LMFDB - Embedded newform 8005.2.a.f.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8005,2,Mod(1,8005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8005 = 5 \cdot 1601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8005.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:	$63.9202468180$
Analytic rank:	$1$
Dimension:	$127$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.09752 q^{2} -1.19582 q^{3} +2.39960 q^{4} -1.00000 q^{5} +2.50825 q^{6} +4.08912 q^{7} -0.838178 q^{8} -1.57003 q^{9} +O(q^{10})$	\(q-2.09752 q^{2} -1.19582 q^{3} +2.39960 q^{4} -1.00000 q^{5} +2.50825 q^{6} +4.08912 q^{7} -0.838178 q^{8} -1.57003 q^{9} +2.09752 q^{10} -0.139958 q^{11} -2.86948 q^{12} -3.69291 q^{13} -8.57702 q^{14} +1.19582 q^{15} -3.04111 q^{16} -1.21585 q^{17} +3.29317 q^{18} -2.86628 q^{19} -2.39960 q^{20} -4.88983 q^{21} +0.293566 q^{22} -7.68924 q^{23} +1.00231 q^{24} +1.00000 q^{25} +7.74597 q^{26} +5.46491 q^{27} +9.81227 q^{28} -2.63406 q^{29} -2.50825 q^{30} +9.05554 q^{31} +8.05515 q^{32} +0.167364 q^{33} +2.55028 q^{34} -4.08912 q^{35} -3.76744 q^{36} +9.81412 q^{37} +6.01210 q^{38} +4.41604 q^{39} +0.838178 q^{40} +3.06916 q^{41} +10.2565 q^{42} -12.2352 q^{43} -0.335844 q^{44} +1.57003 q^{45} +16.1284 q^{46} +8.67272 q^{47} +3.63660 q^{48} +9.72090 q^{49} -2.09752 q^{50} +1.45394 q^{51} -8.86153 q^{52} -5.48317 q^{53} -11.4628 q^{54} +0.139958 q^{55} -3.42741 q^{56} +3.42755 q^{57} +5.52499 q^{58} +12.8315 q^{59} +2.86948 q^{60} +1.14285 q^{61} -18.9942 q^{62} -6.42002 q^{63} -10.8137 q^{64} +3.69291 q^{65} -0.351050 q^{66} -8.57482 q^{67} -2.91757 q^{68} +9.19491 q^{69} +8.57702 q^{70} +10.5672 q^{71} +1.31596 q^{72} +16.0617 q^{73} -20.5853 q^{74} -1.19582 q^{75} -6.87795 q^{76} -0.572306 q^{77} -9.26275 q^{78} -9.44767 q^{79} +3.04111 q^{80} -1.82494 q^{81} -6.43764 q^{82} -5.92807 q^{83} -11.7337 q^{84} +1.21585 q^{85} +25.6637 q^{86} +3.14984 q^{87} +0.117310 q^{88} -15.0748 q^{89} -3.29317 q^{90} -15.1008 q^{91} -18.4511 q^{92} -10.8288 q^{93} -18.1912 q^{94} +2.86628 q^{95} -9.63248 q^{96} +6.67720 q^{97} -20.3898 q^{98} +0.219738 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9}+O(q^{10}) $ 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9	\( 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9} + 6 q^{10} - 45 q^{11} - 30 q^{12} - 53 q^{14} + 18 q^{15} + 84 q^{16} - 36 q^{17} - 10 q^{18} - 49 q^{19} - 114 q^{20} - 48 q^{21} + 13 q^{22} - 29 q^{23} - 63 q^{24} + 127 q^{25} - 55 q^{26} - 75 q^{27} + 44 q^{28} - 45 q^{29} + 20 q^{30} - 49 q^{31} - 32 q^{32} - 8 q^{33} - 52 q^{34} - 28 q^{35} + 44 q^{36} + 36 q^{37} - 65 q^{38} - 52 q^{39} + 18 q^{40} - 66 q^{41} - 18 q^{42} - 5 q^{43} - 93 q^{44} - 101 q^{45} - 25 q^{46} - 32 q^{47} - 54 q^{48} + 77 q^{49} - 6 q^{50} - 102 q^{51} - 13 q^{52} - 67 q^{53} - 53 q^{54} + 45 q^{55} - 158 q^{56} + 16 q^{57} + 35 q^{58} - 213 q^{59} + 30 q^{60} - 62 q^{61} - 33 q^{62} + 59 q^{63} + 34 q^{64} - 60 q^{66} + 10 q^{67} - 94 q^{68} - 93 q^{69} + 53 q^{70} - 118 q^{71} - 24 q^{72} + 35 q^{73} - 107 q^{74} - 18 q^{75} - 98 q^{76} - 93 q^{77} + 21 q^{78} - 64 q^{79} - 84 q^{80} + 15 q^{81} + 15 q^{82} - 187 q^{83} - 118 q^{84} + 36 q^{85} - 126 q^{86} - 53 q^{87} + 15 q^{88} - 138 q^{89} + 10 q^{90} - 138 q^{91} - 86 q^{92} + 23 q^{93} - 60 q^{94} + 49 q^{95} - 92 q^{96} + 9 q^{97} - 67 q^{98} - 147 q^{99}+O(q^{100}) \) 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9 + 6 * q^10 - 45 * q^11 - 30 * q^12 - 53 * q^14 + 18 * q^15 + 84 * q^16 - 36 * q^17 - 10 * q^18 - 49 * q^19 - 114 * q^20 - 48 * q^21 + 13 * q^22 - 29 * q^23 - 63 * q^24 + 127 * q^25 - 55 * q^26 - 75 * q^27 + 44 * q^28 - 45 * q^29 + 20 * q^30 - 49 * q^31 - 32 * q^32 - 8 * q^33 - 52 * q^34 - 28 * q^35 + 44 * q^36 + 36 * q^37 - 65 * q^38 - 52 * q^39 + 18 * q^40 - 66 * q^41 - 18 * q^42 - 5 * q^43 - 93 * q^44 - 101 * q^45 - 25 * q^46 - 32 * q^47 - 54 * q^48 + 77 * q^49 - 6 * q^50 - 102 * q^51 - 13 * q^52 - 67 * q^53 - 53 * q^54 + 45 * q^55 - 158 * q^56 + 16 * q^57 + 35 * q^58 - 213 * q^59 + 30 * q^60 - 62 * q^61 - 33 * q^62 + 59 * q^63 + 34 * q^64 - 60 * q^66 + 10 * q^67 - 94 * q^68 - 93 * q^69 + 53 * q^70 - 118 * q^71 - 24 * q^72 + 35 * q^73 - 107 * q^74 - 18 * q^75 - 98 * q^76 - 93 * q^77 + 21 * q^78 - 64 * q^79 - 84 * q^80 + 15 * q^81 + 15 * q^82 - 187 * q^83 - 118 * q^84 + 36 * q^85 - 126 * q^86 - 53 * q^87 + 15 * q^88 - 138 * q^89 + 10 * q^90 - 138 * q^91 - 86 * q^92 + 23 * q^93 - 60 * q^94 + 49 * q^95 - 92 * q^96 + 9 * q^97 - 67 * q^98 - 147 * 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 $

$2$	−2.09752	−1.48317	−0.741586	−	0.670857i	$-0.765926\pi$
$2$	−2.09752	−1.48317	−0.741586	+	0.670857i	$0.765926\pi$
$3$	−1.19582	−0.690404	−0.345202	−	0.938528i	$-0.612190\pi$
$3$	−1.19582	−0.690404	−0.345202	+	0.938528i	$0.612190\pi$
$4$	2.39960	1.19980
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.50825	1.02399
$7$	4.08912	1.54554	0.772771	−	0.634685i	$-0.218870\pi$
$7$	4.08912	1.54554	0.772771	+	0.634685i	$0.218870\pi$
$8$	−0.838178	−0.296341
$9$	−1.57003	−0.523342
$10$	2.09752	0.663295
$11$	−0.139958	−0.0421990	−0.0210995	−	0.999777i	$-0.506717\pi$
$11$	−0.139958	−0.0421990	−0.0210995	+	0.999777i	$0.506717\pi$
$12$	−2.86948	−0.828348
$13$	−3.69291	−1.02423	−0.512115	−	0.858917i	$-0.671138\pi$
$13$	−3.69291	−1.02423	−0.512115	+	0.858917i	$0.671138\pi$
$14$	−8.57702	−2.29231
$15$	1.19582	0.308758
$16$	−3.04111	−0.760277
$17$	−1.21585	−0.294888	−0.147444	−	0.989070i	$-0.547105\pi$
$17$	−1.21585	−0.294888	−0.147444	+	0.989070i	$0.547105\pi$
$18$	3.29317	0.776207
$19$	−2.86628	−0.657571	−0.328785	−	0.944405i	$-0.606639\pi$
$19$	−2.86628	−0.657571	−0.328785	+	0.944405i	$0.606639\pi$
$20$	−2.39960	−0.536568
$21$	−4.88983	−1.06705
$22$	0.293566	0.0625884
$23$	−7.68924	−1.60332	−0.801659	−	0.597782i	$-0.796049\pi$
$23$	−7.68924	−1.60332	−0.801659	+	0.597782i	$0.796049\pi$
$24$	1.00231	0.204595
$25$	1.00000	0.200000
$26$	7.74597	1.51911
$27$	5.46491	1.05172
$28$	9.81227	1.85434
$29$	−2.63406	−0.489132	−0.244566	−	0.969633i	$-0.578645\pi$
$29$	−2.63406	−0.489132	−0.244566	+	0.969633i	$0.578645\pi$
$30$	−2.50825	−0.457942
$31$	9.05554	1.62642	0.813212	−	0.581968i	$-0.197717\pi$
$31$	9.05554	1.62642	0.813212	+	0.581968i	$0.197717\pi$
$32$	8.05515	1.42396
$33$	0.167364	0.0291344
$34$	2.55028	0.437370
$35$	−4.08912	−0.691187
$36$	−3.76744	−0.627907
$37$	9.81412	1.61343	0.806716	−	0.590940i	$-0.201243\pi$
$37$	9.81412	1.61343	0.806716	+	0.590940i	$0.201243\pi$
$38$	6.01210	0.975291
$39$	4.41604	0.707133
$40$	0.838178	0.132528
$41$	3.06916	0.479322	0.239661	−	0.970857i	$-0.422964\pi$
$41$	3.06916	0.479322	0.239661	+	0.970857i	$0.422964\pi$
$42$	10.2565	1.58262
$43$	−12.2352	−1.86586	−0.932928	−	0.360063i	$-0.882755\pi$
$43$	−12.2352	−1.86586	−0.932928	+	0.360063i	$0.882755\pi$
$44$	−0.335844	−0.0506304
$45$	1.57003	0.234046
$46$	16.1284	2.37800
$47$	8.67272	1.26505	0.632523	−	0.774541i	$-0.282019\pi$
$47$	8.67272	1.26505	0.632523	+	0.774541i	$0.282019\pi$
$48$	3.63660	0.524899
$49$	9.72090	1.38870
$50$	−2.09752	−0.296635
$51$	1.45394	0.203592
$52$	−8.86153	−1.22887
$53$	−5.48317	−0.753171	−0.376586	−	0.926382i	$-0.622902\pi$
$53$	−5.48317	−0.753171	−0.376586	+	0.926382i	$0.622902\pi$
$54$	−11.4628	−1.55989
$55$	0.139958	0.0188720
$56$	−3.42741	−0.458007
$57$	3.42755	0.453990
$58$	5.52499	0.725467
$59$	12.8315	1.67052	0.835261	−	0.549854i	$-0.185317\pi$
$59$	12.8315	1.67052	0.835261	+	0.549854i	$0.185317\pi$
$60$	2.86948	0.370449
$61$	1.14285	0.146327	0.0731635	−	0.997320i	$-0.476691\pi$
$61$	1.14285	0.146327	0.0731635	+	0.997320i	$0.476691\pi$
$62$	−18.9942	−2.41227
$63$	−6.42002	−0.808847
$64$	−10.8137	−1.35171
$65$	3.69291	0.458050
$66$	−0.351050	−0.0432113
$67$	−8.57482	−1.04758	−0.523791	−	0.851847i	$-0.675483\pi$
$67$	−8.57482	−1.04758	−0.523791	+	0.851847i	$0.675483\pi$
$68$	−2.91757	−0.353807
$69$	9.19491	1.10694
$70$	8.57702	1.02515
$71$	10.5672	1.25410	0.627049	−	0.778980i	$-0.284263\pi$
$71$	10.5672	1.25410	0.627049	+	0.778980i	$0.284263\pi$
$72$	1.31596	0.155088
$73$	16.0617	1.87988	0.939941	−	0.341336i	$-0.110880\pi$
$73$	16.0617	1.87988	0.939941	+	0.341336i	$0.110880\pi$
$74$	−20.5853	−2.39300
$75$	−1.19582	−0.138081
$76$	−6.87795	−0.788955
$77$	−0.572306	−0.0652203
$78$	−9.26275	−1.04880
$79$	−9.44767	−1.06295	−0.531473	−	0.847075i	$-0.678361\pi$
$79$	−9.44767	−1.06295	−0.531473	+	0.847075i	$0.678361\pi$
$80$	3.04111	0.340006
$81$	−1.82494	−0.202771
$82$	−6.43764	−0.710918
$83$	−5.92807	−0.650690	−0.325345	−	0.945595i	$-0.605480\pi$
$83$	−5.92807	−0.650690	−0.325345	+	0.945595i	$0.605480\pi$
$84$	−11.7337	−1.28025
$85$	1.21585	0.131878
$86$	25.6637	2.76739
$87$	3.14984	0.337699
$88$	0.117310	0.0125053
$89$	−15.0748	−1.59792	−0.798962	−	0.601381i	$-0.794617\pi$
$89$	−15.0748	−1.59792	−0.798962	+	0.601381i	$0.794617\pi$
$90$	−3.29317	−0.347130
$91$	−15.1008	−1.58299
$92$	−18.4511	−1.92366
$93$	−10.8288	−1.12289
$94$	−18.1912	−1.87628
$95$	2.86628	0.294075
$96$	−9.63248	−0.983110
$97$	6.67720	0.677967	0.338984	−	0.940792i	$-0.389917\pi$
$97$	6.67720	0.677967	0.338984	+	0.940792i	$0.389917\pi$
$98$	−20.3898	−2.05968
$99$	0.219738	0.0220845
$100$	2.39960	0.239960
$101$	−0.295887	−0.0294419	−0.0147210	−	0.999892i	$-0.504686\pi$
$101$	−0.295887	−0.0294419	−0.0147210	+	0.999892i	$0.504686\pi$
$102$	−3.04966	−0.301962
$103$	8.71859	0.859068	0.429534	−	0.903051i	$-0.358678\pi$
$103$	8.71859	0.859068	0.429534	+	0.903051i	$0.358678\pi$
$104$	3.09532	0.303521
$105$	4.88983	0.477199
$106$	11.5011	1.11708
$107$	−7.50595	−0.725627	−0.362814	−	0.931862i	$-0.618184\pi$
$107$	−7.50595	−0.725627	−0.362814	+	0.931862i	$0.618184\pi$
$108$	13.1136	1.26186
$109$	−8.49616	−0.813785	−0.406892	−	0.913476i	$-0.633388\pi$
$109$	−8.49616	−0.813785	−0.406892	+	0.913476i	$0.633388\pi$
$110$	−0.293566	−0.0279904
$111$	−11.7359	−1.11392
$112$	−12.4355	−1.17504
$113$	−5.01330	−0.471611	−0.235806	−	0.971800i	$-0.575773\pi$
$113$	−5.01330	−0.471611	−0.235806	+	0.971800i	$0.575773\pi$
$114$	−7.18936	−0.673345
$115$	7.68924	0.717025
$116$	−6.32069	−0.586861
$117$	5.79797	0.536023
$118$	−26.9144	−2.47767
$119$	−4.97177	−0.455761
$120$	−1.00231	−0.0914976
$121$	−10.9804	−0.998219
$122$	−2.39716	−0.217028
$123$	−3.67015	−0.330926
$124$	21.7297	1.95139
$125$	−1.00000	−0.0894427
$126$	13.4661	1.19966
$127$	20.2779	1.79937	0.899687	−	0.436536i	$-0.143795\pi$
$127$	20.2779	1.79937	0.899687	+	0.436536i	$0.143795\pi$
$128$	6.57158	0.580851
$129$	14.6311	1.28820
$130$	−7.74597	−0.679367
$131$	−10.3008	−0.899981	−0.449991	−	0.893033i	$-0.648573\pi$
$131$	−10.3008	−0.899981	−0.449991	+	0.893033i	$0.648573\pi$
$132$	0.401608	0.0349555
$133$	−11.7206	−1.01630
$134$	17.9859	1.55374
$135$	−5.46491	−0.470344
$136$	1.01910	0.0873873
$137$	6.41147	0.547769	0.273885	−	0.961763i	$-0.411691\pi$
$137$	6.41147	0.547769	0.273885	+	0.961763i	$0.411691\pi$
$138$	−19.2865	−1.64178
$139$	13.5246	1.14714	0.573570	−	0.819157i	$-0.305558\pi$
$139$	13.5246	1.14714	0.573570	+	0.819157i	$0.305558\pi$
$140$	−9.81227	−0.829288
$141$	−10.3710	−0.873393
$142$	−22.1650	−1.86004
$143$	0.516854	0.0432215
$144$	4.77462	0.397885
$145$	2.63406	0.218746
$146$	−33.6898	−2.78819
$147$	−11.6244	−0.958764
$148$	23.5500	1.93580
$149$	−14.5315	−1.19047	−0.595233	−	0.803553i	$-0.702940\pi$
$149$	−14.5315	−1.19047	−0.595233	+	0.803553i	$0.702940\pi$
$150$	2.50825	0.204798
$151$	8.68386	0.706683	0.353341	−	0.935494i	$-0.385045\pi$
$151$	8.68386	0.706683	0.353341	+	0.935494i	$0.385045\pi$
$152$	2.40246	0.194865
$153$	1.90892	0.154327
$154$	1.20042	0.0967330
$155$	−9.05554	−0.727359
$156$	10.5968	0.848419
$157$	11.2468	0.897590	0.448795	−	0.893635i	$-0.351853\pi$
$157$	11.2468	0.897590	0.448795	+	0.893635i	$0.351853\pi$
$158$	19.8167	1.57653
$159$	6.55686	0.519993
$160$	−8.05515	−0.636816
$161$	−31.4422	−2.47799
$162$	3.82785	0.300745
$163$	20.5747	1.61153	0.805766	−	0.592234i	$-0.201754\pi$
$163$	20.5747	1.61153	0.805766	+	0.592234i	$0.201754\pi$
$164$	7.36477	0.575092
$165$	−0.167364	−0.0130293
$166$	12.4343	0.965086
$167$	10.8739	0.841444	0.420722	−	0.907190i	$-0.361777\pi$
$167$	10.8739	0.841444	0.420722	+	0.907190i	$0.361777\pi$
$168$	4.09855	0.316210
$169$	0.637610	0.0490469
$170$	−2.55028	−0.195598
$171$	4.50014	0.344134
$172$	−29.3597	−2.23866
$173$	−6.03118	−0.458542	−0.229271	−	0.973363i	$-0.573634\pi$
$173$	−6.03118	−0.458542	−0.229271	+	0.973363i	$0.573634\pi$
$174$	−6.60687	−0.500866
$175$	4.08912	0.309108
$176$	0.425628	0.0320829
$177$	−15.3441	−1.15334
$178$	31.6197	2.37000
$179$	−13.4651	−1.00643	−0.503213	−	0.864162i	$-0.667849\pi$
$179$	−13.4651	−1.00643	−0.503213	+	0.864162i	$0.667849\pi$
$180$	3.76744	0.280808
$181$	19.3229	1.43626	0.718130	−	0.695909i	$-0.244999\pi$
$181$	19.3229	1.43626	0.718130	+	0.695909i	$0.244999\pi$
$182$	31.6742	2.34785
$183$	−1.36664	−0.101025
$184$	6.44495	0.475128
$185$	−9.81412	−0.721549
$186$	22.7136	1.66544
$187$	0.170169	0.0124440
$188$	20.8111	1.51781
$189$	22.3467	1.62548
$190$	−6.01210	−0.436164
$191$	−20.5471	−1.48673	−0.743367	−	0.668884i	$-0.766772\pi$
$191$	−20.5471	−1.48673	−0.743367	+	0.668884i	$0.766772\pi$
$192$	12.9311	0.933224
$193$	−11.4263	−0.822486	−0.411243	−	0.911526i	$-0.634905\pi$
$193$	−11.4263	−0.822486	−0.411243	+	0.911526i	$0.634905\pi$
$194$	−14.0056	−1.00554
$195$	−4.41604	−0.316239
$196$	23.3263	1.66616
$197$	−12.4420	−0.886459	−0.443229	−	0.896408i	$-0.646167\pi$
$197$	−12.4420	−0.886459	−0.443229	+	0.896408i	$0.646167\pi$
$198$	−0.460906	−0.0327551
$199$	−19.3251	−1.36992	−0.684959	−	0.728582i	$-0.740180\pi$
$199$	−19.3251	−1.36992	−0.684959	+	0.728582i	$0.740180\pi$
$200$	−0.838178	−0.0592682
$201$	10.2539	0.723255
$202$	0.620631	0.0436674
$203$	−10.7710	−0.755974
$204$	3.48887	0.244270
$205$	−3.06916	−0.214360
$206$	−18.2874	−1.27415
$207$	12.0723	0.839083
$208$	11.2306	0.778699
$209$	0.401160	0.0277488
$210$	−10.2565	−0.707768
$211$	14.3718	0.989394	0.494697	−	0.869066i	$-0.335279\pi$
$211$	14.3718	0.989394	0.494697	+	0.869066i	$0.335279\pi$
$212$	−13.1574	−0.903656
$213$	−12.6364	−0.865834
$214$	15.7439	1.07623
$215$	12.2352	0.834436
$216$	−4.58057	−0.311668
$217$	37.0292	2.51371
$218$	17.8209	1.20698
$219$	−19.2069	−1.29788
$220$	0.335844	0.0226426
$221$	4.49004	0.302033
$222$	24.6163	1.65214
$223$	3.71101	0.248507	0.124254	−	0.992250i	$-0.460346\pi$
$223$	3.71101	0.248507	0.124254	+	0.992250i	$0.460346\pi$
$224$	32.9385	2.20080
$225$	−1.57003	−0.104668
$226$	10.5155	0.699481
$227$	−5.65984	−0.375657	−0.187828	−	0.982202i	$-0.560145\pi$
$227$	−5.65984	−0.375657	−0.187828	+	0.982202i	$0.560145\pi$
$228$	8.22476	0.544698
$229$	−25.1732	−1.66350	−0.831748	−	0.555154i	$-0.812659\pi$
$229$	−25.1732	−1.66350	−0.831748	+	0.555154i	$0.812659\pi$
$230$	−16.1284	−1.06347
$231$	0.684372	0.0450284
$232$	2.20781	0.144950
$233$	22.3944	1.46710	0.733552	−	0.679633i	$-0.237861\pi$
$233$	22.3944	1.46710	0.733552	+	0.679633i	$0.237861\pi$
$234$	−12.1614	−0.795014
$235$	−8.67272	−0.565746
$236$	30.7906	2.00429
$237$	11.2977	0.733863
$238$	10.4284	0.675973
$239$	12.0496	0.779426	0.389713	−	0.920936i	$-0.372574\pi$
$239$	12.0496	0.779426	0.389713	+	0.920936i	$0.372574\pi$
$240$	−3.63660	−0.234742
$241$	13.6787	0.881121	0.440561	−	0.897723i	$-0.354780\pi$
$241$	13.6787	0.881121	0.440561	+	0.897723i	$0.354780\pi$
$242$	23.0317	1.48053
$243$	−14.2124	−0.911728
$244$	2.74239	0.175563
$245$	−9.72090	−0.621045
$246$	7.69822	0.490821
$247$	10.5849	0.673504
$248$	−7.59016	−0.481976
$249$	7.08888	0.449239
$250$	2.09752	0.132659
$251$	−11.0749	−0.699044	−0.349522	−	0.936928i	$-0.613656\pi$
$251$	−11.0749	−0.699044	−0.349522	+	0.936928i	$0.613656\pi$
$252$	−15.4055	−0.970456
$253$	1.07617	0.0676584
$254$	−42.5334	−2.66878
$255$	−1.45394	−0.0910490
$256$	7.84326	0.490204
$257$	22.9281	1.43022	0.715108	−	0.699014i	$-0.246378\pi$
$257$	22.9281	1.43022	0.715108	+	0.699014i	$0.246378\pi$
$258$	−30.6890	−1.91062
$259$	40.1311	2.49363
$260$	8.86153	0.549569
$261$	4.13554	0.255983
$262$	21.6061	1.33483
$263$	10.0198	0.617849	0.308925	−	0.951087i	$-0.400031\pi$
$263$	10.0198	0.617849	0.308925	+	0.951087i	$0.400031\pi$
$264$	−0.140281	−0.00863370
$265$	5.48317	0.336828
$266$	24.5842	1.50735
$267$	18.0267	1.10321
$268$	−20.5762	−1.25689
$269$	−3.02493	−0.184433	−0.0922166	−	0.995739i	$-0.529395\pi$
$269$	−3.02493	−0.184433	−0.0922166	+	0.995739i	$0.529395\pi$
$270$	11.4628	0.697602
$271$	−10.1771	−0.618214	−0.309107	−	0.951027i	$-0.600030\pi$
$271$	−10.1771	−0.618214	−0.309107	+	0.951027i	$0.600030\pi$
$272$	3.69754	0.224196
$273$	18.0577	1.09290
$274$	−13.4482	−0.812437
$275$	−0.139958	−0.00843980
$276$	22.0641	1.32811
$277$	18.7411	1.12604	0.563022	−	0.826442i	$-0.309639\pi$
$277$	18.7411	1.12604	0.563022	+	0.826442i	$0.309639\pi$
$278$	−28.3681	−1.70141
$279$	−14.2174	−0.851176
$280$	3.42741	0.204827
$281$	−22.5214	−1.34351	−0.671757	−	0.740772i	$-0.734460\pi$
$281$	−22.5214	−1.34351	−0.671757	+	0.740772i	$0.734460\pi$
$282$	21.7534	1.29539
$283$	16.9734	1.00896	0.504481	−	0.863423i	$-0.331684\pi$
$283$	16.9734	1.00896	0.504481	+	0.863423i	$0.331684\pi$
$284$	25.3571	1.50467
$285$	−3.42755	−0.203030
$286$	−1.08411	−0.0641049
$287$	12.5502	0.740813
$288$	−12.6468	−0.745220
$289$	−15.5217	−0.913041
$290$	−5.52499	−0.324439
$291$	−7.98470	−0.468071
$292$	38.5418	2.25549
$293$	−10.8754	−0.635345	−0.317673	−	0.948200i	$-0.602901\pi$
$293$	−10.8754	−0.635345	−0.317673	+	0.948200i	$0.602901\pi$
$294$	24.3824	1.42201
$295$	−12.8315	−0.747080
$296$	−8.22598	−0.478126
$297$	−0.764858	−0.0443816
$298$	30.4801	1.76567
$299$	28.3957	1.64217
$300$	−2.86948	−0.165670
$301$	−50.0313	−2.88376
$302$	−18.2146	−1.04813
$303$	0.353827	0.0203268
$304$	8.71668	0.499936
$305$	−1.14285	−0.0654394
$306$	−4.00401	−0.228894
$307$	15.5496	0.887461	0.443730	−	0.896160i	$-0.353655\pi$
$307$	15.5496	0.887461	0.443730	+	0.896160i	$0.353655\pi$
$308$	−1.37331	−0.0782514
$309$	−10.4258	−0.593104
$310$	18.9942	1.07880
$311$	−16.2279	−0.920202	−0.460101	−	0.887867i	$-0.652187\pi$
$311$	−16.2279	−0.920202	−0.460101	+	0.887867i	$0.652187\pi$
$312$	−3.70143	−0.209552
$313$	−24.8885	−1.40678	−0.703390	−	0.710804i	$-0.748331\pi$
$313$	−24.8885	−1.40678	−0.703390	+	0.710804i	$0.748331\pi$
$314$	−23.5904	−1.33128
$315$	6.42002	0.361727
$316$	−22.6707	−1.27533
$317$	−22.1974	−1.24673	−0.623365	−	0.781931i	$-0.714235\pi$
$317$	−22.1974	−1.24673	−0.623365	+	0.781931i	$0.714235\pi$
$318$	−13.7532	−0.771239
$319$	0.368658	0.0206409
$320$	10.8137	0.604502
$321$	8.97573	0.500976
$322$	65.9508	3.67529
$323$	3.48498	0.193910
$324$	−4.37913	−0.243285
$325$	−3.69291	−0.204846
$326$	−43.1558	−2.39018
$327$	10.1598	0.561840
$328$	−2.57250	−0.142043
$329$	35.4638	1.95518
$330$	0.351050	0.0193247
$331$	7.73244	0.425013	0.212507	−	0.977160i	$-0.431837\pi$
$331$	7.73244	0.425013	0.212507	+	0.977160i	$0.431837\pi$
$332$	−14.2250	−0.780699
$333$	−15.4084	−0.844377
$334$	−22.8082	−1.24801
$335$	8.57482	0.468493
$336$	14.8705	0.811253
$337$	−19.1883	−1.04525	−0.522626	−	0.852562i	$-0.675047\pi$
$337$	−19.1883	−1.04525	−0.522626	+	0.852562i	$0.675047\pi$
$338$	−1.33740	−0.0727451
$339$	5.99498	0.325603
$340$	2.91757	0.158227
$341$	−1.26740	−0.0686334
$342$	−9.43915	−0.510411
$343$	11.1261	0.600752
$344$	10.2553	0.552929
$345$	−9.19491	−0.495037
$346$	12.6505	0.680098
$347$	7.97307	0.428017	0.214008	−	0.976832i	$-0.431348\pi$
$347$	7.97307	0.428017	0.214008	+	0.976832i	$0.431348\pi$
$348$	7.55838	0.405172
$349$	−8.59454	−0.460055	−0.230028	−	0.973184i	$-0.573882\pi$
$349$	−8.59454	−0.460055	−0.230028	+	0.973184i	$0.573882\pi$
$350$	−8.57702	−0.458461
$351$	−20.1814	−1.07720
$352$	−1.12738	−0.0600898
$353$	21.6708	1.15342	0.576711	−	0.816948i	$-0.304336\pi$
$353$	21.6708	1.15342	0.576711	+	0.816948i	$0.304336\pi$
$354$	32.1847	1.71060
$355$	−10.5672	−0.560849
$356$	−36.1735	−1.91719
$357$	5.94532	0.314660
$358$	28.2433	1.49271
$359$	−20.4095	−1.07717	−0.538586	−	0.842570i	$-0.681041\pi$
$359$	−20.4095	−1.07717	−0.538586	+	0.842570i	$0.681041\pi$
$360$	−1.31596	−0.0693573
$361$	−10.7844	−0.567601
$362$	−40.5302	−2.13022
$363$	13.1305	0.689175
$364$	−36.2359	−1.89927
$365$	−16.0617	−0.840709
$366$	2.86656	0.149837
$367$	−37.6935	−1.96759	−0.983793	−	0.179310i	$-0.942613\pi$
$367$	−37.6935	−1.96759	−0.983793	+	0.179310i	$0.942613\pi$
$368$	23.3838	1.21897
$369$	−4.81866	−0.250850
$370$	20.5853	1.07018
$371$	−22.4213	−1.16406
$372$	−25.9847	−1.34725
$373$	2.71645	0.140652	0.0703262	−	0.997524i	$-0.477596\pi$
$373$	2.71645	0.140652	0.0703262	+	0.997524i	$0.477596\pi$
$374$	−0.356933	−0.0184566
$375$	1.19582	0.0617516
$376$	−7.26929	−0.374885
$377$	9.72734	0.500983
$378$	−46.8726	−2.41087
$379$	−9.78505	−0.502624	−0.251312	−	0.967906i	$-0.580862\pi$
$379$	−9.78505	−0.502624	−0.251312	+	0.967906i	$0.580862\pi$
$380$	6.87795	0.352831
$381$	−24.2486	−1.24230
$382$	43.0980	2.20508
$383$	19.9277	1.01826	0.509129	−	0.860690i	$-0.329968\pi$
$383$	19.9277	1.01826	0.509129	+	0.860690i	$0.329968\pi$
$384$	−7.85840	−0.401022
$385$	0.572306	0.0291674
$386$	23.9670	1.21989
$387$	19.2096	0.976481
$388$	16.0226	0.813426
$389$	−26.5980	−1.34857	−0.674286	−	0.738470i	$-0.735549\pi$
$389$	−26.5980	−1.34857	−0.674286	+	0.738470i	$0.735549\pi$
$390$	9.26275	0.469038
$391$	9.34899	0.472799
$392$	−8.14785	−0.411528
$393$	12.3178	0.621351
$394$	26.0975	1.31477
$395$	9.44767	0.475364
$396$	0.527284	0.0264970
$397$	−11.7067	−0.587543	−0.293771	−	0.955876i	$-0.594910\pi$
$397$	−11.7067	−0.587543	−0.293771	+	0.955876i	$0.594910\pi$
$398$	40.5348	2.03183
$399$	14.0156	0.701660
$400$	−3.04111	−0.152055
$401$	25.7615	1.28647	0.643235	−	0.765669i	$-0.277592\pi$
$401$	25.7615	1.28647	0.643235	+	0.765669i	$0.277592\pi$
$402$	−21.5078	−1.07271
$403$	−33.4413	−1.66583
$404$	−0.710013	−0.0353244
$405$	1.82494	0.0906820
$406$	22.5924	1.12124
$407$	−1.37357	−0.0680852
$408$	−1.21866	−0.0603325
$409$	18.7521	0.927230	0.463615	−	0.886037i	$-0.346552\pi$
$409$	18.7521	0.927230	0.463615	+	0.886037i	$0.346552\pi$
$410$	6.43764	0.317932
$411$	−7.66694	−0.378182
$412$	20.9212	1.03071
$413$	52.4696	2.58186
$414$	−25.3219	−1.24451
$415$	5.92807	0.290998
$416$	−29.7470	−1.45847
$417$	−16.1729	−0.791990
$418$	−0.841443	−0.0411563
$419$	29.2237	1.42767	0.713836	−	0.700313i	$-0.246956\pi$
$419$	29.2237	1.42767	0.713836	+	0.700313i	$0.246956\pi$
$420$	11.7337	0.572544
$421$	−17.7216	−0.863696	−0.431848	−	0.901946i	$-0.642138\pi$
$421$	−17.7216	−0.863696	−0.431848	+	0.901946i	$0.642138\pi$
$422$	−30.1451	−1.46744
$423$	−13.6164	−0.662052
$424$	4.59587	0.223195
$425$	−1.21585	−0.0589775
$426$	26.5052	1.28418
$427$	4.67325	0.226155
$428$	−18.0113	−0.870609
$429$	−0.618061	−0.0298403
$430$	−25.6637	−1.23761
$431$	−12.2218	−0.588703	−0.294352	−	0.955697i	$-0.595104\pi$
$431$	−12.2218	−0.588703	−0.294352	+	0.955697i	$0.595104\pi$
$432$	−16.6194	−0.799600
$433$	19.4917	0.936712	0.468356	−	0.883540i	$-0.344846\pi$
$433$	19.4917	0.936712	0.468356	+	0.883540i	$0.344846\pi$
$434$	−77.6696	−3.72826
$435$	−3.14984	−0.151023
$436$	−20.3874	−0.976381
$437$	22.0395	1.05429
$438$	40.2868	1.92498
$439$	29.7939	1.42198	0.710992	−	0.703200i	$-0.248246\pi$
$439$	29.7939	1.42198	0.710992	+	0.703200i	$0.248246\pi$
$440$	−0.117310	−0.00559253
$441$	−15.2621	−0.726765
$442$	−9.41797	−0.447967
$443$	−1.34689	−0.0639925	−0.0319962	−	0.999488i	$-0.510186\pi$
$443$	−1.34689	−0.0639925	−0.0319962	+	0.999488i	$0.510186\pi$
$444$	−28.1615	−1.33648
$445$	15.0748	0.714614
$446$	−7.78392	−0.368579
$447$	17.3770	0.821902
$448$	−44.2183	−2.08912
$449$	−24.4875	−1.15564	−0.577819	−	0.816165i	$-0.696096\pi$
$449$	−24.4875	−1.15564	−0.577819	+	0.816165i	$0.696096\pi$
$450$	3.29317	0.155241
$451$	−0.429554	−0.0202269
$452$	−12.0299	−0.565840
$453$	−10.3843	−0.487897
$454$	11.8716	0.557164
$455$	15.1008	0.707935
$456$	−2.87290	−0.134536
$457$	−33.1742	−1.55183	−0.775913	−	0.630840i	$-0.782710\pi$
$457$	−33.1742	−1.55183	−0.775913	+	0.630840i	$0.782710\pi$
$458$	52.8015	2.46725
$459$	−6.64452	−0.310140
$460$	18.4511	0.860288
$461$	14.6642	0.682980	0.341490	−	0.939885i	$-0.389068\pi$
$461$	14.6642	0.682980	0.341490	+	0.939885i	$0.389068\pi$
$462$	−1.43549	−0.0667849
$463$	35.5467	1.65200	0.825998	−	0.563673i	$-0.190612\pi$
$463$	35.5467	1.65200	0.825998	+	0.563673i	$0.190612\pi$
$464$	8.01045	0.371876
$465$	10.8288	0.502172
$466$	−46.9727	−2.17597
$467$	−28.8650	−1.33571	−0.667857	−	0.744290i	$-0.732788\pi$
$467$	−28.8650	−1.33571	−0.667857	+	0.744290i	$0.732788\pi$
$468$	13.9128	0.643121
$469$	−35.0635	−1.61908
$470$	18.1912	0.839099
$471$	−13.4491	−0.619700
$472$	−10.7551	−0.495044
$473$	1.71242	0.0787372
$474$	−23.6971	−1.08845
$475$	−2.86628	−0.131514
$476$	−11.9303	−0.546823
$477$	8.60872	0.394166
$478$	−25.2744	−1.15602
$479$	−4.89701	−0.223750	−0.111875	−	0.993722i	$-0.535686\pi$
$479$	−4.89701	−0.223750	−0.111875	+	0.993722i	$0.535686\pi$
$480$	9.63248	0.439660
$481$	−36.2427	−1.65253
$482$	−28.6913	−1.30685
$483$	37.5991	1.71082
$484$	−26.3486	−1.19767
$485$	−6.67720	−0.303196
$486$	29.8109	1.35225
$487$	−5.34582	−0.242242	−0.121121	−	0.992638i	$-0.538649\pi$
$487$	−5.34582	−0.242242	−0.121121	+	0.992638i	$0.538649\pi$
$488$	−0.957913	−0.0433627
$489$	−24.6035	−1.11261
$490$	20.3898	0.921118
$491$	−16.5223	−0.745643	−0.372821	−	0.927903i	$-0.621610\pi$
$491$	−16.5223	−0.745643	−0.372821	+	0.927903i	$0.621610\pi$
$492$	−8.80691	−0.397046
$493$	3.20263	0.144239
$494$	−22.2022	−0.998923
$495$	−0.219738	−0.00987649
$496$	−27.5389	−1.23653
$497$	43.2106	1.93826
$498$	−14.8691	−0.666300
$499$	−6.72549	−0.301074	−0.150537	−	0.988604i	$-0.548100\pi$
$499$	−6.72549	−0.301074	−0.150537	+	0.988604i	$0.548100\pi$
$500$	−2.39960	−0.107314
$501$	−13.0031	−0.580936
$502$	23.2299	1.03680
$503$	25.1228	1.12017	0.560084	−	0.828436i	$-0.310769\pi$
$503$	25.1228	1.12017	0.560084	+	0.828436i	$0.310769\pi$
$504$	5.38113	0.239694
$505$	0.295887	0.0131668
$506$	−2.25730	−0.100349
$507$	−0.762464	−0.0338622
$508$	48.6589	2.15889
$509$	−38.7773	−1.71877	−0.859386	−	0.511328i	$-0.829154\pi$
$509$	−38.7773	−1.71877	−0.859386	+	0.511328i	$0.829154\pi$
$510$	3.04966	0.135041
$511$	65.6783	2.90544
$512$	−29.5946	−1.30791
$513$	−15.6640	−0.691582
$514$	−48.0922	−2.12126
$515$	−8.71859	−0.384187
$516$	35.1088	1.54558
$517$	−1.21382	−0.0533837
$518$	−84.1760	−3.69848
$519$	7.21218	0.316580
$520$	−3.09532	−0.135739
$521$	−9.34111	−0.409242	−0.204621	−	0.978841i	$-0.565596\pi$
$521$	−9.34111	−0.409242	−0.204621	+	0.978841i	$0.565596\pi$
$522$	−8.67438	−0.379667
$523$	−24.1676	−1.05677	−0.528387	−	0.849004i	$-0.677203\pi$
$523$	−24.1676	−1.05677	−0.528387	+	0.849004i	$0.677203\pi$
$524$	−24.7177	−1.07980
$525$	−4.88983	−0.213410
$526$	−21.0168	−0.916377
$527$	−11.0102	−0.479612
$528$	−0.508973	−0.0221502
$529$	36.1244	1.57063
$530$	−11.5011	−0.499575
$531$	−20.1458	−0.874254
$532$	−28.1248	−1.21936
$533$	−11.3341	−0.490936
$534$	−37.8113	−1.63626
$535$	7.50595	0.324510
$536$	7.18723	0.310441
$537$	16.1017	0.694841
$538$	6.34486	0.273546
$539$	−1.36052	−0.0586017
$540$	−13.1136	−0.564320
$541$	−12.0463	−0.517911	−0.258956	−	0.965889i	$-0.583378\pi$
$541$	−12.0463	−0.517911	−0.258956	+	0.965889i	$0.583378\pi$
$542$	21.3467	0.916918
$543$	−23.1066	−0.991599
$544$	−9.79389	−0.419909
$545$	8.49616	0.363936
$546$	−37.8765	−1.62096
$547$	−0.253716	−0.0108481	−0.00542406	−	0.999985i	$-0.501727\pi$
$547$	−0.253716	−0.0108481	−0.00542406	+	0.999985i	$0.501727\pi$
$548$	15.3850	0.657215
$549$	−1.79431	−0.0765791
$550$	0.293566	0.0125177
$551$	7.54995	0.321639
$552$	−7.70697	−0.328031
$553$	−38.6327	−1.64283
$554$	−39.3099	−1.67012
$555$	11.7359	0.498160
$556$	32.4536	1.37634
$557$	−6.18398	−0.262024	−0.131012	−	0.991381i	$-0.541823\pi$
$557$	−6.18398	−0.262024	−0.131012	+	0.991381i	$0.541823\pi$
$558$	29.8214	1.26244
$559$	45.1837	1.91107
$560$	12.4355	0.525494
$561$	−0.203490	−0.00859137
$562$	47.2392	1.99266
$563$	23.0630	0.971990	0.485995	−	0.873962i	$-0.338457\pi$
$563$	23.0630	0.971990	0.485995	+	0.873962i	$0.338457\pi$
$564$	−24.8862	−1.04790
$565$	5.01330	0.210911
$566$	−35.6020	−1.49647
$567$	−7.46240	−0.313391
$568$	−8.85721	−0.371640
$569$	2.97459	0.124701	0.0623506	−	0.998054i	$-0.480140\pi$
$569$	2.97459	0.124701	0.0623506	+	0.998054i	$0.480140\pi$
$570$	7.18936	0.301129
$571$	3.56555	0.149214	0.0746068	−	0.997213i	$-0.476230\pi$
$571$	3.56555	0.149214	0.0746068	+	0.997213i	$0.476230\pi$
$572$	1.24024	0.0518572
$573$	24.5705	1.02645
$574$	−26.3243	−1.09875
$575$	−7.68924	−0.320663
$576$	16.9777	0.707405
$577$	−43.7788	−1.82254	−0.911268	−	0.411814i	$-0.864895\pi$
$577$	−43.7788	−1.82254	−0.911268	+	0.411814i	$0.864895\pi$
$578$	32.5571	1.35420
$579$	13.6638	0.567848
$580$	6.32069	0.262452
$581$	−24.2406	−1.00567
$582$	16.7481	0.694231
$583$	0.767415	0.0317831
$584$	−13.4626	−0.557086
$585$	−5.79797	−0.239717
$586$	22.8113	0.942327
$587$	−16.5988	−0.685106	−0.342553	−	0.939498i	$-0.611292\pi$
$587$	−16.5988	−0.685106	−0.342553	+	0.939498i	$0.611292\pi$
$588$	−27.8939	−1.15033
$589$	−25.9558	−1.06949
$590$	26.9144	1.10805
$591$	14.8784	0.612015
$592$	−29.8458	−1.22666
$593$	−15.3464	−0.630202	−0.315101	−	0.949058i	$-0.602038\pi$
$593$	−15.3464	−0.630202	−0.315101	+	0.949058i	$0.602038\pi$
$594$	1.60431	0.0658256
$595$	4.97177	0.203823
$596$	−34.8698	−1.42832
$597$	23.1092	0.945797
$598$	−59.5606	−2.43562
$599$	25.9911	1.06197	0.530984	−	0.847382i	$-0.321823\pi$
$599$	25.9911	1.06197	0.530984	+	0.847382i	$0.321823\pi$
$600$	1.00231	0.0409190
$601$	12.4366	0.507301	0.253650	−	0.967296i	$-0.418369\pi$
$601$	12.4366	0.507301	0.253650	+	0.967296i	$0.418369\pi$
$602$	104.942	4.27711
$603$	13.4627	0.548243
$604$	20.8378	0.847879
$605$	10.9804	0.446417
$606$	−0.742160	−0.0301482
$607$	−28.6675	−1.16358	−0.581789	−	0.813340i	$-0.697647\pi$
$607$	−28.6675	−1.16358	−0.581789	+	0.813340i	$0.697647\pi$
$608$	−23.0884	−0.936357
$609$	12.8801	0.521927
$610$	2.39716	0.0970580
$611$	−32.0276	−1.29570
$612$	4.58065	0.185162
$613$	20.7525	0.838187	0.419094	−	0.907943i	$-0.362348\pi$
$613$	20.7525	0.838187	0.419094	+	0.907943i	$0.362348\pi$
$614$	−32.6156	−1.31626
$615$	3.67015	0.147995
$616$	0.479694	0.0193274
$617$	−39.6214	−1.59510	−0.797549	−	0.603254i	$-0.793871\pi$
$617$	−39.6214	−1.59510	−0.797549	+	0.603254i	$0.793871\pi$
$618$	21.8684	0.879676
$619$	43.9301	1.76570	0.882851	−	0.469653i	$-0.155621\pi$
$619$	43.9301	1.76570	0.882851	+	0.469653i	$0.155621\pi$
$620$	−21.7297	−0.872686
$621$	−42.0210	−1.68624
$622$	34.0385	1.36482
$623$	−61.6426	−2.46966
$624$	−13.4297	−0.537617
$625$	1.00000	0.0400000
$626$	52.2042	2.08650
$627$	−0.479713	−0.0191579
$628$	26.9878	1.07693
$629$	−11.9325	−0.475781
$630$	−13.4661	−0.536504
$631$	1.67700	0.0667604	0.0333802	−	0.999443i	$-0.489373\pi$
$631$	1.67700	0.0667604	0.0333802	+	0.999443i	$0.489373\pi$
$632$	7.91884	0.314994
$633$	−17.1860	−0.683082
$634$	46.5595	1.84912
$635$	−20.2779	−0.804704
$636$	15.7339	0.623888
$637$	−35.8984	−1.42235
$638$	−0.773268	−0.0306140
$639$	−16.5908	−0.656322
$640$	−6.57158	−0.259765
$641$	13.4317	0.530520	0.265260	−	0.964177i	$-0.414542\pi$
$641$	13.4317	0.530520	0.265260	+	0.964177i	$0.414542\pi$
$642$	−18.8268	−0.743034
$643$	−24.3026	−0.958401	−0.479201	−	0.877705i	$-0.659073\pi$
$643$	−24.3026	−0.958401	−0.479201	+	0.877705i	$0.659073\pi$
$644$	−75.4489	−2.97310
$645$	−14.6311	−0.576098
$646$	−7.30983	−0.287601
$647$	−33.4586	−1.31539	−0.657696	−	0.753283i	$-0.728469\pi$
$647$	−33.4586	−1.31539	−0.657696	+	0.753283i	$0.728469\pi$
$648$	1.52963	0.0600894
$649$	−1.79588	−0.0704943
$650$	7.74597	0.303822
$651$	−44.2801	−1.73547
$652$	49.3710	1.93352
$653$	7.93564	0.310546	0.155273	−	0.987872i	$-0.450374\pi$
$653$	7.93564	0.310546	0.155273	+	0.987872i	$0.450374\pi$
$654$	−21.3105	−0.833307
$655$	10.3008	0.402484
$656$	−9.33365	−0.364418
$657$	−25.2173	−0.983821
$658$	−74.3861	−2.89987
$659$	−17.1911	−0.669672	−0.334836	−	0.942276i	$-0.608681\pi$
$659$	−17.1911	−0.669672	−0.334836	+	0.942276i	$0.608681\pi$
$660$	−0.401608	−0.0156326
$661$	25.9887	1.01084	0.505421	−	0.862873i	$-0.331337\pi$
$661$	25.9887	1.01084	0.505421	+	0.862873i	$0.331337\pi$
$662$	−16.2190	−0.630368
$663$	−5.36926	−0.208525
$664$	4.96878	0.192826
$665$	11.7206	0.454505
$666$	32.3195	1.25236
$667$	20.2539	0.784233
$668$	26.0929	1.00957
$669$	−4.43768	−0.171570
$670$	−17.9859	−0.694856
$671$	−0.159951	−0.00617485
$672$	−39.3883	−1.51944
$673$	18.6322	0.718219	0.359110	−	0.933295i	$-0.383080\pi$
$673$	18.6322	0.718219	0.359110	+	0.933295i	$0.383080\pi$
$674$	40.2478	1.55029
$675$	5.46491	0.210344
$676$	1.53001	0.0588466
$677$	25.3240	0.973279	0.486640	−	0.873603i	$-0.338222\pi$
$677$	25.3240	0.973279	0.486640	+	0.873603i	$0.338222\pi$
$678$	−12.5746	−0.482925
$679$	27.3039	1.04783
$680$	−1.01910	−0.0390808
$681$	6.76812	0.259355
$682$	2.65840	0.101795
$683$	42.5903	1.62967	0.814836	−	0.579692i	$-0.196827\pi$
$683$	42.5903	1.62967	0.814836	+	0.579692i	$0.196827\pi$
$684$	10.7986	0.412893
$685$	−6.41147	−0.244970
$686$	−23.3372	−0.891019
$687$	30.1026	1.14848
$688$	37.2087	1.41857
$689$	20.2489	0.771421
$690$	19.2865	0.734226
$691$	44.4759	1.69194	0.845971	−	0.533229i	$-0.179021\pi$
$691$	44.4759	1.69194	0.845971	+	0.533229i	$0.179021\pi$
$692$	−14.4725	−0.550160
$693$	0.898535	0.0341325
$694$	−16.7237	−0.634823
$695$	−13.5246	−0.513016
$696$	−2.64013	−0.100074
$697$	−3.73165	−0.141346
$698$	18.0272	0.682341
$699$	−26.7795	−1.01290
$700$	9.81227	0.370869
$701$	−31.5825	−1.19285	−0.596427	−	0.802667i	$-0.703414\pi$
$701$	−31.5825	−1.19285	−0.596427	+	0.802667i	$0.703414\pi$
$702$	42.3310	1.59768
$703$	−28.1301	−1.06095
$704$	1.51346	0.0570407
$705$	10.3710	0.390593
$706$	−45.4551	−1.71072
$707$	−1.20992	−0.0455037
$708$	−36.8198	−1.38377
$709$	−20.9386	−0.786367	−0.393183	−	0.919460i	$-0.628626\pi$
$709$	−20.9386	−0.786367	−0.393183	+	0.919460i	$0.628626\pi$
$710$	22.1650	0.831837
$711$	14.8331	0.556284
$712$	12.6354	0.473530
$713$	−69.6302	−2.60767
$714$	−12.4704	−0.466695
$715$	−0.516854	−0.0193292
$716$	−32.3108	−1.20751
$717$	−14.4091	−0.538119
$718$	42.8094	1.59763
$719$	−11.7959	−0.439913	−0.219956	−	0.975510i	$-0.570591\pi$
$719$	−11.7959	−0.439913	−0.219956	+	0.975510i	$0.570591\pi$
$720$	−4.77462	−0.177940
$721$	35.6514	1.32773
$722$	22.6206	0.841850
$723$	−16.3572	−0.608330
$724$	46.3673	1.72323
$725$	−2.63406	−0.0978264
$726$	−27.5416	−1.02217
$727$	28.7750	1.06720	0.533602	−	0.845736i	$-0.320838\pi$
$727$	28.7750	1.06720	0.533602	+	0.845736i	$0.320838\pi$
$728$	12.6571	0.469105
$729$	22.4703	0.832232
$730$	33.6898	1.24692
$731$	14.8763	0.550218
$732$	−3.27939	−0.121210
$733$	−23.5387	−0.869422	−0.434711	−	0.900570i	$-0.643149\pi$
$733$	−23.5387	−0.869422	−0.434711	+	0.900570i	$0.643149\pi$
$734$	79.0630	2.91827
$735$	11.6244	0.428772
$736$	−61.9380	−2.28307
$737$	1.20012	0.0442069
$738$	10.1073	0.372053
$739$	12.8737	0.473568	0.236784	−	0.971562i	$-0.423907\pi$
$739$	12.8737	0.473568	0.236784	+	0.971562i	$0.423907\pi$
$740$	−23.5500	−0.865715
$741$	−12.6576	−0.464990
$742$	47.0293	1.72650
$743$	−41.5349	−1.52377	−0.761883	−	0.647714i	$-0.775725\pi$
$743$	−41.5349	−1.52377	−0.761883	+	0.647714i	$0.775725\pi$
$744$	9.07643	0.332758
$745$	14.5315	0.532392
$746$	−5.69782	−0.208612
$747$	9.30723	0.340534
$748$	0.408337	0.0149303
$749$	−30.6927	−1.12149
$750$	−2.50825	−0.0915883
$751$	32.8343	1.19814	0.599070	−	0.800697i	$-0.295537\pi$
$751$	32.8343	1.19814	0.599070	+	0.800697i	$0.295537\pi$
$752$	−26.3747	−0.961786
$753$	13.2436	0.482623
$754$	−20.4033	−0.743045
$755$	−8.68386	−0.316038
$756$	53.6231	1.95025
$757$	−4.19286	−0.152392	−0.0761960	−	0.997093i	$-0.524277\pi$
$757$	−4.19286	−0.152392	−0.0761960	+	0.997093i	$0.524277\pi$
$758$	20.5244	0.745479
$759$	−1.28690	−0.0467116
$760$	−2.40246	−0.0871463
$761$	0.0272117	0.000986424 0	0.000493212	−	1.00000i	$-0.499843\pi$
$761$	0.0272117	0.000986424 0	0.000493212		1.00000i	$0.499843\pi$
$762$	50.8621	1.84254
$763$	−34.7418	−1.25774
$764$	−49.3048	−1.78379
$765$	−1.90892	−0.0690172
$766$	−41.7988	−1.51025
$767$	−47.3857	−1.71100
$768$	−9.37909	−0.338439
$769$	−32.5234	−1.17282	−0.586412	−	0.810013i	$-0.699460\pi$
$769$	−32.5234	−1.17282	−0.586412	+	0.810013i	$0.699460\pi$
$770$	−1.20042	−0.0432603
$771$	−27.4178	−0.987427
$772$	−27.4187	−0.986820
$773$	−39.0371	−1.40407	−0.702033	−	0.712145i	$-0.747724\pi$
$773$	−39.0371	−1.40407	−0.702033	+	0.712145i	$0.747724\pi$
$774$	−40.2927	−1.44829
$775$	9.05554	0.325285
$776$	−5.59669	−0.200909
$777$	−47.9894	−1.72161
$778$	55.7899	2.00017
$779$	−8.79709	−0.315188
$780$	−10.5968	−0.379425
$781$	−1.47897	−0.0529216
$782$	−19.6097	−0.701242
$783$	−14.3949	−0.514431
$784$	−29.5623	−1.05580
$785$	−11.2468	−0.401414
$786$	−25.8369	−0.921571
$787$	42.2866	1.50736	0.753678	−	0.657244i	$-0.228278\pi$
$787$	42.2866	1.50736	0.753678	+	0.657244i	$0.228278\pi$
$788$	−29.8560	−1.06358
$789$	−11.9819	−0.426566
$790$	−19.8167	−0.705047
$791$	−20.5000	−0.728895
$792$	−0.184180	−0.00654454
$793$	−4.22045	−0.149873
$794$	24.5551	0.871428
$795$	−6.55686	−0.232548
$796$	−46.3725	−1.64363
$797$	34.0930	1.20764	0.603819	−	0.797122i	$-0.293645\pi$
$797$	34.0930	1.20764	0.603819	+	0.797122i	$0.293645\pi$
$798$	−29.3982	−1.04068
$799$	−10.5448	−0.373047
$800$	8.05515	0.284793
$801$	23.6678	0.836261
$802$	−54.0354	−1.90806
$803$	−2.24797	−0.0793291
$804$	24.6053	0.867762
$805$	31.4422	1.10819
$806$	70.1440	2.47072
$807$	3.61726	0.127333
$808$	0.248006	0.00872484
$809$	33.7788	1.18760	0.593799	−	0.804613i	$-0.297627\pi$
$809$	33.7788	1.18760	0.593799	+	0.804613i	$0.297627\pi$
$810$	−3.82785	−0.134497
$811$	−48.2791	−1.69531	−0.847655	−	0.530548i	$-0.821986\pi$
$811$	−48.2791	−1.69531	−0.847655	+	0.530548i	$0.821986\pi$
$812$	−25.8461	−0.907019
$813$	12.1699	0.426817
$814$	2.88109	0.100982
$815$	−20.5747	−0.720699
$816$	−4.42158	−0.154786
$817$	35.0697	1.22693
$818$	−39.3329	−1.37524
$819$	23.7086	0.828445
$820$	−7.36477	−0.257189
$821$	22.7409	0.793662	0.396831	−	0.917892i	$-0.370110\pi$
$821$	22.7409	0.793662	0.396831	+	0.917892i	$0.370110\pi$
$822$	16.0816	0.560910
$823$	−11.7946	−0.411133	−0.205567	−	0.978643i	$-0.565904\pi$
$823$	−11.7946	−0.411133	−0.205567	+	0.978643i	$0.565904\pi$
$824$	−7.30773	−0.254577
$825$	0.167364	0.00582687
$826$	−110.056	−3.82935
$827$	−38.4772	−1.33798	−0.668991	−	0.743270i	$-0.733274\pi$
$827$	−38.4772	−1.33798	−0.668991	+	0.743270i	$0.733274\pi$
$828$	28.9688	1.00673
$829$	−41.6228	−1.44562	−0.722809	−	0.691048i	$-0.757149\pi$
$829$	−41.6228	−1.44562	−0.722809	+	0.691048i	$0.757149\pi$
$830$	−12.4343	−0.431600
$831$	−22.4109	−0.777425
$832$	39.9339	1.38446
$833$	−11.8192	−0.409511
$834$	33.9230	1.17466
$835$	−10.8739	−0.376305
$836$	0.962625	0.0332931
$837$	49.4877	1.71055
$838$	−61.2975	−2.11749
$839$	11.1870	0.386218	0.193109	−	0.981177i	$-0.438143\pi$
$839$	11.1870	0.386218	0.193109	+	0.981177i	$0.438143\pi$
$840$	−4.09855	−0.141413
$841$	−22.0618	−0.760750
$842$	37.1714	1.28101
$843$	26.9314	0.927568
$844$	34.4866	1.18708
$845$	−0.637610	−0.0219344
$846$	28.5607	0.981938
$847$	−44.9002	−1.54279
$848$	16.6749	0.572619
$849$	−20.2970	−0.696592
$850$	2.55028	0.0874739
$851$	−75.4631	−2.58684
$852$	−30.3224	−1.03883
$853$	56.8535	1.94663	0.973313	−	0.229480i	$-0.0737024\pi$
$853$	56.8535	1.94663	0.973313	+	0.229480i	$0.0737024\pi$
$854$	−9.80226	−0.335426
$855$	−4.50014	−0.153902
$856$	6.29132	0.215033
$857$	7.26178	0.248058	0.124029	−	0.992279i	$-0.460418\pi$
$857$	7.26178	0.248058	0.124029	+	0.992279i	$0.460418\pi$
$858$	1.29640	0.0442583
$859$	−37.7167	−1.28688	−0.643438	−	0.765498i	$-0.722493\pi$
$859$	−37.7167	−1.28688	−0.643438	+	0.765498i	$0.722493\pi$
$860$	29.3597	1.00116
$861$	−15.0077	−0.511460
$862$	25.6355	0.873148
$863$	−19.9269	−0.678320	−0.339160	−	0.940729i	$-0.610143\pi$
$863$	−19.9269	−0.678320	−0.339160	+	0.940729i	$0.610143\pi$
$864$	44.0207	1.49761
$865$	6.03118	0.205066
$866$	−40.8843	−1.38931
$867$	18.5611	0.630368
$868$	88.8554	3.01595
$869$	1.32228	0.0448553
$870$	6.60687	0.223994
$871$	31.6661	1.07296
$872$	7.12130	0.241158
$873$	−10.4834	−0.354809
$874$	−46.2285	−1.56370
$875$	−4.08912	−0.138237
$876$	−46.0888	−1.55720
$877$	−13.9286	−0.470335	−0.235167	−	0.971955i	$-0.575564\pi$
$877$	−13.9286	−0.470335	−0.235167	+	0.971955i	$0.575564\pi$
$878$	−62.4933	−2.10905
$879$	13.0049	0.438645
$880$	−0.425628	−0.0143479
$881$	9.42769	0.317627	0.158813	−	0.987309i	$-0.449233\pi$
$881$	9.42769	0.317627	0.158813	+	0.987309i	$0.449233\pi$
$882$	32.0125	1.07792
$883$	−51.2606	−1.72506	−0.862529	−	0.506008i	$-0.831121\pi$
$883$	−51.2606	−1.72506	−0.862529	+	0.506008i	$0.831121\pi$
$884$	10.7743	0.362380
$885$	15.3441	0.515787
$886$	2.82513	0.0949119
$887$	−13.6235	−0.457434	−0.228717	−	0.973493i	$-0.573453\pi$
$887$	−13.6235	−0.457434	−0.228717	+	0.973493i	$0.573453\pi$
$888$	9.83676	0.330100
$889$	82.9188	2.78101
$890$	−31.6197	−1.05990
$891$	0.255415	0.00855674
$892$	8.90494	0.298160
$893$	−24.8585	−0.831858
$894$	−36.4486	−1.21902
$895$	13.4651	0.450088
$896$	26.8720	0.897730
$897$	−33.9560	−1.13376
$898$	51.3631	1.71401
$899$	−23.8528	−0.795536
$900$	−3.76744	−0.125581
$901$	6.66673	0.222101
$902$	0.901000	0.0300000
$903$	59.8282	1.99096
$904$	4.20204	0.139758
$905$	−19.3229	−0.642315
$906$	21.7813	0.723635
$907$	−23.0135	−0.764151	−0.382076	−	0.924131i	$-0.624791\pi$
$907$	−23.0135	−0.764151	−0.382076	+	0.924131i	$0.624791\pi$
$908$	−13.5814	−0.450714
$909$	0.464551	0.0154082
$910$	−31.6742	−1.04999
$911$	9.52488	0.315573	0.157787	−	0.987473i	$-0.449564\pi$
$911$	9.52488	0.315573	0.157787	+	0.987473i	$0.449564\pi$
$912$	−10.4235	−0.345158
$913$	0.829682	0.0274585
$914$	69.5837	2.30163
$915$	1.36664	0.0451797
$916$	−60.4058	−1.99586
$917$	−42.1210	−1.39096
$918$	13.9370	0.459991
$919$	−4.11527	−0.135750	−0.0678751	−	0.997694i	$-0.521622\pi$
$919$	−4.11527	−0.135750	−0.0678751	+	0.997694i	$0.521622\pi$
$920$	−6.44495	−0.212484
$921$	−18.5944	−0.612707
$922$	−30.7585	−1.01298
$923$	−39.0238	−1.28448
$924$	1.64222	0.0540251
$925$	9.81412	0.322686
$926$	−74.5601	−2.45020
$927$	−13.6884	−0.449586
$928$	−21.2177	−0.696506
$929$	−33.7759	−1.10815	−0.554075	−	0.832467i	$-0.686928\pi$
$929$	−33.7759	−1.10815	−0.554075	+	0.832467i	$0.686928\pi$
$930$	−22.7136	−0.744807
$931$	−27.8629	−0.913168
$932$	53.7377	1.76024
$933$	19.4056	0.635311
$934$	60.5451	1.98110
$935$	−0.170169	−0.00556511
$936$	−4.85973	−0.158845
$937$	34.7617	1.13561	0.567807	−	0.823162i	$-0.307792\pi$
$937$	34.7617	1.13561	0.567807	+	0.823162i	$0.307792\pi$
$938$	73.5465	2.40138
$939$	29.7620	0.971247
$940$	−20.8111	−0.678783
$941$	30.8355	1.00521	0.502604	−	0.864517i	$-0.332375\pi$
$941$	30.8355	1.00521	0.502604	+	0.864517i	$0.332375\pi$
$942$	28.2097	0.919122
$943$	−23.5995	−0.768506
$944$	−39.0221	−1.27006
$945$	−22.3467	−0.726937
$946$	−3.59184	−0.116781
$947$	−15.8595	−0.515364	−0.257682	−	0.966230i	$-0.582959\pi$
$947$	−15.8595	−0.515364	−0.257682	+	0.966230i	$0.582959\pi$
$948$	27.1099	0.880490
$949$	−59.3146	−1.92543
$950$	6.01210	0.195058
$951$	26.5440	0.860747
$952$	4.16723	0.135061
$953$	3.03305	0.0982502	0.0491251	−	0.998793i	$-0.484357\pi$
$953$	3.03305	0.0982502	0.0491251	+	0.998793i	$0.484357\pi$
$954$	−18.0570	−0.584617
$955$	20.5471	0.664888
$956$	28.9144	0.935157
$957$	−0.440846	−0.0142505
$958$	10.2716	0.331860
$959$	26.2173	0.846600
$960$	−12.9311	−0.417350
$961$	51.0029	1.64525
$962$	76.0199	2.45098
$963$	11.7845	0.379751
$964$	32.8234	1.05717
$965$	11.4263	0.367827
$966$	−78.8649	−2.53744
$967$	−3.11441	−0.100153	−0.0500764	−	0.998745i	$-0.515946\pi$
$967$	−3.11441	−0.100153	−0.0500764	+	0.998745i	$0.515946\pi$
$968$	9.20354	0.295813
$969$	−4.16739	−0.133876
$970$	14.0056	0.449692
$971$	−30.6773	−0.984483	−0.492241	−	0.870459i	$-0.663822\pi$
$971$	−30.6773	−0.984483	−0.492241	+	0.870459i	$0.663822\pi$
$972$	−34.1042	−1.09389
$973$	55.3036	1.77295
$974$	11.2130	0.359287
$975$	4.41604	0.141427
$976$	−3.47553	−0.111249
$977$	−41.3356	−1.32244	−0.661221	−	0.750191i	$-0.729961\pi$
$977$	−41.3356	−1.32244	−0.661221	+	0.750191i	$0.729961\pi$
$978$	51.6064	1.65019
$979$	2.10984	0.0674308
$980$	−23.3263	−0.745131
$981$	13.3392	0.425888
$982$	34.6560	1.10592
$983$	10.4157	0.332210	0.166105	−	0.986108i	$-0.446881\pi$
$983$	10.4157	0.332210	0.166105	+	0.986108i	$0.446881\pi$
$984$	3.07624	0.0980669
$985$	12.4420	0.396436
$986$	−6.71758	−0.213931
$987$	−42.4081	−1.34987
$988$	25.3997	0.808071
$989$	94.0797	2.99156
$990$	0.460906	0.0146485
$991$	−33.5801	−1.06671	−0.533353	−	0.845893i	$-0.679068\pi$
$991$	−33.5801	−1.06671	−0.533353	+	0.845893i	$0.679068\pi$
$992$	72.9438	2.31597
$993$	−9.24657	−0.293431
$994$	−90.6352	−2.87477
$995$	19.3251	0.612646
$996$	17.0105	0.538998
$997$	6.84841	0.216891	0.108446	−	0.994102i	$-0.465413\pi$
$997$	6.84841	0.216891	0.108446	+	0.994102i	$0.465413\pi$
$998$	14.1069	0.446545
$999$	53.6333	1.69688

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8005.2.a.f.1.20	✓	127

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8005.2.a.f.1.20	✓	127	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:	\( N \)	\(=\)	\( 8005 = 5 \cdot 1601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.09752 q^{2} -1.19582 q^{3} +2.39960 q^{4} -1.00000 q^{5} +2.50825 q^{6} +4.08912 q^{7} -0.838178 q^{8} -1.57003 q^{9} +O(q^{10})\)	\(q-2.09752 q^{2} -1.19582 q^{3} +2.39960 q^{4} -1.00000 q^{5} +2.50825 q^{6} +4.08912 q^{7} -0.838178 q^{8} -1.57003 q^{9} +2.09752 q^{10} -0.139958 q^{11} -2.86948 q^{12} -3.69291 q^{13} -8.57702 q^{14} +1.19582 q^{15} -3.04111 q^{16} -1.21585 q^{17} +3.29317 q^{18} -2.86628 q^{19} -2.39960 q^{20} -4.88983 q^{21} +0.293566 q^{22} -7.68924 q^{23} +1.00231 q^{24} +1.00000 q^{25} +7.74597 q^{26} +5.46491 q^{27} +9.81227 q^{28} -2.63406 q^{29} -2.50825 q^{30} +9.05554 q^{31} +8.05515 q^{32} +0.167364 q^{33} +2.55028 q^{34} -4.08912 q^{35} -3.76744 q^{36} +9.81412 q^{37} +6.01210 q^{38} +4.41604 q^{39} +0.838178 q^{40} +3.06916 q^{41} +10.2565 q^{42} -12.2352 q^{43} -0.335844 q^{44} +1.57003 q^{45} +16.1284 q^{46} +8.67272 q^{47} +3.63660 q^{48} +9.72090 q^{49} -2.09752 q^{50} +1.45394 q^{51} -8.86153 q^{52} -5.48317 q^{53} -11.4628 q^{54} +0.139958 q^{55} -3.42741 q^{56} +3.42755 q^{57} +5.52499 q^{58} +12.8315 q^{59} +2.86948 q^{60} +1.14285 q^{61} -18.9942 q^{62} -6.42002 q^{63} -10.8137 q^{64} +3.69291 q^{65} -0.351050 q^{66} -8.57482 q^{67} -2.91757 q^{68} +9.19491 q^{69} +8.57702 q^{70} +10.5672 q^{71} +1.31596 q^{72} +16.0617 q^{73} -20.5853 q^{74} -1.19582 q^{75} -6.87795 q^{76} -0.572306 q^{77} -9.26275 q^{78} -9.44767 q^{79} +3.04111 q^{80} -1.82494 q^{81} -6.43764 q^{82} -5.92807 q^{83} -11.7337 q^{84} +1.21585 q^{85} +25.6637 q^{86} +3.14984 q^{87} +0.117310 q^{88} -15.0748 q^{89} -3.29317 q^{90} -15.1008 q^{91} -18.4511 q^{92} -10.8288 q^{93} -18.1912 q^{94} +2.86628 q^{95} -9.63248 q^{96} +6.67720 q^{97} -20.3898 q^{98} +0.219738 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9}+O(q^{10}) \) 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9	\( 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9} + 6 q^{10} - 45 q^{11} - 30 q^{12} - 53 q^{14} + 18 q^{15} + 84 q^{16} - 36 q^{17} - 10 q^{18} - 49 q^{19} - 114 q^{20} - 48 q^{21} + 13 q^{22} - 29 q^{23} - 63 q^{24} + 127 q^{25} - 55 q^{26} - 75 q^{27} + 44 q^{28} - 45 q^{29} + 20 q^{30} - 49 q^{31} - 32 q^{32} - 8 q^{33} - 52 q^{34} - 28 q^{35} + 44 q^{36} + 36 q^{37} - 65 q^{38} - 52 q^{39} + 18 q^{40} - 66 q^{41} - 18 q^{42} - 5 q^{43} - 93 q^{44} - 101 q^{45} - 25 q^{46} - 32 q^{47} - 54 q^{48} + 77 q^{49} - 6 q^{50} - 102 q^{51} - 13 q^{52} - 67 q^{53} - 53 q^{54} + 45 q^{55} - 158 q^{56} + 16 q^{57} + 35 q^{58} - 213 q^{59} + 30 q^{60} - 62 q^{61} - 33 q^{62} + 59 q^{63} + 34 q^{64} - 60 q^{66} + 10 q^{67} - 94 q^{68} - 93 q^{69} + 53 q^{70} - 118 q^{71} - 24 q^{72} + 35 q^{73} - 107 q^{74} - 18 q^{75} - 98 q^{76} - 93 q^{77} + 21 q^{78} - 64 q^{79} - 84 q^{80} + 15 q^{81} + 15 q^{82} - 187 q^{83} - 118 q^{84} + 36 q^{85} - 126 q^{86} - 53 q^{87} + 15 q^{88} - 138 q^{89} + 10 q^{90} - 138 q^{91} - 86 q^{92} + 23 q^{93} - 60 q^{94} + 49 q^{95} - 92 q^{96} + 9 q^{97} - 67 q^{98} - 147 q^{99}+O(q^{100}) \) 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9 + 6 * q^10 - 45 * q^11 - 30 * q^12 - 53 * q^14 + 18 * q^15 + 84 * q^16 - 36 * q^17 - 10 * q^18 - 49 * q^19 - 114 * q^20 - 48 * q^21 + 13 * q^22 - 29 * q^23 - 63 * q^24 + 127 * q^25 - 55 * q^26 - 75 * q^27 + 44 * q^28 - 45 * q^29 + 20 * q^30 - 49 * q^31 - 32 * q^32 - 8 * q^33 - 52 * q^34 - 28 * q^35 + 44 * q^36 + 36 * q^37 - 65 * q^38 - 52 * q^39 + 18 * q^40 - 66 * q^41 - 18 * q^42 - 5 * q^43 - 93 * q^44 - 101 * q^45 - 25 * q^46 - 32 * q^47 - 54 * q^48 + 77 * q^49 - 6 * q^50 - 102 * q^51 - 13 * q^52 - 67 * q^53 - 53 * q^54 + 45 * q^55 - 158 * q^56 + 16 * q^57 + 35 * q^58 - 213 * q^59 + 30 * q^60 - 62 * q^61 - 33 * q^62 + 59 * q^63 + 34 * q^64 - 60 * q^66 + 10 * q^67 - 94 * q^68 - 93 * q^69 + 53 * q^70 - 118 * q^71 - 24 * q^72 + 35 * q^73 - 107 * q^74 - 18 * q^75 - 98 * q^76 - 93 * q^77 + 21 * q^78 - 64 * q^79 - 84 * q^80 + 15 * q^81 + 15 * q^82 - 187 * q^83 - 118 * q^84 + 36 * q^85 - 126 * q^86 - 53 * q^87 + 15 * q^88 - 138 * q^89 + 10 * q^90 - 138 * q^91 - 86 * q^92 + 23 * q^93 - 60 * q^94 + 49 * q^95 - 92 * q^96 + 9 * q^97 - 67 * q^98 - 147 * q^99

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