LMFDB - Embedded newform 8045.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8045,2,Mod(1,8045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8045, 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("8045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8045 = 5 \cdot 1609 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8045.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.2396484261$
Analytic rank:	$0$
Dimension:	$142$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77343 q^{2} +2.65510 q^{3} +5.69191 q^{4} +1.00000 q^{5} -7.36373 q^{6} +0.492807 q^{7} -10.2393 q^{8} +4.04956 q^{9} +O(q^{10})$	\(q-2.77343 q^{2} +2.65510 q^{3} +5.69191 q^{4} +1.00000 q^{5} -7.36373 q^{6} +0.492807 q^{7} -10.2393 q^{8} +4.04956 q^{9} -2.77343 q^{10} +1.79985 q^{11} +15.1126 q^{12} +1.84914 q^{13} -1.36676 q^{14} +2.65510 q^{15} +17.0140 q^{16} +5.86033 q^{17} -11.2312 q^{18} +7.66632 q^{19} +5.69191 q^{20} +1.30845 q^{21} -4.99176 q^{22} +3.86038 q^{23} -27.1862 q^{24} +1.00000 q^{25} -5.12847 q^{26} +2.78668 q^{27} +2.80501 q^{28} -1.53408 q^{29} -7.36373 q^{30} +2.40119 q^{31} -26.7087 q^{32} +4.77879 q^{33} -16.2532 q^{34} +0.492807 q^{35} +23.0497 q^{36} -1.91881 q^{37} -21.2620 q^{38} +4.90966 q^{39} -10.2393 q^{40} -2.07211 q^{41} -3.62890 q^{42} +12.2185 q^{43} +10.2446 q^{44} +4.04956 q^{45} -10.7065 q^{46} -4.61965 q^{47} +45.1740 q^{48} -6.75714 q^{49} -2.77343 q^{50} +15.5598 q^{51} +10.5252 q^{52} +3.82864 q^{53} -7.72867 q^{54} +1.79985 q^{55} -5.04597 q^{56} +20.3549 q^{57} +4.25465 q^{58} +6.89844 q^{59} +15.1126 q^{60} -11.1830 q^{61} -6.65952 q^{62} +1.99565 q^{63} +40.0466 q^{64} +1.84914 q^{65} -13.2536 q^{66} +15.5119 q^{67} +33.3565 q^{68} +10.2497 q^{69} -1.36676 q^{70} -11.9724 q^{71} -41.4645 q^{72} +12.4456 q^{73} +5.32168 q^{74} +2.65510 q^{75} +43.6360 q^{76} +0.886980 q^{77} -13.6166 q^{78} +0.963263 q^{79} +17.0140 q^{80} -4.74975 q^{81} +5.74686 q^{82} -9.48831 q^{83} +7.44759 q^{84} +5.86033 q^{85} -33.8870 q^{86} -4.07312 q^{87} -18.4291 q^{88} -13.3533 q^{89} -11.2312 q^{90} +0.911270 q^{91} +21.9729 q^{92} +6.37539 q^{93} +12.8123 q^{94} +7.66632 q^{95} -70.9143 q^{96} -1.46110 q^{97} +18.7405 q^{98} +7.28861 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 142 q + 21 q^{2} + 33 q^{3} + 157 q^{4} + 142 q^{5} + 15 q^{6} + 63 q^{7} + 60 q^{8} + 157 q^{9}+O(q^{10}) $ 142 * q + 21 * q^2 + 33 * q^3 + 157 * q^4 + 142 * q^5 + 15 * q^6 + 63 * q^7 + 60 * q^8 + 157 * q^9	\( 142 q + 21 q^{2} + 33 q^{3} + 157 q^{4} + 142 q^{5} + 15 q^{6} + 63 q^{7} + 60 q^{8} + 157 q^{9} + 21 q^{10} + 36 q^{11} + 55 q^{12} + 57 q^{13} + 2 q^{14} + 33 q^{15} + 179 q^{16} + 55 q^{17} + 65 q^{18} + 130 q^{19} + 157 q^{20} + 28 q^{21} + 30 q^{22} + 117 q^{23} + 21 q^{24} + 142 q^{25} + 21 q^{26} + 120 q^{27} + 135 q^{28} + 12 q^{29} + 15 q^{30} + 74 q^{31} + 126 q^{32} + 55 q^{33} + 35 q^{34} + 63 q^{35} + 186 q^{36} + 75 q^{37} + 65 q^{38} + 23 q^{39} + 60 q^{40} + 22 q^{41} + 10 q^{42} + 190 q^{43} + 22 q^{44} + 157 q^{45} + 56 q^{46} + 102 q^{47} + 78 q^{48} + 197 q^{49} + 21 q^{50} + 30 q^{51} + 120 q^{52} + 56 q^{53} - 6 q^{54} + 36 q^{55} + 3 q^{56} + 68 q^{57} + 31 q^{58} + 55 q^{59} + 55 q^{60} + 90 q^{61} + 68 q^{62} + 167 q^{63} + 180 q^{64} + 57 q^{65} + 17 q^{66} + 151 q^{67} + 119 q^{68} + 21 q^{69} + 2 q^{70} + 4 q^{71} + 130 q^{72} + 143 q^{73} - 46 q^{74} + 33 q^{75} + 213 q^{76} + 75 q^{77} - 24 q^{78} + 47 q^{79} + 179 q^{80} + 150 q^{81} + 69 q^{82} + 201 q^{83} - 31 q^{84} + 55 q^{85} - 4 q^{86} + 153 q^{87} + 37 q^{88} + 25 q^{89} + 65 q^{90} + 132 q^{91} + 194 q^{92} + 52 q^{93} + 18 q^{94} + 130 q^{95} + 13 q^{96} + 80 q^{97} + 58 q^{98} + 103 q^{99}+O(q^{100}) \) 142 * q + 21 * q^2 + 33 * q^3 + 157 * q^4 + 142 * q^5 + 15 * q^6 + 63 * q^7 + 60 * q^8 + 157 * q^9 + 21 * q^10 + 36 * q^11 + 55 * q^12 + 57 * q^13 + 2 * q^14 + 33 * q^15 + 179 * q^16 + 55 * q^17 + 65 * q^18 + 130 * q^19 + 157 * q^20 + 28 * q^21 + 30 * q^22 + 117 * q^23 + 21 * q^24 + 142 * q^25 + 21 * q^26 + 120 * q^27 + 135 * q^28 + 12 * q^29 + 15 * q^30 + 74 * q^31 + 126 * q^32 + 55 * q^33 + 35 * q^34 + 63 * q^35 + 186 * q^36 + 75 * q^37 + 65 * q^38 + 23 * q^39 + 60 * q^40 + 22 * q^41 + 10 * q^42 + 190 * q^43 + 22 * q^44 + 157 * q^45 + 56 * q^46 + 102 * q^47 + 78 * q^48 + 197 * q^49 + 21 * q^50 + 30 * q^51 + 120 * q^52 + 56 * q^53 - 6 * q^54 + 36 * q^55 + 3 * q^56 + 68 * q^57 + 31 * q^58 + 55 * q^59 + 55 * q^60 + 90 * q^61 + 68 * q^62 + 167 * q^63 + 180 * q^64 + 57 * q^65 + 17 * q^66 + 151 * q^67 + 119 * q^68 + 21 * q^69 + 2 * q^70 + 4 * q^71 + 130 * q^72 + 143 * q^73 - 46 * q^74 + 33 * q^75 + 213 * q^76 + 75 * q^77 - 24 * q^78 + 47 * q^79 + 179 * q^80 + 150 * q^81 + 69 * q^82 + 201 * q^83 - 31 * q^84 + 55 * q^85 - 4 * q^86 + 153 * q^87 + 37 * q^88 + 25 * q^89 + 65 * q^90 + 132 * q^91 + 194 * q^92 + 52 * q^93 + 18 * q^94 + 130 * q^95 + 13 * q^96 + 80 * q^97 + 58 * q^98 + 103 * 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 $

$2$	−2.77343	−1.96111	−0.980555	−	0.196243i	$-0.937126\pi$
$2$	−2.77343	−1.96111	−0.980555	+	0.196243i	$0.937126\pi$
$3$	2.65510	1.53292	0.766461	−	0.642290i	$-0.222016\pi$
$3$	2.65510	1.53292	0.766461	+	0.642290i	$0.222016\pi$
$4$	5.69191	2.84596
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−7.36373	−3.00623
$7$	0.492807	0.186263	0.0931317	−	0.995654i	$-0.470312\pi$
$7$	0.492807	0.186263	0.0931317	+	0.995654i	$0.470312\pi$
$8$	−10.2393	−3.62012
$9$	4.04956	1.34985
$10$	−2.77343	−0.877035
$11$	1.79985	0.542676	0.271338	−	0.962484i	$-0.412534\pi$
$11$	1.79985	0.542676	0.271338	+	0.962484i	$0.412534\pi$
$12$	15.1126	4.36263
$13$	1.84914	0.512860	0.256430	−	0.966563i	$-0.417454\pi$
$13$	1.84914	0.512860	0.256430	+	0.966563i	$0.417454\pi$
$14$	−1.36676	−0.365283
$15$	2.65510	0.685544
$16$	17.0140	4.25351
$17$	5.86033	1.42134	0.710670	−	0.703526i	$-0.248392\pi$
$17$	5.86033	1.42134	0.710670	+	0.703526i	$0.248392\pi$
$18$	−11.2312	−2.64721
$19$	7.66632	1.75877	0.879387	−	0.476107i	$-0.157952\pi$
$19$	7.66632	1.75877	0.879387	+	0.476107i	$0.157952\pi$
$20$	5.69191	1.27275
$21$	1.30845	0.285528
$22$	−4.99176	−1.06425
$23$	3.86038	0.804945	0.402472	−	0.915432i	$-0.368151\pi$
$23$	3.86038	0.804945	0.402472	+	0.915432i	$0.368151\pi$
$24$	−27.1862	−5.54937
$25$	1.00000	0.200000
$26$	−5.12847	−1.00578
$27$	2.78668	0.536297
$28$	2.80501	0.530097
$29$	−1.53408	−0.284871	−0.142435	−	0.989804i	$-0.545493\pi$
$29$	−1.53408	−0.284871	−0.142435	+	0.989804i	$0.545493\pi$
$30$	−7.36373	−1.34443
$31$	2.40119	0.431266	0.215633	−	0.976474i	$-0.430819\pi$
$31$	2.40119	0.431266	0.215633	+	0.976474i	$0.430819\pi$
$32$	−26.7087	−4.72148
$33$	4.77879	0.831880
$34$	−16.2532	−2.78740
$35$	0.492807	0.0832995
$36$	23.0497	3.84162
$37$	−1.91881	−0.315450	−0.157725	−	0.987483i	$-0.550416\pi$
$37$	−1.91881	−0.315450	−0.157725	+	0.987483i	$0.550416\pi$
$38$	−21.2620	−3.44915
$39$	4.90966	0.786175
$40$	−10.2393	−1.61897
$41$	−2.07211	−0.323610	−0.161805	−	0.986823i	$-0.551732\pi$
$41$	−2.07211	−0.323610	−0.161805	+	0.986823i	$0.551732\pi$
$42$	−3.62890	−0.559951
$43$	12.2185	1.86330	0.931648	−	0.363362i	$-0.118371\pi$
$43$	12.2185	1.86330	0.931648	+	0.363362i	$0.118371\pi$
$44$	10.2446	1.54443
$45$	4.04956	0.603673
$46$	−10.7065	−1.57859
$47$	−4.61965	−0.673845	−0.336923	−	0.941532i	$-0.609386\pi$
$47$	−4.61965	−0.673845	−0.336923	+	0.941532i	$0.609386\pi$
$48$	45.1740	6.52030
$49$	−6.75714	−0.965306
$50$	−2.77343	−0.392222
$51$	15.5598	2.17880
$52$	10.5252	1.45958
$53$	3.82864	0.525905	0.262952	−	0.964809i	$-0.415304\pi$
$53$	3.82864	0.525905	0.262952	+	0.964809i	$0.415304\pi$
$54$	−7.72867	−1.05174
$55$	1.79985	0.242692
$56$	−5.04597	−0.674297
$57$	20.3549	2.69607
$58$	4.25465	0.558663
$59$	6.89844	0.898100	0.449050	−	0.893507i	$-0.351762\pi$
$59$	6.89844	0.898100	0.449050	+	0.893507i	$0.351762\pi$
$60$	15.1126	1.95103
$61$	−11.1830	−1.43184	−0.715921	−	0.698182i	$-0.753993\pi$
$61$	−11.1830	−1.43184	−0.715921	+	0.698182i	$0.753993\pi$
$62$	−6.65952	−0.845761
$63$	1.99565	0.251428
$64$	40.0466	5.00583
$65$	1.84914	0.229358
$66$	−13.2536	−1.63141
$67$	15.5119	1.89508	0.947538	−	0.319643i	$-0.103563\pi$
$67$	15.5119	1.89508	0.947538	+	0.319643i	$0.103563\pi$
$68$	33.3565	4.04507
$69$	10.2497	1.23392
$70$	−1.36676	−0.163360
$71$	−11.9724	−1.42086	−0.710430	−	0.703768i	$-0.751500\pi$
$71$	−11.9724	−1.42086	−0.710430	+	0.703768i	$0.751500\pi$
$72$	−41.4645	−4.88663
$73$	12.4456	1.45665	0.728323	−	0.685234i	$-0.240300\pi$
$73$	12.4456	1.45665	0.728323	+	0.685234i	$0.240300\pi$
$74$	5.32168	0.618633
$75$	2.65510	0.306585
$76$	43.6360	5.00539
$77$	0.886980	0.101081
$78$	−13.6166	−1.54178
$79$	0.963263	0.108376	0.0541878	−	0.998531i	$-0.482743\pi$
$79$	0.963263	0.108376	0.0541878	+	0.998531i	$0.482743\pi$
$80$	17.0140	1.90223
$81$	−4.74975	−0.527750
$82$	5.74686	0.634635
$83$	−9.48831	−1.04148	−0.520739	−	0.853716i	$-0.674343\pi$
$83$	−9.48831	−1.04148	−0.520739	+	0.853716i	$0.674343\pi$
$84$	7.44759	0.812599
$85$	5.86033	0.635642
$86$	−33.8870	−3.65413
$87$	−4.07312	−0.436685
$88$	−18.4291	−1.96455
$89$	−13.3533	−1.41545	−0.707723	−	0.706490i	$-0.750278\pi$
$89$	−13.3533	−1.41545	−0.707723	+	0.706490i	$0.750278\pi$
$90$	−11.2312	−1.18387
$91$	0.911270	0.0955271
$92$	21.9729	2.29084
$93$	6.37539	0.661098
$94$	12.8123	1.32149
$95$	7.66632	0.786548
$96$	−70.9143	−7.23766
$97$	−1.46110	−0.148352	−0.0741761	−	0.997245i	$-0.523633\pi$
$97$	−1.46110	−0.148352	−0.0741761	+	0.997245i	$0.523633\pi$
$98$	18.7405	1.89307
$99$	7.28861	0.732533
$100$	5.69191	0.569191
$101$	−8.96040	−0.891593	−0.445797	−	0.895134i	$-0.647080\pi$
$101$	−8.96040	−0.891593	−0.445797	+	0.895134i	$0.647080\pi$
$102$	−43.1539	−4.27287
$103$	−16.4573	−1.62158	−0.810791	−	0.585336i	$-0.800963\pi$
$103$	−16.4573	−1.62158	−0.810791	+	0.585336i	$0.800963\pi$
$104$	−18.9338	−1.85662
$105$	1.30845	0.127692
$106$	−10.6185	−1.03136
$107$	−1.34980	−0.130490	−0.0652449	−	0.997869i	$-0.520783\pi$
$107$	−1.34980	−0.130490	−0.0652449	+	0.997869i	$0.520783\pi$
$108$	15.8616	1.52628
$109$	14.6732	1.40544	0.702719	−	0.711467i	$-0.251969\pi$
$109$	14.6732	1.40544	0.702719	+	0.711467i	$0.251969\pi$
$110$	−4.99176	−0.475946
$111$	−5.09463	−0.483561
$112$	8.38463	0.792273
$113$	13.4842	1.26849	0.634245	−	0.773132i	$-0.281311\pi$
$113$	13.4842	1.26849	0.634245	+	0.773132i	$0.281311\pi$
$114$	−56.4528	−5.28728
$115$	3.86038	0.359982
$116$	−8.73182	−0.810729
$117$	7.48821	0.692286
$118$	−19.1323	−1.76127
$119$	2.88801	0.264744
$120$	−27.1862	−2.48175
$121$	−7.76053	−0.705503
$122$	31.0154	2.80800
$123$	−5.50167	−0.496069
$124$	13.6673	1.22736
$125$	1.00000	0.0894427
$126$	−5.53479	−0.493079
$127$	−21.2219	−1.88314	−0.941568	−	0.336823i	$-0.890648\pi$
$127$	−21.2219	−1.88314	−0.941568	+	0.336823i	$0.890648\pi$
$128$	−57.6491	−5.09551
$129$	32.4412	2.85629
$130$	−5.12847	−0.449796
$131$	9.17620	0.801728	0.400864	−	0.916138i	$-0.368710\pi$
$131$	9.17620	0.801728	0.400864	+	0.916138i	$0.368710\pi$
$132$	27.2004	2.36749
$133$	3.77802	0.327595
$134$	−43.0211	−3.71645
$135$	2.78668	0.239839
$136$	−60.0054	−5.14542
$137$	2.02323	0.172856	0.0864279	−	0.996258i	$-0.472455\pi$
$137$	2.02323	0.172856	0.0864279	+	0.996258i	$0.472455\pi$
$138$	−28.4268	−2.41985
$139$	−11.0721	−0.939122	−0.469561	−	0.882900i	$-0.655588\pi$
$139$	−11.0721	−0.939122	−0.469561	+	0.882900i	$0.655588\pi$
$140$	2.80501	0.237067
$141$	−12.2656	−1.03295
$142$	33.2046	2.78647
$143$	3.32819	0.278317
$144$	68.8993	5.74161
$145$	−1.53408	−0.127398
$146$	−34.5169	−2.85664
$147$	−17.9409	−1.47974
$148$	−10.9217	−0.897757
$149$	15.9856	1.30959	0.654796	−	0.755805i	$-0.272754\pi$
$149$	15.9856	1.30959	0.654796	+	0.755805i	$0.272754\pi$
$150$	−7.36373	−0.601246
$151$	−0.571045	−0.0464710	−0.0232355	−	0.999730i	$-0.507397\pi$
$151$	−0.571045	−0.0464710	−0.0232355	+	0.999730i	$0.507397\pi$
$152$	−78.4974	−6.36698
$153$	23.7318	1.91860
$154$	−2.45998	−0.198230
$155$	2.40119	0.192868
$156$	27.9454	2.23742
$157$	−9.44530	−0.753817	−0.376908	−	0.926251i	$-0.623013\pi$
$157$	−9.44530	−0.753817	−0.376908	+	0.926251i	$0.623013\pi$
$158$	−2.67154	−0.212536
$159$	10.1654	0.806171
$160$	−26.7087	−2.11151
$161$	1.90242	0.149932
$162$	13.1731	1.03498
$163$	14.6743	1.14938	0.574690	−	0.818371i	$-0.305123\pi$
$163$	14.6743	1.14938	0.574690	+	0.818371i	$0.305123\pi$
$164$	−11.7943	−0.920980
$165$	4.77879	0.372028
$166$	26.3152	2.04245
$167$	−5.47871	−0.423955	−0.211978	−	0.977275i	$-0.567990\pi$
$167$	−5.47871	−0.423955	−0.211978	+	0.977275i	$0.567990\pi$
$168$	−13.3976	−1.03364
$169$	−9.58067	−0.736975
$170$	−16.2532	−1.24656
$171$	31.0452	2.37409
$172$	69.5463	5.30286
$173$	−17.2618	−1.31239	−0.656194	−	0.754592i	$-0.727835\pi$
$173$	−17.2618	−1.31239	−0.656194	+	0.754592i	$0.727835\pi$
$174$	11.2965	0.856387
$175$	0.492807	0.0372527
$176$	30.6227	2.30828
$177$	18.3160	1.37672
$178$	37.0344	2.77585
$179$	−16.6851	−1.24710	−0.623551	−	0.781783i	$-0.714311\pi$
$179$	−16.6851	−1.24710	−0.623551	+	0.781783i	$0.714311\pi$
$180$	23.0497	1.71803
$181$	−23.5295	−1.74893	−0.874466	−	0.485086i	$-0.838788\pi$
$181$	−23.5295	−1.74893	−0.874466	+	0.485086i	$0.838788\pi$
$182$	−2.52734	−0.187339
$183$	−29.6921	−2.19490
$184$	−39.5274	−2.91400
$185$	−1.91881	−0.141074
$186$	−17.6817	−1.29649
$187$	10.5477	0.771327
$188$	−26.2946	−1.91773
$189$	1.37330	0.0998926
$190$	−21.2620	−1.54251
$191$	−13.4024	−0.969763	−0.484881	−	0.874580i	$-0.661137\pi$
$191$	−13.4024	−0.969763	−0.484881	+	0.874580i	$0.661137\pi$
$192$	106.328	7.67355
$193$	−5.03715	−0.362582	−0.181291	−	0.983429i	$-0.558028\pi$
$193$	−5.03715	−0.362582	−0.181291	+	0.983429i	$0.558028\pi$
$194$	4.05226	0.290935
$195$	4.90966	0.351588
$196$	−38.4610	−2.74722
$197$	5.74014	0.408968	0.204484	−	0.978870i	$-0.434448\pi$
$197$	5.74014	0.408968	0.204484	+	0.978870i	$0.434448\pi$
$198$	−20.2144	−1.43658
$199$	−9.00875	−0.638613	−0.319307	−	0.947651i	$-0.603450\pi$
$199$	−9.00875	−0.638613	−0.319307	+	0.947651i	$0.603450\pi$
$200$	−10.2393	−0.724025
$201$	41.1856	2.90501
$202$	24.8510	1.74851
$203$	−0.756003	−0.0530610
$204$	88.5648	6.20078
$205$	−2.07211	−0.144723
$206$	45.6430	3.18010
$207$	15.6328	1.08656
$208$	31.4614	2.18145
$209$	13.7982	0.954445
$210$	−3.62890	−0.250418
$211$	−21.9332	−1.50994	−0.754971	−	0.655759i	$-0.772349\pi$
$211$	−21.9332	−1.50994	−0.754971	+	0.655759i	$0.772349\pi$
$212$	21.7923	1.49670
$213$	−31.7879	−2.17807
$214$	3.74357	0.255905
$215$	12.2185	0.833291
$216$	−28.5336	−1.94146
$217$	1.18332	0.0803291
$218$	−40.6951	−2.75622
$219$	33.0443	2.23292
$220$	10.2446	0.690691
$221$	10.8366	0.728948
$222$	14.1296	0.948317
$223$	−2.29917	−0.153964	−0.0769818	−	0.997033i	$-0.524528\pi$
$223$	−2.29917	−0.153964	−0.0769818	+	0.997033i	$0.524528\pi$
$224$	−13.1622	−0.879438
$225$	4.04956	0.269971
$226$	−37.3976	−2.48765
$227$	−17.0228	−1.12984	−0.564922	−	0.825144i	$-0.691094\pi$
$227$	−17.0228	−1.12984	−0.564922	+	0.825144i	$0.691094\pi$
$228$	115.858	7.67288
$229$	20.7814	1.37327	0.686637	−	0.727000i	$-0.259086\pi$
$229$	20.7814	1.37327	0.686637	+	0.727000i	$0.259086\pi$
$230$	−10.7065	−0.705965
$231$	2.35502	0.154949
$232$	15.7078	1.03127
$233$	23.8916	1.56519	0.782595	−	0.622531i	$-0.213896\pi$
$233$	23.8916	1.56519	0.782595	+	0.622531i	$0.213896\pi$
$234$	−20.7680	−1.35765
$235$	−4.61965	−0.301353
$236$	39.2653	2.55595
$237$	2.55756	0.166131
$238$	−8.00969	−0.519191
$239$	−1.27289	−0.0823361	−0.0411681	−	0.999152i	$-0.513108\pi$
$239$	−1.27289	−0.0823361	−0.0411681	+	0.999152i	$0.513108\pi$
$240$	45.1740	2.91597
$241$	29.8413	1.92225	0.961123	−	0.276122i	$-0.0890493\pi$
$241$	29.8413	1.92225	0.961123	+	0.276122i	$0.0890493\pi$
$242$	21.5233	1.38357
$243$	−20.9711	−1.34530
$244$	−63.6529	−4.07496
$245$	−6.75714	−0.431698
$246$	15.2585	0.972847
$247$	14.1761	0.902005
$248$	−24.5864	−1.56124
$249$	−25.1924	−1.59650
$250$	−2.77343	−0.175407
$251$	6.59265	0.416125	0.208062	−	0.978116i	$-0.433284\pi$
$251$	6.59265	0.416125	0.208062	+	0.978116i	$0.433284\pi$
$252$	11.3591	0.715554
$253$	6.94811	0.436824
$254$	58.8573	3.69304
$255$	15.5598	0.974390
$256$	79.7925	4.98703
$257$	−6.96030	−0.434171	−0.217086	−	0.976153i	$-0.569655\pi$
$257$	−6.96030	−0.434171	−0.217086	+	0.976153i	$0.569655\pi$
$258$	−89.9734	−5.60150
$259$	−0.945602	−0.0587568
$260$	10.5252	0.652743
$261$	−6.21233	−0.384533
$262$	−25.4495	−1.57228
$263$	−24.7629	−1.52695	−0.763473	−	0.645840i	$-0.776507\pi$
$263$	−24.7629	−1.52695	−0.763473	+	0.645840i	$0.776507\pi$
$264$	−48.9312	−3.01151
$265$	3.82864	0.235192
$266$	−10.4781	−0.642451
$267$	−35.4544	−2.16977
$268$	88.2922	5.39330
$269$	−22.4065	−1.36615	−0.683074	−	0.730349i	$-0.739357\pi$
$269$	−22.4065	−1.36615	−0.683074	+	0.730349i	$0.739357\pi$
$270$	−7.72867	−0.470352
$271$	5.23069	0.317742	0.158871	−	0.987299i	$-0.449215\pi$
$271$	5.23069	0.317742	0.158871	+	0.987299i	$0.449215\pi$
$272$	99.7078	6.04568
$273$	2.41951	0.146436
$274$	−5.61128	−0.338990
$275$	1.79985	0.108535
$276$	58.3403	3.51168
$277$	22.7714	1.36820	0.684099	−	0.729389i	$-0.260195\pi$
$277$	22.7714	1.36820	0.684099	+	0.729389i	$0.260195\pi$
$278$	30.7077	1.84172
$279$	9.72375	0.582146
$280$	−5.04597	−0.301555
$281$	2.81274	0.167794	0.0838971	−	0.996474i	$-0.473263\pi$
$281$	2.81274	0.167794	0.0838971	+	0.996474i	$0.473263\pi$
$282$	34.0179	2.02574
$283$	−10.5392	−0.626490	−0.313245	−	0.949672i	$-0.601416\pi$
$283$	−10.5392	−0.626490	−0.313245	+	0.949672i	$0.601416\pi$
$284$	−68.1457	−4.04371
$285$	20.3549	1.20572
$286$	−9.23049	−0.545810
$287$	−1.02115	−0.0602767
$288$	−108.158	−6.37330
$289$	17.3435	1.02020
$290$	4.25465	0.249842
$291$	−3.87937	−0.227413
$292$	70.8391	4.14555
$293$	−22.6807	−1.32502	−0.662509	−	0.749054i	$-0.730508\pi$
$293$	−22.6807	−1.32502	−0.662509	+	0.749054i	$0.730508\pi$
$294$	49.7578	2.90193
$295$	6.89844	0.401643
$296$	19.6472	1.14197
$297$	5.01562	0.291036
$298$	−44.3350	−2.56826
$299$	7.13839	0.412824
$300$	15.1126	0.872526
$301$	6.02134	0.347064
$302$	1.58375	0.0911347
$303$	−23.7908	−1.36674
$304$	130.435	7.48096
$305$	−11.1830	−0.640339
$306$	−65.8183	−3.76258
$307$	17.0831	0.974986	0.487493	−	0.873127i	$-0.337911\pi$
$307$	17.0831	0.974986	0.487493	+	0.873127i	$0.337911\pi$
$308$	5.04861	0.287671
$309$	−43.6957	−2.48576
$310$	−6.65952	−0.378236
$311$	7.34674	0.416595	0.208298	−	0.978065i	$-0.433208\pi$
$311$	7.34674	0.416595	0.208298	+	0.978065i	$0.433208\pi$
$312$	−50.2713	−2.84605
$313$	25.1140	1.41953	0.709764	−	0.704439i	$-0.248802\pi$
$313$	25.1140	1.41953	0.709764	+	0.704439i	$0.248802\pi$
$314$	26.1959	1.47832
$315$	1.99565	0.112442
$316$	5.48281	0.308432
$317$	25.2710	1.41936	0.709681	−	0.704523i	$-0.248839\pi$
$317$	25.2710	1.41936	0.709681	+	0.704523i	$0.248839\pi$
$318$	−28.1931	−1.58099
$319$	−2.76111	−0.154592
$320$	40.0466	2.23867
$321$	−3.58385	−0.200031
$322$	−5.27623	−0.294033
$323$	44.9272	2.49982
$324$	−27.0352	−1.50195
$325$	1.84914	0.102572
$326$	−40.6981	−2.25406
$327$	38.9588	2.15443
$328$	21.2169	1.17151
$329$	−2.27660	−0.125513
$330$	−13.2536	−0.729589
$331$	−18.7271	−1.02933	−0.514667	−	0.857390i	$-0.672084\pi$
$331$	−18.7271	−1.02933	−0.514667	+	0.857390i	$0.672084\pi$
$332$	−54.0066	−2.96400
$333$	−7.77033	−0.425811
$334$	15.1948	0.831423
$335$	15.5119	0.847504
$336$	22.2620	1.21449
$337$	6.04707	0.329405	0.164702	−	0.986343i	$-0.447334\pi$
$337$	6.04707	0.329405	0.164702	+	0.986343i	$0.447334\pi$
$338$	26.5713	1.44529
$339$	35.8020	1.94450
$340$	33.3565	1.80901
$341$	4.32178	0.234038
$342$	−86.1017	−4.65585
$343$	−6.77961	−0.366065
$344$	−125.108	−6.74536
$345$	10.2497	0.551825
$346$	47.8743	2.57374
$347$	12.5237	0.672306	0.336153	−	0.941807i	$-0.390874\pi$
$347$	12.5237	0.672306	0.336153	+	0.941807i	$0.390874\pi$
$348$	−23.1839	−1.24279
$349$	2.21287	0.118452	0.0592260	−	0.998245i	$-0.481137\pi$
$349$	2.21287	0.118452	0.0592260	+	0.998245i	$0.481137\pi$
$350$	−1.36676	−0.0730567
$351$	5.15298	0.275046
$352$	−48.0717	−2.56223
$353$	−20.3029	−1.08061	−0.540307	−	0.841468i	$-0.681692\pi$
$353$	−20.3029	−1.08061	−0.540307	+	0.841468i	$0.681692\pi$
$354$	−50.7983	−2.69990
$355$	−11.9724	−0.635428
$356$	−76.0058	−4.02830
$357$	7.66796	0.405831
$358$	46.2749	2.44570
$359$	−4.10623	−0.216718	−0.108359	−	0.994112i	$-0.534560\pi$
$359$	−4.10623	−0.216718	−0.108359	+	0.994112i	$0.534560\pi$
$360$	−41.4645	−2.18537
$361$	39.7725	2.09329
$362$	65.2574	3.42985
$363$	−20.6050	−1.08148
$364$	5.18687	0.271866
$365$	12.4456	0.651431
$366$	82.3489	4.30445
$367$	12.0007	0.626429	0.313214	−	0.949682i	$-0.398594\pi$
$367$	12.0007	0.626429	0.313214	+	0.949682i	$0.398594\pi$
$368$	65.6806	3.42384
$369$	−8.39115	−0.436826
$370$	5.32168	0.276661
$371$	1.88678	0.0979568
$372$	36.2882	1.88145
$373$	9.04874	0.468526	0.234263	−	0.972173i	$-0.424732\pi$
$373$	9.04874	0.468526	0.234263	+	0.972173i	$0.424732\pi$
$374$	−29.2534	−1.51266
$375$	2.65510	0.137109
$376$	47.3018	2.43940
$377$	−2.83672	−0.146099
$378$	−3.80874	−0.195900
$379$	−7.75687	−0.398444	−0.199222	−	0.979954i	$-0.563841\pi$
$379$	−7.75687	−0.398444	−0.199222	+	0.979954i	$0.563841\pi$
$380$	43.6360	2.23848
$381$	−56.3462	−2.88670
$382$	37.1706	1.90181
$383$	−31.7571	−1.62271	−0.811356	−	0.584552i	$-0.801270\pi$
$383$	−31.7571	−1.62271	−0.811356	+	0.584552i	$0.801270\pi$
$384$	−153.064	−7.81102
$385$	0.886980	0.0452047
$386$	13.9702	0.711064
$387$	49.4793	2.51518
$388$	−8.31645	−0.422204
$389$	−20.3320	−1.03088	−0.515438	−	0.856927i	$-0.672371\pi$
$389$	−20.3320	−1.03088	−0.515438	+	0.856927i	$0.672371\pi$
$390$	−13.6166	−0.689503
$391$	22.6231	1.14410
$392$	69.1881	3.49453
$393$	24.3637	1.22899
$394$	−15.9199	−0.802031
$395$	0.963263	0.0484670
$396$	41.4861	2.08476
$397$	−3.03343	−0.152244	−0.0761218	−	0.997099i	$-0.524254\pi$
$397$	−3.03343	−0.152244	−0.0761218	+	0.997099i	$0.524254\pi$
$398$	24.9851	1.25239
$399$	10.0310	0.502179
$400$	17.0140	0.850701
$401$	2.17194	0.108461	0.0542306	−	0.998528i	$-0.482729\pi$
$401$	2.17194	0.108461	0.0542306	+	0.998528i	$0.482729\pi$
$402$	−114.225	−5.69704
$403$	4.44014	0.221179
$404$	−51.0018	−2.53744
$405$	−4.74975	−0.236017
$406$	2.09672	0.104058
$407$	−3.45357	−0.171187
$408$	−159.320	−7.88754
$409$	5.61090	0.277441	0.138720	−	0.990332i	$-0.455701\pi$
$409$	5.61090	0.277441	0.138720	+	0.990332i	$0.455701\pi$
$410$	5.74686	0.283817
$411$	5.37187	0.264975
$412$	−93.6733	−4.61495
$413$	3.39960	0.167283
$414$	−43.3566	−2.13086
$415$	−9.48831	−0.465763
$416$	−49.3882	−2.42146
$417$	−29.3975	−1.43960
$418$	−38.2685	−1.87177
$419$	−24.2117	−1.18282	−0.591409	−	0.806372i	$-0.701428\pi$
$419$	−24.2117	−1.18282	−0.591409	+	0.806372i	$0.701428\pi$
$420$	7.44759	0.363405
$421$	−10.1020	−0.492343	−0.246172	−	0.969226i	$-0.579173\pi$
$421$	−10.1020	−0.492343	−0.246172	+	0.969226i	$0.579173\pi$
$422$	60.8301	2.96116
$423$	−18.7075	−0.909592
$424$	−39.2025	−1.90384
$425$	5.86033	0.284268
$426$	88.1614	4.27144
$427$	−5.51108	−0.266700
$428$	−7.68292	−0.371368
$429$	8.83667	0.426638
$430$	−33.8870	−1.63418
$431$	−4.12709	−0.198795	−0.0993974	−	0.995048i	$-0.531692\pi$
$431$	−4.12709	−0.198795	−0.0993974	+	0.995048i	$0.531692\pi$
$432$	47.4127	2.28114
$433$	30.9923	1.48940	0.744698	−	0.667402i	$-0.232594\pi$
$433$	30.9923	1.48940	0.744698	+	0.667402i	$0.232594\pi$
$434$	−3.28186	−0.157534
$435$	−4.07312	−0.195291
$436$	83.5186	3.99981
$437$	29.5949	1.41572
$438$	−91.6459	−4.37901
$439$	23.7784	1.13488	0.567441	−	0.823414i	$-0.307934\pi$
$439$	23.7784	1.13488	0.567441	+	0.823414i	$0.307934\pi$
$440$	−18.4291	−0.878575
$441$	−27.3634	−1.30302
$442$	−30.0545	−1.42955
$443$	−30.4576	−1.44708	−0.723542	−	0.690280i	$-0.757487\pi$
$443$	−30.4576	−1.44708	−0.723542	+	0.690280i	$0.757487\pi$
$444$	−28.9982	−1.37619
$445$	−13.3533	−0.633007
$446$	6.37657	0.301940
$447$	42.4434	2.00751
$448$	19.7353	0.932403
$449$	−27.9561	−1.31933	−0.659665	−	0.751560i	$-0.729302\pi$
$449$	−27.9561	−1.31933	−0.659665	+	0.751560i	$0.729302\pi$
$450$	−11.2312	−0.529442
$451$	−3.72950	−0.175615
$452$	76.7511	3.61007
$453$	−1.51618	−0.0712364
$454$	47.2116	2.21575
$455$	0.911270	0.0427210
$456$	−208.419	−9.76009
$457$	−6.16309	−0.288297	−0.144149	−	0.989556i	$-0.546044\pi$
$457$	−6.16309	−0.288297	−0.144149	+	0.989556i	$0.546044\pi$
$458$	−57.6358	−2.69314
$459$	16.3309	0.762260
$460$	21.9729	1.02449
$461$	−13.5916	−0.633025	−0.316512	−	0.948588i	$-0.602512\pi$
$461$	−13.5916	−0.633025	−0.316512	+	0.948588i	$0.602512\pi$
$462$	−6.53148	−0.303872
$463$	−2.56198	−0.119065	−0.0595327	−	0.998226i	$-0.518961\pi$
$463$	−2.56198	−0.119065	−0.0595327	+	0.998226i	$0.518961\pi$
$464$	−26.1008	−1.21170
$465$	6.37539	0.295652
$466$	−66.2616	−3.06951
$467$	3.74406	0.173254	0.0866271	−	0.996241i	$-0.472391\pi$
$467$	3.74406	0.173254	0.0866271	+	0.996241i	$0.472391\pi$
$468$	42.6222	1.97021
$469$	7.64435	0.352983
$470$	12.8123	0.590986
$471$	−25.0782	−1.15554
$472$	−70.6349	−3.25123
$473$	21.9914	1.01117
$474$	−7.09321	−0.325802
$475$	7.66632	0.351755
$476$	16.4383	0.753448
$477$	15.5043	0.709894
$478$	3.53026	0.161470
$479$	26.2473	1.19927	0.599635	−	0.800274i	$-0.295313\pi$
$479$	26.2473	1.19927	0.599635	+	0.800274i	$0.295313\pi$
$480$	−70.9143	−3.23678
$481$	−3.54815	−0.161782
$482$	−82.7627	−3.76974
$483$	5.05112	0.229834
$484$	−44.1722	−2.00783
$485$	−1.46110	−0.0663452
$486$	58.1619	2.63828
$487$	23.5449	1.06692	0.533460	−	0.845825i	$-0.320891\pi$
$487$	23.5449	1.06692	0.533460	+	0.845825i	$0.320891\pi$
$488$	114.506	5.18344
$489$	38.9618	1.76191
$490$	18.7405	0.846607
$491$	−10.5564	−0.476404	−0.238202	−	0.971216i	$-0.576558\pi$
$491$	−10.5564	−0.476404	−0.238202	+	0.971216i	$0.576558\pi$
$492$	−31.3150	−1.41179
$493$	−8.99019	−0.404898
$494$	−39.3165	−1.76893
$495$	7.28861	0.327599
$496$	40.8539	1.83439
$497$	−5.90007	−0.264654
$498$	69.8694	3.13092
$499$	20.5411	0.919545	0.459773	−	0.888037i	$-0.347931\pi$
$499$	20.5411	0.919545	0.459773	+	0.888037i	$0.347931\pi$
$500$	5.69191	0.254550
$501$	−14.5465	−0.649891
$502$	−18.2843	−0.816066
$503$	20.5283	0.915314	0.457657	−	0.889129i	$-0.348689\pi$
$503$	20.5283	0.915314	0.457657	+	0.889129i	$0.348689\pi$
$504$	−20.4340	−0.910201
$505$	−8.96040	−0.398733
$506$	−19.2701	−0.856661
$507$	−25.4376	−1.12973
$508$	−120.793	−5.35932
$509$	4.68119	0.207490	0.103745	−	0.994604i	$-0.466917\pi$
$509$	4.68119	0.207490	0.103745	+	0.994604i	$0.466917\pi$
$510$	−43.1539	−1.91089
$511$	6.13327	0.271320
$512$	−106.001	−4.68461
$513$	21.3636	0.943226
$514$	19.3039	0.851458
$515$	−16.4573	−0.725193
$516$	184.653	8.12887
$517$	−8.31469	−0.365680
$518$	2.62256	0.115229
$519$	−45.8318	−2.01179
$520$	−18.9338	−0.830304
$521$	−18.2973	−0.801619	−0.400810	−	0.916161i	$-0.631271\pi$
$521$	−18.2973	−0.801619	−0.400810	+	0.916161i	$0.631271\pi$
$522$	17.2295	0.754113
$523$	3.97783	0.173938	0.0869692	−	0.996211i	$-0.472282\pi$
$523$	3.97783	0.173938	0.0869692	+	0.996211i	$0.472282\pi$
$524$	52.2301	2.28168
$525$	1.30845	0.0571055
$526$	68.6782	2.99451
$527$	14.0718	0.612975
$528$	81.3065	3.53841
$529$	−8.09747	−0.352064
$530$	−10.6185	−0.461237
$531$	27.9356	1.21230
$532$	21.5041	0.932322
$533$	−3.83164	−0.165967
$534$	98.3301	4.25516
$535$	−1.34980	−0.0583568
$536$	−158.830	−6.86041
$537$	−44.3006	−1.91171
$538$	62.1429	2.67917
$539$	−12.1619	−0.523848
$540$	15.8616	0.682573
$541$	−9.54517	−0.410379	−0.205189	−	0.978722i	$-0.565781\pi$
$541$	−9.54517	−0.410379	−0.205189	+	0.978722i	$0.565781\pi$
$542$	−14.5069	−0.623126
$543$	−62.4731	−2.68098
$544$	−156.522	−6.71082
$545$	14.6732	0.628531
$546$	−6.71035	−0.287177
$547$	−26.1992	−1.12020	−0.560098	−	0.828426i	$-0.689237\pi$
$547$	−26.1992	−1.12020	−0.560098	+	0.828426i	$0.689237\pi$
$548$	11.5160	0.491940
$549$	−45.2864	−1.93277
$550$	−4.99176	−0.212850
$551$	−11.7607	−0.501023
$552$	−104.949	−4.46694
$553$	0.474702	0.0201864
$554$	−63.1548	−2.68319
$555$	−5.09463	−0.216255
$556$	−63.0213	−2.67270
$557$	−1.38292	−0.0585963	−0.0292981	−	0.999571i	$-0.509327\pi$
$557$	−1.38292	−0.0585963	−0.0292981	+	0.999571i	$0.509327\pi$
$558$	−26.9681	−1.14165
$559$	22.5937	0.955610
$560$	8.38463	0.354315
$561$	28.0053	1.18238
$562$	−7.80095	−0.329063
$563$	22.4881	0.947758	0.473879	−	0.880590i	$-0.342853\pi$
$563$	22.4881	0.947758	0.473879	+	0.880590i	$0.342853\pi$
$564$	−69.8149	−2.93974
$565$	13.4842	0.567286
$566$	29.2297	1.22862
$567$	−2.34071	−0.0983006
$568$	122.588	5.14369
$569$	11.3601	0.476241	0.238121	−	0.971236i	$-0.423469\pi$
$569$	11.3601	0.476241	0.238121	+	0.971236i	$0.423469\pi$
$570$	−56.4528	−2.36455
$571$	29.0655	1.21635	0.608177	−	0.793801i	$-0.291901\pi$
$571$	29.0655	1.21635	0.608177	+	0.793801i	$0.291901\pi$
$572$	18.9437	0.792077
$573$	−35.5847	−1.48657
$574$	2.83209	0.118209
$575$	3.86038	0.160989
$576$	162.171	6.75713
$577$	27.4397	1.14233	0.571165	−	0.820835i	$-0.306492\pi$
$577$	27.4397	1.14233	0.571165	+	0.820835i	$0.306492\pi$
$578$	−48.1009	−2.00073
$579$	−13.3741	−0.555811
$580$	−8.73182	−0.362569
$581$	−4.67590	−0.193989
$582$	10.7592	0.445981
$583$	6.89099	0.285396
$584$	−127.433	−5.27323
$585$	7.48821	0.309600
$586$	62.9032	2.59851
$587$	−31.4766	−1.29918	−0.649588	−	0.760286i	$-0.725059\pi$
$587$	−31.4766	−1.29918	−0.649588	+	0.760286i	$0.725059\pi$
$588$	−102.118	−4.21127
$589$	18.4083	0.758500
$590$	−19.1323	−0.787666
$591$	15.2406	0.626916
$592$	−32.6467	−1.34177
$593$	−3.99895	−0.164217	−0.0821086	−	0.996623i	$-0.526165\pi$
$593$	−3.99895	−0.164217	−0.0821086	+	0.996623i	$0.526165\pi$
$594$	−13.9105	−0.570753
$595$	2.88801	0.118397
$596$	90.9887	3.72704
$597$	−23.9191	−0.978945
$598$	−19.7978	−0.809594
$599$	46.4007	1.89588	0.947940	−	0.318448i	$-0.103162\pi$
$599$	46.4007	1.89588	0.947940	+	0.318448i	$0.103162\pi$
$600$	−27.1862	−1.10987
$601$	5.01695	0.204645	0.102323	−	0.994751i	$-0.467373\pi$
$601$	5.01695	0.204645	0.102323	+	0.994751i	$0.467373\pi$
$602$	−16.6997	−0.680631
$603$	62.8162	2.55807
$604$	−3.25034	−0.132254
$605$	−7.76053	−0.315510
$606$	65.9820	2.68034
$607$	−30.6861	−1.24551	−0.622756	−	0.782416i	$-0.713987\pi$
$607$	−30.6861	−1.24551	−0.622756	+	0.782416i	$0.713987\pi$
$608$	−204.757	−8.30401
$609$	−2.00726	−0.0813384
$610$	31.0154	1.25578
$611$	−8.54240	−0.345588
$612$	135.079	5.46025
$613$	24.4233	0.986449	0.493224	−	0.869902i	$-0.335818\pi$
$613$	24.4233	0.986449	0.493224	+	0.869902i	$0.335818\pi$
$614$	−47.3789	−1.91206
$615$	−5.50167	−0.221849
$616$	−9.08201	−0.365925
$617$	−34.1705	−1.37565	−0.687826	−	0.725876i	$-0.741435\pi$
$617$	−34.1705	−1.37565	−0.687826	+	0.725876i	$0.741435\pi$
$618$	121.187	4.87485
$619$	−41.5118	−1.66850	−0.834250	−	0.551386i	$-0.814099\pi$
$619$	−41.5118	−1.66850	−0.834250	+	0.551386i	$0.814099\pi$
$620$	13.6673	0.548894
$621$	10.7577	0.431690
$622$	−20.3757	−0.816990
$623$	−6.58060	−0.263646
$624$	83.5331	3.34400
$625$	1.00000	0.0400000
$626$	−69.6520	−2.78385
$627$	36.6357	1.46309
$628$	−53.7618	−2.14533
$629$	−11.2449	−0.448362
$630$	−5.53479	−0.220511
$631$	−24.6451	−0.981104	−0.490552	−	0.871412i	$-0.663205\pi$
$631$	−24.6451	−0.981104	−0.490552	+	0.871412i	$0.663205\pi$
$632$	−9.86309	−0.392333
$633$	−58.2348	−2.31462
$634$	−70.0874	−2.78353
$635$	−21.2219	−0.842164
$636$	57.8607	2.29433
$637$	−12.4949	−0.495067
$638$	7.65774	0.303173
$639$	−48.4829	−1.91795
$640$	−57.6491	−2.27878
$641$	−13.5245	−0.534187	−0.267094	−	0.963671i	$-0.586063\pi$
$641$	−13.5245	−0.534187	−0.267094	+	0.963671i	$0.586063\pi$
$642$	9.93954	0.392282
$643$	3.72775	0.147008	0.0735040	−	0.997295i	$-0.476582\pi$
$643$	3.72775	0.147008	0.0735040	+	0.997295i	$0.476582\pi$
$644$	10.8284	0.426699
$645$	32.4412	1.27737
$646$	−124.602	−4.90241
$647$	31.2130	1.22711	0.613554	−	0.789653i	$-0.289739\pi$
$647$	31.2130	1.22711	0.613554	+	0.789653i	$0.289739\pi$
$648$	48.6339	1.91052
$649$	12.4162	0.487377
$650$	−5.12847	−0.201155
$651$	3.14184	0.123138
$652$	83.5248	3.27108
$653$	−23.2433	−0.909581	−0.454790	−	0.890599i	$-0.650286\pi$
$653$	−23.2433	−0.909581	−0.454790	+	0.890599i	$0.650286\pi$
$654$	−108.050	−4.22507
$655$	9.17620	0.358544
$656$	−35.2550	−1.37648
$657$	50.3991	1.96626
$658$	6.31398	0.246144
$659$	−39.6539	−1.54470	−0.772348	−	0.635199i	$-0.780918\pi$
$659$	−39.6539	−1.54470	−0.772348	+	0.635199i	$0.780918\pi$
$660$	27.2004	1.05878
$661$	−33.6178	−1.30758	−0.653790	−	0.756676i	$-0.726822\pi$
$661$	−33.6178	−1.30758	−0.653790	+	0.756676i	$0.726822\pi$
$662$	51.9382	2.01864
$663$	28.7722	1.11742
$664$	97.1532	3.77028
$665$	3.77802	0.146505
$666$	21.5505	0.835063
$667$	−5.92211	−0.229305
$668$	−31.1843	−1.20656
$669$	−6.10452	−0.236014
$670$	−43.0211	−1.66205
$671$	−20.1278	−0.777026
$672$	−34.9470	−1.34811
$673$	30.5527	1.17772	0.588859	−	0.808236i	$-0.299577\pi$
$673$	30.5527	1.17772	0.588859	+	0.808236i	$0.299577\pi$
$674$	−16.7711	−0.645999
$675$	2.78668	0.107259
$676$	−54.5323	−2.09740
$677$	−15.1957	−0.584017	−0.292008	−	0.956416i	$-0.594324\pi$
$677$	−15.1957	−0.584017	−0.292008	+	0.956416i	$0.594324\pi$
$678$	−99.2944	−3.81338
$679$	−0.720040	−0.0276326
$680$	−60.0054	−2.30110
$681$	−45.1973	−1.73196
$682$	−11.9862	−0.458974
$683$	6.22297	0.238115	0.119058	−	0.992887i	$-0.462013\pi$
$683$	6.22297	0.238115	0.119058	+	0.992887i	$0.462013\pi$
$684$	176.707	6.75655
$685$	2.02323	0.0773035
$686$	18.8028	0.717893
$687$	55.1767	2.10512
$688$	207.885	7.92554
$689$	7.07971	0.269715
$690$	−28.4268	−1.08219
$691$	39.1033	1.48756	0.743780	−	0.668424i	$-0.233031\pi$
$691$	39.1033	1.48756	0.743780	+	0.668424i	$0.233031\pi$
$692$	−98.2525	−3.73500
$693$	3.59188	0.136444
$694$	−34.7335	−1.31847
$695$	−11.0721	−0.419988
$696$	41.7057	1.58085
$697$	−12.1433	−0.459960
$698$	−6.13723	−0.232298
$699$	63.4346	2.39932
$700$	2.80501	0.106019
$701$	9.94793	0.375728	0.187864	−	0.982195i	$-0.439844\pi$
$701$	9.94793	0.375728	0.187864	+	0.982195i	$0.439844\pi$
$702$	−14.2914	−0.539395
$703$	−14.7102	−0.554806
$704$	72.0780	2.71654
$705$	−12.2656	−0.461951
$706$	56.3087	2.11921
$707$	−4.41575	−0.166071
$708$	104.253	3.91808
$709$	−15.5648	−0.584547	−0.292274	−	0.956335i	$-0.594412\pi$
$709$	−15.5648	−0.584547	−0.292274	+	0.956335i	$0.594412\pi$
$710$	33.2046	1.24615
$711$	3.90079	0.146291
$712$	136.728	5.12409
$713$	9.26949	0.347145
$714$	−21.2665	−0.795880
$715$	3.32819	0.124467
$716$	−94.9700	−3.54920
$717$	−3.37964	−0.126215
$718$	11.3883	0.425009
$719$	45.7354	1.70564	0.852822	−	0.522202i	$-0.174889\pi$
$719$	45.7354	1.70564	0.852822	+	0.522202i	$0.174889\pi$
$720$	68.8993	2.56773
$721$	−8.11025	−0.302041
$722$	−110.306	−4.10517
$723$	79.2316	2.94665
$724$	−133.928	−4.97738
$725$	−1.53408	−0.0569741
$726$	57.1465	2.12090
$727$	38.9134	1.44322	0.721609	−	0.692301i	$-0.243403\pi$
$727$	38.9134	1.44322	0.721609	+	0.692301i	$0.243403\pi$
$728$	−9.33073	−0.345820
$729$	−41.4312	−1.53449
$730$	−34.5169	−1.27753
$731$	71.6042	2.64838
$732$	−169.005	−6.24659
$733$	25.3781	0.937362	0.468681	−	0.883368i	$-0.344729\pi$
$733$	25.3781	0.937362	0.468681	+	0.883368i	$0.344729\pi$
$734$	−33.2830	−1.22850
$735$	−17.9409	−0.661760
$736$	−103.106	−3.80053
$737$	27.9191	1.02841
$738$	23.2723	0.856664
$739$	28.6280	1.05310	0.526549	−	0.850145i	$-0.323486\pi$
$739$	28.6280	1.05310	0.526549	+	0.850145i	$0.323486\pi$
$740$	−10.9217	−0.401489
$741$	37.6390	1.38270
$742$	−5.23285	−0.192104
$743$	26.2492	0.962989	0.481494	−	0.876449i	$-0.340094\pi$
$743$	26.2492	0.962989	0.481494	+	0.876449i	$0.340094\pi$
$744$	−65.2793	−2.39325
$745$	15.9856	0.585668
$746$	−25.0960	−0.918831
$747$	−38.4235	−1.40584
$748$	60.0368	2.19516
$749$	−0.665189	−0.0243055
$750$	−7.36373	−0.268886
$751$	−10.3506	−0.377699	−0.188849	−	0.982006i	$-0.560476\pi$
$751$	−10.3506	−0.377699	−0.188849	+	0.982006i	$0.560476\pi$
$752$	−78.5989	−2.86621
$753$	17.5042	0.637887
$754$	7.86746	0.286516
$755$	−0.571045	−0.0207825
$756$	7.81668	0.284290
$757$	21.8936	0.795735	0.397868	−	0.917443i	$-0.369750\pi$
$757$	21.8936	0.795735	0.397868	+	0.917443i	$0.369750\pi$
$758$	21.5131	0.781392
$759$	18.4479	0.669618
$760$	−78.4974	−2.84740
$761$	41.2979	1.49705	0.748524	−	0.663107i	$-0.230763\pi$
$761$	41.2979	1.49705	0.748524	+	0.663107i	$0.230763\pi$
$762$	156.272	5.66114
$763$	7.23106	0.261782
$764$	−76.2852	−2.75990
$765$	23.7318	0.858023
$766$	88.0761	3.18232
$767$	12.7562	0.460600
$768$	211.857	7.64473
$769$	40.4605	1.45904	0.729522	−	0.683957i	$-0.239742\pi$
$769$	40.4605	1.45904	0.729522	+	0.683957i	$0.239742\pi$
$770$	−2.45998	−0.0886514
$771$	−18.4803	−0.665551
$772$	−28.6710	−1.03189
$773$	22.3283	0.803093	0.401546	−	0.915839i	$-0.368473\pi$
$773$	22.3283	0.803093	0.401546	+	0.915839i	$0.368473\pi$
$774$	−137.227	−4.93254
$775$	2.40119	0.0862532
$776$	14.9606	0.537054
$777$	−2.51067	−0.0900697
$778$	56.3895	2.02166
$779$	−15.8855	−0.569157
$780$	27.9454	1.00060
$781$	−21.5485	−0.771067
$782$	−62.7436	−2.24371
$783$	−4.27498	−0.152775
$784$	−114.966	−4.10594
$785$	−9.44530	−0.337117
$786$	−67.5711	−2.41018
$787$	−31.7192	−1.13067	−0.565334	−	0.824862i	$-0.691253\pi$
$787$	−31.7192	−1.13067	−0.565334	+	0.824862i	$0.691253\pi$
$788$	32.6723	1.16390
$789$	−65.7480	−2.34069
$790$	−2.67154	−0.0950492
$791$	6.64513	0.236273
$792$	−74.6299	−2.65186
$793$	−20.6790	−0.734334
$794$	8.41301	0.298567
$795$	10.1654	0.360531
$796$	−51.2770	−1.81747
$797$	24.0226	0.850924	0.425462	−	0.904976i	$-0.360112\pi$
$797$	24.0226	0.850924	0.425462	+	0.904976i	$0.360112\pi$
$798$	−27.8203	−0.984828
$799$	−27.0727	−0.957763
$800$	−26.7087	−0.944295
$801$	−54.0750	−1.91064
$802$	−6.02371	−0.212705
$803$	22.4002	0.790486
$804$	234.425	8.26752
$805$	1.90242	0.0670515
$806$	−12.3144	−0.433757
$807$	−59.4915	−2.09420
$808$	91.7478	3.22768
$809$	−30.1692	−1.06069	−0.530346	−	0.847781i	$-0.677938\pi$
$809$	−30.1692	−1.06069	−0.530346	+	0.847781i	$0.677938\pi$
$810$	13.1731	0.462856
$811$	−3.56734	−0.125266	−0.0626331	−	0.998037i	$-0.519950\pi$
$811$	−3.56734	−0.125266	−0.0626331	+	0.998037i	$0.519950\pi$
$812$	−4.30310	−0.151009
$813$	13.8880	0.487073
$814$	9.57824	0.335717
$815$	14.6743	0.514018
$816$	264.734	9.26755
$817$	93.6706	3.27712
$818$	−15.5614	−0.544092
$819$	3.69024	0.128948
$820$	−11.7943	−0.411875
$821$	40.7493	1.42216	0.711081	−	0.703110i	$-0.248206\pi$
$821$	40.7493	1.42216	0.711081	+	0.703110i	$0.248206\pi$
$822$	−14.8985	−0.519645
$823$	−18.2768	−0.637089	−0.318545	−	0.947908i	$-0.603194\pi$
$823$	−18.2768	−0.637089	−0.318545	+	0.947908i	$0.603194\pi$
$824$	168.510	5.87033
$825$	4.77879	0.166376
$826$	−9.42854	−0.328061
$827$	48.0630	1.67131	0.835656	−	0.549253i	$-0.185088\pi$
$827$	48.0630	1.67131	0.835656	+	0.549253i	$0.185088\pi$
$828$	88.9807	3.09229
$829$	−53.7457	−1.86666	−0.933332	−	0.359015i	$-0.883113\pi$
$829$	−53.7457	−1.86666	−0.933332	+	0.359015i	$0.883113\pi$
$830$	26.3152	0.913413
$831$	60.4603	2.09734
$832$	74.0520	2.56729
$833$	−39.5991	−1.37203
$834$	81.5319	2.82322
$835$	−5.47871	−0.189599
$836$	78.5384	2.71631
$837$	6.69135	0.231287
$838$	67.1494	2.31964
$839$	29.7978	1.02874	0.514368	−	0.857570i	$-0.328027\pi$
$839$	29.7978	1.02874	0.514368	+	0.857570i	$0.328027\pi$
$840$	−13.3976	−0.462260
$841$	−26.6466	−0.918849
$842$	28.0173	0.965540
$843$	7.46812	0.257216
$844$	−124.842	−4.29723
$845$	−9.58067	−0.329585
$846$	51.8841	1.78381
$847$	−3.82444	−0.131409
$848$	65.1406	2.23694
$849$	−27.9826	−0.960362
$850$	−16.2532	−0.557481
$851$	−7.40733	−0.253920
$852$	−180.934	−6.19869
$853$	36.5686	1.25208	0.626042	−	0.779789i	$-0.284674\pi$
$853$	36.5686	1.25208	0.626042	+	0.779789i	$0.284674\pi$
$854$	15.2846	0.523028
$855$	31.0452	1.06172
$856$	13.8209	0.472389
$857$	32.5596	1.11221	0.556107	−	0.831111i	$-0.312294\pi$
$857$	32.5596	1.11221	0.556107	+	0.831111i	$0.312294\pi$
$858$	−24.5079	−0.836685
$859$	−29.4339	−1.00427	−0.502136	−	0.864789i	$-0.667452\pi$
$859$	−29.4339	−1.00427	−0.502136	+	0.864789i	$0.667452\pi$
$860$	69.5463	2.37151
$861$	−2.71126	−0.0923996
$862$	11.4462	0.389859
$863$	−44.9274	−1.52935	−0.764673	−	0.644418i	$-0.777100\pi$
$863$	−44.9274	−1.52935	−0.764673	+	0.644418i	$0.777100\pi$
$864$	−74.4287	−2.53212
$865$	−17.2618	−0.586918
$866$	−85.9550	−2.92087
$867$	46.0487	1.56390
$868$	6.73536	0.228613
$869$	1.73373	0.0588128
$870$	11.2965	0.382988
$871$	28.6837	0.971909
$872$	−150.243	−5.08786
$873$	−5.91681	−0.200254
$874$	−82.0794	−2.77638
$875$	0.492807	0.0166599
$876$	188.085	6.35480
$877$	−12.3093	−0.415655	−0.207828	−	0.978165i	$-0.566639\pi$
$877$	−12.3093	−0.415655	−0.207828	+	0.978165i	$0.566639\pi$
$878$	−65.9477	−2.22563
$879$	−60.2194	−2.03115
$880$	30.6227	1.03229
$881$	−3.33586	−0.112388	−0.0561940	−	0.998420i	$-0.517897\pi$
$881$	−3.33586	−0.112388	−0.0561940	+	0.998420i	$0.517897\pi$
$882$	75.8906	2.55537
$883$	−12.9266	−0.435014	−0.217507	−	0.976059i	$-0.569792\pi$
$883$	−12.9266	−0.435014	−0.217507	+	0.976059i	$0.569792\pi$
$884$	61.6809	2.07455
$885$	18.3160	0.615687
$886$	84.4720	2.83789
$887$	53.0679	1.78185	0.890923	−	0.454155i	$-0.150059\pi$
$887$	53.0679	1.78185	0.890923	+	0.454155i	$0.150059\pi$
$888$	52.1652	1.75055
$889$	−10.4583	−0.350759
$890$	37.0344	1.24140
$891$	−8.54885	−0.286397
$892$	−13.0866	−0.438173
$893$	−35.4157	−1.18514
$894$	−117.714	−3.93694
$895$	−16.6851	−0.557721
$896$	−28.4099	−0.949107
$897$	18.9532	0.632827
$898$	77.5342	2.58735
$899$	−3.68360	−0.122855
$900$	23.0497	0.768324
$901$	22.4371	0.747489
$902$	10.3435	0.344401
$903$	15.9872	0.532022
$904$	−138.069	−4.59209
$905$	−23.5295	−0.782146
$906$	4.20502	0.139703
$907$	−6.48330	−0.215275	−0.107637	−	0.994190i	$-0.534329\pi$
$907$	−6.48330	−0.215275	−0.107637	+	0.994190i	$0.534329\pi$
$908$	−96.8924	−3.21549
$909$	−36.2857	−1.20352
$910$	−2.52734	−0.0837806
$911$	−38.3147	−1.26942	−0.634712	−	0.772749i	$-0.718881\pi$
$911$	−38.3147	−1.26942	−0.634712	+	0.772749i	$0.718881\pi$
$912$	346.318	11.4677
$913$	−17.0776	−0.565185
$914$	17.0929	0.565383
$915$	−29.6921	−0.981590
$916$	118.286	3.90828
$917$	4.52209	0.149333
$918$	−45.2926	−1.49488
$919$	15.6205	0.515271	0.257636	−	0.966242i	$-0.417057\pi$
$919$	15.6205	0.515271	0.257636	+	0.966242i	$0.417057\pi$
$920$	−39.5274	−1.30318
$921$	45.3575	1.49458
$922$	37.6954	1.24143
$923$	−22.1387	−0.728703
$924$	13.4046	0.440978
$925$	−1.91881	−0.0630900
$926$	7.10548	0.233500
$927$	−66.6446	−2.18890
$928$	40.9731	1.34501
$929$	−24.7128	−0.810801	−0.405400	−	0.914139i	$-0.632868\pi$
$929$	−24.7128	−0.810801	−0.405400	+	0.914139i	$0.632868\pi$
$930$	−17.6817	−0.579806
$931$	−51.8024	−1.69776
$932$	135.989	4.45446
$933$	19.5063	0.638609
$934$	−10.3839	−0.339771
$935$	10.5477	0.344948
$936$	−76.6737	−2.50616
$937$	−4.36981	−0.142755	−0.0713777	−	0.997449i	$-0.522740\pi$
$937$	−4.36981	−0.142755	−0.0713777	+	0.997449i	$0.522740\pi$
$938$	−21.2011	−0.692240
$939$	66.6802	2.17603
$940$	−26.2946	−0.857637
$941$	27.1944	0.886511	0.443255	−	0.896395i	$-0.353823\pi$
$941$	27.1944	0.886511	0.443255	+	0.896395i	$0.353823\pi$
$942$	69.5527	2.26615
$943$	−7.99915	−0.260488
$944$	117.370	3.82008
$945$	1.37330	0.0446733
$946$	−60.9916	−1.98301
$947$	19.1234	0.621428	0.310714	−	0.950503i	$-0.399432\pi$
$947$	19.1234	0.621428	0.310714	+	0.950503i	$0.399432\pi$
$948$	14.5574	0.472802
$949$	23.0137	0.747055
$950$	−21.2620	−0.689830
$951$	67.0971	2.17577
$952$	−29.5711	−0.958404
$953$	33.6728	1.09077	0.545385	−	0.838185i	$-0.316383\pi$
$953$	33.6728	1.09077	0.545385	+	0.838185i	$0.316383\pi$
$954$	−43.0001	−1.39218
$955$	−13.4024	−0.433691
$956$	−7.24515	−0.234325
$957$	−7.33102	−0.236978
$958$	−72.7950	−2.35190
$959$	0.997060	0.0321967
$960$	106.328	3.43172
$961$	−25.2343	−0.814010
$962$	9.84055	0.317272
$963$	−5.46608	−0.176142
$964$	169.854	5.47062
$965$	−5.03715	−0.162152
$966$	−14.0089	−0.450730
$967$	−48.0406	−1.54488	−0.772441	−	0.635087i	$-0.780964\pi$
$967$	−48.0406	−1.54488	−0.772441	+	0.635087i	$0.780964\pi$
$968$	79.4620	2.55401
$969$	119.286	3.83202
$970$	4.05226	0.130110
$971$	18.7520	0.601781	0.300891	−	0.953659i	$-0.402716\pi$
$971$	18.7520	0.601781	0.300891	+	0.953659i	$0.402716\pi$
$972$	−119.366	−3.82866
$973$	−5.45640	−0.174924
$974$	−65.3001	−2.09235
$975$	4.90966	0.157235
$976$	−190.269	−6.09035
$977$	−21.1537	−0.676765	−0.338383	−	0.941009i	$-0.609880\pi$
$977$	−21.1537	−0.676765	−0.338383	+	0.941009i	$0.609880\pi$
$978$	−108.058	−3.45530
$979$	−24.0340	−0.768129
$980$	−38.4610	−1.22859
$981$	59.4200	1.89713
$982$	29.2775	0.934282
$983$	38.7779	1.23682	0.618411	−	0.785855i	$-0.287777\pi$
$983$	38.7779	1.23682	0.618411	+	0.785855i	$0.287777\pi$
$984$	56.3330	1.79583
$985$	5.74014	0.182896
$986$	24.9337	0.794049
$987$	−6.04459	−0.192401
$988$	80.6893	2.56707
$989$	47.1679	1.49985
$990$	−20.2144	−0.642457
$991$	42.3622	1.34568	0.672841	−	0.739787i	$-0.265074\pi$
$991$	42.3622	1.34568	0.672841	+	0.739787i	$0.265074\pi$
$992$	−64.1326	−2.03621
$993$	−49.7223	−1.57789
$994$	16.3634	0.519017
$995$	−9.00875	−0.285597
$996$	−143.393	−4.54358
$997$	14.8169	0.469255	0.234627	−	0.972085i	$-0.424613\pi$
$997$	14.8169	0.469255	0.234627	+	0.972085i	$0.424613\pi$
$998$	−56.9692	−1.80333
$999$	−5.34711	−0.169175

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8045.2.a.e.1.1	✓	142

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8045.2.a.e.1.1	✓	142	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:	\( N \)	\(=\)	\( 8045 = 5 \cdot 1609 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77343 q^{2} +2.65510 q^{3} +5.69191 q^{4} +1.00000 q^{5} -7.36373 q^{6} +0.492807 q^{7} -10.2393 q^{8} +4.04956 q^{9} +O(q^{10})\)	\(q-2.77343 q^{2} +2.65510 q^{3} +5.69191 q^{4} +1.00000 q^{5} -7.36373 q^{6} +0.492807 q^{7} -10.2393 q^{8} +4.04956 q^{9} -2.77343 q^{10} +1.79985 q^{11} +15.1126 q^{12} +1.84914 q^{13} -1.36676 q^{14} +2.65510 q^{15} +17.0140 q^{16} +5.86033 q^{17} -11.2312 q^{18} +7.66632 q^{19} +5.69191 q^{20} +1.30845 q^{21} -4.99176 q^{22} +3.86038 q^{23} -27.1862 q^{24} +1.00000 q^{25} -5.12847 q^{26} +2.78668 q^{27} +2.80501 q^{28} -1.53408 q^{29} -7.36373 q^{30} +2.40119 q^{31} -26.7087 q^{32} +4.77879 q^{33} -16.2532 q^{34} +0.492807 q^{35} +23.0497 q^{36} -1.91881 q^{37} -21.2620 q^{38} +4.90966 q^{39} -10.2393 q^{40} -2.07211 q^{41} -3.62890 q^{42} +12.2185 q^{43} +10.2446 q^{44} +4.04956 q^{45} -10.7065 q^{46} -4.61965 q^{47} +45.1740 q^{48} -6.75714 q^{49} -2.77343 q^{50} +15.5598 q^{51} +10.5252 q^{52} +3.82864 q^{53} -7.72867 q^{54} +1.79985 q^{55} -5.04597 q^{56} +20.3549 q^{57} +4.25465 q^{58} +6.89844 q^{59} +15.1126 q^{60} -11.1830 q^{61} -6.65952 q^{62} +1.99565 q^{63} +40.0466 q^{64} +1.84914 q^{65} -13.2536 q^{66} +15.5119 q^{67} +33.3565 q^{68} +10.2497 q^{69} -1.36676 q^{70} -11.9724 q^{71} -41.4645 q^{72} +12.4456 q^{73} +5.32168 q^{74} +2.65510 q^{75} +43.6360 q^{76} +0.886980 q^{77} -13.6166 q^{78} +0.963263 q^{79} +17.0140 q^{80} -4.74975 q^{81} +5.74686 q^{82} -9.48831 q^{83} +7.44759 q^{84} +5.86033 q^{85} -33.8870 q^{86} -4.07312 q^{87} -18.4291 q^{88} -13.3533 q^{89} -11.2312 q^{90} +0.911270 q^{91} +21.9729 q^{92} +6.37539 q^{93} +12.8123 q^{94} +7.66632 q^{95} -70.9143 q^{96} -1.46110 q^{97} +18.7405 q^{98} +7.28861 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 142 q + 21 q^{2} + 33 q^{3} + 157 q^{4} + 142 q^{5} + 15 q^{6} + 63 q^{7} + 60 q^{8} + 157 q^{9}+O(q^{10}) \) 142 * q + 21 * q^2 + 33 * q^3 + 157 * q^4 + 142 * q^5 + 15 * q^6 + 63 * q^7 + 60 * q^8 + 157 * q^9	\( 142 q + 21 q^{2} + 33 q^{3} + 157 q^{4} + 142 q^{5} + 15 q^{6} + 63 q^{7} + 60 q^{8} + 157 q^{9} + 21 q^{10} + 36 q^{11} + 55 q^{12} + 57 q^{13} + 2 q^{14} + 33 q^{15} + 179 q^{16} + 55 q^{17} + 65 q^{18} + 130 q^{19} + 157 q^{20} + 28 q^{21} + 30 q^{22} + 117 q^{23} + 21 q^{24} + 142 q^{25} + 21 q^{26} + 120 q^{27} + 135 q^{28} + 12 q^{29} + 15 q^{30} + 74 q^{31} + 126 q^{32} + 55 q^{33} + 35 q^{34} + 63 q^{35} + 186 q^{36} + 75 q^{37} + 65 q^{38} + 23 q^{39} + 60 q^{40} + 22 q^{41} + 10 q^{42} + 190 q^{43} + 22 q^{44} + 157 q^{45} + 56 q^{46} + 102 q^{47} + 78 q^{48} + 197 q^{49} + 21 q^{50} + 30 q^{51} + 120 q^{52} + 56 q^{53} - 6 q^{54} + 36 q^{55} + 3 q^{56} + 68 q^{57} + 31 q^{58} + 55 q^{59} + 55 q^{60} + 90 q^{61} + 68 q^{62} + 167 q^{63} + 180 q^{64} + 57 q^{65} + 17 q^{66} + 151 q^{67} + 119 q^{68} + 21 q^{69} + 2 q^{70} + 4 q^{71} + 130 q^{72} + 143 q^{73} - 46 q^{74} + 33 q^{75} + 213 q^{76} + 75 q^{77} - 24 q^{78} + 47 q^{79} + 179 q^{80} + 150 q^{81} + 69 q^{82} + 201 q^{83} - 31 q^{84} + 55 q^{85} - 4 q^{86} + 153 q^{87} + 37 q^{88} + 25 q^{89} + 65 q^{90} + 132 q^{91} + 194 q^{92} + 52 q^{93} + 18 q^{94} + 130 q^{95} + 13 q^{96} + 80 q^{97} + 58 q^{98} + 103 q^{99}+O(q^{100}) \) 142 * q + 21 * q^2 + 33 * q^3 + 157 * q^4 + 142 * q^5 + 15 * q^6 + 63 * q^7 + 60 * q^8 + 157 * q^9 + 21 * q^10 + 36 * q^11 + 55 * q^12 + 57 * q^13 + 2 * q^14 + 33 * q^15 + 179 * q^16 + 55 * q^17 + 65 * q^18 + 130 * q^19 + 157 * q^20 + 28 * q^21 + 30 * q^22 + 117 * q^23 + 21 * q^24 + 142 * q^25 + 21 * q^26 + 120 * q^27 + 135 * q^28 + 12 * q^29 + 15 * q^30 + 74 * q^31 + 126 * q^32 + 55 * q^33 + 35 * q^34 + 63 * q^35 + 186 * q^36 + 75 * q^37 + 65 * q^38 + 23 * q^39 + 60 * q^40 + 22 * q^41 + 10 * q^42 + 190 * q^43 + 22 * q^44 + 157 * q^45 + 56 * q^46 + 102 * q^47 + 78 * q^48 + 197 * q^49 + 21 * q^50 + 30 * q^51 + 120 * q^52 + 56 * q^53 - 6 * q^54 + 36 * q^55 + 3 * q^56 + 68 * q^57 + 31 * q^58 + 55 * q^59 + 55 * q^60 + 90 * q^61 + 68 * q^62 + 167 * q^63 + 180 * q^64 + 57 * q^65 + 17 * q^66 + 151 * q^67 + 119 * q^68 + 21 * q^69 + 2 * q^70 + 4 * q^71 + 130 * q^72 + 143 * q^73 - 46 * q^74 + 33 * q^75 + 213 * q^76 + 75 * q^77 - 24 * q^78 + 47 * q^79 + 179 * q^80 + 150 * q^81 + 69 * q^82 + 201 * q^83 - 31 * q^84 + 55 * q^85 - 4 * q^86 + 153 * q^87 + 37 * q^88 + 25 * q^89 + 65 * q^90 + 132 * q^91 + 194 * q^92 + 52 * q^93 + 18 * q^94 + 130 * q^95 + 13 * q^96 + 80 * q^97 + 58 * q^98 + 103 * q^99

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