LMFDB - Embedded newform 1003.2.a.h.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, 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("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.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:	$8.00899532273$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} - 5 x^{14} + 90 x^{13} - 82 x^{12} - 456 x^{11} + 723 x^{10} + 951 x^{9} - 2105 x^{8} + \cdots - 1 $ x^16 - 6x^15 - 5x^14 + 90x^13 - 82x^12 - 456x^11 + 723x^10 + 951x^9 - 2105x^8 - 695x^7 + 2641x^6 - 151x^5 - 1323x^4 + 301x^3 + 179x^2 - 50*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.79724$ of defining polynomial
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.79724 q^{2} -2.09283 q^{3} +1.23006 q^{4} -2.26932 q^{5} +3.76130 q^{6} -0.408229 q^{7} +1.38377 q^{8} +1.37993 q^{9} +O(q^{10})$	\(q-1.79724 q^{2} -2.09283 q^{3} +1.23006 q^{4} -2.26932 q^{5} +3.76130 q^{6} -0.408229 q^{7} +1.38377 q^{8} +1.37993 q^{9} +4.07850 q^{10} -5.30925 q^{11} -2.57429 q^{12} +4.40136 q^{13} +0.733683 q^{14} +4.74929 q^{15} -4.94707 q^{16} +1.00000 q^{17} -2.48005 q^{18} +6.57252 q^{19} -2.79139 q^{20} +0.854352 q^{21} +9.54197 q^{22} -3.22305 q^{23} -2.89599 q^{24} +0.149808 q^{25} -7.91029 q^{26} +3.39054 q^{27} -0.502144 q^{28} +5.31587 q^{29} -8.53560 q^{30} +8.06505 q^{31} +6.12352 q^{32} +11.1113 q^{33} -1.79724 q^{34} +0.926401 q^{35} +1.69739 q^{36} -7.46060 q^{37} -11.8124 q^{38} -9.21129 q^{39} -3.14022 q^{40} +0.557550 q^{41} -1.53547 q^{42} +7.66459 q^{43} -6.53067 q^{44} -3.13149 q^{45} +5.79258 q^{46} +10.2475 q^{47} +10.3534 q^{48} -6.83335 q^{49} -0.269241 q^{50} -2.09283 q^{51} +5.41392 q^{52} -13.4282 q^{53} -6.09359 q^{54} +12.0484 q^{55} -0.564895 q^{56} -13.7551 q^{57} -9.55387 q^{58} +1.00000 q^{59} +5.84190 q^{60} +2.66493 q^{61} -14.4948 q^{62} -0.563325 q^{63} -1.11125 q^{64} -9.98810 q^{65} -19.9697 q^{66} -7.99404 q^{67} +1.23006 q^{68} +6.74528 q^{69} -1.66496 q^{70} -6.23963 q^{71} +1.90950 q^{72} -11.2914 q^{73} +13.4084 q^{74} -0.313523 q^{75} +8.08457 q^{76} +2.16739 q^{77} +16.5549 q^{78} +10.6386 q^{79} +11.2265 q^{80} -11.2356 q^{81} -1.00205 q^{82} -7.40405 q^{83} +1.05090 q^{84} -2.26932 q^{85} -13.7751 q^{86} -11.1252 q^{87} -7.34678 q^{88} +7.94689 q^{89} +5.62803 q^{90} -1.79676 q^{91} -3.96453 q^{92} -16.8788 q^{93} -18.4173 q^{94} -14.9151 q^{95} -12.8155 q^{96} -10.0130 q^{97} +12.2811 q^{98} -7.32637 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9} + 12 q^{10} - 7 q^{11} - 4 q^{12} - 16 q^{13} + 11 q^{14} + 7 q^{15} + 22 q^{16} + 16 q^{17} + 11 q^{18} + q^{19} - 43 q^{20} - 8 q^{21} - 18 q^{22} - 8 q^{23} - 39 q^{24} + 23 q^{25} - 49 q^{26} - 7 q^{27} - 15 q^{28} - 39 q^{29} + q^{30} - 3 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{35} - 17 q^{36} - 28 q^{37} - 27 q^{38} - 4 q^{39} + 26 q^{40} - 31 q^{41} - 45 q^{42} + 5 q^{43} - 19 q^{44} - 79 q^{45} - 39 q^{46} - 47 q^{47} - 31 q^{48} + 35 q^{49} - 13 q^{50} - 7 q^{51} + 9 q^{52} - 36 q^{53} + 9 q^{54} + 32 q^{55} + 3 q^{56} + 6 q^{57} + 22 q^{58} + 16 q^{59} + 6 q^{60} - 22 q^{61} + q^{62} - 19 q^{63} + 32 q^{64} - 19 q^{65} + 48 q^{66} + 4 q^{67} + 14 q^{68} + 14 q^{69} - 11 q^{70} - 5 q^{71} + 40 q^{72} - 35 q^{73} + 31 q^{74} - 12 q^{75} + q^{76} - 79 q^{77} + 31 q^{78} - 48 q^{79} - 127 q^{80} - 28 q^{81} - 7 q^{82} - 42 q^{83} + 28 q^{84} - 21 q^{85} + 58 q^{86} - 16 q^{87} - 2 q^{88} + 20 q^{89} - 14 q^{90} + 49 q^{91} - 21 q^{92} - 55 q^{93} - 22 q^{95} + 24 q^{96} - 2 q^{97} - 78 q^{98} - 35 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9 + 12 * q^10 - 7 * q^11 - 4 * q^12 - 16 * q^13 + 11 * q^14 + 7 * q^15 + 22 * q^16 + 16 * q^17 + 11 * q^18 + q^19 - 43 * q^20 - 8 * q^21 - 18 * q^22 - 8 * q^23 - 39 * q^24 + 23 * q^25 - 49 * q^26 - 7 * q^27 - 15 * q^28 - 39 * q^29 + q^30 - 3 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^35 - 17 * q^36 - 28 * q^37 - 27 * q^38 - 4 * q^39 + 26 * q^40 - 31 * q^41 - 45 * q^42 + 5 * q^43 - 19 * q^44 - 79 * q^45 - 39 * q^46 - 47 * q^47 - 31 * q^48 + 35 * q^49 - 13 * q^50 - 7 * q^51 + 9 * q^52 - 36 * q^53 + 9 * q^54 + 32 * q^55 + 3 * q^56 + 6 * q^57 + 22 * q^58 + 16 * q^59 + 6 * q^60 - 22 * q^61 + q^62 - 19 * q^63 + 32 * q^64 - 19 * q^65 + 48 * q^66 + 4 * q^67 + 14 * q^68 + 14 * q^69 - 11 * q^70 - 5 * q^71 + 40 * q^72 - 35 * q^73 + 31 * q^74 - 12 * q^75 + q^76 - 79 * q^77 + 31 * q^78 - 48 * q^79 - 127 * q^80 - 28 * q^81 - 7 * q^82 - 42 * q^83 + 28 * q^84 - 21 * q^85 + 58 * q^86 - 16 * q^87 - 2 * q^88 + 20 * q^89 - 14 * q^90 + 49 * q^91 - 21 * q^92 - 55 * q^93 - 22 * q^95 + 24 * q^96 - 2 * q^97 - 78 * q^98 - 35 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.79724	−1.27084	−0.635419	−	0.772168i	$-0.719172\pi$
$2$	−1.79724	−1.27084	−0.635419	+	0.772168i	$0.719172\pi$
$3$	−2.09283	−1.20829	−0.604147	−	0.796873i	$-0.706486\pi$
$3$	−2.09283	−1.20829	−0.604147	+	0.796873i	$0.706486\pi$
$4$	1.23006	0.615028
$5$	−2.26932	−1.01487	−0.507435	−	0.861690i	$-0.669406\pi$
$5$	−2.26932	−1.01487	−0.507435	+	0.861690i	$0.669406\pi$
$6$	3.76130	1.53555
$7$	−0.408229	−0.154296	−0.0771480	−	0.997020i	$-0.524581\pi$
$7$	−0.408229	−0.154296	−0.0771480	+	0.997020i	$0.524581\pi$
$8$	1.38377	0.489237
$9$	1.37993	0.459975
$10$	4.07850	1.28974
$11$	−5.30925	−1.60080	−0.800399	−	0.599467i	$-0.795379\pi$
$11$	−5.30925	−1.60080	−0.800399	+	0.599467i	$0.795379\pi$
$12$	−2.57429	−0.743135
$13$	4.40136	1.22072	0.610359	−	0.792125i	$-0.291025\pi$
$13$	4.40136	1.22072	0.610359	+	0.792125i	$0.291025\pi$
$14$	0.733683	0.196085
$15$	4.74929	1.22626
$16$	−4.94707	−1.23677
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.48005	−0.584554
$19$	6.57252	1.50784	0.753920	−	0.656967i	$-0.228161\pi$
$19$	6.57252	1.50784	0.753920	+	0.656967i	$0.228161\pi$
$20$	−2.79139	−0.624174
$21$	0.854352	0.186435
$22$	9.54197	2.03436
$23$	−3.22305	−0.672052	−0.336026	−	0.941853i	$-0.609083\pi$
$23$	−3.22305	−0.672052	−0.336026	+	0.941853i	$0.609083\pi$
$24$	−2.89599	−0.591142
$25$	0.149808	0.0299617
$26$	−7.91029	−1.55133
$27$	3.39054	0.652509
$28$	−0.502144	−0.0948963
$29$	5.31587	0.987133	0.493566	−	0.869708i	$-0.335693\pi$
$29$	5.31587	0.987133	0.493566	+	0.869708i	$0.335693\pi$
$30$	−8.53560	−1.55838
$31$	8.06505	1.44853	0.724263	−	0.689524i	$-0.242180\pi$
$31$	8.06505	1.44853	0.724263	+	0.689524i	$0.242180\pi$
$32$	6.12352	1.08250
$33$	11.1113	1.93424
$34$	−1.79724	−0.308223
$35$	0.926401	0.156590
$36$	1.69739	0.282898
$37$	−7.46060	−1.22651	−0.613257	−	0.789883i	$-0.710141\pi$
$37$	−7.46060	−1.22651	−0.613257	+	0.789883i	$0.710141\pi$
$38$	−11.8124	−1.91622
$39$	−9.21129	−1.47499
$40$	−3.14022	−0.496512
$41$	0.557550	0.0870748	0.0435374	−	0.999052i	$-0.486137\pi$
$41$	0.557550	0.0870748	0.0435374	+	0.999052i	$0.486137\pi$
$42$	−1.53547	−0.236929
$43$	7.66459	1.16884	0.584420	−	0.811452i	$-0.301322\pi$
$43$	7.66459	1.16884	0.584420	+	0.811452i	$0.301322\pi$
$44$	−6.53067	−0.984536
$45$	−3.13149	−0.466815
$46$	5.79258	0.854069
$47$	10.2475	1.49476	0.747379	−	0.664398i	$-0.231312\pi$
$47$	10.2475	1.49476	0.747379	+	0.664398i	$0.231312\pi$
$48$	10.3534	1.49438
$49$	−6.83335	−0.976193
$50$	−0.269241	−0.0380764
$51$	−2.09283	−0.293054
$52$	5.41392	0.750776
$53$	−13.4282	−1.84450	−0.922249	−	0.386595i	$-0.873651\pi$
$53$	−13.4282	−1.84450	−0.922249	+	0.386595i	$0.873651\pi$
$54$	−6.09359	−0.829233
$55$	12.0484	1.62460
$56$	−0.564895	−0.0754873
$57$	−13.7551	−1.82191
$58$	−9.55387	−1.25449
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	5.84190	0.754185
$61$	2.66493	0.341209	0.170604	−	0.985340i	$-0.445428\pi$
$61$	2.66493	0.341209	0.170604	+	0.985340i	$0.445428\pi$
$62$	−14.4948	−1.84084
$63$	−0.563325	−0.0709723
$64$	−1.11125	−0.138907
$65$	−9.98810	−1.23887
$66$	−19.9697	−2.45810
$67$	−7.99404	−0.976627	−0.488313	−	0.872668i	$-0.662388\pi$
$67$	−7.99404	−0.976627	−0.488313	+	0.872668i	$0.662388\pi$
$68$	1.23006	0.149166
$69$	6.74528	0.812036
$70$	−1.66496	−0.199001
$71$	−6.23963	−0.740508	−0.370254	−	0.928931i	$-0.620729\pi$
$71$	−6.23963	−0.740508	−0.370254	+	0.928931i	$0.620729\pi$
$72$	1.90950	0.225037
$73$	−11.2914	−1.32156	−0.660782	−	0.750578i	$-0.729775\pi$
$73$	−11.2914	−1.32156	−0.660782	+	0.750578i	$0.729775\pi$
$74$	13.4084	1.55870
$75$	−0.313523	−0.0362025
$76$	8.08457	0.927363
$77$	2.16739	0.246997
$78$	16.5549	1.87447
$79$	10.6386	1.19693	0.598466	−	0.801148i	$-0.295777\pi$
$79$	10.6386	1.19693	0.598466	+	0.801148i	$0.295777\pi$
$80$	11.2265	1.25516
$81$	−11.2356	−1.24840
$82$	−1.00205	−0.110658
$83$	−7.40405	−0.812700	−0.406350	−	0.913718i	$-0.633199\pi$
$83$	−7.40405	−0.812700	−0.406350	+	0.913718i	$0.633199\pi$
$84$	1.05090	0.114663
$85$	−2.26932	−0.246142
$86$	−13.7751	−1.48541
$87$	−11.1252	−1.19275
$88$	−7.34678	−0.783170
$89$	7.94689	0.842369	0.421184	−	0.906975i	$-0.361615\pi$
$89$	7.94689	0.842369	0.421184	+	0.906975i	$0.361615\pi$
$90$	5.62803	0.593246
$91$	−1.79676	−0.188352
$92$	−3.96453	−0.413331
$93$	−16.8788	−1.75025
$94$	−18.4173	−1.89959
$95$	−14.9151	−1.53026
$96$	−12.8155	−1.30797
$97$	−10.0130	−1.01666	−0.508331	−	0.861161i	$-0.669738\pi$
$97$	−10.0130	−1.01666	−0.508331	+	0.861161i	$0.669738\pi$
$98$	12.2811	1.24058
$99$	−7.32637	−0.736328
$100$	0.184273	0.0184273
$101$	−13.4990	−1.34320	−0.671600	−	0.740914i	$-0.734393\pi$
$101$	−13.4990	−1.34320	−0.671600	+	0.740914i	$0.734393\pi$
$102$	3.76130	0.372425
$103$	11.9951	1.18191	0.590955	−	0.806705i	$-0.298751\pi$
$103$	11.9951	1.18191	0.590955	+	0.806705i	$0.298751\pi$
$104$	6.09048	0.597221
$105$	−1.93880	−0.189207
$106$	24.1336	2.34406
$107$	−8.04700	−0.777933	−0.388966	−	0.921252i	$-0.627168\pi$
$107$	−8.04700	−0.777933	−0.388966	+	0.921252i	$0.627168\pi$
$108$	4.17055	0.401311
$109$	−9.33510	−0.894141	−0.447070	−	0.894499i	$-0.647533\pi$
$109$	−9.33510	−0.894141	−0.447070	+	0.894499i	$0.647533\pi$
$110$	−21.6538	−2.06461
$111$	15.6137	1.48199
$112$	2.01954	0.190828
$113$	−0.517224	−0.0486564	−0.0243282	−	0.999704i	$-0.507745\pi$
$113$	−0.517224	−0.0486564	−0.0243282	+	0.999704i	$0.507745\pi$
$114$	24.7212	2.31536
$115$	7.31412	0.682045
$116$	6.53882	0.607114
$117$	6.07355	0.561500
$118$	−1.79724	−0.165449
$119$	−0.408229	−0.0374223
$120$	6.57193	0.599933
$121$	17.1881	1.56256
$122$	−4.78950	−0.433621
$123$	−1.16686	−0.105212
$124$	9.92047	0.890884
$125$	11.0066	0.984463
$126$	1.01243	0.0901943
$127$	−16.3025	−1.44661	−0.723305	−	0.690529i	$-0.757378\pi$
$127$	−16.3025	−1.44661	−0.723305	+	0.690529i	$0.757378\pi$
$128$	−10.2498	−0.905967
$129$	−16.0407	−1.41230
$130$	17.9510	1.57440
$131$	−0.386273	−0.0337488	−0.0168744	−	0.999858i	$-0.505372\pi$
$131$	−0.386273	−0.0337488	−0.0168744	+	0.999858i	$0.505372\pi$
$132$	13.6676	1.18961
$133$	−2.68309	−0.232653
$134$	14.3672	1.24113
$135$	−7.69421	−0.662212
$136$	1.38377	0.118657
$137$	15.9224	1.36034	0.680170	−	0.733054i	$-0.261906\pi$
$137$	15.9224	1.36034	0.680170	+	0.733054i	$0.261906\pi$
$138$	−12.1229	−1.03197
$139$	2.19073	0.185816	0.0929078	−	0.995675i	$-0.470384\pi$
$139$	2.19073	0.185816	0.0929078	+	0.995675i	$0.470384\pi$
$140$	1.13953	0.0963075
$141$	−21.4463	−1.80611
$142$	11.2141	0.941065
$143$	−23.3679	−1.95412
$144$	−6.82659	−0.568883
$145$	−12.0634	−1.00181
$146$	20.2934	1.67949
$147$	14.3010	1.17953
$148$	−9.17695	−0.754341
$149$	15.1567	1.24169	0.620843	−	0.783935i	$-0.286791\pi$
$149$	15.1567	1.24169	0.620843	+	0.783935i	$0.286791\pi$
$150$	0.563474	0.0460075
$151$	1.44767	0.117810	0.0589050	−	0.998264i	$-0.481239\pi$
$151$	1.44767	0.117810	0.0589050	+	0.998264i	$0.481239\pi$
$152$	9.09486	0.737690
$153$	1.37993	0.111560
$154$	−3.89531	−0.313893
$155$	−18.3022	−1.47007
$156$	−11.3304	−0.907158
$157$	14.7791	1.17950	0.589750	−	0.807586i	$-0.299226\pi$
$157$	14.7791	1.17950	0.589750	+	0.807586i	$0.299226\pi$
$158$	−19.1200	−1.52111
$159$	28.1028	2.22870
$160$	−13.8962	−1.09859
$161$	1.31574	0.103695
$162$	20.1930	1.58651
$163$	−18.8295	−1.47484	−0.737420	−	0.675434i	$-0.763956\pi$
$163$	−18.8295	−1.47484	−0.737420	+	0.675434i	$0.763956\pi$
$164$	0.685818	0.0535534
$165$	−25.2152	−1.96300
$166$	13.3068	1.03281
$167$	−2.98946	−0.231331	−0.115666	−	0.993288i	$-0.536900\pi$
$167$	−2.98946	−0.231331	−0.115666	+	0.993288i	$0.536900\pi$
$168$	1.18223	0.0912108
$169$	6.37200	0.490154
$170$	4.07850	0.312807
$171$	9.06958	0.693568
$172$	9.42788	0.718869
$173$	−19.2358	−1.46247	−0.731237	−	0.682123i	$-0.761057\pi$
$173$	−19.2358	−1.46247	−0.731237	+	0.682123i	$0.761057\pi$
$174$	19.9946	1.51579
$175$	−0.0611561	−0.00462296
$176$	26.2653	1.97982
$177$	−2.09283	−0.157307
$178$	−14.2824	−1.07051
$179$	−14.0525	−1.05033	−0.525166	−	0.851000i	$-0.675997\pi$
$179$	−14.0525	−1.05033	−0.525166	+	0.851000i	$0.675997\pi$
$180$	−3.85191	−0.287104
$181$	−15.0117	−1.11581	−0.557905	−	0.829905i	$-0.688395\pi$
$181$	−15.0117	−1.11581	−0.557905	+	0.829905i	$0.688395\pi$
$182$	3.22921	0.239365
$183$	−5.57723	−0.412281
$184$	−4.45996	−0.328793
$185$	16.9305	1.24475
$186$	30.3351	2.22428
$187$	−5.30925	−0.388251
$188$	12.6051	0.919318
$189$	−1.38411	−0.100680
$190$	26.8060	1.94471
$191$	8.34634	0.603920	0.301960	−	0.953321i	$-0.402359\pi$
$191$	8.34634	0.603920	0.301960	+	0.953321i	$0.402359\pi$
$192$	2.32566	0.167840
$193$	24.6445	1.77395	0.886975	−	0.461818i	$-0.152803\pi$
$193$	24.6445	1.77395	0.886975	+	0.461818i	$0.152803\pi$
$194$	17.9957	1.29201
$195$	20.9034	1.49692
$196$	−8.40540	−0.600386
$197$	−14.1500	−1.00815	−0.504073	−	0.863661i	$-0.668166\pi$
$197$	−14.1500	−1.00815	−0.504073	+	0.863661i	$0.668166\pi$
$198$	13.1672	0.935753
$199$	2.23545	0.158467	0.0792335	−	0.996856i	$-0.474753\pi$
$199$	2.23545	0.158467	0.0792335	+	0.996856i	$0.474753\pi$
$200$	0.207300	0.0146583
$201$	16.7301	1.18005
$202$	24.2609	1.70699
$203$	−2.17009	−0.152311
$204$	−2.57429	−0.180237
$205$	−1.26526	−0.0883696
$206$	−21.5580	−1.50201
$207$	−4.44756	−0.309127
$208$	−21.7739	−1.50975
$209$	−34.8951	−2.41375
$210$	3.48448	0.240452
$211$	22.8014	1.56971	0.784857	−	0.619678i	$-0.212737\pi$
$211$	22.8014	1.56971	0.784857	+	0.619678i	$0.212737\pi$
$212$	−16.5174	−1.13442
$213$	13.0585	0.894751
$214$	14.4624	0.988626
$215$	−17.3934	−1.18622
$216$	4.69173	0.319231
$217$	−3.29239	−0.223502
$218$	16.7774	1.13631
$219$	23.6310	1.59684
$220$	14.8202	0.999176
$221$	4.40136	0.296068
$222$	−28.0616	−1.88337
$223$	5.42718	0.363431	0.181715	−	0.983351i	$-0.441835\pi$
$223$	5.42718	0.363431	0.181715	+	0.983351i	$0.441835\pi$
$224$	−2.49980	−0.167025
$225$	0.206724	0.0137816
$226$	0.929574	0.0618344
$227$	−20.0954	−1.33378	−0.666890	−	0.745156i	$-0.732375\pi$
$227$	−20.0954	−1.33378	−0.666890	+	0.745156i	$0.732375\pi$
$228$	−16.9196	−1.12053
$229$	−10.7871	−0.712831	−0.356415	−	0.934328i	$-0.616001\pi$
$229$	−10.7871	−0.712831	−0.356415	+	0.934328i	$0.616001\pi$
$230$	−13.1452	−0.866769
$231$	−4.53597	−0.298445
$232$	7.35595	0.482942
$233$	−7.83103	−0.513028	−0.256514	−	0.966541i	$-0.582574\pi$
$233$	−7.83103	−0.513028	−0.256514	+	0.966541i	$0.582574\pi$
$234$	−10.9156	−0.713575
$235$	−23.2549	−1.51699
$236$	1.23006	0.0800698
$237$	−22.2647	−1.44625
$238$	0.733683	0.0475576
$239$	10.0166	0.647919	0.323960	−	0.946071i	$-0.394986\pi$
$239$	10.0166	0.647919	0.323960	+	0.946071i	$0.394986\pi$
$240$	−23.4951	−1.51660
$241$	26.5106	1.70769	0.853847	−	0.520523i	$-0.174263\pi$
$241$	26.5106	1.70769	0.853847	+	0.520523i	$0.174263\pi$
$242$	−30.8911	−1.98576
$243$	13.3425	0.855923
$244$	3.27801	0.209853
$245$	15.5070	0.990709
$246$	2.09712	0.133707
$247$	28.9280	1.84065
$248$	11.1602	0.708673
$249$	15.4954	0.981981
$250$	−19.7815	−1.25109
$251$	18.0754	1.14091	0.570456	−	0.821328i	$-0.306767\pi$
$251$	18.0754	1.14091	0.570456	+	0.821328i	$0.306767\pi$
$252$	−0.692922	−0.0436500
$253$	17.1120	1.07582
$254$	29.2994	1.83841
$255$	4.74929	0.297412
$256$	20.6439	1.29024
$257$	−21.7862	−1.35899	−0.679493	−	0.733682i	$-0.737800\pi$
$257$	−21.7862	−1.35899	−0.679493	+	0.733682i	$0.737800\pi$
$258$	28.8289	1.79481
$259$	3.04563	0.189246
$260$	−12.2859	−0.761940
$261$	7.33551	0.454056
$262$	0.694224	0.0428893
$263$	15.2245	0.938784	0.469392	−	0.882990i	$-0.344473\pi$
$263$	15.2245	0.938784	0.469392	+	0.882990i	$0.344473\pi$
$264$	15.3755	0.946300
$265$	30.4728	1.87193
$266$	4.82215	0.295665
$267$	−16.6315	−1.01783
$268$	−9.83311	−0.600653
$269$	9.27880	0.565738	0.282869	−	0.959159i	$-0.408714\pi$
$269$	9.27880	0.565738	0.282869	+	0.959159i	$0.408714\pi$
$270$	13.8283	0.841564
$271$	−0.801732	−0.0487017	−0.0243509	−	0.999703i	$-0.507752\pi$
$271$	−0.801732	−0.0487017	−0.0243509	+	0.999703i	$0.507752\pi$
$272$	−4.94707	−0.299960
$273$	3.76031	0.227585
$274$	−28.6163	−1.72877
$275$	−0.795370	−0.0479626
$276$	8.29707	0.499425
$277$	0.776227	0.0466389	0.0233195	−	0.999728i	$-0.492577\pi$
$277$	0.776227	0.0466389	0.0233195	+	0.999728i	$0.492577\pi$
$278$	−3.93727	−0.236142
$279$	11.1292	0.666286
$280$	1.28193	0.0766098
$281$	−9.76558	−0.582566	−0.291283	−	0.956637i	$-0.594082\pi$
$281$	−9.76558	−0.582566	−0.291283	+	0.956637i	$0.594082\pi$
$282$	38.5441	2.29527
$283$	15.9857	0.950251	0.475126	−	0.879918i	$-0.342403\pi$
$283$	15.9857	0.950251	0.475126	+	0.879918i	$0.342403\pi$
$284$	−7.67509	−0.455433
$285$	31.2148	1.84901
$286$	41.9977	2.48338
$287$	−0.227608	−0.0134353
$288$	8.45000	0.497921
$289$	1.00000	0.0588235
$290$	21.6808	1.27314
$291$	20.9554	1.22843
$292$	−13.8891	−0.812799
$293$	−26.0983	−1.52468	−0.762339	−	0.647178i	$-0.775949\pi$
$293$	−26.0983	−1.52468	−0.762339	+	0.647178i	$0.775949\pi$
$294$	−25.7023	−1.49899
$295$	−2.26932	−0.132125
$296$	−10.3238	−0.600056
$297$	−18.0012	−1.04454
$298$	−27.2402	−1.57798
$299$	−14.1858	−0.820386
$300$	−0.385651	−0.0222656
$301$	−3.12891	−0.180347
$302$	−2.60181	−0.149717
$303$	28.2511	1.62298
$304$	−32.5147	−1.86485
$305$	−6.04757	−0.346283
$306$	−2.48005	−0.141775
$307$	6.13677	0.350244	0.175122	−	0.984547i	$-0.443968\pi$
$307$	6.13677	0.350244	0.175122	+	0.984547i	$0.443968\pi$
$308$	2.66601	0.151910
$309$	−25.1036	−1.42809
$310$	32.8933	1.86822
$311$	29.9029	1.69564	0.847819	−	0.530285i	$-0.177915\pi$
$311$	29.9029	1.69564	0.847819	+	0.530285i	$0.177915\pi$
$312$	−12.7463	−0.721618
$313$	−35.2016	−1.98971	−0.994857	−	0.101293i	$-0.967702\pi$
$313$	−35.2016	−1.98971	−0.994857	+	0.101293i	$0.967702\pi$
$314$	−26.5615	−1.49895
$315$	1.27836	0.0720277
$316$	13.0860	0.736147
$317$	6.02594	0.338451	0.169225	−	0.985577i	$-0.445873\pi$
$317$	6.02594	0.338451	0.169225	+	0.985577i	$0.445873\pi$
$318$	−50.5074	−2.83231
$319$	−28.2233	−1.58020
$320$	2.52179	0.140972
$321$	16.8410	0.939972
$322$	−2.36470	−0.131779
$323$	6.57252	0.365705
$324$	−13.8204	−0.767800
$325$	0.659361	0.0365748
$326$	33.8411	1.87428
$327$	19.5368	1.08039
$328$	0.771522	0.0426002
$329$	−4.18334	−0.230635
$330$	45.3176	2.49465
$331$	−26.4681	−1.45482	−0.727409	−	0.686204i	$-0.759276\pi$
$331$	−26.4681	−1.45482	−0.727409	+	0.686204i	$0.759276\pi$
$332$	−9.10740	−0.499833
$333$	−10.2951	−0.564166
$334$	5.37277	0.293985
$335$	18.1410	0.991150
$336$	−4.22654	−0.230577
$337$	−7.25909	−0.395428	−0.197714	−	0.980260i	$-0.563352\pi$
$337$	−7.25909	−0.395428	−0.197714	+	0.980260i	$0.563352\pi$
$338$	−11.4520	−0.622906
$339$	1.08246	0.0587912
$340$	−2.79139	−0.151384
$341$	−42.8194	−2.31880
$342$	−16.3002	−0.881413
$343$	5.64717	0.304919
$344$	10.6060	0.571839
$345$	−15.3072	−0.824112
$346$	34.5714	1.85857
$347$	−32.6943	−1.75512	−0.877561	−	0.479465i	$-0.840831\pi$
$347$	−32.6943	−1.75512	−0.877561	+	0.479465i	$0.840831\pi$
$348$	−13.6846	−0.733573
$349$	−25.5156	−1.36582	−0.682911	−	0.730502i	$-0.739286\pi$
$349$	−25.5156	−1.36582	−0.682911	+	0.730502i	$0.739286\pi$
$350$	0.109912	0.00587503
$351$	14.9230	0.796530
$352$	−32.5113	−1.73286
$353$	−15.9141	−0.847021	−0.423510	−	0.905891i	$-0.639202\pi$
$353$	−15.9141	−0.847021	−0.423510	+	0.905891i	$0.639202\pi$
$354$	3.76130	0.199911
$355$	14.1597	0.751519
$356$	9.77512	0.518080
$357$	0.854352	0.0452171
$358$	25.2556	1.33480
$359$	−24.6043	−1.29856	−0.649282	−	0.760548i	$-0.724930\pi$
$359$	−24.6043	−1.29856	−0.649282	+	0.760548i	$0.724930\pi$
$360$	−4.33327	−0.228383
$361$	24.1980	1.27358
$362$	26.9795	1.41801
$363$	−35.9718	−1.88803
$364$	−2.21012	−0.115842
$365$	25.6239	1.34122
$366$	10.0236	0.523942
$367$	−28.9531	−1.51134	−0.755670	−	0.654952i	$-0.772689\pi$
$367$	−28.9531	−1.51134	−0.755670	+	0.654952i	$0.772689\pi$
$368$	15.9447	0.831173
$369$	0.769378	0.0400522
$370$	−30.4280	−1.58188
$371$	5.48176	0.284599
$372$	−20.7618	−1.07645
$373$	−10.8727	−0.562966	−0.281483	−	0.959566i	$-0.590826\pi$
$373$	−10.8727	−0.562966	−0.281483	+	0.959566i	$0.590826\pi$
$374$	9.54197	0.493404
$375$	−23.0350	−1.18952
$376$	14.1803	0.731291
$377$	23.3971	1.20501
$378$	2.48758	0.127947
$379$	−22.9098	−1.17680	−0.588399	−	0.808570i	$-0.700242\pi$
$379$	−22.9098	−1.17680	−0.588399	+	0.808570i	$0.700242\pi$
$380$	−18.3465	−0.941153
$381$	34.1182	1.74793
$382$	−15.0003	−0.767484
$383$	23.4323	1.19734	0.598668	−	0.800997i	$-0.295697\pi$
$383$	23.4323	1.19734	0.598668	+	0.800997i	$0.295697\pi$
$384$	21.4512	1.09467
$385$	−4.91850	−0.250670
$386$	−44.2920	−2.25440
$387$	10.5766	0.537637
$388$	−12.3165	−0.625276
$389$	−5.62843	−0.285373	−0.142686	−	0.989768i	$-0.545574\pi$
$389$	−5.62843	−0.285373	−0.142686	+	0.989768i	$0.545574\pi$
$390$	−37.5683	−1.90234
$391$	−3.22305	−0.162997
$392$	−9.45579	−0.477589
$393$	0.808403	0.0407785
$394$	25.4309	1.28119
$395$	−24.1423	−1.21473
$396$	−9.01184	−0.452862
$397$	0.711987	0.0357336	0.0178668	−	0.999840i	$-0.494313\pi$
$397$	0.711987	0.0357336	0.0178668	+	0.999840i	$0.494313\pi$
$398$	−4.01763	−0.201386
$399$	5.61525	0.281114
$400$	−0.741113	−0.0370556
$401$	24.4706	1.22200	0.611001	−	0.791630i	$-0.290767\pi$
$401$	24.4706	1.22200	0.611001	+	0.791630i	$0.290767\pi$
$402$	−30.0680	−1.49966
$403$	35.4972	1.76824
$404$	−16.6045	−0.826105
$405$	25.4971	1.26696
$406$	3.90017	0.193562
$407$	39.6102	1.96340
$408$	−2.89599	−0.143373
$409$	−30.3699	−1.50170	−0.750848	−	0.660475i	$-0.770355\pi$
$409$	−30.3699	−1.50170	−0.750848	+	0.660475i	$0.770355\pi$
$410$	2.27397	0.112303
$411$	−33.3228	−1.64369
$412$	14.7546	0.726907
$413$	−0.408229	−0.0200876
$414$	7.99332	0.392850
$415$	16.8021	0.824785
$416$	26.9518	1.32142
$417$	−4.58483	−0.224520
$418$	62.7148	3.06748
$419$	−23.1375	−1.13034	−0.565171	−	0.824973i	$-0.691190\pi$
$419$	−23.1375	−1.13034	−0.565171	+	0.824973i	$0.691190\pi$
$420$	−2.38483	−0.116368
$421$	5.21432	0.254131	0.127065	−	0.991894i	$-0.459444\pi$
$421$	5.21432	0.254131	0.127065	+	0.991894i	$0.459444\pi$
$422$	−40.9795	−1.99485
$423$	14.1408	0.687552
$424$	−18.5815	−0.902397
$425$	0.149808	0.00726677
$426$	−23.4691	−1.13708
$427$	−1.08790	−0.0526472
$428$	−9.89826	−0.478450
$429$	48.9050	2.36116
$430$	31.2600	1.50749
$431$	−4.52664	−0.218041	−0.109020	−	0.994040i	$-0.534771\pi$
$431$	−4.52664	−0.218041	−0.109020	+	0.994040i	$0.534771\pi$
$432$	−16.7732	−0.807003
$433$	−17.8875	−0.859618	−0.429809	−	0.902920i	$-0.641419\pi$
$433$	−17.8875	−0.859618	−0.429809	+	0.902920i	$0.641419\pi$
$434$	5.91720	0.284034
$435$	25.2466	1.21048
$436$	−11.4827	−0.549922
$437$	−21.1835	−1.01335
$438$	−42.4706	−2.02932
$439$	−31.1495	−1.48668	−0.743342	−	0.668911i	$-0.766761\pi$
$439$	−31.1495	−1.48668	−0.743342	+	0.668911i	$0.766761\pi$
$440$	16.6722	0.794816
$441$	−9.42951	−0.449024
$442$	−7.91029	−0.376254
$443$	−15.7170	−0.746736	−0.373368	−	0.927683i	$-0.621797\pi$
$443$	−15.7170	−0.746736	−0.373368	+	0.927683i	$0.621797\pi$
$444$	19.2058	0.911466
$445$	−18.0340	−0.854895
$446$	−9.75392	−0.461862
$447$	−31.7204	−1.50032
$448$	0.453646	0.0214327
$449$	−28.3350	−1.33721	−0.668605	−	0.743618i	$-0.733108\pi$
$449$	−28.3350	−1.33721	−0.668605	+	0.743618i	$0.733108\pi$
$450$	−0.371532	−0.0175142
$451$	−2.96017	−0.139389
$452$	−0.636215	−0.0299250
$453$	−3.02973	−0.142349
$454$	36.1162	1.69502
$455$	4.07743	0.191153
$456$	−19.0340	−0.891347
$457$	1.11900	0.0523446	0.0261723	−	0.999657i	$-0.491668\pi$
$457$	1.11900	0.0523446	0.0261723	+	0.999657i	$0.491668\pi$
$458$	19.3869	0.905892
$459$	3.39054	0.158257
$460$	8.99678	0.419477
$461$	30.7432	1.43185	0.715927	−	0.698176i	$-0.246004\pi$
$461$	30.7432	1.43185	0.715927	+	0.698176i	$0.246004\pi$
$462$	8.15221	0.379275
$463$	−1.62186	−0.0753744	−0.0376872	−	0.999290i	$-0.511999\pi$
$463$	−1.62186	−0.0753744	−0.0376872	+	0.999290i	$0.511999\pi$
$464$	−26.2980	−1.22085
$465$	38.3033	1.77627
$466$	14.0742	0.651975
$467$	25.9946	1.20288	0.601442	−	0.798916i	$-0.294593\pi$
$467$	25.9946	1.20288	0.601442	+	0.798916i	$0.294593\pi$
$468$	7.47081	0.345338
$469$	3.26340	0.150690
$470$	41.7946	1.92784
$471$	−30.9301	−1.42518
$472$	1.38377	0.0636932
$473$	−40.6932	−1.87108
$474$	40.0149	1.83794
$475$	0.984618	0.0451774
$476$	−0.502144	−0.0230157
$477$	−18.5299	−0.848424
$478$	−18.0022	−0.823400
$479$	14.4383	0.659703	0.329851	−	0.944033i	$-0.393001\pi$
$479$	14.4383	0.659703	0.329851	+	0.944033i	$0.393001\pi$
$480$	29.0824	1.32742
$481$	−32.8368	−1.49723
$482$	−47.6457	−2.17020
$483$	−2.75362	−0.125294
$484$	21.1424	0.961016
$485$	22.7226	1.03178
$486$	−23.9797	−1.08774
$487$	−6.25038	−0.283232	−0.141616	−	0.989922i	$-0.545230\pi$
$487$	−6.25038	−0.283232	−0.141616	+	0.989922i	$0.545230\pi$
$488$	3.68765	0.166932
$489$	39.4069	1.78204
$490$	−27.8698	−1.25903
$491$	−28.9856	−1.30810	−0.654050	−	0.756451i	$-0.726931\pi$
$491$	−28.9856	−1.30810	−0.654050	+	0.756451i	$0.726931\pi$
$492$	−1.43530	−0.0647083
$493$	5.31587	0.239415
$494$	−51.9905	−2.33916
$495$	16.6259	0.747277
$496$	−39.8984	−1.79149
$497$	2.54720	0.114257
$498$	−27.8489	−1.24794
$499$	10.7084	0.479373	0.239686	−	0.970850i	$-0.422955\pi$
$499$	10.7084	0.479373	0.239686	+	0.970850i	$0.422955\pi$
$500$	13.5388	0.605472
$501$	6.25643	0.279517
$502$	−32.4858	−1.44991
$503$	−35.2508	−1.57175	−0.785877	−	0.618383i	$-0.787788\pi$
$503$	−35.2508	−1.57175	−0.785877	+	0.618383i	$0.787788\pi$
$504$	−0.779513	−0.0347223
$505$	30.6335	1.36317
$506$	−30.7542	−1.36719
$507$	−13.3355	−0.592250
$508$	−20.0529	−0.889705
$509$	9.17040	0.406471	0.203235	−	0.979130i	$-0.434854\pi$
$509$	9.17040	0.406471	0.203235	+	0.979130i	$0.434854\pi$
$510$	−8.53560	−0.377963
$511$	4.60949	0.203912
$512$	−16.6023	−0.733723
$513$	22.2844	0.983879
$514$	39.1549	1.72705
$515$	−27.2206	−1.19948
$516$	−19.7309	−0.868605
$517$	−54.4068	−2.39281
$518$	−5.47371	−0.240501
$519$	40.2573	1.76710
$520$	−13.8212	−0.606101
$521$	38.8660	1.70275	0.851375	−	0.524558i	$-0.175769\pi$
$521$	38.8660	1.70275	0.851375	+	0.524558i	$0.175769\pi$
$522$	−13.1836	−0.577032
$523$	−10.1174	−0.442403	−0.221202	−	0.975228i	$-0.570998\pi$
$523$	−10.1174	−0.442403	−0.221202	+	0.975228i	$0.570998\pi$
$524$	−0.475138	−0.0207565
$525$	0.127989	0.00558590
$526$	−27.3621	−1.19304
$527$	8.06505	0.351319
$528$	−54.9686	−2.39220
$529$	−12.6120	−0.548346
$530$	−54.7667	−2.37892
$531$	1.37993	0.0598837
$532$	−3.30035	−0.143088
$533$	2.45398	0.106294
$534$	29.8907	1.29350
$535$	18.2612	0.789501
$536$	−11.0619	−0.477802
$537$	29.4094	1.26911
$538$	−16.6762	−0.718962
$539$	36.2800	1.56269
$540$	−9.46431	−0.407279
$541$	−10.3499	−0.444976	−0.222488	−	0.974935i	$-0.571418\pi$
$541$	−10.3499	−0.444976	−0.222488	+	0.974935i	$0.571418\pi$
$542$	1.44090	0.0618920
$543$	31.4169	1.34823
$544$	6.12352	0.262544
$545$	21.1843	0.907437
$546$	−6.75817	−0.289223
$547$	−11.9498	−0.510938	−0.255469	−	0.966817i	$-0.582230\pi$
$547$	−11.9498	−0.510938	−0.255469	+	0.966817i	$0.582230\pi$
$548$	19.5854	0.836647
$549$	3.67740	0.156948
$550$	1.42947	0.0609527
$551$	34.9387	1.48844
$552$	9.33392	0.397278
$553$	−4.34297	−0.184682
$554$	−1.39506	−0.0592705
$555$	−35.4325	−1.50403
$556$	2.69473	0.114282
$557$	−24.7373	−1.04815	−0.524077	−	0.851671i	$-0.675590\pi$
$557$	−24.7373	−1.04815	−0.524077	+	0.851671i	$0.675590\pi$
$558$	−20.0017	−0.846741
$559$	33.7347	1.42682
$560$	−4.58298	−0.193666
$561$	11.1113	0.469121
$562$	17.5511	0.740346
$563$	17.7673	0.748804	0.374402	−	0.927267i	$-0.377848\pi$
$563$	17.7673	0.748804	0.374402	+	0.927267i	$0.377848\pi$
$564$	−26.3802	−1.11081
$565$	1.17375	0.0493799
$566$	−28.7301	−1.20762
$567$	4.58669	0.192623
$568$	−8.63422	−0.362284
$569$	−28.0317	−1.17515	−0.587575	−	0.809170i	$-0.699917\pi$
$569$	−28.0317	−1.17515	−0.587575	+	0.809170i	$0.699917\pi$
$570$	−56.1004	−2.34979
$571$	−0.218760	−0.00915482	−0.00457741	−	0.999990i	$-0.501457\pi$
$571$	−0.218760	−0.00915482	−0.00457741	+	0.999990i	$0.501457\pi$
$572$	−28.7439	−1.20184
$573$	−17.4674	−0.729713
$574$	0.409065	0.0170741
$575$	−0.482839	−0.0201358
$576$	−1.53345	−0.0638936
$577$	16.9609	0.706090	0.353045	−	0.935606i	$-0.385146\pi$
$577$	16.9609	0.706090	0.353045	+	0.935606i	$0.385146\pi$
$578$	−1.79724	−0.0747551
$579$	−51.5767	−2.14345
$580$	−14.8387	−0.616142
$581$	3.02255	0.125396
$582$	−37.6618	−1.56113
$583$	71.2934	2.95267
$584$	−15.6248	−0.646558
$585$	−13.7828	−0.569850
$586$	46.9048	1.93762
$587$	7.82542	0.322990	0.161495	−	0.986874i	$-0.448369\pi$
$587$	7.82542	0.322990	0.161495	+	0.986874i	$0.448369\pi$
$588$	17.5911	0.725443
$589$	53.0077	2.18414
$590$	4.07850	0.167909
$591$	29.6135	1.21814
$592$	36.9081	1.51691
$593$	−20.3342	−0.835025	−0.417512	−	0.908671i	$-0.637098\pi$
$593$	−20.3342	−0.835025	−0.417512	+	0.908671i	$0.637098\pi$
$594$	32.3524	1.32744
$595$	0.926401	0.0379787
$596$	18.6436	0.763671
$597$	−4.67841	−0.191475
$598$	25.4952	1.04258
$599$	−0.288963	−0.0118067	−0.00590335	−	0.999983i	$-0.501879\pi$
$599$	−0.288963	−0.0118067	−0.00590335	+	0.999983i	$0.501879\pi$
$600$	−0.433844	−0.0177116
$601$	35.0164	1.42835	0.714174	−	0.699968i	$-0.246802\pi$
$601$	35.0164	1.42835	0.714174	+	0.699968i	$0.246802\pi$
$602$	5.62338	0.229192
$603$	−11.0312	−0.449224
$604$	1.78072	0.0724564
$605$	−39.0053	−1.58579
$606$	−50.7738	−2.06254
$607$	29.8372	1.21106	0.605528	−	0.795824i	$-0.292962\pi$
$607$	29.8372	1.21106	0.605528	+	0.795824i	$0.292962\pi$
$608$	40.2469	1.63223
$609$	4.54163	0.184036
$610$	10.8689	0.440069
$611$	45.1032	1.82468
$612$	1.69739	0.0686127
$613$	−31.4163	−1.26889	−0.634447	−	0.772967i	$-0.718772\pi$
$613$	−31.4163	−1.26889	−0.634447	+	0.772967i	$0.718772\pi$
$614$	−11.0292	−0.445103
$615$	2.64797	0.106776
$616$	2.99917	0.120840
$617$	−2.88720	−0.116234	−0.0581171	−	0.998310i	$-0.518510\pi$
$617$	−2.88720	−0.116234	−0.0581171	+	0.998310i	$0.518510\pi$
$618$	45.1171	1.81488
$619$	22.9640	0.923002	0.461501	−	0.887140i	$-0.347311\pi$
$619$	22.9640	0.923002	0.461501	+	0.887140i	$0.347311\pi$
$620$	−22.5127	−0.904132
$621$	−10.9279	−0.438520
$622$	−53.7426	−2.15488
$623$	−3.24415	−0.129974
$624$	45.5689	1.82422
$625$	−25.7266	−1.02906
$626$	63.2656	2.52860
$627$	73.0295	2.91652
$628$	18.1791	0.725426
$629$	−7.46060	−0.297473
$630$	−2.29752	−0.0915355
$631$	7.02466	0.279647	0.139824	−	0.990176i	$-0.455346\pi$
$631$	7.02466	0.279647	0.139824	+	0.990176i	$0.455346\pi$
$632$	14.7213	0.585583
$633$	−47.7194	−1.89668
$634$	−10.8300	−0.430116
$635$	36.9955	1.46812
$636$	34.5680	1.37071
$637$	−30.0761	−1.19166
$638$	50.7239	2.00818
$639$	−8.61022	−0.340615
$640$	23.2602	0.919439
$641$	−14.8212	−0.585401	−0.292700	−	0.956204i	$-0.594554\pi$
$641$	−14.8212	−0.585401	−0.292700	+	0.956204i	$0.594554\pi$
$642$	−30.2672	−1.19455
$643$	−13.5317	−0.533637	−0.266819	−	0.963747i	$-0.585972\pi$
$643$	−13.5317	−0.533637	−0.266819	+	0.963747i	$0.585972\pi$
$644$	1.61843	0.0637753
$645$	36.4014	1.43330
$646$	−11.8124	−0.464751
$647$	−1.58681	−0.0623840	−0.0311920	−	0.999513i	$-0.509930\pi$
$647$	−1.58681	−0.0623840	−0.0311920	+	0.999513i	$0.509930\pi$
$648$	−15.5475	−0.610762
$649$	−5.30925	−0.208406
$650$	−1.18503	−0.0464806
$651$	6.89040	0.270056
$652$	−23.1613	−0.907068
$653$	−3.79245	−0.148410	−0.0742051	−	0.997243i	$-0.523642\pi$
$653$	−3.79245	−0.148410	−0.0742051	+	0.997243i	$0.523642\pi$
$654$	−35.1122	−1.37299
$655$	0.876577	0.0342507
$656$	−2.75824	−0.107691
$657$	−15.5814	−0.607887
$658$	7.51845	0.293100
$659$	−14.3354	−0.558429	−0.279215	−	0.960229i	$-0.590074\pi$
$659$	−14.3354	−0.558429	−0.279215	+	0.960229i	$0.590074\pi$
$660$	−31.0161	−1.20730
$661$	−32.8805	−1.27890	−0.639451	−	0.768832i	$-0.720838\pi$
$661$	−32.8805	−1.27890	−0.639451	+	0.768832i	$0.720838\pi$
$662$	47.5694	1.84884
$663$	−9.21129	−0.357737
$664$	−10.2455	−0.397603
$665$	6.08879	0.236113
$666$	18.5027	0.716963
$667$	−17.1333	−0.663404
$668$	−3.67721	−0.142275
$669$	−11.3582	−0.439132
$670$	−32.6037	−1.25959
$671$	−14.1488	−0.546207
$672$	5.23164	0.201815
$673$	12.7775	0.492536	0.246268	−	0.969202i	$-0.420796\pi$
$673$	12.7775	0.492536	0.246268	+	0.969202i	$0.420796\pi$
$674$	13.0463	0.502524
$675$	0.507930	0.0195503
$676$	7.83791	0.301458
$677$	11.3002	0.434301	0.217151	−	0.976138i	$-0.430324\pi$
$677$	11.3002	0.434301	0.217151	+	0.976138i	$0.430324\pi$
$678$	−1.94544	−0.0747141
$679$	4.08758	0.156867
$680$	−3.14022	−0.120422
$681$	42.0563	1.61160
$682$	76.9565	2.94682
$683$	34.4759	1.31918	0.659591	−	0.751625i	$-0.270730\pi$
$683$	34.4759	1.31918	0.659591	+	0.751625i	$0.270730\pi$
$684$	11.1561	0.426564
$685$	−36.1329	−1.38057
$686$	−10.1493	−0.387502
$687$	22.5755	0.861310
$688$	−37.9173	−1.44558
$689$	−59.1022	−2.25161
$690$	27.5106	1.04731
$691$	−45.8225	−1.74317	−0.871586	−	0.490243i	$-0.836908\pi$
$691$	−45.8225	−1.74317	−0.871586	+	0.490243i	$0.836908\pi$
$692$	−23.6612	−0.899463
$693$	2.99083	0.113612
$694$	58.7594	2.23047
$695$	−4.97148	−0.188579
$696$	−15.3947	−0.583536
$697$	0.557550	0.0211187
$698$	45.8576	1.73574
$699$	16.3890	0.619889
$700$	−0.0752254	−0.00284325
$701$	36.1668	1.36600	0.683000	−	0.730418i	$-0.260675\pi$
$701$	36.1668	1.36600	0.683000	+	0.730418i	$0.260675\pi$
$702$	−26.8201	−1.01226
$703$	−49.0349	−1.84939
$704$	5.89992	0.222362
$705$	48.6686	1.83297
$706$	28.6013	1.07643
$707$	5.51068	0.207250
$708$	−2.57429	−0.0967479
$709$	−14.9976	−0.563248	−0.281624	−	0.959525i	$-0.590873\pi$
$709$	−14.9976	−0.563248	−0.281624	+	0.959525i	$0.590873\pi$
$710$	−25.4483	−0.955059
$711$	14.6804	0.550559
$712$	10.9967	0.412118
$713$	−25.9941	−0.973485
$714$	−1.53547	−0.0574636
$715$	53.0293	1.98318
$716$	−17.2853	−0.645983
$717$	−20.9630	−0.782877
$718$	44.2197	1.65026
$719$	14.8293	0.553040	0.276520	−	0.961008i	$-0.410819\pi$
$719$	14.8293	0.553040	0.276520	+	0.961008i	$0.410819\pi$
$720$	15.4917	0.577342
$721$	−4.89673	−0.182364
$722$	−43.4895	−1.61851
$723$	−55.4820	−2.06340
$724$	−18.4652	−0.686254
$725$	0.796362	0.0295761
$726$	64.6498	2.39938
$727$	19.7502	0.732495	0.366248	−	0.930517i	$-0.380642\pi$
$727$	19.7502	0.732495	0.366248	+	0.930517i	$0.380642\pi$
$728$	−2.48631	−0.0921487
$729$	5.78315	0.214191
$730$	−46.0522	−1.70447
$731$	7.66459	0.283485
$732$	−6.86031	−0.253564
$733$	−1.57449	−0.0581551	−0.0290775	−	0.999577i	$-0.509257\pi$
$733$	−1.57449	−0.0581551	−0.0290775	+	0.999577i	$0.509257\pi$
$734$	52.0356	1.92067
$735$	−32.4536	−1.19707
$736$	−19.7364	−0.727493
$737$	42.4423	1.56338
$738$	−1.38275	−0.0508999
$739$	28.4966	1.04826	0.524132	−	0.851637i	$-0.324390\pi$
$739$	28.4966	1.04826	0.524132	+	0.851637i	$0.324390\pi$
$740$	20.8254	0.765558
$741$	−60.5414	−2.22404
$742$	−9.85201	−0.361679
$743$	24.9050	0.913676	0.456838	−	0.889550i	$-0.348982\pi$
$743$	24.9050	0.913676	0.456838	+	0.889550i	$0.348982\pi$
$744$	−23.3563	−0.856285
$745$	−34.3954	−1.26015
$746$	19.5408	0.715438
$747$	−10.2170	−0.373822
$748$	−6.53067	−0.238785
$749$	3.28502	0.120032
$750$	41.3993	1.51169
$751$	8.59795	0.313744	0.156872	−	0.987619i	$-0.449859\pi$
$751$	8.59795	0.313744	0.156872	+	0.987619i	$0.449859\pi$
$752$	−50.6954	−1.84867
$753$	−37.8288	−1.37856
$754$	−42.0501	−1.53137
$755$	−3.28523	−0.119562
$756$	−1.70254	−0.0619207
$757$	5.83207	0.211970	0.105985	−	0.994368i	$-0.466200\pi$
$757$	5.83207	0.211970	0.105985	+	0.994368i	$0.466200\pi$
$758$	41.1744	1.49552
$759$	−35.8124	−1.29991
$760$	−20.6391	−0.748660
$761$	6.51484	0.236163	0.118081	−	0.993004i	$-0.462326\pi$
$761$	6.51484	0.236163	0.118081	+	0.993004i	$0.462326\pi$
$762$	−61.3185	−2.22134
$763$	3.81086	0.137962
$764$	10.2665	0.371428
$765$	−3.13149	−0.113219
$766$	−42.1134	−1.52162
$767$	4.40136	0.158924
$768$	−43.2041	−1.55899
$769$	−28.7287	−1.03598	−0.517991	−	0.855386i	$-0.673320\pi$
$769$	−28.7287	−1.03598	−0.517991	+	0.855386i	$0.673320\pi$
$770$	8.83969	0.318560
$771$	45.5947	1.64205
$772$	30.3141	1.09103
$773$	−38.8799	−1.39841	−0.699206	−	0.714920i	$-0.746463\pi$
$773$	−38.8799	−1.39841	−0.699206	+	0.714920i	$0.746463\pi$
$774$	−19.0086	−0.683249
$775$	1.20821	0.0434003
$776$	−13.8557	−0.497389
$777$	−6.37398	−0.228665
$778$	10.1156	0.362663
$779$	3.66451	0.131295
$780$	25.7123	0.920648
$781$	33.1278	1.18540
$782$	5.79258	0.207142
$783$	18.0237	0.644113
$784$	33.8051	1.20732
$785$	−33.5385	−1.19704
$786$	−1.45289	−0.0518229
$787$	−23.6692	−0.843714	−0.421857	−	0.906662i	$-0.638622\pi$
$787$	−23.6692	−0.843714	−0.421857	+	0.906662i	$0.638622\pi$
$788$	−17.4053	−0.620038
$789$	−31.8623	−1.13433
$790$	43.3894	1.54373
$791$	0.211146	0.00750748
$792$	−10.1380	−0.360239
$793$	11.7293	0.416520
$794$	−1.27961	−0.0454116
$795$	−63.7742	−2.26184
$796$	2.74973	0.0974616
$797$	14.9176	0.528407	0.264204	−	0.964467i	$-0.414891\pi$
$797$	14.9176	0.528407	0.264204	+	0.964467i	$0.414891\pi$
$798$	−10.0919	−0.357250
$799$	10.2475	0.362532
$800$	0.917354	0.0324333
$801$	10.9661	0.387469
$802$	−43.9794	−1.55297
$803$	59.9491	2.11556
$804$	20.5790	0.725765
$805$	−2.98584	−0.105237
$806$	−63.7969	−2.24715
$807$	−19.4189	−0.683578
$808$	−18.6795	−0.657143
$809$	25.5094	0.896863	0.448431	−	0.893817i	$-0.351983\pi$
$809$	25.5094	0.896863	0.448431	+	0.893817i	$0.351983\pi$
$810$	−45.8243	−1.61010
$811$	−49.7245	−1.74606	−0.873032	−	0.487663i	$-0.837849\pi$
$811$	−49.7245	−1.74606	−0.873032	+	0.487663i	$0.837849\pi$
$812$	−2.66933	−0.0936753
$813$	1.67789	0.0588460
$814$	−71.1888	−2.49517
$815$	42.7301	1.49677
$816$	10.3534	0.362440
$817$	50.3757	1.76242
$818$	54.5819	1.90841
$819$	−2.47940	−0.0866372
$820$	−1.55634	−0.0543498
$821$	−20.1530	−0.703343	−0.351672	−	0.936123i	$-0.614387\pi$
$821$	−20.1530	−0.703343	−0.351672	+	0.936123i	$0.614387\pi$
$822$	59.8889	2.08886
$823$	8.61139	0.300174	0.150087	−	0.988673i	$-0.452045\pi$
$823$	8.61139	0.300174	0.150087	+	0.988673i	$0.452045\pi$
$824$	16.5984	0.578234
$825$	1.66457	0.0579529
$826$	0.733683	0.0255281
$827$	14.4015	0.500790	0.250395	−	0.968144i	$-0.419439\pi$
$827$	14.4015	0.500790	0.250395	+	0.968144i	$0.419439\pi$
$828$	−5.47075	−0.190122
$829$	−33.2471	−1.15472	−0.577359	−	0.816490i	$-0.695917\pi$
$829$	−33.2471	−1.15472	−0.577359	+	0.816490i	$0.695917\pi$
$830$	−30.1974	−1.04817
$831$	−1.62451	−0.0563536
$832$	−4.89103	−0.169566
$833$	−6.83335	−0.236762
$834$	8.24002	0.285328
$835$	6.78404	0.234771
$836$	−42.9230	−1.48452
$837$	27.3449	0.945177
$838$	41.5836	1.43648
$839$	−25.8256	−0.891597	−0.445799	−	0.895133i	$-0.647080\pi$
$839$	−25.8256	−0.891597	−0.445799	+	0.895133i	$0.647080\pi$
$840$	−2.68285	−0.0925672
$841$	−0.741505	−0.0255692
$842$	−9.37137	−0.322959
$843$	20.4377	0.703911
$844$	28.0470	0.965417
$845$	−14.4601	−0.497442
$846$	−25.4144	−0.873766
$847$	−7.01669	−0.241096
$848$	66.4301	2.28122
$849$	−33.4553	−1.14818
$850$	−0.269241	−0.00923488
$851$	24.0459	0.824281
$852$	16.0626	0.550297
$853$	−25.1851	−0.862322	−0.431161	−	0.902275i	$-0.641896\pi$
$853$	−25.1851	−0.862322	−0.431161	+	0.902275i	$0.641896\pi$
$854$	1.95521	0.0669060
$855$	−20.5818	−0.703882
$856$	−11.1352	−0.380593
$857$	51.4921	1.75894	0.879468	−	0.475958i	$-0.157898\pi$
$857$	51.4921	1.75894	0.879468	+	0.475958i	$0.157898\pi$
$858$	−87.8939	−3.00065
$859$	−20.3915	−0.695750	−0.347875	−	0.937541i	$-0.613097\pi$
$859$	−20.3915	−0.695750	−0.347875	+	0.937541i	$0.613097\pi$
$860$	−21.3949	−0.729559
$861$	0.476344	0.0162338
$862$	8.13544	0.277094
$863$	8.20953	0.279456	0.139728	−	0.990190i	$-0.455377\pi$
$863$	8.20953	0.279456	0.139728	+	0.990190i	$0.455377\pi$
$864$	20.7620	0.706338
$865$	43.6523	1.48422
$866$	32.1480	1.09244
$867$	−2.09283	−0.0710761
$868$	−4.04982	−0.137460
$869$	−56.4828	−1.91605
$870$	−45.3741	−1.53833
$871$	−35.1847	−1.19219
$872$	−12.9176	−0.437447
$873$	−13.8171	−0.467640
$874$	38.0718	1.28780
$875$	−4.49322	−0.151899
$876$	29.0675	0.982100
$877$	−23.0204	−0.777344	−0.388672	−	0.921376i	$-0.627066\pi$
$877$	−23.0204	−0.777344	−0.388672	+	0.921376i	$0.627066\pi$
$878$	55.9830	1.88933
$879$	54.6192	1.84226
$880$	−59.6042	−2.00926
$881$	45.7149	1.54018	0.770088	−	0.637938i	$-0.220212\pi$
$881$	45.7149	1.54018	0.770088	+	0.637938i	$0.220212\pi$
$882$	16.9471	0.570637
$883$	7.54632	0.253954	0.126977	−	0.991906i	$-0.459473\pi$
$883$	7.54632	0.253954	0.126977	+	0.991906i	$0.459473\pi$
$884$	5.41392	0.182090
$885$	4.74929	0.159646
$886$	28.2471	0.948980
$887$	30.7200	1.03148	0.515738	−	0.856746i	$-0.327518\pi$
$887$	30.7200	1.03148	0.515738	+	0.856746i	$0.327518\pi$
$888$	21.6058	0.725044
$889$	6.65513	0.223206
$890$	32.4114	1.08643
$891$	59.6525	1.99843
$892$	6.67574	0.223520
$893$	67.3522	2.25385
$894$	57.0090	1.90666
$895$	31.8896	1.06595
$896$	4.18428	0.139787
$897$	29.6884	0.991268
$898$	50.9246	1.69938
$899$	42.8728	1.42989
$900$	0.254282	0.00847608
$901$	−13.4282	−0.447357
$902$	5.32013	0.177141
$903$	6.54826	0.217913
$904$	−0.715720	−0.0238045
$905$	34.0663	1.13240
$906$	5.44514	0.180903
$907$	4.99822	0.165963	0.0829816	−	0.996551i	$-0.473556\pi$
$907$	4.99822	0.165963	0.0829816	+	0.996551i	$0.473556\pi$
$908$	−24.7185	−0.820312
$909$	−18.6276	−0.617838
$910$	−7.32810	−0.242924
$911$	31.8672	1.05581	0.527904	−	0.849304i	$-0.322978\pi$
$911$	31.8672	1.05581	0.527904	+	0.849304i	$0.322978\pi$
$912$	68.0477	2.25329
$913$	39.3099	1.30097
$914$	−2.01111	−0.0665215
$915$	12.6565	0.418411
$916$	−13.2687	−0.438411
$917$	0.157688	0.00520731
$918$	−6.09359	−0.201119
$919$	−9.91638	−0.327111	−0.163556	−	0.986534i	$-0.552296\pi$
$919$	−9.91638	−0.327111	−0.163556	+	0.986534i	$0.552296\pi$
$920$	10.1211	0.333682
$921$	−12.8432	−0.423198
$922$	−55.2528	−1.81965
$923$	−27.4629	−0.903952
$924$	−5.57950	−0.183552
$925$	−1.11766	−0.0367484
$926$	2.91487	0.0957886
$927$	16.5523	0.543649
$928$	32.5518	1.06857
$929$	35.4484	1.16302	0.581512	−	0.813538i	$-0.302461\pi$
$929$	35.4484	1.16302	0.581512	+	0.813538i	$0.302461\pi$
$930$	−68.8401	−2.25735
$931$	−44.9123	−1.47194
$932$	−9.63261	−0.315527
$933$	−62.5816	−2.04883
$934$	−46.7183	−1.52867
$935$	12.0484	0.394024
$936$	8.40441	0.274707
$937$	59.5242	1.94457	0.972286	−	0.233794i	$-0.0751141\pi$
$937$	59.5242	1.94457	0.972286	+	0.233794i	$0.0751141\pi$
$938$	−5.86509	−0.191502
$939$	73.6709	2.40416
$940$	−28.6049	−0.932989
$941$	−13.8932	−0.452906	−0.226453	−	0.974022i	$-0.572713\pi$
$941$	−13.8932	−0.452906	−0.226453	+	0.974022i	$0.572713\pi$
$942$	55.5887	1.81118
$943$	−1.79701	−0.0585187
$944$	−4.94707	−0.161014
$945$	3.14100	0.102177
$946$	73.1353	2.37783
$947$	−35.4283	−1.15126	−0.575632	−	0.817709i	$-0.695244\pi$
$947$	−35.4283	−1.15126	−0.575632	+	0.817709i	$0.695244\pi$
$948$	−27.3868	−0.889482
$949$	−49.6978	−1.61326
$950$	−1.76959	−0.0574131
$951$	−12.6113	−0.408948
$952$	−0.564895	−0.0183084
$953$	−33.6497	−1.09002	−0.545010	−	0.838430i	$-0.683474\pi$
$953$	−33.6497	−1.09002	−0.545010	+	0.838430i	$0.683474\pi$
$954$	33.3025	1.07821
$955$	−18.9405	−0.612900
$956$	12.3210	0.398489
$957$	59.0665	1.90935
$958$	−25.9490	−0.838375
$959$	−6.49997	−0.209895
$960$	−5.27767	−0.170336
$961$	34.0451	1.09823
$962$	59.0155	1.90273
$963$	−11.1043	−0.357830
$964$	32.6095	1.05028
$965$	−55.9262	−1.80033
$966$	4.94890	0.159228
$967$	−15.8010	−0.508125	−0.254063	−	0.967188i	$-0.581767\pi$
$967$	−15.8010	−0.508125	−0.254063	+	0.967188i	$0.581767\pi$
$968$	23.7844	0.764461
$969$	−13.7551	−0.441879
$970$	−40.8379	−1.31123
$971$	43.9672	1.41097	0.705487	−	0.708723i	$-0.250728\pi$
$971$	43.9672	1.41097	0.705487	+	0.708723i	$0.250728\pi$
$972$	16.4120	0.526417
$973$	−0.894321	−0.0286706
$974$	11.2334	0.359942
$975$	−1.37993	−0.0441931
$976$	−13.1836	−0.421996
$977$	37.1651	1.18902	0.594508	−	0.804090i	$-0.297347\pi$
$977$	37.1651	1.18902	0.594508	+	0.804090i	$0.297347\pi$
$978$	−70.8235	−2.26469
$979$	−42.1920	−1.34846
$980$	19.0745	0.609314
$981$	−12.8817	−0.411282
$982$	52.0939	1.66238
$983$	−19.5853	−0.624674	−0.312337	−	0.949971i	$-0.601112\pi$
$983$	−19.5853	−0.624674	−0.312337	+	0.949971i	$0.601112\pi$
$984$	−1.61466	−0.0514736
$985$	32.1109	1.02314
$986$	−9.55387	−0.304257
$987$	8.75501	0.278675
$988$	35.5831	1.13205
$989$	−24.7033	−0.785521
$990$	−29.8806	−0.949668
$991$	−13.8116	−0.438741	−0.219371	−	0.975642i	$-0.570400\pi$
$991$	−13.8116	−0.438741	−0.219371	+	0.975642i	$0.570400\pi$
$992$	49.3865	1.56802
$993$	55.3932	1.75785
$994$	−4.57791	−0.145203
$995$	−5.07295	−0.160823
$996$	19.0602	0.603946
$997$	−38.7439	−1.22703	−0.613515	−	0.789683i	$-0.710245\pi$
$997$	−38.7439	−1.22703	−0.613515	+	0.789683i	$0.710245\pi$
$998$	−19.2455	−0.609205
$999$	−25.2954	−0.800312

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.h.1.5	✓	16
3.2	odd	2		9027.2.a.n.1.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.h.1.5	✓	16	1.1	even	1	trivial
9027.2.a.n.1.12		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q-1.79724 q^{2} -2.09283 q^{3} +1.23006 q^{4} -2.26932 q^{5} +3.76130 q^{6} -0.408229 q^{7} +1.38377 q^{8} +1.37993 q^{9} +O(q^{10})\)	\(q-1.79724 q^{2} -2.09283 q^{3} +1.23006 q^{4} -2.26932 q^{5} +3.76130 q^{6} -0.408229 q^{7} +1.38377 q^{8} +1.37993 q^{9} +4.07850 q^{10} -5.30925 q^{11} -2.57429 q^{12} +4.40136 q^{13} +0.733683 q^{14} +4.74929 q^{15} -4.94707 q^{16} +1.00000 q^{17} -2.48005 q^{18} +6.57252 q^{19} -2.79139 q^{20} +0.854352 q^{21} +9.54197 q^{22} -3.22305 q^{23} -2.89599 q^{24} +0.149808 q^{25} -7.91029 q^{26} +3.39054 q^{27} -0.502144 q^{28} +5.31587 q^{29} -8.53560 q^{30} +8.06505 q^{31} +6.12352 q^{32} +11.1113 q^{33} -1.79724 q^{34} +0.926401 q^{35} +1.69739 q^{36} -7.46060 q^{37} -11.8124 q^{38} -9.21129 q^{39} -3.14022 q^{40} +0.557550 q^{41} -1.53547 q^{42} +7.66459 q^{43} -6.53067 q^{44} -3.13149 q^{45} +5.79258 q^{46} +10.2475 q^{47} +10.3534 q^{48} -6.83335 q^{49} -0.269241 q^{50} -2.09283 q^{51} +5.41392 q^{52} -13.4282 q^{53} -6.09359 q^{54} +12.0484 q^{55} -0.564895 q^{56} -13.7551 q^{57} -9.55387 q^{58} +1.00000 q^{59} +5.84190 q^{60} +2.66493 q^{61} -14.4948 q^{62} -0.563325 q^{63} -1.11125 q^{64} -9.98810 q^{65} -19.9697 q^{66} -7.99404 q^{67} +1.23006 q^{68} +6.74528 q^{69} -1.66496 q^{70} -6.23963 q^{71} +1.90950 q^{72} -11.2914 q^{73} +13.4084 q^{74} -0.313523 q^{75} +8.08457 q^{76} +2.16739 q^{77} +16.5549 q^{78} +10.6386 q^{79} +11.2265 q^{80} -11.2356 q^{81} -1.00205 q^{82} -7.40405 q^{83} +1.05090 q^{84} -2.26932 q^{85} -13.7751 q^{86} -11.1252 q^{87} -7.34678 q^{88} +7.94689 q^{89} +5.62803 q^{90} -1.79676 q^{91} -3.96453 q^{92} -16.8788 q^{93} -18.4173 q^{94} -14.9151 q^{95} -12.8155 q^{96} -10.0130 q^{97} +12.2811 q^{98} -7.32637 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9} + 12 q^{10} - 7 q^{11} - 4 q^{12} - 16 q^{13} + 11 q^{14} + 7 q^{15} + 22 q^{16} + 16 q^{17} + 11 q^{18} + q^{19} - 43 q^{20} - 8 q^{21} - 18 q^{22} - 8 q^{23} - 39 q^{24} + 23 q^{25} - 49 q^{26} - 7 q^{27} - 15 q^{28} - 39 q^{29} + q^{30} - 3 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{35} - 17 q^{36} - 28 q^{37} - 27 q^{38} - 4 q^{39} + 26 q^{40} - 31 q^{41} - 45 q^{42} + 5 q^{43} - 19 q^{44} - 79 q^{45} - 39 q^{46} - 47 q^{47} - 31 q^{48} + 35 q^{49} - 13 q^{50} - 7 q^{51} + 9 q^{52} - 36 q^{53} + 9 q^{54} + 32 q^{55} + 3 q^{56} + 6 q^{57} + 22 q^{58} + 16 q^{59} + 6 q^{60} - 22 q^{61} + q^{62} - 19 q^{63} + 32 q^{64} - 19 q^{65} + 48 q^{66} + 4 q^{67} + 14 q^{68} + 14 q^{69} - 11 q^{70} - 5 q^{71} + 40 q^{72} - 35 q^{73} + 31 q^{74} - 12 q^{75} + q^{76} - 79 q^{77} + 31 q^{78} - 48 q^{79} - 127 q^{80} - 28 q^{81} - 7 q^{82} - 42 q^{83} + 28 q^{84} - 21 q^{85} + 58 q^{86} - 16 q^{87} - 2 q^{88} + 20 q^{89} - 14 q^{90} + 49 q^{91} - 21 q^{92} - 55 q^{93} - 22 q^{95} + 24 q^{96} - 2 q^{97} - 78 q^{98} - 35 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9 + 12 * q^10 - 7 * q^11 - 4 * q^12 - 16 * q^13 + 11 * q^14 + 7 * q^15 + 22 * q^16 + 16 * q^17 + 11 * q^18 + q^19 - 43 * q^20 - 8 * q^21 - 18 * q^22 - 8 * q^23 - 39 * q^24 + 23 * q^25 - 49 * q^26 - 7 * q^27 - 15 * q^28 - 39 * q^29 + q^30 - 3 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^35 - 17 * q^36 - 28 * q^37 - 27 * q^38 - 4 * q^39 + 26 * q^40 - 31 * q^41 - 45 * q^42 + 5 * q^43 - 19 * q^44 - 79 * q^45 - 39 * q^46 - 47 * q^47 - 31 * q^48 + 35 * q^49 - 13 * q^50 - 7 * q^51 + 9 * q^52 - 36 * q^53 + 9 * q^54 + 32 * q^55 + 3 * q^56 + 6 * q^57 + 22 * q^58 + 16 * q^59 + 6 * q^60 - 22 * q^61 + q^62 - 19 * q^63 + 32 * q^64 - 19 * q^65 + 48 * q^66 + 4 * q^67 + 14 * q^68 + 14 * q^69 - 11 * q^70 - 5 * q^71 + 40 * q^72 - 35 * q^73 + 31 * q^74 - 12 * q^75 + q^76 - 79 * q^77 + 31 * q^78 - 48 * q^79 - 127 * q^80 - 28 * q^81 - 7 * q^82 - 42 * q^83 + 28 * q^84 - 21 * q^85 + 58 * q^86 - 16 * q^87 - 2 * q^88 + 20 * q^89 - 14 * q^90 + 49 * q^91 - 21 * q^92 - 55 * q^93 - 22 * q^95 + 24 * q^96 - 2 * q^97 - 78 * q^98 - 35 * q^99

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