LMFDB - Embedded newform 4003.2.a.c.1.17

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			1.17
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)

$f(q)$	$=$	$q-2.34837 q^{2} -3.35198 q^{3} +3.51485 q^{4} -2.33127 q^{5} +7.87170 q^{6} -2.55818 q^{7} -3.55742 q^{8} +8.23579 q^{9} +O(q^{10})$	\(q-2.34837 q^{2} -3.35198 q^{3} +3.51485 q^{4} -2.33127 q^{5} +7.87170 q^{6} -2.55818 q^{7} -3.55742 q^{8} +8.23579 q^{9} +5.47468 q^{10} -5.01759 q^{11} -11.7817 q^{12} +2.16479 q^{13} +6.00757 q^{14} +7.81437 q^{15} +1.32445 q^{16} +6.46936 q^{17} -19.3407 q^{18} +2.40547 q^{19} -8.19405 q^{20} +8.57499 q^{21} +11.7832 q^{22} +8.42083 q^{23} +11.9244 q^{24} +0.434808 q^{25} -5.08373 q^{26} -17.5503 q^{27} -8.99162 q^{28} +9.20678 q^{29} -18.3510 q^{30} -8.50137 q^{31} +4.00454 q^{32} +16.8189 q^{33} -15.1925 q^{34} +5.96381 q^{35} +28.9475 q^{36} +9.55203 q^{37} -5.64895 q^{38} -7.25633 q^{39} +8.29330 q^{40} +1.38908 q^{41} -20.1373 q^{42} +11.1994 q^{43} -17.6360 q^{44} -19.1998 q^{45} -19.7752 q^{46} -2.04731 q^{47} -4.43953 q^{48} -0.455691 q^{49} -1.02109 q^{50} -21.6852 q^{51} +7.60890 q^{52} +12.9487 q^{53} +41.2146 q^{54} +11.6973 q^{55} +9.10054 q^{56} -8.06311 q^{57} -21.6209 q^{58} +0.380262 q^{59} +27.4663 q^{60} +7.31995 q^{61} +19.9644 q^{62} -21.0687 q^{63} -12.0530 q^{64} -5.04670 q^{65} -39.4969 q^{66} +3.63536 q^{67} +22.7388 q^{68} -28.2265 q^{69} -14.0052 q^{70} +4.61567 q^{71} -29.2982 q^{72} -0.625275 q^{73} -22.4317 q^{74} -1.45747 q^{75} +8.45487 q^{76} +12.8359 q^{77} +17.0406 q^{78} +0.553808 q^{79} -3.08765 q^{80} +34.1209 q^{81} -3.26209 q^{82} +9.65313 q^{83} +30.1398 q^{84} -15.0818 q^{85} -26.3004 q^{86} -30.8610 q^{87} +17.8497 q^{88} +1.30307 q^{89} +45.0883 q^{90} -5.53793 q^{91} +29.5979 q^{92} +28.4965 q^{93} +4.80784 q^{94} -5.60780 q^{95} -13.4232 q^{96} -4.63431 q^{97} +1.07013 q^{98} -41.3238 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.34837	−1.66055	−0.830274	−	0.557355i	$-0.811816\pi$
$2$	−2.34837	−1.66055	−0.830274	+	0.557355i	$0.811816\pi$
$3$	−3.35198	−1.93527	−0.967634	−	0.252357i	$-0.918794\pi$
$3$	−3.35198	−1.93527	−0.967634	+	0.252357i	$0.918794\pi$
$4$	3.51485	1.75742
$5$	−2.33127	−1.04257	−0.521287	−	0.853381i	$-0.674548\pi$
$5$	−2.33127	−1.04257	−0.521287	+	0.853381i	$0.674548\pi$
$6$	7.87170	3.21361
$7$	−2.55818	−0.966903	−0.483451	−	0.875371i	$-0.660617\pi$
$7$	−2.55818	−0.966903	−0.483451	+	0.875371i	$0.660617\pi$
$8$	−3.55742	−1.25774
$9$	8.23579	2.74526
$10$	5.47468	1.73125
$11$	−5.01759	−1.51286	−0.756430	−	0.654075i	$-0.773058\pi$
$11$	−5.01759	−1.51286	−0.756430	+	0.654075i	$0.773058\pi$
$12$	−11.7817	−3.40109
$13$	2.16479	0.600404	0.300202	−	0.953876i	$-0.402946\pi$
$13$	2.16479	0.600404	0.300202	+	0.953876i	$0.402946\pi$
$14$	6.00757	1.60559
$15$	7.81437	2.01766
$16$	1.32445	0.331112
$17$	6.46936	1.56905	0.784525	−	0.620097i	$-0.212907\pi$
$17$	6.46936	1.56905	0.784525	+	0.620097i	$0.212907\pi$
$18$	−19.3407	−4.55865
$19$	2.40547	0.551854	0.275927	−	0.961179i	$-0.411015\pi$
$19$	2.40547	0.551854	0.275927	+	0.961179i	$0.411015\pi$
$20$	−8.19405	−1.83224
$21$	8.57499	1.87122
$22$	11.7832	2.51218
$23$	8.42083	1.75586	0.877932	−	0.478785i	$-0.158923\pi$
$23$	8.42083	1.75586	0.877932	+	0.478785i	$0.158923\pi$
$24$	11.9244	2.43406
$25$	0.434808	0.0869616
$26$	−5.08373	−0.997001
$27$	−17.5503	−3.37755
$28$	−8.99162	−1.69926
$29$	9.20678	1.70966	0.854828	−	0.518911i	$-0.173663\pi$
$29$	9.20678	1.70966	0.854828	+	0.518911i	$0.173663\pi$
$30$	−18.3510	−3.35043
$31$	−8.50137	−1.52689	−0.763446	−	0.645872i	$-0.776494\pi$
$31$	−8.50137	−1.52689	−0.763446	+	0.645872i	$0.776494\pi$
$32$	4.00454	0.707910
$33$	16.8189	2.92779
$34$	−15.1925	−2.60549
$35$	5.96381	1.00807
$36$	28.9475	4.82459
$37$	9.55203	1.57034	0.785172	−	0.619278i	$-0.212575\pi$
$37$	9.55203	1.57034	0.785172	+	0.619278i	$0.212575\pi$
$38$	−5.64895	−0.916380
$39$	−7.25633	−1.16194
$40$	8.29330	1.31129
$41$	1.38908	0.216939	0.108469	−	0.994100i	$-0.465405\pi$
$41$	1.38908	0.216939	0.108469	+	0.994100i	$0.465405\pi$
$42$	−20.1373	−3.10725
$43$	11.1994	1.70789	0.853947	−	0.520360i	$-0.174202\pi$
$43$	11.1994	1.70789	0.853947	+	0.520360i	$0.174202\pi$
$44$	−17.6360	−2.65873
$45$	−19.1998	−2.86214
$46$	−19.7752	−2.91570
$47$	−2.04731	−0.298631	−0.149315	−	0.988790i	$-0.547707\pi$
$47$	−2.04731	−0.298631	−0.149315	+	0.988790i	$0.547707\pi$
$48$	−4.43953	−0.640791
$49$	−0.455691	−0.0650987
$50$	−1.02109	−0.144404
$51$	−21.6852	−3.03653
$52$	7.60890	1.05516
$53$	12.9487	1.77864	0.889322	−	0.457282i	$-0.151177\pi$
$53$	12.9487	1.77864	0.889322	+	0.457282i	$0.151177\pi$
$54$	41.2146	5.60859
$55$	11.6973	1.57727
$56$	9.10054	1.21611
$57$	−8.06311	−1.06799
$58$	−21.6209	−2.83897
$59$	0.380262	0.0495058	0.0247529	−	0.999694i	$-0.492120\pi$
$59$	0.380262	0.0495058	0.0247529	+	0.999694i	$0.492120\pi$
$60$	27.4663	3.54588
$61$	7.31995	0.937223	0.468612	−	0.883404i	$-0.344754\pi$
$61$	7.31995	0.937223	0.468612	+	0.883404i	$0.344754\pi$
$62$	19.9644	2.53548
$63$	−21.0687	−2.65440
$64$	−12.0530	−1.50663
$65$	−5.04670	−0.625966
$66$	−39.4969	−4.86174
$67$	3.63536	0.444129	0.222065	−	0.975032i	$-0.428720\pi$
$67$	3.63536	0.444129	0.222065	+	0.975032i	$0.428720\pi$
$68$	22.7388	2.75749
$69$	−28.2265	−3.39807
$70$	−14.0052	−1.67395
$71$	4.61567	0.547779	0.273890	−	0.961761i	$-0.411690\pi$
$71$	4.61567	0.547779	0.273890	+	0.961761i	$0.411690\pi$
$72$	−29.2982	−3.45282
$73$	−0.625275	−0.0731829	−0.0365914	−	0.999330i	$-0.511650\pi$
$73$	−0.625275	−0.0731829	−0.0365914	+	0.999330i	$0.511650\pi$
$74$	−22.4317	−2.60763
$75$	−1.45747	−0.168294
$76$	8.45487	0.969840
$77$	12.8359	1.46279
$78$	17.0406	1.92946
$79$	0.553808	0.0623083	0.0311541	−	0.999515i	$-0.490082\pi$
$79$	0.553808	0.0623083	0.0311541	+	0.999515i	$0.490082\pi$
$80$	−3.08765	−0.345209
$81$	34.1209	3.79121
$82$	−3.26209	−0.360237
$83$	9.65313	1.05957	0.529784	−	0.848132i	$-0.322273\pi$
$83$	9.65313	1.05957	0.529784	+	0.848132i	$0.322273\pi$
$84$	30.1398	3.28852
$85$	−15.0818	−1.63585
$86$	−26.3004	−2.83604
$87$	−30.8610	−3.30864
$88$	17.8497	1.90278
$89$	1.30307	0.138125	0.0690627	−	0.997612i	$-0.477999\pi$
$89$	1.30307	0.138125	0.0690627	+	0.997612i	$0.477999\pi$
$90$	45.0883	4.75273
$91$	−5.53793	−0.580533
$92$	29.5979	3.08580
$93$	28.4965	2.95495
$94$	4.80784	0.495891
$95$	−5.60780	−0.575349
$96$	−13.4232	−1.36999
$97$	−4.63431	−0.470542	−0.235271	−	0.971930i	$-0.575598\pi$
$97$	−4.63431	−0.470542	−0.235271	+	0.971930i	$0.575598\pi$
$98$	1.07013	0.108100
$99$	−41.3238	−4.15320
$100$	1.52828	0.152828
$101$	8.72026	0.867699	0.433849	−	0.900985i	$-0.357155\pi$
$101$	8.72026	0.867699	0.433849	+	0.900985i	$0.357155\pi$
$102$	50.9249	5.04231
$103$	−14.4897	−1.42771	−0.713854	−	0.700294i	$-0.753052\pi$
$103$	−14.4897	−1.42771	−0.713854	+	0.700294i	$0.753052\pi$
$104$	−7.70106	−0.755151
$105$	−19.9906	−1.95088
$106$	−30.4084	−2.95352
$107$	1.13406	0.109634	0.0548170	−	0.998496i	$-0.482542\pi$
$107$	1.13406	0.109634	0.0548170	+	0.998496i	$0.482542\pi$
$108$	−61.6866	−5.93579
$109$	−8.29776	−0.794781	−0.397391	−	0.917650i	$-0.630084\pi$
$109$	−8.29776	−0.794781	−0.397391	+	0.917650i	$0.630084\pi$
$110$	−27.4697	−2.61913
$111$	−32.0182	−3.03904
$112$	−3.38819	−0.320154
$113$	0.873059	0.0821305	0.0410652	−	0.999156i	$-0.486925\pi$
$113$	0.873059	0.0821305	0.0410652	+	0.999156i	$0.486925\pi$
$114$	18.9352	1.77344
$115$	−19.6312	−1.83062
$116$	32.3604	3.00459
$117$	17.8287	1.64827
$118$	−0.892995	−0.0822069
$119$	−16.5498	−1.51712
$120$	−27.7990	−2.53769
$121$	14.1762	1.28874
$122$	−17.1899	−1.55630
$123$	−4.65619	−0.419834
$124$	−29.8810	−2.68339
$125$	10.6427	0.951911
$126$	49.4771	4.40777
$127$	4.17780	0.370720	0.185360	−	0.982671i	$-0.440655\pi$
$127$	4.17780	0.370720	0.185360	+	0.982671i	$0.440655\pi$
$128$	20.2959	1.79392
$129$	−37.5402	−3.30523
$130$	11.8515	1.03945
$131$	5.85221	0.511310	0.255655	−	0.966768i	$-0.417709\pi$
$131$	5.85221	0.511310	0.255655	+	0.966768i	$0.417709\pi$
$132$	59.1157	5.14536
$133$	−6.15365	−0.533589
$134$	−8.53716	−0.737499
$135$	40.9144	3.52135
$136$	−23.0142	−1.97345
$137$	−9.20645	−0.786561	−0.393280	−	0.919419i	$-0.628660\pi$
$137$	−9.20645	−0.786561	−0.393280	+	0.919419i	$0.628660\pi$
$138$	66.2862	5.64266
$139$	−3.53429	−0.299775	−0.149887	−	0.988703i	$-0.547891\pi$
$139$	−3.53429	−0.299775	−0.149887	+	0.988703i	$0.547891\pi$
$140$	20.9619	1.77160
$141$	6.86254	0.577931
$142$	−10.8393	−0.909614
$143$	−10.8620	−0.908327
$144$	10.9079	0.908991
$145$	−21.4635	−1.78244
$146$	1.46838	0.121524
$147$	1.52747	0.125983
$148$	33.5739	2.75976
$149$	−4.19058	−0.343306	−0.171653	−	0.985157i	$-0.554911\pi$
$149$	−4.19058	−0.343306	−0.171653	+	0.985157i	$0.554911\pi$
$150$	3.42268	0.279461
$151$	5.95922	0.484954	0.242477	−	0.970157i	$-0.422040\pi$
$151$	5.95922	0.484954	0.242477	+	0.970157i	$0.422040\pi$
$152$	−8.55728	−0.694087
$153$	53.2803	4.30746
$154$	−30.1435	−2.42903
$155$	19.8190	1.59190
$156$	−25.5049	−2.04203
$157$	−13.8794	−1.10770	−0.553850	−	0.832616i	$-0.686842\pi$
$157$	−13.8794	−1.10770	−0.553850	+	0.832616i	$0.686842\pi$
$158$	−1.30055	−0.103466
$159$	−43.4039	−3.44215
$160$	−9.33566	−0.738048
$161$	−21.5420	−1.69775
$162$	−80.1285	−6.29549
$163$	10.4746	0.820437	0.410218	−	0.911987i	$-0.365453\pi$
$163$	10.4746	0.820437	0.410218	+	0.911987i	$0.365453\pi$
$164$	4.88242	0.381253
$165$	−39.2093	−3.05244
$166$	−22.6691	−1.75947
$167$	−6.90718	−0.534493	−0.267247	−	0.963628i	$-0.586114\pi$
$167$	−6.90718	−0.534493	−0.267247	+	0.963628i	$0.586114\pi$
$168$	−30.5048	−2.35350
$169$	−8.31369	−0.639515
$170$	35.4177	2.71641
$171$	19.8110	1.51498
$172$	39.3642	3.00149
$173$	−21.9224	−1.66673	−0.833365	−	0.552723i	$-0.813589\pi$
$173$	−21.9224	−1.66673	−0.833365	+	0.552723i	$0.813589\pi$
$174$	72.4730	5.49416
$175$	−1.11232	−0.0840834
$176$	−6.64554	−0.500926
$177$	−1.27463	−0.0958071
$178$	−3.06010	−0.229364
$179$	2.24464	0.167772	0.0838862	−	0.996475i	$-0.473267\pi$
$179$	2.24464	0.167772	0.0838862	+	0.996475i	$0.473267\pi$
$180$	−67.4845	−5.02999
$181$	11.7608	0.874170	0.437085	−	0.899420i	$-0.356011\pi$
$181$	11.7608	0.874170	0.437085	+	0.899420i	$0.356011\pi$
$182$	13.0051	0.964003
$183$	−24.5363	−1.81378
$184$	−29.9564	−2.20842
$185$	−22.2683	−1.63720
$186$	−66.9203	−4.90683
$187$	−32.4606	−2.37375
$188$	−7.19597	−0.524820
$189$	44.8969	3.26577
$190$	13.1692	0.955395
$191$	12.5971	0.911497	0.455749	−	0.890108i	$-0.349372\pi$
$191$	12.5971	0.911497	0.455749	+	0.890108i	$0.349372\pi$
$192$	40.4016	2.91574
$193$	−5.00262	−0.360096	−0.180048	−	0.983658i	$-0.557625\pi$
$193$	−5.00262	−0.360096	−0.180048	+	0.983658i	$0.557625\pi$
$194$	10.8831	0.781359
$195$	16.9165	1.21141
$196$	−1.60168	−0.114406
$197$	−13.4058	−0.955123	−0.477562	−	0.878598i	$-0.658479\pi$
$197$	−13.4058	−0.955123	−0.477562	+	0.878598i	$0.658479\pi$
$198$	97.0436	6.89659
$199$	−21.5031	−1.52431	−0.762156	−	0.647394i	$-0.775859\pi$
$199$	−21.5031	−1.52431	−0.762156	+	0.647394i	$0.775859\pi$
$200$	−1.54679	−0.109375
$201$	−12.1857	−0.859510
$202$	−20.4784	−1.44086
$203$	−23.5526	−1.65307
$204$	−76.2201	−5.33648
$205$	−3.23833	−0.226175
$206$	34.0271	2.37078
$207$	69.3522	4.82031
$208$	2.86715	0.198801
$209$	−12.0697	−0.834877
$210$	46.9453	3.23954
$211$	−5.54882	−0.381996	−0.190998	−	0.981590i	$-0.561172\pi$
$211$	−5.54882	−0.381996	−0.190998	+	0.981590i	$0.561172\pi$
$212$	45.5127	3.12583
$213$	−15.4717	−1.06010
$214$	−2.66320	−0.182052
$215$	−26.1088	−1.78061
$216$	62.4337	4.24808
$217$	21.7481	1.47636
$218$	19.4862	1.31977
$219$	2.09591	0.141629
$220$	41.1143	2.77193
$221$	14.0048	0.942065
$222$	75.1907	5.04647
$223$	23.9664	1.60491	0.802453	−	0.596715i	$-0.203528\pi$
$223$	23.9664	1.60491	0.802453	+	0.596715i	$0.203528\pi$
$224$	−10.2444	−0.684480
$225$	3.58099	0.238733
$226$	−2.05027	−0.136382
$227$	19.7136	1.30844	0.654220	−	0.756304i	$-0.272997\pi$
$227$	19.7136	1.30844	0.654220	+	0.756304i	$0.272997\pi$
$228$	−28.3406	−1.87690
$229$	5.67747	0.375178	0.187589	−	0.982248i	$-0.439933\pi$
$229$	5.67747	0.375178	0.187589	+	0.982248i	$0.439933\pi$
$230$	46.1013	3.03983
$231$	−43.0258	−2.83089
$232$	−32.7524	−2.15030
$233$	13.1975	0.864597	0.432298	−	0.901731i	$-0.357703\pi$
$233$	13.1975	0.864597	0.432298	+	0.901731i	$0.357703\pi$
$234$	−41.8685	−2.73703
$235$	4.77282	0.311345
$236$	1.33656	0.0870027
$237$	−1.85636	−0.120583
$238$	38.8651	2.51925
$239$	19.7106	1.27497	0.637487	−	0.770461i	$-0.279974\pi$
$239$	19.7106	1.27497	0.637487	+	0.770461i	$0.279974\pi$
$240$	10.3497	0.668073
$241$	2.11242	0.136073	0.0680365	−	0.997683i	$-0.478327\pi$
$241$	2.11242	0.136073	0.0680365	+	0.997683i	$0.478327\pi$
$242$	−33.2909	−2.14002
$243$	−61.7218	−3.95946
$244$	25.7285	1.64710
$245$	1.06234	0.0678702
$246$	10.9345	0.697156
$247$	5.20734	0.331335
$248$	30.2430	1.92043
$249$	−32.3571	−2.05055
$250$	−24.9930	−1.58069
$251$	−9.75347	−0.615633	−0.307817	−	0.951446i	$-0.599598\pi$
$251$	−9.75347	−0.615633	−0.307817	+	0.951446i	$0.599598\pi$
$252$	−74.0532	−4.66491
$253$	−42.2522	−2.65638
$254$	−9.81103	−0.615599
$255$	50.5540	3.16581
$256$	−23.5563	−1.47227
$257$	20.2417	1.26265	0.631323	−	0.775520i	$-0.282512\pi$
$257$	20.2417	1.26265	0.631323	+	0.775520i	$0.282512\pi$
$258$	88.1584	5.48850
$259$	−24.4359	−1.51837
$260$	−17.7384	−1.10009
$261$	75.8251	4.69346
$262$	−13.7432	−0.849055
$263$	12.7769	0.787855	0.393928	−	0.919142i	$-0.371116\pi$
$263$	12.7769	0.787855	0.393928	+	0.919142i	$0.371116\pi$
$264$	−59.8318	−3.68239
$265$	−30.1869	−1.85437
$266$	14.4510	0.886051
$267$	−4.36787	−0.267310
$268$	12.7777	0.780523
$269$	−6.64960	−0.405433	−0.202717	−	0.979237i	$-0.564977\pi$
$269$	−6.64960	−0.405433	−0.202717	+	0.979237i	$0.564977\pi$
$270$	−96.0822	−5.84738
$271$	14.0441	0.853120	0.426560	−	0.904459i	$-0.359725\pi$
$271$	14.0441	0.853120	0.426560	+	0.904459i	$0.359725\pi$
$272$	8.56834	0.519532
$273$	18.5630	1.12349
$274$	21.6202	1.30612
$275$	−2.18169	−0.131561
$276$	−99.2117	−5.97184
$277$	9.62697	0.578429	0.289214	−	0.957264i	$-0.406606\pi$
$277$	9.62697	0.578429	0.289214	+	0.957264i	$0.406606\pi$
$278$	8.29983	0.497791
$279$	−70.0155	−4.19172
$280$	−21.2158	−1.26789
$281$	−0.293482	−0.0175077	−0.00875383	−	0.999962i	$-0.502786\pi$
$281$	−0.293482	−0.0175077	−0.00875383	+	0.999962i	$0.502786\pi$
$282$	−16.1158	−0.959682
$283$	−16.0668	−0.955073	−0.477536	−	0.878612i	$-0.658470\pi$
$283$	−16.0668	−0.955073	−0.477536	+	0.878612i	$0.658470\pi$
$284$	16.2234	0.962680
$285$	18.7973	1.11345
$286$	25.5080	1.50832
$287$	−3.55353	−0.209759
$288$	32.9806	1.94340
$289$	24.8527	1.46192
$290$	50.4042	2.95984
$291$	15.5341	0.910626
$292$	−2.19774	−0.128613
$293$	14.3964	0.841048	0.420524	−	0.907281i	$-0.361846\pi$
$293$	14.3964	0.841048	0.420524	+	0.907281i	$0.361846\pi$
$294$	−3.58706	−0.209202
$295$	−0.886492	−0.0516135
$296$	−33.9806	−1.97508
$297$	88.0601	5.10976
$298$	9.84104	0.570076
$299$	18.2293	1.05423
$300$	−5.12278	−0.295764
$301$	−28.6502	−1.65137
$302$	−13.9945	−0.805290
$303$	−29.2302	−1.67923
$304$	3.18593	0.182726
$305$	−17.0648	−0.977125
$306$	−125.122	−7.15275
$307$	34.0961	1.94597	0.972984	−	0.230871i	$-0.0741576\pi$
$307$	34.0961	1.94597	0.972984	+	0.230871i	$0.0741576\pi$
$308$	45.1163	2.57074
$309$	48.5691	2.76300
$310$	−46.5423	−2.64342
$311$	−5.73215	−0.325041	−0.162520	−	0.986705i	$-0.551962\pi$
$311$	−5.73215	−0.325041	−0.162520	+	0.986705i	$0.551962\pi$
$312$	25.8138	1.46142
$313$	31.3084	1.76966	0.884828	−	0.465917i	$-0.154276\pi$
$313$	31.3084	1.76966	0.884828	+	0.465917i	$0.154276\pi$
$314$	32.5941	1.83939
$315$	49.1167	2.76741
$316$	1.94655	0.109502
$317$	−4.73628	−0.266016	−0.133008	−	0.991115i	$-0.542464\pi$
$317$	−4.73628	−0.266016	−0.133008	+	0.991115i	$0.542464\pi$
$318$	101.928	5.71586
$319$	−46.1958	−2.58647
$320$	28.0989	1.57077
$321$	−3.80136	−0.212171
$322$	50.5887	2.81920
$323$	15.5619	0.865887
$324$	119.930	6.66276
$325$	0.941267	0.0522121
$326$	−24.5983	−1.36238
$327$	27.8140	1.53812
$328$	−4.94156	−0.272852
$329$	5.23739	0.288747
$330$	92.0779	5.06872
$331$	0.731781	0.0402223	0.0201112	−	0.999798i	$-0.493598\pi$
$331$	0.731781	0.0402223	0.0201112	+	0.999798i	$0.493598\pi$
$332$	33.9293	1.86211
$333$	78.6685	4.31101
$334$	16.2206	0.887552
$335$	−8.47499	−0.463038
$336$	11.3571	0.619583
$337$	15.4726	0.842847	0.421424	−	0.906864i	$-0.361531\pi$
$337$	15.4726	0.842847	0.421424	+	0.906864i	$0.361531\pi$
$338$	19.5236	1.06195
$339$	−2.92648	−0.158945
$340$	−53.0103	−2.87488
$341$	42.6564	2.30997
$342$	−46.5235	−2.51571
$343$	19.0730	1.02985
$344$	−39.8410	−2.14808
$345$	65.8035	3.54274
$346$	51.4820	2.76769
$347$	28.4847	1.52914	0.764570	−	0.644541i	$-0.222951\pi$
$347$	28.4847	1.52914	0.764570	+	0.644541i	$0.222951\pi$
$348$	−108.472	−5.81469
$349$	0.509260	0.0272601	0.0136300	−	0.999907i	$-0.495661\pi$
$349$	0.509260	0.0272601	0.0136300	+	0.999907i	$0.495661\pi$
$350$	2.61214	0.139625
$351$	−37.9927	−2.02790
$352$	−20.0931	−1.07097
$353$	−28.6602	−1.52543	−0.762713	−	0.646737i	$-0.776133\pi$
$353$	−28.6602	−1.52543	−0.762713	+	0.646737i	$0.776133\pi$
$354$	2.99331	0.159092
$355$	−10.7604	−0.571101
$356$	4.58010	0.242745
$357$	55.4747	2.93603
$358$	−5.27125	−0.278594
$359$	−2.02732	−0.106998	−0.0534988	−	0.998568i	$-0.517037\pi$
$359$	−2.02732	−0.106998	−0.0534988	+	0.998568i	$0.517037\pi$
$360$	68.3019	3.59982
$361$	−13.2137	−0.695458
$362$	−27.6186	−1.45160
$363$	−47.5183	−2.49406
$364$	−19.4650	−1.02024
$365$	1.45768	0.0762986
$366$	57.6204	3.01187
$367$	−16.9759	−0.886137	−0.443068	−	0.896488i	$-0.646110\pi$
$367$	−16.9759	−0.886137	−0.443068	+	0.896488i	$0.646110\pi$
$368$	11.1530	0.581388
$369$	11.4402	0.595554
$370$	52.2943	2.71865
$371$	−33.1252	−1.71978
$372$	100.161	5.19309
$373$	−7.40719	−0.383530	−0.191765	−	0.981441i	$-0.561421\pi$
$373$	−7.40719	−0.383530	−0.191765	+	0.981441i	$0.561421\pi$
$374$	76.2295	3.94173
$375$	−35.6741	−1.84220
$376$	7.28314	0.375599
$377$	19.9307	1.02648
$378$	−105.435	−5.42297
$379$	−12.0836	−0.620691	−0.310345	−	0.950624i	$-0.600445\pi$
$379$	−12.0836	−0.620691	−0.310345	+	0.950624i	$0.600445\pi$
$380$	−19.7106	−1.01113
$381$	−14.0039	−0.717443
$382$	−29.5828	−1.51359
$383$	−11.0936	−0.566856	−0.283428	−	0.958994i	$-0.591472\pi$
$383$	−11.0936	−0.566856	−0.283428	+	0.958994i	$0.591472\pi$
$384$	−68.0317	−3.47173
$385$	−29.9239	−1.52507
$386$	11.7480	0.597957
$387$	92.2360	4.68862
$388$	−16.2889	−0.826942
$389$	−24.3086	−1.23250	−0.616248	−	0.787552i	$-0.711348\pi$
$389$	−24.3086	−1.23250	−0.616248	+	0.787552i	$0.711348\pi$
$390$	−39.7261	−2.01161
$391$	54.4774	2.75504
$392$	1.62108	0.0818771
$393$	−19.6165	−0.989522
$394$	31.4818	1.58603
$395$	−1.29107	−0.0649610
$396$	−145.247	−7.29893
$397$	−0.411585	−0.0206569	−0.0103284	−	0.999947i	$-0.503288\pi$
$397$	−0.411585	−0.0206569	−0.0103284	+	0.999947i	$0.503288\pi$
$398$	50.4971	2.53119
$399$	20.6269	1.03264
$400$	0.575881	0.0287941
$401$	−14.3825	−0.718229	−0.359115	−	0.933293i	$-0.616921\pi$
$401$	−14.3825	−0.718229	−0.359115	+	0.933293i	$0.616921\pi$
$402$	28.6164	1.42726
$403$	−18.4037	−0.916752
$404$	30.6504	1.52491
$405$	−79.5449	−3.95262
$406$	55.3103	2.74501
$407$	−47.9281	−2.37571
$408$	77.1433	3.81916
$409$	22.9567	1.13514	0.567568	−	0.823327i	$-0.307885\pi$
$409$	22.9567	1.13514	0.567568	+	0.823327i	$0.307885\pi$
$410$	7.60479	0.375574
$411$	30.8599	1.52221
$412$	−50.9289	−2.50909
$413$	−0.972779	−0.0478673
$414$	−162.865	−8.00436
$415$	−22.5040	−1.10468
$416$	8.66898	0.425032
$417$	11.8469	0.580145
$418$	28.3441	1.38635
$419$	25.9209	1.26632	0.633160	−	0.774021i	$-0.281757\pi$
$419$	25.9209	1.26632	0.633160	+	0.774021i	$0.281757\pi$
$420$	−70.2639	−3.42853
$421$	−33.2524	−1.62062	−0.810311	−	0.585999i	$-0.800702\pi$
$421$	−33.2524	−1.62062	−0.810311	+	0.585999i	$0.800702\pi$
$422$	13.0307	0.634324
$423$	−16.8612	−0.819820
$424$	−46.0640	−2.23707
$425$	2.81293	0.136447
$426$	36.3332	1.76035
$427$	−18.7258	−0.906204
$428$	3.98605	0.192673
$429$	36.4093	1.75786
$430$	61.3132	2.95678
$431$	28.5586	1.37562	0.687809	−	0.725892i	$-0.258573\pi$
$431$	28.5586	1.37562	0.687809	+	0.725892i	$0.258573\pi$
$432$	−23.2445	−1.11835
$433$	28.4687	1.36812	0.684060	−	0.729426i	$-0.260213\pi$
$433$	28.4687	1.36812	0.684060	+	0.729426i	$0.260213\pi$
$434$	−51.0726	−2.45156
$435$	71.9452	3.44951
$436$	−29.1654	−1.39677
$437$	20.2561	0.968980
$438$	−4.92198	−0.235181
$439$	−15.0407	−0.717851	−0.358926	−	0.933366i	$-0.616857\pi$
$439$	−15.0407	−0.717851	−0.358926	+	0.933366i	$0.616857\pi$
$440$	−41.6123	−1.98379
$441$	−3.75298	−0.178713
$442$	−32.8885	−1.56434
$443$	1.04456	0.0496285	0.0248142	−	0.999692i	$-0.492101\pi$
$443$	1.04456	0.0496285	0.0248142	+	0.999692i	$0.492101\pi$
$444$	−112.539	−5.34087
$445$	−3.03781	−0.144006
$446$	−56.2819	−2.66503
$447$	14.0468	0.664389
$448$	30.8339	1.45677
$449$	−9.12813	−0.430783	−0.215391	−	0.976528i	$-0.569103\pi$
$449$	−9.12813	−0.430783	−0.215391	+	0.976528i	$0.569103\pi$
$450$	−8.40949	−0.396427
$451$	−6.96985	−0.328198
$452$	3.06867	0.144338
$453$	−19.9752	−0.938517
$454$	−46.2949	−2.17273
$455$	12.9104	0.605248
$456$	28.6839	1.34325
$457$	−20.2093	−0.945349	−0.472675	−	0.881237i	$-0.656711\pi$
$457$	−20.2093	−0.945349	−0.472675	+	0.881237i	$0.656711\pi$
$458$	−13.3328	−0.623001
$459$	−113.539	−5.29956
$460$	−69.0006	−3.21717
$461$	−5.58958	−0.260333	−0.130166	−	0.991492i	$-0.541551\pi$
$461$	−5.58958	−0.260333	−0.130166	+	0.991492i	$0.541551\pi$
$462$	101.040	4.70083
$463$	−22.2166	−1.03249	−0.516246	−	0.856440i	$-0.672671\pi$
$463$	−22.2166	−1.03249	−0.516246	+	0.856440i	$0.672671\pi$
$464$	12.1939	0.566088
$465$	−66.4329	−3.08075
$466$	−30.9926	−1.43571
$467$	4.99723	0.231244	0.115622	−	0.993293i	$-0.463114\pi$
$467$	4.99723	0.231244	0.115622	+	0.993293i	$0.463114\pi$
$468$	62.6653	2.89670
$469$	−9.29991	−0.429430
$470$	−11.2084	−0.517003
$471$	46.5237	2.14370
$472$	−1.35275	−0.0622654
$473$	−56.1940	−2.58380
$474$	4.35941	0.200234
$475$	1.04592	0.0479901
$476$	−58.1701	−2.66622
$477$	106.643	4.88285
$478$	−46.2879	−2.11716
$479$	−13.9884	−0.639146	−0.319573	−	0.947562i	$-0.603539\pi$
$479$	−13.9884	−0.639146	−0.319573	+	0.947562i	$0.603539\pi$
$480$	31.2930	1.42832
$481$	20.6781	0.942841
$482$	−4.96075	−0.225956
$483$	72.2085	3.28560
$484$	49.8271	2.26487
$485$	10.8038	0.490576
$486$	144.946	6.57487
$487$	6.57673	0.298020	0.149010	−	0.988836i	$-0.452391\pi$
$487$	6.57673	0.298020	0.149010	+	0.988836i	$0.452391\pi$
$488$	−26.0401	−1.17878
$489$	−35.1108	−1.58777
$490$	−2.49476	−0.112702
$491$	38.1736	1.72275	0.861375	−	0.507970i	$-0.169604\pi$
$491$	38.1736	1.72275	0.861375	+	0.507970i	$0.169604\pi$
$492$	−16.3658	−0.737827
$493$	59.5620	2.68254
$494$	−12.2288	−0.550198
$495$	96.3368	4.33002
$496$	−11.2596	−0.505573
$497$	−11.8077	−0.529649
$498$	75.9865	3.40504
$499$	−6.36117	−0.284765	−0.142383	−	0.989812i	$-0.545476\pi$
$499$	−6.36117	−0.284765	−0.142383	+	0.989812i	$0.545476\pi$
$500$	37.4074	1.67291
$501$	23.1527	1.03439
$502$	22.9048	1.02229
$503$	4.05126	0.180637	0.0903184	−	0.995913i	$-0.471212\pi$
$503$	4.05126	0.180637	0.0903184	+	0.995913i	$0.471212\pi$
$504$	74.9501	3.33854
$505$	−20.3293	−0.904640
$506$	99.2239	4.41104
$507$	27.8674	1.23763
$508$	14.6843	0.651512
$509$	25.8712	1.14672	0.573361	−	0.819303i	$-0.305639\pi$
$509$	25.8712	1.14672	0.573361	+	0.819303i	$0.305639\pi$
$510$	−118.720	−5.25699
$511$	1.59957	0.0707607
$512$	14.7271	0.650850
$513$	−42.2168	−1.86392
$514$	−47.5351	−2.09668
$515$	33.7793	1.48849
$516$	−131.948	−5.80869
$517$	10.2725	0.451786
$518$	57.3844	2.52133
$519$	73.4836	3.22557
$520$	17.9532	0.787301
$521$	−1.07627	−0.0471522	−0.0235761	−	0.999722i	$-0.507505\pi$
$521$	−1.07627	−0.0471522	−0.0235761	+	0.999722i	$0.507505\pi$
$522$	−178.066	−7.79372
$523$	37.7227	1.64950	0.824748	−	0.565500i	$-0.191317\pi$
$523$	37.7227	1.64950	0.824748	+	0.565500i	$0.191317\pi$
$524$	20.5696	0.898588
$525$	3.72848	0.162724
$526$	−30.0048	−1.30827
$527$	−54.9985	−2.39577
$528$	22.2757	0.969427
$529$	47.9103	2.08306
$530$	70.8901	3.07927
$531$	3.13176	0.135907
$532$	−21.6291	−0.937741
$533$	3.00707	0.130251
$534$	10.2574	0.443881
$535$	−2.64380	−0.114302
$536$	−12.9325	−0.558598
$537$	−7.52400	−0.324685
$538$	15.6157	0.673242
$539$	2.28647	0.0984852
$540$	143.808	6.18851
$541$	37.0227	1.59173	0.795866	−	0.605473i	$-0.207016\pi$
$541$	37.0227	1.59173	0.795866	+	0.605473i	$0.207016\pi$
$542$	−32.9808	−1.41665
$543$	−39.4219	−1.69175
$544$	25.9068	1.11075
$545$	19.3443	0.828619
$546$	−43.5929	−1.86560
$547$	−30.6705	−1.31137	−0.655687	−	0.755033i	$-0.727621\pi$
$547$	−30.6705	−1.31137	−0.655687	+	0.755033i	$0.727621\pi$
$548$	−32.3593	−1.38232
$549$	60.2856	2.57292
$550$	5.12341	0.218463
$551$	22.1467	0.943480
$552$	100.413	4.27388
$553$	−1.41674	−0.0602460
$554$	−22.6077	−0.960509
$555$	74.6431	3.16842
$556$	−12.4225	−0.526831
$557$	27.5702	1.16819	0.584094	−	0.811686i	$-0.301450\pi$
$557$	27.5702	1.16819	0.584094	+	0.811686i	$0.301450\pi$
$558$	164.422	6.96056
$559$	24.2443	1.02543
$560$	7.89877	0.333784
$561$	108.807	4.59385
$562$	0.689205	0.0290723
$563$	19.8423	0.836254	0.418127	−	0.908388i	$-0.362687\pi$
$563$	19.8423	0.836254	0.418127	+	0.908388i	$0.362687\pi$
$564$	24.1208	1.01567
$565$	−2.03533	−0.0856271
$566$	37.7308	1.58594
$567$	−87.2876	−3.66573
$568$	−16.4199	−0.688963
$569$	−23.9841	−1.00547	−0.502733	−	0.864442i	$-0.667672\pi$
$569$	−23.9841	−1.00547	−0.502733	+	0.864442i	$0.667672\pi$
$570$	−44.1430	−1.84894
$571$	26.8357	1.12304	0.561520	−	0.827463i	$-0.310217\pi$
$571$	26.8357	1.12304	0.561520	+	0.827463i	$0.310217\pi$
$572$	−38.1783	−1.59631
$573$	−42.2254	−1.76399
$574$	8.34502	0.348314
$575$	3.66144	0.152693
$576$	−99.2664	−4.13610
$577$	−41.7175	−1.73672	−0.868360	−	0.495934i	$-0.834826\pi$
$577$	−41.7175	−1.73672	−0.868360	+	0.495934i	$0.834826\pi$
$578$	−58.3633	−2.42759
$579$	16.7687	0.696883
$580$	−75.4408	−3.13251
$581$	−24.6945	−1.02450
$582$	−36.4799	−1.51214
$583$	−64.9713	−2.69084
$584$	2.22437	0.0920449
$585$	−41.5636	−1.71844
$586$	−33.8082	−1.39660
$587$	−43.9966	−1.81593	−0.907967	−	0.419041i	$-0.862366\pi$
$587$	−43.9966	−1.81593	−0.907967	+	0.419041i	$0.862366\pi$
$588$	5.36882	0.221406
$589$	−20.4498	−0.842621
$590$	2.08181	0.0857068
$591$	44.9360	1.84842
$592$	12.6512	0.519960
$593$	24.1414	0.991367	0.495683	−	0.868503i	$-0.334918\pi$
$593$	24.1414	0.991367	0.495683	+	0.868503i	$0.334918\pi$
$594$	−206.798	−8.48501
$595$	38.5821	1.58171
$596$	−14.7292	−0.603334
$597$	72.0779	2.94995
$598$	−42.8092	−1.75060
$599$	−14.2352	−0.581633	−0.290817	−	0.956779i	$-0.593927\pi$
$599$	−14.2352	−0.581633	−0.290817	+	0.956779i	$0.593927\pi$
$600$	5.18483	0.211670
$601$	−27.9009	−1.13810	−0.569052	−	0.822302i	$-0.692690\pi$
$601$	−27.9009	−1.13810	−0.569052	+	0.822302i	$0.692690\pi$
$602$	67.2812	2.74218
$603$	29.9400	1.21925
$604$	20.9457	0.852270
$605$	−33.0485	−1.34361
$606$	68.6433	2.78844
$607$	26.7049	1.08392	0.541959	−	0.840405i	$-0.317683\pi$
$607$	26.7049	1.08392	0.541959	+	0.840405i	$0.317683\pi$
$608$	9.63282	0.390662
$609$	78.9481	3.19914
$610$	40.0744	1.62256
$611$	−4.43199	−0.179299
$612$	187.272	7.57003
$613$	7.82828	0.316181	0.158091	−	0.987425i	$-0.449466\pi$
$613$	7.82828	0.316181	0.158091	+	0.987425i	$0.449466\pi$
$614$	−80.0703	−3.23138
$615$	10.8548	0.437709
$616$	−45.6627	−1.83980
$617$	−20.0774	−0.808286	−0.404143	−	0.914696i	$-0.632430\pi$
$617$	−20.0774	−0.808286	−0.404143	+	0.914696i	$0.632430\pi$
$618$	−114.058	−4.58810
$619$	−9.94420	−0.399691	−0.199846	−	0.979827i	$-0.564044\pi$
$619$	−9.94420	−0.399691	−0.199846	+	0.979827i	$0.564044\pi$
$620$	69.6606	2.79764
$621$	−147.788	−5.93053
$622$	13.4612	0.539746
$623$	−3.33350	−0.133554
$624$	−9.61065	−0.384734
$625$	−26.9850	−1.07940
$626$	−73.5238	−2.93860
$627$	40.4574	1.61571
$628$	−48.7841	−1.94670
$629$	61.7955	2.46395
$630$	−115.344	−4.59543
$631$	33.1269	1.31876	0.659381	−	0.751809i	$-0.270819\pi$
$631$	33.1269	1.31876	0.659381	+	0.751809i	$0.270819\pi$
$632$	−1.97013	−0.0783675
$633$	18.5995	0.739266
$634$	11.1225	0.441733
$635$	−9.73958	−0.386503
$636$	−152.558	−6.04932
$637$	−0.986474	−0.0390855
$638$	108.485	4.29496
$639$	38.0137	1.50380
$640$	−47.3153	−1.87030
$641$	−41.4471	−1.63706	−0.818532	−	0.574461i	$-0.805212\pi$
$641$	−41.4471	−1.63706	−0.818532	+	0.574461i	$0.805212\pi$
$642$	8.92700	0.352320
$643$	10.7638	0.424485	0.212242	−	0.977217i	$-0.431923\pi$
$643$	10.7638	0.424485	0.212242	+	0.977217i	$0.431923\pi$
$644$	−75.7169	−2.98366
$645$	87.5163	3.44595
$646$	−36.5451	−1.43785
$647$	−34.8785	−1.37122	−0.685608	−	0.727971i	$-0.740464\pi$
$647$	−34.8785	−1.37122	−0.685608	+	0.727971i	$0.740464\pi$
$648$	−121.382	−4.76835
$649$	−1.90800	−0.0748954
$650$	−2.21044	−0.0867008
$651$	−72.8992	−2.85715
$652$	36.8167	1.44185
$653$	12.1977	0.477331	0.238666	−	0.971102i	$-0.423290\pi$
$653$	12.1977	0.477331	0.238666	+	0.971102i	$0.423290\pi$
$654$	−65.3175	−2.55412
$655$	−13.6431	−0.533079
$656$	1.83977	0.0718310
$657$	−5.14963	−0.200906
$658$	−12.2993	−0.479478
$659$	30.2241	1.17736	0.588681	−	0.808365i	$-0.299647\pi$
$659$	30.2241	1.17736	0.588681	+	0.808365i	$0.299647\pi$
$660$	−137.815	−5.36442
$661$	−16.1415	−0.627830	−0.313915	−	0.949451i	$-0.601641\pi$
$661$	−16.1415	−0.627830	−0.313915	+	0.949451i	$0.601641\pi$
$662$	−1.71849	−0.0667912
$663$	−46.9439	−1.82315
$664$	−34.3402	−1.33266
$665$	14.3458	0.556306
$666$	−184.743	−7.15864
$667$	77.5287	3.00192
$668$	−24.2777	−0.939331
$669$	−80.3348	−3.10592
$670$	19.9024	0.768897
$671$	−36.7285	−1.41789
$672$	34.3389	1.32465
$673$	−11.6709	−0.449878	−0.224939	−	0.974373i	$-0.572218\pi$
$673$	−11.6709	−0.449878	−0.224939	+	0.974373i	$0.572218\pi$
$674$	−36.3355	−1.39959
$675$	−7.63101	−0.293718
$676$	−29.2213	−1.12390
$677$	−37.4911	−1.44090	−0.720450	−	0.693507i	$-0.756065\pi$
$677$	−37.4911	−1.44090	−0.720450	+	0.693507i	$0.756065\pi$
$678$	6.87246	0.263935
$679$	11.8554	0.454969
$680$	53.6523	2.05747
$681$	−66.0798	−2.53218
$682$	−100.173	−3.83582
$683$	45.8571	1.75467	0.877337	−	0.479874i	$-0.159318\pi$
$683$	45.8571	1.75467	0.877337	+	0.479874i	$0.159318\pi$
$684$	69.6326	2.66247
$685$	21.4627	0.820048
$686$	−44.7906	−1.71011
$687$	−19.0308	−0.726070
$688$	14.8331	0.565505
$689$	28.0312	1.06790
$690$	−154.531	−5.88289
$691$	18.9082	0.719304	0.359652	−	0.933087i	$-0.382895\pi$
$691$	18.9082	0.719304	0.359652	+	0.933087i	$0.382895\pi$
$692$	−77.0539	−2.92915
$693$	105.714	4.01574
$694$	−66.8927	−2.53921
$695$	8.23939	0.312538
$696$	109.785	4.16141
$697$	8.98649	0.340388
$698$	−1.19593	−0.0452667
$699$	−44.2378	−1.67323
$700$	−3.90963	−0.147770
$701$	23.9743	0.905497	0.452749	−	0.891638i	$-0.350443\pi$
$701$	23.9743	0.905497	0.452749	+	0.891638i	$0.350443\pi$
$702$	89.2208	3.36742
$703$	22.9772	0.866600
$704$	60.4772	2.27932
$705$	−15.9984	−0.602536
$706$	67.3047	2.53304
$707$	−22.3080	−0.838980
$708$	−4.48013	−0.168374
$709$	−9.18817	−0.345069	−0.172534	−	0.985003i	$-0.555196\pi$
$709$	−9.18817	−0.345069	−0.172534	+	0.985003i	$0.555196\pi$
$710$	25.2693	0.948341
$711$	4.56105	0.171053
$712$	−4.63557	−0.173725
$713$	−71.5886	−2.68101
$714$	−130.275	−4.87543
$715$	25.3223	0.946999
$716$	7.88957	0.294847
$717$	−66.0697	−2.46742
$718$	4.76089	0.177675
$719$	−31.2302	−1.16469	−0.582345	−	0.812942i	$-0.697865\pi$
$719$	−31.2302	−1.16469	−0.582345	+	0.812942i	$0.697865\pi$
$720$	−25.4292	−0.947691
$721$	37.0672	1.38046
$722$	31.0307	1.15484
$723$	−7.08080	−0.263338
$724$	41.3372	1.53629
$725$	4.00318	0.148674
$726$	111.591	4.14152
$727$	−50.7900	−1.88370	−0.941849	−	0.336037i	$-0.890913\pi$
$727$	−50.7900	−1.88370	−0.941849	+	0.336037i	$0.890913\pi$
$728$	19.7007	0.730158
$729$	104.528	3.87140
$730$	−3.42318	−0.126698
$731$	72.4530	2.67977
$732$	−86.2414	−3.18758
$733$	35.8726	1.32498	0.662492	−	0.749069i	$-0.269499\pi$
$733$	35.8726	1.32498	0.662492	+	0.749069i	$0.269499\pi$
$734$	39.8658	1.47147
$735$	−3.56094	−0.131347
$736$	33.7215	1.24299
$737$	−18.2407	−0.671905
$738$	−26.8659	−0.988946
$739$	7.15515	0.263206	0.131603	−	0.991302i	$-0.457988\pi$
$739$	7.15515	0.263206	0.131603	+	0.991302i	$0.457988\pi$
$740$	−78.2698	−2.87725
$741$	−17.4549	−0.641223
$742$	77.7903	2.85577
$743$	31.1184	1.14163	0.570813	−	0.821080i	$-0.306628\pi$
$743$	31.1184	1.14163	0.570813	+	0.821080i	$0.306628\pi$
$744$	−101.374	−3.71655
$745$	9.76937	0.357922
$746$	17.3948	0.636870
$747$	79.5012	2.90880
$748$	−114.094	−4.17169
$749$	−2.90114	−0.106005
$750$	83.7760	3.05907
$751$	−1.45272	−0.0530107	−0.0265053	−	0.999649i	$-0.508438\pi$
$751$	−1.45272	−0.0530107	−0.0265053	+	0.999649i	$0.508438\pi$
$752$	−2.71156	−0.0988803
$753$	32.6935	1.19142
$754$	−46.8047	−1.70453
$755$	−13.8925	−0.505601
$756$	157.806	5.73933
$757$	−9.78833	−0.355763	−0.177882	−	0.984052i	$-0.556924\pi$
$757$	−9.78833	−0.355763	−0.177882	+	0.984052i	$0.556924\pi$
$758$	28.3767	1.03069
$759$	141.629	5.14080
$760$	19.9493	0.723638
$761$	−3.00244	−0.108838	−0.0544192	−	0.998518i	$-0.517331\pi$
$761$	−3.00244	−0.108838	−0.0544192	+	0.998518i	$0.517331\pi$
$762$	32.8864	1.19135
$763$	21.2272	0.768477
$764$	44.2770	1.60189
$765$	−124.211	−4.49085
$766$	26.0519	0.941292
$767$	0.823186	0.0297235
$768$	78.9603	2.84924
$769$	−9.23066	−0.332866	−0.166433	−	0.986053i	$-0.553225\pi$
$769$	−9.23066	−0.332866	−0.166433	+	0.986053i	$0.553225\pi$
$770$	70.2725	2.53245
$771$	−67.8500	−2.44356
$772$	−17.5834	−0.632841
$773$	9.33847	0.335881	0.167941	−	0.985797i	$-0.446288\pi$
$773$	9.33847	0.335881	0.167941	+	0.985797i	$0.446288\pi$
$774$	−216.604	−7.78568
$775$	−3.69647	−0.132781
$776$	16.4862	0.591819
$777$	81.9086	2.93845
$778$	57.0857	2.04662
$779$	3.34141	0.119718
$780$	59.4587	2.12896
$781$	−23.1595	−0.828713
$782$	−127.933	−4.57488
$783$	−161.582	−5.77446
$784$	−0.603540	−0.0215550
$785$	32.3567	1.15486
$786$	46.0669	1.64315
$787$	15.9068	0.567015	0.283507	−	0.958970i	$-0.408502\pi$
$787$	15.9068	0.567015	0.283507	+	0.958970i	$0.408502\pi$
$788$	−47.1193	−1.67856
$789$	−42.8278	−1.52471
$790$	3.03192	0.107871
$791$	−2.23345	−0.0794122
$792$	147.006	5.22363
$793$	15.8461	0.562713
$794$	0.966554	0.0343017
$795$	101.186	3.58870
$796$	−75.5799	−2.67886
$797$	−50.1374	−1.77596	−0.887979	−	0.459884i	$-0.847891\pi$
$797$	−50.1374	−1.77596	−0.887979	+	0.459884i	$0.847891\pi$
$798$	−48.4397	−1.71475
$799$	−13.2448	−0.468567
$800$	1.74121	0.0615610
$801$	10.7318	0.379190
$802$	33.7755	1.19265
$803$	3.13737	0.110715
$804$	−42.8307	−1.51052
$805$	50.2202	1.77003
$806$	43.2186	1.52231
$807$	22.2893	0.784622
$808$	−31.0216	−1.09134
$809$	−19.0548	−0.669933	−0.334966	−	0.942230i	$-0.608725\pi$
$809$	−19.0548	−0.669933	−0.334966	+	0.942230i	$0.608725\pi$
$810$	186.801	6.56352
$811$	−37.9004	−1.33086	−0.665431	−	0.746460i	$-0.731752\pi$
$811$	−37.9004	−1.33086	−0.665431	+	0.746460i	$0.731752\pi$
$812$	−82.7839	−2.90515
$813$	−47.0757	−1.65102
$814$	112.553	3.94498
$815$	−24.4192	−0.855366
$816$	−28.7209	−1.00543
$817$	26.9399	0.942508
$818$	−53.9108	−1.88495
$819$	−45.6092	−1.59372
$820$	−11.3822	−0.397484
$821$	−28.7539	−1.00352	−0.501759	−	0.865007i	$-0.667314\pi$
$821$	−28.7539	−1.00352	−0.501759	+	0.865007i	$0.667314\pi$
$822$	−72.4705	−2.52770
$823$	−31.1456	−1.08567	−0.542834	−	0.839840i	$-0.682649\pi$
$823$	−31.1456	−1.08567	−0.542834	+	0.839840i	$0.682649\pi$
$824$	51.5458	1.79568
$825$	7.31298	0.254605
$826$	2.28445	0.0794861
$827$	−36.7521	−1.27800	−0.638998	−	0.769209i	$-0.720651\pi$
$827$	−36.7521	−1.27800	−0.638998	+	0.769209i	$0.720651\pi$
$828$	243.762	8.47132
$829$	−2.69920	−0.0937471	−0.0468736	−	0.998901i	$-0.514926\pi$
$829$	−2.69920	−0.0937471	−0.0468736	+	0.998901i	$0.514926\pi$
$830$	52.8478	1.83437
$831$	−32.2695	−1.11941
$832$	−26.0923	−0.904587
$833$	−2.94803	−0.102143
$834$	−27.8209	−0.963359
$835$	16.1025	0.557249
$836$	−42.4231	−1.46723
$837$	149.202	5.15716
$838$	−60.8720	−2.10279
$839$	−38.7361	−1.33732	−0.668659	−	0.743569i	$-0.733131\pi$
$839$	−38.7361	−1.33732	−0.668659	+	0.743569i	$0.733131\pi$
$840$	71.1150	2.45370
$841$	55.7648	1.92292
$842$	78.0890	2.69112
$843$	0.983747	0.0338820
$844$	−19.5032	−0.671329
$845$	19.3814	0.666742
$846$	39.5964	1.36135
$847$	−36.2653	−1.24609
$848$	17.1499	0.588931
$849$	53.8557	1.84832
$850$	−6.60581	−0.226577
$851$	80.4360	2.75731
$852$	−54.3805	−1.86304
$853$	−9.27382	−0.317529	−0.158765	−	0.987316i	$-0.550751\pi$
$853$	−9.27382	−0.317529	−0.158765	+	0.987316i	$0.550751\pi$
$854$	43.9751	1.50480
$855$	−46.1847	−1.57948
$856$	−4.03433	−0.137891
$857$	54.4467	1.85986	0.929932	−	0.367731i	$-0.119865\pi$
$857$	54.4467	1.85986	0.929932	+	0.367731i	$0.119865\pi$
$858$	−85.5025	−2.91901
$859$	−35.5638	−1.21342	−0.606710	−	0.794923i	$-0.707511\pi$
$859$	−35.5638	−1.21342	−0.606710	+	0.794923i	$0.707511\pi$
$860$	−91.7685	−3.12928
$861$	11.9114	0.405939
$862$	−67.0661	−2.28428
$863$	−17.4543	−0.594152	−0.297076	−	0.954854i	$-0.596011\pi$
$863$	−17.4543	−0.594152	−0.297076	+	0.954854i	$0.596011\pi$
$864$	−70.2808	−2.39100
$865$	51.1070	1.73769
$866$	−66.8552	−2.27183
$867$	−83.3057	−2.82921
$868$	76.4412	2.59458
$869$	−2.77878	−0.0942636
$870$	−168.954	−5.72808
$871$	7.86978	0.266657
$872$	29.5186	0.999627
$873$	−38.1672	−1.29176
$874$	−47.5688	−1.60904
$875$	−27.2260	−0.920405
$876$	7.36680	0.248901
$877$	−48.3978	−1.63428	−0.817139	−	0.576441i	$-0.804441\pi$
$877$	−48.3978	−1.63428	−0.817139	+	0.576441i	$0.804441\pi$
$878$	35.3210	1.19203
$879$	−48.2566	−1.62765
$880$	15.4925	0.522253
$881$	−5.75008	−0.193725	−0.0968626	−	0.995298i	$-0.530881\pi$
$881$	−5.75008	−0.193725	−0.0968626	+	0.995298i	$0.530881\pi$
$882$	8.81338	0.296762
$883$	−6.01517	−0.202427	−0.101213	−	0.994865i	$-0.532272\pi$
$883$	−6.01517	−0.202427	−0.101213	+	0.994865i	$0.532272\pi$
$884$	49.2247	1.65561
$885$	2.97150	0.0998860
$886$	−2.45301	−0.0824105
$887$	9.87434	0.331548	0.165774	−	0.986164i	$-0.446988\pi$
$887$	9.87434	0.331548	0.165774	+	0.986164i	$0.446988\pi$
$888$	113.902	3.82231
$889$	−10.6876	−0.358450
$890$	7.13390	0.239129
$891$	−171.205	−5.73557
$892$	84.2381	2.82050
$893$	−4.92475	−0.164800
$894$	−32.9870	−1.10325
$895$	−5.23286	−0.174915
$896$	−51.9208	−1.73455
$897$	−61.1043	−2.04021
$898$	21.4362	0.715336
$899$	−78.2703	−2.61046
$900$	12.5866	0.419554
$901$	83.7700	2.79078
$902$	16.3678	0.544988
$903$	96.0349	3.19584
$904$	−3.10584	−0.103299
$905$	−27.4175	−0.911387
$906$	46.9092	1.55845
$907$	31.5257	1.04679	0.523397	−	0.852089i	$-0.324664\pi$
$907$	31.5257	1.04679	0.523397	+	0.852089i	$0.324664\pi$
$908$	69.2904	2.29948
$909$	71.8183	2.38206
$910$	−30.3184	−1.00504
$911$	−52.7733	−1.74846	−0.874229	−	0.485513i	$-0.838633\pi$
$911$	−52.7733	−1.74846	−0.874229	+	0.485513i	$0.838633\pi$
$912$	−10.6792	−0.353623
$913$	−48.4354	−1.60298
$914$	47.4588	1.56980
$915$	57.2008	1.89100
$916$	19.9554	0.659346
$917$	−14.9710	−0.494387
$918$	266.632	8.80017
$919$	47.8561	1.57863	0.789314	−	0.613990i	$-0.210437\pi$
$919$	47.8561	1.57863	0.789314	+	0.613990i	$0.210437\pi$
$920$	69.8364	2.30244
$921$	−114.290	−3.76597
$922$	13.1264	0.432295
$923$	9.99195	0.328889
$924$	−151.229	−4.97507
$925$	4.15330	0.136560
$926$	52.1728	1.71450
$927$	−119.334	−3.91944
$928$	36.8689	1.21028
$929$	8.70839	0.285713	0.142857	−	0.989743i	$-0.454371\pi$
$929$	8.70839	0.285713	0.142857	+	0.989743i	$0.454371\pi$
$930$	156.009	5.11574
$931$	−1.09615	−0.0359250
$932$	46.3872	1.51946
$933$	19.2141	0.629041
$934$	−11.7354	−0.383993
$935$	75.6743	2.47481
$936$	−63.4243	−2.07309
$937$	−42.2895	−1.38154	−0.690768	−	0.723076i	$-0.742728\pi$
$937$	−42.2895	−1.38154	−0.690768	+	0.723076i	$0.742728\pi$
$938$	21.8396	0.713090
$939$	−104.945	−3.42476
$940$	16.7757	0.547164
$941$	−47.8757	−1.56070	−0.780351	−	0.625341i	$-0.784960\pi$
$941$	−47.8757	−1.56070	−0.780351	+	0.625341i	$0.784960\pi$
$942$	−109.255	−3.55971
$943$	11.6972	0.380915
$944$	0.503637	0.0163920
$945$	−104.667	−3.40481
$946$	131.964	4.29053
$947$	−4.00507	−0.130147	−0.0650737	−	0.997880i	$-0.520728\pi$
$947$	−4.00507	−0.130147	−0.0650737	+	0.997880i	$0.520728\pi$
$948$	−6.52480	−0.211916
$949$	−1.35359	−0.0439393
$950$	−2.45621	−0.0796899
$951$	15.8759	0.514813
$952$	58.8747	1.90814
$953$	−1.22460	−0.0396686	−0.0198343	−	0.999803i	$-0.506314\pi$
$953$	−1.22460	−0.0396686	−0.0198343	+	0.999803i	$0.506314\pi$
$954$	−250.437	−8.10820
$955$	−29.3673	−0.950304
$956$	69.2798	2.24067
$957$	154.848	5.00551
$958$	32.8499	1.06133
$959$	23.5518	0.760528
$960$	−94.1870	−3.03987
$961$	41.2733	1.33140
$962$	−48.5599	−1.56563
$963$	9.33990	0.300974
$964$	7.42483	0.239138
$965$	11.6624	0.375427
$966$	−169.572	−5.45590
$967$	−48.2682	−1.55220	−0.776101	−	0.630609i	$-0.782805\pi$
$967$	−48.2682	−1.55220	−0.776101	+	0.630609i	$0.782805\pi$
$968$	−50.4306	−1.62090
$969$	−52.1632	−1.67572
$970$	−25.3713	−0.814625
$971$	−16.8708	−0.541408	−0.270704	−	0.962663i	$-0.587257\pi$
$971$	−16.8708	−0.541408	−0.270704	+	0.962663i	$0.587257\pi$
$972$	−216.943	−6.95844
$973$	9.04138	0.289853
$974$	−15.4446	−0.494877
$975$	−3.15511	−0.101044
$976$	9.69490	0.310326
$977$	−15.5000	−0.495888	−0.247944	−	0.968774i	$-0.579755\pi$
$977$	−15.5000	−0.495888	−0.247944	+	0.968774i	$0.579755\pi$
$978$	82.4532	2.63656
$979$	−6.53827	−0.208964
$980$	3.73395	0.119277
$981$	−68.3386	−2.18189
$982$	−89.6457	−2.86071
$983$	−14.6282	−0.466567	−0.233284	−	0.972409i	$-0.574947\pi$
$983$	−14.6282	−0.466567	−0.233284	+	0.972409i	$0.574947\pi$
$984$	16.5640	0.528042
$985$	31.2525	0.995787
$986$	−139.874	−4.45448
$987$	−17.5557	−0.558803
$988$	18.3030	0.582296
$989$	94.3083	2.99883
$990$	−226.235	−7.19021
$991$	50.5842	1.60686	0.803430	−	0.595399i	$-0.203006\pi$
$991$	50.5842	1.60686	0.803430	+	0.595399i	$0.203006\pi$
$992$	−34.0441	−1.08090
$993$	−2.45292	−0.0778410
$994$	27.7289	0.879509
$995$	50.1294	1.58921
$996$	−113.730	−3.60368
$997$	−7.54852	−0.239064	−0.119532	−	0.992830i	$-0.538139\pi$
$997$	−7.54852	−0.239064	−0.119532	+	0.992830i	$0.538139\pi$
$998$	14.9384	0.472866
$999$	−167.641	−5.30392

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.c.1.17	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.c.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-2.34837 q^{2} -3.35198 q^{3} +3.51485 q^{4} -2.33127 q^{5} +7.87170 q^{6} -2.55818 q^{7} -3.55742 q^{8} +8.23579 q^{9} +O(q^{10})\)	\(q-2.34837 q^{2} -3.35198 q^{3} +3.51485 q^{4} -2.33127 q^{5} +7.87170 q^{6} -2.55818 q^{7} -3.55742 q^{8} +8.23579 q^{9} +5.47468 q^{10} -5.01759 q^{11} -11.7817 q^{12} +2.16479 q^{13} +6.00757 q^{14} +7.81437 q^{15} +1.32445 q^{16} +6.46936 q^{17} -19.3407 q^{18} +2.40547 q^{19} -8.19405 q^{20} +8.57499 q^{21} +11.7832 q^{22} +8.42083 q^{23} +11.9244 q^{24} +0.434808 q^{25} -5.08373 q^{26} -17.5503 q^{27} -8.99162 q^{28} +9.20678 q^{29} -18.3510 q^{30} -8.50137 q^{31} +4.00454 q^{32} +16.8189 q^{33} -15.1925 q^{34} +5.96381 q^{35} +28.9475 q^{36} +9.55203 q^{37} -5.64895 q^{38} -7.25633 q^{39} +8.29330 q^{40} +1.38908 q^{41} -20.1373 q^{42} +11.1994 q^{43} -17.6360 q^{44} -19.1998 q^{45} -19.7752 q^{46} -2.04731 q^{47} -4.43953 q^{48} -0.455691 q^{49} -1.02109 q^{50} -21.6852 q^{51} +7.60890 q^{52} +12.9487 q^{53} +41.2146 q^{54} +11.6973 q^{55} +9.10054 q^{56} -8.06311 q^{57} -21.6209 q^{58} +0.380262 q^{59} +27.4663 q^{60} +7.31995 q^{61} +19.9644 q^{62} -21.0687 q^{63} -12.0530 q^{64} -5.04670 q^{65} -39.4969 q^{66} +3.63536 q^{67} +22.7388 q^{68} -28.2265 q^{69} -14.0052 q^{70} +4.61567 q^{71} -29.2982 q^{72} -0.625275 q^{73} -22.4317 q^{74} -1.45747 q^{75} +8.45487 q^{76} +12.8359 q^{77} +17.0406 q^{78} +0.553808 q^{79} -3.08765 q^{80} +34.1209 q^{81} -3.26209 q^{82} +9.65313 q^{83} +30.1398 q^{84} -15.0818 q^{85} -26.3004 q^{86} -30.8610 q^{87} +17.8497 q^{88} +1.30307 q^{89} +45.0883 q^{90} -5.53793 q^{91} +29.5979 q^{92} +28.4965 q^{93} +4.80784 q^{94} -5.60780 q^{95} -13.4232 q^{96} -4.63431 q^{97} +1.07013 q^{98} -41.3238 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) \) 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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