LMFDB - Embedded newform 6041.2.a.f.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$132$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23793 q^{2} +1.90424 q^{3} +3.00834 q^{4} +4.23440 q^{5} -4.26157 q^{6} +1.00000 q^{7} -2.25659 q^{8} +0.626144 q^{9} +O(q^{10})$	\(q-2.23793 q^{2} +1.90424 q^{3} +3.00834 q^{4} +4.23440 q^{5} -4.26157 q^{6} +1.00000 q^{7} -2.25659 q^{8} +0.626144 q^{9} -9.47631 q^{10} -0.780283 q^{11} +5.72861 q^{12} -5.45043 q^{13} -2.23793 q^{14} +8.06334 q^{15} -0.966582 q^{16} +1.79938 q^{17} -1.40127 q^{18} -4.44901 q^{19} +12.7385 q^{20} +1.90424 q^{21} +1.74622 q^{22} +7.54904 q^{23} -4.29710 q^{24} +12.9302 q^{25} +12.1977 q^{26} -4.52040 q^{27} +3.00834 q^{28} +4.65814 q^{29} -18.0452 q^{30} +9.66318 q^{31} +6.67632 q^{32} -1.48585 q^{33} -4.02690 q^{34} +4.23440 q^{35} +1.88365 q^{36} -2.02034 q^{37} +9.95657 q^{38} -10.3790 q^{39} -9.55531 q^{40} +9.44210 q^{41} -4.26157 q^{42} -8.07255 q^{43} -2.34736 q^{44} +2.65135 q^{45} -16.8942 q^{46} +8.51500 q^{47} -1.84061 q^{48} +1.00000 q^{49} -28.9369 q^{50} +3.42646 q^{51} -16.3967 q^{52} -11.9054 q^{53} +10.1163 q^{54} -3.30404 q^{55} -2.25659 q^{56} -8.47199 q^{57} -10.4246 q^{58} +8.64103 q^{59} +24.2572 q^{60} -4.55315 q^{61} -21.6255 q^{62} +0.626144 q^{63} -13.0080 q^{64} -23.0793 q^{65} +3.32523 q^{66} -4.69394 q^{67} +5.41315 q^{68} +14.3752 q^{69} -9.47631 q^{70} +14.4213 q^{71} -1.41295 q^{72} +8.77726 q^{73} +4.52139 q^{74} +24.6222 q^{75} -13.3841 q^{76} -0.780283 q^{77} +23.2274 q^{78} -6.49617 q^{79} -4.09290 q^{80} -10.4864 q^{81} -21.1308 q^{82} -0.00279464 q^{83} +5.72861 q^{84} +7.61932 q^{85} +18.0658 q^{86} +8.87023 q^{87} +1.76078 q^{88} +8.85786 q^{89} -5.93353 q^{90} -5.45043 q^{91} +22.7101 q^{92} +18.4011 q^{93} -19.0560 q^{94} -18.8389 q^{95} +12.7133 q^{96} +5.10013 q^{97} -2.23793 q^{98} -0.488570 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) $ 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * 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 $

$2$	−2.23793	−1.58246	−0.791228	−	0.611521i	$-0.790558\pi$
$2$	−2.23793	−1.58246	−0.791228	+	0.611521i	$0.790558\pi$
$3$	1.90424	1.09942	0.549708	−	0.835357i	$-0.314739\pi$
$3$	1.90424	1.09942	0.549708	+	0.835357i	$0.314739\pi$
$4$	3.00834	1.50417
$5$	4.23440	1.89368	0.946842	−	0.321700i	$-0.104254\pi$
$5$	4.23440	1.89368	0.946842	+	0.321700i	$0.104254\pi$
$6$	−4.26157	−1.73978
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.25659	−0.797825
$9$	0.626144	0.208715
$10$	−9.47631	−2.99667
$11$	−0.780283	−0.235264	−0.117632	−	0.993057i	$-0.537530\pi$
$11$	−0.780283	−0.235264	−0.117632	+	0.993057i	$0.537530\pi$
$12$	5.72861	1.65371
$13$	−5.45043	−1.51168	−0.755839	−	0.654757i	$-0.772771\pi$
$13$	−5.45043	−1.51168	−0.755839	+	0.654757i	$0.772771\pi$
$14$	−2.23793	−0.598112
$15$	8.06334	2.08195
$16$	−0.966582	−0.241645
$17$	1.79938	0.436414	0.218207	−	0.975902i	$-0.429979\pi$
$17$	1.79938	0.436414	0.218207	+	0.975902i	$0.429979\pi$
$18$	−1.40127	−0.330282
$19$	−4.44901	−1.02067	−0.510336	−	0.859975i	$-0.670479\pi$
$19$	−4.44901	−1.02067	−0.510336	+	0.859975i	$0.670479\pi$
$20$	12.7385	2.84842
$21$	1.90424	0.415540
$22$	1.74622	0.372296
$23$	7.54904	1.57408	0.787042	−	0.616900i	$-0.211612\pi$
$23$	7.54904	1.57408	0.787042	+	0.616900i	$0.211612\pi$
$24$	−4.29710	−0.877141
$25$	12.9302	2.58604
$26$	12.1977	2.39216
$27$	−4.52040	−0.869951
$28$	3.00834	0.568522
$29$	4.65814	0.864994	0.432497	−	0.901635i	$-0.357633\pi$
$29$	4.65814	0.864994	0.432497	+	0.901635i	$0.357633\pi$
$30$	−18.0452	−3.29459
$31$	9.66318	1.73556	0.867780	−	0.496949i	$-0.165546\pi$
$31$	9.66318	1.73556	0.867780	+	0.496949i	$0.165546\pi$
$32$	6.67632	1.18022
$33$	−1.48585	−0.258653
$34$	−4.02690	−0.690607
$35$	4.23440	0.715745
$36$	1.88365	0.313942
$37$	−2.02034	−0.332143	−0.166071	−	0.986114i	$-0.553108\pi$
$37$	−2.02034	−0.332143	−0.166071	+	0.986114i	$0.553108\pi$
$38$	9.95657	1.61517
$39$	−10.3790	−1.66196
$40$	−9.55531	−1.51083
$41$	9.44210	1.47461	0.737304	−	0.675561i	$-0.236099\pi$
$41$	9.44210	1.47461	0.737304	+	0.675561i	$0.236099\pi$
$42$	−4.26157	−0.657574
$43$	−8.07255	−1.23105	−0.615526	−	0.788117i	$-0.711056\pi$
$43$	−8.07255	−1.23105	−0.615526	+	0.788117i	$0.711056\pi$
$44$	−2.34736	−0.353877
$45$	2.65135	0.395240
$46$	−16.8942	−2.49092
$47$	8.51500	1.24204	0.621020	−	0.783794i	$-0.286718\pi$
$47$	8.51500	1.24204	0.621020	+	0.783794i	$0.286718\pi$
$48$	−1.84061	−0.265669
$49$	1.00000	0.142857
$50$	−28.9369	−4.09229
$51$	3.42646	0.479801
$52$	−16.3967	−2.27382
$53$	−11.9054	−1.63534	−0.817668	−	0.575691i	$-0.804733\pi$
$53$	−11.9054	−1.63534	−0.817668	+	0.575691i	$0.804733\pi$
$54$	10.1163	1.37666
$55$	−3.30404	−0.445516
$56$	−2.25659	−0.301549
$57$	−8.47199	−1.12214
$58$	−10.4246	−1.36882
$59$	8.64103	1.12497	0.562483	−	0.826809i	$-0.309846\pi$
$59$	8.64103	1.12497	0.562483	+	0.826809i	$0.309846\pi$
$60$	24.2572	3.13160
$61$	−4.55315	−0.582971	−0.291485	−	0.956575i	$-0.594149\pi$
$61$	−4.55315	−0.582971	−0.291485	+	0.956575i	$0.594149\pi$
$62$	−21.6255	−2.74645
$63$	0.626144	0.0788867
$64$	−13.0080	−1.62600
$65$	−23.0793	−2.86264
$66$	3.32523	0.409308
$67$	−4.69394	−0.573455	−0.286728	−	0.958012i	$-0.592568\pi$
$67$	−4.69394	−0.573455	−0.286728	+	0.958012i	$0.592568\pi$
$68$	5.41315	0.656441
$69$	14.3752	1.73057
$70$	−9.47631	−1.13264
$71$	14.4213	1.71150	0.855748	−	0.517393i	$-0.173097\pi$
$71$	14.4213	1.71150	0.855748	+	0.517393i	$0.173097\pi$
$72$	−1.41295	−0.166518
$73$	8.77726	1.02730	0.513650	−	0.858000i	$-0.328293\pi$
$73$	8.77726	1.02730	0.513650	+	0.858000i	$0.328293\pi$
$74$	4.52139	0.525601
$75$	24.6222	2.84313
$76$	−13.3841	−1.53526
$77$	−0.780283	−0.0889215
$78$	23.2274	2.62998
$79$	−6.49617	−0.730876	−0.365438	−	0.930836i	$-0.619081\pi$
$79$	−6.49617	−0.730876	−0.365438	+	0.930836i	$0.619081\pi$
$80$	−4.09290	−0.457600
$81$	−10.4864	−1.16515
$82$	−21.1308	−2.33350
$83$	−0.00279464	−0.000306752 0	−0.000153376	−	1.00000i	$-0.500049\pi$
$83$	−0.00279464	−0.000306752 0	−0.000153376		1.00000i	$0.500049\pi$
$84$	5.72861	0.625042
$85$	7.61932	0.826431
$86$	18.0658	1.94809
$87$	8.87023	0.950988
$88$	1.76078	0.187700
$89$	8.85786	0.938931	0.469466	−	0.882951i	$-0.344447\pi$
$89$	8.85786	0.938931	0.469466	+	0.882951i	$0.344447\pi$
$90$	−5.93353	−0.625449
$91$	−5.45043	−0.571361
$92$	22.7101	2.36769
$93$	18.4011	1.90810
$94$	−19.0560	−1.96548
$95$	−18.8389	−1.93283
$96$	12.7133	1.29755
$97$	5.10013	0.517840	0.258920	−	0.965899i	$-0.416633\pi$
$97$	5.10013	0.517840	0.258920	+	0.965899i	$0.416633\pi$
$98$	−2.23793	−0.226065
$99$	−0.488570	−0.0491031
$100$	38.8984	3.88984
$101$	7.80750	0.776875	0.388438	−	0.921475i	$-0.373015\pi$
$101$	7.80750	0.776875	0.388438	+	0.921475i	$0.373015\pi$
$102$	−7.66819	−0.759264
$103$	−6.10831	−0.601870	−0.300935	−	0.953645i	$-0.597299\pi$
$103$	−6.10831	−0.601870	−0.300935	+	0.953645i	$0.597299\pi$
$104$	12.2994	1.20605
$105$	8.06334	0.786901
$106$	26.6435	2.58785
$107$	−15.0486	−1.45481	−0.727404	−	0.686210i	$-0.759273\pi$
$107$	−15.0486	−1.45481	−0.727404	+	0.686210i	$0.759273\pi$
$108$	−13.5989	−1.30855
$109$	8.87387	0.849963	0.424981	−	0.905202i	$-0.360281\pi$
$109$	8.87387	0.849963	0.424981	+	0.905202i	$0.360281\pi$
$110$	7.39421	0.705010
$111$	−3.84723	−0.365163
$112$	−0.966582	−0.0913334
$113$	−8.23910	−0.775069	−0.387534	−	0.921855i	$-0.626673\pi$
$113$	−8.23910	−0.775069	−0.387534	+	0.921855i	$0.626673\pi$
$114$	18.9597	1.77574
$115$	31.9657	2.98082
$116$	14.0132	1.30110
$117$	−3.41276	−0.315509
$118$	−19.3380	−1.78021
$119$	1.79938	0.164949
$120$	−18.1956	−1.66103
$121$	−10.3912	−0.944651
$122$	10.1896	0.922526
$123$	17.9801	1.62121
$124$	29.0701	2.61057
$125$	33.5796	3.00345
$126$	−1.40127	−0.124835
$127$	−0.0938159	−0.00832482	−0.00416241	−	0.999991i	$-0.501325\pi$
$127$	−0.0938159	−0.00832482	−0.00416241	+	0.999991i	$0.501325\pi$
$128$	15.7583	1.39285
$129$	−15.3721	−1.35344
$130$	51.6500	4.53000
$131$	9.13967	0.798537	0.399268	−	0.916834i	$-0.369264\pi$
$131$	9.13967	0.798537	0.399268	+	0.916834i	$0.369264\pi$
$132$	−4.46994	−0.389058
$133$	−4.44901	−0.385778
$134$	10.5047	0.907468
$135$	−19.1412	−1.64741
$136$	−4.06047	−0.348182
$137$	6.41396	0.547981	0.273991	−	0.961732i	$-0.411656\pi$
$137$	6.41396	0.547981	0.273991	+	0.961732i	$0.411656\pi$
$138$	−32.1707	−2.73855
$139$	−17.9791	−1.52497	−0.762483	−	0.647008i	$-0.776020\pi$
$139$	−17.9791	−1.52497	−0.762483	+	0.647008i	$0.776020\pi$
$140$	12.7385	1.07660
$141$	16.2146	1.36552
$142$	−32.2739	−2.70837
$143$	4.25288	0.355644
$144$	−0.605219	−0.0504350
$145$	19.7244	1.63803
$146$	−19.6429	−1.62566
$147$	1.90424	0.157059
$148$	−6.07788	−0.499599
$149$	−17.0364	−1.39568	−0.697838	−	0.716256i	$-0.745854\pi$
$149$	−17.0364	−1.39568	−0.697838	+	0.716256i	$0.745854\pi$
$150$	−55.1028	−4.49913
$151$	19.4012	1.57884	0.789422	−	0.613850i	$-0.210380\pi$
$151$	19.4012	1.57884	0.789422	+	0.613850i	$0.210380\pi$
$152$	10.0396	0.814318
$153$	1.12667	0.0910861
$154$	1.74622	0.140714
$155$	40.9178	3.28660
$156$	−31.2234	−2.49987
$157$	16.4556	1.31330	0.656649	−	0.754196i	$-0.271973\pi$
$157$	16.4556	1.31330	0.656649	+	0.754196i	$0.271973\pi$
$158$	14.5380	1.15658
$159$	−22.6708	−1.79791
$160$	28.2703	2.23496
$161$	7.54904	0.594948
$162$	23.4678	1.84380
$163$	16.3744	1.28254	0.641269	−	0.767316i	$-0.278408\pi$
$163$	16.3744	1.28254	0.641269	+	0.767316i	$0.278408\pi$
$164$	28.4050	2.21806
$165$	−6.29169	−0.489807
$166$	0.00625422	0.000485421 0
$167$	−8.56460	−0.662748	−0.331374	−	0.943499i	$-0.607512\pi$
$167$	−8.56460	−0.662748	−0.331374	+	0.943499i	$0.607512\pi$
$168$	−4.29710	−0.331528
$169$	16.7072	1.28517
$170$	−17.0515	−1.30779
$171$	−2.78572	−0.213029
$172$	−24.2849	−1.85171
$173$	7.37599	0.560786	0.280393	−	0.959885i	$-0.409535\pi$
$173$	7.37599	0.560786	0.280393	+	0.959885i	$0.409535\pi$
$174$	−19.8510	−1.50490
$175$	12.9302	0.977430
$176$	0.754208	0.0568505
$177$	16.4546	1.23681
$178$	−19.8233	−1.48582
$179$	16.4120	1.22669	0.613346	−	0.789815i	$-0.289823\pi$
$179$	16.4120	1.22669	0.613346	+	0.789815i	$0.289823\pi$
$180$	7.97615	0.594507
$181$	−17.4423	−1.29648	−0.648240	−	0.761436i	$-0.724495\pi$
$181$	−17.4423	−1.29648	−0.648240	+	0.761436i	$0.724495\pi$
$182$	12.1977	0.904153
$183$	−8.67030	−0.640927
$184$	−17.0351	−1.25584
$185$	−8.55496	−0.628973
$186$	−41.1803	−3.01949
$187$	−1.40403	−0.102673
$188$	25.6160	1.86824
$189$	−4.52040	−0.328811
$190$	42.1602	3.05862
$191$	−15.0200	−1.08681	−0.543406	−	0.839470i	$-0.682866\pi$
$191$	−15.0200	−1.08681	−0.543406	+	0.839470i	$0.682866\pi$
$192$	−24.7704	−1.78765
$193$	10.6285	0.765055	0.382527	−	0.923944i	$-0.375054\pi$
$193$	10.6285	0.765055	0.382527	+	0.923944i	$0.375054\pi$
$194$	−11.4137	−0.819459
$195$	−43.9487	−3.14723
$196$	3.00834	0.214881
$197$	−6.49218	−0.462549	−0.231274	−	0.972889i	$-0.574289\pi$
$197$	−6.49218	−0.462549	−0.231274	+	0.972889i	$0.574289\pi$
$198$	1.09339	0.0777035
$199$	−23.2383	−1.64732	−0.823661	−	0.567083i	$-0.808072\pi$
$199$	−23.2383	−1.64732	−0.823661	+	0.567083i	$0.808072\pi$
$200$	−29.1781	−2.06320
$201$	−8.93840	−0.630466
$202$	−17.4726	−1.22937
$203$	4.65814	0.326937
$204$	10.3080	0.721701
$205$	39.9817	2.79244
$206$	13.6700	0.952433
$207$	4.72679	0.328534
$208$	5.26829	0.365290
$209$	3.47149	0.240128
$210$	−18.0452	−1.24524
$211$	−11.2526	−0.774660	−0.387330	−	0.921941i	$-0.626603\pi$
$211$	−11.2526	−0.774660	−0.387330	+	0.921941i	$0.626603\pi$
$212$	−35.8155	−2.45982
$213$	27.4617	1.88165
$214$	33.6778	2.30217
$215$	−34.1824	−2.33122
$216$	10.2007	0.694069
$217$	9.66318	0.655980
$218$	−19.8591	−1.34503
$219$	16.7140	1.12943
$220$	−9.93965	−0.670131
$221$	−9.80742	−0.659718
$222$	8.60984	0.577854
$223$	3.09800	0.207458	0.103729	−	0.994606i	$-0.466923\pi$
$223$	3.09800	0.207458	0.103729	+	0.994606i	$0.466923\pi$
$224$	6.67632	0.446081
$225$	8.09616	0.539744
$226$	18.4385	1.22651
$227$	7.62786	0.506279	0.253139	−	0.967430i	$-0.418537\pi$
$227$	7.62786	0.506279	0.253139	+	0.967430i	$0.418537\pi$
$228$	−25.4866	−1.68789
$229$	9.39304	0.620709	0.310355	−	0.950621i	$-0.399552\pi$
$229$	9.39304	0.620709	0.310355	+	0.950621i	$0.399552\pi$
$230$	−71.5370	−4.71701
$231$	−1.48585	−0.0977617
$232$	−10.5115	−0.690114
$233$	13.7944	0.903699	0.451849	−	0.892094i	$-0.350764\pi$
$233$	13.7944	0.903699	0.451849	+	0.892094i	$0.350764\pi$
$234$	7.63752	0.499280
$235$	36.0560	2.35203
$236$	25.9951	1.69214
$237$	−12.3703	−0.803536
$238$	−4.02690	−0.261025
$239$	16.4955	1.06700	0.533501	−	0.845799i	$-0.320876\pi$
$239$	16.4955	1.06700	0.533501	+	0.845799i	$0.320876\pi$
$240$	−7.79388	−0.503093
$241$	−2.85396	−0.183840	−0.0919198	−	0.995766i	$-0.529300\pi$
$241$	−2.85396	−0.183840	−0.0919198	+	0.995766i	$0.529300\pi$
$242$	23.2547	1.49487
$243$	−6.40741	−0.411036
$244$	−13.6974	−0.876886
$245$	4.23440	0.270526
$246$	−40.2381	−2.56549
$247$	24.2490	1.54293
$248$	−21.8058	−1.38467
$249$	−0.00532168	−0.000337248 0
$250$	−75.1489	−4.75283
$251$	11.3670	0.717479	0.358739	−	0.933438i	$-0.383207\pi$
$251$	11.3670	0.717479	0.358739	+	0.933438i	$0.383207\pi$
$252$	1.88365	0.118659
$253$	−5.89039	−0.370326
$254$	0.209954	0.0131737
$255$	14.5090	0.908591
$256$	−9.25011	−0.578132
$257$	25.7357	1.60535	0.802676	−	0.596415i	$-0.203409\pi$
$257$	25.7357	1.60535	0.802676	+	0.596415i	$0.203409\pi$
$258$	34.4017	2.14176
$259$	−2.02034	−0.125538
$260$	−69.4304	−4.30589
$261$	2.91667	0.180537
$262$	−20.4540	−1.26365
$263$	12.2326	0.754297	0.377148	−	0.926153i	$-0.376905\pi$
$263$	12.2326	0.754297	0.377148	+	0.926153i	$0.376905\pi$
$264$	3.35295	0.206360
$265$	−50.4124	−3.09681
$266$	9.95657	0.610477
$267$	16.8675	1.03228
$268$	−14.1209	−0.862574
$269$	2.04516	0.124696	0.0623478	−	0.998054i	$-0.480141\pi$
$269$	2.04516	0.124696	0.0623478	+	0.998054i	$0.480141\pi$
$270$	42.8367	2.60696
$271$	12.5732	0.763770	0.381885	−	0.924210i	$-0.375275\pi$
$271$	12.5732	0.763770	0.381885	+	0.924210i	$0.375275\pi$
$272$	−1.73925	−0.105458
$273$	−10.3790	−0.628163
$274$	−14.3540	−0.867157
$275$	−10.0892	−0.608402
$276$	43.2455	2.60307
$277$	−17.7884	−1.06880	−0.534401	−	0.845231i	$-0.679463\pi$
$277$	−17.7884	−1.06880	−0.534401	+	0.845231i	$0.679463\pi$
$278$	40.2360	2.41319
$279$	6.05055	0.362237
$280$	−9.55531	−0.571039
$281$	−14.7088	−0.877455	−0.438727	−	0.898620i	$-0.644571\pi$
$281$	−14.7088	−0.877455	−0.438727	+	0.898620i	$0.644571\pi$
$282$	−36.2873	−2.16087
$283$	14.1547	0.841409	0.420704	−	0.907198i	$-0.361783\pi$
$283$	14.1547	0.841409	0.420704	+	0.907198i	$0.361783\pi$
$284$	43.3842	2.57438
$285$	−35.8738	−2.12498
$286$	−9.51766	−0.562791
$287$	9.44210	0.557349
$288$	4.18034	0.246329
$289$	−13.7622	−0.809542
$290$	−44.1419	−2.59210
$291$	9.71189	0.569321
$292$	26.4050	1.54523
$293$	4.05424	0.236851	0.118426	−	0.992963i	$-0.462215\pi$
$293$	4.05424	0.236851	0.118426	+	0.992963i	$0.462215\pi$
$294$	−4.26157	−0.248540
$295$	36.5896	2.13033
$296$	4.55909	0.264992
$297$	3.52719	0.204669
$298$	38.1263	2.20860
$299$	−41.1455	−2.37951
$300$	74.0719	4.27655
$301$	−8.07255	−0.465294
$302$	−43.4185	−2.49845
$303$	14.8674	0.854109
$304$	4.30033	0.246641
$305$	−19.2799	−1.10396
$306$	−2.52142	−0.144140
$307$	5.72061	0.326492	0.163246	−	0.986585i	$-0.447804\pi$
$307$	5.72061	0.326492	0.163246	+	0.986585i	$0.447804\pi$
$308$	−2.34736	−0.133753
$309$	−11.6317	−0.661705
$310$	−91.5713	−5.20090
$311$	2.26376	0.128366	0.0641830	−	0.997938i	$-0.479556\pi$
$311$	2.26376	0.128366	0.0641830	+	0.997938i	$0.479556\pi$
$312$	23.4210	1.32596
$313$	−8.47529	−0.479052	−0.239526	−	0.970890i	$-0.576992\pi$
$313$	−8.47529	−0.479052	−0.239526	+	0.970890i	$0.576992\pi$
$314$	−36.8265	−2.07824
$315$	2.65135	0.149387
$316$	−19.5427	−1.09936
$317$	21.5313	1.20932	0.604658	−	0.796485i	$-0.293310\pi$
$317$	21.5313	1.20932	0.604658	+	0.796485i	$0.293310\pi$
$318$	50.7357	2.84512
$319$	−3.63467	−0.203502
$320$	−55.0811	−3.07913
$321$	−28.6563	−1.59944
$322$	−16.8942	−0.941479
$323$	−8.00547	−0.445436
$324$	−31.5466	−1.75259
$325$	−70.4751	−3.90926
$326$	−36.6447	−2.02956
$327$	16.8980	0.934462
$328$	−21.3069	−1.17648
$329$	8.51500	0.469447
$330$	14.0804	0.775099
$331$	−17.8763	−0.982568	−0.491284	−	0.870999i	$-0.663472\pi$
$331$	−17.8763	−0.982568	−0.491284	+	0.870999i	$0.663472\pi$
$332$	−0.00840723	−0.000461407 0
$333$	−1.26503	−0.0693231
$334$	19.1670	1.04877
$335$	−19.8760	−1.08594
$336$	−1.84061	−0.100413
$337$	−9.61868	−0.523963	−0.261982	−	0.965073i	$-0.584376\pi$
$337$	−9.61868	−0.523963	−0.261982	+	0.965073i	$0.584376\pi$
$338$	−37.3896	−2.03373
$339$	−15.6892	−0.852123
$340$	22.9215	1.24309
$341$	−7.54002	−0.408315
$342$	6.23425	0.337110
$343$	1.00000	0.0539949
$344$	18.2164	0.982164
$345$	60.8705	3.27716
$346$	−16.5070	−0.887420
$347$	−13.9224	−0.747394	−0.373697	−	0.927551i	$-0.621910\pi$
$347$	−13.9224	−0.747394	−0.373697	+	0.927551i	$0.621910\pi$
$348$	26.6846	1.43045
$349$	2.49357	0.133478	0.0667388	−	0.997770i	$-0.478741\pi$
$349$	2.49357	0.133478	0.0667388	+	0.997770i	$0.478741\pi$
$350$	−28.9369	−1.54674
$351$	24.6381	1.31509
$352$	−5.20942	−0.277663
$353$	−16.2742	−0.866188	−0.433094	−	0.901349i	$-0.642578\pi$
$353$	−16.2742	−0.866188	−0.433094	+	0.901349i	$0.642578\pi$
$354$	−36.8243	−1.95719
$355$	61.0657	3.24103
$356$	26.6474	1.41231
$357$	3.42646	0.181348
$358$	−36.7290	−1.94119
$359$	−8.64553	−0.456294	−0.228147	−	0.973627i	$-0.573267\pi$
$359$	−8.64553	−0.456294	−0.228147	+	0.973627i	$0.573267\pi$
$360$	−5.98300	−0.315332
$361$	0.793661	0.0417717
$362$	39.0348	2.05162
$363$	−19.7873	−1.03856
$364$	−16.3967	−0.859423
$365$	37.1665	1.94538
$366$	19.4035	1.01424
$367$	17.5346	0.915300	0.457650	−	0.889132i	$-0.348691\pi$
$367$	17.5346	0.915300	0.457650	+	0.889132i	$0.348691\pi$
$368$	−7.29676	−0.380370
$369$	5.91211	0.307772
$370$	19.1454	0.995323
$371$	−11.9054	−0.618099
$372$	55.3566	2.87011
$373$	5.93136	0.307114	0.153557	−	0.988140i	$-0.450927\pi$
$373$	5.93136	0.307114	0.153557	+	0.988140i	$0.450927\pi$
$374$	3.14212	0.162475
$375$	63.9438	3.30204
$376$	−19.2149	−0.990931
$377$	−25.3889	−1.30759
$378$	10.1163	0.520329
$379$	6.61805	0.339946	0.169973	−	0.985449i	$-0.445632\pi$
$379$	6.61805	0.339946	0.169973	+	0.985449i	$0.445632\pi$
$380$	−56.6737	−2.90730
$381$	−0.178648	−0.00915244
$382$	33.6138	1.71983
$383$	−7.88970	−0.403145	−0.201573	−	0.979474i	$-0.564605\pi$
$383$	−7.88970	−0.403145	−0.201573	+	0.979474i	$0.564605\pi$
$384$	30.0077	1.53133
$385$	−3.30404	−0.168389
$386$	−23.7858	−1.21067
$387$	−5.05458	−0.256939
$388$	15.3429	0.778918
$389$	−3.94552	−0.200046	−0.100023	−	0.994985i	$-0.531892\pi$
$389$	−3.94552	−0.200046	−0.100023	+	0.994985i	$0.531892\pi$
$390$	98.3542	4.98036
$391$	13.5836	0.686953
$392$	−2.25659	−0.113975
$393$	17.4042	0.877924
$394$	14.5291	0.731963
$395$	−27.5074	−1.38405
$396$	−1.46978	−0.0738594
$397$	−30.8311	−1.54737	−0.773685	−	0.633570i	$-0.781589\pi$
$397$	−30.8311	−1.54737	−0.773685	+	0.633570i	$0.781589\pi$
$398$	52.0058	2.60681
$399$	−8.47199	−0.424130
$400$	−12.4981	−0.624904
$401$	−19.0739	−0.952508	−0.476254	−	0.879308i	$-0.658006\pi$
$401$	−19.0739	−0.952508	−0.476254	+	0.879308i	$0.658006\pi$
$402$	20.0035	0.997685
$403$	−52.6685	−2.62361
$404$	23.4876	1.16855
$405$	−44.4036	−2.20643
$406$	−10.4246	−0.517364
$407$	1.57644	0.0781413
$408$	−7.73212	−0.382797
$409$	9.11863	0.450887	0.225444	−	0.974256i	$-0.427617\pi$
$409$	9.11863	0.450887	0.225444	+	0.974256i	$0.427617\pi$
$410$	−89.4762	−4.41892
$411$	12.2137	0.602459
$412$	−18.3759	−0.905314
$413$	8.64103	0.425197
$414$	−10.5782	−0.519891
$415$	−0.0118336	−0.000580891 0
$416$	−36.3889	−1.78411
$417$	−34.2366	−1.67657
$418$	−7.76895	−0.379992
$419$	−13.7693	−0.672674	−0.336337	−	0.941742i	$-0.609188\pi$
$419$	−13.7693	−0.672674	−0.336337	+	0.941742i	$0.609188\pi$
$420$	24.2572	1.18363
$421$	−15.8348	−0.771743	−0.385872	−	0.922553i	$-0.626099\pi$
$421$	−15.8348	−0.771743	−0.385872	+	0.922553i	$0.626099\pi$
$422$	25.1825	1.22587
$423$	5.33162	0.259232
$424$	26.8656	1.30471
$425$	23.2664	1.12858
$426$	−61.4574	−2.97762
$427$	−4.55315	−0.220342
$428$	−45.2714	−2.18828
$429$	8.09852	0.391000
$430$	76.4980	3.68906
$431$	−25.7789	−1.24173	−0.620864	−	0.783918i	$-0.713218\pi$
$431$	−25.7789	−1.24173	−0.620864	+	0.783918i	$0.713218\pi$
$432$	4.36934	0.210220
$433$	39.9652	1.92060	0.960302	−	0.278964i	$-0.0899909\pi$
$433$	39.9652	1.92060	0.960302	+	0.278964i	$0.0899909\pi$
$434$	−21.6255	−1.03806
$435$	37.5601	1.80087
$436$	26.6956	1.27849
$437$	−33.5857	−1.60662
$438$	−37.4049	−1.78727
$439$	33.6744	1.60719	0.803597	−	0.595174i	$-0.202917\pi$
$439$	33.6744	1.60719	0.803597	+	0.595174i	$0.202917\pi$
$440$	7.45585	0.355444
$441$	0.626144	0.0298164
$442$	21.9483	1.04398
$443$	−16.4230	−0.780282	−0.390141	−	0.920755i	$-0.627574\pi$
$443$	−16.4230	−0.780282	−0.390141	+	0.920755i	$0.627574\pi$
$444$	−11.5738	−0.549266
$445$	37.5078	1.77804
$446$	−6.93312	−0.328293
$447$	−32.4414	−1.53443
$448$	−13.0080	−0.614570
$449$	15.5613	0.734385	0.367193	−	0.930145i	$-0.380319\pi$
$449$	15.5613	0.734385	0.367193	+	0.930145i	$0.380319\pi$
$450$	−18.1186	−0.854121
$451$	−7.36751	−0.346923
$452$	−24.7860	−1.16583
$453$	36.9446	1.73581
$454$	−17.0706	−0.801164
$455$	−23.0793	−1.08198
$456$	19.1178	0.895274
$457$	16.7543	0.783735	0.391868	−	0.920022i	$-0.371829\pi$
$457$	16.7543	0.783735	0.391868	+	0.920022i	$0.371829\pi$
$458$	−21.0210	−0.982246
$459$	−8.13393	−0.379659
$460$	96.1636	4.48365
$461$	27.6748	1.28894	0.644472	−	0.764628i	$-0.277077\pi$
$461$	27.6748	1.28894	0.644472	+	0.764628i	$0.277077\pi$
$462$	3.32523	0.154704
$463$	−34.3806	−1.59780	−0.798902	−	0.601461i	$-0.794585\pi$
$463$	−34.3806	−1.59780	−0.798902	+	0.601461i	$0.794585\pi$
$464$	−4.50247	−0.209022
$465$	77.9175	3.61334
$466$	−30.8708	−1.43006
$467$	35.6963	1.65183	0.825915	−	0.563795i	$-0.190659\pi$
$467$	35.6963	1.65183	0.825915	+	0.563795i	$0.190659\pi$
$468$	−10.2667	−0.474579
$469$	−4.69394	−0.216746
$470$	−80.6908	−3.72199
$471$	31.3355	1.44386
$472$	−19.4993	−0.897526
$473$	6.29888	0.289623
$474$	27.6838	1.27156
$475$	−57.5265	−2.63950
$476$	5.41315	0.248111
$477$	−7.45451	−0.341318
$478$	−36.9157	−1.68849
$479$	19.0655	0.871124	0.435562	−	0.900159i	$-0.356550\pi$
$479$	19.0655	0.871124	0.435562	+	0.900159i	$0.356550\pi$
$480$	53.8335	2.45715
$481$	11.0118	0.502093
$482$	6.38696	0.290918
$483$	14.3752	0.654095
$484$	−31.2601	−1.42091
$485$	21.5960	0.980625
$486$	14.3394	0.650446
$487$	−28.0193	−1.26968	−0.634838	−	0.772645i	$-0.718933\pi$
$487$	−28.0193	−1.26968	−0.634838	+	0.772645i	$0.718933\pi$
$488$	10.2746	0.465108
$489$	31.1808	1.41004
$490$	−9.47631	−0.428096
$491$	26.7259	1.20612	0.603062	−	0.797695i	$-0.293947\pi$
$491$	26.7259	1.20612	0.603062	+	0.797695i	$0.293947\pi$
$492$	54.0901	2.43857
$493$	8.38177	0.377496
$494$	−54.2676	−2.44162
$495$	−2.06880	−0.0929858
$496$	−9.34026	−0.419390
$497$	14.4213	0.646885
$498$	0.0119096	0.000533680 0
$499$	15.9997	0.716246	0.358123	−	0.933674i	$-0.383417\pi$
$499$	15.9997	0.716246	0.358123	+	0.933674i	$0.383417\pi$
$500$	101.019	4.51770
$501$	−16.3091	−0.728636
$502$	−25.4386	−1.13538
$503$	−6.61831	−0.295096	−0.147548	−	0.989055i	$-0.547138\pi$
$503$	−6.61831	−0.295096	−0.147548	+	0.989055i	$0.547138\pi$
$504$	−1.41295	−0.0629378
$505$	33.0601	1.47116
$506$	13.1823	0.586024
$507$	31.8146	1.41294
$508$	−0.282230	−0.0125219
$509$	−24.7080	−1.09516	−0.547582	−	0.836752i	$-0.684452\pi$
$509$	−24.7080	−1.09516	−0.547582	+	0.836752i	$0.684452\pi$
$510$	−32.4702	−1.43781
$511$	8.77726	0.388283
$512$	−10.8156	−0.477985
$513$	20.1113	0.887935
$514$	−57.5948	−2.54040
$515$	−25.8651	−1.13975
$516$	−46.2445	−2.03580
$517$	−6.64412	−0.292208
$518$	4.52139	0.198659
$519$	14.0457	0.616537
$520$	52.0806	2.28389
$521$	40.3144	1.76621	0.883103	−	0.469180i	$-0.155450\pi$
$521$	40.3144	1.76621	0.883103	+	0.469180i	$0.155450\pi$
$522$	−6.52730	−0.285692
$523$	−10.3379	−0.452046	−0.226023	−	0.974122i	$-0.572572\pi$
$523$	−10.3379	−0.452046	−0.226023	+	0.974122i	$0.572572\pi$
$524$	27.4952	1.20113
$525$	24.6222	1.07460
$526$	−27.3758	−1.19364
$527$	17.3878	0.757423
$528$	1.43620	0.0625024
$529$	33.9880	1.47774
$530$	112.819	4.90056
$531$	5.41053	0.234797
$532$	−13.3841	−0.580275
$533$	−51.4635	−2.22913
$534$	−37.7484	−1.63353
$535$	−63.7221	−2.75494
$536$	10.5923	0.457517
$537$	31.2525	1.34864
$538$	−4.57693	−0.197325
$539$	−0.780283	−0.0336092
$540$	−57.5832	−2.47799
$541$	9.41479	0.404773	0.202387	−	0.979306i	$-0.435130\pi$
$541$	9.41479	0.404773	0.202387	+	0.979306i	$0.435130\pi$
$542$	−28.1380	−1.20863
$543$	−33.2145	−1.42537
$544$	12.0133	0.515064
$545$	37.5756	1.60956
$546$	23.2274	0.994040
$547$	−1.02258	−0.0437222	−0.0218611	−	0.999761i	$-0.506959\pi$
$547$	−1.02258	−0.0437222	−0.0218611	+	0.999761i	$0.506959\pi$
$548$	19.2953	0.824256
$549$	−2.85093	−0.121675
$550$	22.5790	0.962770
$551$	−20.7241	−0.882876
$552$	−32.4389	−1.38069
$553$	−6.49617	−0.276245
$554$	39.8093	1.69133
$555$	−16.2907	−0.691503
$556$	−54.0872	−2.29381
$557$	5.97881	0.253330	0.126665	−	0.991946i	$-0.459573\pi$
$557$	5.97881	0.253330	0.126665	+	0.991946i	$0.459573\pi$
$558$	−13.5407	−0.573224
$559$	43.9989	1.86095
$560$	−4.09290	−0.172957
$561$	−2.67361	−0.112880
$562$	32.9173	1.38853
$563$	−44.6473	−1.88166	−0.940830	−	0.338879i	$-0.889952\pi$
$563$	−44.6473	−1.88166	−0.940830	+	0.338879i	$0.889952\pi$
$564$	48.7791	2.05397
$565$	−34.8877	−1.46774
$566$	−31.6772	−1.33149
$567$	−10.4864	−0.440386
$568$	−32.5430	−1.36547
$569$	−16.7375	−0.701671	−0.350835	−	0.936437i	$-0.614102\pi$
$569$	−16.7375	−0.701671	−0.350835	+	0.936437i	$0.614102\pi$
$570$	80.2832	3.36269
$571$	1.66825	0.0698140	0.0349070	−	0.999391i	$-0.488886\pi$
$571$	1.66825	0.0698140	0.0349070	+	0.999391i	$0.488886\pi$
$572$	12.7941	0.534948
$573$	−28.6018	−1.19486
$574$	−21.1308	−0.881981
$575$	97.6105	4.07064
$576$	−8.14488	−0.339370
$577$	10.2857	0.428198	0.214099	−	0.976812i	$-0.431318\pi$
$577$	10.2857	0.428198	0.214099	+	0.976812i	$0.431318\pi$
$578$	30.7989	1.28107
$579$	20.2392	0.841113
$580$	59.3378	2.46387
$581$	−0.00279464	−0.000115941 0
$582$	−21.7345	−0.900926
$583$	9.28960	0.384736
$584$	−19.8067	−0.819606
$585$	−14.4510	−0.597475
$586$	−9.07311	−0.374807
$587$	39.6359	1.63595	0.817975	−	0.575254i	$-0.195097\pi$
$587$	39.6359	1.63595	0.817975	+	0.575254i	$0.195097\pi$
$588$	5.72861	0.236244
$589$	−42.9916	−1.77144
$590$	−81.8850	−3.37115
$591$	−12.3627	−0.508533
$592$	1.95283	0.0802608
$593$	−32.1884	−1.32182	−0.660910	−	0.750465i	$-0.729830\pi$
$593$	−32.1884	−1.32182	−0.660910	+	0.750465i	$0.729830\pi$
$594$	−7.89362	−0.323879
$595$	7.61932	0.312361
$596$	−51.2512	−2.09933
$597$	−44.2514	−1.81109
$598$	92.0809	3.76547
$599$	−34.0952	−1.39309	−0.696547	−	0.717512i	$-0.745281\pi$
$599$	−34.0952	−1.39309	−0.696547	+	0.717512i	$0.745281\pi$
$600$	−55.5622	−2.26832
$601$	−9.01124	−0.367576	−0.183788	−	0.982966i	$-0.558836\pi$
$601$	−9.01124	−0.367576	−0.183788	+	0.982966i	$0.558836\pi$
$602$	18.0658	0.736307
$603$	−2.93908	−0.119689
$604$	58.3653	2.37485
$605$	−44.0004	−1.78887
$606$	−33.2722	−1.35159
$607$	5.59646	0.227153	0.113577	−	0.993529i	$-0.463769\pi$
$607$	5.59646	0.227153	0.113577	+	0.993529i	$0.463769\pi$
$608$	−29.7030	−1.20462
$609$	8.87023	0.359440
$610$	43.1470	1.74697
$611$	−46.4105	−1.87757
$612$	3.38941	0.137009
$613$	−4.20474	−0.169828	−0.0849139	−	0.996388i	$-0.527062\pi$
$613$	−4.20474	−0.169828	−0.0849139	+	0.996388i	$0.527062\pi$
$614$	−12.8023	−0.516660
$615$	76.1348	3.07005
$616$	1.76078	0.0709438
$617$	−27.9644	−1.12580	−0.562902	−	0.826524i	$-0.690315\pi$
$617$	−27.9644	−1.12580	−0.562902	+	0.826524i	$0.690315\pi$
$618$	26.0310	1.04712
$619$	20.5778	0.827090	0.413545	−	0.910484i	$-0.364290\pi$
$619$	20.5778	0.827090	0.413545	+	0.910484i	$0.364290\pi$
$620$	123.095	4.94360
$621$	−34.1247	−1.36938
$622$	−5.06614	−0.203134
$623$	8.85786	0.354883
$624$	10.0321	0.401606
$625$	77.5387	3.10155
$626$	18.9671	0.758079
$627$	6.61056	0.264000
$628$	49.5040	1.97542
$629$	−3.63537	−0.144952
$630$	−5.93353	−0.236398
$631$	29.9688	1.19304	0.596520	−	0.802598i	$-0.296550\pi$
$631$	29.9688	1.19304	0.596520	+	0.802598i	$0.296550\pi$
$632$	14.6592	0.583111
$633$	−21.4277	−0.851673
$634$	−48.1855	−1.91369
$635$	−0.397255	−0.0157646
$636$	−68.2015	−2.70436
$637$	−5.45043	−0.215954
$638$	8.13414	0.322034
$639$	9.02982	0.357214
$640$	66.7272	2.63762
$641$	−20.3207	−0.802618	−0.401309	−	0.915943i	$-0.631445\pi$
$641$	−20.3207	−0.802618	−0.401309	+	0.915943i	$0.631445\pi$
$642$	64.1308	2.53104
$643$	−1.16807	−0.0460644	−0.0230322	−	0.999735i	$-0.507332\pi$
$643$	−1.16807	−0.0460644	−0.0230322	+	0.999735i	$0.507332\pi$
$644$	22.7101	0.894901
$645$	−65.0917	−2.56298
$646$	17.9157	0.704883
$647$	−42.6597	−1.67712	−0.838562	−	0.544806i	$-0.816603\pi$
$647$	−42.6597	−1.67712	−0.838562	+	0.544806i	$0.816603\pi$
$648$	23.6634	0.929588
$649$	−6.74245	−0.264664
$650$	157.718	6.18623
$651$	18.4011	0.721194
$652$	49.2596	1.92915
$653$	10.4011	0.407025	0.203513	−	0.979072i	$-0.434764\pi$
$653$	10.4011	0.407025	0.203513	+	0.979072i	$0.434764\pi$
$654$	−37.8166	−1.47875
$655$	38.7011	1.51218
$656$	−9.12656	−0.356332
$657$	5.49583	0.214413
$658$	−19.0560	−0.742880
$659$	−3.73389	−0.145452	−0.0727258	−	0.997352i	$-0.523170\pi$
$659$	−3.73389	−0.145452	−0.0727258	+	0.997352i	$0.523170\pi$
$660$	−18.9275	−0.736753
$661$	−28.1953	−1.09667	−0.548335	−	0.836259i	$-0.684738\pi$
$661$	−28.1953	−1.09667	−0.548335	+	0.836259i	$0.684738\pi$
$662$	40.0058	1.55487
$663$	−18.6757	−0.725304
$664$	0.00630636	0.000244734 0
$665$	−18.8389	−0.730541
$666$	2.83104	0.109701
$667$	35.1645	1.36157
$668$	−25.7652	−0.996885
$669$	5.89935	0.228082
$670$	44.4812	1.71846
$671$	3.55274	0.137152
$672$	12.7133	0.490428
$673$	−16.0766	−0.619707	−0.309853	−	0.950784i	$-0.600280\pi$
$673$	−16.0766	−0.619707	−0.309853	+	0.950784i	$0.600280\pi$
$674$	21.5260	0.829149
$675$	−58.4496	−2.24973
$676$	50.2610	1.93311
$677$	−45.9928	−1.76765	−0.883824	−	0.467819i	$-0.845040\pi$
$677$	−45.9928	−1.76765	−0.883824	+	0.467819i	$0.845040\pi$
$678$	35.1115	1.34845
$679$	5.10013	0.195725
$680$	−17.1937	−0.659347
$681$	14.5253	0.556611
$682$	16.8741	0.646141
$683$	11.2252	0.429519	0.214759	−	0.976667i	$-0.431103\pi$
$683$	11.2252	0.429519	0.214759	+	0.976667i	$0.431103\pi$
$684$	−8.38038	−0.320432
$685$	27.1593	1.03770
$686$	−2.23793	−0.0854446
$687$	17.8866	0.682418
$688$	7.80278	0.297478
$689$	64.8897	2.47210
$690$	−136.224	−5.18596
$691$	19.0803	0.725850	0.362925	−	0.931818i	$-0.381778\pi$
$691$	19.0803	0.725850	0.362925	+	0.931818i	$0.381778\pi$
$692$	22.1895	0.843517
$693$	−0.488570	−0.0185592
$694$	31.1574	1.18272
$695$	−76.1308	−2.88780
$696$	−20.0165	−0.758722
$697$	16.9900	0.643540
$698$	−5.58043	−0.211222
$699$	26.2678	0.993540
$700$	38.8984	1.47022
$701$	12.2294	0.461897	0.230948	−	0.972966i	$-0.425817\pi$
$701$	12.2294	0.461897	0.230948	+	0.972966i	$0.425817\pi$
$702$	−55.1385	−2.08107
$703$	8.98853	0.339009
$704$	10.1499	0.382539
$705$	68.6593	2.58586
$706$	36.4205	1.37070
$707$	7.80750	0.293631
$708$	49.5011	1.86036
$709$	18.4448	0.692710	0.346355	−	0.938103i	$-0.387419\pi$
$709$	18.4448	0.692710	0.346355	+	0.938103i	$0.387419\pi$
$710$	−136.661	−5.12879
$711$	−4.06754	−0.152544
$712$	−19.9885	−0.749103
$713$	72.9478	2.73191
$714$	−7.66819	−0.286975
$715$	18.0084	0.673477
$716$	49.3729	1.84515
$717$	31.4114	1.17308
$718$	19.3481	0.722065
$719$	−7.97734	−0.297505	−0.148752	−	0.988874i	$-0.547526\pi$
$719$	−7.97734	−0.297505	−0.148752	+	0.988874i	$0.547526\pi$
$720$	−2.56274	−0.0955078
$721$	−6.10831	−0.227486
$722$	−1.77616	−0.0661018
$723$	−5.43463	−0.202116
$724$	−52.4725	−1.95012
$725$	60.2306	2.23691
$726$	44.2826	1.64348
$727$	−0.553970	−0.0205456	−0.0102728	−	0.999947i	$-0.503270\pi$
$727$	−0.553970	−0.0205456	−0.0102728	+	0.999947i	$0.503270\pi$
$728$	12.2994	0.455846
$729$	19.2578	0.713254
$730$	−83.1760	−3.07848
$731$	−14.5256	−0.537249
$732$	−26.0832	−0.964062
$733$	−42.8652	−1.58326	−0.791632	−	0.610998i	$-0.790768\pi$
$733$	−42.8652	−1.58326	−0.791632	+	0.610998i	$0.790768\pi$
$734$	−39.2413	−1.44842
$735$	8.06334	0.297421
$736$	50.3998	1.85776
$737$	3.66260	0.134914
$738$	−13.2309	−0.487036
$739$	−8.92735	−0.328398	−0.164199	−	0.986427i	$-0.552504\pi$
$739$	−8.92735	−0.328398	−0.164199	+	0.986427i	$0.552504\pi$
$740$	−25.7362	−0.946082
$741$	46.1760	1.69632
$742$	26.6435	0.978114
$743$	6.35803	0.233253	0.116627	−	0.993176i	$-0.462792\pi$
$743$	6.35803	0.233253	0.116627	+	0.993176i	$0.462792\pi$
$744$	−41.5236	−1.52233
$745$	−72.1390	−2.64297
$746$	−13.2740	−0.485995
$747$	−0.00174985	−6.40236e−5 0
$748$	−4.22379	−0.154437
$749$	−15.0486	−0.549866
$750$	−143.102	−5.22534
$751$	12.2653	0.447566	0.223783	−	0.974639i	$-0.428159\pi$
$751$	12.2653	0.447566	0.223783	+	0.974639i	$0.428159\pi$
$752$	−8.23045	−0.300133
$753$	21.6455	0.788808
$754$	56.8185	2.06921
$755$	82.1524	2.98983
$756$	−13.5989	−0.494587
$757$	−0.000105885 0	−3.84844e−6 0	−1.92422e−6	−	1.00000i	$-0.500001\pi$
$757$	−0.000105885 0	−3.84844e−6 0	−1.92422e−6		1.00000i	$0.500001\pi$
$758$	−14.8107	−0.537950
$759$	−11.2167	−0.407142
$760$	42.5117	1.54206
$761$	41.4132	1.50123	0.750613	−	0.660742i	$-0.229758\pi$
$761$	41.4132	1.50123	0.750613	+	0.660742i	$0.229758\pi$
$762$	0.399803	0.0144833
$763$	8.87387	0.321256
$764$	−45.1853	−1.63475
$765$	4.77079	0.172488
$766$	17.6566	0.637959
$767$	−47.0973	−1.70059
$768$	−17.6145	−0.635607
$769$	−39.5973	−1.42792	−0.713958	−	0.700188i	$-0.753099\pi$
$769$	−39.5973	−1.42792	−0.713958	+	0.700188i	$0.753099\pi$
$770$	7.39421	0.266469
$771$	49.0071	1.76495
$772$	31.9741	1.15077
$773$	−22.6307	−0.813969	−0.406984	−	0.913435i	$-0.633420\pi$
$773$	−22.6307	−0.813969	−0.406984	+	0.913435i	$0.633420\pi$
$774$	11.3118	0.406594
$775$	124.947	4.48822
$776$	−11.5089	−0.413145
$777$	−3.84723	−0.138019
$778$	8.82980	0.316563
$779$	−42.0080	−1.50509
$780$	−132.212	−4.73397
$781$	−11.2527	−0.402654
$782$	−30.3992	−1.08707
$783$	−21.0566	−0.752503
$784$	−0.966582	−0.0345208
$785$	69.6796	2.48697
$786$	−38.9493	−1.38928
$787$	23.0942	0.823220	0.411610	−	0.911360i	$-0.364967\pi$
$787$	23.0942	0.823220	0.411610	+	0.911360i	$0.364967\pi$
$788$	−19.5307	−0.695751
$789$	23.2939	0.829286
$790$	61.5597	2.19019
$791$	−8.23910	−0.292949
$792$	1.10250	0.0391757
$793$	24.8166	0.881264
$794$	68.9980	2.44865
$795$	−95.9974	−3.40468
$796$	−69.9087	−2.47785
$797$	−14.3777	−0.509284	−0.254642	−	0.967035i	$-0.581958\pi$
$797$	−14.3777	−0.509284	−0.254642	+	0.967035i	$0.581958\pi$
$798$	18.9597	0.671168
$799$	15.3217	0.542045
$800$	86.3261	3.05209
$801$	5.54630	0.195969
$802$	42.6862	1.50730
$803$	−6.84875	−0.241687
$804$	−26.8897	−0.948327
$805$	31.9657	1.12664
$806$	117.869	4.15174
$807$	3.89448	0.137092
$808$	−17.6183	−0.619810
$809$	10.5974	0.372583	0.186292	−	0.982494i	$-0.440353\pi$
$809$	10.5974	0.372583	0.186292	+	0.982494i	$0.440353\pi$
$810$	99.3721	3.49158
$811$	−35.0589	−1.23108	−0.615542	−	0.788104i	$-0.711063\pi$
$811$	−35.0589	−1.23108	−0.615542	+	0.788104i	$0.711063\pi$
$812$	14.0132	0.491769
$813$	23.9425	0.839700
$814$	−3.52797	−0.123655
$815$	69.3356	2.42872
$816$	−3.31196	−0.115942
$817$	35.9148	1.25650
$818$	−20.4069	−0.713510
$819$	−3.41276	−0.119251
$820$	120.278	4.20030
$821$	16.0098	0.558747	0.279374	−	0.960182i	$-0.409873\pi$
$821$	16.0098	0.558747	0.279374	+	0.960182i	$0.409873\pi$
$822$	−27.3335	−0.953365
$823$	−30.7692	−1.07255	−0.536273	−	0.844044i	$-0.680168\pi$
$823$	−30.7692	−1.07255	−0.536273	+	0.844044i	$0.680168\pi$
$824$	13.7840	0.480187
$825$	−19.2123	−0.668887
$826$	−19.3380	−0.672856
$827$	−28.7589	−1.00004	−0.500022	−	0.866013i	$-0.666675\pi$
$827$	−28.7589	−1.00004	−0.500022	+	0.866013i	$0.666675\pi$
$828$	14.2198	0.494171
$829$	−25.3858	−0.881686	−0.440843	−	0.897584i	$-0.645320\pi$
$829$	−25.3858	−0.881686	−0.440843	+	0.897584i	$0.645320\pi$
$830$	0.0264829	0.000919235 0
$831$	−33.8735	−1.17506
$832$	70.8992	2.45799
$833$	1.79938	0.0623449
$834$	76.6191	2.65310
$835$	−36.2660	−1.25504
$836$	10.4434	0.361193
$837$	−43.6815	−1.50985
$838$	30.8148	1.06448
$839$	−2.51518	−0.0868336	−0.0434168	−	0.999057i	$-0.513824\pi$
$839$	−2.51518	−0.0868336	−0.0434168	+	0.999057i	$0.513824\pi$
$840$	−18.1956	−0.627809
$841$	−7.30175	−0.251785
$842$	35.4373	1.22125
$843$	−28.0092	−0.964688
$844$	−33.8516	−1.16522
$845$	70.7451	2.43371
$846$	−11.9318	−0.410224
$847$	−10.3912	−0.357044
$848$	11.5076	0.395171
$849$	26.9540	0.925058
$850$	−52.0685	−1.78593
$851$	−15.2517	−0.522820
$852$	82.6141	2.83031
$853$	−39.1245	−1.33960	−0.669799	−	0.742542i	$-0.733620\pi$
$853$	−39.1245	−1.33960	−0.669799	+	0.742542i	$0.733620\pi$
$854$	10.1896	0.348682
$855$	−11.7959	−0.403410
$856$	33.9586	1.16068
$857$	−17.9728	−0.613938	−0.306969	−	0.951719i	$-0.599315\pi$
$857$	−17.9728	−0.613938	−0.306969	+	0.951719i	$0.599315\pi$
$858$	−18.1239	−0.618741
$859$	−10.6897	−0.364727	−0.182363	−	0.983231i	$-0.558375\pi$
$859$	−10.6897	−0.364727	−0.182363	+	0.983231i	$0.558375\pi$
$860$	−102.832	−3.50655
$861$	17.9801	0.612759
$862$	57.6915	1.96498
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	−30.1797	−1.02673
$865$	31.2329	1.06195
$866$	−89.4393	−3.03927
$867$	−26.2066	−0.890024
$868$	29.0701	0.986704
$869$	5.06885	0.171949
$870$	−84.0570	−2.84980
$871$	25.5840	0.866880
$872$	−20.0247	−0.678121
$873$	3.19342	0.108081
$874$	75.1625	2.54241
$875$	33.5796	1.13520
$876$	50.2815	1.69885
$877$	21.2618	0.717959	0.358979	−	0.933345i	$-0.383125\pi$
$877$	21.2618	0.717959	0.358979	+	0.933345i	$0.383125\pi$
$878$	−75.3611	−2.54331
$879$	7.72026	0.260398
$880$	3.19362	0.107657
$881$	43.4081	1.46246	0.731229	−	0.682133i	$-0.238947\pi$
$881$	43.4081	1.46246	0.731229	+	0.682133i	$0.238947\pi$
$882$	−1.40127	−0.0471831
$883$	−39.5040	−1.32942	−0.664708	−	0.747103i	$-0.731444\pi$
$883$	−39.5040	−1.32942	−0.664708	+	0.747103i	$0.731444\pi$
$884$	−29.5040	−0.992327
$885$	69.6755	2.34212
$886$	36.7537	1.23476
$887$	4.54739	0.152686	0.0763432	−	0.997082i	$-0.475676\pi$
$887$	4.54739	0.152686	0.0763432	+	0.997082i	$0.475676\pi$
$888$	8.68162	0.291336
$889$	−0.0938159	−0.00314649
$890$	−83.9398	−2.81367
$891$	8.18235	0.274119
$892$	9.31984	0.312051
$893$	−37.8833	−1.26772
$894$	72.6017	2.42816
$895$	69.4951	2.32297
$896$	15.7583	0.526449
$897$	−78.3511	−2.61607
$898$	−34.8252	−1.16213
$899$	45.0124	1.50125
$900$	24.3560	0.811866
$901$	−21.4224	−0.713684
$902$	16.4880	0.548990
$903$	−15.3721	−0.511551
$904$	18.5923	0.618369
$905$	−73.8580	−2.45512
$906$	−82.6794	−2.74684
$907$	36.2902	1.20500	0.602499	−	0.798120i	$-0.294172\pi$
$907$	36.2902	1.20500	0.602499	+	0.798120i	$0.294172\pi$
$908$	22.9472	0.761528
$909$	4.88862	0.162145
$910$	51.6500	1.71218
$911$	−15.0322	−0.498038	−0.249019	−	0.968499i	$-0.580108\pi$
$911$	−15.0322	−0.498038	−0.249019	+	0.968499i	$0.580108\pi$
$912$	8.18887	0.271161
$913$	0.00218061	7.21678e−5 0
$914$	−37.4951	−1.24023
$915$	−36.7136	−1.21371
$916$	28.2574	0.933652
$917$	9.13967	0.301818
$918$	18.2032	0.600794
$919$	4.76330	0.157127	0.0785634	−	0.996909i	$-0.474967\pi$
$919$	4.76330	0.157127	0.0785634	+	0.996909i	$0.474967\pi$
$920$	−72.1334	−2.37817
$921$	10.8934	0.358951
$922$	−61.9343	−2.03970
$923$	−78.6024	−2.58723
$924$	−4.46994	−0.147050
$925$	−26.1234	−0.858933
$926$	76.9415	2.52845
$927$	−3.82469	−0.125619
$928$	31.0992	1.02088
$929$	29.4215	0.965287	0.482643	−	0.875817i	$-0.339677\pi$
$929$	29.4215	0.965287	0.482643	+	0.875817i	$0.339677\pi$
$930$	−174.374	−5.71795
$931$	−4.44901	−0.145810
$932$	41.4981	1.35931
$933$	4.31075	0.141128
$934$	−79.8860	−2.61395
$935$	−5.94523	−0.194430
$936$	7.70119	0.251721
$937$	−46.3376	−1.51378	−0.756892	−	0.653540i	$-0.773283\pi$
$937$	−46.3376	−1.51378	−0.756892	+	0.653540i	$0.773283\pi$
$938$	10.5047	0.342991
$939$	−16.1390	−0.526677
$940$	108.469	3.53785
$941$	−25.4229	−0.828762	−0.414381	−	0.910104i	$-0.636002\pi$
$941$	−25.4229	−0.828762	−0.414381	+	0.910104i	$0.636002\pi$
$942$	−70.1266	−2.28485
$943$	71.2788	2.32116
$944$	−8.35226	−0.271843
$945$	−19.1412	−0.622663
$946$	−14.0965	−0.458315
$947$	19.6320	0.637955	0.318978	−	0.947762i	$-0.396660\pi$
$947$	19.6320	0.637955	0.318978	+	0.947762i	$0.396660\pi$
$948$	−37.2140	−1.20865
$949$	−47.8399	−1.55295
$950$	128.740	4.17689
$951$	41.0008	1.32954
$952$	−4.06047	−0.131601
$953$	−23.8559	−0.772767	−0.386384	−	0.922338i	$-0.626276\pi$
$953$	−23.8559	−0.772767	−0.386384	+	0.922338i	$0.626276\pi$
$954$	16.6827	0.540122
$955$	−63.6009	−2.05808
$956$	49.6239	1.60495
$957$	−6.92129	−0.223734
$958$	−42.6672	−1.37852
$959$	6.41396	0.207117
$960$	−104.888	−3.38524
$961$	62.3771	2.01217
$962$	−24.6436	−0.794540
$963$	−9.42262	−0.303640
$964$	−8.58567	−0.276526
$965$	45.0053	1.44877
$966$	−32.1707	−1.03508
$967$	7.92873	0.254971	0.127485	−	0.991840i	$-0.459309\pi$
$967$	7.92873	0.254971	0.127485	+	0.991840i	$0.459309\pi$
$968$	23.4486	0.753666
$969$	−15.2444	−0.489719
$970$	−48.3304	−1.55180
$971$	40.4870	1.29929	0.649644	−	0.760239i	$-0.274918\pi$
$971$	40.4870	1.29929	0.649644	+	0.760239i	$0.274918\pi$
$972$	−19.2757	−0.618267
$973$	−17.9791	−0.576383
$974$	62.7053	2.00921
$975$	−134.202	−4.29790
$976$	4.40099	0.140872
$977$	−59.1027	−1.89086	−0.945432	−	0.325820i	$-0.894360\pi$
$977$	−59.1027	−1.89086	−0.945432	+	0.325820i	$0.894360\pi$
$978$	−69.7804	−2.23133
$979$	−6.91164	−0.220897
$980$	12.7385	0.406917
$981$	5.55632	0.177400
$982$	−59.8108	−1.90864
$983$	−6.75717	−0.215520	−0.107760	−	0.994177i	$-0.534368\pi$
$983$	−6.75717	−0.215520	−0.107760	+	0.994177i	$0.534368\pi$
$984$	−40.5736	−1.29344
$985$	−27.4905	−0.875921
$986$	−18.7578	−0.597371
$987$	16.2146	0.516118
$988$	72.9492	2.32082
$989$	−60.9400	−1.93778
$990$	4.62984	0.147146
$991$	−17.6290	−0.560002	−0.280001	−	0.960000i	$-0.590335\pi$
$991$	−17.6290	−0.560002	−0.280001	+	0.960000i	$0.590335\pi$
$992$	64.5145	2.04834
$993$	−34.0408	−1.08025
$994$	−32.2739	−1.02367
$995$	−98.4005	−3.11950
$996$	−0.0160094	−0.000507278 0
$997$	31.1846	0.987625	0.493813	−	0.869568i	$-0.335603\pi$
$997$	31.1846	0.987625	0.493813	+	0.869568i	$0.335603\pi$
$998$	−35.8063	−1.13343
$999$	9.13277	0.288948

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.f.1.19	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.f.1.19	✓	132	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23793 q^{2} +1.90424 q^{3} +3.00834 q^{4} +4.23440 q^{5} -4.26157 q^{6} +1.00000 q^{7} -2.25659 q^{8} +0.626144 q^{9} +O(q^{10})\)	\(q-2.23793 q^{2} +1.90424 q^{3} +3.00834 q^{4} +4.23440 q^{5} -4.26157 q^{6} +1.00000 q^{7} -2.25659 q^{8} +0.626144 q^{9} -9.47631 q^{10} -0.780283 q^{11} +5.72861 q^{12} -5.45043 q^{13} -2.23793 q^{14} +8.06334 q^{15} -0.966582 q^{16} +1.79938 q^{17} -1.40127 q^{18} -4.44901 q^{19} +12.7385 q^{20} +1.90424 q^{21} +1.74622 q^{22} +7.54904 q^{23} -4.29710 q^{24} +12.9302 q^{25} +12.1977 q^{26} -4.52040 q^{27} +3.00834 q^{28} +4.65814 q^{29} -18.0452 q^{30} +9.66318 q^{31} +6.67632 q^{32} -1.48585 q^{33} -4.02690 q^{34} +4.23440 q^{35} +1.88365 q^{36} -2.02034 q^{37} +9.95657 q^{38} -10.3790 q^{39} -9.55531 q^{40} +9.44210 q^{41} -4.26157 q^{42} -8.07255 q^{43} -2.34736 q^{44} +2.65135 q^{45} -16.8942 q^{46} +8.51500 q^{47} -1.84061 q^{48} +1.00000 q^{49} -28.9369 q^{50} +3.42646 q^{51} -16.3967 q^{52} -11.9054 q^{53} +10.1163 q^{54} -3.30404 q^{55} -2.25659 q^{56} -8.47199 q^{57} -10.4246 q^{58} +8.64103 q^{59} +24.2572 q^{60} -4.55315 q^{61} -21.6255 q^{62} +0.626144 q^{63} -13.0080 q^{64} -23.0793 q^{65} +3.32523 q^{66} -4.69394 q^{67} +5.41315 q^{68} +14.3752 q^{69} -9.47631 q^{70} +14.4213 q^{71} -1.41295 q^{72} +8.77726 q^{73} +4.52139 q^{74} +24.6222 q^{75} -13.3841 q^{76} -0.780283 q^{77} +23.2274 q^{78} -6.49617 q^{79} -4.09290 q^{80} -10.4864 q^{81} -21.1308 q^{82} -0.00279464 q^{83} +5.72861 q^{84} +7.61932 q^{85} +18.0658 q^{86} +8.87023 q^{87} +1.76078 q^{88} +8.85786 q^{89} -5.93353 q^{90} -5.45043 q^{91} +22.7101 q^{92} +18.4011 q^{93} -19.0560 q^{94} -18.8389 q^{95} +12.7133 q^{96} +5.10013 q^{97} -2.23793 q^{98} -0.488570 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * q^99

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