LMFDB - Embedded newform 8015.2.a.m.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.42994 q^{2} -3.33526 q^{3} +0.0447232 q^{4} +1.00000 q^{5} +4.76921 q^{6} -1.00000 q^{7} +2.79592 q^{8} +8.12394 q^{9} +O(q^{10})$	\(q-1.42994 q^{2} -3.33526 q^{3} +0.0447232 q^{4} +1.00000 q^{5} +4.76921 q^{6} -1.00000 q^{7} +2.79592 q^{8} +8.12394 q^{9} -1.42994 q^{10} -4.54568 q^{11} -0.149163 q^{12} -5.29038 q^{13} +1.42994 q^{14} -3.33526 q^{15} -4.08745 q^{16} +4.25548 q^{17} -11.6167 q^{18} +4.09779 q^{19} +0.0447232 q^{20} +3.33526 q^{21} +6.50004 q^{22} -7.31885 q^{23} -9.32513 q^{24} +1.00000 q^{25} +7.56491 q^{26} -17.0897 q^{27} -0.0447232 q^{28} +7.64742 q^{29} +4.76921 q^{30} -3.95674 q^{31} +0.252946 q^{32} +15.1610 q^{33} -6.08507 q^{34} -1.00000 q^{35} +0.363329 q^{36} -8.26228 q^{37} -5.85959 q^{38} +17.6448 q^{39} +2.79592 q^{40} -11.3750 q^{41} -4.76921 q^{42} -7.75203 q^{43} -0.203297 q^{44} +8.12394 q^{45} +10.4655 q^{46} -2.69016 q^{47} +13.6327 q^{48} +1.00000 q^{49} -1.42994 q^{50} -14.1931 q^{51} -0.236603 q^{52} +10.9402 q^{53} +24.4372 q^{54} -4.54568 q^{55} -2.79592 q^{56} -13.6672 q^{57} -10.9353 q^{58} +8.18109 q^{59} -0.149163 q^{60} -6.86525 q^{61} +5.65790 q^{62} -8.12394 q^{63} +7.81320 q^{64} -5.29038 q^{65} -21.6793 q^{66} +1.49602 q^{67} +0.190319 q^{68} +24.4102 q^{69} +1.42994 q^{70} +2.39596 q^{71} +22.7139 q^{72} +12.6342 q^{73} +11.8145 q^{74} -3.33526 q^{75} +0.183266 q^{76} +4.54568 q^{77} -25.2309 q^{78} -3.80369 q^{79} -4.08745 q^{80} +32.6266 q^{81} +16.2655 q^{82} -4.32815 q^{83} +0.149163 q^{84} +4.25548 q^{85} +11.0849 q^{86} -25.5061 q^{87} -12.7094 q^{88} +8.42446 q^{89} -11.6167 q^{90} +5.29038 q^{91} -0.327322 q^{92} +13.1967 q^{93} +3.84676 q^{94} +4.09779 q^{95} -0.843639 q^{96} +10.9584 q^{97} -1.42994 q^{98} -36.9288 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) $ 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * 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 $

$2$	−1.42994	−1.01112	−0.505559	−	0.862792i	$-0.668714\pi$
$2$	−1.42994	−1.01112	−0.505559	+	0.862792i	$0.668714\pi$
$3$	−3.33526	−1.92561	−0.962806	−	0.270194i	$-0.912912\pi$
$3$	−3.33526	−1.92561	−0.962806	+	0.270194i	$0.912912\pi$
$4$	0.0447232	0.0223616
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	4.76921	1.94702
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.79592	0.988509
$9$	8.12394	2.70798
$10$	−1.42994	−0.452186
$11$	−4.54568	−1.37057	−0.685287	−	0.728273i	$-0.740323\pi$
$11$	−4.54568	−1.37057	−0.685287	+	0.728273i	$0.740323\pi$
$12$	−0.149163	−0.0430598
$13$	−5.29038	−1.46729	−0.733643	−	0.679535i	$-0.762182\pi$
$13$	−5.29038	−1.46729	−0.733643	+	0.679535i	$0.762182\pi$
$14$	1.42994	0.382167
$15$	−3.33526	−0.861160
$16$	−4.08745	−1.02186
$17$	4.25548	1.03210	0.516052	−	0.856557i	$-0.327401\pi$
$17$	4.25548	1.03210	0.516052	+	0.856557i	$0.327401\pi$
$18$	−11.6167	−2.73809
$19$	4.09779	0.940098	0.470049	−	0.882640i	$-0.344236\pi$
$19$	4.09779	0.940098	0.470049	+	0.882640i	$0.344236\pi$
$20$	0.0447232	0.0100004
$21$	3.33526	0.727813
$22$	6.50004	1.38581
$23$	−7.31885	−1.52609	−0.763043	−	0.646348i	$-0.776295\pi$
$23$	−7.31885	−1.52609	−0.763043	+	0.646348i	$0.776295\pi$
$24$	−9.32513	−1.90348
$25$	1.00000	0.200000
$26$	7.56491	1.48360
$27$	−17.0897	−3.28891
$28$	−0.0447232	−0.00845190
$29$	7.64742	1.42009	0.710046	−	0.704156i	$-0.248674\pi$
$29$	7.64742	1.42009	0.710046	+	0.704156i	$0.248674\pi$
$30$	4.76921	0.870735
$31$	−3.95674	−0.710652	−0.355326	−	0.934743i	$-0.615630\pi$
$31$	−3.95674	−0.710652	−0.355326	+	0.934743i	$0.615630\pi$
$32$	0.252946	0.0447149
$33$	15.1610	2.63919
$34$	−6.08507	−1.04358
$35$	−1.00000	−0.169031
$36$	0.363329	0.0605548
$37$	−8.26228	−1.35831	−0.679155	−	0.733995i	$-0.737654\pi$
$37$	−8.26228	−1.35831	−0.679155	+	0.733995i	$0.737654\pi$
$38$	−5.85959	−0.950551
$39$	17.6448	2.82542
$40$	2.79592	0.442075
$41$	−11.3750	−1.77647	−0.888236	−	0.459386i	$-0.848069\pi$
$41$	−11.3750	−1.77647	−0.888236	+	0.459386i	$0.848069\pi$
$42$	−4.76921	−0.735905
$43$	−7.75203	−1.18217	−0.591087	−	0.806608i	$-0.701301\pi$
$43$	−7.75203	−1.18217	−0.591087	+	0.806608i	$0.701301\pi$
$44$	−0.203297	−0.0306483
$45$	8.12394	1.21105
$46$	10.4655	1.54305
$47$	−2.69016	−0.392400	−0.196200	−	0.980564i	$-0.562860\pi$
$47$	−2.69016	−0.392400	−0.196200	+	0.980564i	$0.562860\pi$
$48$	13.6327	1.96771
$49$	1.00000	0.142857
$50$	−1.42994	−0.202224
$51$	−14.1931	−1.98743
$52$	−0.236603	−0.0328109
$53$	10.9402	1.50275	0.751375	−	0.659875i	$-0.229391\pi$
$53$	10.9402	1.50275	0.751375	+	0.659875i	$0.229391\pi$
$54$	24.4372	3.32548
$55$	−4.54568	−0.612939
$56$	−2.79592	−0.373621
$57$	−13.6672	−1.81026
$58$	−10.9353	−1.43588
$59$	8.18109	1.06509	0.532543	−	0.846403i	$-0.321236\pi$
$59$	8.18109	1.06509	0.532543	+	0.846403i	$0.321236\pi$
$60$	−0.149163	−0.0192569
$61$	−6.86525	−0.879005	−0.439503	−	0.898241i	$-0.644845\pi$
$61$	−6.86525	−0.879005	−0.439503	+	0.898241i	$0.644845\pi$
$62$	5.65790	0.718553
$63$	−8.12394	−1.02352
$64$	7.81320	0.976649
$65$	−5.29038	−0.656190
$66$	−21.6793	−2.66854
$67$	1.49602	0.182768	0.0913839	−	0.995816i	$-0.470871\pi$
$67$	1.49602	0.182768	0.0913839	+	0.995816i	$0.470871\pi$
$68$	0.190319	0.0230795
$69$	24.4102	2.93865
$70$	1.42994	0.170910
$71$	2.39596	0.284348	0.142174	−	0.989842i	$-0.454591\pi$
$71$	2.39596	0.284348	0.142174	+	0.989842i	$0.454591\pi$
$72$	22.7139	2.67686
$73$	12.6342	1.47872	0.739359	−	0.673311i	$-0.235129\pi$
$73$	12.6342	1.47872	0.739359	+	0.673311i	$0.235129\pi$
$74$	11.8145	1.37341
$75$	−3.33526	−0.385122
$76$	0.183266	0.0210221
$77$	4.54568	0.518028
$78$	−25.2309	−2.85684
$79$	−3.80369	−0.427949	−0.213974	−	0.976839i	$-0.568641\pi$
$79$	−3.80369	−0.427949	−0.213974	+	0.976839i	$0.568641\pi$
$80$	−4.08745	−0.456990
$81$	32.6266	3.62518
$82$	16.2655	1.79623
$83$	−4.32815	−0.475076	−0.237538	−	0.971378i	$-0.576340\pi$
$83$	−4.32815	−0.475076	−0.237538	+	0.971378i	$0.576340\pi$
$84$	0.149163	0.0162751
$85$	4.25548	0.461571
$86$	11.0849	1.19532
$87$	−25.5061	−2.73454
$88$	−12.7094	−1.35482
$89$	8.42446	0.892991	0.446496	−	0.894786i	$-0.352672\pi$
$89$	8.42446	0.892991	0.446496	+	0.894786i	$0.352672\pi$
$90$	−11.6167	−1.22451
$91$	5.29038	0.554582
$92$	−0.327322	−0.0341257
$93$	13.1967	1.36844
$94$	3.84676	0.396763
$95$	4.09779	0.420424
$96$	−0.843639	−0.0861035
$97$	10.9584	1.11265	0.556327	−	0.830963i	$-0.312210\pi$
$97$	10.9584	1.11265	0.556327	+	0.830963i	$0.312210\pi$
$98$	−1.42994	−0.144446
$99$	−36.9288	−3.71149
$100$	0.0447232	0.00447232
$101$	−8.37677	−0.833520	−0.416760	−	0.909017i	$-0.636834\pi$
$101$	−8.37677	−0.833520	−0.416760	+	0.909017i	$0.636834\pi$
$102$	20.2953	2.00953
$103$	−6.64093	−0.654351	−0.327175	−	0.944964i	$-0.606097\pi$
$103$	−6.64093	−0.654351	−0.327175	+	0.944964i	$0.606097\pi$
$104$	−14.7915	−1.45043
$105$	3.33526	0.325488
$106$	−15.6438	−1.51946
$107$	−7.95333	−0.768878	−0.384439	−	0.923150i	$-0.625605\pi$
$107$	−7.95333	−0.768878	−0.384439	+	0.923150i	$0.625605\pi$
$108$	−0.764305	−0.0735453
$109$	−13.6209	−1.30464	−0.652321	−	0.757942i	$-0.726205\pi$
$109$	−13.6209	−1.30464	−0.652321	+	0.757942i	$0.726205\pi$
$110$	6.50004	0.619755
$111$	27.5568	2.61558
$112$	4.08745	0.386227
$113$	−14.8060	−1.39283	−0.696415	−	0.717639i	$-0.745223\pi$
$113$	−14.8060	−1.39283	−0.696415	+	0.717639i	$0.745223\pi$
$114$	19.5432	1.83039
$115$	−7.31885	−0.682486
$116$	0.342017	0.0317555
$117$	−42.9787	−3.97338
$118$	−11.6984	−1.07693
$119$	−4.25548	−0.390099
$120$	−9.32513	−0.851264
$121$	9.66321	0.878474
$122$	9.81689	0.888779
$123$	37.9385	3.42080
$124$	−0.176958	−0.0158913
$125$	1.00000	0.0894427
$126$	11.6167	1.03490
$127$	−9.53576	−0.846162	−0.423081	−	0.906092i	$-0.639051\pi$
$127$	−9.53576	−0.846162	−0.423081	+	0.906092i	$0.639051\pi$
$128$	−11.6783	−1.03222
$129$	25.8550	2.27641
$130$	7.56491	0.663487
$131$	6.92419	0.604969	0.302485	−	0.953154i	$-0.402184\pi$
$131$	6.92419	0.604969	0.302485	+	0.953154i	$0.402184\pi$
$132$	0.678049	0.0590166
$133$	−4.09779	−0.355324
$134$	−2.13921	−0.184800
$135$	−17.0897	−1.47084
$136$	11.8980	1.02024
$137$	18.7331	1.60048	0.800238	−	0.599683i	$-0.204707\pi$
$137$	18.7331	1.60048	0.800238	+	0.599683i	$0.204707\pi$
$138$	−34.9051	−2.97132
$139$	3.58671	0.304221	0.152110	−	0.988364i	$-0.451393\pi$
$139$	3.58671	0.304221	0.152110	+	0.988364i	$0.451393\pi$
$140$	−0.0447232	−0.00377980
$141$	8.97237	0.755609
$142$	−3.42608	−0.287510
$143$	24.0484	2.01102
$144$	−33.2062	−2.76718
$145$	7.64742	0.635084
$146$	−18.0661	−1.49516
$147$	−3.33526	−0.275087
$148$	−0.369516	−0.0303740
$149$	−4.93102	−0.403965	−0.201983	−	0.979389i	$-0.564738\pi$
$149$	−4.93102	−0.403965	−0.201983	+	0.979389i	$0.564738\pi$
$150$	4.76921	0.389404
$151$	4.56452	0.371456	0.185728	−	0.982601i	$-0.440536\pi$
$151$	4.56452	0.371456	0.185728	+	0.982601i	$0.440536\pi$
$152$	11.4571	0.929295
$153$	34.5712	2.79492
$154$	−6.50004	−0.523788
$155$	−3.95674	−0.317813
$156$	0.789131	0.0631810
$157$	−22.6990	−1.81158	−0.905788	−	0.423730i	$-0.860720\pi$
$157$	−22.6990	−1.81158	−0.905788	+	0.423730i	$0.860720\pi$
$158$	5.43904	0.432707
$159$	−36.4883	−2.89371
$160$	0.252946	0.0199971
$161$	7.31885	0.576806
$162$	−46.6540	−3.66548
$163$	−15.1136	−1.18379	−0.591895	−	0.806015i	$-0.701620\pi$
$163$	−15.1136	−1.18379	−0.591895	+	0.806015i	$0.701620\pi$
$164$	−0.508726	−0.0397248
$165$	15.1610	1.18028
$166$	6.18898	0.480358
$167$	0.734327	0.0568239	0.0284120	−	0.999596i	$-0.490955\pi$
$167$	0.734327	0.0568239	0.0284120	+	0.999596i	$0.490955\pi$
$168$	9.32513	0.719449
$169$	14.9881	1.15293
$170$	−6.08507	−0.466703
$171$	33.2902	2.54577
$172$	−0.346696	−0.0264353
$173$	−19.5031	−1.48280	−0.741398	−	0.671065i	$-0.765837\pi$
$173$	−19.5031	−1.48280	−0.741398	+	0.671065i	$0.765837\pi$
$174$	36.4722	2.76495
$175$	−1.00000	−0.0755929
$176$	18.5802	1.40054
$177$	−27.2860	−2.05094
$178$	−12.0465	−0.902921
$179$	7.06550	0.528100	0.264050	−	0.964509i	$-0.414942\pi$
$179$	7.06550	0.528100	0.264050	+	0.964509i	$0.414942\pi$
$180$	0.363329	0.0270809
$181$	−25.7788	−1.91613	−0.958063	−	0.286557i	$-0.907489\pi$
$181$	−25.7788	−1.91613	−0.958063	+	0.286557i	$0.907489\pi$
$182$	−7.56491	−0.560749
$183$	22.8974	1.69262
$184$	−20.4629	−1.50855
$185$	−8.26228	−0.607455
$186$	−18.8705	−1.38365
$187$	−19.3440	−1.41458
$188$	−0.120313	−0.00877469
$189$	17.0897	1.24309
$190$	−5.85959	−0.425099
$191$	8.31722	0.601813	0.300906	−	0.953654i	$-0.402711\pi$
$191$	8.31722	0.601813	0.300906	+	0.953654i	$0.402711\pi$
$192$	−26.0590	−1.88065
$193$	25.2945	1.82074	0.910370	−	0.413796i	$-0.135797\pi$
$193$	25.2945	1.82074	0.910370	+	0.413796i	$0.135797\pi$
$194$	−15.6698	−1.12503
$195$	17.6448	1.26357
$196$	0.0447232	0.00319452
$197$	−11.4224	−0.813810	−0.406905	−	0.913471i	$-0.633392\pi$
$197$	−11.4224	−0.813810	−0.406905	+	0.913471i	$0.633392\pi$
$198$	52.8060	3.75276
$199$	5.23632	0.371193	0.185596	−	0.982626i	$-0.440578\pi$
$199$	5.23632	0.371193	0.185596	+	0.982626i	$0.440578\pi$
$200$	2.79592	0.197702
$201$	−4.98961	−0.351940
$202$	11.9783	0.842788
$203$	−7.64742	−0.536744
$204$	−0.634761	−0.0444422
$205$	−11.3750	−0.794463
$206$	9.49612	0.661626
$207$	−59.4579	−4.13261
$208$	21.6241	1.49936
$209$	−18.6272	−1.28847
$210$	−4.76921	−0.329107
$211$	−23.4811	−1.61651	−0.808253	−	0.588835i	$-0.799587\pi$
$211$	−23.4811	−1.61651	−0.808253	+	0.588835i	$0.799587\pi$
$212$	0.489281	0.0336039
$213$	−7.99115	−0.547545
$214$	11.3728	0.777427
$215$	−7.75203	−0.528684
$216$	−47.7814	−3.25111
$217$	3.95674	0.268601
$218$	19.4770	1.31915
$219$	−42.1382	−2.84744
$220$	−0.203297	−0.0137063
$221$	−22.5131	−1.51439
$222$	−39.4045	−2.64466
$223$	−16.1979	−1.08469	−0.542346	−	0.840155i	$-0.682464\pi$
$223$	−16.1979	−1.08469	−0.542346	+	0.840155i	$0.682464\pi$
$224$	−0.252946	−0.0169006
$225$	8.12394	0.541596
$226$	21.1716	1.40832
$227$	−14.1945	−0.942124	−0.471062	−	0.882100i	$-0.656129\pi$
$227$	−14.1945	−0.942124	−0.471062	+	0.882100i	$0.656129\pi$
$228$	−0.611241	−0.0404804
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	10.4655	0.690075
$231$	−15.1610	−0.997521
$232$	21.3816	1.40377
$233$	−22.7789	−1.49230	−0.746149	−	0.665779i	$-0.768099\pi$
$233$	−22.7789	−1.49230	−0.746149	+	0.665779i	$0.768099\pi$
$234$	61.4569	4.01756
$235$	−2.69016	−0.175486
$236$	0.365885	0.0238171
$237$	12.6863	0.824063
$238$	6.08507	0.394436
$239$	−28.3257	−1.83224	−0.916118	−	0.400910i	$-0.868694\pi$
$239$	−28.3257	−1.83224	−0.916118	+	0.400910i	$0.868694\pi$
$240$	13.6327	0.879986
$241$	5.31468	0.342349	0.171174	−	0.985241i	$-0.445244\pi$
$241$	5.31468	0.342349	0.171174	+	0.985241i	$0.445244\pi$
$242$	−13.8178	−0.888242
$243$	−57.5491	−3.69178
$244$	−0.307036	−0.0196560
$245$	1.00000	0.0638877
$246$	−54.2497	−3.45883
$247$	−21.6789	−1.37939
$248$	−11.0628	−0.702485
$249$	14.4355	0.914811
$250$	−1.42994	−0.0904372
$251$	27.7286	1.75021	0.875106	−	0.483931i	$-0.160792\pi$
$251$	27.7286	1.75021	0.875106	+	0.483931i	$0.160792\pi$
$252$	−0.363329	−0.0228876
$253$	33.2691	2.09161
$254$	13.6355	0.855570
$255$	−14.1931	−0.888807
$256$	1.07282	0.0670515
$257$	26.3423	1.64319	0.821594	−	0.570073i	$-0.193085\pi$
$257$	26.3423	1.64319	0.821594	+	0.570073i	$0.193085\pi$
$258$	−36.9711	−2.30172
$259$	8.26228	0.513393
$260$	−0.236603	−0.0146735
$261$	62.1272	3.84558
$262$	−9.90116	−0.611696
$263$	−17.0663	−1.05235	−0.526176	−	0.850376i	$-0.676375\pi$
$263$	−17.0663	−1.05235	−0.526176	+	0.850376i	$0.676375\pi$
$264$	42.3891	2.60887
$265$	10.9402	0.672051
$266$	5.85959	0.359274
$267$	−28.0978	−1.71955
$268$	0.0669068	0.00408698
$269$	24.8340	1.51415	0.757077	−	0.653326i	$-0.226627\pi$
$269$	24.8340	1.51415	0.757077	+	0.653326i	$0.226627\pi$
$270$	24.4372	1.48720
$271$	−16.5615	−1.00604	−0.503020	−	0.864275i	$-0.667778\pi$
$271$	−16.5615	−1.00604	−0.503020	+	0.864275i	$0.667778\pi$
$272$	−17.3940	−1.05467
$273$	−17.6448	−1.06791
$274$	−26.7872	−1.61827
$275$	−4.54568	−0.274115
$276$	1.09170	0.0657129
$277$	−15.4819	−0.930219	−0.465110	−	0.885253i	$-0.653985\pi$
$277$	−15.4819	−0.930219	−0.465110	+	0.885253i	$0.653985\pi$
$278$	−5.12877	−0.307603
$279$	−32.1443	−1.92443
$280$	−2.79592	−0.167088
$281$	−8.35056	−0.498153	−0.249076	−	0.968484i	$-0.580127\pi$
$281$	−8.35056	−0.498153	−0.249076	+	0.968484i	$0.580127\pi$
$282$	−12.8299	−0.764011
$283$	9.30137	0.552909	0.276454	−	0.961027i	$-0.410841\pi$
$283$	9.30137	0.552909	0.276454	+	0.961027i	$0.410841\pi$
$284$	0.107155	0.00635849
$285$	−13.6672	−0.809574
$286$	−34.3877	−2.03339
$287$	11.3750	0.671444
$288$	2.05492	0.121087
$289$	1.10907	0.0652396
$290$	−10.9353	−0.642145
$291$	−36.5490	−2.14254
$292$	0.565041	0.0330665
$293$	−28.7298	−1.67841	−0.839206	−	0.543814i	$-0.816980\pi$
$293$	−28.7298	−1.67841	−0.839206	+	0.543814i	$0.816980\pi$
$294$	4.76921	0.278146
$295$	8.18109	0.476321
$296$	−23.1007	−1.34270
$297$	77.6841	4.50769
$298$	7.05106	0.408457
$299$	38.7195	2.23920
$300$	−0.149163	−0.00861196
$301$	7.75203	0.446820
$302$	−6.52699	−0.375586
$303$	27.9387	1.60504
$304$	−16.7495	−0.960650
$305$	−6.86525	−0.393103
$306$	−49.4347	−2.82600
$307$	−1.01439	−0.0578941	−0.0289470	−	0.999581i	$-0.509215\pi$
$307$	−1.01439	−0.0578941	−0.0289470	+	0.999581i	$0.509215\pi$
$308$	0.203297	0.0115840
$309$	22.1492	1.26003
$310$	5.65790	0.321347
$311$	16.6455	0.943881	0.471940	−	0.881630i	$-0.343554\pi$
$311$	16.6455	0.943881	0.471940	+	0.881630i	$0.343554\pi$
$312$	49.3334	2.79296
$313$	−1.68550	−0.0952703	−0.0476352	−	0.998865i	$-0.515168\pi$
$313$	−1.68550	−0.0952703	−0.0476352	+	0.998865i	$0.515168\pi$
$314$	32.4582	1.83172
$315$	−8.12394	−0.457732
$316$	−0.170113	−0.00956962
$317$	22.7824	1.27959	0.639794	−	0.768547i	$-0.279020\pi$
$317$	22.7824	1.27959	0.639794	+	0.768547i	$0.279020\pi$
$318$	52.1761	2.92589
$319$	−34.7627	−1.94634
$320$	7.81320	0.436771
$321$	26.5264	1.48056
$322$	−10.4655	−0.583219
$323$	17.4380	0.970279
$324$	1.45917	0.0810648
$325$	−5.29038	−0.293457
$326$	21.6116	1.19695
$327$	45.4291	2.51224
$328$	−31.8036	−1.75606
$329$	2.69016	0.148313
$330$	−21.6793	−1.19341
$331$	11.5597	0.635376	0.317688	−	0.948195i	$-0.397094\pi$
$331$	11.5597	0.635376	0.317688	+	0.948195i	$0.397094\pi$
$332$	−0.193569	−0.0106235
$333$	−67.1222	−3.67828
$334$	−1.05004	−0.0574557
$335$	1.49602	0.0817362
$336$	−13.6327	−0.743724
$337$	−12.0403	−0.655879	−0.327939	−	0.944699i	$-0.606354\pi$
$337$	−12.0403	−0.655879	−0.327939	+	0.944699i	$0.606354\pi$
$338$	−21.4320	−1.16575
$339$	49.3818	2.68205
$340$	0.190319	0.0103215
$341$	17.9861	0.974001
$342$	−47.6029	−2.57407
$343$	−1.00000	−0.0539949
$344$	−21.6741	−1.16859
$345$	24.4102	1.31420
$346$	27.8883	1.49928
$347$	−7.89492	−0.423822	−0.211911	−	0.977289i	$-0.567969\pi$
$347$	−7.89492	−0.423822	−0.211911	+	0.977289i	$0.567969\pi$
$348$	−1.14072	−0.0611488
$349$	−24.1086	−1.29050	−0.645251	−	0.763971i	$-0.723247\pi$
$349$	−24.1086	−1.29050	−0.645251	+	0.763971i	$0.723247\pi$
$350$	1.42994	0.0764334
$351$	90.4107	4.82577
$352$	−1.14981	−0.0612851
$353$	−18.6663	−0.993506	−0.496753	−	0.867892i	$-0.665475\pi$
$353$	−18.6663	−0.993506	−0.496753	+	0.867892i	$0.665475\pi$
$354$	39.0173	2.07375
$355$	2.39596	0.127164
$356$	0.376769	0.0199687
$357$	14.1931	0.751179
$358$	−10.1032	−0.533972
$359$	−28.2600	−1.49150	−0.745752	−	0.666223i	$-0.767910\pi$
$359$	−28.2600	−1.49150	−0.745752	+	0.666223i	$0.767910\pi$
$360$	22.7139	1.19713
$361$	−2.20811	−0.116216
$362$	36.8622	1.93743
$363$	−32.2293	−1.69160
$364$	0.236603	0.0124014
$365$	12.6342	0.661303
$366$	−32.7418	−1.71144
$367$	−24.9119	−1.30039	−0.650195	−	0.759767i	$-0.725313\pi$
$367$	−24.9119	−1.30039	−0.650195	+	0.759767i	$0.725313\pi$
$368$	29.9154	1.55945
$369$	−92.4096	−4.81065
$370$	11.8145	0.614209
$371$	−10.9402	−0.567986
$372$	0.590201	0.0306005
$373$	−6.09760	−0.315722	−0.157861	−	0.987461i	$-0.550460\pi$
$373$	−6.09760	−0.315722	−0.157861	+	0.987461i	$0.550460\pi$
$374$	27.6608	1.43030
$375$	−3.33526	−0.172232
$376$	−7.52148	−0.387891
$377$	−40.4578	−2.08368
$378$	−24.4372	−1.25691
$379$	13.8525	0.711554	0.355777	−	0.934571i	$-0.384216\pi$
$379$	13.8525	0.711554	0.355777	+	0.934571i	$0.384216\pi$
$380$	0.183266	0.00940137
$381$	31.8042	1.62938
$382$	−11.8931	−0.608504
$383$	−27.7351	−1.41720	−0.708598	−	0.705613i	$-0.750672\pi$
$383$	−27.7351	−1.41720	−0.708598	+	0.705613i	$0.750672\pi$
$384$	38.9501	1.98766
$385$	4.54568	0.231669
$386$	−36.1696	−1.84098
$387$	−62.9770	−3.20130
$388$	0.490094	0.0248808
$389$	−10.6581	−0.540387	−0.270194	−	0.962806i	$-0.587088\pi$
$389$	−10.6581	−0.540387	−0.270194	+	0.962806i	$0.587088\pi$
$390$	−25.2309	−1.27762
$391$	−31.1452	−1.57508
$392$	2.79592	0.141216
$393$	−23.0939	−1.16494
$394$	16.3333	0.822859
$395$	−3.80369	−0.191384
$396$	−1.65158	−0.0829949
$397$	25.4749	1.27855	0.639274	−	0.768979i	$-0.279235\pi$
$397$	25.4749	1.27855	0.639274	+	0.768979i	$0.279235\pi$
$398$	−7.48761	−0.375320
$399$	13.6672	0.684215
$400$	−4.08745	−0.204372
$401$	4.83976	0.241686	0.120843	−	0.992672i	$-0.461440\pi$
$401$	4.83976	0.241686	0.120843	+	0.992672i	$0.461440\pi$
$402$	7.13483	0.355853
$403$	20.9326	1.04273
$404$	−0.374636	−0.0186389
$405$	32.6266	1.62123
$406$	10.9353	0.542712
$407$	37.5577	1.86166
$408$	−39.6829	−1.96459
$409$	−0.00770904	−0.000381187 0	−0.000190594	−	1.00000i	$-0.500061\pi$
$409$	−0.00770904	−0.000381187 0	−0.000190594		1.00000i	$0.500061\pi$
$410$	16.2655	0.803296
$411$	−62.4797	−3.08189
$412$	−0.297004	−0.0146323
$413$	−8.18109	−0.402565
$414$	85.0211	4.17856
$415$	−4.32815	−0.212460
$416$	−1.33818	−0.0656096
$417$	−11.9626	−0.585811
$418$	26.6358	1.30280
$419$	13.4027	0.654767	0.327383	−	0.944892i	$-0.393833\pi$
$419$	13.4027	0.654767	0.327383	+	0.944892i	$0.393833\pi$
$420$	0.149163	0.00727843
$421$	10.7128	0.522111	0.261056	−	0.965324i	$-0.415929\pi$
$421$	10.7128	0.522111	0.261056	+	0.965324i	$0.415929\pi$
$422$	33.5765	1.63448
$423$	−21.8547	−1.06261
$424$	30.5879	1.48548
$425$	4.25548	0.206421
$426$	11.4269	0.553633
$427$	6.86525	0.332233
$428$	−0.355699	−0.0171933
$429$	−80.2075	−3.87245
$430$	11.0849	0.534563
$431$	15.5669	0.749830	0.374915	−	0.927059i	$-0.377672\pi$
$431$	15.5669	0.749830	0.374915	+	0.927059i	$0.377672\pi$
$432$	69.8531	3.36081
$433$	3.74090	0.179776	0.0898880	−	0.995952i	$-0.471349\pi$
$433$	3.74090	0.179776	0.0898880	+	0.995952i	$0.471349\pi$
$434$	−5.65790	−0.271588
$435$	−25.5061	−1.22293
$436$	−0.609169	−0.0291739
$437$	−29.9911	−1.43467
$438$	60.2551	2.87910
$439$	21.3190	1.01750	0.508749	−	0.860915i	$-0.330108\pi$
$439$	21.3190	1.01750	0.508749	+	0.860915i	$0.330108\pi$
$440$	−12.7094	−0.605896
$441$	8.12394	0.386854
$442$	32.1923	1.53123
$443$	−0.559783	−0.0265961	−0.0132980	−	0.999912i	$-0.504233\pi$
$443$	−0.559783	−0.0265961	−0.0132980	+	0.999912i	$0.504233\pi$
$444$	1.23243	0.0584885
$445$	8.42446	0.399358
$446$	23.1620	1.09675
$447$	16.4462	0.777880
$448$	−7.81320	−0.369139
$449$	11.8451	0.559006	0.279503	−	0.960145i	$-0.409830\pi$
$449$	11.8451	0.559006	0.279503	+	0.960145i	$0.409830\pi$
$450$	−11.6167	−0.547618
$451$	51.7070	2.43479
$452$	−0.662172	−0.0311459
$453$	−15.2239	−0.715279
$454$	20.2973	0.952599
$455$	5.29038	0.248017
$456$	−38.2124	−1.78946
$457$	−3.96649	−0.185544	−0.0927722	−	0.995687i	$-0.529573\pi$
$457$	−3.96649	−0.185544	−0.0927722	+	0.995687i	$0.529573\pi$
$458$	1.42994	0.0668166
$459$	−72.7246	−3.39449
$460$	−0.327322	−0.0152615
$461$	−29.4311	−1.37074	−0.685371	−	0.728194i	$-0.740360\pi$
$461$	−29.4311	−1.37074	−0.685371	+	0.728194i	$0.740360\pi$
$462$	21.6793	1.00861
$463$	12.7417	0.592159	0.296079	−	0.955163i	$-0.404321\pi$
$463$	12.7417	0.592159	0.296079	+	0.955163i	$0.404321\pi$
$464$	−31.2584	−1.45114
$465$	13.1967	0.611985
$466$	32.5725	1.50889
$467$	20.3927	0.943661	0.471831	−	0.881689i	$-0.343593\pi$
$467$	20.3927	0.943661	0.471831	+	0.881689i	$0.343593\pi$
$468$	−1.92215	−0.0888512
$469$	−1.49602	−0.0690797
$470$	3.84676	0.177438
$471$	75.7070	3.48839
$472$	22.8737	1.05285
$473$	35.2383	1.62026
$474$	−18.1406	−0.833226
$475$	4.09779	0.188020
$476$	−0.190319	−0.00872324
$477$	88.8775	4.06942
$478$	40.5040	1.85261
$479$	16.2607	0.742971	0.371485	−	0.928439i	$-0.378849\pi$
$479$	16.2607	0.742971	0.371485	+	0.928439i	$0.378849\pi$
$480$	−0.843639	−0.0385067
$481$	43.7106	1.99303
$482$	−7.59967	−0.346155
$483$	−24.4102	−1.11070
$484$	0.432170	0.0196441
$485$	10.9584	0.497594
$486$	82.2916	3.73282
$487$	−1.33995	−0.0607187	−0.0303594	−	0.999539i	$-0.509665\pi$
$487$	−1.33995	−0.0607187	−0.0303594	+	0.999539i	$0.509665\pi$
$488$	−19.1947	−0.868905
$489$	50.4078	2.27952
$490$	−1.42994	−0.0645980
$491$	−18.3009	−0.825908	−0.412954	−	0.910752i	$-0.635503\pi$
$491$	−18.3009	−0.825908	−0.412954	+	0.910752i	$0.635503\pi$
$492$	1.69673	0.0764945
$493$	32.5434	1.46568
$494$	30.9994	1.39473
$495$	−36.9288	−1.65983
$496$	16.1730	0.726188
$497$	−2.39596	−0.107474
$498$	−20.6418	−0.924983
$499$	5.60312	0.250830	0.125415	−	0.992104i	$-0.459974\pi$
$499$	5.60312	0.250830	0.125415	+	0.992104i	$0.459974\pi$
$500$	0.0447232	0.00200008
$501$	−2.44917	−0.109421
$502$	−39.6501	−1.76967
$503$	20.7430	0.924884	0.462442	−	0.886650i	$-0.346973\pi$
$503$	20.7430	0.924884	0.462442	+	0.886650i	$0.346973\pi$
$504$	−22.7139	−1.01176
$505$	−8.37677	−0.372762
$506$	−47.5728	−2.11487
$507$	−49.9891	−2.22009
$508$	−0.426470	−0.0189215
$509$	3.72437	0.165080	0.0825399	−	0.996588i	$-0.473697\pi$
$509$	3.72437	0.165080	0.0825399	+	0.996588i	$0.473697\pi$
$510$	20.2953	0.898689
$511$	−12.6342	−0.558903
$512$	21.8225	0.964427
$513$	−70.0298	−3.09189
$514$	−37.6679	−1.66146
$515$	−6.64093	−0.292634
$516$	1.15632	0.0509041
$517$	12.2286	0.537813
$518$	−11.8145	−0.519101
$519$	65.0480	2.85529
$520$	−14.7915	−0.648650
$521$	29.1441	1.27683	0.638414	−	0.769693i	$-0.279591\pi$
$521$	29.1441	1.27683	0.638414	+	0.769693i	$0.279591\pi$
$522$	−88.8381	−3.88834
$523$	36.5649	1.59887	0.799436	−	0.600751i	$-0.205132\pi$
$523$	36.5649	1.59887	0.799436	+	0.600751i	$0.205132\pi$
$524$	0.309672	0.0135281
$525$	3.33526	0.145563
$526$	24.4037	1.06405
$527$	−16.8378	−0.733467
$528$	−61.9698	−2.69689
$529$	30.5655	1.32894
$530$	−15.6438	−0.679523
$531$	66.4627	2.88423
$532$	−0.183266	−0.00794561
$533$	60.1779	2.60659
$534$	40.1781	1.73867
$535$	−7.95333	−0.343853
$536$	4.18276	0.180668
$537$	−23.5652	−1.01692
$538$	−35.5110	−1.53099
$539$	−4.54568	−0.195796
$540$	−0.764305	−0.0328904
$541$	−4.72131	−0.202985	−0.101493	−	0.994836i	$-0.532362\pi$
$541$	−4.72131	−0.202985	−0.101493	+	0.994836i	$0.532362\pi$
$542$	23.6819	1.01723
$543$	85.9791	3.68972
$544$	1.07640	0.0461504
$545$	−13.6209	−0.583454
$546$	25.2309	1.07978
$547$	29.4127	1.25760	0.628799	−	0.777568i	$-0.283547\pi$
$547$	29.4127	1.25760	0.628799	+	0.777568i	$0.283547\pi$
$548$	0.837804	0.0357892
$549$	−55.7729	−2.38033
$550$	6.50004	0.277163
$551$	31.3375	1.33502
$552$	68.2492	2.90488
$553$	3.80369	0.161749
$554$	22.1382	0.940562
$555$	27.5568	1.16972
$556$	0.160409	0.00680286
$557$	31.6715	1.34197	0.670983	−	0.741473i	$-0.265872\pi$
$557$	31.6715	1.34197	0.670983	+	0.741473i	$0.265872\pi$
$558$	45.9644	1.94583
$559$	41.0112	1.73459
$560$	4.08745	0.172726
$561$	64.5173	2.72392
$562$	11.9408	0.503692
$563$	−39.5518	−1.66691	−0.833455	−	0.552588i	$-0.813640\pi$
$563$	−39.5518	−1.66691	−0.833455	+	0.552588i	$0.813640\pi$
$564$	0.401273	0.0168966
$565$	−14.8060	−0.622893
$566$	−13.3004	−0.559057
$567$	−32.6266	−1.37019
$568$	6.69893	0.281081
$569$	29.3543	1.23060	0.615298	−	0.788294i	$-0.289036\pi$
$569$	29.3543	1.23060	0.615298	+	0.788294i	$0.289036\pi$
$570$	19.5432	0.818576
$571$	10.3478	0.433043	0.216522	−	0.976278i	$-0.430529\pi$
$571$	10.3478	0.433043	0.216522	+	0.976278i	$0.430529\pi$
$572$	1.07552	0.0449698
$573$	−27.7401	−1.15886
$574$	−16.2655	−0.678909
$575$	−7.31885	−0.305217
$576$	63.4739	2.64475
$577$	31.6649	1.31823	0.659113	−	0.752044i	$-0.270932\pi$
$577$	31.6649	1.31823	0.659113	+	0.752044i	$0.270932\pi$
$578$	−1.58591	−0.0659650
$579$	−84.3637	−3.50604
$580$	0.342017	0.0142015
$581$	4.32815	0.179562
$582$	52.2628	2.16636
$583$	−49.7306	−2.05963
$584$	35.3242	1.46173
$585$	−42.9787	−1.77695
$586$	41.0818	1.69707
$587$	26.1957	1.08121	0.540607	−	0.841275i	$-0.318195\pi$
$587$	26.1957	1.08121	0.540607	+	0.841275i	$0.318195\pi$
$588$	−0.149163	−0.00615140
$589$	−16.2139	−0.668082
$590$	−11.6984	−0.481618
$591$	38.0965	1.56708
$592$	33.7716	1.38800
$593$	−1.39073	−0.0571103	−0.0285552	−	0.999592i	$-0.509091\pi$
$593$	−1.39073	−0.0571103	−0.0285552	+	0.999592i	$0.509091\pi$
$594$	−111.084	−4.55781
$595$	−4.25548	−0.174457
$596$	−0.220531	−0.00903331
$597$	−17.4645	−0.714773
$598$	−55.3664	−2.26410
$599$	−20.3658	−0.832123	−0.416061	−	0.909337i	$-0.636590\pi$
$599$	−20.3658	−0.832123	−0.416061	+	0.909337i	$0.636590\pi$
$600$	−9.32513	−0.380697
$601$	−14.3564	−0.585609	−0.292804	−	0.956172i	$-0.594589\pi$
$601$	−14.3564	−0.585609	−0.292804	+	0.956172i	$0.594589\pi$
$602$	−11.0849	−0.451788
$603$	12.1536	0.494931
$604$	0.204140	0.00830635
$605$	9.66321	0.392865
$606$	−39.9506	−1.62288
$607$	33.3681	1.35437	0.677186	−	0.735812i	$-0.263199\pi$
$607$	33.3681	1.35437	0.677186	+	0.735812i	$0.263199\pi$
$608$	1.03652	0.0420364
$609$	25.5061	1.03356
$610$	9.81689	0.397474
$611$	14.2319	0.575763
$612$	1.54614	0.0624989
$613$	−26.6170	−1.07505	−0.537525	−	0.843248i	$-0.680641\pi$
$613$	−26.6170	−1.07505	−0.537525	+	0.843248i	$0.680641\pi$
$614$	1.45051	0.0585378
$615$	37.9385	1.52983
$616$	12.7094	0.512076
$617$	−16.8308	−0.677581	−0.338791	−	0.940862i	$-0.610018\pi$
$617$	−16.8308	−0.677581	−0.338791	+	0.940862i	$0.610018\pi$
$618$	−31.6720	−1.27404
$619$	8.24225	0.331284	0.165642	−	0.986186i	$-0.447030\pi$
$619$	8.24225	0.331284	0.165642	+	0.986186i	$0.447030\pi$
$620$	−0.176958	−0.00710681
$621$	125.077	5.01915
$622$	−23.8021	−0.954376
$623$	−8.42446	−0.337519
$624$	−72.1220	−2.88719
$625$	1.00000	0.0400000
$626$	2.41017	0.0963296
$627$	62.1267	2.48110
$628$	−1.01517	−0.0405098
$629$	−35.1599	−1.40192
$630$	11.6167	0.462822
$631$	−25.9558	−1.03329	−0.516643	−	0.856201i	$-0.672818\pi$
$631$	−25.9558	−1.03329	−0.516643	+	0.856201i	$0.672818\pi$
$632$	−10.6348	−0.423031
$633$	78.3156	3.11276
$634$	−32.5774	−1.29382
$635$	−9.53576	−0.378415
$636$	−1.63188	−0.0647081
$637$	−5.29038	−0.209612
$638$	49.7086	1.96798
$639$	19.4647	0.770010
$640$	−11.6783	−0.461624
$641$	−18.7596	−0.740960	−0.370480	−	0.928841i	$-0.620807\pi$
$641$	−18.7596	−0.740960	−0.370480	+	0.928841i	$0.620807\pi$
$642$	−37.9311	−1.49702
$643$	−6.00027	−0.236628	−0.118314	−	0.992976i	$-0.537749\pi$
$643$	−6.00027	−0.236628	−0.118314	+	0.992976i	$0.537749\pi$
$644$	0.327322	0.0128983
$645$	25.8550	1.01804
$646$	−24.9353	−0.981068
$647$	−20.2229	−0.795045	−0.397523	−	0.917592i	$-0.630130\pi$
$647$	−20.2229	−0.795045	−0.397523	+	0.917592i	$0.630130\pi$
$648$	91.2215	3.58352
$649$	−37.1886	−1.45978
$650$	7.56491	0.296720
$651$	−13.1967	−0.517221
$652$	−0.675930	−0.0264715
$653$	37.6975	1.47522	0.737608	−	0.675229i	$-0.235955\pi$
$653$	37.6975	1.47522	0.737608	+	0.675229i	$0.235955\pi$
$654$	−64.9608	−2.54017
$655$	6.92419	0.270550
$656$	46.4946	1.81531
$657$	102.639	4.00434
$658$	−3.84676	−0.149962
$659$	−10.4288	−0.406247	−0.203123	−	0.979153i	$-0.565109\pi$
$659$	−10.4288	−0.406247	−0.203123	+	0.979153i	$0.565109\pi$
$660$	0.678049	0.0263930
$661$	0.886673	0.0344876	0.0172438	−	0.999851i	$-0.494511\pi$
$661$	0.886673	0.0344876	0.0172438	+	0.999851i	$0.494511\pi$
$662$	−16.5296	−0.642441
$663$	75.0869	2.91613
$664$	−12.1012	−0.469617
$665$	−4.09779	−0.158906
$666$	95.9807	3.71918
$667$	−55.9703	−2.16718
$668$	0.0328415	0.00127067
$669$	54.0242	2.08870
$670$	−2.13921	−0.0826450
$671$	31.2072	1.20474
$672$	0.843639	0.0325441
$673$	−28.0623	−1.08172	−0.540861	−	0.841112i	$-0.681901\pi$
$673$	−28.0623	−1.08172	−0.540861	+	0.841112i	$0.681901\pi$
$674$	17.2169	0.663172
$675$	−17.0897	−0.657781
$676$	0.670315	0.0257814
$677$	−21.9638	−0.844137	−0.422069	−	0.906564i	$-0.638696\pi$
$677$	−21.9638	−0.844137	−0.422069	+	0.906564i	$0.638696\pi$
$678$	−70.6129	−2.71187
$679$	−10.9584	−0.420544
$680$	11.8980	0.456267
$681$	47.3424	1.81416
$682$	−25.7190	−0.984831
$683$	−38.2438	−1.46336	−0.731679	−	0.681650i	$-0.761263\pi$
$683$	−38.2438	−1.46336	−0.731679	+	0.681650i	$0.761263\pi$
$684$	1.48885	0.0569274
$685$	18.7331	0.715755
$686$	1.42994	0.0545953
$687$	3.33526	0.127248
$688$	31.6860	1.20802
$689$	−57.8777	−2.20497
$690$	−34.9051	−1.32882
$691$	−0.942369	−0.0358494	−0.0179247	−	0.999839i	$-0.505706\pi$
$691$	−0.942369	−0.0358494	−0.0179247	+	0.999839i	$0.505706\pi$
$692$	−0.872244	−0.0331577
$693$	36.9288	1.40281
$694$	11.2892	0.428534
$695$	3.58671	0.136052
$696$	−71.3132	−2.70312
$697$	−48.4059	−1.83351
$698$	34.4737	1.30485
$699$	75.9736	2.87359
$700$	−0.0447232	−0.00169038
$701$	−15.4449	−0.583346	−0.291673	−	0.956518i	$-0.594212\pi$
$701$	−15.4449	−0.583346	−0.291673	+	0.956518i	$0.594212\pi$
$702$	−129.282	−4.87943
$703$	−33.8571	−1.27694
$704$	−35.5163	−1.33857
$705$	8.97237	0.337919
$706$	26.6916	1.00455
$707$	8.37677	0.315041
$708$	−1.22032	−0.0458624
$709$	−37.4169	−1.40522	−0.702610	−	0.711575i	$-0.747982\pi$
$709$	−37.4169	−1.40522	−0.702610	+	0.711575i	$0.747982\pi$
$710$	−3.42608	−0.128578
$711$	−30.9010	−1.15888
$712$	23.5542	0.882730
$713$	28.9588	1.08451
$714$	−20.2953	−0.759531
$715$	24.0484	0.899358
$716$	0.315992	0.0118092
$717$	94.4734	3.52817
$718$	40.4100	1.50809
$719$	20.3747	0.759847	0.379923	−	0.925018i	$-0.375950\pi$
$719$	20.3747	0.759847	0.379923	+	0.925018i	$0.375950\pi$
$720$	−33.2062	−1.23752
$721$	6.64093	0.247321
$722$	3.15746	0.117509
$723$	−17.7258	−0.659231
$724$	−1.15291	−0.0428477
$725$	7.64742	0.284018
$726$	46.0859	1.71041
$727$	−0.396365	−0.0147004	−0.00735019	−	0.999973i	$-0.502340\pi$
$727$	−0.396365	−0.0147004	−0.00735019	+	0.999973i	$0.502340\pi$
$728$	14.7915	0.548209
$729$	94.0612	3.48375
$730$	−18.0661	−0.668656
$731$	−32.9886	−1.22013
$732$	1.02404	0.0378498
$733$	−4.97004	−0.183573	−0.0917863	−	0.995779i	$-0.529258\pi$
$733$	−4.97004	−0.183573	−0.0917863	+	0.995779i	$0.529258\pi$
$734$	35.6225	1.31485
$735$	−3.33526	−0.123023
$736$	−1.85127	−0.0682387
$737$	−6.80042	−0.250497
$738$	132.140	4.86414
$739$	31.0003	1.14036	0.570182	−	0.821518i	$-0.306873\pi$
$739$	31.0003	1.14036	0.570182	+	0.821518i	$0.306873\pi$
$740$	−0.369516	−0.0135837
$741$	72.3046	2.65617
$742$	15.6438	0.574302
$743$	19.3419	0.709584	0.354792	−	0.934945i	$-0.384552\pi$
$743$	19.3419	0.709584	0.354792	+	0.934945i	$0.384552\pi$
$744$	36.8971	1.35271
$745$	−4.93102	−0.180659
$746$	8.71919	0.319232
$747$	−35.1616	−1.28650
$748$	−0.865128	−0.0316322
$749$	7.95333	0.290609
$750$	4.76921	0.174147
$751$	30.2429	1.10358	0.551790	−	0.833983i	$-0.313945\pi$
$751$	30.2429	1.10358	0.551790	+	0.833983i	$0.313945\pi$
$752$	10.9959	0.400978
$753$	−92.4819	−3.37023
$754$	57.8521	2.10685
$755$	4.56452	0.166120
$756$	0.764305	0.0277975
$757$	−47.8425	−1.73886	−0.869432	−	0.494053i	$-0.835515\pi$
$757$	−47.8425	−1.73886	−0.869432	+	0.494053i	$0.835515\pi$
$758$	−19.8082	−0.719466
$759$	−110.961	−4.02763
$760$	11.4571	0.415593
$761$	25.4318	0.921903	0.460952	−	0.887425i	$-0.347508\pi$
$761$	25.4318	0.921903	0.460952	+	0.887425i	$0.347508\pi$
$762$	−45.4781	−1.64750
$763$	13.6209	0.493109
$764$	0.371973	0.0134575
$765$	34.5712	1.24993
$766$	39.6594	1.43295
$767$	−43.2810	−1.56279
$768$	−3.57815	−0.129115
$769$	27.2472	0.982559	0.491280	−	0.871002i	$-0.336529\pi$
$769$	27.2472	0.982559	0.491280	+	0.871002i	$0.336529\pi$
$770$	−6.50004	−0.234245
$771$	−87.8584	−3.16414
$772$	1.13125	0.0407147
$773$	42.6557	1.53422	0.767109	−	0.641517i	$-0.221695\pi$
$773$	42.6557	1.53422	0.767109	+	0.641517i	$0.221695\pi$
$774$	90.0533	3.23690
$775$	−3.95674	−0.142130
$776$	30.6388	1.09987
$777$	−27.5568	−0.988595
$778$	15.2404	0.546396
$779$	−46.6123	−1.67006
$780$	0.789131	0.0282554
$781$	−10.8913	−0.389721
$782$	44.5357	1.59259
$783$	−130.692	−4.67055
$784$	−4.08745	−0.145980
$785$	−22.6990	−0.810162
$786$	33.0229	1.17789
$787$	25.5606	0.911138	0.455569	−	0.890200i	$-0.349436\pi$
$787$	25.5606	0.911138	0.455569	+	0.890200i	$0.349436\pi$
$788$	−0.510845	−0.0181981
$789$	56.9205	2.02642
$790$	5.43904	0.193512
$791$	14.8060	0.526440
$792$	−103.250	−3.66884
$793$	36.3198	1.28975
$794$	−36.4275	−1.29276
$795$	−36.4883	−1.29411
$796$	0.234185	0.00830047
$797$	22.6524	0.802389	0.401194	−	0.915993i	$-0.368595\pi$
$797$	22.6524	0.802389	0.401194	+	0.915993i	$0.368595\pi$
$798$	−19.5432	−0.691823
$799$	−11.4479	−0.404998
$800$	0.252946	0.00894298
$801$	68.4398	2.41820
$802$	−6.92056	−0.244373
$803$	−57.4309	−2.02669
$804$	−0.223151	−0.00786994
$805$	7.31885	0.257955
$806$	−29.9324	−1.05432
$807$	−82.8276	−2.91567
$808$	−23.4208	−0.823942
$809$	−4.17972	−0.146951	−0.0734755	−	0.997297i	$-0.523409\pi$
$809$	−4.17972	−0.146951	−0.0734755	+	0.997297i	$0.523409\pi$
$810$	−46.6540	−1.63925
$811$	−25.0363	−0.879144	−0.439572	−	0.898207i	$-0.644870\pi$
$811$	−25.0363	−0.879144	−0.439572	+	0.898207i	$0.644870\pi$
$812$	−0.342017	−0.0120025
$813$	55.2369	1.93724
$814$	−53.7052	−1.88236
$815$	−15.1136	−0.529407
$816$	58.0136	2.03088
$817$	−31.7662	−1.11136
$818$	0.0110234	0.000385426 0
$819$	42.9787	1.50180
$820$	−0.508726	−0.0177655
$821$	28.3346	0.988886	0.494443	−	0.869210i	$-0.335372\pi$
$821$	28.3346	0.988886	0.494443	+	0.869210i	$0.335372\pi$
$822$	89.3421	3.11616
$823$	8.05754	0.280868	0.140434	−	0.990090i	$-0.455150\pi$
$823$	8.05754	0.280868	0.140434	+	0.990090i	$0.455150\pi$
$824$	−18.5676	−0.646831
$825$	15.1610	0.527839
$826$	11.6984	0.407041
$827$	−30.1451	−1.04825	−0.524123	−	0.851642i	$-0.675607\pi$
$827$	−30.1451	−1.04825	−0.524123	+	0.851642i	$0.675607\pi$
$828$	−2.65915	−0.0924118
$829$	9.99998	0.347314	0.173657	−	0.984806i	$-0.444442\pi$
$829$	9.99998	0.347314	0.173657	+	0.984806i	$0.444442\pi$
$830$	6.18898	0.214823
$831$	51.6362	1.79124
$832$	−41.3347	−1.43302
$833$	4.25548	0.147443
$834$	17.1058	0.592324
$835$	0.734327	0.0254124
$836$	−0.833071	−0.0288123
$837$	67.6194	2.33727
$838$	−19.1651	−0.662047
$839$	−26.6129	−0.918780	−0.459390	−	0.888235i	$-0.651932\pi$
$839$	−26.6129	−0.918780	−0.459390	+	0.888235i	$0.651932\pi$
$840$	9.32513	0.321748
$841$	29.4831	1.01666
$842$	−15.3187	−0.527917
$843$	27.8513	0.959249
$844$	−1.05015	−0.0361477
$845$	14.9881	0.515606
$846$	31.2508	1.07443
$847$	−9.66321	−0.332032
$848$	−44.7174	−1.53560
$849$	−31.0225	−1.06469
$850$	−6.08507	−0.208716
$851$	60.4703	2.07290
$852$	−0.357390	−0.0122440
$853$	42.1317	1.44256	0.721282	−	0.692642i	$-0.243553\pi$
$853$	42.1317	1.44256	0.721282	+	0.692642i	$0.243553\pi$
$854$	−9.81689	−0.335927
$855$	33.2902	1.13850
$856$	−22.2369	−0.760042
$857$	−0.681458	−0.0232782	−0.0116391	−	0.999932i	$-0.503705\pi$
$857$	−0.681458	−0.0232782	−0.0116391	+	0.999932i	$0.503705\pi$
$858$	114.692	3.91551
$859$	42.3735	1.44577	0.722883	−	0.690970i	$-0.242817\pi$
$859$	42.3735	1.44577	0.722883	+	0.690970i	$0.242817\pi$
$860$	−0.346696	−0.0118222
$861$	−37.9385	−1.29294
$862$	−22.2597	−0.758168
$863$	−13.6335	−0.464090	−0.232045	−	0.972705i	$-0.574542\pi$
$863$	−13.6335	−0.464090	−0.232045	+	0.972705i	$0.574542\pi$
$864$	−4.32276	−0.147063
$865$	−19.5031	−0.663127
$866$	−5.34925	−0.181775
$867$	−3.69904	−0.125626
$868$	0.176958	0.00600635
$869$	17.2904	0.586536
$870$	36.4722	1.23652
$871$	−7.91450	−0.268173
$872$	−38.0829	−1.28965
$873$	89.0252	3.01305
$874$	42.8854	1.45062
$875$	−1.00000	−0.0338062
$876$	−1.88456	−0.0636733
$877$	5.12799	0.173160	0.0865800	−	0.996245i	$-0.472406\pi$
$877$	5.12799	0.173160	0.0865800	+	0.996245i	$0.472406\pi$
$878$	−30.4848	−1.02881
$879$	95.8212	3.23197
$880$	18.5802	0.626339
$881$	6.56178	0.221072	0.110536	−	0.993872i	$-0.464743\pi$
$881$	6.56178	0.221072	0.110536	+	0.993872i	$0.464743\pi$
$882$	−11.6167	−0.391156
$883$	−46.0107	−1.54838	−0.774191	−	0.632952i	$-0.781843\pi$
$883$	−46.0107	−1.54838	−0.774191	+	0.632952i	$0.781843\pi$
$884$	−1.00686	−0.0338643
$885$	−27.2860	−0.917210
$886$	0.800455	0.0268918
$887$	−3.70923	−0.124544	−0.0622719	−	0.998059i	$-0.519835\pi$
$887$	−3.70923	−0.124544	−0.0622719	+	0.998059i	$0.519835\pi$
$888$	77.0468	2.58552
$889$	9.53576	0.319819
$890$	−12.0465	−0.403798
$891$	−148.310	−4.96857
$892$	−0.724422	−0.0242555
$893$	−11.0237	−0.368894
$894$	−23.5171	−0.786529
$895$	7.06550	0.236174
$896$	11.6783	0.390144
$897$	−129.139	−4.31184
$898$	−16.9378	−0.565221
$899$	−30.2589	−1.00919
$900$	0.363329	0.0121110
$901$	46.5557	1.55100
$902$	−73.9378	−2.46186
$903$	−25.8550	−0.860401
$904$	−41.3964	−1.37682
$905$	−25.7788	−0.856918
$906$	21.7692	0.723232
$907$	−29.5827	−0.982276	−0.491138	−	0.871082i	$-0.663419\pi$
$907$	−29.5827	−0.982276	−0.491138	+	0.871082i	$0.663419\pi$
$908$	−0.634825	−0.0210674
$909$	−68.0524	−2.25716
$910$	−7.56491	−0.250774
$911$	3.79863	0.125854	0.0629271	−	0.998018i	$-0.479956\pi$
$911$	3.79863	0.125854	0.0629271	+	0.998018i	$0.479956\pi$
$912$	55.8639	1.84984
$913$	19.6744	0.651127
$914$	5.67183	0.187607
$915$	22.8974	0.756964
$916$	−0.0447232	−0.00147770
$917$	−6.92419	−0.228657
$918$	103.992	3.43224
$919$	42.3283	1.39628	0.698140	−	0.715961i	$-0.254011\pi$
$919$	42.3283	1.39628	0.698140	+	0.715961i	$0.254011\pi$
$920$	−20.4629	−0.674643
$921$	3.38324	0.111481
$922$	42.0846	1.38598
$923$	−12.6755	−0.417221
$924$	−0.678049	−0.0223062
$925$	−8.26228	−0.271662
$926$	−18.2199	−0.598743
$927$	−53.9505	−1.77197
$928$	1.93438	0.0634992
$929$	−30.4869	−1.00024	−0.500122	−	0.865955i	$-0.666711\pi$
$929$	−30.4869	−1.00024	−0.500122	+	0.865955i	$0.666711\pi$
$930$	−18.8705	−0.618789
$931$	4.09779	0.134300
$932$	−1.01875	−0.0333702
$933$	−55.5171	−1.81755
$934$	−29.1603	−0.954154
$935$	−19.3440	−0.632618
$936$	−120.165	−3.92772
$937$	49.1679	1.60625	0.803123	−	0.595813i	$-0.203170\pi$
$937$	49.1679	1.60625	0.803123	+	0.595813i	$0.203170\pi$
$938$	2.13921	0.0698478
$939$	5.62159	0.183454
$940$	−0.120313	−0.00392416
$941$	−38.6441	−1.25976	−0.629881	−	0.776692i	$-0.716896\pi$
$941$	−38.6441	−1.25976	−0.629881	+	0.776692i	$0.716896\pi$
$942$	−108.256	−3.52718
$943$	83.2517	2.71105
$944$	−33.4398	−1.08837
$945$	17.0897	0.555927
$946$	−50.3885	−1.63827
$947$	−21.9546	−0.713429	−0.356714	−	0.934214i	$-0.616103\pi$
$947$	−21.9546	−0.713429	−0.356714	+	0.934214i	$0.616103\pi$
$948$	0.567372	0.0184274
$949$	−66.8395	−2.16970
$950$	−5.85959	−0.190110
$951$	−75.9852	−2.46399
$952$	−11.8980	−0.385616
$953$	51.9645	1.68329	0.841647	−	0.540028i	$-0.181586\pi$
$953$	51.9645	1.68329	0.841647	+	0.540028i	$0.181586\pi$
$954$	−127.089	−4.11467
$955$	8.31722	0.269139
$956$	−1.26682	−0.0409717
$957$	115.943	3.74790
$958$	−23.2518	−0.751232
$959$	−18.7331	−0.604923
$960$	−26.0590	−0.841051
$961$	−15.3442	−0.494974
$962$	−62.5034	−2.01519
$963$	−64.6124	−2.08211
$964$	0.237690	0.00765547
$965$	25.2945	0.814259
$966$	34.9051	1.12305
$967$	2.98388	0.0959551	0.0479775	−	0.998848i	$-0.484722\pi$
$967$	2.98388	0.0959551	0.0479775	+	0.998848i	$0.484722\pi$
$968$	27.0176	0.868379
$969$	−58.1604	−1.86838
$970$	−15.6698	−0.503127
$971$	10.4510	0.335388	0.167694	−	0.985839i	$-0.446368\pi$
$971$	10.4510	0.335388	0.167694	+	0.985839i	$0.446368\pi$
$972$	−2.57378	−0.0825540
$973$	−3.58671	−0.114985
$974$	1.91604	0.0613939
$975$	17.6448	0.565085
$976$	28.0613	0.898222
$977$	30.2235	0.966937	0.483468	−	0.875362i	$-0.339377\pi$
$977$	30.2235	0.966937	0.483468	+	0.875362i	$0.339377\pi$
$978$	−72.0801	−2.30487
$979$	−38.2949	−1.22391
$980$	0.0447232	0.00142863
$981$	−110.655	−3.53295
$982$	26.1692	0.835091
$983$	−20.1355	−0.642222	−0.321111	−	0.947042i	$-0.604056\pi$
$983$	−20.1355	−0.642222	−0.321111	+	0.947042i	$0.604056\pi$
$984$	106.073	3.38149
$985$	−11.4224	−0.363947
$986$	−46.5351	−1.48198
$987$	−8.97237	−0.285594
$988$	−0.969548	−0.0308454
$989$	56.7359	1.80410
$990$	52.8060	1.67828
$991$	−30.3937	−0.965486	−0.482743	−	0.875762i	$-0.660360\pi$
$991$	−30.3937	−0.965486	−0.482743	+	0.875762i	$0.660360\pi$
$992$	−1.00084	−0.0317767
$993$	−38.5544	−1.22349
$994$	3.42608	0.108669
$995$	5.23632	0.166002
$996$	0.645601	0.0204567
$997$	48.0169	1.52071	0.760355	−	0.649508i	$-0.225025\pi$
$997$	48.0169	1.52071	0.760355	+	0.649508i	$0.225025\pi$
$998$	−8.01212	−0.253619
$999$	141.199	4.46735

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.m.1.20	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.m.1.20	✓	67	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.42994 q^{2} -3.33526 q^{3} +0.0447232 q^{4} +1.00000 q^{5} +4.76921 q^{6} -1.00000 q^{7} +2.79592 q^{8} +8.12394 q^{9} +O(q^{10})\)	\(q-1.42994 q^{2} -3.33526 q^{3} +0.0447232 q^{4} +1.00000 q^{5} +4.76921 q^{6} -1.00000 q^{7} +2.79592 q^{8} +8.12394 q^{9} -1.42994 q^{10} -4.54568 q^{11} -0.149163 q^{12} -5.29038 q^{13} +1.42994 q^{14} -3.33526 q^{15} -4.08745 q^{16} +4.25548 q^{17} -11.6167 q^{18} +4.09779 q^{19} +0.0447232 q^{20} +3.33526 q^{21} +6.50004 q^{22} -7.31885 q^{23} -9.32513 q^{24} +1.00000 q^{25} +7.56491 q^{26} -17.0897 q^{27} -0.0447232 q^{28} +7.64742 q^{29} +4.76921 q^{30} -3.95674 q^{31} +0.252946 q^{32} +15.1610 q^{33} -6.08507 q^{34} -1.00000 q^{35} +0.363329 q^{36} -8.26228 q^{37} -5.85959 q^{38} +17.6448 q^{39} +2.79592 q^{40} -11.3750 q^{41} -4.76921 q^{42} -7.75203 q^{43} -0.203297 q^{44} +8.12394 q^{45} +10.4655 q^{46} -2.69016 q^{47} +13.6327 q^{48} +1.00000 q^{49} -1.42994 q^{50} -14.1931 q^{51} -0.236603 q^{52} +10.9402 q^{53} +24.4372 q^{54} -4.54568 q^{55} -2.79592 q^{56} -13.6672 q^{57} -10.9353 q^{58} +8.18109 q^{59} -0.149163 q^{60} -6.86525 q^{61} +5.65790 q^{62} -8.12394 q^{63} +7.81320 q^{64} -5.29038 q^{65} -21.6793 q^{66} +1.49602 q^{67} +0.190319 q^{68} +24.4102 q^{69} +1.42994 q^{70} +2.39596 q^{71} +22.7139 q^{72} +12.6342 q^{73} +11.8145 q^{74} -3.33526 q^{75} +0.183266 q^{76} +4.54568 q^{77} -25.2309 q^{78} -3.80369 q^{79} -4.08745 q^{80} +32.6266 q^{81} +16.2655 q^{82} -4.32815 q^{83} +0.149163 q^{84} +4.25548 q^{85} +11.0849 q^{86} -25.5061 q^{87} -12.7094 q^{88} +8.42446 q^{89} -11.6167 q^{90} +5.29038 q^{91} -0.327322 q^{92} +13.1967 q^{93} +3.84676 q^{94} +4.09779 q^{95} -0.843639 q^{96} +10.9584 q^{97} -1.42994 q^{98} -36.9288 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * q^99

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