LMFDB - Embedded newform 8041.2.a.g.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53420 q^{2} -1.82986 q^{3} +4.42217 q^{4} -1.56039 q^{5} +4.63723 q^{6} -0.999486 q^{7} -6.13827 q^{8} +0.348383 q^{9} +O(q^{10})$	\(q-2.53420 q^{2} -1.82986 q^{3} +4.42217 q^{4} -1.56039 q^{5} +4.63723 q^{6} -0.999486 q^{7} -6.13827 q^{8} +0.348383 q^{9} +3.95435 q^{10} -1.00000 q^{11} -8.09195 q^{12} +6.16556 q^{13} +2.53290 q^{14} +2.85530 q^{15} +6.71126 q^{16} +1.00000 q^{17} -0.882871 q^{18} +7.13266 q^{19} -6.90033 q^{20} +1.82892 q^{21} +2.53420 q^{22} -0.590579 q^{23} +11.2322 q^{24} -2.56517 q^{25} -15.6248 q^{26} +4.85209 q^{27} -4.41990 q^{28} -6.99808 q^{29} -7.23591 q^{30} -0.245102 q^{31} -4.73114 q^{32} +1.82986 q^{33} -2.53420 q^{34} +1.55959 q^{35} +1.54061 q^{36} +5.61492 q^{37} -18.0756 q^{38} -11.2821 q^{39} +9.57812 q^{40} +3.92741 q^{41} -4.63485 q^{42} +1.00000 q^{43} -4.42217 q^{44} -0.543614 q^{45} +1.49665 q^{46} -10.9149 q^{47} -12.2807 q^{48} -6.00103 q^{49} +6.50065 q^{50} -1.82986 q^{51} +27.2652 q^{52} -10.7404 q^{53} -12.2962 q^{54} +1.56039 q^{55} +6.13512 q^{56} -13.0518 q^{57} +17.7345 q^{58} -0.228064 q^{59} +12.6266 q^{60} +5.23588 q^{61} +0.621137 q^{62} -0.348204 q^{63} -1.43286 q^{64} -9.62071 q^{65} -4.63723 q^{66} -11.4120 q^{67} +4.42217 q^{68} +1.08068 q^{69} -3.95232 q^{70} -4.95010 q^{71} -2.13847 q^{72} +0.454673 q^{73} -14.2293 q^{74} +4.69390 q^{75} +31.5418 q^{76} +0.999486 q^{77} +28.5911 q^{78} +2.99823 q^{79} -10.4722 q^{80} -9.92378 q^{81} -9.95285 q^{82} +3.32888 q^{83} +8.08779 q^{84} -1.56039 q^{85} -2.53420 q^{86} +12.8055 q^{87} +6.13827 q^{88} +6.66593 q^{89} +1.37763 q^{90} -6.16239 q^{91} -2.61164 q^{92} +0.448502 q^{93} +27.6605 q^{94} -11.1298 q^{95} +8.65732 q^{96} +10.3922 q^{97} +15.2078 q^{98} -0.348383 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) $ 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * 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 $

$2$	−2.53420	−1.79195	−0.895975	−	0.444104i	$-0.853522\pi$
$2$	−2.53420	−1.79195	−0.895975	+	0.444104i	$0.853522\pi$
$3$	−1.82986	−1.05647	−0.528235	−	0.849098i	$-0.677146\pi$
$3$	−1.82986	−1.05647	−0.528235	+	0.849098i	$0.677146\pi$
$4$	4.42217	2.21109
$5$	−1.56039	−0.697830	−0.348915	−	0.937154i	$-0.613450\pi$
$5$	−1.56039	−0.697830	−0.348915	+	0.937154i	$0.613450\pi$
$6$	4.63723	1.89314
$7$	−0.999486	−0.377770	−0.188885	−	0.981999i	$-0.560487\pi$
$7$	−0.999486	−0.377770	−0.188885	+	0.981999i	$0.560487\pi$
$8$	−6.13827	−2.17021
$9$	0.348383	0.116128
$10$	3.95435	1.25048
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−8.09195	−2.33594
$13$	6.16556	1.71002	0.855010	−	0.518612i	$-0.173551\pi$
$13$	6.16556	1.71002	0.855010	+	0.518612i	$0.173551\pi$
$14$	2.53290	0.676946
$15$	2.85530	0.737236
$16$	6.71126	1.67781
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.882871	−0.208095
$19$	7.13266	1.63634	0.818172	−	0.574973i	$-0.194988\pi$
$19$	7.13266	1.63634	0.818172	+	0.574973i	$0.194988\pi$
$20$	−6.90033	−1.54296
$21$	1.82892	0.399103
$22$	2.53420	0.540293
$23$	−0.590579	−0.123144	−0.0615722	−	0.998103i	$-0.519611\pi$
$23$	−0.590579	−0.123144	−0.0615722	+	0.998103i	$0.519611\pi$
$24$	11.2322	2.29276
$25$	−2.56517	−0.513034
$26$	−15.6248	−3.06427
$27$	4.85209	0.933784
$28$	−4.41990	−0.835283
$29$	−6.99808	−1.29951	−0.649755	−	0.760143i	$-0.725129\pi$
$29$	−6.99808	−1.29951	−0.649755	+	0.760143i	$0.725129\pi$
$30$	−7.23591	−1.32109
$31$	−0.245102	−0.0440216	−0.0220108	−	0.999758i	$-0.507007\pi$
$31$	−0.245102	−0.0440216	−0.0220108	+	0.999758i	$0.507007\pi$
$32$	−4.73114	−0.836355
$33$	1.82986	0.318537
$34$	−2.53420	−0.434612
$35$	1.55959	0.263619
$36$	1.54061	0.256768
$37$	5.61492	0.923088	0.461544	−	0.887117i	$-0.347296\pi$
$37$	5.61492	0.923088	0.461544	+	0.887117i	$0.347296\pi$
$38$	−18.0756	−2.93225
$39$	−11.2821	−1.80658
$40$	9.57812	1.51443
$41$	3.92741	0.613359	0.306679	−	0.951813i	$-0.400782\pi$
$41$	3.92741	0.613359	0.306679	+	0.951813i	$0.400782\pi$
$42$	−4.63485	−0.715172
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−4.42217	−0.666667
$45$	−0.543614	−0.0810372
$46$	1.49665	0.220669
$47$	−10.9149	−1.59210	−0.796049	−	0.605232i	$-0.793080\pi$
$47$	−10.9149	−1.59210	−0.796049	+	0.605232i	$0.793080\pi$
$48$	−12.2807	−1.77256
$49$	−6.00103	−0.857290
$50$	6.50065	0.919331
$51$	−1.82986	−0.256231
$52$	27.2652	3.78100
$53$	−10.7404	−1.47531	−0.737655	−	0.675178i	$-0.764067\pi$
$53$	−10.7404	−1.47531	−0.737655	+	0.675178i	$0.764067\pi$
$54$	−12.2962	−1.67329
$55$	1.56039	0.210404
$56$	6.13512	0.819839
$57$	−13.0518	−1.72875
$58$	17.7345	2.32866
$59$	−0.228064	−0.0296914	−0.0148457	−	0.999890i	$-0.504726\pi$
$59$	−0.228064	−0.0296914	−0.0148457	+	0.999890i	$0.504726\pi$
$60$	12.6266	1.63009
$61$	5.23588	0.670385	0.335193	−	0.942150i	$-0.391199\pi$
$61$	5.23588	0.670385	0.335193	+	0.942150i	$0.391199\pi$
$62$	0.621137	0.0788845
$63$	−0.348204	−0.0438695
$64$	−1.43286	−0.179108
$65$	−9.62071	−1.19330
$66$	−4.63723	−0.570803
$67$	−11.4120	−1.39420	−0.697100	−	0.716974i	$-0.745526\pi$
$67$	−11.4120	−1.39420	−0.697100	+	0.716974i	$0.745526\pi$
$68$	4.42217	0.536267
$69$	1.08068	0.130098
$70$	−3.95232	−0.472393
$71$	−4.95010	−0.587468	−0.293734	−	0.955887i	$-0.594898\pi$
$71$	−4.95010	−0.587468	−0.293734	+	0.955887i	$0.594898\pi$
$72$	−2.13847	−0.252021
$73$	0.454673	0.0532154	0.0266077	−	0.999646i	$-0.491530\pi$
$73$	0.454673	0.0532154	0.0266077	+	0.999646i	$0.491530\pi$
$74$	−14.2293	−1.65413
$75$	4.69390	0.542004
$76$	31.5418	3.61810
$77$	0.999486	0.113902
$78$	28.5911	3.23731
$79$	2.99823	0.337327	0.168664	−	0.985674i	$-0.446055\pi$
$79$	2.99823	0.337327	0.168664	+	0.985674i	$0.446055\pi$
$80$	−10.4722	−1.17083
$81$	−9.92378	−1.10264
$82$	−9.95285	−1.09911
$83$	3.32888	0.365392	0.182696	−	0.983169i	$-0.441518\pi$
$83$	3.32888	0.365392	0.182696	+	0.983169i	$0.441518\pi$
$84$	8.08779	0.882451
$85$	−1.56039	−0.169249
$86$	−2.53420	−0.273270
$87$	12.8055	1.37289
$88$	6.13827	0.654342
$89$	6.66593	0.706587	0.353294	−	0.935512i	$-0.385062\pi$
$89$	6.66593	0.706587	0.353294	+	0.935512i	$0.385062\pi$
$90$	1.37763	0.145215
$91$	−6.16239	−0.645994
$92$	−2.61164	−0.272283
$93$	0.448502	0.0465075
$94$	27.6605	2.85296
$95$	−11.1298	−1.14189
$96$	8.65732	0.883584
$97$	10.3922	1.05517	0.527586	−	0.849502i	$-0.323097\pi$
$97$	10.3922	1.05517	0.527586	+	0.849502i	$0.323097\pi$
$98$	15.2078	1.53622
$99$	−0.348383	−0.0350138
$100$	−11.3436	−1.13436
$101$	−8.75457	−0.871112	−0.435556	−	0.900162i	$-0.643448\pi$
$101$	−8.75457	−0.871112	−0.435556	+	0.900162i	$0.643448\pi$
$102$	4.63723	0.459154
$103$	−9.30483	−0.916832	−0.458416	−	0.888738i	$-0.651583\pi$
$103$	−9.30483	−0.916832	−0.458416	+	0.888738i	$0.651583\pi$
$104$	−37.8459	−3.71109
$105$	−2.85384	−0.278506
$106$	27.2184	2.64368
$107$	8.41358	0.813372	0.406686	−	0.913568i	$-0.366684\pi$
$107$	8.41358	0.813372	0.406686	+	0.913568i	$0.366684\pi$
$108$	21.4568	2.06468
$109$	3.87041	0.370718	0.185359	−	0.982671i	$-0.440655\pi$
$109$	3.87041	0.370718	0.185359	+	0.982671i	$0.440655\pi$
$110$	−3.95435	−0.377033
$111$	−10.2745	−0.975214
$112$	−6.70781	−0.633829
$113$	11.1784	1.05158	0.525788	−	0.850615i	$-0.323770\pi$
$113$	11.1784	1.05158	0.525788	+	0.850615i	$0.323770\pi$
$114$	33.0758	3.09783
$115$	0.921537	0.0859338
$116$	−30.9467	−2.87333
$117$	2.14797	0.198580
$118$	0.577959	0.0532055
$119$	−0.999486	−0.0916228
$120$	−17.5266	−1.59995
$121$	1.00000	0.0909091
$122$	−13.2688	−1.20130
$123$	−7.18661	−0.647995
$124$	−1.08388	−0.0973355
$125$	11.8046	1.05584
$126$	0.882418	0.0786120
$127$	17.0223	1.51049	0.755244	−	0.655444i	$-0.227519\pi$
$127$	17.0223	1.51049	0.755244	+	0.655444i	$0.227519\pi$
$128$	13.0934	1.15731
$129$	−1.82986	−0.161110
$130$	24.3808	2.13834
$131$	5.89092	0.514692	0.257346	−	0.966319i	$-0.417152\pi$
$131$	5.89092	0.514692	0.257346	+	0.966319i	$0.417152\pi$
$132$	8.09195	0.704314
$133$	−7.12900	−0.618162
$134$	28.9203	2.49834
$135$	−7.57117	−0.651622
$136$	−6.13827	−0.526352
$137$	11.6193	0.992707	0.496354	−	0.868120i	$-0.334672\pi$
$137$	11.6193	0.992707	0.496354	+	0.868120i	$0.334672\pi$
$138$	−2.73865	−0.233130
$139$	−13.8811	−1.17738	−0.588690	−	0.808359i	$-0.700356\pi$
$139$	−13.8811	−1.17738	−0.588690	+	0.808359i	$0.700356\pi$
$140$	6.89679	0.582885
$141$	19.9727	1.68200
$142$	12.5445	1.05271
$143$	−6.16556	−0.515590
$144$	2.33809	0.194840
$145$	10.9198	0.906837
$146$	−1.15223	−0.0953594
$147$	10.9810	0.905700
$148$	24.8302	2.04103
$149$	−7.74179	−0.634232	−0.317116	−	0.948387i	$-0.602715\pi$
$149$	−7.74179	−0.634232	−0.317116	+	0.948387i	$0.602715\pi$
$150$	−11.8953	−0.971245
$151$	−2.21864	−0.180550	−0.0902751	−	0.995917i	$-0.528775\pi$
$151$	−2.21864	−0.180550	−0.0902751	+	0.995917i	$0.528775\pi$
$152$	−43.7822	−3.55120
$153$	0.348383	0.0281651
$154$	−2.53290	−0.204107
$155$	0.382456	0.0307196
$156$	−49.8914	−3.99451
$157$	−22.6023	−1.80386	−0.901929	−	0.431884i	$-0.857849\pi$
$157$	−22.6023	−1.80386	−0.901929	+	0.431884i	$0.857849\pi$
$158$	−7.59812	−0.604474
$159$	19.6534	1.55862
$160$	7.38245	0.583634
$161$	0.590276	0.0465203
$162$	25.1488	1.97588
$163$	14.6058	1.14401	0.572007	−	0.820249i	$-0.306165\pi$
$163$	14.6058	1.14401	0.572007	+	0.820249i	$0.306165\pi$
$164$	17.3677	1.35619
$165$	−2.85530	−0.222285
$166$	−8.43605	−0.654765
$167$	−6.00698	−0.464834	−0.232417	−	0.972616i	$-0.574663\pi$
$167$	−6.00698	−0.464834	−0.232417	+	0.972616i	$0.574663\pi$
$168$	−11.2264	−0.866135
$169$	25.0141	1.92417
$170$	3.95435	0.303285
$171$	2.48489	0.190025
$172$	4.42217	0.337187
$173$	−24.8736	−1.89110	−0.945551	−	0.325474i	$-0.894476\pi$
$173$	−24.8736	−1.89110	−0.945551	+	0.325474i	$0.894476\pi$
$174$	−32.4517	−2.46016
$175$	2.56385	0.193809
$176$	−6.71126	−0.505880
$177$	0.417325	0.0313680
$178$	−16.8928	−1.26617
$179$	14.7713	1.10406	0.552030	−	0.833824i	$-0.313853\pi$
$179$	14.7713	1.10406	0.552030	+	0.833824i	$0.313853\pi$
$180$	−2.40396	−0.179180
$181$	−11.3612	−0.844473	−0.422236	−	0.906486i	$-0.638755\pi$
$181$	−11.3612	−0.844473	−0.422236	+	0.906486i	$0.638755\pi$
$182$	15.6167	1.15759
$183$	−9.58092	−0.708242
$184$	3.62514	0.267249
$185$	−8.76150	−0.644158
$186$	−1.13659	−0.0833391
$187$	−1.00000	−0.0731272
$188$	−48.2675	−3.52027
$189$	−4.84959	−0.352756
$190$	28.2051	2.04621
$191$	12.9882	0.939792	0.469896	−	0.882722i	$-0.344291\pi$
$191$	12.9882	0.939792	0.469896	+	0.882722i	$0.344291\pi$
$192$	2.62194	0.189222
$193$	6.32406	0.455216	0.227608	−	0.973753i	$-0.426910\pi$
$193$	6.32406	0.455216	0.227608	+	0.973753i	$0.426910\pi$
$194$	−26.3360	−1.89081
$195$	17.6045	1.26069
$196$	−26.5376	−1.89554
$197$	−1.03181	−0.0735138	−0.0367569	−	0.999324i	$-0.511703\pi$
$197$	−1.03181	−0.0735138	−0.0367569	+	0.999324i	$0.511703\pi$
$198$	0.882871	0.0627429
$199$	−22.4072	−1.58840	−0.794201	−	0.607655i	$-0.792110\pi$
$199$	−22.4072	−1.58840	−0.794201	+	0.607655i	$0.792110\pi$
$200$	15.7457	1.11339
$201$	20.8824	1.47293
$202$	22.1858	1.56099
$203$	6.99449	0.490917
$204$	−8.09195	−0.566550
$205$	−6.12831	−0.428020
$206$	23.5803	1.64292
$207$	−0.205748	−0.0143004
$208$	41.3787	2.86910
$209$	−7.13266	−0.493376
$210$	7.23219	0.499069
$211$	−13.5361	−0.931866	−0.465933	−	0.884820i	$-0.654281\pi$
$211$	−13.5361	−0.931866	−0.465933	+	0.884820i	$0.654281\pi$
$212$	−47.4960	−3.26204
$213$	9.05797	0.620642
$214$	−21.3217	−1.45752
$215$	−1.56039	−0.106418
$216$	−29.7834	−2.02650
$217$	0.244976	0.0166301
$218$	−9.80840	−0.664308
$219$	−0.831987	−0.0562205
$220$	6.90033	0.465220
$221$	6.16556	0.414741
$222$	26.0377	1.74754
$223$	−8.53589	−0.571605	−0.285803	−	0.958289i	$-0.592260\pi$
$223$	−8.53589	−0.571605	−0.285803	+	0.958289i	$0.592260\pi$
$224$	4.72871	0.315950
$225$	−0.893660	−0.0595773
$226$	−28.3283	−1.88437
$227$	22.2825	1.47894	0.739469	−	0.673190i	$-0.235077\pi$
$227$	22.2825	1.47894	0.739469	+	0.673190i	$0.235077\pi$
$228$	−57.7171	−3.82241
$229$	−20.4312	−1.35013	−0.675066	−	0.737757i	$-0.735885\pi$
$229$	−20.4312	−1.35013	−0.675066	+	0.737757i	$0.735885\pi$
$230$	−2.33536	−0.153989
$231$	−1.82892	−0.120334
$232$	42.9561	2.82021
$233$	15.4588	1.01274	0.506369	−	0.862317i	$-0.330988\pi$
$233$	15.4588	1.01274	0.506369	+	0.862317i	$0.330988\pi$
$234$	−5.44340	−0.355846
$235$	17.0315	1.11101
$236$	−1.00854	−0.0656502
$237$	−5.48634	−0.356376
$238$	2.53290	0.164183
$239$	−7.43154	−0.480707	−0.240353	−	0.970685i	$-0.577263\pi$
$239$	−7.43154	−0.480707	−0.240353	+	0.970685i	$0.577263\pi$
$240$	19.1627	1.23695
$241$	19.8654	1.27965	0.639823	−	0.768522i	$-0.279008\pi$
$241$	19.8654	1.27965	0.639823	+	0.768522i	$0.279008\pi$
$242$	−2.53420	−0.162905
$243$	3.60285	0.231123
$244$	23.1539	1.48228
$245$	9.36397	0.598242
$246$	18.2123	1.16117
$247$	43.9768	2.79818
$248$	1.50450	0.0955359
$249$	−6.09138	−0.386026
$250$	−29.9153	−1.89201
$251$	−30.4715	−1.92334	−0.961672	−	0.274203i	$-0.911586\pi$
$251$	−30.4715	−1.92334	−0.961672	+	0.274203i	$0.911586\pi$
$252$	−1.53982	−0.0969993
$253$	0.590579	0.0371294
$254$	−43.1380	−2.70672
$255$	2.85530	0.178806
$256$	−30.3157	−1.89473
$257$	21.7124	1.35438	0.677191	−	0.735807i	$-0.263197\pi$
$257$	21.7124	1.35438	0.677191	+	0.735807i	$0.263197\pi$
$258$	4.63723	0.288701
$259$	−5.61204	−0.348715
$260$	−42.5444	−2.63849
$261$	−2.43801	−0.150909
$262$	−14.9288	−0.922302
$263$	−18.2135	−1.12309	−0.561545	−	0.827446i	$-0.689793\pi$
$263$	−18.2135	−1.12309	−0.561545	+	0.827446i	$0.689793\pi$
$264$	−11.2322	−0.691292
$265$	16.7593	1.02952
$266$	18.0663	1.10772
$267$	−12.1977	−0.746488
$268$	−50.4659	−3.08269
$269$	6.47725	0.394925	0.197462	−	0.980310i	$-0.436730\pi$
$269$	6.47725	0.394925	0.197462	+	0.980310i	$0.436730\pi$
$270$	19.1869	1.16767
$271$	22.3713	1.35896	0.679479	−	0.733695i	$-0.262206\pi$
$271$	22.3713	1.35896	0.679479	+	0.733695i	$0.262206\pi$
$272$	6.71126	0.406930
$273$	11.2763	0.682473
$274$	−29.4457	−1.77888
$275$	2.56517	0.154685
$276$	4.77894	0.287658
$277$	−25.6123	−1.53889	−0.769447	−	0.638711i	$-0.779468\pi$
$277$	−25.6123	−1.53889	−0.769447	+	0.638711i	$0.779468\pi$
$278$	35.1775	2.10981
$279$	−0.0853892	−0.00511212
$280$	−9.57320	−0.572108
$281$	−5.90690	−0.352376	−0.176188	−	0.984357i	$-0.556377\pi$
$281$	−5.90690	−0.352376	−0.176188	+	0.984357i	$0.556377\pi$
$282$	−50.6148	−3.01407
$283$	19.2251	1.14281	0.571405	−	0.820668i	$-0.306398\pi$
$283$	19.2251	1.14281	0.571405	+	0.820668i	$0.306398\pi$
$284$	−21.8902	−1.29894
$285$	20.3659	1.20637
$286$	15.6248	0.923912
$287$	−3.92539	−0.231709
$288$	−1.64825	−0.0971238
$289$	1.00000	0.0588235
$290$	−27.6729	−1.62501
$291$	−19.0163	−1.11476
$292$	2.01064	0.117664
$293$	23.8140	1.39123	0.695614	−	0.718416i	$-0.255133\pi$
$293$	23.8140	1.39123	0.695614	+	0.718416i	$0.255133\pi$
$294$	−27.8281	−1.62297
$295$	0.355870	0.0207195
$296$	−34.4659	−2.00329
$297$	−4.85209	−0.281547
$298$	19.6193	1.13651
$299$	−3.64125	−0.210579
$300$	20.7572	1.19842
$301$	−0.999486	−0.0576094
$302$	5.62248	0.323537
$303$	16.0196	0.920303
$304$	47.8691	2.74548
$305$	−8.17004	−0.467815
$306$	−0.882871	−0.0504704
$307$	19.3343	1.10347	0.551733	−	0.834021i	$-0.313967\pi$
$307$	19.3343	1.10347	0.551733	+	0.834021i	$0.313967\pi$
$308$	4.41990	0.251847
$309$	17.0265	0.968605
$310$	−0.969219	−0.0550480
$311$	−19.2356	−1.09075	−0.545375	−	0.838192i	$-0.683613\pi$
$311$	−19.2356	−1.09075	−0.545375	+	0.838192i	$0.683613\pi$
$312$	69.2526	3.92066
$313$	11.4858	0.649215	0.324608	−	0.945849i	$-0.394768\pi$
$313$	11.4858	0.649215	0.324608	+	0.945849i	$0.394768\pi$
$314$	57.2787	3.23243
$315$	0.543335	0.0306135
$316$	13.2587	0.745860
$317$	−7.51031	−0.421821	−0.210911	−	0.977505i	$-0.567643\pi$
$317$	−7.51031	−0.421821	−0.210911	+	0.977505i	$0.567643\pi$
$318$	−49.8058	−2.79297
$319$	6.99808	0.391817
$320$	2.23583	0.124987
$321$	−15.3957	−0.859302
$322$	−1.49588	−0.0833620
$323$	7.13266	0.396872
$324$	−43.8846	−2.43804
$325$	−15.8157	−0.877297
$326$	−37.0140	−2.05001
$327$	−7.08230	−0.391652
$328$	−24.1075	−1.33111
$329$	10.9093	0.601448
$330$	7.23591	0.398324
$331$	−26.1653	−1.43818	−0.719088	−	0.694919i	$-0.755440\pi$
$331$	−26.1653	−1.43818	−0.719088	+	0.694919i	$0.755440\pi$
$332$	14.7209	0.807914
$333$	1.95614	0.107196
$334$	15.2229	0.832960
$335$	17.8072	0.972914
$336$	12.2743	0.669621
$337$	3.45741	0.188337	0.0941685	−	0.995556i	$-0.469981\pi$
$337$	3.45741	0.188337	0.0941685	+	0.995556i	$0.469981\pi$
$338$	−63.3909	−3.44801
$339$	−20.4549	−1.11096
$340$	−6.90033	−0.374223
$341$	0.245102	0.0132730
$342$	−6.29722	−0.340515
$343$	12.9943	0.701629
$344$	−6.13827	−0.330953
$345$	−1.68628	−0.0907864
$346$	63.0346	3.38876
$347$	26.3086	1.41232	0.706161	−	0.708052i	$-0.250426\pi$
$347$	26.3086	1.41232	0.706161	+	0.708052i	$0.250426\pi$
$348$	56.6281	3.03559
$349$	−12.9494	−0.693164	−0.346582	−	0.938020i	$-0.612658\pi$
$349$	−12.9494	−0.693164	−0.346582	+	0.938020i	$0.612658\pi$
$350$	−6.49731	−0.347296
$351$	29.9158	1.59679
$352$	4.73114	0.252171
$353$	4.51734	0.240434	0.120217	−	0.992748i	$-0.461641\pi$
$353$	4.51734	0.240434	0.120217	+	0.992748i	$0.461641\pi$
$354$	−1.05758	−0.0562100
$355$	7.72410	0.409953
$356$	29.4779	1.56233
$357$	1.82892	0.0967966
$358$	−37.4335	−1.97842
$359$	16.3531	0.863082	0.431541	−	0.902093i	$-0.357970\pi$
$359$	16.3531	0.863082	0.431541	+	0.902093i	$0.357970\pi$
$360$	3.33685	0.175867
$361$	31.8748	1.67762
$362$	28.7916	1.51325
$363$	−1.82986	−0.0960427
$364$	−27.2512	−1.42835
$365$	−0.709469	−0.0371353
$366$	24.2800	1.26913
$367$	15.8528	0.827508	0.413754	−	0.910389i	$-0.364217\pi$
$367$	15.8528	0.827508	0.413754	+	0.910389i	$0.364217\pi$
$368$	−3.96353	−0.206613
$369$	1.36824	0.0712278
$370$	22.2034	1.15430
$371$	10.7349	0.557328
$372$	1.98335	0.102832
$373$	16.1901	0.838291	0.419146	−	0.907919i	$-0.362330\pi$
$373$	16.1901	0.838291	0.419146	+	0.907919i	$0.362330\pi$
$374$	2.53420	0.131040
$375$	−21.6008	−1.11546
$376$	66.9984	3.45518
$377$	−43.1471	−2.22219
$378$	12.2898	0.632121
$379$	24.9685	1.28254	0.641272	−	0.767313i	$-0.278407\pi$
$379$	24.9685	1.28254	0.641272	+	0.767313i	$0.278407\pi$
$380$	−49.2177	−2.52482
$381$	−31.1484	−1.59578
$382$	−32.9147	−1.68406
$383$	16.9048	0.863793	0.431896	−	0.901923i	$-0.357845\pi$
$383$	16.9048	0.863793	0.431896	+	0.901923i	$0.357845\pi$
$384$	−23.9591	−1.22266
$385$	−1.55959	−0.0794842
$386$	−16.0264	−0.815724
$387$	0.348383	0.0177093
$388$	45.9562	2.33307
$389$	20.3241	1.03047	0.515237	−	0.857048i	$-0.327704\pi$
$389$	20.3241	1.03047	0.515237	+	0.857048i	$0.327704\pi$
$390$	−44.6134	−2.25909
$391$	−0.590579	−0.0298669
$392$	36.8359	1.86049
$393$	−10.7795	−0.543756
$394$	2.61483	0.131733
$395$	−4.67843	−0.235397
$396$	−1.54061	−0.0774184
$397$	31.1292	1.56233	0.781164	−	0.624326i	$-0.214626\pi$
$397$	31.1292	1.56233	0.781164	+	0.624326i	$0.214626\pi$
$398$	56.7842	2.84634
$399$	13.0451	0.653069
$400$	−17.2155	−0.860776
$401$	32.6496	1.63045	0.815223	−	0.579148i	$-0.196615\pi$
$401$	32.6496	1.63045	0.815223	+	0.579148i	$0.196615\pi$
$402$	−52.9201	−2.63942
$403$	−1.51119	−0.0752778
$404$	−38.7142	−1.92610
$405$	15.4850	0.769456
$406$	−17.7254	−0.879698
$407$	−5.61492	−0.278321
$408$	11.2322	0.556075
$409$	26.7380	1.32211	0.661055	−	0.750338i	$-0.270109\pi$
$409$	26.7380	1.32211	0.661055	+	0.750338i	$0.270109\pi$
$410$	15.5304	0.766990
$411$	−21.2618	−1.04876
$412$	−41.1475	−2.02719
$413$	0.227947	0.0112165
$414$	0.521406	0.0256257
$415$	−5.19437	−0.254982
$416$	−29.1701	−1.43018
$417$	25.4005	1.24387
$418$	18.0756	0.884106
$419$	−37.8247	−1.84786	−0.923928	−	0.382565i	$-0.875041\pi$
$419$	−37.8247	−1.84786	−0.923928	+	0.382565i	$0.875041\pi$
$420$	−12.6201	−0.615800
$421$	−17.2477	−0.840601	−0.420300	−	0.907385i	$-0.638075\pi$
$421$	−17.2477	−0.840601	−0.420300	+	0.907385i	$0.638075\pi$
$422$	34.3033	1.66986
$423$	−3.80255	−0.184886
$424$	65.9276	3.20173
$425$	−2.56517	−0.124429
$426$	−22.9547	−1.11216
$427$	−5.23319	−0.253252
$428$	37.2063	1.79843
$429$	11.2821	0.544705
$430$	3.95435	0.190696
$431$	−23.0283	−1.10924	−0.554618	−	0.832105i	$-0.687136\pi$
$431$	−23.0283	−1.10924	−0.554618	+	0.832105i	$0.687136\pi$
$432$	32.5636	1.56672
$433$	20.8049	0.999821	0.499910	−	0.866077i	$-0.333366\pi$
$433$	20.8049	0.999821	0.499910	+	0.866077i	$0.333366\pi$
$434$	−0.620818	−0.0298002
$435$	−19.9816	−0.958046
$436$	17.1156	0.819690
$437$	−4.21240	−0.201507
$438$	2.10842	0.100744
$439$	−14.1932	−0.677406	−0.338703	−	0.940893i	$-0.609988\pi$
$439$	−14.1932	−0.677406	−0.338703	+	0.940893i	$0.609988\pi$
$440$	−9.57812	−0.456619
$441$	−2.09065	−0.0995549
$442$	−15.6248	−0.743194
$443$	6.66269	0.316554	0.158277	−	0.987395i	$-0.449406\pi$
$443$	6.66269	0.316554	0.158277	+	0.987395i	$0.449406\pi$
$444$	−45.4357	−2.15628
$445$	−10.4015	−0.493078
$446$	21.6316	1.02429
$447$	14.1664	0.670047
$448$	1.43213	0.0676616
$449$	−40.6818	−1.91989	−0.959946	−	0.280187i	$-0.909604\pi$
$449$	−40.6818	−1.91989	−0.959946	+	0.280187i	$0.909604\pi$
$450$	2.26471	0.106760
$451$	−3.92741	−0.184935
$452$	49.4329	2.32513
$453$	4.05980	0.190746
$454$	−56.4682	−2.65018
$455$	9.61577	0.450794
$456$	80.1152	3.75174
$457$	−25.9993	−1.21620	−0.608098	−	0.793862i	$-0.708067\pi$
$457$	−25.9993	−1.21620	−0.608098	+	0.793862i	$0.708067\pi$
$458$	51.7768	2.41937
$459$	4.85209	0.226476
$460$	4.07520	0.190007
$461$	−29.3223	−1.36568	−0.682838	−	0.730570i	$-0.739254\pi$
$461$	−29.3223	−1.36568	−0.682838	+	0.730570i	$0.739254\pi$
$462$	4.63485	0.215633
$463$	20.1021	0.934222	0.467111	−	0.884199i	$-0.345295\pi$
$463$	20.1021	0.934222	0.467111	+	0.884199i	$0.345295\pi$
$464$	−46.9659	−2.18034
$465$	−0.699840	−0.0324543
$466$	−39.1756	−1.81477
$467$	24.6721	1.14169	0.570845	−	0.821058i	$-0.306616\pi$
$467$	24.6721	1.14169	0.570845	+	0.821058i	$0.306616\pi$
$468$	9.49871	0.439078
$469$	11.4062	0.526687
$470$	−43.1613	−1.99088
$471$	41.3590	1.90572
$472$	1.39992	0.0644364
$473$	−1.00000	−0.0459800
$474$	13.9035	0.638608
$475$	−18.2965	−0.839500
$476$	−4.41990	−0.202586
$477$	−3.74177	−0.171324
$478$	18.8330	0.861402
$479$	−27.5992	−1.26104	−0.630519	−	0.776174i	$-0.717158\pi$
$479$	−27.5992	−1.26104	−0.630519	+	0.776174i	$0.717158\pi$
$480$	−13.5088	−0.616591
$481$	34.6192	1.57850
$482$	−50.3430	−2.29306
$483$	−1.08012	−0.0491472
$484$	4.42217	0.201008
$485$	−16.2160	−0.736330
$486$	−9.13035	−0.414161
$487$	5.59841	0.253688	0.126844	−	0.991923i	$-0.459515\pi$
$487$	5.59841	0.253688	0.126844	+	0.991923i	$0.459515\pi$
$488$	−32.1392	−1.45487
$489$	−26.7265	−1.20861
$490$	−23.7302	−1.07202
$491$	−4.77195	−0.215355	−0.107678	−	0.994186i	$-0.534341\pi$
$491$	−4.77195	−0.215355	−0.107678	+	0.994186i	$0.534341\pi$
$492$	−31.7804	−1.43277
$493$	−6.99808	−0.315178
$494$	−111.446	−5.01420
$495$	0.543614	0.0244336
$496$	−1.64494	−0.0738601
$497$	4.94755	0.221928
$498$	15.4368	0.691739
$499$	−14.3057	−0.640413	−0.320206	−	0.947348i	$-0.603752\pi$
$499$	−14.3057	−0.640413	−0.320206	+	0.947348i	$0.603752\pi$
$500$	52.2022	2.33455
$501$	10.9919	0.491083
$502$	77.2209	3.44654
$503$	−0.201806	−0.00899810	−0.00449905	−	0.999990i	$-0.501432\pi$
$503$	−0.201806	−0.00899810	−0.00449905	+	0.999990i	$0.501432\pi$
$504$	2.13737	0.0952059
$505$	13.6606	0.607888
$506$	−1.49665	−0.0665341
$507$	−45.7724	−2.03282
$508$	75.2756	3.33982
$509$	21.5438	0.954910	0.477455	−	0.878656i	$-0.341559\pi$
$509$	21.5438	0.954910	0.477455	+	0.878656i	$0.341559\pi$
$510$	−7.23591	−0.320411
$511$	−0.454439	−0.0201032
$512$	50.6391	2.23795
$513$	34.6083	1.52799
$514$	−55.0236	−2.42699
$515$	14.5192	0.639793
$516$	−8.09195	−0.356228
$517$	10.9149	0.480036
$518$	14.2220	0.624880
$519$	45.5151	1.99789
$520$	59.0545	2.58971
$521$	27.2057	1.19190	0.595952	−	0.803020i	$-0.296775\pi$
$521$	27.2057	1.19190	0.595952	+	0.803020i	$0.296775\pi$
$522$	6.17840	0.270421
$523$	−10.7506	−0.470089	−0.235044	−	0.971985i	$-0.575524\pi$
$523$	−10.7506	−0.470089	−0.235044	+	0.971985i	$0.575524\pi$
$524$	26.0507	1.13803
$525$	−4.69148	−0.204753
$526$	46.1566	2.01252
$527$	−0.245102	−0.0106768
$528$	12.2807	0.534447
$529$	−22.6512	−0.984835
$530$	−42.4714	−1.84484
$531$	−0.0794535	−0.00344799
$532$	−31.5256	−1.36681
$533$	24.2147	1.04885
$534$	30.9114	1.33767
$535$	−13.1285	−0.567595
$536$	70.0500	3.02570
$537$	−27.0294	−1.16641
$538$	−16.4146	−0.707685
$539$	6.00103	0.258483
$540$	−33.4810	−1.44079
$541$	21.0234	0.903865	0.451933	−	0.892052i	$-0.350735\pi$
$541$	21.0234	0.903865	0.451933	+	0.892052i	$0.350735\pi$
$542$	−56.6933	−2.43518
$543$	20.7894	0.892159
$544$	−4.73114	−0.202846
$545$	−6.03937	−0.258698
$546$	−28.5764	−1.22296
$547$	−25.3715	−1.08481	−0.542404	−	0.840118i	$-0.682486\pi$
$547$	−25.3715	−1.08481	−0.542404	+	0.840118i	$0.682486\pi$
$548$	51.3827	2.19496
$549$	1.82409	0.0778502
$550$	−6.50065	−0.277189
$551$	−49.9149	−2.12645
$552$	−6.63349	−0.282340
$553$	−2.99669	−0.127432
$554$	64.9067	2.75762
$555$	16.0323	0.680533
$556$	−61.3847	−2.60329
$557$	−29.5235	−1.25095	−0.625476	−	0.780243i	$-0.715095\pi$
$557$	−29.5235	−1.25095	−0.625476	+	0.780243i	$0.715095\pi$
$558$	0.216393	0.00916066
$559$	6.16556	0.260775
$560$	10.4668	0.442305
$561$	1.82986	0.0772567
$562$	14.9693	0.631441
$563$	−24.5612	−1.03513	−0.517565	−	0.855644i	$-0.673161\pi$
$563$	−24.5612	−1.03513	−0.517565	+	0.855644i	$0.673161\pi$
$564$	88.3226	3.71905
$565$	−17.4427	−0.733822
$566$	−48.7201	−2.04786
$567$	9.91868	0.416545
$568$	30.3850	1.27493
$569$	39.2346	1.64480	0.822399	−	0.568911i	$-0.192635\pi$
$569$	39.2346	1.64480	0.822399	+	0.568911i	$0.192635\pi$
$570$	−51.6113	−2.16176
$571$	−11.8389	−0.495444	−0.247722	−	0.968831i	$-0.579682\pi$
$571$	−11.8389	−0.495444	−0.247722	+	0.968831i	$0.579682\pi$
$572$	−27.2652	−1.14001
$573$	−23.7665	−0.992861
$574$	9.94774	0.415210
$575$	1.51494	0.0631772
$576$	−0.499184	−0.0207994
$577$	−7.16119	−0.298124	−0.149062	−	0.988828i	$-0.547625\pi$
$577$	−7.16119	−0.298124	−0.149062	+	0.988828i	$0.547625\pi$
$578$	−2.53420	−0.105409
$579$	−11.5721	−0.480921
$580$	48.2891	2.00510
$581$	−3.32717	−0.138034
$582$	48.1911	1.99759
$583$	10.7404	0.444823
$584$	−2.79090	−0.115488
$585$	−3.35169	−0.138575
$586$	−60.3494	−2.49301
$587$	−33.1945	−1.37008	−0.685042	−	0.728504i	$-0.740216\pi$
$587$	−33.1945	−1.37008	−0.685042	+	0.728504i	$0.740216\pi$
$588$	48.5600	2.00258
$589$	−1.74823	−0.0720345
$590$	−0.901845	−0.0371284
$591$	1.88807	0.0776650
$592$	37.6832	1.54877
$593$	−39.1547	−1.60789	−0.803945	−	0.594703i	$-0.797270\pi$
$593$	−39.1547	−1.60789	−0.803945	+	0.594703i	$0.797270\pi$
$594$	12.2962	0.504517
$595$	1.55959	0.0639371
$596$	−34.2355	−1.40234
$597$	41.0019	1.67810
$598$	9.22767	0.377347
$599$	−21.9570	−0.897137	−0.448568	−	0.893748i	$-0.648066\pi$
$599$	−21.9570	−0.897137	−0.448568	+	0.893748i	$0.648066\pi$
$600$	−28.8124	−1.17626
$601$	−41.3225	−1.68558	−0.842790	−	0.538242i	$-0.819089\pi$
$601$	−41.3225	−1.68558	−0.842790	+	0.538242i	$0.819089\pi$
$602$	2.53290	0.103233
$603$	−3.97575	−0.161905
$604$	−9.81120	−0.399212
$605$	−1.56039	−0.0634391
$606$	−40.5969	−1.64914
$607$	−5.14936	−0.209006	−0.104503	−	0.994525i	$-0.533325\pi$
$607$	−5.14936	−0.209006	−0.104503	+	0.994525i	$0.533325\pi$
$608$	−33.7456	−1.36857
$609$	−12.7989	−0.518638
$610$	20.7045	0.838301
$611$	−67.2963	−2.72252
$612$	1.54061	0.0622754
$613$	−13.9140	−0.561981	−0.280991	−	0.959711i	$-0.590663\pi$
$613$	−13.9140	−0.561981	−0.280991	+	0.959711i	$0.590663\pi$
$614$	−48.9969	−1.97735
$615$	11.2139	0.452190
$616$	−6.13512	−0.247191
$617$	−46.3163	−1.86462	−0.932312	−	0.361655i	$-0.882212\pi$
$617$	−46.3163	−1.86462	−0.932312	+	0.361655i	$0.882212\pi$
$618$	−43.1486	−1.73569
$619$	31.7634	1.27668	0.638339	−	0.769755i	$-0.279622\pi$
$619$	31.7634	1.27668	0.638339	+	0.769755i	$0.279622\pi$
$620$	1.69128	0.0679236
$621$	−2.86554	−0.114990
$622$	48.7469	1.95457
$623$	−6.66251	−0.266928
$624$	−75.7171	−3.03111
$625$	−5.59407	−0.223763
$626$	−29.1073	−1.16336
$627$	13.0518	0.521237
$628$	−99.9512	−3.98849
$629$	5.61492	0.223882
$630$	−1.37692	−0.0548578
$631$	−42.3794	−1.68710	−0.843550	−	0.537051i	$-0.819538\pi$
$631$	−42.3794	−1.68710	−0.843550	+	0.537051i	$0.819538\pi$
$632$	−18.4040	−0.732070
$633$	24.7692	0.984487
$634$	19.0326	0.755883
$635$	−26.5615	−1.05406
$636$	86.9109	3.44624
$637$	−36.9997	−1.46598
$638$	−17.7345	−0.702117
$639$	−1.72453	−0.0682212
$640$	−20.4309	−0.807604
$641$	−10.5519	−0.416775	−0.208388	−	0.978046i	$-0.566822\pi$
$641$	−10.5519	−0.416775	−0.208388	+	0.978046i	$0.566822\pi$
$642$	39.0157	1.53983
$643$	−36.8441	−1.45299	−0.726495	−	0.687171i	$-0.758852\pi$
$643$	−36.8441	−1.45299	−0.726495	+	0.687171i	$0.758852\pi$
$644$	2.61030	0.102860
$645$	2.85530	0.112427
$646$	−18.0756	−0.711174
$647$	−48.5244	−1.90769	−0.953845	−	0.300300i	$-0.902913\pi$
$647$	−48.5244	−1.90769	−0.953845	+	0.300300i	$0.902913\pi$
$648$	60.9148	2.39296
$649$	0.228064	0.00895229
$650$	40.0802	1.57207
$651$	−0.448271	−0.0175691
$652$	64.5893	2.52951
$653$	47.8464	1.87237	0.936187	−	0.351502i	$-0.114329\pi$
$653$	47.8464	1.87237	0.936187	+	0.351502i	$0.114329\pi$
$654$	17.9480	0.701822
$655$	−9.19216	−0.359167
$656$	26.3579	1.02910
$657$	0.158400	0.00617977
$658$	−27.6463	−1.07776
$659$	−2.81094	−0.109499	−0.0547494	−	0.998500i	$-0.517436\pi$
$659$	−2.81094	−0.109499	−0.0547494	+	0.998500i	$0.517436\pi$
$660$	−12.6266	−0.491491
$661$	13.4126	0.521690	0.260845	−	0.965381i	$-0.415999\pi$
$661$	13.4126	0.521690	0.260845	+	0.965381i	$0.415999\pi$
$662$	66.3082	2.57714
$663$	−11.2821	−0.438161
$664$	−20.4336	−0.792976
$665$	11.1240	0.431372
$666$	−4.95725	−0.192090
$667$	4.13292	0.160027
$668$	−26.5639	−1.02779
$669$	15.6195	0.603883
$670$	−45.1271	−1.74341
$671$	−5.23588	−0.202129
$672$	−8.65287	−0.333792
$673$	22.3841	0.862845	0.431423	−	0.902150i	$-0.358012\pi$
$673$	22.3841	0.862845	0.431423	+	0.902150i	$0.358012\pi$
$674$	−8.76176	−0.337490
$675$	−12.4464	−0.479063
$676$	110.617	4.25449
$677$	30.3551	1.16664	0.583321	−	0.812242i	$-0.301753\pi$
$677$	30.3551	1.16664	0.583321	+	0.812242i	$0.301753\pi$
$678$	51.8369	1.99078
$679$	−10.3869	−0.398612
$680$	9.57812	0.367304
$681$	−40.7737	−1.56245
$682$	−0.621137	−0.0237846
$683$	−9.77309	−0.373957	−0.186978	−	0.982364i	$-0.559869\pi$
$683$	−9.77309	−0.373957	−0.186978	+	0.982364i	$0.559869\pi$
$684$	10.9886	0.420161
$685$	−18.1308	−0.692741
$686$	−32.9303	−1.25728
$687$	37.3862	1.42637
$688$	6.71126	0.255864
$689$	−66.2207	−2.52281
$690$	4.27338	0.162685
$691$	−29.9971	−1.14114	−0.570572	−	0.821248i	$-0.693278\pi$
$691$	−29.9971	−1.14114	−0.570572	+	0.821248i	$0.693278\pi$
$692$	−109.995	−4.18139
$693$	0.348204	0.0132272
$694$	−66.6713	−2.53081
$695$	21.6600	0.821611
$696$	−78.6036	−2.97946
$697$	3.92741	0.148761
$698$	32.8163	1.24212
$699$	−28.2873	−1.06993
$700$	11.3378	0.428528
$701$	−6.96038	−0.262890	−0.131445	−	0.991323i	$-0.541962\pi$
$701$	−6.96038	−0.262890	−0.131445	+	0.991323i	$0.541962\pi$
$702$	−75.8127	−2.86137
$703$	40.0493	1.51049
$704$	1.43286	0.0540031
$705$	−31.1653	−1.17375
$706$	−11.4478	−0.430845
$707$	8.75007	0.329080
$708$	1.84548	0.0693574
$709$	−20.7004	−0.777419	−0.388710	−	0.921360i	$-0.627079\pi$
$709$	−20.7004	−0.777419	−0.388710	+	0.921360i	$0.627079\pi$
$710$	−19.5744	−0.734615
$711$	1.04453	0.0391730
$712$	−40.9173	−1.53344
$713$	0.144752	0.00542101
$714$	−4.63485	−0.173455
$715$	9.62071	0.359794
$716$	65.3213	2.44117
$717$	13.5987	0.507852
$718$	−41.4420	−1.54660
$719$	7.51047	0.280093	0.140047	−	0.990145i	$-0.455275\pi$
$719$	7.51047	0.280093	0.140047	+	0.990145i	$0.455275\pi$
$720$	−3.64834	−0.135965
$721$	9.30005	0.346352
$722$	−80.7772	−3.00622
$723$	−36.3510	−1.35191
$724$	−50.2413	−1.86720
$725$	17.9513	0.666693
$726$	4.63723	0.172104
$727$	−24.7367	−0.917433	−0.458716	−	0.888583i	$-0.651691\pi$
$727$	−24.7367	−0.917433	−0.458716	+	0.888583i	$0.651691\pi$
$728$	37.8264	1.40194
$729$	23.1786	0.858467
$730$	1.79794	0.0665446
$731$	1.00000	0.0369863
$732$	−42.3685	−1.56598
$733$	−19.0462	−0.703488	−0.351744	−	0.936096i	$-0.614411\pi$
$733$	−19.0462	−0.703488	−0.351744	+	0.936096i	$0.614411\pi$
$734$	−40.1741	−1.48285
$735$	−17.1347	−0.632025
$736$	2.79411	0.102992
$737$	11.4120	0.420367
$738$	−3.46740	−0.127637
$739$	11.2024	0.412088	0.206044	−	0.978543i	$-0.433941\pi$
$739$	11.2024	0.412088	0.206044	+	0.978543i	$0.433941\pi$
$740$	−38.7448	−1.42429
$741$	−80.4714	−2.95619
$742$	−27.2044	−0.998705
$743$	1.75684	0.0644520	0.0322260	−	0.999481i	$-0.489740\pi$
$743$	1.75684	0.0644520	0.0322260	+	0.999481i	$0.489740\pi$
$744$	−2.75302	−0.100931
$745$	12.0803	0.442586
$746$	−41.0289	−1.50218
$747$	1.15972	0.0424321
$748$	−4.42217	−0.161691
$749$	−8.40926	−0.307268
$750$	54.7409	1.99885
$751$	9.29772	0.339279	0.169639	−	0.985506i	$-0.445740\pi$
$751$	9.29772	0.339279	0.169639	+	0.985506i	$0.445740\pi$
$752$	−73.2526	−2.67125
$753$	55.7585	2.03195
$754$	109.343	3.98205
$755$	3.46195	0.125993
$756$	−21.4457	−0.779974
$757$	−5.01203	−0.182165	−0.0910826	−	0.995843i	$-0.529033\pi$
$757$	−5.01203	−0.182165	−0.0910826	+	0.995843i	$0.529033\pi$
$758$	−63.2751	−2.29826
$759$	−1.08068	−0.0392261
$760$	68.3175	2.47814
$761$	−23.9912	−0.869681	−0.434840	−	0.900508i	$-0.643195\pi$
$761$	−23.9912	−0.869681	−0.434840	+	0.900508i	$0.643195\pi$
$762$	78.9364	2.85956
$763$	−3.86842	−0.140046
$764$	57.4360	2.07796
$765$	−0.543614	−0.0196544
$766$	−42.8400	−1.54787
$767$	−1.40614	−0.0507728
$768$	55.4734	2.00172
$769$	16.0113	0.577381	0.288690	−	0.957423i	$-0.406780\pi$
$769$	16.0113	0.577381	0.288690	+	0.957423i	$0.406780\pi$
$770$	3.95232	0.142432
$771$	−39.7306	−1.43086
$772$	27.9661	1.00652
$773$	20.5736	0.739980	0.369990	−	0.929036i	$-0.379361\pi$
$773$	20.5736	0.739980	0.369990	+	0.929036i	$0.379361\pi$
$774$	−0.882871	−0.0317341
$775$	0.628727	0.0225846
$776$	−63.7903	−2.28994
$777$	10.2692	0.368407
$778$	−51.5054	−1.84656
$779$	28.0129	1.00367
$780$	77.8503	2.78749
$781$	4.95010	0.177128
$782$	1.49665	0.0535200
$783$	−33.9553	−1.21346
$784$	−40.2745	−1.43837
$785$	35.2685	1.25879
$786$	27.3175	0.974384
$787$	−4.00865	−0.142893	−0.0714465	−	0.997444i	$-0.522762\pi$
$787$	−4.00865	−0.142893	−0.0714465	+	0.997444i	$0.522762\pi$
$788$	−4.56286	−0.162545
$789$	33.3281	1.18651
$790$	11.8561	0.421820
$791$	−11.1727	−0.397255
$792$	2.13847	0.0759871
$793$	32.2821	1.14637
$794$	−78.8875	−2.79961
$795$	−30.6671	−1.08765
$796$	−99.0883	−3.51209
$797$	47.1126	1.66882	0.834408	−	0.551148i	$-0.185810\pi$
$797$	47.1126	1.66882	0.834408	+	0.551148i	$0.185810\pi$
$798$	−33.0588	−1.17027
$799$	−10.9149	−0.386141
$800$	12.1362	0.429078
$801$	2.32229	0.0820542
$802$	−82.7407	−2.92168
$803$	−0.454673	−0.0160450
$804$	92.3454	3.25677
$805$	−0.921064	−0.0324632
$806$	3.82966	0.134894
$807$	−11.8524	−0.417226
$808$	53.7379	1.89049
$809$	−8.95830	−0.314957	−0.157479	−	0.987522i	$-0.550337\pi$
$809$	−8.95830	−0.314957	−0.157479	+	0.987522i	$0.550337\pi$
$810$	−39.2421	−1.37883
$811$	10.5605	0.370831	0.185415	−	0.982660i	$-0.440637\pi$
$811$	10.5605	0.370831	0.185415	+	0.982660i	$0.440637\pi$
$812$	30.9308	1.08546
$813$	−40.9363	−1.43570
$814$	14.2293	0.498738
$815$	−22.7908	−0.798326
$816$	−12.2807	−0.429909
$817$	7.13266	0.249540
$818$	−67.7595	−2.36915
$819$	−2.14687	−0.0750177
$820$	−27.1005	−0.946389
$821$	−1.28468	−0.0448357	−0.0224178	−	0.999749i	$-0.507136\pi$
$821$	−1.28468	−0.0448357	−0.0224178	+	0.999749i	$0.507136\pi$
$822$	53.8815	1.87933
$823$	36.8236	1.28359	0.641795	−	0.766876i	$-0.278190\pi$
$823$	36.8236	1.28359	0.641795	+	0.766876i	$0.278190\pi$
$824$	57.1155	1.98971
$825$	−4.69390	−0.163420
$826$	−0.577663	−0.0200995
$827$	−4.95661	−0.172358	−0.0861791	−	0.996280i	$-0.527466\pi$
$827$	−4.95661	−0.172358	−0.0861791	+	0.996280i	$0.527466\pi$
$828$	−0.909851	−0.0316195
$829$	−52.0271	−1.80698	−0.903488	−	0.428613i	$-0.859002\pi$
$829$	−52.0271	−1.80698	−0.903488	+	0.428613i	$0.859002\pi$
$830$	13.1636	0.456914
$831$	46.8669	1.62579
$832$	−8.83440	−0.306278
$833$	−6.00103	−0.207923
$834$	−64.3699	−2.22895
$835$	9.37327	0.324375
$836$	−31.5418	−1.09090
$837$	−1.18926	−0.0411067
$838$	95.8553	3.31127
$839$	−37.4066	−1.29142	−0.645710	−	0.763583i	$-0.723438\pi$
$839$	−37.4066	−1.29142	−0.645710	+	0.763583i	$0.723438\pi$
$840$	17.5176	0.604415
$841$	19.9731	0.688728
$842$	43.7091	1.50631
$843$	10.8088	0.372275
$844$	−59.8591	−2.06043
$845$	−39.0319	−1.34274
$846$	9.63643	0.331307
$847$	−0.999486	−0.0343428
$848$	−72.0817	−2.47530
$849$	−35.1791	−1.20734
$850$	6.50065	0.222970
$851$	−3.31606	−0.113673
$852$	40.0559	1.37229
$853$	11.3056	0.387095	0.193548	−	0.981091i	$-0.438001\pi$
$853$	11.3056	0.387095	0.193548	+	0.981091i	$0.438001\pi$
$854$	13.2619	0.453814
$855$	−3.87741	−0.132605
$856$	−51.6448	−1.76518
$857$	−13.5190	−0.461800	−0.230900	−	0.972978i	$-0.574167\pi$
$857$	−13.5190	−0.461800	−0.230900	+	0.972978i	$0.574167\pi$
$858$	−28.5911	−0.976085
$859$	−25.9491	−0.885370	−0.442685	−	0.896677i	$-0.645974\pi$
$859$	−25.9491	−0.885370	−0.442685	+	0.896677i	$0.645974\pi$
$860$	−6.90033	−0.235299
$861$	7.18292	0.244793
$862$	58.3584	1.98770
$863$	−9.25524	−0.315052	−0.157526	−	0.987515i	$-0.550352\pi$
$863$	−9.25524	−0.315052	−0.157526	+	0.987515i	$0.550352\pi$
$864$	−22.9559	−0.780975
$865$	38.8126	1.31967
$866$	−52.7238	−1.79163
$867$	−1.82986	−0.0621453
$868$	1.08333	0.0367705
$869$	−2.99823	−0.101708
$870$	50.6375	1.71677
$871$	−70.3615	−2.38411
$872$	−23.7576	−0.804535
$873$	3.62047	0.122534
$874$	10.6751	0.361090
$875$	−11.7986	−0.398865
$876$	−3.67919	−0.124308
$877$	−1.10220	−0.0372188	−0.0186094	−	0.999827i	$-0.505924\pi$
$877$	−1.10220	−0.0372188	−0.0186094	+	0.999827i	$0.505924\pi$
$878$	35.9685	1.21388
$879$	−43.5762	−1.46979
$880$	10.4722	0.353018
$881$	43.0100	1.44904	0.724521	−	0.689252i	$-0.242061\pi$
$881$	43.0100	1.44904	0.724521	+	0.689252i	$0.242061\pi$
$882$	5.29813	0.178397
$883$	28.7762	0.968395	0.484198	−	0.874959i	$-0.339112\pi$
$883$	28.7762	0.968395	0.484198	+	0.874959i	$0.339112\pi$
$884$	27.2652	0.917027
$885$	−0.651191	−0.0218895
$886$	−16.8846	−0.567249
$887$	42.2820	1.41969	0.709845	−	0.704358i	$-0.248765\pi$
$887$	42.2820	1.41969	0.709845	+	0.704358i	$0.248765\pi$
$888$	63.0677	2.11642
$889$	−17.0136	−0.570617
$890$	26.3594	0.883571
$891$	9.92378	0.332459
$892$	−37.7472	−1.26387
$893$	−77.8521	−2.60522
$894$	−35.9005	−1.20069
$895$	−23.0491	−0.770446
$896$	−13.0867	−0.437197
$897$	6.66298	0.222470
$898$	103.096	3.44035
$899$	1.71524	0.0572065
$900$	−3.95192	−0.131731
$901$	−10.7404	−0.357815
$902$	9.95285	0.331394
$903$	1.82892	0.0608626
$904$	−68.6161	−2.28214
$905$	17.7280	0.589298
$906$	−10.2883	−0.341807
$907$	46.4361	1.54188	0.770942	−	0.636905i	$-0.219786\pi$
$907$	46.4361	1.54188	0.770942	+	0.636905i	$0.219786\pi$
$908$	98.5368	3.27006
$909$	−3.04994	−0.101160
$910$	−24.3683	−0.807801
$911$	−14.8927	−0.493418	−0.246709	−	0.969090i	$-0.579349\pi$
$911$	−14.8927	−0.493418	−0.246709	+	0.969090i	$0.579349\pi$
$912$	−87.5937	−2.90052
$913$	−3.32888	−0.110170
$914$	65.8875	2.17936
$915$	14.9500	0.494232
$916$	−90.3503	−2.98526
$917$	−5.88789	−0.194435
$918$	−12.2962	−0.405834
$919$	−21.8544	−0.720909	−0.360454	−	0.932777i	$-0.617378\pi$
$919$	−21.8544	−0.720909	−0.360454	+	0.932777i	$0.617378\pi$
$920$	−5.65664	−0.186494
$921$	−35.3790	−1.16578
$922$	74.3086	2.44722
$923$	−30.5201	−1.00458
$924$	−8.08779	−0.266069
$925$	−14.4032	−0.473575
$926$	−50.9427	−1.67408
$927$	−3.24164	−0.106469
$928$	33.1089	1.08685
$929$	26.5534	0.871188	0.435594	−	0.900143i	$-0.356538\pi$
$929$	26.5534	0.871188	0.435594	+	0.900143i	$0.356538\pi$
$930$	1.77353	0.0581565
$931$	−42.8033	−1.40282
$932$	68.3613	2.23925
$933$	35.1984	1.15234
$934$	−62.5241	−2.04585
$935$	1.56039	0.0510304
$936$	−13.1848	−0.430960
$937$	−48.4100	−1.58149	−0.790743	−	0.612148i	$-0.790306\pi$
$937$	−48.4100	−1.58149	−0.790743	+	0.612148i	$0.790306\pi$
$938$	−28.9055	−0.943797
$939$	−21.0174	−0.685876
$940$	75.3163	2.45655
$941$	−3.82329	−0.124636	−0.0623178	−	0.998056i	$-0.519849\pi$
$941$	−3.82329	−0.124636	−0.0623178	+	0.998056i	$0.519849\pi$
$942$	−104.812	−3.41496
$943$	−2.31945	−0.0755316
$944$	−1.53060	−0.0498166
$945$	7.56728	0.246164
$946$	2.53420	0.0823940
$947$	46.4013	1.50784	0.753920	−	0.656966i	$-0.228160\pi$
$947$	46.4013	1.50784	0.753920	+	0.656966i	$0.228160\pi$
$948$	−24.2615	−0.787978
$949$	2.80331	0.0909994
$950$	46.3669	1.50434
$951$	13.7428	0.445641
$952$	6.13512	0.198840
$953$	11.7784	0.381540	0.190770	−	0.981635i	$-0.438901\pi$
$953$	11.7784	0.381540	0.190770	+	0.981635i	$0.438901\pi$
$954$	9.48241	0.307004
$955$	−20.2667	−0.655815
$956$	−32.8636	−1.06288
$957$	−12.8055	−0.413943
$958$	69.9418	2.25972
$959$	−11.6134	−0.375015
$960$	−4.09126	−0.132045
$961$	−30.9399	−0.998062
$962$	−87.7319	−2.82859
$963$	2.93114	0.0944548
$964$	87.8484	2.82941
$965$	−9.86802	−0.317663
$966$	2.73725	0.0880694
$967$	28.2883	0.909691	0.454846	−	0.890570i	$-0.349694\pi$
$967$	28.2883	0.909691	0.454846	+	0.890570i	$0.349694\pi$
$968$	−6.13827	−0.197291
$969$	−13.0518	−0.419283
$970$	41.0946	1.31947
$971$	18.6356	0.598044	0.299022	−	0.954246i	$-0.403340\pi$
$971$	18.6356	0.598044	0.299022	+	0.954246i	$0.403340\pi$
$972$	15.9324	0.511033
$973$	13.8740	0.444779
$974$	−14.1875	−0.454597
$975$	28.9405	0.926838
$976$	35.1393	1.12478
$977$	−43.2957	−1.38515	−0.692576	−	0.721345i	$-0.743524\pi$
$977$	−43.2957	−1.38515	−0.692576	+	0.721345i	$0.743524\pi$
$978$	67.7303	2.16578
$979$	−6.66593	−0.213044
$980$	41.4091	1.32276
$981$	1.34838	0.0430506
$982$	12.0931	0.385906
$983$	−16.0999	−0.513506	−0.256753	−	0.966477i	$-0.582653\pi$
$983$	−16.0999	−0.513506	−0.256753	+	0.966477i	$0.582653\pi$
$984$	44.1133	1.40628
$985$	1.61004	0.0513001
$986$	17.7345	0.564783
$987$	−19.9624	−0.635411
$988$	194.473	6.18702
$989$	−0.590579	−0.0187793
$990$	−1.37763	−0.0437839
$991$	40.4822	1.28596	0.642980	−	0.765883i	$-0.277698\pi$
$991$	40.4822	1.28596	0.642980	+	0.765883i	$0.277698\pi$
$992$	1.15961	0.0368177
$993$	47.8788	1.51939
$994$	−12.5381	−0.397684
$995$	34.9640	1.10843
$996$	−26.9371	−0.853536
$997$	26.2912	0.832649	0.416325	−	0.909216i	$-0.363318\pi$
$997$	26.2912	0.832649	0.416325	+	0.909216i	$0.363318\pi$
$998$	36.2536	1.14759
$999$	27.2441	0.861965

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.g.1.6	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.g.1.6	✓	69	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53420 q^{2} -1.82986 q^{3} +4.42217 q^{4} -1.56039 q^{5} +4.63723 q^{6} -0.999486 q^{7} -6.13827 q^{8} +0.348383 q^{9} +O(q^{10})\)	\(q-2.53420 q^{2} -1.82986 q^{3} +4.42217 q^{4} -1.56039 q^{5} +4.63723 q^{6} -0.999486 q^{7} -6.13827 q^{8} +0.348383 q^{9} +3.95435 q^{10} -1.00000 q^{11} -8.09195 q^{12} +6.16556 q^{13} +2.53290 q^{14} +2.85530 q^{15} +6.71126 q^{16} +1.00000 q^{17} -0.882871 q^{18} +7.13266 q^{19} -6.90033 q^{20} +1.82892 q^{21} +2.53420 q^{22} -0.590579 q^{23} +11.2322 q^{24} -2.56517 q^{25} -15.6248 q^{26} +4.85209 q^{27} -4.41990 q^{28} -6.99808 q^{29} -7.23591 q^{30} -0.245102 q^{31} -4.73114 q^{32} +1.82986 q^{33} -2.53420 q^{34} +1.55959 q^{35} +1.54061 q^{36} +5.61492 q^{37} -18.0756 q^{38} -11.2821 q^{39} +9.57812 q^{40} +3.92741 q^{41} -4.63485 q^{42} +1.00000 q^{43} -4.42217 q^{44} -0.543614 q^{45} +1.49665 q^{46} -10.9149 q^{47} -12.2807 q^{48} -6.00103 q^{49} +6.50065 q^{50} -1.82986 q^{51} +27.2652 q^{52} -10.7404 q^{53} -12.2962 q^{54} +1.56039 q^{55} +6.13512 q^{56} -13.0518 q^{57} +17.7345 q^{58} -0.228064 q^{59} +12.6266 q^{60} +5.23588 q^{61} +0.621137 q^{62} -0.348204 q^{63} -1.43286 q^{64} -9.62071 q^{65} -4.63723 q^{66} -11.4120 q^{67} +4.42217 q^{68} +1.08068 q^{69} -3.95232 q^{70} -4.95010 q^{71} -2.13847 q^{72} +0.454673 q^{73} -14.2293 q^{74} +4.69390 q^{75} +31.5418 q^{76} +0.999486 q^{77} +28.5911 q^{78} +2.99823 q^{79} -10.4722 q^{80} -9.92378 q^{81} -9.95285 q^{82} +3.32888 q^{83} +8.08779 q^{84} -1.56039 q^{85} -2.53420 q^{86} +12.8055 q^{87} +6.13827 q^{88} +6.66593 q^{89} +1.37763 q^{90} -6.16239 q^{91} -2.61164 q^{92} +0.448502 q^{93} +27.6605 q^{94} -11.1298 q^{95} +8.65732 q^{96} +10.3922 q^{97} +15.2078 q^{98} -0.348383 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * q^99

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