LMFDB - Embedded newform 8023.2.a.c.1.17

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			1.17
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)

$f(q)$	$=$	$q-2.44908 q^{2} -0.864554 q^{3} +3.99799 q^{4} +2.08542 q^{5} +2.11736 q^{6} -1.35512 q^{7} -4.89325 q^{8} -2.25255 q^{9} +O(q^{10})$	\(q-2.44908 q^{2} -0.864554 q^{3} +3.99799 q^{4} +2.08542 q^{5} +2.11736 q^{6} -1.35512 q^{7} -4.89325 q^{8} -2.25255 q^{9} -5.10735 q^{10} +1.47121 q^{11} -3.45648 q^{12} +5.96106 q^{13} +3.31881 q^{14} -1.80295 q^{15} +3.98797 q^{16} -1.61074 q^{17} +5.51667 q^{18} -6.49286 q^{19} +8.33748 q^{20} +1.17158 q^{21} -3.60312 q^{22} +5.72671 q^{23} +4.23048 q^{24} -0.651039 q^{25} -14.5991 q^{26} +4.54111 q^{27} -5.41778 q^{28} +7.46702 q^{29} +4.41558 q^{30} -9.92398 q^{31} +0.0196355 q^{32} -1.27194 q^{33} +3.94483 q^{34} -2.82600 q^{35} -9.00567 q^{36} -6.38891 q^{37} +15.9015 q^{38} -5.15366 q^{39} -10.2045 q^{40} +10.6962 q^{41} -2.86929 q^{42} +6.09363 q^{43} +5.88190 q^{44} -4.69750 q^{45} -14.0252 q^{46} -5.75546 q^{47} -3.44782 q^{48} -5.16364 q^{49} +1.59445 q^{50} +1.39257 q^{51} +23.8323 q^{52} -11.1072 q^{53} -11.1215 q^{54} +3.06809 q^{55} +6.63096 q^{56} +5.61343 q^{57} -18.2873 q^{58} -0.156976 q^{59} -7.20820 q^{60} -5.80708 q^{61} +24.3046 q^{62} +3.05248 q^{63} -8.02403 q^{64} +12.4313 q^{65} +3.11509 q^{66} +10.2973 q^{67} -6.43973 q^{68} -4.95105 q^{69} +6.92110 q^{70} -1.00000 q^{71} +11.0223 q^{72} -9.98717 q^{73} +15.6470 q^{74} +0.562858 q^{75} -25.9584 q^{76} -1.99368 q^{77} +12.6217 q^{78} +15.2568 q^{79} +8.31658 q^{80} +2.83161 q^{81} -26.1959 q^{82} -4.92825 q^{83} +4.68396 q^{84} -3.35907 q^{85} -14.9238 q^{86} -6.45564 q^{87} -7.19901 q^{88} -7.42802 q^{89} +11.5046 q^{90} -8.07798 q^{91} +22.8954 q^{92} +8.57981 q^{93} +14.0956 q^{94} -13.5403 q^{95} -0.0169760 q^{96} -1.44322 q^{97} +12.6462 q^{98} -3.31397 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.44908	−1.73176	−0.865881	−	0.500251i	$-0.833241\pi$
$2$	−2.44908	−1.73176	−0.865881	+	0.500251i	$0.833241\pi$
$3$	−0.864554	−0.499150	−0.249575	−	0.968355i	$-0.580291\pi$
$3$	−0.864554	−0.499150	−0.249575	+	0.968355i	$0.580291\pi$
$4$	3.99799	1.99900
$5$	2.08542	0.932627	0.466313	−	0.884620i	$-0.345582\pi$
$5$	2.08542	0.932627	0.466313	+	0.884620i	$0.345582\pi$
$6$	2.11736	0.864409
$7$	−1.35512	−0.512189	−0.256094	−	0.966652i	$-0.582436\pi$
$7$	−1.35512	−0.512189	−0.256094	+	0.966652i	$0.582436\pi$
$8$	−4.89325	−1.73002
$9$	−2.25255	−0.750849
$10$	−5.10735	−1.61509
$11$	1.47121	0.443587	0.221794	−	0.975094i	$-0.428809\pi$
$11$	1.47121	0.443587	0.221794	+	0.975094i	$0.428809\pi$
$12$	−3.45648	−0.997800
$13$	5.96106	1.65330	0.826651	−	0.562715i	$-0.190243\pi$
$13$	5.96106	1.65330	0.826651	+	0.562715i	$0.190243\pi$
$14$	3.31881	0.886989
$15$	−1.80295	−0.465521
$16$	3.98797	0.996993
$17$	−1.61074	−0.390662	−0.195331	−	0.980737i	$-0.562578\pi$
$17$	−1.61074	−0.390662	−0.195331	+	0.980737i	$0.562578\pi$
$18$	5.51667	1.30029
$19$	−6.49286	−1.48957	−0.744783	−	0.667307i	$-0.767447\pi$
$19$	−6.49286	−1.48957	−0.744783	+	0.667307i	$0.767447\pi$
$20$	8.33748	1.86432
$21$	1.17158	0.255659
$22$	−3.60312	−0.768187
$23$	5.72671	1.19410	0.597051	−	0.802203i	$-0.296339\pi$
$23$	5.72671	1.19410	0.597051	+	0.802203i	$0.296339\pi$
$24$	4.23048	0.863542
$25$	−0.651039	−0.130208
$26$	−14.5991	−2.86312
$27$	4.54111	0.873937
$28$	−5.41778	−1.02386
$29$	7.46702	1.38659	0.693296	−	0.720653i	$-0.256158\pi$
$29$	7.46702	1.38659	0.693296	+	0.720653i	$0.256158\pi$
$30$	4.41558	0.806171
$31$	−9.92398	−1.78240	−0.891200	−	0.453611i	$-0.850135\pi$
$31$	−9.92398	−1.78240	−0.891200	+	0.453611i	$0.850135\pi$
$32$	0.0196355	0.00347110
$33$	−1.27194	−0.221417
$34$	3.94483	0.676534
$35$	−2.82600	−0.477681
$36$	−9.00567	−1.50095
$37$	−6.38891	−1.05033	−0.525165	−	0.851000i	$-0.675996\pi$
$37$	−6.38891	−1.05033	−0.525165	+	0.851000i	$0.675996\pi$
$38$	15.9015	2.57957
$39$	−5.15366	−0.825246
$40$	−10.2045	−1.61347
$41$	10.6962	1.67047	0.835234	−	0.549895i	$-0.185332\pi$
$41$	10.6962	1.67047	0.835234	+	0.549895i	$0.185332\pi$
$42$	−2.86929	−0.442741
$43$	6.09363	0.929270	0.464635	−	0.885502i	$-0.346186\pi$
$43$	6.09363	0.929270	0.464635	+	0.885502i	$0.346186\pi$
$44$	5.88190	0.886730
$45$	−4.69750	−0.700262
$46$	−14.0252	−2.06790
$47$	−5.75546	−0.839521	−0.419760	−	0.907635i	$-0.637886\pi$
$47$	−5.75546	−0.839521	−0.419760	+	0.907635i	$0.637886\pi$
$48$	−3.44782	−0.497649
$49$	−5.16364	−0.737663
$50$	1.59445	0.225489
$51$	1.39257	0.194999
$52$	23.8323	3.30494
$53$	−11.1072	−1.52569	−0.762844	−	0.646583i	$-0.776197\pi$
$53$	−11.1072	−1.52569	−0.762844	+	0.646583i	$0.776197\pi$
$54$	−11.1215	−1.51345
$55$	3.06809	0.413701
$56$	6.63096	0.886099
$57$	5.61343	0.743517
$58$	−18.2873	−2.40124
$59$	−0.156976	−0.0204365	−0.0102182	−	0.999948i	$-0.503253\pi$
$59$	−0.156976	−0.0204365	−0.0102182	+	0.999948i	$0.503253\pi$
$60$	−7.20820	−0.930575
$61$	−5.80708	−0.743521	−0.371760	−	0.928329i	$-0.621246\pi$
$61$	−5.80708	−0.743521	−0.371760	+	0.928329i	$0.621246\pi$
$62$	24.3046	3.08669
$63$	3.05248	0.384576
$64$	−8.02403	−1.00300
$65$	12.4313	1.54191
$66$	3.11509	0.383441
$67$	10.2973	1.25801	0.629007	−	0.777400i	$-0.283462\pi$
$67$	10.2973	1.25801	0.629007	+	0.777400i	$0.283462\pi$
$68$	−6.43973	−0.780933
$69$	−4.95105	−0.596036
$70$	6.92110	0.827229
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	11.0223	1.29899
$73$	−9.98717	−1.16891	−0.584455	−	0.811426i	$-0.698692\pi$
$73$	−9.98717	−1.16891	−0.584455	+	0.811426i	$0.698692\pi$
$74$	15.6470	1.81892
$75$	0.562858	0.0649933
$76$	−25.9584	−2.97764
$77$	−1.99368	−0.227200
$78$	12.6217	1.42913
$79$	15.2568	1.71652	0.858259	−	0.513216i	$-0.171546\pi$
$79$	15.2568	1.71652	0.858259	+	0.513216i	$0.171546\pi$
$80$	8.31658	0.929822
$81$	2.83161	0.314623
$82$	−26.1959	−2.89285
$83$	−4.92825	−0.540945	−0.270473	−	0.962728i	$-0.587180\pi$
$83$	−4.92825	−0.540945	−0.270473	+	0.962728i	$0.587180\pi$
$84$	4.68396	0.511062
$85$	−3.35907	−0.364342
$86$	−14.9238	−1.60927
$87$	−6.45564	−0.692117
$88$	−7.19901	−0.767417
$89$	−7.42802	−0.787369	−0.393684	−	0.919246i	$-0.628800\pi$
$89$	−7.42802	−0.787369	−0.393684	+	0.919246i	$0.628800\pi$
$90$	11.5046	1.21269
$91$	−8.07798	−0.846802
$92$	22.8954	2.38701
$93$	8.57981	0.889685
$94$	14.0956	1.45385
$95$	−13.5403	−1.38921
$96$	−0.0169760	−0.00173260
$97$	−1.44322	−0.146537	−0.0732686	−	0.997312i	$-0.523343\pi$
$97$	−1.44322	−0.146537	−0.0732686	+	0.997312i	$0.523343\pi$
$98$	12.6462	1.27746
$99$	−3.31397	−0.333067
$100$	−2.60285	−0.260285
$101$	7.52388	0.748654	0.374327	−	0.927297i	$-0.377874\pi$
$101$	7.52388	0.748654	0.374327	+	0.927297i	$0.377874\pi$
$102$	−3.41052	−0.337692
$103$	15.4335	1.52071	0.760356	−	0.649507i	$-0.225024\pi$
$103$	15.4335	1.52071	0.760356	+	0.649507i	$0.225024\pi$
$104$	−29.1690	−2.86025
$105$	2.44323	0.238435
$106$	27.2024	2.64213
$107$	11.1130	1.07434	0.537168	−	0.843475i	$-0.319494\pi$
$107$	11.1130	1.07434	0.537168	+	0.843475i	$0.319494\pi$
$108$	18.1553	1.74700
$109$	7.19380	0.689041	0.344520	−	0.938779i	$-0.388042\pi$
$109$	7.19380	0.689041	0.344520	+	0.938779i	$0.388042\pi$
$110$	−7.51400	−0.716432
$111$	5.52356	0.524273
$112$	−5.40420	−0.510649
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	−13.7477	−1.28759
$115$	11.9426	1.11365
$116$	29.8531	2.77179
$117$	−13.4276	−1.24138
$118$	0.384446	0.0353911
$119$	2.18275	0.200093
$120$	8.82230	0.805363
$121$	−8.83553	−0.803230
$122$	14.2220	1.28760
$123$	−9.24745	−0.833814
$124$	−39.6760	−3.56301
$125$	−11.7848	−1.05406
$126$	−7.47577	−0.665995
$127$	11.9197	1.05771	0.528853	−	0.848714i	$-0.322622\pi$
$127$	11.9197	1.05771	0.528853	+	0.848714i	$0.322622\pi$
$128$	19.6122	1.73349
$129$	−5.26827	−0.463845
$130$	−30.4452	−2.67022
$131$	−13.8354	−1.20881	−0.604403	−	0.796678i	$-0.706588\pi$
$131$	−13.8354	−1.20881	−0.604403	+	0.796678i	$0.706588\pi$
$132$	−5.08522	−0.442611
$133$	8.79864	0.762939
$134$	−25.2189	−2.17858
$135$	9.47010	0.815057
$136$	7.88176	0.675855
$137$	−21.1300	−1.80526	−0.902628	−	0.430421i	$-0.858365\pi$
$137$	−21.1300	−1.80526	−0.902628	+	0.430421i	$0.858365\pi$
$138$	12.1255	1.03219
$139$	−3.59876	−0.305243	−0.152621	−	0.988285i	$-0.548772\pi$
$139$	−3.59876	−0.305243	−0.152621	+	0.988285i	$0.548772\pi$
$140$	−11.2983	−0.954883
$141$	4.97591	0.419047
$142$	2.44908	0.205522
$143$	8.76999	0.733383
$144$	−8.98309	−0.748591
$145$	15.5718	1.29317
$146$	24.4594	2.02427
$147$	4.46424	0.368205
$148$	−25.5428	−2.09961
$149$	−18.6704	−1.52954	−0.764768	−	0.644305i	$-0.777147\pi$
$149$	−18.6704	−1.52954	−0.764768	+	0.644305i	$0.777147\pi$
$150$	−1.37848	−0.112553
$151$	−14.6861	−1.19514	−0.597569	−	0.801818i	$-0.703866\pi$
$151$	−14.6861	−1.19514	−0.597569	+	0.801818i	$0.703866\pi$
$152$	31.7712	2.57698
$153$	3.62827	0.293328
$154$	4.88267	0.393457
$155$	−20.6956	−1.66231
$156$	−20.6043	−1.64966
$157$	1.05125	0.0838988	0.0419494	−	0.999120i	$-0.486643\pi$
$157$	1.05125	0.0838988	0.0419494	+	0.999120i	$0.486643\pi$
$158$	−37.3650	−2.97260
$159$	9.60275	0.761547
$160$	0.0409483	0.00323724
$161$	−7.76041	−0.611606
$162$	−6.93484	−0.544852
$163$	−15.1265	−1.18480	−0.592401	−	0.805643i	$-0.701820\pi$
$163$	−15.1265	−1.18480	−0.592401	+	0.805643i	$0.701820\pi$
$164$	42.7634	3.33926
$165$	−2.65253	−0.206499
$166$	12.0697	0.936788
$167$	−22.4133	−1.73439	−0.867197	−	0.497965i	$-0.834081\pi$
$167$	−22.4133	−1.73439	−0.867197	+	0.497965i	$0.834081\pi$
$168$	−5.73282	−0.442297
$169$	22.5343	1.73341
$170$	8.22662	0.630953
$171$	14.6255	1.11844
$172$	24.3623	1.85761
$173$	−4.22624	−0.321315	−0.160658	−	0.987010i	$-0.551362\pi$
$173$	−4.22624	−0.321315	−0.160658	+	0.987010i	$0.551362\pi$
$174$	15.8104	1.19858
$175$	0.882239	0.0666910
$176$	5.86715	0.442253
$177$	0.135714	0.0102009
$178$	18.1918	1.36353
$179$	22.5991	1.68914	0.844569	−	0.535447i	$-0.179857\pi$
$179$	22.5991	1.68914	0.844569	+	0.535447i	$0.179857\pi$
$180$	−18.7806	−1.39982
$181$	14.3464	1.06636	0.533181	−	0.846001i	$-0.320996\pi$
$181$	14.3464	1.06636	0.533181	+	0.846001i	$0.320996\pi$
$182$	19.7836	1.46646
$183$	5.02053	0.371128
$184$	−28.0222	−2.06583
$185$	−13.3235	−0.979566
$186$	−21.0126	−1.54072
$187$	−2.36974	−0.173293
$188$	−23.0103	−1.67820
$189$	−6.15377	−0.447621
$190$	33.1613	2.40578
$191$	−16.4509	−1.19034	−0.595171	−	0.803599i	$-0.702916\pi$
$191$	−16.4509	−1.19034	−0.595171	+	0.803599i	$0.702916\pi$
$192$	6.93721	0.500650
$193$	−7.37814	−0.531090	−0.265545	−	0.964098i	$-0.585552\pi$
$193$	−7.37814	−0.531090	−0.265545	+	0.964098i	$0.585552\pi$
$194$	3.53457	0.253767
$195$	−10.7475	−0.769646
$196$	−20.6442	−1.47459
$197$	−4.04485	−0.288183	−0.144092	−	0.989564i	$-0.546026\pi$
$197$	−4.04485	−0.288183	−0.144092	+	0.989564i	$0.546026\pi$
$198$	8.11619	0.576793
$199$	10.9601	0.776939	0.388470	−	0.921462i	$-0.373004\pi$
$199$	10.9601	0.776939	0.388470	+	0.921462i	$0.373004\pi$
$200$	3.18570	0.225263
$201$	−8.90256	−0.627938
$202$	−18.4266	−1.29649
$203$	−10.1187	−0.710196
$204$	5.56750	0.389803
$205$	22.3061	1.55792
$206$	−37.7980	−2.63351
$207$	−12.8997	−0.896590
$208$	23.7725	1.64833
$209$	−9.55238	−0.660752
$210$	−5.98366	−0.412912
$211$	2.63498	0.181399	0.0906997	−	0.995878i	$-0.471090\pi$
$211$	2.63498	0.181399	0.0906997	+	0.995878i	$0.471090\pi$
$212$	−44.4064	−3.04984
$213$	0.864554	0.0592382
$214$	−27.2167	−1.86049
$215$	12.7078	0.866662
$216$	−22.2208	−1.51193
$217$	13.4482	0.912925
$218$	−17.6182	−1.19325
$219$	8.63444	0.583461
$220$	12.2662	0.826988
$221$	−9.60173	−0.645882
$222$	−13.5276	−0.907915
$223$	4.58869	0.307281	0.153641	−	0.988127i	$-0.450900\pi$
$223$	4.58869	0.307281	0.153641	+	0.988127i	$0.450900\pi$
$224$	−0.0266086	−0.00177786
$225$	1.46650	0.0977664
$226$	2.44908	0.162910
$227$	4.40742	0.292531	0.146265	−	0.989245i	$-0.453275\pi$
$227$	4.40742	0.292531	0.146265	+	0.989245i	$0.453275\pi$
$228$	22.4425	1.48629
$229$	2.84757	0.188173	0.0940863	−	0.995564i	$-0.470007\pi$
$229$	2.84757	0.188173	0.0940863	+	0.995564i	$0.470007\pi$
$230$	−29.2483	−1.92858
$231$	1.72364	0.113407
$232$	−36.5380	−2.39884
$233$	−23.9930	−1.57183	−0.785916	−	0.618333i	$-0.787808\pi$
$233$	−23.9930	−1.57183	−0.785916	+	0.618333i	$0.787808\pi$
$234$	32.8852	2.14977
$235$	−12.0025	−0.782959
$236$	−0.627588	−0.0408525
$237$	−13.1903	−0.856801
$238$	−5.34574	−0.346513
$239$	0.535564	0.0346428	0.0173214	−	0.999850i	$-0.494486\pi$
$239$	0.535564	0.0346428	0.0173214	+	0.999850i	$0.494486\pi$
$240$	−7.19013	−0.464121
$241$	−6.95189	−0.447810	−0.223905	−	0.974611i	$-0.571881\pi$
$241$	−6.95189	−0.447810	−0.223905	+	0.974611i	$0.571881\pi$
$242$	21.6389	1.39100
$243$	−16.0714	−1.03098
$244$	−23.2167	−1.48630
$245$	−10.7683	−0.687964
$246$	22.6477	1.44397
$247$	−38.7044	−2.46270
$248$	48.5605	3.08360
$249$	4.26073	0.270013
$250$	28.8618	1.82538
$251$	−2.24810	−0.141899	−0.0709494	−	0.997480i	$-0.522603\pi$
$251$	−2.24810	−0.141899	−0.0709494	+	0.997480i	$0.522603\pi$
$252$	12.2038	0.768767
$253$	8.42521	0.529688
$254$	−29.1924	−1.83169
$255$	2.90409	0.181861
$256$	−31.9839	−1.99899
$257$	−6.58419	−0.410710	−0.205355	−	0.978688i	$-0.565835\pi$
$257$	−6.58419	−0.410710	−0.205355	+	0.978688i	$0.565835\pi$
$258$	12.9024	0.803270
$259$	8.65777	0.537967
$260$	49.7003	3.08228
$261$	−16.8198	−1.04112
$262$	33.8841	2.09336
$263$	−19.7920	−1.22043	−0.610214	−	0.792237i	$-0.708916\pi$
$263$	−19.7920	−1.22043	−0.610214	+	0.792237i	$0.708916\pi$
$264$	6.22393	0.383056
$265$	−23.1631	−1.42290
$266$	−21.5486	−1.32123
$267$	6.42192	0.393015
$268$	41.1685	2.51477
$269$	25.6567	1.56432	0.782158	−	0.623080i	$-0.214119\pi$
$269$	25.6567	1.56432	0.782158	+	0.623080i	$0.214119\pi$
$270$	−23.1930	−1.41148
$271$	23.5312	1.42942	0.714710	−	0.699421i	$-0.246559\pi$
$271$	23.5312	1.42942	0.714710	+	0.699421i	$0.246559\pi$
$272$	−6.42359	−0.389487
$273$	6.98385	0.422682
$274$	51.7490	3.12627
$275$	−0.957817	−0.0577585
$276$	−19.7943	−1.19147
$277$	19.1637	1.15143	0.575717	−	0.817649i	$-0.304723\pi$
$277$	19.1637	1.15143	0.575717	+	0.817649i	$0.304723\pi$
$278$	8.81365	0.528608
$279$	22.3542	1.33831
$280$	13.8283	0.826400
$281$	9.91591	0.591533	0.295767	−	0.955260i	$-0.404425\pi$
$281$	9.91591	0.591533	0.295767	+	0.955260i	$0.404425\pi$
$282$	−12.1864	−0.725689
$283$	21.3353	1.26825	0.634127	−	0.773229i	$-0.281359\pi$
$283$	21.3353	1.26825	0.634127	+	0.773229i	$0.281359\pi$
$284$	−3.99799	−0.237237
$285$	11.7063	0.693424
$286$	−21.4784	−1.27004
$287$	−14.4947	−0.855595
$288$	−0.0442300	−0.00260627
$289$	−14.4055	−0.847383
$290$	−38.1367	−2.23946
$291$	1.24774	0.0731441
$292$	−39.9286	−2.33665
$293$	−23.0255	−1.34516	−0.672581	−	0.740024i	$-0.734814\pi$
$293$	−23.0255	−1.34516	−0.672581	+	0.740024i	$0.734814\pi$
$294$	−10.9333	−0.637642
$295$	−0.327360	−0.0190596
$296$	31.2625	1.81710
$297$	6.68093	0.387667
$298$	45.7252	2.64879
$299$	34.1373	1.97421
$300$	2.25030	0.129921
$301$	−8.25763	−0.475962
$302$	35.9674	2.06969
$303$	−6.50480	−0.373691
$304$	−25.8934	−1.48509
$305$	−12.1102	−0.693427
$306$	−8.88593	−0.507975
$307$	21.0297	1.20023	0.600114	−	0.799914i	$-0.295122\pi$
$307$	21.0297	1.20023	0.600114	+	0.799914i	$0.295122\pi$
$308$	−7.97070	−0.454173
$309$	−13.3431	−0.759064
$310$	50.6853	2.87873
$311$	10.4687	0.593624	0.296812	−	0.954936i	$-0.404077\pi$
$311$	10.4687	0.593624	0.296812	+	0.954936i	$0.404077\pi$
$312$	25.2181	1.42770
$313$	−33.5417	−1.89589	−0.947944	−	0.318438i	$-0.896842\pi$
$313$	−33.5417	−1.89589	−0.947944	+	0.318438i	$0.896842\pi$
$314$	−2.57459	−0.145293
$315$	6.36569	0.358666
$316$	60.9964	3.43132
$317$	−9.89314	−0.555654	−0.277827	−	0.960631i	$-0.589614\pi$
$317$	−9.89314	−0.555654	−0.277827	+	0.960631i	$0.589614\pi$
$318$	−23.5179	−1.31882
$319$	10.9856	0.615074
$320$	−16.7334	−0.935428
$321$	−9.60780	−0.536255
$322$	19.0059	1.05915
$323$	10.4583	0.581917
$324$	11.3208	0.628931
$325$	−3.88088	−0.215273
$326$	37.0461	2.05179
$327$	−6.21942	−0.343935
$328$	−52.3392	−2.88995
$329$	7.79937	0.429993
$330$	6.49626	0.357607
$331$	−23.7035	−1.30286	−0.651430	−	0.758709i	$-0.725831\pi$
$331$	−23.7035	−1.30286	−0.651430	+	0.758709i	$0.725831\pi$
$332$	−19.7031	−1.08135
$333$	14.3913	0.788640
$334$	54.8920	3.00356
$335$	21.4741	1.17326
$336$	4.67222	0.254890
$337$	12.0155	0.654523	0.327262	−	0.944934i	$-0.393874\pi$
$337$	12.0155	0.654523	0.327262	+	0.944934i	$0.393874\pi$
$338$	−55.1882	−3.00184
$339$	0.864554	0.0469561
$340$	−13.4295	−0.728318
$341$	−14.6003	−0.790649
$342$	−35.8190	−1.93687
$343$	16.4832	0.890011
$344$	−29.8177	−1.60766
$345$	−10.3250	−0.555879
$346$	10.3504	0.556441
$347$	35.1027	1.88441	0.942206	−	0.335033i	$-0.108747\pi$
$347$	35.1027	1.88441	0.942206	+	0.335033i	$0.108747\pi$
$348$	−25.8096	−1.38354
$349$	−30.2834	−1.62103	−0.810517	−	0.585715i	$-0.800814\pi$
$349$	−30.2834	−1.62103	−0.810517	+	0.585715i	$0.800814\pi$
$350$	−2.16067	−0.115493
$351$	27.0698	1.44488
$352$	0.0288880	0.00153974
$353$	−15.9204	−0.847357	−0.423678	−	0.905813i	$-0.639261\pi$
$353$	−15.9204	−0.847357	−0.423678	+	0.905813i	$0.639261\pi$
$354$	−0.332374	−0.0176655
$355$	−2.08542	−0.110682
$356$	−29.6972	−1.57395
$357$	−1.88711	−0.0998764
$358$	−55.3471	−2.92518
$359$	29.7326	1.56923	0.784614	−	0.619985i	$-0.212861\pi$
$359$	29.7326	1.56923	0.784614	+	0.619985i	$0.212861\pi$
$360$	22.9860	1.21147
$361$	23.1573	1.21880
$362$	−35.1356	−1.84668
$363$	7.63879	0.400933
$364$	−32.2957	−1.69276
$365$	−20.8274	−1.09016
$366$	−12.2957	−0.642706
$367$	8.54500	0.446046	0.223023	−	0.974813i	$-0.428408\pi$
$367$	8.54500	0.446046	0.223023	+	0.974813i	$0.428408\pi$
$368$	22.8380	1.19051
$369$	−24.0937	−1.25427
$370$	32.6304	1.69637
$371$	15.0516	0.781440
$372$	34.3020	1.77848
$373$	−15.3775	−0.796214	−0.398107	−	0.917339i	$-0.630333\pi$
$373$	−15.3775	−0.796214	−0.398107	+	0.917339i	$0.630333\pi$
$374$	5.80369	0.300102
$375$	10.1886	0.526135
$376$	28.1629	1.45239
$377$	44.5114	2.29245
$378$	15.0711	0.775172
$379$	−24.3022	−1.24832	−0.624160	−	0.781296i	$-0.714559\pi$
$379$	−24.3022	−1.24832	−0.624160	+	0.781296i	$0.714559\pi$
$380$	−54.1341	−2.77702
$381$	−10.3053	−0.527954
$382$	40.2895	2.06139
$383$	−23.2475	−1.18789	−0.593947	−	0.804504i	$-0.702431\pi$
$383$	−23.2475	−1.18789	−0.593947	+	0.804504i	$0.702431\pi$
$384$	−16.9558	−0.865273
$385$	−4.15764	−0.211893
$386$	18.0696	0.919721
$387$	−13.7262	−0.697742
$388$	−5.77000	−0.292927
$389$	29.0483	1.47281	0.736404	−	0.676542i	$-0.236522\pi$
$389$	29.0483	1.47281	0.736404	+	0.676542i	$0.236522\pi$
$390$	26.3215	1.33284
$391$	−9.22425	−0.466490
$392$	25.2670	1.27617
$393$	11.9615	0.603376
$394$	9.90615	0.499065
$395$	31.8167	1.60087
$396$	−13.2493	−0.665800
$397$	3.58867	0.180110	0.0900551	−	0.995937i	$-0.471296\pi$
$397$	3.58867	0.180110	0.0900551	+	0.995937i	$0.471296\pi$
$398$	−26.8421	−1.34547
$399$	−7.60689	−0.380821
$400$	−2.59633	−0.129816
$401$	23.4606	1.17157	0.585784	−	0.810467i	$-0.300787\pi$
$401$	23.4606	1.17157	0.585784	+	0.810467i	$0.300787\pi$
$402$	21.8031	1.08744
$403$	−59.1575	−2.94684
$404$	30.0804	1.49656
$405$	5.90508	0.293426
$406$	24.7816	1.22989
$407$	−9.39944	−0.465913
$408$	−6.81420	−0.337353
$409$	4.08861	0.202169	0.101084	−	0.994878i	$-0.467769\pi$
$409$	4.08861	0.202169	0.101084	+	0.994878i	$0.467769\pi$
$410$	−54.6293	−2.69795
$411$	18.2680	0.901094
$412$	61.7032	3.03990
$413$	0.212722	0.0104673
$414$	31.5924	1.55268
$415$	−10.2774	−0.504500
$416$	0.117049	0.00573878
$417$	3.11132	0.152362
$418$	23.3945	1.14426
$419$	0.792388	0.0387107	0.0193553	−	0.999813i	$-0.493839\pi$
$419$	0.792388	0.0387107	0.0193553	+	0.999813i	$0.493839\pi$
$420$	9.76801	0.476630
$421$	27.9728	1.36331	0.681656	−	0.731673i	$-0.261260\pi$
$421$	27.9728	1.36331	0.681656	+	0.731673i	$0.261260\pi$
$422$	−6.45327	−0.314140
$423$	12.9645	0.630353
$424$	54.3502	2.63948
$425$	1.04866	0.0508673
$426$	−2.11736	−0.102586
$427$	7.86932	0.380823
$428$	44.4298	2.14759
$429$	−7.58213	−0.366068
$430$	−31.1223	−1.50085
$431$	−1.39614	−0.0672495	−0.0336248	−	0.999435i	$-0.510705\pi$
$431$	−1.39614	−0.0672495	−0.0336248	+	0.999435i	$0.510705\pi$
$432$	18.1098	0.871309
$433$	−5.56443	−0.267410	−0.133705	−	0.991021i	$-0.542687\pi$
$433$	−5.56443	−0.267410	−0.133705	+	0.991021i	$0.542687\pi$
$434$	−32.9358	−1.58097
$435$	−13.4627	−0.645487
$436$	28.7608	1.37739
$437$	−37.1828	−1.77869
$438$	−21.1464	−1.01042
$439$	23.1446	1.10463	0.552316	−	0.833635i	$-0.313744\pi$
$439$	23.1446	1.10463	0.552316	+	0.833635i	$0.313744\pi$
$440$	−15.0129	−0.715713
$441$	11.6313	0.553873
$442$	23.5154	1.11851
$443$	21.8189	1.03665	0.518324	−	0.855184i	$-0.326556\pi$
$443$	21.8189	1.03665	0.518324	+	0.855184i	$0.326556\pi$
$444$	22.0831	1.04802
$445$	−15.4905	−0.734321
$446$	−11.2381	−0.532138
$447$	16.1415	0.763469
$448$	10.8736	0.513727
$449$	−30.2810	−1.42905	−0.714525	−	0.699610i	$-0.753357\pi$
$449$	−30.2810	−1.42905	−0.714525	+	0.699610i	$0.753357\pi$
$450$	−3.59157	−0.169308
$451$	15.7364	0.740998
$452$	−3.99799	−0.188050
$453$	12.6969	0.596553
$454$	−10.7941	−0.506594
$455$	−16.8460	−0.789750
$456$	−27.4679	−1.28630
$457$	1.56632	0.0732693	0.0366347	−	0.999329i	$-0.488336\pi$
$457$	1.56632	0.0732693	0.0366347	+	0.999329i	$0.488336\pi$
$458$	−6.97392	−0.325870
$459$	−7.31455	−0.341414
$460$	47.7464	2.22619
$461$	−24.4301	−1.13782	−0.568911	−	0.822399i	$-0.692635\pi$
$461$	−24.4301	−1.13782	−0.568911	+	0.822399i	$0.692635\pi$
$462$	−4.22133	−0.196394
$463$	−23.4823	−1.09132	−0.545658	−	0.838008i	$-0.683720\pi$
$463$	−23.4823	−1.09132	−0.545658	+	0.838008i	$0.683720\pi$
$464$	29.7783	1.38242
$465$	17.8925	0.829744
$466$	58.7607	2.72204
$467$	−12.9173	−0.597740	−0.298870	−	0.954294i	$-0.596610\pi$
$467$	−12.9173	−0.597740	−0.298870	+	0.954294i	$0.596610\pi$
$468$	−53.6834	−2.48151
$469$	−13.9541	−0.644341
$470$	29.3952	1.35590
$471$	−0.908861	−0.0418781
$472$	0.768121	0.0353556
$473$	8.96503	0.412212
$474$	32.3041	1.48377
$475$	4.22711	0.193953
$476$	8.72664	0.399985
$477$	25.0194	1.14556
$478$	−1.31164	−0.0599930
$479$	22.7754	1.04064	0.520318	−	0.853972i	$-0.325813\pi$
$479$	22.7754	1.04064	0.520318	+	0.853972i	$0.325813\pi$
$480$	−0.0354020	−0.00161587
$481$	−38.0847	−1.73651
$482$	17.0257	0.775501
$483$	6.70929	0.305283
$484$	−35.3244	−1.60566
$485$	−3.00972	−0.136664
$486$	39.3602	1.78541
$487$	41.9663	1.90167	0.950837	−	0.309692i	$-0.100226\pi$
$487$	41.9663	1.90167	0.950837	+	0.309692i	$0.100226\pi$
$488$	28.4155	1.28631
$489$	13.0777	0.591394
$490$	26.3725	1.19139
$491$	24.4468	1.10327	0.551635	−	0.834086i	$-0.314004\pi$
$491$	24.4468	1.10327	0.551635	+	0.834086i	$0.314004\pi$
$492$	−36.9713	−1.66679
$493$	−12.0274	−0.541689
$494$	94.7901	4.26481
$495$	−6.91102	−0.310627
$496$	−39.5765	−1.77704
$497$	1.35512	0.0607856
$498$	−10.4349	−0.467598
$499$	30.8452	1.38082	0.690410	−	0.723418i	$-0.257430\pi$
$499$	30.8452	1.38082	0.690410	+	0.723418i	$0.257430\pi$
$500$	−47.1154	−2.10707
$501$	19.3775	0.865723
$502$	5.50578	0.245735
$503$	−7.91484	−0.352905	−0.176453	−	0.984309i	$-0.556462\pi$
$503$	−7.91484	−0.352905	−0.176453	+	0.984309i	$0.556462\pi$
$504$	−14.9365	−0.665327
$505$	15.6904	0.698215
$506$	−20.6340	−0.917294
$507$	−19.4821	−0.865230
$508$	47.6550	2.11435
$509$	−21.6493	−0.959588	−0.479794	−	0.877381i	$-0.659289\pi$
$509$	−21.6493	−0.959588	−0.479794	+	0.877381i	$0.659289\pi$
$510$	−7.11236	−0.314940
$511$	13.5338	0.598702
$512$	39.1066	1.72828
$513$	−29.4848	−1.30179
$514$	16.1252	0.711252
$515$	32.1854	1.41826
$516$	−21.0625	−0.927226
$517$	−8.46751	−0.372401
$518$	−21.2036	−0.931631
$519$	3.65381	0.160385
$520$	−60.8294	−2.66755
$521$	−30.5129	−1.33679	−0.668397	−	0.743804i	$-0.733019\pi$
$521$	−30.5129	−1.33679	−0.668397	+	0.743804i	$0.733019\pi$
$522$	41.1931	1.80297
$523$	−35.2936	−1.54328	−0.771640	−	0.636060i	$-0.780563\pi$
$523$	−35.2936	−1.54328	−0.771640	+	0.636060i	$0.780563\pi$
$524$	−55.3140	−2.41640
$525$	−0.762743	−0.0332888
$526$	48.4722	2.11349
$527$	15.9850	0.696316
$528$	−5.07247	−0.220751
$529$	9.79523	0.425879
$530$	56.7282	2.46412
$531$	0.353595	0.0153447
$532$	35.1769	1.52511
$533$	63.7608	2.76179
$534$	−15.7278	−0.680609
$535$	23.1753	1.00195
$536$	−50.3872	−2.17640
$537$	−19.5382	−0.843133
$538$	−62.8353	−2.70902
$539$	−7.59681	−0.327218
$540$	37.8614	1.62930
$541$	−1.28420	−0.0552123	−0.0276061	−	0.999619i	$-0.508788\pi$
$541$	−1.28420	−0.0552123	−0.0276061	+	0.999619i	$0.508788\pi$
$542$	−57.6299	−2.47541
$543$	−12.4033	−0.532275
$544$	−0.0316278	−0.00135603
$545$	15.0021	0.642618
$546$	−17.1040	−0.731984
$547$	15.8614	0.678185	0.339093	−	0.940753i	$-0.389880\pi$
$547$	15.8614	0.678185	0.339093	+	0.940753i	$0.389880\pi$
$548$	−84.4776	−3.60870
$549$	13.0807	0.558272
$550$	2.34577	0.100024
$551$	−48.4824	−2.06542
$552$	24.2267	1.03116
$553$	−20.6748	−0.879182
$554$	−46.9334	−1.99401
$555$	11.5189	0.488951
$556$	−14.3878	−0.610179
$557$	−11.5059	−0.487521	−0.243760	−	0.969836i	$-0.578381\pi$
$557$	−11.5059	−0.487521	−0.243760	+	0.969836i	$0.578381\pi$
$558$	−54.7473	−2.31764
$559$	36.3245	1.53636
$560$	−11.2700	−0.476244
$561$	2.04877	0.0864991
$562$	−24.2849	−1.02439
$563$	−17.2585	−0.727361	−0.363680	−	0.931524i	$-0.618480\pi$
$563$	−17.2585	−0.727361	−0.363680	+	0.931524i	$0.618480\pi$
$564$	19.8936	0.837674
$565$	−2.08542	−0.0877341
$566$	−52.2520	−2.19631
$567$	−3.83718	−0.161146
$568$	4.89325	0.205316
$569$	21.0424	0.882144	0.441072	−	0.897472i	$-0.354598\pi$
$569$	21.0424	0.882144	0.441072	+	0.897472i	$0.354598\pi$
$570$	−28.6698	−1.20084
$571$	−15.9225	−0.666334	−0.333167	−	0.942868i	$-0.608117\pi$
$571$	−15.9225	−0.666334	−0.333167	+	0.942868i	$0.608117\pi$
$572$	35.0624	1.46603
$573$	14.2226	0.594160
$574$	35.4987	1.48169
$575$	−3.72831	−0.155481
$576$	18.0745	0.753105
$577$	−26.1480	−1.08855	−0.544277	−	0.838905i	$-0.683196\pi$
$577$	−26.1480	−1.08855	−0.544277	+	0.838905i	$0.683196\pi$
$578$	35.2803	1.46747
$579$	6.37879	0.265094
$580$	62.2562	2.58505
$581$	6.67838	0.277066
$582$	−3.05583	−0.126668
$583$	−16.3410	−0.676775
$584$	48.8697	2.02224
$585$	−28.0021	−1.15774
$586$	56.3912	2.32950
$587$	−22.8786	−0.944301	−0.472151	−	0.881518i	$-0.656522\pi$
$587$	−22.8786	−0.944301	−0.472151	+	0.881518i	$0.656522\pi$
$588$	17.8480	0.736040
$589$	64.4350	2.65500
$590$	0.801730	0.0330067
$591$	3.49699	0.143847
$592$	−25.4788	−1.04717
$593$	28.6707	1.17737	0.588683	−	0.808364i	$-0.299647\pi$
$593$	28.6707	1.17737	0.588683	+	0.808364i	$0.299647\pi$
$594$	−16.3621	−0.671347
$595$	4.55195	0.186612
$596$	−74.6441	−3.05754
$597$	−9.47558	−0.387810
$598$	−83.6050	−3.41886
$599$	−17.5970	−0.718995	−0.359498	−	0.933146i	$-0.617052\pi$
$599$	−17.5970	−0.718995	−0.359498	+	0.933146i	$0.617052\pi$
$600$	−2.75421	−0.112440
$601$	−39.3729	−1.60605	−0.803027	−	0.595942i	$-0.796779\pi$
$601$	−39.3729	−1.60605	−0.803027	+	0.595942i	$0.796779\pi$
$602$	20.2236	0.824252
$603$	−23.1951	−0.944579
$604$	−58.7149	−2.38908
$605$	−18.4258	−0.749114
$606$	15.9308	0.647144
$607$	−19.8124	−0.804161	−0.402081	−	0.915604i	$-0.631713\pi$
$607$	−19.8124	−0.804161	−0.402081	+	0.915604i	$0.631713\pi$
$608$	−0.127491	−0.00517044
$609$	8.74819	0.354495
$610$	29.6588	1.20085
$611$	−34.3087	−1.38798
$612$	14.5058	0.586362
$613$	4.87598	0.196939	0.0984694	−	0.995140i	$-0.468605\pi$
$613$	4.87598	0.196939	0.0984694	+	0.995140i	$0.468605\pi$
$614$	−51.5034	−2.07851
$615$	−19.2848	−0.777637
$616$	9.75555	0.393062
$617$	42.6838	1.71839	0.859193	−	0.511652i	$-0.170966\pi$
$617$	42.6838	1.71839	0.859193	+	0.511652i	$0.170966\pi$
$618$	32.6784	1.31452
$619$	−39.1413	−1.57322	−0.786611	−	0.617448i	$-0.788166\pi$
$619$	−39.1413	−1.57322	−0.786611	+	0.617448i	$0.788166\pi$
$620$	−82.7410	−3.32296
$621$	26.0056	1.04357
$622$	−25.6386	−1.02801
$623$	10.0659	0.403281
$624$	−20.5526	−0.822764
$625$	−21.3210	−0.852838
$626$	82.1462	3.28322
$627$	8.25855	0.329815
$628$	4.20289	0.167714
$629$	10.2909	0.410324
$630$	−15.5901	−0.621124
$631$	31.1728	1.24097	0.620484	−	0.784219i	$-0.286936\pi$
$631$	31.1728	1.24097	0.620484	+	0.784219i	$0.286936\pi$
$632$	−74.6551	−2.96962
$633$	−2.27808	−0.0905456
$634$	24.2291	0.962261
$635$	24.8576	0.986444
$636$	38.3917	1.52233
$637$	−30.7808	−1.21958
$638$	−26.9046	−1.06516
$639$	2.25255	0.0891094
$640$	40.8997	1.61670
$641$	5.27277	0.208262	0.104131	−	0.994564i	$-0.466794\pi$
$641$	5.27277	0.208262	0.104131	+	0.994564i	$0.466794\pi$
$642$	23.5303	0.928666
$643$	−35.4983	−1.39992	−0.699958	−	0.714184i	$-0.746798\pi$
$643$	−35.4983	−1.39992	−0.699958	+	0.714184i	$0.746798\pi$
$644$	−31.0261	−1.22260
$645$	−10.9865	−0.432595
$646$	−25.6133	−1.00774
$647$	8.74239	0.343699	0.171849	−	0.985123i	$-0.445026\pi$
$647$	8.74239	0.343699	0.171849	+	0.985123i	$0.445026\pi$
$648$	−13.8558	−0.544306
$649$	−0.230945	−0.00906537
$650$	9.50460	0.372801
$651$	−11.6267	−0.455687
$652$	−60.4758	−2.36841
$653$	−12.1886	−0.476977	−0.238488	−	0.971145i	$-0.576652\pi$
$653$	−12.1886	−0.476977	−0.238488	+	0.971145i	$0.576652\pi$
$654$	15.2319	0.595613
$655$	−28.8526	−1.12737
$656$	42.6562	1.66544
$657$	22.4966	0.877674
$658$	−19.1013	−0.744645
$659$	−20.9704	−0.816891	−0.408446	−	0.912783i	$-0.633929\pi$
$659$	−20.9704	−0.816891	−0.408446	+	0.912783i	$0.633929\pi$
$660$	−10.6048	−0.412791
$661$	10.7768	0.419169	0.209585	−	0.977791i	$-0.432789\pi$
$661$	10.7768	0.419169	0.209585	+	0.977791i	$0.432789\pi$
$662$	58.0517	2.25624
$663$	8.30121	0.322392
$664$	24.1151	0.935849
$665$	18.3488	0.711537
$666$	−35.2455	−1.36574
$667$	42.7615	1.65573
$668$	−89.6083	−3.46705
$669$	−3.96717	−0.153380
$670$	−52.5919	−2.03180
$671$	−8.54345	−0.329816
$672$	0.0230045	0.000887420 0
$673$	17.9406	0.691558	0.345779	−	0.938316i	$-0.387615\pi$
$673$	17.9406	0.691558	0.345779	+	0.938316i	$0.387615\pi$
$674$	−29.4268	−1.13348
$675$	−2.95644	−0.113793
$676$	90.0919	3.46507
$677$	−47.2978	−1.81780	−0.908901	−	0.417012i	$-0.863077\pi$
$677$	−47.2978	−1.81780	−0.908901	+	0.417012i	$0.863077\pi$
$678$	−2.11736	−0.0813168
$679$	1.95575	0.0750547
$680$	16.4367	0.630320
$681$	−3.81045	−0.146017
$682$	35.7573	1.36922
$683$	0.639679	0.0244766	0.0122383	−	0.999925i	$-0.496104\pi$
$683$	0.639679	0.0244766	0.0122383	+	0.999925i	$0.496104\pi$
$684$	58.4726	2.23576
$685$	−44.0648	−1.68363
$686$	−40.3688	−1.54129
$687$	−2.46187	−0.0939264
$688$	24.3012	0.926476
$689$	−66.2105	−2.52242
$690$	25.2868	0.962650
$691$	−44.3739	−1.68806	−0.844031	−	0.536294i	$-0.819824\pi$
$691$	−44.3739	−1.68806	−0.844031	+	0.536294i	$0.819824\pi$
$692$	−16.8965	−0.642308
$693$	4.49085	0.170593
$694$	−85.9694	−3.26335
$695$	−7.50491	−0.284678
$696$	31.5891	1.19738
$697$	−17.2288	−0.652588
$698$	74.1665	2.80724
$699$	20.7432	0.784580
$700$	3.52719	0.133315
$701$	16.8460	0.636265	0.318133	−	0.948046i	$-0.396944\pi$
$701$	16.8460	0.636265	0.318133	+	0.948046i	$0.396944\pi$
$702$	−66.2962	−2.50219
$703$	41.4823	1.56454
$704$	−11.8051	−0.444920
$705$	10.3768	0.390814
$706$	38.9903	1.46742
$707$	−10.1958	−0.383452
$708$	0.542584	0.0203915
$709$	1.10791	0.0416083	0.0208042	−	0.999784i	$-0.493377\pi$
$709$	1.10791	0.0416083	0.0208042	+	0.999784i	$0.493377\pi$
$710$	5.10735	0.191676
$711$	−34.3666	−1.28885
$712$	36.3472	1.36217
$713$	−56.8318	−2.12837
$714$	4.62168	0.172962
$715$	18.2891	0.683973
$716$	90.3512	3.37658
$717$	−0.463024	−0.0172920
$718$	−72.8175	−2.71753
$719$	−22.4076	−0.835664	−0.417832	−	0.908524i	$-0.637210\pi$
$719$	−22.4076	−0.835664	−0.417832	+	0.908524i	$0.637210\pi$
$720$	−18.7335	−0.698156
$721$	−20.9144	−0.778892
$722$	−56.7140	−2.11068
$723$	6.01028	0.223525
$724$	57.3570	2.13165
$725$	−4.86132	−0.180545
$726$	−18.7080	−0.694320
$727$	−20.8038	−0.771570	−0.385785	−	0.922589i	$-0.626069\pi$
$727$	−20.8038	−0.771570	−0.385785	+	0.922589i	$0.626069\pi$
$728$	39.5276	1.46499
$729$	5.39976	0.199991
$730$	51.0080	1.88789
$731$	−9.81526	−0.363031
$732$	20.0721	0.741885
$733$	−42.0747	−1.55407	−0.777033	−	0.629460i	$-0.783276\pi$
$733$	−42.0747	−1.55407	−0.777033	+	0.629460i	$0.783276\pi$
$734$	−20.9274	−0.772444
$735$	9.30980	0.343397
$736$	0.112447	0.00414485
$737$	15.1495	0.558039
$738$	59.0075	2.17209
$739$	11.9650	0.440141	0.220070	−	0.975484i	$-0.429371\pi$
$739$	11.9650	0.440141	0.220070	+	0.975484i	$0.429371\pi$
$740$	−53.2674	−1.95815
$741$	33.4620	1.22926
$742$	−36.8626	−1.35327
$743$	−34.1527	−1.25294	−0.626470	−	0.779445i	$-0.715501\pi$
$743$	−34.1527	−1.25294	−0.626470	+	0.779445i	$0.715501\pi$
$744$	−41.9832	−1.53918
$745$	−38.9355	−1.42649
$746$	37.6606	1.37885
$747$	11.1011	0.406168
$748$	−9.47422	−0.346412
$749$	−15.0595	−0.550263
$750$	−24.9526	−0.911141
$751$	43.8020	1.59836	0.799179	−	0.601093i	$-0.205268\pi$
$751$	43.8020	1.59836	0.799179	+	0.601093i	$0.205268\pi$
$752$	−22.9526	−0.836996
$753$	1.94360	0.0708289
$754$	−109.012	−3.96998
$755$	−30.6266	−1.11462
$756$	−24.6027	−0.894792
$757$	5.81934	0.211507	0.105754	−	0.994392i	$-0.466274\pi$
$757$	5.81934	0.211507	0.105754	+	0.994392i	$0.466274\pi$
$758$	59.5181	2.16179
$759$	−7.28404	−0.264394
$760$	66.2562	2.40336
$761$	1.24970	0.0453016	0.0226508	−	0.999743i	$-0.492789\pi$
$761$	1.24970	0.0453016	0.0226508	+	0.999743i	$0.492789\pi$
$762$	25.2384	0.914290
$763$	−9.74849	−0.352919
$764$	−65.7704	−2.37949
$765$	7.56645	0.273566
$766$	56.9351	2.05715
$767$	−0.935742	−0.0337877
$768$	27.6518	0.997797
$769$	−1.02219	−0.0368611	−0.0184306	−	0.999830i	$-0.505867\pi$
$769$	−1.02219	−0.0368611	−0.0184306	+	0.999830i	$0.505867\pi$
$770$	10.1824	0.366948
$771$	5.69238	0.205006
$772$	−29.4977	−1.06165
$773$	−7.62955	−0.274416	−0.137208	−	0.990542i	$-0.543813\pi$
$773$	−7.62955	−0.274416	−0.137208	+	0.990542i	$0.543813\pi$
$774$	33.6165	1.20832
$775$	6.46090	0.232082
$776$	7.06205	0.253513
$777$	−7.48510	−0.268527
$778$	−71.1417	−2.55055
$779$	−69.4490	−2.48827
$780$	−42.9685	−1.53852
$781$	−1.47121	−0.0526441
$782$	22.5909	0.807850
$783$	33.9086	1.21179
$784$	−20.5924	−0.735444
$785$	2.19229	0.0782463
$786$	−29.2946	−1.04490
$787$	−20.8999	−0.745002	−0.372501	−	0.928032i	$-0.621500\pi$
$787$	−20.8999	−0.745002	−0.372501	+	0.928032i	$0.621500\pi$
$788$	−16.1713	−0.576078
$789$	17.1113	0.609177
$790$	−77.9216	−2.77233
$791$	1.35512	0.0481827
$792$	16.2161	0.576214
$793$	−34.6164	−1.22926
$794$	−8.78894	−0.311908
$795$	20.0257	0.710239
$796$	43.8183	1.55310
$797$	−9.73088	−0.344686	−0.172343	−	0.985037i	$-0.555134\pi$
$797$	−9.73088	−0.344686	−0.172343	+	0.985037i	$0.555134\pi$
$798$	18.6299	0.659491
$799$	9.27056	0.327969
$800$	−0.0127835	−0.000451965 0
$801$	16.7320	0.591195
$802$	−57.4570	−2.02888
$803$	−14.6932	−0.518513
$804$	−35.5924	−1.25525
$805$	−16.1837	−0.570400
$806$	144.881	5.10323
$807$	−22.1816	−0.780829
$808$	−36.8162	−1.29519
$809$	−28.5975	−1.00543	−0.502717	−	0.864451i	$-0.667666\pi$
$809$	−28.5975	−1.00543	−0.502717	+	0.864451i	$0.667666\pi$
$810$	−14.4620	−0.508144
$811$	−18.0658	−0.634375	−0.317187	−	0.948363i	$-0.602738\pi$
$811$	−18.0658	−0.634375	−0.317187	+	0.948363i	$0.602738\pi$
$812$	−40.4547	−1.41968
$813$	−20.3440	−0.713495
$814$	23.0200	0.806850
$815$	−31.5451	−1.10498
$816$	5.55354	0.194413
$817$	−39.5651	−1.38421
$818$	−10.0133	−0.350108
$819$	18.1960	0.635821
$820$	89.1795	3.11428
$821$	−37.5775	−1.31147	−0.655733	−	0.754993i	$-0.727640\pi$
$821$	−37.5775	−1.31147	−0.655733	+	0.754993i	$0.727640\pi$
$822$	−44.7398	−1.56048
$823$	−33.8817	−1.18104	−0.590521	−	0.807022i	$-0.701078\pi$
$823$	−33.8817	−1.18104	−0.590521	+	0.807022i	$0.701078\pi$
$824$	−75.5202	−2.63087
$825$	0.828084	0.0288302
$826$	−0.520972	−0.0181269
$827$	−19.9806	−0.694793	−0.347397	−	0.937718i	$-0.612934\pi$
$827$	−19.9806	−0.694793	−0.347397	+	0.937718i	$0.612934\pi$
$828$	−51.5729	−1.79228
$829$	−20.0184	−0.695268	−0.347634	−	0.937630i	$-0.613015\pi$
$829$	−20.0184	−0.695268	−0.347634	+	0.937630i	$0.613015\pi$
$830$	25.1703	0.873673
$831$	−16.5680	−0.574739
$832$	−47.8318	−1.65827
$833$	8.31729	0.288177
$834$	−7.61987	−0.263855
$835$	−46.7411	−1.61754
$836$	−38.1904	−1.32084
$837$	−45.0659	−1.55770
$838$	−1.94062	−0.0670377
$839$	26.9539	0.930551	0.465275	−	0.885166i	$-0.345955\pi$
$839$	26.9539	0.930551	0.465275	+	0.885166i	$0.345955\pi$
$840$	−11.9553	−0.412498
$841$	26.7564	0.922635
$842$	−68.5077	−2.36093
$843$	−8.57283	−0.295264
$844$	10.5346	0.362617
$845$	46.9933	1.61662
$846$	−31.7510	−1.09162
$847$	11.9732	0.411406
$848$	−44.2951	−1.52110
$849$	−18.4456	−0.633050
$850$	−2.56824	−0.0880899
$851$	−36.5874	−1.25420
$852$	3.45648	0.118417
$853$	−53.3140	−1.82544	−0.912719	−	0.408588i	$-0.866021\pi$
$853$	−53.3140	−1.82544	−0.912719	+	0.408588i	$0.866021\pi$
$854$	−19.2726	−0.659494
$855$	30.5002	1.04309
$856$	−54.3788	−1.85863
$857$	39.7102	1.35647	0.678237	−	0.734843i	$-0.262744\pi$
$857$	39.7102	1.35647	0.678237	+	0.734843i	$0.262744\pi$
$858$	18.5692	0.633943
$859$	2.16148	0.0737486	0.0368743	−	0.999320i	$-0.488260\pi$
$859$	2.16148	0.0737486	0.0368743	+	0.999320i	$0.488260\pi$
$860$	50.8056	1.73246
$861$	12.5314	0.427070
$862$	3.41925	0.116460
$863$	−37.8709	−1.28914	−0.644570	−	0.764545i	$-0.722964\pi$
$863$	−37.8709	−1.28914	−0.644570	+	0.764545i	$0.722964\pi$
$864$	0.0891671	0.00303353
$865$	−8.81348	−0.299667
$866$	13.6277	0.463089
$867$	12.4543	0.422972
$868$	53.7659	1.82493
$869$	22.4459	0.761426
$870$	32.9712	1.11783
$871$	61.3828	2.07988
$872$	−35.2010	−1.19206
$873$	3.25093	0.110027
$874$	91.0636	3.08027
$875$	15.9698	0.539879
$876$	34.5204	1.16634
$877$	−17.9900	−0.607477	−0.303739	−	0.952755i	$-0.598235\pi$
$877$	−17.9900	−0.607477	−0.303739	+	0.952755i	$0.598235\pi$
$878$	−56.6830	−1.91296
$879$	19.9067	0.671438
$880$	12.2355	0.412457
$881$	15.5504	0.523906	0.261953	−	0.965081i	$-0.415633\pi$
$881$	15.5504	0.523906	0.261953	+	0.965081i	$0.415633\pi$
$882$	−28.4861	−0.959176
$883$	25.6121	0.861916	0.430958	−	0.902372i	$-0.358176\pi$
$883$	25.6121	0.861916	0.430958	+	0.902372i	$0.358176\pi$
$884$	−38.3877	−1.29112
$885$	0.283020	0.00951361
$886$	−53.4363	−1.79523
$887$	−52.0324	−1.74708	−0.873538	−	0.486756i	$-0.838180\pi$
$887$	−52.0324	−1.74708	−0.873538	+	0.486756i	$0.838180\pi$
$888$	−27.0281	−0.907005
$889$	−16.1527	−0.541745
$890$	37.9375	1.27167
$891$	4.16590	0.139563
$892$	18.3456	0.614255
$893$	37.3694	1.25052
$894$	−39.5319	−1.32215
$895$	47.1286	1.57533
$896$	−26.5770	−0.887875
$897$	−29.5135	−0.985428
$898$	74.1607	2.47477
$899$	−74.1026	−2.47146
$900$	5.86304	0.195435
$901$	17.8908	0.596028
$902$	−38.5397	−1.28323
$903$	7.13916	0.237576
$904$	4.89325	0.162747
$905$	29.9183	0.994517
$906$	−31.0958	−1.03309
$907$	−14.7406	−0.489454	−0.244727	−	0.969592i	$-0.578698\pi$
$907$	−14.7406	−0.489454	−0.244727	+	0.969592i	$0.578698\pi$
$908$	17.6208	0.584768
$909$	−16.9479	−0.562126
$910$	41.2571	1.36766
$911$	6.98453	0.231408	0.115704	−	0.993284i	$-0.463088\pi$
$911$	6.98453	0.231408	0.115704	+	0.993284i	$0.463088\pi$
$912$	22.3862	0.741281
$913$	−7.25050	−0.239956
$914$	−3.83604	−0.126885
$915$	10.4699	0.346124
$916$	11.3846	0.376156
$917$	18.7487	0.619137
$918$	17.9139	0.591248
$919$	−11.0893	−0.365803	−0.182901	−	0.983131i	$-0.558549\pi$
$919$	−11.0893	−0.365803	−0.182901	+	0.983131i	$0.558549\pi$
$920$	−58.4380	−1.92664
$921$	−18.1813	−0.599094
$922$	59.8312	1.97044
$923$	−5.96106	−0.196211
$924$	6.89110	0.226701
$925$	4.15943	0.136761
$926$	57.5100	1.88990
$927$	−34.7648	−1.14183
$928$	0.146619	0.00481300
$929$	6.56344	0.215339	0.107670	−	0.994187i	$-0.465661\pi$
$929$	6.56344	0.215339	0.107670	+	0.994187i	$0.465661\pi$
$930$	−43.8201	−1.43692
$931$	33.5268	1.09880
$932$	−95.9238	−3.14209
$933$	−9.05073	−0.296308
$934$	31.6354	1.03514
$935$	−4.94190	−0.161617
$936$	65.7045	2.14762
$937$	15.8966	0.519318	0.259659	−	0.965700i	$-0.416390\pi$
$937$	15.8966	0.519318	0.259659	+	0.965700i	$0.416390\pi$
$938$	34.1747	1.11584
$939$	28.9986	0.946333
$940$	−47.9861	−1.56513
$941$	−8.57197	−0.279438	−0.139719	−	0.990191i	$-0.544620\pi$
$941$	−8.57197	−0.279438	−0.139719	+	0.990191i	$0.544620\pi$
$942$	2.22587	0.0725229
$943$	61.2541	1.99471
$944$	−0.626015	−0.0203750
$945$	−12.8332	−0.417463
$946$	−21.9561	−0.713853
$947$	35.4116	1.15072	0.575361	−	0.817899i	$-0.304861\pi$
$947$	35.4116	1.15072	0.575361	+	0.817899i	$0.304861\pi$
$948$	−52.7347	−1.71274
$949$	−59.5341	−1.93256
$950$	−10.3525	−0.335880
$951$	8.55315	0.277355
$952$	−10.6808	−0.346165
$953$	21.9178	0.709987	0.354994	−	0.934869i	$-0.384483\pi$
$953$	21.9178	0.709987	0.354994	+	0.934869i	$0.384483\pi$
$954$	−61.2746	−1.98384
$955$	−34.3069	−1.11014
$956$	2.14118	0.0692508
$957$	−9.49762	−0.307014
$958$	−55.7789	−1.80213
$959$	28.6338	0.924632
$960$	14.4670	0.466919
$961$	67.4854	2.17695
$962$	93.2725	3.00723
$963$	−25.0326	−0.806664
$964$	−27.7936	−0.895172
$965$	−15.3865	−0.495309
$966$	−16.4316	−0.528677
$967$	−51.9498	−1.67059	−0.835297	−	0.549800i	$-0.814704\pi$
$967$	−51.9498	−1.67059	−0.835297	+	0.549800i	$0.814704\pi$
$968$	43.2345	1.38961
$969$	−9.04178	−0.290464
$970$	7.37105	0.236670
$971$	−22.7215	−0.729169	−0.364584	−	0.931170i	$-0.618789\pi$
$971$	−22.7215	−0.729169	−0.364584	+	0.931170i	$0.618789\pi$
$972$	−64.2534	−2.06093
$973$	4.87677	0.156342
$974$	−102.779	−3.29325
$975$	3.35523	0.107453
$976$	−23.1585	−0.741285
$977$	−1.10046	−0.0352070	−0.0176035	−	0.999845i	$-0.505604\pi$
$977$	−1.10046	−0.0352070	−0.0176035	+	0.999845i	$0.505604\pi$
$978$	−32.0283	−1.02415
$979$	−10.9282	−0.349267
$980$	−43.0517	−1.37524
$981$	−16.2044	−0.517365
$982$	−59.8723	−1.91060
$983$	2.10873	0.0672581	0.0336291	−	0.999434i	$-0.489294\pi$
$983$	2.10873	0.0672581	0.0336291	+	0.999434i	$0.489294\pi$
$984$	45.2501	1.44252
$985$	−8.43519	−0.268767
$986$	29.4562	0.938075
$987$	−6.74297	−0.214631
$988$	−154.740	−4.92293
$989$	34.8965	1.10964
$990$	16.9256	0.537932
$991$	−7.37805	−0.234371	−0.117186	−	0.993110i	$-0.537387\pi$
$991$	−7.37805	−0.234371	−0.117186	+	0.993110i	$0.537387\pi$
$992$	−0.194863	−0.00618689
$993$	20.4929	0.650323
$994$	−3.31881	−0.105266
$995$	22.8563	0.724594
$996$	17.0344	0.539755
$997$	−15.6697	−0.496263	−0.248131	−	0.968726i	$-0.579817\pi$
$997$	−15.6697	−0.496263	−0.248131	+	0.968726i	$0.579817\pi$
$998$	−75.5423	−2.39125
$999$	−29.0127	−0.917922

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.c.1.17	✓	158

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.c.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-2.44908 q^{2} -0.864554 q^{3} +3.99799 q^{4} +2.08542 q^{5} +2.11736 q^{6} -1.35512 q^{7} -4.89325 q^{8} -2.25255 q^{9} +O(q^{10})\)	\(q-2.44908 q^{2} -0.864554 q^{3} +3.99799 q^{4} +2.08542 q^{5} +2.11736 q^{6} -1.35512 q^{7} -4.89325 q^{8} -2.25255 q^{9} -5.10735 q^{10} +1.47121 q^{11} -3.45648 q^{12} +5.96106 q^{13} +3.31881 q^{14} -1.80295 q^{15} +3.98797 q^{16} -1.61074 q^{17} +5.51667 q^{18} -6.49286 q^{19} +8.33748 q^{20} +1.17158 q^{21} -3.60312 q^{22} +5.72671 q^{23} +4.23048 q^{24} -0.651039 q^{25} -14.5991 q^{26} +4.54111 q^{27} -5.41778 q^{28} +7.46702 q^{29} +4.41558 q^{30} -9.92398 q^{31} +0.0196355 q^{32} -1.27194 q^{33} +3.94483 q^{34} -2.82600 q^{35} -9.00567 q^{36} -6.38891 q^{37} +15.9015 q^{38} -5.15366 q^{39} -10.2045 q^{40} +10.6962 q^{41} -2.86929 q^{42} +6.09363 q^{43} +5.88190 q^{44} -4.69750 q^{45} -14.0252 q^{46} -5.75546 q^{47} -3.44782 q^{48} -5.16364 q^{49} +1.59445 q^{50} +1.39257 q^{51} +23.8323 q^{52} -11.1072 q^{53} -11.1215 q^{54} +3.06809 q^{55} +6.63096 q^{56} +5.61343 q^{57} -18.2873 q^{58} -0.156976 q^{59} -7.20820 q^{60} -5.80708 q^{61} +24.3046 q^{62} +3.05248 q^{63} -8.02403 q^{64} +12.4313 q^{65} +3.11509 q^{66} +10.2973 q^{67} -6.43973 q^{68} -4.95105 q^{69} +6.92110 q^{70} -1.00000 q^{71} +11.0223 q^{72} -9.98717 q^{73} +15.6470 q^{74} +0.562858 q^{75} -25.9584 q^{76} -1.99368 q^{77} +12.6217 q^{78} +15.2568 q^{79} +8.31658 q^{80} +2.83161 q^{81} -26.1959 q^{82} -4.92825 q^{83} +4.68396 q^{84} -3.35907 q^{85} -14.9238 q^{86} -6.45564 q^{87} -7.19901 q^{88} -7.42802 q^{89} +11.5046 q^{90} -8.07798 q^{91} +22.8954 q^{92} +8.57981 q^{93} +14.0956 q^{94} -13.5403 q^{95} -0.0169760 q^{96} -1.44322 q^{97} +12.6462 q^{98} -3.31397 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) \) 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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