LMFDB - Embedded newform 4033.2.a.d.1.51

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			1.51
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)

$f(q)$	$=$	$q+0.764117 q^{2} +2.96846 q^{3} -1.41612 q^{4} -3.17843 q^{5} +2.26826 q^{6} +2.68082 q^{7} -2.61032 q^{8} +5.81178 q^{9} +O(q^{10})$	\(q+0.764117 q^{2} +2.96846 q^{3} -1.41612 q^{4} -3.17843 q^{5} +2.26826 q^{6} +2.68082 q^{7} -2.61032 q^{8} +5.81178 q^{9} -2.42870 q^{10} -5.47292 q^{11} -4.20372 q^{12} +6.18115 q^{13} +2.04846 q^{14} -9.43506 q^{15} +0.837658 q^{16} -3.41961 q^{17} +4.44088 q^{18} -6.86830 q^{19} +4.50106 q^{20} +7.95793 q^{21} -4.18195 q^{22} -2.31526 q^{23} -7.74864 q^{24} +5.10243 q^{25} +4.72312 q^{26} +8.34667 q^{27} -3.79638 q^{28} -6.01455 q^{29} -7.20950 q^{30} +4.93756 q^{31} +5.86071 q^{32} -16.2462 q^{33} -2.61298 q^{34} -8.52082 q^{35} -8.23020 q^{36} -1.00000 q^{37} -5.24819 q^{38} +18.3485 q^{39} +8.29673 q^{40} +0.425505 q^{41} +6.08079 q^{42} +0.301906 q^{43} +7.75033 q^{44} -18.4724 q^{45} -1.76913 q^{46} -9.03645 q^{47} +2.48656 q^{48} +0.186814 q^{49} +3.89886 q^{50} -10.1510 q^{51} -8.75328 q^{52} -3.14454 q^{53} +6.37784 q^{54} +17.3953 q^{55} -6.99781 q^{56} -20.3883 q^{57} -4.59582 q^{58} +3.02866 q^{59} +13.3612 q^{60} -11.7519 q^{61} +3.77288 q^{62} +15.5804 q^{63} +2.80295 q^{64} -19.6464 q^{65} -12.4140 q^{66} +5.42120 q^{67} +4.84259 q^{68} -6.87277 q^{69} -6.51090 q^{70} +14.8811 q^{71} -15.1706 q^{72} -10.8972 q^{73} -0.764117 q^{74} +15.1464 q^{75} +9.72636 q^{76} -14.6719 q^{77} +14.0204 q^{78} -15.9455 q^{79} -2.66244 q^{80} +7.34145 q^{81} +0.325136 q^{82} -12.2046 q^{83} -11.2694 q^{84} +10.8690 q^{85} +0.230692 q^{86} -17.8540 q^{87} +14.2861 q^{88} -5.03245 q^{89} -14.1150 q^{90} +16.5706 q^{91} +3.27870 q^{92} +14.6570 q^{93} -6.90491 q^{94} +21.8304 q^{95} +17.3973 q^{96} -8.71861 q^{97} +0.142748 q^{98} -31.8074 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.764117	0.540313	0.270156	−	0.962816i	$-0.412925\pi$
$2$	0.764117	0.540313	0.270156	+	0.962816i	$0.412925\pi$
$3$	2.96846	1.71384	0.856922	−	0.515446i	$-0.172374\pi$
$3$	2.96846	1.71384	0.856922	+	0.515446i	$0.172374\pi$
$4$	−1.41612	−0.708062
$5$	−3.17843	−1.42144	−0.710719	−	0.703476i	$-0.751630\pi$
$5$	−3.17843	−1.42144	−0.710719	+	0.703476i	$0.751630\pi$
$6$	2.26826	0.926011
$7$	2.68082	1.01326	0.506628	−	0.862165i	$-0.330892\pi$
$7$	2.68082	1.01326	0.506628	+	0.862165i	$0.330892\pi$
$8$	−2.61032	−0.922888
$9$	5.81178	1.93726
$10$	−2.42870	−0.768021
$11$	−5.47292	−1.65015	−0.825074	−	0.565025i	$-0.808866\pi$
$11$	−5.47292	−1.65015	−0.825074	+	0.565025i	$0.808866\pi$
$12$	−4.20372	−1.21351
$13$	6.18115	1.71434	0.857171	−	0.515031i	$-0.172220\pi$
$13$	6.18115	1.71434	0.857171	+	0.515031i	$0.172220\pi$
$14$	2.04846	0.547475
$15$	−9.43506	−2.43612
$16$	0.837658	0.209414
$17$	−3.41961	−0.829377	−0.414688	−	0.909963i	$-0.636109\pi$
$17$	−3.41961	−0.829377	−0.414688	+	0.909963i	$0.636109\pi$
$18$	4.44088	1.04673
$19$	−6.86830	−1.57570	−0.787848	−	0.615870i	$-0.788805\pi$
$19$	−6.86830	−1.57570	−0.787848	+	0.615870i	$0.788805\pi$
$20$	4.50106	1.00647
$21$	7.95793	1.73656
$22$	−4.18195	−0.891595
$23$	−2.31526	−0.482766	−0.241383	−	0.970430i	$-0.577601\pi$
$23$	−2.31526	−0.482766	−0.241383	+	0.970430i	$0.577601\pi$
$24$	−7.74864	−1.58169
$25$	5.10243	1.02049
$26$	4.72312	0.926281
$27$	8.34667	1.60632
$28$	−3.79638	−0.717448
$29$	−6.01455	−1.11687	−0.558437	−	0.829547i	$-0.688599\pi$
$29$	−6.01455	−1.11687	−0.558437	+	0.829547i	$0.688599\pi$
$30$	−7.20950	−1.31627
$31$	4.93756	0.886812	0.443406	−	0.896321i	$-0.353770\pi$
$31$	4.93756	0.886812	0.443406	+	0.896321i	$0.353770\pi$
$32$	5.86071	1.03604
$33$	−16.2462	−2.82809
$34$	−2.61298	−0.448123
$35$	−8.52082	−1.44028
$36$	−8.23020	−1.37170
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−5.24819	−0.851368
$39$	18.3485	2.93812
$40$	8.29673	1.31183
$41$	0.425505	0.0664528	0.0332264	−	0.999448i	$-0.489422\pi$
$41$	0.425505	0.0664528	0.0332264	+	0.999448i	$0.489422\pi$
$42$	6.08079	0.938287
$43$	0.301906	0.0460403	0.0230202	−	0.999735i	$-0.492672\pi$
$43$	0.301906	0.0460403	0.0230202	+	0.999735i	$0.492672\pi$
$44$	7.75033	1.16841
$45$	−18.4724	−2.75370
$46$	−1.76913	−0.260844
$47$	−9.03645	−1.31810	−0.659051	−	0.752099i	$-0.729042\pi$
$47$	−9.03645	−1.31810	−0.659051	+	0.752099i	$0.729042\pi$
$48$	2.48656	0.358904
$49$	0.186814	0.0266877
$50$	3.89886	0.551382
$51$	−10.1510	−1.42142
$52$	−8.75328	−1.21386
$53$	−3.14454	−0.431936	−0.215968	−	0.976400i	$-0.569291\pi$
$53$	−3.14454	−0.431936	−0.215968	+	0.976400i	$0.569291\pi$
$54$	6.37784	0.867913
$55$	17.3953	2.34558
$56$	−6.99781	−0.935121
$57$	−20.3883	−2.70050
$58$	−4.59582	−0.603461
$59$	3.02866	0.394298	0.197149	−	0.980374i	$-0.436832\pi$
$59$	3.02866	0.394298	0.197149	+	0.980374i	$0.436832\pi$
$60$	13.3612	1.72493
$61$	−11.7519	−1.50468	−0.752338	−	0.658777i	$-0.771074\pi$
$61$	−11.7519	−1.50468	−0.752338	+	0.658777i	$0.771074\pi$
$62$	3.77288	0.479156
$63$	15.5804	1.96294
$64$	2.80295	0.350369
$65$	−19.6464	−2.43683
$66$	−12.4140	−1.52805
$67$	5.42120	0.662306	0.331153	−	0.943577i	$-0.392562\pi$
$67$	5.42120	0.662306	0.331153	+	0.943577i	$0.392562\pi$
$68$	4.84259	0.587250
$69$	−6.87277	−0.827385
$70$	−6.51090	−0.778202
$71$	14.8811	1.76606	0.883030	−	0.469317i	$-0.155500\pi$
$71$	14.8811	1.76606	0.883030	+	0.469317i	$0.155500\pi$
$72$	−15.1706	−1.78787
$73$	−10.8972	−1.27542	−0.637710	−	0.770276i	$-0.720118\pi$
$73$	−10.8972	−1.27542	−0.637710	+	0.770276i	$0.720118\pi$
$74$	−0.764117	−0.0888268
$75$	15.1464	1.74895
$76$	9.72636	1.11569
$77$	−14.6719	−1.67202
$78$	14.0204	1.58750
$79$	−15.9455	−1.79401	−0.897007	−	0.442016i	$-0.854263\pi$
$79$	−15.9455	−1.79401	−0.897007	+	0.442016i	$0.854263\pi$
$80$	−2.66244	−0.297670
$81$	7.34145	0.815717
$82$	0.325136	0.0359053
$83$	−12.2046	−1.33963	−0.669817	−	0.742526i	$-0.733627\pi$
$83$	−12.2046	−1.33963	−0.669817	+	0.742526i	$0.733627\pi$
$84$	−11.2694	−1.22959
$85$	10.8690	1.17891
$86$	0.230692	0.0248762
$87$	−17.8540	−1.91415
$88$	14.2861	1.52290
$89$	−5.03245	−0.533438	−0.266719	−	0.963774i	$-0.585940\pi$
$89$	−5.03245	−0.533438	−0.266719	+	0.963774i	$0.585940\pi$
$90$	−14.1150	−1.48786
$91$	16.5706	1.73707
$92$	3.27870	0.341828
$93$	14.6570	1.51986
$94$	−6.90491	−0.712187
$95$	21.8304	2.23975
$96$	17.3973	1.77561
$97$	−8.71861	−0.885241	−0.442620	−	0.896709i	$-0.645951\pi$
$97$	−8.71861	−0.885241	−0.442620	+	0.896709i	$0.645951\pi$
$98$	0.142748	0.0144197
$99$	−31.8074	−3.19676
$100$	−7.22568	−0.722568
$101$	−1.73650	−0.172788	−0.0863939	−	0.996261i	$-0.527534\pi$
$101$	−1.73650	−0.172788	−0.0863939	+	0.996261i	$0.527534\pi$
$102$	−7.75654	−0.768012
$103$	−7.66401	−0.755158	−0.377579	−	0.925977i	$-0.623243\pi$
$103$	−7.66401	−0.755158	−0.377579	+	0.925977i	$0.623243\pi$
$104$	−16.1348	−1.58215
$105$	−25.2937	−2.46842
$106$	−2.40280	−0.233381
$107$	−8.32792	−0.805090	−0.402545	−	0.915400i	$-0.631874\pi$
$107$	−8.32792	−0.805090	−0.402545	+	0.915400i	$0.631874\pi$
$108$	−11.8199	−1.13737
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	13.2921	1.26735
$111$	−2.96846	−0.281754
$112$	2.24561	0.212190
$113$	0.962559	0.0905499	0.0452750	−	0.998975i	$-0.485584\pi$
$113$	0.962559	0.0905499	0.0452750	+	0.998975i	$0.485584\pi$
$114$	−15.5791	−1.45911
$115$	7.35890	0.686221
$116$	8.51735	0.790816
$117$	35.9235	3.32113
$118$	2.31425	0.213044
$119$	−9.16737	−0.840371
$120$	24.6285	2.24827
$121$	18.9528	1.72299
$122$	−8.97983	−0.812996
$123$	1.26310	0.113890
$124$	−6.99220	−0.627918
$125$	−0.325578	−0.0291205
$126$	11.9052	1.06060
$127$	9.96139	0.883930	0.441965	−	0.897032i	$-0.354282\pi$
$127$	9.96139	0.883930	0.441965	+	0.897032i	$0.354282\pi$
$128$	−9.57963	−0.846728
$129$	0.896199	0.0789059
$130$	−15.0121	−1.31665
$131$	1.29448	0.113100	0.0565498	−	0.998400i	$-0.481990\pi$
$131$	1.29448	0.113100	0.0565498	+	0.998400i	$0.481990\pi$
$132$	23.0066	2.00247
$133$	−18.4127	−1.59658
$134$	4.14244	0.357852
$135$	−26.5293	−2.28328
$136$	8.92627	0.765422
$137$	−5.80697	−0.496123	−0.248062	−	0.968744i	$-0.579794\pi$
$137$	−5.80697	−0.496123	−0.248062	+	0.968744i	$0.579794\pi$
$138$	−5.25161	−0.447046
$139$	−0.680828	−0.0577471	−0.0288735	−	0.999583i	$-0.509192\pi$
$139$	−0.680828	−0.0577471	−0.0288735	+	0.999583i	$0.509192\pi$
$140$	12.0665	1.01981
$141$	−26.8244	−2.25902
$142$	11.3709	0.954224
$143$	−33.8289	−2.82892
$144$	4.86828	0.405690
$145$	19.1168	1.58757
$146$	−8.32674	−0.689126
$147$	0.554551	0.0457386
$148$	1.41612	0.116405
$149$	22.1476	1.81440	0.907199	−	0.420702i	$-0.138216\pi$
$149$	22.1476	1.81440	0.907199	+	0.420702i	$0.138216\pi$
$150$	11.5736	0.944982
$151$	24.3110	1.97840	0.989200	−	0.146570i	$-0.0468234\pi$
$151$	24.3110	1.97840	0.989200	+	0.146570i	$0.0468234\pi$
$152$	17.9285	1.45419
$153$	−19.8740	−1.60672
$154$	−11.2111	−0.903414
$155$	−15.6937	−1.26055
$156$	−25.9838	−2.08037
$157$	−4.35372	−0.347465	−0.173732	−	0.984793i	$-0.555583\pi$
$157$	−4.35372	−0.347465	−0.173732	+	0.984793i	$0.555583\pi$
$158$	−12.1843	−0.969329
$159$	−9.33447	−0.740272
$160$	−18.6279	−1.47266
$161$	−6.20681	−0.489165
$162$	5.60973	0.440742
$163$	−16.4290	−1.28682	−0.643411	−	0.765521i	$-0.722481\pi$
$163$	−16.4290	−1.28682	−0.643411	+	0.765521i	$0.722481\pi$
$164$	−0.602568	−0.0470527
$165$	51.6373	4.01996
$166$	−9.32578	−0.723821
$167$	1.42188	0.110028	0.0550141	−	0.998486i	$-0.482480\pi$
$167$	1.42188	0.110028	0.0550141	+	0.998486i	$0.482480\pi$
$168$	−20.7727	−1.60265
$169$	25.2066	1.93897
$170$	8.30519	0.636979
$171$	−39.9170	−3.05253
$172$	−0.427537	−0.0325994
$173$	3.06875	0.233313	0.116656	−	0.993172i	$-0.462782\pi$
$173$	3.06875	0.233313	0.116656	+	0.993172i	$0.462782\pi$
$174$	−13.6425	−1.03424
$175$	13.6787	1.03401
$176$	−4.58443	−0.345565
$177$	8.99047	0.675765
$178$	−3.84538	−0.288224
$179$	21.2457	1.58798	0.793989	−	0.607932i	$-0.208001\pi$
$179$	21.2457	1.58798	0.793989	+	0.607932i	$0.208001\pi$
$180$	26.1592	1.94979
$181$	18.7112	1.39079	0.695396	−	0.718627i	$-0.255229\pi$
$181$	18.7112	1.39079	0.695396	+	0.718627i	$0.255229\pi$
$182$	12.6619	0.938560
$183$	−34.8851	−2.57878
$184$	6.04358	0.445538
$185$	3.17843	0.233683
$186$	11.1996	0.821198
$187$	18.7152	1.36859
$188$	12.7967	0.933298
$189$	22.3759	1.62761
$190$	16.6810	1.21017
$191$	−1.47734	−0.106896	−0.0534482	−	0.998571i	$-0.517021\pi$
$191$	−1.47734	−0.106896	−0.0534482	+	0.998571i	$0.517021\pi$
$192$	8.32047	0.600478
$193$	3.54922	0.255478	0.127739	−	0.991808i	$-0.459228\pi$
$193$	3.54922	0.255478	0.127739	+	0.991808i	$0.459228\pi$
$194$	−6.66204	−0.478307
$195$	−58.3195	−4.17635
$196$	−0.264552	−0.0188966
$197$	10.3693	0.738779	0.369389	−	0.929275i	$-0.379567\pi$
$197$	10.3693	0.738779	0.369389	+	0.929275i	$0.379567\pi$
$198$	−24.3046	−1.72725
$199$	5.41620	0.383944	0.191972	−	0.981400i	$-0.438512\pi$
$199$	5.41620	0.383944	0.191972	+	0.981400i	$0.438512\pi$
$200$	−13.3190	−0.941795
$201$	16.0927	1.13509
$202$	−1.32689	−0.0933594
$203$	−16.1239	−1.13168
$204$	14.3751	1.00646
$205$	−1.35244	−0.0944585
$206$	−5.85621	−0.408021
$207$	−13.4558	−0.935242
$208$	5.17769	0.359008
$209$	37.5896	2.60013
$210$	−19.3274	−1.33372
$211$	10.1962	0.701933	0.350966	−	0.936388i	$-0.385853\pi$
$211$	10.1962	0.701933	0.350966	+	0.936388i	$0.385853\pi$
$212$	4.45307	0.305838
$213$	44.1740	3.02675
$214$	−6.36351	−0.435000
$215$	−0.959589	−0.0654435
$216$	−21.7875	−1.48245
$217$	13.2367	0.898568
$218$	−0.764117	−0.0517526
$219$	−32.3479	−2.18587
$220$	−24.6339	−1.66082
$221$	−21.1371	−1.42184
$222$	−2.26826	−0.152235
$223$	−19.5041	−1.30609	−0.653044	−	0.757320i	$-0.726509\pi$
$223$	−19.5041	−1.30609	−0.653044	+	0.757320i	$0.726509\pi$
$224$	15.7115	1.04977
$225$	29.6542	1.97695
$226$	0.735508	0.0489253
$227$	7.20447	0.478177	0.239089	−	0.970998i	$-0.423151\pi$
$227$	7.20447	0.478177	0.239089	+	0.970998i	$0.423151\pi$
$228$	28.8724	1.91212
$229$	−9.88660	−0.653325	−0.326662	−	0.945141i	$-0.605924\pi$
$229$	−9.88660	−0.653325	−0.326662	+	0.945141i	$0.605924\pi$
$230$	5.62307	0.370774
$231$	−43.5531	−2.86558
$232$	15.6999	1.03075
$233$	−17.0144	−1.11465	−0.557324	−	0.830295i	$-0.688172\pi$
$233$	−17.0144	−1.11465	−0.557324	+	0.830295i	$0.688172\pi$
$234$	27.4498	1.79445
$235$	28.7217	1.87360
$236$	−4.28896	−0.279187
$237$	−47.3338	−3.07466
$238$	−7.00494	−0.454063
$239$	−13.4994	−0.873204	−0.436602	−	0.899655i	$-0.643818\pi$
$239$	−13.4994	−0.873204	−0.436602	+	0.899655i	$0.643818\pi$
$240$	−7.90335	−0.510159
$241$	−3.38342	−0.217945	−0.108973	−	0.994045i	$-0.534756\pi$
$241$	−3.38342	−0.217945	−0.108973	+	0.994045i	$0.534756\pi$
$242$	14.4822	0.930951
$243$	−3.24718	−0.208307
$244$	16.6422	1.06540
$245$	−0.593776	−0.0379350
$246$	0.965155	0.0615360
$247$	−42.4540	−2.70128
$248$	−12.8886	−0.818428
$249$	−36.2291	−2.29592
$250$	−0.248780	−0.0157342
$251$	−15.6153	−0.985629	−0.492814	−	0.870134i	$-0.664032\pi$
$251$	−15.6153	−0.985629	−0.492814	+	0.870134i	$0.664032\pi$
$252$	−22.0637	−1.38988
$253$	12.6712	0.796634
$254$	7.61167	0.477599
$255$	32.2642	2.02046
$256$	−12.9259	−0.807867
$257$	−29.8900	−1.86449	−0.932244	−	0.361831i	$-0.882152\pi$
$257$	−29.8900	−1.86449	−0.932244	+	0.361831i	$0.882152\pi$
$258$	0.684801	0.0426338
$259$	−2.68082	−0.166578
$260$	27.8217	1.72543
$261$	−34.9552	−2.16367
$262$	0.989138	0.0611092
$263$	−17.6263	−1.08688	−0.543441	−	0.839447i	$-0.682879\pi$
$263$	−17.6263	−1.08688	−0.543441	+	0.839447i	$0.682879\pi$
$264$	42.4077	2.61001
$265$	9.99472	0.613971
$266$	−14.0695	−0.862654
$267$	−14.9386	−0.914230
$268$	−7.67710	−0.468954
$269$	2.85781	0.174244	0.0871220	−	0.996198i	$-0.472233\pi$
$269$	2.85781	0.174244	0.0871220	+	0.996198i	$0.472233\pi$
$270$	−20.2715	−1.23369
$271$	−8.35008	−0.507231	−0.253616	−	0.967305i	$-0.581620\pi$
$271$	−8.35008	−0.507231	−0.253616	+	0.967305i	$0.581620\pi$
$272$	−2.86446	−0.173683
$273$	49.1892	2.97706
$274$	−4.43721	−0.268062
$275$	−27.9252	−1.68395
$276$	9.73270	0.585840
$277$	20.6795	1.24251	0.621255	−	0.783609i	$-0.286623\pi$
$277$	20.6795	1.24251	0.621255	+	0.783609i	$0.286623\pi$
$278$	−0.520233	−0.0312015
$279$	28.6960	1.71799
$280$	22.2421	1.32922
$281$	−14.7188	−0.878051	−0.439025	−	0.898475i	$-0.644676\pi$
$281$	−14.7188	−0.878051	−0.439025	+	0.898475i	$0.644676\pi$
$282$	−20.4970	−1.22058
$283$	15.7014	0.933351	0.466675	−	0.884429i	$-0.345452\pi$
$283$	15.7014	0.933351	0.466675	+	0.884429i	$0.345452\pi$
$284$	−21.0735	−1.25048
$285$	64.8028	3.83859
$286$	−25.8493	−1.52850
$287$	1.14070	0.0673337
$288$	34.0612	2.00707
$289$	−5.30628	−0.312134
$290$	14.6075	0.857782
$291$	−25.8809	−1.51716
$292$	15.4318	0.903077
$293$	27.5871	1.61166	0.805829	−	0.592149i	$-0.201720\pi$
$293$	27.5871	1.61166	0.805829	+	0.592149i	$0.201720\pi$
$294$	0.423742	0.0247132
$295$	−9.62639	−0.560470
$296$	2.61032	0.151722
$297$	−45.6806	−2.65066
$298$	16.9233	0.980342
$299$	−14.3110	−0.827626
$300$	−21.4492	−1.23837
$301$	0.809358	0.0466506
$302$	18.5765	1.06895
$303$	−5.15472	−0.296131
$304$	−5.75328	−0.329973
$305$	37.3526	2.13880
$306$	−15.1861	−0.868130
$307$	−7.75216	−0.442439	−0.221220	−	0.975224i	$-0.571004\pi$
$307$	−7.75216	−0.442439	−0.221220	+	0.975224i	$0.571004\pi$
$308$	20.7773	1.18390
$309$	−22.7504	−1.29422
$310$	−11.9918	−0.681090
$311$	8.37688	0.475009	0.237505	−	0.971386i	$-0.423671\pi$
$311$	8.37688	0.475009	0.237505	+	0.971386i	$0.423671\pi$
$312$	−47.8955	−2.71155
$313$	−6.89200	−0.389559	−0.194779	−	0.980847i	$-0.562399\pi$
$313$	−6.89200	−0.389559	−0.194779	+	0.980847i	$0.562399\pi$
$314$	−3.32675	−0.187740
$315$	−49.5211	−2.79020
$316$	22.5809	1.27027
$317$	−32.8834	−1.84692	−0.923458	−	0.383698i	$-0.874650\pi$
$317$	−32.8834	−1.84692	−0.923458	+	0.383698i	$0.874650\pi$
$318$	−7.13263	−0.399978
$319$	32.9171	1.84300
$320$	−8.90900	−0.498028
$321$	−24.7211	−1.37980
$322$	−4.74273	−0.264302
$323$	23.4869	1.30685
$324$	−10.3964	−0.577578
$325$	31.5389	1.74946
$326$	−12.5537	−0.695286
$327$	−2.96846	−0.164156
$328$	−1.11070	−0.0613284
$329$	−24.2251	−1.33557
$330$	39.4570	2.17204
$331$	29.2120	1.60563	0.802817	−	0.596225i	$-0.203333\pi$
$331$	29.2120	1.60563	0.802817	+	0.596225i	$0.203333\pi$
$332$	17.2833	0.948544
$333$	−5.81178	−0.318484
$334$	1.08648	0.0594497
$335$	−17.2309	−0.941426
$336$	6.66602	0.363661
$337$	−16.6108	−0.904847	−0.452424	−	0.891803i	$-0.649440\pi$
$337$	−16.6108	−0.904847	−0.452424	+	0.891803i	$0.649440\pi$
$338$	19.2608	1.04765
$339$	2.85732	0.155188
$340$	−15.3918	−0.834740
$341$	−27.0229	−1.46337
$342$	−30.5013	−1.64932
$343$	−18.2649	−0.986214
$344$	−0.788073	−0.0424900
$345$	21.8446	1.17608
$346$	2.34488	0.126062
$347$	20.1107	1.07960	0.539799	−	0.841794i	$-0.318500\pi$
$347$	20.1107	1.07960	0.539799	+	0.841794i	$0.318500\pi$
$348$	25.2834	1.35533
$349$	27.6158	1.47824	0.739121	−	0.673573i	$-0.235241\pi$
$349$	27.6158	1.47824	0.739121	+	0.673573i	$0.235241\pi$
$350$	10.4522	0.558691
$351$	51.5920	2.75378
$352$	−32.0752	−1.70961
$353$	−17.3079	−0.921209	−0.460605	−	0.887605i	$-0.652367\pi$
$353$	−17.3079	−0.921209	−0.460605	+	0.887605i	$0.652367\pi$
$354$	6.86977	0.365124
$355$	−47.2985	−2.51034
$356$	7.12657	0.377708
$357$	−27.2130	−1.44026
$358$	16.2342	0.858005
$359$	24.4777	1.29188	0.645941	−	0.763387i	$-0.276465\pi$
$359$	24.4777	1.29188	0.645941	+	0.763387i	$0.276465\pi$
$360$	48.2188	2.54135
$361$	28.1735	1.48282
$362$	14.2975	0.751462
$363$	56.2608	2.95293
$364$	−23.4660	−1.22995
$365$	34.6360	1.81293
$366$	−26.6563	−1.39335
$367$	27.9878	1.46095	0.730477	−	0.682938i	$-0.239298\pi$
$367$	27.9878	1.46095	0.730477	+	0.682938i	$0.239298\pi$
$368$	−1.93940	−0.101098
$369$	2.47294	0.128736
$370$	2.42870	0.126262
$371$	−8.42997	−0.437662
$372$	−20.7561	−1.07615
$373$	−4.25335	−0.220230	−0.110115	−	0.993919i	$-0.535122\pi$
$373$	−4.25335	−0.220230	−0.110115	+	0.993919i	$0.535122\pi$
$374$	14.3006	0.739468
$375$	−0.966466	−0.0499081
$376$	23.5880	1.21646
$377$	−37.1768	−1.91470
$378$	17.0979	0.879419
$379$	−16.9148	−0.868857	−0.434429	−	0.900706i	$-0.643050\pi$
$379$	−16.9148	−0.868857	−0.434429	+	0.900706i	$0.643050\pi$
$380$	−30.9146	−1.58588
$381$	29.5700	1.51492
$382$	−1.12886	−0.0577575
$383$	−28.8350	−1.47340	−0.736701	−	0.676219i	$-0.763617\pi$
$383$	−28.8350	−1.47340	−0.736701	+	0.676219i	$0.763617\pi$
$384$	−28.4368	−1.45116
$385$	46.6337	2.37668
$386$	2.71202	0.138038
$387$	1.75461	0.0891920
$388$	12.3466	0.626806
$389$	−9.21849	−0.467396	−0.233698	−	0.972309i	$-0.575083\pi$
$389$	−9.21849	−0.467396	−0.233698	+	0.972309i	$0.575083\pi$
$390$	−44.5630	−2.25653
$391$	7.91729	0.400395
$392$	−0.487645	−0.0246298
$393$	3.84263	0.193835
$394$	7.92333	0.399172
$395$	50.6818	2.55008
$396$	45.0432	2.26351
$397$	23.3992	1.17437	0.587187	−	0.809451i	$-0.300235\pi$
$397$	23.3992	1.17437	0.587187	+	0.809451i	$0.300235\pi$
$398$	4.13862	0.207450
$399$	−54.6574	−2.73629
$400$	4.27409	0.213705
$401$	32.7537	1.63564	0.817820	−	0.575474i	$-0.195183\pi$
$401$	32.7537	1.63564	0.817820	+	0.575474i	$0.195183\pi$
$402$	12.2967	0.613302
$403$	30.5198	1.52030
$404$	2.45909	0.122344
$405$	−23.3343	−1.15949
$406$	−12.3206	−0.611460
$407$	5.47292	0.271283
$408$	26.4973	1.31181
$409$	32.4346	1.60379	0.801894	−	0.597467i	$-0.203826\pi$
$409$	32.4346	1.60379	0.801894	+	0.597467i	$0.203826\pi$
$410$	−1.03342	−0.0510371
$411$	−17.2378	−0.850277
$412$	10.8532	0.534699
$413$	8.11930	0.399525
$414$	−10.2818	−0.505323
$415$	38.7916	1.90421
$416$	36.2259	1.77612
$417$	−2.02101	−0.0989695
$418$	28.7229	1.40488
$419$	27.9968	1.36773	0.683867	−	0.729607i	$-0.260297\pi$
$419$	27.9968	1.36773	0.683867	+	0.729607i	$0.260297\pi$
$420$	35.8191	1.74779
$421$	25.1425	1.22537	0.612685	−	0.790327i	$-0.290089\pi$
$421$	25.1425	1.22537	0.612685	+	0.790327i	$0.290089\pi$
$422$	7.79107	0.379263
$423$	−52.5178	−2.55350
$424$	8.20827	0.398629
$425$	−17.4483	−0.846368
$426$	33.7541	1.63539
$427$	−31.5048	−1.52462
$428$	11.7934	0.570054
$429$	−100.420	−4.84832
$430$	−0.733239	−0.0353599
$431$	−0.534023	−0.0257230	−0.0128615	−	0.999917i	$-0.504094\pi$
$431$	−0.534023	−0.0257230	−0.0128615	+	0.999917i	$0.504094\pi$
$432$	6.99165	0.336386
$433$	−22.0669	−1.06047	−0.530233	−	0.847852i	$-0.677895\pi$
$433$	−22.0669	−1.06047	−0.530233	+	0.847852i	$0.677895\pi$
$434$	10.1144	0.485507
$435$	56.7476	2.72084
$436$	1.41612	0.0678201
$437$	15.9019	0.760691
$438$	−24.7176	−1.18105
$439$	12.0073	0.573078	0.286539	−	0.958069i	$-0.407495\pi$
$439$	12.0073	0.573078	0.286539	+	0.958069i	$0.407495\pi$
$440$	−45.4073	−2.16471
$441$	1.08572	0.0517011
$442$	−16.1512	−0.768236
$443$	−28.0077	−1.33069	−0.665344	−	0.746537i	$-0.731715\pi$
$443$	−28.0077	−1.33069	−0.665344	+	0.746537i	$0.731715\pi$
$444$	4.20372	0.199499
$445$	15.9953	0.758250
$446$	−14.9034	−0.705696
$447$	65.7442	3.10959
$448$	7.51423	0.355014
$449$	−10.3898	−0.490323	−0.245162	−	0.969482i	$-0.578841\pi$
$449$	−10.3898	−0.490323	−0.245162	+	0.969482i	$0.578841\pi$
$450$	22.6593	1.06817
$451$	−2.32876	−0.109657
$452$	−1.36310	−0.0641150
$453$	72.1663	3.39067
$454$	5.50506	0.258365
$455$	−52.6684	−2.46913
$456$	53.2200	2.49225
$457$	5.21186	0.243801	0.121900	−	0.992542i	$-0.461101\pi$
$457$	5.21186	0.243801	0.121900	+	0.992542i	$0.461101\pi$
$458$	−7.55452	−0.353000
$459$	−28.5423	−1.33224
$460$	−10.4211	−0.485887
$461$	−21.9567	−1.02263	−0.511313	−	0.859394i	$-0.670841\pi$
$461$	−21.9567	−1.02263	−0.511313	+	0.859394i	$0.670841\pi$
$462$	−33.2797	−1.54831
$463$	−1.29776	−0.0603120	−0.0301560	−	0.999545i	$-0.509600\pi$
$463$	−1.29776	−0.0603120	−0.0301560	+	0.999545i	$0.509600\pi$
$464$	−5.03813	−0.233889
$465$	−46.5862	−2.16038
$466$	−13.0010	−0.602259
$467$	39.7870	1.84112	0.920561	−	0.390599i	$-0.127732\pi$
$467$	39.7870	1.84112	0.920561	+	0.390599i	$0.127732\pi$
$468$	−50.8721	−2.35157
$469$	14.5333	0.671085
$470$	21.9468	1.01233
$471$	−12.9239	−0.595500
$472$	−7.90577	−0.363893
$473$	−1.65231	−0.0759733
$474$	−36.1686	−1.66128
$475$	−35.0450	−1.60798
$476$	12.9821	0.595035
$477$	−18.2754	−0.836773
$478$	−10.3151	−0.471803
$479$	−36.3758	−1.66205	−0.831026	−	0.556233i	$-0.812246\pi$
$479$	−36.3758	−1.66205	−0.831026	+	0.556233i	$0.812246\pi$
$480$	−55.2962	−2.52391
$481$	−6.18115	−0.281836
$482$	−2.58533	−0.117759
$483$	−18.4247	−0.838352
$484$	−26.8396	−1.21998
$485$	27.7115	1.25832
$486$	−2.48123	−0.112551
$487$	−4.08643	−0.185174	−0.0925870	−	0.995705i	$-0.529514\pi$
$487$	−4.08643	−0.185174	−0.0925870	+	0.995705i	$0.529514\pi$
$488$	30.6762	1.38865
$489$	−48.7690	−2.20541
$490$	−0.453715	−0.0204968
$491$	18.5872	0.838829	0.419415	−	0.907795i	$-0.362235\pi$
$491$	18.5872	0.838829	0.419415	+	0.907795i	$0.362235\pi$
$492$	−1.78870	−0.0806410
$493$	20.5674	0.926309
$494$	−32.4398	−1.45954
$495$	101.098	4.54400
$496$	4.13599	0.185711
$497$	39.8935	1.78947
$498$	−27.6833	−1.24052
$499$	5.19830	0.232708	0.116354	−	0.993208i	$-0.462879\pi$
$499$	5.19830	0.232708	0.116354	+	0.993208i	$0.462879\pi$
$500$	0.461058	0.0206192
$501$	4.22080	0.188571
$502$	−11.9319	−0.532548
$503$	−19.7909	−0.882431	−0.441216	−	0.897401i	$-0.645453\pi$
$503$	−19.7909	−0.882431	−0.441216	+	0.897401i	$0.645453\pi$
$504$	−40.6697	−1.81157
$505$	5.51933	0.245607
$506$	9.68232	0.430431
$507$	74.8249	3.32309
$508$	−14.1066	−0.625878
$509$	8.01105	0.355083	0.177542	−	0.984113i	$-0.443186\pi$
$509$	8.01105	0.355083	0.177542	+	0.984113i	$0.443186\pi$
$510$	24.6537	1.09168
$511$	−29.2135	−1.29233
$512$	9.28238	0.410227
$513$	−57.3274	−2.53107
$514$	−22.8395	−1.00741
$515$	24.3596	1.07341
$516$	−1.26913	−0.0558703
$517$	49.4557	2.17506
$518$	−2.04846	−0.0900043
$519$	9.10947	0.399861
$520$	51.2833	2.24892
$521$	−4.57850	−0.200588	−0.100294	−	0.994958i	$-0.531978\pi$
$521$	−4.57850	−0.200588	−0.100294	+	0.994958i	$0.531978\pi$
$522$	−26.7099	−1.16906
$523$	19.9218	0.871121	0.435560	−	0.900160i	$-0.356550\pi$
$523$	19.9218	0.871121	0.435560	+	0.900160i	$0.356550\pi$
$524$	−1.83315	−0.0800816
$525$	40.6048	1.77214
$526$	−13.4685	−0.587256
$527$	−16.8845	−0.735501
$528$	−13.6087	−0.592244
$529$	−17.6396	−0.766937
$530$	7.63714	0.331736
$531$	17.6019	0.763857
$532$	26.0747	1.13048
$533$	2.63011	0.113923
$534$	−11.4149	−0.493970
$535$	26.4697	1.14439
$536$	−14.1511	−0.611234
$537$	63.0671	2.72155
$538$	2.18371	0.0941462
$539$	−1.02242	−0.0440387
$540$	37.5688	1.61670
$541$	−1.28751	−0.0553544	−0.0276772	−	0.999617i	$-0.508811\pi$
$541$	−1.28751	−0.0553544	−0.0276772	+	0.999617i	$0.508811\pi$
$542$	−6.38044	−0.274063
$543$	55.5435	2.38360
$544$	−20.0413	−0.859265
$545$	3.17843	0.136149
$546$	37.5863	1.60854
$547$	2.64539	0.113109	0.0565543	−	0.998400i	$-0.481989\pi$
$547$	2.64539	0.113109	0.0565543	+	0.998400i	$0.481989\pi$
$548$	8.22339	0.351286
$549$	−68.2994	−2.91495
$550$	−21.3381	−0.909861
$551$	41.3097	1.75985
$552$	17.9401	0.763583
$553$	−42.7472	−1.81780
$554$	15.8016	0.671344
$555$	9.43506	0.400496
$556$	0.964138	0.0408885
$557$	−30.5627	−1.29498	−0.647492	−	0.762072i	$-0.724182\pi$
$557$	−30.5627	−1.29498	−0.647492	+	0.762072i	$0.724182\pi$
$558$	21.9271	0.928249
$559$	1.86613	0.0789289
$560$	−7.13753	−0.301616
$561$	55.5555	2.34556
$562$	−11.2469	−0.474422
$563$	−8.99257	−0.378992	−0.189496	−	0.981882i	$-0.560685\pi$
$563$	−8.99257	−0.378992	−0.189496	+	0.981882i	$0.560685\pi$
$564$	37.9866	1.59953
$565$	−3.05943	−0.128711
$566$	11.9977	0.504301
$567$	19.6811	0.826530
$568$	−38.8444	−1.62987
$569$	17.8129	0.746758	0.373379	−	0.927679i	$-0.378199\pi$
$569$	17.8129	0.746758	0.373379	+	0.927679i	$0.378199\pi$
$570$	49.5170	2.07404
$571$	40.7412	1.70496	0.852482	−	0.522756i	$-0.175096\pi$
$571$	40.7412	1.70496	0.852482	+	0.522756i	$0.175096\pi$
$572$	47.9060	2.00305
$573$	−4.38543	−0.183204
$574$	0.871632	0.0363812
$575$	−11.8135	−0.492656
$576$	16.2902	0.678757
$577$	18.0525	0.751537	0.375768	−	0.926714i	$-0.377379\pi$
$577$	18.0525	0.751537	0.375768	+	0.926714i	$0.377379\pi$
$578$	−4.05462	−0.168650
$579$	10.5357	0.437850
$580$	−27.0718	−1.12410
$581$	−32.7185	−1.35739
$582$	−19.7760	−0.819743
$583$	17.2098	0.712759
$584$	28.4452	1.17707
$585$	−114.180	−4.72078
$586$	21.0798	0.870799
$587$	−4.33265	−0.178828	−0.0894138	−	0.995995i	$-0.528499\pi$
$587$	−4.33265	−0.178828	−0.0894138	+	0.995995i	$0.528499\pi$
$588$	−0.785314	−0.0323858
$589$	−33.9126	−1.39735
$590$	−7.35569	−0.302829
$591$	30.7808	1.26615
$592$	−0.837658	−0.0344275
$593$	41.3833	1.69941	0.849704	−	0.527260i	$-0.176780\pi$
$593$	41.3833	1.69941	0.849704	+	0.527260i	$0.176780\pi$
$594$	−34.9054	−1.43218
$595$	29.1379	1.19454
$596$	−31.3637	−1.28471
$597$	16.0778	0.658021
$598$	−10.9353	−0.447177
$599$	−5.59078	−0.228433	−0.114217	−	0.993456i	$-0.536436\pi$
$599$	−5.59078	−0.228433	−0.114217	+	0.993456i	$0.536436\pi$
$600$	−39.5369	−1.61409
$601$	−23.3603	−0.952886	−0.476443	−	0.879205i	$-0.658074\pi$
$601$	−23.3603	−0.952886	−0.476443	+	0.879205i	$0.658074\pi$
$602$	0.618445	0.0252059
$603$	31.5068	1.28306
$604$	−34.4274	−1.40083
$605$	−60.2403	−2.44912
$606$	−3.93881	−0.160003
$607$	−21.8457	−0.886690	−0.443345	−	0.896351i	$-0.646208\pi$
$607$	−21.8457	−0.886690	−0.443345	+	0.896351i	$0.646208\pi$
$608$	−40.2531	−1.63248
$609$	−47.8633	−1.93952
$610$	28.5418	1.15562
$611$	−55.8556	−2.25968
$612$	28.1441	1.13766
$613$	−8.48197	−0.342584	−0.171292	−	0.985220i	$-0.554794\pi$
$613$	−8.48197	−0.342584	−0.171292	+	0.985220i	$0.554794\pi$
$614$	−5.92356	−0.239055
$615$	−4.01467	−0.161887
$616$	38.2984	1.54309
$617$	45.9908	1.85152	0.925761	−	0.378110i	$-0.123426\pi$
$617$	45.9908	1.85152	0.925761	+	0.378110i	$0.123426\pi$
$618$	−17.3839	−0.699285
$619$	27.9992	1.12538	0.562691	−	0.826667i	$-0.309766\pi$
$619$	27.9992	1.12538	0.562691	+	0.826667i	$0.309766\pi$
$620$	22.2242	0.892547
$621$	−19.3247	−0.775475
$622$	6.40092	0.256653
$623$	−13.4911	−0.540510
$624$	15.3698	0.615284
$625$	−24.4773	−0.979094
$626$	−5.26629	−0.210483
$627$	111.583	4.45621
$628$	6.16541	0.246027
$629$	3.41961	0.136349
$630$	−37.8399	−1.50758
$631$	−35.7134	−1.42173	−0.710864	−	0.703330i	$-0.751696\pi$
$631$	−35.7134	−1.42173	−0.710864	+	0.703330i	$0.751696\pi$
$632$	41.6230	1.65567
$633$	30.2670	1.20300
$634$	−25.1268	−0.997913
$635$	−31.6616	−1.25645
$636$	13.2188	0.524158
$637$	1.15473	0.0457519
$638$	25.1525	0.995799
$639$	86.4856	3.42132
$640$	30.4482	1.20357
$641$	−4.49164	−0.177409	−0.0887047	−	0.996058i	$-0.528273\pi$
$641$	−4.49164	−0.177409	−0.0887047	+	0.996058i	$0.528273\pi$
$642$	−18.8898	−0.745522
$643$	−10.2171	−0.402921	−0.201461	−	0.979497i	$-0.564569\pi$
$643$	−10.2171	−0.402921	−0.201461	+	0.979497i	$0.564569\pi$
$644$	8.78961	0.346359
$645$	−2.84851	−0.112160
$646$	17.9467	0.706105
$647$	−32.7994	−1.28948	−0.644739	−	0.764403i	$-0.723034\pi$
$647$	−32.7994	−1.28948	−0.644739	+	0.764403i	$0.723034\pi$
$648$	−19.1635	−0.752815
$649$	−16.5756	−0.650649
$650$	24.0994	0.945257
$651$	39.2928	1.54000
$652$	23.2656	0.911149
$653$	11.1309	0.435585	0.217792	−	0.975995i	$-0.430114\pi$
$653$	11.1309	0.435585	0.217792	+	0.975995i	$0.430114\pi$
$654$	−2.26826	−0.0886958
$655$	−4.11443	−0.160764
$656$	0.356428	0.0139162
$657$	−63.3321	−2.47082
$658$	−18.5108	−0.721627
$659$	18.8421	0.733983	0.366991	−	0.930224i	$-0.380388\pi$
$659$	18.8421	0.733983	0.366991	+	0.930224i	$0.380388\pi$
$660$	−73.1249	−2.84638
$661$	21.2228	0.825470	0.412735	−	0.910851i	$-0.364574\pi$
$661$	21.2228	0.825470	0.412735	+	0.910851i	$0.364574\pi$
$662$	22.3214	0.867545
$663$	−62.7448	−2.43680
$664$	31.8580	1.23633
$665$	58.5235	2.26944
$666$	−4.44088	−0.172081
$667$	13.9253	0.539188
$668$	−2.01356	−0.0779069
$669$	−57.8971	−2.23843
$670$	−13.1665	−0.508665
$671$	64.3172	2.48294
$672$	46.6391	1.79914
$673$	14.1684	0.546153	0.273076	−	0.961992i	$-0.411959\pi$
$673$	14.1684	0.546153	0.273076	+	0.961992i	$0.411959\pi$
$674$	−12.6926	−0.488900
$675$	42.5883	1.63923
$676$	−35.6957	−1.37291
$677$	−1.03772	−0.0398827	−0.0199414	−	0.999801i	$-0.506348\pi$
$677$	−1.03772	−0.0398827	−0.0199414	+	0.999801i	$0.506348\pi$
$678$	2.18333	0.0838502
$679$	−23.3731	−0.896975
$680$	−28.3716	−1.08800
$681$	21.3862	0.819521
$682$	−20.6486	−0.790678
$683$	24.8919	0.952464	0.476232	−	0.879320i	$-0.342002\pi$
$683$	24.8919	0.952464	0.476232	+	0.879320i	$0.342002\pi$
$684$	56.5275	2.16138
$685$	18.4571	0.705208
$686$	−13.9566	−0.532864
$687$	−29.3480	−1.11970
$688$	0.252894	0.00964150
$689$	−19.4369	−0.740487
$690$	16.6919	0.635449
$691$	25.0220	0.951884	0.475942	−	0.879477i	$-0.342107\pi$
$691$	25.0220	0.951884	0.475942	+	0.879477i	$0.342107\pi$
$692$	−4.34573	−0.165200
$693$	−85.2700	−3.23914
$694$	15.3669	0.583321
$695$	2.16397	0.0820839
$696$	46.6046	1.76654
$697$	−1.45506	−0.0551144
$698$	21.1017	0.798713
$699$	−50.5065	−1.91033
$700$	−19.3708	−0.732146
$701$	35.6667	1.34711	0.673557	−	0.739135i	$-0.264766\pi$
$701$	35.6667	1.34711	0.673557	+	0.739135i	$0.264766\pi$
$702$	39.4224	1.48790
$703$	6.86830	0.259043
$704$	−15.3403	−0.578161
$705$	85.2594	3.21106
$706$	−13.2253	−0.497741
$707$	−4.65524	−0.175078
$708$	−12.7316	−0.478484
$709$	−2.09942	−0.0788452	−0.0394226	−	0.999223i	$-0.512552\pi$
$709$	−2.09942	−0.0788452	−0.0394226	+	0.999223i	$0.512552\pi$
$710$	−36.1416	−1.35637
$711$	−92.6720	−3.47547
$712$	13.1363	0.492304
$713$	−11.4317	−0.428122
$714$	−20.7939	−0.778193
$715$	107.523	4.02113
$716$	−30.0866	−1.12439
$717$	−40.0725	−1.49653
$718$	18.7038	0.698020
$719$	−8.13682	−0.303452	−0.151726	−	0.988423i	$-0.548483\pi$
$719$	−8.13682	−0.303452	−0.151726	+	0.988423i	$0.548483\pi$
$720$	−15.4735	−0.576664
$721$	−20.5459	−0.765168
$722$	21.5279	0.801184
$723$	−10.0436	−0.373524
$724$	−26.4974	−0.984767
$725$	−30.6888	−1.13975
$726$	42.9899	1.59550
$727$	−51.3930	−1.90606	−0.953030	−	0.302876i	$-0.902053\pi$
$727$	−51.3930	−1.90606	−0.953030	+	0.302876i	$0.902053\pi$
$728$	−43.2545	−1.60312
$729$	−31.6635	−1.17272
$730$	26.4660	0.979550
$731$	−1.03240	−0.0381848
$732$	49.4016	1.82594
$733$	−17.6615	−0.652344	−0.326172	−	0.945311i	$-0.605759\pi$
$733$	−17.6615	−0.652344	−0.326172	+	0.945311i	$0.605759\pi$
$734$	21.3860	0.789372
$735$	−1.76260	−0.0650146
$736$	−13.5691	−0.500163
$737$	−29.6698	−1.09290
$738$	1.88962	0.0695578
$739$	−21.9552	−0.807636	−0.403818	−	0.914839i	$-0.632317\pi$
$739$	−21.9552	−0.807636	−0.403818	+	0.914839i	$0.632317\pi$
$740$	−4.50106	−0.165462
$741$	−126.023	−4.62957
$742$	−6.44149	−0.236474
$743$	0.594446	0.0218081	0.0109041	−	0.999941i	$-0.496529\pi$
$743$	0.594446	0.0218081	0.0109041	+	0.999941i	$0.496529\pi$
$744$	−38.2594	−1.40266
$745$	−70.3945	−2.57905
$746$	−3.25006	−0.118993
$747$	−70.9307	−2.59522
$748$	−26.5031	−0.969050
$749$	−22.3257	−0.815762
$750$	−0.738493	−0.0269660
$751$	52.2996	1.90844	0.954220	−	0.299106i	$-0.0966886\pi$
$751$	52.2996	1.90844	0.954220	+	0.299106i	$0.0966886\pi$
$752$	−7.56945	−0.276029
$753$	−46.3535	−1.68921
$754$	−28.4075	−1.03454
$755$	−77.2709	−2.81217
$756$	−31.6871	−1.15245
$757$	−51.0227	−1.85445	−0.927226	−	0.374502i	$-0.877814\pi$
$757$	−51.0227	−1.85445	−0.927226	+	0.374502i	$0.877814\pi$
$758$	−12.9249	−0.469454
$759$	37.6141	1.36531
$760$	−56.9844	−2.06704
$761$	12.3206	0.446620	0.223310	−	0.974747i	$-0.428314\pi$
$761$	12.3206	0.446620	0.223310	+	0.974747i	$0.428314\pi$
$762$	22.5950	0.818529
$763$	−2.68082	−0.0970523
$764$	2.09209	0.0756893
$765$	63.1682	2.28385
$766$	−22.0334	−0.796098
$767$	18.7206	0.675962
$768$	−38.3700	−1.38456
$769$	51.7104	1.86472	0.932362	−	0.361526i	$-0.117744\pi$
$769$	51.7104	1.86472	0.932362	+	0.361526i	$0.117744\pi$
$770$	35.6337	1.28415
$771$	−88.7274	−3.19544
$772$	−5.02614	−0.180895
$773$	24.6326	0.885974	0.442987	−	0.896528i	$-0.353919\pi$
$773$	24.6326	0.885974	0.442987	+	0.896528i	$0.353919\pi$
$774$	1.34073	0.0481916
$775$	25.1936	0.904980
$776$	22.7584	0.816978
$777$	−7.95793	−0.285489
$778$	−7.04401	−0.252540
$779$	−2.92250	−0.104709
$780$	82.5877	2.95712
$781$	−81.4429	−2.91426
$782$	6.04974	0.216338
$783$	−50.2014	−1.79405
$784$	0.156486	0.00558880
$785$	13.8380	0.493900
$786$	2.93622	0.104732
$787$	−49.2592	−1.75590	−0.877951	−	0.478751i	$-0.841090\pi$
$787$	−49.2592	−1.75590	−0.877951	+	0.478751i	$0.841090\pi$
$788$	−14.6842	−0.523101
$789$	−52.3229	−1.86275
$790$	38.7269	1.37784
$791$	2.58045	0.0917502
$792$	83.0275	2.95025
$793$	−72.6402	−2.57953
$794$	17.8798	0.634529
$795$	29.6690	1.05225
$796$	−7.67002	−0.271857
$797$	12.6083	0.446611	0.223305	−	0.974749i	$-0.428315\pi$
$797$	12.6083	0.446611	0.223305	+	0.974749i	$0.428315\pi$
$798$	−41.7647	−1.47845
$799$	30.9011	1.09320
$800$	29.9039	1.05726
$801$	−29.2475	−1.03341
$802$	25.0276	0.883757
$803$	59.6395	2.10463
$804$	−22.7892	−0.803713
$805$	19.7279	0.695318
$806$	23.3207	0.821437
$807$	8.48332	0.298627
$808$	4.53281	0.159464
$809$	−6.60981	−0.232389	−0.116194	−	0.993227i	$-0.537070\pi$
$809$	−6.60981	−0.232389	−0.116194	+	0.993227i	$0.537070\pi$
$810$	−17.8301	−0.626487
$811$	2.88379	0.101264	0.0506318	−	0.998717i	$-0.483877\pi$
$811$	2.88379	0.101264	0.0506318	+	0.998717i	$0.483877\pi$
$812$	22.8335	0.801299
$813$	−24.7869	−0.869315
$814$	4.18195	0.146577
$815$	52.2186	1.82914
$816$	−8.50305	−0.297666
$817$	−2.07358	−0.0725455
$818$	24.7838	0.866546
$819$	96.3045	3.36515
$820$	1.91522	0.0668825
$821$	8.63501	0.301364	0.150682	−	0.988582i	$-0.451853\pi$
$821$	8.63501	0.301364	0.150682	+	0.988582i	$0.451853\pi$
$822$	−13.1717	−0.459416
$823$	−15.9012	−0.554279	−0.277140	−	0.960830i	$-0.589386\pi$
$823$	−15.9012	−0.554279	−0.277140	+	0.960830i	$0.589386\pi$
$824$	20.0055	0.696926
$825$	−82.8950	−2.88603
$826$	6.20410	0.215868
$827$	−29.1605	−1.01401	−0.507006	−	0.861943i	$-0.669248\pi$
$827$	−29.1605	−1.01401	−0.507006	+	0.861943i	$0.669248\pi$
$828$	19.0551	0.662210
$829$	−29.7360	−1.03277	−0.516387	−	0.856355i	$-0.672723\pi$
$829$	−29.7360	−1.03277	−0.516387	+	0.856355i	$0.672723\pi$
$830$	29.6414	1.02887
$831$	61.3863	2.12947
$832$	17.3255	0.600653
$833$	−0.638832	−0.0221342
$834$	−1.54429	−0.0534745
$835$	−4.51935	−0.156398
$836$	−53.2316	−1.84105
$837$	41.2122	1.42450
$838$	21.3928	0.739004
$839$	−27.2214	−0.939786	−0.469893	−	0.882723i	$-0.655708\pi$
$839$	−27.2214	−0.939786	−0.469893	+	0.882723i	$0.655708\pi$
$840$	66.0248	2.27807
$841$	7.17476	0.247406
$842$	19.2118	0.662083
$843$	−43.6923	−1.50484
$844$	−14.4390	−0.497012
$845$	−80.1175	−2.75613
$846$	−40.1298	−1.37969
$847$	50.8092	1.74583
$848$	−2.63405	−0.0904537
$849$	46.6090	1.59962
$850$	−13.3326	−0.457303
$851$	2.31526	0.0793662
$852$	−62.5558	−2.14313
$853$	−12.6405	−0.432803	−0.216402	−	0.976304i	$-0.569432\pi$
$853$	−12.6405	−0.432803	−0.216402	+	0.976304i	$0.569432\pi$
$854$	−24.0733	−0.823773
$855$	126.874	4.33899
$856$	21.7385	0.743008
$857$	15.4504	0.527776	0.263888	−	0.964553i	$-0.414995\pi$
$857$	15.4504	0.527776	0.263888	+	0.964553i	$0.414995\pi$
$858$	−76.7327	−2.61961
$859$	15.0987	0.515160	0.257580	−	0.966257i	$-0.417075\pi$
$859$	15.0987	0.515160	0.257580	+	0.966257i	$0.417075\pi$
$860$	1.35890	0.0463380
$861$	3.38614	0.115399
$862$	−0.408056	−0.0138984
$863$	−54.7738	−1.86452	−0.932262	−	0.361785i	$-0.882168\pi$
$863$	−54.7738	−1.86452	−0.932262	+	0.361785i	$0.882168\pi$
$864$	48.9174	1.66420
$865$	−9.75381	−0.331639
$866$	−16.8617	−0.572983
$867$	−15.7515	−0.534949
$868$	−18.7449	−0.636242
$869$	87.2687	2.96039
$870$	43.3618	1.47010
$871$	33.5093	1.13542
$872$	2.61032	0.0883966
$873$	−50.6706	−1.71494
$874$	12.1509	0.411011
$875$	−0.872816	−0.0295066
$876$	45.8087	1.54773
$877$	−0.963924	−0.0325494	−0.0162747	−	0.999868i	$-0.505181\pi$
$877$	−0.963924	−0.0325494	−0.0162747	+	0.999868i	$0.505181\pi$
$878$	9.17500	0.309641
$879$	81.8914	2.76213
$880$	14.5713	0.491199
$881$	55.9735	1.88580	0.942898	−	0.333081i	$-0.108088\pi$
$881$	55.9735	1.88580	0.942898	+	0.333081i	$0.108088\pi$
$882$	0.829620	0.0279348
$883$	−28.1685	−0.947946	−0.473973	−	0.880539i	$-0.657181\pi$
$883$	−28.1685	−0.947946	−0.473973	+	0.880539i	$0.657181\pi$
$884$	29.9328	1.00675
$885$	−28.5756	−0.960558
$886$	−21.4012	−0.718987
$887$	−23.5218	−0.789785	−0.394893	−	0.918727i	$-0.629218\pi$
$887$	−23.5218	−0.789785	−0.394893	+	0.918727i	$0.629218\pi$
$888$	7.74864	0.260027
$889$	26.7047	0.895647
$890$	12.2223	0.409692
$891$	−40.1792	−1.34605
$892$	27.6202	0.924792
$893$	62.0650	2.07693
$894$	50.2363	1.68015
$895$	−67.5280	−2.25721
$896$	−25.6813	−0.857952
$897$	−42.4816	−1.41842
$898$	−7.93900	−0.264928
$899$	−29.6972	−0.990457
$900$	−41.9941	−1.39980
$901$	10.7531	0.358238
$902$	−1.77944	−0.0592490
$903$	2.40255	0.0799519
$904$	−2.51259	−0.0835674
$905$	−59.4722	−1.97692
$906$	55.1435	1.83202
$907$	34.3699	1.14124	0.570618	−	0.821216i	$-0.306704\pi$
$907$	34.3699	1.14124	0.570618	+	0.821216i	$0.306704\pi$
$908$	−10.2024	−0.338579
$909$	−10.0921	−0.334735
$910$	−40.2449	−1.33410
$911$	−32.9996	−1.09332	−0.546662	−	0.837353i	$-0.684102\pi$
$911$	−32.9996	−1.09332	−0.546662	+	0.837353i	$0.684102\pi$
$912$	−17.0784	−0.565523
$913$	66.7950	2.21059
$914$	3.98247	0.131729
$915$	110.880	3.66558
$916$	14.0007	0.462595
$917$	3.47028	0.114599
$918$	−21.8097	−0.719827
$919$	−45.1715	−1.49007	−0.745035	−	0.667026i	$-0.767567\pi$
$919$	−45.1715	−1.49007	−0.745035	+	0.667026i	$0.767567\pi$
$920$	−19.2091	−0.633305
$921$	−23.0120	−0.758271
$922$	−16.7775	−0.552538
$923$	91.9822	3.02763
$924$	61.6766	2.02901
$925$	−5.10243	−0.167767
$926$	−0.991641	−0.0325874
$927$	−44.5416	−1.46294
$928$	−35.2495	−1.15712
$929$	47.4831	1.55787	0.778935	−	0.627104i	$-0.215760\pi$
$929$	47.4831	1.55787	0.778935	+	0.627104i	$0.215760\pi$
$930$	−35.5973	−1.16728
$931$	−1.28310	−0.0420518
$932$	24.0945	0.789240
$933$	24.8665	0.814091
$934$	30.4019	0.994781
$935$	−59.4851	−1.94537
$936$	−93.7718	−3.06503
$937$	−49.1679	−1.60625	−0.803123	−	0.595813i	$-0.796830\pi$
$937$	−49.1679	−1.60625	−0.803123	+	0.595813i	$0.796830\pi$
$938$	11.1051	0.362596
$939$	−20.4586	−0.667643
$940$	−40.6736	−1.32662
$941$	−20.1977	−0.658427	−0.329213	−	0.944256i	$-0.606784\pi$
$941$	−20.1977	−0.658427	−0.329213	+	0.944256i	$0.606784\pi$
$942$	−9.87535	−0.321756
$943$	−0.985156	−0.0320811
$944$	2.53698	0.0825717
$945$	−71.1204	−2.31355
$946$	−1.26256	−0.0410493
$947$	6.78837	0.220592	0.110296	−	0.993899i	$-0.464820\pi$
$947$	6.78837	0.220592	0.110296	+	0.993899i	$0.464820\pi$
$948$	67.0305	2.17705
$949$	−67.3572	−2.18651
$950$	−26.7785	−0.868810
$951$	−97.6133	−3.16533
$952$	23.9298	0.775568
$953$	29.9206	0.969223	0.484612	−	0.874729i	$-0.338961\pi$
$953$	29.9206	0.969223	0.484612	+	0.874729i	$0.338961\pi$
$954$	−13.9646	−0.452119
$955$	4.69562	0.151947
$956$	19.1168	0.618283
$957$	97.7133	3.15862
$958$	−27.7954	−0.898028
$959$	−15.5675	−0.502700
$960$	−26.4461	−0.853543
$961$	−6.62049	−0.213564
$962$	−4.72312	−0.152280
$963$	−48.4000	−1.55967
$964$	4.79134	0.154319
$965$	−11.2810	−0.363147
$966$	−14.0786	−0.452972
$967$	−34.7461	−1.11736	−0.558680	−	0.829383i	$-0.688692\pi$
$967$	−34.7461	−1.11736	−0.558680	+	0.829383i	$0.688692\pi$
$968$	−49.4730	−1.59012
$969$	69.7200	2.23973
$970$	21.1749	0.679883
$971$	4.18498	0.134302	0.0671512	−	0.997743i	$-0.478609\pi$
$971$	4.18498	0.134302	0.0671512	+	0.997743i	$0.478609\pi$
$972$	4.59841	0.147494
$973$	−1.82518	−0.0585126
$974$	−3.12252	−0.100052
$975$	93.6221	2.99831
$976$	−9.84407	−0.315101
$977$	−21.1231	−0.675788	−0.337894	−	0.941184i	$-0.609715\pi$
$977$	−21.1231	−0.675788	−0.337894	+	0.941184i	$0.609715\pi$
$978$	−37.2652	−1.19161
$979$	27.5422	0.880252
$980$	0.840861	0.0268603
$981$	−5.81178	−0.185556
$982$	14.2028	0.453230
$983$	22.3581	0.713113	0.356556	−	0.934274i	$-0.383951\pi$
$983$	22.3581	0.713113	0.356556	+	0.934274i	$0.383951\pi$
$984$	−3.29709	−0.105107
$985$	−32.9580	−1.05013
$986$	15.7159	0.500496
$987$	−71.9114	−2.28896
$988$	60.1201	1.91268
$989$	−0.698993	−0.0222267
$990$	77.2505	2.45518
$991$	−16.5008	−0.524166	−0.262083	−	0.965045i	$-0.584410\pi$
$991$	−16.5008	−0.524166	−0.262083	+	0.965045i	$0.584410\pi$
$992$	28.9376	0.918770
$993$	86.7147	2.75181
$994$	30.4834	0.966873
$995$	−17.2150	−0.545753
$996$	51.3049	1.62566
$997$	−8.83161	−0.279700	−0.139850	−	0.990173i	$-0.544662\pi$
$997$	−8.83161	−0.279700	−0.139850	+	0.990173i	$0.544662\pi$
$998$	3.97211	0.125735
$999$	−8.34667	−0.264077

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.51	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.51	✓	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)

\(f(q)\)	\(=\)	\(q+0.764117 q^{2} +2.96846 q^{3} -1.41612 q^{4} -3.17843 q^{5} +2.26826 q^{6} +2.68082 q^{7} -2.61032 q^{8} +5.81178 q^{9} +O(q^{10})\)	\(q+0.764117 q^{2} +2.96846 q^{3} -1.41612 q^{4} -3.17843 q^{5} +2.26826 q^{6} +2.68082 q^{7} -2.61032 q^{8} +5.81178 q^{9} -2.42870 q^{10} -5.47292 q^{11} -4.20372 q^{12} +6.18115 q^{13} +2.04846 q^{14} -9.43506 q^{15} +0.837658 q^{16} -3.41961 q^{17} +4.44088 q^{18} -6.86830 q^{19} +4.50106 q^{20} +7.95793 q^{21} -4.18195 q^{22} -2.31526 q^{23} -7.74864 q^{24} +5.10243 q^{25} +4.72312 q^{26} +8.34667 q^{27} -3.79638 q^{28} -6.01455 q^{29} -7.20950 q^{30} +4.93756 q^{31} +5.86071 q^{32} -16.2462 q^{33} -2.61298 q^{34} -8.52082 q^{35} -8.23020 q^{36} -1.00000 q^{37} -5.24819 q^{38} +18.3485 q^{39} +8.29673 q^{40} +0.425505 q^{41} +6.08079 q^{42} +0.301906 q^{43} +7.75033 q^{44} -18.4724 q^{45} -1.76913 q^{46} -9.03645 q^{47} +2.48656 q^{48} +0.186814 q^{49} +3.89886 q^{50} -10.1510 q^{51} -8.75328 q^{52} -3.14454 q^{53} +6.37784 q^{54} +17.3953 q^{55} -6.99781 q^{56} -20.3883 q^{57} -4.59582 q^{58} +3.02866 q^{59} +13.3612 q^{60} -11.7519 q^{61} +3.77288 q^{62} +15.5804 q^{63} +2.80295 q^{64} -19.6464 q^{65} -12.4140 q^{66} +5.42120 q^{67} +4.84259 q^{68} -6.87277 q^{69} -6.51090 q^{70} +14.8811 q^{71} -15.1706 q^{72} -10.8972 q^{73} -0.764117 q^{74} +15.1464 q^{75} +9.72636 q^{76} -14.6719 q^{77} +14.0204 q^{78} -15.9455 q^{79} -2.66244 q^{80} +7.34145 q^{81} +0.325136 q^{82} -12.2046 q^{83} -11.2694 q^{84} +10.8690 q^{85} +0.230692 q^{86} -17.8540 q^{87} +14.2861 q^{88} -5.03245 q^{89} -14.1150 q^{90} +16.5706 q^{91} +3.27870 q^{92} +14.6570 q^{93} -6.90491 q^{94} +21.8304 q^{95} +17.3973 q^{96} -8.71861 q^{97} +0.142748 q^{98} -31.8074 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 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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