.280110\pi$
$811$	36.2901	1.27432	0.637159	+	0.770732i	$0.280110\pi$
$812$	−2.74703	−0.0964020
$813$	−10.2428	−0.359231
$814$	−0.901157	−0.0315855
$815$	30.8298	1.07992
$816$	−3.92776	−0.137499
$817$	1.32854	0.0464798
$818$	−35.9996	−1.25870
$819$	−4.24179	−0.148220
$820$	4.97948	0.173891
$821$	−36.3438	−1.26841	−0.634204	−	0.773166i	$-0.718672\pi$
$821$	−36.3438	−1.26841	−0.634204	+	0.773166i	$0.718672\pi$
$822$	12.4775	0.435202
$823$	−17.3625	−0.605219	−0.302610	−	0.953115i	$-0.597858\pi$
$823$	−17.3625	−0.605219	−0.302610	+	0.953115i	$0.597858\pi$
$824$	−13.4787	−0.469553
$825$	−2.23713	−0.0778867
$826$	21.6576	0.753564
$827$	−30.9284	−1.07548	−0.537742	−	0.843109i	$-0.680723\pi$
$827$	−30.9284	−1.07548	−0.537742	+	0.843109i	$0.680723\pi$
$828$	10.5905	0.368045
$829$	32.2258	1.11925	0.559624	−	0.828747i	$-0.310946\pi$
$829$	32.2258	1.11925	0.559624	+	0.828747i	$0.310946\pi$
$830$	−9.36479	−0.325057
$831$	−2.31226	−0.0802115
$832$	−1.20114	−0.0416421
$833$	24.0077	0.831817
$834$	13.2508	0.458837
$835$	4.21282	0.145790
$836$	−0.167324	−0.00578703
$837$	−6.17966	−0.213600
$838$	6.88795	0.237940
$839$	−12.9114	−0.445750	−0.222875	−	0.974847i	$-0.571544\pi$
$839$	−12.9114	−0.445750	−0.222875	+	0.974847i	$0.571544\pi$
$840$	1.82879	0.0630991
$841$	−25.5652	−0.881560
$842$	3.65448	0.125942
$843$	23.7705	0.818700
$844$	−16.7938	−0.578067
$845$	−18.1466	−0.624263
$846$	−20.6000	−0.708242
$847$	14.4345	0.495975
$848$	−7.34095	−0.252089
$849$	−4.70356	−0.161426
$850$	−12.6693	−0.434554
$851$	−3.56622	−0.122248
$852$	−7.10519	−0.243420
$853$	10.4481	0.357737	0.178869	−	0.983873i	$-0.442756\pi$
$853$	10.4481	0.357737	0.178869	+	0.983873i	$0.442756\pi$
$854$	0.738016	0.0252544
$855$	0.557275	0.0190584
$856$	−3.25270	−0.111175
$857$	−16.8262	−0.574773	−0.287386	−	0.957815i	$-0.592786\pi$
$857$	−16.8262	−0.574773	−0.287386	+	0.957815i	$0.592786\pi$
$858$	1.06015	0.0361931
$859$	−2.39566	−0.0817388	−0.0408694	−	0.999164i	$-0.513013\pi$
$859$	−2.39566	−0.0817388	−0.0408694	+	0.999164i	$0.513013\pi$
$860$	−14.0032	−0.477504
$861$	−3.69373	−0.125882
$862$	−33.2769	−1.13342
$863$	16.1019	0.548114	0.274057	−	0.961714i	$-0.411634\pi$
$863$	16.1019	0.548114	0.274057	+	0.961714i	$0.411634\pi$
$864$	4.22954	0.143892
$865$	−40.3567	−1.37217
$866$	28.7825	0.978069
$867$	6.27439	0.213090
$868$	−2.16564	−0.0735067
$869$	0.884062	0.0299898
$870$	−2.28663	−0.0775240
$871$	13.2869	0.450211
$872$	13.2735	0.449499
$873$	−30.7083	−1.03932
$874$	−0.662165	−0.0223981
$875$	17.5355	0.592809
$876$	7.34209	0.248066
$877$	−32.3171	−1.09127	−0.545635	−	0.838023i	$-0.683712\pi$
$877$	−32.3171	−1.09127	−0.545635	+	0.838023i	$0.683712\pi$
$878$	−16.3681	−0.552397
$879$	26.4285	0.891411
$880$	1.76364	0.0594523
$881$	33.6465	1.13358	0.566789	−	0.823863i	$-0.308186\pi$
$881$	33.6465	1.13358	0.566789	+	0.823863i	$0.308186\pi$
$882$	−11.4433	−0.385316
$883$	−23.4966	−0.790725	−0.395363	−	0.918525i	$-0.629381\pi$
$883$	−23.4966	−0.790725	−0.395363	+	0.918525i	$0.629381\pi$
$884$	6.00388	0.201932
$885$	18.0278	0.605997
$886$	1.62213	0.0544967
$887$	17.2265	0.578408	0.289204	−	0.957267i	$-0.406609\pi$
$887$	17.2265	0.578408	0.289204	+	0.957267i	$0.406609\pi$
$888$	−0.630432	−0.0211559
$889$	−10.1008	−0.338771
$890$	−9.46740	−0.317348
$891$	4.29532	0.143899
$892$	23.4951	0.786675
$893$	1.28800	0.0431014
$894$	−8.22442	−0.275066
$895$	31.8210	1.06366
$896$	1.48223	0.0495178
$897$	4.19543	0.140081
$898$	4.57903	0.152804
$899$	2.70782	0.0903109
$900$	6.03885	0.201295
$901$	36.6936	1.22244
$902$	−3.56215	−0.118607
$903$	10.3874	0.345672
$904$	12.1726	0.404853
$905$	−27.0636	−0.899623
$906$	9.18677	0.305210
$907$	−11.4601	−0.380526	−0.190263	−	0.981733i	$-0.560934\pi$
$907$	−11.4601	−0.380526	−0.190263	+	0.981733i	$0.560934\pi$
$908$	21.8781	0.726049
$909$	−17.3137	−0.574258
$910$	−2.79544	−0.0926680
$911$	−9.82328	−0.325460	−0.162730	−	0.986671i	$-0.552030\pi$
$911$	−9.82328	−0.325460	−0.162730	+	0.986671i	$0.552030\pi$
$912$	−0.117057	−0.00387613
$913$	6.69925	0.221713
$914$	8.95623	0.296246
$915$	0.614324	0.0203089
$916$	−26.4789	−0.874888
$917$	10.2083	0.337109
$918$	−21.1413	−0.697766
$919$	28.8611	0.952040	0.476020	−	0.879434i	$-0.342079\pi$
$919$	28.8611	0.952040	0.476020	+	0.879434i	$0.342079\pi$
$920$	6.97939	0.230104
$921$	−15.8524	−0.522354
$922$	−2.61266	−0.0860433
$923$	10.8608	0.357489
$924$	−1.30825	−0.0430383
$925$	−2.03351	−0.0668614
$926$	39.3068	1.29170
$927$	−32.1135	−1.05474
$928$	−1.85331	−0.0608379
$929$	27.6531	0.907267	0.453634	−	0.891188i	$-0.350127\pi$
$929$	27.6531	0.907267	0.453634	+	0.891188i	$0.350127\pi$
$930$	−1.80268	−0.0591122
$931$	0.715487	0.0234491
$932$	3.58171	0.117323
$933$	21.0811	0.690164
$934$	−15.6584	−0.512360
$935$	−8.81552	−0.288298
$936$	−2.86176	−0.0935396
$937$	−2.27959	−0.0744709	−0.0372354	−	0.999307i	$-0.511855\pi$
$937$	−2.27959	−0.0744709	−0.0372354	+	0.999307i	$0.511855\pi$
$938$	−16.3963	−0.535359
$939$	5.49612	0.179359
$940$	−13.5759	−0.442797
$941$	11.8877	0.387526	0.193763	−	0.981048i	$-0.437931\pi$
$941$	11.8877	0.387526	0.193763	+	0.981048i	$0.437931\pi$
$942$	16.9112	0.550996
$943$	−14.0968	−0.459054
$944$	14.6115	0.475564
$945$	9.84350	0.320209
$946$	10.0174	0.325693
$947$	−43.4093	−1.41061	−0.705306	−	0.708903i	$-0.749191\pi$
$947$	−43.4093	−1.41061	−0.705306	+	0.708903i	$0.749191\pi$
$948$	0.618472	0.0200870
$949$	−11.2230	−0.364313
$950$	−0.377576	−0.0122502
$951$	7.50718	0.243437
$952$	−7.40890	−0.240124
$953$	−29.9829	−0.971240	−0.485620	−	0.874170i	$-0.661406\pi$
$953$	−29.9829	−0.971240	−0.485620	+	0.874170i	$0.661406\pi$
$954$	−17.4901	−0.566262
$955$	7.71685	0.249711
$956$	20.3035	0.656661
$957$	1.63578	0.0528771
$958$	−20.5117	−0.662703
$959$	23.5362	0.760023
$960$	1.23381	0.0398209
$961$	−28.8653	−0.931138
$962$	0.963664	0.0310698
$963$	−7.74967	−0.249730
$964$	6.95275	0.223933
$965$	−12.9718	−0.417578
$966$	−5.17724	−0.166575
$967$	−3.59526	−0.115616	−0.0578078	−	0.998328i	$-0.518411\pi$
$967$	−3.59526	−0.115616	−0.0578078	+	0.998328i	$0.518411\pi$
$968$	9.73835	0.313003
$969$	0.585106	0.0187963
$970$	−20.2375	−0.649787
$971$	8.95642	0.287425	0.143713	−	0.989619i	$-0.454096\pi$
$971$	8.95642	0.287425	0.143713	+	0.989619i	$0.454096\pi$
$972$	15.6935	0.503371
$973$	24.9949	0.801299
$974$	−38.7408	−1.24134
$975$	2.39230	0.0766149
$976$	0.497909	0.0159377
$977$	−33.3802	−1.06793	−0.533964	−	0.845507i	$-0.679298\pi$
$977$	−33.3802	−1.06793	−0.533964	+	0.845507i	$0.679298\pi$
$978$	−15.4289	−0.493363
$979$	6.77265	0.216455
$980$	−7.54142	−0.240902
$981$	31.6247	1.00970
$982$	18.7683	0.598919
$983$	−5.74063	−0.183098	−0.0915489	−	0.995801i	$-0.529182\pi$
$983$	−5.74063	−0.183098	−0.0915489	+	0.995801i	$0.529182\pi$
$984$	−2.49201	−0.0794423
$985$	3.88633	0.123829
$986$	9.26375	0.295018
$987$	10.0705	0.320546
$988$	0.178930	0.00569253
$989$	39.6426	1.26056
$990$	4.20193	0.133546
$991$	−18.4615	−0.586450	−0.293225	−	0.956044i	$-0.594728\pi$
$991$	−18.4615	−0.586450	−0.293225	+	0.956044i	$0.594728\pi$
$992$	−1.46107	−0.0463891
$993$	0.215838	0.00684940
$994$	−13.4025	−0.425101
$995$	23.2501	0.737078
$996$	4.68666	0.148503
$997$	11.5448	0.365629	0.182815	−	0.983147i	$-0.441479\pi$
$997$	11.5448	0.365629	0.182815	+	0.983147i	$0.441479\pi$
$998$	24.8176	0.785589
$999$	−3.39332	−0.107360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.e.1.8	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.e.1.8	✓	11	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:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.785790 q^{3} +1.00000 q^{4} +1.57015 q^{5} -0.785790 q^{6} -1.48223 q^{7} -1.00000 q^{8} -2.38253 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.785790 q^{3} +1.00000 q^{4} +1.57015 q^{5} -0.785790 q^{6} -1.48223 q^{7} -1.00000 q^{8} -2.38253 q^{9} -1.57015 q^{10} +1.12323 q^{11} +0.785790 q^{12} -1.20114 q^{13} +1.48223 q^{14} +1.23381 q^{15} +1.00000 q^{16} -4.99848 q^{17} +2.38253 q^{18} -0.148967 q^{19} +1.57015 q^{20} -1.16472 q^{21} -1.12323 q^{22} -4.44505 q^{23} -0.785790 q^{24} -2.53463 q^{25} +1.20114 q^{26} -4.22954 q^{27} -1.48223 q^{28} +1.85331 q^{29} -1.23381 q^{30} +1.46107 q^{31} -1.00000 q^{32} +0.882623 q^{33} +4.99848 q^{34} -2.32732 q^{35} -2.38253 q^{36} +0.802290 q^{37} +0.148967 q^{38} -0.943844 q^{39} -1.57015 q^{40} +3.17134 q^{41} +1.16472 q^{42} -8.91837 q^{43} +1.12323 q^{44} -3.74093 q^{45} +4.44505 q^{46} -8.64624 q^{47} +0.785790 q^{48} -4.80299 q^{49} +2.53463 q^{50} -3.92776 q^{51} -1.20114 q^{52} -7.34095 q^{53} +4.22954 q^{54} +1.76364 q^{55} +1.48223 q^{56} -0.117057 q^{57} -1.85331 q^{58} +14.6115 q^{59} +1.23381 q^{60} +0.497909 q^{61} -1.46107 q^{62} +3.53146 q^{63} +1.00000 q^{64} -1.88597 q^{65} -0.882623 q^{66} -11.0619 q^{67} -4.99848 q^{68} -3.49287 q^{69} +2.32732 q^{70} -9.04210 q^{71} +2.38253 q^{72} +9.34359 q^{73} -0.802290 q^{74} -1.99169 q^{75} -0.148967 q^{76} -1.66489 q^{77} +0.943844 q^{78} +0.787071 q^{79} +1.57015 q^{80} +3.82407 q^{81} -3.17134 q^{82} +5.96427 q^{83} -1.16472 q^{84} -7.84836 q^{85} +8.91837 q^{86} +1.45631 q^{87} -1.12323 q^{88} +6.02962 q^{89} +3.74093 q^{90} +1.78037 q^{91} -4.44505 q^{92} +1.14809 q^{93} +8.64624 q^{94} -0.233900 q^{95} -0.785790 q^{96} +12.8889 q^{97} +4.80299 q^{98} -2.67614 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 19 q^{13} + 6 q^{14} + q^{15} + 11 q^{16} - 8 q^{17} - 3 q^{18} - 9 q^{19} + q^{20} - 6 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 2 q^{25} + 19 q^{26} - 16 q^{27} - 6 q^{28} + 13 q^{29} - q^{30} - 19 q^{31} - 11 q^{32} - 37 q^{33} + 8 q^{34} + 3 q^{35} + 3 q^{36} - 29 q^{37} + 9 q^{38} + 8 q^{39} - q^{40} - 23 q^{41} + 6 q^{42} - 13 q^{43} + 4 q^{44} - 6 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 5 q^{49} + 2 q^{50} + 33 q^{51} - 19 q^{52} - 25 q^{53} + 16 q^{54} - 14 q^{55} + 6 q^{56} + 4 q^{57} - 13 q^{58} + 6 q^{59} + q^{60} + 10 q^{61} + 19 q^{62} - 7 q^{63} + 11 q^{64} - 19 q^{65} + 37 q^{66} - 16 q^{67} - 8 q^{68} - 25 q^{69} - 3 q^{70} + 8 q^{71} - 3 q^{72} - 56 q^{73} + 29 q^{74} - 50 q^{75} - 9 q^{76} - 7 q^{77} - 8 q^{78} + 2 q^{79} + q^{80} - 5 q^{81} + 23 q^{82} + 21 q^{83} - 6 q^{84} - 55 q^{85} + 13 q^{86} - 11 q^{87} - 4 q^{88} - 24 q^{89} + 6 q^{90} - 43 q^{91} + 2 q^{92} + 10 q^{93} + 16 q^{94} + 25 q^{95} + 4 q^{96} - 84 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9 - q^10 + 4 * q^11 - 4 * q^12 - 19 * q^13 + 6 * q^14 + q^15 + 11 * q^16 - 8 * q^17 - 3 * q^18 - 9 * q^19 + q^20 - 6 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 2 * q^25 + 19 * q^26 - 16 * q^27 - 6 * q^28 + 13 * q^29 - q^30 - 19 * q^31 - 11 * q^32 - 37 * q^33 + 8 * q^34 + 3 * q^35 + 3 * q^36 - 29 * q^37 + 9 * q^38 + 8 * q^39 - q^40 - 23 * q^41 + 6 * q^42 - 13 * q^43 + 4 * q^44 - 6 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 5 * q^49 + 2 * q^50 + 33 * q^51 - 19 * q^52 - 25 * q^53 + 16 * q^54 - 14 * q^55 + 6 * q^56 + 4 * q^57 - 13 * q^58 + 6 * q^59 + q^60 + 10 * q^61 + 19 * q^62 - 7 * q^63 + 11 * q^64 - 19 * q^65 + 37 * q^66 - 16 * q^67 - 8 * q^68 - 25 * q^69 - 3 * q^70 + 8 * q^71 - 3 * q^72 - 56 * q^73 + 29 * q^74 - 50 * q^75 - 9 * q^76 - 7 * q^77 - 8 * q^78 + 2 * q^79 + q^80 - 5 * q^81 + 23 * q^82 + 21 * q^83 - 6 * q^84 - 55 * q^85 + 13 * q^86 - 11 * q^87 - 4 * q^88 - 24 * q^89 + 6 * q^90 - 43 * q^91 + 2 * q^92 + 10 * q^93 + 16 * q^94 + 25 * q^95 + 4 * q^96 - 84 * q^97 + 5 * q^98 + 14 * q^99

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