LMFDB - Embedded newform 4029.2.a.l.1.19

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			1.19
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)

$f(q)$	$=$	$q+0.437930 q^{2} -1.00000 q^{3} -1.80822 q^{4} -1.50297 q^{5} -0.437930 q^{6} -4.33772 q^{7} -1.66773 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.437930 q^{2} -1.00000 q^{3} -1.80822 q^{4} -1.50297 q^{5} -0.437930 q^{6} -4.33772 q^{7} -1.66773 q^{8} +1.00000 q^{9} -0.658196 q^{10} +3.26197 q^{11} +1.80822 q^{12} -1.64522 q^{13} -1.89962 q^{14} +1.50297 q^{15} +2.88608 q^{16} -1.00000 q^{17} +0.437930 q^{18} -5.97637 q^{19} +2.71770 q^{20} +4.33772 q^{21} +1.42851 q^{22} -5.62341 q^{23} +1.66773 q^{24} -2.74108 q^{25} -0.720490 q^{26} -1.00000 q^{27} +7.84354 q^{28} -9.77865 q^{29} +0.658196 q^{30} -9.36283 q^{31} +4.59937 q^{32} -3.26197 q^{33} -0.437930 q^{34} +6.51947 q^{35} -1.80822 q^{36} -4.38216 q^{37} -2.61723 q^{38} +1.64522 q^{39} +2.50655 q^{40} -1.29358 q^{41} +1.89962 q^{42} -3.12682 q^{43} -5.89834 q^{44} -1.50297 q^{45} -2.46266 q^{46} -3.57872 q^{47} -2.88608 q^{48} +11.8158 q^{49} -1.20040 q^{50} +1.00000 q^{51} +2.97491 q^{52} -1.24099 q^{53} -0.437930 q^{54} -4.90264 q^{55} +7.23416 q^{56} +5.97637 q^{57} -4.28236 q^{58} +12.9970 q^{59} -2.71770 q^{60} -4.49618 q^{61} -4.10027 q^{62} -4.33772 q^{63} -3.75797 q^{64} +2.47271 q^{65} -1.42851 q^{66} -8.36592 q^{67} +1.80822 q^{68} +5.62341 q^{69} +2.85507 q^{70} +2.73938 q^{71} -1.66773 q^{72} -15.4337 q^{73} -1.91908 q^{74} +2.74108 q^{75} +10.8066 q^{76} -14.1495 q^{77} +0.720490 q^{78} +1.00000 q^{79} -4.33770 q^{80} +1.00000 q^{81} -0.566495 q^{82} +2.32456 q^{83} -7.84354 q^{84} +1.50297 q^{85} -1.36933 q^{86} +9.77865 q^{87} -5.44009 q^{88} +1.70984 q^{89} -0.658196 q^{90} +7.13650 q^{91} +10.1683 q^{92} +9.36283 q^{93} -1.56723 q^{94} +8.98231 q^{95} -4.59937 q^{96} +1.17467 q^{97} +5.17450 q^{98} +3.26197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.437930	0.309663	0.154832	−	0.987941i	$-0.450516\pi$
$2$	0.437930	0.309663	0.154832	+	0.987941i	$0.450516\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.80822	−0.904109
$5$	−1.50297	−0.672149	−0.336074	−	0.941835i	$-0.609099\pi$
$5$	−1.50297	−0.672149	−0.336074	+	0.941835i	$0.609099\pi$
$6$	−0.437930	−0.178784
$7$	−4.33772	−1.63950	−0.819752	−	0.572718i	$-0.805889\pi$
$7$	−4.33772	−1.63950	−0.819752	+	0.572718i	$0.805889\pi$
$8$	−1.66773	−0.589632
$9$	1.00000	0.333333
$10$	−0.658196	−0.208140
$11$	3.26197	0.983520	0.491760	−	0.870731i	$-0.336354\pi$
$11$	3.26197	0.983520	0.491760	+	0.870731i	$0.336354\pi$
$12$	1.80822	0.521987
$13$	−1.64522	−0.456301	−0.228151	−	0.973626i	$-0.573268\pi$
$13$	−1.64522	−0.456301	−0.228151	+	0.973626i	$0.573268\pi$
$14$	−1.89962	−0.507694
$15$	1.50297	0.388065
$16$	2.88608	0.721521
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.437930	0.103221
$19$	−5.97637	−1.37107	−0.685537	−	0.728038i	$-0.740432\pi$
$19$	−5.97637	−1.37107	−0.685537	+	0.728038i	$0.740432\pi$
$20$	2.71770	0.607696
$21$	4.33772	0.946568
$22$	1.42851	0.304560
$23$	−5.62341	−1.17256	−0.586281	−	0.810108i	$-0.699408\pi$
$23$	−5.62341	−1.17256	−0.586281	+	0.810108i	$0.699408\pi$
$24$	1.66773	0.340424
$25$	−2.74108	−0.548216
$26$	−0.720490	−0.141300
$27$	−1.00000	−0.192450
$28$	7.84354	1.48229
$29$	−9.77865	−1.81585	−0.907925	−	0.419133i	$-0.862334\pi$
$29$	−9.77865	−1.81585	−0.907925	+	0.419133i	$0.862334\pi$
$30$	0.658196	0.120170
$31$	−9.36283	−1.68161	−0.840807	−	0.541335i	$-0.817919\pi$
$31$	−9.36283	−1.68161	−0.840807	+	0.541335i	$0.817919\pi$
$32$	4.59937	0.813061
$33$	−3.26197	−0.567835
$34$	−0.437930	−0.0751044
$35$	6.51947	1.10199
$36$	−1.80822	−0.301370
$37$	−4.38216	−0.720422	−0.360211	−	0.932871i	$-0.617295\pi$
$37$	−4.38216	−0.720422	−0.360211	+	0.932871i	$0.617295\pi$
$38$	−2.61723	−0.424571
$39$	1.64522	0.263446
$40$	2.50655	0.396321
$41$	−1.29358	−0.202022	−0.101011	−	0.994885i	$-0.532208\pi$
$41$	−1.29358	−0.202022	−0.101011	+	0.994885i	$0.532208\pi$
$42$	1.89962	0.293117
$43$	−3.12682	−0.476836	−0.238418	−	0.971163i	$-0.576629\pi$
$43$	−3.12682	−0.476836	−0.238418	+	0.971163i	$0.576629\pi$
$44$	−5.89834	−0.889209
$45$	−1.50297	−0.224050
$46$	−2.46266	−0.363099
$47$	−3.57872	−0.522011	−0.261005	−	0.965337i	$-0.584054\pi$
$47$	−3.57872	−0.522011	−0.261005	+	0.965337i	$0.584054\pi$
$48$	−2.88608	−0.416570
$49$	11.8158	1.68797
$50$	−1.20040	−0.169762
$51$	1.00000	0.140028
$52$	2.97491	0.412546
$53$	−1.24099	−0.170464	−0.0852319	−	0.996361i	$-0.527163\pi$
$53$	−1.24099	−0.170464	−0.0852319	+	0.996361i	$0.527163\pi$
$54$	−0.437930	−0.0595947
$55$	−4.90264	−0.661072
$56$	7.23416	0.966705
$57$	5.97637	0.791589
$58$	−4.28236	−0.562302
$59$	12.9970	1.69206	0.846030	−	0.533136i	$-0.178987\pi$
$59$	12.9970	1.69206	0.846030	+	0.533136i	$0.178987\pi$
$60$	−2.71770	−0.350853
$61$	−4.49618	−0.575677	−0.287838	−	0.957679i	$-0.592937\pi$
$61$	−4.49618	−0.575677	−0.287838	+	0.957679i	$0.592937\pi$
$62$	−4.10027	−0.520734
$63$	−4.33772	−0.546501
$64$	−3.75797	−0.469746
$65$	2.47271	0.306702
$66$	−1.42851	−0.175838
$67$	−8.36592	−1.02206	−0.511030	−	0.859563i	$-0.670736\pi$
$67$	−8.36592	−1.02206	−0.511030	+	0.859563i	$0.670736\pi$
$68$	1.80822	0.219279
$69$	5.62341	0.676978
$70$	2.85507	0.341246
$71$	2.73938	0.325105	0.162552	−	0.986700i	$-0.448027\pi$
$71$	2.73938	0.325105	0.162552	+	0.986700i	$0.448027\pi$
$72$	−1.66773	−0.196544
$73$	−15.4337	−1.80638	−0.903189	−	0.429242i	$-0.858781\pi$
$73$	−15.4337	−1.80638	−0.903189	+	0.429242i	$0.858781\pi$
$74$	−1.91908	−0.223088
$75$	2.74108	0.316513
$76$	10.8066	1.23960
$77$	−14.1495	−1.61248
$78$	0.720490	0.0815795
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−4.33770	−0.484970
$81$	1.00000	0.111111
$82$	−0.566495	−0.0625589
$83$	2.32456	0.255153	0.127577	−	0.991829i	$-0.459280\pi$
$83$	2.32456	0.255153	0.127577	+	0.991829i	$0.459280\pi$
$84$	−7.84354	−0.855801
$85$	1.50297	0.163020
$86$	−1.36933	−0.147659
$87$	9.77865	1.04838
$88$	−5.44009	−0.579915
$89$	1.70984	0.181242	0.0906211	−	0.995885i	$-0.471115\pi$
$89$	1.70984	0.181242	0.0906211	+	0.995885i	$0.471115\pi$
$90$	−0.658196	−0.0693799
$91$	7.13650	0.748108
$92$	10.1683	1.06012
$93$	9.36283	0.970881
$94$	−1.56723	−0.161647
$95$	8.98231	0.921565
$96$	−4.59937	−0.469421
$97$	1.17467	0.119270	0.0596350	−	0.998220i	$-0.481006\pi$
$97$	1.17467	0.119270	0.0596350	+	0.998220i	$0.481006\pi$
$98$	5.17450	0.522704
$99$	3.26197	0.327840
$100$	4.95647	0.495647
$101$	9.86589	0.981693	0.490846	−	0.871246i	$-0.336688\pi$
$101$	9.86589	0.981693	0.490846	+	0.871246i	$0.336688\pi$
$102$	0.437930	0.0433615
$103$	−1.75170	−0.172600	−0.0863000	−	0.996269i	$-0.527504\pi$
$103$	−1.75170	−0.172600	−0.0863000	+	0.996269i	$0.527504\pi$
$104$	2.74378	0.269050
$105$	−6.51947	−0.636235
$106$	−0.543469	−0.0527864
$107$	8.03891	0.777151	0.388576	−	0.921417i	$-0.372967\pi$
$107$	8.03891	0.777151	0.388576	+	0.921417i	$0.372967\pi$
$108$	1.80822	0.173996
$109$	−6.17934	−0.591873	−0.295937	−	0.955208i	$-0.595632\pi$
$109$	−6.17934	−0.591873	−0.295937	+	0.955208i	$0.595632\pi$
$110$	−2.14701	−0.204710
$111$	4.38216	0.415936
$112$	−12.5190	−1.18294
$113$	4.11575	0.387177	0.193588	−	0.981083i	$-0.437987\pi$
$113$	4.11575	0.387177	0.193588	+	0.981083i	$0.437987\pi$
$114$	2.61723	0.245126
$115$	8.45181	0.788135
$116$	17.6819	1.64173
$117$	−1.64522	−0.152100
$118$	5.69176	0.523969
$119$	4.33772	0.397638
$120$	−2.50655	−0.228816
$121$	−0.359578	−0.0326889
$122$	−1.96901	−0.178266
$123$	1.29358	0.116638
$124$	16.9300	1.52036
$125$	11.6346	1.04063
$126$	−1.89962	−0.169231
$127$	18.6911	1.65857	0.829285	−	0.558826i	$-0.188748\pi$
$127$	18.6911	1.65857	0.829285	+	0.558826i	$0.188748\pi$
$128$	−10.8445	−0.958524
$129$	3.12682	0.275301
$130$	1.08288	0.0949745
$131$	0.435527	0.0380522	0.0190261	−	0.999819i	$-0.493943\pi$
$131$	0.435527	0.0380522	0.0190261	+	0.999819i	$0.493943\pi$
$132$	5.89834	0.513385
$133$	25.9238	2.24788
$134$	−3.66369	−0.316494
$135$	1.50297	0.129355
$136$	1.66773	0.143007
$137$	−2.12012	−0.181134	−0.0905669	−	0.995890i	$-0.528868\pi$
$137$	−2.12012	−0.181134	−0.0905669	+	0.995890i	$0.528868\pi$
$138$	2.46266	0.209635
$139$	−6.71447	−0.569514	−0.284757	−	0.958600i	$-0.591913\pi$
$139$	−6.71447	−0.569514	−0.284757	+	0.958600i	$0.591913\pi$
$140$	−11.7886	−0.996320
$141$	3.57872	0.301383
$142$	1.19966	0.100673
$143$	−5.36665	−0.448781
$144$	2.88608	0.240507
$145$	14.6970	1.22052
$146$	−6.75888	−0.559369
$147$	−11.8158	−0.974553
$148$	7.92389	0.651340
$149$	−12.9832	−1.06363	−0.531814	−	0.846861i	$-0.678489\pi$
$149$	−12.9832	−1.06363	−0.531814	+	0.846861i	$0.678489\pi$
$150$	1.20040	0.0980123
$151$	16.6997	1.35901	0.679503	−	0.733673i	$-0.262195\pi$
$151$	16.6997	1.35901	0.679503	+	0.733673i	$0.262195\pi$
$152$	9.96699	0.808429
$153$	−1.00000	−0.0808452
$154$	−6.19649	−0.499327
$155$	14.0721	1.13030
$156$	−2.97491	−0.238184
$157$	0.833868	0.0665499	0.0332749	−	0.999446i	$-0.489406\pi$
$157$	0.833868	0.0665499	0.0332749	+	0.999446i	$0.489406\pi$
$158$	0.437930	0.0348398
$159$	1.24099	0.0984173
$160$	−6.91271	−0.546498
$161$	24.3928	1.92242
$162$	0.437930	0.0344070
$163$	−14.3333	−1.12267	−0.561336	−	0.827588i	$-0.689712\pi$
$163$	−14.3333	−1.12267	−0.561336	+	0.827588i	$0.689712\pi$
$164$	2.33906	0.182650
$165$	4.90264	0.381670
$166$	1.01799	0.0790116
$167$	6.31714	0.488835	0.244418	−	0.969670i	$-0.421403\pi$
$167$	6.31714	0.488835	0.244418	+	0.969670i	$0.421403\pi$
$168$	−7.23416	−0.558127
$169$	−10.2933	−0.791789
$170$	0.658196	0.0504813
$171$	−5.97637	−0.457024
$172$	5.65398	0.431112
$173$	7.06072	0.536816	0.268408	−	0.963305i	$-0.413502\pi$
$173$	7.06072	0.536816	0.268408	+	0.963305i	$0.413502\pi$
$174$	4.28236	0.324645
$175$	11.8900	0.898803
$176$	9.41431	0.709630
$177$	−12.9970	−0.976911
$178$	0.748788	0.0561241
$179$	−8.51845	−0.636699	−0.318350	−	0.947973i	$-0.603129\pi$
$179$	−8.51845	−0.636699	−0.318350	+	0.947973i	$0.603129\pi$
$180$	2.71770	0.202565
$181$	14.1809	1.05406	0.527028	−	0.849848i	$-0.323306\pi$
$181$	14.1809	1.05406	0.527028	+	0.849848i	$0.323306\pi$
$182$	3.12529	0.231662
$183$	4.49618	0.332367
$184$	9.37834	0.691380
$185$	6.58625	0.484231
$186$	4.10027	0.300646
$187$	−3.26197	−0.238539
$188$	6.47111	0.471954
$189$	4.33772	0.315523
$190$	3.93362	0.285375
$191$	−8.16727	−0.590963	−0.295481	−	0.955348i	$-0.595480\pi$
$191$	−8.16727	−0.590963	−0.295481	+	0.955348i	$0.595480\pi$
$192$	3.75797	0.271208
$193$	−11.3104	−0.814138	−0.407069	−	0.913397i	$-0.633449\pi$
$193$	−11.3104	−0.814138	−0.407069	+	0.913397i	$0.633449\pi$
$194$	0.514425	0.0369335
$195$	−2.47271	−0.177075
$196$	−21.3656	−1.52611
$197$	−18.4207	−1.31242	−0.656210	−	0.754578i	$-0.727842\pi$
$197$	−18.4207	−1.31242	−0.656210	+	0.754578i	$0.727842\pi$
$198$	1.42851	0.101520
$199$	14.4105	1.02153	0.510767	−	0.859719i	$-0.329362\pi$
$199$	14.4105	1.02153	0.510767	+	0.859719i	$0.329362\pi$
$200$	4.57139	0.323246
$201$	8.36592	0.590087
$202$	4.32057	0.303994
$203$	42.4170	2.97709
$204$	−1.80822	−0.126601
$205$	1.94420	0.135789
$206$	−0.767121	−0.0534479
$207$	−5.62341	−0.390854
$208$	−4.74824	−0.329231
$209$	−19.4947	−1.34848
$210$	−2.85507	−0.197019
$211$	−4.16963	−0.287049	−0.143525	−	0.989647i	$-0.545844\pi$
$211$	−4.16963	−0.287049	−0.143525	+	0.989647i	$0.545844\pi$
$212$	2.24399	0.154118
$213$	−2.73938	−0.187699
$214$	3.52048	0.240655
$215$	4.69952	0.320505
$216$	1.66773	0.113475
$217$	40.6134	2.75701
$218$	−2.70612	−0.183281
$219$	15.4337	1.04291
$220$	8.86504	0.597681
$221$	1.64522	0.110669
$222$	1.91908	0.128800
$223$	−12.0628	−0.807785	−0.403892	−	0.914806i	$-0.632343\pi$
$223$	−12.0628	−0.807785	−0.403892	+	0.914806i	$0.632343\pi$
$224$	−19.9508	−1.33302
$225$	−2.74108	−0.182739
$226$	1.80241	0.119894
$227$	25.4171	1.68699	0.843495	−	0.537138i	$-0.180494\pi$
$227$	25.4171	1.68699	0.843495	+	0.537138i	$0.180494\pi$
$228$	−10.8066	−0.715683
$229$	−11.6866	−0.772270	−0.386135	−	0.922442i	$-0.626190\pi$
$229$	−11.6866	−0.772270	−0.386135	+	0.922442i	$0.626190\pi$
$230$	3.70130	0.244057
$231$	14.1495	0.930969
$232$	16.3082	1.07068
$233$	−1.16569	−0.0763670	−0.0381835	−	0.999271i	$-0.512157\pi$
$233$	−1.16569	−0.0763670	−0.0381835	+	0.999271i	$0.512157\pi$
$234$	−0.720490	−0.0470999
$235$	5.37872	0.350869
$236$	−23.5013	−1.52981
$237$	−1.00000	−0.0649570
$238$	1.89962	0.123134
$239$	11.1389	0.720517	0.360259	−	0.932853i	$-0.382688\pi$
$239$	11.1389	0.720517	0.360259	+	0.932853i	$0.382688\pi$
$240$	4.33770	0.279997
$241$	0.100901	0.00649959	0.00324980	−	0.999995i	$-0.498966\pi$
$241$	0.100901	0.00649959	0.00324980	+	0.999995i	$0.498966\pi$
$242$	−0.157470	−0.0101225
$243$	−1.00000	−0.0641500
$244$	8.13007	0.520474
$245$	−17.7588	−1.13457
$246$	0.566495	0.0361184
$247$	9.83243	0.625623
$248$	15.6147	0.991535
$249$	−2.32456	−0.147313
$250$	5.09515	0.322245
$251$	−12.5737	−0.793643	−0.396821	−	0.917896i	$-0.629887\pi$
$251$	−12.5737	−0.793643	−0.396821	+	0.917896i	$0.629887\pi$
$252$	7.84354	0.494097
$253$	−18.3434	−1.15324
$254$	8.18541	0.513598
$255$	−1.50297	−0.0941197
$256$	2.76682	0.172926
$257$	−23.0907	−1.44036	−0.720179	−	0.693788i	$-0.755941\pi$
$257$	−23.0907	−1.44036	−0.720179	+	0.693788i	$0.755941\pi$
$258$	1.36933	0.0852507
$259$	19.0086	1.18114
$260$	−4.47120	−0.277292
$261$	−9.77865	−0.605283
$262$	0.190730	0.0117834
$263$	−24.4508	−1.50770	−0.753851	−	0.657045i	$-0.771806\pi$
$263$	−24.4508	−1.50770	−0.753851	+	0.657045i	$0.771806\pi$
$264$	5.44009	0.334814
$265$	1.86518	0.114577
$266$	11.3528	0.696086
$267$	−1.70984	−0.104640
$268$	15.1274	0.924054
$269$	−23.7625	−1.44882	−0.724412	−	0.689368i	$-0.757888\pi$
$269$	−23.7625	−1.44882	−0.724412	+	0.689368i	$0.757888\pi$
$270$	0.658196	0.0400565
$271$	−0.000261783 0	−1.59022e−5 0	−7.95110e−6	−	1.00000i	$-0.500003\pi$
$271$	−0.000261783 0	−1.59022e−5 0	−7.95110e−6		1.00000i	$0.500003\pi$
$272$	−2.88608	−0.174995
$273$	−7.13650	−0.431920
$274$	−0.928463	−0.0560905
$275$	−8.94131	−0.539181
$276$	−10.1683	−0.612062
$277$	−1.16032	−0.0697168	−0.0348584	−	0.999392i	$-0.511098\pi$
$277$	−1.16032	−0.0697168	−0.0348584	+	0.999392i	$0.511098\pi$
$278$	−2.94047	−0.176358
$279$	−9.36283	−0.560538
$280$	−10.8727	−0.649770
$281$	12.5464	0.748454	0.374227	−	0.927337i	$-0.377908\pi$
$281$	12.5464	0.748454	0.374227	+	0.927337i	$0.377908\pi$
$282$	1.56723	0.0933272
$283$	−6.68518	−0.397393	−0.198696	−	0.980061i	$-0.563671\pi$
$283$	−6.68518	−0.397393	−0.198696	+	0.980061i	$0.563671\pi$
$284$	−4.95339	−0.293930
$285$	−8.98231	−0.532066
$286$	−2.35021	−0.138971
$287$	5.61117	0.331217
$288$	4.59937	0.271020
$289$	1.00000	0.0588235
$290$	6.43626	0.377950
$291$	−1.17467	−0.0688606
$292$	27.9075	1.63316
$293$	−27.7696	−1.62231	−0.811157	−	0.584828i	$-0.801162\pi$
$293$	−27.7696	−1.62231	−0.811157	+	0.584828i	$0.801162\pi$
$294$	−5.17450	−0.301783
$295$	−19.5340	−1.13732
$296$	7.30826	0.424784
$297$	−3.26197	−0.189278
$298$	−5.68575	−0.329366
$299$	9.25173	0.535041
$300$	−4.95647	−0.286162
$301$	13.5633	0.781775
$302$	7.31332	0.420834
$303$	−9.86589	−0.566781
$304$	−17.2483	−0.989258
$305$	6.75762	0.386940
$306$	−0.437930	−0.0250348
$307$	−22.2905	−1.27219	−0.636094	−	0.771611i	$-0.719451\pi$
$307$	−22.2905	−1.27219	−0.636094	+	0.771611i	$0.719451\pi$
$308$	25.5854	1.45786
$309$	1.75170	0.0996507
$310$	6.16258	0.350011
$311$	14.5941	0.827558	0.413779	−	0.910377i	$-0.364209\pi$
$311$	14.5941	0.827558	0.413779	+	0.910377i	$0.364209\pi$
$312$	−2.74378	−0.155336
$313$	26.0956	1.47501	0.737505	−	0.675341i	$-0.236004\pi$
$313$	26.0956	1.47501	0.737505	+	0.675341i	$0.236004\pi$
$314$	0.365176	0.0206081
$315$	6.51947	0.367330
$316$	−1.80822	−0.101720
$317$	−24.8218	−1.39413	−0.697065	−	0.717008i	$-0.745511\pi$
$317$	−24.8218	−1.39413	−0.697065	+	0.717008i	$0.745511\pi$
$318$	0.543469	0.0304762
$319$	−31.8976	−1.78592
$320$	5.64811	0.315739
$321$	−8.03891	−0.448688
$322$	10.6823	0.595303
$323$	5.97637	0.332534
$324$	−1.80822	−0.100457
$325$	4.50967	0.250152
$326$	−6.27698	−0.347650
$327$	6.17934	0.341718
$328$	2.15734	0.119119
$329$	15.5235	0.855839
$330$	2.14701	0.118189
$331$	21.1658	1.16338	0.581688	−	0.813412i	$-0.302393\pi$
$331$	21.1658	1.16338	0.581688	+	0.813412i	$0.302393\pi$
$332$	−4.20330	−0.230686
$333$	−4.38216	−0.240141
$334$	2.76647	0.151374
$335$	12.5737	0.686977
$336$	12.5190	0.682969
$337$	18.0523	0.983369	0.491684	−	0.870773i	$-0.336381\pi$
$337$	18.0523	0.983369	0.491684	+	0.870773i	$0.336381\pi$
$338$	−4.50773	−0.245188
$339$	−4.11575	−0.223537
$340$	−2.71770	−0.147388
$341$	−30.5412	−1.65390
$342$	−2.61723	−0.141524
$343$	−20.8897	−1.12794
$344$	5.21470	0.281158
$345$	−8.45181	−0.455030
$346$	3.09210	0.166232
$347$	−6.55557	−0.351922	−0.175961	−	0.984397i	$-0.556303\pi$
$347$	−6.55557	−0.351922	−0.175961	+	0.984397i	$0.556303\pi$
$348$	−17.6819	−0.947850
$349$	−0.809831	−0.0433493	−0.0216746	−	0.999765i	$-0.506900\pi$
$349$	−0.809831	−0.0433493	−0.0216746	+	0.999765i	$0.506900\pi$
$350$	5.20701	0.278326
$351$	1.64522	0.0878152
$352$	15.0030	0.799662
$353$	16.7760	0.892894	0.446447	−	0.894810i	$-0.352689\pi$
$353$	16.7760	0.892894	0.446447	+	0.894810i	$0.352689\pi$
$354$	−5.69176	−0.302513
$355$	−4.11721	−0.218519
$356$	−3.09175	−0.163863
$357$	−4.33772	−0.229577
$358$	−3.73049	−0.197162
$359$	−0.886341	−0.0467793	−0.0233896	−	0.999726i	$-0.507446\pi$
$359$	−0.886341	−0.0467793	−0.0233896	+	0.999726i	$0.507446\pi$
$360$	2.50655	0.132107
$361$	16.7170	0.879842
$362$	6.21023	0.326403
$363$	0.359578	0.0188729
$364$	−12.9043	−0.676371
$365$	23.1964	1.21416
$366$	1.96901	0.102922
$367$	−1.57783	−0.0823620	−0.0411810	−	0.999152i	$-0.513112\pi$
$367$	−1.57783	−0.0823620	−0.0411810	+	0.999152i	$0.513112\pi$
$368$	−16.2296	−0.846028
$369$	−1.29358	−0.0673408
$370$	2.88432	0.149948
$371$	5.38309	0.279476
$372$	−16.9300	−0.877782
$373$	−25.0838	−1.29879	−0.649394	−	0.760452i	$-0.724978\pi$
$373$	−25.0838	−1.29879	−0.649394	+	0.760452i	$0.724978\pi$
$374$	−1.42851	−0.0738666
$375$	−11.6346	−0.600809
$376$	5.96835	0.307794
$377$	16.0880	0.828575
$378$	1.89962	0.0977058
$379$	−33.7423	−1.73322	−0.866612	−	0.498983i	$-0.833707\pi$
$379$	−33.7423	−1.73322	−0.866612	+	0.498983i	$0.833707\pi$
$380$	−16.2420	−0.833195
$381$	−18.6911	−0.957576
$382$	−3.57669	−0.183000
$383$	−20.4661	−1.04577	−0.522885	−	0.852403i	$-0.675144\pi$
$383$	−20.4661	−1.04577	−0.522885	+	0.852403i	$0.675144\pi$
$384$	10.8445	0.553404
$385$	21.2663	1.08383
$386$	−4.95315	−0.252109
$387$	−3.12682	−0.158945
$388$	−2.12407	−0.107833
$389$	13.8163	0.700514	0.350257	−	0.936654i	$-0.386094\pi$
$389$	13.8163	0.700514	0.350257	+	0.936654i	$0.386094\pi$
$390$	−1.08288	−0.0548335
$391$	5.62341	0.284388
$392$	−19.7056	−0.995285
$393$	−0.435527	−0.0219694
$394$	−8.06697	−0.406408
$395$	−1.50297	−0.0756226
$396$	−5.89834	−0.296403
$397$	25.9013	1.29995	0.649974	−	0.759956i	$-0.274780\pi$
$397$	25.9013	1.29995	0.649974	+	0.759956i	$0.274780\pi$
$398$	6.31079	0.316331
$399$	−25.9238	−1.29781
$400$	−7.91099	−0.395549
$401$	−6.54455	−0.326819	−0.163410	−	0.986558i	$-0.552249\pi$
$401$	−6.54455	−0.326819	−0.163410	+	0.986558i	$0.552249\pi$
$402$	3.66369	0.182728
$403$	15.4039	0.767323
$404$	−17.8397	−0.887557
$405$	−1.50297	−0.0746832
$406$	18.5757	0.921896
$407$	−14.2944	−0.708549
$408$	−1.66773	−0.0825651
$409$	26.4569	1.30821	0.654104	−	0.756405i	$-0.273046\pi$
$409$	26.4569	1.30821	0.654104	+	0.756405i	$0.273046\pi$
$410$	0.851426	0.0420489
$411$	2.12012	0.104578
$412$	3.16745	0.156049
$413$	−56.3772	−2.77414
$414$	−2.46266	−0.121033
$415$	−3.49374	−0.171501
$416$	−7.56696	−0.371001
$417$	6.71447	0.328809
$418$	−8.53732	−0.417574
$419$	15.6430	0.764212	0.382106	−	0.924118i	$-0.375199\pi$
$419$	15.6430	0.764212	0.382106	+	0.924118i	$0.375199\pi$
$420$	11.7886	0.575225
$421$	−0.461461	−0.0224902	−0.0112451	−	0.999937i	$-0.503580\pi$
$421$	−0.461461	−0.0224902	−0.0112451	+	0.999937i	$0.503580\pi$
$422$	−1.82601	−0.0888886
$423$	−3.57872	−0.174004
$424$	2.06965	0.100511
$425$	2.74108	0.132962
$426$	−1.19966	−0.0581235
$427$	19.5032	0.943825
$428$	−14.5361	−0.702629
$429$	5.36665	0.259104
$430$	2.05806	0.0992485
$431$	−40.4790	−1.94981	−0.974903	−	0.222629i	$-0.928536\pi$
$431$	−40.4790	−1.94981	−0.974903	+	0.222629i	$0.928536\pi$
$432$	−2.88608	−0.138857
$433$	−26.2372	−1.26088	−0.630439	−	0.776238i	$-0.717125\pi$
$433$	−26.2372	−1.26088	−0.630439	+	0.776238i	$0.717125\pi$
$434$	17.7858	0.853746
$435$	−14.6970	−0.704668
$436$	11.1736	0.535118
$437$	33.6075	1.60767
$438$	6.75888	0.322952
$439$	16.4759	0.786350	0.393175	−	0.919464i	$-0.371377\pi$
$439$	16.4759	0.786350	0.393175	+	0.919464i	$0.371377\pi$
$440$	8.17629	0.389789
$441$	11.8158	0.562658
$442$	0.720490	0.0342702
$443$	18.5159	0.879719	0.439859	−	0.898067i	$-0.355028\pi$
$443$	18.5159	0.879719	0.439859	+	0.898067i	$0.355028\pi$
$444$	−7.92389	−0.376051
$445$	−2.56983	−0.121822
$446$	−5.28266	−0.250141
$447$	12.9832	0.614086
$448$	16.3010	0.770151
$449$	−33.5917	−1.58529	−0.792646	−	0.609682i	$-0.791297\pi$
$449$	−33.5917	−1.58529	−0.792646	+	0.609682i	$0.791297\pi$
$450$	−1.20040	−0.0565875
$451$	−4.21960	−0.198693
$452$	−7.44216	−0.350050
$453$	−16.6997	−0.784622
$454$	11.1309	0.522399
$455$	−10.7259	−0.502840
$456$	−9.96699	−0.466747
$457$	27.8456	1.30256	0.651282	−	0.758836i	$-0.274232\pi$
$457$	27.8456	1.30256	0.651282	+	0.758836i	$0.274232\pi$
$458$	−5.11790	−0.239144
$459$	1.00000	0.0466760
$460$	−15.2827	−0.712560
$461$	2.59011	0.120633	0.0603166	−	0.998179i	$-0.480789\pi$
$461$	2.59011	0.120633	0.0603166	+	0.998179i	$0.480789\pi$
$462$	6.19649	0.288287
$463$	−24.1873	−1.12408	−0.562040	−	0.827110i	$-0.689983\pi$
$463$	−24.1873	−1.12408	−0.562040	+	0.827110i	$0.689983\pi$
$464$	−28.2220	−1.31017
$465$	−14.0721	−0.652576
$466$	−0.510491	−0.0236480
$467$	38.6618	1.78905	0.894526	−	0.447015i	$-0.147513\pi$
$467$	38.6618	1.78905	0.894526	+	0.447015i	$0.147513\pi$
$468$	2.97491	0.137515
$469$	36.2890	1.67567
$470$	2.35550	0.108651
$471$	−0.833868	−0.0384226
$472$	−21.6754	−0.997693
$473$	−10.1996	−0.468978
$474$	−0.437930	−0.0201148
$475$	16.3817	0.751644
$476$	−7.84354	−0.359508
$477$	−1.24099	−0.0568212
$478$	4.87807	0.223118
$479$	−16.3504	−0.747069	−0.373535	−	0.927616i	$-0.621854\pi$
$479$	−16.3504	−0.747069	−0.373535	+	0.927616i	$0.621854\pi$
$480$	6.91271	0.315521
$481$	7.20960	0.328730
$482$	0.0441875	0.00201269
$483$	−24.3928	−1.10991
$484$	0.650195	0.0295543
$485$	−1.76550	−0.0801672
$486$	−0.437930	−0.0198649
$487$	9.18913	0.416399	0.208200	−	0.978086i	$-0.433240\pi$
$487$	9.18913	0.416399	0.208200	+	0.978086i	$0.433240\pi$
$488$	7.49842	0.339438
$489$	14.3333	0.648174
$490$	−7.77712	−0.351335
$491$	27.9077	1.25946	0.629729	−	0.776815i	$-0.283166\pi$
$491$	27.9077	1.25946	0.629729	+	0.776815i	$0.283166\pi$
$492$	−2.33906	−0.105453
$493$	9.77865	0.440408
$494$	4.30592	0.193732
$495$	−4.90264	−0.220357
$496$	−27.0219	−1.21332
$497$	−11.8827	−0.533010
$498$	−1.01799	−0.0456174
$499$	9.56301	0.428099	0.214049	−	0.976823i	$-0.431335\pi$
$499$	9.56301	0.428099	0.214049	+	0.976823i	$0.431335\pi$
$500$	−21.0379	−0.940844
$501$	−6.31714	−0.282229
$502$	−5.50638	−0.245762
$503$	−21.6535	−0.965484	−0.482742	−	0.875763i	$-0.660359\pi$
$503$	−21.6535	−0.965484	−0.482742	+	0.875763i	$0.660359\pi$
$504$	7.23416	0.322235
$505$	−14.8281	−0.659844
$506$	−8.03311	−0.357115
$507$	10.2933	0.457140
$508$	−33.7976	−1.49953
$509$	8.12136	0.359973	0.179987	−	0.983669i	$-0.442395\pi$
$509$	8.12136	0.359973	0.179987	+	0.983669i	$0.442395\pi$
$510$	−0.658196	−0.0291454
$511$	66.9471	2.96157
$512$	22.9006	1.01207
$513$	5.97637	0.263863
$514$	−10.1121	−0.446026
$515$	2.63275	0.116013
$516$	−5.65398	−0.248902
$517$	−11.6737	−0.513408
$518$	8.32442	0.365754
$519$	−7.06072	−0.309931
$520$	−4.12383	−0.180842
$521$	6.67701	0.292525	0.146263	−	0.989246i	$-0.453276\pi$
$521$	6.67701	0.292525	0.146263	+	0.989246i	$0.453276\pi$
$522$	−4.28236	−0.187434
$523$	12.5513	0.548829	0.274414	−	0.961612i	$-0.411516\pi$
$523$	12.5513	0.548829	0.274414	+	0.961612i	$0.411516\pi$
$524$	−0.787528	−0.0344033
$525$	−11.8900	−0.518924
$526$	−10.7078	−0.466880
$527$	9.36283	0.407851
$528$	−9.41431	−0.409705
$529$	8.62269	0.374899
$530$	0.816818	0.0354803
$531$	12.9970	0.564020
$532$	−46.8759	−2.03233
$533$	2.12821	0.0921831
$534$	−0.748788	−0.0324032
$535$	−12.0822	−0.522361
$536$	13.9521	0.602640
$537$	8.51845	0.367598
$538$	−10.4063	−0.448647
$539$	38.5428	1.66016
$540$	−2.71770	−0.116951
$541$	−25.1800	−1.08257	−0.541286	−	0.840838i	$-0.682062\pi$
$541$	−25.1800	−1.08257	−0.541286	+	0.840838i	$0.682062\pi$
$542$	−0.000114643 0	−4.92433e−6 0
$543$	−14.1809	−0.608560
$544$	−4.59937	−0.197196
$545$	9.28736	0.397827
$546$	−3.12529	−0.133750
$547$	32.8011	1.40247	0.701236	−	0.712929i	$-0.252632\pi$
$547$	32.8011	1.40247	0.701236	+	0.712929i	$0.252632\pi$
$548$	3.83363	0.163765
$549$	−4.49618	−0.191892
$550$	−3.91567	−0.166965
$551$	58.4408	2.48966
$552$	−9.37834	−0.399168
$553$	−4.33772	−0.184459
$554$	−0.508139	−0.0215887
$555$	−6.58625	−0.279571
$556$	12.1412	0.514903
$557$	−13.7616	−0.583097	−0.291548	−	0.956556i	$-0.594170\pi$
$557$	−13.7616	−0.583097	−0.291548	+	0.956556i	$0.594170\pi$
$558$	−4.10027	−0.173578
$559$	5.14431	0.217581
$560$	18.8157	0.795110
$561$	3.26197	0.137720
$562$	5.49443	0.231769
$563$	21.1445	0.891136	0.445568	−	0.895248i	$-0.353002\pi$
$563$	21.1445	0.891136	0.445568	+	0.895248i	$0.353002\pi$
$564$	−6.47111	−0.272483
$565$	−6.18584	−0.260240
$566$	−2.92764	−0.123058
$567$	−4.33772	−0.182167
$568$	−4.56855	−0.191692
$569$	−16.6952	−0.699901	−0.349950	−	0.936768i	$-0.613802\pi$
$569$	−16.6952	−0.699901	−0.349950	+	0.936768i	$0.613802\pi$
$570$	−3.93362	−0.164761
$571$	11.6810	0.488833	0.244417	−	0.969670i	$-0.421404\pi$
$571$	11.6810	0.488833	0.244417	+	0.969670i	$0.421404\pi$
$572$	9.70406	0.405747
$573$	8.16727	0.341193
$574$	2.45730	0.102566
$575$	15.4142	0.642817
$576$	−3.75797	−0.156582
$577$	−32.3742	−1.34776	−0.673878	−	0.738842i	$-0.735373\pi$
$577$	−32.3742	−1.34776	−0.673878	+	0.738842i	$0.735373\pi$
$578$	0.437930	0.0182155
$579$	11.3104	0.470043
$580$	−26.5754	−1.10348
$581$	−10.0833	−0.418325
$582$	−0.514425	−0.0213236
$583$	−4.04808	−0.167654
$584$	25.7393	1.06510
$585$	2.47271	0.102234
$586$	−12.1611	−0.502371
$587$	−3.67784	−0.151801	−0.0759003	−	0.997115i	$-0.524183\pi$
$587$	−3.67784	−0.151801	−0.0759003	+	0.997115i	$0.524183\pi$
$588$	21.3656	0.881101
$589$	55.9558	2.30562
$590$	−8.55454	−0.352185
$591$	18.4207	0.757726
$592$	−12.6473	−0.519800
$593$	34.5520	1.41888	0.709440	−	0.704766i	$-0.248948\pi$
$593$	34.5520	1.41888	0.709440	+	0.704766i	$0.248948\pi$
$594$	−1.42851	−0.0586126
$595$	−6.51947	−0.267272
$596$	23.4765	0.961635
$597$	−14.4105	−0.589782
$598$	4.05161	0.165683
$599$	30.9296	1.26375	0.631875	−	0.775071i	$-0.282286\pi$
$599$	30.9296	1.26375	0.631875	+	0.775071i	$0.282286\pi$
$600$	−4.57139	−0.186626
$601$	26.2993	1.07277	0.536385	−	0.843973i	$-0.319789\pi$
$601$	26.2993	1.07277	0.536385	+	0.843973i	$0.319789\pi$
$602$	5.93977	0.242087
$603$	−8.36592	−0.340687
$604$	−30.1968	−1.22869
$605$	0.540435	0.0219718
$606$	−4.32057	−0.175511
$607$	−38.6827	−1.57008	−0.785042	−	0.619442i	$-0.787359\pi$
$607$	−38.6827	−1.57008	−0.785042	+	0.619442i	$0.787359\pi$
$608$	−27.4875	−1.11477
$609$	−42.4170	−1.71883
$610$	2.95937	0.119821
$611$	5.88778	0.238194
$612$	1.80822	0.0730929
$613$	37.1429	1.50019	0.750094	−	0.661332i	$-0.230008\pi$
$613$	37.1429	1.50019	0.750094	+	0.661332i	$0.230008\pi$
$614$	−9.76170	−0.393950
$615$	−1.94420	−0.0783979
$616$	23.5976	0.950773
$617$	−12.1463	−0.488991	−0.244495	−	0.969650i	$-0.578622\pi$
$617$	−12.1463	−0.488991	−0.244495	+	0.969650i	$0.578622\pi$
$618$	0.767121	0.0308582
$619$	−14.3051	−0.574970	−0.287485	−	0.957785i	$-0.592819\pi$
$619$	−14.3051	−0.574970	−0.287485	+	0.957785i	$0.592819\pi$
$620$	−25.4453	−1.02191
$621$	5.62341	0.225659
$622$	6.39122	0.256264
$623$	−7.41679	−0.297147
$624$	4.74824	0.190082
$625$	−3.78108	−0.151243
$626$	11.4280	0.456757
$627$	19.4947	0.778544
$628$	−1.50781	−0.0601683
$629$	4.38216	0.174728
$630$	2.85507	0.113749
$631$	14.3547	0.571452	0.285726	−	0.958311i	$-0.407765\pi$
$631$	14.3547	0.571452	0.285726	+	0.958311i	$0.407765\pi$
$632$	−1.66773	−0.0663388
$633$	4.16963	0.165728
$634$	−10.8702	−0.431711
$635$	−28.0922	−1.11481
$636$	−2.24399	−0.0889799
$637$	−19.4396	−0.770225
$638$	−13.9689	−0.553035
$639$	2.73938	0.108368
$640$	16.2989	0.644271
$641$	−17.0613	−0.673882	−0.336941	−	0.941526i	$-0.609392\pi$
$641$	−17.0613	−0.673882	−0.336941	+	0.941526i	$0.609392\pi$
$642$	−3.52048	−0.138942
$643$	−30.4812	−1.20206	−0.601031	−	0.799226i	$-0.705243\pi$
$643$	−30.4812	−1.20206	−0.601031	+	0.799226i	$0.705243\pi$
$644$	−44.1074	−1.73808
$645$	−4.69952	−0.185044
$646$	2.61723	0.102974
$647$	−17.8193	−0.700550	−0.350275	−	0.936647i	$-0.613912\pi$
$647$	−17.8193	−0.700550	−0.350275	+	0.936647i	$0.613912\pi$
$648$	−1.66773	−0.0655147
$649$	42.3956	1.66417
$650$	1.97492	0.0774628
$651$	−40.6134	−1.59176
$652$	25.9177	1.01502
$653$	−27.5261	−1.07718	−0.538589	−	0.842569i	$-0.681042\pi$
$653$	−27.5261	−1.07718	−0.538589	+	0.842569i	$0.681042\pi$
$654$	2.70612	0.105818
$655$	−0.654585	−0.0255767
$656$	−3.73337	−0.145763
$657$	−15.4337	−0.602126
$658$	6.79821	0.265022
$659$	−13.3927	−0.521707	−0.260853	−	0.965378i	$-0.584004\pi$
$659$	−13.3927	−0.521707	−0.260853	+	0.965378i	$0.584004\pi$
$660$	−8.86504	−0.345071
$661$	−19.3318	−0.751919	−0.375960	−	0.926636i	$-0.622687\pi$
$661$	−19.3318	−0.751919	−0.375960	+	0.926636i	$0.622687\pi$
$662$	9.26912	0.360255
$663$	−1.64522	−0.0638950
$664$	−3.87674	−0.150447
$665$	−38.9627	−1.51091
$666$	−1.91908	−0.0743627
$667$	54.9893	2.12919
$668$	−11.4228	−0.441960
$669$	12.0628	0.466375
$670$	5.50642	0.212731
$671$	−14.6664	−0.566190
$672$	19.9508	0.769618
$673$	−43.0773	−1.66051	−0.830254	−	0.557386i	$-0.811804\pi$
$673$	−43.0773	−1.66051	−0.830254	+	0.557386i	$0.811804\pi$
$674$	7.90562	0.304513
$675$	2.74108	0.105504
$676$	18.6124	0.715863
$677$	−43.7804	−1.68262	−0.841309	−	0.540554i	$-0.818215\pi$
$677$	−43.7804	−1.68262	−0.841309	+	0.540554i	$0.818215\pi$
$678$	−1.80241	−0.0692211
$679$	−5.09541	−0.195544
$680$	−2.50655	−0.0961219
$681$	−25.4171	−0.973984
$682$	−13.3749	−0.512152
$683$	−28.2765	−1.08197	−0.540985	−	0.841032i	$-0.681949\pi$
$683$	−28.2765	−1.08197	−0.540985	+	0.841032i	$0.681949\pi$
$684$	10.8066	0.413200
$685$	3.18647	0.121749
$686$	−9.14822	−0.349281
$687$	11.6866	0.445870
$688$	−9.02428	−0.344047
$689$	2.04171	0.0777828
$690$	−3.70130	−0.140906
$691$	18.9171	0.719642	0.359821	−	0.933021i	$-0.382838\pi$
$691$	18.9171	0.719642	0.359821	+	0.933021i	$0.382838\pi$
$692$	−12.7673	−0.485340
$693$	−14.1495	−0.537495
$694$	−2.87088	−0.108977
$695$	10.0917	0.382798
$696$	−16.3082	−0.618160
$697$	1.29358	0.0489976
$698$	−0.354649	−0.0134237
$699$	1.16569	0.0440905
$700$	−21.4998	−0.812615
$701$	10.8657	0.410391	0.205196	−	0.978721i	$-0.434217\pi$
$701$	10.8657	0.410391	0.205196	+	0.978721i	$0.434217\pi$
$702$	0.720490	0.0271932
$703$	26.1894	0.987751
$704$	−12.2584	−0.462005
$705$	−5.37872	−0.202574
$706$	7.34670	0.276497
$707$	−42.7955	−1.60949
$708$	23.5013	0.883234
$709$	1.72491	0.0647802	0.0323901	−	0.999475i	$-0.489688\pi$
$709$	1.72491	0.0647802	0.0323901	+	0.999475i	$0.489688\pi$
$710$	−1.80305	−0.0676672
$711$	1.00000	0.0375029
$712$	−2.85155	−0.106866
$713$	52.6510	1.97180
$714$	−1.89962	−0.0710914
$715$	8.06591	0.301648
$716$	15.4032	0.575645
$717$	−11.1389	−0.415991
$718$	−0.388155	−0.0144858
$719$	−22.6198	−0.843577	−0.421788	−	0.906694i	$-0.638597\pi$
$719$	−22.6198	−0.843577	−0.421788	+	0.906694i	$0.638597\pi$
$720$	−4.33770	−0.161657
$721$	7.59838	0.282979
$722$	7.32087	0.272455
$723$	−0.100901	−0.00375254
$724$	−25.6421	−0.952982
$725$	26.8041	0.995478
$726$	0.157470	0.00584426
$727$	44.2704	1.64190	0.820950	−	0.571000i	$-0.193444\pi$
$727$	44.2704	1.64190	0.820950	+	0.571000i	$0.193444\pi$
$728$	−11.9018	−0.441109
$729$	1.00000	0.0370370
$730$	10.1584	0.375979
$731$	3.12682	0.115650
$732$	−8.13007	−0.300496
$733$	−1.87683	−0.0693224	−0.0346612	−	0.999399i	$-0.511035\pi$
$733$	−1.87683	−0.0693224	−0.0346612	+	0.999399i	$0.511035\pi$
$734$	−0.690978	−0.0255045
$735$	17.7588	0.655044
$736$	−25.8641	−0.953364
$737$	−27.2894	−1.00522
$738$	−0.566495	−0.0208530
$739$	22.4601	0.826209	0.413105	−	0.910684i	$-0.364444\pi$
$739$	22.4601	0.826209	0.413105	+	0.910684i	$0.364444\pi$
$740$	−11.9094	−0.437797
$741$	−9.83243	−0.361203
$742$	2.35742	0.0865435
$743$	27.0418	0.992068	0.496034	−	0.868303i	$-0.334789\pi$
$743$	27.0418	0.992068	0.496034	+	0.868303i	$0.334789\pi$
$744$	−15.6147	−0.572463
$745$	19.5134	0.714916
$746$	−10.9849	−0.402187
$747$	2.32456	0.0850511
$748$	5.89834	0.215665
$749$	−34.8706	−1.27414
$750$	−5.09515	−0.186048
$751$	−4.61891	−0.168546	−0.0842732	−	0.996443i	$-0.526857\pi$
$751$	−4.61891	−0.168546	−0.0842732	+	0.996443i	$0.526857\pi$
$752$	−10.3285	−0.376642
$753$	12.5737	0.458210
$754$	7.04542	0.256579
$755$	−25.0992	−0.913454
$756$	−7.84354	−0.285267
$757$	−38.6018	−1.40301	−0.701503	−	0.712666i	$-0.747487\pi$
$757$	−38.6018	−1.40301	−0.701503	+	0.712666i	$0.747487\pi$
$758$	−14.7767	−0.536716
$759$	18.3434	0.665822
$760$	−14.9801	−0.543385
$761$	45.3944	1.64554	0.822772	−	0.568371i	$-0.192426\pi$
$761$	45.3944	1.64554	0.822772	+	0.568371i	$0.192426\pi$
$762$	−8.18541	−0.296526
$763$	26.8042	0.970379
$764$	14.7682	0.534295
$765$	1.50297	0.0543400
$766$	−8.96273	−0.323837
$767$	−21.3828	−0.772089
$768$	−2.76682	−0.0998391
$769$	−33.2058	−1.19743	−0.598717	−	0.800961i	$-0.704322\pi$
$769$	−33.2058	−1.19743	−0.598717	+	0.800961i	$0.704322\pi$
$770$	9.31314	0.335622
$771$	23.0907	0.831592
$772$	20.4516	0.736069
$773$	−15.8934	−0.571646	−0.285823	−	0.958283i	$-0.592267\pi$
$773$	−15.8934	−0.571646	−0.285823	+	0.958283i	$0.592267\pi$
$774$	−1.36933	−0.0492195
$775$	25.6643	0.921888
$776$	−1.95904	−0.0703255
$777$	−19.0086	−0.681929
$778$	6.05057	0.216923
$779$	7.73088	0.276988
$780$	4.47120	0.160095
$781$	8.93576	0.319747
$782$	2.46266	0.0880645
$783$	9.77865	0.349460
$784$	34.1015	1.21791
$785$	−1.25328	−0.0447314
$786$	−0.190730	−0.00680313
$787$	−38.6133	−1.37642	−0.688208	−	0.725513i	$-0.741602\pi$
$787$	−38.6133	−1.37642	−0.688208	+	0.725513i	$0.741602\pi$
$788$	33.3086	1.18657
$789$	24.4508	0.870473
$790$	−0.658196	−0.0234176
$791$	−17.8530	−0.634778
$792$	−5.44009	−0.193305
$793$	7.39720	0.262682
$794$	11.3429	0.402546
$795$	−1.86518	−0.0661511
$796$	−26.0573	−0.923577
$797$	−7.87321	−0.278883	−0.139442	−	0.990230i	$-0.544531\pi$
$797$	−7.87321	−0.278883	−0.139442	+	0.990230i	$0.544531\pi$
$798$	−11.3528	−0.401885
$799$	3.57872	0.126606
$800$	−12.6072	−0.445733
$801$	1.70984	0.0604141
$802$	−2.86606	−0.101204
$803$	−50.3442	−1.77661
$804$	−15.1274	−0.533503
$805$	−36.6616	−1.29215
$806$	6.74583	0.237612
$807$	23.7625	0.836479
$808$	−16.4537	−0.578838
$809$	−38.2955	−1.34640	−0.673198	−	0.739462i	$-0.735080\pi$
$809$	−38.2955	−1.34640	−0.673198	+	0.739462i	$0.735080\pi$
$810$	−0.658196	−0.0231266
$811$	19.9033	0.698900	0.349450	−	0.936955i	$-0.386368\pi$
$811$	19.9033	0.698900	0.349450	+	0.936955i	$0.386368\pi$
$812$	−76.6992	−2.69162
$813$	0.000261783 0	9.18114e−6 0
$814$	−6.25997	−0.219412
$815$	21.5425	0.754602
$816$	2.88608	0.101033
$817$	18.6870	0.653777
$818$	11.5863	0.405104
$819$	7.13650	0.249369
$820$	−3.51555	−0.122768
$821$	−5.55919	−0.194017	−0.0970086	−	0.995284i	$-0.530927\pi$
$821$	−5.55919	−0.194017	−0.0970086	+	0.995284i	$0.530927\pi$
$822$	0.928463	0.0323839
$823$	−55.2647	−1.92641	−0.963203	−	0.268773i	$-0.913382\pi$
$823$	−55.2647	−1.92641	−0.963203	+	0.268773i	$0.913382\pi$
$824$	2.92137	0.101771
$825$	8.94131	0.311296
$826$	−24.6892	−0.859049
$827$	−23.6024	−0.820737	−0.410368	−	0.911920i	$-0.634600\pi$
$827$	−23.6024	−0.820737	−0.410368	+	0.911920i	$0.634600\pi$
$828$	10.1683	0.353374
$829$	50.5661	1.75623	0.878116	−	0.478448i	$-0.158800\pi$
$829$	50.5661	1.75623	0.878116	+	0.478448i	$0.158800\pi$
$830$	−1.53001	−0.0531075
$831$	1.16032	0.0402510
$832$	6.18268	0.214346
$833$	−11.8158	−0.409394
$834$	2.94047	0.101820
$835$	−9.49448	−0.328570
$836$	35.2507	1.21917
$837$	9.36283	0.323627
$838$	6.85055	0.236648
$839$	−8.51786	−0.294069	−0.147035	−	0.989131i	$-0.546973\pi$
$839$	−8.51786	−0.294069	−0.147035	+	0.989131i	$0.546973\pi$
$840$	10.8727	0.375145
$841$	66.6220	2.29731
$842$	−0.202088	−0.00696440
$843$	−12.5464	−0.432120
$844$	7.53960	0.259524
$845$	15.4705	0.532200
$846$	−1.56723	−0.0538825
$847$	1.55975	0.0535936
$848$	−3.58162	−0.122993
$849$	6.68518	0.229435
$850$	1.20040	0.0411734
$851$	24.6426	0.844739
$852$	4.95339	0.169700
$853$	3.31587	0.113533	0.0567667	−	0.998387i	$-0.481921\pi$
$853$	3.31587	0.113533	0.0567667	+	0.998387i	$0.481921\pi$
$854$	8.54102	0.292268
$855$	8.98231	0.307188
$856$	−13.4068	−0.458234
$857$	13.5889	0.464189	0.232094	−	0.972693i	$-0.425442\pi$
$857$	13.5889	0.464189	0.232094	+	0.972693i	$0.425442\pi$
$858$	2.35021	0.0802350
$859$	17.4120	0.594089	0.297045	−	0.954864i	$-0.403999\pi$
$859$	17.4120	0.594089	0.297045	+	0.954864i	$0.403999\pi$
$860$	−8.49776	−0.289771
$861$	−5.61117	−0.191228
$862$	−17.7270	−0.603783
$863$	−45.2505	−1.54034	−0.770172	−	0.637836i	$-0.779830\pi$
$863$	−45.2505	−1.54034	−0.770172	+	0.637836i	$0.779830\pi$
$864$	−4.59937	−0.156474
$865$	−10.6121	−0.360821
$866$	−11.4901	−0.390448
$867$	−1.00000	−0.0339618
$868$	−73.4378	−2.49264
$869$	3.26197	0.110655
$870$	−6.43626	−0.218210
$871$	13.7638	0.466368
$872$	10.3055	0.348988
$873$	1.17467	0.0397567
$874$	14.7178	0.497835
$875$	−50.4677	−1.70612
$876$	−27.9075	−0.942907
$877$	−6.01006	−0.202945	−0.101473	−	0.994838i	$-0.532355\pi$
$877$	−6.01006	−0.202945	−0.101473	+	0.994838i	$0.532355\pi$
$878$	7.21528	0.243504
$879$	27.7696	0.936644
$880$	−14.1494	−0.476977
$881$	8.13198	0.273973	0.136987	−	0.990573i	$-0.456258\pi$
$881$	8.13198	0.273973	0.136987	+	0.990573i	$0.456258\pi$
$882$	5.17450	0.174235
$883$	−56.5172	−1.90195	−0.950977	−	0.309261i	$-0.899918\pi$
$883$	−56.5172	−1.90195	−0.950977	+	0.309261i	$0.899918\pi$
$884$	−2.97491	−0.100057
$885$	19.5340	0.656629
$886$	8.10868	0.272417
$887$	−5.02720	−0.168797	−0.0843984	−	0.996432i	$-0.526897\pi$
$887$	−5.02720	−0.168797	−0.0843984	+	0.996432i	$0.526897\pi$
$888$	−7.30826	−0.245249
$889$	−81.0769	−2.71923
$890$	−1.12541	−0.0377237
$891$	3.26197	0.109280
$892$	21.8122	0.730325
$893$	21.3878	0.715715
$894$	5.68575	0.190160
$895$	12.8030	0.427956
$896$	47.0403	1.57150
$897$	−9.25173	−0.308906
$898$	−14.7108	−0.490907
$899$	91.5559	3.05356
$900$	4.95647	0.165216
$901$	1.24099	0.0413435
$902$	−1.84789	−0.0615280
$903$	−13.5633	−0.451358
$904$	−6.86396	−0.228292
$905$	−21.3134	−0.708483
$906$	−7.31332	−0.242969
$907$	4.36007	0.144774	0.0723869	−	0.997377i	$-0.476938\pi$
$907$	4.36007	0.144774	0.0723869	+	0.997377i	$0.476938\pi$
$908$	−45.9596	−1.52522
$909$	9.86589	0.327231
$910$	−4.69721	−0.155711
$911$	−18.2410	−0.604350	−0.302175	−	0.953252i	$-0.597713\pi$
$911$	−18.2410	−0.604350	−0.302175	+	0.953252i	$0.597713\pi$
$912$	17.2483	0.571149
$913$	7.58263	0.250948
$914$	12.1944	0.403356
$915$	−6.75762	−0.223400
$916$	21.1318	0.698216
$917$	−1.88920	−0.0623868
$918$	0.437930	0.0144538
$919$	−23.7165	−0.782334	−0.391167	−	0.920320i	$-0.627929\pi$
$919$	−23.7165	−0.782334	−0.391167	+	0.920320i	$0.627929\pi$
$920$	−14.0954	−0.464710
$921$	22.2905	0.734498
$922$	1.13428	0.0373557
$923$	−4.50688	−0.148346
$924$	−25.5854	−0.841697
$925$	12.0118	0.394947
$926$	−10.5923	−0.348086
$927$	−1.75170	−0.0575333
$928$	−44.9756	−1.47640
$929$	−12.9490	−0.424844	−0.212422	−	0.977178i	$-0.568135\pi$
$929$	−12.9490	−0.424844	−0.212422	+	0.977178i	$0.568135\pi$
$930$	−6.16258	−0.202079
$931$	−70.6157	−2.31434
$932$	2.10782	0.0690440
$933$	−14.5941	−0.477791
$934$	16.9311	0.554004
$935$	4.90264	0.160333
$936$	2.74378	0.0896834
$937$	−23.0205	−0.752046	−0.376023	−	0.926610i	$-0.622709\pi$
$937$	−23.0205	−0.752046	−0.376023	+	0.926610i	$0.622709\pi$
$938$	15.8921	0.518894
$939$	−26.0956	−0.851598
$940$	−9.72589	−0.317223
$941$	−24.7050	−0.805360	−0.402680	−	0.915341i	$-0.631921\pi$
$941$	−24.7050	−0.805360	−0.402680	+	0.915341i	$0.631921\pi$
$942$	−0.365176	−0.0118981
$943$	7.27430	0.236884
$944$	37.5103	1.22086
$945$	−6.51947	−0.212078
$946$	−4.46671	−0.145225
$947$	−8.35855	−0.271616	−0.135808	−	0.990735i	$-0.543363\pi$
$947$	−8.35855	−0.271616	−0.135808	+	0.990735i	$0.543363\pi$
$948$	1.80822	0.0587282
$949$	25.3918	0.824253
$950$	7.17404	0.232757
$951$	24.8218	0.804901
$952$	−7.23416	−0.234460
$953$	−43.8717	−1.42114	−0.710571	−	0.703625i	$-0.751563\pi$
$953$	−43.8717	−1.42114	−0.710571	+	0.703625i	$0.751563\pi$
$954$	−0.543469	−0.0175955
$955$	12.2752	0.397215
$956$	−20.1416	−0.651426
$957$	31.8976	1.03110
$958$	−7.16033	−0.231340
$959$	9.19648	0.296970
$960$	−5.64811	−0.182292
$961$	56.6627	1.82783
$962$	3.15730	0.101795
$963$	8.03891	0.259050
$964$	−0.182451	−0.00587634
$965$	16.9992	0.547222
$966$	−10.6823	−0.343698
$967$	51.6076	1.65959	0.829794	−	0.558070i	$-0.188458\pi$
$967$	51.6076	1.65959	0.829794	+	0.558070i	$0.188458\pi$
$968$	0.599680	0.0192744
$969$	−5.97637	−0.191989
$970$	−0.773165	−0.0248248
$971$	17.9100	0.574758	0.287379	−	0.957817i	$-0.407216\pi$
$971$	17.9100	0.574758	0.287379	+	0.957817i	$0.407216\pi$
$972$	1.80822	0.0579986
$973$	29.1255	0.933721
$974$	4.02420	0.128944
$975$	−4.50967	−0.144425
$976$	−12.9764	−0.415363
$977$	−47.5348	−1.52077	−0.760386	−	0.649471i	$-0.774990\pi$
$977$	−47.5348	−1.52077	−0.760386	+	0.649471i	$0.774990\pi$
$978$	6.27698	0.200716
$979$	5.57743	0.178255
$980$	32.1118	1.02577
$981$	−6.17934	−0.197291
$982$	12.2216	0.390008
$983$	40.5653	1.29383	0.646916	−	0.762561i	$-0.276058\pi$
$983$	40.5653	1.29383	0.646916	+	0.762561i	$0.276058\pi$
$984$	−2.15734	−0.0687734
$985$	27.6858	0.882142
$986$	4.28236	0.136378
$987$	−15.5235	−0.494119
$988$	−17.7792	−0.565631
$989$	17.5834	0.559119
$990$	−2.14701	−0.0682365
$991$	−19.1569	−0.608540	−0.304270	−	0.952586i	$-0.598413\pi$
$991$	−19.1569	−0.608540	−0.304270	+	0.952586i	$0.598413\pi$
$992$	−43.0631	−1.36726
$993$	−21.1658	−0.671675
$994$	−5.20377	−0.165054
$995$	−21.6586	−0.686622
$996$	4.20330	0.133187
$997$	−35.9163	−1.13748	−0.568740	−	0.822517i	$-0.692569\pi$
$997$	−35.9163	−1.13748	−0.568740	+	0.822517i	$0.692569\pi$
$998$	4.18793	0.132567
$999$	4.38216	0.138645

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.l.1.19	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.l.1.19	✓	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)

\(f(q)\)	\(=\)	\(q+0.437930 q^{2} -1.00000 q^{3} -1.80822 q^{4} -1.50297 q^{5} -0.437930 q^{6} -4.33772 q^{7} -1.66773 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.437930 q^{2} -1.00000 q^{3} -1.80822 q^{4} -1.50297 q^{5} -0.437930 q^{6} -4.33772 q^{7} -1.66773 q^{8} +1.00000 q^{9} -0.658196 q^{10} +3.26197 q^{11} +1.80822 q^{12} -1.64522 q^{13} -1.89962 q^{14} +1.50297 q^{15} +2.88608 q^{16} -1.00000 q^{17} +0.437930 q^{18} -5.97637 q^{19} +2.71770 q^{20} +4.33772 q^{21} +1.42851 q^{22} -5.62341 q^{23} +1.66773 q^{24} -2.74108 q^{25} -0.720490 q^{26} -1.00000 q^{27} +7.84354 q^{28} -9.77865 q^{29} +0.658196 q^{30} -9.36283 q^{31} +4.59937 q^{32} -3.26197 q^{33} -0.437930 q^{34} +6.51947 q^{35} -1.80822 q^{36} -4.38216 q^{37} -2.61723 q^{38} +1.64522 q^{39} +2.50655 q^{40} -1.29358 q^{41} +1.89962 q^{42} -3.12682 q^{43} -5.89834 q^{44} -1.50297 q^{45} -2.46266 q^{46} -3.57872 q^{47} -2.88608 q^{48} +11.8158 q^{49} -1.20040 q^{50} +1.00000 q^{51} +2.97491 q^{52} -1.24099 q^{53} -0.437930 q^{54} -4.90264 q^{55} +7.23416 q^{56} +5.97637 q^{57} -4.28236 q^{58} +12.9970 q^{59} -2.71770 q^{60} -4.49618 q^{61} -4.10027 q^{62} -4.33772 q^{63} -3.75797 q^{64} +2.47271 q^{65} -1.42851 q^{66} -8.36592 q^{67} +1.80822 q^{68} +5.62341 q^{69} +2.85507 q^{70} +2.73938 q^{71} -1.66773 q^{72} -15.4337 q^{73} -1.91908 q^{74} +2.74108 q^{75} +10.8066 q^{76} -14.1495 q^{77} +0.720490 q^{78} +1.00000 q^{79} -4.33770 q^{80} +1.00000 q^{81} -0.566495 q^{82} +2.32456 q^{83} -7.84354 q^{84} +1.50297 q^{85} -1.36933 q^{86} +9.77865 q^{87} -5.44009 q^{88} +1.70984 q^{89} -0.658196 q^{90} +7.13650 q^{91} +10.1683 q^{92} +9.36283 q^{93} -1.56723 q^{94} +8.98231 q^{95} -4.59937 q^{96} +1.17467 q^{97} +5.17450 q^{98} +3.26197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) \) 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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