LMFDB - Embedded newform 2006.2.a.v.1.12

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 21 x^{10} + 62 x^{9} + 144 x^{8} - 418 x^{7} - 370 x^{6} + 1042 x^{5} + 417 x^{4} + \cdots + 62 $ x^12 - 3x^11 - 21x^10 + 62x^9 + 144x^8 - 418x^7 - 370x^6 + 1042x^5 + 417x^4 - 935x^3 - 233x^2 + 228*x + 62
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-3.06872$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +3.06872 q^{3} +1.00000 q^{4} -2.96683 q^{5} -3.06872 q^{6} +2.62570 q^{7} -1.00000 q^{8} +6.41702 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.06872 q^{3} +1.00000 q^{4} -2.96683 q^{5} -3.06872 q^{6} +2.62570 q^{7} -1.00000 q^{8} +6.41702 q^{9} +2.96683 q^{10} +2.16480 q^{11} +3.06872 q^{12} +0.453812 q^{13} -2.62570 q^{14} -9.10435 q^{15} +1.00000 q^{16} -1.00000 q^{17} -6.41702 q^{18} -2.51406 q^{19} -2.96683 q^{20} +8.05753 q^{21} -2.16480 q^{22} -0.198807 q^{23} -3.06872 q^{24} +3.80207 q^{25} -0.453812 q^{26} +10.4859 q^{27} +2.62570 q^{28} +4.75652 q^{29} +9.10435 q^{30} +9.40641 q^{31} -1.00000 q^{32} +6.64316 q^{33} +1.00000 q^{34} -7.79001 q^{35} +6.41702 q^{36} +4.14115 q^{37} +2.51406 q^{38} +1.39262 q^{39} +2.96683 q^{40} -2.27829 q^{41} -8.05753 q^{42} +5.08881 q^{43} +2.16480 q^{44} -19.0382 q^{45} +0.198807 q^{46} -5.85069 q^{47} +3.06872 q^{48} -0.105691 q^{49} -3.80207 q^{50} -3.06872 q^{51} +0.453812 q^{52} +4.62790 q^{53} -10.4859 q^{54} -6.42259 q^{55} -2.62570 q^{56} -7.71494 q^{57} -4.75652 q^{58} +1.00000 q^{59} -9.10435 q^{60} +6.17265 q^{61} -9.40641 q^{62} +16.8492 q^{63} +1.00000 q^{64} -1.34638 q^{65} -6.64316 q^{66} -9.85393 q^{67} -1.00000 q^{68} -0.610081 q^{69} +7.79001 q^{70} +1.77365 q^{71} -6.41702 q^{72} +4.50071 q^{73} -4.14115 q^{74} +11.6675 q^{75} -2.51406 q^{76} +5.68412 q^{77} -1.39262 q^{78} +3.64127 q^{79} -2.96683 q^{80} +12.9271 q^{81} +2.27829 q^{82} -16.7499 q^{83} +8.05753 q^{84} +2.96683 q^{85} -5.08881 q^{86} +14.5964 q^{87} -2.16480 q^{88} +2.84540 q^{89} +19.0382 q^{90} +1.19157 q^{91} -0.198807 q^{92} +28.8656 q^{93} +5.85069 q^{94} +7.45879 q^{95} -3.06872 q^{96} +3.92103 q^{97} +0.105691 q^{98} +13.8916 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} - q^{5} + 3 q^{6} + 4 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 - q^5 + 3 * q^6 + 4 * q^7 - 12 * q^8 + 15 * q^9	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} - q^{5} + 3 q^{6} + 4 q^{7} - 12 q^{8} + 15 q^{9} + q^{10} - 3 q^{11} - 3 q^{12} + 15 q^{13} - 4 q^{14} - 3 q^{15} + 12 q^{16} - 12 q^{17} - 15 q^{18} + 16 q^{19} - q^{20} + 15 q^{21} + 3 q^{22} - 14 q^{23} + 3 q^{24} + 19 q^{25} - 15 q^{26} - 12 q^{27} + 4 q^{28} + 14 q^{29} + 3 q^{30} + 26 q^{31} - 12 q^{32} + 13 q^{33} + 12 q^{34} - 5 q^{35} + 15 q^{36} + 15 q^{37} - 16 q^{38} + 4 q^{39} + q^{40} - 2 q^{41} - 15 q^{42} + 8 q^{43} - 3 q^{44} - 17 q^{45} + 14 q^{46} - 6 q^{47} - 3 q^{48} + 30 q^{49} - 19 q^{50} + 3 q^{51} + 15 q^{52} + q^{53} + 12 q^{54} + q^{55} - 4 q^{56} + 3 q^{57} - 14 q^{58} + 12 q^{59} - 3 q^{60} + 30 q^{61} - 26 q^{62} + q^{63} + 12 q^{64} - 4 q^{65} - 13 q^{66} + 10 q^{67} - 12 q^{68} + 8 q^{69} + 5 q^{70} + 6 q^{71} - 15 q^{72} + 26 q^{73} - 15 q^{74} + 7 q^{75} + 16 q^{76} + 45 q^{77} - 4 q^{78} - 11 q^{79} - q^{80} + 48 q^{81} + 2 q^{82} - 21 q^{83} + 15 q^{84} + q^{85} - 8 q^{86} + 2 q^{87} + 3 q^{88} - 2 q^{89} + 17 q^{90} + 31 q^{91} - 14 q^{92} + 41 q^{93} + 6 q^{94} - 29 q^{95} + 3 q^{96} + 27 q^{97} - 30 q^{98} + 9 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 - q^5 + 3 * q^6 + 4 * q^7 - 12 * q^8 + 15 * q^9 + q^10 - 3 * q^11 - 3 * q^12 + 15 * q^13 - 4 * q^14 - 3 * q^15 + 12 * q^16 - 12 * q^17 - 15 * q^18 + 16 * q^19 - q^20 + 15 * q^21 + 3 * q^22 - 14 * q^23 + 3 * q^24 + 19 * q^25 - 15 * q^26 - 12 * q^27 + 4 * q^28 + 14 * q^29 + 3 * q^30 + 26 * q^31 - 12 * q^32 + 13 * q^33 + 12 * q^34 - 5 * q^35 + 15 * q^36 + 15 * q^37 - 16 * q^38 + 4 * q^39 + q^40 - 2 * q^41 - 15 * q^42 + 8 * q^43 - 3 * q^44 - 17 * q^45 + 14 * q^46 - 6 * q^47 - 3 * q^48 + 30 * q^49 - 19 * q^50 + 3 * q^51 + 15 * q^52 + q^53 + 12 * q^54 + q^55 - 4 * q^56 + 3 * q^57 - 14 * q^58 + 12 * q^59 - 3 * q^60 + 30 * q^61 - 26 * q^62 + q^63 + 12 * q^64 - 4 * q^65 - 13 * q^66 + 10 * q^67 - 12 * q^68 + 8 * q^69 + 5 * q^70 + 6 * q^71 - 15 * q^72 + 26 * q^73 - 15 * q^74 + 7 * q^75 + 16 * q^76 + 45 * q^77 - 4 * q^78 - 11 * q^79 - q^80 + 48 * q^81 + 2 * q^82 - 21 * q^83 + 15 * q^84 + q^85 - 8 * q^86 + 2 * q^87 + 3 * q^88 - 2 * q^89 + 17 * q^90 + 31 * q^91 - 14 * q^92 + 41 * q^93 + 6 * q^94 - 29 * q^95 + 3 * q^96 + 27 * q^97 - 30 * q^98 + 9 * 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
$3$	3.06872	1.77172	0.885862	−	0.463949i	$-0.153568\pi$
$3$	3.06872	1.77172	0.885862	+	0.463949i	$0.153568\pi$
$4$	1.00000	0.500000
$5$	−2.96683	−1.32681	−0.663403	−	0.748262i	$-0.730889\pi$
$5$	−2.96683	−1.32681	−0.663403	+	0.748262i	$0.730889\pi$
$6$	−3.06872	−1.25280
$7$	2.62570	0.992422	0.496211	−	0.868202i	$-0.334724\pi$
$7$	2.62570	0.992422	0.496211	+	0.868202i	$0.334724\pi$
$8$	−1.00000	−0.353553
$9$	6.41702	2.13901
$10$	2.96683	0.938194
$11$	2.16480	0.652712	0.326356	−	0.945247i	$-0.394179\pi$
$11$	2.16480	0.652712	0.326356	+	0.945247i	$0.394179\pi$
$12$	3.06872	0.885862
$13$	0.453812	0.125865	0.0629324	−	0.998018i	$-0.479955\pi$
$13$	0.453812	0.125865	0.0629324	+	0.998018i	$0.479955\pi$
$14$	−2.62570	−0.701748
$15$	−9.10435	−2.35073
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−6.41702	−1.51251
$19$	−2.51406	−0.576765	−0.288383	−	0.957515i	$-0.593118\pi$
$19$	−2.51406	−0.576765	−0.288383	+	0.957515i	$0.593118\pi$
$20$	−2.96683	−0.663403
$21$	8.05753	1.75830
$22$	−2.16480	−0.461537
$23$	−0.198807	−0.0414541	−0.0207270	−	0.999785i	$-0.506598\pi$
$23$	−0.198807	−0.0414541	−0.0207270	+	0.999785i	$0.506598\pi$
$24$	−3.06872	−0.626399
$25$	3.80207	0.760415
$26$	−0.453812	−0.0889998
$27$	10.4859	2.01800
$28$	2.62570	0.496211
$29$	4.75652	0.883263	0.441632	−	0.897197i	$-0.354400\pi$
$29$	4.75652	0.883263	0.441632	+	0.897197i	$0.354400\pi$
$30$	9.10435	1.66222
$31$	9.40641	1.68944	0.844720	−	0.535208i	$-0.179767\pi$
$31$	9.40641	1.68944	0.844720	+	0.535208i	$0.179767\pi$
$32$	−1.00000	−0.176777
$33$	6.64316	1.15643
$34$	1.00000	0.171499
$35$	−7.79001	−1.31675
$36$	6.41702	1.06950
$37$	4.14115	0.680801	0.340400	−	0.940281i	$-0.389437\pi$
$37$	4.14115	0.680801	0.340400	+	0.940281i	$0.389437\pi$
$38$	2.51406	0.407835
$39$	1.39262	0.222998
$40$	2.96683	0.469097
$41$	−2.27829	−0.355809	−0.177904	−	0.984048i	$-0.556932\pi$
$41$	−2.27829	−0.355809	−0.177904	+	0.984048i	$0.556932\pi$
$42$	−8.05753	−1.24330
$43$	5.08881	0.776036	0.388018	−	0.921652i	$-0.373160\pi$
$43$	5.08881	0.776036	0.388018	+	0.921652i	$0.373160\pi$
$44$	2.16480	0.326356
$45$	−19.0382	−2.83805
$46$	0.198807	0.0293124
$47$	−5.85069	−0.853411	−0.426705	−	0.904391i	$-0.640326\pi$
$47$	−5.85069	−0.853411	−0.426705	+	0.904391i	$0.640326\pi$
$48$	3.06872	0.442931
$49$	−0.105691	−0.0150986
$50$	−3.80207	−0.537694
$51$	−3.06872	−0.429706
$52$	0.453812	0.0629324
$53$	4.62790	0.635692	0.317846	−	0.948142i	$-0.397041\pi$
$53$	4.62790	0.635692	0.317846	+	0.948142i	$0.397041\pi$
$54$	−10.4859	−1.42694
$55$	−6.42259	−0.866022
$56$	−2.62570	−0.350874
$57$	−7.71494	−1.02187
$58$	−4.75652	−0.624561
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−9.10435	−1.17537
$61$	6.17265	0.790327	0.395164	−	0.918611i	$-0.370688\pi$
$61$	6.17265	0.790327	0.395164	+	0.918611i	$0.370688\pi$
$62$	−9.40641	−1.19461
$63$	16.8492	2.12280
$64$	1.00000	0.125000
$65$	−1.34638	−0.166998
$66$	−6.64316	−0.817716
$67$	−9.85393	−1.20385	−0.601924	−	0.798553i	$-0.705599\pi$
$67$	−9.85393	−1.20385	−0.601924	+	0.798553i	$0.705599\pi$
$68$	−1.00000	−0.121268
$69$	−0.610081	−0.0734451
$70$	7.79001	0.931084
$71$	1.77365	0.210494	0.105247	−	0.994446i	$-0.466437\pi$
$71$	1.77365	0.210494	0.105247	+	0.994446i	$0.466437\pi$
$72$	−6.41702	−0.756253
$73$	4.50071	0.526768	0.263384	−	0.964691i	$-0.415161\pi$
$73$	4.50071	0.526768	0.263384	+	0.964691i	$0.415161\pi$
$74$	−4.14115	−0.481399
$75$	11.6675	1.34724
$76$	−2.51406	−0.288383
$77$	5.68412	0.647765
$78$	−1.39262	−0.157683
$79$	3.64127	0.409675	0.204838	−	0.978796i	$-0.434333\pi$
$79$	3.64127	0.409675	0.204838	+	0.978796i	$0.434333\pi$
$80$	−2.96683	−0.331702
$81$	12.9271	1.43634
$82$	2.27829	0.251595
$83$	−16.7499	−1.83854	−0.919271	−	0.393624i	$-0.871221\pi$
$83$	−16.7499	−1.83854	−0.919271	+	0.393624i	$0.871221\pi$
$84$	8.05753	0.879149
$85$	2.96683	0.321798
$86$	−5.08881	−0.548740
$87$	14.5964	1.56490
$88$	−2.16480	−0.230768
$89$	2.84540	0.301612	0.150806	−	0.988563i	$-0.451813\pi$
$89$	2.84540	0.301612	0.150806	+	0.988563i	$0.451813\pi$
$90$	19.0382	2.00680
$91$	1.19157	0.124911
$92$	−0.198807	−0.0207270
$93$	28.8656	2.99322
$94$	5.85069	0.603452
$95$	7.45879	0.765256
$96$	−3.06872	−0.313200
$97$	3.92103	0.398121	0.199060	−	0.979987i	$-0.436211\pi$
$97$	3.92103	0.398121	0.199060	+	0.979987i	$0.436211\pi$
$98$	0.105691	0.0106764
$99$	13.8916	1.39615
$100$	3.80207	0.380207
$101$	6.47478	0.644264	0.322132	−	0.946695i	$-0.395600\pi$
$101$	6.47478	0.644264	0.322132	+	0.946695i	$0.395600\pi$
$102$	3.06872	0.303848
$103$	3.29244	0.324414	0.162207	−	0.986757i	$-0.448139\pi$
$103$	3.29244	0.324414	0.162207	+	0.986757i	$0.448139\pi$
$104$	−0.453812	−0.0444999
$105$	−23.9053	−2.33292
$106$	−4.62790	−0.449502
$107$	12.2188	1.18123	0.590616	−	0.806953i	$-0.298885\pi$
$107$	12.2188	1.18123	0.590616	+	0.806953i	$0.298885\pi$
$108$	10.4859	1.00900
$109$	4.63112	0.443581	0.221790	−	0.975094i	$-0.428810\pi$
$109$	4.63112	0.443581	0.221790	+	0.975094i	$0.428810\pi$
$110$	6.42259	0.612370
$111$	12.7080	1.20619
$112$	2.62570	0.248105
$113$	−12.3846	−1.16504	−0.582521	−	0.812816i	$-0.697934\pi$
$113$	−12.3846	−1.16504	−0.582521	+	0.812816i	$0.697934\pi$
$114$	7.71494	0.722570
$115$	0.589825	0.0550015
$116$	4.75652	0.441632
$117$	2.91212	0.269225
$118$	−1.00000	−0.0920575
$119$	−2.62570	−0.240698
$120$	9.10435	0.831110
$121$	−6.31364	−0.573967
$122$	−6.17265	−0.558846
$123$	−6.99142	−0.630395
$124$	9.40641	0.844720
$125$	3.55404	0.317883
$126$	−16.8492	−1.50104
$127$	7.92198	0.702962	0.351481	−	0.936195i	$-0.385678\pi$
$127$	7.92198	0.702962	0.351481	+	0.936195i	$0.385678\pi$
$128$	−1.00000	−0.0883883
$129$	15.6161	1.37492
$130$	1.34638	0.118086
$131$	11.9651	1.04540	0.522698	−	0.852518i	$-0.324926\pi$
$131$	11.9651	1.04540	0.522698	+	0.852518i	$0.324926\pi$
$132$	6.64316	0.578213
$133$	−6.60118	−0.572395
$134$	9.85393	0.851249
$135$	−31.1097	−2.67750
$136$	1.00000	0.0857493
$137$	−17.9970	−1.53758	−0.768792	−	0.639499i	$-0.779142\pi$
$137$	−17.9970	−1.53758	−0.768792	+	0.639499i	$0.779142\pi$
$138$	0.610081	0.0519336
$139$	−5.23382	−0.443927	−0.221963	−	0.975055i	$-0.571247\pi$
$139$	−5.23382	−0.443927	−0.221963	+	0.975055i	$0.571247\pi$
$140$	−7.79001	−0.658376
$141$	−17.9541	−1.51201
$142$	−1.77365	−0.148842
$143$	0.982412	0.0821534
$144$	6.41702	0.534751
$145$	−14.1118	−1.17192
$146$	−4.50071	−0.372481
$147$	−0.324334	−0.0267506
$148$	4.14115	0.340400
$149$	−15.6130	−1.27907	−0.639534	−	0.768763i	$-0.720873\pi$
$149$	−15.6130	−1.27907	−0.639534	+	0.768763i	$0.720873\pi$
$150$	−11.6675	−0.952646
$151$	12.3893	1.00823	0.504114	−	0.863637i	$-0.331819\pi$
$151$	12.3893	1.00823	0.504114	+	0.863637i	$0.331819\pi$
$152$	2.51406	0.203917
$153$	−6.41702	−0.518785
$154$	−5.68412	−0.458039
$155$	−27.9072	−2.24156
$156$	1.39262	0.111499
$157$	16.6323	1.32740	0.663700	−	0.747999i	$-0.268985\pi$
$157$	16.6323	1.32740	0.663700	+	0.747999i	$0.268985\pi$
$158$	−3.64127	−0.289684
$159$	14.2017	1.12627
$160$	2.96683	0.234548
$161$	−0.522007	−0.0411399
$162$	−12.9271	−1.01565
$163$	11.0739	0.867375	0.433688	−	0.901063i	$-0.357212\pi$
$163$	11.0739	0.867375	0.433688	+	0.901063i	$0.357212\pi$
$164$	−2.27829	−0.177904
$165$	−19.7091	−1.53435
$166$	16.7499	1.30005
$167$	14.9404	1.15612	0.578062	−	0.815993i	$-0.303809\pi$
$167$	14.9404	1.15612	0.578062	+	0.815993i	$0.303809\pi$
$168$	−8.05753	−0.621652
$169$	−12.7941	−0.984158
$170$	−2.96683	−0.227545
$171$	−16.1328	−1.23370
$172$	5.08881	0.388018
$173$	−21.3743	−1.62506	−0.812530	−	0.582920i	$-0.801910\pi$
$173$	−21.3743	−1.62506	−0.812530	+	0.582920i	$0.801910\pi$
$174$	−14.5964	−1.10655
$175$	9.98311	0.754652
$176$	2.16480	0.163178
$177$	3.06872	0.230659
$178$	−2.84540	−0.213272
$179$	−8.51252	−0.636256	−0.318128	−	0.948048i	$-0.603054\pi$
$179$	−8.51252	−0.636256	−0.318128	+	0.948048i	$0.603054\pi$
$180$	−19.0382	−1.41902
$181$	−9.47975	−0.704624	−0.352312	−	0.935883i	$-0.614604\pi$
$181$	−9.47975	−0.704624	−0.352312	+	0.935883i	$0.614604\pi$
$182$	−1.19157	−0.0883254
$183$	18.9421	1.40024
$184$	0.198807	0.0146562
$185$	−12.2861	−0.903291
$186$	−28.8656	−2.11653
$187$	−2.16480	−0.158306
$188$	−5.85069	−0.426705
$189$	27.5327	2.00271
$190$	−7.45879	−0.541118
$191$	13.8388	1.00134	0.500670	−	0.865638i	$-0.333087\pi$
$191$	13.8388	1.00134	0.500670	+	0.865638i	$0.333087\pi$
$192$	3.06872	0.221465
$193$	−13.8353	−0.995890	−0.497945	−	0.867209i	$-0.665912\pi$
$193$	−13.8353	−0.995890	−0.497945	+	0.867209i	$0.665912\pi$
$194$	−3.92103	−0.281514
$195$	−4.13166	−0.295875
$196$	−0.105691	−0.00754932
$197$	−14.3830	−1.02475	−0.512374	−	0.858762i	$-0.671234\pi$
$197$	−14.3830	−1.02475	−0.512374	+	0.858762i	$0.671234\pi$
$198$	−13.8916	−0.987230
$199$	20.4468	1.44943	0.724717	−	0.689047i	$-0.241971\pi$
$199$	20.4468	1.44943	0.724717	+	0.689047i	$0.241971\pi$
$200$	−3.80207	−0.268847
$201$	−30.2389	−2.13289
$202$	−6.47478	−0.455564
$203$	12.4892	0.876570
$204$	−3.06872	−0.214853
$205$	6.75929	0.472089
$206$	−3.29244	−0.229395
$207$	−1.27575	−0.0886705
$208$	0.453812	0.0314662
$209$	−5.44244	−0.376461
$210$	23.9053	1.64962
$211$	−5.40534	−0.372119	−0.186060	−	0.982538i	$-0.559572\pi$
$211$	−5.40534	−0.372119	−0.186060	+	0.982538i	$0.559572\pi$
$212$	4.62790	0.317846
$213$	5.44283	0.372937
$214$	−12.2188	−0.835257
$215$	−15.0976	−1.02965
$216$	−10.4859	−0.713472
$217$	24.6984	1.67664
$218$	−4.63112	−0.313659
$219$	13.8114	0.933287
$220$	−6.42259	−0.433011
$221$	−0.453812	−0.0305267
$222$	−12.7080	−0.852906
$223$	−20.7034	−1.38640	−0.693200	−	0.720746i	$-0.743800\pi$
$223$	−20.7034	−1.38640	−0.693200	+	0.720746i	$0.743800\pi$
$224$	−2.62570	−0.175437
$225$	24.3980	1.62653
$226$	12.3846	0.823809
$227$	16.6210	1.10317	0.551586	−	0.834118i	$-0.314023\pi$
$227$	16.6210	1.10317	0.551586	+	0.834118i	$0.314023\pi$
$228$	−7.71494	−0.510934
$229$	−2.34529	−0.154981	−0.0774907	−	0.996993i	$-0.524691\pi$
$229$	−2.34529	−0.154981	−0.0774907	+	0.996993i	$0.524691\pi$
$230$	−0.589825	−0.0388919
$231$	17.4429	1.14766
$232$	−4.75652	−0.312281
$233$	5.06340	0.331715	0.165857	−	0.986150i	$-0.446961\pi$
$233$	5.06340	0.331715	0.165857	+	0.986150i	$0.446961\pi$
$234$	−2.91212	−0.190371
$235$	17.3580	1.13231
$236$	1.00000	0.0650945
$237$	11.1740	0.725831
$238$	2.62570	0.170199
$239$	4.45339	0.288066	0.144033	−	0.989573i	$-0.453993\pi$
$239$	4.45339	0.288066	0.144033	+	0.989573i	$0.453993\pi$
$240$	−9.10435	−0.587684
$241$	1.35080	0.0870125	0.0435063	−	0.999053i	$-0.486147\pi$
$241$	1.35080	0.0870125	0.0435063	+	0.999053i	$0.486147\pi$
$242$	6.31364	0.405856
$243$	8.21191	0.526794
$244$	6.17265	0.395164
$245$	0.313566	0.0200330
$246$	6.99142	0.445757
$247$	−1.14091	−0.0725944
$248$	−9.40641	−0.597307
$249$	−51.4008	−3.25739
$250$	−3.55404	−0.224777
$251$	−14.8177	−0.935284	−0.467642	−	0.883918i	$-0.654896\pi$
$251$	−14.8177	−0.935284	−0.467642	+	0.883918i	$0.654896\pi$
$252$	16.8492	1.06140
$253$	−0.430377	−0.0270575
$254$	−7.92198	−0.497069
$255$	9.10435	0.570137
$256$	1.00000	0.0625000
$257$	−0.724339	−0.0451830	−0.0225915	−	0.999745i	$-0.507192\pi$
$257$	−0.724339	−0.0451830	−0.0225915	+	0.999745i	$0.507192\pi$
$258$	−15.6161	−0.972216
$259$	10.8734	0.675642
$260$	−1.34638	−0.0834991
$261$	30.5227	1.88930
$262$	−11.9651	−0.739206
$263$	−22.7384	−1.40211	−0.701056	−	0.713106i	$-0.747288\pi$
$263$	−22.7384	−1.40211	−0.701056	+	0.713106i	$0.747288\pi$
$264$	−6.64316	−0.408858
$265$	−13.7302	−0.843439
$266$	6.60118	0.404744
$267$	8.73172	0.534373
$268$	−9.85393	−0.601924
$269$	23.4025	1.42687	0.713437	−	0.700720i	$-0.247138\pi$
$269$	23.4025	1.42687	0.713437	+	0.700720i	$0.247138\pi$
$270$	31.1097	1.89328
$271$	9.93775	0.603675	0.301838	−	0.953359i	$-0.402400\pi$
$271$	9.93775	0.603675	0.301838	+	0.953359i	$0.402400\pi$
$272$	−1.00000	−0.0606339
$273$	3.65660	0.221308
$274$	17.9970	1.08724
$275$	8.23073	0.496332
$276$	−0.610081	−0.0367226
$277$	−14.6257	−0.878775	−0.439388	−	0.898298i	$-0.644805\pi$
$277$	−14.6257	−0.878775	−0.439388	+	0.898298i	$0.644805\pi$
$278$	5.23382	0.313903
$279$	60.3611	3.61372
$280$	7.79001	0.465542
$281$	−13.1102	−0.782091	−0.391045	−	0.920371i	$-0.627886\pi$
$281$	−13.1102	−0.782091	−0.391045	+	0.920371i	$0.627886\pi$
$282$	17.9541	1.06915
$283$	−15.0356	−0.893772	−0.446886	−	0.894591i	$-0.647467\pi$
$283$	−15.0356	−0.893772	−0.446886	+	0.894591i	$0.647467\pi$
$284$	1.77365	0.105247
$285$	22.8889	1.35582
$286$	−0.982412	−0.0580912
$287$	−5.98211	−0.353113
$288$	−6.41702	−0.378126
$289$	1.00000	0.0588235
$290$	14.1118	0.828672
$291$	12.0325	0.705360
$292$	4.50071	0.263384
$293$	−22.2242	−1.29835	−0.649176	−	0.760638i	$-0.724886\pi$
$293$	−22.2242	−1.29835	−0.649176	+	0.760638i	$0.724886\pi$
$294$	0.324334	0.0189156
$295$	−2.96683	−0.172735
$296$	−4.14115	−0.240699
$297$	22.6998	1.31717
$298$	15.6130	0.904437
$299$	−0.0902208	−0.00521760
$300$	11.6675	0.673622
$301$	13.3617	0.770155
$302$	−12.3893	−0.712924
$303$	19.8692	1.14146
$304$	−2.51406	−0.144191
$305$	−18.3132	−1.04861
$306$	6.41702	0.366836
$307$	32.3245	1.84485	0.922427	−	0.386171i	$-0.126203\pi$
$307$	32.3245	1.84485	0.922427	+	0.386171i	$0.126203\pi$
$308$	5.68412	0.323883
$309$	10.1036	0.574772
$310$	27.9072	1.58502
$311$	−21.9046	−1.24210	−0.621049	−	0.783772i	$-0.713293\pi$
$311$	−21.9046	−1.24210	−0.621049	+	0.783772i	$0.713293\pi$
$312$	−1.39262	−0.0788416
$313$	20.6515	1.16729	0.583645	−	0.812009i	$-0.301626\pi$
$313$	20.6515	1.16729	0.583645	+	0.812009i	$0.301626\pi$
$314$	−16.6323	−0.938614
$315$	−49.9886	−2.81654
$316$	3.64127	0.204838
$317$	−11.2117	−0.629709	−0.314855	−	0.949140i	$-0.601956\pi$
$317$	−11.2117	−0.629709	−0.314855	+	0.949140i	$0.601956\pi$
$318$	−14.2017	−0.796393
$319$	10.2969	0.576516
$320$	−2.96683	−0.165851
$321$	37.4959	2.09282
$322$	0.522007	0.0290903
$323$	2.51406	0.139886
$324$	12.9271	0.718170
$325$	1.72543	0.0957094
$326$	−11.0739	−0.613327
$327$	14.2116	0.785902
$328$	2.27829	0.125797
$329$	−15.3622	−0.846943
$330$	19.7091	1.08495
$331$	−2.30713	−0.126811	−0.0634057	−	0.997988i	$-0.520196\pi$
$331$	−2.30713	−0.126811	−0.0634057	+	0.997988i	$0.520196\pi$
$332$	−16.7499	−0.919271
$333$	26.5738	1.45624
$334$	−14.9404	−0.817503
$335$	29.2349	1.59727
$336$	8.05753	0.439574
$337$	13.0462	0.710672	0.355336	−	0.934739i	$-0.384366\pi$
$337$	13.0462	0.710672	0.355336	+	0.934739i	$0.384366\pi$
$338$	12.7941	0.695905
$339$	−38.0047	−2.06413
$340$	2.96683	0.160899
$341$	20.3630	1.10272
$342$	16.1328	0.872361
$343$	−18.6574	−1.00741
$344$	−5.08881	−0.274370
$345$	1.81001	0.0974475
$346$	21.3743	1.14909
$347$	−15.7878	−0.847532	−0.423766	−	0.905772i	$-0.639292\pi$
$347$	−15.7878	−0.847532	−0.423766	+	0.905772i	$0.639292\pi$
$348$	14.5964	0.782449
$349$	−27.6649	−1.48087	−0.740433	−	0.672130i	$-0.765380\pi$
$349$	−27.6649	−1.48087	−0.740433	+	0.672130i	$0.765380\pi$
$350$	−9.98311	−0.533620
$351$	4.75861	0.253996
$352$	−2.16480	−0.115384
$353$	28.3006	1.50629	0.753145	−	0.657855i	$-0.228536\pi$
$353$	28.3006	1.50629	0.753145	+	0.657855i	$0.228536\pi$
$354$	−3.06872	−0.163100
$355$	−5.26212	−0.279284
$356$	2.84540	0.150806
$357$	−8.05753	−0.426450
$358$	8.51252	0.449901
$359$	3.48262	0.183806	0.0919029	−	0.995768i	$-0.470705\pi$
$359$	3.48262	0.183806	0.0919029	+	0.995768i	$0.470705\pi$
$360$	19.0382	1.00340
$361$	−12.6795	−0.667342
$362$	9.47975	0.498245
$363$	−19.3748	−1.01691
$364$	1.19157	0.0624555
$365$	−13.3528	−0.698919
$366$	−18.9421	−0.990121
$367$	−26.7273	−1.39515	−0.697576	−	0.716511i	$-0.745738\pi$
$367$	−26.7273	−1.39515	−0.697576	+	0.716511i	$0.745738\pi$
$368$	−0.198807	−0.0103635
$369$	−14.6198	−0.761077
$370$	12.2861	0.638723
$371$	12.1515	0.630874
$372$	28.8656	1.49661
$373$	−13.0550	−0.675965	−0.337982	−	0.941152i	$-0.609744\pi$
$373$	−13.0550	−0.675965	−0.337982	+	0.941152i	$0.609744\pi$
$374$	2.16480	0.111939
$375$	10.9063	0.563201
$376$	5.85069	0.301726
$377$	2.15856	0.111172
$378$	−27.5327	−1.41613
$379$	−23.8831	−1.22679	−0.613395	−	0.789776i	$-0.710197\pi$
$379$	−23.8831	−1.22679	−0.613395	+	0.789776i	$0.710197\pi$
$380$	7.45879	0.382628
$381$	24.3103	1.24545
$382$	−13.8388	−0.708054
$383$	−31.2837	−1.59852	−0.799262	−	0.600983i	$-0.794776\pi$
$383$	−31.2837	−1.59852	−0.799262	+	0.600983i	$0.794776\pi$
$384$	−3.06872	−0.156600
$385$	−16.8638	−0.859459
$386$	13.8353	0.704201
$387$	32.6550	1.65994
$388$	3.92103	0.199060
$389$	−15.5936	−0.790629	−0.395315	−	0.918546i	$-0.629364\pi$
$389$	−15.5936	−0.790629	−0.395315	+	0.918546i	$0.629364\pi$
$390$	4.13166	0.209215
$391$	0.198807	0.0100541
$392$	0.105691	0.00533818
$393$	36.7175	1.85215
$394$	14.3830	0.724606
$395$	−10.8030	−0.543560
$396$	13.8916	0.698077
$397$	−3.99206	−0.200356	−0.100178	−	0.994970i	$-0.531941\pi$
$397$	−3.99206	−0.200356	−0.100178	+	0.994970i	$0.531941\pi$
$398$	−20.4468	−1.02490
$399$	−20.2571	−1.01413
$400$	3.80207	0.190104
$401$	−11.8898	−0.593746	−0.296873	−	0.954917i	$-0.595944\pi$
$401$	−11.8898	−0.593746	−0.296873	+	0.954917i	$0.595944\pi$
$402$	30.2389	1.50818
$403$	4.26874	0.212641
$404$	6.47478	0.322132
$405$	−38.3524	−1.90574
$406$	−12.4892	−0.619828
$407$	8.96476	0.444367
$408$	3.06872	0.151924
$409$	−31.5088	−1.55801	−0.779006	−	0.627017i	$-0.784276\pi$
$409$	−31.5088	−1.55801	−0.779006	+	0.627017i	$0.784276\pi$
$410$	−6.75929	−0.333818
$411$	−55.2275	−2.72417
$412$	3.29244	0.162207
$413$	2.62570	0.129202
$414$	1.27575	0.0626995
$415$	49.6942	2.43939
$416$	−0.453812	−0.0222500
$417$	−16.0611	−0.786515
$418$	5.44244	0.266198
$419$	1.32977	0.0649635	0.0324817	−	0.999472i	$-0.489659\pi$
$419$	1.32977	0.0649635	0.0324817	+	0.999472i	$0.489659\pi$
$420$	−23.9053	−1.16646
$421$	−22.1245	−1.07828	−0.539141	−	0.842215i	$-0.681251\pi$
$421$	−22.1245	−1.07828	−0.539141	+	0.842215i	$0.681251\pi$
$422$	5.40534	0.263128
$423$	−37.5440	−1.82545
$424$	−4.62790	−0.224751
$425$	−3.80207	−0.184428
$426$	−5.44283	−0.263706
$427$	16.2075	0.784338
$428$	12.2188	0.590616
$429$	3.01474	0.145553
$430$	15.0976	0.728072
$431$	−4.82429	−0.232378	−0.116189	−	0.993227i	$-0.537068\pi$
$431$	−4.82429	−0.232378	−0.116189	+	0.993227i	$0.537068\pi$
$432$	10.4859	0.504501
$433$	0.307559	0.0147804	0.00739018	−	0.999973i	$-0.497648\pi$
$433$	0.307559	0.0147804	0.00739018	+	0.999973i	$0.497648\pi$
$434$	−24.6984	−1.18556
$435$	−43.3050	−2.07632
$436$	4.63112	0.221790
$437$	0.499812	0.0239093
$438$	−13.8114	−0.659934
$439$	−8.45441	−0.403507	−0.201753	−	0.979436i	$-0.564664\pi$
$439$	−8.45441	−0.403507	−0.201753	+	0.979436i	$0.564664\pi$
$440$	6.42259	0.306185
$441$	−0.678218	−0.0322961
$442$	0.453812	0.0215856
$443$	29.9844	1.42460	0.712300	−	0.701875i	$-0.247653\pi$
$443$	29.9844	1.42460	0.712300	+	0.701875i	$0.247653\pi$
$444$	12.7080	0.603096
$445$	−8.44181	−0.400180
$446$	20.7034	0.980332
$447$	−47.9119	−2.26615
$448$	2.62570	0.124053
$449$	−27.2807	−1.28746	−0.643729	−	0.765254i	$-0.722614\pi$
$449$	−27.2807	−1.28746	−0.643729	+	0.765254i	$0.722614\pi$
$450$	−24.3980	−1.15013
$451$	−4.93204	−0.232241
$452$	−12.3846	−0.582521
$453$	38.0193	1.78630
$454$	−16.6210	−0.780061
$455$	−3.53520	−0.165733
$456$	7.71494	0.361285
$457$	−5.53972	−0.259137	−0.129569	−	0.991570i	$-0.541359\pi$
$457$	−5.53972	−0.259137	−0.129569	+	0.991570i	$0.541359\pi$
$458$	2.34529	0.109588
$459$	−10.4859	−0.489438
$460$	0.589825	0.0275007
$461$	14.9061	0.694248	0.347124	−	0.937819i	$-0.387158\pi$
$461$	14.9061	0.694248	0.347124	+	0.937819i	$0.387158\pi$
$462$	−17.4429	−0.811519
$463$	6.63837	0.308511	0.154256	−	0.988031i	$-0.450702\pi$
$463$	6.63837	0.308511	0.154256	+	0.988031i	$0.450702\pi$
$464$	4.75652	0.220816
$465$	−85.6393	−3.97143
$466$	−5.06340	−0.234558
$467$	−8.97243	−0.415194	−0.207597	−	0.978214i	$-0.566564\pi$
$467$	−8.97243	−0.415194	−0.207597	+	0.978214i	$0.566564\pi$
$468$	2.91212	0.134613
$469$	−25.8735	−1.19473
$470$	−17.3580	−0.800664
$471$	51.0397	2.35179
$472$	−1.00000	−0.0460287
$473$	11.0162	0.506528
$474$	−11.1740	−0.513240
$475$	−9.55865	−0.438581
$476$	−2.62570	−0.120349
$477$	29.6973	1.35975
$478$	−4.45339	−0.203693
$479$	7.37889	0.337150	0.168575	−	0.985689i	$-0.446083\pi$
$479$	7.37889	0.337150	0.168575	+	0.985689i	$0.446083\pi$
$480$	9.10435	0.415555
$481$	1.87930	0.0856888
$482$	−1.35080	−0.0615272
$483$	−1.60189	−0.0728886
$484$	−6.31364	−0.286984
$485$	−11.6330	−0.528229
$486$	−8.21191	−0.372500
$487$	−26.1443	−1.18471	−0.592355	−	0.805677i	$-0.701802\pi$
$487$	−26.1443	−1.18471	−0.592355	+	0.805677i	$0.701802\pi$
$488$	−6.17265	−0.279423
$489$	33.9827	1.53675
$490$	−0.313566	−0.0141655
$491$	42.4731	1.91678	0.958392	−	0.285455i	$-0.0921448\pi$
$491$	42.4731	1.91678	0.958392	+	0.285455i	$0.0921448\pi$
$492$	−6.99142	−0.315198
$493$	−4.75652	−0.214223
$494$	1.14091	0.0513320
$495$	−41.2139	−1.85243
$496$	9.40641	0.422360
$497$	4.65708	0.208899
$498$	51.4008	2.30332
$499$	−39.6364	−1.77437	−0.887184	−	0.461417i	$-0.847341\pi$
$499$	−39.6364	−1.77437	−0.887184	+	0.461417i	$0.847341\pi$
$500$	3.55404	0.158942
$501$	45.8479	2.04833
$502$	14.8177	0.661346
$503$	−8.12306	−0.362189	−0.181095	−	0.983466i	$-0.557964\pi$
$503$	−8.12306	−0.362189	−0.181095	+	0.983466i	$0.557964\pi$
$504$	−16.8492	−0.750522
$505$	−19.2096	−0.854814
$506$	0.430377	0.0191326
$507$	−39.2613	−1.74366
$508$	7.92198	0.351481
$509$	36.5175	1.61861	0.809305	−	0.587388i	$-0.199844\pi$
$509$	36.5175	1.61861	0.809305	+	0.587388i	$0.199844\pi$
$510$	−9.10435	−0.403148
$511$	11.8175	0.522776
$512$	−1.00000	−0.0441942
$513$	−26.3621	−1.16391
$514$	0.724339	0.0319492
$515$	−9.76812	−0.430435
$516$	15.6161	0.687460
$517$	−12.6656	−0.557031
$518$	−10.8734	−0.477751
$519$	−65.5917	−2.87916
$520$	1.34638	0.0590428
$521$	12.3456	0.540872	0.270436	−	0.962738i	$-0.412832\pi$
$521$	12.3456	0.540872	0.270436	+	0.962738i	$0.412832\pi$
$522$	−30.5227	−1.33594
$523$	−0.765575	−0.0334763	−0.0167381	−	0.999860i	$-0.505328\pi$
$523$	−0.765575	−0.0334763	−0.0167381	+	0.999860i	$0.505328\pi$
$524$	11.9651	0.522698
$525$	30.6353	1.33704
$526$	22.7384	0.991443
$527$	−9.40641	−0.409749
$528$	6.64316	0.289106
$529$	−22.9605	−0.998282
$530$	13.7302	0.596402
$531$	6.41702	0.278475
$532$	−6.60118	−0.286197
$533$	−1.03391	−0.0447838
$534$	−8.73172	−0.377859
$535$	−36.2509	−1.56726
$536$	9.85393	0.425625
$537$	−26.1225	−1.12727
$538$	−23.4025	−1.00895
$539$	−0.228799	−0.00985506
$540$	−31.1097	−1.33875
$541$	19.2669	0.828349	0.414175	−	0.910197i	$-0.364070\pi$
$541$	19.2669	0.828349	0.414175	+	0.910197i	$0.364070\pi$
$542$	−9.93775	−0.426863
$543$	−29.0907	−1.24840
$544$	1.00000	0.0428746
$545$	−13.7397	−0.588545
$546$	−3.65660	−0.156488
$547$	35.4030	1.51372	0.756861	−	0.653576i	$-0.226732\pi$
$547$	35.4030	1.51372	0.756861	+	0.653576i	$0.226732\pi$
$548$	−17.9970	−0.768792
$549$	39.6100	1.69051
$550$	−8.23073	−0.350959
$551$	−11.9582	−0.509435
$552$	0.610081	0.0259668
$553$	9.56090	0.406571
$554$	14.6257	0.621388
$555$	−37.7025	−1.60038
$556$	−5.23382	−0.221963
$557$	5.95764	0.252433	0.126217	−	0.992003i	$-0.459717\pi$
$557$	5.95764	0.252433	0.126217	+	0.992003i	$0.459717\pi$
$558$	−60.3611	−2.55529
$559$	2.30936	0.0976755
$560$	−7.79001	−0.329188
$561$	−6.64316	−0.280474
$562$	13.1102	0.553022
$563$	20.6245	0.869219	0.434610	−	0.900619i	$-0.356886\pi$
$563$	20.6245	0.869219	0.434610	+	0.900619i	$0.356886\pi$
$564$	−17.9541	−0.756004
$565$	36.7429	1.54578
$566$	15.0356	0.631992
$567$	33.9426	1.42546
$568$	−1.77365	−0.0744208
$569$	−0.478216	−0.0200479	−0.0100239	−	0.999950i	$-0.503191\pi$
$569$	−0.478216	−0.0200479	−0.0100239	+	0.999950i	$0.503191\pi$
$570$	−22.8889	−0.958711
$571$	33.5129	1.40247	0.701235	−	0.712930i	$-0.252632\pi$
$571$	33.5129	1.40247	0.701235	+	0.712930i	$0.252632\pi$
$572$	0.982412	0.0410767
$573$	42.4673	1.77410
$574$	5.98211	0.249688
$575$	−0.755877	−0.0315223
$576$	6.41702	0.267376
$577$	6.99238	0.291097	0.145548	−	0.989351i	$-0.453505\pi$
$577$	6.99238	0.291097	0.145548	+	0.989351i	$0.453505\pi$
$578$	−1.00000	−0.0415945
$579$	−42.4568	−1.76444
$580$	−14.1118	−0.585959
$581$	−43.9803	−1.82461
$582$	−12.0325	−0.498765
$583$	10.0185	0.414923
$584$	−4.50071	−0.186241
$585$	−8.63976	−0.357210
$586$	22.2242	0.918073
$587$	17.6327	0.727778	0.363889	−	0.931442i	$-0.381449\pi$
$587$	17.6327	0.727778	0.363889	+	0.931442i	$0.381449\pi$
$588$	−0.324334	−0.0133753
$589$	−23.6483	−0.974411
$590$	2.96683	0.122142
$591$	−44.1374	−1.81557
$592$	4.14115	0.170200
$593$	22.4912	0.923605	0.461802	−	0.886983i	$-0.347203\pi$
$593$	22.4912	0.923605	0.461802	+	0.886983i	$0.347203\pi$
$594$	−22.6998	−0.931383
$595$	7.79001	0.319359
$596$	−15.6130	−0.639534
$597$	62.7454	2.56800
$598$	0.0902208	0.00368940
$599$	−41.2003	−1.68340	−0.841700	−	0.539946i	$-0.818445\pi$
$599$	−41.2003	−1.68340	−0.841700	+	0.539946i	$0.818445\pi$
$600$	−11.6675	−0.476323
$601$	−31.7796	−1.29632	−0.648159	−	0.761505i	$-0.724461\pi$
$601$	−31.7796	−1.29632	−0.648159	+	0.761505i	$0.724461\pi$
$602$	−13.3617	−0.544582
$603$	−63.2328	−2.57504
$604$	12.3893	0.504114
$605$	18.7315	0.761543
$606$	−19.8692	−0.807133
$607$	−14.4136	−0.585030	−0.292515	−	0.956261i	$-0.594492\pi$
$607$	−14.4136	−0.585030	−0.292515	+	0.956261i	$0.594492\pi$
$608$	2.51406	0.101959
$609$	38.3258	1.55304
$610$	18.3132	0.741480
$611$	−2.65511	−0.107414
$612$	−6.41702	−0.259393
$613$	−5.81855	−0.235009	−0.117505	−	0.993072i	$-0.537489\pi$
$613$	−5.81855	−0.235009	−0.117505	+	0.993072i	$0.537489\pi$
$614$	−32.3245	−1.30451
$615$	20.7423	0.836412
$616$	−5.68412	−0.229020
$617$	−21.5521	−0.867655	−0.433827	−	0.900996i	$-0.642837\pi$
$617$	−21.5521	−0.867655	−0.433827	+	0.900996i	$0.642837\pi$
$618$	−10.1036	−0.406425
$619$	−24.2957	−0.976526	−0.488263	−	0.872697i	$-0.662369\pi$
$619$	−24.2957	−0.976526	−0.488263	+	0.872697i	$0.662369\pi$
$620$	−27.9072	−1.12078
$621$	−2.08466	−0.0836544
$622$	21.9046	0.878295
$623$	7.47117	0.299326
$624$	1.39262	0.0557494
$625$	−29.5546	−1.18218
$626$	−20.6515	−0.825398
$627$	−16.7013	−0.666986
$628$	16.6323	0.663700
$629$	−4.14115	−0.165118
$630$	49.9886	1.99159
$631$	−30.2875	−1.20573	−0.602864	−	0.797844i	$-0.705974\pi$
$631$	−30.2875	−1.20573	−0.602864	+	0.797844i	$0.705974\pi$
$632$	−3.64127	−0.144842
$633$	−16.5875	−0.659292
$634$	11.2117	0.445272
$635$	−23.5032	−0.932694
$636$	14.2017	0.563135
$637$	−0.0479636	−0.00190039
$638$	−10.2969	−0.407658
$639$	11.3816	0.450247
$640$	2.96683	0.117274
$641$	−28.7729	−1.13646	−0.568231	−	0.822869i	$-0.692372\pi$
$641$	−28.7729	−1.13646	−0.568231	+	0.822869i	$0.692372\pi$
$642$	−37.4959	−1.47984
$643$	−12.6851	−0.500250	−0.250125	−	0.968214i	$-0.580472\pi$
$643$	−12.6851	−0.500250	−0.250125	+	0.968214i	$0.580472\pi$
$644$	−0.522007	−0.0205700
$645$	−46.3303	−1.82425
$646$	−2.51406	−0.0989144
$647$	−27.1404	−1.06700	−0.533500	−	0.845800i	$-0.679124\pi$
$647$	−27.1404	−1.06700	−0.533500	+	0.845800i	$0.679124\pi$
$648$	−12.9271	−0.507823
$649$	2.16480	0.0849758
$650$	−1.72543	−0.0676768
$651$	75.7924	2.97054
$652$	11.0739	0.433688
$653$	36.7628	1.43864	0.719319	−	0.694680i	$-0.244454\pi$
$653$	36.7628	1.43864	0.719319	+	0.694680i	$0.244454\pi$
$654$	−14.2116	−0.555717
$655$	−35.4984	−1.38704
$656$	−2.27829	−0.0889522
$657$	28.8811	1.12676
$658$	15.3622	0.598879
$659$	−30.3984	−1.18415	−0.592077	−	0.805881i	$-0.701692\pi$
$659$	−30.3984	−1.18415	−0.592077	+	0.805881i	$0.701692\pi$
$660$	−19.7091	−0.767176
$661$	−22.6622	−0.881458	−0.440729	−	0.897640i	$-0.645280\pi$
$661$	−22.6622	−0.881458	−0.440729	+	0.897640i	$0.645280\pi$
$662$	2.30713	0.0896692
$663$	−1.39262	−0.0540849
$664$	16.7499	0.650023
$665$	19.5846	0.759457
$666$	−26.5738	−1.02971
$667$	−0.945627	−0.0366148
$668$	14.9404	0.578062
$669$	−63.5327	−2.45632
$670$	−29.2349	−1.12944
$671$	13.3626	0.515856
$672$	−8.05753	−0.310826
$673$	−45.8132	−1.76597	−0.882985	−	0.469401i	$-0.844470\pi$
$673$	−45.8132	−1.76597	−0.882985	+	0.469401i	$0.844470\pi$
$674$	−13.0462	−0.502521
$675$	39.8680	1.53452
$676$	−12.7941	−0.492079
$677$	41.8028	1.60661	0.803306	−	0.595567i	$-0.203073\pi$
$677$	41.8028	1.60661	0.803306	+	0.595567i	$0.203073\pi$
$678$	38.0047	1.45956
$679$	10.2955	0.395104
$680$	−2.96683	−0.113773
$681$	51.0050	1.95452
$682$	−20.3630	−0.779739
$683$	−25.7666	−0.985931	−0.492966	−	0.870049i	$-0.664087\pi$
$683$	−25.7666	−0.985931	−0.492966	+	0.870049i	$0.664087\pi$
$684$	−16.1328	−0.616852
$685$	53.3939	2.04008
$686$	18.6574	0.712344
$687$	−7.19704	−0.274584
$688$	5.08881	0.194009
$689$	2.10020	0.0800112
$690$	−1.81001	−0.0689058
$691$	21.2919	0.809982	0.404991	−	0.914321i	$-0.367275\pi$
$691$	21.2919	0.809982	0.404991	+	0.914321i	$0.367275\pi$
$692$	−21.3743	−0.812530
$693$	36.4751	1.38557
$694$	15.7878	0.599295
$695$	15.5278	0.589004
$696$	−14.5964	−0.553275
$697$	2.27829	0.0862963
$698$	27.6649	1.04713
$699$	15.5381	0.587707
$700$	9.98311	0.377326
$701$	32.4807	1.22678	0.613390	−	0.789780i	$-0.289805\pi$
$701$	32.4807	1.22678	0.613390	+	0.789780i	$0.289805\pi$
$702$	−4.75861	−0.179602
$703$	−10.4111	−0.392662
$704$	2.16480	0.0815890
$705$	53.2667	2.00614
$706$	−28.3006	−1.06511
$707$	17.0008	0.639382
$708$	3.06872	0.115329
$709$	23.6662	0.888802	0.444401	−	0.895828i	$-0.353417\pi$
$709$	23.6662	0.888802	0.444401	+	0.895828i	$0.353417\pi$
$710$	5.26212	0.197484
$711$	23.3661	0.876298
$712$	−2.84540	−0.106636
$713$	−1.87006	−0.0700341
$714$	8.05753	0.301546
$715$	−2.91465	−0.109002
$716$	−8.51252	−0.318128
$717$	13.6662	0.510373
$718$	−3.48262	−0.129970
$719$	36.6948	1.36849	0.684243	−	0.729254i	$-0.260133\pi$
$719$	36.6948	1.36849	0.684243	+	0.729254i	$0.260133\pi$
$720$	−19.0382	−0.709512
$721$	8.64498	0.321956
$722$	12.6795	0.471882
$723$	4.14521	0.154162
$724$	−9.47975	−0.352312
$725$	18.0846	0.671646
$726$	19.3748	0.719065
$727$	47.8259	1.77376	0.886882	−	0.461996i	$-0.152867\pi$
$727$	47.8259	1.77376	0.886882	+	0.461996i	$0.152867\pi$
$728$	−1.19157	−0.0441627
$729$	−13.5812	−0.503006
$730$	13.3528	0.494210
$731$	−5.08881	−0.188216
$732$	18.9421	0.700121
$733$	2.66444	0.0984132	0.0492066	−	0.998789i	$-0.484331\pi$
$733$	2.66444	0.0984132	0.0492066	+	0.998789i	$0.484331\pi$
$734$	26.7273	0.986522
$735$	0.962244	0.0354929
$736$	0.198807	0.00732811
$737$	−21.3318	−0.785766
$738$	14.6198	0.538163
$739$	6.44588	0.237116	0.118558	−	0.992947i	$-0.462173\pi$
$739$	6.44588	0.237116	0.118558	+	0.992947i	$0.462173\pi$
$740$	−12.2861	−0.451645
$741$	−3.50113	−0.128617
$742$	−12.1515	−0.446095
$743$	−0.623547	−0.0228757	−0.0114379	−	0.999935i	$-0.503641\pi$
$743$	−0.623547	−0.0228757	−0.0114379	+	0.999935i	$0.503641\pi$
$744$	−28.8656	−1.05826
$745$	46.3211	1.69708
$746$	13.0550	0.477979
$747$	−107.485	−3.93265
$748$	−2.16480	−0.0791529
$749$	32.0828	1.17228
$750$	−10.9063	−0.398244
$751$	37.1871	1.35698	0.678488	−	0.734611i	$-0.262636\pi$
$751$	37.1871	1.35698	0.678488	+	0.734611i	$0.262636\pi$
$752$	−5.85069	−0.213353
$753$	−45.4713	−1.65707
$754$	−2.15856	−0.0786103
$755$	−36.7569	−1.33772
$756$	27.5327	1.00136
$757$	6.59105	0.239556	0.119778	−	0.992801i	$-0.461782\pi$
$757$	6.59105	0.239556	0.119778	+	0.992801i	$0.461782\pi$
$758$	23.8831	0.867472
$759$	−1.32070	−0.0479385
$760$	−7.45879	−0.270559
$761$	−17.6524	−0.639900	−0.319950	−	0.947434i	$-0.603666\pi$
$761$	−17.6524	−0.639900	−0.319950	+	0.947434i	$0.603666\pi$
$762$	−24.3103	−0.880669
$763$	12.1599	0.440219
$764$	13.8388	0.500670
$765$	19.0382	0.688327
$766$	31.2837	1.13033
$767$	0.453812	0.0163862
$768$	3.06872	0.110733
$769$	−14.0678	−0.507299	−0.253650	−	0.967296i	$-0.581631\pi$
$769$	−14.0678	−0.507299	−0.253650	+	0.967296i	$0.581631\pi$
$770$	16.8638	0.607729
$771$	−2.22279	−0.0800519
$772$	−13.8353	−0.497945
$773$	10.3391	0.371872	0.185936	−	0.982562i	$-0.440468\pi$
$773$	10.3391	0.371872	0.185936	+	0.982562i	$0.440468\pi$
$774$	−32.6550	−1.17376
$775$	35.7638	1.28468
$776$	−3.92103	−0.140757
$777$	33.3674	1.19705
$778$	15.5936	0.559059
$779$	5.72776	0.205218
$780$	−4.13166	−0.147937
$781$	3.83960	0.137392
$782$	−0.198807	−0.00710931
$783$	49.8761	1.78243
$784$	−0.105691	−0.00377466
$785$	−49.3451	−1.76120
$786$	−36.7175	−1.30967
$787$	−39.0400	−1.39162	−0.695812	−	0.718224i	$-0.744955\pi$
$787$	−39.0400	−1.39162	−0.695812	+	0.718224i	$0.744955\pi$
$788$	−14.3830	−0.512374
$789$	−69.7778	−2.48416
$790$	10.8030	0.384355
$791$	−32.5182	−1.15621
$792$	−13.8916	−0.493615
$793$	2.80122	0.0994744
$794$	3.99206	0.141673
$795$	−42.1341	−1.49434
$796$	20.4468	0.724717
$797$	−28.7823	−1.01952	−0.509761	−	0.860316i	$-0.670266\pi$
$797$	−28.7823	−1.01952	−0.509761	+	0.860316i	$0.670266\pi$
$798$	20.2571	0.717095
$799$	5.85069	0.206982
$800$	−3.80207	−0.134424
$801$	18.2590	0.645149
$802$	11.8898	0.419842
$803$	9.74313	0.343828
$804$	−30.2389	−1.06644
$805$	1.54871	0.0545847
$806$	−4.26874	−0.150360
$807$	71.8155	2.52803
$808$	−6.47478	−0.227782
$809$	23.0407	0.810070	0.405035	−	0.914301i	$-0.367259\pi$
$809$	23.0407	0.810070	0.405035	+	0.914301i	$0.367259\pi$
$810$	38.3524	1.34757
$811$	46.0213	1.61603	0.808013	−	0.589165i	$-0.200543\pi$
$811$	46.0213	1.61603	0.808013	+	0.589165i	$0.200543\pi$
$812$	12.4892	0.438285
$813$	30.4961	1.06955
$814$	−8.96476	−0.314215
$815$	−32.8544	−1.15084
$816$	−3.06872	−0.107427
$817$	−12.7936	−0.447590
$818$	31.5088	1.10168
$819$	7.64636	0.267185
$820$	6.75929	0.236045
$821$	0.317759	0.0110899	0.00554493	−	0.999985i	$-0.498235\pi$
$821$	0.317759	0.0110899	0.00554493	+	0.999985i	$0.498235\pi$
$822$	55.2275	1.92628
$823$	4.82558	0.168209	0.0841046	−	0.996457i	$-0.473197\pi$
$823$	4.82558	0.168209	0.0841046	+	0.996457i	$0.473197\pi$
$824$	−3.29244	−0.114698
$825$	25.2578	0.879363
$826$	−2.62570	−0.0913598
$827$	−0.0608346	−0.00211543	−0.00105771	−	0.999999i	$-0.500337\pi$
$827$	−0.0608346	−0.00211543	−0.00105771	+	0.999999i	$0.500337\pi$
$828$	−1.27575	−0.0443352
$829$	14.5247	0.504464	0.252232	−	0.967667i	$-0.418835\pi$
$829$	14.5247	0.504464	0.252232	+	0.967667i	$0.418835\pi$
$830$	−49.6942	−1.72491
$831$	−44.8822	−1.55695
$832$	0.453812	0.0157331
$833$	0.105691	0.00366196
$834$	16.0611	0.556150
$835$	−44.3256	−1.53395
$836$	−5.44244	−0.188231
$837$	98.6342	3.40930
$838$	−1.32977	−0.0459361
$839$	15.8874	0.548492	0.274246	−	0.961660i	$-0.411572\pi$
$839$	15.8874	0.548492	0.274246	+	0.961660i	$0.411572\pi$
$840$	23.9053	0.824812
$841$	−6.37555	−0.219846
$842$	22.1245	0.762461
$843$	−40.2316	−1.38565
$844$	−5.40534	−0.186060
$845$	37.9578	1.30579
$846$	37.5440	1.29079
$847$	−16.5777	−0.569618
$848$	4.62790	0.158923
$849$	−46.1399	−1.58352
$850$	3.80207	0.130410
$851$	−0.823288	−0.0282219
$852$	5.44283	0.186468
$853$	10.1646	0.348029	0.174015	−	0.984743i	$-0.444326\pi$
$853$	10.1646	0.348029	0.174015	+	0.984743i	$0.444326\pi$
$854$	−16.2075	−0.554611
$855$	47.8632	1.63689
$856$	−12.2188	−0.417628
$857$	−16.1313	−0.551036	−0.275518	−	0.961296i	$-0.588849\pi$
$857$	−16.1313	−0.551036	−0.275518	+	0.961296i	$0.588849\pi$
$858$	−3.01474	−0.102922
$859$	1.62635	0.0554904	0.0277452	−	0.999615i	$-0.491167\pi$
$859$	1.62635	0.0554904	0.0277452	+	0.999615i	$0.491167\pi$
$860$	−15.0976	−0.514824
$861$	−18.3574	−0.625618
$862$	4.82429	0.164316
$863$	−46.7628	−1.59183	−0.795913	−	0.605411i	$-0.793009\pi$
$863$	−46.7628	−1.59183	−0.795913	+	0.605411i	$0.793009\pi$
$864$	−10.4859	−0.356736
$865$	63.4139	2.15614
$866$	−0.307559	−0.0104513
$867$	3.06872	0.104219
$868$	24.6984	0.838319
$869$	7.88263	0.267400
$870$	43.3050	1.46818
$871$	−4.47183	−0.151522
$872$	−4.63112	−0.156829
$873$	25.1613	0.851583
$874$	−0.499812	−0.0169064
$875$	9.33186	0.315474
$876$	13.8114	0.466644
$877$	−26.7677	−0.903880	−0.451940	−	0.892048i	$-0.649268\pi$
$877$	−26.7677	−0.903880	−0.451940	+	0.892048i	$0.649268\pi$
$878$	8.45441	0.285322
$879$	−68.1998	−2.30032
$880$	−6.42259	−0.216505
$881$	48.2447	1.62541	0.812703	−	0.582678i	$-0.197995\pi$
$881$	48.2447	1.62541	0.812703	+	0.582678i	$0.197995\pi$
$882$	0.678218	0.0228368
$883$	−11.1129	−0.373978	−0.186989	−	0.982362i	$-0.559873\pi$
$883$	−11.1129	−0.373978	−0.186989	+	0.982362i	$0.559873\pi$
$884$	−0.453812	−0.0152633
$885$	−9.10435	−0.306040
$886$	−29.9844	−1.00734
$887$	20.7386	0.696335	0.348167	−	0.937432i	$-0.386804\pi$
$887$	20.7386	0.696335	0.348167	+	0.937432i	$0.386804\pi$
$888$	−12.7080	−0.426453
$889$	20.8007	0.697635
$890$	8.44181	0.282970
$891$	27.9845	0.937516
$892$	−20.7034	−0.693200
$893$	14.7090	0.492218
$894$	47.9119	1.60241
$895$	25.2552	0.844188
$896$	−2.62570	−0.0877185
$897$	−0.276862	−0.00924416
$898$	27.2807	0.910370
$899$	44.7417	1.49222
$900$	24.3980	0.813266
$901$	−4.62790	−0.154178
$902$	4.93204	0.164219
$903$	41.0032	1.36450
$904$	12.3846	0.411904
$905$	28.1248	0.934900
$906$	−38.0193	−1.26311
$907$	10.1953	0.338528	0.169264	−	0.985571i	$-0.445861\pi$
$907$	10.1953	0.338528	0.169264	+	0.985571i	$0.445861\pi$
$908$	16.6210	0.551586
$909$	41.5487	1.37808
$910$	3.53520	0.117191
$911$	−22.1904	−0.735199	−0.367600	−	0.929984i	$-0.619820\pi$
$911$	−22.1904	−0.735199	−0.367600	+	0.929984i	$0.619820\pi$
$912$	−7.71494	−0.255467
$913$	−36.2602	−1.20004
$914$	5.53972	0.183238
$915$	−56.1980	−1.85785
$916$	−2.34529	−0.0774907
$917$	31.4168	1.03747
$918$	10.4859	0.346085
$919$	34.7463	1.14618	0.573088	−	0.819494i	$-0.305745\pi$
$919$	34.7463	1.14618	0.573088	+	0.819494i	$0.305745\pi$
$920$	−0.589825	−0.0194460
$921$	99.1946	3.26857
$922$	−14.9061	−0.490908
$923$	0.804904	0.0264937
$924$	17.4429	0.573831
$925$	15.7450	0.517691
$926$	−6.63837	−0.218150
$927$	21.1277	0.693924
$928$	−4.75652	−0.156140
$929$	45.2766	1.48548	0.742739	−	0.669581i	$-0.233527\pi$
$929$	45.2766	1.48548	0.742739	+	0.669581i	$0.233527\pi$
$930$	85.6393	2.80822
$931$	0.265712	0.00870838
$932$	5.06340	0.165857
$933$	−67.2191	−2.20065
$934$	8.97243	0.293587
$935$	6.42259	0.210041
$936$	−2.91212	−0.0951856
$937$	−33.9026	−1.10755	−0.553774	−	0.832667i	$-0.686813\pi$
$937$	−33.9026	−1.10755	−0.553774	+	0.832667i	$0.686813\pi$
$938$	25.8735	0.844799
$939$	63.3735	2.06811
$940$	17.3580	0.566155
$941$	−35.7023	−1.16386	−0.581931	−	0.813238i	$-0.697703\pi$
$941$	−35.7023	−1.16386	−0.581931	+	0.813238i	$0.697703\pi$
$942$	−51.0397	−1.66296
$943$	0.452939	0.0147497
$944$	1.00000	0.0325472
$945$	−81.6849	−2.65721
$946$	−11.0162	−0.358169
$947$	3.83081	0.124485	0.0622423	−	0.998061i	$-0.480175\pi$
$947$	3.83081	0.124485	0.0622423	+	0.998061i	$0.480175\pi$
$948$	11.1740	0.362916
$949$	2.04247	0.0663015
$950$	9.55865	0.310123
$951$	−34.4054	−1.11567
$952$	2.62570	0.0850995
$953$	17.9519	0.581518	0.290759	−	0.956796i	$-0.406092\pi$
$953$	17.9519	0.581518	0.290759	+	0.956796i	$0.406092\pi$
$954$	−29.6973	−0.961487
$955$	−41.0573	−1.32858
$956$	4.45339	0.144033
$957$	31.5983	1.02143
$958$	−7.37889	−0.238401
$959$	−47.2546	−1.52593
$960$	−9.10435	−0.293842
$961$	57.4805	1.85421
$962$	−1.87930	−0.0605912
$963$	78.4079	2.52666
$964$	1.35080	0.0435063
$965$	41.0471	1.32135
$966$	1.60189	0.0515400
$967$	38.3156	1.23215	0.616074	−	0.787688i	$-0.288722\pi$
$967$	38.3156	1.23215	0.616074	+	0.787688i	$0.288722\pi$
$968$	6.31364	0.202928
$969$	7.71494	0.247840
$970$	11.6330	0.373514
$971$	−3.03143	−0.0972831	−0.0486416	−	0.998816i	$-0.515489\pi$
$971$	−3.03143	−0.0972831	−0.0486416	+	0.998816i	$0.515489\pi$
$972$	8.21191	0.263397
$973$	−13.7424	−0.440562
$974$	26.1443	0.837717
$975$	5.29484	0.169571
$976$	6.17265	0.197582
$977$	−33.9579	−1.08641	−0.543205	−	0.839600i	$-0.682790\pi$
$977$	−33.9579	−1.08641	−0.543205	+	0.839600i	$0.682790\pi$
$978$	−33.9827	−1.08665
$979$	6.15972	0.196865
$980$	0.313566	0.0100165
$981$	29.7180	0.948821
$982$	−42.4731	−1.35537
$983$	−39.1075	−1.24733	−0.623667	−	0.781690i	$-0.714358\pi$
$983$	−39.1075	−1.24733	−0.623667	+	0.781690i	$0.714358\pi$
$984$	6.99142	0.222878
$985$	42.6720	1.35964
$986$	4.75652	0.151478
$987$	−47.1421	−1.50055
$988$	−1.14091	−0.0362972
$989$	−1.01169	−0.0321698
$990$	41.2139	1.30986
$991$	−32.5708	−1.03464	−0.517322	−	0.855791i	$-0.673071\pi$
$991$	−32.5708	−1.03464	−0.517322	+	0.855791i	$0.673071\pi$
$992$	−9.40641	−0.298654
$993$	−7.07993	−0.224675
$994$	−4.65708	−0.147714
$995$	−60.6621	−1.92312
$996$	−51.4008	−1.62870
$997$	15.1892	0.481048	0.240524	−	0.970643i	$-0.422681\pi$
$997$	15.1892	0.481048	0.240524	+	0.970643i	$0.422681\pi$
$998$	39.6364	1.25467
$999$	43.4235	1.37386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.v.1.12	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.v.1.12	✓	12	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.06872 q^{3} +1.00000 q^{4} -2.96683 q^{5} -3.06872 q^{6} +2.62570 q^{7} -1.00000 q^{8} +6.41702 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.06872 q^{3} +1.00000 q^{4} -2.96683 q^{5} -3.06872 q^{6} +2.62570 q^{7} -1.00000 q^{8} +6.41702 q^{9} +2.96683 q^{10} +2.16480 q^{11} +3.06872 q^{12} +0.453812 q^{13} -2.62570 q^{14} -9.10435 q^{15} +1.00000 q^{16} -1.00000 q^{17} -6.41702 q^{18} -2.51406 q^{19} -2.96683 q^{20} +8.05753 q^{21} -2.16480 q^{22} -0.198807 q^{23} -3.06872 q^{24} +3.80207 q^{25} -0.453812 q^{26} +10.4859 q^{27} +2.62570 q^{28} +4.75652 q^{29} +9.10435 q^{30} +9.40641 q^{31} -1.00000 q^{32} +6.64316 q^{33} +1.00000 q^{34} -7.79001 q^{35} +6.41702 q^{36} +4.14115 q^{37} +2.51406 q^{38} +1.39262 q^{39} +2.96683 q^{40} -2.27829 q^{41} -8.05753 q^{42} +5.08881 q^{43} +2.16480 q^{44} -19.0382 q^{45} +0.198807 q^{46} -5.85069 q^{47} +3.06872 q^{48} -0.105691 q^{49} -3.80207 q^{50} -3.06872 q^{51} +0.453812 q^{52} +4.62790 q^{53} -10.4859 q^{54} -6.42259 q^{55} -2.62570 q^{56} -7.71494 q^{57} -4.75652 q^{58} +1.00000 q^{59} -9.10435 q^{60} +6.17265 q^{61} -9.40641 q^{62} +16.8492 q^{63} +1.00000 q^{64} -1.34638 q^{65} -6.64316 q^{66} -9.85393 q^{67} -1.00000 q^{68} -0.610081 q^{69} +7.79001 q^{70} +1.77365 q^{71} -6.41702 q^{72} +4.50071 q^{73} -4.14115 q^{74} +11.6675 q^{75} -2.51406 q^{76} +5.68412 q^{77} -1.39262 q^{78} +3.64127 q^{79} -2.96683 q^{80} +12.9271 q^{81} +2.27829 q^{82} -16.7499 q^{83} +8.05753 q^{84} +2.96683 q^{85} -5.08881 q^{86} +14.5964 q^{87} -2.16480 q^{88} +2.84540 q^{89} +19.0382 q^{90} +1.19157 q^{91} -0.198807 q^{92} +28.8656 q^{93} +5.85069 q^{94} +7.45879 q^{95} -3.06872 q^{96} +3.92103 q^{97} +0.105691 q^{98} +13.8916 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} - q^{5} + 3 q^{6} + 4 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 - q^5 + 3 * q^6 + 4 * q^7 - 12 * q^8 + 15 * q^9	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} - q^{5} + 3 q^{6} + 4 q^{7} - 12 q^{8} + 15 q^{9} + q^{10} - 3 q^{11} - 3 q^{12} + 15 q^{13} - 4 q^{14} - 3 q^{15} + 12 q^{16} - 12 q^{17} - 15 q^{18} + 16 q^{19} - q^{20} + 15 q^{21} + 3 q^{22} - 14 q^{23} + 3 q^{24} + 19 q^{25} - 15 q^{26} - 12 q^{27} + 4 q^{28} + 14 q^{29} + 3 q^{30} + 26 q^{31} - 12 q^{32} + 13 q^{33} + 12 q^{34} - 5 q^{35} + 15 q^{36} + 15 q^{37} - 16 q^{38} + 4 q^{39} + q^{40} - 2 q^{41} - 15 q^{42} + 8 q^{43} - 3 q^{44} - 17 q^{45} + 14 q^{46} - 6 q^{47} - 3 q^{48} + 30 q^{49} - 19 q^{50} + 3 q^{51} + 15 q^{52} + q^{53} + 12 q^{54} + q^{55} - 4 q^{56} + 3 q^{57} - 14 q^{58} + 12 q^{59} - 3 q^{60} + 30 q^{61} - 26 q^{62} + q^{63} + 12 q^{64} - 4 q^{65} - 13 q^{66} + 10 q^{67} - 12 q^{68} + 8 q^{69} + 5 q^{70} + 6 q^{71} - 15 q^{72} + 26 q^{73} - 15 q^{74} + 7 q^{75} + 16 q^{76} + 45 q^{77} - 4 q^{78} - 11 q^{79} - q^{80} + 48 q^{81} + 2 q^{82} - 21 q^{83} + 15 q^{84} + q^{85} - 8 q^{86} + 2 q^{87} + 3 q^{88} - 2 q^{89} + 17 q^{90} + 31 q^{91} - 14 q^{92} + 41 q^{93} + 6 q^{94} - 29 q^{95} + 3 q^{96} + 27 q^{97} - 30 q^{98} + 9 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 - q^5 + 3 * q^6 + 4 * q^7 - 12 * q^8 + 15 * q^9 + q^10 - 3 * q^11 - 3 * q^12 + 15 * q^13 - 4 * q^14 - 3 * q^15 + 12 * q^16 - 12 * q^17 - 15 * q^18 + 16 * q^19 - q^20 + 15 * q^21 + 3 * q^22 - 14 * q^23 + 3 * q^24 + 19 * q^25 - 15 * q^26 - 12 * q^27 + 4 * q^28 + 14 * q^29 + 3 * q^30 + 26 * q^31 - 12 * q^32 + 13 * q^33 + 12 * q^34 - 5 * q^35 + 15 * q^36 + 15 * q^37 - 16 * q^38 + 4 * q^39 + q^40 - 2 * q^41 - 15 * q^42 + 8 * q^43 - 3 * q^44 - 17 * q^45 + 14 * q^46 - 6 * q^47 - 3 * q^48 + 30 * q^49 - 19 * q^50 + 3 * q^51 + 15 * q^52 + q^53 + 12 * q^54 + q^55 - 4 * q^56 + 3 * q^57 - 14 * q^58 + 12 * q^59 - 3 * q^60 + 30 * q^61 - 26 * q^62 + q^63 + 12 * q^64 - 4 * q^65 - 13 * q^66 + 10 * q^67 - 12 * q^68 + 8 * q^69 + 5 * q^70 + 6 * q^71 - 15 * q^72 + 26 * q^73 - 15 * q^74 + 7 * q^75 + 16 * q^76 + 45 * q^77 - 4 * q^78 - 11 * q^79 - q^80 + 48 * q^81 + 2 * q^82 - 21 * q^83 + 15 * q^84 + q^85 - 8 * q^86 + 2 * q^87 + 3 * q^88 - 2 * q^89 + 17 * q^90 + 31 * q^91 - 14 * q^92 + 41 * q^93 + 6 * q^94 - 29 * q^95 + 3 * q^96 + 27 * q^97 - 30 * q^98 + 9 * q^99

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