LMFDB - Embedded newform 8041.2.a.c.1.8

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:	$60$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-2.36766 q^{2} +0.323518 q^{3} +3.60581 q^{4} -3.56257 q^{5} -0.765980 q^{6} +3.82937 q^{7} -3.80202 q^{8} -2.89534 q^{9} +O(q^{10})$	\(q-2.36766 q^{2} +0.323518 q^{3} +3.60581 q^{4} -3.56257 q^{5} -0.765980 q^{6} +3.82937 q^{7} -3.80202 q^{8} -2.89534 q^{9} +8.43496 q^{10} +1.00000 q^{11} +1.16655 q^{12} +5.24999 q^{13} -9.06664 q^{14} -1.15256 q^{15} +1.79026 q^{16} +1.00000 q^{17} +6.85517 q^{18} +0.126978 q^{19} -12.8460 q^{20} +1.23887 q^{21} -2.36766 q^{22} -1.44840 q^{23} -1.23002 q^{24} +7.69192 q^{25} -12.4302 q^{26} -1.90725 q^{27} +13.8080 q^{28} -8.11905 q^{29} +2.72886 q^{30} +3.73592 q^{31} +3.36531 q^{32} +0.323518 q^{33} -2.36766 q^{34} -13.6424 q^{35} -10.4400 q^{36} -1.31069 q^{37} -0.300640 q^{38} +1.69847 q^{39} +13.5450 q^{40} +4.48390 q^{41} -2.93322 q^{42} -1.00000 q^{43} +3.60581 q^{44} +10.3148 q^{45} +3.42933 q^{46} -2.15828 q^{47} +0.579181 q^{48} +7.66405 q^{49} -18.2119 q^{50} +0.323518 q^{51} +18.9305 q^{52} -2.06667 q^{53} +4.51571 q^{54} -3.56257 q^{55} -14.5593 q^{56} +0.0410796 q^{57} +19.2231 q^{58} +3.98929 q^{59} -4.15590 q^{60} -10.3035 q^{61} -8.84538 q^{62} -11.0873 q^{63} -11.5484 q^{64} -18.7035 q^{65} -0.765980 q^{66} +2.01212 q^{67} +3.60581 q^{68} -0.468585 q^{69} +32.3006 q^{70} -2.01387 q^{71} +11.0081 q^{72} -7.40491 q^{73} +3.10327 q^{74} +2.48848 q^{75} +0.457858 q^{76} +3.82937 q^{77} -4.02139 q^{78} -6.76504 q^{79} -6.37793 q^{80} +8.06898 q^{81} -10.6163 q^{82} -18.0048 q^{83} +4.46713 q^{84} -3.56257 q^{85} +2.36766 q^{86} -2.62666 q^{87} -3.80202 q^{88} +10.4946 q^{89} -24.4220 q^{90} +20.1042 q^{91} -5.22267 q^{92} +1.20864 q^{93} +5.11007 q^{94} -0.452367 q^{95} +1.08874 q^{96} +0.0988980 q^{97} -18.1459 q^{98} -2.89534 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) $ 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.36766	−1.67419	−0.837094	−	0.547059i	$-0.815747\pi$
$2$	−2.36766	−1.67419	−0.837094	+	0.547059i	$0.815747\pi$
$3$	0.323518	0.186783	0.0933916	−	0.995629i	$-0.470229\pi$
$3$	0.323518	0.186783	0.0933916	+	0.995629i	$0.470229\pi$
$4$	3.60581	1.80291
$5$	−3.56257	−1.59323	−0.796615	−	0.604486i	$-0.793378\pi$
$5$	−3.56257	−1.59323	−0.796615	+	0.604486i	$0.793378\pi$
$6$	−0.765980	−0.312710
$7$	3.82937	1.44736	0.723682	−	0.690133i	$-0.242448\pi$
$7$	3.82937	1.44736	0.723682	+	0.690133i	$0.242448\pi$
$8$	−3.80202	−1.34422
$9$	−2.89534	−0.965112
$10$	8.43496	2.66737
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.16655	0.336753
$13$	5.24999	1.45609	0.728043	−	0.685531i	$-0.240430\pi$
$13$	5.24999	1.45609	0.728043	+	0.685531i	$0.240430\pi$
$14$	−9.06664	−2.42316
$15$	−1.15256	−0.297589
$16$	1.79026	0.447565
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	6.85517	1.61578
$19$	0.126978	0.0291307	0.0145653	−	0.999894i	$-0.495364\pi$
$19$	0.126978	0.0291307	0.0145653	+	0.999894i	$0.495364\pi$
$20$	−12.8460	−2.87245
$21$	1.23887	0.270343
$22$	−2.36766	−0.504787
$23$	−1.44840	−0.302013	−0.151007	−	0.988533i	$-0.548251\pi$
$23$	−1.44840	−0.302013	−0.151007	+	0.988533i	$0.548251\pi$
$24$	−1.23002	−0.251077
$25$	7.69192	1.53838
$26$	−12.4302	−2.43776
$27$	−1.90725	−0.367050
$28$	13.8080	2.60946
$29$	−8.11905	−1.50767	−0.753834	−	0.657064i	$-0.771798\pi$
$29$	−8.11905	−1.50767	−0.753834	+	0.657064i	$0.771798\pi$
$30$	2.72886	0.498220
$31$	3.73592	0.670991	0.335495	−	0.942042i	$-0.391096\pi$
$31$	3.73592	0.670991	0.335495	+	0.942042i	$0.391096\pi$
$32$	3.36531	0.594908
$33$	0.323518	0.0563172
$34$	−2.36766	−0.406050
$35$	−13.6424	−2.30599
$36$	−10.4400	−1.74001
$37$	−1.31069	−0.215476	−0.107738	−	0.994179i	$-0.534361\pi$
$37$	−1.31069	−0.215476	−0.107738	+	0.994179i	$0.534361\pi$
$38$	−0.300640	−0.0487702
$39$	1.69847	0.271972
$40$	13.5450	2.14165
$41$	4.48390	0.700268	0.350134	−	0.936700i	$-0.386136\pi$
$41$	4.48390	0.700268	0.350134	+	0.936700i	$0.386136\pi$
$42$	−2.93322	−0.452606
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	3.60581	0.543597
$45$	10.3148	1.53765
$46$	3.42933	0.505627
$47$	−2.15828	−0.314817	−0.157409	−	0.987534i	$-0.550314\pi$
$47$	−2.15828	−0.314817	−0.157409	+	0.987534i	$0.550314\pi$
$48$	0.579181	0.0835976
$49$	7.66405	1.09486
$50$	−18.2119	−2.57555
$51$	0.323518	0.0453016
$52$	18.9305	2.62519
$53$	−2.06667	−0.283878	−0.141939	−	0.989875i	$-0.545334\pi$
$53$	−2.06667	−0.283878	−0.141939	+	0.989875i	$0.545334\pi$
$54$	4.51571	0.614511
$55$	−3.56257	−0.480377
$56$	−14.5593	−1.94557
$57$	0.0410796	0.00544112
$58$	19.2231	2.52412
$59$	3.98929	0.519362	0.259681	−	0.965694i	$-0.416383\pi$
$59$	3.98929	0.519362	0.259681	+	0.965694i	$0.416383\pi$
$60$	−4.15590	−0.536525
$61$	−10.3035	−1.31922	−0.659611	−	0.751607i	$-0.729279\pi$
$61$	−10.3035	−1.31922	−0.659611	+	0.751607i	$0.729279\pi$
$62$	−8.84538	−1.12336
$63$	−11.0873	−1.39687
$64$	−11.5484	−1.44355
$65$	−18.7035	−2.31988
$66$	−0.765980	−0.0942857
$67$	2.01212	0.245820	0.122910	−	0.992418i	$-0.460777\pi$
$67$	2.01212	0.245820	0.122910	+	0.992418i	$0.460777\pi$
$68$	3.60581	0.437269
$69$	−0.468585	−0.0564110
$70$	32.3006	3.86065
$71$	−2.01387	−0.239002	−0.119501	−	0.992834i	$-0.538130\pi$
$71$	−2.01387	−0.239002	−0.119501	+	0.992834i	$0.538130\pi$
$72$	11.0081	1.29732
$73$	−7.40491	−0.866679	−0.433340	−	0.901231i	$-0.642665\pi$
$73$	−7.40491	−0.866679	−0.433340	+	0.901231i	$0.642665\pi$
$74$	3.10327	0.360748
$75$	2.48848	0.287344
$76$	0.457858	0.0525199
$77$	3.82937	0.436397
$78$	−4.02139	−0.455333
$79$	−6.76504	−0.761127	−0.380563	−	0.924755i	$-0.624270\pi$
$79$	−6.76504	−0.761127	−0.380563	+	0.924755i	$0.624270\pi$
$80$	−6.37793	−0.713074
$81$	8.06898	0.896553
$82$	−10.6163	−1.17238
$83$	−18.0048	−1.97628	−0.988142	−	0.153542i	$-0.950932\pi$
$83$	−18.0048	−1.97628	−0.988142	+	0.153542i	$0.950932\pi$
$84$	4.46713	0.487404
$85$	−3.56257	−0.386415
$86$	2.36766	0.255311
$87$	−2.62666	−0.281607
$88$	−3.80202	−0.405296
$89$	10.4946	1.11242	0.556211	−	0.831041i	$-0.312255\pi$
$89$	10.4946	1.11242	0.556211	+	0.831041i	$0.312255\pi$
$90$	−24.4220	−2.57431
$91$	20.1042	2.10749
$92$	−5.22267	−0.544501
$93$	1.20864	0.125330
$94$	5.11007	0.527063
$95$	−0.452367	−0.0464119
$96$	1.08874	0.111119
$97$	0.0988980	0.0100416	0.00502078	−	0.999987i	$-0.498402\pi$
$97$	0.0988980	0.0100416	0.00502078	+	0.999987i	$0.498402\pi$
$98$	−18.1459	−1.83301
$99$	−2.89534	−0.290992
$100$	27.7356	2.77356
$101$	4.46310	0.444095	0.222047	−	0.975036i	$-0.428726\pi$
$101$	4.46310	0.444095	0.222047	+	0.975036i	$0.428726\pi$
$102$	−0.765980	−0.0758434
$103$	1.67202	0.164750	0.0823748	−	0.996601i	$-0.473750\pi$
$103$	1.67202	0.164750	0.0823748	+	0.996601i	$0.473750\pi$
$104$	−19.9606	−1.95730
$105$	−4.41356	−0.430719
$106$	4.89316	0.475266
$107$	−5.01250	−0.484577	−0.242289	−	0.970204i	$-0.577898\pi$
$107$	−5.01250	−0.484577	−0.242289	+	0.970204i	$0.577898\pi$
$108$	−6.87718	−0.661756
$109$	8.09379	0.775244	0.387622	−	0.921818i	$-0.373297\pi$
$109$	8.09379	0.775244	0.387622	+	0.921818i	$0.373297\pi$
$110$	8.43496	0.804242
$111$	−0.424032	−0.0402473
$112$	6.85556	0.647790
$113$	−7.59897	−0.714851	−0.357425	−	0.933942i	$-0.616345\pi$
$113$	−7.59897	−0.714851	−0.357425	+	0.933942i	$0.616345\pi$
$114$	−0.0972624	−0.00910946
$115$	5.16005	0.481177
$116$	−29.2758	−2.71819
$117$	−15.2005	−1.40529
$118$	−9.44529	−0.869510
$119$	3.82937	0.351037
$120$	4.38204	0.400024
$121$	1.00000	0.0909091
$122$	24.3951	2.20863
$123$	1.45062	0.130798
$124$	13.4710	1.20973
$125$	−9.59017	−0.857771
$126$	26.2510	2.33862
$127$	−6.65534	−0.590566	−0.295283	−	0.955410i	$-0.595414\pi$
$127$	−6.65534	−0.590566	−0.295283	+	0.955410i	$0.595414\pi$
$128$	20.6121	1.82187
$129$	−0.323518	−0.0284842
$130$	44.2835	3.88392
$131$	−9.97414	−0.871445	−0.435723	−	0.900081i	$-0.643507\pi$
$131$	−9.97414	−0.871445	−0.435723	+	0.900081i	$0.643507\pi$
$132$	1.16655	0.101535
$133$	0.486244	0.0421627
$134$	−4.76401	−0.411548
$135$	6.79471	0.584795
$136$	−3.80202	−0.326020
$137$	−10.2320	−0.874181	−0.437091	−	0.899417i	$-0.643991\pi$
$137$	−10.2320	−0.874181	−0.437091	+	0.899417i	$0.643991\pi$
$138$	1.10945	0.0944426
$139$	7.95399	0.674649	0.337324	−	0.941388i	$-0.390478\pi$
$139$	7.95399	0.674649	0.337324	+	0.941388i	$0.390478\pi$
$140$	−49.1919	−4.15748
$141$	−0.698241	−0.0588025
$142$	4.76816	0.400135
$143$	5.24999	0.439027
$144$	−5.18340	−0.431950
$145$	28.9247	2.40206
$146$	17.5323	1.45098
$147$	2.47946	0.204502
$148$	−4.72610	−0.388483
$149$	−3.59163	−0.294238	−0.147119	−	0.989119i	$-0.547000\pi$
$149$	−3.59163	−0.294238	−0.147119	+	0.989119i	$0.547000\pi$
$150$	−5.89186	−0.481069
$151$	−10.5476	−0.858355	−0.429177	−	0.903220i	$-0.641196\pi$
$151$	−10.5476	−0.858355	−0.429177	+	0.903220i	$0.641196\pi$
$152$	−0.482771	−0.0391579
$153$	−2.89534	−0.234074
$154$	−9.06664	−0.730610
$155$	−13.3095	−1.06904
$156$	6.12435	0.490341
$157$	−11.0868	−0.884820	−0.442410	−	0.896813i	$-0.645876\pi$
$157$	−11.0868	−0.884820	−0.442410	+	0.896813i	$0.645876\pi$
$158$	16.0173	1.27427
$159$	−0.668603	−0.0530237
$160$	−11.9892	−0.947826
$161$	−5.54647	−0.437123
$162$	−19.1046	−1.50100
$163$	12.3504	0.967358	0.483679	−	0.875245i	$-0.339300\pi$
$163$	12.3504	0.967358	0.483679	+	0.875245i	$0.339300\pi$
$164$	16.1681	1.26252
$165$	−1.15256	−0.0897264
$166$	42.6293	3.30867
$167$	−2.22531	−0.172200	−0.0860998	−	0.996287i	$-0.527440\pi$
$167$	−2.22531	−0.172200	−0.0860998	+	0.996287i	$0.527440\pi$
$168$	−4.71020	−0.363400
$169$	14.5624	1.12019
$170$	8.43496	0.646932
$171$	−0.367643	−0.0281144
$172$	−3.60581	−0.274941
$173$	18.2465	1.38725	0.693627	−	0.720334i	$-0.256011\pi$
$173$	18.2465	1.38725	0.693627	+	0.720334i	$0.256011\pi$
$174$	6.21903	0.471463
$175$	29.4552	2.22660
$176$	1.79026	0.134946
$177$	1.29061	0.0970081
$178$	−24.8476	−1.86240
$179$	22.1120	1.65273	0.826364	−	0.563136i	$-0.190405\pi$
$179$	22.1120	1.65273	0.826364	+	0.563136i	$0.190405\pi$
$180$	37.1934	2.77223
$181$	4.53224	0.336879	0.168439	−	0.985712i	$-0.446127\pi$
$181$	4.53224	0.336879	0.168439	+	0.985712i	$0.446127\pi$
$182$	−47.5998	−3.52833
$183$	−3.33335	−0.246408
$184$	5.50686	0.405971
$185$	4.66943	0.343303
$186$	−2.86164	−0.209826
$187$	1.00000	0.0731272
$188$	−7.78234	−0.567586
$189$	−7.30355	−0.531255
$190$	1.07105	0.0777022
$191$	−20.2409	−1.46458	−0.732291	−	0.680992i	$-0.761549\pi$
$191$	−20.2409	−1.46458	−0.732291	+	0.680992i	$0.761549\pi$
$192$	−3.73612	−0.269632
$193$	6.89280	0.496155	0.248077	−	0.968740i	$-0.420201\pi$
$193$	6.89280	0.496155	0.248077	+	0.968740i	$0.420201\pi$
$194$	−0.234157	−0.0168115
$195$	−6.05091	−0.433315
$196$	27.6351	1.97394
$197$	22.1445	1.57773	0.788864	−	0.614568i	$-0.210670\pi$
$197$	22.1445	1.57773	0.788864	+	0.614568i	$0.210670\pi$
$198$	6.85517	0.487176
$199$	−24.1739	−1.71364	−0.856820	−	0.515616i	$-0.827563\pi$
$199$	−24.1739	−1.71364	−0.856820	+	0.515616i	$0.827563\pi$
$200$	−29.2448	−2.06792
$201$	0.650957	0.0459150
$202$	−10.5671	−0.743498
$203$	−31.0908	−2.18215
$204$	1.16655	0.0816745
$205$	−15.9742	−1.11569
$206$	−3.95879	−0.275822
$207$	4.19362	0.291477
$208$	9.39885	0.651693
$209$	0.126978	0.00878323
$210$	10.4498	0.721105
$211$	22.6099	1.55653	0.778266	−	0.627935i	$-0.216100\pi$
$211$	22.6099	1.55653	0.778266	+	0.627935i	$0.216100\pi$
$212$	−7.45201	−0.511806
$213$	−0.651523	−0.0446416
$214$	11.8679	0.811273
$215$	3.56257	0.242965
$216$	7.25139	0.493394
$217$	14.3062	0.971168
$218$	−19.1633	−1.29791
$219$	−2.39562	−0.161881
$220$	−12.8460	−0.866075
$221$	5.24999	0.353153
$222$	1.00396	0.0673816
$223$	−13.9934	−0.937067	−0.468533	−	0.883446i	$-0.655217\pi$
$223$	−13.9934	−0.937067	−0.468533	+	0.883446i	$0.655217\pi$
$224$	12.8870	0.861049
$225$	−22.2707	−1.48471
$226$	17.9918	1.19679
$227$	17.6713	1.17289	0.586444	−	0.809990i	$-0.300527\pi$
$227$	17.6713	1.17289	0.586444	+	0.809990i	$0.300527\pi$
$228$	0.148125	0.00980983
$229$	6.43674	0.425352	0.212676	−	0.977123i	$-0.431782\pi$
$229$	6.43674	0.425352	0.212676	+	0.977123i	$0.431782\pi$
$230$	−12.2172	−0.805580
$231$	1.23887	0.0815116
$232$	30.8688	2.02663
$233$	−15.0581	−0.986489	−0.493244	−	0.869891i	$-0.664189\pi$
$233$	−15.0581	−0.986489	−0.493244	+	0.869891i	$0.664189\pi$
$234$	35.9896	2.35271
$235$	7.68902	0.501576
$236$	14.3846	0.936361
$237$	−2.18861	−0.142166
$238$	−9.06664	−0.587703
$239$	15.5241	1.00417	0.502086	−	0.864818i	$-0.332566\pi$
$239$	15.5241	1.00417	0.502086	+	0.864818i	$0.332566\pi$
$240$	−2.06337	−0.133190
$241$	13.5638	0.873721	0.436861	−	0.899529i	$-0.356090\pi$
$241$	13.5638	0.873721	0.436861	+	0.899529i	$0.356090\pi$
$242$	−2.36766	−0.152199
$243$	8.33220	0.534511
$244$	−37.1523	−2.37843
$245$	−27.3037	−1.74437
$246$	−3.43458	−0.218981
$247$	0.666632	0.0424168
$248$	−14.2040	−0.901957
$249$	−5.82488	−0.369137
$250$	22.7063	1.43607
$251$	−24.1052	−1.52151	−0.760754	−	0.649041i	$-0.775170\pi$
$251$	−24.1052	−1.52151	−0.760754	+	0.649041i	$0.775170\pi$
$252$	−39.9787	−2.51842
$253$	−1.44840	−0.0910604
$254$	15.7576	0.988719
$255$	−1.15256	−0.0721759
$256$	−25.7057	−1.60660
$257$	14.7439	0.919700	0.459850	−	0.887997i	$-0.347903\pi$
$257$	14.7439	0.919700	0.459850	+	0.887997i	$0.347903\pi$
$258$	0.765980	0.0476879
$259$	−5.01911	−0.311873
$260$	−67.4413	−4.18253
$261$	23.5074	1.45507
$262$	23.6154	1.45896
$263$	5.99877	0.369900	0.184950	−	0.982748i	$-0.440788\pi$
$263$	5.99877	0.369900	0.184950	+	0.982748i	$0.440788\pi$
$264$	−1.23002	−0.0757026
$265$	7.36264	0.452284
$266$	−1.15126	−0.0705883
$267$	3.39518	0.207782
$268$	7.25533	0.443190
$269$	26.9691	1.64434	0.822168	−	0.569244i	$-0.192764\pi$
$269$	26.9691	1.64434	0.822168	+	0.569244i	$0.192764\pi$
$270$	−16.0876	−0.979057
$271$	−18.4825	−1.12273	−0.561365	−	0.827568i	$-0.689724\pi$
$271$	−18.4825	−1.12273	−0.561365	+	0.827568i	$0.689724\pi$
$272$	1.79026	0.108550
$273$	6.50405	0.393643
$274$	24.2260	1.46354
$275$	7.69192	0.463840
$276$	−1.68963	−0.101704
$277$	−14.6138	−0.878056	−0.439028	−	0.898473i	$-0.644677\pi$
$277$	−14.6138	−0.878056	−0.439028	+	0.898473i	$0.644677\pi$
$278$	−18.8324	−1.12949
$279$	−10.8167	−0.647581
$280$	51.8686	3.09974
$281$	−19.1397	−1.14178	−0.570888	−	0.821028i	$-0.693401\pi$
$281$	−19.1397	−1.14178	−0.570888	+	0.821028i	$0.693401\pi$
$282$	1.65320	0.0984465
$283$	−11.1186	−0.660935	−0.330467	−	0.943817i	$-0.607206\pi$
$283$	−11.1186	−0.660935	−0.330467	+	0.943817i	$0.607206\pi$
$284$	−7.26164	−0.430899
$285$	−0.146349	−0.00866896
$286$	−12.4302	−0.735013
$287$	17.1705	1.01354
$288$	−9.74370	−0.574153
$289$	1.00000	0.0588235
$290$	−68.4838	−4.02151
$291$	0.0319953	0.00187560
$292$	−26.7007	−1.56254
$293$	−30.0609	−1.75617	−0.878087	−	0.478501i	$-0.841180\pi$
$293$	−30.0609	−1.75617	−0.878087	+	0.478501i	$0.841180\pi$
$294$	−5.87051	−0.342375
$295$	−14.2122	−0.827463
$296$	4.98327	0.289647
$297$	−1.90725	−0.110670
$298$	8.50376	0.492610
$299$	−7.60411	−0.439757
$300$	8.97298	0.518055
$301$	−3.82937	−0.220721
$302$	24.9732	1.43705
$303$	1.44389	0.0829494
$304$	0.227323	0.0130379
$305$	36.7068	2.10182
$306$	6.85517	0.391884
$307$	−7.88729	−0.450151	−0.225076	−	0.974341i	$-0.572263\pi$
$307$	−7.88729	−0.450151	−0.225076	+	0.974341i	$0.572263\pi$
$308$	13.8080	0.786783
$309$	0.540930	0.0307724
$310$	31.5123	1.78978
$311$	−26.8267	−1.52120	−0.760601	−	0.649219i	$-0.775096\pi$
$311$	−26.8267	−1.52120	−0.760601	+	0.649219i	$0.775096\pi$
$312$	−6.45760	−0.365590
$313$	−6.30365	−0.356303	−0.178152	−	0.984003i	$-0.557012\pi$
$313$	−6.30365	−0.356303	−0.178152	+	0.984003i	$0.557012\pi$
$314$	26.2497	1.48136
$315$	39.4993	2.22553
$316$	−24.3935	−1.37224
$317$	−12.4983	−0.701974	−0.350987	−	0.936380i	$-0.614154\pi$
$317$	−12.4983	−0.701974	−0.350987	+	0.936380i	$0.614154\pi$
$318$	1.58302	0.0887716
$319$	−8.11905	−0.454579
$320$	41.1421	2.29991
$321$	−1.62164	−0.0905108
$322$	13.1322	0.731826
$323$	0.126978	0.00706523
$324$	29.0952	1.61640
$325$	40.3826	2.24002
$326$	−29.2416	−1.61954
$327$	2.61849	0.144803
$328$	−17.0479	−0.941311
$329$	−8.26483	−0.455655
$330$	2.72886	0.150219
$331$	13.6087	0.748004	0.374002	−	0.927428i	$-0.377985\pi$
$331$	13.6087	0.748004	0.374002	+	0.927428i	$0.377985\pi$
$332$	−64.9220	−3.56306
$333$	3.79489	0.207959
$334$	5.26877	0.288295
$335$	−7.16832	−0.391647
$336$	2.21790	0.120996
$337$	−5.26917	−0.287030	−0.143515	−	0.989648i	$-0.545841\pi$
$337$	−5.26917	−0.287030	−0.143515	+	0.989648i	$0.545841\pi$
$338$	−34.4789	−1.87540
$339$	−2.45840	−0.133522
$340$	−12.8460	−0.696671
$341$	3.73592	0.202311
$342$	0.870454	0.0470687
$343$	2.54288	0.137303
$344$	3.80202	0.204991
$345$	1.66937	0.0898757
$346$	−43.2015	−2.32253
$347$	−14.3411	−0.769868	−0.384934	−	0.922944i	$-0.625776\pi$
$347$	−14.3411	−0.769868	−0.384934	+	0.922944i	$0.625776\pi$
$348$	−9.47123	−0.507711
$349$	23.2833	1.24632	0.623162	−	0.782093i	$-0.285848\pi$
$349$	23.2833	1.24632	0.623162	+	0.782093i	$0.285848\pi$
$350$	−69.7399	−3.72775
$351$	−10.0130	−0.534456
$352$	3.36531	0.179372
$353$	14.7128	0.783084	0.391542	−	0.920160i	$-0.371942\pi$
$353$	14.7128	0.783084	0.391542	+	0.920160i	$0.371942\pi$
$354$	−3.05572	−0.162410
$355$	7.17456	0.380786
$356$	37.8415	2.00559
$357$	1.23887	0.0655679
$358$	−52.3537	−2.76698
$359$	4.47556	0.236211	0.118105	−	0.993001i	$-0.462318\pi$
$359$	4.47556	0.236211	0.118105	+	0.993001i	$0.462318\pi$
$360$	−39.2172	−2.06693
$361$	−18.9839	−0.999151
$362$	−10.7308	−0.563999
$363$	0.323518	0.0169803
$364$	72.4918	3.79960
$365$	26.3805	1.38082
$366$	7.89224	0.412534
$367$	−27.5962	−1.44051	−0.720255	−	0.693709i	$-0.755975\pi$
$367$	−27.5962	−1.44051	−0.720255	+	0.693709i	$0.755975\pi$
$368$	−2.59302	−0.135171
$369$	−12.9824	−0.675837
$370$	−11.0556	−0.574754
$371$	−7.91402	−0.410875
$372$	4.35812	0.225958
$373$	14.4865	0.750084	0.375042	−	0.927008i	$-0.377628\pi$
$373$	14.4865	0.750084	0.375042	+	0.927008i	$0.377628\pi$
$374$	−2.36766	−0.122429
$375$	−3.10259	−0.160217
$376$	8.20581	0.423182
$377$	−42.6249	−2.19530
$378$	17.2923	0.889421
$379$	25.1128	1.28996	0.644979	−	0.764200i	$-0.276866\pi$
$379$	25.1128	1.28996	0.644979	+	0.764200i	$0.276866\pi$
$380$	−1.63115	−0.0836763
$381$	−2.15312	−0.110308
$382$	47.9236	2.45199
$383$	35.9766	1.83832	0.919159	−	0.393887i	$-0.128870\pi$
$383$	35.9766	1.83832	0.919159	+	0.393887i	$0.128870\pi$
$384$	6.66839	0.340295
$385$	−13.6424	−0.695281
$386$	−16.3198	−0.830656
$387$	2.89534	0.147178
$388$	0.356608	0.0181040
$389$	−25.3411	−1.28484	−0.642421	−	0.766352i	$-0.722070\pi$
$389$	−25.3411	−1.28484	−0.642421	+	0.766352i	$0.722070\pi$
$390$	14.3265	0.725451
$391$	−1.44840	−0.0732489
$392$	−29.1389	−1.47173
$393$	−3.22681	−0.162771
$394$	−52.4305	−2.64141
$395$	24.1010	1.21265
$396$	−10.4400	−0.524632
$397$	32.8544	1.64891	0.824457	−	0.565925i	$-0.191481\pi$
$397$	32.8544	1.64891	0.824457	+	0.565925i	$0.191481\pi$
$398$	57.2355	2.86895
$399$	0.157309	0.00787528
$400$	13.7705	0.688527
$401$	−0.718916	−0.0359009	−0.0179505	−	0.999839i	$-0.505714\pi$
$401$	−0.718916	−0.0359009	−0.0179505	+	0.999839i	$0.505714\pi$
$402$	−1.54124	−0.0768703
$403$	19.6135	0.977020
$404$	16.0931	0.800661
$405$	−28.7463	−1.42842
$406$	73.6124	3.65332
$407$	−1.31069	−0.0649685
$408$	−1.23002	−0.0608951
$409$	−7.28907	−0.360421	−0.180211	−	0.983628i	$-0.557678\pi$
$409$	−7.28907	−0.360421	−0.180211	+	0.983628i	$0.557678\pi$
$410$	37.8215	1.86787
$411$	−3.31025	−0.163282
$412$	6.02901	0.297028
$413$	15.2765	0.751706
$414$	−9.92906	−0.487987
$415$	64.1434	3.14868
$416$	17.6679	0.866238
$417$	2.57326	0.126013
$418$	−0.300640	−0.0147048
$419$	31.3299	1.53057	0.765284	−	0.643693i	$-0.222598\pi$
$419$	31.3299	1.53057	0.765284	+	0.643693i	$0.222598\pi$
$420$	−15.9145	−0.776547
$421$	1.68877	0.0823058	0.0411529	−	0.999153i	$-0.486897\pi$
$421$	1.68877	0.0823058	0.0411529	+	0.999153i	$0.486897\pi$
$422$	−53.5326	−2.60593
$423$	6.24894	0.303834
$424$	7.85750	0.381594
$425$	7.69192	0.373113
$426$	1.54259	0.0747385
$427$	−39.4557	−1.90939
$428$	−18.0742	−0.873647
$429$	1.69847	0.0820028
$430$	−8.43496	−0.406770
$431$	35.8570	1.72717	0.863585	−	0.504204i	$-0.168214\pi$
$431$	35.8570	1.72717	0.863585	+	0.504204i	$0.168214\pi$
$432$	−3.41447	−0.164279
$433$	−20.4955	−0.984952	−0.492476	−	0.870326i	$-0.663908\pi$
$433$	−20.4955	−0.984952	−0.492476	+	0.870326i	$0.663908\pi$
$434$	−33.8722	−1.62592
$435$	9.35766	0.448665
$436$	29.1847	1.39769
$437$	−0.183915	−0.00879785
$438$	5.67202	0.271019
$439$	−2.86454	−0.136717	−0.0683585	−	0.997661i	$-0.521776\pi$
$439$	−2.86454	−0.136717	−0.0683585	+	0.997661i	$0.521776\pi$
$440$	13.5450	0.645731
$441$	−22.1900	−1.05667
$442$	−12.4302	−0.591244
$443$	−8.67834	−0.412320	−0.206160	−	0.978518i	$-0.566097\pi$
$443$	−8.67834	−0.412320	−0.206160	+	0.978518i	$0.566097\pi$
$444$	−1.52898	−0.0725622
$445$	−37.3877	−1.77235
$446$	33.1316	1.56883
$447$	−1.16196	−0.0549587
$448$	−44.2232	−2.08935
$449$	−13.3457	−0.629821	−0.314910	−	0.949121i	$-0.601974\pi$
$449$	−13.3457	−0.629821	−0.314910	+	0.949121i	$0.601974\pi$
$450$	52.7295	2.48569
$451$	4.48390	0.211139
$452$	−27.4004	−1.28881
$453$	−3.41235	−0.160326
$454$	−41.8397	−1.96364
$455$	−71.6225	−3.35771
$456$	−0.156185	−0.00731404
$457$	−6.12472	−0.286502	−0.143251	−	0.989686i	$-0.545756\pi$
$457$	−6.12472	−0.286502	−0.143251	+	0.989686i	$0.545756\pi$
$458$	−15.2400	−0.712119
$459$	−1.90725	−0.0890227
$460$	18.6062	0.867517
$461$	−16.8970	−0.786970	−0.393485	−	0.919331i	$-0.628731\pi$
$461$	−16.8970	−0.786970	−0.393485	+	0.919331i	$0.628731\pi$
$462$	−2.93322	−0.136466
$463$	−36.5553	−1.69887	−0.849433	−	0.527696i	$-0.823056\pi$
$463$	−36.5553	−1.69887	−0.849433	+	0.527696i	$0.823056\pi$
$464$	−14.5352	−0.674780
$465$	−4.30585	−0.199679
$466$	35.6525	1.65157
$467$	−7.84928	−0.363221	−0.181611	−	0.983371i	$-0.558131\pi$
$467$	−7.84928	−0.363221	−0.181611	+	0.983371i	$0.558131\pi$
$468$	−54.8101	−2.53360
$469$	7.70514	0.355790
$470$	−18.2050	−0.839733
$471$	−3.58677	−0.165270
$472$	−15.1674	−0.698135
$473$	−1.00000	−0.0459800
$474$	5.18189	0.238012
$475$	0.976703	0.0448142
$476$	13.8080	0.632888
$477$	5.98369	0.273974
$478$	−36.7558	−1.68117
$479$	−0.509081	−0.0232605	−0.0116302	−	0.999932i	$-0.503702\pi$
$479$	−0.509081	−0.0232605	−0.0116302	+	0.999932i	$0.503702\pi$
$480$	−3.87871	−0.177038
$481$	−6.88112	−0.313752
$482$	−32.1145	−1.46277
$483$	−1.79438	−0.0816472
$484$	3.60581	0.163901
$485$	−0.352331	−0.0159985
$486$	−19.7278	−0.894872
$487$	16.5403	0.749514	0.374757	−	0.927123i	$-0.377726\pi$
$487$	16.5403	0.749514	0.374757	+	0.927123i	$0.377726\pi$
$488$	39.1739	1.77332
$489$	3.99558	0.180686
$490$	64.6459	2.92041
$491$	−7.35856	−0.332087	−0.166044	−	0.986118i	$-0.553099\pi$
$491$	−7.35856	−0.332087	−0.166044	+	0.986118i	$0.553099\pi$
$492$	5.23067	0.235817
$493$	−8.11905	−0.365663
$494$	−1.57836	−0.0710137
$495$	10.3148	0.463618
$496$	6.68826	0.300312
$497$	−7.71185	−0.345924
$498$	13.7913	0.618004
$499$	27.5973	1.23542	0.617712	−	0.786404i	$-0.288060\pi$
$499$	27.5973	1.23542	0.617712	+	0.786404i	$0.288060\pi$
$500$	−34.5804	−1.54648
$501$	−0.719927	−0.0321640
$502$	57.0729	2.54729
$503$	−2.96285	−0.132107	−0.0660536	−	0.997816i	$-0.521041\pi$
$503$	−2.96285	−0.132107	−0.0660536	+	0.997816i	$0.521041\pi$
$504$	42.1541	1.87769
$505$	−15.9001	−0.707546
$506$	3.42933	0.152452
$507$	4.71121	0.209232
$508$	−23.9979	−1.06474
$509$	−35.9861	−1.59506	−0.797529	−	0.603281i	$-0.793860\pi$
$509$	−35.9861	−1.59506	−0.797529	+	0.603281i	$0.793860\pi$
$510$	2.72886	0.120836
$511$	−28.3561	−1.25440
$512$	19.6380	0.867884
$513$	−0.242178	−0.0106924
$514$	−34.9086	−1.53975
$515$	−5.95671	−0.262484
$516$	−1.16655	−0.0513543
$517$	−2.15828	−0.0949209
$518$	11.8836	0.522133
$519$	5.90307	0.259116
$520$	71.1110	3.11842
$521$	−17.9689	−0.787231	−0.393615	−	0.919275i	$-0.628776\pi$
$521$	−17.9689	−0.787231	−0.393615	+	0.919275i	$0.628776\pi$
$522$	−55.6574	−2.43606
$523$	4.78806	0.209367	0.104684	−	0.994506i	$-0.466617\pi$
$523$	4.78806	0.209367	0.104684	+	0.994506i	$0.466617\pi$
$524$	−35.9649	−1.57113
$525$	9.52928	0.415892
$526$	−14.2031	−0.619283
$527$	3.73592	0.162739
$528$	0.579181	0.0252056
$529$	−20.9021	−0.908788
$530$	−17.4322	−0.757208
$531$	−11.5503	−0.501242
$532$	1.75331	0.0760154
$533$	23.5404	1.01965
$534$	−8.03864	−0.347866
$535$	17.8574	0.772043
$536$	−7.65012	−0.330435
$537$	7.15363	0.308702
$538$	−63.8537	−2.75293
$539$	7.66405	0.330114
$540$	24.5004	1.05433
$541$	−44.3624	−1.90729	−0.953644	−	0.300938i	$-0.902700\pi$
$541$	−44.3624	−1.90729	−0.953644	+	0.300938i	$0.902700\pi$
$542$	43.7602	1.87966
$543$	1.46626	0.0629233
$544$	3.36531	0.144286
$545$	−28.8347	−1.23514
$546$	−15.3994	−0.659033
$547$	−11.8084	−0.504891	−0.252446	−	0.967611i	$-0.581235\pi$
$547$	−11.8084	−0.504891	−0.252446	+	0.967611i	$0.581235\pi$
$548$	−36.8948	−1.57607
$549$	29.8320	1.27320
$550$	−18.2119	−0.776556
$551$	−1.03094	−0.0439194
$552$	1.78157	0.0758286
$553$	−25.9058	−1.10163
$554$	34.6004	1.47003
$555$	1.51064	0.0641233
$556$	28.6806	1.21633
$557$	−10.9933	−0.465801	−0.232900	−	0.972501i	$-0.574822\pi$
$557$	−10.9933	−0.465801	−0.232900	+	0.972501i	$0.574822\pi$
$558$	25.6104	1.08417
$559$	−5.24999	−0.222051
$560$	−24.4234	−1.03208
$561$	0.323518	0.0136589
$562$	45.3162	1.91155
$563$	−35.1925	−1.48319	−0.741594	−	0.670849i	$-0.765930\pi$
$563$	−35.1925	−1.48319	−0.741594	+	0.670849i	$0.765930\pi$
$564$	−2.51773	−0.106015
$565$	27.0719	1.13892
$566$	26.3252	1.10653
$567$	30.8991	1.29764
$568$	7.65677	0.321271
$569$	15.1790	0.636335	0.318168	−	0.948034i	$-0.396933\pi$
$569$	15.1790	0.636335	0.318168	+	0.948034i	$0.396933\pi$
$570$	0.346504	0.0145135
$571$	23.5749	0.986580	0.493290	−	0.869865i	$-0.335794\pi$
$571$	23.5749	0.986580	0.493290	+	0.869865i	$0.335794\pi$
$572$	18.9305	0.791524
$573$	−6.54830	−0.273559
$574$	−40.6539	−1.69686
$575$	−11.1410	−0.464612
$576$	33.4366	1.39319
$577$	−19.0793	−0.794283	−0.397142	−	0.917757i	$-0.629998\pi$
$577$	−19.0793	−0.794283	−0.397142	+	0.917757i	$0.629998\pi$
$578$	−2.36766	−0.0984817
$579$	2.22994	0.0926733
$580$	104.297	4.33070
$581$	−68.9470	−2.86040
$582$	−0.0757539	−0.00314010
$583$	−2.06667	−0.0855925
$584$	28.1536	1.16500
$585$	54.1529	2.23895
$586$	71.1739	2.94017
$587$	21.4186	0.884039	0.442019	−	0.897005i	$-0.354262\pi$
$587$	21.4186	0.884039	0.442019	+	0.897005i	$0.354262\pi$
$588$	8.94046	0.368698
$589$	0.474378	0.0195464
$590$	33.6495	1.38533
$591$	7.16413	0.294693
$592$	−2.34648	−0.0964396
$593$	24.1564	0.991984	0.495992	−	0.868327i	$-0.334805\pi$
$593$	24.1564	0.991984	0.495992	+	0.868327i	$0.334805\pi$
$594$	4.51571	0.185282
$595$	−13.6424	−0.559284
$596$	−12.9508	−0.530484
$597$	−7.82068	−0.320079
$598$	18.0040	0.736236
$599$	12.1113	0.494853	0.247426	−	0.968907i	$-0.420415\pi$
$599$	12.1113	0.494853	0.247426	+	0.968907i	$0.420415\pi$
$600$	−9.46123	−0.386253
$601$	−35.2163	−1.43650	−0.718251	−	0.695784i	$-0.755057\pi$
$601$	−35.2163	−1.43650	−0.718251	+	0.695784i	$0.755057\pi$
$602$	9.06664	0.369529
$603$	−5.82576	−0.237243
$604$	−38.0328	−1.54753
$605$	−3.56257	−0.144839
$606$	−3.41865	−0.138873
$607$	−21.2597	−0.862904	−0.431452	−	0.902136i	$-0.641999\pi$
$607$	−21.2597	−0.862904	−0.431452	+	0.902136i	$0.641999\pi$
$608$	0.427319	0.0173301
$609$	−10.0584	−0.407588
$610$	−86.9092	−3.51885
$611$	−11.3309	−0.458401
$612$	−10.4400	−0.422014
$613$	25.5613	1.03241	0.516205	−	0.856465i	$-0.327344\pi$
$613$	25.5613	1.03241	0.516205	+	0.856465i	$0.327344\pi$
$614$	18.6744	0.753638
$615$	−5.16795	−0.208392
$616$	−14.5593	−0.586612
$617$	24.6577	0.992680	0.496340	−	0.868128i	$-0.334677\pi$
$617$	24.6577	0.992680	0.496340	+	0.868128i	$0.334677\pi$
$618$	−1.28074	−0.0515188
$619$	−42.6415	−1.71390	−0.856952	−	0.515395i	$-0.827645\pi$
$619$	−42.6415	−1.71390	−0.856952	+	0.515395i	$0.827645\pi$
$620$	−47.9915	−1.92738
$621$	2.76246	0.110854
$622$	63.5165	2.54678
$623$	40.1876	1.61008
$624$	3.04070	0.121725
$625$	−4.29393	−0.171757
$626$	14.9249	0.596519
$627$	0.0410796	0.00164056
$628$	−39.9768	−1.59525
$629$	−1.31069	−0.0522607
$630$	−93.5210	−3.72596
$631$	−18.4190	−0.733248	−0.366624	−	0.930369i	$-0.619486\pi$
$631$	−18.4190	−0.733248	−0.366624	+	0.930369i	$0.619486\pi$
$632$	25.7208	1.02312
$633$	7.31472	0.290734
$634$	29.5917	1.17524
$635$	23.7101	0.940908
$636$	−2.41086	−0.0955967
$637$	40.2362	1.59422
$638$	19.2231	0.761051
$639$	5.83083	0.230664
$640$	−73.4322	−2.90266
$641$	31.0170	1.22510	0.612549	−	0.790433i	$-0.290144\pi$
$641$	31.0170	1.22510	0.612549	+	0.790433i	$0.290144\pi$
$642$	3.83948	0.151532
$643$	−31.1975	−1.23031	−0.615155	−	0.788406i	$-0.710907\pi$
$643$	−31.1975	−1.23031	−0.615155	+	0.788406i	$0.710907\pi$
$644$	−19.9995	−0.788092
$645$	1.15256	0.0453819
$646$	−0.300640	−0.0118285
$647$	11.1884	0.439863	0.219932	−	0.975515i	$-0.429417\pi$
$647$	11.1884	0.439863	0.219932	+	0.975515i	$0.429417\pi$
$648$	−30.6784	−1.20516
$649$	3.98929	0.156593
$650$	−95.6121	−3.75022
$651$	4.62831	0.181398
$652$	44.5333	1.74406
$653$	−41.2351	−1.61366	−0.806828	−	0.590787i	$-0.798817\pi$
$653$	−41.2351	−1.61366	−0.806828	+	0.590787i	$0.798817\pi$
$654$	−6.19968	−0.242427
$655$	35.5336	1.38841
$656$	8.02735	0.313415
$657$	21.4397	0.836443
$658$	19.5683	0.762852
$659$	30.2085	1.17676	0.588378	−	0.808586i	$-0.299767\pi$
$659$	30.2085	1.17676	0.588378	+	0.808586i	$0.299767\pi$
$660$	−4.15590	−0.161768
$661$	−1.10256	−0.0428846	−0.0214423	−	0.999770i	$-0.506826\pi$
$661$	−1.10256	−0.0428846	−0.0214423	+	0.999770i	$0.506826\pi$
$662$	−32.2209	−1.25230
$663$	1.69847	0.0659630
$664$	68.4546	2.65655
$665$	−1.73228	−0.0671749
$666$	−8.98501	−0.348162
$667$	11.7597	0.455336
$668$	−8.02405	−0.310460
$669$	−4.52711	−0.175028
$670$	16.9721	0.655691
$671$	−10.3035	−0.397760
$672$	4.16918	0.160830
$673$	−29.5527	−1.13917	−0.569587	−	0.821931i	$-0.692897\pi$
$673$	−29.5527	−1.13917	−0.569587	+	0.821931i	$0.692897\pi$
$674$	12.4756	0.480542
$675$	−14.6704	−0.564664
$676$	52.5094	2.01959
$677$	−1.69304	−0.0650688	−0.0325344	−	0.999471i	$-0.510358\pi$
$677$	−1.69304	−0.0650688	−0.0325344	+	0.999471i	$0.510358\pi$
$678$	5.82066	0.223541
$679$	0.378717	0.0145338
$680$	13.5450	0.519426
$681$	5.71699	0.219076
$682$	−8.84538	−0.338707
$683$	12.0652	0.461662	0.230831	−	0.972994i	$-0.425855\pi$
$683$	12.0652	0.461662	0.230831	+	0.972994i	$0.425855\pi$
$684$	−1.32565	−0.0506876
$685$	36.4524	1.39277
$686$	−6.02069	−0.229871
$687$	2.08240	0.0794486
$688$	−1.79026	−0.0682530
$689$	−10.8500	−0.413351
$690$	−3.95249	−0.150469
$691$	−27.1863	−1.03422	−0.517108	−	0.855920i	$-0.672992\pi$
$691$	−27.1863	−1.03422	−0.517108	+	0.855920i	$0.672992\pi$
$692$	65.7934	2.50109
$693$	−11.0873	−0.421172
$694$	33.9547	1.28890
$695$	−28.3367	−1.07487
$696$	9.98660	0.378541
$697$	4.48390	0.169840
$698$	−55.1268	−2.08658
$699$	−4.87156	−0.184259
$700$	106.210	4.01436
$701$	−11.9224	−0.450302	−0.225151	−	0.974324i	$-0.572288\pi$
$701$	−11.9224	−0.450302	−0.225151	+	0.974324i	$0.572288\pi$
$702$	23.7075	0.894780
$703$	−0.166428	−0.00627697
$704$	−11.5484	−0.435248
$705$	2.48754	0.0936860
$706$	−34.8349	−1.31103
$707$	17.0908	0.642767
$708$	4.65369	0.174896
$709$	28.4323	1.06780	0.533898	−	0.845549i	$-0.320727\pi$
$709$	28.4323	1.06780	0.533898	+	0.845549i	$0.320727\pi$
$710$	−16.9869	−0.637508
$711$	19.5871	0.734573
$712$	−39.9006	−1.49534
$713$	−5.41112	−0.202648
$714$	−2.93322	−0.109773
$715$	−18.7035	−0.699471
$716$	79.7317	2.97971
$717$	5.02233	0.187562
$718$	−10.5966	−0.395462
$719$	35.8957	1.33868	0.669341	−	0.742955i	$-0.266576\pi$
$719$	35.8957	1.33868	0.669341	+	0.742955i	$0.266576\pi$
$720$	18.4663	0.688197
$721$	6.40280	0.238453
$722$	44.9474	1.67277
$723$	4.38813	0.163196
$724$	16.3424	0.607361
$725$	−62.4511	−2.31937
$726$	−0.765980	−0.0284282
$727$	41.9764	1.55682	0.778409	−	0.627757i	$-0.216027\pi$
$727$	41.9764	1.55682	0.778409	+	0.627757i	$0.216027\pi$
$728$	−76.4363	−2.83292
$729$	−21.5113	−0.796716
$730$	−62.4601	−2.31175
$731$	−1.00000	−0.0369863
$732$	−12.0194	−0.444251
$733$	−26.0953	−0.963854	−0.481927	−	0.876211i	$-0.660063\pi$
$733$	−26.0953	−0.963854	−0.481927	+	0.876211i	$0.660063\pi$
$734$	65.3384	2.41169
$735$	−8.83325	−0.325819
$736$	−4.87433	−0.179670
$737$	2.01212	0.0741174
$738$	30.7379	1.13148
$739$	−11.2800	−0.414942	−0.207471	−	0.978241i	$-0.566523\pi$
$739$	−11.2800	−0.414942	−0.207471	+	0.978241i	$0.566523\pi$
$740$	16.8371	0.618944
$741$	0.215667	0.00792274
$742$	18.7377	0.687883
$743$	23.1388	0.848881	0.424441	−	0.905456i	$-0.360471\pi$
$743$	23.1388	0.848881	0.424441	+	0.905456i	$0.360471\pi$
$744$	−4.59526	−0.168470
$745$	12.7955	0.468789
$746$	−34.2992	−1.25578
$747$	52.1300	1.90734
$748$	3.60581	0.131842
$749$	−19.1947	−0.701360
$750$	7.34589	0.268234
$751$	1.74184	0.0635606	0.0317803	−	0.999495i	$-0.489882\pi$
$751$	1.74184	0.0635606	0.0317803	+	0.999495i	$0.489882\pi$
$752$	−3.86388	−0.140901
$753$	−7.79847	−0.284192
$754$	100.921	3.67534
$755$	37.5767	1.36756
$756$	−26.3352	−0.957803
$757$	25.0903	0.911924	0.455962	−	0.889999i	$-0.349295\pi$
$757$	25.0903	0.911924	0.455962	+	0.889999i	$0.349295\pi$
$758$	−59.4586	−2.15963
$759$	−0.468585	−0.0170085
$760$	1.71991	0.0623876
$761$	7.21490	0.261540	0.130770	−	0.991413i	$-0.458255\pi$
$761$	7.21490	0.261540	0.130770	+	0.991413i	$0.458255\pi$
$762$	5.09786	0.184676
$763$	30.9941	1.12206
$764$	−72.9850	−2.64050
$765$	10.3148	0.372934
$766$	−85.1803	−3.07769
$767$	20.9438	0.756236
$768$	−8.31624	−0.300086
$769$	−16.1432	−0.582140	−0.291070	−	0.956702i	$-0.594011\pi$
$769$	−16.1432	−0.582140	−0.291070	+	0.956702i	$0.594011\pi$
$770$	32.3006	1.16403
$771$	4.76992	0.171785
$772$	24.8541	0.894520
$773$	7.29503	0.262384	0.131192	−	0.991357i	$-0.458120\pi$
$773$	7.29503	0.262384	0.131192	+	0.991357i	$0.458120\pi$
$774$	−6.85517	−0.246404
$775$	28.7364	1.03224
$776$	−0.376012	−0.0134980
$777$	−1.62377	−0.0582526
$778$	59.9990	2.15107
$779$	0.569355	0.0203993
$780$	−21.8185	−0.781226
$781$	−2.01387	−0.0720619
$782$	3.42933	0.122633
$783$	15.4850	0.553390
$784$	13.7206	0.490023
$785$	39.4974	1.40972
$786$	7.64000	0.272510
$787$	29.2562	1.04287	0.521436	−	0.853291i	$-0.325397\pi$
$787$	29.2562	1.04287	0.521436	+	0.853291i	$0.325397\pi$
$788$	79.8488	2.84449
$789$	1.94071	0.0690911
$790$	−57.0629	−2.03021
$791$	−29.0992	−1.03465
$792$	11.0081	0.391157
$793$	−54.0931	−1.92090
$794$	−77.7880	−2.76059
$795$	2.38195	0.0844790
$796$	−87.1664	−3.08953
$797$	−3.44401	−0.121993	−0.0609966	−	0.998138i	$-0.519428\pi$
$797$	−3.44401	−0.121993	−0.0609966	+	0.998138i	$0.519428\pi$
$798$	−0.372453	−0.0131847
$799$	−2.15828	−0.0763543
$800$	25.8857	0.915198
$801$	−30.3853	−1.07361
$802$	1.70215	0.0601049
$803$	−7.40491	−0.261314
$804$	2.34723	0.0827804
$805$	19.7597	0.696438
$806$	−46.4382	−1.63572
$807$	8.72500	0.307134
$808$	−16.9688	−0.596960
$809$	−38.5639	−1.35583	−0.677917	−	0.735138i	$-0.737117\pi$
$809$	−38.5639	−1.35583	−0.677917	+	0.735138i	$0.737117\pi$
$810$	68.0615	2.39144
$811$	−38.6514	−1.35724	−0.678618	−	0.734492i	$-0.737421\pi$
$811$	−38.6514	−1.35724	−0.678618	+	0.734492i	$0.737421\pi$
$812$	−112.108	−3.93421
$813$	−5.97941	−0.209707
$814$	3.10327	0.108770
$815$	−43.9992	−1.54123
$816$	0.579181	0.0202754
$817$	−0.126978	−0.00444239
$818$	17.2580	0.603413
$819$	−58.2083	−2.03396
$820$	−57.6000	−2.01148
$821$	−29.7449	−1.03811	−0.519053	−	0.854742i	$-0.673715\pi$
$821$	−29.7449	−1.03811	−0.519053	+	0.854742i	$0.673715\pi$
$822$	7.83753	0.273365
$823$	31.7561	1.10695	0.553474	−	0.832866i	$-0.313302\pi$
$823$	31.7561	1.10695	0.553474	+	0.832866i	$0.313302\pi$
$824$	−6.35707	−0.221459
$825$	2.48848	0.0866376
$826$	−36.1695	−1.25850
$827$	−33.6200	−1.16908	−0.584541	−	0.811364i	$-0.698726\pi$
$827$	−33.6200	−1.16908	−0.584541	+	0.811364i	$0.698726\pi$
$828$	15.1214	0.525505
$829$	−15.0016	−0.521026	−0.260513	−	0.965470i	$-0.583892\pi$
$829$	−15.0016	−0.521026	−0.260513	+	0.965470i	$0.583892\pi$
$830$	−151.870	−5.27148
$831$	−4.72781	−0.164006
$832$	−60.6292	−2.10194
$833$	7.66405	0.265544
$834$	−6.09260	−0.210970
$835$	7.92783	0.274354
$836$	0.457858	0.0158353
$837$	−7.12532	−0.246287
$838$	−74.1787	−2.56246
$839$	−15.6368	−0.539841	−0.269921	−	0.962883i	$-0.586998\pi$
$839$	−15.6368	−0.539841	−0.269921	+	0.962883i	$0.586998\pi$
$840$	16.7804	0.578980
$841$	36.9189	1.27307
$842$	−3.99844	−0.137795
$843$	−6.19203	−0.213265
$844$	81.5272	2.80628
$845$	−51.8797	−1.78472
$846$	−14.7954	−0.508675
$847$	3.82937	0.131579
$848$	−3.69987	−0.127054
$849$	−3.59708	−0.123451
$850$	−18.2119	−0.624662
$851$	1.89841	0.0650766
$852$	−2.34927	−0.0804847
$853$	24.6538	0.844132	0.422066	−	0.906565i	$-0.361305\pi$
$853$	24.6538	0.844132	0.422066	+	0.906565i	$0.361305\pi$
$854$	93.4176	3.19669
$855$	1.30976	0.0447927
$856$	19.0576	0.651377
$857$	−21.9258	−0.748970	−0.374485	−	0.927233i	$-0.622180\pi$
$857$	−21.9258	−0.748970	−0.374485	+	0.927233i	$0.622180\pi$
$858$	−4.02139	−0.137288
$859$	−55.9028	−1.90738	−0.953689	−	0.300795i	$-0.902748\pi$
$859$	−55.9028	−1.90738	−0.953689	+	0.300795i	$0.902748\pi$
$860$	12.8460	0.438044
$861$	5.55496	0.189313
$862$	−84.8971	−2.89161
$863$	−41.2749	−1.40501	−0.702507	−	0.711677i	$-0.747936\pi$
$863$	−41.2749	−1.40501	−0.702507	+	0.711677i	$0.747936\pi$
$864$	−6.41848	−0.218361
$865$	−65.0044	−2.21022
$866$	48.5264	1.64900
$867$	0.323518	0.0109872
$868$	51.5855	1.75092
$869$	−6.76504	−0.229488
$870$	−22.1557	−0.751150
$871$	10.5636	0.357934
$872$	−30.7727	−1.04210
$873$	−0.286343	−0.00969124
$874$	0.435448	0.0147293
$875$	−36.7243	−1.24151
$876$	−8.63816	−0.291857
$877$	−7.05612	−0.238268	−0.119134	−	0.992878i	$-0.538012\pi$
$877$	−7.05612	−0.238268	−0.119134	+	0.992878i	$0.538012\pi$
$878$	6.78226	0.228890
$879$	−9.72523	−0.328024
$880$	−6.37793	−0.215000
$881$	−9.13527	−0.307775	−0.153888	−	0.988088i	$-0.549179\pi$
$881$	−9.13527	−0.307775	−0.153888	+	0.988088i	$0.549179\pi$
$882$	52.5384	1.76906
$883$	−25.8631	−0.870363	−0.435181	−	0.900343i	$-0.643316\pi$
$883$	−25.8631	−0.870363	−0.435181	+	0.900343i	$0.643316\pi$
$884$	18.9305	0.636701
$885$	−4.59789	−0.154556
$886$	20.5473	0.690302
$887$	−31.0244	−1.04170	−0.520849	−	0.853649i	$-0.674385\pi$
$887$	−31.0244	−1.04170	−0.520849	+	0.853649i	$0.674385\pi$
$888$	1.61218	0.0541011
$889$	−25.4857	−0.854764
$890$	88.5213	2.96724
$891$	8.06898	0.270321
$892$	−50.4575	−1.68944
$893$	−0.274053	−0.00917083
$894$	2.75112	0.0920112
$895$	−78.7756	−2.63318
$896$	78.9314	2.63691
$897$	−2.46007	−0.0821392
$898$	31.5980	1.05444
$899$	−30.3321	−1.01163
$900$	−80.3040	−2.67680
$901$	−2.06667	−0.0688506
$902$	−10.6163	−0.353486
$903$	−1.23887	−0.0412270
$904$	28.8914	0.960914
$905$	−16.1464	−0.536726
$906$	8.07928	0.268416
$907$	32.6961	1.08566	0.542828	−	0.839844i	$-0.317354\pi$
$907$	32.6961	1.08566	0.542828	+	0.839844i	$0.317354\pi$
$908$	63.7195	2.11461
$909$	−12.9222	−0.428601
$910$	169.578	5.62145
$911$	−19.5306	−0.647079	−0.323539	−	0.946215i	$-0.604873\pi$
$911$	−19.5306	−0.647079	−0.323539	+	0.946215i	$0.604873\pi$
$912$	0.0735431	0.00243525
$913$	−18.0048	−0.595872
$914$	14.5013	0.479659
$915$	11.8753	0.392585
$916$	23.2097	0.766870
$917$	−38.1947	−1.26130
$918$	4.51571	0.149041
$919$	40.0416	1.32085	0.660426	−	0.750891i	$-0.270376\pi$
$919$	40.0416	1.32085	0.660426	+	0.750891i	$0.270376\pi$
$920$	−19.6186	−0.646806
$921$	−2.55168	−0.0840807
$922$	40.0063	1.31754
$923$	−10.5728	−0.348008
$924$	4.46713	0.146958
$925$	−10.0817	−0.331485
$926$	86.5504	2.84422
$927$	−4.84107	−0.159002
$928$	−27.3231	−0.896925
$929$	−32.3560	−1.06157	−0.530783	−	0.847508i	$-0.678102\pi$
$929$	−32.3560	−1.06157	−0.530783	+	0.847508i	$0.678102\pi$
$930$	10.1948	0.334301
$931$	0.973163	0.0318941
$932$	−54.2967	−1.77855
$933$	−8.67892	−0.284135
$934$	18.5844	0.608101
$935$	−3.56257	−0.116509
$936$	57.7926	1.88901
$937$	−51.6846	−1.68846	−0.844232	−	0.535978i	$-0.819943\pi$
$937$	−51.6846	−1.68846	−0.844232	+	0.535978i	$0.819943\pi$
$938$	−18.2432	−0.595660
$939$	−2.03934	−0.0665515
$940$	27.7252	0.904295
$941$	−26.3737	−0.859757	−0.429879	−	0.902887i	$-0.641444\pi$
$941$	−26.3737	−0.859757	−0.429879	+	0.902887i	$0.641444\pi$
$942$	8.49225	0.276692
$943$	−6.49450	−0.211490
$944$	7.14187	0.232448
$945$	26.0194	0.846412
$946$	2.36766	0.0769793
$947$	40.0907	1.30277	0.651387	−	0.758746i	$-0.274188\pi$
$947$	40.0907	1.30277	0.651387	+	0.758746i	$0.274188\pi$
$948$	−7.89173	−0.256311
$949$	−38.8757	−1.26196
$950$	−2.31250	−0.0750274
$951$	−4.04342	−0.131117
$952$	−14.5593	−0.471870
$953$	−38.3185	−1.24126	−0.620630	−	0.784104i	$-0.713123\pi$
$953$	−38.3185	−1.24126	−0.620630	+	0.784104i	$0.713123\pi$
$954$	−14.1673	−0.458685
$955$	72.1098	2.33342
$956$	55.9771	1.81043
$957$	−2.62666	−0.0849078
$958$	1.20533	0.0389425
$959$	−39.1822	−1.26526
$960$	13.3102	0.429585
$961$	−17.0429	−0.549772
$962$	16.2921	0.525280
$963$	14.5129	0.467671
$964$	48.9085	1.57524
$965$	−24.5561	−0.790489
$966$	4.24849	0.136693
$967$	−25.4003	−0.816817	−0.408409	−	0.912799i	$-0.633916\pi$
$967$	−25.4003	−0.816817	−0.408409	+	0.912799i	$0.633916\pi$
$968$	−3.80202	−0.122201
$969$	0.0410796	0.00131967
$970$	0.834201	0.0267846
$971$	−42.1019	−1.35111	−0.675557	−	0.737308i	$-0.736097\pi$
$971$	−42.1019	−1.35111	−0.675557	+	0.737308i	$0.736097\pi$
$972$	30.0444	0.963673
$973$	30.4588	0.976463
$974$	−39.1619	−1.25483
$975$	13.0645	0.418398
$976$	−18.4459	−0.590437
$977$	−0.0885699	−0.00283360	−0.00141680	−	0.999999i	$-0.500451\pi$
$977$	−0.0885699	−0.00283360	−0.00141680	+	0.999999i	$0.500451\pi$
$978$	−9.46017	−0.302503
$979$	10.4946	0.335408
$980$	−98.4521	−3.14494
$981$	−23.4342	−0.748198
$982$	17.4226	0.555976
$983$	0.981025	0.0312898	0.0156449	−	0.999878i	$-0.495020\pi$
$983$	0.981025	0.0312898	0.0156449	+	0.999878i	$0.495020\pi$
$984$	−5.51529	−0.175821
$985$	−78.8912	−2.51368
$986$	19.2231	0.612189
$987$	−2.67382	−0.0851087
$988$	2.40375	0.0764735
$989$	1.44840	0.0460566
$990$	−24.4220	−0.776184
$991$	−3.34524	−0.106265	−0.0531325	−	0.998587i	$-0.516921\pi$
$991$	−3.34524	−0.106265	−0.0531325	+	0.998587i	$0.516921\pi$
$992$	12.5725	0.399178
$993$	4.40267	0.139714
$994$	18.2590	0.579141
$995$	86.1211	2.73022
$996$	−21.0034	−0.665519
$997$	−40.8279	−1.29303	−0.646516	−	0.762900i	$-0.723775\pi$
$997$	−40.8279	−1.29303	−0.646516	+	0.762900i	$0.723775\pi$
$998$	−65.3410	−2.06833
$999$	2.49981	0.0790905

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.c.1.8	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.c.1.8	✓	60	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)

\(f(q)\)	\(=\)	\(q-2.36766 q^{2} +0.323518 q^{3} +3.60581 q^{4} -3.56257 q^{5} -0.765980 q^{6} +3.82937 q^{7} -3.80202 q^{8} -2.89534 q^{9} +O(q^{10})\)	\(q-2.36766 q^{2} +0.323518 q^{3} +3.60581 q^{4} -3.56257 q^{5} -0.765980 q^{6} +3.82937 q^{7} -3.80202 q^{8} -2.89534 q^{9} +8.43496 q^{10} +1.00000 q^{11} +1.16655 q^{12} +5.24999 q^{13} -9.06664 q^{14} -1.15256 q^{15} +1.79026 q^{16} +1.00000 q^{17} +6.85517 q^{18} +0.126978 q^{19} -12.8460 q^{20} +1.23887 q^{21} -2.36766 q^{22} -1.44840 q^{23} -1.23002 q^{24} +7.69192 q^{25} -12.4302 q^{26} -1.90725 q^{27} +13.8080 q^{28} -8.11905 q^{29} +2.72886 q^{30} +3.73592 q^{31} +3.36531 q^{32} +0.323518 q^{33} -2.36766 q^{34} -13.6424 q^{35} -10.4400 q^{36} -1.31069 q^{37} -0.300640 q^{38} +1.69847 q^{39} +13.5450 q^{40} +4.48390 q^{41} -2.93322 q^{42} -1.00000 q^{43} +3.60581 q^{44} +10.3148 q^{45} +3.42933 q^{46} -2.15828 q^{47} +0.579181 q^{48} +7.66405 q^{49} -18.2119 q^{50} +0.323518 q^{51} +18.9305 q^{52} -2.06667 q^{53} +4.51571 q^{54} -3.56257 q^{55} -14.5593 q^{56} +0.0410796 q^{57} +19.2231 q^{58} +3.98929 q^{59} -4.15590 q^{60} -10.3035 q^{61} -8.84538 q^{62} -11.0873 q^{63} -11.5484 q^{64} -18.7035 q^{65} -0.765980 q^{66} +2.01212 q^{67} +3.60581 q^{68} -0.468585 q^{69} +32.3006 q^{70} -2.01387 q^{71} +11.0081 q^{72} -7.40491 q^{73} +3.10327 q^{74} +2.48848 q^{75} +0.457858 q^{76} +3.82937 q^{77} -4.02139 q^{78} -6.76504 q^{79} -6.37793 q^{80} +8.06898 q^{81} -10.6163 q^{82} -18.0048 q^{83} +4.46713 q^{84} -3.56257 q^{85} +2.36766 q^{86} -2.62666 q^{87} -3.80202 q^{88} +10.4946 q^{89} -24.4220 q^{90} +20.1042 q^{91} -5.22267 q^{92} +1.20864 q^{93} +5.11007 q^{94} -0.452367 q^{95} +1.08874 q^{96} +0.0988980 q^{97} -18.1459 q^{98} -2.89534 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * q^99

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