LMFDB - Embedded newform 8041.2.a.h.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.83407 q^{2} +2.68858 q^{3} +1.36381 q^{4} -0.219056 q^{5} -4.93104 q^{6} +2.19442 q^{7} +1.16682 q^{8} +4.22847 q^{9} +O(q^{10})$	\(q-1.83407 q^{2} +2.68858 q^{3} +1.36381 q^{4} -0.219056 q^{5} -4.93104 q^{6} +2.19442 q^{7} +1.16682 q^{8} +4.22847 q^{9} +0.401763 q^{10} -1.00000 q^{11} +3.66671 q^{12} +4.10926 q^{13} -4.02472 q^{14} -0.588949 q^{15} -4.86764 q^{16} -1.00000 q^{17} -7.75531 q^{18} -5.63273 q^{19} -0.298749 q^{20} +5.89988 q^{21} +1.83407 q^{22} -1.59663 q^{23} +3.13710 q^{24} -4.95201 q^{25} -7.53666 q^{26} +3.30285 q^{27} +2.99277 q^{28} -0.641874 q^{29} +1.08017 q^{30} -9.73424 q^{31} +6.59395 q^{32} -2.68858 q^{33} +1.83407 q^{34} -0.480700 q^{35} +5.76682 q^{36} +1.89536 q^{37} +10.3308 q^{38} +11.0481 q^{39} -0.255599 q^{40} -4.74827 q^{41} -10.8208 q^{42} -1.00000 q^{43} -1.36381 q^{44} -0.926271 q^{45} +2.92833 q^{46} -0.817013 q^{47} -13.0871 q^{48} -2.18452 q^{49} +9.08233 q^{50} -2.68858 q^{51} +5.60424 q^{52} +7.01904 q^{53} -6.05766 q^{54} +0.219056 q^{55} +2.56050 q^{56} -15.1440 q^{57} +1.17724 q^{58} -14.1749 q^{59} -0.803212 q^{60} +5.71986 q^{61} +17.8533 q^{62} +9.27905 q^{63} -2.35847 q^{64} -0.900156 q^{65} +4.93104 q^{66} +1.06305 q^{67} -1.36381 q^{68} -4.29268 q^{69} +0.881637 q^{70} -3.44103 q^{71} +4.93388 q^{72} -12.7655 q^{73} -3.47623 q^{74} -13.3139 q^{75} -7.68195 q^{76} -2.19442 q^{77} -20.2629 q^{78} -6.87441 q^{79} +1.06628 q^{80} -3.80543 q^{81} +8.70865 q^{82} -9.87762 q^{83} +8.04630 q^{84} +0.219056 q^{85} +1.83407 q^{86} -1.72573 q^{87} -1.16682 q^{88} -3.36582 q^{89} +1.69884 q^{90} +9.01745 q^{91} -2.17750 q^{92} -26.1713 q^{93} +1.49846 q^{94} +1.23388 q^{95} +17.7284 q^{96} -0.804736 q^{97} +4.00655 q^{98} -4.22847 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) $ 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * 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 $

$2$	−1.83407	−1.29688	−0.648441	−	0.761265i	$-0.724579\pi$
$2$	−1.83407	−1.29688	−0.648441	+	0.761265i	$0.724579\pi$
$3$	2.68858	1.55225	0.776127	−	0.630577i	$-0.217182\pi$
$3$	2.68858	1.55225	0.776127	+	0.630577i	$0.217182\pi$
$4$	1.36381	0.681903
$5$	−0.219056	−0.0979646	−0.0489823	−	0.998800i	$-0.515598\pi$
$5$	−0.219056	−0.0979646	−0.0489823	+	0.998800i	$0.515598\pi$
$6$	−4.93104	−2.01309
$7$	2.19442	0.829413	0.414707	−	0.909955i	$-0.363884\pi$
$7$	2.19442	0.829413	0.414707	+	0.909955i	$0.363884\pi$
$8$	1.16682	0.412534
$9$	4.22847	1.40949
$10$	0.401763	0.127049
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.66671	1.05849
$13$	4.10926	1.13970	0.569852	−	0.821747i	$-0.307001\pi$
$13$	4.10926	1.13970	0.569852	+	0.821747i	$0.307001\pi$
$14$	−4.02472	−1.07565
$15$	−0.588949	−0.152066
$16$	−4.86764	−1.21691
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−7.75531	−1.82794
$19$	−5.63273	−1.29224	−0.646118	−	0.763238i	$-0.723609\pi$
$19$	−5.63273	−1.29224	−0.646118	+	0.763238i	$0.723609\pi$
$20$	−0.298749	−0.0668024
$21$	5.89988	1.28746
$22$	1.83407	0.391025
$23$	−1.59663	−0.332921	−0.166460	−	0.986048i	$-0.553234\pi$
$23$	−1.59663	−0.332921	−0.166460	+	0.986048i	$0.553234\pi$
$24$	3.13710	0.640357
$25$	−4.95201	−0.990403
$26$	−7.53666	−1.47806
$27$	3.30285	0.635635
$28$	2.99277	0.565580
$29$	−0.641874	−0.119193	−0.0595965	−	0.998223i	$-0.518981\pi$
$29$	−0.641874	−0.119193	−0.0595965	+	0.998223i	$0.518981\pi$
$30$	1.08017	0.197212
$31$	−9.73424	−1.74832	−0.874161	−	0.485637i	$-0.838588\pi$
$31$	−9.73424	−1.74832	−0.874161	+	0.485637i	$0.838588\pi$
$32$	6.59395	1.16566
$33$	−2.68858	−0.468022
$34$	1.83407	0.314540
$35$	−0.480700	−0.0812531
$36$	5.76682	0.961137
$37$	1.89536	0.311596	0.155798	−	0.987789i	$-0.450205\pi$
$37$	1.89536	0.311596	0.155798	+	0.987789i	$0.450205\pi$
$38$	10.3308	1.67588
$39$	11.0481	1.76911
$40$	−0.255599	−0.0404137
$41$	−4.74827	−0.741555	−0.370777	−	0.928722i	$-0.620909\pi$
$41$	−4.74827	−0.741555	−0.370777	+	0.928722i	$0.620909\pi$
$42$	−10.8208	−1.66968
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−1.36381	−0.205602
$45$	−0.926271	−0.138080
$46$	2.92833	0.431759
$47$	−0.817013	−0.119174	−0.0595868	−	0.998223i	$-0.518978\pi$
$47$	−0.817013	−0.119174	−0.0595868	+	0.998223i	$0.518978\pi$
$48$	−13.0871	−1.88895
$49$	−2.18452	−0.312074
$50$	9.08233	1.28444
$51$	−2.68858	−0.376477
$52$	5.60424	0.777168
$53$	7.01904	0.964140	0.482070	−	0.876133i	$-0.339885\pi$
$53$	7.01904	0.964140	0.482070	+	0.876133i	$0.339885\pi$
$54$	−6.05766	−0.824343
$55$	0.219056	0.0295374
$56$	2.56050	0.342161
$57$	−15.1440	−2.00588
$58$	1.17724	0.154579
$59$	−14.1749	−1.84541	−0.922707	−	0.385501i	$-0.874028\pi$
$59$	−14.1749	−1.84541	−0.922707	+	0.385501i	$0.874028\pi$
$60$	−0.803212	−0.103694
$61$	5.71986	0.732353	0.366176	−	0.930545i	$-0.380667\pi$
$61$	5.71986	0.732353	0.366176	+	0.930545i	$0.380667\pi$
$62$	17.8533	2.26737
$63$	9.27905	1.16905
$64$	−2.35847	−0.294808
$65$	−0.900156	−0.111651
$66$	4.93104	0.606970
$67$	1.06305	0.129872	0.0649361	−	0.997889i	$-0.479316\pi$
$67$	1.06305	0.129872	0.0649361	+	0.997889i	$0.479316\pi$
$68$	−1.36381	−0.165386
$69$	−4.29268	−0.516778
$70$	0.881637	0.105376
$71$	−3.44103	−0.408375	−0.204187	−	0.978932i	$-0.565455\pi$
$71$	−3.44103	−0.408375	−0.204187	+	0.978932i	$0.565455\pi$
$72$	4.93388	0.581463
$73$	−12.7655	−1.49408	−0.747042	−	0.664777i	$-0.768527\pi$
$73$	−12.7655	−1.49408	−0.747042	+	0.664777i	$0.768527\pi$
$74$	−3.47623	−0.404103
$75$	−13.3139	−1.53736
$76$	−7.68195	−0.881180
$77$	−2.19442	−0.250077
$78$	−20.2629	−2.29433
$79$	−6.87441	−0.773432	−0.386716	−	0.922199i	$-0.626391\pi$
$79$	−6.87441	−0.773432	−0.386716	+	0.922199i	$0.626391\pi$
$80$	1.06628	0.119214
$81$	−3.80543	−0.422825
$82$	8.70865	0.961709
$83$	−9.87762	−1.08421	−0.542105	−	0.840311i	$-0.682372\pi$
$83$	−9.87762	−1.08421	−0.542105	+	0.840311i	$0.682372\pi$
$84$	8.04630	0.877923
$85$	0.219056	0.0237599
$86$	1.83407	0.197773
$87$	−1.72573	−0.185018
$88$	−1.16682	−0.124384
$89$	−3.36582	−0.356776	−0.178388	−	0.983960i	$-0.557088\pi$
$89$	−3.36582	−0.356776	−0.178388	+	0.983960i	$0.557088\pi$
$90$	1.69884	0.179074
$91$	9.01745	0.945285
$92$	−2.17750	−0.227020
$93$	−26.1713	−2.71384
$94$	1.49846	0.154554
$95$	1.23388	0.126593
$96$	17.7284	1.80939
$97$	−0.804736	−0.0817085	−0.0408543	−	0.999165i	$-0.513008\pi$
$97$	−0.804736	−0.0817085	−0.0408543	+	0.999165i	$0.513008\pi$
$98$	4.00655	0.404723
$99$	−4.22847	−0.424978
$100$	−6.75359	−0.675359
$101$	2.59606	0.258318	0.129159	−	0.991624i	$-0.458772\pi$
$101$	2.59606	0.258318	0.129159	+	0.991624i	$0.458772\pi$
$102$	4.93104	0.488246
$103$	5.10966	0.503469	0.251735	−	0.967796i	$-0.418999\pi$
$103$	5.10966	0.503469	0.251735	+	0.967796i	$0.418999\pi$
$104$	4.79477	0.470166
$105$	−1.29240	−0.126125
$106$	−12.8734	−1.25038
$107$	−4.61839	−0.446477	−0.223238	−	0.974764i	$-0.571663\pi$
$107$	−4.61839	−0.446477	−0.223238	+	0.974764i	$0.571663\pi$
$108$	4.50446	0.433442
$109$	−11.5120	−1.10265	−0.551323	−	0.834292i	$-0.685877\pi$
$109$	−11.5120	−1.10265	−0.551323	+	0.834292i	$0.685877\pi$
$110$	−0.401763	−0.0383066
$111$	5.09584	0.483676
$112$	−10.6817	−1.00932
$113$	−6.08516	−0.572443	−0.286222	−	0.958163i	$-0.592399\pi$
$113$	−6.08516	−0.572443	−0.286222	+	0.958163i	$0.592399\pi$
$114$	27.7752	2.60139
$115$	0.349751	0.0326145
$116$	−0.875392	−0.0812781
$117$	17.3759	1.60640
$118$	25.9977	2.39329
$119$	−2.19442	−0.201162
$120$	−0.687198	−0.0627323
$121$	1.00000	0.0909091
$122$	−10.4906	−0.949775
$123$	−12.7661	−1.15108
$124$	−13.2756	−1.19219
$125$	2.18004	0.194989
$126$	−17.0184	−1.51612
$127$	−14.0733	−1.24880	−0.624402	−	0.781103i	$-0.714657\pi$
$127$	−14.0733	−1.24880	−0.624402	+	0.781103i	$0.714657\pi$
$128$	−8.86231	−0.783325
$129$	−2.68858	−0.236716
$130$	1.65095	0.144798
$131$	−14.8793	−1.30001	−0.650005	−	0.759930i	$-0.725233\pi$
$131$	−14.8793	−1.30001	−0.650005	+	0.759930i	$0.725233\pi$
$132$	−3.66671	−0.319146
$133$	−12.3606	−1.07180
$134$	−1.94971	−0.168429
$135$	−0.723509	−0.0622697
$136$	−1.16682	−0.100054
$137$	−9.54556	−0.815533	−0.407766	−	0.913086i	$-0.633692\pi$
$137$	−9.54556	−0.815533	−0.407766	+	0.913086i	$0.633692\pi$
$138$	7.87306	0.670200
$139$	−7.61061	−0.645524	−0.322762	−	0.946480i	$-0.604611\pi$
$139$	−7.61061	−0.645524	−0.322762	+	0.946480i	$0.604611\pi$
$140$	−0.655582	−0.0554068
$141$	−2.19661	−0.184988
$142$	6.31108	0.529614
$143$	−4.10926	−0.343634
$144$	−20.5827	−1.71523
$145$	0.140606	0.0116767
$146$	23.4127	1.93765
$147$	−5.87325	−0.484418
$148$	2.58491	0.212478
$149$	4.67947	0.383357	0.191679	−	0.981458i	$-0.438607\pi$
$149$	4.67947	0.383357	0.191679	+	0.981458i	$0.438607\pi$
$150$	24.4186	1.99377
$151$	8.49875	0.691618	0.345809	−	0.938305i	$-0.387604\pi$
$151$	8.49875	0.691618	0.345809	+	0.938305i	$0.387604\pi$
$152$	−6.57239	−0.533091
$153$	−4.22847	−0.341852
$154$	4.02472	0.324321
$155$	2.13234	0.171274
$156$	15.0675	1.20636
$157$	16.0182	1.27839	0.639196	−	0.769044i	$-0.279267\pi$
$157$	16.0182	1.27839	0.639196	+	0.769044i	$0.279267\pi$
$158$	12.6081	1.00305
$159$	18.8713	1.49659
$160$	−1.44444	−0.114193
$161$	−3.50368	−0.276129
$162$	6.97941	0.548354
$163$	17.4946	1.37029	0.685143	−	0.728409i	$-0.259740\pi$
$163$	17.4946	1.37029	0.685143	+	0.728409i	$0.259740\pi$
$164$	−6.47572	−0.505669
$165$	0.588949	0.0458496
$166$	18.1162	1.40609
$167$	−24.3676	−1.88562	−0.942812	−	0.333325i	$-0.891829\pi$
$167$	−24.3676	−1.88562	−0.942812	+	0.333325i	$0.891829\pi$
$168$	6.88411	0.531121
$169$	3.88602	0.298924
$170$	−0.401763	−0.0308138
$171$	−23.8178	−1.82140
$172$	−1.36381	−0.103989
$173$	8.59666	0.653592	0.326796	−	0.945095i	$-0.394031\pi$
$173$	8.59666	0.653592	0.326796	+	0.945095i	$0.394031\pi$
$174$	3.16511	0.239946
$175$	−10.8668	−0.821453
$176$	4.86764	0.366913
$177$	−38.1104	−2.86455
$178$	6.17314	0.462696
$179$	2.98518	0.223123	0.111561	−	0.993758i	$-0.464415\pi$
$179$	2.98518	0.223123	0.111561	+	0.993758i	$0.464415\pi$
$180$	−1.26325	−0.0941574
$181$	13.4180	0.997351	0.498676	−	0.866789i	$-0.333820\pi$
$181$	13.4180	0.997351	0.498676	+	0.866789i	$0.333820\pi$
$182$	−16.5386	−1.22592
$183$	15.3783	1.13680
$184$	−1.86298	−0.137341
$185$	−0.415190	−0.0305254
$186$	48.0000	3.51953
$187$	1.00000	0.0731272
$188$	−1.11425	−0.0812649
$189$	7.24785	0.527204
$190$	−2.26302	−0.164177
$191$	26.3367	1.90566	0.952829	−	0.303509i	$-0.0981581\pi$
$191$	26.3367	1.90566	0.952829	+	0.303509i	$0.0981581\pi$
$192$	−6.34093	−0.457617
$193$	23.1113	1.66359	0.831794	−	0.555084i	$-0.187314\pi$
$193$	23.1113	1.66359	0.831794	+	0.555084i	$0.187314\pi$
$194$	1.47594	0.105966
$195$	−2.42014	−0.173310
$196$	−2.97926	−0.212804
$197$	0.256726	0.0182909	0.00914547	−	0.999958i	$-0.497089\pi$
$197$	0.256726	0.0182909	0.00914547	+	0.999958i	$0.497089\pi$
$198$	7.75531	0.551146
$199$	13.8948	0.984979	0.492489	−	0.870318i	$-0.336087\pi$
$199$	13.8948	0.984979	0.492489	+	0.870318i	$0.336087\pi$
$200$	−5.77812	−0.408575
$201$	2.85810	0.201595
$202$	−4.76135	−0.335007
$203$	−1.40854	−0.0988602
$204$	−3.66671	−0.256721
$205$	1.04013	0.0726461
$206$	−9.37146	−0.652940
$207$	−6.75132	−0.469249
$208$	−20.0024	−1.38692
$209$	5.63273	0.389624
$210$	2.37035	0.163570
$211$	12.0111	0.826878	0.413439	−	0.910532i	$-0.364328\pi$
$211$	12.0111	0.826878	0.413439	+	0.910532i	$0.364328\pi$
$212$	9.57262	0.657450
$213$	−9.25148	−0.633901
$214$	8.47044	0.579028
$215$	0.219056	0.0149395
$216$	3.85384	0.262221
$217$	−21.3610	−1.45008
$218$	21.1137	1.43000
$219$	−34.3210	−2.31920
$220$	0.298749	0.0201417
$221$	−4.10926	−0.276419
$222$	−9.34613	−0.627271
$223$	28.3094	1.89573	0.947867	−	0.318665i	$-0.103235\pi$
$223$	28.3094	1.89573	0.947867	+	0.318665i	$0.103235\pi$
$224$	14.4699	0.966811
$225$	−20.9395	−1.39596
$226$	11.1606	0.742392
$227$	−18.8052	−1.24814	−0.624072	−	0.781367i	$-0.714523\pi$
$227$	−18.8052	−1.24814	−0.624072	+	0.781367i	$0.714523\pi$
$228$	−20.6536	−1.36782
$229$	16.3033	1.07735	0.538677	−	0.842512i	$-0.318924\pi$
$229$	16.3033	1.07735	0.538677	+	0.842512i	$0.318924\pi$
$230$	−0.641467	−0.0422971
$231$	−5.89988	−0.388184
$232$	−0.748952	−0.0491711
$233$	9.08120	0.594929	0.297465	−	0.954733i	$-0.403859\pi$
$233$	9.08120	0.594929	0.297465	+	0.954733i	$0.403859\pi$
$234$	−31.8686	−2.08331
$235$	0.178971	0.0116748
$236$	−19.3318	−1.25839
$237$	−18.4824	−1.20056
$238$	4.02472	0.260884
$239$	13.7346	0.888415	0.444207	−	0.895924i	$-0.353485\pi$
$239$	13.7346	0.888415	0.444207	+	0.895924i	$0.353485\pi$
$240$	2.86679	0.185051
$241$	3.61976	0.233169	0.116585	−	0.993181i	$-0.462805\pi$
$241$	3.61976	0.233169	0.116585	+	0.993181i	$0.462805\pi$
$242$	−1.83407	−0.117898
$243$	−20.1398	−1.29197
$244$	7.80078	0.499394
$245$	0.478530	0.0305722
$246$	23.4139	1.49282
$247$	−23.1463	−1.47277
$248$	−11.3581	−0.721241
$249$	−26.5568	−1.68297
$250$	−3.99835	−0.252878
$251$	−25.7128	−1.62298	−0.811490	−	0.584367i	$-0.801343\pi$
$251$	−25.7128	−1.62298	−0.811490	+	0.584367i	$0.801343\pi$
$252$	12.6548	0.797180
$253$	1.59663	0.100379
$254$	25.8114	1.61955
$255$	0.588949	0.0368814
$256$	20.9710	1.31069
$257$	26.1396	1.63054	0.815272	−	0.579078i	$-0.196587\pi$
$257$	26.1396	1.63054	0.815272	+	0.579078i	$0.196587\pi$
$258$	4.93104	0.306993
$259$	4.15923	0.258442
$260$	−1.22764	−0.0761349
$261$	−2.71415	−0.168001
$262$	27.2897	1.68596
$263$	−14.3571	−0.885295	−0.442647	−	0.896696i	$-0.645961\pi$
$263$	−14.3571	−0.885295	−0.442647	+	0.896696i	$0.645961\pi$
$264$	−3.13710	−0.193075
$265$	−1.53756	−0.0944516
$266$	22.6701	1.39000
$267$	−9.04928	−0.553807
$268$	1.44979	0.0885603
$269$	8.94774	0.545553	0.272777	−	0.962077i	$-0.412058\pi$
$269$	8.94774	0.545553	0.272777	+	0.962077i	$0.412058\pi$
$270$	1.32696	0.0807565
$271$	−1.87578	−0.113946	−0.0569728	−	0.998376i	$-0.518145\pi$
$271$	−1.87578	−0.113946	−0.0569728	+	0.998376i	$0.518145\pi$
$272$	4.86764	0.295144
$273$	24.2441	1.46732
$274$	17.5072	1.05765
$275$	4.95201	0.298618
$276$	−5.85438	−0.352392
$277$	20.2104	1.21433	0.607163	−	0.794577i	$-0.292307\pi$
$277$	20.2104	1.21433	0.607163	+	0.794577i	$0.292307\pi$
$278$	13.9584	0.837168
$279$	−41.1610	−2.46424
$280$	−0.560891	−0.0335197
$281$	19.6312	1.17110	0.585550	−	0.810637i	$-0.300879\pi$
$281$	19.6312	1.17110	0.585550	+	0.810637i	$0.300879\pi$
$282$	4.02873	0.239907
$283$	15.2766	0.908099	0.454049	−	0.890976i	$-0.349979\pi$
$283$	15.2766	0.908099	0.454049	+	0.890976i	$0.349979\pi$
$284$	−4.69289	−0.278472
$285$	3.31739	0.196505
$286$	7.53666	0.445652
$287$	−10.4197	−0.615055
$288$	27.8823	1.64298
$289$	1.00000	0.0588235
$290$	−0.257881	−0.0151433
$291$	−2.16360	−0.126832
$292$	−17.4096	−1.01882
$293$	−25.0816	−1.46528	−0.732642	−	0.680614i	$-0.761713\pi$
$293$	−25.0816	−1.46528	−0.732642	+	0.680614i	$0.761713\pi$
$294$	10.7719	0.628233
$295$	3.10509	0.180785
$296$	2.21155	0.128544
$297$	−3.30285	−0.191651
$298$	−8.58247	−0.497169
$299$	−6.56098	−0.379431
$300$	−18.1576	−1.04833
$301$	−2.19442	−0.126484
$302$	−15.5873	−0.896948
$303$	6.97972	0.400974
$304$	27.4181	1.57254
$305$	−1.25297	−0.0717447
$306$	7.75531	0.443342
$307$	−25.4052	−1.44995	−0.724975	−	0.688775i	$-0.758149\pi$
$307$	−25.4052	−1.44995	−0.724975	+	0.688775i	$0.758149\pi$
$308$	−2.99277	−0.170529
$309$	13.7377	0.781512
$310$	−3.91086	−0.222122
$311$	4.17462	0.236721	0.118360	−	0.992971i	$-0.462236\pi$
$311$	4.17462	0.236721	0.118360	+	0.992971i	$0.462236\pi$
$312$	12.8911	0.729817
$313$	16.6984	0.943849	0.471925	−	0.881639i	$-0.343559\pi$
$313$	16.6984	0.943849	0.471925	+	0.881639i	$0.343559\pi$
$314$	−29.3785	−1.65792
$315$	−2.03263	−0.114526
$316$	−9.37537	−0.527406
$317$	1.44889	0.0813776	0.0406888	−	0.999172i	$-0.487045\pi$
$317$	1.44889	0.0813776	0.0406888	+	0.999172i	$0.487045\pi$
$318$	−34.6112	−1.94090
$319$	0.641874	0.0359380
$320$	0.516635	0.0288808
$321$	−12.4169	−0.693045
$322$	6.42599	0.358107
$323$	5.63273	0.313413
$324$	−5.18987	−0.288326
$325$	−20.3491	−1.12877
$326$	−32.0864	−1.77710
$327$	−30.9509	−1.71159
$328$	−5.54038	−0.305916
$329$	−1.79287	−0.0988442
$330$	−1.08017	−0.0594615
$331$	24.2967	1.33547	0.667733	−	0.744400i	$-0.267265\pi$
$331$	24.2967	1.33547	0.667733	+	0.744400i	$0.267265\pi$
$332$	−13.4712	−0.739326
$333$	8.01450	0.439192
$334$	44.6919	2.44543
$335$	−0.232867	−0.0127229
$336$	−28.7185	−1.56672
$337$	−1.13241	−0.0616861	−0.0308430	−	0.999524i	$-0.509819\pi$
$337$	−1.13241	−0.0616861	−0.0308430	+	0.999524i	$0.509819\pi$
$338$	−7.12722	−0.387670
$339$	−16.3604	−0.888577
$340$	0.298749	0.0162020
$341$	9.73424	0.527139
$342$	43.6835	2.36214
$343$	−20.1547	−1.08825
$344$	−1.16682	−0.0629108
$345$	0.940335	0.0506259
$346$	−15.7669	−0.847632
$347$	−9.57209	−0.513857	−0.256928	−	0.966430i	$-0.582710\pi$
$347$	−9.57209	−0.513857	−0.256928	+	0.966430i	$0.582710\pi$
$348$	−2.35356	−0.126164
$349$	26.0472	1.39427	0.697137	−	0.716938i	$-0.254457\pi$
$349$	26.0472	1.39427	0.697137	+	0.716938i	$0.254457\pi$
$350$	19.9305	1.06533
$351$	13.5723	0.724435
$352$	−6.59395	−0.351459
$353$	−19.4835	−1.03700	−0.518500	−	0.855078i	$-0.673509\pi$
$353$	−19.4835	−1.03700	−0.518500	+	0.855078i	$0.673509\pi$
$354$	69.8970	3.71499
$355$	0.753776	0.0400063
$356$	−4.59033	−0.243287
$357$	−5.89988	−0.312255
$358$	−5.47503	−0.289364
$359$	−3.92982	−0.207408	−0.103704	−	0.994608i	$-0.533069\pi$
$359$	−3.92982	−0.207408	−0.103704	+	0.994608i	$0.533069\pi$
$360$	−1.08079	−0.0569628
$361$	12.7276	0.669874
$362$	−24.6095	−1.29345
$363$	2.68858	0.141114
$364$	12.2981	0.644593
$365$	2.79634	0.146367
$366$	−28.2049	−1.47429
$367$	−10.0166	−0.522860	−0.261430	−	0.965222i	$-0.584194\pi$
$367$	−10.0166	−0.522860	−0.261430	+	0.965222i	$0.584194\pi$
$368$	7.77184	0.405135
$369$	−20.0779	−1.04522
$370$	0.761487	0.0395878
$371$	15.4027	0.799670
$372$	−35.6926	−1.85058
$373$	13.4282	0.695286	0.347643	−	0.937627i	$-0.386982\pi$
$373$	13.4282	0.695286	0.347643	+	0.937627i	$0.386982\pi$
$374$	−1.83407	−0.0948374
$375$	5.86123	0.302672
$376$	−0.953309	−0.0491632
$377$	−2.63763	−0.135845
$378$	−13.2931	−0.683721
$379$	−35.1355	−1.80479	−0.902394	−	0.430912i	$-0.858192\pi$
$379$	−35.1355	−1.80479	−0.902394	+	0.430912i	$0.858192\pi$
$380$	1.68277	0.0863245
$381$	−37.8372	−1.93846
$382$	−48.3033	−2.47141
$383$	26.1543	1.33642	0.668211	−	0.743971i	$-0.267060\pi$
$383$	26.1543	1.33642	0.668211	+	0.743971i	$0.267060\pi$
$384$	−23.8271	−1.21592
$385$	0.480700	0.0244987
$386$	−42.3877	−2.15748
$387$	−4.22847	−0.214945
$388$	−1.09750	−0.0557173
$389$	−28.2685	−1.43327	−0.716635	−	0.697448i	$-0.754319\pi$
$389$	−28.2685	−1.43327	−0.716635	+	0.697448i	$0.754319\pi$
$390$	4.43871	0.224763
$391$	1.59663	0.0807452
$392$	−2.54894	−0.128741
$393$	−40.0042	−2.01795
$394$	−0.470852	−0.0237212
$395$	1.50588	0.0757689
$396$	−5.76682	−0.289794
$397$	30.1695	1.51417	0.757083	−	0.653319i	$-0.226624\pi$
$397$	30.1695	1.51417	0.757083	+	0.653319i	$0.226624\pi$
$398$	−25.4841	−1.27740
$399$	−33.2324	−1.66370
$400$	24.1046	1.20523
$401$	−6.65785	−0.332477	−0.166239	−	0.986086i	$-0.553162\pi$
$401$	−6.65785	−0.332477	−0.166239	+	0.986086i	$0.553162\pi$
$402$	−5.24195	−0.261445
$403$	−40.0005	−1.99257
$404$	3.54052	0.176148
$405$	0.833600	0.0414219
$406$	2.58336	0.128210
$407$	−1.89536	−0.0939498
$408$	−3.13710	−0.155309
$409$	23.3546	1.15481	0.577406	−	0.816457i	$-0.304065\pi$
$409$	23.3546	1.15481	0.577406	+	0.816457i	$0.304065\pi$
$410$	−1.90768	−0.0942135
$411$	−25.6640	−1.26591
$412$	6.96858	0.343317
$413$	−31.1057	−1.53061
$414$	12.3824	0.608561
$415$	2.16375	0.106214
$416$	27.0963	1.32850
$417$	−20.4618	−1.00202
$418$	−10.3308	−0.505296
$419$	8.73593	0.426778	0.213389	−	0.976967i	$-0.431550\pi$
$419$	8.73593	0.426778	0.213389	+	0.976967i	$0.431550\pi$
$420$	−1.76259	−0.0860054
$421$	−19.4567	−0.948262	−0.474131	−	0.880454i	$-0.657238\pi$
$421$	−19.4567	−0.948262	−0.474131	+	0.880454i	$0.657238\pi$
$422$	−22.0292	−1.07236
$423$	−3.45472	−0.167974
$424$	8.18997	0.397740
$425$	4.95201	0.240208
$426$	16.9678	0.822095
$427$	12.5518	0.607423
$428$	−6.29859	−0.304454
$429$	−11.0481	−0.533406
$430$	−0.401763	−0.0193747
$431$	24.2189	1.16658	0.583291	−	0.812263i	$-0.301765\pi$
$431$	24.2189	1.16658	0.583291	+	0.812263i	$0.301765\pi$
$432$	−16.0771	−0.773511
$433$	−24.5003	−1.17741	−0.588706	−	0.808347i	$-0.700362\pi$
$433$	−24.5003	−1.17741	−0.588706	+	0.808347i	$0.700362\pi$
$434$	39.1776	1.88058
$435$	0.378031	0.0181252
$436$	−15.7001	−0.751899
$437$	8.99339	0.430212
$438$	62.9470	3.00773
$439$	−35.4573	−1.69228	−0.846142	−	0.532957i	$-0.821081\pi$
$439$	−35.4573	−1.69228	−0.846142	+	0.532957i	$0.821081\pi$
$440$	0.255599	0.0121852
$441$	−9.23717	−0.439865
$442$	7.53666	0.358483
$443$	23.6693	1.12456	0.562282	−	0.826946i	$-0.309924\pi$
$443$	23.6693	1.12456	0.562282	+	0.826946i	$0.309924\pi$
$444$	6.94975	0.329820
$445$	0.737301	0.0349514
$446$	−51.9213	−2.45854
$447$	12.5811	0.595068
$448$	−5.17547	−0.244518
$449$	−33.1704	−1.56541	−0.782705	−	0.622393i	$-0.786160\pi$
$449$	−33.1704	−1.56541	−0.782705	+	0.622393i	$0.786160\pi$
$450$	38.4044	1.81040
$451$	4.74827	0.223587
$452$	−8.29898	−0.390351
$453$	22.8496	1.07357
$454$	34.4900	1.61870
$455$	−1.97532	−0.0926045
$456$	−17.6704	−0.827492
$457$	13.1565	0.615434	0.307717	−	0.951478i	$-0.400435\pi$
$457$	13.1565	0.615434	0.307717	+	0.951478i	$0.400435\pi$
$458$	−29.9014	−1.39720
$459$	−3.30285	−0.154164
$460$	0.476993	0.0222399
$461$	0.769545	0.0358413	0.0179206	−	0.999839i	$-0.494295\pi$
$461$	0.769545	0.0358413	0.0179206	+	0.999839i	$0.494295\pi$
$462$	10.8208	0.503429
$463$	36.4650	1.69467	0.847336	−	0.531057i	$-0.178205\pi$
$463$	36.4650	1.69467	0.847336	+	0.531057i	$0.178205\pi$
$464$	3.12441	0.145047
$465$	5.73297	0.265860
$466$	−16.6555	−0.771553
$467$	−3.20804	−0.148451	−0.0742253	−	0.997242i	$-0.523648\pi$
$467$	−3.20804	−0.148451	−0.0742253	+	0.997242i	$0.523648\pi$
$468$	23.6974	1.09541
$469$	2.33278	0.107718
$470$	−0.328246	−0.0151408
$471$	43.0662	1.98439
$472$	−16.5396	−0.761296
$473$	1.00000	0.0459800
$474$	33.8980	1.55699
$475$	27.8933	1.27983
$476$	−2.99277	−0.137173
$477$	29.6799	1.35895
$478$	−25.1901	−1.15217
$479$	1.59236	0.0727566	0.0363783	−	0.999338i	$-0.488418\pi$
$479$	1.59236	0.0727566	0.0363783	+	0.999338i	$0.488418\pi$
$480$	−3.88350	−0.177257
$481$	7.78855	0.355127
$482$	−6.63889	−0.302393
$483$	−9.41994	−0.428622
$484$	1.36381	0.0619912
$485$	0.176282	0.00800454
$486$	36.9377	1.67553
$487$	−9.52878	−0.431790	−0.215895	−	0.976417i	$-0.569267\pi$
$487$	−9.52878	−0.431790	−0.215895	+	0.976417i	$0.569267\pi$
$488$	6.67405	0.302120
$489$	47.0358	2.12703
$490$	−0.877657	−0.0396485
$491$	10.3662	0.467820	0.233910	−	0.972258i	$-0.424848\pi$
$491$	10.3662	0.467820	0.233910	+	0.972258i	$0.424848\pi$
$492$	−17.4105	−0.784926
$493$	0.641874	0.0289085
$494$	42.4520	1.91000
$495$	0.926271	0.0416328
$496$	47.3828	2.12755
$497$	−7.55106	−0.338711
$498$	48.7070	2.18261
$499$	−20.4532	−0.915612	−0.457806	−	0.889052i	$-0.651365\pi$
$499$	−20.4532	−0.915612	−0.457806	+	0.889052i	$0.651365\pi$
$500$	2.97316	0.132964
$501$	−65.5144	−2.92697
$502$	47.1591	2.10481
$503$	−3.24391	−0.144639	−0.0723193	−	0.997382i	$-0.523040\pi$
$503$	−3.24391	−0.144639	−0.0723193	+	0.997382i	$0.523040\pi$
$504$	10.8270	0.482273
$505$	−0.568681	−0.0253060
$506$	−2.92833	−0.130180
$507$	10.4479	0.464006
$508$	−19.1933	−0.851564
$509$	−27.9700	−1.23975	−0.619874	−	0.784701i	$-0.712816\pi$
$509$	−27.9700	−1.23975	−0.619874	+	0.784701i	$0.712816\pi$
$510$	−1.08017	−0.0478308
$511$	−28.0128	−1.23921
$512$	−20.7377	−0.916484
$513$	−18.6041	−0.821390
$514$	−47.9419	−2.11462
$515$	−1.11930	−0.0493222
$516$	−3.66671	−0.161418
$517$	0.817013	0.0359322
$518$	−7.62831	−0.335169
$519$	23.1128	1.01454
$520$	−1.05032	−0.0460596
$521$	13.7731	0.603409	0.301704	−	0.953402i	$-0.402444\pi$
$521$	13.7731	0.603409	0.301704	+	0.953402i	$0.402444\pi$
$522$	4.97793	0.217878
$523$	−40.1697	−1.75650	−0.878250	−	0.478202i	$-0.841289\pi$
$523$	−40.1697	−1.75650	−0.878250	+	0.478202i	$0.841289\pi$
$524$	−20.2925	−0.886482
$525$	−29.2163	−1.27510
$526$	26.3318	1.14812
$527$	9.73424	0.424030
$528$	13.0871	0.569541
$529$	−20.4508	−0.889164
$530$	2.81999	0.122493
$531$	−59.9382	−2.60110
$532$	−16.8574	−0.730862
$533$	−19.5119	−0.845153
$534$	16.5970	0.718222
$535$	1.01168	0.0437389
$536$	1.24039	0.0535767
$537$	8.02590	0.346343
$538$	−16.4108	−0.707518
$539$	2.18452	0.0940938
$540$	−0.986726	−0.0424619
$541$	44.2944	1.90437	0.952183	−	0.305529i	$-0.0988332\pi$
$541$	44.2944	1.90437	0.952183	+	0.305529i	$0.0988332\pi$
$542$	3.44031	0.147774
$543$	36.0754	1.54814
$544$	−6.59395	−0.282713
$545$	2.52176	0.108020
$546$	−44.4654	−1.90294
$547$	8.59958	0.367691	0.183846	−	0.982955i	$-0.441145\pi$
$547$	8.59958	0.367691	0.183846	+	0.982955i	$0.441145\pi$
$548$	−13.0183	−0.556114
$549$	24.1863	1.03225
$550$	−9.08233	−0.387272
$551$	3.61550	0.154025
$552$	−5.00879	−0.213188
$553$	−15.0854	−0.641495
$554$	−37.0673	−1.57484
$555$	−1.11627	−0.0473831
$556$	−10.3794	−0.440185
$557$	−9.49015	−0.402111	−0.201055	−	0.979580i	$-0.564437\pi$
$557$	−9.49015	−0.402111	−0.201055	+	0.979580i	$0.564437\pi$
$558$	75.4921	3.19583
$559$	−4.10926	−0.173803
$560$	2.33988	0.0988779
$561$	2.68858	0.113512
$562$	−36.0050	−1.51878
$563$	−46.3510	−1.95346	−0.976732	−	0.214466i	$-0.931199\pi$
$563$	−46.3510	−1.95346	−0.976732	+	0.214466i	$0.931199\pi$
$564$	−2.99575	−0.126144
$565$	1.33299	0.0560792
$566$	−28.0183	−1.17770
$567$	−8.35071	−0.350697
$568$	−4.01506	−0.168468
$569$	37.1431	1.55712	0.778559	−	0.627571i	$-0.215951\pi$
$569$	37.1431	1.55712	0.778559	+	0.627571i	$0.215951\pi$
$570$	−6.08431	−0.254844
$571$	−24.3408	−1.01863	−0.509315	−	0.860580i	$-0.670101\pi$
$571$	−24.3408	−1.01863	−0.509315	+	0.860580i	$0.670101\pi$
$572$	−5.60424	−0.234325
$573$	70.8084	2.95806
$574$	19.1104	0.797654
$575$	7.90655	0.329726
$576$	−9.97271	−0.415530
$577$	28.8361	1.20046	0.600232	−	0.799826i	$-0.295075\pi$
$577$	28.8361	1.20046	0.600232	+	0.799826i	$0.295075\pi$
$578$	−1.83407	−0.0762872
$579$	62.1367	2.58231
$580$	0.191759	0.00796237
$581$	−21.6757	−0.899258
$582$	3.96819	0.164487
$583$	−7.01904	−0.290699
$584$	−14.8950	−0.616360
$585$	−3.80629	−0.157371
$586$	46.0014	1.90030
$587$	−13.5175	−0.557925	−0.278963	−	0.960302i	$-0.589991\pi$
$587$	−13.5175	−0.557925	−0.278963	+	0.960302i	$0.589991\pi$
$588$	−8.00998	−0.330326
$589$	54.8303	2.25924
$590$	−5.69495	−0.234457
$591$	0.690228	0.0283922
$592$	−9.22596	−0.379185
$593$	−5.14960	−0.211469	−0.105734	−	0.994394i	$-0.533719\pi$
$593$	−5.14960	−0.211469	−0.105734	+	0.994394i	$0.533719\pi$
$594$	6.05766	0.248549
$595$	0.480700	0.0197068
$596$	6.38190	0.261413
$597$	37.3574	1.52894
$598$	12.0333	0.492077
$599$	−25.3254	−1.03477	−0.517385	−	0.855753i	$-0.673094\pi$
$599$	−25.3254	−1.03477	−0.517385	+	0.855753i	$0.673094\pi$
$600$	−15.5349	−0.634211
$601$	7.76877	0.316895	0.158447	−	0.987367i	$-0.449351\pi$
$601$	7.76877	0.316895	0.158447	+	0.987367i	$0.449351\pi$
$602$	4.02472	0.164035
$603$	4.49508	0.183054
$604$	11.5907	0.471617
$605$	−0.219056	−0.00890587
$606$	−12.8013	−0.520017
$607$	−22.7788	−0.924563	−0.462282	−	0.886733i	$-0.652969\pi$
$607$	−22.7788	−0.924563	−0.462282	+	0.886733i	$0.652969\pi$
$608$	−37.1419	−1.50630
$609$	−3.78698	−0.153456
$610$	2.29803	0.0930444
$611$	−3.35732	−0.135823
$612$	−5.76682	−0.233110
$613$	−26.7175	−1.07911	−0.539554	−	0.841951i	$-0.681407\pi$
$613$	−26.7175	−1.07911	−0.539554	+	0.841951i	$0.681407\pi$
$614$	46.5948	1.88041
$615$	2.79649	0.112765
$616$	−2.56050	−0.103165
$617$	−14.6927	−0.591506	−0.295753	−	0.955265i	$-0.595570\pi$
$617$	−14.6927	−0.591506	−0.295753	+	0.955265i	$0.595570\pi$
$618$	−25.1959	−1.01353
$619$	47.4438	1.90693	0.953464	−	0.301506i	$-0.0974894\pi$
$619$	47.4438	1.90693	0.953464	+	0.301506i	$0.0974894\pi$
$620$	2.90810	0.116792
$621$	−5.27344	−0.211616
$622$	−7.65654	−0.306999
$623$	−7.38602	−0.295915
$624$	−53.7781	−2.15285
$625$	24.2825	0.971301
$626$	−30.6260	−1.22406
$627$	15.1440	0.604795
$628$	21.8457	0.871740
$629$	−1.89536	−0.0755731
$630$	3.72798	0.148526
$631$	−5.39637	−0.214826	−0.107413	−	0.994214i	$-0.534257\pi$
$631$	−5.39637	−0.214826	−0.107413	+	0.994214i	$0.534257\pi$
$632$	−8.02121	−0.319067
$633$	32.2928	1.28352
$634$	−2.65736	−0.105537
$635$	3.08284	0.122339
$636$	25.7368	1.02053
$637$	−8.97674	−0.355672
$638$	−1.17724	−0.0466074
$639$	−14.5503	−0.575601
$640$	1.94134	0.0767381
$641$	5.74021	0.226724	0.113362	−	0.993554i	$-0.463838\pi$
$641$	5.74021	0.226724	0.113362	+	0.993554i	$0.463838\pi$
$642$	22.7735	0.898798
$643$	−12.7574	−0.503102	−0.251551	−	0.967844i	$-0.580941\pi$
$643$	−12.7574	−0.503102	−0.251551	+	0.967844i	$0.580941\pi$
$644$	−4.77835	−0.188293
$645$	0.588949	0.0231898
$646$	−10.3308	−0.406460
$647$	39.5990	1.55680	0.778399	−	0.627770i	$-0.216032\pi$
$647$	39.5990	1.55680	0.778399	+	0.627770i	$0.216032\pi$
$648$	−4.44025	−0.174430
$649$	14.1749	0.556413
$650$	37.3217	1.46388
$651$	−57.4309	−2.25089
$652$	23.8593	0.934402
$653$	−33.8633	−1.32517	−0.662586	−	0.748986i	$-0.730541\pi$
$653$	−33.8633	−1.32517	−0.662586	+	0.748986i	$0.730541\pi$
$654$	56.7660	2.21973
$655$	3.25939	0.127355
$656$	23.1129	0.902406
$657$	−53.9784	−2.10590
$658$	3.28825	0.128189
$659$	−21.1664	−0.824525	−0.412262	−	0.911065i	$-0.635261\pi$
$659$	−21.1664	−0.824525	−0.412262	+	0.911065i	$0.635261\pi$
$660$	0.803212	0.0312650
$661$	36.7896	1.43095	0.715474	−	0.698639i	$-0.246211\pi$
$661$	36.7896	1.43095	0.715474	+	0.698639i	$0.246211\pi$
$662$	−44.5618	−1.73194
$663$	−11.0481	−0.429072
$664$	−11.5254	−0.447273
$665$	2.70765	0.104998
$666$	−14.6991	−0.569580
$667$	1.02484	0.0396818
$668$	−33.2327	−1.28581
$669$	76.1120	2.94266
$670$	0.427094	0.0165001
$671$	−5.71986	−0.220813
$672$	38.9035	1.50074
$673$	49.0769	1.89178	0.945889	−	0.324492i	$-0.105193\pi$
$673$	49.0769	1.89178	0.945889	+	0.324492i	$0.105193\pi$
$674$	2.07691	0.0799996
$675$	−16.3558	−0.629534
$676$	5.29977	0.203837
$677$	−13.4324	−0.516250	−0.258125	−	0.966111i	$-0.583105\pi$
$677$	−13.4324	−0.516250	−0.258125	+	0.966111i	$0.583105\pi$
$678$	30.0062	1.15238
$679$	−1.76593	−0.0677701
$680$	0.255599	0.00980176
$681$	−50.5593	−1.93744
$682$	−17.8533	−0.683637
$683$	−6.29458	−0.240855	−0.120428	−	0.992722i	$-0.538427\pi$
$683$	−6.29458	−0.240855	−0.120428	+	0.992722i	$0.538427\pi$
$684$	−32.4829	−1.24202
$685$	2.09101	0.0798933
$686$	36.9651	1.41133
$687$	43.8329	1.67233
$688$	4.86764	0.185577
$689$	28.8431	1.09883
$690$	−1.72464	−0.0656558
$691$	−4.72135	−0.179609	−0.0898043	−	0.995959i	$-0.528624\pi$
$691$	−4.72135	−0.179609	−0.0898043	+	0.995959i	$0.528624\pi$
$692$	11.7242	0.445687
$693$	−9.27905	−0.352482
$694$	17.5559	0.666412
$695$	1.66715	0.0632385
$696$	−2.01362	−0.0763260
$697$	4.74827	0.179853
$698$	−47.7723	−1.80821
$699$	24.4156	0.923481
$700$	−14.8202	−0.560152
$701$	21.7610	0.821903	0.410952	−	0.911657i	$-0.365196\pi$
$701$	21.7610	0.821903	0.410952	+	0.911657i	$0.365196\pi$
$702$	−24.8925	−0.939507
$703$	−10.6761	−0.402656
$704$	2.35847	0.0888880
$705$	0.481179	0.0181223
$706$	35.7340	1.34487
$707$	5.69685	0.214252
$708$	−51.9752	−1.95335
$709$	9.71712	0.364934	0.182467	−	0.983212i	$-0.441592\pi$
$709$	9.71712	0.364934	0.182467	+	0.983212i	$0.441592\pi$
$710$	−1.38248	−0.0518834
$711$	−29.0683	−1.09015
$712$	−3.92731	−0.147182
$713$	15.5420	0.582053
$714$	10.8208	0.404958
$715$	0.900156	0.0336639
$716$	4.07121	0.152148
$717$	36.9265	1.37904
$718$	7.20757	0.268984
$719$	14.5547	0.542797	0.271399	−	0.962467i	$-0.412514\pi$
$719$	14.5547	0.542797	0.271399	+	0.962467i	$0.412514\pi$
$720$	4.50876	0.168031
$721$	11.2127	0.417584
$722$	−23.3433	−0.868747
$723$	9.73203	0.361938
$724$	18.2995	0.680097
$725$	3.17857	0.118049
$726$	−4.93104	−0.183008
$727$	3.48622	0.129297	0.0646483	−	0.997908i	$-0.479407\pi$
$727$	3.48622	0.129297	0.0646483	+	0.997908i	$0.479407\pi$
$728$	10.5218	0.389962
$729$	−42.7311	−1.58263
$730$	−5.12869	−0.189821
$731$	1.00000	0.0369863
$732$	20.9730	0.775186
$733$	−6.89794	−0.254781	−0.127391	−	0.991853i	$-0.540660\pi$
$733$	−6.89794	−0.254781	−0.127391	+	0.991853i	$0.540660\pi$
$734$	18.3710	0.678087
$735$	1.28657	0.0474558
$736$	−10.5281	−0.388071
$737$	−1.06305	−0.0391580
$738$	36.8243	1.35552
$739$	−42.3092	−1.55637	−0.778184	−	0.628036i	$-0.783859\pi$
$739$	−42.3092	−1.55637	−0.778184	+	0.628036i	$0.783859\pi$
$740$	−0.566239	−0.0208154
$741$	−62.2308	−2.28611
$742$	−28.2497	−1.03708
$743$	32.3940	1.18842	0.594211	−	0.804309i	$-0.297464\pi$
$743$	32.3940	1.18842	0.594211	+	0.804309i	$0.297464\pi$
$744$	−30.5372	−1.11955
$745$	−1.02506	−0.0375554
$746$	−24.6283	−0.901705
$747$	−41.7673	−1.52818
$748$	1.36381	0.0498657
$749$	−10.1347	−0.370314
$750$	−10.7499	−0.392531
$751$	−46.1167	−1.68282	−0.841412	−	0.540395i	$-0.818275\pi$
$751$	−46.1167	−1.68282	−0.841412	+	0.540395i	$0.818275\pi$
$752$	3.97693	0.145024
$753$	−69.1311	−2.51928
$754$	4.83759	0.176174
$755$	−1.86170	−0.0677541
$756$	9.88467	0.359502
$757$	−29.8781	−1.08594	−0.542968	−	0.839753i	$-0.682700\pi$
$757$	−29.8781	−1.08594	−0.542968	+	0.839753i	$0.682700\pi$
$758$	64.4409	2.34060
$759$	4.29268	0.155814
$760$	1.43972	0.0522240
$761$	30.0074	1.08777	0.543884	−	0.839160i	$-0.316953\pi$
$761$	30.0074	1.08777	0.543884	+	0.839160i	$0.316953\pi$
$762$	69.3961	2.51396
$763$	−25.2621	−0.914550
$764$	35.9182	1.29947
$765$	0.926271	0.0334894
$766$	−47.9688	−1.73318
$767$	−58.2483	−2.10323
$768$	56.3823	2.03452
$769$	20.9907	0.756945	0.378473	−	0.925613i	$-0.376449\pi$
$769$	20.9907	0.756945	0.378473	+	0.925613i	$0.376449\pi$
$770$	−0.881637	−0.0317720
$771$	70.2785	2.53102
$772$	31.5194	1.13441
$773$	−11.2876	−0.405988	−0.202994	−	0.979180i	$-0.565067\pi$
$773$	−11.2876	−0.405988	−0.202994	+	0.979180i	$0.565067\pi$
$774$	7.75531	0.278759
$775$	48.2041	1.73154
$776$	−0.938983	−0.0337075
$777$	11.1824	0.401167
$778$	51.8464	1.85878
$779$	26.7457	0.958264
$780$	−3.30061	−0.118181
$781$	3.44103	0.123130
$782$	−2.92833	−0.104717
$783$	−2.12002	−0.0757632
$784$	10.6334	0.379766
$785$	−3.50888	−0.125237
$786$	73.3705	2.61704
$787$	17.3186	0.617342	0.308671	−	0.951169i	$-0.400116\pi$
$787$	17.3186	0.617342	0.308671	+	0.951169i	$0.400116\pi$
$788$	0.350124	0.0124727
$789$	−38.6002	−1.37420
$790$	−2.76188	−0.0982634
$791$	−13.3534	−0.474792
$792$	−4.93388	−0.175318
$793$	23.5044	0.834665
$794$	−55.3330	−1.96369
$795$	−4.13386	−0.146613
$796$	18.9499	0.671660
$797$	−5.23886	−0.185570	−0.0927849	−	0.995686i	$-0.529577\pi$
$797$	−5.23886	−0.185570	−0.0927849	+	0.995686i	$0.529577\pi$
$798$	60.9505	2.15763
$799$	0.817013	0.0289039
$800$	−32.6533	−1.15447
$801$	−14.2323	−0.502873
$802$	12.2110	0.431184
$803$	12.7655	0.450483
$804$	3.89789	0.137468
$805$	0.767501	0.0270509
$806$	73.3637	2.58413
$807$	24.0567	0.846837
$808$	3.02914	0.106565
$809$	28.2087	0.991764	0.495882	−	0.868390i	$-0.334845\pi$
$809$	28.2087	0.991764	0.495882	+	0.868390i	$0.334845\pi$
$810$	−1.52888	−0.0537193
$811$	30.5599	1.07310	0.536551	−	0.843868i	$-0.319727\pi$
$811$	30.5599	1.07310	0.536551	+	0.843868i	$0.319727\pi$
$812$	−1.92098	−0.0674131
$813$	−5.04319	−0.176872
$814$	3.47623	0.121842
$815$	−3.83230	−0.134239
$816$	13.0871	0.458139
$817$	5.63273	0.197064
$818$	−42.8340	−1.49766
$819$	38.1300	1.33237
$820$	1.41854	0.0495377
$821$	−47.9323	−1.67285	−0.836425	−	0.548081i	$-0.815359\pi$
$821$	−47.9323	−1.67285	−0.836425	+	0.548081i	$0.815359\pi$
$822$	47.0696	1.64174
$823$	47.4389	1.65362	0.826808	−	0.562485i	$-0.190154\pi$
$823$	47.4389	1.65362	0.826808	+	0.562485i	$0.190154\pi$
$824$	5.96206	0.207698
$825$	13.3139	0.463530
$826$	57.0500	1.98502
$827$	−28.5985	−0.994467	−0.497234	−	0.867617i	$-0.665651\pi$
$827$	−28.5985	−0.994467	−0.497234	+	0.867617i	$0.665651\pi$
$828$	−9.20749	−0.319983
$829$	21.2774	0.738995	0.369498	−	0.929232i	$-0.379530\pi$
$829$	21.2774	0.738995	0.369498	+	0.929232i	$0.379530\pi$
$830$	−3.96846	−0.137747
$831$	54.3374	1.88494
$832$	−9.69155	−0.335994
$833$	2.18452	0.0756890
$834$	37.5283	1.29950
$835$	5.33786	0.184724
$836$	7.68195	0.265686
$837$	−32.1508	−1.11129
$838$	−16.0223	−0.553481
$839$	7.91806	0.273362	0.136681	−	0.990615i	$-0.456356\pi$
$839$	7.91806	0.273362	0.136681	+	0.990615i	$0.456356\pi$
$840$	−1.50800	−0.0520310
$841$	−28.5880	−0.985793
$842$	35.6849	1.22978
$843$	52.7801	1.81784
$844$	16.3808	0.563851
$845$	−0.851253	−0.0292840
$846$	6.33619	0.217843
$847$	2.19442	0.0754012
$848$	−34.1662	−1.17327
$849$	41.0724	1.40960
$850$	−9.08233	−0.311521
$851$	−3.02620	−0.103737
$852$	−12.6172	−0.432259
$853$	−16.5852	−0.567867	−0.283933	−	0.958844i	$-0.591639\pi$
$853$	−16.5852	−0.567867	−0.283933	+	0.958844i	$0.591639\pi$
$854$	−23.0208	−0.787756
$855$	5.21743	0.178432
$856$	−5.38884	−0.184187
$857$	−0.0102757	−0.000351011 0	−0.000175506	−	1.00000i	$-0.500056\pi$
$857$	−0.0102757	−0.000351011 0	−0.000175506		1.00000i	$0.500056\pi$
$858$	20.2629	0.691765
$859$	−7.02038	−0.239532	−0.119766	−	0.992802i	$-0.538214\pi$
$859$	−7.02038	−0.239532	−0.119766	+	0.992802i	$0.538214\pi$
$860$	0.298749	0.0101873
$861$	−28.0142	−0.954722
$862$	−44.4191	−1.51292
$863$	19.0807	0.649515	0.324758	−	0.945797i	$-0.394717\pi$
$863$	19.0807	0.649515	0.324758	+	0.945797i	$0.394717\pi$
$864$	21.7789	0.740932
$865$	−1.88315	−0.0640289
$866$	44.9353	1.52696
$867$	2.68858	0.0913090
$868$	−29.1323	−0.988815
$869$	6.87441	0.233198
$870$	−0.693334	−0.0235062
$871$	4.36835	0.148016
$872$	−13.4324	−0.454879
$873$	−3.40280	−0.115167
$874$	−16.4945	−0.557935
$875$	4.78393	0.161726
$876$	−46.8072	−1.58147
$877$	−30.0413	−1.01442	−0.507212	−	0.861822i	$-0.669324\pi$
$877$	−30.0413	−1.01442	−0.507212	+	0.861822i	$0.669324\pi$
$878$	65.0311	2.19469
$879$	−67.4340	−2.27449
$880$	−1.06628	−0.0359444
$881$	17.3012	0.582891	0.291446	−	0.956587i	$-0.405864\pi$
$881$	17.3012	0.582891	0.291446	+	0.956587i	$0.405864\pi$
$882$	16.9416	0.570453
$883$	15.9310	0.536121	0.268061	−	0.963402i	$-0.413617\pi$
$883$	15.9310	0.536121	0.268061	+	0.963402i	$0.413617\pi$
$884$	−5.60424	−0.188491
$885$	8.34829	0.280625
$886$	−43.4112	−1.45843
$887$	−23.3725	−0.784772	−0.392386	−	0.919801i	$-0.628350\pi$
$887$	−23.3725	−0.784772	−0.392386	+	0.919801i	$0.628350\pi$
$888$	5.94594	0.199533
$889$	−30.8828	−1.03577
$890$	−1.35226	−0.0453279
$891$	3.80543	0.127487
$892$	38.6085	1.29271
$893$	4.60201	0.154000
$894$	−23.0747	−0.771733
$895$	−0.653920	−0.0218581
$896$	−19.4476	−0.649700
$897$	−17.6397	−0.588973
$898$	60.8368	2.03015
$899$	6.24815	0.208388
$900$	−28.5574	−0.951913
$901$	−7.01904	−0.233838
$902$	−8.70865	−0.289966
$903$	−5.89988	−0.196336
$904$	−7.10029	−0.236152
$905$	−2.93928	−0.0977051
$906$	−41.9077	−1.39229
$907$	−32.8755	−1.09161	−0.545806	−	0.837912i	$-0.683776\pi$
$907$	−32.8755	−1.09161	−0.545806	+	0.837912i	$0.683776\pi$
$908$	−25.6467	−0.851114
$909$	10.9774	0.364096
$910$	3.62287	0.120097
$911$	−33.7071	−1.11677	−0.558383	−	0.829583i	$-0.688578\pi$
$911$	−33.7071	−1.11677	−0.558383	+	0.829583i	$0.688578\pi$
$912$	73.7158	2.44098
$913$	9.87762	0.326901
$914$	−24.1299	−0.798145
$915$	−3.36870	−0.111366
$916$	22.2346	0.734652
$917$	−32.6515	−1.07825
$918$	6.05766	0.199933
$919$	−28.7049	−0.946888	−0.473444	−	0.880824i	$-0.656989\pi$
$919$	−28.7049	−0.946888	−0.473444	+	0.880824i	$0.656989\pi$
$920$	0.408097	0.0134546
$921$	−68.3039	−2.25069
$922$	−1.41140	−0.0464819
$923$	−14.1401	−0.465426
$924$	−8.04630	−0.264704
$925$	−9.38588	−0.308606
$926$	−66.8793	−2.19779
$927$	21.6060	0.709636
$928$	−4.23248	−0.138938
$929$	19.4675	0.638707	0.319353	−	0.947636i	$-0.396534\pi$
$929$	19.4675	0.638707	0.319353	+	0.947636i	$0.396534\pi$
$930$	−10.5147	−0.344789
$931$	12.3048	0.403273
$932$	12.3850	0.405684
$933$	11.2238	0.367451
$934$	5.88377	0.192523
$935$	−0.219056	−0.00716388
$936$	20.2746	0.662695
$937$	−53.7292	−1.75526	−0.877628	−	0.479343i	$-0.840875\pi$
$937$	−53.7292	−1.75526	−0.877628	+	0.479343i	$0.840875\pi$
$938$	−4.27848	−0.139697
$939$	44.8950	1.46509
$940$	0.244082	0.00796109
$941$	53.2113	1.73464	0.867319	−	0.497753i	$-0.165841\pi$
$941$	53.2113	1.73464	0.867319	+	0.497753i	$0.165841\pi$
$942$	−78.9864	−2.57352
$943$	7.58124	0.246879
$944$	68.9984	2.24571
$945$	−1.58768	−0.0516473
$946$	−1.83407	−0.0596307
$947$	−49.5637	−1.61060	−0.805302	−	0.592864i	$-0.797997\pi$
$947$	−49.5637	−1.61060	−0.805302	+	0.592864i	$0.797997\pi$
$948$	−25.2065	−0.818668
$949$	−52.4566	−1.70281
$950$	−51.1583	−1.65979
$951$	3.89545	0.126319
$952$	−2.56050	−0.0829862
$953$	20.2307	0.655337	0.327669	−	0.944793i	$-0.393737\pi$
$953$	20.2307	0.655337	0.327669	+	0.944793i	$0.393737\pi$
$954$	−54.4349	−1.76239
$955$	−5.76920	−0.186687
$956$	18.7313	0.605813
$957$	1.72573	0.0557849
$958$	−2.92049	−0.0943567
$959$	−20.9470	−0.676413
$960$	1.38902	0.0448303
$961$	63.7554	2.05663
$962$	−14.2847	−0.460558
$963$	−19.5287	−0.629305
$964$	4.93666	0.158999
$965$	−5.06266	−0.162973
$966$	17.2768	0.555872
$967$	−42.6737	−1.37229	−0.686146	−	0.727464i	$-0.740699\pi$
$967$	−42.6737	−1.37229	−0.686146	+	0.727464i	$0.740699\pi$
$968$	1.16682	0.0375031
$969$	15.1440	0.486497
$970$	−0.323313	−0.0103810
$971$	2.57201	0.0825396	0.0412698	−	0.999148i	$-0.486860\pi$
$971$	2.57201	0.0825396	0.0412698	+	0.999148i	$0.486860\pi$
$972$	−27.4668	−0.880997
$973$	−16.7009	−0.535406
$974$	17.4764	0.559981
$975$	−54.7103	−1.75213
$976$	−27.8422	−0.891208
$977$	−40.5244	−1.29649	−0.648245	−	0.761432i	$-0.724497\pi$
$977$	−40.5244	−1.29649	−0.648245	+	0.761432i	$0.724497\pi$
$978$	−86.2668	−2.75851
$979$	3.36582	0.107572
$980$	0.652623	0.0208473
$981$	−48.6781	−1.55417
$982$	−19.0123	−0.606707
$983$	−44.2266	−1.41061	−0.705305	−	0.708904i	$-0.749190\pi$
$983$	−44.2266	−1.41061	−0.705305	+	0.708904i	$0.749190\pi$
$984$	−14.8958	−0.474860
$985$	−0.0562372	−0.00179186
$986$	−1.17724	−0.0374910
$987$	−4.82028	−0.153431
$988$	−31.5671	−1.00428
$989$	1.59663	0.0507699
$990$	−1.69884	−0.0539928
$991$	20.7909	0.660446	0.330223	−	0.943903i	$-0.392876\pi$
$991$	20.7909	0.660446	0.330223	+	0.943903i	$0.392876\pi$
$992$	−64.1871	−2.03794
$993$	65.3237	2.07298
$994$	13.8492	0.439269
$995$	−3.04374	−0.0964931
$996$	−36.2183	−1.14762
$997$	−14.0706	−0.445622	−0.222811	−	0.974862i	$-0.571523\pi$
$997$	−14.0706	−0.445622	−0.222811	+	0.974862i	$0.571523\pi$
$998$	37.5126	1.18744
$999$	6.26012	0.198061

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.h.1.18	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.h.1.18	✓	74	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.83407 q^{2} +2.68858 q^{3} +1.36381 q^{4} -0.219056 q^{5} -4.93104 q^{6} +2.19442 q^{7} +1.16682 q^{8} +4.22847 q^{9} +O(q^{10})\)	\(q-1.83407 q^{2} +2.68858 q^{3} +1.36381 q^{4} -0.219056 q^{5} -4.93104 q^{6} +2.19442 q^{7} +1.16682 q^{8} +4.22847 q^{9} +0.401763 q^{10} -1.00000 q^{11} +3.66671 q^{12} +4.10926 q^{13} -4.02472 q^{14} -0.588949 q^{15} -4.86764 q^{16} -1.00000 q^{17} -7.75531 q^{18} -5.63273 q^{19} -0.298749 q^{20} +5.89988 q^{21} +1.83407 q^{22} -1.59663 q^{23} +3.13710 q^{24} -4.95201 q^{25} -7.53666 q^{26} +3.30285 q^{27} +2.99277 q^{28} -0.641874 q^{29} +1.08017 q^{30} -9.73424 q^{31} +6.59395 q^{32} -2.68858 q^{33} +1.83407 q^{34} -0.480700 q^{35} +5.76682 q^{36} +1.89536 q^{37} +10.3308 q^{38} +11.0481 q^{39} -0.255599 q^{40} -4.74827 q^{41} -10.8208 q^{42} -1.00000 q^{43} -1.36381 q^{44} -0.926271 q^{45} +2.92833 q^{46} -0.817013 q^{47} -13.0871 q^{48} -2.18452 q^{49} +9.08233 q^{50} -2.68858 q^{51} +5.60424 q^{52} +7.01904 q^{53} -6.05766 q^{54} +0.219056 q^{55} +2.56050 q^{56} -15.1440 q^{57} +1.17724 q^{58} -14.1749 q^{59} -0.803212 q^{60} +5.71986 q^{61} +17.8533 q^{62} +9.27905 q^{63} -2.35847 q^{64} -0.900156 q^{65} +4.93104 q^{66} +1.06305 q^{67} -1.36381 q^{68} -4.29268 q^{69} +0.881637 q^{70} -3.44103 q^{71} +4.93388 q^{72} -12.7655 q^{73} -3.47623 q^{74} -13.3139 q^{75} -7.68195 q^{76} -2.19442 q^{77} -20.2629 q^{78} -6.87441 q^{79} +1.06628 q^{80} -3.80543 q^{81} +8.70865 q^{82} -9.87762 q^{83} +8.04630 q^{84} +0.219056 q^{85} +1.83407 q^{86} -1.72573 q^{87} -1.16682 q^{88} -3.36582 q^{89} +1.69884 q^{90} +9.01745 q^{91} -2.17750 q^{92} -26.1713 q^{93} +1.49846 q^{94} +1.23388 q^{95} +17.7284 q^{96} -0.804736 q^{97} +4.00655 q^{98} -4.22847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * q^99

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