LMFDB - Embedded newform 4011.2.a.l.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.03548 q^{2} -1.00000 q^{3} -0.927780 q^{4} -1.23903 q^{5} -1.03548 q^{6} +1.00000 q^{7} -3.03166 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.03548 q^{2} -1.00000 q^{3} -0.927780 q^{4} -1.23903 q^{5} -1.03548 q^{6} +1.00000 q^{7} -3.03166 q^{8} +1.00000 q^{9} -1.28299 q^{10} +3.83036 q^{11} +0.927780 q^{12} -5.12270 q^{13} +1.03548 q^{14} +1.23903 q^{15} -1.28367 q^{16} +8.19673 q^{17} +1.03548 q^{18} -5.60125 q^{19} +1.14955 q^{20} -1.00000 q^{21} +3.96627 q^{22} -6.61860 q^{23} +3.03166 q^{24} -3.46481 q^{25} -5.30446 q^{26} -1.00000 q^{27} -0.927780 q^{28} +2.48459 q^{29} +1.28299 q^{30} -2.69886 q^{31} +4.73411 q^{32} -3.83036 q^{33} +8.48756 q^{34} -1.23903 q^{35} -0.927780 q^{36} -4.88041 q^{37} -5.79999 q^{38} +5.12270 q^{39} +3.75631 q^{40} +4.66419 q^{41} -1.03548 q^{42} +0.832065 q^{43} -3.55373 q^{44} -1.23903 q^{45} -6.85343 q^{46} +11.2552 q^{47} +1.28367 q^{48} +1.00000 q^{49} -3.58774 q^{50} -8.19673 q^{51} +4.75274 q^{52} +8.81550 q^{53} -1.03548 q^{54} -4.74593 q^{55} -3.03166 q^{56} +5.60125 q^{57} +2.57274 q^{58} +3.93054 q^{59} -1.14955 q^{60} +10.4880 q^{61} -2.79462 q^{62} +1.00000 q^{63} +7.46941 q^{64} +6.34717 q^{65} -3.96627 q^{66} -14.2487 q^{67} -7.60476 q^{68} +6.61860 q^{69} -1.28299 q^{70} -5.94230 q^{71} -3.03166 q^{72} -7.41430 q^{73} -5.05357 q^{74} +3.46481 q^{75} +5.19673 q^{76} +3.83036 q^{77} +5.30446 q^{78} -11.7057 q^{79} +1.59050 q^{80} +1.00000 q^{81} +4.82968 q^{82} +3.95863 q^{83} +0.927780 q^{84} -10.1560 q^{85} +0.861588 q^{86} -2.48459 q^{87} -11.6124 q^{88} -11.8742 q^{89} -1.28299 q^{90} -5.12270 q^{91} +6.14060 q^{92} +2.69886 q^{93} +11.6545 q^{94} +6.94011 q^{95} -4.73411 q^{96} +13.7072 q^{97} +1.03548 q^{98} +3.83036 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) $ 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9 + 4 * q^10 - 8 * q^11 - 34 * q^12 + 26 * q^13 - 6 * q^14 - 8 * q^15 + 62 * q^16 + 9 * q^17 - 6 * q^18 + 25 * q^19 + 20 * q^20 - 28 * q^21 + 3 * q^22 - 30 * q^23 + 15 * q^24 + 42 * q^25 + 25 * q^26 - 28 * q^27 + 34 * q^28 - 5 * q^29 - 4 * q^30 + 18 * q^31 - 26 * q^32 + 8 * q^33 + 30 * q^34 + 8 * q^35 + 34 * q^36 + 36 * q^37 - 2 * q^38 - 26 * q^39 + 28 * q^40 + 21 * q^41 + 6 * q^42 + 8 * q^43 - 20 * q^44 + 8 * q^45 + 24 * q^46 + 6 * q^47 - 62 * q^48 + 28 * q^49 - 48 * q^50 - 9 * q^51 + 54 * q^52 - 12 * q^53 + 6 * q^54 + 15 * q^55 - 15 * q^56 - 25 * q^57 + 19 * q^58 + 33 * q^59 - 20 * q^60 + 48 * q^61 + 28 * q^63 + 75 * q^64 + 21 * q^65 - 3 * q^66 + 27 * q^67 + 19 * q^68 + 30 * q^69 + 4 * q^70 - 45 * q^71 - 15 * q^72 + 61 * q^73 - 31 * q^74 - 42 * q^75 + 63 * q^76 - 8 * q^77 - 25 * q^78 + 35 * q^79 + 84 * q^80 + 28 * q^81 + 11 * q^82 + 43 * q^83 - 34 * q^84 + 43 * q^85 - q^86 + 5 * q^87 - 27 * q^88 + 25 * q^89 + 4 * q^90 + 26 * q^91 - 102 * q^92 - 18 * q^93 + 55 * q^94 - 43 * q^95 + 26 * q^96 + 40 * q^97 - 6 * q^98 - 8 * 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 $

$2$	1.03548	0.732195	0.366098	−	0.930576i	$-0.380694\pi$
$2$	1.03548	0.732195	0.366098	+	0.930576i	$0.380694\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.927780	−0.463890
$5$	−1.23903	−0.554110	−0.277055	−	0.960854i	$-0.589358\pi$
$5$	−1.23903	−0.554110	−0.277055	+	0.960854i	$0.589358\pi$
$6$	−1.03548	−0.422733
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.03166	−1.07185
$9$	1.00000	0.333333
$10$	−1.28299	−0.405717
$11$	3.83036	1.15490	0.577449	−	0.816427i	$-0.304048\pi$
$11$	3.83036	1.15490	0.577449	+	0.816427i	$0.304048\pi$
$12$	0.927780	0.267827
$13$	−5.12270	−1.42078	−0.710391	−	0.703807i	$-0.751482\pi$
$13$	−5.12270	−1.42078	−0.710391	+	0.703807i	$0.751482\pi$
$14$	1.03548	0.276744
$15$	1.23903	0.319916
$16$	−1.28367	−0.320916
$17$	8.19673	1.98800	0.994000	−	0.109383i	$-0.0348874\pi$
$17$	8.19673	1.98800	0.994000	+	0.109383i	$0.0348874\pi$
$18$	1.03548	0.244065
$19$	−5.60125	−1.28502	−0.642508	−	0.766279i	$-0.722106\pi$
$19$	−5.60125	−1.28502	−0.642508	+	0.766279i	$0.722106\pi$
$20$	1.14955	0.257046
$21$	−1.00000	−0.218218
$22$	3.96627	0.845611
$23$	−6.61860	−1.38007	−0.690036	−	0.723775i	$-0.742405\pi$
$23$	−6.61860	−1.38007	−0.690036	+	0.723775i	$0.742405\pi$
$24$	3.03166	0.618835
$25$	−3.46481	−0.692962
$26$	−5.30446	−1.04029
$27$	−1.00000	−0.192450
$28$	−0.927780	−0.175334
$29$	2.48459	0.461377	0.230688	−	0.973028i	$-0.425902\pi$
$29$	2.48459	0.461377	0.230688	+	0.973028i	$0.425902\pi$
$30$	1.28299	0.234241
$31$	−2.69886	−0.484730	−0.242365	−	0.970185i	$-0.577923\pi$
$31$	−2.69886	−0.484730	−0.242365	+	0.970185i	$0.577923\pi$
$32$	4.73411	0.836880
$33$	−3.83036	−0.666780
$34$	8.48756	1.45560
$35$	−1.23903	−0.209434
$36$	−0.927780	−0.154630
$37$	−4.88041	−0.802334	−0.401167	−	0.916005i	$-0.631395\pi$
$37$	−4.88041	−0.802334	−0.401167	+	0.916005i	$0.631395\pi$
$38$	−5.79999	−0.940882
$39$	5.12270	0.820289
$40$	3.75631	0.593925
$41$	4.66419	0.728425	0.364212	−	0.931316i	$-0.381338\pi$
$41$	4.66419	0.728425	0.364212	+	0.931316i	$0.381338\pi$
$42$	−1.03548	−0.159778
$43$	0.832065	0.126889	0.0634444	−	0.997985i	$-0.479791\pi$
$43$	0.832065	0.126889	0.0634444	+	0.997985i	$0.479791\pi$
$44$	−3.55373	−0.535745
$45$	−1.23903	−0.184703
$46$	−6.85343	−1.01048
$47$	11.2552	1.64174	0.820868	−	0.571118i	$-0.193490\pi$
$47$	11.2552	1.64174	0.820868	+	0.571118i	$0.193490\pi$
$48$	1.28367	0.185281
$49$	1.00000	0.142857
$50$	−3.58774	−0.507383
$51$	−8.19673	−1.14777
$52$	4.75274	0.659086
$53$	8.81550	1.21090	0.605451	−	0.795882i	$-0.292993\pi$
$53$	8.81550	1.21090	0.605451	+	0.795882i	$0.292993\pi$
$54$	−1.03548	−0.140911
$55$	−4.74593	−0.639941
$56$	−3.03166	−0.405123
$57$	5.60125	0.741904
$58$	2.57274	0.337818
$59$	3.93054	0.511712	0.255856	−	0.966715i	$-0.417643\pi$
$59$	3.93054	0.511712	0.255856	+	0.966715i	$0.417643\pi$
$60$	−1.14955	−0.148406
$61$	10.4880	1.34285	0.671427	−	0.741071i	$-0.265682\pi$
$61$	10.4880	1.34285	0.671427	+	0.741071i	$0.265682\pi$
$62$	−2.79462	−0.354917
$63$	1.00000	0.125988
$64$	7.46941	0.933676
$65$	6.34717	0.787270
$66$	−3.96627	−0.488214
$67$	−14.2487	−1.74076	−0.870380	−	0.492381i	$-0.836127\pi$
$67$	−14.2487	−1.74076	−0.870380	+	0.492381i	$0.836127\pi$
$68$	−7.60476	−0.922213
$69$	6.61860	0.796785
$70$	−1.28299	−0.153347
$71$	−5.94230	−0.705222	−0.352611	−	0.935770i	$-0.614706\pi$
$71$	−5.94230	−0.705222	−0.352611	+	0.935770i	$0.614706\pi$
$72$	−3.03166	−0.357284
$73$	−7.41430	−0.867778	−0.433889	−	0.900966i	$-0.642859\pi$
$73$	−7.41430	−0.867778	−0.433889	+	0.900966i	$0.642859\pi$
$74$	−5.05357	−0.587466
$75$	3.46481	0.400082
$76$	5.19673	0.596105
$77$	3.83036	0.436510
$78$	5.30446	0.600612
$79$	−11.7057	−1.31699	−0.658494	−	0.752586i	$-0.728806\pi$
$79$	−11.7057	−1.31699	−0.658494	+	0.752586i	$0.728806\pi$
$80$	1.59050	0.177823
$81$	1.00000	0.111111
$82$	4.82968	0.533349
$83$	3.95863	0.434516	0.217258	−	0.976114i	$-0.430289\pi$
$83$	3.95863	0.434516	0.217258	+	0.976114i	$0.430289\pi$
$84$	0.927780	0.101229
$85$	−10.1560	−1.10157
$86$	0.861588	0.0929074
$87$	−2.48459	−0.266376
$88$	−11.6124	−1.23788
$89$	−11.8742	−1.25867	−0.629334	−	0.777135i	$-0.716672\pi$
$89$	−11.8742	−1.25867	−0.629334	+	0.777135i	$0.716672\pi$
$90$	−1.28299	−0.135239
$91$	−5.12270	−0.537005
$92$	6.14060	0.640202
$93$	2.69886	0.279859
$94$	11.6545	1.20207
$95$	6.94011	0.712040
$96$	−4.73411	−0.483173
$97$	13.7072	1.39176	0.695880	−	0.718159i	$-0.255015\pi$
$97$	13.7072	1.39176	0.695880	+	0.718159i	$0.255015\pi$
$98$	1.03548	0.104599
$99$	3.83036	0.384966
$100$	3.21458	0.321458
$101$	6.10771	0.607740	0.303870	−	0.952714i	$-0.401721\pi$
$101$	6.10771	0.607740	0.303870	+	0.952714i	$0.401721\pi$
$102$	−8.48756	−0.840393
$103$	16.6172	1.63734	0.818670	−	0.574264i	$-0.194712\pi$
$103$	16.6172	1.63734	0.818670	+	0.574264i	$0.194712\pi$
$104$	15.5303	1.52287
$105$	1.23903	0.120917
$106$	9.12828	0.886617
$107$	−8.58131	−0.829587	−0.414793	−	0.909916i	$-0.636146\pi$
$107$	−8.58131	−0.829587	−0.414793	+	0.909916i	$0.636146\pi$
$108$	0.927780	0.0892756
$109$	16.0391	1.53627	0.768136	−	0.640287i	$-0.221185\pi$
$109$	16.0391	1.53627	0.768136	+	0.640287i	$0.221185\pi$
$110$	−4.91432	−0.468562
$111$	4.88041	0.463228
$112$	−1.28367	−0.121295
$113$	−11.8028	−1.11031	−0.555155	−	0.831747i	$-0.687341\pi$
$113$	−11.8028	−1.11031	−0.555155	+	0.831747i	$0.687341\pi$
$114$	5.79999	0.543219
$115$	8.20063	0.764712
$116$	−2.30515	−0.214028
$117$	−5.12270	−0.473594
$118$	4.07000	0.374673
$119$	8.19673	0.751393
$120$	−3.75631	−0.342903
$121$	3.67167	0.333788
$122$	10.8601	0.983231
$123$	−4.66419	−0.420556
$124$	2.50395	0.224861
$125$	10.4881	0.938088
$126$	1.03548	0.0922480
$127$	14.4486	1.28211	0.641054	−	0.767495i	$-0.278497\pi$
$127$	14.4486	1.28211	0.641054	+	0.767495i	$0.278497\pi$
$128$	−1.73379	−0.153247
$129$	−0.832065	−0.0732593
$130$	6.57237	0.576435
$131$	18.5110	1.61732	0.808658	−	0.588279i	$-0.200194\pi$
$131$	18.5110	1.61732	0.808658	+	0.588279i	$0.200194\pi$
$132$	3.55373	0.309313
$133$	−5.60125	−0.485690
$134$	−14.7543	−1.27458
$135$	1.23903	0.106639
$136$	−24.8497	−2.13084
$137$	7.05472	0.602725	0.301363	−	0.953510i	$-0.402559\pi$
$137$	7.05472	0.602725	0.301363	+	0.953510i	$0.402559\pi$
$138$	6.85343	0.583403
$139$	6.10390	0.517726	0.258863	−	0.965914i	$-0.416652\pi$
$139$	6.10390	0.517726	0.258863	+	0.965914i	$0.416652\pi$
$140$	1.14955	0.0971543
$141$	−11.2552	−0.947857
$142$	−6.15314	−0.516360
$143$	−19.6218	−1.64086
$144$	−1.28367	−0.106972
$145$	−3.07848	−0.255654
$146$	−7.67736	−0.635383
$147$	−1.00000	−0.0824786
$148$	4.52795	0.372195
$149$	21.0560	1.72497	0.862486	−	0.506080i	$-0.168906\pi$
$149$	21.0560	1.72497	0.862486	+	0.506080i	$0.168906\pi$
$150$	3.58774	0.292938
$151$	16.0552	1.30656	0.653279	−	0.757118i	$-0.273393\pi$
$151$	16.0552	1.30656	0.653279	+	0.757118i	$0.273393\pi$
$152$	16.9811	1.37735
$153$	8.19673	0.662666
$154$	3.96627	0.319611
$155$	3.34397	0.268594
$156$	−4.75274	−0.380524
$157$	20.4675	1.63348	0.816741	−	0.577005i	$-0.195779\pi$
$157$	20.4675	1.63348	0.816741	+	0.577005i	$0.195779\pi$
$158$	−12.1210	−0.964293
$159$	−8.81550	−0.699115
$160$	−5.86569	−0.463724
$161$	−6.61860	−0.521618
$162$	1.03548	0.0813551
$163$	21.7920	1.70688	0.853442	−	0.521188i	$-0.174511\pi$
$163$	21.7920	1.70688	0.853442	+	0.521188i	$0.174511\pi$
$164$	−4.32734	−0.337909
$165$	4.74593	0.369470
$166$	4.09909	0.318151
$167$	8.03636	0.621872	0.310936	−	0.950431i	$-0.399357\pi$
$167$	8.03636	0.621872	0.310936	+	0.950431i	$0.399357\pi$
$168$	3.03166	0.233898
$169$	13.2421	1.01862
$170$	−10.5163	−0.806565
$171$	−5.60125	−0.428338
$172$	−0.771973	−0.0588624
$173$	−13.5462	−1.02990	−0.514951	−	0.857220i	$-0.672190\pi$
$173$	−13.5462	−1.02990	−0.514951	+	0.857220i	$0.672190\pi$
$174$	−2.57274	−0.195039
$175$	−3.46481	−0.261915
$176$	−4.91690	−0.370626
$177$	−3.93054	−0.295437
$178$	−12.2956	−0.921591
$179$	23.5248	1.75833	0.879164	−	0.476518i	$-0.158101\pi$
$179$	23.5248	1.75833	0.879164	+	0.476518i	$0.158101\pi$
$180$	1.14955	0.0856820
$181$	11.9287	0.886651	0.443325	−	0.896361i	$-0.353799\pi$
$181$	11.9287	0.886651	0.443325	+	0.896361i	$0.353799\pi$
$182$	−5.30446	−0.393193
$183$	−10.4880	−0.775297
$184$	20.0653	1.47924
$185$	6.04697	0.444582
$186$	2.79462	0.204911
$187$	31.3964	2.29594
$188$	−10.4423	−0.761585
$189$	−1.00000	−0.0727393
$190$	7.18635	0.521353
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	−7.46941	−0.539058
$193$	16.9232	1.21816	0.609079	−	0.793109i	$-0.291539\pi$
$193$	16.9232	1.21816	0.609079	+	0.793109i	$0.291539\pi$
$194$	14.1936	1.01904
$195$	−6.34717	−0.454530
$196$	−0.927780	−0.0662700
$197$	−7.23547	−0.515506	−0.257753	−	0.966211i	$-0.582982\pi$
$197$	−7.23547	−0.515506	−0.257753	+	0.966211i	$0.582982\pi$
$198$	3.96627	0.281870
$199$	−15.4495	−1.09519	−0.547593	−	0.836745i	$-0.684456\pi$
$199$	−15.4495	−1.09519	−0.547593	+	0.836745i	$0.684456\pi$
$200$	10.5041	0.742753
$201$	14.2487	1.00503
$202$	6.32442	0.444984
$203$	2.48459	0.174384
$204$	7.60476	0.532440
$205$	−5.77907	−0.403628
$206$	17.2068	1.19885
$207$	−6.61860	−0.460024
$208$	6.57584	0.455952
$209$	−21.4548	−1.48406
$210$	1.28299	0.0885347
$211$	7.83218	0.539189	0.269595	−	0.962974i	$-0.413110\pi$
$211$	7.83218	0.539189	0.269595	+	0.962974i	$0.413110\pi$
$212$	−8.17884	−0.561725
$213$	5.94230	0.407160
$214$	−8.88578	−0.607420
$215$	−1.03095	−0.0703104
$216$	3.03166	0.206278
$217$	−2.69886	−0.183211
$218$	16.6082	1.12485
$219$	7.41430	0.501012
$220$	4.40317	0.296862
$221$	−41.9894	−2.82451
$222$	5.05357	0.339173
$223$	−0.887704	−0.0594450	−0.0297225	−	0.999558i	$-0.509462\pi$
$223$	−0.887704	−0.0594450	−0.0297225	+	0.999558i	$0.509462\pi$
$224$	4.73411	0.316311
$225$	−3.46481	−0.230987
$226$	−12.2215	−0.812965
$227$	19.0891	1.26699	0.633493	−	0.773748i	$-0.281621\pi$
$227$	19.0891	1.26699	0.633493	+	0.773748i	$0.281621\pi$
$228$	−5.19673	−0.344162
$229$	7.15988	0.473138	0.236569	−	0.971615i	$-0.423977\pi$
$229$	7.15988	0.473138	0.236569	+	0.971615i	$0.423977\pi$
$230$	8.49159	0.559919
$231$	−3.83036	−0.252019
$232$	−7.53243	−0.494528
$233$	−12.1478	−0.795827	−0.397913	−	0.917423i	$-0.630266\pi$
$233$	−12.1478	−0.795827	−0.397913	+	0.917423i	$0.630266\pi$
$234$	−5.30446	−0.346763
$235$	−13.9455	−0.909703
$236$	−3.64667	−0.237378
$237$	11.7057	0.760364
$238$	8.48756	0.550167
$239$	−25.7944	−1.66850	−0.834252	−	0.551383i	$-0.814100\pi$
$239$	−25.7944	−1.66850	−0.834252	+	0.551383i	$0.814100\pi$
$240$	−1.59050	−0.102666
$241$	−20.8634	−1.34393	−0.671966	−	0.740582i	$-0.734550\pi$
$241$	−20.8634	−1.34393	−0.671966	+	0.740582i	$0.734550\pi$
$242$	3.80194	0.244398
$243$	−1.00000	−0.0641500
$244$	−9.73057	−0.622936
$245$	−1.23903	−0.0791586
$246$	−4.82968	−0.307929
$247$	28.6935	1.82573
$248$	8.18203	0.519559
$249$	−3.95863	−0.250868
$250$	10.8603	0.686863
$251$	1.81295	0.114432	0.0572162	−	0.998362i	$-0.481778\pi$
$251$	1.81295	0.114432	0.0572162	+	0.998362i	$0.481778\pi$
$252$	−0.927780	−0.0584446
$253$	−25.3516	−1.59384
$254$	14.9613	0.938754
$255$	10.1560	0.635992
$256$	−16.7341	−1.04588
$257$	8.52307	0.531654	0.265827	−	0.964021i	$-0.414355\pi$
$257$	8.52307	0.531654	0.265827	+	0.964021i	$0.414355\pi$
$258$	−0.861588	−0.0536401
$259$	−4.88041	−0.303254
$260$	−5.88878	−0.365206
$261$	2.48459	0.153792
$262$	19.1678	1.18419
$263$	−4.24451	−0.261728	−0.130864	−	0.991400i	$-0.541775\pi$
$263$	−4.24451	−0.261728	−0.130864	+	0.991400i	$0.541775\pi$
$264$	11.6124	0.714691
$265$	−10.9227	−0.670973
$266$	−5.79999	−0.355620
$267$	11.8742	0.726692
$268$	13.2197	0.807521
$269$	8.97669	0.547318	0.273659	−	0.961827i	$-0.411766\pi$
$269$	8.97669	0.547318	0.273659	+	0.961827i	$0.411766\pi$
$270$	1.28299	0.0780803
$271$	−18.0420	−1.09597	−0.547986	−	0.836488i	$-0.684605\pi$
$271$	−18.0420	−1.09597	−0.547986	+	0.836488i	$0.684605\pi$
$272$	−10.5219	−0.637982
$273$	5.12270	0.310040
$274$	7.30503	0.441313
$275$	−13.2715	−0.800300
$276$	−6.14060	−0.369621
$277$	−27.1151	−1.62919	−0.814594	−	0.580032i	$-0.803040\pi$
$277$	−27.1151	−1.62919	−0.814594	+	0.580032i	$0.803040\pi$
$278$	6.32047	0.379077
$279$	−2.69886	−0.161577
$280$	3.75631	0.224483
$281$	−9.15118	−0.545914	−0.272957	−	0.962026i	$-0.588002\pi$
$281$	−9.15118	−0.545914	−0.272957	+	0.962026i	$0.588002\pi$
$282$	−11.6545	−0.694017
$283$	5.37462	0.319488	0.159744	−	0.987158i	$-0.448933\pi$
$283$	5.37462	0.319488	0.159744	+	0.987158i	$0.448933\pi$
$284$	5.51315	0.327145
$285$	−6.94011	−0.411097
$286$	−20.3180	−1.20143
$287$	4.66419	0.275319
$288$	4.73411	0.278960
$289$	50.1864	2.95214
$290$	−3.18770	−0.187188
$291$	−13.7072	−0.803532
$292$	6.87883	0.402553
$293$	−0.496635	−0.0290137	−0.0145069	−	0.999895i	$-0.504618\pi$
$293$	−0.496635	−0.0290137	−0.0145069	+	0.999895i	$0.504618\pi$
$294$	−1.03548	−0.0603905
$295$	−4.87005	−0.283545
$296$	14.7957	0.859985
$297$	−3.83036	−0.222260
$298$	21.8031	1.26302
$299$	33.9051	1.96078
$300$	−3.21458	−0.185594
$301$	0.832065	0.0479595
$302$	16.6249	0.956655
$303$	−6.10771	−0.350879
$304$	7.19013	0.412382
$305$	−12.9950	−0.744089
$306$	8.48756	0.485201
$307$	−20.3271	−1.16013	−0.580065	−	0.814570i	$-0.696973\pi$
$307$	−20.3271	−1.16013	−0.580065	+	0.814570i	$0.696973\pi$
$308$	−3.55373	−0.202493
$309$	−16.6172	−0.945319
$310$	3.46261	0.196663
$311$	−15.9129	−0.902339	−0.451169	−	0.892438i	$-0.648993\pi$
$311$	−15.9129	−0.902339	−0.451169	+	0.892438i	$0.648993\pi$
$312$	−15.5303	−0.879229
$313$	−6.32660	−0.357601	−0.178800	−	0.983885i	$-0.557222\pi$
$313$	−6.32660	−0.357601	−0.178800	+	0.983885i	$0.557222\pi$
$314$	21.1937	1.19603
$315$	−1.23903	−0.0698113
$316$	10.8603	0.610938
$317$	12.6494	0.710463	0.355232	−	0.934778i	$-0.384402\pi$
$317$	12.6494	0.710463	0.355232	+	0.934778i	$0.384402\pi$
$318$	−9.12828	−0.511889
$319$	9.51688	0.532843
$320$	−9.25481	−0.517360
$321$	8.58131	0.478962
$322$	−6.85343	−0.381927
$323$	−45.9120	−2.55461
$324$	−0.927780	−0.0515433
$325$	17.7492	0.984547
$326$	22.5652	1.24977
$327$	−16.0391	−0.886966
$328$	−14.1402	−0.780764
$329$	11.2552	0.620518
$330$	4.91432	0.270524
$331$	−8.80956	−0.484217	−0.242109	−	0.970249i	$-0.577839\pi$
$331$	−8.80956	−0.484217	−0.242109	+	0.970249i	$0.577839\pi$
$332$	−3.67274	−0.201568
$333$	−4.88041	−0.267445
$334$	8.32150	0.455332
$335$	17.6546	0.964573
$336$	1.28367	0.0700297
$337$	−13.9721	−0.761107	−0.380554	−	0.924759i	$-0.624267\pi$
$337$	−13.9721	−0.761107	−0.380554	+	0.924759i	$0.624267\pi$
$338$	13.7119	0.745829
$339$	11.8028	0.641038
$340$	9.42251	0.511008
$341$	−10.3376	−0.559813
$342$	−5.79999	−0.313627
$343$	1.00000	0.0539949
$344$	−2.52254	−0.136006
$345$	−8.20063	−0.441507
$346$	−14.0269	−0.754089
$347$	−10.6632	−0.572428	−0.286214	−	0.958166i	$-0.592397\pi$
$347$	−10.6632	−0.572428	−0.286214	+	0.958166i	$0.592397\pi$
$348$	2.30515	0.123569
$349$	15.5601	0.832915	0.416458	−	0.909155i	$-0.363271\pi$
$349$	15.5601	0.832915	0.416458	+	0.909155i	$0.363271\pi$
$350$	−3.58774	−0.191773
$351$	5.12270	0.273430
$352$	18.1333	0.966510
$353$	−8.40425	−0.447313	−0.223657	−	0.974668i	$-0.571799\pi$
$353$	−8.40425	−0.447313	−0.223657	+	0.974668i	$0.571799\pi$
$354$	−4.07000	−0.216318
$355$	7.36268	0.390771
$356$	11.0167	0.583883
$357$	−8.19673	−0.433817
$358$	24.3595	1.28744
$359$	−0.934350	−0.0493131	−0.0246566	−	0.999696i	$-0.507849\pi$
$359$	−0.934350	−0.0493131	−0.0246566	+	0.999696i	$0.507849\pi$
$360$	3.75631	0.197975
$361$	12.3740	0.651264
$362$	12.3519	0.649202
$363$	−3.67167	−0.192713
$364$	4.75274	0.249111
$365$	9.18652	0.480845
$366$	−10.8601	−0.567669
$367$	32.1892	1.68026	0.840130	−	0.542385i	$-0.182478\pi$
$367$	32.1892	1.68026	0.840130	+	0.542385i	$0.182478\pi$
$368$	8.49606	0.442888
$369$	4.66419	0.242808
$370$	6.26152	0.325521
$371$	8.81550	0.457678
$372$	−2.50395	−0.129824
$373$	−12.6410	−0.654526	−0.327263	−	0.944933i	$-0.606126\pi$
$373$	−12.6410	−0.654526	−0.327263	+	0.944933i	$0.606126\pi$
$374$	32.5104	1.68107
$375$	−10.4881	−0.541605
$376$	−34.1219	−1.75970
$377$	−12.7278	−0.655515
$378$	−1.03548	−0.0532594
$379$	−31.1978	−1.60252	−0.801262	−	0.598314i	$-0.795837\pi$
$379$	−31.1978	−1.60252	−0.801262	+	0.598314i	$0.795837\pi$
$380$	−6.43889	−0.330308
$381$	−14.4486	−0.740226
$382$	−1.03548	−0.0529798
$383$	15.3609	0.784905	0.392453	−	0.919772i	$-0.371627\pi$
$383$	15.3609	0.784905	0.392453	+	0.919772i	$0.371627\pi$
$384$	1.73379	0.0884769
$385$	−4.74593	−0.241875
$386$	17.5236	0.891930
$387$	0.832065	0.0422963
$388$	−12.7173	−0.645623
$389$	25.6288	1.29943	0.649716	−	0.760177i	$-0.274888\pi$
$389$	25.6288	1.29943	0.649716	+	0.760177i	$0.274888\pi$
$390$	−6.57237	−0.332805
$391$	−54.2509	−2.74358
$392$	−3.03166	−0.153122
$393$	−18.5110	−0.933758
$394$	−7.49219	−0.377451
$395$	14.5036	0.729757
$396$	−3.55373	−0.178582
$397$	−18.3487	−0.920896	−0.460448	−	0.887687i	$-0.652311\pi$
$397$	−18.3487	−0.920896	−0.460448	+	0.887687i	$0.652311\pi$
$398$	−15.9977	−0.801890
$399$	5.60125	0.280413
$400$	4.44766	0.222383
$401$	−5.97823	−0.298539	−0.149269	−	0.988797i	$-0.547692\pi$
$401$	−5.97823	−0.298539	−0.149269	+	0.988797i	$0.547692\pi$
$402$	14.7543	0.735877
$403$	13.8255	0.688695
$404$	−5.66661	−0.281924
$405$	−1.23903	−0.0615678
$406$	2.57274	0.127683
$407$	−18.6937	−0.926614
$408$	24.8497	1.23024
$409$	−3.60182	−0.178099	−0.0890494	−	0.996027i	$-0.528383\pi$
$409$	−3.60182	−0.178099	−0.0890494	+	0.996027i	$0.528383\pi$
$410$	−5.98411	−0.295534
$411$	−7.05472	−0.347984
$412$	−15.4171	−0.759545
$413$	3.93054	0.193409
$414$	−6.85343	−0.336828
$415$	−4.90486	−0.240770
$416$	−24.2514	−1.18902
$417$	−6.10390	−0.298909
$418$	−22.2160	−1.08662
$419$	15.2335	0.744203	0.372102	−	0.928192i	$-0.378637\pi$
$419$	15.2335	0.744203	0.372102	+	0.928192i	$0.378637\pi$
$420$	−1.14955	−0.0560921
$421$	26.7843	1.30539	0.652693	−	0.757623i	$-0.273639\pi$
$421$	26.7843	1.30539	0.652693	+	0.757623i	$0.273639\pi$
$422$	8.11007	0.394792
$423$	11.2552	0.547245
$424$	−26.7256	−1.29791
$425$	−28.4001	−1.37761
$426$	6.15314	0.298121
$427$	10.4880	0.507551
$428$	7.96157	0.384837
$429$	19.6218	0.947349
$430$	−1.06753	−0.0514809
$431$	33.5761	1.61731	0.808653	−	0.588286i	$-0.200197\pi$
$431$	33.5761	1.61731	0.808653	+	0.588286i	$0.200197\pi$
$432$	1.28367	0.0617604
$433$	−35.8077	−1.72081	−0.860405	−	0.509611i	$-0.829789\pi$
$433$	−35.8077	−1.72081	−0.860405	+	0.509611i	$0.829789\pi$
$434$	−2.79462	−0.134146
$435$	3.07848	0.147602
$436$	−14.8808	−0.712660
$437$	37.0724	1.77341
$438$	7.67736	0.366838
$439$	−2.42248	−0.115619	−0.0578093	−	0.998328i	$-0.518412\pi$
$439$	−2.42248	−0.115619	−0.0578093	+	0.998328i	$0.518412\pi$
$440$	14.3880	0.685923
$441$	1.00000	0.0476190
$442$	−43.4792	−2.06810
$443$	1.00578	0.0477863	0.0238931	−	0.999715i	$-0.492394\pi$
$443$	1.00578	0.0477863	0.0238931	+	0.999715i	$0.492394\pi$
$444$	−4.52795	−0.214887
$445$	14.7125	0.697441
$446$	−0.919200	−0.0435254
$447$	−21.0560	−0.995914
$448$	7.46941	0.352896
$449$	−33.4083	−1.57664	−0.788318	−	0.615268i	$-0.789048\pi$
$449$	−33.4083	−1.57664	−0.788318	+	0.615268i	$0.789048\pi$
$450$	−3.58774	−0.169128
$451$	17.8655	0.841256
$452$	10.9504	0.515062
$453$	−16.0552	−0.754341
$454$	19.7664	0.927681
$455$	6.34717	0.297560
$456$	−16.9811	−0.795212
$457$	−11.3183	−0.529448	−0.264724	−	0.964324i	$-0.585281\pi$
$457$	−11.3183	−0.529448	−0.264724	+	0.964324i	$0.585281\pi$
$458$	7.41391	0.346429
$459$	−8.19673	−0.382591
$460$	−7.60837	−0.354742
$461$	24.0057	1.11806	0.559028	−	0.829149i	$-0.311174\pi$
$461$	24.0057	1.11806	0.559028	+	0.829149i	$0.311174\pi$
$462$	−3.96627	−0.184527
$463$	−24.4560	−1.13657	−0.568284	−	0.822832i	$-0.692393\pi$
$463$	−24.4560	−1.13657	−0.568284	+	0.822832i	$0.692393\pi$
$464$	−3.18938	−0.148063
$465$	−3.34397	−0.155073
$466$	−12.5788	−0.582701
$467$	36.4231	1.68546	0.842730	−	0.538337i	$-0.180947\pi$
$467$	36.4231	1.68546	0.842730	+	0.538337i	$0.180947\pi$
$468$	4.75274	0.219695
$469$	−14.2487	−0.657945
$470$	−14.4403	−0.666080
$471$	−20.4675	−0.943091
$472$	−11.9161	−0.548481
$473$	3.18711	0.146544
$474$	12.1210	0.556735
$475$	19.4073	0.890466
$476$	−7.60476	−0.348564
$477$	8.81550	0.403634
$478$	−26.7097	−1.22167
$479$	−2.84767	−0.130113	−0.0650566	−	0.997882i	$-0.520723\pi$
$479$	−2.84767	−0.130113	−0.0650566	+	0.997882i	$0.520723\pi$
$480$	5.86569	0.267731
$481$	25.0009	1.13994
$482$	−21.6037	−0.984021
$483$	6.61860	0.301157
$484$	−3.40650	−0.154841
$485$	−16.9837	−0.771188
$486$	−1.03548	−0.0469704
$487$	−23.1098	−1.04721	−0.523603	−	0.851962i	$-0.675413\pi$
$487$	−23.1098	−1.04721	−0.523603	+	0.851962i	$0.675413\pi$
$488$	−31.7961	−1.43934
$489$	−21.7920	−0.985470
$490$	−1.28299	−0.0579596
$491$	−25.6490	−1.15752	−0.578761	−	0.815497i	$-0.696464\pi$
$491$	−25.6490	−1.15752	−0.578761	+	0.815497i	$0.696464\pi$
$492$	4.32734	0.195092
$493$	20.3655	0.917217
$494$	29.7116	1.33679
$495$	−4.74593	−0.213314
$496$	3.46444	0.155558
$497$	−5.94230	−0.266549
$498$	−4.09909	−0.183685
$499$	−7.56274	−0.338555	−0.169277	−	0.985568i	$-0.554143\pi$
$499$	−7.56274	−0.338555	−0.169277	+	0.985568i	$0.554143\pi$
$500$	−9.73068	−0.435169
$501$	−8.03636	−0.359038
$502$	1.87727	0.0837868
$503$	9.87745	0.440414	0.220207	−	0.975453i	$-0.429327\pi$
$503$	9.87745	0.440414	0.220207	+	0.975453i	$0.429327\pi$
$504$	−3.03166	−0.135041
$505$	−7.56762	−0.336755
$506$	−26.2511	−1.16700
$507$	−13.2421	−0.588101
$508$	−13.4051	−0.594757
$509$	33.4259	1.48158	0.740789	−	0.671738i	$-0.234452\pi$
$509$	33.4259	1.48158	0.740789	+	0.671738i	$0.234452\pi$
$510$	10.5163	0.465671
$511$	−7.41430	−0.327989
$512$	−13.8603	−0.612544
$513$	5.60125	0.247301
$514$	8.82547	0.389275
$515$	−20.5892	−0.907267
$516$	0.771973	0.0339842
$517$	43.1114	1.89604
$518$	−5.05357	−0.222041
$519$	13.5462	0.594614
$520$	−19.2425	−0.843838
$521$	0.866290	0.0379529	0.0189764	−	0.999820i	$-0.493959\pi$
$521$	0.866290	0.0379529	0.0189764	+	0.999820i	$0.493959\pi$
$522$	2.57274	0.112606
$523$	−2.25721	−0.0987010	−0.0493505	−	0.998782i	$-0.515715\pi$
$523$	−2.25721	−0.0987010	−0.0493505	+	0.998782i	$0.515715\pi$
$524$	−17.1742	−0.750256
$525$	3.46481	0.151217
$526$	−4.39511	−0.191636
$527$	−22.1218	−0.963642
$528$	4.91690	0.213981
$529$	20.8058	0.904600
$530$	−11.3102	−0.491284
$531$	3.93054	0.170571
$532$	5.19673	0.225307
$533$	−23.8933	−1.03493
$534$	12.2956	0.532081
$535$	10.6325	0.459682
$536$	43.1973	1.86584
$537$	−23.5248	−1.01517
$538$	9.29518	0.400744
$539$	3.83036	0.164985
$540$	−1.14955	−0.0494686
$541$	26.7012	1.14797	0.573986	−	0.818865i	$-0.305396\pi$
$541$	26.7012	1.14797	0.573986	+	0.818865i	$0.305396\pi$
$542$	−18.6821	−0.802466
$543$	−11.9287	−0.511908
$544$	38.8042	1.66372
$545$	−19.8729	−0.851264
$546$	5.30446	0.227010
$547$	−14.9914	−0.640985	−0.320493	−	0.947251i	$-0.603848\pi$
$547$	−14.9914	−0.640985	−0.320493	+	0.947251i	$0.603848\pi$
$548$	−6.54522	−0.279598
$549$	10.4880	0.447618
$550$	−13.7424	−0.585976
$551$	−13.9168	−0.592876
$552$	−20.0653	−0.854037
$553$	−11.7057	−0.497775
$554$	−28.0772	−1.19288
$555$	−6.04697	−0.256679
$556$	−5.66307	−0.240168
$557$	35.3420	1.49749	0.748743	−	0.662860i	$-0.230658\pi$
$557$	35.3420	1.49749	0.748743	+	0.662860i	$0.230658\pi$
$558$	−2.79462	−0.118306
$559$	−4.26242	−0.180281
$560$	1.59050	0.0672108
$561$	−31.3964	−1.32556
$562$	−9.47587	−0.399716
$563$	−12.8090	−0.539836	−0.269918	−	0.962883i	$-0.586997\pi$
$563$	−12.8090	−0.539836	−0.269918	+	0.962883i	$0.586997\pi$
$564$	10.4423	0.439701
$565$	14.6240	0.615235
$566$	5.56531	0.233928
$567$	1.00000	0.0419961
$568$	18.0150	0.755894
$569$	−14.9950	−0.628624	−0.314312	−	0.949320i	$-0.601774\pi$
$569$	−14.9950	−0.628624	−0.314312	+	0.949320i	$0.601774\pi$
$570$	−7.18635	−0.301003
$571$	17.8079	0.745237	0.372618	−	0.927985i	$-0.378460\pi$
$571$	17.8079	0.745237	0.372618	+	0.927985i	$0.378460\pi$
$572$	18.2047	0.761177
$573$	1.00000	0.0417756
$574$	4.82968	0.201587
$575$	22.9322	0.956338
$576$	7.46941	0.311225
$577$	−17.7604	−0.739376	−0.369688	−	0.929156i	$-0.620535\pi$
$577$	−17.7604	−0.739376	−0.369688	+	0.929156i	$0.620535\pi$
$578$	51.9671	2.16154
$579$	−16.9232	−0.703304
$580$	2.85615	0.118595
$581$	3.95863	0.164232
$582$	−14.1936	−0.588343
$583$	33.7666	1.39847
$584$	22.4776	0.930131
$585$	6.34717	0.262423
$586$	−0.514256	−0.0212437
$587$	−43.8320	−1.80914	−0.904570	−	0.426325i	$-0.859808\pi$
$587$	−43.8320	−1.80914	−0.904570	+	0.426325i	$0.859808\pi$
$588$	0.927780	0.0382610
$589$	15.1170	0.622885
$590$	−5.04284	−0.207610
$591$	7.23547	0.297628
$592$	6.26481	0.257482
$593$	28.9429	1.18854	0.594271	−	0.804265i	$-0.297441\pi$
$593$	28.9429	1.18854	0.594271	+	0.804265i	$0.297441\pi$
$594$	−3.96627	−0.162738
$595$	−10.1560	−0.416355
$596$	−19.5353	−0.800197
$597$	15.4495	0.632306
$598$	35.1081	1.43568
$599$	5.84676	0.238892	0.119446	−	0.992841i	$-0.461888\pi$
$599$	5.84676	0.238892	0.119446	+	0.992841i	$0.461888\pi$
$600$	−10.5041	−0.428829
$601$	13.8434	0.564685	0.282342	−	0.959314i	$-0.408889\pi$
$601$	13.8434	0.564685	0.282342	+	0.959314i	$0.408889\pi$
$602$	0.861588	0.0351157
$603$	−14.2487	−0.580253
$604$	−14.8957	−0.606099
$605$	−4.54930	−0.184955
$606$	−6.32442	−0.256912
$607$	−8.80332	−0.357316	−0.178658	−	0.983911i	$-0.557176\pi$
$607$	−8.80332	−0.357316	−0.178658	+	0.983911i	$0.557176\pi$
$608$	−26.5169	−1.07540
$609$	−2.48459	−0.100681
$610$	−13.4560	−0.544818
$611$	−57.6569	−2.33255
$612$	−7.60476	−0.307404
$613$	3.82811	0.154616	0.0773080	−	0.997007i	$-0.475368\pi$
$613$	3.82811	0.154616	0.0773080	+	0.997007i	$0.475368\pi$
$614$	−21.0483	−0.849442
$615$	5.77907	0.233034
$616$	−11.6124	−0.467875
$617$	−16.1738	−0.651134	−0.325567	−	0.945519i	$-0.605555\pi$
$617$	−16.1738	−0.651134	−0.325567	+	0.945519i	$0.605555\pi$
$618$	−17.2068	−0.692158
$619$	14.0786	0.565867	0.282933	−	0.959140i	$-0.408692\pi$
$619$	14.0786	0.565867	0.282933	+	0.959140i	$0.408692\pi$
$620$	−3.10246	−0.124598
$621$	6.61860	0.265595
$622$	−16.4775	−0.660688
$623$	−11.8742	−0.475732
$624$	−6.57584	−0.263244
$625$	4.32894	0.173158
$626$	−6.55107	−0.261833
$627$	21.4548	0.856823
$628$	−18.9893	−0.757755
$629$	−40.0034	−1.59504
$630$	−1.28299	−0.0511155
$631$	27.2900	1.08640	0.543198	−	0.839605i	$-0.317213\pi$
$631$	27.2900	1.08640	0.543198	+	0.839605i	$0.317213\pi$
$632$	35.4875	1.41162
$633$	−7.83218	−0.311301
$634$	13.0983	0.520198
$635$	−17.9023	−0.710430
$636$	8.17884	0.324312
$637$	−5.12270	−0.202969
$638$	9.85454	0.390145
$639$	−5.94230	−0.235074
$640$	2.14821	0.0849155
$641$	−10.9172	−0.431203	−0.215602	−	0.976481i	$-0.569171\pi$
$641$	−10.9172	−0.431203	−0.215602	+	0.976481i	$0.569171\pi$
$642$	8.88578	0.350694
$643$	−13.7672	−0.542927	−0.271463	−	0.962449i	$-0.587508\pi$
$643$	−13.7672	−0.542927	−0.271463	+	0.962449i	$0.587508\pi$
$644$	6.14060	0.241973
$645$	1.03095	0.0405937
$646$	−47.5409	−1.87047
$647$	−17.3544	−0.682273	−0.341136	−	0.940014i	$-0.610812\pi$
$647$	−17.3544	−0.682273	−0.341136	+	0.940014i	$0.610812\pi$
$648$	−3.03166	−0.119095
$649$	15.0554	0.590975
$650$	18.3789	0.720881
$651$	2.69886	0.105777
$652$	−20.2182	−0.791806
$653$	3.04672	0.119228	0.0596138	−	0.998222i	$-0.481013\pi$
$653$	3.04672	0.119228	0.0596138	+	0.998222i	$0.481013\pi$
$654$	−16.6082	−0.649433
$655$	−22.9357	−0.896171
$656$	−5.98726	−0.233763
$657$	−7.41430	−0.289259
$658$	11.6545	0.454340
$659$	−6.91247	−0.269271	−0.134636	−	0.990895i	$-0.542986\pi$
$659$	−6.91247	−0.269271	−0.134636	+	0.990895i	$0.542986\pi$
$660$	−4.40317	−0.171393
$661$	14.9233	0.580450	0.290225	−	0.956958i	$-0.406270\pi$
$661$	14.9233	0.580450	0.290225	+	0.956958i	$0.406270\pi$
$662$	−9.12213	−0.354542
$663$	41.9894	1.63073
$664$	−12.0012	−0.465738
$665$	6.94011	0.269126
$666$	−5.05357	−0.195822
$667$	−16.4445	−0.636733
$668$	−7.45597	−0.288480
$669$	0.887704	0.0343206
$670$	18.2810	0.706256
$671$	40.1729	1.55086
$672$	−4.73411	−0.182622
$673$	26.9290	1.03804	0.519019	−	0.854763i	$-0.326297\pi$
$673$	26.9290	1.03804	0.519019	+	0.854763i	$0.326297\pi$
$674$	−14.4678	−0.557279
$675$	3.46481	0.133361
$676$	−12.2857	−0.472528
$677$	6.28677	0.241620	0.120810	−	0.992676i	$-0.461451\pi$
$677$	6.28677	0.241620	0.120810	+	0.992676i	$0.461451\pi$
$678$	12.2215	0.469365
$679$	13.7072	0.526036
$680$	30.7895	1.18072
$681$	−19.0891	−0.731495
$682$	−10.7044	−0.409893
$683$	25.9587	0.993280	0.496640	−	0.867957i	$-0.334567\pi$
$683$	25.9587	0.993280	0.496640	+	0.867957i	$0.334567\pi$
$684$	5.19673	0.198702
$685$	−8.74100	−0.333976
$686$	1.03548	0.0395348
$687$	−7.15988	−0.273166
$688$	−1.06809	−0.0407207
$689$	−45.1592	−1.72043
$690$	−8.49159	−0.323269
$691$	5.97760	0.227399	0.113699	−	0.993515i	$-0.463730\pi$
$691$	5.97760	0.227399	0.113699	+	0.993515i	$0.463730\pi$
$692$	12.5679	0.477761
$693$	3.83036	0.145503
$694$	−11.0415	−0.419129
$695$	−7.56291	−0.286877
$696$	7.53243	0.285516
$697$	38.2311	1.44811
$698$	16.1122	0.609857
$699$	12.1478	0.459471
$700$	3.21458	0.121500
$701$	26.6366	1.00605	0.503025	−	0.864272i	$-0.332220\pi$
$701$	26.6366	1.00605	0.503025	+	0.864272i	$0.332220\pi$
$702$	5.30446	0.200204
$703$	27.3364	1.03101
$704$	28.6105	1.07830
$705$	13.9455	0.525217
$706$	−8.70244	−0.327521
$707$	6.10771	0.229704
$708$	3.64667	0.137050
$709$	16.8165	0.631558	0.315779	−	0.948833i	$-0.397734\pi$
$709$	16.8165	0.631558	0.315779	+	0.948833i	$0.397734\pi$
$710$	7.62392	0.286120
$711$	−11.7057	−0.438996
$712$	35.9987	1.34911
$713$	17.8627	0.668962
$714$	−8.48756	−0.317639
$715$	24.3120	0.909216
$716$	−21.8259	−0.815671
$717$	25.7944	0.963311
$718$	−0.967502	−0.0361068
$719$	−8.74812	−0.326250	−0.163125	−	0.986605i	$-0.552157\pi$
$719$	−8.74812	−0.326250	−0.163125	+	0.986605i	$0.552157\pi$
$720$	1.59050	0.0592744
$721$	16.6172	0.618856
$722$	12.8131	0.476852
$723$	20.8634	0.775919
$724$	−11.0672	−0.411308
$725$	−8.60863	−0.319716
$726$	−3.80194	−0.141103
$727$	−1.47591	−0.0547384	−0.0273692	−	0.999625i	$-0.508713\pi$
$727$	−1.47591	−0.0547384	−0.0273692	+	0.999625i	$0.508713\pi$
$728$	15.5303	0.575591
$729$	1.00000	0.0370370
$730$	9.51247	0.352072
$731$	6.82022	0.252255
$732$	9.73057	0.359652
$733$	49.1283	1.81460	0.907298	−	0.420489i	$-0.138141\pi$
$733$	49.1283	1.81460	0.907298	+	0.420489i	$0.138141\pi$
$734$	33.3313	1.23028
$735$	1.23903	0.0457022
$736$	−31.3331	−1.15496
$737$	−54.5778	−2.01040
$738$	4.82968	0.177783
$739$	3.95747	0.145578	0.0727889	−	0.997347i	$-0.476810\pi$
$739$	3.95747	0.145578	0.0727889	+	0.997347i	$0.476810\pi$
$740$	−5.61025	−0.206237
$741$	−28.6935	−1.05408
$742$	9.12828	0.335110
$743$	−16.0435	−0.588580	−0.294290	−	0.955716i	$-0.595083\pi$
$743$	−16.0435	−0.588580	−0.294290	+	0.955716i	$0.595083\pi$
$744$	−8.18203	−0.299968
$745$	−26.0890	−0.955825
$746$	−13.0895	−0.479241
$747$	3.95863	0.144839
$748$	−29.1290	−1.06506
$749$	−8.58131	−0.313554
$750$	−10.8603	−0.396561
$751$	−17.6973	−0.645783	−0.322892	−	0.946436i	$-0.604655\pi$
$751$	−17.6973	−0.645783	−0.322892	+	0.946436i	$0.604655\pi$
$752$	−14.4479	−0.526860
$753$	−1.81295	−0.0660675
$754$	−13.1794	−0.479965
$755$	−19.8929	−0.723977
$756$	0.927780	0.0337430
$757$	−32.6516	−1.18674	−0.593372	−	0.804929i	$-0.702204\pi$
$757$	−32.6516	−1.18674	−0.593372	+	0.804929i	$0.702204\pi$
$758$	−32.3047	−1.17336
$759$	25.3516	0.920205
$760$	−21.0400	−0.763203
$761$	−0.230812	−0.00836692	−0.00418346	−	0.999991i	$-0.501332\pi$
$761$	−0.230812	−0.00836692	−0.00418346	+	0.999991i	$0.501332\pi$
$762$	−14.9613	−0.541990
$763$	16.0391	0.580656
$764$	0.927780	0.0335659
$765$	−10.1560	−0.367190
$766$	15.9059	0.574704
$767$	−20.1350	−0.727032
$768$	16.7341	0.603841
$769$	32.6341	1.17682	0.588408	−	0.808564i	$-0.299755\pi$
$769$	32.6341	1.17682	0.588408	+	0.808564i	$0.299755\pi$
$770$	−4.91432	−0.177100
$771$	−8.52307	−0.306951
$772$	−15.7010	−0.565091
$773$	−52.2980	−1.88103	−0.940515	−	0.339754i	$-0.889656\pi$
$773$	−52.2980	−1.88103	−0.940515	+	0.339754i	$0.889656\pi$
$774$	0.861588	0.0309691
$775$	9.35104	0.335899
$776$	−41.5557	−1.49176
$777$	4.88041	0.175084
$778$	26.5381	0.951438
$779$	−26.1253	−0.936037
$780$	5.88878	0.210852
$781$	−22.7612	−0.814459
$782$	−56.1757	−2.00884
$783$	−2.48459	−0.0887920
$784$	−1.28367	−0.0458452
$785$	−25.3598	−0.905129
$786$	−19.1678	−0.683693
$787$	−6.56073	−0.233865	−0.116932	−	0.993140i	$-0.537306\pi$
$787$	−6.56073	−0.233865	−0.116932	+	0.993140i	$0.537306\pi$
$788$	6.71293	0.239138
$789$	4.24451	0.151109
$790$	15.0182	0.534325
$791$	−11.8028	−0.419658
$792$	−11.6124	−0.412627
$793$	−53.7270	−1.90790
$794$	−18.9998	−0.674276
$795$	10.9227	0.387387
$796$	14.3337	0.508045
$797$	−1.35342	−0.0479407	−0.0239703	−	0.999713i	$-0.507631\pi$
$797$	−1.35342	−0.0479407	−0.0239703	+	0.999713i	$0.507631\pi$
$798$	5.79999	0.205317
$799$	92.2557	3.26377
$800$	−16.4028	−0.579926
$801$	−11.8742	−0.419556
$802$	−6.19035	−0.218589
$803$	−28.3994	−1.00219
$804$	−13.2197	−0.466222
$805$	8.20063	0.289034
$806$	14.3160	0.504259
$807$	−8.97669	−0.315994
$808$	−18.5165	−0.651408
$809$	8.74726	0.307537	0.153769	−	0.988107i	$-0.450859\pi$
$809$	8.74726	0.307537	0.153769	+	0.988107i	$0.450859\pi$
$810$	−1.28299	−0.0450797
$811$	−14.0354	−0.492848	−0.246424	−	0.969162i	$-0.579256\pi$
$811$	−14.0354	−0.492848	−0.246424	+	0.969162i	$0.579256\pi$
$812$	−2.30515	−0.0808950
$813$	18.0420	0.632760
$814$	−19.3570	−0.678463
$815$	−27.0009	−0.945802
$816$	10.5219	0.368339
$817$	−4.66061	−0.163054
$818$	−3.72962	−0.130403
$819$	−5.12270	−0.179002
$820$	5.36170	0.187239
$821$	−25.5355	−0.891196	−0.445598	−	0.895233i	$-0.647009\pi$
$821$	−25.5355	−0.891196	−0.445598	+	0.895233i	$0.647009\pi$
$822$	−7.30503	−0.254792
$823$	47.0500	1.64006	0.820029	−	0.572322i	$-0.193957\pi$
$823$	47.0500	1.64006	0.820029	+	0.572322i	$0.193957\pi$
$824$	−50.3777	−1.75499
$825$	13.2715	0.462053
$826$	4.07000	0.141613
$827$	18.2998	0.636346	0.318173	−	0.948033i	$-0.396931\pi$
$827$	18.2998	0.636346	0.318173	+	0.948033i	$0.396931\pi$
$828$	6.14060	0.213401
$829$	−36.4853	−1.26719	−0.633594	−	0.773665i	$-0.718421\pi$
$829$	−36.4853	−1.26719	−0.633594	+	0.773665i	$0.718421\pi$
$830$	−5.07889	−0.176291
$831$	27.1151	0.940612
$832$	−38.2635	−1.32655
$833$	8.19673	0.284000
$834$	−6.32047	−0.218860
$835$	−9.95728	−0.344586
$836$	19.9053	0.688441
$837$	2.69886	0.0932863
$838$	15.7740	0.544902
$839$	39.8482	1.37571	0.687857	−	0.725846i	$-0.258552\pi$
$839$	39.8482	1.37571	0.687857	+	0.725846i	$0.258552\pi$
$840$	−3.75631	−0.129605
$841$	−22.8268	−0.787132
$842$	27.7346	0.955797
$843$	9.15118	0.315184
$844$	−7.26654	−0.250124
$845$	−16.4073	−0.564428
$846$	11.6545	0.400691
$847$	3.67167	0.126160
$848$	−11.3162	−0.388598
$849$	−5.37462	−0.184456
$850$	−29.4078	−1.00868
$851$	32.3015	1.10728
$852$	−5.51315	−0.188877
$853$	12.8208	0.438975	0.219488	−	0.975615i	$-0.429561\pi$
$853$	12.8208	0.438975	0.219488	+	0.975615i	$0.429561\pi$
$854$	10.8601	0.371626
$855$	6.94011	0.237347
$856$	26.0156	0.889195
$857$	−29.2405	−0.998838	−0.499419	−	0.866361i	$-0.666453\pi$
$857$	−29.2405	−0.998838	−0.499419	+	0.866361i	$0.666453\pi$
$858$	20.3180	0.693645
$859$	−40.5745	−1.38438	−0.692192	−	0.721714i	$-0.743355\pi$
$859$	−40.5745	−1.38438	−0.692192	+	0.721714i	$0.743355\pi$
$860$	0.956497	0.0326163
$861$	−4.66419	−0.158955
$862$	34.7674	1.18418
$863$	20.9432	0.712915	0.356458	−	0.934311i	$-0.383984\pi$
$863$	20.9432	0.712915	0.356458	+	0.934311i	$0.383984\pi$
$864$	−4.73411	−0.161058
$865$	16.7842	0.570679
$866$	−37.0782	−1.25997
$867$	−50.1864	−1.70442
$868$	2.50395	0.0849895
$869$	−44.8369	−1.52099
$870$	3.18770	0.108073
$871$	72.9920	2.47324
$872$	−48.6252	−1.64666
$873$	13.7072	0.463920
$874$	38.3878	1.29849
$875$	10.4881	0.354564
$876$	−6.87883	−0.232414
$877$	24.1235	0.814594	0.407297	−	0.913296i	$-0.366471\pi$
$877$	24.1235	0.814594	0.407297	+	0.913296i	$0.366471\pi$
$878$	−2.50843	−0.0846554
$879$	0.496635	0.0167511
$880$	6.09218	0.205367
$881$	50.0546	1.68638	0.843191	−	0.537615i	$-0.180675\pi$
$881$	50.0546	1.68638	0.843191	+	0.537615i	$0.180675\pi$
$882$	1.03548	0.0348665
$883$	−43.1155	−1.45095	−0.725476	−	0.688248i	$-0.758380\pi$
$883$	−43.1155	−1.45095	−0.725476	+	0.688248i	$0.758380\pi$
$884$	38.9569	1.31026
$885$	4.87005	0.163705
$886$	1.04147	0.0349889
$887$	33.6337	1.12931	0.564655	−	0.825327i	$-0.309009\pi$
$887$	33.6337	1.12931	0.564655	+	0.825327i	$0.309009\pi$
$888$	−14.7957	−0.496513
$889$	14.4486	0.484592
$890$	15.2345	0.510663
$891$	3.83036	0.128322
$892$	0.823593	0.0275759
$893$	−63.0431	−2.10966
$894$	−21.8031	−0.729203
$895$	−29.1479	−0.974308
$896$	−1.73379	−0.0579217
$897$	−33.9051	−1.13206
$898$	−34.5937	−1.15441
$899$	−6.70556	−0.223643
$900$	3.21458	0.107153
$901$	72.2583	2.40727
$902$	18.4994	0.615964
$903$	−0.832065	−0.0276894
$904$	35.7820	1.19009
$905$	−14.7800	−0.491302
$906$	−16.6249	−0.552325
$907$	35.9648	1.19419	0.597095	−	0.802171i	$-0.296322\pi$
$907$	35.9648	1.19419	0.597095	+	0.802171i	$0.296322\pi$
$908$	−17.7104	−0.587742
$909$	6.10771	0.202580
$910$	6.57237	0.217872
$911$	2.30081	0.0762292	0.0381146	−	0.999273i	$-0.487865\pi$
$911$	2.30081	0.0762292	0.0381146	+	0.999273i	$0.487865\pi$
$912$	−7.19013	−0.238089
$913$	15.1630	0.501822
$914$	−11.7199	−0.387659
$915$	12.9950	0.429600
$916$	−6.64279	−0.219484
$917$	18.5110	0.611288
$918$	−8.48756	−0.280131
$919$	0.384600	0.0126868	0.00634339	−	0.999980i	$-0.497981\pi$
$919$	0.384600	0.0126868	0.00634339	+	0.999980i	$0.497981\pi$
$920$	−24.8615	−0.819660
$921$	20.3271	0.669801
$922$	24.8574	0.818636
$923$	30.4406	1.00197
$924$	3.55373	0.116909
$925$	16.9097	0.555987
$926$	−25.3238	−0.832190
$927$	16.6172	0.545780
$928$	11.7623	0.386117
$929$	−11.2518	−0.369161	−0.184580	−	0.982817i	$-0.559093\pi$
$929$	−11.2518	−0.369161	−0.184580	+	0.982817i	$0.559093\pi$
$930$	−3.46261	−0.113544
$931$	−5.60125	−0.183574
$932$	11.2705	0.369176
$933$	15.9129	0.520965
$934$	37.7154	1.23409
$935$	−38.9011	−1.27220
$936$	15.5303	0.507623
$937$	−39.3918	−1.28687	−0.643437	−	0.765499i	$-0.722492\pi$
$937$	−39.3918	−1.28687	−0.643437	+	0.765499i	$0.722492\pi$
$938$	−14.7543	−0.481745
$939$	6.32660	0.206461
$940$	12.9383	0.422002
$941$	8.20737	0.267553	0.133776	−	0.991012i	$-0.457290\pi$
$941$	8.20737	0.267553	0.133776	+	0.991012i	$0.457290\pi$
$942$	−21.1937	−0.690527
$943$	−30.8704	−1.00528
$944$	−5.04550	−0.164217
$945$	1.23903	0.0403056
$946$	3.30019	0.107299
$947$	−28.7034	−0.932734	−0.466367	−	0.884591i	$-0.654437\pi$
$947$	−28.7034	−0.932734	−0.466367	+	0.884591i	$0.654437\pi$
$948$	−10.8603	−0.352725
$949$	37.9812	1.23292
$950$	20.0958	0.651995
$951$	−12.6494	−0.410186
$952$	−24.8497	−0.805383
$953$	30.1159	0.975549	0.487774	−	0.872970i	$-0.337809\pi$
$953$	30.1159	0.975549	0.487774	+	0.872970i	$0.337809\pi$
$954$	9.12828	0.295539
$955$	1.23903	0.0400940
$956$	23.9316	0.774002
$957$	−9.51688	−0.307637
$958$	−2.94871	−0.0952683
$959$	7.05472	0.227809
$960$	9.25481	0.298698
$961$	−23.7161	−0.765037
$962$	25.8879	0.834660
$963$	−8.58131	−0.276529
$964$	19.3567	0.623436
$965$	−20.9683	−0.674994
$966$	6.85343	0.220505
$967$	17.7704	0.571457	0.285729	−	0.958311i	$-0.407764\pi$
$967$	17.7704	0.571457	0.285729	+	0.958311i	$0.407764\pi$
$968$	−11.1313	−0.357772
$969$	45.9120	1.47490
$970$	−17.5862	−0.564660
$971$	−8.46689	−0.271716	−0.135858	−	0.990728i	$-0.543379\pi$
$971$	−8.46689	−0.271716	−0.135858	+	0.990728i	$0.543379\pi$
$972$	0.927780	0.0297585
$973$	6.10390	0.195682
$974$	−23.9298	−0.766760
$975$	−17.7492	−0.568429
$976$	−13.4631	−0.430944
$977$	27.0824	0.866444	0.433222	−	0.901287i	$-0.357377\pi$
$977$	27.0824	0.866444	0.433222	+	0.901287i	$0.357377\pi$
$978$	−22.5652	−0.721556
$979$	−45.4827	−1.45363
$980$	1.14955	0.0367209
$981$	16.0391	0.512090
$982$	−26.5590	−0.847532
$983$	−41.1798	−1.31343	−0.656716	−	0.754138i	$-0.728055\pi$
$983$	−41.1798	−1.31343	−0.656716	+	0.754138i	$0.728055\pi$
$984$	14.1402	0.450775
$985$	8.96496	0.285647
$986$	21.0881	0.671582
$987$	−11.2552	−0.358256
$988$	−26.6213	−0.846936
$989$	−5.50710	−0.175116
$990$	−4.91432	−0.156187
$991$	−35.4471	−1.12602	−0.563008	−	0.826452i	$-0.690356\pi$
$991$	−35.4471	−1.12602	−0.563008	+	0.826452i	$0.690356\pi$
$992$	−12.7767	−0.405661
$993$	8.80956	0.279563
$994$	−6.15314	−0.195166
$995$	19.1424	0.606854
$996$	3.67274	0.116375
$997$	22.3218	0.706939	0.353469	−	0.935446i	$-0.385002\pi$
$997$	22.3218	0.706939	0.353469	+	0.935446i	$0.385002\pi$
$998$	−7.83107	−0.247888
$999$	4.88041	0.154409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.l.1.20	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.l.1.20	✓	28	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q+1.03548 q^{2} -1.00000 q^{3} -0.927780 q^{4} -1.23903 q^{5} -1.03548 q^{6} +1.00000 q^{7} -3.03166 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.03548 q^{2} -1.00000 q^{3} -0.927780 q^{4} -1.23903 q^{5} -1.03548 q^{6} +1.00000 q^{7} -3.03166 q^{8} +1.00000 q^{9} -1.28299 q^{10} +3.83036 q^{11} +0.927780 q^{12} -5.12270 q^{13} +1.03548 q^{14} +1.23903 q^{15} -1.28367 q^{16} +8.19673 q^{17} +1.03548 q^{18} -5.60125 q^{19} +1.14955 q^{20} -1.00000 q^{21} +3.96627 q^{22} -6.61860 q^{23} +3.03166 q^{24} -3.46481 q^{25} -5.30446 q^{26} -1.00000 q^{27} -0.927780 q^{28} +2.48459 q^{29} +1.28299 q^{30} -2.69886 q^{31} +4.73411 q^{32} -3.83036 q^{33} +8.48756 q^{34} -1.23903 q^{35} -0.927780 q^{36} -4.88041 q^{37} -5.79999 q^{38} +5.12270 q^{39} +3.75631 q^{40} +4.66419 q^{41} -1.03548 q^{42} +0.832065 q^{43} -3.55373 q^{44} -1.23903 q^{45} -6.85343 q^{46} +11.2552 q^{47} +1.28367 q^{48} +1.00000 q^{49} -3.58774 q^{50} -8.19673 q^{51} +4.75274 q^{52} +8.81550 q^{53} -1.03548 q^{54} -4.74593 q^{55} -3.03166 q^{56} +5.60125 q^{57} +2.57274 q^{58} +3.93054 q^{59} -1.14955 q^{60} +10.4880 q^{61} -2.79462 q^{62} +1.00000 q^{63} +7.46941 q^{64} +6.34717 q^{65} -3.96627 q^{66} -14.2487 q^{67} -7.60476 q^{68} +6.61860 q^{69} -1.28299 q^{70} -5.94230 q^{71} -3.03166 q^{72} -7.41430 q^{73} -5.05357 q^{74} +3.46481 q^{75} +5.19673 q^{76} +3.83036 q^{77} +5.30446 q^{78} -11.7057 q^{79} +1.59050 q^{80} +1.00000 q^{81} +4.82968 q^{82} +3.95863 q^{83} +0.927780 q^{84} -10.1560 q^{85} +0.861588 q^{86} -2.48459 q^{87} -11.6124 q^{88} -11.8742 q^{89} -1.28299 q^{90} -5.12270 q^{91} +6.14060 q^{92} +2.69886 q^{93} +11.6545 q^{94} +6.94011 q^{95} -4.73411 q^{96} +13.7072 q^{97} +1.03548 q^{98} +3.83036 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9 + 4 * q^10 - 8 * q^11 - 34 * q^12 + 26 * q^13 - 6 * q^14 - 8 * q^15 + 62 * q^16 + 9 * q^17 - 6 * q^18 + 25 * q^19 + 20 * q^20 - 28 * q^21 + 3 * q^22 - 30 * q^23 + 15 * q^24 + 42 * q^25 + 25 * q^26 - 28 * q^27 + 34 * q^28 - 5 * q^29 - 4 * q^30 + 18 * q^31 - 26 * q^32 + 8 * q^33 + 30 * q^34 + 8 * q^35 + 34 * q^36 + 36 * q^37 - 2 * q^38 - 26 * q^39 + 28 * q^40 + 21 * q^41 + 6 * q^42 + 8 * q^43 - 20 * q^44 + 8 * q^45 + 24 * q^46 + 6 * q^47 - 62 * q^48 + 28 * q^49 - 48 * q^50 - 9 * q^51 + 54 * q^52 - 12 * q^53 + 6 * q^54 + 15 * q^55 - 15 * q^56 - 25 * q^57 + 19 * q^58 + 33 * q^59 - 20 * q^60 + 48 * q^61 + 28 * q^63 + 75 * q^64 + 21 * q^65 - 3 * q^66 + 27 * q^67 + 19 * q^68 + 30 * q^69 + 4 * q^70 - 45 * q^71 - 15 * q^72 + 61 * q^73 - 31 * q^74 - 42 * q^75 + 63 * q^76 - 8 * q^77 - 25 * q^78 + 35 * q^79 + 84 * q^80 + 28 * q^81 + 11 * q^82 + 43 * q^83 - 34 * q^84 + 43 * q^85 - q^86 + 5 * q^87 - 27 * q^88 + 25 * q^89 + 4 * q^90 + 26 * q^91 - 102 * q^92 - 18 * q^93 + 55 * q^94 - 43 * q^95 + 26 * q^96 + 40 * q^97 - 6 * q^98 - 8 * q^99

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