LMFDB - Embedded newform 845.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(1,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, 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("845.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.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:	$6.74735897080$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 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			$1.80194$ of defining polynomial
Character	$\chi$	$=$	845.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.80194 q^{2} -1.55496 q^{3} +1.24698 q^{4} +1.00000 q^{5} +2.80194 q^{6} -1.55496 q^{7} +1.35690 q^{8} -0.582105 q^{9} +O(q^{10})$	\(q-1.80194 q^{2} -1.55496 q^{3} +1.24698 q^{4} +1.00000 q^{5} +2.80194 q^{6} -1.55496 q^{7} +1.35690 q^{8} -0.582105 q^{9} -1.80194 q^{10} +0.356896 q^{11} -1.93900 q^{12} +2.80194 q^{14} -1.55496 q^{15} -4.93900 q^{16} -1.33513 q^{17} +1.04892 q^{18} +8.65279 q^{19} +1.24698 q^{20} +2.41789 q^{21} -0.643104 q^{22} -8.00969 q^{23} -2.10992 q^{24} +1.00000 q^{25} +5.57002 q^{27} -1.93900 q^{28} +7.14675 q^{29} +2.80194 q^{30} -5.43296 q^{31} +6.18598 q^{32} -0.554958 q^{33} +2.40581 q^{34} -1.55496 q^{35} -0.725873 q^{36} +4.60388 q^{37} -15.5918 q^{38} +1.35690 q^{40} +8.58211 q^{41} -4.35690 q^{42} -9.24698 q^{43} +0.445042 q^{44} -0.582105 q^{45} +14.4330 q^{46} -3.41789 q^{47} +7.67994 q^{48} -4.58211 q^{49} -1.80194 q^{50} +2.07606 q^{51} -2.24698 q^{53} -10.0368 q^{54} +0.356896 q^{55} -2.10992 q^{56} -13.4547 q^{57} -12.8780 q^{58} -0.506041 q^{59} -1.93900 q^{60} -7.24698 q^{61} +9.78986 q^{62} +0.905149 q^{63} -1.26875 q^{64} +1.00000 q^{66} -4.48188 q^{67} -1.66487 q^{68} +12.4547 q^{69} +2.80194 q^{70} -6.39373 q^{71} -0.789856 q^{72} -15.5254 q^{73} -8.29590 q^{74} -1.55496 q^{75} +10.7899 q^{76} -0.554958 q^{77} -4.65519 q^{79} -4.93900 q^{80} -6.91484 q^{81} -15.4644 q^{82} -5.48427 q^{83} +3.01507 q^{84} -1.33513 q^{85} +16.6625 q^{86} -11.1129 q^{87} +0.484271 q^{88} -16.5797 q^{89} +1.04892 q^{90} -9.98792 q^{92} +8.44803 q^{93} +6.15883 q^{94} +8.65279 q^{95} -9.61894 q^{96} -10.4330 q^{97} +8.25667 q^{98} -0.207751 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} - 5 q^{3} - q^{4} + 3 q^{5} + 4 q^{6} - 5 q^{7} + 4 q^{9}+O(q^{10}) $ 3 * q - q^2 - 5 * q^3 - q^4 + 3 * q^5 + 4 * q^6 - 5 * q^7 + 4 * q^9	$ 3 q - q^{2} - 5 q^{3} - q^{4} + 3 q^{5} + 4 q^{6} - 5 q^{7} + 4 q^{9} - q^{10} - 3 q^{11} + 4 q^{12} + 4 q^{14} - 5 q^{15} - 5 q^{16} - 3 q^{17} - 6 q^{18} + 8 q^{19} - q^{20} + 13 q^{21} - 6 q^{22} - 2 q^{23} - 7 q^{24} + 3 q^{25} - 8 q^{27} + 4 q^{28} - 6 q^{29} + 4 q^{30} + 3 q^{31} + 4 q^{32} - 2 q^{33} - 6 q^{34} - 5 q^{35} - 13 q^{36} + 5 q^{37} - 19 q^{38} + 20 q^{41} - 9 q^{42} - 23 q^{43} + q^{44} + 4 q^{45} + 24 q^{46} - 16 q^{47} - q^{48} - 8 q^{49} - q^{50} - 9 q^{51} - 2 q^{53} - 2 q^{54} - 3 q^{55} - 7 q^{56} - 18 q^{57} - 19 q^{58} - 11 q^{59} + 4 q^{60} - 17 q^{61} + 6 q^{62} - 23 q^{63} + 4 q^{64} + 3 q^{66} + 15 q^{67} - 6 q^{68} + 15 q^{69} + 4 q^{70} + 13 q^{71} + 21 q^{72} - 12 q^{73} - 11 q^{74} - 5 q^{75} + 9 q^{76} - 2 q^{77} - 37 q^{79} - 5 q^{80} + 27 q^{81} - 2 q^{82} - 29 q^{83} - 16 q^{84} - 3 q^{85} + 10 q^{86} + 10 q^{87} + 14 q^{88} - 3 q^{89} - 6 q^{90} - 11 q^{92} - 19 q^{93} + 10 q^{94} + 8 q^{95} + 5 q^{96} - 12 q^{97} - 2 q^{98} + 17 q^{99}+O(q^{100}) $ 3 * q - q^2 - 5 * q^3 - q^4 + 3 * q^5 + 4 * q^6 - 5 * q^7 + 4 * q^9 - q^10 - 3 * q^11 + 4 * q^12 + 4 * q^14 - 5 * q^15 - 5 * q^16 - 3 * q^17 - 6 * q^18 + 8 * q^19 - q^20 + 13 * q^21 - 6 * q^22 - 2 * q^23 - 7 * q^24 + 3 * q^25 - 8 * q^27 + 4 * q^28 - 6 * q^29 + 4 * q^30 + 3 * q^31 + 4 * q^32 - 2 * q^33 - 6 * q^34 - 5 * q^35 - 13 * q^36 + 5 * q^37 - 19 * q^38 + 20 * q^41 - 9 * q^42 - 23 * q^43 + q^44 + 4 * q^45 + 24 * q^46 - 16 * q^47 - q^48 - 8 * q^49 - q^50 - 9 * q^51 - 2 * q^53 - 2 * q^54 - 3 * q^55 - 7 * q^56 - 18 * q^57 - 19 * q^58 - 11 * q^59 + 4 * q^60 - 17 * q^61 + 6 * q^62 - 23 * q^63 + 4 * q^64 + 3 * q^66 + 15 * q^67 - 6 * q^68 + 15 * q^69 + 4 * q^70 + 13 * q^71 + 21 * q^72 - 12 * q^73 - 11 * q^74 - 5 * q^75 + 9 * q^76 - 2 * q^77 - 37 * q^79 - 5 * q^80 + 27 * q^81 - 2 * q^82 - 29 * q^83 - 16 * q^84 - 3 * q^85 + 10 * q^86 + 10 * q^87 + 14 * q^88 - 3 * q^89 - 6 * q^90 - 11 * q^92 - 19 * q^93 + 10 * q^94 + 8 * q^95 + 5 * q^96 - 12 * q^97 - 2 * q^98 + 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.80194	−1.27416	−0.637081	−	0.770797i	$-0.719858\pi$
$2$	−1.80194	−1.27416	−0.637081	+	0.770797i	$0.719858\pi$
$3$	−1.55496	−0.897755	−0.448878	−	0.893593i	$-0.648176\pi$
$3$	−1.55496	−0.897755	−0.448878	+	0.893593i	$0.648176\pi$
$4$	1.24698	0.623490
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.80194	1.14389
$7$	−1.55496	−0.587719	−0.293859	−	0.955849i	$-0.594940\pi$
$7$	−1.55496	−0.587719	−0.293859	+	0.955849i	$0.594940\pi$
$8$	1.35690	0.479735
$9$	−0.582105	−0.194035
$10$	−1.80194	−0.569823
$11$	0.356896	0.107608	0.0538041	−	0.998552i	$-0.482865\pi$
$11$	0.356896	0.107608	0.0538041	+	0.998552i	$0.482865\pi$
$12$	−1.93900	−0.559741
$13$	0	0
$13$	0	0
$14$	2.80194	0.748849
$15$	−1.55496	−0.401488
$16$	−4.93900	−1.23475
$17$	−1.33513	−0.323816	−0.161908	−	0.986806i	$-0.551765\pi$
$17$	−1.33513	−0.323816	−0.161908	+	0.986806i	$0.551765\pi$
$18$	1.04892	0.247232
$19$	8.65279	1.98509	0.992543	−	0.121892i	$-0.0388961\pi$
$19$	8.65279	1.98509	0.992543	+	0.121892i	$0.0388961\pi$
$20$	1.24698	0.278833
$21$	2.41789	0.527628
$22$	−0.643104	−0.137110
$23$	−8.00969	−1.67014	−0.835068	−	0.550147i	$-0.814572\pi$
$23$	−8.00969	−1.67014	−0.835068	+	0.550147i	$0.814572\pi$
$24$	−2.10992	−0.430685
$25$	1.00000	0.200000
$26$	0	0
$27$	5.57002	1.07195
$28$	−1.93900	−0.366437
$29$	7.14675	1.32712	0.663559	−	0.748124i	$-0.269045\pi$
$29$	7.14675	1.32712	0.663559	+	0.748124i	$0.269045\pi$
$30$	2.80194	0.511562
$31$	−5.43296	−0.975788	−0.487894	−	0.872903i	$-0.662235\pi$
$31$	−5.43296	−0.975788	−0.487894	+	0.872903i	$0.662235\pi$
$32$	6.18598	1.09354
$33$	−0.554958	−0.0966058
$34$	2.40581	0.412594
$35$	−1.55496	−0.262836
$36$	−0.725873	−0.120979
$37$	4.60388	0.756872	0.378436	−	0.925627i	$-0.376462\pi$
$37$	4.60388	0.756872	0.378436	+	0.925627i	$0.376462\pi$
$38$	−15.5918	−2.52932
$39$	0	0
$40$	1.35690	0.214544
$41$	8.58211	1.34030	0.670150	−	0.742226i	$-0.266230\pi$
$41$	8.58211	1.34030	0.670150	+	0.742226i	$0.266230\pi$
$42$	−4.35690	−0.672284
$43$	−9.24698	−1.41015	−0.705076	−	0.709132i	$-0.749087\pi$
$43$	−9.24698	−1.41015	−0.705076	+	0.709132i	$0.749087\pi$
$44$	0.445042	0.0670926
$45$	−0.582105	−0.0867751
$46$	14.4330	2.12802
$47$	−3.41789	−0.498551	−0.249276	−	0.968433i	$-0.580192\pi$
$47$	−3.41789	−0.498551	−0.249276	+	0.968433i	$0.580192\pi$
$48$	7.67994	1.10850
$49$	−4.58211	−0.654586
$50$	−1.80194	−0.254832
$51$	2.07606	0.290707
$52$	0	0
$53$	−2.24698	−0.308646	−0.154323	−	0.988020i	$-0.549320\pi$
$53$	−2.24698	−0.308646	−0.154323	+	0.988020i	$0.549320\pi$
$54$	−10.0368	−1.36584
$55$	0.356896	0.0481238
$56$	−2.10992	−0.281949
$57$	−13.4547	−1.78212
$58$	−12.8780	−1.69096
$59$	−0.506041	−0.0658809	−0.0329404	−	0.999457i	$-0.510487\pi$
$59$	−0.506041	−0.0658809	−0.0329404	+	0.999457i	$0.510487\pi$
$60$	−1.93900	−0.250324
$61$	−7.24698	−0.927881	−0.463940	−	0.885866i	$-0.653565\pi$
$61$	−7.24698	−0.927881	−0.463940	+	0.885866i	$0.653565\pi$
$62$	9.78986	1.24331
$63$	0.905149	0.114038
$64$	−1.26875	−0.158594
$65$	0	0
$66$	1.00000	0.123091
$67$	−4.48188	−0.547548	−0.273774	−	0.961794i	$-0.588272\pi$
$67$	−4.48188	−0.547548	−0.273774	+	0.961794i	$0.588272\pi$
$68$	−1.66487	−0.201896
$69$	12.4547	1.49937
$70$	2.80194	0.334896
$71$	−6.39373	−0.758796	−0.379398	−	0.925233i	$-0.623869\pi$
$71$	−6.39373	−0.758796	−0.379398	+	0.925233i	$0.623869\pi$
$72$	−0.789856	−0.0930854
$73$	−15.5254	−1.81711	−0.908556	−	0.417762i	$-0.862814\pi$
$73$	−15.5254	−1.81711	−0.908556	+	0.417762i	$0.862814\pi$
$74$	−8.29590	−0.964378
$75$	−1.55496	−0.179551
$76$	10.7899	1.23768
$77$	−0.554958	−0.0632433
$78$	0	0
$79$	−4.65519	−0.523749	−0.261875	−	0.965102i	$-0.584341\pi$
$79$	−4.65519	−0.523749	−0.261875	+	0.965102i	$0.584341\pi$
$80$	−4.93900	−0.552197
$81$	−6.91484	−0.768315
$82$	−15.4644	−1.70776
$83$	−5.48427	−0.601977	−0.300988	−	0.953628i	$-0.597317\pi$
$83$	−5.48427	−0.601977	−0.300988	+	0.953628i	$0.597317\pi$
$84$	3.01507	0.328971
$85$	−1.33513	−0.144815
$86$	16.6625	1.79676
$87$	−11.1129	−1.19143
$88$	0.484271	0.0516234
$89$	−16.5797	−1.75745	−0.878723	−	0.477332i	$-0.841604\pi$
$89$	−16.5797	−1.75745	−0.878723	+	0.477332i	$0.841604\pi$
$90$	1.04892	0.110566
$91$	0	0
$92$	−9.98792	−1.04131
$93$	8.44803	0.876019
$94$	6.15883	0.635235
$95$	8.65279	0.887758
$96$	−9.61894	−0.981729
$97$	−10.4330	−1.05931	−0.529653	−	0.848214i	$-0.677678\pi$
$97$	−10.4330	−1.05931	−0.529653	+	0.848214i	$0.677678\pi$
$98$	8.25667	0.834049
$99$	−0.207751	−0.0208798
$100$	1.24698	0.124698
$101$	1.62565	0.161758	0.0808789	−	0.996724i	$-0.474227\pi$
$101$	1.62565	0.161758	0.0808789	+	0.996724i	$0.474227\pi$
$102$	−3.74094	−0.370408
$103$	−9.33513	−0.919817	−0.459909	−	0.887966i	$-0.652118\pi$
$103$	−9.33513	−0.919817	−0.459909	+	0.887966i	$0.652118\pi$
$104$	0	0
$105$	2.41789	0.235962
$106$	4.04892	0.393266
$107$	16.2228	1.56832	0.784159	−	0.620559i	$-0.213094\pi$
$107$	16.2228	1.56832	0.784159	+	0.620559i	$0.213094\pi$
$108$	6.94571	0.668351
$109$	5.06638	0.485271	0.242635	−	0.970118i	$-0.421988\pi$
$109$	5.06638	0.485271	0.242635	+	0.970118i	$0.421988\pi$
$110$	−0.643104	−0.0613176
$111$	−7.15883	−0.679486
$112$	7.67994	0.725686
$113$	10.1153	0.951567	0.475783	−	0.879562i	$-0.342165\pi$
$113$	10.1153	0.951567	0.475783	+	0.879562i	$0.342165\pi$
$114$	24.2446	2.27071
$115$	−8.00969	−0.746907
$116$	8.91185	0.827445
$117$	0	0
$118$	0.911854	0.0839430
$119$	2.07606	0.190313
$120$	−2.10992	−0.192608
$121$	−10.8726	−0.988420
$122$	13.0586	1.18227
$123$	−13.3448	−1.20326
$124$	−6.77479	−0.608394
$125$	1.00000	0.0894427
$126$	−1.63102	−0.145303
$127$	−6.02715	−0.534823	−0.267411	−	0.963582i	$-0.586168\pi$
$127$	−6.02715	−0.534823	−0.267411	+	0.963582i	$0.586168\pi$
$128$	−10.0858	−0.891463
$129$	14.3787	1.26597
$130$	0	0
$131$	−10.1075	−0.883098	−0.441549	−	0.897237i	$-0.645571\pi$
$131$	−10.1075	−0.883098	−0.441549	+	0.897237i	$0.645571\pi$
$132$	−0.692021	−0.0602327
$133$	−13.4547	−1.16667
$134$	8.07606	0.697666
$135$	5.57002	0.479391
$136$	−1.81163	−0.155346
$137$	−4.96077	−0.423827	−0.211914	−	0.977288i	$-0.567970\pi$
$137$	−4.96077	−0.423827	−0.211914	+	0.977288i	$0.567970\pi$
$138$	−22.4426	−1.91045
$139$	−9.02177	−0.765217	−0.382608	−	0.923911i	$-0.624974\pi$
$139$	−9.02177	−0.765217	−0.382608	+	0.923911i	$0.624974\pi$
$140$	−1.93900	−0.163876
$141$	5.31468	0.447577
$142$	11.5211	0.966830
$143$	0	0
$144$	2.87502	0.239585
$145$	7.14675	0.593505
$146$	27.9758	2.31530
$147$	7.12498	0.587659
$148$	5.74094	0.471902
$149$	18.1957	1.49065	0.745324	−	0.666703i	$-0.232295\pi$
$149$	18.1957	1.49065	0.745324	+	0.666703i	$0.232295\pi$
$150$	2.80194	0.228777
$151$	7.22521	0.587979	0.293990	−	0.955809i	$-0.405017\pi$
$151$	7.22521	0.587979	0.293990	+	0.955809i	$0.405017\pi$
$152$	11.7409	0.952316
$153$	0.777184	0.0628316
$154$	1.00000	0.0805823
$155$	−5.43296	−0.436386
$156$	0	0
$157$	−8.79954	−0.702280	−0.351140	−	0.936323i	$-0.614206\pi$
$157$	−8.79954	−0.702280	−0.351140	+	0.936323i	$0.614206\pi$
$158$	8.38835	0.667342
$159$	3.49396	0.277089
$160$	6.18598	0.489045
$161$	12.4547	0.981570
$162$	12.4601	0.978958
$163$	−5.91723	−0.463473	−0.231737	−	0.972779i	$-0.574441\pi$
$163$	−5.91723	−0.463473	−0.231737	+	0.972779i	$0.574441\pi$
$164$	10.7017	0.835663
$165$	−0.554958	−0.0432034
$166$	9.88231	0.767016
$167$	6.00431	0.464628	0.232314	−	0.972641i	$-0.425370\pi$
$167$	6.00431	0.464628	0.232314	+	0.972641i	$0.425370\pi$
$168$	3.28083	0.253122
$169$	0	0
$170$	2.40581	0.184517
$171$	−5.03684	−0.385176
$172$	−11.5308	−0.879215
$173$	17.7506	1.34956	0.674778	−	0.738021i	$-0.264240\pi$
$173$	17.7506	1.34956	0.674778	+	0.738021i	$0.264240\pi$
$174$	20.0248	1.51807
$175$	−1.55496	−0.117544
$176$	−1.76271	−0.132869
$177$	0.786872	0.0591449
$178$	29.8756	2.23927
$179$	−16.5550	−1.23738	−0.618688	−	0.785637i	$-0.712335\pi$
$179$	−16.5550	−1.23738	−0.618688	+	0.785637i	$0.712335\pi$
$180$	−0.725873	−0.0541034
$181$	11.1739	0.830549	0.415275	−	0.909696i	$-0.363685\pi$
$181$	11.1739	0.830549	0.415275	+	0.909696i	$0.363685\pi$
$182$	0	0
$183$	11.2687	0.833010
$184$	−10.8683	−0.801223
$185$	4.60388	0.338484
$186$	−15.2228	−1.11619
$187$	−0.476501	−0.0348452
$188$	−4.26205	−0.310842
$189$	−8.66115	−0.630006
$190$	−15.5918	−1.13115
$191$	−8.03684	−0.581525	−0.290763	−	0.956795i	$-0.593909\pi$
$191$	−8.03684	−0.581525	−0.290763	+	0.956795i	$0.593909\pi$
$192$	1.97285	0.142378
$193$	15.8931	1.14401	0.572004	−	0.820251i	$-0.306166\pi$
$193$	15.8931	1.14401	0.572004	+	0.820251i	$0.306166\pi$
$194$	18.7995	1.34973
$195$	0	0
$196$	−5.71379	−0.408128
$197$	20.1715	1.43716	0.718580	−	0.695444i	$-0.244792\pi$
$197$	20.1715	1.43716	0.718580	+	0.695444i	$0.244792\pi$
$198$	0.374354	0.0266042
$199$	−11.8116	−0.837304	−0.418652	−	0.908147i	$-0.637497\pi$
$199$	−11.8116	−0.837304	−0.418652	+	0.908147i	$0.637497\pi$
$200$	1.35690	0.0959470
$201$	6.96913	0.491565
$202$	−2.92931	−0.206106
$203$	−11.1129	−0.779973
$204$	2.58881	0.181253
$205$	8.58211	0.599400
$206$	16.8213	1.17200
$207$	4.66248	0.324065
$208$	0	0
$209$	3.08815	0.213612
$210$	−4.35690	−0.300654
$211$	−24.0978	−1.65896	−0.829482	−	0.558534i	$-0.811364\pi$
$211$	−24.0978	−1.65896	−0.829482	+	0.558534i	$0.811364\pi$
$212$	−2.80194	−0.192438
$213$	9.94198	0.681214
$214$	−29.2325	−1.99829
$215$	−9.24698	−0.630639
$216$	7.55794	0.514253
$217$	8.44803	0.573489
$218$	−9.12929	−0.618314
$219$	24.1414	1.63132
$220$	0.445042	0.0300047
$221$	0	0
$222$	12.8998	0.865776
$223$	−10.2034	−0.683273	−0.341636	−	0.939832i	$-0.610981\pi$
$223$	−10.2034	−0.683273	−0.341636	+	0.939832i	$0.610981\pi$
$224$	−9.61894	−0.642693
$225$	−0.582105	−0.0388070
$226$	−18.2271	−1.21245
$227$	7.83446	0.519991	0.259996	−	0.965610i	$-0.416279\pi$
$227$	7.83446	0.519991	0.259996	+	0.965610i	$0.416279\pi$
$228$	−16.7778	−1.11114
$229$	−6.61596	−0.437195	−0.218597	−	0.975815i	$-0.570148\pi$
$229$	−6.61596	−0.437195	−0.218597	+	0.975815i	$0.570148\pi$
$230$	14.4330	0.951681
$231$	0.862937	0.0567771
$232$	9.69740	0.636665
$233$	1.37196	0.0898802	0.0449401	−	0.998990i	$-0.485690\pi$
$233$	1.37196	0.0898802	0.0449401	+	0.998990i	$0.485690\pi$
$234$	0	0
$235$	−3.41789	−0.222959
$236$	−0.631023	−0.0410761
$237$	7.23862	0.470199
$238$	−3.74094	−0.242489
$239$	2.10454	0.136131	0.0680657	−	0.997681i	$-0.478317\pi$
$239$	2.10454	0.136131	0.0680657	+	0.997681i	$0.478317\pi$
$240$	7.67994	0.495738
$241$	−19.1890	−1.23607	−0.618035	−	0.786151i	$-0.712071\pi$
$241$	−19.1890	−1.23607	−0.618035	+	0.786151i	$0.712071\pi$
$242$	19.5918	1.25941
$243$	−5.95779	−0.382192
$244$	−9.03684	−0.578524
$245$	−4.58211	−0.292740
$246$	24.0465	1.53315
$247$	0	0
$248$	−7.37196	−0.468120
$249$	8.52781	0.540428
$250$	−1.80194	−0.113965
$251$	−10.0653	−0.635317	−0.317658	−	0.948205i	$-0.602897\pi$
$251$	−10.0653	−0.635317	−0.317658	+	0.948205i	$0.602897\pi$
$252$	1.12870	0.0711016
$253$	−2.85862	−0.179720
$254$	10.8605	0.681451
$255$	2.07606	0.130008
$256$	20.7114	1.29446
$257$	10.9095	0.680513	0.340257	−	0.940333i	$-0.389486\pi$
$257$	10.9095	0.680513	0.340257	+	0.940333i	$0.389486\pi$
$258$	−25.9095	−1.61305
$259$	−7.15883	−0.444828
$260$	0	0
$261$	−4.16016	−0.257508
$262$	18.2131	1.12521
$263$	−8.41789	−0.519070	−0.259535	−	0.965734i	$-0.583569\pi$
$263$	−8.41789	−0.519070	−0.259535	+	0.965734i	$0.583569\pi$
$264$	−0.753020	−0.0463452
$265$	−2.24698	−0.138031
$266$	24.2446	1.48653
$267$	25.7808	1.57776
$268$	−5.58881	−0.341391
$269$	19.3991	1.18278	0.591392	−	0.806384i	$-0.298579\pi$
$269$	19.3991	1.18278	0.591392	+	0.806384i	$0.298579\pi$
$270$	−10.0368	−0.610822
$271$	−3.10023	−0.188325	−0.0941627	−	0.995557i	$-0.530017\pi$
$271$	−3.10023	−0.188325	−0.0941627	+	0.995557i	$0.530017\pi$
$272$	6.59419	0.399831
$273$	0	0
$274$	8.93900	0.540025
$275$	0.356896	0.0215216
$276$	15.5308	0.934844
$277$	7.10752	0.427050	0.213525	−	0.976938i	$-0.431506\pi$
$277$	7.10752	0.427050	0.213525	+	0.976938i	$0.431506\pi$
$278$	16.2567	0.975010
$279$	3.16255	0.189337
$280$	−2.10992	−0.126092
$281$	8.80492	0.525258	0.262629	−	0.964897i	$-0.415411\pi$
$281$	8.80492	0.525258	0.262629	+	0.964897i	$0.415411\pi$
$282$	−9.57673	−0.570286
$283$	−7.59419	−0.451428	−0.225714	−	0.974194i	$-0.572471\pi$
$283$	−7.59419	−0.451428	−0.225714	+	0.974194i	$0.572471\pi$
$284$	−7.97285	−0.473102
$285$	−13.4547	−0.796989
$286$	0	0
$287$	−13.3448	−0.787719
$288$	−3.60089	−0.212185
$289$	−15.2174	−0.895144
$290$	−12.8780	−0.756222
$291$	16.2228	0.950998
$292$	−19.3599	−1.13295
$293$	−6.96615	−0.406967	−0.203483	−	0.979078i	$-0.565226\pi$
$293$	−6.96615	−0.406967	−0.203483	+	0.979078i	$0.565226\pi$
$294$	−12.8388	−0.748772
$295$	−0.506041	−0.0294628
$296$	6.24698	0.363098
$297$	1.98792	0.115351
$298$	−32.7875	−1.89933
$299$	0	0
$300$	−1.93900	−0.111948
$301$	14.3787	0.828773
$302$	−13.0194	−0.749181
$303$	−2.52781	−0.145219
$304$	−42.7362	−2.45109
$305$	−7.24698	−0.414961
$306$	−1.40044	−0.0800576
$307$	21.3153	1.21653	0.608263	−	0.793735i	$-0.291866\pi$
$307$	21.3153	1.21653	0.608263	+	0.793735i	$0.291866\pi$
$308$	−0.692021	−0.0394316
$309$	14.5157	0.825771
$310$	9.78986	0.556026
$311$	−29.3672	−1.66526	−0.832630	−	0.553830i	$-0.813166\pi$
$311$	−29.3672	−1.66526	−0.832630	+	0.553830i	$0.813166\pi$
$312$	0	0
$313$	2.09246	0.118273	0.0591364	−	0.998250i	$-0.481165\pi$
$313$	2.09246	0.118273	0.0591364	+	0.998250i	$0.481165\pi$
$314$	15.8562	0.894819
$315$	0.905149	0.0509994
$316$	−5.80492	−0.326552
$317$	−10.1981	−0.572780	−0.286390	−	0.958113i	$-0.592455\pi$
$317$	−10.1981	−0.572780	−0.286390	+	0.958113i	$0.592455\pi$
$318$	−6.29590	−0.353056
$319$	2.55065	0.142809
$320$	−1.26875	−0.0709253
$321$	−25.2258	−1.40797
$322$	−22.4426	−1.25068
$323$	−11.5526	−0.642802
$324$	−8.62266	−0.479037
$325$	0	0
$326$	10.6625	0.590540
$327$	−7.87800	−0.435655
$328$	11.6450	0.642989
$329$	5.31468	0.293008
$330$	1.00000	0.0550482
$331$	15.2282	0.837017	0.418509	−	0.908213i	$-0.362553\pi$
$331$	15.2282	0.837017	0.418509	+	0.908213i	$0.362553\pi$
$332$	−6.83877	−0.375326
$333$	−2.67994	−0.146860
$334$	−10.8194	−0.592011
$335$	−4.48188	−0.244871
$336$	−11.9420	−0.651489
$337$	−0.869641	−0.0473724	−0.0236862	−	0.999719i	$-0.507540\pi$
$337$	−0.869641	−0.0473724	−0.0236862	+	0.999719i	$0.507540\pi$
$338$	0	0
$339$	−15.7289	−0.854274
$340$	−1.66487	−0.0902905
$341$	−1.93900	−0.105003
$342$	9.07606	0.490777
$343$	18.0097	0.972432
$344$	−12.5472	−0.676499
$345$	12.4547	0.670540
$346$	−31.9855	−1.71955
$347$	−16.7614	−0.899798	−0.449899	−	0.893079i	$-0.648540\pi$
$347$	−16.7614	−0.899798	−0.449899	+	0.893079i	$0.648540\pi$
$348$	−13.8576	−0.742843
$349$	23.3381	1.24926	0.624630	−	0.780921i	$-0.285250\pi$
$349$	23.3381	1.24926	0.624630	+	0.780921i	$0.285250\pi$
$350$	2.80194	0.149770
$351$	0	0
$352$	2.20775	0.117674
$353$	−30.5870	−1.62798	−0.813991	−	0.580877i	$-0.802710\pi$
$353$	−30.5870	−1.62798	−0.813991	+	0.580877i	$0.802710\pi$
$354$	−1.41789	−0.0753603
$355$	−6.39373	−0.339344
$356$	−20.6746	−1.09575
$357$	−3.22819	−0.170854
$358$	29.8310	1.57662
$359$	12.3418	0.651377	0.325688	−	0.945477i	$-0.394404\pi$
$359$	12.3418	0.651377	0.325688	+	0.945477i	$0.394404\pi$
$360$	−0.789856	−0.0416291
$361$	55.8708	2.94057
$362$	−20.1347	−1.05825
$363$	16.9065	0.887360
$364$	0	0
$365$	−15.5254	−0.812638
$366$	−20.3056	−1.06139
$367$	18.5569	0.968661	0.484331	−	0.874885i	$-0.339063\pi$
$367$	18.5569	0.968661	0.484331	+	0.874885i	$0.339063\pi$
$368$	39.5599	2.06220
$369$	−4.99569	−0.260065
$370$	−8.29590	−0.431283
$371$	3.49396	0.181397
$372$	10.5345	0.546189
$373$	−23.9245	−1.23877	−0.619383	−	0.785089i	$-0.712617\pi$
$373$	−23.9245	−1.23877	−0.619383	+	0.785089i	$0.712617\pi$
$374$	0.858625	0.0443984
$375$	−1.55496	−0.0802977
$376$	−4.63773	−0.239173
$377$	0	0
$378$	15.6069	0.802730
$379$	7.85623	0.403548	0.201774	−	0.979432i	$-0.435329\pi$
$379$	7.85623	0.403548	0.201774	+	0.979432i	$0.435329\pi$
$380$	10.7899	0.553508
$381$	9.37196	0.480140
$382$	14.4819	0.740957
$383$	5.45473	0.278724	0.139362	−	0.990242i	$-0.455495\pi$
$383$	5.45473	0.278724	0.139362	+	0.990242i	$0.455495\pi$
$384$	15.6829	0.800316
$385$	−0.554958	−0.0282833
$386$	−28.6383	−1.45765
$387$	5.38271	0.273619
$388$	−13.0097	−0.660467
$389$	−18.0084	−0.913060	−0.456530	−	0.889708i	$-0.650908\pi$
$389$	−18.0084	−0.913060	−0.456530	+	0.889708i	$0.650908\pi$
$390$	0	0
$391$	10.6939	0.540816
$392$	−6.21744	−0.314028
$393$	15.7168	0.792806
$394$	−36.3478	−1.83118
$395$	−4.65519	−0.234228
$396$	−0.259061	−0.0130183
$397$	18.3080	0.918851	0.459426	−	0.888216i	$-0.348055\pi$
$397$	18.3080	0.918851	0.459426	+	0.888216i	$0.348055\pi$
$398$	21.2838	1.06686
$399$	20.9215	1.04739
$400$	−4.93900	−0.246950
$401$	−19.1728	−0.957446	−0.478723	−	0.877966i	$-0.658900\pi$
$401$	−19.1728	−0.957446	−0.478723	+	0.877966i	$0.658900\pi$
$402$	−12.5579	−0.626333
$403$	0	0
$404$	2.02715	0.100854
$405$	−6.91484	−0.343601
$406$	20.0248	0.993812
$407$	1.64310	0.0814456
$408$	2.81700	0.139462
$409$	−7.22223	−0.357116	−0.178558	−	0.983929i	$-0.557143\pi$
$409$	−7.22223	−0.357116	−0.178558	+	0.983929i	$0.557143\pi$
$410$	−15.4644	−0.763733
$411$	7.71379	0.380493
$412$	−11.6407	−0.573497
$413$	0.786872	0.0387195
$414$	−8.40150	−0.412911
$415$	−5.48427	−0.269212
$416$	0	0
$417$	14.0285	0.686977
$418$	−5.56465	−0.272176
$419$	0.271143	0.0132462	0.00662310	−	0.999978i	$-0.497892\pi$
$419$	0.271143	0.0132462	0.00662310	+	0.999978i	$0.497892\pi$
$420$	3.01507	0.147120
$421$	−35.6286	−1.73643	−0.868217	−	0.496185i	$-0.834734\pi$
$421$	−35.6286	−1.73643	−0.868217	+	0.496185i	$0.834734\pi$
$422$	43.4228	2.11379
$423$	1.98957	0.0967364
$424$	−3.04892	−0.148069
$425$	−1.33513	−0.0647631
$426$	−17.9148	−0.867977
$427$	11.2687	0.545333
$428$	20.2295	0.977831
$429$	0	0
$430$	16.6625	0.803536
$431$	−35.4959	−1.70978	−0.854888	−	0.518812i	$-0.826374\pi$
$431$	−35.4959	−1.70978	−0.854888	+	0.518812i	$0.826374\pi$
$432$	−27.5104	−1.32359
$433$	15.8605	0.762209	0.381105	−	0.924532i	$-0.375544\pi$
$433$	15.8605	0.762209	0.381105	+	0.924532i	$0.375544\pi$
$434$	−15.2228	−0.730719
$435$	−11.1129	−0.532823
$436$	6.31767	0.302561
$437$	−69.3062	−3.31536
$438$	−43.5013	−2.07857
$439$	−25.9312	−1.23763	−0.618815	−	0.785537i	$-0.712387\pi$
$439$	−25.9312	−1.23763	−0.618815	+	0.785537i	$0.712387\pi$
$440$	0.484271	0.0230867
$441$	2.66727	0.127013
$442$	0	0
$443$	−11.2306	−0.533581	−0.266791	−	0.963755i	$-0.585963\pi$
$443$	−11.2306	−0.533581	−0.266791	+	0.963755i	$0.585963\pi$
$444$	−8.92692	−0.423653
$445$	−16.5797	−0.785954
$446$	18.3860	0.870601
$447$	−28.2935	−1.33824
$448$	1.97285	0.0932085
$449$	36.8471	1.73892	0.869462	−	0.494000i	$-0.164466\pi$
$449$	36.8471	1.73892	0.869462	+	0.494000i	$0.164466\pi$
$450$	1.04892	0.0494464
$451$	3.06292	0.144227
$452$	12.6136	0.593292
$453$	−11.2349	−0.527862
$454$	−14.1172	−0.662554
$455$	0	0
$456$	−18.2567	−0.854947
$457$	−21.9879	−1.02855	−0.514276	−	0.857625i	$-0.671939\pi$
$457$	−21.9879	−1.02855	−0.514276	+	0.857625i	$0.671939\pi$
$458$	11.9215	0.557057
$459$	−7.43668	−0.347115
$460$	−9.98792	−0.465689
$461$	8.53750	0.397631	0.198816	−	0.980037i	$-0.436291\pi$
$461$	8.53750	0.397631	0.198816	+	0.980037i	$0.436291\pi$
$462$	−1.55496	−0.0723432
$463$	20.9922	0.975592	0.487796	−	0.872958i	$-0.337801\pi$
$463$	20.9922	0.975592	0.487796	+	0.872958i	$0.337801\pi$
$464$	−35.2978	−1.63866
$465$	8.44803	0.391768
$466$	−2.47219	−0.114522
$467$	13.9976	0.647732	0.323866	−	0.946103i	$-0.395017\pi$
$467$	13.9976	0.647732	0.323866	+	0.946103i	$0.395017\pi$
$468$	0	0
$469$	6.96913	0.321805
$470$	6.15883	0.284086
$471$	13.6829	0.630476
$472$	−0.686645	−0.0316054
$473$	−3.30021	−0.151744
$474$	−13.0435	−0.599110
$475$	8.65279	0.397017
$476$	2.58881	0.118658
$477$	1.30798	0.0598882
$478$	−3.79225	−0.173453
$479$	14.6136	0.667711	0.333855	−	0.942624i	$-0.391650\pi$
$479$	14.6136	0.667711	0.333855	+	0.942624i	$0.391650\pi$
$480$	−9.61894	−0.439043
$481$	0	0
$482$	34.5773	1.57495
$483$	−19.3666	−0.881210
$484$	−13.5579	−0.616270
$485$	−10.4330	−0.473736
$486$	10.7356	0.486975
$487$	−39.0616	−1.77005	−0.885025	−	0.465544i	$-0.845859\pi$
$487$	−39.0616	−1.77005	−0.885025	+	0.465544i	$0.845859\pi$
$488$	−9.83340	−0.445137
$489$	9.20105	0.416086
$490$	8.25667	0.372998
$491$	−25.6082	−1.15568	−0.577841	−	0.816150i	$-0.696104\pi$
$491$	−25.6082	−1.15568	−0.577841	+	0.816150i	$0.696104\pi$
$492$	−16.6407	−0.750221
$493$	−9.54181	−0.429742
$494$	0	0
$495$	−0.207751	−0.00933771
$496$	26.8334	1.20486
$497$	9.94198	0.445959
$498$	−15.3666	−0.688593
$499$	−1.67563	−0.0750114	−0.0375057	−	0.999296i	$-0.511941\pi$
$499$	−1.67563	−0.0750114	−0.0375057	+	0.999296i	$0.511941\pi$
$500$	1.24698	0.0557666
$501$	−9.33645	−0.417122
$502$	18.1371	0.809497
$503$	24.5569	1.09494	0.547469	−	0.836826i	$-0.315592\pi$
$503$	24.5569	1.09494	0.547469	+	0.836826i	$0.315592\pi$
$504$	1.22819	0.0547081
$505$	1.62565	0.0723403
$506$	5.15106	0.228993
$507$	0	0
$508$	−7.51573	−0.333457
$509$	21.8767	0.969667	0.484833	−	0.874607i	$-0.338880\pi$
$509$	21.8767	0.969667	0.484833	+	0.874607i	$0.338880\pi$
$510$	−3.74094	−0.165652
$511$	24.1414	1.06795
$512$	−17.1491	−0.757892
$513$	48.1963	2.12792
$514$	−19.6582	−0.867085
$515$	−9.33513	−0.411355
$516$	17.9299	0.789320
$517$	−1.21983	−0.0536482
$518$	12.8998	0.566783
$519$	−27.6015	−1.21157
$520$	0	0
$521$	30.2131	1.32366	0.661831	−	0.749653i	$-0.269780\pi$
$521$	30.2131	1.32366	0.661831	+	0.749653i	$0.269780\pi$
$522$	7.49635	0.328106
$523$	21.1957	0.926822	0.463411	−	0.886143i	$-0.346625\pi$
$523$	21.1957	0.926822	0.463411	+	0.886143i	$0.346625\pi$
$524$	−12.6039	−0.550603
$525$	2.41789	0.105526
$526$	15.1685	0.661379
$527$	7.25368	0.315975
$528$	2.74094	0.119284
$529$	41.1551	1.78935
$530$	4.04892	0.175874
$531$	0.294569	0.0127832
$532$	−16.7778	−0.727409
$533$	0	0
$534$	−46.4553	−2.01032
$535$	16.2228	0.701374
$536$	−6.08144	−0.262678
$537$	25.7423	1.11086
$538$	−34.9560	−1.50706
$539$	−1.63533	−0.0704388
$540$	6.94571	0.298896
$541$	15.4373	0.663700	0.331850	−	0.943332i	$-0.392327\pi$
$541$	15.4373	0.663700	0.331850	+	0.943332i	$0.392327\pi$
$542$	5.58642	0.239957
$543$	−17.3749	−0.745630
$544$	−8.25906	−0.354104
$545$	5.06638	0.217020
$546$	0	0
$547$	−38.6722	−1.65350	−0.826751	−	0.562568i	$-0.809814\pi$
$547$	−38.6722	−1.65350	−0.826751	+	0.562568i	$0.809814\pi$
$548$	−6.18598	−0.264252
$549$	4.21850	0.180041
$550$	−0.643104	−0.0274221
$551$	61.8394	2.63445
$552$	16.8998	0.719302
$553$	7.23862	0.307817
$554$	−12.8073	−0.544131
$555$	−7.15883	−0.303876
$556$	−11.2500	−0.477105
$557$	−21.9782	−0.931247	−0.465624	−	0.884983i	$-0.654170\pi$
$557$	−21.9782	−0.931247	−0.465624	+	0.884983i	$0.654170\pi$
$558$	−5.69873	−0.241246
$559$	0	0
$560$	7.67994	0.324537
$561$	0.740939	0.0312825
$562$	−15.8659	−0.669263
$563$	14.4474	0.608887	0.304443	−	0.952530i	$-0.401530\pi$
$563$	14.4474	0.608887	0.304443	+	0.952530i	$0.401530\pi$
$564$	6.62730	0.279060
$565$	10.1153	0.425554
$566$	13.6843	0.575192
$567$	10.7523	0.451553
$568$	−8.67563	−0.364021
$569$	−0.305586	−0.0128108	−0.00640541	−	0.999979i	$-0.502039\pi$
$569$	−0.305586	−0.0128108	−0.00640541	+	0.999979i	$0.502039\pi$
$570$	24.2446	1.01549
$571$	−19.8629	−0.831238	−0.415619	−	0.909539i	$-0.636435\pi$
$571$	−19.8629	−0.831238	−0.415619	+	0.909539i	$0.636435\pi$
$572$	0	0
$573$	12.4969	0.522067
$574$	24.0465	1.00368
$575$	−8.00969	−0.334027
$576$	0.738546	0.0307727
$577$	18.3254	0.762898	0.381449	−	0.924390i	$-0.375425\pi$
$577$	18.3254	0.762898	0.381449	+	0.924390i	$0.375425\pi$
$578$	27.4209	1.14056
$579$	−24.7131	−1.02704
$580$	8.91185	0.370045
$581$	8.52781	0.353793
$582$	−29.2325	−1.21173
$583$	−0.801938	−0.0332129
$584$	−21.0664	−0.871733
$585$	0	0
$586$	12.5526	0.518542
$587$	−27.0476	−1.11637	−0.558187	−	0.829715i	$-0.688503\pi$
$587$	−27.0476	−1.11637	−0.558187	+	0.829715i	$0.688503\pi$
$588$	8.88471	0.366399
$589$	−47.0103	−1.93702
$590$	0.911854	0.0375404
$591$	−31.3658	−1.29022
$592$	−22.7385	−0.934548
$593$	−10.6907	−0.439014	−0.219507	−	0.975611i	$-0.570445\pi$
$593$	−10.6907	−0.439014	−0.219507	+	0.975611i	$0.570445\pi$
$594$	−3.58211	−0.146976
$595$	2.07606	0.0851103
$596$	22.6896	0.929403
$597$	18.3666	0.751694
$598$	0	0
$599$	32.8702	1.34304	0.671521	−	0.740986i	$-0.265641\pi$
$599$	32.8702	1.34304	0.671521	+	0.740986i	$0.265641\pi$
$600$	−2.10992	−0.0861370
$601$	−42.1702	−1.72016	−0.860079	−	0.510161i	$-0.829586\pi$
$601$	−42.1702	−1.72016	−0.860079	+	0.510161i	$0.829586\pi$
$602$	−25.9095	−1.05599
$603$	2.60892	0.106244
$604$	9.00969	0.366599
$605$	−10.8726	−0.442035
$606$	4.55496	0.185033
$607$	0.687710	0.0279133	0.0139566	−	0.999903i	$-0.495557\pi$
$607$	0.687710	0.0279133	0.0139566	+	0.999903i	$0.495557\pi$
$608$	53.5260	2.17077
$609$	17.2801	0.700225
$610$	13.0586	0.528728
$611$	0	0
$612$	0.969132	0.0391748
$613$	34.5080	1.39376	0.696882	−	0.717186i	$-0.254570\pi$
$613$	34.5080	1.39376	0.696882	+	0.717186i	$0.254570\pi$
$614$	−38.4088	−1.55005
$615$	−13.3448	−0.538115
$616$	−0.753020	−0.0303401
$617$	−10.1612	−0.409076	−0.204538	−	0.978859i	$-0.565569\pi$
$617$	−10.1612	−0.409076	−0.204538	+	0.978859i	$0.565569\pi$
$618$	−26.1564	−1.05217
$619$	12.8442	0.516250	0.258125	−	0.966112i	$-0.416895\pi$
$619$	12.8442	0.516250	0.258125	+	0.966112i	$0.416895\pi$
$620$	−6.77479	−0.272082
$621$	−44.6142	−1.79030
$622$	52.9178	2.12181
$623$	25.7808	1.03288
$624$	0	0
$625$	1.00000	0.0400000
$626$	−3.77048	−0.150699
$627$	−4.80194	−0.191771
$628$	−10.9729	−0.437865
$629$	−6.14675	−0.245087
$630$	−1.63102	−0.0649815
$631$	17.2489	0.686668	0.343334	−	0.939213i	$-0.388444\pi$
$631$	17.2489	0.686668	0.343334	+	0.939213i	$0.388444\pi$
$632$	−6.31660	−0.251261
$633$	37.4711	1.48934
$634$	18.3763	0.729815
$635$	−6.02715	−0.239180
$636$	4.35690	0.172762
$637$	0	0
$638$	−4.59611	−0.181962
$639$	3.72182	0.147233
$640$	−10.0858	−0.398674
$641$	−11.5526	−0.456299	−0.228149	−	0.973626i	$-0.573267\pi$
$641$	−11.5526	−0.456299	−0.228149	+	0.973626i	$0.573267\pi$
$642$	45.4553	1.79398
$643$	24.9661	0.984569	0.492284	−	0.870434i	$-0.336162\pi$
$643$	24.9661	0.984569	0.492284	+	0.870434i	$0.336162\pi$
$644$	15.5308	0.611999
$645$	14.3787	0.566159
$646$	20.8170	0.819034
$647$	17.0852	0.671687	0.335844	−	0.941918i	$-0.390979\pi$
$647$	17.0852	0.671687	0.335844	+	0.941918i	$0.390979\pi$
$648$	−9.38271	−0.368588
$649$	−0.180604	−0.00708932
$650$	0	0
$651$	−13.1363	−0.514853
$652$	−7.37867	−0.288971
$653$	−37.5773	−1.47051	−0.735257	−	0.677788i	$-0.762939\pi$
$653$	−37.5773	−1.47051	−0.735257	+	0.677788i	$0.762939\pi$
$654$	14.1957	0.555095
$655$	−10.1075	−0.394934
$656$	−42.3870	−1.65494
$657$	9.03743	0.352584
$658$	−9.57673	−0.373340
$659$	24.4131	0.951000	0.475500	−	0.879716i	$-0.342267\pi$
$659$	24.4131	0.951000	0.475500	+	0.879716i	$0.342267\pi$
$660$	−0.692021	−0.0269369
$661$	−9.13467	−0.355298	−0.177649	−	0.984094i	$-0.556849\pi$
$661$	−9.13467	−0.355298	−0.177649	+	0.984094i	$0.556849\pi$
$662$	−27.4403	−1.06650
$663$	0	0
$664$	−7.44158	−0.288789
$665$	−13.4547	−0.521752
$666$	4.82908	0.187123
$667$	−57.2433	−2.21647
$668$	7.48725	0.289691
$669$	15.8659	0.613412
$670$	8.07606	0.312006
$671$	−2.58642	−0.0998475
$672$	14.9571	0.576981
$673$	36.0810	1.39082	0.695410	−	0.718614i	$-0.255223\pi$
$673$	36.0810	1.39082	0.695410	+	0.718614i	$0.255223\pi$
$674$	1.56704	0.0603601
$675$	5.57002	0.214390
$676$	0	0
$677$	20.5905	0.791356	0.395678	−	0.918389i	$-0.370510\pi$
$677$	20.5905	0.791356	0.395678	+	0.918389i	$0.370510\pi$
$678$	28.3424	1.08848
$679$	16.2228	0.622575
$680$	−1.81163	−0.0694727
$681$	−12.1823	−0.466825
$682$	3.49396	0.133791
$683$	6.40821	0.245203	0.122602	−	0.992456i	$-0.460876\pi$
$683$	6.40821	0.245203	0.122602	+	0.992456i	$0.460876\pi$
$684$	−6.28083	−0.240154
$685$	−4.96077	−0.189541
$686$	−32.4523	−1.23904
$687$	10.2875	0.392494
$688$	45.6708	1.74118
$689$	0	0
$690$	−22.4426	−0.854377
$691$	1.76032	0.0669656	0.0334828	−	0.999439i	$-0.489340\pi$
$691$	1.76032	0.0669656	0.0334828	+	0.999439i	$0.489340\pi$
$692$	22.1347	0.841434
$693$	0.323044	0.0122714
$694$	30.2030	1.14649
$695$	−9.02177	−0.342215
$696$	−15.0790	−0.571570
$697$	−11.4582	−0.434010
$698$	−42.0538	−1.59176
$699$	−2.13334	−0.0806904
$700$	−1.93900	−0.0732874
$701$	24.3532	0.919807	0.459903	−	0.887969i	$-0.347884\pi$
$701$	24.3532	0.919807	0.459903	+	0.887969i	$0.347884\pi$
$702$	0	0
$703$	39.8364	1.50246
$704$	−0.452812	−0.0170660
$705$	5.31468	0.200163
$706$	55.1159	2.07431
$707$	−2.52781	−0.0950681
$708$	0.981214	0.0368763
$709$	−31.4916	−1.18269	−0.591345	−	0.806418i	$-0.701403\pi$
$709$	−31.4916	−1.18269	−0.591345	+	0.806418i	$0.701403\pi$
$710$	11.5211	0.432379
$711$	2.70981	0.101626
$712$	−22.4969	−0.843109
$713$	43.5163	1.62970
$714$	5.81700	0.217696
$715$	0	0
$716$	−20.6437	−0.771491
$717$	−3.27247	−0.122213
$718$	−22.2392	−0.829960
$719$	20.1304	0.750736	0.375368	−	0.926876i	$-0.377516\pi$
$719$	20.1304	0.750736	0.375368	+	0.926876i	$0.377516\pi$
$720$	2.87502	0.107146
$721$	14.5157	0.540594
$722$	−100.676	−3.74676
$723$	29.8380	1.10969
$724$	13.9336	0.517839
$725$	7.14675	0.265424
$726$	−30.4644	−1.13064
$727$	13.8183	0.512494	0.256247	−	0.966611i	$-0.417514\pi$
$727$	13.8183	0.512494	0.256247	+	0.966611i	$0.417514\pi$
$728$	0	0
$729$	30.0086	1.11143
$730$	27.9758	1.03543
$731$	12.3459	0.456629
$732$	14.0519	0.519373
$733$	3.47086	0.128199	0.0640996	−	0.997944i	$-0.479582\pi$
$733$	3.47086	0.128199	0.0640996	+	0.997944i	$0.479582\pi$
$734$	−33.4383	−1.23423
$735$	7.12498	0.262809
$736$	−49.5478	−1.82636
$737$	−1.59956	−0.0589207
$738$	9.00192	0.331365
$739$	−33.0495	−1.21575	−0.607873	−	0.794034i	$-0.707977\pi$
$739$	−33.0495	−1.21575	−0.607873	+	0.794034i	$0.707977\pi$
$740$	5.74094	0.211041
$741$	0	0
$742$	−6.29590	−0.231130
$743$	18.3840	0.674445	0.337223	−	0.941425i	$-0.390513\pi$
$743$	18.3840	0.674445	0.337223	+	0.941425i	$0.390513\pi$
$744$	11.4631	0.420257
$745$	18.1957	0.666638
$746$	43.1105	1.57839
$747$	3.19242	0.116805
$748$	−0.594187	−0.0217256
$749$	−25.2258	−0.921731
$750$	2.80194	0.102312
$751$	28.8127	1.05139	0.525695	−	0.850673i	$-0.323805\pi$
$751$	28.8127	1.05139	0.525695	+	0.850673i	$0.323805\pi$
$752$	16.8810	0.615586
$753$	15.6511	0.570359
$754$	0	0
$755$	7.22521	0.262952
$756$	−10.8003	−0.392802
$757$	31.3435	1.13920	0.569599	−	0.821923i	$-0.307098\pi$
$757$	31.3435	1.13920	0.569599	+	0.821923i	$0.307098\pi$
$758$	−14.1564	−0.514185
$759$	4.44504	0.161345
$760$	11.7409	0.425889
$761$	18.0489	0.654273	0.327136	−	0.944977i	$-0.393916\pi$
$761$	18.0489	0.654273	0.327136	+	0.944977i	$0.393916\pi$
$762$	−16.8877	−0.611776
$763$	−7.87800	−0.285203
$764$	−10.0218	−0.362575
$765$	0.777184	0.0280991
$766$	−9.82908	−0.355139
$767$	0	0
$768$	−32.2054	−1.16211
$769$	−9.42626	−0.339919	−0.169960	−	0.985451i	$-0.554364\pi$
$769$	−9.42626	−0.339919	−0.169960	+	0.985451i	$0.554364\pi$
$770$	1.00000	0.0360375
$771$	−16.9638	−0.610935
$772$	19.8183	0.713277
$773$	−23.6305	−0.849932	−0.424966	−	0.905209i	$-0.639714\pi$
$773$	−23.6305	−0.849932	−0.424966	+	0.905209i	$0.639714\pi$
$774$	−9.69932	−0.348635
$775$	−5.43296	−0.195158
$776$	−14.1564	−0.508187
$777$	11.1317	0.399347
$778$	32.4499	1.16339
$779$	74.2592	2.66061
$780$	0	0
$781$	−2.28190	−0.0816527
$782$	−19.2698	−0.689087
$783$	39.8076	1.42261
$784$	22.6310	0.808251
$785$	−8.79954	−0.314069
$786$	−28.3207	−1.01016
$787$	17.5948	0.627186	0.313593	−	0.949557i	$-0.398467\pi$
$787$	17.5948	0.627186	0.313593	+	0.949557i	$0.398467\pi$
$788$	25.1535	0.896055
$789$	13.0895	0.465998
$790$	8.38835	0.298444
$791$	−15.7289	−0.559254
$792$	−0.281896	−0.0100168
$793$	0	0
$794$	−32.9898	−1.17077
$795$	3.49396	0.123918
$796$	−14.7289	−0.522051
$797$	15.6813	0.555459	0.277730	−	0.960659i	$-0.410418\pi$
$797$	15.6813	0.555459	0.277730	+	0.960659i	$0.410418\pi$
$798$	−37.6993	−1.33454
$799$	4.56332	0.161439
$800$	6.18598	0.218707
$801$	9.65114	0.341006
$802$	34.5483	1.21994
$803$	−5.54096	−0.195536
$804$	8.69037	0.306486
$805$	12.4547	0.438972
$806$	0	0
$807$	−30.1648	−1.06185
$808$	2.20583	0.0776009
$809$	−19.2301	−0.676095	−0.338047	−	0.941129i	$-0.609766\pi$
$809$	−19.2301	−0.676095	−0.338047	+	0.941129i	$0.609766\pi$
$810$	12.4601	0.437804
$811$	31.4432	1.10412	0.552061	−	0.833804i	$-0.313842\pi$
$811$	31.4432	1.10412	0.552061	+	0.833804i	$0.313842\pi$
$812$	−13.8576	−0.486305
$813$	4.82072	0.169070
$814$	−2.96077	−0.103775
$815$	−5.91723	−0.207272
$816$	−10.2537	−0.358951
$817$	−80.0122	−2.79927
$818$	13.0140	0.455024
$819$	0	0
$820$	10.7017	0.373720
$821$	10.6286	0.370942	0.185471	−	0.982650i	$-0.440619\pi$
$821$	10.6286	0.370942	0.185471	+	0.982650i	$0.440619\pi$
$822$	−13.8998	−0.484810
$823$	−36.8963	−1.28612	−0.643062	−	0.765814i	$-0.722336\pi$
$823$	−36.8963	−1.28612	−0.643062	+	0.765814i	$0.722336\pi$
$824$	−12.6668	−0.441269
$825$	−0.554958	−0.0193212
$826$	−1.41789	−0.0493349
$827$	−18.7006	−0.650285	−0.325143	−	0.945665i	$-0.605412\pi$
$827$	−18.7006	−0.650285	−0.325143	+	0.945665i	$0.605412\pi$
$828$	5.81402	0.202051
$829$	−13.4437	−0.466919	−0.233460	−	0.972366i	$-0.575005\pi$
$829$	−13.4437	−0.466919	−0.233460	+	0.972366i	$0.575005\pi$
$830$	9.88231	0.343020
$831$	−11.0519	−0.383386
$832$	0	0
$833$	6.11769	0.211965
$834$	−25.2784	−0.875321
$835$	6.00431	0.207788
$836$	3.85086	0.133185
$837$	−30.2617	−1.04600
$838$	−0.488582	−0.0168778
$839$	−26.4547	−0.913319	−0.456659	−	0.889642i	$-0.650954\pi$
$839$	−26.4547	−0.913319	−0.456659	+	0.889642i	$0.650954\pi$
$840$	3.28083	0.113199
$841$	22.0761	0.761244
$842$	64.2006	2.21250
$843$	−13.6913	−0.471553
$844$	−30.0495	−1.03435
$845$	0	0
$846$	−3.58509	−0.123258
$847$	16.9065	0.580913
$848$	11.0978	0.381101
$849$	11.8086	0.405272
$850$	2.40581	0.0825187
$851$	−36.8756	−1.26408
$852$	12.3975	0.424730
$853$	44.7222	1.53126	0.765629	−	0.643283i	$-0.222428\pi$
$853$	44.7222	1.53126	0.765629	+	0.643283i	$0.222428\pi$
$854$	−20.3056	−0.694843
$855$	−5.03684	−0.172256
$856$	22.0127	0.752378
$857$	−23.6969	−0.809472	−0.404736	−	0.914434i	$-0.632636\pi$
$857$	−23.6969	−0.809472	−0.404736	+	0.914434i	$0.632636\pi$
$858$	0	0
$859$	−35.0814	−1.19696	−0.598482	−	0.801137i	$-0.704229\pi$
$859$	−35.0814	−1.19696	−0.598482	+	0.801137i	$0.704229\pi$
$860$	−11.5308	−0.393197
$861$	20.7506	0.707179
$862$	63.9614	2.17853
$863$	−22.7439	−0.774212	−0.387106	−	0.922035i	$-0.626525\pi$
$863$	−22.7439	−0.774212	−0.387106	+	0.922035i	$0.626525\pi$
$864$	34.4561	1.17222
$865$	17.7506	0.603539
$866$	−28.5797	−0.971178
$867$	23.6625	0.803620
$868$	10.5345	0.357565
$869$	−1.66142	−0.0563597
$870$	20.0248	0.678903
$871$	0	0
$872$	6.87454	0.232801
$873$	6.07308	0.205543
$874$	124.885	4.22431
$875$	−1.55496	−0.0525672
$876$	30.1038	1.01711
$877$	−6.14483	−0.207496	−0.103748	−	0.994604i	$-0.533084\pi$
$877$	−6.14483	−0.207496	−0.103748	+	0.994604i	$0.533084\pi$
$878$	46.7265	1.57694
$879$	10.8321	0.365357
$880$	−1.76271	−0.0594209
$881$	−11.6517	−0.392557	−0.196278	−	0.980548i	$-0.562886\pi$
$881$	−11.6517	−0.392557	−0.196278	+	0.980548i	$0.562886\pi$
$882$	−4.80625	−0.161835
$883$	12.7694	0.429725	0.214862	−	0.976644i	$-0.431070\pi$
$883$	12.7694	0.429725	0.214862	+	0.976644i	$0.431070\pi$
$884$	0	0
$885$	0.786872	0.0264504
$886$	20.2368	0.679869
$887$	27.4993	0.923337	0.461669	−	0.887052i	$-0.347251\pi$
$887$	27.4993	0.923337	0.461669	+	0.887052i	$0.347251\pi$
$888$	−9.71379	−0.325974
$889$	9.37196	0.314325
$890$	29.8756	1.00143
$891$	−2.46788	−0.0826770
$892$	−12.7235	−0.426014
$893$	−29.5743	−0.989667
$894$	50.9831	1.70513
$895$	−16.5550	−0.553371
$896$	15.6829	0.523930
$897$	0	0
$898$	−66.3962	−2.21567
$899$	−38.8280	−1.29499
$900$	−0.725873	−0.0241958
$901$	3.00000	0.0999445
$902$	−5.51919	−0.183769
$903$	−22.3582	−0.744035
$904$	13.7254	0.456500
$905$	11.1739	0.371433
$906$	20.2446	0.672581
$907$	−11.4668	−0.380749	−0.190375	−	0.981712i	$-0.560970\pi$
$907$	−11.4668	−0.380749	−0.190375	+	0.981712i	$0.560970\pi$
$908$	9.76941	0.324209
$909$	−0.946297	−0.0313867
$910$	0	0
$911$	−23.1943	−0.768463	−0.384231	−	0.923237i	$-0.625534\pi$
$911$	−23.1943	−0.768463	−0.384231	+	0.923237i	$0.625534\pi$
$912$	66.4529	2.20048
$913$	−1.95731	−0.0647776
$914$	39.6209	1.31054
$915$	11.2687	0.372533
$916$	−8.24996	−0.272586
$917$	15.7168	0.519014
$918$	13.4004	0.442280
$919$	−59.0702	−1.94855	−0.974273	−	0.225370i	$-0.927641\pi$
$919$	−59.0702	−1.94855	−0.974273	+	0.225370i	$0.927641\pi$
$920$	−10.8683	−0.358318
$921$	−33.1444	−1.09214
$922$	−15.3840	−0.506646
$923$	0	0
$924$	1.07606	0.0353999
$925$	4.60388	0.151374
$926$	−37.8267	−1.24306
$927$	5.43403	0.178477
$928$	44.2097	1.45125
$929$	−23.9124	−0.784542	−0.392271	−	0.919850i	$-0.628310\pi$
$929$	−23.9124	−0.784542	−0.392271	+	0.919850i	$0.628310\pi$
$930$	−15.2228	−0.499176
$931$	−39.6480	−1.29941
$932$	1.71081	0.0560394
$933$	45.6647	1.49500
$934$	−25.2228	−0.825316
$935$	−0.476501	−0.0155832
$936$	0	0
$937$	−12.9667	−0.423605	−0.211802	−	0.977312i	$-0.567933\pi$
$937$	−12.9667	−0.423605	−0.211802	+	0.977312i	$0.567933\pi$
$938$	−12.5579	−0.410031
$939$	−3.25368	−0.106180
$940$	−4.26205	−0.139013
$941$	−45.5585	−1.48517	−0.742583	−	0.669754i	$-0.766399\pi$
$941$	−45.5585	−1.48517	−0.742583	+	0.669754i	$0.766399\pi$
$942$	−24.6558	−0.803329
$943$	−68.7400	−2.23848
$944$	2.49934	0.0813465
$945$	−8.66115	−0.281747
$946$	5.94677	0.193346
$947$	−5.78017	−0.187830	−0.0939151	−	0.995580i	$-0.529938\pi$
$947$	−5.78017	−0.187830	−0.0939151	+	0.995580i	$0.529938\pi$
$948$	9.02641	0.293164
$949$	0	0
$950$	−15.5918	−0.505865
$951$	15.8576	0.514217
$952$	2.81700	0.0912996
$953$	−47.4058	−1.53562	−0.767812	−	0.640675i	$-0.778655\pi$
$953$	−47.4058	−1.53562	−0.767812	+	0.640675i	$0.778655\pi$
$954$	−2.35690	−0.0763073
$955$	−8.03684	−0.260066
$956$	2.62432	0.0848765
$957$	−3.96615	−0.128207
$958$	−26.3327	−0.850772
$959$	7.71379	0.249091
$960$	1.97285	0.0636736
$961$	−1.48294	−0.0478369
$962$	0	0
$963$	−9.44339	−0.304309
$964$	−23.9282	−0.770677
$965$	15.8931	0.511616
$966$	34.8974	1.12280
$967$	7.63102	0.245397	0.122699	−	0.992444i	$-0.460845\pi$
$967$	7.63102	0.245397	0.122699	+	0.992444i	$0.460845\pi$
$968$	−14.7530	−0.474180
$969$	17.9638	0.577079
$970$	18.7995	0.603617
$971$	45.8273	1.47067	0.735334	−	0.677705i	$-0.237025\pi$
$971$	45.8273	1.47067	0.735334	+	0.677705i	$0.237025\pi$
$972$	−7.42924	−0.238293
$973$	14.0285	0.449732
$974$	70.3866	2.25533
$975$	0	0
$976$	35.7928	1.14570
$977$	4.59983	0.147161	0.0735807	−	0.997289i	$-0.476557\pi$
$977$	4.59983	0.147161	0.0735807	+	0.997289i	$0.476557\pi$
$978$	−16.5797	−0.530161
$979$	−5.91723	−0.189116
$980$	−5.71379	−0.182520
$981$	−2.94916	−0.0941596
$982$	46.1444	1.47253
$983$	16.2728	0.519022	0.259511	−	0.965740i	$-0.416439\pi$
$983$	16.2728	0.519022	0.259511	+	0.965740i	$0.416439\pi$
$984$	−18.1075	−0.577247
$985$	20.1715	0.642718
$986$	17.1938	0.547561
$987$	−8.26411	−0.263050
$988$	0	0
$989$	74.0654	2.35514
$990$	0.374354	0.0118978
$991$	−34.9898	−1.11149	−0.555744	−	0.831353i	$-0.687567\pi$
$991$	−34.9898	−1.11149	−0.555744	+	0.831353i	$0.687567\pi$
$992$	−33.6082	−1.06706
$993$	−23.6792	−0.751437
$994$	−17.9148	−0.568224
$995$	−11.8116	−0.374454
$996$	10.6340	0.336951
$997$	−37.8353	−1.19826	−0.599128	−	0.800653i	$-0.704486\pi$
$997$	−37.8353	−1.19826	−0.599128	+	0.800653i	$0.704486\pi$
$998$	3.01938	0.0955767
$999$	25.6437	0.811331

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.a.h.1.1	✓	3
3.2	odd	2		7605.2.a.by.1.3		3
5.4	even	2		4225.2.a.bf.1.3		3
13.2	odd	12		845.2.m.i.316.1		12
13.3	even	3		845.2.e.l.191.3		6
13.4	even	6		845.2.e.j.146.1		6
13.5	odd	4		845.2.c.f.506.6		6
13.6	odd	12		845.2.m.i.361.6		12
13.7	odd	12		845.2.m.i.361.1		12
13.8	odd	4		845.2.c.f.506.1		6
13.9	even	3		845.2.e.l.146.3		6
13.10	even	6		845.2.e.j.191.1		6
13.11	odd	12		845.2.m.i.316.6		12
13.12	even	2		845.2.a.j.1.3	yes	3
39.38	odd	2		7605.2.a.br.1.1		3
65.64	even	2		4225.2.a.bd.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.a.h.1.1	✓	3	1.1	even	1	trivial
845.2.a.j.1.3	yes	3	13.12	even	2
845.2.c.f.506.1		6	13.8	odd	4
845.2.c.f.506.6		6	13.5	odd	4
845.2.e.j.146.1		6	13.4	even	6
845.2.e.j.191.1		6	13.10	even	6
845.2.e.l.146.3		6	13.9	even	3
845.2.e.l.191.3		6	13.3	even	3
845.2.m.i.316.1		12	13.2	odd	12
845.2.m.i.316.6		12	13.11	odd	12
845.2.m.i.361.1		12	13.7	odd	12
845.2.m.i.361.6		12	13.6	odd	12
4225.2.a.bd.1.1		3	65.64	even	2
4225.2.a.bf.1.3		3	5.4	even	2
7605.2.a.br.1.1		3	39.38	odd	2
7605.2.a.by.1.3		3	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.a (trivial)

\(f(q)\)	\(=\)	\(q-1.80194 q^{2} -1.55496 q^{3} +1.24698 q^{4} +1.00000 q^{5} +2.80194 q^{6} -1.55496 q^{7} +1.35690 q^{8} -0.582105 q^{9} +O(q^{10})\)	\(q-1.80194 q^{2} -1.55496 q^{3} +1.24698 q^{4} +1.00000 q^{5} +2.80194 q^{6} -1.55496 q^{7} +1.35690 q^{8} -0.582105 q^{9} -1.80194 q^{10} +0.356896 q^{11} -1.93900 q^{12} +2.80194 q^{14} -1.55496 q^{15} -4.93900 q^{16} -1.33513 q^{17} +1.04892 q^{18} +8.65279 q^{19} +1.24698 q^{20} +2.41789 q^{21} -0.643104 q^{22} -8.00969 q^{23} -2.10992 q^{24} +1.00000 q^{25} +5.57002 q^{27} -1.93900 q^{28} +7.14675 q^{29} +2.80194 q^{30} -5.43296 q^{31} +6.18598 q^{32} -0.554958 q^{33} +2.40581 q^{34} -1.55496 q^{35} -0.725873 q^{36} +4.60388 q^{37} -15.5918 q^{38} +1.35690 q^{40} +8.58211 q^{41} -4.35690 q^{42} -9.24698 q^{43} +0.445042 q^{44} -0.582105 q^{45} +14.4330 q^{46} -3.41789 q^{47} +7.67994 q^{48} -4.58211 q^{49} -1.80194 q^{50} +2.07606 q^{51} -2.24698 q^{53} -10.0368 q^{54} +0.356896 q^{55} -2.10992 q^{56} -13.4547 q^{57} -12.8780 q^{58} -0.506041 q^{59} -1.93900 q^{60} -7.24698 q^{61} +9.78986 q^{62} +0.905149 q^{63} -1.26875 q^{64} +1.00000 q^{66} -4.48188 q^{67} -1.66487 q^{68} +12.4547 q^{69} +2.80194 q^{70} -6.39373 q^{71} -0.789856 q^{72} -15.5254 q^{73} -8.29590 q^{74} -1.55496 q^{75} +10.7899 q^{76} -0.554958 q^{77} -4.65519 q^{79} -4.93900 q^{80} -6.91484 q^{81} -15.4644 q^{82} -5.48427 q^{83} +3.01507 q^{84} -1.33513 q^{85} +16.6625 q^{86} -11.1129 q^{87} +0.484271 q^{88} -16.5797 q^{89} +1.04892 q^{90} -9.98792 q^{92} +8.44803 q^{93} +6.15883 q^{94} +8.65279 q^{95} -9.61894 q^{96} -10.4330 q^{97} +8.25667 q^{98} -0.207751 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} - 5 q^{3} - q^{4} + 3 q^{5} + 4 q^{6} - 5 q^{7} + 4 q^{9}+O(q^{10}) \) 3 * q - q^2 - 5 * q^3 - q^4 + 3 * q^5 + 4 * q^6 - 5 * q^7 + 4 * q^9	\( 3 q - q^{2} - 5 q^{3} - q^{4} + 3 q^{5} + 4 q^{6} - 5 q^{7} + 4 q^{9} - q^{10} - 3 q^{11} + 4 q^{12} + 4 q^{14} - 5 q^{15} - 5 q^{16} - 3 q^{17} - 6 q^{18} + 8 q^{19} - q^{20} + 13 q^{21} - 6 q^{22} - 2 q^{23} - 7 q^{24} + 3 q^{25} - 8 q^{27} + 4 q^{28} - 6 q^{29} + 4 q^{30} + 3 q^{31} + 4 q^{32} - 2 q^{33} - 6 q^{34} - 5 q^{35} - 13 q^{36} + 5 q^{37} - 19 q^{38} + 20 q^{41} - 9 q^{42} - 23 q^{43} + q^{44} + 4 q^{45} + 24 q^{46} - 16 q^{47} - q^{48} - 8 q^{49} - q^{50} - 9 q^{51} - 2 q^{53} - 2 q^{54} - 3 q^{55} - 7 q^{56} - 18 q^{57} - 19 q^{58} - 11 q^{59} + 4 q^{60} - 17 q^{61} + 6 q^{62} - 23 q^{63} + 4 q^{64} + 3 q^{66} + 15 q^{67} - 6 q^{68} + 15 q^{69} + 4 q^{70} + 13 q^{71} + 21 q^{72} - 12 q^{73} - 11 q^{74} - 5 q^{75} + 9 q^{76} - 2 q^{77} - 37 q^{79} - 5 q^{80} + 27 q^{81} - 2 q^{82} - 29 q^{83} - 16 q^{84} - 3 q^{85} + 10 q^{86} + 10 q^{87} + 14 q^{88} - 3 q^{89} - 6 q^{90} - 11 q^{92} - 19 q^{93} + 10 q^{94} + 8 q^{95} + 5 q^{96} - 12 q^{97} - 2 q^{98} + 17 q^{99}+O(q^{100}) \) 3 * q - q^2 - 5 * q^3 - q^4 + 3 * q^5 + 4 * q^6 - 5 * q^7 + 4 * q^9 - q^10 - 3 * q^11 + 4 * q^12 + 4 * q^14 - 5 * q^15 - 5 * q^16 - 3 * q^17 - 6 * q^18 + 8 * q^19 - q^20 + 13 * q^21 - 6 * q^22 - 2 * q^23 - 7 * q^24 + 3 * q^25 - 8 * q^27 + 4 * q^28 - 6 * q^29 + 4 * q^30 + 3 * q^31 + 4 * q^32 - 2 * q^33 - 6 * q^34 - 5 * q^35 - 13 * q^36 + 5 * q^37 - 19 * q^38 + 20 * q^41 - 9 * q^42 - 23 * q^43 + q^44 + 4 * q^45 + 24 * q^46 - 16 * q^47 - q^48 - 8 * q^49 - q^50 - 9 * q^51 - 2 * q^53 - 2 * q^54 - 3 * q^55 - 7 * q^56 - 18 * q^57 - 19 * q^58 - 11 * q^59 + 4 * q^60 - 17 * q^61 + 6 * q^62 - 23 * q^63 + 4 * q^64 + 3 * q^66 + 15 * q^67 - 6 * q^68 + 15 * q^69 + 4 * q^70 + 13 * q^71 + 21 * q^72 - 12 * q^73 - 11 * q^74 - 5 * q^75 + 9 * q^76 - 2 * q^77 - 37 * q^79 - 5 * q^80 + 27 * q^81 - 2 * q^82 - 29 * q^83 - 16 * q^84 - 3 * q^85 + 10 * q^86 + 10 * q^87 + 14 * q^88 - 3 * q^89 - 6 * q^90 - 11 * q^92 - 19 * q^93 + 10 * q^94 + 8 * q^95 + 5 * q^96 - 12 * q^97 - 2 * q^98 + 17 * q^99

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