LMFDB - Embedded newform 6010.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + \cdots - 10 $ x^16 - 8x^15 + 9x^14 + 75x^13 - 178x^12 - 232x^11 + 872x^10 + 228x^9 - 1986x^8 + 164x^7 + 2332x^6 - 440x^5 - 1344x^4 + 244x^3 + 295x^2 - 41*x - 10
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.28136$ of defining polynomial
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.28136 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.28136 q^{6} +1.99437 q^{7} +1.00000 q^{8} +2.20462 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.28136 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.28136 q^{6} +1.99437 q^{7} +1.00000 q^{8} +2.20462 q^{9} +1.00000 q^{10} +1.87428 q^{11} -2.28136 q^{12} -4.38275 q^{13} +1.99437 q^{14} -2.28136 q^{15} +1.00000 q^{16} -2.44884 q^{17} +2.20462 q^{18} -5.14004 q^{19} +1.00000 q^{20} -4.54988 q^{21} +1.87428 q^{22} +5.32780 q^{23} -2.28136 q^{24} +1.00000 q^{25} -4.38275 q^{26} +1.81455 q^{27} +1.99437 q^{28} +8.18089 q^{29} -2.28136 q^{30} -9.68099 q^{31} +1.00000 q^{32} -4.27591 q^{33} -2.44884 q^{34} +1.99437 q^{35} +2.20462 q^{36} -4.69319 q^{37} -5.14004 q^{38} +9.99864 q^{39} +1.00000 q^{40} -2.34952 q^{41} -4.54988 q^{42} -9.31769 q^{43} +1.87428 q^{44} +2.20462 q^{45} +5.32780 q^{46} -1.00015 q^{47} -2.28136 q^{48} -3.02249 q^{49} +1.00000 q^{50} +5.58669 q^{51} -4.38275 q^{52} -3.26390 q^{53} +1.81455 q^{54} +1.87428 q^{55} +1.99437 q^{56} +11.7263 q^{57} +8.18089 q^{58} -2.78044 q^{59} -2.28136 q^{60} -0.527106 q^{61} -9.68099 q^{62} +4.39683 q^{63} +1.00000 q^{64} -4.38275 q^{65} -4.27591 q^{66} +6.25111 q^{67} -2.44884 q^{68} -12.1546 q^{69} +1.99437 q^{70} -12.4228 q^{71} +2.20462 q^{72} -9.22198 q^{73} -4.69319 q^{74} -2.28136 q^{75} -5.14004 q^{76} +3.73801 q^{77} +9.99864 q^{78} -4.06354 q^{79} +1.00000 q^{80} -10.7535 q^{81} -2.34952 q^{82} +10.7147 q^{83} -4.54988 q^{84} -2.44884 q^{85} -9.31769 q^{86} -18.6636 q^{87} +1.87428 q^{88} +1.69710 q^{89} +2.20462 q^{90} -8.74082 q^{91} +5.32780 q^{92} +22.0859 q^{93} -1.00015 q^{94} -5.14004 q^{95} -2.28136 q^{96} +13.8088 q^{97} -3.02249 q^{98} +4.13207 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * 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
$3$	−2.28136	−1.31715	−0.658573	−	0.752517i	$-0.728840\pi$
$3$	−2.28136	−1.31715	−0.658573	+	0.752517i	$0.728840\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.28136	−0.931363
$7$	1.99437	0.753801	0.376901	−	0.926254i	$-0.376990\pi$
$7$	1.99437	0.753801	0.376901	+	0.926254i	$0.376990\pi$
$8$	1.00000	0.353553
$9$	2.20462	0.734873
$10$	1.00000	0.316228
$11$	1.87428	0.565116	0.282558	−	0.959250i	$-0.408817\pi$
$11$	1.87428	0.565116	0.282558	+	0.959250i	$0.408817\pi$
$12$	−2.28136	−0.658573
$13$	−4.38275	−1.21556	−0.607778	−	0.794107i	$-0.707939\pi$
$13$	−4.38275	−1.21556	−0.607778	+	0.794107i	$0.707939\pi$
$14$	1.99437	0.533018
$15$	−2.28136	−0.589046
$16$	1.00000	0.250000
$17$	−2.44884	−0.593931	−0.296965	−	0.954888i	$-0.595975\pi$
$17$	−2.44884	−0.593931	−0.296965	+	0.954888i	$0.595975\pi$
$18$	2.20462	0.519634
$19$	−5.14004	−1.17921	−0.589603	−	0.807693i	$-0.700716\pi$
$19$	−5.14004	−1.17921	−0.589603	+	0.807693i	$0.700716\pi$
$20$	1.00000	0.223607
$21$	−4.54988	−0.992866
$22$	1.87428	0.399598
$23$	5.32780	1.11092	0.555462	−	0.831542i	$-0.312542\pi$
$23$	5.32780	1.11092	0.555462	+	0.831542i	$0.312542\pi$
$24$	−2.28136	−0.465681
$25$	1.00000	0.200000
$26$	−4.38275	−0.859528
$27$	1.81455	0.349210
$28$	1.99437	0.376901
$29$	8.18089	1.51915	0.759576	−	0.650418i	$-0.225406\pi$
$29$	8.18089	1.51915	0.759576	+	0.650418i	$0.225406\pi$
$30$	−2.28136	−0.416518
$31$	−9.68099	−1.73876	−0.869379	−	0.494146i	$-0.835481\pi$
$31$	−9.68099	−1.73876	−0.869379	+	0.494146i	$0.835481\pi$
$32$	1.00000	0.176777
$33$	−4.27591	−0.744341
$34$	−2.44884	−0.419973
$35$	1.99437	0.337110
$36$	2.20462	0.367437
$37$	−4.69319	−0.771556	−0.385778	−	0.922592i	$-0.626067\pi$
$37$	−4.69319	−0.771556	−0.385778	+	0.922592i	$0.626067\pi$
$38$	−5.14004	−0.833825
$39$	9.99864	1.60106
$40$	1.00000	0.158114
$41$	−2.34952	−0.366934	−0.183467	−	0.983026i	$-0.558732\pi$
$41$	−2.34952	−0.366934	−0.183467	+	0.983026i	$0.558732\pi$
$42$	−4.54988	−0.702062
$43$	−9.31769	−1.42093	−0.710467	−	0.703731i	$-0.751516\pi$
$43$	−9.31769	−1.42093	−0.710467	+	0.703731i	$0.751516\pi$
$44$	1.87428	0.282558
$45$	2.20462	0.328645
$46$	5.32780	0.785541
$47$	−1.00015	−0.145887	−0.0729436	−	0.997336i	$-0.523239\pi$
$47$	−1.00015	−0.145887	−0.0729436	+	0.997336i	$0.523239\pi$
$48$	−2.28136	−0.329286
$49$	−3.02249	−0.431784
$50$	1.00000	0.141421
$51$	5.58669	0.782294
$52$	−4.38275	−0.607778
$53$	−3.26390	−0.448331	−0.224165	−	0.974551i	$-0.571966\pi$
$53$	−3.26390	−0.448331	−0.224165	+	0.974551i	$0.571966\pi$
$54$	1.81455	0.246929
$55$	1.87428	0.252728
$56$	1.99437	0.266509
$57$	11.7263	1.55319
$58$	8.18089	1.07420
$59$	−2.78044	−0.361983	−0.180991	−	0.983485i	$-0.557931\pi$
$59$	−2.78044	−0.361983	−0.180991	+	0.983485i	$0.557931\pi$
$60$	−2.28136	−0.294523
$61$	−0.527106	−0.0674890	−0.0337445	−	0.999430i	$-0.510743\pi$
$61$	−0.527106	−0.0674890	−0.0337445	+	0.999430i	$0.510743\pi$
$62$	−9.68099	−1.22949
$63$	4.39683	0.553948
$64$	1.00000	0.125000
$65$	−4.38275	−0.543613
$66$	−4.27591	−0.526328
$67$	6.25111	0.763695	0.381848	−	0.924225i	$-0.375288\pi$
$67$	6.25111	0.763695	0.381848	+	0.924225i	$0.375288\pi$
$68$	−2.44884	−0.296965
$69$	−12.1546	−1.46325
$70$	1.99437	0.238373
$71$	−12.4228	−1.47432	−0.737158	−	0.675721i	$-0.763832\pi$
$71$	−12.4228	−1.47432	−0.737158	+	0.675721i	$0.763832\pi$
$72$	2.20462	0.259817
$73$	−9.22198	−1.07935	−0.539675	−	0.841873i	$-0.681453\pi$
$73$	−9.22198	−1.07935	−0.539675	+	0.841873i	$0.681453\pi$
$74$	−4.69319	−0.545573
$75$	−2.28136	−0.263429
$76$	−5.14004	−0.589603
$77$	3.73801	0.425985
$78$	9.99864	1.13212
$79$	−4.06354	−0.457184	−0.228592	−	0.973522i	$-0.573412\pi$
$79$	−4.06354	−0.457184	−0.228592	+	0.973522i	$0.573412\pi$
$80$	1.00000	0.111803
$81$	−10.7535	−1.19483
$82$	−2.34952	−0.259461
$83$	10.7147	1.17610	0.588048	−	0.808826i	$-0.299897\pi$
$83$	10.7147	1.17610	0.588048	+	0.808826i	$0.299897\pi$
$84$	−4.54988	−0.496433
$85$	−2.44884	−0.265614
$86$	−9.31769	−1.00475
$87$	−18.6636	−2.00095
$88$	1.87428	0.199799
$89$	1.69710	0.179892	0.0899461	−	0.995947i	$-0.471331\pi$
$89$	1.69710	0.179892	0.0899461	+	0.995947i	$0.471331\pi$
$90$	2.20462	0.232387
$91$	−8.74082	−0.916287
$92$	5.32780	0.555462
$93$	22.0859	2.29020
$94$	−1.00015	−0.103158
$95$	−5.14004	−0.527357
$96$	−2.28136	−0.232841
$97$	13.8088	1.40208	0.701038	−	0.713124i	$-0.252720\pi$
$97$	13.8088	1.40208	0.701038	+	0.713124i	$0.252720\pi$
$98$	−3.02249	−0.305317
$99$	4.13207	0.415289
$100$	1.00000	0.100000
$101$	−1.36351	−0.135675	−0.0678374	−	0.997696i	$-0.521610\pi$
$101$	−1.36351	−0.135675	−0.0678374	+	0.997696i	$0.521610\pi$
$102$	5.58669	0.553165
$103$	−6.73160	−0.663284	−0.331642	−	0.943405i	$-0.607603\pi$
$103$	−6.73160	−0.663284	−0.331642	+	0.943405i	$0.607603\pi$
$104$	−4.38275	−0.429764
$105$	−4.54988	−0.444023
$106$	−3.26390	−0.317018
$107$	−1.21947	−0.117890	−0.0589452	−	0.998261i	$-0.518774\pi$
$107$	−1.21947	−0.117890	−0.0589452	+	0.998261i	$0.518774\pi$
$108$	1.81455	0.174605
$109$	7.55973	0.724091	0.362046	−	0.932160i	$-0.382078\pi$
$109$	7.55973	0.724091	0.362046	+	0.932160i	$0.382078\pi$
$110$	1.87428	0.178705
$111$	10.7069	1.01625
$112$	1.99437	0.188450
$113$	16.9666	1.59608	0.798042	−	0.602602i	$-0.205869\pi$
$113$	16.9666	1.59608	0.798042	+	0.602602i	$0.205869\pi$
$114$	11.7263	1.09827
$115$	5.32780	0.496820
$116$	8.18089	0.759576
$117$	−9.66230	−0.893280
$118$	−2.78044	−0.255961
$119$	−4.88389	−0.447706
$120$	−2.28136	−0.208259
$121$	−7.48708	−0.680644
$122$	−0.527106	−0.0477219
$123$	5.36011	0.483305
$124$	−9.68099	−0.869379
$125$	1.00000	0.0894427
$126$	4.39683	0.391701
$127$	−6.40287	−0.568163	−0.284081	−	0.958800i	$-0.591689\pi$
$127$	−6.40287	−0.568163	−0.284081	+	0.958800i	$0.591689\pi$
$128$	1.00000	0.0883883
$129$	21.2570	1.87158
$130$	−4.38275	−0.384392
$131$	7.53069	0.657959	0.328980	−	0.944337i	$-0.393295\pi$
$131$	7.53069	0.657959	0.328980	+	0.944337i	$0.393295\pi$
$132$	−4.27591	−0.372170
$133$	−10.2511	−0.888887
$134$	6.25111	0.540014
$135$	1.81455	0.156172
$136$	−2.44884	−0.209986
$137$	17.6455	1.50755	0.753777	−	0.657130i	$-0.228230\pi$
$137$	17.6455	1.50755	0.753777	+	0.657130i	$0.228230\pi$
$138$	−12.1546	−1.03467
$139$	−11.7390	−0.995692	−0.497846	−	0.867265i	$-0.665875\pi$
$139$	−11.7390	−0.995692	−0.497846	+	0.867265i	$0.665875\pi$
$140$	1.99437	0.168555
$141$	2.28171	0.192155
$142$	−12.4228	−1.04250
$143$	−8.21449	−0.686930
$144$	2.20462	0.183718
$145$	8.18089	0.679386
$146$	−9.22198	−0.763216
$147$	6.89540	0.568723
$148$	−4.69319	−0.385778
$149$	−7.41774	−0.607685	−0.303842	−	0.952722i	$-0.598270\pi$
$149$	−7.41774	−0.607685	−0.303842	+	0.952722i	$0.598270\pi$
$150$	−2.28136	−0.186273
$151$	−13.2359	−1.07712	−0.538562	−	0.842586i	$-0.681032\pi$
$151$	−13.2359	−1.07712	−0.538562	+	0.842586i	$0.681032\pi$
$152$	−5.14004	−0.416913
$153$	−5.39876	−0.436464
$154$	3.73801	0.301217
$155$	−9.68099	−0.777596
$156$	9.99864	0.800532
$157$	−11.5379	−0.920822	−0.460411	−	0.887706i	$-0.652298\pi$
$157$	−11.5379	−0.920822	−0.460411	+	0.887706i	$0.652298\pi$
$158$	−4.06354	−0.323278
$159$	7.44614	0.590517
$160$	1.00000	0.0790569
$161$	10.6256	0.837415
$162$	−10.7535	−0.844876
$163$	6.06917	0.475374	0.237687	−	0.971342i	$-0.423611\pi$
$163$	6.06917	0.475374	0.237687	+	0.971342i	$0.423611\pi$
$164$	−2.34952	−0.183467
$165$	−4.27591	−0.332879
$166$	10.7147	0.831625
$167$	13.6921	1.05953	0.529765	−	0.848145i	$-0.322280\pi$
$167$	13.6921	1.05953	0.529765	+	0.848145i	$0.322280\pi$
$168$	−4.54988	−0.351031
$169$	6.20849	0.477576
$170$	−2.44884	−0.187817
$171$	−11.3318	−0.866568
$172$	−9.31769	−0.710467
$173$	−19.4834	−1.48130	−0.740648	−	0.671893i	$-0.765481\pi$
$173$	−19.4834	−1.48130	−0.740648	+	0.671893i	$0.765481\pi$
$174$	−18.6636	−1.41488
$175$	1.99437	0.150760
$176$	1.87428	0.141279
$177$	6.34320	0.476784
$178$	1.69710	0.127203
$179$	7.94386	0.593752	0.296876	−	0.954916i	$-0.404055\pi$
$179$	7.94386	0.593752	0.296876	+	0.954916i	$0.404055\pi$
$180$	2.20462	0.164323
$181$	−12.1441	−0.902660	−0.451330	−	0.892357i	$-0.649050\pi$
$181$	−12.1441	−0.902660	−0.451330	+	0.892357i	$0.649050\pi$
$182$	−8.74082	−0.647913
$183$	1.20252	0.0888928
$184$	5.32780	0.392771
$185$	−4.69319	−0.345051
$186$	22.0859	1.61941
$187$	−4.58981	−0.335640
$188$	−1.00015	−0.0729436
$189$	3.61888	0.263235
$190$	−5.14004	−0.372898
$191$	21.8649	1.58209	0.791045	−	0.611758i	$-0.209537\pi$
$191$	21.8649	1.58209	0.791045	+	0.611758i	$0.209537\pi$
$192$	−2.28136	−0.164643
$193$	−25.8490	−1.86065	−0.930324	−	0.366738i	$-0.880475\pi$
$193$	−25.8490	−1.86065	−0.930324	+	0.366738i	$0.880475\pi$
$194$	13.8088	0.991418
$195$	9.99864	0.716018
$196$	−3.02249	−0.215892
$197$	−7.50208	−0.534501	−0.267250	−	0.963627i	$-0.586115\pi$
$197$	−7.50208	−0.534501	−0.267250	+	0.963627i	$0.586115\pi$
$198$	4.13207	0.293654
$199$	1.81387	0.128582	0.0642908	−	0.997931i	$-0.479521\pi$
$199$	1.81387	0.128582	0.0642908	+	0.997931i	$0.479521\pi$
$200$	1.00000	0.0707107
$201$	−14.2611	−1.00590
$202$	−1.36351	−0.0959365
$203$	16.3157	1.14514
$204$	5.58669	0.391147
$205$	−2.34952	−0.164098
$206$	−6.73160	−0.469013
$207$	11.7458	0.816388
$208$	−4.38275	−0.303889
$209$	−9.63387	−0.666389
$210$	−4.54988	−0.313972
$211$	12.3024	0.846931	0.423466	−	0.905912i	$-0.360813\pi$
$211$	12.3024	0.846931	0.423466	+	0.905912i	$0.360813\pi$
$212$	−3.26390	−0.224165
$213$	28.3409	1.94189
$214$	−1.21947	−0.0833611
$215$	−9.31769	−0.635461
$216$	1.81455	0.123465
$217$	−19.3075	−1.31068
$218$	7.55973	0.512010
$219$	21.0387	1.42166
$220$	1.87428	0.126364
$221$	10.7326	0.721956
$222$	10.7069	0.718599
$223$	−5.44946	−0.364923	−0.182461	−	0.983213i	$-0.558406\pi$
$223$	−5.44946	−0.364923	−0.182461	+	0.983213i	$0.558406\pi$
$224$	1.99437	0.133254
$225$	2.20462	0.146975
$226$	16.9666	1.12860
$227$	−17.8644	−1.18570	−0.592852	−	0.805311i	$-0.701998\pi$
$227$	−17.8644	−1.18570	−0.592852	+	0.805311i	$0.701998\pi$
$228$	11.7263	0.776594
$229$	−13.3168	−0.879996	−0.439998	−	0.897999i	$-0.645021\pi$
$229$	−13.3168	−0.879996	−0.439998	+	0.897999i	$0.645021\pi$
$230$	5.32780	0.351305
$231$	−8.52775	−0.561085
$232$	8.18089	0.537101
$233$	−4.00562	−0.262417	−0.131209	−	0.991355i	$-0.541886\pi$
$233$	−4.00562	−0.262417	−0.131209	+	0.991355i	$0.541886\pi$
$234$	−9.66230	−0.631644
$235$	−1.00015	−0.0652427
$236$	−2.78044	−0.180991
$237$	9.27042	0.602179
$238$	−4.88389	−0.316576
$239$	10.2326	0.661893	0.330946	−	0.943650i	$-0.392632\pi$
$239$	10.2326	0.661893	0.330946	+	0.943650i	$0.392632\pi$
$240$	−2.28136	−0.147261
$241$	−29.0639	−1.87217	−0.936084	−	0.351777i	$-0.885578\pi$
$241$	−29.0639	−1.87217	−0.936084	+	0.351777i	$0.885578\pi$
$242$	−7.48708	−0.481288
$243$	19.0890	1.22456
$244$	−0.527106	−0.0337445
$245$	−3.02249	−0.193100
$246$	5.36011	0.341748
$247$	22.5275	1.43339
$248$	−9.68099	−0.614744
$249$	−24.4442	−1.54909
$250$	1.00000	0.0632456
$251$	−10.3519	−0.653406	−0.326703	−	0.945127i	$-0.605938\pi$
$251$	−10.3519	−0.653406	−0.326703	+	0.945127i	$0.605938\pi$
$252$	4.39683	0.276974
$253$	9.98578	0.627801
$254$	−6.40287	−0.401752
$255$	5.58669	0.349852
$256$	1.00000	0.0625000
$257$	−27.5708	−1.71982	−0.859909	−	0.510448i	$-0.829480\pi$
$257$	−27.5708	−1.71982	−0.859909	+	0.510448i	$0.829480\pi$
$258$	21.2570	1.32340
$259$	−9.35997	−0.581600
$260$	−4.38275	−0.271807
$261$	18.0357	1.11638
$262$	7.53069	0.465247
$263$	31.1715	1.92212	0.961058	−	0.276347i	$-0.0891237\pi$
$263$	31.1715	1.92212	0.961058	+	0.276347i	$0.0891237\pi$
$264$	−4.27591	−0.263164
$265$	−3.26390	−0.200500
$266$	−10.2511	−0.628538
$267$	−3.87170	−0.236944
$268$	6.25111	0.381848
$269$	−8.33487	−0.508186	−0.254093	−	0.967180i	$-0.581777\pi$
$269$	−8.33487	−0.508186	−0.254093	+	0.967180i	$0.581777\pi$
$270$	1.81455	0.110430
$271$	−19.7981	−1.20265	−0.601324	−	0.799005i	$-0.705360\pi$
$271$	−19.7981	−1.20265	−0.601324	+	0.799005i	$0.705360\pi$
$272$	−2.44884	−0.148483
$273$	19.9410	1.20688
$274$	17.6455	1.06600
$275$	1.87428	0.113023
$276$	−12.1546	−0.731624
$277$	−13.6513	−0.820227	−0.410114	−	0.912034i	$-0.634511\pi$
$277$	−13.6513	−0.820227	−0.410114	+	0.912034i	$0.634511\pi$
$278$	−11.7390	−0.704060
$279$	−21.3429	−1.27777
$280$	1.99437	0.119186
$281$	−14.9118	−0.889564	−0.444782	−	0.895639i	$-0.646719\pi$
$281$	−14.9118	−0.889564	−0.444782	+	0.895639i	$0.646719\pi$
$282$	2.28171	0.135874
$283$	14.8349	0.881843	0.440921	−	0.897546i	$-0.354652\pi$
$283$	14.8349	0.881843	0.440921	+	0.897546i	$0.354652\pi$
$284$	−12.4228	−0.737158
$285$	11.7263	0.694607
$286$	−8.21449	−0.485733
$287$	−4.68582	−0.276595
$288$	2.20462	0.129908
$289$	−11.0032	−0.647246
$290$	8.18089	0.480398
$291$	−31.5030	−1.84674
$292$	−9.22198	−0.539675
$293$	15.8005	0.923076	0.461538	−	0.887120i	$-0.347298\pi$
$293$	15.8005	0.923076	0.461538	+	0.887120i	$0.347298\pi$
$294$	6.89540	0.402148
$295$	−2.78044	−0.161884
$296$	−4.69319	−0.272786
$297$	3.40097	0.197344
$298$	−7.41774	−0.429698
$299$	−23.3504	−1.35039
$300$	−2.28136	−0.131715
$301$	−18.5829	−1.07110
$302$	−13.2359	−0.761642
$303$	3.11067	0.178703
$304$	−5.14004	−0.294802
$305$	−0.527106	−0.0301820
$306$	−5.39876	−0.308627
$307$	−19.8280	−1.13165	−0.565823	−	0.824527i	$-0.691442\pi$
$307$	−19.8280	−1.13165	−0.565823	+	0.824527i	$0.691442\pi$
$308$	3.73801	0.212993
$309$	15.3572	0.873642
$310$	−9.68099	−0.549843
$311$	−4.80236	−0.272317	−0.136158	−	0.990687i	$-0.543476\pi$
$311$	−4.80236	−0.272317	−0.136158	+	0.990687i	$0.543476\pi$
$312$	9.99864	0.566062
$313$	−9.73399	−0.550198	−0.275099	−	0.961416i	$-0.588711\pi$
$313$	−9.73399	−0.550198	−0.275099	+	0.961416i	$0.588711\pi$
$314$	−11.5379	−0.651119
$315$	4.39683	0.247733
$316$	−4.06354	−0.228592
$317$	−3.27762	−0.184090	−0.0920448	−	0.995755i	$-0.529340\pi$
$317$	−3.27762	−0.184090	−0.0920448	+	0.995755i	$0.529340\pi$
$318$	7.44614	0.417559
$319$	15.3333	0.858498
$320$	1.00000	0.0559017
$321$	2.78205	0.155279
$322$	10.6256	0.592142
$323$	12.5871	0.700367
$324$	−10.7535	−0.597417
$325$	−4.38275	−0.243111
$326$	6.06917	0.336140
$327$	−17.2465	−0.953734
$328$	−2.34952	−0.129731
$329$	−1.99467	−0.109970
$330$	−4.27591	−0.235381
$331$	6.01441	0.330582	0.165291	−	0.986245i	$-0.447144\pi$
$331$	6.01441	0.330582	0.165291	+	0.986245i	$0.447144\pi$
$332$	10.7147	0.588048
$333$	−10.3467	−0.566996
$334$	13.6921	0.749201
$335$	6.25111	0.341535
$336$	−4.54988	−0.248216
$337$	−16.7042	−0.909934	−0.454967	−	0.890508i	$-0.650349\pi$
$337$	−16.7042	−0.909934	−0.454967	+	0.890508i	$0.650349\pi$
$338$	6.20849	0.337697
$339$	−38.7070	−2.10227
$340$	−2.44884	−0.132807
$341$	−18.1449	−0.982600
$342$	−11.3318	−0.612756
$343$	−19.9886	−1.07928
$344$	−9.31769	−0.502376
$345$	−12.1546	−0.654384
$346$	−19.4834	−1.04743
$347$	−20.2128	−1.08508	−0.542540	−	0.840030i	$-0.682537\pi$
$347$	−20.2128	−1.08508	−0.542540	+	0.840030i	$0.682537\pi$
$348$	−18.6636	−1.00047
$349$	32.1542	1.72118	0.860588	−	0.509302i	$-0.170096\pi$
$349$	32.1542	1.72118	0.860588	+	0.509302i	$0.170096\pi$
$350$	1.99437	0.106604
$351$	−7.95272	−0.424485
$352$	1.87428	0.0998994
$353$	20.1440	1.07216	0.536080	−	0.844167i	$-0.319905\pi$
$353$	20.1440	1.07216	0.536080	+	0.844167i	$0.319905\pi$
$354$	6.34320	0.337137
$355$	−12.4228	−0.659334
$356$	1.69710	0.0899461
$357$	11.1419	0.589694
$358$	7.94386	0.419846
$359$	−27.2113	−1.43616	−0.718078	−	0.695963i	$-0.754978\pi$
$359$	−27.2113	−1.43616	−0.718078	+	0.695963i	$0.754978\pi$
$360$	2.20462	0.116194
$361$	7.42004	0.390529
$362$	−12.1441	−0.638277
$363$	17.0808	0.896507
$364$	−8.74082	−0.458144
$365$	−9.22198	−0.482700
$366$	1.20252	0.0628567
$367$	28.2878	1.47661	0.738306	−	0.674466i	$-0.235626\pi$
$367$	28.2878	1.47661	0.738306	+	0.674466i	$0.235626\pi$
$368$	5.32780	0.277731
$369$	−5.17980	−0.269650
$370$	−4.69319	−0.243988
$371$	−6.50942	−0.337952
$372$	22.0859	1.14510
$373$	−0.976114	−0.0505413	−0.0252706	−	0.999681i	$-0.508045\pi$
$373$	−0.976114	−0.0505413	−0.0252706	+	0.999681i	$0.508045\pi$
$374$	−4.58981	−0.237333
$375$	−2.28136	−0.117809
$376$	−1.00015	−0.0515789
$377$	−35.8548	−1.84661
$378$	3.61888	0.186135
$379$	8.48882	0.436042	0.218021	−	0.975944i	$-0.430040\pi$
$379$	8.48882	0.436042	0.218021	+	0.975944i	$0.430040\pi$
$380$	−5.14004	−0.263679
$381$	14.6073	0.748354
$382$	21.8649	1.11871
$383$	−10.1052	−0.516354	−0.258177	−	0.966098i	$-0.583122\pi$
$383$	−10.1052	−0.516354	−0.258177	+	0.966098i	$0.583122\pi$
$384$	−2.28136	−0.116420
$385$	3.73801	0.190506
$386$	−25.8490	−1.31568
$387$	−20.5420	−1.04421
$388$	13.8088	0.701038
$389$	−18.1330	−0.919380	−0.459690	−	0.888080i	$-0.652039\pi$
$389$	−18.1330	−0.919380	−0.459690	+	0.888080i	$0.652039\pi$
$390$	9.99864	0.506301
$391$	−13.0469	−0.659811
$392$	−3.02249	−0.152659
$393$	−17.1802	−0.866628
$394$	−7.50208	−0.377949
$395$	−4.06354	−0.204459
$396$	4.13207	0.207644
$397$	13.6402	0.684584	0.342292	−	0.939594i	$-0.388797\pi$
$397$	13.6402	0.684584	0.342292	+	0.939594i	$0.388797\pi$
$398$	1.81387	0.0909209
$399$	23.3866	1.17079
$400$	1.00000	0.0500000
$401$	−2.29121	−0.114417	−0.0572087	−	0.998362i	$-0.518220\pi$
$401$	−2.29121	−0.114417	−0.0572087	+	0.998362i	$0.518220\pi$
$402$	−14.2611	−0.711277
$403$	42.4294	2.11356
$404$	−1.36351	−0.0678374
$405$	−10.7535	−0.534346
$406$	16.3157	0.809735
$407$	−8.79635	−0.436019
$408$	5.58669	0.276583
$409$	−18.8708	−0.933101	−0.466551	−	0.884495i	$-0.654503\pi$
$409$	−18.8708	−0.933101	−0.466551	+	0.884495i	$0.654503\pi$
$410$	−2.34952	−0.116035
$411$	−40.2557	−1.98567
$412$	−6.73160	−0.331642
$413$	−5.54523	−0.272863
$414$	11.7458	0.577273
$415$	10.7147	0.525966
$416$	−4.38275	−0.214882
$417$	26.7810	1.31147
$418$	−9.63387	−0.471208
$419$	8.02753	0.392170	0.196085	−	0.980587i	$-0.437177\pi$
$419$	8.02753	0.392170	0.196085	+	0.980587i	$0.437177\pi$
$420$	−4.54988	−0.222012
$421$	−32.1899	−1.56884	−0.784420	−	0.620230i	$-0.787039\pi$
$421$	−32.1899	−1.56884	−0.784420	+	0.620230i	$0.787039\pi$
$422$	12.3024	0.598871
$423$	−2.20496	−0.107209
$424$	−3.26390	−0.158509
$425$	−2.44884	−0.118786
$426$	28.3409	1.37312
$427$	−1.05124	−0.0508733
$428$	−1.21947	−0.0589452
$429$	18.7402	0.904788
$430$	−9.31769	−0.449339
$431$	−38.2579	−1.84282	−0.921408	−	0.388597i	$-0.872960\pi$
$431$	−38.2579	−1.84282	−0.921408	+	0.388597i	$0.872960\pi$
$432$	1.81455	0.0873026
$433$	−0.870006	−0.0418098	−0.0209049	−	0.999781i	$-0.506655\pi$
$433$	−0.870006	−0.0418098	−0.0209049	+	0.999781i	$0.506655\pi$
$434$	−19.3075	−0.926789
$435$	−18.6636	−0.894850
$436$	7.55973	0.362046
$437$	−27.3851	−1.31001
$438$	21.0387	1.00527
$439$	15.3880	0.734431	0.367216	−	0.930136i	$-0.380311\pi$
$439$	15.3880	0.734431	0.367216	+	0.930136i	$0.380311\pi$
$440$	1.87428	0.0893527
$441$	−6.66344	−0.317307
$442$	10.7326	0.510500
$443$	13.5024	0.641519	0.320759	−	0.947161i	$-0.396062\pi$
$443$	13.5024	0.641519	0.320759	+	0.947161i	$0.396062\pi$
$444$	10.7069	0.508126
$445$	1.69710	0.0804502
$446$	−5.44946	−0.258039
$447$	16.9226	0.800409
$448$	1.99437	0.0942251
$449$	1.21920	0.0575376	0.0287688	−	0.999586i	$-0.490841\pi$
$449$	1.21920	0.0575376	0.0287688	+	0.999586i	$0.490841\pi$
$450$	2.20462	0.103927
$451$	−4.40366	−0.207360
$452$	16.9666	0.798042
$453$	30.1960	1.41873
$454$	−17.8644	−0.838420
$455$	−8.74082	−0.409776
$456$	11.7263	0.549135
$457$	−14.6280	−0.684267	−0.342133	−	0.939651i	$-0.611149\pi$
$457$	−14.6280	−0.684267	−0.342133	+	0.939651i	$0.611149\pi$
$458$	−13.3168	−0.622251
$459$	−4.44354	−0.207407
$460$	5.32780	0.248410
$461$	−38.2518	−1.78156	−0.890782	−	0.454430i	$-0.849843\pi$
$461$	−38.2518	−1.78156	−0.890782	+	0.454430i	$0.849843\pi$
$462$	−8.52775	−0.396747
$463$	29.1991	1.35700	0.678498	−	0.734602i	$-0.262631\pi$
$463$	29.1991	1.35700	0.678498	+	0.734602i	$0.262631\pi$
$464$	8.18089	0.379788
$465$	22.0859	1.02421
$466$	−4.00562	−0.185557
$467$	32.0814	1.48455	0.742276	−	0.670094i	$-0.233746\pi$
$467$	32.0814	1.48455	0.742276	+	0.670094i	$0.233746\pi$
$468$	−9.66230	−0.446640
$469$	12.4670	0.575674
$470$	−1.00015	−0.0461336
$471$	26.3221	1.21286
$472$	−2.78044	−0.127980
$473$	−17.4639	−0.802993
$474$	9.27042	0.425805
$475$	−5.14004	−0.235841
$476$	−4.88389	−0.223853
$477$	−7.19566	−0.329467
$478$	10.2326	0.468029
$479$	2.21543	0.101226	0.0506129	−	0.998718i	$-0.483883\pi$
$479$	2.21543	0.101226	0.0506129	+	0.998718i	$0.483883\pi$
$480$	−2.28136	−0.104130
$481$	20.5691	0.937870
$482$	−29.0639	−1.32382
$483$	−24.2409	−1.10300
$484$	−7.48708	−0.340322
$485$	13.8088	0.627028
$486$	19.0890	0.865895
$487$	6.19322	0.280642	0.140321	−	0.990106i	$-0.455187\pi$
$487$	6.19322	0.280642	0.140321	+	0.990106i	$0.455187\pi$
$488$	−0.527106	−0.0238610
$489$	−13.8460	−0.626137
$490$	−3.02249	−0.136542
$491$	7.75169	0.349829	0.174914	−	0.984584i	$-0.444035\pi$
$491$	7.75169	0.349829	0.174914	+	0.984584i	$0.444035\pi$
$492$	5.36011	0.241653
$493$	−20.0337	−0.902271
$494$	22.5275	1.01356
$495$	4.13207	0.185723
$496$	−9.68099	−0.434689
$497$	−24.7757	−1.11134
$498$	−24.4442	−1.09537
$499$	−1.76473	−0.0790003	−0.0395002	−	0.999220i	$-0.512577\pi$
$499$	−1.76473	−0.0790003	−0.0395002	+	0.999220i	$0.512577\pi$
$500$	1.00000	0.0447214
$501$	−31.2368	−1.39556
$502$	−10.3519	−0.462028
$503$	−16.8768	−0.752499	−0.376249	−	0.926518i	$-0.622786\pi$
$503$	−16.8768	−0.752499	−0.376249	+	0.926518i	$0.622786\pi$
$504$	4.39683	0.195850
$505$	−1.36351	−0.0606756
$506$	9.98578	0.443922
$507$	−14.1638	−0.629037
$508$	−6.40287	−0.284081
$509$	45.0177	1.99538	0.997688	−	0.0679615i	$-0.0216495\pi$
$509$	45.0177	1.99538	0.997688	+	0.0679615i	$0.0216495\pi$
$510$	5.58669	0.247383
$511$	−18.3920	−0.813616
$512$	1.00000	0.0441942
$513$	−9.32687	−0.411791
$514$	−27.5708	−1.21609
$515$	−6.73160	−0.296630
$516$	21.2570	0.935789
$517$	−1.87456	−0.0824432
$518$	−9.35997	−0.411253
$519$	44.4488	1.95108
$520$	−4.38275	−0.192196
$521$	−6.30714	−0.276321	−0.138160	−	0.990410i	$-0.544119\pi$
$521$	−6.30714	−0.276321	−0.138160	+	0.990410i	$0.544119\pi$
$522$	18.0357	0.789403
$523$	−37.5327	−1.64119	−0.820595	−	0.571510i	$-0.806358\pi$
$523$	−37.5327	−1.64119	−0.820595	+	0.571510i	$0.806358\pi$
$524$	7.53069	0.328980
$525$	−4.54988	−0.198573
$526$	31.1715	1.35914
$527$	23.7072	1.03270
$528$	−4.27591	−0.186085
$529$	5.38545	0.234150
$530$	−3.26390	−0.141775
$531$	−6.12982	−0.266012
$532$	−10.2511	−0.444444
$533$	10.2974	0.446028
$534$	−3.87170	−0.167545
$535$	−1.21947	−0.0527222
$536$	6.25111	0.270007
$537$	−18.1228	−0.782058
$538$	−8.33487	−0.359342
$539$	−5.66499	−0.244008
$540$	1.81455	0.0780858
$541$	−4.46479	−0.191956	−0.0959782	−	0.995383i	$-0.530598\pi$
$541$	−4.46479	−0.191956	−0.0959782	+	0.995383i	$0.530598\pi$
$542$	−19.7981	−0.850401
$543$	27.7050	1.18894
$544$	−2.44884	−0.104993
$545$	7.55973	0.323823
$546$	19.9410	0.853396
$547$	26.3218	1.12544	0.562720	−	0.826648i	$-0.309755\pi$
$547$	26.3218	1.12544	0.562720	+	0.826648i	$0.309755\pi$
$548$	17.6455	0.753777
$549$	−1.16207	−0.0495959
$550$	1.87428	0.0799195
$551$	−42.0501	−1.79139
$552$	−12.1546	−0.517336
$553$	−8.10421	−0.344626
$554$	−13.6513	−0.579988
$555$	10.7069	0.454482
$556$	−11.7390	−0.497846
$557$	1.70559	0.0722680	0.0361340	−	0.999347i	$-0.488496\pi$
$557$	1.70559	0.0722680	0.0361340	+	0.999347i	$0.488496\pi$
$558$	−21.3429	−0.903518
$559$	40.8371	1.72722
$560$	1.99437	0.0842775
$561$	10.4710	0.442087
$562$	−14.9118	−0.629017
$563$	44.0436	1.85622	0.928109	−	0.372309i	$-0.121434\pi$
$563$	44.0436	1.85622	0.928109	+	0.372309i	$0.121434\pi$
$564$	2.28171	0.0960774
$565$	16.9666	0.713790
$566$	14.8349	0.623557
$567$	−21.4465	−0.900667
$568$	−12.4228	−0.521249
$569$	14.8842	0.623978	0.311989	−	0.950086i	$-0.399005\pi$
$569$	14.8842	0.623978	0.311989	+	0.950086i	$0.399005\pi$
$570$	11.7263	0.491161
$571$	29.4256	1.23142	0.615712	−	0.787972i	$-0.288869\pi$
$571$	29.4256	1.23142	0.615712	+	0.787972i	$0.288869\pi$
$572$	−8.21449	−0.343465
$573$	−49.8818	−2.08384
$574$	−4.68582	−0.195582
$575$	5.32780	0.222185
$576$	2.20462	0.0918592
$577$	9.19120	0.382635	0.191317	−	0.981528i	$-0.438724\pi$
$577$	9.19120	0.382635	0.191317	+	0.981528i	$0.438724\pi$
$578$	−11.0032	−0.457672
$579$	58.9709	2.45075
$580$	8.18089	0.339693
$581$	21.3692	0.886542
$582$	−31.5030	−1.30584
$583$	−6.11746	−0.253359
$584$	−9.22198	−0.381608
$585$	−9.66230	−0.399487
$586$	15.8005	0.652714
$587$	47.8954	1.97685	0.988426	−	0.151701i	$-0.0484752\pi$
$587$	47.8954	1.97685	0.988426	+	0.151701i	$0.0484752\pi$
$588$	6.89540	0.284361
$589$	49.7607	2.05035
$590$	−2.78044	−0.114469
$591$	17.1150	0.704016
$592$	−4.69319	−0.192889
$593$	6.26015	0.257073	0.128537	−	0.991705i	$-0.458972\pi$
$593$	6.26015	0.257073	0.128537	+	0.991705i	$0.458972\pi$
$594$	3.40097	0.139544
$595$	−4.88389	−0.200220
$596$	−7.41774	−0.303842
$597$	−4.13809	−0.169361
$598$	−23.3504	−0.954869
$599$	−9.68059	−0.395538	−0.197769	−	0.980249i	$-0.563370\pi$
$599$	−9.68059	−0.395538	−0.197769	+	0.980249i	$0.563370\pi$
$600$	−2.28136	−0.0931363
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	−18.5829	−0.757383
$603$	13.7813	0.561219
$604$	−13.2359	−0.538562
$605$	−7.48708	−0.304393
$606$	3.11067	0.126362
$607$	−36.2345	−1.47071	−0.735357	−	0.677680i	$-0.762986\pi$
$607$	−36.2345	−1.47071	−0.735357	+	0.677680i	$0.762986\pi$
$608$	−5.14004	−0.208456
$609$	−37.2221	−1.50831
$610$	−0.527106	−0.0213419
$611$	4.38342	0.177334
$612$	−5.39876	−0.218232
$613$	36.1691	1.46086	0.730428	−	0.682990i	$-0.239321\pi$
$613$	36.1691	1.46086	0.730428	+	0.682990i	$0.239321\pi$
$614$	−19.8280	−0.800195
$615$	5.36011	0.216141
$616$	3.73801	0.150609
$617$	−28.2435	−1.13704	−0.568520	−	0.822669i	$-0.692484\pi$
$617$	−28.2435	−1.13704	−0.568520	+	0.822669i	$0.692484\pi$
$618$	15.3572	0.617758
$619$	35.3820	1.42212	0.711061	−	0.703130i	$-0.248215\pi$
$619$	35.3820	1.42212	0.711061	+	0.703130i	$0.248215\pi$
$620$	−9.68099	−0.388798
$621$	9.66756	0.387946
$622$	−4.80236	−0.192557
$623$	3.38464	0.135603
$624$	9.99864	0.400266
$625$	1.00000	0.0400000
$626$	−9.73399	−0.389049
$627$	21.9784	0.877731
$628$	−11.5379	−0.460411
$629$	11.4929	0.458251
$630$	4.39683	0.175174
$631$	−20.1738	−0.803107	−0.401553	−	0.915836i	$-0.631530\pi$
$631$	−20.1738	−0.803107	−0.401553	+	0.915836i	$0.631530\pi$
$632$	−4.06354	−0.161639
$633$	−28.0662	−1.11553
$634$	−3.27762	−0.130171
$635$	−6.40287	−0.254090
$636$	7.44614	0.295259
$637$	13.2468	0.524858
$638$	15.3333	0.607050
$639$	−27.3876	−1.08343
$640$	1.00000	0.0395285
$641$	23.3534	0.922405	0.461203	−	0.887295i	$-0.347418\pi$
$641$	23.3534	0.922405	0.461203	+	0.887295i	$0.347418\pi$
$642$	2.78205	0.109799
$643$	39.7730	1.56849	0.784247	−	0.620449i	$-0.213049\pi$
$643$	39.7730	1.56849	0.784247	+	0.620449i	$0.213049\pi$
$644$	10.6256	0.418707
$645$	21.2570	0.836995
$646$	12.5871	0.495234
$647$	−28.9077	−1.13648	−0.568240	−	0.822863i	$-0.692376\pi$
$647$	−28.9077	−1.13648	−0.568240	+	0.822863i	$0.692376\pi$
$648$	−10.7535	−0.422438
$649$	−5.21132	−0.204562
$650$	−4.38275	−0.171906
$651$	44.0474	1.72635
$652$	6.06917	0.237687
$653$	23.0429	0.901737	0.450869	−	0.892590i	$-0.351114\pi$
$653$	23.0429	0.901737	0.450869	+	0.892590i	$0.351114\pi$
$654$	−17.2465	−0.674391
$655$	7.53069	0.294248
$656$	−2.34952	−0.0917334
$657$	−20.3310	−0.793186
$658$	−1.99467	−0.0777605
$659$	−11.5214	−0.448811	−0.224405	−	0.974496i	$-0.572044\pi$
$659$	−11.5214	−0.448811	−0.224405	+	0.974496i	$0.572044\pi$
$660$	−4.27591	−0.166440
$661$	34.2954	1.33394	0.666969	−	0.745086i	$-0.267591\pi$
$661$	34.2954	1.33394	0.666969	+	0.745086i	$0.267591\pi$
$662$	6.01441	0.233757
$663$	−24.4851	−0.950922
$664$	10.7147	0.415813
$665$	−10.2511	−0.397522
$666$	−10.3467	−0.400927
$667$	43.5861	1.68766
$668$	13.6921	0.529765
$669$	12.4322	0.480656
$670$	6.25111	0.241502
$671$	−0.987943	−0.0381391
$672$	−4.54988	−0.175516
$673$	1.47480	0.0568495	0.0284247	−	0.999596i	$-0.490951\pi$
$673$	1.47480	0.0568495	0.0284247	+	0.999596i	$0.490951\pi$
$674$	−16.7042	−0.643420
$675$	1.81455	0.0698421
$676$	6.20849	0.238788
$677$	−1.61020	−0.0618849	−0.0309424	−	0.999521i	$-0.509851\pi$
$677$	−1.61020	−0.0618849	−0.0309424	+	0.999521i	$0.509851\pi$
$678$	−38.7070	−1.48653
$679$	27.5400	1.05689
$680$	−2.44884	−0.0939087
$681$	40.7553	1.56175
$682$	−18.1449	−0.694803
$683$	47.2327	1.80731	0.903655	−	0.428261i	$-0.140874\pi$
$683$	47.2327	1.80731	0.903655	+	0.428261i	$0.140874\pi$
$684$	−11.3318	−0.433284
$685$	17.6455	0.674199
$686$	−19.9886	−0.763166
$687$	30.3804	1.15908
$688$	−9.31769	−0.355233
$689$	14.3048	0.544971
$690$	−12.1546	−0.462720
$691$	−30.5215	−1.16109	−0.580547	−	0.814227i	$-0.697161\pi$
$691$	−30.5215	−1.16109	−0.580547	+	0.814227i	$0.697161\pi$
$692$	−19.4834	−0.740648
$693$	8.24088	0.313045
$694$	−20.2128	−0.767268
$695$	−11.7390	−0.445287
$696$	−18.6636	−0.707441
$697$	5.75360	0.217933
$698$	32.1542	1.21706
$699$	9.13828	0.345642
$700$	1.99437	0.0753801
$701$	43.5429	1.64459	0.822296	−	0.569059i	$-0.192693\pi$
$701$	43.5429	1.64459	0.822296	+	0.569059i	$0.192693\pi$
$702$	−7.95272	−0.300156
$703$	24.1232	0.909824
$704$	1.87428	0.0706395
$705$	2.28171	0.0859342
$706$	20.1440	0.758131
$707$	−2.71935	−0.102272
$708$	6.34320	0.238392
$709$	−23.2550	−0.873361	−0.436680	−	0.899617i	$-0.643846\pi$
$709$	−23.2550	−0.873361	−0.436680	+	0.899617i	$0.643846\pi$
$710$	−12.4228	−0.466219
$711$	−8.95857	−0.335973
$712$	1.69710	0.0636015
$713$	−51.5784	−1.93163
$714$	11.1419	0.416976
$715$	−8.21449	−0.307205
$716$	7.94386	0.296876
$717$	−23.3443	−0.871809
$718$	−27.2113	−1.01552
$719$	−29.4691	−1.09901	−0.549506	−	0.835490i	$-0.685184\pi$
$719$	−29.4691	−1.09901	−0.549506	+	0.835490i	$0.685184\pi$
$720$	2.20462	0.0821613
$721$	−13.4253	−0.499984
$722$	7.42004	0.276145
$723$	66.3052	2.46592
$724$	−12.1441	−0.451330
$725$	8.18089	0.303830
$726$	17.0808	0.633926
$727$	7.82904	0.290363	0.145182	−	0.989405i	$-0.453623\pi$
$727$	7.82904	0.290363	0.145182	+	0.989405i	$0.453623\pi$
$728$	−8.74082	−0.323956
$729$	−11.2885	−0.418091
$730$	−9.22198	−0.341321
$731$	22.8175	0.843936
$732$	1.20252	0.0444464
$733$	−17.0264	−0.628883	−0.314441	−	0.949277i	$-0.601817\pi$
$733$	−17.0264	−0.628883	−0.314441	+	0.949277i	$0.601817\pi$
$734$	28.2878	1.04412
$735$	6.89540	0.254340
$736$	5.32780	0.196385
$737$	11.7163	0.431577
$738$	−5.17980	−0.190671
$739$	42.5442	1.56502	0.782508	−	0.622641i	$-0.213940\pi$
$739$	42.5442	1.56502	0.782508	+	0.622641i	$0.213940\pi$
$740$	−4.69319	−0.172525
$741$	−51.3935	−1.88799
$742$	−6.50942	−0.238968
$743$	−13.0719	−0.479561	−0.239780	−	0.970827i	$-0.577075\pi$
$743$	−13.0719	−0.479561	−0.239780	+	0.970827i	$0.577075\pi$
$744$	22.0859	0.809707
$745$	−7.41774	−0.271765
$746$	−0.976114	−0.0357381
$747$	23.6219	0.864281
$748$	−4.58981	−0.167820
$749$	−2.43207	−0.0888659
$750$	−2.28136	−0.0833036
$751$	−40.7815	−1.48814	−0.744069	−	0.668103i	$-0.767107\pi$
$751$	−40.7815	−1.48814	−0.744069	+	0.668103i	$0.767107\pi$
$752$	−1.00015	−0.0364718
$753$	23.6164	0.860631
$754$	−35.8548	−1.30575
$755$	−13.2359	−0.481705
$756$	3.61888	0.131618
$757$	−46.8948	−1.70442	−0.852210	−	0.523200i	$-0.824738\pi$
$757$	−46.8948	−1.70442	−0.852210	+	0.523200i	$0.824738\pi$
$758$	8.48882	0.308328
$759$	−22.7812	−0.826905
$760$	−5.14004	−0.186449
$761$	35.6949	1.29394	0.646970	−	0.762516i	$-0.276036\pi$
$761$	35.6949	1.29394	0.646970	+	0.762516i	$0.276036\pi$
$762$	14.6073	0.529166
$763$	15.0769	0.545821
$764$	21.8649	0.791045
$765$	−5.39876	−0.195193
$766$	−10.1052	−0.365118
$767$	12.1860	0.440010
$768$	−2.28136	−0.0823216
$769$	−15.2231	−0.548958	−0.274479	−	0.961593i	$-0.588505\pi$
$769$	−15.2231	−0.548958	−0.274479	+	0.961593i	$0.588505\pi$
$770$	3.73801	0.134708
$771$	62.8989	2.26525
$772$	−25.8490	−0.930324
$773$	−2.98771	−0.107461	−0.0537303	−	0.998555i	$-0.517111\pi$
$773$	−2.98771	−0.107461	−0.0537303	+	0.998555i	$0.517111\pi$
$774$	−20.5420	−0.738366
$775$	−9.68099	−0.347752
$776$	13.8088	0.495709
$777$	21.3535	0.766052
$778$	−18.1330	−0.650100
$779$	12.0766	0.432691
$780$	9.99864	0.358009
$781$	−23.2838	−0.833159
$782$	−13.0469	−0.466557
$783$	14.8446	0.530504
$784$	−3.02249	−0.107946
$785$	−11.5379	−0.411804
$786$	−17.1802	−0.612799
$787$	−4.70167	−0.167596	−0.0837982	−	0.996483i	$-0.526705\pi$
$787$	−4.70167	−0.167596	−0.0837982	+	0.996483i	$0.526705\pi$
$788$	−7.50208	−0.267250
$789$	−71.1135	−2.53171
$790$	−4.06354	−0.144574
$791$	33.8377	1.20313
$792$	4.13207	0.146827
$793$	2.31017	0.0820366
$794$	13.6402	0.484074
$795$	7.44614	0.264087
$796$	1.81387	0.0642908
$797$	33.6753	1.19284	0.596420	−	0.802672i	$-0.296589\pi$
$797$	33.6753	1.19284	0.596420	+	0.802672i	$0.296589\pi$
$798$	23.3866	0.827877
$799$	2.44921	0.0866469
$800$	1.00000	0.0353553
$801$	3.74146	0.132198
$802$	−2.29121	−0.0809053
$803$	−17.2846	−0.609959
$804$	−14.2611	−0.502949
$805$	10.6256	0.374503
$806$	42.4294	1.49451
$807$	19.0149	0.669355
$808$	−1.36351	−0.0479683
$809$	−36.1134	−1.26968	−0.634839	−	0.772644i	$-0.718934\pi$
$809$	−36.1134	−1.26968	−0.634839	+	0.772644i	$0.718934\pi$
$810$	−10.7535	−0.377840
$811$	28.2962	0.993614	0.496807	−	0.867861i	$-0.334506\pi$
$811$	28.2962	0.993614	0.496807	+	0.867861i	$0.334506\pi$
$812$	16.3157	0.572569
$813$	45.1666	1.58406
$814$	−8.79635	−0.308312
$815$	6.06917	0.212594
$816$	5.58669	0.195573
$817$	47.8933	1.67557
$818$	−18.8708	−0.659802
$819$	−19.2702	−0.673355
$820$	−2.34952	−0.0820489
$821$	−13.2379	−0.462004	−0.231002	−	0.972953i	$-0.574200\pi$
$821$	−13.2379	−0.462004	−0.231002	+	0.972953i	$0.574200\pi$
$822$	−40.2557	−1.40408
$823$	27.9186	0.973180	0.486590	−	0.873630i	$-0.338240\pi$
$823$	27.9186	0.973180	0.486590	+	0.873630i	$0.338240\pi$
$824$	−6.73160	−0.234506
$825$	−4.27591	−0.148868
$826$	−5.54523	−0.192943
$827$	−51.3407	−1.78529	−0.892646	−	0.450759i	$-0.851153\pi$
$827$	−51.3407	−1.78529	−0.892646	+	0.450759i	$0.851153\pi$
$828$	11.7458	0.408194
$829$	6.35055	0.220564	0.110282	−	0.993900i	$-0.464825\pi$
$829$	6.35055	0.220564	0.110282	+	0.993900i	$0.464825\pi$
$830$	10.7147	0.371914
$831$	31.1436	1.08036
$832$	−4.38275	−0.151944
$833$	7.40159	0.256450
$834$	26.7810	0.927350
$835$	13.6921	0.473836
$836$	−9.63387	−0.333194
$837$	−17.5666	−0.607192
$838$	8.02753	0.277306
$839$	14.6234	0.504857	0.252429	−	0.967615i	$-0.418771\pi$
$839$	14.6234	0.504857	0.252429	+	0.967615i	$0.418771\pi$
$840$	−4.54988	−0.156986
$841$	37.9269	1.30782
$842$	−32.1899	−1.10934
$843$	34.0193	1.17169
$844$	12.3024	0.423466
$845$	6.20849	0.213578
$846$	−2.20496	−0.0758080
$847$	−14.9320	−0.513070
$848$	−3.26390	−0.112083
$849$	−33.8438	−1.16152
$850$	−2.44884	−0.0839945
$851$	−25.0044	−0.857140
$852$	28.3409	0.970944
$853$	−23.5105	−0.804985	−0.402493	−	0.915423i	$-0.631856\pi$
$853$	−23.5105	−0.804985	−0.402493	+	0.915423i	$0.631856\pi$
$854$	−1.05124	−0.0359728
$855$	−11.3318	−0.387541
$856$	−1.21947	−0.0416805
$857$	−1.38976	−0.0474732	−0.0237366	−	0.999718i	$-0.507556\pi$
$857$	−1.38976	−0.0474732	−0.0237366	+	0.999718i	$0.507556\pi$
$858$	18.7402	0.639781
$859$	−18.0488	−0.615817	−0.307909	−	0.951416i	$-0.599629\pi$
$859$	−18.0488	−0.615817	−0.307909	+	0.951416i	$0.599629\pi$
$860$	−9.31769	−0.317730
$861$	10.6901	0.364316
$862$	−38.2579	−1.30307
$863$	1.45594	0.0495606	0.0247803	−	0.999693i	$-0.492111\pi$
$863$	1.45594	0.0495606	0.0247803	+	0.999693i	$0.492111\pi$
$864$	1.81455	0.0617323
$865$	−19.4834	−0.662456
$866$	−0.870006	−0.0295640
$867$	25.1023	0.852518
$868$	−19.3075	−0.655339
$869$	−7.61621	−0.258362
$870$	−18.6636	−0.632754
$871$	−27.3971	−0.928314
$872$	7.55973	0.256005
$873$	30.4433	1.03035
$874$	−27.3851	−0.926315
$875$	1.99437	0.0674220
$876$	21.0387	0.710831
$877$	−0.775510	−0.0261871	−0.0130936	−	0.999914i	$-0.504168\pi$
$877$	−0.775510	−0.0261871	−0.0130936	+	0.999914i	$0.504168\pi$
$878$	15.3880	0.519321
$879$	−36.0467	−1.21583
$880$	1.87428	0.0631819
$881$	5.60615	0.188876	0.0944381	−	0.995531i	$-0.469895\pi$
$881$	5.60615	0.188876	0.0944381	+	0.995531i	$0.469895\pi$
$882$	−6.66344	−0.224370
$883$	23.5277	0.791769	0.395885	−	0.918300i	$-0.370438\pi$
$883$	23.5277	0.791769	0.395885	+	0.918300i	$0.370438\pi$
$884$	10.7326	0.360978
$885$	6.34320	0.213224
$886$	13.5024	0.453622
$887$	49.6539	1.66721	0.833607	−	0.552358i	$-0.186272\pi$
$887$	49.6539	1.66721	0.833607	+	0.552358i	$0.186272\pi$
$888$	10.7069	0.359299
$889$	−12.7697	−0.428282
$890$	1.69710	0.0568869
$891$	−20.1551	−0.675220
$892$	−5.44946	−0.182461
$893$	5.14083	0.172031
$894$	16.9226	0.565975
$895$	7.94386	0.265534
$896$	1.99437	0.0666272
$897$	53.2708	1.77866
$898$	1.21920	0.0406852
$899$	−79.1991	−2.64144
$900$	2.20462	0.0734873
$901$	7.99276	0.266278
$902$	−4.40366	−0.146626
$903$	42.3944	1.41080
$904$	16.9666	0.564301
$905$	−12.1441	−0.403682
$906$	30.1960	1.00319
$907$	22.4359	0.744971	0.372485	−	0.928038i	$-0.378506\pi$
$907$	22.4359	0.744971	0.372485	+	0.928038i	$0.378506\pi$
$908$	−17.8644	−0.592852
$909$	−3.00603	−0.0997038
$910$	−8.74082	−0.289755
$911$	26.1208	0.865421	0.432711	−	0.901533i	$-0.357557\pi$
$911$	26.1208	0.865421	0.432711	+	0.901533i	$0.357557\pi$
$912$	11.7263	0.388297
$913$	20.0824	0.664631
$914$	−14.6280	−0.483850
$915$	1.20252	0.0397541
$916$	−13.3168	−0.439998
$917$	15.0190	0.495970
$918$	−4.44354	−0.146659
$919$	8.28053	0.273149	0.136575	−	0.990630i	$-0.456391\pi$
$919$	8.28053	0.273149	0.136575	+	0.990630i	$0.456391\pi$
$920$	5.32780	0.175652
$921$	45.2350	1.49054
$922$	−38.2518	−1.25976
$923$	54.4460	1.79211
$924$	−8.52775	−0.280542
$925$	−4.69319	−0.154311
$926$	29.1991	0.959541
$927$	−14.8406	−0.487430
$928$	8.18089	0.268551
$929$	−21.3883	−0.701726	−0.350863	−	0.936427i	$-0.614112\pi$
$929$	−21.3883	−0.701726	−0.350863	+	0.936427i	$0.614112\pi$
$930$	22.0859	0.724224
$931$	15.5357	0.509163
$932$	−4.00562	−0.131209
$933$	10.9559	0.358681
$934$	32.0814	1.04974
$935$	−4.58981	−0.150103
$936$	−9.66230	−0.315822
$937$	−3.48138	−0.113732	−0.0568659	−	0.998382i	$-0.518111\pi$
$937$	−3.48138	−0.113732	−0.0568659	+	0.998382i	$0.518111\pi$
$938$	12.4670	0.407063
$939$	22.2068	0.724691
$940$	−1.00015	−0.0326214
$941$	−35.1196	−1.14486	−0.572432	−	0.819952i	$-0.694000\pi$
$941$	−35.1196	−1.14486	−0.572432	+	0.819952i	$0.694000\pi$
$942$	26.3221	0.857619
$943$	−12.5178	−0.407635
$944$	−2.78044	−0.0904957
$945$	3.61888	0.117722
$946$	−17.4639	−0.567802
$947$	7.69518	0.250060	0.125030	−	0.992153i	$-0.460097\pi$
$947$	7.69518	0.250060	0.125030	+	0.992153i	$0.460097\pi$
$948$	9.27042	0.301089
$949$	40.4176	1.31201
$950$	−5.14004	−0.166765
$951$	7.47744	0.242473
$952$	−4.88389	−0.158288
$953$	−2.58696	−0.0837999	−0.0419000	−	0.999122i	$-0.513341\pi$
$953$	−2.58696	−0.0837999	−0.0419000	+	0.999122i	$0.513341\pi$
$954$	−7.19566	−0.232968
$955$	21.8649	0.707532
$956$	10.2326	0.330946
$957$	−34.9807	−1.13077
$958$	2.21543	0.0715774
$959$	35.1916	1.13640
$960$	−2.28136	−0.0736307
$961$	62.7216	2.02328
$962$	20.5691	0.663174
$963$	−2.68846	−0.0866345
$964$	−29.0639	−0.936084
$965$	−25.8490	−0.832107
$966$	−24.2409	−0.779937
$967$	5.67466	0.182485	0.0912424	−	0.995829i	$-0.470916\pi$
$967$	5.67466	0.182485	0.0912424	+	0.995829i	$0.470916\pi$
$968$	−7.48708	−0.240644
$969$	−28.7158	−0.922486
$970$	13.8088	0.443375
$971$	−26.5535	−0.852142	−0.426071	−	0.904690i	$-0.640103\pi$
$971$	−26.5535	−0.852142	−0.426071	+	0.904690i	$0.640103\pi$
$972$	19.0890	0.612281
$973$	−23.4120	−0.750554
$974$	6.19322	0.198444
$975$	9.99864	0.320213
$976$	−0.527106	−0.0168722
$977$	−26.7138	−0.854651	−0.427325	−	0.904098i	$-0.640544\pi$
$977$	−26.7138	−0.854651	−0.427325	+	0.904098i	$0.640544\pi$
$978$	−13.8460	−0.442746
$979$	3.18084	0.101660
$980$	−3.02249	−0.0965498
$981$	16.6663	0.532115
$982$	7.75169	0.247366
$983$	54.5247	1.73907	0.869535	−	0.493872i	$-0.164419\pi$
$983$	54.5247	1.73907	0.869535	+	0.493872i	$0.164419\pi$
$984$	5.36011	0.170874
$985$	−7.50208	−0.239036
$986$	−20.0337	−0.638002
$987$	4.55058	0.144846
$988$	22.5275	0.716696
$989$	−49.6428	−1.57855
$990$	4.13207	0.131326
$991$	−20.7124	−0.657952	−0.328976	−	0.944338i	$-0.606704\pi$
$991$	−20.7124	−0.657952	−0.328976	+	0.944338i	$0.606704\pi$
$992$	−9.68099	−0.307372
$993$	−13.7211	−0.435425
$994$	−24.7757	−0.785836
$995$	1.81387	0.0575034
$996$	−24.4442	−0.774545
$997$	42.7101	1.35264	0.676321	−	0.736607i	$-0.263573\pi$
$997$	42.7101	1.35264	0.676321	+	0.736607i	$0.263573\pi$
$998$	−1.76473	−0.0558617
$999$	−8.51604	−0.269435

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.c.1.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.c.1.3	✓	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.28136 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.28136 q^{6} +1.99437 q^{7} +1.00000 q^{8} +2.20462 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.28136 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.28136 q^{6} +1.99437 q^{7} +1.00000 q^{8} +2.20462 q^{9} +1.00000 q^{10} +1.87428 q^{11} -2.28136 q^{12} -4.38275 q^{13} +1.99437 q^{14} -2.28136 q^{15} +1.00000 q^{16} -2.44884 q^{17} +2.20462 q^{18} -5.14004 q^{19} +1.00000 q^{20} -4.54988 q^{21} +1.87428 q^{22} +5.32780 q^{23} -2.28136 q^{24} +1.00000 q^{25} -4.38275 q^{26} +1.81455 q^{27} +1.99437 q^{28} +8.18089 q^{29} -2.28136 q^{30} -9.68099 q^{31} +1.00000 q^{32} -4.27591 q^{33} -2.44884 q^{34} +1.99437 q^{35} +2.20462 q^{36} -4.69319 q^{37} -5.14004 q^{38} +9.99864 q^{39} +1.00000 q^{40} -2.34952 q^{41} -4.54988 q^{42} -9.31769 q^{43} +1.87428 q^{44} +2.20462 q^{45} +5.32780 q^{46} -1.00015 q^{47} -2.28136 q^{48} -3.02249 q^{49} +1.00000 q^{50} +5.58669 q^{51} -4.38275 q^{52} -3.26390 q^{53} +1.81455 q^{54} +1.87428 q^{55} +1.99437 q^{56} +11.7263 q^{57} +8.18089 q^{58} -2.78044 q^{59} -2.28136 q^{60} -0.527106 q^{61} -9.68099 q^{62} +4.39683 q^{63} +1.00000 q^{64} -4.38275 q^{65} -4.27591 q^{66} +6.25111 q^{67} -2.44884 q^{68} -12.1546 q^{69} +1.99437 q^{70} -12.4228 q^{71} +2.20462 q^{72} -9.22198 q^{73} -4.69319 q^{74} -2.28136 q^{75} -5.14004 q^{76} +3.73801 q^{77} +9.99864 q^{78} -4.06354 q^{79} +1.00000 q^{80} -10.7535 q^{81} -2.34952 q^{82} +10.7147 q^{83} -4.54988 q^{84} -2.44884 q^{85} -9.31769 q^{86} -18.6636 q^{87} +1.87428 q^{88} +1.69710 q^{89} +2.20462 q^{90} -8.74082 q^{91} +5.32780 q^{92} +22.0859 q^{93} -1.00015 q^{94} -5.14004 q^{95} -2.28136 q^{96} +13.8088 q^{97} -3.02249 q^{98} +4.13207 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * q^99

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