LMFDB - Embedded newform 8023.2.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, 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("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$1$
Dimension:	$158$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70862 q^{2} +0.748763 q^{3} +5.33660 q^{4} -3.98594 q^{5} -2.02811 q^{6} +0.912141 q^{7} -9.03756 q^{8} -2.43935 q^{9} +O(q^{10})$	\(q-2.70862 q^{2} +0.748763 q^{3} +5.33660 q^{4} -3.98594 q^{5} -2.02811 q^{6} +0.912141 q^{7} -9.03756 q^{8} -2.43935 q^{9} +10.7964 q^{10} -1.43215 q^{11} +3.99585 q^{12} -3.27590 q^{13} -2.47064 q^{14} -2.98453 q^{15} +13.8061 q^{16} +3.55832 q^{17} +6.60727 q^{18} -1.62050 q^{19} -21.2714 q^{20} +0.682978 q^{21} +3.87914 q^{22} -1.25726 q^{23} -6.76700 q^{24} +10.8877 q^{25} +8.87315 q^{26} -4.07279 q^{27} +4.86773 q^{28} +6.41914 q^{29} +8.08394 q^{30} -1.29634 q^{31} -19.3203 q^{32} -1.07234 q^{33} -9.63813 q^{34} -3.63574 q^{35} -13.0179 q^{36} -2.43016 q^{37} +4.38930 q^{38} -2.45287 q^{39} +36.0232 q^{40} +2.70524 q^{41} -1.84993 q^{42} +7.66248 q^{43} -7.64280 q^{44} +9.72312 q^{45} +3.40544 q^{46} -8.91948 q^{47} +10.3375 q^{48} -6.16800 q^{49} -29.4907 q^{50} +2.66434 q^{51} -17.4822 q^{52} -6.14645 q^{53} +11.0316 q^{54} +5.70846 q^{55} -8.24354 q^{56} -1.21337 q^{57} -17.3870 q^{58} -5.15399 q^{59} -15.9272 q^{60} +12.2559 q^{61} +3.51130 q^{62} -2.22504 q^{63} +24.7190 q^{64} +13.0575 q^{65} +2.90456 q^{66} +15.1183 q^{67} +18.9893 q^{68} -0.941392 q^{69} +9.84783 q^{70} -1.00000 q^{71} +22.0458 q^{72} +0.774711 q^{73} +6.58236 q^{74} +8.15235 q^{75} -8.64794 q^{76} -1.30632 q^{77} +6.64389 q^{78} +15.0796 q^{79} -55.0303 q^{80} +4.26850 q^{81} -7.32746 q^{82} -16.4118 q^{83} +3.64478 q^{84} -14.1833 q^{85} -20.7547 q^{86} +4.80642 q^{87} +12.9431 q^{88} +2.35548 q^{89} -26.3362 q^{90} -2.98808 q^{91} -6.70950 q^{92} -0.970655 q^{93} +24.1594 q^{94} +6.45921 q^{95} -14.4663 q^{96} -8.35135 q^{97} +16.7067 q^{98} +3.49352 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) $ 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * 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 $

$2$	−2.70862	−1.91528	−0.957640	−	0.287967i	$-0.907021\pi$
$2$	−2.70862	−1.91528	−0.957640	+	0.287967i	$0.907021\pi$
$3$	0.748763	0.432299	0.216149	−	0.976360i	$-0.430650\pi$
$3$	0.748763	0.432299	0.216149	+	0.976360i	$0.430650\pi$
$4$	5.33660	2.66830
$5$	−3.98594	−1.78257	−0.891284	−	0.453445i	$-0.850195\pi$
$5$	−3.98594	−1.78257	−0.891284	+	0.453445i	$0.850195\pi$
$6$	−2.02811	−0.827973
$7$	0.912141	0.344757	0.172379	−	0.985031i	$-0.444855\pi$
$7$	0.912141	0.344757	0.172379	+	0.985031i	$0.444855\pi$
$8$	−9.03756	−3.19526
$9$	−2.43935	−0.813118
$10$	10.7964	3.41412
$11$	−1.43215	−0.431809	−0.215905	−	0.976414i	$-0.569270\pi$
$11$	−1.43215	−0.431809	−0.215905	+	0.976414i	$0.569270\pi$
$12$	3.99585	1.15350
$13$	−3.27590	−0.908570	−0.454285	−	0.890856i	$-0.650105\pi$
$13$	−3.27590	−0.908570	−0.454285	+	0.890856i	$0.650105\pi$
$14$	−2.47064	−0.660307
$15$	−2.98453	−0.770602
$16$	13.8061	3.45152
$17$	3.55832	0.863020	0.431510	−	0.902108i	$-0.357981\pi$
$17$	3.55832	0.863020	0.431510	+	0.902108i	$0.357981\pi$
$18$	6.60727	1.55735
$19$	−1.62050	−0.371767	−0.185884	−	0.982572i	$-0.559515\pi$
$19$	−1.62050	−0.371767	−0.185884	+	0.982572i	$0.559515\pi$
$20$	−21.2714	−4.75643
$21$	0.682978	0.149038
$22$	3.87914	0.827035
$23$	−1.25726	−0.262157	−0.131079	−	0.991372i	$-0.541844\pi$
$23$	−1.25726	−0.262157	−0.131079	+	0.991372i	$0.541844\pi$
$24$	−6.76700	−1.38131
$25$	10.8877	2.17755
$26$	8.87315	1.74017
$27$	−4.07279	−0.783809
$28$	4.86773	0.919915
$29$	6.41914	1.19201	0.596003	−	0.802983i	$-0.296755\pi$
$29$	6.41914	1.19201	0.596003	+	0.802983i	$0.296755\pi$
$30$	8.08394	1.47592
$31$	−1.29634	−0.232830	−0.116415	−	0.993201i	$-0.537140\pi$
$31$	−1.29634	−0.232830	−0.116415	+	0.993201i	$0.537140\pi$
$32$	−19.3203	−3.41537
$33$	−1.07234	−0.186671
$34$	−9.63813	−1.65293
$35$	−3.63574	−0.614553
$36$	−13.0179	−2.16964
$37$	−2.43016	−0.399515	−0.199758	−	0.979845i	$-0.564015\pi$
$37$	−2.43016	−0.399515	−0.199758	+	0.979845i	$0.564015\pi$
$38$	4.38930	0.712039
$39$	−2.45287	−0.392774
$40$	36.0232	5.69577
$41$	2.70524	0.422488	0.211244	−	0.977433i	$-0.432249\pi$
$41$	2.70524	0.422488	0.211244	+	0.977433i	$0.432249\pi$
$42$	−1.84993	−0.285450
$43$	7.66248	1.16852	0.584259	−	0.811567i	$-0.301385\pi$
$43$	7.66248	1.16852	0.584259	+	0.811567i	$0.301385\pi$
$44$	−7.64280	−1.15220
$45$	9.72312	1.44944
$46$	3.40544	0.502105
$47$	−8.91948	−1.30104	−0.650520	−	0.759489i	$-0.725449\pi$
$47$	−8.91948	−1.30104	−0.650520	+	0.759489i	$0.725449\pi$
$48$	10.3375	1.49209
$49$	−6.16800	−0.881143
$50$	−29.4907	−4.17062
$51$	2.66434	0.373083
$52$	−17.4822	−2.42434
$53$	−6.14645	−0.844280	−0.422140	−	0.906531i	$-0.638721\pi$
$53$	−6.14645	−0.844280	−0.422140	+	0.906531i	$0.638721\pi$
$54$	11.0316	1.50121
$55$	5.70846	0.769729
$56$	−8.24354	−1.10159
$57$	−1.21337	−0.160715
$58$	−17.3870	−2.28302
$59$	−5.15399	−0.670993	−0.335496	−	0.942041i	$-0.608904\pi$
$59$	−5.15399	−0.670993	−0.335496	+	0.942041i	$0.608904\pi$
$60$	−15.9272	−2.05620
$61$	12.2559	1.56920	0.784601	−	0.620002i	$-0.212868\pi$
$61$	12.2559	1.56920	0.784601	+	0.620002i	$0.212868\pi$
$62$	3.51130	0.445935
$63$	−2.22504	−0.280328
$64$	24.7190	3.08987
$65$	13.0575	1.61959
$66$	2.90456	0.357526
$67$	15.1183	1.84700	0.923499	−	0.383601i	$-0.125316\pi$
$67$	15.1183	1.84700	0.923499	+	0.383601i	$0.125316\pi$
$68$	18.9893	2.30280
$69$	−0.941392	−0.113330
$70$	9.84783	1.17704
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	22.0458	2.59812
$73$	0.774711	0.0906731	0.0453365	−	0.998972i	$-0.485564\pi$
$73$	0.774711	0.0906731	0.0453365	+	0.998972i	$0.485564\pi$
$74$	6.58236	0.765184
$75$	8.15235	0.941352
$76$	−8.64794	−0.991987
$77$	−1.30632	−0.148869
$78$	6.64389	0.752272
$79$	15.0796	1.69659	0.848293	−	0.529527i	$-0.177630\pi$
$79$	15.0796	1.69659	0.848293	+	0.529527i	$0.177630\pi$
$80$	−55.0303	−6.15257
$81$	4.26850	0.474278
$82$	−7.32746	−0.809182
$83$	−16.4118	−1.80143	−0.900714	−	0.434413i	$-0.856956\pi$
$83$	−16.4118	−1.80143	−0.900714	+	0.434413i	$0.856956\pi$
$84$	3.64478	0.397678
$85$	−14.1833	−1.53839
$86$	−20.7547	−2.23804
$87$	4.80642	0.515302
$88$	12.9431	1.37974
$89$	2.35548	0.249681	0.124840	−	0.992177i	$-0.460158\pi$
$89$	2.35548	0.249681	0.124840	+	0.992177i	$0.460158\pi$
$90$	−26.3362	−2.77608
$91$	−2.98808	−0.313236
$92$	−6.70950	−0.699514
$93$	−0.970655	−0.100652
$94$	24.1594	2.49186
$95$	6.45921	0.662701
$96$	−14.4663	−1.47646
$97$	−8.35135	−0.847951	−0.423976	−	0.905674i	$-0.639366\pi$
$97$	−8.35135	−0.847951	−0.423976	+	0.905674i	$0.639366\pi$
$98$	16.7067	1.68764
$99$	3.49352	0.351112
$100$	58.1035	5.81035
$101$	−6.61098	−0.657818	−0.328909	−	0.944362i	$-0.606681\pi$
$101$	−6.61098	−0.657818	−0.328909	+	0.944362i	$0.606681\pi$
$102$	−7.21668	−0.714558
$103$	0.0657150	0.00647509	0.00323754	−	0.999995i	$-0.498969\pi$
$103$	0.0657150	0.00647509	0.00323754	+	0.999995i	$0.498969\pi$
$104$	29.6061	2.90312
$105$	−2.72231	−0.265671
$106$	16.6484	1.61703
$107$	4.41657	0.426965	0.213483	−	0.976947i	$-0.431519\pi$
$107$	4.41657	0.426965	0.213483	+	0.976947i	$0.431519\pi$
$108$	−21.7348	−2.09144
$109$	10.9260	1.04652	0.523260	−	0.852173i	$-0.324716\pi$
$109$	10.9260	1.04652	0.523260	+	0.852173i	$0.324716\pi$
$110$	−15.4620	−1.47425
$111$	−1.81961	−0.172710
$112$	12.5931	1.18994
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	3.28655	0.307813
$115$	5.01137	0.467313
$116$	34.2564	3.18063
$117$	7.99107	0.738775
$118$	13.9602	1.28514
$119$	3.24569	0.297532
$120$	26.9729	2.46227
$121$	−8.94895	−0.813541
$122$	−33.1964	−3.00546
$123$	2.02559	0.182641
$124$	−6.91807	−0.621261
$125$	−23.4682	−2.09906
$126$	6.02677	0.536907
$127$	12.7108	1.12790	0.563950	−	0.825809i	$-0.309281\pi$
$127$	12.7108	1.12790	0.563950	+	0.825809i	$0.309281\pi$
$128$	−28.3137	−2.50260
$129$	5.73739	0.505149
$130$	−35.3679	−3.10197
$131$	20.4376	1.78564	0.892822	−	0.450409i	$-0.148722\pi$
$131$	20.4376	1.78564	0.892822	+	0.450409i	$0.148722\pi$
$132$	−5.72265	−0.498093
$133$	−1.47812	−0.128169
$134$	−40.9498	−3.53752
$135$	16.2339	1.39719
$136$	−32.1586	−2.75758
$137$	13.8559	1.18379	0.591893	−	0.806017i	$-0.298381\pi$
$137$	13.8559	1.18379	0.591893	+	0.806017i	$0.298381\pi$
$138$	2.54987	0.217059
$139$	7.62312	0.646585	0.323292	−	0.946299i	$-0.395210\pi$
$139$	7.62312	0.646585	0.323292	+	0.946299i	$0.395210\pi$
$140$	−19.4025	−1.63981
$141$	−6.67858	−0.562438
$142$	2.70862	0.227302
$143$	4.69157	0.392329
$144$	−33.6779	−2.80649
$145$	−25.5863	−2.12483
$146$	−2.09839	−0.173664
$147$	−4.61837	−0.380917
$148$	−12.9688	−1.06603
$149$	17.1316	1.40347	0.701737	−	0.712436i	$-0.252408\pi$
$149$	17.1316	1.40347	0.701737	+	0.712436i	$0.252408\pi$
$150$	−22.0816	−1.80295
$151$	4.75003	0.386552	0.193276	−	0.981144i	$-0.438089\pi$
$151$	4.75003	0.386552	0.193276	+	0.981144i	$0.438089\pi$
$152$	14.6453	1.18789
$153$	−8.68001	−0.701737
$154$	3.53832	0.285126
$155$	5.16715	0.415036
$156$	−13.0900	−1.04804
$157$	13.5555	1.08185	0.540924	−	0.841072i	$-0.318075\pi$
$157$	13.5555	1.08185	0.540924	+	0.841072i	$0.318075\pi$
$158$	−40.8448	−3.24944
$159$	−4.60224	−0.364981
$160$	77.0095	6.08813
$161$	−1.14680	−0.0903805
$162$	−11.5617	−0.908376
$163$	−9.81288	−0.768604	−0.384302	−	0.923207i	$-0.625558\pi$
$163$	−9.81288	−0.768604	−0.384302	+	0.923207i	$0.625558\pi$
$164$	14.4368	1.12732
$165$	4.27429	0.332753
$166$	44.4532	3.45024
$167$	3.81946	0.295559	0.147779	−	0.989020i	$-0.452787\pi$
$167$	3.81946	0.295559	0.147779	+	0.989020i	$0.452787\pi$
$168$	−6.17246	−0.476216
$169$	−2.26850	−0.174500
$170$	38.4170	2.94645
$171$	3.95296	0.302291
$172$	40.8916	3.11796
$173$	5.50622	0.418630	0.209315	−	0.977848i	$-0.432877\pi$
$173$	5.50622	0.418630	0.209315	+	0.977848i	$0.432877\pi$
$174$	−13.0187	−0.986949
$175$	9.93116	0.750725
$176$	−19.7724	−1.49040
$177$	−3.85912	−0.290069
$178$	−6.38010	−0.478209
$179$	−10.7058	−0.800190	−0.400095	−	0.916474i	$-0.631023\pi$
$179$	−10.7058	−0.800190	−0.400095	+	0.916474i	$0.631023\pi$
$180$	51.8884	3.86753
$181$	−3.40862	−0.253361	−0.126681	−	0.991944i	$-0.540432\pi$
$181$	−3.40862	−0.253361	−0.126681	+	0.991944i	$0.540432\pi$
$182$	8.09357	0.599935
$183$	9.17673	0.678364
$184$	11.3626	0.837661
$185$	9.68647	0.712163
$186$	2.62913	0.192777
$187$	−5.09605	−0.372660
$188$	−47.5997	−3.47156
$189$	−3.71496	−0.270224
$190$	−17.4955	−1.26926
$191$	10.6151	0.768081	0.384040	−	0.923316i	$-0.374532\pi$
$191$	10.6151	0.768081	0.384040	+	0.923316i	$0.374532\pi$
$192$	18.5087	1.33575
$193$	−3.51604	−0.253090	−0.126545	−	0.991961i	$-0.540389\pi$
$193$	−3.51604	−0.253090	−0.126545	+	0.991961i	$0.540389\pi$
$194$	22.6206	1.62406
$195$	9.77701	0.700146
$196$	−32.9161	−2.35115
$197$	1.34905	0.0961162	0.0480581	−	0.998845i	$-0.484697\pi$
$197$	1.34905	0.0961162	0.0480581	+	0.998845i	$0.484697\pi$
$198$	−9.46259	−0.672477
$199$	−19.9417	−1.41363	−0.706814	−	0.707400i	$-0.749868\pi$
$199$	−19.9417	−1.41363	−0.706814	+	0.707400i	$0.749868\pi$
$200$	−98.3987	−6.95784
$201$	11.3201	0.798455
$202$	17.9066	1.25991
$203$	5.85517	0.410952
$204$	14.2185	0.995496
$205$	−10.7829	−0.753113
$206$	−0.177997	−0.0124016
$207$	3.06691	0.213165
$208$	−45.2273	−3.13595
$209$	2.32079	0.160532
$210$	7.37370	0.508834
$211$	4.89531	0.337007	0.168503	−	0.985701i	$-0.446107\pi$
$211$	4.89531	0.337007	0.168503	+	0.985701i	$0.446107\pi$
$212$	−32.8011	−2.25279
$213$	−0.748763	−0.0513044
$214$	−11.9628	−0.817759
$215$	−30.5422	−2.08296
$216$	36.8081	2.50447
$217$	−1.18245	−0.0802699
$218$	−29.5943	−2.00438
$219$	0.580075	0.0391979
$220$	30.4638	2.05387
$221$	−11.6567	−0.784115
$222$	4.92863	0.330788
$223$	15.2903	1.02391	0.511957	−	0.859011i	$-0.328921\pi$
$223$	15.2903	1.02391	0.511957	+	0.859011i	$0.328921\pi$
$224$	−17.6228	−1.17747
$225$	−26.5591	−1.77060
$226$	2.70862	0.180174
$227$	−19.2461	−1.27741	−0.638704	−	0.769452i	$-0.720529\pi$
$227$	−19.2461	−1.27741	−0.638704	+	0.769452i	$0.720529\pi$
$228$	−6.47526	−0.428835
$229$	−17.9326	−1.18502	−0.592511	−	0.805562i	$-0.701863\pi$
$229$	−17.9326	−1.18502	−0.592511	+	0.805562i	$0.701863\pi$
$230$	−13.5739	−0.895035
$231$	−0.978126	−0.0643560
$232$	−58.0134	−3.80877
$233$	11.7215	0.767898	0.383949	−	0.923354i	$-0.374564\pi$
$233$	11.7215	0.767898	0.383949	+	0.923354i	$0.374564\pi$
$234$	−21.6447	−1.41496
$235$	35.5525	2.31919
$236$	−27.5048	−1.79041
$237$	11.2910	0.733432
$238$	−8.79134	−0.569858
$239$	−18.4110	−1.19091	−0.595454	−	0.803389i	$-0.703028\pi$
$239$	−18.4110	−1.19091	−0.595454	+	0.803389i	$0.703028\pi$
$240$	−41.2047	−2.65975
$241$	−6.89501	−0.444147	−0.222073	−	0.975030i	$-0.571282\pi$
$241$	−6.89501	−0.444147	−0.222073	+	0.975030i	$0.571282\pi$
$242$	24.2393	1.55816
$243$	15.4145	0.988839
$244$	65.4046	4.18710
$245$	24.5853	1.57070
$246$	−5.48653	−0.349808
$247$	5.30858	0.337777
$248$	11.7158	0.743953
$249$	−12.2885	−0.778755
$250$	63.5664	4.02029
$251$	−5.84727	−0.369076	−0.184538	−	0.982825i	$-0.559079\pi$
$251$	−5.84727	−0.369076	−0.184538	+	0.982825i	$0.559079\pi$
$252$	−11.8741	−0.747999
$253$	1.80059	0.113202
$254$	−34.4287	−2.16025
$255$	−10.6199	−0.665045
$256$	27.2530	1.70331
$257$	4.37391	0.272837	0.136418	−	0.990651i	$-0.456441\pi$
$257$	4.37391	0.272837	0.136418	+	0.990651i	$0.456441\pi$
$258$	−15.5404	−0.967502
$259$	−2.21665	−0.137736
$260$	69.6829	4.32155
$261$	−15.6586	−0.969241
$262$	−55.3577	−3.42001
$263$	18.3415	1.13099	0.565493	−	0.824753i	$-0.308686\pi$
$263$	18.3415	1.13099	0.565493	+	0.824753i	$0.308686\pi$
$264$	9.69135	0.596461
$265$	24.4994	1.50499
$266$	4.00366	0.245480
$267$	1.76370	0.107937
$268$	80.6805	4.92834
$269$	−29.4085	−1.79307	−0.896535	−	0.442973i	$-0.853924\pi$
$269$	−29.4085	−1.79307	−0.896535	+	0.442973i	$0.853924\pi$
$270$	−43.9714	−2.67601
$271$	7.14665	0.434128	0.217064	−	0.976157i	$-0.430352\pi$
$271$	7.14665	0.434128	0.217064	+	0.976157i	$0.430352\pi$
$272$	49.1265	2.97873
$273$	−2.23737	−0.135412
$274$	−37.5302	−2.26728
$275$	−15.5929	−0.940285
$276$	−5.02383	−0.302399
$277$	6.64724	0.399394	0.199697	−	0.979858i	$-0.436004\pi$
$277$	6.64724	0.399394	0.199697	+	0.979858i	$0.436004\pi$
$278$	−20.6481	−1.23839
$279$	3.16224	0.189318
$280$	32.8583	1.96366
$281$	−20.8212	−1.24209	−0.621044	−	0.783776i	$-0.713291\pi$
$281$	−20.8212	−1.24209	−0.621044	+	0.783776i	$0.713291\pi$
$282$	18.0897	1.07723
$283$	−8.34621	−0.496131	−0.248065	−	0.968743i	$-0.579795\pi$
$283$	−8.34621	−0.496131	−0.248065	+	0.968743i	$0.579795\pi$
$284$	−5.33660	−0.316669
$285$	4.83642	0.286485
$286$	−12.7077	−0.751420
$287$	2.46756	0.145656
$288$	47.1290	2.77710
$289$	−4.33833	−0.255196
$290$	69.3036	4.06965
$291$	−6.25319	−0.366568
$292$	4.13432	0.241943
$293$	27.0509	1.58033	0.790165	−	0.612895i	$-0.209995\pi$
$293$	27.0509	1.58033	0.790165	+	0.612895i	$0.209995\pi$
$294$	12.5094	0.729563
$295$	20.5435	1.19609
$296$	21.9627	1.27656
$297$	5.83284	0.338456
$298$	−46.4029	−2.68805
$299$	4.11866	0.238188
$300$	43.5058	2.51181
$301$	6.98927	0.402855
$302$	−12.8660	−0.740356
$303$	−4.95006	−0.284374
$304$	−22.3727	−1.28316
$305$	−48.8511	−2.79721
$306$	23.5108	1.34402
$307$	−4.94756	−0.282372	−0.141186	−	0.989983i	$-0.545092\pi$
$307$	−4.94756	−0.282372	−0.141186	+	0.989983i	$0.545092\pi$
$308$	−6.97132	−0.397228
$309$	0.0492050	0.00279917
$310$	−13.9958	−0.794910
$311$	−12.4990	−0.708751	−0.354376	−	0.935103i	$-0.615307\pi$
$311$	−12.4990	−0.708751	−0.354376	+	0.935103i	$0.615307\pi$
$312$	22.1680	1.25502
$313$	−25.9006	−1.46399	−0.731994	−	0.681311i	$-0.761410\pi$
$313$	−25.9006	−1.46399	−0.731994	+	0.681311i	$0.761410\pi$
$314$	−36.7167	−2.07204
$315$	8.86886	0.499704
$316$	80.4737	4.52700
$317$	3.05519	0.171597	0.0857983	−	0.996313i	$-0.472656\pi$
$317$	3.05519	0.171597	0.0857983	+	0.996313i	$0.472656\pi$
$318$	12.4657	0.699041
$319$	−9.19317	−0.514719
$320$	−98.5285	−5.50791
$321$	3.30696	0.184577
$322$	3.10624	0.173104
$323$	−5.76625	−0.320843
$324$	22.7793	1.26552
$325$	−35.6671	−1.97846
$326$	26.5793	1.47209
$327$	8.18099	0.452410
$328$	−24.4488	−1.34996
$329$	−8.13583	−0.448543
$330$	−11.5774	−0.637315
$331$	24.8088	1.36361	0.681807	−	0.731532i	$-0.261194\pi$
$331$	24.8088	1.36361	0.681807	+	0.731532i	$0.261194\pi$
$332$	−87.5831	−4.80675
$333$	5.92801	0.324853
$334$	−10.3455	−0.566078
$335$	−60.2608	−3.29240
$336$	9.42926	0.514408
$337$	−30.2374	−1.64714	−0.823569	−	0.567216i	$-0.808021\pi$
$337$	−30.2374	−1.64714	−0.823569	+	0.567216i	$0.808021\pi$
$338$	6.14449	0.334216
$339$	−0.748763	−0.0406672
$340$	−75.6905	−4.10489
$341$	1.85656	0.100538
$342$	−10.7071	−0.578971
$343$	−12.0111	−0.648537
$344$	−69.2502	−3.73372
$345$	3.75233	0.202019
$346$	−14.9142	−0.801793
$347$	23.3414	1.25303	0.626516	−	0.779408i	$-0.284480\pi$
$347$	23.3414	1.25303	0.626516	+	0.779408i	$0.284480\pi$
$348$	25.6499	1.37498
$349$	−16.7935	−0.898935	−0.449467	−	0.893297i	$-0.648386\pi$
$349$	−16.7935	−0.898935	−0.449467	+	0.893297i	$0.648386\pi$
$350$	−26.8997	−1.43785
$351$	13.3420	0.712145
$352$	27.6695	1.47479
$353$	−7.11191	−0.378529	−0.189264	−	0.981926i	$-0.560610\pi$
$353$	−7.11191	−0.378529	−0.189264	+	0.981926i	$0.560610\pi$
$354$	10.4529	0.555564
$355$	3.98594	0.211552
$356$	12.5703	0.666223
$357$	2.43026	0.128623
$358$	28.9979	1.53259
$359$	−7.30190	−0.385380	−0.192690	−	0.981260i	$-0.561721\pi$
$359$	−7.30190	−0.385380	−0.192690	+	0.981260i	$0.561721\pi$
$360$	−87.8734	−4.63133
$361$	−16.3740	−0.861789
$362$	9.23265	0.485258
$363$	−6.70065	−0.351693
$364$	−15.9462	−0.835808
$365$	−3.08795	−0.161631
$366$	−24.8562	−1.29926
$367$	−7.54315	−0.393749	−0.196875	−	0.980429i	$-0.563079\pi$
$367$	−7.54315	−0.393749	−0.196875	+	0.980429i	$0.563079\pi$
$368$	−17.3579	−0.904841
$369$	−6.59904	−0.343532
$370$	−26.2369	−1.36399
$371$	−5.60643	−0.291071
$372$	−5.18000	−0.268570
$373$	−30.5427	−1.58144	−0.790720	−	0.612178i	$-0.790293\pi$
$373$	−30.5427	−1.58144	−0.790720	+	0.612178i	$0.790293\pi$
$374$	13.8032	0.713748
$375$	−17.5721	−0.907421
$376$	80.6104	4.15716
$377$	−21.0285	−1.08302
$378$	10.0624	0.517554
$379$	21.9396	1.12696	0.563481	−	0.826129i	$-0.309462\pi$
$379$	21.9396	1.12696	0.563481	+	0.826129i	$0.309462\pi$
$380$	34.4702	1.76828
$381$	9.51738	0.487590
$382$	−28.7522	−1.47109
$383$	−31.9447	−1.63230	−0.816148	−	0.577842i	$-0.803895\pi$
$383$	−31.9447	−1.63230	−0.816148	+	0.577842i	$0.803895\pi$
$384$	−21.2003	−1.08187
$385$	5.20693	0.265370
$386$	9.52361	0.484739
$387$	−18.6915	−0.950143
$388$	−44.5678	−2.26259
$389$	14.8660	0.753736	0.376868	−	0.926267i	$-0.377001\pi$
$389$	14.8660	0.753736	0.376868	+	0.926267i	$0.377001\pi$
$390$	−26.4822	−1.34098
$391$	−4.47374	−0.226247
$392$	55.7437	2.81548
$393$	15.3030	0.771932
$394$	−3.65407	−0.184089
$395$	−60.1064	−3.02428
$396$	18.6435	0.936871
$397$	14.3745	0.721434	0.360717	−	0.932675i	$-0.382532\pi$
$397$	14.3745	0.721434	0.360717	+	0.932675i	$0.382532\pi$
$398$	54.0143	2.70749
$399$	−1.10676	−0.0554075
$400$	150.317	7.51586
$401$	10.1155	0.505144	0.252572	−	0.967578i	$-0.418724\pi$
$401$	10.1155	0.505144	0.252572	+	0.967578i	$0.418724\pi$
$402$	−30.6617	−1.52927
$403$	4.24669	0.211543
$404$	−35.2802	−1.75525
$405$	−17.0140	−0.845433
$406$	−15.8594	−0.787089
$407$	3.48035	0.172514
$408$	−24.0792	−1.19210
$409$	−8.97727	−0.443898	−0.221949	−	0.975058i	$-0.571242\pi$
$409$	−8.97727	−0.443898	−0.221949	+	0.975058i	$0.571242\pi$
$410$	29.2068	1.44242
$411$	10.3748	0.511749
$412$	0.350694	0.0172775
$413$	−4.70117	−0.231330
$414$	−8.30707	−0.408270
$415$	65.4164	3.21117
$416$	63.2912	3.10311
$417$	5.70791	0.279518
$418$	−6.28613	−0.307465
$419$	−31.6460	−1.54601	−0.773005	−	0.634400i	$-0.781247\pi$
$419$	−31.6460	−1.54601	−0.773005	+	0.634400i	$0.781247\pi$
$420$	−14.5279	−0.708888
$421$	−6.22844	−0.303555	−0.151778	−	0.988415i	$-0.548500\pi$
$421$	−6.22844	−0.303555	−0.151778	+	0.988415i	$0.548500\pi$
$422$	−13.2595	−0.645463
$423$	21.7578	1.05790
$424$	55.5489	2.69769
$425$	38.7421	1.87927
$426$	2.02811	0.0982624
$427$	11.1791	0.540993
$428$	23.5694	1.13927
$429$	3.51288	0.169603
$430$	82.7272	3.98946
$431$	31.5869	1.52149	0.760744	−	0.649052i	$-0.224834\pi$
$431$	31.5869	1.52149	0.760744	+	0.649052i	$0.224834\pi$
$432$	−56.2293	−2.70533
$433$	5.81410	0.279408	0.139704	−	0.990193i	$-0.455385\pi$
$433$	5.81410	0.279408	0.139704	+	0.990193i	$0.455385\pi$
$434$	3.20280	0.153739
$435$	−19.1581	−0.918562
$436$	58.3077	2.79243
$437$	2.03739	0.0974615
$438$	−1.57120	−0.0750749
$439$	34.5312	1.64808	0.824042	−	0.566529i	$-0.191714\pi$
$439$	34.5312	1.64808	0.824042	+	0.566529i	$0.191714\pi$
$440$	−51.5906	−2.45949
$441$	15.0459	0.716473
$442$	31.5735	1.50180
$443$	1.48642	0.0706218	0.0353109	−	0.999376i	$-0.488758\pi$
$443$	1.48642	0.0706218	0.0353109	+	0.999376i	$0.488758\pi$
$444$	−9.71054	−0.460842
$445$	−9.38882	−0.445073
$446$	−41.4155	−1.96108
$447$	12.8275	0.606720
$448$	22.5472	1.06526
$449$	29.4685	1.39071	0.695353	−	0.718668i	$-0.255248\pi$
$449$	29.4685	1.39071	0.695353	+	0.718668i	$0.255248\pi$
$450$	71.9383	3.39120
$451$	−3.87431	−0.182434
$452$	−5.33660	−0.251013
$453$	3.55665	0.167106
$454$	52.1303	2.44660
$455$	11.9103	0.558365
$456$	10.9659	0.513525
$457$	−1.65144	−0.0772511	−0.0386255	−	0.999254i	$-0.512298\pi$
$457$	−1.65144	−0.0772511	−0.0386255	+	0.999254i	$0.512298\pi$
$458$	48.5726	2.26965
$459$	−14.4923	−0.676443
$460$	26.7437	1.24693
$461$	−1.95428	−0.0910198	−0.0455099	−	0.998964i	$-0.514491\pi$
$461$	−1.95428	−0.0910198	−0.0455099	+	0.998964i	$0.514491\pi$
$462$	2.64937	0.123260
$463$	−13.6009	−0.632089	−0.316044	−	0.948744i	$-0.602355\pi$
$463$	−13.6009	−0.632089	−0.316044	+	0.948744i	$0.602355\pi$
$464$	88.6233	4.11423
$465$	3.86897	0.179419
$466$	−31.7489	−1.47074
$467$	−13.4410	−0.621977	−0.310988	−	0.950414i	$-0.600660\pi$
$467$	−13.4410	−0.621977	−0.310988	+	0.950414i	$0.600660\pi$
$468$	42.6451	1.97127
$469$	13.7901	0.636766
$470$	−96.2982	−4.44190
$471$	10.1499	0.467681
$472$	46.5796	2.14400
$473$	−10.9738	−0.504577
$474$	−30.5831	−1.40473
$475$	−17.6435	−0.809541
$476$	17.3210	0.793905
$477$	14.9934	0.686499
$478$	49.8683	2.28092
$479$	−25.8889	−1.18289	−0.591447	−	0.806344i	$-0.701443\pi$
$479$	−25.8889	−1.18289	−0.591447	+	0.806344i	$0.701443\pi$
$480$	57.6619	2.63189
$481$	7.96094	0.362988
$482$	18.6759	0.850665
$483$	−0.858682	−0.0390714
$484$	−47.7570	−2.17077
$485$	33.2880	1.51153
$486$	−41.7519	−1.89390
$487$	−20.5703	−0.932131	−0.466066	−	0.884750i	$-0.654329\pi$
$487$	−20.5703	−0.932131	−0.466066	+	0.884750i	$0.654329\pi$
$488$	−110.763	−5.01401
$489$	−7.34753	−0.332267
$490$	−66.5921	−3.00832
$491$	14.8702	0.671084	0.335542	−	0.942025i	$-0.391081\pi$
$491$	14.8702	0.671084	0.335542	+	0.942025i	$0.391081\pi$
$492$	10.8097	0.487341
$493$	22.8414	1.02872
$494$	−14.3789	−0.646937
$495$	−13.9250	−0.625880
$496$	−17.8974	−0.803619
$497$	−0.912141	−0.0409151
$498$	33.2849	1.49153
$499$	16.1355	0.722326	0.361163	−	0.932503i	$-0.382380\pi$
$499$	16.1355	0.722326	0.361163	+	0.932503i	$0.382380\pi$
$500$	−125.240	−5.60092
$501$	2.85987	0.127770
$502$	15.8380	0.706885
$503$	−6.46730	−0.288363	−0.144181	−	0.989551i	$-0.546055\pi$
$503$	−6.46730	−0.288363	−0.144181	+	0.989551i	$0.546055\pi$
$504$	20.1089	0.895722
$505$	26.3510	1.17260
$506$	−4.87709	−0.216813
$507$	−1.69857	−0.0754360
$508$	67.8324	3.00958
$509$	30.0668	1.33269	0.666343	−	0.745645i	$-0.267859\pi$
$509$	30.0668	1.33269	0.666343	+	0.745645i	$0.267859\pi$
$510$	28.7653	1.27375
$511$	0.706646	0.0312602
$512$	−17.1905	−0.759719
$513$	6.59994	0.291394
$514$	−11.8472	−0.522559
$515$	−0.261936	−0.0115423
$516$	30.6181	1.34789
$517$	12.7740	0.561801
$518$	6.00404	0.263803
$519$	4.12285	0.180973
$520$	−118.008	−5.17501
$521$	−0.674971	−0.0295710	−0.0147855	−	0.999891i	$-0.504707\pi$
$521$	−0.674971	−0.0295710	−0.0147855	+	0.999891i	$0.504707\pi$
$522$	42.4130	1.85637
$523$	−3.42474	−0.149753	−0.0748766	−	0.997193i	$-0.523856\pi$
$523$	−3.42474	−0.149753	−0.0748766	+	0.997193i	$0.523856\pi$
$524$	109.067	4.76464
$525$	7.43609	0.324538
$526$	−49.6801	−2.16615
$527$	−4.61281	−0.200937
$528$	−14.8048	−0.644298
$529$	−21.4193	−0.931274
$530$	−66.3595	−2.88247
$531$	12.5724	0.545596
$532$	−7.88814	−0.341994
$533$	−8.86209	−0.383860
$534$	−4.77719	−0.206729
$535$	−17.6042	−0.761095
$536$	−136.633	−5.90164
$537$	−8.01612	−0.345921
$538$	79.6564	3.43423
$539$	8.83349	0.380485
$540$	86.6338	3.72813
$541$	42.2052	1.81454	0.907272	−	0.420544i	$-0.138161\pi$
$541$	42.2052	1.81454	0.907272	+	0.420544i	$0.138161\pi$
$542$	−19.3575	−0.831477
$543$	−2.55225	−0.109528
$544$	−68.7478	−2.94754
$545$	−43.5504	−1.86549
$546$	6.06017	0.259351
$547$	−34.7310	−1.48499	−0.742496	−	0.669851i	$-0.766358\pi$
$547$	−34.7310	−1.48499	−0.742496	+	0.669851i	$0.766358\pi$
$548$	73.9431	3.15869
$549$	−29.8964	−1.27595
$550$	42.2351	1.80091
$551$	−10.4022	−0.443149
$552$	8.50789	0.362120
$553$	13.7547	0.584910
$554$	−18.0048	−0.764951
$555$	7.25287	0.307867
$556$	40.6815	1.72528
$557$	−33.6060	−1.42393	−0.711965	−	0.702215i	$-0.752195\pi$
$557$	−33.6060	−1.42393	−0.711965	+	0.702215i	$0.752195\pi$
$558$	−8.56529	−0.362598
$559$	−25.1015	−1.06168
$560$	−50.1954	−2.12114
$561$	−3.81574	−0.161100
$562$	56.3966	2.37895
$563$	−18.8058	−0.792570	−0.396285	−	0.918127i	$-0.629701\pi$
$563$	−18.8058	−0.792570	−0.396285	+	0.918127i	$0.629701\pi$
$564$	−35.6409	−1.50075
$565$	3.98594	0.167690
$566$	22.6067	0.950230
$567$	3.89348	0.163511
$568$	9.03756	0.379208
$569$	17.2585	0.723516	0.361758	−	0.932272i	$-0.382177\pi$
$569$	17.2585	0.723516	0.361758	+	0.932272i	$0.382177\pi$
$570$	−13.1000	−0.548698
$571$	−1.14730	−0.0480130	−0.0240065	−	0.999712i	$-0.507642\pi$
$571$	−1.14730	−0.0480130	−0.0240065	+	0.999712i	$0.507642\pi$
$572$	25.0370	1.04685
$573$	7.94819	0.332040
$574$	−6.68368	−0.278971
$575$	−13.6887	−0.570860
$576$	−60.2984	−2.51243
$577$	29.7016	1.23650	0.618248	−	0.785983i	$-0.287843\pi$
$577$	29.7016	1.23650	0.618248	+	0.785983i	$0.287843\pi$
$578$	11.7509	0.488772
$579$	−2.63268	−0.109411
$580$	−136.544	−5.66968
$581$	−14.9699	−0.621055
$582$	16.9375	0.702081
$583$	8.80263	0.364568
$584$	−7.00150	−0.289724
$585$	−31.8520	−1.31692
$586$	−73.2704	−3.02677
$587$	−0.801683	−0.0330890	−0.0165445	−	0.999863i	$-0.505267\pi$
$587$	−0.801683	−0.0330890	−0.0165445	+	0.999863i	$0.505267\pi$
$588$	−24.6464	−1.01640
$589$	2.10072	0.0865587
$590$	−55.6445	−2.29085
$591$	1.01012	0.0415509
$592$	−33.5510	−1.37894
$593$	−2.85792	−0.117361	−0.0586804	−	0.998277i	$-0.518689\pi$
$593$	−2.85792	−0.117361	−0.0586804	+	0.998277i	$0.518689\pi$
$594$	−15.7989	−0.648238
$595$	−12.9372	−0.530372
$596$	91.4244	3.74489
$597$	−14.9316	−0.611109
$598$	−11.1559	−0.456197
$599$	10.3741	0.423876	0.211938	−	0.977283i	$-0.432023\pi$
$599$	10.3741	0.423876	0.211938	+	0.977283i	$0.432023\pi$
$600$	−73.6773	−3.00786
$601$	−6.48619	−0.264577	−0.132289	−	0.991211i	$-0.542233\pi$
$601$	−6.48619	−0.264577	−0.132289	+	0.991211i	$0.542233\pi$
$602$	−18.9312	−0.771580
$603$	−36.8790	−1.50183
$604$	25.3490	1.03144
$605$	35.6700	1.45019
$606$	13.4078	0.544655
$607$	−1.64123	−0.0666157	−0.0333078	−	0.999445i	$-0.510604\pi$
$607$	−1.64123	−0.0666157	−0.0333078	+	0.999445i	$0.510604\pi$
$608$	31.3084	1.26972
$609$	4.38414	0.177654
$610$	132.319	5.35744
$611$	29.2193	1.18209
$612$	−46.3217	−1.87244
$613$	20.4776	0.827082	0.413541	−	0.910485i	$-0.364292\pi$
$613$	20.4776	0.827082	0.413541	+	0.910485i	$0.364292\pi$
$614$	13.4010	0.540822
$615$	−8.07387	−0.325570
$616$	11.8060	0.475676
$617$	−23.2480	−0.935930	−0.467965	−	0.883747i	$-0.655013\pi$
$617$	−23.2480	−0.935930	−0.467965	+	0.883747i	$0.655013\pi$
$618$	−0.133277	−0.00536120
$619$	12.9089	0.518852	0.259426	−	0.965763i	$-0.416467\pi$
$619$	12.9089	0.518852	0.259426	+	0.965763i	$0.416467\pi$
$620$	27.5750	1.10744
$621$	5.12056	0.205481
$622$	33.8549	1.35746
$623$	2.14853	0.0860792
$624$	−33.8646	−1.35567
$625$	39.1043	1.56417
$626$	70.1547	2.80395
$627$	1.73772	0.0693980
$628$	72.3403	2.88669
$629$	−8.64728	−0.344790
$630$	−24.0223	−0.957073
$631$	−34.4391	−1.37100	−0.685499	−	0.728074i	$-0.740416\pi$
$631$	−34.4391	−1.37100	−0.685499	+	0.728074i	$0.740416\pi$
$632$	−136.283	−5.42104
$633$	3.66543	0.145688
$634$	−8.27533	−0.328656
$635$	−50.6645	−2.01056
$636$	−24.5603	−0.973879
$637$	20.2057	0.800580
$638$	24.9008	0.985831
$639$	2.43935	0.0964993
$640$	112.857	4.46106
$641$	3.65825	0.144492	0.0722461	−	0.997387i	$-0.476983\pi$
$641$	3.65825	0.144492	0.0722461	+	0.997387i	$0.476983\pi$
$642$	−8.95729	−0.353516
$643$	−21.4227	−0.844828	−0.422414	−	0.906403i	$-0.638817\pi$
$643$	−21.4227	−0.844828	−0.422414	+	0.906403i	$0.638817\pi$
$644$	−6.12001	−0.241162
$645$	−22.8689	−0.900462
$646$	15.6186	0.614504
$647$	7.43844	0.292435	0.146218	−	0.989252i	$-0.453290\pi$
$647$	7.43844	0.292435	0.146218	+	0.989252i	$0.453290\pi$
$648$	−38.5769	−1.51544
$649$	7.38129	0.289741
$650$	96.6086	3.78930
$651$	−0.885374	−0.0347006
$652$	−52.3674	−2.05087
$653$	−13.6620	−0.534637	−0.267319	−	0.963608i	$-0.586138\pi$
$653$	−13.6620	−0.534637	−0.267319	+	0.963608i	$0.586138\pi$
$654$	−22.1592	−0.866491
$655$	−81.4633	−3.18303
$656$	37.3488	1.45823
$657$	−1.88979	−0.0737279
$658$	22.0368	0.859085
$659$	24.0406	0.936490	0.468245	−	0.883599i	$-0.344886\pi$
$659$	24.0406	0.936490	0.468245	+	0.883599i	$0.344886\pi$
$660$	22.8102	0.887884
$661$	18.8492	0.733148	0.366574	−	0.930389i	$-0.380531\pi$
$661$	18.8492	0.733148	0.366574	+	0.930389i	$0.380531\pi$
$662$	−67.1974	−2.61170
$663$	−8.72811	−0.338972
$664$	148.323	5.75603
$665$	5.89171	0.228471
$666$	−16.0567	−0.622185
$667$	−8.07054	−0.312493
$668$	20.3829	0.788639
$669$	11.4488	0.442637
$670$	163.223	6.30587
$671$	−17.5522	−0.677595
$672$	−13.1953	−0.509021
$673$	−40.1378	−1.54720	−0.773599	−	0.633675i	$-0.781545\pi$
$673$	−40.1378	−1.54720	−0.773599	+	0.633675i	$0.781545\pi$
$674$	81.9016	3.15473
$675$	−44.3435	−1.70678
$676$	−12.1061	−0.465618
$677$	9.21275	0.354075	0.177037	−	0.984204i	$-0.443349\pi$
$677$	9.21275	0.354075	0.177037	+	0.984204i	$0.443349\pi$
$678$	2.02811	0.0778892
$679$	−7.61761	−0.292337
$680$	128.182	4.91557
$681$	−14.4108	−0.552222
$682$	−5.02870	−0.192559
$683$	11.5761	0.442949	0.221474	−	0.975166i	$-0.428913\pi$
$683$	11.5761	0.442949	0.221474	+	0.975166i	$0.428913\pi$
$684$	21.0954	0.806602
$685$	−55.2286	−2.11018
$686$	32.5334	1.24213
$687$	−13.4273	−0.512284
$688$	105.789	4.03317
$689$	20.1351	0.767088
$690$	−10.1636	−0.386923
$691$	−12.3409	−0.469468	−0.234734	−	0.972060i	$-0.575422\pi$
$691$	−12.3409	−0.469468	−0.234734	+	0.972060i	$0.575422\pi$
$692$	29.3845	1.11703
$693$	3.18658	0.121048
$694$	−63.2229	−2.39991
$695$	−30.3853	−1.15258
$696$	−43.4383	−1.64653
$697$	9.62612	0.364615
$698$	45.4871	1.72171
$699$	8.77659	0.331961
$700$	52.9986	2.00316
$701$	−17.6089	−0.665078	−0.332539	−	0.943089i	$-0.607905\pi$
$701$	−17.6089	−0.665078	−0.332539	+	0.943089i	$0.607905\pi$
$702$	−36.1385	−1.36396
$703$	3.93806	0.148527
$704$	−35.4013	−1.33424
$705$	26.6204	1.00258
$706$	19.2634	0.724989
$707$	−6.03015	−0.226787
$708$	−20.5946	−0.773992
$709$	52.6488	1.97727	0.988634	−	0.150341i	$-0.0480371\pi$
$709$	52.6488	1.97727	0.988634	+	0.150341i	$0.0480371\pi$
$710$	−10.7964	−0.405181
$711$	−36.7845	−1.37952
$712$	−21.2878	−0.797795
$713$	1.62984	0.0610381
$714$	−6.58263	−0.246349
$715$	−18.7003	−0.699353
$716$	−57.1326	−2.13515
$717$	−13.7855	−0.514828
$718$	19.7781	0.738110
$719$	−28.7662	−1.07280	−0.536399	−	0.843965i	$-0.680216\pi$
$719$	−28.7662	−1.07280	−0.536399	+	0.843965i	$0.680216\pi$
$720$	134.238	5.00277
$721$	0.0599413	0.00223233
$722$	44.3509	1.65057
$723$	−5.16273	−0.192004
$724$	−18.1905	−0.676043
$725$	69.8900	2.59565
$726$	18.1495	0.673590
$727$	−2.89966	−0.107542	−0.0537712	−	0.998553i	$-0.517124\pi$
$727$	−2.89966	−0.107542	−0.0537712	+	0.998553i	$0.517124\pi$
$728$	27.0050	1.00087
$729$	−1.26372	−0.0468045
$730$	8.36408	0.309568
$731$	27.2656	1.00845
$732$	48.9726	1.81008
$733$	11.4829	0.424132	0.212066	−	0.977255i	$-0.431981\pi$
$733$	11.4829	0.424132	0.212066	+	0.977255i	$0.431981\pi$
$734$	20.4315	0.754140
$735$	18.4086	0.679010
$736$	24.2906	0.895364
$737$	−21.6517	−0.797551
$738$	17.8743	0.657960
$739$	0.714710	0.0262910	0.0131455	−	0.999914i	$-0.495816\pi$
$739$	0.714710	0.0262910	0.0131455	+	0.999914i	$0.495816\pi$
$740$	51.6928	1.90026
$741$	3.97487	0.146020
$742$	15.1857	0.557483
$743$	−17.8664	−0.655455	−0.327727	−	0.944772i	$-0.606283\pi$
$743$	−17.8664	−0.655455	−0.327727	+	0.944772i	$0.606283\pi$
$744$	8.77235	0.321610
$745$	−68.2856	−2.50179
$746$	82.7283	3.02890
$747$	40.0341	1.46477
$748$	−27.1956	−0.994368
$749$	4.02853	0.147199
$750$	47.5962	1.73797
$751$	37.2948	1.36091	0.680454	−	0.732791i	$-0.261783\pi$
$751$	37.2948	1.36091	0.680454	+	0.732791i	$0.261783\pi$
$752$	−123.143	−4.49057
$753$	−4.37822	−0.159551
$754$	56.9580	2.07429
$755$	−18.9334	−0.689056
$756$	−19.8253	−0.721037
$757$	−30.3008	−1.10130	−0.550651	−	0.834736i	$-0.685620\pi$
$757$	−30.3008	−1.10130	−0.550651	+	0.834736i	$0.685620\pi$
$758$	−59.4260	−2.15845
$759$	1.34821	0.0489370
$760$	−58.3755	−2.11750
$761$	0.132741	0.00481184	0.00240592	−	0.999997i	$-0.499234\pi$
$761$	0.132741	0.00481184	0.00240592	+	0.999997i	$0.499234\pi$
$762$	−25.7789	−0.933872
$763$	9.96606	0.360795
$764$	56.6485	2.04947
$765$	34.5980	1.25089
$766$	86.5259	3.12631
$767$	16.8840	0.609644
$768$	20.4061	0.736340
$769$	19.3907	0.699246	0.349623	−	0.936890i	$-0.386310\pi$
$769$	19.3907	0.699246	0.349623	+	0.936890i	$0.386310\pi$
$770$	−14.1036	−0.508257
$771$	3.27502	0.117947
$772$	−18.7637	−0.675321
$773$	−25.3106	−0.910360	−0.455180	−	0.890399i	$-0.650425\pi$
$773$	−25.3106	−0.910360	−0.455180	+	0.890399i	$0.650425\pi$
$774$	50.6281	1.81979
$775$	−14.1143	−0.506999
$776$	75.4759	2.70943
$777$	−1.65974	−0.0595430
$778$	−40.2663	−1.44362
$779$	−4.38383	−0.157067
$780$	52.1760	1.86820
$781$	1.43215	0.0512463
$782$	12.1177	0.433326
$783$	−26.1438	−0.934304
$784$	−85.1559	−3.04128
$785$	−54.0315	−1.92847
$786$	−41.4498	−1.47847
$787$	−55.4960	−1.97822	−0.989110	−	0.147180i	$-0.952980\pi$
$787$	−55.4960	−1.97822	−0.989110	+	0.147180i	$0.952980\pi$
$788$	7.19936	0.256467
$789$	13.7334	0.488924
$790$	162.805	5.79235
$791$	−0.912141	−0.0324320
$792$	−31.5729	−1.12189
$793$	−40.1489	−1.42573
$794$	−38.9349	−1.38175
$795$	18.3443	0.650604
$796$	−106.421	−3.77198
$797$	10.6582	0.377534	0.188767	−	0.982022i	$-0.439551\pi$
$797$	10.6582	0.377534	0.188767	+	0.982022i	$0.439551\pi$
$798$	2.99780	0.106121
$799$	−31.7384	−1.12282
$800$	−210.354	−7.43714
$801$	−5.74586	−0.203020
$802$	−27.3990	−0.967493
$803$	−1.10950	−0.0391534
$804$	60.4106	2.13052
$805$	4.57108	0.161109
$806$	−11.5026	−0.405163
$807$	−22.0200	−0.775142
$808$	59.7472	2.10190
$809$	−13.2400	−0.465495	−0.232748	−	0.972537i	$-0.574772\pi$
$809$	−13.2400	−0.465495	−0.232748	+	0.972537i	$0.574772\pi$
$810$	46.0844	1.61924
$811$	3.35248	0.117721	0.0588607	−	0.998266i	$-0.481253\pi$
$811$	3.35248	0.117721	0.0588607	+	0.998266i	$0.481253\pi$
$812$	31.2467	1.09654
$813$	5.35115	0.187673
$814$	−9.42692	−0.330413
$815$	39.1136	1.37009
$816$	36.7842	1.28770
$817$	−12.4170	−0.434417
$818$	24.3160	0.850188
$819$	7.28899	0.254698
$820$	−57.5442	−2.00953
$821$	54.9230	1.91683	0.958414	−	0.285382i	$-0.0921206\pi$
$821$	54.9230	1.91683	0.958414	+	0.285382i	$0.0921206\pi$
$822$	−28.1012	−0.980143
$823$	−10.8079	−0.376741	−0.188370	−	0.982098i	$-0.560321\pi$
$823$	−10.8079	−0.376741	−0.188370	+	0.982098i	$0.560321\pi$
$824$	−0.593903	−0.0206896
$825$	−11.6754	−0.406484
$826$	12.7337	0.443061
$827$	−21.6437	−0.752626	−0.376313	−	0.926493i	$-0.622808\pi$
$827$	−21.6437	−0.752626	−0.376313	+	0.926493i	$0.622808\pi$
$828$	16.3668	0.568787
$829$	−29.7101	−1.03188	−0.515938	−	0.856626i	$-0.672557\pi$
$829$	−29.7101	−1.03188	−0.515938	+	0.856626i	$0.672557\pi$
$830$	−177.188	−6.15028
$831$	4.97721	0.172658
$832$	−80.9769	−2.80737
$833$	−21.9477	−0.760444
$834$	−15.4605	−0.535355
$835$	−15.2242	−0.526854
$836$	12.3851	0.428349
$837$	5.27973	0.182494
$838$	85.7169	2.96104
$839$	16.0247	0.553234	0.276617	−	0.960980i	$-0.410787\pi$
$839$	16.0247	0.553234	0.276617	+	0.960980i	$0.410787\pi$
$840$	24.6031	0.848887
$841$	12.2054	0.420876
$842$	16.8704	0.581394
$843$	−15.5901	−0.536953
$844$	26.1243	0.899235
$845$	9.04210	0.311058
$846$	−58.9334	−2.02617
$847$	−8.16271	−0.280474
$848$	−84.8584	−2.91405
$849$	−6.24934	−0.214477
$850$	−104.938	−3.59933
$851$	3.05534	0.104736
$852$	−3.99585	−0.136896
$853$	−38.6351	−1.32284	−0.661420	−	0.750016i	$-0.730046\pi$
$853$	−38.6351	−1.32284	−0.661420	+	0.750016i	$0.730046\pi$
$854$	−30.2798	−1.03615
$855$	−15.7563	−0.538854
$856$	−39.9150	−1.36427
$857$	−21.9064	−0.748310	−0.374155	−	0.927366i	$-0.622067\pi$
$857$	−21.9064	−0.748310	−0.374155	+	0.927366i	$0.622067\pi$
$858$	−9.51504	−0.324838
$859$	−36.4789	−1.24464	−0.622322	−	0.782761i	$-0.713811\pi$
$859$	−36.4789	−1.24464	−0.622322	+	0.782761i	$0.713811\pi$
$860$	−162.992	−5.55797
$861$	1.84762	0.0629667
$862$	−85.5569	−2.91408
$863$	−51.4502	−1.75138	−0.875692	−	0.482869i	$-0.839595\pi$
$863$	−51.4502	−1.75138	−0.875692	+	0.482869i	$0.839595\pi$
$864$	78.6874	2.67700
$865$	−21.9475	−0.746236
$866$	−15.7482	−0.535145
$867$	−3.24838	−0.110321
$868$	−6.31026	−0.214184
$869$	−21.5962	−0.732601
$870$	51.8920	1.75930
$871$	−49.5261	−1.67813
$872$	−98.7444	−3.34391
$873$	20.3719	0.689484
$874$	−5.51850	−0.186666
$875$	−21.4063	−0.723666
$876$	3.09563	0.104592
$877$	−35.8209	−1.20959	−0.604793	−	0.796382i	$-0.706744\pi$
$877$	−35.8209	−1.20959	−0.604793	+	0.796382i	$0.706744\pi$
$878$	−93.5317	−3.15654
$879$	20.2547	0.683174
$880$	78.8116	2.65674
$881$	25.6573	0.864415	0.432207	−	0.901774i	$-0.357735\pi$
$881$	25.6573	0.864415	0.432207	+	0.901774i	$0.357735\pi$
$882$	−40.7536	−1.37225
$883$	−25.2048	−0.848208	−0.424104	−	0.905613i	$-0.639411\pi$
$883$	−25.2048	−0.848208	−0.424104	+	0.905613i	$0.639411\pi$
$884$	−62.2072	−2.09225
$885$	15.3822	0.517069
$886$	−4.02614	−0.135261
$887$	−0.569316	−0.0191157	−0.00955787	−	0.999954i	$-0.503042\pi$
$887$	−0.569316	−0.0191157	−0.00955787	+	0.999954i	$0.503042\pi$
$888$	16.4449	0.551854
$889$	11.5940	0.388852
$890$	25.4307	0.852440
$891$	−6.11313	−0.204798
$892$	81.5982	2.73211
$893$	14.4540	0.483684
$894$	−34.7448	−1.16204
$895$	42.6728	1.42639
$896$	−25.8261	−0.862790
$897$	3.08390	0.102968
$898$	−79.8189	−2.66359
$899$	−8.32142	−0.277535
$900$	−141.735	−4.72450
$901$	−21.8711	−0.728631
$902$	10.4940	0.349412
$903$	5.23331	0.174154
$904$	9.03756	0.300585
$905$	13.5866	0.451633
$906$	−9.63360	−0.320055
$907$	−31.3531	−1.04106	−0.520531	−	0.853843i	$-0.674266\pi$
$907$	−31.3531	−1.04106	−0.520531	+	0.853843i	$0.674266\pi$
$908$	−102.709	−3.40851
$909$	16.1265	0.534883
$910$	−32.2605	−1.06942
$911$	42.0364	1.39273	0.696364	−	0.717688i	$-0.254800\pi$
$911$	42.0364	1.39273	0.696364	+	0.717688i	$0.254800\pi$
$912$	−16.7519	−0.554710
$913$	23.5041	0.777873
$914$	4.47311	0.147957
$915$	−36.5779	−1.20923
$916$	−95.6993	−3.16199
$917$	18.6420	0.615614
$918$	39.2541	1.29558
$919$	−36.9675	−1.21945	−0.609723	−	0.792615i	$-0.708719\pi$
$919$	−36.9675	−1.21945	−0.609723	+	0.792615i	$0.708719\pi$
$920$	−45.2906	−1.49319
$921$	−3.70455	−0.122069
$922$	5.29339	0.174328
$923$	3.27590	0.107827
$924$	−5.21987	−0.171721
$925$	−26.4589	−0.869964
$926$	36.8397	1.21063
$927$	−0.160302	−0.00526501
$928$	−124.020	−4.07114
$929$	−8.82033	−0.289386	−0.144693	−	0.989477i	$-0.546219\pi$
$929$	−8.82033	−0.289386	−0.144693	+	0.989477i	$0.546219\pi$
$930$	−10.4796	−0.343639
$931$	9.99522	0.327580
$932$	62.5527	2.04898
$933$	−9.35877	−0.306392
$934$	36.4066	1.19126
$935$	20.3126	0.664292
$936$	−72.2198	−2.36058
$937$	12.6870	0.414465	0.207233	−	0.978292i	$-0.433554\pi$
$937$	12.6870	0.414465	0.207233	+	0.978292i	$0.433554\pi$
$938$	−37.3520	−1.21958
$939$	−19.3934	−0.632880
$940$	189.730	6.18830
$941$	−19.0629	−0.621432	−0.310716	−	0.950503i	$-0.600569\pi$
$941$	−19.0629	−0.621432	−0.310716	+	0.950503i	$0.600569\pi$
$942$	−27.4921	−0.895741
$943$	−3.40119	−0.110758
$944$	−71.1565	−2.31595
$945$	14.8076	0.481692
$946$	29.7239	0.966406
$947$	−56.0404	−1.82107	−0.910533	−	0.413435i	$-0.864329\pi$
$947$	−56.0404	−1.82107	−0.910533	+	0.413435i	$0.864329\pi$
$948$	60.2558	1.95702
$949$	−2.53787	−0.0823829
$950$	47.7896	1.55050
$951$	2.28761	0.0741810
$952$	−29.3332	−0.950694
$953$	15.6501	0.506958	0.253479	−	0.967341i	$-0.418425\pi$
$953$	15.6501	0.506958	0.253479	+	0.967341i	$0.418425\pi$
$954$	−40.6113	−1.31484
$955$	−42.3111	−1.36916
$956$	−98.2521	−3.17770
$957$	−6.88351	−0.222512
$958$	70.1231	2.26558
$959$	12.6385	0.408118
$960$	−73.7745	−2.38106
$961$	−29.3195	−0.945790
$962$	−21.5631	−0.695223
$963$	−10.7736	−0.347173
$964$	−36.7959	−1.18512
$965$	14.0147	0.451151
$966$	2.32584	0.0748327
$967$	30.2670	0.973320	0.486660	−	0.873592i	$-0.338215\pi$
$967$	30.2670	0.973320	0.486660	+	0.873592i	$0.338215\pi$
$968$	80.8767	2.59948
$969$	−4.31756	−0.138700
$970$	−90.1644	−2.89500
$971$	15.2688	0.490000	0.245000	−	0.969523i	$-0.421212\pi$
$971$	15.2688	0.490000	0.245000	+	0.969523i	$0.421212\pi$
$972$	82.2608	2.63852
$973$	6.95336	0.222915
$974$	55.7172	1.78529
$975$	−26.7062	−0.855284
$976$	169.205	5.41613
$977$	−4.47235	−0.143083	−0.0715415	−	0.997438i	$-0.522792\pi$
$977$	−4.47235	−0.143083	−0.0715415	+	0.997438i	$0.522792\pi$
$978$	19.9016	0.636384
$979$	−3.37340	−0.107814
$980$	131.202	4.19109
$981$	−26.6524	−0.850945
$982$	−40.2777	−1.28531
$983$	47.5911	1.51792	0.758960	−	0.651138i	$-0.225708\pi$
$983$	47.5911	1.51792	0.758960	+	0.651138i	$0.225708\pi$
$984$	−18.3064	−0.583585
$985$	−5.37726	−0.171334
$986$	−61.8686	−1.97030
$987$	−6.09181	−0.193904
$988$	28.3298	0.901290
$989$	−9.63375	−0.306335
$990$	37.7174	1.19874
$991$	−22.4691	−0.713756	−0.356878	−	0.934151i	$-0.616159\pi$
$991$	−22.4691	−0.713756	−0.356878	+	0.934151i	$0.616159\pi$
$992$	25.0457	0.795202
$993$	18.5759	0.589489
$994$	2.47064	0.0783640
$995$	79.4864	2.51989
$996$	−65.5790	−2.07795
$997$	−35.4199	−1.12176	−0.560880	−	0.827897i	$-0.689537\pi$
$997$	−35.4199	−1.12176	−0.560880	+	0.827897i	$0.689537\pi$
$998$	−43.7050	−1.38346
$999$	9.89751	0.313144

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.c.1.7	✓	158

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.c.1.7	✓	158	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70862 q^{2} +0.748763 q^{3} +5.33660 q^{4} -3.98594 q^{5} -2.02811 q^{6} +0.912141 q^{7} -9.03756 q^{8} -2.43935 q^{9} +O(q^{10})\)	\(q-2.70862 q^{2} +0.748763 q^{3} +5.33660 q^{4} -3.98594 q^{5} -2.02811 q^{6} +0.912141 q^{7} -9.03756 q^{8} -2.43935 q^{9} +10.7964 q^{10} -1.43215 q^{11} +3.99585 q^{12} -3.27590 q^{13} -2.47064 q^{14} -2.98453 q^{15} +13.8061 q^{16} +3.55832 q^{17} +6.60727 q^{18} -1.62050 q^{19} -21.2714 q^{20} +0.682978 q^{21} +3.87914 q^{22} -1.25726 q^{23} -6.76700 q^{24} +10.8877 q^{25} +8.87315 q^{26} -4.07279 q^{27} +4.86773 q^{28} +6.41914 q^{29} +8.08394 q^{30} -1.29634 q^{31} -19.3203 q^{32} -1.07234 q^{33} -9.63813 q^{34} -3.63574 q^{35} -13.0179 q^{36} -2.43016 q^{37} +4.38930 q^{38} -2.45287 q^{39} +36.0232 q^{40} +2.70524 q^{41} -1.84993 q^{42} +7.66248 q^{43} -7.64280 q^{44} +9.72312 q^{45} +3.40544 q^{46} -8.91948 q^{47} +10.3375 q^{48} -6.16800 q^{49} -29.4907 q^{50} +2.66434 q^{51} -17.4822 q^{52} -6.14645 q^{53} +11.0316 q^{54} +5.70846 q^{55} -8.24354 q^{56} -1.21337 q^{57} -17.3870 q^{58} -5.15399 q^{59} -15.9272 q^{60} +12.2559 q^{61} +3.51130 q^{62} -2.22504 q^{63} +24.7190 q^{64} +13.0575 q^{65} +2.90456 q^{66} +15.1183 q^{67} +18.9893 q^{68} -0.941392 q^{69} +9.84783 q^{70} -1.00000 q^{71} +22.0458 q^{72} +0.774711 q^{73} +6.58236 q^{74} +8.15235 q^{75} -8.64794 q^{76} -1.30632 q^{77} +6.64389 q^{78} +15.0796 q^{79} -55.0303 q^{80} +4.26850 q^{81} -7.32746 q^{82} -16.4118 q^{83} +3.64478 q^{84} -14.1833 q^{85} -20.7547 q^{86} +4.80642 q^{87} +12.9431 q^{88} +2.35548 q^{89} -26.3362 q^{90} -2.98808 q^{91} -6.70950 q^{92} -0.970655 q^{93} +24.1594 q^{94} +6.45921 q^{95} -14.4663 q^{96} -8.35135 q^{97} +16.7067 q^{98} +3.49352 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * q^99

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