LMFDB - Embedded newform 6045.2.a.bh.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.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:	$48.2695680219$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 25 x^{15} + 47 x^{14} + 252 x^{13} - 437 x^{12} - 1319 x^{11} + 2056 x^{10} + \cdots + 8 $ x^17 - 2x^16 - 25x^15 + 47x^14 + 252x^13 - 437x^12 - 1319x^11 + 2056x^10 + 3854x^9 - 5201x^8 - 6304x^7 + 6915x^6 + 5469x^5 - 4238x^4 - 2198x^3 + 760x^2 + 306x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$2.54626$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.54626 q^{2} -1.00000 q^{3} +4.48346 q^{4} +1.00000 q^{5} -2.54626 q^{6} -1.02990 q^{7} +6.32355 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.54626 q^{2} -1.00000 q^{3} +4.48346 q^{4} +1.00000 q^{5} -2.54626 q^{6} -1.02990 q^{7} +6.32355 q^{8} +1.00000 q^{9} +2.54626 q^{10} +2.98909 q^{11} -4.48346 q^{12} +1.00000 q^{13} -2.62239 q^{14} -1.00000 q^{15} +7.13450 q^{16} +5.98536 q^{17} +2.54626 q^{18} -2.06421 q^{19} +4.48346 q^{20} +1.02990 q^{21} +7.61102 q^{22} +4.10895 q^{23} -6.32355 q^{24} +1.00000 q^{25} +2.54626 q^{26} -1.00000 q^{27} -4.61751 q^{28} +2.98050 q^{29} -2.54626 q^{30} +1.00000 q^{31} +5.51923 q^{32} -2.98909 q^{33} +15.2403 q^{34} -1.02990 q^{35} +4.48346 q^{36} -4.03351 q^{37} -5.25601 q^{38} -1.00000 q^{39} +6.32355 q^{40} +0.184510 q^{41} +2.62239 q^{42} -0.571830 q^{43} +13.4015 q^{44} +1.00000 q^{45} +10.4625 q^{46} -9.24553 q^{47} -7.13450 q^{48} -5.93931 q^{49} +2.54626 q^{50} -5.98536 q^{51} +4.48346 q^{52} -6.11650 q^{53} -2.54626 q^{54} +2.98909 q^{55} -6.51262 q^{56} +2.06421 q^{57} +7.58913 q^{58} +13.2766 q^{59} -4.48346 q^{60} -10.5214 q^{61} +2.54626 q^{62} -1.02990 q^{63} -0.215586 q^{64} +1.00000 q^{65} -7.61102 q^{66} +3.87908 q^{67} +26.8351 q^{68} -4.10895 q^{69} -2.62239 q^{70} -2.68065 q^{71} +6.32355 q^{72} +1.90612 q^{73} -10.2704 q^{74} -1.00000 q^{75} -9.25478 q^{76} -3.07846 q^{77} -2.54626 q^{78} +4.03783 q^{79} +7.13450 q^{80} +1.00000 q^{81} +0.469812 q^{82} +10.2125 q^{83} +4.61751 q^{84} +5.98536 q^{85} -1.45603 q^{86} -2.98050 q^{87} +18.9017 q^{88} +5.50706 q^{89} +2.54626 q^{90} -1.02990 q^{91} +18.4223 q^{92} -1.00000 q^{93} -23.5416 q^{94} -2.06421 q^{95} -5.51923 q^{96} +14.5645 q^{97} -15.1230 q^{98} +2.98909 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) $ 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9} + 2 q^{10} + 3 q^{11} - 20 q^{12} + 17 q^{13} + q^{14} - 17 q^{15} + 26 q^{16} + 2 q^{18} + 10 q^{19} + 20 q^{20} - 18 q^{21} + 5 q^{22} + 16 q^{23} - 9 q^{24} + 17 q^{25} + 2 q^{26} - 17 q^{27} + 36 q^{28} - 3 q^{29} - 2 q^{30} + 17 q^{31} + 20 q^{32} - 3 q^{33} + q^{34} + 18 q^{35} + 20 q^{36} + 14 q^{37} + 22 q^{38} - 17 q^{39} + 9 q^{40} - 6 q^{41} - q^{42} + 24 q^{43} - 15 q^{44} + 17 q^{45} + 6 q^{46} + 25 q^{47} - 26 q^{48} + 31 q^{49} + 2 q^{50} + 20 q^{52} - 15 q^{53} - 2 q^{54} + 3 q^{55} + 31 q^{56} - 10 q^{57} + 44 q^{58} + 16 q^{59} - 20 q^{60} - 5 q^{61} + 2 q^{62} + 18 q^{63} + 35 q^{64} + 17 q^{65} - 5 q^{66} + 50 q^{67} + 13 q^{68} - 16 q^{69} + q^{70} + 16 q^{71} + 9 q^{72} + 33 q^{73} + 2 q^{74} - 17 q^{75} + 9 q^{77} - 2 q^{78} - 10 q^{79} + 26 q^{80} + 17 q^{81} + 61 q^{82} + 27 q^{83} - 36 q^{84} - 12 q^{86} + 3 q^{87} + 23 q^{88} - 24 q^{89} + 2 q^{90} + 18 q^{91} - 21 q^{92} - 17 q^{93} + 6 q^{94} + 10 q^{95} - 20 q^{96} + 48 q^{97} + 14 q^{98} + 3 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9 + 2 * q^10 + 3 * q^11 - 20 * q^12 + 17 * q^13 + q^14 - 17 * q^15 + 26 * q^16 + 2 * q^18 + 10 * q^19 + 20 * q^20 - 18 * q^21 + 5 * q^22 + 16 * q^23 - 9 * q^24 + 17 * q^25 + 2 * q^26 - 17 * q^27 + 36 * q^28 - 3 * q^29 - 2 * q^30 + 17 * q^31 + 20 * q^32 - 3 * q^33 + q^34 + 18 * q^35 + 20 * q^36 + 14 * q^37 + 22 * q^38 - 17 * q^39 + 9 * q^40 - 6 * q^41 - q^42 + 24 * q^43 - 15 * q^44 + 17 * q^45 + 6 * q^46 + 25 * q^47 - 26 * q^48 + 31 * q^49 + 2 * q^50 + 20 * q^52 - 15 * q^53 - 2 * q^54 + 3 * q^55 + 31 * q^56 - 10 * q^57 + 44 * q^58 + 16 * q^59 - 20 * q^60 - 5 * q^61 + 2 * q^62 + 18 * q^63 + 35 * q^64 + 17 * q^65 - 5 * q^66 + 50 * q^67 + 13 * q^68 - 16 * q^69 + q^70 + 16 * q^71 + 9 * q^72 + 33 * q^73 + 2 * q^74 - 17 * q^75 + 9 * q^77 - 2 * q^78 - 10 * q^79 + 26 * q^80 + 17 * q^81 + 61 * q^82 + 27 * q^83 - 36 * q^84 - 12 * q^86 + 3 * q^87 + 23 * q^88 - 24 * q^89 + 2 * q^90 + 18 * q^91 - 21 * q^92 - 17 * q^93 + 6 * q^94 + 10 * q^95 - 20 * q^96 + 48 * q^97 + 14 * q^98 + 3 * 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 $

$2$	2.54626	1.80048	0.900240	−	0.435393i	$-0.143391\pi$
$2$	2.54626	1.80048	0.900240	+	0.435393i	$0.143391\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.48346	2.24173
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.54626	−1.03951
$7$	−1.02990	−0.389265	−0.194633	−	0.980876i	$-0.562351\pi$
$7$	−1.02990	−0.389265	−0.194633	+	0.980876i	$0.562351\pi$
$8$	6.32355	2.23571
$9$	1.00000	0.333333
$10$	2.54626	0.805199
$11$	2.98909	0.901246	0.450623	−	0.892714i	$-0.351202\pi$
$11$	2.98909	0.901246	0.450623	+	0.892714i	$0.351202\pi$
$12$	−4.48346	−1.29426
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.62239	−0.700864
$15$	−1.00000	−0.258199
$16$	7.13450	1.78363
$17$	5.98536	1.45166	0.725832	−	0.687872i	$-0.241455\pi$
$17$	5.98536	1.45166	0.725832	+	0.687872i	$0.241455\pi$
$18$	2.54626	0.600160
$19$	−2.06421	−0.473561	−0.236781	−	0.971563i	$-0.576092\pi$
$19$	−2.06421	−0.473561	−0.236781	+	0.971563i	$0.576092\pi$
$20$	4.48346	1.00253
$21$	1.02990	0.224742
$22$	7.61102	1.62268
$23$	4.10895	0.856775	0.428387	−	0.903595i	$-0.359082\pi$
$23$	4.10895	0.856775	0.428387	+	0.903595i	$0.359082\pi$
$24$	−6.32355	−1.29079
$25$	1.00000	0.200000
$26$	2.54626	0.499363
$27$	−1.00000	−0.192450
$28$	−4.61751	−0.872628
$29$	2.98050	0.553464	0.276732	−	0.960947i	$-0.410749\pi$
$29$	2.98050	0.553464	0.276732	+	0.960947i	$0.410749\pi$
$30$	−2.54626	−0.464882
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	5.51923	0.975671
$33$	−2.98909	−0.520334
$34$	15.2403	2.61369
$35$	−1.02990	−0.174085
$36$	4.48346	0.747244
$37$	−4.03351	−0.663105	−0.331552	−	0.943437i	$-0.607572\pi$
$37$	−4.03351	−0.663105	−0.331552	+	0.943437i	$0.607572\pi$
$38$	−5.25601	−0.852638
$39$	−1.00000	−0.160128
$40$	6.32355	0.999841
$41$	0.184510	0.0288157	0.0144078	−	0.999896i	$-0.495414\pi$
$41$	0.184510	0.0288157	0.0144078	+	0.999896i	$0.495414\pi$
$42$	2.62239	0.404644
$43$	−0.571830	−0.0872032	−0.0436016	−	0.999049i	$-0.513883\pi$
$43$	−0.571830	−0.0872032	−0.0436016	+	0.999049i	$0.513883\pi$
$44$	13.4015	2.02035
$45$	1.00000	0.149071
$46$	10.4625	1.54261
$47$	−9.24553	−1.34860	−0.674299	−	0.738458i	$-0.735554\pi$
$47$	−9.24553	−1.34860	−0.674299	+	0.738458i	$0.735554\pi$
$48$	−7.13450	−1.02978
$49$	−5.93931	−0.848473
$50$	2.54626	0.360096
$51$	−5.98536	−0.838119
$52$	4.48346	0.621744
$53$	−6.11650	−0.840165	−0.420083	−	0.907486i	$-0.637999\pi$
$53$	−6.11650	−0.840165	−0.420083	+	0.907486i	$0.637999\pi$
$54$	−2.54626	−0.346503
$55$	2.98909	0.403049
$56$	−6.51262	−0.870285
$57$	2.06421	0.273411
$58$	7.58913	0.996502
$59$	13.2766	1.72847	0.864236	−	0.503087i	$-0.167802\pi$
$59$	13.2766	1.72847	0.864236	+	0.503087i	$0.167802\pi$
$60$	−4.48346	−0.578812
$61$	−10.5214	−1.34712	−0.673561	−	0.739132i	$-0.735236\pi$
$61$	−10.5214	−1.34712	−0.673561	+	0.739132i	$0.735236\pi$
$62$	2.54626	0.323376
$63$	−1.02990	−0.129755
$64$	−0.215586	−0.0269483
$65$	1.00000	0.124035
$66$	−7.61102	−0.936852
$67$	3.87908	0.473905	0.236953	−	0.971521i	$-0.423851\pi$
$67$	3.87908	0.473905	0.236953	+	0.971521i	$0.423851\pi$
$68$	26.8351	3.25424
$69$	−4.10895	−0.494659
$70$	−2.62239	−0.313436
$71$	−2.68065	−0.318135	−0.159067	−	0.987268i	$-0.550849\pi$
$71$	−2.68065	−0.318135	−0.159067	+	0.987268i	$0.550849\pi$
$72$	6.32355	0.745237
$73$	1.90612	0.223095	0.111547	−	0.993759i	$-0.464419\pi$
$73$	1.90612	0.223095	0.111547	+	0.993759i	$0.464419\pi$
$74$	−10.2704	−1.19391
$75$	−1.00000	−0.115470
$76$	−9.25478	−1.06160
$77$	−3.07846	−0.350824
$78$	−2.54626	−0.288308
$79$	4.03783	0.454291	0.227145	−	0.973861i	$-0.427061\pi$
$79$	4.03783	0.454291	0.227145	+	0.973861i	$0.427061\pi$
$80$	7.13450	0.797662
$81$	1.00000	0.111111
$82$	0.469812	0.0518821
$83$	10.2125	1.12096	0.560481	−	0.828167i	$-0.310616\pi$
$83$	10.2125	1.12096	0.560481	+	0.828167i	$0.310616\pi$
$84$	4.61751	0.503812
$85$	5.98536	0.649204
$86$	−1.45603	−0.157008
$87$	−2.98050	−0.319543
$88$	18.9017	2.01493
$89$	5.50706	0.583748	0.291874	−	0.956457i	$-0.405721\pi$
$89$	5.50706	0.583748	0.291874	+	0.956457i	$0.405721\pi$
$90$	2.54626	0.268400
$91$	−1.02990	−0.107963
$92$	18.4223	1.92066
$93$	−1.00000	−0.103695
$94$	−23.5416	−2.42813
$95$	−2.06421	−0.211783
$96$	−5.51923	−0.563304
$97$	14.5645	1.47880	0.739402	−	0.673264i	$-0.235108\pi$
$97$	14.5645	1.47880	0.739402	+	0.673264i	$0.235108\pi$
$98$	−15.1230	−1.52766
$99$	2.98909	0.300415
$100$	4.48346	0.448346
$101$	13.1527	1.30874	0.654371	−	0.756174i	$-0.272934\pi$
$101$	13.1527	1.30874	0.654371	+	0.756174i	$0.272934\pi$
$102$	−15.2403	−1.50902
$103$	15.5954	1.53666	0.768328	−	0.640056i	$-0.221089\pi$
$103$	15.5954	1.53666	0.768328	+	0.640056i	$0.221089\pi$
$104$	6.32355	0.620075
$105$	1.02990	0.100508
$106$	−15.5742	−1.51270
$107$	17.4613	1.68805	0.844023	−	0.536307i	$-0.180181\pi$
$107$	17.4613	1.68805	0.844023	+	0.536307i	$0.180181\pi$
$108$	−4.48346	−0.431421
$109$	−11.7879	−1.12908	−0.564540	−	0.825406i	$-0.690946\pi$
$109$	−11.7879	−1.12908	−0.564540	+	0.825406i	$0.690946\pi$
$110$	7.61102	0.725682
$111$	4.03351	0.382844
$112$	−7.34782	−0.694303
$113$	9.33207	0.877888	0.438944	−	0.898514i	$-0.355353\pi$
$113$	9.33207	0.877888	0.438944	+	0.898514i	$0.355353\pi$
$114$	5.25601	0.492271
$115$	4.10895	0.383161
$116$	13.3629	1.24072
$117$	1.00000	0.0924500
$118$	33.8058	3.11208
$119$	−6.16432	−0.565082
$120$	−6.32355	−0.577258
$121$	−2.06532	−0.187757
$122$	−26.7902	−2.42547
$123$	−0.184510	−0.0166367
$124$	4.48346	0.402627
$125$	1.00000	0.0894427
$126$	−2.62239	−0.233621
$127$	−19.2252	−1.70596	−0.852980	−	0.521944i	$-0.825207\pi$
$127$	−19.2252	−1.70596	−0.852980	+	0.521944i	$0.825207\pi$
$128$	−11.5874	−1.02419
$129$	0.571830	0.0503468
$130$	2.54626	0.223322
$131$	17.5732	1.53538	0.767690	−	0.640821i	$-0.221406\pi$
$131$	17.5732	1.53538	0.767690	+	0.640821i	$0.221406\pi$
$132$	−13.4015	−1.16645
$133$	2.12592	0.184341
$134$	9.87717	0.853258
$135$	−1.00000	−0.0860663
$136$	37.8487	3.24550
$137$	16.0467	1.37096	0.685480	−	0.728092i	$-0.259592\pi$
$137$	16.0467	1.37096	0.685480	+	0.728092i	$0.259592\pi$
$138$	−10.4625	−0.890624
$139$	−3.71894	−0.315436	−0.157718	−	0.987484i	$-0.550414\pi$
$139$	−3.71894	−0.315436	−0.157718	+	0.987484i	$0.550414\pi$
$140$	−4.61751	−0.390251
$141$	9.24553	0.778614
$142$	−6.82565	−0.572796
$143$	2.98909	0.249961
$144$	7.13450	0.594542
$145$	2.98050	0.247517
$146$	4.85349	0.401678
$147$	5.93931	0.489866
$148$	−18.0841	−1.48650
$149$	−7.10280	−0.581884	−0.290942	−	0.956741i	$-0.593969\pi$
$149$	−7.10280	−0.581884	−0.290942	+	0.956741i	$0.593969\pi$
$150$	−2.54626	−0.207902
$151$	3.51700	0.286209	0.143105	−	0.989708i	$-0.454291\pi$
$151$	3.51700	0.286209	0.143105	+	0.989708i	$0.454291\pi$
$152$	−13.0531	−1.05875
$153$	5.98536	0.483888
$154$	−7.83858	−0.631651
$155$	1.00000	0.0803219
$156$	−4.48346	−0.358964
$157$	9.43952	0.753356	0.376678	−	0.926344i	$-0.377066\pi$
$157$	9.43952	0.753356	0.376678	+	0.926344i	$0.377066\pi$
$158$	10.2814	0.817942
$159$	6.11650	0.485070
$160$	5.51923	0.436333
$161$	−4.23180	−0.333513
$162$	2.54626	0.200053
$163$	−23.4792	−1.83903	−0.919517	−	0.393050i	$-0.871420\pi$
$163$	−23.4792	−1.83903	−0.919517	+	0.393050i	$0.871420\pi$
$164$	0.827245	0.0645970
$165$	−2.98909	−0.232701
$166$	26.0036	2.01827
$167$	−16.5512	−1.28077	−0.640384	−	0.768055i	$-0.721225\pi$
$167$	−16.5512	−1.28077	−0.640384	+	0.768055i	$0.721225\pi$
$168$	6.51262	0.502459
$169$	1.00000	0.0769231
$170$	15.2403	1.16888
$171$	−2.06421	−0.157854
$172$	−2.56378	−0.195486
$173$	−10.4571	−0.795037	−0.397519	−	0.917594i	$-0.630129\pi$
$173$	−10.4571	−0.795037	−0.397519	+	0.917594i	$0.630129\pi$
$174$	−7.58913	−0.575331
$175$	−1.02990	−0.0778530
$176$	21.3257	1.60748
$177$	−13.2766	−0.997934
$178$	14.0224	1.05103
$179$	17.3282	1.29517	0.647585	−	0.761994i	$-0.275779\pi$
$179$	17.3282	1.29517	0.647585	+	0.761994i	$0.275779\pi$
$180$	4.48346	0.334177
$181$	−19.9080	−1.47975	−0.739877	−	0.672743i	$-0.765116\pi$
$181$	−19.9080	−1.47975	−0.739877	+	0.672743i	$0.765116\pi$
$182$	−2.62239	−0.194385
$183$	10.5214	0.777761
$184$	25.9831	1.91550
$185$	−4.03351	−0.296550
$186$	−2.54626	−0.186701
$187$	17.8908	1.30831
$188$	−41.4520	−3.02319
$189$	1.02990	0.0749141
$190$	−5.25601	−0.381311
$191$	0.704657	0.0509872	0.0254936	−	0.999675i	$-0.491884\pi$
$191$	0.704657	0.0509872	0.0254936	+	0.999675i	$0.491884\pi$
$192$	0.215586	0.0155586
$193$	−9.84575	−0.708713	−0.354356	−	0.935110i	$-0.615300\pi$
$193$	−9.84575	−0.708713	−0.354356	+	0.935110i	$0.615300\pi$
$194$	37.0852	2.66256
$195$	−1.00000	−0.0716115
$196$	−26.6287	−1.90205
$197$	−21.8244	−1.55493	−0.777463	−	0.628928i	$-0.783494\pi$
$197$	−21.8244	−1.55493	−0.777463	+	0.628928i	$0.783494\pi$
$198$	7.61102	0.540892
$199$	6.36012	0.450857	0.225429	−	0.974260i	$-0.427622\pi$
$199$	6.36012	0.450857	0.225429	+	0.974260i	$0.427622\pi$
$200$	6.32355	0.447142
$201$	−3.87908	−0.273609
$202$	33.4902	2.35636
$203$	−3.06961	−0.215444
$204$	−26.8351	−1.87884
$205$	0.184510	0.0128868
$206$	39.7099	2.76672
$207$	4.10895	0.285592
$208$	7.13450	0.494689
$209$	−6.17010	−0.426795
$210$	2.62239	0.180962
$211$	−6.35199	−0.437289	−0.218645	−	0.975805i	$-0.570164\pi$
$211$	−6.35199	−0.437289	−0.218645	+	0.975805i	$0.570164\pi$
$212$	−27.4231	−1.88342
$213$	2.68065	0.183675
$214$	44.4610	3.03929
$215$	−0.571830	−0.0389985
$216$	−6.32355	−0.430263
$217$	−1.02990	−0.0699141
$218$	−30.0152	−2.03288
$219$	−1.90612	−0.128804
$220$	13.4015	0.903528
$221$	5.98536	0.402619
$222$	10.2704	0.689303
$223$	−4.60136	−0.308130	−0.154065	−	0.988061i	$-0.549236\pi$
$223$	−4.60136	−0.308130	−0.154065	+	0.988061i	$0.549236\pi$
$224$	−5.68425	−0.379795
$225$	1.00000	0.0666667
$226$	23.7619	1.58062
$227$	25.2676	1.67707	0.838533	−	0.544851i	$-0.183414\pi$
$227$	25.2676	1.67707	0.838533	+	0.544851i	$0.183414\pi$
$228$	9.25478	0.612913
$229$	−28.8995	−1.90973	−0.954867	−	0.297033i	$-0.904003\pi$
$229$	−28.8995	−1.90973	−0.954867	+	0.297033i	$0.904003\pi$
$230$	10.4625	0.689875
$231$	3.07846	0.202548
$232$	18.8473	1.23739
$233$	−18.4093	−1.20603	−0.603017	−	0.797729i	$-0.706035\pi$
$233$	−18.4093	−1.20603	−0.603017	+	0.797729i	$0.706035\pi$
$234$	2.54626	0.166454
$235$	−9.24553	−0.603112
$236$	59.5253	3.87477
$237$	−4.03783	−0.262285
$238$	−15.6960	−1.01742
$239$	−3.95948	−0.256117	−0.128059	−	0.991767i	$-0.540875\pi$
$239$	−3.95948	−0.256117	−0.128059	+	0.991767i	$0.540875\pi$
$240$	−7.13450	−0.460530
$241$	22.2978	1.43633	0.718164	−	0.695874i	$-0.244983\pi$
$241$	22.2978	1.43633	0.718164	+	0.695874i	$0.244983\pi$
$242$	−5.25885	−0.338052
$243$	−1.00000	−0.0641500
$244$	−47.1721	−3.01988
$245$	−5.93931	−0.379448
$246$	−0.469812	−0.0299541
$247$	−2.06421	−0.131342
$248$	6.32355	0.401546
$249$	−10.2125	−0.647188
$250$	2.54626	0.161040
$251$	9.88327	0.623826	0.311913	−	0.950111i	$-0.399030\pi$
$251$	9.88327	0.623826	0.311913	+	0.950111i	$0.399030\pi$
$252$	−4.61751	−0.290876
$253$	12.2820	0.772164
$254$	−48.9524	−3.07155
$255$	−5.98536	−0.374818
$256$	−29.0734	−1.81709
$257$	16.4824	1.02815	0.514073	−	0.857747i	$-0.328136\pi$
$257$	16.4824	1.02815	0.514073	+	0.857747i	$0.328136\pi$
$258$	1.45603	0.0906484
$259$	4.15411	0.258124
$260$	4.48346	0.278052
$261$	2.98050	0.184488
$262$	44.7461	2.76442
$263$	−26.5559	−1.63750	−0.818752	−	0.574147i	$-0.805334\pi$
$263$	−26.5559	−1.63750	−0.818752	+	0.574147i	$0.805334\pi$
$264$	−18.9017	−1.16332
$265$	−6.11650	−0.375733
$266$	5.41316	0.331902
$267$	−5.50706	−0.337027
$268$	17.3917	1.06237
$269$	−17.0294	−1.03830	−0.519151	−	0.854683i	$-0.673752\pi$
$269$	−17.0294	−1.03830	−0.519151	+	0.854683i	$0.673752\pi$
$270$	−2.54626	−0.154961
$271$	−16.0825	−0.976945	−0.488473	−	0.872579i	$-0.662446\pi$
$271$	−16.0825	−0.976945	−0.488473	+	0.872579i	$0.662446\pi$
$272$	42.7026	2.58922
$273$	1.02990	0.0623323
$274$	40.8591	2.46839
$275$	2.98909	0.180249
$276$	−18.4223	−1.10889
$277$	−14.3164	−0.860191	−0.430095	−	0.902783i	$-0.641520\pi$
$277$	−14.3164	−0.860191	−0.430095	+	0.902783i	$0.641520\pi$
$278$	−9.46940	−0.567937
$279$	1.00000	0.0598684
$280$	−6.51262	−0.389203
$281$	−1.36079	−0.0811779	−0.0405889	−	0.999176i	$-0.512923\pi$
$281$	−1.36079	−0.0811779	−0.0405889	+	0.999176i	$0.512923\pi$
$282$	23.5416	1.40188
$283$	−17.6046	−1.04648	−0.523241	−	0.852185i	$-0.675277\pi$
$283$	−17.6046	−1.04648	−0.523241	+	0.852185i	$0.675277\pi$
$284$	−12.0186	−0.713173
$285$	2.06421	0.122273
$286$	7.61102	0.450049
$287$	−0.190027	−0.0112169
$288$	5.51923	0.325224
$289$	18.8246	1.10733
$290$	7.58913	0.445649
$291$	−14.5645	−0.853788
$292$	8.54602	0.500118
$293$	24.1496	1.41084	0.705419	−	0.708791i	$-0.250759\pi$
$293$	24.1496	1.41084	0.705419	+	0.708791i	$0.250759\pi$
$294$	15.1230	0.881994
$295$	13.2766	0.772996
$296$	−25.5061	−1.48251
$297$	−2.98909	−0.173445
$298$	−18.0856	−1.04767
$299$	4.10895	0.237627
$300$	−4.48346	−0.258853
$301$	0.588927	0.0339452
$302$	8.95520	0.515314
$303$	−13.1527	−0.755602
$304$	−14.7271	−0.844656
$305$	−10.5214	−0.602451
$306$	15.2403	0.871231
$307$	14.1858	0.809627	0.404814	−	0.914399i	$-0.367336\pi$
$307$	14.1858	0.809627	0.404814	+	0.914399i	$0.367336\pi$
$308$	−13.8022	−0.786452
$309$	−15.5954	−0.887189
$310$	2.54626	0.144618
$311$	−22.0702	−1.25149	−0.625744	−	0.780029i	$-0.715204\pi$
$311$	−22.0702	−1.25149	−0.625744	+	0.780029i	$0.715204\pi$
$312$	−6.32355	−0.358000
$313$	−30.5339	−1.72588	−0.862940	−	0.505307i	$-0.831379\pi$
$313$	−30.5339	−1.72588	−0.862940	+	0.505307i	$0.831379\pi$
$314$	24.0355	1.35640
$315$	−1.02990	−0.0580282
$316$	18.1034	1.01840
$317$	10.7132	0.601712	0.300856	−	0.953670i	$-0.402728\pi$
$317$	10.7132	0.601712	0.300856	+	0.953670i	$0.402728\pi$
$318$	15.5742	0.873359
$319$	8.90898	0.498807
$320$	−0.215586	−0.0120516
$321$	−17.4613	−0.974594
$322$	−10.7753	−0.600483
$323$	−12.3550	−0.687452
$324$	4.48346	0.249081
$325$	1.00000	0.0554700
$326$	−59.7843	−3.31115
$327$	11.7879	0.651874
$328$	1.16676	0.0644236
$329$	9.52196	0.524963
$330$	−7.61102	−0.418973
$331$	−17.4529	−0.959299	−0.479650	−	0.877460i	$-0.659236\pi$
$331$	−17.4529	−0.959299	−0.479650	+	0.877460i	$0.659236\pi$
$332$	45.7871	2.51290
$333$	−4.03351	−0.221035
$334$	−42.1437	−2.30600
$335$	3.87908	0.211937
$336$	7.34782	0.400856
$337$	−18.0176	−0.981480	−0.490740	−	0.871306i	$-0.663273\pi$
$337$	−18.0176	−0.981480	−0.490740	+	0.871306i	$0.663273\pi$
$338$	2.54626	0.138499
$339$	−9.33207	−0.506849
$340$	26.8351	1.45534
$341$	2.98909	0.161868
$342$	−5.25601	−0.284213
$343$	13.3262	0.719546
$344$	−3.61599	−0.194961
$345$	−4.10895	−0.221218
$346$	−26.6265	−1.43145
$347$	23.0409	1.23690	0.618449	−	0.785825i	$-0.287761\pi$
$347$	23.0409	1.23690	0.618449	+	0.785825i	$0.287761\pi$
$348$	−13.3629	−0.716329
$349$	−20.3725	−1.09052	−0.545258	−	0.838268i	$-0.683568\pi$
$349$	−20.3725	−1.09052	−0.545258	+	0.838268i	$0.683568\pi$
$350$	−2.62239	−0.140173
$351$	−1.00000	−0.0533761
$352$	16.4975	0.879319
$353$	15.1058	0.803998	0.401999	−	0.915640i	$-0.368315\pi$
$353$	15.1058	0.803998	0.401999	+	0.915640i	$0.368315\pi$
$354$	−33.8058	−1.79676
$355$	−2.68065	−0.142274
$356$	24.6907	1.30860
$357$	6.16432	0.326250
$358$	44.1221	2.33193
$359$	−23.3231	−1.23094	−0.615472	−	0.788159i	$-0.711035\pi$
$359$	−23.3231	−1.23094	−0.615472	+	0.788159i	$0.711035\pi$
$360$	6.32355	0.333280
$361$	−14.7391	−0.775740
$362$	−50.6911	−2.66427
$363$	2.06532	0.108401
$364$	−4.61751	−0.242023
$365$	1.90612	0.0997709
$366$	26.7902	1.40034
$367$	30.5957	1.59708	0.798541	−	0.601940i	$-0.205605\pi$
$367$	30.5957	1.59708	0.798541	+	0.601940i	$0.205605\pi$
$368$	29.3153	1.52817
$369$	0.184510	0.00960523
$370$	−10.2704	−0.533932
$371$	6.29937	0.327047
$372$	−4.48346	−0.232457
$373$	−25.9370	−1.34297	−0.671483	−	0.741020i	$-0.734342\pi$
$373$	−25.9370	−1.34297	−0.671483	+	0.741020i	$0.734342\pi$
$374$	45.5547	2.35558
$375$	−1.00000	−0.0516398
$376$	−58.4645	−3.01508
$377$	2.98050	0.153503
$378$	2.62239	0.134881
$379$	36.8095	1.89078	0.945388	−	0.325946i	$-0.105683\pi$
$379$	36.8095	1.89078	0.945388	+	0.325946i	$0.105683\pi$
$380$	−9.25478	−0.474760
$381$	19.2252	0.984936
$382$	1.79424	0.0918014
$383$	−13.7763	−0.703938	−0.351969	−	0.936012i	$-0.614488\pi$
$383$	−13.7763	−0.703938	−0.351969	+	0.936012i	$0.614488\pi$
$384$	11.5874	0.591317
$385$	−3.07846	−0.156893
$386$	−25.0699	−1.27602
$387$	−0.571830	−0.0290677
$388$	65.2995	3.31508
$389$	−11.3914	−0.577565	−0.288783	−	0.957395i	$-0.593250\pi$
$389$	−11.3914	−0.577565	−0.288783	+	0.957395i	$0.593250\pi$
$390$	−2.54626	−0.128935
$391$	24.5935	1.24375
$392$	−37.5575	−1.89694
$393$	−17.5732	−0.886452
$394$	−55.5708	−2.79962
$395$	4.03783	0.203165
$396$	13.4015	0.673450
$397$	12.8893	0.646897	0.323449	−	0.946246i	$-0.395158\pi$
$397$	12.8893	0.646897	0.323449	+	0.946246i	$0.395158\pi$
$398$	16.1946	0.811760
$399$	−2.12592	−0.106429
$400$	7.13450	0.356725
$401$	−20.9202	−1.04470	−0.522352	−	0.852730i	$-0.674945\pi$
$401$	−20.9202	−1.04470	−0.522352	+	0.852730i	$0.674945\pi$
$402$	−9.87717	−0.492629
$403$	1.00000	0.0498135
$404$	58.9696	2.93385
$405$	1.00000	0.0496904
$406$	−7.81604	−0.387903
$407$	−12.0565	−0.597620
$408$	−37.8487	−1.87379
$409$	−28.3919	−1.40389	−0.701945	−	0.712231i	$-0.747685\pi$
$409$	−28.3919	−1.40389	−0.701945	+	0.712231i	$0.747685\pi$
$410$	0.469812	0.0232024
$411$	−16.0467	−0.791524
$412$	69.9212	3.44477
$413$	−13.6736	−0.672834
$414$	10.4625	0.514202
$415$	10.2125	0.501310
$416$	5.51923	0.270603
$417$	3.71894	0.182117
$418$	−15.7107	−0.768436
$419$	2.40036	0.117265	0.0586326	−	0.998280i	$-0.481326\pi$
$419$	2.40036	0.117265	0.0586326	+	0.998280i	$0.481326\pi$
$420$	4.61751	0.225312
$421$	−3.44590	−0.167943	−0.0839714	−	0.996468i	$-0.526760\pi$
$421$	−3.44590	−0.167943	−0.0839714	+	0.996468i	$0.526760\pi$
$422$	−16.1738	−0.787331
$423$	−9.24553	−0.449533
$424$	−38.6780	−1.87837
$425$	5.98536	0.290333
$426$	6.82565	0.330704
$427$	10.8359	0.524388
$428$	78.2870	3.78414
$429$	−2.98909	−0.144315
$430$	−1.45603	−0.0702160
$431$	7.92699	0.381830	0.190915	−	0.981607i	$-0.438855\pi$
$431$	7.92699	0.381830	0.190915	+	0.981607i	$0.438855\pi$
$432$	−7.13450	−0.343259
$433$	−18.2173	−0.875467	−0.437734	−	0.899105i	$-0.644219\pi$
$433$	−18.2173	−0.875467	−0.437734	+	0.899105i	$0.644219\pi$
$434$	−2.62239	−0.125879
$435$	−2.98050	−0.142904
$436$	−52.8507	−2.53109
$437$	−8.48171	−0.405735
$438$	−4.85349	−0.231909
$439$	−14.8335	−0.707964	−0.353982	−	0.935252i	$-0.615173\pi$
$439$	−14.8335	−0.707964	−0.353982	+	0.935252i	$0.615173\pi$
$440$	18.9017	0.901102
$441$	−5.93931	−0.282824
$442$	15.2403	0.724908
$443$	3.05615	0.145202	0.0726010	−	0.997361i	$-0.476870\pi$
$443$	3.05615	0.145202	0.0726010	+	0.997361i	$0.476870\pi$
$444$	18.0841	0.858233
$445$	5.50706	0.261060
$446$	−11.7163	−0.554781
$447$	7.10280	0.335951
$448$	0.222032	0.0104900
$449$	−15.2214	−0.718345	−0.359172	−	0.933271i	$-0.616941\pi$
$449$	−15.2214	−0.718345	−0.359172	+	0.933271i	$0.616941\pi$
$450$	2.54626	0.120032
$451$	0.551519	0.0259700
$452$	41.8400	1.96799
$453$	−3.51700	−0.165243
$454$	64.3379	3.01953
$455$	−1.02990	−0.0482824
$456$	13.0531	0.611268
$457$	27.0921	1.26732	0.633659	−	0.773613i	$-0.281552\pi$
$457$	27.0921	1.26732	0.633659	+	0.773613i	$0.281552\pi$
$458$	−73.5858	−3.43844
$459$	−5.98536	−0.279373
$460$	18.4223	0.858944
$461$	2.23692	0.104184	0.0520919	−	0.998642i	$-0.483411\pi$
$461$	2.23692	0.104184	0.0520919	+	0.998642i	$0.483411\pi$
$462$	7.83858	0.364684
$463$	29.5767	1.37454	0.687272	−	0.726400i	$-0.258808\pi$
$463$	29.5767	1.37454	0.687272	+	0.726400i	$0.258808\pi$
$464$	21.2644	0.987173
$465$	−1.00000	−0.0463739
$466$	−46.8749	−2.17144
$467$	8.76483	0.405588	0.202794	−	0.979221i	$-0.434998\pi$
$467$	8.76483	0.405588	0.202794	+	0.979221i	$0.434998\pi$
$468$	4.48346	0.207248
$469$	−3.99506	−0.184475
$470$	−23.5416	−1.08589
$471$	−9.43952	−0.434950
$472$	83.9555	3.86436
$473$	−1.70925	−0.0785915
$474$	−10.2814	−0.472239
$475$	−2.06421	−0.0947122
$476$	−27.6375	−1.26676
$477$	−6.11650	−0.280055
$478$	−10.0819	−0.461134
$479$	18.6669	0.852913	0.426457	−	0.904508i	$-0.359762\pi$
$479$	18.6669	0.852913	0.426457	+	0.904508i	$0.359762\pi$
$480$	−5.51923	−0.251917
$481$	−4.03351	−0.183912
$482$	56.7761	2.58608
$483$	4.23180	0.192554
$484$	−9.25979	−0.420900
$485$	14.5645	0.661342
$486$	−2.54626	−0.115501
$487$	36.4892	1.65348	0.826742	−	0.562581i	$-0.190191\pi$
$487$	36.4892	1.65348	0.826742	+	0.562581i	$0.190191\pi$
$488$	−66.5323	−3.01178
$489$	23.4792	1.06177
$490$	−15.1230	−0.683190
$491$	31.9476	1.44177	0.720887	−	0.693052i	$-0.243735\pi$
$491$	31.9476	1.44177	0.720887	+	0.693052i	$0.243735\pi$
$492$	−0.827245	−0.0372951
$493$	17.8394	0.803444
$494$	−5.25601	−0.236479
$495$	2.98909	0.134350
$496$	7.13450	0.320349
$497$	2.76080	0.123839
$498$	−26.0036	−1.16525
$499$	15.6012	0.698406	0.349203	−	0.937047i	$-0.386452\pi$
$499$	15.6012	0.698406	0.349203	+	0.937047i	$0.386452\pi$
$500$	4.48346	0.200506
$501$	16.5512	0.739452
$502$	25.1654	1.12319
$503$	−30.8788	−1.37682	−0.688409	−	0.725323i	$-0.741690\pi$
$503$	−30.8788	−1.37682	−0.688409	+	0.725323i	$0.741690\pi$
$504$	−6.51262	−0.290095
$505$	13.1527	0.585287
$506$	31.2733	1.39027
$507$	−1.00000	−0.0444116
$508$	−86.1954	−3.82430
$509$	−26.7054	−1.18370	−0.591848	−	0.806049i	$-0.701602\pi$
$509$	−26.7054	−1.18370	−0.591848	+	0.806049i	$0.701602\pi$
$510$	−15.2403	−0.674853
$511$	−1.96311	−0.0868430
$512$	−50.8538	−2.24744
$513$	2.06421	0.0911369
$514$	41.9686	1.85116
$515$	15.5954	0.687214
$516$	2.56378	0.112864
$517$	−27.6357	−1.21542
$518$	10.5775	0.464747
$519$	10.4571	0.459015
$520$	6.32355	0.277306
$521$	8.72083	0.382066	0.191033	−	0.981584i	$-0.438816\pi$
$521$	8.72083	0.382066	0.191033	+	0.981584i	$0.438816\pi$
$522$	7.58913	0.332167
$523$	−11.9681	−0.523329	−0.261665	−	0.965159i	$-0.584271\pi$
$523$	−11.9681	−0.523329	−0.261665	+	0.965159i	$0.584271\pi$
$524$	78.7889	3.44191
$525$	1.02990	0.0449485
$526$	−67.6182	−2.94830
$527$	5.98536	0.260727
$528$	−21.3257	−0.928082
$529$	−6.11655	−0.265937
$530$	−15.5742	−0.676501
$531$	13.2766	0.576157
$532$	9.53149	0.413243
$533$	0.184510	0.00799203
$534$	−14.0224	−0.606810
$535$	17.4613	0.754917
$536$	24.5296	1.05952
$537$	−17.3282	−0.747766
$538$	−43.3614	−1.86944
$539$	−17.7531	−0.764682
$540$	−4.48346	−0.192937
$541$	14.3912	0.618725	0.309363	−	0.950944i	$-0.399884\pi$
$541$	14.3912	0.618725	0.309363	+	0.950944i	$0.399884\pi$
$542$	−40.9504	−1.75897
$543$	19.9080	0.854336
$544$	33.0346	1.41635
$545$	−11.7879	−0.504939
$546$	2.62239	0.112228
$547$	4.62695	0.197834	0.0989171	−	0.995096i	$-0.468462\pi$
$547$	4.62695	0.197834	0.0989171	+	0.995096i	$0.468462\pi$
$548$	71.9446	3.07332
$549$	−10.5214	−0.449041
$550$	7.61102	0.324535
$551$	−6.15236	−0.262099
$552$	−25.9831	−1.10592
$553$	−4.15855	−0.176840
$554$	−36.4534	−1.54876
$555$	4.03351	0.171213
$556$	−16.6737	−0.707123
$557$	−25.1268	−1.06466	−0.532329	−	0.846538i	$-0.678683\pi$
$557$	−25.1268	−1.06466	−0.532329	+	0.846538i	$0.678683\pi$
$558$	2.54626	0.107792
$559$	−0.571830	−0.0241858
$560$	−7.34782	−0.310502
$561$	−17.8908	−0.755351
$562$	−3.46493	−0.146159
$563$	−33.3074	−1.40374	−0.701870	−	0.712305i	$-0.747651\pi$
$563$	−33.3074	−1.40374	−0.701870	+	0.712305i	$0.747651\pi$
$564$	41.4520	1.74544
$565$	9.33207	0.392603
$566$	−44.8258	−1.88417
$567$	−1.02990	−0.0432517
$568$	−16.9512	−0.711258
$569$	−43.8888	−1.83991	−0.919957	−	0.392019i	$-0.871777\pi$
$569$	−43.8888	−1.83991	−0.919957	+	0.392019i	$0.871777\pi$
$570$	5.25601	0.220150
$571$	−31.1265	−1.30260	−0.651301	−	0.758820i	$-0.725776\pi$
$571$	−31.1265	−1.30260	−0.651301	+	0.758820i	$0.725776\pi$
$572$	13.4015	0.560344
$573$	−0.704657	−0.0294375
$574$	−0.483859	−0.0201959
$575$	4.10895	0.171355
$576$	−0.215586	−0.00898277
$577$	26.1014	1.08661	0.543307	−	0.839534i	$-0.317172\pi$
$577$	26.1014	1.08661	0.543307	+	0.839534i	$0.317172\pi$
$578$	47.9323	1.99372
$579$	9.84575	0.409175
$580$	13.3629	0.554866
$581$	−10.5178	−0.436352
$582$	−37.0852	−1.53723
$583$	−18.2828	−0.757195
$584$	12.0534	0.498775
$585$	1.00000	0.0413449
$586$	61.4914	2.54019
$587$	−26.8276	−1.10729	−0.553647	−	0.832752i	$-0.686764\pi$
$587$	−26.8276	−1.10729	−0.553647	+	0.832752i	$0.686764\pi$
$588$	26.6287	1.09815
$589$	−2.06421	−0.0850541
$590$	33.8058	1.39176
$591$	21.8244	0.897737
$592$	−28.7771	−1.18273
$593$	−21.1052	−0.866688	−0.433344	−	0.901229i	$-0.642667\pi$
$593$	−21.1052	−0.866688	−0.433344	+	0.901229i	$0.642667\pi$
$594$	−7.61102	−0.312284
$595$	−6.16432	−0.252712
$596$	−31.8451	−1.30443
$597$	−6.36012	−0.260302
$598$	10.4625	0.427842
$599$	3.19247	0.130441	0.0652204	−	0.997871i	$-0.479225\pi$
$599$	3.19247	0.130441	0.0652204	+	0.997871i	$0.479225\pi$
$600$	−6.32355	−0.258158
$601$	−11.8287	−0.482501	−0.241251	−	0.970463i	$-0.577558\pi$
$601$	−11.8287	−0.482501	−0.241251	+	0.970463i	$0.577558\pi$
$602$	1.49956	0.0611176
$603$	3.87908	0.157968
$604$	15.7683	0.641604
$605$	−2.06532	−0.0839673
$606$	−33.4902	−1.36045
$607$	−27.1084	−1.10030	−0.550149	−	0.835067i	$-0.685429\pi$
$607$	−27.1084	−1.10030	−0.550149	+	0.835067i	$0.685429\pi$
$608$	−11.3928	−0.462040
$609$	3.06961	0.124387
$610$	−26.7902	−1.08470
$611$	−9.24553	−0.374034
$612$	26.8351	1.08475
$613$	12.8802	0.520225	0.260112	−	0.965578i	$-0.416240\pi$
$613$	12.8802	0.520225	0.260112	+	0.965578i	$0.416240\pi$
$614$	36.1208	1.45772
$615$	−0.184510	−0.00744018
$616$	−19.4668	−0.784340
$617$	21.0379	0.846956	0.423478	−	0.905906i	$-0.360809\pi$
$617$	21.0379	0.846956	0.423478	+	0.905906i	$0.360809\pi$
$618$	−39.7099	−1.59737
$619$	28.6853	1.15296	0.576480	−	0.817111i	$-0.304426\pi$
$619$	28.6853	1.15296	0.576480	+	0.817111i	$0.304426\pi$
$620$	4.48346	0.180060
$621$	−4.10895	−0.164886
$622$	−56.1966	−2.25328
$623$	−5.67172	−0.227233
$624$	−7.13450	−0.285609
$625$	1.00000	0.0400000
$626$	−77.7474	−3.10741
$627$	6.17010	0.246410
$628$	42.3217	1.68882
$629$	−24.1420	−0.962605
$630$	−2.62239	−0.104479
$631$	−26.2936	−1.04673	−0.523366	−	0.852108i	$-0.675324\pi$
$631$	−26.2936	−1.04673	−0.523366	+	0.852108i	$0.675324\pi$
$632$	25.5334	1.01566
$633$	6.35199	0.252469
$634$	27.2786	1.08337
$635$	−19.2252	−0.762928
$636$	27.4231	1.08740
$637$	−5.93931	−0.235324
$638$	22.6846	0.898093
$639$	−2.68065	−0.106045
$640$	−11.5874	−0.458032
$641$	−30.4820	−1.20397	−0.601983	−	0.798509i	$-0.705623\pi$
$641$	−30.4820	−1.20397	−0.601983	+	0.798509i	$0.705623\pi$
$642$	−44.4610	−1.75474
$643$	−11.7036	−0.461544	−0.230772	−	0.973008i	$-0.574125\pi$
$643$	−11.7036	−0.461544	−0.230772	+	0.973008i	$0.574125\pi$
$644$	−18.9731	−0.747645
$645$	0.571830	0.0225158
$646$	−31.4591	−1.23774
$647$	−7.15157	−0.281157	−0.140579	−	0.990070i	$-0.544896\pi$
$647$	−7.15157	−0.281157	−0.140579	+	0.990070i	$0.544896\pi$
$648$	6.32355	0.248412
$649$	39.6851	1.55778
$650$	2.54626	0.0998727
$651$	1.02990	0.0403649
$652$	−105.268	−4.12262
$653$	−18.7502	−0.733752	−0.366876	−	0.930270i	$-0.619573\pi$
$653$	−18.7502	−0.733752	−0.366876	+	0.930270i	$0.619573\pi$
$654$	30.0152	1.17369
$655$	17.5732	0.686643
$656$	1.31639	0.0513964
$657$	1.90612	0.0743649
$658$	24.2454	0.945185
$659$	−35.2215	−1.37203	−0.686017	−	0.727585i	$-0.740643\pi$
$659$	−35.2215	−1.37203	−0.686017	+	0.727585i	$0.740643\pi$
$660$	−13.4015	−0.521652
$661$	9.17490	0.356862	0.178431	−	0.983952i	$-0.442898\pi$
$661$	9.17490	0.356862	0.178431	+	0.983952i	$0.442898\pi$
$662$	−44.4397	−1.72720
$663$	−5.98536	−0.232452
$664$	64.5789	2.50615
$665$	2.12592	0.0824398
$666$	−10.2704	−0.397969
$667$	12.2467	0.474194
$668$	−74.2066	−2.87114
$669$	4.60136	0.177899
$670$	9.87717	0.381588
$671$	−31.4493	−1.21409
$672$	5.68425	0.219275
$673$	10.7394	0.413973	0.206987	−	0.978344i	$-0.433634\pi$
$673$	10.7394	0.413973	0.206987	+	0.978344i	$0.433634\pi$
$674$	−45.8775	−1.76714
$675$	−1.00000	−0.0384900
$676$	4.48346	0.172441
$677$	22.6753	0.871481	0.435741	−	0.900072i	$-0.356486\pi$
$677$	22.6753	0.871481	0.435741	+	0.900072i	$0.356486\pi$
$678$	−23.7619	−0.912571
$679$	−15.0000	−0.575647
$680$	37.8487	1.45143
$681$	−25.2676	−0.968255
$682$	7.61102	0.291441
$683$	19.4597	0.744603	0.372301	−	0.928112i	$-0.378569\pi$
$683$	19.4597	0.744603	0.372301	+	0.928112i	$0.378569\pi$
$684$	−9.25478	−0.353866
$685$	16.0467	0.613112
$686$	33.9320	1.29553
$687$	28.8995	1.10259
$688$	−4.07972	−0.155538
$689$	−6.11650	−0.233020
$690$	−10.4625	−0.398299
$691$	−31.3908	−1.19416	−0.597082	−	0.802180i	$-0.703673\pi$
$691$	−31.3908	−1.19416	−0.597082	+	0.802180i	$0.703673\pi$
$692$	−46.8839	−1.78226
$693$	−3.07846	−0.116941
$694$	58.6681	2.22701
$695$	−3.71894	−0.141067
$696$	−18.8473	−0.714406
$697$	1.10436	0.0418307
$698$	−51.8738	−1.96345
$699$	18.4093	0.696304
$700$	−4.61751	−0.174526
$701$	25.7856	0.973910	0.486955	−	0.873427i	$-0.338108\pi$
$701$	25.7856	0.973910	0.486955	+	0.873427i	$0.338108\pi$
$702$	−2.54626	−0.0961025
$703$	8.32599	0.314021
$704$	−0.644408	−0.0242870
$705$	9.24553	0.348207
$706$	38.4632	1.44758
$707$	−13.5459	−0.509447
$708$	−59.5253	−2.23710
$709$	2.11047	0.0792603	0.0396301	−	0.999214i	$-0.487382\pi$
$709$	2.11047	0.0792603	0.0396301	+	0.999214i	$0.487382\pi$
$710$	−6.82565	−0.256162
$711$	4.03783	0.151430
$712$	34.8242	1.30509
$713$	4.10895	0.153881
$714$	15.6960	0.587407
$715$	2.98909	0.111786
$716$	77.6902	2.90342
$717$	3.95948	0.147869
$718$	−59.3867	−2.21629
$719$	26.6750	0.994811	0.497405	−	0.867518i	$-0.334286\pi$
$719$	26.6750	0.994811	0.497405	+	0.867518i	$0.334286\pi$
$720$	7.13450	0.265887
$721$	−16.0616	−0.598167
$722$	−37.5295	−1.39670
$723$	−22.2978	−0.829265
$724$	−89.2569	−3.31721
$725$	2.98050	0.110693
$726$	5.25885	0.195174
$727$	−10.1824	−0.377643	−0.188822	−	0.982011i	$-0.560467\pi$
$727$	−10.1824	−0.377643	−0.188822	+	0.982011i	$0.560467\pi$
$728$	−6.51262	−0.241374
$729$	1.00000	0.0370370
$730$	4.85349	0.179636
$731$	−3.42261	−0.126590
$732$	47.1721	1.74353
$733$	−1.33430	−0.0492836	−0.0246418	−	0.999696i	$-0.507845\pi$
$733$	−1.33430	−0.0492836	−0.0246418	+	0.999696i	$0.507845\pi$
$734$	77.9047	2.87552
$735$	5.93931	0.219075
$736$	22.6782	0.835930
$737$	11.5949	0.427105
$738$	0.469812	0.0172940
$739$	−37.2444	−1.37006	−0.685028	−	0.728517i	$-0.740210\pi$
$739$	−37.2444	−1.37006	−0.685028	+	0.728517i	$0.740210\pi$
$740$	−18.0841	−0.664784
$741$	2.06421	0.0758305
$742$	16.0399	0.588842
$743$	29.6029	1.08602	0.543012	−	0.839725i	$-0.317284\pi$
$743$	29.6029	1.08602	0.543012	+	0.839725i	$0.317284\pi$
$744$	−6.32355	−0.231833
$745$	−7.10280	−0.260227
$746$	−66.0424	−2.41798
$747$	10.2125	0.373654
$748$	80.2127	2.93287
$749$	−17.9834	−0.657098
$750$	−2.54626	−0.0929764
$751$	−40.2013	−1.46697	−0.733483	−	0.679708i	$-0.762106\pi$
$751$	−40.2013	−1.46697	−0.733483	+	0.679708i	$0.762106\pi$
$752$	−65.9622	−2.40539
$753$	−9.88327	−0.360166
$754$	7.58913	0.276380
$755$	3.51700	0.127997
$756$	4.61751	0.167937
$757$	39.3618	1.43063	0.715314	−	0.698803i	$-0.246284\pi$
$757$	39.3618	1.43063	0.715314	+	0.698803i	$0.246284\pi$
$758$	93.7267	3.40431
$759$	−12.2820	−0.445809
$760$	−13.0531	−0.473486
$761$	1.38032	0.0500364	0.0250182	−	0.999687i	$-0.492036\pi$
$761$	1.38032	0.0500364	0.0250182	+	0.999687i	$0.492036\pi$
$762$	48.9524	1.77336
$763$	12.1404	0.439511
$764$	3.15930	0.114300
$765$	5.98536	0.216401
$766$	−35.0782	−1.26743
$767$	13.2766	0.479392
$768$	29.0734	1.04910
$769$	40.8468	1.47297	0.736487	−	0.676451i	$-0.236483\pi$
$769$	40.8468	1.47297	0.736487	+	0.676451i	$0.236483\pi$
$770$	−7.83858	−0.282483
$771$	−16.4824	−0.593600
$772$	−44.1430	−1.58874
$773$	−6.42680	−0.231156	−0.115578	−	0.993298i	$-0.536872\pi$
$773$	−6.42680	−0.231156	−0.115578	+	0.993298i	$0.536872\pi$
$774$	−1.45603	−0.0523359
$775$	1.00000	0.0359211
$776$	92.0996	3.30618
$777$	−4.15411	−0.149028
$778$	−29.0054	−1.03989
$779$	−0.380867	−0.0136460
$780$	−4.48346	−0.160534
$781$	−8.01272	−0.286718
$782$	62.6217	2.23935
$783$	−2.98050	−0.106514
$784$	−42.3740	−1.51336
$785$	9.43952	0.336911
$786$	−44.7461	−1.59604
$787$	−13.3250	−0.474985	−0.237493	−	0.971389i	$-0.576326\pi$
$787$	−13.3250	−0.474985	−0.237493	+	0.971389i	$0.576326\pi$
$788$	−97.8490	−3.48573
$789$	26.5559	0.945414
$790$	10.2814	0.365795
$791$	−9.61109	−0.341731
$792$	18.9017	0.671642
$793$	−10.5214	−0.373624
$794$	32.8197	1.16473
$795$	6.11650	0.216930
$796$	28.5154	1.01070
$797$	−34.6416	−1.22707	−0.613534	−	0.789668i	$-0.710253\pi$
$797$	−34.6416	−1.22707	−0.613534	+	0.789668i	$0.710253\pi$
$798$	−5.41316	−0.191624
$799$	−55.3378	−1.95771
$800$	5.51923	0.195134
$801$	5.50706	0.194583
$802$	−53.2683	−1.88097
$803$	5.69757	0.201063
$804$	−17.3917	−0.613359
$805$	−4.23180	−0.149151
$806$	2.54626	0.0896883
$807$	17.0294	0.599463
$808$	83.1716	2.92597
$809$	5.24719	0.184481	0.0922406	−	0.995737i	$-0.470597\pi$
$809$	5.24719	0.184481	0.0922406	+	0.995737i	$0.470597\pi$
$810$	2.54626	0.0894666
$811$	−15.2806	−0.536575	−0.268288	−	0.963339i	$-0.586458\pi$
$811$	−15.2806	−0.536575	−0.268288	+	0.963339i	$0.586458\pi$
$812$	−13.7625	−0.482968
$813$	16.0825	0.564039
$814$	−30.6991	−1.07600
$815$	−23.4792	−0.822441
$816$	−42.7026	−1.49489
$817$	1.18037	0.0412961
$818$	−72.2934	−2.52768
$819$	−1.02990	−0.0359876
$820$	0.827245	0.0288886
$821$	32.3116	1.12768	0.563841	−	0.825883i	$-0.309323\pi$
$821$	32.3116	1.12768	0.563841	+	0.825883i	$0.309323\pi$
$822$	−40.8591	−1.42512
$823$	−36.8710	−1.28524	−0.642621	−	0.766184i	$-0.722153\pi$
$823$	−36.8710	−1.28524	−0.642621	+	0.766184i	$0.722153\pi$
$824$	98.6180	3.43552
$825$	−2.98909	−0.104067
$826$	−34.8166	−1.21142
$827$	49.4955	1.72113	0.860564	−	0.509343i	$-0.170111\pi$
$827$	49.4955	1.72113	0.860564	+	0.509343i	$0.170111\pi$
$828$	18.4223	0.640219
$829$	29.1011	1.01072	0.505361	−	0.862908i	$-0.331359\pi$
$829$	29.1011	1.01072	0.505361	+	0.862908i	$0.331359\pi$
$830$	26.0036	0.902598
$831$	14.3164	0.496631
$832$	−0.215586	−0.00747412
$833$	−35.5489	−1.23170
$834$	9.46940	0.327899
$835$	−16.5512	−0.572777
$836$	−27.6634	−0.956759
$837$	−1.00000	−0.0345651
$838$	6.11195	0.211134
$839$	26.7611	0.923897	0.461948	−	0.886907i	$-0.347151\pi$
$839$	26.7611	0.923897	0.461948	+	0.886907i	$0.347151\pi$
$840$	6.51262	0.224707
$841$	−20.1166	−0.693677
$842$	−8.77417	−0.302378
$843$	1.36079	0.0468681
$844$	−28.4789	−0.980284
$845$	1.00000	0.0344010
$846$	−23.5416	−0.809375
$847$	2.12707	0.0730871
$848$	−43.6382	−1.49854
$849$	17.6046	0.604187
$850$	15.2403	0.522739
$851$	−16.5735	−0.568132
$852$	12.0186	0.411751
$853$	8.78342	0.300739	0.150369	−	0.988630i	$-0.451954\pi$
$853$	8.78342	0.300739	0.150369	+	0.988630i	$0.451954\pi$
$854$	27.5912	0.944150
$855$	−2.06421	−0.0705943
$856$	110.417	3.77398
$857$	6.53948	0.223384	0.111692	−	0.993743i	$-0.464373\pi$
$857$	6.53948	0.223384	0.111692	+	0.993743i	$0.464373\pi$
$858$	−7.61102	−0.259836
$859$	1.01343	0.0345780	0.0172890	−	0.999851i	$-0.494496\pi$
$859$	1.01343	0.0345780	0.0172890	+	0.999851i	$0.494496\pi$
$860$	−2.56378	−0.0874240
$861$	0.190027	0.00647610
$862$	20.1842	0.687477
$863$	0.410115	0.0139605	0.00698024	−	0.999976i	$-0.497778\pi$
$863$	0.410115	0.0139605	0.00698024	+	0.999976i	$0.497778\pi$
$864$	−5.51923	−0.187768
$865$	−10.4571	−0.355552
$866$	−46.3860	−1.57626
$867$	−18.8246	−0.639316
$868$	−4.61751	−0.156729
$869$	12.0694	0.409428
$870$	−7.58913	−0.257296
$871$	3.87908	0.131438
$872$	−74.5416	−2.52430
$873$	14.5645	0.492935
$874$	−21.5967	−0.730518
$875$	−1.02990	−0.0348169
$876$	−8.54602	−0.288743
$877$	−53.8975	−1.81999	−0.909994	−	0.414622i	$-0.863914\pi$
$877$	−53.8975	−1.81999	−0.909994	+	0.414622i	$0.863914\pi$
$878$	−37.7700	−1.27467
$879$	−24.1496	−0.814547
$880$	21.3257	0.718889
$881$	−42.5548	−1.43371	−0.716854	−	0.697223i	$-0.754419\pi$
$881$	−42.5548	−1.43371	−0.716854	+	0.697223i	$0.754419\pi$
$882$	−15.1230	−0.509219
$883$	40.9687	1.37871	0.689354	−	0.724425i	$-0.257895\pi$
$883$	40.9687	1.37871	0.689354	+	0.724425i	$0.257895\pi$
$884$	26.8351	0.902564
$885$	−13.2766	−0.446289
$886$	7.78177	0.261434
$887$	8.44077	0.283413	0.141707	−	0.989909i	$-0.454741\pi$
$887$	8.44077	0.283413	0.141707	+	0.989909i	$0.454741\pi$
$888$	25.5061	0.855928
$889$	19.8000	0.664071
$890$	14.0224	0.470033
$891$	2.98909	0.100138
$892$	−20.6300	−0.690744
$893$	19.0847	0.638644
$894$	18.0856	0.604873
$895$	17.3282	0.579217
$896$	11.9339	0.398682
$897$	−4.10895	−0.137194
$898$	−38.7578	−1.29337
$899$	2.98050	0.0994051
$900$	4.48346	0.149449
$901$	−36.6095	−1.21964
$902$	1.40431	0.0467585
$903$	−0.588927	−0.0195983
$904$	59.0118	1.96270
$905$	−19.9080	−0.661766
$906$	−8.95520	−0.297517
$907$	−6.79221	−0.225532	−0.112766	−	0.993622i	$-0.535971\pi$
$907$	−6.79221	−0.225532	−0.112766	+	0.993622i	$0.535971\pi$
$908$	113.286	3.75953
$909$	13.1527	0.436247
$910$	−2.62239	−0.0869315
$911$	1.83902	0.0609295	0.0304647	−	0.999536i	$-0.490301\pi$
$911$	1.83902	0.0609295	0.0304647	+	0.999536i	$0.490301\pi$
$912$	14.7271	0.487662
$913$	30.5260	1.01026
$914$	68.9838	2.28178
$915$	10.5214	0.347825
$916$	−129.570	−4.28111
$917$	−18.0987	−0.597670
$918$	−15.2403	−0.503005
$919$	12.7552	0.420757	0.210378	−	0.977620i	$-0.432530\pi$
$919$	12.7552	0.420757	0.210378	+	0.977620i	$0.432530\pi$
$920$	25.9831	0.856638
$921$	−14.1858	−0.467438
$922$	5.69579	0.187581
$923$	−2.68065	−0.0882348
$924$	13.8022	0.454058
$925$	−4.03351	−0.132621
$926$	75.3100	2.47484
$927$	15.5954	0.512219
$928$	16.4500	0.539999
$929$	−30.9896	−1.01674	−0.508368	−	0.861140i	$-0.669751\pi$
$929$	−30.9896	−1.01674	−0.508368	+	0.861140i	$0.669751\pi$
$930$	−2.54626	−0.0834953
$931$	12.2600	0.401804
$932$	−82.5374	−2.70360
$933$	22.0702	0.722546
$934$	22.3176	0.730254
$935$	17.8908	0.585092
$936$	6.32355	0.206692
$937$	−0.000644290 0	−2.10480e−5 0	−1.05240e−5	−	1.00000i	$-0.500003\pi$
$937$	−0.000644290 0	−2.10480e−5 0	−1.05240e−5		1.00000i	$0.500003\pi$
$938$	−10.1725	−0.332144
$939$	30.5339	0.996437
$940$	−41.4520	−1.35201
$941$	25.3483	0.826332	0.413166	−	0.910656i	$-0.364423\pi$
$941$	25.3483	0.826332	0.413166	+	0.910656i	$0.364423\pi$
$942$	−24.0355	−0.783120
$943$	0.758143	0.0246885
$944$	94.7222	3.08295
$945$	1.02990	0.0335026
$946$	−4.35221	−0.141502
$947$	−18.8142	−0.611378	−0.305689	−	0.952131i	$-0.598887\pi$
$947$	−18.8142	−0.611378	−0.305689	+	0.952131i	$0.598887\pi$
$948$	−18.1034	−0.587972
$949$	1.90612	0.0618753
$950$	−5.25601	−0.170528
$951$	−10.7132	−0.347398
$952$	−38.9804	−1.26336
$953$	43.2871	1.40221	0.701103	−	0.713060i	$-0.252691\pi$
$953$	43.2871	1.40221	0.701103	+	0.713060i	$0.252691\pi$
$954$	−15.5742	−0.504234
$955$	0.704657	0.0228022
$956$	−17.7522	−0.574146
$957$	−8.90898	−0.287986
$958$	47.5309	1.53565
$959$	−16.5265	−0.533667
$960$	0.215586	0.00695802
$961$	1.00000	0.0322581
$962$	−10.2704	−0.331130
$963$	17.4613	0.562682
$964$	99.9714	3.21986
$965$	−9.84575	−0.316946
$966$	10.7753	0.346689
$967$	−14.8781	−0.478448	−0.239224	−	0.970964i	$-0.576893\pi$
$967$	−14.8781	−0.478448	−0.239224	+	0.970964i	$0.576893\pi$
$968$	−13.0602	−0.419770
$969$	12.3550	0.396900
$970$	37.0852	1.19073
$971$	40.3860	1.29605	0.648025	−	0.761619i	$-0.275595\pi$
$971$	40.3860	1.29605	0.648025	+	0.761619i	$0.275595\pi$
$972$	−4.48346	−0.143807
$973$	3.83013	0.122788
$974$	92.9112	2.97707
$975$	−1.00000	−0.0320256
$976$	−75.0647	−2.40276
$977$	42.0759	1.34613	0.673063	−	0.739585i	$-0.264978\pi$
$977$	42.0759	1.34613	0.673063	+	0.739585i	$0.264978\pi$
$978$	59.7843	1.91169
$979$	16.4611	0.526100
$980$	−26.6287	−0.850621
$981$	−11.7879	−0.376360
$982$	81.3470	2.59589
$983$	28.8047	0.918727	0.459363	−	0.888248i	$-0.348078\pi$
$983$	28.8047	0.918727	0.459363	+	0.888248i	$0.348078\pi$
$984$	−1.16676	−0.0371950
$985$	−21.8244	−0.695384
$986$	45.4237	1.44659
$987$	−9.52196	−0.303087
$988$	−9.25478	−0.294434
$989$	−2.34962	−0.0747135
$990$	7.61102	0.241894
$991$	−22.5487	−0.716284	−0.358142	−	0.933667i	$-0.616590\pi$
$991$	−22.5487	−0.716284	−0.358142	+	0.933667i	$0.616590\pi$
$992$	5.51923	0.175236
$993$	17.4529	0.553852
$994$	7.02973	0.222969
$995$	6.36012	0.201629
$996$	−45.7871	−1.45082
$997$	50.0207	1.58417	0.792086	−	0.610409i	$-0.208995\pi$
$997$	50.0207	1.58417	0.792086	+	0.610409i	$0.208995\pi$
$998$	39.7248	1.25747
$999$	4.03351	0.127615

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.bh.1.15	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.bh.1.15	✓	17	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:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q+2.54626 q^{2} -1.00000 q^{3} +4.48346 q^{4} +1.00000 q^{5} -2.54626 q^{6} -1.02990 q^{7} +6.32355 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.54626 q^{2} -1.00000 q^{3} +4.48346 q^{4} +1.00000 q^{5} -2.54626 q^{6} -1.02990 q^{7} +6.32355 q^{8} +1.00000 q^{9} +2.54626 q^{10} +2.98909 q^{11} -4.48346 q^{12} +1.00000 q^{13} -2.62239 q^{14} -1.00000 q^{15} +7.13450 q^{16} +5.98536 q^{17} +2.54626 q^{18} -2.06421 q^{19} +4.48346 q^{20} +1.02990 q^{21} +7.61102 q^{22} +4.10895 q^{23} -6.32355 q^{24} +1.00000 q^{25} +2.54626 q^{26} -1.00000 q^{27} -4.61751 q^{28} +2.98050 q^{29} -2.54626 q^{30} +1.00000 q^{31} +5.51923 q^{32} -2.98909 q^{33} +15.2403 q^{34} -1.02990 q^{35} +4.48346 q^{36} -4.03351 q^{37} -5.25601 q^{38} -1.00000 q^{39} +6.32355 q^{40} +0.184510 q^{41} +2.62239 q^{42} -0.571830 q^{43} +13.4015 q^{44} +1.00000 q^{45} +10.4625 q^{46} -9.24553 q^{47} -7.13450 q^{48} -5.93931 q^{49} +2.54626 q^{50} -5.98536 q^{51} +4.48346 q^{52} -6.11650 q^{53} -2.54626 q^{54} +2.98909 q^{55} -6.51262 q^{56} +2.06421 q^{57} +7.58913 q^{58} +13.2766 q^{59} -4.48346 q^{60} -10.5214 q^{61} +2.54626 q^{62} -1.02990 q^{63} -0.215586 q^{64} +1.00000 q^{65} -7.61102 q^{66} +3.87908 q^{67} +26.8351 q^{68} -4.10895 q^{69} -2.62239 q^{70} -2.68065 q^{71} +6.32355 q^{72} +1.90612 q^{73} -10.2704 q^{74} -1.00000 q^{75} -9.25478 q^{76} -3.07846 q^{77} -2.54626 q^{78} +4.03783 q^{79} +7.13450 q^{80} +1.00000 q^{81} +0.469812 q^{82} +10.2125 q^{83} +4.61751 q^{84} +5.98536 q^{85} -1.45603 q^{86} -2.98050 q^{87} +18.9017 q^{88} +5.50706 q^{89} +2.54626 q^{90} -1.02990 q^{91} +18.4223 q^{92} -1.00000 q^{93} -23.5416 q^{94} -2.06421 q^{95} -5.51923 q^{96} +14.5645 q^{97} -15.1230 q^{98} +2.98909 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9} + 2 q^{10} + 3 q^{11} - 20 q^{12} + 17 q^{13} + q^{14} - 17 q^{15} + 26 q^{16} + 2 q^{18} + 10 q^{19} + 20 q^{20} - 18 q^{21} + 5 q^{22} + 16 q^{23} - 9 q^{24} + 17 q^{25} + 2 q^{26} - 17 q^{27} + 36 q^{28} - 3 q^{29} - 2 q^{30} + 17 q^{31} + 20 q^{32} - 3 q^{33} + q^{34} + 18 q^{35} + 20 q^{36} + 14 q^{37} + 22 q^{38} - 17 q^{39} + 9 q^{40} - 6 q^{41} - q^{42} + 24 q^{43} - 15 q^{44} + 17 q^{45} + 6 q^{46} + 25 q^{47} - 26 q^{48} + 31 q^{49} + 2 q^{50} + 20 q^{52} - 15 q^{53} - 2 q^{54} + 3 q^{55} + 31 q^{56} - 10 q^{57} + 44 q^{58} + 16 q^{59} - 20 q^{60} - 5 q^{61} + 2 q^{62} + 18 q^{63} + 35 q^{64} + 17 q^{65} - 5 q^{66} + 50 q^{67} + 13 q^{68} - 16 q^{69} + q^{70} + 16 q^{71} + 9 q^{72} + 33 q^{73} + 2 q^{74} - 17 q^{75} + 9 q^{77} - 2 q^{78} - 10 q^{79} + 26 q^{80} + 17 q^{81} + 61 q^{82} + 27 q^{83} - 36 q^{84} - 12 q^{86} + 3 q^{87} + 23 q^{88} - 24 q^{89} + 2 q^{90} + 18 q^{91} - 21 q^{92} - 17 q^{93} + 6 q^{94} + 10 q^{95} - 20 q^{96} + 48 q^{97} + 14 q^{98} + 3 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9 + 2 * q^10 + 3 * q^11 - 20 * q^12 + 17 * q^13 + q^14 - 17 * q^15 + 26 * q^16 + 2 * q^18 + 10 * q^19 + 20 * q^20 - 18 * q^21 + 5 * q^22 + 16 * q^23 - 9 * q^24 + 17 * q^25 + 2 * q^26 - 17 * q^27 + 36 * q^28 - 3 * q^29 - 2 * q^30 + 17 * q^31 + 20 * q^32 - 3 * q^33 + q^34 + 18 * q^35 + 20 * q^36 + 14 * q^37 + 22 * q^38 - 17 * q^39 + 9 * q^40 - 6 * q^41 - q^42 + 24 * q^43 - 15 * q^44 + 17 * q^45 + 6 * q^46 + 25 * q^47 - 26 * q^48 + 31 * q^49 + 2 * q^50 + 20 * q^52 - 15 * q^53 - 2 * q^54 + 3 * q^55 + 31 * q^56 - 10 * q^57 + 44 * q^58 + 16 * q^59 - 20 * q^60 - 5 * q^61 + 2 * q^62 + 18 * q^63 + 35 * q^64 + 17 * q^65 - 5 * q^66 + 50 * q^67 + 13 * q^68 - 16 * q^69 + q^70 + 16 * q^71 + 9 * q^72 + 33 * q^73 + 2 * q^74 - 17 * q^75 + 9 * q^77 - 2 * q^78 - 10 * q^79 + 26 * q^80 + 17 * q^81 + 61 * q^82 + 27 * q^83 - 36 * q^84 - 12 * q^86 + 3 * q^87 + 23 * q^88 - 24 * q^89 + 2 * q^90 + 18 * q^91 - 21 * q^92 - 17 * q^93 + 6 * q^94 + 10 * q^95 - 20 * q^96 + 48 * q^97 + 14 * q^98 + 3 * q^99

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