LMFDB - Embedded newform 4033.2.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, 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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50943 q^{2} +1.55716 q^{3} +4.29722 q^{4} -3.66304 q^{5} -3.90758 q^{6} +4.73862 q^{7} -5.76470 q^{8} -0.575254 q^{9} +O(q^{10})$	\(q-2.50943 q^{2} +1.55716 q^{3} +4.29722 q^{4} -3.66304 q^{5} -3.90758 q^{6} +4.73862 q^{7} -5.76470 q^{8} -0.575254 q^{9} +9.19213 q^{10} +5.22371 q^{11} +6.69145 q^{12} -3.90099 q^{13} -11.8912 q^{14} -5.70394 q^{15} +5.87164 q^{16} -3.68586 q^{17} +1.44356 q^{18} -5.02658 q^{19} -15.7409 q^{20} +7.37878 q^{21} -13.1085 q^{22} -0.531824 q^{23} -8.97655 q^{24} +8.41787 q^{25} +9.78925 q^{26} -5.56724 q^{27} +20.3629 q^{28} +7.93297 q^{29} +14.3136 q^{30} +9.09986 q^{31} -3.20506 q^{32} +8.13415 q^{33} +9.24940 q^{34} -17.3577 q^{35} -2.47199 q^{36} -1.00000 q^{37} +12.6138 q^{38} -6.07447 q^{39} +21.1163 q^{40} -9.30734 q^{41} -18.5165 q^{42} -1.44956 q^{43} +22.4474 q^{44} +2.10718 q^{45} +1.33457 q^{46} -4.67692 q^{47} +9.14309 q^{48} +15.4545 q^{49} -21.1240 q^{50} -5.73948 q^{51} -16.7634 q^{52} -9.23111 q^{53} +13.9706 q^{54} -19.1347 q^{55} -27.3167 q^{56} -7.82719 q^{57} -19.9072 q^{58} -13.6370 q^{59} -24.5111 q^{60} +7.43229 q^{61} -22.8354 q^{62} -2.72591 q^{63} -3.70043 q^{64} +14.2895 q^{65} -20.4120 q^{66} +6.71252 q^{67} -15.8390 q^{68} -0.828134 q^{69} +43.5580 q^{70} -3.82404 q^{71} +3.31617 q^{72} -14.4234 q^{73} +2.50943 q^{74} +13.1080 q^{75} -21.6003 q^{76} +24.7532 q^{77} +15.2434 q^{78} +3.11017 q^{79} -21.5081 q^{80} -6.94332 q^{81} +23.3561 q^{82} -6.20380 q^{83} +31.7082 q^{84} +13.5015 q^{85} +3.63757 q^{86} +12.3529 q^{87} -30.1131 q^{88} -2.99085 q^{89} -5.28781 q^{90} -18.4853 q^{91} -2.28536 q^{92} +14.1699 q^{93} +11.7364 q^{94} +18.4126 q^{95} -4.99079 q^{96} +16.5707 q^{97} -38.7819 q^{98} -3.00496 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + 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 $

$2$	−2.50943	−1.77443	−0.887216	−	0.461354i	$-0.847364\pi$
$2$	−2.50943	−1.77443	−0.887216	+	0.461354i	$0.847364\pi$
$3$	1.55716	0.899026	0.449513	−	0.893274i	$-0.351597\pi$
$3$	1.55716	0.899026	0.449513	+	0.893274i	$0.351597\pi$
$4$	4.29722	2.14861
$5$	−3.66304	−1.63816	−0.819081	−	0.573678i	$-0.805516\pi$
$5$	−3.66304	−1.63816	−0.819081	+	0.573678i	$0.805516\pi$
$6$	−3.90758	−1.59526
$7$	4.73862	1.79103	0.895514	−	0.445033i	$-0.146808\pi$
$7$	4.73862	1.79103	0.895514	+	0.445033i	$0.146808\pi$
$8$	−5.76470	−2.03813
$9$	−0.575254	−0.191751
$10$	9.19213	2.90681
$11$	5.22371	1.57501	0.787504	−	0.616310i	$-0.211373\pi$
$11$	5.22371	1.57501	0.787504	+	0.616310i	$0.211373\pi$
$12$	6.69145	1.93166
$13$	−3.90099	−1.08194	−0.540970	−	0.841042i	$-0.681943\pi$
$13$	−3.90099	−1.08194	−0.540970	+	0.841042i	$0.681943\pi$
$14$	−11.8912	−3.17806
$15$	−5.70394	−1.47275
$16$	5.87164	1.46791
$17$	−3.68586	−0.893953	−0.446976	−	0.894546i	$-0.647499\pi$
$17$	−3.68586	−0.893953	−0.446976	+	0.894546i	$0.647499\pi$
$18$	1.44356	0.340250
$19$	−5.02658	−1.15318	−0.576589	−	0.817034i	$-0.695617\pi$
$19$	−5.02658	−1.15318	−0.576589	+	0.817034i	$0.695617\pi$
$20$	−15.7409	−3.51977
$21$	7.37878	1.61018
$22$	−13.1085	−2.79474
$23$	−0.531824	−0.110893	−0.0554464	−	0.998462i	$-0.517658\pi$
$23$	−0.531824	−0.110893	−0.0554464	+	0.998462i	$0.517658\pi$
$24$	−8.97655	−1.83233
$25$	8.41787	1.68357
$26$	9.78925	1.91983
$27$	−5.56724	−1.07142
$28$	20.3629	3.84822
$29$	7.93297	1.47312	0.736558	−	0.676374i	$-0.236450\pi$
$29$	7.93297	1.47312	0.736558	+	0.676374i	$0.236450\pi$
$30$	14.3136	2.61330
$31$	9.09986	1.63438	0.817192	−	0.576366i	$-0.195530\pi$
$31$	9.09986	1.63438	0.817192	+	0.576366i	$0.195530\pi$
$32$	−3.20506	−0.566580
$33$	8.13415	1.41597
$34$	9.24940	1.58626
$35$	−17.3577	−2.93399
$36$	−2.47199	−0.411999
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	12.6138	2.04624
$39$	−6.07447	−0.972693
$40$	21.1163	3.33878
$41$	−9.30734	−1.45356	−0.726781	−	0.686869i	$-0.758985\pi$
$41$	−9.30734	−1.45356	−0.726781	+	0.686869i	$0.758985\pi$
$42$	−18.5165	−2.85716
$43$	−1.44956	−0.221056	−0.110528	−	0.993873i	$-0.535254\pi$
$43$	−1.44956	−0.221056	−0.110528	+	0.993873i	$0.535254\pi$
$44$	22.4474	3.38408
$45$	2.10718	0.314120
$46$	1.33457	0.196772
$47$	−4.67692	−0.682199	−0.341100	−	0.940027i	$-0.610799\pi$
$47$	−4.67692	−0.682199	−0.341100	+	0.940027i	$0.610799\pi$
$48$	9.14309	1.31969
$49$	15.4545	2.20778
$50$	−21.1240	−2.98739
$51$	−5.73948	−0.803687
$52$	−16.7634	−2.32467
$53$	−9.23111	−1.26799	−0.633995	−	0.773337i	$-0.718586\pi$
$53$	−9.23111	−1.26799	−0.633995	+	0.773337i	$0.718586\pi$
$54$	13.9706	1.90115
$55$	−19.1347	−2.58012
$56$	−27.3167	−3.65035
$57$	−7.82719	−1.03674
$58$	−19.9072	−2.61394
$59$	−13.6370	−1.77538	−0.887692	−	0.460438i	$-0.847693\pi$
$59$	−13.6370	−1.77538	−0.887692	+	0.460438i	$0.847693\pi$
$60$	−24.5111	−3.16437
$61$	7.43229	0.951607	0.475804	−	0.879552i	$-0.342157\pi$
$61$	7.43229	0.951607	0.475804	+	0.879552i	$0.342157\pi$
$62$	−22.8354	−2.90010
$63$	−2.72591	−0.343432
$64$	−3.70043	−0.462554
$65$	14.2895	1.77239
$66$	−20.4120	−2.51255
$67$	6.71252	0.820065	0.410032	−	0.912071i	$-0.365517\pi$
$67$	6.71252	0.820065	0.410032	+	0.912071i	$0.365517\pi$
$68$	−15.8390	−1.92076
$69$	−0.828134	−0.0996956
$70$	43.5580	5.20617
$71$	−3.82404	−0.453831	−0.226915	−	0.973914i	$-0.572864\pi$
$71$	−3.82404	−0.453831	−0.226915	+	0.973914i	$0.572864\pi$
$72$	3.31617	0.390814
$73$	−14.4234	−1.68813	−0.844066	−	0.536240i	$-0.819844\pi$
$73$	−14.4234	−1.68813	−0.844066	+	0.536240i	$0.819844\pi$
$74$	2.50943	0.291715
$75$	13.1080	1.51358
$76$	−21.6003	−2.47773
$77$	24.7532	2.82088
$78$	15.2434	1.72598
$79$	3.11017	0.349922	0.174961	−	0.984575i	$-0.444020\pi$
$79$	3.11017	0.349922	0.174961	+	0.984575i	$0.444020\pi$
$80$	−21.5081	−2.40468
$81$	−6.94332	−0.771480
$82$	23.3561	2.57925
$83$	−6.20380	−0.680956	−0.340478	−	0.940253i	$-0.610589\pi$
$83$	−6.20380	−0.680956	−0.340478	+	0.940253i	$0.610589\pi$
$84$	31.7082	3.45965
$85$	13.5015	1.46444
$86$	3.63757	0.392249
$87$	12.3529	1.32437
$88$	−30.1131	−3.21007
$89$	−2.99085	−0.317029	−0.158515	−	0.987357i	$-0.550671\pi$
$89$	−2.99085	−0.317029	−0.158515	+	0.987357i	$0.550671\pi$
$90$	−5.28781	−0.557384
$91$	−18.4853	−1.93779
$92$	−2.28536	−0.238265
$93$	14.1699	1.46935
$94$	11.7364	1.21052
$95$	18.4126	1.88909
$96$	−4.99079	−0.509370
$97$	16.5707	1.68250	0.841252	−	0.540644i	$-0.181819\pi$
$97$	16.5707	1.68250	0.841252	+	0.540644i	$0.181819\pi$
$98$	−38.7819	−3.91756
$99$	−3.00496	−0.302010
$100$	36.1734	3.61734
$101$	−4.02565	−0.400567	−0.200283	−	0.979738i	$-0.564186\pi$
$101$	−4.02565	−0.400567	−0.200283	+	0.979738i	$0.564186\pi$
$102$	14.4028	1.42609
$103$	−5.99485	−0.590690	−0.295345	−	0.955391i	$-0.595435\pi$
$103$	−5.99485	−0.590690	−0.295345	+	0.955391i	$0.595435\pi$
$104$	22.4880	2.20513
$105$	−27.0288	−2.63774
$106$	23.1648	2.24996
$107$	−6.82101	−0.659412	−0.329706	−	0.944084i	$-0.606950\pi$
$107$	−6.82101	−0.659412	−0.329706	+	0.944084i	$0.606950\pi$
$108$	−23.9236	−2.30205
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	48.0170	4.57824
$111$	−1.55716	−0.147799
$112$	27.8235	2.62907
$113$	−18.3601	−1.72717	−0.863586	−	0.504202i	$-0.831787\pi$
$113$	−18.3601	−1.72717	−0.863586	+	0.504202i	$0.831787\pi$
$114$	19.6418	1.83962
$115$	1.94809	0.181660
$116$	34.0897	3.16515
$117$	2.24406	0.207464
$118$	34.2210	3.15030
$119$	−17.4659	−1.60110
$120$	32.8815	3.00165
$121$	16.2871	1.48065
$122$	−18.6508	−1.68856
$123$	−14.4930	−1.30679
$124$	39.1041	3.51165
$125$	−12.5198	−1.11980
$126$	6.84046	0.609397
$127$	−9.74732	−0.864934	−0.432467	−	0.901650i	$-0.642357\pi$
$127$	−9.74732	−0.864934	−0.432467	+	0.901650i	$0.642357\pi$
$128$	15.6961	1.38735
$129$	−2.25720	−0.198735
$130$	−35.8584	−3.14499
$131$	15.9375	1.39246	0.696232	−	0.717817i	$-0.254858\pi$
$131$	15.9375	1.39246	0.696232	+	0.717817i	$0.254858\pi$
$132$	34.9542	3.04237
$133$	−23.8191	−2.06537
$134$	−16.8446	−1.45515
$135$	20.3930	1.75515
$136$	21.2479	1.82199
$137$	11.4835	0.981098	0.490549	−	0.871414i	$-0.336796\pi$
$137$	11.4835	0.981098	0.490549	+	0.871414i	$0.336796\pi$
$138$	2.07814	0.176903
$139$	11.6112	0.984845	0.492423	−	0.870356i	$-0.336111\pi$
$139$	11.6112	0.984845	0.492423	+	0.870356i	$0.336111\pi$
$140$	−74.5900	−6.30401
$141$	−7.28272	−0.613315
$142$	9.59616	0.805291
$143$	−20.3776	−1.70406
$144$	−3.37769	−0.281474
$145$	−29.0588	−2.41320
$146$	36.1944	2.99547
$147$	24.0651	1.98485
$148$	−4.29722	−0.353229
$149$	9.55511	0.782785	0.391392	−	0.920224i	$-0.371994\pi$
$149$	9.55511	0.782785	0.391392	+	0.920224i	$0.371994\pi$
$150$	−32.8935	−2.68574
$151$	−15.5153	−1.26262	−0.631308	−	0.775533i	$-0.717481\pi$
$151$	−15.5153	−1.26262	−0.631308	+	0.775533i	$0.717481\pi$
$152$	28.9767	2.35032
$153$	2.12031	0.171417
$154$	−62.1162	−5.00547
$155$	−33.3332	−2.67738
$156$	−26.1033	−2.08994
$157$	−10.5711	−0.843668	−0.421834	−	0.906673i	$-0.638614\pi$
$157$	−10.5711	−0.843668	−0.421834	+	0.906673i	$0.638614\pi$
$158$	−7.80475	−0.620912
$159$	−14.3743	−1.13996
$160$	11.7403	0.928149
$161$	−2.52011	−0.198612
$162$	17.4237	1.36894
$163$	3.97477	0.311328	0.155664	−	0.987810i	$-0.450248\pi$
$163$	3.97477	0.311328	0.155664	+	0.987810i	$0.450248\pi$
$164$	−39.9957	−3.12314
$165$	−29.7957	−2.31959
$166$	15.5680	1.20831
$167$	1.19905	0.0927855	0.0463927	−	0.998923i	$-0.485227\pi$
$167$	1.19905	0.0927855	0.0463927	+	0.998923i	$0.485227\pi$
$168$	−42.5364	−3.28176
$169$	2.21774	0.170595
$170$	−33.8809	−2.59855
$171$	2.89156	0.221123
$172$	−6.22908	−0.474963
$173$	10.8966	0.828457	0.414228	−	0.910173i	$-0.364052\pi$
$173$	10.8966	0.828457	0.414228	+	0.910173i	$0.364052\pi$
$174$	−30.9987	−2.35001
$175$	39.8891	3.01533
$176$	30.6718	2.31197
$177$	−21.2350	−1.59612
$178$	7.50531	0.562547
$179$	9.55455	0.714141	0.357070	−	0.934077i	$-0.383776\pi$
$179$	9.55455	0.714141	0.357070	+	0.934077i	$0.383776\pi$
$180$	9.05501	0.674920
$181$	−8.00091	−0.594703	−0.297352	−	0.954768i	$-0.596103\pi$
$181$	−8.00091	−0.594703	−0.297352	+	0.954768i	$0.596103\pi$
$182$	46.3875	3.43847
$183$	11.5733	0.855520
$184$	3.06580	0.226014
$185$	3.66304	0.269312
$186$	−35.5584	−2.60727
$187$	−19.2539	−1.40798
$188$	−20.0978	−1.46578
$189$	−26.3810	−1.91894
$190$	−46.2050	−3.35206
$191$	−9.95153	−0.720067	−0.360034	−	0.932939i	$-0.617235\pi$
$191$	−9.95153	−0.720067	−0.360034	+	0.932939i	$0.617235\pi$
$192$	−5.76216	−0.415848
$193$	7.33322	0.527857	0.263928	−	0.964542i	$-0.414982\pi$
$193$	7.33322	0.527857	0.263928	+	0.964542i	$0.414982\pi$
$194$	−41.5830	−2.98549
$195$	22.2510	1.59343
$196$	66.4113	4.74366
$197$	5.47193	0.389859	0.194929	−	0.980817i	$-0.437552\pi$
$197$	5.47193	0.389859	0.194929	+	0.980817i	$0.437552\pi$
$198$	7.54072	0.535896
$199$	5.04693	0.357767	0.178884	−	0.983870i	$-0.442751\pi$
$199$	5.04693	0.357767	0.178884	+	0.983870i	$0.442751\pi$
$200$	−48.5265	−3.43134
$201$	10.4525	0.737260
$202$	10.1021	0.710778
$203$	37.5913	2.63839
$204$	−24.6638	−1.72681
$205$	34.0932	2.38117
$206$	15.0436	1.04814
$207$	0.305934	0.0212639
$208$	−22.9052	−1.58819
$209$	−26.2574	−1.81626
$210$	67.8267	4.68049
$211$	9.84430	0.677710	0.338855	−	0.940839i	$-0.389960\pi$
$211$	9.84430	0.677710	0.338855	+	0.940839i	$0.389960\pi$
$212$	−39.6681	−2.72442
$213$	−5.95465	−0.408006
$214$	17.1168	1.17008
$215$	5.30980	0.362126
$216$	32.0935	2.18368
$217$	43.1207	2.92723
$218$	2.50943	0.169960
$219$	−22.4595	−1.51767
$220$	−82.2258	−5.54366
$221$	14.3785	0.967204
$222$	3.90758	0.262259
$223$	−24.1510	−1.61727	−0.808634	−	0.588312i	$-0.799793\pi$
$223$	−24.1510	−1.61727	−0.808634	+	0.588312i	$0.799793\pi$
$224$	−15.1875	−1.01476
$225$	−4.84241	−0.322828
$226$	46.0733	3.06475
$227$	8.18538	0.543283	0.271641	−	0.962399i	$-0.412434\pi$
$227$	8.18538	0.543283	0.271641	+	0.962399i	$0.412434\pi$
$228$	−33.6352	−2.22754
$229$	−14.2098	−0.939012	−0.469506	−	0.882929i	$-0.655568\pi$
$229$	−14.2098	−0.939012	−0.469506	+	0.882929i	$0.655568\pi$
$230$	−4.88859	−0.322344
$231$	38.5446	2.53605
$232$	−45.7312	−3.00240
$233$	−8.44981	−0.553565	−0.276783	−	0.960933i	$-0.589268\pi$
$233$	−8.44981	−0.553565	−0.276783	+	0.960933i	$0.589268\pi$
$234$	−5.63131	−0.368130
$235$	17.1318	1.11755
$236$	−58.6011	−3.81461
$237$	4.84304	0.314589
$238$	43.8293	2.84103
$239$	−0.337644	−0.0218404	−0.0109202	−	0.999940i	$-0.503476\pi$
$239$	−0.337644	−0.0218404	−0.0109202	+	0.999940i	$0.503476\pi$
$240$	−33.4915	−2.16187
$241$	−1.69229	−0.109010	−0.0545049	−	0.998514i	$-0.517358\pi$
$241$	−1.69229	−0.109010	−0.0545049	+	0.998514i	$0.517358\pi$
$242$	−40.8714	−2.62731
$243$	5.88987	0.377835
$244$	31.9382	2.04463
$245$	−56.6104	−3.61670
$246$	36.3692	2.31881
$247$	19.6087	1.24767
$248$	−52.4579	−3.33108
$249$	−9.66031	−0.612197
$250$	31.4175	1.98702
$251$	−13.3167	−0.840540	−0.420270	−	0.907399i	$-0.638065\pi$
$251$	−13.3167	−0.840540	−0.420270	+	0.907399i	$0.638065\pi$
$252$	−11.7138	−0.737901
$253$	−2.77809	−0.174657
$254$	24.4602	1.53477
$255$	21.0239	1.31657
$256$	−31.9873	−1.99920
$257$	−18.7641	−1.17047	−0.585235	−	0.810864i	$-0.698998\pi$
$257$	−18.7641	−1.17047	−0.585235	+	0.810864i	$0.698998\pi$
$258$	5.66427	0.352642
$259$	−4.73862	−0.294443
$260$	61.4051	3.80818
$261$	−4.56348	−0.282472
$262$	−39.9939	−2.47083
$263$	−6.87208	−0.423751	−0.211875	−	0.977297i	$-0.567957\pi$
$263$	−6.87208	−0.423751	−0.211875	+	0.977297i	$0.567957\pi$
$264$	−46.8909	−2.88594
$265$	33.8139	2.07717
$266$	59.7721	3.66487
$267$	−4.65723	−0.285018
$268$	28.8452	1.76200
$269$	−5.47400	−0.333756	−0.166878	−	0.985978i	$-0.553369\pi$
$269$	−5.47400	−0.333756	−0.166878	+	0.985978i	$0.553369\pi$
$270$	−51.1748	−3.11440
$271$	−2.04932	−0.124488	−0.0622438	−	0.998061i	$-0.519826\pi$
$271$	−2.04932	−0.124488	−0.0622438	+	0.998061i	$0.519826\pi$
$272$	−21.6421	−1.31224
$273$	−28.7846	−1.74212
$274$	−28.8169	−1.74089
$275$	43.9725	2.65164
$276$	−3.55867	−0.214207
$277$	−9.80283	−0.588995	−0.294498	−	0.955652i	$-0.595152\pi$
$277$	−9.80283	−0.588995	−0.294498	+	0.955652i	$0.595152\pi$
$278$	−29.1373	−1.74754
$279$	−5.23473	−0.313395
$280$	100.062	5.97986
$281$	−19.7388	−1.17752	−0.588759	−	0.808308i	$-0.700383\pi$
$281$	−19.7388	−1.17752	−0.588759	+	0.808308i	$0.700383\pi$
$282$	18.2754	1.08829
$283$	−31.2603	−1.85823	−0.929117	−	0.369785i	$-0.879431\pi$
$283$	−31.2603	−1.85823	−0.929117	+	0.369785i	$0.879431\pi$
$284$	−16.4328	−0.975104
$285$	28.6713	1.69834
$286$	51.1362	3.02375
$287$	−44.1039	−2.60337
$288$	1.84372	0.108642
$289$	−3.41442	−0.200848
$290$	72.9209	4.28206
$291$	25.8033	1.51262
$292$	−61.9805	−3.62713
$293$	8.12219	0.474504	0.237252	−	0.971448i	$-0.423753\pi$
$293$	8.12219	0.474504	0.237252	+	0.971448i	$0.423753\pi$
$294$	−60.3896	−3.52199
$295$	49.9528	2.90837
$296$	5.76470	0.335066
$297$	−29.0817	−1.68749
$298$	−23.9778	−1.38900
$299$	2.07464	0.119979
$300$	56.3278	3.25209
$301$	−6.86892	−0.395918
$302$	38.9344	2.24042
$303$	−6.26857	−0.360120
$304$	−29.5143	−1.69276
$305$	−27.2248	−1.55889
$306$	−5.32075	−0.304167
$307$	−2.84533	−0.162392	−0.0811959	−	0.996698i	$-0.525874\pi$
$307$	−2.84533	−0.162392	−0.0811959	+	0.996698i	$0.525874\pi$
$308$	106.370	6.06097
$309$	−9.33494	−0.531046
$310$	83.6471	4.75084
$311$	14.5820	0.826871	0.413435	−	0.910533i	$-0.364329\pi$
$311$	14.5820	0.826871	0.413435	+	0.910533i	$0.364329\pi$
$312$	35.0175	1.98247
$313$	−2.09216	−0.118256	−0.0591279	−	0.998250i	$-0.518832\pi$
$313$	−2.09216	−0.118256	−0.0591279	+	0.998250i	$0.518832\pi$
$314$	26.5275	1.49703
$315$	9.98511	0.562597
$316$	13.3651	0.751845
$317$	8.86131	0.497701	0.248850	−	0.968542i	$-0.419947\pi$
$317$	8.86131	0.497701	0.248850	+	0.968542i	$0.419947\pi$
$318$	36.0713	2.02278
$319$	41.4395	2.32017
$320$	13.5548	0.757738
$321$	−10.6214	−0.592829
$322$	6.32402	0.352424
$323$	18.5273	1.03089
$324$	−29.8370	−1.65761
$325$	−32.8380	−1.82153
$326$	−9.97440	−0.552431
$327$	−1.55716	−0.0861111
$328$	53.6540	2.96255
$329$	−22.1621	−1.22184
$330$	74.7702	4.11596
$331$	−21.4004	−1.17627	−0.588135	−	0.808762i	$-0.700138\pi$
$331$	−21.4004	−1.17627	−0.588135	+	0.808762i	$0.700138\pi$
$332$	−26.6591	−1.46311
$333$	0.575254	0.0315237
$334$	−3.00893	−0.164641
$335$	−24.5882	−1.34340
$336$	43.3256	2.36360
$337$	−10.5330	−0.573772	−0.286886	−	0.957965i	$-0.592620\pi$
$337$	−10.5330	−0.573772	−0.286886	+	0.957965i	$0.592620\pi$
$338$	−5.56525	−0.302710
$339$	−28.5896	−1.55277
$340$	58.0187	3.14651
$341$	47.5350	2.57417
$342$	−7.25616	−0.392368
$343$	40.0625	2.16317
$344$	8.35628	0.450541
$345$	3.03349	0.163318
$346$	−27.3443	−1.47004
$347$	−15.5095	−0.832595	−0.416298	−	0.909228i	$-0.636673\pi$
$347$	−15.5095	−0.832595	−0.416298	+	0.909228i	$0.636673\pi$
$348$	53.0831	2.84555
$349$	−14.5770	−0.780291	−0.390146	−	0.920753i	$-0.627575\pi$
$349$	−14.5770	−0.780291	−0.390146	+	0.920753i	$0.627575\pi$
$350$	−100.099	−5.35050
$351$	21.7178	1.15921
$352$	−16.7423	−0.892368
$353$	22.1867	1.18088	0.590439	−	0.807083i	$-0.298955\pi$
$353$	22.1867	1.18088	0.590439	+	0.807083i	$0.298955\pi$
$354$	53.2876	2.83220
$355$	14.0076	0.743448
$356$	−12.8523	−0.681172
$357$	−27.1972	−1.43943
$358$	−23.9764	−1.26719
$359$	−15.3418	−0.809709	−0.404854	−	0.914381i	$-0.632678\pi$
$359$	−15.3418	−0.809709	−0.404854	+	0.914381i	$0.632678\pi$
$360$	−12.1473	−0.640216
$361$	6.26655	0.329819
$362$	20.0777	1.05526
$363$	25.3617	1.33114
$364$	−79.4354	−4.16354
$365$	52.8335	2.76543
$366$	−29.0422	−1.51806
$367$	20.5887	1.07472	0.537361	−	0.843352i	$-0.319421\pi$
$367$	20.5887	1.07472	0.537361	+	0.843352i	$0.319421\pi$
$368$	−3.12268	−0.162781
$369$	5.35409	0.278723
$370$	−9.19213	−0.477876
$371$	−43.7427	−2.27101
$372$	60.8913	3.15707
$373$	−30.3559	−1.57177	−0.785885	−	0.618373i	$-0.787792\pi$
$373$	−30.3559	−1.57177	−0.785885	+	0.618373i	$0.787792\pi$
$374$	48.3162	2.49837
$375$	−19.4953	−1.00673
$376$	26.9610	1.39041
$377$	−30.9465	−1.59382
$378$	66.2012	3.40502
$379$	15.2665	0.784188	0.392094	−	0.919925i	$-0.371751\pi$
$379$	15.2665	0.784188	0.392094	+	0.919925i	$0.371751\pi$
$380$	79.1229	4.05892
$381$	−15.1781	−0.777599
$382$	24.9726	1.27771
$383$	−8.75892	−0.447560	−0.223780	−	0.974640i	$-0.571840\pi$
$383$	−8.75892	−0.447560	−0.223780	+	0.974640i	$0.571840\pi$
$384$	24.4413	1.24726
$385$	−90.6718	−4.62106
$386$	−18.4022	−0.936646
$387$	0.833866	0.0423878
$388$	71.2081	3.61504
$389$	15.4119	0.781412	0.390706	−	0.920516i	$-0.372231\pi$
$389$	15.4119	0.781412	0.390706	+	0.920516i	$0.372231\pi$
$390$	−55.8373	−2.82743
$391$	1.96023	0.0991330
$392$	−89.0904	−4.49974
$393$	24.8172	1.25186
$394$	−13.7314	−0.691778
$395$	−11.3927	−0.573229
$396$	−12.9130	−0.648901
$397$	26.4379	1.32688	0.663440	−	0.748229i	$-0.269096\pi$
$397$	26.4379	1.32688	0.663440	+	0.748229i	$0.269096\pi$
$398$	−12.6649	−0.634833
$399$	−37.0901	−1.85683
$400$	49.4267	2.47134
$401$	−32.3352	−1.61474	−0.807371	−	0.590044i	$-0.799110\pi$
$401$	−32.3352	−1.61474	−0.807371	+	0.590044i	$0.799110\pi$
$402$	−26.2297	−1.30822
$403$	−35.4985	−1.76831
$404$	−17.2991	−0.860661
$405$	25.4337	1.26381
$406$	−94.3326	−4.68165
$407$	−5.22371	−0.258930
$408$	33.0863	1.63802
$409$	−24.2044	−1.19683	−0.598414	−	0.801187i	$-0.704202\pi$
$409$	−24.2044	−1.19683	−0.598414	+	0.801187i	$0.704202\pi$
$410$	−85.5543	−4.22523
$411$	17.8816	0.882033
$412$	−25.7612	−1.26916
$413$	−64.6204	−3.17976
$414$	−0.767718	−0.0377313
$415$	22.7248	1.11552
$416$	12.5029	0.613006
$417$	18.0804	0.885402
$418$	65.8910	3.22284
$419$	24.2859	1.18645	0.593223	−	0.805038i	$-0.297855\pi$
$419$	24.2859	1.18645	0.593223	+	0.805038i	$0.297855\pi$
$420$	−116.149	−5.66747
$421$	−11.4156	−0.556363	−0.278181	−	0.960529i	$-0.589732\pi$
$421$	−11.4156	−0.556363	−0.278181	+	0.960529i	$0.589732\pi$
$422$	−24.7035	−1.20255
$423$	2.69042	0.130813
$424$	53.2145	2.58433
$425$	−31.0271	−1.50504
$426$	14.9427	0.723978
$427$	35.2188	1.70436
$428$	−29.3114	−1.41682
$429$	−31.7313	−1.53200
$430$	−13.3246	−0.642567
$431$	−6.27698	−0.302352	−0.151176	−	0.988507i	$-0.548306\pi$
$431$	−6.27698	−0.302352	−0.151176	+	0.988507i	$0.548306\pi$
$432$	−32.6889	−1.57274
$433$	−14.9111	−0.716582	−0.358291	−	0.933610i	$-0.616640\pi$
$433$	−14.9111	−0.716582	−0.358291	+	0.933610i	$0.616640\pi$
$434$	−108.208	−5.19416
$435$	−45.2492	−2.16953
$436$	−4.29722	−0.205799
$437$	2.67326	0.127879
$438$	56.3605	2.69301
$439$	−29.6766	−1.41639	−0.708195	−	0.706017i	$-0.750490\pi$
$439$	−29.6766	−1.41639	−0.708195	+	0.706017i	$0.750490\pi$
$440$	110.306	5.25861
$441$	−8.89025	−0.423345
$442$	−36.0818	−1.71624
$443$	22.5315	1.07051	0.535253	−	0.844692i	$-0.320216\pi$
$443$	22.5315	1.07051	0.535253	+	0.844692i	$0.320216\pi$
$444$	−6.69145	−0.317562
$445$	10.9556	0.519345
$446$	60.6051	2.86973
$447$	14.8788	0.703744
$448$	−17.5349	−0.828446
$449$	−36.4547	−1.72040	−0.860202	−	0.509953i	$-0.829663\pi$
$449$	−36.4547	−1.72040	−0.860202	+	0.509953i	$0.829663\pi$
$450$	12.1517	0.572836
$451$	−48.6189	−2.28937
$452$	−78.8973	−3.71102
$453$	−24.1598	−1.13512
$454$	−20.5406	−0.964019
$455$	67.7124	3.17441
$456$	45.1214	2.11300
$457$	3.45807	0.161762	0.0808808	−	0.996724i	$-0.474227\pi$
$457$	3.45807	0.161762	0.0808808	+	0.996724i	$0.474227\pi$
$458$	35.6585	1.66621
$459$	20.5201	0.957796
$460$	8.37137	0.390317
$461$	−4.04873	−0.188568	−0.0942841	−	0.995545i	$-0.530056\pi$
$461$	−4.04873	−0.188568	−0.0942841	+	0.995545i	$0.530056\pi$
$462$	−96.7248	−4.50005
$463$	4.48700	0.208528	0.104264	−	0.994550i	$-0.466751\pi$
$463$	4.48700	0.208528	0.104264	+	0.994550i	$0.466751\pi$
$464$	46.5796	2.16240
$465$	−51.9051	−2.40704
$466$	21.2042	0.982264
$467$	27.8009	1.28647	0.643235	−	0.765669i	$-0.277592\pi$
$467$	27.8009	1.28647	0.643235	+	0.765669i	$0.277592\pi$
$468$	9.64322	0.445758
$469$	31.8080	1.46876
$470$	−42.9909	−1.98302
$471$	−16.4609	−0.758480
$472$	78.6131	3.61846
$473$	−7.57209	−0.348165
$474$	−12.1532	−0.558217
$475$	−42.3131	−1.94146
$476$	−75.0547	−3.44013
$477$	5.31023	0.243139
$478$	0.847293	0.0387543
$479$	22.0749	1.00863	0.504314	−	0.863520i	$-0.331745\pi$
$479$	22.0749	1.00863	0.504314	+	0.863520i	$0.331745\pi$
$480$	18.2815	0.834431
$481$	3.90099	0.177870
$482$	4.24667	0.193430
$483$	−3.92421	−0.178558
$484$	69.9894	3.18134
$485$	−60.6993	−2.75621
$486$	−14.7802	−0.670443
$487$	9.65733	0.437616	0.218808	−	0.975768i	$-0.429783\pi$
$487$	9.65733	0.437616	0.218808	+	0.975768i	$0.429783\pi$
$488$	−42.8449	−1.93950
$489$	6.18936	0.279892
$490$	142.060	6.41760
$491$	−10.8227	−0.488421	−0.244210	−	0.969722i	$-0.578529\pi$
$491$	−10.8227	−0.488421	−0.244210	+	0.969722i	$0.578529\pi$
$492$	−62.2797	−2.80778
$493$	−29.2398	−1.31690
$494$	−49.2065	−2.21390
$495$	11.0073	0.494741
$496$	53.4311	2.39913
$497$	−18.1207	−0.812823
$498$	24.2418	1.08630
$499$	8.82635	0.395122	0.197561	−	0.980291i	$-0.436698\pi$
$499$	8.82635	0.395122	0.197561	+	0.980291i	$0.436698\pi$
$500$	−53.8003	−2.40602
$501$	1.86712	0.0834166
$502$	33.4172	1.49148
$503$	−40.2122	−1.79297	−0.896487	−	0.443071i	$-0.853889\pi$
$503$	−40.2122	−1.79297	−0.896487	+	0.443071i	$0.853889\pi$
$504$	15.7140	0.699959
$505$	14.7461	0.656193
$506$	6.97141	0.309917
$507$	3.45337	0.153370
$508$	−41.8863	−1.85841
$509$	−9.29491	−0.411990	−0.205995	−	0.978553i	$-0.566043\pi$
$509$	−9.29491	−0.411990	−0.205995	+	0.978553i	$0.566043\pi$
$510$	−52.7580	−2.33616
$511$	−68.3469	−3.02349
$512$	48.8775	2.16010
$513$	27.9842	1.23553
$514$	47.0870	2.07692
$515$	21.9594	0.967646
$516$	−9.69967	−0.427004
$517$	−24.4309	−1.07447
$518$	11.8912	0.522470
$519$	16.9678	0.744804
$520$	−82.3746	−3.61237
$521$	30.4907	1.33582	0.667911	−	0.744241i	$-0.267189\pi$
$521$	30.4907	1.33582	0.667911	+	0.744241i	$0.267189\pi$
$522$	11.4517	0.501227
$523$	−29.7316	−1.30007	−0.650037	−	0.759903i	$-0.725247\pi$
$523$	−29.7316	−1.30007	−0.650037	+	0.759903i	$0.725247\pi$
$524$	68.4868	2.99186
$525$	62.1136	2.71086
$526$	17.2450	0.751916
$527$	−33.5408	−1.46106
$528$	47.7608	2.07852
$529$	−22.7172	−0.987703
$530$	−84.8536	−3.68580
$531$	7.84473	0.340432
$532$	−102.356	−4.43768
$533$	36.3079	1.57267
$534$	11.6870	0.505745
$535$	24.9856	1.08022
$536$	−38.6956	−1.67140
$537$	14.8780	0.642031
$538$	13.7366	0.592227
$539$	80.7297	3.47727
$540$	87.6333	3.77114
$541$	−38.1722	−1.64115	−0.820575	−	0.571538i	$-0.806347\pi$
$541$	−38.1722	−1.64115	−0.820575	+	0.571538i	$0.806347\pi$
$542$	5.14263	0.220895
$543$	−12.4587	−0.534654
$544$	11.8134	0.506496
$545$	3.66304	0.156907
$546$	72.2327	3.09128
$547$	19.5715	0.836817	0.418409	−	0.908259i	$-0.362588\pi$
$547$	19.5715	0.836817	0.418409	+	0.908259i	$0.362588\pi$
$548$	49.3469	2.10800
$549$	−4.27545	−0.182472
$550$	−110.346	−4.70516
$551$	−39.8758	−1.69876
$552$	4.77394	0.203192
$553$	14.7379	0.626720
$554$	24.5995	1.04513
$555$	5.70394	0.242119
$556$	49.8956	2.11605
$557$	−25.3215	−1.07291	−0.536453	−	0.843930i	$-0.680236\pi$
$557$	−25.3215	−1.07291	−0.536453	+	0.843930i	$0.680236\pi$
$558$	13.1362	0.556099
$559$	5.65473	0.239170
$560$	−101.918	−4.30684
$561$	−29.9814	−1.26581
$562$	49.5331	2.08943
$563$	−6.23855	−0.262923	−0.131462	−	0.991321i	$-0.541967\pi$
$563$	−6.23855	−0.262923	−0.131462	+	0.991321i	$0.541967\pi$
$564$	−31.2954	−1.31777
$565$	67.2537	2.82939
$566$	78.4455	3.29731
$567$	−32.9017	−1.38174
$568$	22.0445	0.924965
$569$	40.2415	1.68701	0.843506	−	0.537120i	$-0.180488\pi$
$569$	40.2415	1.68701	0.843506	+	0.537120i	$0.180488\pi$
$570$	−71.9486	−3.01359
$571$	13.1388	0.549842	0.274921	−	0.961467i	$-0.411348\pi$
$571$	13.1388	0.549842	0.274921	+	0.961467i	$0.411348\pi$
$572$	−87.5672	−3.66137
$573$	−15.4961	−0.647360
$574$	110.676	4.61951
$575$	−4.47682	−0.186696
$576$	2.12869	0.0886953
$577$	3.63653	0.151391	0.0756955	−	0.997131i	$-0.475882\pi$
$577$	3.63653	0.151391	0.0756955	+	0.997131i	$0.475882\pi$
$578$	8.56823	0.356391
$579$	11.4190	0.474557
$580$	−124.872	−5.18503
$581$	−29.3974	−1.21961
$582$	−64.7514	−2.68403
$583$	−48.2206	−1.99709
$584$	83.1465	3.44063
$585$	−8.22009	−0.339859
$586$	−20.3820	−0.841974
$587$	21.3888	0.882811	0.441405	−	0.897308i	$-0.354480\pi$
$587$	21.3888	0.882811	0.441405	+	0.897308i	$0.354480\pi$
$588$	103.413	4.26468
$589$	−45.7412	−1.88473
$590$	−125.353	−5.16070
$591$	8.52066	0.350493
$592$	−5.87164	−0.241323
$593$	−40.3708	−1.65783	−0.828916	−	0.559373i	$-0.811042\pi$
$593$	−40.3708	−1.65783	−0.828916	+	0.559373i	$0.811042\pi$
$594$	72.9782	2.99433
$595$	63.9783	2.62285
$596$	41.0604	1.68190
$597$	7.85887	0.321642
$598$	−5.20615	−0.212895
$599$	14.3270	0.585386	0.292693	−	0.956207i	$-0.405449\pi$
$599$	14.3270	0.585386	0.292693	+	0.956207i	$0.405449\pi$
$600$	−75.5635	−3.08487
$601$	−15.6938	−0.640165	−0.320083	−	0.947390i	$-0.603711\pi$
$601$	−15.6938	−0.640165	−0.320083	+	0.947390i	$0.603711\pi$
$602$	17.2370	0.702529
$603$	−3.86140	−0.157249
$604$	−66.6725	−2.71287
$605$	−59.6605	−2.42554
$606$	15.7305	0.639009
$607$	−13.3386	−0.541398	−0.270699	−	0.962664i	$-0.587255\pi$
$607$	−13.3386	−0.541398	−0.270699	+	0.962664i	$0.587255\pi$
$608$	16.1105	0.653367
$609$	58.5357	2.37198
$610$	68.3186	2.76614
$611$	18.2446	0.738099
$612$	9.11142	0.368307
$613$	21.3728	0.863239	0.431620	−	0.902056i	$-0.357942\pi$
$613$	21.3728	0.863239	0.431620	+	0.902056i	$0.357942\pi$
$614$	7.14016	0.288153
$615$	53.0885	2.14074
$616$	−142.694	−5.74932
$617$	−40.3810	−1.62568	−0.812840	−	0.582488i	$-0.802079\pi$
$617$	−40.3810	−1.62568	−0.812840	+	0.582488i	$0.802079\pi$
$618$	23.4253	0.942305
$619$	−15.6995	−0.631018	−0.315509	−	0.948923i	$-0.602175\pi$
$619$	−15.6995	−0.631018	−0.315509	+	0.948923i	$0.602175\pi$
$620$	−143.240	−5.75265
$621$	2.96079	0.118812
$622$	−36.5925	−1.46723
$623$	−14.1725	−0.567809
$624$	−35.6671	−1.42783
$625$	3.77119	0.150847
$626$	5.25012	0.209837
$627$	−40.8870	−1.63287
$628$	−45.4264	−1.81271
$629$	3.68586	0.146965
$630$	−25.0569	−0.998291
$631$	−6.34405	−0.252553	−0.126276	−	0.991995i	$-0.540303\pi$
$631$	−6.34405	−0.252553	−0.126276	+	0.991995i	$0.540303\pi$
$632$	−17.9292	−0.713185
$633$	15.3291	0.609279
$634$	−22.2368	−0.883136
$635$	35.7048	1.41690
$636$	−61.7695	−2.44932
$637$	−60.2878	−2.38869
$638$	−103.989	−4.11698
$639$	2.19980	0.0870226
$640$	−57.4953	−2.27270
$641$	−44.0719	−1.74074	−0.870368	−	0.492402i	$-0.836119\pi$
$641$	−44.0719	−1.74074	−0.870368	+	0.492402i	$0.836119\pi$
$642$	26.6536	1.05193
$643$	3.68166	0.145191	0.0725953	−	0.997361i	$-0.476872\pi$
$643$	3.68166	0.145191	0.0725953	+	0.997361i	$0.476872\pi$
$644$	−10.8294	−0.426740
$645$	8.26821	0.325561
$646$	−46.4929	−1.82924
$647$	−50.6441	−1.99103	−0.995513	−	0.0946247i	$-0.969835\pi$
$647$	−50.6441	−1.99103	−0.995513	+	0.0946247i	$0.969835\pi$
$648$	40.0261	1.57238
$649$	−71.2356	−2.79624
$650$	82.4046	3.23218
$651$	67.1459	2.63165
$652$	17.0805	0.668923
$653$	44.6441	1.74706	0.873530	−	0.486770i	$-0.161825\pi$
$653$	44.6441	1.74706	0.873530	+	0.486770i	$0.161825\pi$
$654$	3.90758	0.152798
$655$	−58.3797	−2.28108
$656$	−54.6494	−2.13370
$657$	8.29712	0.323701
$658$	55.6142	2.16807
$659$	31.2563	1.21757	0.608786	−	0.793335i	$-0.291657\pi$
$659$	31.2563	1.21757	0.608786	+	0.793335i	$0.291657\pi$
$660$	−128.039	−4.98390
$661$	−27.3462	−1.06364	−0.531822	−	0.846856i	$-0.678492\pi$
$661$	−27.3462	−1.06364	−0.531822	+	0.846856i	$0.678492\pi$
$662$	53.7026	2.08721
$663$	22.3897	0.869542
$664$	35.7630	1.38788
$665$	87.2502	3.38342
$666$	−1.44356	−0.0559367
$667$	−4.21894	−0.163358
$668$	5.15259	0.199360
$669$	−37.6069	−1.45397
$670$	61.7023	2.38377
$671$	38.8241	1.49879
$672$	−23.6494	−0.912297
$673$	10.5837	0.407973	0.203987	−	0.978974i	$-0.434610\pi$
$673$	10.5837	0.407973	0.203987	+	0.978974i	$0.434610\pi$
$674$	26.4319	1.01812
$675$	−46.8643	−1.80381
$676$	9.53011	0.366543
$677$	8.00730	0.307746	0.153873	−	0.988091i	$-0.450825\pi$
$677$	8.00730	0.307746	0.153873	+	0.988091i	$0.450825\pi$
$678$	71.7434	2.75529
$679$	78.5224	3.01341
$680$	−77.8319	−2.98472
$681$	12.7459	0.488426
$682$	−119.286	−4.56768
$683$	13.9415	0.533455	0.266728	−	0.963772i	$-0.414058\pi$
$683$	13.9415	0.533455	0.266728	+	0.963772i	$0.414058\pi$
$684$	12.4257	0.475108
$685$	−42.0644	−1.60720
$686$	−100.534	−3.83840
$687$	−22.1270	−0.844196
$688$	−8.51131	−0.324491
$689$	36.0105	1.37189
$690$	−7.61232	−0.289796
$691$	47.4223	1.80403	0.902015	−	0.431704i	$-0.142087\pi$
$691$	47.4223	1.80403	0.902015	+	0.431704i	$0.142087\pi$
$692$	46.8253	1.78003
$693$	−14.2394	−0.540908
$694$	38.9200	1.47738
$695$	−42.5321	−1.61334
$696$	−71.2107	−2.69924
$697$	34.3056	1.29942
$698$	36.5800	1.38457
$699$	−13.1577	−0.497670
$700$	171.412	6.47876
$701$	−18.2394	−0.688892	−0.344446	−	0.938806i	$-0.611933\pi$
$701$	−18.2394	−0.688892	−0.344446	+	0.938806i	$0.611933\pi$
$702$	−54.4991	−2.05694
$703$	5.02658	0.189581
$704$	−19.3300	−0.728525
$705$	26.6769	1.00471
$706$	−55.6758	−2.09539
$707$	−19.0760	−0.717426
$708$	−91.2512	−3.42943
$709$	21.8973	0.822372	0.411186	−	0.911552i	$-0.365115\pi$
$709$	21.8973	0.822372	0.411186	+	0.911552i	$0.365115\pi$
$710$	−35.1511	−1.31920
$711$	−1.78914	−0.0670980
$712$	17.2413	0.646147
$713$	−4.83952	−0.181241
$714$	68.2493	2.55417
$715$	74.6442	2.79153
$716$	41.0580	1.53441
$717$	−0.525766	−0.0196351
$718$	38.4991	1.43677
$719$	−11.2021	−0.417770	−0.208885	−	0.977940i	$-0.566983\pi$
$719$	−11.2021	−0.417770	−0.208885	+	0.977940i	$0.566983\pi$
$720$	12.3726	0.461100
$721$	−28.4073	−1.05794
$722$	−15.7254	−0.585241
$723$	−2.63516	−0.0980027
$724$	−34.3817	−1.27778
$725$	66.7787	2.48010
$726$	−63.6432	−2.36202
$727$	−30.8841	−1.14543	−0.572715	−	0.819755i	$-0.694110\pi$
$727$	−30.8841	−1.14543	−0.572715	+	0.819755i	$0.694110\pi$
$728$	106.562	3.94946
$729$	30.0014	1.11116
$730$	−132.582	−4.90707
$731$	5.34288	0.197614
$732$	49.7328	1.83818
$733$	51.2138	1.89162	0.945812	−	0.324713i	$-0.105268\pi$
$733$	51.2138	1.89162	0.945812	+	0.324713i	$0.105268\pi$
$734$	−51.6658	−1.90702
$735$	−88.1514	−3.25151
$736$	1.70453	0.0628297
$737$	35.0643	1.29161
$738$	−13.4357	−0.494574
$739$	18.0742	0.664872	0.332436	−	0.943126i	$-0.392130\pi$
$739$	18.0742	0.664872	0.332436	+	0.943126i	$0.392130\pi$
$740$	15.7409	0.578646
$741$	30.5338	1.12169
$742$	109.769	4.02975
$743$	40.4259	1.48308	0.741542	−	0.670906i	$-0.234095\pi$
$743$	40.4259	1.48308	0.741542	+	0.670906i	$0.234095\pi$
$744$	−81.6854	−2.99473
$745$	−35.0008	−1.28233
$746$	76.1759	2.78900
$747$	3.56876	0.130574
$748$	−82.7381	−3.02520
$749$	−32.3221	−1.18103
$750$	48.9221	1.78638
$751$	17.7809	0.648834	0.324417	−	0.945914i	$-0.394832\pi$
$751$	17.7809	0.648834	0.324417	+	0.945914i	$0.394832\pi$
$752$	−27.4612	−1.00141
$753$	−20.7362	−0.755668
$754$	77.6579	2.82813
$755$	56.8331	2.06837
$756$	−113.365	−4.12304
$757$	−28.6166	−1.04009	−0.520043	−	0.854140i	$-0.674084\pi$
$757$	−28.6166	−1.04009	−0.520043	+	0.854140i	$0.674084\pi$
$758$	−38.3102	−1.39149
$759$	−4.32593	−0.157021
$760$	−106.143	−3.85021
$761$	−4.05011	−0.146816	−0.0734082	−	0.997302i	$-0.523388\pi$
$761$	−4.05011	−0.146816	−0.0734082	+	0.997302i	$0.523388\pi$
$762$	38.0884	1.37980
$763$	−4.73862	−0.171549
$764$	−42.7639	−1.54714
$765$	−7.76677	−0.280808
$766$	21.9799	0.794165
$767$	53.1978	1.92086
$768$	−49.8093	−1.79734
$769$	14.7109	0.530487	0.265244	−	0.964181i	$-0.414548\pi$
$769$	14.7109	0.530487	0.265244	+	0.964181i	$0.414548\pi$
$770$	227.534	8.19976
$771$	−29.2186	−1.05228
$772$	31.5124	1.13416
$773$	−8.56342	−0.308005	−0.154002	−	0.988070i	$-0.549216\pi$
$773$	−8.56342	−0.308005	−0.154002	+	0.988070i	$0.549216\pi$
$774$	−2.09253	−0.0752143
$775$	76.6014	2.75161
$776$	−95.5253	−3.42916
$777$	−7.37878	−0.264712
$778$	−38.6749	−1.38656
$779$	46.7842	1.67622
$780$	95.6175	3.42366
$781$	−19.9757	−0.714787
$782$	−4.91905	−0.175905
$783$	−44.1648	−1.57832
$784$	90.7432	3.24083
$785$	38.7225	1.38206
$786$	−62.2769	−2.22134
$787$	−21.5824	−0.769330	−0.384665	−	0.923056i	$-0.625683\pi$
$787$	−21.5824	−0.769330	−0.384665	+	0.923056i	$0.625683\pi$
$788$	23.5141	0.837654
$789$	−10.7009	−0.380963
$790$	28.5891	1.01716
$791$	−87.0014	−3.09341
$792$	17.3227	0.615535
$793$	−28.9933	−1.02958
$794$	−66.3440	−2.35446
$795$	52.6537	1.86743
$796$	21.6877	0.768702
$797$	11.3298	0.401320	0.200660	−	0.979661i	$-0.435691\pi$
$797$	11.3298	0.401320	0.200660	+	0.979661i	$0.435691\pi$
$798$	93.0748	3.29481
$799$	17.2385	0.609854
$800$	−26.9798	−0.953879
$801$	1.72050	0.0607908
$802$	81.1428	2.86525
$803$	−75.3436	−2.65882
$804$	44.9165	1.58408
$805$	9.23126	0.325359
$806$	89.0808	3.13774
$807$	−8.52389	−0.300055
$808$	23.2066	0.816406
$809$	−14.5982	−0.513244	−0.256622	−	0.966512i	$-0.582610\pi$
$809$	−14.5982	−0.513244	−0.256622	+	0.966512i	$0.582610\pi$
$810$	−63.8239	−2.24254
$811$	3.90842	0.137243	0.0686216	−	0.997643i	$-0.478140\pi$
$811$	3.90842	0.137243	0.0686216	+	0.997643i	$0.478140\pi$
$812$	161.538	5.66887
$813$	−3.19112	−0.111918
$814$	13.1085	0.459453
$815$	−14.5598	−0.510006
$816$	−33.7002	−1.17974
$817$	7.28634	0.254917
$818$	60.7390	2.12369
$819$	10.6337	0.371573
$820$	146.506	5.11621
$821$	19.8006	0.691047	0.345524	−	0.938410i	$-0.387701\pi$
$821$	19.8006	0.691047	0.345524	+	0.938410i	$0.387701\pi$
$822$	−44.8725	−1.56511
$823$	−3.83510	−0.133683	−0.0668416	−	0.997764i	$-0.521292\pi$
$823$	−3.83510	−0.133683	−0.0668416	+	0.997764i	$0.521292\pi$
$824$	34.5585	1.20390
$825$	68.4722	2.38390
$826$	162.160	5.64227
$827$	37.7819	1.31381	0.656903	−	0.753975i	$-0.271866\pi$
$827$	37.7819	1.31381	0.656903	+	0.753975i	$0.271866\pi$
$828$	1.31466	0.0456877
$829$	−31.4880	−1.09362	−0.546811	−	0.837256i	$-0.684158\pi$
$829$	−31.4880	−1.09362	−0.546811	+	0.837256i	$0.684158\pi$
$830$	−57.0262	−1.97941
$831$	−15.2646	−0.529522
$832$	14.4353	0.500455
$833$	−56.9631	−1.97365
$834$	−45.3715	−1.57109
$835$	−4.39218	−0.151998
$836$	−112.834	−3.90244
$837$	−50.6611	−1.75110
$838$	−60.9438	−2.10527
$839$	46.3153	1.59898	0.799490	−	0.600679i	$-0.205103\pi$
$839$	46.3153	1.59898	0.799490	+	0.600679i	$0.205103\pi$
$840$	155.813	5.37605
$841$	33.9321	1.17007
$842$	28.6466	0.987228
$843$	−30.7365	−1.05862
$844$	42.3031	1.45613
$845$	−8.12367	−0.279463
$846$	−6.75141	−0.232118
$847$	77.1785	2.65188
$848$	−54.2018	−1.86130
$849$	−48.6773	−1.67060
$850$	77.8602	2.67058
$851$	0.531824	0.0182307
$852$	−25.5884	−0.876645
$853$	−27.6240	−0.945828	−0.472914	−	0.881109i	$-0.656798\pi$
$853$	−27.6240	−0.945828	−0.472914	+	0.881109i	$0.656798\pi$
$854$	−88.3789	−3.02426
$855$	−10.5919	−0.362236
$856$	39.3211	1.34397
$857$	48.9285	1.67137	0.835683	−	0.549212i	$-0.185072\pi$
$857$	48.9285	1.67137	0.835683	+	0.549212i	$0.185072\pi$
$858$	79.6272	2.71843
$859$	26.3969	0.900650	0.450325	−	0.892865i	$-0.351308\pi$
$859$	26.3969	0.900650	0.450325	+	0.892865i	$0.351308\pi$
$860$	22.8174	0.778066
$861$	−68.6768	−2.34050
$862$	15.7516	0.536503
$863$	35.0054	1.19160	0.595799	−	0.803134i	$-0.296835\pi$
$863$	35.0054	1.19160	0.595799	+	0.803134i	$0.296835\pi$
$864$	17.8433	0.607043
$865$	−39.9149	−1.35715
$866$	37.4183	1.27153
$867$	−5.31679	−0.180568
$868$	185.299	6.28947
$869$	16.2466	0.551130
$870$	113.549	3.84969
$871$	−26.1855	−0.887261
$872$	5.76470	0.195217
$873$	−9.53238	−0.322622
$874$	−6.70834	−0.226913
$875$	−59.3265	−2.00560
$876$	−96.5135	−3.26089
$877$	7.59709	0.256535	0.128268	−	0.991740i	$-0.459058\pi$
$877$	7.59709	0.256535	0.128268	+	0.991740i	$0.459058\pi$
$878$	74.4713	2.51329
$879$	12.6475	0.426591
$880$	−112.352	−3.78738
$881$	28.6671	0.965818	0.482909	−	0.875670i	$-0.339580\pi$
$881$	28.6671	0.965818	0.482909	+	0.875670i	$0.339580\pi$
$882$	22.3094	0.751197
$883$	−35.0356	−1.17904	−0.589521	−	0.807753i	$-0.700683\pi$
$883$	−35.0356	−1.17904	−0.589521	+	0.807753i	$0.700683\pi$
$884$	61.7876	2.07814
$885$	77.7845	2.61470
$886$	−56.5412	−1.89954
$887$	−51.1100	−1.71611	−0.858053	−	0.513561i	$-0.828326\pi$
$887$	−51.1100	−1.71611	−0.858053	+	0.513561i	$0.828326\pi$
$888$	8.97655	0.301233
$889$	−46.1888	−1.54912
$890$	−27.4923	−0.921543
$891$	−36.2699	−1.21509
$892$	−103.782	−3.47488
$893$	23.5089	0.786697
$894$	−37.3373	−1.24875
$895$	−34.9987	−1.16988
$896$	74.3776	2.48478
$897$	3.23054	0.107865
$898$	91.4804	3.05274
$899$	72.1890	2.40764
$900$	−20.8089	−0.693630
$901$	34.0246	1.13352
$902$	122.005	4.06234
$903$	−10.6960	−0.355940
$904$	105.840	3.52020
$905$	29.3077	0.974220
$906$	60.6271	2.01420
$907$	−29.1580	−0.968175	−0.484087	−	0.875020i	$-0.660848\pi$
$907$	−29.1580	−0.968175	−0.484087	+	0.875020i	$0.660848\pi$
$908$	35.1744	1.16730
$909$	2.31577	0.0768092
$910$	−169.919	−5.63277
$911$	15.0994	0.500264	0.250132	−	0.968212i	$-0.419526\pi$
$911$	15.0994	0.500264	0.250132	+	0.968212i	$0.419526\pi$
$912$	−45.9585	−1.52184
$913$	−32.4069	−1.07251
$914$	−8.67776	−0.287035
$915$	−42.3933	−1.40148
$916$	−61.0627	−2.01757
$917$	75.5216	2.49394
$918$	−51.4936	−1.69954
$919$	−45.0741	−1.48686	−0.743428	−	0.668816i	$-0.766801\pi$
$919$	−45.0741	−1.48686	−0.743428	+	0.668816i	$0.766801\pi$
$920$	−11.2302	−0.370247
$921$	−4.43064	−0.145995
$922$	10.1600	0.334602
$923$	14.9176	0.491018
$924$	165.635	5.44898
$925$	−8.41787	−0.276778
$926$	−11.2598	−0.370019
$927$	3.44856	0.113266
$928$	−25.4256	−0.834638
$929$	42.2910	1.38752	0.693761	−	0.720205i	$-0.255952\pi$
$929$	42.2910	1.38752	0.693761	+	0.720205i	$0.255952\pi$
$930$	130.252	4.27113
$931$	−77.6832	−2.54597
$932$	−36.3107	−1.18940
$933$	22.7065	0.743379
$934$	−69.7642	−2.28275
$935$	70.5277	2.30650
$936$	−12.9363	−0.422837
$937$	−6.96123	−0.227413	−0.113707	−	0.993514i	$-0.536272\pi$
$937$	−6.96123	−0.227413	−0.113707	+	0.993514i	$0.536272\pi$
$938$	−79.8199	−2.60621
$939$	−3.25783	−0.106315
$940$	73.6189	2.40118
$941$	29.0893	0.948284	0.474142	−	0.880448i	$-0.342758\pi$
$941$	29.0893	0.948284	0.474142	+	0.880448i	$0.342758\pi$
$942$	41.3075	1.34587
$943$	4.94986	0.161190
$944$	−80.0715	−2.60611
$945$	96.6347	3.14353
$946$	19.0016	0.617795
$947$	−18.5406	−0.602488	−0.301244	−	0.953547i	$-0.597402\pi$
$947$	−18.5406	−0.602488	−0.301244	+	0.953547i	$0.597402\pi$
$948$	20.8116	0.675929
$949$	56.2656	1.82646
$950$	106.182	3.44499
$951$	13.7985	0.447446
$952$	100.686	3.26324
$953$	53.3908	1.72950	0.864749	−	0.502205i	$-0.167478\pi$
$953$	53.3908	1.72950	0.864749	+	0.502205i	$0.167478\pi$
$954$	−13.3256	−0.431433
$955$	36.4529	1.17959
$956$	−1.45093	−0.0469264
$957$	64.5280	2.08589
$958$	−55.3954	−1.78974
$959$	54.4157	1.75717
$960$	21.1070	0.681226
$961$	51.8075	1.67121
$962$	−9.78925	−0.315618
$963$	3.92381	0.126443
$964$	−7.27213	−0.234219
$965$	−26.8619	−0.864715
$966$	9.84751	0.316838
$967$	−40.8793	−1.31459	−0.657295	−	0.753634i	$-0.728299\pi$
$967$	−40.8793	−1.31459	−0.657295	+	0.753634i	$0.728299\pi$
$968$	−93.8904	−3.01775
$969$	28.8500	0.926794
$970$	152.320	4.89071
$971$	−33.3048	−1.06880	−0.534402	−	0.845231i	$-0.679463\pi$
$971$	−33.3048	−1.06880	−0.534402	+	0.845231i	$0.679463\pi$
$972$	25.3100	0.811820
$973$	55.0208	1.76389
$974$	−24.2344	−0.776519
$975$	−51.1341	−1.63760
$976$	43.6398	1.39687
$977$	−28.1602	−0.900923	−0.450462	−	0.892796i	$-0.648741\pi$
$977$	−28.1602	−0.900923	−0.450462	+	0.892796i	$0.648741\pi$
$978$	−15.5317	−0.496650
$979$	−15.6233	−0.499324
$980$	−243.267	−7.77088
$981$	0.575254	0.0183664
$982$	27.1587	0.866669
$983$	−46.1640	−1.47240	−0.736201	−	0.676763i	$-0.763382\pi$
$983$	−46.1640	−1.47240	−0.736201	+	0.676763i	$0.763382\pi$
$984$	83.5479	2.66341
$985$	−20.0439	−0.638652
$986$	73.3752	2.33674
$987$	−34.5100	−1.09847
$988$	84.2627	2.68075
$989$	0.770911	0.0245135
$990$	−27.6220	−0.877884
$991$	7.13537	0.226662	0.113331	−	0.993557i	$-0.463848\pi$
$991$	7.13537	0.226662	0.113331	+	0.993557i	$0.463848\pi$
$992$	−29.1656	−0.926009
$993$	−33.3238	−1.05750
$994$	45.4725	1.44230
$995$	−18.4871	−0.586080
$996$	−41.5125	−1.31537
$997$	−48.3396	−1.53093	−0.765465	−	0.643478i	$-0.777491\pi$
$997$	−48.3396	−1.53093	−0.765465	+	0.643478i	$0.777491\pi$
$998$	−22.1491	−0.701117
$999$	5.56724	0.176140

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.8	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.8	✓	79	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.50943 q^{2} +1.55716 q^{3} +4.29722 q^{4} -3.66304 q^{5} -3.90758 q^{6} +4.73862 q^{7} -5.76470 q^{8} -0.575254 q^{9} +O(q^{10})\)	\(q-2.50943 q^{2} +1.55716 q^{3} +4.29722 q^{4} -3.66304 q^{5} -3.90758 q^{6} +4.73862 q^{7} -5.76470 q^{8} -0.575254 q^{9} +9.19213 q^{10} +5.22371 q^{11} +6.69145 q^{12} -3.90099 q^{13} -11.8912 q^{14} -5.70394 q^{15} +5.87164 q^{16} -3.68586 q^{17} +1.44356 q^{18} -5.02658 q^{19} -15.7409 q^{20} +7.37878 q^{21} -13.1085 q^{22} -0.531824 q^{23} -8.97655 q^{24} +8.41787 q^{25} +9.78925 q^{26} -5.56724 q^{27} +20.3629 q^{28} +7.93297 q^{29} +14.3136 q^{30} +9.09986 q^{31} -3.20506 q^{32} +8.13415 q^{33} +9.24940 q^{34} -17.3577 q^{35} -2.47199 q^{36} -1.00000 q^{37} +12.6138 q^{38} -6.07447 q^{39} +21.1163 q^{40} -9.30734 q^{41} -18.5165 q^{42} -1.44956 q^{43} +22.4474 q^{44} +2.10718 q^{45} +1.33457 q^{46} -4.67692 q^{47} +9.14309 q^{48} +15.4545 q^{49} -21.1240 q^{50} -5.73948 q^{51} -16.7634 q^{52} -9.23111 q^{53} +13.9706 q^{54} -19.1347 q^{55} -27.3167 q^{56} -7.82719 q^{57} -19.9072 q^{58} -13.6370 q^{59} -24.5111 q^{60} +7.43229 q^{61} -22.8354 q^{62} -2.72591 q^{63} -3.70043 q^{64} +14.2895 q^{65} -20.4120 q^{66} +6.71252 q^{67} -15.8390 q^{68} -0.828134 q^{69} +43.5580 q^{70} -3.82404 q^{71} +3.31617 q^{72} -14.4234 q^{73} +2.50943 q^{74} +13.1080 q^{75} -21.6003 q^{76} +24.7532 q^{77} +15.2434 q^{78} +3.11017 q^{79} -21.5081 q^{80} -6.94332 q^{81} +23.3561 q^{82} -6.20380 q^{83} +31.7082 q^{84} +13.5015 q^{85} +3.63757 q^{86} +12.3529 q^{87} -30.1131 q^{88} -2.99085 q^{89} -5.28781 q^{90} -18.4853 q^{91} -2.28536 q^{92} +14.1699 q^{93} +11.7364 q^{94} +18.4126 q^{95} -4.99079 q^{96} +16.5707 q^{97} -38.7819 q^{98} -3.00496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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