LMFDB - Embedded newform 4003.2.a.c.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.64748 q^{2} +2.89261 q^{3} +5.00915 q^{4} +3.62616 q^{5} -7.65814 q^{6} +1.08314 q^{7} -7.96667 q^{8} +5.36721 q^{9} +O(q^{10})$	\(q-2.64748 q^{2} +2.89261 q^{3} +5.00915 q^{4} +3.62616 q^{5} -7.65814 q^{6} +1.08314 q^{7} -7.96667 q^{8} +5.36721 q^{9} -9.60018 q^{10} -4.28161 q^{11} +14.4895 q^{12} +5.59638 q^{13} -2.86759 q^{14} +10.4891 q^{15} +11.0733 q^{16} +1.81985 q^{17} -14.2096 q^{18} -7.75770 q^{19} +18.1640 q^{20} +3.13311 q^{21} +11.3355 q^{22} +4.67094 q^{23} -23.0445 q^{24} +8.14901 q^{25} -14.8163 q^{26} +6.84743 q^{27} +5.42561 q^{28} +9.07311 q^{29} -27.7696 q^{30} +5.85538 q^{31} -13.3830 q^{32} -12.3850 q^{33} -4.81801 q^{34} +3.92764 q^{35} +26.8852 q^{36} -0.0758430 q^{37} +20.5383 q^{38} +16.1882 q^{39} -28.8884 q^{40} +8.62838 q^{41} -8.29483 q^{42} -5.57989 q^{43} -21.4472 q^{44} +19.4624 q^{45} -12.3662 q^{46} -10.9631 q^{47} +32.0308 q^{48} -5.82681 q^{49} -21.5744 q^{50} +5.26412 q^{51} +28.0331 q^{52} +4.13375 q^{53} -18.1284 q^{54} -15.5258 q^{55} -8.62902 q^{56} -22.4400 q^{57} -24.0209 q^{58} +14.6491 q^{59} +52.5414 q^{60} -11.0384 q^{61} -15.5020 q^{62} +5.81344 q^{63} +13.2846 q^{64} +20.2933 q^{65} +32.7891 q^{66} -6.78760 q^{67} +9.11589 q^{68} +13.5112 q^{69} -10.3983 q^{70} -5.11064 q^{71} -42.7588 q^{72} -13.7830 q^{73} +0.200793 q^{74} +23.5719 q^{75} -38.8595 q^{76} -4.63758 q^{77} -42.8578 q^{78} -5.34405 q^{79} +40.1535 q^{80} +3.70534 q^{81} -22.8435 q^{82} -10.2636 q^{83} +15.6942 q^{84} +6.59905 q^{85} +14.7727 q^{86} +26.2450 q^{87} +34.1101 q^{88} +0.730464 q^{89} -51.5262 q^{90} +6.06166 q^{91} +23.3975 q^{92} +16.9374 q^{93} +29.0247 q^{94} -28.1306 q^{95} -38.7119 q^{96} +9.43142 q^{97} +15.4264 q^{98} -22.9803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.64748	−1.87205	−0.936026	−	0.351932i	$-0.885525\pi$
$2$	−2.64748	−1.87205	−0.936026	+	0.351932i	$0.885525\pi$
$3$	2.89261	1.67005	0.835026	−	0.550211i	$-0.185453\pi$
$3$	2.89261	1.67005	0.835026	+	0.550211i	$0.185453\pi$
$4$	5.00915	2.50458
$5$	3.62616	1.62167	0.810833	−	0.585277i	$-0.199014\pi$
$5$	3.62616	1.62167	0.810833	+	0.585277i	$0.199014\pi$
$6$	−7.65814	−3.12642
$7$	1.08314	0.409388	0.204694	−	0.978826i	$-0.434380\pi$
$7$	1.08314	0.409388	0.204694	+	0.978826i	$0.434380\pi$
$8$	−7.96667	−2.81664
$9$	5.36721	1.78907
$10$	−9.60018	−3.03584
$11$	−4.28161	−1.29095	−0.645476	−	0.763780i	$-0.723341\pi$
$11$	−4.28161	−1.29095	−0.645476	+	0.763780i	$0.723341\pi$
$12$	14.4895	4.18277
$13$	5.59638	1.55216	0.776078	−	0.630637i	$-0.217206\pi$
$13$	5.59638	1.55216	0.776078	+	0.630637i	$0.217206\pi$
$14$	−2.86759	−0.766396
$15$	10.4891	2.70827
$16$	11.0733	2.76833
$17$	1.81985	0.441378	0.220689	−	0.975344i	$-0.429169\pi$
$17$	1.81985	0.441378	0.220689	+	0.975344i	$0.429169\pi$
$18$	−14.2096	−3.34923
$19$	−7.75770	−1.77974	−0.889869	−	0.456217i	$-0.849204\pi$
$19$	−7.75770	−1.77974	−0.889869	+	0.456217i	$0.849204\pi$
$20$	18.1640	4.06159
$21$	3.13311	0.683700
$22$	11.3355	2.41673
$23$	4.67094	0.973959	0.486979	−	0.873413i	$-0.338099\pi$
$23$	4.67094	0.973959	0.486979	+	0.873413i	$0.338099\pi$
$24$	−23.0445	−4.70394
$25$	8.14901	1.62980
$26$	−14.8163	−2.90571
$27$	6.84743	1.31779
$28$	5.42561	1.02534
$29$	9.07311	1.68483	0.842417	−	0.538826i	$-0.181132\pi$
$29$	9.07311	1.68483	0.842417	+	0.538826i	$0.181132\pi$
$30$	−27.7696	−5.07001
$31$	5.85538	1.05166	0.525829	−	0.850590i	$-0.323755\pi$
$31$	5.85538	1.05166	0.525829	+	0.850590i	$0.323755\pi$
$32$	−13.3830	−2.36580
$33$	−12.3850	−2.15596
$34$	−4.81801	−0.826282
$35$	3.92764	0.663892
$36$	26.8852	4.48087
$37$	−0.0758430	−0.0124685	−0.00623425	−	0.999981i	$-0.501984\pi$
$37$	−0.0758430	−0.0124685	−0.00623425	+	0.999981i	$0.501984\pi$
$38$	20.5383	3.33176
$39$	16.1882	2.59218
$40$	−28.8884	−4.56766
$41$	8.62838	1.34753	0.673764	−	0.738947i	$-0.264677\pi$
$41$	8.62838	1.34753	0.673764	+	0.738947i	$0.264677\pi$
$42$	−8.29483	−1.27992
$43$	−5.57989	−0.850925	−0.425463	−	0.904976i	$-0.639889\pi$
$43$	−5.57989	−0.850925	−0.425463	+	0.904976i	$0.639889\pi$
$44$	−21.4472	−3.23329
$45$	19.4624	2.90128
$46$	−12.3662	−1.82330
$47$	−10.9631	−1.59914	−0.799569	−	0.600574i	$-0.794939\pi$
$47$	−10.9631	−1.59914	−0.799569	+	0.600574i	$0.794939\pi$
$48$	32.0308	4.62325
$49$	−5.82681	−0.832401
$50$	−21.5744	−3.05107
$51$	5.26412	0.737124
$52$	28.0331	3.88749
$53$	4.13375	0.567814	0.283907	−	0.958852i	$-0.408369\pi$
$53$	4.13375	0.567814	0.283907	+	0.958852i	$0.408369\pi$
$54$	−18.1284	−2.46697
$55$	−15.5258	−2.09349
$56$	−8.62902	−1.15310
$57$	−22.4400	−2.97225
$58$	−24.0209	−3.15410
$59$	14.6491	1.90716	0.953578	−	0.301147i	$-0.0973694\pi$
$59$	14.6491	1.90716	0.953578	+	0.301147i	$0.0973694\pi$
$60$	52.5414	6.78306
$61$	−11.0384	−1.41332	−0.706658	−	0.707555i	$-0.749798\pi$
$61$	−11.0384	−1.41332	−0.706658	+	0.707555i	$0.749798\pi$
$62$	−15.5020	−1.96876
$63$	5.81344	0.732425
$64$	13.2846	1.66058
$65$	20.2933	2.51708
$66$	32.7891	4.03606
$67$	−6.78760	−0.829237	−0.414618	−	0.909995i	$-0.636085\pi$
$67$	−6.78760	−0.829237	−0.414618	+	0.909995i	$0.636085\pi$
$68$	9.11589	1.10546
$69$	13.5112	1.62656
$70$	−10.3983	−1.24284
$71$	−5.11064	−0.606521	−0.303261	−	0.952908i	$-0.598075\pi$
$71$	−5.11064	−0.606521	−0.303261	+	0.952908i	$0.598075\pi$
$72$	−42.7588	−5.03918
$73$	−13.7830	−1.61317	−0.806587	−	0.591116i	$-0.798688\pi$
$73$	−13.7830	−1.61317	−0.806587	+	0.591116i	$0.798688\pi$
$74$	0.200793	0.0233417
$75$	23.5719	2.72185
$76$	−38.8595	−4.45749
$77$	−4.63758	−0.528501
$78$	−42.8578	−4.85269
$79$	−5.34405	−0.601252	−0.300626	−	0.953742i	$-0.597196\pi$
$79$	−5.34405	−0.601252	−0.300626	+	0.953742i	$0.597196\pi$
$80$	40.1535	4.48930
$81$	3.70534	0.411704
$82$	−22.8435	−2.52264
$83$	−10.2636	−1.12658	−0.563288	−	0.826261i	$-0.690464\pi$
$83$	−10.2636	−1.12658	−0.563288	+	0.826261i	$0.690464\pi$
$84$	15.6942	1.71238
$85$	6.59905	0.715768
$86$	14.7727	1.59298
$87$	26.2450	2.81376
$88$	34.1101	3.63615
$89$	0.730464	0.0774290	0.0387145	−	0.999250i	$-0.487674\pi$
$89$	0.730464	0.0774290	0.0387145	+	0.999250i	$0.487674\pi$
$90$	−51.5262	−5.43134
$91$	6.06166	0.635434
$92$	23.3975	2.43935
$93$	16.9374	1.75632
$94$	29.0247	2.99367
$95$	−28.1306	−2.88614
$96$	−38.7119	−3.95101
$97$	9.43142	0.957616	0.478808	−	0.877920i	$-0.341069\pi$
$97$	9.43142	0.957616	0.478808	+	0.877920i	$0.341069\pi$
$98$	15.4264	1.55830
$99$	−22.9803	−2.30961
$100$	40.8196	4.08196
$101$	−6.89393	−0.685972	−0.342986	−	0.939341i	$-0.611438\pi$
$101$	−6.89393	−0.685972	−0.342986	+	0.939341i	$0.611438\pi$
$102$	−13.9366	−1.37993
$103$	12.3202	1.21395	0.606974	−	0.794722i	$-0.292383\pi$
$103$	12.3202	1.21395	0.606974	+	0.794722i	$0.292383\pi$
$104$	−44.5845	−4.37187
$105$	11.3611	1.10873
$106$	−10.9440	−1.06298
$107$	10.0047	0.967190	0.483595	−	0.875292i	$-0.339331\pi$
$107$	10.0047	0.967190	0.483595	+	0.875292i	$0.339331\pi$
$108$	34.2998	3.30050
$109$	−1.52346	−0.145921	−0.0729603	−	0.997335i	$-0.523245\pi$
$109$	−1.52346	−0.145921	−0.0729603	+	0.997335i	$0.523245\pi$
$110$	41.1042	3.91913
$111$	−0.219384	−0.0208230
$112$	11.9939	1.13332
$113$	3.01613	0.283734	0.141867	−	0.989886i	$-0.454690\pi$
$113$	3.01613	0.283734	0.141867	+	0.989886i	$0.454690\pi$
$114$	59.4095	5.56421
$115$	16.9376	1.57944
$116$	45.4486	4.21980
$117$	30.0369	2.77692
$118$	−38.7833	−3.57029
$119$	1.97115	0.180695
$120$	−83.5630	−7.62822
$121$	7.33214	0.666559
$122$	29.2238	2.64580
$123$	24.9586	2.25044
$124$	29.3305	2.63396
$125$	11.4188	1.02133
$126$	−15.3910	−1.37114
$127$	−0.197600	−0.0175341	−0.00876707	−	0.999962i	$-0.502791\pi$
$127$	−0.197600	−0.0175341	−0.00876707	+	0.999962i	$0.502791\pi$
$128$	−8.40482	−0.742889
$129$	−16.1405	−1.42109
$130$	−53.7262	−4.71210
$131$	6.83446	0.597130	0.298565	−	0.954389i	$-0.403492\pi$
$131$	6.83446	0.597130	0.298565	+	0.954389i	$0.403492\pi$
$132$	−62.0385	−5.39976
$133$	−8.40267	−0.728604
$134$	17.9700	1.55237
$135$	24.8299	2.13701
$136$	−14.4981	−1.24320
$137$	16.3806	1.39949	0.699744	−	0.714393i	$-0.253297\pi$
$137$	16.3806	1.39949	0.699744	+	0.714393i	$0.253297\pi$
$138$	−35.7707	−3.04501
$139$	−0.374348	−0.0317517	−0.0158759	−	0.999874i	$-0.505054\pi$
$139$	−0.374348	−0.0317517	−0.0158759	+	0.999874i	$0.505054\pi$
$140$	19.6741	1.66277
$141$	−31.7121	−2.67064
$142$	13.5303	1.13544
$143$	−23.9615	−2.00376
$144$	59.4328	4.95273
$145$	32.9005	2.73224
$146$	36.4901	3.01994
$147$	−16.8547	−1.39015
$148$	−0.379909	−0.0312283
$149$	3.75611	0.307712	0.153856	−	0.988093i	$-0.450831\pi$
$149$	3.75611	0.307712	0.153856	+	0.988093i	$0.450831\pi$
$150$	−62.4063	−5.09545
$151$	−5.76659	−0.469278	−0.234639	−	0.972083i	$-0.575391\pi$
$151$	−5.76659	−0.469278	−0.234639	+	0.972083i	$0.575391\pi$
$152$	61.8030	5.01289
$153$	9.76751	0.789656
$154$	12.2779	0.989381
$155$	21.2325	1.70544
$156$	81.0889	6.49231
$157$	−14.9576	−1.19375	−0.596873	−	0.802336i	$-0.703590\pi$
$157$	−14.9576	−1.19375	−0.596873	+	0.802336i	$0.703590\pi$
$158$	14.1483	1.12557
$159$	11.9573	0.948279
$160$	−48.5289	−3.83655
$161$	5.05928	0.398727
$162$	−9.80982	−0.770732
$163$	−19.7624	−1.54791	−0.773957	−	0.633238i	$-0.781725\pi$
$163$	−19.7624	−1.54791	−0.773957	+	0.633238i	$0.781725\pi$
$164$	43.2209	3.37498
$165$	−44.9101	−3.49624
$166$	27.1727	2.10901
$167$	−13.0546	−1.01020	−0.505099	−	0.863061i	$-0.668544\pi$
$167$	−13.0546	−1.01020	−0.505099	+	0.863061i	$0.668544\pi$
$168$	−24.9604	−1.92574
$169$	18.3194	1.40919
$170$	−17.4709	−1.33995
$171$	−41.6372	−3.18408
$172$	−27.9505	−2.13121
$173$	−22.4559	−1.70729	−0.853646	−	0.520854i	$-0.825614\pi$
$173$	−22.4559	−1.70729	−0.853646	+	0.520854i	$0.825614\pi$
$174$	−69.4831	−5.26750
$175$	8.82652	0.667222
$176$	−47.4115	−3.57378
$177$	42.3743	3.18505
$178$	−1.93389	−0.144951
$179$	13.2450	0.989977	0.494988	−	0.868900i	$-0.335172\pi$
$179$	13.2450	0.989977	0.494988	+	0.868900i	$0.335172\pi$
$180$	97.4899	7.26647
$181$	14.1328	1.05048	0.525242	−	0.850953i	$-0.323975\pi$
$181$	14.1328	1.05048	0.525242	+	0.850953i	$0.323975\pi$
$182$	−16.0481	−1.18957
$183$	−31.9297	−2.36031
$184$	−37.2119	−2.74330
$185$	−0.275019	−0.0202198
$186$	−44.8413	−3.28793
$187$	−7.79187	−0.569798
$188$	−54.9160	−4.00516
$189$	7.41673	0.539488
$190$	74.4753	5.40300
$191$	−5.81177	−0.420525	−0.210263	−	0.977645i	$-0.567432\pi$
$191$	−5.81177	−0.420525	−0.210263	+	0.977645i	$0.567432\pi$
$192$	38.4273	2.77326
$193$	7.21340	0.519232	0.259616	−	0.965712i	$-0.416404\pi$
$193$	7.21340	0.519232	0.259616	+	0.965712i	$0.416404\pi$
$194$	−24.9695	−1.79271
$195$	58.7008	4.20365
$196$	−29.1874	−2.08481
$197$	−6.42877	−0.458031	−0.229015	−	0.973423i	$-0.573551\pi$
$197$	−6.42877	−0.458031	−0.229015	+	0.973423i	$0.573551\pi$
$198$	60.8399	4.32370
$199$	26.7237	1.89439	0.947197	−	0.320651i	$-0.103902\pi$
$199$	26.7237	1.89439	0.947197	+	0.320651i	$0.103902\pi$
$200$	−64.9205	−4.59057
$201$	−19.6339	−1.38487
$202$	18.2515	1.28417
$203$	9.82745	0.689752
$204$	26.3688	1.84618
$205$	31.2879	2.18524
$206$	−32.6176	−2.27257
$207$	25.0699	1.74248
$208$	61.9704	4.29687
$209$	33.2154	2.29756
$210$	−30.0784	−2.07560
$211$	−8.88244	−0.611493	−0.305746	−	0.952113i	$-0.598906\pi$
$211$	−8.88244	−0.611493	−0.305746	+	0.952113i	$0.598906\pi$
$212$	20.7066	1.42213
$213$	−14.7831	−1.01292
$214$	−26.4872	−1.81063
$215$	−20.2336	−1.37992
$216$	−54.5513	−3.71174
$217$	6.34220	0.430537
$218$	4.03332	0.273171
$219$	−39.8688	−2.69408
$220$	−77.7710	−5.24332
$221$	10.1846	0.685087
$222$	0.580816	0.0389818
$223$	−3.25366	−0.217881	−0.108941	−	0.994048i	$-0.534746\pi$
$223$	−3.25366	−0.217881	−0.108941	+	0.994048i	$0.534746\pi$
$224$	−14.4957	−0.968533
$225$	43.7375	2.91583
$226$	−7.98515	−0.531164
$227$	15.1823	1.00768	0.503842	−	0.863796i	$-0.331919\pi$
$227$	15.1823	1.00768	0.503842	+	0.863796i	$0.331919\pi$
$228$	−112.405	−7.44423
$229$	−2.33262	−0.154144	−0.0770719	−	0.997026i	$-0.524557\pi$
$229$	−2.33262	−0.154144	−0.0770719	+	0.997026i	$0.524557\pi$
$230$	−44.8419	−2.95679
$231$	−13.4147	−0.882624
$232$	−72.2825	−4.74558
$233$	−9.45867	−0.619658	−0.309829	−	0.950792i	$-0.600272\pi$
$233$	−9.45867	−0.619658	−0.309829	+	0.950792i	$0.600272\pi$
$234$	−79.5222	−5.19853
$235$	−39.7541	−2.59327
$236$	73.3798	4.77662
$237$	−15.4583	−1.00412
$238$	−5.21858	−0.338270
$239$	−26.7926	−1.73307	−0.866533	−	0.499119i	$-0.833657\pi$
$239$	−26.7926	−1.73307	−0.866533	+	0.499119i	$0.833657\pi$
$240$	116.149	7.49736
$241$	−13.6719	−0.880686	−0.440343	−	0.897830i	$-0.645143\pi$
$241$	−13.6719	−0.880686	−0.440343	+	0.897830i	$0.645143\pi$
$242$	−19.4117	−1.24783
$243$	−9.82418	−0.630222
$244$	−55.2928	−3.53976
$245$	−21.1289	−1.34988
$246$	−66.0774	−4.21294
$247$	−43.4150	−2.76243
$248$	−46.6479	−2.96215
$249$	−29.6886	−1.88144
$250$	−30.2311	−1.91198
$251$	−5.25740	−0.331844	−0.165922	−	0.986139i	$-0.553060\pi$
$251$	−5.25740	−0.331844	−0.165922	+	0.986139i	$0.553060\pi$
$252$	29.1204	1.83441
$253$	−19.9991	−1.25733
$254$	0.523141	0.0328248
$255$	19.0885	1.19537
$256$	−4.31769	−0.269855
$257$	2.72408	0.169923	0.0849616	−	0.996384i	$-0.472923\pi$
$257$	2.72408	0.169923	0.0849616	+	0.996384i	$0.472923\pi$
$258$	42.7316	2.66035
$259$	−0.0821486	−0.00510446
$260$	101.652	6.30422
$261$	48.6973	3.01429
$262$	−18.0941	−1.11786
$263$	9.87419	0.608869	0.304434	−	0.952533i	$-0.401533\pi$
$263$	9.87419	0.608869	0.304434	+	0.952533i	$0.401533\pi$
$264$	98.6675	6.07256
$265$	14.9896	0.920805
$266$	22.2459	1.36398
$267$	2.11295	0.129310
$268$	−34.0001	−2.07689
$269$	−1.39306	−0.0849364	−0.0424682	−	0.999098i	$-0.513522\pi$
$269$	−1.39306	−0.0849364	−0.0424682	+	0.999098i	$0.513522\pi$
$270$	−65.7366	−4.00060
$271$	22.6658	1.37685	0.688425	−	0.725307i	$-0.258302\pi$
$271$	22.6658	1.37685	0.688425	+	0.725307i	$0.258302\pi$
$272$	20.1517	1.22188
$273$	17.5340	1.06121
$274$	−43.3673	−2.61991
$275$	−34.8909	−2.10400
$276$	67.6798	4.07385
$277$	21.4396	1.28818	0.644090	−	0.764949i	$-0.277236\pi$
$277$	21.4396	1.28818	0.644090	+	0.764949i	$0.277236\pi$
$278$	0.991078	0.0594409
$279$	31.4271	1.88149
$280$	−31.2902	−1.86995
$281$	24.5703	1.46574	0.732870	−	0.680368i	$-0.238180\pi$
$281$	24.5703	1.46574	0.732870	+	0.680368i	$0.238180\pi$
$282$	83.9572	4.99958
$283$	9.30052	0.552859	0.276429	−	0.961034i	$-0.410849\pi$
$283$	9.30052	0.552859	0.276429	+	0.961034i	$0.410849\pi$
$284$	−25.6000	−1.51908
$285$	−81.3710	−4.82000
$286$	63.4375	3.75114
$287$	9.34575	0.551662
$288$	−71.8295	−4.23259
$289$	−13.6882	−0.805186
$290$	−87.1035	−5.11489
$291$	27.2815	1.59927
$292$	−69.0410	−4.04032
$293$	15.8700	0.927137	0.463569	−	0.886061i	$-0.346569\pi$
$293$	15.8700	0.927137	0.463569	+	0.886061i	$0.346569\pi$
$294$	44.6225	2.60244
$295$	53.1201	3.09277
$296$	0.604216	0.0351193
$297$	−29.3180	−1.70120
$298$	−9.94421	−0.576053
$299$	26.1404	1.51174
$300$	118.075	6.81709
$301$	−6.04380	−0.348359
$302$	15.2669	0.878513
$303$	−19.9415	−1.14561
$304$	−85.9033	−4.92689
$305$	−40.0268	−2.29193
$306$	−25.8593	−1.47828
$307$	−8.17943	−0.466825	−0.233412	−	0.972378i	$-0.574989\pi$
$307$	−8.17943	−0.466825	−0.233412	+	0.972378i	$0.574989\pi$
$308$	−23.2303	−1.32367
$309$	35.6377	2.02736
$310$	−56.2127	−3.19267
$311$	9.29348	0.526985	0.263492	−	0.964661i	$-0.415126\pi$
$311$	9.29348	0.526985	0.263492	+	0.964661i	$0.415126\pi$
$312$	−128.966	−7.30125
$313$	25.2307	1.42612	0.713062	−	0.701101i	$-0.247308\pi$
$313$	25.2307	1.42612	0.713062	+	0.701101i	$0.247308\pi$
$314$	39.5999	2.23475
$315$	21.0805	1.18775
$316$	−26.7691	−1.50588
$317$	−12.3336	−0.692726	−0.346363	−	0.938101i	$-0.612583\pi$
$317$	−12.3336	−0.692726	−0.346363	+	0.938101i	$0.612583\pi$
$318$	−31.6568	−1.77523
$319$	−38.8475	−2.17504
$320$	48.1722	2.69291
$321$	28.9397	1.61526
$322$	−13.3944	−0.746438
$323$	−14.1178	−0.785537
$324$	18.5606	1.03115
$325$	45.6049	2.52971
$326$	52.3207	2.89777
$327$	−4.40677	−0.243695
$328$	−68.7395	−3.79550
$329$	−11.8746	−0.654669
$330$	118.899	6.54515
$331$	−9.53761	−0.524234	−0.262117	−	0.965036i	$-0.584421\pi$
$331$	−9.53761	−0.524234	−0.262117	+	0.965036i	$0.584421\pi$
$332$	−51.4119	−2.82159
$333$	−0.407065	−0.0223070
$334$	34.5619	1.89114
$335$	−24.6129	−1.34475
$336$	34.6938	1.89270
$337$	15.3667	0.837076	0.418538	−	0.908199i	$-0.362543\pi$
$337$	15.3667	0.837076	0.418538	+	0.908199i	$0.362543\pi$
$338$	−48.5003	−2.63807
$339$	8.72450	0.473850
$340$	33.0557	1.79269
$341$	−25.0704	−1.35764
$342$	110.234	5.96076
$343$	−13.8932	−0.750164
$344$	44.4532	2.39675
$345$	48.9938	2.63774
$346$	59.4516	3.19614
$347$	−7.15827	−0.384276	−0.192138	−	0.981368i	$-0.561542\pi$
$347$	−7.15827	−0.384276	−0.192138	+	0.981368i	$0.561542\pi$
$348$	131.465	7.04728
$349$	−15.6055	−0.835343	−0.417671	−	0.908598i	$-0.637154\pi$
$349$	−15.6055	−0.835343	−0.417671	+	0.908598i	$0.637154\pi$
$350$	−23.3680	−1.24907
$351$	38.3208	2.04541
$352$	57.3008	3.05414
$353$	−35.1808	−1.87248	−0.936242	−	0.351356i	$-0.885721\pi$
$353$	−35.1808	−1.87248	−0.936242	+	0.351356i	$0.885721\pi$
$354$	−112.185	−5.96257
$355$	−18.5320	−0.983576
$356$	3.65900	0.193927
$357$	5.70177	0.301770
$358$	−35.0658	−1.85329
$359$	12.9142	0.681583	0.340792	−	0.940139i	$-0.389305\pi$
$359$	12.9142	0.681583	0.340792	+	0.940139i	$0.389305\pi$
$360$	−155.050	−8.17186
$361$	41.1818	2.16747
$362$	−37.4163	−1.96656
$363$	21.2091	1.11319
$364$	30.3638	1.59149
$365$	−49.9792	−2.61603
$366$	84.5332	4.41862
$367$	−22.6161	−1.18055	−0.590275	−	0.807202i	$-0.700981\pi$
$367$	−22.6161	−1.18055	−0.590275	+	0.807202i	$0.700981\pi$
$368$	51.7228	2.69624
$369$	46.3104	2.41082
$370$	0.728106	0.0378524
$371$	4.47743	0.232457
$372$	84.8418	4.39884
$373$	−17.6455	−0.913650	−0.456825	−	0.889557i	$-0.651013\pi$
$373$	−17.6455	−0.913650	−0.456825	+	0.889557i	$0.651013\pi$
$374$	20.6288	1.06669
$375$	33.0302	1.70567
$376$	87.3397	4.50420
$377$	50.7765	2.61513
$378$	−19.6356	−1.00995
$379$	−19.0429	−0.978167	−0.489083	−	0.872237i	$-0.662669\pi$
$379$	−19.0429	−0.978167	−0.489083	+	0.872237i	$0.662669\pi$
$380$	−140.911	−7.22856
$381$	−0.571580	−0.0292829
$382$	15.3866	0.787245
$383$	−12.9167	−0.660010	−0.330005	−	0.943979i	$-0.607051\pi$
$383$	−12.9167	−0.660010	−0.330005	+	0.943979i	$0.607051\pi$
$384$	−24.3119	−1.24066
$385$	−16.8166	−0.857052
$386$	−19.0973	−0.972028
$387$	−29.9485	−1.52237
$388$	47.2434	2.39842
$389$	29.7573	1.50875	0.754376	−	0.656442i	$-0.227939\pi$
$389$	29.7573	1.50875	0.754376	+	0.656442i	$0.227939\pi$
$390$	−155.409	−7.86945
$391$	8.50040	0.429884
$392$	46.4203	2.34458
$393$	19.7695	0.997237
$394$	17.0200	0.857458
$395$	−19.3783	−0.975030
$396$	−115.112	−5.78458
$397$	22.3698	1.12271	0.561355	−	0.827575i	$-0.310280\pi$
$397$	22.3698	1.12271	0.561355	+	0.827575i	$0.310280\pi$
$398$	−70.7505	−3.54640
$399$	−24.3057	−1.21681
$400$	90.2365	4.51182
$401$	−11.6158	−0.580066	−0.290033	−	0.957017i	$-0.593666\pi$
$401$	−11.6158	−0.580066	−0.290033	+	0.957017i	$0.593666\pi$
$402$	51.9803	2.59254
$403$	32.7689	1.63234
$404$	−34.5328	−1.71807
$405$	13.4361	0.667647
$406$	−26.0180	−1.29125
$407$	0.324730	0.0160963
$408$	−41.9375	−2.07621
$409$	12.9847	0.642051	0.321025	−	0.947071i	$-0.395973\pi$
$409$	12.9847	0.642051	0.321025	+	0.947071i	$0.395973\pi$
$410$	−82.8340	−4.09088
$411$	47.3827	2.33722
$412$	61.7139	3.04042
$413$	15.8671	0.780767
$414$	−66.3722	−3.26202
$415$	−37.2174	−1.82693
$416$	−74.8964	−3.67210
$417$	−1.08284	−0.0530270
$418$	−87.9371	−4.30114
$419$	−3.17947	−0.155327	−0.0776635	−	0.996980i	$-0.524746\pi$
$419$	−3.17947	−0.155327	−0.0776635	+	0.996980i	$0.524746\pi$
$420$	56.9096	2.77691
$421$	6.80322	0.331569	0.165784	−	0.986162i	$-0.446984\pi$
$421$	6.80322	0.331569	0.165784	+	0.986162i	$0.446984\pi$
$422$	23.5161	1.14475
$423$	−58.8415	−2.86097
$424$	−32.9322	−1.59933
$425$	14.8300	0.719359
$426$	39.1380	1.89624
$427$	−11.9561	−0.578595
$428$	50.1150	2.42240
$429$	−69.3113	−3.34638
$430$	53.5679	2.58328
$431$	−3.44615	−0.165995	−0.0829975	−	0.996550i	$-0.526449\pi$
$431$	−3.44615	−0.165995	−0.0829975	+	0.996550i	$0.526449\pi$
$432$	75.8237	3.64807
$433$	−8.31846	−0.399760	−0.199880	−	0.979820i	$-0.564055\pi$
$433$	−8.31846	−0.399760	−0.199880	+	0.979820i	$0.564055\pi$
$434$	−16.7908	−0.805987
$435$	95.1685	4.56298
$436$	−7.63122	−0.365469
$437$	−36.2358	−1.73339
$438$	105.552	5.04346
$439$	−12.8921	−0.615306	−0.307653	−	0.951499i	$-0.599544\pi$
$439$	−12.8921	−0.615306	−0.307653	+	0.951499i	$0.599544\pi$
$440$	123.689	5.89663
$441$	−31.2737	−1.48922
$442$	−26.9634	−1.28252
$443$	7.60334	0.361245	0.180623	−	0.983552i	$-0.442189\pi$
$443$	7.60334	0.361245	0.180623	+	0.983552i	$0.442189\pi$
$444$	−1.09893	−0.0521529
$445$	2.64878	0.125564
$446$	8.61400	0.407885
$447$	10.8650	0.513895
$448$	14.3891	0.679823
$449$	−33.5784	−1.58466	−0.792331	−	0.610091i	$-0.791133\pi$
$449$	−33.5784	−1.58466	−0.792331	+	0.610091i	$0.791133\pi$
$450$	−115.794	−5.45859
$451$	−36.9433	−1.73959
$452$	15.1083	0.710633
$453$	−16.6805	−0.783719
$454$	−40.1948	−1.88644
$455$	21.9805	1.03046
$456$	178.772	8.37178
$457$	21.3349	0.998004	0.499002	−	0.866601i	$-0.333700\pi$
$457$	21.3349	0.998004	0.499002	+	0.866601i	$0.333700\pi$
$458$	6.17557	0.288565
$459$	12.4613	0.581643
$460$	84.8429	3.95582
$461$	14.1583	0.659419	0.329709	−	0.944082i	$-0.393049\pi$
$461$	14.1583	0.659419	0.329709	+	0.944082i	$0.393049\pi$
$462$	35.5152	1.65232
$463$	−36.8277	−1.71153	−0.855764	−	0.517367i	$-0.826912\pi$
$463$	−36.8277	−1.71153	−0.855764	+	0.517367i	$0.826912\pi$
$464$	100.469	4.66417
$465$	61.4175	2.84817
$466$	25.0416	1.16003
$467$	24.9682	1.15539	0.577696	−	0.816252i	$-0.303952\pi$
$467$	24.9682	1.15539	0.577696	+	0.816252i	$0.303952\pi$
$468$	150.460	6.95500
$469$	−7.35192	−0.339480
$470$	105.248	4.85473
$471$	−43.2665	−1.99362
$472$	−116.705	−5.37178
$473$	23.8909	1.09850
$474$	40.9254	1.87977
$475$	−63.2176	−2.90062
$476$	9.87379	0.452564
$477$	22.1867	1.01586
$478$	70.9328	3.24439
$479$	−18.6823	−0.853618	−0.426809	−	0.904342i	$-0.640362\pi$
$479$	−18.6823	−0.853618	−0.426809	+	0.904342i	$0.640362\pi$
$480$	−140.375	−6.40723
$481$	−0.424446	−0.0193531
$482$	36.1962	1.64869
$483$	14.6346	0.665895
$484$	36.7278	1.66945
$485$	34.1998	1.55293
$486$	26.0093	1.17981
$487$	12.4357	0.563515	0.281757	−	0.959486i	$-0.409083\pi$
$487$	12.4357	0.563515	0.281757	+	0.959486i	$0.409083\pi$
$488$	87.9389	3.98081
$489$	−57.1651	−2.58510
$490$	55.9384	2.52704
$491$	4.15707	0.187606	0.0938031	−	0.995591i	$-0.470098\pi$
$491$	4.15707	0.187606	0.0938031	+	0.995591i	$0.470098\pi$
$492$	125.021	5.63640
$493$	16.5117	0.743649
$494$	114.940	5.17141
$495$	−83.3301	−3.74541
$496$	64.8384	2.91133
$497$	−5.53554	−0.248303
$498$	78.6000	3.52215
$499$	−6.33437	−0.283566	−0.141783	−	0.989898i	$-0.545283\pi$
$499$	−6.33437	−0.283566	−0.141783	+	0.989898i	$0.545283\pi$
$500$	57.1986	2.55800
$501$	−37.7620	−1.68708
$502$	13.9189	0.621230
$503$	−10.4867	−0.467579	−0.233789	−	0.972287i	$-0.575113\pi$
$503$	−10.4867	−0.467579	−0.233789	+	0.972287i	$0.575113\pi$
$504$	−46.3138	−2.06298
$505$	−24.9985	−1.11242
$506$	52.9473	2.35380
$507$	52.9910	2.35341
$508$	−0.989807	−0.0439156
$509$	−33.5799	−1.48840	−0.744202	−	0.667954i	$-0.767170\pi$
$509$	−33.5799	−1.48840	−0.744202	+	0.667954i	$0.767170\pi$
$510$	−50.5365	−2.23779
$511$	−14.9289	−0.660415
$512$	28.2406	1.24807
$513$	−53.1203	−2.34532
$514$	−7.21194	−0.318105
$515$	44.6751	1.96862
$516$	−80.8501	−3.55923
$517$	46.9398	2.06441
$518$	0.217487	0.00955582
$519$	−64.9563	−2.85127
$520$	−161.670	−7.08971
$521$	39.4913	1.73014	0.865072	−	0.501649i	$-0.167273\pi$
$521$	39.4913	1.73014	0.865072	+	0.501649i	$0.167273\pi$
$522$	−128.925	−5.64290
$523$	40.4774	1.76995	0.884976	−	0.465636i	$-0.154174\pi$
$523$	40.4774	1.76995	0.884976	+	0.465636i	$0.154174\pi$
$524$	34.2349	1.49556
$525$	25.5317	1.11430
$526$	−26.1417	−1.13983
$527$	10.6559	0.464178
$528$	−137.143	−5.96839
$529$	−1.18229	−0.0514041
$530$	−39.6847	−1.72379
$531$	78.6251	3.41204
$532$	−42.0903	−1.82484
$533$	48.2877	2.09157
$534$	−5.59399	−0.242076
$535$	36.2786	1.56846
$536$	54.0745	2.33566
$537$	38.3126	1.65331
$538$	3.68810	0.159005
$539$	24.9481	1.07459
$540$	124.377	5.35232
$541$	37.5916	1.61619	0.808094	−	0.589054i	$-0.200499\pi$
$541$	37.5916	1.61619	0.808094	+	0.589054i	$0.200499\pi$
$542$	−60.0073	−2.57753
$543$	40.8808	1.75436
$544$	−24.3550	−1.04421
$545$	−5.52429	−0.236635
$546$	−46.4210	−1.98664
$547$	−16.7892	−0.717855	−0.358927	−	0.933366i	$-0.616857\pi$
$547$	−16.7892	−0.717855	−0.358927	+	0.933366i	$0.616857\pi$
$548$	82.0529	3.50513
$549$	−59.2452	−2.52852
$550$	92.3729	3.93879
$551$	−70.3864	−2.99856
$552$	−107.640	−4.58144
$553$	−5.78835	−0.246146
$554$	−56.7609	−2.41154
$555$	−0.795522	−0.0337680
$556$	−1.87516	−0.0795247
$557$	5.76993	0.244480	0.122240	−	0.992501i	$-0.460992\pi$
$557$	5.76993	0.244480	0.122240	+	0.992501i	$0.460992\pi$
$558$	−83.2026	−3.52225
$559$	−31.2272	−1.32077
$560$	43.4919	1.83787
$561$	−22.5389	−0.951592
$562$	−65.0494	−2.74394
$563$	−12.1989	−0.514124	−0.257062	−	0.966395i	$-0.582754\pi$
$563$	−12.1989	−0.514124	−0.257062	+	0.966395i	$0.582754\pi$
$564$	−158.851	−6.68883
$565$	10.9370	0.460121
$566$	−24.6230	−1.03498
$567$	4.01340	0.168547
$568$	40.7148	1.70836
$569$	31.9559	1.33966	0.669830	−	0.742515i	$-0.266367\pi$
$569$	31.9559	1.33966	0.669830	+	0.742515i	$0.266367\pi$
$570$	215.428	9.02329
$571$	−35.2509	−1.47521	−0.737603	−	0.675234i	$-0.764042\pi$
$571$	−35.2509	−1.47521	−0.737603	+	0.675234i	$0.764042\pi$
$572$	−120.027	−5.01857
$573$	−16.8112	−0.702298
$574$	−24.7427	−1.03274
$575$	38.0636	1.58736
$576$	71.3015	2.97090
$577$	−17.7779	−0.740103	−0.370051	−	0.929011i	$-0.620660\pi$
$577$	−17.7779	−0.740103	−0.370051	+	0.929011i	$0.620660\pi$
$578$	36.2391	1.50735
$579$	20.8656	0.867144
$580$	164.804	6.84310
$581$	−11.1169	−0.461207
$582$	−72.2271	−2.99391
$583$	−17.6991	−0.733021
$584$	109.804	4.54374
$585$	108.919	4.50323
$586$	−42.0156	−1.73565
$587$	40.2878	1.66285	0.831427	−	0.555634i	$-0.187524\pi$
$587$	40.2878	1.66285	0.831427	+	0.555634i	$0.187524\pi$
$588$	−84.4278	−3.48174
$589$	−45.4243	−1.87167
$590$	−140.634	−5.78983
$591$	−18.5960	−0.764935
$592$	−0.839832	−0.0345169
$593$	15.8728	0.651817	0.325908	−	0.945401i	$-0.394330\pi$
$593$	15.8728	0.651817	0.325908	+	0.945401i	$0.394330\pi$
$594$	77.6189	3.18474
$595$	7.14770	0.293027
$596$	18.8149	0.770688
$597$	77.3014	3.16374
$598$	−69.2061	−2.83005
$599$	−8.67101	−0.354288	−0.177144	−	0.984185i	$-0.556686\pi$
$599$	−8.67101	−0.354288	−0.177144	+	0.984185i	$0.556686\pi$
$600$	−187.790	−7.66649
$601$	−26.3945	−1.07665	−0.538327	−	0.842736i	$-0.680943\pi$
$601$	−26.3945	−1.07665	−0.538327	+	0.842736i	$0.680943\pi$
$602$	16.0008	0.652146
$603$	−36.4305	−1.48356
$604$	−28.8857	−1.17534
$605$	26.5875	1.08094
$606$	52.7947	2.14464
$607$	−4.02326	−0.163299	−0.0816496	−	0.996661i	$-0.526019\pi$
$607$	−4.02326	−0.163299	−0.0816496	+	0.996661i	$0.526019\pi$
$608$	103.821	4.21051
$609$	28.4270	1.15192
$610$	105.970	4.29061
$611$	−61.3539	−2.48211
$612$	48.9269	1.97775
$613$	5.25999	0.212449	0.106224	−	0.994342i	$-0.466124\pi$
$613$	5.25999	0.212449	0.106224	+	0.994342i	$0.466124\pi$
$614$	21.6549	0.873920
$615$	90.5037	3.64946
$616$	36.9461	1.48860
$617$	−11.6549	−0.469209	−0.234604	−	0.972091i	$-0.575379\pi$
$617$	−11.6549	−0.469209	−0.234604	+	0.972091i	$0.575379\pi$
$618$	−94.3500	−3.79531
$619$	−9.86867	−0.396656	−0.198328	−	0.980136i	$-0.563551\pi$
$619$	−9.86867	−0.396656	−0.198328	+	0.980136i	$0.563551\pi$
$620$	106.357	4.27140
$621$	31.9840	1.28347
$622$	−24.6043	−0.986542
$623$	0.791194	0.0316985
$624$	179.256	7.17600
$625$	0.661348	0.0264539
$626$	−66.7978	−2.66978
$627$	96.0793	3.83704
$628$	−74.9249	−2.98983
$629$	−0.138023	−0.00550332
$630$	−55.8101	−2.22353
$631$	4.02347	0.160172	0.0800859	−	0.996788i	$-0.474481\pi$
$631$	4.02347	0.160172	0.0800859	+	0.996788i	$0.474481\pi$
$632$	42.5743	1.69351
$633$	−25.6935	−1.02122
$634$	32.6530	1.29682
$635$	−0.716528	−0.0284345
$636$	59.8961	2.37504
$637$	−32.6090	−1.29202
$638$	102.848	4.07179
$639$	−27.4299	−1.08511
$640$	−30.4772	−1.20472
$641$	17.7703	0.701885	0.350942	−	0.936397i	$-0.385861\pi$
$641$	17.7703	0.701885	0.350942	+	0.936397i	$0.385861\pi$
$642$	−76.6173	−3.02384
$643$	14.3452	0.565719	0.282860	−	0.959161i	$-0.408717\pi$
$643$	14.3452	0.565719	0.282860	+	0.959161i	$0.408717\pi$
$644$	25.3427	0.998643
$645$	−58.5279	−2.30453
$646$	37.3767	1.47056
$647$	−25.3910	−0.998224	−0.499112	−	0.866537i	$-0.666340\pi$
$647$	−25.3910	−0.998224	−0.499112	+	0.866537i	$0.666340\pi$
$648$	−29.5192	−1.15962
$649$	−62.7218	−2.46205
$650$	−120.738	−4.73574
$651$	18.3455	0.719018
$652$	−98.9931	−3.87687
$653$	15.8088	0.618646	0.309323	−	0.950957i	$-0.399898\pi$
$653$	15.8088	0.618646	0.309323	+	0.950957i	$0.399898\pi$
$654$	11.6668	0.456209
$655$	24.7828	0.968345
$656$	95.5447	3.73039
$657$	−73.9761	−2.88608
$658$	31.4378	1.22557
$659$	3.07014	0.119596	0.0597979	−	0.998211i	$-0.480954\pi$
$659$	3.07014	0.119596	0.0597979	+	0.998211i	$0.480954\pi$
$660$	−224.961	−8.75661
$661$	−19.9291	−0.775151	−0.387575	−	0.921838i	$-0.626687\pi$
$661$	−19.9291	−0.775151	−0.387575	+	0.921838i	$0.626687\pi$
$662$	25.2506	0.981394
$663$	29.4600	1.14413
$664$	81.7667	3.17316
$665$	−30.4694	−1.18155
$666$	1.07770	0.0417599
$667$	42.3800	1.64096
$668$	−65.3927	−2.53012
$669$	−9.41158	−0.363873
$670$	65.1621	2.51743
$671$	47.2619	1.82452
$672$	−41.9304	−1.61750
$673$	−28.4756	−1.09765	−0.548826	−	0.835937i	$-0.684925\pi$
$673$	−28.4756	−1.09765	−0.548826	+	0.835937i	$0.684925\pi$
$674$	−40.6830	−1.56705
$675$	55.7998	2.14774
$676$	91.7648	3.52942
$677$	−14.6200	−0.561893	−0.280946	−	0.959723i	$-0.590648\pi$
$677$	−14.6200	−0.561893	−0.280946	+	0.959723i	$0.590648\pi$
$678$	−23.0979	−0.887071
$679$	10.2156	0.392037
$680$	−52.5725	−2.01606
$681$	43.9165	1.68288
$682$	66.3735	2.54157
$683$	30.3090	1.15974	0.579870	−	0.814709i	$-0.303103\pi$
$683$	30.3090	1.15974	0.579870	+	0.814709i	$0.303103\pi$
$684$	−208.567	−7.97476
$685$	59.3986	2.26950
$686$	36.7820	1.40435
$687$	−6.74737	−0.257428
$688$	−61.7878	−2.35564
$689$	23.1340	0.881336
$690$	−129.710	−4.93798
$691$	−20.4529	−0.778064	−0.389032	−	0.921224i	$-0.627190\pi$
$691$	−20.4529	−0.778064	−0.389032	+	0.921224i	$0.627190\pi$
$692$	−112.485	−4.27604
$693$	−24.8909	−0.945526
$694$	18.9514	0.719385
$695$	−1.35744	−0.0514907
$696$	−209.085	−7.92536
$697$	15.7023	0.594769
$698$	41.3152	1.56380
$699$	−27.3603	−1.03486
$700$	44.2134	1.67111
$701$	7.05619	0.266509	0.133254	−	0.991082i	$-0.457457\pi$
$701$	7.05619	0.266509	0.133254	+	0.991082i	$0.457457\pi$
$702$	−101.454	−3.82912
$703$	0.588367	0.0221907
$704$	−56.8796	−2.14373
$705$	−114.993	−4.33089
$706$	93.1404	3.50539
$707$	−7.46709	−0.280829
$708$	212.259	7.97719
$709$	−45.7817	−1.71937	−0.859683	−	0.510827i	$-0.829339\pi$
$709$	−45.7817	−1.71937	−0.859683	+	0.510827i	$0.829339\pi$
$710$	49.0631	1.84130
$711$	−28.6826	−1.07568
$712$	−5.81936	−0.218090
$713$	27.3502	1.02427
$714$	−15.0953	−0.564929
$715$	−86.8881	−3.24943
$716$	66.3462	2.47947
$717$	−77.5005	−2.89431
$718$	−34.1900	−1.27596
$719$	−10.4873	−0.391110	−0.195555	−	0.980693i	$-0.562651\pi$
$719$	−10.4873	−0.391110	−0.195555	+	0.980693i	$0.562651\pi$
$720$	215.513	8.03168
$721$	13.3445	0.496976
$722$	−109.028	−4.05761
$723$	−39.5476	−1.47079
$724$	70.7934	2.63102
$725$	73.9369	2.74595
$726$	−56.1506	−2.08394
$727$	15.8430	0.587585	0.293792	−	0.955869i	$-0.405083\pi$
$727$	15.8430	0.587585	0.293792	+	0.955869i	$0.405083\pi$
$728$	−48.2912	−1.78979
$729$	−39.5336	−1.46421
$730$	132.319	4.89734
$731$	−10.1545	−0.375580
$732$	−159.941	−5.91158
$733$	−5.74382	−0.212153	−0.106076	−	0.994358i	$-0.533829\pi$
$733$	−5.74382	−0.212153	−0.106076	+	0.994358i	$0.533829\pi$
$734$	59.8757	2.21005
$735$	−61.1178	−2.25436
$736$	−62.5113	−2.30420
$737$	29.0618	1.07051
$738$	−122.606	−4.51318
$739$	14.4032	0.529830	0.264915	−	0.964272i	$-0.414656\pi$
$739$	14.4032	0.529830	0.264915	+	0.964272i	$0.414656\pi$
$740$	−1.37761	−0.0506419
$741$	−125.583	−4.61340
$742$	−11.8539	−0.435171
$743$	−37.1271	−1.36206	−0.681031	−	0.732255i	$-0.738468\pi$
$743$	−37.1271	−1.36206	−0.681031	+	0.732255i	$0.738468\pi$
$744$	−134.934	−4.94694
$745$	13.6202	0.499006
$746$	46.7161	1.71040
$747$	−55.0869	−2.01552
$748$	−39.0307	−1.42710
$749$	10.8365	0.395956
$750$	−87.4469	−3.19311
$751$	15.6616	0.571501	0.285751	−	0.958304i	$-0.407757\pi$
$751$	15.6616	0.571501	0.285751	+	0.958304i	$0.407757\pi$
$752$	−121.398	−4.42694
$753$	−15.2076	−0.554197
$754$	−134.430	−4.89565
$755$	−20.9106	−0.761013
$756$	37.1515	1.35119
$757$	44.9984	1.63549	0.817747	−	0.575578i	$-0.195223\pi$
$757$	44.9984	1.63549	0.817747	+	0.575578i	$0.195223\pi$
$758$	50.4156	1.83118
$759$	−57.8498	−2.09981
$760$	224.107	8.12923
$761$	−18.7194	−0.678579	−0.339290	−	0.940682i	$-0.610187\pi$
$761$	−18.7194	−0.678579	−0.339290	+	0.940682i	$0.610187\pi$
$762$	1.51325	0.0548191
$763$	−1.65012	−0.0597382
$764$	−29.1121	−1.05324
$765$	35.4185	1.28056
$766$	34.1966	1.23557
$767$	81.9821	2.96020
$768$	−12.4894	−0.450672
$769$	−11.2397	−0.405314	−0.202657	−	0.979250i	$-0.564958\pi$
$769$	−11.2397	−0.405314	−0.202657	+	0.979250i	$0.564958\pi$
$770$	44.5216	1.60445
$771$	7.87970	0.283780
$772$	36.1330	1.30046
$773$	16.3028	0.586371	0.293185	−	0.956056i	$-0.405285\pi$
$773$	16.3028	0.586371	0.293185	+	0.956056i	$0.405285\pi$
$774$	79.2880	2.84995
$775$	47.7156	1.71399
$776$	−75.1371	−2.69726
$777$	−0.237624	−0.00852471
$778$	−78.7817	−2.82446
$779$	−66.9364	−2.39824
$780$	294.041	10.5284
$781$	21.8817	0.782991
$782$	−22.5047	−0.804765
$783$	62.1275	2.22026
$784$	−64.5220	−2.30436
$785$	−54.2386	−1.93586
$786$	−52.3392	−1.86688
$787$	22.1732	0.790389	0.395194	−	0.918598i	$-0.370677\pi$
$787$	22.1732	0.790389	0.395194	+	0.918598i	$0.370677\pi$
$788$	−32.2027	−1.14717
$789$	28.5622	1.01684
$790$	51.3038	1.82531
$791$	3.26689	0.116157
$792$	183.076	6.50534
$793$	−61.7748	−2.19369
$794$	−59.2237	−2.10177
$795$	43.3592	1.53779
$796$	133.863	4.74466
$797$	−19.8872	−0.704442	−0.352221	−	0.935917i	$-0.614573\pi$
$797$	−19.8872	−0.704442	−0.352221	+	0.935917i	$0.614573\pi$
$798$	64.3488	2.27792
$799$	−19.9512	−0.705824
$800$	−109.058	−3.85579
$801$	3.92055	0.138526
$802$	30.7526	1.08591
$803$	59.0132	2.08253
$804$	−98.3492	−3.46851
$805$	18.3458	0.646603
$806$	−86.7551	−3.05582
$807$	−4.02959	−0.141848
$808$	54.9217	1.93214
$809$	−15.0672	−0.529733	−0.264867	−	0.964285i	$-0.585328\pi$
$809$	−15.0672	−0.529733	−0.264867	+	0.964285i	$0.585328\pi$
$810$	−35.5719	−1.24987
$811$	−36.2069	−1.27139	−0.635697	−	0.771938i	$-0.719287\pi$
$811$	−36.2069	−1.27139	−0.635697	+	0.771938i	$0.719287\pi$
$812$	49.2272	1.72754
$813$	65.5634	2.29941
$814$	−0.859715	−0.0301330
$815$	−71.6617	−2.51020
$816$	58.2911	2.04060
$817$	43.2871	1.51442
$818$	−34.3767	−1.20195
$819$	32.5342	1.13684
$820$	156.726	5.47310
$821$	33.9167	1.18370	0.591851	−	0.806047i	$-0.298397\pi$
$821$	33.9167	1.18370	0.591851	+	0.806047i	$0.298397\pi$
$822$	−125.445	−4.37539
$823$	−26.3234	−0.917575	−0.458788	−	0.888546i	$-0.651716\pi$
$823$	−26.3234	−0.917575	−0.458788	+	0.888546i	$0.651716\pi$
$824$	−98.1512	−3.41926
$825$	−100.926	−3.51378
$826$	−42.0078	−1.46164
$827$	15.3608	0.534149	0.267074	−	0.963676i	$-0.413943\pi$
$827$	15.3608	0.534149	0.267074	+	0.963676i	$0.413943\pi$
$828$	125.579	4.36418
$829$	−23.3827	−0.812115	−0.406057	−	0.913848i	$-0.633097\pi$
$829$	−23.3827	−0.812115	−0.406057	+	0.913848i	$0.633097\pi$
$830$	98.5323	3.42011
$831$	62.0165	2.15133
$832$	74.3459	2.57748
$833$	−10.6039	−0.367403
$834$	2.86681	0.0992693
$835$	−47.3382	−1.63820
$836$	166.381	5.75441
$837$	40.0944	1.38586
$838$	8.41757	0.290780
$839$	44.4168	1.53344	0.766719	−	0.641982i	$-0.221888\pi$
$839$	44.4168	1.53344	0.766719	+	0.641982i	$0.221888\pi$
$840$	−90.5104	−3.12291
$841$	53.3213	1.83867
$842$	−18.0114	−0.620713
$843$	71.0724	2.44786
$844$	−44.4935	−1.53153
$845$	66.4291	2.28523
$846$	155.782	5.35589
$847$	7.94174	0.272881
$848$	45.7743	1.57189
$849$	26.9028	0.923303
$850$	−39.2620	−1.34668
$851$	−0.354258	−0.0121438
$852$	−74.0508	−2.53694
$853$	−41.4600	−1.41956	−0.709782	−	0.704421i	$-0.751207\pi$
$853$	−41.4600	−1.41956	−0.709782	+	0.704421i	$0.751207\pi$
$854$	31.6535	1.08316
$855$	−150.983	−5.16351
$856$	−79.7041	−2.72423
$857$	−9.23705	−0.315531	−0.157766	−	0.987477i	$-0.550429\pi$
$857$	−9.23705	−0.315531	−0.157766	+	0.987477i	$0.550429\pi$
$858$	183.500	6.26460
$859$	−28.2804	−0.964915	−0.482458	−	0.875919i	$-0.660256\pi$
$859$	−28.2804	−0.964915	−0.482458	+	0.875919i	$0.660256\pi$
$860$	−101.353	−3.45611
$861$	27.0336	0.921304
$862$	9.12360	0.310751
$863$	−3.49136	−0.118847	−0.0594237	−	0.998233i	$-0.518926\pi$
$863$	−3.49136	−0.118847	−0.0594237	+	0.998233i	$0.518926\pi$
$864$	−91.6393	−3.11763
$865$	−81.4287	−2.76866
$866$	22.0230	0.748370
$867$	−39.5945	−1.34470
$868$	31.7690	1.07831
$869$	22.8811	0.776188
$870$	−251.957	−8.54213
$871$	−37.9859	−1.28710
$872$	12.1369	0.411006
$873$	50.6205	1.71324
$874$	95.9334	3.24500
$875$	12.3682	0.418121
$876$	−199.709	−6.74754
$877$	−18.9583	−0.640175	−0.320088	−	0.947388i	$-0.603712\pi$
$877$	−18.9583	−0.640175	−0.320088	+	0.947388i	$0.603712\pi$
$878$	34.1316	1.15188
$879$	45.9059	1.54837
$880$	−171.922	−5.79548
$881$	−40.7163	−1.37177	−0.685883	−	0.727712i	$-0.740584\pi$
$881$	−40.7163	−1.37177	−0.685883	+	0.727712i	$0.740584\pi$
$882$	82.7966	2.78791
$883$	−8.94377	−0.300982	−0.150491	−	0.988611i	$-0.548085\pi$
$883$	−8.94377	−0.300982	−0.150491	+	0.988611i	$0.548085\pi$
$884$	51.0160	1.71585
$885$	153.656	5.16509
$886$	−20.1297	−0.676270
$887$	−15.5298	−0.521439	−0.260719	−	0.965415i	$-0.583960\pi$
$887$	−15.5298	−0.521439	−0.260719	+	0.965415i	$0.583960\pi$
$888$	1.74776	0.0586511
$889$	−0.214028	−0.00717828
$890$	−7.01258	−0.235062
$891$	−15.8648	−0.531491
$892$	−16.2981	−0.545700
$893$	85.0487	2.84605
$894$	−28.7648	−0.962038
$895$	48.0284	1.60541
$896$	−9.10360	−0.304130
$897$	75.6139	2.52468
$898$	88.8981	2.96657
$899$	53.1265	1.77187
$900$	219.088	7.30293
$901$	7.52279	0.250621
$902$	97.8068	3.25661
$903$	−17.4824	−0.581777
$904$	−24.0285	−0.799177
$905$	51.2478	1.70353
$906$	44.1613	1.46716
$907$	22.0161	0.731031	0.365516	−	0.930805i	$-0.380893\pi$
$907$	22.0161	0.731031	0.365516	+	0.930805i	$0.380893\pi$
$908$	76.0504	2.52382
$909$	−37.0012	−1.22725
$910$	−58.1930	−1.92908
$911$	0.623853	0.0206692	0.0103346	−	0.999947i	$-0.496710\pi$
$911$	0.623853	0.0206692	0.0103346	+	0.999947i	$0.496710\pi$
$912$	−248.485	−8.22816
$913$	43.9447	1.45436
$914$	−56.4837	−1.86831
$915$	−115.782	−3.82764
$916$	−11.6845	−0.386065
$917$	7.40268	0.244458
$918$	−32.9910	−1.08887
$919$	−14.9507	−0.493179	−0.246589	−	0.969120i	$-0.579310\pi$
$919$	−14.9507	−0.493179	−0.246589	+	0.969120i	$0.579310\pi$
$920$	−134.936	−4.44871
$921$	−23.6599	−0.779622
$922$	−37.4839	−1.23447
$923$	−28.6011	−0.941416
$924$	−67.1964	−2.21060
$925$	−0.618045	−0.0203212
$926$	97.5006	3.20407
$927$	66.1253	2.17184
$928$	−121.426	−3.98599
$929$	−48.5592	−1.59318	−0.796588	−	0.604523i	$-0.793364\pi$
$929$	−48.5592	−1.59318	−0.796588	+	0.604523i	$0.793364\pi$
$930$	−162.602	−5.33192
$931$	45.2026	1.48146
$932$	−47.3799	−1.55198
$933$	26.8824	0.880091
$934$	−66.1029	−2.16295
$935$	−28.2545	−0.924022
$936$	−239.294	−7.82159
$937$	−44.0875	−1.44028	−0.720138	−	0.693831i	$-0.755922\pi$
$937$	−44.0875	−1.44028	−0.720138	+	0.693831i	$0.755922\pi$
$938$	19.4641	0.635524
$939$	72.9827	2.38170
$940$	−199.134	−6.49504
$941$	−20.5729	−0.670657	−0.335328	−	0.942101i	$-0.608847\pi$
$941$	−20.5729	−0.670657	−0.335328	+	0.942101i	$0.608847\pi$
$942$	114.547	3.73215
$943$	40.3027	1.31244
$944$	162.214	5.27963
$945$	26.8942	0.874869
$946$	−63.2507	−2.05646
$947$	−2.11136	−0.0686101	−0.0343050	−	0.999411i	$-0.510922\pi$
$947$	−2.11136	−0.0686101	−0.0343050	+	0.999411i	$0.510922\pi$
$948$	−77.4328	−2.51490
$949$	−77.1346	−2.50390
$950$	167.367	5.43011
$951$	−35.6764	−1.15689
$952$	−15.7035	−0.508953
$953$	9.19987	0.298013	0.149007	−	0.988836i	$-0.452392\pi$
$953$	9.19987	0.298013	0.149007	+	0.988836i	$0.452392\pi$
$954$	−58.7389	−1.90174
$955$	−21.0744	−0.681952
$956$	−134.208	−4.34060
$957$	−112.371	−3.63243
$958$	49.4611	1.59802
$959$	17.7425	0.572934
$960$	139.344	4.49730
$961$	3.28551	0.105984
$962$	1.12371	0.0362299
$963$	53.6973	1.73037
$964$	−68.4848	−2.20575
$965$	26.1569	0.842021
$966$	−38.7447	−1.24659
$967$	41.8641	1.34626	0.673129	−	0.739525i	$-0.264950\pi$
$967$	41.8641	1.34626	0.673129	+	0.739525i	$0.264950\pi$
$968$	−58.4128	−1.87746
$969$	−40.8374	−1.31189
$970$	−90.5433	−2.90717
$971$	−39.8545	−1.27899	−0.639495	−	0.768795i	$-0.720857\pi$
$971$	−39.8545	−1.27899	−0.639495	+	0.768795i	$0.720857\pi$
$972$	−49.2108	−1.57844
$973$	−0.405471	−0.0129988
$974$	−32.9232	−1.05493
$975$	131.917	4.22474
$976$	−122.231	−3.91252
$977$	56.8097	1.81750	0.908752	−	0.417337i	$-0.137036\pi$
$977$	56.8097	1.81750	0.908752	+	0.417337i	$0.137036\pi$
$978$	151.344	4.83943
$979$	−3.12756	−0.0999572
$980$	−105.838	−3.38087
$981$	−8.17671	−0.261062
$982$	−11.0058	−0.351208
$983$	−13.8591	−0.442036	−0.221018	−	0.975270i	$-0.570938\pi$
$983$	−13.8591	−0.442036	−0.221018	+	0.975270i	$0.570938\pi$
$984$	−198.837	−6.33869
$985$	−23.3117	−0.742774
$986$	−43.7143	−1.39215
$987$	−34.3487	−1.09333
$988$	−217.472	−6.91871
$989$	−26.0633	−0.828766
$990$	220.615	7.01160
$991$	−13.7035	−0.435305	−0.217653	−	0.976026i	$-0.569840\pi$
$991$	−13.7035	−0.435305	−0.217653	+	0.976026i	$0.569840\pi$
$992$	−78.3626	−2.48802
$993$	−27.5886	−0.875498
$994$	14.6552	0.464836
$995$	96.9044	3.07208
$996$	−148.715	−4.71221
$997$	23.8106	0.754088	0.377044	−	0.926195i	$-0.376940\pi$
$997$	23.8106	0.754088	0.377044	+	0.926195i	$0.376940\pi$
$998$	16.7701	0.530849
$999$	−0.519330	−0.0164309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.c.1.4	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.c.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.64748 q^{2} +2.89261 q^{3} +5.00915 q^{4} +3.62616 q^{5} -7.65814 q^{6} +1.08314 q^{7} -7.96667 q^{8} +5.36721 q^{9} +O(q^{10})\)	\(q-2.64748 q^{2} +2.89261 q^{3} +5.00915 q^{4} +3.62616 q^{5} -7.65814 q^{6} +1.08314 q^{7} -7.96667 q^{8} +5.36721 q^{9} -9.60018 q^{10} -4.28161 q^{11} +14.4895 q^{12} +5.59638 q^{13} -2.86759 q^{14} +10.4891 q^{15} +11.0733 q^{16} +1.81985 q^{17} -14.2096 q^{18} -7.75770 q^{19} +18.1640 q^{20} +3.13311 q^{21} +11.3355 q^{22} +4.67094 q^{23} -23.0445 q^{24} +8.14901 q^{25} -14.8163 q^{26} +6.84743 q^{27} +5.42561 q^{28} +9.07311 q^{29} -27.7696 q^{30} +5.85538 q^{31} -13.3830 q^{32} -12.3850 q^{33} -4.81801 q^{34} +3.92764 q^{35} +26.8852 q^{36} -0.0758430 q^{37} +20.5383 q^{38} +16.1882 q^{39} -28.8884 q^{40} +8.62838 q^{41} -8.29483 q^{42} -5.57989 q^{43} -21.4472 q^{44} +19.4624 q^{45} -12.3662 q^{46} -10.9631 q^{47} +32.0308 q^{48} -5.82681 q^{49} -21.5744 q^{50} +5.26412 q^{51} +28.0331 q^{52} +4.13375 q^{53} -18.1284 q^{54} -15.5258 q^{55} -8.62902 q^{56} -22.4400 q^{57} -24.0209 q^{58} +14.6491 q^{59} +52.5414 q^{60} -11.0384 q^{61} -15.5020 q^{62} +5.81344 q^{63} +13.2846 q^{64} +20.2933 q^{65} +32.7891 q^{66} -6.78760 q^{67} +9.11589 q^{68} +13.5112 q^{69} -10.3983 q^{70} -5.11064 q^{71} -42.7588 q^{72} -13.7830 q^{73} +0.200793 q^{74} +23.5719 q^{75} -38.8595 q^{76} -4.63758 q^{77} -42.8578 q^{78} -5.34405 q^{79} +40.1535 q^{80} +3.70534 q^{81} -22.8435 q^{82} -10.2636 q^{83} +15.6942 q^{84} +6.59905 q^{85} +14.7727 q^{86} +26.2450 q^{87} +34.1101 q^{88} +0.730464 q^{89} -51.5262 q^{90} +6.06166 q^{91} +23.3975 q^{92} +16.9374 q^{93} +29.0247 q^{94} -28.1306 q^{95} -38.7119 q^{96} +9.43142 q^{97} +15.4264 q^{98} -22.9803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) \) 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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