LMFDB - Embedded newform 2006.2.a.w.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2006,2,Mod(1,2006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2006, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2006 = 2 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2006.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$16.0179906455$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 6 x^{12} - 9 x^{11} + 91 x^{10} + 14 x^{9} - 517 x^{8} + 70 x^{7} + 1296 x^{6} - 300 x^{5} + \cdots + 16 $ x^13 - 6x^12 - 9x^11 + 91x^10 + 14x^9 - 517x^8 + 70x^7 + 1296x^6 - 300x^5 - 1312x^4 + 472x^3 + 368x^2 - 176x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-1.58918$ of defining polynomial
Character	$\chi$	$=$	2006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.58918 q^{3} +1.00000 q^{4} +2.47054 q^{5} +2.58918 q^{6} -1.02544 q^{7} +1.00000 q^{8} +3.70384 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.58918 q^{3} +1.00000 q^{4} +2.47054 q^{5} +2.58918 q^{6} -1.02544 q^{7} +1.00000 q^{8} +3.70384 q^{9} +2.47054 q^{10} -3.15988 q^{11} +2.58918 q^{12} +1.78916 q^{13} -1.02544 q^{14} +6.39668 q^{15} +1.00000 q^{16} +1.00000 q^{17} +3.70384 q^{18} +5.49560 q^{19} +2.47054 q^{20} -2.65504 q^{21} -3.15988 q^{22} -5.73487 q^{23} +2.58918 q^{24} +1.10359 q^{25} +1.78916 q^{26} +1.82236 q^{27} -1.02544 q^{28} -1.10571 q^{29} +6.39668 q^{30} +4.53303 q^{31} +1.00000 q^{32} -8.18149 q^{33} +1.00000 q^{34} -2.53339 q^{35} +3.70384 q^{36} +9.71380 q^{37} +5.49560 q^{38} +4.63246 q^{39} +2.47054 q^{40} -7.11984 q^{41} -2.65504 q^{42} -7.22645 q^{43} -3.15988 q^{44} +9.15050 q^{45} -5.73487 q^{46} +10.5215 q^{47} +2.58918 q^{48} -5.94848 q^{49} +1.10359 q^{50} +2.58918 q^{51} +1.78916 q^{52} -10.3913 q^{53} +1.82236 q^{54} -7.80662 q^{55} -1.02544 q^{56} +14.2291 q^{57} -1.10571 q^{58} +1.00000 q^{59} +6.39668 q^{60} -1.55831 q^{61} +4.53303 q^{62} -3.79805 q^{63} +1.00000 q^{64} +4.42021 q^{65} -8.18149 q^{66} +11.3522 q^{67} +1.00000 q^{68} -14.8486 q^{69} -2.53339 q^{70} -10.9816 q^{71} +3.70384 q^{72} +4.88344 q^{73} +9.71380 q^{74} +2.85739 q^{75} +5.49560 q^{76} +3.24026 q^{77} +4.63246 q^{78} +11.9072 q^{79} +2.47054 q^{80} -6.39309 q^{81} -7.11984 q^{82} +1.96708 q^{83} -2.65504 q^{84} +2.47054 q^{85} -7.22645 q^{86} -2.86288 q^{87} -3.15988 q^{88} -12.9976 q^{89} +9.15050 q^{90} -1.83467 q^{91} -5.73487 q^{92} +11.7368 q^{93} +10.5215 q^{94} +13.5771 q^{95} +2.58918 q^{96} +1.40274 q^{97} -5.94848 q^{98} -11.7037 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9	\( 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9} + q^{10} + 13 q^{11} + 7 q^{12} + 9 q^{13} + 8 q^{14} - 9 q^{15} + 13 q^{16} + 13 q^{17} + 16 q^{18} + 16 q^{19} + q^{20} - 3 q^{21} + 13 q^{22} + 18 q^{23} + 7 q^{24} + 14 q^{25} + 9 q^{26} + 10 q^{27} + 8 q^{28} + 8 q^{29} - 9 q^{30} + 32 q^{31} + 13 q^{32} + 13 q^{33} + 13 q^{34} - q^{35} + 16 q^{36} - 3 q^{37} + 16 q^{38} + 20 q^{39} + q^{40} + 24 q^{41} - 3 q^{42} - 2 q^{43} + 13 q^{44} - 3 q^{45} + 18 q^{46} + 26 q^{47} + 7 q^{48} + 23 q^{49} + 14 q^{50} + 7 q^{51} + 9 q^{52} - 27 q^{53} + 10 q^{54} - 7 q^{55} + 8 q^{56} - 21 q^{57} + 8 q^{58} + 13 q^{59} - 9 q^{60} + 20 q^{61} + 32 q^{62} - 3 q^{63} + 13 q^{64} + 16 q^{65} + 13 q^{66} + 4 q^{67} + 13 q^{68} - 2 q^{69} - q^{70} - 8 q^{71} + 16 q^{72} + 10 q^{73} - 3 q^{74} + 39 q^{75} + 16 q^{76} - 15 q^{77} + 20 q^{78} + 35 q^{79} + q^{80} + 29 q^{81} + 24 q^{82} - q^{83} - 3 q^{84} + q^{85} - 2 q^{86} - 32 q^{87} + 13 q^{88} - 20 q^{89} - 3 q^{90} - 15 q^{91} + 18 q^{92} - 7 q^{93} + 26 q^{94} - 3 q^{95} + 7 q^{96} - 3 q^{97} + 23 q^{98} + 65 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9 + q^10 + 13 * q^11 + 7 * q^12 + 9 * q^13 + 8 * q^14 - 9 * q^15 + 13 * q^16 + 13 * q^17 + 16 * q^18 + 16 * q^19 + q^20 - 3 * q^21 + 13 * q^22 + 18 * q^23 + 7 * q^24 + 14 * q^25 + 9 * q^26 + 10 * q^27 + 8 * q^28 + 8 * q^29 - 9 * q^30 + 32 * q^31 + 13 * q^32 + 13 * q^33 + 13 * q^34 - q^35 + 16 * q^36 - 3 * q^37 + 16 * q^38 + 20 * q^39 + q^40 + 24 * q^41 - 3 * q^42 - 2 * q^43 + 13 * q^44 - 3 * q^45 + 18 * q^46 + 26 * q^47 + 7 * q^48 + 23 * q^49 + 14 * q^50 + 7 * q^51 + 9 * q^52 - 27 * q^53 + 10 * q^54 - 7 * q^55 + 8 * q^56 - 21 * q^57 + 8 * q^58 + 13 * q^59 - 9 * q^60 + 20 * q^61 + 32 * q^62 - 3 * q^63 + 13 * q^64 + 16 * q^65 + 13 * q^66 + 4 * q^67 + 13 * q^68 - 2 * q^69 - q^70 - 8 * q^71 + 16 * q^72 + 10 * q^73 - 3 * q^74 + 39 * q^75 + 16 * q^76 - 15 * q^77 + 20 * q^78 + 35 * q^79 + q^80 + 29 * q^81 + 24 * q^82 - q^83 - 3 * q^84 + q^85 - 2 * q^86 - 32 * q^87 + 13 * q^88 - 20 * q^89 - 3 * q^90 - 15 * q^91 + 18 * q^92 - 7 * q^93 + 26 * q^94 - 3 * q^95 + 7 * q^96 - 3 * q^97 + 23 * q^98 + 65 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.58918	1.49486	0.747431	−	0.664339i	$-0.231287\pi$
$3$	2.58918	1.49486	0.747431	+	0.664339i	$0.231287\pi$
$4$	1.00000	0.500000
$5$	2.47054	1.10486	0.552431	−	0.833559i	$-0.313700\pi$
$5$	2.47054	1.10486	0.552431	+	0.833559i	$0.313700\pi$
$6$	2.58918	1.05703
$7$	−1.02544	−0.387578	−0.193789	−	0.981043i	$-0.562078\pi$
$7$	−1.02544	−0.387578	−0.193789	+	0.981043i	$0.562078\pi$
$8$	1.00000	0.353553
$9$	3.70384	1.23461
$10$	2.47054	0.781255
$11$	−3.15988	−0.952740	−0.476370	−	0.879245i	$-0.658048\pi$
$11$	−3.15988	−0.952740	−0.476370	+	0.879245i	$0.658048\pi$
$12$	2.58918	0.747431
$13$	1.78916	0.496225	0.248112	−	0.968731i	$-0.420190\pi$
$13$	1.78916	0.496225	0.248112	+	0.968731i	$0.420190\pi$
$14$	−1.02544	−0.274059
$15$	6.39668	1.65162
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	3.70384	0.873003
$19$	5.49560	1.26078	0.630389	−	0.776280i	$-0.282896\pi$
$19$	5.49560	1.26078	0.630389	+	0.776280i	$0.282896\pi$
$20$	2.47054	0.552431
$21$	−2.65504	−0.579376
$22$	−3.15988	−0.673689
$23$	−5.73487	−1.19580	−0.597902	−	0.801569i	$-0.703999\pi$
$23$	−5.73487	−1.19580	−0.597902	+	0.801569i	$0.703999\pi$
$24$	2.58918	0.528514
$25$	1.10359	0.220718
$26$	1.78916	0.350884
$27$	1.82236	0.350714
$28$	−1.02544	−0.193789
$29$	−1.10571	−0.205325	−0.102663	−	0.994716i	$-0.532736\pi$
$29$	−1.10571	−0.205325	−0.102663	+	0.994716i	$0.532736\pi$
$30$	6.39668	1.16787
$31$	4.53303	0.814156	0.407078	−	0.913393i	$-0.366548\pi$
$31$	4.53303	0.814156	0.407078	+	0.913393i	$0.366548\pi$
$32$	1.00000	0.176777
$33$	−8.18149	−1.42421
$34$	1.00000	0.171499
$35$	−2.53339	−0.428220
$36$	3.70384	0.617306
$37$	9.71380	1.59694	0.798469	−	0.602035i	$-0.205643\pi$
$37$	9.71380	1.59694	0.798469	+	0.602035i	$0.205643\pi$
$38$	5.49560	0.891504
$39$	4.63246	0.741787
$40$	2.47054	0.390627
$41$	−7.11984	−1.11193	−0.555966	−	0.831205i	$-0.687652\pi$
$41$	−7.11984	−1.11193	−0.555966	+	0.831205i	$0.687652\pi$
$42$	−2.65504	−0.409681
$43$	−7.22645	−1.10202	−0.551011	−	0.834498i	$-0.685758\pi$
$43$	−7.22645	−1.10202	−0.551011	+	0.834498i	$0.685758\pi$
$44$	−3.15988	−0.476370
$45$	9.15050	1.36408
$46$	−5.73487	−0.845561
$47$	10.5215	1.53472	0.767359	−	0.641218i	$-0.221571\pi$
$47$	10.5215	1.53472	0.767359	+	0.641218i	$0.221571\pi$
$48$	2.58918	0.373716
$49$	−5.94848	−0.849783
$50$	1.10359	0.156071
$51$	2.58918	0.362557
$52$	1.78916	0.248112
$53$	−10.3913	−1.42735	−0.713676	−	0.700476i	$-0.752971\pi$
$53$	−10.3913	−1.42735	−0.713676	+	0.700476i	$0.752971\pi$
$54$	1.82236	0.247992
$55$	−7.80662	−1.05264
$56$	−1.02544	−0.137030
$57$	14.2291	1.88469
$58$	−1.10571	−0.145187
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	6.39668	0.825808
$61$	−1.55831	−0.199521	−0.0997606	−	0.995011i	$-0.531808\pi$
$61$	−1.55831	−0.199521	−0.0997606	+	0.995011i	$0.531808\pi$
$62$	4.53303	0.575695
$63$	−3.79805	−0.478509
$64$	1.00000	0.125000
$65$	4.42021	0.548259
$66$	−8.18149	−1.00707
$67$	11.3522	1.38690	0.693449	−	0.720506i	$-0.256090\pi$
$67$	11.3522	1.38690	0.693449	+	0.720506i	$0.256090\pi$
$68$	1.00000	0.121268
$69$	−14.8486	−1.78756
$70$	−2.53339	−0.302798
$71$	−10.9816	−1.30327	−0.651637	−	0.758531i	$-0.725918\pi$
$71$	−10.9816	−1.30327	−0.651637	+	0.758531i	$0.725918\pi$
$72$	3.70384	0.436502
$73$	4.88344	0.571563	0.285782	−	0.958295i	$-0.407747\pi$
$73$	4.88344	0.571563	0.285782	+	0.958295i	$0.407747\pi$
$74$	9.71380	1.12921
$75$	2.85739	0.329943
$76$	5.49560	0.630389
$77$	3.24026	0.369261
$78$	4.63246	0.524523
$79$	11.9072	1.33967	0.669834	−	0.742511i	$-0.266365\pi$
$79$	11.9072	1.33967	0.669834	+	0.742511i	$0.266365\pi$
$80$	2.47054	0.276215
$81$	−6.39309	−0.710344
$82$	−7.11984	−0.786255
$83$	1.96708	0.215915	0.107958	−	0.994155i	$-0.465569\pi$
$83$	1.96708	0.215915	0.107958	+	0.994155i	$0.465569\pi$
$84$	−2.65504	−0.289688
$85$	2.47054	0.267968
$86$	−7.22645	−0.779248
$87$	−2.86288	−0.306933
$88$	−3.15988	−0.336844
$89$	−12.9976	−1.37774	−0.688871	−	0.724884i	$-0.741893\pi$
$89$	−12.9976	−1.37774	−0.688871	+	0.724884i	$0.741893\pi$
$90$	9.15050	0.964547
$91$	−1.83467	−0.192326
$92$	−5.73487	−0.597902
$93$	11.7368	1.21705
$94$	10.5215	1.08521
$95$	13.5771	1.39298
$96$	2.58918	0.264257
$97$	1.40274	0.142427	0.0712133	−	0.997461i	$-0.477313\pi$
$97$	1.40274	0.142427	0.0712133	+	0.997461i	$0.477313\pi$
$98$	−5.94848	−0.600887
$99$	−11.7037	−1.17626
$100$	1.10359	0.110359
$101$	−14.8612	−1.47874	−0.739371	−	0.673298i	$-0.764877\pi$
$101$	−14.8612	−1.47874	−0.739371	+	0.673298i	$0.764877\pi$
$102$	2.58918	0.256367
$103$	−8.98471	−0.885290	−0.442645	−	0.896697i	$-0.645960\pi$
$103$	−8.98471	−0.885290	−0.442645	+	0.896697i	$0.645960\pi$
$104$	1.78916	0.175442
$105$	−6.55938	−0.640130
$106$	−10.3913	−1.00929
$107$	−0.969100	−0.0936864	−0.0468432	−	0.998902i	$-0.514916\pi$
$107$	−0.969100	−0.0936864	−0.0468432	+	0.998902i	$0.514916\pi$
$108$	1.82236	0.175357
$109$	−9.02849	−0.864773	−0.432386	−	0.901688i	$-0.642328\pi$
$109$	−9.02849	−0.864773	−0.432386	+	0.901688i	$0.642328\pi$
$110$	−7.80662	−0.744332
$111$	25.1507	2.38720
$112$	−1.02544	−0.0968946
$113$	−1.49771	−0.140893	−0.0704465	−	0.997516i	$-0.522442\pi$
$113$	−1.49771	−0.140893	−0.0704465	+	0.997516i	$0.522442\pi$
$114$	14.2291	1.33268
$115$	−14.1683	−1.32120
$116$	−1.10571	−0.102663
$117$	6.62677	0.612645
$118$	1.00000	0.0920575
$119$	−1.02544	−0.0940016
$120$	6.39668	0.583934
$121$	−1.01516	−0.0922872
$122$	−1.55831	−0.141083
$123$	−18.4345	−1.66218
$124$	4.53303	0.407078
$125$	−9.62625	−0.860998
$126$	−3.79805	−0.338357
$127$	−18.3758	−1.63059	−0.815295	−	0.579045i	$-0.803425\pi$
$127$	−18.3758	−1.63059	−0.815295	+	0.579045i	$0.803425\pi$
$128$	1.00000	0.0883883
$129$	−18.7105	−1.64737
$130$	4.42021	0.387678
$131$	14.9865	1.30938	0.654688	−	0.755899i	$-0.272800\pi$
$131$	14.9865	1.30938	0.654688	+	0.755899i	$0.272800\pi$
$132$	−8.18149	−0.712107
$133$	−5.63539	−0.488650
$134$	11.3522	0.980685
$135$	4.50223	0.387490
$136$	1.00000	0.0857493
$137$	−16.7609	−1.43198	−0.715991	−	0.698110i	$-0.754025\pi$
$137$	−16.7609	−1.43198	−0.715991	+	0.698110i	$0.754025\pi$
$138$	−14.8486	−1.26400
$139$	13.3830	1.13513	0.567565	−	0.823328i	$-0.307885\pi$
$139$	13.3830	1.13513	0.567565	+	0.823328i	$0.307885\pi$
$140$	−2.53339	−0.214110
$141$	27.2420	2.29419
$142$	−10.9816	−0.921554
$143$	−5.65354	−0.472773
$144$	3.70384	0.308653
$145$	−2.73170	−0.226856
$146$	4.88344	0.404156
$147$	−15.4017	−1.27031
$148$	9.71380	0.798469
$149$	2.36890	0.194068	0.0970338	−	0.995281i	$-0.469065\pi$
$149$	2.36890	0.194068	0.0970338	+	0.995281i	$0.469065\pi$
$150$	2.85739	0.233305
$151$	12.0781	0.982902	0.491451	−	0.870905i	$-0.336467\pi$
$151$	12.0781	0.982902	0.491451	+	0.870905i	$0.336467\pi$
$152$	5.49560	0.445752
$153$	3.70384	0.299438
$154$	3.24026	0.261107
$155$	11.1990	0.899529
$156$	4.63246	0.370894
$157$	−15.1601	−1.20991	−0.604956	−	0.796259i	$-0.706809\pi$
$157$	−15.1601	−1.20991	−0.604956	+	0.796259i	$0.706809\pi$
$158$	11.9072	0.947288
$159$	−26.9049	−2.13370
$160$	2.47054	0.195314
$161$	5.88075	0.463468
$162$	−6.39309	−0.502289
$163$	17.1637	1.34437	0.672183	−	0.740385i	$-0.265357\pi$
$163$	17.1637	1.34437	0.672183	+	0.740385i	$0.265357\pi$
$164$	−7.11984	−0.555966
$165$	−20.2127	−1.57356
$166$	1.96708	0.152675
$167$	−5.16600	−0.399757	−0.199879	−	0.979821i	$-0.564055\pi$
$167$	−5.16600	−0.399757	−0.199879	+	0.979821i	$0.564055\pi$
$168$	−2.65504	−0.204840
$169$	−9.79889	−0.753761
$170$	2.47054	0.189482
$171$	20.3548	1.55657
$172$	−7.22645	−0.551011
$173$	11.6401	0.884978	0.442489	−	0.896774i	$-0.354096\pi$
$173$	11.6401	0.884978	0.442489	+	0.896774i	$0.354096\pi$
$174$	−2.86288	−0.217034
$175$	−1.13166	−0.0855456
$176$	−3.15988	−0.238185
$177$	2.58918	0.194614
$178$	−12.9976	−0.974210
$179$	7.40798	0.553698	0.276849	−	0.960913i	$-0.410710\pi$
$179$	7.40798	0.553698	0.276849	+	0.960913i	$0.410710\pi$
$180$	9.15050	0.682038
$181$	−4.32208	−0.321258	−0.160629	−	0.987015i	$-0.551352\pi$
$181$	−4.32208	−0.321258	−0.160629	+	0.987015i	$0.551352\pi$
$182$	−1.83467	−0.135995
$183$	−4.03474	−0.298257
$184$	−5.73487	−0.422780
$185$	23.9984	1.76440
$186$	11.7368	0.860585
$187$	−3.15988	−0.231073
$188$	10.5215	0.767359
$189$	−1.86872	−0.135929
$190$	13.5771	0.984988
$191$	23.2865	1.68495	0.842475	−	0.538735i	$-0.181098\pi$
$191$	23.2865	1.68495	0.842475	+	0.538735i	$0.181098\pi$
$192$	2.58918	0.186858
$193$	12.9909	0.935105	0.467552	−	0.883965i	$-0.345136\pi$
$193$	12.9909	0.935105	0.467552	+	0.883965i	$0.345136\pi$
$194$	1.40274	0.100711
$195$	11.4447	0.819572
$196$	−5.94848	−0.424891
$197$	3.21190	0.228838	0.114419	−	0.993433i	$-0.463499\pi$
$197$	3.21190	0.228838	0.114419	+	0.993433i	$0.463499\pi$
$198$	−11.7037	−0.831745
$199$	7.47981	0.530229	0.265115	−	0.964217i	$-0.414590\pi$
$199$	7.47981	0.530229	0.265115	+	0.964217i	$0.414590\pi$
$200$	1.10359	0.0780356
$201$	29.3930	2.07322
$202$	−14.8612	−1.04563
$203$	1.13383	0.0795796
$204$	2.58918	0.181279
$205$	−17.5899	−1.22853
$206$	−8.98471	−0.625994
$207$	−21.2410	−1.47635
$208$	1.78916	0.124056
$209$	−17.3654	−1.20119
$210$	−6.55938	−0.452641
$211$	−18.3324	−1.26205	−0.631027	−	0.775761i	$-0.717366\pi$
$211$	−18.3324	−1.26205	−0.631027	+	0.775761i	$0.717366\pi$
$212$	−10.3913	−0.713676
$213$	−28.4333	−1.94822
$214$	−0.969100	−0.0662463
$215$	−17.8533	−1.21758
$216$	1.82236	0.123996
$217$	−4.64833	−0.315549
$218$	−9.02849	−0.611487
$219$	12.6441	0.854408
$220$	−7.80662	−0.526322
$221$	1.78916	0.120352
$222$	25.1507	1.68801
$223$	−2.70488	−0.181132	−0.0905662	−	0.995890i	$-0.528868\pi$
$223$	−2.70488	−0.181132	−0.0905662	+	0.995890i	$0.528868\pi$
$224$	−1.02544	−0.0685148
$225$	4.08752	0.272501
$226$	−1.49771	−0.0996264
$227$	0.812909	0.0539546	0.0269773	−	0.999636i	$-0.491412\pi$
$227$	0.812909	0.0539546	0.0269773	+	0.999636i	$0.491412\pi$
$228$	14.2291	0.942344
$229$	−2.51932	−0.166481	−0.0832407	−	0.996529i	$-0.526527\pi$
$229$	−2.51932	−0.166481	−0.0832407	+	0.996529i	$0.526527\pi$
$230$	−14.1683	−0.934227
$231$	8.38959	0.551995
$232$	−1.10571	−0.0725934
$233$	22.5905	1.47995	0.739976	−	0.672633i	$-0.234837\pi$
$233$	22.5905	1.47995	0.739976	+	0.672633i	$0.234837\pi$
$234$	6.62677	0.433206
$235$	25.9938	1.69565
$236$	1.00000	0.0650945
$237$	30.8299	2.00262
$238$	−1.02544	−0.0664692
$239$	−15.9818	−1.03378	−0.516889	−	0.856053i	$-0.672910\pi$
$239$	−15.9818	−1.03378	−0.516889	+	0.856053i	$0.672910\pi$
$240$	6.39668	0.412904
$241$	−5.08175	−0.327344	−0.163672	−	0.986515i	$-0.552334\pi$
$241$	−5.08175	−0.327344	−0.163672	+	0.986515i	$0.552334\pi$
$242$	−1.01516	−0.0652569
$243$	−22.0199	−1.41258
$244$	−1.55831	−0.0997606
$245$	−14.6960	−0.938892
$246$	−18.4345	−1.17534
$247$	9.83253	0.625629
$248$	4.53303	0.287847
$249$	5.09312	0.322764
$250$	−9.62625	−0.608818
$251$	0.900077	0.0568123	0.0284062	−	0.999596i	$-0.490957\pi$
$251$	0.900077	0.0568123	0.0284062	+	0.999596i	$0.490957\pi$
$252$	−3.79805	−0.239255
$253$	18.1215	1.13929
$254$	−18.3758	−1.15300
$255$	6.39668	0.400576
$256$	1.00000	0.0625000
$257$	−27.2929	−1.70248	−0.851241	−	0.524775i	$-0.824149\pi$
$257$	−27.2929	−1.70248	−0.851241	+	0.524775i	$0.824149\pi$
$258$	−18.7105	−1.16487
$259$	−9.96088	−0.618939
$260$	4.42021	0.274130
$261$	−4.09537	−0.253497
$262$	14.9865	0.925869
$263$	24.1912	1.49169	0.745847	−	0.666117i	$-0.232045\pi$
$263$	24.1912	1.49169	0.745847	+	0.666117i	$0.232045\pi$
$264$	−8.18149	−0.503536
$265$	−25.6721	−1.57703
$266$	−5.63539	−0.345528
$267$	−33.6530	−2.05953
$268$	11.3522	0.693449
$269$	21.7744	1.32761	0.663803	−	0.747907i	$-0.268941\pi$
$269$	21.7744	1.32761	0.663803	+	0.747907i	$0.268941\pi$
$270$	4.50223	0.273997
$271$	−2.75053	−0.167083	−0.0835414	−	0.996504i	$-0.526623\pi$
$271$	−2.75053	−0.167083	−0.0835414	+	0.996504i	$0.526623\pi$
$272$	1.00000	0.0606339
$273$	−4.75029	−0.287501
$274$	−16.7609	−1.01256
$275$	−3.48721	−0.210287
$276$	−14.8486	−0.893781
$277$	−17.9707	−1.07975	−0.539877	−	0.841744i	$-0.681529\pi$
$277$	−17.9707	−1.07975	−0.539877	+	0.841744i	$0.681529\pi$
$278$	13.3830	0.802659
$279$	16.7896	1.00517
$280$	−2.53339	−0.151399
$281$	28.4931	1.69975	0.849877	−	0.526980i	$-0.176676\pi$
$281$	28.4931	1.69975	0.849877	+	0.526980i	$0.176676\pi$
$282$	27.2420	1.62224
$283$	−15.1427	−0.900139	−0.450070	−	0.892993i	$-0.648601\pi$
$283$	−15.1427	−0.900139	−0.450070	+	0.892993i	$0.648601\pi$
$284$	−10.9816	−0.651637
$285$	35.1536	2.08232
$286$	−5.65354	−0.334301
$287$	7.30094	0.430961
$288$	3.70384	0.218251
$289$	1.00000	0.0588235
$290$	−2.73170	−0.160411
$291$	3.63194	0.212908
$292$	4.88344	0.285782
$293$	−11.1377	−0.650673	−0.325337	−	0.945598i	$-0.605478\pi$
$293$	−11.1377	−0.650673	−0.325337	+	0.945598i	$0.605478\pi$
$294$	−15.4017	−0.898244
$295$	2.47054	0.143841
$296$	9.71380	0.564603
$297$	−5.75845	−0.334139
$298$	2.36890	0.137226
$299$	−10.2606	−0.593387
$300$	2.85739	0.164972
$301$	7.41026	0.427120
$302$	12.0781	0.695016
$303$	−38.4782	−2.21052
$304$	5.49560	0.315194
$305$	−3.84987	−0.220443
$306$	3.70384	0.211734
$307$	25.4164	1.45059	0.725296	−	0.688437i	$-0.241703\pi$
$307$	25.4164	1.45059	0.725296	+	0.688437i	$0.241703\pi$
$308$	3.24026	0.184631
$309$	−23.2630	−1.32339
$310$	11.1990	0.636063
$311$	−30.7502	−1.74368	−0.871842	−	0.489787i	$-0.837074\pi$
$311$	−30.7502	−1.74368	−0.871842	+	0.489787i	$0.837074\pi$
$312$	4.63246	0.262261
$313$	0.603581	0.0341164	0.0170582	−	0.999854i	$-0.494570\pi$
$313$	0.603581	0.0341164	0.0170582	+	0.999854i	$0.494570\pi$
$314$	−15.1601	−0.855536
$315$	−9.38325	−0.528686
$316$	11.9072	0.669834
$317$	32.1093	1.80344	0.901719	−	0.432323i	$-0.142306\pi$
$317$	32.1093	1.80344	0.901719	+	0.432323i	$0.142306\pi$
$318$	−26.9049	−1.50875
$319$	3.49391	0.195621
$320$	2.47054	0.138108
$321$	−2.50917	−0.140048
$322$	5.88075	0.327721
$323$	5.49560	0.305783
$324$	−6.39309	−0.355172
$325$	1.97450	0.109526
$326$	17.1637	0.950610
$327$	−23.3764	−1.29272
$328$	−7.11984	−0.393127
$329$	−10.7891	−0.594823
$330$	−20.2127	−1.11267
$331$	19.0063	1.04468	0.522340	−	0.852737i	$-0.325059\pi$
$331$	19.0063	1.04468	0.522340	+	0.852737i	$0.325059\pi$
$332$	1.96708	0.107958
$333$	35.9783	1.97160
$334$	−5.16600	−0.282671
$335$	28.0462	1.53233
$336$	−2.65504	−0.144844
$337$	8.73571	0.475864	0.237932	−	0.971282i	$-0.423530\pi$
$337$	8.73571	0.475864	0.237932	+	0.971282i	$0.423530\pi$
$338$	−9.79889	−0.532990
$339$	−3.87785	−0.210616
$340$	2.47054	0.133984
$341$	−14.3238	−0.775678
$342$	20.3548	1.10066
$343$	13.2778	0.716936
$344$	−7.22645	−0.389624
$345$	−36.6841	−1.97501
$346$	11.6401	0.625774
$347$	6.01893	0.323113	0.161557	−	0.986863i	$-0.448349\pi$
$347$	6.01893	0.323113	0.161557	+	0.986863i	$0.448349\pi$
$348$	−2.86288	−0.153466
$349$	18.3746	0.983570	0.491785	−	0.870717i	$-0.336345\pi$
$349$	18.3746	0.983570	0.491785	+	0.870717i	$0.336345\pi$
$350$	−1.13166	−0.0604899
$351$	3.26051	0.174033
$352$	−3.15988	−0.168422
$353$	32.4758	1.72851	0.864257	−	0.503051i	$-0.167789\pi$
$353$	32.4758	1.72851	0.864257	+	0.503051i	$0.167789\pi$
$354$	2.58918	0.137613
$355$	−27.1305	−1.43994
$356$	−12.9976	−0.688871
$357$	−2.65504	−0.140519
$358$	7.40798	0.391524
$359$	−12.4013	−0.654516	−0.327258	−	0.944935i	$-0.606125\pi$
$359$	−12.4013	−0.654516	−0.327258	+	0.944935i	$0.606125\pi$
$360$	9.15050	0.482274
$361$	11.2016	0.589559
$362$	−4.32208	−0.227164
$363$	−2.62843	−0.137957
$364$	−1.83467	−0.0961630
$365$	12.0648	0.631498
$366$	−4.03474	−0.210899
$367$	29.3875	1.53401	0.767006	−	0.641639i	$-0.221745\pi$
$367$	29.3875	1.53401	0.767006	+	0.641639i	$0.221745\pi$
$368$	−5.73487	−0.298951
$369$	−26.3707	−1.37281
$370$	23.9984	1.24762
$371$	10.6556	0.553211
$372$	11.7368	0.608525
$373$	−7.43642	−0.385043	−0.192522	−	0.981293i	$-0.561667\pi$
$373$	−7.43642	−0.385043	−0.192522	+	0.981293i	$0.561667\pi$
$374$	−3.15988	−0.163393
$375$	−24.9241	−1.28707
$376$	10.5215	0.542604
$377$	−1.97829	−0.101887
$378$	−1.86872	−0.0961165
$379$	4.26581	0.219120	0.109560	−	0.993980i	$-0.465056\pi$
$379$	4.26581	0.219120	0.109560	+	0.993980i	$0.465056\pi$
$380$	13.5771	0.696492
$381$	−47.5783	−2.43751
$382$	23.2865	1.19144
$383$	11.1319	0.568815	0.284408	−	0.958703i	$-0.408203\pi$
$383$	11.1319	0.568815	0.284408	+	0.958703i	$0.408203\pi$
$384$	2.58918	0.132128
$385$	8.00519	0.407982
$386$	12.9909	0.661219
$387$	−26.7656	−1.36057
$388$	1.40274	0.0712133
$389$	7.58274	0.384460	0.192230	−	0.981350i	$-0.438428\pi$
$389$	7.58274	0.384460	0.192230	+	0.981350i	$0.438428\pi$
$390$	11.4447	0.579525
$391$	−5.73487	−0.290025
$392$	−5.94848	−0.300444
$393$	38.8027	1.95734
$394$	3.21190	0.161813
$395$	29.4173	1.48015
$396$	−11.7037	−0.588132
$397$	−33.1047	−1.66148	−0.830739	−	0.556661i	$-0.812082\pi$
$397$	−33.1047	−1.66148	−0.830739	+	0.556661i	$0.812082\pi$
$398$	7.47981	0.374929
$399$	−14.5910	−0.730464
$400$	1.10359	0.0551795
$401$	10.5010	0.524395	0.262198	−	0.965014i	$-0.415553\pi$
$401$	10.5010	0.524395	0.262198	+	0.965014i	$0.415553\pi$
$402$	29.3930	1.46599
$403$	8.11032	0.404004
$404$	−14.8612	−0.739371
$405$	−15.7944	−0.784831
$406$	1.13383	0.0562713
$407$	−30.6944	−1.52147
$408$	2.58918	0.128183
$409$	13.4321	0.664173	0.332086	−	0.943249i	$-0.392247\pi$
$409$	13.4321	0.664173	0.332086	+	0.943249i	$0.392247\pi$
$410$	−17.5899	−0.868702
$411$	−43.3970	−2.14061
$412$	−8.98471	−0.442645
$413$	−1.02544	−0.0504584
$414$	−21.2410	−1.04394
$415$	4.85976	0.238556
$416$	1.78916	0.0877209
$417$	34.6509	1.69686
$418$	−17.3654	−0.849371
$419$	−25.7867	−1.25976	−0.629882	−	0.776691i	$-0.716897\pi$
$419$	−25.7867	−1.25976	−0.629882	+	0.776691i	$0.716897\pi$
$420$	−6.55938	−0.320065
$421$	10.1457	0.494469	0.247235	−	0.968956i	$-0.420478\pi$
$421$	10.1457	0.494469	0.247235	+	0.968956i	$0.420478\pi$
$422$	−18.3324	−0.892407
$423$	38.9699	1.89478
$424$	−10.3913	−0.504645
$425$	1.10359	0.0535320
$426$	−28.4333	−1.37760
$427$	1.59795	0.0773301
$428$	−0.969100	−0.0468432
$429$	−14.6380	−0.706730
$430$	−17.8533	−0.860960
$431$	−22.7131	−1.09405	−0.547025	−	0.837116i	$-0.684240\pi$
$431$	−22.7131	−1.09405	−0.547025	+	0.837116i	$0.684240\pi$
$432$	1.82236	0.0876785
$433$	−27.6916	−1.33077	−0.665387	−	0.746499i	$-0.731733\pi$
$433$	−27.6916	−1.33077	−0.665387	+	0.746499i	$0.731733\pi$
$434$	−4.64833	−0.223127
$435$	−7.07287	−0.339118
$436$	−9.02849	−0.432386
$437$	−31.5166	−1.50764
$438$	12.6441	0.604158
$439$	0.348362	0.0166264	0.00831321	−	0.999965i	$-0.497354\pi$
$439$	0.348362	0.0166264	0.00831321	+	0.999965i	$0.497354\pi$
$440$	−7.80662	−0.372166
$441$	−22.0322	−1.04915
$442$	1.78916	0.0851018
$443$	−2.87143	−0.136426	−0.0682129	−	0.997671i	$-0.521730\pi$
$443$	−2.87143	−0.136426	−0.0682129	+	0.997671i	$0.521730\pi$
$444$	25.1507	1.19360
$445$	−32.1111	−1.52221
$446$	−2.70488	−0.128080
$447$	6.13349	0.290104
$448$	−1.02544	−0.0484473
$449$	30.1071	1.42084	0.710420	−	0.703778i	$-0.248505\pi$
$449$	30.1071	1.42084	0.710420	+	0.703778i	$0.248505\pi$
$450$	4.08752	0.192688
$451$	22.4978	1.05938
$452$	−1.49771	−0.0704465
$453$	31.2723	1.46930
$454$	0.812909	0.0381517
$455$	−4.53264	−0.212493
$456$	14.2291	0.666338
$457$	−10.3641	−0.484813	−0.242406	−	0.970175i	$-0.577937\pi$
$457$	−10.3641	−0.484813	−0.242406	+	0.970175i	$0.577937\pi$
$458$	−2.51932	−0.117720
$459$	1.82236	0.0850607
$460$	−14.1683	−0.660599
$461$	−26.1717	−1.21894	−0.609468	−	0.792810i	$-0.708617\pi$
$461$	−26.1717	−1.21894	−0.609468	+	0.792810i	$0.708617\pi$
$462$	8.38959	0.390319
$463$	−23.3676	−1.08599	−0.542993	−	0.839737i	$-0.682709\pi$
$463$	−23.3676	−1.08599	−0.542993	+	0.839737i	$0.682709\pi$
$464$	−1.10571	−0.0513313
$465$	28.9963	1.34467
$466$	22.5905	1.04648
$467$	21.9379	1.01517	0.507583	−	0.861603i	$-0.330539\pi$
$467$	21.9379	1.01517	0.507583	+	0.861603i	$0.330539\pi$
$468$	6.62677	0.306323
$469$	−11.6410	−0.537532
$470$	25.9938	1.19901
$471$	−39.2523	−1.80865
$472$	1.00000	0.0460287
$473$	22.8347	1.04994
$474$	30.8299	1.41606
$475$	6.06489	0.278276
$476$	−1.02544	−0.0470008
$477$	−38.4876	−1.76223
$478$	−15.9818	−0.730991
$479$	12.8313	0.586277	0.293138	−	0.956070i	$-0.405300\pi$
$479$	12.8313	0.586277	0.293138	+	0.956070i	$0.405300\pi$
$480$	6.39668	0.291967
$481$	17.3796	0.792440
$482$	−5.08175	−0.231467
$483$	15.2263	0.692820
$484$	−1.01516	−0.0461436
$485$	3.46553	0.157362
$486$	−22.0199	−0.998845
$487$	−38.2597	−1.73371	−0.866856	−	0.498559i	$-0.833863\pi$
$487$	−38.2597	−1.73371	−0.866856	+	0.498559i	$0.833863\pi$
$488$	−1.55831	−0.0705414
$489$	44.4399	2.00964
$490$	−14.6960	−0.663897
$491$	8.44936	0.381314	0.190657	−	0.981657i	$-0.438938\pi$
$491$	8.44936	0.381314	0.190657	+	0.981657i	$0.438938\pi$
$492$	−18.4345	−0.831092
$493$	−1.10571	−0.0497986
$494$	9.83253	0.442386
$495$	−28.9145	−1.29961
$496$	4.53303	0.203539
$497$	11.2609	0.505121
$498$	5.09312	0.228228
$499$	0.537695	0.0240705	0.0120353	−	0.999928i	$-0.496169\pi$
$499$	0.537695	0.0240705	0.0120353	+	0.999928i	$0.496169\pi$
$500$	−9.62625	−0.430499
$501$	−13.3757	−0.597582
$502$	0.900077	0.0401724
$503$	−34.3745	−1.53268	−0.766341	−	0.642434i	$-0.777925\pi$
$503$	−34.3745	−1.53268	−0.766341	+	0.642434i	$0.777925\pi$
$504$	−3.79805	−0.169179
$505$	−36.7152	−1.63381
$506$	18.1215	0.805599
$507$	−25.3711	−1.12677
$508$	−18.3758	−0.815295
$509$	13.2687	0.588123	0.294062	−	0.955786i	$-0.404993\pi$
$509$	13.2687	0.588123	0.294062	+	0.955786i	$0.404993\pi$
$510$	6.39668	0.283250
$511$	−5.00765	−0.221526
$512$	1.00000	0.0441942
$513$	10.0150	0.442172
$514$	−27.2929	−1.20384
$515$	−22.1971	−0.978122
$516$	−18.7105	−0.823686
$517$	−33.2466	−1.46219
$518$	−9.96088	−0.437656
$519$	30.1382	1.32292
$520$	4.42021	0.193839
$521$	21.5453	0.943918	0.471959	−	0.881621i	$-0.343547\pi$
$521$	21.5453	0.943918	0.471959	+	0.881621i	$0.343547\pi$
$522$	−4.09537	−0.179249
$523$	18.6346	0.814833	0.407416	−	0.913243i	$-0.366430\pi$
$523$	18.6346	0.814833	0.407416	+	0.913243i	$0.366430\pi$
$524$	14.9865	0.654688
$525$	−2.93007	−0.127879
$526$	24.1912	1.05479
$527$	4.53303	0.197462
$528$	−8.18149	−0.356054
$529$	9.88878	0.429947
$530$	−25.6721	−1.11513
$531$	3.70384	0.160733
$532$	−5.63539	−0.244325
$533$	−12.7386	−0.551768
$534$	−33.6530	−1.45631
$535$	−2.39420	−0.103510
$536$	11.3522	0.490342
$537$	19.1806	0.827702
$538$	21.7744	0.938759
$539$	18.7965	0.809622
$540$	4.50223	0.193745
$541$	33.6253	1.44566	0.722832	−	0.691024i	$-0.242840\pi$
$541$	33.6253	1.44566	0.722832	+	0.691024i	$0.242840\pi$
$542$	−2.75053	−0.118145
$543$	−11.1906	−0.480236
$544$	1.00000	0.0428746
$545$	−22.3053	−0.955454
$546$	−4.75029	−0.203294
$547$	−2.39228	−0.102286	−0.0511432	−	0.998691i	$-0.516287\pi$
$547$	−2.39228	−0.102286	−0.0511432	+	0.998691i	$0.516287\pi$
$548$	−16.7609	−0.715991
$549$	−5.77173	−0.246331
$550$	−3.48721	−0.148695
$551$	−6.07654	−0.258869
$552$	−14.8486	−0.631999
$553$	−12.2101	−0.519226
$554$	−17.9707	−0.763502
$555$	62.1360	2.63753
$556$	13.3830	0.567565
$557$	2.90023	0.122887	0.0614433	−	0.998111i	$-0.480430\pi$
$557$	2.90023	0.122887	0.0614433	+	0.998111i	$0.480430\pi$
$558$	16.7896	0.710760
$559$	−12.9293	−0.546851
$560$	−2.53339	−0.107055
$561$	−8.18149	−0.345423
$562$	28.4931	1.20191
$563$	26.3288	1.10963	0.554814	−	0.831974i	$-0.312789\pi$
$563$	26.3288	1.10963	0.554814	+	0.831974i	$0.312789\pi$
$564$	27.2420	1.14710
$565$	−3.70017	−0.155667
$566$	−15.1427	−0.636495
$567$	6.55571	0.275314
$568$	−10.9816	−0.460777
$569$	−40.4594	−1.69615	−0.848073	−	0.529879i	$-0.822237\pi$
$569$	−40.4594	−1.69615	−0.848073	+	0.529879i	$0.822237\pi$
$570$	35.1536	1.47242
$571$	25.3951	1.06275	0.531376	−	0.847136i	$-0.321675\pi$
$571$	25.3951	1.06275	0.531376	+	0.847136i	$0.321675\pi$
$572$	−5.65354	−0.236386
$573$	60.2928	2.51877
$574$	7.30094	0.304735
$575$	−6.32895	−0.263936
$576$	3.70384	0.154327
$577$	45.2540	1.88395	0.941974	−	0.335687i	$-0.108969\pi$
$577$	45.2540	1.88395	0.941974	+	0.335687i	$0.108969\pi$
$578$	1.00000	0.0415945
$579$	33.6357	1.39785
$580$	−2.73170	−0.113428
$581$	−2.01712	−0.0836841
$582$	3.63194	0.150549
$583$	32.8352	1.35990
$584$	4.88344	0.202078
$585$	16.3717	0.676888
$586$	−11.1377	−0.460095
$587$	−12.4842	−0.515278	−0.257639	−	0.966241i	$-0.582945\pi$
$587$	−12.4842	−0.515278	−0.257639	+	0.966241i	$0.582945\pi$
$588$	−15.4017	−0.635154
$589$	24.9117	1.02647
$590$	2.47054	0.101711
$591$	8.31617	0.342082
$592$	9.71380	0.399235
$593$	−34.9934	−1.43700	−0.718502	−	0.695524i	$-0.755172\pi$
$593$	−34.9934	−1.43700	−0.718502	+	0.695524i	$0.755172\pi$
$594$	−5.75845	−0.236272
$595$	−2.53339	−0.103859
$596$	2.36890	0.0970338
$597$	19.3665	0.792620
$598$	−10.2606	−0.419588
$599$	−37.6001	−1.53630	−0.768148	−	0.640272i	$-0.778822\pi$
$599$	−37.6001	−1.53630	−0.768148	+	0.640272i	$0.778822\pi$
$600$	2.85739	0.116653
$601$	12.3122	0.502227	0.251113	−	0.967958i	$-0.419203\pi$
$601$	12.3122	0.502227	0.251113	+	0.967958i	$0.419203\pi$
$602$	7.41026	0.302020
$603$	42.0469	1.71228
$604$	12.0781	0.491451
$605$	−2.50800	−0.101965
$606$	−38.4782	−1.56307
$607$	33.4419	1.35736	0.678682	−	0.734432i	$-0.262551\pi$
$607$	33.4419	1.35736	0.678682	+	0.734432i	$0.262551\pi$
$608$	5.49560	0.222876
$609$	2.93570	0.118960
$610$	−3.84987	−0.155877
$611$	18.8247	0.761564
$612$	3.70384	0.149719
$613$	18.8883	0.762889	0.381445	−	0.924392i	$-0.375427\pi$
$613$	18.8883	0.762889	0.381445	+	0.924392i	$0.375427\pi$
$614$	25.4164	1.02572
$615$	−45.5433	−1.83648
$616$	3.24026	0.130554
$617$	−4.24317	−0.170824	−0.0854119	−	0.996346i	$-0.527221\pi$
$617$	−4.24317	−0.170824	−0.0854119	+	0.996346i	$0.527221\pi$
$618$	−23.2630	−0.935775
$619$	8.37431	0.336592	0.168296	−	0.985737i	$-0.446174\pi$
$619$	8.37431	0.336592	0.168296	+	0.985737i	$0.446174\pi$
$620$	11.1990	0.449764
$621$	−10.4510	−0.419385
$622$	−30.7502	−1.23297
$623$	13.3282	0.533983
$624$	4.63246	0.185447
$625$	−29.3000	−1.17200
$626$	0.603581	0.0241240
$627$	−44.9622	−1.79562
$628$	−15.1601	−0.604956
$629$	9.71380	0.387315
$630$	−9.38325	−0.373838
$631$	−45.1179	−1.79612	−0.898058	−	0.439878i	$-0.855022\pi$
$631$	−45.1179	−1.79612	−0.898058	+	0.439878i	$0.855022\pi$
$632$	11.9072	0.473644
$633$	−47.4658	−1.88660
$634$	32.1093	1.27522
$635$	−45.3983	−1.80158
$636$	−26.9049	−1.06685
$637$	−10.6428	−0.421683
$638$	3.49391	0.138325
$639$	−40.6740	−1.60904
$640$	2.47054	0.0976568
$641$	−35.9810	−1.42116	−0.710582	−	0.703614i	$-0.751568\pi$
$641$	−35.9810	−1.42116	−0.710582	+	0.703614i	$0.751568\pi$
$642$	−2.50917	−0.0990291
$643$	−16.9934	−0.670153	−0.335076	−	0.942191i	$-0.608762\pi$
$643$	−16.9934	−0.670153	−0.335076	+	0.942191i	$0.608762\pi$
$644$	5.88075	0.231734
$645$	−46.2252	−1.82012
$646$	5.49560	0.216221
$647$	−47.3230	−1.86046	−0.930230	−	0.366978i	$-0.880392\pi$
$647$	−47.3230	−1.86046	−0.930230	+	0.366978i	$0.880392\pi$
$648$	−6.39309	−0.251144
$649$	−3.15988	−0.124036
$650$	1.97450	0.0774464
$651$	−12.0353	−0.471703
$652$	17.1637	0.672183
$653$	23.7546	0.929590	0.464795	−	0.885418i	$-0.346128\pi$
$653$	23.7546	0.929590	0.464795	+	0.885418i	$0.346128\pi$
$654$	−23.3764	−0.914088
$655$	37.0248	1.44668
$656$	−7.11984	−0.277983
$657$	18.0875	0.705659
$658$	−10.7891	−0.420604
$659$	3.15486	0.122896	0.0614479	−	0.998110i	$-0.480428\pi$
$659$	3.15486	0.122896	0.0614479	+	0.998110i	$0.480428\pi$
$660$	−20.2127	−0.786780
$661$	−6.70263	−0.260702	−0.130351	−	0.991468i	$-0.541610\pi$
$661$	−6.70263	−0.260702	−0.130351	+	0.991468i	$0.541610\pi$
$662$	19.0063	0.738701
$663$	4.63246	0.179910
$664$	1.96708	0.0763376
$665$	−13.9225	−0.539890
$666$	35.9783	1.39413
$667$	6.34110	0.245528
$668$	−5.16600	−0.199879
$669$	−7.00343	−0.270768
$670$	28.0462	1.08352
$671$	4.92407	0.190092
$672$	−2.65504	−0.102420
$673$	22.4199	0.864225	0.432112	−	0.901820i	$-0.357768\pi$
$673$	22.4199	0.864225	0.432112	+	0.901820i	$0.357768\pi$
$674$	8.73571	0.336487
$675$	2.01114	0.0774089
$676$	−9.79889	−0.376881
$677$	−15.1486	−0.582207	−0.291103	−	0.956692i	$-0.594022\pi$
$677$	−15.1486	−0.582207	−0.291103	+	0.956692i	$0.594022\pi$
$678$	−3.87785	−0.148928
$679$	−1.43842	−0.0552015
$680$	2.47054	0.0947411
$681$	2.10476	0.0806548
$682$	−14.3238	−0.548487
$683$	−9.48021	−0.362750	−0.181375	−	0.983414i	$-0.558055\pi$
$683$	−9.48021	−0.362750	−0.181375	+	0.983414i	$0.558055\pi$
$684$	20.3548	0.778286
$685$	−41.4086	−1.58214
$686$	13.2778	0.506950
$687$	−6.52296	−0.248867
$688$	−7.22645	−0.275506
$689$	−18.5917	−0.708287
$690$	−36.6841	−1.39654
$691$	−6.49452	−0.247063	−0.123532	−	0.992341i	$-0.539422\pi$
$691$	−6.49452	−0.247063	−0.123532	+	0.992341i	$0.539422\pi$
$692$	11.6401	0.442489
$693$	12.0014	0.455895
$694$	6.01893	0.228476
$695$	33.0633	1.25416
$696$	−2.86288	−0.108517
$697$	−7.11984	−0.269683
$698$	18.3746	0.695489
$699$	58.4908	2.21233
$700$	−1.13166	−0.0427728
$701$	−0.298298	−0.0112666	−0.00563328	−	0.999984i	$-0.501793\pi$
$701$	−0.298298	−0.0112666	−0.00563328	+	0.999984i	$0.501793\pi$
$702$	3.26051	0.123060
$703$	53.3832	2.01338
$704$	−3.15988	−0.119092
$705$	67.3026	2.53476
$706$	32.4758	1.22224
$707$	15.2392	0.573129
$708$	2.58918	0.0973072
$709$	24.3175	0.913261	0.456631	−	0.889656i	$-0.349056\pi$
$709$	24.3175	0.913261	0.456631	+	0.889656i	$0.349056\pi$
$710$	−27.1305	−1.01819
$711$	44.1024	1.65397
$712$	−12.9976	−0.487105
$713$	−25.9963	−0.973570
$714$	−2.65504	−0.0993622
$715$	−13.9673	−0.522348
$716$	7.40798	0.276849
$717$	−41.3797	−1.54535
$718$	−12.4013	−0.462813
$719$	−21.4084	−0.798399	−0.399199	−	0.916864i	$-0.630712\pi$
$719$	−21.4084	−0.798399	−0.399199	+	0.916864i	$0.630712\pi$
$720$	9.15050	0.341019
$721$	9.21325	0.343119
$722$	11.2016	0.416881
$723$	−13.1576	−0.489335
$724$	−4.32208	−0.160629
$725$	−1.22025	−0.0453190
$726$	−2.62843	−0.0975501
$727$	36.1896	1.34220	0.671099	−	0.741368i	$-0.265823\pi$
$727$	36.1896	1.34220	0.671099	+	0.741368i	$0.265823\pi$
$728$	−1.83467	−0.0679975
$729$	−37.8343	−1.40127
$730$	12.0648	0.446536
$731$	−7.22645	−0.267280
$732$	−4.03474	−0.149128
$733$	6.92114	0.255638	0.127819	−	0.991798i	$-0.459202\pi$
$733$	6.92114	0.255638	0.127819	+	0.991798i	$0.459202\pi$
$734$	29.3875	1.08471
$735$	−38.0505	−1.40351
$736$	−5.73487	−0.211390
$737$	−35.8717	−1.32135
$738$	−26.3707	−0.970720
$739$	37.2559	1.37048	0.685240	−	0.728317i	$-0.259697\pi$
$739$	37.2559	1.37048	0.685240	+	0.728317i	$0.259697\pi$
$740$	23.9984	0.882198
$741$	25.4582	0.935229
$742$	10.6556	0.391179
$743$	14.6370	0.536978	0.268489	−	0.963283i	$-0.413476\pi$
$743$	14.6370	0.536978	0.268489	+	0.963283i	$0.413476\pi$
$744$	11.7368	0.430292
$745$	5.85246	0.214418
$746$	−7.43642	−0.272267
$747$	7.28575	0.266572
$748$	−3.15988	−0.115537
$749$	0.993750	0.0363108
$750$	−24.9241	−0.910099
$751$	−11.3586	−0.414482	−0.207241	−	0.978290i	$-0.566448\pi$
$751$	−11.3586	−0.414482	−0.207241	+	0.978290i	$0.566448\pi$
$752$	10.5215	0.383679
$753$	2.33046	0.0849266
$754$	−1.97829	−0.0720452
$755$	29.8395	1.08597
$756$	−1.86872	−0.0679646
$757$	−12.4865	−0.453829	−0.226914	−	0.973915i	$-0.572864\pi$
$757$	−12.4865	−0.453829	−0.226914	+	0.973915i	$0.572864\pi$
$758$	4.26581	0.154941
$759$	46.9198	1.70308
$760$	13.5771	0.492494
$761$	−31.1694	−1.12989	−0.564945	−	0.825129i	$-0.691103\pi$
$761$	−31.1694	−1.12989	−0.564945	+	0.825129i	$0.691103\pi$
$762$	−47.5783	−1.72358
$763$	9.25814	0.335167
$764$	23.2865	0.842475
$765$	9.15050	0.330837
$766$	11.1319	0.402213
$767$	1.78916	0.0646029
$768$	2.58918	0.0934289
$769$	33.0220	1.19080	0.595401	−	0.803428i	$-0.296993\pi$
$769$	33.0220	1.19080	0.595401	+	0.803428i	$0.296993\pi$
$770$	8.00519	0.288487
$771$	−70.6660	−2.54498
$772$	12.9909	0.467552
$773$	11.4644	0.412347	0.206174	−	0.978515i	$-0.433899\pi$
$773$	11.4644	0.412347	0.206174	+	0.978515i	$0.433899\pi$
$774$	−26.7656	−0.962069
$775$	5.00260	0.179699
$776$	1.40274	0.0503554
$777$	−25.7905	−0.925229
$778$	7.58274	0.271854
$779$	−39.1278	−1.40190
$780$	11.4447	0.409786
$781$	34.7005	1.24168
$782$	−5.73487	−0.205079
$783$	−2.01500	−0.0720104
$784$	−5.94848	−0.212446
$785$	−37.4538	−1.33678
$786$	38.8027	1.38405
$787$	13.6557	0.486773	0.243387	−	0.969929i	$-0.421742\pi$
$787$	13.6557	0.486773	0.243387	+	0.969929i	$0.421742\pi$
$788$	3.21190	0.114419
$789$	62.6354	2.22988
$790$	29.4173	1.04662
$791$	1.53581	0.0546071
$792$	−11.7037	−0.415872
$793$	−2.78807	−0.0990073
$794$	−33.1047	−1.17484
$795$	−66.4697	−2.35744
$796$	7.47981	0.265115
$797$	−29.4804	−1.04425	−0.522125	−	0.852869i	$-0.674860\pi$
$797$	−29.4804	−1.04425	−0.522125	+	0.852869i	$0.674860\pi$
$798$	−14.5910	−0.516516
$799$	10.5215	0.372224
$800$	1.10359	0.0390178
$801$	−48.1410	−1.70098
$802$	10.5010	0.370803
$803$	−15.4311	−0.544551
$804$	29.3930	1.03661
$805$	14.5286	0.512068
$806$	8.11032	0.285674
$807$	56.3777	1.98459
$808$	−14.8612	−0.522814
$809$	−5.26617	−0.185149	−0.0925743	−	0.995706i	$-0.529510\pi$
$809$	−5.26617	−0.185149	−0.0925743	+	0.995706i	$0.529510\pi$
$810$	−15.7944	−0.554959
$811$	37.5927	1.32006	0.660029	−	0.751240i	$-0.270544\pi$
$811$	37.5927	1.32006	0.660029	+	0.751240i	$0.270544\pi$
$812$	1.13383	0.0397898
$813$	−7.12161	−0.249766
$814$	−30.6944	−1.07584
$815$	42.4037	1.48534
$816$	2.58918	0.0906393
$817$	−39.7137	−1.38940
$818$	13.4321	0.469641
$819$	−6.79533	−0.237448
$820$	−17.5899	−0.614265
$821$	21.2239	0.740719	0.370360	−	0.928888i	$-0.379234\pi$
$821$	21.2239	0.740719	0.370360	+	0.928888i	$0.379234\pi$
$822$	−43.3970	−1.51364
$823$	33.9908	1.18485	0.592423	−	0.805627i	$-0.298171\pi$
$823$	33.9908	1.18485	0.592423	+	0.805627i	$0.298171\pi$
$824$	−8.98471	−0.312997
$825$	−9.02901	−0.314350
$826$	−1.02544	−0.0356795
$827$	30.2842	1.05308	0.526542	−	0.850149i	$-0.323488\pi$
$827$	30.2842	1.05308	0.526542	+	0.850149i	$0.323488\pi$
$828$	−21.2410	−0.738177
$829$	−23.7618	−0.825283	−0.412642	−	0.910894i	$-0.635394\pi$
$829$	−23.7618	−0.825283	−0.412642	+	0.910894i	$0.635394\pi$
$830$	4.85976	0.168685
$831$	−46.5293	−1.61408
$832$	1.78916	0.0620281
$833$	−5.94848	−0.206103
$834$	34.6509	1.19986
$835$	−12.7628	−0.441676
$836$	−17.3654	−0.600596
$837$	8.26082	0.285536
$838$	−25.7867	−0.890787
$839$	−33.4893	−1.15618	−0.578090	−	0.815973i	$-0.696202\pi$
$839$	−33.4893	−1.15618	−0.578090	+	0.815973i	$0.696202\pi$
$840$	−6.55938	−0.226320
$841$	−27.7774	−0.957842
$842$	10.1457	0.349643
$843$	73.7736	2.54090
$844$	−18.3324	−0.631027
$845$	−24.2086	−0.832801
$846$	38.9699	1.33981
$847$	1.04098	0.0357685
$848$	−10.3913	−0.356838
$849$	−39.2071	−1.34558
$850$	1.10359	0.0378528
$851$	−55.7074	−1.90963
$852$	−28.4333	−0.974108
$853$	6.08881	0.208477	0.104239	−	0.994552i	$-0.466759\pi$
$853$	6.08881	0.208477	0.104239	+	0.994552i	$0.466759\pi$
$854$	1.59795	0.0546806
$855$	50.2875	1.71980
$856$	−0.969100	−0.0331231
$857$	−22.4568	−0.767109	−0.383554	−	0.923518i	$-0.625300\pi$
$857$	−22.4568	−0.767109	−0.383554	+	0.923518i	$0.625300\pi$
$858$	−14.6380	−0.499734
$859$	14.5227	0.495509	0.247754	−	0.968823i	$-0.420307\pi$
$859$	14.5227	0.495509	0.247754	+	0.968823i	$0.420307\pi$
$860$	−17.8533	−0.608791
$861$	18.9034	0.644227
$862$	−22.7131	−0.773610
$863$	6.98233	0.237681	0.118841	−	0.992913i	$-0.462082\pi$
$863$	6.98233	0.237681	0.118841	+	0.992913i	$0.462082\pi$
$864$	1.82236	0.0619981
$865$	28.7573	0.977777
$866$	−27.6916	−0.940999
$867$	2.58918	0.0879331
$868$	−4.64833	−0.157775
$869$	−37.6254	−1.27635
$870$	−7.07287	−0.239793
$871$	20.3110	0.688213
$872$	−9.02849	−0.305743
$873$	5.19552	0.175842
$874$	−31.5166	−1.06606
$875$	9.87111	0.333704
$876$	12.6441	0.427204
$877$	32.6398	1.10217	0.551085	−	0.834449i	$-0.314214\pi$
$877$	32.6398	1.10217	0.551085	+	0.834449i	$0.314214\pi$
$878$	0.348362	0.0117567
$879$	−28.8376	−0.972667
$880$	−7.80662	−0.263161
$881$	−16.4566	−0.554437	−0.277218	−	0.960807i	$-0.589413\pi$
$881$	−16.4566	−0.554437	−0.277218	+	0.960807i	$0.589413\pi$
$882$	−22.0322	−0.741863
$883$	−6.43618	−0.216595	−0.108297	−	0.994119i	$-0.534540\pi$
$883$	−6.43618	−0.216595	−0.108297	+	0.994119i	$0.534540\pi$
$884$	1.78916	0.0601761
$885$	6.39668	0.215022
$886$	−2.87143	−0.0964676
$887$	18.9022	0.634673	0.317336	−	0.948313i	$-0.397212\pi$
$887$	18.9022	0.634673	0.317336	+	0.948313i	$0.397212\pi$
$888$	25.1507	0.844004
$889$	18.8432	0.631982
$890$	−32.1111	−1.07637
$891$	20.2014	0.676773
$892$	−2.70488	−0.0905662
$893$	57.8219	1.93494
$894$	6.13349	0.205135
$895$	18.3017	0.611760
$896$	−1.02544	−0.0342574
$897$	−26.5666	−0.887032
$898$	30.1071	1.00469
$899$	−5.01221	−0.167167
$900$	4.08752	0.136251
$901$	−10.3913	−0.346184
$902$	22.4978	0.749096
$903$	19.1865	0.638486
$904$	−1.49771	−0.0498132
$905$	−10.6779	−0.354945
$906$	31.2723	1.03895
$907$	28.4511	0.944703	0.472351	−	0.881410i	$-0.343405\pi$
$907$	28.4511	0.944703	0.472351	+	0.881410i	$0.343405\pi$
$908$	0.812909	0.0269773
$909$	−55.0434	−1.82567
$910$	−4.53264	−0.150256
$911$	18.2533	0.604757	0.302379	−	0.953188i	$-0.402219\pi$
$911$	18.2533	0.604757	0.302379	+	0.953188i	$0.402219\pi$
$912$	14.2291	0.471172
$913$	−6.21574	−0.205711
$914$	−10.3641	−0.342814
$915$	−9.96800	−0.329532
$916$	−2.51932	−0.0832407
$917$	−15.3677	−0.507486
$918$	1.82236	0.0601470
$919$	−7.71935	−0.254638	−0.127319	−	0.991862i	$-0.540637\pi$
$919$	−7.71935	−0.254638	−0.127319	+	0.991862i	$0.540637\pi$
$920$	−14.1683	−0.467114
$921$	65.8076	2.16843
$922$	−26.1717	−0.861918
$923$	−19.6479	−0.646717
$924$	8.38959	0.275997
$925$	10.7201	0.352473
$926$	−23.3676	−0.767908
$927$	−33.2779	−1.09299
$928$	−1.10571	−0.0362967
$929$	18.8496	0.618434	0.309217	−	0.950992i	$-0.399933\pi$
$929$	18.8496	0.618434	0.309217	+	0.950992i	$0.399933\pi$
$930$	28.9963	0.950827
$931$	−32.6905	−1.07139
$932$	22.5905	0.739976
$933$	−79.6177	−2.60657
$934$	21.9379	0.717831
$935$	−7.80662	−0.255304
$936$	6.62677	0.216603
$937$	−51.1384	−1.67062	−0.835310	−	0.549779i	$-0.814712\pi$
$937$	−51.1384	−1.67062	−0.835310	+	0.549779i	$0.814712\pi$
$938$	−11.6410	−0.380092
$939$	1.56278	0.0509994
$940$	25.9938	0.847825
$941$	−12.6390	−0.412018	−0.206009	−	0.978550i	$-0.566048\pi$
$941$	−12.6390	−0.412018	−0.206009	+	0.978550i	$0.566048\pi$
$942$	−39.2523	−1.27891
$943$	40.8314	1.32965
$944$	1.00000	0.0325472
$945$	−4.61675	−0.150183
$946$	22.8347	0.742420
$947$	47.5303	1.54453	0.772263	−	0.635303i	$-0.219125\pi$
$947$	47.5303	1.54453	0.772263	+	0.635303i	$0.219125\pi$
$948$	30.8299	1.00131
$949$	8.73727	0.283624
$950$	6.06489	0.196771
$951$	83.1367	2.69589
$952$	−1.02544	−0.0332346
$953$	12.5579	0.406791	0.203395	−	0.979097i	$-0.434802\pi$
$953$	12.5579	0.406791	0.203395	+	0.979097i	$0.434802\pi$
$954$	−38.4876	−1.24608
$955$	57.5303	1.86164
$956$	−15.9818	−0.516889
$957$	9.04635	0.292427
$958$	12.8313	0.414560
$959$	17.1872	0.555005
$960$	6.39668	0.206452
$961$	−10.4517	−0.337151
$962$	17.3796	0.560340
$963$	−3.58939	−0.115666
$964$	−5.08175	−0.163672
$965$	32.0946	1.03316
$966$	15.2263	0.489898
$967$	−52.5492	−1.68987	−0.844934	−	0.534871i	$-0.820360\pi$
$967$	−52.5492	−1.68987	−0.844934	+	0.534871i	$0.820360\pi$
$968$	−1.01516	−0.0326285
$969$	14.2291	0.457104
$970$	3.46553	0.111272
$971$	57.7795	1.85423	0.927116	−	0.374775i	$-0.122280\pi$
$971$	57.7795	1.85423	0.927116	+	0.374775i	$0.122280\pi$
$972$	−22.0199	−0.706290
$973$	−13.7234	−0.439952
$974$	−38.2597	−1.22592
$975$	5.11234	0.163726
$976$	−1.55831	−0.0498803
$977$	28.5030	0.911892	0.455946	−	0.890007i	$-0.349301\pi$
$977$	28.5030	0.911892	0.455946	+	0.890007i	$0.349301\pi$
$978$	44.4399	1.42103
$979$	41.0708	1.31263
$980$	−14.6960	−0.469446
$981$	−33.4401	−1.06766
$982$	8.44936	0.269630
$983$	16.1638	0.515546	0.257773	−	0.966205i	$-0.417011\pi$
$983$	16.1638	0.515546	0.257773	+	0.966205i	$0.417011\pi$
$984$	−18.4345	−0.587671
$985$	7.93514	0.252835
$986$	−1.10571	−0.0352130
$987$	−27.9349	−0.889179
$988$	9.83253	0.312814
$989$	41.4428	1.31780
$990$	−28.9145	−0.918962
$991$	0.207558	0.00659329	0.00329664	−	0.999995i	$-0.498951\pi$
$991$	0.207558	0.00659329	0.00329664	+	0.999995i	$0.498951\pi$
$992$	4.53303	0.143924
$993$	49.2107	1.56165
$994$	11.2609	0.357175
$995$	18.4792	0.585830
$996$	5.09312	0.161382
$997$	6.19551	0.196214	0.0981069	−	0.995176i	$-0.468721\pi$
$997$	6.19551	0.196214	0.0981069	+	0.995176i	$0.468721\pi$
$998$	0.537695	0.0170204
$999$	17.7021	0.560069

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.w.1.10	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.w.1.10	✓	13	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2006 = 2 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.58918 q^{3} +1.00000 q^{4} +2.47054 q^{5} +2.58918 q^{6} -1.02544 q^{7} +1.00000 q^{8} +3.70384 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.58918 q^{3} +1.00000 q^{4} +2.47054 q^{5} +2.58918 q^{6} -1.02544 q^{7} +1.00000 q^{8} +3.70384 q^{9} +2.47054 q^{10} -3.15988 q^{11} +2.58918 q^{12} +1.78916 q^{13} -1.02544 q^{14} +6.39668 q^{15} +1.00000 q^{16} +1.00000 q^{17} +3.70384 q^{18} +5.49560 q^{19} +2.47054 q^{20} -2.65504 q^{21} -3.15988 q^{22} -5.73487 q^{23} +2.58918 q^{24} +1.10359 q^{25} +1.78916 q^{26} +1.82236 q^{27} -1.02544 q^{28} -1.10571 q^{29} +6.39668 q^{30} +4.53303 q^{31} +1.00000 q^{32} -8.18149 q^{33} +1.00000 q^{34} -2.53339 q^{35} +3.70384 q^{36} +9.71380 q^{37} +5.49560 q^{38} +4.63246 q^{39} +2.47054 q^{40} -7.11984 q^{41} -2.65504 q^{42} -7.22645 q^{43} -3.15988 q^{44} +9.15050 q^{45} -5.73487 q^{46} +10.5215 q^{47} +2.58918 q^{48} -5.94848 q^{49} +1.10359 q^{50} +2.58918 q^{51} +1.78916 q^{52} -10.3913 q^{53} +1.82236 q^{54} -7.80662 q^{55} -1.02544 q^{56} +14.2291 q^{57} -1.10571 q^{58} +1.00000 q^{59} +6.39668 q^{60} -1.55831 q^{61} +4.53303 q^{62} -3.79805 q^{63} +1.00000 q^{64} +4.42021 q^{65} -8.18149 q^{66} +11.3522 q^{67} +1.00000 q^{68} -14.8486 q^{69} -2.53339 q^{70} -10.9816 q^{71} +3.70384 q^{72} +4.88344 q^{73} +9.71380 q^{74} +2.85739 q^{75} +5.49560 q^{76} +3.24026 q^{77} +4.63246 q^{78} +11.9072 q^{79} +2.47054 q^{80} -6.39309 q^{81} -7.11984 q^{82} +1.96708 q^{83} -2.65504 q^{84} +2.47054 q^{85} -7.22645 q^{86} -2.86288 q^{87} -3.15988 q^{88} -12.9976 q^{89} +9.15050 q^{90} -1.83467 q^{91} -5.73487 q^{92} +11.7368 q^{93} +10.5215 q^{94} +13.5771 q^{95} +2.58918 q^{96} +1.40274 q^{97} -5.94848 q^{98} -11.7037 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9	\( 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9} + q^{10} + 13 q^{11} + 7 q^{12} + 9 q^{13} + 8 q^{14} - 9 q^{15} + 13 q^{16} + 13 q^{17} + 16 q^{18} + 16 q^{19} + q^{20} - 3 q^{21} + 13 q^{22} + 18 q^{23} + 7 q^{24} + 14 q^{25} + 9 q^{26} + 10 q^{27} + 8 q^{28} + 8 q^{29} - 9 q^{30} + 32 q^{31} + 13 q^{32} + 13 q^{33} + 13 q^{34} - q^{35} + 16 q^{36} - 3 q^{37} + 16 q^{38} + 20 q^{39} + q^{40} + 24 q^{41} - 3 q^{42} - 2 q^{43} + 13 q^{44} - 3 q^{45} + 18 q^{46} + 26 q^{47} + 7 q^{48} + 23 q^{49} + 14 q^{50} + 7 q^{51} + 9 q^{52} - 27 q^{53} + 10 q^{54} - 7 q^{55} + 8 q^{56} - 21 q^{57} + 8 q^{58} + 13 q^{59} - 9 q^{60} + 20 q^{61} + 32 q^{62} - 3 q^{63} + 13 q^{64} + 16 q^{65} + 13 q^{66} + 4 q^{67} + 13 q^{68} - 2 q^{69} - q^{70} - 8 q^{71} + 16 q^{72} + 10 q^{73} - 3 q^{74} + 39 q^{75} + 16 q^{76} - 15 q^{77} + 20 q^{78} + 35 q^{79} + q^{80} + 29 q^{81} + 24 q^{82} - q^{83} - 3 q^{84} + q^{85} - 2 q^{86} - 32 q^{87} + 13 q^{88} - 20 q^{89} - 3 q^{90} - 15 q^{91} + 18 q^{92} - 7 q^{93} + 26 q^{94} - 3 q^{95} + 7 q^{96} - 3 q^{97} + 23 q^{98} + 65 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9 + q^10 + 13 * q^11 + 7 * q^12 + 9 * q^13 + 8 * q^14 - 9 * q^15 + 13 * q^16 + 13 * q^17 + 16 * q^18 + 16 * q^19 + q^20 - 3 * q^21 + 13 * q^22 + 18 * q^23 + 7 * q^24 + 14 * q^25 + 9 * q^26 + 10 * q^27 + 8 * q^28 + 8 * q^29 - 9 * q^30 + 32 * q^31 + 13 * q^32 + 13 * q^33 + 13 * q^34 - q^35 + 16 * q^36 - 3 * q^37 + 16 * q^38 + 20 * q^39 + q^40 + 24 * q^41 - 3 * q^42 - 2 * q^43 + 13 * q^44 - 3 * q^45 + 18 * q^46 + 26 * q^47 + 7 * q^48 + 23 * q^49 + 14 * q^50 + 7 * q^51 + 9 * q^52 - 27 * q^53 + 10 * q^54 - 7 * q^55 + 8 * q^56 - 21 * q^57 + 8 * q^58 + 13 * q^59 - 9 * q^60 + 20 * q^61 + 32 * q^62 - 3 * q^63 + 13 * q^64 + 16 * q^65 + 13 * q^66 + 4 * q^67 + 13 * q^68 - 2 * q^69 - q^70 - 8 * q^71 + 16 * q^72 + 10 * q^73 - 3 * q^74 + 39 * q^75 + 16 * q^76 - 15 * q^77 + 20 * q^78 + 35 * q^79 + q^80 + 29 * q^81 + 24 * q^82 - q^83 - 3 * q^84 + q^85 - 2 * q^86 - 32 * q^87 + 13 * q^88 - 20 * q^89 - 3 * q^90 - 15 * q^91 + 18 * q^92 - 7 * q^93 + 26 * q^94 - 3 * q^95 + 7 * q^96 - 3 * q^97 + 23 * q^98 + 65 * q^99

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