LMFDB - Embedded newform 4029.2.a.l.1.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.28
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.29130 q^{2} -1.00000 q^{3} +3.25006 q^{4} +3.13615 q^{5} -2.29130 q^{6} +0.344445 q^{7} +2.86426 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.29130 q^{2} -1.00000 q^{3} +3.25006 q^{4} +3.13615 q^{5} -2.29130 q^{6} +0.344445 q^{7} +2.86426 q^{8} +1.00000 q^{9} +7.18585 q^{10} +5.23682 q^{11} -3.25006 q^{12} +2.96491 q^{13} +0.789227 q^{14} -3.13615 q^{15} +0.0627600 q^{16} -1.00000 q^{17} +2.29130 q^{18} -2.69703 q^{19} +10.1927 q^{20} -0.344445 q^{21} +11.9991 q^{22} +7.52621 q^{23} -2.86426 q^{24} +4.83541 q^{25} +6.79351 q^{26} -1.00000 q^{27} +1.11947 q^{28} -1.77304 q^{29} -7.18585 q^{30} -0.447226 q^{31} -5.58471 q^{32} -5.23682 q^{33} -2.29130 q^{34} +1.08023 q^{35} +3.25006 q^{36} -0.229108 q^{37} -6.17970 q^{38} -2.96491 q^{39} +8.98273 q^{40} -7.81931 q^{41} -0.789227 q^{42} -6.20506 q^{43} +17.0200 q^{44} +3.13615 q^{45} +17.2448 q^{46} -3.09524 q^{47} -0.0627600 q^{48} -6.88136 q^{49} +11.0794 q^{50} +1.00000 q^{51} +9.63614 q^{52} +1.46841 q^{53} -2.29130 q^{54} +16.4234 q^{55} +0.986579 q^{56} +2.69703 q^{57} -4.06257 q^{58} +10.7658 q^{59} -10.1927 q^{60} +8.00416 q^{61} -1.02473 q^{62} +0.344445 q^{63} -12.9218 q^{64} +9.29840 q^{65} -11.9991 q^{66} -10.2637 q^{67} -3.25006 q^{68} -7.52621 q^{69} +2.47513 q^{70} -0.297132 q^{71} +2.86426 q^{72} -5.70357 q^{73} -0.524956 q^{74} -4.83541 q^{75} -8.76550 q^{76} +1.80380 q^{77} -6.79351 q^{78} +1.00000 q^{79} +0.196824 q^{80} +1.00000 q^{81} -17.9164 q^{82} +4.51994 q^{83} -1.11947 q^{84} -3.13615 q^{85} -14.2177 q^{86} +1.77304 q^{87} +14.9996 q^{88} +13.7770 q^{89} +7.18585 q^{90} +1.02125 q^{91} +24.4606 q^{92} +0.447226 q^{93} -7.09213 q^{94} -8.45827 q^{95} +5.58471 q^{96} +12.0659 q^{97} -15.7673 q^{98} +5.23682 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * 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 $

$2$	2.29130	1.62019	0.810097	−	0.586296i	$-0.199414\pi$
$2$	2.29130	1.62019	0.810097	+	0.586296i	$0.199414\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.25006	1.62503
$5$	3.13615	1.40253	0.701263	−	0.712902i	$-0.252620\pi$
$5$	3.13615	1.40253	0.701263	+	0.712902i	$0.252620\pi$
$6$	−2.29130	−0.935419
$7$	0.344445	0.130188	0.0650940	−	0.997879i	$-0.479265\pi$
$7$	0.344445	0.130188	0.0650940	+	0.997879i	$0.479265\pi$
$8$	2.86426	1.01267
$9$	1.00000	0.333333
$10$	7.18585	2.27237
$11$	5.23682	1.57896	0.789481	−	0.613775i	$-0.210350\pi$
$11$	5.23682	1.57896	0.789481	+	0.613775i	$0.210350\pi$
$12$	−3.25006	−0.938211
$13$	2.96491	0.822319	0.411160	−	0.911563i	$-0.365124\pi$
$13$	2.96491	0.822319	0.411160	+	0.911563i	$0.365124\pi$
$14$	0.789227	0.210930
$15$	−3.13615	−0.809749
$16$	0.0627600	0.0156900
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.29130	0.540065
$19$	−2.69703	−0.618741	−0.309370	−	0.950942i	$-0.600118\pi$
$19$	−2.69703	−0.618741	−0.309370	+	0.950942i	$0.600118\pi$
$20$	10.1927	2.27915
$21$	−0.344445	−0.0751641
$22$	11.9991	2.55822
$23$	7.52621	1.56932	0.784662	−	0.619924i	$-0.212837\pi$
$23$	7.52621	1.56932	0.784662	+	0.619924i	$0.212837\pi$
$24$	−2.86426	−0.584664
$25$	4.83541	0.967082
$26$	6.79351	1.33232
$27$	−1.00000	−0.192450
$28$	1.11947	0.211559
$29$	−1.77304	−0.329246	−0.164623	−	0.986357i	$-0.552641\pi$
$29$	−1.77304	−0.329246	−0.164623	+	0.986357i	$0.552641\pi$
$30$	−7.18585	−1.31195
$31$	−0.447226	−0.0803242	−0.0401621	−	0.999193i	$-0.512787\pi$
$31$	−0.447226	−0.0803242	−0.0401621	+	0.999193i	$0.512787\pi$
$32$	−5.58471	−0.987247
$33$	−5.23682	−0.911614
$34$	−2.29130	−0.392955
$35$	1.08023	0.182592
$36$	3.25006	0.541676
$37$	−0.229108	−0.0376652	−0.0188326	−	0.999823i	$-0.505995\pi$
$37$	−0.229108	−0.0376652	−0.0188326	+	0.999823i	$0.505995\pi$
$38$	−6.17970	−1.00248
$39$	−2.96491	−0.474766
$40$	8.98273	1.42029
$41$	−7.81931	−1.22117	−0.610585	−	0.791951i	$-0.709066\pi$
$41$	−7.81931	−1.22117	−0.610585	+	0.791951i	$0.709066\pi$
$42$	−0.789227	−0.121780
$43$	−6.20506	−0.946263	−0.473132	−	0.880992i	$-0.656876\pi$
$43$	−6.20506	−0.946263	−0.473132	+	0.880992i	$0.656876\pi$
$44$	17.0200	2.56586
$45$	3.13615	0.467509
$46$	17.2448	2.54261
$47$	−3.09524	−0.451488	−0.225744	−	0.974187i	$-0.572481\pi$
$47$	−3.09524	−0.451488	−0.225744	+	0.974187i	$0.572481\pi$
$48$	−0.0627600	−0.00905862
$49$	−6.88136	−0.983051
$50$	11.0794	1.56686
$51$	1.00000	0.140028
$52$	9.63614	1.33629
$53$	1.46841	0.201702	0.100851	−	0.994902i	$-0.467843\pi$
$53$	1.46841	0.201702	0.100851	+	0.994902i	$0.467843\pi$
$54$	−2.29130	−0.311806
$55$	16.4234	2.21454
$56$	0.986579	0.131837
$57$	2.69703	0.357230
$58$	−4.06257	−0.533442
$59$	10.7658	1.40158	0.700792	−	0.713366i	$-0.252830\pi$
$59$	10.7658	1.40158	0.700792	+	0.713366i	$0.252830\pi$
$60$	−10.1927	−1.31587
$61$	8.00416	1.02483	0.512414	−	0.858739i	$-0.328751\pi$
$61$	8.00416	1.02483	0.512414	+	0.858739i	$0.328751\pi$
$62$	−1.02473	−0.130141
$63$	0.344445	0.0433960
$64$	−12.9218	−1.61522
$65$	9.29840	1.15333
$66$	−11.9991	−1.47699
$67$	−10.2637	−1.25392	−0.626958	−	0.779053i	$-0.715700\pi$
$67$	−10.2637	−1.25392	−0.626958	+	0.779053i	$0.715700\pi$
$68$	−3.25006	−0.394127
$69$	−7.52621	−0.906049
$70$	2.47513	0.295835
$71$	−0.297132	−0.0352630	−0.0176315	−	0.999845i	$-0.505613\pi$
$71$	−0.297132	−0.0352630	−0.0176315	+	0.999845i	$0.505613\pi$
$72$	2.86426	0.337556
$73$	−5.70357	−0.667552	−0.333776	−	0.942652i	$-0.608323\pi$
$73$	−5.70357	−0.667552	−0.333776	+	0.942652i	$0.608323\pi$
$74$	−0.524956	−0.0610249
$75$	−4.83541	−0.558345
$76$	−8.76550	−1.00547
$77$	1.80380	0.205562
$78$	−6.79351	−0.769214
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	0.196824	0.0220056
$81$	1.00000	0.111111
$82$	−17.9164	−1.97853
$83$	4.51994	0.496128	0.248064	−	0.968744i	$-0.420206\pi$
$83$	4.51994	0.496128	0.248064	+	0.968744i	$0.420206\pi$
$84$	−1.11947	−0.122144
$85$	−3.13615	−0.340163
$86$	−14.2177	−1.53313
$87$	1.77304	0.190090
$88$	14.9996	1.59896
$89$	13.7770	1.46036	0.730178	−	0.683257i	$-0.239437\pi$
$89$	13.7770	1.46036	0.730178	+	0.683257i	$0.239437\pi$
$90$	7.18585	0.757455
$91$	1.02125	0.107056
$92$	24.4606	2.55020
$93$	0.447226	0.0463752
$94$	−7.09213	−0.731497
$95$	−8.45827	−0.867800
$96$	5.58471	0.569987
$97$	12.0659	1.22511	0.612555	−	0.790428i	$-0.290142\pi$
$97$	12.0659	1.22511	0.612555	+	0.790428i	$0.290142\pi$
$98$	−15.7673	−1.59273
$99$	5.23682	0.526320
$100$	15.7154	1.57154
$101$	−4.95312	−0.492854	−0.246427	−	0.969161i	$-0.579257\pi$
$101$	−4.95312	−0.492854	−0.246427	+	0.969161i	$0.579257\pi$
$102$	2.29130	0.226873
$103$	−5.95784	−0.587043	−0.293522	−	0.955952i	$-0.594827\pi$
$103$	−5.95784	−0.587043	−0.293522	+	0.955952i	$0.594827\pi$
$104$	8.49228	0.832737
$105$	−1.08023	−0.105420
$106$	3.36457	0.326796
$107$	3.45232	0.333748	0.166874	−	0.985978i	$-0.446633\pi$
$107$	3.45232	0.333748	0.166874	+	0.985978i	$0.446633\pi$
$108$	−3.25006	−0.312737
$109$	−11.9979	−1.14919	−0.574594	−	0.818439i	$-0.694840\pi$
$109$	−11.9979	−1.14919	−0.574594	+	0.818439i	$0.694840\pi$
$110$	37.6310	3.58798
$111$	0.229108	0.0217460
$112$	0.0216174	0.00204265
$113$	11.6917	1.09987	0.549933	−	0.835209i	$-0.314653\pi$
$113$	11.6917	1.09987	0.549933	+	0.835209i	$0.314653\pi$
$114$	6.17970	0.578782
$115$	23.6033	2.20102
$116$	−5.76249	−0.535034
$117$	2.96491	0.274106
$118$	24.6676	2.27084
$119$	−0.344445	−0.0315752
$120$	−8.98273	−0.820007
$121$	16.4243	1.49312
$122$	18.3399	1.66042
$123$	7.81931	0.705043
$124$	−1.45351	−0.130529
$125$	−0.516183	−0.0461688
$126$	0.789227	0.0703099
$127$	−9.05863	−0.803823	−0.401912	−	0.915678i	$-0.631654\pi$
$127$	−9.05863	−0.803823	−0.401912	+	0.915678i	$0.631654\pi$
$128$	−18.4382	−1.62973
$129$	6.20506	0.546325
$130$	21.3054	1.86861
$131$	10.0609	0.879026	0.439513	−	0.898236i	$-0.355151\pi$
$131$	10.0609	0.879026	0.439513	+	0.898236i	$0.355151\pi$
$132$	−17.0200	−1.48140
$133$	−0.928978	−0.0805526
$134$	−23.5173	−2.03159
$135$	−3.13615	−0.269916
$136$	−2.86426	−0.245608
$137$	−14.3256	−1.22392	−0.611959	−	0.790889i	$-0.709618\pi$
$137$	−14.3256	−1.22392	−0.611959	+	0.790889i	$0.709618\pi$
$138$	−17.2448	−1.46798
$139$	−5.22574	−0.443242	−0.221621	−	0.975133i	$-0.571135\pi$
$139$	−5.22574	−0.443242	−0.221621	+	0.975133i	$0.571135\pi$
$140$	3.51081	0.296717
$141$	3.09524	0.260666
$142$	−0.680818	−0.0571330
$143$	15.5267	1.29841
$144$	0.0627600	0.00523000
$145$	−5.56052	−0.461776
$146$	−13.0686	−1.08156
$147$	6.88136	0.567565
$148$	−0.744616	−0.0612070
$149$	−10.6431	−0.871916	−0.435958	−	0.899967i	$-0.643590\pi$
$149$	−10.6431	−0.871916	−0.435958	+	0.899967i	$0.643590\pi$
$150$	−11.0794	−0.904627
$151$	10.7718	0.876596	0.438298	−	0.898830i	$-0.355582\pi$
$151$	10.7718	0.876596	0.438298	+	0.898830i	$0.355582\pi$
$152$	−7.72498	−0.626579
$153$	−1.00000	−0.0808452
$154$	4.13304	0.333050
$155$	−1.40257	−0.112657
$156$	−9.63614	−0.771509
$157$	11.5008	0.917861	0.458931	−	0.888472i	$-0.348233\pi$
$157$	11.5008	0.917861	0.458931	+	0.888472i	$0.348233\pi$
$158$	2.29130	0.182286
$159$	−1.46841	−0.116453
$160$	−17.5145	−1.38464
$161$	2.59237	0.204307
$162$	2.29130	0.180022
$163$	−20.0529	−1.57066	−0.785331	−	0.619076i	$-0.787507\pi$
$163$	−20.0529	−1.57066	−0.785331	+	0.619076i	$0.787507\pi$
$164$	−25.4132	−1.98444
$165$	−16.4234	−1.27856
$166$	10.3565	0.803824
$167$	−6.49641	−0.502707	−0.251354	−	0.967895i	$-0.580876\pi$
$167$	−6.49641	−0.502707	−0.251354	+	0.967895i	$0.580876\pi$
$168$	−0.986579	−0.0761162
$169$	−4.20928	−0.323791
$170$	−7.18585	−0.551130
$171$	−2.69703	−0.206247
$172$	−20.1668	−1.53771
$173$	2.03494	0.154713	0.0773567	−	0.997003i	$-0.475352\pi$
$173$	2.03494	0.154713	0.0773567	+	0.997003i	$0.475352\pi$
$174$	4.06257	0.307983
$175$	1.66553	0.125902
$176$	0.328663	0.0247739
$177$	−10.7658	−0.809205
$178$	31.5672	2.36606
$179$	14.0069	1.04692	0.523462	−	0.852049i	$-0.324640\pi$
$179$	14.0069	1.04692	0.523462	+	0.852049i	$0.324640\pi$
$180$	10.1927	0.759716
$181$	6.51210	0.484041	0.242020	−	0.970271i	$-0.422190\pi$
$181$	6.51210	0.484041	0.242020	+	0.970271i	$0.422190\pi$
$182$	2.33999	0.173452
$183$	−8.00416	−0.591684
$184$	21.5570	1.58920
$185$	−0.718517	−0.0528264
$186$	1.02473	0.0751369
$187$	−5.23682	−0.382954
$188$	−10.0597	−0.733680
$189$	−0.344445	−0.0250547
$190$	−19.3804	−1.40600
$191$	0.721682	0.0522191	0.0261095	−	0.999659i	$-0.491688\pi$
$191$	0.721682	0.0522191	0.0261095	+	0.999659i	$0.491688\pi$
$192$	12.9218	0.932549
$193$	−22.3243	−1.60694	−0.803470	−	0.595345i	$-0.797015\pi$
$193$	−22.3243	−1.60694	−0.803470	+	0.595345i	$0.797015\pi$
$194$	27.6467	1.98492
$195$	−9.29840	−0.665873
$196$	−22.3648	−1.59749
$197$	9.53728	0.679503	0.339752	−	0.940515i	$-0.389657\pi$
$197$	9.53728	0.679503	0.339752	+	0.940515i	$0.389657\pi$
$198$	11.9991	0.852741
$199$	−9.31052	−0.660006	−0.330003	−	0.943980i	$-0.607050\pi$
$199$	−9.31052	−0.660006	−0.330003	+	0.943980i	$0.607050\pi$
$200$	13.8499	0.979333
$201$	10.2637	0.723949
$202$	−11.3491	−0.798519
$203$	−0.610715	−0.0428638
$204$	3.25006	0.227550
$205$	−24.5225	−1.71272
$206$	−13.6512	−0.951124
$207$	7.52621	0.523108
$208$	0.186078	0.0129022
$209$	−14.1239	−0.976967
$210$	−2.47513	−0.170800
$211$	1.67678	0.115434	0.0577170	−	0.998333i	$-0.481618\pi$
$211$	1.67678	0.115434	0.0577170	+	0.998333i	$0.481618\pi$
$212$	4.77242	0.327771
$213$	0.297132	0.0203591
$214$	7.91030	0.540737
$215$	−19.4600	−1.32716
$216$	−2.86426	−0.194888
$217$	−0.154045	−0.0104573
$218$	−27.4907	−1.86191
$219$	5.70357	0.385411
$220$	53.3771	3.59868
$221$	−2.96491	−0.199442
$222$	0.524956	0.0352328
$223$	6.38693	0.427700	0.213850	−	0.976866i	$-0.431400\pi$
$223$	6.38693	0.427700	0.213850	+	0.976866i	$0.431400\pi$
$224$	−1.92363	−0.128528
$225$	4.83541	0.322361
$226$	26.7893	1.78200
$227$	4.76689	0.316390	0.158195	−	0.987408i	$-0.449433\pi$
$227$	4.76689	0.316390	0.158195	+	0.987408i	$0.449433\pi$
$228$	8.76550	0.580509
$229$	12.2425	0.809010	0.404505	−	0.914536i	$-0.367444\pi$
$229$	12.2425	0.809010	0.404505	+	0.914536i	$0.367444\pi$
$230$	54.0822	3.56608
$231$	−1.80380	−0.118681
$232$	−5.07845	−0.333417
$233$	9.72668	0.637216	0.318608	−	0.947887i	$-0.396785\pi$
$233$	9.72668	0.637216	0.318608	+	0.947887i	$0.396785\pi$
$234$	6.79351	0.444106
$235$	−9.70713	−0.633223
$236$	34.9894	2.27761
$237$	−1.00000	−0.0649570
$238$	−0.789227	−0.0511580
$239$	29.0625	1.87990	0.939948	−	0.341318i	$-0.110873\pi$
$239$	29.0625	1.87990	0.939948	+	0.341318i	$0.110873\pi$
$240$	−0.196824	−0.0127050
$241$	−7.78050	−0.501186	−0.250593	−	0.968093i	$-0.580626\pi$
$241$	−7.78050	−0.501186	−0.250593	+	0.968093i	$0.580626\pi$
$242$	37.6330	2.41914
$243$	−1.00000	−0.0641500
$244$	26.0140	1.66537
$245$	−21.5809	−1.37876
$246$	17.9164	1.14231
$247$	−7.99646	−0.508802
$248$	−1.28097	−0.0813418
$249$	−4.51994	−0.286440
$250$	−1.18273	−0.0748024
$251$	−7.38981	−0.466441	−0.233220	−	0.972424i	$-0.574926\pi$
$251$	−7.38981	−0.466441	−0.233220	+	0.972424i	$0.574926\pi$
$252$	1.11947	0.0705197
$253$	39.4134	2.47790
$254$	−20.7560	−1.30235
$255$	3.13615	0.196393
$256$	−16.4040	−1.02525
$257$	−0.684745	−0.0427132	−0.0213566	−	0.999772i	$-0.506799\pi$
$257$	−0.684745	−0.0427132	−0.0213566	+	0.999772i	$0.506799\pi$
$258$	14.2177	0.885153
$259$	−0.0789152	−0.00490355
$260$	30.2204	1.87419
$261$	−1.77304	−0.109749
$262$	23.0526	1.42419
$263$	3.21135	0.198020	0.0990102	−	0.995086i	$-0.468432\pi$
$263$	3.21135	0.198020	0.0990102	+	0.995086i	$0.468432\pi$
$264$	−14.9996	−0.923162
$265$	4.60515	0.282892
$266$	−2.12857	−0.130511
$267$	−13.7770	−0.843137
$268$	−33.3578	−2.03765
$269$	2.49091	0.151873	0.0759366	−	0.997113i	$-0.475805\pi$
$269$	2.49091	0.151873	0.0759366	+	0.997113i	$0.475805\pi$
$270$	−7.18585	−0.437317
$271$	9.98520	0.606558	0.303279	−	0.952902i	$-0.401919\pi$
$271$	9.98520	0.606558	0.303279	+	0.952902i	$0.401919\pi$
$272$	−0.0627600	−0.00380538
$273$	−1.02125	−0.0618089
$274$	−32.8243	−1.98299
$275$	25.3222	1.52698
$276$	−24.4606	−1.47236
$277$	−5.19393	−0.312073	−0.156036	−	0.987751i	$-0.549872\pi$
$277$	−5.19393	−0.312073	−0.156036	+	0.987751i	$0.549872\pi$
$278$	−11.9737	−0.718138
$279$	−0.447226	−0.0267747
$280$	3.09406	0.184905
$281$	−22.0088	−1.31293	−0.656467	−	0.754355i	$-0.727950\pi$
$281$	−22.0088	−1.31293	−0.656467	+	0.754355i	$0.727950\pi$
$282$	7.09213	0.422330
$283$	−0.862266	−0.0512564	−0.0256282	−	0.999672i	$-0.508159\pi$
$283$	−0.862266	−0.0512564	−0.0256282	+	0.999672i	$0.508159\pi$
$284$	−0.965695	−0.0573035
$285$	8.45827	0.501025
$286$	35.5764	2.10368
$287$	−2.69332	−0.158982
$288$	−5.58471	−0.329082
$289$	1.00000	0.0588235
$290$	−12.7408	−0.748166
$291$	−12.0659	−0.707317
$292$	−18.5369	−1.08479
$293$	6.07836	0.355102	0.177551	−	0.984112i	$-0.443183\pi$
$293$	6.07836	0.355102	0.177551	+	0.984112i	$0.443183\pi$
$294$	15.7673	0.919565
$295$	33.7630	1.96576
$296$	−0.656226	−0.0381423
$297$	−5.23682	−0.303871
$298$	−24.3865	−1.41267
$299$	22.3146	1.29049
$300$	−15.7154	−0.907327
$301$	−2.13730	−0.123192
$302$	24.6814	1.42025
$303$	4.95312	0.284549
$304$	−0.169265	−0.00970803
$305$	25.1022	1.43735
$306$	−2.29130	−0.130985
$307$	−0.782039	−0.0446333	−0.0223167	−	0.999751i	$-0.507104\pi$
$307$	−0.782039	−0.0446333	−0.0223167	+	0.999751i	$0.507104\pi$
$308$	5.86245	0.334044
$309$	5.95784	0.338929
$310$	−3.21370	−0.182526
$311$	0.327480	0.0185697	0.00928485	−	0.999957i	$-0.497044\pi$
$311$	0.327480	0.0185697	0.00928485	+	0.999957i	$0.497044\pi$
$312$	−8.49228	−0.480781
$313$	−28.4507	−1.60813	−0.804063	−	0.594544i	$-0.797333\pi$
$313$	−28.4507	−1.60813	−0.804063	+	0.594544i	$0.797333\pi$
$314$	26.3517	1.48711
$315$	1.08023	0.0608640
$316$	3.25006	0.182830
$317$	−16.2326	−0.911713	−0.455857	−	0.890053i	$-0.650667\pi$
$317$	−16.2326	−0.911713	−0.455857	+	0.890053i	$0.650667\pi$
$318$	−3.36457	−0.188676
$319$	−9.28511	−0.519866
$320$	−40.5246	−2.26539
$321$	−3.45232	−0.192690
$322$	5.93989	0.331017
$323$	2.69703	0.150067
$324$	3.25006	0.180559
$325$	14.3366	0.795250
$326$	−45.9471	−2.54478
$327$	11.9979	0.663484
$328$	−22.3965	−1.23664
$329$	−1.06614	−0.0587782
$330$	−37.6310	−2.07152
$331$	−8.99597	−0.494463	−0.247232	−	0.968956i	$-0.579521\pi$
$331$	−8.99597	−0.494463	−0.247232	+	0.968956i	$0.579521\pi$
$332$	14.6901	0.806223
$333$	−0.229108	−0.0125551
$334$	−14.8852	−0.814483
$335$	−32.1886	−1.75865
$336$	−0.0216174	−0.00117932
$337$	9.23104	0.502847	0.251423	−	0.967877i	$-0.419101\pi$
$337$	9.23104	0.502847	0.251423	+	0.967877i	$0.419101\pi$
$338$	−9.64472	−0.524604
$339$	−11.6917	−0.635008
$340$	−10.1927	−0.552774
$341$	−2.34205	−0.126829
$342$	−6.17970	−0.334160
$343$	−4.78136	−0.258169
$344$	−17.7729	−0.958251
$345$	−23.6033	−1.27076
$346$	4.66265	0.250666
$347$	30.9083	1.65925	0.829624	−	0.558323i	$-0.188555\pi$
$347$	30.9083	1.65925	0.829624	+	0.558323i	$0.188555\pi$
$348$	5.76249	0.308902
$349$	10.7378	0.574783	0.287391	−	0.957813i	$-0.407212\pi$
$349$	10.7378	0.574783	0.287391	+	0.957813i	$0.407212\pi$
$350$	3.81623	0.203986
$351$	−2.96491	−0.158255
$352$	−29.2462	−1.55883
$353$	−19.4990	−1.03783	−0.518915	−	0.854826i	$-0.673664\pi$
$353$	−19.4990	−1.03783	−0.518915	+	0.854826i	$0.673664\pi$
$354$	−24.6676	−1.31107
$355$	−0.931848	−0.0494574
$356$	44.7759	2.37312
$357$	0.344445	0.0182300
$358$	32.0940	1.69622
$359$	20.4210	1.07778	0.538890	−	0.842376i	$-0.318844\pi$
$359$	20.4210	1.07778	0.538890	+	0.842376i	$0.318844\pi$
$360$	8.98273	0.473431
$361$	−11.7260	−0.617160
$362$	14.9212	0.784240
$363$	−16.4243	−0.862053
$364$	3.31912	0.173969
$365$	−17.8872	−0.936259
$366$	−18.3399	−0.958643
$367$	15.9057	0.830269	0.415135	−	0.909760i	$-0.363734\pi$
$367$	15.9057	0.830269	0.415135	+	0.909760i	$0.363734\pi$
$368$	0.472345	0.0246227
$369$	−7.81931	−0.407057
$370$	−1.64634	−0.0855891
$371$	0.505787	0.0262592
$372$	1.45351	0.0753611
$373$	−22.5079	−1.16541	−0.582707	−	0.812682i	$-0.698006\pi$
$373$	−22.5079	−1.16541	−0.582707	+	0.812682i	$0.698006\pi$
$374$	−11.9991	−0.620460
$375$	0.516183	0.0266556
$376$	−8.86557	−0.457207
$377$	−5.25692	−0.270745
$378$	−0.789227	−0.0405935
$379$	−8.36222	−0.429538	−0.214769	−	0.976665i	$-0.568900\pi$
$379$	−8.36222	−0.429538	−0.214769	+	0.976665i	$0.568900\pi$
$380$	−27.4899	−1.41020
$381$	9.05863	0.464088
$382$	1.65359	0.0846051
$383$	34.8274	1.77960	0.889798	−	0.456355i	$-0.150845\pi$
$383$	34.8274	1.77960	0.889798	+	0.456355i	$0.150845\pi$
$384$	18.4382	0.940923
$385$	5.65697	0.288306
$386$	−51.1517	−2.60355
$387$	−6.20506	−0.315421
$388$	39.2150	1.99084
$389$	−13.8860	−0.704049	−0.352024	−	0.935991i	$-0.614507\pi$
$389$	−13.8860	−0.704049	−0.352024	+	0.935991i	$0.614507\pi$
$390$	−21.3054	−1.07884
$391$	−7.52621	−0.380617
$392$	−19.7100	−0.995504
$393$	−10.0609	−0.507506
$394$	21.8528	1.10093
$395$	3.13615	0.157797
$396$	17.0200	0.855286
$397$	−32.9267	−1.65255	−0.826273	−	0.563270i	$-0.809543\pi$
$397$	−32.9267	−1.65255	−0.826273	+	0.563270i	$0.809543\pi$
$398$	−21.3332	−1.06934
$399$	0.928978	0.0465071
$400$	0.303470	0.0151735
$401$	−11.6823	−0.583384	−0.291692	−	0.956512i	$-0.594218\pi$
$401$	−11.6823	−0.583384	−0.291692	+	0.956512i	$0.594218\pi$
$402$	23.5173	1.17294
$403$	−1.32599	−0.0660522
$404$	−16.0979	−0.800902
$405$	3.13615	0.155836
$406$	−1.39933	−0.0694477
$407$	−1.19980	−0.0594719
$408$	2.86426	0.141802
$409$	−12.4742	−0.616812	−0.308406	−	0.951255i	$-0.599796\pi$
$409$	−12.4742	−0.616812	−0.308406	+	0.951255i	$0.599796\pi$
$410$	−56.1884	−2.77495
$411$	14.3256	0.706630
$412$	−19.3633	−0.953962
$413$	3.70821	0.182469
$414$	17.2448	0.847536
$415$	14.1752	0.695833
$416$	−16.5582	−0.811833
$417$	5.22574	0.255906
$418$	−32.3620	−1.58288
$419$	−39.0914	−1.90974	−0.954871	−	0.297021i	$-0.904007\pi$
$419$	−39.0914	−1.90974	−0.954871	+	0.297021i	$0.904007\pi$
$420$	−3.51081	−0.171310
$421$	−28.2451	−1.37658	−0.688292	−	0.725434i	$-0.741639\pi$
$421$	−28.2451	−1.37658	−0.688292	+	0.725434i	$0.741639\pi$
$422$	3.84200	0.187026
$423$	−3.09524	−0.150496
$424$	4.20591	0.204257
$425$	−4.83541	−0.234552
$426$	0.680818	0.0329857
$427$	2.75699	0.133420
$428$	11.2202	0.542350
$429$	−15.5267	−0.749638
$430$	−44.5887	−2.15026
$431$	4.76828	0.229680	0.114840	−	0.993384i	$-0.463364\pi$
$431$	4.76828	0.229680	0.114840	+	0.993384i	$0.463364\pi$
$432$	−0.0627600	−0.00301954
$433$	22.5593	1.08413	0.542066	−	0.840336i	$-0.317642\pi$
$433$	22.5593	1.08413	0.542066	+	0.840336i	$0.317642\pi$
$434$	−0.352963	−0.0169428
$435$	5.56052	0.266606
$436$	−38.9938	−1.86746
$437$	−20.2984	−0.971004
$438$	13.0686	0.624441
$439$	−6.05932	−0.289196	−0.144598	−	0.989491i	$-0.546189\pi$
$439$	−6.05932	−0.289196	−0.144598	+	0.989491i	$0.546189\pi$
$440$	47.0410	2.24259
$441$	−6.88136	−0.327684
$442$	−6.79351	−0.323134
$443$	−29.6291	−1.40772	−0.703861	−	0.710337i	$-0.748542\pi$
$443$	−29.6291	−1.40772	−0.703861	+	0.710337i	$0.748542\pi$
$444$	0.744616	0.0353379
$445$	43.2066	2.04819
$446$	14.6344	0.692958
$447$	10.6431	0.503401
$448$	−4.45084	−0.210282
$449$	−15.3166	−0.722837	−0.361419	−	0.932404i	$-0.617707\pi$
$449$	−15.3166	−0.722837	−0.361419	+	0.932404i	$0.617707\pi$
$450$	11.0794	0.522287
$451$	−40.9483	−1.92818
$452$	37.9988	1.78731
$453$	−10.7718	−0.506103
$454$	10.9224	0.512613
$455$	3.20279	0.150149
$456$	7.72498	0.361755
$457$	−22.1995	−1.03845	−0.519223	−	0.854639i	$-0.673779\pi$
$457$	−22.1995	−1.03845	−0.519223	+	0.854639i	$0.673779\pi$
$458$	28.0513	1.31075
$459$	1.00000	0.0466760
$460$	76.7121	3.57672
$461$	−18.3345	−0.853922	−0.426961	−	0.904270i	$-0.640416\pi$
$461$	−18.3345	−0.853922	−0.426961	+	0.904270i	$0.640416\pi$
$462$	−4.13304	−0.192286
$463$	26.2093	1.21805	0.609026	−	0.793151i	$-0.291561\pi$
$463$	26.2093	1.21805	0.609026	+	0.793151i	$0.291561\pi$
$464$	−0.111276	−0.00516586
$465$	1.40257	0.0650425
$466$	22.2867	1.03241
$467$	6.18319	0.286124	0.143062	−	0.989714i	$-0.454305\pi$
$467$	6.18319	0.286124	0.143062	+	0.989714i	$0.454305\pi$
$468$	9.63614	0.445431
$469$	−3.53529	−0.163245
$470$	−22.2420	−1.02594
$471$	−11.5008	−0.529928
$472$	30.8359	1.41934
$473$	−32.4948	−1.49411
$474$	−2.29130	−0.105243
$475$	−13.0412	−0.598373
$476$	−1.11947	−0.0513106
$477$	1.46841	0.0672340
$478$	66.5909	3.04580
$479$	−19.5375	−0.892691	−0.446345	−	0.894861i	$-0.647275\pi$
$479$	−19.5375	−0.892691	−0.446345	+	0.894861i	$0.647275\pi$
$480$	17.5145	0.799423
$481$	−0.679287	−0.0309728
$482$	−17.8275	−0.812018
$483$	−2.59237	−0.117957
$484$	53.3800	2.42636
$485$	37.8405	1.71825
$486$	−2.29130	−0.103935
$487$	−24.8885	−1.12781	−0.563903	−	0.825841i	$-0.690701\pi$
$487$	−24.8885	−1.12781	−0.563903	+	0.825841i	$0.690701\pi$
$488$	22.9260	1.03781
$489$	20.0529	0.906822
$490$	−49.4484	−2.23385
$491$	37.6065	1.69716	0.848579	−	0.529069i	$-0.177459\pi$
$491$	37.6065	1.69716	0.848579	+	0.529069i	$0.177459\pi$
$492$	25.4132	1.14572
$493$	1.77304	0.0798538
$494$	−18.3223	−0.824359
$495$	16.4234	0.738179
$496$	−0.0280679	−0.00126029
$497$	−0.102346	−0.00459082
$498$	−10.3565	−0.464088
$499$	−38.6811	−1.73160	−0.865802	−	0.500387i	$-0.833191\pi$
$499$	−38.6811	−1.73160	−0.865802	+	0.500387i	$0.833191\pi$
$500$	−1.67762	−0.0750256
$501$	6.49641	0.290238
$502$	−16.9323	−0.755725
$503$	41.1375	1.83423	0.917115	−	0.398623i	$-0.130512\pi$
$503$	41.1375	1.83423	0.917115	+	0.398623i	$0.130512\pi$
$504$	0.986579	0.0439457
$505$	−15.5337	−0.691241
$506$	90.3080	4.01468
$507$	4.20928	0.186941
$508$	−29.4411	−1.30624
$509$	8.02946	0.355900	0.177950	−	0.984040i	$-0.443054\pi$
$509$	8.02946	0.355900	0.177950	+	0.984040i	$0.443054\pi$
$510$	7.18585	0.318195
$511$	−1.96456	−0.0869072
$512$	−0.710018	−0.0313787
$513$	2.69703	0.119077
$514$	−1.56896	−0.0692037
$515$	−18.6846	−0.823344
$516$	20.1668	0.887794
$517$	−16.2092	−0.712881
$518$	−0.180819	−0.00794471
$519$	−2.03494	−0.0893238
$520$	26.6330	1.16794
$521$	−44.5755	−1.95289	−0.976445	−	0.215767i	$-0.930775\pi$
$521$	−44.5755	−1.95289	−0.976445	+	0.215767i	$0.930775\pi$
$522$	−4.06257	−0.177814
$523$	28.3536	1.23982	0.619908	−	0.784674i	$-0.287170\pi$
$523$	28.3536	1.23982	0.619908	+	0.784674i	$0.287170\pi$
$524$	32.6986	1.42844
$525$	−1.66553	−0.0726898
$526$	7.35817	0.320832
$527$	0.447226	0.0194815
$528$	−0.328663	−0.0143032
$529$	33.6438	1.46278
$530$	10.5518	0.458341
$531$	10.7658	0.467195
$532$	−3.01923	−0.130900
$533$	−23.1836	−1.00419
$534$	−31.5672	−1.36605
$535$	10.8270	0.468091
$536$	−29.3980	−1.26980
$537$	−14.0069	−0.604442
$538$	5.70741	0.246064
$539$	−36.0364	−1.55220
$540$	−10.1927	−0.438622
$541$	1.40364	0.0603473	0.0301736	−	0.999545i	$-0.490394\pi$
$541$	1.40364	0.0603473	0.0301736	+	0.999545i	$0.490394\pi$
$542$	22.8791	0.982741
$543$	−6.51210	−0.279461
$544$	5.58471	0.239443
$545$	−37.6271	−1.61177
$546$	−2.33999	−0.100142
$547$	28.9638	1.23840	0.619201	−	0.785233i	$-0.287457\pi$
$547$	28.9638	1.23840	0.619201	+	0.785233i	$0.287457\pi$
$548$	−46.5590	−1.98890
$549$	8.00416	0.341609
$550$	58.0207	2.47401
$551$	4.78194	0.203718
$552$	−21.5570	−0.917527
$553$	0.344445	0.0146473
$554$	−11.9009	−0.505619
$555$	0.718517	0.0304994
$556$	−16.9840	−0.720281
$557$	−37.5733	−1.59203	−0.796015	−	0.605277i	$-0.793062\pi$
$557$	−37.5733	−1.59203	−0.796015	+	0.605277i	$0.793062\pi$
$558$	−1.02473	−0.0433803
$559$	−18.3975	−0.778131
$560$	0.0677952	0.00286487
$561$	5.23682	0.221099
$562$	−50.4287	−2.12721
$563$	4.77987	0.201447	0.100724	−	0.994914i	$-0.467884\pi$
$563$	4.77987	0.201447	0.100724	+	0.994914i	$0.467884\pi$
$564$	10.0597	0.423590
$565$	36.6670	1.54259
$566$	−1.97571	−0.0830453
$567$	0.344445	0.0144653
$568$	−0.851062	−0.0357098
$569$	32.1241	1.34671	0.673355	−	0.739319i	$-0.264852\pi$
$569$	32.1241	1.34671	0.673355	+	0.739319i	$0.264852\pi$
$570$	19.3804	0.811757
$571$	−5.48371	−0.229486	−0.114743	−	0.993395i	$-0.536604\pi$
$571$	−5.48371	−0.229486	−0.114743	+	0.993395i	$0.536604\pi$
$572$	50.4628	2.10995
$573$	−0.721682	−0.0301487
$574$	−6.17121	−0.257581
$575$	36.3923	1.51766
$576$	−12.9218	−0.538407
$577$	7.90488	0.329085	0.164542	−	0.986370i	$-0.447385\pi$
$577$	7.90488	0.329085	0.164542	+	0.986370i	$0.447385\pi$
$578$	2.29130	0.0953055
$579$	22.3243	0.927767
$580$	−18.0720	−0.750399
$581$	1.55687	0.0645899
$582$	−27.6467	−1.14599
$583$	7.68981	0.318480
$584$	−16.3365	−0.676008
$585$	9.29840	0.384442
$586$	13.9274	0.575334
$587$	34.5390	1.42558	0.712789	−	0.701379i	$-0.247432\pi$
$587$	34.5390	1.42558	0.712789	+	0.701379i	$0.247432\pi$
$588$	22.3648	0.922309
$589$	1.20618	0.0496999
$590$	77.3612	3.18491
$591$	−9.53728	−0.392311
$592$	−0.0143788	−0.000590966 0
$593$	−17.7397	−0.728483	−0.364242	−	0.931304i	$-0.618672\pi$
$593$	−17.7397	−0.728483	−0.364242	+	0.931304i	$0.618672\pi$
$594$	−11.9991	−0.492330
$595$	−1.08023	−0.0442851
$596$	−34.5907	−1.41689
$597$	9.31052	0.381054
$598$	51.1294	2.09084
$599$	−21.3039	−0.870454	−0.435227	−	0.900321i	$-0.643332\pi$
$599$	−21.3039	−0.870454	−0.435227	+	0.900321i	$0.643332\pi$
$600$	−13.8499	−0.565418
$601$	8.56076	0.349201	0.174600	−	0.984639i	$-0.444137\pi$
$601$	8.56076	0.349201	0.174600	+	0.984639i	$0.444137\pi$
$602$	−4.89720	−0.199595
$603$	−10.2637	−0.417972
$604$	35.0089	1.42449
$605$	51.5090	2.09414
$606$	11.3491	0.461025
$607$	30.4224	1.23481	0.617404	−	0.786647i	$-0.288185\pi$
$607$	30.4224	1.23481	0.617404	+	0.786647i	$0.288185\pi$
$608$	15.0621	0.610850
$609$	0.610715	0.0247474
$610$	57.5167	2.32878
$611$	−9.17713	−0.371267
$612$	−3.25006	−0.131376
$613$	10.1291	0.409109	0.204554	−	0.978855i	$-0.434425\pi$
$613$	10.1291	0.409109	0.204554	+	0.978855i	$0.434425\pi$
$614$	−1.79189	−0.0723146
$615$	24.5225	0.988842
$616$	5.16654	0.208166
$617$	−24.6201	−0.991169	−0.495585	−	0.868560i	$-0.665046\pi$
$617$	−24.6201	−0.991169	−0.495585	+	0.868560i	$0.665046\pi$
$618$	13.6512	0.549131
$619$	−48.7908	−1.96107	−0.980534	−	0.196349i	$-0.937092\pi$
$619$	−48.7908	−1.96107	−0.980534	+	0.196349i	$0.937092\pi$
$620$	−4.55842	−0.183071
$621$	−7.52621	−0.302016
$622$	0.750356	0.0300865
$623$	4.74541	0.190121
$624$	−0.186078	−0.00744908
$625$	−25.7959	−1.03183
$626$	−65.1890	−2.60548
$627$	14.1239	0.564052
$628$	37.3782	1.49155
$629$	0.229108	0.00913515
$630$	2.47513	0.0986116
$631$	−2.35328	−0.0936826	−0.0468413	−	0.998902i	$-0.514916\pi$
$631$	−2.35328	−0.0936826	−0.0468413	+	0.998902i	$0.514916\pi$
$632$	2.86426	0.113934
$633$	−1.67678	−0.0666459
$634$	−37.1937	−1.47715
$635$	−28.4092	−1.12738
$636$	−4.77242	−0.189239
$637$	−20.4026	−0.808382
$638$	−21.2750	−0.842284
$639$	−0.297132	−0.0117543
$640$	−57.8250	−2.28573
$641$	13.7190	0.541868	0.270934	−	0.962598i	$-0.412668\pi$
$641$	13.7190	0.541868	0.270934	+	0.962598i	$0.412668\pi$
$642$	−7.91030	−0.312195
$643$	−28.9909	−1.14329	−0.571644	−	0.820502i	$-0.693694\pi$
$643$	−28.9909	−1.14329	−0.571644	+	0.820502i	$0.693694\pi$
$644$	8.42534	0.332005
$645$	19.4600	0.766236
$646$	6.17970	0.243137
$647$	−36.3379	−1.42859	−0.714296	−	0.699844i	$-0.753253\pi$
$647$	−36.3379	−1.42859	−0.714296	+	0.699844i	$0.753253\pi$
$648$	2.86426	0.112519
$649$	56.3784	2.21305
$650$	32.8494	1.28846
$651$	0.154045	0.00603750
$652$	−65.1730	−2.55237
$653$	−7.48129	−0.292766	−0.146383	−	0.989228i	$-0.546763\pi$
$653$	−7.48129	−0.292766	−0.146383	+	0.989228i	$0.546763\pi$
$654$	27.4907	1.07497
$655$	31.5525	1.23286
$656$	−0.490739	−0.0191602
$657$	−5.70357	−0.222517
$658$	−2.44285	−0.0952322
$659$	−28.1202	−1.09541	−0.547703	−	0.836673i	$-0.684498\pi$
$659$	−28.1202	−1.09541	−0.547703	+	0.836673i	$0.684498\pi$
$660$	−53.3771	−2.07770
$661$	−0.243966	−0.00948917	−0.00474458	−	0.999989i	$-0.501510\pi$
$661$	−0.243966	−0.00948917	−0.00474458	+	0.999989i	$0.501510\pi$
$662$	−20.6125	−0.801126
$663$	2.96491	0.115148
$664$	12.9463	0.502413
$665$	−2.91341	−0.112977
$666$	−0.524956	−0.0203416
$667$	−13.3443	−0.516693
$668$	−21.1137	−0.816914
$669$	−6.38693	−0.246933
$670$	−73.7537	−2.84936
$671$	41.9164	1.61816
$672$	1.92363	0.0742055
$673$	17.4992	0.674543	0.337271	−	0.941407i	$-0.390496\pi$
$673$	17.4992	0.674543	0.337271	+	0.941407i	$0.390496\pi$
$674$	21.1511	0.814710
$675$	−4.83541	−0.186115
$676$	−13.6804	−0.526169
$677$	−7.75219	−0.297941	−0.148970	−	0.988842i	$-0.547596\pi$
$677$	−7.75219	−0.297941	−0.148970	+	0.988842i	$0.547596\pi$
$678$	−26.7893	−1.02884
$679$	4.15605	0.159495
$680$	−8.98273	−0.344472
$681$	−4.76689	−0.182668
$682$	−5.36633	−0.205487
$683$	32.5312	1.24477	0.622386	−	0.782711i	$-0.286164\pi$
$683$	32.5312	1.24477	0.622386	+	0.782711i	$0.286164\pi$
$684$	−8.76550	−0.335157
$685$	−44.9272	−1.71658
$686$	−10.9555	−0.418285
$687$	−12.2425	−0.467082
$688$	−0.389429	−0.0148469
$689$	4.35372	0.165863
$690$	−54.0822	−2.05888
$691$	−7.37506	−0.280561	−0.140280	−	0.990112i	$-0.544800\pi$
$691$	−7.37506	−0.280561	−0.140280	+	0.990112i	$0.544800\pi$
$692$	6.61366	0.251414
$693$	1.80380	0.0685206
$694$	70.8203	2.68830
$695$	−16.3887	−0.621658
$696$	5.07845	0.192498
$697$	7.81931	0.296177
$698$	24.6036	0.931260
$699$	−9.72668	−0.367897
$700$	5.41308	0.204595
$701$	−13.7660	−0.519933	−0.259967	−	0.965618i	$-0.583712\pi$
$701$	−13.7660	−0.519933	−0.259967	+	0.965618i	$0.583712\pi$
$702$	−6.79351	−0.256405
$703$	0.617912	0.0233050
$704$	−67.6691	−2.55037
$705$	9.70713	0.365592
$706$	−44.6782	−1.68148
$707$	−1.70608	−0.0641636
$708$	−34.9894	−1.31498
$709$	−6.62389	−0.248766	−0.124383	−	0.992234i	$-0.539695\pi$
$709$	−6.62389	−0.248766	−0.124383	+	0.992234i	$0.539695\pi$
$710$	−2.13514	−0.0801305
$711$	1.00000	0.0375029
$712$	39.4608	1.47886
$713$	−3.36592	−0.126055
$714$	0.789227	0.0295361
$715$	48.6941	1.82106
$716$	45.5232	1.70128
$717$	−29.0625	−1.08536
$718$	46.7907	1.74621
$719$	−44.7892	−1.67036	−0.835178	−	0.549979i	$-0.814636\pi$
$719$	−44.7892	−1.67036	−0.835178	+	0.549979i	$0.814636\pi$
$720$	0.196824	0.00733521
$721$	−2.05215	−0.0764259
$722$	−26.8679	−0.999919
$723$	7.78050	0.289360
$724$	21.1647	0.786580
$725$	−8.57338	−0.318407
$726$	−37.6330	−1.39669
$727$	32.6613	1.21134	0.605670	−	0.795716i	$-0.292905\pi$
$727$	32.6613	1.21134	0.605670	+	0.795716i	$0.292905\pi$
$728$	2.92512	0.108412
$729$	1.00000	0.0370370
$730$	−40.9850	−1.51692
$731$	6.20506	0.229503
$732$	−26.0140	−0.961504
$733$	17.4312	0.643835	0.321918	−	0.946768i	$-0.395673\pi$
$733$	17.4312	0.643835	0.321918	+	0.946768i	$0.395673\pi$
$734$	36.4447	1.34520
$735$	21.5809	0.796025
$736$	−42.0317	−1.54931
$737$	−53.7494	−1.97988
$738$	−17.9164	−0.659511
$739$	−16.9260	−0.622632	−0.311316	−	0.950306i	$-0.600770\pi$
$739$	−16.9260	−0.622632	−0.311316	+	0.950306i	$0.600770\pi$
$740$	−2.33522	−0.0858445
$741$	7.99646	0.293757
$742$	1.15891	0.0425449
$743$	36.1803	1.32733	0.663663	−	0.748032i	$-0.269001\pi$
$743$	36.1803	1.32733	0.663663	+	0.748032i	$0.269001\pi$
$744$	1.28097	0.0469627
$745$	−33.3783	−1.22289
$746$	−51.5723	−1.88820
$747$	4.51994	0.165376
$748$	−17.0200	−0.622312
$749$	1.18913	0.0434500
$750$	1.18273	0.0431872
$751$	31.0542	1.13318	0.566591	−	0.823999i	$-0.308262\pi$
$751$	31.0542	1.13318	0.566591	+	0.823999i	$0.308262\pi$
$752$	−0.194257	−0.00708383
$753$	7.38981	0.269300
$754$	−12.0452	−0.438660
$755$	33.7819	1.22945
$756$	−1.11947	−0.0407146
$757$	23.0176	0.836591	0.418295	−	0.908311i	$-0.362628\pi$
$757$	23.0176	0.836591	0.418295	+	0.908311i	$0.362628\pi$
$758$	−19.1604	−0.695936
$759$	−39.4134	−1.43062
$760$	−24.2267	−0.878794
$761$	14.6819	0.532218	0.266109	−	0.963943i	$-0.414262\pi$
$761$	14.6819	0.532218	0.266109	+	0.963943i	$0.414262\pi$
$762$	20.7560	0.751912
$763$	−4.13261	−0.149610
$764$	2.34551	0.0848575
$765$	−3.13615	−0.113388
$766$	79.8000	2.88329
$767$	31.9196	1.15255
$768$	16.4040	0.591929
$769$	23.9057	0.862061	0.431030	−	0.902337i	$-0.358150\pi$
$769$	23.9057	0.862061	0.431030	+	0.902337i	$0.358150\pi$
$770$	12.9618	0.467112
$771$	0.684745	0.0246605
$772$	−72.5554	−2.61132
$773$	17.3373	0.623579	0.311789	−	0.950151i	$-0.399072\pi$
$773$	17.3373	0.623579	0.311789	+	0.950151i	$0.399072\pi$
$774$	−14.2177	−0.511043
$775$	−2.16252	−0.0776801
$776$	34.5599	1.24063
$777$	0.0789152	0.00283107
$778$	−31.8170	−1.14070
$779$	21.0889	0.755588
$780$	−30.2204	−1.08206
$781$	−1.55603	−0.0556790
$782$	−17.2448	−0.616673
$783$	1.77304	0.0633633
$784$	−0.431874	−0.0154241
$785$	36.0681	1.28733
$786$	−23.0526	−0.822258
$787$	1.25459	0.0447212	0.0223606	−	0.999750i	$-0.492882\pi$
$787$	1.25459	0.0447212	0.0223606	+	0.999750i	$0.492882\pi$
$788$	30.9967	1.10421
$789$	−3.21135	−0.114327
$790$	7.18585	0.255661
$791$	4.02716	0.143189
$792$	14.9996	0.532988
$793$	23.7316	0.842735
$794$	−75.4450	−2.67744
$795$	−4.60515	−0.163328
$796$	−30.2597	−1.07253
$797$	−22.9704	−0.813652	−0.406826	−	0.913506i	$-0.633365\pi$
$797$	−22.9704	−0.813652	−0.406826	+	0.913506i	$0.633365\pi$
$798$	2.12857	0.0753505
$799$	3.09524	0.109502
$800$	−27.0044	−0.954749
$801$	13.7770	0.486785
$802$	−26.7676	−0.945196
$803$	−29.8686	−1.05404
$804$	33.3578	1.17644
$805$	8.13004	0.286546
$806$	−3.03824	−0.107017
$807$	−2.49091	−0.0876840
$808$	−14.1870	−0.499097
$809$	12.3886	0.435561	0.217781	−	0.975998i	$-0.430118\pi$
$809$	12.3886	0.435561	0.217781	+	0.975998i	$0.430118\pi$
$810$	7.18585	0.252485
$811$	−1.52266	−0.0534677	−0.0267338	−	0.999643i	$-0.508511\pi$
$811$	−1.52266	−0.0534677	−0.0267338	+	0.999643i	$0.508511\pi$
$812$	−1.98486	−0.0696549
$813$	−9.98520	−0.350196
$814$	−2.74910	−0.0963560
$815$	−62.8887	−2.20289
$816$	0.0627600	0.00219704
$817$	16.7352	0.585491
$818$	−28.5822	−0.999355
$819$	1.02125	0.0356854
$820$	−79.6995	−2.78323
$821$	37.1334	1.29596	0.647982	−	0.761656i	$-0.275613\pi$
$821$	37.1334	1.29596	0.647982	+	0.761656i	$0.275613\pi$
$822$	32.8243	1.14488
$823$	7.39591	0.257805	0.128903	−	0.991657i	$-0.458855\pi$
$823$	7.39591	0.257805	0.128903	+	0.991657i	$0.458855\pi$
$824$	−17.0648	−0.594480
$825$	−25.3222	−0.881605
$826$	8.49663	0.295636
$827$	30.2219	1.05092	0.525459	−	0.850819i	$-0.323894\pi$
$827$	30.2219	1.05092	0.525459	+	0.850819i	$0.323894\pi$
$828$	24.4606	0.850065
$829$	27.5697	0.957535	0.478768	−	0.877942i	$-0.341084\pi$
$829$	27.5697	0.957535	0.478768	+	0.877942i	$0.341084\pi$
$830$	32.4796	1.12738
$831$	5.19393	0.180175
$832$	−38.3120	−1.32823
$833$	6.88136	0.238425
$834$	11.9737	0.414617
$835$	−20.3737	−0.705060
$836$	−45.9033	−1.58760
$837$	0.447226	0.0154584
$838$	−89.5702	−3.09415
$839$	42.6970	1.47407	0.737033	−	0.675857i	$-0.236226\pi$
$839$	42.6970	1.47407	0.737033	+	0.675857i	$0.236226\pi$
$840$	−3.09406	−0.106755
$841$	−25.8563	−0.891597
$842$	−64.7181	−2.23033
$843$	22.0088	0.758023
$844$	5.44962	0.187584
$845$	−13.2009	−0.454125
$846$	−7.09213	−0.243832
$847$	5.65727	0.194386
$848$	0.0921575	0.00316470
$849$	0.862266	0.0295929
$850$	−11.0794	−0.380019
$851$	−1.72432	−0.0591089
$852$	0.965695	0.0330842
$853$	0.922063	0.0315708	0.0157854	−	0.999875i	$-0.494975\pi$
$853$	0.922063	0.0315708	0.0157854	+	0.999875i	$0.494975\pi$
$854$	6.31710	0.216167
$855$	−8.45827	−0.289267
$856$	9.88833	0.337976
$857$	−11.5204	−0.393530	−0.196765	−	0.980451i	$-0.563044\pi$
$857$	−11.5204	−0.393530	−0.196765	+	0.980451i	$0.563044\pi$
$858$	−35.5764	−1.21456
$859$	35.2485	1.20266	0.601331	−	0.799000i	$-0.294637\pi$
$859$	35.2485	1.20266	0.601331	+	0.799000i	$0.294637\pi$
$860$	−63.2461	−2.15667
$861$	2.69332	0.0917881
$862$	10.9256	0.372126
$863$	39.8819	1.35760	0.678798	−	0.734325i	$-0.262501\pi$
$863$	39.8819	1.35760	0.678798	+	0.734325i	$0.262501\pi$
$864$	5.58471	0.189996
$865$	6.38185	0.216990
$866$	51.6902	1.75650
$867$	−1.00000	−0.0339618
$868$	−0.500655	−0.0169933
$869$	5.23682	0.177647
$870$	12.7408	0.431954
$871$	−30.4311	−1.03112
$872$	−34.3650	−1.16375
$873$	12.0659	0.408370
$874$	−46.5097	−1.57321
$875$	−0.177797	−0.00601062
$876$	18.5369	0.626304
$877$	−16.5488	−0.558812	−0.279406	−	0.960173i	$-0.590137\pi$
$877$	−16.5488	−0.558812	−0.279406	+	0.960173i	$0.590137\pi$
$878$	−13.8837	−0.468553
$879$	−6.07836	−0.205018
$880$	1.03073	0.0347460
$881$	7.22976	0.243577	0.121788	−	0.992556i	$-0.461137\pi$
$881$	7.22976	0.243577	0.121788	+	0.992556i	$0.461137\pi$
$882$	−15.7673	−0.530911
$883$	27.3337	0.919852	0.459926	−	0.887957i	$-0.347876\pi$
$883$	27.3337	0.919852	0.459926	+	0.887957i	$0.347876\pi$
$884$	−9.63614	−0.324099
$885$	−33.7630	−1.13493
$886$	−67.8892	−2.28078
$887$	−17.6903	−0.593983	−0.296991	−	0.954880i	$-0.595983\pi$
$887$	−17.6903	−0.593983	−0.296991	+	0.954880i	$0.595983\pi$
$888$	0.656226	0.0220215
$889$	−3.12020	−0.104648
$890$	98.9993	3.31846
$891$	5.23682	0.175440
$892$	20.7579	0.695025
$893$	8.34795	0.279354
$894$	24.3865	0.815607
$895$	43.9277	1.46834
$896$	−6.35096	−0.212171
$897$	−22.3146	−0.745062
$898$	−35.0950	−1.17114
$899$	0.792951	0.0264464
$900$	15.7154	0.523845
$901$	−1.46841	−0.0489199
$902$	−93.8249	−3.12403
$903$	2.13730	0.0711250
$904$	33.4881	1.11380
$905$	20.4229	0.678880
$906$	−24.6814	−0.819985
$907$	−41.6312	−1.38234	−0.691171	−	0.722691i	$-0.742905\pi$
$907$	−41.6312	−1.38234	−0.691171	+	0.722691i	$0.742905\pi$
$908$	15.4927	0.514143
$909$	−4.95312	−0.164285
$910$	7.33855	0.243271
$911$	−3.64692	−0.120828	−0.0604140	−	0.998173i	$-0.519242\pi$
$911$	−3.64692	−0.120828	−0.0604140	+	0.998173i	$0.519242\pi$
$912$	0.169265	0.00560494
$913$	23.6701	0.783367
$914$	−50.8656	−1.68249
$915$	−25.1022	−0.829853
$916$	39.7890	1.31466
$917$	3.46543	0.114439
$918$	2.29130	0.0756242
$919$	3.59614	0.118626	0.0593128	−	0.998239i	$-0.481109\pi$
$919$	3.59614	0.118626	0.0593128	+	0.998239i	$0.481109\pi$
$920$	67.6059	2.22890
$921$	0.782039	0.0257690
$922$	−42.0098	−1.38352
$923$	−0.880970	−0.0289975
$924$	−5.86245	−0.192860
$925$	−1.10783	−0.0364253
$926$	60.0535	1.97348
$927$	−5.95784	−0.195681
$928$	9.90193	0.325047
$929$	−10.3656	−0.340083	−0.170042	−	0.985437i	$-0.554390\pi$
$929$	−10.3656	−0.340083	−0.170042	+	0.985437i	$0.554390\pi$
$930$	3.21370	0.105381
$931$	18.5592	0.608254
$932$	31.6123	1.03549
$933$	−0.327480	−0.0107212
$934$	14.1675	0.463576
$935$	−16.4234	−0.537104
$936$	8.49228	0.277579
$937$	18.2382	0.595815	0.297907	−	0.954595i	$-0.403711\pi$
$937$	18.2382	0.595815	0.297907	+	0.954595i	$0.403711\pi$
$938$	−8.10042	−0.264488
$939$	28.4507	0.928452
$940$	−31.5487	−1.02901
$941$	40.9477	1.33486	0.667429	−	0.744674i	$-0.267395\pi$
$941$	40.9477	1.33486	0.667429	+	0.744674i	$0.267395\pi$
$942$	−26.3517	−0.858585
$943$	−58.8497	−1.91641
$944$	0.675659	0.0219908
$945$	−1.08023	−0.0351399
$946$	−74.4554	−2.42075
$947$	−53.0226	−1.72300	−0.861501	−	0.507756i	$-0.830475\pi$
$947$	−53.0226	−1.72300	−0.861501	+	0.507756i	$0.830475\pi$
$948$	−3.25006	−0.105557
$949$	−16.9106	−0.548941
$950$	−29.8814	−0.969480
$951$	16.2326	0.526378
$952$	−0.986579	−0.0319752
$953$	−0.178211	−0.00577281	−0.00288640	−	0.999996i	$-0.500919\pi$
$953$	−0.178211	−0.00577281	−0.00288640	+	0.999996i	$0.500919\pi$
$954$	3.36457	0.108932
$955$	2.26330	0.0732387
$956$	94.4547	3.05488
$957$	9.28511	0.300145
$958$	−44.7663	−1.44633
$959$	−4.93438	−0.159340
$960$	40.5246	1.30793
$961$	−30.8000	−0.993548
$962$	−1.55645	−0.0501820
$963$	3.45232	0.111249
$964$	−25.2871	−0.814441
$965$	−70.0123	−2.25378
$966$	−5.93989	−0.191113
$967$	17.8079	0.572664	0.286332	−	0.958131i	$-0.407564\pi$
$967$	17.8079	0.572664	0.286332	+	0.958131i	$0.407564\pi$
$968$	47.0435	1.51203
$969$	−2.69703	−0.0866410
$970$	86.7040	2.78390
$971$	24.9421	0.800431	0.400215	−	0.916421i	$-0.368935\pi$
$971$	24.9421	0.800431	0.400215	+	0.916421i	$0.368935\pi$
$972$	−3.25006	−0.104246
$973$	−1.79998	−0.0577047
$974$	−57.0270	−1.82726
$975$	−14.3366	−0.459138
$976$	0.502341	0.0160795
$977$	−26.2005	−0.838229	−0.419114	−	0.907933i	$-0.637659\pi$
$977$	−26.2005	−0.838229	−0.419114	+	0.907933i	$0.637659\pi$
$978$	45.9471	1.46923
$979$	72.1475	2.30585
$980$	−70.1393	−2.24052
$981$	−11.9979	−0.383063
$982$	86.1678	2.74972
$983$	−14.3901	−0.458974	−0.229487	−	0.973312i	$-0.573705\pi$
$983$	−14.3901	−0.458974	−0.229487	+	0.973312i	$0.573705\pi$
$984$	22.3965	0.713975
$985$	29.9103	0.953022
$986$	4.06257	0.129379
$987$	1.06614	0.0339356
$988$	−25.9889	−0.826819
$989$	−46.7006	−1.48499
$990$	37.6310	1.19599
$991$	17.3167	0.550085	0.275042	−	0.961432i	$-0.411308\pi$
$991$	17.3167	0.550085	0.275042	+	0.961432i	$0.411308\pi$
$992$	2.49763	0.0792999
$993$	8.99597	0.285479
$994$	−0.234504	−0.00743803
$995$	−29.1992	−0.925676
$996$	−14.6901	−0.465473
$997$	−36.6298	−1.16008	−0.580038	−	0.814589i	$-0.696962\pi$
$997$	−36.6298	−1.16008	−0.580038	+	0.814589i	$0.696962\pi$
$998$	−88.6300	−2.80553
$999$	0.229108	0.00724867

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.l.1.28	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.l.1.28	✓	32	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+2.29130 q^{2} -1.00000 q^{3} +3.25006 q^{4} +3.13615 q^{5} -2.29130 q^{6} +0.344445 q^{7} +2.86426 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.29130 q^{2} -1.00000 q^{3} +3.25006 q^{4} +3.13615 q^{5} -2.29130 q^{6} +0.344445 q^{7} +2.86426 q^{8} +1.00000 q^{9} +7.18585 q^{10} +5.23682 q^{11} -3.25006 q^{12} +2.96491 q^{13} +0.789227 q^{14} -3.13615 q^{15} +0.0627600 q^{16} -1.00000 q^{17} +2.29130 q^{18} -2.69703 q^{19} +10.1927 q^{20} -0.344445 q^{21} +11.9991 q^{22} +7.52621 q^{23} -2.86426 q^{24} +4.83541 q^{25} +6.79351 q^{26} -1.00000 q^{27} +1.11947 q^{28} -1.77304 q^{29} -7.18585 q^{30} -0.447226 q^{31} -5.58471 q^{32} -5.23682 q^{33} -2.29130 q^{34} +1.08023 q^{35} +3.25006 q^{36} -0.229108 q^{37} -6.17970 q^{38} -2.96491 q^{39} +8.98273 q^{40} -7.81931 q^{41} -0.789227 q^{42} -6.20506 q^{43} +17.0200 q^{44} +3.13615 q^{45} +17.2448 q^{46} -3.09524 q^{47} -0.0627600 q^{48} -6.88136 q^{49} +11.0794 q^{50} +1.00000 q^{51} +9.63614 q^{52} +1.46841 q^{53} -2.29130 q^{54} +16.4234 q^{55} +0.986579 q^{56} +2.69703 q^{57} -4.06257 q^{58} +10.7658 q^{59} -10.1927 q^{60} +8.00416 q^{61} -1.02473 q^{62} +0.344445 q^{63} -12.9218 q^{64} +9.29840 q^{65} -11.9991 q^{66} -10.2637 q^{67} -3.25006 q^{68} -7.52621 q^{69} +2.47513 q^{70} -0.297132 q^{71} +2.86426 q^{72} -5.70357 q^{73} -0.524956 q^{74} -4.83541 q^{75} -8.76550 q^{76} +1.80380 q^{77} -6.79351 q^{78} +1.00000 q^{79} +0.196824 q^{80} +1.00000 q^{81} -17.9164 q^{82} +4.51994 q^{83} -1.11947 q^{84} -3.13615 q^{85} -14.2177 q^{86} +1.77304 q^{87} +14.9996 q^{88} +13.7770 q^{89} +7.18585 q^{90} +1.02125 q^{91} +24.4606 q^{92} +0.447226 q^{93} -7.09213 q^{94} -8.45827 q^{95} +5.58471 q^{96} +12.0659 q^{97} -15.7673 q^{98} +5.23682 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * q^99

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