LMFDB - Embedded newform 6018.2.a.bb.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
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} - 4 x^{12} - 41 x^{11} + 179 x^{10} + 540 x^{9} - 2773 x^{8} - 2260 x^{7} + 17621 x^{6} + \cdots + 128 $ x^13 - 4x^12 - 41x^11 + 179x^10 + 540x^9 - 2773x^8 - 2260x^7 + 17621x^6 - 838x^5 - 44478x^4 + 16472x^3 + 29944x^2 - 6856x + 128
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-4.21367$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.21367 q^{5} +1.00000 q^{6} +1.46512 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.21367 q^{5} +1.00000 q^{6} +1.46512 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.21367 q^{10} +2.34927 q^{11} +1.00000 q^{12} -5.14252 q^{13} +1.46512 q^{14} -4.21367 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +3.77047 q^{19} -4.21367 q^{20} +1.46512 q^{21} +2.34927 q^{22} +0.976527 q^{23} +1.00000 q^{24} +12.7551 q^{25} -5.14252 q^{26} +1.00000 q^{27} +1.46512 q^{28} -1.57264 q^{29} -4.21367 q^{30} -8.54603 q^{31} +1.00000 q^{32} +2.34927 q^{33} +1.00000 q^{34} -6.17355 q^{35} +1.00000 q^{36} +1.17725 q^{37} +3.77047 q^{38} -5.14252 q^{39} -4.21367 q^{40} +8.81213 q^{41} +1.46512 q^{42} +5.09941 q^{43} +2.34927 q^{44} -4.21367 q^{45} +0.976527 q^{46} -2.66349 q^{47} +1.00000 q^{48} -4.85342 q^{49} +12.7551 q^{50} +1.00000 q^{51} -5.14252 q^{52} +8.01977 q^{53} +1.00000 q^{54} -9.89905 q^{55} +1.46512 q^{56} +3.77047 q^{57} -1.57264 q^{58} -1.00000 q^{59} -4.21367 q^{60} +9.05698 q^{61} -8.54603 q^{62} +1.46512 q^{63} +1.00000 q^{64} +21.6689 q^{65} +2.34927 q^{66} -1.84238 q^{67} +1.00000 q^{68} +0.976527 q^{69} -6.17355 q^{70} +3.02124 q^{71} +1.00000 q^{72} -12.2860 q^{73} +1.17725 q^{74} +12.7551 q^{75} +3.77047 q^{76} +3.44196 q^{77} -5.14252 q^{78} -11.8546 q^{79} -4.21367 q^{80} +1.00000 q^{81} +8.81213 q^{82} +5.37381 q^{83} +1.46512 q^{84} -4.21367 q^{85} +5.09941 q^{86} -1.57264 q^{87} +2.34927 q^{88} +17.0732 q^{89} -4.21367 q^{90} -7.53442 q^{91} +0.976527 q^{92} -8.54603 q^{93} -2.66349 q^{94} -15.8876 q^{95} +1.00000 q^{96} +2.69494 q^{97} -4.85342 q^{98} +2.34927 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9} + 4 q^{10} + 7 q^{11} + 13 q^{12} + 6 q^{13} + 11 q^{14} + 4 q^{15} + 13 q^{16} + 13 q^{17} + 13 q^{18} + 9 q^{19} + 4 q^{20} + 11 q^{21} + 7 q^{22} + 2 q^{23} + 13 q^{24} + 33 q^{25} + 6 q^{26} + 13 q^{27} + 11 q^{28} + 14 q^{29} + 4 q^{30} - 5 q^{31} + 13 q^{32} + 7 q^{33} + 13 q^{34} + 24 q^{35} + 13 q^{36} + 4 q^{37} + 9 q^{38} + 6 q^{39} + 4 q^{40} + 28 q^{41} + 11 q^{42} + q^{43} + 7 q^{44} + 4 q^{45} + 2 q^{46} + 12 q^{47} + 13 q^{48} + 32 q^{49} + 33 q^{50} + 13 q^{51} + 6 q^{52} + 22 q^{53} + 13 q^{54} - 7 q^{55} + 11 q^{56} + 9 q^{57} + 14 q^{58} - 13 q^{59} + 4 q^{60} - 9 q^{61} - 5 q^{62} + 11 q^{63} + 13 q^{64} + 34 q^{65} + 7 q^{66} + 26 q^{67} + 13 q^{68} + 2 q^{69} + 24 q^{70} + 8 q^{71} + 13 q^{72} + 4 q^{73} + 4 q^{74} + 33 q^{75} + 9 q^{76} + 38 q^{77} + 6 q^{78} - 17 q^{79} + 4 q^{80} + 13 q^{81} + 28 q^{82} + 14 q^{83} + 11 q^{84} + 4 q^{85} + q^{86} + 14 q^{87} + 7 q^{88} + 19 q^{89} + 4 q^{90} - 5 q^{91} + 2 q^{92} - 5 q^{93} + 12 q^{94} + 25 q^{95} + 13 q^{96} - 5 q^{97} + 32 q^{98} + 7 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9 + 4 * q^10 + 7 * q^11 + 13 * q^12 + 6 * q^13 + 11 * q^14 + 4 * q^15 + 13 * q^16 + 13 * q^17 + 13 * q^18 + 9 * q^19 + 4 * q^20 + 11 * q^21 + 7 * q^22 + 2 * q^23 + 13 * q^24 + 33 * q^25 + 6 * q^26 + 13 * q^27 + 11 * q^28 + 14 * q^29 + 4 * q^30 - 5 * q^31 + 13 * q^32 + 7 * q^33 + 13 * q^34 + 24 * q^35 + 13 * q^36 + 4 * q^37 + 9 * q^38 + 6 * q^39 + 4 * q^40 + 28 * q^41 + 11 * q^42 + q^43 + 7 * q^44 + 4 * q^45 + 2 * q^46 + 12 * q^47 + 13 * q^48 + 32 * q^49 + 33 * q^50 + 13 * q^51 + 6 * q^52 + 22 * q^53 + 13 * q^54 - 7 * q^55 + 11 * q^56 + 9 * q^57 + 14 * q^58 - 13 * q^59 + 4 * q^60 - 9 * q^61 - 5 * q^62 + 11 * q^63 + 13 * q^64 + 34 * q^65 + 7 * q^66 + 26 * q^67 + 13 * q^68 + 2 * q^69 + 24 * q^70 + 8 * q^71 + 13 * q^72 + 4 * q^73 + 4 * q^74 + 33 * q^75 + 9 * q^76 + 38 * q^77 + 6 * q^78 - 17 * q^79 + 4 * q^80 + 13 * q^81 + 28 * q^82 + 14 * q^83 + 11 * q^84 + 4 * q^85 + q^86 + 14 * q^87 + 7 * q^88 + 19 * q^89 + 4 * q^90 - 5 * q^91 + 2 * q^92 - 5 * q^93 + 12 * q^94 + 25 * q^95 + 13 * q^96 - 5 * q^97 + 32 * q^98 + 7 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−4.21367	−1.88441	−0.942206	−	0.335033i	$-0.891252\pi$
$5$	−4.21367	−1.88441	−0.942206	+	0.335033i	$0.891252\pi$
$6$	1.00000	0.408248
$7$	1.46512	0.553764	0.276882	−	0.960904i	$-0.410699\pi$
$7$	1.46512	0.553764	0.276882	+	0.960904i	$0.410699\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−4.21367	−1.33248
$11$	2.34927	0.708331	0.354165	−	0.935183i	$-0.384765\pi$
$11$	2.34927	0.708331	0.354165	+	0.935183i	$0.384765\pi$
$12$	1.00000	0.288675
$13$	−5.14252	−1.42628	−0.713139	−	0.701023i	$-0.752727\pi$
$13$	−5.14252	−1.42628	−0.713139	+	0.701023i	$0.752727\pi$
$14$	1.46512	0.391570
$15$	−4.21367	−1.08797
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	3.77047	0.865006	0.432503	−	0.901632i	$-0.357630\pi$
$19$	3.77047	0.865006	0.432503	+	0.901632i	$0.357630\pi$
$20$	−4.21367	−0.942206
$21$	1.46512	0.319716
$22$	2.34927	0.500865
$23$	0.976527	0.203620	0.101810	−	0.994804i	$-0.467537\pi$
$23$	0.976527	0.203620	0.101810	+	0.994804i	$0.467537\pi$
$24$	1.00000	0.204124
$25$	12.7551	2.55101
$26$	−5.14252	−1.00853
$27$	1.00000	0.192450
$28$	1.46512	0.276882
$29$	−1.57264	−0.292032	−0.146016	−	0.989282i	$-0.546645\pi$
$29$	−1.57264	−0.292032	−0.146016	+	0.989282i	$0.546645\pi$
$30$	−4.21367	−0.769308
$31$	−8.54603	−1.53491	−0.767456	−	0.641102i	$-0.778478\pi$
$31$	−8.54603	−1.53491	−0.767456	+	0.641102i	$0.778478\pi$
$32$	1.00000	0.176777
$33$	2.34927	0.408955
$34$	1.00000	0.171499
$35$	−6.17355	−1.04352
$36$	1.00000	0.166667
$37$	1.17725	0.193538	0.0967691	−	0.995307i	$-0.469149\pi$
$37$	1.17725	0.193538	0.0967691	+	0.995307i	$0.469149\pi$
$38$	3.77047	0.611652
$39$	−5.14252	−0.823462
$40$	−4.21367	−0.666240
$41$	8.81213	1.37622	0.688112	−	0.725605i	$-0.258440\pi$
$41$	8.81213	1.37622	0.688112	+	0.725605i	$0.258440\pi$
$42$	1.46512	0.226073
$43$	5.09941	0.777652	0.388826	−	0.921311i	$-0.372881\pi$
$43$	5.09941	0.777652	0.388826	+	0.921311i	$0.372881\pi$
$44$	2.34927	0.354165
$45$	−4.21367	−0.628138
$46$	0.976527	0.143981
$47$	−2.66349	−0.388510	−0.194255	−	0.980951i	$-0.562229\pi$
$47$	−2.66349	−0.388510	−0.194255	+	0.980951i	$0.562229\pi$
$48$	1.00000	0.144338
$49$	−4.85342	−0.693345
$50$	12.7551	1.80384
$51$	1.00000	0.140028
$52$	−5.14252	−0.713139
$53$	8.01977	1.10160	0.550800	−	0.834637i	$-0.314323\pi$
$53$	8.01977	1.10160	0.550800	+	0.834637i	$0.314323\pi$
$54$	1.00000	0.136083
$55$	−9.89905	−1.33479
$56$	1.46512	0.195785
$57$	3.77047	0.499411
$58$	−1.57264	−0.206498
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−4.21367	−0.543983
$61$	9.05698	1.15963	0.579814	−	0.814749i	$-0.303125\pi$
$61$	9.05698	1.15963	0.579814	+	0.814749i	$0.303125\pi$
$62$	−8.54603	−1.08535
$63$	1.46512	0.184588
$64$	1.00000	0.125000
$65$	21.6689	2.68770
$66$	2.34927	0.289175
$67$	−1.84238	−0.225083	−0.112541	−	0.993647i	$-0.535899\pi$
$67$	−1.84238	−0.225083	−0.112541	+	0.993647i	$0.535899\pi$
$68$	1.00000	0.121268
$69$	0.976527	0.117560
$70$	−6.17355	−0.737880
$71$	3.02124	0.358556	0.179278	−	0.983798i	$-0.442624\pi$
$71$	3.02124	0.358556	0.179278	+	0.983798i	$0.442624\pi$
$72$	1.00000	0.117851
$73$	−12.2860	−1.43797	−0.718983	−	0.695028i	$-0.755392\pi$
$73$	−12.2860	−1.43797	−0.718983	+	0.695028i	$0.755392\pi$
$74$	1.17725	0.136852
$75$	12.7551	1.47283
$76$	3.77047	0.432503
$77$	3.44196	0.392248
$78$	−5.14252	−0.582275
$79$	−11.8546	−1.33375	−0.666876	−	0.745169i	$-0.732369\pi$
$79$	−11.8546	−1.33375	−0.666876	+	0.745169i	$0.732369\pi$
$80$	−4.21367	−0.471103
$81$	1.00000	0.111111
$82$	8.81213	0.973137
$83$	5.37381	0.589852	0.294926	−	0.955520i	$-0.404705\pi$
$83$	5.37381	0.589852	0.294926	+	0.955520i	$0.404705\pi$
$84$	1.46512	0.159858
$85$	−4.21367	−0.457037
$86$	5.09941	0.549883
$87$	−1.57264	−0.168605
$88$	2.34927	0.250433
$89$	17.0732	1.80976	0.904878	−	0.425670i	$-0.139962\pi$
$89$	17.0732	1.80976	0.904878	+	0.425670i	$0.139962\pi$
$90$	−4.21367	−0.444160
$91$	−7.53442	−0.789821
$92$	0.976527	0.101810
$93$	−8.54603	−0.886182
$94$	−2.66349	−0.274718
$95$	−15.8876	−1.63003
$96$	1.00000	0.102062
$97$	2.69494	0.273629	0.136815	−	0.990597i	$-0.456313\pi$
$97$	2.69494	0.273629	0.136815	+	0.990597i	$0.456313\pi$
$98$	−4.85342	−0.490269
$99$	2.34927	0.236110
$100$	12.7551	1.27551
$101$	−4.80419	−0.478034	−0.239017	−	0.971015i	$-0.576825\pi$
$101$	−4.80419	−0.478034	−0.239017	+	0.971015i	$0.576825\pi$
$102$	1.00000	0.0990148
$103$	11.1649	1.10011	0.550055	−	0.835129i	$-0.314607\pi$
$103$	11.1649	1.10011	0.550055	+	0.835129i	$0.314607\pi$
$104$	−5.14252	−0.504265
$105$	−6.17355	−0.602477
$106$	8.01977	0.778949
$107$	19.5382	1.88883	0.944413	−	0.328760i	$-0.106631\pi$
$107$	19.5382	1.88883	0.944413	+	0.328760i	$0.106631\pi$
$108$	1.00000	0.0962250
$109$	17.2953	1.65658	0.828292	−	0.560296i	$-0.189313\pi$
$109$	17.2953	1.65658	0.828292	+	0.560296i	$0.189313\pi$
$110$	−9.89905	−0.943837
$111$	1.17725	0.111739
$112$	1.46512	0.138441
$113$	15.1734	1.42739	0.713697	−	0.700455i	$-0.247019\pi$
$113$	15.1734	1.42739	0.713697	+	0.700455i	$0.247019\pi$
$114$	3.77047	0.353137
$115$	−4.11477	−0.383704
$116$	−1.57264	−0.146016
$117$	−5.14252	−0.475426
$118$	−1.00000	−0.0920575
$119$	1.46512	0.134308
$120$	−4.21367	−0.384654
$121$	−5.48095	−0.498268
$122$	9.05698	0.819980
$123$	8.81213	0.794563
$124$	−8.54603	−0.767456
$125$	−32.6773	−2.92274
$126$	1.46512	0.130523
$127$	19.4432	1.72530	0.862652	−	0.505798i	$-0.168802\pi$
$127$	19.4432	1.72530	0.862652	+	0.505798i	$0.168802\pi$
$128$	1.00000	0.0883883
$129$	5.09941	0.448978
$130$	21.6689	1.90049
$131$	14.8066	1.29366	0.646829	−	0.762635i	$-0.276095\pi$
$131$	14.8066	1.29366	0.646829	+	0.762635i	$0.276095\pi$
$132$	2.34927	0.204477
$133$	5.52421	0.479009
$134$	−1.84238	−0.159157
$135$	−4.21367	−0.362655
$136$	1.00000	0.0857493
$137$	−6.13571	−0.524209	−0.262105	−	0.965039i	$-0.584417\pi$
$137$	−6.13571	−0.524209	−0.262105	+	0.965039i	$0.584417\pi$
$138$	0.976527	0.0831275
$139$	14.4847	1.22858	0.614289	−	0.789081i	$-0.289443\pi$
$139$	14.4847	1.22858	0.614289	+	0.789081i	$0.289443\pi$
$140$	−6.17355	−0.521760
$141$	−2.66349	−0.224306
$142$	3.02124	0.253537
$143$	−12.0811	−1.01028
$144$	1.00000	0.0833333
$145$	6.62660	0.550309
$146$	−12.2860	−1.01680
$147$	−4.85342	−0.400303
$148$	1.17725	0.0967691
$149$	−2.15518	−0.176560	−0.0882798	−	0.996096i	$-0.528137\pi$
$149$	−2.15518	−0.176560	−0.0882798	+	0.996096i	$0.528137\pi$
$150$	12.7551	1.04145
$151$	−0.183913	−0.0149666	−0.00748331	−	0.999972i	$-0.502382\pi$
$151$	−0.183913	−0.0149666	−0.00748331	+	0.999972i	$0.502382\pi$
$152$	3.77047	0.305826
$153$	1.00000	0.0808452
$154$	3.44196	0.277361
$155$	36.0102	2.89241
$156$	−5.14252	−0.411731
$157$	−5.67036	−0.452544	−0.226272	−	0.974064i	$-0.572654\pi$
$157$	−5.67036	−0.452544	−0.226272	+	0.974064i	$0.572654\pi$
$158$	−11.8546	−0.943104
$159$	8.01977	0.636010
$160$	−4.21367	−0.333120
$161$	1.43073	0.112757
$162$	1.00000	0.0785674
$163$	3.21209	0.251591	0.125795	−	0.992056i	$-0.459852\pi$
$163$	3.21209	0.251591	0.125795	+	0.992056i	$0.459852\pi$
$164$	8.81213	0.688112
$165$	−9.89905	−0.770640
$166$	5.37381	0.417089
$167$	12.2561	0.948408	0.474204	−	0.880415i	$-0.342736\pi$
$167$	12.2561	0.948408	0.474204	+	0.880415i	$0.342736\pi$
$168$	1.46512	0.113037
$169$	13.4455	1.03427
$170$	−4.21367	−0.323174
$171$	3.77047	0.288335
$172$	5.09941	0.388826
$173$	−8.63903	−0.656814	−0.328407	−	0.944536i	$-0.606512\pi$
$173$	−8.63903	−0.656814	−0.328407	+	0.944536i	$0.606512\pi$
$174$	−1.57264	−0.119222
$175$	18.6877	1.41266
$176$	2.34927	0.177083
$177$	−1.00000	−0.0751646
$178$	17.0732	1.27969
$179$	13.7718	1.02935	0.514675	−	0.857385i	$-0.327913\pi$
$179$	13.7718	1.02935	0.514675	+	0.857385i	$0.327913\pi$
$180$	−4.21367	−0.314069
$181$	6.46338	0.480420	0.240210	−	0.970721i	$-0.422784\pi$
$181$	6.46338	0.480420	0.240210	+	0.970721i	$0.422784\pi$
$182$	−7.53442	−0.558488
$183$	9.05698	0.669511
$184$	0.976527	0.0719905
$185$	−4.96054	−0.364706
$186$	−8.54603	−0.626625
$187$	2.34927	0.171795
$188$	−2.66349	−0.194255
$189$	1.46512	0.106572
$190$	−15.8876	−1.15260
$191$	22.3517	1.61731	0.808657	−	0.588280i	$-0.200195\pi$
$191$	22.3517	1.61731	0.808657	+	0.588280i	$0.200195\pi$
$192$	1.00000	0.0721688
$193$	−18.7283	−1.34809	−0.674046	−	0.738689i	$-0.735445\pi$
$193$	−18.7283	−1.34809	−0.674046	+	0.738689i	$0.735445\pi$
$194$	2.69494	0.193485
$195$	21.6689	1.55174
$196$	−4.85342	−0.346673
$197$	−23.3864	−1.66621	−0.833105	−	0.553115i	$-0.813439\pi$
$197$	−23.3864	−1.66621	−0.833105	+	0.553115i	$0.813439\pi$
$198$	2.34927	0.166955
$199$	−18.4041	−1.30463	−0.652315	−	0.757948i	$-0.726202\pi$
$199$	−18.4041	−1.30463	−0.652315	+	0.757948i	$0.726202\pi$
$200$	12.7551	0.901919
$201$	−1.84238	−0.129952
$202$	−4.80419	−0.338021
$203$	−2.30411	−0.161717
$204$	1.00000	0.0700140
$205$	−37.1314	−2.59337
$206$	11.1649	0.777895
$207$	0.976527	0.0678733
$208$	−5.14252	−0.356569
$209$	8.85785	0.612710
$210$	−6.17355	−0.426015
$211$	−5.77830	−0.397795	−0.198897	−	0.980020i	$-0.563736\pi$
$211$	−5.77830	−0.397795	−0.198897	+	0.980020i	$0.563736\pi$
$212$	8.01977	0.550800
$213$	3.02124	0.207012
$214$	19.5382	1.33560
$215$	−21.4872	−1.46542
$216$	1.00000	0.0680414
$217$	−12.5210	−0.849979
$218$	17.2953	1.17138
$219$	−12.2860	−0.830210
$220$	−9.89905	−0.667393
$221$	−5.14252	−0.345923
$222$	1.17725	0.0790117
$223$	9.81570	0.657308	0.328654	−	0.944450i	$-0.393405\pi$
$223$	9.81570	0.657308	0.328654	+	0.944450i	$0.393405\pi$
$224$	1.46512	0.0978926
$225$	12.7551	0.850337
$226$	15.1734	1.00932
$227$	17.7579	1.17863	0.589317	−	0.807902i	$-0.299397\pi$
$227$	17.7579	1.17863	0.589317	+	0.807902i	$0.299397\pi$
$228$	3.77047	0.249706
$229$	12.3852	0.818437	0.409218	−	0.912436i	$-0.365801\pi$
$229$	12.3852	0.818437	0.409218	+	0.912436i	$0.365801\pi$
$230$	−4.11477	−0.271320
$231$	3.44196	0.226465
$232$	−1.57264	−0.103249
$233$	−0.349336	−0.0228857	−0.0114429	−	0.999935i	$-0.503642\pi$
$233$	−0.349336	−0.0228857	−0.0114429	+	0.999935i	$0.503642\pi$
$234$	−5.14252	−0.336177
$235$	11.2231	0.732113
$236$	−1.00000	−0.0650945
$237$	−11.8546	−0.770042
$238$	1.46512	0.0949698
$239$	−19.7387	−1.27679	−0.638394	−	0.769709i	$-0.720401\pi$
$239$	−19.7387	−1.27679	−0.638394	+	0.769709i	$0.720401\pi$
$240$	−4.21367	−0.271992
$241$	−14.1617	−0.912238	−0.456119	−	0.889919i	$-0.650761\pi$
$241$	−14.1617	−0.912238	−0.456119	+	0.889919i	$0.650761\pi$
$242$	−5.48095	−0.352329
$243$	1.00000	0.0641500
$244$	9.05698	0.579814
$245$	20.4507	1.30655
$246$	8.81213	0.561841
$247$	−19.3897	−1.23374
$248$	−8.54603	−0.542673
$249$	5.37381	0.340551
$250$	−32.6773	−2.06669
$251$	−30.3362	−1.91480	−0.957402	−	0.288758i	$-0.906758\pi$
$251$	−30.3362	−1.91480	−0.957402	+	0.288758i	$0.906758\pi$
$252$	1.46512	0.0922940
$253$	2.29412	0.144230
$254$	19.4432	1.21997
$255$	−4.21367	−0.263871
$256$	1.00000	0.0625000
$257$	13.3150	0.830566	0.415283	−	0.909692i	$-0.363683\pi$
$257$	13.3150	0.830566	0.415283	+	0.909692i	$0.363683\pi$
$258$	5.09941	0.317475
$259$	1.72481	0.107175
$260$	21.6689	1.34385
$261$	−1.57264	−0.0973440
$262$	14.8066	0.914755
$263$	1.55696	0.0960060	0.0480030	−	0.998847i	$-0.484714\pi$
$263$	1.55696	0.0960060	0.0480030	+	0.998847i	$0.484714\pi$
$264$	2.34927	0.144587
$265$	−33.7927	−2.07587
$266$	5.52421	0.338711
$267$	17.0732	1.04486
$268$	−1.84238	−0.112541
$269$	−23.4522	−1.42991	−0.714953	−	0.699172i	$-0.753552\pi$
$269$	−23.4522	−1.42991	−0.714953	+	0.699172i	$0.753552\pi$
$270$	−4.21367	−0.256436
$271$	7.68374	0.466754	0.233377	−	0.972386i	$-0.425022\pi$
$271$	7.68374	0.466754	0.233377	+	0.972386i	$0.425022\pi$
$272$	1.00000	0.0606339
$273$	−7.53442	−0.456004
$274$	−6.13571	−0.370672
$275$	29.9650	1.80696
$276$	0.976527	0.0587800
$277$	22.3715	1.34417	0.672087	−	0.740472i	$-0.265398\pi$
$277$	22.3715	1.34417	0.672087	+	0.740472i	$0.265398\pi$
$278$	14.4847	0.868735
$279$	−8.54603	−0.511637
$280$	−6.17355	−0.368940
$281$	26.7158	1.59373	0.796866	−	0.604156i	$-0.206490\pi$
$281$	26.7158	1.59373	0.796866	+	0.604156i	$0.206490\pi$
$282$	−2.66349	−0.158609
$283$	−23.3907	−1.39043	−0.695217	−	0.718800i	$-0.744692\pi$
$283$	−23.3907	−1.39043	−0.695217	+	0.718800i	$0.744692\pi$
$284$	3.02124	0.179278
$285$	−15.8876	−0.941097
$286$	−12.0811	−0.714373
$287$	12.9108	0.762103
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	6.62660	0.389127
$291$	2.69494	0.157980
$292$	−12.2860	−0.718983
$293$	15.0828	0.881147	0.440574	−	0.897716i	$-0.354775\pi$
$293$	15.0828	0.881147	0.440574	+	0.897716i	$0.354775\pi$
$294$	−4.85342	−0.283057
$295$	4.21367	0.245330
$296$	1.17725	0.0684261
$297$	2.34927	0.136318
$298$	−2.15518	−0.124846
$299$	−5.02181	−0.290419
$300$	12.7551	0.736413
$301$	7.47126	0.430636
$302$	−0.183913	−0.0105830
$303$	−4.80419	−0.275993
$304$	3.77047	0.216251
$305$	−38.1632	−2.18522
$306$	1.00000	0.0571662
$307$	−10.5871	−0.604237	−0.302119	−	0.953270i	$-0.597694\pi$
$307$	−10.5871	−0.604237	−0.302119	+	0.953270i	$0.597694\pi$
$308$	3.44196	0.196124
$309$	11.1649	0.635148
$310$	36.0102	2.04524
$311$	−9.22088	−0.522868	−0.261434	−	0.965221i	$-0.584195\pi$
$311$	−9.22088	−0.522868	−0.261434	+	0.965221i	$0.584195\pi$
$312$	−5.14252	−0.291138
$313$	−19.3753	−1.09516	−0.547578	−	0.836755i	$-0.684450\pi$
$313$	−19.3753	−1.09516	−0.547578	+	0.836755i	$0.684450\pi$
$314$	−5.67036	−0.319997
$315$	−6.17355	−0.347840
$316$	−11.8546	−0.666876
$317$	−16.1831	−0.908932	−0.454466	−	0.890764i	$-0.650170\pi$
$317$	−16.1831	−0.908932	−0.454466	+	0.890764i	$0.650170\pi$
$318$	8.01977	0.449727
$319$	−3.69455	−0.206855
$320$	−4.21367	−0.235552
$321$	19.5382	1.09051
$322$	1.43073	0.0797316
$323$	3.77047	0.209795
$324$	1.00000	0.0555556
$325$	−65.5931	−3.63845
$326$	3.21209	0.177901
$327$	17.2953	0.956430
$328$	8.81213	0.486568
$329$	−3.90234	−0.215143
$330$	−9.89905	−0.544924
$331$	10.0269	0.551130	0.275565	−	0.961282i	$-0.411135\pi$
$331$	10.0269	0.551130	0.275565	+	0.961282i	$0.411135\pi$
$332$	5.37381	0.294926
$333$	1.17725	0.0645128
$334$	12.2561	0.670626
$335$	7.76319	0.424149
$336$	1.46512	0.0799290
$337$	−9.98793	−0.544077	−0.272039	−	0.962286i	$-0.587698\pi$
$337$	−9.98793	−0.544077	−0.272039	+	0.962286i	$0.587698\pi$
$338$	13.4455	0.731338
$339$	15.1734	0.824106
$340$	−4.21367	−0.228519
$341$	−20.0769	−1.08722
$342$	3.77047	0.203884
$343$	−17.3667	−0.937714
$344$	5.09941	0.274942
$345$	−4.11477	−0.221532
$346$	−8.63903	−0.464437
$347$	3.70851	0.199083	0.0995417	−	0.995033i	$-0.468262\pi$
$347$	3.70851	0.199083	0.0995417	+	0.995033i	$0.468262\pi$
$348$	−1.57264	−0.0843024
$349$	6.02341	0.322426	0.161213	−	0.986920i	$-0.448459\pi$
$349$	6.02341	0.322426	0.161213	+	0.986920i	$0.448459\pi$
$350$	18.6877	0.998900
$351$	−5.14252	−0.274487
$352$	2.34927	0.125216
$353$	16.5147	0.878987	0.439494	−	0.898246i	$-0.355158\pi$
$353$	16.5147	0.878987	0.439494	+	0.898246i	$0.355158\pi$
$354$	−1.00000	−0.0531494
$355$	−12.7305	−0.675667
$356$	17.0732	0.904878
$357$	1.46512	0.0775425
$358$	13.7718	0.727860
$359$	18.5478	0.978915	0.489457	−	0.872027i	$-0.337195\pi$
$359$	18.5478	0.978915	0.489457	+	0.872027i	$0.337195\pi$
$360$	−4.21367	−0.222080
$361$	−4.78353	−0.251765
$362$	6.46338	0.339708
$363$	−5.48095	−0.287675
$364$	−7.53442	−0.394911
$365$	51.7692	2.70972
$366$	9.05698	0.473416
$367$	14.8278	0.774006	0.387003	−	0.922078i	$-0.373510\pi$
$367$	14.8278	0.774006	0.387003	+	0.922078i	$0.373510\pi$
$368$	0.976527	0.0509050
$369$	8.81213	0.458741
$370$	−4.96054	−0.257886
$371$	11.7500	0.610027
$372$	−8.54603	−0.443091
$373$	10.6468	0.551270	0.275635	−	0.961262i	$-0.411112\pi$
$373$	10.6468	0.551270	0.275635	+	0.961262i	$0.411112\pi$
$374$	2.34927	0.121478
$375$	−32.6773	−1.68745
$376$	−2.66349	−0.137359
$377$	8.08733	0.416519
$378$	1.46512	0.0753578
$379$	−18.8948	−0.970563	−0.485282	−	0.874358i	$-0.661283\pi$
$379$	−18.8948	−0.970563	−0.485282	+	0.874358i	$0.661283\pi$
$380$	−15.8876	−0.815014
$381$	19.4432	0.996105
$382$	22.3517	1.14361
$383$	20.9377	1.06987	0.534933	−	0.844894i	$-0.320337\pi$
$383$	20.9377	1.06987	0.534933	+	0.844894i	$0.320337\pi$
$384$	1.00000	0.0510310
$385$	−14.5033	−0.739157
$386$	−18.7283	−0.953246
$387$	5.09941	0.259217
$388$	2.69494	0.136815
$389$	18.7037	0.948314	0.474157	−	0.880440i	$-0.342753\pi$
$389$	18.7037	0.948314	0.474157	+	0.880440i	$0.342753\pi$
$390$	21.6689	1.09725
$391$	0.976527	0.0493851
$392$	−4.85342	−0.245135
$393$	14.8066	0.746894
$394$	−23.3864	−1.17819
$395$	49.9516	2.51334
$396$	2.34927	0.118055
$397$	−6.12137	−0.307223	−0.153611	−	0.988131i	$-0.549090\pi$
$397$	−6.12137	−0.307223	−0.153611	+	0.988131i	$0.549090\pi$
$398$	−18.4041	−0.922512
$399$	5.52421	0.276556
$400$	12.7551	0.637753
$401$	14.7263	0.735394	0.367697	−	0.929946i	$-0.380146\pi$
$401$	14.7263	0.735394	0.367697	+	0.929946i	$0.380146\pi$
$402$	−1.84238	−0.0918896
$403$	43.9481	2.18921
$404$	−4.80419	−0.239017
$405$	−4.21367	−0.209379
$406$	−2.30411	−0.114351
$407$	2.76567	0.137089
$408$	1.00000	0.0495074
$409$	−18.7827	−0.928745	−0.464372	−	0.885640i	$-0.653720\pi$
$409$	−18.7827	−0.928745	−0.464372	+	0.885640i	$0.653720\pi$
$410$	−37.1314	−1.83379
$411$	−6.13571	−0.302652
$412$	11.1649	0.550055
$413$	−1.46512	−0.0720940
$414$	0.976527	0.0479937
$415$	−22.6435	−1.11153
$416$	−5.14252	−0.252133
$417$	14.4847	0.709320
$418$	8.85785	0.433251
$419$	−21.0778	−1.02972	−0.514859	−	0.857275i	$-0.672156\pi$
$419$	−21.0778	−1.02972	−0.514859	+	0.857275i	$0.672156\pi$
$420$	−6.17355	−0.301238
$421$	9.21574	0.449148	0.224574	−	0.974457i	$-0.427901\pi$
$421$	9.21574	0.449148	0.224574	+	0.974457i	$0.427901\pi$
$422$	−5.77830	−0.281283
$423$	−2.66349	−0.129503
$424$	8.01977	0.389475
$425$	12.7551	0.618711
$426$	3.02124	0.146380
$427$	13.2696	0.642160
$428$	19.5382	0.944413
$429$	−12.0811	−0.583283
$430$	−21.4872	−1.03621
$431$	27.6452	1.33162	0.665811	−	0.746121i	$-0.268086\pi$
$431$	27.6452	1.33162	0.665811	+	0.746121i	$0.268086\pi$
$432$	1.00000	0.0481125
$433$	−28.4710	−1.36823	−0.684116	−	0.729374i	$-0.739812\pi$
$433$	−28.4710	−1.36823	−0.684116	+	0.729374i	$0.739812\pi$
$434$	−12.5210	−0.601026
$435$	6.62660	0.317721
$436$	17.2953	0.828292
$437$	3.68197	0.176132
$438$	−12.2860	−0.587047
$439$	28.8665	1.37772	0.688861	−	0.724893i	$-0.258111\pi$
$439$	28.8665	1.37772	0.688861	+	0.724893i	$0.258111\pi$
$440$	−9.89905	−0.471918
$441$	−4.85342	−0.231115
$442$	−5.14252	−0.244605
$443$	13.8142	0.656332	0.328166	−	0.944620i	$-0.393569\pi$
$443$	13.8142	0.656332	0.328166	+	0.944620i	$0.393569\pi$
$444$	1.17725	0.0558697
$445$	−71.9410	−3.41033
$446$	9.81570	0.464787
$447$	−2.15518	−0.101937
$448$	1.46512	0.0692205
$449$	−15.7149	−0.741630	−0.370815	−	0.928707i	$-0.620922\pi$
$449$	−15.7149	−0.741630	−0.370815	+	0.928707i	$0.620922\pi$
$450$	12.7551	0.601279
$451$	20.7020	0.974821
$452$	15.1734	0.713697
$453$	−0.183913	−0.00864098
$454$	17.7579	0.833420
$455$	31.7476	1.48835
$456$	3.77047	0.176569
$457$	−25.8898	−1.21108	−0.605538	−	0.795817i	$-0.707042\pi$
$457$	−25.8898	−1.21108	−0.605538	+	0.795817i	$0.707042\pi$
$458$	12.3852	0.578722
$459$	1.00000	0.0466760
$460$	−4.11477	−0.191852
$461$	4.45680	0.207574	0.103787	−	0.994600i	$-0.466904\pi$
$461$	4.45680	0.207574	0.103787	+	0.994600i	$0.466904\pi$
$462$	3.44196	0.160135
$463$	−15.2591	−0.709150	−0.354575	−	0.935028i	$-0.615374\pi$
$463$	−15.2591	−0.709150	−0.354575	+	0.935028i	$0.615374\pi$
$464$	−1.57264	−0.0730080
$465$	36.0102	1.66993
$466$	−0.349336	−0.0161827
$467$	−18.1408	−0.839455	−0.419727	−	0.907650i	$-0.637874\pi$
$467$	−18.1408	−0.839455	−0.419727	+	0.907650i	$0.637874\pi$
$468$	−5.14252	−0.237713
$469$	−2.69931	−0.124643
$470$	11.2231	0.517682
$471$	−5.67036	−0.261276
$472$	−1.00000	−0.0460287
$473$	11.9799	0.550835
$474$	−11.8546	−0.544502
$475$	48.0926	2.20664
$476$	1.46512	0.0671538
$477$	8.01977	0.367200
$478$	−19.7387	−0.902826
$479$	−13.8404	−0.632386	−0.316193	−	0.948695i	$-0.602405\pi$
$479$	−13.8404	−0.632386	−0.316193	+	0.948695i	$0.602405\pi$
$480$	−4.21367	−0.192327
$481$	−6.05401	−0.276039
$482$	−14.1617	−0.645050
$483$	1.43073	0.0651005
$484$	−5.48095	−0.249134
$485$	−11.3556	−0.515631
$486$	1.00000	0.0453609
$487$	−2.79573	−0.126687	−0.0633434	−	0.997992i	$-0.520176\pi$
$487$	−2.79573	−0.126687	−0.0633434	+	0.997992i	$0.520176\pi$
$488$	9.05698	0.409990
$489$	3.21209	0.145256
$490$	20.4507	0.923869
$491$	10.2225	0.461334	0.230667	−	0.973033i	$-0.425909\pi$
$491$	10.2225	0.461334	0.230667	+	0.973033i	$0.425909\pi$
$492$	8.81213	0.397281
$493$	−1.57264	−0.0708282
$494$	−19.3897	−0.872385
$495$	−9.89905	−0.444929
$496$	−8.54603	−0.383728
$497$	4.42649	0.198555
$498$	5.37381	0.240806
$499$	−0.826933	−0.0370186	−0.0185093	−	0.999829i	$-0.505892\pi$
$499$	−0.826933	−0.0370186	−0.0185093	+	0.999829i	$0.505892\pi$
$500$	−32.6773	−1.46137
$501$	12.2561	0.547564
$502$	−30.3362	−1.35397
$503$	−41.2191	−1.83787	−0.918934	−	0.394410i	$-0.870949\pi$
$503$	−41.2191	−1.83787	−0.918934	+	0.394410i	$0.870949\pi$
$504$	1.46512	0.0652617
$505$	20.2433	0.900814
$506$	2.29412	0.101986
$507$	13.4455	0.597135
$508$	19.4432	0.862652
$509$	−3.81234	−0.168979	−0.0844894	−	0.996424i	$-0.526926\pi$
$509$	−3.81234	−0.168979	−0.0844894	+	0.996424i	$0.526926\pi$
$510$	−4.21367	−0.186585
$511$	−18.0005	−0.796294
$512$	1.00000	0.0441942
$513$	3.77047	0.166470
$514$	13.3150	0.587299
$515$	−47.0452	−2.07306
$516$	5.09941	0.224489
$517$	−6.25725	−0.275193
$518$	1.72481	0.0757839
$519$	−8.63903	−0.379212
$520$	21.6689	0.950244
$521$	26.1455	1.14546	0.572728	−	0.819746i	$-0.305885\pi$
$521$	26.1455	1.14546	0.572728	+	0.819746i	$0.305885\pi$
$522$	−1.57264	−0.0688326
$523$	−16.3020	−0.712837	−0.356418	−	0.934327i	$-0.616002\pi$
$523$	−16.3020	−0.712837	−0.356418	+	0.934327i	$0.616002\pi$
$524$	14.8066	0.646829
$525$	18.6877	0.815599
$526$	1.55696	0.0678865
$527$	−8.54603	−0.372271
$528$	2.34927	0.102239
$529$	−22.0464	−0.958539
$530$	−33.7927	−1.46786
$531$	−1.00000	−0.0433963
$532$	5.52421	0.239505
$533$	−45.3165	−1.96288
$534$	17.0732	0.738830
$535$	−82.3275	−3.55933
$536$	−1.84238	−0.0795787
$537$	13.7718	0.594295
$538$	−23.4522	−1.01110
$539$	−11.4020	−0.491118
$540$	−4.21367	−0.181328
$541$	−37.7655	−1.62366	−0.811832	−	0.583891i	$-0.801530\pi$
$541$	−37.7655	−1.62366	−0.811832	+	0.583891i	$0.801530\pi$
$542$	7.68374	0.330045
$543$	6.46338	0.277370
$544$	1.00000	0.0428746
$545$	−72.8766	−3.12169
$546$	−7.53442	−0.322443
$547$	14.6735	0.627392	0.313696	−	0.949524i	$-0.398433\pi$
$547$	14.6735	0.627392	0.313696	+	0.949524i	$0.398433\pi$
$548$	−6.13571	−0.262105
$549$	9.05698	0.386542
$550$	29.9650	1.27771
$551$	−5.92960	−0.252609
$552$	0.976527	0.0415637
$553$	−17.3685	−0.738584
$554$	22.3715	0.950475
$555$	−4.96054	−0.210563
$556$	14.4847	0.614289
$557$	19.1858	0.812928	0.406464	−	0.913667i	$-0.366762\pi$
$557$	19.1858	0.812928	0.406464	+	0.913667i	$0.366762\pi$
$558$	−8.54603	−0.361782
$559$	−26.2238	−1.10915
$560$	−6.17355	−0.260880
$561$	2.34927	0.0991861
$562$	26.7158	1.12694
$563$	10.4239	0.439315	0.219657	−	0.975577i	$-0.429506\pi$
$563$	10.4239	0.439315	0.219657	+	0.975577i	$0.429506\pi$
$564$	−2.66349	−0.112153
$565$	−63.9358	−2.68980
$566$	−23.3907	−0.983186
$567$	1.46512	0.0615294
$568$	3.02124	0.126769
$569$	0.313698	0.0131509	0.00657545	−	0.999978i	$-0.497907\pi$
$569$	0.313698	0.0131509	0.00657545	+	0.999978i	$0.497907\pi$
$570$	−15.8876	−0.665456
$571$	32.1625	1.34596	0.672980	−	0.739661i	$-0.265014\pi$
$571$	32.1625	1.34596	0.672980	+	0.739661i	$0.265014\pi$
$572$	−12.0811	−0.505138
$573$	22.3517	0.933757
$574$	12.9108	0.538888
$575$	12.4557	0.519437
$576$	1.00000	0.0416667
$577$	14.5633	0.606279	0.303139	−	0.952946i	$-0.401965\pi$
$577$	14.5633	0.606279	0.303139	+	0.952946i	$0.401965\pi$
$578$	1.00000	0.0415945
$579$	−18.7283	−0.778322
$580$	6.62660	0.275154
$581$	7.87329	0.326639
$582$	2.69494	0.111709
$583$	18.8406	0.780297
$584$	−12.2860	−0.508398
$585$	21.6689	0.895898
$586$	15.0828	0.623065
$587$	19.1388	0.789941	0.394970	−	0.918694i	$-0.370755\pi$
$587$	19.1388	0.789941	0.394970	+	0.918694i	$0.370755\pi$
$588$	−4.85342	−0.200152
$589$	−32.2226	−1.32771
$590$	4.21367	0.173474
$591$	−23.3864	−0.961987
$592$	1.17725	0.0483846
$593$	−34.2385	−1.40601	−0.703003	−	0.711187i	$-0.748158\pi$
$593$	−34.2385	−1.40601	−0.703003	+	0.711187i	$0.748158\pi$
$594$	2.34927	0.0963916
$595$	−6.17355	−0.253091
$596$	−2.15518	−0.0882798
$597$	−18.4041	−0.753228
$598$	−5.02181	−0.205357
$599$	−36.8348	−1.50503	−0.752515	−	0.658575i	$-0.771160\pi$
$599$	−36.8348	−1.50503	−0.752515	+	0.658575i	$0.771160\pi$
$600$	12.7551	0.520723
$601$	−43.2006	−1.76219	−0.881095	−	0.472940i	$-0.843193\pi$
$601$	−43.2006	−1.76219	−0.881095	+	0.472940i	$0.843193\pi$
$602$	7.47126	0.304506
$603$	−1.84238	−0.0750275
$604$	−0.183913	−0.00748331
$605$	23.0949	0.938942
$606$	−4.80419	−0.195157
$607$	28.1938	1.14435	0.572176	−	0.820131i	$-0.306099\pi$
$607$	28.1938	1.14435	0.572176	+	0.820131i	$0.306099\pi$
$608$	3.77047	0.152913
$609$	−2.30411	−0.0933673
$610$	−38.1632	−1.54518
$611$	13.6970	0.554123
$612$	1.00000	0.0404226
$613$	7.01268	0.283239	0.141620	−	0.989921i	$-0.454769\pi$
$613$	7.01268	0.283239	0.141620	+	0.989921i	$0.454769\pi$
$614$	−10.5871	−0.427260
$615$	−37.1314	−1.49728
$616$	3.44196	0.138681
$617$	−20.7543	−0.835538	−0.417769	−	0.908553i	$-0.637188\pi$
$617$	−20.7543	−0.835538	−0.417769	+	0.908553i	$0.637188\pi$
$618$	11.1649	0.449118
$619$	44.2364	1.77801	0.889005	−	0.457898i	$-0.151398\pi$
$619$	44.2364	1.77801	0.889005	+	0.457898i	$0.151398\pi$
$620$	36.0102	1.44620
$621$	0.976527	0.0391867
$622$	−9.22088	−0.369724
$623$	25.0143	1.00218
$624$	−5.14252	−0.205865
$625$	73.9162	2.95665
$626$	−19.3753	−0.774392
$627$	8.85785	0.353748
$628$	−5.67036	−0.226272
$629$	1.17725	0.0469399
$630$	−6.17355	−0.245960
$631$	−23.2592	−0.925935	−0.462967	−	0.886375i	$-0.653215\pi$
$631$	−23.2592	−0.925935	−0.462967	+	0.886375i	$0.653215\pi$
$632$	−11.8546	−0.471552
$633$	−5.77830	−0.229667
$634$	−16.1831	−0.642712
$635$	−81.9273	−3.25118
$636$	8.01977	0.318005
$637$	24.9588	0.988903
$638$	−3.69455	−0.146269
$639$	3.02124	0.119519
$640$	−4.21367	−0.166560
$641$	49.0145	1.93596	0.967978	−	0.251036i	$-0.0807712\pi$
$641$	49.0145	1.93596	0.967978	+	0.251036i	$0.0807712\pi$
$642$	19.5382	0.771110
$643$	35.2230	1.38906	0.694530	−	0.719464i	$-0.255612\pi$
$643$	35.2230	1.38906	0.694530	+	0.719464i	$0.255612\pi$
$644$	1.43073	0.0563787
$645$	−21.4872	−0.846060
$646$	3.77047	0.148347
$647$	−42.1244	−1.65608	−0.828041	−	0.560668i	$-0.810545\pi$
$647$	−42.1244	−1.65608	−0.828041	+	0.560668i	$0.810545\pi$
$648$	1.00000	0.0392837
$649$	−2.34927	−0.0922168
$650$	−65.5931	−2.57277
$651$	−12.5210	−0.490736
$652$	3.21209	0.125795
$653$	−8.18475	−0.320294	−0.160147	−	0.987093i	$-0.551197\pi$
$653$	−8.18475	−0.320294	−0.160147	+	0.987093i	$0.551197\pi$
$654$	17.2953	0.676298
$655$	−62.3902	−2.43779
$656$	8.81213	0.344056
$657$	−12.2860	−0.479322
$658$	−3.90234	−0.152129
$659$	−29.9216	−1.16558	−0.582791	−	0.812622i	$-0.698039\pi$
$659$	−29.9216	−1.16558	−0.582791	+	0.812622i	$0.698039\pi$
$660$	−9.89905	−0.385320
$661$	23.9742	0.932489	0.466245	−	0.884656i	$-0.345607\pi$
$661$	23.9742	0.932489	0.466245	+	0.884656i	$0.345607\pi$
$662$	10.0269	0.389708
$663$	−5.14252	−0.199719
$664$	5.37381	0.208544
$665$	−23.2772	−0.902651
$666$	1.17725	0.0456174
$667$	−1.53573	−0.0594635
$668$	12.2561	0.474204
$669$	9.81570	0.379497
$670$	7.76319	0.299918
$671$	21.2773	0.821399
$672$	1.46512	0.0565183
$673$	−7.41913	−0.285987	−0.142993	−	0.989724i	$-0.545673\pi$
$673$	−7.41913	−0.285987	−0.142993	+	0.989724i	$0.545673\pi$
$674$	−9.98793	−0.384721
$675$	12.7551	0.490942
$676$	13.4455	0.517134
$677$	−47.1897	−1.81365	−0.906823	−	0.421512i	$-0.861500\pi$
$677$	−47.1897	−1.81365	−0.906823	+	0.421512i	$0.861500\pi$
$678$	15.1734	0.582731
$679$	3.94841	0.151526
$680$	−4.21367	−0.161587
$681$	17.7579	0.680485
$682$	−20.0769	−0.768784
$683$	−26.1197	−0.999442	−0.499721	−	0.866186i	$-0.666564\pi$
$683$	−26.1197	−0.999442	−0.499721	+	0.866186i	$0.666564\pi$
$684$	3.77047	0.144168
$685$	25.8539	0.987827
$686$	−17.3667	−0.663064
$687$	12.3852	0.472525
$688$	5.09941	0.194413
$689$	−41.2418	−1.57119
$690$	−4.11477	−0.156647
$691$	−20.2166	−0.769076	−0.384538	−	0.923109i	$-0.625639\pi$
$691$	−20.2166	−0.769076	−0.384538	+	0.923109i	$0.625639\pi$
$692$	−8.63903	−0.328407
$693$	3.44196	0.130749
$694$	3.70851	0.140773
$695$	−61.0339	−2.31515
$696$	−1.57264	−0.0596108
$697$	8.81213	0.333783
$698$	6.02341	0.227989
$699$	−0.349336	−0.0132131
$700$	18.6877	0.706329
$701$	42.9045	1.62048	0.810241	−	0.586097i	$-0.199336\pi$
$701$	42.9045	1.62048	0.810241	+	0.586097i	$0.199336\pi$
$702$	−5.14252	−0.194092
$703$	4.43878	0.167412
$704$	2.34927	0.0885413
$705$	11.2231	0.422686
$706$	16.5147	0.621538
$707$	−7.03872	−0.264718
$708$	−1.00000	−0.0375823
$709$	−19.0735	−0.716321	−0.358160	−	0.933660i	$-0.616596\pi$
$709$	−19.0735	−0.716321	−0.358160	+	0.933660i	$0.616596\pi$
$710$	−12.7305	−0.477769
$711$	−11.8546	−0.444584
$712$	17.0732	0.639846
$713$	−8.34542	−0.312539
$714$	1.46512	0.0548308
$715$	50.9060	1.90378
$716$	13.7718	0.514675
$717$	−19.7387	−0.737154
$718$	18.5478	0.692197
$719$	−6.56575	−0.244861	−0.122431	−	0.992477i	$-0.539069\pi$
$719$	−6.56575	−0.244861	−0.122431	+	0.992477i	$0.539069\pi$
$720$	−4.21367	−0.157034
$721$	16.3579	0.609201
$722$	−4.78353	−0.178024
$723$	−14.1617	−0.526681
$724$	6.46338	0.240210
$725$	−20.0591	−0.744977
$726$	−5.48095	−0.203417
$727$	28.0858	1.04164	0.520822	−	0.853666i	$-0.325626\pi$
$727$	28.0858	1.04164	0.520822	+	0.853666i	$0.325626\pi$
$728$	−7.53442	−0.279244
$729$	1.00000	0.0370370
$730$	51.7692	1.91606
$731$	5.09941	0.188608
$732$	9.05698	0.334756
$733$	−45.0058	−1.66233	−0.831163	−	0.556028i	$-0.812325\pi$
$733$	−45.0058	−1.66233	−0.831163	+	0.556028i	$0.812325\pi$
$734$	14.8278	0.547305
$735$	20.4507	0.754336
$736$	0.976527	0.0359953
$737$	−4.32824	−0.159433
$738$	8.81213	0.324379
$739$	1.81328	0.0667024	0.0333512	−	0.999444i	$-0.489382\pi$
$739$	1.81328	0.0667024	0.0333512	+	0.999444i	$0.489382\pi$
$740$	−4.96054	−0.182353
$741$	−19.3897	−0.712299
$742$	11.7500	0.431354
$743$	−23.5932	−0.865551	−0.432775	−	0.901502i	$-0.642466\pi$
$743$	−23.5932	−0.865551	−0.432775	+	0.901502i	$0.642466\pi$
$744$	−8.54603	−0.313313
$745$	9.08125	0.332711
$746$	10.6468	0.389807
$747$	5.37381	0.196617
$748$	2.34927	0.0858977
$749$	28.6258	1.04596
$750$	−32.6773	−1.19321
$751$	13.4458	0.490645	0.245323	−	0.969441i	$-0.421106\pi$
$751$	13.4458	0.490645	0.245323	+	0.969441i	$0.421106\pi$
$752$	−2.66349	−0.0971275
$753$	−30.3362	−1.10551
$754$	8.08733	0.294523
$755$	0.774949	0.0282033
$756$	1.46512	0.0532860
$757$	30.5357	1.10984	0.554920	−	0.831904i	$-0.312749\pi$
$757$	30.5357	1.10984	0.554920	+	0.831904i	$0.312749\pi$
$758$	−18.8948	−0.686292
$759$	2.29412	0.0832714
$760$	−15.8876	−0.576302
$761$	−34.3441	−1.24497	−0.622486	−	0.782631i	$-0.713877\pi$
$761$	−34.3441	−1.24497	−0.622486	+	0.782631i	$0.713877\pi$
$762$	19.4432	0.704352
$763$	25.3397	0.917357
$764$	22.3517	0.808657
$765$	−4.21367	−0.152346
$766$	20.9377	0.756510
$767$	5.14252	0.185686
$768$	1.00000	0.0360844
$769$	−45.5641	−1.64309	−0.821543	−	0.570147i	$-0.806886\pi$
$769$	−45.5641	−1.64309	−0.821543	+	0.570147i	$0.806886\pi$
$770$	−14.5033	−0.522663
$771$	13.3150	0.479527
$772$	−18.7283	−0.674046
$773$	25.0663	0.901572	0.450786	−	0.892632i	$-0.351144\pi$
$773$	25.0663	0.901572	0.450786	+	0.892632i	$0.351144\pi$
$774$	5.09941	0.183294
$775$	−109.005	−3.91558
$776$	2.69494	0.0967426
$777$	1.72481	0.0618773
$778$	18.7037	0.670559
$779$	33.2259	1.19044
$780$	21.6689	0.775871
$781$	7.09771	0.253976
$782$	0.976527	0.0349205
$783$	−1.57264	−0.0562016
$784$	−4.85342	−0.173336
$785$	23.8931	0.852780
$786$	14.8066	0.528134
$787$	45.1863	1.61072	0.805358	−	0.592789i	$-0.201973\pi$
$787$	45.1863	1.61072	0.805358	+	0.592789i	$0.201973\pi$
$788$	−23.3864	−0.833105
$789$	1.55696	0.0554291
$790$	49.9516	1.77720
$791$	22.2309	0.790439
$792$	2.34927	0.0834776
$793$	−46.5757	−1.65395
$794$	−6.12137	−0.217239
$795$	−33.7927	−1.19850
$796$	−18.4041	−0.652315
$797$	14.1067	0.499684	0.249842	−	0.968287i	$-0.419621\pi$
$797$	14.1067	0.499684	0.249842	+	0.968287i	$0.419621\pi$
$798$	5.52421	0.195555
$799$	−2.66349	−0.0942275
$800$	12.7551	0.450959
$801$	17.0732	0.603252
$802$	14.7263	0.520002
$803$	−28.8631	−1.01856
$804$	−1.84238	−0.0649758
$805$	−6.02864	−0.212482
$806$	43.9481	1.54801
$807$	−23.4522	−0.825557
$808$	−4.80419	−0.169011
$809$	27.8950	0.980735	0.490368	−	0.871516i	$-0.336863\pi$
$809$	27.8950	0.980735	0.490368	+	0.871516i	$0.336863\pi$
$810$	−4.21367	−0.148053
$811$	−43.7594	−1.53660	−0.768301	−	0.640089i	$-0.778898\pi$
$811$	−43.7594	−1.53660	−0.768301	+	0.640089i	$0.778898\pi$
$812$	−2.30411	−0.0808584
$813$	7.68374	0.269481
$814$	2.76567	0.0969366
$815$	−13.5347	−0.474100
$816$	1.00000	0.0350070
$817$	19.2272	0.672674
$818$	−18.7827	−0.656722
$819$	−7.53442	−0.263274
$820$	−37.1314	−1.29669
$821$	−39.8214	−1.38978	−0.694889	−	0.719117i	$-0.744546\pi$
$821$	−39.8214	−1.38978	−0.694889	+	0.719117i	$0.744546\pi$
$822$	−6.13571	−0.214008
$823$	41.3713	1.44211	0.721057	−	0.692876i	$-0.243657\pi$
$823$	41.3713	1.44211	0.721057	+	0.692876i	$0.243657\pi$
$824$	11.1649	0.388947
$825$	29.9650	1.04325
$826$	−1.46512	−0.0509781
$827$	21.1913	0.736893	0.368446	−	0.929649i	$-0.379890\pi$
$827$	21.1913	0.736893	0.368446	+	0.929649i	$0.379890\pi$
$828$	0.976527	0.0339367
$829$	−14.0001	−0.486244	−0.243122	−	0.969996i	$-0.578172\pi$
$829$	−14.0001	−0.486244	−0.243122	+	0.969996i	$0.578172\pi$
$830$	−22.6435	−0.785967
$831$	22.3715	0.776060
$832$	−5.14252	−0.178285
$833$	−4.85342	−0.168161
$834$	14.4847	0.501565
$835$	−51.6433	−1.78719
$836$	8.85785	0.306355
$837$	−8.54603	−0.295394
$838$	−21.0778	−0.728121
$839$	−38.5210	−1.32989	−0.664947	−	0.746891i	$-0.731546\pi$
$839$	−38.5210	−1.32989	−0.664947	+	0.746891i	$0.731546\pi$
$840$	−6.17355	−0.213008
$841$	−26.5268	−0.914717
$842$	9.21574	0.317595
$843$	26.7158	0.920141
$844$	−5.77830	−0.198897
$845$	−56.6549	−1.94899
$846$	−2.66349	−0.0915727
$847$	−8.03026	−0.275923
$848$	8.01977	0.275400
$849$	−23.3907	−0.802768
$850$	12.7551	0.437495
$851$	1.14961	0.0394083
$852$	3.02124	0.103506
$853$	−19.1323	−0.655076	−0.327538	−	0.944838i	$-0.606219\pi$
$853$	−19.1323	−0.655076	−0.327538	+	0.944838i	$0.606219\pi$
$854$	13.2696	0.454076
$855$	−15.8876	−0.543343
$856$	19.5382	0.667801
$857$	−4.88815	−0.166976	−0.0834880	−	0.996509i	$-0.526606\pi$
$857$	−4.88815	−0.166976	−0.0834880	+	0.996509i	$0.526606\pi$
$858$	−12.0811	−0.412443
$859$	36.2745	1.23767	0.618835	−	0.785521i	$-0.287605\pi$
$859$	36.2745	1.23767	0.618835	+	0.785521i	$0.287605\pi$
$860$	−21.4872	−0.732709
$861$	12.9108	0.440001
$862$	27.6452	0.941599
$863$	−19.5353	−0.664990	−0.332495	−	0.943105i	$-0.607890\pi$
$863$	−19.5353	−0.664990	−0.332495	+	0.943105i	$0.607890\pi$
$864$	1.00000	0.0340207
$865$	36.4021	1.23771
$866$	−28.4710	−0.967486
$867$	1.00000	0.0339618
$868$	−12.5210	−0.424990
$869$	−27.8497	−0.944737
$870$	6.62660	0.224663
$871$	9.47447	0.321030
$872$	17.2953	0.585691
$873$	2.69494	0.0912098
$874$	3.68197	0.124544
$875$	−47.8762	−1.61851
$876$	−12.2860	−0.415105
$877$	36.8891	1.24566	0.622829	−	0.782358i	$-0.285983\pi$
$877$	36.8891	1.24566	0.622829	+	0.782358i	$0.285983\pi$
$878$	28.8665	0.974197
$879$	15.0828	0.508731
$880$	−9.89905	−0.333697
$881$	−18.6579	−0.628601	−0.314301	−	0.949324i	$-0.601770\pi$
$881$	−18.6579	−0.628601	−0.314301	+	0.949324i	$0.601770\pi$
$882$	−4.85342	−0.163423
$883$	−3.86127	−0.129942	−0.0649711	−	0.997887i	$-0.520696\pi$
$883$	−3.86127	−0.129942	−0.0649711	+	0.997887i	$0.520696\pi$
$884$	−5.14252	−0.172962
$885$	4.21367	0.141641
$886$	13.8142	0.464097
$887$	36.1843	1.21495	0.607475	−	0.794338i	$-0.292182\pi$
$887$	36.1843	1.21495	0.607475	+	0.794338i	$0.292182\pi$
$888$	1.17725	0.0395058
$889$	28.4867	0.955412
$890$	−71.9410	−2.41147
$891$	2.34927	0.0787034
$892$	9.81570	0.328654
$893$	−10.0426	−0.336063
$894$	−2.15518	−0.0720802
$895$	−58.0297	−1.93972
$896$	1.46512	0.0489463
$897$	−5.02181	−0.167673
$898$	−15.7149	−0.524412
$899$	13.4398	0.448243
$900$	12.7551	0.425169
$901$	8.01977	0.267177
$902$	20.7020	0.689303
$903$	7.47126	0.248628
$904$	15.1734	0.504660
$905$	−27.2346	−0.905309
$906$	−0.183913	−0.00611010
$907$	28.7160	0.953498	0.476749	−	0.879040i	$-0.341815\pi$
$907$	28.7160	0.953498	0.476749	+	0.879040i	$0.341815\pi$
$908$	17.7579	0.589317
$909$	−4.80419	−0.159345
$910$	31.7476	1.05242
$911$	23.5475	0.780164	0.390082	−	0.920780i	$-0.372447\pi$
$911$	23.5475	0.780164	0.390082	+	0.920780i	$0.372447\pi$
$912$	3.77047	0.124853
$913$	12.6245	0.417810
$914$	−25.8898	−0.856359
$915$	−38.1632	−1.26164
$916$	12.3852	0.409218
$917$	21.6935	0.716382
$918$	1.00000	0.0330049
$919$	−48.0543	−1.58517	−0.792583	−	0.609764i	$-0.791264\pi$
$919$	−48.0543	−1.58517	−0.792583	+	0.609764i	$0.791264\pi$
$920$	−4.11477	−0.135660
$921$	−10.5871	−0.348857
$922$	4.45680	0.146777
$923$	−15.5368	−0.511400
$924$	3.44196	0.113232
$925$	15.0159	0.493718
$926$	−15.2591	−0.501445
$927$	11.1649	0.366703
$928$	−1.57264	−0.0516245
$929$	−46.9051	−1.53891	−0.769453	−	0.638704i	$-0.779471\pi$
$929$	−46.9051	−1.53891	−0.769453	+	0.638704i	$0.779471\pi$
$930$	36.0102	1.18082
$931$	−18.2997	−0.599748
$932$	−0.349336	−0.0114429
$933$	−9.22088	−0.301878
$934$	−18.1408	−0.593584
$935$	−9.89905	−0.323733
$936$	−5.14252	−0.168088
$937$	−35.6940	−1.16607	−0.583037	−	0.812446i	$-0.698136\pi$
$937$	−35.6940	−1.16607	−0.583037	+	0.812446i	$0.698136\pi$
$938$	−2.69931	−0.0881357
$939$	−19.3753	−0.632289
$940$	11.2231	0.366057
$941$	−18.6355	−0.607500	−0.303750	−	0.952752i	$-0.598239\pi$
$941$	−18.6355	−0.607500	−0.303750	+	0.952752i	$0.598239\pi$
$942$	−5.67036	−0.184750
$943$	8.60528	0.280227
$944$	−1.00000	−0.0325472
$945$	−6.17355	−0.200826
$946$	11.9799	0.389499
$947$	−4.92272	−0.159967	−0.0799834	−	0.996796i	$-0.525487\pi$
$947$	−4.92272	−0.159967	−0.0799834	+	0.996796i	$0.525487\pi$
$948$	−11.8546	−0.385021
$949$	63.1809	2.05094
$950$	48.0926	1.56033
$951$	−16.1831	−0.524772
$952$	1.46512	0.0474849
$953$	33.8236	1.09566	0.547828	−	0.836591i	$-0.315455\pi$
$953$	33.8236	1.09566	0.547828	+	0.836591i	$0.315455\pi$
$954$	8.01977	0.259650
$955$	−94.1829	−3.04769
$956$	−19.7387	−0.638394
$957$	−3.69455	−0.119428
$958$	−13.8404	−0.447165
$959$	−8.98957	−0.290288
$960$	−4.21367	−0.135996
$961$	42.0346	1.35595
$962$	−6.05401	−0.195189
$963$	19.5382	0.629609
$964$	−14.1617	−0.456119
$965$	78.9150	2.54036
$966$	1.43073	0.0460330
$967$	−32.6524	−1.05003	−0.525015	−	0.851093i	$-0.675940\pi$
$967$	−32.6524	−1.05003	−0.525015	+	0.851093i	$0.675940\pi$
$968$	−5.48095	−0.176164
$969$	3.77047	0.121125
$970$	−11.3556	−0.364606
$971$	−40.3740	−1.29566	−0.647832	−	0.761784i	$-0.724324\pi$
$971$	−40.3740	−1.29566	−0.647832	+	0.761784i	$0.724324\pi$
$972$	1.00000	0.0320750
$973$	21.2219	0.680342
$974$	−2.79573	−0.0895811
$975$	−65.5931	−2.10066
$976$	9.05698	0.289907
$977$	17.9317	0.573686	0.286843	−	0.957978i	$-0.407394\pi$
$977$	17.9317	0.573686	0.286843	+	0.957978i	$0.407394\pi$
$978$	3.21209	0.102711
$979$	40.1095	1.28191
$980$	20.4507	0.653274
$981$	17.2953	0.552195
$982$	10.2225	0.326212
$983$	−3.40365	−0.108560	−0.0542798	−	0.998526i	$-0.517286\pi$
$983$	−3.40365	−0.108560	−0.0542798	+	0.998526i	$0.517286\pi$
$984$	8.81213	0.280920
$985$	98.5426	3.13983
$986$	−1.57264	−0.0500831
$987$	−3.90234	−0.124213
$988$	−19.3897	−0.616869
$989$	4.97971	0.158346
$990$	−9.89905	−0.314612
$991$	−51.6879	−1.64192	−0.820961	−	0.570985i	$-0.806562\pi$
$991$	−51.6879	−1.64192	−0.820961	+	0.570985i	$0.806562\pi$
$992$	−8.54603	−0.271337
$993$	10.0269	0.318195
$994$	4.42649	0.140400
$995$	77.5487	2.45846
$996$	5.37381	0.170276
$997$	−9.05329	−0.286721	−0.143360	−	0.989671i	$-0.545791\pi$
$997$	−9.05329	−0.286721	−0.143360	+	0.989671i	$0.545791\pi$
$998$	−0.826933	−0.0261761
$999$	1.17725	0.0372465

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.bb.1.1	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.bb.1.1	✓	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.21367 q^{5} +1.00000 q^{6} +1.46512 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.21367 q^{5} +1.00000 q^{6} +1.46512 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.21367 q^{10} +2.34927 q^{11} +1.00000 q^{12} -5.14252 q^{13} +1.46512 q^{14} -4.21367 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +3.77047 q^{19} -4.21367 q^{20} +1.46512 q^{21} +2.34927 q^{22} +0.976527 q^{23} +1.00000 q^{24} +12.7551 q^{25} -5.14252 q^{26} +1.00000 q^{27} +1.46512 q^{28} -1.57264 q^{29} -4.21367 q^{30} -8.54603 q^{31} +1.00000 q^{32} +2.34927 q^{33} +1.00000 q^{34} -6.17355 q^{35} +1.00000 q^{36} +1.17725 q^{37} +3.77047 q^{38} -5.14252 q^{39} -4.21367 q^{40} +8.81213 q^{41} +1.46512 q^{42} +5.09941 q^{43} +2.34927 q^{44} -4.21367 q^{45} +0.976527 q^{46} -2.66349 q^{47} +1.00000 q^{48} -4.85342 q^{49} +12.7551 q^{50} +1.00000 q^{51} -5.14252 q^{52} +8.01977 q^{53} +1.00000 q^{54} -9.89905 q^{55} +1.46512 q^{56} +3.77047 q^{57} -1.57264 q^{58} -1.00000 q^{59} -4.21367 q^{60} +9.05698 q^{61} -8.54603 q^{62} +1.46512 q^{63} +1.00000 q^{64} +21.6689 q^{65} +2.34927 q^{66} -1.84238 q^{67} +1.00000 q^{68} +0.976527 q^{69} -6.17355 q^{70} +3.02124 q^{71} +1.00000 q^{72} -12.2860 q^{73} +1.17725 q^{74} +12.7551 q^{75} +3.77047 q^{76} +3.44196 q^{77} -5.14252 q^{78} -11.8546 q^{79} -4.21367 q^{80} +1.00000 q^{81} +8.81213 q^{82} +5.37381 q^{83} +1.46512 q^{84} -4.21367 q^{85} +5.09941 q^{86} -1.57264 q^{87} +2.34927 q^{88} +17.0732 q^{89} -4.21367 q^{90} -7.53442 q^{91} +0.976527 q^{92} -8.54603 q^{93} -2.66349 q^{94} -15.8876 q^{95} +1.00000 q^{96} +2.69494 q^{97} -4.85342 q^{98} +2.34927 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9} + 4 q^{10} + 7 q^{11} + 13 q^{12} + 6 q^{13} + 11 q^{14} + 4 q^{15} + 13 q^{16} + 13 q^{17} + 13 q^{18} + 9 q^{19} + 4 q^{20} + 11 q^{21} + 7 q^{22} + 2 q^{23} + 13 q^{24} + 33 q^{25} + 6 q^{26} + 13 q^{27} + 11 q^{28} + 14 q^{29} + 4 q^{30} - 5 q^{31} + 13 q^{32} + 7 q^{33} + 13 q^{34} + 24 q^{35} + 13 q^{36} + 4 q^{37} + 9 q^{38} + 6 q^{39} + 4 q^{40} + 28 q^{41} + 11 q^{42} + q^{43} + 7 q^{44} + 4 q^{45} + 2 q^{46} + 12 q^{47} + 13 q^{48} + 32 q^{49} + 33 q^{50} + 13 q^{51} + 6 q^{52} + 22 q^{53} + 13 q^{54} - 7 q^{55} + 11 q^{56} + 9 q^{57} + 14 q^{58} - 13 q^{59} + 4 q^{60} - 9 q^{61} - 5 q^{62} + 11 q^{63} + 13 q^{64} + 34 q^{65} + 7 q^{66} + 26 q^{67} + 13 q^{68} + 2 q^{69} + 24 q^{70} + 8 q^{71} + 13 q^{72} + 4 q^{73} + 4 q^{74} + 33 q^{75} + 9 q^{76} + 38 q^{77} + 6 q^{78} - 17 q^{79} + 4 q^{80} + 13 q^{81} + 28 q^{82} + 14 q^{83} + 11 q^{84} + 4 q^{85} + q^{86} + 14 q^{87} + 7 q^{88} + 19 q^{89} + 4 q^{90} - 5 q^{91} + 2 q^{92} - 5 q^{93} + 12 q^{94} + 25 q^{95} + 13 q^{96} - 5 q^{97} + 32 q^{98} + 7 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9 + 4 * q^10 + 7 * q^11 + 13 * q^12 + 6 * q^13 + 11 * q^14 + 4 * q^15 + 13 * q^16 + 13 * q^17 + 13 * q^18 + 9 * q^19 + 4 * q^20 + 11 * q^21 + 7 * q^22 + 2 * q^23 + 13 * q^24 + 33 * q^25 + 6 * q^26 + 13 * q^27 + 11 * q^28 + 14 * q^29 + 4 * q^30 - 5 * q^31 + 13 * q^32 + 7 * q^33 + 13 * q^34 + 24 * q^35 + 13 * q^36 + 4 * q^37 + 9 * q^38 + 6 * q^39 + 4 * q^40 + 28 * q^41 + 11 * q^42 + q^43 + 7 * q^44 + 4 * q^45 + 2 * q^46 + 12 * q^47 + 13 * q^48 + 32 * q^49 + 33 * q^50 + 13 * q^51 + 6 * q^52 + 22 * q^53 + 13 * q^54 - 7 * q^55 + 11 * q^56 + 9 * q^57 + 14 * q^58 - 13 * q^59 + 4 * q^60 - 9 * q^61 - 5 * q^62 + 11 * q^63 + 13 * q^64 + 34 * q^65 + 7 * q^66 + 26 * q^67 + 13 * q^68 + 2 * q^69 + 24 * q^70 + 8 * q^71 + 13 * q^72 + 4 * q^73 + 4 * q^74 + 33 * q^75 + 9 * q^76 + 38 * q^77 + 6 * q^78 - 17 * q^79 + 4 * q^80 + 13 * q^81 + 28 * q^82 + 14 * q^83 + 11 * q^84 + 4 * q^85 + q^86 + 14 * q^87 + 7 * q^88 + 19 * q^89 + 4 * q^90 - 5 * q^91 + 2 * q^92 - 5 * q^93 + 12 * q^94 + 25 * q^95 + 13 * q^96 - 5 * q^97 + 32 * q^98 + 7 * q^99

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