LMFDB - Embedded newform 8035.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, 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("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.1597980241$
Analytic rank:	$0$
Dimension:	$127$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.25182 q^{2} +0.156734 q^{3} +3.07069 q^{4} -1.00000 q^{5} -0.352938 q^{6} +4.92465 q^{7} -2.41100 q^{8} -2.97543 q^{9} +O(q^{10})$	\(q-2.25182 q^{2} +0.156734 q^{3} +3.07069 q^{4} -1.00000 q^{5} -0.352938 q^{6} +4.92465 q^{7} -2.41100 q^{8} -2.97543 q^{9} +2.25182 q^{10} +1.62991 q^{11} +0.481283 q^{12} -3.16650 q^{13} -11.0894 q^{14} -0.156734 q^{15} -0.712243 q^{16} +3.17458 q^{17} +6.70014 q^{18} +5.12744 q^{19} -3.07069 q^{20} +0.771862 q^{21} -3.67027 q^{22} +2.13830 q^{23} -0.377887 q^{24} +1.00000 q^{25} +7.13039 q^{26} -0.936557 q^{27} +15.1221 q^{28} +1.75742 q^{29} +0.352938 q^{30} -2.47728 q^{31} +6.42584 q^{32} +0.255464 q^{33} -7.14857 q^{34} -4.92465 q^{35} -9.13664 q^{36} -4.03755 q^{37} -11.5461 q^{38} -0.496300 q^{39} +2.41100 q^{40} +9.88647 q^{41} -1.73809 q^{42} -0.426675 q^{43} +5.00496 q^{44} +2.97543 q^{45} -4.81506 q^{46} -6.14356 q^{47} -0.111633 q^{48} +17.2522 q^{49} -2.25182 q^{50} +0.497566 q^{51} -9.72335 q^{52} +6.63139 q^{53} +2.10896 q^{54} -1.62991 q^{55} -11.8733 q^{56} +0.803646 q^{57} -3.95738 q^{58} -5.62554 q^{59} -0.481283 q^{60} +2.28751 q^{61} +5.57838 q^{62} -14.6530 q^{63} -13.0454 q^{64} +3.16650 q^{65} -0.575258 q^{66} -2.08372 q^{67} +9.74814 q^{68} +0.335145 q^{69} +11.0894 q^{70} +8.12636 q^{71} +7.17377 q^{72} -7.25447 q^{73} +9.09184 q^{74} +0.156734 q^{75} +15.7448 q^{76} +8.02675 q^{77} +1.11758 q^{78} +0.404882 q^{79} +0.712243 q^{80} +8.77951 q^{81} -22.2626 q^{82} -1.48329 q^{83} +2.37015 q^{84} -3.17458 q^{85} +0.960794 q^{86} +0.275448 q^{87} -3.92972 q^{88} -15.7693 q^{89} -6.70014 q^{90} -15.5939 q^{91} +6.56605 q^{92} -0.388275 q^{93} +13.8342 q^{94} -5.12744 q^{95} +1.00715 q^{96} -2.13658 q^{97} -38.8487 q^{98} -4.84970 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) $ 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9 - 19 * q^10 + 30 * q^11 + 35 * q^12 + 30 * q^13 + 39 * q^14 - 10 * q^15 + 121 * q^16 + 63 * q^17 + 53 * q^18 - 35 * q^19 - 125 * q^20 + 33 * q^21 + 49 * q^22 + 61 * q^23 - 5 * q^24 + 127 * q^25 + 10 * q^26 + 40 * q^27 + 32 * q^28 + 134 * q^29 - 25 * q^31 + 122 * q^32 + 48 * q^33 - 21 * q^34 - 13 * q^35 + 133 * q^36 + 60 * q^37 + 33 * q^38 + 26 * q^39 - 54 * q^40 + 9 * q^41 + 45 * q^42 + 48 * q^43 + 85 * q^44 - 123 * q^45 - 11 * q^46 + 57 * q^47 + 71 * q^48 + 70 * q^49 + 19 * q^50 + 45 * q^51 + 68 * q^52 + 182 * q^53 - 29 * q^54 - 30 * q^55 + 96 * q^56 + 74 * q^57 + 47 * q^58 + 19 * q^59 - 35 * q^60 + 16 * q^61 + 43 * q^62 + 73 * q^63 + 110 * q^64 - 30 * q^65 + 8 * q^66 + 40 * q^67 + 129 * q^68 + 2 * q^69 - 39 * q^70 + 48 * q^71 + 151 * q^72 + 30 * q^73 + 117 * q^74 + 10 * q^75 - 98 * q^76 + 134 * q^77 + 54 * q^78 + 23 * q^79 - 121 * q^80 + 111 * q^81 + 4 * q^82 + 92 * q^83 + 48 * q^84 - 63 * q^85 + 42 * q^86 + 69 * q^87 + 121 * q^88 + 12 * q^89 - 53 * q^90 - 30 * q^91 + 175 * q^92 + 82 * q^93 - 23 * q^94 + 35 * q^95 + 6 * q^96 + 67 * q^97 + 122 * q^98 + 73 * 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 $

$2$	−2.25182	−1.59228	−0.796138	−	0.605115i	$-0.793127\pi$
$2$	−2.25182	−1.59228	−0.796138	+	0.605115i	$0.793127\pi$
$3$	0.156734	0.0904907	0.0452453	−	0.998976i	$-0.485593\pi$
$3$	0.156734	0.0904907	0.0452453	+	0.998976i	$0.485593\pi$
$4$	3.07069	1.53535
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.352938	−0.144086
$7$	4.92465	1.86134	0.930671	−	0.365858i	$-0.119224\pi$
$7$	4.92465	1.86134	0.930671	+	0.365858i	$0.119224\pi$
$8$	−2.41100	−0.852417
$9$	−2.97543	−0.991811
$10$	2.25182	0.712088
$11$	1.62991	0.491437	0.245719	−	0.969341i	$-0.420976\pi$
$11$	1.62991	0.491437	0.245719	+	0.969341i	$0.420976\pi$
$12$	0.481283	0.138934
$13$	−3.16650	−0.878230	−0.439115	−	0.898431i	$-0.644708\pi$
$13$	−3.16650	−0.878230	−0.439115	+	0.898431i	$0.644708\pi$
$14$	−11.0894	−2.96377
$15$	−0.156734	−0.0404687
$16$	−0.712243	−0.178061
$17$	3.17458	0.769948	0.384974	−	0.922927i	$-0.374210\pi$
$17$	3.17458	0.769948	0.384974	+	0.922927i	$0.374210\pi$
$18$	6.70014	1.57924
$19$	5.12744	1.17632	0.588158	−	0.808746i	$-0.299853\pi$
$19$	5.12744	1.17632	0.588158	+	0.808746i	$0.299853\pi$
$20$	−3.07069	−0.686627
$21$	0.771862	0.168434
$22$	−3.67027	−0.782504
$23$	2.13830	0.445866	0.222933	−	0.974834i	$-0.428437\pi$
$23$	2.13830	0.445866	0.222933	+	0.974834i	$0.428437\pi$
$24$	−0.377887	−0.0771358
$25$	1.00000	0.200000
$26$	7.13039	1.39838
$27$	−0.936557	−0.180240
$28$	15.1221	2.85780
$29$	1.75742	0.326344	0.163172	−	0.986598i	$-0.447827\pi$
$29$	1.75742	0.326344	0.163172	+	0.986598i	$0.447827\pi$
$30$	0.352938	0.0644373
$31$	−2.47728	−0.444932	−0.222466	−	0.974940i	$-0.571411\pi$
$31$	−2.47728	−0.444932	−0.222466	+	0.974940i	$0.571411\pi$
$32$	6.42584	1.13594
$33$	0.255464	0.0444705
$34$	−7.14857	−1.22597
$35$	−4.92465	−0.832417
$36$	−9.13664	−1.52277
$37$	−4.03755	−0.663770	−0.331885	−	0.943320i	$-0.607685\pi$
$37$	−4.03755	−0.663770	−0.331885	+	0.943320i	$0.607685\pi$
$38$	−11.5461	−1.87302
$39$	−0.496300	−0.0794716
$40$	2.41100	0.381213
$41$	9.88647	1.54401	0.772004	−	0.635618i	$-0.219255\pi$
$41$	9.88647	1.54401	0.772004	+	0.635618i	$0.219255\pi$
$42$	−1.73809	−0.268194
$43$	−0.426675	−0.0650673	−0.0325336	−	0.999471i	$-0.510358\pi$
$43$	−0.426675	−0.0650673	−0.0325336	+	0.999471i	$0.510358\pi$
$44$	5.00496	0.754526
$45$	2.97543	0.443552
$46$	−4.81506	−0.709942
$47$	−6.14356	−0.896130	−0.448065	−	0.894001i	$-0.647887\pi$
$47$	−6.14356	−0.896130	−0.448065	+	0.894001i	$0.647887\pi$
$48$	−0.111633	−0.0161128
$49$	17.2522	2.46459
$50$	−2.25182	−0.318455
$51$	0.497566	0.0696731
$52$	−9.72335	−1.34839
$53$	6.63139	0.910892	0.455446	−	0.890263i	$-0.349480\pi$
$53$	6.63139	0.910892	0.455446	+	0.890263i	$0.349480\pi$
$54$	2.10896	0.286993
$55$	−1.62991	−0.219778
$56$	−11.8733	−1.58664
$57$	0.803646	0.106446
$58$	−3.95738	−0.519630
$59$	−5.62554	−0.732383	−0.366192	−	0.930539i	$-0.619339\pi$
$59$	−5.62554	−0.732383	−0.366192	+	0.930539i	$0.619339\pi$
$60$	−0.481283	−0.0621334
$61$	2.28751	0.292886	0.146443	−	0.989219i	$-0.453218\pi$
$61$	2.28751	0.292886	0.146443	+	0.989219i	$0.453218\pi$
$62$	5.57838	0.708455
$63$	−14.6530	−1.84610
$64$	−13.0454	−1.63067
$65$	3.16650	0.392756
$66$	−0.575258	−0.0708094
$67$	−2.08372	−0.254567	−0.127283	−	0.991866i	$-0.540626\pi$
$67$	−2.08372	−0.254567	−0.127283	+	0.991866i	$0.540626\pi$
$68$	9.74814	1.18214
$69$	0.335145	0.0403467
$70$	11.0894	1.32544
$71$	8.12636	0.964421	0.482211	−	0.876055i	$-0.339834\pi$
$71$	8.12636	0.964421	0.482211	+	0.876055i	$0.339834\pi$
$72$	7.17377	0.845437
$73$	−7.25447	−0.849072	−0.424536	−	0.905411i	$-0.639563\pi$
$73$	−7.25447	−0.849072	−0.424536	+	0.905411i	$0.639563\pi$
$74$	9.09184	1.05691
$75$	0.156734	0.0180981
$76$	15.7448	1.80605
$77$	8.02675	0.914733
$78$	1.11758	0.126541
$79$	0.404882	0.0455528	0.0227764	−	0.999741i	$-0.492749\pi$
$79$	0.404882	0.0455528	0.0227764	+	0.999741i	$0.492749\pi$
$80$	0.712243	0.0796312
$81$	8.77951	0.975501
$82$	−22.2626	−2.45849
$83$	−1.48329	−0.162812	−0.0814060	−	0.996681i	$-0.525941\pi$
$83$	−1.48329	−0.162812	−0.0814060	+	0.996681i	$0.525941\pi$
$84$	2.37015	0.258604
$85$	−3.17458	−0.344331
$86$	0.960794	0.103605
$87$	0.275448	0.0295311
$88$	−3.92972	−0.418910
$89$	−15.7693	−1.67154	−0.835770	−	0.549079i	$-0.814978\pi$
$89$	−15.7693	−1.67154	−0.835770	+	0.549079i	$0.814978\pi$
$90$	−6.70014	−0.706257
$91$	−15.5939	−1.63469
$92$	6.56605	0.684558
$93$	−0.388275	−0.0402622
$94$	13.8342	1.42689
$95$	−5.12744	−0.526064
$96$	1.00715	0.102792
$97$	−2.13658	−0.216937	−0.108468	−	0.994100i	$-0.534595\pi$
$97$	−2.13658	−0.216937	−0.108468	+	0.994100i	$0.534595\pi$
$98$	−38.8487	−3.92431
$99$	−4.84970	−0.487413
$100$	3.07069	0.307069
$101$	19.9007	1.98020	0.990099	−	0.140369i	$-0.0448290\pi$
$101$	19.9007	1.98020	0.990099	+	0.140369i	$0.0448290\pi$
$102$	−1.12043	−0.110939
$103$	−9.57849	−0.943797	−0.471898	−	0.881653i	$-0.656431\pi$
$103$	−9.57849	−0.943797	−0.471898	+	0.881653i	$0.656431\pi$
$104$	7.63444	0.748618
$105$	−0.771862	−0.0753260
$106$	−14.9327	−1.45039
$107$	17.7266	1.71370	0.856848	−	0.515570i	$-0.172420\pi$
$107$	17.7266	1.71370	0.856848	+	0.515570i	$0.172420\pi$
$108$	−2.87587	−0.276731
$109$	−9.13395	−0.874873	−0.437437	−	0.899249i	$-0.644114\pi$
$109$	−9.13395	−0.874873	−0.437437	+	0.899249i	$0.644114\pi$
$110$	3.67027	0.349947
$111$	−0.632824	−0.0600650
$112$	−3.50754	−0.331432
$113$	19.7699	1.85979	0.929897	−	0.367821i	$-0.119896\pi$
$113$	19.7699	1.85979	0.929897	+	0.367821i	$0.119896\pi$
$114$	−1.80967	−0.169491
$115$	−2.13830	−0.199397
$116$	5.39648	0.501050
$117$	9.42172	0.871038
$118$	12.6677	1.16616
$119$	15.6337	1.43314
$120$	0.377887	0.0344962
$121$	−8.34338	−0.758489
$122$	−5.15106	−0.466355
$123$	1.54955	0.139718
$124$	−7.60695	−0.683124
$125$	−1.00000	−0.0894427
$126$	32.9958	2.93950
$127$	7.95130	0.705564	0.352782	−	0.935706i	$-0.385236\pi$
$127$	7.95130	0.705564	0.352782	+	0.935706i	$0.385236\pi$
$128$	16.5241	1.46054
$129$	−0.0668746	−0.00588798
$130$	−7.13039	−0.625377
$131$	17.5960	1.53737	0.768685	−	0.639627i	$-0.220911\pi$
$131$	17.5960	1.53737	0.768685	+	0.639627i	$0.220911\pi$
$132$	0.784450	0.0682776
$133$	25.2508	2.18952
$134$	4.69216	0.405341
$135$	0.936557	0.0806060
$136$	−7.65391	−0.656317
$137$	−3.43836	−0.293759	−0.146880	−	0.989154i	$-0.546923\pi$
$137$	−3.43836	−0.293759	−0.146880	+	0.989154i	$0.546923\pi$
$138$	−0.754686	−0.0642431
$139$	−15.1066	−1.28133	−0.640664	−	0.767822i	$-0.721341\pi$
$139$	−15.1066	−1.28133	−0.640664	+	0.767822i	$0.721341\pi$
$140$	−15.1221	−1.27805
$141$	−0.962907	−0.0810914
$142$	−18.2991	−1.53563
$143$	−5.16113	−0.431595
$144$	2.11923	0.176603
$145$	−1.75742	−0.145945
$146$	16.3358	1.35196
$147$	2.70401	0.223023
$148$	−12.3981	−1.01912
$149$	−8.56903	−0.702002	−0.351001	−	0.936375i	$-0.614159\pi$
$149$	−8.56903	−0.702002	−0.351001	+	0.936375i	$0.614159\pi$
$150$	−0.352938	−0.0288172
$151$	1.43490	0.116770	0.0583851	−	0.998294i	$-0.481405\pi$
$151$	1.43490	0.116770	0.0583851	+	0.998294i	$0.481405\pi$
$152$	−12.3623	−1.00271
$153$	−9.44574	−0.763643
$154$	−18.0748	−1.45651
$155$	2.47728	0.198980
$156$	−1.52398	−0.122016
$157$	5.35700	0.427535	0.213767	−	0.976885i	$-0.431427\pi$
$157$	5.35700	0.427535	0.213767	+	0.976885i	$0.431427\pi$
$158$	−0.911722	−0.0725327
$159$	1.03937	0.0824273
$160$	−6.42584	−0.508007
$161$	10.5304	0.829909
$162$	−19.7699	−1.55327
$163$	18.5487	1.45285	0.726425	−	0.687246i	$-0.241180\pi$
$163$	18.5487	1.45285	0.726425	+	0.687246i	$0.241180\pi$
$164$	30.3583	2.37058
$165$	−0.255464	−0.0198878
$166$	3.34009	0.259242
$167$	−5.86248	−0.453653	−0.226826	−	0.973935i	$-0.572835\pi$
$167$	−5.86248	−0.453653	−0.226826	+	0.973935i	$0.572835\pi$
$168$	−1.86096	−0.143576
$169$	−2.97326	−0.228713
$170$	7.14857	0.548270
$171$	−15.2564	−1.16668
$172$	−1.31019	−0.0999007
$173$	1.21936	0.0927062	0.0463531	−	0.998925i	$-0.485240\pi$
$173$	1.21936	0.0927062	0.0463531	+	0.998925i	$0.485240\pi$
$174$	−0.620258	−0.0470217
$175$	4.92465	0.372268
$176$	−1.16089	−0.0875057
$177$	−0.881717	−0.0662739
$178$	35.5096	2.66155
$179$	14.9860	1.12011	0.560055	−	0.828456i	$-0.310780\pi$
$179$	14.9860	1.12011	0.560055	+	0.828456i	$0.310780\pi$
$180$	9.13664	0.681005
$181$	−1.47474	−0.109617	−0.0548083	−	0.998497i	$-0.517455\pi$
$181$	−1.47474	−0.109617	−0.0548083	+	0.998497i	$0.517455\pi$
$182$	35.1147	2.60287
$183$	0.358532	0.0265035
$184$	−5.15544	−0.380064
$185$	4.03755	0.296847
$186$	0.874324	0.0641086
$187$	5.17429	0.378381
$188$	−18.8650	−1.37587
$189$	−4.61221	−0.335489
$190$	11.5461	0.837640
$191$	−19.0777	−1.38042	−0.690208	−	0.723611i	$-0.742481\pi$
$191$	−19.0777	−1.38042	−0.690208	+	0.723611i	$0.742481\pi$
$192$	−2.04466	−0.147560
$193$	13.5858	0.977931	0.488965	−	0.872303i	$-0.337374\pi$
$193$	13.5858	0.977931	0.488965	+	0.872303i	$0.337374\pi$
$194$	4.81119	0.345423
$195$	0.496300	0.0355408
$196$	52.9760	3.78400
$197$	5.04665	0.359559	0.179779	−	0.983707i	$-0.442462\pi$
$197$	5.04665	0.359559	0.179779	+	0.983707i	$0.442462\pi$
$198$	10.9207	0.776097
$199$	24.7086	1.75155	0.875774	−	0.482721i	$-0.160351\pi$
$199$	24.7086	1.75155	0.875774	+	0.482721i	$0.160351\pi$
$200$	−2.41100	−0.170483
$201$	−0.326590	−0.0230359
$202$	−44.8129	−3.15302
$203$	8.65465	0.607437
$204$	1.52787	0.106972
$205$	−9.88647	−0.690501
$206$	21.5690	1.50279
$207$	−6.36236	−0.442215
$208$	2.25532	0.156378
$209$	8.35728	0.578085
$210$	1.73809	0.119940
$211$	13.3063	0.916044	0.458022	−	0.888941i	$-0.348558\pi$
$211$	13.3063	0.916044	0.458022	+	0.888941i	$0.348558\pi$
$212$	20.3630	1.39853
$213$	1.27368	0.0872711
$214$	−39.9171	−2.72868
$215$	0.426675	0.0290990
$216$	2.25804	0.153640
$217$	−12.1997	−0.828170
$218$	20.5680	1.39304
$219$	−1.13703	−0.0768331
$220$	−5.00496	−0.337434
$221$	−10.0523	−0.676191
$222$	1.42501	0.0956401
$223$	9.69861	0.649467	0.324733	−	0.945806i	$-0.394725\pi$
$223$	9.69861	0.649467	0.324733	+	0.945806i	$0.394725\pi$
$224$	31.6450	2.11437
$225$	−2.97543	−0.198362
$226$	−44.5182	−2.96131
$227$	−3.85890	−0.256124	−0.128062	−	0.991766i	$-0.540876\pi$
$227$	−3.85890	−0.256124	−0.128062	+	0.991766i	$0.540876\pi$
$228$	2.46775	0.163431
$229$	−4.33794	−0.286659	−0.143330	−	0.989675i	$-0.545781\pi$
$229$	−4.33794	−0.286659	−0.143330	+	0.989675i	$0.545781\pi$
$230$	4.81506	0.317496
$231$	1.25807	0.0827748
$232$	−4.23713	−0.278181
$233$	−9.91896	−0.649813	−0.324906	−	0.945746i	$-0.605333\pi$
$233$	−9.91896	−0.649813	−0.324906	+	0.945746i	$0.605333\pi$
$234$	−21.2160	−1.38693
$235$	6.14356	0.400761
$236$	−17.2743	−1.12446
$237$	0.0634590	0.00412211
$238$	−35.2042	−2.28195
$239$	−14.7636	−0.954980	−0.477490	−	0.878637i	$-0.658453\pi$
$239$	−14.7636	−0.954980	−0.477490	+	0.878637i	$0.658453\pi$
$240$	0.111633	0.00720588
$241$	−1.46268	−0.0942197	−0.0471098	−	0.998890i	$-0.515001\pi$
$241$	−1.46268	−0.0942197	−0.0471098	+	0.998890i	$0.515001\pi$
$242$	18.7878	1.20772
$243$	4.18572	0.268514
$244$	7.02424	0.449681
$245$	−17.2522	−1.10220
$246$	−3.48931	−0.222470
$247$	−16.2360	−1.03307
$248$	5.97271	0.379268
$249$	−0.232482	−0.0147330
$250$	2.25182	0.142418
$251$	−20.1546	−1.27214	−0.636072	−	0.771630i	$-0.719442\pi$
$251$	−20.1546	−1.27214	−0.636072	+	0.771630i	$0.719442\pi$
$252$	−44.9947	−2.83440
$253$	3.48524	0.219115
$254$	−17.9049	−1.12345
$255$	−0.497566	−0.0311588
$256$	−11.1186	−0.694910
$257$	21.0670	1.31413	0.657063	−	0.753836i	$-0.271799\pi$
$257$	21.0670	1.31413	0.657063	+	0.753836i	$0.271799\pi$
$258$	0.150590	0.00937530
$259$	−19.8835	−1.23550
$260$	9.72335	0.603016
$261$	−5.22907	−0.323672
$262$	−39.6230	−2.44792
$263$	9.09333	0.560718	0.280359	−	0.959895i	$-0.409546\pi$
$263$	9.09333	0.560718	0.280359	+	0.959895i	$0.409546\pi$
$264$	−0.615923	−0.0379074
$265$	−6.63139	−0.407363
$266$	−56.8603	−3.48633
$267$	−2.47159	−0.151259
$268$	−6.39845	−0.390848
$269$	−16.8801	−1.02920	−0.514598	−	0.857432i	$-0.672059\pi$
$269$	−16.8801	−1.02920	−0.514598	+	0.857432i	$0.672059\pi$
$270$	−2.10896	−0.128347
$271$	−10.7795	−0.654805	−0.327403	−	0.944885i	$-0.606173\pi$
$271$	−10.7795	−0.654805	−0.327403	+	0.944885i	$0.606173\pi$
$272$	−2.26107	−0.137097
$273$	−2.44410	−0.147924
$274$	7.74257	0.467746
$275$	1.62991	0.0982875
$276$	1.02913	0.0619461
$277$	−3.52446	−0.211764	−0.105882	−	0.994379i	$-0.533767\pi$
$277$	−3.52446	−0.211764	−0.105882	+	0.994379i	$0.533767\pi$
$278$	34.0174	2.04023
$279$	7.37097	0.441289
$280$	11.8733	0.709567
$281$	−4.70914	−0.280924	−0.140462	−	0.990086i	$-0.544859\pi$
$281$	−4.70914	−0.280924	−0.140462	+	0.990086i	$0.544859\pi$
$282$	2.16829	0.129120
$283$	−18.0172	−1.07101	−0.535506	−	0.844531i	$-0.679879\pi$
$283$	−18.0172	−1.07101	−0.535506	+	0.844531i	$0.679879\pi$
$284$	24.9535	1.48072
$285$	−0.803646	−0.0476039
$286$	11.6219	0.687219
$287$	48.6874	2.87393
$288$	−19.1197	−1.12664
$289$	−6.92206	−0.407180
$290$	3.95738	0.232385
$291$	−0.334876	−0.0196308
$292$	−22.2762	−1.30362
$293$	−2.80063	−0.163615	−0.0818073	−	0.996648i	$-0.526069\pi$
$293$	−2.80063	−0.163615	−0.0818073	+	0.996648i	$0.526069\pi$
$294$	−6.08893	−0.355114
$295$	5.62554	0.327532
$296$	9.73455	0.565809
$297$	−1.52651	−0.0885769
$298$	19.2959	1.11778
$299$	−6.77092	−0.391573
$300$	0.481283	0.0277869
$301$	−2.10122	−0.121112
$302$	−3.23113	−0.185931
$303$	3.11913	0.179190
$304$	−3.65198	−0.209456
$305$	−2.28751	−0.130983
$306$	21.2701	1.21593
$307$	−12.3834	−0.706759	−0.353380	−	0.935480i	$-0.614968\pi$
$307$	−12.3834	−0.706759	−0.353380	+	0.935480i	$0.614968\pi$
$308$	24.6477	1.40443
$309$	−1.50128	−0.0854048
$310$	−5.57838	−0.316831
$311$	5.45080	0.309086	0.154543	−	0.987986i	$-0.450609\pi$
$311$	5.45080	0.309086	0.154543	+	0.987986i	$0.450609\pi$
$312$	1.19658	0.0677430
$313$	−6.47318	−0.365886	−0.182943	−	0.983124i	$-0.558562\pi$
$313$	−6.47318	−0.365886	−0.182943	+	0.983124i	$0.558562\pi$
$314$	−12.0630	−0.680754
$315$	14.6530	0.825601
$316$	1.24327	0.0699393
$317$	8.97739	0.504221	0.252110	−	0.967698i	$-0.418875\pi$
$317$	8.97739	0.504221	0.252110	+	0.967698i	$0.418875\pi$
$318$	−2.34047	−0.131247
$319$	2.86444	0.160378
$320$	13.0454	0.729257
$321$	2.77837	0.155073
$322$	−23.7125	−1.32144
$323$	16.2774	0.905701
$324$	26.9592	1.49773
$325$	−3.16650	−0.175646
$326$	−41.7684	−2.31334
$327$	−1.43160	−0.0791679
$328$	−23.8363	−1.31614
$329$	−30.2549	−1.66800
$330$	0.575258	0.0316669
$331$	−27.6041	−1.51726	−0.758628	−	0.651524i	$-0.774130\pi$
$331$	−27.6041	−1.51726	−0.758628	+	0.651524i	$0.774130\pi$
$332$	−4.55472	−0.249972
$333$	12.0135	0.658335
$334$	13.2013	0.722340
$335$	2.08372	0.113846
$336$	−0.549753	−0.0299915
$337$	8.54410	0.465427	0.232713	−	0.972545i	$-0.425240\pi$
$337$	8.54410	0.465427	0.232713	+	0.972545i	$0.425240\pi$
$338$	6.69525	0.364174
$339$	3.09862	0.168294
$340$	−9.74814	−0.528667
$341$	−4.03775	−0.218656
$342$	34.3546	1.85768
$343$	50.4882	2.72611
$344$	1.02871	0.0554645
$345$	−0.335145	−0.0180436
$346$	−2.74578	−0.147614
$347$	33.9374	1.82185	0.910927	−	0.412567i	$-0.135368\pi$
$347$	33.9374	1.82185	0.910927	+	0.412567i	$0.135368\pi$
$348$	0.845814	0.0453404
$349$	17.8583	0.955935	0.477967	−	0.878378i	$-0.341374\pi$
$349$	17.8583	0.955935	0.477967	+	0.878378i	$0.341374\pi$
$350$	−11.0894	−0.592754
$351$	2.96561	0.158292
$352$	10.4736	0.558243
$353$	−6.89777	−0.367131	−0.183566	−	0.983007i	$-0.558764\pi$
$353$	−6.89777	−0.367131	−0.183566	+	0.983007i	$0.558764\pi$
$354$	1.98547	0.105526
$355$	−8.12636	−0.431302
$356$	−48.4226	−2.56639
$357$	2.45034	0.129685
$358$	−33.7459	−1.78352
$359$	−22.5148	−1.18829	−0.594144	−	0.804359i	$-0.702509\pi$
$359$	−22.5148	−1.18829	−0.594144	+	0.804359i	$0.702509\pi$
$360$	−7.17377	−0.378091
$361$	7.29063	0.383717
$362$	3.32085	0.174540
$363$	−1.30770	−0.0686362
$364$	−47.8841	−2.50981
$365$	7.25447	0.379716
$366$	−0.807349	−0.0422008
$367$	0.265157	0.0138411	0.00692053	−	0.999976i	$-0.497797\pi$
$367$	0.265157	0.0138411	0.00692053	+	0.999976i	$0.497797\pi$
$368$	−1.52299	−0.0793912
$369$	−29.4166	−1.53136
$370$	−9.09184	−0.472662
$371$	32.6573	1.69548
$372$	−1.19227	−0.0618164
$373$	−19.5127	−1.01033	−0.505166	−	0.863022i	$-0.668569\pi$
$373$	−19.5127	−1.01033	−0.505166	+	0.863022i	$0.668569\pi$
$374$	−11.6516	−0.602488
$375$	−0.156734	−0.00809373
$376$	14.8121	0.763877
$377$	−5.56486	−0.286605
$378$	10.3859	0.534191
$379$	2.13412	0.109622	0.0548111	−	0.998497i	$-0.482544\pi$
$379$	2.13412	0.109622	0.0548111	+	0.998497i	$0.482544\pi$
$380$	−15.7448	−0.807690
$381$	1.24624	0.0638469
$382$	42.9596	2.19800
$383$	24.3820	1.24586	0.622932	−	0.782276i	$-0.285941\pi$
$383$	24.3820	1.24586	0.622932	+	0.782276i	$0.285941\pi$
$384$	2.58989	0.132165
$385$	−8.02675	−0.409081
$386$	−30.5929	−1.55714
$387$	1.26954	0.0645345
$388$	−6.56077	−0.333073
$389$	−7.29720	−0.369983	−0.184991	−	0.982740i	$-0.559226\pi$
$389$	−7.29720	−0.369983	−0.184991	+	0.982740i	$0.559226\pi$
$390$	−1.11758	−0.0565908
$391$	6.78819	0.343293
$392$	−41.5949	−2.10086
$393$	2.75790	0.139118
$394$	−11.3641	−0.572517
$395$	−0.404882	−0.0203718
$396$	−14.8919	−0.748348
$397$	12.5852	0.631634	0.315817	−	0.948820i	$-0.397721\pi$
$397$	12.5852	0.631634	0.315817	+	0.948820i	$0.397721\pi$
$398$	−55.6394	−2.78895
$399$	3.95768	0.198132
$400$	−0.712243	−0.0356121
$401$	−3.20626	−0.160113	−0.0800565	−	0.996790i	$-0.525510\pi$
$401$	−3.20626	−0.160113	−0.0800565	+	0.996790i	$0.525510\pi$
$402$	0.735423	0.0366795
$403$	7.84430	0.390752
$404$	61.1090	3.04029
$405$	−8.77951	−0.436257
$406$	−19.4887	−0.967208
$407$	−6.58087	−0.326201
$408$	−1.19963	−0.0593906
$409$	−29.6736	−1.46727	−0.733633	−	0.679546i	$-0.762177\pi$
$409$	−29.6736	−1.46727	−0.733633	+	0.679546i	$0.762177\pi$
$410$	22.2626	1.09947
$411$	−0.538910	−0.0265825
$412$	−29.4126	−1.44905
$413$	−27.7038	−1.36322
$414$	14.3269	0.704128
$415$	1.48329	0.0728117
$416$	−20.3474	−0.997616
$417$	−2.36773	−0.115948
$418$	−18.8191	−0.920472
$419$	10.5983	0.517760	0.258880	−	0.965909i	$-0.416647\pi$
$419$	10.5983	0.517760	0.258880	+	0.965909i	$0.416647\pi$
$420$	−2.37015	−0.115651
$421$	11.6251	0.566573	0.283286	−	0.959035i	$-0.408575\pi$
$421$	11.6251	0.566573	0.283286	+	0.959035i	$0.408575\pi$
$422$	−29.9634	−1.45860
$423$	18.2798	0.888792
$424$	−15.9883	−0.776460
$425$	3.17458	0.153990
$426$	−2.86810	−0.138960
$427$	11.2652	0.545161
$428$	54.4329	2.63111
$429$	−0.808926	−0.0390553
$430$	−0.960794	−0.0463336
$431$	7.69293	0.370556	0.185278	−	0.982686i	$-0.440682\pi$
$431$	7.69293	0.370556	0.185278	+	0.982686i	$0.440682\pi$
$432$	0.667056	0.0320937
$433$	−22.7935	−1.09539	−0.547694	−	0.836679i	$-0.684494\pi$
$433$	−22.7935	−1.09539	−0.547694	+	0.836679i	$0.684494\pi$
$434$	27.4715	1.31868
$435$	−0.275448	−0.0132067
$436$	−28.0475	−1.34323
$437$	10.9640	0.524479
$438$	2.56038	0.122340
$439$	−4.59035	−0.219085	−0.109543	−	0.993982i	$-0.534939\pi$
$439$	−4.59035	−0.219085	−0.109543	+	0.993982i	$0.534939\pi$
$440$	3.92972	0.187342
$441$	−51.3326	−2.44441
$442$	22.6360	1.07668
$443$	−20.7334	−0.985076	−0.492538	−	0.870291i	$-0.663931\pi$
$443$	−20.7334	−0.985076	−0.492538	+	0.870291i	$0.663931\pi$
$444$	−1.94321	−0.0922205
$445$	15.7693	0.747536
$446$	−21.8395	−1.03413
$447$	−1.34306	−0.0635247
$448$	−64.2438	−3.03523
$449$	0.0579530	0.00273497	0.00136749	−	0.999999i	$-0.499565\pi$
$449$	0.0579530	0.00273497	0.00136749	+	0.999999i	$0.499565\pi$
$450$	6.70014	0.315848
$451$	16.1141	0.758783
$452$	60.7072	2.85542
$453$	0.224898	0.0105666
$454$	8.68954	0.407821
$455$	15.5939	0.731054
$456$	−1.93759	−0.0907361
$457$	29.3654	1.37366	0.686829	−	0.726819i	$-0.259002\pi$
$457$	29.3654	1.37366	0.686829	+	0.726819i	$0.259002\pi$
$458$	9.76827	0.456441
$459$	−2.97317	−0.138776
$460$	−6.56605	−0.306144
$461$	27.4968	1.28065	0.640327	−	0.768102i	$-0.278799\pi$
$461$	27.4968	1.28065	0.640327	+	0.768102i	$0.278799\pi$
$462$	−2.83294	−0.131800
$463$	33.3442	1.54963	0.774817	−	0.632185i	$-0.217842\pi$
$463$	33.3442	1.54963	0.774817	+	0.632185i	$0.217842\pi$
$464$	−1.25171	−0.0581090
$465$	0.388275	0.0180058
$466$	22.3357	1.03468
$467$	9.64409	0.446275	0.223138	−	0.974787i	$-0.428370\pi$
$467$	9.64409	0.446275	0.223138	+	0.974787i	$0.428370\pi$
$468$	28.9312	1.33734
$469$	−10.2616	−0.473835
$470$	−13.8342	−0.638123
$471$	0.839626	0.0386879
$472$	13.5632	0.624296
$473$	−0.695443	−0.0319765
$474$	−0.142898	−0.00656354
$475$	5.12744	0.235263
$476$	48.0062	2.20036
$477$	−19.7313	−0.903433
$478$	33.2450	1.52059
$479$	−10.4858	−0.479110	−0.239555	−	0.970883i	$-0.577001\pi$
$479$	−10.4858	−0.479110	−0.239555	+	0.970883i	$0.577001\pi$
$480$	−1.00715	−0.0459700
$481$	12.7849	0.582942
$482$	3.29370	0.150024
$483$	1.65047	0.0750990
$484$	−25.6199	−1.16454
$485$	2.13658	0.0970171
$486$	−9.42549	−0.427549
$487$	41.4947	1.88031	0.940153	−	0.340753i	$-0.110682\pi$
$487$	41.4947	1.88031	0.940153	+	0.340753i	$0.110682\pi$
$488$	−5.51519	−0.249661
$489$	2.90723	0.131469
$490$	38.8487	1.75501
$491$	8.37937	0.378156	0.189078	−	0.981962i	$-0.439450\pi$
$491$	8.37937	0.378156	0.189078	+	0.981962i	$0.439450\pi$
$492$	4.75819	0.214516
$493$	5.57905	0.251268
$494$	36.5606	1.64494
$495$	4.84970	0.217978
$496$	1.76442	0.0792249
$497$	40.0194	1.79512
$498$	0.523508	0.0234590
$499$	39.9192	1.78703	0.893514	−	0.449035i	$-0.148232\pi$
$499$	39.9192	1.78703	0.893514	+	0.449035i	$0.148232\pi$
$500$	−3.07069	−0.137325
$501$	−0.918853	−0.0410513
$502$	45.3844	2.02561
$503$	17.0810	0.761603	0.380802	−	0.924657i	$-0.375648\pi$
$503$	17.0810	0.761603	0.380802	+	0.924657i	$0.375648\pi$
$504$	35.3283	1.57365
$505$	−19.9007	−0.885572
$506$	−7.84813	−0.348892
$507$	−0.466013	−0.0206964
$508$	24.4160	1.08328
$509$	9.30932	0.412628	0.206314	−	0.978486i	$-0.433853\pi$
$509$	9.30932	0.412628	0.206314	+	0.978486i	$0.433853\pi$
$510$	1.12043	0.0496134
$511$	−35.7257	−1.58041
$512$	−8.01120	−0.354048
$513$	−4.80214	−0.212020
$514$	−47.4392	−2.09245
$515$	9.57849	0.422079
$516$	−0.205351	−0.00904009
$517$	−10.0135	−0.440392
$518$	44.7741	1.96726
$519$	0.191116	0.00838905
$520$	−7.63444	−0.334792
$521$	5.19897	0.227771	0.113885	−	0.993494i	$-0.463670\pi$
$521$	5.19897	0.227771	0.113885	+	0.993494i	$0.463670\pi$
$522$	11.7749	0.515375
$523$	−13.7611	−0.601731	−0.300866	−	0.953667i	$-0.597276\pi$
$523$	−13.7611	−0.601731	−0.300866	+	0.953667i	$0.597276\pi$
$524$	54.0319	2.36039
$525$	0.771862	0.0336868
$526$	−20.4765	−0.892819
$527$	−7.86430	−0.342574
$528$	−0.181952	−0.00791845
$529$	−18.4277	−0.801204
$530$	14.9327	0.648635
$531$	16.7384	0.726386
$532$	77.5375	3.36168
$533$	−31.3055	−1.35599
$534$	5.56557	0.240846
$535$	−17.7266	−0.766388
$536$	5.02384	0.216997
$537$	2.34883	0.101359
$538$	38.0109	1.63876
$539$	28.1195	1.21119
$540$	2.87587	0.123758
$541$	−15.1820	−0.652724	−0.326362	−	0.945245i	$-0.605823\pi$
$541$	−15.1820	−0.652724	−0.326362	+	0.945245i	$0.605823\pi$
$542$	24.2734	1.04263
$543$	−0.231143	−0.00991929
$544$	20.3993	0.874614
$545$	9.13395	0.391255
$546$	5.50368	0.235536
$547$	−23.2388	−0.993621	−0.496811	−	0.867859i	$-0.665496\pi$
$547$	−23.2388	−0.993621	−0.496811	+	0.867859i	$0.665496\pi$
$548$	−10.5581	−0.451022
$549$	−6.80634	−0.290488
$550$	−3.67027	−0.156501
$551$	9.01104	0.383883
$552$	−0.808035	−0.0343922
$553$	1.99390	0.0847894
$554$	7.93645	0.337187
$555$	0.632824	0.0268619
$556$	−46.3878	−1.96728
$557$	−9.42793	−0.399474	−0.199737	−	0.979850i	$-0.564009\pi$
$557$	−9.42793	−0.399474	−0.199737	+	0.979850i	$0.564009\pi$
$558$	−16.5981	−0.702653
$559$	1.35107	0.0571440
$560$	3.50754	0.148221
$561$	0.810989	0.0342400
$562$	10.6041	0.447309
$563$	10.1826	0.429146	0.214573	−	0.976708i	$-0.431164\pi$
$563$	10.1826	0.429146	0.214573	+	0.976708i	$0.431164\pi$
$564$	−2.95679	−0.124503
$565$	−19.7699	−0.831725
$566$	40.5715	1.70535
$567$	43.2360	1.81574
$568$	−19.5927	−0.822089
$569$	12.7471	0.534388	0.267194	−	0.963643i	$-0.413904\pi$
$569$	12.7471	0.534388	0.267194	+	0.963643i	$0.413904\pi$
$570$	1.80967	0.0757986
$571$	−13.7683	−0.576187	−0.288093	−	0.957602i	$-0.593021\pi$
$571$	−13.7683	−0.576187	−0.288093	+	0.957602i	$0.593021\pi$
$572$	−15.8482	−0.662647
$573$	−2.99014	−0.124915
$574$	−109.635	−4.57609
$575$	2.13830	0.0891732
$576$	38.8156	1.61732
$577$	−21.4753	−0.894029	−0.447014	−	0.894527i	$-0.647513\pi$
$577$	−21.4753	−0.894029	−0.447014	+	0.894527i	$0.647513\pi$
$578$	15.5872	0.648344
$579$	2.12937	0.0884936
$580$	−5.39648	−0.224077
$581$	−7.30467	−0.303049
$582$	0.754080	0.0312576
$583$	10.8086	0.447646
$584$	17.4905	0.723764
$585$	−9.42172	−0.389540
$586$	6.30651	0.260520
$587$	7.58490	0.313062	0.156531	−	0.987673i	$-0.449969\pi$
$587$	7.58490	0.313062	0.156531	+	0.987673i	$0.449969\pi$
$588$	8.30317	0.342417
$589$	−12.7021	−0.523380
$590$	−12.6677	−0.521521
$591$	0.790983	0.0325367
$592$	2.87572	0.118191
$593$	−41.7878	−1.71602	−0.858009	−	0.513634i	$-0.828299\pi$
$593$	−41.7878	−1.71602	−0.858009	+	0.513634i	$0.828299\pi$
$594$	3.43742	0.141039
$595$	−15.6337	−0.640918
$596$	−26.3128	−1.07782
$597$	3.87270	0.158499
$598$	15.2469	0.623492
$599$	45.0336	1.84002	0.920012	−	0.391890i	$-0.128178\pi$
$599$	45.0336	1.84002	0.920012	+	0.391890i	$0.128178\pi$
$600$	−0.377887	−0.0154272
$601$	−28.2342	−1.15170	−0.575848	−	0.817557i	$-0.695328\pi$
$601$	−28.2342	−1.15170	−0.575848	+	0.817557i	$0.695328\pi$
$602$	4.73157	0.192845
$603$	6.19997	0.252482
$604$	4.40612	0.179283
$605$	8.34338	0.339207
$606$	−7.02372	−0.285319
$607$	−0.323261	−0.0131208	−0.00656038	−	0.999978i	$-0.502088\pi$
$607$	−0.323261	−0.0131208	−0.00656038	+	0.999978i	$0.502088\pi$
$608$	32.9481	1.33622
$609$	1.35648	0.0549674
$610$	5.15106	0.208561
$611$	19.4536	0.787008
$612$	−29.0050	−1.17246
$613$	39.3535	1.58947	0.794736	−	0.606955i	$-0.207609\pi$
$613$	39.3535	1.58947	0.794736	+	0.606955i	$0.207609\pi$
$614$	27.8852	1.12536
$615$	−1.54955	−0.0624839
$616$	−19.3525	−0.779734
$617$	−7.97675	−0.321132	−0.160566	−	0.987025i	$-0.551332\pi$
$617$	−7.97675	−0.321132	−0.160566	+	0.987025i	$0.551332\pi$
$618$	3.38061	0.135988
$619$	5.59592	0.224919	0.112459	−	0.993656i	$-0.464127\pi$
$619$	5.59592	0.224919	0.112459	+	0.993656i	$0.464127\pi$
$620$	7.60695	0.305502
$621$	−2.00264	−0.0803630
$622$	−12.2742	−0.492151
$623$	−77.6581	−3.11131
$624$	0.353486	0.0141508
$625$	1.00000	0.0400000
$626$	14.5764	0.582592
$627$	1.30987	0.0523113
$628$	16.4497	0.656414
$629$	−12.8175	−0.511068
$630$	−32.9958	−1.31459
$631$	22.5544	0.897876	0.448938	−	0.893563i	$-0.351802\pi$
$631$	22.5544	0.897876	0.448938	+	0.893563i	$0.351802\pi$
$632$	−0.976172	−0.0388300
$633$	2.08556	0.0828934
$634$	−20.2155	−0.802859
$635$	−7.95130	−0.315538
$636$	3.19158	0.126554
$637$	−54.6290	−2.16448
$638$	−6.45019	−0.255366
$639$	−24.1794	−0.956524
$640$	−16.5241	−0.653172
$641$	20.0534	0.792062	0.396031	−	0.918237i	$-0.370387\pi$
$641$	20.0534	0.792062	0.396031	+	0.918237i	$0.370387\pi$
$642$	−6.25639	−0.246920
$643$	−21.9422	−0.865315	−0.432657	−	0.901558i	$-0.642424\pi$
$643$	−21.9422	−0.865315	−0.432657	+	0.901558i	$0.642424\pi$
$644$	32.3355	1.27420
$645$	0.0668746	0.00263319
$646$	−36.6539	−1.44213
$647$	27.3817	1.07649	0.538243	−	0.842790i	$-0.319088\pi$
$647$	27.3817	1.07649	0.538243	+	0.842790i	$0.319088\pi$
$648$	−21.1674	−0.831534
$649$	−9.16915	−0.359921
$650$	7.13039	0.279677
$651$	−1.91212	−0.0749417
$652$	56.9574	2.23063
$653$	0.939456	0.0367637	0.0183819	−	0.999831i	$-0.494149\pi$
$653$	0.939456	0.0367637	0.0183819	+	0.999831i	$0.494149\pi$
$654$	3.22371	0.126057
$655$	−17.5960	−0.687533
$656$	−7.04157	−0.274927
$657$	21.5852	0.842119
$658$	68.1285	2.65592
$659$	45.2551	1.76289	0.881445	−	0.472287i	$-0.156571\pi$
$659$	45.2551	1.76289	0.881445	+	0.472287i	$0.156571\pi$
$660$	−0.784450	−0.0305347
$661$	25.8384	1.00500	0.502498	−	0.864578i	$-0.332414\pi$
$661$	25.8384	1.00500	0.502498	+	0.864578i	$0.332414\pi$
$662$	62.1594	2.41589
$663$	−1.57554	−0.0611890
$664$	3.57621	0.138784
$665$	−25.2508	−0.979185
$666$	−27.0522	−1.04825
$667$	3.75788	0.145506
$668$	−18.0019	−0.696513
$669$	1.52011	0.0587707
$670$	−4.69216	−0.181274
$671$	3.72845	0.143935
$672$	4.95986	0.191331
$673$	−4.29014	−0.165373	−0.0826863	−	0.996576i	$-0.526350\pi$
$673$	−4.29014	−0.165373	−0.0826863	+	0.996576i	$0.526350\pi$
$674$	−19.2398	−0.741088
$675$	−0.936557	−0.0360481
$676$	−9.12997	−0.351153
$677$	5.44961	0.209445	0.104723	−	0.994501i	$-0.466604\pi$
$677$	5.44961	0.209445	0.104723	+	0.994501i	$0.466604\pi$
$678$	−6.97753	−0.267971
$679$	−10.5219	−0.403794
$680$	7.65391	0.293514
$681$	−0.604823	−0.0231769
$682$	9.09227	0.348161
$683$	26.3056	1.00656	0.503278	−	0.864125i	$-0.332127\pi$
$683$	26.3056	1.00656	0.503278	+	0.864125i	$0.332127\pi$
$684$	−46.8475	−1.79126
$685$	3.43836	0.131373
$686$	−113.690	−4.34072
$687$	−0.679905	−0.0259400
$688$	0.303896	0.0115859
$689$	−20.9983	−0.799972
$690$	0.754686	0.0287304
$691$	−32.1341	−1.22244	−0.611219	−	0.791462i	$-0.709320\pi$
$691$	−32.1341	−1.22244	−0.611219	+	0.791462i	$0.709320\pi$
$692$	3.74428	0.142336
$693$	−23.8831	−0.907243
$694$	−76.4209	−2.90090
$695$	15.1066	0.573027
$696$	−0.664104	−0.0251728
$697$	31.3854	1.18881
$698$	−40.2137	−1.52211
$699$	−1.55464	−0.0588020
$700$	15.1221	0.571560
$701$	−25.1059	−0.948236	−0.474118	−	0.880461i	$-0.657233\pi$
$701$	−25.1059	−0.948236	−0.474118	+	0.880461i	$0.657233\pi$
$702$	−6.67801	−0.252045
$703$	−20.7023	−0.780803
$704$	−21.2628	−0.801372
$705$	0.962907	0.0362652
$706$	15.5325	0.584574
$707$	98.0042	3.68583
$708$	−2.70748	−0.101753
$709$	−28.9196	−1.08610	−0.543050	−	0.839700i	$-0.682731\pi$
$709$	−28.9196	−1.08610	−0.543050	+	0.839700i	$0.682731\pi$
$710$	18.2991	0.686753
$711$	−1.20470	−0.0451798
$712$	38.0197	1.42485
$713$	−5.29715	−0.198380
$714$	−5.51771	−0.206495
$715$	5.16113	0.193015
$716$	46.0175	1.71975
$717$	−2.31397	−0.0864168
$718$	50.6993	1.89208
$719$	−26.5554	−0.990349	−0.495175	−	0.868793i	$-0.664896\pi$
$719$	−26.5554	−0.990349	−0.495175	+	0.868793i	$0.664896\pi$
$720$	−2.11923	−0.0789791
$721$	−47.1707	−1.75673
$722$	−16.4172	−0.610984
$723$	−0.229253	−0.00852601
$724$	−4.52847	−0.168299
$725$	1.75742	0.0652688
$726$	2.94469	0.109288
$727$	−2.07370	−0.0769093	−0.0384546	−	0.999260i	$-0.512244\pi$
$727$	−2.07370	−0.0769093	−0.0384546	+	0.999260i	$0.512244\pi$
$728$	37.5969	1.39343
$729$	−25.6825	−0.951203
$730$	−16.3358	−0.604614
$731$	−1.35451	−0.0500984
$732$	1.10094	0.0406919
$733$	1.24841	0.0461109	0.0230555	−	0.999734i	$-0.492661\pi$
$733$	1.24841	0.0461109	0.0230555	+	0.999734i	$0.492661\pi$
$734$	−0.597085	−0.0220388
$735$	−2.70401	−0.0997388
$736$	13.7404	0.506476
$737$	−3.39628	−0.125104
$738$	66.2408	2.43836
$739$	22.6354	0.832658	0.416329	−	0.909214i	$-0.363316\pi$
$739$	22.6354	0.832658	0.416329	+	0.909214i	$0.363316\pi$
$740$	12.3981	0.455762
$741$	−2.54475	−0.0934837
$742$	−73.5383	−2.69968
$743$	−39.6603	−1.45500	−0.727498	−	0.686109i	$-0.759317\pi$
$743$	−39.6603	−1.45500	−0.727498	+	0.686109i	$0.759317\pi$
$744$	0.936130	0.0343202
$745$	8.56903	0.313945
$746$	43.9392	1.60873
$747$	4.41342	0.161479
$748$	15.8886	0.580946
$749$	87.2973	3.18977
$750$	0.352938	0.0128875
$751$	14.4089	0.525789	0.262894	−	0.964825i	$-0.415323\pi$
$751$	14.4089	0.525789	0.262894	+	0.964825i	$0.415323\pi$
$752$	4.37570	0.159566
$753$	−3.15891	−0.115117
$754$	12.5311	0.456354
$755$	−1.43490	−0.0522213
$756$	−14.1627	−0.515091
$757$	45.8578	1.66673	0.833364	−	0.552724i	$-0.186412\pi$
$757$	45.8578	1.66673	0.833364	+	0.552724i	$0.186412\pi$
$758$	−4.80565	−0.174549
$759$	0.546257	0.0198279
$760$	12.3623	0.448426
$761$	23.5921	0.855213	0.427607	−	0.903965i	$-0.359357\pi$
$761$	23.5921	0.855213	0.427607	+	0.903965i	$0.359357\pi$
$762$	−2.80631	−0.101662
$763$	−44.9815	−1.62844
$764$	−58.5818	−2.11942
$765$	9.44574	0.341512
$766$	−54.9040	−1.98376
$767$	17.8133	0.643201
$768$	−1.74266	−0.0628829
$769$	8.48410	0.305944	0.152972	−	0.988230i	$-0.451116\pi$
$769$	8.48410	0.305944	0.152972	+	0.988230i	$0.451116\pi$
$770$	18.0748	0.651370
$771$	3.30193	0.118916
$772$	41.7179	1.50146
$773$	−41.5237	−1.49350	−0.746752	−	0.665103i	$-0.768388\pi$
$773$	−41.5237	−1.49350	−0.746752	+	0.665103i	$0.768388\pi$
$774$	−2.85878	−0.102757
$775$	−2.47728	−0.0889864
$776$	5.15129	0.184921
$777$	−3.11644	−0.111801
$778$	16.4320	0.589115
$779$	50.6923	1.81624
$780$	1.52398	0.0545674
$781$	13.2453	0.473953
$782$	−15.2858	−0.546618
$783$	−1.64592	−0.0588203
$784$	−12.2877	−0.438847
$785$	−5.35700	−0.191199
$786$	−6.21029	−0.221514
$787$	10.3327	0.368319	0.184160	−	0.982896i	$-0.441044\pi$
$787$	10.3327	0.368319	0.184160	+	0.982896i	$0.441044\pi$
$788$	15.4967	0.552047
$789$	1.42524	0.0507398
$790$	0.911722	0.0324376
$791$	97.3597	3.46171
$792$	11.6926	0.415480
$793$	−7.24341	−0.257221
$794$	−28.3396	−1.00574
$795$	−1.03937	−0.0368626
$796$	75.8726	2.68923
$797$	13.6632	0.483976	0.241988	−	0.970279i	$-0.422201\pi$
$797$	13.6632	0.483976	0.241988	+	0.970279i	$0.422201\pi$
$798$	−8.91197	−0.315480
$799$	−19.5032	−0.689973
$800$	6.42584	0.227188
$801$	46.9205	1.65785
$802$	7.21992	0.254944
$803$	−11.8242	−0.417266
$804$	−1.00286	−0.0353681
$805$	−10.5304	−0.371146
$806$	−17.6639	−0.622186
$807$	−2.64569	−0.0931327
$808$	−47.9807	−1.68796
$809$	−31.8284	−1.11903	−0.559514	−	0.828821i	$-0.689012\pi$
$809$	−31.8284	−1.11903	−0.559514	+	0.828821i	$0.689012\pi$
$810$	19.7699	0.694643
$811$	38.1637	1.34011	0.670054	−	0.742313i	$-0.266271\pi$
$811$	38.1637	1.34011	0.670054	+	0.742313i	$0.266271\pi$
$812$	26.5758	0.932626
$813$	−1.68951	−0.0592538
$814$	14.8189	0.519403
$815$	−18.5487	−0.649734
$816$	−0.354388	−0.0124060
$817$	−2.18775	−0.0765396
$818$	66.8196	2.33629
$819$	46.3986	1.62130
$820$	−30.3583	−1.06016
$821$	−6.12550	−0.213781	−0.106891	−	0.994271i	$-0.534089\pi$
$821$	−6.12550	−0.213781	−0.106891	+	0.994271i	$0.534089\pi$
$822$	1.21353	0.0423266
$823$	−11.9947	−0.418108	−0.209054	−	0.977904i	$-0.567038\pi$
$823$	−11.9947	−0.418108	−0.209054	+	0.977904i	$0.567038\pi$
$824$	23.0937	0.804509
$825$	0.255464	0.00889410
$826$	62.3840	2.17062
$827$	−29.3722	−1.02137	−0.510686	−	0.859767i	$-0.670609\pi$
$827$	−29.3722	−1.02137	−0.510686	+	0.859767i	$0.670609\pi$
$828$	−19.5368	−0.678952
$829$	46.4186	1.61218	0.806092	−	0.591791i	$-0.201579\pi$
$829$	46.4186	1.61218	0.806092	+	0.591791i	$0.201579\pi$
$830$	−3.34009	−0.115936
$831$	−0.552405	−0.0191627
$832$	41.3081	1.43210
$833$	54.7683	1.89761
$834$	5.33170	0.184622
$835$	5.86248	0.202880
$836$	25.6626	0.887560
$837$	2.32011	0.0801947
$838$	−23.8654	−0.824418
$839$	−45.2473	−1.56211	−0.781056	−	0.624461i	$-0.785319\pi$
$839$	−45.2473	−1.56211	−0.781056	+	0.624461i	$0.785319\pi$
$840$	1.86096	0.0642092
$841$	−25.9115	−0.893500
$842$	−26.1776	−0.902141
$843$	−0.738085	−0.0254210
$844$	40.8595	1.40644
$845$	2.97326	0.102283
$846$	−41.1627	−1.41520
$847$	−41.0882	−1.41181
$848$	−4.72316	−0.162194
$849$	−2.82392	−0.0969167
$850$	−7.14857	−0.245194
$851$	−8.63349	−0.295952
$852$	3.91108	0.133991
$853$	38.3995	1.31478	0.657388	−	0.753553i	$-0.271661\pi$
$853$	38.3995	1.31478	0.657388	+	0.753553i	$0.271661\pi$
$854$	−25.3672	−0.868047
$855$	15.2564	0.521756
$856$	−42.7389	−1.46078
$857$	52.0127	1.77672	0.888360	−	0.459148i	$-0.151845\pi$
$857$	52.0127	1.77672	0.888360	+	0.459148i	$0.151845\pi$
$858$	1.82156	0.0621869
$859$	7.69322	0.262489	0.131245	−	0.991350i	$-0.458103\pi$
$859$	7.69322	0.262489	0.131245	+	0.991350i	$0.458103\pi$
$860$	1.31019	0.0446770
$861$	7.63099	0.260064
$862$	−17.3231	−0.590027
$863$	5.68034	0.193361	0.0966806	−	0.995315i	$-0.469177\pi$
$863$	5.68034	0.193361	0.0966806	+	0.995315i	$0.469177\pi$
$864$	−6.01817	−0.204742
$865$	−1.21936	−0.0414595
$866$	51.3269	1.74416
$867$	−1.08493	−0.0368460
$868$	−37.4615	−1.27153
$869$	0.659924	0.0223864
$870$	0.620258	0.0210287
$871$	6.59810	0.223568
$872$	22.0219	0.745757
$873$	6.35725	0.215160
$874$	−24.6889	−0.835115
$875$	−4.92465	−0.166483
$876$	−3.49145	−0.117965
$877$	42.9887	1.45162	0.725812	−	0.687893i	$-0.241464\pi$
$877$	42.9887	1.45162	0.725812	+	0.687893i	$0.241464\pi$
$878$	10.3366	0.348844
$879$	−0.438955	−0.0148056
$880$	1.16089	0.0391337
$881$	−4.08763	−0.137716	−0.0688579	−	0.997626i	$-0.521936\pi$
$881$	−4.08763	−0.137716	−0.0688579	+	0.997626i	$0.521936\pi$
$882$	115.592	3.89218
$883$	10.3594	0.348620	0.174310	−	0.984691i	$-0.444230\pi$
$883$	10.3594	0.348620	0.174310	+	0.984691i	$0.444230\pi$
$884$	−30.8675	−1.03819
$885$	0.881717	0.0296386
$886$	46.6880	1.56851
$887$	51.0806	1.71512	0.857559	−	0.514385i	$-0.171980\pi$
$887$	51.0806	1.71512	0.857559	+	0.514385i	$0.171980\pi$
$888$	1.52574	0.0512004
$889$	39.1573	1.31329
$890$	−35.5096	−1.19028
$891$	14.3098	0.479398
$892$	29.7814	0.997156
$893$	−31.5007	−1.05413
$894$	3.02433	0.101149
$895$	−14.9860	−0.500928
$896$	81.3753	2.71856
$897$	−1.06124	−0.0354337
$898$	−0.130500	−0.00435483
$899$	−4.35360	−0.145201
$900$	−9.13664	−0.304555
$901$	21.0519	0.701339
$902$	−36.2860	−1.20819
$903$	−0.329334	−0.0109595
$904$	−47.6652	−1.58532
$905$	1.47474	0.0490221
$906$	−0.506429	−0.0168250
$907$	6.16794	0.204803	0.102402	−	0.994743i	$-0.467347\pi$
$907$	6.16794	0.204803	0.102402	+	0.994743i	$0.467347\pi$
$908$	−11.8495	−0.393239
$909$	−59.2134	−1.96398
$910$	−35.1147	−1.16404
$911$	39.2167	1.29931	0.649654	−	0.760230i	$-0.274914\pi$
$911$	39.2167	1.29931	0.649654	+	0.760230i	$0.274914\pi$
$912$	−0.572391	−0.0189538
$913$	−2.41763	−0.0800119
$914$	−66.1257	−2.18724
$915$	−0.358532	−0.0118527
$916$	−13.3205	−0.440121
$917$	86.6541	2.86157
$918$	6.69504	0.220969
$919$	23.5580	0.777107	0.388554	−	0.921426i	$-0.372975\pi$
$919$	23.5580	0.777107	0.388554	+	0.921426i	$0.372975\pi$
$920$	5.15544	0.169970
$921$	−1.94091	−0.0639551
$922$	−61.9179	−2.03916
$923$	−25.7321	−0.846983
$924$	3.86314	0.127088
$925$	−4.03755	−0.132754
$926$	−75.0850	−2.46745
$927$	28.5002	0.936068
$928$	11.2929	0.370707
$929$	−6.40657	−0.210193	−0.105096	−	0.994462i	$-0.533515\pi$
$929$	−6.40657	−0.210193	−0.105096	+	0.994462i	$0.533515\pi$
$930$	−0.874324	−0.0286702
$931$	88.4594	2.89914
$932$	−30.4581	−0.997687
$933$	0.854328	0.0279694
$934$	−21.7167	−0.710594
$935$	−5.17429	−0.169217
$936$	−22.7158	−0.742488
$937$	−21.9206	−0.716116	−0.358058	−	0.933699i	$-0.616561\pi$
$937$	−21.9206	−0.716116	−0.358058	+	0.933699i	$0.616561\pi$
$938$	23.1072	0.754477
$939$	−1.01457	−0.0331093
$940$	18.8650	0.615307
$941$	26.1415	0.852190	0.426095	−	0.904678i	$-0.359889\pi$
$941$	26.1415	0.852190	0.426095	+	0.904678i	$0.359889\pi$
$942$	−1.89069	−0.0616019
$943$	21.1402	0.688420
$944$	4.00675	0.130409
$945$	4.61221	0.150035
$946$	1.56601	0.0509154
$947$	44.1279	1.43396	0.716982	−	0.697091i	$-0.245523\pi$
$947$	44.1279	1.43396	0.716982	+	0.697091i	$0.245523\pi$
$948$	0.194863	0.00632886
$949$	22.9713	0.745680
$950$	−11.5461	−0.374604
$951$	1.40707	0.0456273
$952$	−37.6928	−1.22163
$953$	−46.6890	−1.51240	−0.756202	−	0.654338i	$-0.772947\pi$
$953$	−46.6890	−1.51240	−0.756202	+	0.654338i	$0.772947\pi$
$954$	44.4313	1.43852
$955$	19.0777	0.617341
$956$	−45.3345	−1.46622
$957$	0.448956	0.0145127
$958$	23.6122	0.762875
$959$	−16.9327	−0.546786
$960$	2.04466	0.0659910
$961$	−24.8631	−0.802036
$962$	−28.7893	−0.928206
$963$	−52.7443	−1.69966
$964$	−4.49145	−0.144660
$965$	−13.5858	−0.437344
$966$	−3.71656	−0.119578
$967$	54.3710	1.74845	0.874227	−	0.485518i	$-0.161369\pi$
$967$	54.3710	1.74845	0.874227	+	0.485518i	$0.161369\pi$
$968$	20.1159	0.646549
$969$	2.55124	0.0819575
$970$	−4.81119	−0.154478
$971$	59.4867	1.90902	0.954509	−	0.298181i	$-0.0963799\pi$
$971$	59.4867	1.90902	0.954509	+	0.298181i	$0.0963799\pi$
$972$	12.8531	0.412262
$973$	−74.3948	−2.38499
$974$	−93.4387	−2.99397
$975$	−0.496300	−0.0158943
$976$	−1.62926	−0.0521515
$977$	24.8400	0.794701	0.397351	−	0.917667i	$-0.369930\pi$
$977$	24.8400	0.794701	0.397351	+	0.917667i	$0.369930\pi$
$978$	−6.54655	−0.209336
$979$	−25.7026	−0.821458
$980$	−52.9760	−1.69226
$981$	27.1775	0.867709
$982$	−18.8688	−0.602128
$983$	18.3211	0.584351	0.292176	−	0.956365i	$-0.405621\pi$
$983$	18.3211	0.584351	0.292176	+	0.956365i	$0.405621\pi$
$984$	−3.73597	−0.119098
$985$	−5.04665	−0.160800
$986$	−12.5630	−0.400088
$987$	−4.74198	−0.150939
$988$	−49.8559	−1.58613
$989$	−0.912357	−0.0290113
$990$	−10.9207	−0.347081
$991$	−0.255941	−0.00813024	−0.00406512	−	0.999992i	$-0.501294\pi$
$991$	−0.255941	−0.00813024	−0.00406512	+	0.999992i	$0.501294\pi$
$992$	−15.9186	−0.505416
$993$	−4.32651	−0.137298
$994$	−90.1166	−2.85832
$995$	−24.7086	−0.783316
$996$	−0.713881	−0.0226202
$997$	5.91158	0.187222	0.0936108	−	0.995609i	$-0.470159\pi$
$997$	5.91158	0.187222	0.0936108	+	0.995609i	$0.470159\pi$
$998$	−89.8908	−2.84544
$999$	3.78140	0.119638

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.c.1.13	✓	127

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.c.1.13	✓	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.25182 q^{2} +0.156734 q^{3} +3.07069 q^{4} -1.00000 q^{5} -0.352938 q^{6} +4.92465 q^{7} -2.41100 q^{8} -2.97543 q^{9} +O(q^{10})\)	\(q-2.25182 q^{2} +0.156734 q^{3} +3.07069 q^{4} -1.00000 q^{5} -0.352938 q^{6} +4.92465 q^{7} -2.41100 q^{8} -2.97543 q^{9} +2.25182 q^{10} +1.62991 q^{11} +0.481283 q^{12} -3.16650 q^{13} -11.0894 q^{14} -0.156734 q^{15} -0.712243 q^{16} +3.17458 q^{17} +6.70014 q^{18} +5.12744 q^{19} -3.07069 q^{20} +0.771862 q^{21} -3.67027 q^{22} +2.13830 q^{23} -0.377887 q^{24} +1.00000 q^{25} +7.13039 q^{26} -0.936557 q^{27} +15.1221 q^{28} +1.75742 q^{29} +0.352938 q^{30} -2.47728 q^{31} +6.42584 q^{32} +0.255464 q^{33} -7.14857 q^{34} -4.92465 q^{35} -9.13664 q^{36} -4.03755 q^{37} -11.5461 q^{38} -0.496300 q^{39} +2.41100 q^{40} +9.88647 q^{41} -1.73809 q^{42} -0.426675 q^{43} +5.00496 q^{44} +2.97543 q^{45} -4.81506 q^{46} -6.14356 q^{47} -0.111633 q^{48} +17.2522 q^{49} -2.25182 q^{50} +0.497566 q^{51} -9.72335 q^{52} +6.63139 q^{53} +2.10896 q^{54} -1.62991 q^{55} -11.8733 q^{56} +0.803646 q^{57} -3.95738 q^{58} -5.62554 q^{59} -0.481283 q^{60} +2.28751 q^{61} +5.57838 q^{62} -14.6530 q^{63} -13.0454 q^{64} +3.16650 q^{65} -0.575258 q^{66} -2.08372 q^{67} +9.74814 q^{68} +0.335145 q^{69} +11.0894 q^{70} +8.12636 q^{71} +7.17377 q^{72} -7.25447 q^{73} +9.09184 q^{74} +0.156734 q^{75} +15.7448 q^{76} +8.02675 q^{77} +1.11758 q^{78} +0.404882 q^{79} +0.712243 q^{80} +8.77951 q^{81} -22.2626 q^{82} -1.48329 q^{83} +2.37015 q^{84} -3.17458 q^{85} +0.960794 q^{86} +0.275448 q^{87} -3.92972 q^{88} -15.7693 q^{89} -6.70014 q^{90} -15.5939 q^{91} +6.56605 q^{92} -0.388275 q^{93} +13.8342 q^{94} -5.12744 q^{95} +1.00715 q^{96} -2.13658 q^{97} -38.8487 q^{98} -4.84970 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9 - 19 * q^10 + 30 * q^11 + 35 * q^12 + 30 * q^13 + 39 * q^14 - 10 * q^15 + 121 * q^16 + 63 * q^17 + 53 * q^18 - 35 * q^19 - 125 * q^20 + 33 * q^21 + 49 * q^22 + 61 * q^23 - 5 * q^24 + 127 * q^25 + 10 * q^26 + 40 * q^27 + 32 * q^28 + 134 * q^29 - 25 * q^31 + 122 * q^32 + 48 * q^33 - 21 * q^34 - 13 * q^35 + 133 * q^36 + 60 * q^37 + 33 * q^38 + 26 * q^39 - 54 * q^40 + 9 * q^41 + 45 * q^42 + 48 * q^43 + 85 * q^44 - 123 * q^45 - 11 * q^46 + 57 * q^47 + 71 * q^48 + 70 * q^49 + 19 * q^50 + 45 * q^51 + 68 * q^52 + 182 * q^53 - 29 * q^54 - 30 * q^55 + 96 * q^56 + 74 * q^57 + 47 * q^58 + 19 * q^59 - 35 * q^60 + 16 * q^61 + 43 * q^62 + 73 * q^63 + 110 * q^64 - 30 * q^65 + 8 * q^66 + 40 * q^67 + 129 * q^68 + 2 * q^69 - 39 * q^70 + 48 * q^71 + 151 * q^72 + 30 * q^73 + 117 * q^74 + 10 * q^75 - 98 * q^76 + 134 * q^77 + 54 * q^78 + 23 * q^79 - 121 * q^80 + 111 * q^81 + 4 * q^82 + 92 * q^83 + 48 * q^84 - 63 * q^85 + 42 * q^86 + 69 * q^87 + 121 * q^88 + 12 * q^89 - 53 * q^90 - 30 * q^91 + 175 * q^92 + 82 * q^93 - 23 * q^94 + 35 * q^95 + 6 * q^96 + 67 * q^97 + 122 * q^98 + 73 * q^99

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