LMFDB - Embedded newform 2006.2.a.w.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:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 6 x^{12} - 9 x^{11} + 91 x^{10} + 14 x^{9} - 517 x^{8} + 70 x^{7} + 1296 x^{6} - 300 x^{5} + \cdots + 16 $ x^13 - 6x^12 - 9x^11 + 91x^10 + 14x^9 - 517x^8 + 70x^7 + 1296x^6 - 300x^5 - 1312x^4 + 472x^3 + 368x^2 - 176x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.13025$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.13025 q^{3} +1.00000 q^{4} -0.954710 q^{5} -2.13025 q^{6} -2.87838 q^{7} +1.00000 q^{8} +1.53797 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.13025 q^{3} +1.00000 q^{4} -0.954710 q^{5} -2.13025 q^{6} -2.87838 q^{7} +1.00000 q^{8} +1.53797 q^{9} -0.954710 q^{10} -2.38271 q^{11} -2.13025 q^{12} -5.49266 q^{13} -2.87838 q^{14} +2.03377 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.53797 q^{18} -1.53697 q^{19} -0.954710 q^{20} +6.13167 q^{21} -2.38271 q^{22} +7.94790 q^{23} -2.13025 q^{24} -4.08853 q^{25} -5.49266 q^{26} +3.11450 q^{27} -2.87838 q^{28} +7.87482 q^{29} +2.03377 q^{30} +6.99757 q^{31} +1.00000 q^{32} +5.07577 q^{33} +1.00000 q^{34} +2.74802 q^{35} +1.53797 q^{36} -9.30103 q^{37} -1.53697 q^{38} +11.7007 q^{39} -0.954710 q^{40} +8.04385 q^{41} +6.13167 q^{42} -8.40965 q^{43} -2.38271 q^{44} -1.46831 q^{45} +7.94790 q^{46} +8.53547 q^{47} -2.13025 q^{48} +1.28507 q^{49} -4.08853 q^{50} -2.13025 q^{51} -5.49266 q^{52} +1.04754 q^{53} +3.11450 q^{54} +2.27480 q^{55} -2.87838 q^{56} +3.27412 q^{57} +7.87482 q^{58} +1.00000 q^{59} +2.03377 q^{60} -0.376722 q^{61} +6.99757 q^{62} -4.42685 q^{63} +1.00000 q^{64} +5.24390 q^{65} +5.07577 q^{66} -9.41144 q^{67} +1.00000 q^{68} -16.9310 q^{69} +2.74802 q^{70} -4.73931 q^{71} +1.53797 q^{72} +11.4588 q^{73} -9.30103 q^{74} +8.70959 q^{75} -1.53697 q^{76} +6.85835 q^{77} +11.7007 q^{78} +12.4143 q^{79} -0.954710 q^{80} -11.2486 q^{81} +8.04385 q^{82} +8.15569 q^{83} +6.13167 q^{84} -0.954710 q^{85} -8.40965 q^{86} -16.7753 q^{87} -2.38271 q^{88} -2.60510 q^{89} -1.46831 q^{90} +15.8100 q^{91} +7.94790 q^{92} -14.9066 q^{93} +8.53547 q^{94} +1.46736 q^{95} -2.13025 q^{96} -3.38636 q^{97} +1.28507 q^{98} -3.66453 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9	\( 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9} + q^{10} + 13 q^{11} + 7 q^{12} + 9 q^{13} + 8 q^{14} - 9 q^{15} + 13 q^{16} + 13 q^{17} + 16 q^{18} + 16 q^{19} + q^{20} - 3 q^{21} + 13 q^{22} + 18 q^{23} + 7 q^{24} + 14 q^{25} + 9 q^{26} + 10 q^{27} + 8 q^{28} + 8 q^{29} - 9 q^{30} + 32 q^{31} + 13 q^{32} + 13 q^{33} + 13 q^{34} - q^{35} + 16 q^{36} - 3 q^{37} + 16 q^{38} + 20 q^{39} + q^{40} + 24 q^{41} - 3 q^{42} - 2 q^{43} + 13 q^{44} - 3 q^{45} + 18 q^{46} + 26 q^{47} + 7 q^{48} + 23 q^{49} + 14 q^{50} + 7 q^{51} + 9 q^{52} - 27 q^{53} + 10 q^{54} - 7 q^{55} + 8 q^{56} - 21 q^{57} + 8 q^{58} + 13 q^{59} - 9 q^{60} + 20 q^{61} + 32 q^{62} - 3 q^{63} + 13 q^{64} + 16 q^{65} + 13 q^{66} + 4 q^{67} + 13 q^{68} - 2 q^{69} - q^{70} - 8 q^{71} + 16 q^{72} + 10 q^{73} - 3 q^{74} + 39 q^{75} + 16 q^{76} - 15 q^{77} + 20 q^{78} + 35 q^{79} + q^{80} + 29 q^{81} + 24 q^{82} - q^{83} - 3 q^{84} + q^{85} - 2 q^{86} - 32 q^{87} + 13 q^{88} - 20 q^{89} - 3 q^{90} - 15 q^{91} + 18 q^{92} - 7 q^{93} + 26 q^{94} - 3 q^{95} + 7 q^{96} - 3 q^{97} + 23 q^{98} + 65 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9 + q^10 + 13 * q^11 + 7 * q^12 + 9 * q^13 + 8 * q^14 - 9 * q^15 + 13 * q^16 + 13 * q^17 + 16 * q^18 + 16 * q^19 + q^20 - 3 * q^21 + 13 * q^22 + 18 * q^23 + 7 * q^24 + 14 * q^25 + 9 * q^26 + 10 * q^27 + 8 * q^28 + 8 * q^29 - 9 * q^30 + 32 * q^31 + 13 * q^32 + 13 * q^33 + 13 * q^34 - q^35 + 16 * q^36 - 3 * q^37 + 16 * q^38 + 20 * q^39 + q^40 + 24 * q^41 - 3 * q^42 - 2 * q^43 + 13 * q^44 - 3 * q^45 + 18 * q^46 + 26 * q^47 + 7 * q^48 + 23 * q^49 + 14 * q^50 + 7 * q^51 + 9 * q^52 - 27 * q^53 + 10 * q^54 - 7 * q^55 + 8 * q^56 - 21 * q^57 + 8 * q^58 + 13 * q^59 - 9 * q^60 + 20 * q^61 + 32 * q^62 - 3 * q^63 + 13 * q^64 + 16 * q^65 + 13 * q^66 + 4 * q^67 + 13 * q^68 - 2 * q^69 - q^70 - 8 * q^71 + 16 * q^72 + 10 * q^73 - 3 * q^74 + 39 * q^75 + 16 * q^76 - 15 * q^77 + 20 * q^78 + 35 * q^79 + q^80 + 29 * q^81 + 24 * q^82 - q^83 - 3 * q^84 + q^85 - 2 * q^86 - 32 * q^87 + 13 * q^88 - 20 * q^89 - 3 * q^90 - 15 * q^91 + 18 * q^92 - 7 * q^93 + 26 * q^94 - 3 * q^95 + 7 * q^96 - 3 * q^97 + 23 * q^98 + 65 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.13025	−1.22990	−0.614950	−	0.788566i	$-0.710824\pi$
$3$	−2.13025	−1.22990	−0.614950	+	0.788566i	$0.710824\pi$
$4$	1.00000	0.500000
$5$	−0.954710	−0.426959	−0.213480	−	0.976948i	$-0.568480\pi$
$5$	−0.954710	−0.426959	−0.213480	+	0.976948i	$0.568480\pi$
$6$	−2.13025	−0.869671
$7$	−2.87838	−1.08793	−0.543963	−	0.839109i	$-0.683077\pi$
$7$	−2.87838	−1.08793	−0.543963	+	0.839109i	$0.683077\pi$
$8$	1.00000	0.353553
$9$	1.53797	0.512655
$10$	−0.954710	−0.301906
$11$	−2.38271	−0.718415	−0.359207	−	0.933258i	$-0.616953\pi$
$11$	−2.38271	−0.718415	−0.359207	+	0.933258i	$0.616953\pi$
$12$	−2.13025	−0.614950
$13$	−5.49266	−1.52339	−0.761695	−	0.647935i	$-0.775633\pi$
$13$	−5.49266	−1.52339	−0.761695	+	0.647935i	$0.775633\pi$
$14$	−2.87838	−0.769279
$15$	2.03377	0.525117
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.53797	0.362502
$19$	−1.53697	−0.352604	−0.176302	−	0.984336i	$-0.556414\pi$
$19$	−1.53697	−0.352604	−0.176302	+	0.984336i	$0.556414\pi$
$20$	−0.954710	−0.213480
$21$	6.13167	1.33804
$22$	−2.38271	−0.507996
$23$	7.94790	1.65725	0.828625	−	0.559803i	$-0.189123\pi$
$23$	7.94790	1.65725	0.828625	+	0.559803i	$0.189123\pi$
$24$	−2.13025	−0.434835
$25$	−4.08853	−0.817706
$26$	−5.49266	−1.07720
$27$	3.11450	0.599386
$28$	−2.87838	−0.543963
$29$	7.87482	1.46232	0.731159	−	0.682208i	$-0.238980\pi$
$29$	7.87482	1.46232	0.731159	+	0.682208i	$0.238980\pi$
$30$	2.03377	0.371314
$31$	6.99757	1.25680	0.628401	−	0.777890i	$-0.283710\pi$
$31$	6.99757	1.25680	0.628401	+	0.777890i	$0.283710\pi$
$32$	1.00000	0.176777
$33$	5.07577	0.883579
$34$	1.00000	0.171499
$35$	2.74802	0.464500
$36$	1.53797	0.256328
$37$	−9.30103	−1.52908	−0.764540	−	0.644576i	$-0.777034\pi$
$37$	−9.30103	−1.52908	−0.764540	+	0.644576i	$0.777034\pi$
$38$	−1.53697	−0.249329
$39$	11.7007	1.87362
$40$	−0.954710	−0.150953
$41$	8.04385	1.25624	0.628119	−	0.778117i	$-0.283825\pi$
$41$	8.04385	1.25624	0.628119	+	0.778117i	$0.283825\pi$
$42$	6.13167	0.946137
$43$	−8.40965	−1.28246	−0.641230	−	0.767349i	$-0.721575\pi$
$43$	−8.40965	−1.28246	−0.641230	+	0.767349i	$0.721575\pi$
$44$	−2.38271	−0.359207
$45$	−1.46831	−0.218883
$46$	7.94790	1.17185
$47$	8.53547	1.24503	0.622513	−	0.782609i	$-0.286112\pi$
$47$	8.53547	1.24503	0.622513	+	0.782609i	$0.286112\pi$
$48$	−2.13025	−0.307475
$49$	1.28507	0.183581
$50$	−4.08853	−0.578205
$51$	−2.13025	−0.298295
$52$	−5.49266	−0.761695
$53$	1.04754	0.143890	0.0719450	−	0.997409i	$-0.477079\pi$
$53$	1.04754	0.143890	0.0719450	+	0.997409i	$0.477079\pi$
$54$	3.11450	0.423830
$55$	2.27480	0.306734
$56$	−2.87838	−0.384640
$57$	3.27412	0.433668
$58$	7.87482	1.03401
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	2.03377	0.262559
$61$	−0.376722	−0.0482343	−0.0241171	−	0.999709i	$-0.507677\pi$
$61$	−0.376722	−0.0482343	−0.0241171	+	0.999709i	$0.507677\pi$
$62$	6.99757	0.888693
$63$	−4.42685	−0.557730
$64$	1.00000	0.125000
$65$	5.24390	0.650426
$66$	5.07577	0.624784
$67$	−9.41144	−1.14979	−0.574895	−	0.818227i	$-0.694957\pi$
$67$	−9.41144	−1.14979	−0.574895	+	0.818227i	$0.694957\pi$
$68$	1.00000	0.121268
$69$	−16.9310	−2.03825
$70$	2.74802	0.328451
$71$	−4.73931	−0.562452	−0.281226	−	0.959642i	$-0.590741\pi$
$71$	−4.73931	−0.562452	−0.281226	+	0.959642i	$0.590741\pi$
$72$	1.53797	0.181251
$73$	11.4588	1.34115	0.670576	−	0.741841i	$-0.266047\pi$
$73$	11.4588	1.34115	0.670576	+	0.741841i	$0.266047\pi$
$74$	−9.30103	−1.08122
$75$	8.70959	1.00570
$76$	−1.53697	−0.176302
$77$	6.85835	0.781581
$78$	11.7007	1.32485
$79$	12.4143	1.39672	0.698361	−	0.715746i	$-0.253913\pi$
$79$	12.4143	1.39672	0.698361	+	0.715746i	$0.253913\pi$
$80$	−0.954710	−0.106740
$81$	−11.2486	−1.24984
$82$	8.04385	0.888294
$83$	8.15569	0.895204	0.447602	−	0.894233i	$-0.352278\pi$
$83$	8.15569	0.895204	0.447602	+	0.894233i	$0.352278\pi$
$84$	6.13167	0.669020
$85$	−0.954710	−0.103553
$86$	−8.40965	−0.906836
$87$	−16.7753	−1.79850
$88$	−2.38271	−0.253998
$89$	−2.60510	−0.276140	−0.138070	−	0.990422i	$-0.544090\pi$
$89$	−2.60510	−0.276140	−0.138070	+	0.990422i	$0.544090\pi$
$90$	−1.46831	−0.154774
$91$	15.8100	1.65734
$92$	7.94790	0.828625
$93$	−14.9066	−1.54574
$94$	8.53547	0.880366
$95$	1.46736	0.150548
$96$	−2.13025	−0.217418
$97$	−3.38636	−0.343832	−0.171916	−	0.985112i	$-0.554996\pi$
$97$	−3.38636	−0.343832	−0.171916	+	0.985112i	$0.554996\pi$
$98$	1.28507	0.129811
$99$	−3.66453	−0.368299
$100$	−4.08853	−0.408853
$101$	7.67081	0.763274	0.381637	−	0.924312i	$-0.375360\pi$
$101$	7.67081	0.763274	0.381637	+	0.924312i	$0.375360\pi$
$102$	−2.13025	−0.210926
$103$	8.76198	0.863344	0.431672	−	0.902031i	$-0.357924\pi$
$103$	8.76198	0.863344	0.431672	+	0.902031i	$0.357924\pi$
$104$	−5.49266	−0.538600
$105$	−5.85396	−0.571288
$106$	1.04754	0.101746
$107$	6.47543	0.626004	0.313002	−	0.949753i	$-0.398665\pi$
$107$	6.47543	0.626004	0.313002	+	0.949753i	$0.398665\pi$
$108$	3.11450	0.299693
$109$	8.79441	0.842351	0.421176	−	0.906979i	$-0.361618\pi$
$109$	8.79441	0.842351	0.421176	+	0.906979i	$0.361618\pi$
$110$	2.27480	0.216894
$111$	19.8135	1.88062
$112$	−2.87838	−0.271981
$113$	−18.8136	−1.76983	−0.884916	−	0.465751i	$-0.845784\pi$
$113$	−18.8136	−1.76983	−0.884916	+	0.465751i	$0.845784\pi$
$114$	3.27412	0.306650
$115$	−7.58794	−0.707579
$116$	7.87482	0.731159
$117$	−8.44753	−0.780974
$118$	1.00000	0.0920575
$119$	−2.87838	−0.263861
$120$	2.03377	0.185657
$121$	−5.32268	−0.483880
$122$	−0.376722	−0.0341068
$123$	−17.1354	−1.54505
$124$	6.99757	0.628401
$125$	8.67691	0.776086
$126$	−4.42685	−0.394375
$127$	7.80925	0.692959	0.346480	−	0.938058i	$-0.387377\pi$
$127$	7.80925	0.692959	0.346480	+	0.938058i	$0.387377\pi$
$128$	1.00000	0.0883883
$129$	17.9147	1.57730
$130$	5.24390	0.459921
$131$	4.89424	0.427612	0.213806	−	0.976876i	$-0.431414\pi$
$131$	4.89424	0.427612	0.213806	+	0.976876i	$0.431414\pi$
$132$	5.07577	0.441789
$133$	4.42397	0.383607
$134$	−9.41144	−0.813025
$135$	−2.97344	−0.255913
$136$	1.00000	0.0857493
$137$	8.85228	0.756302	0.378151	−	0.925744i	$-0.376560\pi$
$137$	8.85228	0.756302	0.378151	+	0.925744i	$0.376560\pi$
$138$	−16.9310	−1.44126
$139$	15.4471	1.31020	0.655102	−	0.755540i	$-0.272626\pi$
$139$	15.4471	1.31020	0.655102	+	0.755540i	$0.272626\pi$
$140$	2.74802	0.232250
$141$	−18.1827	−1.53126
$142$	−4.73931	−0.397714
$143$	13.0874	1.09443
$144$	1.53797	0.128164
$145$	−7.51817	−0.624350
$146$	11.4588	0.948337
$147$	−2.73751	−0.225786
$148$	−9.30103	−0.764540
$149$	−18.8093	−1.54092	−0.770461	−	0.637487i	$-0.779974\pi$
$149$	−18.8093	−1.54092	−0.770461	+	0.637487i	$0.779974\pi$
$150$	8.70959	0.711135
$151$	17.3165	1.40920	0.704598	−	0.709607i	$-0.251128\pi$
$151$	17.3165	1.40920	0.704598	+	0.709607i	$0.251128\pi$
$152$	−1.53697	−0.124664
$153$	1.53797	0.124337
$154$	6.85835	0.552661
$155$	−6.68065	−0.536603
$156$	11.7007	0.936810
$157$	5.43540	0.433792	0.216896	−	0.976195i	$-0.430407\pi$
$157$	5.43540	0.433792	0.216896	+	0.976195i	$0.430407\pi$
$158$	12.4143	0.987631
$159$	−2.23151	−0.176970
$160$	−0.954710	−0.0754765
$161$	−22.8771	−1.80296
$162$	−11.2486	−0.883770
$163$	6.73914	0.527850	0.263925	−	0.964543i	$-0.414983\pi$
$163$	6.73914	0.527850	0.263925	+	0.964543i	$0.414983\pi$
$164$	8.04385	0.628119
$165$	−4.84589	−0.377252
$166$	8.15569	0.633004
$167$	4.17107	0.322767	0.161384	−	0.986892i	$-0.448404\pi$
$167$	4.17107	0.322767	0.161384	+	0.986892i	$0.448404\pi$
$168$	6.13167	0.473068
$169$	17.1694	1.32072
$170$	−0.954710	−0.0732229
$171$	−2.36380	−0.180764
$172$	−8.40965	−0.641230
$173$	−1.86060	−0.141459	−0.0707293	−	0.997496i	$-0.522533\pi$
$173$	−1.86060	−0.141459	−0.0707293	+	0.997496i	$0.522533\pi$
$174$	−16.7753	−1.27173
$175$	11.7683	0.889603
$176$	−2.38271	−0.179604
$177$	−2.13025	−0.160119
$178$	−2.60510	−0.195261
$179$	3.65963	0.273534	0.136767	−	0.990603i	$-0.456329\pi$
$179$	3.65963	0.273534	0.136767	+	0.990603i	$0.456329\pi$
$180$	−1.46831	−0.109441
$181$	6.49672	0.482898	0.241449	−	0.970414i	$-0.422377\pi$
$181$	6.49672	0.482898	0.241449	+	0.970414i	$0.422377\pi$
$182$	15.8100	1.17191
$183$	0.802512	0.0593234
$184$	7.94790	0.585927
$185$	8.87979	0.652855
$186$	−14.9066	−1.09300
$187$	−2.38271	−0.174241
$188$	8.53547	0.622513
$189$	−8.96471	−0.652087
$190$	1.46736	0.106453
$191$	16.2585	1.17642	0.588210	−	0.808708i	$-0.299833\pi$
$191$	16.2585	1.17642	0.588210	+	0.808708i	$0.299833\pi$
$192$	−2.13025	−0.153738
$193$	−18.6409	−1.34180	−0.670902	−	0.741546i	$-0.734093\pi$
$193$	−18.6409	−1.34180	−0.670902	+	0.741546i	$0.734093\pi$
$194$	−3.38636	−0.243126
$195$	−11.1708	−0.799959
$196$	1.28507	0.0917905
$197$	−27.7360	−1.97611	−0.988054	−	0.154110i	$-0.950749\pi$
$197$	−27.7360	−1.97611	−0.988054	+	0.154110i	$0.950749\pi$
$198$	−3.66453	−0.260427
$199$	2.11908	0.150218	0.0751088	−	0.997175i	$-0.476070\pi$
$199$	2.11908	0.150218	0.0751088	+	0.997175i	$0.476070\pi$
$200$	−4.08853	−0.289103
$201$	20.0487	1.41413
$202$	7.67081	0.539716
$203$	−22.6667	−1.59089
$204$	−2.13025	−0.149147
$205$	−7.67954	−0.536362
$206$	8.76198	0.610476
$207$	12.2236	0.849598
$208$	−5.49266	−0.380848
$209$	3.66215	0.253316
$210$	−5.85396	−0.403962
$211$	−9.17407	−0.631569	−0.315784	−	0.948831i	$-0.602268\pi$
$211$	−9.17407	−0.631569	−0.315784	+	0.948831i	$0.602268\pi$
$212$	1.04754	0.0719450
$213$	10.0959	0.691760
$214$	6.47543	0.442651
$215$	8.02878	0.547558
$216$	3.11450	0.211915
$217$	−20.1417	−1.36731
$218$	8.79441	0.595632
$219$	−24.4101	−1.64948
$220$	2.27480	0.153367
$221$	−5.49266	−0.369477
$222$	19.8135	1.32980
$223$	−21.7882	−1.45905	−0.729524	−	0.683956i	$-0.760258\pi$
$223$	−21.7882	−1.45905	−0.729524	+	0.683956i	$0.760258\pi$
$224$	−2.87838	−0.192320
$225$	−6.28802	−0.419201
$226$	−18.8136	−1.25146
$227$	−21.9873	−1.45935	−0.729675	−	0.683794i	$-0.760328\pi$
$227$	−21.9873	−1.45935	−0.729675	+	0.683794i	$0.760328\pi$
$228$	3.27412	0.216834
$229$	2.11697	0.139893	0.0699467	−	0.997551i	$-0.477717\pi$
$229$	2.11697	0.139893	0.0699467	+	0.997551i	$0.477717\pi$
$230$	−7.58794	−0.500334
$231$	−14.6100	−0.961267
$232$	7.87482	0.517007
$233$	−1.19201	−0.0780911	−0.0390456	−	0.999237i	$-0.512432\pi$
$233$	−1.19201	−0.0780911	−0.0390456	+	0.999237i	$0.512432\pi$
$234$	−8.44753	−0.552232
$235$	−8.14890	−0.531575
$236$	1.00000	0.0650945
$237$	−26.4456	−1.71783
$238$	−2.87838	−0.186578
$239$	6.66122	0.430879	0.215439	−	0.976517i	$-0.430882\pi$
$239$	6.66122	0.430879	0.215439	+	0.976517i	$0.430882\pi$
$240$	2.03377	0.131279
$241$	−14.1123	−0.909052	−0.454526	−	0.890733i	$-0.650191\pi$
$241$	−14.1123	−0.909052	−0.454526	+	0.890733i	$0.650191\pi$
$242$	−5.32268	−0.342155
$243$	14.6187	0.937793
$244$	−0.376722	−0.0241171
$245$	−1.22687	−0.0783816
$246$	−17.1354	−1.09251
$247$	8.44204	0.537154
$248$	6.99757	0.444346
$249$	−17.3737	−1.10101
$250$	8.67691	0.548776
$251$	−1.47976	−0.0934018	−0.0467009	−	0.998909i	$-0.514871\pi$
$251$	−1.47976	−0.0934018	−0.0467009	+	0.998909i	$0.514871\pi$
$252$	−4.42685	−0.278865
$253$	−18.9375	−1.19059
$254$	7.80925	0.489996
$255$	2.03377	0.127360
$256$	1.00000	0.0625000
$257$	28.0271	1.74828	0.874141	−	0.485672i	$-0.161425\pi$
$257$	28.0271	1.74828	0.874141	+	0.485672i	$0.161425\pi$
$258$	17.9147	1.11532
$259$	26.7719	1.66352
$260$	5.24390	0.325213
$261$	12.1112	0.749664
$262$	4.89424	0.302367
$263$	−29.4361	−1.81511	−0.907555	−	0.419933i	$-0.862053\pi$
$263$	−29.4361	−1.81511	−0.907555	+	0.419933i	$0.862053\pi$
$264$	5.07577	0.312392
$265$	−1.00009	−0.0614352
$266$	4.42397	0.271251
$267$	5.54952	0.339625
$268$	−9.41144	−0.574895
$269$	2.79321	0.170305	0.0851525	−	0.996368i	$-0.472862\pi$
$269$	2.79321	0.170305	0.0851525	+	0.996368i	$0.472862\pi$
$270$	−2.97344	−0.180958
$271$	−26.0587	−1.58296	−0.791478	−	0.611198i	$-0.790688\pi$
$271$	−26.0587	−1.58296	−0.791478	+	0.611198i	$0.790688\pi$
$272$	1.00000	0.0606339
$273$	−33.6792	−2.03836
$274$	8.85228	0.534786
$275$	9.74179	0.587452
$276$	−16.9310	−1.01913
$277$	10.0227	0.602203	0.301102	−	0.953592i	$-0.402646\pi$
$277$	10.0227	0.602203	0.301102	+	0.953592i	$0.402646\pi$
$278$	15.4471	0.926454
$279$	10.7620	0.644306
$280$	2.74802	0.164225
$281$	−1.21027	−0.0721987	−0.0360994	−	0.999348i	$-0.511493\pi$
$281$	−1.21027	−0.0721987	−0.0360994	+	0.999348i	$0.511493\pi$
$282$	−18.1827	−1.08276
$283$	9.04546	0.537697	0.268848	−	0.963183i	$-0.413357\pi$
$283$	9.04546	0.537697	0.268848	+	0.963183i	$0.413357\pi$
$284$	−4.73931	−0.281226
$285$	−3.12584	−0.185159
$286$	13.0874	0.773876
$287$	−23.1532	−1.36669
$288$	1.53797	0.0906255
$289$	1.00000	0.0588235
$290$	−7.51817	−0.441482
$291$	7.21378	0.422879
$292$	11.4588	0.670576
$293$	19.7942	1.15639	0.578194	−	0.815900i	$-0.303758\pi$
$293$	19.7942	1.15639	0.578194	+	0.815900i	$0.303758\pi$
$294$	−2.73751	−0.159655
$295$	−0.954710	−0.0555854
$296$	−9.30103	−0.540612
$297$	−7.42095	−0.430607
$298$	−18.8093	−1.08960
$299$	−43.6551	−2.52464
$300$	8.70959	0.502848
$301$	24.2062	1.39522
$302$	17.3165	0.996451
$303$	−16.3407	−0.938751
$304$	−1.53697	−0.0881511
$305$	0.359660	0.0205941
$306$	1.53797	0.0879196
$307$	25.0628	1.43041	0.715205	−	0.698914i	$-0.246333\pi$
$307$	25.0628	1.43041	0.715205	+	0.698914i	$0.246333\pi$
$308$	6.85835	0.390791
$309$	−18.6652	−1.06183
$310$	−6.68065	−0.379436
$311$	2.87967	0.163291	0.0816455	−	0.996661i	$-0.473982\pi$
$311$	2.87967	0.163291	0.0816455	+	0.996661i	$0.473982\pi$
$312$	11.7007	0.662424
$313$	9.82632	0.555417	0.277708	−	0.960665i	$-0.410425\pi$
$313$	9.82632	0.555417	0.277708	+	0.960665i	$0.410425\pi$
$314$	5.43540	0.306737
$315$	4.22636	0.238128
$316$	12.4143	0.698361
$317$	15.1133	0.848847	0.424423	−	0.905464i	$-0.360477\pi$
$317$	15.1133	0.848847	0.424423	+	0.905464i	$0.360477\pi$
$318$	−2.23151	−0.125137
$319$	−18.7634	−1.05055
$320$	−0.954710	−0.0533699
$321$	−13.7943	−0.769922
$322$	−22.8771	−1.27489
$323$	−1.53697	−0.0855191
$324$	−11.2486	−0.624920
$325$	22.4569	1.24569
$326$	6.73914	0.373247
$327$	−18.7343	−1.03601
$328$	8.04385	0.444147
$329$	−24.5683	−1.35450
$330$	−4.84589	−0.266758
$331$	33.3802	1.83474	0.917371	−	0.398032i	$-0.130307\pi$
$331$	33.3802	1.83474	0.917371	+	0.398032i	$0.130307\pi$
$332$	8.15569	0.447602
$333$	−14.3047	−0.783891
$334$	4.17107	0.228231
$335$	8.98520	0.490914
$336$	6.13167	0.334510
$337$	8.44583	0.460074	0.230037	−	0.973182i	$-0.426115\pi$
$337$	8.44583	0.460074	0.230037	+	0.973182i	$0.426115\pi$
$338$	17.1694	0.933890
$339$	40.0776	2.17672
$340$	−0.954710	−0.0517764
$341$	−16.6732	−0.902904
$342$	−2.36380	−0.127820
$343$	16.4497	0.888203
$344$	−8.40965	−0.453418
$345$	16.1642	0.870251
$346$	−1.86060	−0.100026
$347$	28.1483	1.51108	0.755540	−	0.655103i	$-0.227375\pi$
$347$	28.1483	1.51108	0.755540	+	0.655103i	$0.227375\pi$
$348$	−16.7753	−0.899252
$349$	−6.56107	−0.351206	−0.175603	−	0.984461i	$-0.556187\pi$
$349$	−6.56107	−0.351206	−0.175603	+	0.984461i	$0.556187\pi$
$350$	11.7683	0.629044
$351$	−17.1069	−0.913099
$352$	−2.38271	−0.126999
$353$	25.8191	1.37421	0.687106	−	0.726557i	$-0.258881\pi$
$353$	25.8191	1.37421	0.687106	+	0.726557i	$0.258881\pi$
$354$	−2.13025	−0.113222
$355$	4.52466	0.240144
$356$	−2.60510	−0.138070
$357$	6.13167	0.324522
$358$	3.65963	0.193417
$359$	8.00624	0.422553	0.211277	−	0.977426i	$-0.432238\pi$
$359$	8.00624	0.422553	0.211277	+	0.977426i	$0.432238\pi$
$360$	−1.46831	−0.0773868
$361$	−16.6377	−0.875670
$362$	6.49672	0.341460
$363$	11.3386	0.595125
$364$	15.8100	0.828668
$365$	−10.9398	−0.572617
$366$	0.802512	0.0419480
$367$	−0.231178	−0.0120674	−0.00603371	−	0.999982i	$-0.501921\pi$
$367$	−0.231178	−0.0120674	−0.00603371	+	0.999982i	$0.501921\pi$
$368$	7.94790	0.414313
$369$	12.3712	0.644017
$370$	8.87979	0.461638
$371$	−3.01520	−0.156542
$372$	−14.9066	−0.772870
$373$	−18.5038	−0.958088	−0.479044	−	0.877791i	$-0.659017\pi$
$373$	−18.5038	−0.958088	−0.479044	+	0.877791i	$0.659017\pi$
$374$	−2.38271	−0.123207
$375$	−18.4840	−0.954509
$376$	8.53547	0.440183
$377$	−43.2537	−2.22768
$378$	−8.96471	−0.461095
$379$	9.13464	0.469215	0.234608	−	0.972090i	$-0.424620\pi$
$379$	9.13464	0.469215	0.234608	+	0.972090i	$0.424620\pi$
$380$	1.46736	0.0752738
$381$	−16.6357	−0.852271
$382$	16.2585	0.831855
$383$	−8.38767	−0.428590	−0.214295	−	0.976769i	$-0.568745\pi$
$383$	−8.38767	−0.428590	−0.214295	+	0.976769i	$0.568745\pi$
$384$	−2.13025	−0.108709
$385$	−6.54773	−0.333703
$386$	−18.6409	−0.948799
$387$	−12.9338	−0.657459
$388$	−3.38636	−0.171916
$389$	−34.6887	−1.75879	−0.879393	−	0.476097i	$-0.842051\pi$
$389$	−34.6887	−1.75879	−0.879393	+	0.476097i	$0.842051\pi$
$390$	−11.1708	−0.565657
$391$	7.94790	0.401942
$392$	1.28507	0.0649057
$393$	−10.4260	−0.525920
$394$	−27.7360	−1.39732
$395$	−11.8521	−0.596343
$396$	−3.66453	−0.184150
$397$	−14.2778	−0.716581	−0.358291	−	0.933610i	$-0.616640\pi$
$397$	−14.2778	−0.716581	−0.358291	+	0.933610i	$0.616640\pi$
$398$	2.11908	0.106220
$399$	−9.42417	−0.471798
$400$	−4.08853	−0.204426
$401$	4.07720	0.203606	0.101803	−	0.994805i	$-0.467539\pi$
$401$	4.07720	0.203606	0.101803	+	0.994805i	$0.467539\pi$
$402$	20.0487	0.999939
$403$	−38.4353	−1.91460
$404$	7.67081	0.381637
$405$	10.7391	0.533631
$406$	−22.6667	−1.12493
$407$	22.1617	1.09851
$408$	−2.13025	−0.105463
$409$	6.82173	0.337313	0.168656	−	0.985675i	$-0.446057\pi$
$409$	6.82173	0.337313	0.168656	+	0.985675i	$0.446057\pi$
$410$	−7.67954	−0.379266
$411$	−18.8576	−0.930176
$412$	8.76198	0.431672
$413$	−2.87838	−0.141636
$414$	12.2236	0.600757
$415$	−7.78632	−0.382215
$416$	−5.49266	−0.269300
$417$	−32.9061	−1.61142
$418$	3.66215	0.179122
$419$	2.92296	0.142796	0.0713980	−	0.997448i	$-0.477254\pi$
$419$	2.92296	0.142796	0.0713980	+	0.997448i	$0.477254\pi$
$420$	−5.85396	−0.285644
$421$	−2.05292	−0.100053	−0.0500267	−	0.998748i	$-0.515931\pi$
$421$	−2.05292	−0.100053	−0.0500267	+	0.998748i	$0.515931\pi$
$422$	−9.17407	−0.446587
$423$	13.1273	0.638269
$424$	1.04754	0.0508728
$425$	−4.08853	−0.198323
$426$	10.0959	0.489148
$427$	1.08435	0.0524753
$428$	6.47543	0.313002
$429$	−27.8795	−1.34604
$430$	8.02878	0.387182
$431$	3.98530	0.191965	0.0959826	−	0.995383i	$-0.469401\pi$
$431$	3.98530	0.191965	0.0959826	+	0.995383i	$0.469401\pi$
$432$	3.11450	0.149846
$433$	−6.81831	−0.327667	−0.163834	−	0.986488i	$-0.552386\pi$
$433$	−6.81831	−0.327667	−0.163834	+	0.986488i	$0.552386\pi$
$434$	−20.1417	−0.966831
$435$	16.0156	0.767888
$436$	8.79441	0.421176
$437$	−12.2156	−0.584354
$438$	−24.4101	−1.16636
$439$	13.0677	0.623686	0.311843	−	0.950134i	$-0.399054\pi$
$439$	13.0677	0.623686	0.311843	+	0.950134i	$0.399054\pi$
$440$	2.27480	0.108447
$441$	1.97639	0.0941138
$442$	−5.49266	−0.261259
$443$	15.9155	0.756168	0.378084	−	0.925771i	$-0.376583\pi$
$443$	15.9155	0.756168	0.378084	+	0.925771i	$0.376583\pi$
$444$	19.8135	0.940308
$445$	2.48712	0.117901
$446$	−21.7882	−1.03170
$447$	40.0686	1.89518
$448$	−2.87838	−0.135991
$449$	33.9710	1.60319	0.801596	−	0.597866i	$-0.203985\pi$
$449$	33.9710	1.60319	0.801596	+	0.597866i	$0.203985\pi$
$450$	−6.28802	−0.296420
$451$	−19.1662	−0.902500
$452$	−18.8136	−0.884916
$453$	−36.8884	−1.73317
$454$	−21.9873	−1.03192
$455$	−15.0939	−0.707615
$456$	3.27412	0.153325
$457$	20.7306	0.969739	0.484869	−	0.874587i	$-0.338867\pi$
$457$	20.7306	0.969739	0.484869	+	0.874587i	$0.338867\pi$
$458$	2.11697	0.0989196
$459$	3.11450	0.145372
$460$	−7.58794	−0.353789
$461$	8.24218	0.383876	0.191938	−	0.981407i	$-0.438523\pi$
$461$	8.24218	0.383876	0.191938	+	0.981407i	$0.438523\pi$
$462$	−14.6100	−0.679719
$463$	−39.8502	−1.85200	−0.925998	−	0.377529i	$-0.876774\pi$
$463$	−39.8502	−1.85200	−0.925998	+	0.377529i	$0.876774\pi$
$464$	7.87482	0.365579
$465$	14.2315	0.659968
$466$	−1.19201	−0.0552188
$467$	8.09024	0.374372	0.187186	−	0.982325i	$-0.440063\pi$
$467$	8.09024	0.374372	0.187186	+	0.982325i	$0.440063\pi$
$468$	−8.44753	−0.390487
$469$	27.0897	1.25089
$470$	−8.14890	−0.375881
$471$	−11.5788	−0.533521
$472$	1.00000	0.0460287
$473$	20.0378	0.921338
$474$	−26.4456	−1.21469
$475$	6.28393	0.288327
$476$	−2.87838	−0.131930
$477$	1.61107	0.0737660
$478$	6.66122	0.304677
$479$	−30.0455	−1.37282	−0.686408	−	0.727217i	$-0.740813\pi$
$479$	−30.0455	−1.37282	−0.686408	+	0.727217i	$0.740813\pi$
$480$	2.03377	0.0928285
$481$	51.0874	2.32939
$482$	−14.1123	−0.642797
$483$	48.7339	2.21747
$484$	−5.32268	−0.241940
$485$	3.23299	0.146802
$486$	14.6187	0.663120
$487$	16.0948	0.729325	0.364662	−	0.931140i	$-0.381184\pi$
$487$	16.0948	0.729325	0.364662	+	0.931140i	$0.381184\pi$
$488$	−0.376722	−0.0170534
$489$	−14.3561	−0.649204
$490$	−1.22687	−0.0554242
$491$	−8.40591	−0.379353	−0.189677	−	0.981847i	$-0.560744\pi$
$491$	−8.40591	−0.379353	−0.189677	+	0.981847i	$0.560744\pi$
$492$	−17.1354	−0.772524
$493$	7.87482	0.354664
$494$	8.44204	0.379825
$495$	3.49856	0.157249
$496$	6.99757	0.314200
$497$	13.6415	0.611906
$498$	−17.3737	−0.778533
$499$	−8.77202	−0.392690	−0.196345	−	0.980535i	$-0.562907\pi$
$499$	−8.77202	−0.392690	−0.196345	+	0.980535i	$0.562907\pi$
$500$	8.67691	0.388043
$501$	−8.88542	−0.396971
$502$	−1.47976	−0.0660451
$503$	2.41503	0.107681	0.0538405	−	0.998550i	$-0.482854\pi$
$503$	2.41503	0.107681	0.0538405	+	0.998550i	$0.482854\pi$
$504$	−4.42685	−0.197187
$505$	−7.32340	−0.325887
$506$	−18.9375	−0.841877
$507$	−36.5750	−1.62435
$508$	7.80925	0.346480
$509$	−13.7024	−0.607346	−0.303673	−	0.952776i	$-0.598213\pi$
$509$	−13.7024	−0.607346	−0.303673	+	0.952776i	$0.598213\pi$
$510$	2.03377	0.0900569
$511$	−32.9828	−1.45907
$512$	1.00000	0.0441942
$513$	−4.78688	−0.211346
$514$	28.0271	1.23622
$515$	−8.36515	−0.368613
$516$	17.9147	0.788649
$517$	−20.3376	−0.894445
$518$	26.7719	1.17629
$519$	3.96354	0.173980
$520$	5.24390	0.229960
$521$	5.09032	0.223011	0.111505	−	0.993764i	$-0.464433\pi$
$521$	5.09032	0.223011	0.111505	+	0.993764i	$0.464433\pi$
$522$	12.1112	0.530093
$523$	−19.8772	−0.869170	−0.434585	−	0.900631i	$-0.643105\pi$
$523$	−19.8772	−0.869170	−0.434585	+	0.900631i	$0.643105\pi$
$524$	4.89424	0.213806
$525$	−25.0695	−1.09412
$526$	−29.4361	−1.28348
$527$	6.99757	0.304819
$528$	5.07577	0.220895
$529$	40.1690	1.74648
$530$	−1.00009	−0.0434412
$531$	1.53797	0.0667420
$532$	4.42397	0.191804
$533$	−44.1822	−1.91374
$534$	5.54952	0.240151
$535$	−6.18216	−0.267278
$536$	−9.41144	−0.406512
$537$	−7.79593	−0.336419
$538$	2.79321	0.120424
$539$	−3.06194	−0.131887
$540$	−2.97344	−0.127957
$541$	−16.0053	−0.688121	−0.344060	−	0.938948i	$-0.611802\pi$
$541$	−16.0053	−0.688121	−0.344060	+	0.938948i	$0.611802\pi$
$542$	−26.0587	−1.11932
$543$	−13.8396	−0.593916
$544$	1.00000	0.0428746
$545$	−8.39611	−0.359650
$546$	−33.6792	−1.44134
$547$	−36.1914	−1.54743	−0.773716	−	0.633533i	$-0.781604\pi$
$547$	−36.1914	−1.54743	−0.773716	+	0.633533i	$0.781604\pi$
$548$	8.85228	0.378151
$549$	−0.579385	−0.0247276
$550$	9.74179	0.415391
$551$	−12.1033	−0.515619
$552$	−16.9310	−0.720631
$553$	−35.7332	−1.51953
$554$	10.0227	0.425822
$555$	−18.9162	−0.802947
$556$	15.4471	0.655102
$557$	23.3329	0.988649	0.494324	−	0.869278i	$-0.335416\pi$
$557$	23.3329	0.988649	0.494324	+	0.869278i	$0.335416\pi$
$558$	10.7620	0.455593
$559$	46.1914	1.95369
$560$	2.74802	0.116125
$561$	5.07577	0.214299
$562$	−1.21027	−0.0510522
$563$	−6.97140	−0.293810	−0.146905	−	0.989151i	$-0.546931\pi$
$563$	−6.97140	−0.293810	−0.146905	+	0.989151i	$0.546931\pi$
$564$	−18.1827	−0.765629
$565$	17.9615	0.755646
$566$	9.04546	0.380209
$567$	32.3776	1.35973
$568$	−4.73931	−0.198857
$569$	39.1767	1.64237	0.821186	−	0.570660i	$-0.193313\pi$
$569$	39.1767	1.64237	0.821186	+	0.570660i	$0.193313\pi$
$570$	−3.12584	−0.130927
$571$	42.4196	1.77521	0.887603	−	0.460610i	$-0.152369\pi$
$571$	42.4196	1.77521	0.887603	+	0.460610i	$0.152369\pi$
$572$	13.0874	0.547213
$573$	−34.6346	−1.44688
$574$	−23.1532	−0.966398
$575$	−32.4952	−1.35514
$576$	1.53797	0.0640819
$577$	36.5061	1.51977	0.759884	−	0.650059i	$-0.225256\pi$
$577$	36.5061	1.51977	0.759884	+	0.650059i	$0.225256\pi$
$578$	1.00000	0.0415945
$579$	39.7099	1.65029
$580$	−7.51817	−0.312175
$581$	−23.4752	−0.973914
$582$	7.21378	0.299021
$583$	−2.49598	−0.103373
$584$	11.4588	0.474169
$585$	8.06494	0.333444
$586$	19.7942	0.817689
$587$	32.2091	1.32941	0.664705	−	0.747106i	$-0.268557\pi$
$587$	32.2091	1.32941	0.664705	+	0.747106i	$0.268557\pi$
$588$	−2.73751	−0.112893
$589$	−10.7550	−0.443153
$590$	−0.954710	−0.0393048
$591$	59.0846	2.43042
$592$	−9.30103	−0.382270
$593$	−34.9167	−1.43386	−0.716928	−	0.697147i	$-0.754452\pi$
$593$	−34.9167	−1.43386	−0.716928	+	0.697147i	$0.754452\pi$
$594$	−7.42095	−0.304485
$595$	2.74802	0.112658
$596$	−18.8093	−0.770461
$597$	−4.51417	−0.184753
$598$	−43.6551	−1.78519
$599$	31.8013	1.29937	0.649684	−	0.760205i	$-0.274901\pi$
$599$	31.8013	1.29937	0.649684	+	0.760205i	$0.274901\pi$
$600$	8.70959	0.355567
$601$	18.3430	0.748225	0.374112	−	0.927383i	$-0.377947\pi$
$601$	18.3430	0.748225	0.374112	+	0.927383i	$0.377947\pi$
$602$	24.2062	0.986569
$603$	−14.4745	−0.589446
$604$	17.3165	0.704598
$605$	5.08162	0.206597
$606$	−16.3407	−0.663797
$607$	−1.03424	−0.0419786	−0.0209893	−	0.999780i	$-0.506682\pi$
$607$	−1.03424	−0.0419786	−0.0209893	+	0.999780i	$0.506682\pi$
$608$	−1.53697	−0.0623322
$609$	48.2858	1.95664
$610$	0.359660	0.0145622
$611$	−46.8825	−1.89666
$612$	1.53797	0.0621686
$613$	42.6374	1.72211	0.861055	−	0.508512i	$-0.169804\pi$
$613$	42.6374	1.72211	0.861055	+	0.508512i	$0.169804\pi$
$614$	25.0628	1.01145
$615$	16.3593	0.659672
$616$	6.85835	0.276331
$617$	−10.4158	−0.419325	−0.209663	−	0.977774i	$-0.567237\pi$
$617$	−10.4158	−0.419325	−0.209663	+	0.977774i	$0.567237\pi$
$618$	−18.6652	−0.750825
$619$	44.2063	1.77680	0.888400	−	0.459070i	$-0.151817\pi$
$619$	44.2063	1.77680	0.888400	+	0.459070i	$0.151817\pi$
$620$	−6.68065	−0.268301
$621$	24.7537	0.993332
$622$	2.87967	0.115464
$623$	7.49847	0.300420
$624$	11.7007	0.468405
$625$	12.1587	0.486348
$626$	9.82632	0.392739
$627$	−7.80129	−0.311554
$628$	5.43540	0.216896
$629$	−9.30103	−0.370856
$630$	4.22636	0.168382
$631$	−40.4207	−1.60912	−0.804562	−	0.593869i	$-0.797600\pi$
$631$	−40.4207	−1.60912	−0.804562	+	0.593869i	$0.797600\pi$
$632$	12.4143	0.493816
$633$	19.5431	0.776767
$634$	15.1133	0.600225
$635$	−7.45557	−0.295865
$636$	−2.23151	−0.0884852
$637$	−7.05844	−0.279666
$638$	−18.7634	−0.742851
$639$	−7.28889	−0.288344
$640$	−0.954710	−0.0377382
$641$	23.5314	0.929436	0.464718	−	0.885459i	$-0.346156\pi$
$641$	23.5314	0.929436	0.464718	+	0.885459i	$0.346156\pi$
$642$	−13.7943	−0.544417
$643$	−34.1573	−1.34703	−0.673516	−	0.739173i	$-0.735217\pi$
$643$	−34.1573	−1.34703	−0.673516	+	0.739173i	$0.735217\pi$
$644$	−22.8771	−0.901482
$645$	−17.1033	−0.673442
$646$	−1.53697	−0.0604711
$647$	−5.41982	−0.213075	−0.106538	−	0.994309i	$-0.533976\pi$
$647$	−5.41982	−0.213075	−0.106538	+	0.994309i	$0.533976\pi$
$648$	−11.2486	−0.441885
$649$	−2.38271	−0.0935296
$650$	22.4569	0.880833
$651$	42.9068	1.68165
$652$	6.73914	0.263925
$653$	−0.0284785	−0.00111445	−0.000557225	−	1.00000i	$-0.500177\pi$
$653$	−0.0284785	−0.00111445	−0.000557225		1.00000i	$0.500177\pi$
$654$	−18.7343	−0.732569
$655$	−4.67258	−0.182573
$656$	8.04385	0.314059
$657$	17.6232	0.687548
$658$	−24.5683	−0.957773
$659$	31.5026	1.22717	0.613584	−	0.789629i	$-0.289727\pi$
$659$	31.5026	1.22717	0.613584	+	0.789629i	$0.289727\pi$
$660$	−4.84589	−0.188626
$661$	41.5847	1.61746	0.808729	−	0.588182i	$-0.200156\pi$
$661$	41.5847	1.61746	0.808729	+	0.588182i	$0.200156\pi$
$662$	33.3802	1.29736
$663$	11.7007	0.454419
$664$	8.15569	0.316502
$665$	−4.22361	−0.163785
$666$	−14.3047	−0.554295
$667$	62.5882	2.42343
$668$	4.17107	0.161384
$669$	46.4144	1.79448
$670$	8.98520	0.347128
$671$	0.897620	0.0346522
$672$	6.13167	0.236534
$673$	−51.2833	−1.97683	−0.988413	−	0.151790i	$-0.951496\pi$
$673$	−51.2833	−1.97683	−0.988413	+	0.151790i	$0.951496\pi$
$674$	8.44583	0.325321
$675$	−12.7337	−0.490121
$676$	17.1694	0.660360
$677$	−34.5040	−1.32610	−0.663049	−	0.748576i	$-0.730738\pi$
$677$	−34.5040	−1.32610	−0.663049	+	0.748576i	$0.730738\pi$
$678$	40.0776	1.53917
$679$	9.74721	0.374064
$680$	−0.954710	−0.0366115
$681$	46.8385	1.79485
$682$	−16.6732	−0.638450
$683$	0.335716	0.0128458	0.00642291	−	0.999979i	$-0.497956\pi$
$683$	0.335716	0.0128458	0.00642291	+	0.999979i	$0.497956\pi$
$684$	−2.36380	−0.0903822
$685$	−8.45136	−0.322910
$686$	16.4497	0.628054
$687$	−4.50968	−0.172055
$688$	−8.40965	−0.320615
$689$	−5.75376	−0.219201
$690$	16.1642	0.615361
$691$	30.1103	1.14545	0.572725	−	0.819747i	$-0.305886\pi$
$691$	30.1103	1.14545	0.572725	+	0.819747i	$0.305886\pi$
$692$	−1.86060	−0.0707293
$693$	10.5479	0.400682
$694$	28.1483	1.06849
$695$	−14.7475	−0.559404
$696$	−16.7753	−0.635867
$697$	8.04385	0.304682
$698$	−6.56107	−0.248340
$699$	2.53928	0.0960443
$700$	11.7683	0.444801
$701$	6.99983	0.264380	0.132190	−	0.991224i	$-0.457799\pi$
$701$	6.99983	0.264380	0.132190	+	0.991224i	$0.457799\pi$
$702$	−17.1069	−0.645658
$703$	14.2954	0.539160
$704$	−2.38271	−0.0898018
$705$	17.3592	0.653785
$706$	25.8191	0.971715
$707$	−22.0795	−0.830385
$708$	−2.13025	−0.0800597
$709$	8.64028	0.324493	0.162246	−	0.986750i	$-0.448126\pi$
$709$	8.64028	0.324493	0.162246	+	0.986750i	$0.448126\pi$
$710$	4.52466	0.169808
$711$	19.0928	0.716037
$712$	−2.60510	−0.0976303
$713$	55.6160	2.08283
$714$	6.13167	0.229472
$715$	−12.4947	−0.467276
$716$	3.65963	0.136767
$717$	−14.1901	−0.529938
$718$	8.00624	0.298790
$719$	33.4350	1.24691	0.623457	−	0.781858i	$-0.285728\pi$
$719$	33.4350	1.24691	0.623457	+	0.781858i	$0.285728\pi$
$720$	−1.46831	−0.0547207
$721$	−25.2203	−0.939254
$722$	−16.6377	−0.619192
$723$	30.0627	1.11804
$724$	6.49672	0.241449
$725$	−32.1964	−1.19575
$726$	11.3386	0.420817
$727$	24.4063	0.905180	0.452590	−	0.891719i	$-0.350500\pi$
$727$	24.4063	0.905180	0.452590	+	0.891719i	$0.350500\pi$
$728$	15.8100	0.585956
$729$	2.60409	0.0964477
$730$	−10.9398	−0.404901
$731$	−8.40965	−0.311042
$732$	0.802512	0.0296617
$733$	−3.23813	−0.119603	−0.0598015	−	0.998210i	$-0.519047\pi$
$733$	−3.23813	−0.119603	−0.0598015	+	0.998210i	$0.519047\pi$
$734$	−0.231178	−0.00853295
$735$	2.61353	0.0964016
$736$	7.94790	0.292963
$737$	22.4248	0.826026
$738$	12.3712	0.455389
$739$	24.0360	0.884178	0.442089	−	0.896971i	$-0.354238\pi$
$739$	24.0360	0.884178	0.442089	+	0.896971i	$0.354238\pi$
$740$	8.87979	0.326428
$741$	−17.9837	−0.660646
$742$	−3.01520	−0.110692
$743$	0.538551	0.0197575	0.00987877	−	0.999951i	$-0.496855\pi$
$743$	0.538551	0.0197575	0.00987877	+	0.999951i	$0.496855\pi$
$744$	−14.9066	−0.546502
$745$	17.9575	0.657911
$746$	−18.5038	−0.677471
$747$	12.5432	0.458931
$748$	−2.38271	−0.0871206
$749$	−18.6388	−0.681045
$750$	−18.4840	−0.674940
$751$	−19.6810	−0.718171	−0.359085	−	0.933305i	$-0.616911\pi$
$751$	−19.6810	−0.718171	−0.359085	+	0.933305i	$0.616911\pi$
$752$	8.53547	0.311256
$753$	3.15227	0.114875
$754$	−43.2537	−1.57521
$755$	−16.5322	−0.601669
$756$	−8.96471	−0.326043
$757$	−22.4235	−0.814995	−0.407498	−	0.913206i	$-0.633599\pi$
$757$	−22.4235	−0.814995	−0.407498	+	0.913206i	$0.633599\pi$
$758$	9.13464	0.331785
$759$	40.3417	1.46431
$760$	1.46736	0.0532266
$761$	13.3491	0.483905	0.241952	−	0.970288i	$-0.422212\pi$
$761$	13.3491	0.483905	0.241952	+	0.970288i	$0.422212\pi$
$762$	−16.6357	−0.602646
$763$	−25.3136	−0.916415
$764$	16.2585	0.588210
$765$	−1.46831	−0.0530869
$766$	−8.38767	−0.303059
$767$	−5.49266	−0.198329
$768$	−2.13025	−0.0768688
$769$	−47.2268	−1.70304	−0.851522	−	0.524320i	$-0.824320\pi$
$769$	−47.2268	−1.70304	−0.851522	+	0.524320i	$0.824320\pi$
$770$	−6.54773	−0.235964
$771$	−59.7047	−2.15021
$772$	−18.6409	−0.670902
$773$	−22.1275	−0.795872	−0.397936	−	0.917413i	$-0.630273\pi$
$773$	−22.1275	−0.795872	−0.397936	+	0.917413i	$0.630273\pi$
$774$	−12.9338	−0.464894
$775$	−28.6098	−1.02769
$776$	−3.38636	−0.121563
$777$	−57.0308	−2.04597
$778$	−34.6887	−1.24365
$779$	−12.3631	−0.442955
$780$	−11.1708	−0.399980
$781$	11.2924	0.404074
$782$	7.94790	0.284216
$783$	24.5261	0.876492
$784$	1.28507	0.0458952
$785$	−5.18923	−0.185212
$786$	−10.4260	−0.371882
$787$	4.05939	0.144701	0.0723507	−	0.997379i	$-0.476950\pi$
$787$	4.05939	0.144701	0.0723507	+	0.997379i	$0.476950\pi$
$788$	−27.7360	−0.988054
$789$	62.7063	2.23240
$790$	−11.8521	−0.421678
$791$	54.1526	1.92544
$792$	−3.66453	−0.130213
$793$	2.06921	0.0734797
$794$	−14.2778	−0.506699
$795$	2.13045	0.0755592
$796$	2.11908	0.0751088
$797$	−37.3471	−1.32290	−0.661450	−	0.749989i	$-0.730059\pi$
$797$	−37.3471	−1.32290	−0.661450	+	0.749989i	$0.730059\pi$
$798$	−9.42417	−0.333612
$799$	8.53547	0.301963
$800$	−4.08853	−0.144551
$801$	−4.00656	−0.141565
$802$	4.07720	0.143971
$803$	−27.3030	−0.963503
$804$	20.0487	0.707064
$805$	21.8410	0.769793
$806$	−38.4353	−1.35383
$807$	−5.95024	−0.209458
$808$	7.67081	0.269858
$809$	12.8703	0.452497	0.226248	−	0.974070i	$-0.427354\pi$
$809$	12.8703	0.452497	0.226248	+	0.974070i	$0.427354\pi$
$810$	10.7391	0.377334
$811$	−15.8115	−0.555215	−0.277608	−	0.960695i	$-0.589541\pi$
$811$	−15.8115	−0.555215	−0.277608	+	0.960695i	$0.589541\pi$
$812$	−22.6667	−0.795446
$813$	55.5116	1.94688
$814$	22.1617	0.776767
$815$	−6.43393	−0.225371
$816$	−2.13025	−0.0745737
$817$	12.9253	0.452201
$818$	6.82173	0.238516
$819$	24.3152	0.849642
$820$	−7.67954	−0.268181
$821$	5.66735	0.197792	0.0988959	−	0.995098i	$-0.468469\pi$
$821$	5.66735	0.197792	0.0988959	+	0.995098i	$0.468469\pi$
$822$	−18.8576	−0.657734
$823$	31.4260	1.09544	0.547720	−	0.836662i	$-0.315496\pi$
$823$	31.4260	1.09544	0.547720	+	0.836662i	$0.315496\pi$
$824$	8.76198	0.305238
$825$	−20.7524	−0.722507
$826$	−2.87838	−0.100152
$827$	−44.7967	−1.55774	−0.778868	−	0.627188i	$-0.784206\pi$
$827$	−44.7967	−1.55774	−0.778868	+	0.627188i	$0.784206\pi$
$828$	12.2236	0.424799
$829$	11.6245	0.403737	0.201869	−	0.979413i	$-0.435299\pi$
$829$	11.6245	0.403737	0.201869	+	0.979413i	$0.435299\pi$
$830$	−7.78632	−0.270267
$831$	−21.3508	−0.740650
$832$	−5.49266	−0.190424
$833$	1.28507	0.0445249
$834$	−32.9061	−1.13945
$835$	−3.98216	−0.137808
$836$	3.66215	0.126658
$837$	21.7939	0.753309
$838$	2.92296	0.100972
$839$	49.8170	1.71987	0.859937	−	0.510400i	$-0.170503\pi$
$839$	49.8170	1.71987	0.859937	+	0.510400i	$0.170503\pi$
$840$	−5.85396	−0.201981
$841$	33.0128	1.13837
$842$	−2.05292	−0.0707484
$843$	2.57818	0.0887973
$844$	−9.17407	−0.315784
$845$	−16.3918	−0.563894
$846$	13.1273	0.451324
$847$	15.3207	0.526426
$848$	1.04754	0.0359725
$849$	−19.2691	−0.661313
$850$	−4.08853	−0.140235
$851$	−73.9236	−2.53407
$852$	10.0959	0.345880
$853$	−47.3411	−1.62093	−0.810465	−	0.585787i	$-0.800785\pi$
$853$	−47.3411	−1.62093	−0.810465	+	0.585787i	$0.800785\pi$
$854$	1.08435	0.0371056
$855$	2.25674	0.0771790
$856$	6.47543	0.221326
$857$	−17.6869	−0.604174	−0.302087	−	0.953280i	$-0.597683\pi$
$857$	−17.6869	−0.604174	−0.302087	+	0.953280i	$0.597683\pi$
$858$	−27.8795	−0.951791
$859$	−56.2544	−1.91938	−0.959688	−	0.281067i	$-0.909312\pi$
$859$	−56.2544	−1.91938	−0.959688	+	0.281067i	$0.909312\pi$
$860$	8.02878	0.273779
$861$	49.3222	1.68090
$862$	3.98530	0.135740
$863$	12.7897	0.435368	0.217684	−	0.976019i	$-0.430150\pi$
$863$	12.7897	0.435368	0.217684	+	0.976019i	$0.430150\pi$
$864$	3.11450	0.105957
$865$	1.77633	0.0603970
$866$	−6.81831	−0.231696
$867$	−2.13025	−0.0723471
$868$	−20.1417	−0.683653
$869$	−29.5798	−1.00343
$870$	16.0156	0.542979
$871$	51.6939	1.75158
$872$	8.79441	0.297816
$873$	−5.20810	−0.176267
$874$	−12.2156	−0.413200
$875$	−24.9754	−0.844324
$876$	−24.4101	−0.824741
$877$	−16.2938	−0.550203	−0.275102	−	0.961415i	$-0.588712\pi$
$877$	−16.2938	−0.550203	−0.275102	+	0.961415i	$0.588712\pi$
$878$	13.0677	0.441013
$879$	−42.1665	−1.42224
$880$	2.27480	0.0766835
$881$	15.3139	0.515939	0.257969	−	0.966153i	$-0.416947\pi$
$881$	15.3139	0.515939	0.257969	+	0.966153i	$0.416947\pi$
$882$	1.97639	0.0665485
$883$	47.7321	1.60631	0.803156	−	0.595769i	$-0.203153\pi$
$883$	47.7321	1.60631	0.803156	+	0.595769i	$0.203153\pi$
$884$	−5.49266	−0.184738
$885$	2.03377	0.0683645
$886$	15.9155	0.534691
$887$	41.6324	1.39788	0.698939	−	0.715181i	$-0.253656\pi$
$887$	41.6324	1.39788	0.698939	+	0.715181i	$0.253656\pi$
$888$	19.8135	0.664898
$889$	−22.4780	−0.753888
$890$	2.48712	0.0833683
$891$	26.8021	0.897903
$892$	−21.7882	−0.729524
$893$	−13.1187	−0.439001
$894$	40.0686	1.34009
$895$	−3.49388	−0.116788
$896$	−2.87838	−0.0961599
$897$	92.9963	3.10506
$898$	33.9710	1.13363
$899$	55.1046	1.83784
$900$	−6.28802	−0.209601
$901$	1.04754	0.0348985
$902$	−19.1662	−0.638164
$903$	−51.5652	−1.71598
$904$	−18.8136	−0.625730
$905$	−6.20249	−0.206178
$906$	−36.8884	−1.22554
$907$	−22.5330	−0.748196	−0.374098	−	0.927389i	$-0.622048\pi$
$907$	−22.5330	−0.748196	−0.374098	+	0.927389i	$0.622048\pi$
$908$	−21.9873	−0.729675
$909$	11.7974	0.391296
$910$	−15.0939	−0.500359
$911$	35.9606	1.19143	0.595714	−	0.803196i	$-0.296869\pi$
$911$	35.9606	1.19143	0.595714	+	0.803196i	$0.296869\pi$
$912$	3.27412	0.108417
$913$	−19.4327	−0.643127
$914$	20.7306	0.685709
$915$	−0.766166	−0.0253287
$916$	2.11697	0.0699467
$917$	−14.0875	−0.465210
$918$	3.11450	0.102794
$919$	−8.11232	−0.267601	−0.133800	−	0.991008i	$-0.542718\pi$
$919$	−8.11232	−0.267601	−0.133800	+	0.991008i	$0.542718\pi$
$920$	−7.58794	−0.250167
$921$	−53.3901	−1.75926
$922$	8.24218	0.271442
$923$	26.0314	0.856835
$924$	−14.6100	−0.480634
$925$	38.0275	1.25034
$926$	−39.8502	−1.30956
$927$	13.4756	0.442598
$928$	7.87482	0.258504
$929$	38.6798	1.26904	0.634521	−	0.772906i	$-0.281197\pi$
$929$	38.6798	1.26904	0.634521	+	0.772906i	$0.281197\pi$
$930$	14.2315	0.466668
$931$	−1.97510	−0.0647314
$932$	−1.19201	−0.0390456
$933$	−6.13441	−0.200832
$934$	8.09024	0.264721
$935$	2.27480	0.0743939
$936$	−8.44753	−0.276116
$937$	−11.1927	−0.365651	−0.182825	−	0.983145i	$-0.558524\pi$
$937$	−11.1927	−0.365651	−0.182825	+	0.983145i	$0.558524\pi$
$938$	27.0897	0.884510
$939$	−20.9325	−0.683107
$940$	−8.14890	−0.265788
$941$	−33.9437	−1.10653	−0.553267	−	0.833004i	$-0.686619\pi$
$941$	−33.9437	−1.10653	−0.553267	+	0.833004i	$0.686619\pi$
$942$	−11.5788	−0.377257
$943$	63.9317	2.08190
$944$	1.00000	0.0325472
$945$	8.55870	0.278414
$946$	20.0378	0.651484
$947$	56.8656	1.84788	0.923942	−	0.382532i	$-0.124948\pi$
$947$	56.8656	1.84788	0.923942	+	0.382532i	$0.124948\pi$
$948$	−26.4456	−0.858914
$949$	−62.9394	−2.04310
$950$	6.28393	0.203878
$951$	−32.1951	−1.04400
$952$	−2.87838	−0.0932888
$953$	16.2748	0.527192	0.263596	−	0.964633i	$-0.415091\pi$
$953$	16.2748	0.527192	0.263596	+	0.964633i	$0.415091\pi$
$954$	1.61107	0.0521604
$955$	−15.5221	−0.502284
$956$	6.66122	0.215439
$957$	39.9708	1.29207
$958$	−30.0455	−0.970727
$959$	−25.4802	−0.822799
$960$	2.03377	0.0656397
$961$	17.9660	0.579549
$962$	51.0874	1.64713
$963$	9.95899	0.320924
$964$	−14.1123	−0.454526
$965$	17.7967	0.572896
$966$	48.7339	1.56799
$967$	29.6856	0.954625	0.477313	−	0.878734i	$-0.341611\pi$
$967$	29.6856	0.954625	0.477313	+	0.878734i	$0.341611\pi$
$968$	−5.32268	−0.171078
$969$	3.27412	0.105180
$970$	3.23299	0.103805
$971$	47.9004	1.53720	0.768598	−	0.639732i	$-0.220954\pi$
$971$	47.9004	1.53720	0.768598	+	0.639732i	$0.220954\pi$
$972$	14.6187	0.468897
$973$	−44.4626	−1.42540
$974$	16.0948	0.515710
$975$	−47.8388	−1.53207
$976$	−0.376722	−0.0120586
$977$	−46.6485	−1.49242	−0.746209	−	0.665712i	$-0.768128\pi$
$977$	−46.6485	−1.49242	−0.746209	+	0.665712i	$0.768128\pi$
$978$	−14.3561	−0.459056
$979$	6.20721	0.198383
$980$	−1.22687	−0.0391908
$981$	13.5255	0.431836
$982$	−8.40591	−0.268243
$983$	−28.4706	−0.908072	−0.454036	−	0.890983i	$-0.650016\pi$
$983$	−28.4706	−0.908072	−0.454036	+	0.890983i	$0.650016\pi$
$984$	−17.1354	−0.546257
$985$	26.4798	0.843717
$986$	7.87482	0.250785
$987$	52.3367	1.66589
$988$	8.44204	0.268577
$989$	−66.8390	−2.12536
$990$	3.49856	0.111192
$991$	36.4593	1.15817	0.579084	−	0.815268i	$-0.303410\pi$
$991$	36.4593	1.15817	0.579084	+	0.815268i	$0.303410\pi$
$992$	6.99757	0.222173
$993$	−71.1082	−2.25655
$994$	13.6415	0.432683
$995$	−2.02311	−0.0641368
$996$	−17.3737	−0.550506
$997$	58.2082	1.84347	0.921735	−	0.387819i	$-0.126772\pi$
$997$	58.2082	1.84347	0.921735	+	0.387819i	$0.126772\pi$
$998$	−8.77202	−0.277673
$999$	−28.9681	−0.916509

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.w.1.2	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.w.1.2	✓	13	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.13025 q^{3} +1.00000 q^{4} -0.954710 q^{5} -2.13025 q^{6} -2.87838 q^{7} +1.00000 q^{8} +1.53797 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.13025 q^{3} +1.00000 q^{4} -0.954710 q^{5} -2.13025 q^{6} -2.87838 q^{7} +1.00000 q^{8} +1.53797 q^{9} -0.954710 q^{10} -2.38271 q^{11} -2.13025 q^{12} -5.49266 q^{13} -2.87838 q^{14} +2.03377 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.53797 q^{18} -1.53697 q^{19} -0.954710 q^{20} +6.13167 q^{21} -2.38271 q^{22} +7.94790 q^{23} -2.13025 q^{24} -4.08853 q^{25} -5.49266 q^{26} +3.11450 q^{27} -2.87838 q^{28} +7.87482 q^{29} +2.03377 q^{30} +6.99757 q^{31} +1.00000 q^{32} +5.07577 q^{33} +1.00000 q^{34} +2.74802 q^{35} +1.53797 q^{36} -9.30103 q^{37} -1.53697 q^{38} +11.7007 q^{39} -0.954710 q^{40} +8.04385 q^{41} +6.13167 q^{42} -8.40965 q^{43} -2.38271 q^{44} -1.46831 q^{45} +7.94790 q^{46} +8.53547 q^{47} -2.13025 q^{48} +1.28507 q^{49} -4.08853 q^{50} -2.13025 q^{51} -5.49266 q^{52} +1.04754 q^{53} +3.11450 q^{54} +2.27480 q^{55} -2.87838 q^{56} +3.27412 q^{57} +7.87482 q^{58} +1.00000 q^{59} +2.03377 q^{60} -0.376722 q^{61} +6.99757 q^{62} -4.42685 q^{63} +1.00000 q^{64} +5.24390 q^{65} +5.07577 q^{66} -9.41144 q^{67} +1.00000 q^{68} -16.9310 q^{69} +2.74802 q^{70} -4.73931 q^{71} +1.53797 q^{72} +11.4588 q^{73} -9.30103 q^{74} +8.70959 q^{75} -1.53697 q^{76} +6.85835 q^{77} +11.7007 q^{78} +12.4143 q^{79} -0.954710 q^{80} -11.2486 q^{81} +8.04385 q^{82} +8.15569 q^{83} +6.13167 q^{84} -0.954710 q^{85} -8.40965 q^{86} -16.7753 q^{87} -2.38271 q^{88} -2.60510 q^{89} -1.46831 q^{90} +15.8100 q^{91} +7.94790 q^{92} -14.9066 q^{93} +8.53547 q^{94} +1.46736 q^{95} -2.13025 q^{96} -3.38636 q^{97} +1.28507 q^{98} -3.66453 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9	\( 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9} + q^{10} + 13 q^{11} + 7 q^{12} + 9 q^{13} + 8 q^{14} - 9 q^{15} + 13 q^{16} + 13 q^{17} + 16 q^{18} + 16 q^{19} + q^{20} - 3 q^{21} + 13 q^{22} + 18 q^{23} + 7 q^{24} + 14 q^{25} + 9 q^{26} + 10 q^{27} + 8 q^{28} + 8 q^{29} - 9 q^{30} + 32 q^{31} + 13 q^{32} + 13 q^{33} + 13 q^{34} - q^{35} + 16 q^{36} - 3 q^{37} + 16 q^{38} + 20 q^{39} + q^{40} + 24 q^{41} - 3 q^{42} - 2 q^{43} + 13 q^{44} - 3 q^{45} + 18 q^{46} + 26 q^{47} + 7 q^{48} + 23 q^{49} + 14 q^{50} + 7 q^{51} + 9 q^{52} - 27 q^{53} + 10 q^{54} - 7 q^{55} + 8 q^{56} - 21 q^{57} + 8 q^{58} + 13 q^{59} - 9 q^{60} + 20 q^{61} + 32 q^{62} - 3 q^{63} + 13 q^{64} + 16 q^{65} + 13 q^{66} + 4 q^{67} + 13 q^{68} - 2 q^{69} - q^{70} - 8 q^{71} + 16 q^{72} + 10 q^{73} - 3 q^{74} + 39 q^{75} + 16 q^{76} - 15 q^{77} + 20 q^{78} + 35 q^{79} + q^{80} + 29 q^{81} + 24 q^{82} - q^{83} - 3 q^{84} + q^{85} - 2 q^{86} - 32 q^{87} + 13 q^{88} - 20 q^{89} - 3 q^{90} - 15 q^{91} + 18 q^{92} - 7 q^{93} + 26 q^{94} - 3 q^{95} + 7 q^{96} - 3 q^{97} + 23 q^{98} + 65 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9 + q^10 + 13 * q^11 + 7 * q^12 + 9 * q^13 + 8 * q^14 - 9 * q^15 + 13 * q^16 + 13 * q^17 + 16 * q^18 + 16 * q^19 + q^20 - 3 * q^21 + 13 * q^22 + 18 * q^23 + 7 * q^24 + 14 * q^25 + 9 * q^26 + 10 * q^27 + 8 * q^28 + 8 * q^29 - 9 * q^30 + 32 * q^31 + 13 * q^32 + 13 * q^33 + 13 * q^34 - q^35 + 16 * q^36 - 3 * q^37 + 16 * q^38 + 20 * q^39 + q^40 + 24 * q^41 - 3 * q^42 - 2 * q^43 + 13 * q^44 - 3 * q^45 + 18 * q^46 + 26 * q^47 + 7 * q^48 + 23 * q^49 + 14 * q^50 + 7 * q^51 + 9 * q^52 - 27 * q^53 + 10 * q^54 - 7 * q^55 + 8 * q^56 - 21 * q^57 + 8 * q^58 + 13 * q^59 - 9 * q^60 + 20 * q^61 + 32 * q^62 - 3 * q^63 + 13 * q^64 + 16 * q^65 + 13 * q^66 + 4 * q^67 + 13 * q^68 - 2 * q^69 - q^70 - 8 * q^71 + 16 * q^72 + 10 * q^73 - 3 * q^74 + 39 * q^75 + 16 * q^76 - 15 * q^77 + 20 * q^78 + 35 * q^79 + q^80 + 29 * q^81 + 24 * q^82 - q^83 - 3 * q^84 + q^85 - 2 * q^86 - 32 * q^87 + 13 * q^88 - 20 * q^89 - 3 * q^90 - 15 * q^91 + 18 * q^92 - 7 * q^93 + 26 * q^94 - 3 * q^95 + 7 * q^96 - 3 * q^97 + 23 * q^98 + 65 * q^99

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