LMFDB - Embedded newform 4029.2.a.f.1.1

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:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-2.46822 q^{2} -1.00000 q^{3} +4.09210 q^{4} +0.833166 q^{5} +2.46822 q^{6} -0.715489 q^{7} -5.16375 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.46822 q^{2} -1.00000 q^{3} +4.09210 q^{4} +0.833166 q^{5} +2.46822 q^{6} -0.715489 q^{7} -5.16375 q^{8} +1.00000 q^{9} -2.05644 q^{10} -5.81952 q^{11} -4.09210 q^{12} -2.33755 q^{13} +1.76598 q^{14} -0.833166 q^{15} +4.56107 q^{16} +1.00000 q^{17} -2.46822 q^{18} -7.40433 q^{19} +3.40940 q^{20} +0.715489 q^{21} +14.3638 q^{22} +5.79065 q^{23} +5.16375 q^{24} -4.30583 q^{25} +5.76959 q^{26} -1.00000 q^{27} -2.92785 q^{28} +8.60039 q^{29} +2.05644 q^{30} +10.1599 q^{31} -0.930203 q^{32} +5.81952 q^{33} -2.46822 q^{34} -0.596121 q^{35} +4.09210 q^{36} +3.80433 q^{37} +18.2755 q^{38} +2.33755 q^{39} -4.30226 q^{40} +12.4254 q^{41} -1.76598 q^{42} -5.00468 q^{43} -23.8141 q^{44} +0.833166 q^{45} -14.2926 q^{46} -1.90344 q^{47} -4.56107 q^{48} -6.48808 q^{49} +10.6277 q^{50} -1.00000 q^{51} -9.56550 q^{52} +5.59018 q^{53} +2.46822 q^{54} -4.84863 q^{55} +3.69461 q^{56} +7.40433 q^{57} -21.2276 q^{58} +13.6148 q^{59} -3.40940 q^{60} -6.21619 q^{61} -25.0768 q^{62} -0.715489 q^{63} -6.82619 q^{64} -1.94757 q^{65} -14.3638 q^{66} -1.14433 q^{67} +4.09210 q^{68} -5.79065 q^{69} +1.47136 q^{70} -0.475589 q^{71} -5.16375 q^{72} +15.0001 q^{73} -9.38991 q^{74} +4.30583 q^{75} -30.2993 q^{76} +4.16380 q^{77} -5.76959 q^{78} +1.00000 q^{79} +3.80013 q^{80} +1.00000 q^{81} -30.6685 q^{82} -10.4139 q^{83} +2.92785 q^{84} +0.833166 q^{85} +12.3526 q^{86} -8.60039 q^{87} +30.0506 q^{88} -13.7233 q^{89} -2.05644 q^{90} +1.67249 q^{91} +23.6959 q^{92} -10.1599 q^{93} +4.69811 q^{94} -6.16904 q^{95} +0.930203 q^{96} +8.39126 q^{97} +16.0140 q^{98} -5.81952 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9}+O(q^{10}) $ 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9} - 13 q^{10} - 23 q^{11} - 19 q^{12} - 18 q^{13} - 9 q^{14} - q^{15} + 21 q^{16} + 22 q^{17} + q^{18} - 30 q^{19} - 7 q^{20} + 15 q^{21} + 4 q^{22} - 3 q^{23} - 15 q^{24} + 19 q^{25} - 7 q^{26} - 22 q^{27} - 25 q^{28} - 7 q^{29} + 13 q^{30} - 10 q^{31} + 31 q^{32} + 23 q^{33} + q^{34} - 11 q^{35} + 19 q^{36} - q^{37} - 29 q^{38} + 18 q^{39} - 59 q^{40} + 9 q^{42} - 43 q^{43} - 80 q^{44} + q^{45} - 43 q^{46} + 2 q^{47} - 21 q^{48} + 43 q^{49} + 25 q^{50} - 22 q^{51} - 5 q^{52} - q^{53} - q^{54} - 19 q^{55} - 8 q^{56} + 30 q^{57} - 43 q^{58} - 28 q^{59} + 7 q^{60} - 29 q^{61} - 3 q^{62} - 15 q^{63} + 23 q^{64} + 19 q^{65} - 4 q^{66} - 16 q^{67} + 19 q^{68} + 3 q^{69} - 5 q^{70} - q^{71} + 15 q^{72} - 19 q^{73} - 24 q^{74} - 19 q^{75} - 72 q^{76} + 24 q^{77} + 7 q^{78} + 22 q^{79} - 82 q^{80} + 22 q^{81} - 81 q^{82} - 29 q^{83} + 25 q^{84} + q^{85} - 42 q^{86} + 7 q^{87} - 43 q^{88} - 28 q^{89} - 13 q^{90} - 96 q^{91} - 11 q^{92} + 10 q^{93} - 63 q^{94} - 23 q^{95} - 31 q^{96} - 51 q^{97} + 12 q^{98} - 23 q^{99}+O(q^{100}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9 - 13 * q^10 - 23 * q^11 - 19 * q^12 - 18 * q^13 - 9 * q^14 - q^15 + 21 * q^16 + 22 * q^17 + q^18 - 30 * q^19 - 7 * q^20 + 15 * q^21 + 4 * q^22 - 3 * q^23 - 15 * q^24 + 19 * q^25 - 7 * q^26 - 22 * q^27 - 25 * q^28 - 7 * q^29 + 13 * q^30 - 10 * q^31 + 31 * q^32 + 23 * q^33 + q^34 - 11 * q^35 + 19 * q^36 - q^37 - 29 * q^38 + 18 * q^39 - 59 * q^40 + 9 * q^42 - 43 * q^43 - 80 * q^44 + q^45 - 43 * q^46 + 2 * q^47 - 21 * q^48 + 43 * q^49 + 25 * q^50 - 22 * q^51 - 5 * q^52 - q^53 - q^54 - 19 * q^55 - 8 * q^56 + 30 * q^57 - 43 * q^58 - 28 * q^59 + 7 * q^60 - 29 * q^61 - 3 * q^62 - 15 * q^63 + 23 * q^64 + 19 * q^65 - 4 * q^66 - 16 * q^67 + 19 * q^68 + 3 * q^69 - 5 * q^70 - q^71 + 15 * q^72 - 19 * q^73 - 24 * q^74 - 19 * q^75 - 72 * q^76 + 24 * q^77 + 7 * q^78 + 22 * q^79 - 82 * q^80 + 22 * q^81 - 81 * q^82 - 29 * q^83 + 25 * q^84 + q^85 - 42 * q^86 + 7 * q^87 - 43 * q^88 - 28 * q^89 - 13 * q^90 - 96 * q^91 - 11 * q^92 + 10 * q^93 - 63 * q^94 - 23 * q^95 - 31 * q^96 - 51 * q^97 + 12 * q^98 - 23 * 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 $

$2$	−2.46822	−1.74529	−0.872647	−	0.488352i	$-0.837598\pi$
$2$	−2.46822	−1.74529	−0.872647	+	0.488352i	$0.837598\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.09210	2.04605
$5$	0.833166	0.372603	0.186302	−	0.982493i	$-0.440350\pi$
$5$	0.833166	0.372603	0.186302	+	0.982493i	$0.440350\pi$
$6$	2.46822	1.00765
$7$	−0.715489	−0.270429	−0.135215	−	0.990816i	$-0.543172\pi$
$7$	−0.715489	−0.270429	−0.135215	+	0.990816i	$0.543172\pi$
$8$	−5.16375	−1.82566
$9$	1.00000	0.333333
$10$	−2.05644	−0.650302
$11$	−5.81952	−1.75465	−0.877326	−	0.479895i	$-0.840675\pi$
$11$	−5.81952	−1.75465	−0.877326	+	0.479895i	$0.840675\pi$
$12$	−4.09210	−1.18129
$13$	−2.33755	−0.648321	−0.324160	−	0.946002i	$-0.605082\pi$
$13$	−2.33755	−0.648321	−0.324160	+	0.946002i	$0.605082\pi$
$14$	1.76598	0.471979
$15$	−0.833166	−0.215123
$16$	4.56107	1.14027
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.46822	−0.581764
$19$	−7.40433	−1.69867	−0.849335	−	0.527854i	$-0.822997\pi$
$19$	−7.40433	−1.69867	−0.849335	+	0.527854i	$0.822997\pi$
$20$	3.40940	0.762365
$21$	0.715489	0.156132
$22$	14.3638	3.06238
$23$	5.79065	1.20743	0.603717	−	0.797199i	$-0.293686\pi$
$23$	5.79065	1.20743	0.603717	+	0.797199i	$0.293686\pi$
$24$	5.16375	1.05405
$25$	−4.30583	−0.861167
$26$	5.76959	1.13151
$27$	−1.00000	−0.192450
$28$	−2.92785	−0.553312
$29$	8.60039	1.59705	0.798526	−	0.601960i	$-0.205613\pi$
$29$	8.60039	1.59705	0.798526	+	0.601960i	$0.205613\pi$
$30$	2.05644	0.375452
$31$	10.1599	1.82477	0.912384	−	0.409334i	$-0.134239\pi$
$31$	10.1599	1.82477	0.912384	+	0.409334i	$0.134239\pi$
$32$	−0.930203	−0.164438
$33$	5.81952	1.01305
$34$	−2.46822	−0.423296
$35$	−0.596121	−0.100763
$36$	4.09210	0.682016
$37$	3.80433	0.625428	0.312714	−	0.949847i	$-0.398762\pi$
$37$	3.80433	0.625428	0.312714	+	0.949847i	$0.398762\pi$
$38$	18.2755	2.96468
$39$	2.33755	0.374308
$40$	−4.30226	−0.680248
$41$	12.4254	1.94052	0.970258	−	0.242073i	$-0.0778274\pi$
$41$	12.4254	1.94052	0.970258	+	0.242073i	$0.0778274\pi$
$42$	−1.76598	−0.272497
$43$	−5.00468	−0.763207	−0.381604	−	0.924326i	$-0.624628\pi$
$43$	−5.00468	−0.763207	−0.381604	+	0.924326i	$0.624628\pi$
$44$	−23.8141	−3.59010
$45$	0.833166	0.124201
$46$	−14.2926	−2.10733
$47$	−1.90344	−0.277646	−0.138823	−	0.990317i	$-0.544332\pi$
$47$	−1.90344	−0.277646	−0.138823	+	0.990317i	$0.544332\pi$
$48$	−4.56107	−0.658333
$49$	−6.48808	−0.926868
$50$	10.6277	1.50299
$51$	−1.00000	−0.140028
$52$	−9.56550	−1.32650
$53$	5.59018	0.767871	0.383935	−	0.923360i	$-0.374569\pi$
$53$	5.59018	0.767871	0.383935	+	0.923360i	$0.374569\pi$
$54$	2.46822	0.335882
$55$	−4.84863	−0.653789
$56$	3.69461	0.493713
$57$	7.40433	0.980728
$58$	−21.2276	−2.78733
$59$	13.6148	1.77250	0.886251	−	0.463205i	$-0.153301\pi$
$59$	13.6148	1.77250	0.886251	+	0.463205i	$0.153301\pi$
$60$	−3.40940	−0.440151
$61$	−6.21619	−0.795902	−0.397951	−	0.917407i	$-0.630279\pi$
$61$	−6.21619	−0.795902	−0.397951	+	0.917407i	$0.630279\pi$
$62$	−25.0768	−3.18476
$63$	−0.715489	−0.0901431
$64$	−6.82619	−0.853274
$65$	−1.94757	−0.241567
$66$	−14.3638	−1.76807
$67$	−1.14433	−0.139803	−0.0699013	−	0.997554i	$-0.522268\pi$
$67$	−1.14433	−0.139803	−0.0699013	+	0.997554i	$0.522268\pi$
$68$	4.09210	0.496240
$69$	−5.79065	−0.697112
$70$	1.47136	0.175861
$71$	−0.475589	−0.0564420	−0.0282210	−	0.999602i	$-0.508984\pi$
$71$	−0.475589	−0.0564420	−0.0282210	+	0.999602i	$0.508984\pi$
$72$	−5.16375	−0.608554
$73$	15.0001	1.75563	0.877817	−	0.478995i	$-0.158999\pi$
$73$	15.0001	1.75563	0.877817	+	0.478995i	$0.158999\pi$
$74$	−9.38991	−1.09155
$75$	4.30583	0.497195
$76$	−30.2993	−3.47556
$77$	4.16380	0.474509
$78$	−5.76959	−0.653278
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	3.80013	0.424867
$81$	1.00000	0.111111
$82$	−30.6685	−3.38677
$83$	−10.4139	−1.14308	−0.571539	−	0.820575i	$-0.693653\pi$
$83$	−10.4139	−1.14308	−0.571539	+	0.820575i	$0.693653\pi$
$84$	2.92785	0.319455
$85$	0.833166	0.0903696
$86$	12.3526	1.33202
$87$	−8.60039	−0.922059
$88$	30.0506	3.20340
$89$	−13.7233	−1.45466	−0.727332	−	0.686285i	$-0.759240\pi$
$89$	−13.7233	−1.45466	−0.727332	+	0.686285i	$0.759240\pi$
$90$	−2.05644	−0.216767
$91$	1.67249	0.175325
$92$	23.6959	2.47047
$93$	−10.1599	−1.05353
$94$	4.69811	0.484573
$95$	−6.16904	−0.632930
$96$	0.930203	0.0949385
$97$	8.39126	0.852004	0.426002	−	0.904722i	$-0.359922\pi$
$97$	8.39126	0.852004	0.426002	+	0.904722i	$0.359922\pi$
$98$	16.0140	1.61766
$99$	−5.81952	−0.584884
$100$	−17.6199	−1.76199
$101$	−3.28496	−0.326865	−0.163433	−	0.986554i	$-0.552257\pi$
$101$	−3.28496	−0.326865	−0.163433	+	0.986554i	$0.552257\pi$
$102$	2.46822	0.244390
$103$	11.5905	1.14204	0.571022	−	0.820935i	$-0.306547\pi$
$103$	11.5905	1.14204	0.571022	+	0.820935i	$0.306547\pi$
$104$	12.0706	1.18362
$105$	0.596121	0.0581755
$106$	−13.7978	−1.34016
$107$	−3.36177	−0.324995	−0.162497	−	0.986709i	$-0.551955\pi$
$107$	−3.36177	−0.324995	−0.162497	+	0.986709i	$0.551955\pi$
$108$	−4.09210	−0.393762
$109$	−5.45742	−0.522726	−0.261363	−	0.965241i	$-0.584172\pi$
$109$	−5.45742	−0.522726	−0.261363	+	0.965241i	$0.584172\pi$
$110$	11.9675	1.14105
$111$	−3.80433	−0.361091
$112$	−3.26339	−0.308362
$113$	−3.79995	−0.357469	−0.178734	−	0.983897i	$-0.557200\pi$
$113$	−3.79995	−0.357469	−0.178734	+	0.983897i	$0.557200\pi$
$114$	−18.2755	−1.71166
$115$	4.82457	0.449894
$116$	35.1936	3.26765
$117$	−2.33755	−0.216107
$118$	−33.6044	−3.09354
$119$	−0.715489	−0.0655888
$120$	4.30226	0.392741
$121$	22.8668	2.07880
$122$	15.3429	1.38908
$123$	−12.4254	−1.12036
$124$	41.5752	3.73357
$125$	−7.75331	−0.693477
$126$	1.76598	0.157326
$127$	−19.5796	−1.73741	−0.868703	−	0.495333i	$-0.835046\pi$
$127$	−19.5796	−1.73741	−0.868703	+	0.495333i	$0.835046\pi$
$128$	18.7089	1.65365
$129$	5.00468	0.440638
$130$	4.80703	0.421605
$131$	−15.8331	−1.38335	−0.691674	−	0.722210i	$-0.743127\pi$
$131$	−15.8331	−1.38335	−0.691674	+	0.722210i	$0.743127\pi$
$132$	23.8141	2.07275
$133$	5.29772	0.459370
$134$	2.82446	0.243997
$135$	−0.833166	−0.0717075
$136$	−5.16375	−0.442788
$137$	−6.13223	−0.523912	−0.261956	−	0.965080i	$-0.584367\pi$
$137$	−6.13223	−0.523912	−0.261956	+	0.965080i	$0.584367\pi$
$138$	14.2926	1.21666
$139$	−16.2611	−1.37925	−0.689625	−	0.724167i	$-0.742224\pi$
$139$	−16.2611	−1.37925	−0.689625	+	0.724167i	$0.742224\pi$
$140$	−2.43939	−0.206166
$141$	1.90344	0.160299
$142$	1.17386	0.0985078
$143$	13.6035	1.13758
$144$	4.56107	0.380089
$145$	7.16556	0.595067
$146$	−37.0236	−3.06410
$147$	6.48808	0.535127
$148$	15.5677	1.27966
$149$	−14.4738	−1.18574	−0.592870	−	0.805298i	$-0.702005\pi$
$149$	−14.4738	−1.18574	−0.592870	+	0.805298i	$0.702005\pi$
$150$	−10.6277	−0.867751
$151$	−10.9420	−0.890444	−0.445222	−	0.895420i	$-0.646875\pi$
$151$	−10.9420	−0.890444	−0.445222	+	0.895420i	$0.646875\pi$
$152$	38.2341	3.10120
$153$	1.00000	0.0808452
$154$	−10.2772	−0.828158
$155$	8.46487	0.679915
$156$	9.56550	0.765853
$157$	13.7142	1.09451	0.547255	−	0.836966i	$-0.315673\pi$
$157$	13.7142	1.09451	0.547255	+	0.836966i	$0.315673\pi$
$158$	−2.46822	−0.196361
$159$	−5.59018	−0.443330
$160$	−0.775014	−0.0612703
$161$	−4.14314	−0.326525
$162$	−2.46822	−0.193921
$163$	12.0371	0.942820	0.471410	−	0.881914i	$-0.343745\pi$
$163$	12.0371	0.942820	0.471410	+	0.881914i	$0.343745\pi$
$164$	50.8458	3.97039
$165$	4.84863	0.377465
$166$	25.7039	1.99501
$167$	10.2101	0.790082	0.395041	−	0.918663i	$-0.370730\pi$
$167$	10.2101	0.790082	0.395041	+	0.918663i	$0.370730\pi$
$168$	−3.69461	−0.285045
$169$	−7.53584	−0.579680
$170$	−2.05644	−0.157721
$171$	−7.40433	−0.566224
$172$	−20.4797	−1.56156
$173$	−0.388142	−0.0295099	−0.0147549	−	0.999891i	$-0.504697\pi$
$173$	−0.388142	−0.0295099	−0.0147549	+	0.999891i	$0.504697\pi$
$174$	21.2276	1.60926
$175$	3.08078	0.232885
$176$	−26.5432	−2.00077
$177$	−13.6148	−1.02335
$178$	33.8720	2.53882
$179$	8.16160	0.610027	0.305013	−	0.952348i	$-0.401339\pi$
$179$	8.16160	0.610027	0.305013	+	0.952348i	$0.401339\pi$
$180$	3.40940	0.254122
$181$	−7.85298	−0.583707	−0.291854	−	0.956463i	$-0.594272\pi$
$181$	−7.85298	−0.583707	−0.291854	+	0.956463i	$0.594272\pi$
$182$	−4.12808	−0.305994
$183$	6.21619	0.459514
$184$	−29.9015	−2.20437
$185$	3.16964	0.233036
$186$	25.0768	1.83872
$187$	−5.81952	−0.425566
$188$	−7.78908	−0.568077
$189$	0.715489	0.0520442
$190$	15.2265	1.10465
$191$	−8.05933	−0.583153	−0.291576	−	0.956548i	$-0.594180\pi$
$191$	−8.05933	−0.583153	−0.291576	+	0.956548i	$0.594180\pi$
$192$	6.82619	0.492638
$193$	−16.2872	−1.17238	−0.586190	−	0.810174i	$-0.699373\pi$
$193$	−16.2872	−1.17238	−0.586190	+	0.810174i	$0.699373\pi$
$194$	−20.7115	−1.48700
$195$	1.94757	0.139469
$196$	−26.5498	−1.89642
$197$	15.5364	1.10693	0.553463	−	0.832874i	$-0.313306\pi$
$197$	15.5364	1.10693	0.553463	+	0.832874i	$0.313306\pi$
$198$	14.3638	1.02079
$199$	−23.8354	−1.68965	−0.844824	−	0.535045i	$-0.820295\pi$
$199$	−23.8354	−1.68965	−0.844824	+	0.535045i	$0.820295\pi$
$200$	22.2343	1.57220
$201$	1.14433	0.0807151
$202$	8.10799	0.570476
$203$	−6.15348	−0.431890
$204$	−4.09210	−0.286504
$205$	10.3524	0.723043
$206$	−28.6078	−1.99320
$207$	5.79065	0.402478
$208$	−10.6617	−0.739259
$209$	43.0897	2.98058
$210$	−1.47136	−0.101533
$211$	7.76231	0.534379	0.267190	−	0.963644i	$-0.413905\pi$
$211$	7.76231	0.534379	0.267190	+	0.963644i	$0.413905\pi$
$212$	22.8756	1.57110
$213$	0.475589	0.0325868
$214$	8.29758	0.567211
$215$	−4.16973	−0.284374
$216$	5.16375	0.351349
$217$	−7.26928	−0.493471
$218$	13.4701	0.912311
$219$	−15.0001	−1.01362
$220$	−19.8411	−1.33768
$221$	−2.33755	−0.157241
$222$	9.38991	0.630209
$223$	−8.32167	−0.557260	−0.278630	−	0.960398i	$-0.589880\pi$
$223$	−8.32167	−0.557260	−0.278630	+	0.960398i	$0.589880\pi$
$224$	0.665550	0.0444689
$225$	−4.30583	−0.287056
$226$	9.37910	0.623888
$227$	−3.95648	−0.262601	−0.131300	−	0.991343i	$-0.541915\pi$
$227$	−3.95648	−0.262601	−0.131300	+	0.991343i	$0.541915\pi$
$228$	30.2993	2.00662
$229$	10.9347	0.722583	0.361291	−	0.932453i	$-0.382336\pi$
$229$	10.9347	0.722583	0.361291	+	0.932453i	$0.382336\pi$
$230$	−11.9081	−0.785196
$231$	−4.16380	−0.273958
$232$	−44.4103	−2.91568
$233$	20.1727	1.32156	0.660779	−	0.750580i	$-0.270226\pi$
$233$	20.1727	1.32156	0.660779	+	0.750580i	$0.270226\pi$
$234$	5.76959	0.377170
$235$	−1.58589	−0.103452
$236$	55.7133	3.62663
$237$	−1.00000	−0.0649570
$238$	1.76598	0.114472
$239$	5.70635	0.369113	0.184557	−	0.982822i	$-0.440915\pi$
$239$	5.70635	0.369113	0.184557	+	0.982822i	$0.440915\pi$
$240$	−3.80013	−0.245297
$241$	−1.50966	−0.0972460	−0.0486230	−	0.998817i	$-0.515483\pi$
$241$	−1.50966	−0.0972460	−0.0486230	+	0.998817i	$0.515483\pi$
$242$	−56.4404	−3.62812
$243$	−1.00000	−0.0641500
$244$	−25.4373	−1.62845
$245$	−5.40565	−0.345354
$246$	30.6685	1.95535
$247$	17.3080	1.10128
$248$	−52.4631	−3.33141
$249$	10.4139	0.659956
$250$	19.1369	1.21032
$251$	−17.4724	−1.10285	−0.551425	−	0.834225i	$-0.685916\pi$
$251$	−17.4724	−1.10285	−0.551425	+	0.834225i	$0.685916\pi$
$252$	−2.92785	−0.184437
$253$	−33.6988	−2.11863
$254$	48.3267	3.03228
$255$	−0.833166	−0.0521749
$256$	−32.5253	−2.03283
$257$	21.8771	1.36466	0.682328	−	0.731046i	$-0.260968\pi$
$257$	21.8771	1.36466	0.682328	+	0.731046i	$0.260968\pi$
$258$	−12.3526	−0.769042
$259$	−2.72195	−0.169134
$260$	−7.96965	−0.494257
$261$	8.60039	0.532351
$262$	39.0796	2.41435
$263$	4.32975	0.266984	0.133492	−	0.991050i	$-0.457381\pi$
$263$	4.32975	0.266984	0.133492	+	0.991050i	$0.457381\pi$
$264$	−30.0506	−1.84948
$265$	4.65755	0.286111
$266$	−13.0759	−0.801736
$267$	13.7233	0.839851
$268$	−4.68272	−0.286043
$269$	11.5088	0.701707	0.350853	−	0.936430i	$-0.385892\pi$
$269$	11.5088	0.701707	0.350853	+	0.936430i	$0.385892\pi$
$270$	2.05644	0.125151
$271$	−3.23069	−0.196251	−0.0981253	−	0.995174i	$-0.531285\pi$
$271$	−3.23069	−0.196251	−0.0981253	+	0.995174i	$0.531285\pi$
$272$	4.56107	0.276555
$273$	−1.67249	−0.101224
$274$	15.1357	0.914380
$275$	25.0579	1.51105
$276$	−23.6959	−1.42633
$277$	−7.64903	−0.459585	−0.229793	−	0.973240i	$-0.573805\pi$
$277$	−7.64903	−0.459585	−0.229793	+	0.973240i	$0.573805\pi$
$278$	40.1359	2.40719
$279$	10.1599	0.608256
$280$	3.07822	0.183959
$281$	−8.50997	−0.507662	−0.253831	−	0.967249i	$-0.581691\pi$
$281$	−8.50997	−0.507662	−0.253831	+	0.967249i	$0.581691\pi$
$282$	−4.69811	−0.279769
$283$	−17.2502	−1.02542	−0.512710	−	0.858562i	$-0.671358\pi$
$283$	−17.2502	−1.02542	−0.512710	+	0.858562i	$0.671358\pi$
$284$	−1.94615	−0.115483
$285$	6.16904	0.365423
$286$	−33.5763	−1.98541
$287$	−8.89021	−0.524773
$288$	−0.930203	−0.0548128
$289$	1.00000	0.0588235
$290$	−17.6862	−1.03857
$291$	−8.39126	−0.491905
$292$	61.3821	3.59211
$293$	−19.3262	−1.12905	−0.564525	−	0.825416i	$-0.690940\pi$
$293$	−19.3262	−1.12905	−0.564525	+	0.825416i	$0.690940\pi$
$294$	−16.0140	−0.933954
$295$	11.3434	0.660440
$296$	−19.6446	−1.14182
$297$	5.81952	0.337683
$298$	35.7245	2.06946
$299$	−13.5360	−0.782804
$300$	17.6199	1.01728
$301$	3.58080	0.206394
$302$	27.0071	1.55409
$303$	3.28496	0.188716
$304$	−33.7717	−1.93694
$305$	−5.17912	−0.296556
$306$	−2.46822	−0.141099
$307$	−4.88089	−0.278567	−0.139284	−	0.990253i	$-0.544480\pi$
$307$	−4.88089	−0.278567	−0.139284	+	0.990253i	$0.544480\pi$
$308$	17.0387	0.970870
$309$	−11.5905	−0.659360
$310$	−20.8931	−1.18665
$311$	−9.04396	−0.512836	−0.256418	−	0.966566i	$-0.582542\pi$
$311$	−9.04396	−0.512836	−0.256418	+	0.966566i	$0.582542\pi$
$312$	−12.0706	−0.683360
$313$	−4.67628	−0.264319	−0.132159	−	0.991228i	$-0.542191\pi$
$313$	−4.67628	−0.264319	−0.132159	+	0.991228i	$0.542191\pi$
$314$	−33.8496	−1.91024
$315$	−0.596121	−0.0335876
$316$	4.09210	0.230198
$317$	−25.3157	−1.42187	−0.710935	−	0.703257i	$-0.751728\pi$
$317$	−25.3157	−1.42187	−0.710935	+	0.703257i	$0.751728\pi$
$318$	13.7978	0.773741
$319$	−50.0502	−2.80227
$320$	−5.68735	−0.317933
$321$	3.36177	0.187636
$322$	10.2262	0.569883
$323$	−7.40433	−0.411988
$324$	4.09210	0.227339
$325$	10.0651	0.558312
$326$	−29.7102	−1.64550
$327$	5.45742	0.301796
$328$	−64.1615	−3.54273
$329$	1.36189	0.0750836
$330$	−11.9675	−0.658788
$331$	−25.0288	−1.37571	−0.687854	−	0.725849i	$-0.741447\pi$
$331$	−25.0288	−1.37571	−0.687854	+	0.725849i	$0.741447\pi$
$332$	−42.6148	−2.33879
$333$	3.80433	0.208476
$334$	−25.2008	−1.37893
$335$	−0.953420	−0.0520909
$336$	3.26339	0.178033
$337$	−8.65069	−0.471233	−0.235616	−	0.971846i	$-0.575711\pi$
$337$	−8.65069	−0.471233	−0.235616	+	0.971846i	$0.575711\pi$
$338$	18.6001	1.01171
$339$	3.79995	0.206385
$340$	3.40940	0.184901
$341$	−59.1257	−3.20183
$342$	18.2755	0.988226
$343$	9.65057	0.521082
$344$	25.8429	1.39336
$345$	−4.82457	−0.259746
$346$	0.958019	0.0515034
$347$	21.6642	1.16299	0.581497	−	0.813549i	$-0.302467\pi$
$347$	21.6642	1.16299	0.581497	+	0.813549i	$0.302467\pi$
$348$	−35.1936	−1.88658
$349$	−12.5692	−0.672813	−0.336407	−	0.941717i	$-0.609212\pi$
$349$	−12.5692	−0.672813	−0.336407	+	0.941717i	$0.609212\pi$
$350$	−7.60403	−0.406452
$351$	2.33755	0.124769
$352$	5.41334	0.288532
$353$	−23.2323	−1.23653	−0.618265	−	0.785970i	$-0.712164\pi$
$353$	−23.2323	−1.23653	−0.618265	+	0.785970i	$0.712164\pi$
$354$	33.6044	1.78605
$355$	−0.396244	−0.0210305
$356$	−56.1570	−2.97631
$357$	0.715489	0.0378677
$358$	−20.1446	−1.06468
$359$	−23.0391	−1.21596	−0.607978	−	0.793954i	$-0.708019\pi$
$359$	−23.0391	−1.21596	−0.607978	+	0.793954i	$0.708019\pi$
$360$	−4.30226	−0.226749
$361$	35.8242	1.88548
$362$	19.3829	1.01874
$363$	−22.8668	−1.20020
$364$	6.84401	0.358724
$365$	12.4976	0.654155
$366$	−15.3429	−0.801987
$367$	−22.9380	−1.19735	−0.598676	−	0.800991i	$-0.704306\pi$
$367$	−22.9380	−1.19735	−0.598676	+	0.800991i	$0.704306\pi$
$368$	26.4115	1.37680
$369$	12.4254	0.646839
$370$	−7.82336	−0.406717
$371$	−3.99971	−0.207655
$372$	−41.5752	−2.15558
$373$	−12.7809	−0.661771	−0.330885	−	0.943671i	$-0.607347\pi$
$373$	−12.7809	−0.661771	−0.330885	+	0.943671i	$0.607347\pi$
$374$	14.3638	0.742737
$375$	7.75331	0.400379
$376$	9.82891	0.506888
$377$	−20.1039	−1.03540
$378$	−1.76598	−0.0908323
$379$	−7.17819	−0.368719	−0.184360	−	0.982859i	$-0.559021\pi$
$379$	−7.17819	−0.368719	−0.184360	+	0.982859i	$0.559021\pi$
$380$	−25.2443	−1.29501
$381$	19.5796	1.00309
$382$	19.8922	1.01777
$383$	3.11072	0.158951	0.0794753	−	0.996837i	$-0.474676\pi$
$383$	3.11072	0.158951	0.0794753	+	0.996837i	$0.474676\pi$
$384$	−18.7089	−0.954736
$385$	3.46914	0.176804
$386$	40.2004	2.04615
$387$	−5.00468	−0.254402
$388$	34.3379	1.74324
$389$	−23.7910	−1.20625	−0.603127	−	0.797645i	$-0.706079\pi$
$389$	−23.7910	−1.20625	−0.603127	+	0.797645i	$0.706079\pi$
$390$	−4.80703	−0.243413
$391$	5.79065	0.292846
$392$	33.5028	1.69215
$393$	15.8331	0.798676
$394$	−38.3473	−1.93191
$395$	0.833166	0.0419212
$396$	−23.8141	−1.19670
$397$	27.1622	1.36323	0.681617	−	0.731709i	$-0.261277\pi$
$397$	27.1622	1.36323	0.681617	+	0.731709i	$0.261277\pi$
$398$	58.8310	2.94893
$399$	−5.29772	−0.265218
$400$	−19.6392	−0.981960
$401$	4.90186	0.244787	0.122394	−	0.992482i	$-0.460943\pi$
$401$	4.90186	0.244787	0.122394	+	0.992482i	$0.460943\pi$
$402$	−2.82446	−0.140871
$403$	−23.7493	−1.18304
$404$	−13.4424	−0.668783
$405$	0.833166	0.0414004
$406$	15.1881	0.753775
$407$	−22.1394	−1.09741
$408$	5.16375	0.255644
$409$	9.93643	0.491325	0.245662	−	0.969355i	$-0.420995\pi$
$409$	9.93643	0.491325	0.245662	+	0.969355i	$0.420995\pi$
$410$	−25.5520	−1.26192
$411$	6.13223	0.302481
$412$	47.4294	2.33668
$413$	−9.74127	−0.479337
$414$	−14.2926	−0.702442
$415$	−8.67654	−0.425915
$416$	2.17440	0.106609
$417$	16.2611	0.796310
$418$	−106.355	−5.20198
$419$	18.2797	0.893020	0.446510	−	0.894779i	$-0.352667\pi$
$419$	18.2797	0.893020	0.446510	+	0.894779i	$0.352667\pi$
$420$	2.43939	0.119030
$421$	−1.46608	−0.0714524	−0.0357262	−	0.999362i	$-0.511374\pi$
$421$	−1.46608	−0.0714524	−0.0357262	+	0.999362i	$0.511374\pi$
$422$	−19.1591	−0.932649
$423$	−1.90344	−0.0925486
$424$	−28.8663	−1.40187
$425$	−4.30583	−0.208864
$426$	−1.17386	−0.0568735
$427$	4.44761	0.215235
$428$	−13.7567	−0.664955
$429$	−13.6035	−0.656781
$430$	10.2918	0.496315
$431$	2.83544	0.136579	0.0682893	−	0.997666i	$-0.478246\pi$
$431$	2.83544	0.136579	0.0682893	+	0.997666i	$0.478246\pi$
$432$	−4.56107	−0.219444
$433$	17.1436	0.823869	0.411935	−	0.911213i	$-0.364853\pi$
$433$	17.1436	0.823869	0.411935	+	0.911213i	$0.364853\pi$
$434$	17.9422	0.861252
$435$	−7.16556	−0.343562
$436$	−22.3323	−1.06952
$437$	−42.8759	−2.05103
$438$	37.0236	1.76906
$439$	19.2406	0.918304	0.459152	−	0.888358i	$-0.348153\pi$
$439$	19.2406	0.918304	0.459152	+	0.888358i	$0.348153\pi$
$440$	25.0371	1.19360
$441$	−6.48808	−0.308956
$442$	5.76959	0.274432
$443$	14.4911	0.688495	0.344247	−	0.938879i	$-0.388134\pi$
$443$	14.4911	0.688495	0.344247	+	0.938879i	$0.388134\pi$
$444$	−15.5677	−0.738809
$445$	−11.4338	−0.542013
$446$	20.5397	0.972583
$447$	14.4738	0.684587
$448$	4.88406	0.230750
$449$	−0.814559	−0.0384414	−0.0192207	−	0.999815i	$-0.506119\pi$
$449$	−0.814559	−0.0384414	−0.0192207	+	0.999815i	$0.506119\pi$
$450$	10.6277	0.500996
$451$	−72.3097	−3.40493
$452$	−15.5498	−0.731399
$453$	10.9420	0.514098
$454$	9.76545	0.458315
$455$	1.39347	0.0653267
$456$	−38.2341	−1.79048
$457$	21.5711	1.00905	0.504527	−	0.863396i	$-0.331667\pi$
$457$	21.5711	1.00905	0.504527	+	0.863396i	$0.331667\pi$
$458$	−26.9891	−1.26112
$459$	−1.00000	−0.0466760
$460$	19.7426	0.920504
$461$	−1.55192	−0.0722801	−0.0361400	−	0.999347i	$-0.511506\pi$
$461$	−1.55192	−0.0722801	−0.0361400	+	0.999347i	$0.511506\pi$
$462$	10.2772	0.478137
$463$	−31.8488	−1.48014	−0.740069	−	0.672531i	$-0.765207\pi$
$463$	−31.8488	−1.48014	−0.740069	+	0.672531i	$0.765207\pi$
$464$	39.2270	1.82107
$465$	−8.46487	−0.392549
$466$	−49.7907	−2.30651
$467$	−21.3681	−0.988796	−0.494398	−	0.869236i	$-0.664611\pi$
$467$	−21.3681	−0.988796	−0.494398	+	0.869236i	$0.664611\pi$
$468$	−9.56550	−0.442165
$469$	0.818758	0.0378067
$470$	3.91431	0.180554
$471$	−13.7142	−0.631916
$472$	−70.3037	−3.23599
$473$	29.1249	1.33916
$474$	2.46822	0.113369
$475$	31.8818	1.46284
$476$	−2.92785	−0.134198
$477$	5.59018	0.255957
$478$	−14.0845	−0.644211
$479$	39.8309	1.81992	0.909960	−	0.414696i	$-0.136112\pi$
$479$	39.8309	1.81992	0.909960	+	0.414696i	$0.136112\pi$
$480$	0.775014	0.0353744
$481$	−8.89282	−0.405478
$482$	3.72618	0.169723
$483$	4.14314	0.188520
$484$	93.5734	4.25333
$485$	6.99132	0.317459
$486$	2.46822	0.111961
$487$	23.8842	1.08229	0.541147	−	0.840928i	$-0.317990\pi$
$487$	23.8842	1.08229	0.541147	+	0.840928i	$0.317990\pi$
$488$	32.0989	1.45305
$489$	−12.0371	−0.544337
$490$	13.3423	0.602744
$491$	−16.7474	−0.755799	−0.377900	−	0.925847i	$-0.623354\pi$
$491$	−16.7474	−0.755799	−0.377900	+	0.925847i	$0.623354\pi$
$492$	−50.8458	−2.29231
$493$	8.60039	0.387342
$494$	−42.7200	−1.92206
$495$	−4.84863	−0.217930
$496$	46.3399	2.08072
$497$	0.340278	0.0152636
$498$	−25.7039	−1.15182
$499$	−31.4437	−1.40761	−0.703806	−	0.710392i	$-0.748517\pi$
$499$	−31.4437	−1.40761	−0.703806	+	0.710392i	$0.748517\pi$
$500$	−31.7273	−1.41889
$501$	−10.2101	−0.456154
$502$	43.1258	1.92480
$503$	−25.9278	−1.15606	−0.578031	−	0.816015i	$-0.696179\pi$
$503$	−25.9278	−1.15606	−0.578031	+	0.816015i	$0.696179\pi$
$504$	3.69461	0.164571
$505$	−2.73692	−0.121791
$506$	83.1760	3.69762
$507$	7.53584	0.334678
$508$	−80.1216	−3.55482
$509$	2.76118	0.122387	0.0611935	−	0.998126i	$-0.480509\pi$
$509$	2.76118	0.122387	0.0611935	+	0.998126i	$0.480509\pi$
$510$	2.05644	0.0910605
$511$	−10.7324	−0.474775
$512$	42.8617	1.89424
$513$	7.40433	0.326909
$514$	−53.9975	−2.38173
$515$	9.65680	0.425530
$516$	20.4797	0.901566
$517$	11.0771	0.487172
$518$	6.71837	0.295188
$519$	0.388142	0.0170375
$520$	10.0568	0.441019
$521$	−37.2111	−1.63025	−0.815124	−	0.579286i	$-0.803332\pi$
$521$	−37.2111	−1.63025	−0.815124	+	0.579286i	$0.803332\pi$
$522$	−21.2276	−0.929109
$523$	35.0055	1.53068	0.765341	−	0.643625i	$-0.222570\pi$
$523$	35.0055	1.53068	0.765341	+	0.643625i	$0.222570\pi$
$524$	−64.7908	−2.83040
$525$	−3.08078	−0.134456
$526$	−10.6868	−0.465965
$527$	10.1599	0.442571
$528$	26.5432	1.15515
$529$	10.5316	0.457895
$530$	−11.4959	−0.499348
$531$	13.6148	0.590834
$532$	21.6788	0.939894
$533$	−29.0450	−1.25808
$534$	−33.8720	−1.46579
$535$	−2.80091	−0.121094
$536$	5.90905	0.255232
$537$	−8.16160	−0.352199
$538$	−28.4063	−1.22468
$539$	37.7575	1.62633
$540$	−3.40940	−0.146717
$541$	3.27428	0.140772	0.0703861	−	0.997520i	$-0.477577\pi$
$541$	3.27428	0.140772	0.0703861	+	0.997520i	$0.477577\pi$
$542$	7.97405	0.342515
$543$	7.85298	0.337004
$544$	−0.930203	−0.0398821
$545$	−4.54694	−0.194770
$546$	4.12808	0.176665
$547$	−26.1456	−1.11790	−0.558952	−	0.829200i	$-0.688796\pi$
$547$	−26.1456	−1.11790	−0.558952	+	0.829200i	$0.688796\pi$
$548$	−25.0937	−1.07195
$549$	−6.21619	−0.265301
$550$	−61.8483	−2.63722
$551$	−63.6802	−2.71287
$552$	29.9015	1.27269
$553$	−0.715489	−0.0304257
$554$	18.8795	0.802111
$555$	−3.16964	−0.134544
$556$	−66.5420	−2.82201
$557$	−38.2918	−1.62248	−0.811238	−	0.584716i	$-0.801206\pi$
$557$	−38.2918	−1.62248	−0.811238	+	0.584716i	$0.801206\pi$
$558$	−25.0768	−1.06159
$559$	11.6987	0.494803
$560$	−2.71895	−0.114897
$561$	5.81952	0.245700
$562$	21.0045	0.886020
$563$	−1.99562	−0.0841054	−0.0420527	−	0.999115i	$-0.513390\pi$
$563$	−1.99562	−0.0841054	−0.0420527	+	0.999115i	$0.513390\pi$
$564$	7.78908	0.327979
$565$	−3.16599	−0.133194
$566$	42.5773	1.78966
$567$	−0.715489	−0.0300477
$568$	2.45582	0.103044
$569$	22.4680	0.941907	0.470954	−	0.882158i	$-0.343910\pi$
$569$	22.4680	0.941907	0.470954	+	0.882158i	$0.343910\pi$
$570$	−15.2265	−0.637769
$571$	−13.4191	−0.561570	−0.280785	−	0.959771i	$-0.590595\pi$
$571$	−13.4191	−0.561570	−0.280785	+	0.959771i	$0.590595\pi$
$572$	55.6667	2.32754
$573$	8.05933	0.336683
$574$	21.9430	0.915882
$575$	−24.9336	−1.03980
$576$	−6.82619	−0.284425
$577$	6.53191	0.271927	0.135963	−	0.990714i	$-0.456587\pi$
$577$	6.53191	0.271927	0.135963	+	0.990714i	$0.456587\pi$
$578$	−2.46822	−0.102664
$579$	16.2872	0.676874
$580$	29.3222	1.21754
$581$	7.45106	0.309122
$582$	20.7115	0.858518
$583$	−32.5322	−1.34735
$584$	−77.4571	−3.20520
$585$	−1.94757	−0.0805222
$586$	47.7013	1.97052
$587$	24.0936	0.994451	0.497226	−	0.867621i	$-0.334352\pi$
$587$	24.0936	0.994451	0.497226	+	0.867621i	$0.334352\pi$
$588$	26.5498	1.09490
$589$	−75.2272	−3.09968
$590$	−27.9981	−1.15266
$591$	−15.5364	−0.639084
$592$	17.3518	0.713154
$593$	21.7036	0.891261	0.445630	−	0.895217i	$-0.352980\pi$
$593$	21.7036	0.891261	0.445630	+	0.895217i	$0.352980\pi$
$594$	−14.3638	−0.589356
$595$	−0.596121	−0.0244386
$596$	−59.2282	−2.42608
$597$	23.8354	0.975518
$598$	33.4097	1.36622
$599$	−26.6624	−1.08940	−0.544699	−	0.838632i	$-0.683356\pi$
$599$	−26.6624	−1.08940	−0.544699	+	0.838632i	$0.683356\pi$
$600$	−22.2343	−0.907710
$601$	25.3671	1.03474	0.517372	−	0.855761i	$-0.326910\pi$
$601$	25.3671	1.03474	0.517372	+	0.855761i	$0.326910\pi$
$602$	−8.83818	−0.360217
$603$	−1.14433	−0.0466009
$604$	−44.7756	−1.82189
$605$	19.0519	0.774569
$606$	−8.10799	−0.329365
$607$	8.96620	0.363927	0.181963	−	0.983305i	$-0.441755\pi$
$607$	8.96620	0.363927	0.181963	+	0.983305i	$0.441755\pi$
$608$	6.88754	0.279326
$609$	6.15348	0.249352
$610$	12.7832	0.517577
$611$	4.44940	0.180004
$612$	4.09210	0.165413
$613$	11.2535	0.454523	0.227262	−	0.973834i	$-0.427023\pi$
$613$	11.2535	0.454523	0.227262	+	0.973834i	$0.427023\pi$
$614$	12.0471	0.486182
$615$	−10.3524	−0.417449
$616$	−21.5009	−0.866294
$617$	23.6517	0.952182	0.476091	−	0.879396i	$-0.342053\pi$
$617$	23.6517	0.952182	0.476091	+	0.879396i	$0.342053\pi$
$618$	28.6078	1.15078
$619$	−23.1184	−0.929208	−0.464604	−	0.885519i	$-0.653803\pi$
$619$	−23.1184	−0.929208	−0.464604	+	0.885519i	$0.653803\pi$
$620$	34.6391	1.39114
$621$	−5.79065	−0.232371
$622$	22.3225	0.895049
$623$	9.81885	0.393384
$624$	10.6617	0.426811
$625$	15.0694	0.602775
$626$	11.5421	0.461314
$627$	−43.0897	−1.72084
$628$	56.1197	2.23942
$629$	3.80433	0.151688
$630$	1.47136	0.0586203
$631$	15.1874	0.604601	0.302300	−	0.953213i	$-0.402245\pi$
$631$	15.1874	0.604601	0.302300	+	0.953213i	$0.402245\pi$
$632$	−5.16375	−0.205403
$633$	−7.76231	−0.308524
$634$	62.4846	2.48158
$635$	−16.3130	−0.647364
$636$	−22.8756	−0.907075
$637$	15.1662	0.600908
$638$	123.535	4.89079
$639$	−0.475589	−0.0188140
$640$	15.5877	0.616156
$641$	34.6347	1.36799	0.683994	−	0.729487i	$-0.260241\pi$
$641$	34.6347	1.36799	0.683994	+	0.729487i	$0.260241\pi$
$642$	−8.29758	−0.327479
$643$	49.3785	1.94730	0.973650	−	0.228049i	$-0.0732347\pi$
$643$	49.3785	1.94730	0.973650	+	0.228049i	$0.0732347\pi$
$644$	−16.9541	−0.668087
$645$	4.16973	0.164183
$646$	18.2755	0.719040
$647$	45.3543	1.78306	0.891532	−	0.452958i	$-0.149631\pi$
$647$	45.3543	1.78306	0.891532	+	0.452958i	$0.149631\pi$
$648$	−5.16375	−0.202851
$649$	−79.2319	−3.11012
$650$	−24.8429	−0.974419
$651$	7.26928	0.284906
$652$	49.2571	1.92906
$653$	7.00372	0.274077	0.137038	−	0.990566i	$-0.456242\pi$
$653$	7.00372	0.274077	0.137038	+	0.990566i	$0.456242\pi$
$654$	−13.4701	−0.526723
$655$	−13.1916	−0.515440
$656$	56.6729	2.21271
$657$	15.0001	0.585212
$658$	−3.36145	−0.131043
$659$	−30.9632	−1.20616	−0.603078	−	0.797682i	$-0.706059\pi$
$659$	−30.9632	−1.20616	−0.603078	+	0.797682i	$0.706059\pi$
$660$	19.8411	0.772313
$661$	−32.0629	−1.24710	−0.623550	−	0.781783i	$-0.714310\pi$
$661$	−32.0629	−1.24710	−0.623550	+	0.781783i	$0.714310\pi$
$662$	61.7766	2.40101
$663$	2.33755	0.0907831
$664$	53.7750	2.08687
$665$	4.41388	0.171163
$666$	−9.38991	−0.363852
$667$	49.8018	1.92833
$668$	41.7808	1.61655
$669$	8.32167	0.321734
$670$	2.35325	0.0909139
$671$	36.1753	1.39653
$672$	−0.665550	−0.0256742
$673$	−51.1985	−1.97356	−0.986778	−	0.162077i	$-0.948181\pi$
$673$	−51.1985	−1.97356	−0.986778	+	0.162077i	$0.948181\pi$
$674$	21.3518	0.822440
$675$	4.30583	0.165732
$676$	−30.8374	−1.18605
$677$	−9.37042	−0.360135	−0.180067	−	0.983654i	$-0.557632\pi$
$677$	−9.37042	−0.360135	−0.180067	+	0.983654i	$0.557632\pi$
$678$	−9.37910	−0.360202
$679$	−6.00386	−0.230407
$680$	−4.30226	−0.164984
$681$	3.95648	0.151613
$682$	145.935	5.58814
$683$	−2.24327	−0.0858363	−0.0429182	−	0.999079i	$-0.513665\pi$
$683$	−2.24327	−0.0858363	−0.0429182	+	0.999079i	$0.513665\pi$
$684$	−30.2993	−1.15852
$685$	−5.10917	−0.195211
$686$	−23.8197	−0.909440
$687$	−10.9347	−0.417183
$688$	−22.8267	−0.870260
$689$	−13.0674	−0.497827
$690$	11.9081	0.453333
$691$	25.3106	0.962860	0.481430	−	0.876484i	$-0.340117\pi$
$691$	25.3106	0.962860	0.481430	+	0.876484i	$0.340117\pi$
$692$	−1.58831	−0.0603787
$693$	4.16380	0.158170
$694$	−53.4719	−2.02977
$695$	−13.5482	−0.513913
$696$	44.4103	1.68337
$697$	12.4254	0.470644
$698$	31.0235	1.17426
$699$	−20.1727	−0.763002
$700$	12.6068	0.476494
$701$	−8.27839	−0.312670	−0.156335	−	0.987704i	$-0.549968\pi$
$701$	−8.27839	−0.312670	−0.156335	+	0.987704i	$0.549968\pi$
$702$	−5.76959	−0.217759
$703$	−28.1685	−1.06240
$704$	39.7252	1.49720
$705$	1.58589	0.0597279
$706$	57.3423	2.15811
$707$	2.35035	0.0883940
$708$	−55.7133	−2.09383
$709$	−19.0875	−0.716847	−0.358423	−	0.933559i	$-0.616686\pi$
$709$	−19.0875	−0.716847	−0.358423	+	0.933559i	$0.616686\pi$
$710$	0.978017	0.0367043
$711$	1.00000	0.0375029
$712$	70.8636	2.65573
$713$	58.8323	2.20329
$714$	−1.76598	−0.0660902
$715$	11.3339	0.423865
$716$	33.3981	1.24814
$717$	−5.70635	−0.213108
$718$	56.8654	2.12220
$719$	−35.4045	−1.32036	−0.660182	−	0.751106i	$-0.729521\pi$
$719$	−35.4045	−1.32036	−0.660182	+	0.751106i	$0.729521\pi$
$720$	3.80013	0.141622
$721$	−8.29286	−0.308842
$722$	−88.4218	−3.29072
$723$	1.50966	0.0561450
$724$	−32.1352	−1.19429
$725$	−37.0319	−1.37533
$726$	56.4404	2.09470
$727$	−26.2802	−0.974678	−0.487339	−	0.873213i	$-0.662032\pi$
$727$	−26.2802	−0.974678	−0.487339	+	0.873213i	$0.662032\pi$
$728$	−8.63635	−0.320084
$729$	1.00000	0.0370370
$730$	−30.8468	−1.14169
$731$	−5.00468	−0.185105
$732$	25.4373	0.940188
$733$	−13.0934	−0.483616	−0.241808	−	0.970324i	$-0.577740\pi$
$733$	−13.0934	−0.483616	−0.241808	+	0.970324i	$0.577740\pi$
$734$	56.6159	2.08973
$735$	5.40565	0.199390
$736$	−5.38648	−0.198548
$737$	6.65947	0.245305
$738$	−30.6685	−1.12892
$739$	44.1940	1.62570	0.812851	−	0.582472i	$-0.197914\pi$
$739$	44.1940	1.62570	0.812851	+	0.582472i	$0.197914\pi$
$740$	12.9705	0.476804
$741$	−17.3080	−0.635827
$742$	9.87216	0.362418
$743$	−17.4945	−0.641810	−0.320905	−	0.947111i	$-0.603987\pi$
$743$	−17.4945	−0.641810	−0.320905	+	0.947111i	$0.603987\pi$
$744$	52.4631	1.92339
$745$	−12.0591	−0.441811
$746$	31.5461	1.15498
$747$	−10.4139	−0.381026
$748$	−23.8141	−0.870728
$749$	2.40531	0.0878881
$750$	−19.1369	−0.698779
$751$	−16.6330	−0.606946	−0.303473	−	0.952840i	$-0.598146\pi$
$751$	−16.6330	−0.606946	−0.303473	+	0.952840i	$0.598146\pi$
$752$	−8.68174	−0.316590
$753$	17.4724	0.636731
$754$	49.6208	1.80708
$755$	−9.11647	−0.331782
$756$	2.92785	0.106485
$757$	31.2089	1.13431	0.567153	−	0.823613i	$-0.308045\pi$
$757$	31.2089	1.13431	0.567153	+	0.823613i	$0.308045\pi$
$758$	17.7173	0.643523
$759$	33.6988	1.22319
$760$	31.8554	1.15552
$761$	21.2105	0.768880	0.384440	−	0.923150i	$-0.374394\pi$
$761$	21.2105	0.768880	0.384440	+	0.923150i	$0.374394\pi$
$762$	−48.3267	−1.75069
$763$	3.90472	0.141361
$764$	−32.9796	−1.19316
$765$	0.833166	0.0301232
$766$	−7.67795	−0.277415
$767$	−31.8254	−1.14915
$768$	32.5253	1.17366
$769$	−38.8765	−1.40192	−0.700961	−	0.713200i	$-0.747245\pi$
$769$	−38.8765	−1.40192	−0.700961	+	0.713200i	$0.747245\pi$
$770$	−8.56260	−0.308575
$771$	−21.8771	−0.787885
$772$	−66.6489	−2.39875
$773$	8.60076	0.309348	0.154674	−	0.987966i	$-0.450567\pi$
$773$	8.60076	0.309348	0.154674	+	0.987966i	$0.450567\pi$
$774$	12.3526	0.444007
$775$	−43.7468	−1.57143
$776$	−43.3304	−1.55547
$777$	2.72195	0.0976496
$778$	58.7215	2.10527
$779$	−92.0016	−3.29630
$780$	7.96965	0.285359
$781$	2.76770	0.0990360
$782$	−14.2926	−0.511101
$783$	−8.60039	−0.307353
$784$	−29.5926	−1.05688
$785$	11.4262	0.407818
$786$	−39.0796	−1.39392
$787$	18.2055	0.648955	0.324477	−	0.945893i	$-0.394812\pi$
$787$	18.2055	0.648955	0.324477	+	0.945893i	$0.394812\pi$
$788$	63.5766	2.26482
$789$	−4.32975	−0.154143
$790$	−2.05644	−0.0731647
$791$	2.71882	0.0966701
$792$	30.0506	1.06780
$793$	14.5307	0.516000
$794$	−67.0423	−2.37924
$795$	−4.65755	−0.165186
$796$	−97.5368	−3.45710
$797$	−11.9452	−0.423120	−0.211560	−	0.977365i	$-0.567854\pi$
$797$	−11.9452	−0.423120	−0.211560	+	0.977365i	$0.567854\pi$
$798$	13.0759	0.462883
$799$	−1.90344	−0.0673390
$800$	4.00530	0.141609
$801$	−13.7233	−0.484888
$802$	−12.0989	−0.427225
$803$	−87.2937	−3.08053
$804$	4.68272	0.165147
$805$	−3.45193	−0.121664
$806$	58.6184	2.06474
$807$	−11.5088	−0.405131
$808$	16.9627	0.596746
$809$	0.281385	0.00989296	0.00494648	−	0.999988i	$-0.498425\pi$
$809$	0.281385	0.00989296	0.00494648	+	0.999988i	$0.498425\pi$
$810$	−2.05644	−0.0722558
$811$	−16.6382	−0.584245	−0.292123	−	0.956381i	$-0.594362\pi$
$811$	−16.6382	−0.584245	−0.292123	+	0.956381i	$0.594362\pi$
$812$	−25.1807	−0.883668
$813$	3.23069	0.113305
$814$	54.6448	1.91530
$815$	10.0289	0.351298
$816$	−4.56107	−0.159669
$817$	37.0563	1.29644
$818$	−24.5253	−0.857506
$819$	1.67249	0.0584417
$820$	42.3630	1.47938
$821$	43.6918	1.52485	0.762427	−	0.647075i	$-0.224008\pi$
$821$	43.6918	1.52485	0.762427	+	0.647075i	$0.224008\pi$
$822$	−15.1357	−0.527917
$823$	−6.32412	−0.220445	−0.110222	−	0.993907i	$-0.535156\pi$
$823$	−6.32412	−0.220445	−0.110222	+	0.993907i	$0.535156\pi$
$824$	−59.8504	−2.08499
$825$	−25.0579	−0.872404
$826$	24.0436	0.836583
$827$	−32.2792	−1.12246	−0.561229	−	0.827661i	$-0.689671\pi$
$827$	−32.2792	−1.12246	−0.561229	+	0.827661i	$0.689671\pi$
$828$	23.6959	0.823489
$829$	57.5015	1.99711	0.998555	−	0.0537302i	$-0.0171111\pi$
$829$	57.5015	1.99711	0.998555	+	0.0537302i	$0.0171111\pi$
$830$	21.4156	0.743346
$831$	7.64903	0.265342
$832$	15.9566	0.553195
$833$	−6.48808	−0.224798
$834$	−40.1359	−1.38979
$835$	8.50672	0.294387
$836$	176.327	6.09840
$837$	−10.1599	−0.351177
$838$	−45.1182	−1.55858
$839$	−52.7910	−1.82255	−0.911275	−	0.411799i	$-0.864901\pi$
$839$	−52.7910	−1.82255	−0.911275	+	0.411799i	$0.864901\pi$
$840$	−3.07822	−0.106209
$841$	44.9668	1.55058
$842$	3.61861	0.124705
$843$	8.50997	0.293099
$844$	31.7641	1.09337
$845$	−6.27861	−0.215991
$846$	4.69811	0.161524
$847$	−16.3610	−0.562170
$848$	25.4972	0.875577
$849$	17.2502	0.592026
$850$	10.6277	0.364528
$851$	22.0295	0.755162
$852$	1.94615	0.0666742
$853$	−31.7680	−1.08772	−0.543858	−	0.839178i	$-0.683037\pi$
$853$	−31.7680	−1.08772	−0.543858	+	0.839178i	$0.683037\pi$
$854$	−10.9777	−0.375649
$855$	−6.16904	−0.210977
$856$	17.3594	0.593330
$857$	21.0045	0.717499	0.358749	−	0.933434i	$-0.383203\pi$
$857$	21.0045	0.717499	0.358749	+	0.933434i	$0.383203\pi$
$858$	33.5763	1.14628
$859$	−23.6029	−0.805321	−0.402661	−	0.915349i	$-0.631915\pi$
$859$	−23.6029	−0.805321	−0.402661	+	0.915349i	$0.631915\pi$
$860$	−17.0630	−0.581842
$861$	8.89021	0.302978
$862$	−6.99849	−0.238370
$863$	31.7146	1.07958	0.539789	−	0.841800i	$-0.318504\pi$
$863$	31.7146	1.07958	0.539789	+	0.841800i	$0.318504\pi$
$864$	0.930203	0.0316462
$865$	−0.323387	−0.0109955
$866$	−42.3142	−1.43789
$867$	−1.00000	−0.0339618
$868$	−29.7466	−1.00967
$869$	−5.81952	−0.197414
$870$	17.6862	0.599617
$871$	2.67494	0.0906369
$872$	28.1808	0.954321
$873$	8.39126	0.284001
$874$	105.827	3.57965
$875$	5.54741	0.187537
$876$	−61.3821	−2.07391
$877$	8.34546	0.281806	0.140903	−	0.990023i	$-0.454999\pi$
$877$	8.34546	0.281806	0.140903	+	0.990023i	$0.454999\pi$
$878$	−47.4900	−1.60271
$879$	19.3262	0.651857
$880$	−22.1149	−0.745494
$881$	−0.584013	−0.0196759	−0.00983795	−	0.999952i	$-0.503132\pi$
$881$	−0.584013	−0.0196759	−0.00983795	+	0.999952i	$0.503132\pi$
$882$	16.0140	0.539219
$883$	−27.8072	−0.935788	−0.467894	−	0.883785i	$-0.654987\pi$
$883$	−27.8072	−0.935788	−0.467894	+	0.883785i	$0.654987\pi$
$884$	−9.56550	−0.321723
$885$	−11.3434	−0.381305
$886$	−35.7673	−1.20163
$887$	18.9236	0.635392	0.317696	−	0.948193i	$-0.397091\pi$
$887$	18.9236	0.635392	0.317696	+	0.948193i	$0.397091\pi$
$888$	19.6446	0.659230
$889$	14.0090	0.469846
$890$	28.2210	0.945972
$891$	−5.81952	−0.194961
$892$	−34.0531	−1.14018
$893$	14.0937	0.471629
$894$	−35.7245	−1.19481
$895$	6.79997	0.227298
$896$	−13.3860	−0.447196
$897$	13.5360	0.451952
$898$	2.01051	0.0670916
$899$	87.3790	2.91425
$900$	−17.6199	−0.587330
$901$	5.59018	0.186236
$902$	178.476	5.94260
$903$	−3.58080	−0.119161
$904$	19.6220	0.652618
$905$	−6.54284	−0.217491
$906$	−27.0071	−0.897252
$907$	9.89607	0.328594	0.164297	−	0.986411i	$-0.447464\pi$
$907$	9.89607	0.328594	0.164297	+	0.986411i	$0.447464\pi$
$908$	−16.1903	−0.537294
$909$	−3.28496	−0.108955
$910$	−3.43938	−0.114014
$911$	50.8702	1.68540	0.842702	−	0.538381i	$-0.180964\pi$
$911$	50.8702	1.68540	0.842702	+	0.538381i	$0.180964\pi$
$912$	33.7717	1.11829
$913$	60.6041	2.00570
$914$	−53.2421	−1.76109
$915$	5.17912	0.171216
$916$	44.7457	1.47844
$917$	11.3284	0.374098
$918$	2.46822	0.0814633
$919$	−26.7655	−0.882913	−0.441456	−	0.897283i	$-0.645538\pi$
$919$	−26.7655	−0.882913	−0.441456	+	0.897283i	$0.645538\pi$
$920$	−24.9129	−0.821354
$921$	4.88089	0.160831
$922$	3.83047	0.126150
$923$	1.11171	0.0365925
$924$	−17.0387	−0.560532
$925$	−16.3808	−0.538597
$926$	78.6097	2.58328
$927$	11.5905	0.380681
$928$	−8.00011	−0.262617
$929$	−2.50638	−0.0822315	−0.0411158	−	0.999154i	$-0.513091\pi$
$929$	−2.50638	−0.0822315	−0.0411158	+	0.999154i	$0.513091\pi$
$930$	20.8931	0.685113
$931$	48.0399	1.57444
$932$	82.5487	2.70397
$933$	9.04396	0.296086
$934$	52.7410	1.72574
$935$	−4.84863	−0.158567
$936$	12.0706	0.394538
$937$	−48.6886	−1.59059	−0.795293	−	0.606225i	$-0.792683\pi$
$937$	−48.6886	−1.59059	−0.795293	+	0.606225i	$0.792683\pi$
$938$	−2.02087	−0.0659838
$939$	4.67628	0.152605
$940$	−6.48960	−0.211667
$941$	9.25816	0.301807	0.150904	−	0.988548i	$-0.451782\pi$
$941$	9.25816	0.301807	0.150904	+	0.988548i	$0.451782\pi$
$942$	33.8496	1.10288
$943$	71.9509	2.34304
$944$	62.0982	2.02113
$945$	0.596121	0.0193918
$946$	−71.8865	−2.33723
$947$	31.1992	1.01384	0.506919	−	0.861994i	$-0.330784\pi$
$947$	31.1992	1.01384	0.506919	+	0.861994i	$0.330784\pi$
$948$	−4.09210	−0.132905
$949$	−35.0637	−1.13821
$950$	−78.6913	−2.55308
$951$	25.3157	0.820917
$952$	3.69461	0.119743
$953$	35.9086	1.16319	0.581597	−	0.813477i	$-0.302428\pi$
$953$	35.9086	1.16319	0.581597	+	0.813477i	$0.302428\pi$
$954$	−13.7978	−0.446720
$955$	−6.71476	−0.217285
$956$	23.3510	0.755224
$957$	50.0502	1.61789
$958$	−98.3113	−3.17629
$959$	4.38754	0.141681
$960$	5.68735	0.183559
$961$	72.2232	2.32978
$962$	21.9494	0.707678
$963$	−3.36177	−0.108332
$964$	−6.17769	−0.198970
$965$	−13.5700	−0.436833
$966$	−10.2262	−0.329022
$967$	−33.0894	−1.06408	−0.532042	−	0.846718i	$-0.678575\pi$
$967$	−33.0894	−1.06408	−0.532042	+	0.846718i	$0.678575\pi$
$968$	−118.079	−3.79519
$969$	7.40433	0.237861
$970$	−17.2561	−0.554060
$971$	−33.8549	−1.08646	−0.543228	−	0.839585i	$-0.682798\pi$
$971$	−33.8549	−1.08646	−0.543228	+	0.839585i	$0.682798\pi$
$972$	−4.09210	−0.131254
$973$	11.6346	0.372989
$974$	−58.9513	−1.88892
$975$	−10.0651	−0.322342
$976$	−28.3525	−0.907540
$977$	40.5637	1.29775	0.648873	−	0.760897i	$-0.275241\pi$
$977$	40.5637	1.29775	0.648873	+	0.760897i	$0.275241\pi$
$978$	29.7102	0.950028
$979$	79.8629	2.55243
$980$	−22.1204	−0.706611
$981$	−5.45742	−0.174242
$982$	41.3362	1.31909
$983$	−2.11612	−0.0674936	−0.0337468	−	0.999430i	$-0.510744\pi$
$983$	−2.11612	−0.0674936	−0.0337468	+	0.999430i	$0.510744\pi$
$984$	64.1615	2.04539
$985$	12.9444	0.412444
$986$	−21.2276	−0.676026
$987$	−1.36189	−0.0433495
$988$	70.8262	2.25328
$989$	−28.9804	−0.921522
$990$	11.9675	0.380351
$991$	2.62065	0.0832478	0.0416239	−	0.999133i	$-0.486747\pi$
$991$	2.62065	0.0832478	0.0416239	+	0.999133i	$0.486747\pi$
$992$	−9.45076	−0.300062
$993$	25.0288	0.794266
$994$	−0.839881	−0.0266394
$995$	−19.8589	−0.629568
$996$	42.6148	1.35030
$997$	−50.8316	−1.60985	−0.804927	−	0.593374i	$-0.797796\pi$
$997$	−50.8316	−1.60985	−0.804927	+	0.593374i	$0.797796\pi$
$998$	77.6098	2.45670
$999$	−3.80433	−0.120364

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.f.1.1	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.f.1.1	✓	22	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)

\(f(q)\)	\(=\)	\(q-2.46822 q^{2} -1.00000 q^{3} +4.09210 q^{4} +0.833166 q^{5} +2.46822 q^{6} -0.715489 q^{7} -5.16375 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.46822 q^{2} -1.00000 q^{3} +4.09210 q^{4} +0.833166 q^{5} +2.46822 q^{6} -0.715489 q^{7} -5.16375 q^{8} +1.00000 q^{9} -2.05644 q^{10} -5.81952 q^{11} -4.09210 q^{12} -2.33755 q^{13} +1.76598 q^{14} -0.833166 q^{15} +4.56107 q^{16} +1.00000 q^{17} -2.46822 q^{18} -7.40433 q^{19} +3.40940 q^{20} +0.715489 q^{21} +14.3638 q^{22} +5.79065 q^{23} +5.16375 q^{24} -4.30583 q^{25} +5.76959 q^{26} -1.00000 q^{27} -2.92785 q^{28} +8.60039 q^{29} +2.05644 q^{30} +10.1599 q^{31} -0.930203 q^{32} +5.81952 q^{33} -2.46822 q^{34} -0.596121 q^{35} +4.09210 q^{36} +3.80433 q^{37} +18.2755 q^{38} +2.33755 q^{39} -4.30226 q^{40} +12.4254 q^{41} -1.76598 q^{42} -5.00468 q^{43} -23.8141 q^{44} +0.833166 q^{45} -14.2926 q^{46} -1.90344 q^{47} -4.56107 q^{48} -6.48808 q^{49} +10.6277 q^{50} -1.00000 q^{51} -9.56550 q^{52} +5.59018 q^{53} +2.46822 q^{54} -4.84863 q^{55} +3.69461 q^{56} +7.40433 q^{57} -21.2276 q^{58} +13.6148 q^{59} -3.40940 q^{60} -6.21619 q^{61} -25.0768 q^{62} -0.715489 q^{63} -6.82619 q^{64} -1.94757 q^{65} -14.3638 q^{66} -1.14433 q^{67} +4.09210 q^{68} -5.79065 q^{69} +1.47136 q^{70} -0.475589 q^{71} -5.16375 q^{72} +15.0001 q^{73} -9.38991 q^{74} +4.30583 q^{75} -30.2993 q^{76} +4.16380 q^{77} -5.76959 q^{78} +1.00000 q^{79} +3.80013 q^{80} +1.00000 q^{81} -30.6685 q^{82} -10.4139 q^{83} +2.92785 q^{84} +0.833166 q^{85} +12.3526 q^{86} -8.60039 q^{87} +30.0506 q^{88} -13.7233 q^{89} -2.05644 q^{90} +1.67249 q^{91} +23.6959 q^{92} -10.1599 q^{93} +4.69811 q^{94} -6.16904 q^{95} +0.930203 q^{96} +8.39126 q^{97} +16.0140 q^{98} -5.81952 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9}+O(q^{10}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9} - 13 q^{10} - 23 q^{11} - 19 q^{12} - 18 q^{13} - 9 q^{14} - q^{15} + 21 q^{16} + 22 q^{17} + q^{18} - 30 q^{19} - 7 q^{20} + 15 q^{21} + 4 q^{22} - 3 q^{23} - 15 q^{24} + 19 q^{25} - 7 q^{26} - 22 q^{27} - 25 q^{28} - 7 q^{29} + 13 q^{30} - 10 q^{31} + 31 q^{32} + 23 q^{33} + q^{34} - 11 q^{35} + 19 q^{36} - q^{37} - 29 q^{38} + 18 q^{39} - 59 q^{40} + 9 q^{42} - 43 q^{43} - 80 q^{44} + q^{45} - 43 q^{46} + 2 q^{47} - 21 q^{48} + 43 q^{49} + 25 q^{50} - 22 q^{51} - 5 q^{52} - q^{53} - q^{54} - 19 q^{55} - 8 q^{56} + 30 q^{57} - 43 q^{58} - 28 q^{59} + 7 q^{60} - 29 q^{61} - 3 q^{62} - 15 q^{63} + 23 q^{64} + 19 q^{65} - 4 q^{66} - 16 q^{67} + 19 q^{68} + 3 q^{69} - 5 q^{70} - q^{71} + 15 q^{72} - 19 q^{73} - 24 q^{74} - 19 q^{75} - 72 q^{76} + 24 q^{77} + 7 q^{78} + 22 q^{79} - 82 q^{80} + 22 q^{81} - 81 q^{82} - 29 q^{83} + 25 q^{84} + q^{85} - 42 q^{86} + 7 q^{87} - 43 q^{88} - 28 q^{89} - 13 q^{90} - 96 q^{91} - 11 q^{92} + 10 q^{93} - 63 q^{94} - 23 q^{95} - 31 q^{96} - 51 q^{97} + 12 q^{98} - 23 q^{99}+O(q^{100}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9 - 13 * q^10 - 23 * q^11 - 19 * q^12 - 18 * q^13 - 9 * q^14 - q^15 + 21 * q^16 + 22 * q^17 + q^18 - 30 * q^19 - 7 * q^20 + 15 * q^21 + 4 * q^22 - 3 * q^23 - 15 * q^24 + 19 * q^25 - 7 * q^26 - 22 * q^27 - 25 * q^28 - 7 * q^29 + 13 * q^30 - 10 * q^31 + 31 * q^32 + 23 * q^33 + q^34 - 11 * q^35 + 19 * q^36 - q^37 - 29 * q^38 + 18 * q^39 - 59 * q^40 + 9 * q^42 - 43 * q^43 - 80 * q^44 + q^45 - 43 * q^46 + 2 * q^47 - 21 * q^48 + 43 * q^49 + 25 * q^50 - 22 * q^51 - 5 * q^52 - q^53 - q^54 - 19 * q^55 - 8 * q^56 + 30 * q^57 - 43 * q^58 - 28 * q^59 + 7 * q^60 - 29 * q^61 - 3 * q^62 - 15 * q^63 + 23 * q^64 + 19 * q^65 - 4 * q^66 - 16 * q^67 + 19 * q^68 + 3 * q^69 - 5 * q^70 - q^71 + 15 * q^72 - 19 * q^73 - 24 * q^74 - 19 * q^75 - 72 * q^76 + 24 * q^77 + 7 * q^78 + 22 * q^79 - 82 * q^80 + 22 * q^81 - 81 * q^82 - 29 * q^83 + 25 * q^84 + q^85 - 42 * q^86 + 7 * q^87 - 43 * q^88 - 28 * q^89 - 13 * q^90 - 96 * q^91 - 11 * q^92 + 10 * q^93 - 63 * q^94 - 23 * q^95 - 31 * q^96 - 51 * q^97 + 12 * q^98 - 23 * q^99

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