LMFDB - Embedded newform 8015.2.a.i.1.2

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:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-2.53948 q^{2} +2.62786 q^{3} +4.44894 q^{4} +1.00000 q^{5} -6.67339 q^{6} -1.00000 q^{7} -6.21901 q^{8} +3.90566 q^{9} +O(q^{10})$	\(q-2.53948 q^{2} +2.62786 q^{3} +4.44894 q^{4} +1.00000 q^{5} -6.67339 q^{6} -1.00000 q^{7} -6.21901 q^{8} +3.90566 q^{9} -2.53948 q^{10} +2.08708 q^{11} +11.6912 q^{12} +3.62064 q^{13} +2.53948 q^{14} +2.62786 q^{15} +6.89516 q^{16} -1.95159 q^{17} -9.91832 q^{18} -5.09822 q^{19} +4.44894 q^{20} -2.62786 q^{21} -5.30008 q^{22} -6.01387 q^{23} -16.3427 q^{24} +1.00000 q^{25} -9.19453 q^{26} +2.37994 q^{27} -4.44894 q^{28} -4.27768 q^{29} -6.67339 q^{30} -7.16004 q^{31} -5.07206 q^{32} +5.48455 q^{33} +4.95601 q^{34} -1.00000 q^{35} +17.3760 q^{36} +0.0520641 q^{37} +12.9468 q^{38} +9.51454 q^{39} -6.21901 q^{40} +4.88126 q^{41} +6.67339 q^{42} -2.70162 q^{43} +9.28527 q^{44} +3.90566 q^{45} +15.2721 q^{46} +9.43679 q^{47} +18.1195 q^{48} +1.00000 q^{49} -2.53948 q^{50} -5.12850 q^{51} +16.1080 q^{52} -12.1952 q^{53} -6.04381 q^{54} +2.08708 q^{55} +6.21901 q^{56} -13.3974 q^{57} +10.8631 q^{58} -6.87625 q^{59} +11.6912 q^{60} -7.57783 q^{61} +18.1827 q^{62} -3.90566 q^{63} -0.909948 q^{64} +3.62064 q^{65} -13.9279 q^{66} -11.6499 q^{67} -8.68249 q^{68} -15.8036 q^{69} +2.53948 q^{70} -7.24494 q^{71} -24.2893 q^{72} -5.45645 q^{73} -0.132215 q^{74} +2.62786 q^{75} -22.6816 q^{76} -2.08708 q^{77} -24.1619 q^{78} +4.76620 q^{79} +6.89516 q^{80} -5.46281 q^{81} -12.3958 q^{82} +2.96373 q^{83} -11.6912 q^{84} -1.95159 q^{85} +6.86070 q^{86} -11.2412 q^{87} -12.9796 q^{88} -0.584731 q^{89} -9.91832 q^{90} -3.62064 q^{91} -26.7553 q^{92} -18.8156 q^{93} -23.9645 q^{94} -5.09822 q^{95} -13.3287 q^{96} +7.92337 q^{97} -2.53948 q^{98} +8.15141 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) $ 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.53948	−1.79568	−0.897840	−	0.440322i	$-0.854864\pi$
$2$	−2.53948	−1.79568	−0.897840	+	0.440322i	$0.854864\pi$
$3$	2.62786	1.51720	0.758598	−	0.651559i	$-0.225885\pi$
$3$	2.62786	1.51720	0.758598	+	0.651559i	$0.225885\pi$
$4$	4.44894	2.22447
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−6.67339	−2.72440
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−6.21901	−2.19875
$9$	3.90566	1.30189
$10$	−2.53948	−0.803053
$11$	2.08708	0.629277	0.314639	−	0.949212i	$-0.398117\pi$
$11$	2.08708	0.629277	0.314639	+	0.949212i	$0.398117\pi$
$12$	11.6912	3.37496
$13$	3.62064	1.00419	0.502093	−	0.864814i	$-0.332564\pi$
$13$	3.62064	1.00419	0.502093	+	0.864814i	$0.332564\pi$
$14$	2.53948	0.678703
$15$	2.62786	0.678511
$16$	6.89516	1.72379
$17$	−1.95159	−0.473329	−0.236665	−	0.971591i	$-0.576054\pi$
$17$	−1.95159	−0.473329	−0.236665	+	0.971591i	$0.576054\pi$
$18$	−9.91832	−2.33777
$19$	−5.09822	−1.16961	−0.584806	−	0.811174i	$-0.698829\pi$
$19$	−5.09822	−1.16961	−0.584806	+	0.811174i	$0.698829\pi$
$20$	4.44894	0.994812
$21$	−2.62786	−0.573446
$22$	−5.30008	−1.12998
$23$	−6.01387	−1.25398	−0.626989	−	0.779028i	$-0.715713\pi$
$23$	−6.01387	−1.25398	−0.626989	+	0.779028i	$0.715713\pi$
$24$	−16.3427	−3.33594
$25$	1.00000	0.200000
$26$	−9.19453	−1.80320
$27$	2.37994	0.458020
$28$	−4.44894	−0.840770
$29$	−4.27768	−0.794345	−0.397173	−	0.917744i	$-0.630009\pi$
$29$	−4.27768	−0.794345	−0.397173	+	0.917744i	$0.630009\pi$
$30$	−6.67339	−1.21839
$31$	−7.16004	−1.28598	−0.642990	−	0.765874i	$-0.722306\pi$
$31$	−7.16004	−1.28598	−0.642990	+	0.765874i	$0.722306\pi$
$32$	−5.07206	−0.896621
$33$	5.48455	0.954737
$34$	4.95601	0.849948
$35$	−1.00000	−0.169031
$36$	17.3760	2.89600
$37$	0.0520641	0.00855928	0.00427964	−	0.999991i	$-0.498638\pi$
$37$	0.0520641	0.00855928	0.00427964	+	0.999991i	$0.498638\pi$
$38$	12.9468	2.10025
$39$	9.51454	1.52355
$40$	−6.21901	−0.983312
$41$	4.88126	0.762325	0.381163	−	0.924508i	$-0.375524\pi$
$41$	4.88126	0.762325	0.381163	+	0.924508i	$0.375524\pi$
$42$	6.67339	1.02973
$43$	−2.70162	−0.411993	−0.205997	−	0.978553i	$-0.566044\pi$
$43$	−2.70162	−0.411993	−0.205997	+	0.978553i	$0.566044\pi$
$44$	9.28527	1.39981
$45$	3.90566	0.582221
$46$	15.2721	2.25174
$47$	9.43679	1.37650	0.688249	−	0.725475i	$-0.258380\pi$
$47$	9.43679	1.37650	0.688249	+	0.725475i	$0.258380\pi$
$48$	18.1195	2.61533
$49$	1.00000	0.142857
$50$	−2.53948	−0.359136
$51$	−5.12850	−0.718134
$52$	16.1080	2.23378
$53$	−12.1952	−1.67514	−0.837570	−	0.546330i	$-0.816024\pi$
$53$	−12.1952	−1.67514	−0.837570	+	0.546330i	$0.816024\pi$
$54$	−6.04381	−0.822458
$55$	2.08708	0.281421
$56$	6.21901	0.831050
$57$	−13.3974	−1.77453
$58$	10.8631	1.42639
$59$	−6.87625	−0.895212	−0.447606	−	0.894231i	$-0.647723\pi$
$59$	−6.87625	−0.895212	−0.447606	+	0.894231i	$0.647723\pi$
$60$	11.6912	1.50933
$61$	−7.57783	−0.970242	−0.485121	−	0.874447i	$-0.661224\pi$
$61$	−7.57783	−0.970242	−0.485121	+	0.874447i	$0.661224\pi$
$62$	18.1827	2.30921
$63$	−3.90566	−0.492067
$64$	−0.909948	−0.113744
$65$	3.62064	0.449085
$66$	−13.9279	−1.71440
$67$	−11.6499	−1.42327	−0.711633	−	0.702551i	$-0.752044\pi$
$67$	−11.6499	−1.42327	−0.711633	+	0.702551i	$0.752044\pi$
$68$	−8.68249	−1.05291
$69$	−15.8036	−1.90253
$70$	2.53948	0.303525
$71$	−7.24494	−0.859816	−0.429908	−	0.902873i	$-0.641454\pi$
$71$	−7.24494	−0.859816	−0.429908	+	0.902873i	$0.641454\pi$
$72$	−24.2893	−2.86253
$73$	−5.45645	−0.638629	−0.319315	−	0.947649i	$-0.603453\pi$
$73$	−5.45645	−0.638629	−0.319315	+	0.947649i	$0.603453\pi$
$74$	−0.132215	−0.0153697
$75$	2.62786	0.303439
$76$	−22.6816	−2.60176
$77$	−2.08708	−0.237844
$78$	−24.1619	−2.73580
$79$	4.76620	0.536239	0.268120	−	0.963386i	$-0.413598\pi$
$79$	4.76620	0.536239	0.268120	+	0.963386i	$0.413598\pi$
$80$	6.89516	0.770902
$81$	−5.46281	−0.606979
$82$	−12.3958	−1.36889
$83$	2.96373	0.325312	0.162656	−	0.986683i	$-0.447994\pi$
$83$	2.96373	0.325312	0.162656	+	0.986683i	$0.447994\pi$
$84$	−11.6912	−1.27561
$85$	−1.95159	−0.211679
$86$	6.86070	0.739808
$87$	−11.2412	−1.20518
$88$	−12.9796	−1.38362
$89$	−0.584731	−0.0619814	−0.0309907	−	0.999520i	$-0.509866\pi$
$89$	−0.584731	−0.0619814	−0.0309907	+	0.999520i	$0.509866\pi$
$90$	−9.91832	−1.04548
$91$	−3.62064	−0.379546
$92$	−26.7553	−2.78943
$93$	−18.8156	−1.95109
$94$	−23.9645	−2.47175
$95$	−5.09822	−0.523066
$96$	−13.3287	−1.36035
$97$	7.92337	0.804496	0.402248	−	0.915531i	$-0.368229\pi$
$97$	7.92337	0.804496	0.402248	+	0.915531i	$0.368229\pi$
$98$	−2.53948	−0.256526
$99$	8.15141	0.819247
$100$	4.44894	0.444894
$101$	19.2728	1.91772	0.958859	−	0.283883i	$-0.0916229\pi$
$101$	19.2728	1.91772	0.958859	+	0.283883i	$0.0916229\pi$
$102$	13.0237	1.28954
$103$	−2.81294	−0.277167	−0.138584	−	0.990351i	$-0.544255\pi$
$103$	−2.81294	−0.277167	−0.138584	+	0.990351i	$0.544255\pi$
$104$	−22.5168	−2.20795
$105$	−2.62786	−0.256453
$106$	30.9694	3.00801
$107$	−9.38897	−0.907666	−0.453833	−	0.891087i	$-0.649944\pi$
$107$	−9.38897	−0.907666	−0.453833	+	0.891087i	$0.649944\pi$
$108$	10.5882	1.01885
$109$	−17.7022	−1.69556	−0.847782	−	0.530345i	$-0.822062\pi$
$109$	−17.7022	−1.69556	−0.847782	+	0.530345i	$0.822062\pi$
$110$	−5.30008	−0.505343
$111$	0.136817	0.0129861
$112$	−6.89516	−0.651531
$113$	−6.95664	−0.654425	−0.327213	−	0.944951i	$-0.606109\pi$
$113$	−6.95664	−0.654425	−0.327213	+	0.944951i	$0.606109\pi$
$114$	34.0224	3.18649
$115$	−6.01387	−0.560796
$116$	−19.0311	−1.76700
$117$	14.1410	1.30733
$118$	17.4621	1.60751
$119$	1.95159	0.178902
$120$	−16.3427	−1.49188
$121$	−6.64411	−0.604010
$122$	19.2437	1.74224
$123$	12.8273	1.15660
$124$	−31.8545	−2.86062
$125$	1.00000	0.0894427
$126$	9.91832	0.883594
$127$	7.14009	0.633580	0.316790	−	0.948496i	$-0.397395\pi$
$127$	7.14009	0.633580	0.316790	+	0.948496i	$0.397395\pi$
$128$	12.4549	1.10087
$129$	−7.09948	−0.625075
$130$	−9.19453	−0.806413
$131$	3.30608	0.288854	0.144427	−	0.989515i	$-0.453866\pi$
$131$	3.30608	0.288854	0.144427	+	0.989515i	$0.453866\pi$
$132$	24.4004	2.12378
$133$	5.09822	0.442071
$134$	29.5847	2.55573
$135$	2.37994	0.204833
$136$	12.1369	1.04073
$137$	16.0076	1.36762	0.683809	−	0.729661i	$-0.260322\pi$
$137$	16.0076	1.36762	0.683809	+	0.729661i	$0.260322\pi$
$138$	40.1329	3.41634
$139$	4.39081	0.372424	0.186212	−	0.982510i	$-0.440379\pi$
$139$	4.39081	0.372424	0.186212	+	0.982510i	$0.440379\pi$
$140$	−4.44894	−0.376004
$141$	24.7986	2.08842
$142$	18.3983	1.54395
$143$	7.55655	0.631911
$144$	26.9301	2.24418
$145$	−4.27768	−0.355242
$146$	13.8565	1.14677
$147$	2.62786	0.216742
$148$	0.231630	0.0190398
$149$	−15.0539	−1.23326	−0.616631	−	0.787252i	$-0.711503\pi$
$149$	−15.0539	−1.23326	−0.616631	+	0.787252i	$0.711503\pi$
$150$	−6.67339	−0.544880
$151$	−10.4836	−0.853141	−0.426570	−	0.904454i	$-0.640278\pi$
$151$	−10.4836	−0.853141	−0.426570	+	0.904454i	$0.640278\pi$
$152$	31.7059	2.57169
$153$	−7.62223	−0.616221
$154$	5.30008	0.427093
$155$	−7.16004	−0.575108
$156$	42.3296	3.38908
$157$	5.46007	0.435761	0.217880	−	0.975975i	$-0.430086\pi$
$157$	5.46007	0.435761	0.217880	+	0.975975i	$0.430086\pi$
$158$	−12.1036	−0.962915
$159$	−32.0473	−2.54152
$160$	−5.07206	−0.400981
$161$	6.01387	0.473959
$162$	13.8727	1.08994
$163$	−7.04703	−0.551966	−0.275983	−	0.961163i	$-0.589003\pi$
$163$	−7.04703	−0.551966	−0.275983	+	0.961163i	$0.589003\pi$
$164$	21.7164	1.69577
$165$	5.48455	0.426971
$166$	−7.52632	−0.584156
$167$	19.6111	1.51755	0.758776	−	0.651352i	$-0.225798\pi$
$167$	19.6111	1.51755	0.758776	+	0.651352i	$0.225798\pi$
$168$	16.3427	1.26087
$169$	0.109039	0.00838759
$170$	4.95601	0.380108
$171$	−19.9119	−1.52270
$172$	−12.0193	−0.916466
$173$	3.61170	0.274592	0.137296	−	0.990530i	$-0.456159\pi$
$173$	3.61170	0.274592	0.137296	+	0.990530i	$0.456159\pi$
$174$	28.5466	2.16411
$175$	−1.00000	−0.0755929
$176$	14.3907	1.08474
$177$	−18.0698	−1.35821
$178$	1.48491	0.111299
$179$	−26.3421	−1.96890	−0.984450	−	0.175667i	$-0.943792\pi$
$179$	−26.3421	−1.96890	−0.984450	+	0.175667i	$0.943792\pi$
$180$	17.3760	1.29513
$181$	−22.2697	−1.65530	−0.827648	−	0.561247i	$-0.810322\pi$
$181$	−22.2697	−1.65530	−0.827648	+	0.561247i	$0.810322\pi$
$182$	9.19453	0.681544
$183$	−19.9135	−1.47205
$184$	37.4003	2.75719
$185$	0.0520641	0.00382783
$186$	47.7817	3.50353
$187$	−4.07311	−0.297855
$188$	41.9837	3.06197
$189$	−2.37994	−0.173115
$190$	12.9468	0.939259
$191$	2.57866	0.186585	0.0932927	−	0.995639i	$-0.470261\pi$
$191$	2.57866	0.186585	0.0932927	+	0.995639i	$0.470261\pi$
$192$	−2.39122	−0.172571
$193$	−14.6381	−1.05367	−0.526837	−	0.849966i	$-0.676622\pi$
$193$	−14.6381	−1.05367	−0.526837	+	0.849966i	$0.676622\pi$
$194$	−20.1212	−1.44462
$195$	9.51454	0.681351
$196$	4.44894	0.317781
$197$	9.19786	0.655321	0.327660	−	0.944796i	$-0.393740\pi$
$197$	9.19786	0.655321	0.327660	+	0.944796i	$0.393740\pi$
$198$	−20.7003	−1.47111
$199$	12.3769	0.877377	0.438688	−	0.898639i	$-0.355443\pi$
$199$	12.3769	0.877377	0.438688	+	0.898639i	$0.355443\pi$
$200$	−6.21901	−0.439751
$201$	−30.6144	−2.15938
$202$	−48.9429	−3.44361
$203$	4.27768	0.300234
$204$	−22.8164	−1.59747
$205$	4.88126	0.340922
$206$	7.14340	0.497704
$207$	−23.4881	−1.63254
$208$	24.9649	1.73100
$209$	−10.6404	−0.736010
$210$	6.67339	0.460508
$211$	19.4214	1.33702	0.668511	−	0.743702i	$-0.266932\pi$
$211$	19.4214	1.33702	0.668511	+	0.743702i	$0.266932\pi$
$212$	−54.2557	−3.72629
$213$	−19.0387	−1.30451
$214$	23.8431	1.62988
$215$	−2.70162	−0.184249
$216$	−14.8009	−1.00707
$217$	7.16004	0.486055
$218$	44.9543	3.04469
$219$	−14.3388	−0.968926
$220$	9.28527	0.626013
$221$	−7.06600	−0.475310
$222$	−0.347444	−0.0233189
$223$	−7.94966	−0.532348	−0.266174	−	0.963925i	$-0.585760\pi$
$223$	−7.94966	−0.532348	−0.266174	+	0.963925i	$0.585760\pi$
$224$	5.07206	0.338891
$225$	3.90566	0.260377
$226$	17.6662	1.17514
$227$	3.77776	0.250738	0.125369	−	0.992110i	$-0.459988\pi$
$227$	3.77776	0.250738	0.125369	+	0.992110i	$0.459988\pi$
$228$	−59.6042	−3.94738
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	15.2721	1.00701
$231$	−5.48455	−0.360857
$232$	26.6029	1.74657
$233$	−4.59505	−0.301031	−0.150516	−	0.988608i	$-0.548093\pi$
$233$	−4.59505	−0.301031	−0.150516	+	0.988608i	$0.548093\pi$
$234$	−35.9107	−2.34755
$235$	9.43679	0.615588
$236$	−30.5920	−1.99137
$237$	12.5249	0.813581
$238$	−4.95601	−0.321250
$239$	−7.96425	−0.515164	−0.257582	−	0.966256i	$-0.582926\pi$
$239$	−7.96425	−0.515164	−0.257582	+	0.966256i	$0.582926\pi$
$240$	18.1195	1.16961
$241$	1.84778	0.119026	0.0595128	−	0.998228i	$-0.481045\pi$
$241$	1.84778	0.119026	0.0595128	+	0.998228i	$0.481045\pi$
$242$	16.8726	1.08461
$243$	−21.4953	−1.37893
$244$	−33.7133	−2.15827
$245$	1.00000	0.0638877
$246$	−32.5746	−2.07688
$247$	−18.4588	−1.17451
$248$	44.5284	2.82755
$249$	7.78828	0.493562
$250$	−2.53948	−0.160611
$251$	17.9267	1.13152	0.565760	−	0.824570i	$-0.308583\pi$
$251$	17.9267	1.13152	0.565760	+	0.824570i	$0.308583\pi$
$252$	−17.3760	−1.09459
$253$	−12.5514	−0.789100
$254$	−18.1321	−1.13771
$255$	−5.12850	−0.321159
$256$	−29.8090	−1.86306
$257$	−20.8626	−1.30137	−0.650685	−	0.759347i	$-0.725518\pi$
$257$	−20.8626	−1.30137	−0.650685	+	0.759347i	$0.725518\pi$
$258$	18.0290	1.12243
$259$	−0.0520641	−0.00323510
$260$	16.1080	0.998976
$261$	−16.7072	−1.03415
$262$	−8.39572	−0.518689
$263$	9.87332	0.608815	0.304407	−	0.952542i	$-0.401542\pi$
$263$	9.87332	0.608815	0.304407	+	0.952542i	$0.401542\pi$
$264$	−34.1085	−2.09923
$265$	−12.1952	−0.749145
$266$	−12.9468	−0.793819
$267$	−1.53659	−0.0940380
$268$	−51.8298	−3.16601
$269$	−8.05126	−0.490894	−0.245447	−	0.969410i	$-0.578935\pi$
$269$	−8.05126	−0.490894	−0.245447	+	0.969410i	$0.578935\pi$
$270$	−6.04381	−0.367814
$271$	21.8913	1.32980	0.664900	−	0.746932i	$-0.268474\pi$
$271$	21.8913	1.32980	0.664900	+	0.746932i	$0.268474\pi$
$272$	−13.4565	−0.815920
$273$	−9.51454	−0.575846
$274$	−40.6508	−2.45580
$275$	2.08708	0.125855
$276$	−70.3093	−4.23212
$277$	31.6770	1.90328	0.951642	−	0.307208i	$-0.0993948\pi$
$277$	31.6770	1.90328	0.951642	+	0.307208i	$0.0993948\pi$
$278$	−11.1504	−0.668754
$279$	−27.9647	−1.67420
$280$	6.21901	0.371657
$281$	15.4229	0.920051	0.460025	−	0.887906i	$-0.347840\pi$
$281$	15.4229	0.920051	0.460025	+	0.887906i	$0.347840\pi$
$282$	−62.9754	−3.75013
$283$	28.4446	1.69086	0.845428	−	0.534089i	$-0.179345\pi$
$283$	28.4446	1.69086	0.845428	+	0.534089i	$0.179345\pi$
$284$	−32.2323	−1.91263
$285$	−13.3974	−0.793594
$286$	−19.1897	−1.13471
$287$	−4.88126	−0.288132
$288$	−19.8097	−1.16730
$289$	−13.1913	−0.775959
$290$	10.8631	0.637901
$291$	20.8215	1.22058
$292$	−24.2754	−1.42061
$293$	−5.07546	−0.296512	−0.148256	−	0.988949i	$-0.547366\pi$
$293$	−5.07546	−0.296512	−0.148256	+	0.988949i	$0.547366\pi$
$294$	−6.67339	−0.389200
$295$	−6.87625	−0.400351
$296$	−0.323787	−0.0188197
$297$	4.96712	0.288222
$298$	38.2290	2.21455
$299$	−21.7741	−1.25923
$300$	11.6912	0.674991
$301$	2.70162	0.155719
$302$	26.6228	1.53197
$303$	50.6463	2.90955
$304$	−35.1530	−2.01616
$305$	−7.57783	−0.433905
$306$	19.3565	1.10654
$307$	15.4585	0.882261	0.441130	−	0.897443i	$-0.354578\pi$
$307$	15.4585	0.882261	0.441130	+	0.897443i	$0.354578\pi$
$308$	−9.28527	−0.529077
$309$	−7.39202	−0.420517
$310$	18.1827	1.03271
$311$	23.9826	1.35993	0.679964	−	0.733245i	$-0.261995\pi$
$311$	23.9826	1.35993	0.679964	+	0.733245i	$0.261995\pi$
$312$	−59.1711	−3.34990
$313$	7.79099	0.440373	0.220186	−	0.975458i	$-0.429333\pi$
$313$	7.79099	0.440373	0.220186	+	0.975458i	$0.429333\pi$
$314$	−13.8657	−0.782487
$315$	−3.90566	−0.220059
$316$	21.2045	1.19285
$317$	−6.63389	−0.372597	−0.186298	−	0.982493i	$-0.559649\pi$
$317$	−6.63389	−0.372597	−0.186298	+	0.982493i	$0.559649\pi$
$318$	81.3833	4.56375
$319$	−8.92784	−0.499863
$320$	−0.909948	−0.0508677
$321$	−24.6729	−1.37711
$322$	−15.2721	−0.851079
$323$	9.94961	0.553611
$324$	−24.3037	−1.35021
$325$	3.62064	0.200837
$326$	17.8958	0.991154
$327$	−46.5190	−2.57250
$328$	−30.3566	−1.67616
$329$	−9.43679	−0.520267
$330$	−13.9279	−0.766704
$331$	−18.8344	−1.03523	−0.517616	−	0.855613i	$-0.673180\pi$
$331$	−18.8344	−1.03523	−0.517616	+	0.855613i	$0.673180\pi$
$332$	13.1854	0.723646
$333$	0.203344	0.0111432
$334$	−49.8019	−2.72504
$335$	−11.6499	−0.636504
$336$	−18.1195	−0.988501
$337$	−24.4349	−1.33105	−0.665527	−	0.746374i	$-0.731793\pi$
$337$	−24.4349	−1.33105	−0.665527	+	0.746374i	$0.731793\pi$
$338$	−0.276901	−0.0150614
$339$	−18.2811	−0.992892
$340$	−8.68249	−0.470874
$341$	−14.9435	−0.809238
$342$	50.5657	2.73428
$343$	−1.00000	−0.0539949
$344$	16.8014	0.905871
$345$	−15.8036	−0.850838
$346$	−9.17181	−0.493080
$347$	−7.98547	−0.428683	−0.214341	−	0.976759i	$-0.568760\pi$
$347$	−7.98547	−0.428683	−0.214341	+	0.976759i	$0.568760\pi$
$348$	−50.0112	−2.68088
$349$	7.24379	0.387751	0.193876	−	0.981026i	$-0.437894\pi$
$349$	7.24379	0.387751	0.193876	+	0.981026i	$0.437894\pi$
$350$	2.53948	0.135741
$351$	8.61692	0.459937
$352$	−10.5858	−0.564223
$353$	11.0739	0.589405	0.294702	−	0.955589i	$-0.404780\pi$
$353$	11.0739	0.589405	0.294702	+	0.955589i	$0.404780\pi$
$354$	45.8879	2.43892
$355$	−7.24494	−0.384521
$356$	−2.60143	−0.137876
$357$	5.12850	0.271429
$358$	66.8951	3.53551
$359$	0.800907	0.0422703	0.0211351	−	0.999777i	$-0.493272\pi$
$359$	0.800907	0.0422703	0.0211351	+	0.999777i	$0.493272\pi$
$360$	−24.2893	−1.28016
$361$	6.99181	0.367990
$362$	56.5535	2.97238
$363$	−17.4598	−0.916402
$364$	−16.1080	−0.844288
$365$	−5.45645	−0.285604
$366$	50.5698	2.64333
$367$	36.2561	1.89255	0.946276	−	0.323361i	$-0.104813\pi$
$367$	36.2561	1.89255	0.946276	+	0.323361i	$0.104813\pi$
$368$	−41.4666	−2.16159
$369$	19.0645	0.992460
$370$	−0.132215	−0.00687355
$371$	12.1952	0.633143
$372$	−83.7093	−4.34013
$373$	30.7505	1.59220	0.796101	−	0.605164i	$-0.206893\pi$
$373$	30.7505	1.59220	0.796101	+	0.605164i	$0.206893\pi$
$374$	10.3436	0.534853
$375$	2.62786	0.135702
$376$	−58.6875	−3.02658
$377$	−15.4879	−0.797670
$378$	6.04381	0.310860
$379$	−17.9035	−0.919640	−0.459820	−	0.888012i	$-0.652086\pi$
$379$	−17.9035	−0.919640	−0.459820	+	0.888012i	$0.652086\pi$
$380$	−22.6816	−1.16354
$381$	18.7632	0.961266
$382$	−6.54845	−0.335048
$383$	−23.9253	−1.22252	−0.611262	−	0.791428i	$-0.709338\pi$
$383$	−23.9253	−1.22252	−0.611262	+	0.791428i	$0.709338\pi$
$384$	32.7298	1.67023
$385$	−2.08708	−0.106367
$386$	37.1731	1.89206
$387$	−10.5516	−0.536368
$388$	35.2506	1.78958
$389$	0.922022	0.0467484	0.0233742	−	0.999727i	$-0.492559\pi$
$389$	0.922022	0.0467484	0.0233742	+	0.999727i	$0.492559\pi$
$390$	−24.1619	−1.22349
$391$	11.7366	0.593545
$392$	−6.21901	−0.314108
$393$	8.68793	0.438248
$394$	−23.3577	−1.17675
$395$	4.76620	0.239814
$396$	36.2651	1.82239
$397$	−35.1517	−1.76421	−0.882107	−	0.471049i	$-0.843875\pi$
$397$	−35.1517	−1.76421	−0.882107	+	0.471049i	$0.843875\pi$
$398$	−31.4309	−1.57549
$399$	13.3974	0.670709
$400$	6.89516	0.344758
$401$	−16.3302	−0.815492	−0.407746	−	0.913095i	$-0.633685\pi$
$401$	−16.3302	−0.815492	−0.407746	+	0.913095i	$0.633685\pi$
$402$	77.7446	3.87755
$403$	−25.9239	−1.29136
$404$	85.7435	4.26590
$405$	−5.46281	−0.271449
$406$	−10.8631	−0.539125
$407$	0.108662	0.00538616
$408$	31.8942	1.57900
$409$	−31.3526	−1.55029	−0.775143	−	0.631786i	$-0.782322\pi$
$409$	−31.3526	−1.55029	−0.775143	+	0.631786i	$0.782322\pi$
$410$	−12.3958	−0.612187
$411$	42.0656	2.07495
$412$	−12.5146	−0.616550
$413$	6.87625	0.338358
$414$	59.6475	2.93151
$415$	2.96373	0.145484
$416$	−18.3641	−0.900374
$417$	11.5384	0.565040
$418$	27.0209	1.32164
$419$	36.3806	1.77731	0.888654	−	0.458578i	$-0.151641\pi$
$419$	36.3806	1.77731	0.888654	+	0.458578i	$0.151641\pi$
$420$	−11.6912	−0.570472
$421$	−32.6987	−1.59363	−0.796817	−	0.604220i	$-0.793485\pi$
$421$	−32.6987	−1.59363	−0.796817	+	0.604220i	$0.793485\pi$
$422$	−49.3201	−2.40086
$423$	36.8569	1.79204
$424$	75.8421	3.68322
$425$	−1.95159	−0.0946659
$426$	48.3483	2.34248
$427$	7.57783	0.366717
$428$	−41.7709	−2.01907
$429$	19.8576	0.958733
$430$	6.86070	0.330852
$431$	13.1552	0.633664	0.316832	−	0.948482i	$-0.397381\pi$
$431$	13.1552	0.633664	0.316832	+	0.948482i	$0.397381\pi$
$432$	16.4101	0.789530
$433$	−5.39576	−0.259304	−0.129652	−	0.991560i	$-0.541386\pi$
$433$	−5.39576	−0.259304	−0.129652	+	0.991560i	$0.541386\pi$
$434$	−18.1827	−0.872799
$435$	−11.2412	−0.538972
$436$	−78.7560	−3.77173
$437$	30.6600	1.46667
$438$	36.4130	1.73988
$439$	−39.2491	−1.87326	−0.936630	−	0.350321i	$-0.886073\pi$
$439$	−39.2491	−1.87326	−0.936630	+	0.350321i	$0.886073\pi$
$440$	−12.9796	−0.618776
$441$	3.90566	0.185984
$442$	17.9439	0.853505
$443$	24.3092	1.15497	0.577483	−	0.816402i	$-0.304035\pi$
$443$	24.3092	1.15497	0.577483	+	0.816402i	$0.304035\pi$
$444$	0.608691	0.0288872
$445$	−0.584731	−0.0277189
$446$	20.1880	0.955928
$447$	−39.5595	−1.87110
$448$	0.909948	0.0429910
$449$	26.0158	1.22776	0.613881	−	0.789399i	$-0.289608\pi$
$449$	26.0158	1.22776	0.613881	+	0.789399i	$0.289608\pi$
$450$	−9.91832	−0.467554
$451$	10.1876	0.479714
$452$	−30.9496	−1.45575
$453$	−27.5494	−1.29438
$454$	−9.59352	−0.450246
$455$	−3.62064	−0.169738
$456$	83.3186	3.90175
$457$	−20.8597	−0.975776	−0.487888	−	0.872906i	$-0.662233\pi$
$457$	−20.8597	−0.975776	−0.487888	+	0.872906i	$0.662233\pi$
$458$	−2.53948	−0.118662
$459$	−4.64467	−0.216794
$460$	−26.7553	−1.24747
$461$	15.1290	0.704628	0.352314	−	0.935882i	$-0.385395\pi$
$461$	15.1290	0.704628	0.352314	+	0.935882i	$0.385395\pi$
$462$	13.9279	0.647983
$463$	29.3516	1.36409	0.682043	−	0.731312i	$-0.261092\pi$
$463$	29.3516	1.36409	0.682043	+	0.731312i	$0.261092\pi$
$464$	−29.4953	−1.36928
$465$	−18.8156	−0.872552
$466$	11.6690	0.540556
$467$	19.4745	0.901171	0.450585	−	0.892733i	$-0.351215\pi$
$467$	19.4745	0.901171	0.450585	+	0.892733i	$0.351215\pi$
$468$	62.9123	2.90812
$469$	11.6499	0.537944
$470$	−23.9645	−1.10540
$471$	14.3483	0.661135
$472$	42.7635	1.96835
$473$	−5.63849	−0.259258
$474$	−31.8067	−1.46093
$475$	−5.09822	−0.233922
$476$	8.68249	0.397961
$477$	−47.6303	−2.18084
$478$	20.2250	0.925071
$479$	−6.72388	−0.307222	−0.153611	−	0.988131i	$-0.549090\pi$
$479$	−6.72388	−0.307222	−0.153611	+	0.988131i	$0.549090\pi$
$480$	−13.3287	−0.608368
$481$	0.188505	0.00859510
$482$	−4.69238	−0.213732
$483$	15.8036	0.719089
$484$	−29.5592	−1.34360
$485$	7.92337	0.359782
$486$	54.5869	2.47611
$487$	−14.4489	−0.654742	−0.327371	−	0.944896i	$-0.606163\pi$
$487$	−14.4489	−0.654742	−0.327371	+	0.944896i	$0.606163\pi$
$488$	47.1266	2.13332
$489$	−18.5186	−0.837441
$490$	−2.53948	−0.114722
$491$	21.6908	0.978892	0.489446	−	0.872034i	$-0.337199\pi$
$491$	21.6908	0.978892	0.489446	+	0.872034i	$0.337199\pi$
$492$	57.0678	2.57281
$493$	8.34827	0.375987
$494$	46.8757	2.10904
$495$	8.15141	0.366378
$496$	−49.3696	−2.21676
$497$	7.24494	0.324980
$498$	−19.7781	−0.886279
$499$	20.9687	0.938689	0.469345	−	0.883015i	$-0.344490\pi$
$499$	20.9687	0.938689	0.469345	+	0.883015i	$0.344490\pi$
$500$	4.44894	0.198962
$501$	51.5352	2.30242
$502$	−45.5243	−2.03185
$503$	35.9747	1.60403	0.802017	−	0.597301i	$-0.203760\pi$
$503$	35.9747	1.60403	0.802017	+	0.597301i	$0.203760\pi$
$504$	24.2893	1.08193
$505$	19.2728	0.857629
$506$	31.8740	1.41697
$507$	0.286539	0.0127256
$508$	31.7658	1.40938
$509$	2.02578	0.0897912	0.0448956	−	0.998992i	$-0.485704\pi$
$509$	2.02578	0.0897912	0.0448956	+	0.998992i	$0.485704\pi$
$510$	13.0237	0.576699
$511$	5.45645	0.241379
$512$	50.7895	2.24460
$513$	−12.1335	−0.535706
$514$	52.9800	2.33685
$515$	−2.81294	−0.123953
$516$	−31.5851	−1.39046
$517$	19.6953	0.866199
$518$	0.132215	0.00580921
$519$	9.49104	0.416610
$520$	−22.5168	−0.987427
$521$	10.8103	0.473606	0.236803	−	0.971558i	$-0.423900\pi$
$521$	10.8103	0.473606	0.236803	+	0.971558i	$0.423900\pi$
$522$	42.4274	1.85700
$523$	12.8650	0.562547	0.281274	−	0.959628i	$-0.409243\pi$
$523$	12.8650	0.562547	0.281274	+	0.959628i	$0.409243\pi$
$524$	14.7086	0.642546
$525$	−2.62786	−0.114689
$526$	−25.0731	−1.09324
$527$	13.9734	0.608692
$528$	37.8168	1.64577
$529$	13.1666	0.572462
$530$	30.9694	1.34523
$531$	−26.8563	−1.16546
$532$	22.6816	0.983374
$533$	17.6733	0.765515
$534$	3.90214	0.168862
$535$	−9.38897	−0.405921
$536$	72.4511	3.12941
$537$	−69.2233	−2.98721
$538$	20.4460	0.881489
$539$	2.08708	0.0898967
$540$	10.5882	0.455644
$541$	−40.1560	−1.72644	−0.863220	−	0.504828i	$-0.831556\pi$
$541$	−40.1560	−1.72644	−0.863220	+	0.504828i	$0.831556\pi$
$542$	−55.5923	−2.38790
$543$	−58.5218	−2.51141
$544$	9.89856	0.424397
$545$	−17.7022	−0.758279
$546$	24.1619	1.03404
$547$	−8.87717	−0.379560	−0.189780	−	0.981827i	$-0.560778\pi$
$547$	−8.87717	−0.379560	−0.189780	+	0.981827i	$0.560778\pi$
$548$	71.2166	3.04222
$549$	−29.5964	−1.26314
$550$	−5.30008	−0.225996
$551$	21.8085	0.929075
$552$	98.2829	4.18320
$553$	−4.76620	−0.202679
$554$	−80.4429	−3.41769
$555$	0.136817	0.00580757
$556$	19.5344	0.828444
$557$	−0.340910	−0.0144448	−0.00722242	−	0.999974i	$-0.502299\pi$
$557$	−0.340910	−0.0144448	−0.00722242	+	0.999974i	$0.502299\pi$
$558$	71.0155	3.00633
$559$	−9.78160	−0.413717
$560$	−6.89516	−0.291374
$561$	−10.7036	−0.451905
$562$	−39.1660	−1.65212
$563$	16.7815	0.707256	0.353628	−	0.935386i	$-0.384948\pi$
$563$	16.7815	0.707256	0.353628	+	0.935386i	$0.384948\pi$
$564$	110.327	4.64562
$565$	−6.95664	−0.292668
$566$	−72.2344	−3.03624
$567$	5.46281	0.229417
$568$	45.0564	1.89052
$569$	−10.6215	−0.445277	−0.222638	−	0.974901i	$-0.571467\pi$
$569$	−10.6215	−0.445277	−0.222638	+	0.974901i	$0.571467\pi$
$570$	34.0224	1.42504
$571$	−40.6819	−1.70249	−0.851243	−	0.524772i	$-0.824151\pi$
$571$	−40.6819	−1.70249	−0.851243	+	0.524772i	$0.824151\pi$
$572$	33.6186	1.40567
$573$	6.77636	0.283087
$574$	12.3958	0.517393
$575$	−6.01387	−0.250796
$576$	−3.55395	−0.148081
$577$	−18.8445	−0.784508	−0.392254	−	0.919857i	$-0.628305\pi$
$577$	−18.8445	−0.784508	−0.392254	+	0.919857i	$0.628305\pi$
$578$	33.4990	1.39337
$579$	−38.4669	−1.59863
$580$	−19.0311	−0.790224
$581$	−2.96373	−0.122956
$582$	−52.8757	−2.19177
$583$	−25.4523	−1.05413
$584$	33.9337	1.40419
$585$	14.1410	0.584658
$586$	12.8890	0.532440
$587$	−4.43206	−0.182931	−0.0914654	−	0.995808i	$-0.529155\pi$
$587$	−4.43206	−0.182931	−0.0914654	+	0.995808i	$0.529155\pi$
$588$	11.6912	0.482136
$589$	36.5034	1.50410
$590$	17.4621	0.718902
$591$	24.1707	0.994250
$592$	0.358990	0.0147544
$593$	−44.5093	−1.82778	−0.913889	−	0.405965i	$-0.866936\pi$
$593$	−44.5093	−1.82778	−0.913889	+	0.405965i	$0.866936\pi$
$594$	−12.6139	−0.517554
$595$	1.95159	0.0800073
$596$	−66.9738	−2.74335
$597$	32.5248	1.33115
$598$	55.2947	2.26117
$599$	−0.368265	−0.0150469	−0.00752345	−	0.999972i	$-0.502395\pi$
$599$	−0.368265	−0.0150469	−0.00752345	+	0.999972i	$0.502395\pi$
$600$	−16.3427	−0.667188
$601$	14.6994	0.599603	0.299801	−	0.954002i	$-0.403080\pi$
$601$	14.6994	0.599603	0.299801	+	0.954002i	$0.403080\pi$
$602$	−6.86070	−0.279621
$603$	−45.5007	−1.85293
$604$	−46.6407	−1.89778
$605$	−6.64411	−0.270122
$606$	−128.615	−5.22463
$607$	2.43456	0.0988156	0.0494078	−	0.998779i	$-0.484267\pi$
$607$	2.43456	0.0988156	0.0494078	+	0.998779i	$0.484267\pi$
$608$	25.8584	1.04870
$609$	11.2412	0.455514
$610$	19.2437	0.779155
$611$	34.1672	1.38226
$612$	−33.9108	−1.37076
$613$	−8.67833	−0.350514	−0.175257	−	0.984523i	$-0.556076\pi$
$613$	−8.67833	−0.350514	−0.175257	+	0.984523i	$0.556076\pi$
$614$	−39.2564	−1.58426
$615$	12.8273	0.517246
$616$	12.9796	0.522961
$617$	−22.9249	−0.922921	−0.461460	−	0.887161i	$-0.652674\pi$
$617$	−22.9249	−0.922921	−0.461460	+	0.887161i	$0.652674\pi$
$618$	18.7719	0.755115
$619$	22.0055	0.884475	0.442238	−	0.896898i	$-0.354185\pi$
$619$	22.0055	0.884475	0.442238	+	0.896898i	$0.354185\pi$
$620$	−31.8545	−1.27931
$621$	−14.3127	−0.574347
$622$	−60.9032	−2.44200
$623$	0.584731	0.0234268
$624$	65.6043	2.62627
$625$	1.00000	0.0400000
$626$	−19.7850	−0.790769
$627$	−27.9614	−1.11667
$628$	24.2915	0.969336
$629$	−0.101608	−0.00405136
$630$	9.91832	0.395155
$631$	−4.69890	−0.187060	−0.0935301	−	0.995616i	$-0.529815\pi$
$631$	−4.69890	−0.187060	−0.0935301	+	0.995616i	$0.529815\pi$
$632$	−29.6411	−1.17906
$633$	51.0367	2.02853
$634$	16.8466	0.669064
$635$	7.14009	0.283346
$636$	−142.576	−5.65352
$637$	3.62064	0.143455
$638$	22.6720	0.897595
$639$	−28.2962	−1.11938
$640$	12.4549	0.492323
$641$	31.5128	1.24468	0.622340	−	0.782747i	$-0.286182\pi$
$641$	31.5128	1.24468	0.622340	+	0.782747i	$0.286182\pi$
$642$	62.6563	2.47285
$643$	−38.6235	−1.52316	−0.761581	−	0.648070i	$-0.775576\pi$
$643$	−38.6235	−1.52316	−0.761581	+	0.648070i	$0.775576\pi$
$644$	26.7553	1.05431
$645$	−7.09948	−0.279542
$646$	−25.2668	−0.994109
$647$	−18.5547	−0.729462	−0.364731	−	0.931113i	$-0.618839\pi$
$647$	−18.5547	−0.729462	−0.364731	+	0.931113i	$0.618839\pi$
$648$	33.9733	1.33460
$649$	−14.3513	−0.563336
$650$	−9.19453	−0.360639
$651$	18.8156	0.737441
$652$	−31.3518	−1.22783
$653$	32.9506	1.28946	0.644728	−	0.764412i	$-0.276971\pi$
$653$	32.9506	1.28946	0.644728	+	0.764412i	$0.276971\pi$
$654$	118.134	4.61939
$655$	3.30608	0.129179
$656$	33.6571	1.31409
$657$	−21.3110	−0.831422
$658$	23.9645	0.934234
$659$	25.0731	0.976709	0.488354	−	0.872645i	$-0.337597\pi$
$659$	25.0731	0.976709	0.488354	+	0.872645i	$0.337597\pi$
$660$	24.4004	0.949784
$661$	−26.8628	−1.04484	−0.522422	−	0.852687i	$-0.674971\pi$
$661$	−26.8628	−1.04484	−0.522422	+	0.852687i	$0.674971\pi$
$662$	47.8295	1.85895
$663$	−18.5685	−0.721139
$664$	−18.4315	−0.715280
$665$	5.09822	0.197700
$666$	−0.516388	−0.0200096
$667$	25.7254	0.996092
$668$	87.2485	3.37574
$669$	−20.8906	−0.807677
$670$	29.5847	1.14296
$671$	−15.8155	−0.610551
$672$	13.3287	0.514164
$673$	6.80678	0.262382	0.131191	−	0.991357i	$-0.458120\pi$
$673$	6.80678	0.262382	0.131191	+	0.991357i	$0.458120\pi$
$674$	62.0519	2.39015
$675$	2.37994	0.0916040
$676$	0.485106	0.0186579
$677$	9.43843	0.362748	0.181374	−	0.983414i	$-0.441946\pi$
$677$	9.43843	0.362748	0.181374	+	0.983414i	$0.441946\pi$
$678$	46.4244	1.78292
$679$	−7.92337	−0.304071
$680$	12.1369	0.465431
$681$	9.92742	0.380420
$682$	37.9488	1.45313
$683$	19.0441	0.728701	0.364351	−	0.931262i	$-0.381291\pi$
$683$	19.0441	0.728701	0.364351	+	0.931262i	$0.381291\pi$
$684$	−88.5867	−3.38720
$685$	16.0076	0.611617
$686$	2.53948	0.0969576
$687$	2.62786	0.100259
$688$	−18.6281	−0.710189
$689$	−44.1544	−1.68215
$690$	40.1329	1.52783
$691$	35.3606	1.34518	0.672591	−	0.740014i	$-0.265181\pi$
$691$	35.3606	1.34518	0.672591	+	0.740014i	$0.265181\pi$
$692$	16.0682	0.610821
$693$	−8.15141	−0.309646
$694$	20.2789	0.769777
$695$	4.39081	0.166553
$696$	69.9089	2.64989
$697$	−9.52621	−0.360831
$698$	−18.3954	−0.696277
$699$	−12.0751	−0.456724
$700$	−4.44894	−0.168154
$701$	−25.5567	−0.965263	−0.482631	−	0.875824i	$-0.660319\pi$
$701$	−25.5567	−0.965263	−0.482631	+	0.875824i	$0.660319\pi$
$702$	−21.8825	−0.825900
$703$	−0.265434	−0.0100110
$704$	−1.89913	−0.0715762
$705$	24.7986	0.933969
$706$	−28.1219	−1.05838
$707$	−19.2728	−0.724829
$708$	−80.3916	−3.02130
$709$	18.4111	0.691445	0.345722	−	0.938337i	$-0.387634\pi$
$709$	18.4111	0.691445	0.345722	+	0.938337i	$0.387634\pi$
$710$	18.3983	0.690477
$711$	18.6151	0.698123
$712$	3.63645	0.136282
$713$	43.0595	1.61259
$714$	−13.0237	−0.487400
$715$	7.55655	0.282599
$716$	−117.194	−4.37975
$717$	−20.9289	−0.781606
$718$	−2.03388	−0.0759039
$719$	−37.9009	−1.41346	−0.706732	−	0.707482i	$-0.749831\pi$
$719$	−37.9009	−1.41346	−0.706732	+	0.707482i	$0.749831\pi$
$720$	26.9301	1.00363
$721$	2.81294	0.104759
$722$	−17.7555	−0.660792
$723$	4.85570	0.180585
$724$	−99.0766	−3.68215
$725$	−4.27768	−0.158869
$726$	44.3388	1.64557
$727$	27.7423	1.02891	0.514453	−	0.857518i	$-0.327995\pi$
$727$	27.7423	1.02891	0.514453	+	0.857518i	$0.327995\pi$
$728$	22.5168	0.834528
$729$	−40.0984	−1.48512
$730$	13.8565	0.512853
$731$	5.27245	0.195008
$732$	−88.5938	−3.27452
$733$	8.76871	0.323880	0.161940	−	0.986801i	$-0.448225\pi$
$733$	8.76871	0.323880	0.161940	+	0.986801i	$0.448225\pi$
$734$	−92.0714	−3.39842
$735$	2.62786	0.0969301
$736$	30.5027	1.12434
$737$	−24.3143	−0.895629
$738$	−48.4139	−1.78214
$739$	18.0125	0.662601	0.331300	−	0.943525i	$-0.392513\pi$
$739$	18.0125	0.662601	0.331300	+	0.943525i	$0.392513\pi$
$740$	0.231630	0.00851488
$741$	−48.5072	−1.78196
$742$	−30.9694	−1.13692
$743$	4.70333	0.172549	0.0862743	−	0.996271i	$-0.472504\pi$
$743$	4.70333	0.172549	0.0862743	+	0.996271i	$0.472504\pi$
$744$	117.014	4.28995
$745$	−15.0539	−0.551532
$746$	−78.0902	−2.85908
$747$	11.5753	0.423519
$748$	−18.1210	−0.662570
$749$	9.38897	0.343066
$750$	−6.67339	−0.243678
$751$	11.7314	0.428085	0.214042	−	0.976824i	$-0.431337\pi$
$751$	11.7314	0.428085	0.214042	+	0.976824i	$0.431337\pi$
$752$	65.0682	2.37279
$753$	47.1088	1.71674
$754$	39.3312	1.43236
$755$	−10.4836	−0.381536
$756$	−10.5882	−0.385090
$757$	18.9428	0.688489	0.344244	−	0.938880i	$-0.388135\pi$
$757$	18.9428	0.688489	0.344244	+	0.938880i	$0.388135\pi$
$758$	45.4654	1.65138
$759$	−32.9834	−1.19722
$760$	31.7059	1.15009
$761$	1.99515	0.0723243	0.0361621	−	0.999346i	$-0.488487\pi$
$761$	1.99515	0.0723243	0.0361621	+	0.999346i	$0.488487\pi$
$762$	−47.6486	−1.72613
$763$	17.7022	0.640863
$764$	11.4723	0.415053
$765$	−7.62223	−0.275582
$766$	60.7576	2.19526
$767$	−24.8964	−0.898958
$768$	−78.3340	−2.82664
$769$	−35.8963	−1.29445	−0.647227	−	0.762297i	$-0.724071\pi$
$769$	−35.8963	−1.29445	−0.647227	+	0.762297i	$0.724071\pi$
$770$	5.30008	0.191002
$771$	−54.8239	−1.97444
$772$	−65.1240	−2.34386
$773$	33.5075	1.20518	0.602591	−	0.798051i	$-0.294135\pi$
$773$	33.5075	1.20518	0.602591	+	0.798051i	$0.294135\pi$
$774$	26.7955	0.963146
$775$	−7.16004	−0.257196
$776$	−49.2755	−1.76889
$777$	−0.136817	−0.00490829
$778$	−2.34145	−0.0839451
$779$	−24.8857	−0.891624
$780$	42.3296	1.51564
$781$	−15.1207	−0.541063
$782$	−29.8048	−1.06582
$783$	−10.1806	−0.363826
$784$	6.89516	0.246256
$785$	5.46007	0.194878
$786$	−22.0628	−0.786954
$787$	40.6324	1.44839	0.724194	−	0.689596i	$-0.242212\pi$
$787$	40.6324	1.44839	0.724194	+	0.689596i	$0.242212\pi$
$788$	40.9207	1.45774
$789$	25.9457	0.923692
$790$	−12.1036	−0.430629
$791$	6.95664	0.247350
$792$	−50.6937	−1.80132
$793$	−27.4366	−0.974302
$794$	89.2669	3.16796
$795$	−32.0473	−1.13660
$796$	55.0641	1.95170
$797$	37.7845	1.33840	0.669198	−	0.743084i	$-0.266638\pi$
$797$	37.7845	1.33840	0.669198	+	0.743084i	$0.266638\pi$
$798$	−34.0224	−1.20438
$799$	−18.4167	−0.651537
$800$	−5.07206	−0.179324
$801$	−2.28376	−0.0806927
$802$	41.4702	1.46436
$803$	−11.3880	−0.401875
$804$	−136.202	−4.80346
$805$	6.01387	0.211961
$806$	65.8332	2.31887
$807$	−21.1576	−0.744783
$808$	−119.858	−4.21659
$809$	−47.9182	−1.68471	−0.842357	−	0.538920i	$-0.818832\pi$
$809$	−47.9182	−1.68471	−0.842357	+	0.538920i	$0.818832\pi$
$810$	13.8727	0.487436
$811$	−37.6893	−1.32345	−0.661725	−	0.749746i	$-0.730175\pi$
$811$	−37.6893	−1.32345	−0.661725	+	0.749746i	$0.730175\pi$
$812$	19.0311	0.667861
$813$	57.5272	2.01757
$814$	−0.275944	−0.00967182
$815$	−7.04703	−0.246847
$816$	−35.3618	−1.23791
$817$	13.7734	0.481872
$818$	79.6191	2.78382
$819$	−14.1410	−0.494126
$820$	21.7164	0.758370
$821$	40.4425	1.41145	0.705727	−	0.708484i	$-0.250620\pi$
$821$	40.4425	1.41145	0.705727	+	0.708484i	$0.250620\pi$
$822$	−106.825	−3.72594
$823$	11.1093	0.387244	0.193622	−	0.981076i	$-0.437976\pi$
$823$	11.1093	0.387244	0.193622	+	0.981076i	$0.437976\pi$
$824$	17.4937	0.609423
$825$	5.48455	0.190947
$826$	−17.4621	−0.607583
$827$	18.6235	0.647603	0.323801	−	0.946125i	$-0.395039\pi$
$827$	18.6235	0.647603	0.323801	+	0.946125i	$0.395039\pi$
$828$	−104.497	−3.63153
$829$	−18.9419	−0.657878	−0.328939	−	0.944351i	$-0.606691\pi$
$829$	−18.9419	−0.657878	−0.328939	+	0.944351i	$0.606691\pi$
$830$	−7.52632	−0.261242
$831$	83.2427	2.88766
$832$	−3.29460	−0.114220
$833$	−1.95159	−0.0676185
$834$	−29.3016	−1.01463
$835$	19.6111	0.678670
$836$	−47.3383	−1.63723
$837$	−17.0405	−0.589005
$838$	−92.3876	−3.19148
$839$	−21.4899	−0.741912	−0.370956	−	0.928650i	$-0.620970\pi$
$839$	−21.4899	−0.741912	−0.370956	+	0.928650i	$0.620970\pi$
$840$	16.3427	0.563877
$841$	−10.7015	−0.369016
$842$	83.0374	2.86166
$843$	40.5292	1.39590
$844$	86.4044	2.97416
$845$	0.109039	0.00375105
$846$	−93.5971	−3.21794
$847$	6.64411	0.228294
$848$	−84.0878	−2.88759
$849$	74.7485	2.56536
$850$	4.95601	0.169990
$851$	−0.313107	−0.0107332
$852$	−84.7019	−2.90184
$853$	−55.2389	−1.89134	−0.945672	−	0.325122i	$-0.894595\pi$
$853$	−55.2389	−1.89134	−0.945672	+	0.325122i	$0.894595\pi$
$854$	−19.2437	−0.658506
$855$	−19.9119	−0.680972
$856$	58.3901	1.99573
$857$	43.4803	1.48526	0.742629	−	0.669703i	$-0.233579\pi$
$857$	43.4803	1.48526	0.742629	+	0.669703i	$0.233579\pi$
$858$	−50.4278	−1.72158
$859$	−29.3418	−1.00113	−0.500565	−	0.865699i	$-0.666874\pi$
$859$	−29.3418	−1.00113	−0.500565	+	0.865699i	$0.666874\pi$
$860$	−12.0193	−0.409856
$861$	−12.8273	−0.437153
$862$	−33.4073	−1.13786
$863$	−17.8110	−0.606294	−0.303147	−	0.952944i	$-0.598037\pi$
$863$	−17.8110	−0.606294	−0.303147	+	0.952944i	$0.598037\pi$
$864$	−12.0712	−0.410671
$865$	3.61170	0.122801
$866$	13.7024	0.465627
$867$	−34.6649	−1.17728
$868$	31.8545	1.08121
$869$	9.94742	0.337443
$870$	28.5466	0.967821
$871$	−42.1802	−1.42922
$872$	110.090	3.72813
$873$	30.9460	1.04736
$874$	−77.8603	−2.63366
$875$	−1.00000	−0.0338062
$876$	−63.7924	−2.15534
$877$	25.1252	0.848417	0.424209	−	0.905565i	$-0.360552\pi$
$877$	25.1252	0.848417	0.424209	+	0.905565i	$0.360552\pi$
$878$	99.6722	3.36378
$879$	−13.3376	−0.449866
$880$	14.3907	0.485111
$881$	−0.779077	−0.0262478	−0.0131239	−	0.999914i	$-0.504178\pi$
$881$	−0.779077	−0.0262478	−0.0131239	+	0.999914i	$0.504178\pi$
$882$	−9.91832	−0.333967
$883$	31.7473	1.06838	0.534191	−	0.845364i	$-0.320616\pi$
$883$	31.7473	1.06838	0.534191	+	0.845364i	$0.320616\pi$
$884$	−31.4362	−1.05731
$885$	−18.0698	−0.607411
$886$	−61.7327	−2.07395
$887$	−3.00597	−0.100931	−0.0504653	−	0.998726i	$-0.516070\pi$
$887$	−3.00597	−0.100931	−0.0504653	+	0.998726i	$0.516070\pi$
$888$	−0.850868	−0.0285533
$889$	−7.14009	−0.239471
$890$	1.48491	0.0497743
$891$	−11.4013	−0.381958
$892$	−35.3675	−1.18419
$893$	−48.1108	−1.60997
$894$	100.460	3.35990
$895$	−26.3421	−0.880518
$896$	−12.4549	−0.416089
$897$	−57.2192	−1.91049
$898$	−66.0665	−2.20467
$899$	30.6283	1.02151
$900$	17.3760	0.579201
$901$	23.8000	0.792893
$902$	−25.8711	−0.861413
$903$	7.09948	0.236256
$904$	43.2634	1.43892
$905$	−22.2697	−0.740271
$906$	69.9610	2.32430
$907$	−3.03148	−0.100659	−0.0503294	−	0.998733i	$-0.516027\pi$
$907$	−3.03148	−0.100659	−0.0503294	+	0.998733i	$0.516027\pi$
$908$	16.8070	0.557760
$909$	75.2730	2.49665
$910$	9.19453	0.304796
$911$	35.4717	1.17523	0.587614	−	0.809141i	$-0.300067\pi$
$911$	35.4717	1.17523	0.587614	+	0.809141i	$0.300067\pi$
$912$	−92.3772	−3.05892
$913$	6.18553	0.204711
$914$	52.9727	1.75218
$915$	−19.9135	−0.658320
$916$	4.44894	0.146997
$917$	−3.30608	−0.109177
$918$	11.7950	0.389294
$919$	22.0135	0.726157	0.363079	−	0.931758i	$-0.381726\pi$
$919$	22.0135	0.726157	0.363079	+	0.931758i	$0.381726\pi$
$920$	37.4003	1.23305
$921$	40.6227	1.33856
$922$	−38.4197	−1.26529
$923$	−26.2313	−0.863414
$924$	−24.4004	−0.802714
$925$	0.0520641	0.00171186
$926$	−74.5378	−2.44946
$927$	−10.9864	−0.360840
$928$	21.6966	0.712227
$929$	−40.2624	−1.32097	−0.660483	−	0.750841i	$-0.729648\pi$
$929$	−40.2624	−1.32097	−0.660483	+	0.750841i	$0.729648\pi$
$930$	47.7817	1.56682
$931$	−5.09822	−0.167087
$932$	−20.4431	−0.669635
$933$	63.0230	2.06328
$934$	−49.4549	−1.61821
$935$	−4.07311	−0.133205
$936$	−87.9429	−2.87450
$937$	17.1825	0.561328	0.280664	−	0.959806i	$-0.409445\pi$
$937$	17.1825	0.561328	0.280664	+	0.959806i	$0.409445\pi$
$938$	−29.5847	−0.965976
$939$	20.4737	0.668132
$940$	41.9837	1.36936
$941$	9.68229	0.315633	0.157817	−	0.987468i	$-0.449554\pi$
$941$	9.68229	0.315633	0.157817	+	0.987468i	$0.449554\pi$
$942$	−36.4372	−1.18719
$943$	−29.3553	−0.955939
$944$	−47.4128	−1.54316
$945$	−2.37994	−0.0774196
$946$	14.3188	0.465544
$947$	−30.2794	−0.983950	−0.491975	−	0.870609i	$-0.663725\pi$
$947$	−30.2794	−0.983950	−0.491975	+	0.870609i	$0.663725\pi$
$948$	55.7225	1.80978
$949$	−19.7558	−0.641302
$950$	12.9468	0.420049
$951$	−17.4330	−0.565302
$952$	−12.1369	−0.393361
$953$	24.2811	0.786543	0.393272	−	0.919422i	$-0.371343\pi$
$953$	24.2811	0.786543	0.393272	+	0.919422i	$0.371343\pi$
$954$	120.956	3.91609
$955$	2.57866	0.0834435
$956$	−35.4324	−1.14597
$957$	−23.4611	−0.758391
$958$	17.0751	0.551672
$959$	−16.0076	−0.516911
$960$	−2.39122	−0.0771762
$961$	20.2661	0.653746
$962$	−0.478705	−0.0154341
$963$	−36.6701	−1.18168
$964$	8.22063	0.264769
$965$	−14.6381	−0.471217
$966$	−40.1329	−1.29125
$967$	37.4691	1.20493	0.602463	−	0.798147i	$-0.294186\pi$
$967$	37.4691	1.20493	0.602463	+	0.798147i	$0.294186\pi$
$968$	41.3198	1.32807
$969$	26.1462	0.839937
$970$	−20.1212	−0.646053
$971$	−38.0286	−1.22040	−0.610199	−	0.792248i	$-0.708910\pi$
$971$	−38.0286	−1.22040	−0.610199	+	0.792248i	$0.708910\pi$
$972$	−95.6314	−3.06738
$973$	−4.39081	−0.140763
$974$	36.6926	1.17571
$975$	9.51454	0.304709
$976$	−52.2503	−1.67249
$977$	−28.9935	−0.927585	−0.463792	−	0.885944i	$-0.653512\pi$
$977$	−28.9935	−0.927585	−0.463792	+	0.885944i	$0.653512\pi$
$978$	47.0276	1.50378
$979$	−1.22038	−0.0390035
$980$	4.44894	0.142116
$981$	−69.1388	−2.20743
$982$	−55.0833	−1.75778
$983$	33.7804	1.07743	0.538714	−	0.842489i	$-0.318910\pi$
$983$	33.7804	1.07743	0.538714	+	0.842489i	$0.318910\pi$
$984$	−79.7730	−2.54307
$985$	9.19786	0.293068
$986$	−21.2002	−0.675152
$987$	−24.7986	−0.789348
$988$	−82.1221	−2.61265
$989$	16.2472	0.516631
$990$	−20.7003	−0.657899
$991$	−22.7985	−0.724220	−0.362110	−	0.932135i	$-0.617943\pi$
$991$	−22.7985	−0.724220	−0.362110	+	0.932135i	$0.617943\pi$
$992$	36.3161	1.15304
$993$	−49.4942	−1.57065
$994$	−18.3983	−0.583560
$995$	12.3769	0.392375
$996$	34.6495	1.09791
$997$	2.43770	0.0772029	0.0386014	−	0.999255i	$-0.487710\pi$
$997$	2.43770	0.0772029	0.0386014	+	0.999255i	$0.487710\pi$
$998$	−53.2496	−1.68559
$999$	0.123910	0.00392032

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.i.1.2	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.i.1.2	✓	44	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)

\(f(q)\)	\(=\)	\(q-2.53948 q^{2} +2.62786 q^{3} +4.44894 q^{4} +1.00000 q^{5} -6.67339 q^{6} -1.00000 q^{7} -6.21901 q^{8} +3.90566 q^{9} +O(q^{10})\)	\(q-2.53948 q^{2} +2.62786 q^{3} +4.44894 q^{4} +1.00000 q^{5} -6.67339 q^{6} -1.00000 q^{7} -6.21901 q^{8} +3.90566 q^{9} -2.53948 q^{10} +2.08708 q^{11} +11.6912 q^{12} +3.62064 q^{13} +2.53948 q^{14} +2.62786 q^{15} +6.89516 q^{16} -1.95159 q^{17} -9.91832 q^{18} -5.09822 q^{19} +4.44894 q^{20} -2.62786 q^{21} -5.30008 q^{22} -6.01387 q^{23} -16.3427 q^{24} +1.00000 q^{25} -9.19453 q^{26} +2.37994 q^{27} -4.44894 q^{28} -4.27768 q^{29} -6.67339 q^{30} -7.16004 q^{31} -5.07206 q^{32} +5.48455 q^{33} +4.95601 q^{34} -1.00000 q^{35} +17.3760 q^{36} +0.0520641 q^{37} +12.9468 q^{38} +9.51454 q^{39} -6.21901 q^{40} +4.88126 q^{41} +6.67339 q^{42} -2.70162 q^{43} +9.28527 q^{44} +3.90566 q^{45} +15.2721 q^{46} +9.43679 q^{47} +18.1195 q^{48} +1.00000 q^{49} -2.53948 q^{50} -5.12850 q^{51} +16.1080 q^{52} -12.1952 q^{53} -6.04381 q^{54} +2.08708 q^{55} +6.21901 q^{56} -13.3974 q^{57} +10.8631 q^{58} -6.87625 q^{59} +11.6912 q^{60} -7.57783 q^{61} +18.1827 q^{62} -3.90566 q^{63} -0.909948 q^{64} +3.62064 q^{65} -13.9279 q^{66} -11.6499 q^{67} -8.68249 q^{68} -15.8036 q^{69} +2.53948 q^{70} -7.24494 q^{71} -24.2893 q^{72} -5.45645 q^{73} -0.132215 q^{74} +2.62786 q^{75} -22.6816 q^{76} -2.08708 q^{77} -24.1619 q^{78} +4.76620 q^{79} +6.89516 q^{80} -5.46281 q^{81} -12.3958 q^{82} +2.96373 q^{83} -11.6912 q^{84} -1.95159 q^{85} +6.86070 q^{86} -11.2412 q^{87} -12.9796 q^{88} -0.584731 q^{89} -9.91832 q^{90} -3.62064 q^{91} -26.7553 q^{92} -18.8156 q^{93} -23.9645 q^{94} -5.09822 q^{95} -13.3287 q^{96} +7.92337 q^{97} -2.53948 q^{98} +8.15141 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * q^99

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