LMFDB - Embedded newform 4015.2.a.g.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.962434 q^{2} +2.32544 q^{3} -1.07372 q^{4} -1.00000 q^{5} -2.23808 q^{6} +2.98112 q^{7} +2.95825 q^{8} +2.40766 q^{9} +O(q^{10})$	\(q-0.962434 q^{2} +2.32544 q^{3} -1.07372 q^{4} -1.00000 q^{5} -2.23808 q^{6} +2.98112 q^{7} +2.95825 q^{8} +2.40766 q^{9} +0.962434 q^{10} -1.00000 q^{11} -2.49687 q^{12} -0.728112 q^{13} -2.86913 q^{14} -2.32544 q^{15} -0.699685 q^{16} +0.869989 q^{17} -2.31722 q^{18} -5.99563 q^{19} +1.07372 q^{20} +6.93241 q^{21} +0.962434 q^{22} -4.15988 q^{23} +6.87924 q^{24} +1.00000 q^{25} +0.700760 q^{26} -1.37744 q^{27} -3.20089 q^{28} -0.861362 q^{29} +2.23808 q^{30} -6.34355 q^{31} -5.24311 q^{32} -2.32544 q^{33} -0.837307 q^{34} -2.98112 q^{35} -2.58516 q^{36} -0.518033 q^{37} +5.77040 q^{38} -1.69318 q^{39} -2.95825 q^{40} +0.372643 q^{41} -6.67199 q^{42} -9.97481 q^{43} +1.07372 q^{44} -2.40766 q^{45} +4.00361 q^{46} +8.16208 q^{47} -1.62707 q^{48} +1.88708 q^{49} -0.962434 q^{50} +2.02310 q^{51} +0.781789 q^{52} -0.188379 q^{53} +1.32570 q^{54} +1.00000 q^{55} +8.81891 q^{56} -13.9425 q^{57} +0.829004 q^{58} -2.73614 q^{59} +2.49687 q^{60} -4.92422 q^{61} +6.10525 q^{62} +7.17754 q^{63} +6.44552 q^{64} +0.728112 q^{65} +2.23808 q^{66} +10.4943 q^{67} -0.934124 q^{68} -9.67354 q^{69} +2.86913 q^{70} -14.3880 q^{71} +7.12248 q^{72} -1.00000 q^{73} +0.498573 q^{74} +2.32544 q^{75} +6.43763 q^{76} -2.98112 q^{77} +1.62957 q^{78} -15.9628 q^{79} +0.699685 q^{80} -10.4261 q^{81} -0.358645 q^{82} +8.81283 q^{83} -7.44347 q^{84} -0.869989 q^{85} +9.60010 q^{86} -2.00304 q^{87} -2.95825 q^{88} -1.13920 q^{89} +2.31722 q^{90} -2.17059 q^{91} +4.46655 q^{92} -14.7515 q^{93} -7.85547 q^{94} +5.99563 q^{95} -12.1925 q^{96} +5.75100 q^{97} -1.81619 q^{98} -2.40766 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) $ 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * 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 $

$2$	−0.962434	−0.680544	−0.340272	−	0.940327i	$-0.610519\pi$
$2$	−0.962434	−0.680544	−0.340272	+	0.940327i	$0.610519\pi$
$3$	2.32544	1.34259	0.671296	−	0.741189i	$-0.265738\pi$
$3$	2.32544	1.34259	0.671296	+	0.741189i	$0.265738\pi$
$4$	−1.07372	−0.536860
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.23808	−0.913693
$7$	2.98112	1.12676	0.563379	−	0.826199i	$-0.309501\pi$
$7$	2.98112	1.12676	0.563379	+	0.826199i	$0.309501\pi$
$8$	2.95825	1.04590
$9$	2.40766	0.802554
$10$	0.962434	0.304348
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.49687	−0.720784
$13$	−0.728112	−0.201942	−0.100971	−	0.994889i	$-0.532195\pi$
$13$	−0.728112	−0.201942	−0.100971	+	0.994889i	$0.532195\pi$
$14$	−2.86913	−0.766808
$15$	−2.32544	−0.600426
$16$	−0.699685	−0.174921
$17$	0.869989	0.211003	0.105502	−	0.994419i	$-0.466355\pi$
$17$	0.869989	0.211003	0.105502	+	0.994419i	$0.466355\pi$
$18$	−2.31722	−0.546174
$19$	−5.99563	−1.37549	−0.687746	−	0.725952i	$-0.741400\pi$
$19$	−5.99563	−1.37549	−0.687746	+	0.725952i	$0.741400\pi$
$20$	1.07372	0.240091
$21$	6.93241	1.51278
$22$	0.962434	0.205192
$23$	−4.15988	−0.867395	−0.433697	−	0.901059i	$-0.642791\pi$
$23$	−4.15988	−0.867395	−0.433697	+	0.901059i	$0.642791\pi$
$24$	6.87924	1.40422
$25$	1.00000	0.200000
$26$	0.700760	0.137430
$27$	−1.37744	−0.265089
$28$	−3.20089	−0.604911
$29$	−0.861362	−0.159951	−0.0799754	−	0.996797i	$-0.525484\pi$
$29$	−0.861362	−0.159951	−0.0799754	+	0.996797i	$0.525484\pi$
$30$	2.23808	0.408616
$31$	−6.34355	−1.13934	−0.569668	−	0.821875i	$-0.692928\pi$
$31$	−6.34355	−1.13934	−0.569668	+	0.821875i	$0.692928\pi$
$32$	−5.24311	−0.926859
$33$	−2.32544	−0.404807
$34$	−0.837307	−0.143597
$35$	−2.98112	−0.503901
$36$	−2.58516	−0.430859
$37$	−0.518033	−0.0851642	−0.0425821	−	0.999093i	$-0.513558\pi$
$37$	−0.518033	−0.0851642	−0.0425821	+	0.999093i	$0.513558\pi$
$38$	5.77040	0.936082
$39$	−1.69318	−0.271126
$40$	−2.95825	−0.467741
$41$	0.372643	0.0581971	0.0290986	−	0.999577i	$-0.490736\pi$
$41$	0.372643	0.0581971	0.0290986	+	0.999577i	$0.490736\pi$
$42$	−6.67199	−1.02951
$43$	−9.97481	−1.52114	−0.760572	−	0.649253i	$-0.775081\pi$
$43$	−9.97481	−1.52114	−0.760572	+	0.649253i	$0.775081\pi$
$44$	1.07372	0.161869
$45$	−2.40766	−0.358913
$46$	4.00361	0.590300
$47$	8.16208	1.19056	0.595281	−	0.803518i	$-0.297041\pi$
$47$	8.16208	1.19056	0.595281	+	0.803518i	$0.297041\pi$
$48$	−1.62707	−0.234848
$49$	1.88708	0.269583
$50$	−0.962434	−0.136109
$51$	2.02310	0.283291
$52$	0.781789	0.108415
$53$	−0.188379	−0.0258758	−0.0129379	−	0.999916i	$-0.504118\pi$
$53$	−0.188379	−0.0258758	−0.0129379	+	0.999916i	$0.504118\pi$
$54$	1.32570	0.180405
$55$	1.00000	0.134840
$56$	8.81891	1.17848
$57$	−13.9425	−1.84672
$58$	0.829004	0.108854
$59$	−2.73614	−0.356216	−0.178108	−	0.984011i	$-0.556998\pi$
$59$	−2.73614	−0.356216	−0.178108	+	0.984011i	$0.556998\pi$
$60$	2.49687	0.322344
$61$	−4.92422	−0.630482	−0.315241	−	0.949012i	$-0.602085\pi$
$61$	−4.92422	−0.630482	−0.315241	+	0.949012i	$0.602085\pi$
$62$	6.10525	0.775368
$63$	7.17754	0.904285
$64$	6.44552	0.805690
$65$	0.728112	0.0903112
$66$	2.23808	0.275489
$67$	10.4943	1.28209	0.641044	−	0.767504i	$-0.278502\pi$
$67$	10.4943	1.28209	0.641044	+	0.767504i	$0.278502\pi$
$68$	−0.934124	−0.113279
$69$	−9.67354	−1.16456
$70$	2.86913	0.342927
$71$	−14.3880	−1.70754	−0.853769	−	0.520653i	$-0.825689\pi$
$71$	−14.3880	−1.70754	−0.853769	+	0.520653i	$0.825689\pi$
$72$	7.12248	0.839392
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	0.498573	0.0579580
$75$	2.32544	0.268518
$76$	6.43763	0.738446
$77$	−2.98112	−0.339730
$78$	1.62957	0.184513
$79$	−15.9628	−1.79595	−0.897977	−	0.440043i	$-0.854963\pi$
$79$	−15.9628	−1.79595	−0.897977	+	0.440043i	$0.854963\pi$
$80$	0.699685	0.0782272
$81$	−10.4261	−1.15846
$82$	−0.358645	−0.0396057
$83$	8.81283	0.967334	0.483667	−	0.875252i	$-0.339305\pi$
$83$	8.81283	0.967334	0.483667	+	0.875252i	$0.339305\pi$
$84$	−7.44347	−0.812149
$85$	−0.869989	−0.0943635
$86$	9.60010	1.03521
$87$	−2.00304	−0.214749
$88$	−2.95825	−0.315351
$89$	−1.13920	−0.120755	−0.0603773	−	0.998176i	$-0.519230\pi$
$89$	−1.13920	−0.120755	−0.0603773	+	0.998176i	$0.519230\pi$
$90$	2.31722	0.244256
$91$	−2.17059	−0.227540
$92$	4.46655	0.465670
$93$	−14.7515	−1.52966
$94$	−7.85547	−0.810229
$95$	5.99563	0.615138
$96$	−12.1925	−1.24439
$97$	5.75100	0.583926	0.291963	−	0.956430i	$-0.405692\pi$
$97$	5.75100	0.583926	0.291963	+	0.956430i	$0.405692\pi$
$98$	−1.81619	−0.183463
$99$	−2.40766	−0.241979
$100$	−1.07372	−0.107372
$101$	−11.7113	−1.16532	−0.582659	−	0.812716i	$-0.697988\pi$
$101$	−11.7113	−1.16532	−0.582659	+	0.812716i	$0.697988\pi$
$102$	−1.94711	−0.192792
$103$	15.9047	1.56713	0.783567	−	0.621308i	$-0.213398\pi$
$103$	15.9047	1.56713	0.783567	+	0.621308i	$0.213398\pi$
$104$	−2.15394	−0.211211
$105$	−6.93241	−0.676534
$106$	0.181302	0.0176096
$107$	1.11583	0.107871	0.0539356	−	0.998544i	$-0.482823\pi$
$107$	1.11583	0.107871	0.0539356	+	0.998544i	$0.482823\pi$
$108$	1.47899	0.142316
$109$	6.93234	0.663998	0.331999	−	0.943280i	$-0.392277\pi$
$109$	6.93234	0.663998	0.331999	+	0.943280i	$0.392277\pi$
$110$	−0.962434	−0.0917645
$111$	−1.20465	−0.114341
$112$	−2.08585	−0.197094
$113$	−10.8137	−1.01727	−0.508634	−	0.860983i	$-0.669849\pi$
$113$	−10.8137	−1.01727	−0.508634	+	0.860983i	$0.669849\pi$
$114$	13.4187	1.25678
$115$	4.15988	0.387911
$116$	0.924861	0.0858712
$117$	−1.75305	−0.162069
$118$	2.63336	0.242420
$119$	2.59354	0.237750
$120$	−6.87924	−0.627986
$121$	1.00000	0.0909091
$122$	4.73924	0.429071
$123$	0.866559	0.0781350
$124$	6.81120	0.611664
$125$	−1.00000	−0.0894427
$126$	−6.90791	−0.615405
$127$	20.0410	1.77835	0.889175	−	0.457567i	$-0.151279\pi$
$127$	20.0410	1.77835	0.889175	+	0.457567i	$0.151279\pi$
$128$	4.28283	0.378552
$129$	−23.1958	−2.04228
$130$	−0.700760	−0.0614607
$131$	−1.80065	−0.157323	−0.0786616	−	0.996901i	$-0.525065\pi$
$131$	−1.80065	−0.157323	−0.0786616	+	0.996901i	$0.525065\pi$
$132$	2.49687	0.217325
$133$	−17.8737	−1.54985
$134$	−10.1001	−0.872517
$135$	1.37744	0.118551
$136$	2.57365	0.220688
$137$	5.01593	0.428539	0.214270	−	0.976775i	$-0.431263\pi$
$137$	5.01593	0.428539	0.214270	+	0.976775i	$0.431263\pi$
$138$	9.31015	0.792533
$139$	2.91029	0.246848	0.123424	−	0.992354i	$-0.460613\pi$
$139$	2.91029	0.246848	0.123424	+	0.992354i	$0.460613\pi$
$140$	3.20089	0.270525
$141$	18.9804	1.59844
$142$	13.8475	1.16205
$143$	0.728112	0.0608878
$144$	−1.68461	−0.140384
$145$	0.861362	0.0715322
$146$	0.962434	0.0796516
$147$	4.38829	0.361940
$148$	0.556223	0.0457212
$149$	−14.4424	−1.18316	−0.591582	−	0.806244i	$-0.701497\pi$
$149$	−14.4424	−1.18316	−0.591582	+	0.806244i	$0.701497\pi$
$150$	−2.23808	−0.182739
$151$	14.6359	1.19105	0.595525	−	0.803337i	$-0.296944\pi$
$151$	14.6359	1.19105	0.595525	+	0.803337i	$0.296944\pi$
$152$	−17.7366	−1.43863
$153$	2.09464	0.169342
$154$	2.86913	0.231201
$155$	6.34355	0.509526
$156$	1.81800	0.145557
$157$	15.9332	1.27161	0.635804	−	0.771851i	$-0.280669\pi$
$157$	15.9332	1.27161	0.635804	+	0.771851i	$0.280669\pi$
$158$	15.3631	1.22223
$159$	−0.438064	−0.0347407
$160$	5.24311	0.414504
$161$	−12.4011	−0.977344
$162$	10.0345	0.788383
$163$	−10.9228	−0.855539	−0.427769	−	0.903888i	$-0.640700\pi$
$163$	−10.9228	−0.855539	−0.427769	+	0.903888i	$0.640700\pi$
$164$	−0.400115	−0.0312437
$165$	2.32544	0.181035
$166$	−8.48178	−0.658313
$167$	−11.8615	−0.917869	−0.458934	−	0.888470i	$-0.651769\pi$
$167$	−11.8615	−0.917869	−0.458934	+	0.888470i	$0.651769\pi$
$168$	20.5078	1.58221
$169$	−12.4699	−0.959219
$170$	0.837307	0.0642185
$171$	−14.4355	−1.10391
$172$	10.7102	0.816642
$173$	7.19662	0.547149	0.273574	−	0.961851i	$-0.411794\pi$
$173$	7.19662	0.547149	0.273574	+	0.961851i	$0.411794\pi$
$174$	1.92780	0.146146
$175$	2.98112	0.225352
$176$	0.699685	0.0527408
$177$	−6.36273	−0.478252
$178$	1.09640	0.0821788
$179$	−2.50017	−0.186871	−0.0934356	−	0.995625i	$-0.529785\pi$
$179$	−2.50017	−0.186871	−0.0934356	+	0.995625i	$0.529785\pi$
$180$	2.58516	0.192686
$181$	1.90127	0.141320	0.0706602	−	0.997500i	$-0.477489\pi$
$181$	1.90127	0.141320	0.0706602	+	0.997500i	$0.477489\pi$
$182$	2.08905	0.154851
$183$	−11.4510	−0.846480
$184$	−12.3060	−0.907209
$185$	0.518033	0.0380866
$186$	14.1974	1.04100
$187$	−0.869989	−0.0636199
$188$	−8.76379	−0.639165
$189$	−4.10632	−0.298691
$190$	−5.77040	−0.418629
$191$	−26.6673	−1.92958	−0.964790	−	0.263023i	$-0.915281\pi$
$191$	−26.6673	−1.92958	−0.964790	+	0.263023i	$0.915281\pi$
$192$	14.9887	1.08171
$193$	−19.0972	−1.37465	−0.687323	−	0.726351i	$-0.741214\pi$
$193$	−19.0972	−1.37465	−0.687323	+	0.726351i	$0.741214\pi$
$194$	−5.53496	−0.397387
$195$	1.69318	0.121251
$196$	−2.02620	−0.144728
$197$	−3.58147	−0.255169	−0.127584	−	0.991828i	$-0.540722\pi$
$197$	−3.58147	−0.255169	−0.127584	+	0.991828i	$0.540722\pi$
$198$	2.31722	0.164678
$199$	−7.20264	−0.510582	−0.255291	−	0.966864i	$-0.582171\pi$
$199$	−7.20264	−0.510582	−0.255291	+	0.966864i	$0.582171\pi$
$200$	2.95825	0.209180
$201$	24.4040	1.72132
$202$	11.2714	0.793051
$203$	−2.56782	−0.180226
$204$	−2.17225	−0.152088
$205$	−0.372643	−0.0260265
$206$	−15.3072	−1.06650
$207$	−10.0156	−0.696131
$208$	0.509449	0.0353240
$209$	5.99563	0.414726
$210$	6.67199	0.460411
$211$	3.69317	0.254248	0.127124	−	0.991887i	$-0.459425\pi$
$211$	3.69317	0.254248	0.127124	+	0.991887i	$0.459425\pi$
$212$	0.202266	0.0138917
$213$	−33.4583	−2.29253
$214$	−1.07391	−0.0734110
$215$	9.97481	0.680276
$216$	−4.07482	−0.277257
$217$	−18.9109	−1.28376
$218$	−6.67192	−0.451880
$219$	−2.32544	−0.157139
$220$	−1.07372	−0.0723902
$221$	−0.633449	−0.0426104
$222$	1.15940	0.0778139
$223$	2.09882	0.140547	0.0702736	−	0.997528i	$-0.477613\pi$
$223$	2.09882	0.140547	0.0702736	+	0.997528i	$0.477613\pi$
$224$	−15.6303	−1.04435
$225$	2.40766	0.160511
$226$	10.4075	0.692296
$227$	29.7464	1.97434	0.987170	−	0.159673i	$-0.0510439\pi$
$227$	29.7464	1.97434	0.987170	+	0.159673i	$0.0510439\pi$
$228$	14.9703	0.991432
$229$	−9.39125	−0.620591	−0.310296	−	0.950640i	$-0.600428\pi$
$229$	−9.39125	−0.620591	−0.310296	+	0.950640i	$0.600428\pi$
$230$	−4.00361	−0.263990
$231$	−6.93241	−0.456119
$232$	−2.54813	−0.167293
$233$	−28.9544	−1.89686	−0.948432	−	0.316981i	$-0.897331\pi$
$233$	−28.9544	−1.89686	−0.948432	+	0.316981i	$0.897331\pi$
$234$	1.68720	0.110295
$235$	−8.16208	−0.532435
$236$	2.93785	0.191238
$237$	−37.1205	−2.41123
$238$	−2.49611	−0.161799
$239$	11.7425	0.759559	0.379780	−	0.925077i	$-0.376000\pi$
$239$	11.7425	0.759559	0.379780	+	0.925077i	$0.376000\pi$
$240$	1.62707	0.105027
$241$	6.15260	0.396324	0.198162	−	0.980169i	$-0.436503\pi$
$241$	6.15260	0.396324	0.198162	+	0.980169i	$0.436503\pi$
$242$	−0.962434	−0.0618676
$243$	−20.1130	−1.29025
$244$	5.28723	0.338481
$245$	−1.88708	−0.120561
$246$	−0.834006	−0.0531743
$247$	4.36549	0.277770
$248$	−18.7658	−1.19163
$249$	20.4937	1.29874
$250$	0.962434	0.0608697
$251$	−20.7015	−1.30667	−0.653335	−	0.757069i	$-0.726630\pi$
$251$	−20.7015	−1.30667	−0.653335	+	0.757069i	$0.726630\pi$
$252$	−7.70666	−0.485474
$253$	4.15988	0.261529
$254$	−19.2881	−1.21025
$255$	−2.02310	−0.126692
$256$	−17.0130	−1.06331
$257$	9.47587	0.591088	0.295544	−	0.955329i	$-0.404499\pi$
$257$	9.47587	0.591088	0.295544	+	0.955329i	$0.404499\pi$
$258$	22.3244	1.38986
$259$	−1.54432	−0.0959594
$260$	−0.781789	−0.0484845
$261$	−2.07387	−0.128369
$262$	1.73300	0.107065
$263$	−24.3493	−1.50144	−0.750722	−	0.660618i	$-0.770294\pi$
$263$	−24.3493	−1.50144	−0.750722	+	0.660618i	$0.770294\pi$
$264$	−6.87924	−0.423388
$265$	0.188379	0.0115720
$266$	17.2023	1.05474
$267$	−2.64913	−0.162124
$268$	−11.2680	−0.688302
$269$	−2.38243	−0.145259	−0.0726297	−	0.997359i	$-0.523139\pi$
$269$	−2.38243	−0.145259	−0.0726297	+	0.997359i	$0.523139\pi$
$270$	−1.32570	−0.0806794
$271$	−5.44739	−0.330906	−0.165453	−	0.986218i	$-0.552909\pi$
$271$	−5.44739	−0.330906	−0.165453	+	0.986218i	$0.552909\pi$
$272$	−0.608718	−0.0369090
$273$	−5.04758	−0.305493
$274$	−4.82750	−0.291640
$275$	−1.00000	−0.0603023
$276$	10.3867	0.625204
$277$	−23.4286	−1.40769	−0.703845	−	0.710354i	$-0.748535\pi$
$277$	−23.4286	−1.40769	−0.703845	+	0.710354i	$0.748535\pi$
$278$	−2.80097	−0.167991
$279$	−15.2731	−0.914379
$280$	−8.81891	−0.527031
$281$	−12.4511	−0.742771	−0.371385	−	0.928479i	$-0.621117\pi$
$281$	−12.4511	−0.742771	−0.371385	+	0.928479i	$0.621117\pi$
$282$	−18.2674	−1.08781
$283$	27.7921	1.65207	0.826033	−	0.563622i	$-0.190592\pi$
$283$	27.7921	1.65207	0.826033	+	0.563622i	$0.190592\pi$
$284$	15.4486	0.916708
$285$	13.9425	0.825880
$286$	−0.700760	−0.0414368
$287$	1.11089	0.0655740
$288$	−12.6236	−0.743855
$289$	−16.2431	−0.955478
$290$	−0.829004	−0.0486808
$291$	13.3736	0.783975
$292$	1.07372	0.0628347
$293$	−8.78817	−0.513410	−0.256705	−	0.966490i	$-0.582637\pi$
$293$	−8.78817	−0.513410	−0.256705	+	0.966490i	$0.582637\pi$
$294$	−4.22344	−0.246316
$295$	2.73614	0.159304
$296$	−1.53247	−0.0890733
$297$	1.37744	0.0799273
$298$	13.8998	0.805196
$299$	3.02886	0.175163
$300$	−2.49687	−0.144157
$301$	−29.7361	−1.71396
$302$	−14.0861	−0.810561
$303$	−27.2339	−1.56455
$304$	4.19505	0.240603
$305$	4.92422	0.281960
$306$	−2.01595	−0.115244
$307$	22.2874	1.27201	0.636004	−	0.771686i	$-0.280586\pi$
$307$	22.2874	1.27201	0.636004	+	0.771686i	$0.280586\pi$
$308$	3.20089	0.182388
$309$	36.9853	2.10402
$310$	−6.10525	−0.346755
$311$	18.0753	1.02495	0.512477	−	0.858701i	$-0.328728\pi$
$311$	18.0753	1.02495	0.512477	+	0.858701i	$0.328728\pi$
$312$	−5.00886	−0.283571
$313$	−0.728738	−0.0411907	−0.0205953	−	0.999788i	$-0.506556\pi$
$313$	−0.728738	−0.0411907	−0.0205953	+	0.999788i	$0.506556\pi$
$314$	−15.3347	−0.865385
$315$	−7.17754	−0.404408
$316$	17.1396	0.964176
$317$	23.6434	1.32794	0.663972	−	0.747758i	$-0.268870\pi$
$317$	23.6434	1.32794	0.663972	+	0.747758i	$0.268870\pi$
$318$	0.421608	0.0236426
$319$	0.861362	0.0482270
$320$	−6.44552	−0.360315
$321$	2.59479	0.144827
$322$	11.9352	0.665125
$323$	−5.21613	−0.290233
$324$	11.1948	0.621931
$325$	−0.728112	−0.0403884
$326$	10.5125	0.582232
$327$	16.1207	0.891478
$328$	1.10237	0.0608684
$329$	24.3321	1.34147
$330$	−2.23808	−0.123202
$331$	−21.4676	−1.17997	−0.589983	−	0.807416i	$-0.700866\pi$
$331$	−21.4676	−1.17997	−0.589983	+	0.807416i	$0.700866\pi$
$332$	−9.46252	−0.519323
$333$	−1.24725	−0.0683489
$334$	11.4159	0.624650
$335$	−10.4943	−0.573367
$336$	−4.85051	−0.264617
$337$	35.0838	1.91114	0.955569	−	0.294768i	$-0.0952425\pi$
$337$	35.0838	1.91114	0.955569	+	0.294768i	$0.0952425\pi$
$338$	12.0014	0.652791
$339$	−25.1466	−1.36578
$340$	0.934124	0.0506600
$341$	6.34355	0.343523
$342$	13.8932	0.751257
$343$	−15.2422	−0.823003
$344$	−29.5080	−1.59097
$345$	9.67354	0.520806
$346$	−6.92627	−0.372359
$347$	−25.2700	−1.35656	−0.678282	−	0.734801i	$-0.737275\pi$
$347$	−25.2700	−1.35656	−0.678282	+	0.734801i	$0.737275\pi$
$348$	2.15071	0.115290
$349$	−3.55798	−0.190454	−0.0952271	−	0.995456i	$-0.530358\pi$
$349$	−3.55798	−0.190454	−0.0952271	+	0.995456i	$0.530358\pi$
$350$	−2.86913	−0.153362
$351$	1.00293	0.0535326
$352$	5.24311	0.279459
$353$	1.73469	0.0923281	0.0461640	−	0.998934i	$-0.485300\pi$
$353$	1.73469	0.0923281	0.0461640	+	0.998934i	$0.485300\pi$
$354$	6.12371	0.325472
$355$	14.3880	0.763634
$356$	1.22318	0.0648283
$357$	6.03112	0.319201
$358$	2.40624	0.127174
$359$	−8.43334	−0.445095	−0.222547	−	0.974922i	$-0.571437\pi$
$359$	−8.43334	−0.445095	−0.222547	+	0.974922i	$0.571437\pi$
$360$	−7.12248	−0.375388
$361$	16.9476	0.891977
$362$	−1.82985	−0.0961748
$363$	2.32544	0.122054
$364$	2.33061	0.122157
$365$	1.00000	0.0523424
$366$	11.0208	0.576067
$367$	0.0451672	0.00235771	0.00117885	−	0.999999i	$-0.499625\pi$
$367$	0.0451672	0.00235771	0.00117885	+	0.999999i	$0.499625\pi$
$368$	2.91061	0.151726
$369$	0.897200	0.0467063
$370$	−0.498573	−0.0259196
$371$	−0.561580	−0.0291558
$372$	15.8390	0.821215
$373$	29.1543	1.50955	0.754775	−	0.655983i	$-0.227746\pi$
$373$	29.1543	1.50955	0.754775	+	0.655983i	$0.227746\pi$
$374$	0.837307	0.0432961
$375$	−2.32544	−0.120085
$376$	24.1455	1.24521
$377$	0.627168	0.0323008
$378$	3.95206	0.203272
$379$	−26.9662	−1.38516	−0.692580	−	0.721341i	$-0.743526\pi$
$379$	−26.9662	−1.38516	−0.692580	+	0.721341i	$0.743526\pi$
$380$	−6.43763	−0.330243
$381$	46.6041	2.38760
$382$	25.6655	1.31316
$383$	13.9855	0.714626	0.357313	−	0.933985i	$-0.383693\pi$
$383$	13.9855	0.714626	0.357313	+	0.933985i	$0.383693\pi$
$384$	9.95945	0.508241
$385$	2.98112	0.151932
$386$	18.3798	0.935508
$387$	−24.0160	−1.22080
$388$	−6.17497	−0.313487
$389$	−15.0288	−0.761992	−0.380996	−	0.924577i	$-0.624419\pi$
$389$	−15.0288	−0.761992	−0.380996	+	0.924577i	$0.624419\pi$
$390$	−1.62957	−0.0825167
$391$	−3.61905	−0.183023
$392$	5.58247	0.281957
$393$	−4.18729	−0.211221
$394$	3.44693	0.173654
$395$	15.9628	0.803175
$396$	2.58516	0.129909
$397$	19.3788	0.972595	0.486297	−	0.873793i	$-0.338347\pi$
$397$	19.3788	0.972595	0.486297	+	0.873793i	$0.338347\pi$
$398$	6.93207	0.347473
$399$	−41.5642	−2.08081
$400$	−0.699685	−0.0349843
$401$	−16.4485	−0.821398	−0.410699	−	0.911771i	$-0.634715\pi$
$401$	−16.4485	−0.821398	−0.410699	+	0.911771i	$0.634715\pi$
$402$	−23.4872	−1.17144
$403$	4.61882	0.230080
$404$	12.5747	0.625613
$405$	10.4261	0.518079
$406$	2.47136	0.122652
$407$	0.518033	0.0256780
$408$	5.98486	0.296295
$409$	22.2673	1.10105	0.550524	−	0.834819i	$-0.314428\pi$
$409$	22.2673	1.10105	0.550524	+	0.834819i	$0.314428\pi$
$410$	0.358645	0.0177122
$411$	11.6642	0.575354
$412$	−17.0772	−0.841331
$413$	−8.15678	−0.401369
$414$	9.63935	0.473748
$415$	−8.81283	−0.432605
$416$	3.81757	0.187172
$417$	6.76771	0.331416
$418$	−5.77040	−0.282239
$419$	1.80068	0.0879690	0.0439845	−	0.999032i	$-0.485995\pi$
$419$	1.80068	0.0879690	0.0439845	+	0.999032i	$0.485995\pi$
$420$	7.44347	0.363204
$421$	23.3988	1.14039	0.570193	−	0.821511i	$-0.306868\pi$
$421$	23.3988	1.14039	0.570193	+	0.821511i	$0.306868\pi$
$422$	−3.55443	−0.173027
$423$	19.6515	0.955490
$424$	−0.557273	−0.0270636
$425$	0.869989	0.0422006
$426$	32.2014	1.56016
$427$	−14.6797	−0.710400
$428$	−1.19809	−0.0579117
$429$	1.69318	0.0817475
$430$	−9.60010	−0.462958
$431$	21.8294	1.05149	0.525743	−	0.850643i	$-0.323787\pi$
$431$	21.8294	1.05149	0.525743	+	0.850643i	$0.323787\pi$
$432$	0.963776	0.0463697
$433$	−24.4450	−1.17475	−0.587376	−	0.809314i	$-0.699839\pi$
$433$	−24.4450	−1.17475	−0.587376	+	0.809314i	$0.699839\pi$
$434$	18.2005	0.873652
$435$	2.00304	0.0960386
$436$	−7.44339	−0.356474
$437$	24.9411	1.19309
$438$	2.23808	0.106940
$439$	9.13074	0.435786	0.217893	−	0.975973i	$-0.430082\pi$
$439$	9.13074	0.435786	0.217893	+	0.975973i	$0.430082\pi$
$440$	2.95825	0.141029
$441$	4.54346	0.216355
$442$	0.609654	0.0289983
$443$	12.6315	0.600140	0.300070	−	0.953917i	$-0.402990\pi$
$443$	12.6315	0.600140	0.300070	+	0.953917i	$0.402990\pi$
$444$	1.29346	0.0613850
$445$	1.13920	0.0540031
$446$	−2.01997	−0.0956485
$447$	−33.5848	−1.58851
$448$	19.2149	0.907817
$449$	−22.3031	−1.05255	−0.526274	−	0.850315i	$-0.676411\pi$
$449$	−22.3031	−1.05255	−0.526274	+	0.850315i	$0.676411\pi$
$450$	−2.31722	−0.109235
$451$	−0.372643	−0.0175471
$452$	11.6109	0.546131
$453$	34.0348	1.59909
$454$	−28.6290	−1.34363
$455$	2.17059	0.101759
$456$	−41.2453	−1.93149
$457$	−9.31308	−0.435647	−0.217824	−	0.975988i	$-0.569896\pi$
$457$	−9.31308	−0.435647	−0.217824	+	0.975988i	$0.569896\pi$
$458$	9.03846	0.422340
$459$	−1.19836	−0.0559346
$460$	−4.46655	−0.208254
$461$	−30.9368	−1.44087	−0.720436	−	0.693522i	$-0.756058\pi$
$461$	−30.9368	−1.44087	−0.720436	+	0.693522i	$0.756058\pi$
$462$	6.67199	0.310409
$463$	1.37586	0.0639415	0.0319707	−	0.999489i	$-0.489822\pi$
$463$	1.37586	0.0639415	0.0319707	+	0.999489i	$0.489822\pi$
$464$	0.602682	0.0279788
$465$	14.7515	0.684086
$466$	27.8667	1.29090
$467$	−24.2923	−1.12412	−0.562058	−	0.827098i	$-0.689990\pi$
$467$	−24.2923	−1.12412	−0.562058	+	0.827098i	$0.689990\pi$
$468$	1.88228	0.0870086
$469$	31.2849	1.44460
$470$	7.85547	0.362346
$471$	37.0517	1.70725
$472$	−8.09421	−0.372566
$473$	9.97481	0.458642
$474$	35.7260	1.64095
$475$	−5.99563	−0.275098
$476$	−2.78474	−0.127638
$477$	−0.453553	−0.0207668
$478$	−11.3014	−0.516914
$479$	−13.5496	−0.619096	−0.309548	−	0.950884i	$-0.600178\pi$
$479$	−13.5496	−0.619096	−0.309548	+	0.950884i	$0.600178\pi$
$480$	12.1925	0.556510
$481$	0.377187	0.0171982
$482$	−5.92147	−0.269716
$483$	−28.8380	−1.31217
$484$	−1.07372	−0.0488055
$485$	−5.75100	−0.261140
$486$	19.3575	0.878073
$487$	−16.8834	−0.765061	−0.382531	−	0.923943i	$-0.624947\pi$
$487$	−16.8834	−0.765061	−0.382531	+	0.923943i	$0.624947\pi$
$488$	−14.5671	−0.659421
$489$	−25.4003	−1.14864
$490$	1.81619	0.0820472
$491$	30.7784	1.38901	0.694506	−	0.719487i	$-0.255623\pi$
$491$	30.7784	1.38901	0.694506	+	0.719487i	$0.255623\pi$
$492$	−0.930442	−0.0419476
$493$	−0.749375	−0.0337501
$494$	−4.20150	−0.189034
$495$	2.40766	0.108216
$496$	4.43849	0.199294
$497$	−42.8923	−1.92398
$498$	−19.7238	−0.883847
$499$	6.37948	0.285585	0.142792	−	0.989753i	$-0.454392\pi$
$499$	6.37948	0.285585	0.142792	+	0.989753i	$0.454392\pi$
$500$	1.07372	0.0480182
$501$	−27.5831	−1.23232
$502$	19.9239	0.889246
$503$	−11.4595	−0.510956	−0.255478	−	0.966815i	$-0.582233\pi$
$503$	−11.4595	−0.510956	−0.255478	+	0.966815i	$0.582233\pi$
$504$	21.2330	0.945792
$505$	11.7113	0.521146
$506$	−4.00361	−0.177982
$507$	−28.9979	−1.28784
$508$	−21.5184	−0.954725
$509$	−22.5844	−1.00104	−0.500519	−	0.865726i	$-0.666857\pi$
$509$	−22.5844	−1.00104	−0.500519	+	0.865726i	$0.666857\pi$
$510$	1.94711	0.0862193
$511$	−2.98112	−0.131877
$512$	7.80822	0.345078
$513$	8.25863	0.364627
$514$	−9.11990	−0.402262
$515$	−15.9047	−0.700843
$516$	24.9058	1.09642
$517$	−8.16208	−0.358968
$518$	1.48631	0.0653046
$519$	16.7353	0.734598
$520$	2.15394	0.0944566
$521$	−0.455557	−0.0199583	−0.00997915	−	0.999950i	$-0.503177\pi$
$521$	−0.455557	−0.0199583	−0.00997915	+	0.999950i	$0.503177\pi$
$522$	1.99596	0.0873609
$523$	22.7044	0.992796	0.496398	−	0.868095i	$-0.334656\pi$
$523$	22.7044	0.992796	0.496398	+	0.868095i	$0.334656\pi$
$524$	1.93339	0.0844605
$525$	6.93241	0.302555
$526$	23.4346	1.02180
$527$	−5.51882	−0.240404
$528$	1.62707	0.0708093
$529$	−5.69541	−0.247626
$530$	−0.181302	−0.00787527
$531$	−6.58771	−0.285882
$532$	19.1913	0.832050
$533$	−0.271326	−0.0117524
$534$	2.54961	0.110333
$535$	−1.11583	−0.0482414
$536$	31.0449	1.34094
$537$	−5.81398	−0.250892
$538$	2.29293	0.0988554
$539$	−1.88708	−0.0812824
$540$	−1.47899	−0.0636455
$541$	46.3475	1.99263	0.996317	−	0.0857420i	$-0.0273261\pi$
$541$	46.3475	1.99263	0.996317	+	0.0857420i	$0.0273261\pi$
$542$	5.24276	0.225196
$543$	4.42129	0.189736
$544$	−4.56144	−0.195570
$545$	−6.93234	−0.296949
$546$	4.85796	0.207901
$547$	5.76774	0.246611	0.123305	−	0.992369i	$-0.460651\pi$
$547$	5.76774	0.246611	0.123305	+	0.992369i	$0.460651\pi$
$548$	−5.38570	−0.230066
$549$	−11.8559	−0.505996
$550$	0.962434	0.0410383
$551$	5.16440	0.220011
$552$	−28.6168	−1.21801
$553$	−47.5870	−2.02360
$554$	22.5485	0.957994
$555$	1.20465	0.0511347
$556$	−3.12484	−0.132523
$557$	4.05293	0.171728	0.0858641	−	0.996307i	$-0.472635\pi$
$557$	4.05293	0.171728	0.0858641	+	0.996307i	$0.472635\pi$
$558$	14.6994	0.622275
$559$	7.26278	0.307183
$560$	2.08585	0.0881431
$561$	−2.02310	−0.0854156
$562$	11.9834	0.505488
$563$	40.2191	1.69503	0.847516	−	0.530770i	$-0.178097\pi$
$563$	40.2191	1.69503	0.847516	+	0.530770i	$0.178097\pi$
$564$	−20.3796	−0.858138
$565$	10.8137	0.454936
$566$	−26.7480	−1.12430
$567$	−31.0816	−1.30530
$568$	−42.5632	−1.78591
$569$	14.7320	0.617599	0.308800	−	0.951127i	$-0.400073\pi$
$569$	14.7320	0.617599	0.308800	+	0.951127i	$0.400073\pi$
$570$	−13.4187	−0.562048
$571$	−25.6922	−1.07519	−0.537593	−	0.843205i	$-0.680666\pi$
$571$	−25.6922	−1.07519	−0.537593	+	0.843205i	$0.680666\pi$
$572$	−0.781789	−0.0326882
$573$	−62.0132	−2.59064
$574$	−1.06916	−0.0446260
$575$	−4.15988	−0.173479
$576$	15.5186	0.646610
$577$	8.04944	0.335103	0.167551	−	0.985863i	$-0.446414\pi$
$577$	8.04944	0.335103	0.167551	+	0.985863i	$0.446414\pi$
$578$	15.6329	0.650244
$579$	−44.4094	−1.84559
$580$	−0.924861	−0.0384028
$581$	26.2721	1.08995
$582$	−12.8712	−0.533529
$583$	0.188379	0.00780186
$584$	−2.95825	−0.122413
$585$	1.75305	0.0724797
$586$	8.45803	0.349398
$587$	0.956030	0.0394596	0.0197298	−	0.999805i	$-0.493719\pi$
$587$	0.956030	0.0394596	0.0197298	+	0.999805i	$0.493719\pi$
$588$	−4.71180	−0.194311
$589$	38.0336	1.56715
$590$	−2.63336	−0.108414
$591$	−8.32848	−0.342588
$592$	0.362460	0.0148970
$593$	−0.246335	−0.0101158	−0.00505788	−	0.999987i	$-0.501610\pi$
$593$	−0.246335	−0.0101158	−0.00505788	+	0.999987i	$0.501610\pi$
$594$	−1.32570	−0.0543940
$595$	−2.59354	−0.106325
$596$	15.5071	0.635194
$597$	−16.7493	−0.685503
$598$	−2.91508	−0.119206
$599$	9.53550	0.389610	0.194805	−	0.980842i	$-0.437593\pi$
$599$	9.53550	0.389610	0.194805	+	0.980842i	$0.437593\pi$
$600$	6.87924	0.280844
$601$	20.1773	0.823048	0.411524	−	0.911399i	$-0.364997\pi$
$601$	20.1773	0.823048	0.411524	+	0.911399i	$0.364997\pi$
$602$	28.6191	1.16643
$603$	25.2669	1.02895
$604$	−15.7148	−0.639427
$605$	−1.00000	−0.0406558
$606$	26.2109	1.06474
$607$	13.1180	0.532445	0.266222	−	0.963912i	$-0.414224\pi$
$607$	13.1180	0.532445	0.266222	+	0.963912i	$0.414224\pi$
$608$	31.4357	1.27489
$609$	−5.97131	−0.241970
$610$	−4.73924	−0.191886
$611$	−5.94291	−0.240424
$612$	−2.24906	−0.0909127
$613$	11.4090	0.460804	0.230402	−	0.973095i	$-0.425996\pi$
$613$	11.4090	0.460804	0.230402	+	0.973095i	$0.425996\pi$
$614$	−21.4501	−0.865657
$615$	−0.866559	−0.0349430
$616$	−8.81891	−0.355324
$617$	−17.8020	−0.716683	−0.358342	−	0.933591i	$-0.616658\pi$
$617$	−17.8020	−0.716683	−0.358342	+	0.933591i	$0.616658\pi$
$618$	−35.5959	−1.43188
$619$	−25.5500	−1.02694	−0.513471	−	0.858107i	$-0.671641\pi$
$619$	−25.5500	−1.02694	−0.513471	+	0.858107i	$0.671641\pi$
$620$	−6.81120	−0.273544
$621$	5.72999	0.229937
$622$	−17.3962	−0.697526
$623$	−3.39608	−0.136061
$624$	1.18469	0.0474257
$625$	1.00000	0.0400000
$626$	0.701362	0.0280321
$627$	13.9425	0.556808
$628$	−17.1078	−0.682675
$629$	−0.450683	−0.0179699
$630$	6.90791	0.275218
$631$	−35.6108	−1.41764	−0.708821	−	0.705388i	$-0.750773\pi$
$631$	−35.6108	−1.41764	−0.708821	+	0.705388i	$0.750773\pi$
$632$	−47.2220	−1.87839
$633$	8.58824	0.341352
$634$	−22.7552	−0.903724
$635$	−20.0410	−0.795302
$636$	0.470358	0.0186509
$637$	−1.37401	−0.0544402
$638$	−0.829004	−0.0328206
$639$	−34.6414	−1.37039
$640$	−4.28283	−0.169294
$641$	26.7973	1.05843	0.529216	−	0.848487i	$-0.322486\pi$
$641$	26.7973	1.05843	0.529216	+	0.848487i	$0.322486\pi$
$642$	−2.49731	−0.0985611
$643$	−12.2173	−0.481803	−0.240902	−	0.970550i	$-0.577443\pi$
$643$	−12.2173	−0.481803	−0.240902	+	0.970550i	$0.577443\pi$
$644$	13.3153	0.524697
$645$	23.1958	0.913334
$646$	5.02018	0.197516
$647$	−31.0370	−1.22019	−0.610095	−	0.792328i	$-0.708869\pi$
$647$	−31.0370	−1.22019	−0.610095	+	0.792328i	$0.708869\pi$
$648$	−30.8432	−1.21163
$649$	2.73614	0.107403
$650$	0.700760	0.0274861
$651$	−43.9761	−1.72356
$652$	11.7280	0.459304
$653$	−20.0286	−0.783778	−0.391889	−	0.920013i	$-0.628178\pi$
$653$	−20.0286	−0.783778	−0.391889	+	0.920013i	$0.628178\pi$
$654$	−15.5151	−0.606690
$655$	1.80065	0.0703570
$656$	−0.260733	−0.0101799
$657$	−2.40766	−0.0939319
$658$	−23.4181	−0.912932
$659$	43.3076	1.68702	0.843512	−	0.537110i	$-0.180484\pi$
$659$	43.3076	1.68702	0.843512	+	0.537110i	$0.180484\pi$
$660$	−2.49687	−0.0971905
$661$	34.1492	1.32825	0.664125	−	0.747622i	$-0.268804\pi$
$661$	34.1492	1.32825	0.664125	+	0.747622i	$0.268804\pi$
$662$	20.6612	0.803019
$663$	−1.47305	−0.0572084
$664$	26.0706	1.01174
$665$	17.8737	0.693112
$666$	1.20040	0.0465144
$667$	3.58316	0.138741
$668$	12.7359	0.492767
$669$	4.88067	0.188698
$670$	10.1001	0.390202
$671$	4.92422	0.190097
$672$	−36.3474	−1.40213
$673$	3.63665	0.140183	0.0700913	−	0.997541i	$-0.477671\pi$
$673$	3.63665	0.140183	0.0700913	+	0.997541i	$0.477671\pi$
$674$	−33.7659	−1.30061
$675$	−1.37744	−0.0530178
$676$	13.3891	0.514967
$677$	−24.9409	−0.958557	−0.479279	−	0.877663i	$-0.659102\pi$
$677$	−24.9409	−0.958557	−0.479279	+	0.877663i	$0.659102\pi$
$678$	24.2020	0.929471
$679$	17.1444	0.657943
$680$	−2.57365	−0.0986949
$681$	69.1735	2.65073
$682$	−6.10525	−0.233782
$683$	17.6362	0.674829	0.337414	−	0.941356i	$-0.390448\pi$
$683$	17.6362	0.674829	0.337414	+	0.941356i	$0.390448\pi$
$684$	15.4996	0.592643
$685$	−5.01593	−0.191649
$686$	14.6696	0.560090
$687$	−21.8388	−0.833201
$688$	6.97923	0.266081
$689$	0.137161	0.00522542
$690$	−9.31015	−0.354431
$691$	23.3315	0.887573	0.443787	−	0.896133i	$-0.353635\pi$
$691$	23.3315	0.887573	0.443787	+	0.896133i	$0.353635\pi$
$692$	−7.72715	−0.293742
$693$	−7.17754	−0.272652
$694$	24.3207	0.923202
$695$	−2.91029	−0.110394
$696$	−5.92551	−0.224606
$697$	0.324195	0.0122798
$698$	3.42432	0.129612
$699$	−67.3316	−2.54672
$700$	−3.20089	−0.120982
$701$	43.5761	1.64585	0.822923	−	0.568153i	$-0.192342\pi$
$701$	43.5761	1.64585	0.822923	+	0.568153i	$0.192342\pi$
$702$	−0.965257	−0.0364313
$703$	3.10594	0.117143
$704$	−6.44552	−0.242925
$705$	−18.9804	−0.714844
$706$	−1.66952	−0.0628333
$707$	−34.9128	−1.31303
$708$	6.83179	0.256755
$709$	−34.1984	−1.28435	−0.642173	−	0.766559i	$-0.721967\pi$
$709$	−34.1984	−1.28435	−0.642173	+	0.766559i	$0.721967\pi$
$710$	−13.8475	−0.519686
$711$	−38.4330	−1.44135
$712$	−3.37003	−0.126297
$713$	26.3884	0.988254
$714$	−5.80456	−0.217230
$715$	−0.728112	−0.0272299
$716$	2.68448	0.100324
$717$	27.3065	1.01978
$718$	8.11654	0.302906
$719$	−0.407073	−0.0151812	−0.00759062	−	0.999971i	$-0.502416\pi$
$719$	−0.407073	−0.0151812	−0.00759062	+	0.999971i	$0.502416\pi$
$720$	1.68461	0.0627816
$721$	47.4137	1.76578
$722$	−16.3109	−0.607029
$723$	14.3075	0.532101
$724$	−2.04143	−0.0758693
$725$	−0.861362	−0.0319902
$726$	−2.23808	−0.0830630
$727$	35.1609	1.30405	0.652023	−	0.758199i	$-0.273921\pi$
$727$	35.1609	1.30405	0.652023	+	0.758199i	$0.273921\pi$
$728$	−6.42116	−0.237984
$729$	−15.4932	−0.573822
$730$	−0.962434	−0.0356213
$731$	−8.67797	−0.320966
$732$	12.2951	0.454441
$733$	50.5136	1.86576	0.932881	−	0.360185i	$-0.117286\pi$
$733$	50.5136	1.86576	0.932881	+	0.360185i	$0.117286\pi$
$734$	−0.0434704	−0.00160452
$735$	−4.38829	−0.161865
$736$	21.8107	0.803953
$737$	−10.4943	−0.386564
$738$	−0.863496	−0.0317857
$739$	−4.37254	−0.160846	−0.0804232	−	0.996761i	$-0.525627\pi$
$739$	−4.37254	−0.160846	−0.0804232	+	0.996761i	$0.525627\pi$
$740$	−0.556223	−0.0204472
$741$	10.1517	0.372931
$742$	0.540484	0.0198418
$743$	−41.7785	−1.53270	−0.766351	−	0.642422i	$-0.777930\pi$
$743$	−41.7785	−1.53270	−0.766351	+	0.642422i	$0.777930\pi$
$744$	−43.6388	−1.59988
$745$	14.4424	0.529127
$746$	−28.0591	−1.02732
$747$	21.2183	0.776338
$748$	0.934124	0.0341550
$749$	3.32642	0.121545
$750$	2.23808	0.0817232
$751$	23.5985	0.861123	0.430562	−	0.902561i	$-0.358316\pi$
$751$	23.5985	0.861123	0.430562	+	0.902561i	$0.358316\pi$
$752$	−5.71089	−0.208255
$753$	−48.1401	−1.75432
$754$	−0.603608	−0.0219821
$755$	−14.6359	−0.532653
$756$	4.40904	0.160355
$757$	−29.4602	−1.07075	−0.535375	−	0.844615i	$-0.679830\pi$
$757$	−29.4602	−1.07075	−0.535375	+	0.844615i	$0.679830\pi$
$758$	25.9532	0.942663
$759$	9.67354	0.351127
$760$	17.7366	0.643374
$761$	−23.1649	−0.839728	−0.419864	−	0.907587i	$-0.637922\pi$
$761$	−23.1649	−0.839728	−0.419864	+	0.907587i	$0.637922\pi$
$762$	−44.8534	−1.62487
$763$	20.6661	0.748165
$764$	28.6332	1.03591
$765$	−2.09464	−0.0757319
$766$	−13.4601	−0.486334
$767$	1.99222	0.0719349
$768$	−39.5626	−1.42759
$769$	−13.8132	−0.498117	−0.249059	−	0.968488i	$-0.580121\pi$
$769$	−13.8132	−0.498117	−0.249059	+	0.968488i	$0.580121\pi$
$770$	−2.86913	−0.103396
$771$	22.0355	0.793591
$772$	20.5051	0.737993
$773$	−6.42481	−0.231084	−0.115542	−	0.993303i	$-0.536861\pi$
$773$	−6.42481	−0.231084	−0.115542	+	0.993303i	$0.536861\pi$
$774$	23.1138	0.830809
$775$	−6.34355	−0.227867
$776$	17.0129	0.610729
$777$	−3.59122	−0.128834
$778$	14.4643	0.518569
$779$	−2.23423	−0.0800496
$780$	−1.81800	−0.0650949
$781$	14.3880	0.514842
$782$	3.48310	0.124555
$783$	1.18648	0.0424012
$784$	−1.32036	−0.0471558
$785$	−15.9332	−0.568680
$786$	4.02999	0.143745
$787$	6.92710	0.246924	0.123462	−	0.992349i	$-0.460600\pi$
$787$	6.92710	0.246924	0.123462	+	0.992349i	$0.460600\pi$
$788$	3.84549	0.136990
$789$	−56.6229	−2.01583
$790$	−15.3631	−0.546596
$791$	−32.2370	−1.14622
$792$	−7.12248	−0.253086
$793$	3.58539	0.127321
$794$	−18.6508	−0.661893
$795$	0.438064	0.0155365
$796$	7.73362	0.274111
$797$	−12.5508	−0.444572	−0.222286	−	0.974981i	$-0.571352\pi$
$797$	−12.5508	−0.444572	−0.222286	+	0.974981i	$0.571352\pi$
$798$	40.0028	1.41608
$799$	7.10092	0.251212
$800$	−5.24311	−0.185372
$801$	−2.74280	−0.0969121
$802$	15.8306	0.558997
$803$	1.00000	0.0352892
$804$	−26.2030	−0.924109
$805$	12.4011	0.437081
$806$	−4.44531	−0.156579
$807$	−5.54020	−0.195024
$808$	−34.6450	−1.21881
$809$	−0.904894	−0.0318144	−0.0159072	−	0.999873i	$-0.505064\pi$
$809$	−0.904894	−0.0318144	−0.0159072	+	0.999873i	$0.505064\pi$
$810$	−10.0345	−0.352576
$811$	−52.6406	−1.84846	−0.924230	−	0.381835i	$-0.875292\pi$
$811$	−52.6406	−1.84846	−0.924230	+	0.381835i	$0.875292\pi$
$812$	2.75712	0.0967561
$813$	−12.6676	−0.444271
$814$	−0.498573	−0.0174750
$815$	10.9228	0.382609
$816$	−1.41554	−0.0495537
$817$	59.8052	2.09232
$818$	−21.4308	−0.749312
$819$	−5.22605	−0.182613
$820$	0.400115	0.0139726
$821$	−1.87661	−0.0654941	−0.0327470	−	0.999464i	$-0.510426\pi$
$821$	−1.87661	−0.0654941	−0.0327470	+	0.999464i	$0.510426\pi$
$822$	−11.2261	−0.391554
$823$	−31.4350	−1.09576	−0.547878	−	0.836559i	$-0.684564\pi$
$823$	−31.4350	−1.09576	−0.547878	+	0.836559i	$0.684564\pi$
$824$	47.0500	1.63907
$825$	−2.32544	−0.0809614
$826$	7.85036	0.273149
$827$	14.5610	0.506335	0.253168	−	0.967422i	$-0.418528\pi$
$827$	14.5610	0.506335	0.253168	+	0.967422i	$0.418528\pi$
$828$	10.7539	0.373725
$829$	−0.256645	−0.00891366	−0.00445683	−	0.999990i	$-0.501419\pi$
$829$	−0.256645	−0.00891366	−0.00445683	+	0.999990i	$0.501419\pi$
$830$	8.48178	0.294407
$831$	−54.4818	−1.88995
$832$	−4.69306	−0.162703
$833$	1.64174	0.0568829
$834$	−6.51347	−0.225543
$835$	11.8615	0.410483
$836$	−6.43763	−0.222650
$837$	8.73788	0.302025
$838$	−1.73304	−0.0598668
$839$	−17.6213	−0.608355	−0.304177	−	0.952615i	$-0.598382\pi$
$839$	−17.6213	−0.608355	−0.304177	+	0.952615i	$0.598382\pi$
$840$	−20.5078	−0.707588
$841$	−28.2581	−0.974416
$842$	−22.5198	−0.776083
$843$	−28.9543	−0.997239
$844$	−3.96543	−0.136496
$845$	12.4699	0.428976
$846$	−18.9133	−0.650253
$847$	2.98112	0.102433
$848$	0.131806	0.00452624
$849$	64.6287	2.21805
$850$	−0.837307	−0.0287194
$851$	2.15496	0.0738709
$852$	35.9249	1.23077
$853$	6.54554	0.224115	0.112058	−	0.993702i	$-0.464256\pi$
$853$	6.54554	0.224115	0.112058	+	0.993702i	$0.464256\pi$
$854$	14.1282	0.483459
$855$	14.4355	0.493682
$856$	3.30090	0.112822
$857$	−11.1722	−0.381634	−0.190817	−	0.981626i	$-0.561114\pi$
$857$	−11.1722	−0.381634	−0.190817	+	0.981626i	$0.561114\pi$
$858$	−1.62957	−0.0556328
$859$	28.4856	0.971918	0.485959	−	0.873982i	$-0.338470\pi$
$859$	28.4856	0.971918	0.485959	+	0.873982i	$0.338470\pi$
$860$	−10.7102	−0.365213
$861$	2.58332	0.0880392
$862$	−21.0094	−0.715583
$863$	13.7635	0.468515	0.234257	−	0.972175i	$-0.424734\pi$
$863$	13.7635	0.468515	0.234257	+	0.972175i	$0.424734\pi$
$864$	7.22208	0.245700
$865$	−7.19662	−0.244692
$866$	23.5267	0.799470
$867$	−37.7724	−1.28282
$868$	20.3050	0.689197
$869$	15.9628	0.541500
$870$	−1.92780	−0.0653585
$871$	−7.64106	−0.258908
$872$	20.5076	0.694476
$873$	13.8465	0.468632
$874$	−24.0042	−0.811953
$875$	−2.98112	−0.100780
$876$	2.49687	0.0843614
$877$	−0.107783	−0.00363958	−0.00181979	−	0.999998i	$-0.500579\pi$
$877$	−0.107783	−0.00363958	−0.00181979	+	0.999998i	$0.500579\pi$
$878$	−8.78774	−0.296572
$879$	−20.4363	−0.689301
$880$	−0.699685	−0.0235864
$881$	1.49009	0.0502023	0.0251011	−	0.999685i	$-0.492009\pi$
$881$	1.49009	0.0502023	0.0251011	+	0.999685i	$0.492009\pi$
$882$	−4.37278	−0.147239
$883$	−32.6576	−1.09901	−0.549507	−	0.835489i	$-0.685185\pi$
$883$	−32.6576	−1.09901	−0.549507	+	0.835489i	$0.685185\pi$
$884$	0.680147	0.0228758
$885$	6.36273	0.213881
$886$	−12.1570	−0.408421
$887$	12.4843	0.419180	0.209590	−	0.977789i	$-0.432787\pi$
$887$	12.4843	0.419180	0.209590	+	0.977789i	$0.432787\pi$
$888$	−3.56367	−0.119589
$889$	59.7446	2.00377
$890$	−1.09640	−0.0367515
$891$	10.4261	0.349289
$892$	−2.25354	−0.0754542
$893$	−48.9368	−1.63761
$894$	32.3232	1.08105
$895$	2.50017	0.0835713
$896$	12.7676	0.426536
$897$	7.04342	0.235173
$898$	21.4653	0.716305
$899$	5.46409	0.182238
$900$	−2.58516	−0.0861719
$901$	−0.163888	−0.00545989
$902$	0.358645	0.0119416
$903$	−69.1495	−2.30115
$904$	−31.9897	−1.06396
$905$	−1.90127	−0.0632004
$906$	−32.7562	−1.08825
$907$	49.3738	1.63943	0.819715	−	0.572772i	$-0.194132\pi$
$907$	49.3738	1.63943	0.819715	+	0.572772i	$0.194132\pi$
$908$	−31.9393	−1.05994
$909$	−28.1969	−0.935232
$910$	−2.08905	−0.0692514
$911$	8.49057	0.281305	0.140653	−	0.990059i	$-0.455080\pi$
$911$	8.49057	0.281305	0.140653	+	0.990059i	$0.455080\pi$
$912$	9.75534	0.323031
$913$	−8.81283	−0.291662
$914$	8.96323	0.296477
$915$	11.4510	0.378557
$916$	10.0836	0.333171
$917$	−5.36794	−0.177265
$918$	1.15334	0.0380660
$919$	33.0730	1.09098	0.545488	−	0.838119i	$-0.316344\pi$
$919$	33.0730	1.09098	0.545488	+	0.838119i	$0.316344\pi$
$920$	12.3060	0.405716
$921$	51.8279	1.70779
$922$	29.7747	0.980576
$923$	10.4761	0.344823
$924$	7.44347	0.244872
$925$	−0.518033	−0.0170328
$926$	−1.32417	−0.0435150
$927$	38.2931	1.25771
$928$	4.51621	0.148252
$929$	5.27326	0.173010	0.0865050	−	0.996251i	$-0.472430\pi$
$929$	5.27326	0.173010	0.0865050	+	0.996251i	$0.472430\pi$
$930$	−14.1974	−0.465551
$931$	−11.3142	−0.370809
$932$	31.0889	1.01835
$933$	42.0329	1.37610
$934$	23.3798	0.765010
$935$	0.869989	0.0284517
$936$	−5.18597	−0.169509
$937$	26.8336	0.876616	0.438308	−	0.898825i	$-0.355578\pi$
$937$	26.8336	0.876616	0.438308	+	0.898825i	$0.355578\pi$
$938$	−30.1097	−0.983116
$939$	−1.69463	−0.0553023
$940$	8.76379	0.285843
$941$	−24.7175	−0.805767	−0.402883	−	0.915251i	$-0.631992\pi$
$941$	−24.7175	−0.805767	−0.402883	+	0.915251i	$0.631992\pi$
$942$	−35.6598	−1.16186
$943$	−1.55015	−0.0504799
$944$	1.91444	0.0623097
$945$	4.10632	0.133579
$946$	−9.60010	−0.312126
$947$	−17.1240	−0.556456	−0.278228	−	0.960515i	$-0.589747\pi$
$947$	−17.1240	−0.556456	−0.278228	+	0.960515i	$0.589747\pi$
$948$	39.8570	1.29450
$949$	0.728112	0.0236355
$950$	5.77040	0.187216
$951$	54.9812	1.78289
$952$	7.67235	0.248662
$953$	−28.2101	−0.913816	−0.456908	−	0.889514i	$-0.651043\pi$
$953$	−28.2101	−0.913816	−0.456908	+	0.889514i	$0.651043\pi$
$954$	0.436515	0.0141327
$955$	26.6673	0.862934
$956$	−12.6082	−0.407777
$957$	2.00304	0.0647492
$958$	13.0406	0.421322
$959$	14.9531	0.482860
$960$	−14.9887	−0.483757
$961$	9.24066	0.298086
$962$	−0.363017	−0.0117041
$963$	2.68654	0.0865724
$964$	−6.60616	−0.212770
$965$	19.0972	0.614761
$966$	27.7547	0.892992
$967$	29.1731	0.938145	0.469072	−	0.883160i	$-0.344588\pi$
$967$	29.1731	0.938145	0.469072	+	0.883160i	$0.344588\pi$
$968$	2.95825	0.0950819
$969$	−12.1298	−0.389665
$970$	5.53496	0.177717
$971$	52.2788	1.67771	0.838853	−	0.544359i	$-0.183227\pi$
$971$	52.2788	1.67771	0.838853	+	0.544359i	$0.183227\pi$
$972$	21.5958	0.692685
$973$	8.67594	0.278138
$974$	16.2492	0.520658
$975$	−1.69318	−0.0542252
$976$	3.44540	0.110285
$977$	27.5494	0.881385	0.440692	−	0.897658i	$-0.354733\pi$
$977$	27.5494	0.881385	0.440692	+	0.897658i	$0.354733\pi$
$978$	24.4461	0.781700
$979$	1.13920	0.0364089
$980$	2.02620	0.0647245
$981$	16.6907	0.532894
$982$	−29.6222	−0.945283
$983$	−11.9990	−0.382709	−0.191354	−	0.981521i	$-0.561288\pi$
$983$	−11.9990	−0.382709	−0.191354	+	0.981521i	$0.561288\pi$
$984$	2.56350	0.0817214
$985$	3.58147	0.114115
$986$	0.721224	0.0229685
$987$	56.5829	1.80105
$988$	−4.68731	−0.149123
$989$	41.4940	1.31943
$990$	−2.31722	−0.0736460
$991$	−10.4107	−0.330707	−0.165354	−	0.986234i	$-0.552877\pi$
$991$	−10.4107	−0.330707	−0.165354	+	0.986234i	$0.552877\pi$
$992$	33.2599	1.05600
$993$	−49.9216	−1.58421
$994$	41.2810	1.30935
$995$	7.20264	0.228339
$996$	−22.0045	−0.697239
$997$	−32.7834	−1.03826	−0.519130	−	0.854695i	$-0.673744\pi$
$997$	−32.7834	−1.03826	−0.519130	+	0.854695i	$0.673744\pi$
$998$	−6.13983	−0.194353
$999$	0.713561	0.0225761

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.g.1.12	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.g.1.12	✓	32	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.962434 q^{2} +2.32544 q^{3} -1.07372 q^{4} -1.00000 q^{5} -2.23808 q^{6} +2.98112 q^{7} +2.95825 q^{8} +2.40766 q^{9} +O(q^{10})\)	\(q-0.962434 q^{2} +2.32544 q^{3} -1.07372 q^{4} -1.00000 q^{5} -2.23808 q^{6} +2.98112 q^{7} +2.95825 q^{8} +2.40766 q^{9} +0.962434 q^{10} -1.00000 q^{11} -2.49687 q^{12} -0.728112 q^{13} -2.86913 q^{14} -2.32544 q^{15} -0.699685 q^{16} +0.869989 q^{17} -2.31722 q^{18} -5.99563 q^{19} +1.07372 q^{20} +6.93241 q^{21} +0.962434 q^{22} -4.15988 q^{23} +6.87924 q^{24} +1.00000 q^{25} +0.700760 q^{26} -1.37744 q^{27} -3.20089 q^{28} -0.861362 q^{29} +2.23808 q^{30} -6.34355 q^{31} -5.24311 q^{32} -2.32544 q^{33} -0.837307 q^{34} -2.98112 q^{35} -2.58516 q^{36} -0.518033 q^{37} +5.77040 q^{38} -1.69318 q^{39} -2.95825 q^{40} +0.372643 q^{41} -6.67199 q^{42} -9.97481 q^{43} +1.07372 q^{44} -2.40766 q^{45} +4.00361 q^{46} +8.16208 q^{47} -1.62707 q^{48} +1.88708 q^{49} -0.962434 q^{50} +2.02310 q^{51} +0.781789 q^{52} -0.188379 q^{53} +1.32570 q^{54} +1.00000 q^{55} +8.81891 q^{56} -13.9425 q^{57} +0.829004 q^{58} -2.73614 q^{59} +2.49687 q^{60} -4.92422 q^{61} +6.10525 q^{62} +7.17754 q^{63} +6.44552 q^{64} +0.728112 q^{65} +2.23808 q^{66} +10.4943 q^{67} -0.934124 q^{68} -9.67354 q^{69} +2.86913 q^{70} -14.3880 q^{71} +7.12248 q^{72} -1.00000 q^{73} +0.498573 q^{74} +2.32544 q^{75} +6.43763 q^{76} -2.98112 q^{77} +1.62957 q^{78} -15.9628 q^{79} +0.699685 q^{80} -10.4261 q^{81} -0.358645 q^{82} +8.81283 q^{83} -7.44347 q^{84} -0.869989 q^{85} +9.60010 q^{86} -2.00304 q^{87} -2.95825 q^{88} -1.13920 q^{89} +2.31722 q^{90} -2.17059 q^{91} +4.46655 q^{92} -14.7515 q^{93} -7.85547 q^{94} +5.99563 q^{95} -12.1925 q^{96} +5.75100 q^{97} -1.81619 q^{98} -2.40766 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * q^99

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