LMFDB - Embedded newform 1805.2.a.q.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.5822000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 5x^{3} + 14x^{2} + x - 1 $ x^6 - x^5 - 8x^4 + 5x^3 + 14*x^2 + x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.47848$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.860448 q^{2} -0.867394 q^{3} -1.25963 q^{4} -1.00000 q^{5} -0.746348 q^{6} -0.263921 q^{7} -2.80474 q^{8} -2.24763 q^{9} +O(q^{10})$	\(q+0.860448 q^{2} -0.867394 q^{3} -1.25963 q^{4} -1.00000 q^{5} -0.746348 q^{6} -0.263921 q^{7} -2.80474 q^{8} -2.24763 q^{9} -0.860448 q^{10} -5.32135 q^{11} +1.09259 q^{12} -1.19606 q^{13} -0.227090 q^{14} +0.867394 q^{15} +0.105921 q^{16} +4.46010 q^{17} -1.93397 q^{18} +1.25963 q^{20} +0.228924 q^{21} -4.57874 q^{22} -0.920897 q^{23} +2.43282 q^{24} +1.00000 q^{25} -1.02914 q^{26} +4.55176 q^{27} +0.332443 q^{28} +9.87581 q^{29} +0.746348 q^{30} +0.0400121 q^{31} +5.70062 q^{32} +4.61570 q^{33} +3.83769 q^{34} +0.263921 q^{35} +2.83118 q^{36} -7.76091 q^{37} +1.03745 q^{39} +2.80474 q^{40} -6.27419 q^{41} +0.196977 q^{42} +10.0853 q^{43} +6.70292 q^{44} +2.24763 q^{45} -0.792384 q^{46} +8.44271 q^{47} -0.0918755 q^{48} -6.93035 q^{49} +0.860448 q^{50} -3.86866 q^{51} +1.50659 q^{52} -4.20047 q^{53} +3.91655 q^{54} +5.32135 q^{55} +0.740231 q^{56} +8.49762 q^{58} +8.10775 q^{59} -1.09259 q^{60} +0.218505 q^{61} +0.0344283 q^{62} +0.593196 q^{63} +4.69325 q^{64} +1.19606 q^{65} +3.97157 q^{66} -3.76600 q^{67} -5.61807 q^{68} +0.798780 q^{69} +0.227090 q^{70} -10.1077 q^{71} +6.30402 q^{72} +9.91093 q^{73} -6.67786 q^{74} -0.867394 q^{75} +1.40442 q^{77} +0.892673 q^{78} -0.00558375 q^{79} -0.105921 q^{80} +2.79472 q^{81} -5.39862 q^{82} +8.82190 q^{83} -0.288359 q^{84} -4.46010 q^{85} +8.67786 q^{86} -8.56621 q^{87} +14.9250 q^{88} +0.431648 q^{89} +1.93397 q^{90} +0.315664 q^{91} +1.15999 q^{92} -0.0347063 q^{93} +7.26452 q^{94} -4.94469 q^{96} +17.3729 q^{97} -5.96320 q^{98} +11.9604 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9} + 2 q^{10} + 15 q^{11} + 20 q^{12} - 6 q^{13} - 20 q^{14} + 4 q^{15} + 20 q^{16} + 5 q^{17} + 8 q^{18} - 8 q^{20} - 7 q^{21} - 14 q^{22} + 18 q^{24} + 6 q^{25} - 22 q^{26} - 28 q^{27} + 10 q^{28} + 20 q^{29} - 8 q^{30} - 12 q^{31} + 8 q^{32} - q^{33} - 7 q^{35} - 14 q^{36} - 20 q^{37} + 16 q^{39} - 8 q^{41} - 30 q^{42} + 27 q^{43} + 46 q^{44} - 10 q^{45} - 16 q^{46} - 8 q^{47} + 24 q^{48} + 11 q^{49} - 2 q^{50} + 11 q^{51} - 4 q^{52} - 19 q^{53} + 30 q^{54} - 15 q^{55} - 62 q^{56} + 20 q^{58} + 41 q^{59} - 20 q^{60} + 6 q^{61} - 30 q^{62} - 18 q^{63} + 48 q^{64} + 6 q^{65} + 46 q^{66} + 15 q^{67} - 14 q^{68} + 10 q^{69} + 20 q^{70} - 2 q^{71} + 68 q^{72} + 8 q^{73} + 2 q^{74} - 4 q^{75} + 21 q^{77} - 46 q^{78} - 18 q^{79} - 20 q^{80} + 50 q^{81} - 18 q^{82} - 10 q^{83} - 4 q^{84} - 5 q^{85} + 10 q^{86} - 14 q^{87} + 52 q^{88} - 17 q^{89} - 8 q^{90} + 23 q^{91} + 28 q^{92} + 10 q^{93} + 28 q^{94} + 26 q^{96} + 4 q^{97} - 50 q^{98} + 58 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9 + 2 * q^10 + 15 * q^11 + 20 * q^12 - 6 * q^13 - 20 * q^14 + 4 * q^15 + 20 * q^16 + 5 * q^17 + 8 * q^18 - 8 * q^20 - 7 * q^21 - 14 * q^22 + 18 * q^24 + 6 * q^25 - 22 * q^26 - 28 * q^27 + 10 * q^28 + 20 * q^29 - 8 * q^30 - 12 * q^31 + 8 * q^32 - q^33 - 7 * q^35 - 14 * q^36 - 20 * q^37 + 16 * q^39 - 8 * q^41 - 30 * q^42 + 27 * q^43 + 46 * q^44 - 10 * q^45 - 16 * q^46 - 8 * q^47 + 24 * q^48 + 11 * q^49 - 2 * q^50 + 11 * q^51 - 4 * q^52 - 19 * q^53 + 30 * q^54 - 15 * q^55 - 62 * q^56 + 20 * q^58 + 41 * q^59 - 20 * q^60 + 6 * q^61 - 30 * q^62 - 18 * q^63 + 48 * q^64 + 6 * q^65 + 46 * q^66 + 15 * q^67 - 14 * q^68 + 10 * q^69 + 20 * q^70 - 2 * q^71 + 68 * q^72 + 8 * q^73 + 2 * q^74 - 4 * q^75 + 21 * q^77 - 46 * q^78 - 18 * q^79 - 20 * q^80 + 50 * q^81 - 18 * q^82 - 10 * q^83 - 4 * q^84 - 5 * q^85 + 10 * q^86 - 14 * q^87 + 52 * q^88 - 17 * q^89 - 8 * q^90 + 23 * q^91 + 28 * q^92 + 10 * q^93 + 28 * q^94 + 26 * q^96 + 4 * q^97 - 50 * q^98 + 58 * 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 $

$2$	0.860448	0.608429	0.304214	−	0.952604i	$-0.401606\pi$
$2$	0.860448	0.608429	0.304214	+	0.952604i	$0.401606\pi$
$3$	−0.867394	−0.500790	−0.250395	−	0.968144i	$-0.580560\pi$
$3$	−0.867394	−0.500790	−0.250395	+	0.968144i	$0.580560\pi$
$4$	−1.25963	−0.629814
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.746348	−0.304695
$7$	−0.263921	−0.0997528	−0.0498764	−	0.998755i	$-0.515883\pi$
$7$	−0.263921	−0.0997528	−0.0498764	+	0.998755i	$0.515883\pi$
$8$	−2.80474	−0.991626
$9$	−2.24763	−0.749209
$10$	−0.860448	−0.272098
$11$	−5.32135	−1.60445	−0.802223	−	0.597024i	$-0.796350\pi$
$11$	−5.32135	−1.60445	−0.802223	+	0.597024i	$0.796350\pi$
$12$	1.09259	0.315405
$13$	−1.19606	−0.331726	−0.165863	−	0.986149i	$-0.553041\pi$
$13$	−1.19606	−0.331726	−0.165863	+	0.986149i	$0.553041\pi$
$14$	−0.227090	−0.0606925
$15$	0.867394	0.223960
$16$	0.105921	0.0264803
$17$	4.46010	1.08173	0.540867	−	0.841108i	$-0.318096\pi$
$17$	4.46010	1.08173	0.540867	+	0.841108i	$0.318096\pi$
$18$	−1.93397	−0.455841
$19$	0	0
$19$	0	0
$20$	1.25963	0.281662
$21$	0.228924	0.0499552
$22$	−4.57874	−0.976191
$23$	−0.920897	−0.192020	−0.0960101	−	0.995380i	$-0.530608\pi$
$23$	−0.920897	−0.192020	−0.0960101	+	0.995380i	$0.530608\pi$
$24$	2.43282	0.496596
$25$	1.00000	0.200000
$26$	−1.02914	−0.201832
$27$	4.55176	0.875987
$28$	0.332443	0.0628257
$29$	9.87581	1.83389	0.916946	−	0.399012i	$-0.130647\pi$
$29$	9.87581	1.83389	0.916946	+	0.399012i	$0.130647\pi$
$30$	0.746348	0.136264
$31$	0.0400121	0.00718639	0.00359319	−	0.999994i	$-0.498856\pi$
$31$	0.0400121	0.00718639	0.00359319	+	0.999994i	$0.498856\pi$
$32$	5.70062	1.00774
$33$	4.61570	0.803491
$34$	3.83769	0.658158
$35$	0.263921	0.0446108
$36$	2.83118	0.471863
$37$	−7.76091	−1.27589	−0.637943	−	0.770084i	$-0.720214\pi$
$37$	−7.76091	−1.27589	−0.637943	+	0.770084i	$0.720214\pi$
$38$	0	0
$39$	1.03745	0.166125
$40$	2.80474	0.443469
$41$	−6.27419	−0.979864	−0.489932	−	0.871761i	$-0.662978\pi$
$41$	−6.27419	−0.979864	−0.489932	+	0.871761i	$0.662978\pi$
$42$	0.196977	0.0303942
$43$	10.0853	1.53799	0.768995	−	0.639254i	$-0.220757\pi$
$43$	10.0853	1.53799	0.768995	+	0.639254i	$0.220757\pi$
$44$	6.70292	1.01050
$45$	2.24763	0.335057
$46$	−0.792384	−0.116831
$47$	8.44271	1.23150	0.615748	−	0.787943i	$-0.288854\pi$
$47$	8.44271	1.23150	0.615748	+	0.787943i	$0.288854\pi$
$48$	−0.0918755	−0.0132611
$49$	−6.93035	−0.990049
$50$	0.860448	0.121686
$51$	−3.86866	−0.541721
$52$	1.50659	0.208926
$53$	−4.20047	−0.576979	−0.288490	−	0.957483i	$-0.593153\pi$
$53$	−4.20047	−0.576979	−0.288490	+	0.957483i	$0.593153\pi$
$54$	3.91655	0.532976
$55$	5.32135	0.717530
$56$	0.740231	0.0989175
$57$	0	0
$58$	8.49762	1.11579
$59$	8.10775	1.05554	0.527770	−	0.849387i	$-0.323028\pi$
$59$	8.10775	1.05554	0.527770	+	0.849387i	$0.323028\pi$
$60$	−1.09259	−0.141053
$61$	0.218505	0.0279768	0.0139884	−	0.999902i	$-0.495547\pi$
$61$	0.218505	0.0279768	0.0139884	+	0.999902i	$0.495547\pi$
$62$	0.0344283	0.00437240
$63$	0.593196	0.0747357
$64$	4.69325	0.586656
$65$	1.19606	0.148352
$66$	3.97157	0.488867
$67$	−3.76600	−0.460090	−0.230045	−	0.973180i	$-0.573887\pi$
$67$	−3.76600	−0.460090	−0.230045	+	0.973180i	$0.573887\pi$
$68$	−5.61807	−0.681291
$69$	0.798780	0.0961618
$70$	0.227090	0.0271425
$71$	−10.1077	−1.19956	−0.599780	−	0.800165i	$-0.704745\pi$
$71$	−10.1077	−1.19956	−0.599780	+	0.800165i	$0.704745\pi$
$72$	6.30402	0.742936
$73$	9.91093	1.15999	0.579993	−	0.814621i	$-0.303055\pi$
$73$	9.91093	1.15999	0.579993	+	0.814621i	$0.303055\pi$
$74$	−6.67786	−0.776286
$75$	−0.867394	−0.100158
$76$	0	0
$77$	1.40442	0.160048
$78$	0.892673	0.101075
$79$	−0.00558375	−0.000628221 0	−0.000314111	−	1.00000i	$-0.500100\pi$
$79$	−0.00558375	−0.000628221 0	−0.000314111		1.00000i	$0.500100\pi$
$80$	−0.105921	−0.0118424
$81$	2.79472	0.310524
$82$	−5.39862	−0.596177
$83$	8.82190	0.968329	0.484165	−	0.874977i	$-0.339124\pi$
$83$	8.82190	0.968329	0.484165	+	0.874977i	$0.339124\pi$
$84$	−0.288359	−0.0314625
$85$	−4.46010	−0.483766
$86$	8.67786	0.935758
$87$	−8.56621	−0.918395
$88$	14.9250	1.59101
$89$	0.431648	0.0457546	0.0228773	−	0.999738i	$-0.492717\pi$
$89$	0.431648	0.0457546	0.0228773	+	0.999738i	$0.492717\pi$
$90$	1.93397	0.203858
$91$	0.315664	0.0330906
$92$	1.15999	0.120937
$93$	−0.0347063	−0.00359887
$94$	7.26452	0.749278
$95$	0	0
$96$	−4.94469	−0.504665
$97$	17.3729	1.76395	0.881973	−	0.471299i	$-0.156215\pi$
$97$	17.3729	1.76395	0.881973	+	0.471299i	$0.156215\pi$
$98$	−5.96320	−0.602375
$99$	11.9604	1.20207
$100$	−1.25963	−0.125963
$101$	−8.95142	−0.890699	−0.445350	−	0.895357i	$-0.646921\pi$
$101$	−8.95142	−0.890699	−0.445350	+	0.895357i	$0.646921\pi$
$102$	−3.32879	−0.329599
$103$	−5.66535	−0.558224	−0.279112	−	0.960259i	$-0.590040\pi$
$103$	−5.66535	−0.558224	−0.279112	+	0.960259i	$0.590040\pi$
$104$	3.35463	0.328948
$105$	−0.228924	−0.0223406
$106$	−3.61429	−0.351051
$107$	−8.52693	−0.824329	−0.412165	−	0.911109i	$-0.635227\pi$
$107$	−8.52693	−0.824329	−0.412165	+	0.911109i	$0.635227\pi$
$108$	−5.73353	−0.551709
$109$	−7.01751	−0.672156	−0.336078	−	0.941834i	$-0.609101\pi$
$109$	−7.01751	−0.672156	−0.336078	+	0.941834i	$0.609101\pi$
$110$	4.57874	0.436566
$111$	6.73176	0.638951
$112$	−0.0279549	−0.00264149
$113$	−8.74027	−0.822215	−0.411108	−	0.911587i	$-0.634858\pi$
$113$	−8.74027	−0.822215	−0.411108	+	0.911587i	$0.634858\pi$
$114$	0	0
$115$	0.920897	0.0858741
$116$	−12.4398	−1.15501
$117$	2.68829	0.248532
$118$	6.97630	0.642221
$119$	−1.17711	−0.107906
$120$	−2.43282	−0.222085
$121$	17.3167	1.57425
$122$	0.188013	0.0170219
$123$	5.44219	0.490706
$124$	−0.0504004	−0.00452609
$125$	−1.00000	−0.0894427
$126$	0.510415	0.0454714
$127$	−6.80930	−0.604228	−0.302114	−	0.953272i	$-0.597692\pi$
$127$	−6.80930	−0.604228	−0.302114	+	0.953272i	$0.597692\pi$
$128$	−7.36295	−0.650799
$129$	−8.74791	−0.770210
$130$	1.02914	0.0902619
$131$	11.4004	0.996055	0.498028	−	0.867161i	$-0.334058\pi$
$131$	11.4004	0.996055	0.498028	+	0.867161i	$0.334058\pi$
$132$	−5.81407	−0.506050
$133$	0	0
$134$	−3.24045	−0.279932
$135$	−4.55176	−0.391753
$136$	−12.5094	−1.07267
$137$	−17.1356	−1.46400	−0.731998	−	0.681307i	$-0.761412\pi$
$137$	−17.1356	−1.46400	−0.731998	+	0.681307i	$0.761412\pi$
$138$	0.687309	0.0585076
$139$	13.4272	1.13888	0.569439	−	0.822034i	$-0.307160\pi$
$139$	13.4272	1.13888	0.569439	+	0.822034i	$0.307160\pi$
$140$	−0.332443	−0.0280965
$141$	−7.32316	−0.616721
$142$	−8.69713	−0.729847
$143$	6.36463	0.532237
$144$	−0.238072	−0.0198393
$145$	−9.87581	−0.820141
$146$	8.52784	0.705769
$147$	6.01134	0.495807
$148$	9.77586	0.803571
$149$	19.3771	1.58743	0.793716	−	0.608289i	$-0.208144\pi$
$149$	19.3771	1.58743	0.793716	+	0.608289i	$0.208144\pi$
$150$	−0.746348	−0.0609390
$151$	15.2903	1.24431	0.622153	−	0.782896i	$-0.286258\pi$
$151$	15.2903	1.24431	0.622153	+	0.782896i	$0.286258\pi$
$152$	0	0
$153$	−10.0246	−0.810445
$154$	1.20843	0.0973778
$155$	−0.0400121	−0.00321385
$156$	−1.30680	−0.104628
$157$	16.7845	1.33955	0.669773	−	0.742566i	$-0.266392\pi$
$157$	16.7845	1.33955	0.669773	+	0.742566i	$0.266392\pi$
$158$	−0.00480453	−0.000382228 0
$159$	3.64346	0.288945
$160$	−5.70062	−0.450674
$161$	0.243044	0.0191546
$162$	2.40471	0.188932
$163$	20.1558	1.57872	0.789361	−	0.613929i	$-0.210412\pi$
$163$	20.1558	1.57872	0.789361	+	0.613929i	$0.210412\pi$
$164$	7.90315	0.617132
$165$	−4.61570	−0.359332
$166$	7.59079	0.589159
$167$	23.6089	1.82691	0.913454	−	0.406942i	$-0.133405\pi$
$167$	23.6089	1.82691	0.913454	+	0.406942i	$0.133405\pi$
$168$	−0.642071	−0.0495369
$169$	−11.5695	−0.889958
$170$	−3.83769	−0.294337
$171$	0	0
$172$	−12.7037	−0.968648
$173$	−7.10025	−0.539822	−0.269911	−	0.962885i	$-0.586994\pi$
$173$	−7.10025	−0.539822	−0.269911	+	0.962885i	$0.586994\pi$
$174$	−7.37079	−0.558778
$175$	−0.263921	−0.0199506
$176$	−0.563644	−0.0424863
$177$	−7.03262	−0.528604
$178$	0.371411	0.0278384
$179$	3.65176	0.272946	0.136473	−	0.990644i	$-0.456423\pi$
$179$	3.65176	0.272946	0.136473	+	0.990644i	$0.456423\pi$
$180$	−2.83118	−0.211023
$181$	−8.74210	−0.649796	−0.324898	−	0.945749i	$-0.605330\pi$
$181$	−8.74210	−0.649796	−0.324898	+	0.945749i	$0.605330\pi$
$182$	0.271613	0.0201333
$183$	−0.189530	−0.0140105
$184$	2.58288	0.190412
$185$	7.76091	0.570593
$186$	−0.0298629	−0.00218966
$187$	−23.7337	−1.73558
$188$	−10.6347	−0.775614
$189$	−1.20131	−0.0873821
$190$	0	0
$191$	3.41340	0.246985	0.123492	−	0.992346i	$-0.460591\pi$
$191$	3.41340	0.246985	0.123492	+	0.992346i	$0.460591\pi$
$192$	−4.07090	−0.293792
$193$	13.7389	0.988946	0.494473	−	0.869193i	$-0.335361\pi$
$193$	13.7389	0.988946	0.494473	+	0.869193i	$0.335361\pi$
$194$	14.9485	1.07324
$195$	−1.03745	−0.0742934
$196$	8.72966	0.623547
$197$	−12.4598	−0.887722	−0.443861	−	0.896096i	$-0.646392\pi$
$197$	−12.4598	−0.887722	−0.443861	+	0.896096i	$0.646392\pi$
$198$	10.2913	0.731372
$199$	27.1939	1.92772	0.963861	−	0.266407i	$-0.0858364\pi$
$199$	27.1939	1.92772	0.963861	+	0.266407i	$0.0858364\pi$
$200$	−2.80474	−0.198325
$201$	3.26660	0.230409
$202$	−7.70223	−0.541927
$203$	−2.60643	−0.182936
$204$	4.87308	0.341184
$205$	6.27419	0.438208
$206$	−4.87474	−0.339640
$207$	2.06983	0.143863
$208$	−0.126688	−0.00878422
$209$	0	0
$210$	−0.196977	−0.0135927
$211$	15.6319	1.07614	0.538071	−	0.842899i	$-0.319153\pi$
$211$	15.6319	1.07614	0.538071	+	0.842899i	$0.319153\pi$
$212$	5.29103	0.363390
$213$	8.76733	0.600728
$214$	−7.33698	−0.501546
$215$	−10.0853	−0.687810
$216$	−12.7665	−0.868651
$217$	−0.0105600	−0.000716862 0
$218$	−6.03821	−0.408959
$219$	−8.59668	−0.580910
$220$	−6.70292	−0.451911
$221$	−5.33453	−0.358839
$222$	5.79234	0.388756
$223$	−19.1486	−1.28229	−0.641143	−	0.767421i	$-0.721540\pi$
$223$	−19.1486	−1.28229	−0.641143	+	0.767421i	$0.721540\pi$
$224$	−1.50451	−0.100525
$225$	−2.24763	−0.149842
$226$	−7.52055	−0.500259
$227$	−27.9989	−1.85835	−0.929175	−	0.369641i	$-0.879481\pi$
$227$	−27.9989	−1.85835	−0.929175	+	0.369641i	$0.879481\pi$
$228$	0	0
$229$	7.43209	0.491126	0.245563	−	0.969381i	$-0.421027\pi$
$229$	7.43209	0.491126	0.245563	+	0.969381i	$0.421027\pi$
$230$	0.792384	0.0522483
$231$	−1.21818	−0.0801505
$232$	−27.6991	−1.81853
$233$	−14.2940	−0.936431	−0.468215	−	0.883614i	$-0.655103\pi$
$233$	−14.2940	−0.936431	−0.468215	+	0.883614i	$0.655103\pi$
$234$	2.31313	0.151214
$235$	−8.44271	−0.550742
$236$	−10.2128	−0.664794
$237$	0.00484331	0.000314607 0
$238$	−1.01285	−0.0656531
$239$	1.04233	0.0674225	0.0337113	−	0.999432i	$-0.489267\pi$
$239$	1.04233	0.0674225	0.0337113	+	0.999432i	$0.489267\pi$
$240$	0.0918755	0.00593054
$241$	−18.2225	−1.17381	−0.586907	−	0.809655i	$-0.699654\pi$
$241$	−18.2225	−1.17381	−0.586907	+	0.809655i	$0.699654\pi$
$242$	14.9001	0.957818
$243$	−16.0794	−1.03149
$244$	−0.275236	−0.0176202
$245$	6.93035	0.442764
$246$	4.68273	0.298560
$247$	0	0
$248$	−0.112224	−0.00712621
$249$	−7.65206	−0.484930
$250$	−0.860448	−0.0544195
$251$	2.92399	0.184561	0.0922804	−	0.995733i	$-0.470584\pi$
$251$	2.92399	0.184561	0.0922804	+	0.995733i	$0.470584\pi$
$252$	−0.747207	−0.0470696
$253$	4.90041	0.308086
$254$	−5.85905	−0.367630
$255$	3.86866	0.242265
$256$	−15.7219	−0.982621
$257$	−13.8615	−0.864659	−0.432330	−	0.901716i	$-0.642308\pi$
$257$	−13.8615	−0.864659	−0.432330	+	0.901716i	$0.642308\pi$
$258$	−7.52712	−0.468618
$259$	2.04827	0.127273
$260$	−1.50659	−0.0934345
$261$	−22.1971	−1.37397
$262$	9.80944	0.606029
$263$	−12.4674	−0.768776	−0.384388	−	0.923172i	$-0.625587\pi$
$263$	−12.4674	−0.768776	−0.384388	+	0.923172i	$0.625587\pi$
$264$	−12.9459	−0.796762
$265$	4.20047	0.258033
$266$	0	0
$267$	−0.374409	−0.0229134
$268$	4.74376	0.289771
$269$	27.2482	1.66135	0.830676	−	0.556755i	$-0.187954\pi$
$269$	27.2482	1.66135	0.830676	+	0.556755i	$0.187954\pi$
$270$	−3.91655	−0.238354
$271$	−25.6315	−1.55700	−0.778501	−	0.627644i	$-0.784020\pi$
$271$	−25.6315	−1.55700	−0.778501	+	0.627644i	$0.784020\pi$
$272$	0.472420	0.0286446
$273$	−0.273805	−0.0165715
$274$	−14.7443	−0.890737
$275$	−5.32135	−0.320889
$276$	−1.00617	−0.0605641
$277$	21.1317	1.26968	0.634841	−	0.772643i	$-0.281066\pi$
$277$	21.1317	1.26968	0.634841	+	0.772643i	$0.281066\pi$
$278$	11.5534	0.692926
$279$	−0.0899323	−0.00538411
$280$	−0.740231	−0.0442372
$281$	1.59925	0.0954033	0.0477017	−	0.998862i	$-0.484810\pi$
$281$	1.59925	0.0954033	0.0477017	+	0.998862i	$0.484810\pi$
$282$	−6.30120	−0.375231
$283$	2.19141	0.130266	0.0651328	−	0.997877i	$-0.479253\pi$
$283$	2.19141	0.130266	0.0651328	+	0.997877i	$0.479253\pi$
$284$	12.7319	0.755500
$285$	0	0
$286$	5.47643	0.323828
$287$	1.65589	0.0977442
$288$	−12.8129	−0.755006
$289$	2.89249	0.170147
$290$	−8.49762	−0.498998
$291$	−15.0691	−0.883367
$292$	−12.4841	−0.730576
$293$	14.0044	0.818145	0.409073	−	0.912502i	$-0.365852\pi$
$293$	14.0044	0.818145	0.409073	+	0.912502i	$0.365852\pi$
$294$	5.17245	0.301663
$295$	−8.10775	−0.472052
$296$	21.7673	1.26520
$297$	−24.2215	−1.40547
$298$	16.6730	0.965839
$299$	1.10144	0.0636982
$300$	1.09259	0.0630809
$301$	−2.66172	−0.153419
$302$	13.1565	0.757072
$303$	7.76440	0.446053
$304$	0	0
$305$	−0.218505	−0.0125116
$306$	−8.62569	−0.493098
$307$	−4.81646	−0.274890	−0.137445	−	0.990509i	$-0.543889\pi$
$307$	−4.81646	−0.274890	−0.137445	+	0.990509i	$0.543889\pi$
$308$	−1.76904	−0.100801
$309$	4.91409	0.279553
$310$	−0.0344283	−0.00195540
$311$	19.4101	1.10064	0.550322	−	0.834952i	$-0.314505\pi$
$311$	19.4101	1.10064	0.550322	+	0.834952i	$0.314505\pi$
$312$	−2.90978	−0.164734
$313$	−5.71724	−0.323157	−0.161579	−	0.986860i	$-0.551659\pi$
$313$	−5.71724	−0.323157	−0.161579	+	0.986860i	$0.551659\pi$
$314$	14.4422	0.815018
$315$	−0.593196	−0.0334228
$316$	0.00703346	0.000395663 0
$317$	14.8729	0.835348	0.417674	−	0.908597i	$-0.362845\pi$
$317$	14.8729	0.835348	0.417674	+	0.908597i	$0.362845\pi$
$318$	3.13501	0.175803
$319$	−52.5526	−2.94238
$320$	−4.69325	−0.262361
$321$	7.39621	0.412816
$322$	0.209127	0.0116542
$323$	0	0
$324$	−3.52030	−0.195572
$325$	−1.19606	−0.0663452
$326$	17.3430	0.960540
$327$	6.08695	0.336609
$328$	17.5975	0.971659
$329$	−2.22821	−0.122845
$330$	−3.97157	−0.218628
$331$	−0.0342375	−0.00188187	−0.000940933	−	1.00000i	$-0.500300\pi$
$331$	−0.0342375	−0.00188187	−0.000940933		1.00000i	$0.500300\pi$
$332$	−11.1123	−0.609868
$333$	17.4436	0.955905
$334$	20.3142	1.11154
$335$	3.76600	0.205759
$336$	0.0242479	0.00132283
$337$	23.8249	1.29782	0.648911	−	0.760864i	$-0.275225\pi$
$337$	23.8249	1.29782	0.648911	+	0.760864i	$0.275225\pi$
$338$	−9.95491	−0.541476
$339$	7.58125	0.411757
$340$	5.61807	0.304683
$341$	−0.212918	−0.0115302
$342$	0	0
$343$	3.67651	0.198513
$344$	−28.2866	−1.52511
$345$	−0.798780	−0.0430049
$346$	−6.10940	−0.328443
$347$	−32.4568	−1.74237	−0.871186	−	0.490952i	$-0.836649\pi$
$347$	−32.4568	−1.74237	−0.871186	+	0.490952i	$0.836649\pi$
$348$	10.7902	0.578418
$349$	2.59566	0.138943	0.0694713	−	0.997584i	$-0.477869\pi$
$349$	2.59566	0.138943	0.0694713	+	0.997584i	$0.477869\pi$
$350$	−0.227090	−0.0121385
$351$	−5.44416	−0.290588
$352$	−30.3350	−1.61686
$353$	2.39072	0.127245	0.0636226	−	0.997974i	$-0.479735\pi$
$353$	2.39072	0.127245	0.0636226	+	0.997974i	$0.479735\pi$
$354$	−6.05120	−0.321618
$355$	10.1077	0.536459
$356$	−0.543716	−0.0288169
$357$	1.02102	0.0540382
$358$	3.14215	0.166068
$359$	−15.6300	−0.824918	−0.412459	−	0.910976i	$-0.635330\pi$
$359$	−15.6300	−0.824918	−0.412459	+	0.910976i	$0.635330\pi$
$360$	−6.30402	−0.332251
$361$	0	0
$362$	−7.52213	−0.395354
$363$	−15.0204	−0.788368
$364$	−0.397620	−0.0208409
$365$	−9.91093	−0.518762
$366$	−0.163081	−0.00852438
$367$	−6.19364	−0.323305	−0.161653	−	0.986848i	$-0.551682\pi$
$367$	−6.19364	−0.323305	−0.161653	+	0.986848i	$0.551682\pi$
$368$	−0.0975426	−0.00508476
$369$	14.1020	0.734123
$370$	6.67786	0.347165
$371$	1.10859	0.0575553
$372$	0.0437170	0.00226662
$373$	−26.9063	−1.39316	−0.696578	−	0.717481i	$-0.745295\pi$
$373$	−26.9063	−1.39316	−0.696578	+	0.717481i	$0.745295\pi$
$374$	−20.4217	−1.05598
$375$	0.867394	0.0447920
$376$	−23.6796	−1.22118
$377$	−11.8120	−0.608350
$378$	−1.03366	−0.0531658
$379$	27.0655	1.39026	0.695129	−	0.718885i	$-0.255347\pi$
$379$	27.0655	1.39026	0.695129	+	0.718885i	$0.255347\pi$
$380$	0	0
$381$	5.90634	0.302591
$382$	2.93705	0.150273
$383$	30.5061	1.55879	0.779394	−	0.626533i	$-0.215527\pi$
$383$	30.5061	1.55879	0.779394	+	0.626533i	$0.215527\pi$
$384$	6.38658	0.325914
$385$	−1.40442	−0.0715756
$386$	11.8216	0.601704
$387$	−22.6680	−1.15228
$388$	−21.8834	−1.11096
$389$	−13.3023	−0.674453	−0.337226	−	0.941424i	$-0.609489\pi$
$389$	−13.3023	−0.674453	−0.337226	+	0.941424i	$0.609489\pi$
$390$	−0.892673	−0.0452023
$391$	−4.10729	−0.207715
$392$	19.4378	0.981759
$393$	−9.88862	−0.498815
$394$	−10.7210	−0.540116
$395$	0.00558375	0.000280949 0
$396$	−15.0657	−0.757078
$397$	23.0108	1.15488	0.577440	−	0.816433i	$-0.304052\pi$
$397$	23.0108	1.15488	0.577440	+	0.816433i	$0.304052\pi$
$398$	23.3989	1.17288
$399$	0	0
$400$	0.105921	0.00529606
$401$	−35.9215	−1.79383	−0.896917	−	0.442199i	$-0.854198\pi$
$401$	−35.9215	−1.79383	−0.896917	+	0.442199i	$0.854198\pi$
$402$	2.81074	0.140187
$403$	−0.0478567	−0.00238391
$404$	11.2755	0.560975
$405$	−2.79472	−0.138871
$406$	−2.24270	−0.111303
$407$	41.2985	2.04709
$408$	10.8506	0.537185
$409$	32.3379	1.59900	0.799502	−	0.600663i	$-0.205097\pi$
$409$	32.3379	1.59900	0.799502	+	0.600663i	$0.205097\pi$
$410$	5.39862	0.266619
$411$	14.8633	0.733154
$412$	7.13624	0.351577
$413$	−2.13981	−0.105293
$414$	1.78098	0.0875306
$415$	−8.82190	−0.433050
$416$	−6.81826	−0.334293
$417$	−11.6466	−0.570339
$418$	0	0
$419$	12.6510	0.618041	0.309021	−	0.951055i	$-0.399999\pi$
$419$	12.6510	0.618041	0.309021	+	0.951055i	$0.399999\pi$
$420$	0.288359	0.0140705
$421$	14.6787	0.715396	0.357698	−	0.933837i	$-0.383562\pi$
$421$	14.6787	0.715396	0.357698	+	0.933837i	$0.383562\pi$
$422$	13.4504	0.654756
$423$	−18.9761	−0.922649
$424$	11.7812	0.572148
$425$	4.46010	0.216347
$426$	7.54384	0.365500
$427$	−0.0576682	−0.00279076
$428$	10.7408	0.519174
$429$	−5.52064	−0.266539
$430$	−8.67786	−0.418484
$431$	12.9971	0.626049	0.313025	−	0.949745i	$-0.398658\pi$
$431$	12.9971	0.626049	0.313025	+	0.949745i	$0.398658\pi$
$432$	0.482128	0.0231964
$433$	−25.3993	−1.22061	−0.610305	−	0.792166i	$-0.708953\pi$
$433$	−25.3993	−1.22061	−0.610305	+	0.792166i	$0.708953\pi$
$434$	−0.00908637	−0.000436160 0
$435$	8.56621	0.410719
$436$	8.83946	0.423333
$437$	0	0
$438$	−7.39700	−0.353442
$439$	18.6099	0.888203	0.444101	−	0.895977i	$-0.353523\pi$
$439$	18.6099	0.888203	0.444101	+	0.895977i	$0.353523\pi$
$440$	−14.9250	−0.711522
$441$	15.5768	0.741754
$442$	−4.59009	−0.218328
$443$	−10.3665	−0.492527	−0.246263	−	0.969203i	$-0.579203\pi$
$443$	−10.3665	−0.492527	−0.246263	+	0.969203i	$0.579203\pi$
$444$	−8.47952	−0.402420
$445$	−0.431648	−0.0204621
$446$	−16.4764	−0.780180
$447$	−16.8075	−0.794970
$448$	−1.23865	−0.0585206
$449$	12.9229	0.609869	0.304934	−	0.952373i	$-0.401365\pi$
$449$	12.9229	0.609869	0.304934	+	0.952373i	$0.401365\pi$
$450$	−1.93397	−0.0911681
$451$	33.3871	1.57214
$452$	11.0095	0.517843
$453$	−13.2627	−0.623136
$454$	−24.0916	−1.13067
$455$	−0.315664	−0.0147986
$456$	0	0
$457$	21.6446	1.01249	0.506246	−	0.862389i	$-0.331033\pi$
$457$	21.6446	1.01249	0.506246	+	0.862389i	$0.331033\pi$
$458$	6.39493	0.298815
$459$	20.3013	0.947584
$460$	−1.15999	−0.0540847
$461$	25.6902	1.19651	0.598255	−	0.801306i	$-0.295861\pi$
$461$	25.6902	1.19651	0.598255	+	0.801306i	$0.295861\pi$
$462$	−1.04818	−0.0487659
$463$	−5.30550	−0.246567	−0.123284	−	0.992371i	$-0.539343\pi$
$463$	−5.30550	−0.246567	−0.123284	+	0.992371i	$0.539343\pi$
$464$	1.04606	0.0485620
$465$	0.0347063	0.00160946
$466$	−12.2992	−0.569751
$467$	0.970711	0.0449191	0.0224596	−	0.999748i	$-0.492850\pi$
$467$	0.970711	0.0449191	0.0224596	+	0.999748i	$0.492850\pi$
$468$	−3.38625	−0.156529
$469$	0.993927	0.0458953
$470$	−7.26452	−0.335087
$471$	−14.5587	−0.670831
$472$	−22.7402	−1.04670
$473$	−53.6673	−2.46762
$474$	0.00416742	0.000191416 0
$475$	0	0
$476$	1.48273	0.0679607
$477$	9.44110	0.432278
$478$	0.896868	0.0410218
$479$	0.227190	0.0103806	0.00519030	−	0.999987i	$-0.498348\pi$
$479$	0.227190	0.0103806	0.00519030	+	0.999987i	$0.498348\pi$
$480$	4.94469	0.225693
$481$	9.28248	0.423245
$482$	−15.6795	−0.714182
$483$	−0.210815	−0.00959241
$484$	−21.8126	−0.991484
$485$	−17.3729	−0.788861
$486$	−13.8355	−0.627591
$487$	16.5677	0.750753	0.375376	−	0.926872i	$-0.377513\pi$
$487$	16.5677	0.750753	0.375376	+	0.926872i	$0.377513\pi$
$488$	−0.612851	−0.0277425
$489$	−17.4830	−0.790608
$490$	5.96320	0.269390
$491$	22.0413	0.994709	0.497354	−	0.867547i	$-0.334305\pi$
$491$	22.0413	0.994709	0.497354	+	0.867547i	$0.334305\pi$
$492$	−6.85514	−0.309054
$493$	44.0471	1.98378
$494$	0	0
$495$	−11.9604	−0.537580
$496$	0.00423813	0.000190298 0
$497$	2.66763	0.119659
$498$	−6.58420	−0.295045
$499$	25.3168	1.13334	0.566669	−	0.823946i	$-0.308232\pi$
$499$	25.3168	1.13334	0.566669	+	0.823946i	$0.308232\pi$
$500$	1.25963	0.0563323
$501$	−20.4782	−0.914897
$502$	2.51595	0.112292
$503$	17.2941	0.771104	0.385552	−	0.922686i	$-0.374011\pi$
$503$	17.2941	0.771104	0.385552	+	0.922686i	$0.374011\pi$
$504$	−1.66376	−0.0741099
$505$	8.95142	0.398333
$506$	4.21655	0.187449
$507$	10.0353	0.445682
$508$	8.57719	0.380551
$509$	−11.2867	−0.500272	−0.250136	−	0.968211i	$-0.580475\pi$
$509$	−11.2867	−0.500272	−0.250136	+	0.968211i	$0.580475\pi$
$510$	3.32879	0.147401
$511$	−2.61570	−0.115712
$512$	1.19798	0.0529438
$513$	0	0
$514$	−11.9271	−0.526084
$515$	5.66535	0.249645
$516$	11.0191	0.485090
$517$	−44.9266	−1.97587
$518$	1.76243	0.0774367
$519$	6.15872	0.270338
$520$	−3.35463	−0.147110
$521$	19.6658	0.861573	0.430787	−	0.902454i	$-0.358236\pi$
$521$	19.6658	0.861573	0.430787	+	0.902454i	$0.358236\pi$
$522$	−19.0995	−0.835962
$523$	−35.4632	−1.55070	−0.775349	−	0.631534i	$-0.782426\pi$
$523$	−35.4632	−1.55070	−0.775349	+	0.631534i	$0.782426\pi$
$524$	−14.3602	−0.627330
$525$	0.228924	0.00999104
$526$	−10.7276	−0.467745
$527$	0.178458	0.00777375
$528$	0.488901	0.0212767
$529$	−22.1519	−0.963128
$530$	3.61429	0.156995
$531$	−18.2232	−0.790820
$532$	0	0
$533$	7.50428	0.325047
$534$	−0.322159	−0.0139412
$535$	8.52693	0.368651
$536$	10.5627	0.456237
$537$	−3.16752	−0.136688
$538$	23.4457	1.01082
$539$	36.8788	1.58848
$540$	5.73353	0.246732
$541$	7.58701	0.326191	0.163095	−	0.986610i	$-0.447852\pi$
$541$	7.58701	0.326191	0.163095	+	0.986610i	$0.447852\pi$
$542$	−22.0546	−0.947325
$543$	7.58285	0.325411
$544$	25.4254	1.09010
$545$	7.01751	0.300597
$546$	−0.235595	−0.0100826
$547$	16.6909	0.713650	0.356825	−	0.934171i	$-0.383859\pi$
$547$	16.6909	0.713650	0.356825	+	0.934171i	$0.383859\pi$
$548$	21.5845	0.922045
$549$	−0.491119	−0.0209604
$550$	−4.57874	−0.195238
$551$	0	0
$552$	−2.24037	−0.0953566
$553$	0.00147367	6.26668e−5 0
$554$	18.1828	0.772511
$555$	−6.73176	−0.285747
$556$	−16.9133	−0.717282
$557$	−18.6607	−0.790680	−0.395340	−	0.918535i	$-0.629373\pi$
$557$	−18.6607	−0.790680	−0.395340	+	0.918535i	$0.629373\pi$
$558$	−0.0773821	−0.00327585
$559$	−12.0626	−0.510192
$560$	0.0279549	0.00118131
$561$	20.5865	0.869163
$562$	1.37607	0.0580462
$563$	6.21513	0.261936	0.130968	−	0.991387i	$-0.458191\pi$
$563$	6.21513	0.261936	0.130968	+	0.991387i	$0.458191\pi$
$564$	9.22446	0.388420
$565$	8.74027	0.367706
$566$	1.88559	0.0792573
$567$	−0.737584	−0.0309756
$568$	28.3494	1.18951
$569$	16.6738	0.699003	0.349501	−	0.936936i	$-0.386351\pi$
$569$	16.6738	0.699003	0.349501	+	0.936936i	$0.386351\pi$
$570$	0	0
$571$	−14.4171	−0.603337	−0.301669	−	0.953413i	$-0.597544\pi$
$571$	−14.4171	−0.603337	−0.301669	+	0.953413i	$0.597544\pi$
$572$	−8.01707	−0.335210
$573$	−2.96076	−0.123688
$574$	1.42481	0.0594704
$575$	−0.920897	−0.0384041
$576$	−10.5487	−0.439528
$577$	22.2199	0.925028	0.462514	−	0.886612i	$-0.346947\pi$
$577$	22.2199	0.925028	0.462514	+	0.886612i	$0.346947\pi$
$578$	2.48884	0.103522
$579$	−11.9170	−0.495255
$580$	12.4398	0.516537
$581$	−2.32829	−0.0965936
$582$	−12.9662	−0.537466
$583$	22.3522	0.925732
$584$	−27.7976	−1.15027
$585$	−2.68829	−0.111147
$586$	12.0501	0.497783
$587$	41.5186	1.71366	0.856828	−	0.515602i	$-0.172432\pi$
$587$	41.5186	1.71366	0.856828	+	0.515602i	$0.172432\pi$
$588$	−7.57205	−0.312266
$589$	0	0
$590$	−6.97630	−0.287210
$591$	10.8075	0.444562
$592$	−0.822045	−0.0337859
$593$	−8.48062	−0.348257	−0.174129	−	0.984723i	$-0.555711\pi$
$593$	−8.48062	−0.348257	−0.174129	+	0.984723i	$0.555711\pi$
$594$	−20.8413	−0.855131
$595$	1.17711	0.0482570
$596$	−24.4079	−0.999787
$597$	−23.5878	−0.965384
$598$	0.947736	0.0387558
$599$	15.1403	0.618614	0.309307	−	0.950962i	$-0.399903\pi$
$599$	15.1403	0.618614	0.309307	+	0.950962i	$0.399903\pi$
$600$	2.43282	0.0993193
$601$	−24.4130	−0.995826	−0.497913	−	0.867227i	$-0.665900\pi$
$601$	−24.4130	−0.995826	−0.497913	+	0.867227i	$0.665900\pi$
$602$	−2.29027	−0.0933445
$603$	8.46457	0.344704
$604$	−19.2601	−0.783682
$605$	−17.3167	−0.704025
$606$	6.68087	0.271392
$607$	−22.1867	−0.900532	−0.450266	−	0.892894i	$-0.648671\pi$
$607$	−22.1867	−0.900532	−0.450266	+	0.892894i	$0.648671\pi$
$608$	0	0
$609$	2.26080	0.0916124
$610$	−0.188013	−0.00761241
$611$	−10.0980	−0.408520
$612$	12.6273	0.510430
$613$	11.2934	0.456135	0.228068	−	0.973645i	$-0.426759\pi$
$613$	11.2934	0.456135	0.228068	+	0.973645i	$0.426759\pi$
$614$	−4.14432	−0.167251
$615$	−5.44219	−0.219450
$616$	−3.93902	−0.158708
$617$	−8.72864	−0.351402	−0.175701	−	0.984444i	$-0.556219\pi$
$617$	−8.72864	−0.351402	−0.175701	+	0.984444i	$0.556219\pi$
$618$	4.22832	0.170088
$619$	46.3421	1.86265	0.931323	−	0.364194i	$-0.118655\pi$
$619$	46.3421	1.86265	0.931323	+	0.364194i	$0.118655\pi$
$620$	0.0504004	0.00202413
$621$	−4.19170	−0.168207
$622$	16.7014	0.669664
$623$	−0.113921	−0.00456415
$624$	0.109888	0.00439905
$625$	1.00000	0.0400000
$626$	−4.91939	−0.196618
$627$	0	0
$628$	−21.1422	−0.843665
$629$	−34.6144	−1.38017
$630$	−0.510415	−0.0203354
$631$	14.1200	0.562108	0.281054	−	0.959692i	$-0.409316\pi$
$631$	14.1200	0.562108	0.281054	+	0.959692i	$0.409316\pi$
$632$	0.0156610	0.000622961 0
$633$	−13.5590	−0.538922
$634$	12.7974	0.508250
$635$	6.80930	0.270219
$636$	−4.58941	−0.181982
$637$	8.28908	0.328425
$638$	−45.2188	−1.79023
$639$	22.7183	0.898721
$640$	7.36295	0.291046
$641$	14.0331	0.554273	0.277136	−	0.960831i	$-0.410615\pi$
$641$	14.0331	0.554273	0.277136	+	0.960831i	$0.410615\pi$
$642$	6.36405	0.251169
$643$	20.4083	0.804823	0.402411	−	0.915459i	$-0.368172\pi$
$643$	20.4083	0.804823	0.402411	+	0.915459i	$0.368172\pi$
$644$	−0.306145	−0.0120638
$645$	8.74791	0.344449
$646$	0	0
$647$	−14.5688	−0.572757	−0.286379	−	0.958117i	$-0.592452\pi$
$647$	−14.5688	−0.572757	−0.286379	+	0.958117i	$0.592452\pi$
$648$	−7.83846	−0.307924
$649$	−43.1442	−1.69356
$650$	−1.02914	−0.0403664
$651$	0.00915971	0.000358997 0
$652$	−25.3888	−0.994302
$653$	−26.9592	−1.05500	−0.527498	−	0.849556i	$-0.676870\pi$
$653$	−26.9592	−1.05500	−0.527498	+	0.849556i	$0.676870\pi$
$654$	5.23751	0.204803
$655$	−11.4004	−0.445450
$656$	−0.664570	−0.0259471
$657$	−22.2761	−0.869073
$658$	−1.91726	−0.0747426
$659$	14.3259	0.558059	0.279029	−	0.960283i	$-0.409987\pi$
$659$	14.3259	0.558059	0.279029	+	0.960283i	$0.409987\pi$
$660$	5.81407	0.226312
$661$	45.9785	1.78836	0.894179	−	0.447710i	$-0.147760\pi$
$661$	45.9785	1.78836	0.894179	+	0.447710i	$0.147760\pi$
$662$	−0.0294596	−0.00114498
$663$	4.62714	0.179703
$664$	−24.7432	−0.960221
$665$	0	0
$666$	15.0093	0.581600
$667$	−9.09460	−0.352144
$668$	−29.7384	−1.15061
$669$	16.6094	0.642156
$670$	3.24045	0.125189
$671$	−1.16274	−0.0448872
$672$	1.30501	0.0503417
$673$	−3.81843	−0.147190	−0.0735948	−	0.997288i	$-0.523447\pi$
$673$	−3.81843	−0.147190	−0.0735948	+	0.997288i	$0.523447\pi$
$674$	20.5001	0.789633
$675$	4.55176	0.175197
$676$	14.5732	0.560508
$677$	−48.8890	−1.87896	−0.939479	−	0.342607i	$-0.888690\pi$
$677$	−48.8890	−1.87896	−0.939479	+	0.342607i	$0.888690\pi$
$678$	6.52328	0.250525
$679$	−4.58506	−0.175959
$680$	12.5094	0.479715
$681$	24.2860	0.930643
$682$	−0.183205	−0.00701529
$683$	15.9118	0.608849	0.304425	−	0.952536i	$-0.401536\pi$
$683$	15.9118	0.608849	0.304425	+	0.952536i	$0.401536\pi$
$684$	0	0
$685$	17.1356	0.654719
$686$	3.16345	0.120781
$687$	−6.44655	−0.245951
$688$	1.06825	0.0407265
$689$	5.02400	0.191399
$690$	−0.687309	−0.0261654
$691$	36.6387	1.39380	0.696902	−	0.717167i	$-0.254561\pi$
$691$	36.6387	1.39380	0.696902	+	0.717167i	$0.254561\pi$
$692$	8.94368	0.339988
$693$	−3.15660	−0.119909
$694$	−27.9274	−1.06011
$695$	−13.4272	−0.509322
$696$	24.0260	0.910704
$697$	−27.9835	−1.05995
$698$	2.23343	0.0845367
$699$	12.3985	0.468955
$700$	0.332443	0.0125651
$701$	−17.6715	−0.667442	−0.333721	−	0.942672i	$-0.608304\pi$
$701$	−17.6715	−0.667442	−0.333721	+	0.942672i	$0.608304\pi$
$702$	−4.68442	−0.176802
$703$	0	0
$704$	−24.9744	−0.941258
$705$	7.32316	0.275806
$706$	2.05709	0.0774196
$707$	2.36247	0.0888497
$708$	8.85848	0.332922
$709$	15.3223	0.575442	0.287721	−	0.957714i	$-0.407102\pi$
$709$	15.3223	0.575442	0.287721	+	0.957714i	$0.407102\pi$
$710$	8.69713	0.326397
$711$	0.0125502	0.000470669 0
$712$	−1.21066	−0.0453714
$713$	−0.0368470	−0.00137993
$714$	0.878537	0.0328784
$715$	−6.36463	−0.238024
$716$	−4.59986	−0.171905
$717$	−0.904108	−0.0337645
$718$	−13.4488	−0.501904
$719$	1.62082	0.0604462	0.0302231	−	0.999543i	$-0.490378\pi$
$719$	1.62082	0.0604462	0.0302231	+	0.999543i	$0.490378\pi$
$720$	0.238072	0.00887241
$721$	1.49521	0.0556844
$722$	0	0
$723$	15.8061	0.587834
$724$	11.0118	0.409250
$725$	9.87581	0.366778
$726$	−12.9243	−0.479666
$727$	11.1635	0.414031	0.207016	−	0.978338i	$-0.433625\pi$
$727$	11.1635	0.414031	0.207016	+	0.978338i	$0.433625\pi$
$728$	−0.885357	−0.0328135
$729$	5.56303	0.206038
$730$	−8.52784	−0.315630
$731$	44.9813	1.66370
$732$	0.238738	0.00882400
$733$	12.1110	0.447331	0.223666	−	0.974666i	$-0.428198\pi$
$733$	12.1110	0.447331	0.223666	+	0.974666i	$0.428198\pi$
$734$	−5.32931	−0.196708
$735$	−6.01134	−0.221732
$736$	−5.24969	−0.193506
$737$	20.0402	0.738190
$738$	12.1341	0.446662
$739$	40.0688	1.47395	0.736977	−	0.675918i	$-0.236253\pi$
$739$	40.0688	1.47395	0.736977	+	0.675918i	$0.236253\pi$
$740$	−9.77586	−0.359368
$741$	0	0
$742$	0.953887	0.0350183
$743$	23.3715	0.857416	0.428708	−	0.903443i	$-0.358969\pi$
$743$	23.3715	0.857416	0.428708	+	0.903443i	$0.358969\pi$
$744$	0.0973421	0.00356873
$745$	−19.3771	−0.709921
$746$	−23.1515	−0.847636
$747$	−19.8283	−0.725481
$748$	29.8957	1.09309
$749$	2.25044	0.0822292
$750$	0.746348	0.0272528
$751$	−16.6615	−0.607986	−0.303993	−	0.952674i	$-0.598320\pi$
$751$	−16.6615	−0.607986	−0.303993	+	0.952674i	$0.598320\pi$
$752$	0.894263	0.0326104
$753$	−2.53625	−0.0924262
$754$	−10.1636	−0.370138
$755$	−15.2903	−0.556470
$756$	1.51320	0.0550345
$757$	23.5257	0.855057	0.427528	−	0.904002i	$-0.359384\pi$
$757$	23.5257	0.855057	0.427528	+	0.904002i	$0.359384\pi$
$758$	23.2884	0.845874
$759$	−4.25059	−0.154287
$760$	0	0
$761$	−8.20495	−0.297429	−0.148715	−	0.988880i	$-0.547514\pi$
$761$	−8.20495	−0.297429	−0.148715	+	0.988880i	$0.547514\pi$
$762$	5.08210	0.184105
$763$	1.85207	0.0670494
$764$	−4.29961	−0.155555
$765$	10.0246	0.362442
$766$	26.2489	0.948412
$767$	−9.69733	−0.350150
$768$	13.6371	0.492087
$769$	18.8871	0.681087	0.340544	−	0.940229i	$-0.389389\pi$
$769$	18.8871	0.681087	0.340544	+	0.940229i	$0.389389\pi$
$770$	−1.20843	−0.0435487
$771$	12.0234	0.433013
$772$	−17.3059	−0.622853
$773$	−42.4983	−1.52856	−0.764279	−	0.644886i	$-0.776905\pi$
$773$	−42.4983	−1.52856	−0.764279	+	0.644886i	$0.776905\pi$
$774$	−19.5046	−0.701079
$775$	0.0400121	0.00143728
$776$	−48.7264	−1.74918
$777$	−1.77665	−0.0637371
$778$	−11.4459	−0.410356
$779$	0	0
$780$	1.30680	0.0467911
$781$	53.7864	1.92463
$782$	−3.53411	−0.126380
$783$	44.9523	1.60646
$784$	−0.734071	−0.0262168
$785$	−16.7845	−0.599063
$786$	−8.50864	−0.303493
$787$	−44.4450	−1.58429	−0.792146	−	0.610331i	$-0.791036\pi$
$787$	−44.4450	−1.58429	−0.792146	+	0.610331i	$0.791036\pi$
$788$	15.6947	0.559100
$789$	10.8142	0.384995
$790$	0.00480453	0.000170938 0
$791$	2.30674	0.0820183
$792$	−33.5459	−1.19200
$793$	−0.261345	−0.00928062
$794$	19.7996	0.702662
$795$	−3.64346	−0.129220
$796$	−34.2542	−1.21411
$797$	0.711060	0.0251870	0.0125935	−	0.999921i	$-0.495991\pi$
$797$	0.711060	0.0251870	0.0125935	+	0.999921i	$0.495991\pi$
$798$	0	0
$799$	37.6554	1.33215
$800$	5.70062	0.201547
$801$	−0.970184	−0.0342798
$802$	−30.9086	−1.09142
$803$	−52.7395	−1.86114
$804$	−4.11471	−0.145115
$805$	−0.243044	−0.00856618
$806$	−0.0411782	−0.00145044
$807$	−23.6349	−0.831989
$808$	25.1064	0.883241
$809$	−37.2669	−1.31023	−0.655117	−	0.755528i	$-0.727381\pi$
$809$	−37.2669	−1.31023	−0.655117	+	0.755528i	$0.727381\pi$
$810$	−2.40471	−0.0844928
$811$	26.0182	0.913622	0.456811	−	0.889564i	$-0.348992\pi$
$811$	26.0182	0.913622	0.456811	+	0.889564i	$0.348992\pi$
$812$	3.28314	0.115216
$813$	22.2326	0.779731
$814$	35.5352	1.24551
$815$	−20.1558	−0.706026
$816$	−0.409774	−0.0143450
$817$	0	0
$818$	27.8251	0.972881
$819$	−0.709496	−0.0247918
$820$	−7.90315	−0.275990
$821$	1.15939	0.0404631	0.0202316	−	0.999795i	$-0.493560\pi$
$821$	1.15939	0.0404631	0.0202316	+	0.999795i	$0.493560\pi$
$822$	12.7891	0.446072
$823$	15.4136	0.537284	0.268642	−	0.963240i	$-0.413425\pi$
$823$	15.4136	0.537284	0.268642	+	0.963240i	$0.413425\pi$
$824$	15.8899	0.553549
$825$	4.61570	0.160698
$826$	−1.84119	−0.0640633
$827$	37.9042	1.31806	0.659029	−	0.752118i	$-0.270968\pi$
$827$	37.9042	1.31806	0.659029	+	0.752118i	$0.270968\pi$
$828$	−2.60722	−0.0906072
$829$	12.1577	0.422254	0.211127	−	0.977459i	$-0.432287\pi$
$829$	12.1577	0.422254	0.211127	+	0.977459i	$0.432287\pi$
$830$	−7.59079	−0.263480
$831$	−18.3295	−0.635844
$832$	−5.61339	−0.194609
$833$	−30.9100	−1.07097
$834$	−10.0213	−0.347011
$835$	−23.6089	−0.817018
$836$	0	0
$837$	0.182125	0.00629518
$838$	10.8855	0.376034
$839$	−47.7649	−1.64903	−0.824513	−	0.565843i	$-0.808551\pi$
$839$	−47.7649	−1.64903	−0.824513	+	0.565843i	$0.808551\pi$
$840$	0.642071	0.0221536
$841$	68.5316	2.36316
$842$	12.6303	0.435267
$843$	−1.38718	−0.0477770
$844$	−19.6904	−0.677770
$845$	11.5695	0.398001
$846$	−16.3279	−0.561366
$847$	−4.57025	−0.157036
$848$	−0.444919	−0.0152786
$849$	−1.90081	−0.0652357
$850$	3.83769	0.131632
$851$	7.14700	0.244996
$852$	−11.0436	−0.378347
$853$	−27.5081	−0.941859	−0.470930	−	0.882171i	$-0.656081\pi$
$853$	−27.5081	−0.941859	−0.470930	+	0.882171i	$0.656081\pi$
$854$	−0.0496205	−0.00169798
$855$	0	0
$856$	23.9158	0.817427
$857$	7.97761	0.272510	0.136255	−	0.990674i	$-0.456493\pi$
$857$	7.97761	0.272510	0.136255	+	0.990674i	$0.456493\pi$
$858$	−4.75022	−0.162170
$859$	2.43789	0.0831798	0.0415899	−	0.999135i	$-0.486758\pi$
$859$	2.43789	0.0831798	0.0415899	+	0.999135i	$0.486758\pi$
$860$	12.7037	0.433193
$861$	−1.43631	−0.0489493
$862$	11.1833	0.380906
$863$	−19.8250	−0.674852	−0.337426	−	0.941352i	$-0.609556\pi$
$863$	−19.8250	−0.674852	−0.337426	+	0.941352i	$0.609556\pi$
$864$	25.9479	0.882765
$865$	7.10025	0.241416
$866$	−21.8547	−0.742655
$867$	−2.50893	−0.0852077
$868$	0.0133017	0.000451490 0
$869$	0.0297131	0.00100795
$870$	7.37079	0.249893
$871$	4.50435	0.152624
$872$	19.6823	0.666527
$873$	−39.0477	−1.32157
$874$	0	0
$875$	0.263921	0.00892216
$876$	10.8286	0.365865
$877$	−8.63651	−0.291634	−0.145817	−	0.989312i	$-0.546581\pi$
$877$	−8.63651	−0.291634	−0.145817	+	0.989312i	$0.546581\pi$
$878$	16.0129	0.540408
$879$	−12.1473	−0.409719
$880$	0.563644	0.0190004
$881$	−6.78634	−0.228638	−0.114319	−	0.993444i	$-0.536469\pi$
$881$	−6.78634	−0.228638	−0.114319	+	0.993444i	$0.536469\pi$
$882$	13.4031	0.451305
$883$	22.2213	0.747807	0.373904	−	0.927468i	$-0.378019\pi$
$883$	22.2213	0.747807	0.373904	+	0.927468i	$0.378019\pi$
$884$	6.71952	0.226002
$885$	7.03262	0.236399
$886$	−8.91983	−0.299668
$887$	3.22267	0.108207	0.0541033	−	0.998535i	$-0.482770\pi$
$887$	3.22267	0.108207	0.0541033	+	0.998535i	$0.482770\pi$
$888$	−18.8809	−0.633600
$889$	1.79712	0.0602734
$890$	−0.371411	−0.0124497
$891$	−14.8716	−0.498219
$892$	24.1202	0.807602
$893$	0	0
$894$	−14.4620	−0.483683
$895$	−3.65176	−0.122065
$896$	1.94324	0.0649190
$897$	−0.955386	−0.0318994
$898$	11.1195	0.371062
$899$	0.395152	0.0131791
$900$	2.83118	0.0943725
$901$	−18.7345	−0.624137
$902$	28.7279	0.956535
$903$	2.30876	0.0768306
$904$	24.5142	0.815330
$905$	8.74210	0.290597
$906$	−11.4119	−0.379134
$907$	−0.911956	−0.0302810	−0.0151405	−	0.999885i	$-0.504820\pi$
$907$	−0.911956	−0.0302810	−0.0151405	+	0.999885i	$0.504820\pi$
$908$	35.2682	1.17042
$909$	20.1195	0.667320
$910$	−0.271613	−0.00900388
$911$	−51.6358	−1.71077	−0.855385	−	0.517992i	$-0.826680\pi$
$911$	−51.6358	−1.71077	−0.855385	+	0.517992i	$0.826680\pi$
$912$	0	0
$913$	−46.9444	−1.55363
$914$	18.6241	0.616029
$915$	0.189530	0.00626568
$916$	−9.36167	−0.309318
$917$	−3.00880	−0.0993593
$918$	17.4682	0.576537
$919$	−16.5629	−0.546361	−0.273180	−	0.961963i	$-0.588076\pi$
$919$	−16.5629	−0.546361	−0.273180	+	0.961963i	$0.588076\pi$
$920$	−2.58288	−0.0851550
$921$	4.17777	0.137662
$922$	22.1051	0.727991
$923$	12.0893	0.397925
$924$	1.53446	0.0504799
$925$	−7.76091	−0.255177
$926$	−4.56511	−0.150019
$927$	12.7336	0.418227
$928$	56.2983	1.84808
$929$	−25.5753	−0.839098	−0.419549	−	0.907733i	$-0.637812\pi$
$929$	−25.5753	−0.839098	−0.419549	+	0.907733i	$0.637812\pi$
$930$	0.0298629	0.000979244 0
$931$	0	0
$932$	18.0051	0.589777
$933$	−16.8362	−0.551192
$934$	0.835247	0.0273301
$935$	23.7337	0.776176
$936$	−7.53996	−0.246451
$937$	−1.00369	−0.0327890	−0.0163945	−	0.999866i	$-0.505219\pi$
$937$	−1.00369	−0.0327890	−0.0163945	+	0.999866i	$0.505219\pi$
$938$	0.855223	0.0279240
$939$	4.95910	0.161834
$940$	10.6347	0.346865
$941$	55.6685	1.81474	0.907371	−	0.420331i	$-0.138086\pi$
$941$	55.6685	1.81474	0.907371	+	0.420331i	$0.138086\pi$
$942$	−12.5270	−0.408153
$943$	5.77788	0.188154
$944$	0.858784	0.0279510
$945$	1.20131	0.0390785
$946$	−46.1779	−1.50137
$947$	28.8174	0.936438	0.468219	−	0.883612i	$-0.344896\pi$
$947$	28.8174	0.936438	0.468219	+	0.883612i	$0.344896\pi$
$948$	−0.00610078	−0.000198144 0
$949$	−11.8540	−0.384798
$950$	0	0
$951$	−12.9007	−0.418334
$952$	3.30150	0.107002
$953$	8.08279	0.261827	0.130914	−	0.991394i	$-0.458209\pi$
$953$	8.08279	0.261827	0.130914	+	0.991394i	$0.458209\pi$
$954$	8.12358	0.263011
$955$	−3.41340	−0.110455
$956$	−1.31294	−0.0424637
$957$	45.5838	1.47351
$958$	0.195486	0.00631585
$959$	4.52245	0.146038
$960$	4.07090	0.131388
$961$	−30.9984	−0.999948
$962$	7.98710	0.257514
$963$	19.1654	0.617595
$964$	22.9536	0.739285
$965$	−13.7389	−0.442270
$966$	−0.181395	−0.00583630
$967$	9.84792	0.316688	0.158344	−	0.987384i	$-0.449385\pi$
$967$	9.84792	0.316688	0.158344	+	0.987384i	$0.449385\pi$
$968$	−48.5690	−1.56107
$969$	0	0
$970$	−14.9485	−0.479966
$971$	1.84777	0.0592979	0.0296489	−	0.999560i	$-0.490561\pi$
$971$	1.84777	0.0592979	0.0296489	+	0.999560i	$0.490561\pi$
$972$	20.2541	0.649650
$973$	−3.54371	−0.113606
$974$	14.2556	0.456780
$975$	1.03745	0.0332250
$976$	0.0231444	0.000740833 0
$977$	−26.4611	−0.846567	−0.423283	−	0.905997i	$-0.639123\pi$
$977$	−26.4611	−0.846567	−0.423283	+	0.905997i	$0.639123\pi$
$978$	−15.0432	−0.481029
$979$	−2.29695	−0.0734108
$980$	−8.72966	−0.278859
$981$	15.7728	0.503586
$982$	18.9654	0.605210
$983$	−35.5543	−1.13401	−0.567003	−	0.823716i	$-0.691897\pi$
$983$	−35.5543	−1.13401	−0.567003	+	0.823716i	$0.691897\pi$
$984$	−15.2639	−0.486597
$985$	12.4598	0.397001
$986$	37.9002	1.20699
$987$	1.93274	0.0615197
$988$	0	0
$989$	−9.28750	−0.295325
$990$	−10.2913	−0.327079
$991$	−39.1942	−1.24504	−0.622522	−	0.782603i	$-0.713892\pi$
$991$	−39.1942	−1.24504	−0.622522	+	0.782603i	$0.713892\pi$
$992$	0.228094	0.00724199
$993$	0.0296974	0.000942420 0
$994$	2.29536	0.0728043
$995$	−27.1939	−0.862103
$996$	9.63875	0.305416
$997$	−3.55869	−0.112705	−0.0563524	−	0.998411i	$-0.517947\pi$
$997$	−3.55869	−0.112705	−0.0563524	+	0.998411i	$0.517947\pi$
$998$	21.7838	0.689555
$999$	−35.3258	−1.11766

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.q.1.5	✓	6
5.4	even	2		9025.2.a.ca.1.2		6
19.18	odd	2		1805.2.a.r.1.2	yes	6
95.94	odd	2		9025.2.a.bq.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.a.q.1.5	✓	6	1.1	even	1	trivial
1805.2.a.r.1.2	yes	6	19.18	odd	2
9025.2.a.bq.1.5		6	95.94	odd	2
9025.2.a.ca.1.2		6	5.4	even	2

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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q+0.860448 q^{2} -0.867394 q^{3} -1.25963 q^{4} -1.00000 q^{5} -0.746348 q^{6} -0.263921 q^{7} -2.80474 q^{8} -2.24763 q^{9} +O(q^{10})\)	\(q+0.860448 q^{2} -0.867394 q^{3} -1.25963 q^{4} -1.00000 q^{5} -0.746348 q^{6} -0.263921 q^{7} -2.80474 q^{8} -2.24763 q^{9} -0.860448 q^{10} -5.32135 q^{11} +1.09259 q^{12} -1.19606 q^{13} -0.227090 q^{14} +0.867394 q^{15} +0.105921 q^{16} +4.46010 q^{17} -1.93397 q^{18} +1.25963 q^{20} +0.228924 q^{21} -4.57874 q^{22} -0.920897 q^{23} +2.43282 q^{24} +1.00000 q^{25} -1.02914 q^{26} +4.55176 q^{27} +0.332443 q^{28} +9.87581 q^{29} +0.746348 q^{30} +0.0400121 q^{31} +5.70062 q^{32} +4.61570 q^{33} +3.83769 q^{34} +0.263921 q^{35} +2.83118 q^{36} -7.76091 q^{37} +1.03745 q^{39} +2.80474 q^{40} -6.27419 q^{41} +0.196977 q^{42} +10.0853 q^{43} +6.70292 q^{44} +2.24763 q^{45} -0.792384 q^{46} +8.44271 q^{47} -0.0918755 q^{48} -6.93035 q^{49} +0.860448 q^{50} -3.86866 q^{51} +1.50659 q^{52} -4.20047 q^{53} +3.91655 q^{54} +5.32135 q^{55} +0.740231 q^{56} +8.49762 q^{58} +8.10775 q^{59} -1.09259 q^{60} +0.218505 q^{61} +0.0344283 q^{62} +0.593196 q^{63} +4.69325 q^{64} +1.19606 q^{65} +3.97157 q^{66} -3.76600 q^{67} -5.61807 q^{68} +0.798780 q^{69} +0.227090 q^{70} -10.1077 q^{71} +6.30402 q^{72} +9.91093 q^{73} -6.67786 q^{74} -0.867394 q^{75} +1.40442 q^{77} +0.892673 q^{78} -0.00558375 q^{79} -0.105921 q^{80} +2.79472 q^{81} -5.39862 q^{82} +8.82190 q^{83} -0.288359 q^{84} -4.46010 q^{85} +8.67786 q^{86} -8.56621 q^{87} +14.9250 q^{88} +0.431648 q^{89} +1.93397 q^{90} +0.315664 q^{91} +1.15999 q^{92} -0.0347063 q^{93} +7.26452 q^{94} -4.94469 q^{96} +17.3729 q^{97} -5.96320 q^{98} +11.9604 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9} + 2 q^{10} + 15 q^{11} + 20 q^{12} - 6 q^{13} - 20 q^{14} + 4 q^{15} + 20 q^{16} + 5 q^{17} + 8 q^{18} - 8 q^{20} - 7 q^{21} - 14 q^{22} + 18 q^{24} + 6 q^{25} - 22 q^{26} - 28 q^{27} + 10 q^{28} + 20 q^{29} - 8 q^{30} - 12 q^{31} + 8 q^{32} - q^{33} - 7 q^{35} - 14 q^{36} - 20 q^{37} + 16 q^{39} - 8 q^{41} - 30 q^{42} + 27 q^{43} + 46 q^{44} - 10 q^{45} - 16 q^{46} - 8 q^{47} + 24 q^{48} + 11 q^{49} - 2 q^{50} + 11 q^{51} - 4 q^{52} - 19 q^{53} + 30 q^{54} - 15 q^{55} - 62 q^{56} + 20 q^{58} + 41 q^{59} - 20 q^{60} + 6 q^{61} - 30 q^{62} - 18 q^{63} + 48 q^{64} + 6 q^{65} + 46 q^{66} + 15 q^{67} - 14 q^{68} + 10 q^{69} + 20 q^{70} - 2 q^{71} + 68 q^{72} + 8 q^{73} + 2 q^{74} - 4 q^{75} + 21 q^{77} - 46 q^{78} - 18 q^{79} - 20 q^{80} + 50 q^{81} - 18 q^{82} - 10 q^{83} - 4 q^{84} - 5 q^{85} + 10 q^{86} - 14 q^{87} + 52 q^{88} - 17 q^{89} - 8 q^{90} + 23 q^{91} + 28 q^{92} + 10 q^{93} + 28 q^{94} + 26 q^{96} + 4 q^{97} - 50 q^{98} + 58 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9 + 2 * q^10 + 15 * q^11 + 20 * q^12 - 6 * q^13 - 20 * q^14 + 4 * q^15 + 20 * q^16 + 5 * q^17 + 8 * q^18 - 8 * q^20 - 7 * q^21 - 14 * q^22 + 18 * q^24 + 6 * q^25 - 22 * q^26 - 28 * q^27 + 10 * q^28 + 20 * q^29 - 8 * q^30 - 12 * q^31 + 8 * q^32 - q^33 - 7 * q^35 - 14 * q^36 - 20 * q^37 + 16 * q^39 - 8 * q^41 - 30 * q^42 + 27 * q^43 + 46 * q^44 - 10 * q^45 - 16 * q^46 - 8 * q^47 + 24 * q^48 + 11 * q^49 - 2 * q^50 + 11 * q^51 - 4 * q^52 - 19 * q^53 + 30 * q^54 - 15 * q^55 - 62 * q^56 + 20 * q^58 + 41 * q^59 - 20 * q^60 + 6 * q^61 - 30 * q^62 - 18 * q^63 + 48 * q^64 + 6 * q^65 + 46 * q^66 + 15 * q^67 - 14 * q^68 + 10 * q^69 + 20 * q^70 - 2 * q^71 + 68 * q^72 + 8 * q^73 + 2 * q^74 - 4 * q^75 + 21 * q^77 - 46 * q^78 - 18 * q^79 - 20 * q^80 + 50 * q^81 - 18 * q^82 - 10 * q^83 - 4 * q^84 - 5 * q^85 + 10 * q^86 - 14 * q^87 + 52 * q^88 - 17 * q^89 - 8 * q^90 + 23 * q^91 + 28 * q^92 + 10 * q^93 + 28 * q^94 + 26 * q^96 + 4 * q^97 - 50 * q^98 + 58 * q^99

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