LMFDB - Embedded newform 4031.2.a.e.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$0$
Dimension:	$103$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59576 q^{2} -0.589470 q^{3} +4.73795 q^{4} +2.97822 q^{5} +1.53012 q^{6} -2.97611 q^{7} -7.10705 q^{8} -2.65253 q^{9} +O(q^{10})$	\(q-2.59576 q^{2} -0.589470 q^{3} +4.73795 q^{4} +2.97822 q^{5} +1.53012 q^{6} -2.97611 q^{7} -7.10705 q^{8} -2.65253 q^{9} -7.73074 q^{10} -4.94201 q^{11} -2.79288 q^{12} -6.38960 q^{13} +7.72526 q^{14} -1.75557 q^{15} +8.97226 q^{16} +6.28598 q^{17} +6.88531 q^{18} -5.57074 q^{19} +14.1107 q^{20} +1.75433 q^{21} +12.8282 q^{22} -6.32366 q^{23} +4.18939 q^{24} +3.86980 q^{25} +16.5858 q^{26} +3.33199 q^{27} -14.1007 q^{28} -1.00000 q^{29} +4.55703 q^{30} -1.16462 q^{31} -9.07571 q^{32} +2.91316 q^{33} -16.3169 q^{34} -8.86352 q^{35} -12.5675 q^{36} -10.7597 q^{37} +14.4603 q^{38} +3.76648 q^{39} -21.1664 q^{40} -5.05639 q^{41} -4.55381 q^{42} -4.91780 q^{43} -23.4150 q^{44} -7.89981 q^{45} +16.4147 q^{46} -5.81978 q^{47} -5.28888 q^{48} +1.85724 q^{49} -10.0451 q^{50} -3.70540 q^{51} -30.2736 q^{52} +4.29954 q^{53} -8.64904 q^{54} -14.7184 q^{55} +21.1514 q^{56} +3.28379 q^{57} +2.59576 q^{58} +2.70428 q^{59} -8.31781 q^{60} +14.5274 q^{61} +3.02307 q^{62} +7.89421 q^{63} +5.61380 q^{64} -19.0296 q^{65} -7.56186 q^{66} +0.993219 q^{67} +29.7827 q^{68} +3.72761 q^{69} +23.0075 q^{70} +2.76208 q^{71} +18.8516 q^{72} +16.7568 q^{73} +27.9295 q^{74} -2.28113 q^{75} -26.3939 q^{76} +14.7080 q^{77} -9.77685 q^{78} -5.02738 q^{79} +26.7214 q^{80} +5.99347 q^{81} +13.1251 q^{82} +9.74519 q^{83} +8.31191 q^{84} +18.7211 q^{85} +12.7654 q^{86} +0.589470 q^{87} +35.1231 q^{88} -10.6856 q^{89} +20.5060 q^{90} +19.0162 q^{91} -29.9612 q^{92} +0.686508 q^{93} +15.1067 q^{94} -16.5909 q^{95} +5.34985 q^{96} -15.2934 q^{97} -4.82093 q^{98} +13.1088 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) $ 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9 + 20 * q^10 + 9 * q^11 + 36 * q^13 - 10 * q^14 + 16 * q^15 + 179 * q^16 + 21 * q^17 + 7 * q^18 + 42 * q^19 + 24 * q^20 + 28 * q^21 + 32 * q^22 + 25 * q^23 + 68 * q^24 + 194 * q^25 - 5 * q^26 + 14 * q^27 + 59 * q^28 - 103 * q^29 + 84 * q^30 + 34 * q^31 + 11 * q^32 + 42 * q^33 + 54 * q^34 + 35 * q^35 + 214 * q^36 + 34 * q^37 + 9 * q^38 + 23 * q^39 + 46 * q^40 + 16 * q^41 + 13 * q^42 + 68 * q^43 - 6 * q^44 + 25 * q^45 + 60 * q^46 + 6 * q^47 + 5 * q^48 + 257 * q^49 - 51 * q^50 + 68 * q^51 + 37 * q^52 + 35 * q^53 + 30 * q^54 + 66 * q^55 - 54 * q^56 + 78 * q^57 - q^58 + 10 * q^59 - 24 * q^60 + 70 * q^61 + 29 * q^62 + 26 * q^63 + 276 * q^64 + 95 * q^65 + 77 * q^66 + 71 * q^67 - 21 * q^68 - 20 * q^69 + 48 * q^70 + 32 * q^71 + 32 * q^72 + 94 * q^73 + 35 * q^74 + 7 * q^75 + 134 * q^76 + 17 * q^77 + 58 * q^78 + 110 * q^79 + 78 * q^80 + 267 * q^81 - 71 * q^82 + 35 * q^83 + 96 * q^84 + 71 * q^85 + 33 * q^86 - 2 * q^87 + 100 * q^88 + 22 * q^89 - 134 * q^90 + 108 * q^91 - 11 * q^92 + 78 * q^93 + 90 * q^94 + 12 * q^95 + 177 * q^96 + 44 * q^97 - 18 * q^98 + 83 * 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 $

$2$	−2.59576	−1.83548	−0.917738	−	0.397186i	$-0.869987\pi$
$2$	−2.59576	−1.83548	−0.917738	+	0.397186i	$0.869987\pi$
$3$	−0.589470	−0.340331	−0.170165	−	0.985416i	$-0.554430\pi$
$3$	−0.589470	−0.340331	−0.170165	+	0.985416i	$0.554430\pi$
$4$	4.73795	2.36897
$5$	2.97822	1.33190	0.665951	−	0.745996i	$-0.268026\pi$
$5$	2.97822	1.33190	0.665951	+	0.745996i	$0.268026\pi$
$6$	1.53012	0.624669
$7$	−2.97611	−1.12486	−0.562432	−	0.826843i	$-0.690134\pi$
$7$	−2.97611	−1.12486	−0.562432	+	0.826843i	$0.690134\pi$
$8$	−7.10705	−2.51272
$9$	−2.65253	−0.884175
$10$	−7.73074	−2.44467
$11$	−4.94201	−1.49007	−0.745035	−	0.667025i	$-0.767567\pi$
$11$	−4.94201	−1.49007	−0.745035	+	0.667025i	$0.767567\pi$
$12$	−2.79288	−0.806234
$13$	−6.38960	−1.77216	−0.886078	−	0.463536i	$-0.846580\pi$
$13$	−6.38960	−1.77216	−0.886078	+	0.463536i	$0.846580\pi$
$14$	7.72526	2.06466
$15$	−1.75557	−0.453287
$16$	8.97226	2.24307
$17$	6.28598	1.52458	0.762288	−	0.647238i	$-0.224076\pi$
$17$	6.28598	1.52458	0.762288	+	0.647238i	$0.224076\pi$
$18$	6.88531	1.62288
$19$	−5.57074	−1.27802	−0.639008	−	0.769200i	$-0.720655\pi$
$19$	−5.57074	−1.27802	−0.639008	+	0.769200i	$0.720655\pi$
$20$	14.1107	3.15524
$21$	1.75433	0.382826
$22$	12.8282	2.73499
$23$	−6.32366	−1.31858	−0.659288	−	0.751891i	$-0.729142\pi$
$23$	−6.32366	−1.31858	−0.659288	+	0.751891i	$0.729142\pi$
$24$	4.18939	0.855155
$25$	3.86980	0.773961
$26$	16.5858	3.25275
$27$	3.33199	0.641242
$28$	−14.1007	−2.66477
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	4.55703	0.831997
$31$	−1.16462	−0.209172	−0.104586	−	0.994516i	$-0.533352\pi$
$31$	−1.16462	−0.209172	−0.104586	+	0.994516i	$0.533352\pi$
$32$	−9.07571	−1.60437
$33$	2.91316	0.507117
$34$	−16.3169	−2.79832
$35$	−8.86352	−1.49821
$36$	−12.5675	−2.09459
$37$	−10.7597	−1.76888	−0.884441	−	0.466652i	$-0.845460\pi$
$37$	−10.7597	−1.76888	−0.884441	+	0.466652i	$0.845460\pi$
$38$	14.4603	2.34577
$39$	3.76648	0.603119
$40$	−21.1664	−3.34670
$41$	−5.05639	−0.789675	−0.394837	−	0.918751i	$-0.629199\pi$
$41$	−5.05639	−0.789675	−0.394837	+	0.918751i	$0.629199\pi$
$42$	−4.55381	−0.702667
$43$	−4.91780	−0.749958	−0.374979	−	0.927033i	$-0.622350\pi$
$43$	−4.91780	−0.749958	−0.374979	+	0.927033i	$0.622350\pi$
$44$	−23.4150	−3.52994
$45$	−7.89981	−1.17763
$46$	16.4147	2.42021
$47$	−5.81978	−0.848903	−0.424451	−	0.905451i	$-0.639533\pi$
$47$	−5.81978	−0.848903	−0.424451	+	0.905451i	$0.639533\pi$
$48$	−5.28888	−0.763384
$49$	1.85724	0.265319
$50$	−10.0451	−1.42059
$51$	−3.70540	−0.518859
$52$	−30.2736	−4.19819
$53$	4.29954	0.590587	0.295293	−	0.955407i	$-0.404583\pi$
$53$	4.29954	0.590587	0.295293	+	0.955407i	$0.404583\pi$
$54$	−8.64904	−1.17699
$55$	−14.7184	−1.98463
$56$	21.1514	2.82647
$57$	3.28379	0.434948
$58$	2.59576	0.340839
$59$	2.70428	0.352067	0.176034	−	0.984384i	$-0.443673\pi$
$59$	2.70428	0.352067	0.176034	+	0.984384i	$0.443673\pi$
$60$	−8.31781	−1.07382
$61$	14.5274	1.86005	0.930024	−	0.367498i	$-0.119786\pi$
$61$	14.5274	1.86005	0.930024	+	0.367498i	$0.119786\pi$
$62$	3.02307	0.383930
$63$	7.89421	0.994577
$64$	5.61380	0.701724
$65$	−19.0296	−2.36034
$66$	−7.56186	−0.930800
$67$	0.993219	0.121341	0.0606705	−	0.998158i	$-0.480676\pi$
$67$	0.993219	0.121341	0.0606705	+	0.998158i	$0.480676\pi$
$68$	29.7827	3.61168
$69$	3.72761	0.448751
$70$	23.0075	2.74993
$71$	2.76208	0.327799	0.163899	−	0.986477i	$-0.447593\pi$
$71$	2.76208	0.327799	0.163899	+	0.986477i	$0.447593\pi$
$72$	18.8516	2.22168
$73$	16.7568	1.96124	0.980620	−	0.195920i	$-0.0627694\pi$
$73$	16.7568	1.96124	0.980620	+	0.195920i	$0.0627694\pi$
$74$	27.9295	3.24674
$75$	−2.28113	−0.263402
$76$	−26.3939	−3.02759
$77$	14.7080	1.67613
$78$	−9.77685	−1.10701
$79$	−5.02738	−0.565624	−0.282812	−	0.959175i	$-0.591267\pi$
$79$	−5.02738	−0.565624	−0.282812	+	0.959175i	$0.591267\pi$
$80$	26.7214	2.98754
$81$	5.99347	0.665941
$82$	13.1251	1.44943
$83$	9.74519	1.06967	0.534837	−	0.844956i	$-0.320373\pi$
$83$	9.74519	1.06967	0.534837	+	0.844956i	$0.320373\pi$
$84$	8.31191	0.906904
$85$	18.7211	2.03058
$86$	12.7654	1.37653
$87$	0.589470	0.0631978
$88$	35.1231	3.74413
$89$	−10.6856	−1.13267	−0.566334	−	0.824176i	$-0.691639\pi$
$89$	−10.6856	−1.13267	−0.566334	+	0.824176i	$0.691639\pi$
$90$	20.5060	2.16152
$91$	19.0162	1.99343
$92$	−29.9612	−3.12367
$93$	0.686508	0.0711876
$94$	15.1067	1.55814
$95$	−16.5909	−1.70219
$96$	5.34985	0.546017
$97$	−15.2934	−1.55281	−0.776403	−	0.630237i	$-0.782958\pi$
$97$	−15.2934	−1.55281	−0.776403	+	0.630237i	$0.782958\pi$
$98$	−4.82093	−0.486988
$99$	13.1088	1.31748
$100$	18.3349	1.83349
$101$	1.12489	0.111931	0.0559654	−	0.998433i	$-0.482176\pi$
$101$	1.12489	0.111931	0.0559654	+	0.998433i	$0.482176\pi$
$102$	9.61831	0.952354
$103$	−9.09801	−0.896453	−0.448227	−	0.893920i	$-0.647944\pi$
$103$	−9.09801	−0.896453	−0.448227	+	0.893920i	$0.647944\pi$
$104$	45.4112	4.45293
$105$	5.22478	0.509886
$106$	−11.1605	−1.08401
$107$	−12.3669	−1.19555	−0.597776	−	0.801663i	$-0.703949\pi$
$107$	−12.3669	−1.19555	−0.597776	+	0.801663i	$0.703949\pi$
$108$	15.7868	1.51909
$109$	16.9103	1.61971	0.809855	−	0.586630i	$-0.199546\pi$
$109$	16.9103	1.61971	0.809855	+	0.586630i	$0.199546\pi$
$110$	38.2053	3.64274
$111$	6.34251	0.602005
$112$	−26.7024	−2.52314
$113$	−15.8353	−1.48966	−0.744829	−	0.667256i	$-0.767469\pi$
$113$	−15.8353	−1.48966	−0.744829	+	0.667256i	$0.767469\pi$
$114$	−8.52391	−0.798337
$115$	−18.8333	−1.75621
$116$	−4.73795	−0.439907
$117$	16.9486	1.56690
$118$	−7.01965	−0.646211
$119$	−18.7078	−1.71494
$120$	12.4769	1.13898
$121$	13.4234	1.22031
$122$	−37.7097	−3.41408
$123$	2.98059	0.268750
$124$	−5.51791	−0.495523
$125$	−3.36598	−0.301062
$126$	−20.4914	−1.82552
$127$	3.20963	0.284809	0.142404	−	0.989809i	$-0.454517\pi$
$127$	3.20963	0.284809	0.142404	+	0.989809i	$0.454517\pi$
$128$	3.57937	0.316375
$129$	2.89889	0.255233
$130$	49.3963	4.33234
$131$	1.79251	0.156612	0.0783061	−	0.996929i	$-0.475049\pi$
$131$	1.79251	0.156612	0.0783061	+	0.996929i	$0.475049\pi$
$132$	13.8024	1.20135
$133$	16.5792	1.43760
$134$	−2.57816	−0.222719
$135$	9.92341	0.854071
$136$	−44.6748	−3.83083
$137$	−3.41422	−0.291696	−0.145848	−	0.989307i	$-0.546591\pi$
$137$	−3.41422	−0.291696	−0.145848	+	0.989307i	$0.546591\pi$
$138$	−9.67596	−0.823673
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	−41.9949	−3.54922
$141$	3.43059	0.288908
$142$	−7.16968	−0.601667
$143$	31.5774	2.64064
$144$	−23.7992	−1.98326
$145$	−2.97822	−0.247328
$146$	−43.4967	−3.59981
$147$	−1.09478	−0.0902963
$148$	−50.9789	−4.19044
$149$	16.0496	1.31483	0.657416	−	0.753528i	$-0.271650\pi$
$149$	16.0496	1.31483	0.657416	+	0.753528i	$0.271650\pi$
$150$	5.92126	0.483469
$151$	19.4718	1.58459	0.792296	−	0.610137i	$-0.208886\pi$
$151$	19.4718	1.58459	0.792296	+	0.610137i	$0.208886\pi$
$152$	39.5915	3.21130
$153$	−16.6737	−1.34799
$154$	−38.1783	−3.07649
$155$	−3.46850	−0.278596
$156$	17.8454	1.42877
$157$	3.78157	0.301802	0.150901	−	0.988549i	$-0.451783\pi$
$157$	3.78157	0.301802	0.150901	+	0.988549i	$0.451783\pi$
$158$	13.0498	1.03819
$159$	−2.53445	−0.200995
$160$	−27.0295	−2.13687
$161$	18.8199	1.48322
$162$	−15.5576	−1.22232
$163$	4.38520	0.343475	0.171738	−	0.985143i	$-0.445062\pi$
$163$	4.38520	0.343475	0.171738	+	0.985143i	$0.445062\pi$
$164$	−23.9569	−1.87072
$165$	8.67604	0.675429
$166$	−25.2961	−1.96336
$167$	10.9842	0.849981	0.424991	−	0.905198i	$-0.360277\pi$
$167$	10.9842	0.849981	0.424991	+	0.905198i	$0.360277\pi$
$168$	−12.4681	−0.961934
$169$	27.8270	2.14054
$170$	−48.5953	−3.72709
$171$	14.7765	1.12999
$172$	−23.3003	−1.77663
$173$	6.43645	0.489355	0.244677	−	0.969605i	$-0.421318\pi$
$173$	6.43645	0.489355	0.244677	+	0.969605i	$0.421318\pi$
$174$	−1.53012	−0.115998
$175$	−11.5170	−0.870601
$176$	−44.3410	−3.34233
$177$	−1.59409	−0.119819
$178$	27.7371	2.07899
$179$	11.5256	0.861465	0.430733	−	0.902480i	$-0.358255\pi$
$179$	11.5256	0.861465	0.430733	+	0.902480i	$0.358255\pi$
$180$	−37.4289	−2.78978
$181$	13.7972	1.02554	0.512768	−	0.858527i	$-0.328620\pi$
$181$	13.7972	1.02554	0.512768	+	0.858527i	$0.328620\pi$
$182$	−49.3613	−3.65890
$183$	−8.56349	−0.633031
$184$	44.9426	3.31321
$185$	−32.0447	−2.35598
$186$	−1.78201	−0.130663
$187$	−31.0654	−2.27172
$188$	−27.5738	−2.01103
$189$	−9.91638	−0.721311
$190$	43.0660	3.12433
$191$	−6.12948	−0.443513	−0.221757	−	0.975102i	$-0.571179\pi$
$191$	−6.12948	−0.443513	−0.221757	+	0.975102i	$0.571179\pi$
$192$	−3.30916	−0.238818
$193$	−6.60227	−0.475242	−0.237621	−	0.971358i	$-0.576368\pi$
$193$	−6.60227	−0.475242	−0.237621	+	0.971358i	$0.576368\pi$
$194$	39.6978	2.85014
$195$	11.2174	0.803295
$196$	8.79949	0.628535
$197$	−19.2042	−1.36824	−0.684122	−	0.729368i	$-0.739814\pi$
$197$	−19.2042	−1.36824	−0.684122	+	0.729368i	$0.739814\pi$
$198$	−34.0272	−2.41821
$199$	−8.01954	−0.568490	−0.284245	−	0.958752i	$-0.591743\pi$
$199$	−8.01954	−0.568490	−0.284245	+	0.958752i	$0.591743\pi$
$200$	−27.5029	−1.94475
$201$	−0.585473	−0.0412961
$202$	−2.91994	−0.205446
$203$	2.97611	0.208882
$204$	−17.5560	−1.22916
$205$	−15.0590	−1.05177
$206$	23.6162	1.64542
$207$	16.7737	1.16585
$208$	−57.3292	−3.97506
$209$	27.5307	1.90433
$210$	−13.5622	−0.935884
$211$	13.2291	0.910728	0.455364	−	0.890305i	$-0.349509\pi$
$211$	13.2291	0.910728	0.455364	+	0.890305i	$0.349509\pi$
$212$	20.3710	1.39908
$213$	−1.62816	−0.111560
$214$	32.1014	2.19441
$215$	−14.6463	−0.998869
$216$	−23.6806	−1.61126
$217$	3.46604	0.235290
$218$	−43.8949	−2.97294
$219$	−9.87765	−0.667470
$220$	−69.7350	−4.70153
$221$	−40.1649	−2.70179
$222$	−16.4636	−1.10497
$223$	−22.3086	−1.49389	−0.746947	−	0.664884i	$-0.768481\pi$
$223$	−22.3086	−1.49389	−0.746947	+	0.664884i	$0.768481\pi$
$224$	27.0103	1.80470
$225$	−10.2648	−0.684317
$226$	41.1045	2.73423
$227$	−15.9700	−1.05997	−0.529984	−	0.848007i	$-0.677802\pi$
$227$	−15.9700	−1.05997	−0.529984	+	0.848007i	$0.677802\pi$
$228$	15.5584	1.03038
$229$	−2.46282	−0.162748	−0.0813738	−	0.996684i	$-0.525931\pi$
$229$	−2.46282	−0.162748	−0.0813738	+	0.996684i	$0.525931\pi$
$230$	48.8866	3.22349
$231$	−8.66989	−0.570437
$232$	7.10705	0.466600
$233$	−9.34757	−0.612379	−0.306190	−	0.951971i	$-0.599054\pi$
$233$	−9.34757	−0.612379	−0.306190	+	0.951971i	$0.599054\pi$
$234$	−43.9944	−2.87600
$235$	−17.3326	−1.13065
$236$	12.8127	0.834039
$237$	2.96349	0.192499
$238$	48.5609	3.14773
$239$	−1.37438	−0.0889015	−0.0444508	−	0.999012i	$-0.514154\pi$
$239$	−1.37438	−0.0889015	−0.0444508	+	0.999012i	$0.514154\pi$
$240$	−15.7514	−1.01675
$241$	17.4708	1.12540	0.562698	−	0.826663i	$-0.309763\pi$
$241$	17.4708	1.12540	0.562698	+	0.826663i	$0.309763\pi$
$242$	−34.8439	−2.23985
$243$	−13.5289	−0.867882
$244$	68.8303	4.40641
$245$	5.53126	0.353379
$246$	−7.73688	−0.493285
$247$	35.5948	2.26484
$248$	8.27701	0.525591
$249$	−5.74449	−0.364042
$250$	8.73725	0.552592
$251$	−24.1116	−1.52191	−0.760956	−	0.648803i	$-0.775270\pi$
$251$	−24.1116	−1.52191	−0.760956	+	0.648803i	$0.775270\pi$
$252$	37.4024	2.35613
$253$	31.2516	1.96477
$254$	−8.33142	−0.522760
$255$	−11.0355	−0.691070
$256$	−20.5188	−1.28242
$257$	19.7914	1.23455	0.617275	−	0.786747i	$-0.288236\pi$
$257$	19.7914	1.23455	0.617275	+	0.786747i	$0.288236\pi$
$258$	−7.52482	−0.468475
$259$	32.0220	1.98975
$260$	−90.1615	−5.59158
$261$	2.65253	0.164187
$262$	−4.65292	−0.287458
$263$	−24.2841	−1.49742	−0.748710	−	0.662898i	$-0.769326\pi$
$263$	−24.2841	−1.49742	−0.748710	+	0.662898i	$0.769326\pi$
$264$	−20.7040	−1.27424
$265$	12.8050	0.786603
$266$	−43.0354	−2.63867
$267$	6.29882	0.385482
$268$	4.70582	0.287454
$269$	23.1604	1.41212	0.706058	−	0.708154i	$-0.250472\pi$
$269$	23.1604	1.41212	0.706058	+	0.708154i	$0.250472\pi$
$270$	−25.7588	−1.56763
$271$	−17.0858	−1.03789	−0.518943	−	0.854809i	$-0.673674\pi$
$271$	−17.0858	−1.03789	−0.518943	+	0.854809i	$0.673674\pi$
$272$	56.3995	3.41972
$273$	−11.2094	−0.678427
$274$	8.86248	0.535402
$275$	−19.1246	−1.15326
$276$	17.6612	1.06308
$277$	−25.2785	−1.51884	−0.759419	−	0.650601i	$-0.774517\pi$
$277$	−25.2785	−1.51884	−0.759419	+	0.650601i	$0.774517\pi$
$278$	−2.59576	−0.155683
$279$	3.08918	0.184945
$280$	62.9934	3.76458
$281$	15.6122	0.931347	0.465673	−	0.884957i	$-0.345812\pi$
$281$	15.6122	0.931347	0.465673	+	0.884957i	$0.345812\pi$
$282$	−8.90497	−0.530283
$283$	20.5568	1.22197	0.610986	−	0.791641i	$-0.290773\pi$
$283$	20.5568	1.22197	0.610986	+	0.791641i	$0.290773\pi$
$284$	13.0866	0.776546
$285$	9.77984	0.579308
$286$	−81.9673	−4.84683
$287$	15.0484	0.888277
$288$	24.0735	1.41855
$289$	22.5136	1.32433
$290$	7.73074	0.453964
$291$	9.01498	0.528467
$292$	79.3930	4.64613
$293$	−12.3861	−0.723607	−0.361803	−	0.932254i	$-0.617839\pi$
$293$	−12.3861	−0.723607	−0.361803	+	0.932254i	$0.617839\pi$
$294$	2.84179	0.165737
$295$	8.05395	0.468919
$296$	76.4696	4.44471
$297$	−16.4667	−0.955496
$298$	−41.6607	−2.41334
$299$	40.4057	2.33672
$300$	−10.8079	−0.623994
$301$	14.6359	0.843600
$302$	−50.5440	−2.90848
$303$	−0.663088	−0.0380934
$304$	−49.9822	−2.86667
$305$	43.2659	2.47740
$306$	43.2809	2.47421
$307$	−2.18632	−0.124780	−0.0623901	−	0.998052i	$-0.519872\pi$
$307$	−2.18632	−0.124780	−0.0623901	+	0.998052i	$0.519872\pi$
$308$	69.6855	3.97070
$309$	5.36300	0.305090
$310$	9.00337	0.511357
$311$	18.4261	1.04485	0.522425	−	0.852685i	$-0.325027\pi$
$311$	18.4261	1.04485	0.522425	+	0.852685i	$0.325027\pi$
$312$	−26.7685	−1.51547
$313$	17.4508	0.986377	0.493189	−	0.869922i	$-0.335831\pi$
$313$	17.4508	0.986377	0.493189	+	0.869922i	$0.335831\pi$
$314$	−9.81603	−0.553950
$315$	23.5107	1.32468
$316$	−23.8195	−1.33995
$317$	−30.7395	−1.72650	−0.863251	−	0.504776i	$-0.831575\pi$
$317$	−30.7395	−1.72650	−0.863251	+	0.504776i	$0.831575\pi$
$318$	6.57880	0.368921
$319$	4.94201	0.276699
$320$	16.7191	0.934628
$321$	7.28990	0.406883
$322$	−48.8519	−2.72241
$323$	−35.0176	−1.94843
$324$	28.3967	1.57760
$325$	−24.7265	−1.37158
$326$	−11.3829	−0.630441
$327$	−9.96810	−0.551237
$328$	35.9360	1.98423
$329$	17.3203	0.954900
$330$	−22.5209	−1.23973
$331$	−28.5321	−1.56827	−0.784133	−	0.620592i	$-0.786892\pi$
$331$	−28.5321	−1.56827	−0.784133	+	0.620592i	$0.786892\pi$
$332$	46.1722	2.53403
$333$	28.5403	1.56400
$334$	−28.5122	−1.56012
$335$	2.95803	0.161614
$336$	15.7403	0.858703
$337$	12.1571	0.662242	0.331121	−	0.943588i	$-0.392573\pi$
$337$	12.1571	0.662242	0.331121	+	0.943588i	$0.392573\pi$
$338$	−72.2321	−3.92891
$339$	9.33441	0.506976
$340$	88.6994	4.81040
$341$	5.75556	0.311681
$342$	−38.3563	−2.07407
$343$	15.3054	0.826416
$344$	34.9510	1.88443
$345$	11.1016	0.597692
$346$	−16.7075	−0.898199
$347$	−0.714807	−0.0383729	−0.0191864	−	0.999816i	$-0.506108\pi$
$347$	−0.714807	−0.0383729	−0.0191864	+	0.999816i	$0.506108\pi$
$348$	2.79288	0.149714
$349$	−14.8969	−0.797410	−0.398705	−	0.917079i	$-0.630540\pi$
$349$	−14.8969	−0.797410	−0.398705	+	0.917079i	$0.630540\pi$
$350$	29.8952	1.59797
$351$	−21.2901	−1.13638
$352$	44.8522	2.39063
$353$	−0.0986490	−0.00525056	−0.00262528	−	0.999997i	$-0.500836\pi$
$353$	−0.0986490	−0.00525056	−0.00262528	+	0.999997i	$0.500836\pi$
$354$	4.13787	0.219925
$355$	8.22608	0.436595
$356$	−50.6277	−2.68326
$357$	11.0277	0.583646
$358$	−29.9177	−1.58120
$359$	−20.9542	−1.10592	−0.552960	−	0.833208i	$-0.686502\pi$
$359$	−20.9542	−1.10592	−0.552960	+	0.833208i	$0.686502\pi$
$360$	56.1443	2.95906
$361$	12.0332	0.633326
$362$	−35.8141	−1.88235
$363$	−7.91270	−0.415309
$364$	90.0976	4.72240
$365$	49.9056	2.61218
$366$	22.2287	1.16191
$367$	−6.91376	−0.360895	−0.180448	−	0.983585i	$-0.557755\pi$
$367$	−6.91376	−0.360895	−0.180448	+	0.983585i	$0.557755\pi$
$368$	−56.7376	−2.95765
$369$	13.4122	0.698211
$370$	83.1803	4.32434
$371$	−12.7959	−0.664330
$372$	3.25264	0.168642
$373$	−27.0774	−1.40201	−0.701007	−	0.713155i	$-0.747266\pi$
$373$	−27.0774	−1.40201	−0.701007	+	0.713155i	$0.747266\pi$
$374$	80.6381	4.16970
$375$	1.98414	0.102461
$376$	41.3615	2.13306
$377$	6.38960	0.329081
$378$	25.7405	1.32395
$379$	3.94551	0.202667	0.101334	−	0.994853i	$-0.467689\pi$
$379$	3.94551	0.202667	0.101334	+	0.994853i	$0.467689\pi$
$380$	−78.6069	−4.03245
$381$	−1.89198	−0.0969291
$382$	15.9106	0.814058
$383$	−25.1194	−1.28354	−0.641771	−	0.766896i	$-0.721800\pi$
$383$	−25.1194	−1.28354	−0.641771	+	0.766896i	$0.721800\pi$
$384$	−2.10993	−0.107672
$385$	43.8036	2.23244
$386$	17.1379	0.872295
$387$	13.0446	0.663094
$388$	−72.4592	−3.67856
$389$	−1.87786	−0.0952111	−0.0476056	−	0.998866i	$-0.515159\pi$
$389$	−1.87786	−0.0952111	−0.0476056	+	0.998866i	$0.515159\pi$
$390$	−29.1176	−1.47443
$391$	−39.7505	−2.01027
$392$	−13.1995	−0.666674
$393$	−1.05663	−0.0532999
$394$	49.8494	2.51138
$395$	−14.9726	−0.753355
$396$	62.1088	3.12108
$397$	25.4222	1.27590	0.637952	−	0.770076i	$-0.279782\pi$
$397$	25.4222	1.27590	0.637952	+	0.770076i	$0.279782\pi$
$398$	20.8168	1.04345
$399$	−9.77291	−0.489257
$400$	34.7209	1.73604
$401$	−39.6413	−1.97959	−0.989795	−	0.142497i	$-0.954487\pi$
$401$	−39.6413	−1.97959	−0.989795	+	0.142497i	$0.954487\pi$
$402$	1.51974	0.0757980
$403$	7.44146	0.370685
$404$	5.32967	0.265161
$405$	17.8499	0.886967
$406$	−7.72526	−0.383398
$407$	53.1744	2.63576
$408$	26.3344	1.30375
$409$	−13.6357	−0.674243	−0.337121	−	0.941461i	$-0.609453\pi$
$409$	−13.6357	−0.674243	−0.337121	+	0.941461i	$0.609453\pi$
$410$	39.0896	1.93050
$411$	2.01258	0.0992732
$412$	−43.1059	−2.12367
$413$	−8.04824	−0.396028
$414$	−43.5404	−2.13989
$415$	29.0233	1.42470
$416$	57.9901	2.84320
$417$	−0.589470	−0.0288665
$418$	−71.4629	−3.49536
$419$	22.7740	1.11258	0.556291	−	0.830988i	$-0.312224\pi$
$419$	22.7740	1.11258	0.556291	+	0.830988i	$0.312224\pi$
$420$	24.7547	1.20791
$421$	−25.8868	−1.26165	−0.630823	−	0.775927i	$-0.717282\pi$
$421$	−25.8868	−1.26165	−0.630823	+	0.775927i	$0.717282\pi$
$422$	−34.3395	−1.67162
$423$	15.4371	0.750579
$424$	−30.5570	−1.48398
$425$	24.3255	1.17996
$426$	4.22631	0.204765
$427$	−43.2353	−2.09230
$428$	−58.5936	−2.83223
$429$	−18.6139	−0.898690
$430$	38.0182	1.83340
$431$	11.6451	0.560924	0.280462	−	0.959865i	$-0.409512\pi$
$431$	11.6451	0.560924	0.280462	+	0.959865i	$0.409512\pi$
$432$	29.8955	1.43835
$433$	−11.6224	−0.558536	−0.279268	−	0.960213i	$-0.590092\pi$
$433$	−11.6224	−0.558536	−0.279268	+	0.960213i	$0.590092\pi$
$434$	−8.99699	−0.431869
$435$	1.75557	0.0841732
$436$	80.1200	3.83705
$437$	35.2275	1.68516
$438$	25.6400	1.22513
$439$	−16.4820	−0.786641	−0.393321	−	0.919401i	$-0.628674\pi$
$439$	−16.4820	−0.786641	−0.393321	+	0.919401i	$0.628674\pi$
$440$	104.604	4.98681
$441$	−4.92637	−0.234589
$442$	104.258	4.95906
$443$	−28.9345	−1.37472	−0.687359	−	0.726318i	$-0.741230\pi$
$443$	−28.9345	−1.37472	−0.687359	+	0.726318i	$0.741230\pi$
$444$	30.0505	1.42613
$445$	−31.8240	−1.50860
$446$	57.9076	2.74201
$447$	−9.46073	−0.447477
$448$	−16.7073	−0.789345
$449$	4.46099	0.210527	0.105264	−	0.994444i	$-0.466431\pi$
$449$	4.46099	0.210527	0.105264	+	0.994444i	$0.466431\pi$
$450$	26.6448	1.25605
$451$	24.9887	1.17667
$452$	−75.0267	−3.52896
$453$	−11.4780	−0.539285
$454$	41.4543	1.94555
$455$	56.6343	2.65506
$456$	−23.3380	−1.09290
$457$	−3.16722	−0.148156	−0.0740782	−	0.997252i	$-0.523601\pi$
$457$	−3.16722	−0.148156	−0.0740782	+	0.997252i	$0.523601\pi$
$458$	6.39288	0.298720
$459$	20.9449	0.977622
$460$	−89.2311	−4.16042
$461$	−1.74091	−0.0810824	−0.0405412	−	0.999178i	$-0.512908\pi$
$461$	−1.74091	−0.0810824	−0.0405412	+	0.999178i	$0.512908\pi$
$462$	22.5049	1.04702
$463$	23.8455	1.10819	0.554097	−	0.832452i	$-0.313064\pi$
$463$	23.8455	1.10819	0.554097	+	0.832452i	$0.313064\pi$
$464$	−8.97226	−0.416527
$465$	2.04457	0.0948148
$466$	24.2640	1.12401
$467$	19.8859	0.920209	0.460105	−	0.887865i	$-0.347812\pi$
$467$	19.8859	0.920209	0.460105	+	0.887865i	$0.347812\pi$
$468$	80.3015	3.71194
$469$	−2.95593	−0.136492
$470$	44.9912	2.07529
$471$	−2.22912	−0.102712
$472$	−19.2194	−0.884647
$473$	24.3038	1.11749
$474$	−7.69249	−0.353328
$475$	−21.5577	−0.989135
$476$	−88.6365	−4.06265
$477$	−11.4046	−0.522182
$478$	3.56757	0.163177
$479$	−38.2378	−1.74713	−0.873565	−	0.486708i	$-0.838198\pi$
$479$	−38.2378	−1.74713	−0.873565	+	0.486708i	$0.838198\pi$
$480$	15.9331	0.727241
$481$	68.7501	3.13474
$482$	−45.3500	−2.06564
$483$	−11.0938	−0.504784
$484$	63.5995	2.89088
$485$	−45.5470	−2.06818
$486$	35.1178	1.59298
$487$	33.2455	1.50650	0.753248	−	0.657737i	$-0.228486\pi$
$487$	33.2455	1.50650	0.753248	+	0.657737i	$0.228486\pi$
$488$	−103.247	−4.67378
$489$	−2.58494	−0.116895
$490$	−14.3578	−0.648619
$491$	42.8832	1.93529	0.967645	−	0.252315i	$-0.0811919\pi$
$491$	42.8832	1.93529	0.967645	+	0.252315i	$0.0811919\pi$
$492$	14.1219	0.636663
$493$	−6.28598	−0.283107
$494$	−92.3955	−4.15707
$495$	39.0409	1.75476
$496$	−10.4493	−0.469186
$497$	−8.22025	−0.368729
$498$	14.9113	0.668191
$499$	−14.4656	−0.647571	−0.323785	−	0.946131i	$-0.604956\pi$
$499$	−14.4656	−0.647571	−0.323785	+	0.946131i	$0.604956\pi$
$500$	−15.9478	−0.713208
$501$	−6.47484	−0.289275
$502$	62.5879	2.79343
$503$	29.3189	1.30726	0.653632	−	0.756812i	$-0.273244\pi$
$503$	29.3189	1.30726	0.653632	+	0.756812i	$0.273244\pi$
$504$	−56.1045	−2.49909
$505$	3.35017	0.149081
$506$	−81.1215	−3.60629
$507$	−16.4032	−0.728490
$508$	15.2071	0.674704
$509$	−5.38363	−0.238625	−0.119312	−	0.992857i	$-0.538069\pi$
$509$	−5.38363	−0.238625	−0.119312	+	0.992857i	$0.538069\pi$
$510$	28.6455	1.26844
$511$	−49.8702	−2.20613
$512$	46.1030	2.03748
$513$	−18.5617	−0.819518
$514$	−51.3735	−2.26599
$515$	−27.0959	−1.19399
$516$	13.7348	0.604642
$517$	28.7614	1.26493
$518$	−83.1214	−3.65214
$519$	−3.79409	−0.166542
$520$	135.245	5.93087
$521$	−1.31780	−0.0577338	−0.0288669	−	0.999583i	$-0.509190\pi$
$521$	−1.31780	−0.0577338	−0.0288669	+	0.999583i	$0.509190\pi$
$522$	−6.88531	−0.301362
$523$	38.2013	1.67043	0.835214	−	0.549925i	$-0.185344\pi$
$523$	38.2013	1.67043	0.835214	+	0.549925i	$0.185344\pi$
$524$	8.49282	0.371010
$525$	6.78890	0.296292
$526$	63.0355	2.74848
$527$	−7.32078	−0.318898
$528$	26.1377	1.13750
$529$	16.9887	0.738641
$530$	−33.2386	−1.44379
$531$	−7.17317	−0.311289
$532$	78.5512	3.40563
$533$	32.3083	1.39943
$534$	−16.3502	−0.707542
$535$	−36.8313	−1.59236
$536$	−7.05886	−0.304896
$537$	−6.79400	−0.293183
$538$	−60.1188	−2.59191
$539$	−9.17847	−0.395345
$540$	47.0166	2.02327
$541$	27.1312	1.16646	0.583231	−	0.812306i	$-0.301788\pi$
$541$	27.1312	1.16646	0.583231	+	0.812306i	$0.301788\pi$
$542$	44.3505	1.90502
$543$	−8.13302	−0.349021
$544$	−57.0497	−2.44599
$545$	50.3625	2.15729
$546$	29.0970	1.24524
$547$	−27.5583	−1.17831	−0.589153	−	0.808021i	$-0.700538\pi$
$547$	−27.5583	−1.17831	−0.589153	+	0.808021i	$0.700538\pi$
$548$	−16.1764	−0.691021
$549$	−38.5344	−1.64461
$550$	49.6428	2.11677
$551$	5.57074	0.237322
$552$	−26.4923	−1.12759
$553$	14.9620	0.636250
$554$	65.6169	2.78779
$555$	18.8894	0.801810
$556$	4.73795	0.200934
$557$	−33.2284	−1.40793	−0.703965	−	0.710234i	$-0.748589\pi$
$557$	−33.2284	−1.40793	−0.703965	+	0.710234i	$0.748589\pi$
$558$	−8.01877	−0.339462
$559$	31.4228	1.32904
$560$	−79.5258	−3.36058
$561$	18.3121	0.773137
$562$	−40.5255	−1.70947
$563$	18.3259	0.772345	0.386172	−	0.922427i	$-0.373797\pi$
$563$	18.3259	0.772345	0.386172	+	0.922427i	$0.373797\pi$
$564$	16.2539	0.684414
$565$	−47.1609	−1.98408
$566$	−53.3603	−2.24290
$567$	−17.8372	−0.749093
$568$	−19.6302	−0.823666
$569$	13.9096	0.583119	0.291559	−	0.956553i	$-0.405826\pi$
$569$	13.9096	0.583119	0.291559	+	0.956553i	$0.405826\pi$
$570$	−25.3861	−1.06331
$571$	9.66839	0.404609	0.202305	−	0.979323i	$-0.435157\pi$
$571$	9.66839	0.404609	0.202305	+	0.979323i	$0.435157\pi$
$572$	149.612	6.25560
$573$	3.61314	0.150941
$574$	−39.0619	−1.63041
$575$	−24.4713	−1.02053
$576$	−14.8907	−0.620447
$577$	43.9263	1.82868	0.914338	−	0.404952i	$-0.132712\pi$
$577$	43.9263	1.82868	0.914338	+	0.404952i	$0.132712\pi$
$578$	−58.4398	−2.43078
$579$	3.89184	0.161739
$580$	−14.1107	−0.585913
$581$	−29.0028	−1.20324
$582$	−23.4007	−0.969989
$583$	−21.2483	−0.880016
$584$	−119.092	−4.92805
$585$	50.4766	2.08695
$586$	32.1514	1.32816
$587$	−36.3661	−1.50099	−0.750496	−	0.660875i	$-0.770185\pi$
$587$	−36.3661	−1.50099	−0.750496	+	0.660875i	$0.770185\pi$
$588$	−5.18703	−0.213910
$589$	6.48780	0.267325
$590$	−20.9061	−0.860690
$591$	11.3203	0.465655
$592$	−96.5387	−3.96772
$593$	12.5873	0.516896	0.258448	−	0.966025i	$-0.416789\pi$
$593$	12.5873	0.516896	0.258448	+	0.966025i	$0.416789\pi$
$594$	42.7436	1.75379
$595$	−55.7159	−2.28413
$596$	76.0420	3.11480
$597$	4.72727	0.193474
$598$	−104.883	−4.28900
$599$	−13.3203	−0.544251	−0.272126	−	0.962262i	$-0.587727\pi$
$599$	−13.3203	−0.544251	−0.272126	+	0.962262i	$0.587727\pi$
$600$	16.2121	0.661857
$601$	43.0810	1.75731	0.878655	−	0.477458i	$-0.158442\pi$
$601$	43.0810	1.75731	0.878655	+	0.477458i	$0.158442\pi$
$602$	−37.9913	−1.54841
$603$	−2.63454	−0.107287
$604$	92.2563	3.75386
$605$	39.9779	1.62533
$606$	1.72122	0.0699196
$607$	−19.1330	−0.776583	−0.388292	−	0.921536i	$-0.626935\pi$
$607$	−19.1330	−0.776583	−0.388292	+	0.921536i	$0.626935\pi$
$608$	50.5584	2.05042
$609$	−1.75433	−0.0710889
$610$	−112.308	−4.54721
$611$	37.1861	1.50439
$612$	−78.9993	−3.19336
$613$	−22.3187	−0.901445	−0.450723	−	0.892664i	$-0.648834\pi$
$613$	−22.3187	−0.901445	−0.450723	+	0.892664i	$0.648834\pi$
$614$	5.67517	0.229031
$615$	8.87685	0.357949
$616$	−104.530	−4.21164
$617$	−10.7113	−0.431219	−0.215609	−	0.976480i	$-0.569174\pi$
$617$	−10.7113	−0.431219	−0.215609	+	0.976480i	$0.569174\pi$
$618$	−13.9210	−0.559986
$619$	−6.61839	−0.266016	−0.133008	−	0.991115i	$-0.542464\pi$
$619$	−6.61839	−0.266016	−0.133008	+	0.991115i	$0.542464\pi$
$620$	−16.4336	−0.659988
$621$	−21.0704	−0.845526
$622$	−47.8297	−1.91780
$623$	31.8014	1.27410
$624$	33.7938	1.35283
$625$	−29.3736	−1.17495
$626$	−45.2980	−1.81047
$627$	−16.2285	−0.648103
$628$	17.9169	0.714961
$629$	−67.6352	−2.69679
$630$	−61.0281	−2.43142
$631$	20.5707	0.818906	0.409453	−	0.912331i	$-0.365720\pi$
$631$	20.5707	0.818906	0.409453	+	0.912331i	$0.365720\pi$
$632$	35.7298	1.42126
$633$	−7.79815	−0.309949
$634$	79.7922	3.16895
$635$	9.55899	0.379337
$636$	−12.0081	−0.476151
$637$	−11.8670	−0.470188
$638$	−12.8282	−0.507875
$639$	−7.32649	−0.289831
$640$	10.6602	0.421380
$641$	−37.9127	−1.49746	−0.748730	−	0.662875i	$-0.769336\pi$
$641$	−37.9127	−1.49746	−0.748730	+	0.662875i	$0.769336\pi$
$642$	−18.9228	−0.746824
$643$	32.4120	1.27820	0.639102	−	0.769122i	$-0.279306\pi$
$643$	32.4120	1.27820	0.639102	+	0.769122i	$0.279306\pi$
$644$	89.1679	3.51371
$645$	8.63355	0.339946
$646$	90.8972	3.57630
$647$	10.8245	0.425553	0.212777	−	0.977101i	$-0.431749\pi$
$647$	10.8245	0.425553	0.212777	+	0.977101i	$0.431749\pi$
$648$	−42.5959	−1.67332
$649$	−13.3646	−0.524605
$650$	64.1839	2.51750
$651$	−2.04312	−0.0800764
$652$	20.7768	0.813684
$653$	3.39854	0.132995	0.0664976	−	0.997787i	$-0.478818\pi$
$653$	3.39854	0.132995	0.0664976	+	0.997787i	$0.478818\pi$
$654$	25.8747	1.01178
$655$	5.33849	0.208592
$656$	−45.3672	−1.77129
$657$	−44.4479	−1.73408
$658$	−44.9593	−1.75270
$659$	−3.78753	−0.147541	−0.0737705	−	0.997275i	$-0.523503\pi$
$659$	−3.78753	−0.147541	−0.0737705	+	0.997275i	$0.523503\pi$
$660$	41.1066	1.60007
$661$	27.7731	1.08025	0.540124	−	0.841586i	$-0.318377\pi$
$661$	27.7731	1.08025	0.540124	+	0.841586i	$0.318377\pi$
$662$	74.0624	2.87852
$663$	23.6760	0.919500
$664$	−69.2595	−2.68779
$665$	49.3764	1.91473
$666$	−74.0838	−2.87069
$667$	6.32366	0.244853
$668$	52.0425	2.01358
$669$	13.1502	0.508417
$670$	−7.67832	−0.296639
$671$	−71.7947	−2.77160
$672$	−15.9218	−0.614195
$673$	17.3889	0.670295	0.335147	−	0.942166i	$-0.391214\pi$
$673$	17.3889	0.670295	0.335147	+	0.942166i	$0.391214\pi$
$674$	−31.5570	−1.21553
$675$	12.8942	0.496296
$676$	131.843	5.07088
$677$	17.1480	0.659051	0.329525	−	0.944147i	$-0.393111\pi$
$677$	17.1480	0.659051	0.329525	+	0.944147i	$0.393111\pi$
$678$	−24.2299	−0.930542
$679$	45.5148	1.74670
$680$	−133.051	−5.10229
$681$	9.41385	0.360740
$682$	−14.9400	−0.572083
$683$	−25.4440	−0.973587	−0.486794	−	0.873517i	$-0.661834\pi$
$683$	−25.4440	−0.973587	−0.486794	+	0.873517i	$0.661834\pi$
$684$	70.0105	2.67692
$685$	−10.1683	−0.388511
$686$	−39.7292	−1.51687
$687$	1.45176	0.0553880
$688$	−44.1238	−1.68220
$689$	−27.4723	−1.04661
$690$	−28.8172	−1.09705
$691$	19.1501	0.728503	0.364252	−	0.931301i	$-0.381325\pi$
$691$	19.1501	0.728503	0.364252	+	0.931301i	$0.381325\pi$
$692$	30.4956	1.15927
$693$	−39.0132	−1.48199
$694$	1.85547	0.0704325
$695$	2.97822	0.112970
$696$	−4.18939	−0.158798
$697$	−31.7844	−1.20392
$698$	38.6686	1.46363
$699$	5.51011	0.208411
$700$	−54.5668	−2.06243
$701$	−12.3150	−0.465132	−0.232566	−	0.972581i	$-0.574712\pi$
$701$	−12.3150	−0.465132	−0.232566	+	0.972581i	$0.574712\pi$
$702$	55.2639	2.08580
$703$	59.9395	2.26066
$704$	−27.7434	−1.04562
$705$	10.2170	0.384796
$706$	0.256069	0.00963728
$707$	−3.34780	−0.125907
$708$	−7.55272	−0.283849
$709$	15.4661	0.580842	0.290421	−	0.956899i	$-0.406205\pi$
$709$	15.4661	0.580842	0.290421	+	0.956899i	$0.406205\pi$
$710$	−21.3529	−0.801360
$711$	13.3352	0.500111
$712$	75.9429	2.84608
$713$	7.36467	0.275809
$714$	−28.6252	−1.07127
$715$	94.0446	3.51707
$716$	54.6078	2.04079
$717$	0.810158	0.0302559
$718$	54.3919	2.02989
$719$	−11.6227	−0.433454	−0.216727	−	0.976232i	$-0.569538\pi$
$719$	−11.6227	−0.433454	−0.216727	+	0.976232i	$0.569538\pi$
$720$	−70.8791	−2.64151
$721$	27.0767	1.00839
$722$	−31.2352	−1.16246
$723$	−10.2985	−0.383007
$724$	65.3703	2.42947
$725$	−3.86980	−0.143721
$726$	20.5394	0.762290
$727$	31.9577	1.18525	0.592623	−	0.805480i	$-0.298093\pi$
$727$	31.9577	1.18525	0.592623	+	0.805480i	$0.298093\pi$
$728$	−135.149	−5.00894
$729$	−10.0055	−0.370574
$730$	−129.543	−4.79459
$731$	−30.9132	−1.14337
$732$	−40.5734	−1.49963
$733$	−7.41534	−0.273892	−0.136946	−	0.990579i	$-0.543729\pi$
$733$	−7.41534	−0.273892	−0.136946	+	0.990579i	$0.543729\pi$
$734$	17.9464	0.662415
$735$	−3.26051	−0.120266
$736$	57.3917	2.11549
$737$	−4.90850	−0.180807
$738$	−34.8148	−1.28155
$739$	−27.5022	−1.01169	−0.505843	−	0.862625i	$-0.668819\pi$
$739$	−27.5022	−1.01169	−0.505843	+	0.862625i	$0.668819\pi$
$740$	−151.826	−5.58125
$741$	−20.9821	−0.770796
$742$	33.2150	1.21936
$743$	40.6260	1.49042	0.745212	−	0.666828i	$-0.232348\pi$
$743$	40.6260	1.49042	0.745212	+	0.666828i	$0.232348\pi$
$744$	−4.87905	−0.178875
$745$	47.7991	1.75123
$746$	70.2862	2.57336
$747$	−25.8494	−0.945778
$748$	−147.186	−5.38166
$749$	36.8052	1.34483
$750$	−5.15035	−0.188064
$751$	−17.2671	−0.630084	−0.315042	−	0.949078i	$-0.602019\pi$
$751$	−17.2671	−0.630084	−0.315042	+	0.949078i	$0.602019\pi$
$752$	−52.2166	−1.90414
$753$	14.2131	0.517953
$754$	−16.5858	−0.604021
$755$	57.9913	2.11052
$756$	−46.9833	−1.70877
$757$	−42.1372	−1.53150	−0.765751	−	0.643137i	$-0.777633\pi$
$757$	−42.1372	−1.53150	−0.765751	+	0.643137i	$0.777633\pi$
$758$	−10.2416	−0.371991
$759$	−18.4219	−0.668671
$760$	117.912	4.27713
$761$	7.23932	0.262425	0.131213	−	0.991354i	$-0.458113\pi$
$761$	7.23932	0.262425	0.131213	+	0.991354i	$0.458113\pi$
$762$	4.91112	0.177911
$763$	−50.3269	−1.82195
$764$	−29.0411	−1.05067
$765$	−49.6581	−1.79539
$766$	65.2039	2.35591
$767$	−17.2793	−0.623918
$768$	12.0952	0.436447
$769$	22.4353	0.809037	0.404519	−	0.914530i	$-0.367439\pi$
$769$	22.4353	0.809037	0.404519	+	0.914530i	$0.367439\pi$
$770$	−113.703	−4.09758
$771$	−11.6664	−0.420155
$772$	−31.2812	−1.12584
$773$	−2.31489	−0.0832608	−0.0416304	−	0.999133i	$-0.513255\pi$
$773$	−2.31489	−0.0832608	−0.0416304	+	0.999133i	$0.513255\pi$
$774$	−33.8606	−1.21709
$775$	−4.50685	−0.161891
$776$	108.691	3.90177
$777$	−18.8760	−0.677173
$778$	4.87446	0.174758
$779$	28.1678	1.00922
$780$	53.1475	1.90298
$781$	−13.6502	−0.488443
$782$	103.182	3.68980
$783$	−3.33199	−0.119076
$784$	16.6636	0.595129
$785$	11.2623	0.401970
$786$	2.74275	0.0978308
$787$	−29.1564	−1.03931	−0.519657	−	0.854375i	$-0.673940\pi$
$787$	−29.1564	−1.03931	−0.519657	+	0.854375i	$0.673940\pi$
$788$	−90.9886	−3.24133
$789$	14.3147	0.509618
$790$	38.8653	1.38277
$791$	47.1275	1.67566
$792$	−93.1648	−3.31047
$793$	−92.8245	−3.29630
$794$	−65.9898	−2.34189
$795$	−7.54814	−0.267705
$796$	−37.9962	−1.34674
$797$	32.8572	1.16386	0.581931	−	0.813238i	$-0.302297\pi$
$797$	32.8572	1.16386	0.581931	+	0.813238i	$0.302297\pi$
$798$	25.3681	0.898021
$799$	−36.5831	−1.29422
$800$	−35.1212	−1.24172
$801$	28.3437	1.00148
$802$	102.899	3.63349
$803$	−82.8124	−2.92239
$804$	−2.77394	−0.0978293
$805$	56.0499	1.97550
$806$	−19.3162	−0.680384
$807$	−13.6524	−0.480586
$808$	−7.99464	−0.281251
$809$	22.0443	0.775035	0.387518	−	0.921862i	$-0.373333\pi$
$809$	22.0443	0.775035	0.387518	+	0.921862i	$0.373333\pi$
$810$	−46.3339	−1.62801
$811$	−1.29848	−0.0455959	−0.0227980	−	0.999740i	$-0.507257\pi$
$811$	−1.29848	−0.0455959	−0.0227980	+	0.999740i	$0.507257\pi$
$812$	14.1007	0.494836
$813$	10.0715	0.353225
$814$	−138.028	−4.83787
$815$	13.0601	0.457475
$816$	−33.2458	−1.16384
$817$	27.3958	0.958458
$818$	35.3950	1.23756
$819$	−50.4408	−1.76255
$820$	−71.3490	−2.49161
$821$	27.4849	0.959231	0.479615	−	0.877479i	$-0.340776\pi$
$821$	27.4849	0.959231	0.479615	+	0.877479i	$0.340776\pi$
$822$	−5.22416	−0.182214
$823$	8.85316	0.308602	0.154301	−	0.988024i	$-0.450688\pi$
$823$	8.85316	0.308602	0.154301	+	0.988024i	$0.450688\pi$
$824$	64.6600	2.25254
$825$	11.2734	0.392488
$826$	20.8913	0.726900
$827$	−40.6781	−1.41452	−0.707259	−	0.706955i	$-0.750068\pi$
$827$	−40.6781	−1.41452	−0.707259	+	0.706955i	$0.750068\pi$
$828$	79.4728	2.76187
$829$	19.6957	0.684061	0.342030	−	0.939689i	$-0.388885\pi$
$829$	19.6957	0.684061	0.342030	+	0.939689i	$0.388885\pi$
$830$	−75.3375	−2.61500
$831$	14.9009	0.516907
$832$	−35.8699	−1.24357
$833$	11.6746	0.404499
$834$	1.53012	0.0529837
$835$	32.7133	1.13209
$836$	130.439	4.51132
$837$	−3.88051	−0.134130
$838$	−59.1157	−2.04212
$839$	−16.2607	−0.561381	−0.280691	−	0.959798i	$-0.590563\pi$
$839$	−16.2607	−0.561381	−0.280691	+	0.959798i	$0.590563\pi$
$840$	−37.1327	−1.28120
$841$	1.00000	0.0344828
$842$	67.1958	2.31572
$843$	−9.20293	−0.316966
$844$	62.6788	2.15749
$845$	82.8749	2.85098
$846$	−40.0710	−1.37767
$847$	−39.9496	−1.37268
$848$	38.5766	1.32472
$849$	−12.1176	−0.415875
$850$	−63.1431	−2.16579
$851$	68.0407	2.33240
$852$	−7.71415	−0.264282
$853$	21.9738	0.752368	0.376184	−	0.926545i	$-0.377236\pi$
$853$	21.9738	0.752368	0.376184	+	0.926545i	$0.377236\pi$
$854$	112.228	3.84037
$855$	44.0078	1.50504
$856$	87.8920	3.00409
$857$	−3.58409	−0.122430	−0.0612150	−	0.998125i	$-0.519498\pi$
$857$	−3.58409	−0.122430	−0.0612150	+	0.998125i	$0.519498\pi$
$858$	48.3173	1.64952
$859$	13.3422	0.455230	0.227615	−	0.973751i	$-0.426907\pi$
$859$	13.3422	0.455230	0.227615	+	0.973751i	$0.426907\pi$
$860$	−69.3934	−2.36630
$861$	−8.87056	−0.302308
$862$	−30.2278	−1.02956
$863$	11.8717	0.404118	0.202059	−	0.979373i	$-0.435237\pi$
$863$	11.8717	0.404118	0.202059	+	0.979373i	$0.435237\pi$
$864$	−30.2402	−1.02879
$865$	19.1692	0.651772
$866$	30.1688	1.02518
$867$	−13.2711	−0.450710
$868$	16.4219	0.557396
$869$	24.8453	0.842820
$870$	−4.55703	−0.154498
$871$	−6.34628	−0.215035
$872$	−120.182	−4.06988
$873$	40.5660	1.37295
$874$	−91.4420	−3.09307
$875$	10.0175	0.338654
$876$	−46.7998	−1.58122
$877$	−36.1891	−1.22202	−0.611010	−	0.791623i	$-0.709236\pi$
$877$	−36.1891	−1.22202	−0.611010	+	0.791623i	$0.709236\pi$
$878$	42.7832	1.44386
$879$	7.30126	0.246265
$880$	−132.057	−4.45165
$881$	1.12969	0.0380603	0.0190301	−	0.999819i	$-0.493942\pi$
$881$	1.12969	0.0380603	0.0190301	+	0.999819i	$0.493942\pi$
$882$	12.7876	0.430582
$883$	−26.5096	−0.892120	−0.446060	−	0.895003i	$-0.647173\pi$
$883$	−26.5096	−0.892120	−0.446060	+	0.895003i	$0.647173\pi$
$884$	−190.299	−6.40046
$885$	−4.74756	−0.159587
$886$	75.1068	2.52326
$887$	−14.3564	−0.482041	−0.241021	−	0.970520i	$-0.577482\pi$
$887$	−14.3564	−0.482041	−0.241021	+	0.970520i	$0.577482\pi$
$888$	−45.0765	−1.51267
$889$	−9.55221	−0.320371
$890$	82.6073	2.76900
$891$	−29.6197	−0.992299
$892$	−105.697	−3.53899
$893$	32.4205	1.08491
$894$	24.5577	0.821334
$895$	34.3258	1.14739
$896$	−10.6526	−0.355878
$897$	−23.8179	−0.795258
$898$	−11.5796	−0.386418
$899$	1.16462	0.0388423
$900$	−48.6339	−1.62113
$901$	27.0268	0.900394
$902$	−64.8645	−2.15975
$903$	−8.62743	−0.287103
$904$	112.542	3.74309
$905$	41.0910	1.36591
$906$	29.7942	0.989845
$907$	23.0039	0.763834	0.381917	−	0.924197i	$-0.375264\pi$
$907$	23.0039	0.763834	0.381917	+	0.924197i	$0.375264\pi$
$908$	−75.6652	−2.51104
$909$	−2.98380	−0.0989664
$910$	−147.009	−4.87330
$911$	−32.8618	−1.08876	−0.544380	−	0.838839i	$-0.683235\pi$
$911$	−32.8618	−1.08876	−0.544380	+	0.838839i	$0.683235\pi$
$912$	29.4630	0.975617
$913$	−48.1608	−1.59389
$914$	8.22133	0.271938
$915$	−25.5040	−0.843135
$916$	−11.6687	−0.385545
$917$	−5.33471	−0.176168
$918$	−54.3677	−1.79440
$919$	30.3062	0.999708	0.499854	−	0.866110i	$-0.333387\pi$
$919$	30.3062	0.999708	0.499854	+	0.866110i	$0.333387\pi$
$920$	133.849	4.41287
$921$	1.28877	0.0424665
$922$	4.51899	0.148825
$923$	−17.6486	−0.580910
$924$	−41.0775	−1.35135
$925$	−41.6379	−1.36905
$926$	−61.8971	−2.03406
$927$	24.1327	0.792622
$928$	9.07571	0.297925
$929$	13.3630	0.438426	0.219213	−	0.975677i	$-0.429651\pi$
$929$	13.3630	0.438426	0.219213	+	0.975677i	$0.429651\pi$
$930$	−5.30721	−0.174030
$931$	−10.3462	−0.339083
$932$	−44.2883	−1.45071
$933$	−10.8616	−0.355594
$934$	−51.6189	−1.68902
$935$	−92.5195	−3.02571
$936$	−120.454	−3.93717
$937$	−20.5239	−0.670486	−0.335243	−	0.942132i	$-0.608818\pi$
$937$	−20.5239	−0.670486	−0.335243	+	0.942132i	$0.608818\pi$
$938$	7.67288	0.250528
$939$	−10.2867	−0.335694
$940$	−82.1210	−2.67849
$941$	−31.3041	−1.02048	−0.510241	−	0.860031i	$-0.670444\pi$
$941$	−31.3041	−1.02048	−0.510241	+	0.860031i	$0.670444\pi$
$942$	5.78625	0.188526
$943$	31.9749	1.04125
$944$	24.2635	0.789710
$945$	−29.5332	−0.960714
$946$	−63.0867	−2.05113
$947$	−21.4039	−0.695532	−0.347766	−	0.937581i	$-0.613060\pi$
$947$	−21.4039	−0.695532	−0.347766	+	0.937581i	$0.613060\pi$
$948$	14.0408	0.456025
$949$	−107.069	−3.47562
$950$	55.9585	1.81553
$951$	18.1200	0.587581
$952$	132.957	4.30916
$953$	32.6814	1.05865	0.529327	−	0.848418i	$-0.322444\pi$
$953$	32.6814	1.05865	0.529327	+	0.848418i	$0.322444\pi$
$954$	29.6036	0.958453
$955$	−18.2549	−0.590716
$956$	−6.51176	−0.210605
$957$	−2.91316	−0.0941692
$958$	99.2560	3.20682
$959$	10.1611	0.328119
$960$	−9.85542	−0.318082
$961$	−29.6437	−0.956247
$962$	−178.458	−5.75373
$963$	32.8035	1.05708
$964$	82.7759	2.66603
$965$	−19.6630	−0.632975
$966$	28.7967	0.926520
$967$	−6.36748	−0.204764	−0.102382	−	0.994745i	$-0.532646\pi$
$967$	−6.36748	−0.204764	−0.102382	+	0.994745i	$0.532646\pi$
$968$	−95.4008	−3.06630
$969$	20.6418	0.663111
$970$	118.229	3.79610
$971$	−19.2843	−0.618862	−0.309431	−	0.950922i	$-0.600139\pi$
$971$	−19.2843	−0.618862	−0.309431	+	0.950922i	$0.600139\pi$
$972$	−64.0995	−2.05599
$973$	−2.97611	−0.0954097
$974$	−86.2971	−2.76514
$975$	14.5755	0.466790
$976$	130.344	4.17221
$977$	45.7909	1.46498	0.732490	−	0.680777i	$-0.238358\pi$
$977$	45.7909	1.46498	0.732490	+	0.680777i	$0.238358\pi$
$978$	6.70988	0.214558
$979$	52.8081	1.68776
$980$	26.2068	0.837147
$981$	−44.8549	−1.43211
$982$	−111.314	−3.55218
$983$	7.78579	0.248328	0.124164	−	0.992262i	$-0.460375\pi$
$983$	7.78579	0.248328	0.124164	+	0.992262i	$0.460375\pi$
$984$	−21.1832	−0.675295
$985$	−57.1944	−1.82236
$986$	16.3169	0.519635
$987$	−10.2098	−0.324982
$988$	168.646	5.36536
$989$	31.0985	0.988876
$990$	−101.341	−3.22082
$991$	26.1929	0.832044	0.416022	−	0.909355i	$-0.363424\pi$
$991$	26.1929	0.832044	0.416022	+	0.909355i	$0.363424\pi$
$992$	10.5697	0.335590
$993$	16.8188	0.533729
$994$	21.3378	0.676793
$995$	−23.8840	−0.757172
$996$	−27.2171	−0.862407
$997$	23.4022	0.741155	0.370577	−	0.928802i	$-0.379160\pi$
$997$	23.4022	0.741155	0.370577	+	0.928802i	$0.379160\pi$
$998$	37.5492	1.18860
$999$	−35.8512	−1.13428

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.e.1.8	✓	103

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.e.1.8	✓	103	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59576 q^{2} -0.589470 q^{3} +4.73795 q^{4} +2.97822 q^{5} +1.53012 q^{6} -2.97611 q^{7} -7.10705 q^{8} -2.65253 q^{9} +O(q^{10})\)	\(q-2.59576 q^{2} -0.589470 q^{3} +4.73795 q^{4} +2.97822 q^{5} +1.53012 q^{6} -2.97611 q^{7} -7.10705 q^{8} -2.65253 q^{9} -7.73074 q^{10} -4.94201 q^{11} -2.79288 q^{12} -6.38960 q^{13} +7.72526 q^{14} -1.75557 q^{15} +8.97226 q^{16} +6.28598 q^{17} +6.88531 q^{18} -5.57074 q^{19} +14.1107 q^{20} +1.75433 q^{21} +12.8282 q^{22} -6.32366 q^{23} +4.18939 q^{24} +3.86980 q^{25} +16.5858 q^{26} +3.33199 q^{27} -14.1007 q^{28} -1.00000 q^{29} +4.55703 q^{30} -1.16462 q^{31} -9.07571 q^{32} +2.91316 q^{33} -16.3169 q^{34} -8.86352 q^{35} -12.5675 q^{36} -10.7597 q^{37} +14.4603 q^{38} +3.76648 q^{39} -21.1664 q^{40} -5.05639 q^{41} -4.55381 q^{42} -4.91780 q^{43} -23.4150 q^{44} -7.89981 q^{45} +16.4147 q^{46} -5.81978 q^{47} -5.28888 q^{48} +1.85724 q^{49} -10.0451 q^{50} -3.70540 q^{51} -30.2736 q^{52} +4.29954 q^{53} -8.64904 q^{54} -14.7184 q^{55} +21.1514 q^{56} +3.28379 q^{57} +2.59576 q^{58} +2.70428 q^{59} -8.31781 q^{60} +14.5274 q^{61} +3.02307 q^{62} +7.89421 q^{63} +5.61380 q^{64} -19.0296 q^{65} -7.56186 q^{66} +0.993219 q^{67} +29.7827 q^{68} +3.72761 q^{69} +23.0075 q^{70} +2.76208 q^{71} +18.8516 q^{72} +16.7568 q^{73} +27.9295 q^{74} -2.28113 q^{75} -26.3939 q^{76} +14.7080 q^{77} -9.77685 q^{78} -5.02738 q^{79} +26.7214 q^{80} +5.99347 q^{81} +13.1251 q^{82} +9.74519 q^{83} +8.31191 q^{84} +18.7211 q^{85} +12.7654 q^{86} +0.589470 q^{87} +35.1231 q^{88} -10.6856 q^{89} +20.5060 q^{90} +19.0162 q^{91} -29.9612 q^{92} +0.686508 q^{93} +15.1067 q^{94} -16.5909 q^{95} +5.34985 q^{96} -15.2934 q^{97} -4.82093 q^{98} +13.1088 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9 + 20 * q^10 + 9 * q^11 + 36 * q^13 - 10 * q^14 + 16 * q^15 + 179 * q^16 + 21 * q^17 + 7 * q^18 + 42 * q^19 + 24 * q^20 + 28 * q^21 + 32 * q^22 + 25 * q^23 + 68 * q^24 + 194 * q^25 - 5 * q^26 + 14 * q^27 + 59 * q^28 - 103 * q^29 + 84 * q^30 + 34 * q^31 + 11 * q^32 + 42 * q^33 + 54 * q^34 + 35 * q^35 + 214 * q^36 + 34 * q^37 + 9 * q^38 + 23 * q^39 + 46 * q^40 + 16 * q^41 + 13 * q^42 + 68 * q^43 - 6 * q^44 + 25 * q^45 + 60 * q^46 + 6 * q^47 + 5 * q^48 + 257 * q^49 - 51 * q^50 + 68 * q^51 + 37 * q^52 + 35 * q^53 + 30 * q^54 + 66 * q^55 - 54 * q^56 + 78 * q^57 - q^58 + 10 * q^59 - 24 * q^60 + 70 * q^61 + 29 * q^62 + 26 * q^63 + 276 * q^64 + 95 * q^65 + 77 * q^66 + 71 * q^67 - 21 * q^68 - 20 * q^69 + 48 * q^70 + 32 * q^71 + 32 * q^72 + 94 * q^73 + 35 * q^74 + 7 * q^75 + 134 * q^76 + 17 * q^77 + 58 * q^78 + 110 * q^79 + 78 * q^80 + 267 * q^81 - 71 * q^82 + 35 * q^83 + 96 * q^84 + 71 * q^85 + 33 * q^86 - 2 * q^87 + 100 * q^88 + 22 * q^89 - 134 * q^90 + 108 * q^91 - 11 * q^92 + 78 * q^93 + 90 * q^94 + 12 * q^95 + 177 * q^96 + 44 * q^97 - 18 * q^98 + 83 * q^99

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