LMFDB - Embedded newform 2006.2.a.u.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2006,2,Mod(1,2006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2006, 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("2006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2006 = 2 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2006.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:	$16.0179906455$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 23x^{7} + 18x^{6} + 185x^{5} - 91x^{4} - 615x^{3} + 126x^{2} + 668x - 44 $ x^9 - x^8 - 23x^7 + 18x^6 + 185x^5 - 91x^4 - 615x^3 + 126x^2 + 668*x - 44
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-3.17249$ of defining polynomial
Character	$\chi$	$=$	2006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.17249 q^{3} +1.00000 q^{4} -0.981527 q^{5} -3.17249 q^{6} -4.36977 q^{7} -1.00000 q^{8} +7.06469 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.17249 q^{3} +1.00000 q^{4} -0.981527 q^{5} -3.17249 q^{6} -4.36977 q^{7} -1.00000 q^{8} +7.06469 q^{9} +0.981527 q^{10} -5.66760 q^{11} +3.17249 q^{12} +4.51095 q^{13} +4.36977 q^{14} -3.11388 q^{15} +1.00000 q^{16} +1.00000 q^{17} -7.06469 q^{18} +6.02994 q^{19} -0.981527 q^{20} -13.8631 q^{21} +5.66760 q^{22} +8.45189 q^{23} -3.17249 q^{24} -4.03660 q^{25} -4.51095 q^{26} +12.8952 q^{27} -4.36977 q^{28} +6.80855 q^{29} +3.11388 q^{30} +7.63586 q^{31} -1.00000 q^{32} -17.9804 q^{33} -1.00000 q^{34} +4.28905 q^{35} +7.06469 q^{36} -1.22307 q^{37} -6.02994 q^{38} +14.3109 q^{39} +0.981527 q^{40} -1.81353 q^{41} +13.8631 q^{42} +0.435861 q^{43} -5.66760 q^{44} -6.93418 q^{45} -8.45189 q^{46} -5.55534 q^{47} +3.17249 q^{48} +12.0949 q^{49} +4.03660 q^{50} +3.17249 q^{51} +4.51095 q^{52} -5.88073 q^{53} -12.8952 q^{54} +5.56291 q^{55} +4.36977 q^{56} +19.1299 q^{57} -6.80855 q^{58} -1.00000 q^{59} -3.11388 q^{60} +5.82568 q^{61} -7.63586 q^{62} -30.8711 q^{63} +1.00000 q^{64} -4.42762 q^{65} +17.9804 q^{66} +1.75244 q^{67} +1.00000 q^{68} +26.8135 q^{69} -4.28905 q^{70} +7.79928 q^{71} -7.06469 q^{72} +8.01813 q^{73} +1.22307 q^{74} -12.8061 q^{75} +6.02994 q^{76} +24.7661 q^{77} -14.3109 q^{78} +14.6059 q^{79} -0.981527 q^{80} +19.7157 q^{81} +1.81353 q^{82} +7.70106 q^{83} -13.8631 q^{84} -0.981527 q^{85} -0.435861 q^{86} +21.6001 q^{87} +5.66760 q^{88} -9.83671 q^{89} +6.93418 q^{90} -19.7118 q^{91} +8.45189 q^{92} +24.2247 q^{93} +5.55534 q^{94} -5.91855 q^{95} -3.17249 q^{96} -2.56483 q^{97} -12.0949 q^{98} -40.0398 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9	\( 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9} - 7 q^{10} + 5 q^{11} - q^{12} + 25 q^{13} - 5 q^{15} + 9 q^{16} + 9 q^{17} - 20 q^{18} + 14 q^{19} + 7 q^{20} - 7 q^{21} - 5 q^{22} + 2 q^{23} + q^{24} + 20 q^{25} - 25 q^{26} - 10 q^{27} + 18 q^{29} + 5 q^{30} + 6 q^{31} - 9 q^{32} - 9 q^{33} - 9 q^{34} - 17 q^{35} + 20 q^{36} + 11 q^{37} - 14 q^{38} - 8 q^{39} - 7 q^{40} + 18 q^{41} + 7 q^{42} - 10 q^{43} + 5 q^{44} + 27 q^{45} - 2 q^{46} - 20 q^{47} - q^{48} + 13 q^{49} - 20 q^{50} - q^{51} + 25 q^{52} - 7 q^{53} + 10 q^{54} + 29 q^{55} + 17 q^{57} - 18 q^{58} - 9 q^{59} - 5 q^{60} + 30 q^{61} - 6 q^{62} - 47 q^{63} + 9 q^{64} + 8 q^{65} + 9 q^{66} + 6 q^{67} + 9 q^{68} + 20 q^{69} + 17 q^{70} + 30 q^{71} - 20 q^{72} - 11 q^{74} - 7 q^{75} + 14 q^{76} - 3 q^{77} + 8 q^{78} + 29 q^{79} + 7 q^{80} - 3 q^{81} - 18 q^{82} + 9 q^{83} - 7 q^{84} + 7 q^{85} + 10 q^{86} + 44 q^{87} - 5 q^{88} + 8 q^{89} - 27 q^{90} + 13 q^{91} + 2 q^{92} + 7 q^{93} + 20 q^{94} + 27 q^{95} + q^{96} - 13 q^{97} - 13 q^{98} - 19 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9 - 7 * q^10 + 5 * q^11 - q^12 + 25 * q^13 - 5 * q^15 + 9 * q^16 + 9 * q^17 - 20 * q^18 + 14 * q^19 + 7 * q^20 - 7 * q^21 - 5 * q^22 + 2 * q^23 + q^24 + 20 * q^25 - 25 * q^26 - 10 * q^27 + 18 * q^29 + 5 * q^30 + 6 * q^31 - 9 * q^32 - 9 * q^33 - 9 * q^34 - 17 * q^35 + 20 * q^36 + 11 * q^37 - 14 * q^38 - 8 * q^39 - 7 * q^40 + 18 * q^41 + 7 * q^42 - 10 * q^43 + 5 * q^44 + 27 * q^45 - 2 * q^46 - 20 * q^47 - q^48 + 13 * q^49 - 20 * q^50 - q^51 + 25 * q^52 - 7 * q^53 + 10 * q^54 + 29 * q^55 + 17 * q^57 - 18 * q^58 - 9 * q^59 - 5 * q^60 + 30 * q^61 - 6 * q^62 - 47 * q^63 + 9 * q^64 + 8 * q^65 + 9 * q^66 + 6 * q^67 + 9 * q^68 + 20 * q^69 + 17 * q^70 + 30 * q^71 - 20 * q^72 - 11 * q^74 - 7 * q^75 + 14 * q^76 - 3 * q^77 + 8 * q^78 + 29 * q^79 + 7 * q^80 - 3 * q^81 - 18 * q^82 + 9 * q^83 - 7 * q^84 + 7 * q^85 + 10 * q^86 + 44 * q^87 - 5 * q^88 + 8 * q^89 - 27 * q^90 + 13 * q^91 + 2 * q^92 + 7 * q^93 + 20 * q^94 + 27 * q^95 + q^96 - 13 * q^97 - 13 * q^98 - 19 * 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
$3$	3.17249	1.83164	0.915819	−	0.401592i	$-0.131543\pi$
$3$	3.17249	1.83164	0.915819	+	0.401592i	$0.131543\pi$
$4$	1.00000	0.500000
$5$	−0.981527	−0.438952	−0.219476	−	0.975618i	$-0.570435\pi$
$5$	−0.981527	−0.438952	−0.219476	+	0.975618i	$0.570435\pi$
$6$	−3.17249	−1.29516
$7$	−4.36977	−1.65162	−0.825810	−	0.563949i	$-0.809281\pi$
$7$	−4.36977	−1.65162	−0.825810	+	0.563949i	$0.809281\pi$
$8$	−1.00000	−0.353553
$9$	7.06469	2.35490
$10$	0.981527	0.310386
$11$	−5.66760	−1.70885	−0.854423	−	0.519578i	$-0.826089\pi$
$11$	−5.66760	−1.70885	−0.854423	+	0.519578i	$0.826089\pi$
$12$	3.17249	0.915819
$13$	4.51095	1.25111	0.625556	−	0.780180i	$-0.284872\pi$
$13$	4.51095	1.25111	0.625556	+	0.780180i	$0.284872\pi$
$14$	4.36977	1.16787
$15$	−3.11388	−0.804002
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−7.06469	−1.66516
$19$	6.02994	1.38336	0.691681	−	0.722203i	$-0.256870\pi$
$19$	6.02994	1.38336	0.691681	+	0.722203i	$0.256870\pi$
$20$	−0.981527	−0.219476
$21$	−13.8631	−3.02517
$22$	5.66760	1.20834
$23$	8.45189	1.76234	0.881171	−	0.472798i	$-0.156756\pi$
$23$	8.45189	1.76234	0.881171	+	0.472798i	$0.156756\pi$
$24$	−3.17249	−0.647582
$25$	−4.03660	−0.807321
$26$	−4.51095	−0.884669
$27$	12.8952	2.48168
$28$	−4.36977	−0.825810
$29$	6.80855	1.26432	0.632158	−	0.774839i	$-0.282169\pi$
$29$	6.80855	1.26432	0.632158	+	0.774839i	$0.282169\pi$
$30$	3.11388	0.568515
$31$	7.63586	1.37144	0.685720	−	0.727865i	$-0.259487\pi$
$31$	7.63586	1.37144	0.685720	+	0.727865i	$0.259487\pi$
$32$	−1.00000	−0.176777
$33$	−17.9804	−3.12999
$34$	−1.00000	−0.171499
$35$	4.28905	0.724982
$36$	7.06469	1.17745
$37$	−1.22307	−0.201071	−0.100536	−	0.994933i	$-0.532056\pi$
$37$	−1.22307	−0.201071	−0.100536	+	0.994933i	$0.532056\pi$
$38$	−6.02994	−0.978185
$39$	14.3109	2.29158
$40$	0.981527	0.155193
$41$	−1.81353	−0.283226	−0.141613	−	0.989922i	$-0.545229\pi$
$41$	−1.81353	−0.283226	−0.141613	+	0.989922i	$0.545229\pi$
$42$	13.8631	2.13912
$43$	0.435861	0.0664681	0.0332341	−	0.999448i	$-0.489419\pi$
$43$	0.435861	0.0664681	0.0332341	+	0.999448i	$0.489419\pi$
$44$	−5.66760	−0.854423
$45$	−6.93418	−1.03369
$46$	−8.45189	−1.24616
$47$	−5.55534	−0.810330	−0.405165	−	0.914244i	$-0.632786\pi$
$47$	−5.55534	−0.810330	−0.405165	+	0.914244i	$0.632786\pi$
$48$	3.17249	0.457909
$49$	12.0949	1.72785
$50$	4.03660	0.570862
$51$	3.17249	0.444237
$52$	4.51095	0.625556
$53$	−5.88073	−0.807781	−0.403890	−	0.914807i	$-0.632342\pi$
$53$	−5.88073	−0.807781	−0.403890	+	0.914807i	$0.632342\pi$
$54$	−12.8952	−1.75481
$55$	5.56291	0.750102
$56$	4.36977	0.583936
$57$	19.1299	2.53382
$58$	−6.80855	−0.894007
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−3.11388	−0.402001
$61$	5.82568	0.745902	0.372951	−	0.927851i	$-0.378346\pi$
$61$	5.82568	0.745902	0.372951	+	0.927851i	$0.378346\pi$
$62$	−7.63586	−0.969755
$63$	−30.8711	−3.88939
$64$	1.00000	0.125000
$65$	−4.42762	−0.549178
$66$	17.9804	2.21323
$67$	1.75244	0.214094	0.107047	−	0.994254i	$-0.465860\pi$
$67$	1.75244	0.214094	0.107047	+	0.994254i	$0.465860\pi$
$68$	1.00000	0.121268
$69$	26.8135	3.22797
$70$	−4.28905	−0.512640
$71$	7.79928	0.925605	0.462802	−	0.886462i	$-0.346844\pi$
$71$	7.79928	0.925605	0.462802	+	0.886462i	$0.346844\pi$
$72$	−7.06469	−0.832581
$73$	8.01813	0.938451	0.469226	−	0.883078i	$-0.344533\pi$
$73$	8.01813	0.938451	0.469226	+	0.883078i	$0.344533\pi$
$74$	1.22307	0.142179
$75$	−12.8061	−1.47872
$76$	6.02994	0.691681
$77$	24.7661	2.82236
$78$	−14.3109	−1.62039
$79$	14.6059	1.64329	0.821645	−	0.569999i	$-0.193057\pi$
$79$	14.6059	1.64329	0.821645	+	0.569999i	$0.193057\pi$
$80$	−0.981527	−0.109738
$81$	19.7157	2.19064
$82$	1.81353	0.200271
$83$	7.70106	0.845302	0.422651	−	0.906293i	$-0.361100\pi$
$83$	7.70106	0.845302	0.422651	+	0.906293i	$0.361100\pi$
$84$	−13.8631	−1.51258
$85$	−0.981527	−0.106462
$86$	−0.435861	−0.0470001
$87$	21.6001	2.31577
$88$	5.66760	0.604168
$89$	−9.83671	−1.04269	−0.521345	−	0.853346i	$-0.674569\pi$
$89$	−9.83671	−1.04269	−0.521345	+	0.853346i	$0.674569\pi$
$90$	6.93418	0.730927
$91$	−19.7118	−2.06636
$92$	8.45189	0.881171
$93$	24.2247	2.51198
$94$	5.55534	0.572990
$95$	−5.91855	−0.607230
$96$	−3.17249	−0.323791
$97$	−2.56483	−0.260419	−0.130210	−	0.991486i	$-0.541565\pi$
$97$	−2.56483	−0.260419	−0.130210	+	0.991486i	$0.541565\pi$
$98$	−12.0949	−1.22177
$99$	−40.0398	−4.02415
$100$	−4.03660	−0.403660
$101$	14.1560	1.40857	0.704287	−	0.709915i	$-0.251267\pi$
$101$	14.1560	1.40857	0.704287	+	0.709915i	$0.251267\pi$
$102$	−3.17249	−0.314123
$103$	−17.9463	−1.76830	−0.884149	−	0.467206i	$-0.845261\pi$
$103$	−17.9463	−1.76830	−0.884149	+	0.467206i	$0.845261\pi$
$104$	−4.51095	−0.442335
$105$	13.6070	1.32790
$106$	5.88073	0.571187
$107$	−5.30802	−0.513146	−0.256573	−	0.966525i	$-0.582593\pi$
$107$	−5.30802	−0.513146	−0.256573	+	0.966525i	$0.582593\pi$
$108$	12.8952	1.24084
$109$	2.84413	0.272418	0.136209	−	0.990680i	$-0.456508\pi$
$109$	2.84413	0.272418	0.136209	+	0.990680i	$0.456508\pi$
$110$	−5.56291	−0.530402
$111$	−3.88017	−0.368290
$112$	−4.36977	−0.412905
$113$	−2.21790	−0.208643	−0.104321	−	0.994544i	$-0.533267\pi$
$113$	−2.21790	−0.208643	−0.104321	+	0.994544i	$0.533267\pi$
$114$	−19.1299	−1.79168
$115$	−8.29577	−0.773584
$116$	6.80855	0.632158
$117$	31.8684	2.94624
$118$	1.00000	0.0920575
$119$	−4.36977	−0.400577
$120$	3.11388	0.284258
$121$	21.1217	1.92016
$122$	−5.82568	−0.527433
$123$	−5.75342	−0.518768
$124$	7.63586	0.685720
$125$	8.86967	0.793328
$126$	30.8711	2.75021
$127$	16.2543	1.44233	0.721167	−	0.692761i	$-0.243606\pi$
$127$	16.2543	1.44233	0.721167	+	0.692761i	$0.243606\pi$
$128$	−1.00000	−0.0883883
$129$	1.38276	0.121746
$130$	4.42762	0.388328
$131$	−11.3988	−0.995919	−0.497959	−	0.867200i	$-0.665917\pi$
$131$	−11.3988	−0.995919	−0.497959	+	0.867200i	$0.665917\pi$
$132$	−17.9804	−1.56499
$133$	−26.3495	−2.28479
$134$	−1.75244	−0.151388
$135$	−12.6570	−1.08934
$136$	−1.00000	−0.0857493
$137$	−9.20791	−0.786685	−0.393342	−	0.919392i	$-0.628681\pi$
$137$	−9.20791	−0.786685	−0.393342	+	0.919392i	$0.628681\pi$
$138$	−26.8135	−2.28252
$139$	−0.0476975	−0.00404565	−0.00202282	−	0.999998i	$-0.500644\pi$
$139$	−0.0476975	−0.00404565	−0.00202282	+	0.999998i	$0.500644\pi$
$140$	4.28905	0.362491
$141$	−17.6243	−1.48423
$142$	−7.79928	−0.654501
$143$	−25.5662	−2.13796
$144$	7.06469	0.588724
$145$	−6.68278	−0.554975
$146$	−8.01813	−0.663585
$147$	38.3710	3.16479
$148$	−1.22307	−0.100536
$149$	−16.5292	−1.35412	−0.677062	−	0.735926i	$-0.736747\pi$
$149$	−16.5292	−1.35412	−0.677062	+	0.735926i	$0.736747\pi$
$150$	12.8061	1.04561
$151$	−12.7165	−1.03486	−0.517429	−	0.855726i	$-0.673111\pi$
$151$	−12.7165	−1.03486	−0.517429	+	0.855726i	$0.673111\pi$
$152$	−6.02994	−0.489092
$153$	7.06469	0.571146
$154$	−24.7661	−1.99571
$155$	−7.49481	−0.601997
$156$	14.3109	1.14579
$157$	8.38966	0.669568	0.334784	−	0.942295i	$-0.391337\pi$
$157$	8.38966	0.669568	0.334784	+	0.942295i	$0.391337\pi$
$158$	−14.6059	−1.16198
$159$	−18.6566	−1.47956
$160$	0.981527	0.0775966
$161$	−36.9329	−2.91072
$162$	−19.7157	−1.54901
$163$	−19.9915	−1.56585	−0.782927	−	0.622113i	$-0.786274\pi$
$163$	−19.9915	−1.56585	−0.782927	+	0.622113i	$0.786274\pi$
$164$	−1.81353	−0.141613
$165$	17.6483	1.37392
$166$	−7.70106	−0.597718
$167$	6.87636	0.532109	0.266055	−	0.963958i	$-0.414280\pi$
$167$	6.87636	0.532109	0.266055	+	0.963958i	$0.414280\pi$
$168$	13.8631	1.06956
$169$	7.34863	0.565279
$170$	0.981527	0.0752797
$171$	42.5996	3.25767
$172$	0.435861	0.0332341
$173$	24.8765	1.89133	0.945663	−	0.325148i	$-0.105414\pi$
$173$	24.8765	1.89133	0.945663	+	0.325148i	$0.105414\pi$
$174$	−21.6001	−1.63750
$175$	17.6390	1.33339
$176$	−5.66760	−0.427212
$177$	−3.17249	−0.238459
$178$	9.83671	0.737293
$179$	−18.6871	−1.39674	−0.698369	−	0.715738i	$-0.746090\pi$
$179$	−18.6871	−1.39674	−0.698369	+	0.715738i	$0.746090\pi$
$180$	−6.93418	−0.516843
$181$	−5.59332	−0.415748	−0.207874	−	0.978156i	$-0.566654\pi$
$181$	−5.59332	−0.415748	−0.207874	+	0.978156i	$0.566654\pi$
$182$	19.7118	1.46114
$183$	18.4819	1.36622
$184$	−8.45189	−0.623082
$185$	1.20048	0.0882608
$186$	−24.2247	−1.77624
$187$	−5.66760	−0.414456
$188$	−5.55534	−0.405165
$189$	−56.3490	−4.09878
$190$	5.91855	0.429377
$191$	−22.4086	−1.62143	−0.810716	−	0.585440i	$-0.800922\pi$
$191$	−22.4086	−1.62143	−0.810716	+	0.585440i	$0.800922\pi$
$192$	3.17249	0.228955
$193$	17.1452	1.23414	0.617069	−	0.786909i	$-0.288320\pi$
$193$	17.1452	1.23414	0.617069	+	0.786909i	$0.288320\pi$
$194$	2.56483	0.184144
$195$	−14.0466	−1.00590
$196$	12.0949	0.863923
$197$	9.50161	0.676962	0.338481	−	0.940973i	$-0.390087\pi$
$197$	9.50161	0.676962	0.338481	+	0.940973i	$0.390087\pi$
$198$	40.0398	2.84551
$199$	3.79356	0.268918	0.134459	−	0.990919i	$-0.457070\pi$
$199$	3.79356	0.268918	0.134459	+	0.990919i	$0.457070\pi$
$200$	4.03660	0.285431
$201$	5.55959	0.392143
$202$	−14.1560	−0.996013
$203$	−29.7518	−2.08817
$204$	3.17249	0.222119
$205$	1.78003	0.124323
$206$	17.9463	1.25037
$207$	59.7100	4.15013
$208$	4.51095	0.312778
$209$	−34.1753	−2.36395
$210$	−13.6070	−0.938970
$211$	−15.7950	−1.08738	−0.543688	−	0.839288i	$-0.682972\pi$
$211$	−15.7950	−1.08738	−0.543688	+	0.839288i	$0.682972\pi$
$212$	−5.88073	−0.403890
$213$	24.7431	1.69537
$214$	5.30802	0.362849
$215$	−0.427809	−0.0291764
$216$	−12.8952	−0.877405
$217$	−33.3670	−2.26510
$218$	−2.84413	−0.192629
$219$	25.4374	1.71890
$220$	5.56291	0.375051
$221$	4.51095	0.303439
$222$	3.88017	0.260420
$223$	−2.01148	−0.134698	−0.0673492	−	0.997729i	$-0.521454\pi$
$223$	−2.01148	−0.134698	−0.0673492	+	0.997729i	$0.521454\pi$
$224$	4.36977	0.291968
$225$	−28.5173	−1.90116
$226$	2.21790	0.147533
$227$	4.93139	0.327308	0.163654	−	0.986518i	$-0.447672\pi$
$227$	4.93139	0.327308	0.163654	+	0.986518i	$0.447672\pi$
$228$	19.1299	1.26691
$229$	−6.72077	−0.444121	−0.222061	−	0.975033i	$-0.571278\pi$
$229$	−6.72077	−0.444121	−0.222061	+	0.975033i	$0.571278\pi$
$230$	8.29577	0.547007
$231$	78.5703	5.16955
$232$	−6.80855	−0.447003
$233$	−16.1682	−1.05921	−0.529607	−	0.848243i	$-0.677661\pi$
$233$	−16.1682	−1.05921	−0.529607	+	0.848243i	$0.677661\pi$
$234$	−31.8684	−2.08330
$235$	5.45272	0.355696
$236$	−1.00000	−0.0650945
$237$	46.3370	3.00991
$238$	4.36977	0.283250
$239$	3.07329	0.198794	0.0993972	−	0.995048i	$-0.468309\pi$
$239$	3.07329	0.198794	0.0993972	+	0.995048i	$0.468309\pi$
$240$	−3.11388	−0.201000
$241$	15.8599	1.02162	0.510811	−	0.859693i	$-0.329345\pi$
$241$	15.8599	1.02162	0.510811	+	0.859693i	$0.329345\pi$
$242$	−21.1217	−1.35776
$243$	23.8624	1.53077
$244$	5.82568	0.372951
$245$	−11.8715	−0.758442
$246$	5.75342	0.366824
$247$	27.2007	1.73074
$248$	−7.63586	−0.484878
$249$	24.4315	1.54829
$250$	−8.86967	−0.560967
$251$	8.07175	0.509485	0.254742	−	0.967009i	$-0.418009\pi$
$251$	8.07175	0.509485	0.254742	+	0.967009i	$0.418009\pi$
$252$	−30.8711	−1.94470
$253$	−47.9020	−3.01157
$254$	−16.2543	−1.01988
$255$	−3.11388	−0.194999
$256$	1.00000	0.0625000
$257$	0.984940	0.0614389	0.0307194	−	0.999528i	$-0.490220\pi$
$257$	0.984940	0.0614389	0.0307194	+	0.999528i	$0.490220\pi$
$258$	−1.38276	−0.0860871
$259$	5.34454	0.332093
$260$	−4.42762	−0.274589
$261$	48.1003	2.97733
$262$	11.3988	0.704221
$263$	−11.6075	−0.715749	−0.357875	−	0.933770i	$-0.616498\pi$
$263$	−11.6075	−0.715749	−0.357875	+	0.933770i	$0.616498\pi$
$264$	17.9804	1.10662
$265$	5.77210	0.354577
$266$	26.3495	1.61559
$267$	−31.2069	−1.90983
$268$	1.75244	0.107047
$269$	−6.40628	−0.390598	−0.195299	−	0.980744i	$-0.562568\pi$
$269$	−6.40628	−0.390598	−0.195299	+	0.980744i	$0.562568\pi$
$270$	12.6570	0.770278
$271$	−9.50798	−0.577568	−0.288784	−	0.957394i	$-0.593251\pi$
$271$	−9.50798	−0.577568	−0.288784	+	0.957394i	$0.593251\pi$
$272$	1.00000	0.0606339
$273$	−62.5355	−3.78482
$274$	9.20791	0.556270
$275$	22.8779	1.37959
$276$	26.8135	1.61399
$277$	−23.9649	−1.43991	−0.719957	−	0.694019i	$-0.755838\pi$
$277$	−23.9649	−1.43991	−0.719957	+	0.694019i	$0.755838\pi$
$278$	0.0476975	0.00286070
$279$	53.9449	3.22960
$280$	−4.28905	−0.256320
$281$	21.7780	1.29916	0.649582	−	0.760291i	$-0.274944\pi$
$281$	21.7780	1.29916	0.649582	+	0.760291i	$0.274944\pi$
$282$	17.6243	1.04951
$283$	0.824032	0.0489836	0.0244918	−	0.999700i	$-0.492203\pi$
$283$	0.824032	0.0489836	0.0244918	+	0.999700i	$0.492203\pi$
$284$	7.79928	0.462802
$285$	−18.7765	−1.11223
$286$	25.5662	1.51176
$287$	7.92473	0.467782
$288$	−7.06469	−0.416291
$289$	1.00000	0.0588235
$290$	6.68278	0.392426
$291$	−8.13690	−0.476994
$292$	8.01813	0.469226
$293$	13.3667	0.780890	0.390445	−	0.920626i	$-0.372321\pi$
$293$	13.3667	0.780890	0.390445	+	0.920626i	$0.372321\pi$
$294$	−38.3710	−2.23784
$295$	0.981527	0.0571467
$296$	1.22307	0.0710895
$297$	−73.0847	−4.24080
$298$	16.5292	0.957511
$299$	38.1260	2.20489
$300$	−12.8061	−0.739359
$301$	−1.90461	−0.109780
$302$	12.7165	0.731755
$303$	44.9098	2.58000
$304$	6.02994	0.345841
$305$	−5.71807	−0.327416
$306$	−7.06469	−0.403861
$307$	−30.1179	−1.71892	−0.859461	−	0.511201i	$-0.829201\pi$
$307$	−30.1179	−1.71892	−0.859461	+	0.511201i	$0.829201\pi$
$308$	24.7661	1.41118
$309$	−56.9343	−3.23888
$310$	7.49481	0.425676
$311$	−11.9913	−0.679967	−0.339983	−	0.940431i	$-0.610421\pi$
$311$	−11.9913	−0.679967	−0.339983	+	0.940431i	$0.610421\pi$
$312$	−14.3109	−0.810197
$313$	15.6928	0.887011	0.443505	−	0.896272i	$-0.353735\pi$
$313$	15.6928	0.887011	0.443505	+	0.896272i	$0.353735\pi$
$314$	−8.38966	−0.473456
$315$	30.3008	1.70726
$316$	14.6059	0.821645
$317$	17.5448	0.985416	0.492708	−	0.870195i	$-0.336007\pi$
$317$	17.5448	0.985416	0.492708	+	0.870195i	$0.336007\pi$
$318$	18.6566	1.04621
$319$	−38.5882	−2.16052
$320$	−0.981527	−0.0548691
$321$	−16.8396	−0.939897
$322$	36.9329	2.05819
$323$	6.02994	0.335515
$324$	19.7157	1.09532
$325$	−18.2089	−1.01005
$326$	19.9915	1.10723
$327$	9.02296	0.498971
$328$	1.81353	0.100136
$329$	24.2756	1.33836
$330$	−17.6483	−0.971505
$331$	29.3168	1.61140	0.805699	−	0.592325i	$-0.201790\pi$
$331$	29.3168	1.61140	0.805699	+	0.592325i	$0.201790\pi$
$332$	7.70106	0.422651
$333$	−8.64060	−0.473502
$334$	−6.87636	−0.376258
$335$	−1.72007	−0.0939773
$336$	−13.8631	−0.756292
$337$	7.60905	0.414491	0.207246	−	0.978289i	$-0.433550\pi$
$337$	7.60905	0.414491	0.207246	+	0.978289i	$0.433550\pi$
$338$	−7.34863	−0.399713
$339$	−7.03627	−0.382158
$340$	−0.981527	−0.0532308
$341$	−43.2770	−2.34358
$342$	−42.5996	−2.30352
$343$	−22.2637	−1.20213
$344$	−0.435861	−0.0235000
$345$	−26.3182	−1.41693
$346$	−24.8765	−1.33737
$347$	−14.2809	−0.766640	−0.383320	−	0.923616i	$-0.625219\pi$
$347$	−14.2809	−0.766640	−0.383320	+	0.923616i	$0.625219\pi$
$348$	21.6001	1.15788
$349$	17.3069	0.926417	0.463209	−	0.886249i	$-0.346698\pi$
$349$	17.3069	0.926417	0.463209	+	0.886249i	$0.346698\pi$
$350$	−17.6390	−0.942847
$351$	58.1694	3.10485
$352$	5.66760	0.302084
$353$	−20.7060	−1.10207	−0.551034	−	0.834483i	$-0.685767\pi$
$353$	−20.7060	−1.10207	−0.551034	+	0.834483i	$0.685767\pi$
$354$	3.17249	0.168616
$355$	−7.65521	−0.406296
$356$	−9.83671	−0.521345
$357$	−13.8631	−0.733711
$358$	18.6871	0.987642
$359$	14.8643	0.784508	0.392254	−	0.919857i	$-0.371695\pi$
$359$	14.8643	0.784508	0.392254	+	0.919857i	$0.371695\pi$
$360$	6.93418	0.365464
$361$	17.3601	0.913691
$362$	5.59332	0.293978
$363$	67.0084	3.51703
$364$	−19.7118	−1.03318
$365$	−7.87002	−0.411935
$366$	−18.4819	−0.966065
$367$	−19.9014	−1.03884	−0.519422	−	0.854518i	$-0.673853\pi$
$367$	−19.9014	−1.03884	−0.519422	+	0.854518i	$0.673853\pi$
$368$	8.45189	0.440585
$369$	−12.8120	−0.666969
$370$	−1.20048	−0.0624098
$371$	25.6975	1.33415
$372$	24.2247	1.25599
$373$	11.3441	0.587373	0.293686	−	0.955902i	$-0.405118\pi$
$373$	11.3441	0.587373	0.293686	+	0.955902i	$0.405118\pi$
$374$	5.66760	0.293065
$375$	28.1389	1.45309
$376$	5.55534	0.286495
$377$	30.7130	1.58180
$378$	56.3490	2.89828
$379$	13.2341	0.679790	0.339895	−	0.940463i	$-0.389608\pi$
$379$	13.2341	0.679790	0.339895	+	0.940463i	$0.389608\pi$
$380$	−5.91855	−0.303615
$381$	51.5665	2.64183
$382$	22.4086	1.14653
$383$	−10.0049	−0.511227	−0.255613	−	0.966779i	$-0.582277\pi$
$383$	−10.0049	−0.511227	−0.255613	+	0.966779i	$0.582277\pi$
$384$	−3.17249	−0.161895
$385$	−24.3086	−1.23888
$386$	−17.1452	−0.872668
$387$	3.07922	0.156526
$388$	−2.56483	−0.130210
$389$	3.93281	0.199402	0.0997008	−	0.995017i	$-0.468211\pi$
$389$	3.93281	0.199402	0.0997008	+	0.995017i	$0.468211\pi$
$390$	14.0466	0.711276
$391$	8.45189	0.427431
$392$	−12.0949	−0.610886
$393$	−36.1626	−1.82416
$394$	−9.50161	−0.478684
$395$	−14.3361	−0.721326
$396$	−40.0398	−2.01208
$397$	30.1626	1.51382	0.756908	−	0.653521i	$-0.226709\pi$
$397$	30.1626	1.51382	0.756908	+	0.653521i	$0.226709\pi$
$398$	−3.79356	−0.190154
$399$	−83.5934	−4.18490
$400$	−4.03660	−0.201830
$401$	−1.47097	−0.0734569	−0.0367285	−	0.999325i	$-0.511694\pi$
$401$	−1.47097	−0.0734569	−0.0367285	+	0.999325i	$0.511694\pi$
$402$	−5.55959	−0.277287
$403$	34.4449	1.71583
$404$	14.1560	0.704287
$405$	−19.3515	−0.961585
$406$	29.7518	1.47656
$407$	6.93187	0.343600
$408$	−3.17249	−0.157062
$409$	20.0841	0.993097	0.496548	−	0.868009i	$-0.334601\pi$
$409$	20.0841	0.993097	0.496548	+	0.868009i	$0.334601\pi$
$410$	−1.78003	−0.0879096
$411$	−29.2120	−1.44092
$412$	−17.9463	−0.884149
$413$	4.36977	0.215023
$414$	−59.7100	−2.93458
$415$	−7.55881	−0.371047
$416$	−4.51095	−0.221167
$417$	−0.151320	−0.00741016
$418$	34.1753	1.67157
$419$	−5.31209	−0.259512	−0.129756	−	0.991546i	$-0.541419\pi$
$419$	−5.31209	−0.259512	−0.129756	+	0.991546i	$0.541419\pi$
$420$	13.6070	0.663952
$421$	26.3779	1.28558	0.642790	−	0.766042i	$-0.277777\pi$
$421$	26.3779	1.28558	0.642790	+	0.766042i	$0.277777\pi$
$422$	15.7950	0.768891
$423$	−39.2467	−1.90824
$424$	5.88073	0.285594
$425$	−4.03660	−0.195804
$426$	−24.7431	−1.19881
$427$	−25.4569	−1.23195
$428$	−5.30802	−0.256573
$429$	−81.1086	−3.91596
$430$	0.427809	0.0206308
$431$	−30.0335	−1.44667	−0.723333	−	0.690500i	$-0.757391\pi$
$431$	−30.0335	−1.44667	−0.723333	+	0.690500i	$0.757391\pi$
$432$	12.8952	0.620419
$433$	−37.1371	−1.78470	−0.892349	−	0.451347i	$-0.850944\pi$
$433$	−37.1371	−1.78470	−0.892349	+	0.451347i	$0.850944\pi$
$434$	33.3670	1.60167
$435$	−21.2010	−1.01651
$436$	2.84413	0.136209
$437$	50.9644	2.43796
$438$	−25.4374	−1.21545
$439$	−7.21785	−0.344489	−0.172245	−	0.985054i	$-0.555102\pi$
$439$	−7.21785	−0.344489	−0.172245	+	0.985054i	$0.555102\pi$
$440$	−5.56291	−0.265201
$441$	85.4468	4.06890
$442$	−4.51095	−0.214564
$443$	−3.47866	−0.165276	−0.0826381	−	0.996580i	$-0.526335\pi$
$443$	−3.47866	−0.165276	−0.0826381	+	0.996580i	$0.526335\pi$
$444$	−3.88017	−0.184145
$445$	9.65500	0.457691
$446$	2.01148	0.0952462
$447$	−52.4387	−2.48026
$448$	−4.36977	−0.206452
$449$	−19.2194	−0.907019	−0.453510	−	0.891251i	$-0.649828\pi$
$449$	−19.2194	−0.907019	−0.453510	+	0.891251i	$0.649828\pi$
$450$	28.5173	1.34432
$451$	10.2784	0.483991
$452$	−2.21790	−0.104321
$453$	−40.3431	−1.89548
$454$	−4.93139	−0.231442
$455$	19.3477	0.907034
$456$	−19.1299	−0.895840
$457$	6.58851	0.308197	0.154099	−	0.988055i	$-0.450753\pi$
$457$	6.58851	0.308197	0.154099	+	0.988055i	$0.450753\pi$
$458$	6.72077	0.314041
$459$	12.8952	0.601895
$460$	−8.29577	−0.386792
$461$	−22.4005	−1.04329	−0.521647	−	0.853162i	$-0.674682\pi$
$461$	−22.4005	−1.04329	−0.521647	+	0.853162i	$0.674682\pi$
$462$	−78.5703	−3.65542
$463$	−3.61388	−0.167951	−0.0839757	−	0.996468i	$-0.526762\pi$
$463$	−3.61388	−0.167951	−0.0839757	+	0.996468i	$0.526762\pi$
$464$	6.80855	0.316079
$465$	−23.7772	−1.10264
$466$	16.1682	0.748978
$467$	−37.7440	−1.74658	−0.873291	−	0.487199i	$-0.838019\pi$
$467$	−37.7440	−1.74658	−0.873291	+	0.487199i	$0.838019\pi$
$468$	31.8684	1.47312
$469$	−7.65776	−0.353602
$470$	−5.45272	−0.251515
$471$	26.6161	1.22641
$472$	1.00000	0.0460287
$473$	−2.47029	−0.113584
$474$	−46.3370	−2.12833
$475$	−24.3405	−1.11682
$476$	−4.36977	−0.200288
$477$	−41.5455	−1.90224
$478$	−3.07329	−0.140569
$479$	10.3145	0.471282	0.235641	−	0.971840i	$-0.424281\pi$
$479$	10.3145	0.471282	0.235641	+	0.971840i	$0.424281\pi$
$480$	3.11388	0.142129
$481$	−5.51720	−0.251563
$482$	−15.8599	−0.722397
$483$	−117.169	−5.33138
$484$	21.1217	0.960078
$485$	2.51745	0.114312
$486$	−23.8624	−1.08242
$487$	21.5034	0.974410	0.487205	−	0.873288i	$-0.338016\pi$
$487$	21.5034	0.974410	0.487205	+	0.873288i	$0.338016\pi$
$488$	−5.82568	−0.263716
$489$	−63.4228	−2.86808
$490$	11.8715	0.536300
$491$	−29.8313	−1.34627	−0.673134	−	0.739521i	$-0.735052\pi$
$491$	−29.8313	−1.34627	−0.673134	+	0.739521i	$0.735052\pi$
$492$	−5.75342	−0.259384
$493$	6.80855	0.306642
$494$	−27.2007	−1.22382
$495$	39.3002	1.76641
$496$	7.63586	0.342860
$497$	−34.0811	−1.52875
$498$	−24.4315	−1.09480
$499$	30.9708	1.38645	0.693223	−	0.720723i	$-0.256190\pi$
$499$	30.9708	1.38645	0.693223	+	0.720723i	$0.256190\pi$
$500$	8.86967	0.396664
$501$	21.8152	0.974631
$502$	−8.07175	−0.360260
$503$	−39.0143	−1.73956	−0.869781	−	0.493437i	$-0.835740\pi$
$503$	−39.0143	−1.73956	−0.869781	+	0.493437i	$0.835740\pi$
$504$	30.8711	1.37511
$505$	−13.8945	−0.618297
$506$	47.9020	2.12950
$507$	23.3135	1.03539
$508$	16.2543	0.721167
$509$	−1.46586	−0.0649733	−0.0324867	−	0.999472i	$-0.510343\pi$
$509$	−1.46586	−0.0649733	−0.0324867	+	0.999472i	$0.510343\pi$
$510$	3.11388	0.137885
$511$	−35.0374	−1.54996
$512$	−1.00000	−0.0441942
$513$	77.7570	3.43306
$514$	−0.984940	−0.0434438
$515$	17.6147	0.776198
$516$	1.38276	0.0608728
$517$	31.4855	1.38473
$518$	−5.34454	−0.234826
$519$	78.9205	3.46422
$520$	4.42762	0.194164
$521$	−0.946144	−0.0414513	−0.0207257	−	0.999785i	$-0.506598\pi$
$521$	−0.946144	−0.0414513	−0.0207257	+	0.999785i	$0.506598\pi$
$522$	−48.1003	−2.10529
$523$	22.7624	0.995332	0.497666	−	0.867369i	$-0.334191\pi$
$523$	22.7624	0.995332	0.497666	+	0.867369i	$0.334191\pi$
$524$	−11.3988	−0.497959
$525$	55.9597	2.44228
$526$	11.6075	0.506111
$527$	7.63586	0.332623
$528$	−17.9804	−0.782497
$529$	48.4345	2.10585
$530$	−5.77210	−0.250724
$531$	−7.06469	−0.306581
$532$	−26.3495	−1.14239
$533$	−8.18075	−0.354348
$534$	31.2069	1.35045
$535$	5.20997	0.225247
$536$	−1.75244	−0.0756938
$537$	−59.2845	−2.55832
$538$	6.40628	0.276194
$539$	−68.5492	−2.95262
$540$	−12.6570	−0.544669
$541$	−30.6703	−1.31862	−0.659309	−	0.751872i	$-0.729151\pi$
$541$	−30.6703	−1.31862	−0.659309	+	0.751872i	$0.729151\pi$
$542$	9.50798	0.408403
$543$	−17.7447	−0.761500
$544$	−1.00000	−0.0428746
$545$	−2.79159	−0.119579
$546$	62.5355	2.67627
$547$	4.61080	0.197144	0.0985718	−	0.995130i	$-0.468573\pi$
$547$	4.61080	0.197144	0.0985718	+	0.995130i	$0.468573\pi$
$548$	−9.20791	−0.393342
$549$	41.1566	1.75652
$550$	−22.8779	−0.975515
$551$	41.0551	1.74901
$552$	−26.8135	−1.14126
$553$	−63.8244	−2.71409
$554$	23.9649	1.01817
$555$	3.80850	0.161662
$556$	−0.0476975	−0.00202282
$557$	−31.3570	−1.32864	−0.664319	−	0.747449i	$-0.731278\pi$
$557$	−31.3570	−1.32864	−0.664319	+	0.747449i	$0.731278\pi$
$558$	−53.9449	−2.28367
$559$	1.96614	0.0831590
$560$	4.28905	0.181246
$561$	−17.9804	−0.759133
$562$	−21.7780	−0.918648
$563$	−33.1725	−1.39806	−0.699028	−	0.715094i	$-0.746384\pi$
$563$	−33.1725	−1.39806	−0.699028	+	0.715094i	$0.746384\pi$
$564$	−17.6243	−0.742115
$565$	2.17693	0.0915842
$566$	−0.824032	−0.0346367
$567$	−86.1532	−3.61810
$568$	−7.79928	−0.327251
$569$	−9.89467	−0.414806	−0.207403	−	0.978256i	$-0.566501\pi$
$569$	−9.89467	−0.414806	−0.207403	+	0.978256i	$0.566501\pi$
$570$	18.7765	0.786462
$571$	−36.0512	−1.50869	−0.754347	−	0.656476i	$-0.772047\pi$
$571$	−36.0512	−1.50869	−0.754347	+	0.656476i	$0.772047\pi$
$572$	−25.5662	−1.06898
$573$	−71.0911	−2.96987
$574$	−7.92473	−0.330772
$575$	−34.1169	−1.42278
$576$	7.06469	0.294362
$577$	−4.87714	−0.203038	−0.101519	−	0.994834i	$-0.532370\pi$
$577$	−4.87714	−0.203038	−0.101519	+	0.994834i	$0.532370\pi$
$578$	−1.00000	−0.0415945
$579$	54.3930	2.26049
$580$	−6.68278	−0.277487
$581$	−33.6519	−1.39612
$582$	8.13690	0.337286
$583$	33.3296	1.38037
$584$	−8.01813	−0.331793
$585$	−31.2797	−1.29326
$586$	−13.3667	−0.552173
$587$	−20.8975	−0.862532	−0.431266	−	0.902225i	$-0.641933\pi$
$587$	−20.8975	−0.862532	−0.431266	+	0.902225i	$0.641933\pi$
$588$	38.3710	1.58239
$589$	46.0437	1.89720
$590$	−0.981527	−0.0404088
$591$	30.1437	1.23995
$592$	−1.22307	−0.0502679
$593$	1.83440	0.0753299	0.0376650	−	0.999290i	$-0.488008\pi$
$593$	1.83440	0.0753299	0.0376650	+	0.999290i	$0.488008\pi$
$594$	73.0847	2.99870
$595$	4.28905	0.175834
$596$	−16.5292	−0.677062
$597$	12.0350	0.492561
$598$	−38.1260	−1.55909
$599$	−4.71385	−0.192603	−0.0963014	−	0.995352i	$-0.530701\pi$
$599$	−4.71385	−0.192603	−0.0963014	+	0.995352i	$0.530701\pi$
$600$	12.8061	0.522806
$601$	12.2164	0.498316	0.249158	−	0.968463i	$-0.419846\pi$
$601$	12.2164	0.498316	0.249158	+	0.968463i	$0.419846\pi$
$602$	1.90461	0.0776262
$603$	12.3804	0.504170
$604$	−12.7165	−0.517429
$605$	−20.7315	−0.842857
$606$	−44.9098	−1.82433
$607$	23.3693	0.948531	0.474265	−	0.880382i	$-0.342714\pi$
$607$	23.3693	0.948531	0.474265	+	0.880382i	$0.342714\pi$
$608$	−6.02994	−0.244546
$609$	−94.3874	−3.82477
$610$	5.71807	0.231518
$611$	−25.0598	−1.01381
$612$	7.06469	0.285573
$613$	29.3915	1.18711	0.593556	−	0.804792i	$-0.297723\pi$
$613$	29.3915	1.18711	0.593556	+	0.804792i	$0.297723\pi$
$614$	30.1179	1.21546
$615$	5.64714	0.227715
$616$	−24.7661	−0.997856
$617$	42.5639	1.71356	0.856779	−	0.515684i	$-0.172462\pi$
$617$	42.5639	1.71356	0.856779	+	0.515684i	$0.172462\pi$
$618$	56.9343	2.29023
$619$	−31.6952	−1.27394	−0.636969	−	0.770889i	$-0.719812\pi$
$619$	−31.6952	−1.27394	−0.636969	+	0.770889i	$0.719812\pi$
$620$	−7.49481	−0.300999
$621$	108.989	4.37356
$622$	11.9913	0.480809
$623$	42.9842	1.72213
$624$	14.3109	0.572895
$625$	11.4772	0.459088
$626$	−15.6928	−0.627211
$627$	−108.421	−4.32991
$628$	8.38966	0.334784
$629$	−1.22307	−0.0487670
$630$	−30.3008	−1.20721
$631$	31.5553	1.25620	0.628099	−	0.778133i	$-0.283833\pi$
$631$	31.5553	1.25620	0.628099	+	0.778133i	$0.283833\pi$
$632$	−14.6059	−0.580991
$633$	−50.1096	−1.99168
$634$	−17.5448	−0.696794
$635$	−15.9540	−0.633116
$636$	−18.6566	−0.739780
$637$	54.5596	2.16173
$638$	38.5882	1.52772
$639$	55.0995	2.17970
$640$	0.981527	0.0387983
$641$	19.9547	0.788164	0.394082	−	0.919075i	$-0.371063\pi$
$641$	19.9547	0.788164	0.394082	+	0.919075i	$0.371063\pi$
$642$	16.8396	0.664607
$643$	−4.51673	−0.178122	−0.0890611	−	0.996026i	$-0.528387\pi$
$643$	−4.51673	−0.178122	−0.0890611	+	0.996026i	$0.528387\pi$
$644$	−36.9329	−1.45536
$645$	−1.35722	−0.0534405
$646$	−6.02994	−0.237245
$647$	−46.2144	−1.81688	−0.908438	−	0.418020i	$-0.862724\pi$
$647$	−46.2144	−1.81688	−0.908438	+	0.418020i	$0.862724\pi$
$648$	−19.7157	−0.774507
$649$	5.66760	0.222473
$650$	18.2089	0.714212
$651$	−105.856	−4.14884
$652$	−19.9915	−0.782927
$653$	41.3165	1.61684	0.808420	−	0.588606i	$-0.200323\pi$
$653$	41.3165	1.61684	0.808420	+	0.588606i	$0.200323\pi$
$654$	−9.02296	−0.352826
$655$	11.1882	0.437161
$656$	−1.81353	−0.0708066
$657$	56.6456	2.20995
$658$	−24.2756	−0.946361
$659$	16.8362	0.655847	0.327923	−	0.944704i	$-0.393651\pi$
$659$	16.8362	0.655847	0.327923	+	0.944704i	$0.393651\pi$
$660$	17.6483	0.686958
$661$	10.7738	0.419052	0.209526	−	0.977803i	$-0.432808\pi$
$661$	10.7738	0.419052	0.209526	+	0.977803i	$0.432808\pi$
$662$	−29.3168	−1.13943
$663$	14.3109	0.555790
$664$	−7.70106	−0.298859
$665$	25.8627	1.00291
$666$	8.64060	0.334817
$667$	57.5452	2.22816
$668$	6.87636	0.266055
$669$	−6.38139	−0.246719
$670$	1.72007	0.0664520
$671$	−33.0177	−1.27463
$672$	13.8631	0.534779
$673$	−26.3793	−1.01685	−0.508423	−	0.861108i	$-0.669771\pi$
$673$	−26.3793	−1.01685	−0.508423	+	0.861108i	$0.669771\pi$
$674$	−7.60905	−0.293090
$675$	−52.0527	−2.00351
$676$	7.34863	0.282640
$677$	−2.61825	−0.100627	−0.0503137	−	0.998733i	$-0.516022\pi$
$677$	−2.61825	−0.100627	−0.0503137	+	0.998733i	$0.516022\pi$
$678$	7.03627	0.270226
$679$	11.2077	0.430114
$680$	0.981527	0.0376399
$681$	15.6448	0.599509
$682$	43.2770	1.65716
$683$	8.00137	0.306164	0.153082	−	0.988213i	$-0.451080\pi$
$683$	8.00137	0.306164	0.153082	+	0.988213i	$0.451080\pi$
$684$	42.5996	1.62884
$685$	9.03782	0.345317
$686$	22.2637	0.850031
$687$	−21.3216	−0.813469
$688$	0.435861	0.0166170
$689$	−26.5277	−1.01062
$690$	26.3182	1.00192
$691$	−19.4361	−0.739383	−0.369692	−	0.929155i	$-0.620537\pi$
$691$	−19.4361	−0.739383	−0.369692	+	0.929155i	$0.620537\pi$
$692$	24.8765	0.945663
$693$	174.965	6.64637
$694$	14.2809	0.542096
$695$	0.0468164	0.00177585
$696$	−21.6001	−0.818748
$697$	−1.81353	−0.0686925
$698$	−17.3069	−0.655076
$699$	−51.2935	−1.94010
$700$	17.6390	0.666693
$701$	41.6151	1.57178	0.785891	−	0.618365i	$-0.212205\pi$
$701$	41.6151	1.57178	0.785891	+	0.618365i	$0.212205\pi$
$702$	−58.1694	−2.19546
$703$	−7.37503	−0.278155
$704$	−5.66760	−0.213606
$705$	17.2987	0.651507
$706$	20.7060	0.779280
$707$	−61.8585	−2.32643
$708$	−3.17249	−0.119229
$709$	11.6240	0.436548	0.218274	−	0.975888i	$-0.429957\pi$
$709$	11.6240	0.436548	0.218274	+	0.975888i	$0.429957\pi$
$710$	7.65521	0.287295
$711$	103.186	3.86978
$712$	9.83671	0.368646
$713$	64.5375	2.41695
$714$	13.8631	0.518812
$715$	25.0940	0.938461
$716$	−18.6871	−0.698369
$717$	9.74997	0.364119
$718$	−14.8643	−0.554731
$719$	5.81445	0.216842	0.108421	−	0.994105i	$-0.465420\pi$
$719$	5.81445	0.216842	0.108421	+	0.994105i	$0.465420\pi$
$720$	−6.93418	−0.258422
$721$	78.4211	2.92055
$722$	−17.3601	−0.646077
$723$	50.3152	1.87124
$724$	−5.59332	−0.207874
$725$	−27.4834	−1.02071
$726$	−67.0084	−2.48692
$727$	−4.27644	−0.158604	−0.0793022	−	0.996851i	$-0.525269\pi$
$727$	−4.27644	−0.158604	−0.0793022	+	0.996851i	$0.525269\pi$
$728$	19.7118	0.730568
$729$	16.5560	0.613186
$730$	7.87002	0.291282
$731$	0.435861	0.0161209
$732$	18.4819	0.683111
$733$	−24.0765	−0.889284	−0.444642	−	0.895708i	$-0.646669\pi$
$733$	−24.0765	−0.889284	−0.444642	+	0.895708i	$0.646669\pi$
$734$	19.9014	0.734574
$735$	−37.6622	−1.38919
$736$	−8.45189	−0.311541
$737$	−9.93212	−0.365854
$738$	12.8120	0.471618
$739$	35.5461	1.30758	0.653792	−	0.756674i	$-0.273177\pi$
$739$	35.5461	1.30758	0.653792	+	0.756674i	$0.273177\pi$
$740$	1.20048	0.0441304
$741$	86.2940	3.17009
$742$	−25.6975	−0.943384
$743$	25.8249	0.947424	0.473712	−	0.880680i	$-0.342914\pi$
$743$	25.8249	0.947424	0.473712	+	0.880680i	$0.342914\pi$
$744$	−24.2247	−0.888120
$745$	16.2239	0.594396
$746$	−11.3441	−0.415335
$747$	54.4056	1.99060
$748$	−5.66760	−0.207228
$749$	23.1949	0.847521
$750$	−28.1389	−1.02749
$751$	23.4614	0.856118	0.428059	−	0.903751i	$-0.359198\pi$
$751$	23.4614	0.856118	0.428059	+	0.903751i	$0.359198\pi$
$752$	−5.55534	−0.202582
$753$	25.6075	0.933191
$754$	−30.7130	−1.11850
$755$	12.4816	0.454253
$756$	−56.3490	−2.04939
$757$	3.50407	0.127358	0.0636789	−	0.997970i	$-0.479717\pi$
$757$	3.50407	0.127358	0.0636789	+	0.997970i	$0.479717\pi$
$758$	−13.2341	−0.480684
$759$	−151.968	−5.51611
$760$	5.91855	0.214688
$761$	15.0162	0.544336	0.272168	−	0.962250i	$-0.412259\pi$
$761$	15.0162	0.544336	0.272168	+	0.962250i	$0.412259\pi$
$762$	−51.5665	−1.86806
$763$	−12.4282	−0.449931
$764$	−22.4086	−0.810716
$765$	−6.93418	−0.250706
$766$	10.0049	0.361492
$767$	−4.51095	−0.162881
$768$	3.17249	0.114477
$769$	3.57208	0.128813	0.0644063	−	0.997924i	$-0.479485\pi$
$769$	3.57208	0.128813	0.0644063	+	0.997924i	$0.479485\pi$
$770$	24.3086	0.876023
$771$	3.12471	0.112534
$772$	17.1452	0.617069
$773$	11.7091	0.421148	0.210574	−	0.977578i	$-0.432467\pi$
$773$	11.7091	0.421148	0.210574	+	0.977578i	$0.432467\pi$
$774$	−3.07922	−0.110680
$775$	−30.8229	−1.10719
$776$	2.56483	0.0920721
$777$	16.9555	0.608275
$778$	−3.93281	−0.140998
$779$	−10.9355	−0.391805
$780$	−14.0466	−0.502948
$781$	−44.2032	−1.58172
$782$	−8.45189	−0.302239
$783$	87.7974	3.13762
$784$	12.0949	0.431962
$785$	−8.23468	−0.293908
$786$	36.1626	1.28988
$787$	38.5246	1.37325	0.686627	−	0.727010i	$-0.259091\pi$
$787$	38.5246	1.37325	0.686627	+	0.727010i	$0.259091\pi$
$788$	9.50161	0.338481
$789$	−36.8247	−1.31099
$790$	14.3361	0.510055
$791$	9.69173	0.344598
$792$	40.0398	1.42275
$793$	26.2793	0.933207
$794$	−30.1626	−1.07043
$795$	18.3119	0.649457
$796$	3.79356	0.134459
$797$	13.8105	0.489193	0.244597	−	0.969625i	$-0.421344\pi$
$797$	13.8105	0.489193	0.244597	+	0.969625i	$0.421344\pi$
$798$	83.5934	2.95917
$799$	−5.55534	−0.196534
$800$	4.03660	0.142715
$801$	−69.4933	−2.45542
$802$	1.47097	0.0519419
$803$	−45.4436	−1.60367
$804$	5.55959	0.196072
$805$	36.2506	1.27767
$806$	−34.4449	−1.21327
$807$	−20.3239	−0.715433
$808$	−14.1560	−0.498006
$809$	37.6925	1.32520	0.662599	−	0.748975i	$-0.269454\pi$
$809$	37.6925	1.32520	0.662599	+	0.748975i	$0.269454\pi$
$810$	19.3515	0.679943
$811$	−35.8209	−1.25784	−0.628922	−	0.777469i	$-0.716503\pi$
$811$	−35.8209	−1.25784	−0.628922	+	0.777469i	$0.716503\pi$
$812$	−29.7518	−1.04408
$813$	−30.1639	−1.05790
$814$	−6.93187	−0.242962
$815$	19.6222	0.687336
$816$	3.17249	0.111059
$817$	2.62821	0.0919495
$818$	−20.0841	−0.702225
$819$	−139.258	−4.86606
$820$	1.78003	0.0621615
$821$	−39.3668	−1.37391	−0.686956	−	0.726699i	$-0.741053\pi$
$821$	−39.3668	−1.37391	−0.686956	+	0.726699i	$0.741053\pi$
$822$	29.2120	1.01889
$823$	−3.76592	−0.131272	−0.0656359	−	0.997844i	$-0.520908\pi$
$823$	−3.76592	−0.131272	−0.0656359	+	0.997844i	$0.520908\pi$
$824$	17.9463	0.625187
$825$	72.5798	2.52690
$826$	−4.36977	−0.152044
$827$	−49.7988	−1.73167	−0.865837	−	0.500326i	$-0.833213\pi$
$827$	−49.7988	−1.73167	−0.865837	+	0.500326i	$0.833213\pi$
$828$	59.7100	2.07506
$829$	−29.4566	−1.02307	−0.511534	−	0.859263i	$-0.670923\pi$
$829$	−29.4566	−1.02307	−0.511534	+	0.859263i	$0.670923\pi$
$830$	7.55881	0.262370
$831$	−76.0285	−2.63740
$832$	4.51095	0.156389
$833$	12.0949	0.419064
$834$	0.151320	0.00523977
$835$	−6.74934	−0.233571
$836$	−34.1753	−1.18198
$837$	98.4657	3.40347
$838$	5.31209	0.183503
$839$	52.7730	1.82193	0.910963	−	0.412489i	$-0.135340\pi$
$839$	52.7730	1.82193	0.910963	+	0.412489i	$0.135340\pi$
$840$	−13.6070	−0.469485
$841$	17.3564	0.598496
$842$	−26.3779	−0.909043
$843$	69.0904	2.37960
$844$	−15.7950	−0.543688
$845$	−7.21288	−0.248131
$846$	39.2467	1.34933
$847$	−92.2971	−3.17137
$848$	−5.88073	−0.201945
$849$	2.61423	0.0897203
$850$	4.03660	0.138454
$851$	−10.3373	−0.354357
$852$	24.7431	0.847686
$853$	27.8018	0.951915	0.475957	−	0.879468i	$-0.342102\pi$
$853$	27.8018	0.951915	0.475957	+	0.879468i	$0.342102\pi$
$854$	25.4569	0.871118
$855$	−41.8127	−1.42996
$856$	5.30802	0.181424
$857$	4.36600	0.149140	0.0745699	−	0.997216i	$-0.476242\pi$
$857$	4.36600	0.149140	0.0745699	+	0.997216i	$0.476242\pi$
$858$	81.1086	2.76900
$859$	−21.9623	−0.749344	−0.374672	−	0.927157i	$-0.622245\pi$
$859$	−21.9623	−0.749344	−0.374672	+	0.927157i	$0.622245\pi$
$860$	−0.427809	−0.0145882
$861$	25.1411	0.856807
$862$	30.0335	1.02295
$863$	−23.3543	−0.794989	−0.397495	−	0.917605i	$-0.630120\pi$
$863$	−23.3543	−0.794989	−0.397495	+	0.917605i	$0.630120\pi$
$864$	−12.8952	−0.438703
$865$	−24.4170	−0.830202
$866$	37.1371	1.26197
$867$	3.17249	0.107743
$868$	−33.3670	−1.13255
$869$	−82.7803	−2.80813
$870$	21.2010	0.718783
$871$	7.90515	0.267856
$872$	−2.84413	−0.0963143
$873$	−18.1197	−0.613260
$874$	−50.9644	−1.72390
$875$	−38.7585	−1.31028
$876$	25.4374	0.859451
$877$	−49.9380	−1.68629	−0.843143	−	0.537689i	$-0.819298\pi$
$877$	−49.9380	−1.68629	−0.843143	+	0.537689i	$0.819298\pi$
$878$	7.21785	0.243591
$879$	42.4057	1.43031
$880$	5.56291	0.187526
$881$	8.15171	0.274638	0.137319	−	0.990527i	$-0.456151\pi$
$881$	8.15171	0.274638	0.137319	+	0.990527i	$0.456151\pi$
$882$	−85.4468	−2.87714
$883$	0.782003	0.0263165	0.0131582	−	0.999913i	$-0.495811\pi$
$883$	0.782003	0.0263165	0.0131582	+	0.999913i	$0.495811\pi$
$884$	4.51095	0.151720
$885$	3.11388	0.104672
$886$	3.47866	0.116868
$887$	12.6358	0.424269	0.212135	−	0.977240i	$-0.431958\pi$
$887$	12.6358	0.424269	0.212135	+	0.977240i	$0.431958\pi$
$888$	3.88017	0.130210
$889$	−71.0275	−2.38219
$890$	−9.65500	−0.323636
$891$	−111.741	−3.74346
$892$	−2.01148	−0.0673492
$893$	−33.4984	−1.12098
$894$	52.4387	1.75381
$895$	18.3419	0.613101
$896$	4.36977	0.145984
$897$	120.954	4.03855
$898$	19.2194	0.641360
$899$	51.9891	1.73394
$900$	−28.5173	−0.950578
$901$	−5.88073	−0.195916
$902$	−10.2784	−0.342233
$903$	−6.04236	−0.201077
$904$	2.21790	0.0737663
$905$	5.48999	0.182494
$906$	40.3431	1.34031
$907$	2.89342	0.0960746	0.0480373	−	0.998846i	$-0.484703\pi$
$907$	2.89342	0.0960746	0.0480373	+	0.998846i	$0.484703\pi$
$908$	4.93139	0.163654
$909$	100.008	3.31705
$910$	−19.3477	−0.641370
$911$	−10.3524	−0.342989	−0.171494	−	0.985185i	$-0.554860\pi$
$911$	−10.3524	−0.342989	−0.171494	+	0.985185i	$0.554860\pi$
$912$	19.1299	0.633454
$913$	−43.6466	−1.44449
$914$	−6.58851	−0.217929
$915$	−18.1405	−0.599707
$916$	−6.72077	−0.222061
$917$	49.8102	1.64488
$918$	−12.8952	−0.425604
$919$	−14.3425	−0.473115	−0.236557	−	0.971618i	$-0.576019\pi$
$919$	−14.3425	−0.473115	−0.236557	+	0.971618i	$0.576019\pi$
$920$	8.29577	0.273503
$921$	−95.5488	−3.14844
$922$	22.4005	0.737720
$923$	35.1821	1.15803
$924$	78.5703	2.58477
$925$	4.93705	0.162329
$926$	3.61388	0.118760
$927$	−126.785	−4.16415
$928$	−6.80855	−0.223502
$929$	3.75103	0.123067	0.0615337	−	0.998105i	$-0.480401\pi$
$929$	3.75103	0.123067	0.0615337	+	0.998105i	$0.480401\pi$
$930$	23.7772	0.779685
$931$	72.9316	2.39024
$932$	−16.1682	−0.529607
$933$	−38.0424	−1.24545
$934$	37.7440	1.23502
$935$	5.56291	0.181927
$936$	−31.8684	−1.04165
$937$	−48.4515	−1.58284	−0.791422	−	0.611271i	$-0.790659\pi$
$937$	−48.4515	−1.58284	−0.791422	+	0.611271i	$0.790659\pi$
$938$	7.65776	0.250035
$939$	49.7853	1.62468
$940$	5.45272	0.177848
$941$	−28.3858	−0.925349	−0.462675	−	0.886528i	$-0.653110\pi$
$941$	−28.3858	−0.925349	−0.462675	+	0.886528i	$0.653110\pi$
$942$	−26.6161	−0.867200
$943$	−15.3278	−0.499142
$944$	−1.00000	−0.0325472
$945$	55.3081	1.79917
$946$	2.47029	0.0803159
$947$	43.6663	1.41896	0.709482	−	0.704724i	$-0.248929\pi$
$947$	43.6663	1.41896	0.709482	+	0.704724i	$0.248929\pi$
$948$	46.3370	1.50496
$949$	36.1694	1.17411
$950$	24.3405	0.789709
$951$	55.6608	1.80492
$952$	4.36977	0.141625
$953$	−27.8642	−0.902609	−0.451305	−	0.892370i	$-0.649041\pi$
$953$	−27.8642	−0.902609	−0.451305	+	0.892370i	$0.649041\pi$
$954$	41.5455	1.34509
$955$	21.9947	0.711731
$956$	3.07329	0.0993972
$957$	−122.421	−3.95729
$958$	−10.3145	−0.333246
$959$	40.2365	1.29930
$960$	−3.11388	−0.100500
$961$	27.3064	0.880850
$962$	5.51720	0.177882
$963$	−37.4995	−1.20840
$964$	15.8599	0.510811
$965$	−16.8285	−0.541728
$966$	117.169	3.76985
$967$	33.0780	1.06372	0.531858	−	0.846834i	$-0.321494\pi$
$967$	33.0780	1.06372	0.531858	+	0.846834i	$0.321494\pi$
$968$	−21.1217	−0.678878
$969$	19.1299	0.614541
$970$	−2.51745	−0.0808306
$971$	−11.0240	−0.353776	−0.176888	−	0.984231i	$-0.556603\pi$
$971$	−11.0240	−0.353776	−0.176888	+	0.984231i	$0.556603\pi$
$972$	23.8624	0.765387
$973$	0.208427	0.00668187
$974$	−21.5034	−0.689012
$975$	−57.7675	−1.85004
$976$	5.82568	0.186476
$977$	14.2755	0.456714	0.228357	−	0.973577i	$-0.426665\pi$
$977$	14.2755	0.456714	0.228357	+	0.973577i	$0.426665\pi$
$978$	63.4228	2.02804
$979$	55.7506	1.78180
$980$	−11.8715	−0.379221
$981$	20.0929	0.641516
$982$	29.8313	0.951955
$983$	−40.4948	−1.29158	−0.645792	−	0.763513i	$-0.723473\pi$
$983$	−40.4948	−1.29158	−0.645792	+	0.763513i	$0.723473\pi$
$984$	5.75342	0.183412
$985$	−9.32609	−0.297154
$986$	−6.80855	−0.216828
$987$	77.0140	2.45138
$988$	27.2007	0.865370
$989$	3.68385	0.117140
$990$	−39.3002	−1.24904
$991$	−19.0310	−0.604539	−0.302269	−	0.953223i	$-0.597744\pi$
$991$	−19.0310	−0.604539	−0.302269	+	0.953223i	$0.597744\pi$
$992$	−7.63586	−0.242439
$993$	93.0073	2.95150
$994$	34.0811	1.08099
$995$	−3.72348	−0.118042
$996$	24.4315	0.774143
$997$	−40.7387	−1.29021	−0.645104	−	0.764095i	$-0.723186\pi$
$997$	−40.7387	−1.29021	−0.645104	+	0.764095i	$0.723186\pi$
$998$	−30.9708	−0.980365
$999$	−15.7717	−0.498994

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.u.1.9	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.u.1.9	✓	9	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:	\( N \)	\(=\)	\( 2006 = 2 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.17249 q^{3} +1.00000 q^{4} -0.981527 q^{5} -3.17249 q^{6} -4.36977 q^{7} -1.00000 q^{8} +7.06469 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.17249 q^{3} +1.00000 q^{4} -0.981527 q^{5} -3.17249 q^{6} -4.36977 q^{7} -1.00000 q^{8} +7.06469 q^{9} +0.981527 q^{10} -5.66760 q^{11} +3.17249 q^{12} +4.51095 q^{13} +4.36977 q^{14} -3.11388 q^{15} +1.00000 q^{16} +1.00000 q^{17} -7.06469 q^{18} +6.02994 q^{19} -0.981527 q^{20} -13.8631 q^{21} +5.66760 q^{22} +8.45189 q^{23} -3.17249 q^{24} -4.03660 q^{25} -4.51095 q^{26} +12.8952 q^{27} -4.36977 q^{28} +6.80855 q^{29} +3.11388 q^{30} +7.63586 q^{31} -1.00000 q^{32} -17.9804 q^{33} -1.00000 q^{34} +4.28905 q^{35} +7.06469 q^{36} -1.22307 q^{37} -6.02994 q^{38} +14.3109 q^{39} +0.981527 q^{40} -1.81353 q^{41} +13.8631 q^{42} +0.435861 q^{43} -5.66760 q^{44} -6.93418 q^{45} -8.45189 q^{46} -5.55534 q^{47} +3.17249 q^{48} +12.0949 q^{49} +4.03660 q^{50} +3.17249 q^{51} +4.51095 q^{52} -5.88073 q^{53} -12.8952 q^{54} +5.56291 q^{55} +4.36977 q^{56} +19.1299 q^{57} -6.80855 q^{58} -1.00000 q^{59} -3.11388 q^{60} +5.82568 q^{61} -7.63586 q^{62} -30.8711 q^{63} +1.00000 q^{64} -4.42762 q^{65} +17.9804 q^{66} +1.75244 q^{67} +1.00000 q^{68} +26.8135 q^{69} -4.28905 q^{70} +7.79928 q^{71} -7.06469 q^{72} +8.01813 q^{73} +1.22307 q^{74} -12.8061 q^{75} +6.02994 q^{76} +24.7661 q^{77} -14.3109 q^{78} +14.6059 q^{79} -0.981527 q^{80} +19.7157 q^{81} +1.81353 q^{82} +7.70106 q^{83} -13.8631 q^{84} -0.981527 q^{85} -0.435861 q^{86} +21.6001 q^{87} +5.66760 q^{88} -9.83671 q^{89} +6.93418 q^{90} -19.7118 q^{91} +8.45189 q^{92} +24.2247 q^{93} +5.55534 q^{94} -5.91855 q^{95} -3.17249 q^{96} -2.56483 q^{97} -12.0949 q^{98} -40.0398 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9	\( 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9} - 7 q^{10} + 5 q^{11} - q^{12} + 25 q^{13} - 5 q^{15} + 9 q^{16} + 9 q^{17} - 20 q^{18} + 14 q^{19} + 7 q^{20} - 7 q^{21} - 5 q^{22} + 2 q^{23} + q^{24} + 20 q^{25} - 25 q^{26} - 10 q^{27} + 18 q^{29} + 5 q^{30} + 6 q^{31} - 9 q^{32} - 9 q^{33} - 9 q^{34} - 17 q^{35} + 20 q^{36} + 11 q^{37} - 14 q^{38} - 8 q^{39} - 7 q^{40} + 18 q^{41} + 7 q^{42} - 10 q^{43} + 5 q^{44} + 27 q^{45} - 2 q^{46} - 20 q^{47} - q^{48} + 13 q^{49} - 20 q^{50} - q^{51} + 25 q^{52} - 7 q^{53} + 10 q^{54} + 29 q^{55} + 17 q^{57} - 18 q^{58} - 9 q^{59} - 5 q^{60} + 30 q^{61} - 6 q^{62} - 47 q^{63} + 9 q^{64} + 8 q^{65} + 9 q^{66} + 6 q^{67} + 9 q^{68} + 20 q^{69} + 17 q^{70} + 30 q^{71} - 20 q^{72} - 11 q^{74} - 7 q^{75} + 14 q^{76} - 3 q^{77} + 8 q^{78} + 29 q^{79} + 7 q^{80} - 3 q^{81} - 18 q^{82} + 9 q^{83} - 7 q^{84} + 7 q^{85} + 10 q^{86} + 44 q^{87} - 5 q^{88} + 8 q^{89} - 27 q^{90} + 13 q^{91} + 2 q^{92} + 7 q^{93} + 20 q^{94} + 27 q^{95} + q^{96} - 13 q^{97} - 13 q^{98} - 19 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9 - 7 * q^10 + 5 * q^11 - q^12 + 25 * q^13 - 5 * q^15 + 9 * q^16 + 9 * q^17 - 20 * q^18 + 14 * q^19 + 7 * q^20 - 7 * q^21 - 5 * q^22 + 2 * q^23 + q^24 + 20 * q^25 - 25 * q^26 - 10 * q^27 + 18 * q^29 + 5 * q^30 + 6 * q^31 - 9 * q^32 - 9 * q^33 - 9 * q^34 - 17 * q^35 + 20 * q^36 + 11 * q^37 - 14 * q^38 - 8 * q^39 - 7 * q^40 + 18 * q^41 + 7 * q^42 - 10 * q^43 + 5 * q^44 + 27 * q^45 - 2 * q^46 - 20 * q^47 - q^48 + 13 * q^49 - 20 * q^50 - q^51 + 25 * q^52 - 7 * q^53 + 10 * q^54 + 29 * q^55 + 17 * q^57 - 18 * q^58 - 9 * q^59 - 5 * q^60 + 30 * q^61 - 6 * q^62 - 47 * q^63 + 9 * q^64 + 8 * q^65 + 9 * q^66 + 6 * q^67 + 9 * q^68 + 20 * q^69 + 17 * q^70 + 30 * q^71 - 20 * q^72 - 11 * q^74 - 7 * q^75 + 14 * q^76 - 3 * q^77 + 8 * q^78 + 29 * q^79 + 7 * q^80 - 3 * q^81 - 18 * q^82 + 9 * q^83 - 7 * q^84 + 7 * q^85 + 10 * q^86 + 44 * q^87 - 5 * q^88 + 8 * q^89 - 27 * q^90 + 13 * q^91 + 2 * q^92 + 7 * q^93 + 20 * q^94 + 27 * q^95 + q^96 - 13 * q^97 - 13 * q^98 - 19 * q^99

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