LMFDB - Embedded newform 4010.2.a.l.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, 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("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 24 x^{15} + 70 x^{14} + 228 x^{13} - 638 x^{12} - 1075 x^{11} + 2854 x^{10} + \cdots - 2 $ x^17 - 3x^16 - 24x^15 + 70x^14 + 228x^13 - 638x^12 - 1075x^11 + 2854x^10 + 2544x^9 - 6415x^8 - 2573x^7 + 6456x^6 + 485x^5 - 1839x^4 + 67x^3 + 136x^2 - 8x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$2.94584$ of defining polynomial
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.94584 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.94584 q^{6} +2.56799 q^{7} -1.00000 q^{8} +5.67796 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.94584 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.94584 q^{6} +2.56799 q^{7} -1.00000 q^{8} +5.67796 q^{9} +1.00000 q^{10} +2.28041 q^{11} +2.94584 q^{12} -5.38582 q^{13} -2.56799 q^{14} -2.94584 q^{15} +1.00000 q^{16} -1.40684 q^{17} -5.67796 q^{18} +5.12283 q^{19} -1.00000 q^{20} +7.56487 q^{21} -2.28041 q^{22} +7.76902 q^{23} -2.94584 q^{24} +1.00000 q^{25} +5.38582 q^{26} +7.88884 q^{27} +2.56799 q^{28} -3.83685 q^{29} +2.94584 q^{30} +3.25428 q^{31} -1.00000 q^{32} +6.71773 q^{33} +1.40684 q^{34} -2.56799 q^{35} +5.67796 q^{36} +4.27113 q^{37} -5.12283 q^{38} -15.8657 q^{39} +1.00000 q^{40} -7.79807 q^{41} -7.56487 q^{42} +3.63299 q^{43} +2.28041 q^{44} -5.67796 q^{45} -7.76902 q^{46} -5.10448 q^{47} +2.94584 q^{48} -0.405444 q^{49} -1.00000 q^{50} -4.14433 q^{51} -5.38582 q^{52} +3.44016 q^{53} -7.88884 q^{54} -2.28041 q^{55} -2.56799 q^{56} +15.0910 q^{57} +3.83685 q^{58} +13.3838 q^{59} -2.94584 q^{60} +2.97293 q^{61} -3.25428 q^{62} +14.5809 q^{63} +1.00000 q^{64} +5.38582 q^{65} -6.71773 q^{66} -0.166775 q^{67} -1.40684 q^{68} +22.8863 q^{69} +2.56799 q^{70} +1.16612 q^{71} -5.67796 q^{72} +13.6515 q^{73} -4.27113 q^{74} +2.94584 q^{75} +5.12283 q^{76} +5.85607 q^{77} +15.8657 q^{78} -5.91203 q^{79} -1.00000 q^{80} +6.20535 q^{81} +7.79807 q^{82} -9.66124 q^{83} +7.56487 q^{84} +1.40684 q^{85} -3.63299 q^{86} -11.3027 q^{87} -2.28041 q^{88} -7.33819 q^{89} +5.67796 q^{90} -13.8307 q^{91} +7.76902 q^{92} +9.58657 q^{93} +5.10448 q^{94} -5.12283 q^{95} -2.94584 q^{96} +16.5480 q^{97} +0.405444 q^{98} +12.9481 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * 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
$3$	2.94584	1.70078	0.850390	−	0.526153i	$-0.176366\pi$
$3$	2.94584	1.70078	0.850390	+	0.526153i	$0.176366\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.94584	−1.20263
$7$	2.56799	0.970608	0.485304	−	0.874346i	$-0.338709\pi$
$7$	2.56799	0.970608	0.485304	+	0.874346i	$0.338709\pi$
$8$	−1.00000	−0.353553
$9$	5.67796	1.89265
$10$	1.00000	0.316228
$11$	2.28041	0.687570	0.343785	−	0.939048i	$-0.388291\pi$
$11$	2.28041	0.687570	0.343785	+	0.939048i	$0.388291\pi$
$12$	2.94584	0.850390
$13$	−5.38582	−1.49376	−0.746878	−	0.664961i	$-0.768448\pi$
$13$	−5.38582	−1.49376	−0.746878	+	0.664961i	$0.768448\pi$
$14$	−2.56799	−0.686323
$15$	−2.94584	−0.760612
$16$	1.00000	0.250000
$17$	−1.40684	−0.341209	−0.170605	−	0.985340i	$-0.554572\pi$
$17$	−1.40684	−0.341209	−0.170605	+	0.985340i	$0.554572\pi$
$18$	−5.67796	−1.33831
$19$	5.12283	1.17526	0.587629	−	0.809130i	$-0.300061\pi$
$19$	5.12283	1.17526	0.587629	+	0.809130i	$0.300061\pi$
$20$	−1.00000	−0.223607
$21$	7.56487	1.65079
$22$	−2.28041	−0.486186
$23$	7.76902	1.61995	0.809977	−	0.586462i	$-0.199480\pi$
$23$	7.76902	1.61995	0.809977	+	0.586462i	$0.199480\pi$
$24$	−2.94584	−0.601317
$25$	1.00000	0.200000
$26$	5.38582	1.05625
$27$	7.88884	1.51821
$28$	2.56799	0.485304
$29$	−3.83685	−0.712484	−0.356242	−	0.934394i	$-0.615942\pi$
$29$	−3.83685	−0.712484	−0.356242	+	0.934394i	$0.615942\pi$
$30$	2.94584	0.537834
$31$	3.25428	0.584485	0.292243	−	0.956344i	$-0.405598\pi$
$31$	3.25428	0.584485	0.292243	+	0.956344i	$0.405598\pi$
$32$	−1.00000	−0.176777
$33$	6.71773	1.16941
$34$	1.40684	0.241272
$35$	−2.56799	−0.434069
$36$	5.67796	0.946327
$37$	4.27113	0.702169	0.351085	−	0.936344i	$-0.385813\pi$
$37$	4.27113	0.702169	0.351085	+	0.936344i	$0.385813\pi$
$38$	−5.12283	−0.831033
$39$	−15.8657	−2.54055
$40$	1.00000	0.158114
$41$	−7.79807	−1.21785	−0.608927	−	0.793226i	$-0.708400\pi$
$41$	−7.79807	−1.21785	−0.608927	+	0.793226i	$0.708400\pi$
$42$	−7.56487	−1.16729
$43$	3.63299	0.554026	0.277013	−	0.960866i	$-0.410656\pi$
$43$	3.63299	0.554026	0.277013	+	0.960866i	$0.410656\pi$
$44$	2.28041	0.343785
$45$	−5.67796	−0.846420
$46$	−7.76902	−1.14548
$47$	−5.10448	−0.744566	−0.372283	−	0.928119i	$-0.621425\pi$
$47$	−5.10448	−0.744566	−0.372283	+	0.928119i	$0.621425\pi$
$48$	2.94584	0.425195
$49$	−0.405444	−0.0579206
$50$	−1.00000	−0.141421
$51$	−4.14433	−0.580322
$52$	−5.38582	−0.746878
$53$	3.44016	0.472543	0.236271	−	0.971687i	$-0.424075\pi$
$53$	3.44016	0.472543	0.236271	+	0.971687i	$0.424075\pi$
$54$	−7.88884	−1.07353
$55$	−2.28041	−0.307491
$56$	−2.56799	−0.343162
$57$	15.0910	1.99886
$58$	3.83685	0.503803
$59$	13.3838	1.74243	0.871213	−	0.490905i	$-0.163334\pi$
$59$	13.3838	1.74243	0.871213	+	0.490905i	$0.163334\pi$
$60$	−2.94584	−0.380306
$61$	2.97293	0.380644	0.190322	−	0.981722i	$-0.439047\pi$
$61$	2.97293	0.380644	0.190322	+	0.981722i	$0.439047\pi$
$62$	−3.25428	−0.413294
$63$	14.5809	1.83702
$64$	1.00000	0.125000
$65$	5.38582	0.668028
$66$	−6.71773	−0.826895
$67$	−0.166775	−0.0203748	−0.0101874	−	0.999948i	$-0.503243\pi$
$67$	−0.166775	−0.0203748	−0.0101874	+	0.999948i	$0.503243\pi$
$68$	−1.40684	−0.170605
$69$	22.8863	2.75519
$70$	2.56799	0.306933
$71$	1.16612	0.138393	0.0691963	−	0.997603i	$-0.477957\pi$
$71$	1.16612	0.138393	0.0691963	+	0.997603i	$0.477957\pi$
$72$	−5.67796	−0.669154
$73$	13.6515	1.59778	0.798891	−	0.601476i	$-0.205420\pi$
$73$	13.6515	1.59778	0.798891	+	0.601476i	$0.205420\pi$
$74$	−4.27113	−0.496509
$75$	2.94584	0.340156
$76$	5.12283	0.587629
$77$	5.85607	0.667361
$78$	15.8657	1.79644
$79$	−5.91203	−0.665155	−0.332577	−	0.943076i	$-0.607918\pi$
$79$	−5.91203	−0.665155	−0.332577	+	0.943076i	$0.607918\pi$
$80$	−1.00000	−0.111803
$81$	6.20535	0.689484
$82$	7.79807	0.861152
$83$	−9.66124	−1.06046	−0.530229	−	0.847854i	$-0.677894\pi$
$83$	−9.66124	−1.06046	−0.530229	+	0.847854i	$0.677894\pi$
$84$	7.56487	0.825395
$85$	1.40684	0.152593
$86$	−3.63299	−0.391755
$87$	−11.3027	−1.21178
$88$	−2.28041	−0.243093
$89$	−7.33819	−0.777847	−0.388923	−	0.921270i	$-0.627153\pi$
$89$	−7.33819	−0.777847	−0.388923	+	0.921270i	$0.627153\pi$
$90$	5.67796	0.598510
$91$	−13.8307	−1.44985
$92$	7.76902	0.809977
$93$	9.58657	0.994081
$94$	5.10448	0.526487
$95$	−5.12283	−0.525592
$96$	−2.94584	−0.300658
$97$	16.5480	1.68020	0.840100	−	0.542432i	$-0.182496\pi$
$97$	16.5480	1.68020	0.840100	+	0.542432i	$0.182496\pi$
$98$	0.405444	0.0409560
$99$	12.9481	1.30133
$100$	1.00000	0.100000
$101$	2.36112	0.234940	0.117470	−	0.993076i	$-0.462522\pi$
$101$	2.36112	0.234940	0.117470	+	0.993076i	$0.462522\pi$
$102$	4.14433	0.410350
$103$	−4.52115	−0.445482	−0.222741	−	0.974878i	$-0.571500\pi$
$103$	−4.52115	−0.445482	−0.222741	+	0.974878i	$0.571500\pi$
$104$	5.38582	0.528123
$105$	−7.56487	−0.738256
$106$	−3.44016	−0.334138
$107$	9.83954	0.951224	0.475612	−	0.879655i	$-0.342227\pi$
$107$	9.83954	0.951224	0.475612	+	0.879655i	$0.342227\pi$
$108$	7.88884	0.759104
$109$	−4.04786	−0.387714	−0.193857	−	0.981030i	$-0.562100\pi$
$109$	−4.04786	−0.387714	−0.193857	+	0.981030i	$0.562100\pi$
$110$	2.28041	0.217429
$111$	12.5821	1.19424
$112$	2.56799	0.242652
$113$	2.61257	0.245770	0.122885	−	0.992421i	$-0.460785\pi$
$113$	2.61257	0.245770	0.122885	+	0.992421i	$0.460785\pi$
$114$	−15.0910	−1.41341
$115$	−7.76902	−0.724465
$116$	−3.83685	−0.356242
$117$	−30.5804	−2.82716
$118$	−13.3838	−1.23208
$119$	−3.61275	−0.331181
$120$	2.94584	0.268917
$121$	−5.79972	−0.527247
$122$	−2.97293	−0.269156
$123$	−22.9718	−2.07130
$124$	3.25428	0.292243
$125$	−1.00000	−0.0894427
$126$	−14.5809	−1.29897
$127$	10.1960	0.904748	0.452374	−	0.891828i	$-0.350577\pi$
$127$	10.1960	0.904748	0.452374	+	0.891828i	$0.350577\pi$
$128$	−1.00000	−0.0883883
$129$	10.7022	0.942276
$130$	−5.38582	−0.472367
$131$	−9.40559	−0.821770	−0.410885	−	0.911687i	$-0.634780\pi$
$131$	−9.40559	−0.821770	−0.410885	+	0.911687i	$0.634780\pi$
$132$	6.71773	0.584703
$133$	13.1554	1.14072
$134$	0.166775	0.0144071
$135$	−7.88884	−0.678963
$136$	1.40684	0.120636
$137$	7.83368	0.669276	0.334638	−	0.942347i	$-0.391386\pi$
$137$	7.83368	0.669276	0.334638	+	0.942347i	$0.391386\pi$
$138$	−22.8863	−1.94821
$139$	15.7822	1.33863	0.669316	−	0.742978i	$-0.266587\pi$
$139$	15.7822	1.33863	0.669316	+	0.742978i	$0.266587\pi$
$140$	−2.56799	−0.217034
$141$	−15.0370	−1.26634
$142$	−1.16612	−0.0978583
$143$	−12.2819	−1.02706
$144$	5.67796	0.473163
$145$	3.83685	0.318633
$146$	−13.6515	−1.12980
$147$	−1.19437	−0.0985102
$148$	4.27113	0.351085
$149$	−13.2020	−1.08155	−0.540776	−	0.841166i	$-0.681869\pi$
$149$	−13.2020	−1.08155	−0.540776	+	0.841166i	$0.681869\pi$
$150$	−2.94584	−0.240527
$151$	−15.4152	−1.25447	−0.627235	−	0.778830i	$-0.715813\pi$
$151$	−15.4152	−1.25447	−0.627235	+	0.778830i	$0.715813\pi$
$152$	−5.12283	−0.415517
$153$	−7.98800	−0.645791
$154$	−5.85607	−0.471896
$155$	−3.25428	−0.261390
$156$	−15.8657	−1.27028
$157$	−2.60337	−0.207772	−0.103886	−	0.994589i	$-0.533128\pi$
$157$	−2.60337	−0.207772	−0.103886	+	0.994589i	$0.533128\pi$
$158$	5.91203	0.470336
$159$	10.1342	0.803692
$160$	1.00000	0.0790569
$161$	19.9508	1.57234
$162$	−6.20535	−0.487539
$163$	−12.0817	−0.946315	−0.473157	−	0.880978i	$-0.656886\pi$
$163$	−12.0817	−0.946315	−0.473157	+	0.880978i	$0.656886\pi$
$164$	−7.79807	−0.608927
$165$	−6.71773	−0.522974
$166$	9.66124	0.749858
$167$	6.30384	0.487806	0.243903	−	0.969800i	$-0.421572\pi$
$167$	6.30384	0.487806	0.243903	+	0.969800i	$0.421572\pi$
$168$	−7.56487	−0.583643
$169$	16.0070	1.23131
$170$	−1.40684	−0.107900
$171$	29.0872	2.22436
$172$	3.63299	0.277013
$173$	−1.32474	−0.100718	−0.0503591	−	0.998731i	$-0.516037\pi$
$173$	−1.32474	−0.100718	−0.0503591	+	0.998731i	$0.516037\pi$
$174$	11.3027	0.856857
$175$	2.56799	0.194122
$176$	2.28041	0.171893
$177$	39.4266	2.96348
$178$	7.33819	0.550021
$179$	9.19865	0.687539	0.343770	−	0.939054i	$-0.388296\pi$
$179$	9.19865	0.687539	0.343770	+	0.939054i	$0.388296\pi$
$180$	−5.67796	−0.423210
$181$	23.1462	1.72045	0.860224	−	0.509917i	$-0.170324\pi$
$181$	23.1462	1.72045	0.860224	+	0.509917i	$0.170324\pi$
$182$	13.8307	1.02520
$183$	8.75776	0.647392
$184$	−7.76902	−0.572740
$185$	−4.27113	−0.314020
$186$	−9.58657	−0.702922
$187$	−3.20818	−0.234605
$188$	−5.10448	−0.372283
$189$	20.2584	1.47358
$190$	5.12283	0.371649
$191$	5.82810	0.421707	0.210853	−	0.977518i	$-0.432376\pi$
$191$	5.82810	0.421707	0.210853	+	0.977518i	$0.432376\pi$
$192$	2.94584	0.212598
$193$	2.39465	0.172370	0.0861852	−	0.996279i	$-0.472532\pi$
$193$	2.39465	0.172370	0.0861852	+	0.996279i	$0.472532\pi$
$194$	−16.5480	−1.18808
$195$	15.8657	1.13617
$196$	−0.405444	−0.0289603
$197$	−10.5909	−0.754569	−0.377284	−	0.926097i	$-0.623142\pi$
$197$	−10.5909	−0.754569	−0.377284	+	0.926097i	$0.623142\pi$
$198$	−12.9481	−0.920181
$199$	2.22324	0.157602	0.0788008	−	0.996890i	$-0.474891\pi$
$199$	2.22324	0.157602	0.0788008	+	0.996890i	$0.474891\pi$
$200$	−1.00000	−0.0707107
$201$	−0.491291	−0.0346530
$202$	−2.36112	−0.166128
$203$	−9.85297	−0.691543
$204$	−4.14433	−0.290161
$205$	7.79807	0.544641
$206$	4.52115	0.315003
$207$	44.1122	3.06601
$208$	−5.38582	−0.373439
$209$	11.6822	0.808073
$210$	7.56487	0.522026
$211$	−3.95240	−0.272094	−0.136047	−	0.990702i	$-0.543440\pi$
$211$	−3.95240	−0.272094	−0.136047	+	0.990702i	$0.543440\pi$
$212$	3.44016	0.236271
$213$	3.43519	0.235375
$214$	−9.83954	−0.672617
$215$	−3.63299	−0.247768
$216$	−7.88884	−0.536767
$217$	8.35694	0.567306
$218$	4.04786	0.274155
$219$	40.2150	2.71748
$220$	−2.28041	−0.153745
$221$	7.57699	0.509684
$222$	−12.5821	−0.844452
$223$	−22.3347	−1.49564	−0.747821	−	0.663901i	$-0.768900\pi$
$223$	−22.3347	−1.49564	−0.747821	+	0.663901i	$0.768900\pi$
$224$	−2.56799	−0.171581
$225$	5.67796	0.378531
$226$	−2.61257	−0.173786
$227$	1.83568	0.121839	0.0609193	−	0.998143i	$-0.480597\pi$
$227$	1.83568	0.121839	0.0609193	+	0.998143i	$0.480597\pi$
$228$	15.0910	0.999428
$229$	−6.13613	−0.405487	−0.202743	−	0.979232i	$-0.564986\pi$
$229$	−6.13613	−0.405487	−0.202743	+	0.979232i	$0.564986\pi$
$230$	7.76902	0.512274
$231$	17.2510	1.13503
$232$	3.83685	0.251901
$233$	−12.5500	−0.822177	−0.411088	−	0.911595i	$-0.634851\pi$
$233$	−12.5500	−0.822177	−0.411088	+	0.911595i	$0.634851\pi$
$234$	30.5804	1.99911
$235$	5.10448	0.332980
$236$	13.3838	0.871213
$237$	−17.4159	−1.13128
$238$	3.61275	0.234180
$239$	4.78332	0.309407	0.154703	−	0.987961i	$-0.450558\pi$
$239$	4.78332	0.309407	0.154703	+	0.987961i	$0.450558\pi$
$240$	−2.94584	−0.190153
$241$	−8.49201	−0.547018	−0.273509	−	0.961869i	$-0.588184\pi$
$241$	−8.49201	−0.547018	−0.273509	+	0.961869i	$0.588184\pi$
$242$	5.79972	0.372820
$243$	−5.38654	−0.345547
$244$	2.97293	0.190322
$245$	0.405444	0.0259029
$246$	22.9718	1.46463
$247$	−27.5906	−1.75555
$248$	−3.25428	−0.206647
$249$	−28.4604	−1.80361
$250$	1.00000	0.0632456
$251$	−19.7844	−1.24878	−0.624392	−	0.781111i	$-0.714653\pi$
$251$	−19.7844	−1.24878	−0.624392	+	0.781111i	$0.714653\pi$
$252$	14.5809	0.918512
$253$	17.7166	1.11383
$254$	−10.1960	−0.639753
$255$	4.14433	0.259528
$256$	1.00000	0.0625000
$257$	14.7779	0.921819	0.460909	−	0.887447i	$-0.347523\pi$
$257$	14.7779	0.921819	0.460909	+	0.887447i	$0.347523\pi$
$258$	−10.7022	−0.666290
$259$	10.9682	0.681531
$260$	5.38582	0.334014
$261$	−21.7855	−1.34849
$262$	9.40559	0.581079
$263$	−5.49039	−0.338552	−0.169276	−	0.985569i	$-0.554143\pi$
$263$	−5.49039	−0.338552	−0.169276	+	0.985569i	$0.554143\pi$
$264$	−6.71773	−0.413447
$265$	−3.44016	−0.211328
$266$	−13.1554	−0.806607
$267$	−21.6171	−1.32295
$268$	−0.166775	−0.0101874
$269$	−4.07115	−0.248223	−0.124111	−	0.992268i	$-0.539608\pi$
$269$	−4.07115	−0.248223	−0.124111	+	0.992268i	$0.539608\pi$
$270$	7.88884	0.480099
$271$	8.48096	0.515181	0.257591	−	0.966254i	$-0.417071\pi$
$271$	8.48096	0.515181	0.257591	+	0.966254i	$0.417071\pi$
$272$	−1.40684	−0.0853024
$273$	−40.7430	−2.46588
$274$	−7.83368	−0.473250
$275$	2.28041	0.137514
$276$	22.8863	1.37759
$277$	−10.9508	−0.657971	−0.328985	−	0.944335i	$-0.606707\pi$
$277$	−10.9508	−0.657971	−0.328985	+	0.944335i	$0.606707\pi$
$278$	−15.7822	−0.946555
$279$	18.4777	1.10623
$280$	2.56799	0.153467
$281$	11.8909	0.709351	0.354676	−	0.934989i	$-0.384591\pi$
$281$	11.8909	0.709351	0.354676	+	0.934989i	$0.384591\pi$
$282$	15.0370	0.895439
$283$	−8.46273	−0.503057	−0.251528	−	0.967850i	$-0.580933\pi$
$283$	−8.46273	−0.503057	−0.251528	+	0.967850i	$0.580933\pi$
$284$	1.16612	0.0691963
$285$	−15.0910	−0.893916
$286$	12.2819	0.726243
$287$	−20.0253	−1.18206
$288$	−5.67796	−0.334577
$289$	−15.0208	−0.883576
$290$	−3.83685	−0.225307
$291$	48.7479	2.85765
$292$	13.6515	0.798891
$293$	−5.51680	−0.322295	−0.161147	−	0.986930i	$-0.551519\pi$
$293$	−5.51680	−0.322295	−0.161147	+	0.986930i	$0.551519\pi$
$294$	1.19437	0.0696572
$295$	−13.3838	−0.779237
$296$	−4.27113	−0.248254
$297$	17.9898	1.04387
$298$	13.2020	0.764773
$299$	−41.8425	−2.41982
$300$	2.94584	0.170078
$301$	9.32947	0.537742
$302$	15.4152	0.887044
$303$	6.95547	0.399582
$304$	5.12283	0.293815
$305$	−2.97293	−0.170229
$306$	7.98800	0.456643
$307$	14.7692	0.842925	0.421463	−	0.906846i	$-0.361517\pi$
$307$	14.7692	0.842925	0.421463	+	0.906846i	$0.361517\pi$
$308$	5.85607	0.333681
$309$	−13.3186	−0.757667
$310$	3.25428	0.184831
$311$	5.07818	0.287957	0.143979	−	0.989581i	$-0.454010\pi$
$311$	5.07818	0.287957	0.143979	+	0.989581i	$0.454010\pi$
$312$	15.8657	0.898221
$313$	8.77729	0.496122	0.248061	−	0.968744i	$-0.420207\pi$
$313$	8.77729	0.496122	0.248061	+	0.968744i	$0.420207\pi$
$314$	2.60337	0.146917
$315$	−14.5809	−0.821542
$316$	−5.91203	−0.332577
$317$	−27.1554	−1.52520	−0.762601	−	0.646869i	$-0.776078\pi$
$317$	−27.1554	−1.52520	−0.762601	+	0.646869i	$0.776078\pi$
$318$	−10.1342	−0.568296
$319$	−8.74959	−0.489883
$320$	−1.00000	−0.0559017
$321$	28.9857	1.61782
$322$	−19.9508	−1.11181
$323$	−7.20702	−0.401009
$324$	6.20535	0.344742
$325$	−5.38582	−0.298751
$326$	12.0817	0.669145
$327$	−11.9243	−0.659417
$328$	7.79807	0.430576
$329$	−13.1082	−0.722681
$330$	6.71773	0.369799
$331$	14.0219	0.770711	0.385355	−	0.922768i	$-0.374079\pi$
$331$	14.0219	0.770711	0.385355	+	0.922768i	$0.374079\pi$
$332$	−9.66124	−0.530229
$333$	24.2513	1.32896
$334$	−6.30384	−0.344931
$335$	0.166775	0.00911188
$336$	7.56487	0.412698
$337$	−1.92072	−0.104628	−0.0523140	−	0.998631i	$-0.516660\pi$
$337$	−1.92072	−0.104628	−0.0523140	+	0.998631i	$0.516660\pi$
$338$	−16.0070	−0.870667
$339$	7.69621	0.418001
$340$	1.40684	0.0762967
$341$	7.42110	0.401875
$342$	−29.0872	−1.57286
$343$	−19.0171	−1.02683
$344$	−3.63299	−0.195878
$345$	−22.8863	−1.23216
$346$	1.32474	0.0712185
$347$	−0.406441	−0.0218189	−0.0109094	−	0.999940i	$-0.503473\pi$
$347$	−0.406441	−0.0218189	−0.0109094	+	0.999940i	$0.503473\pi$
$348$	−11.3027	−0.605890
$349$	12.0599	0.645552	0.322776	−	0.946475i	$-0.395384\pi$
$349$	12.0599	0.645552	0.322776	+	0.946475i	$0.395384\pi$
$350$	−2.56799	−0.137265
$351$	−42.4878	−2.26783
$352$	−2.28041	−0.121546
$353$	16.3714	0.871364	0.435682	−	0.900101i	$-0.356507\pi$
$353$	16.3714	0.871364	0.435682	+	0.900101i	$0.356507\pi$
$354$	−39.4266	−2.09550
$355$	−1.16612	−0.0618910
$356$	−7.33819	−0.388923
$357$	−10.6426	−0.563265
$358$	−9.19865	−0.486164
$359$	−35.3150	−1.86385	−0.931926	−	0.362648i	$-0.881873\pi$
$359$	−35.3150	−1.86385	−0.931926	+	0.362648i	$0.881873\pi$
$360$	5.67796	0.299255
$361$	7.24342	0.381233
$362$	−23.1462	−1.21654
$363$	−17.0850	−0.896731
$364$	−13.8307	−0.724926
$365$	−13.6515	−0.714550
$366$	−8.75776	−0.457775
$367$	12.9076	0.673770	0.336885	−	0.941546i	$-0.390627\pi$
$367$	12.9076	0.673770	0.336885	+	0.941546i	$0.390627\pi$
$368$	7.76902	0.404988
$369$	−44.2771	−2.30497
$370$	4.27113	0.222045
$371$	8.83430	0.458654
$372$	9.58657	0.497041
$373$	9.50083	0.491935	0.245967	−	0.969278i	$-0.420894\pi$
$373$	9.50083	0.491935	0.245967	+	0.969278i	$0.420894\pi$
$374$	3.20818	0.165891
$375$	−2.94584	−0.152122
$376$	5.10448	0.263244
$377$	20.6645	1.06428
$378$	−20.2584	−1.04198
$379$	29.6192	1.52143	0.760717	−	0.649083i	$-0.224847\pi$
$379$	29.6192	1.52143	0.760717	+	0.649083i	$0.224847\pi$
$380$	−5.12283	−0.262796
$381$	30.0357	1.53878
$382$	−5.82810	−0.298192
$383$	−21.1132	−1.07883	−0.539416	−	0.842039i	$-0.681355\pi$
$383$	−21.1132	−1.07883	−0.539416	+	0.842039i	$0.681355\pi$
$384$	−2.94584	−0.150329
$385$	−5.85607	−0.298453
$386$	−2.39465	−0.121884
$387$	20.6280	1.04858
$388$	16.5480	0.840100
$389$	−30.3463	−1.53862	−0.769309	−	0.638877i	$-0.779399\pi$
$389$	−30.3463	−1.53862	−0.769309	+	0.638877i	$0.779399\pi$
$390$	−15.8657	−0.803393
$391$	−10.9298	−0.552743
$392$	0.405444	0.0204780
$393$	−27.7073	−1.39765
$394$	10.5909	0.533561
$395$	5.91203	0.297466
$396$	12.9481	0.650666
$397$	16.4946	0.827840	0.413920	−	0.910313i	$-0.364159\pi$
$397$	16.4946	0.827840	0.413920	+	0.910313i	$0.364159\pi$
$398$	−2.22324	−0.111441
$399$	38.7536	1.94011
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	0.491291	0.0245034
$403$	−17.5269	−0.873079
$404$	2.36112	0.117470
$405$	−6.20535	−0.308347
$406$	9.85297	0.488995
$407$	9.73994	0.482791
$408$	4.14433	0.205175
$409$	24.1892	1.19608	0.598039	−	0.801467i	$-0.295947\pi$
$409$	24.1892	1.19608	0.598039	+	0.801467i	$0.295947\pi$
$410$	−7.79807	−0.385119
$411$	23.0767	1.13829
$412$	−4.52115	−0.222741
$413$	34.3695	1.69121
$414$	−44.1122	−2.16800
$415$	9.66124	0.474252
$416$	5.38582	0.264061
$417$	46.4919	2.27672
$418$	−11.6822	−0.571394
$419$	−21.1570	−1.03359	−0.516794	−	0.856110i	$-0.672875\pi$
$419$	−21.1570	−1.03359	−0.516794	+	0.856110i	$0.672875\pi$
$420$	−7.56487	−0.369128
$421$	−10.5406	−0.513717	−0.256858	−	0.966449i	$-0.582687\pi$
$421$	−10.5406	−0.513717	−0.256858	+	0.966449i	$0.582687\pi$
$422$	3.95240	0.192400
$423$	−28.9831	−1.40920
$424$	−3.44016	−0.167069
$425$	−1.40684	−0.0682419
$426$	−3.43519	−0.166436
$427$	7.63444	0.369456
$428$	9.83954	0.475612
$429$	−36.1804	−1.74681
$430$	3.63299	0.175198
$431$	−1.98063	−0.0954034	−0.0477017	−	0.998862i	$-0.515190\pi$
$431$	−1.98063	−0.0954034	−0.0477017	+	0.998862i	$0.515190\pi$
$432$	7.88884	0.379552
$433$	38.9083	1.86981	0.934906	−	0.354895i	$-0.115483\pi$
$433$	38.9083	1.86981	0.934906	+	0.354895i	$0.115483\pi$
$434$	−8.35694	−0.401146
$435$	11.3027	0.541924
$436$	−4.04786	−0.193857
$437$	39.7994	1.90386
$438$	−40.2150	−1.92155
$439$	−20.3147	−0.969566	−0.484783	−	0.874634i	$-0.661102\pi$
$439$	−20.3147	−0.969566	−0.484783	+	0.874634i	$0.661102\pi$
$440$	2.28041	0.108714
$441$	−2.30210	−0.109624
$442$	−7.57699	−0.360401
$443$	−30.8826	−1.46727	−0.733637	−	0.679541i	$-0.762179\pi$
$443$	−30.8826	−1.46727	−0.733637	+	0.679541i	$0.762179\pi$
$444$	12.5821	0.597118
$445$	7.33819	0.347864
$446$	22.3347	1.05758
$447$	−38.8911	−1.83948
$448$	2.56799	0.121326
$449$	14.6913	0.693324	0.346662	−	0.937990i	$-0.387315\pi$
$449$	14.6913	0.693324	0.346662	+	0.937990i	$0.387315\pi$
$450$	−5.67796	−0.267662
$451$	−17.7828	−0.837360
$452$	2.61257	0.122885
$453$	−45.4106	−2.13358
$454$	−1.83568	−0.0861529
$455$	13.8307	0.648393
$456$	−15.0910	−0.706703
$457$	1.09430	0.0511892	0.0255946	−	0.999672i	$-0.491852\pi$
$457$	1.09430	0.0511892	0.0255946	+	0.999672i	$0.491852\pi$
$458$	6.13613	0.286722
$459$	−11.0984	−0.518027
$460$	−7.76902	−0.362233
$461$	−37.0142	−1.72392	−0.861961	−	0.506974i	$-0.830764\pi$
$461$	−37.0142	−1.72392	−0.861961	+	0.506974i	$0.830764\pi$
$462$	−17.2510	−0.802591
$463$	2.78743	0.129543	0.0647714	−	0.997900i	$-0.479368\pi$
$463$	2.78743	0.129543	0.0647714	+	0.997900i	$0.479368\pi$
$464$	−3.83685	−0.178121
$465$	−9.58657	−0.444567
$466$	12.5500	0.581367
$467$	−10.0653	−0.465765	−0.232883	−	0.972505i	$-0.574816\pi$
$467$	−10.0653	−0.465765	−0.232883	+	0.972505i	$0.574816\pi$
$468$	−30.5804	−1.41358
$469$	−0.428275	−0.0197759
$470$	−5.10448	−0.235452
$471$	−7.66911	−0.353374
$472$	−13.3838	−0.616041
$473$	8.28472	0.380932
$474$	17.4159	0.799937
$475$	5.12283	0.235052
$476$	−3.61275	−0.165590
$477$	19.5331	0.894360
$478$	−4.78332	−0.218784
$479$	−35.9421	−1.64223	−0.821117	−	0.570760i	$-0.806649\pi$
$479$	−35.9421	−1.64223	−0.821117	+	0.570760i	$0.806649\pi$
$480$	2.94584	0.134458
$481$	−23.0035	−1.04887
$482$	8.49201	0.386800
$483$	58.7717	2.67420
$484$	−5.79972	−0.263624
$485$	−16.5480	−0.751408
$486$	5.38654	0.244339
$487$	27.1565	1.23058	0.615289	−	0.788302i	$-0.289039\pi$
$487$	27.1565	1.23058	0.615289	+	0.788302i	$0.289039\pi$
$488$	−2.97293	−0.134578
$489$	−35.5908	−1.60947
$490$	−0.405444	−0.0183161
$491$	33.1747	1.49715	0.748576	−	0.663049i	$-0.230738\pi$
$491$	33.1747	1.49715	0.748576	+	0.663049i	$0.230738\pi$
$492$	−22.9718	−1.03565
$493$	5.39784	0.243106
$494$	27.5906	1.24136
$495$	−12.9481	−0.581974
$496$	3.25428	0.146121
$497$	2.99457	0.134325
$498$	28.4604	1.27534
$499$	−5.04645	−0.225910	−0.112955	−	0.993600i	$-0.536032\pi$
$499$	−5.04645	−0.225910	−0.112955	+	0.993600i	$0.536032\pi$
$500$	−1.00000	−0.0447214
$501$	18.5701	0.829650
$502$	19.7844	0.883023
$503$	−29.2775	−1.30542	−0.652709	−	0.757609i	$-0.726367\pi$
$503$	−29.2775	−1.30542	−0.652709	+	0.757609i	$0.726367\pi$
$504$	−14.5809	−0.649486
$505$	−2.36112	−0.105068
$506$	−17.7166	−0.787598
$507$	47.1541	2.09419
$508$	10.1960	0.452374
$509$	−20.3836	−0.903488	−0.451744	−	0.892147i	$-0.649198\pi$
$509$	−20.3836	−0.903488	−0.451744	+	0.892147i	$0.649198\pi$
$510$	−4.14433	−0.183514
$511$	35.0568	1.55082
$512$	−1.00000	−0.0441942
$513$	40.4132	1.78429
$514$	−14.7779	−0.651824
$515$	4.52115	0.199226
$516$	10.7022	0.471138
$517$	−11.6403	−0.511941
$518$	−10.9682	−0.481915
$519$	−3.90247	−0.171299
$520$	−5.38582	−0.236184
$521$	−26.9579	−1.18105	−0.590523	−	0.807021i	$-0.701078\pi$
$521$	−26.9579	−1.18105	−0.590523	+	0.807021i	$0.701078\pi$
$522$	21.7855	0.953524
$523$	5.73421	0.250739	0.125370	−	0.992110i	$-0.459988\pi$
$523$	5.73421	0.250739	0.125370	+	0.992110i	$0.459988\pi$
$524$	−9.40559	−0.410885
$525$	7.56487	0.330158
$526$	5.49039	0.239392
$527$	−4.57826	−0.199432
$528$	6.71773	0.292352
$529$	37.3577	1.62425
$530$	3.44016	0.149431
$531$	75.9929	3.29781
$532$	13.1554	0.570358
$533$	41.9990	1.81918
$534$	21.6171	0.935464
$535$	−9.83954	−0.425400
$536$	0.166775	0.00720357
$537$	27.0977	1.16935
$538$	4.07115	0.175520
$539$	−0.924580	−0.0398245
$540$	−7.88884	−0.339482
$541$	23.4086	1.00642	0.503208	−	0.864165i	$-0.332153\pi$
$541$	23.4086	1.00642	0.503208	+	0.864165i	$0.332153\pi$
$542$	−8.48096	−0.364288
$543$	68.1851	2.92610
$544$	1.40684	0.0603179
$545$	4.04786	0.173391
$546$	40.7430	1.74364
$547$	−32.1950	−1.37656	−0.688279	−	0.725447i	$-0.741633\pi$
$547$	−32.1950	−1.37656	−0.688279	+	0.725447i	$0.741633\pi$
$548$	7.83368	0.334638
$549$	16.8802	0.720428
$550$	−2.28041	−0.0972371
$551$	−19.6555	−0.837353
$552$	−22.8863	−0.974105
$553$	−15.1820	−0.645604
$554$	10.9508	0.465256
$555$	−12.5821	−0.534078
$556$	15.7822	0.669316
$557$	37.1045	1.57217	0.786085	−	0.618118i	$-0.212105\pi$
$557$	37.1045	1.57217	0.786085	+	0.618118i	$0.212105\pi$
$558$	−18.4777	−0.782222
$559$	−19.5666	−0.827580
$560$	−2.56799	−0.108517
$561$	−9.45078	−0.399012
$562$	−11.8909	−0.501587
$563$	5.73905	0.241872	0.120936	−	0.992660i	$-0.461410\pi$
$563$	5.73905	0.241872	0.120936	+	0.992660i	$0.461410\pi$
$564$	−15.0370	−0.633171
$565$	−2.61257	−0.109912
$566$	8.46273	0.355715
$567$	15.9353	0.669218
$568$	−1.16612	−0.0489292
$569$	−36.6990	−1.53850	−0.769250	−	0.638947i	$-0.779370\pi$
$569$	−36.6990	−1.53850	−0.769250	+	0.638947i	$0.779370\pi$
$570$	15.0910	0.632094
$571$	11.2554	0.471022	0.235511	−	0.971872i	$-0.424324\pi$
$571$	11.2554	0.471022	0.235511	+	0.971872i	$0.424324\pi$
$572$	−12.2819	−0.513531
$573$	17.1686	0.717230
$574$	20.0253	0.835841
$575$	7.76902	0.323991
$576$	5.67796	0.236582
$577$	35.9366	1.49606	0.748031	−	0.663664i	$-0.231000\pi$
$577$	35.9366	1.49606	0.748031	+	0.663664i	$0.231000\pi$
$578$	15.0208	0.624783
$579$	7.05424	0.293164
$580$	3.83685	0.159316
$581$	−24.8099	−1.02929
$582$	−48.7479	−2.02066
$583$	7.84499	0.324906
$584$	−13.6515	−0.564901
$585$	30.5804	1.26435
$586$	5.51680	0.227897
$587$	43.1362	1.78042	0.890211	−	0.455548i	$-0.150557\pi$
$587$	43.1362	1.78042	0.890211	+	0.455548i	$0.150557\pi$
$588$	−1.19437	−0.0492551
$589$	16.6711	0.686922
$590$	13.3838	0.551004
$591$	−31.1990	−1.28336
$592$	4.27113	0.175542
$593$	−42.7384	−1.75505	−0.877527	−	0.479527i	$-0.840808\pi$
$593$	−42.7384	−1.75505	−0.877527	+	0.479527i	$0.840808\pi$
$594$	−17.9898	−0.738131
$595$	3.61275	0.148108
$596$	−13.2020	−0.540776
$597$	6.54931	0.268046
$598$	41.8425	1.71107
$599$	−16.7516	−0.684453	−0.342227	−	0.939617i	$-0.611181\pi$
$599$	−16.7516	−0.684453	−0.342227	+	0.939617i	$0.611181\pi$
$600$	−2.94584	−0.120263
$601$	−36.2720	−1.47957	−0.739784	−	0.672845i	$-0.765072\pi$
$601$	−36.2720	−1.47957	−0.739784	+	0.672845i	$0.765072\pi$
$602$	−9.32947	−0.380241
$603$	−0.946941	−0.0385624
$604$	−15.4152	−0.627235
$605$	5.79972	0.235792
$606$	−6.95547	−0.282547
$607$	45.6234	1.85179	0.925897	−	0.377775i	$-0.123311\pi$
$607$	45.6234	1.85179	0.925897	+	0.377775i	$0.123311\pi$
$608$	−5.12283	−0.207758
$609$	−29.0252	−1.17616
$610$	2.97293	0.120370
$611$	27.4918	1.11220
$612$	−7.98800	−0.322896
$613$	−15.9654	−0.644835	−0.322417	−	0.946598i	$-0.604495\pi$
$613$	−15.9654	−0.644835	−0.322417	+	0.946598i	$0.604495\pi$
$614$	−14.7692	−0.596038
$615$	22.9718	0.926314
$616$	−5.85607	−0.235948
$617$	25.8496	1.04067	0.520334	−	0.853963i	$-0.325808\pi$
$617$	25.8496	1.04067	0.520334	+	0.853963i	$0.325808\pi$
$618$	13.3186	0.535752
$619$	30.9474	1.24388	0.621940	−	0.783065i	$-0.286345\pi$
$619$	30.9474	1.24388	0.621940	+	0.783065i	$0.286345\pi$
$620$	−3.25428	−0.130695
$621$	61.2886	2.45943
$622$	−5.07818	−0.203617
$623$	−18.8444	−0.754984
$624$	−15.8657	−0.635138
$625$	1.00000	0.0400000
$626$	−8.77729	−0.350811
$627$	34.4138	1.37435
$628$	−2.60337	−0.103886
$629$	−6.00881	−0.239587
$630$	14.5809	0.580918
$631$	−26.2394	−1.04457	−0.522287	−	0.852770i	$-0.674921\pi$
$631$	−26.2394	−1.04457	−0.522287	+	0.852770i	$0.674921\pi$
$632$	5.91203	0.235168
$633$	−11.6431	−0.462772
$634$	27.1554	1.07848
$635$	−10.1960	−0.404616
$636$	10.1342	0.401846
$637$	2.18365	0.0865193
$638$	8.74959	0.346400
$639$	6.62116	0.261929
$640$	1.00000	0.0395285
$641$	21.6390	0.854689	0.427344	−	0.904089i	$-0.359449\pi$
$641$	21.6390	0.854689	0.427344	+	0.904089i	$0.359449\pi$
$642$	−28.9857	−1.14397
$643$	5.87740	0.231782	0.115891	−	0.993262i	$-0.463028\pi$
$643$	5.87740	0.231782	0.115891	+	0.993262i	$0.463028\pi$
$644$	19.9508	0.786170
$645$	−10.7022	−0.421399
$646$	7.20702	0.283556
$647$	1.48450	0.0583616	0.0291808	−	0.999574i	$-0.490710\pi$
$647$	1.48450	0.0583616	0.0291808	+	0.999574i	$0.490710\pi$
$648$	−6.20535	−0.243769
$649$	30.5207	1.19804
$650$	5.38582	0.211249
$651$	24.6182	0.964863
$652$	−12.0817	−0.473157
$653$	28.5707	1.11806	0.559029	−	0.829148i	$-0.311174\pi$
$653$	28.5707	1.11806	0.559029	+	0.829148i	$0.311174\pi$
$654$	11.9243	0.466278
$655$	9.40559	0.367507
$656$	−7.79807	−0.304463
$657$	77.5124	3.02405
$658$	13.1082	0.511013
$659$	−48.5520	−1.89132	−0.945659	−	0.325159i	$-0.894582\pi$
$659$	−48.5520	−1.89132	−0.945659	+	0.325159i	$0.894582\pi$
$660$	−6.71773	−0.261487
$661$	−2.58199	−0.100428	−0.0502138	−	0.998738i	$-0.515990\pi$
$661$	−2.58199	−0.100428	−0.0502138	+	0.998738i	$0.515990\pi$
$662$	−14.0219	−0.544975
$663$	22.3206	0.866860
$664$	9.66124	0.374929
$665$	−13.1554	−0.510143
$666$	−24.2513	−0.939719
$667$	−29.8085	−1.15419
$668$	6.30384	0.243903
$669$	−65.7944	−2.54376
$670$	−0.166775	−0.00644307
$671$	6.77950	0.261720
$672$	−7.56487	−0.291821
$673$	6.27716	0.241967	0.120983	−	0.992655i	$-0.461395\pi$
$673$	6.27716	0.241967	0.120983	+	0.992655i	$0.461395\pi$
$674$	1.92072	0.0739832
$675$	7.88884	0.303642
$676$	16.0070	0.615654
$677$	−41.3475	−1.58911	−0.794557	−	0.607190i	$-0.792297\pi$
$677$	−41.3475	−1.58911	−0.794557	+	0.607190i	$0.792297\pi$
$678$	−7.69621	−0.295571
$679$	42.4952	1.63081
$680$	−1.40684	−0.0539499
$681$	5.40763	0.207221
$682$	−7.42110	−0.284168
$683$	−18.8361	−0.720745	−0.360372	−	0.932809i	$-0.617350\pi$
$683$	−18.8361	−0.720745	−0.360372	+	0.932809i	$0.617350\pi$
$684$	29.0872	1.11218
$685$	−7.83368	−0.299309
$686$	19.0171	0.726076
$687$	−18.0760	−0.689644
$688$	3.63299	0.138506
$689$	−18.5281	−0.705864
$690$	22.8863	0.871266
$691$	−11.5947	−0.441083	−0.220542	−	0.975378i	$-0.570782\pi$
$691$	−11.5947	−0.441083	−0.220542	+	0.975378i	$0.570782\pi$
$692$	−1.32474	−0.0503591
$693$	33.2505	1.26308
$694$	0.406441	0.0154283
$695$	−15.7822	−0.598654
$696$	11.3027	0.428429
$697$	10.9707	0.415543
$698$	−12.0599	−0.456474
$699$	−36.9702	−1.39834
$700$	2.56799	0.0970608
$701$	5.42711	0.204979	0.102489	−	0.994734i	$-0.467319\pi$
$701$	5.42711	0.204979	0.102489	+	0.994734i	$0.467319\pi$
$702$	42.4878	1.60360
$703$	21.8803	0.825231
$704$	2.28041	0.0859463
$705$	15.0370	0.566326
$706$	−16.3714	−0.616147
$707$	6.06332	0.228035
$708$	39.4266	1.48174
$709$	5.34970	0.200912	0.100456	−	0.994941i	$-0.467970\pi$
$709$	5.34970	0.200912	0.100456	+	0.994941i	$0.467970\pi$
$710$	1.16612	0.0437636
$711$	−33.5682	−1.25891
$712$	7.33819	0.275010
$713$	25.2826	0.946839
$714$	10.6426	0.398289
$715$	12.2819	0.459316
$716$	9.19865	0.343770
$717$	14.0909	0.526233
$718$	35.3150	1.31794
$719$	−28.4370	−1.06052	−0.530261	−	0.847834i	$-0.677906\pi$
$719$	−28.4370	−1.06052	−0.530261	+	0.847834i	$0.677906\pi$
$720$	−5.67796	−0.211605
$721$	−11.6103	−0.432388
$722$	−7.24342	−0.269572
$723$	−25.0161	−0.930358
$724$	23.1462	0.860224
$725$	−3.83685	−0.142497
$726$	17.0850	0.634085
$727$	−7.13507	−0.264625	−0.132313	−	0.991208i	$-0.542240\pi$
$727$	−7.13507	−0.264625	−0.132313	+	0.991208i	$0.542240\pi$
$728$	13.8307	0.512600
$729$	−34.4840	−1.27718
$730$	13.6515	0.505263
$731$	−5.11105	−0.189039
$732$	8.75776	0.323696
$733$	−17.0651	−0.630312	−0.315156	−	0.949040i	$-0.602057\pi$
$733$	−17.0651	−0.630312	−0.315156	+	0.949040i	$0.602057\pi$
$734$	−12.9076	−0.476427
$735$	1.19437	0.0440551
$736$	−7.76902	−0.286370
$737$	−0.380315	−0.0140091
$738$	44.2771	1.62986
$739$	−3.24960	−0.119538	−0.0597692	−	0.998212i	$-0.519036\pi$
$739$	−3.24960	−0.119538	−0.0597692	+	0.998212i	$0.519036\pi$
$740$	−4.27113	−0.157010
$741$	−81.2775	−2.98581
$742$	−8.83430	−0.324317
$743$	27.8524	1.02181	0.510904	−	0.859638i	$-0.329311\pi$
$743$	27.8524	1.02181	0.510904	+	0.859638i	$0.329311\pi$
$744$	−9.58657	−0.351461
$745$	13.2020	0.483685
$746$	−9.50083	−0.347850
$747$	−54.8561	−2.00708
$748$	−3.20818	−0.117303
$749$	25.2678	0.923266
$750$	2.94584	0.107567
$751$	−28.3171	−1.03331	−0.516654	−	0.856194i	$-0.672823\pi$
$751$	−28.3171	−1.03331	−0.516654	+	0.856194i	$0.672823\pi$
$752$	−5.10448	−0.186141
$753$	−58.2818	−2.12391
$754$	−20.6645	−0.752558
$755$	15.4152	0.561016
$756$	20.2584	0.736792
$757$	−33.2848	−1.20976	−0.604878	−	0.796318i	$-0.706778\pi$
$757$	−33.2848	−1.20976	−0.604878	+	0.796318i	$0.706778\pi$
$758$	−29.6192	−1.07582
$759$	52.1902	1.89438
$760$	5.12283	0.185825
$761$	−17.3634	−0.629422	−0.314711	−	0.949188i	$-0.601908\pi$
$761$	−17.3634	−0.629422	−0.314711	+	0.949188i	$0.601908\pi$
$762$	−30.0357	−1.08808
$763$	−10.3948	−0.376319
$764$	5.82810	0.210853
$765$	7.98800	0.288807
$766$	21.1132	0.762849
$767$	−72.0829	−2.60276
$768$	2.94584	0.106299
$769$	−5.84314	−0.210709	−0.105355	−	0.994435i	$-0.533598\pi$
$769$	−5.84314	−0.210709	−0.105355	+	0.994435i	$0.533598\pi$
$770$	5.85607	0.211038
$771$	43.5332	1.56781
$772$	2.39465	0.0861852
$773$	16.6305	0.598157	0.299078	−	0.954229i	$-0.403321\pi$
$773$	16.6305	0.598157	0.299078	+	0.954229i	$0.403321\pi$
$774$	−20.6280	−0.741457
$775$	3.25428	0.116897
$776$	−16.5480	−0.594040
$777$	32.3105	1.15913
$778$	30.3463	1.08797
$779$	−39.9482	−1.43129
$780$	15.8657	0.568085
$781$	2.65923	0.0951546
$782$	10.9298	0.390849
$783$	−30.2683	−1.08170
$784$	−0.405444	−0.0144801
$785$	2.60337	0.0929184
$786$	27.7073	0.988288
$787$	−16.7805	−0.598159	−0.299079	−	0.954228i	$-0.596679\pi$
$787$	−16.7805	−0.598159	−0.299079	+	0.954228i	$0.596679\pi$
$788$	−10.5909	−0.377284
$789$	−16.1738	−0.575802
$790$	−5.91203	−0.210340
$791$	6.70905	0.238546
$792$	−12.9481	−0.460090
$793$	−16.0116	−0.568590
$794$	−16.4946	−0.585372
$795$	−10.1342	−0.359422
$796$	2.22324	0.0788008
$797$	39.4933	1.39893	0.699463	−	0.714669i	$-0.253423\pi$
$797$	39.4933	1.39893	0.699463	+	0.714669i	$0.253423\pi$
$798$	−38.7536	−1.37186
$799$	7.18121	0.254053
$800$	−1.00000	−0.0353553
$801$	−41.6660	−1.47219
$802$	−1.00000	−0.0353112
$803$	31.1310	1.09859
$804$	−0.491291	−0.0173265
$805$	−19.9508	−0.703172
$806$	17.5269	0.617360
$807$	−11.9930	−0.422172
$808$	−2.36112	−0.0830639
$809$	−36.4110	−1.28014	−0.640071	−	0.768316i	$-0.721095\pi$
$809$	−36.4110	−1.28014	−0.640071	+	0.768316i	$0.721095\pi$
$810$	6.20535	0.218034
$811$	−27.1589	−0.953677	−0.476839	−	0.878991i	$-0.658217\pi$
$811$	−27.1589	−0.953677	−0.476839	+	0.878991i	$0.658217\pi$
$812$	−9.85297	−0.345771
$813$	24.9835	0.876210
$814$	−9.73994	−0.341385
$815$	12.0817	0.423205
$816$	−4.14433	−0.145081
$817$	18.6112	0.651124
$818$	−24.1892	−0.845755
$819$	−78.5302	−2.74407
$820$	7.79807	0.272320
$821$	32.1305	1.12136	0.560680	−	0.828032i	$-0.310540\pi$
$821$	32.1305	1.12136	0.560680	+	0.828032i	$0.310540\pi$
$822$	−23.0767	−0.804894
$823$	−37.4482	−1.30536	−0.652681	−	0.757633i	$-0.726356\pi$
$823$	−37.4482	−1.30536	−0.652681	+	0.757633i	$0.726356\pi$
$824$	4.52115	0.157502
$825$	6.71773	0.233881
$826$	−34.3695	−1.19587
$827$	48.8295	1.69797	0.848984	−	0.528419i	$-0.177215\pi$
$827$	48.8295	1.69797	0.848984	+	0.528419i	$0.177215\pi$
$828$	44.1122	1.53301
$829$	−6.22253	−0.216117	−0.108059	−	0.994145i	$-0.534463\pi$
$829$	−6.22253	−0.216117	−0.108059	+	0.994145i	$0.534463\pi$
$830$	−9.66124	−0.335346
$831$	−32.2593	−1.11906
$832$	−5.38582	−0.186720
$833$	0.570396	0.0197631
$834$	−46.4919	−1.60988
$835$	−6.30384	−0.218153
$836$	11.6822	0.404036
$837$	25.6725	0.887370
$838$	21.1570	0.730858
$839$	−18.5979	−0.642072	−0.321036	−	0.947067i	$-0.604031\pi$
$839$	−18.5979	−0.642072	−0.321036	+	0.947067i	$0.604031\pi$
$840$	7.56487	0.261013
$841$	−14.2786	−0.492366
$842$	10.5406	0.363253
$843$	35.0286	1.20645
$844$	−3.95240	−0.136047
$845$	−16.0070	−0.550658
$846$	28.9831	0.996458
$847$	−14.8936	−0.511750
$848$	3.44016	0.118136
$849$	−24.9298	−0.855589
$850$	1.40684	0.0482543
$851$	33.1825	1.13748
$852$	3.43519	0.117688
$853$	38.5375	1.31950	0.659750	−	0.751485i	$-0.270662\pi$
$853$	38.5375	1.31950	0.659750	+	0.751485i	$0.270662\pi$
$854$	−7.63444	−0.261245
$855$	−29.0872	−0.994763
$856$	−9.83954	−0.336309
$857$	9.36053	0.319749	0.159875	−	0.987137i	$-0.448891\pi$
$857$	9.36053	0.319749	0.159875	+	0.987137i	$0.448891\pi$
$858$	36.1804	1.23518
$859$	−5.88265	−0.200713	−0.100357	−	0.994952i	$-0.531998\pi$
$859$	−5.88265	−0.200713	−0.100357	+	0.994952i	$0.531998\pi$
$860$	−3.63299	−0.123884
$861$	−58.9914	−2.01042
$862$	1.98063	0.0674604
$863$	−39.1247	−1.33182	−0.665910	−	0.746032i	$-0.731957\pi$
$863$	−39.1247	−1.33182	−0.665910	+	0.746032i	$0.731957\pi$
$864$	−7.88884	−0.268384
$865$	1.32474	0.0450425
$866$	−38.9083	−1.32216
$867$	−44.2488	−1.50277
$868$	8.35694	0.283653
$869$	−13.4819	−0.457341
$870$	−11.3027	−0.383198
$871$	0.898218	0.0304350
$872$	4.04786	0.137078
$873$	93.9592	3.18004
$874$	−39.7994	−1.34624
$875$	−2.56799	−0.0868138
$876$	40.2150	1.35874
$877$	44.1800	1.49185	0.745926	−	0.666029i	$-0.232007\pi$
$877$	44.1800	1.49185	0.745926	+	0.666029i	$0.232007\pi$
$878$	20.3147	0.685587
$879$	−16.2516	−0.548153
$880$	−2.28041	−0.0768727
$881$	29.5585	0.995851	0.497926	−	0.867220i	$-0.334095\pi$
$881$	29.5585	0.995851	0.497926	+	0.867220i	$0.334095\pi$
$882$	2.30210	0.0775156
$883$	−29.3371	−0.987272	−0.493636	−	0.869669i	$-0.664332\pi$
$883$	−29.3371	−0.987272	−0.493636	+	0.869669i	$0.664332\pi$
$884$	7.57699	0.254842
$885$	−39.4266	−1.32531
$886$	30.8826	1.03752
$887$	46.1793	1.55055	0.775275	−	0.631624i	$-0.217611\pi$
$887$	46.1793	1.55055	0.775275	+	0.631624i	$0.217611\pi$
$888$	−12.5821	−0.422226
$889$	26.1832	0.878155
$890$	−7.33819	−0.245977
$891$	14.1508	0.474069
$892$	−22.3347	−0.747821
$893$	−26.1494	−0.875057
$894$	38.8911	1.30071
$895$	−9.19865	−0.307477
$896$	−2.56799	−0.0857904
$897$	−123.261	−4.11558
$898$	−14.6913	−0.490254
$899$	−12.4862	−0.416437
$900$	5.67796	0.189265
$901$	−4.83977	−0.161236
$902$	17.7828	0.592103
$903$	27.4831	0.914581
$904$	−2.61257	−0.0868928
$905$	−23.1462	−0.769407
$906$	45.4106	1.50867
$907$	−30.5400	−1.01406	−0.507031	−	0.861928i	$-0.669257\pi$
$907$	−30.5400	−1.01406	−0.507031	+	0.861928i	$0.669257\pi$
$908$	1.83568	0.0609193
$909$	13.4063	0.444660
$910$	−13.8307	−0.458483
$911$	−46.0914	−1.52708	−0.763538	−	0.645763i	$-0.776539\pi$
$911$	−46.0914	−1.52708	−0.763538	+	0.645763i	$0.776539\pi$
$912$	15.0910	0.499714
$913$	−22.0316	−0.729140
$914$	−1.09430	−0.0361962
$915$	−8.75776	−0.289523
$916$	−6.13613	−0.202743
$917$	−24.1534	−0.797617
$918$	11.0984	0.366300
$919$	−21.3322	−0.703685	−0.351842	−	0.936059i	$-0.614445\pi$
$919$	−21.3322	−0.703685	−0.351842	+	0.936059i	$0.614445\pi$
$920$	7.76902	0.256137
$921$	43.5078	1.43363
$922$	37.0142	1.21900
$923$	−6.28049	−0.206725
$924$	17.2510	0.567517
$925$	4.27113	0.140434
$926$	−2.78743	−0.0916006
$927$	−25.6709	−0.843143
$928$	3.83685	0.125951
$929$	−1.80120	−0.0590954	−0.0295477	−	0.999563i	$-0.509407\pi$
$929$	−1.80120	−0.0590954	−0.0295477	+	0.999563i	$0.509407\pi$
$930$	9.58657	0.314356
$931$	−2.07702	−0.0680717
$932$	−12.5500	−0.411088
$933$	14.9595	0.489752
$934$	10.0653	0.329346
$935$	3.20818	0.104919
$936$	30.5804	0.999553
$937$	−40.2262	−1.31413	−0.657066	−	0.753833i	$-0.728203\pi$
$937$	−40.2262	−1.31413	−0.657066	+	0.753833i	$0.728203\pi$
$938$	0.428275	0.0139837
$939$	25.8565	0.843794
$940$	5.10448	0.166490
$941$	37.0316	1.20720	0.603598	−	0.797288i	$-0.293733\pi$
$941$	37.0316	1.20720	0.603598	+	0.797288i	$0.293733\pi$
$942$	7.66911	0.249873
$943$	−60.5834	−1.97287
$944$	13.3838	0.435607
$945$	−20.2584	−0.659007
$946$	−8.28472	−0.269359
$947$	36.6802	1.19195	0.595973	−	0.803004i	$-0.296766\pi$
$947$	36.6802	1.19195	0.595973	+	0.803004i	$0.296766\pi$
$948$	−17.4159	−0.565641
$949$	−73.5242	−2.38670
$950$	−5.12283	−0.166207
$951$	−79.9955	−2.59403
$952$	3.61275	0.117090
$953$	−1.57017	−0.0508629	−0.0254314	−	0.999677i	$-0.508096\pi$
$953$	−1.57017	−0.0508629	−0.0254314	+	0.999677i	$0.508096\pi$
$954$	−19.5331	−0.632408
$955$	−5.82810	−0.188593
$956$	4.78332	0.154703
$957$	−25.7749	−0.833183
$958$	35.9421	1.16124
$959$	20.1168	0.649605
$960$	−2.94584	−0.0950765
$961$	−20.4097	−0.658377
$962$	23.0035	0.741663
$963$	55.8685	1.80034
$964$	−8.49201	−0.273509
$965$	−2.39465	−0.0770864
$966$	−58.7717	−1.89095
$967$	21.3852	0.687701	0.343850	−	0.939024i	$-0.388269\pi$
$967$	21.3852	0.687701	0.343850	+	0.939024i	$0.388269\pi$
$968$	5.79972	0.186410
$969$	−21.2307	−0.682029
$970$	16.5480	0.531326
$971$	−43.1791	−1.38568	−0.692841	−	0.721090i	$-0.743641\pi$
$971$	−43.1791	−1.38568	−0.692841	+	0.721090i	$0.743641\pi$
$972$	−5.38654	−0.172773
$973$	40.5285	1.29929
$974$	−27.1565	−0.870150
$975$	−15.8657	−0.508110
$976$	2.97293	0.0951611
$977$	−29.4397	−0.941858	−0.470929	−	0.882171i	$-0.656081\pi$
$977$	−29.4397	−0.941858	−0.470929	+	0.882171i	$0.656081\pi$
$978$	35.5908	1.13807
$979$	−16.7341	−0.534824
$980$	0.405444	0.0129514
$981$	−22.9836	−0.733809
$982$	−33.1747	−1.05865
$983$	−49.3169	−1.57296	−0.786482	−	0.617613i	$-0.788100\pi$
$983$	−49.3169	−1.57296	−0.786482	+	0.617613i	$0.788100\pi$
$984$	22.9718	0.732316
$985$	10.5909	0.337453
$986$	−5.39784	−0.171902
$987$	−38.6148	−1.22912
$988$	−27.5906	−0.877775
$989$	28.2248	0.897496
$990$	12.9481	0.411517
$991$	26.1791	0.831607	0.415803	−	0.909455i	$-0.363500\pi$
$991$	26.1791	0.831607	0.415803	+	0.909455i	$0.363500\pi$
$992$	−3.25428	−0.103323
$993$	41.3061	1.31081
$994$	−2.99457	−0.0949821
$995$	−2.22324	−0.0704815
$996$	−28.4604	−0.901804
$997$	−55.1577	−1.74686	−0.873431	−	0.486948i	$-0.838110\pi$
$997$	−55.1577	−1.74686	−0.873431	+	0.486948i	$0.838110\pi$
$998$	5.04645	0.159742
$999$	33.6942	1.06604

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.l.1.17	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.l.1.17	✓	17	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.94584 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.94584 q^{6} +2.56799 q^{7} -1.00000 q^{8} +5.67796 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.94584 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.94584 q^{6} +2.56799 q^{7} -1.00000 q^{8} +5.67796 q^{9} +1.00000 q^{10} +2.28041 q^{11} +2.94584 q^{12} -5.38582 q^{13} -2.56799 q^{14} -2.94584 q^{15} +1.00000 q^{16} -1.40684 q^{17} -5.67796 q^{18} +5.12283 q^{19} -1.00000 q^{20} +7.56487 q^{21} -2.28041 q^{22} +7.76902 q^{23} -2.94584 q^{24} +1.00000 q^{25} +5.38582 q^{26} +7.88884 q^{27} +2.56799 q^{28} -3.83685 q^{29} +2.94584 q^{30} +3.25428 q^{31} -1.00000 q^{32} +6.71773 q^{33} +1.40684 q^{34} -2.56799 q^{35} +5.67796 q^{36} +4.27113 q^{37} -5.12283 q^{38} -15.8657 q^{39} +1.00000 q^{40} -7.79807 q^{41} -7.56487 q^{42} +3.63299 q^{43} +2.28041 q^{44} -5.67796 q^{45} -7.76902 q^{46} -5.10448 q^{47} +2.94584 q^{48} -0.405444 q^{49} -1.00000 q^{50} -4.14433 q^{51} -5.38582 q^{52} +3.44016 q^{53} -7.88884 q^{54} -2.28041 q^{55} -2.56799 q^{56} +15.0910 q^{57} +3.83685 q^{58} +13.3838 q^{59} -2.94584 q^{60} +2.97293 q^{61} -3.25428 q^{62} +14.5809 q^{63} +1.00000 q^{64} +5.38582 q^{65} -6.71773 q^{66} -0.166775 q^{67} -1.40684 q^{68} +22.8863 q^{69} +2.56799 q^{70} +1.16612 q^{71} -5.67796 q^{72} +13.6515 q^{73} -4.27113 q^{74} +2.94584 q^{75} +5.12283 q^{76} +5.85607 q^{77} +15.8657 q^{78} -5.91203 q^{79} -1.00000 q^{80} +6.20535 q^{81} +7.79807 q^{82} -9.66124 q^{83} +7.56487 q^{84} +1.40684 q^{85} -3.63299 q^{86} -11.3027 q^{87} -2.28041 q^{88} -7.33819 q^{89} +5.67796 q^{90} -13.8307 q^{91} +7.76902 q^{92} +9.58657 q^{93} +5.10448 q^{94} -5.12283 q^{95} -2.94584 q^{96} +16.5480 q^{97} +0.405444 q^{98} +12.9481 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * q^99

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