LMFDB - Embedded newform 2013.2.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,2,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2013.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:	$16.0738859269$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4x^{10} - 6x^{9} + 37x^{8} - 2x^{7} - 109x^{6} + 55x^{5} + 115x^{4} - 76x^{3} - 29x^{2} + 14x + 3 $ x^11 - 4x^10 - 6x^9 + 37x^8 - 2x^7 - 109x^6 + 55x^5 + 115x^4 - 76x^3 - 29x^2 + 14x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.36137$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.36137 q^{2} +1.00000 q^{3} -0.146675 q^{4} -3.87776 q^{5} -1.36137 q^{6} -4.18708 q^{7} +2.92242 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.36137 q^{2} +1.00000 q^{3} -0.146675 q^{4} -3.87776 q^{5} -1.36137 q^{6} -4.18708 q^{7} +2.92242 q^{8} +1.00000 q^{9} +5.27907 q^{10} -1.00000 q^{11} -0.146675 q^{12} +6.69213 q^{13} +5.70016 q^{14} -3.87776 q^{15} -3.68514 q^{16} +2.46824 q^{17} -1.36137 q^{18} +0.542898 q^{19} +0.568769 q^{20} -4.18708 q^{21} +1.36137 q^{22} +2.08289 q^{23} +2.92242 q^{24} +10.0370 q^{25} -9.11046 q^{26} +1.00000 q^{27} +0.614139 q^{28} -2.48240 q^{29} +5.27907 q^{30} -6.44257 q^{31} -0.828001 q^{32} -1.00000 q^{33} -3.36018 q^{34} +16.2365 q^{35} -0.146675 q^{36} +11.3624 q^{37} -0.739084 q^{38} +6.69213 q^{39} -11.3324 q^{40} -12.1540 q^{41} +5.70016 q^{42} -1.28391 q^{43} +0.146675 q^{44} -3.87776 q^{45} -2.83558 q^{46} +6.95084 q^{47} -3.68514 q^{48} +10.5317 q^{49} -13.6641 q^{50} +2.46824 q^{51} -0.981566 q^{52} +11.4569 q^{53} -1.36137 q^{54} +3.87776 q^{55} -12.2364 q^{56} +0.542898 q^{57} +3.37947 q^{58} -10.3751 q^{59} +0.568769 q^{60} +1.00000 q^{61} +8.77071 q^{62} -4.18708 q^{63} +8.49749 q^{64} -25.9505 q^{65} +1.36137 q^{66} +2.88534 q^{67} -0.362028 q^{68} +2.08289 q^{69} -22.1039 q^{70} -12.6125 q^{71} +2.92242 q^{72} +3.24241 q^{73} -15.4685 q^{74} +10.0370 q^{75} -0.0796293 q^{76} +4.18708 q^{77} -9.11046 q^{78} -8.60065 q^{79} +14.2901 q^{80} +1.00000 q^{81} +16.5461 q^{82} -11.8532 q^{83} +0.614139 q^{84} -9.57124 q^{85} +1.74787 q^{86} -2.48240 q^{87} -2.92242 q^{88} -7.77300 q^{89} +5.27907 q^{90} -28.0205 q^{91} -0.305507 q^{92} -6.44257 q^{93} -9.46266 q^{94} -2.10523 q^{95} -0.828001 q^{96} -8.63349 q^{97} -14.3375 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 4 q^{2} + 11 q^{3} + 6 q^{4} - 13 q^{5} - 4 q^{6} - 5 q^{7} - 9 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q - 4 * q^2 + 11 * q^3 + 6 * q^4 - 13 * q^5 - 4 * q^6 - 5 * q^7 - 9 * q^8 + 11 * q^9	\( 11 q - 4 q^{2} + 11 q^{3} + 6 q^{4} - 13 q^{5} - 4 q^{6} - 5 q^{7} - 9 q^{8} + 11 q^{9} + 6 q^{10} - 11 q^{11} + 6 q^{12} - 3 q^{13} - 9 q^{14} - 13 q^{15} + 4 q^{16} - 7 q^{17} - 4 q^{18} - 8 q^{19} - 25 q^{20} - 5 q^{21} + 4 q^{22} - 15 q^{23} - 9 q^{24} + 4 q^{25} - 2 q^{26} + 11 q^{27} + 13 q^{28} - 8 q^{29} + 6 q^{30} - 17 q^{31} - 27 q^{32} - 11 q^{33} - 18 q^{34} - 2 q^{35} + 6 q^{36} - 10 q^{37} - 30 q^{38} - 3 q^{39} + 10 q^{40} - 25 q^{41} - 9 q^{42} - 7 q^{43} - 6 q^{44} - 13 q^{45} + 32 q^{46} - 30 q^{47} + 4 q^{48} - 2 q^{49} + 11 q^{50} - 7 q^{51} - 7 q^{52} - 18 q^{53} - 4 q^{54} + 13 q^{55} - 20 q^{56} - 8 q^{57} - 13 q^{58} - 43 q^{59} - 25 q^{60} + 11 q^{61} + 7 q^{62} - 5 q^{63} + 25 q^{64} - 27 q^{65} + 4 q^{66} - 30 q^{67} + 10 q^{68} - 15 q^{69} - 4 q^{70} - 7 q^{71} - 9 q^{72} + 6 q^{73} - 44 q^{74} + 4 q^{75} - 19 q^{76} + 5 q^{77} - 2 q^{78} + 17 q^{79} - 22 q^{80} + 11 q^{81} + 8 q^{82} - 34 q^{83} + 13 q^{84} + 10 q^{85} + 2 q^{86} - 8 q^{87} + 9 q^{88} - 41 q^{89} + 6 q^{90} - 39 q^{91} - 32 q^{92} - 17 q^{93} + 55 q^{94} - 9 q^{95} - 27 q^{96} - 41 q^{97} - 29 q^{98} - 11 q^{99}+O(q^{100}) \) 11 * q - 4 * q^2 + 11 * q^3 + 6 * q^4 - 13 * q^5 - 4 * q^6 - 5 * q^7 - 9 * q^8 + 11 * q^9 + 6 * q^10 - 11 * q^11 + 6 * q^12 - 3 * q^13 - 9 * q^14 - 13 * q^15 + 4 * q^16 - 7 * q^17 - 4 * q^18 - 8 * q^19 - 25 * q^20 - 5 * q^21 + 4 * q^22 - 15 * q^23 - 9 * q^24 + 4 * q^25 - 2 * q^26 + 11 * q^27 + 13 * q^28 - 8 * q^29 + 6 * q^30 - 17 * q^31 - 27 * q^32 - 11 * q^33 - 18 * q^34 - 2 * q^35 + 6 * q^36 - 10 * q^37 - 30 * q^38 - 3 * q^39 + 10 * q^40 - 25 * q^41 - 9 * q^42 - 7 * q^43 - 6 * q^44 - 13 * q^45 + 32 * q^46 - 30 * q^47 + 4 * q^48 - 2 * q^49 + 11 * q^50 - 7 * q^51 - 7 * q^52 - 18 * q^53 - 4 * q^54 + 13 * q^55 - 20 * q^56 - 8 * q^57 - 13 * q^58 - 43 * q^59 - 25 * q^60 + 11 * q^61 + 7 * q^62 - 5 * q^63 + 25 * q^64 - 27 * q^65 + 4 * q^66 - 30 * q^67 + 10 * q^68 - 15 * q^69 - 4 * q^70 - 7 * q^71 - 9 * q^72 + 6 * q^73 - 44 * q^74 + 4 * q^75 - 19 * q^76 + 5 * q^77 - 2 * q^78 + 17 * q^79 - 22 * q^80 + 11 * q^81 + 8 * q^82 - 34 * q^83 + 13 * q^84 + 10 * q^85 + 2 * q^86 - 8 * q^87 + 9 * q^88 - 41 * q^89 + 6 * q^90 - 39 * q^91 - 32 * q^92 - 17 * q^93 + 55 * q^94 - 9 * q^95 - 27 * q^96 - 41 * q^97 - 29 * 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 $

$2$	−1.36137	−0.962633	−0.481317	−	0.876547i	$-0.659841\pi$
$2$	−1.36137	−0.962633	−0.481317	+	0.876547i	$0.659841\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.146675	−0.0733373
$5$	−3.87776	−1.73419	−0.867094	−	0.498144i	$-0.834015\pi$
$5$	−3.87776	−1.73419	−0.867094	+	0.498144i	$0.834015\pi$
$6$	−1.36137	−0.555777
$7$	−4.18708	−1.58257	−0.791284	−	0.611449i	$-0.790587\pi$
$7$	−4.18708	−1.58257	−0.791284	+	0.611449i	$0.790587\pi$
$8$	2.92242	1.03323
$9$	1.00000	0.333333
$10$	5.27907	1.66939
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.146675	−0.0423413
$13$	6.69213	1.85606	0.928031	−	0.372502i	$-0.121500\pi$
$13$	6.69213	1.85606	0.928031	+	0.372502i	$0.121500\pi$
$14$	5.70016	1.52343
$15$	−3.87776	−1.00123
$16$	−3.68514	−0.921284
$17$	2.46824	0.598636	0.299318	−	0.954153i	$-0.403241\pi$
$17$	2.46824	0.598636	0.299318	+	0.954153i	$0.403241\pi$
$18$	−1.36137	−0.320878
$19$	0.542898	0.124549	0.0622746	−	0.998059i	$-0.480165\pi$
$19$	0.542898	0.124549	0.0622746	+	0.998059i	$0.480165\pi$
$20$	0.568769	0.127181
$21$	−4.18708	−0.913696
$22$	1.36137	0.290245
$23$	2.08289	0.434312	0.217156	−	0.976137i	$-0.430322\pi$
$23$	2.08289	0.434312	0.217156	+	0.976137i	$0.430322\pi$
$24$	2.92242	0.596536
$25$	10.0370	2.00741
$26$	−9.11046	−1.78671
$27$	1.00000	0.192450
$28$	0.614139	0.116061
$29$	−2.48240	−0.460971	−0.230485	−	0.973076i	$-0.574031\pi$
$29$	−2.48240	−0.460971	−0.230485	+	0.973076i	$0.574031\pi$
$30$	5.27907	0.963821
$31$	−6.44257	−1.15712	−0.578559	−	0.815640i	$-0.696385\pi$
$31$	−6.44257	−1.15712	−0.578559	+	0.815640i	$0.696385\pi$
$32$	−0.828001	−0.146371
$33$	−1.00000	−0.174078
$34$	−3.36018	−0.576267
$35$	16.2365	2.74447
$36$	−0.146675	−0.0244458
$37$	11.3624	1.86797	0.933987	−	0.357307i	$-0.116305\pi$
$37$	11.3624	1.86797	0.933987	+	0.357307i	$0.116305\pi$
$38$	−0.739084	−0.119895
$39$	6.69213	1.07160
$40$	−11.3324	−1.79182
$41$	−12.1540	−1.89813	−0.949067	−	0.315076i	$-0.897970\pi$
$41$	−12.1540	−1.89813	−0.949067	+	0.315076i	$0.897970\pi$
$42$	5.70016	0.879554
$43$	−1.28391	−0.195794	−0.0978970	−	0.995197i	$-0.531212\pi$
$43$	−1.28391	−0.195794	−0.0978970	+	0.995197i	$0.531212\pi$
$44$	0.146675	0.0221120
$45$	−3.87776	−0.578063
$46$	−2.83558	−0.418083
$47$	6.95084	1.01388	0.506942	−	0.861980i	$-0.330776\pi$
$47$	6.95084	1.01388	0.506942	+	0.861980i	$0.330776\pi$
$48$	−3.68514	−0.531904
$49$	10.5317	1.50452
$50$	−13.6641	−1.93240
$51$	2.46824	0.345623
$52$	−0.981566	−0.136119
$53$	11.4569	1.57372	0.786861	−	0.617130i	$-0.211705\pi$
$53$	11.4569	1.57372	0.786861	+	0.617130i	$0.211705\pi$
$54$	−1.36137	−0.185259
$55$	3.87776	0.522877
$56$	−12.2364	−1.63516
$57$	0.542898	0.0719086
$58$	3.37947	0.443746
$59$	−10.3751	−1.35072	−0.675360	−	0.737488i	$-0.736012\pi$
$59$	−10.3751	−1.35072	−0.675360	+	0.737488i	$0.736012\pi$
$60$	0.568769	0.0734278
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	8.77071	1.11388
$63$	−4.18708	−0.527523
$64$	8.49749	1.06219
$65$	−25.9505	−3.21876
$66$	1.36137	0.167573
$67$	2.88534	0.352500	0.176250	−	0.984345i	$-0.443603\pi$
$67$	2.88534	0.352500	0.176250	+	0.984345i	$0.443603\pi$
$68$	−0.362028	−0.0439023
$69$	2.08289	0.250750
$70$	−22.1039	−2.64192
$71$	−12.6125	−1.49683	−0.748416	−	0.663229i	$-0.769186\pi$
$71$	−12.6125	−1.49683	−0.748416	+	0.663229i	$0.769186\pi$
$72$	2.92242	0.344410
$73$	3.24241	0.379495	0.189748	−	0.981833i	$-0.439233\pi$
$73$	3.24241	0.379495	0.189748	+	0.981833i	$0.439233\pi$
$74$	−15.4685	−1.79817
$75$	10.0370	1.15898
$76$	−0.0796293	−0.00913411
$77$	4.18708	0.477162
$78$	−9.11046	−1.03156
$79$	−8.60065	−0.967648	−0.483824	−	0.875165i	$-0.660753\pi$
$79$	−8.60065	−0.967648	−0.483824	+	0.875165i	$0.660753\pi$
$80$	14.2901	1.59768
$81$	1.00000	0.111111
$82$	16.5461	1.82721
$83$	−11.8532	−1.30106	−0.650529	−	0.759482i	$-0.725453\pi$
$83$	−11.8532	−1.30106	−0.650529	+	0.759482i	$0.725453\pi$
$84$	0.614139	0.0670080
$85$	−9.57124	−1.03815
$86$	1.74787	0.188478
$87$	−2.48240	−0.266142
$88$	−2.92242	−0.311531
$89$	−7.77300	−0.823936	−0.411968	−	0.911198i	$-0.635158\pi$
$89$	−7.77300	−0.823936	−0.411968	+	0.911198i	$0.635158\pi$
$90$	5.27907	0.556462
$91$	−28.0205	−2.93735
$92$	−0.305507	−0.0318513
$93$	−6.44257	−0.668063
$94$	−9.46266	−0.975998
$95$	−2.10523	−0.215992
$96$	−0.828001	−0.0845075
$97$	−8.63349	−0.876598	−0.438299	−	0.898829i	$-0.644419\pi$
$97$	−8.63349	−0.876598	−0.438299	+	0.898829i	$0.644419\pi$
$98$	−14.3375	−1.44830
$99$	−1.00000	−0.100504
$100$	−1.47218	−0.147218
$101$	13.8546	1.37858	0.689292	−	0.724484i	$-0.257922\pi$
$101$	13.8546	1.37858	0.689292	+	0.724484i	$0.257922\pi$
$102$	−3.36018	−0.332708
$103$	−10.1640	−1.00149	−0.500744	−	0.865595i	$-0.666940\pi$
$103$	−10.1640	−1.00149	−0.500744	+	0.865595i	$0.666940\pi$
$104$	19.5572	1.91774
$105$	16.2365	1.58452
$106$	−15.5970	−1.51492
$107$	−6.89839	−0.666892	−0.333446	−	0.942769i	$-0.608212\pi$
$107$	−6.89839	−0.666892	−0.333446	+	0.942769i	$0.608212\pi$
$108$	−0.146675	−0.0141138
$109$	4.32572	0.414329	0.207165	−	0.978306i	$-0.433576\pi$
$109$	4.32572	0.414329	0.207165	+	0.978306i	$0.433576\pi$
$110$	−5.27907	−0.503339
$111$	11.3624	1.07848
$112$	15.4300	1.45800
$113$	−16.4131	−1.54401	−0.772007	−	0.635614i	$-0.780747\pi$
$113$	−16.4131	−1.54401	−0.772007	+	0.635614i	$0.780747\pi$
$114$	−0.739084	−0.0692216
$115$	−8.07694	−0.753179
$116$	0.364106	0.0338064
$117$	6.69213	0.618688
$118$	14.1243	1.30025
$119$	−10.3347	−0.947382
$120$	−11.3324	−1.03451
$121$	1.00000	0.0909091
$122$	−1.36137	−0.123253
$123$	−12.1540	−1.09589
$124$	0.944961	0.0848600
$125$	−19.5325	−1.74704
$126$	5.70016	0.507811
$127$	6.40220	0.568103	0.284052	−	0.958809i	$-0.408321\pi$
$127$	6.40220	0.568103	0.284052	+	0.958809i	$0.408321\pi$
$128$	−9.91222	−0.876124
$129$	−1.28391	−0.113042
$130$	35.3282	3.09849
$131$	−8.59775	−0.751189	−0.375594	−	0.926784i	$-0.622561\pi$
$131$	−8.59775	−0.751189	−0.375594	+	0.926784i	$0.622561\pi$
$132$	0.146675	0.0127664
$133$	−2.27316	−0.197108
$134$	−3.92801	−0.339328
$135$	−3.87776	−0.333745
$136$	7.21322	0.618529
$137$	−1.42796	−0.121999	−0.0609996	−	0.998138i	$-0.519429\pi$
$137$	−1.42796	−0.121999	−0.0609996	+	0.998138i	$0.519429\pi$
$138$	−2.83558	−0.241380
$139$	5.70099	0.483552	0.241776	−	0.970332i	$-0.422270\pi$
$139$	5.70099	0.483552	0.241776	+	0.970332i	$0.422270\pi$
$140$	−2.38148	−0.201272
$141$	6.95084	0.585366
$142$	17.1703	1.44090
$143$	−6.69213	−0.559624
$144$	−3.68514	−0.307095
$145$	9.62617	0.799410
$146$	−4.41411	−0.365315
$147$	10.5317	0.868636
$148$	−1.66658	−0.136992
$149$	−8.09426	−0.663107	−0.331554	−	0.943436i	$-0.607573\pi$
$149$	−8.09426	−0.663107	−0.331554	+	0.943436i	$0.607573\pi$
$150$	−13.6641	−1.11567
$151$	23.7308	1.93118	0.965592	−	0.260062i	$-0.0837429\pi$
$151$	23.7308	1.93118	0.965592	+	0.260062i	$0.0837429\pi$
$152$	1.58657	0.128688
$153$	2.46824	0.199545
$154$	−5.70016	−0.459332
$155$	24.9827	2.00666
$156$	−0.981566	−0.0785881
$157$	9.39417	0.749736	0.374868	−	0.927078i	$-0.377688\pi$
$157$	9.39417	0.749736	0.374868	+	0.927078i	$0.377688\pi$
$158$	11.7087	0.931490
$159$	11.4569	0.908589
$160$	3.21079	0.253835
$161$	−8.72122	−0.687328
$162$	−1.36137	−0.106959
$163$	−21.6836	−1.69839	−0.849194	−	0.528081i	$-0.822912\pi$
$163$	−21.6836	−1.69839	−0.849194	+	0.528081i	$0.822912\pi$
$164$	1.78268	0.139204
$165$	3.87776	0.301883
$166$	16.1366	1.25244
$167$	−2.13907	−0.165526	−0.0827632	−	0.996569i	$-0.526375\pi$
$167$	−2.13907	−0.165526	−0.0827632	+	0.996569i	$0.526375\pi$
$168$	−12.2364	−0.944058
$169$	31.7846	2.44497
$170$	13.0300	0.999355
$171$	0.542898	0.0415164
$172$	0.188317	0.0143590
$173$	7.13624	0.542559	0.271279	−	0.962501i	$-0.412553\pi$
$173$	7.13624	0.542559	0.271279	+	0.962501i	$0.412553\pi$
$174$	3.37947	0.256197
$175$	−42.0259	−3.17686
$176$	3.68514	0.277778
$177$	−10.3751	−0.779839
$178$	10.5819	0.793148
$179$	10.1795	0.760853	0.380426	−	0.924811i	$-0.375777\pi$
$179$	10.1795	0.760853	0.380426	+	0.924811i	$0.375777\pi$
$180$	0.568769	0.0423936
$181$	−18.1842	−1.35162	−0.675809	−	0.737077i	$-0.736206\pi$
$181$	−18.1842	−1.35162	−0.675809	+	0.737077i	$0.736206\pi$
$182$	38.1462	2.82759
$183$	1.00000	0.0739221
$184$	6.08706	0.448744
$185$	−44.0608	−3.23942
$186$	8.77071	0.643100
$187$	−2.46824	−0.180496
$188$	−1.01951	−0.0743555
$189$	−4.18708	−0.304565
$190$	2.86599	0.207921
$191$	−24.4619	−1.77000	−0.885001	−	0.465590i	$-0.845842\pi$
$191$	−24.4619	−1.77000	−0.885001	+	0.465590i	$0.845842\pi$
$192$	8.49749	0.613253
$193$	9.15753	0.659174	0.329587	−	0.944125i	$-0.393091\pi$
$193$	9.15753	0.659174	0.329587	+	0.944125i	$0.393091\pi$
$194$	11.7534	0.843842
$195$	−25.9505	−1.85835
$196$	−1.54473	−0.110338
$197$	6.78587	0.483473	0.241737	−	0.970342i	$-0.422283\pi$
$197$	6.78587	0.483473	0.241737	+	0.970342i	$0.422283\pi$
$198$	1.36137	0.0967483
$199$	−9.29788	−0.659110	−0.329555	−	0.944136i	$-0.606899\pi$
$199$	−9.29788	−0.659110	−0.329555	+	0.944136i	$0.606899\pi$
$200$	29.3324	2.07411
$201$	2.88534	0.203516
$202$	−18.8612	−1.32707
$203$	10.3940	0.729518
$204$	−0.362028	−0.0253470
$205$	47.1303	3.29172
$206$	13.8369	0.964065
$207$	2.08289	0.144771
$208$	−24.6614	−1.70996
$209$	−0.542898	−0.0375530
$210$	−22.1039	−1.52531
$211$	23.3423	1.60695	0.803475	−	0.595338i	$-0.202982\pi$
$211$	23.3423	1.60695	0.803475	+	0.595338i	$0.202982\pi$
$212$	−1.68043	−0.115413
$213$	−12.6125	−0.864197
$214$	9.39125	0.641973
$215$	4.97868	0.339543
$216$	2.92242	0.198845
$217$	26.9756	1.83122
$218$	−5.88890	−0.398847
$219$	3.24241	0.219102
$220$	−0.568769	−0.0383464
$221$	16.5178	1.11111
$222$	−15.4685	−1.03818
$223$	−29.2785	−1.96064	−0.980318	−	0.197424i	$-0.936742\pi$
$223$	−29.2785	−1.96064	−0.980318	+	0.197424i	$0.936742\pi$
$224$	3.46691	0.231643
$225$	10.0370	0.669136
$226$	22.3443	1.48632
$227$	−5.38706	−0.357552	−0.178776	−	0.983890i	$-0.557214\pi$
$227$	−5.38706	−0.357552	−0.178776	+	0.983890i	$0.557214\pi$
$228$	−0.0796293	−0.00527358
$229$	10.7826	0.712535	0.356267	−	0.934384i	$-0.384049\pi$
$229$	10.7826	0.712535	0.356267	+	0.934384i	$0.384049\pi$
$230$	10.9957	0.725035
$231$	4.18708	0.275490
$232$	−7.25462	−0.476289
$233$	17.4971	1.14627	0.573135	−	0.819461i	$-0.305727\pi$
$233$	17.4971	1.14627	0.573135	+	0.819461i	$0.305727\pi$
$234$	−9.11046	−0.595569
$235$	−26.9537	−1.75827
$236$	1.52176	0.0990582
$237$	−8.60065	−0.558672
$238$	14.0694	0.911982
$239$	−11.7135	−0.757684	−0.378842	−	0.925461i	$-0.623678\pi$
$239$	−11.7135	−0.757684	−0.378842	+	0.925461i	$0.623678\pi$
$240$	14.2901	0.922421
$241$	4.78270	0.308081	0.154040	−	0.988065i	$-0.450771\pi$
$241$	4.78270	0.308081	0.154040	+	0.988065i	$0.450771\pi$
$242$	−1.36137	−0.0875121
$243$	1.00000	0.0641500
$244$	−0.146675	−0.00938988
$245$	−40.8393	−2.60912
$246$	16.5461	1.05494
$247$	3.63314	0.231171
$248$	−18.8279	−1.19557
$249$	−11.8532	−0.751166
$250$	26.5909	1.68175
$251$	−7.22749	−0.456195	−0.228098	−	0.973638i	$-0.573251\pi$
$251$	−7.22749	−0.456195	−0.228098	+	0.973638i	$0.573251\pi$
$252$	0.614139	0.0386871
$253$	−2.08289	−0.130950
$254$	−8.71576	−0.546875
$255$	−9.57124	−0.599375
$256$	−3.50080	−0.218800
$257$	−22.7298	−1.41784	−0.708922	−	0.705287i	$-0.750818\pi$
$257$	−22.7298	−1.41784	−0.708922	+	0.705287i	$0.750818\pi$
$258$	1.74787	0.108818
$259$	−47.5755	−2.95620
$260$	3.80628	0.236055
$261$	−2.48240	−0.153657
$262$	11.7047	0.723119
$263$	2.90532	0.179149	0.0895747	−	0.995980i	$-0.471449\pi$
$263$	2.90532	0.179149	0.0895747	+	0.995980i	$0.471449\pi$
$264$	−2.92242	−0.179862
$265$	−44.4270	−2.72913
$266$	3.09461	0.189742
$267$	−7.77300	−0.475700
$268$	−0.423206	−0.0258514
$269$	0.359962	0.0219473	0.0109736	−	0.999940i	$-0.496507\pi$
$269$	0.359962	0.0219473	0.0109736	+	0.999940i	$0.496507\pi$
$270$	5.27907	0.321274
$271$	−11.3193	−0.687601	−0.343800	−	0.939043i	$-0.611714\pi$
$271$	−11.3193	−0.687601	−0.343800	+	0.939043i	$0.611714\pi$
$272$	−9.09580	−0.551514
$273$	−28.0205	−1.69588
$274$	1.94398	0.117440
$275$	−10.0370	−0.605256
$276$	−0.305507	−0.0183893
$277$	−26.1993	−1.57416	−0.787080	−	0.616850i	$-0.788408\pi$
$277$	−26.1993	−1.57416	−0.787080	+	0.616850i	$0.788408\pi$
$278$	−7.76115	−0.465483
$279$	−6.44257	−0.385706
$280$	47.4498	2.83567
$281$	−21.0286	−1.25446	−0.627232	−	0.778833i	$-0.715812\pi$
$281$	−21.0286	−1.25446	−0.627232	+	0.778833i	$0.715812\pi$
$282$	−9.46266	−0.563493
$283$	−11.6793	−0.694265	−0.347132	−	0.937816i	$-0.612845\pi$
$283$	−11.6793	−0.694265	−0.347132	+	0.937816i	$0.612845\pi$
$284$	1.84994	0.109774
$285$	−2.10523	−0.124703
$286$	9.11046	0.538713
$287$	50.8897	3.00393
$288$	−0.828001	−0.0487904
$289$	−10.9078	−0.641635
$290$	−13.1048	−0.769539
$291$	−8.63349	−0.506104
$292$	−0.475579	−0.0278311
$293$	6.80140	0.397342	0.198671	−	0.980066i	$-0.436338\pi$
$293$	6.80140	0.397342	0.198671	+	0.980066i	$0.436338\pi$
$294$	−14.3375	−0.836178
$295$	40.2321	2.34240
$296$	33.2058	1.93005
$297$	−1.00000	−0.0580259
$298$	11.0193	0.638329
$299$	13.9389	0.806110
$300$	−1.47218	−0.0849963
$301$	5.37582	0.309857
$302$	−32.3064	−1.85902
$303$	13.8546	0.795926
$304$	−2.00065	−0.114745
$305$	−3.87776	−0.222040
$306$	−3.36018	−0.192089
$307$	−2.02246	−0.115428	−0.0577139	−	0.998333i	$-0.518381\pi$
$307$	−2.02246	−0.115428	−0.0577139	+	0.998333i	$0.518381\pi$
$308$	−0.614139	−0.0349938
$309$	−10.1640	−0.578209
$310$	−34.0107	−1.93168
$311$	21.5828	1.22385	0.611925	−	0.790915i	$-0.290395\pi$
$311$	21.5828	1.22385	0.611925	+	0.790915i	$0.290395\pi$
$312$	19.5572	1.10721
$313$	−2.88840	−0.163262	−0.0816310	−	0.996663i	$-0.526013\pi$
$313$	−2.88840	−0.163262	−0.0816310	+	0.996663i	$0.526013\pi$
$314$	−12.7889	−0.721721
$315$	16.2365	0.914824
$316$	1.26150	0.0709647
$317$	−1.67422	−0.0940337	−0.0470169	−	0.998894i	$-0.514971\pi$
$317$	−1.67422	−0.0940337	−0.0470169	+	0.998894i	$0.514971\pi$
$318$	−15.5970	−0.874638
$319$	2.48240	0.138988
$320$	−32.9512	−1.84203
$321$	−6.89839	−0.385030
$322$	11.8728	0.661645
$323$	1.34000	0.0745597
$324$	−0.146675	−0.00814859
$325$	67.1692	3.72588
$326$	29.5193	1.63493
$327$	4.32572	0.239213
$328$	−35.5190	−1.96121
$329$	−29.1037	−1.60454
$330$	−5.27907	−0.290603
$331$	29.3112	1.61109	0.805544	−	0.592537i	$-0.201873\pi$
$331$	29.3112	1.61109	0.805544	+	0.592537i	$0.201873\pi$
$332$	1.73856	0.0954160
$333$	11.3624	0.622658
$334$	2.91207	0.159341
$335$	−11.1886	−0.611301
$336$	15.4300	0.841774
$337$	1.54901	0.0843802	0.0421901	−	0.999110i	$-0.486566\pi$
$337$	1.54901	0.0843802	0.0421901	+	0.999110i	$0.486566\pi$
$338$	−43.2706	−2.35361
$339$	−16.4131	−0.891437
$340$	1.40386	0.0761349
$341$	6.44257	0.348884
$342$	−0.739084	−0.0399651
$343$	−14.7873	−0.798441
$344$	−3.75211	−0.202300
$345$	−8.07694	−0.434848
$346$	−9.71506	−0.522285
$347$	−17.4874	−0.938773	−0.469387	−	0.882993i	$-0.655525\pi$
$347$	−17.4874	−0.938773	−0.469387	+	0.882993i	$0.655525\pi$
$348$	0.364106	0.0195181
$349$	−2.92513	−0.156579	−0.0782893	−	0.996931i	$-0.524946\pi$
$349$	−2.92513	−0.156579	−0.0782893	+	0.996931i	$0.524946\pi$
$350$	57.2128	3.05815
$351$	6.69213	0.357199
$352$	0.828001	0.0441326
$353$	−20.5083	−1.09155	−0.545773	−	0.837933i	$-0.683764\pi$
$353$	−20.5083	−1.09155	−0.545773	+	0.837933i	$0.683764\pi$
$354$	14.1243	0.750699
$355$	48.9084	2.59579
$356$	1.14010	0.0604253
$357$	−10.3347	−0.546971
$358$	−13.8581	−0.732422
$359$	32.0915	1.69372	0.846862	−	0.531812i	$-0.178489\pi$
$359$	32.0915	1.69372	0.846862	+	0.531812i	$0.178489\pi$
$360$	−11.3324	−0.597272
$361$	−18.7053	−0.984487
$362$	24.7553	1.30111
$363$	1.00000	0.0524864
$364$	4.10990	0.215417
$365$	−12.5733	−0.658116
$366$	−1.36137	−0.0711599
$367$	24.6284	1.28559	0.642795	−	0.766038i	$-0.277775\pi$
$367$	24.6284	1.28559	0.642795	+	0.766038i	$0.277775\pi$
$368$	−7.67572	−0.400125
$369$	−12.1540	−0.632711
$370$	59.9831	3.11837
$371$	−47.9709	−2.49052
$372$	0.944961	0.0489939
$373$	−26.5765	−1.37608	−0.688040	−	0.725673i	$-0.741529\pi$
$373$	−26.5765	−1.37608	−0.688040	+	0.725673i	$0.741529\pi$
$374$	3.36018	0.173751
$375$	−19.5325	−1.00865
$376$	20.3132	1.04758
$377$	−16.6126	−0.855591
$378$	5.70016	0.293185
$379$	−16.3160	−0.838098	−0.419049	−	0.907964i	$-0.637636\pi$
$379$	−16.3160	−0.838098	−0.419049	+	0.907964i	$0.637636\pi$
$380$	0.308784	0.0158403
$381$	6.40220	0.327995
$382$	33.3017	1.70386
$383$	28.0979	1.43574	0.717868	−	0.696179i	$-0.245118\pi$
$383$	28.0979	1.43574	0.717868	+	0.696179i	$0.245118\pi$
$384$	−9.91222	−0.505831
$385$	−16.2365	−0.827489
$386$	−12.4668	−0.634542
$387$	−1.28391	−0.0652646
$388$	1.26631	0.0642873
$389$	22.0946	1.12024	0.560119	−	0.828412i	$-0.310755\pi$
$389$	22.0946	1.12024	0.560119	+	0.828412i	$0.310755\pi$
$390$	35.3282	1.78891
$391$	5.14106	0.259995
$392$	30.7779	1.55452
$393$	−8.59775	−0.433699
$394$	−9.23808	−0.465408
$395$	33.3513	1.67808
$396$	0.146675	0.00737068
$397$	−0.667673	−0.0335095	−0.0167548	−	0.999860i	$-0.505333\pi$
$397$	−0.667673	−0.0335095	−0.0167548	+	0.999860i	$0.505333\pi$
$398$	12.6579	0.634481
$399$	−2.27316	−0.113800
$400$	−36.9879	−1.84939
$401$	−5.22811	−0.261080	−0.130540	−	0.991443i	$-0.541671\pi$
$401$	−5.22811	−0.261080	−0.130540	+	0.991443i	$0.541671\pi$
$402$	−3.92801	−0.195911
$403$	−43.1145	−2.14769
$404$	−2.03212	−0.101102
$405$	−3.87776	−0.192688
$406$	−14.1501	−0.702258
$407$	−11.3624	−0.563215
$408$	7.21322	0.357108
$409$	14.8127	0.732441	0.366220	−	0.930528i	$-0.380652\pi$
$409$	14.8127	0.732441	0.366220	+	0.930528i	$0.380652\pi$
$410$	−64.1617	−3.16872
$411$	−1.42796	−0.0704362
$412$	1.49080	0.0734464
$413$	43.4413	2.13761
$414$	−2.83558	−0.139361
$415$	45.9639	2.25628
$416$	−5.54109	−0.271674
$417$	5.70099	0.279179
$418$	0.739084	0.0361498
$419$	−21.6455	−1.05745	−0.528726	−	0.848793i	$-0.677330\pi$
$419$	−21.6455	−1.05745	−0.528726	+	0.848793i	$0.677330\pi$
$420$	−2.38148	−0.116205
$421$	−38.8002	−1.89100	−0.945502	−	0.325615i	$-0.894429\pi$
$421$	−38.8002	−1.89100	−0.945502	+	0.325615i	$0.894429\pi$
$422$	−31.7775	−1.54690
$423$	6.95084	0.337961
$424$	33.4818	1.62602
$425$	24.7738	1.20171
$426$	17.1703	0.831905
$427$	−4.18708	−0.202627
$428$	1.01182	0.0489081
$429$	−6.69213	−0.323099
$430$	−6.77783	−0.326856
$431$	−25.2944	−1.21839	−0.609193	−	0.793022i	$-0.708507\pi$
$431$	−25.2944	−1.21839	−0.609193	+	0.793022i	$0.708507\pi$
$432$	−3.68514	−0.177301
$433$	−19.4376	−0.934112	−0.467056	−	0.884228i	$-0.654685\pi$
$433$	−19.4376	−0.934112	−0.467056	+	0.884228i	$0.654685\pi$
$434$	−36.7237	−1.76279
$435$	9.62617	0.461540
$436$	−0.634474	−0.0303858
$437$	1.13079	0.0540932
$438$	−4.41411	−0.210914
$439$	−31.9998	−1.52727	−0.763634	−	0.645650i	$-0.776587\pi$
$439$	−31.9998	−1.52727	−0.763634	+	0.645650i	$0.776587\pi$
$440$	11.3324	0.540253
$441$	10.5317	0.501507
$442$	−22.4868	−1.06959
$443$	8.28628	0.393693	0.196846	−	0.980434i	$-0.436930\pi$
$443$	8.28628	0.393693	0.196846	+	0.980434i	$0.436930\pi$
$444$	−1.66658	−0.0790925
$445$	30.1418	1.42886
$446$	39.8589	1.88737
$447$	−8.09426	−0.382845
$448$	−35.5797	−1.68098
$449$	−0.0397784	−0.00187726	−0.000938629	−	1.00000i	$-0.500299\pi$
$449$	−0.0397784	−0.00187726	−0.000938629		1.00000i	$0.500299\pi$
$450$	−13.6641	−0.644133
$451$	12.1540	0.572309
$452$	2.40739	0.113234
$453$	23.7308	1.11497
$454$	7.33377	0.344191
$455$	108.657	5.09391
$456$	1.58657	0.0742981
$457$	−21.7886	−1.01923	−0.509613	−	0.860404i	$-0.670211\pi$
$457$	−21.7886	−1.01923	−0.509613	+	0.860404i	$0.670211\pi$
$458$	−14.6791	−0.685910
$459$	2.46824	0.115208
$460$	1.18468	0.0552361
$461$	2.61987	0.122020	0.0610098	−	0.998137i	$-0.480568\pi$
$461$	2.61987	0.122020	0.0610098	+	0.998137i	$0.480568\pi$
$462$	−5.70016	−0.265196
$463$	−5.53154	−0.257072	−0.128536	−	0.991705i	$-0.541028\pi$
$463$	−5.53154	−0.257072	−0.128536	+	0.991705i	$0.541028\pi$
$464$	9.14800	0.424685
$465$	24.9827	1.15855
$466$	−23.8199	−1.10344
$467$	−38.7915	−1.79506	−0.897528	−	0.440956i	$-0.854639\pi$
$467$	−38.7915	−1.79506	−0.897528	+	0.440956i	$0.854639\pi$
$468$	−0.981566	−0.0453729
$469$	−12.0811	−0.557855
$470$	36.6939	1.69257
$471$	9.39417	0.432860
$472$	−30.3203	−1.39561
$473$	1.28391	0.0590341
$474$	11.7087	0.537796
$475$	5.44909	0.250021
$476$	1.51584	0.0694785
$477$	11.4569	0.524574
$478$	15.9464	0.729372
$479$	18.1553	0.829536	0.414768	−	0.909927i	$-0.363863\pi$
$479$	18.1553	0.829536	0.414768	+	0.909927i	$0.363863\pi$
$480$	3.21079	0.146552
$481$	76.0389	3.46708
$482$	−6.51102	−0.296569
$483$	−8.72122	−0.396829
$484$	−0.146675	−0.00666703
$485$	33.4786	1.52019
$486$	−1.36137	−0.0617529
$487$	32.2397	1.46092	0.730460	−	0.682955i	$-0.239306\pi$
$487$	32.2397	1.46092	0.730460	+	0.682955i	$0.239306\pi$
$488$	2.92242	0.132292
$489$	−21.6836	−0.980565
$490$	55.5973	2.51163
$491$	−6.67527	−0.301251	−0.150625	−	0.988591i	$-0.548129\pi$
$491$	−6.67527	−0.301251	−0.150625	+	0.988591i	$0.548129\pi$
$492$	1.78268	0.0803695
$493$	−6.12716	−0.275954
$494$	−4.94605	−0.222533
$495$	3.87776	0.174292
$496$	23.7417	1.06604
$497$	52.8097	2.36884
$498$	16.1366	0.723097
$499$	−9.68119	−0.433390	−0.216695	−	0.976239i	$-0.569528\pi$
$499$	−9.68119	−0.433390	−0.216695	+	0.976239i	$0.569528\pi$
$500$	2.86492	0.128123
$501$	−2.13907	−0.0955667
$502$	9.83928	0.439149
$503$	12.4346	0.554433	0.277217	−	0.960807i	$-0.410588\pi$
$503$	12.4346	0.554433	0.277217	+	0.960807i	$0.410588\pi$
$504$	−12.2364	−0.545052
$505$	−53.7248	−2.39072
$506$	2.83558	0.126057
$507$	31.7846	1.41160
$508$	−0.939040	−0.0416632
$509$	0.184761	0.00818937	0.00409469	−	0.999992i	$-0.498697\pi$
$509$	0.184761	0.00818937	0.00409469	+	0.999992i	$0.498697\pi$
$510$	13.0300	0.576978
$511$	−13.5762	−0.600577
$512$	24.5903	1.08675
$513$	0.542898	0.0239695
$514$	30.9436	1.36486
$515$	39.4135	1.73677
$516$	0.188317	0.00829017
$517$	−6.95084	−0.305698
$518$	64.7678	2.84573
$519$	7.13624	0.313246
$520$	−75.8381	−3.32572
$521$	31.8838	1.39686	0.698428	−	0.715680i	$-0.253883\pi$
$521$	31.8838	1.39686	0.698428	+	0.715680i	$0.253883\pi$
$522$	3.37947	0.147915
$523$	25.8648	1.13099	0.565494	−	0.824753i	$-0.308686\pi$
$523$	25.8648	1.13099	0.565494	+	0.824753i	$0.308686\pi$
$524$	1.26107	0.0550902
$525$	−42.0259	−1.83416
$526$	−3.95521	−0.172455
$527$	−15.9018	−0.692693
$528$	3.68514	0.160375
$529$	−18.6616	−0.811373
$530$	60.4816	2.62715
$531$	−10.3751	−0.450240
$532$	0.333415	0.0144554
$533$	−81.3360	−3.52305
$534$	10.5819	0.457924
$535$	26.7503	1.15652
$536$	8.43215	0.364214
$537$	10.1795	0.439278
$538$	−0.490041	−0.0211272
$539$	−10.5317	−0.453631
$540$	0.568769	0.0244759
$541$	−2.53064	−0.108801	−0.0544004	−	0.998519i	$-0.517325\pi$
$541$	−2.53064	−0.108801	−0.0544004	+	0.998519i	$0.517325\pi$
$542$	15.4098	0.661907
$543$	−18.1842	−0.780357
$544$	−2.04370	−0.0876231
$545$	−16.7741	−0.718524
$546$	38.1462	1.63251
$547$	21.8175	0.932851	0.466425	−	0.884561i	$-0.345542\pi$
$547$	21.8175	0.932851	0.466425	+	0.884561i	$0.345542\pi$
$548$	0.209446	0.00894709
$549$	1.00000	0.0426790
$550$	13.6641	0.582640
$551$	−1.34769	−0.0574136
$552$	6.08706	0.259083
$553$	36.0116	1.53137
$554$	35.6669	1.51534
$555$	−44.0608	−1.87028
$556$	−0.836191	−0.0354624
$557$	5.41490	0.229437	0.114718	−	0.993398i	$-0.463403\pi$
$557$	5.41490	0.229437	0.114718	+	0.993398i	$0.463403\pi$
$558$	8.77071	0.371294
$559$	−8.59207	−0.363406
$560$	−59.8338	−2.52844
$561$	−2.46824	−0.104209
$562$	28.6277	1.20759
$563$	−22.5530	−0.950494	−0.475247	−	0.879852i	$-0.657641\pi$
$563$	−22.5530	−0.950494	−0.475247	+	0.879852i	$0.657641\pi$
$564$	−1.01951	−0.0429292
$565$	63.6461	2.67761
$566$	15.8999	0.668322
$567$	−4.18708	−0.175841
$568$	−36.8591	−1.54657
$569$	12.7940	0.536352	0.268176	−	0.963370i	$-0.413579\pi$
$569$	12.7940	0.536352	0.268176	+	0.963370i	$0.413579\pi$
$570$	2.86599	0.120043
$571$	13.5653	0.567688	0.283844	−	0.958870i	$-0.408390\pi$
$571$	13.5653	0.567688	0.283844	+	0.958870i	$0.408390\pi$
$572$	0.981566	0.0410413
$573$	−24.4619	−1.02191
$574$	−69.2797	−2.89168
$575$	20.9060	0.871841
$576$	8.49749	0.354062
$577$	−38.2936	−1.59418	−0.797091	−	0.603859i	$-0.793629\pi$
$577$	−38.2936	−1.59418	−0.797091	+	0.603859i	$0.793629\pi$
$578$	14.8495	0.617659
$579$	9.15753	0.380574
$580$	−1.41191	−0.0586266
$581$	49.6303	2.05901
$582$	11.7534	0.487192
$583$	−11.4569	−0.474495
$584$	9.47566	0.392106
$585$	−25.9505	−1.07292
$586$	−9.25921	−0.382494
$587$	22.8211	0.941927	0.470963	−	0.882153i	$-0.343906\pi$
$587$	22.8211	0.941927	0.470963	+	0.882153i	$0.343906\pi$
$588$	−1.54473	−0.0637035
$589$	−3.49765	−0.144118
$590$	−54.7707	−2.25488
$591$	6.78587	0.279133
$592$	−41.8722	−1.72093
$593$	−33.1642	−1.36189	−0.680945	−	0.732334i	$-0.738431\pi$
$593$	−33.1642	−1.36189	−0.680945	+	0.732334i	$0.738431\pi$
$594$	1.36137	0.0558576
$595$	40.0756	1.64294
$596$	1.18722	0.0486305
$597$	−9.29788	−0.380537
$598$	−18.9761	−0.775988
$599$	1.05436	0.0430801	0.0215400	−	0.999768i	$-0.493143\pi$
$599$	1.05436	0.0430801	0.0215400	+	0.999768i	$0.493143\pi$
$600$	29.3324	1.19749
$601$	−20.9815	−0.855855	−0.427927	−	0.903813i	$-0.640756\pi$
$601$	−20.9815	−0.855855	−0.427927	+	0.903813i	$0.640756\pi$
$602$	−7.31848	−0.298279
$603$	2.88534	0.117500
$604$	−3.48070	−0.141628
$605$	−3.87776	−0.157653
$606$	−18.8612	−0.766185
$607$	−5.21231	−0.211561	−0.105780	−	0.994390i	$-0.533734\pi$
$607$	−5.21231	−0.211561	−0.105780	+	0.994390i	$0.533734\pi$
$608$	−0.449520	−0.0182304
$609$	10.3940	0.421187
$610$	5.27907	0.213743
$611$	46.5159	1.88183
$612$	−0.362028	−0.0146341
$613$	5.26202	0.212531	0.106266	−	0.994338i	$-0.466111\pi$
$613$	5.26202	0.212531	0.106266	+	0.994338i	$0.466111\pi$
$614$	2.75331	0.111115
$615$	47.1303	1.90048
$616$	12.2364	0.493018
$617$	27.8663	1.12186	0.560928	−	0.827865i	$-0.310445\pi$
$617$	27.8663	1.12186	0.560928	+	0.827865i	$0.310445\pi$
$618$	13.8369	0.556603
$619$	−6.36381	−0.255783	−0.127892	−	0.991788i	$-0.540821\pi$
$619$	−6.36381	−0.255783	−0.127892	+	0.991788i	$0.540821\pi$
$620$	−3.66433	−0.147163
$621$	2.08289	0.0835834
$622$	−29.3822	−1.17812
$623$	32.5462	1.30394
$624$	−24.6614	−0.987247
$625$	25.5570	1.02228
$626$	3.93218	0.157161
$627$	−0.542898	−0.0216812
$628$	−1.37789	−0.0549836
$629$	28.0452	1.11824
$630$	−22.1039	−0.880640
$631$	−8.51121	−0.338826	−0.169413	−	0.985545i	$-0.554187\pi$
$631$	−8.51121	−0.338826	−0.169413	+	0.985545i	$0.554187\pi$
$632$	−25.1347	−0.999803
$633$	23.3423	0.927773
$634$	2.27923	0.0905200
$635$	−24.8262	−0.985198
$636$	−1.68043	−0.0666335
$637$	70.4792	2.79249
$638$	−3.37947	−0.133794
$639$	−12.6125	−0.498944
$640$	38.4372	1.51936
$641$	−22.0359	−0.870366	−0.435183	−	0.900342i	$-0.643316\pi$
$641$	−22.0359	−0.870366	−0.435183	+	0.900342i	$0.643316\pi$
$642$	9.39125	0.370643
$643$	4.04352	0.159461	0.0797304	−	0.996816i	$-0.474594\pi$
$643$	4.04352	0.159461	0.0797304	+	0.996816i	$0.474594\pi$
$644$	1.27918	0.0504068
$645$	4.97868	0.196036
$646$	−1.82424	−0.0717736
$647$	−23.3871	−0.919442	−0.459721	−	0.888063i	$-0.652051\pi$
$647$	−23.3871	−0.919442	−0.459721	+	0.888063i	$0.652051\pi$
$648$	2.92242	0.114803
$649$	10.3751	0.407258
$650$	−91.4420	−3.58665
$651$	26.9756	1.05726
$652$	3.18043	0.124555
$653$	−16.9014	−0.661405	−0.330702	−	0.943735i	$-0.607286\pi$
$653$	−16.9014	−0.661405	−0.330702	+	0.943735i	$0.607286\pi$
$654$	−5.88890	−0.230274
$655$	33.3400	1.30270
$656$	44.7891	1.74872
$657$	3.24241	0.126498
$658$	39.6209	1.54458
$659$	2.02972	0.0790668	0.0395334	−	0.999218i	$-0.487413\pi$
$659$	2.02972	0.0790668	0.0395334	+	0.999218i	$0.487413\pi$
$660$	−0.568769	−0.0221393
$661$	−44.3494	−1.72499	−0.862496	−	0.506065i	$-0.831100\pi$
$661$	−44.3494	−1.72499	−0.862496	+	0.506065i	$0.831100\pi$
$662$	−39.9033	−1.55089
$663$	16.5178	0.641497
$664$	−34.6400	−1.34429
$665$	8.81476	0.341822
$666$	−15.4685	−0.599391
$667$	−5.17057	−0.200205
$668$	0.313748	0.0121393
$669$	−29.2785	−1.13197
$670$	15.2319	0.588459
$671$	−1.00000	−0.0386046
$672$	3.46691	0.133739
$673$	−5.39200	−0.207846	−0.103923	−	0.994585i	$-0.533140\pi$
$673$	−5.39200	−0.207846	−0.103923	+	0.994585i	$0.533140\pi$
$674$	−2.10878	−0.0812272
$675$	10.0370	0.386326
$676$	−4.66199	−0.179307
$677$	−27.7248	−1.06555	−0.532775	−	0.846257i	$-0.678851\pi$
$677$	−27.7248	−1.06555	−0.532775	+	0.846257i	$0.678851\pi$
$678$	22.3443	0.858127
$679$	36.1491	1.38728
$680$	−27.9712	−1.07265
$681$	−5.38706	−0.206432
$682$	−8.77071	−0.335848
$683$	15.7263	0.601748	0.300874	−	0.953664i	$-0.402722\pi$
$683$	15.7263	0.601748	0.300874	+	0.953664i	$0.402722\pi$
$684$	−0.0796293	−0.00304470
$685$	5.53730	0.211569
$686$	20.1310	0.768606
$687$	10.7826	0.411382
$688$	4.73137	0.180382
$689$	76.6709	2.92093
$690$	10.9957	0.418599
$691$	−13.7942	−0.524757	−0.262379	−	0.964965i	$-0.584507\pi$
$691$	−13.7942	−0.524757	−0.262379	+	0.964965i	$0.584507\pi$
$692$	−1.04671	−0.0397898
$693$	4.18708	0.159054
$694$	23.8068	0.903695
$695$	−22.1071	−0.838569
$696$	−7.25462	−0.274985
$697$	−29.9989	−1.13629
$698$	3.98218	0.150728
$699$	17.4971	0.661799
$700$	6.16414	0.232982
$701$	−20.0891	−0.758757	−0.379378	−	0.925242i	$-0.623862\pi$
$701$	−20.0891	−0.758757	−0.379378	+	0.925242i	$0.623862\pi$
$702$	−9.11046	−0.343852
$703$	6.16864	0.232655
$704$	−8.49749	−0.320261
$705$	−26.9537	−1.01514
$706$	27.9194	1.05076
$707$	−58.0103	−2.18170
$708$	1.52176	0.0571913
$709$	−15.6461	−0.587603	−0.293802	−	0.955866i	$-0.594920\pi$
$709$	−15.6461	−0.587603	−0.293802	+	0.955866i	$0.594920\pi$
$710$	−66.5824	−2.49879
$711$	−8.60065	−0.322549
$712$	−22.7159	−0.851316
$713$	−13.4191	−0.502551
$714$	14.0694	0.526533
$715$	25.9505	0.970493
$716$	−1.49308	−0.0557989
$717$	−11.7135	−0.437449
$718$	−43.6884	−1.63044
$719$	27.0208	1.00771	0.503853	−	0.863789i	$-0.331915\pi$
$719$	27.0208	1.00771	0.503853	+	0.863789i	$0.331915\pi$
$720$	14.2901	0.532560
$721$	42.5575	1.58492
$722$	25.4648	0.947700
$723$	4.78270	0.177871
$724$	2.66715	0.0991240
$725$	−24.9160	−0.925357
$726$	−1.36137	−0.0505251
$727$	13.3341	0.494536	0.247268	−	0.968947i	$-0.420467\pi$
$727$	13.3341	0.494536	0.247268	+	0.968947i	$0.420467\pi$
$728$	−81.8875	−3.03495
$729$	1.00000	0.0370370
$730$	17.1169	0.633524
$731$	−3.16899	−0.117209
$732$	−0.146675	−0.00542125
$733$	8.75125	0.323235	0.161617	−	0.986853i	$-0.448329\pi$
$733$	8.75125	0.323235	0.161617	+	0.986853i	$0.448329\pi$
$734$	−33.5283	−1.23755
$735$	−40.8393	−1.50638
$736$	−1.72463	−0.0635708
$737$	−2.88534	−0.106283
$738$	16.5461	0.609069
$739$	1.39583	0.0513464	0.0256732	−	0.999670i	$-0.491827\pi$
$739$	1.39583	0.0513464	0.0256732	+	0.999670i	$0.491827\pi$
$740$	6.46261	0.237570
$741$	3.63314	0.133467
$742$	65.3061	2.39746
$743$	−22.9347	−0.841394	−0.420697	−	0.907201i	$-0.638214\pi$
$743$	−22.9347	−0.841394	−0.420697	+	0.907201i	$0.638214\pi$
$744$	−18.8279	−0.690263
$745$	31.3876	1.14995
$746$	36.1804	1.32466
$747$	−11.8532	−0.433686
$748$	0.362028	0.0132371
$749$	28.8841	1.05540
$750$	26.5909	0.970962
$751$	−21.6879	−0.791402	−0.395701	−	0.918379i	$-0.629498\pi$
$751$	−21.6879	−0.791402	−0.395701	+	0.918379i	$0.629498\pi$
$752$	−25.6148	−0.934076
$753$	−7.22749	−0.263384
$754$	22.6158	0.823620
$755$	−92.0224	−3.34904
$756$	0.614139	0.0223360
$757$	8.03337	0.291978	0.145989	−	0.989286i	$-0.453364\pi$
$757$	8.03337	0.291978	0.145989	+	0.989286i	$0.453364\pi$
$758$	22.2121	0.806781
$759$	−2.08289	−0.0756040
$760$	−6.15235	−0.223169
$761$	32.2248	1.16815	0.584074	−	0.811701i	$-0.301458\pi$
$761$	32.2248	1.16815	0.584074	+	0.811701i	$0.301458\pi$
$762$	−8.71576	−0.315739
$763$	−18.1122	−0.655704
$764$	3.58794	0.129807
$765$	−9.57124	−0.346049
$766$	−38.2516	−1.38209
$767$	−69.4314	−2.50702
$768$	−3.50080	−0.126324
$769$	37.1134	1.33834	0.669172	−	0.743107i	$-0.266649\pi$
$769$	37.1134	1.33834	0.669172	+	0.743107i	$0.266649\pi$
$770$	22.1039	0.796569
$771$	−22.7298	−0.818592
$772$	−1.34318	−0.0483420
$773$	1.47587	0.0530833	0.0265417	−	0.999648i	$-0.491551\pi$
$773$	1.47587	0.0530833	0.0265417	+	0.999648i	$0.491551\pi$
$774$	1.74787	0.0628259
$775$	−64.6643	−2.32281
$776$	−25.2306	−0.905727
$777$	−47.5755	−1.70676
$778$	−30.0789	−1.07838
$779$	−6.59837	−0.236411
$780$	3.80628	0.136287
$781$	12.6125	0.451312
$782$	−6.99888	−0.250280
$783$	−2.48240	−0.0887139
$784$	−38.8106	−1.38609
$785$	−36.4283	−1.30018
$786$	11.7047	0.417493
$787$	−2.36171	−0.0841860	−0.0420930	−	0.999114i	$-0.513403\pi$
$787$	−2.36171	−0.0841860	−0.0420930	+	0.999114i	$0.513403\pi$
$788$	−0.995315	−0.0354566
$789$	2.90532	0.103432
$790$	−45.4034	−1.61538
$791$	68.7230	2.44351
$792$	−2.92242	−0.103844
$793$	6.69213	0.237644
$794$	0.908949	0.0322574
$795$	−44.4270	−1.57566
$796$	1.36376	0.0483373
$797$	3.10211	0.109882	0.0549412	−	0.998490i	$-0.482503\pi$
$797$	3.10211	0.109882	0.0549412	+	0.998490i	$0.482503\pi$
$798$	3.09461	0.109548
$799$	17.1563	0.606947
$800$	−8.31068	−0.293827
$801$	−7.77300	−0.274645
$802$	7.11739	0.251324
$803$	−3.24241	−0.114422
$804$	−0.423206	−0.0149253
$805$	33.8188	1.19196
$806$	58.6947	2.06743
$807$	0.359962	0.0126713
$808$	40.4889	1.42439
$809$	−28.7073	−1.00930	−0.504648	−	0.863325i	$-0.668378\pi$
$809$	−28.7073	−1.00930	−0.504648	+	0.863325i	$0.668378\pi$
$810$	5.27907	0.185487
$811$	−26.7251	−0.938446	−0.469223	−	0.883080i	$-0.655466\pi$
$811$	−26.7251	−0.938446	−0.469223	+	0.883080i	$0.655466\pi$
$812$	−1.52454	−0.0535009
$813$	−11.3193	−0.396986
$814$	15.4685	0.542170
$815$	84.0837	2.94532
$816$	−9.09580	−0.318417
$817$	−0.697030	−0.0243860
$818$	−20.1655	−0.705072
$819$	−28.0205	−0.979115
$820$	−6.91281	−0.241406
$821$	−3.45735	−0.120662	−0.0603312	−	0.998178i	$-0.519216\pi$
$821$	−3.45735	−0.120662	−0.0603312	+	0.998178i	$0.519216\pi$
$822$	1.94398	0.0678042
$823$	35.5363	1.23872	0.619358	−	0.785108i	$-0.287393\pi$
$823$	35.5363	1.23872	0.619358	+	0.785108i	$0.287393\pi$
$824$	−29.7034	−1.03477
$825$	−10.0370	−0.349445
$826$	−59.1397	−2.05773
$827$	24.5703	0.854392	0.427196	−	0.904159i	$-0.359501\pi$
$827$	24.5703	0.854392	0.427196	+	0.904159i	$0.359501\pi$
$828$	−0.305507	−0.0106171
$829$	2.29787	0.0798083	0.0399041	−	0.999204i	$-0.487295\pi$
$829$	2.29787	0.0798083	0.0399041	+	0.999204i	$0.487295\pi$
$830$	−62.5738	−2.17197
$831$	−26.1993	−0.908842
$832$	56.8663	1.97148
$833$	25.9946	0.900661
$834$	−7.76115	−0.268747
$835$	8.29481	0.287054
$836$	0.0796293	0.00275404
$837$	−6.44257	−0.222688
$838$	29.4675	1.01794
$839$	−43.3926	−1.49808	−0.749039	−	0.662526i	$-0.769484\pi$
$839$	−43.3926	−1.49808	−0.749039	+	0.662526i	$0.769484\pi$
$840$	47.4498	1.63717
$841$	−22.8377	−0.787506
$842$	52.8214	1.82034
$843$	−21.0286	−0.724265
$844$	−3.42372	−0.117849
$845$	−123.253	−4.24004
$846$	−9.46266	−0.325333
$847$	−4.18708	−0.143870
$848$	−42.2202	−1.44985
$849$	−11.6793	−0.400834
$850$	−33.7263	−1.15680
$851$	23.6667	0.811283
$852$	1.84994	0.0633779
$853$	−5.87217	−0.201059	−0.100530	−	0.994934i	$-0.532054\pi$
$853$	−5.87217	−0.201059	−0.100530	+	0.994934i	$0.532054\pi$
$854$	5.70016	0.195056
$855$	−2.10523	−0.0719973
$856$	−20.1600	−0.689053
$857$	−3.13979	−0.107253	−0.0536267	−	0.998561i	$-0.517078\pi$
$857$	−3.13979	−0.107253	−0.0536267	+	0.998561i	$0.517078\pi$
$858$	9.11046	0.311026
$859$	9.87831	0.337044	0.168522	−	0.985698i	$-0.446101\pi$
$859$	9.87831	0.337044	0.168522	+	0.985698i	$0.446101\pi$
$860$	−0.730247	−0.0249012
$861$	50.8897	1.73432
$862$	34.4350	1.17286
$863$	16.8134	0.572333	0.286167	−	0.958180i	$-0.407619\pi$
$863$	16.8134	0.572333	0.286167	+	0.958180i	$0.407619\pi$
$864$	−0.828001	−0.0281692
$865$	−27.6727	−0.940899
$866$	26.4618	0.899208
$867$	−10.9078	−0.370448
$868$	−3.95663	−0.134297
$869$	8.60065	0.291757
$870$	−13.1048	−0.444293
$871$	19.3090	0.654262
$872$	12.6416	0.428097
$873$	−8.63349	−0.292199
$874$	−1.53943	−0.0520720
$875$	81.7840	2.76480
$876$	−0.475579	−0.0160683
$877$	−24.2890	−0.820180	−0.410090	−	0.912045i	$-0.634503\pi$
$877$	−24.2890	−0.820180	−0.410090	+	0.912045i	$0.634503\pi$
$878$	43.5635	1.47020
$879$	6.80140	0.229405
$880$	−14.2901	−0.481719
$881$	−35.5958	−1.19925	−0.599626	−	0.800280i	$-0.704684\pi$
$881$	−35.5958	−1.19925	−0.599626	+	0.800280i	$0.704684\pi$
$882$	−14.3375	−0.482768
$883$	5.77221	0.194250	0.0971252	−	0.995272i	$-0.469035\pi$
$883$	5.77221	0.194250	0.0971252	+	0.995272i	$0.469035\pi$
$884$	−2.42274	−0.0814855
$885$	40.2321	1.35239
$886$	−11.2807	−0.378982
$887$	21.6590	0.727238	0.363619	−	0.931548i	$-0.381541\pi$
$887$	21.6590	0.727238	0.363619	+	0.931548i	$0.381541\pi$
$888$	33.2058	1.11431
$889$	−26.8065	−0.899062
$890$	−41.0342	−1.37547
$891$	−1.00000	−0.0335013
$892$	4.29442	0.143788
$893$	3.77360	0.126279
$894$	11.0193	0.368539
$895$	−39.4737	−1.31946
$896$	41.5033	1.38653
$897$	13.9389	0.465408
$898$	0.0541531	0.00180711
$899$	15.9930	0.533398
$900$	−1.47218	−0.0490726
$901$	28.2783	0.942087
$902$	−16.5461	−0.550923
$903$	5.37582	0.178896
$904$	−47.9659	−1.59532
$905$	70.5138	2.34396
$906$	−32.3064	−1.07331
$907$	−46.4167	−1.54124	−0.770620	−	0.637295i	$-0.780053\pi$
$907$	−46.4167	−1.54124	−0.770620	+	0.637295i	$0.780053\pi$
$908$	0.790145	0.0262219
$909$	13.8546	0.459528
$910$	−147.922	−4.90357
$911$	−23.6206	−0.782586	−0.391293	−	0.920266i	$-0.627972\pi$
$911$	−23.6206	−0.782586	−0.391293	+	0.920266i	$0.627972\pi$
$912$	−2.00065	−0.0662482
$913$	11.8532	0.392284
$914$	29.6623	0.981141
$915$	−3.87776	−0.128195
$916$	−1.58153	−0.0522554
$917$	35.9995	1.18881
$918$	−3.36018	−0.110903
$919$	−14.0934	−0.464899	−0.232449	−	0.972609i	$-0.574674\pi$
$919$	−14.0934	−0.464899	−0.232449	+	0.972609i	$0.574674\pi$
$920$	−23.6042	−0.778207
$921$	−2.02246	−0.0666423
$922$	−3.56661	−0.117460
$923$	−84.4047	−2.77822
$924$	−0.614139	−0.0202037
$925$	114.045	3.74979
$926$	7.53046	0.247466
$927$	−10.1640	−0.333829
$928$	2.05543	0.0674729
$929$	−3.81727	−0.125241	−0.0626204	−	0.998037i	$-0.519946\pi$
$929$	−3.81727	−0.125241	−0.0626204	+	0.998037i	$0.519946\pi$
$930$	−34.0107	−1.11526
$931$	5.71761	0.187387
$932$	−2.56637	−0.0840644
$933$	21.5828	0.706591
$934$	52.8096	1.72798
$935$	9.57124	0.313013
$936$	19.5572	0.639247
$937$	9.22141	0.301250	0.150625	−	0.988591i	$-0.451871\pi$
$937$	9.22141	0.301250	0.150625	+	0.988591i	$0.451871\pi$
$938$	16.4469	0.537010
$939$	−2.88840	−0.0942593
$940$	3.95342	0.128946
$941$	−24.1263	−0.786494	−0.393247	−	0.919433i	$-0.628648\pi$
$941$	−24.1263	−0.786494	−0.393247	+	0.919433i	$0.628648\pi$
$942$	−12.7889	−0.416686
$943$	−25.3154	−0.824382
$944$	38.2336	1.24440
$945$	16.2365	0.528174
$946$	−1.74787	−0.0568282
$947$	9.72548	0.316036	0.158018	−	0.987436i	$-0.449490\pi$
$947$	9.72548	0.316036	0.158018	+	0.987436i	$0.449490\pi$
$948$	1.26150	0.0409715
$949$	21.6986	0.704367
$950$	−7.41822	−0.240679
$951$	−1.67422	−0.0542904
$952$	−30.2024	−0.978864
$953$	21.2016	0.686787	0.343394	−	0.939192i	$-0.388424\pi$
$953$	21.2016	0.686787	0.343394	+	0.939192i	$0.388424\pi$
$954$	−15.5970	−0.504973
$955$	94.8574	3.06951
$956$	1.71808	0.0555665
$957$	2.48240	0.0802447
$958$	−24.7160	−0.798539
$959$	5.97900	0.193072
$960$	−32.9512	−1.06350
$961$	10.5067	0.338924
$962$	−103.517	−3.33752
$963$	−6.89839	−0.222297
$964$	−0.701501	−0.0225938
$965$	−35.5107	−1.14313
$966$	11.8728	0.382001
$967$	−7.28973	−0.234422	−0.117211	−	0.993107i	$-0.537395\pi$
$967$	−7.28973	−0.234422	−0.117211	+	0.993107i	$0.537395\pi$
$968$	2.92242	0.0939300
$969$	1.34000	0.0430470
$970$	−45.5767	−1.46338
$971$	−51.5773	−1.65519	−0.827597	−	0.561323i	$-0.810292\pi$
$971$	−51.5773	−1.65519	−0.827597	+	0.561323i	$0.810292\pi$
$972$	−0.146675	−0.00470459
$973$	−23.8705	−0.765253
$974$	−43.8901	−1.40633
$975$	67.1692	2.15114
$976$	−3.68514	−0.117958
$977$	39.3201	1.25796	0.628981	−	0.777421i	$-0.283472\pi$
$977$	39.3201	1.25796	0.628981	+	0.777421i	$0.283472\pi$
$978$	29.5193	0.943924
$979$	7.77300	0.248426
$980$	5.99008	0.191346
$981$	4.32572	0.138110
$982$	9.08750	0.289994
$983$	7.60168	0.242456	0.121228	−	0.992625i	$-0.461317\pi$
$983$	7.60168	0.242456	0.121228	+	0.992625i	$0.461317\pi$
$984$	−35.5190	−1.13230
$985$	−26.3140	−0.838434
$986$	8.34133	0.265642
$987$	−29.1037	−0.926382
$988$	−0.532890	−0.0169535
$989$	−2.67423	−0.0850356
$990$	−5.27907	−0.167780
$991$	−36.9367	−1.17333	−0.586666	−	0.809829i	$-0.699560\pi$
$991$	−36.9367	−1.17333	−0.586666	+	0.809829i	$0.699560\pi$
$992$	5.33445	0.169369
$993$	29.3112	0.930162
$994$	−71.8935	−2.28032
$995$	36.0550	1.14302
$996$	1.73856	0.0550885
$997$	58.0742	1.83923	0.919615	−	0.392822i	$-0.128501\pi$
$997$	58.0742	1.83923	0.919615	+	0.392822i	$0.128501\pi$
$998$	13.1797	0.417195
$999$	11.3624	0.359492

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.a.1.4	✓	11
3.2	odd	2		6039.2.a.d.1.8		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.a.1.4	✓	11	1.1	even	1	trivial
6039.2.a.d.1.8		11	3.2	odd	2

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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-1.36137 q^{2} +1.00000 q^{3} -0.146675 q^{4} -3.87776 q^{5} -1.36137 q^{6} -4.18708 q^{7} +2.92242 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.36137 q^{2} +1.00000 q^{3} -0.146675 q^{4} -3.87776 q^{5} -1.36137 q^{6} -4.18708 q^{7} +2.92242 q^{8} +1.00000 q^{9} +5.27907 q^{10} -1.00000 q^{11} -0.146675 q^{12} +6.69213 q^{13} +5.70016 q^{14} -3.87776 q^{15} -3.68514 q^{16} +2.46824 q^{17} -1.36137 q^{18} +0.542898 q^{19} +0.568769 q^{20} -4.18708 q^{21} +1.36137 q^{22} +2.08289 q^{23} +2.92242 q^{24} +10.0370 q^{25} -9.11046 q^{26} +1.00000 q^{27} +0.614139 q^{28} -2.48240 q^{29} +5.27907 q^{30} -6.44257 q^{31} -0.828001 q^{32} -1.00000 q^{33} -3.36018 q^{34} +16.2365 q^{35} -0.146675 q^{36} +11.3624 q^{37} -0.739084 q^{38} +6.69213 q^{39} -11.3324 q^{40} -12.1540 q^{41} +5.70016 q^{42} -1.28391 q^{43} +0.146675 q^{44} -3.87776 q^{45} -2.83558 q^{46} +6.95084 q^{47} -3.68514 q^{48} +10.5317 q^{49} -13.6641 q^{50} +2.46824 q^{51} -0.981566 q^{52} +11.4569 q^{53} -1.36137 q^{54} +3.87776 q^{55} -12.2364 q^{56} +0.542898 q^{57} +3.37947 q^{58} -10.3751 q^{59} +0.568769 q^{60} +1.00000 q^{61} +8.77071 q^{62} -4.18708 q^{63} +8.49749 q^{64} -25.9505 q^{65} +1.36137 q^{66} +2.88534 q^{67} -0.362028 q^{68} +2.08289 q^{69} -22.1039 q^{70} -12.6125 q^{71} +2.92242 q^{72} +3.24241 q^{73} -15.4685 q^{74} +10.0370 q^{75} -0.0796293 q^{76} +4.18708 q^{77} -9.11046 q^{78} -8.60065 q^{79} +14.2901 q^{80} +1.00000 q^{81} +16.5461 q^{82} -11.8532 q^{83} +0.614139 q^{84} -9.57124 q^{85} +1.74787 q^{86} -2.48240 q^{87} -2.92242 q^{88} -7.77300 q^{89} +5.27907 q^{90} -28.0205 q^{91} -0.305507 q^{92} -6.44257 q^{93} -9.46266 q^{94} -2.10523 q^{95} -0.828001 q^{96} -8.63349 q^{97} -14.3375 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 4 q^{2} + 11 q^{3} + 6 q^{4} - 13 q^{5} - 4 q^{6} - 5 q^{7} - 9 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q - 4 * q^2 + 11 * q^3 + 6 * q^4 - 13 * q^5 - 4 * q^6 - 5 * q^7 - 9 * q^8 + 11 * q^9	\( 11 q - 4 q^{2} + 11 q^{3} + 6 q^{4} - 13 q^{5} - 4 q^{6} - 5 q^{7} - 9 q^{8} + 11 q^{9} + 6 q^{10} - 11 q^{11} + 6 q^{12} - 3 q^{13} - 9 q^{14} - 13 q^{15} + 4 q^{16} - 7 q^{17} - 4 q^{18} - 8 q^{19} - 25 q^{20} - 5 q^{21} + 4 q^{22} - 15 q^{23} - 9 q^{24} + 4 q^{25} - 2 q^{26} + 11 q^{27} + 13 q^{28} - 8 q^{29} + 6 q^{30} - 17 q^{31} - 27 q^{32} - 11 q^{33} - 18 q^{34} - 2 q^{35} + 6 q^{36} - 10 q^{37} - 30 q^{38} - 3 q^{39} + 10 q^{40} - 25 q^{41} - 9 q^{42} - 7 q^{43} - 6 q^{44} - 13 q^{45} + 32 q^{46} - 30 q^{47} + 4 q^{48} - 2 q^{49} + 11 q^{50} - 7 q^{51} - 7 q^{52} - 18 q^{53} - 4 q^{54} + 13 q^{55} - 20 q^{56} - 8 q^{57} - 13 q^{58} - 43 q^{59} - 25 q^{60} + 11 q^{61} + 7 q^{62} - 5 q^{63} + 25 q^{64} - 27 q^{65} + 4 q^{66} - 30 q^{67} + 10 q^{68} - 15 q^{69} - 4 q^{70} - 7 q^{71} - 9 q^{72} + 6 q^{73} - 44 q^{74} + 4 q^{75} - 19 q^{76} + 5 q^{77} - 2 q^{78} + 17 q^{79} - 22 q^{80} + 11 q^{81} + 8 q^{82} - 34 q^{83} + 13 q^{84} + 10 q^{85} + 2 q^{86} - 8 q^{87} + 9 q^{88} - 41 q^{89} + 6 q^{90} - 39 q^{91} - 32 q^{92} - 17 q^{93} + 55 q^{94} - 9 q^{95} - 27 q^{96} - 41 q^{97} - 29 q^{98} - 11 q^{99}+O(q^{100}) \) 11 * q - 4 * q^2 + 11 * q^3 + 6 * q^4 - 13 * q^5 - 4 * q^6 - 5 * q^7 - 9 * q^8 + 11 * q^9 + 6 * q^10 - 11 * q^11 + 6 * q^12 - 3 * q^13 - 9 * q^14 - 13 * q^15 + 4 * q^16 - 7 * q^17 - 4 * q^18 - 8 * q^19 - 25 * q^20 - 5 * q^21 + 4 * q^22 - 15 * q^23 - 9 * q^24 + 4 * q^25 - 2 * q^26 + 11 * q^27 + 13 * q^28 - 8 * q^29 + 6 * q^30 - 17 * q^31 - 27 * q^32 - 11 * q^33 - 18 * q^34 - 2 * q^35 + 6 * q^36 - 10 * q^37 - 30 * q^38 - 3 * q^39 + 10 * q^40 - 25 * q^41 - 9 * q^42 - 7 * q^43 - 6 * q^44 - 13 * q^45 + 32 * q^46 - 30 * q^47 + 4 * q^48 - 2 * q^49 + 11 * q^50 - 7 * q^51 - 7 * q^52 - 18 * q^53 - 4 * q^54 + 13 * q^55 - 20 * q^56 - 8 * q^57 - 13 * q^58 - 43 * q^59 - 25 * q^60 + 11 * q^61 + 7 * q^62 - 5 * q^63 + 25 * q^64 - 27 * q^65 + 4 * q^66 - 30 * q^67 + 10 * q^68 - 15 * q^69 - 4 * q^70 - 7 * q^71 - 9 * q^72 + 6 * q^73 - 44 * q^74 + 4 * q^75 - 19 * q^76 + 5 * q^77 - 2 * q^78 + 17 * q^79 - 22 * q^80 + 11 * q^81 + 8 * q^82 - 34 * q^83 + 13 * q^84 + 10 * q^85 + 2 * q^86 - 8 * q^87 + 9 * q^88 - 41 * q^89 + 6 * q^90 - 39 * q^91 - 32 * q^92 - 17 * q^93 + 55 * q^94 - 9 * q^95 - 27 * q^96 - 41 * q^97 - 29 * q^98 - 11 * q^99

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