LMFDB - Embedded newform 4003.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4003,2,Mod(1,4003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4003, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4003.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:	$31.9641159291$
Analytic rank:	$0$
Dimension:	$179$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71994 q^{2} -1.21777 q^{3} +5.39810 q^{4} +4.02685 q^{5} +3.31228 q^{6} -3.20136 q^{7} -9.24264 q^{8} -1.51703 q^{9} +O(q^{10})$	\(q-2.71994 q^{2} -1.21777 q^{3} +5.39810 q^{4} +4.02685 q^{5} +3.31228 q^{6} -3.20136 q^{7} -9.24264 q^{8} -1.51703 q^{9} -10.9528 q^{10} +0.459418 q^{11} -6.57366 q^{12} +1.82669 q^{13} +8.70752 q^{14} -4.90379 q^{15} +14.3433 q^{16} +6.01389 q^{17} +4.12623 q^{18} +1.50580 q^{19} +21.7373 q^{20} +3.89853 q^{21} -1.24959 q^{22} +9.07350 q^{23} +11.2554 q^{24} +11.2155 q^{25} -4.96850 q^{26} +5.50072 q^{27} -17.2812 q^{28} -8.29688 q^{29} +13.3380 q^{30} +8.55827 q^{31} -20.5276 q^{32} -0.559468 q^{33} -16.3574 q^{34} -12.8914 q^{35} -8.18905 q^{36} +3.64335 q^{37} -4.09570 q^{38} -2.22450 q^{39} -37.2187 q^{40} -3.50776 q^{41} -10.6038 q^{42} +5.04731 q^{43} +2.47998 q^{44} -6.10883 q^{45} -24.6794 q^{46} -3.06088 q^{47} -17.4669 q^{48} +3.24870 q^{49} -30.5055 q^{50} -7.32355 q^{51} +9.86067 q^{52} +8.50203 q^{53} -14.9616 q^{54} +1.85001 q^{55} +29.5890 q^{56} -1.83373 q^{57} +22.5670 q^{58} -7.92925 q^{59} -26.4711 q^{60} +0.108532 q^{61} -23.2780 q^{62} +4.85654 q^{63} +27.1474 q^{64} +7.35581 q^{65} +1.52172 q^{66} -14.4225 q^{67} +32.4635 q^{68} -11.0495 q^{69} +35.0638 q^{70} -7.04938 q^{71} +14.0213 q^{72} +10.0320 q^{73} -9.90970 q^{74} -13.6579 q^{75} +8.12847 q^{76} -1.47076 q^{77} +6.05052 q^{78} -4.30658 q^{79} +57.7581 q^{80} -2.14755 q^{81} +9.54093 q^{82} +9.06454 q^{83} +21.0447 q^{84} +24.2170 q^{85} -13.7284 q^{86} +10.1037 q^{87} -4.24623 q^{88} -3.72076 q^{89} +16.6157 q^{90} -5.84790 q^{91} +48.9796 q^{92} -10.4220 q^{93} +8.32543 q^{94} +6.06364 q^{95} +24.9980 q^{96} +5.86283 q^{97} -8.83628 q^{98} -0.696949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) $ 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9 + 9 * q^10 + 46 * q^11 + 33 * q^12 + 47 * q^13 + 22 * q^14 + 36 * q^15 + 222 * q^16 + 103 * q^17 + 43 * q^18 + 12 * q^19 + 102 * q^20 + 50 * q^21 + 39 * q^22 + 121 * q^23 - 3 * q^24 + 246 * q^25 + 52 * q^26 + 49 * q^27 + 41 * q^28 + 138 * q^29 + 28 * q^30 + 5 * q^31 + 137 * q^32 + 63 * q^33 + 2 * q^34 + 72 * q^35 + 279 * q^36 + 118 * q^37 + 123 * q^38 + q^39 + 9 * q^40 + 50 * q^41 + 48 * q^42 + 48 * q^43 + 108 * q^44 + 158 * q^45 + 13 * q^46 + 85 * q^47 + 50 * q^48 + 230 * q^49 + 78 * q^50 + 15 * q^51 + 41 * q^52 + 399 * q^53 - 5 * q^54 + 24 * q^55 + 53 * q^56 + 45 * q^57 + 27 * q^58 + 48 * q^59 + 66 * q^60 + 46 * q^61 + 81 * q^62 + 78 * q^63 + 252 * q^64 + 153 * q^65 + 6 * q^66 + 70 * q^67 + 240 * q^68 + 120 * q^69 - 31 * q^70 + 86 * q^71 + 89 * q^72 + 45 * q^73 + 68 * q^74 + 17 * q^75 - 13 * q^76 + 362 * q^77 + 69 * q^78 + 31 * q^79 + 169 * q^80 + 303 * q^81 + 25 * q^82 + 106 * q^83 + 13 * q^84 + 115 * q^85 + 95 * q^86 + 32 * q^87 + 83 * q^88 + 105 * q^89 - 38 * q^90 + 3 * q^91 + 310 * q^92 + 298 * q^93 - 17 * q^94 + 102 * q^95 - 82 * q^96 + 34 * q^97 + 81 * q^98 + 58 * 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 $

$2$	−2.71994	−1.92329	−0.961646	−	0.274295i	$-0.911555\pi$
$2$	−2.71994	−1.92329	−0.961646	+	0.274295i	$0.911555\pi$
$3$	−1.21777	−0.703082	−0.351541	−	0.936172i	$-0.614342\pi$
$3$	−1.21777	−0.703082	−0.351541	+	0.936172i	$0.614342\pi$
$4$	5.39810	2.69905
$5$	4.02685	1.80086	0.900430	−	0.435000i	$-0.143252\pi$
$5$	4.02685	1.80086	0.900430	+	0.435000i	$0.143252\pi$
$6$	3.31228	1.35223
$7$	−3.20136	−1.21000	−0.605000	−	0.796226i	$-0.706827\pi$
$7$	−3.20136	−1.21000	−0.605000	+	0.796226i	$0.706827\pi$
$8$	−9.24264	−3.26776
$9$	−1.51703	−0.505675
$10$	−10.9528	−3.46358
$11$	0.459418	0.138520	0.0692599	−	0.997599i	$-0.477936\pi$
$11$	0.459418	0.138520	0.0692599	+	0.997599i	$0.477936\pi$
$12$	−6.57366	−1.89765
$13$	1.82669	0.506633	0.253317	−	0.967383i	$-0.418479\pi$
$13$	1.82669	0.506633	0.253317	+	0.967383i	$0.418479\pi$
$14$	8.70752	2.32718
$15$	−4.90379	−1.26615
$16$	14.3433	3.58581
$17$	6.01389	1.45858	0.729291	−	0.684204i	$-0.239850\pi$
$17$	6.01389	1.45858	0.729291	+	0.684204i	$0.239850\pi$
$18$	4.12623	0.972561
$19$	1.50580	0.345455	0.172727	−	0.984970i	$-0.444742\pi$
$19$	1.50580	0.345455	0.172727	+	0.984970i	$0.444742\pi$
$20$	21.7373	4.86061
$21$	3.89853	0.850729
$22$	−1.24959	−0.266414
$23$	9.07350	1.89196	0.945978	−	0.324231i	$-0.105106\pi$
$23$	9.07350	1.89196	0.945978	+	0.324231i	$0.105106\pi$
$24$	11.2554	2.29751
$25$	11.2155	2.24310
$26$	−4.96850	−0.974404
$27$	5.50072	1.05861
$28$	−17.2812	−3.26585
$29$	−8.29688	−1.54069	−0.770346	−	0.637627i	$-0.779916\pi$
$29$	−8.29688	−1.54069	−0.770346	+	0.637627i	$0.779916\pi$
$30$	13.3380	2.43518
$31$	8.55827	1.53711	0.768555	−	0.639783i	$-0.220976\pi$
$31$	8.55827	1.53711	0.768555	+	0.639783i	$0.220976\pi$
$32$	−20.5276	−3.62880
$33$	−0.559468	−0.0973908
$34$	−16.3574	−2.80528
$35$	−12.8914	−2.17904
$36$	−8.18905	−1.36484
$37$	3.64335	0.598963	0.299481	−	0.954102i	$-0.403186\pi$
$37$	3.64335	0.598963	0.299481	+	0.954102i	$0.403186\pi$
$38$	−4.09570	−0.664410
$39$	−2.22450	−0.356205
$40$	−37.2187	−5.88479
$41$	−3.50776	−0.547821	−0.273910	−	0.961755i	$-0.588317\pi$
$41$	−3.50776	−0.547821	−0.273910	+	0.961755i	$0.588317\pi$
$42$	−10.6038	−1.63620
$43$	5.04731	0.769708	0.384854	−	0.922978i	$-0.374252\pi$
$43$	5.04731	0.769708	0.384854	+	0.922978i	$0.374252\pi$
$44$	2.47998	0.373872
$45$	−6.10883	−0.910651
$46$	−24.6794	−3.63878
$47$	−3.06088	−0.446476	−0.223238	−	0.974764i	$-0.571663\pi$
$47$	−3.06088	−0.446476	−0.223238	+	0.974764i	$0.571663\pi$
$48$	−17.4669	−2.52112
$49$	3.24870	0.464100
$50$	−30.5055	−4.31413
$51$	−7.32355	−1.02550
$52$	9.86067	1.36743
$53$	8.50203	1.16784	0.583922	−	0.811810i	$-0.301518\pi$
$53$	8.50203	1.16784	0.583922	+	0.811810i	$0.301518\pi$
$54$	−14.9616	−2.03602
$55$	1.85001	0.249455
$56$	29.5890	3.95400
$57$	−1.83373	−0.242883
$58$	22.5670	2.96320
$59$	−7.92925	−1.03230	−0.516150	−	0.856498i	$-0.672635\pi$
$59$	−7.92925	−1.03230	−0.516150	+	0.856498i	$0.672635\pi$
$60$	−26.4711	−3.41741
$61$	0.108532	0.0138961	0.00694803	−	0.999976i	$-0.497788\pi$
$61$	0.108532	0.0138961	0.00694803	+	0.999976i	$0.497788\pi$
$62$	−23.2780	−2.95631
$63$	4.85654	0.611867
$64$	27.1474	3.39342
$65$	7.35581	0.912376
$66$	1.52172	0.187311
$67$	−14.4225	−1.76199	−0.880996	−	0.473125i	$-0.843126\pi$
$67$	−14.4225	−1.76199	−0.880996	+	0.473125i	$0.843126\pi$
$68$	32.4635	3.93678
$69$	−11.0495	−1.33020
$70$	35.0638	4.19093
$71$	−7.04938	−0.836607	−0.418304	−	0.908307i	$-0.637375\pi$
$71$	−7.04938	−0.836607	−0.418304	+	0.908307i	$0.637375\pi$
$72$	14.0213	1.65243
$73$	10.0320	1.17415	0.587076	−	0.809532i	$-0.300279\pi$
$73$	10.0320	1.17415	0.587076	+	0.809532i	$0.300279\pi$
$74$	−9.90970	−1.15198
$75$	−13.6579	−1.57708
$76$	8.12847	0.932399
$77$	−1.47076	−0.167609
$78$	6.05052	0.685086
$79$	−4.30658	−0.484528	−0.242264	−	0.970210i	$-0.577890\pi$
$79$	−4.30658	−0.484528	−0.242264	+	0.970210i	$0.577890\pi$
$80$	57.7581	6.45755
$81$	−2.14755	−0.238617
$82$	9.54093	1.05362
$83$	9.06454	0.994963	0.497481	−	0.867475i	$-0.334258\pi$
$83$	9.06454	0.994963	0.497481	+	0.867475i	$0.334258\pi$
$84$	21.0447	2.29616
$85$	24.2170	2.62670
$86$	−13.7284	−1.48037
$87$	10.1037	1.08323
$88$	−4.24623	−0.452650
$89$	−3.72076	−0.394400	−0.197200	−	0.980363i	$-0.563185\pi$
$89$	−3.72076	−0.394400	−0.197200	+	0.980363i	$0.563185\pi$
$90$	16.6157	1.75145
$91$	−5.84790	−0.613026
$92$	48.9796	5.10648
$93$	−10.4220	−1.08072
$94$	8.32543	0.858702
$95$	6.06364	0.622116
$96$	24.9980	2.55135
$97$	5.86283	0.595281	0.297640	−	0.954678i	$-0.403800\pi$
$97$	5.86283	0.595281	0.297640	+	0.954678i	$0.403800\pi$
$98$	−8.83628	−0.892599
$99$	−0.696949	−0.0700460
$100$	60.5423	6.05423
$101$	5.24825	0.522220	0.261110	−	0.965309i	$-0.415911\pi$
$101$	5.24825	0.522220	0.261110	+	0.965309i	$0.415911\pi$
$102$	19.9197	1.97234
$103$	−19.0830	−1.88030	−0.940150	−	0.340761i	$-0.889315\pi$
$103$	−19.0830	−1.88030	−0.940150	+	0.340761i	$0.889315\pi$
$104$	−16.8835	−1.65556
$105$	15.6988	1.53205
$106$	−23.1250	−2.24610
$107$	−16.1210	−1.55847	−0.779237	−	0.626729i	$-0.784393\pi$
$107$	−16.1210	−1.55847	−0.779237	+	0.626729i	$0.784393\pi$
$108$	29.6934	2.85725
$109$	−3.82013	−0.365902	−0.182951	−	0.983122i	$-0.558565\pi$
$109$	−3.82013	−0.365902	−0.182951	+	0.983122i	$0.558565\pi$
$110$	−5.03191	−0.479774
$111$	−4.43678	−0.421120
$112$	−45.9179	−4.33884
$113$	18.6882	1.75804	0.879021	−	0.476783i	$-0.158197\pi$
$113$	18.6882	1.75804	0.879021	+	0.476783i	$0.158197\pi$
$114$	4.98764	0.467135
$115$	36.5376	3.40715
$116$	−44.7873	−4.15840
$117$	−2.77114	−0.256192
$118$	21.5671	1.98541
$119$	−19.2526	−1.76488
$120$	45.3239	4.13749
$121$	−10.7889	−0.980812
$122$	−0.295200	−0.0267262
$123$	4.27167	0.385163
$124$	46.1984	4.14874
$125$	25.0288	2.23865
$126$	−13.2095	−1.17680
$127$	−19.3664	−1.71849	−0.859245	−	0.511564i	$-0.829066\pi$
$127$	−19.3664	−1.71849	−0.859245	+	0.511564i	$0.829066\pi$
$128$	−32.7842	−2.89774
$129$	−6.14649	−0.541168
$130$	−20.0074	−1.75476
$131$	−3.93661	−0.343943	−0.171972	−	0.985102i	$-0.555014\pi$
$131$	−3.93661	−0.343943	−0.171972	+	0.985102i	$0.555014\pi$
$132$	−3.02006	−0.262863
$133$	−4.82061	−0.418000
$134$	39.2284	3.38882
$135$	22.1505	1.90642
$136$	−55.5841	−4.76630
$137$	14.3996	1.23024	0.615121	−	0.788433i	$-0.289107\pi$
$137$	14.3996	1.23024	0.615121	+	0.788433i	$0.289107\pi$
$138$	30.0540	2.55836
$139$	0.951210	0.0806806	0.0403403	−	0.999186i	$-0.487156\pi$
$139$	0.951210	0.0806806	0.0403403	+	0.999186i	$0.487156\pi$
$140$	−69.5889	−5.88134
$141$	3.72746	0.313909
$142$	19.1739	1.60904
$143$	0.839216	0.0701788
$144$	−21.7591	−1.81326
$145$	−33.4102	−2.77457
$146$	−27.2863	−2.25823
$147$	−3.95618	−0.326300
$148$	19.6671	1.61663
$149$	−3.58224	−0.293469	−0.146734	−	0.989176i	$-0.546876\pi$
$149$	−3.58224	−0.293469	−0.146734	+	0.989176i	$0.546876\pi$
$150$	37.1488	3.03319
$151$	15.2762	1.24316	0.621581	−	0.783350i	$-0.286490\pi$
$151$	15.2762	1.24316	0.621581	+	0.783350i	$0.286490\pi$
$152$	−13.9176	−1.12886
$153$	−9.12322	−0.737569
$154$	4.00039	0.322361
$155$	34.4628	2.76812
$156$	−12.0081	−0.961415
$157$	−0.271830	−0.0216944	−0.0108472	−	0.999941i	$-0.503453\pi$
$157$	−0.271830	−0.0216944	−0.0108472	+	0.999941i	$0.503453\pi$
$158$	11.7137	0.931888
$159$	−10.3535	−0.821090
$160$	−82.6615	−6.53496
$161$	−29.0475	−2.28927
$162$	5.84123	0.458930
$163$	−5.05401	−0.395860	−0.197930	−	0.980216i	$-0.563422\pi$
$163$	−5.05401	−0.395860	−0.197930	+	0.980216i	$0.563422\pi$
$164$	−18.9353	−1.47860
$165$	−2.25289	−0.175387
$166$	−24.6551	−1.91360
$167$	0.794472	0.0614781	0.0307390	−	0.999527i	$-0.490214\pi$
$167$	0.794472	0.0614781	0.0307390	+	0.999527i	$0.490214\pi$
$168$	−36.0327	−2.77998
$169$	−9.66319	−0.743323
$170$	−65.8689	−5.05191
$171$	−2.28434	−0.174688
$172$	27.2459	2.07748
$173$	17.1358	1.30281	0.651406	−	0.758729i	$-0.274179\pi$
$173$	17.1358	1.30281	0.651406	+	0.758729i	$0.274179\pi$
$174$	−27.4816	−2.08337
$175$	−35.9048	−2.71415
$176$	6.58955	0.496706
$177$	9.65603	0.725792
$178$	10.1203	0.758546
$179$	16.8766	1.26142	0.630708	−	0.776020i	$-0.282765\pi$
$179$	16.8766	1.26142	0.630708	+	0.776020i	$0.282765\pi$
$180$	−32.9761	−2.45789
$181$	20.6365	1.53390	0.766950	−	0.641707i	$-0.221774\pi$
$181$	20.6365	1.53390	0.766950	+	0.641707i	$0.221774\pi$
$182$	15.9060	1.17903
$183$	−0.132167	−0.00977008
$184$	−83.8631	−6.18247
$185$	14.6712	1.07865
$186$	28.3474	2.07853
$187$	2.76289	0.202042
$188$	−16.5229	−1.20506
$189$	−17.6098	−1.28092
$190$	−16.4927	−1.19651
$191$	19.3645	1.40117	0.700584	−	0.713570i	$-0.252923\pi$
$191$	19.3645	1.40117	0.700584	+	0.713570i	$0.252923\pi$
$192$	−33.0594	−2.38586
$193$	−17.5334	−1.26208	−0.631042	−	0.775748i	$-0.717373\pi$
$193$	−17.5334	−1.26208	−0.631042	+	0.775748i	$0.717373\pi$
$194$	−15.9466	−1.14490
$195$	−8.95772	−0.641476
$196$	17.5368	1.25263
$197$	18.8470	1.34279	0.671395	−	0.741099i	$-0.265695\pi$
$197$	18.8470	1.34279	0.671395	+	0.741099i	$0.265695\pi$
$198$	1.89566	0.134719
$199$	1.63812	0.116124	0.0580618	−	0.998313i	$-0.481508\pi$
$199$	1.63812	0.116124	0.0580618	+	0.998313i	$0.481508\pi$
$200$	−103.661	−7.32992
$201$	17.5634	1.23882
$202$	−14.2749	−1.00438
$203$	26.5613	1.86424
$204$	−39.5333	−2.76788
$205$	−14.1252	−0.986549
$206$	51.9046	3.61636
$207$	−13.7647	−0.956715
$208$	26.2007	1.81669
$209$	0.691793	0.0478523
$210$	−42.6998	−2.94657
$211$	8.40140	0.578376	0.289188	−	0.957272i	$-0.406615\pi$
$211$	8.40140	0.578376	0.289188	+	0.957272i	$0.406615\pi$
$212$	45.8948	3.15207
$213$	8.58455	0.588204
$214$	43.8482	2.99740
$215$	20.3247	1.38614
$216$	−50.8411	−3.45930
$217$	−27.3981	−1.85990
$218$	10.3905	0.703737
$219$	−12.2167	−0.825525
$220$	9.98651	0.673291
$221$	10.9855	0.738966
$222$	12.0678	0.809937
$223$	−4.66209	−0.312196	−0.156098	−	0.987742i	$-0.549892\pi$
$223$	−4.66209	−0.312196	−0.156098	+	0.987742i	$0.549892\pi$
$224$	65.7162	4.39085
$225$	−17.0142	−1.13428
$226$	−50.8310	−3.38123
$227$	12.7598	0.846898	0.423449	−	0.905920i	$-0.360819\pi$
$227$	12.7598	0.846898	0.423449	+	0.905920i	$0.360819\pi$
$228$	−9.89864	−0.655553
$229$	−3.53977	−0.233914	−0.116957	−	0.993137i	$-0.537314\pi$
$229$	−3.53977	−0.233914	−0.116957	+	0.993137i	$0.537314\pi$
$230$	−99.3802	−6.55294
$231$	1.79106	0.117843
$232$	76.6850	5.03462
$233$	−25.7783	−1.68880	−0.844398	−	0.535717i	$-0.820042\pi$
$233$	−25.7783	−1.68880	−0.844398	+	0.535717i	$0.820042\pi$
$234$	7.53735	0.492732
$235$	−12.3257	−0.804040
$236$	−42.8028	−2.78623
$237$	5.24444	0.340663
$238$	52.3660	3.39438
$239$	2.01486	0.130330	0.0651651	−	0.997874i	$-0.479243\pi$
$239$	2.01486	0.130330	0.0651651	+	0.997874i	$0.479243\pi$
$240$	−70.3363	−4.54019
$241$	16.0437	1.03346	0.516732	−	0.856147i	$-0.327148\pi$
$241$	16.0437	1.03346	0.516732	+	0.856147i	$0.327148\pi$
$242$	29.3453	1.88639
$243$	−13.8869	−0.890846
$244$	0.585865	0.0375061
$245$	13.0820	0.835779
$246$	−11.6187	−0.740781
$247$	2.75064	0.175019
$248$	−79.1010	−5.02292
$249$	−11.0386	−0.699541
$250$	−68.0770	−4.30557
$251$	−1.18838	−0.0750098	−0.0375049	−	0.999296i	$-0.511941\pi$
$251$	−1.18838	−0.0750098	−0.0375049	+	0.999296i	$0.511941\pi$
$252$	26.2161	1.65146
$253$	4.16853	0.262073
$254$	52.6755	3.30516
$255$	−29.4908	−1.84679
$256$	34.8765	2.17978
$257$	28.4540	1.77491	0.887455	−	0.460895i	$-0.152472\pi$
$257$	28.4540	1.77491	0.887455	+	0.460895i	$0.152472\pi$
$258$	16.7181	1.04082
$259$	−11.6637	−0.724745
$260$	39.7074	2.46255
$261$	12.5866	0.779089
$262$	10.7074	0.661503
$263$	17.0990	1.05437	0.527186	−	0.849750i	$-0.323247\pi$
$263$	17.0990	1.05437	0.527186	+	0.849750i	$0.323247\pi$
$264$	5.17096	0.318250
$265$	34.2364	2.10312
$266$	13.1118	0.803936
$267$	4.53105	0.277296
$268$	−77.8542	−4.75570
$269$	−0.103272	−0.00629660	−0.00314830	−	0.999995i	$-0.501002\pi$
$269$	−0.103272	−0.00629660	−0.00314830	+	0.999995i	$0.501002\pi$
$270$	−60.2483	−3.66659
$271$	−24.5182	−1.48937	−0.744686	−	0.667415i	$-0.767401\pi$
$271$	−24.5182	−1.48937	−0.744686	+	0.667415i	$0.767401\pi$
$272$	86.2587	5.23020
$273$	7.12142	0.431008
$274$	−39.1661	−2.36611
$275$	5.15260	0.310714
$276$	−59.6461	−3.59028
$277$	−13.3024	−0.799265	−0.399633	−	0.916675i	$-0.630862\pi$
$277$	−13.3024	−0.799265	−0.399633	+	0.916675i	$0.630862\pi$
$278$	−2.58724	−0.155172
$279$	−12.9831	−0.777279
$280$	119.150	7.12059
$281$	0.295352	0.0176192	0.00880962	−	0.999961i	$-0.497196\pi$
$281$	0.295352	0.0176192	0.00880962	+	0.999961i	$0.497196\pi$
$282$	−10.1385	−0.603738
$283$	25.2635	1.50176	0.750878	−	0.660441i	$-0.229630\pi$
$283$	25.2635	1.50176	0.750878	+	0.660441i	$0.229630\pi$
$284$	−38.0532	−2.25804
$285$	−7.38414	−0.437399
$286$	−2.28262	−0.134974
$287$	11.2296	0.662863
$288$	31.1409	1.83499
$289$	19.1668	1.12746
$290$	90.8740	5.33631
$291$	−7.13961	−0.418531
$292$	54.1534	3.16909
$293$	−11.8178	−0.690404	−0.345202	−	0.938528i	$-0.612190\pi$
$293$	−11.8178	−0.690404	−0.345202	+	0.938528i	$0.612190\pi$
$294$	10.7606	0.627570
$295$	−31.9299	−1.85903
$296$	−33.6741	−1.95727
$297$	2.52713	0.146639
$298$	9.74350	0.564426
$299$	16.5745	0.958528
$300$	−73.7269	−4.25662
$301$	−16.1583	−0.931346
$302$	−41.5505	−2.39096
$303$	−6.39118	−0.367164
$304$	21.5981	1.23874
$305$	0.437041	0.0250249
$306$	24.8146	1.41856
$307$	−20.3409	−1.16092	−0.580459	−	0.814289i	$-0.697127\pi$
$307$	−20.3409	−1.16092	−0.580459	+	0.814289i	$0.697127\pi$
$308$	−7.93932	−0.452385
$309$	23.2387	1.32201
$310$	−93.7370	−5.32390
$311$	−13.8424	−0.784933	−0.392466	−	0.919766i	$-0.628378\pi$
$311$	−13.8424	−0.784933	−0.392466	+	0.919766i	$0.628378\pi$
$312$	20.5602	1.16399
$313$	31.0897	1.75729	0.878646	−	0.477474i	$-0.158448\pi$
$313$	31.0897	1.75729	0.878646	+	0.477474i	$0.158448\pi$
$314$	0.739362	0.0417246
$315$	19.5566	1.10189
$316$	−23.2473	−1.30776
$317$	13.1335	0.737652	0.368826	−	0.929498i	$-0.379760\pi$
$317$	13.1335	0.737652	0.368826	+	0.929498i	$0.379760\pi$
$318$	28.1611	1.57919
$319$	−3.81174	−0.213416
$320$	109.318	6.11108
$321$	19.6317	1.09574
$322$	79.0077	4.40292
$323$	9.05572	0.503874
$324$	−11.5927	−0.644039
$325$	20.4873	1.13643
$326$	13.7466	0.761355
$327$	4.65206	0.257259
$328$	32.4210	1.79015
$329$	9.79898	0.540235
$330$	6.12774	0.337321
$331$	−23.1963	−1.27498	−0.637492	−	0.770457i	$-0.720028\pi$
$331$	−23.1963	−1.27498	−0.637492	+	0.770457i	$0.720028\pi$
$332$	48.9313	2.68545
$333$	−5.52705	−0.302881
$334$	−2.16092	−0.118240
$335$	−58.0773	−3.17310
$336$	55.9177	3.05056
$337$	29.8241	1.62462	0.812312	−	0.583224i	$-0.198209\pi$
$337$	29.8241	1.62462	0.812312	+	0.583224i	$0.198209\pi$
$338$	26.2833	1.42963
$339$	−22.7581	−1.23605
$340$	130.726	7.08960
$341$	3.93182	0.212920
$342$	6.21328	0.335976
$343$	12.0093	0.648439
$344$	−46.6505	−2.51522
$345$	−44.4945	−2.39551
$346$	−46.6085	−2.50569
$347$	0.594697	0.0319250	0.0159625	−	0.999873i	$-0.494919\pi$
$347$	0.594697	0.0319250	0.0159625	+	0.999873i	$0.494919\pi$
$348$	54.5409	2.92370
$349$	5.22964	0.279936	0.139968	−	0.990156i	$-0.455300\pi$
$349$	5.22964	0.279936	0.139968	+	0.990156i	$0.455300\pi$
$350$	97.6591	5.22010
$351$	10.0481	0.536329
$352$	−9.43075	−0.502661
$353$	−2.38060	−0.126706	−0.0633532	−	0.997991i	$-0.520179\pi$
$353$	−2.38060	−0.126706	−0.0633532	+	0.997991i	$0.520179\pi$
$354$	−26.2639	−1.39591
$355$	−28.3868	−1.50661
$356$	−20.0850	−1.06450
$357$	23.4453	1.24086
$358$	−45.9034	−2.42607
$359$	−34.2529	−1.80780	−0.903899	−	0.427747i	$-0.859308\pi$
$359$	−34.2529	−1.80780	−0.903899	+	0.427747i	$0.859308\pi$
$360$	56.4617	2.97579
$361$	−16.7326	−0.880661
$362$	−56.1301	−2.95013
$363$	13.1385	0.689592
$364$	−31.5675	−1.65459
$365$	40.3971	2.11448
$366$	0.359487	0.0187907
$367$	−13.3305	−0.695845	−0.347923	−	0.937523i	$-0.613113\pi$
$367$	−13.3305	−0.695845	−0.347923	+	0.937523i	$0.613113\pi$
$368$	130.144	6.78420
$369$	5.32137	0.277019
$370$	−39.9049	−2.07455
$371$	−27.2180	−1.41309
$372$	−56.2592	−2.91690
$373$	17.9688	0.930387	0.465194	−	0.885209i	$-0.345985\pi$
$373$	17.9688	0.930387	0.465194	+	0.885209i	$0.345985\pi$
$374$	−7.51490	−0.388586
$375$	−30.4795	−1.57395
$376$	28.2906	1.45898
$377$	−15.1558	−0.780566
$378$	47.8976	2.46359
$379$	12.2948	0.631543	0.315772	−	0.948835i	$-0.397737\pi$
$379$	12.2948	0.631543	0.315772	+	0.948835i	$0.397737\pi$
$380$	32.7321	1.67912
$381$	23.5839	1.20824
$382$	−52.6704	−2.69485
$383$	6.05097	0.309190	0.154595	−	0.987978i	$-0.450593\pi$
$383$	6.05097	0.309190	0.154595	+	0.987978i	$0.450593\pi$
$384$	39.9238	2.03735
$385$	−5.92253	−0.301840
$386$	47.6900	2.42736
$387$	−7.65690	−0.389222
$388$	31.6481	1.60669
$389$	14.6753	0.744068	0.372034	−	0.928219i	$-0.378660\pi$
$389$	14.6753	0.744068	0.372034	+	0.928219i	$0.378660\pi$
$390$	24.3645	1.23374
$391$	54.5670	2.75957
$392$	−30.0265	−1.51657
$393$	4.79390	0.241820
$394$	−51.2627	−2.58258
$395$	−17.3419	−0.872567
$396$	−3.76220	−0.189058
$397$	22.1773	1.11305	0.556523	−	0.830832i	$-0.312135\pi$
$397$	22.1773	1.11305	0.556523	+	0.830832i	$0.312135\pi$
$398$	−4.45560	−0.223339
$399$	5.87042	0.293889
$400$	160.867	8.04334
$401$	29.2780	1.46208	0.731038	−	0.682337i	$-0.239036\pi$
$401$	29.2780	1.46208	0.731038	+	0.682337i	$0.239036\pi$
$402$	−47.7714	−2.38262
$403$	15.6333	0.778752
$404$	28.3305	1.40950
$405$	−8.64787	−0.429716
$406$	−72.2452	−3.58547
$407$	1.67382	0.0829682
$408$	67.6889	3.35110
$409$	−36.3638	−1.79807	−0.899037	−	0.437872i	$-0.855732\pi$
$409$	−36.3638	−1.79807	−0.899037	+	0.437872i	$0.855732\pi$
$410$	38.4198	1.89742
$411$	−17.5355	−0.864961
$412$	−103.012	−5.07502
$413$	25.3844	1.24908
$414$	37.4393	1.84004
$415$	36.5015	1.79179
$416$	−37.4976	−1.83847
$417$	−1.15836	−0.0567251
$418$	−1.88164	−0.0920339
$419$	11.3644	0.555185	0.277593	−	0.960699i	$-0.410463\pi$
$419$	11.3644	0.555185	0.277593	+	0.960699i	$0.410463\pi$
$420$	84.7436	4.13506
$421$	−2.66252	−0.129763	−0.0648816	−	0.997893i	$-0.520667\pi$
$421$	−2.66252	−0.129763	−0.0648816	+	0.997893i	$0.520667\pi$
$422$	−22.8513	−1.11239
$423$	4.64344	0.225772
$424$	−78.5811	−3.81624
$425$	67.4487	3.27174
$426$	−23.3495	−1.13129
$427$	−0.347449	−0.0168142
$428$	−87.0226	−4.20640
$429$	−1.02198	−0.0493414
$430$	−55.2822	−2.66594
$431$	0.496165	0.0238994	0.0119497	−	0.999929i	$-0.496196\pi$
$431$	0.496165	0.0238994	0.0119497	+	0.999929i	$0.496196\pi$
$432$	78.8982	3.79599
$433$	−3.36511	−0.161717	−0.0808585	−	0.996726i	$-0.525766\pi$
$433$	−3.36511	−0.161717	−0.0808585	+	0.996726i	$0.525766\pi$
$434$	74.5213	3.57714
$435$	40.6861	1.95075
$436$	−20.6214	−0.987588
$437$	13.6629	0.653585
$438$	33.2286	1.58772
$439$	17.1172	0.816960	0.408480	−	0.912767i	$-0.366059\pi$
$439$	17.1172	0.816960	0.408480	+	0.912767i	$0.366059\pi$
$440$	−17.0989	−0.815160
$441$	−4.92836	−0.234684
$442$	−29.8800	−1.42125
$443$	33.7131	1.60176	0.800878	−	0.598828i	$-0.204366\pi$
$443$	33.7131	1.60176	0.800878	+	0.598828i	$0.204366\pi$
$444$	−23.9501	−1.13662
$445$	−14.9829	−0.710259
$446$	12.6806	0.600445
$447$	4.36236	0.206333
$448$	−86.9086	−4.10604
$449$	18.2605	0.861767	0.430884	−	0.902407i	$-0.358202\pi$
$449$	18.2605	0.861767	0.430884	+	0.902407i	$0.358202\pi$
$450$	46.2777	2.18155
$451$	−1.61153	−0.0758840
$452$	100.881	4.74504
$453$	−18.6030	−0.874046
$454$	−34.7060	−1.62883
$455$	−23.5486	−1.10398
$456$	16.9485	0.793685
$457$	−20.0636	−0.938538	−0.469269	−	0.883055i	$-0.655483\pi$
$457$	−20.0636	−0.938538	−0.469269	+	0.883055i	$0.655483\pi$
$458$	9.62797	0.449885
$459$	33.0807	1.54407
$460$	197.233	9.19606
$461$	14.4955	0.675125	0.337562	−	0.941303i	$-0.390398\pi$
$461$	14.4955	0.675125	0.337562	+	0.941303i	$0.390398\pi$
$462$	−4.87157	−0.226646
$463$	−29.4419	−1.36828	−0.684140	−	0.729351i	$-0.739822\pi$
$463$	−29.4419	−1.36828	−0.684140	+	0.729351i	$0.739822\pi$
$464$	−119.004	−5.52463
$465$	−41.9680	−1.94622
$466$	70.1157	3.24805
$467$	−41.3917	−1.91538	−0.957691	−	0.287800i	$-0.907076\pi$
$467$	−41.3917	−1.91538	−0.957691	+	0.287800i	$0.907076\pi$
$468$	−14.9589	−0.691475
$469$	46.1717	2.13201
$470$	33.5252	1.54640
$471$	0.331027	0.0152529
$472$	73.2871	3.37331
$473$	2.31883	0.106620
$474$	−14.2646	−0.655194
$475$	16.8883	0.774889
$476$	−103.927	−4.76351
$477$	−12.8978	−0.590549
$478$	−5.48030	−0.250663
$479$	20.1633	0.921286	0.460643	−	0.887586i	$-0.347619\pi$
$479$	20.1633	0.921286	0.460643	+	0.887586i	$0.347619\pi$
$480$	100.663	4.59462
$481$	6.65528	0.303455
$482$	−43.6379	−1.98765
$483$	35.3733	1.60954
$484$	−58.2397	−2.64726
$485$	23.6087	1.07202
$486$	37.7716	1.71336
$487$	−10.7142	−0.485509	−0.242754	−	0.970088i	$-0.578051\pi$
$487$	−10.7142	−0.485509	−0.242754	+	0.970088i	$0.578051\pi$
$488$	−1.00312	−0.0454091
$489$	6.15464	0.278322
$490$	−35.5823	−1.60745
$491$	−1.10787	−0.0499975	−0.0249988	−	0.999687i	$-0.507958\pi$
$491$	−1.10787	−0.0499975	−0.0249988	+	0.999687i	$0.507958\pi$
$492$	23.0589	1.03957
$493$	−49.8965	−2.24722
$494$	−7.48158	−0.336612
$495$	−2.80651	−0.126143
$496$	122.753	5.51179
$497$	22.5676	1.01229
$498$	30.0243	1.34542
$499$	−10.4445	−0.467562	−0.233781	−	0.972289i	$-0.575110\pi$
$499$	−10.4445	−0.467562	−0.233781	+	0.972289i	$0.575110\pi$
$500$	135.108	6.04222
$501$	−0.967488	−0.0432242
$502$	3.23232	0.144266
$503$	−1.51162	−0.0674000	−0.0337000	−	0.999432i	$-0.510729\pi$
$503$	−1.51162	−0.0674000	−0.0337000	+	0.999432i	$0.510729\pi$
$504$	−44.8873	−1.99944
$505$	21.1339	0.940446
$506$	−11.3382	−0.504043
$507$	11.7676	0.522617
$508$	−104.542	−4.63829
$509$	17.1997	0.762363	0.381181	−	0.924500i	$-0.375517\pi$
$509$	17.1997	0.762363	0.381181	+	0.924500i	$0.375517\pi$
$510$	80.2134	3.55191
$511$	−32.1159	−1.42072
$512$	−29.2936	−1.29461
$513$	8.28299	0.365703
$514$	−77.3932	−3.41367
$515$	−76.8441	−3.38616
$516$	−33.1793	−1.46064
$517$	−1.40622	−0.0618457
$518$	31.7245	1.39390
$519$	−20.8676	−0.915985
$520$	−67.9871	−2.98143
$521$	17.2772	0.756928	0.378464	−	0.925616i	$-0.376452\pi$
$521$	17.2772	0.756928	0.378464	+	0.925616i	$0.376452\pi$
$522$	−34.2348	−1.49842
$523$	13.7550	0.601463	0.300732	−	0.953709i	$-0.402769\pi$
$523$	13.7550	0.601463	0.300732	+	0.953709i	$0.402769\pi$
$524$	−21.2502	−0.928319
$525$	43.7240	1.90827
$526$	−46.5084	−2.02786
$527$	51.4685	2.24200
$528$	−8.02459	−0.349225
$529$	59.3284	2.57950
$530$	−93.1210	−4.04492
$531$	12.0289	0.522009
$532$	−26.0221	−1.12820
$533$	−6.40761	−0.277544
$534$	−12.3242	−0.533320
$535$	−64.9167	−2.80659
$536$	133.302	5.75777
$537$	−20.5519	−0.886879
$538$	0.280894	0.0121102
$539$	1.49251	0.0642870
$540$	119.571	5.14551
$541$	13.9719	0.600697	0.300348	−	0.953830i	$-0.402897\pi$
$541$	13.9719	0.600697	0.300348	+	0.953830i	$0.402897\pi$
$542$	66.6881	2.86450
$543$	−25.1306	−1.07846
$544$	−123.451	−5.29290
$545$	−15.3831	−0.658939
$546$	−19.3699	−0.828954
$547$	0.959405	0.0410212	0.0205106	−	0.999790i	$-0.493471\pi$
$547$	0.959405	0.0410212	0.0205106	+	0.999790i	$0.493471\pi$
$548$	77.7305	3.32048
$549$	−0.164645	−0.00702690
$550$	−14.0148	−0.597593
$551$	−12.4935	−0.532239
$552$	102.126	4.34678
$553$	13.7869	0.586279
$554$	36.1819	1.53722
$555$	−17.8662	−0.758379
$556$	5.13472	0.217761
$557$	−14.7282	−0.624052	−0.312026	−	0.950073i	$-0.601008\pi$
$557$	−14.7282	−0.624052	−0.312026	+	0.950073i	$0.601008\pi$
$558$	35.3134	1.49493
$559$	9.21989	0.389960
$560$	−184.904	−7.81364
$561$	−3.36457	−0.142052
$562$	−0.803341	−0.0338869
$563$	−25.3234	−1.06725	−0.533627	−	0.845720i	$-0.679171\pi$
$563$	−25.3234	−1.06725	−0.533627	+	0.845720i	$0.679171\pi$
$564$	20.1212	0.847256
$565$	75.2547	3.16599
$566$	−68.7152	−2.88831
$567$	6.87509	0.288727
$568$	65.1548	2.73384
$569$	−18.8440	−0.789980	−0.394990	−	0.918685i	$-0.629252\pi$
$569$	−18.8440	−0.789980	−0.394990	+	0.918685i	$0.629252\pi$
$570$	20.0844	0.841245
$571$	34.6258	1.44904	0.724522	−	0.689251i	$-0.242060\pi$
$571$	34.6258	1.44904	0.724522	+	0.689251i	$0.242060\pi$
$572$	4.53017	0.189416
$573$	−23.5816	−0.985136
$574$	−30.5439	−1.27488
$575$	101.764	4.24384
$576$	−41.1833	−1.71597
$577$	42.9720	1.78895	0.894475	−	0.447119i	$-0.147550\pi$
$577$	42.9720	1.78895	0.894475	+	0.447119i	$0.147550\pi$
$578$	−52.1327	−2.16843
$579$	21.3518	0.887350
$580$	−180.352	−7.48870
$581$	−29.0189	−1.20390
$582$	19.4193	0.804957
$583$	3.90599	0.161769
$584$	−92.7217	−3.83685
$585$	−11.1590	−0.461366
$586$	32.1438	1.32785
$587$	−1.73862	−0.0717603	−0.0358802	−	0.999356i	$-0.511423\pi$
$587$	−1.73862	−0.0717603	−0.0358802	+	0.999356i	$0.511423\pi$
$588$	−21.3558	−0.880700
$589$	12.8871	0.531002
$590$	86.8474	3.57545
$591$	−22.9513	−0.944092
$592$	52.2575	2.14777
$593$	−28.6600	−1.17693	−0.588463	−	0.808524i	$-0.700267\pi$
$593$	−28.6600	−1.17693	−0.588463	+	0.808524i	$0.700267\pi$
$594$	−6.87365	−0.282029
$595$	−77.5273	−3.17831
$596$	−19.3373	−0.792086
$597$	−1.99486	−0.0816444
$598$	−45.0817	−1.84353
$599$	−2.77020	−0.113187	−0.0565936	−	0.998397i	$-0.518024\pi$
$599$	−2.77020	−0.113187	−0.0565936	+	0.998397i	$0.518024\pi$
$600$	126.235	5.15354
$601$	−21.7401	−0.886798	−0.443399	−	0.896324i	$-0.646228\pi$
$601$	−21.7401	−0.886798	−0.443399	+	0.896324i	$0.646228\pi$
$602$	43.9496	1.79125
$603$	21.8793	0.890995
$604$	82.4626	3.35536
$605$	−43.4454	−1.76631
$606$	17.3837	0.706163
$607$	−2.65821	−0.107893	−0.0539467	−	0.998544i	$-0.517180\pi$
$607$	−2.65821	−0.107893	−0.0539467	+	0.998544i	$0.517180\pi$
$608$	−30.9105	−1.25359
$609$	−32.3456	−1.31071
$610$	−1.18873	−0.0481301
$611$	−5.59129	−0.226199
$612$	−49.2480	−1.99073
$613$	−10.0197	−0.404693	−0.202346	−	0.979314i	$-0.564857\pi$
$613$	−10.0197	−0.404693	−0.202346	+	0.979314i	$0.564857\pi$
$614$	55.3262	2.23278
$615$	17.2013	0.693625
$616$	13.5937	0.547707
$617$	12.6179	0.507979	0.253989	−	0.967207i	$-0.418257\pi$
$617$	12.6179	0.507979	0.253989	+	0.967207i	$0.418257\pi$
$618$	−63.2081	−2.54260
$619$	−16.6475	−0.669118	−0.334559	−	0.942375i	$-0.608587\pi$
$619$	−16.6475	−0.669118	−0.334559	+	0.942375i	$0.608587\pi$
$620$	186.034	7.47129
$621$	49.9108	2.00285
$622$	37.6507	1.50965
$623$	11.9115	0.477224
$624$	−31.9066	−1.27729
$625$	44.7098	1.78839
$626$	−84.5622	−3.37978
$627$	−0.842448	−0.0336441
$628$	−1.46736	−0.0585542
$629$	21.9107	0.873636
$630$	−53.1927	−2.11925
$631$	29.1968	1.16231	0.581153	−	0.813795i	$-0.302602\pi$
$631$	29.1968	1.16231	0.581153	+	0.813795i	$0.302602\pi$
$632$	39.8041	1.58332
$633$	−10.2310	−0.406646
$634$	−35.7224	−1.41872
$635$	−77.9855	−3.09476
$636$	−55.8895	−2.21616
$637$	5.93437	0.235128
$638$	10.3677	0.410462
$639$	10.6941	0.423052
$640$	−132.017	−5.21843
$641$	11.2945	0.446105	0.223053	−	0.974806i	$-0.428398\pi$
$641$	11.2945	0.446105	0.223053	+	0.974806i	$0.428398\pi$
$642$	−53.3972	−2.10742
$643$	−26.8391	−1.05843	−0.529216	−	0.848487i	$-0.677514\pi$
$643$	−26.8391	−1.05843	−0.529216	+	0.848487i	$0.677514\pi$
$644$	−156.801	−6.17884
$645$	−24.7510	−0.974568
$646$	−24.6311	−0.969096
$647$	1.17367	0.0461417	0.0230708	−	0.999734i	$-0.492656\pi$
$647$	1.17367	0.0461417	0.0230708	+	0.999734i	$0.492656\pi$
$648$	19.8491	0.779745
$649$	−3.64284	−0.142994
$650$	−55.7242	−2.18568
$651$	33.3647	1.30767
$652$	−27.2820	−1.06845
$653$	−23.4210	−0.916533	−0.458267	−	0.888815i	$-0.651530\pi$
$653$	−23.4210	−0.916533	−0.458267	+	0.888815i	$0.651530\pi$
$654$	−12.6533	−0.494785
$655$	−15.8521	−0.619393
$656$	−50.3128	−1.96438
$657$	−15.2187	−0.593739
$658$	−26.6527	−1.03903
$659$	−23.6100	−0.919715	−0.459858	−	0.887993i	$-0.652100\pi$
$659$	−23.6100	−0.919715	−0.459858	+	0.887993i	$0.652100\pi$
$660$	−12.1613	−0.473379
$661$	−3.64224	−0.141667	−0.0708334	−	0.997488i	$-0.522566\pi$
$661$	−3.64224	−0.141667	−0.0708334	+	0.997488i	$0.522566\pi$
$662$	63.0927	2.45217
$663$	−13.3779	−0.519554
$664$	−83.7803	−3.25131
$665$	−19.4119	−0.752760
$666$	15.0333	0.582528
$667$	−75.2817	−2.91492
$668$	4.28864	0.165932
$669$	5.67737	0.219500
$670$	157.967	6.10279
$671$	0.0498614	0.00192488
$672$	−80.0275	−3.08713
$673$	−22.8464	−0.880662	−0.440331	−	0.897835i	$-0.645139\pi$
$673$	−22.8464	−0.880662	−0.440331	+	0.897835i	$0.645139\pi$
$674$	−81.1199	−3.12462
$675$	61.6933	2.37457
$676$	−52.1629	−2.00626
$677$	5.25133	0.201825	0.100913	−	0.994895i	$-0.467824\pi$
$677$	5.25133	0.201825	0.100913	+	0.994895i	$0.467824\pi$
$678$	61.9007	2.37728
$679$	−18.7690	−0.720289
$680$	−223.829	−8.58344
$681$	−15.5386	−0.595439
$682$	−10.6943	−0.409508
$683$	16.7060	0.639236	0.319618	−	0.947546i	$-0.396445\pi$
$683$	16.7060	0.639236	0.319618	+	0.947546i	$0.396445\pi$
$684$	−12.3311	−0.471491
$685$	57.9850	2.21549
$686$	−32.6645	−1.24714
$687$	4.31064	0.164461
$688$	72.3949	2.76003
$689$	15.5306	0.591668
$690$	121.023	4.60725
$691$	25.5190	0.970789	0.485395	−	0.874295i	$-0.338676\pi$
$691$	25.5190	0.970789	0.485395	+	0.874295i	$0.338676\pi$
$692$	92.5009	3.51635
$693$	2.23118	0.0847557
$694$	−1.61754	−0.0614011
$695$	3.83038	0.145294
$696$	−93.3850	−3.53975
$697$	−21.0953	−0.799041
$698$	−14.2243	−0.538399
$699$	31.3922	1.18736
$700$	−193.818	−7.32562
$701$	−4.63599	−0.175099	−0.0875494	−	0.996160i	$-0.527904\pi$
$701$	−4.63599	−0.175099	−0.0875494	+	0.996160i	$0.527904\pi$
$702$	−27.3303	−1.03152
$703$	5.48616	0.206915
$704$	12.4720	0.470056
$705$	15.0099	0.565306
$706$	6.47509	0.243693
$707$	−16.8015	−0.631886
$708$	52.1242	1.95895
$709$	−45.9417	−1.72538	−0.862688	−	0.505737i	$-0.831221\pi$
$709$	−45.9417	−1.72538	−0.862688	+	0.505737i	$0.831221\pi$
$710$	77.2104	2.89765
$711$	6.53319	0.245014
$712$	34.3896	1.28881
$713$	77.6535	2.90814
$714$	−63.7700	−2.38653
$715$	3.37939	0.126382
$716$	91.1015	3.40462
$717$	−2.45364	−0.0916329
$718$	93.1659	3.47692
$719$	−1.55512	−0.0579962	−0.0289981	−	0.999579i	$-0.509232\pi$
$719$	−1.55512	−0.0579962	−0.0289981	+	0.999579i	$0.509232\pi$
$720$	−87.6205	−3.26542
$721$	61.0914	2.27516
$722$	45.5116	1.69377
$723$	−19.5376	−0.726610
$724$	111.398	4.14007
$725$	−93.0535	−3.45592
$726$	−35.7360	−1.32629
$727$	31.4168	1.16518	0.582591	−	0.812765i	$-0.302039\pi$
$727$	31.4168	1.16518	0.582591	+	0.812765i	$0.302039\pi$
$728$	54.0500	2.00323
$729$	23.3538	0.864955
$730$	−109.878	−4.06676
$731$	30.3540	1.12268
$732$	−0.713451	−0.0263699
$733$	−18.3588	−0.678097	−0.339048	−	0.940769i	$-0.610105\pi$
$733$	−18.3588	−0.678097	−0.339048	+	0.940769i	$0.610105\pi$
$734$	36.2582	1.33831
$735$	−15.9309	−0.587621
$736$	−186.257	−6.86553
$737$	−6.62597	−0.244071
$738$	−14.4738	−0.532789
$739$	−5.76090	−0.211918	−0.105959	−	0.994370i	$-0.533791\pi$
$739$	−5.76090	−0.211918	−0.105959	+	0.994370i	$0.533791\pi$
$740$	79.1966	2.91132
$741$	−3.34966	−0.123053
$742$	74.0315	2.71778
$743$	−4.91138	−0.180181	−0.0900905	−	0.995934i	$-0.528716\pi$
$743$	−4.91138	−0.180181	−0.0900905	+	0.995934i	$0.528716\pi$
$744$	96.3271	3.53152
$745$	−14.4251	−0.528496
$746$	−48.8740	−1.78941
$747$	−13.7511	−0.503128
$748$	14.9143	0.545322
$749$	51.6090	1.88575
$750$	82.9025	3.02717
$751$	−23.3605	−0.852438	−0.426219	−	0.904620i	$-0.640155\pi$
$751$	−23.3605	−0.852438	−0.426219	+	0.904620i	$0.640155\pi$
$752$	−43.9030	−1.60098
$753$	1.44718	0.0527380
$754$	41.2231	1.50126
$755$	61.5151	2.23876
$756$	−95.0593	−3.45727
$757$	−38.4371	−1.39702	−0.698510	−	0.715600i	$-0.746153\pi$
$757$	−38.4371	−1.39702	−0.698510	+	0.715600i	$0.746153\pi$
$758$	−33.4413	−1.21464
$759$	−5.07633	−0.184259
$760$	−56.0440	−2.03293
$761$	11.0753	0.401479	0.200739	−	0.979645i	$-0.435666\pi$
$761$	11.0753	0.401479	0.200739	+	0.979645i	$0.435666\pi$
$762$	−64.1469	−2.32380
$763$	12.2296	0.442742
$764$	104.532	3.78182
$765$	−36.7378	−1.32826
$766$	−16.4583	−0.594662
$767$	−14.4843	−0.522998
$768$	−42.4717	−1.53256
$769$	−13.1433	−0.473960	−0.236980	−	0.971515i	$-0.576158\pi$
$769$	−13.1433	−0.473960	−0.236980	+	0.971515i	$0.576158\pi$
$770$	16.1090	0.580527
$771$	−34.6505	−1.24791
$772$	−94.6472	−3.40643
$773$	29.5537	1.06297	0.531487	−	0.847067i	$-0.321634\pi$
$773$	29.5537	1.06297	0.531487	+	0.847067i	$0.321634\pi$
$774$	20.8263	0.748588
$775$	95.9852	3.44789
$776$	−54.1880	−1.94524
$777$	14.2037	0.509555
$778$	−39.9160	−1.43106
$779$	−5.28200	−0.189247
$780$	−48.3546	−1.73137
$781$	−3.23861	−0.115887
$782$	−148.419	−5.30746
$783$	−45.6388	−1.63100
$784$	46.5969	1.66418
$785$	−1.09462	−0.0390685
$786$	−13.0391	−0.465091
$787$	3.46853	0.123640	0.0618199	−	0.998087i	$-0.480310\pi$
$787$	3.46853	0.123640	0.0618199	+	0.998087i	$0.480310\pi$
$788$	101.738	3.62426
$789$	−20.8228	−0.741310
$790$	47.1691	1.67820
$791$	−59.8278	−2.12723
$792$	6.44165	0.228894
$793$	0.198254	0.00704021
$794$	−60.3210	−2.14071
$795$	−41.6921	−1.47867
$796$	8.84275	0.313423
$797$	−18.0708	−0.640100	−0.320050	−	0.947401i	$-0.603700\pi$
$797$	−18.0708	−0.640100	−0.320050	+	0.947401i	$0.603700\pi$
$798$	−15.9672	−0.565233
$799$	−18.4078	−0.651221
$800$	−230.227	−8.13976
$801$	5.64449	0.199438
$802$	−79.6346	−2.81200
$803$	4.60886	0.162643
$804$	94.8088	3.34365
$805$	−116.970	−4.12265
$806$	−42.5218	−1.49777
$807$	0.125762	0.00442703
$808$	−48.5076	−1.70649
$809$	20.4716	0.719743	0.359872	−	0.933002i	$-0.382820\pi$
$809$	20.4716	0.719743	0.359872	+	0.933002i	$0.382820\pi$
$810$	23.5217	0.826470
$811$	10.9773	0.385467	0.192733	−	0.981251i	$-0.438265\pi$
$811$	10.9773	0.385467	0.192733	+	0.981251i	$0.438265\pi$
$812$	143.380	5.03166
$813$	29.8576	1.04715
$814$	−4.55270	−0.159572
$815$	−20.3517	−0.712889
$816$	−105.044	−3.67726
$817$	7.60025	0.265899
$818$	98.9075	3.45822
$819$	8.87141	0.309992
$820$	−76.2494	−2.66274
$821$	−0.274059	−0.00956472	−0.00478236	−	0.999989i	$-0.501522\pi$
$821$	−0.274059	−0.00956472	−0.00478236	+	0.999989i	$0.501522\pi$
$822$	47.6955	1.66357
$823$	24.6248	0.858368	0.429184	−	0.903217i	$-0.358801\pi$
$823$	24.6248	0.858368	0.429184	+	0.903217i	$0.358801\pi$
$824$	176.377	6.14438
$825$	−6.27470	−0.218457
$826$	−69.0441	−2.40235
$827$	33.1968	1.15437	0.577183	−	0.816615i	$-0.304152\pi$
$827$	33.1968	1.15437	0.577183	+	0.816615i	$0.304152\pi$
$828$	−74.3034	−2.58222
$829$	35.3098	1.22636	0.613181	−	0.789943i	$-0.289890\pi$
$829$	35.3098	1.22636	0.613181	+	0.789943i	$0.289890\pi$
$830$	−99.2821	−3.44613
$831$	16.1994	0.561949
$832$	49.5900	1.71922
$833$	19.5373	0.676927
$834$	3.15067	0.109099
$835$	3.19922	0.110713
$836$	3.73437	0.129156
$837$	47.0766	1.62721
$838$	−30.9104	−1.06778
$839$	45.9657	1.58691	0.793456	−	0.608627i	$-0.208280\pi$
$839$	45.9657	1.58691	0.793456	+	0.608627i	$0.208280\pi$
$840$	−145.098	−5.00636
$841$	39.8382	1.37373
$842$	7.24190	0.249572
$843$	−0.359672	−0.0123878
$844$	45.3516	1.56106
$845$	−38.9122	−1.33862
$846$	−12.6299	−0.434225
$847$	34.5393	1.18678
$848$	121.947	4.18767
$849$	−30.7652	−1.05586
$850$	−183.457	−6.29251
$851$	33.0579	1.13321
$852$	46.3402	1.58759
$853$	1.41203	0.0483468	0.0241734	−	0.999708i	$-0.492305\pi$
$853$	1.41203	0.0483468	0.0241734	+	0.999708i	$0.492305\pi$
$854$	0.945042	0.0323387
$855$	−9.19869	−0.314589
$856$	149.000	5.09273
$857$	30.4407	1.03984	0.519918	−	0.854216i	$-0.325963\pi$
$857$	30.4407	1.03984	0.519918	+	0.854216i	$0.325963\pi$
$858$	2.77972	0.0948980
$859$	−24.4971	−0.835829	−0.417914	−	0.908486i	$-0.637239\pi$
$859$	−24.4971	−0.835829	−0.417914	+	0.908486i	$0.637239\pi$
$860$	109.715	3.74125
$861$	−13.6751	−0.466047
$862$	−1.34954	−0.0459655
$863$	29.1106	0.990937	0.495469	−	0.868626i	$-0.334996\pi$
$863$	29.1106	0.990937	0.495469	+	0.868626i	$0.334996\pi$
$864$	−112.917	−3.84150
$865$	69.0033	2.34618
$866$	9.15292	0.311029
$867$	−23.3409	−0.792697
$868$	−147.898	−5.01997
$869$	−1.97852	−0.0671167
$870$	−110.664	−3.75186
$871$	−26.3455	−0.892684
$872$	35.3081	1.19568
$873$	−8.89407	−0.301019
$874$	−37.1623	−1.25703
$875$	−80.1263	−2.70876
$876$	−65.9467	−2.22813
$877$	−41.8799	−1.41418	−0.707092	−	0.707122i	$-0.749993\pi$
$877$	−41.8799	−1.41418	−0.707092	+	0.707122i	$0.749993\pi$
$878$	−46.5579	−1.57125
$879$	14.3914	0.485411
$880$	26.5351	0.894499
$881$	−46.5679	−1.56891	−0.784456	−	0.620185i	$-0.787058\pi$
$881$	−46.5679	−1.56891	−0.784456	+	0.620185i	$0.787058\pi$
$882$	13.4049	0.451365
$883$	0.431972	0.0145370	0.00726851	−	0.999974i	$-0.497686\pi$
$883$	0.431972	0.0145370	0.00726851	+	0.999974i	$0.497686\pi$
$884$	59.3009	1.99451
$885$	38.8834	1.30705
$886$	−91.6977	−3.08064
$887$	41.8907	1.40655	0.703276	−	0.710917i	$-0.251720\pi$
$887$	41.8907	1.40655	0.703276	+	0.710917i	$0.251720\pi$
$888$	41.0075	1.37612
$889$	61.9988	2.07937
$890$	40.7528	1.36604
$891$	−0.986626	−0.0330532
$892$	−25.1664	−0.842633
$893$	−4.60908	−0.154237
$894$	−11.8654	−0.396838
$895$	67.9594	2.27163
$896$	104.954	3.50627
$897$	−20.1840	−0.673924
$898$	−49.6676	−1.65743
$899$	−71.0069	−2.36821
$900$	−91.8443	−3.06148
$901$	51.1302	1.70339
$902$	4.38327	0.145947
$903$	19.6771	0.654813
$904$	−172.729	−5.74487
$905$	83.1000	2.76234
$906$	50.5992	1.68104
$907$	−4.16495	−0.138295	−0.0691475	−	0.997606i	$-0.522028\pi$
$907$	−4.16495	−0.138295	−0.0691475	+	0.997606i	$0.522028\pi$
$908$	68.8787	2.28582
$909$	−7.96173	−0.264074
$910$	64.0509	2.12327
$911$	−36.5179	−1.20989	−0.604945	−	0.796267i	$-0.706805\pi$
$911$	−36.5179	−1.20989	−0.604945	+	0.796267i	$0.706805\pi$
$912$	−26.3016	−0.870934
$913$	4.16442	0.137822
$914$	54.5720	1.80508
$915$	−0.532217	−0.0175945
$916$	−19.1080	−0.631346
$917$	12.6025	0.416171
$918$	−89.9776	−2.96970
$919$	39.0154	1.28700	0.643499	−	0.765447i	$-0.277482\pi$
$919$	39.0154	1.28700	0.643499	+	0.765447i	$0.277482\pi$
$920$	−337.704	−11.1338
$921$	24.7707	0.816221
$922$	−39.4271	−1.29846
$923$	−12.8770	−0.423853
$924$	9.66830	0.318064
$925$	40.8619	1.34353
$926$	80.0802	2.63160
$927$	28.9493	0.950821
$928$	170.315	5.59086
$929$	−13.4461	−0.441153	−0.220577	−	0.975370i	$-0.570794\pi$
$929$	−13.4461	−0.441153	−0.220577	+	0.975370i	$0.570794\pi$
$930$	114.151	3.74314
$931$	4.89190	0.160325
$932$	−139.154	−4.55814
$933$	16.8570	0.551872
$934$	112.583	3.68384
$935$	11.1257	0.363850
$936$	25.6126	0.837175
$937$	29.7410	0.971597	0.485799	−	0.874071i	$-0.338529\pi$
$937$	29.7410	0.971597	0.485799	+	0.874071i	$0.338529\pi$
$938$	−125.584	−4.10047
$939$	−37.8602	−1.23552
$940$	−66.5353	−2.17014
$941$	26.8684	0.875884	0.437942	−	0.899003i	$-0.355708\pi$
$941$	26.8684	0.875884	0.437942	+	0.899003i	$0.355708\pi$
$942$	−0.900376	−0.0293358
$943$	−31.8277	−1.03645
$944$	−113.731	−3.70164
$945$	−70.9118	−2.30676
$946$	−6.30708	−0.205061
$947$	−15.9418	−0.518039	−0.259020	−	0.965872i	$-0.583399\pi$
$947$	−15.9418	−0.518039	−0.259020	+	0.965872i	$0.583399\pi$
$948$	28.3100	0.919466
$949$	18.3253	0.594864
$950$	−45.9353	−1.49034
$951$	−15.9937	−0.518630
$952$	177.945	5.76722
$953$	45.8542	1.48536	0.742681	−	0.669645i	$-0.233554\pi$
$953$	45.8542	1.48536	0.742681	+	0.669645i	$0.233554\pi$
$954$	35.0813	1.13580
$955$	77.9780	2.52331
$956$	10.8764	0.351768
$957$	4.64183	0.150049
$958$	−54.8431	−1.77190
$959$	−46.0983	−1.48859
$960$	−133.125	−4.29660
$961$	42.2440	1.36271
$962$	−18.1020	−0.583631
$963$	24.4559	0.788082
$964$	86.6053	2.78937
$965$	−70.6045	−2.27284
$966$	−96.2135	−3.09562
$967$	10.5685	0.339860	0.169930	−	0.985456i	$-0.445646\pi$
$967$	10.5685	0.339860	0.169930	+	0.985456i	$0.445646\pi$
$968$	99.7182	3.20506
$969$	−11.0278	−0.354265
$970$	−64.2144	−2.06180
$971$	9.29966	0.298440	0.149220	−	0.988804i	$-0.452324\pi$
$971$	9.29966	0.298440	0.149220	+	0.988804i	$0.452324\pi$
$972$	−74.9629	−2.40444
$973$	−3.04516	−0.0976235
$974$	29.1421	0.933774
$975$	−24.9489	−0.799003
$976$	1.55670	0.0498287
$977$	−55.5204	−1.77625	−0.888127	−	0.459598i	$-0.847994\pi$
$977$	−55.5204	−1.77625	−0.888127	+	0.459598i	$0.847994\pi$
$978$	−16.7403	−0.535295
$979$	−1.70939	−0.0546322
$980$	70.6179	2.25581
$981$	5.79524	0.185028
$982$	3.01335	0.0961598
$983$	26.9801	0.860531	0.430266	−	0.902702i	$-0.358420\pi$
$983$	26.9801	0.860531	0.430266	+	0.902702i	$0.358420\pi$
$984$	−39.4814	−1.25862
$985$	75.8938	2.41818
$986$	135.716	4.32207
$987$	−11.9329	−0.379830
$988$	14.8482	0.472385
$989$	45.7968	1.45625
$990$	7.63354	0.242610
$991$	−6.09515	−0.193619	−0.0968094	−	0.995303i	$-0.530864\pi$
$991$	−6.09515	−0.193619	−0.0968094	+	0.995303i	$0.530864\pi$
$992$	−175.681	−5.57787
$993$	28.2479	0.896419
$994$	−61.3826	−1.94694
$995$	6.59647	0.209122
$996$	−59.5873	−1.88809
$997$	0.267082	0.00845856	0.00422928	−	0.999991i	$-0.498654\pi$
$997$	0.267082	0.00845856	0.00422928	+	0.999991i	$0.498654\pi$
$998$	28.4086	0.899258
$999$	20.0410	0.634070

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.c.1.3	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.c.1.3	✓	179	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:	\( N \)	\(=\)	\( 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.71994 q^{2} -1.21777 q^{3} +5.39810 q^{4} +4.02685 q^{5} +3.31228 q^{6} -3.20136 q^{7} -9.24264 q^{8} -1.51703 q^{9} +O(q^{10})\)	\(q-2.71994 q^{2} -1.21777 q^{3} +5.39810 q^{4} +4.02685 q^{5} +3.31228 q^{6} -3.20136 q^{7} -9.24264 q^{8} -1.51703 q^{9} -10.9528 q^{10} +0.459418 q^{11} -6.57366 q^{12} +1.82669 q^{13} +8.70752 q^{14} -4.90379 q^{15} +14.3433 q^{16} +6.01389 q^{17} +4.12623 q^{18} +1.50580 q^{19} +21.7373 q^{20} +3.89853 q^{21} -1.24959 q^{22} +9.07350 q^{23} +11.2554 q^{24} +11.2155 q^{25} -4.96850 q^{26} +5.50072 q^{27} -17.2812 q^{28} -8.29688 q^{29} +13.3380 q^{30} +8.55827 q^{31} -20.5276 q^{32} -0.559468 q^{33} -16.3574 q^{34} -12.8914 q^{35} -8.18905 q^{36} +3.64335 q^{37} -4.09570 q^{38} -2.22450 q^{39} -37.2187 q^{40} -3.50776 q^{41} -10.6038 q^{42} +5.04731 q^{43} +2.47998 q^{44} -6.10883 q^{45} -24.6794 q^{46} -3.06088 q^{47} -17.4669 q^{48} +3.24870 q^{49} -30.5055 q^{50} -7.32355 q^{51} +9.86067 q^{52} +8.50203 q^{53} -14.9616 q^{54} +1.85001 q^{55} +29.5890 q^{56} -1.83373 q^{57} +22.5670 q^{58} -7.92925 q^{59} -26.4711 q^{60} +0.108532 q^{61} -23.2780 q^{62} +4.85654 q^{63} +27.1474 q^{64} +7.35581 q^{65} +1.52172 q^{66} -14.4225 q^{67} +32.4635 q^{68} -11.0495 q^{69} +35.0638 q^{70} -7.04938 q^{71} +14.0213 q^{72} +10.0320 q^{73} -9.90970 q^{74} -13.6579 q^{75} +8.12847 q^{76} -1.47076 q^{77} +6.05052 q^{78} -4.30658 q^{79} +57.7581 q^{80} -2.14755 q^{81} +9.54093 q^{82} +9.06454 q^{83} +21.0447 q^{84} +24.2170 q^{85} -13.7284 q^{86} +10.1037 q^{87} -4.24623 q^{88} -3.72076 q^{89} +16.6157 q^{90} -5.84790 q^{91} +48.9796 q^{92} -10.4220 q^{93} +8.32543 q^{94} +6.06364 q^{95} +24.9980 q^{96} +5.86283 q^{97} -8.83628 q^{98} -0.696949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9 + 9 * q^10 + 46 * q^11 + 33 * q^12 + 47 * q^13 + 22 * q^14 + 36 * q^15 + 222 * q^16 + 103 * q^17 + 43 * q^18 + 12 * q^19 + 102 * q^20 + 50 * q^21 + 39 * q^22 + 121 * q^23 - 3 * q^24 + 246 * q^25 + 52 * q^26 + 49 * q^27 + 41 * q^28 + 138 * q^29 + 28 * q^30 + 5 * q^31 + 137 * q^32 + 63 * q^33 + 2 * q^34 + 72 * q^35 + 279 * q^36 + 118 * q^37 + 123 * q^38 + q^39 + 9 * q^40 + 50 * q^41 + 48 * q^42 + 48 * q^43 + 108 * q^44 + 158 * q^45 + 13 * q^46 + 85 * q^47 + 50 * q^48 + 230 * q^49 + 78 * q^50 + 15 * q^51 + 41 * q^52 + 399 * q^53 - 5 * q^54 + 24 * q^55 + 53 * q^56 + 45 * q^57 + 27 * q^58 + 48 * q^59 + 66 * q^60 + 46 * q^61 + 81 * q^62 + 78 * q^63 + 252 * q^64 + 153 * q^65 + 6 * q^66 + 70 * q^67 + 240 * q^68 + 120 * q^69 - 31 * q^70 + 86 * q^71 + 89 * q^72 + 45 * q^73 + 68 * q^74 + 17 * q^75 - 13 * q^76 + 362 * q^77 + 69 * q^78 + 31 * q^79 + 169 * q^80 + 303 * q^81 + 25 * q^82 + 106 * q^83 + 13 * q^84 + 115 * q^85 + 95 * q^86 + 32 * q^87 + 83 * q^88 + 105 * q^89 - 38 * q^90 + 3 * q^91 + 310 * q^92 + 298 * q^93 - 17 * q^94 + 102 * q^95 - 82 * q^96 + 34 * q^97 + 81 * q^98 + 58 * q^99

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