LMFDB - Embedded newform 2013.2.a.d.1.10

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 16 x^{10} + 13 x^{9} + 93 x^{8} - 59 x^{7} - 238 x^{6} + 108 x^{5} + 257 x^{4} + \cdots + 1 $ x^12 - x^11 - 16x^10 + 13x^9 + 93x^8 - 59x^7 - 238x^6 + 108x^5 + 257x^4 - 71x^3 - 93x^2 + 13x + 1
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			1.10
Root			$2.01091$ 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)

$f(q)$	$=$	$q+2.01091 q^{2} -1.00000 q^{3} +2.04375 q^{4} +2.29360 q^{5} -2.01091 q^{6} -4.38501 q^{7} +0.0879817 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.01091 q^{2} -1.00000 q^{3} +2.04375 q^{4} +2.29360 q^{5} -2.01091 q^{6} -4.38501 q^{7} +0.0879817 q^{8} +1.00000 q^{9} +4.61222 q^{10} -1.00000 q^{11} -2.04375 q^{12} -1.69111 q^{13} -8.81784 q^{14} -2.29360 q^{15} -3.91058 q^{16} -1.38158 q^{17} +2.01091 q^{18} +0.110526 q^{19} +4.68755 q^{20} +4.38501 q^{21} -2.01091 q^{22} -0.503803 q^{23} -0.0879817 q^{24} +0.260612 q^{25} -3.40067 q^{26} -1.00000 q^{27} -8.96186 q^{28} -4.90215 q^{29} -4.61222 q^{30} -3.94262 q^{31} -8.03978 q^{32} +1.00000 q^{33} -2.77824 q^{34} -10.0575 q^{35} +2.04375 q^{36} -3.22228 q^{37} +0.222258 q^{38} +1.69111 q^{39} +0.201795 q^{40} +12.4079 q^{41} +8.81784 q^{42} +1.40887 q^{43} -2.04375 q^{44} +2.29360 q^{45} -1.01310 q^{46} -9.04166 q^{47} +3.91058 q^{48} +12.2283 q^{49} +0.524067 q^{50} +1.38158 q^{51} -3.45621 q^{52} -8.78013 q^{53} -2.01091 q^{54} -2.29360 q^{55} -0.385800 q^{56} -0.110526 q^{57} -9.85777 q^{58} -5.26459 q^{59} -4.68755 q^{60} -1.00000 q^{61} -7.92825 q^{62} -4.38501 q^{63} -8.34611 q^{64} -3.87874 q^{65} +2.01091 q^{66} -8.70560 q^{67} -2.82362 q^{68} +0.503803 q^{69} -20.2246 q^{70} +4.64701 q^{71} +0.0879817 q^{72} -1.09932 q^{73} -6.47971 q^{74} -0.260612 q^{75} +0.225888 q^{76} +4.38501 q^{77} +3.40067 q^{78} +14.4489 q^{79} -8.96932 q^{80} +1.00000 q^{81} +24.9511 q^{82} -0.315020 q^{83} +8.96186 q^{84} -3.16880 q^{85} +2.83311 q^{86} +4.90215 q^{87} -0.0879817 q^{88} +2.05956 q^{89} +4.61222 q^{90} +7.41553 q^{91} -1.02965 q^{92} +3.94262 q^{93} -18.1819 q^{94} +0.253503 q^{95} +8.03978 q^{96} +16.1329 q^{97} +24.5899 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} - 12 q^{3} + 9 q^{4} - 3 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + q^2 - 12 * q^3 + 9 * q^4 - 3 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 12 * q^9	\( 12 q + q^{2} - 12 q^{3} + 9 q^{4} - 3 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 12 q^{9} - 8 q^{10} - 12 q^{11} - 9 q^{12} - q^{13} - 3 q^{14} + 3 q^{15} + 3 q^{16} + 9 q^{17} + q^{18} - 20 q^{19} - 9 q^{20} + 9 q^{21} - q^{22} - 9 q^{23} - 6 q^{24} + 3 q^{25} - 18 q^{26} - 12 q^{27} - 31 q^{28} + 18 q^{29} + 8 q^{30} - 21 q^{31} + 18 q^{32} + 12 q^{33} - 12 q^{34} - 4 q^{35} + 9 q^{36} - 18 q^{37} - 2 q^{38} + q^{39} - 26 q^{40} + 15 q^{41} + 3 q^{42} - 33 q^{43} - 9 q^{44} - 3 q^{45} - 28 q^{46} - 20 q^{47} - 3 q^{48} + 15 q^{49} - 2 q^{50} - 9 q^{51} - 27 q^{52} - q^{54} + 3 q^{55} - 8 q^{56} + 20 q^{57} - 11 q^{58} - 21 q^{59} + 9 q^{60} - 12 q^{61} - 9 q^{62} - 9 q^{63} - 12 q^{64} + 17 q^{65} + q^{66} - 34 q^{67} - 16 q^{68} + 9 q^{69} - 36 q^{70} - 5 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} - 3 q^{75} - 27 q^{76} + 9 q^{77} + 18 q^{78} - 31 q^{79} - 60 q^{80} + 12 q^{81} - 12 q^{82} - 32 q^{83} + 31 q^{84} - 40 q^{85} + 18 q^{86} - 18 q^{87} - 6 q^{88} + 27 q^{89} - 8 q^{90} - 45 q^{91} - 78 q^{92} + 21 q^{93} - 13 q^{94} + 37 q^{95} - 18 q^{96} - 19 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q + q^2 - 12 * q^3 + 9 * q^4 - 3 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 12 * q^9 - 8 * q^10 - 12 * q^11 - 9 * q^12 - q^13 - 3 * q^14 + 3 * q^15 + 3 * q^16 + 9 * q^17 + q^18 - 20 * q^19 - 9 * q^20 + 9 * q^21 - q^22 - 9 * q^23 - 6 * q^24 + 3 * q^25 - 18 * q^26 - 12 * q^27 - 31 * q^28 + 18 * q^29 + 8 * q^30 - 21 * q^31 + 18 * q^32 + 12 * q^33 - 12 * q^34 - 4 * q^35 + 9 * q^36 - 18 * q^37 - 2 * q^38 + q^39 - 26 * q^40 + 15 * q^41 + 3 * q^42 - 33 * q^43 - 9 * q^44 - 3 * q^45 - 28 * q^46 - 20 * q^47 - 3 * q^48 + 15 * q^49 - 2 * q^50 - 9 * q^51 - 27 * q^52 - q^54 + 3 * q^55 - 8 * q^56 + 20 * q^57 - 11 * q^58 - 21 * q^59 + 9 * q^60 - 12 * q^61 - 9 * q^62 - 9 * q^63 - 12 * q^64 + 17 * q^65 + q^66 - 34 * q^67 - 16 * q^68 + 9 * q^69 - 36 * q^70 - 5 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 - 3 * q^75 - 27 * q^76 + 9 * q^77 + 18 * q^78 - 31 * q^79 - 60 * q^80 + 12 * q^81 - 12 * q^82 - 32 * q^83 + 31 * q^84 - 40 * q^85 + 18 * q^86 - 18 * q^87 - 6 * q^88 + 27 * q^89 - 8 * q^90 - 45 * q^91 - 78 * q^92 + 21 * q^93 - 13 * q^94 + 37 * q^95 - 18 * q^96 - 19 * q^97 + 4 * q^98 - 12 * 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 $

$2$	2.01091	1.42193	0.710963	−	0.703229i	$-0.248259\pi$
$2$	2.01091	1.42193	0.710963	+	0.703229i	$0.248259\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.04375	1.02188
$5$	2.29360	1.02573	0.512865	−	0.858469i	$-0.328584\pi$
$5$	2.29360	1.02573	0.512865	+	0.858469i	$0.328584\pi$
$6$	−2.01091	−0.820950
$7$	−4.38501	−1.65738	−0.828688	−	0.559711i	$-0.810912\pi$
$7$	−4.38501	−1.65738	−0.828688	+	0.559711i	$0.810912\pi$
$8$	0.0879817	0.0311062
$9$	1.00000	0.333333
$10$	4.61222	1.45851
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.04375	−0.589980
$13$	−1.69111	−0.469030	−0.234515	−	0.972113i	$-0.575350\pi$
$13$	−1.69111	−0.469030	−0.234515	+	0.972113i	$0.575350\pi$
$14$	−8.81784	−2.35667
$15$	−2.29360	−0.592206
$16$	−3.91058	−0.977645
$17$	−1.38158	−0.335083	−0.167542	−	0.985865i	$-0.553583\pi$
$17$	−1.38158	−0.335083	−0.167542	+	0.985865i	$0.553583\pi$
$18$	2.01091	0.473976
$19$	0.110526	0.0253565	0.0126782	−	0.999920i	$-0.495964\pi$
$19$	0.110526	0.0253565	0.0126782	+	0.999920i	$0.495964\pi$
$20$	4.68755	1.04817
$21$	4.38501	0.956887
$22$	−2.01091	−0.428727
$23$	−0.503803	−0.105050	−0.0525251	−	0.998620i	$-0.516727\pi$
$23$	−0.503803	−0.105050	−0.0525251	+	0.998620i	$0.516727\pi$
$24$	−0.0879817	−0.0179592
$25$	0.260612	0.0521224
$26$	−3.40067	−0.666926
$27$	−1.00000	−0.192450
$28$	−8.96186	−1.69363
$29$	−4.90215	−0.910306	−0.455153	−	0.890413i	$-0.650415\pi$
$29$	−4.90215	−0.910306	−0.455153	+	0.890413i	$0.650415\pi$
$30$	−4.61222	−0.842073
$31$	−3.94262	−0.708116	−0.354058	−	0.935224i	$-0.615198\pi$
$31$	−3.94262	−0.708116	−0.354058	+	0.935224i	$0.615198\pi$
$32$	−8.03978	−1.42125
$33$	1.00000	0.174078
$34$	−2.77824	−0.476464
$35$	−10.0575	−1.70002
$36$	2.04375	0.340625
$37$	−3.22228	−0.529740	−0.264870	−	0.964284i	$-0.585329\pi$
$37$	−3.22228	−0.529740	−0.264870	+	0.964284i	$0.585329\pi$
$38$	0.222258	0.0360550
$39$	1.69111	0.270794
$40$	0.201795	0.0319066
$41$	12.4079	1.93778	0.968891	−	0.247489i	$-0.0796053\pi$
$41$	12.4079	1.93778	0.968891	+	0.247489i	$0.0796053\pi$
$42$	8.81784	1.36062
$43$	1.40887	0.214851	0.107425	−	0.994213i	$-0.465739\pi$
$43$	1.40887	0.214851	0.107425	+	0.994213i	$0.465739\pi$
$44$	−2.04375	−0.308107
$45$	2.29360	0.341910
$46$	−1.01310	−0.149374
$47$	−9.04166	−1.31886	−0.659431	−	0.751765i	$-0.729203\pi$
$47$	−9.04166	−1.31886	−0.659431	+	0.751765i	$0.729203\pi$
$48$	3.91058	0.564444
$49$	12.2283	1.74690
$50$	0.524067	0.0741142
$51$	1.38158	0.193460
$52$	−3.45621	−0.479290
$53$	−8.78013	−1.20604	−0.603022	−	0.797725i	$-0.706037\pi$
$53$	−8.78013	−1.20604	−0.603022	+	0.797725i	$0.706037\pi$
$54$	−2.01091	−0.273650
$55$	−2.29360	−0.309269
$56$	−0.385800	−0.0515547
$57$	−0.110526	−0.0146396
$58$	−9.85777	−1.29439
$59$	−5.26459	−0.685392	−0.342696	−	0.939446i	$-0.611340\pi$
$59$	−5.26459	−0.685392	−0.342696	+	0.939446i	$0.611340\pi$
$60$	−4.68755	−0.605161
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−7.92825	−1.00689
$63$	−4.38501	−0.552459
$64$	−8.34611	−1.04326
$65$	−3.87874	−0.481098
$66$	2.01091	0.247526
$67$	−8.70560	−1.06356	−0.531779	−	0.846883i	$-0.678476\pi$
$67$	−8.70560	−1.06356	−0.531779	+	0.846883i	$0.678476\pi$
$68$	−2.82362	−0.342414
$69$	0.503803	0.0606508
$70$	−20.2246	−2.41731
$71$	4.64701	0.551499	0.275749	−	0.961230i	$-0.411074\pi$
$71$	4.64701	0.551499	0.275749	+	0.961230i	$0.411074\pi$
$72$	0.0879817	0.0103687
$73$	−1.09932	−0.128666	−0.0643331	−	0.997928i	$-0.520492\pi$
$73$	−1.09932	−0.128666	−0.0643331	+	0.997928i	$0.520492\pi$
$74$	−6.47971	−0.753251
$75$	−0.260612	−0.0300929
$76$	0.225888	0.0259112
$77$	4.38501	0.499718
$78$	3.40067	0.385050
$79$	14.4489	1.62563	0.812814	−	0.582524i	$-0.197935\pi$
$79$	14.4489	1.62563	0.812814	+	0.582524i	$0.197935\pi$
$80$	−8.96932	−1.00280
$81$	1.00000	0.111111
$82$	24.9511	2.75538
$83$	−0.315020	−0.0345780	−0.0172890	−	0.999851i	$-0.505504\pi$
$83$	−0.315020	−0.0345780	−0.0172890	+	0.999851i	$0.505504\pi$
$84$	8.96186	0.977820
$85$	−3.16880	−0.343705
$86$	2.83311	0.305502
$87$	4.90215	0.525565
$88$	−0.0879817	−0.00937888
$89$	2.05956	0.218313	0.109156	−	0.994025i	$-0.465185\pi$
$89$	2.05956	0.218313	0.109156	+	0.994025i	$0.465185\pi$
$90$	4.61222	0.486171
$91$	7.41553	0.777359
$92$	−1.02965	−0.107348
$93$	3.94262	0.408831
$94$	−18.1819	−1.87532
$95$	0.253503	0.0260089
$96$	8.03978	0.820557
$97$	16.1329	1.63804	0.819022	−	0.573762i	$-0.194516\pi$
$97$	16.1329	1.63804	0.819022	+	0.573762i	$0.194516\pi$
$98$	24.5899	2.48396
$99$	−1.00000	−0.100504
$100$	0.532626	0.0532626
$101$	−0.0715942	−0.00712389	−0.00356195	−	0.999994i	$-0.501134\pi$
$101$	−0.0715942	−0.00712389	−0.00356195	+	0.999994i	$0.501134\pi$
$102$	2.77824	0.275087
$103$	−4.03904	−0.397978	−0.198989	−	0.980002i	$-0.563766\pi$
$103$	−4.03904	−0.397978	−0.198989	+	0.980002i	$0.563766\pi$
$104$	−0.148787	−0.0145897
$105$	10.0575	0.981508
$106$	−17.6560	−1.71491
$107$	−18.0417	−1.74416	−0.872078	−	0.489367i	$-0.837228\pi$
$107$	−18.0417	−1.74416	−0.872078	+	0.489367i	$0.837228\pi$
$108$	−2.04375	−0.196660
$109$	15.7912	1.51253	0.756263	−	0.654267i	$-0.227023\pi$
$109$	15.7912	1.51253	0.756263	+	0.654267i	$0.227023\pi$
$110$	−4.61222	−0.439758
$111$	3.22228	0.305845
$112$	17.1479	1.62033
$113$	−5.62641	−0.529288	−0.264644	−	0.964346i	$-0.585255\pi$
$113$	−5.62641	−0.529288	−0.264644	+	0.964346i	$0.585255\pi$
$114$	−0.222258	−0.0208164
$115$	−1.15552	−0.107753
$116$	−10.0188	−0.930220
$117$	−1.69111	−0.156343
$118$	−10.5866	−0.974577
$119$	6.05825	0.555359
$120$	−0.201795	−0.0184213
$121$	1.00000	0.0909091
$122$	−2.01091	−0.182059
$123$	−12.4079	−1.11878
$124$	−8.05774	−0.723606
$125$	−10.8703	−0.972267
$126$	−8.81784	−0.785556
$127$	−4.42664	−0.392801	−0.196400	−	0.980524i	$-0.562925\pi$
$127$	−4.42664	−0.392801	−0.196400	+	0.980524i	$0.562925\pi$
$128$	−0.703685	−0.0621976
$129$	−1.40887	−0.124044
$130$	−7.79978	−0.684086
$131$	3.64937	0.318847	0.159423	−	0.987210i	$-0.449036\pi$
$131$	3.64937	0.318847	0.159423	+	0.987210i	$0.449036\pi$
$132$	2.04375	0.177886
$133$	−0.484658	−0.0420252
$134$	−17.5062	−1.51230
$135$	−2.29360	−0.197402
$136$	−0.121554	−0.0104232
$137$	−11.5989	−0.990965	−0.495483	−	0.868618i	$-0.665009\pi$
$137$	−11.5989	−0.990965	−0.495483	+	0.868618i	$0.665009\pi$
$138$	1.01310	0.0862410
$139$	−15.1002	−1.28078	−0.640390	−	0.768050i	$-0.721227\pi$
$139$	−15.1002	−1.28078	−0.640390	+	0.768050i	$0.721227\pi$
$140$	−20.5550	−1.73721
$141$	9.04166	0.761445
$142$	9.34471	0.784191
$143$	1.69111	0.141418
$144$	−3.91058	−0.325882
$145$	−11.2436	−0.933728
$146$	−2.21064	−0.182954
$147$	−12.2283	−1.00857
$148$	−6.58555	−0.541329
$149$	13.2433	1.08494	0.542468	−	0.840076i	$-0.317490\pi$
$149$	13.2433	1.08494	0.542468	+	0.840076i	$0.317490\pi$
$150$	−0.524067	−0.0427899
$151$	16.6453	1.35457	0.677286	−	0.735720i	$-0.263156\pi$
$151$	16.6453	1.35457	0.677286	+	0.735720i	$0.263156\pi$
$152$	0.00972429	0.000788744 0
$153$	−1.38158	−0.111694
$154$	8.81784	0.710562
$155$	−9.04280	−0.726335
$156$	3.45621	0.276718
$157$	11.9301	0.952127	0.476063	−	0.879411i	$-0.342063\pi$
$157$	11.9301	0.952127	0.476063	+	0.879411i	$0.342063\pi$
$158$	29.0554	2.31152
$159$	8.78013	0.696310
$160$	−18.4401	−1.45782
$161$	2.20918	0.174108
$162$	2.01091	0.157992
$163$	−0.505535	−0.0395966	−0.0197983	−	0.999804i	$-0.506302\pi$
$163$	−0.505535	−0.0395966	−0.0197983	+	0.999804i	$0.506302\pi$
$164$	25.3586	1.98017
$165$	2.29360	0.178557
$166$	−0.633477	−0.0491673
$167$	−7.02034	−0.543250	−0.271625	−	0.962403i	$-0.587561\pi$
$167$	−7.02034	−0.543250	−0.271625	+	0.962403i	$0.587561\pi$
$168$	0.385800	0.0297651
$169$	−10.1401	−0.780011
$170$	−6.37218	−0.488724
$171$	0.110526	0.00845215
$172$	2.87938	0.219551
$173$	−5.71737	−0.434684	−0.217342	−	0.976096i	$-0.569739\pi$
$173$	−5.71737	−0.434684	−0.217342	+	0.976096i	$0.569739\pi$
$174$	9.85777	0.747316
$175$	−1.14278	−0.0863864
$176$	3.91058	0.294771
$177$	5.26459	0.395711
$178$	4.14158	0.310425
$179$	5.77529	0.431665	0.215833	−	0.976430i	$-0.430753\pi$
$179$	5.77529	0.431665	0.215833	+	0.976430i	$0.430753\pi$
$180$	4.68755	0.349390
$181$	8.98069	0.667530	0.333765	−	0.942656i	$-0.391681\pi$
$181$	8.98069	0.667530	0.333765	+	0.942656i	$0.391681\pi$
$182$	14.9120	1.10535
$183$	1.00000	0.0739221
$184$	−0.0443255	−0.00326772
$185$	−7.39063	−0.543370
$186$	7.92825	0.581327
$187$	1.38158	0.101031
$188$	−18.4789	−1.34771
$189$	4.38501	0.318962
$190$	0.509772	0.0369827
$191$	−2.79919	−0.202542	−0.101271	−	0.994859i	$-0.532291\pi$
$191$	−2.79919	−0.202542	−0.101271	+	0.994859i	$0.532291\pi$
$192$	8.34611	0.602328
$193$	−10.5823	−0.761729	−0.380865	−	0.924631i	$-0.624374\pi$
$193$	−10.5823	−0.761729	−0.380865	+	0.924631i	$0.624374\pi$
$194$	32.4417	2.32918
$195$	3.87874	0.277762
$196$	24.9916	1.78511
$197$	23.6369	1.68406	0.842031	−	0.539429i	$-0.181360\pi$
$197$	23.6369	1.68406	0.842031	+	0.539429i	$0.181360\pi$
$198$	−2.01091	−0.142909
$199$	0.311922	0.0221116	0.0110558	−	0.999939i	$-0.496481\pi$
$199$	0.311922	0.0221116	0.0110558	+	0.999939i	$0.496481\pi$
$200$	0.0229291	0.00162133
$201$	8.70560	0.614045
$202$	−0.143969	−0.0101297
$203$	21.4959	1.50872
$204$	2.82362	0.197693
$205$	28.4587	1.98764
$206$	−8.12214	−0.565896
$207$	−0.503803	−0.0350167
$208$	6.61323	0.458545
$209$	−0.110526	−0.00764526
$210$	20.2246	1.39563
$211$	−26.1628	−1.80112	−0.900562	−	0.434728i	$-0.856845\pi$
$211$	−26.1628	−1.80112	−0.900562	+	0.434728i	$0.856845\pi$
$212$	−17.9444	−1.23243
$213$	−4.64701	−0.318408
$214$	−36.2802	−2.48006
$215$	3.23139	0.220379
$216$	−0.0879817	−0.00598640
$217$	17.2884	1.17361
$218$	31.7547	2.15070
$219$	1.09932	0.0742854
$220$	−4.68755	−0.316035
$221$	2.33641	0.157164
$222$	6.47971	0.434890
$223$	15.1197	1.01249	0.506244	−	0.862390i	$-0.331034\pi$
$223$	15.1197	1.01249	0.506244	+	0.862390i	$0.331034\pi$
$224$	35.2545	2.35554
$225$	0.260612	0.0173741
$226$	−11.3142	−0.752609
$227$	8.01271	0.531822	0.265911	−	0.963998i	$-0.414327\pi$
$227$	8.01271	0.531822	0.265911	+	0.963998i	$0.414327\pi$
$228$	−0.225888	−0.0149598
$229$	−18.0492	−1.19272	−0.596362	−	0.802716i	$-0.703388\pi$
$229$	−18.0492	−1.19272	−0.596362	+	0.802716i	$0.703388\pi$
$230$	−2.32365	−0.153217
$231$	−4.38501	−0.288512
$232$	−0.431299	−0.0283162
$233$	−11.3922	−0.746330	−0.373165	−	0.927765i	$-0.621727\pi$
$233$	−11.3922	−0.746330	−0.373165	+	0.927765i	$0.621727\pi$
$234$	−3.40067	−0.222309
$235$	−20.7380	−1.35280
$236$	−10.7595	−0.700386
$237$	−14.4489	−0.938556
$238$	12.1826	0.789680
$239$	3.97892	0.257375	0.128688	−	0.991685i	$-0.458924\pi$
$239$	3.97892	0.257375	0.128688	+	0.991685i	$0.458924\pi$
$240$	8.96932	0.578967
$241$	−5.89109	−0.379478	−0.189739	−	0.981835i	$-0.560764\pi$
$241$	−5.89109	−0.379478	−0.189739	+	0.981835i	$0.560764\pi$
$242$	2.01091	0.129266
$243$	−1.00000	−0.0641500
$244$	−2.04375	−0.130838
$245$	28.0468	1.79184
$246$	−24.9511	−1.59082
$247$	−0.186912	−0.0118929
$248$	−0.346878	−0.0220268
$249$	0.315020	0.0199636
$250$	−21.8591	−1.38249
$251$	−21.6615	−1.36726	−0.683631	−	0.729828i	$-0.739600\pi$
$251$	−21.6615	−1.36726	−0.683631	+	0.729828i	$0.739600\pi$
$252$	−8.96186	−0.564544
$253$	0.503803	0.0316738
$254$	−8.90156	−0.558534
$255$	3.16880	0.198438
$256$	15.2772	0.954823
$257$	−8.24914	−0.514567	−0.257284	−	0.966336i	$-0.582827\pi$
$257$	−8.24914	−0.514567	−0.257284	+	0.966336i	$0.582827\pi$
$258$	−2.83311	−0.176382
$259$	14.1297	0.877978
$260$	−7.92717	−0.491623
$261$	−4.90215	−0.303435
$262$	7.33855	0.453377
$263$	26.5861	1.63937	0.819685	−	0.572815i	$-0.194149\pi$
$263$	26.5861	1.63937	0.819685	+	0.572815i	$0.194149\pi$
$264$	0.0879817	0.00541490
$265$	−20.1381	−1.23708
$266$	−0.974603	−0.0597567
$267$	−2.05956	−0.126043
$268$	−17.7921	−1.08682
$269$	−13.7490	−0.838293	−0.419147	−	0.907919i	$-0.637671\pi$
$269$	−13.7490	−0.838293	−0.419147	+	0.907919i	$0.637671\pi$
$270$	−4.61222	−0.280691
$271$	−8.02467	−0.487464	−0.243732	−	0.969843i	$-0.578372\pi$
$271$	−8.02467	−0.487464	−0.243732	+	0.969843i	$0.578372\pi$
$272$	5.40280	0.327593
$273$	−7.41553	−0.448808
$274$	−23.3244	−1.40908
$275$	−0.260612	−0.0157155
$276$	1.02965	0.0619776
$277$	15.6333	0.939314	0.469657	−	0.882849i	$-0.344378\pi$
$277$	15.6333	0.939314	0.469657	+	0.882849i	$0.344378\pi$
$278$	−30.3651	−1.82117
$279$	−3.94262	−0.236039
$280$	−0.884873	−0.0528812
$281$	31.2843	1.86626	0.933132	−	0.359534i	$-0.117064\pi$
$281$	31.2843	1.86626	0.933132	+	0.359534i	$0.117064\pi$
$282$	18.1819	1.08272
$283$	13.7147	0.815255	0.407628	−	0.913148i	$-0.366356\pi$
$283$	13.7147	0.815255	0.407628	+	0.913148i	$0.366356\pi$
$284$	9.49734	0.563563
$285$	−0.253503	−0.0150162
$286$	3.40067	0.201086
$287$	−54.4085	−3.21163
$288$	−8.03978	−0.473749
$289$	−15.0912	−0.887719
$290$	−22.6098	−1.32769
$291$	−16.1329	−0.945726
$292$	−2.24675	−0.131481
$293$	9.57188	0.559195	0.279598	−	0.960117i	$-0.409799\pi$
$293$	9.57188	0.559195	0.279598	+	0.960117i	$0.409799\pi$
$294$	−24.5899	−1.43411
$295$	−12.0749	−0.703027
$296$	−0.283502	−0.0164782
$297$	1.00000	0.0580259
$298$	26.6311	1.54270
$299$	0.851987	0.0492717
$300$	−0.532626	−0.0307512
$301$	−6.17790	−0.356088
$302$	33.4721	1.92610
$303$	0.0715942	0.00411298
$304$	−0.432222	−0.0247896
$305$	−2.29360	−0.131331
$306$	−2.77824	−0.158821
$307$	−11.7940	−0.673120	−0.336560	−	0.941662i	$-0.609263\pi$
$307$	−11.7940	−0.673120	−0.336560	+	0.941662i	$0.609263\pi$
$308$	8.96186	0.510650
$309$	4.03904	0.229773
$310$	−18.1842	−1.03280
$311$	−6.65342	−0.377281	−0.188640	−	0.982046i	$-0.560408\pi$
$311$	−6.65342	−0.377281	−0.188640	+	0.982046i	$0.560408\pi$
$312$	0.148787	0.00842340
$313$	−5.96584	−0.337209	−0.168605	−	0.985684i	$-0.553926\pi$
$313$	−5.96584	−0.337209	−0.168605	+	0.985684i	$0.553926\pi$
$314$	23.9904	1.35385
$315$	−10.0575	−0.566674
$316$	29.5300	1.66119
$317$	16.5911	0.931848	0.465924	−	0.884825i	$-0.345722\pi$
$317$	16.5911	0.931848	0.465924	+	0.884825i	$0.345722\pi$
$318$	17.6560	0.990102
$319$	4.90215	0.274468
$320$	−19.1426	−1.07011
$321$	18.0417	1.00699
$322$	4.44246	0.247568
$323$	−0.152701	−0.00849653
$324$	2.04375	0.113542
$325$	−0.440724	−0.0244469
$326$	−1.01658	−0.0563034
$327$	−15.7912	−0.873258
$328$	1.09166	0.0602771
$329$	39.6477	2.18585
$330$	4.61222	0.253895
$331$	−23.9520	−1.31652	−0.658259	−	0.752791i	$-0.728707\pi$
$331$	−23.9520	−1.31652	−0.658259	+	0.752791i	$0.728707\pi$
$332$	−0.643823	−0.0353344
$333$	−3.22228	−0.176580
$334$	−14.1173	−0.772462
$335$	−19.9672	−1.09092
$336$	−17.1479	−0.935496
$337$	−6.96307	−0.379302	−0.189651	−	0.981852i	$-0.560736\pi$
$337$	−6.96307	−0.379302	−0.189651	+	0.981852i	$0.560736\pi$
$338$	−20.3909	−1.10912
$339$	5.62641	0.305585
$340$	−6.47625	−0.351224
$341$	3.94262	0.213505
$342$	0.222258	0.0120183
$343$	−22.9260	−1.23789
$344$	0.123955	0.00668319
$345$	1.15552	0.0622113
$346$	−11.4971	−0.618088
$347$	20.8345	1.11845	0.559226	−	0.829015i	$-0.311098\pi$
$347$	20.8345	1.11845	0.559226	+	0.829015i	$0.311098\pi$
$348$	10.0188	0.537063
$349$	22.1809	1.18732	0.593659	−	0.804717i	$-0.297683\pi$
$349$	22.1809	1.18732	0.593659	+	0.804717i	$0.297683\pi$
$350$	−2.29803	−0.122835
$351$	1.69111	0.0902648
$352$	8.03978	0.428522
$353$	15.6354	0.832190	0.416095	−	0.909321i	$-0.363398\pi$
$353$	15.6354	0.832190	0.416095	+	0.909321i	$0.363398\pi$
$354$	10.5866	0.562672
$355$	10.6584	0.565689
$356$	4.20923	0.223089
$357$	−6.05825	−0.320637
$358$	11.6136	0.613796
$359$	−22.1078	−1.16680	−0.583402	−	0.812183i	$-0.698279\pi$
$359$	−22.1078	−1.16680	−0.583402	+	0.812183i	$0.698279\pi$
$360$	0.201795	0.0106355
$361$	−18.9878	−0.999357
$362$	18.0593	0.949178
$363$	−1.00000	−0.0524864
$364$	15.1555	0.794364
$365$	−2.52141	−0.131977
$366$	2.01091	0.105112
$367$	9.46184	0.493904	0.246952	−	0.969028i	$-0.420571\pi$
$367$	9.46184	0.493904	0.246952	+	0.969028i	$0.420571\pi$
$368$	1.97016	0.102702
$369$	12.4079	0.645927
$370$	−14.8619	−0.772633
$371$	38.5009	1.99887
$372$	8.05774	0.417774
$373$	−4.34508	−0.224980	−0.112490	−	0.993653i	$-0.535883\pi$
$373$	−4.34508	−0.224980	−0.112490	+	0.993653i	$0.535883\pi$
$374$	2.77824	0.143659
$375$	10.8703	0.561338
$376$	−0.795501	−0.0410248
$377$	8.29008	0.426961
$378$	8.81784	0.453541
$379$	−4.12788	−0.212035	−0.106017	−	0.994364i	$-0.533810\pi$
$379$	−4.12788	−0.212035	−0.106017	+	0.994364i	$0.533810\pi$
$380$	0.518098	0.0265779
$381$	4.42664	0.226784
$382$	−5.62890	−0.288000
$383$	−24.1984	−1.23648	−0.618241	−	0.785989i	$-0.712154\pi$
$383$	−24.1984	−1.23648	−0.618241	+	0.785989i	$0.712154\pi$
$384$	0.703685	0.0359098
$385$	10.0575	0.512576
$386$	−21.2800	−1.08312
$387$	1.40887	0.0716169
$388$	32.9716	1.67388
$389$	19.9003	1.00899	0.504493	−	0.863416i	$-0.331680\pi$
$389$	19.9003	1.00899	0.504493	+	0.863416i	$0.331680\pi$
$390$	7.79978	0.394957
$391$	0.696046	0.0352006
$392$	1.07586	0.0543394
$393$	−3.64937	−0.184086
$394$	47.5317	2.39461
$395$	33.1400	1.66745
$396$	−2.04375	−0.102702
$397$	−14.7767	−0.741620	−0.370810	−	0.928709i	$-0.620920\pi$
$397$	−14.7767	−0.741620	−0.370810	+	0.928709i	$0.620920\pi$
$398$	0.627247	0.0314411
$399$	0.484658	0.0242633
$400$	−1.01914	−0.0509572
$401$	−32.5681	−1.62637	−0.813187	−	0.582002i	$-0.802269\pi$
$401$	−32.5681	−1.62637	−0.813187	+	0.582002i	$0.802269\pi$
$402$	17.5062	0.873128
$403$	6.66741	0.332127
$404$	−0.146321	−0.00727973
$405$	2.29360	0.113970
$406$	43.2264	2.14529
$407$	3.22228	0.159723
$408$	0.121554	0.00601783
$409$	12.4675	0.616476	0.308238	−	0.951309i	$-0.400261\pi$
$409$	12.4675	0.616476	0.308238	+	0.951309i	$0.400261\pi$
$410$	57.2278	2.82628
$411$	11.5989	0.572134
$412$	−8.25480	−0.406685
$413$	23.0853	1.13595
$414$	−1.01310	−0.0497912
$415$	−0.722531	−0.0354677
$416$	13.5962	0.666607
$417$	15.1002	0.739458
$418$	−0.222258	−0.0108710
$419$	−6.15342	−0.300614	−0.150307	−	0.988639i	$-0.548026\pi$
$419$	−6.15342	−0.300614	−0.150307	+	0.988639i	$0.548026\pi$
$420$	20.5550	1.00298
$421$	2.12112	0.103377	0.0516886	−	0.998663i	$-0.483540\pi$
$421$	2.12112	0.103377	0.0516886	+	0.998663i	$0.483540\pi$
$422$	−52.6111	−2.56107
$423$	−9.04166	−0.439620
$424$	−0.772491	−0.0375155
$425$	−0.360057	−0.0174653
$426$	−9.34471	−0.452753
$427$	4.38501	0.212205
$428$	−36.8727	−1.78231
$429$	−1.69111	−0.0816476
$430$	6.49802	0.313363
$431$	−6.48815	−0.312523	−0.156262	−	0.987716i	$-0.549944\pi$
$431$	−6.48815	−0.312523	−0.156262	+	0.987716i	$0.549944\pi$
$432$	3.91058	0.188148
$433$	27.8259	1.33723	0.668614	−	0.743610i	$-0.266888\pi$
$433$	27.8259	1.33723	0.668614	+	0.743610i	$0.266888\pi$
$434$	34.7654	1.66879
$435$	11.2436	0.539088
$436$	32.2734	1.54561
$437$	−0.0556835	−0.00266370
$438$	2.21064	0.105628
$439$	−18.7530	−0.895032	−0.447516	−	0.894276i	$-0.647691\pi$
$439$	−18.7530	−0.895032	−0.447516	+	0.894276i	$0.647691\pi$
$440$	−0.201795	−0.00962020
$441$	12.2283	0.582299
$442$	4.69831	0.223476
$443$	−7.88037	−0.374408	−0.187204	−	0.982321i	$-0.559942\pi$
$443$	−7.88037	−0.374408	−0.187204	+	0.982321i	$0.559942\pi$
$444$	6.58555	0.312536
$445$	4.72381	0.223930
$446$	30.4043	1.43968
$447$	−13.2433	−0.626388
$448$	36.5977	1.72908
$449$	23.4421	1.10630	0.553150	−	0.833082i	$-0.313426\pi$
$449$	23.4421	1.10630	0.553150	+	0.833082i	$0.313426\pi$
$450$	0.524067	0.0247047
$451$	−12.4079	−0.584263
$452$	−11.4990	−0.540867
$453$	−16.6453	−0.782063
$454$	16.1128	0.756212
$455$	17.0083	0.797360
$456$	−0.00972429	−0.000455381 0
$457$	21.7612	1.01795	0.508974	−	0.860782i	$-0.330025\pi$
$457$	21.7612	1.01795	0.508974	+	0.860782i	$0.330025\pi$
$458$	−36.2953	−1.69597
$459$	1.38158	0.0644868
$460$	−2.36160	−0.110110
$461$	3.03355	0.141287	0.0706433	−	0.997502i	$-0.477495\pi$
$461$	3.03355	0.141287	0.0706433	+	0.997502i	$0.477495\pi$
$462$	−8.81784	−0.410243
$463$	28.2066	1.31087	0.655435	−	0.755252i	$-0.272485\pi$
$463$	28.2066	1.31087	0.655435	+	0.755252i	$0.272485\pi$
$464$	19.1703	0.889957
$465$	9.04280	0.419350
$466$	−22.9087	−1.06123
$467$	−37.5563	−1.73790	−0.868949	−	0.494901i	$-0.835204\pi$
$467$	−37.5563	−1.73790	−0.868949	+	0.494901i	$0.835204\pi$
$468$	−3.45621	−0.159763
$469$	38.1741	1.76272
$470$	−41.7021	−1.92358
$471$	−11.9301	−0.549711
$472$	−0.463188	−0.0213200
$473$	−1.40887	−0.0647799
$474$	−29.0554	−1.33456
$475$	0.0288044	0.00132164
$476$	12.3816	0.567508
$477$	−8.78013	−0.402015
$478$	8.00125	0.365969
$479$	−8.43821	−0.385552	−0.192776	−	0.981243i	$-0.561749\pi$
$479$	−8.43821	−0.385552	−0.192776	+	0.981243i	$0.561749\pi$
$480$	18.4401	0.841670
$481$	5.44924	0.248464
$482$	−11.8464	−0.539590
$483$	−2.20918	−0.100521
$484$	2.04375	0.0928978
$485$	37.0024	1.68019
$486$	−2.01091	−0.0912167
$487$	−12.6724	−0.574240	−0.287120	−	0.957895i	$-0.592698\pi$
$487$	−12.6724	−0.574240	−0.287120	+	0.957895i	$0.592698\pi$
$488$	−0.0879817	−0.00398275
$489$	0.505535	0.0228611
$490$	56.3995	2.54787
$491$	13.8805	0.626420	0.313210	−	0.949684i	$-0.398596\pi$
$491$	13.8805	0.626420	0.313210	+	0.949684i	$0.398596\pi$
$492$	−25.3586	−1.14325
$493$	6.77273	0.305028
$494$	−0.375863	−0.0169109
$495$	−2.29360	−0.103090
$496$	15.4179	0.692286
$497$	−20.3772	−0.914041
$498$	0.633477	0.0283868
$499$	−12.0067	−0.537496	−0.268748	−	0.963211i	$-0.586610\pi$
$499$	−12.0067	−0.537496	−0.268748	+	0.963211i	$0.586610\pi$
$500$	−22.2161	−0.993536
$501$	7.02034	0.313646
$502$	−43.5593	−1.94415
$503$	−15.4221	−0.687639	−0.343819	−	0.939036i	$-0.611721\pi$
$503$	−15.4221	−0.687639	−0.343819	+	0.939036i	$0.611721\pi$
$504$	−0.385800	−0.0171849
$505$	−0.164209	−0.00730719
$506$	1.01310	0.0450379
$507$	10.1401	0.450340
$508$	−9.04695	−0.401394
$509$	5.48166	0.242970	0.121485	−	0.992593i	$-0.461234\pi$
$509$	5.48166	0.242970	0.121485	+	0.992593i	$0.461234\pi$
$510$	6.37218	0.282165
$511$	4.82054	0.213248
$512$	32.1283	1.41989
$513$	−0.110526	−0.00487985
$514$	−16.5883	−0.731677
$515$	−9.26395	−0.408218
$516$	−2.87938	−0.126758
$517$	9.04166	0.397652
$518$	28.4136	1.24842
$519$	5.71737	0.250965
$520$	−0.341258	−0.0149651
$521$	−14.2914	−0.626116	−0.313058	−	0.949734i	$-0.601353\pi$
$521$	−14.2914	−0.626116	−0.313058	+	0.949734i	$0.601353\pi$
$522$	−9.85777	−0.431463
$523$	−34.2760	−1.49878	−0.749392	−	0.662127i	$-0.769654\pi$
$523$	−34.2760	−1.49878	−0.749392	+	0.662127i	$0.769654\pi$
$524$	7.45841	0.325822
$525$	1.14278	0.0498752
$526$	53.4622	2.33106
$527$	5.44706	0.237278
$528$	−3.91058	−0.170186
$529$	−22.7462	−0.988964
$530$	−40.4959	−1.75903
$531$	−5.26459	−0.228464
$532$	−0.990521	−0.0429445
$533$	−20.9831	−0.908877
$534$	−4.14158	−0.179224
$535$	−41.3804	−1.78903
$536$	−0.765933	−0.0330833
$537$	−5.77529	−0.249222
$538$	−27.6480	−1.19199
$539$	−12.2283	−0.526709
$540$	−4.68755	−0.201720
$541$	−10.0880	−0.433718	−0.216859	−	0.976203i	$-0.569581\pi$
$541$	−10.0880	−0.433718	−0.216859	+	0.976203i	$0.569581\pi$
$542$	−16.1369	−0.693138
$543$	−8.98069	−0.385398
$544$	11.1076	0.476236
$545$	36.2188	1.55144
$546$	−14.9120	−0.638173
$547$	−13.4837	−0.576521	−0.288261	−	0.957552i	$-0.593077\pi$
$547$	−13.4837	−0.576521	−0.288261	+	0.957552i	$0.593077\pi$
$548$	−23.7054	−1.01264
$549$	−1.00000	−0.0426790
$550$	−0.524067	−0.0223463
$551$	−0.541816	−0.0230821
$552$	0.0443255	0.00188662
$553$	−63.3585	−2.69428
$554$	31.4371	1.33564
$555$	7.39063	0.313715
$556$	−30.8610	−1.30880
$557$	4.31291	0.182744	0.0913719	−	0.995817i	$-0.470875\pi$
$557$	4.31291	0.182744	0.0913719	+	0.995817i	$0.470875\pi$
$558$	−7.92825	−0.335629
$559$	−2.38255	−0.100771
$560$	39.3305	1.66202
$561$	−1.38158	−0.0583305
$562$	62.9098	2.65369
$563$	19.9662	0.841474	0.420737	−	0.907183i	$-0.361772\pi$
$563$	19.9662	0.841474	0.420737	+	0.907183i	$0.361772\pi$
$564$	18.4789	0.778102
$565$	−12.9048	−0.542907
$566$	27.5790	1.15923
$567$	−4.38501	−0.184153
$568$	0.408852	0.0171550
$569$	−24.9722	−1.04689	−0.523445	−	0.852060i	$-0.675353\pi$
$569$	−24.9722	−1.04689	−0.523445	+	0.852060i	$0.675353\pi$
$570$	−0.509772	−0.0213520
$571$	−14.2393	−0.595895	−0.297947	−	0.954582i	$-0.596302\pi$
$571$	−14.2393	−0.595895	−0.297947	+	0.954582i	$0.596302\pi$
$572$	3.45621	0.144511
$573$	2.79919	0.116938
$574$	−109.411	−4.56671
$575$	−0.131297	−0.00547547
$576$	−8.34611	−0.347754
$577$	−30.9745	−1.28948	−0.644742	−	0.764400i	$-0.723035\pi$
$577$	−30.9745	−1.28948	−0.644742	+	0.764400i	$0.723035\pi$
$578$	−30.3471	−1.26227
$579$	10.5823	0.439785
$580$	−22.9791	−0.954155
$581$	1.38137	0.0573087
$582$	−32.4417	−1.34475
$583$	8.78013	0.363636
$584$	−0.0967204	−0.00400232
$585$	−3.87874	−0.160366
$586$	19.2482	0.795135
$587$	−9.67605	−0.399373	−0.199687	−	0.979860i	$-0.563992\pi$
$587$	−9.67605	−0.399373	−0.199687	+	0.979860i	$0.563992\pi$
$588$	−24.9916	−1.03063
$589$	−0.435763	−0.0179553
$590$	−24.2815	−0.999653
$591$	−23.6369	−0.972294
$592$	12.6010	0.517898
$593$	21.0897	0.866052	0.433026	−	0.901381i	$-0.357446\pi$
$593$	21.0897	0.866052	0.433026	+	0.901381i	$0.357446\pi$
$594$	2.01091	0.0825086
$595$	13.8952	0.569649
$596$	27.0661	1.10867
$597$	−0.311922	−0.0127661
$598$	1.71327	0.0700607
$599$	45.4706	1.85788	0.928938	−	0.370234i	$-0.120723\pi$
$599$	45.4706	1.85788	0.928938	+	0.370234i	$0.120723\pi$
$600$	−0.0229291	−0.000936076 0
$601$	−47.2990	−1.92937	−0.964684	−	0.263411i	$-0.915152\pi$
$601$	−47.2990	−1.92937	−0.964684	+	0.263411i	$0.915152\pi$
$602$	−12.4232	−0.506332
$603$	−8.70560	−0.354519
$604$	34.0188	1.38420
$605$	2.29360	0.0932482
$606$	0.143969	0.00584836
$607$	14.6907	0.596279	0.298139	−	0.954522i	$-0.403634\pi$
$607$	14.6907	0.596279	0.298139	+	0.954522i	$0.403634\pi$
$608$	−0.888607	−0.0360378
$609$	−21.4959	−0.871060
$610$	−4.61222	−0.186743
$611$	15.2904	0.618585
$612$	−2.82362	−0.114138
$613$	−18.0321	−0.728308	−0.364154	−	0.931339i	$-0.618642\pi$
$613$	−18.0321	−0.728308	−0.364154	+	0.931339i	$0.618642\pi$
$614$	−23.7167	−0.957127
$615$	−28.4587	−1.14757
$616$	0.385800	0.0155443
$617$	18.5435	0.746534	0.373267	−	0.927724i	$-0.378238\pi$
$617$	18.5435	0.746534	0.373267	+	0.927724i	$0.378238\pi$
$618$	8.12214	0.326720
$619$	26.7079	1.07348	0.536741	−	0.843747i	$-0.319655\pi$
$619$	26.7079	1.07348	0.536741	+	0.843747i	$0.319655\pi$
$620$	−18.4812	−0.742225
$621$	0.503803	0.0202169
$622$	−13.3794	−0.536465
$623$	−9.03118	−0.361826
$624$	−6.61323	−0.264741
$625$	−26.2351	−1.04941
$626$	−11.9968	−0.479487
$627$	0.110526	0.00441399
$628$	24.3822	0.972956
$629$	4.45185	0.177507
$630$	−20.2246	−0.805768
$631$	−12.8556	−0.511775	−0.255887	−	0.966707i	$-0.582368\pi$
$631$	−12.8556	−0.511775	−0.255887	+	0.966707i	$0.582368\pi$
$632$	1.27124	0.0505671
$633$	26.1628	1.03988
$634$	33.3631	1.32502
$635$	−10.1529	−0.402908
$636$	17.9444	0.711542
$637$	−20.6794	−0.819346
$638$	9.85777	0.390273
$639$	4.64701	0.183833
$640$	−1.61397	−0.0637979
$641$	3.35864	0.132658	0.0663292	−	0.997798i	$-0.478871\pi$
$641$	3.35864	0.132658	0.0663292	+	0.997798i	$0.478871\pi$
$642$	36.2802	1.43186
$643$	24.3997	0.962232	0.481116	−	0.876657i	$-0.340232\pi$
$643$	24.3997	0.962232	0.481116	+	0.876657i	$0.340232\pi$
$644$	4.51502	0.177917
$645$	−3.23139	−0.127236
$646$	−0.307068	−0.0120814
$647$	21.3923	0.841018	0.420509	−	0.907288i	$-0.361852\pi$
$647$	21.3923	0.841018	0.420509	+	0.907288i	$0.361852\pi$
$648$	0.0879817	0.00345625
$649$	5.26459	0.206653
$650$	−0.886255	−0.0347618
$651$	−17.2884	−0.677586
$652$	−1.03319	−0.0404628
$653$	−19.6838	−0.770287	−0.385143	−	0.922857i	$-0.625848\pi$
$653$	−19.6838	−0.770287	−0.385143	+	0.922857i	$0.625848\pi$
$654$	−31.7547	−1.24171
$655$	8.37020	0.327051
$656$	−48.5219	−1.89446
$657$	−1.09932	−0.0428887
$658$	79.7279	3.10812
$659$	41.7847	1.62770	0.813851	−	0.581073i	$-0.197367\pi$
$659$	41.7847	1.62770	0.813851	+	0.581073i	$0.197367\pi$
$660$	4.68755	0.182463
$661$	−49.1659	−1.91233	−0.956166	−	0.292827i	$-0.905404\pi$
$661$	−49.1659	−1.91233	−0.956166	+	0.292827i	$0.905404\pi$
$662$	−48.1652	−1.87199
$663$	−2.33641	−0.0907387
$664$	−0.0277160	−0.00107559
$665$	−1.11161	−0.0431065
$666$	−6.47971	−0.251084
$667$	2.46972	0.0956279
$668$	−14.3478	−0.555135
$669$	−15.1197	−0.584560
$670$	−40.1522	−1.55121
$671$	1.00000	0.0386046
$672$	−35.2545	−1.35997
$673$	−26.0028	−1.00233	−0.501166	−	0.865351i	$-0.667096\pi$
$673$	−26.0028	−1.00233	−0.501166	+	0.865351i	$0.667096\pi$
$674$	−14.0021	−0.539340
$675$	−0.260612	−0.0100310
$676$	−20.7239	−0.797075
$677$	−39.4872	−1.51762	−0.758808	−	0.651314i	$-0.774218\pi$
$677$	−39.4872	−1.51762	−0.758808	+	0.651314i	$0.774218\pi$
$678$	11.3142	0.434519
$679$	−70.7427	−2.71486
$680$	−0.278797	−0.0106914
$681$	−8.01271	−0.307048
$682$	7.92825	0.303588
$683$	−30.4225	−1.16408	−0.582042	−	0.813159i	$-0.697746\pi$
$683$	−30.4225	−1.16408	−0.582042	+	0.813159i	$0.697746\pi$
$684$	0.225888	0.00863705
$685$	−26.6034	−1.01646
$686$	−46.1021	−1.76019
$687$	18.0492	0.688620
$688$	−5.50950	−0.210048
$689$	14.8482	0.565670
$690$	2.32365	0.0884600
$691$	−15.2900	−0.581661	−0.290830	−	0.956775i	$-0.593931\pi$
$691$	−15.2900	−0.581661	−0.290830	+	0.956775i	$0.593931\pi$
$692$	−11.6849	−0.444193
$693$	4.38501	0.166573
$694$	41.8962	1.59036
$695$	−34.6338	−1.31373
$696$	0.431299	0.0163484
$697$	−17.1425	−0.649318
$698$	44.6038	1.68828
$699$	11.3922	0.430894
$700$	−2.33557	−0.0882762
$701$	46.4671	1.75504	0.877519	−	0.479542i	$-0.159197\pi$
$701$	46.4671	1.75504	0.877519	+	0.479542i	$0.159197\pi$
$702$	3.40067	0.128350
$703$	−0.356147	−0.0134323
$704$	8.34611	0.314556
$705$	20.7380	0.781037
$706$	31.4414	1.18331
$707$	0.313941	0.0118070
$708$	10.7595	0.404368
$709$	−21.4793	−0.806671	−0.403335	−	0.915052i	$-0.632149\pi$
$709$	−21.4793	−0.806671	−0.403335	+	0.915052i	$0.632149\pi$
$710$	21.4331	0.804368
$711$	14.4489	0.541876
$712$	0.181204	0.00679089
$713$	1.98630	0.0743877
$714$	−12.1826	−0.455922
$715$	3.87874	0.145056
$716$	11.8033	0.441108
$717$	−3.97892	−0.148596
$718$	−44.4568	−1.65911
$719$	26.8421	1.00104	0.500520	−	0.865725i	$-0.333142\pi$
$719$	26.8421	1.00104	0.500520	+	0.865725i	$0.333142\pi$
$720$	−8.96932	−0.334267
$721$	17.7112	0.659600
$722$	−38.1827	−1.42101
$723$	5.89109	0.219092
$724$	18.3543	0.682133
$725$	−1.27756	−0.0474473
$726$	−2.01091	−0.0746318
$727$	−3.22418	−0.119578	−0.0597892	−	0.998211i	$-0.519043\pi$
$727$	−3.22418	−0.119578	−0.0597892	+	0.998211i	$0.519043\pi$
$728$	0.652431	0.0241807
$729$	1.00000	0.0370370
$730$	−5.07033	−0.187661
$731$	−1.94647	−0.0719929
$732$	2.04375	0.0755393
$733$	−13.1514	−0.485758	−0.242879	−	0.970057i	$-0.578092\pi$
$733$	−13.1514	−0.485758	−0.242879	+	0.970057i	$0.578092\pi$
$734$	19.0269	0.702295
$735$	−28.0468	−1.03452
$736$	4.05047	0.149302
$737$	8.70560	0.320675
$738$	24.9511	0.918461
$739$	−11.4422	−0.420908	−0.210454	−	0.977604i	$-0.567494\pi$
$739$	−11.4422	−0.420908	−0.210454	+	0.977604i	$0.567494\pi$
$740$	−15.1046	−0.555257
$741$	0.186912	0.00686639
$742$	77.4218	2.84224
$743$	−5.62720	−0.206442	−0.103221	−	0.994658i	$-0.532915\pi$
$743$	−5.62720	−0.206442	−0.103221	+	0.994658i	$0.532915\pi$
$744$	0.346878	0.0127172
$745$	30.3749	1.11285
$746$	−8.73755	−0.319904
$747$	−0.315020	−0.0115260
$748$	2.82362	0.103242
$749$	79.1129	2.89072
$750$	21.8591	0.798182
$751$	−30.1861	−1.10151	−0.550753	−	0.834668i	$-0.685659\pi$
$751$	−30.1861	−1.10151	−0.550753	+	0.834668i	$0.685659\pi$
$752$	35.3581	1.28938
$753$	21.6615	0.789389
$754$	16.6706	0.607107
$755$	38.1776	1.38943
$756$	8.96186	0.325940
$757$	−20.9910	−0.762931	−0.381466	−	0.924383i	$-0.624581\pi$
$757$	−20.9910	−0.762931	−0.381466	+	0.924383i	$0.624581\pi$
$758$	−8.30078	−0.301498
$759$	−0.503803	−0.0182869
$760$	0.0223036	0.000809038 0
$761$	−41.3479	−1.49886	−0.749429	−	0.662084i	$-0.769672\pi$
$761$	−41.3479	−1.49886	−0.749429	+	0.662084i	$0.769672\pi$
$762$	8.90156	0.322470
$763$	−69.2447	−2.50683
$764$	−5.72084	−0.206973
$765$	−3.16880	−0.114568
$766$	−48.6608	−1.75819
$767$	8.90301	0.321469
$768$	−15.2772	−0.551267
$769$	−38.4423	−1.38627	−0.693133	−	0.720810i	$-0.743770\pi$
$769$	−38.4423	−1.38627	−0.693133	+	0.720810i	$0.743770\pi$
$770$	20.2246	0.728845
$771$	8.24914	0.297086
$772$	−21.6276	−0.778393
$773$	13.3063	0.478593	0.239297	−	0.970946i	$-0.423083\pi$
$773$	13.3063	0.478593	0.239297	+	0.970946i	$0.423083\pi$
$774$	2.83311	0.101834
$775$	−1.02749	−0.0369087
$776$	1.41940	0.0509534
$777$	−14.1297	−0.506901
$778$	40.0177	1.43470
$779$	1.37139	0.0491353
$780$	7.92717	0.283838
$781$	−4.64701	−0.166283
$782$	1.39969	0.0500527
$783$	4.90215	0.175188
$784$	−47.8197	−1.70784
$785$	27.3629	0.976625
$786$	−7.33855	−0.261757
$787$	−35.4872	−1.26498	−0.632491	−	0.774568i	$-0.717967\pi$
$787$	−35.4872	−1.26498	−0.632491	+	0.774568i	$0.717967\pi$
$788$	48.3080	1.72090
$789$	−26.5861	−0.946491
$790$	66.6415	2.37100
$791$	24.6719	0.877230
$792$	−0.0879817	−0.00312629
$793$	1.69111	0.0600531
$794$	−29.7145	−1.05453
$795$	20.1381	0.714226
$796$	0.637492	0.0225953
$797$	−47.3262	−1.67638	−0.838190	−	0.545379i	$-0.816386\pi$
$797$	−47.3262	−1.67638	−0.838190	+	0.545379i	$0.816386\pi$
$798$	0.974603	0.0345006
$799$	12.4918	0.441928
$800$	−2.09526	−0.0740787
$801$	2.05956	0.0727709
$802$	−65.4915	−2.31259
$803$	1.09932	0.0387943
$804$	17.7921	0.627478
$805$	5.06698	0.178588
$806$	13.4075	0.472261
$807$	13.7490	0.483989
$808$	−0.00629898	−0.000221597 0
$809$	18.1512	0.638161	0.319080	−	0.947728i	$-0.396626\pi$
$809$	18.1512	0.638161	0.319080	+	0.947728i	$0.396626\pi$
$810$	4.61222	0.162057
$811$	−28.2877	−0.993317	−0.496658	−	0.867946i	$-0.665440\pi$
$811$	−28.2877	−0.993317	−0.496658	+	0.867946i	$0.665440\pi$
$812$	43.9324	1.54172
$813$	8.02467	0.281437
$814$	6.47971	0.227114
$815$	−1.15950	−0.0406154
$816$	−5.40280	−0.189136
$817$	0.155717	0.00544785
$818$	25.0709	0.876584
$819$	7.41553	0.259120
$820$	58.1625	2.03112
$821$	12.7438	0.444761	0.222380	−	0.974960i	$-0.428617\pi$
$821$	12.7438	0.444761	0.222380	+	0.974960i	$0.428617\pi$
$822$	23.3244	0.813533
$823$	18.2656	0.636699	0.318350	−	0.947973i	$-0.396871\pi$
$823$	18.2656	0.636699	0.318350	+	0.947973i	$0.396871\pi$
$824$	−0.355362	−0.0123796
$825$	0.260612	0.00907334
$826$	46.4224	1.61524
$827$	−24.3560	−0.846940	−0.423470	−	0.905910i	$-0.639188\pi$
$827$	−24.3560	−0.846940	−0.423470	+	0.905910i	$0.639188\pi$
$828$	−1.02965	−0.0357828
$829$	48.5630	1.68666	0.843331	−	0.537394i	$-0.180591\pi$
$829$	48.5630	1.68666	0.843331	+	0.537394i	$0.180591\pi$
$830$	−1.45294	−0.0504324
$831$	−15.6333	−0.542313
$832$	14.1142	0.489321
$833$	−16.8944	−0.585356
$834$	30.3651	1.05146
$835$	−16.1019	−0.557228
$836$	−0.225888	−0.00781251
$837$	3.94262	0.136277
$838$	−12.3740	−0.427451
$839$	−46.5295	−1.60638	−0.803189	−	0.595724i	$-0.796865\pi$
$839$	−46.5295	−1.60638	−0.803189	+	0.595724i	$0.796865\pi$
$840$	0.884873	0.0305310
$841$	−4.96894	−0.171343
$842$	4.26539	0.146995
$843$	−31.2843	−1.07749
$844$	−53.4704	−1.84053
$845$	−23.2575	−0.800081
$846$	−18.1819	−0.625108
$847$	−4.38501	−0.150671
$848$	34.3354	1.17908
$849$	−13.7147	−0.470688
$850$	−0.724042	−0.0248344
$851$	1.62340	0.0556493
$852$	−9.49734	−0.325373
$853$	−53.8273	−1.84301	−0.921506	−	0.388364i	$-0.873040\pi$
$853$	−53.8273	−1.84301	−0.921506	+	0.388364i	$0.873040\pi$
$854$	8.81784	0.301740
$855$	0.253503	0.00866963
$856$	−1.58734	−0.0542541
$857$	−11.7256	−0.400538	−0.200269	−	0.979741i	$-0.564182\pi$
$857$	−11.7256	−0.400538	−0.200269	+	0.979741i	$0.564182\pi$
$858$	−3.40067	−0.116097
$859$	35.5984	1.21460	0.607300	−	0.794472i	$-0.292253\pi$
$859$	35.5984	1.21460	0.607300	+	0.794472i	$0.292253\pi$
$860$	6.60415	0.225200
$861$	54.4085	1.85424
$862$	−13.0471	−0.444385
$863$	−25.4808	−0.867376	−0.433688	−	0.901063i	$-0.642788\pi$
$863$	−25.4808	−0.867376	−0.433688	+	0.901063i	$0.642788\pi$
$864$	8.03978	0.273519
$865$	−13.1134	−0.445868
$866$	55.9553	1.90144
$867$	15.0912	0.512525
$868$	35.3332	1.19929
$869$	−14.4489	−0.490145
$870$	22.6098	0.766544
$871$	14.7221	0.498840
$872$	1.38934	0.0470490
$873$	16.1329	0.546015
$874$	−0.111974	−0.00378759
$875$	47.6662	1.61141
$876$	2.24675	0.0759105
$877$	−25.4906	−0.860756	−0.430378	−	0.902649i	$-0.641620\pi$
$877$	−25.4906	−0.860756	−0.430378	+	0.902649i	$0.641620\pi$
$878$	−37.7106	−1.27267
$879$	−9.57188	−0.322851
$880$	8.96932	0.302356
$881$	−57.5717	−1.93964	−0.969820	−	0.243821i	$-0.921599\pi$
$881$	−57.5717	−1.93964	−0.969820	+	0.243821i	$0.921599\pi$
$882$	24.5899	0.827986
$883$	20.7139	0.697077	0.348538	−	0.937295i	$-0.386678\pi$
$883$	20.7139	0.697077	0.348538	+	0.937295i	$0.386678\pi$
$884$	4.77505	0.160602
$885$	12.0749	0.405893
$886$	−15.8467	−0.532380
$887$	−48.1203	−1.61572	−0.807861	−	0.589373i	$-0.799375\pi$
$887$	−48.1203	−1.61572	−0.807861	+	0.589373i	$0.799375\pi$
$888$	0.283502	0.00951370
$889$	19.4108	0.651019
$890$	9.49915	0.318412
$891$	−1.00000	−0.0335013
$892$	30.9008	1.03464
$893$	−0.999340	−0.0334416
$894$	−26.6311	−0.890678
$895$	13.2462	0.442772
$896$	3.08566	0.103085
$897$	−0.851987	−0.0284470
$898$	47.1398	1.57308
$899$	19.3273	0.644602
$900$	0.532626	0.0177542
$901$	12.1305	0.404125
$902$	−24.9511	−0.830779
$903$	6.17790	0.205588
$904$	−0.495021	−0.0164642
$905$	20.5981	0.684705
$906$	−33.4721	−1.11204
$907$	−27.0508	−0.898205	−0.449103	−	0.893480i	$-0.648256\pi$
$907$	−27.0508	−0.898205	−0.449103	+	0.893480i	$0.648256\pi$
$908$	16.3760	0.543456
$909$	−0.0715942	−0.00237463
$910$	34.2021	1.13379
$911$	5.04031	0.166993	0.0834965	−	0.996508i	$-0.473391\pi$
$911$	5.04031	0.166993	0.0834965	+	0.996508i	$0.473391\pi$
$912$	0.432222	0.0143123
$913$	0.315020	0.0104256
$914$	43.7598	1.44745
$915$	2.29360	0.0758242
$916$	−36.8881	−1.21882
$917$	−16.0025	−0.528449
$918$	2.77824	0.0916955
$919$	11.2458	0.370965	0.185483	−	0.982648i	$-0.440615\pi$
$919$	11.2458	0.370965	0.185483	+	0.982648i	$0.440615\pi$
$920$	−0.101665	−0.00335180
$921$	11.7940	0.388626
$922$	6.10020	0.200899
$923$	−7.85861	−0.258669
$924$	−8.96186	−0.294824
$925$	−0.839765	−0.0276113
$926$	56.7208	1.86396
$927$	−4.03904	−0.132659
$928$	39.4122	1.29377
$929$	−0.644532	−0.0211464	−0.0105732	−	0.999944i	$-0.503366\pi$
$929$	−0.644532	−0.0211464	−0.0105732	+	0.999944i	$0.503366\pi$
$930$	18.1842	0.596285
$931$	1.35155	0.0442951
$932$	−23.2829	−0.762657
$933$	6.65342	0.217823
$934$	−75.5223	−2.47116
$935$	3.16880	0.103631
$936$	−0.148787	−0.00486325
$937$	−42.3215	−1.38258	−0.691291	−	0.722576i	$-0.742958\pi$
$937$	−42.3215	−1.38258	−0.691291	+	0.722576i	$0.742958\pi$
$938$	76.7646	2.50645
$939$	5.96584	0.194688
$940$	−42.3833	−1.38239
$941$	−17.3107	−0.564314	−0.282157	−	0.959368i	$-0.591050\pi$
$941$	−17.3107	−0.564314	−0.282157	+	0.959368i	$0.591050\pi$
$942$	−23.9904	−0.781648
$943$	−6.25112	−0.203564
$944$	20.5876	0.670070
$945$	10.0575	0.327169
$946$	−2.83311	−0.0921123
$947$	−36.6997	−1.19258	−0.596290	−	0.802769i	$-0.703359\pi$
$947$	−36.6997	−1.19258	−0.596290	+	0.802769i	$0.703359\pi$
$948$	−29.5300	−0.959088
$949$	1.85908	0.0603482
$950$	0.0579231	0.00187927
$951$	−16.5911	−0.538003
$952$	0.533016	0.0172751
$953$	3.27584	0.106115	0.0530575	−	0.998591i	$-0.483103\pi$
$953$	3.27584	0.106115	0.0530575	+	0.998591i	$0.483103\pi$
$954$	−17.6560	−0.571635
$955$	−6.42022	−0.207753
$956$	8.13194	0.263006
$957$	−4.90215	−0.158464
$958$	−16.9685	−0.548226
$959$	50.8615	1.64240
$960$	19.1426	0.617826
$961$	−15.4557	−0.498572
$962$	10.9579	0.353297
$963$	−18.0417	−0.581385
$964$	−12.0399	−0.387780
$965$	−24.2715	−0.781329
$966$	−4.44246	−0.142934
$967$	12.4126	0.399163	0.199582	−	0.979881i	$-0.436042\pi$
$967$	12.4126	0.399163	0.199582	+	0.979881i	$0.436042\pi$
$968$	0.0879817	0.00282784
$969$	0.152701	0.00490547
$970$	74.4084	2.38911
$971$	6.15591	0.197553	0.0987763	−	0.995110i	$-0.468507\pi$
$971$	6.15591	0.197553	0.0987763	+	0.995110i	$0.468507\pi$
$972$	−2.04375	−0.0655534
$973$	66.2143	2.12273
$974$	−25.4830	−0.816527
$975$	0.440724	0.0141144
$976$	3.91058	0.125175
$977$	57.1570	1.82861	0.914307	−	0.405021i	$-0.132736\pi$
$977$	57.1570	1.82861	0.914307	+	0.405021i	$0.132736\pi$
$978$	1.01658	0.0325068
$979$	−2.05956	−0.0658238
$980$	57.3207	1.83104
$981$	15.7912	0.504176
$982$	27.9125	0.890723
$983$	39.1647	1.24916	0.624580	−	0.780961i	$-0.285270\pi$
$983$	39.1647	1.24916	0.624580	+	0.780961i	$0.285270\pi$
$984$	−1.09166	−0.0348010
$985$	54.2137	1.72739
$986$	13.6193	0.433728
$987$	−39.6477	−1.26200
$988$	−0.382002	−0.0121531
$989$	−0.709793	−0.0225701
$990$	−4.61222	−0.146586
$991$	−13.8422	−0.439712	−0.219856	−	0.975532i	$-0.570559\pi$
$991$	−13.8422	−0.439712	−0.219856	+	0.975532i	$0.570559\pi$
$992$	31.6978	1.00641
$993$	23.9520	0.760092
$994$	−40.9766	−1.29970
$995$	0.715426	0.0226805
$996$	0.643823	0.0204003
$997$	−16.8632	−0.534064	−0.267032	−	0.963688i	$-0.586043\pi$
$997$	−16.8632	−0.534064	−0.267032	+	0.963688i	$0.586043\pi$
$998$	−24.1445	−0.764279
$999$	3.22228	0.101948

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.d.1.10	✓	12
3.2	odd	2		6039.2.a.e.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.d.1.10	✓	12	1.1	even	1	trivial
6039.2.a.e.1.3		12	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)

\(f(q)\)	\(=\)	\(q+2.01091 q^{2} -1.00000 q^{3} +2.04375 q^{4} +2.29360 q^{5} -2.01091 q^{6} -4.38501 q^{7} +0.0879817 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.01091 q^{2} -1.00000 q^{3} +2.04375 q^{4} +2.29360 q^{5} -2.01091 q^{6} -4.38501 q^{7} +0.0879817 q^{8} +1.00000 q^{9} +4.61222 q^{10} -1.00000 q^{11} -2.04375 q^{12} -1.69111 q^{13} -8.81784 q^{14} -2.29360 q^{15} -3.91058 q^{16} -1.38158 q^{17} +2.01091 q^{18} +0.110526 q^{19} +4.68755 q^{20} +4.38501 q^{21} -2.01091 q^{22} -0.503803 q^{23} -0.0879817 q^{24} +0.260612 q^{25} -3.40067 q^{26} -1.00000 q^{27} -8.96186 q^{28} -4.90215 q^{29} -4.61222 q^{30} -3.94262 q^{31} -8.03978 q^{32} +1.00000 q^{33} -2.77824 q^{34} -10.0575 q^{35} +2.04375 q^{36} -3.22228 q^{37} +0.222258 q^{38} +1.69111 q^{39} +0.201795 q^{40} +12.4079 q^{41} +8.81784 q^{42} +1.40887 q^{43} -2.04375 q^{44} +2.29360 q^{45} -1.01310 q^{46} -9.04166 q^{47} +3.91058 q^{48} +12.2283 q^{49} +0.524067 q^{50} +1.38158 q^{51} -3.45621 q^{52} -8.78013 q^{53} -2.01091 q^{54} -2.29360 q^{55} -0.385800 q^{56} -0.110526 q^{57} -9.85777 q^{58} -5.26459 q^{59} -4.68755 q^{60} -1.00000 q^{61} -7.92825 q^{62} -4.38501 q^{63} -8.34611 q^{64} -3.87874 q^{65} +2.01091 q^{66} -8.70560 q^{67} -2.82362 q^{68} +0.503803 q^{69} -20.2246 q^{70} +4.64701 q^{71} +0.0879817 q^{72} -1.09932 q^{73} -6.47971 q^{74} -0.260612 q^{75} +0.225888 q^{76} +4.38501 q^{77} +3.40067 q^{78} +14.4489 q^{79} -8.96932 q^{80} +1.00000 q^{81} +24.9511 q^{82} -0.315020 q^{83} +8.96186 q^{84} -3.16880 q^{85} +2.83311 q^{86} +4.90215 q^{87} -0.0879817 q^{88} +2.05956 q^{89} +4.61222 q^{90} +7.41553 q^{91} -1.02965 q^{92} +3.94262 q^{93} -18.1819 q^{94} +0.253503 q^{95} +8.03978 q^{96} +16.1329 q^{97} +24.5899 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} - 12 q^{3} + 9 q^{4} - 3 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + q^2 - 12 * q^3 + 9 * q^4 - 3 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 12 * q^9	\( 12 q + q^{2} - 12 q^{3} + 9 q^{4} - 3 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 12 q^{9} - 8 q^{10} - 12 q^{11} - 9 q^{12} - q^{13} - 3 q^{14} + 3 q^{15} + 3 q^{16} + 9 q^{17} + q^{18} - 20 q^{19} - 9 q^{20} + 9 q^{21} - q^{22} - 9 q^{23} - 6 q^{24} + 3 q^{25} - 18 q^{26} - 12 q^{27} - 31 q^{28} + 18 q^{29} + 8 q^{30} - 21 q^{31} + 18 q^{32} + 12 q^{33} - 12 q^{34} - 4 q^{35} + 9 q^{36} - 18 q^{37} - 2 q^{38} + q^{39} - 26 q^{40} + 15 q^{41} + 3 q^{42} - 33 q^{43} - 9 q^{44} - 3 q^{45} - 28 q^{46} - 20 q^{47} - 3 q^{48} + 15 q^{49} - 2 q^{50} - 9 q^{51} - 27 q^{52} - q^{54} + 3 q^{55} - 8 q^{56} + 20 q^{57} - 11 q^{58} - 21 q^{59} + 9 q^{60} - 12 q^{61} - 9 q^{62} - 9 q^{63} - 12 q^{64} + 17 q^{65} + q^{66} - 34 q^{67} - 16 q^{68} + 9 q^{69} - 36 q^{70} - 5 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} - 3 q^{75} - 27 q^{76} + 9 q^{77} + 18 q^{78} - 31 q^{79} - 60 q^{80} + 12 q^{81} - 12 q^{82} - 32 q^{83} + 31 q^{84} - 40 q^{85} + 18 q^{86} - 18 q^{87} - 6 q^{88} + 27 q^{89} - 8 q^{90} - 45 q^{91} - 78 q^{92} + 21 q^{93} - 13 q^{94} + 37 q^{95} - 18 q^{96} - 19 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q + q^2 - 12 * q^3 + 9 * q^4 - 3 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 12 * q^9 - 8 * q^10 - 12 * q^11 - 9 * q^12 - q^13 - 3 * q^14 + 3 * q^15 + 3 * q^16 + 9 * q^17 + q^18 - 20 * q^19 - 9 * q^20 + 9 * q^21 - q^22 - 9 * q^23 - 6 * q^24 + 3 * q^25 - 18 * q^26 - 12 * q^27 - 31 * q^28 + 18 * q^29 + 8 * q^30 - 21 * q^31 + 18 * q^32 + 12 * q^33 - 12 * q^34 - 4 * q^35 + 9 * q^36 - 18 * q^37 - 2 * q^38 + q^39 - 26 * q^40 + 15 * q^41 + 3 * q^42 - 33 * q^43 - 9 * q^44 - 3 * q^45 - 28 * q^46 - 20 * q^47 - 3 * q^48 + 15 * q^49 - 2 * q^50 - 9 * q^51 - 27 * q^52 - q^54 + 3 * q^55 - 8 * q^56 + 20 * q^57 - 11 * q^58 - 21 * q^59 + 9 * q^60 - 12 * q^61 - 9 * q^62 - 9 * q^63 - 12 * q^64 + 17 * q^65 + q^66 - 34 * q^67 - 16 * q^68 + 9 * q^69 - 36 * q^70 - 5 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 - 3 * q^75 - 27 * q^76 + 9 * q^77 + 18 * q^78 - 31 * q^79 - 60 * q^80 + 12 * q^81 - 12 * q^82 - 32 * q^83 + 31 * q^84 - 40 * q^85 + 18 * q^86 - 18 * q^87 - 6 * q^88 + 27 * q^89 - 8 * q^90 - 45 * q^91 - 78 * q^92 + 21 * q^93 - 13 * q^94 + 37 * q^95 - 18 * q^96 - 19 * q^97 + 4 * q^98 - 12 * q^99

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