LMFDB - Embedded newform 2006.2.a.p.1.2

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:	$1$
Dimension:	$4$
Coefficient field:	4.4.2225.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + 2x + 4 $ x^4 - x^3 - 5x^2 + 2x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.13856$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.13856 q^{3} +1.00000 q^{4} -4.37463 q^{5} +1.13856 q^{6} +1.84224 q^{7} -1.00000 q^{8} -1.70367 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.13856 q^{3} +1.00000 q^{4} -4.37463 q^{5} +1.13856 q^{6} +1.84224 q^{7} -1.00000 q^{8} -1.70367 q^{9} +4.37463 q^{10} +5.61070 q^{11} -1.13856 q^{12} -2.98080 q^{13} -1.84224 q^{14} +4.98080 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.70367 q^{18} -4.80118 q^{19} -4.37463 q^{20} -2.09750 q^{21} -5.61070 q^{22} -0.958939 q^{23} +1.13856 q^{24} +14.1374 q^{25} +2.98080 q^{26} +5.35543 q^{27} +1.84224 q^{28} +6.47214 q^{29} -4.98080 q^{30} -6.11936 q^{31} -1.00000 q^{32} -6.38814 q^{33} -1.00000 q^{34} -8.05910 q^{35} -1.70367 q^{36} -2.42654 q^{37} +4.80118 q^{38} +3.39383 q^{39} +4.37463 q^{40} +7.96160 q^{41} +2.09750 q^{42} +3.39383 q^{43} +5.61070 q^{44} +7.45294 q^{45} +0.958939 q^{46} +11.0783 q^{47} -1.13856 q^{48} -3.60617 q^{49} -14.1374 q^{50} -1.13856 q^{51} -2.98080 q^{52} +9.20602 q^{53} -5.35543 q^{54} -24.5448 q^{55} -1.84224 q^{56} +5.46645 q^{57} -6.47214 q^{58} +1.00000 q^{59} +4.98080 q^{60} -6.92170 q^{61} +6.11936 q^{62} -3.13856 q^{63} +1.00000 q^{64} +13.0399 q^{65} +6.38814 q^{66} -12.4856 q^{67} +1.00000 q^{68} +1.09181 q^{69} +8.05910 q^{70} +0.582435 q^{71} +1.70367 q^{72} +11.5120 q^{73} +2.42654 q^{74} -16.0963 q^{75} -4.80118 q^{76} +10.3362 q^{77} -3.39383 q^{78} -6.67549 q^{79} -4.37463 q^{80} -0.986489 q^{81} -7.96160 q^{82} -10.6788 q^{83} -2.09750 q^{84} -4.37463 q^{85} -3.39383 q^{86} -7.36894 q^{87} -5.61070 q^{88} -18.5768 q^{89} -7.45294 q^{90} -5.49134 q^{91} -0.958939 q^{92} +6.96729 q^{93} -11.0783 q^{94} +21.0034 q^{95} +1.13856 q^{96} -4.40165 q^{97} +3.60617 q^{98} -9.55879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - q^{3} + 4 q^{4} - 5 q^{5} + q^{6} - 2 q^{7} - 4 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - q^3 + 4 * q^4 - 5 * q^5 + q^6 - 2 * q^7 - 4 * q^8 - q^9	\( 4 q - 4 q^{2} - q^{3} + 4 q^{4} - 5 q^{5} + q^{6} - 2 q^{7} - 4 q^{8} - q^{9} + 5 q^{10} + q^{11} - q^{12} + q^{13} + 2 q^{14} + 7 q^{15} + 4 q^{16} + 4 q^{17} + q^{18} - 8 q^{19} - 5 q^{20} - 3 q^{21} - q^{22} - 2 q^{23} + q^{24} + 7 q^{25} - q^{26} - 4 q^{27} - 2 q^{28} + 8 q^{29} - 7 q^{30} - 8 q^{31} - 4 q^{32} - q^{33} - 4 q^{34} - q^{35} - q^{36} - 11 q^{37} + 8 q^{38} + 14 q^{39} + 5 q^{40} + 6 q^{41} + 3 q^{42} + 14 q^{43} + q^{44} - q^{45} + 2 q^{46} + 26 q^{47} - q^{48} - 14 q^{49} - 7 q^{50} - q^{51} + q^{52} + 3 q^{53} + 4 q^{54} - 37 q^{55} + 2 q^{56} - 21 q^{57} - 8 q^{58} + 4 q^{59} + 7 q^{60} - 46 q^{61} + 8 q^{62} - 9 q^{63} + 4 q^{64} + 8 q^{65} + q^{66} - 20 q^{67} + 4 q^{68} - 26 q^{69} + q^{70} + 10 q^{71} + q^{72} - 16 q^{73} + 11 q^{74} - 13 q^{75} - 8 q^{76} + 3 q^{77} - 14 q^{78} + q^{79} - 5 q^{80} - 16 q^{81} - 6 q^{82} + q^{83} - 3 q^{84} - 5 q^{85} - 14 q^{86} + 8 q^{87} - q^{88} - 6 q^{89} + q^{90} - 17 q^{91} - 2 q^{92} + 27 q^{93} - 26 q^{94} + 17 q^{95} + q^{96} + 19 q^{97} + 14 q^{98} - 3 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - q^3 + 4 * q^4 - 5 * q^5 + q^6 - 2 * q^7 - 4 * q^8 - q^9 + 5 * q^10 + q^11 - q^12 + q^13 + 2 * q^14 + 7 * q^15 + 4 * q^16 + 4 * q^17 + q^18 - 8 * q^19 - 5 * q^20 - 3 * q^21 - q^22 - 2 * q^23 + q^24 + 7 * q^25 - q^26 - 4 * q^27 - 2 * q^28 + 8 * q^29 - 7 * q^30 - 8 * q^31 - 4 * q^32 - q^33 - 4 * q^34 - q^35 - q^36 - 11 * q^37 + 8 * q^38 + 14 * q^39 + 5 * q^40 + 6 * q^41 + 3 * q^42 + 14 * q^43 + q^44 - q^45 + 2 * q^46 + 26 * q^47 - q^48 - 14 * q^49 - 7 * q^50 - q^51 + q^52 + 3 * q^53 + 4 * q^54 - 37 * q^55 + 2 * q^56 - 21 * q^57 - 8 * q^58 + 4 * q^59 + 7 * q^60 - 46 * q^61 + 8 * q^62 - 9 * q^63 + 4 * q^64 + 8 * q^65 + q^66 - 20 * q^67 + 4 * q^68 - 26 * q^69 + q^70 + 10 * q^71 + q^72 - 16 * q^73 + 11 * q^74 - 13 * q^75 - 8 * q^76 + 3 * q^77 - 14 * q^78 + q^79 - 5 * q^80 - 16 * q^81 - 6 * q^82 + q^83 - 3 * q^84 - 5 * q^85 - 14 * q^86 + 8 * q^87 - q^88 - 6 * q^89 + q^90 - 17 * q^91 - 2 * q^92 + 27 * q^93 - 26 * q^94 + 17 * q^95 + q^96 + 19 * q^97 + 14 * q^98 - 3 * 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
$3$	−1.13856	−0.657350	−0.328675	−	0.944443i	$-0.606602\pi$
$3$	−1.13856	−0.657350	−0.328675	+	0.944443i	$0.606602\pi$
$4$	1.00000	0.500000
$5$	−4.37463	−1.95640	−0.978198	−	0.207677i	$-0.933410\pi$
$5$	−4.37463	−1.95640	−0.978198	+	0.207677i	$0.933410\pi$
$6$	1.13856	0.464817
$7$	1.84224	0.696300	0.348150	−	0.937439i	$-0.386810\pi$
$7$	1.84224	0.696300	0.348150	+	0.937439i	$0.386810\pi$
$8$	−1.00000	−0.353553
$9$	−1.70367	−0.567890
$10$	4.37463	1.38338
$11$	5.61070	1.69169	0.845845	−	0.533429i	$-0.179097\pi$
$11$	5.61070	1.69169	0.845845	+	0.533429i	$0.179097\pi$
$12$	−1.13856	−0.328675
$13$	−2.98080	−0.826725	−0.413363	−	0.910567i	$-0.635646\pi$
$13$	−2.98080	−0.826725	−0.413363	+	0.910567i	$0.635646\pi$
$14$	−1.84224	−0.492358
$15$	4.98080	1.28604
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.70367	0.401559
$19$	−4.80118	−1.10147	−0.550733	−	0.834682i	$-0.685652\pi$
$19$	−4.80118	−1.10147	−0.550733	+	0.834682i	$0.685652\pi$
$20$	−4.37463	−0.978198
$21$	−2.09750	−0.457713
$22$	−5.61070	−1.19621
$23$	−0.958939	−0.199953	−0.0999763	−	0.994990i	$-0.531877\pi$
$23$	−0.958939	−0.199953	−0.0999763	+	0.994990i	$0.531877\pi$
$24$	1.13856	0.232408
$25$	14.1374	2.82748
$26$	2.98080	0.584583
$27$	5.35543	1.03065
$28$	1.84224	0.348150
$29$	6.47214	1.20185	0.600923	−	0.799307i	$-0.294800\pi$
$29$	6.47214	1.20185	0.600923	+	0.799307i	$0.294800\pi$
$30$	−4.98080	−0.909365
$31$	−6.11936	−1.09907	−0.549535	−	0.835471i	$-0.685195\pi$
$31$	−6.11936	−1.09907	−0.549535	+	0.835471i	$0.685195\pi$
$32$	−1.00000	−0.176777
$33$	−6.38814	−1.11203
$34$	−1.00000	−0.171499
$35$	−8.05910	−1.36224
$36$	−1.70367	−0.283945
$37$	−2.42654	−0.398921	−0.199461	−	0.979906i	$-0.563919\pi$
$37$	−2.42654	−0.398921	−0.199461	+	0.979906i	$0.563919\pi$
$38$	4.80118	0.778853
$39$	3.39383	0.543448
$40$	4.37463	0.691690
$41$	7.96160	1.24339	0.621697	−	0.783258i	$-0.286444\pi$
$41$	7.96160	1.24339	0.621697	+	0.783258i	$0.286444\pi$
$42$	2.09750	0.323652
$43$	3.39383	0.517555	0.258777	−	0.965937i	$-0.416680\pi$
$43$	3.39383	0.517555	0.258777	+	0.965937i	$0.416680\pi$
$44$	5.61070	0.845845
$45$	7.45294	1.11102
$46$	0.958939	0.141388
$47$	11.0783	1.61594	0.807968	−	0.589226i	$-0.200567\pi$
$47$	11.0783	1.61594	0.807968	+	0.589226i	$0.200567\pi$
$48$	−1.13856	−0.164338
$49$	−3.60617	−0.515167
$50$	−14.1374	−1.99933
$51$	−1.13856	−0.159431
$52$	−2.98080	−0.413363
$53$	9.20602	1.26454	0.632272	−	0.774747i	$-0.282123\pi$
$53$	9.20602	1.26454	0.632272	+	0.774747i	$0.282123\pi$
$54$	−5.35543	−0.728782
$55$	−24.5448	−3.30961
$56$	−1.84224	−0.246179
$57$	5.46645	0.724049
$58$	−6.47214	−0.849833
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	4.98080	0.643019
$61$	−6.92170	−0.886232	−0.443116	−	0.896464i	$-0.646127\pi$
$61$	−6.92170	−0.886232	−0.443116	+	0.896464i	$0.646127\pi$
$62$	6.11936	0.777160
$63$	−3.13856	−0.395422
$64$	1.00000	0.125000
$65$	13.0399	1.61740
$66$	6.38814	0.786326
$67$	−12.4856	−1.52536	−0.762682	−	0.646773i	$-0.776118\pi$
$67$	−12.4856	−1.52536	−0.762682	+	0.646773i	$0.776118\pi$
$68$	1.00000	0.121268
$69$	1.09181	0.131439
$70$	8.05910	0.963247
$71$	0.582435	0.0691223	0.0345612	−	0.999403i	$-0.488997\pi$
$71$	0.582435	0.0691223	0.0345612	+	0.999403i	$0.488997\pi$
$72$	1.70367	0.200780
$73$	11.5120	1.34738	0.673691	−	0.739013i	$-0.264708\pi$
$73$	11.5120	1.34738	0.673691	+	0.739013i	$0.264708\pi$
$74$	2.42654	0.282080
$75$	−16.0963	−1.85865
$76$	−4.80118	−0.550733
$77$	10.3362	1.17792
$78$	−3.39383	−0.384276
$79$	−6.67549	−0.751052	−0.375526	−	0.926812i	$-0.622538\pi$
$79$	−6.67549	−0.751052	−0.375526	+	0.926812i	$0.622538\pi$
$80$	−4.37463	−0.489099
$81$	−0.986489	−0.109610
$82$	−7.96160	−0.879212
$83$	−10.6788	−1.17215	−0.586074	−	0.810257i	$-0.699327\pi$
$83$	−10.6788	−1.17215	−0.586074	+	0.810257i	$0.699327\pi$
$84$	−2.09750	−0.228856
$85$	−4.37463	−0.474495
$86$	−3.39383	−0.365966
$87$	−7.36894	−0.790034
$88$	−5.61070	−0.598103
$89$	−18.5768	−1.96914	−0.984570	−	0.174990i	$-0.944011\pi$
$89$	−18.5768	−1.96914	−0.984570	+	0.174990i	$0.944011\pi$
$90$	−7.45294	−0.785608
$91$	−5.49134	−0.575648
$92$	−0.958939	−0.0999763
$93$	6.96729	0.722474
$94$	−11.0783	−1.14264
$95$	21.0034	2.15490
$96$	1.13856	0.116204
$97$	−4.40165	−0.446920	−0.223460	−	0.974713i	$-0.571735\pi$
$97$	−4.40165	−0.446920	−0.223460	+	0.974713i	$0.571735\pi$
$98$	3.60617	0.364278
$99$	−9.55879	−0.960694
$100$	14.1374	1.41374
$101$	−17.1695	−1.70843	−0.854214	−	0.519922i	$-0.825961\pi$
$101$	−17.1695	−1.70843	−0.854214	+	0.519922i	$0.825961\pi$
$102$	1.13856	0.112735
$103$	−1.86597	−0.183859	−0.0919297	−	0.995766i	$-0.529303\pi$
$103$	−1.86597	−0.183859	−0.0919297	+	0.995766i	$0.529303\pi$
$104$	2.98080	0.292291
$105$	9.17581	0.895467
$106$	−9.20602	−0.894167
$107$	−2.09234	−0.202274	−0.101137	−	0.994872i	$-0.532248\pi$
$107$	−2.09234	−0.202274	−0.101137	+	0.994872i	$0.532248\pi$
$108$	5.35543	0.515327
$109$	−12.2252	−1.17096	−0.585482	−	0.810686i	$-0.699095\pi$
$109$	−12.2252	−1.17096	−0.585482	+	0.810686i	$0.699095\pi$
$110$	24.5448	2.34025
$111$	2.76278	0.262231
$112$	1.84224	0.174075
$113$	−11.4209	−1.07438	−0.537192	−	0.843460i	$-0.680515\pi$
$113$	−11.4209	−1.07438	−0.537192	+	0.843460i	$0.680515\pi$
$114$	−5.46645	−0.511980
$115$	4.19501	0.391186
$116$	6.47214	0.600923
$117$	5.07830	0.469489
$118$	−1.00000	−0.0920575
$119$	1.84224	0.168877
$120$	−4.98080	−0.454683
$121$	20.4800	1.86181
$122$	6.92170	0.626661
$123$	−9.06479	−0.817345
$124$	−6.11936	−0.549535
$125$	−39.9728	−3.57528
$126$	3.13856	0.279606
$127$	−17.7454	−1.57465	−0.787327	−	0.616536i	$-0.788536\pi$
$127$	−17.7454	−1.57465	−0.787327	+	0.616536i	$0.788536\pi$
$128$	−1.00000	−0.0883883
$129$	−3.86410	−0.340215
$130$	−13.0399	−1.14368
$131$	−5.18860	−0.453330	−0.226665	−	0.973973i	$-0.572782\pi$
$131$	−5.18860	−0.453330	−0.226665	+	0.973973i	$0.572782\pi$
$132$	−6.38814	−0.556016
$133$	−8.84490	−0.766950
$134$	12.4856	1.07860
$135$	−23.4280	−2.01637
$136$	−1.00000	−0.0857493
$137$	22.6878	1.93835	0.969177	−	0.246366i	$-0.0792366\pi$
$137$	22.6878	1.93835	0.969177	+	0.246366i	$0.0792366\pi$
$138$	−1.09181	−0.0929414
$139$	3.21118	0.272369	0.136184	−	0.990684i	$-0.456516\pi$
$139$	3.21118	0.272369	0.136184	+	0.990684i	$0.456516\pi$
$140$	−8.05910	−0.681119
$141$	−12.6134	−1.06224
$142$	−0.582435	−0.0488769
$143$	−16.7244	−1.39856
$144$	−1.70367	−0.141973
$145$	−28.3132	−2.35128
$146$	−11.5120	−0.952743
$147$	4.10585	0.338645
$148$	−2.42654	−0.199461
$149$	12.9578	1.06154	0.530771	−	0.847515i	$-0.321902\pi$
$149$	12.9578	1.06154	0.530771	+	0.847515i	$0.321902\pi$
$150$	16.0963	1.31426
$151$	2.81469	0.229056	0.114528	−	0.993420i	$-0.463464\pi$
$151$	2.81469	0.229056	0.114528	+	0.993420i	$0.463464\pi$
$152$	4.80118	0.389427
$153$	−1.70367	−0.137734
$154$	−10.3362	−0.832917
$155$	26.7700	2.15022
$156$	3.39383	0.271724
$157$	14.3651	1.14646	0.573231	−	0.819394i	$-0.305690\pi$
$157$	14.3651	1.14646	0.573231	+	0.819394i	$0.305690\pi$
$158$	6.67549	0.531074
$159$	−10.4816	−0.831248
$160$	4.37463	0.345845
$161$	−1.76659	−0.139227
$162$	0.986489	0.0775059
$163$	0.352772	0.0276312	0.0138156	−	0.999905i	$-0.495602\pi$
$163$	0.352772	0.0276312	0.0138156	+	0.999905i	$0.495602\pi$
$164$	7.96160	0.621697
$165$	27.9458	2.17558
$166$	10.6788	0.828834
$167$	5.95325	0.460676	0.230338	−	0.973111i	$-0.426017\pi$
$167$	5.95325	0.460676	0.230338	+	0.973111i	$0.426017\pi$
$168$	2.09750	0.161826
$169$	−4.11483	−0.316526
$170$	4.37463	0.335519
$171$	8.17962	0.625512
$172$	3.39383	0.258777
$173$	−19.7621	−1.50249	−0.751244	−	0.660024i	$-0.770546\pi$
$173$	−19.7621	−1.50249	−0.751244	+	0.660024i	$0.770546\pi$
$174$	7.36894	0.558638
$175$	26.0444	1.96877
$176$	5.61070	0.422922
$177$	−1.13856	−0.0855797
$178$	18.5768	1.39239
$179$	−9.80900	−0.733159	−0.366579	−	0.930387i	$-0.619471\pi$
$179$	−9.80900	−0.733159	−0.366579	+	0.930387i	$0.619471\pi$
$180$	7.45294	0.555509
$181$	1.39196	0.103464	0.0517318	−	0.998661i	$-0.483526\pi$
$181$	1.39196	0.103464	0.0517318	+	0.998661i	$0.483526\pi$
$182$	5.49134	0.407045
$183$	7.88080	0.582565
$184$	0.958939	0.0706940
$185$	10.6152	0.780447
$186$	−6.96729	−0.510866
$187$	5.61070	0.410295
$188$	11.0783	0.807968
$189$	9.86597	0.717644
$190$	−21.0034	−1.52375
$191$	0.470264	0.0340271	0.0170136	−	0.999855i	$-0.494584\pi$
$191$	0.470264	0.0340271	0.0170136	+	0.999855i	$0.494584\pi$
$192$	−1.13856	−0.0821688
$193$	22.2138	1.59899	0.799494	−	0.600675i	$-0.205101\pi$
$193$	22.2138	1.59899	0.799494	+	0.600675i	$0.205101\pi$
$194$	4.40165	0.316020
$195$	−14.8468	−1.06320
$196$	−3.60617	−0.257583
$197$	−12.4703	−0.888470	−0.444235	−	0.895910i	$-0.646524\pi$
$197$	−12.4703	−0.888470	−0.444235	+	0.895910i	$0.646524\pi$
$198$	9.55879	0.679314
$199$	−16.2530	−1.15214	−0.576071	−	0.817400i	$-0.695415\pi$
$199$	−16.2530	−1.15214	−0.576071	+	0.817400i	$0.695415\pi$
$200$	−14.1374	−0.999666
$201$	14.2157	1.00270
$202$	17.1695	1.20804
$203$	11.9232	0.836845
$204$	−1.13856	−0.0797154
$205$	−34.8291	−2.43257
$206$	1.86597	0.130008
$207$	1.63372	0.113551
$208$	−2.98080	−0.206681
$209$	−26.9380	−1.86334
$210$	−9.17581	−0.633191
$211$	−14.4754	−0.996529	−0.498265	−	0.867025i	$-0.666029\pi$
$211$	−14.4754	−0.996529	−0.498265	+	0.867025i	$0.666029\pi$
$212$	9.20602	0.632272
$213$	−0.663140	−0.0454376
$214$	2.09234	0.143030
$215$	−14.8468	−1.01254
$216$	−5.35543	−0.364391
$217$	−11.2733	−0.765282
$218$	12.2252	0.827996
$219$	−13.1072	−0.885702
$220$	−24.5448	−1.65481
$221$	−2.98080	−0.200510
$222$	−2.76278	−0.185425
$223$	2.87379	0.192443	0.0962216	−	0.995360i	$-0.469324\pi$
$223$	2.87379	0.192443	0.0962216	+	0.995360i	$0.469324\pi$
$224$	−1.84224	−0.123090
$225$	−24.0855	−1.60570
$226$	11.4209	0.759704
$227$	13.4830	0.894897	0.447449	−	0.894310i	$-0.352333\pi$
$227$	13.4830	0.894897	0.447449	+	0.894310i	$0.352333\pi$
$228$	5.46645	0.362024
$229$	−10.5813	−0.699231	−0.349615	−	0.936893i	$-0.613688\pi$
$229$	−10.5813	−0.699231	−0.349615	+	0.936893i	$0.613688\pi$
$230$	−4.19501	−0.276611
$231$	−11.7685	−0.774308
$232$	−6.47214	−0.424917
$233$	−4.86028	−0.318407	−0.159204	−	0.987246i	$-0.550893\pi$
$233$	−4.86028	−0.318407	−0.159204	+	0.987246i	$0.550893\pi$
$234$	−5.07830	−0.331979
$235$	−48.4635	−3.16141
$236$	1.00000	0.0650945
$237$	7.60048	0.493704
$238$	−1.84224	−0.119414
$239$	−16.0342	−1.03717	−0.518584	−	0.855027i	$-0.673540\pi$
$239$	−16.0342	−1.03717	−0.518584	+	0.855027i	$0.673540\pi$
$240$	4.98080	0.321509
$241$	−7.15323	−0.460780	−0.230390	−	0.973098i	$-0.574000\pi$
$241$	−7.15323	−0.460780	−0.230390	+	0.973098i	$0.574000\pi$
$242$	−20.4800	−1.31650
$243$	−14.9431	−0.958601
$244$	−6.92170	−0.443116
$245$	15.7757	1.00787
$246$	9.06479	0.577950
$247$	14.3113	0.910609
$248$	6.11936	0.388580
$249$	12.1585	0.770512
$250$	39.9728	2.52810
$251$	0.510536	0.0322248	0.0161124	−	0.999870i	$-0.494871\pi$
$251$	0.510536	0.0322248	0.0161124	+	0.999870i	$0.494871\pi$
$252$	−3.13856	−0.197711
$253$	−5.38032	−0.338258
$254$	17.7454	1.11345
$255$	4.98080	0.311910
$256$	1.00000	0.0625000
$257$	28.3683	1.76957	0.884783	−	0.466002i	$-0.154306\pi$
$257$	28.3683	1.76957	0.884783	+	0.466002i	$0.154306\pi$
$258$	3.86410	0.240568
$259$	−4.47026	−0.277769
$260$	13.0399	0.808700
$261$	−11.0264	−0.682517
$262$	5.18860	0.320553
$263$	−24.2364	−1.49448	−0.747241	−	0.664554i	$-0.768622\pi$
$263$	−24.2364	−1.49448	−0.747241	+	0.664554i	$0.768622\pi$
$264$	6.38814	0.393163
$265$	−40.2729	−2.47395
$266$	8.84490	0.542315
$267$	21.1509	1.29442
$268$	−12.4856	−0.762682
$269$	−21.9874	−1.34059	−0.670297	−	0.742093i	$-0.733833\pi$
$269$	−21.9874	−1.34059	−0.670297	+	0.742093i	$0.733833\pi$
$270$	23.4280	1.42579
$271$	25.8578	1.57075	0.785374	−	0.619021i	$-0.212471\pi$
$271$	25.8578	1.57075	0.785374	+	0.619021i	$0.212471\pi$
$272$	1.00000	0.0606339
$273$	6.25224	0.378403
$274$	−22.6878	−1.37062
$275$	79.3208	4.78322
$276$	1.09181	0.0657195
$277$	−3.45738	−0.207734	−0.103867	−	0.994591i	$-0.533122\pi$
$277$	−3.45738	−0.207734	−0.103867	+	0.994591i	$0.533122\pi$
$278$	−3.21118	−0.192594
$279$	10.4254	0.624152
$280$	8.05910	0.481624
$281$	22.2780	1.32899	0.664497	−	0.747291i	$-0.268646\pi$
$281$	22.2780	1.32899	0.664497	+	0.747291i	$0.268646\pi$
$282$	12.6134	0.751115
$283$	2.00072	0.118930	0.0594651	−	0.998230i	$-0.481061\pi$
$283$	2.00072	0.118930	0.0594651	+	0.998230i	$0.481061\pi$
$284$	0.582435	0.0345612
$285$	−23.9137	−1.41652
$286$	16.7244	0.988933
$287$	14.6671	0.865774
$288$	1.70367	0.100390
$289$	1.00000	0.0588235
$290$	28.3132	1.66261
$291$	5.01157	0.293783
$292$	11.5120	0.673691
$293$	−25.3242	−1.47946	−0.739729	−	0.672905i	$-0.765046\pi$
$293$	−25.3242	−1.47946	−0.739729	+	0.672905i	$0.765046\pi$
$294$	−4.10585	−0.239458
$295$	−4.37463	−0.254701
$296$	2.42654	0.141040
$297$	30.0477	1.74355
$298$	−12.9578	−0.750624
$299$	2.85841	0.165306
$300$	−16.0963	−0.929323
$301$	6.25224	0.360373
$302$	−2.81469	−0.161967
$303$	19.5486	1.12304
$304$	−4.80118	−0.275366
$305$	30.2799	1.73382
$306$	1.70367	0.0973924
$307$	−4.89468	−0.279354	−0.139677	−	0.990197i	$-0.544606\pi$
$307$	−4.89468	−0.279354	−0.139677	+	0.990197i	$0.544606\pi$
$308$	10.3362	0.588961
$309$	2.12452	0.120860
$310$	−26.7700	−1.52043
$311$	3.92436	0.222530	0.111265	−	0.993791i	$-0.464510\pi$
$311$	3.92436	0.222530	0.111265	+	0.993791i	$0.464510\pi$
$312$	−3.39383	−0.192138
$313$	−12.6206	−0.713356	−0.356678	−	0.934227i	$-0.616091\pi$
$313$	−12.6206	−0.713356	−0.356678	+	0.934227i	$0.616091\pi$
$314$	−14.3651	−0.810671
$315$	13.7301	0.773601
$316$	−6.67549	−0.375526
$317$	−10.9994	−0.617786	−0.308893	−	0.951097i	$-0.599959\pi$
$317$	−10.9994	−0.617786	−0.308893	+	0.951097i	$0.599959\pi$
$318$	10.4816	0.587781
$319$	36.3132	2.03315
$320$	−4.37463	−0.244549
$321$	2.38227	0.132965
$322$	1.76659	0.0984483
$323$	−4.80118	−0.267145
$324$	−0.986489	−0.0548050
$325$	−42.1408	−2.33755
$326$	−0.352772	−0.0195382
$327$	13.9192	0.769733
$328$	−7.96160	−0.439606
$329$	20.4088	1.12518
$330$	−27.9458	−1.53836
$331$	10.0975	0.555009	0.277504	−	0.960724i	$-0.410493\pi$
$331$	10.0975	0.555009	0.277504	+	0.960724i	$0.410493\pi$
$332$	−10.6788	−0.586074
$333$	4.13403	0.226544
$334$	−5.95325	−0.325747
$335$	54.6201	2.98422
$336$	−2.09750	−0.114428
$337$	2.36831	0.129010	0.0645052	−	0.997917i	$-0.479453\pi$
$337$	2.36831	0.129010	0.0645052	+	0.997917i	$0.479453\pi$
$338$	4.11483	0.223817
$339$	13.0034	0.706246
$340$	−4.37463	−0.237248
$341$	−34.3339	−1.85929
$342$	−8.17962	−0.442303
$343$	−19.5391	−1.05501
$344$	−3.39383	−0.182983
$345$	−4.77629	−0.257147
$346$	19.7621	1.06242
$347$	−0.282289	−0.0151541	−0.00757704	−	0.999971i	$-0.502412\pi$
$347$	−0.282289	−0.0151541	−0.00757704	+	0.999971i	$0.502412\pi$
$348$	−7.36894	−0.395017
$349$	−14.3651	−0.768948	−0.384474	−	0.923136i	$-0.625617\pi$
$349$	−14.3651	−0.768948	−0.384474	+	0.923136i	$0.625617\pi$
$350$	−26.0444	−1.39213
$351$	−15.9635	−0.852067
$352$	−5.61070	−0.299051
$353$	−9.99555	−0.532010	−0.266005	−	0.963972i	$-0.585704\pi$
$353$	−9.99555	−0.532010	−0.266005	+	0.963972i	$0.585704\pi$
$354$	1.13856	0.0605140
$355$	−2.54794	−0.135231
$356$	−18.5768	−0.984570
$357$	−2.09750	−0.111012
$358$	9.80900	0.518422
$359$	24.4856	1.29230	0.646151	−	0.763209i	$-0.276377\pi$
$359$	24.4856	1.29230	0.646151	+	0.763209i	$0.276377\pi$
$360$	−7.45294	−0.392804
$361$	4.05128	0.213225
$362$	−1.39196	−0.0731598
$363$	−23.3177	−1.22386
$364$	−5.49134	−0.287824
$365$	−50.3609	−2.63601
$366$	−7.88080	−0.411936
$367$	29.6417	1.54729	0.773643	−	0.633622i	$-0.218433\pi$
$367$	29.6417	1.54729	0.773643	+	0.633622i	$0.218433\pi$
$368$	−0.958939	−0.0499882
$369$	−13.5640	−0.706111
$370$	−10.6152	−0.551860
$371$	16.9597	0.880501
$372$	6.96729	0.361237
$373$	−33.1644	−1.71719	−0.858595	−	0.512655i	$-0.828662\pi$
$373$	−33.1644	−1.71719	−0.858595	+	0.512655i	$0.828662\pi$
$374$	−5.61070	−0.290122
$375$	45.5116	2.35021
$376$	−11.0783	−0.571320
$377$	−19.2921	−0.993596
$378$	−9.86597	−0.507451
$379$	−5.36191	−0.275423	−0.137711	−	0.990472i	$-0.543975\pi$
$379$	−5.36191	−0.275423	−0.137711	+	0.990472i	$0.543975\pi$
$380$	21.0034	1.07745
$381$	20.2043	1.03510
$382$	−0.470264	−0.0240608
$383$	4.75371	0.242903	0.121452	−	0.992597i	$-0.461245\pi$
$383$	4.75371	0.242903	0.121452	+	0.992597i	$0.461245\pi$
$384$	1.13856	0.0581021
$385$	−45.2172	−2.30448
$386$	−22.2138	−1.13065
$387$	−5.78198	−0.293914
$388$	−4.40165	−0.223460
$389$	23.1581	1.17416	0.587081	−	0.809528i	$-0.300277\pi$
$389$	23.1581	1.17416	0.587081	+	0.809528i	$0.300277\pi$
$390$	14.8468	0.751795
$391$	−0.958939	−0.0484957
$392$	3.60617	0.182139
$393$	5.90756	0.297997
$394$	12.4703	0.628243
$395$	29.2028	1.46935
$396$	−9.55879	−0.480347
$397$	4.68829	0.235298	0.117649	−	0.993055i	$-0.462464\pi$
$397$	4.68829	0.235298	0.117649	+	0.993055i	$0.462464\pi$
$398$	16.2530	0.814687
$399$	10.0705	0.504155
$400$	14.1374	0.706870
$401$	−25.3554	−1.26619	−0.633095	−	0.774074i	$-0.718216\pi$
$401$	−25.3554	−1.26619	−0.633095	+	0.774074i	$0.718216\pi$
$402$	−14.2157	−0.709015
$403$	18.2406	0.908629
$404$	−17.1695	−0.854214
$405$	4.31553	0.214440
$406$	−11.9232	−0.591738
$407$	−13.6146	−0.674851
$408$	1.13856	0.0563673
$409$	−0.851214	−0.0420898	−0.0210449	−	0.999779i	$-0.506699\pi$
$409$	−0.851214	−0.0420898	−0.0210449	+	0.999779i	$0.506699\pi$
$410$	34.8291	1.72009
$411$	−25.8316	−1.27418
$412$	−1.86597	−0.0919297
$413$	1.84224	0.0906505
$414$	−1.63372	−0.0802928
$415$	46.7157	2.29319
$416$	2.98080	0.146146
$417$	−3.65613	−0.179042
$418$	26.9380	1.31758
$419$	−19.0523	−0.930764	−0.465382	−	0.885110i	$-0.654083\pi$
$419$	−19.0523	−0.930764	−0.465382	+	0.885110i	$0.654083\pi$
$420$	9.17581	0.447734
$421$	16.4472	0.801590	0.400795	−	0.916168i	$-0.368734\pi$
$421$	16.4472	0.801590	0.400795	+	0.916168i	$0.368734\pi$
$422$	14.4754	0.704653
$423$	−18.8738	−0.917675
$424$	−9.20602	−0.447084
$425$	14.1374	0.685765
$426$	0.663140	0.0321292
$427$	−12.7514	−0.617083
$428$	−2.09234	−0.101137
$429$	19.0418	0.919346
$430$	14.8468	0.715975
$431$	5.61977	0.270695	0.135347	−	0.990798i	$-0.456785\pi$
$431$	5.61977	0.270695	0.135347	+	0.990798i	$0.456785\pi$
$432$	5.35543	0.257663
$433$	23.8360	1.14549	0.572743	−	0.819735i	$-0.305879\pi$
$433$	23.8360	1.14549	0.572743	+	0.819735i	$0.305879\pi$
$434$	11.2733	0.541136
$435$	32.2364	1.54562
$436$	−12.2252	−0.585482
$437$	4.60404	0.220241
$438$	13.1072	0.626286
$439$	−25.4830	−1.21624	−0.608118	−	0.793846i	$-0.708075\pi$
$439$	−25.4830	−1.21624	−0.608118	+	0.793846i	$0.708075\pi$
$440$	24.5448	1.17013
$441$	6.14372	0.292558
$442$	2.98080	0.141782
$443$	−10.0924	−0.479506	−0.239753	−	0.970834i	$-0.577067\pi$
$443$	−10.0924	−0.479506	−0.239753	+	0.970834i	$0.577067\pi$
$444$	2.76278	0.131115
$445$	81.2668	3.85242
$446$	−2.87379	−0.136078
$447$	−14.7533	−0.697806
$448$	1.84224	0.0870375
$449$	−10.4139	−0.491463	−0.245731	−	0.969338i	$-0.579028\pi$
$449$	−10.4139	−0.491463	−0.245731	+	0.969338i	$0.579028\pi$
$450$	24.0855	1.13540
$451$	44.6702	2.10344
$452$	−11.4209	−0.537192
$453$	−3.20470	−0.150570
$454$	−13.4830	−0.632788
$455$	24.0226	1.12620
$456$	−5.46645	−0.255990
$457$	4.61655	0.215953	0.107977	−	0.994153i	$-0.465563\pi$
$457$	4.61655	0.215953	0.107977	+	0.994153i	$0.465563\pi$
$458$	10.5813	0.494431
$459$	5.35543	0.249970
$460$	4.19501	0.195593
$461$	−9.43755	−0.439551	−0.219775	−	0.975551i	$-0.570532\pi$
$461$	−9.43755	−0.439551	−0.219775	+	0.975551i	$0.570532\pi$
$462$	11.7685	0.547519
$463$	5.25474	0.244208	0.122104	−	0.992517i	$-0.461036\pi$
$463$	5.25474	0.244208	0.122104	+	0.992517i	$0.461036\pi$
$464$	6.47214	0.300461
$465$	−30.4793	−1.41345
$466$	4.86028	0.225148
$467$	9.89530	0.457900	0.228950	−	0.973438i	$-0.426471\pi$
$467$	9.89530	0.457900	0.228950	+	0.973438i	$0.426471\pi$
$468$	5.07830	0.234745
$469$	−23.0015	−1.06211
$470$	48.4635	2.23545
$471$	−16.3556	−0.753627
$472$	−1.00000	−0.0460287
$473$	19.0418	0.875542
$474$	−7.60048	−0.349102
$475$	−67.8762	−3.11437
$476$	1.84224	0.0844387
$477$	−15.6840	−0.718122
$478$	16.0342	0.733388
$479$	−37.5470	−1.71556	−0.857782	−	0.514013i	$-0.828158\pi$
$479$	−37.5470	−1.71556	−0.857782	+	0.514013i	$0.828158\pi$
$480$	−4.98080	−0.227341
$481$	7.23304	0.329798
$482$	7.15323	0.325821
$483$	2.01138	0.0915209
$484$	20.4800	0.930907
$485$	19.2556	0.874352
$486$	14.9431	0.677833
$487$	15.9265	0.721698	0.360849	−	0.932624i	$-0.382487\pi$
$487$	15.9265	0.721698	0.360849	+	0.932624i	$0.382487\pi$
$488$	6.92170	0.313330
$489$	−0.401653	−0.0181634
$490$	−15.7757	−0.712672
$491$	9.33499	0.421282	0.210641	−	0.977563i	$-0.432445\pi$
$491$	9.33499	0.421282	0.210641	+	0.977563i	$0.432445\pi$
$492$	−9.06479	−0.408672
$493$	6.47214	0.291490
$494$	−14.3113	−0.643898
$495$	41.8162	1.87950
$496$	−6.11936	−0.274768
$497$	1.07298	0.0481299
$498$	−12.1585	−0.544834
$499$	22.6818	1.01538	0.507689	−	0.861541i	$-0.330500\pi$
$499$	22.6818	1.01538	0.507689	+	0.861541i	$0.330500\pi$
$500$	−39.9728	−1.78764
$501$	−6.77816	−0.302826
$502$	−0.510536	−0.0227863
$503$	39.8304	1.77595	0.887975	−	0.459891i	$-0.152112\pi$
$503$	39.8304	1.77595	0.887975	+	0.459891i	$0.152112\pi$
$504$	3.13856	0.139803
$505$	75.1102	3.34236
$506$	5.38032	0.239184
$507$	4.68500	0.208068
$508$	−17.7454	−0.787327
$509$	−26.1475	−1.15897	−0.579485	−	0.814983i	$-0.696746\pi$
$509$	−26.1475	−1.15897	−0.579485	+	0.814983i	$0.696746\pi$
$510$	−4.98080	−0.220554
$511$	21.2079	0.938182
$512$	−1.00000	−0.0441942
$513$	−25.7124	−1.13523
$514$	−28.3683	−1.25127
$515$	8.16292	0.359701
$516$	−3.86410	−0.170107
$517$	62.1570	2.73366
$518$	4.47026	0.196412
$519$	22.5005	0.987661
$520$	−13.0399	−0.571838
$521$	8.32085	0.364543	0.182272	−	0.983248i	$-0.441655\pi$
$521$	8.32085	0.364543	0.182272	+	0.983248i	$0.441655\pi$
$522$	11.0264	0.482612
$523$	20.9835	0.917546	0.458773	−	0.888553i	$-0.348289\pi$
$523$	20.9835	0.917546	0.458773	+	0.888553i	$0.348289\pi$
$524$	−5.18860	−0.226665
$525$	−29.6533	−1.29417
$526$	24.2364	1.05676
$527$	−6.11936	−0.266564
$528$	−6.38814	−0.278008
$529$	−22.0804	−0.960019
$530$	40.2729	1.74934
$531$	−1.70367	−0.0739330
$532$	−8.84490	−0.383475
$533$	−23.7319	−1.02794
$534$	−21.1509	−0.915290
$535$	9.15323	0.395729
$536$	12.4856	0.539298
$537$	11.1682	0.481942
$538$	21.9874	0.947943
$539$	−20.2331	−0.871502
$540$	−23.4280	−1.00818
$541$	−19.5884	−0.842171	−0.421085	−	0.907021i	$-0.638351\pi$
$541$	−19.5884	−0.842171	−0.421085	+	0.907021i	$0.638351\pi$
$542$	−25.8578	−1.11069
$543$	−1.58484	−0.0680118
$544$	−1.00000	−0.0428746
$545$	53.4808	2.29087
$546$	−6.25224	−0.267571
$547$	−1.81922	−0.0777842	−0.0388921	−	0.999243i	$-0.512383\pi$
$547$	−1.81922	−0.0777842	−0.0388921	+	0.999243i	$0.512383\pi$
$548$	22.6878	0.969177
$549$	11.7923	0.503283
$550$	−79.3208	−3.38225
$551$	−31.0739	−1.32379
$552$	−1.09181	−0.0464707
$553$	−12.2978	−0.522957
$554$	3.45738	0.146890
$555$	−12.0861	−0.513027
$556$	3.21118	0.136184
$557$	14.9569	0.633744	0.316872	−	0.948468i	$-0.397367\pi$
$557$	14.9569	0.633744	0.316872	+	0.948468i	$0.397367\pi$
$558$	−10.4254	−0.441342
$559$	−10.1163	−0.427875
$560$	−8.05910	−0.340559
$561$	−6.38814	−0.269708
$562$	−22.2780	−0.939741
$563$	−8.36644	−0.352604	−0.176302	−	0.984336i	$-0.556413\pi$
$563$	−8.36644	−0.352604	−0.176302	+	0.984336i	$0.556413\pi$
$564$	−12.6134	−0.531118
$565$	49.9620	2.10192
$566$	−2.00072	−0.0840963
$567$	−1.81735	−0.0763214
$568$	−0.582435	−0.0244384
$569$	−10.3818	−0.435229	−0.217614	−	0.976035i	$-0.569828\pi$
$569$	−10.3818	−0.435229	−0.217614	+	0.976035i	$0.569828\pi$
$570$	23.9137	1.00163
$571$	−16.6101	−0.695110	−0.347555	−	0.937660i	$-0.612988\pi$
$571$	−16.6101	−0.695110	−0.347555	+	0.937660i	$0.612988\pi$
$572$	−16.7244	−0.699281
$573$	−0.535426	−0.0223677
$574$	−14.6671	−0.612195
$575$	−13.5569	−0.565363
$576$	−1.70367	−0.0709863
$577$	−32.6318	−1.35848	−0.679239	−	0.733917i	$-0.737690\pi$
$577$	−32.6318	−1.35848	−0.679239	+	0.733917i	$0.737690\pi$
$578$	−1.00000	−0.0415945
$579$	−25.2919	−1.05109
$580$	−28.3132	−1.17564
$581$	−19.6728	−0.816167
$582$	−5.01157	−0.207736
$583$	51.6522	2.13922
$584$	−11.5120	−0.476372
$585$	−22.2157	−0.918507
$586$	25.3242	1.04613
$587$	13.0770	0.539748	0.269874	−	0.962896i	$-0.413018\pi$
$587$	13.0770	0.539748	0.269874	+	0.962896i	$0.413018\pi$
$588$	4.10585	0.169323
$589$	29.3801	1.21059
$590$	4.37463	0.180101
$591$	14.1982	0.584036
$592$	−2.42654	−0.0997303
$593$	5.22371	0.214512	0.107256	−	0.994231i	$-0.465794\pi$
$593$	5.22371	0.214512	0.107256	+	0.994231i	$0.465794\pi$
$594$	−30.0477	−1.23287
$595$	−8.05910	−0.330391
$596$	12.9578	0.530771
$597$	18.5050	0.757361
$598$	−2.85841	−0.116889
$599$	−11.0059	−0.449691	−0.224845	−	0.974394i	$-0.572188\pi$
$599$	−11.0059	−0.449691	−0.224845	+	0.974394i	$0.572188\pi$
$600$	16.0963	0.657131
$601$	10.4589	0.426627	0.213313	−	0.976984i	$-0.431574\pi$
$601$	10.4589	0.426627	0.213313	+	0.976984i	$0.431574\pi$
$602$	−6.25224	−0.254822
$603$	21.2714	0.866240
$604$	2.81469	0.114528
$605$	−89.5923	−3.64244
$606$	−19.5486	−0.794106
$607$	−40.2580	−1.63402	−0.817011	−	0.576622i	$-0.804371\pi$
$607$	−40.2580	−1.63402	−0.817011	+	0.576622i	$0.804371\pi$
$608$	4.80118	0.194713
$609$	−13.5753	−0.550100
$610$	−30.2799	−1.22600
$611$	−33.0222	−1.33594
$612$	−1.70367	−0.0688668
$613$	38.0926	1.53855	0.769273	−	0.638920i	$-0.220619\pi$
$613$	38.0926	1.53855	0.769273	+	0.638920i	$0.220619\pi$
$614$	4.89468	0.197533
$615$	39.6551	1.59905
$616$	−10.3362	−0.416459
$617$	−13.0285	−0.524509	−0.262254	−	0.964999i	$-0.584466\pi$
$617$	−13.0285	−0.524509	−0.262254	+	0.964999i	$0.584466\pi$
$618$	−2.12452	−0.0854609
$619$	24.0620	0.967131	0.483566	−	0.875308i	$-0.339341\pi$
$619$	24.0620	0.967131	0.483566	+	0.875308i	$0.339341\pi$
$620$	26.7700	1.07511
$621$	−5.13554	−0.206082
$622$	−3.92436	−0.157352
$623$	−34.2229	−1.37111
$624$	3.39383	0.135862
$625$	104.179	4.16717
$626$	12.6206	0.504419
$627$	30.6706	1.22487
$628$	14.3651	0.573231
$629$	−2.42654	−0.0967526
$630$	−13.7301	−0.547019
$631$	−29.6321	−1.17964	−0.589818	−	0.807536i	$-0.700801\pi$
$631$	−29.6321	−1.17964	−0.589818	+	0.807536i	$0.700801\pi$
$632$	6.67549	0.265537
$633$	16.4812	0.655069
$634$	10.9994	0.436841
$635$	77.6298	3.08064
$636$	−10.4816	−0.415624
$637$	10.7493	0.425901
$638$	−36.3132	−1.43765
$639$	−0.992278	−0.0392539
$640$	4.37463	0.172923
$641$	5.43249	0.214571	0.107285	−	0.994228i	$-0.465784\pi$
$641$	5.43249	0.214571	0.107285	+	0.994228i	$0.465784\pi$
$642$	−2.38227	−0.0940206
$643$	−18.3748	−0.724631	−0.362316	−	0.932055i	$-0.618014\pi$
$643$	−18.3748	−0.724631	−0.362316	+	0.932055i	$0.618014\pi$
$644$	−1.76659	−0.0696135
$645$	16.9040	0.665594
$646$	4.80118	0.188900
$647$	−15.0038	−0.589861	−0.294930	−	0.955519i	$-0.595296\pi$
$647$	−15.0038	−0.589861	−0.294930	+	0.955519i	$0.595296\pi$
$648$	0.986489	0.0387530
$649$	5.61070	0.220239
$650$	42.1408	1.65290
$651$	12.8354	0.503059
$652$	0.352772	0.0138156
$653$	−46.5443	−1.82142	−0.910710	−	0.413047i	$-0.864465\pi$
$653$	−46.5443	−1.82142	−0.910710	+	0.413047i	$0.864465\pi$
$654$	−13.9192	−0.544284
$655$	22.6982	0.886893
$656$	7.96160	0.310848
$657$	−19.6127	−0.765166
$658$	−20.4088	−0.795620
$659$	48.8105	1.90139	0.950694	−	0.310132i	$-0.100373\pi$
$659$	48.8105	1.90139	0.950694	+	0.310132i	$0.100373\pi$
$660$	27.9458	1.08779
$661$	−18.8719	−0.734033	−0.367016	−	0.930215i	$-0.619621\pi$
$661$	−18.8719	−0.734033	−0.367016	+	0.930215i	$0.619621\pi$
$662$	−10.0975	−0.392451
$663$	3.39383	0.131806
$664$	10.6788	0.414417
$665$	38.6932	1.50046
$666$	−4.13403	−0.160190
$667$	−6.20639	−0.240312
$668$	5.95325	0.230338
$669$	−3.27199	−0.126503
$670$	−54.6201	−2.11016
$671$	−38.8356	−1.49923
$672$	2.09750	0.0809130
$673$	3.28050	0.126454	0.0632271	−	0.997999i	$-0.479861\pi$
$673$	3.28050	0.126454	0.0632271	+	0.997999i	$0.479861\pi$
$674$	−2.36831	−0.0912241
$675$	75.7119	2.91415
$676$	−4.11483	−0.158263
$677$	−0.0890547	−0.00342265	−0.00171132	−	0.999999i	$-0.500545\pi$
$677$	−0.0890547	−0.00342265	−0.00171132	+	0.999999i	$0.500545\pi$
$678$	−13.0034	−0.499392
$679$	−8.10888	−0.311190
$680$	4.37463	0.167759
$681$	−15.3512	−0.588261
$682$	34.3339	1.31471
$683$	36.3017	1.38905	0.694524	−	0.719470i	$-0.255615\pi$
$683$	36.3017	1.38905	0.694524	+	0.719470i	$0.255615\pi$
$684$	8.17962	0.312756
$685$	−99.2510	−3.79219
$686$	19.5391	0.746005
$687$	12.0475	0.459639
$688$	3.39383	0.129389
$689$	−27.4413	−1.04543
$690$	4.77629	0.181830
$691$	−44.0614	−1.67617	−0.838087	−	0.545536i	$-0.816326\pi$
$691$	−44.0614	−1.67617	−0.838087	+	0.545536i	$0.816326\pi$
$692$	−19.7621	−0.751244
$693$	−17.6095	−0.668931
$694$	0.282289	0.0107155
$695$	−14.0477	−0.532861
$696$	7.36894	0.279319
$697$	7.96160	0.301567
$698$	14.3651	0.543728
$699$	5.53374	0.209305
$700$	26.0444	0.984387
$701$	2.34530	0.0885807	0.0442903	−	0.999019i	$-0.485897\pi$
$701$	2.34530	0.0885807	0.0442903	+	0.999019i	$0.485897\pi$
$702$	15.9635	0.602502
$703$	11.6503	0.439398
$704$	5.61070	0.211461
$705$	55.1788	2.07815
$706$	9.99555	0.376188
$707$	−31.6302	−1.18958
$708$	−1.13856	−0.0427899
$709$	47.2024	1.77272	0.886361	−	0.462994i	$-0.153225\pi$
$709$	47.2024	1.77272	0.886361	+	0.462994i	$0.153225\pi$
$710$	2.54794	0.0956225
$711$	11.3728	0.426515
$712$	18.5768	0.696196
$713$	5.86810	0.219762
$714$	2.09750	0.0784971
$715$	73.1630	2.73614
$716$	−9.80900	−0.366579
$717$	18.2560	0.681782
$718$	−24.4856	−0.913796
$719$	−10.8315	−0.403946	−0.201973	−	0.979391i	$-0.564735\pi$
$719$	−10.8315	−0.403946	−0.201973	+	0.979391i	$0.564735\pi$
$720$	7.45294	0.277755
$721$	−3.43755	−0.128021
$722$	−4.05128	−0.150773
$723$	8.14441	0.302894
$724$	1.39196	0.0517318
$725$	91.4992	3.39820
$726$	23.3177	0.865403
$727$	24.5615	0.910934	0.455467	−	0.890253i	$-0.349472\pi$
$727$	24.5615	0.910934	0.455467	+	0.890253i	$0.349472\pi$
$728$	5.49134	0.203522
$729$	19.9732	0.739747
$730$	50.3609	1.86394
$731$	3.39383	0.125525
$732$	7.88080	0.291283
$733$	−28.7795	−1.06299	−0.531497	−	0.847060i	$-0.678370\pi$
$733$	−28.7795	−1.06299	−0.531497	+	0.847060i	$0.678370\pi$
$734$	−29.6417	−1.09410
$735$	−17.9616	−0.662524
$736$	0.958939	0.0353470
$737$	−70.0532	−2.58044
$738$	13.5640	0.499296
$739$	−26.3164	−0.968065	−0.484032	−	0.875050i	$-0.660828\pi$
$739$	−26.3164	−0.968065	−0.484032	+	0.875050i	$0.660828\pi$
$740$	10.6152	0.390224
$741$	−16.2944	−0.598589
$742$	−16.9597	−0.622609
$743$	6.73834	0.247206	0.123603	−	0.992332i	$-0.460555\pi$
$743$	6.73834	0.247206	0.123603	+	0.992332i	$0.460555\pi$
$744$	−6.96729	−0.255433
$745$	−56.6855	−2.07680
$746$	33.1644	1.21424
$747$	18.1931	0.665652
$748$	5.61070	0.205148
$749$	−3.85459	−0.140844
$750$	−45.5116	−1.66185
$751$	−48.7968	−1.78062	−0.890311	−	0.455353i	$-0.849513\pi$
$751$	−48.7968	−1.78062	−0.890311	+	0.455353i	$0.849513\pi$
$752$	11.0783	0.403984
$753$	−0.581278	−0.0211830
$754$	19.2921	0.702578
$755$	−12.3132	−0.448124
$756$	9.86597	0.358822
$757$	−3.96605	−0.144148	−0.0720742	−	0.997399i	$-0.522962\pi$
$757$	−3.96605	−0.144148	−0.0720742	+	0.997399i	$0.522962\pi$
$758$	5.36191	0.194753
$759$	6.12584	0.222354
$760$	−21.0034	−0.761873
$761$	19.0792	0.691620	0.345810	−	0.938305i	$-0.387604\pi$
$761$	19.0792	0.691620	0.345810	+	0.938305i	$0.387604\pi$
$762$	−20.2043	−0.731926
$763$	−22.5217	−0.815341
$764$	0.470264	0.0170136
$765$	7.45294	0.269461
$766$	−4.75371	−0.171759
$767$	−2.98080	−0.107630
$768$	−1.13856	−0.0410844
$769$	48.1011	1.73457	0.867284	−	0.497813i	$-0.165863\pi$
$769$	48.1011	1.73457	0.867284	+	0.497813i	$0.165863\pi$
$770$	45.2172	1.62952
$771$	−32.2991	−1.16323
$772$	22.2138	0.799494
$773$	−33.3871	−1.20085	−0.600425	−	0.799681i	$-0.705002\pi$
$773$	−33.3871	−1.20085	−0.600425	+	0.799681i	$0.705002\pi$
$774$	5.78198	0.207829
$775$	−86.5119	−3.10760
$776$	4.40165	0.158010
$777$	5.08968	0.182591
$778$	−23.1581	−0.830258
$779$	−38.2250	−1.36955
$780$	−14.8468	−0.531600
$781$	3.26787	0.116934
$782$	0.958939	0.0342916
$783$	34.6611	1.23869
$784$	−3.60617	−0.128792
$785$	−62.8421	−2.24293
$786$	−5.90756	−0.210716
$787$	−34.7011	−1.23696	−0.618480	−	0.785801i	$-0.712251\pi$
$787$	−34.7011	−1.23696	−0.618480	+	0.785801i	$0.712251\pi$
$788$	−12.4703	−0.444235
$789$	27.5947	0.982398
$790$	−29.2028	−1.03899
$791$	−21.0399	−0.748093
$792$	9.55879	0.339657
$793$	20.6322	0.732671
$794$	−4.68829	−0.166381
$795$	45.8533	1.62625
$796$	−16.2530	−0.576071
$797$	29.4384	1.04276	0.521380	−	0.853324i	$-0.325417\pi$
$797$	29.4384	1.04276	0.521380	+	0.853324i	$0.325417\pi$
$798$	−10.0705	−0.356491
$799$	11.0783	0.391922
$800$	−14.1374	−0.499833
$801$	31.6488	1.11826
$802$	25.3554	0.895331
$803$	64.5906	2.27935
$804$	14.2157	0.501349
$805$	7.72819	0.272383
$806$	−18.2406	−0.642498
$807$	25.0340	0.881240
$808$	17.1695	0.604021
$809$	−14.6716	−0.515826	−0.257913	−	0.966168i	$-0.583035\pi$
$809$	−14.6716	−0.515826	−0.257913	+	0.966168i	$0.583035\pi$
$810$	−4.31553	−0.151632
$811$	−34.0824	−1.19679	−0.598397	−	0.801199i	$-0.704196\pi$
$811$	−34.0824	−1.19679	−0.598397	+	0.801199i	$0.704196\pi$
$812$	11.9232	0.418422
$813$	−29.4407	−1.03253
$814$	13.6146	0.477192
$815$	−1.54325	−0.0540576
$816$	−1.13856	−0.0398577
$817$	−16.2944	−0.570068
$818$	0.851214	0.0297620
$819$	9.35543	0.326905
$820$	−34.8291	−1.21628
$821$	−35.5519	−1.24077	−0.620384	−	0.784298i	$-0.713023\pi$
$821$	−35.5519	−1.24077	−0.620384	+	0.784298i	$0.713023\pi$
$822$	25.8316	0.900980
$823$	−32.4649	−1.13166	−0.565828	−	0.824523i	$-0.691443\pi$
$823$	−32.4649	−1.13166	−0.565828	+	0.824523i	$0.691443\pi$
$824$	1.86597	0.0650041
$825$	−90.3118	−3.14425
$826$	−1.84224	−0.0640996
$827$	−28.0246	−0.974511	−0.487256	−	0.873259i	$-0.662002\pi$
$827$	−28.0246	−0.974511	−0.487256	+	0.873259i	$0.662002\pi$
$828$	1.63372	0.0567756
$829$	25.0141	0.868777	0.434388	−	0.900726i	$-0.356965\pi$
$829$	25.0141	0.868777	0.434388	+	0.900726i	$0.356965\pi$
$830$	−46.7157	−1.62153
$831$	3.93645	0.136554
$832$	−2.98080	−0.103341
$833$	−3.60617	−0.124946
$834$	3.65613	0.126602
$835$	−26.0433	−0.901265
$836$	−26.9380	−0.931669
$837$	−32.7718	−1.13276
$838$	19.0523	0.658149
$839$	−31.5943	−1.09076	−0.545379	−	0.838190i	$-0.683614\pi$
$839$	−31.5943	−1.09076	−0.545379	+	0.838190i	$0.683614\pi$
$840$	−9.17581	−0.316595
$841$	12.8885	0.444433
$842$	−16.4472	−0.566810
$843$	−25.3649	−0.873615
$844$	−14.4754	−0.498265
$845$	18.0009	0.619249
$846$	18.8738	0.648894
$847$	37.7289	1.29638
$848$	9.20602	0.316136
$849$	−2.27794	−0.0781788
$850$	−14.1374	−0.484909
$851$	2.32691	0.0797654
$852$	−0.663140	−0.0227188
$853$	−12.2609	−0.419804	−0.209902	−	0.977722i	$-0.567315\pi$
$853$	−12.2609	−0.419804	−0.209902	+	0.977722i	$0.567315\pi$
$854$	12.7514	0.436344
$855$	−35.7829	−1.22375
$856$	2.09234	0.0715148
$857$	−16.1475	−0.551590	−0.275795	−	0.961217i	$-0.588941\pi$
$857$	−16.1475	−0.551590	−0.275795	+	0.961217i	$0.588941\pi$
$858$	−19.0418	−0.650076
$859$	6.72250	0.229369	0.114684	−	0.993402i	$-0.463414\pi$
$859$	6.72250	0.229369	0.114684	+	0.993402i	$0.463414\pi$
$860$	−14.8468	−0.506271
$861$	−16.6995	−0.569117
$862$	−5.61977	−0.191410
$863$	53.9453	1.83632	0.918160	−	0.396209i	$-0.129675\pi$
$863$	53.9453	1.83632	0.918160	+	0.396209i	$0.129675\pi$
$864$	−5.35543	−0.182196
$865$	86.4521	2.93946
$866$	−23.8360	−0.809981
$867$	−1.13856	−0.0386677
$868$	−11.2733	−0.382641
$869$	−37.4542	−1.27055
$870$	−32.2364	−1.09292
$871$	37.2172	1.26106
$872$	12.2252	0.413998
$873$	7.49897	0.253802
$874$	−4.60404	−0.155734
$875$	−73.6393	−2.48946
$876$	−13.1072	−0.442851
$877$	−19.0346	−0.642752	−0.321376	−	0.946952i	$-0.604145\pi$
$877$	−19.0346	−0.642752	−0.321376	+	0.946952i	$0.604145\pi$
$878$	25.4830	0.860009
$879$	28.8333	0.972522
$880$	−24.5448	−0.827403
$881$	−38.9766	−1.31316	−0.656578	−	0.754258i	$-0.727997\pi$
$881$	−38.9766	−1.31316	−0.656578	+	0.754258i	$0.727997\pi$
$882$	−6.14372	−0.206870
$883$	−16.9859	−0.571620	−0.285810	−	0.958286i	$-0.592263\pi$
$883$	−16.9859	−0.571620	−0.285810	+	0.958286i	$0.592263\pi$
$884$	−2.98080	−0.100255
$885$	4.98080	0.167428
$886$	10.0924	0.339062
$887$	7.62002	0.255855	0.127928	−	0.991783i	$-0.459167\pi$
$887$	7.62002	0.255855	0.127928	+	0.991783i	$0.459167\pi$
$888$	−2.76278	−0.0927127
$889$	−32.6913	−1.09643
$890$	−81.2668	−2.72407
$891$	−5.53490	−0.185426
$892$	2.87379	0.0962216
$893$	−53.1889	−1.77990
$894$	14.7533	0.493423
$895$	42.9108	1.43435
$896$	−1.84224	−0.0615448
$897$	−3.25448	−0.108664
$898$	10.4139	0.347517
$899$	−39.6054	−1.32091
$900$	−24.0855	−0.802850
$901$	9.20602	0.306697
$902$	−44.6702	−1.48735
$903$	−7.11858	−0.236891
$904$	11.4209	0.379852
$905$	−6.08931	−0.202416
$906$	3.20470	0.106469
$907$	13.7696	0.457213	0.228606	−	0.973519i	$-0.426583\pi$
$907$	13.7696	0.457213	0.228606	+	0.973519i	$0.426583\pi$
$908$	13.4830	0.447449
$909$	29.2512	0.970200
$910$	−24.0226	−0.796341
$911$	−17.3266	−0.574057	−0.287029	−	0.957922i	$-0.592667\pi$
$911$	−17.3266	−0.574057	−0.287029	+	0.957922i	$0.592667\pi$
$912$	5.46645	0.181012
$913$	−59.9154	−1.98291
$914$	−4.61655	−0.152702
$915$	−34.4756	−1.13973
$916$	−10.5813	−0.349615
$917$	−9.55863	−0.315654
$918$	−5.35543	−0.176756
$919$	14.4332	0.476107	0.238053	−	0.971252i	$-0.423491\pi$
$919$	14.4332	0.476107	0.238053	+	0.971252i	$0.423491\pi$
$920$	−4.19501	−0.138305
$921$	5.57290	0.183633
$922$	9.43755	0.310809
$923$	−1.73612	−0.0571452
$924$	−11.7685	−0.387154
$925$	−34.3050	−1.12794
$926$	−5.25474	−0.172681
$927$	3.17900	0.104412
$928$	−6.47214	−0.212458
$929$	18.1587	0.595769	0.297884	−	0.954602i	$-0.403719\pi$
$929$	18.1587	0.595769	0.297884	+	0.954602i	$0.403719\pi$
$930$	30.4793	0.999457
$931$	17.3138	0.567438
$932$	−4.86028	−0.159204
$933$	−4.46813	−0.146280
$934$	−9.89530	−0.323784
$935$	−24.5448	−0.802699
$936$	−5.07830	−0.165990
$937$	−15.1262	−0.494152	−0.247076	−	0.968996i	$-0.579470\pi$
$937$	−15.1262	−0.494152	−0.247076	+	0.968996i	$0.579470\pi$
$938$	23.0015	0.751026
$939$	14.3693	0.468925
$940$	−48.4635	−1.58071
$941$	−4.52779	−0.147602	−0.0738009	−	0.997273i	$-0.523513\pi$
$941$	−4.52779	−0.147602	−0.0738009	+	0.997273i	$0.523513\pi$
$942$	16.3556	0.532895
$943$	−7.63469	−0.248620
$944$	1.00000	0.0325472
$945$	−43.1600	−1.40399
$946$	−19.0418	−0.619102
$947$	−0.698069	−0.0226842	−0.0113421	−	0.999936i	$-0.503610\pi$
$947$	−0.698069	−0.0226842	−0.0113421	+	0.999936i	$0.503610\pi$
$948$	7.60048	0.246852
$949$	−34.3151	−1.11391
$950$	67.8762	2.20219
$951$	12.5235	0.406102
$952$	−1.84224	−0.0597072
$953$	45.3250	1.46822	0.734111	−	0.679029i	$-0.237599\pi$
$953$	45.3250	1.46822	0.734111	+	0.679029i	$0.237599\pi$
$954$	15.6840	0.507789
$955$	−2.05723	−0.0665704
$956$	−16.0342	−0.518584
$957$	−41.3449	−1.33649
$958$	37.5470	1.21309
$959$	41.7964	1.34967
$960$	4.98080	0.160755
$961$	6.44662	0.207955
$962$	−7.23304	−0.233203
$963$	3.56467	0.114870
$964$	−7.15323	−0.230390
$965$	−97.1774	−3.12825
$966$	−2.01138	−0.0647151
$967$	33.4627	1.07609	0.538044	−	0.842917i	$-0.319163\pi$
$967$	33.4627	1.07609	0.538044	+	0.842917i	$0.319163\pi$
$968$	−20.4800	−0.658251
$969$	5.46645	0.175608
$970$	−19.2556	−0.618261
$971$	−40.6421	−1.30427	−0.652134	−	0.758104i	$-0.726126\pi$
$971$	−40.6421	−1.30427	−0.652134	+	0.758104i	$0.726126\pi$
$972$	−14.9431	−0.479301
$973$	5.91575	0.189650
$974$	−15.9265	−0.510318
$975$	47.9800	1.53659
$976$	−6.92170	−0.221558
$977$	17.1456	0.548536	0.274268	−	0.961653i	$-0.411564\pi$
$977$	17.1456	0.548536	0.274268	+	0.961653i	$0.411564\pi$
$978$	0.401653	0.0128435
$979$	−104.229	−3.33117
$980$	15.7757	0.503935
$981$	20.8278	0.664979
$982$	−9.33499	−0.297891
$983$	58.7304	1.87321	0.936605	−	0.350388i	$-0.113950\pi$
$983$	58.7304	1.87321	0.936605	+	0.350388i	$0.113950\pi$
$984$	9.06479	0.288975
$985$	54.5528	1.73820
$986$	−6.47214	−0.206115
$987$	−23.2368	−0.739635
$988$	14.3113	0.455304
$989$	−3.25448	−0.103486
$990$	−41.8162	−1.32901
$991$	−19.5595	−0.621328	−0.310664	−	0.950520i	$-0.600551\pi$
$991$	−19.5595	−0.621328	−0.310664	+	0.950520i	$0.600551\pi$
$992$	6.11936	0.194290
$993$	−11.4967	−0.364835
$994$	−1.07298	−0.0340329
$995$	71.1007	2.25404
$996$	12.1585	0.385256
$997$	−5.70011	−0.180524	−0.0902622	−	0.995918i	$-0.528771\pi$
$997$	−5.70011	−0.180524	−0.0902622	+	0.995918i	$0.528771\pi$
$998$	−22.6818	−0.717980
$999$	−12.9952	−0.411149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.p.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.p.1.2	✓	4	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.13856 q^{3} +1.00000 q^{4} -4.37463 q^{5} +1.13856 q^{6} +1.84224 q^{7} -1.00000 q^{8} -1.70367 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.13856 q^{3} +1.00000 q^{4} -4.37463 q^{5} +1.13856 q^{6} +1.84224 q^{7} -1.00000 q^{8} -1.70367 q^{9} +4.37463 q^{10} +5.61070 q^{11} -1.13856 q^{12} -2.98080 q^{13} -1.84224 q^{14} +4.98080 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.70367 q^{18} -4.80118 q^{19} -4.37463 q^{20} -2.09750 q^{21} -5.61070 q^{22} -0.958939 q^{23} +1.13856 q^{24} +14.1374 q^{25} +2.98080 q^{26} +5.35543 q^{27} +1.84224 q^{28} +6.47214 q^{29} -4.98080 q^{30} -6.11936 q^{31} -1.00000 q^{32} -6.38814 q^{33} -1.00000 q^{34} -8.05910 q^{35} -1.70367 q^{36} -2.42654 q^{37} +4.80118 q^{38} +3.39383 q^{39} +4.37463 q^{40} +7.96160 q^{41} +2.09750 q^{42} +3.39383 q^{43} +5.61070 q^{44} +7.45294 q^{45} +0.958939 q^{46} +11.0783 q^{47} -1.13856 q^{48} -3.60617 q^{49} -14.1374 q^{50} -1.13856 q^{51} -2.98080 q^{52} +9.20602 q^{53} -5.35543 q^{54} -24.5448 q^{55} -1.84224 q^{56} +5.46645 q^{57} -6.47214 q^{58} +1.00000 q^{59} +4.98080 q^{60} -6.92170 q^{61} +6.11936 q^{62} -3.13856 q^{63} +1.00000 q^{64} +13.0399 q^{65} +6.38814 q^{66} -12.4856 q^{67} +1.00000 q^{68} +1.09181 q^{69} +8.05910 q^{70} +0.582435 q^{71} +1.70367 q^{72} +11.5120 q^{73} +2.42654 q^{74} -16.0963 q^{75} -4.80118 q^{76} +10.3362 q^{77} -3.39383 q^{78} -6.67549 q^{79} -4.37463 q^{80} -0.986489 q^{81} -7.96160 q^{82} -10.6788 q^{83} -2.09750 q^{84} -4.37463 q^{85} -3.39383 q^{86} -7.36894 q^{87} -5.61070 q^{88} -18.5768 q^{89} -7.45294 q^{90} -5.49134 q^{91} -0.958939 q^{92} +6.96729 q^{93} -11.0783 q^{94} +21.0034 q^{95} +1.13856 q^{96} -4.40165 q^{97} +3.60617 q^{98} -9.55879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - q^{3} + 4 q^{4} - 5 q^{5} + q^{6} - 2 q^{7} - 4 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - q^3 + 4 * q^4 - 5 * q^5 + q^6 - 2 * q^7 - 4 * q^8 - q^9	\( 4 q - 4 q^{2} - q^{3} + 4 q^{4} - 5 q^{5} + q^{6} - 2 q^{7} - 4 q^{8} - q^{9} + 5 q^{10} + q^{11} - q^{12} + q^{13} + 2 q^{14} + 7 q^{15} + 4 q^{16} + 4 q^{17} + q^{18} - 8 q^{19} - 5 q^{20} - 3 q^{21} - q^{22} - 2 q^{23} + q^{24} + 7 q^{25} - q^{26} - 4 q^{27} - 2 q^{28} + 8 q^{29} - 7 q^{30} - 8 q^{31} - 4 q^{32} - q^{33} - 4 q^{34} - q^{35} - q^{36} - 11 q^{37} + 8 q^{38} + 14 q^{39} + 5 q^{40} + 6 q^{41} + 3 q^{42} + 14 q^{43} + q^{44} - q^{45} + 2 q^{46} + 26 q^{47} - q^{48} - 14 q^{49} - 7 q^{50} - q^{51} + q^{52} + 3 q^{53} + 4 q^{54} - 37 q^{55} + 2 q^{56} - 21 q^{57} - 8 q^{58} + 4 q^{59} + 7 q^{60} - 46 q^{61} + 8 q^{62} - 9 q^{63} + 4 q^{64} + 8 q^{65} + q^{66} - 20 q^{67} + 4 q^{68} - 26 q^{69} + q^{70} + 10 q^{71} + q^{72} - 16 q^{73} + 11 q^{74} - 13 q^{75} - 8 q^{76} + 3 q^{77} - 14 q^{78} + q^{79} - 5 q^{80} - 16 q^{81} - 6 q^{82} + q^{83} - 3 q^{84} - 5 q^{85} - 14 q^{86} + 8 q^{87} - q^{88} - 6 q^{89} + q^{90} - 17 q^{91} - 2 q^{92} + 27 q^{93} - 26 q^{94} + 17 q^{95} + q^{96} + 19 q^{97} + 14 q^{98} - 3 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - q^3 + 4 * q^4 - 5 * q^5 + q^6 - 2 * q^7 - 4 * q^8 - q^9 + 5 * q^10 + q^11 - q^12 + q^13 + 2 * q^14 + 7 * q^15 + 4 * q^16 + 4 * q^17 + q^18 - 8 * q^19 - 5 * q^20 - 3 * q^21 - q^22 - 2 * q^23 + q^24 + 7 * q^25 - q^26 - 4 * q^27 - 2 * q^28 + 8 * q^29 - 7 * q^30 - 8 * q^31 - 4 * q^32 - q^33 - 4 * q^34 - q^35 - q^36 - 11 * q^37 + 8 * q^38 + 14 * q^39 + 5 * q^40 + 6 * q^41 + 3 * q^42 + 14 * q^43 + q^44 - q^45 + 2 * q^46 + 26 * q^47 - q^48 - 14 * q^49 - 7 * q^50 - q^51 + q^52 + 3 * q^53 + 4 * q^54 - 37 * q^55 + 2 * q^56 - 21 * q^57 - 8 * q^58 + 4 * q^59 + 7 * q^60 - 46 * q^61 + 8 * q^62 - 9 * q^63 + 4 * q^64 + 8 * q^65 + q^66 - 20 * q^67 + 4 * q^68 - 26 * q^69 + q^70 + 10 * q^71 + q^72 - 16 * q^73 + 11 * q^74 - 13 * q^75 - 8 * q^76 + 3 * q^77 - 14 * q^78 + q^79 - 5 * q^80 - 16 * q^81 - 6 * q^82 + q^83 - 3 * q^84 - 5 * q^85 - 14 * q^86 + 8 * q^87 - q^88 - 6 * q^89 + q^90 - 17 * q^91 - 2 * q^92 + 27 * q^93 - 26 * q^94 + 17 * q^95 + q^96 + 19 * q^97 + 14 * q^98 - 3 * q^99

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