LMFDB - Embedded newform 4003.2.a.c.1.16

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			1.16
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)

$f(q)$	$=$	$q-2.38397 q^{2} +1.62509 q^{3} +3.68332 q^{4} -0.985677 q^{5} -3.87416 q^{6} -1.38154 q^{7} -4.01299 q^{8} -0.359094 q^{9} +O(q^{10})$	\(q-2.38397 q^{2} +1.62509 q^{3} +3.68332 q^{4} -0.985677 q^{5} -3.87416 q^{6} -1.38154 q^{7} -4.01299 q^{8} -0.359094 q^{9} +2.34983 q^{10} +3.88920 q^{11} +5.98572 q^{12} +1.26448 q^{13} +3.29355 q^{14} -1.60181 q^{15} +2.20022 q^{16} +1.19457 q^{17} +0.856070 q^{18} +6.37297 q^{19} -3.63057 q^{20} -2.24512 q^{21} -9.27175 q^{22} +1.09885 q^{23} -6.52146 q^{24} -4.02844 q^{25} -3.01449 q^{26} -5.45882 q^{27} -5.08866 q^{28} +3.93133 q^{29} +3.81867 q^{30} +4.35012 q^{31} +2.78073 q^{32} +6.32029 q^{33} -2.84781 q^{34} +1.36175 q^{35} -1.32266 q^{36} +5.82343 q^{37} -15.1930 q^{38} +2.05490 q^{39} +3.95552 q^{40} -1.19420 q^{41} +5.35231 q^{42} +4.92877 q^{43} +14.3252 q^{44} +0.353951 q^{45} -2.61964 q^{46} -2.09466 q^{47} +3.57555 q^{48} -5.09135 q^{49} +9.60369 q^{50} +1.94127 q^{51} +4.65750 q^{52} +1.02747 q^{53} +13.0137 q^{54} -3.83350 q^{55} +5.54411 q^{56} +10.3566 q^{57} -9.37219 q^{58} -3.71709 q^{59} -5.89998 q^{60} -8.30371 q^{61} -10.3706 q^{62} +0.496103 q^{63} -11.0296 q^{64} -1.24637 q^{65} -15.0674 q^{66} -3.61329 q^{67} +4.39997 q^{68} +1.78573 q^{69} -3.24638 q^{70} +6.21892 q^{71} +1.44104 q^{72} -12.0245 q^{73} -13.8829 q^{74} -6.54656 q^{75} +23.4737 q^{76} -5.37309 q^{77} -4.89881 q^{78} -12.5180 q^{79} -2.16871 q^{80} -7.79377 q^{81} +2.84695 q^{82} +14.5960 q^{83} -8.26951 q^{84} -1.17746 q^{85} -11.7501 q^{86} +6.38876 q^{87} -15.6074 q^{88} -11.3971 q^{89} -0.843809 q^{90} -1.74693 q^{91} +4.04744 q^{92} +7.06932 q^{93} +4.99361 q^{94} -6.28169 q^{95} +4.51892 q^{96} +12.5169 q^{97} +12.1376 q^{98} -1.39659 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.38397	−1.68572	−0.842861	−	0.538131i	$-0.819131\pi$
$2$	−2.38397	−1.68572	−0.842861	+	0.538131i	$0.819131\pi$
$3$	1.62509	0.938244	0.469122	−	0.883133i	$-0.344570\pi$
$3$	1.62509	0.938244	0.469122	+	0.883133i	$0.344570\pi$
$4$	3.68332	1.84166
$5$	−0.985677	−0.440808	−0.220404	−	0.975409i	$-0.570738\pi$
$5$	−0.985677	−0.440808	−0.220404	+	0.975409i	$0.570738\pi$
$6$	−3.87416	−1.58162
$7$	−1.38154	−0.522173	−0.261086	−	0.965315i	$-0.584081\pi$
$7$	−1.38154	−0.522173	−0.261086	+	0.965315i	$0.584081\pi$
$8$	−4.01299	−1.41881
$9$	−0.359094	−0.119698
$10$	2.34983	0.743080
$11$	3.88920	1.17264	0.586320	−	0.810080i	$-0.300576\pi$
$11$	3.88920	1.17264	0.586320	+	0.810080i	$0.300576\pi$
$12$	5.98572	1.72793
$13$	1.26448	0.350705	0.175352	−	0.984506i	$-0.443894\pi$
$13$	1.26448	0.350705	0.175352	+	0.984506i	$0.443894\pi$
$14$	3.29355	0.880239
$15$	−1.60181	−0.413586
$16$	2.20022	0.550055
$17$	1.19457	0.289725	0.144862	−	0.989452i	$-0.453726\pi$
$17$	1.19457	0.289725	0.144862	+	0.989452i	$0.453726\pi$
$18$	0.856070	0.201778
$19$	6.37297	1.46206	0.731030	−	0.682345i	$-0.239040\pi$
$19$	6.37297	1.46206	0.731030	+	0.682345i	$0.239040\pi$
$20$	−3.63057	−0.811819
$21$	−2.24512	−0.489926
$22$	−9.27175	−1.97674
$23$	1.09885	0.229127	0.114564	−	0.993416i	$-0.463453\pi$
$23$	1.09885	0.229127	0.114564	+	0.993416i	$0.463453\pi$
$24$	−6.52146	−1.33119
$25$	−4.02844	−0.805688
$26$	−3.01449	−0.591191
$27$	−5.45882	−1.05055
$28$	−5.08866	−0.961666
$29$	3.93133	0.730030	0.365015	−	0.931002i	$-0.381064\pi$
$29$	3.93133	0.730030	0.365015	+	0.931002i	$0.381064\pi$
$30$	3.81867	0.697191
$31$	4.35012	0.781304	0.390652	−	0.920538i	$-0.372250\pi$
$31$	4.35012	0.781304	0.390652	+	0.920538i	$0.372250\pi$
$32$	2.78073	0.491568
$33$	6.32029	1.10022
$34$	−2.84781	−0.488396
$35$	1.36175	0.230178
$36$	−1.32266	−0.220443
$37$	5.82343	0.957366	0.478683	−	0.877988i	$-0.341114\pi$
$37$	5.82343	0.957366	0.478683	+	0.877988i	$0.341114\pi$
$38$	−15.1930	−2.46463
$39$	2.05490	0.329047
$40$	3.95552	0.625422
$41$	−1.19420	−0.186503	−0.0932516	−	0.995643i	$-0.529726\pi$
$41$	−1.19420	−0.186503	−0.0932516	+	0.995643i	$0.529726\pi$
$42$	5.35231	0.825879
$43$	4.92877	0.751631	0.375815	−	0.926695i	$-0.377363\pi$
$43$	4.92877	0.751631	0.375815	+	0.926695i	$0.377363\pi$
$44$	14.3252	2.15960
$45$	0.353951	0.0527639
$46$	−2.61964	−0.386245
$47$	−2.09466	−0.305537	−0.152769	−	0.988262i	$-0.548819\pi$
$47$	−2.09466	−0.305537	−0.152769	+	0.988262i	$0.548819\pi$
$48$	3.57555	0.516086
$49$	−5.09135	−0.727335
$50$	9.60369	1.35817
$51$	1.94127	0.271833
$52$	4.65750	0.645879
$53$	1.02747	0.141133	0.0705667	−	0.997507i	$-0.477519\pi$
$53$	1.02747	0.141133	0.0705667	+	0.997507i	$0.477519\pi$
$54$	13.0137	1.77094
$55$	−3.83350	−0.516909
$56$	5.54411	0.740863
$57$	10.3566	1.37177
$58$	−9.37219	−1.23063
$59$	−3.71709	−0.483924	−0.241962	−	0.970286i	$-0.577791\pi$
$59$	−3.71709	−0.483924	−0.241962	+	0.970286i	$0.577791\pi$
$60$	−5.89998	−0.761685
$61$	−8.30371	−1.06318	−0.531591	−	0.847001i	$-0.678406\pi$
$61$	−8.30371	−1.06318	−0.531591	+	0.847001i	$0.678406\pi$
$62$	−10.3706	−1.31706
$63$	0.496103	0.0625031
$64$	−11.0296	−1.37870
$65$	−1.24637	−0.154594
$66$	−15.0674	−1.85467
$67$	−3.61329	−0.441434	−0.220717	−	0.975338i	$-0.570840\pi$
$67$	−3.61329	−0.441434	−0.220717	+	0.975338i	$0.570840\pi$
$68$	4.39997	0.533575
$69$	1.78573	0.214977
$70$	−3.24638	−0.388016
$71$	6.21892	0.738050	0.369025	−	0.929419i	$-0.379692\pi$
$71$	6.21892	0.738050	0.369025	+	0.929419i	$0.379692\pi$
$72$	1.44104	0.169829
$73$	−12.0245	−1.40736	−0.703679	−	0.710518i	$-0.748460\pi$
$73$	−12.0245	−1.40736	−0.703679	+	0.710518i	$0.748460\pi$
$74$	−13.8829	−1.61385
$75$	−6.54656	−0.755932
$76$	23.4737	2.69262
$77$	−5.37309	−0.612320
$78$	−4.89881	−0.554682
$79$	−12.5180	−1.40839	−0.704193	−	0.710008i	$-0.748691\pi$
$79$	−12.5180	−1.40839	−0.704193	+	0.710008i	$0.748691\pi$
$80$	−2.16871	−0.242469
$81$	−7.79377	−0.865974
$82$	2.84695	0.314393
$83$	14.5960	1.60212	0.801062	−	0.598582i	$-0.204269\pi$
$83$	14.5960	1.60212	0.801062	+	0.598582i	$0.204269\pi$
$84$	−8.26951	−0.902277
$85$	−1.17746	−0.127713
$86$	−11.7501	−1.26704
$87$	6.38876	0.684947
$88$	−15.6074	−1.66375
$89$	−11.3971	−1.20809	−0.604047	−	0.796949i	$-0.706446\pi$
$89$	−11.3971	−1.20809	−0.604047	+	0.796949i	$0.706446\pi$
$90$	−0.843809	−0.0889453
$91$	−1.74693	−0.183129
$92$	4.04744	0.421974
$93$	7.06932	0.733054
$94$	4.99361	0.515051
$95$	−6.28169	−0.644488
$96$	4.51892	0.461210
$97$	12.5169	1.27090	0.635451	−	0.772141i	$-0.280814\pi$
$97$	12.5169	1.27090	0.635451	+	0.772141i	$0.280814\pi$
$98$	12.1376	1.22609
$99$	−1.39659	−0.140363
$100$	−14.8380	−1.48380
$101$	11.4870	1.14300	0.571498	−	0.820603i	$-0.306362\pi$
$101$	11.4870	1.14300	0.571498	+	0.820603i	$0.306362\pi$
$102$	−4.62794	−0.458235
$103$	4.56537	0.449839	0.224920	−	0.974377i	$-0.427788\pi$
$103$	4.56537	0.449839	0.224920	+	0.974377i	$0.427788\pi$
$104$	−5.07437	−0.497583
$105$	2.21296	0.215963
$106$	−2.44945	−0.237912
$107$	15.1394	1.46358	0.731792	−	0.681528i	$-0.238684\pi$
$107$	15.1394	1.46358	0.731792	+	0.681528i	$0.238684\pi$
$108$	−20.1066	−1.93476
$109$	3.64049	0.348696	0.174348	−	0.984684i	$-0.444218\pi$
$109$	3.64049	0.348696	0.174348	+	0.984684i	$0.444218\pi$
$110$	9.13895	0.871365
$111$	9.46358	0.898243
$112$	−3.03969	−0.287224
$113$	4.66060	0.438432	0.219216	−	0.975676i	$-0.429650\pi$
$113$	4.66060	0.438432	0.219216	+	0.975676i	$0.429650\pi$
$114$	−24.6899	−2.31242
$115$	−1.08312	−0.101001
$116$	14.4804	1.34447
$117$	−0.454069	−0.0419787
$118$	8.86144	0.815761
$119$	−1.65034	−0.151286
$120$	6.42805	0.586798
$121$	4.12591	0.375082
$122$	19.7958	1.79223
$123$	−1.94068	−0.174985
$124$	16.0229	1.43890
$125$	8.89913	0.795962
$126$	−1.18270	−0.105363
$127$	4.97369	0.441344	0.220672	−	0.975348i	$-0.429175\pi$
$127$	4.97369	0.441344	0.220672	+	0.975348i	$0.429175\pi$
$128$	20.7328	1.83254
$129$	8.00968	0.705213
$130$	2.97132	0.260602
$131$	3.88753	0.339655	0.169828	−	0.985474i	$-0.445679\pi$
$131$	3.88753	0.339655	0.169828	+	0.985474i	$0.445679\pi$
$132$	23.2797	2.02624
$133$	−8.80452	−0.763448
$134$	8.61398	0.744135
$135$	5.38063	0.463091
$136$	−4.79379	−0.411064
$137$	2.11556	0.180745	0.0903724	−	0.995908i	$-0.471194\pi$
$137$	2.11556	0.180745	0.0903724	+	0.995908i	$0.471194\pi$
$138$	−4.25714	−0.362392
$139$	−9.42170	−0.799138	−0.399569	−	0.916703i	$-0.630840\pi$
$139$	−9.42170	−0.799138	−0.399569	+	0.916703i	$0.630840\pi$
$140$	5.01577	0.423910
$141$	−3.40400	−0.286669
$142$	−14.8257	−1.24415
$143$	4.91784	0.411250
$144$	−0.790086	−0.0658405
$145$	−3.87502	−0.321803
$146$	28.6660	2.37241
$147$	−8.27388	−0.682418
$148$	21.4496	1.76314
$149$	−7.43957	−0.609473	−0.304737	−	0.952437i	$-0.598568\pi$
$149$	−7.43957	−0.609473	−0.304737	+	0.952437i	$0.598568\pi$
$150$	15.6068	1.27429
$151$	17.2817	1.40636	0.703180	−	0.711012i	$-0.251763\pi$
$151$	17.2817	1.40636	0.703180	+	0.711012i	$0.251763\pi$
$152$	−25.5747	−2.07438
$153$	−0.428962	−0.0346795
$154$	12.8093	1.03220
$155$	−4.28781	−0.344405
$156$	7.56884	0.605993
$157$	5.99724	0.478632	0.239316	−	0.970942i	$-0.423077\pi$
$157$	5.99724	0.478632	0.239316	+	0.970942i	$0.423077\pi$
$158$	29.8426	2.37415
$159$	1.66972	0.132417
$160$	−2.74090	−0.216687
$161$	−1.51811	−0.119644
$162$	18.5801	1.45979
$163$	−20.1634	−1.57932	−0.789658	−	0.613547i	$-0.789742\pi$
$163$	−20.1634	−1.57932	−0.789658	+	0.613547i	$0.789742\pi$
$164$	−4.39863	−0.343476
$165$	−6.22977	−0.484987
$166$	−34.7965	−2.70074
$167$	20.8663	1.61468	0.807342	−	0.590083i	$-0.200905\pi$
$167$	20.8663	1.61468	0.807342	+	0.590083i	$0.200905\pi$
$168$	9.00966	0.695110
$169$	−11.4011	−0.877006
$170$	2.80702	0.215289
$171$	−2.28850	−0.175006
$172$	18.1543	1.38425
$173$	−5.97414	−0.454205	−0.227103	−	0.973871i	$-0.572925\pi$
$173$	−5.97414	−0.454205	−0.227103	+	0.973871i	$0.572925\pi$
$174$	−15.2306	−1.15463
$175$	5.56545	0.420709
$176$	8.55710	0.645016
$177$	−6.04059	−0.454039
$178$	27.1704	2.03651
$179$	18.1058	1.35329	0.676647	−	0.736308i	$-0.263432\pi$
$179$	18.1058	1.35329	0.676647	+	0.736308i	$0.263432\pi$
$180$	1.30372	0.0971732
$181$	19.8416	1.47481	0.737406	−	0.675450i	$-0.236051\pi$
$181$	19.8416	1.47481	0.737406	+	0.675450i	$0.236051\pi$
$182$	4.16464	0.308704
$183$	−13.4943	−0.997524
$184$	−4.40970	−0.325087
$185$	−5.74002	−0.422015
$186$	−16.8531	−1.23573
$187$	4.64591	0.339743
$188$	−7.71531	−0.562697
$189$	7.54157	0.548569
$190$	14.9754	1.08643
$191$	−23.4582	−1.69738	−0.848688	−	0.528894i	$-0.822607\pi$
$191$	−23.4582	−1.69738	−0.848688	+	0.528894i	$0.822607\pi$
$192$	−17.9241	−1.29356
$193$	26.7484	1.92539	0.962697	−	0.270581i	$-0.0872157\pi$
$193$	26.7484	1.92539	0.962697	+	0.270581i	$0.0872157\pi$
$194$	−29.8400	−2.14239
$195$	−2.02546	−0.145046
$196$	−18.7531	−1.33951
$197$	−21.9533	−1.56411	−0.782055	−	0.623209i	$-0.785828\pi$
$197$	−21.9533	−1.56411	−0.782055	+	0.623209i	$0.785828\pi$
$198$	3.32943	0.236612
$199$	21.4122	1.51787	0.758935	−	0.651167i	$-0.225720\pi$
$199$	21.4122	1.51787	0.758935	+	0.651167i	$0.225720\pi$
$200$	16.1661	1.14312
$201$	−5.87191	−0.414172
$202$	−27.3846	−1.92678
$203$	−5.43129	−0.381202
$204$	7.15034	0.500624
$205$	1.17710	0.0822121
$206$	−10.8837	−0.758305
$207$	−0.394592	−0.0274261
$208$	2.78214	0.192907
$209$	24.7858	1.71447
$210$	−5.27564	−0.364054
$211$	14.8915	1.02517	0.512587	−	0.858635i	$-0.328687\pi$
$211$	14.8915	1.02517	0.512587	+	0.858635i	$0.328687\pi$
$212$	3.78449	0.259920
$213$	10.1063	0.692471
$214$	−36.0920	−2.46720
$215$	−4.85818	−0.331325
$216$	21.9062	1.49053
$217$	−6.00986	−0.407976
$218$	−8.67883	−0.587804
$219$	−19.5408	−1.32044
$220$	−14.1200	−0.951971
$221$	1.51051	0.101608
$222$	−22.5609	−1.51419
$223$	16.6924	1.11781	0.558903	−	0.829233i	$-0.311222\pi$
$223$	16.6924	1.11781	0.558903	+	0.829233i	$0.311222\pi$
$224$	−3.84168	−0.256683
$225$	1.44659	0.0964393
$226$	−11.1107	−0.739076
$227$	27.5760	1.83029	0.915143	−	0.403130i	$-0.132078\pi$
$227$	27.5760	1.83029	0.915143	+	0.403130i	$0.132078\pi$
$228$	38.1468	2.52633
$229$	−15.7633	−1.04167	−0.520836	−	0.853657i	$-0.674380\pi$
$229$	−15.7633	−1.04167	−0.520836	+	0.853657i	$0.674380\pi$
$230$	2.58212	0.170260
$231$	−8.73173	−0.574506
$232$	−15.7764	−1.03577
$233$	28.5806	1.87238	0.936188	−	0.351500i	$-0.114328\pi$
$233$	28.5806	1.87238	0.936188	+	0.351500i	$0.114328\pi$
$234$	1.08249	0.0707644
$235$	2.06466	0.134683
$236$	−13.6912	−0.891224
$237$	−20.3429	−1.32141
$238$	3.93437	0.255027
$239$	0.441817	0.0285788	0.0142894	−	0.999898i	$-0.495451\pi$
$239$	0.441817	0.0285788	0.0142894	+	0.999898i	$0.495451\pi$
$240$	−3.52433	−0.227495
$241$	−7.51546	−0.484113	−0.242057	−	0.970262i	$-0.577822\pi$
$241$	−7.51546	−0.484113	−0.242057	+	0.970262i	$0.577822\pi$
$242$	−9.83605	−0.632285
$243$	3.71091	0.238055
$244$	−30.5853	−1.95802
$245$	5.01842	0.320615
$246$	4.62653	0.294977
$247$	8.05852	0.512752
$248$	−17.4570	−1.10852
$249$	23.7198	1.50318
$250$	−21.2153	−1.34177
$251$	28.0907	1.77307	0.886534	−	0.462664i	$-0.153106\pi$
$251$	28.0907	1.77307	0.886534	+	0.462664i	$0.153106\pi$
$252$	1.82731	0.115110
$253$	4.27367	0.268683
$254$	−11.8571	−0.743984
$255$	−1.91347	−0.119826
$256$	−27.3673	−1.71045
$257$	30.0704	1.87574	0.937870	−	0.346987i	$-0.112795\pi$
$257$	30.0704	1.87574	0.937870	+	0.346987i	$0.112795\pi$
$258$	−19.0949	−1.18879
$259$	−8.04530	−0.499911
$260$	−4.59079	−0.284709
$261$	−1.41172	−0.0873832
$262$	−9.26777	−0.572565
$263$	−10.6895	−0.659141	−0.329571	−	0.944131i	$-0.606904\pi$
$263$	−10.6895	−0.659141	−0.329571	+	0.944131i	$0.606904\pi$
$264$	−25.3633	−1.56100
$265$	−1.01275	−0.0622127
$266$	20.9897	1.28696
$267$	−18.5213	−1.13349
$268$	−13.3089	−0.812971
$269$	−17.1571	−1.04609	−0.523043	−	0.852306i	$-0.675203\pi$
$269$	−17.1571	−1.04609	−0.523043	+	0.852306i	$0.675203\pi$
$270$	−12.8273	−0.780643
$271$	−2.87675	−0.174750	−0.0873750	−	0.996175i	$-0.527848\pi$
$271$	−2.87675	−0.174750	−0.0873750	+	0.996175i	$0.527848\pi$
$272$	2.62831	0.159365
$273$	−2.83892	−0.171819
$274$	−5.04344	−0.304686
$275$	−15.6674	−0.944781
$276$	6.57743	0.395915
$277$	−20.5033	−1.23192	−0.615962	−	0.787776i	$-0.711233\pi$
$277$	−20.5033	−1.23192	−0.615962	+	0.787776i	$0.711233\pi$
$278$	22.4611	1.34713
$279$	−1.56210	−0.0935206
$280$	−5.46470	−0.326578
$281$	−18.5394	−1.10597	−0.552984	−	0.833192i	$-0.686511\pi$
$281$	−18.5394	−1.10597	−0.552984	+	0.833192i	$0.686511\pi$
$282$	8.11505	0.483244
$283$	−6.45245	−0.383558	−0.191779	−	0.981438i	$-0.561426\pi$
$283$	−6.45245	−0.383558	−0.191779	+	0.981438i	$0.561426\pi$
$284$	22.9063	1.35924
$285$	−10.2083	−0.604687
$286$	−11.7240	−0.693254
$287$	1.64984	0.0973869
$288$	−0.998542	−0.0588397
$289$	−15.5730	−0.916059
$290$	9.23795	0.542471
$291$	20.3411	1.19242
$292$	−44.2900	−2.59188
$293$	−2.30664	−0.134756	−0.0673778	−	0.997728i	$-0.521463\pi$
$293$	−2.30664	−0.134756	−0.0673778	+	0.997728i	$0.521463\pi$
$294$	19.7247	1.15037
$295$	3.66385	0.213318
$296$	−23.3694	−1.35832
$297$	−21.2305	−1.23192
$298$	17.7357	1.02740
$299$	1.38948	0.0803560
$300$	−24.1131	−1.39217
$301$	−6.80930	−0.392481
$302$	−41.1990	−2.37073
$303$	18.6673	1.07241
$304$	14.0219	0.804213
$305$	8.18478	0.468659
$306$	1.02263	0.0584600
$307$	−32.9828	−1.88242	−0.941212	−	0.337815i	$-0.890312\pi$
$307$	−32.9828	−1.88242	−0.941212	+	0.337815i	$0.890312\pi$
$308$	−19.7908	−1.12769
$309$	7.41912	0.422059
$310$	10.2220	0.580572
$311$	5.31422	0.301342	0.150671	−	0.988584i	$-0.451857\pi$
$311$	5.31422	0.301342	0.150671	+	0.988584i	$0.451857\pi$
$312$	−8.24628	−0.466854
$313$	−5.65641	−0.319719	−0.159860	−	0.987140i	$-0.551104\pi$
$313$	−5.65641	−0.319719	−0.159860	+	0.987140i	$0.551104\pi$
$314$	−14.2973	−0.806841
$315$	−0.488997	−0.0275519
$316$	−46.1079	−2.59377
$317$	3.34255	0.187736	0.0938681	−	0.995585i	$-0.470077\pi$
$317$	3.34255	0.187736	0.0938681	+	0.995585i	$0.470077\pi$
$318$	−3.98057	−0.223219
$319$	15.2898	0.856062
$320$	10.8716	0.607743
$321$	24.6029	1.37320
$322$	3.61913	0.201686
$323$	7.61294	0.423595
$324$	−28.7070	−1.59483
$325$	−5.09390	−0.282559
$326$	48.0689	2.66229
$327$	5.91611	0.327162
$328$	4.79233	0.264612
$329$	2.89385	0.159543
$330$	14.8516	0.817553
$331$	−8.30956	−0.456735	−0.228367	−	0.973575i	$-0.573339\pi$
$331$	−8.30956	−0.456735	−0.228367	+	0.973575i	$0.573339\pi$
$332$	53.7619	2.95057
$333$	−2.09116	−0.114595
$334$	−49.7447	−2.72191
$335$	3.56154	0.194587
$336$	−4.93976	−0.269486
$337$	4.26862	0.232526	0.116263	−	0.993218i	$-0.462908\pi$
$337$	4.26862	0.232526	0.116263	+	0.993218i	$0.462908\pi$
$338$	27.1799	1.47839
$339$	7.57388	0.411357
$340$	−4.33695	−0.235204
$341$	16.9185	0.916188
$342$	5.45571	0.295011
$343$	16.7047	0.901968
$344$	−19.7791	−1.06642
$345$	−1.76016	−0.0947636
$346$	14.2422	0.765664
$347$	23.7556	1.27527	0.637634	−	0.770340i	$-0.279913\pi$
$347$	23.7556	1.27527	0.637634	+	0.770340i	$0.279913\pi$
$348$	23.5319	1.26144
$349$	−31.4886	−1.68555	−0.842774	−	0.538268i	$-0.819079\pi$
$349$	−31.4886	−1.68555	−0.842774	+	0.538268i	$0.819079\pi$
$350$	−13.2679	−0.709198
$351$	−6.90259	−0.368433
$352$	10.8148	0.576431
$353$	−0.538111	−0.0286408	−0.0143204	−	0.999897i	$-0.504558\pi$
$353$	−0.538111	−0.0286408	−0.0143204	+	0.999897i	$0.504558\pi$
$354$	14.4006	0.765383
$355$	−6.12985	−0.325338
$356$	−41.9793	−2.22490
$357$	−2.68195	−0.141944
$358$	−43.1638	−2.28128
$359$	−7.98560	−0.421464	−0.210732	−	0.977544i	$-0.567585\pi$
$359$	−7.98560	−0.421464	−0.210732	+	0.977544i	$0.567585\pi$
$360$	−1.42040	−0.0748618
$361$	21.6148	1.13762
$362$	−47.3017	−2.48612
$363$	6.70496	0.351919
$364$	−6.43452	−0.337261
$365$	11.8522	0.620375
$366$	32.1699	1.68155
$367$	24.6772	1.28814	0.644070	−	0.764967i	$-0.277245\pi$
$367$	24.6772	1.28814	0.644070	+	0.764967i	$0.277245\pi$
$368$	2.41772	0.126032
$369$	0.428831	0.0223241
$370$	13.6841	0.711400
$371$	−1.41949	−0.0736960
$372$	26.0386	1.35004
$373$	−20.8355	−1.07882	−0.539410	−	0.842043i	$-0.681353\pi$
$373$	−20.8355	−1.07882	−0.539410	+	0.842043i	$0.681353\pi$
$374$	−11.0757	−0.572712
$375$	14.4618	0.746807
$376$	8.40585	0.433499
$377$	4.97111	0.256025
$378$	−17.9789	−0.924735
$379$	10.8518	0.557417	0.278709	−	0.960376i	$-0.410094\pi$
$379$	10.8518	0.557417	0.278709	+	0.960376i	$0.410094\pi$
$380$	−23.1375	−1.18693
$381$	8.08268	0.414088
$382$	55.9237	2.86130
$383$	−0.999478	−0.0510710	−0.0255355	−	0.999674i	$-0.508129\pi$
$383$	−0.999478	−0.0510710	−0.0255355	+	0.999674i	$0.508129\pi$
$384$	33.6926	1.71937
$385$	5.29613	0.269916
$386$	−63.7675	−3.24568
$387$	−1.76989	−0.0899688
$388$	46.1039	2.34057
$389$	18.5799	0.942038	0.471019	−	0.882123i	$-0.343886\pi$
$389$	18.5799	0.942038	0.471019	+	0.882123i	$0.343886\pi$
$390$	4.82865	0.244508
$391$	1.31265	0.0663838
$392$	20.4315	1.03195
$393$	6.31758	0.318680
$394$	52.3361	2.63666
$395$	12.3387	0.620828
$396$	−5.14409	−0.258500
$397$	30.3144	1.52143	0.760717	−	0.649084i	$-0.224848\pi$
$397$	30.3144	1.52143	0.760717	+	0.649084i	$0.224848\pi$
$398$	−51.0460	−2.55871
$399$	−14.3081	−0.716301
$400$	−8.86345	−0.443173
$401$	37.3576	1.86555	0.932775	−	0.360459i	$-0.117380\pi$
$401$	37.3576	1.86555	0.932775	+	0.360459i	$0.117380\pi$
$402$	13.9985	0.698180
$403$	5.50066	0.274007
$404$	42.3102	2.10501
$405$	7.68214	0.381729
$406$	12.9481	0.642601
$407$	22.6485	1.12265
$408$	−7.79032	−0.385678
$409$	−27.7895	−1.37410	−0.687050	−	0.726610i	$-0.741095\pi$
$409$	−27.7895	−1.37410	−0.687050	+	0.726610i	$0.741095\pi$
$410$	−2.80617	−0.138587
$411$	3.43797	0.169583
$412$	16.8157	0.828452
$413$	5.13531	0.252692
$414$	0.940697	0.0462327
$415$	−14.3870	−0.706229
$416$	3.51618	0.172395
$417$	−15.3111	−0.749787
$418$	−59.0886	−2.89012
$419$	7.73759	0.378006	0.189003	−	0.981977i	$-0.439474\pi$
$419$	7.73759	0.378006	0.189003	+	0.981977i	$0.439474\pi$
$420$	8.15106	0.397731
$421$	30.2169	1.47268	0.736341	−	0.676610i	$-0.236552\pi$
$421$	30.2169	1.47268	0.736341	+	0.676610i	$0.236552\pi$
$422$	−35.5010	−1.72816
$423$	0.752180	0.0365722
$424$	−4.12321	−0.200241
$425$	−4.81224	−0.233428
$426$	−24.0931	−1.16731
$427$	11.4719	0.555165
$428$	55.7634	2.69543
$429$	7.99191	0.385853
$430$	11.5818	0.558522
$431$	34.2524	1.64988	0.824939	−	0.565222i	$-0.191209\pi$
$431$	34.2524	1.64988	0.824939	+	0.565222i	$0.191209\pi$
$432$	−12.0106	−0.577860
$433$	−36.0183	−1.73093	−0.865464	−	0.500971i	$-0.832976\pi$
$433$	−36.0183	−1.73093	−0.865464	+	0.500971i	$0.832976\pi$
$434$	14.3273	0.687734
$435$	−6.29725	−0.301930
$436$	13.4091	0.642180
$437$	7.00297	0.334998
$438$	46.5847	2.22590
$439$	20.2425	0.966123	0.483062	−	0.875586i	$-0.339525\pi$
$439$	20.2425	0.966123	0.483062	+	0.875586i	$0.339525\pi$
$440$	15.3838	0.733394
$441$	1.82827	0.0870606
$442$	−3.60101	−0.171283
$443$	−28.4706	−1.35268	−0.676340	−	0.736590i	$-0.736435\pi$
$443$	−28.4706	−1.35268	−0.676340	+	0.736590i	$0.736435\pi$
$444$	34.8574	1.65426
$445$	11.2339	0.532537
$446$	−39.7942	−1.88431
$447$	−12.0899	−0.571834
$448$	15.2378	0.719920
$449$	21.4256	1.01114	0.505568	−	0.862787i	$-0.331283\pi$
$449$	21.4256	1.01114	0.505568	+	0.862787i	$0.331283\pi$
$450$	−3.44863	−0.162570
$451$	−4.64450	−0.218701
$452$	17.1665	0.807444
$453$	28.0842	1.31951
$454$	−65.7405	−3.08535
$455$	1.72191	0.0807245
$456$	−41.5611	−1.94628
$457$	−2.93875	−0.137469	−0.0687345	−	0.997635i	$-0.521896\pi$
$457$	−2.93875	−0.137469	−0.0687345	+	0.997635i	$0.521896\pi$
$458$	37.5794	1.75597
$459$	−6.52092	−0.304371
$460$	−3.98946	−0.186010
$461$	15.7378	0.732982	0.366491	−	0.930422i	$-0.380559\pi$
$461$	15.7378	0.732982	0.366491	+	0.930422i	$0.380559\pi$
$462$	20.8162	0.968458
$463$	19.7845	0.919466	0.459733	−	0.888057i	$-0.347945\pi$
$463$	19.7845	0.919466	0.459733	+	0.888057i	$0.347945\pi$
$464$	8.64980	0.401557
$465$	−6.96807	−0.323136
$466$	−68.1353	−3.15631
$467$	8.34339	0.386086	0.193043	−	0.981190i	$-0.438164\pi$
$467$	8.34339	0.386086	0.193043	+	0.981190i	$0.438164\pi$
$468$	−1.67248	−0.0773105
$469$	4.99190	0.230505
$470$	−4.92209	−0.227039
$471$	9.74603	0.449074
$472$	14.9167	0.686595
$473$	19.1690	0.881392
$474$	48.4968	2.22753
$475$	−25.6732	−1.17796
$476$	−6.07874	−0.278618
$477$	−0.368957	−0.0168934
$478$	−1.05328	−0.0481759
$479$	−29.5028	−1.34802	−0.674009	−	0.738723i	$-0.735429\pi$
$479$	−29.5028	−1.34802	−0.674009	+	0.738723i	$0.735429\pi$
$480$	−4.45419	−0.203305
$481$	7.36364	0.335753
$482$	17.9166	0.816080
$483$	−2.46706	−0.112255
$484$	15.1970	0.690775
$485$	−12.3376	−0.560224
$486$	−8.84670	−0.401294
$487$	6.58140	0.298232	0.149116	−	0.988820i	$-0.452357\pi$
$487$	6.58140	0.298232	0.149116	+	0.988820i	$0.452357\pi$
$488$	33.3228	1.50845
$489$	−32.7672	−1.48178
$490$	−11.9638	−0.540469
$491$	3.50101	0.157998	0.0789991	−	0.996875i	$-0.474828\pi$
$491$	3.50101	0.157998	0.0789991	+	0.996875i	$0.474828\pi$
$492$	−7.14816	−0.322264
$493$	4.69624	0.211508
$494$	−19.2113	−0.864357
$495$	1.37659	0.0618730
$496$	9.57122	0.429760
$497$	−8.59168	−0.385390
$498$	−56.5474	−2.53395
$499$	8.20477	0.367296	0.183648	−	0.982992i	$-0.441209\pi$
$499$	8.20477	0.367296	0.183648	+	0.982992i	$0.441209\pi$
$500$	32.7784	1.46589
$501$	33.9096	1.51497
$502$	−66.9674	−2.98890
$503$	44.4308	1.98107	0.990536	−	0.137251i	$-0.0438268\pi$
$503$	44.4308	1.98107	0.990536	+	0.137251i	$0.0438268\pi$
$504$	−1.99086	−0.0886798
$505$	−11.3224	−0.503842
$506$	−10.1883	−0.452926
$507$	−18.5277	−0.822846
$508$	18.3197	0.812806
$509$	9.31101	0.412703	0.206352	−	0.978478i	$-0.433841\pi$
$509$	9.31101	0.412703	0.206352	+	0.978478i	$0.433841\pi$
$510$	4.56166	0.201993
$511$	16.6123	0.734884
$512$	23.7771	1.05081
$513$	−34.7889	−1.53597
$514$	−71.6870	−3.16198
$515$	−4.49998	−0.198293
$516$	29.5022	1.29876
$517$	−8.14656	−0.358285
$518$	19.1798	0.842711
$519$	−9.70849	−0.426155
$520$	5.00169	0.219338
$521$	−22.8124	−0.999431	−0.499716	−	0.866190i	$-0.666562\pi$
$521$	−22.8124	−0.999431	−0.499716	+	0.866190i	$0.666562\pi$
$522$	3.36550	0.147304
$523$	−32.9871	−1.44242	−0.721212	−	0.692715i	$-0.756415\pi$
$523$	−32.9871	−1.44242	−0.721212	+	0.692715i	$0.756415\pi$
$524$	14.3190	0.625530
$525$	9.04434	0.394727
$526$	25.4834	1.11113
$527$	5.19651	0.226363
$528$	13.9060	0.605182
$529$	−21.7925	−0.947501
$530$	2.41437	0.104873
$531$	1.33479	0.0579247
$532$	−32.4299	−1.40601
$533$	−1.51005	−0.0654075
$534$	44.1543	1.91074
$535$	−14.9226	−0.645160
$536$	14.5001	0.626309
$537$	29.4235	1.26972
$538$	40.9020	1.76341
$539$	−19.8013	−0.852902
$540$	19.8186	0.852857
$541$	29.7693	1.27988	0.639942	−	0.768423i	$-0.278958\pi$
$541$	29.7693	1.27988	0.639942	+	0.768423i	$0.278958\pi$
$542$	6.85809	0.294580
$543$	32.2442	1.38373
$544$	3.32176	0.142419
$545$	−3.58835	−0.153708
$546$	6.76791	0.289640
$547$	29.7546	1.27222	0.636108	−	0.771600i	$-0.280543\pi$
$547$	29.7546	1.27222	0.636108	+	0.771600i	$0.280543\pi$
$548$	7.79230	0.332871
$549$	2.98182	0.127261
$550$	37.3507	1.59264
$551$	25.0543	1.06735
$552$	−7.16614	−0.305011
$553$	17.2941	0.735421
$554$	48.8793	2.07668
$555$	−9.32803	−0.395953
$556$	−34.7032	−1.47174
$557$	16.6704	0.706349	0.353174	−	0.935558i	$-0.385102\pi$
$557$	16.6704	0.706349	0.353174	+	0.935558i	$0.385102\pi$
$558$	3.72401	0.157650
$559$	6.23236	0.263601
$560$	2.99615	0.126611
$561$	7.55001	0.318762
$562$	44.1974	1.86435
$563$	9.27289	0.390806	0.195403	−	0.980723i	$-0.437399\pi$
$563$	9.27289	0.390806	0.195403	+	0.980723i	$0.437399\pi$
$564$	−12.5380	−0.527947
$565$	−4.59385	−0.193265
$566$	15.3825	0.646573
$567$	10.7674	0.452188
$568$	−24.9565	−1.04715
$569$	−31.5143	−1.32115	−0.660573	−	0.750762i	$-0.729687\pi$
$569$	−31.5143	−1.32115	−0.660573	+	0.750762i	$0.729687\pi$
$570$	24.3363	1.01933
$571$	17.4098	0.728579	0.364290	−	0.931286i	$-0.381312\pi$
$571$	17.4098	0.728579	0.364290	+	0.931286i	$0.381312\pi$
$572$	18.1140	0.757383
$573$	−38.1216	−1.59255
$574$	−3.93317	−0.164167
$575$	−4.42667	−0.184605
$576$	3.96067	0.165028
$577$	1.37427	0.0572115	0.0286058	−	0.999591i	$-0.490893\pi$
$577$	1.37427	0.0572115	0.0286058	+	0.999591i	$0.490893\pi$
$578$	37.1256	1.54422
$579$	43.4685	1.80649
$580$	−14.2730	−0.592653
$581$	−20.1650	−0.836585
$582$	−48.4926	−2.01008
$583$	3.99602	0.165498
$584$	48.2541	1.99677
$585$	0.447565	0.0185045
$586$	5.49898	0.227161
$587$	0.883022	0.0364462	0.0182231	−	0.999834i	$-0.494199\pi$
$587$	0.883022	0.0364462	0.0182231	+	0.999834i	$0.494199\pi$
$588$	−30.4754	−1.25678
$589$	27.7232	1.14231
$590$	−8.73451	−0.359594
$591$	−35.6761	−1.46752
$592$	12.8128	0.526604
$593$	−25.1310	−1.03201	−0.516003	−	0.856587i	$-0.672581\pi$
$593$	−25.1310	−1.03201	−0.516003	+	0.856587i	$0.672581\pi$
$594$	50.6128	2.07667
$595$	1.62670	0.0666883
$596$	−27.4023	−1.12244
$597$	34.7966	1.42413
$598$	−3.31249	−0.135458
$599$	32.2298	1.31687	0.658437	−	0.752636i	$-0.271218\pi$
$599$	32.2298	1.31687	0.658437	+	0.752636i	$0.271218\pi$
$600$	26.2713	1.07252
$601$	17.4491	0.711763	0.355881	−	0.934531i	$-0.384181\pi$
$601$	17.4491	0.711763	0.355881	+	0.934531i	$0.384181\pi$
$602$	16.2332	0.661615
$603$	1.29751	0.0528387
$604$	63.6539	2.59004
$605$	−4.06681	−0.165339
$606$	−44.5024	−1.80779
$607$	19.0974	0.775139	0.387569	−	0.921841i	$-0.373315\pi$
$607$	19.0974	0.775139	0.387569	+	0.921841i	$0.373315\pi$
$608$	17.7215	0.718701
$609$	−8.82632	−0.357661
$610$	−19.5123	−0.790029
$611$	−2.64866	−0.107153
$612$	−1.58000	−0.0638679
$613$	−9.19146	−0.371240	−0.185620	−	0.982622i	$-0.559429\pi$
$613$	−9.19146	−0.371240	−0.185620	+	0.982622i	$0.559429\pi$
$614$	78.6300	3.17325
$615$	1.91289	0.0771350
$616$	21.5622	0.868765
$617$	−11.0770	−0.445942	−0.222971	−	0.974825i	$-0.571576\pi$
$617$	−11.0770	−0.445942	−0.222971	+	0.974825i	$0.571576\pi$
$618$	−17.6870	−0.711475
$619$	−27.6053	−1.10955	−0.554775	−	0.832001i	$-0.687195\pi$
$619$	−27.6053	−1.10955	−0.554775	+	0.832001i	$0.687195\pi$
$620$	−15.7934	−0.634278
$621$	−5.99845	−0.240709
$622$	−12.6690	−0.507979
$623$	15.7456	0.630834
$624$	4.52122	0.180994
$625$	11.3705	0.454822
$626$	13.4847	0.538958
$627$	40.2791	1.60859
$628$	22.0898	0.881478
$629$	6.95648	0.277373
$630$	1.16576	0.0464448
$631$	−13.3080	−0.529784	−0.264892	−	0.964278i	$-0.585336\pi$
$631$	−13.3080	−0.529784	−0.264892	+	0.964278i	$0.585336\pi$
$632$	50.2347	1.99823
$633$	24.2000	0.961864
$634$	−7.96854	−0.316471
$635$	−4.90245	−0.194548
$636$	6.15012	0.243868
$637$	−6.43793	−0.255080
$638$	−36.4504	−1.44308
$639$	−2.23318	−0.0883431
$640$	−20.4359	−0.807799
$641$	20.3014	0.801858	0.400929	−	0.916109i	$-0.368687\pi$
$641$	20.3014	0.801858	0.400929	+	0.916109i	$0.368687\pi$
$642$	−58.6526	−2.31483
$643$	−29.2420	−1.15319	−0.576597	−	0.817029i	$-0.695620\pi$
$643$	−29.2420	−1.15319	−0.576597	+	0.817029i	$0.695620\pi$
$644$	−5.59169	−0.220344
$645$	−7.89496	−0.310864
$646$	−18.1490	−0.714064
$647$	−1.00324	−0.0394416	−0.0197208	−	0.999806i	$-0.506278\pi$
$647$	−1.00324	−0.0394416	−0.0197208	+	0.999806i	$0.506278\pi$
$648$	31.2763	1.22865
$649$	−14.4565	−0.567468
$650$	12.1437	0.476316
$651$	−9.76655	−0.382781
$652$	−74.2682	−2.90857
$653$	9.10509	0.356310	0.178155	−	0.984002i	$-0.442987\pi$
$653$	9.10509	0.356310	0.178155	+	0.984002i	$0.442987\pi$
$654$	−14.1038	−0.551504
$655$	−3.83185	−0.149723
$656$	−2.62751	−0.102587
$657$	4.31792	0.168458
$658$	−6.89887	−0.268946
$659$	−9.61728	−0.374636	−0.187318	−	0.982299i	$-0.559980\pi$
$659$	−9.61728	−0.374636	−0.187318	+	0.982299i	$0.559980\pi$
$660$	−22.9462	−0.893181
$661$	−19.9268	−0.775064	−0.387532	−	0.921856i	$-0.626672\pi$
$661$	−19.9268	−0.775064	−0.387532	+	0.921856i	$0.626672\pi$
$662$	19.8098	0.769928
$663$	2.45471	0.0953330
$664$	−58.5738	−2.27310
$665$	8.67841	0.336534
$666$	4.98527	0.193175
$667$	4.31996	0.167270
$668$	76.8574	2.97370
$669$	27.1266	1.04877
$670$	−8.49060	−0.328021
$671$	−32.2948	−1.24673
$672$	−6.24307	−0.240832
$673$	−2.85519	−0.110060	−0.0550298	−	0.998485i	$-0.517525\pi$
$673$	−2.85519	−0.110060	−0.0550298	+	0.998485i	$0.517525\pi$
$674$	−10.1763	−0.391975
$675$	21.9905	0.846416
$676$	−41.9939	−1.61515
$677$	7.85158	0.301761	0.150880	−	0.988552i	$-0.451789\pi$
$677$	7.85158	0.301761	0.150880	+	0.988552i	$0.451789\pi$
$678$	−18.0559	−0.693433
$679$	−17.2926	−0.663630
$680$	4.72513	0.181200
$681$	44.8134	1.71725
$682$	−40.3332	−1.54444
$683$	−4.40699	−0.168629	−0.0843145	−	0.996439i	$-0.526870\pi$
$683$	−4.40699	−0.168629	−0.0843145	+	0.996439i	$0.526870\pi$
$684$	−8.42928	−0.322301
$685$	−2.08526	−0.0796738
$686$	−39.8235	−1.52047
$687$	−25.6168	−0.977342
$688$	10.8444	0.413438
$689$	1.29921	0.0494961
$690$	4.19616	0.159745
$691$	−3.20181	−0.121803	−0.0609013	−	0.998144i	$-0.519398\pi$
$691$	−3.20181	−0.121803	−0.0609013	+	0.998144i	$0.519398\pi$
$692$	−22.0047	−0.836492
$693$	1.92945	0.0732936
$694$	−56.6327	−2.14975
$695$	9.28675	0.352267
$696$	−25.6380	−0.971807
$697$	−1.42655	−0.0540346
$698$	75.0680	2.84137
$699$	46.4459	1.75675
$700$	20.4993	0.774803
$701$	14.0982	0.532483	0.266242	−	0.963906i	$-0.414218\pi$
$701$	14.0982	0.532483	0.266242	+	0.963906i	$0.414218\pi$
$702$	16.4556	0.621076
$703$	37.1126	1.39973
$704$	−42.8964	−1.61672
$705$	3.35525	0.126366
$706$	1.28284	0.0482804
$707$	−15.8697	−0.596842
$708$	−22.2494	−0.836185
$709$	47.5619	1.78622	0.893112	−	0.449835i	$-0.148517\pi$
$709$	47.5619	1.78622	0.893112	+	0.449835i	$0.148517\pi$
$710$	14.6134	0.548430
$711$	4.49515	0.168581
$712$	45.7366	1.71405
$713$	4.78015	0.179018
$714$	6.39368	0.239278
$715$	−4.84740	−0.181282
$716$	66.6896	2.49231
$717$	0.717991	0.0268139
$718$	19.0374	0.710471
$719$	31.9606	1.19193	0.595965	−	0.803011i	$-0.296770\pi$
$719$	31.9606	1.19193	0.595965	+	0.803011i	$0.296770\pi$
$720$	0.778770	0.0290230
$721$	−6.30724	−0.234894
$722$	−51.5291	−1.91771
$723$	−12.2133	−0.454216
$724$	73.0829	2.71610
$725$	−15.8371	−0.588177
$726$	−15.9844	−0.593238
$727$	7.63297	0.283091	0.141546	−	0.989932i	$-0.454793\pi$
$727$	7.63297	0.283091	0.141546	+	0.989932i	$0.454793\pi$
$728$	7.01044	0.259824
$729$	29.4119	1.08933
$730$	−28.2554	−1.04578
$731$	5.88775	0.217766
$732$	−49.7037	−1.83710
$733$	−46.4847	−1.71695	−0.858475	−	0.512855i	$-0.828588\pi$
$733$	−46.4847	−1.71695	−0.858475	+	0.512855i	$0.828588\pi$
$734$	−58.8298	−2.17145
$735$	8.15537	0.300815
$736$	3.05561	0.112631
$737$	−14.0528	−0.517642
$738$	−1.02232	−0.0376322
$739$	−34.3813	−1.26474	−0.632369	−	0.774667i	$-0.717917\pi$
$739$	−34.3813	−1.26474	−0.632369	+	0.774667i	$0.717917\pi$
$740$	−21.1424	−0.777208
$741$	13.0958	0.481086
$742$	3.38401	0.124231
$743$	−32.4758	−1.19142	−0.595711	−	0.803199i	$-0.703130\pi$
$743$	−32.4758	−1.19142	−0.595711	+	0.803199i	$0.703130\pi$
$744$	−28.3691	−1.04006
$745$	7.33301	0.268661
$746$	49.6712	1.81859
$747$	−5.24135	−0.191771
$748$	17.1124	0.625691
$749$	−20.9157	−0.764244
$750$	−34.4766	−1.25891
$751$	−2.00830	−0.0732840	−0.0366420	−	0.999328i	$-0.511666\pi$
$751$	−2.00830	−0.0732840	−0.0366420	+	0.999328i	$0.511666\pi$
$752$	−4.60871	−0.168062
$753$	45.6498	1.66357
$754$	−11.8510	−0.431587
$755$	−17.0341	−0.619935
$756$	27.7780	1.01028
$757$	−10.1703	−0.369644	−0.184822	−	0.982772i	$-0.559171\pi$
$757$	−10.1703	−0.369644	−0.184822	+	0.982772i	$0.559171\pi$
$758$	−25.8703	−0.939651
$759$	6.94508	0.252091
$760$	25.2084	0.914405
$761$	−16.3519	−0.592756	−0.296378	−	0.955071i	$-0.595779\pi$
$761$	−16.3519	−0.592756	−0.296378	+	0.955071i	$0.595779\pi$
$762$	−19.2689	−0.698038
$763$	−5.02948	−0.182080
$764$	−86.4041	−3.12599
$765$	0.422818	0.0152870
$766$	2.38273	0.0860915
$767$	−4.70020	−0.169714
$768$	−44.4742	−1.60482
$769$	−9.09299	−0.327902	−0.163951	−	0.986469i	$-0.552424\pi$
$769$	−9.09299	−0.327902	−0.163951	+	0.986469i	$0.552424\pi$
$770$	−12.6258	−0.455003
$771$	48.8670	1.75990
$772$	98.5231	3.54592
$773$	40.6120	1.46071	0.730357	−	0.683066i	$-0.239354\pi$
$773$	40.6120	1.46071	0.730357	+	0.683066i	$0.239354\pi$
$774$	4.21938	0.151662
$775$	−17.5242	−0.629488
$776$	−50.2304	−1.80316
$777$	−13.0743	−0.469038
$778$	−44.2939	−1.58801
$779$	−7.61062	−0.272679
$780$	−7.46044	−0.267126
$781$	24.1866	0.865466
$782$	−3.12933	−0.111905
$783$	−21.4604	−0.766933
$784$	−11.2021	−0.400074
$785$	−5.91134	−0.210985
$786$	−15.0609	−0.537205
$787$	−25.1104	−0.895090	−0.447545	−	0.894262i	$-0.647702\pi$
$787$	−25.1104	−0.895090	−0.447545	+	0.894262i	$0.647702\pi$
$788$	−80.8612	−2.88056
$789$	−17.3713	−0.618435
$790$	−29.4152	−1.04654
$791$	−6.43881	−0.228938
$792$	5.60451	0.199148
$793$	−10.4999	−0.372863
$794$	−72.2686	−2.56472
$795$	−1.64581	−0.0583707
$796$	78.8680	2.79540
$797$	−33.6657	−1.19250	−0.596250	−	0.802799i	$-0.703343\pi$
$797$	−33.6657	−1.19250	−0.596250	+	0.802799i	$0.703343\pi$
$798$	34.1101	1.20748
$799$	−2.50221	−0.0885218
$800$	−11.2020	−0.396050
$801$	4.09264	0.144606
$802$	−89.0595	−3.14480
$803$	−46.7656	−1.65032
$804$	−21.6281	−0.762765
$805$	1.49637	0.0527400
$806$	−13.1134	−0.461900
$807$	−27.8818	−0.981485
$808$	−46.0972	−1.62169
$809$	−24.3264	−0.855269	−0.427635	−	0.903952i	$-0.640653\pi$
$809$	−24.3264	−0.855269	−0.427635	+	0.903952i	$0.640653\pi$
$810$	−18.3140	−0.643488
$811$	−30.2095	−1.06080	−0.530400	−	0.847747i	$-0.677958\pi$
$811$	−30.2095	−1.06080	−0.530400	+	0.847747i	$0.677958\pi$
$812$	−20.0052	−0.702045
$813$	−4.67496	−0.163958
$814$	−53.9934	−1.89247
$815$	19.8746	0.696176
$816$	4.27123	0.149523
$817$	31.4109	1.09893
$818$	66.2493	2.31635
$819$	0.627314	0.0219201
$820$	4.33563	0.151407
$821$	−48.5910	−1.69584	−0.847918	−	0.530127i	$-0.822144\pi$
$821$	−48.5910	−1.69584	−0.847918	+	0.530127i	$0.822144\pi$
$822$	−8.19603	−0.285869
$823$	1.21203	0.0422486	0.0211243	−	0.999777i	$-0.493275\pi$
$823$	1.21203	0.0422486	0.0211243	+	0.999777i	$0.493275\pi$
$824$	−18.3208	−0.638235
$825$	−25.4609	−0.886436
$826$	−12.2424	−0.425969
$827$	47.2210	1.64203	0.821017	−	0.570904i	$-0.193407\pi$
$827$	47.2210	1.64203	0.821017	+	0.570904i	$0.193407\pi$
$828$	−1.45341	−0.0505095
$829$	−23.7155	−0.823673	−0.411836	−	0.911258i	$-0.635112\pi$
$829$	−23.7155	−0.823673	−0.411836	+	0.911258i	$0.635112\pi$
$830$	34.2981	1.19051
$831$	−33.3196	−1.15585
$832$	−13.9468	−0.483517
$833$	−6.08195	−0.210727
$834$	36.5012	1.26393
$835$	−20.5675	−0.711766
$836$	91.2941	3.15747
$837$	−23.7465	−0.820799
$838$	−18.4462	−0.637213
$839$	−49.4138	−1.70595	−0.852977	−	0.521948i	$-0.825206\pi$
$839$	−49.4138	−1.70595	−0.852977	+	0.521948i	$0.825206\pi$
$840$	−8.88061	−0.306410
$841$	−13.5446	−0.467056
$842$	−72.0363	−2.48253
$843$	−30.1281	−1.03767
$844$	54.8503	1.88802
$845$	11.2378	0.386591
$846$	−1.79318	−0.0616507
$847$	−5.70010	−0.195858
$848$	2.26065	0.0776311
$849$	−10.4858	−0.359871
$850$	11.4722	0.393495
$851$	6.39911	0.219359
$852$	37.2247	1.27530
$853$	34.1047	1.16772	0.583861	−	0.811854i	$-0.301541\pi$
$853$	34.1047	1.16772	0.583861	+	0.811854i	$0.301541\pi$
$854$	−27.3487	−0.935854
$855$	2.25572	0.0771440
$856$	−60.7545	−2.07655
$857$	45.9077	1.56818	0.784089	−	0.620649i	$-0.213131\pi$
$857$	45.9077	1.56818	0.784089	+	0.620649i	$0.213131\pi$
$858$	−19.0525	−0.650441
$859$	30.0054	1.02377	0.511886	−	0.859053i	$-0.328947\pi$
$859$	30.0054	1.02377	0.511886	+	0.859053i	$0.328947\pi$
$860$	−17.8942	−0.610188
$861$	2.68113	0.0913727
$862$	−81.6567	−2.78124
$863$	33.6886	1.14677	0.573386	−	0.819285i	$-0.305630\pi$
$863$	33.6886	1.14677	0.573386	+	0.819285i	$0.305630\pi$
$864$	−15.1795	−0.516416
$865$	5.88857	0.200217
$866$	85.8666	2.91787
$867$	−25.3075	−0.859487
$868$	−22.1363	−0.751354
$869$	−48.6851	−1.65153
$870$	15.0125	0.508970
$871$	−4.56895	−0.154813
$872$	−14.6093	−0.494732
$873$	−4.49476	−0.152124
$874$	−16.6949	−0.564713
$875$	−12.2945	−0.415630
$876$	−71.9750	−2.43181
$877$	22.0177	0.743485	0.371743	−	0.928336i	$-0.378760\pi$
$877$	22.0177	0.743485	0.371743	+	0.928336i	$0.378760\pi$
$878$	−48.2576	−1.62862
$879$	−3.74850	−0.126434
$880$	−8.43454	−0.284328
$881$	51.8498	1.74686	0.873432	−	0.486947i	$-0.161889\pi$
$881$	51.8498	1.74686	0.873432	+	0.486947i	$0.161889\pi$
$882$	−4.35855	−0.146760
$883$	−20.5448	−0.691386	−0.345693	−	0.938348i	$-0.612356\pi$
$883$	−20.5448	−0.691386	−0.345693	+	0.938348i	$0.612356\pi$
$884$	5.56370	0.187127
$885$	5.95407	0.200144
$886$	67.8731	2.28024
$887$	−23.7931	−0.798893	−0.399447	−	0.916756i	$-0.630798\pi$
$887$	−23.7931	−0.798893	−0.399447	+	0.916756i	$0.630798\pi$
$888$	−37.9773	−1.27443
$889$	−6.87135	−0.230458
$890$	−26.7813	−0.897711
$891$	−30.3116	−1.01548
$892$	61.4835	2.05862
$893$	−13.3492	−0.446714
$894$	28.8221	0.963954
$895$	−17.8465	−0.596543
$896$	−28.6432	−0.956903
$897$	2.25803	0.0753935
$898$	−51.0780	−1.70449
$899$	17.1018	0.570376
$900$	5.32826	0.177609
$901$	1.22738	0.0408898
$902$	11.0724	0.368669
$903$	−11.0657	−0.368243
$904$	−18.7030	−0.622051
$905$	−19.5574	−0.650109
$906$	−66.9519	−2.22433
$907$	30.1290	1.00042	0.500208	−	0.865905i	$-0.333257\pi$
$907$	30.1290	1.00042	0.500208	+	0.865905i	$0.333257\pi$
$908$	101.571	3.37077
$909$	−4.12491	−0.136814
$910$	−4.10499	−0.136079
$911$	−37.0846	−1.22867	−0.614334	−	0.789046i	$-0.710575\pi$
$911$	−37.0846	−1.22867	−0.614334	+	0.789046i	$0.710575\pi$
$912$	22.7869	0.754549
$913$	56.7670	1.87871
$914$	7.00590	0.231735
$915$	13.3010	0.439717
$916$	−58.0615	−1.91841
$917$	−5.37078	−0.177359
$918$	15.5457	0.513084
$919$	28.0924	0.926682	0.463341	−	0.886180i	$-0.346651\pi$
$919$	28.0924	0.926682	0.463341	+	0.886180i	$0.346651\pi$
$920$	4.34654	0.143301
$921$	−53.5998	−1.76617
$922$	−37.5184	−1.23560
$923$	7.86372	0.258838
$924$	−32.1618	−1.05805
$925$	−23.4594	−0.771339
$926$	−47.1658	−1.54996
$927$	−1.63940	−0.0538449
$928$	10.9320	0.358859
$929$	−14.4713	−0.474789	−0.237394	−	0.971413i	$-0.576293\pi$
$929$	−14.4713	−0.474789	−0.237394	+	0.971413i	$0.576293\pi$
$930$	16.6117	0.544718
$931$	−32.4470	−1.06341
$932$	105.271	3.44828
$933$	8.63607	0.282732
$934$	−19.8904	−0.650834
$935$	−4.57937	−0.149761
$936$	1.82218	0.0595597
$937$	−23.5798	−0.770320	−0.385160	−	0.922850i	$-0.625854\pi$
$937$	−23.5798	−0.770320	−0.385160	+	0.922850i	$0.625854\pi$
$938$	−11.9006	−0.388567
$939$	−9.19215	−0.299975
$940$	7.60480	0.248041
$941$	−14.3974	−0.469342	−0.234671	−	0.972075i	$-0.575401\pi$
$941$	−14.3974	−0.469342	−0.234671	+	0.972075i	$0.575401\pi$
$942$	−23.2343	−0.757013
$943$	−1.31226	−0.0427329
$944$	−8.17841	−0.266185
$945$	−7.43356	−0.241814
$946$	−45.6984	−1.48578
$947$	−32.4809	−1.05549	−0.527744	−	0.849403i	$-0.676962\pi$
$947$	−32.4809	−1.05549	−0.527744	+	0.849403i	$0.676962\pi$
$948$	−74.9293	−2.43359
$949$	−15.2047	−0.493567
$950$	61.2041	1.98572
$951$	5.43193	0.176142
$952$	6.62281	0.214646
$953$	−27.6339	−0.895150	−0.447575	−	0.894246i	$-0.647712\pi$
$953$	−27.6339	−0.895150	−0.447575	+	0.894246i	$0.647712\pi$
$954$	0.879583	0.0284776
$955$	23.1222	0.748217
$956$	1.62736	0.0526324
$957$	24.8472	0.803195
$958$	70.3339	2.27239
$959$	−2.92274	−0.0943800
$960$	17.6673	0.570211
$961$	−12.0765	−0.389563
$962$	−17.5547	−0.565986
$963$	−5.43648	−0.175188
$964$	−27.6818	−0.891572
$965$	−26.3653	−0.848730
$966$	5.88141	0.189231
$967$	30.0821	0.967374	0.483687	−	0.875241i	$-0.339297\pi$
$967$	30.0821	0.967374	0.483687	+	0.875241i	$0.339297\pi$
$968$	−16.5572	−0.532170
$969$	12.3717	0.397436
$970$	29.4126	0.944382
$971$	−0.390165	−0.0125210	−0.00626050	−	0.999980i	$-0.501993\pi$
$971$	−0.390165	−0.0125210	−0.00626050	+	0.999980i	$0.501993\pi$
$972$	13.6685	0.438416
$973$	13.0165	0.417288
$974$	−15.6899	−0.502736
$975$	−8.27803	−0.265109
$976$	−18.2700	−0.584808
$977$	−11.5655	−0.370012	−0.185006	−	0.982737i	$-0.559230\pi$
$977$	−11.5655	−0.370012	−0.185006	+	0.982737i	$0.559230\pi$
$978$	78.1161	2.49788
$979$	−44.3258	−1.41666
$980$	18.4845	0.590465
$981$	−1.30728	−0.0417382
$982$	−8.34630	−0.266341
$983$	7.44288	0.237391	0.118696	−	0.992931i	$-0.462129\pi$
$983$	7.44288	0.237391	0.118696	+	0.992931i	$0.462129\pi$
$984$	7.78795	0.248271
$985$	21.6389	0.689472
$986$	−11.1957	−0.356544
$987$	4.70276	0.149691
$988$	29.6821	0.944315
$989$	5.41601	0.172219
$990$	−3.28174	−0.104301
$991$	13.0064	0.413162	0.206581	−	0.978429i	$-0.433766\pi$
$991$	13.0064	0.413162	0.206581	+	0.978429i	$0.433766\pi$
$992$	12.0965	0.384064
$993$	−13.5038	−0.428529
$994$	20.4823	0.649660
$995$	−21.1055	−0.669089
$996$	87.3677	2.76835
$997$	−9.39388	−0.297507	−0.148754	−	0.988874i	$-0.547526\pi$
$997$	−9.39388	−0.297507	−0.148754	+	0.988874i	$0.547526\pi$
$998$	−19.5600	−0.619159
$999$	−31.7891	−1.00576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.c.1.16	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.c.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-2.38397 q^{2} +1.62509 q^{3} +3.68332 q^{4} -0.985677 q^{5} -3.87416 q^{6} -1.38154 q^{7} -4.01299 q^{8} -0.359094 q^{9} +O(q^{10})\)	\(q-2.38397 q^{2} +1.62509 q^{3} +3.68332 q^{4} -0.985677 q^{5} -3.87416 q^{6} -1.38154 q^{7} -4.01299 q^{8} -0.359094 q^{9} +2.34983 q^{10} +3.88920 q^{11} +5.98572 q^{12} +1.26448 q^{13} +3.29355 q^{14} -1.60181 q^{15} +2.20022 q^{16} +1.19457 q^{17} +0.856070 q^{18} +6.37297 q^{19} -3.63057 q^{20} -2.24512 q^{21} -9.27175 q^{22} +1.09885 q^{23} -6.52146 q^{24} -4.02844 q^{25} -3.01449 q^{26} -5.45882 q^{27} -5.08866 q^{28} +3.93133 q^{29} +3.81867 q^{30} +4.35012 q^{31} +2.78073 q^{32} +6.32029 q^{33} -2.84781 q^{34} +1.36175 q^{35} -1.32266 q^{36} +5.82343 q^{37} -15.1930 q^{38} +2.05490 q^{39} +3.95552 q^{40} -1.19420 q^{41} +5.35231 q^{42} +4.92877 q^{43} +14.3252 q^{44} +0.353951 q^{45} -2.61964 q^{46} -2.09466 q^{47} +3.57555 q^{48} -5.09135 q^{49} +9.60369 q^{50} +1.94127 q^{51} +4.65750 q^{52} +1.02747 q^{53} +13.0137 q^{54} -3.83350 q^{55} +5.54411 q^{56} +10.3566 q^{57} -9.37219 q^{58} -3.71709 q^{59} -5.89998 q^{60} -8.30371 q^{61} -10.3706 q^{62} +0.496103 q^{63} -11.0296 q^{64} -1.24637 q^{65} -15.0674 q^{66} -3.61329 q^{67} +4.39997 q^{68} +1.78573 q^{69} -3.24638 q^{70} +6.21892 q^{71} +1.44104 q^{72} -12.0245 q^{73} -13.8829 q^{74} -6.54656 q^{75} +23.4737 q^{76} -5.37309 q^{77} -4.89881 q^{78} -12.5180 q^{79} -2.16871 q^{80} -7.79377 q^{81} +2.84695 q^{82} +14.5960 q^{83} -8.26951 q^{84} -1.17746 q^{85} -11.7501 q^{86} +6.38876 q^{87} -15.6074 q^{88} -11.3971 q^{89} -0.843809 q^{90} -1.74693 q^{91} +4.04744 q^{92} +7.06932 q^{93} +4.99361 q^{94} -6.28169 q^{95} +4.51892 q^{96} +12.5169 q^{97} +12.1376 q^{98} -1.39659 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) \) 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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