LMFDB - Embedded newform 8013.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, 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("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.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:	$63.9841271397$
Analytic rank:	$1$
Dimension:	$116$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42944 q^{2} -1.00000 q^{3} +3.90217 q^{4} -3.31824 q^{5} +2.42944 q^{6} +4.69634 q^{7} -4.62122 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.42944 q^{2} -1.00000 q^{3} +3.90217 q^{4} -3.31824 q^{5} +2.42944 q^{6} +4.69634 q^{7} -4.62122 q^{8} +1.00000 q^{9} +8.06146 q^{10} -2.03672 q^{11} -3.90217 q^{12} -5.53930 q^{13} -11.4095 q^{14} +3.31824 q^{15} +3.42261 q^{16} -0.426323 q^{17} -2.42944 q^{18} -1.00799 q^{19} -12.9483 q^{20} -4.69634 q^{21} +4.94810 q^{22} -0.244244 q^{23} +4.62122 q^{24} +6.01072 q^{25} +13.4574 q^{26} -1.00000 q^{27} +18.3260 q^{28} -0.0614980 q^{29} -8.06146 q^{30} +4.24075 q^{31} +0.927400 q^{32} +2.03672 q^{33} +1.03572 q^{34} -15.5836 q^{35} +3.90217 q^{36} +2.59338 q^{37} +2.44884 q^{38} +5.53930 q^{39} +15.3343 q^{40} -4.52212 q^{41} +11.4095 q^{42} -0.167165 q^{43} -7.94765 q^{44} -3.31824 q^{45} +0.593376 q^{46} -5.90160 q^{47} -3.42261 q^{48} +15.0557 q^{49} -14.6027 q^{50} +0.426323 q^{51} -21.6153 q^{52} -1.70831 q^{53} +2.42944 q^{54} +6.75834 q^{55} -21.7028 q^{56} +1.00799 q^{57} +0.149406 q^{58} +12.8121 q^{59} +12.9483 q^{60} -7.27605 q^{61} -10.3026 q^{62} +4.69634 q^{63} -9.09829 q^{64} +18.3807 q^{65} -4.94810 q^{66} +9.21360 q^{67} -1.66359 q^{68} +0.244244 q^{69} +37.8594 q^{70} +2.50866 q^{71} -4.62122 q^{72} +11.3322 q^{73} -6.30046 q^{74} -6.01072 q^{75} -3.93334 q^{76} -9.56515 q^{77} -13.4574 q^{78} +1.90861 q^{79} -11.3571 q^{80} +1.00000 q^{81} +10.9862 q^{82} +3.93115 q^{83} -18.3260 q^{84} +1.41464 q^{85} +0.406117 q^{86} +0.0614980 q^{87} +9.41214 q^{88} +3.64161 q^{89} +8.06146 q^{90} -26.0145 q^{91} -0.953083 q^{92} -4.24075 q^{93} +14.3376 q^{94} +3.34474 q^{95} -0.927400 q^{96} -6.42908 q^{97} -36.5768 q^{98} -2.03672 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9}+O(q^{10}) $ 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9	\( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9} + 3 q^{10} - 57 q^{11} - 116 q^{12} + 6 q^{13} - 9 q^{14} + 20 q^{15} + 112 q^{16} - 30 q^{17} - 16 q^{18} + 3 q^{19} - 54 q^{20} + 33 q^{21} - 22 q^{22} - 58 q^{23} + 45 q^{24} + 126 q^{25} - 21 q^{26} - 116 q^{27} - 77 q^{28} - 38 q^{29} - 3 q^{30} + 17 q^{31} - 106 q^{32} + 57 q^{33} + 35 q^{34} - 72 q^{35} + 116 q^{36} - 41 q^{37} - 45 q^{38} - 6 q^{39} + 5 q^{40} - 39 q^{41} + 9 q^{42} - 118 q^{43} - 103 q^{44} - 20 q^{45} - 8 q^{46} - 65 q^{47} - 112 q^{48} + 165 q^{49} - 72 q^{50} + 30 q^{51} - 10 q^{52} - 58 q^{53} + 16 q^{54} + 14 q^{55} - 23 q^{56} - 3 q^{57} - 27 q^{58} - 75 q^{59} + 54 q^{60} + 45 q^{61} - 73 q^{62} - 33 q^{63} + 111 q^{64} - 86 q^{65} + 22 q^{66} - 127 q^{67} - 94 q^{68} + 58 q^{69} - 7 q^{70} - 61 q^{71} - 45 q^{72} + 15 q^{73} - 51 q^{74} - 126 q^{75} + 96 q^{76} - 57 q^{77} + 21 q^{78} + 7 q^{79} - 144 q^{80} + 116 q^{81} - 37 q^{82} - 194 q^{83} + 77 q^{84} + 3 q^{85} - 57 q^{86} + 38 q^{87} - 42 q^{88} - 56 q^{89} + 3 q^{90} - 39 q^{91} - 138 q^{92} - 17 q^{93} + 51 q^{94} - 127 q^{95} + 106 q^{96} + 57 q^{97} - 105 q^{98} - 57 q^{99}+O(q^{100}) \) 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9 + 3 * q^10 - 57 * q^11 - 116 * q^12 + 6 * q^13 - 9 * q^14 + 20 * q^15 + 112 * q^16 - 30 * q^17 - 16 * q^18 + 3 * q^19 - 54 * q^20 + 33 * q^21 - 22 * q^22 - 58 * q^23 + 45 * q^24 + 126 * q^25 - 21 * q^26 - 116 * q^27 - 77 * q^28 - 38 * q^29 - 3 * q^30 + 17 * q^31 - 106 * q^32 + 57 * q^33 + 35 * q^34 - 72 * q^35 + 116 * q^36 - 41 * q^37 - 45 * q^38 - 6 * q^39 + 5 * q^40 - 39 * q^41 + 9 * q^42 - 118 * q^43 - 103 * q^44 - 20 * q^45 - 8 * q^46 - 65 * q^47 - 112 * q^48 + 165 * q^49 - 72 * q^50 + 30 * q^51 - 10 * q^52 - 58 * q^53 + 16 * q^54 + 14 * q^55 - 23 * q^56 - 3 * q^57 - 27 * q^58 - 75 * q^59 + 54 * q^60 + 45 * q^61 - 73 * q^62 - 33 * q^63 + 111 * q^64 - 86 * q^65 + 22 * q^66 - 127 * q^67 - 94 * q^68 + 58 * q^69 - 7 * q^70 - 61 * q^71 - 45 * q^72 + 15 * q^73 - 51 * q^74 - 126 * q^75 + 96 * q^76 - 57 * q^77 + 21 * q^78 + 7 * q^79 - 144 * q^80 + 116 * q^81 - 37 * q^82 - 194 * q^83 + 77 * q^84 + 3 * q^85 - 57 * q^86 + 38 * q^87 - 42 * q^88 - 56 * q^89 + 3 * q^90 - 39 * q^91 - 138 * q^92 - 17 * q^93 + 51 * q^94 - 127 * q^95 + 106 * q^96 + 57 * q^97 - 105 * q^98 - 57 * 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 $

$2$	−2.42944	−1.71787	−0.858936	−	0.512082i	$-0.828874\pi$
$2$	−2.42944	−1.71787	−0.858936	+	0.512082i	$0.828874\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.90217	1.95109
$5$	−3.31824	−1.48396	−0.741981	−	0.670421i	$-0.766114\pi$
$5$	−3.31824	−1.48396	−0.741981	+	0.670421i	$0.766114\pi$
$6$	2.42944	0.991814
$7$	4.69634	1.77505	0.887526	−	0.460758i	$-0.152422\pi$
$7$	4.69634	1.77505	0.887526	+	0.460758i	$0.152422\pi$
$8$	−4.62122	−1.63385
$9$	1.00000	0.333333
$10$	8.06146	2.54926
$11$	−2.03672	−0.614095	−0.307048	−	0.951694i	$-0.599341\pi$
$11$	−2.03672	−0.614095	−0.307048	+	0.951694i	$0.599341\pi$
$12$	−3.90217	−1.12646
$13$	−5.53930	−1.53633	−0.768163	−	0.640255i	$-0.778829\pi$
$13$	−5.53930	−1.53633	−0.768163	+	0.640255i	$0.778829\pi$
$14$	−11.4095	−3.04931
$15$	3.31824	0.856766
$16$	3.42261	0.855653
$17$	−0.426323	−0.103398	−0.0516992	−	0.998663i	$-0.516464\pi$
$17$	−0.426323	−0.103398	−0.0516992	+	0.998663i	$0.516464\pi$
$18$	−2.42944	−0.572624
$19$	−1.00799	−0.231248	−0.115624	−	0.993293i	$-0.536887\pi$
$19$	−1.00799	−0.231248	−0.115624	+	0.993293i	$0.536887\pi$
$20$	−12.9483	−2.89534
$21$	−4.69634	−1.02483
$22$	4.94810	1.05494
$23$	−0.244244	−0.0509284	−0.0254642	−	0.999676i	$-0.508106\pi$
$23$	−0.244244	−0.0509284	−0.0254642	+	0.999676i	$0.508106\pi$
$24$	4.62122	0.943302
$25$	6.01072	1.20214
$26$	13.4574	2.63921
$27$	−1.00000	−0.192450
$28$	18.3260	3.46328
$29$	−0.0614980	−0.0114199	−0.00570995	−	0.999984i	$-0.501818\pi$
$29$	−0.0614980	−0.0114199	−0.00570995	+	0.999984i	$0.501818\pi$
$30$	−8.06146	−1.47181
$31$	4.24075	0.761661	0.380831	−	0.924645i	$-0.375638\pi$
$31$	4.24075	0.761661	0.380831	+	0.924645i	$0.375638\pi$
$32$	0.927400	0.163943
$33$	2.03672	0.354548
$34$	1.03572	0.177625
$35$	−15.5836	−2.63411
$36$	3.90217	0.650362
$37$	2.59338	0.426349	0.213175	−	0.977014i	$-0.431620\pi$
$37$	2.59338	0.426349	0.213175	+	0.977014i	$0.431620\pi$
$38$	2.44884	0.397255
$39$	5.53930	0.886998
$40$	15.3343	2.42457
$41$	−4.52212	−0.706236	−0.353118	−	0.935579i	$-0.614879\pi$
$41$	−4.52212	−0.706236	−0.353118	+	0.935579i	$0.614879\pi$
$42$	11.4095	1.76052
$43$	−0.167165	−0.0254924	−0.0127462	−	0.999919i	$-0.504057\pi$
$43$	−0.167165	−0.0254924	−0.0127462	+	0.999919i	$0.504057\pi$
$44$	−7.94765	−1.19815
$45$	−3.31824	−0.494654
$46$	0.593376	0.0874885
$47$	−5.90160	−0.860837	−0.430419	−	0.902629i	$-0.641634\pi$
$47$	−5.90160	−0.860837	−0.430419	+	0.902629i	$0.641634\pi$
$48$	−3.42261	−0.494012
$49$	15.0557	2.15081
$50$	−14.6027	−2.06513
$51$	0.426323	0.0596971
$52$	−21.6153	−2.99750
$53$	−1.70831	−0.234654	−0.117327	−	0.993093i	$-0.537433\pi$
$53$	−1.70831	−0.234654	−0.117327	+	0.993093i	$0.537433\pi$
$54$	2.42944	0.330605
$55$	6.75834	0.911294
$56$	−21.7028	−2.90016
$57$	1.00799	0.133511
$58$	0.149406	0.0196179
$59$	12.8121	1.66799	0.833995	−	0.551772i	$-0.186048\pi$
$59$	12.8121	1.66799	0.833995	+	0.551772i	$0.186048\pi$
$60$	12.9483	1.67162
$61$	−7.27605	−0.931602	−0.465801	−	0.884889i	$-0.654234\pi$
$61$	−7.27605	−0.931602	−0.465801	+	0.884889i	$0.654234\pi$
$62$	−10.3026	−1.30844
$63$	4.69634	0.591684
$64$	−9.09829	−1.13729
$65$	18.3807	2.27985
$66$	−4.94810	−0.609068
$67$	9.21360	1.12562	0.562810	−	0.826586i	$-0.309720\pi$
$67$	9.21360	1.12562	0.562810	+	0.826586i	$0.309720\pi$
$68$	−1.66359	−0.201739
$69$	0.244244	0.0294035
$70$	37.8594	4.52506
$71$	2.50866	0.297723	0.148862	−	0.988858i	$-0.452439\pi$
$71$	2.50866	0.297723	0.148862	+	0.988858i	$0.452439\pi$
$72$	−4.62122	−0.544615
$73$	11.3322	1.32633	0.663167	−	0.748471i	$-0.269212\pi$
$73$	11.3322	1.32633	0.663167	+	0.748471i	$0.269212\pi$
$74$	−6.30046	−0.732414
$75$	−6.01072	−0.694058
$76$	−3.93334	−0.451185
$77$	−9.56515	−1.09005
$78$	−13.4574	−1.52375
$79$	1.90861	0.214736	0.107368	−	0.994219i	$-0.465758\pi$
$79$	1.90861	0.214736	0.107368	+	0.994219i	$0.465758\pi$
$80$	−11.3571	−1.26976
$81$	1.00000	0.111111
$82$	10.9862	1.21322
$83$	3.93115	0.431500	0.215750	−	0.976449i	$-0.430780\pi$
$83$	3.93115	0.431500	0.215750	+	0.976449i	$0.430780\pi$
$84$	−18.3260	−1.99953
$85$	1.41464	0.153439
$86$	0.406117	0.0437927
$87$	0.0614980	0.00659328
$88$	9.41214	1.00334
$89$	3.64161	0.386010	0.193005	−	0.981198i	$-0.438177\pi$
$89$	3.64161	0.386010	0.193005	+	0.981198i	$0.438177\pi$
$90$	8.06146	0.849753
$91$	−26.0145	−2.72706
$92$	−0.953083	−0.0993658
$93$	−4.24075	−0.439745
$94$	14.3376	1.47881
$95$	3.34474	0.343163
$96$	−0.927400	−0.0946524
$97$	−6.42908	−0.652774	−0.326387	−	0.945236i	$-0.605831\pi$
$97$	−6.42908	−0.652774	−0.326387	+	0.945236i	$0.605831\pi$
$98$	−36.5768	−3.69481
$99$	−2.03672	−0.204698
$100$	23.4549	2.34549
$101$	−8.92675	−0.888245	−0.444122	−	0.895966i	$-0.646484\pi$
$101$	−8.92675	−0.888245	−0.444122	+	0.895966i	$0.646484\pi$
$102$	−1.03572	−0.102552
$103$	0.333172	0.0328285	0.0164142	−	0.999865i	$-0.494775\pi$
$103$	0.333172	0.0328285	0.0164142	+	0.999865i	$0.494775\pi$
$104$	25.5983	2.51012
$105$	15.5836	1.52080
$106$	4.15023	0.403106
$107$	−5.22192	−0.504822	−0.252411	−	0.967620i	$-0.581224\pi$
$107$	−5.22192	−0.504822	−0.252411	+	0.967620i	$0.581224\pi$
$108$	−3.90217	−0.375487
$109$	3.37974	0.323721	0.161860	−	0.986814i	$-0.448251\pi$
$109$	3.37974	0.323721	0.161860	+	0.986814i	$0.448251\pi$
$110$	−16.4190	−1.56549
$111$	−2.59338	−0.246153
$112$	16.0738	1.51883
$113$	−3.94931	−0.371520	−0.185760	−	0.982595i	$-0.559475\pi$
$113$	−3.94931	−0.371520	−0.185760	+	0.982595i	$0.559475\pi$
$114$	−2.44884	−0.229355
$115$	0.810461	0.0755758
$116$	−0.239976	−0.0222812
$117$	−5.53930	−0.512108
$118$	−31.1262	−2.86539
$119$	−2.00216	−0.183538
$120$	−15.3343	−1.39982
$121$	−6.85176	−0.622887
$122$	17.6767	1.60037
$123$	4.52212	0.407746
$124$	16.5482	1.48607
$125$	−3.35380	−0.299973
$126$	−11.4095	−1.01644
$127$	−12.2662	−1.08845	−0.544223	−	0.838940i	$-0.683176\pi$
$127$	−12.2662	−1.08845	−0.544223	+	0.838940i	$0.683176\pi$
$128$	20.2489	1.78977
$129$	0.167165	0.0147180
$130$	−44.6548	−3.91649
$131$	2.66846	0.233144	0.116572	−	0.993182i	$-0.462809\pi$
$131$	2.66846	0.233144	0.116572	+	0.993182i	$0.462809\pi$
$132$	7.94765	0.691754
$133$	−4.73385	−0.410477
$134$	−22.3839	−1.93367
$135$	3.31824	0.285589
$136$	1.97013	0.168937
$137$	6.04756	0.516678	0.258339	−	0.966054i	$-0.416825\pi$
$137$	6.04756	0.516678	0.258339	+	0.966054i	$0.416825\pi$
$138$	−0.593376	−0.0505115
$139$	−9.06375	−0.768777	−0.384389	−	0.923171i	$-0.625588\pi$
$139$	−9.06375	−0.768777	−0.384389	+	0.923171i	$0.625588\pi$
$140$	−60.8099	−5.13938
$141$	5.90160	0.497005
$142$	−6.09463	−0.511450
$143$	11.2820	0.943450
$144$	3.42261	0.285218
$145$	0.204065	0.0169467
$146$	−27.5309	−2.27847
$147$	−15.0557	−1.24177
$148$	10.1198	0.831844
$149$	−10.8981	−0.892809	−0.446404	−	0.894831i	$-0.647296\pi$
$149$	−10.8981	−0.892809	−0.446404	+	0.894831i	$0.647296\pi$
$150$	14.6027	1.19230
$151$	5.09927	0.414973	0.207486	−	0.978238i	$-0.433472\pi$
$151$	5.09927	0.414973	0.207486	+	0.978238i	$0.433472\pi$
$152$	4.65812	0.377824
$153$	−0.426323	−0.0344661
$154$	23.2380	1.87257
$155$	−14.0718	−1.13028
$156$	21.6153	1.73061
$157$	−1.86372	−0.148741	−0.0743704	−	0.997231i	$-0.523695\pi$
$157$	−1.86372	−0.148741	−0.0743704	+	0.997231i	$0.523695\pi$
$158$	−4.63686	−0.368889
$159$	1.70831	0.135478
$160$	−3.07734	−0.243285
$161$	−1.14705	−0.0904006
$162$	−2.42944	−0.190875
$163$	8.09837	0.634314	0.317157	−	0.948373i	$-0.397272\pi$
$163$	8.09837	0.634314	0.317157	+	0.948373i	$0.397272\pi$
$164$	−17.6461	−1.37793
$165$	−6.75834	−0.526136
$166$	−9.55050	−0.741263
$167$	−7.25109	−0.561106	−0.280553	−	0.959839i	$-0.590518\pi$
$167$	−7.25109	−0.561106	−0.280553	+	0.959839i	$0.590518\pi$
$168$	21.7028	1.67441
$169$	17.6838	1.36030
$170$	−3.43678	−0.263589
$171$	−1.00799	−0.0770827
$172$	−0.652306	−0.0497379
$173$	0.497009	0.0377869	0.0188935	−	0.999822i	$-0.493986\pi$
$173$	0.497009	0.0377869	0.0188935	+	0.999822i	$0.493986\pi$
$174$	−0.149406	−0.0113264
$175$	28.2284	2.13387
$176$	−6.97092	−0.525453
$177$	−12.8121	−0.963015
$178$	−8.84707	−0.663116
$179$	−5.63113	−0.420891	−0.210445	−	0.977606i	$-0.567491\pi$
$179$	−5.63113	−0.420891	−0.210445	+	0.977606i	$0.567491\pi$
$180$	−12.9483	−0.965113
$181$	15.5879	1.15864	0.579319	−	0.815101i	$-0.303319\pi$
$181$	15.5879	1.15864	0.579319	+	0.815101i	$0.303319\pi$
$182$	63.2005	4.68474
$183$	7.27605	0.537861
$184$	1.12870	0.0832092
$185$	−8.60546	−0.632686
$186$	10.3026	0.755427
$187$	0.868301	0.0634965
$188$	−23.0291	−1.67957
$189$	−4.69634	−0.341609
$190$	−8.12584	−0.589511
$191$	10.4552	0.756512	0.378256	−	0.925701i	$-0.376524\pi$
$191$	10.4552	0.756512	0.378256	+	0.925701i	$0.376524\pi$
$192$	9.09829	0.656612
$193$	−13.0939	−0.942521	−0.471260	−	0.881994i	$-0.656201\pi$
$193$	−13.0939	−0.942521	−0.471260	+	0.881994i	$0.656201\pi$
$194$	15.6190	1.12138
$195$	−18.3807	−1.31627
$196$	58.7498	4.19641
$197$	−7.92548	−0.564667	−0.282334	−	0.959316i	$-0.591109\pi$
$197$	−7.92548	−0.564667	−0.282334	+	0.959316i	$0.591109\pi$
$198$	4.94810	0.351646
$199$	15.4572	1.09573	0.547866	−	0.836566i	$-0.315440\pi$
$199$	15.4572	1.09573	0.547866	+	0.836566i	$0.315440\pi$
$200$	−27.7768	−1.96412
$201$	−9.21360	−0.649877
$202$	21.6870	1.52589
$203$	−0.288816	−0.0202709
$204$	1.66359	0.116474
$205$	15.0055	1.04803
$206$	−0.809422	−0.0563951
$207$	−0.244244	−0.0169761
$208$	−18.9589	−1.31456
$209$	2.05299	0.142008
$210$	−37.8594	−2.61255
$211$	−21.5434	−1.48311	−0.741555	−	0.670892i	$-0.765911\pi$
$211$	−21.5434	−1.48311	−0.741555	+	0.670892i	$0.765911\pi$
$212$	−6.66612	−0.457831
$213$	−2.50866	−0.171890
$214$	12.6863	0.867220
$215$	0.554693	0.0378298
$216$	4.62122	0.314434
$217$	19.9160	1.35199
$218$	−8.21088	−0.556111
$219$	−11.3322	−0.765759
$220$	26.3722	1.77801
$221$	2.36153	0.158854
$222$	6.30046	0.422859
$223$	29.2321	1.95753	0.978764	−	0.204991i	$-0.0657164\pi$
$223$	29.2321	1.95753	0.978764	+	0.204991i	$0.0657164\pi$
$224$	4.35539	0.291007
$225$	6.01072	0.400714
$226$	9.59460	0.638224
$227$	−15.8771	−1.05380	−0.526901	−	0.849927i	$-0.676646\pi$
$227$	−15.8771	−1.05380	−0.526901	+	0.849927i	$0.676646\pi$
$228$	3.93334	0.260492
$229$	7.26256	0.479923	0.239962	−	0.970782i	$-0.422865\pi$
$229$	7.26256	0.479923	0.239962	+	0.970782i	$0.422865\pi$
$230$	−1.96896	−0.129830
$231$	9.56515	0.629341
$232$	0.284196	0.0186584
$233$	−13.4330	−0.880025	−0.440013	−	0.897992i	$-0.645026\pi$
$233$	−13.4330	−0.880025	−0.440013	+	0.897992i	$0.645026\pi$
$234$	13.4574	0.879737
$235$	19.5829	1.27745
$236$	49.9949	3.25439
$237$	−1.90861	−0.123978
$238$	4.86412	0.315294
$239$	−0.0359353	−0.00232446	−0.00116223	−	0.999999i	$-0.500370\pi$
$239$	−0.0359353	−0.00232446	−0.00116223	+	0.999999i	$0.500370\pi$
$240$	11.3571	0.733095
$241$	2.44963	0.157794	0.0788971	−	0.996883i	$-0.474860\pi$
$241$	2.44963	0.157794	0.0788971	+	0.996883i	$0.474860\pi$
$242$	16.6459	1.07004
$243$	−1.00000	−0.0641500
$244$	−28.3924	−1.81764
$245$	−49.9583	−3.19172
$246$	−10.9862	−0.700455
$247$	5.58354	0.355272
$248$	−19.5974	−1.24444
$249$	−3.93115	−0.249127
$250$	8.14784	0.515315
$251$	29.5319	1.86404	0.932020	−	0.362407i	$-0.118045\pi$
$251$	29.5319	1.86404	0.932020	+	0.362407i	$0.118045\pi$
$252$	18.3260	1.15443
$253$	0.497458	0.0312749
$254$	29.7999	1.86981
$255$	−1.41464	−0.0885882
$256$	−30.9970	−1.93731
$257$	18.0774	1.12764	0.563819	−	0.825898i	$-0.309332\pi$
$257$	18.0774	1.12764	0.563819	+	0.825898i	$0.309332\pi$
$258$	−0.406117	−0.0252837
$259$	12.1794	0.756792
$260$	71.7248	4.44818
$261$	−0.0614980	−0.00380663
$262$	−6.48285	−0.400512
$263$	24.5126	1.51151	0.755756	−	0.654853i	$-0.227269\pi$
$263$	24.5126	1.51151	0.755756	+	0.654853i	$0.227269\pi$
$264$	−9.41214	−0.579277
$265$	5.66858	0.348218
$266$	11.5006	0.705147
$267$	−3.64161	−0.222863
$268$	35.9531	2.19618
$269$	−10.0932	−0.615396	−0.307698	−	0.951484i	$-0.599559\pi$
$269$	−10.0932	−0.615396	−0.307698	+	0.951484i	$0.599559\pi$
$270$	−8.06146	−0.490605
$271$	22.7774	1.38363	0.691814	−	0.722076i	$-0.256812\pi$
$271$	22.7774	1.38363	0.691814	+	0.722076i	$0.256812\pi$
$272$	−1.45914	−0.0884732
$273$	26.0145	1.57447
$274$	−14.6922	−0.887586
$275$	−12.2422	−0.738230
$276$	0.953083	0.0573689
$277$	−0.297653	−0.0178842	−0.00894211	−	0.999960i	$-0.502846\pi$
$277$	−0.297653	−0.0178842	−0.00894211	+	0.999960i	$0.502846\pi$
$278$	22.0198	1.32066
$279$	4.24075	0.253887
$280$	72.0152	4.30373
$281$	23.7643	1.41766	0.708830	−	0.705379i	$-0.249223\pi$
$281$	23.7643	1.41766	0.708830	+	0.705379i	$0.249223\pi$
$282$	−14.3376	−0.853791
$283$	−5.01531	−0.298129	−0.149065	−	0.988827i	$-0.547626\pi$
$283$	−5.01531	−0.298129	−0.149065	+	0.988827i	$0.547626\pi$
$284$	9.78922	0.580884
$285$	−3.34474	−0.198125
$286$	−27.4090	−1.62073
$287$	−21.2374	−1.25361
$288$	0.927400	0.0546476
$289$	−16.8182	−0.989309
$290$	−0.495764	−0.0291123
$291$	6.42908	0.376879
$292$	44.2202	2.58779
$293$	−8.96491	−0.523735	−0.261868	−	0.965104i	$-0.584338\pi$
$293$	−8.96491	−0.523735	−0.261868	+	0.965104i	$0.584338\pi$
$294$	36.5768	2.13320
$295$	−42.5135	−2.47523
$296$	−11.9846	−0.696589
$297$	2.03672	0.118183
$298$	26.4763	1.53373
$299$	1.35294	0.0782426
$300$	−23.4549	−1.35417
$301$	−0.785064	−0.0452503
$302$	−12.3884	−0.712871
$303$	8.92675	0.512828
$304$	−3.44995	−0.197868
$305$	24.1437	1.38246
$306$	1.03572	0.0592085
$307$	20.3185	1.15964	0.579819	−	0.814745i	$-0.303123\pi$
$307$	20.3185	1.15964	0.579819	+	0.814745i	$0.303123\pi$
$308$	−37.3249	−2.12678
$309$	−0.333172	−0.0189535
$310$	34.1867	1.94167
$311$	31.9392	1.81110	0.905552	−	0.424235i	$-0.139457\pi$
$311$	31.9392	1.81110	0.905552	+	0.424235i	$0.139457\pi$
$312$	−25.5983	−1.44922
$313$	−27.0732	−1.53027	−0.765133	−	0.643873i	$-0.777327\pi$
$313$	−27.0732	−1.53027	−0.765133	+	0.643873i	$0.777327\pi$
$314$	4.52778	0.255518
$315$	−15.5836	−0.878036
$316$	7.44774	0.418968
$317$	11.0690	0.621697	0.310849	−	0.950459i	$-0.399387\pi$
$317$	11.0690	0.621697	0.310849	+	0.950459i	$0.399387\pi$
$318$	−4.15023	−0.232733
$319$	0.125254	0.00701290
$320$	30.1903	1.68769
$321$	5.22192	0.291459
$322$	2.78670	0.155297
$323$	0.429727	0.0239107
$324$	3.90217	0.216787
$325$	−33.2952	−1.84688
$326$	−19.6745	−1.08967
$327$	−3.37974	−0.186900
$328$	20.8977	1.15388
$329$	−27.7160	−1.52803
$330$	16.4190	0.903834
$331$	6.35280	0.349182	0.174591	−	0.984641i	$-0.444140\pi$
$331$	6.35280	0.349182	0.174591	+	0.984641i	$0.444140\pi$
$332$	15.3400	0.841894
$333$	2.59338	0.142116
$334$	17.6161	0.963908
$335$	−30.5729	−1.67038
$336$	−16.0738	−0.876896
$337$	−32.6958	−1.78105	−0.890527	−	0.454930i	$-0.849664\pi$
$337$	−32.6958	−1.78105	−0.890527	+	0.454930i	$0.849664\pi$
$338$	−42.9618	−2.33681
$339$	3.94931	0.214497
$340$	5.52017	0.299373
$341$	−8.63724	−0.467733
$342$	2.44884	0.132418
$343$	37.8321	2.04274
$344$	0.772505	0.0416507
$345$	−0.810461	−0.0436337
$346$	−1.20745	−0.0649131
$347$	−22.3795	−1.20139	−0.600697	−	0.799477i	$-0.705110\pi$
$347$	−22.3795	−1.20139	−0.600697	+	0.799477i	$0.705110\pi$
$348$	0.239976	0.0128641
$349$	−18.7257	−1.00236	−0.501181	−	0.865343i	$-0.667101\pi$
$349$	−18.7257	−1.00236	−0.501181	+	0.865343i	$0.667101\pi$
$350$	−68.5791	−3.66571
$351$	5.53930	0.295666
$352$	−1.88886	−0.100676
$353$	8.56159	0.455687	0.227844	−	0.973698i	$-0.426832\pi$
$353$	8.56159	0.455687	0.227844	+	0.973698i	$0.426832\pi$
$354$	31.1262	1.65434
$355$	−8.32433	−0.441810
$356$	14.2102	0.753139
$357$	2.00216	0.105965
$358$	13.6805	0.723037
$359$	8.23483	0.434618	0.217309	−	0.976103i	$-0.430272\pi$
$359$	8.23483	0.434618	0.217309	+	0.976103i	$0.430272\pi$
$360$	15.3343	0.808189
$361$	−17.9840	−0.946524
$362$	−37.8698	−1.99039
$363$	6.85176	0.359624
$364$	−101.513	−5.32072
$365$	−37.6030	−1.96823
$366$	−17.6767	−0.923976
$367$	15.6539	0.817124	0.408562	−	0.912730i	$-0.366030\pi$
$367$	15.6539	0.817124	0.408562	+	0.912730i	$0.366030\pi$
$368$	−0.835953	−0.0435771
$369$	−4.52212	−0.235412
$370$	20.9064	1.08687
$371$	−8.02280	−0.416523
$372$	−16.5482	−0.857982
$373$	0.470103	0.0243410	0.0121705	−	0.999926i	$-0.496126\pi$
$373$	0.470103	0.0243410	0.0121705	+	0.999926i	$0.496126\pi$
$374$	−2.10949	−0.109079
$375$	3.35380	0.173189
$376$	27.2726	1.40648
$377$	0.340656	0.0175447
$378$	11.4095	0.586840
$379$	−11.1857	−0.574570	−0.287285	−	0.957845i	$-0.592753\pi$
$379$	−11.1857	−0.574570	−0.287285	+	0.957845i	$0.592753\pi$
$380$	13.0518	0.669541
$381$	12.2662	0.628415
$382$	−25.4003	−1.29959
$383$	−13.3910	−0.684250	−0.342125	−	0.939655i	$-0.611147\pi$
$383$	−13.3910	−0.684250	−0.342125	+	0.939655i	$0.611147\pi$
$384$	−20.2489	−1.03332
$385$	31.7395	1.61759
$386$	31.8109	1.61913
$387$	−0.167165	−0.00849747
$388$	−25.0874	−1.27362
$389$	−6.81951	−0.345763	−0.172881	−	0.984943i	$-0.555308\pi$
$389$	−6.81951	−0.345763	−0.172881	+	0.984943i	$0.555308\pi$
$390$	44.6548	2.26119
$391$	0.104127	0.00526592
$392$	−69.5754	−3.51409
$393$	−2.66846	−0.134606
$394$	19.2545	0.970027
$395$	−6.33324	−0.318660
$396$	−7.94765	−0.399384
$397$	−19.0839	−0.957794	−0.478897	−	0.877871i	$-0.658963\pi$
$397$	−19.0839	−0.957794	−0.478897	+	0.877871i	$0.658963\pi$
$398$	−37.5524	−1.88233
$399$	4.73385	0.236989
$400$	20.5724	1.02862
$401$	9.73492	0.486139	0.243069	−	0.970009i	$-0.421846\pi$
$401$	9.73492	0.486139	0.243069	+	0.970009i	$0.421846\pi$
$402$	22.3839	1.11641
$403$	−23.4908	−1.17016
$404$	−34.8337	−1.73304
$405$	−3.31824	−0.164885
$406$	0.701661	0.0348228
$407$	−5.28200	−0.261819
$408$	−1.97013	−0.0975359
$409$	4.65638	0.230243	0.115122	−	0.993351i	$-0.463274\pi$
$409$	4.65638	0.230243	0.115122	+	0.993351i	$0.463274\pi$
$410$	−36.4549	−1.80038
$411$	−6.04756	−0.298304
$412$	1.30010	0.0640512
$413$	60.1699	2.96077
$414$	0.593376	0.0291628
$415$	−13.0445	−0.640330
$416$	−5.13715	−0.251869
$417$	9.06375	0.443854
$418$	−4.98761	−0.243952
$419$	35.2879	1.72392	0.861962	−	0.506972i	$-0.169235\pi$
$419$	35.2879	1.72392	0.861962	+	0.506972i	$0.169235\pi$
$420$	60.8099	2.96722
$421$	17.9701	0.875808	0.437904	−	0.899022i	$-0.355721\pi$
$421$	17.9701	0.875808	0.437904	+	0.899022i	$0.355721\pi$
$422$	52.3384	2.54779
$423$	−5.90160	−0.286946
$424$	7.89446	0.383389
$425$	−2.56250	−0.124300
$426$	6.09463	0.295286
$427$	−34.1708	−1.65364
$428$	−20.3768	−0.984952
$429$	−11.2820	−0.544701
$430$	−1.34759	−0.0649867
$431$	−1.63577	−0.0787922	−0.0393961	−	0.999224i	$-0.512543\pi$
$431$	−1.63577	−0.0787922	−0.0393961	+	0.999224i	$0.512543\pi$
$432$	−3.42261	−0.164671
$433$	−11.0479	−0.530929	−0.265465	−	0.964121i	$-0.585525\pi$
$433$	−11.0479	−0.530929	−0.265465	+	0.964121i	$0.585525\pi$
$434$	−48.3848	−2.32254
$435$	−0.204065	−0.00978418
$436$	13.1884	0.631608
$437$	0.246195	0.0117771
$438$	27.5309	1.31548
$439$	−8.74981	−0.417605	−0.208803	−	0.977958i	$-0.566957\pi$
$439$	−8.74981	−0.417605	−0.208803	+	0.977958i	$0.566957\pi$
$440$	−31.2317	−1.48891
$441$	15.0557	0.716936
$442$	−5.73719	−0.272890
$443$	13.1114	0.622943	0.311471	−	0.950256i	$-0.399178\pi$
$443$	13.1114	0.622943	0.311471	+	0.950256i	$0.399178\pi$
$444$	−10.1198	−0.480266
$445$	−12.0837	−0.572824
$446$	−71.0177	−3.36278
$447$	10.8981	0.515463
$448$	−42.7287	−2.01874
$449$	−18.4233	−0.869449	−0.434724	−	0.900564i	$-0.643154\pi$
$449$	−18.4233	−0.869449	−0.434724	+	0.900564i	$0.643154\pi$
$450$	−14.6027	−0.688376
$451$	9.21030	0.433696
$452$	−15.4109	−0.724867
$453$	−5.09927	−0.239585
$454$	38.5725	1.81030
$455$	86.3222	4.04685
$456$	−4.65812	−0.218137
$457$	−6.47944	−0.303095	−0.151548	−	0.988450i	$-0.548426\pi$
$457$	−6.47944	−0.303095	−0.151548	+	0.988450i	$0.548426\pi$
$458$	−17.6439	−0.824447
$459$	0.426323	0.0198990
$460$	3.16256	0.147455
$461$	6.82523	0.317882	0.158941	−	0.987288i	$-0.449192\pi$
$461$	6.82523	0.317882	0.158941	+	0.987288i	$0.449192\pi$
$462$	−23.2380	−1.08113
$463$	−13.4207	−0.623712	−0.311856	−	0.950129i	$-0.600951\pi$
$463$	−13.4207	−0.623712	−0.311856	+	0.950129i	$0.600951\pi$
$464$	−0.210484	−0.00977147
$465$	14.0718	0.652566
$466$	32.6347	1.51177
$467$	23.4512	1.08519	0.542596	−	0.839994i	$-0.317442\pi$
$467$	23.4512	1.08519	0.542596	+	0.839994i	$0.317442\pi$
$468$	−21.6153	−0.999168
$469$	43.2702	1.99803
$470$	−47.5755	−2.19450
$471$	1.86372	0.0858755
$472$	−59.2074	−2.72524
$473$	0.340469	0.0156548
$474$	4.63686	0.212978
$475$	−6.05872	−0.277993
$476$	−7.81277	−0.358098
$477$	−1.70831	−0.0782181
$478$	0.0873025	0.00399312
$479$	24.5810	1.12313	0.561566	−	0.827432i	$-0.310199\pi$
$479$	24.5810	1.12313	0.561566	+	0.827432i	$0.310199\pi$
$480$	3.07734	0.140461
$481$	−14.3655	−0.655011
$482$	−5.95122	−0.271070
$483$	1.14705	0.0521928
$484$	−26.7368	−1.21531
$485$	21.3332	0.968691
$486$	2.42944	0.110202
$487$	−19.2090	−0.870443	−0.435221	−	0.900323i	$-0.643330\pi$
$487$	−19.2090	−0.870443	−0.435221	+	0.900323i	$0.643330\pi$
$488$	33.6242	1.52210
$489$	−8.09837	−0.366221
$490$	121.371	5.48296
$491$	−29.7756	−1.34376	−0.671878	−	0.740662i	$-0.734512\pi$
$491$	−29.7756	−1.34376	−0.671878	+	0.740662i	$0.734512\pi$
$492$	17.6461	0.795547
$493$	0.0262180	0.00118080
$494$	−13.5649	−0.610312
$495$	6.75834	0.303765
$496$	14.5145	0.651718
$497$	11.7815	0.528474
$498$	9.55050	0.427968
$499$	−31.8498	−1.42579	−0.712897	−	0.701269i	$-0.752617\pi$
$499$	−31.8498	−1.42579	−0.712897	+	0.701269i	$0.752617\pi$
$500$	−13.0871	−0.585273
$501$	7.25109	0.323955
$502$	−71.7461	−3.20218
$503$	10.9541	0.488418	0.244209	−	0.969723i	$-0.421472\pi$
$503$	10.9541	0.488418	0.244209	+	0.969723i	$0.421472\pi$
$504$	−21.7028	−0.966720
$505$	29.6211	1.31812
$506$	−1.20854	−0.0537263
$507$	−17.6838	−0.785367
$508$	−47.8647	−2.12365
$509$	−36.9902	−1.63956	−0.819781	−	0.572677i	$-0.805905\pi$
$509$	−36.9902	−1.63956	−0.819781	+	0.572677i	$0.805905\pi$
$510$	3.43678	0.152183
$511$	53.2199	2.35431
$512$	34.8074	1.53828
$513$	1.00799	0.0445037
$514$	−43.9180	−1.93714
$515$	−1.10555	−0.0487162
$516$	0.652306	0.0287162
$517$	12.0199	0.528636
$518$	−29.5891	−1.30007
$519$	−0.497009	−0.0218163
$520$	−84.9413	−3.72492
$521$	42.6498	1.86852	0.934260	−	0.356593i	$-0.116062\pi$
$521$	42.6498	1.86852	0.934260	+	0.356593i	$0.116062\pi$
$522$	0.149406	0.00653931
$523$	29.5173	1.29070	0.645351	−	0.763887i	$-0.276711\pi$
$523$	29.5173	1.29070	0.645351	+	0.763887i	$0.276711\pi$
$524$	10.4128	0.454884
$525$	−28.2284	−1.23199
$526$	−59.5519	−2.59659
$527$	−1.80793	−0.0787546
$528$	6.97092	0.303370
$529$	−22.9403	−0.997406
$530$	−13.7715	−0.598194
$531$	12.8121	0.555997
$532$	−18.4723	−0.800876
$533$	25.0494	1.08501
$534$	8.84707	0.382850
$535$	17.3276	0.749137
$536$	−42.5780	−1.83909
$537$	5.63113	0.243001
$538$	24.5209	1.05717
$539$	−30.6642	−1.32080
$540$	12.9483	0.557208
$541$	−16.2705	−0.699524	−0.349762	−	0.936839i	$-0.613738\pi$
$541$	−16.2705	−0.699524	−0.349762	+	0.936839i	$0.613738\pi$
$542$	−55.3363	−2.37690
$543$	−15.5879	−0.668940
$544$	−0.395372	−0.0169514
$545$	−11.2148	−0.480389
$546$	−63.2005	−2.70473
$547$	−31.2551	−1.33637	−0.668185	−	0.743995i	$-0.732929\pi$
$547$	−31.2551	−1.33637	−0.668185	+	0.743995i	$0.732929\pi$
$548$	23.5986	1.00808
$549$	−7.27605	−0.310534
$550$	29.7416	1.26819
$551$	0.0619892	0.00264083
$552$	−1.12870	−0.0480409
$553$	8.96350	0.381167
$554$	0.723129	0.0307228
$555$	8.60546	0.365281
$556$	−35.3683	−1.49995
$557$	−17.9522	−0.760658	−0.380329	−	0.924851i	$-0.624189\pi$
$557$	−17.9522	−0.760658	−0.380329	+	0.924851i	$0.624189\pi$
$558$	−10.3026	−0.436146
$559$	0.925976	0.0391646
$560$	−53.3366	−2.25388
$561$	−0.868301	−0.0366597
$562$	−57.7340	−2.43536
$563$	−6.82276	−0.287545	−0.143773	−	0.989611i	$-0.545923\pi$
$563$	−6.82276	−0.287545	−0.143773	+	0.989611i	$0.545923\pi$
$564$	23.0291	0.969699
$565$	13.1048	0.551321
$566$	12.1844	0.512148
$567$	4.69634	0.197228
$568$	−11.5931	−0.486434
$569$	−4.57274	−0.191699	−0.0958497	−	0.995396i	$-0.530557\pi$
$569$	−4.57274	−0.191699	−0.0958497	+	0.995396i	$0.530557\pi$
$570$	8.12584	0.340354
$571$	7.30453	0.305685	0.152843	−	0.988251i	$-0.451157\pi$
$571$	7.30453	0.305685	0.152843	+	0.988251i	$0.451157\pi$
$572$	44.0244	1.84075
$573$	−10.4552	−0.436772
$574$	51.5950	2.15353
$575$	−1.46808	−0.0612232
$576$	−9.09829	−0.379095
$577$	−26.0069	−1.08268	−0.541341	−	0.840803i	$-0.682083\pi$
$577$	−26.0069	−1.08268	−0.541341	+	0.840803i	$0.682083\pi$
$578$	40.8589	1.69951
$579$	13.0939	0.544165
$580$	0.796298	0.0330645
$581$	18.4621	0.765935
$582$	−15.6190	−0.647430
$583$	3.47935	0.144100
$584$	−52.3686	−2.16703
$585$	18.3807	0.759949
$586$	21.7797	0.899711
$587$	−24.5146	−1.01183	−0.505913	−	0.862584i	$-0.668844\pi$
$587$	−24.5146	−1.01183	−0.505913	+	0.862584i	$0.668844\pi$
$588$	−58.7498	−2.42280
$589$	−4.27462	−0.176133
$590$	103.284	4.25214
$591$	7.92548	0.326011
$592$	8.87614	0.364807
$593$	−28.4482	−1.16823	−0.584115	−	0.811671i	$-0.698558\pi$
$593$	−28.4482	−1.16823	−0.584115	+	0.811671i	$0.698558\pi$
$594$	−4.94810	−0.203023
$595$	6.64364	0.272363
$596$	−42.5264	−1.74195
$597$	−15.4572	−0.632622
$598$	−3.28689	−0.134411
$599$	−31.2475	−1.27674	−0.638370	−	0.769730i	$-0.720391\pi$
$599$	−31.2475	−1.27674	−0.638370	+	0.769730i	$0.720391\pi$
$600$	27.7768	1.13398
$601$	−26.6118	−1.08552	−0.542760	−	0.839888i	$-0.682621\pi$
$601$	−26.6118	−1.08552	−0.542760	+	0.839888i	$0.682621\pi$
$602$	1.90726	0.0777343
$603$	9.21360	0.375207
$604$	19.8983	0.809648
$605$	22.7358	0.924341
$606$	−21.6870	−0.880974
$607$	20.9613	0.850792	0.425396	−	0.905007i	$-0.360135\pi$
$607$	20.9613	0.850792	0.425396	+	0.905007i	$0.360135\pi$
$608$	−0.934807	−0.0379114
$609$	0.288816	0.0117034
$610$	−58.6556	−2.37489
$611$	32.6907	1.32253
$612$	−1.66359	−0.0672464
$613$	−37.3057	−1.50676	−0.753382	−	0.657583i	$-0.771579\pi$
$613$	−37.3057	−1.50676	−0.753382	+	0.657583i	$0.771579\pi$
$614$	−49.3626	−1.99211
$615$	−15.0055	−0.605079
$616$	44.2026	1.78098
$617$	−25.5083	−1.02692	−0.513462	−	0.858112i	$-0.671637\pi$
$617$	−25.5083	−1.02692	−0.513462	+	0.858112i	$0.671637\pi$
$618$	0.809422	0.0325597
$619$	2.43058	0.0976932	0.0488466	−	0.998806i	$-0.484445\pi$
$619$	2.43058	0.0976932	0.0488466	+	0.998806i	$0.484445\pi$
$620$	−54.9107	−2.20527
$621$	0.244244	0.00980118
$622$	−77.5943	−3.11125
$623$	17.1023	0.685188
$624$	18.9589	0.758963
$625$	−18.9249	−0.756995
$626$	65.7726	2.62880
$627$	−2.05299	−0.0819885
$628$	−7.27254	−0.290206
$629$	−1.10562	−0.0440838
$630$	37.8594	1.50835
$631$	27.9408	1.11231	0.556153	−	0.831080i	$-0.312277\pi$
$631$	27.9408	1.11231	0.556153	+	0.831080i	$0.312277\pi$
$632$	−8.82011	−0.350845
$633$	21.5434	0.856274
$634$	−26.8915	−1.06800
$635$	40.7021	1.61521
$636$	6.66612	0.264329
$637$	−83.3978	−3.30434
$638$	−0.304298	−0.0120473
$639$	2.50866	0.0992410
$640$	−67.1908	−2.65595
$641$	17.9488	0.708934	0.354467	−	0.935069i	$-0.384662\pi$
$641$	17.9488	0.708934	0.354467	+	0.935069i	$0.384662\pi$
$642$	−12.6863	−0.500690
$643$	12.6757	0.499882	0.249941	−	0.968261i	$-0.419589\pi$
$643$	12.6757	0.499882	0.249941	+	0.968261i	$0.419589\pi$
$644$	−4.47601	−0.176379
$645$	−0.554693	−0.0218410
$646$	−1.04400	−0.0410755
$647$	17.7451	0.697630	0.348815	−	0.937192i	$-0.386584\pi$
$647$	17.7451	0.697630	0.348815	+	0.937192i	$0.386584\pi$
$648$	−4.62122	−0.181538
$649$	−26.0947	−1.02430
$650$	80.8885	3.17271
$651$	−19.9160	−0.780571
$652$	31.6013	1.23760
$653$	3.44667	0.134879	0.0674394	−	0.997723i	$-0.478517\pi$
$653$	3.44667	0.134879	0.0674394	+	0.997723i	$0.478517\pi$
$654$	8.21088	0.321071
$655$	−8.85458	−0.345977
$656$	−15.4775	−0.604293
$657$	11.3322	0.442111
$658$	67.3342	2.62496
$659$	−8.97706	−0.349697	−0.174848	−	0.984595i	$-0.555944\pi$
$659$	−8.97706	−0.349697	−0.174848	+	0.984595i	$0.555944\pi$
$660$	−26.3722	−1.02654
$661$	−2.46442	−0.0958546	−0.0479273	−	0.998851i	$-0.515262\pi$
$661$	−2.46442	−0.0958546	−0.0479273	+	0.998851i	$0.515262\pi$
$662$	−15.4337	−0.599849
$663$	−2.36153	−0.0917142
$664$	−18.1667	−0.705005
$665$	15.7081	0.609132
$666$	−6.30046	−0.244138
$667$	0.0150205	0.000581597 0
$668$	−28.2950	−1.09477
$669$	−29.2321	−1.13018
$670$	74.2751	2.86950
$671$	14.8193	0.572092
$672$	−4.35539	−0.168013
$673$	−13.0570	−0.503309	−0.251654	−	0.967817i	$-0.580975\pi$
$673$	−13.0570	−0.503309	−0.251654	+	0.967817i	$0.580975\pi$
$674$	79.4325	3.05963
$675$	−6.01072	−0.231353
$676$	69.0054	2.65405
$677$	1.18247	0.0454461	0.0227230	−	0.999742i	$-0.492766\pi$
$677$	1.18247	0.0454461	0.0227230	+	0.999742i	$0.492766\pi$
$678$	−9.59460	−0.368479
$679$	−30.1932	−1.15871
$680$	−6.53736	−0.250696
$681$	15.8771	0.608413
$682$	20.9836	0.803505
$683$	9.79734	0.374885	0.187442	−	0.982276i	$-0.439980\pi$
$683$	9.79734	0.374885	0.187442	+	0.982276i	$0.439980\pi$
$684$	−3.93334	−0.150395
$685$	−20.0672	−0.766730
$686$	−91.9108	−3.50917
$687$	−7.26256	−0.277084
$688$	−0.572141	−0.0218127
$689$	9.46283	0.360505
$690$	1.96896	0.0749572
$691$	−36.9370	−1.40515	−0.702575	−	0.711610i	$-0.747966\pi$
$691$	−36.9370	−1.40515	−0.702575	+	0.711610i	$0.747966\pi$
$692$	1.93942	0.0737255
$693$	−9.56515	−0.363350
$694$	54.3696	2.06384
$695$	30.0757	1.14084
$696$	−0.284196	−0.0107724
$697$	1.92788	0.0730237
$698$	45.4928	1.72193
$699$	13.4330	0.508083
$700$	110.152	4.16336
$701$	42.7392	1.61424	0.807118	−	0.590390i	$-0.201026\pi$
$701$	42.7392	1.61424	0.807118	+	0.590390i	$0.201026\pi$
$702$	−13.4574	−0.507916
$703$	−2.61409	−0.0985924
$704$	18.5307	0.698402
$705$	−19.5829	−0.737536
$706$	−20.7999	−0.782813
$707$	−41.9231	−1.57668
$708$	−49.9949	−1.87893
$709$	1.16850	0.0438839	0.0219419	−	0.999759i	$-0.493015\pi$
$709$	1.16850	0.0438839	0.0219419	+	0.999759i	$0.493015\pi$
$710$	20.2235	0.758973
$711$	1.90861	0.0715786
$712$	−16.8287	−0.630681
$713$	−1.03578	−0.0387902
$714$	−4.86412	−0.182035
$715$	−37.4364	−1.40004
$716$	−21.9737	−0.821194
$717$	0.0359353	0.00134203
$718$	−20.0060	−0.746618
$719$	5.42205	0.202208	0.101104	−	0.994876i	$-0.467762\pi$
$719$	5.42205	0.202208	0.101104	+	0.994876i	$0.467762\pi$
$720$	−11.3571	−0.423252
$721$	1.56469	0.0582722
$722$	43.6909	1.62601
$723$	−2.44963	−0.0911025
$724$	60.8266	2.26060
$725$	−0.369647	−0.0137283
$726$	−16.6459	−0.617788
$727$	41.9677	1.55650	0.778249	−	0.627956i	$-0.216108\pi$
$727$	41.9677	1.55650	0.778249	+	0.627956i	$0.216108\pi$
$728$	120.218	4.45559
$729$	1.00000	0.0370370
$730$	91.3541	3.38117
$731$	0.0712662	0.00263587
$732$	28.3924	1.04941
$733$	−41.6104	−1.53692	−0.768458	−	0.639900i	$-0.778976\pi$
$733$	−41.6104	−1.53692	−0.768458	+	0.639900i	$0.778976\pi$
$734$	−38.0301	−1.40372
$735$	49.9583	1.84274
$736$	−0.226512	−0.00834934
$737$	−18.7655	−0.691238
$738$	10.9862	0.404408
$739$	−34.2411	−1.25958	−0.629789	−	0.776766i	$-0.716859\pi$
$739$	−34.2411	−1.25958	−0.629789	+	0.776766i	$0.716859\pi$
$740$	−33.5800	−1.23443
$741$	−5.58354	−0.205116
$742$	19.4909	0.715534
$743$	−34.8733	−1.27938	−0.639689	−	0.768634i	$-0.720937\pi$
$743$	−34.8733	−1.27938	−0.639689	+	0.768634i	$0.720937\pi$
$744$	19.5974	0.718477
$745$	36.1626	1.32489
$746$	−1.14209	−0.0418148
$747$	3.93115	0.143833
$748$	3.38826	0.123887
$749$	−24.5239	−0.896085
$750$	−8.14784	−0.297517
$751$	8.05939	0.294091	0.147046	−	0.989130i	$-0.453024\pi$
$751$	8.05939	0.294091	0.147046	+	0.989130i	$0.453024\pi$
$752$	−20.1989	−0.736578
$753$	−29.5319	−1.07620
$754$	−0.827603	−0.0301395
$755$	−16.9206	−0.615804
$756$	−18.3260	−0.666508
$757$	−2.60021	−0.0945064	−0.0472532	−	0.998883i	$-0.515047\pi$
$757$	−2.60021	−0.0945064	−0.0472532	+	0.998883i	$0.515047\pi$
$758$	27.1749	0.987038
$759$	−0.497458	−0.0180566
$760$	−15.4568	−0.560676
$761$	34.7930	1.26124	0.630622	−	0.776090i	$-0.282800\pi$
$761$	34.7930	1.26124	0.630622	+	0.776090i	$0.282800\pi$
$762$	−29.7999	−1.07954
$763$	15.8724	0.574621
$764$	40.7980	1.47602
$765$	1.41464	0.0511464
$766$	32.5327	1.17545
$767$	−70.9699	−2.56258
$768$	30.9970	1.11851
$769$	−16.4862	−0.594507	−0.297254	−	0.954799i	$-0.596071\pi$
$769$	−16.4862	−0.594507	−0.297254	+	0.954799i	$0.596071\pi$
$770$	−77.1091	−2.77882
$771$	−18.0774	−0.651042
$772$	−51.0947	−1.83894
$773$	17.1345	0.616287	0.308143	−	0.951340i	$-0.400292\pi$
$773$	17.1345	0.616287	0.308143	+	0.951340i	$0.400292\pi$
$774$	0.406117	0.0145976
$775$	25.4900	0.915626
$776$	29.7101	1.06653
$777$	−12.1794	−0.436934
$778$	16.5676	0.593977
$779$	4.55823	0.163316
$780$	−71.7248	−2.56816
$781$	−5.10944	−0.182830
$782$	−0.252970	−0.00904618
$783$	0.0614980	0.00219776
$784$	51.5297	1.84035
$785$	6.18426	0.220726
$786$	6.48285	0.231236
$787$	25.4770	0.908158	0.454079	−	0.890962i	$-0.349968\pi$
$787$	25.4770	0.908158	0.454079	+	0.890962i	$0.349968\pi$
$788$	−30.9266	−1.10172
$789$	−24.5126	−0.872672
$790$	15.3862	0.547417
$791$	−18.5473	−0.659466
$792$	9.41214	0.334446
$793$	40.3042	1.43124
$794$	46.3632	1.64537
$795$	−5.66858	−0.201044
$796$	60.3167	2.13787
$797$	5.09317	0.180409	0.0902047	−	0.995923i	$-0.471248\pi$
$797$	5.09317	0.180409	0.0902047	+	0.995923i	$0.471248\pi$
$798$	−11.5006	−0.407117
$799$	2.51599	0.0890092
$800$	5.57434	0.197083
$801$	3.64161	0.128670
$802$	−23.6504	−0.835124
$803$	−23.0806	−0.814496
$804$	−35.9531	−1.26797
$805$	3.80620	0.134151
$806$	57.0694	2.01019
$807$	10.0932	0.355299
$808$	41.2524	1.45126
$809$	−10.8006	−0.379730	−0.189865	−	0.981810i	$-0.560805\pi$
$809$	−10.8006	−0.379730	−0.189865	+	0.981810i	$0.560805\pi$
$810$	8.06146	0.283251
$811$	−13.5959	−0.477416	−0.238708	−	0.971091i	$-0.576724\pi$
$811$	−13.5959	−0.477416	−0.238708	+	0.971091i	$0.576724\pi$
$812$	−1.12701	−0.0395503
$813$	−22.7774	−0.798838
$814$	12.8323	0.449772
$815$	−26.8723	−0.941297
$816$	1.45914	0.0510800
$817$	0.168500	0.00589507
$818$	−11.3124	−0.395528
$819$	−26.0145	−0.909019
$820$	58.5539	2.04479
$821$	−36.2637	−1.26561	−0.632807	−	0.774310i	$-0.718097\pi$
$821$	−36.2637	−1.26561	−0.632807	+	0.774310i	$0.718097\pi$
$822$	14.6922	0.512448
$823$	36.1479	1.26004	0.630018	−	0.776580i	$-0.283047\pi$
$823$	36.1479	1.26004	0.630018	+	0.776580i	$0.283047\pi$
$824$	−1.53966	−0.0536367
$825$	12.2422	0.426217
$826$	−146.179	−5.08622
$827$	−16.0457	−0.557965	−0.278982	−	0.960296i	$-0.589997\pi$
$827$	−16.0457	−0.557965	−0.278982	+	0.960296i	$0.589997\pi$
$828$	−0.953083	−0.0331219
$829$	50.3696	1.74941	0.874705	−	0.484656i	$-0.161055\pi$
$829$	50.3696	1.74941	0.874705	+	0.484656i	$0.161055\pi$
$830$	31.6908	1.10001
$831$	0.297653	0.0103255
$832$	50.3981	1.74724
$833$	−6.41856	−0.222390
$834$	−22.0198	−0.762484
$835$	24.0608	0.832660
$836$	8.01112	0.277070
$837$	−4.24075	−0.146582
$838$	−85.7297	−2.96148
$839$	−7.66880	−0.264756	−0.132378	−	0.991199i	$-0.542261\pi$
$839$	−7.66880	−0.264756	−0.132378	+	0.991199i	$0.542261\pi$
$840$	−72.0152	−2.48476
$841$	−28.9962	−0.999870
$842$	−43.6572	−1.50453
$843$	−23.7643	−0.818487
$844$	−84.0661	−2.89368
$845$	−58.6792	−2.01863
$846$	14.3376	0.492936
$847$	−32.1782	−1.10566
$848$	−5.84688	−0.200783
$849$	5.01531	0.172125
$850$	6.22545	0.213531
$851$	−0.633418	−0.0217133
$852$	−9.78922	−0.335373
$853$	−43.3600	−1.48462	−0.742310	−	0.670057i	$-0.766270\pi$
$853$	−43.3600	−1.48462	−0.742310	+	0.670057i	$0.766270\pi$
$854$	83.0159	2.84075
$855$	3.34474	0.114388
$856$	24.1316	0.824802
$857$	−45.5209	−1.55496	−0.777482	−	0.628906i	$-0.783503\pi$
$857$	−45.5209	−1.55496	−0.777482	+	0.628906i	$0.783503\pi$
$858$	27.4090	0.935727
$859$	2.73591	0.0933481	0.0466741	−	0.998910i	$-0.485138\pi$
$859$	2.73591	0.0933481	0.0466741	+	0.998910i	$0.485138\pi$
$860$	2.16451	0.0738092
$861$	21.2374	0.723769
$862$	3.97400	0.135355
$863$	−29.9787	−1.02049	−0.510244	−	0.860030i	$-0.670445\pi$
$863$	−29.9787	−1.02049	−0.510244	+	0.860030i	$0.670445\pi$
$864$	−0.927400	−0.0315508
$865$	−1.64920	−0.0560743
$866$	26.8403	0.912069
$867$	16.8182	0.571178
$868$	77.7158	2.63785
$869$	−3.88732	−0.131868
$870$	0.495764	0.0168080
$871$	−51.0369	−1.72932
$872$	−15.6185	−0.528910
$873$	−6.42908	−0.217591
$874$	−0.598115	−0.0202315
$875$	−15.7506	−0.532467
$876$	−44.2202	−1.49406
$877$	−10.6574	−0.359874	−0.179937	−	0.983678i	$-0.557589\pi$
$877$	−10.6574	−0.359874	−0.179937	+	0.983678i	$0.557589\pi$
$878$	21.2571	0.717393
$879$	8.96491	0.302379
$880$	23.1312	0.779752
$881$	−0.335184	−0.0112926	−0.00564632	−	0.999984i	$-0.501797\pi$
$881$	−0.335184	−0.0112926	−0.00564632	+	0.999984i	$0.501797\pi$
$882$	−36.5768	−1.23160
$883$	14.9763	0.503992	0.251996	−	0.967728i	$-0.418913\pi$
$883$	14.9763	0.503992	0.251996	+	0.967728i	$0.418913\pi$
$884$	9.21510	0.309937
$885$	42.5135	1.42908
$886$	−31.8534	−1.07014
$887$	−45.1599	−1.51632	−0.758161	−	0.652067i	$-0.773902\pi$
$887$	−45.1599	−1.51632	−0.758161	+	0.652067i	$0.773902\pi$
$888$	11.9846	0.402176
$889$	−57.6062	−1.93205
$890$	29.3567	0.984039
$891$	−2.03672	−0.0682328
$892$	114.069	3.81931
$893$	5.94874	0.199067
$894$	−26.4763	−0.885500
$895$	18.6854	0.624586
$896$	95.0960	3.17693
$897$	−1.35294	−0.0451734
$898$	44.7583	1.49360
$899$	−0.260798	−0.00869809
$900$	23.4549	0.781829
$901$	0.728290	0.0242629
$902$	−22.3759	−0.745035
$903$	0.785064	0.0261253
$904$	18.2506	0.607006
$905$	−51.7243	−1.71937
$906$	12.3884	0.411576
$907$	4.27123	0.141824	0.0709120	−	0.997483i	$-0.477409\pi$
$907$	4.27123	0.141824	0.0709120	+	0.997483i	$0.477409\pi$
$908$	−61.9553	−2.05606
$909$	−8.92675	−0.296082
$910$	−209.715	−6.95197
$911$	−14.7498	−0.488682	−0.244341	−	0.969689i	$-0.578572\pi$
$911$	−14.7498	−0.488682	−0.244341	+	0.969689i	$0.578572\pi$
$912$	3.44995	0.114239
$913$	−8.00667	−0.264982
$914$	15.7414	0.520679
$915$	−24.1437	−0.798165
$916$	28.3398	0.936372
$917$	12.5320	0.413843
$918$	−1.03572	−0.0341840
$919$	−23.6284	−0.779430	−0.389715	−	0.920935i	$-0.627427\pi$
$919$	−23.6284	−0.779430	−0.389715	+	0.920935i	$0.627427\pi$
$920$	−3.74531	−0.123479
$921$	−20.3185	−0.669517
$922$	−16.5815	−0.546082
$923$	−13.8962	−0.457399
$924$	37.3249	1.22790
$925$	15.5881	0.512533
$926$	32.6047	1.07146
$927$	0.333172	0.0109428
$928$	−0.0570333	−0.00187221
$929$	0.364074	0.0119449	0.00597244	−	0.999982i	$-0.498099\pi$
$929$	0.364074	0.0119449	0.00597244	+	0.999982i	$0.498099\pi$
$930$	−34.1867	−1.12102
$931$	−15.1759	−0.497370
$932$	−52.4179	−1.71701
$933$	−31.9392	−1.04564
$934$	−56.9732	−1.86422
$935$	−2.88123	−0.0942264
$936$	25.5983	0.836707
$937$	−19.7537	−0.645326	−0.322663	−	0.946514i	$-0.604578\pi$
$937$	−19.7537	−0.645326	−0.322663	+	0.946514i	$0.604578\pi$
$938$	−105.122	−3.43237
$939$	27.0732	0.883499
$940$	76.4160	2.49242
$941$	−60.2270	−1.96334	−0.981672	−	0.190576i	$-0.938965\pi$
$941$	−60.2270	−1.96334	−0.981672	+	0.190576i	$0.938965\pi$
$942$	−4.52778	−0.147523
$943$	1.10450	0.0359675
$944$	43.8508	1.42722
$945$	15.5836	0.506934
$946$	−0.827148	−0.0268929
$947$	−17.1732	−0.558054	−0.279027	−	0.960283i	$-0.590012\pi$
$947$	−17.1732	−0.558054	−0.279027	+	0.960283i	$0.590012\pi$
$948$	−7.44774	−0.241891
$949$	−62.7725	−2.03768
$950$	14.7193	0.477557
$951$	−11.0690	−0.358937
$952$	9.25240	0.299872
$953$	−50.3975	−1.63254	−0.816268	−	0.577673i	$-0.803961\pi$
$953$	−50.3975	−1.63254	−0.816268	+	0.577673i	$0.803961\pi$
$954$	4.15023	0.134369
$955$	−34.6929	−1.12263
$956$	−0.140226	−0.00453522
$957$	−0.125254	−0.00404890
$958$	−59.7179	−1.92940
$959$	28.4014	0.917129
$960$	−30.1903	−0.974388
$961$	−13.0160	−0.419872
$962$	34.9001	1.12523
$963$	−5.22192	−0.168274
$964$	9.55886	0.307870
$965$	43.4488	1.39866
$966$	−2.78670	−0.0896606
$967$	−52.5964	−1.69139	−0.845693	−	0.533670i	$-0.820812\pi$
$967$	−52.5964	−1.69139	−0.845693	+	0.533670i	$0.820812\pi$
$968$	31.6635	1.01770
$969$	−0.429727	−0.0138048
$970$	−51.8277	−1.66409
$971$	−7.29865	−0.234225	−0.117112	−	0.993119i	$-0.537364\pi$
$971$	−7.29865	−0.234225	−0.117112	+	0.993119i	$0.537364\pi$
$972$	−3.90217	−0.125162
$973$	−42.5665	−1.36462
$974$	46.6671	1.49531
$975$	33.2952	1.06630
$976$	−24.9031	−0.797129
$977$	29.5660	0.945901	0.472951	−	0.881089i	$-0.343189\pi$
$977$	29.5660	0.945901	0.472951	+	0.881089i	$0.343189\pi$
$978$	19.6745	0.629121
$979$	−7.41696	−0.237047
$980$	−194.946	−6.22732
$981$	3.37974	0.107907
$982$	72.3381	2.30840
$983$	37.9588	1.21070	0.605348	−	0.795961i	$-0.293034\pi$
$983$	37.9588	1.21070	0.605348	+	0.795961i	$0.293034\pi$
$984$	−20.8977	−0.666194
$985$	26.2987	0.837945
$986$	−0.0636950	−0.00202846
$987$	27.7160	0.882209
$988$	21.7879	0.693167
$989$	0.0408290	0.00129829
$990$	−16.4190	−0.521829
$991$	−10.6905	−0.339594	−0.169797	−	0.985479i	$-0.554311\pi$
$991$	−10.6905	−0.339594	−0.169797	+	0.985479i	$0.554311\pi$
$992$	3.93287	0.124869
$993$	−6.35280	−0.201600
$994$	−28.6225	−0.907851
$995$	−51.2907	−1.62603
$996$	−15.3400	−0.486068
$997$	−41.1538	−1.30335	−0.651677	−	0.758497i	$-0.725934\pi$
$997$	−41.1538	−1.30335	−0.651677	+	0.758497i	$0.725934\pi$
$998$	77.3772	2.44933
$999$	−2.59338	−0.0820509

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.c.1.13	✓	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.c.1.13	✓	116	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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.42944 q^{2} -1.00000 q^{3} +3.90217 q^{4} -3.31824 q^{5} +2.42944 q^{6} +4.69634 q^{7} -4.62122 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.42944 q^{2} -1.00000 q^{3} +3.90217 q^{4} -3.31824 q^{5} +2.42944 q^{6} +4.69634 q^{7} -4.62122 q^{8} +1.00000 q^{9} +8.06146 q^{10} -2.03672 q^{11} -3.90217 q^{12} -5.53930 q^{13} -11.4095 q^{14} +3.31824 q^{15} +3.42261 q^{16} -0.426323 q^{17} -2.42944 q^{18} -1.00799 q^{19} -12.9483 q^{20} -4.69634 q^{21} +4.94810 q^{22} -0.244244 q^{23} +4.62122 q^{24} +6.01072 q^{25} +13.4574 q^{26} -1.00000 q^{27} +18.3260 q^{28} -0.0614980 q^{29} -8.06146 q^{30} +4.24075 q^{31} +0.927400 q^{32} +2.03672 q^{33} +1.03572 q^{34} -15.5836 q^{35} +3.90217 q^{36} +2.59338 q^{37} +2.44884 q^{38} +5.53930 q^{39} +15.3343 q^{40} -4.52212 q^{41} +11.4095 q^{42} -0.167165 q^{43} -7.94765 q^{44} -3.31824 q^{45} +0.593376 q^{46} -5.90160 q^{47} -3.42261 q^{48} +15.0557 q^{49} -14.6027 q^{50} +0.426323 q^{51} -21.6153 q^{52} -1.70831 q^{53} +2.42944 q^{54} +6.75834 q^{55} -21.7028 q^{56} +1.00799 q^{57} +0.149406 q^{58} +12.8121 q^{59} +12.9483 q^{60} -7.27605 q^{61} -10.3026 q^{62} +4.69634 q^{63} -9.09829 q^{64} +18.3807 q^{65} -4.94810 q^{66} +9.21360 q^{67} -1.66359 q^{68} +0.244244 q^{69} +37.8594 q^{70} +2.50866 q^{71} -4.62122 q^{72} +11.3322 q^{73} -6.30046 q^{74} -6.01072 q^{75} -3.93334 q^{76} -9.56515 q^{77} -13.4574 q^{78} +1.90861 q^{79} -11.3571 q^{80} +1.00000 q^{81} +10.9862 q^{82} +3.93115 q^{83} -18.3260 q^{84} +1.41464 q^{85} +0.406117 q^{86} +0.0614980 q^{87} +9.41214 q^{88} +3.64161 q^{89} +8.06146 q^{90} -26.0145 q^{91} -0.953083 q^{92} -4.24075 q^{93} +14.3376 q^{94} +3.34474 q^{95} -0.927400 q^{96} -6.42908 q^{97} -36.5768 q^{98} -2.03672 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9}+O(q^{10}) \) 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9	\( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9} + 3 q^{10} - 57 q^{11} - 116 q^{12} + 6 q^{13} - 9 q^{14} + 20 q^{15} + 112 q^{16} - 30 q^{17} - 16 q^{18} + 3 q^{19} - 54 q^{20} + 33 q^{21} - 22 q^{22} - 58 q^{23} + 45 q^{24} + 126 q^{25} - 21 q^{26} - 116 q^{27} - 77 q^{28} - 38 q^{29} - 3 q^{30} + 17 q^{31} - 106 q^{32} + 57 q^{33} + 35 q^{34} - 72 q^{35} + 116 q^{36} - 41 q^{37} - 45 q^{38} - 6 q^{39} + 5 q^{40} - 39 q^{41} + 9 q^{42} - 118 q^{43} - 103 q^{44} - 20 q^{45} - 8 q^{46} - 65 q^{47} - 112 q^{48} + 165 q^{49} - 72 q^{50} + 30 q^{51} - 10 q^{52} - 58 q^{53} + 16 q^{54} + 14 q^{55} - 23 q^{56} - 3 q^{57} - 27 q^{58} - 75 q^{59} + 54 q^{60} + 45 q^{61} - 73 q^{62} - 33 q^{63} + 111 q^{64} - 86 q^{65} + 22 q^{66} - 127 q^{67} - 94 q^{68} + 58 q^{69} - 7 q^{70} - 61 q^{71} - 45 q^{72} + 15 q^{73} - 51 q^{74} - 126 q^{75} + 96 q^{76} - 57 q^{77} + 21 q^{78} + 7 q^{79} - 144 q^{80} + 116 q^{81} - 37 q^{82} - 194 q^{83} + 77 q^{84} + 3 q^{85} - 57 q^{86} + 38 q^{87} - 42 q^{88} - 56 q^{89} + 3 q^{90} - 39 q^{91} - 138 q^{92} - 17 q^{93} + 51 q^{94} - 127 q^{95} + 106 q^{96} + 57 q^{97} - 105 q^{98} - 57 q^{99}+O(q^{100}) \) 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9 + 3 * q^10 - 57 * q^11 - 116 * q^12 + 6 * q^13 - 9 * q^14 + 20 * q^15 + 112 * q^16 - 30 * q^17 - 16 * q^18 + 3 * q^19 - 54 * q^20 + 33 * q^21 - 22 * q^22 - 58 * q^23 + 45 * q^24 + 126 * q^25 - 21 * q^26 - 116 * q^27 - 77 * q^28 - 38 * q^29 - 3 * q^30 + 17 * q^31 - 106 * q^32 + 57 * q^33 + 35 * q^34 - 72 * q^35 + 116 * q^36 - 41 * q^37 - 45 * q^38 - 6 * q^39 + 5 * q^40 - 39 * q^41 + 9 * q^42 - 118 * q^43 - 103 * q^44 - 20 * q^45 - 8 * q^46 - 65 * q^47 - 112 * q^48 + 165 * q^49 - 72 * q^50 + 30 * q^51 - 10 * q^52 - 58 * q^53 + 16 * q^54 + 14 * q^55 - 23 * q^56 - 3 * q^57 - 27 * q^58 - 75 * q^59 + 54 * q^60 + 45 * q^61 - 73 * q^62 - 33 * q^63 + 111 * q^64 - 86 * q^65 + 22 * q^66 - 127 * q^67 - 94 * q^68 + 58 * q^69 - 7 * q^70 - 61 * q^71 - 45 * q^72 + 15 * q^73 - 51 * q^74 - 126 * q^75 + 96 * q^76 - 57 * q^77 + 21 * q^78 + 7 * q^79 - 144 * q^80 + 116 * q^81 - 37 * q^82 - 194 * q^83 + 77 * q^84 + 3 * q^85 - 57 * q^86 + 38 * q^87 - 42 * q^88 - 56 * q^89 + 3 * q^90 - 39 * q^91 - 138 * q^92 - 17 * q^93 + 51 * q^94 - 127 * q^95 + 106 * q^96 + 57 * q^97 - 105 * q^98 - 57 * q^99

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