LMFDB - Embedded newform 4017.2.a.l.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.238219 q^{2} +1.00000 q^{3} -1.94325 q^{4} +2.19571 q^{5} -0.238219 q^{6} +5.28038 q^{7} +0.939357 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.238219 q^{2} +1.00000 q^{3} -1.94325 q^{4} +2.19571 q^{5} -0.238219 q^{6} +5.28038 q^{7} +0.939357 q^{8} +1.00000 q^{9} -0.523060 q^{10} +4.75715 q^{11} -1.94325 q^{12} -1.00000 q^{13} -1.25788 q^{14} +2.19571 q^{15} +3.66273 q^{16} +2.71112 q^{17} -0.238219 q^{18} -6.38367 q^{19} -4.26682 q^{20} +5.28038 q^{21} -1.13324 q^{22} +8.68320 q^{23} +0.939357 q^{24} -0.178853 q^{25} +0.238219 q^{26} +1.00000 q^{27} -10.2611 q^{28} +6.80245 q^{29} -0.523060 q^{30} -3.94716 q^{31} -2.75124 q^{32} +4.75715 q^{33} -0.645840 q^{34} +11.5942 q^{35} -1.94325 q^{36} -5.52934 q^{37} +1.52071 q^{38} -1.00000 q^{39} +2.06256 q^{40} +4.85834 q^{41} -1.25788 q^{42} +12.1476 q^{43} -9.24435 q^{44} +2.19571 q^{45} -2.06850 q^{46} -1.83308 q^{47} +3.66273 q^{48} +20.8824 q^{49} +0.0426060 q^{50} +2.71112 q^{51} +1.94325 q^{52} -2.35926 q^{53} -0.238219 q^{54} +10.4453 q^{55} +4.96016 q^{56} -6.38367 q^{57} -1.62047 q^{58} -14.0077 q^{59} -4.26682 q^{60} -13.1212 q^{61} +0.940288 q^{62} +5.28038 q^{63} -6.67006 q^{64} -2.19571 q^{65} -1.13324 q^{66} -0.824250 q^{67} -5.26839 q^{68} +8.68320 q^{69} -2.76195 q^{70} -5.55497 q^{71} +0.939357 q^{72} -14.9728 q^{73} +1.31719 q^{74} -0.178853 q^{75} +12.4051 q^{76} +25.1196 q^{77} +0.238219 q^{78} -3.13169 q^{79} +8.04230 q^{80} +1.00000 q^{81} -1.15735 q^{82} -4.17816 q^{83} -10.2611 q^{84} +5.95284 q^{85} -2.89379 q^{86} +6.80245 q^{87} +4.46866 q^{88} +4.45553 q^{89} -0.523060 q^{90} -5.28038 q^{91} -16.8736 q^{92} -3.94716 q^{93} +0.436673 q^{94} -14.0167 q^{95} -2.75124 q^{96} -11.3734 q^{97} -4.97457 q^{98} +4.75715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * 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 $

$2$	−0.238219	−0.168446	−0.0842231	−	0.996447i	$-0.526841\pi$
$2$	−0.238219	−0.168446	−0.0842231	+	0.996447i	$0.526841\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.94325	−0.971626
$5$	2.19571	0.981952	0.490976	−	0.871173i	$-0.336640\pi$
$5$	2.19571	0.981952	0.490976	+	0.871173i	$0.336640\pi$
$6$	−0.238219	−0.0972524
$7$	5.28038	1.99579	0.997897	−	0.0648142i	$-0.0206455\pi$
$7$	5.28038	1.99579	0.997897	+	0.0648142i	$0.0206455\pi$
$8$	0.939357	0.332113
$9$	1.00000	0.333333
$10$	−0.523060	−0.165406
$11$	4.75715	1.43434	0.717168	−	0.696900i	$-0.245438\pi$
$11$	4.75715	1.43434	0.717168	+	0.696900i	$0.245438\pi$
$12$	−1.94325	−0.560968
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.25788	−0.336184
$15$	2.19571	0.566930
$16$	3.66273	0.915683
$17$	2.71112	0.657543	0.328772	−	0.944409i	$-0.393365\pi$
$17$	2.71112	0.657543	0.328772	+	0.944409i	$0.393365\pi$
$18$	−0.238219	−0.0561487
$19$	−6.38367	−1.46451	−0.732257	−	0.681028i	$-0.761533\pi$
$19$	−6.38367	−1.46451	−0.732257	+	0.681028i	$0.761533\pi$
$20$	−4.26682	−0.954090
$21$	5.28038	1.15227
$22$	−1.13324	−0.241608
$23$	8.68320	1.81057	0.905286	−	0.424803i	$-0.139657\pi$
$23$	8.68320	1.81057	0.905286	+	0.424803i	$0.139657\pi$
$24$	0.939357	0.191745
$25$	−0.178853	−0.0357705
$26$	0.238219	0.0467185
$27$	1.00000	0.192450
$28$	−10.2611	−1.93917
$29$	6.80245	1.26318	0.631592	−	0.775301i	$-0.282402\pi$
$29$	6.80245	1.26318	0.631592	+	0.775301i	$0.282402\pi$
$30$	−0.523060	−0.0954972
$31$	−3.94716	−0.708931	−0.354465	−	0.935069i	$-0.615337\pi$
$31$	−3.94716	−0.708931	−0.354465	+	0.935069i	$0.615337\pi$
$32$	−2.75124	−0.486356
$33$	4.75715	0.828114
$34$	−0.645840	−0.110761
$35$	11.5942	1.95977
$36$	−1.94325	−0.323875
$37$	−5.52934	−0.909018	−0.454509	−	0.890742i	$-0.650185\pi$
$37$	−5.52934	−0.909018	−0.454509	+	0.890742i	$0.650185\pi$
$38$	1.52071	0.246692
$39$	−1.00000	−0.160128
$40$	2.06256	0.326119
$41$	4.85834	0.758745	0.379372	−	0.925244i	$-0.376140\pi$
$41$	4.85834	0.758745	0.379372	+	0.925244i	$0.376140\pi$
$42$	−1.25788	−0.194096
$43$	12.1476	1.85249	0.926246	−	0.376920i	$-0.123017\pi$
$43$	12.1476	1.85249	0.926246	+	0.376920i	$0.123017\pi$
$44$	−9.24435	−1.39364
$45$	2.19571	0.327317
$46$	−2.06850	−0.304984
$47$	−1.83308	−0.267382	−0.133691	−	0.991023i	$-0.542683\pi$
$47$	−1.83308	−0.267382	−0.133691	+	0.991023i	$0.542683\pi$
$48$	3.66273	0.528670
$49$	20.8824	2.98320
$50$	0.0426060	0.00602540
$51$	2.71112	0.379633
$52$	1.94325	0.269481
$53$	−2.35926	−0.324069	−0.162034	−	0.986785i	$-0.551806\pi$
$53$	−2.35926	−0.324069	−0.162034	+	0.986785i	$0.551806\pi$
$54$	−0.238219	−0.0324175
$55$	10.4453	1.40845
$56$	4.96016	0.662829
$57$	−6.38367	−0.845538
$58$	−1.62047	−0.212778
$59$	−14.0077	−1.82365	−0.911825	−	0.410580i	$-0.865326\pi$
$59$	−14.0077	−1.82365	−0.911825	+	0.410580i	$0.865326\pi$
$60$	−4.26682	−0.550844
$61$	−13.1212	−1.68000	−0.839998	−	0.542589i	$-0.817444\pi$
$61$	−13.1212	−1.68000	−0.839998	+	0.542589i	$0.817444\pi$
$62$	0.940288	0.119417
$63$	5.28038	0.665265
$64$	−6.67006	−0.833758
$65$	−2.19571	−0.272344
$66$	−1.13324	−0.139493
$67$	−0.824250	−0.100698	−0.0503491	−	0.998732i	$-0.516033\pi$
$67$	−0.824250	−0.100698	−0.0503491	+	0.998732i	$0.516033\pi$
$68$	−5.26839	−0.638886
$69$	8.68320	1.04533
$70$	−2.76195	−0.330116
$71$	−5.55497	−0.659253	−0.329627	−	0.944111i	$-0.606923\pi$
$71$	−5.55497	−0.659253	−0.329627	+	0.944111i	$0.606923\pi$
$72$	0.939357	0.110704
$73$	−14.9728	−1.75244	−0.876218	−	0.481914i	$-0.839942\pi$
$73$	−14.9728	−1.75244	−0.876218	+	0.481914i	$0.839942\pi$
$74$	1.31719	0.153121
$75$	−0.178853	−0.0206521
$76$	12.4051	1.42296
$77$	25.1196	2.86264
$78$	0.238219	0.0269730
$79$	−3.13169	−0.352343	−0.176171	−	0.984360i	$-0.556371\pi$
$79$	−3.13169	−0.352343	−0.176171	+	0.984360i	$0.556371\pi$
$80$	8.04230	0.899156
$81$	1.00000	0.111111
$82$	−1.15735	−0.127808
$83$	−4.17816	−0.458612	−0.229306	−	0.973354i	$-0.573646\pi$
$83$	−4.17816	−0.458612	−0.229306	+	0.973354i	$0.573646\pi$
$84$	−10.2611	−1.11958
$85$	5.95284	0.645676
$86$	−2.89379	−0.312045
$87$	6.80245	0.729300
$88$	4.46866	0.476361
$89$	4.45553	0.472286	0.236143	−	0.971718i	$-0.424117\pi$
$89$	4.45553	0.472286	0.236143	+	0.971718i	$0.424117\pi$
$90$	−0.523060	−0.0551353
$91$	−5.28038	−0.553534
$92$	−16.8736	−1.75920
$93$	−3.94716	−0.409301
$94$	0.436673	0.0450394
$95$	−14.0167	−1.43808
$96$	−2.75124	−0.280798
$97$	−11.3734	−1.15480	−0.577399	−	0.816462i	$-0.695932\pi$
$97$	−11.3734	−1.15480	−0.577399	+	0.816462i	$0.695932\pi$
$98$	−4.97457	−0.502508
$99$	4.75715	0.478112
$100$	0.347556	0.0347556
$101$	−8.79611	−0.875245	−0.437623	−	0.899159i	$-0.644179\pi$
$101$	−8.79611	−0.875245	−0.437623	+	0.899159i	$0.644179\pi$
$102$	−0.645840	−0.0639477
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−0.939357	−0.0921115
$105$	11.5942	1.13148
$106$	0.562020	0.0545882
$107$	−10.4336	−1.00866	−0.504328	−	0.863512i	$-0.668260\pi$
$107$	−10.4336	−1.00866	−0.504328	+	0.863512i	$0.668260\pi$
$108$	−1.94325	−0.186989
$109$	−8.32808	−0.797685	−0.398843	−	0.917019i	$-0.630588\pi$
$109$	−8.32808	−0.797685	−0.398843	+	0.917019i	$0.630588\pi$
$110$	−2.48828	−0.237248
$111$	−5.52934	−0.524822
$112$	19.3406	1.82751
$113$	3.10915	0.292485	0.146242	−	0.989249i	$-0.453282\pi$
$113$	3.10915	0.292485	0.146242	+	0.989249i	$0.453282\pi$
$114$	1.52071	0.142428
$115$	19.0658	1.77789
$116$	−13.2189	−1.22734
$117$	−1.00000	−0.0924500
$118$	3.33690	0.307187
$119$	14.3157	1.31232
$120$	2.06256	0.188285
$121$	11.6305	1.05732
$122$	3.12571	0.282989
$123$	4.85834	0.438061
$124$	7.67033	0.688816
$125$	−11.3713	−1.01708
$126$	−1.25788	−0.112061
$127$	6.14555	0.545329	0.272665	−	0.962109i	$-0.412095\pi$
$127$	6.14555	0.545329	0.272665	+	0.962109i	$0.412095\pi$
$128$	7.09142	0.626799
$129$	12.1476	1.06954
$130$	0.523060	0.0458754
$131$	−6.62605	−0.578920	−0.289460	−	0.957190i	$-0.593476\pi$
$131$	−6.62605	−0.578920	−0.289460	+	0.957190i	$0.593476\pi$
$132$	−9.24435	−0.804617
$133$	−33.7082	−2.92287
$134$	0.196352	0.0169622
$135$	2.19571	0.188977
$136$	2.54671	0.218379
$137$	−0.663504	−0.0566870	−0.0283435	−	0.999598i	$-0.509023\pi$
$137$	−0.663504	−0.0566870	−0.0283435	+	0.999598i	$0.509023\pi$
$138$	−2.06850	−0.176082
$139$	−6.64243	−0.563404	−0.281702	−	0.959502i	$-0.590899\pi$
$139$	−6.64243	−0.563404	−0.281702	+	0.959502i	$0.590899\pi$
$140$	−22.5304	−1.90417
$141$	−1.83308	−0.154373
$142$	1.32330	0.111049
$143$	−4.75715	−0.397813
$144$	3.66273	0.305228
$145$	14.9362	1.24039
$146$	3.56681	0.295191
$147$	20.8824	1.72235
$148$	10.7449	0.883226
$149$	0.417217	0.0341797	0.0170899	−	0.999854i	$-0.494560\pi$
$149$	0.417217	0.0341797	0.0170899	+	0.999854i	$0.494560\pi$
$150$	0.0426060	0.00347877
$151$	13.6104	1.10760	0.553800	−	0.832649i	$-0.313177\pi$
$151$	13.6104	1.10760	0.553800	+	0.832649i	$0.313177\pi$
$152$	−5.99654	−0.486384
$153$	2.71112	0.219181
$154$	−5.98395	−0.482201
$155$	−8.66682	−0.696136
$156$	1.94325	0.155585
$157$	19.0235	1.51824	0.759120	−	0.650951i	$-0.225630\pi$
$157$	19.0235	1.51824	0.759120	+	0.650951i	$0.225630\pi$
$158$	0.746027	0.0593507
$159$	−2.35926	−0.187101
$160$	−6.04094	−0.477578
$161$	45.8505	3.61353
$162$	−0.238219	−0.0187162
$163$	−1.95594	−0.153201	−0.0766004	−	0.997062i	$-0.524407\pi$
$163$	−1.95594	−0.153201	−0.0766004	+	0.997062i	$0.524407\pi$
$164$	−9.44097	−0.737216
$165$	10.4453	0.813168
$166$	0.995315	0.0772515
$167$	−17.8382	−1.38036	−0.690182	−	0.723636i	$-0.742469\pi$
$167$	−17.8382	−1.38036	−0.690182	+	0.723636i	$0.742469\pi$
$168$	4.96016	0.382684
$169$	1.00000	0.0769231
$170$	−1.41808	−0.108762
$171$	−6.38367	−0.488171
$172$	−23.6059	−1.79993
$173$	10.0187	0.761709	0.380854	−	0.924635i	$-0.375630\pi$
$173$	10.0187	0.761709	0.380854	+	0.924635i	$0.375630\pi$
$174$	−1.62047	−0.122848
$175$	−0.944409	−0.0713906
$176$	17.4242	1.31340
$177$	−14.0077	−1.05288
$178$	−1.06139	−0.0795547
$179$	−25.1847	−1.88239	−0.941197	−	0.337859i	$-0.890297\pi$
$179$	−25.1847	−1.88239	−0.941197	+	0.337859i	$0.890297\pi$
$180$	−4.26682	−0.318030
$181$	18.6107	1.38333	0.691663	−	0.722221i	$-0.256879\pi$
$181$	18.6107	1.38333	0.691663	+	0.722221i	$0.256879\pi$
$182$	1.25788	0.0932406
$183$	−13.1212	−0.969947
$184$	8.15662	0.601314
$185$	−12.1408	−0.892612
$186$	0.940288	0.0689452
$187$	12.8972	0.943138
$188$	3.56213	0.259795
$189$	5.28038	0.384091
$190$	3.33904	0.242239
$191$	26.0720	1.88650	0.943251	−	0.332080i	$-0.107750\pi$
$191$	26.0720	1.88650	0.943251	+	0.332080i	$0.107750\pi$
$192$	−6.67006	−0.481370
$193$	−17.3023	−1.24544	−0.622722	−	0.782443i	$-0.713973\pi$
$193$	−17.3023	−1.24544	−0.622722	+	0.782443i	$0.713973\pi$
$194$	2.70937	0.194521
$195$	−2.19571	−0.157238
$196$	−40.5797	−2.89855
$197$	−1.41392	−0.100737	−0.0503687	−	0.998731i	$-0.516040\pi$
$197$	−1.41392	−0.100737	−0.0503687	+	0.998731i	$0.516040\pi$
$198$	−1.13324	−0.0805361
$199$	−17.4134	−1.23440	−0.617200	−	0.786806i	$-0.711733\pi$
$199$	−17.4134	−1.23440	−0.617200	+	0.786806i	$0.711733\pi$
$200$	−0.168006	−0.0118798
$201$	−0.824250	−0.0581381
$202$	2.09540	0.147432
$203$	35.9195	2.52106
$204$	−5.26839	−0.368861
$205$	10.6675	0.745051
$206$	0.238219	0.0165975
$207$	8.68320	0.603524
$208$	−3.66273	−0.253965
$209$	−30.3681	−2.10061
$210$	−2.76195	−0.190593
$211$	5.61181	0.386333	0.193167	−	0.981166i	$-0.438124\pi$
$211$	5.61181	0.386333	0.193167	+	0.981166i	$0.438124\pi$
$212$	4.58463	0.314874
$213$	−5.55497	−0.380620
$214$	2.48548	0.169904
$215$	26.6726	1.81906
$216$	0.939357	0.0639151
$217$	−20.8425	−1.41488
$218$	1.98390	0.134367
$219$	−14.9728	−1.01177
$220$	−20.2979	−1.36849
$221$	−2.71112	−0.182370
$222$	1.31719	0.0884042
$223$	−3.83412	−0.256751	−0.128376	−	0.991726i	$-0.540976\pi$
$223$	−3.83412	−0.256751	−0.128376	+	0.991726i	$0.540976\pi$
$224$	−14.5276	−0.970667
$225$	−0.178853	−0.0119235
$226$	−0.740659	−0.0492679
$227$	−3.99838	−0.265382	−0.132691	−	0.991157i	$-0.542362\pi$
$227$	−3.99838	−0.265382	−0.132691	+	0.991157i	$0.542362\pi$
$228$	12.4051	0.821546
$229$	3.63444	0.240171	0.120085	−	0.992764i	$-0.461683\pi$
$229$	3.63444	0.240171	0.120085	+	0.992764i	$0.461683\pi$
$230$	−4.54183	−0.299479
$231$	25.1196	1.65275
$232$	6.38993	0.419520
$233$	25.8526	1.69366	0.846828	−	0.531866i	$-0.178509\pi$
$233$	25.8526	1.69366	0.846828	+	0.531866i	$0.178509\pi$
$234$	0.238219	0.0155728
$235$	−4.02491	−0.262556
$236$	27.2205	1.77190
$237$	−3.13169	−0.203425
$238$	−3.41028	−0.221056
$239$	14.8702	0.961874	0.480937	−	0.876755i	$-0.340296\pi$
$239$	14.8702	0.961874	0.480937	+	0.876755i	$0.340296\pi$
$240$	8.04230	0.519128
$241$	13.7541	0.885977	0.442989	−	0.896527i	$-0.353918\pi$
$241$	13.7541	0.885977	0.442989	+	0.896527i	$0.353918\pi$
$242$	−2.77061	−0.178101
$243$	1.00000	0.0641500
$244$	25.4978	1.63233
$245$	45.8517	2.92936
$246$	−1.15735	−0.0737897
$247$	6.38367	0.406183
$248$	−3.70779	−0.235445
$249$	−4.17816	−0.264780
$250$	2.70885	0.171323
$251$	11.0765	0.699140	0.349570	−	0.936910i	$-0.386328\pi$
$251$	11.0765	0.699140	0.349570	+	0.936910i	$0.386328\pi$
$252$	−10.2611	−0.646389
$253$	41.3073	2.59697
$254$	−1.46398	−0.0918586
$255$	5.95284	0.372781
$256$	11.6508	0.728176
$257$	9.55928	0.596292	0.298146	−	0.954520i	$-0.403632\pi$
$257$	9.55928	0.596292	0.298146	+	0.954520i	$0.403632\pi$
$258$	−2.89379	−0.180159
$259$	−29.1970	−1.81421
$260$	4.26682	0.264617
$261$	6.80245	0.421061
$262$	1.57845	0.0975169
$263$	4.81938	0.297176	0.148588	−	0.988899i	$-0.452527\pi$
$263$	4.81938	0.297176	0.148588	+	0.988899i	$0.452527\pi$
$264$	4.46866	0.275027
$265$	−5.18025	−0.318220
$266$	8.02992	0.492346
$267$	4.45553	0.272674
$268$	1.60172	0.0978409
$269$	7.22868	0.440740	0.220370	−	0.975416i	$-0.429273\pi$
$269$	7.22868	0.440740	0.220370	+	0.975416i	$0.429273\pi$
$270$	−0.523060	−0.0318324
$271$	4.90211	0.297782	0.148891	−	0.988854i	$-0.452430\pi$
$271$	4.90211	0.297782	0.148891	+	0.988854i	$0.452430\pi$
$272$	9.93011	0.602101
$273$	−5.28038	−0.319583
$274$	0.158059	0.00954870
$275$	−0.850829	−0.0513069
$276$	−16.8736	−1.01567
$277$	−9.36944	−0.562955	−0.281478	−	0.959568i	$-0.590825\pi$
$277$	−9.36944	−0.562955	−0.281478	+	0.959568i	$0.590825\pi$
$278$	1.58235	0.0949032
$279$	−3.94716	−0.236310
$280$	10.8911	0.650866
$281$	4.86563	0.290259	0.145130	−	0.989413i	$-0.453640\pi$
$281$	4.86563	0.290259	0.145130	+	0.989413i	$0.453640\pi$
$282$	0.436673	0.0260035
$283$	16.2539	0.966192	0.483096	−	0.875567i	$-0.339512\pi$
$283$	16.2539	0.966192	0.483096	+	0.875567i	$0.339512\pi$
$284$	10.7947	0.640547
$285$	−14.0167	−0.830277
$286$	1.13324	0.0670101
$287$	25.6538	1.51430
$288$	−2.75124	−0.162119
$289$	−9.64982	−0.567637
$290$	−3.55809	−0.208938
$291$	−11.3734	−0.666723
$292$	29.0960	1.70271
$293$	20.9312	1.22281	0.611407	−	0.791317i	$-0.290604\pi$
$293$	20.9312	1.22281	0.611407	+	0.791317i	$0.290604\pi$
$294$	−4.97457	−0.290123
$295$	−30.7569	−1.79074
$296$	−5.19402	−0.301897
$297$	4.75715	0.276038
$298$	−0.0993888	−0.00575744
$299$	−8.68320	−0.502162
$300$	0.347556	0.0200661
$301$	64.1439	3.69719
$302$	−3.24226	−0.186571
$303$	−8.79611	−0.505323
$304$	−23.3817	−1.34103
$305$	−28.8104	−1.64968
$306$	−0.645840	−0.0369202
$307$	−23.8283	−1.35996	−0.679978	−	0.733233i	$-0.738011\pi$
$307$	−23.8283	−1.35996	−0.679978	+	0.733233i	$0.738011\pi$
$308$	−48.8136	−2.78142
$309$	−1.00000	−0.0568880
$310$	2.06460	0.117261
$311$	−15.4828	−0.877947	−0.438973	−	0.898500i	$-0.644658\pi$
$311$	−15.4828	−0.877947	−0.438973	+	0.898500i	$0.644658\pi$
$312$	−0.939357	−0.0531806
$313$	−23.8113	−1.34589	−0.672946	−	0.739691i	$-0.734972\pi$
$313$	−23.8113	−1.34589	−0.672946	+	0.739691i	$0.734972\pi$
$314$	−4.53175	−0.255742
$315$	11.5942	0.653258
$316$	6.08566	0.342345
$317$	−27.2329	−1.52955	−0.764777	−	0.644295i	$-0.777151\pi$
$317$	−27.2329	−1.52955	−0.764777	+	0.644295i	$0.777151\pi$
$318$	0.562020	0.0315165
$319$	32.3603	1.81183
$320$	−14.6455	−0.818710
$321$	−10.4336	−0.582348
$322$	−10.9225	−0.608685
$323$	−17.3069	−0.962982
$324$	−1.94325	−0.107958
$325$	0.178853	0.00992096
$326$	0.465941	0.0258061
$327$	−8.32808	−0.460544
$328$	4.56371	0.251989
$329$	−9.67933	−0.533639
$330$	−2.48828	−0.136975
$331$	−27.4165	−1.50695	−0.753473	−	0.657479i	$-0.771623\pi$
$331$	−27.4165	−1.50695	−0.753473	+	0.657479i	$0.771623\pi$
$332$	8.11921	0.445600
$333$	−5.52934	−0.303006
$334$	4.24940	0.232517
$335$	−1.80981	−0.0988807
$336$	19.3406	1.05512
$337$	32.4711	1.76882	0.884408	−	0.466715i	$-0.154562\pi$
$337$	32.4711	1.76882	0.884408	+	0.466715i	$0.154562\pi$
$338$	−0.238219	−0.0129574
$339$	3.10915	0.168866
$340$	−11.5679	−0.627356
$341$	−18.7772	−1.01685
$342$	1.52071	0.0822306
$343$	73.3042	3.95805
$344$	11.4109	0.615236
$345$	19.0658	1.02647
$346$	−2.38665	−0.128307
$347$	23.5080	1.26197	0.630987	−	0.775793i	$-0.282650\pi$
$347$	23.5080	1.26197	0.630987	+	0.775793i	$0.282650\pi$
$348$	−13.2189	−0.708606
$349$	−7.99036	−0.427714	−0.213857	−	0.976865i	$-0.568603\pi$
$349$	−7.99036	−0.427714	−0.213857	+	0.976865i	$0.568603\pi$
$350$	0.224976	0.0120255
$351$	−1.00000	−0.0533761
$352$	−13.0881	−0.697598
$353$	4.25800	0.226630	0.113315	−	0.993559i	$-0.463853\pi$
$353$	4.25800	0.226630	0.113315	+	0.993559i	$0.463853\pi$
$354$	3.33690	0.177354
$355$	−12.1971	−0.647355
$356$	−8.65823	−0.458885
$357$	14.3157	0.757669
$358$	5.99947	0.317082
$359$	−10.5971	−0.559292	−0.279646	−	0.960103i	$-0.590217\pi$
$359$	−10.5971	−0.559292	−0.279646	+	0.960103i	$0.590217\pi$
$360$	2.06256	0.108706
$361$	21.7512	1.14480
$362$	−4.43343	−0.233016
$363$	11.6305	0.610444
$364$	10.2611	0.537828
$365$	−32.8760	−1.72081
$366$	3.12571	0.163384
$367$	21.1201	1.10246	0.551229	−	0.834354i	$-0.314159\pi$
$367$	21.1201	1.10246	0.551229	+	0.834354i	$0.314159\pi$
$368$	31.8042	1.65791
$369$	4.85834	0.252915
$370$	2.89218	0.150357
$371$	−12.4578	−0.646775
$372$	7.67033	0.397688
$373$	21.3139	1.10359	0.551796	−	0.833979i	$-0.313943\pi$
$373$	21.3139	1.10359	0.551796	+	0.833979i	$0.313943\pi$
$374$	−3.07236	−0.158868
$375$	−11.3713	−0.587210
$376$	−1.72191	−0.0888009
$377$	−6.80245	−0.350344
$378$	−1.25788	−0.0646986
$379$	14.2405	0.731485	0.365742	−	0.930716i	$-0.380815\pi$
$379$	14.2405	0.731485	0.365742	+	0.930716i	$0.380815\pi$
$380$	27.2380	1.39728
$381$	6.14555	0.314846
$382$	−6.21084	−0.317774
$383$	−21.2790	−1.08731	−0.543653	−	0.839310i	$-0.682959\pi$
$383$	−21.2790	−1.08731	−0.543653	+	0.839310i	$0.682959\pi$
$384$	7.09142	0.361883
$385$	55.1553	2.81097
$386$	4.12172	0.209790
$387$	12.1476	0.617497
$388$	22.1015	1.12203
$389$	−27.3684	−1.38763	−0.693815	−	0.720153i	$-0.744072\pi$
$389$	−27.3684	−1.38763	−0.693815	+	0.720153i	$0.744072\pi$
$390$	0.523060	0.0264862
$391$	23.5412	1.19053
$392$	19.6160	0.990758
$393$	−6.62605	−0.334240
$394$	0.336821	0.0169688
$395$	−6.87629	−0.345983
$396$	−9.24435	−0.464546
$397$	−19.8761	−0.997551	−0.498775	−	0.866731i	$-0.666217\pi$
$397$	−19.8761	−0.997551	−0.498775	+	0.866731i	$0.666217\pi$
$398$	4.14819	0.207930
$399$	−33.7082	−1.68752
$400$	−0.655089	−0.0327544
$401$	1.55920	0.0778629	0.0389315	−	0.999242i	$-0.487605\pi$
$401$	1.55920	0.0778629	0.0389315	+	0.999242i	$0.487605\pi$
$402$	0.196352	0.00979314
$403$	3.94716	0.196622
$404$	17.0931	0.850411
$405$	2.19571	0.109106
$406$	−8.55670	−0.424662
$407$	−26.3039	−1.30384
$408$	2.54671	0.126081
$409$	−13.3166	−0.658464	−0.329232	−	0.944249i	$-0.606790\pi$
$409$	−13.3166	−0.658464	−0.329232	+	0.944249i	$0.606790\pi$
$410$	−2.54120	−0.125501
$411$	−0.663504	−0.0327282
$412$	1.94325	0.0957371
$413$	−73.9660	−3.63963
$414$	−2.06850	−0.101661
$415$	−9.17402	−0.450335
$416$	2.75124	0.134891
$417$	−6.64243	−0.325281
$418$	7.23425	0.353839
$419$	−25.8849	−1.26456	−0.632281	−	0.774739i	$-0.717881\pi$
$419$	−25.8849	−1.26456	−0.632281	+	0.774739i	$0.717881\pi$
$420$	−22.5304	−1.09937
$421$	−7.38313	−0.359832	−0.179916	−	0.983682i	$-0.557583\pi$
$421$	−7.38313	−0.359832	−0.179916	+	0.983682i	$0.557583\pi$
$422$	−1.33684	−0.0650763
$423$	−1.83308	−0.0891272
$424$	−2.21618	−0.107627
$425$	−0.484891	−0.0235207
$426$	1.32330	0.0641140
$427$	−69.2848	−3.35293
$428$	20.2752	0.980037
$429$	−4.75715	−0.229678
$430$	−6.35392	−0.306413
$431$	−17.2268	−0.829785	−0.414892	−	0.909870i	$-0.636181\pi$
$431$	−17.2268	−0.829785	−0.414892	+	0.909870i	$0.636181\pi$
$432$	3.66273	0.176223
$433$	18.3812	0.883345	0.441673	−	0.897176i	$-0.354385\pi$
$433$	18.3812	0.883345	0.441673	+	0.897176i	$0.354385\pi$
$434$	4.96507	0.238331
$435$	14.9362	0.716137
$436$	16.1835	0.775051
$437$	−55.4307	−2.65161
$438$	3.56681	0.170429
$439$	2.52896	0.120701	0.0603503	−	0.998177i	$-0.480778\pi$
$439$	2.52896	0.120701	0.0603503	+	0.998177i	$0.480778\pi$
$440$	9.81190	0.467764
$441$	20.8824	0.994399
$442$	0.645840	0.0307195
$443$	27.9133	1.32620	0.663101	−	0.748530i	$-0.269240\pi$
$443$	27.9133	1.32620	0.663101	+	0.748530i	$0.269240\pi$
$444$	10.7449	0.509931
$445$	9.78307	0.463762
$446$	0.913358	0.0432488
$447$	0.417217	0.0197337
$448$	−35.2205	−1.66401
$449$	38.0583	1.79608	0.898042	−	0.439910i	$-0.144990\pi$
$449$	38.0583	1.79608	0.898042	+	0.439910i	$0.144990\pi$
$450$	0.0426060	0.00200847
$451$	23.1118	1.08829
$452$	−6.04187	−0.284186
$453$	13.6104	0.639474
$454$	0.952489	0.0447025
$455$	−11.5942	−0.543544
$456$	−5.99654	−0.280814
$457$	9.08299	0.424884	0.212442	−	0.977174i	$-0.431858\pi$
$457$	9.08299	0.424884	0.212442	+	0.977174i	$0.431858\pi$
$458$	−0.865792	−0.0404558
$459$	2.71112	0.126544
$460$	−37.0496	−1.72745
$461$	26.4592	1.23233	0.616165	−	0.787617i	$-0.288686\pi$
$461$	26.4592	1.23233	0.616165	+	0.787617i	$0.288686\pi$
$462$	−5.98395	−0.278399
$463$	−17.3017	−0.804078	−0.402039	−	0.915622i	$-0.631698\pi$
$463$	−17.3017	−0.804078	−0.402039	+	0.915622i	$0.631698\pi$
$464$	24.9156	1.15668
$465$	−8.66682	−0.401914
$466$	−6.15856	−0.285290
$467$	−12.0577	−0.557962	−0.278981	−	0.960297i	$-0.589997\pi$
$467$	−12.0577	−0.557962	−0.278981	+	0.960297i	$0.589997\pi$
$468$	1.94325	0.0898268
$469$	−4.35235	−0.200973
$470$	0.958808	0.0442265
$471$	19.0235	0.876556
$472$	−13.1582	−0.605657
$473$	57.7880	2.65710
$474$	0.746027	0.0342662
$475$	1.14174	0.0523864
$476$	−27.8191	−1.27509
$477$	−2.35926	−0.108023
$478$	−3.54237	−0.162024
$479$	−25.2918	−1.15561	−0.577806	−	0.816174i	$-0.696091\pi$
$479$	−25.2918	−1.15561	−0.577806	+	0.816174i	$0.696091\pi$
$480$	−6.04094	−0.275730
$481$	5.52934	0.252116
$482$	−3.27648	−0.149239
$483$	45.8505	2.08627
$484$	−22.6010	−1.02732
$485$	−24.9728	−1.13396
$486$	−0.238219	−0.0108058
$487$	−10.4596	−0.473971	−0.236985	−	0.971513i	$-0.576159\pi$
$487$	−10.4596	−0.473971	−0.236985	+	0.971513i	$0.576159\pi$
$488$	−12.3255	−0.557948
$489$	−1.95594	−0.0884505
$490$	−10.9227	−0.493439
$491$	9.46924	0.427341	0.213670	−	0.976906i	$-0.431458\pi$
$491$	9.46924	0.427341	0.213670	+	0.976906i	$0.431458\pi$
$492$	−9.44097	−0.425632
$493$	18.4423	0.830599
$494$	−1.52071	−0.0684200
$495$	10.4453	0.469483
$496$	−14.4574	−0.649156
$497$	−29.3323	−1.31573
$498$	0.995315	0.0446011
$499$	39.2030	1.75497	0.877485	−	0.479605i	$-0.159220\pi$
$499$	39.2030	1.75497	0.877485	+	0.479605i	$0.159220\pi$
$500$	22.0972	0.988218
$501$	−17.8382	−0.796953
$502$	−2.63862	−0.117767
$503$	−11.0246	−0.491565	−0.245782	−	0.969325i	$-0.579045\pi$
$503$	−11.0246	−0.491565	−0.245782	+	0.969325i	$0.579045\pi$
$504$	4.96016	0.220943
$505$	−19.3137	−0.859449
$506$	−9.84017	−0.437449
$507$	1.00000	0.0444116
$508$	−11.9423	−0.529856
$509$	−33.8615	−1.50088	−0.750441	−	0.660937i	$-0.770159\pi$
$509$	−33.8615	−1.50088	−0.750441	+	0.660937i	$0.770159\pi$
$510$	−1.41808	−0.0627936
$511$	−79.0622	−3.49750
$512$	−16.9583	−0.749458
$513$	−6.38367	−0.281846
$514$	−2.27720	−0.100443
$515$	−2.19571	−0.0967546
$516$	−23.6059	−1.03919
$517$	−8.72023	−0.383515
$518$	6.95528	0.305597
$519$	10.0187	0.439773
$520$	−2.06256	−0.0904491
$521$	5.44340	0.238480	0.119240	−	0.992865i	$-0.461954\pi$
$521$	5.44340	0.238480	0.119240	+	0.992865i	$0.461954\pi$
$522$	−1.62047	−0.0709262
$523$	−3.54053	−0.154817	−0.0774084	−	0.996999i	$-0.524665\pi$
$523$	−3.54053	−0.154817	−0.0774084	+	0.996999i	$0.524665\pi$
$524$	12.8761	0.562494
$525$	−0.944409	−0.0412174
$526$	−1.14807	−0.0500581
$527$	−10.7012	−0.466153
$528$	17.4242	0.758290
$529$	52.3979	2.27817
$530$	1.23403	0.0536029
$531$	−14.0077	−0.607883
$532$	65.5035	2.83994
$533$	−4.85834	−0.210438
$534$	−1.06139	−0.0459309
$535$	−22.9092	−0.990452
$536$	−0.774264	−0.0334431
$537$	−25.1847	−1.08680
$538$	−1.72201	−0.0742410
$539$	99.3407	4.27891
$540$	−4.26682	−0.183615
$541$	6.71916	0.288879	0.144440	−	0.989514i	$-0.453862\pi$
$541$	6.71916	0.288879	0.144440	+	0.989514i	$0.453862\pi$
$542$	−1.16777	−0.0501602
$543$	18.6107	0.798663
$544$	−7.45896	−0.319800
$545$	−18.2861	−0.783288
$546$	1.25788	0.0538325
$547$	12.4600	0.532753	0.266376	−	0.963869i	$-0.414174\pi$
$547$	12.4600	0.532753	0.266376	+	0.963869i	$0.414174\pi$
$548$	1.28936	0.0550785
$549$	−13.1212	−0.559999
$550$	0.202683	0.00864245
$551$	−43.4246	−1.84995
$552$	8.15662	0.347169
$553$	−16.5365	−0.703203
$554$	2.23198	0.0948276
$555$	−12.1408	−0.515350
$556$	12.9079	0.547418
$557$	1.52679	0.0646921	0.0323460	−	0.999477i	$-0.489702\pi$
$557$	1.52679	0.0646921	0.0323460	+	0.999477i	$0.489702\pi$
$558$	0.940288	0.0398056
$559$	−12.1476	−0.513789
$560$	42.4664	1.79453
$561$	12.8972	0.544521
$562$	−1.15909	−0.0488931
$563$	−36.1889	−1.52518	−0.762591	−	0.646881i	$-0.776073\pi$
$563$	−36.1889	−1.52518	−0.762591	+	0.646881i	$0.776073\pi$
$564$	3.56213	0.149993
$565$	6.82680	0.287206
$566$	−3.87198	−0.162751
$567$	5.28038	0.221755
$568$	−5.21809	−0.218946
$569$	7.47866	0.313522	0.156761	−	0.987637i	$-0.449895\pi$
$569$	7.47866	0.313522	0.156761	+	0.987637i	$0.449895\pi$
$570$	3.33904	0.139857
$571$	13.6003	0.569153	0.284577	−	0.958653i	$-0.408147\pi$
$571$	13.6003	0.569153	0.284577	+	0.958653i	$0.408147\pi$
$572$	9.24435	0.386526
$573$	26.0720	1.08917
$574$	−6.11123	−0.255078
$575$	−1.55301	−0.0647651
$576$	−6.67006	−0.277919
$577$	4.05572	0.168842	0.0844208	−	0.996430i	$-0.473096\pi$
$577$	4.05572	0.168842	0.0844208	+	0.996430i	$0.473096\pi$
$578$	2.29877	0.0956162
$579$	−17.3023	−0.719058
$580$	−29.0248	−1.20519
$581$	−22.0622	−0.915296
$582$	2.70937	0.112307
$583$	−11.2234	−0.464824
$584$	−14.0648	−0.582007
$585$	−2.19571	−0.0907815
$586$	−4.98620	−0.205978
$587$	5.59639	0.230988	0.115494	−	0.993308i	$-0.463155\pi$
$587$	5.59639	0.230988	0.115494	+	0.993308i	$0.463155\pi$
$588$	−40.5797	−1.67348
$589$	25.1974	1.03824
$590$	7.32687	0.301642
$591$	−1.41392	−0.0581607
$592$	−20.2525	−0.832373
$593$	−46.8567	−1.92418	−0.962088	−	0.272740i	$-0.912070\pi$
$593$	−46.8567	−1.92418	−0.962088	+	0.272740i	$0.912070\pi$
$594$	−1.13324	−0.0464975
$595$	31.4332	1.28864
$596$	−0.810757	−0.0332099
$597$	−17.4134	−0.712681
$598$	2.06850	0.0845873
$599$	14.3248	0.585297	0.292648	−	0.956220i	$-0.405463\pi$
$599$	14.3248	0.585297	0.292648	+	0.956220i	$0.405463\pi$
$600$	−0.168006	−0.00685883
$601$	7.67543	0.313087	0.156544	−	0.987671i	$-0.449965\pi$
$601$	7.67543	0.313087	0.156544	+	0.987671i	$0.449965\pi$
$602$	−15.2803	−0.622778
$603$	−0.824250	−0.0335660
$604$	−26.4485	−1.07617
$605$	25.5372	1.03824
$606$	2.09540	0.0851197
$607$	−19.6259	−0.796590	−0.398295	−	0.917257i	$-0.630398\pi$
$607$	−19.6259	−0.796590	−0.398295	+	0.917257i	$0.630398\pi$
$608$	17.5630	0.712275
$609$	35.9195	1.45553
$610$	6.86317	0.277881
$611$	1.83308	0.0741583
$612$	−5.26839	−0.212962
$613$	−3.61899	−0.146170	−0.0730849	−	0.997326i	$-0.523284\pi$
$613$	−3.61899	−0.146170	−0.0730849	+	0.997326i	$0.523284\pi$
$614$	5.67636	0.229079
$615$	10.6675	0.430155
$616$	23.5962	0.950719
$617$	−3.75438	−0.151146	−0.0755728	−	0.997140i	$-0.524079\pi$
$617$	−3.75438	−0.151146	−0.0755728	+	0.997140i	$0.524079\pi$
$618$	0.238219	0.00958256
$619$	29.2332	1.17498	0.587490	−	0.809231i	$-0.300116\pi$
$619$	29.2332	1.17498	0.587490	+	0.809231i	$0.300116\pi$
$620$	16.8418	0.676384
$621$	8.68320	0.348445
$622$	3.68828	0.147887
$623$	23.5269	0.942585
$624$	−3.66273	−0.146627
$625$	−24.0737	−0.962950
$626$	5.67229	0.226710
$627$	−30.3681	−1.21279
$628$	−36.9674	−1.47516
$629$	−14.9907	−0.597719
$630$	−2.76195	−0.110039
$631$	19.5630	0.778791	0.389396	−	0.921071i	$-0.372684\pi$
$631$	19.5630	0.778791	0.389396	+	0.921071i	$0.372684\pi$
$632$	−2.94177	−0.117017
$633$	5.61181	0.223050
$634$	6.48740	0.257647
$635$	13.4938	0.535487
$636$	4.58463	0.181792
$637$	−20.8824	−0.827390
$638$	−7.70884	−0.305196
$639$	−5.55497	−0.219751
$640$	15.5707	0.615487
$641$	41.7658	1.64965	0.824825	−	0.565388i	$-0.191274\pi$
$641$	41.7658	1.64965	0.824825	+	0.565388i	$0.191274\pi$
$642$	2.48548	0.0980943
$643$	−18.1233	−0.714711	−0.357356	−	0.933968i	$-0.616322\pi$
$643$	−18.1233	−0.714711	−0.357356	+	0.933968i	$0.616322\pi$
$644$	−89.0992	−3.51100
$645$	26.6726	1.05023
$646$	4.12283	0.162211
$647$	−17.8105	−0.700203	−0.350101	−	0.936712i	$-0.613853\pi$
$647$	−17.8105	−0.700203	−0.350101	+	0.936712i	$0.613853\pi$
$648$	0.939357	0.0369014
$649$	−66.6369	−2.61573
$650$	−0.0426060	−0.00167115
$651$	−20.8425	−0.816882
$652$	3.80088	0.148854
$653$	−9.31626	−0.364574	−0.182287	−	0.983245i	$-0.558350\pi$
$653$	−9.31626	−0.364574	−0.182287	+	0.983245i	$0.558350\pi$
$654$	1.98390	0.0775768
$655$	−14.5489	−0.568472
$656$	17.7948	0.694769
$657$	−14.9728	−0.584146
$658$	2.30580	0.0898894
$659$	−26.9382	−1.04936	−0.524682	−	0.851298i	$-0.675816\pi$
$659$	−26.9382	−1.04936	−0.524682	+	0.851298i	$0.675816\pi$
$660$	−20.2979	−0.790095
$661$	33.3533	1.29729	0.648646	−	0.761090i	$-0.275335\pi$
$661$	33.3533	1.29729	0.648646	+	0.761090i	$0.275335\pi$
$662$	6.53112	0.253839
$663$	−2.71112	−0.105291
$664$	−3.92478	−0.152311
$665$	−74.0134	−2.87012
$666$	1.31719	0.0510402
$667$	59.0670	2.28709
$668$	34.6642	1.34120
$669$	−3.83412	−0.148235
$670$	0.431132	0.0166561
$671$	−62.4195	−2.40968
$672$	−14.5276	−0.560415
$673$	−24.4235	−0.941458	−0.470729	−	0.882278i	$-0.656009\pi$
$673$	−24.4235	−0.941458	−0.470729	+	0.882278i	$0.656009\pi$
$674$	−7.73524	−0.297950
$675$	−0.178853	−0.00688404
$676$	−1.94325	−0.0747405
$677$	−21.4199	−0.823232	−0.411616	−	0.911357i	$-0.635035\pi$
$677$	−21.4199	−0.823232	−0.411616	+	0.911357i	$0.635035\pi$
$678$	−0.740659	−0.0284448
$679$	−60.0560	−2.30474
$680$	5.59184	0.214437
$681$	−3.99838	−0.153218
$682$	4.47309	0.171284
$683$	−14.7911	−0.565965	−0.282982	−	0.959125i	$-0.591324\pi$
$683$	−14.7911	−0.565965	−0.282982	+	0.959125i	$0.591324\pi$
$684$	12.4051	0.474320
$685$	−1.45686	−0.0556639
$686$	−17.4624	−0.666719
$687$	3.63444	0.138663
$688$	44.4934	1.69630
$689$	2.35926	0.0898806
$690$	−4.54183	−0.172904
$691$	13.8854	0.528227	0.264114	−	0.964492i	$-0.414921\pi$
$691$	13.8854	0.528227	0.264114	+	0.964492i	$0.414921\pi$
$692$	−19.4689	−0.740096
$693$	25.1196	0.954213
$694$	−5.60004	−0.212575
$695$	−14.5849	−0.553235
$696$	6.38993	0.242210
$697$	13.1715	0.498908
$698$	1.90345	0.0720468
$699$	25.8526	0.977833
$700$	1.83522	0.0693650
$701$	33.2076	1.25423	0.627116	−	0.778926i	$-0.284235\pi$
$701$	33.2076	1.25423	0.627116	+	0.778926i	$0.284235\pi$
$702$	0.238219	0.00899099
$703$	35.2975	1.33127
$704$	−31.7305	−1.19589
$705$	−4.02491	−0.151587
$706$	−1.01433	−0.0381750
$707$	−46.4468	−1.74681
$708$	27.2205	1.02301
$709$	25.0172	0.939539	0.469770	−	0.882789i	$-0.344337\pi$
$709$	25.0172	0.939539	0.469770	+	0.882789i	$0.344337\pi$
$710$	2.90558	0.109044
$711$	−3.13169	−0.117448
$712$	4.18534	0.156852
$713$	−34.2740	−1.28357
$714$	−3.41028	−0.127626
$715$	−10.4453	−0.390633
$716$	48.9402	1.82898
$717$	14.8702	0.555338
$718$	2.52442	0.0942106
$719$	−20.5929	−0.767985	−0.383993	−	0.923336i	$-0.625451\pi$
$719$	−20.5929	−0.767985	−0.383993	+	0.923336i	$0.625451\pi$
$720$	8.04230	0.299719
$721$	−5.28038	−0.196651
$722$	−5.18155	−0.192837
$723$	13.7541	0.511519
$724$	−36.1654	−1.34407
$725$	−1.21664	−0.0451847
$726$	−2.77061	−0.102827
$727$	−19.6455	−0.728613	−0.364307	−	0.931279i	$-0.618694\pi$
$727$	−19.6455	−0.728613	−0.364307	+	0.931279i	$0.618694\pi$
$728$	−4.96016	−0.183836
$729$	1.00000	0.0370370
$730$	7.83168	0.289864
$731$	32.9336	1.21809
$732$	25.4978	0.942425
$733$	−19.1613	−0.707739	−0.353869	−	0.935295i	$-0.615134\pi$
$733$	−19.1613	−0.707739	−0.353869	+	0.935295i	$0.615134\pi$
$734$	−5.03120	−0.185705
$735$	45.8517	1.69126
$736$	−23.8896	−0.880582
$737$	−3.92108	−0.144435
$738$	−1.15735	−0.0426025
$739$	38.8029	1.42739	0.713693	−	0.700458i	$-0.247021\pi$
$739$	38.8029	1.42739	0.713693	+	0.700458i	$0.247021\pi$
$740$	23.5927	0.867285
$741$	6.38367	0.234510
$742$	2.96767	0.108947
$743$	7.72276	0.283321	0.141660	−	0.989915i	$-0.454756\pi$
$743$	7.72276	0.283321	0.141660	+	0.989915i	$0.454756\pi$
$744$	−3.70779	−0.135934
$745$	0.916087	0.0335628
$746$	−5.07737	−0.185896
$747$	−4.17816	−0.152871
$748$	−25.0625	−0.916378
$749$	−55.0935	−2.01307
$750$	2.70885	0.0989132
$751$	15.7466	0.574600	0.287300	−	0.957841i	$-0.407242\pi$
$751$	15.7466	0.574600	0.287300	+	0.957841i	$0.407242\pi$
$752$	−6.71407	−0.244837
$753$	11.0765	0.403649
$754$	1.62047	0.0590141
$755$	29.8846	1.08761
$756$	−10.2611	−0.373193
$757$	−35.9336	−1.30603	−0.653014	−	0.757346i	$-0.726496\pi$
$757$	−35.9336	−1.30603	−0.653014	+	0.757346i	$0.726496\pi$
$758$	−3.39235	−0.123216
$759$	41.3073	1.49936
$760$	−13.1667	−0.477605
$761$	45.4800	1.64865	0.824324	−	0.566119i	$-0.191556\pi$
$761$	45.4800	1.64865	0.824324	+	0.566119i	$0.191556\pi$
$762$	−1.46398	−0.0530346
$763$	−43.9754	−1.59202
$764$	−50.6644	−1.83297
$765$	5.95284	0.215225
$766$	5.06906	0.183152
$767$	14.0077	0.505789
$768$	11.6508	0.420413
$769$	40.0808	1.44535	0.722676	−	0.691187i	$-0.242912\pi$
$769$	40.0808	1.44535	0.722676	+	0.691187i	$0.242912\pi$
$770$	−13.1390	−0.473498
$771$	9.55928	0.344269
$772$	33.6227	1.21011
$773$	−12.5461	−0.451252	−0.225626	−	0.974214i	$-0.572443\pi$
$773$	−12.5461	−0.451252	−0.225626	+	0.974214i	$0.572443\pi$
$774$	−2.89379	−0.104015
$775$	0.705960	0.0253588
$776$	−10.6837	−0.383523
$777$	−29.1970	−1.04744
$778$	6.51966	0.233741
$779$	−31.0140	−1.11119
$780$	4.26682	0.152777
$781$	−26.4258	−0.945591
$782$	−5.60796	−0.200540
$783$	6.80245	0.243100
$784$	76.4865	2.73166
$785$	41.7701	1.49084
$786$	1.57845	0.0563014
$787$	−18.2871	−0.651865	−0.325933	−	0.945393i	$-0.605678\pi$
$787$	−18.2871	−0.651865	−0.325933	+	0.945393i	$0.605678\pi$
$788$	2.74759	0.0978790
$789$	4.81938	0.171575
$790$	1.63806	0.0582796
$791$	16.4175	0.583739
$792$	4.46866	0.158787
$793$	13.1212	0.465947
$794$	4.73485	0.168034
$795$	−5.18025	−0.183724
$796$	33.8385	1.19938
$797$	4.77578	0.169167	0.0845834	−	0.996416i	$-0.473044\pi$
$797$	4.77578	0.169167	0.0845834	+	0.996416i	$0.473044\pi$
$798$	8.02992	0.284256
$799$	−4.96969	−0.175815
$800$	0.492067	0.0173972
$801$	4.45553	0.157429
$802$	−0.371432	−0.0131157
$803$	−71.2280	−2.51358
$804$	1.60172	0.0564885
$805$	100.675	3.54831
$806$	−0.940288	−0.0331202
$807$	7.22868	0.254462
$808$	−8.26268	−0.290680
$809$	−17.9918	−0.632558	−0.316279	−	0.948666i	$-0.602434\pi$
$809$	−17.9918	−0.632558	−0.316279	+	0.948666i	$0.602434\pi$
$810$	−0.523060	−0.0183784
$811$	−30.0004	−1.05346	−0.526728	−	0.850034i	$-0.676581\pi$
$811$	−30.0004	−1.05346	−0.526728	+	0.850034i	$0.676581\pi$
$812$	−69.8007	−2.44952
$813$	4.90211	0.171924
$814$	6.26609	0.219626
$815$	−4.29467	−0.150436
$816$	9.93011	0.347623
$817$	−77.5463	−2.71300
$818$	3.17226	0.110916
$819$	−5.28038	−0.184511
$820$	−20.7296	−0.723910
$821$	34.6918	1.21075	0.605376	−	0.795939i	$-0.293023\pi$
$821$	34.6918	1.21075	0.605376	+	0.795939i	$0.293023\pi$
$822$	0.158059	0.00551294
$823$	18.3233	0.638709	0.319355	−	0.947635i	$-0.396534\pi$
$823$	18.3233	0.638709	0.319355	+	0.947635i	$0.396534\pi$
$824$	−0.939357	−0.0327240
$825$	−0.850829	−0.0296221
$826$	17.6201	0.613081
$827$	−42.7511	−1.48660	−0.743300	−	0.668958i	$-0.766740\pi$
$827$	−42.7511	−1.48660	−0.743300	+	0.668958i	$0.766740\pi$
$828$	−16.8736	−0.586399
$829$	29.7760	1.03416	0.517082	−	0.855936i	$-0.327018\pi$
$829$	29.7760	1.03416	0.517082	+	0.855936i	$0.327018\pi$
$830$	2.18543	0.0758572
$831$	−9.36944	−0.325022
$832$	6.67006	0.231243
$833$	56.6147	1.96158
$834$	1.58235	0.0547924
$835$	−39.1676	−1.35545
$836$	59.0129	2.04100
$837$	−3.94716	−0.136434
$838$	6.16628	0.213011
$839$	56.2494	1.94194	0.970972	−	0.239194i	$-0.0768832\pi$
$839$	56.2494	1.94194	0.970972	+	0.239194i	$0.0768832\pi$
$840$	10.8911	0.375778
$841$	17.2734	0.595634
$842$	1.75880	0.0606122
$843$	4.86563	0.167581
$844$	−10.9052	−0.375371
$845$	2.19571	0.0755348
$846$	0.436673	0.0150131
$847$	61.4135	2.11019
$848$	−8.64133	−0.296744
$849$	16.2539	0.557831
$850$	0.115510	0.00396197
$851$	−48.0124	−1.64584
$852$	10.7947	0.369820
$853$	−37.6549	−1.28928	−0.644640	−	0.764486i	$-0.722993\pi$
$853$	−37.6549	−1.28928	−0.644640	+	0.764486i	$0.722993\pi$
$854$	16.5050	0.564788
$855$	−14.0167	−0.479361
$856$	−9.80089	−0.334988
$857$	40.4513	1.38179	0.690895	−	0.722955i	$-0.257217\pi$
$857$	40.4513	1.38179	0.690895	+	0.722955i	$0.257217\pi$
$858$	1.13324	0.0386883
$859$	0.514652	0.0175597	0.00877985	−	0.999961i	$-0.497205\pi$
$859$	0.514652	0.0175597	0.00877985	+	0.999961i	$0.497205\pi$
$860$	−51.8316	−1.76744
$861$	25.6538	0.874281
$862$	4.10374	0.139774
$863$	40.5437	1.38013	0.690063	−	0.723750i	$-0.257583\pi$
$863$	40.5437	1.38013	0.690063	+	0.723750i	$0.257583\pi$
$864$	−2.75124	−0.0935992
$865$	21.9982	0.747961
$866$	−4.37875	−0.148796
$867$	−9.64982	−0.327725
$868$	40.5022	1.37473
$869$	−14.8979	−0.505378
$870$	−3.55809	−0.120631
$871$	0.824250	0.0279286
$872$	−7.82303	−0.264921
$873$	−11.3734	−0.384933
$874$	13.2046	0.446653
$875$	−60.0446	−2.02988
$876$	29.0960	0.983062
$877$	26.2892	0.887723	0.443861	−	0.896095i	$-0.353608\pi$
$877$	26.2892	0.887723	0.443861	+	0.896095i	$0.353608\pi$
$878$	−0.602445	−0.0203315
$879$	20.9312	0.705991
$880$	38.2585	1.28969
$881$	4.70849	0.158633	0.0793165	−	0.996849i	$-0.474726\pi$
$881$	4.70849	0.158633	0.0793165	+	0.996849i	$0.474726\pi$
$882$	−4.97457	−0.167503
$883$	38.2588	1.28751	0.643756	−	0.765231i	$-0.277375\pi$
$883$	38.2588	1.28751	0.643756	+	0.765231i	$0.277375\pi$
$884$	5.26839	0.177195
$885$	−30.7569	−1.03388
$886$	−6.64947	−0.223393
$887$	−6.24524	−0.209695	−0.104847	−	0.994488i	$-0.533435\pi$
$887$	−6.24524	−0.209695	−0.104847	+	0.994488i	$0.533435\pi$
$888$	−5.19402	−0.174300
$889$	32.4508	1.08837
$890$	−2.33051	−0.0781189
$891$	4.75715	0.159371
$892$	7.45065	0.249466
$893$	11.7018	0.391584
$894$	−0.0993888	−0.00332406
$895$	−55.2983	−1.84842
$896$	37.4454	1.25096
$897$	−8.68320	−0.289923
$898$	−9.06621	−0.302543
$899$	−26.8504	−0.895510
$900$	0.347556	0.0115852
$901$	−6.39623	−0.213089
$902$	−5.50568	−0.183319
$903$	64.1439	2.13458
$904$	2.92060	0.0971378
$905$	40.8638	1.35836
$906$	−3.24226	−0.107717
$907$	50.4217	1.67423	0.837113	−	0.547030i	$-0.184242\pi$
$907$	50.4217	1.67423	0.837113	+	0.547030i	$0.184242\pi$
$908$	7.76986	0.257852
$909$	−8.79611	−0.291748
$910$	2.76195	0.0915578
$911$	−6.25914	−0.207375	−0.103687	−	0.994610i	$-0.533064\pi$
$911$	−6.25914	−0.207375	−0.103687	+	0.994610i	$0.533064\pi$
$912$	−23.3817	−0.774244
$913$	−19.8761	−0.657804
$914$	−2.16374	−0.0715701
$915$	−28.8104	−0.952441
$916$	−7.06264	−0.233356
$917$	−34.9880	−1.15541
$918$	−0.645840	−0.0213159
$919$	−6.21104	−0.204883	−0.102442	−	0.994739i	$-0.532665\pi$
$919$	−6.21104	−0.204883	−0.102442	+	0.994739i	$0.532665\pi$
$920$	17.9096	0.590461
$921$	−23.8283	−0.785171
$922$	−6.30309	−0.207581
$923$	5.55497	0.182844
$924$	−48.8136	−1.60585
$925$	0.988937	0.0325161
$926$	4.12159	0.135444
$927$	−1.00000	−0.0328443
$928$	−18.7152	−0.614357
$929$	2.58800	0.0849094	0.0424547	−	0.999098i	$-0.486482\pi$
$929$	2.58800	0.0849094	0.0424547	+	0.999098i	$0.486482\pi$
$930$	2.06460	0.0677009
$931$	−133.306	−4.36893
$932$	−50.2380	−1.64560
$933$	−15.4828	−0.506883
$934$	2.87236	0.0939865
$935$	28.3186	0.926116
$936$	−0.939357	−0.0307038
$937$	36.2915	1.18559	0.592796	−	0.805353i	$-0.298024\pi$
$937$	36.2915	1.18559	0.592796	+	0.805353i	$0.298024\pi$
$938$	1.03681	0.0338531
$939$	−23.8113	−0.777051
$940$	7.82141	0.255106
$941$	25.6323	0.835588	0.417794	−	0.908542i	$-0.362803\pi$
$941$	25.6323	0.835588	0.417794	+	0.908542i	$0.362803\pi$
$942$	−4.53175	−0.147652
$943$	42.1859	1.37376
$944$	−51.3065	−1.66988
$945$	11.5942	0.377159
$946$	−13.7662	−0.447577
$947$	6.97075	0.226519	0.113259	−	0.993565i	$-0.463871\pi$
$947$	6.97075	0.226519	0.113259	+	0.993565i	$0.463871\pi$
$948$	6.08566	0.197653
$949$	14.9728	0.486039
$950$	−0.271983	−0.00882429
$951$	−27.2329	−0.883088
$952$	13.4476	0.435839
$953$	−8.78561	−0.284594	−0.142297	−	0.989824i	$-0.545449\pi$
$953$	−8.78561	−0.284594	−0.142297	+	0.989824i	$0.545449\pi$
$954$	0.562020	0.0181961
$955$	57.2465	1.85245
$956$	−28.8966	−0.934582
$957$	32.3603	1.04606
$958$	6.02498	0.194658
$959$	−3.50355	−0.113136
$960$	−14.6455	−0.472683
$961$	−15.4199	−0.497417
$962$	−1.31719	−0.0424680
$963$	−10.4336	−0.336219
$964$	−26.7276	−0.860838
$965$	−37.9908	−1.22297
$966$	−10.9225	−0.351424
$967$	1.74216	0.0560241	0.0280121	−	0.999608i	$-0.491082\pi$
$967$	1.74216	0.0560241	0.0280121	+	0.999608i	$0.491082\pi$
$968$	10.9252	0.351149
$969$	−17.3069	−0.555978
$970$	5.94899	0.191010
$971$	42.3059	1.35766	0.678831	−	0.734295i	$-0.262487\pi$
$971$	42.3059	1.35766	0.678831	+	0.734295i	$0.262487\pi$
$972$	−1.94325	−0.0623298
$973$	−35.0745	−1.12444
$974$	2.49168	0.0798386
$975$	0.178853	0.00572787
$976$	−48.0594	−1.53834
$977$	30.4369	0.973762	0.486881	−	0.873468i	$-0.338134\pi$
$977$	30.4369	0.973762	0.486881	+	0.873468i	$0.338134\pi$
$978$	0.465941	0.0148991
$979$	21.1957	0.677416
$980$	−89.1013	−2.84624
$981$	−8.32808	−0.265895
$982$	−2.25575	−0.0719839
$983$	−1.14635	−0.0365628	−0.0182814	−	0.999833i	$-0.505819\pi$
$983$	−1.14635	−0.0365628	−0.0182814	+	0.999833i	$0.505819\pi$
$984$	4.56371	0.145486
$985$	−3.10455	−0.0989192
$986$	−4.39330	−0.139911
$987$	−9.67933	−0.308097
$988$	−12.4051	−0.394658
$989$	105.480	3.35407
$990$	−2.48828	−0.0790826
$991$	−54.9217	−1.74464	−0.872322	−	0.488931i	$-0.837387\pi$
$991$	−54.9217	−1.74464	−0.872322	+	0.488931i	$0.837387\pi$
$992$	10.8596	0.344793
$993$	−27.4165	−0.870036
$994$	6.98751	0.221630
$995$	−38.2347	−1.21212
$996$	8.11921	0.257267
$997$	−4.52758	−0.143390	−0.0716950	−	0.997427i	$-0.522841\pi$
$997$	−4.52758	−0.143390	−0.0716950	+	0.997427i	$0.522841\pi$
$998$	−9.33890	−0.295618
$999$	−5.52934	−0.174941

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.l.1.14	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.l.1.14	✓	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-0.238219 q^{2} +1.00000 q^{3} -1.94325 q^{4} +2.19571 q^{5} -0.238219 q^{6} +5.28038 q^{7} +0.939357 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.238219 q^{2} +1.00000 q^{3} -1.94325 q^{4} +2.19571 q^{5} -0.238219 q^{6} +5.28038 q^{7} +0.939357 q^{8} +1.00000 q^{9} -0.523060 q^{10} +4.75715 q^{11} -1.94325 q^{12} -1.00000 q^{13} -1.25788 q^{14} +2.19571 q^{15} +3.66273 q^{16} +2.71112 q^{17} -0.238219 q^{18} -6.38367 q^{19} -4.26682 q^{20} +5.28038 q^{21} -1.13324 q^{22} +8.68320 q^{23} +0.939357 q^{24} -0.178853 q^{25} +0.238219 q^{26} +1.00000 q^{27} -10.2611 q^{28} +6.80245 q^{29} -0.523060 q^{30} -3.94716 q^{31} -2.75124 q^{32} +4.75715 q^{33} -0.645840 q^{34} +11.5942 q^{35} -1.94325 q^{36} -5.52934 q^{37} +1.52071 q^{38} -1.00000 q^{39} +2.06256 q^{40} +4.85834 q^{41} -1.25788 q^{42} +12.1476 q^{43} -9.24435 q^{44} +2.19571 q^{45} -2.06850 q^{46} -1.83308 q^{47} +3.66273 q^{48} +20.8824 q^{49} +0.0426060 q^{50} +2.71112 q^{51} +1.94325 q^{52} -2.35926 q^{53} -0.238219 q^{54} +10.4453 q^{55} +4.96016 q^{56} -6.38367 q^{57} -1.62047 q^{58} -14.0077 q^{59} -4.26682 q^{60} -13.1212 q^{61} +0.940288 q^{62} +5.28038 q^{63} -6.67006 q^{64} -2.19571 q^{65} -1.13324 q^{66} -0.824250 q^{67} -5.26839 q^{68} +8.68320 q^{69} -2.76195 q^{70} -5.55497 q^{71} +0.939357 q^{72} -14.9728 q^{73} +1.31719 q^{74} -0.178853 q^{75} +12.4051 q^{76} +25.1196 q^{77} +0.238219 q^{78} -3.13169 q^{79} +8.04230 q^{80} +1.00000 q^{81} -1.15735 q^{82} -4.17816 q^{83} -10.2611 q^{84} +5.95284 q^{85} -2.89379 q^{86} +6.80245 q^{87} +4.46866 q^{88} +4.45553 q^{89} -0.523060 q^{90} -5.28038 q^{91} -16.8736 q^{92} -3.94716 q^{93} +0.436673 q^{94} -14.0167 q^{95} -2.75124 q^{96} -11.3734 q^{97} -4.97457 q^{98} +4.75715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * q^99

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