LMFDB - Embedded newform 4011.2.a.l.1.18

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			1.18
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)

$f(q)$	$=$	$q+0.544491 q^{2} -1.00000 q^{3} -1.70353 q^{4} +2.42913 q^{5} -0.544491 q^{6} +1.00000 q^{7} -2.01654 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.544491 q^{2} -1.00000 q^{3} -1.70353 q^{4} +2.42913 q^{5} -0.544491 q^{6} +1.00000 q^{7} -2.01654 q^{8} +1.00000 q^{9} +1.32264 q^{10} +4.74490 q^{11} +1.70353 q^{12} +6.42081 q^{13} +0.544491 q^{14} -2.42913 q^{15} +2.30907 q^{16} +7.11970 q^{17} +0.544491 q^{18} +0.432535 q^{19} -4.13810 q^{20} -1.00000 q^{21} +2.58356 q^{22} -4.15659 q^{23} +2.01654 q^{24} +0.900695 q^{25} +3.49607 q^{26} -1.00000 q^{27} -1.70353 q^{28} +7.53128 q^{29} -1.32264 q^{30} -2.47841 q^{31} +5.29035 q^{32} -4.74490 q^{33} +3.87661 q^{34} +2.42913 q^{35} -1.70353 q^{36} +5.63424 q^{37} +0.235512 q^{38} -6.42081 q^{39} -4.89844 q^{40} -1.87242 q^{41} -0.544491 q^{42} -8.34532 q^{43} -8.08308 q^{44} +2.42913 q^{45} -2.26323 q^{46} -13.3116 q^{47} -2.30907 q^{48} +1.00000 q^{49} +0.490420 q^{50} -7.11970 q^{51} -10.9380 q^{52} -2.82754 q^{53} -0.544491 q^{54} +11.5260 q^{55} -2.01654 q^{56} -0.432535 q^{57} +4.10071 q^{58} -1.03460 q^{59} +4.13810 q^{60} +0.129499 q^{61} -1.34947 q^{62} +1.00000 q^{63} -1.73760 q^{64} +15.5970 q^{65} -2.58356 q^{66} +0.621432 q^{67} -12.1286 q^{68} +4.15659 q^{69} +1.32264 q^{70} +11.5821 q^{71} -2.01654 q^{72} -5.56783 q^{73} +3.06779 q^{74} -0.900695 q^{75} -0.736837 q^{76} +4.74490 q^{77} -3.49607 q^{78} -3.37327 q^{79} +5.60905 q^{80} +1.00000 q^{81} -1.01952 q^{82} -5.59293 q^{83} +1.70353 q^{84} +17.2947 q^{85} -4.54395 q^{86} -7.53128 q^{87} -9.56827 q^{88} +16.9830 q^{89} +1.32264 q^{90} +6.42081 q^{91} +7.08087 q^{92} +2.47841 q^{93} -7.24803 q^{94} +1.05069 q^{95} -5.29035 q^{96} -5.75638 q^{97} +0.544491 q^{98} +4.74490 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.544491	0.385013	0.192507	−	0.981296i	$-0.438338\pi$
$2$	0.544491	0.385013	0.192507	+	0.981296i	$0.438338\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.70353	−0.851765
$5$	2.42913	1.08634	0.543171	−	0.839622i	$-0.317224\pi$
$5$	2.42913	1.08634	0.543171	+	0.839622i	$0.317224\pi$
$6$	−0.544491	−0.222287
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.01654	−0.712954
$9$	1.00000	0.333333
$10$	1.32264	0.418256
$11$	4.74490	1.43064	0.715321	−	0.698796i	$-0.246281\pi$
$11$	4.74490	1.43064	0.715321	+	0.698796i	$0.246281\pi$
$12$	1.70353	0.491767
$13$	6.42081	1.78081	0.890406	−	0.455167i	$-0.150420\pi$
$13$	6.42081	1.78081	0.890406	+	0.455167i	$0.150420\pi$
$14$	0.544491	0.145521
$15$	−2.42913	−0.627200
$16$	2.30907	0.577268
$17$	7.11970	1.72678	0.863390	−	0.504537i	$-0.168337\pi$
$17$	7.11970	1.72678	0.863390	+	0.504537i	$0.168337\pi$
$18$	0.544491	0.128338
$19$	0.432535	0.0992304	0.0496152	−	0.998768i	$-0.484201\pi$
$19$	0.432535	0.0992304	0.0496152	+	0.998768i	$0.484201\pi$
$20$	−4.13810	−0.925308
$21$	−1.00000	−0.218218
$22$	2.58356	0.550816
$23$	−4.15659	−0.866709	−0.433354	−	0.901224i	$-0.642670\pi$
$23$	−4.15659	−0.866709	−0.433354	+	0.901224i	$0.642670\pi$
$24$	2.01654	0.411624
$25$	0.900695	0.180139
$26$	3.49607	0.685636
$27$	−1.00000	−0.192450
$28$	−1.70353	−0.321937
$29$	7.53128	1.39852	0.699261	−	0.714866i	$-0.253512\pi$
$29$	7.53128	1.39852	0.699261	+	0.714866i	$0.253512\pi$
$30$	−1.32264	−0.241480
$31$	−2.47841	−0.445135	−0.222568	−	0.974917i	$-0.571444\pi$
$31$	−2.47841	−0.445135	−0.222568	+	0.974917i	$0.571444\pi$
$32$	5.29035	0.935210
$33$	−4.74490	−0.825981
$34$	3.87661	0.664833
$35$	2.42913	0.410599
$36$	−1.70353	−0.283922
$37$	5.63424	0.926264	0.463132	−	0.886289i	$-0.346726\pi$
$37$	5.63424	0.926264	0.463132	+	0.886289i	$0.346726\pi$
$38$	0.235512	0.0382050
$39$	−6.42081	−1.02815
$40$	−4.89844	−0.774512
$41$	−1.87242	−0.292423	−0.146212	−	0.989253i	$-0.546708\pi$
$41$	−1.87242	−0.292423	−0.146212	+	0.989253i	$0.546708\pi$
$42$	−0.544491	−0.0840168
$43$	−8.34532	−1.27265	−0.636325	−	0.771421i	$-0.719546\pi$
$43$	−8.34532	−1.27265	−0.636325	+	0.771421i	$0.719546\pi$
$44$	−8.08308	−1.21857
$45$	2.42913	0.362114
$46$	−2.26323	−0.333694
$47$	−13.3116	−1.94169	−0.970847	−	0.239702i	$-0.922950\pi$
$47$	−13.3116	−1.94169	−0.970847	+	0.239702i	$0.922950\pi$
$48$	−2.30907	−0.333286
$49$	1.00000	0.142857
$50$	0.490420	0.0693559
$51$	−7.11970	−0.996957
$52$	−10.9380	−1.51683
$53$	−2.82754	−0.388392	−0.194196	−	0.980963i	$-0.562210\pi$
$53$	−2.82754	−0.388392	−0.194196	+	0.980963i	$0.562210\pi$
$54$	−0.544491	−0.0740958
$55$	11.5260	1.55417
$56$	−2.01654	−0.269471
$57$	−0.432535	−0.0572907
$58$	4.10071	0.538450
$59$	−1.03460	−0.134694	−0.0673468	−	0.997730i	$-0.521453\pi$
$59$	−1.03460	−0.134694	−0.0673468	+	0.997730i	$0.521453\pi$
$60$	4.13810	0.534227
$61$	0.129499	0.0165807	0.00829034	−	0.999966i	$-0.497361\pi$
$61$	0.129499	0.0165807	0.00829034	+	0.999966i	$0.497361\pi$
$62$	−1.34947	−0.171383
$63$	1.00000	0.125988
$64$	−1.73760	−0.217200
$65$	15.5970	1.93457
$66$	−2.58356	−0.318014
$67$	0.621432	0.0759200	0.0379600	−	0.999279i	$-0.487914\pi$
$67$	0.621432	0.0759200	0.0379600	+	0.999279i	$0.487914\pi$
$68$	−12.1286	−1.47081
$69$	4.15659	0.500395
$70$	1.32264	0.158086
$71$	11.5821	1.37454	0.687269	−	0.726403i	$-0.258809\pi$
$71$	11.5821	1.37454	0.687269	+	0.726403i	$0.258809\pi$
$72$	−2.01654	−0.237651
$73$	−5.56783	−0.651666	−0.325833	−	0.945427i	$-0.605645\pi$
$73$	−5.56783	−0.651666	−0.325833	+	0.945427i	$0.605645\pi$
$74$	3.06779	0.356624
$75$	−0.900695	−0.104003
$76$	−0.736837	−0.0845210
$77$	4.74490	0.540732
$78$	−3.49607	−0.395852
$79$	−3.37327	−0.379522	−0.189761	−	0.981830i	$-0.560771\pi$
$79$	−3.37327	−0.379522	−0.189761	+	0.981830i	$0.560771\pi$
$80$	5.60905	0.627111
$81$	1.00000	0.111111
$82$	−1.01952	−0.112587
$83$	−5.59293	−0.613904	−0.306952	−	0.951725i	$-0.599309\pi$
$83$	−5.59293	−0.613904	−0.306952	+	0.951725i	$0.599309\pi$
$84$	1.70353	0.185870
$85$	17.2947	1.87587
$86$	−4.54395	−0.489987
$87$	−7.53128	−0.807437
$88$	−9.56827	−1.01998
$89$	16.9830	1.80020	0.900099	−	0.435686i	$-0.143494\pi$
$89$	16.9830	1.80020	0.900099	+	0.435686i	$0.143494\pi$
$90$	1.32264	0.139419
$91$	6.42081	0.673084
$92$	7.08087	0.738232
$93$	2.47841	0.256999
$94$	−7.24803	−0.747578
$95$	1.05069	0.107798
$96$	−5.29035	−0.539944
$97$	−5.75638	−0.584472	−0.292236	−	0.956346i	$-0.594399\pi$
$97$	−5.75638	−0.584472	−0.292236	+	0.956346i	$0.594399\pi$
$98$	0.544491	0.0550019
$99$	4.74490	0.476880
$100$	−1.53436	−0.153436
$101$	−6.86443	−0.683037	−0.341518	−	0.939875i	$-0.610941\pi$
$101$	−6.86443	−0.683037	−0.341518	+	0.939875i	$0.610941\pi$
$102$	−3.87661	−0.383842
$103$	17.2315	1.69787	0.848937	−	0.528495i	$-0.177243\pi$
$103$	17.2315	1.69787	0.848937	+	0.528495i	$0.177243\pi$
$104$	−12.9478	−1.26964
$105$	−2.42913	−0.237059
$106$	−1.53957	−0.149536
$107$	15.8360	1.53092	0.765460	−	0.643484i	$-0.222512\pi$
$107$	15.8360	1.53092	0.765460	+	0.643484i	$0.222512\pi$
$108$	1.70353	0.163922
$109$	6.48096	0.620764	0.310382	−	0.950612i	$-0.399543\pi$
$109$	6.48096	0.620764	0.310382	+	0.950612i	$0.399543\pi$
$110$	6.27580	0.598374
$111$	−5.63424	−0.534779
$112$	2.30907	0.218187
$113$	−3.78905	−0.356443	−0.178222	−	0.983990i	$-0.557034\pi$
$113$	−3.78905	−0.356443	−0.178222	+	0.983990i	$0.557034\pi$
$114$	−0.235512	−0.0220577
$115$	−10.0969	−0.941542
$116$	−12.8298	−1.19121
$117$	6.42081	0.593604
$118$	−0.563331	−0.0518588
$119$	7.11970	0.652662
$120$	4.89844	0.447165
$121$	11.5141	1.04674
$122$	0.0705112	0.00638378
$123$	1.87242	0.168831
$124$	4.22204	0.379151
$125$	−9.95776	−0.890650
$126$	0.544491	0.0485071
$127$	−17.9006	−1.58842	−0.794212	−	0.607641i	$-0.792116\pi$
$127$	−17.9006	−1.58842	−0.794212	+	0.607641i	$0.792116\pi$
$128$	−11.5268	−1.01883
$129$	8.34532	0.734764
$130$	8.49243	0.744836
$131$	−14.9914	−1.30980	−0.654901	−	0.755715i	$-0.727290\pi$
$131$	−14.9914	−1.30980	−0.654901	+	0.755715i	$0.727290\pi$
$132$	8.08308	0.703542
$133$	0.432535	0.0375056
$134$	0.338364	0.0292302
$135$	−2.42913	−0.209067
$136$	−14.3571	−1.23112
$137$	−4.84422	−0.413869	−0.206935	−	0.978355i	$-0.566349\pi$
$137$	−4.84422	−0.413869	−0.206935	+	0.978355i	$0.566349\pi$
$138$	2.26323	0.192659
$139$	−5.49829	−0.466359	−0.233180	−	0.972434i	$-0.574913\pi$
$139$	−5.49829	−0.466359	−0.233180	+	0.972434i	$0.574913\pi$
$140$	−4.13810	−0.349734
$141$	13.3116	1.12104
$142$	6.30633	0.529215
$143$	30.4661	2.54770
$144$	2.30907	0.192423
$145$	18.2945	1.51927
$146$	−3.03164	−0.250900
$147$	−1.00000	−0.0824786
$148$	−9.59810	−0.788959
$149$	23.3411	1.91218	0.956088	−	0.293081i	$-0.0946806\pi$
$149$	23.3411	1.91218	0.956088	+	0.293081i	$0.0946806\pi$
$150$	−0.490420	−0.0400426
$151$	−17.5395	−1.42734	−0.713671	−	0.700481i	$-0.752969\pi$
$151$	−17.5395	−1.42734	−0.713671	+	0.700481i	$0.752969\pi$
$152$	−0.872224	−0.0707467
$153$	7.11970	0.575594
$154$	2.58356	0.208189
$155$	−6.02039	−0.483569
$156$	10.9380	0.875744
$157$	−14.1672	−1.13066	−0.565332	−	0.824863i	$-0.691252\pi$
$157$	−14.1672	−1.13066	−0.565332	+	0.824863i	$0.691252\pi$
$158$	−1.83671	−0.146121
$159$	2.82754	0.224238
$160$	12.8510	1.01596
$161$	−4.15659	−0.327585
$162$	0.544491	0.0427792
$163$	−7.08946	−0.555289	−0.277645	−	0.960684i	$-0.589554\pi$
$163$	−7.08946	−0.555289	−0.277645	+	0.960684i	$0.589554\pi$
$164$	3.18973	0.249076
$165$	−11.5260	−0.897298
$166$	−3.04530	−0.236361
$167$	3.86265	0.298901	0.149451	−	0.988769i	$-0.452250\pi$
$167$	3.86265	0.298901	0.149451	+	0.988769i	$0.452250\pi$
$168$	2.01654	0.155579
$169$	28.2268	2.17129
$170$	9.41681	0.722236
$171$	0.432535	0.0330768
$172$	14.2165	1.08400
$173$	17.4273	1.32498	0.662488	−	0.749073i	$-0.269501\pi$
$173$	17.4273	1.32498	0.662488	+	0.749073i	$0.269501\pi$
$174$	−4.10071	−0.310874
$175$	0.900695	0.0680861
$176$	10.9563	0.825864
$177$	1.03460	0.0777654
$178$	9.24711	0.693100
$179$	8.48155	0.633941	0.316970	−	0.948435i	$-0.397334\pi$
$179$	8.48155	0.633941	0.316970	+	0.948435i	$0.397334\pi$
$180$	−4.13810	−0.308436
$181$	−13.9616	−1.03776	−0.518879	−	0.854848i	$-0.673651\pi$
$181$	−13.9616	−1.03776	−0.518879	+	0.854848i	$0.673651\pi$
$182$	3.49607	0.259146
$183$	−0.129499	−0.00957286
$184$	8.38192	0.617923
$185$	13.6863	1.00624
$186$	1.34947	0.0989480
$187$	33.7823	2.47040
$188$	22.6767	1.65387
$189$	−1.00000	−0.0727393
$190$	0.572089	0.0415037
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	1.73760	0.125400
$193$	5.17829	0.372741	0.186371	−	0.982480i	$-0.440328\pi$
$193$	5.17829	0.372741	0.186371	+	0.982480i	$0.440328\pi$
$194$	−3.13430	−0.225029
$195$	−15.5970	−1.11693
$196$	−1.70353	−0.121681
$197$	−22.7249	−1.61908	−0.809540	−	0.587065i	$-0.800283\pi$
$197$	−22.7249	−1.61908	−0.809540	+	0.587065i	$0.800283\pi$
$198$	2.58356	0.183605
$199$	24.2629	1.71995	0.859976	−	0.510334i	$-0.170478\pi$
$199$	24.2629	1.71995	0.859976	+	0.510334i	$0.170478\pi$
$200$	−1.81629	−0.128431
$201$	−0.621432	−0.0438325
$202$	−3.73762	−0.262978
$203$	7.53128	0.528592
$204$	12.1286	0.849173
$205$	−4.54836	−0.317672
$206$	9.38241	0.653704
$207$	−4.15659	−0.288903
$208$	14.8261	1.02801
$209$	2.05234	0.141963
$210$	−1.32264	−0.0912710
$211$	−5.91255	−0.407037	−0.203518	−	0.979071i	$-0.565238\pi$
$211$	−5.91255	−0.407037	−0.203518	+	0.979071i	$0.565238\pi$
$212$	4.81680	0.330819
$213$	−11.5821	−0.793590
$214$	8.62253	0.589424
$215$	−20.2719	−1.38253
$216$	2.01654	0.137208
$217$	−2.47841	−0.168245
$218$	3.52883	0.239002
$219$	5.56783	0.376239
$220$	−19.6349	−1.32378
$221$	45.7142	3.07507
$222$	−3.06779	−0.205897
$223$	0.0633748	0.00424389	0.00212195	−	0.999998i	$-0.499325\pi$
$223$	0.0633748	0.00424389	0.00212195	+	0.999998i	$0.499325\pi$
$224$	5.29035	0.353476
$225$	0.900695	0.0600463
$226$	−2.06310	−0.137235
$227$	23.5851	1.56540	0.782700	−	0.622399i	$-0.213842\pi$
$227$	23.5851	1.56540	0.782700	+	0.622399i	$0.213842\pi$
$228$	0.736837	0.0487982
$229$	−22.7420	−1.50284	−0.751418	−	0.659827i	$-0.770630\pi$
$229$	−22.7420	−1.50284	−0.751418	+	0.659827i	$0.770630\pi$
$230$	−5.49768	−0.362506
$231$	−4.74490	−0.312192
$232$	−15.1871	−0.997082
$233$	−0.820877	−0.0537774	−0.0268887	−	0.999638i	$-0.508560\pi$
$233$	−0.820877	−0.0537774	−0.0268887	+	0.999638i	$0.508560\pi$
$234$	3.49607	0.228545
$235$	−32.3356	−2.10934
$236$	1.76247	0.114727
$237$	3.37327	0.219117
$238$	3.87661	0.251283
$239$	5.87988	0.380338	0.190169	−	0.981751i	$-0.439096\pi$
$239$	5.87988	0.380338	0.190169	+	0.981751i	$0.439096\pi$
$240$	−5.60905	−0.362062
$241$	11.3104	0.728570	0.364285	−	0.931288i	$-0.381313\pi$
$241$	11.3104	0.728570	0.364285	+	0.931288i	$0.381313\pi$
$242$	6.26932	0.403007
$243$	−1.00000	−0.0641500
$244$	−0.220606	−0.0141228
$245$	2.42913	0.155192
$246$	1.01952	0.0650020
$247$	2.77723	0.176711
$248$	4.99781	0.317361
$249$	5.59293	0.354437
$250$	−5.42191	−0.342912
$251$	−13.3592	−0.843228	−0.421614	−	0.906776i	$-0.638536\pi$
$251$	−13.3592	−0.843228	−0.421614	+	0.906776i	$0.638536\pi$
$252$	−1.70353	−0.107312
$253$	−19.7226	−1.23995
$254$	−9.74672	−0.611564
$255$	−17.2947	−1.08304
$256$	−2.80104	−0.175065
$257$	16.2238	1.01201	0.506005	−	0.862531i	$-0.331122\pi$
$257$	16.2238	1.01201	0.506005	+	0.862531i	$0.331122\pi$
$258$	4.54395	0.282894
$259$	5.63424	0.350095
$260$	−26.5700	−1.64780
$261$	7.53128	0.466174
$262$	−8.16266	−0.504291
$263$	−17.3748	−1.07137	−0.535687	−	0.844417i	$-0.679947\pi$
$263$	−17.3748	−1.07137	−0.535687	+	0.844417i	$0.679947\pi$
$264$	9.56827	0.588887
$265$	−6.86847	−0.421927
$266$	0.235512	0.0144401
$267$	−16.9830	−1.03934
$268$	−1.05863	−0.0646660
$269$	−25.4818	−1.55365	−0.776827	−	0.629714i	$-0.783172\pi$
$269$	−25.4818	−1.55365	−0.776827	+	0.629714i	$0.783172\pi$
$270$	−1.32264	−0.0804934
$271$	−6.57737	−0.399547	−0.199773	−	0.979842i	$-0.564021\pi$
$271$	−6.57737	−0.399547	−0.199773	+	0.979842i	$0.564021\pi$
$272$	16.4399	0.996815
$273$	−6.42081	−0.388605
$274$	−2.63763	−0.159345
$275$	4.27371	0.257714
$276$	−7.08087	−0.426218
$277$	9.30303	0.558965	0.279482	−	0.960151i	$-0.409837\pi$
$277$	9.30303	0.558965	0.279482	+	0.960151i	$0.409837\pi$
$278$	−2.99377	−0.179554
$279$	−2.47841	−0.148378
$280$	−4.89844	−0.292738
$281$	−12.3651	−0.737639	−0.368820	−	0.929501i	$-0.620238\pi$
$281$	−12.3651	−0.737639	−0.368820	+	0.929501i	$0.620238\pi$
$282$	7.24803	0.431614
$283$	0.812108	0.0482748	0.0241374	−	0.999709i	$-0.492316\pi$
$283$	0.812108	0.0482748	0.0241374	+	0.999709i	$0.492316\pi$
$284$	−19.7304	−1.17078
$285$	−1.05069	−0.0622373
$286$	16.5885	0.980900
$287$	−1.87242	−0.110526
$288$	5.29035	0.311737
$289$	33.6901	1.98177
$290$	9.96118	0.584941
$291$	5.75638	0.337445
$292$	9.48497	0.555066
$293$	9.98309	0.583218	0.291609	−	0.956538i	$-0.405809\pi$
$293$	9.98309	0.583218	0.291609	+	0.956538i	$0.405809\pi$
$294$	−0.544491	−0.0317554
$295$	−2.51319	−0.146323
$296$	−11.3617	−0.660384
$297$	−4.74490	−0.275327
$298$	12.7090	0.736213
$299$	−26.6887	−1.54345
$300$	1.53436	0.0885863
$301$	−8.34532	−0.481016
$302$	−9.55008	−0.549545
$303$	6.86443	0.394351
$304$	0.998755	0.0572826
$305$	0.314571	0.0180123
$306$	3.87661	0.221611
$307$	−23.6603	−1.35036	−0.675182	−	0.737651i	$-0.735935\pi$
$307$	−23.6603	−1.35036	−0.675182	+	0.737651i	$0.735935\pi$
$308$	−8.08308	−0.460576
$309$	−17.2315	−0.980268
$310$	−3.27805	−0.186181
$311$	25.9134	1.46942	0.734708	−	0.678383i	$-0.237319\pi$
$311$	25.9134	1.46942	0.734708	+	0.678383i	$0.237319\pi$
$312$	12.9478	0.733025
$313$	16.1243	0.911398	0.455699	−	0.890134i	$-0.349389\pi$
$313$	16.1243	0.911398	0.455699	+	0.890134i	$0.349389\pi$
$314$	−7.71390	−0.435321
$315$	2.42913	0.136866
$316$	5.74646	0.323264
$317$	−9.46753	−0.531750	−0.265875	−	0.964008i	$-0.585661\pi$
$317$	−9.46753	−0.531750	−0.265875	+	0.964008i	$0.585661\pi$
$318$	1.53957	0.0863348
$319$	35.7352	2.00078
$320$	−4.22086	−0.235953
$321$	−15.8360	−0.883877
$322$	−2.26323	−0.126125
$323$	3.07952	0.171349
$324$	−1.70353	−0.0946405
$325$	5.78319	0.320794
$326$	−3.86015	−0.213794
$327$	−6.48096	−0.358398
$328$	3.77581	0.208484
$329$	−13.3116	−0.733891
$330$	−6.27580	−0.345472
$331$	18.8457	1.03585	0.517927	−	0.855425i	$-0.326704\pi$
$331$	18.8457	1.03585	0.517927	+	0.855425i	$0.326704\pi$
$332$	9.52772	0.522902
$333$	5.63424	0.308755
$334$	2.10318	0.115081
$335$	1.50954	0.0824751
$336$	−2.30907	−0.125970
$337$	12.1608	0.662442	0.331221	−	0.943553i	$-0.392539\pi$
$337$	12.1608	0.662442	0.331221	+	0.943553i	$0.392539\pi$
$338$	15.3692	0.835976
$339$	3.78905	0.205793
$340$	−29.4620	−1.59780
$341$	−11.7598	−0.636829
$342$	0.235512	0.0127350
$343$	1.00000	0.0539949
$344$	16.8287	0.907340
$345$	10.0969	0.543600
$346$	9.48902	0.510133
$347$	18.5222	0.994322	0.497161	−	0.867658i	$-0.334376\pi$
$347$	18.5222	0.994322	0.497161	+	0.867658i	$0.334376\pi$
$348$	12.8298	0.687747
$349$	10.9068	0.583827	0.291914	−	0.956445i	$-0.405708\pi$
$349$	10.9068	0.583827	0.291914	+	0.956445i	$0.405708\pi$
$350$	0.490420	0.0262141
$351$	−6.42081	−0.342717
$352$	25.1022	1.33795
$353$	−36.7408	−1.95552	−0.977759	−	0.209733i	$-0.932740\pi$
$353$	−36.7408	−1.95552	−0.977759	+	0.209733i	$0.932740\pi$
$354$	0.563331	0.0299407
$355$	28.1344	1.49322
$356$	−28.9311	−1.53334
$357$	−7.11970	−0.376814
$358$	4.61813	0.244076
$359$	−20.8095	−1.09828	−0.549141	−	0.835730i	$-0.685045\pi$
$359$	−20.8095	−1.09828	−0.549141	+	0.835730i	$0.685045\pi$
$360$	−4.89844	−0.258171
$361$	−18.8129	−0.990153
$362$	−7.60197	−0.399551
$363$	−11.5141	−0.604333
$364$	−10.9380	−0.573309
$365$	−13.5250	−0.707932
$366$	−0.0705112	−0.00368568
$367$	2.57207	0.134261	0.0671304	−	0.997744i	$-0.478616\pi$
$367$	2.57207	0.134261	0.0671304	+	0.997744i	$0.478616\pi$
$368$	−9.59787	−0.500323
$369$	−1.87242	−0.0974744
$370$	7.45209	0.387416
$371$	−2.82754	−0.146799
$372$	−4.22204	−0.218903
$373$	−7.15087	−0.370258	−0.185129	−	0.982714i	$-0.559270\pi$
$373$	−7.15087	−0.370258	−0.185129	+	0.982714i	$0.559270\pi$
$374$	18.3941	0.951138
$375$	9.95776	0.514217
$376$	26.8433	1.38434
$377$	48.3569	2.49051
$378$	−0.544491	−0.0280056
$379$	6.96955	0.358002	0.179001	−	0.983849i	$-0.442714\pi$
$379$	6.96955	0.358002	0.179001	+	0.983849i	$0.442714\pi$
$380$	−1.78988	−0.0918187
$381$	17.9006	0.917076
$382$	−0.544491	−0.0278586
$383$	23.9335	1.22294	0.611471	−	0.791267i	$-0.290578\pi$
$383$	23.9335	1.22294	0.611471	+	0.791267i	$0.290578\pi$
$384$	11.5268	0.588224
$385$	11.5260	0.587420
$386$	2.81953	0.143510
$387$	−8.34532	−0.424216
$388$	9.80617	0.497833
$389$	7.01715	0.355784	0.177892	−	0.984050i	$-0.443072\pi$
$389$	7.01715	0.355784	0.177892	+	0.984050i	$0.443072\pi$
$390$	−8.49243	−0.430031
$391$	−29.5937	−1.49662
$392$	−2.01654	−0.101851
$393$	14.9914	0.756214
$394$	−12.3735	−0.623367
$395$	−8.19412	−0.412291
$396$	−8.08308	−0.406190
$397$	15.6443	0.785165	0.392583	−	0.919717i	$-0.371582\pi$
$397$	15.6443	0.785165	0.392583	+	0.919717i	$0.371582\pi$
$398$	13.2109	0.662205
$399$	−0.432535	−0.0216539
$400$	2.07977	0.103988
$401$	−28.3634	−1.41640	−0.708202	−	0.706010i	$-0.750493\pi$
$401$	−28.3634	−1.41640	−0.708202	+	0.706010i	$0.750493\pi$
$402$	−0.338364	−0.0168761
$403$	−15.9134	−0.792702
$404$	11.6938	0.581786
$405$	2.42913	0.120705
$406$	4.10071	0.203515
$407$	26.7339	1.32515
$408$	14.3571	0.710785
$409$	−3.40087	−0.168162	−0.0840811	−	0.996459i	$-0.526795\pi$
$409$	−3.40087	−0.168162	−0.0840811	+	0.996459i	$0.526795\pi$
$410$	−2.47654	−0.122308
$411$	4.84422	0.238948
$412$	−29.3544	−1.44619
$413$	−1.03460	−0.0509094
$414$	−2.26323	−0.111231
$415$	−13.5860	−0.666909
$416$	33.9683	1.66543
$417$	5.49829	0.269253
$418$	1.11748	0.0546577
$419$	−30.4267	−1.48644	−0.743221	−	0.669046i	$-0.766703\pi$
$419$	−30.4267	−1.48644	−0.743221	+	0.669046i	$0.766703\pi$
$420$	4.13810	0.201919
$421$	−18.4285	−0.898152	−0.449076	−	0.893493i	$-0.648247\pi$
$421$	−18.4285	−0.898152	−0.449076	+	0.893493i	$0.648247\pi$
$422$	−3.21933	−0.156715
$423$	−13.3116	−0.647231
$424$	5.70184	0.276906
$425$	6.41268	0.311060
$426$	−6.30633	−0.305543
$427$	0.129499	0.00626691
$428$	−26.9770	−1.30398
$429$	−30.4661	−1.47092
$430$	−11.0379	−0.532293
$431$	−7.21904	−0.347729	−0.173865	−	0.984770i	$-0.555625\pi$
$431$	−7.21904	−0.347729	−0.173865	+	0.984770i	$0.555625\pi$
$432$	−2.30907	−0.111095
$433$	0.764506	0.0367398	0.0183699	−	0.999831i	$-0.494152\pi$
$433$	0.764506	0.0367398	0.0183699	+	0.999831i	$0.494152\pi$
$434$	−1.34947	−0.0647767
$435$	−18.2945	−0.877153
$436$	−11.0405	−0.528745
$437$	−1.79787	−0.0860039
$438$	3.03164	0.144857
$439$	23.5722	1.12504	0.562521	−	0.826783i	$-0.309832\pi$
$439$	23.5722	1.12504	0.562521	+	0.826783i	$0.309832\pi$
$440$	−23.2426	−1.10805
$441$	1.00000	0.0476190
$442$	24.8910	1.18394
$443$	−27.5127	−1.30717	−0.653584	−	0.756854i	$-0.726735\pi$
$443$	−27.5127	−1.30717	−0.653584	+	0.756854i	$0.726735\pi$
$444$	9.59810	0.455506
$445$	41.2541	1.95563
$446$	0.0345070	0.00163395
$447$	−23.3411	−1.10399
$448$	−1.73760	−0.0820938
$449$	−1.35927	−0.0641481	−0.0320740	−	0.999485i	$-0.510211\pi$
$449$	−1.35927	−0.0641481	−0.0320740	+	0.999485i	$0.510211\pi$
$450$	0.490420	0.0231186
$451$	−8.88446	−0.418353
$452$	6.45475	0.303606
$453$	17.5395	0.824076
$454$	12.8419	0.602700
$455$	15.5970	0.731199
$456$	0.872224	0.0408456
$457$	8.09899	0.378855	0.189427	−	0.981895i	$-0.439337\pi$
$457$	8.09899	0.378855	0.189427	+	0.981895i	$0.439337\pi$
$458$	−12.3828	−0.578612
$459$	−7.11970	−0.332319
$460$	17.2004	0.801972
$461$	−27.6380	−1.28723	−0.643615	−	0.765349i	$-0.722566\pi$
$461$	−27.6380	−1.28723	−0.643615	+	0.765349i	$0.722566\pi$
$462$	−2.58356	−0.120198
$463$	24.0686	1.11856	0.559281	−	0.828978i	$-0.311077\pi$
$463$	24.0686	1.11856	0.559281	+	0.828978i	$0.311077\pi$
$464$	17.3903	0.807323
$465$	6.02039	0.279189
$466$	−0.446960	−0.0207050
$467$	11.7601	0.544191	0.272096	−	0.962270i	$-0.412283\pi$
$467$	11.7601	0.544191	0.272096	+	0.962270i	$0.412283\pi$
$468$	−10.9380	−0.505611
$469$	0.621432	0.0286951
$470$	−17.6064	−0.812125
$471$	14.1672	0.652789
$472$	2.08631	0.0960304
$473$	−39.5977	−1.82070
$474$	1.83671	0.0843631
$475$	0.389582	0.0178753
$476$	−12.1286	−0.555914
$477$	−2.82754	−0.129464
$478$	3.20154	0.146435
$479$	20.9908	0.959096	0.479548	−	0.877516i	$-0.340801\pi$
$479$	20.9908	0.959096	0.479548	+	0.877516i	$0.340801\pi$
$480$	−12.8510	−0.586563
$481$	36.1764	1.64950
$482$	6.15843	0.280509
$483$	4.15659	0.189131
$484$	−19.6146	−0.891572
$485$	−13.9830	−0.634937
$486$	−0.544491	−0.0246986
$487$	−13.5474	−0.613892	−0.306946	−	0.951727i	$-0.599307\pi$
$487$	−13.5474	−0.613892	−0.306946	+	0.951727i	$0.599307\pi$
$488$	−0.261140	−0.0118213
$489$	7.08946	0.320596
$490$	1.32264	0.0597509
$491$	22.8631	1.03180	0.515899	−	0.856650i	$-0.327458\pi$
$491$	22.8631	1.03180	0.515899	+	0.856650i	$0.327458\pi$
$492$	−3.18973	−0.143804
$493$	53.6204	2.41494
$494$	1.51218	0.0680360
$495$	11.5260	0.518055
$496$	−5.72282	−0.256962
$497$	11.5821	0.519527
$498$	3.04530	0.136463
$499$	−12.4093	−0.555518	−0.277759	−	0.960651i	$-0.589592\pi$
$499$	−12.4093	−0.555518	−0.277759	+	0.960651i	$0.589592\pi$
$500$	16.9633	0.758624
$501$	−3.86265	−0.172571
$502$	−7.27398	−0.324654
$503$	14.1746	0.632013	0.316006	−	0.948757i	$-0.397658\pi$
$503$	14.1746	0.632013	0.316006	+	0.948757i	$0.397658\pi$
$504$	−2.01654	−0.0898238
$505$	−16.6746	−0.742011
$506$	−10.7388	−0.477397
$507$	−28.2268	−1.25360
$508$	30.4942	1.35296
$509$	−3.91962	−0.173734	−0.0868671	−	0.996220i	$-0.527686\pi$
$509$	−3.91962	−0.173734	−0.0868671	+	0.996220i	$0.527686\pi$
$510$	−9.41681	−0.416983
$511$	−5.56783	−0.246306
$512$	21.5285	0.951432
$513$	−0.432535	−0.0190969
$514$	8.83369	0.389637
$515$	41.8577	1.84447
$516$	−14.2165	−0.625846
$517$	−63.1621	−2.77787
$518$	3.06779	0.134791
$519$	−17.4273	−0.764975
$520$	−31.4520	−1.37926
$521$	−17.3403	−0.759691	−0.379845	−	0.925050i	$-0.624023\pi$
$521$	−17.3403	−0.759691	−0.379845	+	0.925050i	$0.624023\pi$
$522$	4.10071	0.179483
$523$	39.7890	1.73985	0.869927	−	0.493181i	$-0.164166\pi$
$523$	39.7890	1.73985	0.869927	+	0.493181i	$0.164166\pi$
$524$	25.5382	1.11564
$525$	−0.900695	−0.0393095
$526$	−9.46039	−0.412493
$527$	−17.6455	−0.768651
$528$	−10.9563	−0.476813
$529$	−5.72277	−0.248816
$530$	−3.73982	−0.162447
$531$	−1.03460	−0.0448979
$532$	−0.736837	−0.0319459
$533$	−12.0225	−0.520751
$534$	−9.24711	−0.400161
$535$	38.4677	1.66310
$536$	−1.25314	−0.0541275
$537$	−8.48155	−0.366006
$538$	−13.8746	−0.598177
$539$	4.74490	0.204377
$540$	4.13810	0.178076
$541$	8.62312	0.370737	0.185369	−	0.982669i	$-0.440652\pi$
$541$	8.62312	0.370737	0.185369	+	0.982669i	$0.440652\pi$
$542$	−3.58132	−0.153831
$543$	13.9616	0.599150
$544$	37.6657	1.61490
$545$	15.7431	0.674362
$546$	−3.49607	−0.149618
$547$	8.81131	0.376744	0.188372	−	0.982098i	$-0.439679\pi$
$547$	8.81131	0.376744	0.188372	+	0.982098i	$0.439679\pi$
$548$	8.25227	0.352519
$549$	0.129499	0.00552689
$550$	2.32699	0.0992234
$551$	3.25754	0.138776
$552$	−8.38192	−0.356758
$553$	−3.37327	−0.143446
$554$	5.06542	0.215209
$555$	−13.6863	−0.580953
$556$	9.36651	0.397228
$557$	8.01392	0.339561	0.169780	−	0.985482i	$-0.445694\pi$
$557$	8.01392	0.339561	0.169780	+	0.985482i	$0.445694\pi$
$558$	−1.34947	−0.0571277
$559$	−53.5837	−2.26635
$560$	5.60905	0.237026
$561$	−33.7823	−1.42629
$562$	−6.73268	−0.284001
$563$	−33.5084	−1.41221	−0.706105	−	0.708107i	$-0.749549\pi$
$563$	−33.5084	−1.41221	−0.706105	+	0.708107i	$0.749549\pi$
$564$	−22.6767	−0.954860
$565$	−9.20410	−0.387220
$566$	0.442185	0.0185864
$567$	1.00000	0.0419961
$568$	−23.3557	−0.979982
$569$	9.95426	0.417304	0.208652	−	0.977990i	$-0.433092\pi$
$569$	9.95426	0.417304	0.208652	+	0.977990i	$0.433092\pi$
$570$	−0.572089	−0.0239622
$571$	−15.1744	−0.635029	−0.317515	−	0.948253i	$-0.602848\pi$
$571$	−15.1744	−0.635029	−0.317515	+	0.948253i	$0.602848\pi$
$572$	−51.8999	−2.17004
$573$	1.00000	0.0417756
$574$	−1.01952	−0.0425538
$575$	−3.74382	−0.156128
$576$	−1.73760	−0.0724000
$577$	−20.1826	−0.840214	−0.420107	−	0.907475i	$-0.638008\pi$
$577$	−20.1826	−0.840214	−0.420107	+	0.907475i	$0.638008\pi$
$578$	18.3440	0.763008
$579$	−5.17829	−0.215202
$580$	−31.1652	−1.29406
$581$	−5.59293	−0.232034
$582$	3.13430	0.129921
$583$	−13.4164	−0.555650
$584$	11.2278	0.464608
$585$	15.5970	0.644857
$586$	5.43570	0.224547
$587$	−30.9428	−1.27714	−0.638572	−	0.769562i	$-0.720475\pi$
$587$	−30.9428	−1.27714	−0.638572	+	0.769562i	$0.720475\pi$
$588$	1.70353	0.0702524
$589$	−1.07200	−0.0441710
$590$	−1.36841	−0.0563364
$591$	22.7249	0.934776
$592$	13.0099	0.534703
$593$	32.6869	1.34229	0.671146	−	0.741325i	$-0.265802\pi$
$593$	32.6869	1.34229	0.671146	+	0.741325i	$0.265802\pi$
$594$	−2.58356	−0.106005
$595$	17.2947	0.709014
$596$	−39.7622	−1.62872
$597$	−24.2629	−0.993015
$598$	−14.5317	−0.594247
$599$	−2.41761	−0.0987807	−0.0493904	−	0.998780i	$-0.515728\pi$
$599$	−2.41761	−0.0987807	−0.0493904	+	0.998780i	$0.515728\pi$
$600$	1.81629	0.0741495
$601$	43.8632	1.78922	0.894610	−	0.446849i	$-0.147454\pi$
$601$	43.8632	1.78922	0.894610	+	0.446849i	$0.147454\pi$
$602$	−4.54395	−0.185198
$603$	0.621432	0.0253067
$604$	29.8790	1.21576
$605$	27.9693	1.13711
$606$	3.73762	0.151830
$607$	36.7493	1.49161	0.745803	−	0.666166i	$-0.232066\pi$
$607$	36.7493	1.49161	0.745803	+	0.666166i	$0.232066\pi$
$608$	2.28826	0.0928013
$609$	−7.53128	−0.305183
$610$	0.171281	0.00693497
$611$	−85.4711	−3.45779
$612$	−12.1286	−0.490270
$613$	−1.47625	−0.0596253	−0.0298127	−	0.999556i	$-0.509491\pi$
$613$	−1.47625	−0.0596253	−0.0298127	+	0.999556i	$0.509491\pi$
$614$	−12.8828	−0.519908
$615$	4.54836	0.183408
$616$	−9.56827	−0.385517
$617$	−17.1846	−0.691827	−0.345914	−	0.938266i	$-0.612431\pi$
$617$	−17.1846	−0.691827	−0.345914	+	0.938266i	$0.612431\pi$
$618$	−9.38241	−0.377416
$619$	22.0122	0.884746	0.442373	−	0.896831i	$-0.354137\pi$
$619$	22.0122	0.884746	0.442373	+	0.896831i	$0.354137\pi$
$620$	10.2559	0.411887
$621$	4.15659	0.166798
$622$	14.1096	0.565745
$623$	16.9830	0.680411
$624$	−14.8261	−0.593520
$625$	−28.6922	−1.14769
$626$	8.77952	0.350900
$627$	−2.05234	−0.0819625
$628$	24.1342	0.963060
$629$	40.1141	1.59945
$630$	1.32264	0.0526953
$631$	26.3817	1.05024	0.525119	−	0.851029i	$-0.324021\pi$
$631$	26.3817	1.05024	0.525119	+	0.851029i	$0.324021\pi$
$632$	6.80233	0.270582
$633$	5.91255	0.235003
$634$	−5.15499	−0.204731
$635$	−43.4830	−1.72557
$636$	−4.81680	−0.190998
$637$	6.42081	0.254402
$638$	19.4575	0.770329
$639$	11.5821	0.458179
$640$	−28.0001	−1.10680
$641$	−15.6297	−0.617337	−0.308668	−	0.951170i	$-0.599883\pi$
$641$	−15.6297	−0.617337	−0.308668	+	0.951170i	$0.599883\pi$
$642$	−8.62253	−0.340304
$643$	38.5805	1.52146	0.760732	−	0.649066i	$-0.224840\pi$
$643$	38.5805	1.52146	0.760732	+	0.649066i	$0.224840\pi$
$644$	7.08087	0.279025
$645$	20.2719	0.798205
$646$	1.67677	0.0659717
$647$	−35.2958	−1.38762	−0.693811	−	0.720157i	$-0.744070\pi$
$647$	−35.2958	−1.38762	−0.693811	+	0.720157i	$0.744070\pi$
$648$	−2.01654	−0.0792171
$649$	−4.90908	−0.192698
$650$	3.14889	0.123510
$651$	2.47841	0.0971365
$652$	12.0771	0.472976
$653$	−15.8391	−0.619834	−0.309917	−	0.950764i	$-0.600301\pi$
$653$	−15.8391	−0.619834	−0.309917	+	0.950764i	$0.600301\pi$
$654$	−3.52883	−0.137988
$655$	−36.4160	−1.42289
$656$	−4.32356	−0.168807
$657$	−5.56783	−0.217222
$658$	−7.24803	−0.282558
$659$	−31.3409	−1.22087	−0.610434	−	0.792067i	$-0.709005\pi$
$659$	−31.3409	−1.22087	−0.610434	+	0.792067i	$0.709005\pi$
$660$	19.6349	0.764287
$661$	−7.48339	−0.291070	−0.145535	−	0.989353i	$-0.546490\pi$
$661$	−7.48339	−0.291070	−0.145535	+	0.989353i	$0.546490\pi$
$662$	10.2613	0.398818
$663$	−45.7142	−1.77539
$664$	11.2784	0.437685
$665$	1.05069	0.0407439
$666$	3.06779	0.118875
$667$	−31.3044	−1.21211
$668$	−6.58014	−0.254593
$669$	−0.0633748	−0.00245021
$670$	0.821932	0.0317540
$671$	0.614461	0.0237210
$672$	−5.29035	−0.204080
$673$	−36.5905	−1.41046	−0.705230	−	0.708979i	$-0.749156\pi$
$673$	−36.5905	−1.41046	−0.705230	+	0.708979i	$0.749156\pi$
$674$	6.62146	0.255049
$675$	−0.900695	−0.0346678
$676$	−48.0852	−1.84943
$677$	−6.93554	−0.266554	−0.133277	−	0.991079i	$-0.542550\pi$
$677$	−6.93554	−0.266554	−0.133277	+	0.991079i	$0.542550\pi$
$678$	2.06310	0.0792329
$679$	−5.75638	−0.220910
$680$	−34.8754	−1.33741
$681$	−23.5851	−0.903785
$682$	−6.40311	−0.245188
$683$	−6.94099	−0.265590	−0.132795	−	0.991144i	$-0.542395\pi$
$683$	−6.94099	−0.265590	−0.132795	+	0.991144i	$0.542395\pi$
$684$	−0.736837	−0.0281737
$685$	−11.7673	−0.449604
$686$	0.544491	0.0207888
$687$	22.7420	0.867662
$688$	−19.2699	−0.734660
$689$	−18.1551	−0.691654
$690$	5.49768	0.209293
$691$	40.9624	1.55828	0.779141	−	0.626849i	$-0.215656\pi$
$691$	40.9624	1.55828	0.779141	+	0.626849i	$0.215656\pi$
$692$	−29.6880	−1.12857
$693$	4.74490	0.180244
$694$	10.0852	0.382827
$695$	−13.3561	−0.506626
$696$	15.1871	0.575666
$697$	−13.3311	−0.504951
$698$	5.93865	0.224781
$699$	0.820877	0.0310484
$700$	−1.53436	−0.0579934
$701$	−0.580865	−0.0219390	−0.0109695	−	0.999940i	$-0.503492\pi$
$701$	−0.580865	−0.0219390	−0.0109695	+	0.999940i	$0.503492\pi$
$702$	−3.49607	−0.131951
$703$	2.43701	0.0919136
$704$	−8.24474	−0.310735
$705$	32.3356	1.21783
$706$	−20.0051	−0.752900
$707$	−6.86443	−0.258164
$708$	−1.76247	−0.0662378
$709$	20.1457	0.756588	0.378294	−	0.925686i	$-0.376511\pi$
$709$	20.1457	0.756588	0.378294	+	0.925686i	$0.376511\pi$
$710$	15.3189	0.574909
$711$	−3.37327	−0.126507
$712$	−34.2469	−1.28346
$713$	10.3017	0.385803
$714$	−3.87661	−0.145079
$715$	74.0063	2.76768
$716$	−14.4486	−0.539968
$717$	−5.87988	−0.219588
$718$	−11.3306	−0.422853
$719$	15.5751	0.580854	0.290427	−	0.956897i	$-0.406203\pi$
$719$	15.5751	0.580854	0.290427	+	0.956897i	$0.406203\pi$
$720$	5.60905	0.209037
$721$	17.2315	0.641736
$722$	−10.2435	−0.381222
$723$	−11.3104	−0.420640
$724$	23.7840	0.883926
$725$	6.78338	0.251928
$726$	−6.26932	−0.232676
$727$	5.81925	0.215824	0.107912	−	0.994160i	$-0.465584\pi$
$727$	5.81925	0.215824	0.107912	+	0.994160i	$0.465584\pi$
$728$	−12.9478	−0.479878
$729$	1.00000	0.0370370
$730$	−7.36425	−0.272563
$731$	−59.4162	−2.19759
$732$	0.220606	0.00815382
$733$	−10.8622	−0.401205	−0.200602	−	0.979673i	$-0.564290\pi$
$733$	−10.8622	−0.401205	−0.200602	+	0.979673i	$0.564290\pi$
$734$	1.40047	0.0516922
$735$	−2.42913	−0.0896000
$736$	−21.9898	−0.810555
$737$	2.94864	0.108614
$738$	−1.01952	−0.0375289
$739$	2.87850	0.105887	0.0529436	−	0.998598i	$-0.483140\pi$
$739$	2.87850	0.105887	0.0529436	+	0.998598i	$0.483140\pi$
$740$	−23.3151	−0.857079
$741$	−2.77723	−0.102024
$742$	−1.53957	−0.0565194
$743$	−17.2443	−0.632631	−0.316316	−	0.948654i	$-0.602446\pi$
$743$	−17.2443	−0.632631	−0.316316	+	0.948654i	$0.602446\pi$
$744$	−4.99781	−0.183228
$745$	56.6986	2.07728
$746$	−3.89358	−0.142554
$747$	−5.59293	−0.204635
$748$	−57.5491	−2.10420
$749$	15.8360	0.578633
$750$	5.42191	0.197980
$751$	14.8278	0.541074	0.270537	−	0.962710i	$-0.412799\pi$
$751$	14.8278	0.541074	0.270537	+	0.962710i	$0.412799\pi$
$752$	−30.7374	−1.12088
$753$	13.3592	0.486838
$754$	26.3299	0.958878
$755$	−42.6057	−1.55058
$756$	1.70353	0.0619568
$757$	20.6458	0.750383	0.375192	−	0.926947i	$-0.377577\pi$
$757$	20.6458	0.750383	0.375192	+	0.926947i	$0.377577\pi$
$758$	3.79486	0.137835
$759$	19.7226	0.715885
$760$	−2.11875	−0.0768551
$761$	40.4100	1.46486	0.732430	−	0.680842i	$-0.238386\pi$
$761$	40.4100	1.46486	0.732430	+	0.680842i	$0.238386\pi$
$762$	9.74672	0.353087
$763$	6.48096	0.234627
$764$	1.70353	0.0616315
$765$	17.2947	0.625291
$766$	13.0316	0.470849
$767$	−6.64298	−0.239864
$768$	2.80104	0.101074
$769$	−15.5961	−0.562408	−0.281204	−	0.959648i	$-0.590734\pi$
$769$	−15.5961	−0.562408	−0.281204	+	0.959648i	$0.590734\pi$
$770$	6.27580	0.226164
$771$	−16.2238	−0.584284
$772$	−8.82136	−0.317488
$773$	−39.0077	−1.40301	−0.701505	−	0.712665i	$-0.747488\pi$
$773$	−39.0077	−1.40301	−0.701505	+	0.712665i	$0.747488\pi$
$774$	−4.54395	−0.163329
$775$	−2.23229	−0.0801862
$776$	11.6080	0.416702
$777$	−5.63424	−0.202127
$778$	3.82078	0.136981
$779$	−0.809889	−0.0290173
$780$	26.5700	0.951358
$781$	54.9557	1.96647
$782$	−16.1135	−0.576217
$783$	−7.53128	−0.269146
$784$	2.30907	0.0824669
$785$	−34.4140	−1.22829
$786$	8.16266	0.291152
$787$	−42.0928	−1.50045	−0.750223	−	0.661185i	$-0.770054\pi$
$787$	−42.0928	−1.50045	−0.750223	+	0.661185i	$0.770054\pi$
$788$	38.7125	1.37908
$789$	17.3748	0.618558
$790$	−4.46163	−0.158738
$791$	−3.78905	−0.134723
$792$	−9.56827	−0.339994
$793$	0.831490	0.0295271
$794$	8.51819	0.302299
$795$	6.86847	0.243600
$796$	−41.3326	−1.46500
$797$	5.02017	0.177824	0.0889118	−	0.996040i	$-0.471661\pi$
$797$	5.02017	0.177824	0.0889118	+	0.996040i	$0.471661\pi$
$798$	−0.235512	−0.00833702
$799$	−94.7744	−3.35288
$800$	4.76499	0.168468
$801$	16.9830	0.600066
$802$	−15.4436	−0.545334
$803$	−26.4188	−0.932300
$804$	1.05863	0.0373349
$805$	−10.0969	−0.355869
$806$	−8.66470	−0.305201
$807$	25.4818	0.897002
$808$	13.8424	0.486974
$809$	−14.0541	−0.494117	−0.247058	−	0.969001i	$-0.579464\pi$
$809$	−14.0541	−0.494117	−0.247058	+	0.969001i	$0.579464\pi$
$810$	1.32264	0.0464729
$811$	16.7276	0.587384	0.293692	−	0.955900i	$-0.405116\pi$
$811$	16.7276	0.587384	0.293692	+	0.955900i	$0.405116\pi$
$812$	−12.8298	−0.450236
$813$	6.57737	0.230678
$814$	14.5564	0.510201
$815$	−17.2213	−0.603234
$816$	−16.4399	−0.575512
$817$	−3.60965	−0.126286
$818$	−1.85174	−0.0647447
$819$	6.42081	0.224361
$820$	7.74827	0.270581
$821$	−7.42690	−0.259201	−0.129600	−	0.991566i	$-0.541369\pi$
$821$	−7.42690	−0.259201	−0.129600	+	0.991566i	$0.541369\pi$
$822$	2.63763	0.0919980
$823$	27.1986	0.948083	0.474042	−	0.880502i	$-0.342795\pi$
$823$	27.1986	0.948083	0.474042	+	0.880502i	$0.342795\pi$
$824$	−34.7480	−1.21051
$825$	−4.27371	−0.148791
$826$	−0.563331	−0.0196008
$827$	17.8260	0.619872	0.309936	−	0.950757i	$-0.399692\pi$
$827$	17.8260	0.619872	0.309936	+	0.950757i	$0.399692\pi$
$828$	7.08087	0.246077
$829$	−24.9615	−0.866949	−0.433475	−	0.901166i	$-0.642713\pi$
$829$	−24.9615	−0.866949	−0.433475	+	0.901166i	$0.642713\pi$
$830$	−7.39744	−0.256769
$831$	−9.30303	−0.322719
$832$	−11.1568	−0.386792
$833$	7.11970	0.246683
$834$	2.99377	0.103666
$835$	9.38291	0.324709
$836$	−3.49622	−0.120919
$837$	2.47841	0.0856663
$838$	−16.5671	−0.572300
$839$	−54.6690	−1.88738	−0.943692	−	0.330824i	$-0.892673\pi$
$839$	−54.6690	−1.88738	−0.943692	+	0.330824i	$0.892673\pi$
$840$	4.89844	0.169012
$841$	27.7201	0.955866
$842$	−10.0342	−0.345801
$843$	12.3651	0.425876
$844$	10.0722	0.346700
$845$	68.5667	2.35877
$846$	−7.24803	−0.249193
$847$	11.5141	0.395629
$848$	−6.52899	−0.224207
$849$	−0.812108	−0.0278715
$850$	3.49164	0.119762
$851$	−23.4192	−0.802801
$852$	19.7304	0.675952
$853$	−3.95191	−0.135311	−0.0676555	−	0.997709i	$-0.521552\pi$
$853$	−3.95191	−0.135311	−0.0676555	+	0.997709i	$0.521552\pi$
$854$	0.0705112	0.00241284
$855$	1.05069	0.0359327
$856$	−31.9338	−1.09148
$857$	−24.9266	−0.851477	−0.425739	−	0.904846i	$-0.639986\pi$
$857$	−24.9266	−0.851477	−0.425739	+	0.904846i	$0.639986\pi$
$858$	−16.5885	−0.566323
$859$	30.4513	1.03898	0.519492	−	0.854475i	$-0.326121\pi$
$859$	30.4513	1.03898	0.519492	+	0.854475i	$0.326121\pi$
$860$	34.5338	1.17759
$861$	1.87242	0.0638120
$862$	−3.93070	−0.133880
$863$	24.6711	0.839815	0.419907	−	0.907567i	$-0.362063\pi$
$863$	24.6711	0.839815	0.419907	+	0.907567i	$0.362063\pi$
$864$	−5.29035	−0.179981
$865$	42.3333	1.43938
$866$	0.416267	0.0141453
$867$	−33.6901	−1.14418
$868$	4.22204	0.143305
$869$	−16.0058	−0.542960
$870$	−9.96118	−0.337716
$871$	3.99010	0.135199
$872$	−13.0691	−0.442576
$873$	−5.75638	−0.194824
$874$	−0.978925	−0.0331126
$875$	−9.95776	−0.336634
$876$	−9.48497	−0.320467
$877$	−26.0779	−0.880589	−0.440294	−	0.897854i	$-0.645126\pi$
$877$	−26.0779	−0.880589	−0.440294	+	0.897854i	$0.645126\pi$
$878$	12.8349	0.433156
$879$	−9.98309	−0.336721
$880$	26.6144	0.897170
$881$	−39.1319	−1.31839	−0.659194	−	0.751973i	$-0.729102\pi$
$881$	−39.1319	−1.31839	−0.659194	+	0.751973i	$0.729102\pi$
$882$	0.544491	0.0183340
$883$	5.50207	0.185160	0.0925798	−	0.995705i	$-0.470489\pi$
$883$	5.50207	0.185160	0.0925798	+	0.995705i	$0.470489\pi$
$884$	−77.8756	−2.61924
$885$	2.51319	0.0844798
$886$	−14.9804	−0.503277
$887$	55.9432	1.87839	0.939195	−	0.343385i	$-0.111573\pi$
$887$	55.9432	1.87839	0.939195	+	0.343385i	$0.111573\pi$
$888$	11.3617	0.381273
$889$	−17.9006	−0.600367
$890$	22.4625	0.752944
$891$	4.74490	0.158960
$892$	−0.107961	−0.00361480
$893$	−5.75773	−0.192675
$894$	−12.7090	−0.425053
$895$	20.6028	0.688677
$896$	−11.5268	−0.385083
$897$	26.6887	0.891109
$898$	−0.740112	−0.0246979
$899$	−18.6656	−0.622532
$900$	−1.53436	−0.0511453
$901$	−20.1312	−0.670669
$902$	−4.83751	−0.161071
$903$	8.34532	0.277715
$904$	7.64076	0.254128
$905$	−33.9146	−1.12736
$906$	9.55008	0.317280
$907$	−21.4376	−0.711824	−0.355912	−	0.934519i	$-0.615830\pi$
$907$	−21.4376	−0.711824	−0.355912	+	0.934519i	$0.615830\pi$
$908$	−40.1780	−1.33335
$909$	−6.86443	−0.227679
$910$	8.49243	0.281521
$911$	8.81580	0.292080	0.146040	−	0.989279i	$-0.453347\pi$
$911$	8.81580	0.292080	0.146040	+	0.989279i	$0.453347\pi$
$912$	−0.998755	−0.0330721
$913$	−26.5379	−0.878276
$914$	4.40983	0.145864
$915$	−0.314571	−0.0103994
$916$	38.7417	1.28006
$917$	−14.9914	−0.495058
$918$	−3.87661	−0.127947
$919$	−11.0852	−0.365667	−0.182834	−	0.983144i	$-0.558527\pi$
$919$	−11.0852	−0.365667	−0.182834	+	0.983144i	$0.558527\pi$
$920$	20.3608	0.671276
$921$	23.6603	0.779633
$922$	−15.0486	−0.495601
$923$	74.3662	2.44779
$924$	8.08308	0.265914
$925$	5.07473	0.166856
$926$	13.1051	0.430662
$927$	17.2315	0.565958
$928$	39.8431	1.30791
$929$	10.3233	0.338697	0.169349	−	0.985556i	$-0.445834\pi$
$929$	10.3233	0.338697	0.169349	+	0.985556i	$0.445834\pi$
$930$	3.27805	0.107491
$931$	0.432535	0.0141758
$932$	1.39839	0.0458057
$933$	−25.9134	−0.848368
$934$	6.40325	0.209521
$935$	82.0617	2.68370
$936$	−12.9478	−0.423212
$937$	−20.7793	−0.678831	−0.339415	−	0.940637i	$-0.610229\pi$
$937$	−20.7793	−0.678831	−0.339415	+	0.940637i	$0.610229\pi$
$938$	0.338364	0.0110480
$939$	−16.1243	−0.526196
$940$	55.0847	1.79666
$941$	26.3082	0.857623	0.428812	−	0.903394i	$-0.358932\pi$
$941$	26.3082	0.857623	0.428812	+	0.903394i	$0.358932\pi$
$942$	7.71390	0.251332
$943$	7.78289	0.253446
$944$	−2.38897	−0.0777543
$945$	−2.42913	−0.0790198
$946$	−21.5606	−0.700995
$947$	−23.9416	−0.777999	−0.388999	−	0.921238i	$-0.627179\pi$
$947$	−23.9416	−0.777999	−0.388999	+	0.921238i	$0.627179\pi$
$948$	−5.74646	−0.186636
$949$	−35.7500	−1.16049
$950$	0.212124	0.00688221
$951$	9.46753	0.307006
$952$	−14.3571	−0.465318
$953$	−48.2753	−1.56379	−0.781895	−	0.623411i	$-0.785746\pi$
$953$	−48.2753	−1.56379	−0.781895	+	0.623411i	$0.785746\pi$
$954$	−1.53957	−0.0498454
$955$	−2.42913	−0.0786049
$956$	−10.0165	−0.323958
$957$	−35.7352	−1.15515
$958$	11.4293	0.369265
$959$	−4.84422	−0.156428
$960$	4.22086	0.136228
$961$	−24.8575	−0.801855
$962$	19.6977	0.635080
$963$	15.8360	0.510307
$964$	−19.2677	−0.620570
$965$	12.5788	0.404924
$966$	2.26323	0.0728181
$967$	−52.2927	−1.68162	−0.840811	−	0.541329i	$-0.817921\pi$
$967$	−52.2927	−1.68162	−0.840811	+	0.541329i	$0.817921\pi$
$968$	−23.2186	−0.746274
$969$	−3.07952	−0.0989285
$970$	−7.61363	−0.244459
$971$	−50.4842	−1.62012	−0.810058	−	0.586349i	$-0.800565\pi$
$971$	−50.4842	−1.62012	−0.810058	+	0.586349i	$0.800565\pi$
$972$	1.70353	0.0546407
$973$	−5.49829	−0.176267
$974$	−7.37644	−0.236356
$975$	−5.78319	−0.185210
$976$	0.299023	0.00957150
$977$	−6.87076	−0.219815	−0.109908	−	0.993942i	$-0.535055\pi$
$977$	−6.87076	−0.219815	−0.109908	+	0.993942i	$0.535055\pi$
$978$	3.86015	0.123434
$979$	80.5828	2.57544
$980$	−4.13810	−0.132187
$981$	6.48096	0.206921
$982$	12.4487	0.397256
$983$	−6.10040	−0.194572	−0.0972862	−	0.995256i	$-0.531016\pi$
$983$	−6.10040	−0.194572	−0.0972862	+	0.995256i	$0.531016\pi$
$984$	−3.77581	−0.120368
$985$	−55.2018	−1.75887
$986$	29.1958	0.929785
$987$	13.3116	0.423712
$988$	−4.73109	−0.150516
$989$	34.6881	1.10302
$990$	6.27580	0.199458
$991$	54.8838	1.74344	0.871721	−	0.490003i	$-0.163004\pi$
$991$	54.8838	1.74344	0.871721	+	0.490003i	$0.163004\pi$
$992$	−13.1116	−0.416295
$993$	−18.8457	−0.598051
$994$	6.30633	0.200025
$995$	58.9379	1.86846
$996$	−9.52772	−0.301897
$997$	−26.1103	−0.826922	−0.413461	−	0.910522i	$-0.635680\pi$
$997$	−26.1103	−0.826922	−0.413461	+	0.910522i	$0.635680\pi$
$998$	−6.75677	−0.213882
$999$	−5.63424	−0.178260

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.l.1.18	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.l.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+0.544491 q^{2} -1.00000 q^{3} -1.70353 q^{4} +2.42913 q^{5} -0.544491 q^{6} +1.00000 q^{7} -2.01654 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.544491 q^{2} -1.00000 q^{3} -1.70353 q^{4} +2.42913 q^{5} -0.544491 q^{6} +1.00000 q^{7} -2.01654 q^{8} +1.00000 q^{9} +1.32264 q^{10} +4.74490 q^{11} +1.70353 q^{12} +6.42081 q^{13} +0.544491 q^{14} -2.42913 q^{15} +2.30907 q^{16} +7.11970 q^{17} +0.544491 q^{18} +0.432535 q^{19} -4.13810 q^{20} -1.00000 q^{21} +2.58356 q^{22} -4.15659 q^{23} +2.01654 q^{24} +0.900695 q^{25} +3.49607 q^{26} -1.00000 q^{27} -1.70353 q^{28} +7.53128 q^{29} -1.32264 q^{30} -2.47841 q^{31} +5.29035 q^{32} -4.74490 q^{33} +3.87661 q^{34} +2.42913 q^{35} -1.70353 q^{36} +5.63424 q^{37} +0.235512 q^{38} -6.42081 q^{39} -4.89844 q^{40} -1.87242 q^{41} -0.544491 q^{42} -8.34532 q^{43} -8.08308 q^{44} +2.42913 q^{45} -2.26323 q^{46} -13.3116 q^{47} -2.30907 q^{48} +1.00000 q^{49} +0.490420 q^{50} -7.11970 q^{51} -10.9380 q^{52} -2.82754 q^{53} -0.544491 q^{54} +11.5260 q^{55} -2.01654 q^{56} -0.432535 q^{57} +4.10071 q^{58} -1.03460 q^{59} +4.13810 q^{60} +0.129499 q^{61} -1.34947 q^{62} +1.00000 q^{63} -1.73760 q^{64} +15.5970 q^{65} -2.58356 q^{66} +0.621432 q^{67} -12.1286 q^{68} +4.15659 q^{69} +1.32264 q^{70} +11.5821 q^{71} -2.01654 q^{72} -5.56783 q^{73} +3.06779 q^{74} -0.900695 q^{75} -0.736837 q^{76} +4.74490 q^{77} -3.49607 q^{78} -3.37327 q^{79} +5.60905 q^{80} +1.00000 q^{81} -1.01952 q^{82} -5.59293 q^{83} +1.70353 q^{84} +17.2947 q^{85} -4.54395 q^{86} -7.53128 q^{87} -9.56827 q^{88} +16.9830 q^{89} +1.32264 q^{90} +6.42081 q^{91} +7.08087 q^{92} +2.47841 q^{93} -7.24803 q^{94} +1.05069 q^{95} -5.29035 q^{96} -5.75638 q^{97} +0.544491 q^{98} +4.74490 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) \) 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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