LMFDB - Embedded newform 93.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(1,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, 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("93.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.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:	$0.742608738798$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	93.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61803 q^{2} -1.00000 q^{3} +4.85410 q^{4} +0.236068 q^{5} +2.61803 q^{6} -4.23607 q^{7} -7.47214 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.61803 q^{2} -1.00000 q^{3} +4.85410 q^{4} +0.236068 q^{5} +2.61803 q^{6} -4.23607 q^{7} -7.47214 q^{8} +1.00000 q^{9} -0.618034 q^{10} -5.23607 q^{11} -4.85410 q^{12} -3.23607 q^{13} +11.0902 q^{14} -0.236068 q^{15} +9.85410 q^{16} +2.47214 q^{17} -2.61803 q^{18} -1.76393 q^{19} +1.14590 q^{20} +4.23607 q^{21} +13.7082 q^{22} +3.23607 q^{23} +7.47214 q^{24} -4.94427 q^{25} +8.47214 q^{26} -1.00000 q^{27} -20.5623 q^{28} -1.23607 q^{29} +0.618034 q^{30} -1.00000 q^{31} -10.8541 q^{32} +5.23607 q^{33} -6.47214 q^{34} -1.00000 q^{35} +4.85410 q^{36} +7.70820 q^{37} +4.61803 q^{38} +3.23607 q^{39} -1.76393 q^{40} -6.70820 q^{41} -11.0902 q^{42} +3.70820 q^{43} -25.4164 q^{44} +0.236068 q^{45} -8.47214 q^{46} +6.47214 q^{47} -9.85410 q^{48} +10.9443 q^{49} +12.9443 q^{50} -2.47214 q^{51} -15.7082 q^{52} -8.94427 q^{53} +2.61803 q^{54} -1.23607 q^{55} +31.6525 q^{56} +1.76393 q^{57} +3.23607 q^{58} -3.00000 q^{59} -1.14590 q^{60} +8.00000 q^{61} +2.61803 q^{62} -4.23607 q^{63} +8.70820 q^{64} -0.763932 q^{65} -13.7082 q^{66} -12.0000 q^{67} +12.0000 q^{68} -3.23607 q^{69} +2.61803 q^{70} +9.00000 q^{71} -7.47214 q^{72} -1.23607 q^{73} -20.1803 q^{74} +4.94427 q^{75} -8.56231 q^{76} +22.1803 q^{77} -8.47214 q^{78} -0.472136 q^{79} +2.32624 q^{80} +1.00000 q^{81} +17.5623 q^{82} -7.52786 q^{83} +20.5623 q^{84} +0.583592 q^{85} -9.70820 q^{86} +1.23607 q^{87} +39.1246 q^{88} -10.9443 q^{89} -0.618034 q^{90} +13.7082 q^{91} +15.7082 q^{92} +1.00000 q^{93} -16.9443 q^{94} -0.416408 q^{95} +10.8541 q^{96} +9.00000 q^{97} -28.6525 q^{98} -5.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - 4 q^{5} + 3 q^{6} - 4 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - 4 * q^5 + 3 * q^6 - 4 * q^7 - 6 * q^8 + 2 * q^9	\( 2 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - 4 q^{5} + 3 q^{6} - 4 q^{7} - 6 q^{8} + 2 q^{9} + q^{10} - 6 q^{11} - 3 q^{12} - 2 q^{13} + 11 q^{14} + 4 q^{15} + 13 q^{16} - 4 q^{17} - 3 q^{18} - 8 q^{19} + 9 q^{20} + 4 q^{21} + 14 q^{22} + 2 q^{23} + 6 q^{24} + 8 q^{25} + 8 q^{26} - 2 q^{27} - 21 q^{28} + 2 q^{29} - q^{30} - 2 q^{31} - 15 q^{32} + 6 q^{33} - 4 q^{34} - 2 q^{35} + 3 q^{36} + 2 q^{37} + 7 q^{38} + 2 q^{39} - 8 q^{40} - 11 q^{42} - 6 q^{43} - 24 q^{44} - 4 q^{45} - 8 q^{46} + 4 q^{47} - 13 q^{48} + 4 q^{49} + 8 q^{50} + 4 q^{51} - 18 q^{52} + 3 q^{54} + 2 q^{55} + 32 q^{56} + 8 q^{57} + 2 q^{58} - 6 q^{59} - 9 q^{60} + 16 q^{61} + 3 q^{62} - 4 q^{63} + 4 q^{64} - 6 q^{65} - 14 q^{66} - 24 q^{67} + 24 q^{68} - 2 q^{69} + 3 q^{70} + 18 q^{71} - 6 q^{72} + 2 q^{73} - 18 q^{74} - 8 q^{75} + 3 q^{76} + 22 q^{77} - 8 q^{78} + 8 q^{79} - 11 q^{80} + 2 q^{81} + 15 q^{82} - 24 q^{83} + 21 q^{84} + 28 q^{85} - 6 q^{86} - 2 q^{87} + 38 q^{88} - 4 q^{89} + q^{90} + 14 q^{91} + 18 q^{92} + 2 q^{93} - 16 q^{94} + 26 q^{95} + 15 q^{96} + 18 q^{97} - 26 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - 4 * q^5 + 3 * q^6 - 4 * q^7 - 6 * q^8 + 2 * q^9 + q^10 - 6 * q^11 - 3 * q^12 - 2 * q^13 + 11 * q^14 + 4 * q^15 + 13 * q^16 - 4 * q^17 - 3 * q^18 - 8 * q^19 + 9 * q^20 + 4 * q^21 + 14 * q^22 + 2 * q^23 + 6 * q^24 + 8 * q^25 + 8 * q^26 - 2 * q^27 - 21 * q^28 + 2 * q^29 - q^30 - 2 * q^31 - 15 * q^32 + 6 * q^33 - 4 * q^34 - 2 * q^35 + 3 * q^36 + 2 * q^37 + 7 * q^38 + 2 * q^39 - 8 * q^40 - 11 * q^42 - 6 * q^43 - 24 * q^44 - 4 * q^45 - 8 * q^46 + 4 * q^47 - 13 * q^48 + 4 * q^49 + 8 * q^50 + 4 * q^51 - 18 * q^52 + 3 * q^54 + 2 * q^55 + 32 * q^56 + 8 * q^57 + 2 * q^58 - 6 * q^59 - 9 * q^60 + 16 * q^61 + 3 * q^62 - 4 * q^63 + 4 * q^64 - 6 * q^65 - 14 * q^66 - 24 * q^67 + 24 * q^68 - 2 * q^69 + 3 * q^70 + 18 * q^71 - 6 * q^72 + 2 * q^73 - 18 * q^74 - 8 * q^75 + 3 * q^76 + 22 * q^77 - 8 * q^78 + 8 * q^79 - 11 * q^80 + 2 * q^81 + 15 * q^82 - 24 * q^83 + 21 * q^84 + 28 * q^85 - 6 * q^86 - 2 * q^87 + 38 * q^88 - 4 * q^89 + q^90 + 14 * q^91 + 18 * q^92 + 2 * q^93 - 16 * q^94 + 26 * q^95 + 15 * q^96 + 18 * q^97 - 26 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.61803	−1.85123	−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−2.61803	−1.85123	−0.925615	+	0.378467i	$0.876451\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.85410	2.42705
$5$	0.236068	0.105573	0.0527864	−	0.998606i	$-0.483190\pi$
$5$	0.236068	0.105573	0.0527864	+	0.998606i	$0.483190\pi$
$6$	2.61803	1.06881
$7$	−4.23607	−1.60108	−0.800542	−	0.599277i	$-0.795455\pi$
$7$	−4.23607	−1.60108	−0.800542	+	0.599277i	$0.795455\pi$
$8$	−7.47214	−2.64180
$9$	1.00000	0.333333
$10$	−0.618034	−0.195440
$11$	−5.23607	−1.57873	−0.789367	−	0.613922i	$-0.789591\pi$
$11$	−5.23607	−1.57873	−0.789367	+	0.613922i	$0.789591\pi$
$12$	−4.85410	−1.40126
$13$	−3.23607	−0.897524	−0.448762	−	0.893651i	$-0.648135\pi$
$13$	−3.23607	−0.897524	−0.448762	+	0.893651i	$0.648135\pi$
$14$	11.0902	2.96397
$15$	−0.236068	−0.0609525
$16$	9.85410	2.46353
$17$	2.47214	0.599581	0.299791	−	0.954005i	$-0.403083\pi$
$17$	2.47214	0.599581	0.299791	+	0.954005i	$0.403083\pi$
$18$	−2.61803	−0.617077
$19$	−1.76393	−0.404674	−0.202337	−	0.979316i	$-0.564854\pi$
$19$	−1.76393	−0.404674	−0.202337	+	0.979316i	$0.564854\pi$
$20$	1.14590	0.256231
$21$	4.23607	0.924386
$22$	13.7082	2.92260
$23$	3.23607	0.674767	0.337383	−	0.941367i	$-0.390458\pi$
$23$	3.23607	0.674767	0.337383	+	0.941367i	$0.390458\pi$
$24$	7.47214	1.52524
$25$	−4.94427	−0.988854
$26$	8.47214	1.66152
$27$	−1.00000	−0.192450
$28$	−20.5623	−3.88591
$29$	−1.23607	−0.229532	−0.114766	−	0.993393i	$-0.536612\pi$
$29$	−1.23607	−0.229532	−0.114766	+	0.993393i	$0.536612\pi$
$30$	0.618034	0.112837
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−10.8541	−1.91875
$33$	5.23607	0.911482
$34$	−6.47214	−1.10996
$35$	−1.00000	−0.169031
$36$	4.85410	0.809017
$37$	7.70820	1.26722	0.633610	−	0.773652i	$-0.281572\pi$
$37$	7.70820	1.26722	0.633610	+	0.773652i	$0.281572\pi$
$38$	4.61803	0.749144
$39$	3.23607	0.518186
$40$	−1.76393	−0.278902
$41$	−6.70820	−1.04765	−0.523823	−	0.851827i	$-0.675495\pi$
$41$	−6.70820	−1.04765	−0.523823	+	0.851827i	$0.675495\pi$
$42$	−11.0902	−1.71125
$43$	3.70820	0.565496	0.282748	−	0.959194i	$-0.408754\pi$
$43$	3.70820	0.565496	0.282748	+	0.959194i	$0.408754\pi$
$44$	−25.4164	−3.83167
$45$	0.236068	0.0351909
$46$	−8.47214	−1.24915
$47$	6.47214	0.944058	0.472029	−	0.881583i	$-0.343522\pi$
$47$	6.47214	0.944058	0.472029	+	0.881583i	$0.343522\pi$
$48$	−9.85410	−1.42232
$49$	10.9443	1.56347
$50$	12.9443	1.83060
$51$	−2.47214	−0.346168
$52$	−15.7082	−2.17834
$53$	−8.94427	−1.22859	−0.614295	−	0.789076i	$-0.710560\pi$
$53$	−8.94427	−1.22859	−0.614295	+	0.789076i	$0.710560\pi$
$54$	2.61803	0.356269
$55$	−1.23607	−0.166671
$56$	31.6525	4.22974
$57$	1.76393	0.233639
$58$	3.23607	0.424917
$59$	−3.00000	−0.390567	−0.195283	−	0.980747i	$-0.562563\pi$
$59$	−3.00000	−0.390567	−0.195283	+	0.980747i	$0.562563\pi$
$60$	−1.14590	−0.147935
$61$	8.00000	1.02430	0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000	1.02430	0.512148	+	0.858898i	$0.328850\pi$
$62$	2.61803	0.332491
$63$	−4.23607	−0.533694
$64$	8.70820	1.08853
$65$	−0.763932	−0.0947541
$66$	−13.7082	−1.68736
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	12.0000	1.45521
$69$	−3.23607	−0.389577
$70$	2.61803	0.312915
$71$	9.00000	1.06810	0.534052	−	0.845452i	$-0.320669\pi$
$71$	9.00000	1.06810	0.534052	+	0.845452i	$0.320669\pi$
$72$	−7.47214	−0.880600
$73$	−1.23607	−0.144671	−0.0723354	−	0.997380i	$-0.523045\pi$
$73$	−1.23607	−0.144671	−0.0723354	+	0.997380i	$0.523045\pi$
$74$	−20.1803	−2.34592
$75$	4.94427	0.570915
$76$	−8.56231	−0.982164
$77$	22.1803	2.52768
$78$	−8.47214	−0.959280
$79$	−0.472136	−0.0531194	−0.0265597	−	0.999647i	$-0.508455\pi$
$79$	−0.472136	−0.0531194	−0.0265597	+	0.999647i	$0.508455\pi$
$80$	2.32624	0.260081
$81$	1.00000	0.111111
$82$	17.5623	1.93943
$83$	−7.52786	−0.826290	−0.413145	−	0.910665i	$-0.635570\pi$
$83$	−7.52786	−0.826290	−0.413145	+	0.910665i	$0.635570\pi$
$84$	20.5623	2.24353
$85$	0.583592	0.0632995
$86$	−9.70820	−1.04686
$87$	1.23607	0.132520
$88$	39.1246	4.17070
$89$	−10.9443	−1.16009	−0.580045	−	0.814584i	$-0.696965\pi$
$89$	−10.9443	−1.16009	−0.580045	+	0.814584i	$0.696965\pi$
$90$	−0.618034	−0.0651465
$91$	13.7082	1.43701
$92$	15.7082	1.63769
$93$	1.00000	0.103695
$94$	−16.9443	−1.74767
$95$	−0.416408	−0.0427225
$96$	10.8541	1.10779
$97$	9.00000	0.913812	0.456906	−	0.889515i	$-0.348958\pi$
$97$	9.00000	0.913812	0.456906	+	0.889515i	$0.348958\pi$
$98$	−28.6525	−2.89434
$99$	−5.23607	−0.526245
$100$	−24.0000	−2.40000
$101$	−10.2361	−1.01853	−0.509263	−	0.860611i	$-0.670082\pi$
$101$	−10.2361	−1.01853	−0.509263	+	0.860611i	$0.670082\pi$
$102$	6.47214	0.640837
$103$	−18.2361	−1.79685	−0.898427	−	0.439124i	$-0.855289\pi$
$103$	−18.2361	−1.79685	−0.898427	+	0.439124i	$0.855289\pi$
$104$	24.1803	2.37108
$105$	1.00000	0.0975900
$106$	23.4164	2.27440
$107$	−7.47214	−0.722359	−0.361179	−	0.932496i	$-0.617626\pi$
$107$	−7.47214	−0.722359	−0.361179	+	0.932496i	$0.617626\pi$
$108$	−4.85410	−0.467086
$109$	−5.00000	−0.478913	−0.239457	−	0.970907i	$-0.576969\pi$
$109$	−5.00000	−0.478913	−0.239457	+	0.970907i	$0.576969\pi$
$110$	3.23607	0.308547
$111$	−7.70820	−0.731630
$112$	−41.7426	−3.94431
$113$	−6.23607	−0.586640	−0.293320	−	0.956014i	$-0.594760\pi$
$113$	−6.23607	−0.586640	−0.293320	+	0.956014i	$0.594760\pi$
$114$	−4.61803	−0.432519
$115$	0.763932	0.0712370
$116$	−6.00000	−0.557086
$117$	−3.23607	−0.299175
$118$	7.85410	0.723029
$119$	−10.4721	−0.959979
$120$	1.76393	0.161024
$121$	16.4164	1.49240
$122$	−20.9443	−1.89621
$123$	6.70820	0.604858
$124$	−4.85410	−0.435911
$125$	−2.34752	−0.209969
$126$	11.0902	0.987991
$127$	2.76393	0.245259	0.122630	−	0.992453i	$-0.460867\pi$
$127$	2.76393	0.245259	0.122630	+	0.992453i	$0.460867\pi$
$128$	−1.09017	−0.0963583
$129$	−3.70820	−0.326489
$130$	2.00000	0.175412
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	25.4164	2.21221
$133$	7.47214	0.647916
$134$	31.4164	2.71396
$135$	−0.236068	−0.0203175
$136$	−18.4721	−1.58397
$137$	12.1803	1.04064	0.520318	−	0.853972i	$-0.325813\pi$
$137$	12.1803	1.04064	0.520318	+	0.853972i	$0.325813\pi$
$138$	8.47214	0.721196
$139$	−7.70820	−0.653801	−0.326901	−	0.945059i	$-0.606004\pi$
$139$	−7.70820	−0.653801	−0.326901	+	0.945059i	$0.606004\pi$
$140$	−4.85410	−0.410246
$141$	−6.47214	−0.545052
$142$	−23.5623	−1.97730
$143$	16.9443	1.41695
$144$	9.85410	0.821175
$145$	−0.291796	−0.0242323
$146$	3.23607	0.267819
$147$	−10.9443	−0.902668
$148$	37.4164	3.07561
$149$	13.4164	1.09911	0.549557	−	0.835456i	$-0.314796\pi$
$149$	13.4164	1.09911	0.549557	+	0.835456i	$0.314796\pi$
$150$	−12.9443	−1.05690
$151$	10.7639	0.875956	0.437978	−	0.898986i	$-0.355695\pi$
$151$	10.7639	0.875956	0.437978	+	0.898986i	$0.355695\pi$
$152$	13.1803	1.06907
$153$	2.47214	0.199860
$154$	−58.0689	−4.67932
$155$	−0.236068	−0.0189614
$156$	15.7082	1.25766
$157$	−21.9443	−1.75134	−0.875672	−	0.482907i	$-0.839581\pi$
$157$	−21.9443	−1.75134	−0.875672	+	0.482907i	$0.839581\pi$
$158$	1.23607	0.0983363
$159$	8.94427	0.709327
$160$	−2.56231	−0.202568
$161$	−13.7082	−1.08036
$162$	−2.61803	−0.205692
$163$	15.1803	1.18902	0.594508	−	0.804090i	$-0.297347\pi$
$163$	15.1803	1.18902	0.594508	+	0.804090i	$0.297347\pi$
$164$	−32.5623	−2.54269
$165$	1.23607	0.0962278
$166$	19.7082	1.52965
$167$	14.6525	1.13384	0.566921	−	0.823772i	$-0.308134\pi$
$167$	14.6525	1.13384	0.566921	+	0.823772i	$0.308134\pi$
$168$	−31.6525	−2.44204
$169$	−2.52786	−0.194451
$170$	−1.52786	−0.117182
$171$	−1.76393	−0.134891
$172$	18.0000	1.37249
$173$	−10.9443	−0.832078	−0.416039	−	0.909347i	$-0.636582\pi$
$173$	−10.9443	−0.832078	−0.416039	+	0.909347i	$0.636582\pi$
$174$	−3.23607	−0.245326
$175$	20.9443	1.58324
$176$	−51.5967	−3.88925
$177$	3.00000	0.225494
$178$	28.6525	2.14759
$179$	−7.41641	−0.554328	−0.277164	−	0.960823i	$-0.589395\pi$
$179$	−7.41641	−0.554328	−0.277164	+	0.960823i	$0.589395\pi$
$180$	1.14590	0.0854102
$181$	−7.41641	−0.551257	−0.275629	−	0.961264i	$-0.588886\pi$
$181$	−7.41641	−0.551257	−0.275629	+	0.961264i	$0.588886\pi$
$182$	−35.8885	−2.66024
$183$	−8.00000	−0.591377
$184$	−24.1803	−1.78260
$185$	1.81966	0.133784
$186$	−2.61803	−0.191964
$187$	−12.9443	−0.946579
$188$	31.4164	2.29128
$189$	4.23607	0.308129
$190$	1.09017	0.0790892
$191$	3.94427	0.285397	0.142699	−	0.989766i	$-0.454422\pi$
$191$	3.94427	0.285397	0.142699	+	0.989766i	$0.454422\pi$
$192$	−8.70820	−0.628460
$193$	−3.00000	−0.215945	−0.107972	−	0.994154i	$-0.534436\pi$
$193$	−3.00000	−0.215945	−0.107972	+	0.994154i	$0.534436\pi$
$194$	−23.5623	−1.69167
$195$	0.763932	0.0547063
$196$	53.1246	3.79462
$197$	0.763932	0.0544279	0.0272140	−	0.999630i	$-0.491336\pi$
$197$	0.763932	0.0544279	0.0272140	+	0.999630i	$0.491336\pi$
$198$	13.7082	0.974200
$199$	10.1803	0.721665	0.360833	−	0.932631i	$-0.382493\pi$
$199$	10.1803	0.721665	0.360833	+	0.932631i	$0.382493\pi$
$200$	36.9443	2.61235
$201$	12.0000	0.846415
$202$	26.7984	1.88553
$203$	5.23607	0.367500
$204$	−12.0000	−0.840168
$205$	−1.58359	−0.110603
$206$	47.7426	3.32639
$207$	3.23607	0.224922
$208$	−31.8885	−2.21107
$209$	9.23607	0.638872
$210$	−2.61803	−0.180662
$211$	−12.7082	−0.874869	−0.437434	−	0.899250i	$-0.644113\pi$
$211$	−12.7082	−0.874869	−0.437434	+	0.899250i	$0.644113\pi$
$212$	−43.4164	−2.98185
$213$	−9.00000	−0.616670
$214$	19.5623	1.33725
$215$	0.875388	0.0597010
$216$	7.47214	0.508414
$217$	4.23607	0.287563
$218$	13.0902	0.886578
$219$	1.23607	0.0835257
$220$	−6.00000	−0.404520
$221$	−8.00000	−0.538138
$222$	20.1803	1.35442
$223$	−24.1803	−1.61924	−0.809618	−	0.586958i	$-0.800326\pi$
$223$	−24.1803	−1.61924	−0.809618	+	0.586958i	$0.800326\pi$
$224$	45.9787	3.07208
$225$	−4.94427	−0.329618
$226$	16.3262	1.08601
$227$	−12.9443	−0.859142	−0.429571	−	0.903033i	$-0.641335\pi$
$227$	−12.9443	−0.859142	−0.429571	+	0.903033i	$0.641335\pi$
$228$	8.56231	0.567053
$229$	−3.70820	−0.245045	−0.122523	−	0.992466i	$-0.539098\pi$
$229$	−3.70820	−0.245045	−0.122523	+	0.992466i	$0.539098\pi$
$230$	−2.00000	−0.131876
$231$	−22.1803	−1.45936
$232$	9.23607	0.606378
$233$	−12.7082	−0.832542	−0.416271	−	0.909241i	$-0.636663\pi$
$233$	−12.7082	−0.832542	−0.416271	+	0.909241i	$0.636663\pi$
$234$	8.47214	0.553841
$235$	1.52786	0.0996669
$236$	−14.5623	−0.947925
$237$	0.472136	0.0306685
$238$	27.4164	1.77714
$239$	23.8885	1.54522	0.772611	−	0.634880i	$-0.218950\pi$
$239$	23.8885	1.54522	0.772611	+	0.634880i	$0.218950\pi$
$240$	−2.32624	−0.150158
$241$	−0.291796	−0.0187962	−0.00939812	−	0.999956i	$-0.502992\pi$
$241$	−0.291796	−0.0187962	−0.00939812	+	0.999956i	$0.502992\pi$
$242$	−42.9787	−2.76278
$243$	−1.00000	−0.0641500
$244$	38.8328	2.48602
$245$	2.58359	0.165060
$246$	−17.5623	−1.11973
$247$	5.70820	0.363204
$248$	7.47214	0.474481
$249$	7.52786	0.477059
$250$	6.14590	0.388701
$251$	−6.76393	−0.426936	−0.213468	−	0.976950i	$-0.568476\pi$
$251$	−6.76393	−0.426936	−0.213468	+	0.976950i	$0.568476\pi$
$252$	−20.5623	−1.29530
$253$	−16.9443	−1.06528
$254$	−7.23607	−0.454031
$255$	−0.583592	−0.0365460
$256$	−14.5623	−0.910144
$257$	18.7082	1.16699	0.583493	−	0.812118i	$-0.301686\pi$
$257$	18.7082	1.16699	0.583493	+	0.812118i	$0.301686\pi$
$258$	9.70820	0.604406
$259$	−32.6525	−2.02893
$260$	−3.70820	−0.229973
$261$	−1.23607	−0.0765107
$262$	0	0
$263$	9.52786	0.587513	0.293757	−	0.955880i	$-0.405094\pi$
$263$	9.52786	0.587513	0.293757	+	0.955880i	$0.405094\pi$
$264$	−39.1246	−2.40795
$265$	−2.11146	−0.129706
$266$	−19.5623	−1.19944
$267$	10.9443	0.669779
$268$	−58.2492	−3.55814
$269$	18.6525	1.13726	0.568631	−	0.822593i	$-0.307473\pi$
$269$	18.6525	1.13726	0.568631	+	0.822593i	$0.307473\pi$
$270$	0.618034	0.0376124
$271$	13.4164	0.814989	0.407494	−	0.913208i	$-0.366403\pi$
$271$	13.4164	0.814989	0.407494	+	0.913208i	$0.366403\pi$
$272$	24.3607	1.47708
$273$	−13.7082	−0.829658
$274$	−31.8885	−1.92646
$275$	25.8885	1.56114
$276$	−15.7082	−0.945523
$277$	0.472136	0.0283679	0.0141840	−	0.999899i	$-0.495485\pi$
$277$	0.472136	0.0283679	0.0141840	+	0.999899i	$0.495485\pi$
$278$	20.1803	1.21034
$279$	−1.00000	−0.0598684
$280$	7.47214	0.446546
$281$	−23.7639	−1.41764	−0.708819	−	0.705391i	$-0.750772\pi$
$281$	−23.7639	−1.41764	−0.708819	+	0.705391i	$0.750772\pi$
$282$	16.9443	1.00902
$283$	−8.00000	−0.475551	−0.237775	−	0.971320i	$-0.576418\pi$
$283$	−8.00000	−0.475551	−0.237775	+	0.971320i	$0.576418\pi$
$284$	43.6869	2.59234
$285$	0.416408	0.0246659
$286$	−44.3607	−2.62310
$287$	28.4164	1.67737
$288$	−10.8541	−0.639584
$289$	−10.8885	−0.640503
$290$	0.763932	0.0448596
$291$	−9.00000	−0.527589
$292$	−6.00000	−0.351123
$293$	−30.3607	−1.77369	−0.886845	−	0.462067i	$-0.847108\pi$
$293$	−30.3607	−1.77369	−0.886845	+	0.462067i	$0.847108\pi$
$294$	28.6525	1.67105
$295$	−0.708204	−0.0412332
$296$	−57.5967	−3.34774
$297$	5.23607	0.303827
$298$	−35.1246	−2.03471
$299$	−10.4721	−0.605619
$300$	24.0000	1.38564
$301$	−15.7082	−0.905406
$302$	−28.1803	−1.62160
$303$	10.2361	0.588047
$304$	−17.3820	−0.996924
$305$	1.88854	0.108138
$306$	−6.47214	−0.369987
$307$	−5.76393	−0.328965	−0.164482	−	0.986380i	$-0.552595\pi$
$307$	−5.76393	−0.328965	−0.164482	+	0.986380i	$0.552595\pi$
$308$	107.666	6.13482
$309$	18.2361	1.03741
$310$	0.618034	0.0351020
$311$	3.47214	0.196887	0.0984434	−	0.995143i	$-0.468614\pi$
$311$	3.47214	0.196887	0.0984434	+	0.995143i	$0.468614\pi$
$312$	−24.1803	−1.36894
$313$	2.47214	0.139733	0.0698667	−	0.997556i	$-0.477743\pi$
$313$	2.47214	0.139733	0.0698667	+	0.997556i	$0.477743\pi$
$314$	57.4508	3.24214
$315$	−1.00000	−0.0563436
$316$	−2.29180	−0.128924
$317$	−8.12461	−0.456324	−0.228162	−	0.973623i	$-0.573272\pi$
$317$	−8.12461	−0.456324	−0.228162	+	0.973623i	$0.573272\pi$
$318$	−23.4164	−1.31313
$319$	6.47214	0.362370
$320$	2.05573	0.114919
$321$	7.47214	0.417054
$322$	35.8885	1.99999
$323$	−4.36068	−0.242635
$324$	4.85410	0.269672
$325$	16.0000	0.887520
$326$	−39.7426	−2.20114
$327$	5.00000	0.276501
$328$	50.1246	2.76767
$329$	−27.4164	−1.51152
$330$	−3.23607	−0.178140
$331$	−32.8328	−1.80465	−0.902327	−	0.431051i	$-0.858143\pi$
$331$	−32.8328	−1.80465	−0.902327	+	0.431051i	$0.858143\pi$
$332$	−36.5410	−2.00545
$333$	7.70820	0.422407
$334$	−38.3607	−2.09900
$335$	−2.83282	−0.154773
$336$	41.7426	2.27725
$337$	34.9443	1.90354	0.951768	−	0.306819i	$-0.0992646\pi$
$337$	34.9443	1.90354	0.951768	+	0.306819i	$0.0992646\pi$
$338$	6.61803	0.359974
$339$	6.23607	0.338697
$340$	2.83282	0.153631
$341$	5.23607	0.283549
$342$	4.61803	0.249715
$343$	−16.7082	−0.902158
$344$	−27.7082	−1.49393
$345$	−0.763932	−0.0411287
$346$	28.6525	1.54037
$347$	34.6525	1.86024	0.930121	−	0.367253i	$-0.119702\pi$
$347$	34.6525	1.86024	0.930121	+	0.367253i	$0.119702\pi$
$348$	6.00000	0.321634
$349$	−7.88854	−0.422264	−0.211132	−	0.977458i	$-0.567715\pi$
$349$	−7.88854	−0.422264	−0.211132	+	0.977458i	$0.567715\pi$
$350$	−54.8328	−2.93094
$351$	3.23607	0.172729
$352$	56.8328	3.02920
$353$	−12.7639	−0.679356	−0.339678	−	0.940542i	$-0.610318\pi$
$353$	−12.7639	−0.679356	−0.339678	+	0.940542i	$0.610318\pi$
$354$	−7.85410	−0.417441
$355$	2.12461	0.112763
$356$	−53.1246	−2.81560
$357$	10.4721	0.554244
$358$	19.4164	1.02619
$359$	26.8885	1.41912	0.709562	−	0.704643i	$-0.248893\pi$
$359$	26.8885	1.41912	0.709562	+	0.704643i	$0.248893\pi$
$360$	−1.76393	−0.0929674
$361$	−15.8885	−0.836239
$362$	19.4164	1.02050
$363$	−16.4164	−0.861638
$364$	66.5410	3.48770
$365$	−0.291796	−0.0152733
$366$	20.9443	1.09477
$367$	34.9443	1.82408	0.912038	−	0.410106i	$-0.134508\pi$
$367$	34.9443	1.82408	0.912038	+	0.410106i	$0.134508\pi$
$368$	31.8885	1.66231
$369$	−6.70820	−0.349215
$370$	−4.76393	−0.247665
$371$	37.8885	1.96708
$372$	4.85410	0.251673
$373$	34.4164	1.78201	0.891007	−	0.453990i	$-0.150000\pi$
$373$	34.4164	1.78201	0.891007	+	0.453990i	$0.150000\pi$
$374$	33.8885	1.75233
$375$	2.34752	0.121226
$376$	−48.3607	−2.49401
$377$	4.00000	0.206010
$378$	−11.0902	−0.570417
$379$	26.4721	1.35978	0.679891	−	0.733313i	$-0.262027\pi$
$379$	26.4721	1.35978	0.679891	+	0.733313i	$0.262027\pi$
$380$	−2.02129	−0.103690
$381$	−2.76393	−0.141601
$382$	−10.3262	−0.528336
$383$	−14.9443	−0.763617	−0.381808	−	0.924242i	$-0.624699\pi$
$383$	−14.9443	−0.763617	−0.381808	+	0.924242i	$0.624699\pi$
$384$	1.09017	0.0556325
$385$	5.23607	0.266855
$386$	7.85410	0.399763
$387$	3.70820	0.188499
$388$	43.6869	2.21787
$389$	3.81966	0.193664	0.0968322	−	0.995301i	$-0.469129\pi$
$389$	3.81966	0.193664	0.0968322	+	0.995301i	$0.469129\pi$
$390$	−2.00000	−0.101274
$391$	8.00000	0.404577
$392$	−81.7771	−4.13037
$393$	0	0
$394$	−2.00000	−0.100759
$395$	−0.111456	−0.00560797
$396$	−25.4164	−1.27722
$397$	−3.58359	−0.179855	−0.0899277	−	0.995948i	$-0.528664\pi$
$397$	−3.58359	−0.179855	−0.0899277	+	0.995948i	$0.528664\pi$
$398$	−26.6525	−1.33597
$399$	−7.47214	−0.374075
$400$	−48.7214	−2.43607
$401$	5.23607	0.261477	0.130738	−	0.991417i	$-0.458265\pi$
$401$	5.23607	0.261477	0.130738	+	0.991417i	$0.458265\pi$
$402$	−31.4164	−1.56691
$403$	3.23607	0.161200
$404$	−49.6869	−2.47202
$405$	0.236068	0.0117303
$406$	−13.7082	−0.680327
$407$	−40.3607	−2.00060
$408$	18.4721	0.914507
$409$	−17.1246	−0.846758	−0.423379	−	0.905953i	$-0.639156\pi$
$409$	−17.1246	−0.846758	−0.423379	+	0.905953i	$0.639156\pi$
$410$	4.14590	0.204751
$411$	−12.1803	−0.600812
$412$	−88.5197	−4.36105
$413$	12.7082	0.625330
$414$	−8.47214	−0.416383
$415$	−1.77709	−0.0872338
$416$	35.1246	1.72213
$417$	7.70820	0.377472
$418$	−24.1803	−1.18270
$419$	9.00000	0.439679	0.219839	−	0.975536i	$-0.429447\pi$
$419$	9.00000	0.439679	0.219839	+	0.975536i	$0.429447\pi$
$420$	4.85410	0.236856
$421$	12.4164	0.605139	0.302569	−	0.953127i	$-0.402156\pi$
$421$	12.4164	0.605139	0.302569	+	0.953127i	$0.402156\pi$
$422$	33.2705	1.61958
$423$	6.47214	0.314686
$424$	66.8328	3.24569
$425$	−12.2229	−0.592898
$426$	23.5623	1.14160
$427$	−33.8885	−1.63998
$428$	−36.2705	−1.75320
$429$	−16.9443	−0.818077
$430$	−2.29180	−0.110520
$431$	2.47214	0.119079	0.0595393	−	0.998226i	$-0.481037\pi$
$431$	2.47214	0.119079	0.0595393	+	0.998226i	$0.481037\pi$
$432$	−9.85410	−0.474106
$433$	3.52786	0.169538	0.0847692	−	0.996401i	$-0.472985\pi$
$433$	3.52786	0.169538	0.0847692	+	0.996401i	$0.472985\pi$
$434$	−11.0902	−0.532345
$435$	0.291796	0.0139906
$436$	−24.2705	−1.16235
$437$	−5.70820	−0.273060
$438$	−3.23607	−0.154625
$439$	2.70820	0.129256	0.0646278	−	0.997909i	$-0.479414\pi$
$439$	2.70820	0.129256	0.0646278	+	0.997909i	$0.479414\pi$
$440$	9.23607	0.440312
$441$	10.9443	0.521156
$442$	20.9443	0.996217
$443$	19.3607	0.919854	0.459927	−	0.887957i	$-0.347876\pi$
$443$	19.3607	0.919854	0.459927	+	0.887957i	$0.347876\pi$
$444$	−37.4164	−1.77570
$445$	−2.58359	−0.122474
$446$	63.3050	2.99758
$447$	−13.4164	−0.634574
$448$	−36.8885	−1.74282
$449$	0.652476	0.0307922	0.0153961	−	0.999881i	$-0.495099\pi$
$449$	0.652476	0.0307922	0.0153961	+	0.999881i	$0.495099\pi$
$450$	12.9443	0.610199
$451$	35.1246	1.65395
$452$	−30.2705	−1.42381
$453$	−10.7639	−0.505734
$454$	33.8885	1.59047
$455$	3.23607	0.151709
$456$	−13.1803	−0.617226
$457$	−29.1246	−1.36239	−0.681196	−	0.732101i	$-0.738540\pi$
$457$	−29.1246	−1.36239	−0.681196	+	0.732101i	$0.738540\pi$
$458$	9.70820	0.453635
$459$	−2.47214	−0.115389
$460$	3.70820	0.172896
$461$	11.8885	0.553705	0.276852	−	0.960912i	$-0.410709\pi$
$461$	11.8885	0.553705	0.276852	+	0.960912i	$0.410709\pi$
$462$	58.0689	2.70161
$463$	28.8328	1.33997	0.669987	−	0.742373i	$-0.266300\pi$
$463$	28.8328	1.33997	0.669987	+	0.742373i	$0.266300\pi$
$464$	−12.1803	−0.565458
$465$	0.236068	0.0109474
$466$	33.2705	1.54123
$467$	37.9443	1.75585	0.877926	−	0.478797i	$-0.158927\pi$
$467$	37.9443	1.75585	0.877926	+	0.478797i	$0.158927\pi$
$468$	−15.7082	−0.726112
$469$	50.8328	2.34724
$470$	−4.00000	−0.184506
$471$	21.9443	1.01114
$472$	22.4164	1.03180
$473$	−19.4164	−0.892767
$474$	−1.23607	−0.0567745
$475$	8.72136	0.400163
$476$	−50.8328	−2.32992
$477$	−8.94427	−0.409530
$478$	−62.5410	−2.86056
$479$	−17.9443	−0.819895	−0.409947	−	0.912109i	$-0.634453\pi$
$479$	−17.9443	−0.819895	−0.409947	+	0.912109i	$0.634453\pi$
$480$	2.56231	0.116953
$481$	−24.9443	−1.13736
$482$	0.763932	0.0347962
$483$	13.7082	0.623745
$484$	79.6869	3.62213
$485$	2.12461	0.0964737
$486$	2.61803	0.118756
$487$	9.70820	0.439921	0.219960	−	0.975509i	$-0.429407\pi$
$487$	9.70820	0.439921	0.219960	+	0.975509i	$0.429407\pi$
$488$	−59.7771	−2.70598
$489$	−15.1803	−0.686479
$490$	−6.76393	−0.305563
$491$	−36.1803	−1.63280	−0.816398	−	0.577490i	$-0.804032\pi$
$491$	−36.1803	−1.63280	−0.816398	+	0.577490i	$0.804032\pi$
$492$	32.5623	1.46802
$493$	−3.05573	−0.137623
$494$	−14.9443	−0.672375
$495$	−1.23607	−0.0555571
$496$	−9.85410	−0.442462
$497$	−38.1246	−1.71012
$498$	−19.7082	−0.883146
$499$	−15.8885	−0.711269	−0.355634	−	0.934625i	$-0.615735\pi$
$499$	−15.8885	−0.711269	−0.355634	+	0.934625i	$0.615735\pi$
$500$	−11.3951	−0.509605
$501$	−14.6525	−0.654624
$502$	17.7082	0.790356
$503$	−31.3607	−1.39830	−0.699152	−	0.714973i	$-0.746439\pi$
$503$	−31.3607	−1.39830	−0.699152	+	0.714973i	$0.746439\pi$
$504$	31.6525	1.40991
$505$	−2.41641	−0.107529
$506$	44.3607	1.97207
$507$	2.52786	0.112266
$508$	13.4164	0.595257
$509$	39.7082	1.76004	0.880018	−	0.474941i	$-0.157531\pi$
$509$	39.7082	1.76004	0.880018	+	0.474941i	$0.157531\pi$
$510$	1.52786	0.0676550
$511$	5.23607	0.231630
$512$	40.3050	1.78124
$513$	1.76393	0.0778795
$514$	−48.9787	−2.16036
$515$	−4.30495	−0.189699
$516$	−18.0000	−0.792406
$517$	−33.8885	−1.49042
$518$	85.4853	3.75601
$519$	10.9443	0.480400
$520$	5.70820	0.250321
$521$	−36.4721	−1.59787	−0.798937	−	0.601415i	$-0.794604\pi$
$521$	−36.4721	−1.59787	−0.798937	+	0.601415i	$0.794604\pi$
$522$	3.23607	0.141639
$523$	−24.5410	−1.07310	−0.536552	−	0.843867i	$-0.680273\pi$
$523$	−24.5410	−1.07310	−0.536552	+	0.843867i	$0.680273\pi$
$524$	0	0
$525$	−20.9443	−0.914083
$526$	−24.9443	−1.08762
$527$	−2.47214	−0.107688
$528$	51.5967	2.24546
$529$	−12.5279	−0.544690
$530$	5.52786	0.240115
$531$	−3.00000	−0.130189
$532$	36.2705	1.57253
$533$	21.7082	0.940287
$534$	−28.6525	−1.23991
$535$	−1.76393	−0.0762614
$536$	89.6656	3.87297
$537$	7.41641	0.320042
$538$	−48.8328	−2.10533
$539$	−57.3050	−2.46830
$540$	−1.14590	−0.0493116
$541$	−9.00000	−0.386940	−0.193470	−	0.981106i	$-0.561974\pi$
$541$	−9.00000	−0.386940	−0.193470	+	0.981106i	$0.561974\pi$
$542$	−35.1246	−1.50873
$543$	7.41641	0.318269
$544$	−26.8328	−1.15045
$545$	−1.18034	−0.0505602
$546$	35.8885	1.53589
$547$	35.5410	1.51962	0.759812	−	0.650143i	$-0.225291\pi$
$547$	35.5410	1.51962	0.759812	+	0.650143i	$0.225291\pi$
$548$	59.1246	2.52568
$549$	8.00000	0.341432
$550$	−67.7771	−2.89002
$551$	2.18034	0.0928856
$552$	24.1803	1.02918
$553$	2.00000	0.0850487
$554$	−1.23607	−0.0525155
$555$	−1.81966	−0.0772403
$556$	−37.4164	−1.58681
$557$	−6.65248	−0.281874	−0.140937	−	0.990019i	$-0.545012\pi$
$557$	−6.65248	−0.281874	−0.140937	+	0.990019i	$0.545012\pi$
$558$	2.61803	0.110830
$559$	−12.0000	−0.507546
$560$	−9.85410	−0.416412
$561$	12.9443	0.546508
$562$	62.2148	2.62437
$563$	−44.8885	−1.89183	−0.945913	−	0.324420i	$-0.894831\pi$
$563$	−44.8885	−1.89183	−0.945913	+	0.324420i	$0.894831\pi$
$564$	−31.4164	−1.32287
$565$	−1.47214	−0.0619332
$566$	20.9443	0.880353
$567$	−4.23607	−0.177898
$568$	−67.2492	−2.82171
$569$	−5.88854	−0.246861	−0.123430	−	0.992353i	$-0.539390\pi$
$569$	−5.88854	−0.246861	−0.123430	+	0.992353i	$0.539390\pi$
$570$	−1.09017	−0.0456622
$571$	10.2918	0.430698	0.215349	−	0.976537i	$-0.430911\pi$
$571$	10.2918	0.430698	0.215349	+	0.976537i	$0.430911\pi$
$572$	82.2492	3.43901
$573$	−3.94427	−0.164774
$574$	−74.3951	−3.10519
$575$	−16.0000	−0.667246
$576$	8.70820	0.362842
$577$	−14.3607	−0.597843	−0.298921	−	0.954278i	$-0.596627\pi$
$577$	−14.3607	−0.597843	−0.298921	+	0.954278i	$0.596627\pi$
$578$	28.5066	1.18572
$579$	3.00000	0.124676
$580$	−1.41641	−0.0588131
$581$	31.8885	1.32296
$582$	23.5623	0.976689
$583$	46.8328	1.93962
$584$	9.23607	0.382191
$585$	−0.763932	−0.0315847
$586$	79.4853	3.28351
$587$	−25.5279	−1.05365	−0.526824	−	0.849974i	$-0.676617\pi$
$587$	−25.5279	−1.05365	−0.526824	+	0.849974i	$0.676617\pi$
$588$	−53.1246	−2.19082
$589$	1.76393	0.0726816
$590$	1.85410	0.0763322
$591$	−0.763932	−0.0314240
$592$	75.9574	3.12183
$593$	−18.7082	−0.768254	−0.384127	−	0.923280i	$-0.625497\pi$
$593$	−18.7082	−0.768254	−0.384127	+	0.923280i	$0.625497\pi$
$594$	−13.7082	−0.562454
$595$	−2.47214	−0.101348
$596$	65.1246	2.66761
$597$	−10.1803	−0.416654
$598$	27.4164	1.12114
$599$	−20.0557	−0.819455	−0.409727	−	0.912208i	$-0.634376\pi$
$599$	−20.0557	−0.819455	−0.409727	+	0.912208i	$0.634376\pi$
$600$	−36.9443	−1.50824
$601$	46.5410	1.89845	0.949224	−	0.314601i	$-0.101871\pi$
$601$	46.5410	1.89845	0.949224	+	0.314601i	$0.101871\pi$
$602$	41.1246	1.67611
$603$	−12.0000	−0.488678
$604$	52.2492	2.12599
$605$	3.87539	0.157557
$606$	−26.7984	−1.08861
$607$	−26.8328	−1.08911	−0.544555	−	0.838725i	$-0.683302\pi$
$607$	−26.8328	−1.08911	−0.544555	+	0.838725i	$0.683302\pi$
$608$	19.1459	0.776469
$609$	−5.23607	−0.212176
$610$	−4.94427	−0.200188
$611$	−20.9443	−0.847315
$612$	12.0000	0.485071
$613$	9.41641	0.380325	0.190163	−	0.981753i	$-0.439098\pi$
$613$	9.41641	0.380325	0.190163	+	0.981753i	$0.439098\pi$
$614$	15.0902	0.608990
$615$	1.58359	0.0638566
$616$	−165.735	−6.67763
$617$	−13.4164	−0.540124	−0.270062	−	0.962843i	$-0.587044\pi$
$617$	−13.4164	−0.540124	−0.270062	+	0.962843i	$0.587044\pi$
$618$	−47.7426	−1.92049
$619$	6.00000	0.241160	0.120580	−	0.992704i	$-0.461525\pi$
$619$	6.00000	0.241160	0.120580	+	0.992704i	$0.461525\pi$
$620$	−1.14590	−0.0460204
$621$	−3.23607	−0.129859
$622$	−9.09017	−0.364483
$623$	46.3607	1.85740
$624$	31.8885	1.27656
$625$	24.1672	0.966687
$626$	−6.47214	−0.258679
$627$	−9.23607	−0.368853
$628$	−106.520	−4.25060
$629$	19.0557	0.759802
$630$	2.61803	0.104305
$631$	28.8328	1.14782	0.573908	−	0.818920i	$-0.305427\pi$
$631$	28.8328	1.14782	0.573908	+	0.818920i	$0.305427\pi$
$632$	3.52786	0.140331
$633$	12.7082	0.505106
$634$	21.2705	0.844760
$635$	0.652476	0.0258927
$636$	43.4164	1.72157
$637$	−35.4164	−1.40325
$638$	−16.9443	−0.670830
$639$	9.00000	0.356034
$640$	−0.257354	−0.0101728
$641$	31.4164	1.24087	0.620437	−	0.784256i	$-0.286955\pi$
$641$	31.4164	1.24087	0.620437	+	0.784256i	$0.286955\pi$
$642$	−19.5623	−0.772063
$643$	−35.5279	−1.40108	−0.700541	−	0.713612i	$-0.747058\pi$
$643$	−35.5279	−1.40108	−0.700541	+	0.713612i	$0.747058\pi$
$644$	−66.5410	−2.62208
$645$	−0.875388	−0.0344684
$646$	11.4164	0.449173
$647$	−39.5967	−1.55671	−0.778354	−	0.627825i	$-0.783945\pi$
$647$	−39.5967	−1.55671	−0.778354	+	0.627825i	$0.783945\pi$
$648$	−7.47214	−0.293533
$649$	15.7082	0.616601
$650$	−41.8885	−1.64300
$651$	−4.23607	−0.166025
$652$	73.6869	2.88580
$653$	11.8885	0.465235	0.232617	−	0.972568i	$-0.425271\pi$
$653$	11.8885	0.465235	0.232617	+	0.972568i	$0.425271\pi$
$654$	−13.0902	−0.511866
$655$	0	0
$656$	−66.1033	−2.58090
$657$	−1.23607	−0.0482236
$658$	71.7771	2.79816
$659$	18.3050	0.713060	0.356530	−	0.934284i	$-0.383960\pi$
$659$	18.3050	0.713060	0.356530	+	0.934284i	$0.383960\pi$
$660$	6.00000	0.233550
$661$	0.527864	0.0205315	0.0102658	−	0.999947i	$-0.496732\pi$
$661$	0.527864	0.0205315	0.0102658	+	0.999947i	$0.496732\pi$
$662$	85.9574	3.34083
$663$	8.00000	0.310694
$664$	56.2492	2.18289
$665$	1.76393	0.0684023
$666$	−20.1803	−0.781972
$667$	−4.00000	−0.154881
$668$	71.1246	2.75189
$669$	24.1803	0.934866
$670$	7.41641	0.286521
$671$	−41.8885	−1.61709
$672$	−45.9787	−1.77367
$673$	7.12461	0.274634	0.137317	−	0.990527i	$-0.456152\pi$
$673$	7.12461	0.274634	0.137317	+	0.990527i	$0.456152\pi$
$674$	−91.4853	−3.52388
$675$	4.94427	0.190305
$676$	−12.2705	−0.471943
$677$	20.6525	0.793739	0.396870	−	0.917875i	$-0.370097\pi$
$677$	20.6525	0.793739	0.396870	+	0.917875i	$0.370097\pi$
$678$	−16.3262	−0.627005
$679$	−38.1246	−1.46309
$680$	−4.36068	−0.167224
$681$	12.9443	0.496026
$682$	−13.7082	−0.524914
$683$	8.88854	0.340111	0.170055	−	0.985435i	$-0.445605\pi$
$683$	8.88854	0.340111	0.170055	+	0.985435i	$0.445605\pi$
$684$	−8.56231	−0.327388
$685$	2.87539	0.109863
$686$	43.7426	1.67010
$687$	3.70820	0.141477
$688$	36.5410	1.39311
$689$	28.9443	1.10269
$690$	2.00000	0.0761387
$691$	−9.29180	−0.353477	−0.176738	−	0.984258i	$-0.556555\pi$
$691$	−9.29180	−0.353477	−0.176738	+	0.984258i	$0.556555\pi$
$692$	−53.1246	−2.01949
$693$	22.1803	0.842561
$694$	−90.7214	−3.44374
$695$	−1.81966	−0.0690236
$696$	−9.23607	−0.350092
$697$	−16.5836	−0.628148
$698$	20.6525	0.781708
$699$	12.7082	0.480668
$700$	101.666	3.84260
$701$	−11.2918	−0.426485	−0.213243	−	0.976999i	$-0.568402\pi$
$701$	−11.2918	−0.426485	−0.213243	+	0.976999i	$0.568402\pi$
$702$	−8.47214	−0.319760
$703$	−13.5967	−0.512811
$704$	−45.5967	−1.71849
$705$	−1.52786	−0.0575427
$706$	33.4164	1.25764
$707$	43.3607	1.63075
$708$	14.5623	0.547285
$709$	14.8328	0.557058	0.278529	−	0.960428i	$-0.410153\pi$
$709$	14.8328	0.557058	0.278529	+	0.960428i	$0.410153\pi$
$710$	−5.56231	−0.208750
$711$	−0.472136	−0.0177065
$712$	81.7771	3.06473
$713$	−3.23607	−0.121192
$714$	−27.4164	−1.02603
$715$	4.00000	0.149592
$716$	−36.0000	−1.34538
$717$	−23.8885	−0.892134
$718$	−70.3951	−2.62712
$719$	−45.1935	−1.68543	−0.842716	−	0.538358i	$-0.819045\pi$
$719$	−45.1935	−1.68543	−0.842716	+	0.538358i	$0.819045\pi$
$720$	2.32624	0.0866938
$721$	77.2492	2.87691
$722$	41.5967	1.54807
$723$	0.291796	0.0108520
$724$	−36.0000	−1.33793
$725$	6.11146	0.226974
$726$	42.9787	1.59509
$727$	−16.1246	−0.598029	−0.299014	−	0.954249i	$-0.596658\pi$
$727$	−16.1246	−0.598029	−0.299014	+	0.954249i	$0.596658\pi$
$728$	−102.430	−3.79629
$729$	1.00000	0.0370370
$730$	0.763932	0.0282744
$731$	9.16718	0.339061
$732$	−38.8328	−1.43530
$733$	−7.00000	−0.258551	−0.129275	−	0.991609i	$-0.541265\pi$
$733$	−7.00000	−0.258551	−0.129275	+	0.991609i	$0.541265\pi$
$734$	−91.4853	−3.37678
$735$	−2.58359	−0.0952972
$736$	−35.1246	−1.29471
$737$	62.8328	2.31448
$738$	17.5623	0.646477
$739$	38.7639	1.42595	0.712977	−	0.701187i	$-0.247346\pi$
$739$	38.7639	1.42595	0.712977	+	0.701187i	$0.247346\pi$
$740$	8.83282	0.324701
$741$	−5.70820	−0.209696
$742$	−99.1935	−3.64151
$743$	−34.7639	−1.27536	−0.637682	−	0.770299i	$-0.720107\pi$
$743$	−34.7639	−1.27536	−0.637682	+	0.770299i	$0.720107\pi$
$744$	−7.47214	−0.273942
$745$	3.16718	0.116037
$746$	−90.1033	−3.29892
$747$	−7.52786	−0.275430
$748$	−62.8328	−2.29740
$749$	31.6525	1.15656
$750$	−6.14590	−0.224416
$751$	−12.7082	−0.463729	−0.231864	−	0.972748i	$-0.574483\pi$
$751$	−12.7082	−0.463729	−0.231864	+	0.972748i	$0.574483\pi$
$752$	63.7771	2.32571
$753$	6.76393	0.246491
$754$	−10.4721	−0.381373
$755$	2.54102	0.0924772
$756$	20.5623	0.747844
$757$	−41.5967	−1.51186	−0.755930	−	0.654653i	$-0.772815\pi$
$757$	−41.5967	−1.51186	−0.755930	+	0.654653i	$0.772815\pi$
$758$	−69.3050	−2.51727
$759$	16.9443	0.615038
$760$	3.11146	0.112864
$761$	−37.2361	−1.34981	−0.674903	−	0.737906i	$-0.735815\pi$
$761$	−37.2361	−1.34981	−0.674903	+	0.737906i	$0.735815\pi$
$762$	7.23607	0.262135
$763$	21.1803	0.766780
$764$	19.1459	0.692674
$765$	0.583592	0.0210998
$766$	39.1246	1.41363
$767$	9.70820	0.350543
$768$	14.5623	0.525472
$769$	52.4164	1.89018	0.945092	−	0.326804i	$-0.105972\pi$
$769$	52.4164	1.89018	0.945092	+	0.326804i	$0.105972\pi$
$770$	−13.7082	−0.494009
$771$	−18.7082	−0.673760
$772$	−14.5623	−0.524109
$773$	33.2361	1.19542	0.597709	−	0.801713i	$-0.296078\pi$
$773$	33.2361	1.19542	0.597709	+	0.801713i	$0.296078\pi$
$774$	−9.70820	−0.348954
$775$	4.94427	0.177603
$776$	−67.2492	−2.41411
$777$	32.6525	1.17140
$778$	−10.0000	−0.358517
$779$	11.8328	0.423955
$780$	3.70820	0.132775
$781$	−47.1246	−1.68625
$782$	−20.9443	−0.748966
$783$	1.23607	0.0441735
$784$	107.846	3.85164
$785$	−5.18034	−0.184894
$786$	0	0
$787$	12.8328	0.457440	0.228720	−	0.973492i	$-0.426546\pi$
$787$	12.8328	0.457440	0.228720	+	0.973492i	$0.426546\pi$
$788$	3.70820	0.132099
$789$	−9.52786	−0.339201
$790$	0.291796	0.0103816
$791$	26.4164	0.939259
$792$	39.1246	1.39023
$793$	−25.8885	−0.919329
$794$	9.38197	0.332954
$795$	2.11146	0.0748856
$796$	49.4164	1.75152
$797$	−47.7771	−1.69235	−0.846176	−	0.532904i	$-0.821101\pi$
$797$	−47.7771	−1.69235	−0.846176	+	0.532904i	$0.821101\pi$
$798$	19.5623	0.692498
$799$	16.0000	0.566039
$800$	53.6656	1.89737
$801$	−10.9443	−0.386697
$802$	−13.7082	−0.484054
$803$	6.47214	0.228397
$804$	58.2492	2.05429
$805$	−3.23607	−0.114056
$806$	−8.47214	−0.298418
$807$	−18.6525	−0.656598
$808$	76.4853	2.69074
$809$	23.0132	0.809099	0.404550	−	0.914516i	$-0.367428\pi$
$809$	23.0132	0.809099	0.404550	+	0.914516i	$0.367428\pi$
$810$	−0.618034	−0.0217155
$811$	6.83282	0.239933	0.119966	−	0.992778i	$-0.461721\pi$
$811$	6.83282	0.239933	0.119966	+	0.992778i	$0.461721\pi$
$812$	25.4164	0.891941
$813$	−13.4164	−0.470534
$814$	105.666	3.70358
$815$	3.58359	0.125528
$816$	−24.3607	−0.852794
$817$	−6.54102	−0.228841
$818$	44.8328	1.56754
$819$	13.7082	0.479003
$820$	−7.68692	−0.268439
$821$	−7.30495	−0.254945	−0.127472	−	0.991842i	$-0.540686\pi$
$821$	−7.30495	−0.254945	−0.127472	+	0.991842i	$0.540686\pi$
$822$	31.8885	1.11224
$823$	−34.8328	−1.21420	−0.607098	−	0.794627i	$-0.707666\pi$
$823$	−34.8328	−1.21420	−0.607098	+	0.794627i	$0.707666\pi$
$824$	136.262	4.74692
$825$	−25.8885	−0.901323
$826$	−33.2705	−1.15763
$827$	−41.1246	−1.43004	−0.715021	−	0.699103i	$-0.753583\pi$
$827$	−41.1246	−1.43004	−0.715021	+	0.699103i	$0.753583\pi$
$828$	15.7082	0.545898
$829$	21.4164	0.743823	0.371911	−	0.928268i	$-0.378703\pi$
$829$	21.4164	0.743823	0.371911	+	0.928268i	$0.378703\pi$
$830$	4.65248	0.161490
$831$	−0.472136	−0.0163782
$832$	−28.1803	−0.976978
$833$	27.0557	0.937425
$834$	−20.1803	−0.698788
$835$	3.45898	0.119703
$836$	44.8328	1.55058
$837$	1.00000	0.0345651
$838$	−23.5623	−0.813946
$839$	−3.05573	−0.105495	−0.0527477	−	0.998608i	$-0.516798\pi$
$839$	−3.05573	−0.105495	−0.0527477	+	0.998608i	$0.516798\pi$
$840$	−7.47214	−0.257813
$841$	−27.4721	−0.947315
$842$	−32.5066	−1.12025
$843$	23.7639	0.818473
$844$	−61.6869	−2.12335
$845$	−0.596748	−0.0205287
$846$	−16.9443	−0.582556
$847$	−69.5410	−2.38946
$848$	−88.1378	−3.02666
$849$	8.00000	0.274559
$850$	32.0000	1.09759
$851$	24.9443	0.855079
$852$	−43.6869	−1.49669
$853$	−32.4721	−1.11182	−0.555912	−	0.831241i	$-0.687631\pi$
$853$	−32.4721	−1.11182	−0.555912	+	0.831241i	$0.687631\pi$
$854$	88.7214	3.03598
$855$	−0.416408	−0.0142408
$856$	55.8328	1.90833
$857$	55.3050	1.88918	0.944591	−	0.328251i	$-0.106459\pi$
$857$	55.3050	1.88918	0.944591	+	0.328251i	$0.106459\pi$
$858$	44.3607	1.51445
$859$	−0.180340	−0.00615312	−0.00307656	−	0.999995i	$-0.500979\pi$
$859$	−0.180340	−0.00615312	−0.00307656	+	0.999995i	$0.500979\pi$
$860$	4.24922	0.144897
$861$	−28.4164	−0.968429
$862$	−6.47214	−0.220442
$863$	51.3050	1.74644	0.873220	−	0.487325i	$-0.162027\pi$
$863$	51.3050	1.74644	0.873220	+	0.487325i	$0.162027\pi$
$864$	10.8541	0.369264
$865$	−2.58359	−0.0878448
$866$	−9.23607	−0.313854
$867$	10.8885	0.369794
$868$	20.5623	0.697930
$869$	2.47214	0.0838615
$870$	−0.763932	−0.0258997
$871$	38.8328	1.31580
$872$	37.3607	1.26519
$873$	9.00000	0.304604
$874$	14.9443	0.505498
$875$	9.94427	0.336178
$876$	6.00000	0.202721
$877$	23.8328	0.804777	0.402389	−	0.915469i	$-0.368180\pi$
$877$	23.8328	0.804777	0.402389	+	0.915469i	$0.368180\pi$
$878$	−7.09017	−0.239282
$879$	30.3607	1.02404
$880$	−12.1803	−0.410599
$881$	−17.3050	−0.583019	−0.291509	−	0.956568i	$-0.594157\pi$
$881$	−17.3050	−0.583019	−0.291509	+	0.956568i	$0.594157\pi$
$882$	−28.6525	−0.964779
$883$	−26.8328	−0.902996	−0.451498	−	0.892272i	$-0.649110\pi$
$883$	−26.8328	−0.902996	−0.451498	+	0.892272i	$0.649110\pi$
$884$	−38.8328	−1.30609
$885$	0.708204	0.0238060
$886$	−50.6869	−1.70286
$887$	46.4164	1.55851	0.779255	−	0.626707i	$-0.215598\pi$
$887$	46.4164	1.55851	0.779255	+	0.626707i	$0.215598\pi$
$888$	57.5967	1.93282
$889$	−11.7082	−0.392681
$890$	6.76393	0.226728
$891$	−5.23607	−0.175415
$892$	−117.374	−3.92997
$893$	−11.4164	−0.382036
$894$	35.1246	1.17474
$895$	−1.75078	−0.0585220
$896$	4.61803	0.154278
$897$	10.4721	0.349654
$898$	−1.70820	−0.0570035
$899$	1.23607	0.0412252
$900$	−24.0000	−0.800000
$901$	−22.1115	−0.736639
$902$	−91.9574	−3.06185
$903$	15.7082	0.522736
$904$	46.5967	1.54978
$905$	−1.75078	−0.0581978
$906$	28.1803	0.936229
$907$	−50.9574	−1.69201	−0.846007	−	0.533172i	$-0.821000\pi$
$907$	−50.9574	−1.69201	−0.846007	+	0.533172i	$0.821000\pi$
$908$	−62.8328	−2.08518
$909$	−10.2361	−0.339509
$910$	−8.47214	−0.280849
$911$	2.18034	0.0722379	0.0361189	−	0.999347i	$-0.488500\pi$
$911$	2.18034	0.0722379	0.0361189	+	0.999347i	$0.488500\pi$
$912$	17.3820	0.575574
$913$	39.4164	1.30449
$914$	76.2492	2.52210
$915$	−1.88854	−0.0624333
$916$	−18.0000	−0.594737
$917$	0	0
$918$	6.47214	0.213612
$919$	−24.0000	−0.791687	−0.395843	−	0.918318i	$-0.629548\pi$
$919$	−24.0000	−0.791687	−0.395843	+	0.918318i	$0.629548\pi$
$920$	−5.70820	−0.188194
$921$	5.76393	0.189928
$922$	−31.1246	−1.02503
$923$	−29.1246	−0.958648
$924$	−107.666	−3.54194
$925$	−38.1115	−1.25310
$926$	−75.4853	−2.48060
$927$	−18.2361	−0.598951
$928$	13.4164	0.440415
$929$	−12.7639	−0.418771	−0.209386	−	0.977833i	$-0.567146\pi$
$929$	−12.7639	−0.418771	−0.209386	+	0.977833i	$0.567146\pi$
$930$	−0.618034	−0.0202661
$931$	−19.3050	−0.632694
$932$	−61.6869	−2.02062
$933$	−3.47214	−0.113673
$934$	−99.3394	−3.25048
$935$	−3.05573	−0.0999330
$936$	24.1803	0.790359
$937$	20.8328	0.680578	0.340289	−	0.940321i	$-0.389475\pi$
$937$	20.8328	0.680578	0.340289	+	0.940321i	$0.389475\pi$
$938$	−133.082	−4.34528
$939$	−2.47214	−0.0806751
$940$	7.41641	0.241897
$941$	−9.05573	−0.295208	−0.147604	−	0.989047i	$-0.547156\pi$
$941$	−9.05573	−0.295208	−0.147604	+	0.989047i	$0.547156\pi$
$942$	−57.4508	−1.87185
$943$	−21.7082	−0.706916
$944$	−29.5623	−0.962171
$945$	1.00000	0.0325300
$946$	50.8328	1.65272
$947$	−30.1803	−0.980729	−0.490365	−	0.871517i	$-0.663136\pi$
$947$	−30.1803	−0.980729	−0.490365	+	0.871517i	$0.663136\pi$
$948$	2.29180	0.0744341
$949$	4.00000	0.129845
$950$	−22.8328	−0.740794
$951$	8.12461	0.263459
$952$	78.2492	2.53607
$953$	16.9443	0.548879	0.274439	−	0.961604i	$-0.411508\pi$
$953$	16.9443	0.548879	0.274439	+	0.961604i	$0.411508\pi$
$954$	23.4164	0.758134
$955$	0.931116	0.0301302
$956$	115.957	3.75033
$957$	−6.47214	−0.209214
$958$	46.9787	1.51781
$959$	−51.5967	−1.66615
$960$	−2.05573	−0.0663483
$961$	1.00000	0.0322581
$962$	65.3050	2.10552
$963$	−7.47214	−0.240786
$964$	−1.41641	−0.0456194
$965$	−0.708204	−0.0227979
$966$	−35.8885	−1.15469
$967$	16.5410	0.531923	0.265962	−	0.963984i	$-0.414311\pi$
$967$	16.5410	0.531923	0.265962	+	0.963984i	$0.414311\pi$
$968$	−122.666	−3.94262
$969$	4.36068	0.140085
$970$	−5.56231	−0.178595
$971$	48.0000	1.54039	0.770197	−	0.637806i	$-0.220158\pi$
$971$	48.0000	1.54039	0.770197	+	0.637806i	$0.220158\pi$
$972$	−4.85410	−0.155695
$973$	32.6525	1.04679
$974$	−25.4164	−0.814394
$975$	−16.0000	−0.512410
$976$	78.8328	2.52338
$977$	24.7082	0.790485	0.395243	−	0.918577i	$-0.370660\pi$
$977$	24.7082	0.790485	0.395243	+	0.918577i	$0.370660\pi$
$978$	39.7426	1.27083
$979$	57.3050	1.83147
$980$	12.5410	0.400608
$981$	−5.00000	−0.159638
$982$	94.7214	3.02268
$983$	−33.2361	−1.06007	−0.530033	−	0.847977i	$-0.677820\pi$
$983$	−33.2361	−1.06007	−0.530033	+	0.847977i	$0.677820\pi$
$984$	−50.1246	−1.59791
$985$	0.180340	0.00574611
$986$	8.00000	0.254772
$987$	27.4164	0.872674
$988$	27.7082	0.881515
$989$	12.0000	0.381578
$990$	3.23607	0.102849
$991$	−52.7214	−1.67475	−0.837375	−	0.546629i	$-0.815911\pi$
$991$	−52.7214	−1.67475	−0.837375	+	0.546629i	$0.815911\pi$
$992$	10.8541	0.344618
$993$	32.8328	1.04192
$994$	99.8115	3.16583
$995$	2.40325	0.0761882
$996$	36.5410	1.15785
$997$	22.4164	0.709935	0.354967	−	0.934879i	$-0.384492\pi$
$997$	22.4164	0.709935	0.354967	+	0.934879i	$0.384492\pi$
$998$	41.5967	1.31672
$999$	−7.70820	−0.243877

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.a.a.1.1	✓	2
3.2	odd	2		279.2.a.b.1.2		2
4.3	odd	2		1488.2.a.q.1.2		2
5.2	odd	4		2325.2.c.h.1024.1		4
5.3	odd	4		2325.2.c.h.1024.4		4
5.4	even	2		2325.2.a.o.1.2		2
7.6	odd	2		4557.2.a.p.1.1		2
8.3	odd	2		5952.2.a.bo.1.1		2
8.5	even	2		5952.2.a.bv.1.1		2
12.11	even	2		4464.2.a.bn.1.1		2
15.14	odd	2		6975.2.a.t.1.1		2
31.30	odd	2		2883.2.a.a.1.1		2
93.92	even	2		8649.2.a.m.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.a.a.1.1	✓	2	1.1	even	1	trivial
279.2.a.b.1.2		2	3.2	odd	2
1488.2.a.q.1.2		2	4.3	odd	2
2325.2.a.o.1.2		2	5.4	even	2
2325.2.c.h.1024.1		4	5.2	odd	4
2325.2.c.h.1024.4		4	5.3	odd	4
2883.2.a.a.1.1		2	31.30	odd	2
4464.2.a.bn.1.1		2	12.11	even	2
4557.2.a.p.1.1		2	7.6	odd	2
5952.2.a.bo.1.1		2	8.3	odd	2
5952.2.a.bv.1.1		2	8.5	even	2
6975.2.a.t.1.1		2	15.14	odd	2
8649.2.a.m.1.2		2	93.92	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61803 q^{2} -1.00000 q^{3} +4.85410 q^{4} +0.236068 q^{5} +2.61803 q^{6} -4.23607 q^{7} -7.47214 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.61803 q^{2} -1.00000 q^{3} +4.85410 q^{4} +0.236068 q^{5} +2.61803 q^{6} -4.23607 q^{7} -7.47214 q^{8} +1.00000 q^{9} -0.618034 q^{10} -5.23607 q^{11} -4.85410 q^{12} -3.23607 q^{13} +11.0902 q^{14} -0.236068 q^{15} +9.85410 q^{16} +2.47214 q^{17} -2.61803 q^{18} -1.76393 q^{19} +1.14590 q^{20} +4.23607 q^{21} +13.7082 q^{22} +3.23607 q^{23} +7.47214 q^{24} -4.94427 q^{25} +8.47214 q^{26} -1.00000 q^{27} -20.5623 q^{28} -1.23607 q^{29} +0.618034 q^{30} -1.00000 q^{31} -10.8541 q^{32} +5.23607 q^{33} -6.47214 q^{34} -1.00000 q^{35} +4.85410 q^{36} +7.70820 q^{37} +4.61803 q^{38} +3.23607 q^{39} -1.76393 q^{40} -6.70820 q^{41} -11.0902 q^{42} +3.70820 q^{43} -25.4164 q^{44} +0.236068 q^{45} -8.47214 q^{46} +6.47214 q^{47} -9.85410 q^{48} +10.9443 q^{49} +12.9443 q^{50} -2.47214 q^{51} -15.7082 q^{52} -8.94427 q^{53} +2.61803 q^{54} -1.23607 q^{55} +31.6525 q^{56} +1.76393 q^{57} +3.23607 q^{58} -3.00000 q^{59} -1.14590 q^{60} +8.00000 q^{61} +2.61803 q^{62} -4.23607 q^{63} +8.70820 q^{64} -0.763932 q^{65} -13.7082 q^{66} -12.0000 q^{67} +12.0000 q^{68} -3.23607 q^{69} +2.61803 q^{70} +9.00000 q^{71} -7.47214 q^{72} -1.23607 q^{73} -20.1803 q^{74} +4.94427 q^{75} -8.56231 q^{76} +22.1803 q^{77} -8.47214 q^{78} -0.472136 q^{79} +2.32624 q^{80} +1.00000 q^{81} +17.5623 q^{82} -7.52786 q^{83} +20.5623 q^{84} +0.583592 q^{85} -9.70820 q^{86} +1.23607 q^{87} +39.1246 q^{88} -10.9443 q^{89} -0.618034 q^{90} +13.7082 q^{91} +15.7082 q^{92} +1.00000 q^{93} -16.9443 q^{94} -0.416408 q^{95} +10.8541 q^{96} +9.00000 q^{97} -28.6525 q^{98} -5.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - 4 q^{5} + 3 q^{6} - 4 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - 4 * q^5 + 3 * q^6 - 4 * q^7 - 6 * q^8 + 2 * q^9	\( 2 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - 4 q^{5} + 3 q^{6} - 4 q^{7} - 6 q^{8} + 2 q^{9} + q^{10} - 6 q^{11} - 3 q^{12} - 2 q^{13} + 11 q^{14} + 4 q^{15} + 13 q^{16} - 4 q^{17} - 3 q^{18} - 8 q^{19} + 9 q^{20} + 4 q^{21} + 14 q^{22} + 2 q^{23} + 6 q^{24} + 8 q^{25} + 8 q^{26} - 2 q^{27} - 21 q^{28} + 2 q^{29} - q^{30} - 2 q^{31} - 15 q^{32} + 6 q^{33} - 4 q^{34} - 2 q^{35} + 3 q^{36} + 2 q^{37} + 7 q^{38} + 2 q^{39} - 8 q^{40} - 11 q^{42} - 6 q^{43} - 24 q^{44} - 4 q^{45} - 8 q^{46} + 4 q^{47} - 13 q^{48} + 4 q^{49} + 8 q^{50} + 4 q^{51} - 18 q^{52} + 3 q^{54} + 2 q^{55} + 32 q^{56} + 8 q^{57} + 2 q^{58} - 6 q^{59} - 9 q^{60} + 16 q^{61} + 3 q^{62} - 4 q^{63} + 4 q^{64} - 6 q^{65} - 14 q^{66} - 24 q^{67} + 24 q^{68} - 2 q^{69} + 3 q^{70} + 18 q^{71} - 6 q^{72} + 2 q^{73} - 18 q^{74} - 8 q^{75} + 3 q^{76} + 22 q^{77} - 8 q^{78} + 8 q^{79} - 11 q^{80} + 2 q^{81} + 15 q^{82} - 24 q^{83} + 21 q^{84} + 28 q^{85} - 6 q^{86} - 2 q^{87} + 38 q^{88} - 4 q^{89} + q^{90} + 14 q^{91} + 18 q^{92} + 2 q^{93} - 16 q^{94} + 26 q^{95} + 15 q^{96} + 18 q^{97} - 26 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - 4 * q^5 + 3 * q^6 - 4 * q^7 - 6 * q^8 + 2 * q^9 + q^10 - 6 * q^11 - 3 * q^12 - 2 * q^13 + 11 * q^14 + 4 * q^15 + 13 * q^16 - 4 * q^17 - 3 * q^18 - 8 * q^19 + 9 * q^20 + 4 * q^21 + 14 * q^22 + 2 * q^23 + 6 * q^24 + 8 * q^25 + 8 * q^26 - 2 * q^27 - 21 * q^28 + 2 * q^29 - q^30 - 2 * q^31 - 15 * q^32 + 6 * q^33 - 4 * q^34 - 2 * q^35 + 3 * q^36 + 2 * q^37 + 7 * q^38 + 2 * q^39 - 8 * q^40 - 11 * q^42 - 6 * q^43 - 24 * q^44 - 4 * q^45 - 8 * q^46 + 4 * q^47 - 13 * q^48 + 4 * q^49 + 8 * q^50 + 4 * q^51 - 18 * q^52 + 3 * q^54 + 2 * q^55 + 32 * q^56 + 8 * q^57 + 2 * q^58 - 6 * q^59 - 9 * q^60 + 16 * q^61 + 3 * q^62 - 4 * q^63 + 4 * q^64 - 6 * q^65 - 14 * q^66 - 24 * q^67 + 24 * q^68 - 2 * q^69 + 3 * q^70 + 18 * q^71 - 6 * q^72 + 2 * q^73 - 18 * q^74 - 8 * q^75 + 3 * q^76 + 22 * q^77 - 8 * q^78 + 8 * q^79 - 11 * q^80 + 2 * q^81 + 15 * q^82 - 24 * q^83 + 21 * q^84 + 28 * q^85 - 6 * q^86 - 2 * q^87 + 38 * q^88 - 4 * q^89 + q^90 + 14 * q^91 + 18 * q^92 + 2 * q^93 - 16 * q^94 + 26 * q^95 + 15 * q^96 + 18 * q^97 - 26 * q^98 - 6 * q^99

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