LMFDB - Embedded newform 805.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(1,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, 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("805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.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:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.61803 q^{2} -2.23607 q^{3} +4.85410 q^{4} -1.00000 q^{5} -5.85410 q^{6} -1.00000 q^{7} +7.47214 q^{8} +2.00000 q^{9} +O(q^{10})$	\(q+2.61803 q^{2} -2.23607 q^{3} +4.85410 q^{4} -1.00000 q^{5} -5.85410 q^{6} -1.00000 q^{7} +7.47214 q^{8} +2.00000 q^{9} -2.61803 q^{10} +6.00000 q^{11} -10.8541 q^{12} +3.00000 q^{13} -2.61803 q^{14} +2.23607 q^{15} +9.85410 q^{16} +3.23607 q^{17} +5.23607 q^{18} -0.472136 q^{19} -4.85410 q^{20} +2.23607 q^{21} +15.7082 q^{22} +1.00000 q^{23} -16.7082 q^{24} +1.00000 q^{25} +7.85410 q^{26} +2.23607 q^{27} -4.85410 q^{28} -1.47214 q^{29} +5.85410 q^{30} +3.47214 q^{31} +10.8541 q^{32} -13.4164 q^{33} +8.47214 q^{34} +1.00000 q^{35} +9.70820 q^{36} -2.76393 q^{37} -1.23607 q^{38} -6.70820 q^{39} -7.47214 q^{40} -6.70820 q^{41} +5.85410 q^{42} -9.70820 q^{43} +29.1246 q^{44} -2.00000 q^{45} +2.61803 q^{46} +0.236068 q^{47} -22.0344 q^{48} +1.00000 q^{49} +2.61803 q^{50} -7.23607 q^{51} +14.5623 q^{52} -13.2361 q^{53} +5.85410 q^{54} -6.00000 q^{55} -7.47214 q^{56} +1.05573 q^{57} -3.85410 q^{58} +2.47214 q^{59} +10.8541 q^{60} +11.7082 q^{61} +9.09017 q^{62} -2.00000 q^{63} +8.70820 q^{64} -3.00000 q^{65} -35.1246 q^{66} -1.23607 q^{67} +15.7082 q^{68} -2.23607 q^{69} +2.61803 q^{70} +0.236068 q^{71} +14.9443 q^{72} +9.00000 q^{73} -7.23607 q^{74} -2.23607 q^{75} -2.29180 q^{76} -6.00000 q^{77} -17.5623 q^{78} +13.4164 q^{79} -9.85410 q^{80} -11.0000 q^{81} -17.5623 q^{82} -9.70820 q^{83} +10.8541 q^{84} -3.23607 q^{85} -25.4164 q^{86} +3.29180 q^{87} +44.8328 q^{88} -4.76393 q^{89} -5.23607 q^{90} -3.00000 q^{91} +4.85410 q^{92} -7.76393 q^{93} +0.618034 q^{94} +0.472136 q^{95} -24.2705 q^{96} -13.7082 q^{97} +2.61803 q^{98} +12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + 3 q^{4} - 2 q^{5} - 5 q^{6} - 2 q^{7} + 6 q^{8} + 4 q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 + 3 * q^4 - 2 * q^5 - 5 * q^6 - 2 * q^7 + 6 * q^8 + 4 * q^9	$ 2 q + 3 q^{2} + 3 q^{4} - 2 q^{5} - 5 q^{6} - 2 q^{7} + 6 q^{8} + 4 q^{9} - 3 q^{10} + 12 q^{11} - 15 q^{12} + 6 q^{13} - 3 q^{14} + 13 q^{16} + 2 q^{17} + 6 q^{18} + 8 q^{19} - 3 q^{20} + 18 q^{22} + 2 q^{23} - 20 q^{24} + 2 q^{25} + 9 q^{26} - 3 q^{28} + 6 q^{29} + 5 q^{30} - 2 q^{31} + 15 q^{32} + 8 q^{34} + 2 q^{35} + 6 q^{36} - 10 q^{37} + 2 q^{38} - 6 q^{40} + 5 q^{42} - 6 q^{43} + 18 q^{44} - 4 q^{45} + 3 q^{46} - 4 q^{47} - 15 q^{48} + 2 q^{49} + 3 q^{50} - 10 q^{51} + 9 q^{52} - 22 q^{53} + 5 q^{54} - 12 q^{55} - 6 q^{56} + 20 q^{57} - q^{58} - 4 q^{59} + 15 q^{60} + 10 q^{61} + 7 q^{62} - 4 q^{63} + 4 q^{64} - 6 q^{65} - 30 q^{66} + 2 q^{67} + 18 q^{68} + 3 q^{70} - 4 q^{71} + 12 q^{72} + 18 q^{73} - 10 q^{74} - 18 q^{76} - 12 q^{77} - 15 q^{78} - 13 q^{80} - 22 q^{81} - 15 q^{82} - 6 q^{83} + 15 q^{84} - 2 q^{85} - 24 q^{86} + 20 q^{87} + 36 q^{88} - 14 q^{89} - 6 q^{90} - 6 q^{91} + 3 q^{92} - 20 q^{93} - q^{94} - 8 q^{95} - 15 q^{96} - 14 q^{97} + 3 q^{98} + 24 q^{99}+O(q^{100}) $ 2 * q + 3 * q^2 + 3 * q^4 - 2 * q^5 - 5 * q^6 - 2 * q^7 + 6 * q^8 + 4 * q^9 - 3 * q^10 + 12 * q^11 - 15 * q^12 + 6 * q^13 - 3 * q^14 + 13 * q^16 + 2 * q^17 + 6 * q^18 + 8 * q^19 - 3 * q^20 + 18 * q^22 + 2 * q^23 - 20 * q^24 + 2 * q^25 + 9 * q^26 - 3 * q^28 + 6 * q^29 + 5 * q^30 - 2 * q^31 + 15 * q^32 + 8 * q^34 + 2 * q^35 + 6 * q^36 - 10 * q^37 + 2 * q^38 - 6 * q^40 + 5 * q^42 - 6 * q^43 + 18 * q^44 - 4 * q^45 + 3 * q^46 - 4 * q^47 - 15 * q^48 + 2 * q^49 + 3 * q^50 - 10 * q^51 + 9 * q^52 - 22 * q^53 + 5 * q^54 - 12 * q^55 - 6 * q^56 + 20 * q^57 - q^58 - 4 * q^59 + 15 * q^60 + 10 * q^61 + 7 * q^62 - 4 * q^63 + 4 * q^64 - 6 * q^65 - 30 * q^66 + 2 * q^67 + 18 * q^68 + 3 * q^70 - 4 * q^71 + 12 * q^72 + 18 * q^73 - 10 * q^74 - 18 * q^76 - 12 * q^77 - 15 * q^78 - 13 * q^80 - 22 * q^81 - 15 * q^82 - 6 * q^83 + 15 * q^84 - 2 * q^85 - 24 * q^86 + 20 * q^87 + 36 * q^88 - 14 * q^89 - 6 * q^90 - 6 * q^91 + 3 * q^92 - 20 * q^93 - q^94 - 8 * q^95 - 15 * q^96 - 14 * q^97 + 3 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.61803	1.85123	0.925615	−	0.378467i	$-0.123549\pi$
$2$	2.61803	1.85123	0.925615	+	0.378467i	$0.123549\pi$
$3$	−2.23607	−1.29099	−0.645497	−	0.763763i	$-0.723350\pi$
$3$	−2.23607	−1.29099	−0.645497	+	0.763763i	$0.723350\pi$
$4$	4.85410	2.42705
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−5.85410	−2.38993
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	7.47214	2.64180
$9$	2.00000	0.666667
$10$	−2.61803	−0.827895
$11$	6.00000	1.80907	0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000	1.80907	0.904534	+	0.426401i	$0.140219\pi$
$12$	−10.8541	−3.13331
$13$	3.00000	0.832050	0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000	0.832050	0.416025	+	0.909353i	$0.363423\pi$
$14$	−2.61803	−0.699699
$15$	2.23607	0.577350
$16$	9.85410	2.46353
$17$	3.23607	0.784862	0.392431	−	0.919781i	$-0.371634\pi$
$17$	3.23607	0.784862	0.392431	+	0.919781i	$0.371634\pi$
$18$	5.23607	1.23415
$19$	−0.472136	−0.108315	−0.0541577	−	0.998532i	$-0.517247\pi$
$19$	−0.472136	−0.108315	−0.0541577	+	0.998532i	$0.517247\pi$
$20$	−4.85410	−1.08541
$21$	2.23607	0.487950
$22$	15.7082	3.34900
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−16.7082	−3.41055
$25$	1.00000	0.200000
$26$	7.85410	1.54032
$27$	2.23607	0.430331
$28$	−4.85410	−0.917339
$29$	−1.47214	−0.273369	−0.136684	−	0.990615i	$-0.543645\pi$
$29$	−1.47214	−0.273369	−0.136684	+	0.990615i	$0.543645\pi$
$30$	5.85410	1.06881
$31$	3.47214	0.623614	0.311807	−	0.950145i	$-0.399066\pi$
$31$	3.47214	0.623614	0.311807	+	0.950145i	$0.399066\pi$
$32$	10.8541	1.91875
$33$	−13.4164	−2.33550
$34$	8.47214	1.45296
$35$	1.00000	0.169031
$36$	9.70820	1.61803
$37$	−2.76393	−0.454388	−0.227194	−	0.973850i	$-0.572955\pi$
$37$	−2.76393	−0.454388	−0.227194	+	0.973850i	$0.572955\pi$
$38$	−1.23607	−0.200517
$39$	−6.70820	−1.07417
$40$	−7.47214	−1.18145
$41$	−6.70820	−1.04765	−0.523823	−	0.851827i	$-0.675495\pi$
$41$	−6.70820	−1.04765	−0.523823	+	0.851827i	$0.675495\pi$
$42$	5.85410	0.903308
$43$	−9.70820	−1.48049	−0.740244	−	0.672339i	$-0.765290\pi$
$43$	−9.70820	−1.48049	−0.740244	+	0.672339i	$0.765290\pi$
$44$	29.1246	4.39070
$45$	−2.00000	−0.298142
$46$	2.61803	0.386008
$47$	0.236068	0.0344341	0.0172170	−	0.999852i	$-0.494519\pi$
$47$	0.236068	0.0344341	0.0172170	+	0.999852i	$0.494519\pi$
$48$	−22.0344	−3.18040
$49$	1.00000	0.142857
$50$	2.61803	0.370246
$51$	−7.23607	−1.01325
$52$	14.5623	2.01943
$53$	−13.2361	−1.81811	−0.909057	−	0.416672i	$-0.863196\pi$
$53$	−13.2361	−1.81811	−0.909057	+	0.416672i	$0.863196\pi$
$54$	5.85410	0.796642
$55$	−6.00000	−0.809040
$56$	−7.47214	−0.998506
$57$	1.05573	0.139835
$58$	−3.85410	−0.506068
$59$	2.47214	0.321845	0.160922	−	0.986967i	$-0.448553\pi$
$59$	2.47214	0.321845	0.160922	+	0.986967i	$0.448553\pi$
$60$	10.8541	1.40126
$61$	11.7082	1.49908	0.749541	−	0.661958i	$-0.230274\pi$
$61$	11.7082	1.49908	0.749541	+	0.661958i	$0.230274\pi$
$62$	9.09017	1.15445
$63$	−2.00000	−0.251976
$64$	8.70820	1.08853
$65$	−3.00000	−0.372104
$66$	−35.1246	−4.32354
$67$	−1.23607	−0.151010	−0.0755049	−	0.997145i	$-0.524057\pi$
$67$	−1.23607	−0.151010	−0.0755049	+	0.997145i	$0.524057\pi$
$68$	15.7082	1.90490
$69$	−2.23607	−0.269191
$70$	2.61803	0.312915
$71$	0.236068	0.0280161	0.0140081	−	0.999902i	$-0.495541\pi$
$71$	0.236068	0.0280161	0.0140081	+	0.999902i	$0.495541\pi$
$72$	14.9443	1.76120
$73$	9.00000	1.05337	0.526685	−	0.850060i	$-0.323435\pi$
$73$	9.00000	1.05337	0.526685	+	0.850060i	$0.323435\pi$
$74$	−7.23607	−0.841176
$75$	−2.23607	−0.258199
$76$	−2.29180	−0.262887
$77$	−6.00000	−0.683763
$78$	−17.5623	−1.98854
$79$	13.4164	1.50946	0.754732	−	0.656033i	$-0.227767\pi$
$79$	13.4164	1.50946	0.754732	+	0.656033i	$0.227767\pi$
$80$	−9.85410	−1.10172
$81$	−11.0000	−1.22222
$82$	−17.5623	−1.93943
$83$	−9.70820	−1.06561	−0.532807	−	0.846237i	$-0.678863\pi$
$83$	−9.70820	−1.06561	−0.532807	+	0.846237i	$0.678863\pi$
$84$	10.8541	1.18428
$85$	−3.23607	−0.351001
$86$	−25.4164	−2.74072
$87$	3.29180	0.352918
$88$	44.8328	4.77919
$89$	−4.76393	−0.504976	−0.252488	−	0.967600i	$-0.581249\pi$
$89$	−4.76393	−0.504976	−0.252488	+	0.967600i	$0.581249\pi$
$90$	−5.23607	−0.551930
$91$	−3.00000	−0.314485
$92$	4.85410	0.506075
$93$	−7.76393	−0.805082
$94$	0.618034	0.0637453
$95$	0.472136	0.0484401
$96$	−24.2705	−2.47710
$97$	−13.7082	−1.39186	−0.695929	−	0.718111i	$-0.745007\pi$
$97$	−13.7082	−1.39186	−0.695929	+	0.718111i	$0.745007\pi$
$98$	2.61803	0.264461
$99$	12.0000	1.20605
$100$	4.85410	0.485410
$101$	−10.9443	−1.08900	−0.544498	−	0.838762i	$-0.683280\pi$
$101$	−10.9443	−1.08900	−0.544498	+	0.838762i	$0.683280\pi$
$102$	−18.9443	−1.87576
$103$	−16.9443	−1.66957	−0.834784	−	0.550577i	$-0.814408\pi$
$103$	−16.9443	−1.66957	−0.834784	+	0.550577i	$0.814408\pi$
$104$	22.4164	2.19811
$105$	−2.23607	−0.218218
$106$	−34.6525	−3.36575
$107$	19.8885	1.92270	0.961349	−	0.275333i	$-0.0887880\pi$
$107$	19.8885	1.92270	0.961349	+	0.275333i	$0.0887880\pi$
$108$	10.8541	1.04444
$109$	−1.70820	−0.163616	−0.0818081	−	0.996648i	$-0.526069\pi$
$109$	−1.70820	−0.163616	−0.0818081	+	0.996648i	$0.526069\pi$
$110$	−15.7082	−1.49772
$111$	6.18034	0.586612
$112$	−9.85410	−0.931125
$113$	−19.4164	−1.82654	−0.913271	−	0.407353i	$-0.866452\pi$
$113$	−19.4164	−1.82654	−0.913271	+	0.407353i	$0.866452\pi$
$114$	2.76393	0.258866
$115$	−1.00000	−0.0932505
$116$	−7.14590	−0.663480
$117$	6.00000	0.554700
$118$	6.47214	0.595808
$119$	−3.23607	−0.296650
$120$	16.7082	1.52524
$121$	25.0000	2.27273
$122$	30.6525	2.77514
$123$	15.0000	1.35250
$124$	16.8541	1.51354
$125$	−1.00000	−0.0894427
$126$	−5.23607	−0.466466
$127$	3.00000	0.266207	0.133103	−	0.991102i	$-0.457506\pi$
$127$	3.00000	0.266207	0.133103	+	0.991102i	$0.457506\pi$
$128$	1.09017	0.0963583
$129$	21.7082	1.91130
$130$	−7.85410	−0.688850
$131$	19.4721	1.70129	0.850644	−	0.525742i	$-0.176212\pi$
$131$	19.4721	1.70129	0.850644	+	0.525742i	$0.176212\pi$
$132$	−65.1246	−5.66837
$133$	0.472136	0.0409394
$134$	−3.23607	−0.279554
$135$	−2.23607	−0.192450
$136$	24.1803	2.07345
$137$	−3.23607	−0.276476	−0.138238	−	0.990399i	$-0.544144\pi$
$137$	−3.23607	−0.276476	−0.138238	+	0.990399i	$0.544144\pi$
$138$	−5.85410	−0.498334
$139$	−2.52786	−0.214411	−0.107205	−	0.994237i	$-0.534190\pi$
$139$	−2.52786	−0.214411	−0.107205	+	0.994237i	$0.534190\pi$
$140$	4.85410	0.410246
$141$	−0.527864	−0.0444542
$142$	0.618034	0.0518643
$143$	18.0000	1.50524
$144$	19.7082	1.64235
$145$	1.47214	0.122254
$146$	23.5623	1.95003
$147$	−2.23607	−0.184428
$148$	−13.4164	−1.10282
$149$	9.23607	0.756648	0.378324	−	0.925673i	$-0.376500\pi$
$149$	9.23607	0.756648	0.378324	+	0.925673i	$0.376500\pi$
$150$	−5.85410	−0.477985
$151$	17.7639	1.44561	0.722804	−	0.691053i	$-0.242853\pi$
$151$	17.7639	1.44561	0.722804	+	0.691053i	$0.242853\pi$
$152$	−3.52786	−0.286148
$153$	6.47214	0.523241
$154$	−15.7082	−1.26580
$155$	−3.47214	−0.278889
$156$	−32.5623	−2.60707
$157$	−19.2361	−1.53521	−0.767603	−	0.640926i	$-0.778551\pi$
$157$	−19.2361	−1.53521	−0.767603	+	0.640926i	$0.778551\pi$
$158$	35.1246	2.79436
$159$	29.5967	2.34717
$160$	−10.8541	−0.858092
$161$	−1.00000	−0.0788110
$162$	−28.7984	−2.26261
$163$	−17.0000	−1.33154	−0.665771	−	0.746156i	$-0.731897\pi$
$163$	−17.0000	−1.33154	−0.665771	+	0.746156i	$0.731897\pi$
$164$	−32.5623	−2.54269
$165$	13.4164	1.04447
$166$	−25.4164	−1.97270
$167$	−0.944272	−0.0730700	−0.0365350	−	0.999332i	$-0.511632\pi$
$167$	−0.944272	−0.0730700	−0.0365350	+	0.999332i	$0.511632\pi$
$168$	16.7082	1.28907
$169$	−4.00000	−0.307692
$170$	−8.47214	−0.649783
$171$	−0.944272	−0.0722103
$172$	−47.1246	−3.59322
$173$	14.9443	1.13619	0.568096	−	0.822962i	$-0.307680\pi$
$173$	14.9443	1.13619	0.568096	+	0.822962i	$0.307680\pi$
$174$	8.61803	0.653331
$175$	−1.00000	−0.0755929
$176$	59.1246	4.45669
$177$	−5.52786	−0.415500
$178$	−12.4721	−0.934826
$179$	5.29180	0.395527	0.197764	−	0.980250i	$-0.436632\pi$
$179$	5.29180	0.395527	0.197764	+	0.980250i	$0.436632\pi$
$180$	−9.70820	−0.723607
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	−7.85410	−0.582185
$183$	−26.1803	−1.93531
$184$	7.47214	0.550853
$185$	2.76393	0.203208
$186$	−20.3262	−1.49039
$187$	19.4164	1.41987
$188$	1.14590	0.0835732
$189$	−2.23607	−0.162650
$190$	1.23607	0.0896738
$191$	−8.47214	−0.613022	−0.306511	−	0.951867i	$-0.599162\pi$
$191$	−8.47214	−0.613022	−0.306511	+	0.951867i	$0.599162\pi$
$192$	−19.4721	−1.40528
$193$	−6.23607	−0.448882	−0.224441	−	0.974488i	$-0.572056\pi$
$193$	−6.23607	−0.448882	−0.224441	+	0.974488i	$0.572056\pi$
$194$	−35.8885	−2.57665
$195$	6.70820	0.480384
$196$	4.85410	0.346722
$197$	18.7082	1.33290	0.666452	−	0.745548i	$-0.267812\pi$
$197$	18.7082	1.33290	0.666452	+	0.745548i	$0.267812\pi$
$198$	31.4164	2.23267
$199$	−25.4164	−1.80172	−0.900861	−	0.434108i	$-0.857064\pi$
$199$	−25.4164	−1.80172	−0.900861	+	0.434108i	$0.857064\pi$
$200$	7.47214	0.528360
$201$	2.76393	0.194953
$202$	−28.6525	−2.01598
$203$	1.47214	0.103324
$204$	−35.1246	−2.45921
$205$	6.70820	0.468521
$206$	−44.3607	−3.09076
$207$	2.00000	0.139010
$208$	29.5623	2.04978
$209$	−2.83282	−0.195950
$210$	−5.85410	−0.403971
$211$	0.944272	0.0650064	0.0325032	−	0.999472i	$-0.489652\pi$
$211$	0.944272	0.0650064	0.0325032	+	0.999472i	$0.489652\pi$
$212$	−64.2492	−4.41265
$213$	−0.527864	−0.0361686
$214$	52.0689	3.55936
$215$	9.70820	0.662094
$216$	16.7082	1.13685
$217$	−3.47214	−0.235704
$218$	−4.47214	−0.302891
$219$	−20.1246	−1.35990
$220$	−29.1246	−1.96358
$221$	9.70820	0.653044
$222$	16.1803	1.08595
$223$	4.94427	0.331093	0.165546	−	0.986202i	$-0.447061\pi$
$223$	4.94427	0.331093	0.165546	+	0.986202i	$0.447061\pi$
$224$	−10.8541	−0.725220
$225$	2.00000	0.133333
$226$	−50.8328	−3.38135
$227$	7.41641	0.492244	0.246122	−	0.969239i	$-0.420844\pi$
$227$	7.41641	0.492244	0.246122	+	0.969239i	$0.420844\pi$
$228$	5.12461	0.339386
$229$	−12.0000	−0.792982	−0.396491	−	0.918039i	$-0.629772\pi$
$229$	−12.0000	−0.792982	−0.396491	+	0.918039i	$0.629772\pi$
$230$	−2.61803	−0.172628
$231$	13.4164	0.882735
$232$	−11.0000	−0.722185
$233$	−6.70820	−0.439469	−0.219735	−	0.975560i	$-0.570519\pi$
$233$	−6.70820	−0.439469	−0.219735	+	0.975560i	$0.570519\pi$
$234$	15.7082	1.02688
$235$	−0.236068	−0.0153994
$236$	12.0000	0.781133
$237$	−30.0000	−1.94871
$238$	−8.47214	−0.549167
$239$	−13.6525	−0.883105	−0.441553	−	0.897235i	$-0.645572\pi$
$239$	−13.6525	−0.883105	−0.441553	+	0.897235i	$0.645572\pi$
$240$	22.0344	1.42232
$241$	11.1246	0.716599	0.358300	−	0.933607i	$-0.383357\pi$
$241$	11.1246	0.716599	0.358300	+	0.933607i	$0.383357\pi$
$242$	65.4508	4.20734
$243$	17.8885	1.14755
$244$	56.8328	3.63835
$245$	−1.00000	−0.0638877
$246$	39.2705	2.50380
$247$	−1.41641	−0.0901239
$248$	25.9443	1.64746
$249$	21.7082	1.37570
$250$	−2.61803	−0.165579
$251$	8.94427	0.564557	0.282279	−	0.959332i	$-0.408910\pi$
$251$	8.94427	0.564557	0.282279	+	0.959332i	$0.408910\pi$
$252$	−9.70820	−0.611559
$253$	6.00000	0.377217
$254$	7.85410	0.492810
$255$	7.23607	0.453140
$256$	−14.5623	−0.910144
$257$	27.3607	1.70671	0.853356	−	0.521328i	$-0.174563\pi$
$257$	27.3607	1.70671	0.853356	+	0.521328i	$0.174563\pi$
$258$	56.8328	3.53826
$259$	2.76393	0.171742
$260$	−14.5623	−0.903116
$261$	−2.94427	−0.182246
$262$	50.9787	3.14948
$263$	25.5967	1.57836	0.789182	−	0.614160i	$-0.210505\pi$
$263$	25.5967	1.57836	0.789182	+	0.614160i	$0.210505\pi$
$264$	−100.249	−6.16991
$265$	13.2361	0.813085
$266$	1.23607	0.0757882
$267$	10.6525	0.651921
$268$	−6.00000	−0.366508
$269$	6.70820	0.409006	0.204503	−	0.978866i	$-0.434442\pi$
$269$	6.70820	0.409006	0.204503	+	0.978866i	$0.434442\pi$
$270$	−5.85410	−0.356269
$271$	−26.4721	−1.60807	−0.804034	−	0.594583i	$-0.797317\pi$
$271$	−26.4721	−1.60807	−0.804034	+	0.594583i	$0.797317\pi$
$272$	31.8885	1.93353
$273$	6.70820	0.405999
$274$	−8.47214	−0.511820
$275$	6.00000	0.361814
$276$	−10.8541	−0.653340
$277$	−33.0689	−1.98692	−0.993458	−	0.114195i	$-0.963571\pi$
$277$	−33.0689	−1.98692	−0.993458	+	0.114195i	$0.963571\pi$
$278$	−6.61803	−0.396923
$279$	6.94427	0.415743
$280$	7.47214	0.446546
$281$	−8.18034	−0.487998	−0.243999	−	0.969775i	$-0.578459\pi$
$281$	−8.18034	−0.487998	−0.243999	+	0.969775i	$0.578459\pi$
$282$	−1.38197	−0.0822949
$283$	11.1246	0.661290	0.330645	−	0.943755i	$-0.392734\pi$
$283$	11.1246	0.661290	0.330645	+	0.943755i	$0.392734\pi$
$284$	1.14590	0.0679965
$285$	−1.05573	−0.0625359
$286$	47.1246	2.78654
$287$	6.70820	0.395973
$288$	21.7082	1.27917
$289$	−6.52786	−0.383992
$290$	3.85410	0.226321
$291$	30.6525	1.79688
$292$	43.6869	2.55658
$293$	−32.1803	−1.88000	−0.939998	−	0.341181i	$-0.889173\pi$
$293$	−32.1803	−1.88000	−0.939998	+	0.341181i	$0.889173\pi$
$294$	−5.85410	−0.341418
$295$	−2.47214	−0.143933
$296$	−20.6525	−1.20040
$297$	13.4164	0.778499
$298$	24.1803	1.40073
$299$	3.00000	0.173494
$300$	−10.8541	−0.626662
$301$	9.70820	0.559572
$302$	46.5066	2.67615
$303$	24.4721	1.40589
$304$	−4.65248	−0.266838
$305$	−11.7082	−0.670410
$306$	16.9443	0.968640
$307$	19.4164	1.10815	0.554076	−	0.832466i	$-0.313072\pi$
$307$	19.4164	1.10815	0.554076	+	0.832466i	$0.313072\pi$
$308$	−29.1246	−1.65953
$309$	37.8885	2.15540
$310$	−9.09017	−0.516287
$311$	−10.4164	−0.590660	−0.295330	−	0.955395i	$-0.595430\pi$
$311$	−10.4164	−0.590660	−0.295330	+	0.955395i	$0.595430\pi$
$312$	−50.1246	−2.83775
$313$	−6.29180	−0.355633	−0.177817	−	0.984064i	$-0.556903\pi$
$313$	−6.29180	−0.355633	−0.177817	+	0.984064i	$0.556903\pi$
$314$	−50.3607	−2.84202
$315$	2.00000	0.112687
$316$	65.1246	3.66355
$317$	−3.52786	−0.198145	−0.0990723	−	0.995080i	$-0.531588\pi$
$317$	−3.52786	−0.198145	−0.0990723	+	0.995080i	$0.531588\pi$
$318$	77.4853	4.34516
$319$	−8.83282	−0.494543
$320$	−8.70820	−0.486803
$321$	−44.4721	−2.48219
$322$	−2.61803	−0.145897
$323$	−1.52786	−0.0850126
$324$	−53.3951	−2.96640
$325$	3.00000	0.166410
$326$	−44.5066	−2.46499
$327$	3.81966	0.211228
$328$	−50.1246	−2.76767
$329$	−0.236068	−0.0130148
$330$	35.1246	1.93355
$331$	20.1246	1.10615	0.553074	−	0.833132i	$-0.313455\pi$
$331$	20.1246	1.10615	0.553074	+	0.833132i	$0.313455\pi$
$332$	−47.1246	−2.58630
$333$	−5.52786	−0.302925
$334$	−2.47214	−0.135269
$335$	1.23607	0.0675336
$336$	22.0344	1.20208
$337$	−7.41641	−0.403997	−0.201999	−	0.979386i	$-0.564744\pi$
$337$	−7.41641	−0.403997	−0.201999	+	0.979386i	$0.564744\pi$
$338$	−10.4721	−0.569609
$339$	43.4164	2.35806
$340$	−15.7082	−0.851897
$341$	20.8328	1.12816
$342$	−2.47214	−0.133678
$343$	−1.00000	−0.0539949
$344$	−72.5410	−3.91115
$345$	2.23607	0.120386
$346$	39.1246	2.10335
$347$	30.4721	1.63583	0.817915	−	0.575339i	$-0.195130\pi$
$347$	30.4721	1.63583	0.817915	+	0.575339i	$0.195130\pi$
$348$	15.9787	0.856549
$349$	−11.7639	−0.629709	−0.314854	−	0.949140i	$-0.601956\pi$
$349$	−11.7639	−0.629709	−0.314854	+	0.949140i	$0.601956\pi$
$350$	−2.61803	−0.139940
$351$	6.70820	0.358057
$352$	65.1246	3.47115
$353$	12.0557	0.641662	0.320831	−	0.947137i	$-0.396038\pi$
$353$	12.0557	0.641662	0.320831	+	0.947137i	$0.396038\pi$
$354$	−14.4721	−0.769185
$355$	−0.236068	−0.0125292
$356$	−23.1246	−1.22560
$357$	7.23607	0.382973
$358$	13.8541	0.732212
$359$	2.94427	0.155393	0.0776964	−	0.996977i	$-0.475244\pi$
$359$	2.94427	0.155393	0.0776964	+	0.996977i	$0.475244\pi$
$360$	−14.9443	−0.787632
$361$	−18.7771	−0.988268
$362$	−26.1803	−1.37601
$363$	−55.9017	−2.93408
$364$	−14.5623	−0.763272
$365$	−9.00000	−0.471082
$366$	−68.5410	−3.58270
$367$	−4.76393	−0.248675	−0.124338	−	0.992240i	$-0.539681\pi$
$367$	−4.76393	−0.248675	−0.124338	+	0.992240i	$0.539681\pi$
$368$	9.85410	0.513681
$369$	−13.4164	−0.698430
$370$	7.23607	0.376185
$371$	13.2361	0.687182
$372$	−37.6869	−1.95398
$373$	−13.2361	−0.685338	−0.342669	−	0.939456i	$-0.611331\pi$
$373$	−13.2361	−0.685338	−0.342669	+	0.939456i	$0.611331\pi$
$374$	50.8328	2.62850
$375$	2.23607	0.115470
$376$	1.76393	0.0909678
$377$	−4.41641	−0.227457
$378$	−5.85410	−0.301103
$379$	31.5967	1.62302	0.811508	−	0.584341i	$-0.198647\pi$
$379$	31.5967	1.62302	0.811508	+	0.584341i	$0.198647\pi$
$380$	2.29180	0.117567
$381$	−6.70820	−0.343672
$382$	−22.1803	−1.13484
$383$	2.47214	0.126320	0.0631601	−	0.998003i	$-0.479882\pi$
$383$	2.47214	0.126320	0.0631601	+	0.998003i	$0.479882\pi$
$384$	−2.43769	−0.124398
$385$	6.00000	0.305788
$386$	−16.3262	−0.830984
$387$	−19.4164	−0.986991
$388$	−66.5410	−3.37811
$389$	25.8885	1.31260	0.656301	−	0.754499i	$-0.272120\pi$
$389$	25.8885	1.31260	0.656301	+	0.754499i	$0.272120\pi$
$390$	17.5623	0.889302
$391$	3.23607	0.163655
$392$	7.47214	0.377400
$393$	−43.5410	−2.19635
$394$	48.9787	2.46751
$395$	−13.4164	−0.675053
$396$	58.2492	2.92713
$397$	−0.416408	−0.0208989	−0.0104495	−	0.999945i	$-0.503326\pi$
$397$	−0.416408	−0.0208989	−0.0104495	+	0.999945i	$0.503326\pi$
$398$	−66.5410	−3.33540
$399$	−1.05573	−0.0528525
$400$	9.85410	0.492705
$401$	−13.5967	−0.678989	−0.339495	−	0.940608i	$-0.610256\pi$
$401$	−13.5967	−0.678989	−0.339495	+	0.940608i	$0.610256\pi$
$402$	7.23607	0.360902
$403$	10.4164	0.518878
$404$	−53.1246	−2.64305
$405$	11.0000	0.546594
$406$	3.85410	0.191276
$407$	−16.5836	−0.822018
$408$	−54.0689	−2.67681
$409$	37.1803	1.83845	0.919225	−	0.393733i	$-0.128817\pi$
$409$	37.1803	1.83845	0.919225	+	0.393733i	$0.128817\pi$
$410$	17.5623	0.867340
$411$	7.23607	0.356929
$412$	−82.2492	−4.05213
$413$	−2.47214	−0.121646
$414$	5.23607	0.257339
$415$	9.70820	0.476557
$416$	32.5623	1.59650
$417$	5.65248	0.276803
$418$	−7.41641	−0.362748
$419$	−14.6525	−0.715820	−0.357910	−	0.933756i	$-0.616511\pi$
$419$	−14.6525	−0.715820	−0.357910	+	0.933756i	$0.616511\pi$
$420$	−10.8541	−0.529626
$421$	32.0000	1.55958	0.779792	−	0.626038i	$-0.215325\pi$
$421$	32.0000	1.55958	0.779792	+	0.626038i	$0.215325\pi$
$422$	2.47214	0.120342
$423$	0.472136	0.0229560
$424$	−98.9017	−4.80309
$425$	3.23607	0.156972
$426$	−1.38197	−0.0669565
$427$	−11.7082	−0.566600
$428$	96.5410	4.66649
$429$	−40.2492	−1.94325
$430$	25.4164	1.22569
$431$	3.05573	0.147189	0.0735946	−	0.997288i	$-0.476553\pi$
$431$	3.05573	0.147189	0.0735946	+	0.997288i	$0.476553\pi$
$432$	22.0344	1.06013
$433$	4.29180	0.206251	0.103125	−	0.994668i	$-0.467116\pi$
$433$	4.29180	0.206251	0.103125	+	0.994668i	$0.467116\pi$
$434$	−9.09017	−0.436342
$435$	−3.29180	−0.157830
$436$	−8.29180	−0.397105
$437$	−0.472136	−0.0225853
$438$	−52.6869	−2.51748
$439$	−9.00000	−0.429547	−0.214773	−	0.976664i	$-0.568901\pi$
$439$	−9.00000	−0.429547	−0.214773	+	0.976664i	$0.568901\pi$
$440$	−44.8328	−2.13732
$441$	2.00000	0.0952381
$442$	25.4164	1.20894
$443$	−7.36068	−0.349716	−0.174858	−	0.984594i	$-0.555947\pi$
$443$	−7.36068	−0.349716	−0.174858	+	0.984594i	$0.555947\pi$
$444$	30.0000	1.42374
$445$	4.76393	0.225832
$446$	12.9443	0.612929
$447$	−20.6525	−0.976829
$448$	−8.70820	−0.411424
$449$	−25.4164	−1.19947	−0.599737	−	0.800197i	$-0.704728\pi$
$449$	−25.4164	−1.19947	−0.599737	+	0.800197i	$0.704728\pi$
$450$	5.23607	0.246831
$451$	−40.2492	−1.89526
$452$	−94.2492	−4.43311
$453$	−39.7214	−1.86627
$454$	19.4164	0.911257
$455$	3.00000	0.140642
$456$	7.88854	0.369415
$457$	−28.7639	−1.34552	−0.672760	−	0.739861i	$-0.734891\pi$
$457$	−28.7639	−1.34552	−0.672760	+	0.739861i	$0.734891\pi$
$458$	−31.4164	−1.46799
$459$	7.23607	0.337751
$460$	−4.85410	−0.226324
$461$	3.65248	0.170113	0.0850564	−	0.996376i	$-0.472893\pi$
$461$	3.65248	0.170113	0.0850564	+	0.996376i	$0.472893\pi$
$462$	35.1246	1.63414
$463$	34.8328	1.61882	0.809409	−	0.587245i	$-0.199788\pi$
$463$	34.8328	1.61882	0.809409	+	0.587245i	$0.199788\pi$
$464$	−14.5066	−0.673451
$465$	7.76393	0.360044
$466$	−17.5623	−0.813558
$467$	9.05573	0.419049	0.209525	−	0.977803i	$-0.432808\pi$
$467$	9.05573	0.419049	0.209525	+	0.977803i	$0.432808\pi$
$468$	29.1246	1.34629
$469$	1.23607	0.0570763
$470$	−0.618034	−0.0285078
$471$	43.0132	1.98194
$472$	18.4721	0.850249
$473$	−58.2492	−2.67830
$474$	−78.5410	−3.60751
$475$	−0.472136	−0.0216631
$476$	−15.7082	−0.719984
$477$	−26.4721	−1.21208
$478$	−35.7426	−1.63483
$479$	−26.8328	−1.22602	−0.613011	−	0.790074i	$-0.710042\pi$
$479$	−26.8328	−1.22602	−0.613011	+	0.790074i	$0.710042\pi$
$480$	24.2705	1.10779
$481$	−8.29180	−0.378073
$482$	29.1246	1.32659
$483$	2.23607	0.101745
$484$	121.353	5.51602
$485$	13.7082	0.622457
$486$	46.8328	2.12438
$487$	−40.4164	−1.83144	−0.915721	−	0.401814i	$-0.868380\pi$
$487$	−40.4164	−1.83144	−0.915721	+	0.401814i	$0.868380\pi$
$488$	87.4853	3.96027
$489$	38.0132	1.71901
$490$	−2.61803	−0.118271
$491$	−9.18034	−0.414303	−0.207151	−	0.978309i	$-0.566419\pi$
$491$	−9.18034	−0.414303	−0.207151	+	0.978309i	$0.566419\pi$
$492$	72.8115	3.28260
$493$	−4.76393	−0.214557
$494$	−3.70820	−0.166840
$495$	−12.0000	−0.539360
$496$	34.2148	1.53629
$497$	−0.236068	−0.0105891
$498$	56.8328	2.54674
$499$	−8.70820	−0.389833	−0.194916	−	0.980820i	$-0.562444\pi$
$499$	−8.70820	−0.389833	−0.194916	+	0.980820i	$0.562444\pi$
$500$	−4.85410	−0.217082
$501$	2.11146	0.0943329
$502$	23.4164	1.04513
$503$	26.7639	1.19334	0.596672	−	0.802485i	$-0.296489\pi$
$503$	26.7639	1.19334	0.596672	+	0.802485i	$0.296489\pi$
$504$	−14.9443	−0.665671
$505$	10.9443	0.487014
$506$	15.7082	0.698315
$507$	8.94427	0.397229
$508$	14.5623	0.646098
$509$	40.0132	1.77355	0.886776	−	0.462200i	$-0.152940\pi$
$509$	40.0132	1.77355	0.886776	+	0.462200i	$0.152940\pi$
$510$	18.9443	0.838866
$511$	−9.00000	−0.398137
$512$	−40.3050	−1.78124
$513$	−1.05573	−0.0466115
$514$	71.6312	3.15952
$515$	16.9443	0.746654
$516$	105.374	4.63882
$517$	1.41641	0.0622935
$518$	7.23607	0.317935
$519$	−33.4164	−1.46682
$520$	−22.4164	−0.983025
$521$	5.88854	0.257982	0.128991	−	0.991646i	$-0.458826\pi$
$521$	5.88854	0.257982	0.128991	+	0.991646i	$0.458826\pi$
$522$	−7.70820	−0.337379
$523$	32.5410	1.42292	0.711460	−	0.702727i	$-0.248034\pi$
$523$	32.5410	1.42292	0.711460	+	0.702727i	$0.248034\pi$
$524$	94.5197	4.12911
$525$	2.23607	0.0975900
$526$	67.0132	2.92191
$527$	11.2361	0.489451
$528$	−132.207	−5.75356
$529$	1.00000	0.0434783
$530$	34.6525	1.50521
$531$	4.94427	0.214563
$532$	2.29180	0.0993620
$533$	−20.1246	−0.871694
$534$	27.8885	1.20686
$535$	−19.8885	−0.859857
$536$	−9.23607	−0.398937
$537$	−11.8328	−0.510624
$538$	17.5623	0.757165
$539$	6.00000	0.258438
$540$	−10.8541	−0.467086
$541$	13.0000	0.558914	0.279457	−	0.960158i	$-0.409846\pi$
$541$	13.0000	0.558914	0.279457	+	0.960158i	$0.409846\pi$
$542$	−69.3050	−2.97690
$543$	22.3607	0.959589
$544$	35.1246	1.50596
$545$	1.70820	0.0731714
$546$	17.5623	0.751597
$547$	33.4721	1.43117	0.715583	−	0.698528i	$-0.246161\pi$
$547$	33.4721	1.43117	0.715583	+	0.698528i	$0.246161\pi$
$548$	−15.7082	−0.671021
$549$	23.4164	0.999388
$550$	15.7082	0.669800
$551$	0.695048	0.0296101
$552$	−16.7082	−0.711148
$553$	−13.4164	−0.570524
$554$	−86.5755	−3.67824
$555$	−6.18034	−0.262341
$556$	−12.2705	−0.520386
$557$	−12.0000	−0.508456	−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000	−0.508456	−0.254228	+	0.967144i	$0.581821\pi$
$558$	18.1803	0.769635
$559$	−29.1246	−1.23184
$560$	9.85410	0.416412
$561$	−43.4164	−1.83304
$562$	−21.4164	−0.903397
$563$	32.1803	1.35624	0.678120	−	0.734951i	$-0.262795\pi$
$563$	32.1803	1.35624	0.678120	+	0.734951i	$0.262795\pi$
$564$	−2.56231	−0.107893
$565$	19.4164	0.816854
$566$	29.1246	1.22420
$567$	11.0000	0.461957
$568$	1.76393	0.0740129
$569$	−27.5279	−1.15403	−0.577014	−	0.816734i	$-0.695782\pi$
$569$	−27.5279	−1.15403	−0.577014	+	0.816734i	$0.695782\pi$
$570$	−2.76393	−0.115768
$571$	0	0		−	1.00000i	$-0.5\pi$
$571$	0	0			1.00000i	$0.5\pi$
$572$	87.3738	3.65328
$573$	18.9443	0.791408
$574$	17.5623	0.733036
$575$	1.00000	0.0417029
$576$	17.4164	0.725684
$577$	−5.11146	−0.212793	−0.106396	−	0.994324i	$-0.533931\pi$
$577$	−5.11146	−0.212793	−0.106396	+	0.994324i	$0.533931\pi$
$578$	−17.0902	−0.710857
$579$	13.9443	0.579504
$580$	7.14590	0.296717
$581$	9.70820	0.402764
$582$	80.2492	3.32644
$583$	−79.4164	−3.28909
$584$	67.2492	2.78279
$585$	−6.00000	−0.248069
$586$	−84.2492	−3.48030
$587$	−37.0689	−1.53000	−0.764998	−	0.644032i	$-0.777260\pi$
$587$	−37.0689	−1.53000	−0.764998	+	0.644032i	$0.777260\pi$
$588$	−10.8541	−0.447616
$589$	−1.63932	−0.0675470
$590$	−6.47214	−0.266454
$591$	−41.8328	−1.72077
$592$	−27.2361	−1.11940
$593$	41.7771	1.71558	0.857790	−	0.514001i	$-0.171837\pi$
$593$	41.7771	1.71558	0.857790	+	0.514001i	$0.171837\pi$
$594$	35.1246	1.44118
$595$	3.23607	0.132666
$596$	44.8328	1.83642
$597$	56.8328	2.32601
$598$	7.85410	0.321178
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	−16.7082	−0.682110
$601$	−34.5967	−1.41123	−0.705615	−	0.708595i	$-0.749329\pi$
$601$	−34.5967	−1.41123	−0.705615	+	0.708595i	$0.749329\pi$
$602$	25.4164	1.03590
$603$	−2.47214	−0.100673
$604$	86.2279	3.50857
$605$	−25.0000	−1.01639
$606$	64.0689	2.60262
$607$	−23.4164	−0.950443	−0.475221	−	0.879866i	$-0.657632\pi$
$607$	−23.4164	−0.950443	−0.475221	+	0.879866i	$0.657632\pi$
$608$	−5.12461	−0.207830
$609$	−3.29180	−0.133390
$610$	−30.6525	−1.24108
$611$	0.708204	0.0286509
$612$	31.4164	1.26993
$613$	−33.5279	−1.35418	−0.677089	−	0.735901i	$-0.736759\pi$
$613$	−33.5279	−1.35418	−0.677089	+	0.735901i	$0.736759\pi$
$614$	50.8328	2.05145
$615$	−15.0000	−0.604858
$616$	−44.8328	−1.80637
$617$	16.4721	0.663143	0.331572	−	0.943430i	$-0.392421\pi$
$617$	16.4721	0.663143	0.331572	+	0.943430i	$0.392421\pi$
$618$	99.1935	3.99015
$619$	−22.6525	−0.910480	−0.455240	−	0.890369i	$-0.650447\pi$
$619$	−22.6525	−0.910480	−0.455240	+	0.890369i	$0.650447\pi$
$620$	−16.8541	−0.676877
$621$	2.23607	0.0897303
$622$	−27.2705	−1.09345
$623$	4.76393	0.190863
$624$	−66.1033	−2.64625
$625$	1.00000	0.0400000
$626$	−16.4721	−0.658359
$627$	6.33437	0.252970
$628$	−93.3738	−3.72602
$629$	−8.94427	−0.356631
$630$	5.23607	0.208610
$631$	−20.7639	−0.826599	−0.413300	−	0.910595i	$-0.635624\pi$
$631$	−20.7639	−0.826599	−0.413300	+	0.910595i	$0.635624\pi$
$632$	100.249	3.98770
$633$	−2.11146	−0.0839228
$634$	−9.23607	−0.366811
$635$	−3.00000	−0.119051
$636$	143.666	5.69671
$637$	3.00000	0.118864
$638$	−23.1246	−0.915512
$639$	0.472136	0.0186774
$640$	−1.09017	−0.0430928
$641$	41.1246	1.62432	0.812162	−	0.583432i	$-0.198290\pi$
$641$	41.1246	1.62432	0.812162	+	0.583432i	$0.198290\pi$
$642$	−116.430	−4.59511
$643$	−43.8885	−1.73080	−0.865398	−	0.501086i	$-0.832934\pi$
$643$	−43.8885	−1.73080	−0.865398	+	0.501086i	$0.832934\pi$
$644$	−4.85410	−0.191278
$645$	−21.7082	−0.854760
$646$	−4.00000	−0.157378
$647$	−27.1803	−1.06857	−0.534285	−	0.845305i	$-0.679419\pi$
$647$	−27.1803	−1.06857	−0.534285	+	0.845305i	$0.679419\pi$
$648$	−82.1935	−3.22887
$649$	14.8328	0.582239
$650$	7.85410	0.308063
$651$	7.76393	0.304292
$652$	−82.5197	−3.23172
$653$	6.59675	0.258151	0.129075	−	0.991635i	$-0.458799\pi$
$653$	6.59675	0.258151	0.129075	+	0.991635i	$0.458799\pi$
$654$	10.0000	0.391031
$655$	−19.4721	−0.760839
$656$	−66.1033	−2.58090
$657$	18.0000	0.702247
$658$	−0.618034	−0.0240935
$659$	15.0557	0.586488	0.293244	−	0.956038i	$-0.405265\pi$
$659$	15.0557	0.586488	0.293244	+	0.956038i	$0.405265\pi$
$660$	65.1246	2.53497
$661$	−12.2918	−0.478095	−0.239048	−	0.971008i	$-0.576835\pi$
$661$	−12.2918	−0.478095	−0.239048	+	0.971008i	$0.576835\pi$
$662$	52.6869	2.04774
$663$	−21.7082	−0.843077
$664$	−72.5410	−2.81514
$665$	−0.472136	−0.0183086
$666$	−14.4721	−0.560784
$667$	−1.47214	−0.0570013
$668$	−4.58359	−0.177345
$669$	−11.0557	−0.427439
$670$	3.23607	0.125020
$671$	70.2492	2.71194
$672$	24.2705	0.936255
$673$	40.7082	1.56919	0.784593	−	0.620011i	$-0.212872\pi$
$673$	40.7082	1.56919	0.784593	+	0.620011i	$0.212872\pi$
$674$	−19.4164	−0.747892
$675$	2.23607	0.0860663
$676$	−19.4164	−0.746785
$677$	−13.8197	−0.531133	−0.265566	−	0.964093i	$-0.585559\pi$
$677$	−13.8197	−0.531133	−0.265566	+	0.964093i	$0.585559\pi$
$678$	113.666	4.36530
$679$	13.7082	0.526073
$680$	−24.1803	−0.927274
$681$	−16.5836	−0.635485
$682$	54.5410	2.08848
$683$	−1.36068	−0.0520650	−0.0260325	−	0.999661i	$-0.508287\pi$
$683$	−1.36068	−0.0520650	−0.0260325	+	0.999661i	$0.508287\pi$
$684$	−4.58359	−0.175258
$685$	3.23607	0.123644
$686$	−2.61803	−0.0999570
$687$	26.8328	1.02374
$688$	−95.6656	−3.64722
$689$	−39.7082	−1.51276
$690$	5.85410	0.222862
$691$	−6.83282	−0.259933	−0.129966	−	0.991518i	$-0.541487\pi$
$691$	−6.83282	−0.259933	−0.129966	+	0.991518i	$0.541487\pi$
$692$	72.5410	2.75760
$693$	−12.0000	−0.455842
$694$	79.7771	3.02830
$695$	2.52786	0.0958873
$696$	24.5967	0.932337
$697$	−21.7082	−0.822257
$698$	−30.7984	−1.16574
$699$	15.0000	0.567352
$700$	−4.85410	−0.183468
$701$	9.70820	0.366674	0.183337	−	0.983050i	$-0.441310\pi$
$701$	9.70820	0.366674	0.183337	+	0.983050i	$0.441310\pi$
$702$	17.5623	0.662847
$703$	1.30495	0.0492172
$704$	52.2492	1.96922
$705$	0.527864	0.0198805
$706$	31.5623	1.18786
$707$	10.9443	0.411602
$708$	−26.8328	−1.00844
$709$	−16.9443	−0.636355	−0.318178	−	0.948031i	$-0.603071\pi$
$709$	−16.9443	−0.636355	−0.318178	+	0.948031i	$0.603071\pi$
$710$	−0.618034	−0.0231944
$711$	26.8328	1.00631
$712$	−35.5967	−1.33404
$713$	3.47214	0.130033
$714$	18.9443	0.708972
$715$	−18.0000	−0.673162
$716$	25.6869	0.959965
$717$	30.5279	1.14008
$718$	7.70820	0.287668
$719$	28.9443	1.07944	0.539720	−	0.841845i	$-0.318530\pi$
$719$	28.9443	1.07944	0.539720	+	0.841845i	$0.318530\pi$
$720$	−19.7082	−0.734481
$721$	16.9443	0.631038
$722$	−49.1591	−1.82951
$723$	−24.8754	−0.925126
$724$	−48.5410	−1.80401
$725$	−1.47214	−0.0546738
$726$	−146.353	−5.43165
$727$	−18.0000	−0.667583	−0.333792	−	0.942647i	$-0.608328\pi$
$727$	−18.0000	−0.667583	−0.333792	+	0.942647i	$0.608328\pi$
$728$	−22.4164	−0.830807
$729$	−7.00000	−0.259259
$730$	−23.5623	−0.872080
$731$	−31.4164	−1.16198
$732$	−127.082	−4.69709
$733$	−9.70820	−0.358581	−0.179290	−	0.983796i	$-0.557380\pi$
$733$	−9.70820	−0.358581	−0.179290	+	0.983796i	$0.557380\pi$
$734$	−12.4721	−0.460355
$735$	2.23607	0.0824786
$736$	10.8541	0.400088
$737$	−7.41641	−0.273187
$738$	−35.1246	−1.29295
$739$	20.1246	0.740296	0.370148	−	0.928973i	$-0.379307\pi$
$739$	20.1246	0.740296	0.370148	+	0.928973i	$0.379307\pi$
$740$	13.4164	0.493197
$741$	3.16718	0.116349
$742$	34.6525	1.27213
$743$	−38.0689	−1.39661	−0.698306	−	0.715799i	$-0.746062\pi$
$743$	−38.0689	−1.39661	−0.698306	+	0.715799i	$0.746062\pi$
$744$	−58.0132	−2.12687
$745$	−9.23607	−0.338383
$746$	−34.6525	−1.26872
$747$	−19.4164	−0.710409
$748$	94.2492	3.44609
$749$	−19.8885	−0.726712
$750$	5.85410	0.213762
$751$	6.87539	0.250886	0.125443	−	0.992101i	$-0.459965\pi$
$751$	6.87539	0.250886	0.125443	+	0.992101i	$0.459965\pi$
$752$	2.32624	0.0848292
$753$	−20.0000	−0.728841
$754$	−11.5623	−0.421074
$755$	−17.7639	−0.646496
$756$	−10.8541	−0.394760
$757$	−27.3050	−0.992415	−0.496208	−	0.868204i	$-0.665275\pi$
$757$	−27.3050	−0.992415	−0.496208	+	0.868204i	$0.665275\pi$
$758$	82.7214	3.00458
$759$	−13.4164	−0.486985
$760$	3.52786	0.127969
$761$	−2.23607	−0.0810574	−0.0405287	−	0.999178i	$-0.512904\pi$
$761$	−2.23607	−0.0810574	−0.0405287	+	0.999178i	$0.512904\pi$
$762$	−17.5623	−0.636215
$763$	1.70820	0.0618411
$764$	−41.1246	−1.48784
$765$	−6.47214	−0.234001
$766$	6.47214	0.233848
$767$	7.41641	0.267791
$768$	32.5623	1.17499
$769$	16.8328	0.607007	0.303503	−	0.952830i	$-0.401844\pi$
$769$	16.8328	0.607007	0.303503	+	0.952830i	$0.401844\pi$
$770$	15.7082	0.566084
$771$	−61.1803	−2.20336
$772$	−30.2705	−1.08946
$773$	−2.83282	−0.101889	−0.0509446	−	0.998701i	$-0.516223\pi$
$773$	−2.83282	−0.101889	−0.0509446	+	0.998701i	$0.516223\pi$
$774$	−50.8328	−1.82715
$775$	3.47214	0.124723
$776$	−102.430	−3.67701
$777$	−6.18034	−0.221718
$778$	67.7771	2.42993
$779$	3.16718	0.113476
$780$	32.5623	1.16592
$781$	1.41641	0.0506831
$782$	8.47214	0.302963
$783$	−3.29180	−0.117639
$784$	9.85410	0.351932
$785$	19.2361	0.686565
$786$	−113.992	−4.06596
$787$	3.63932	0.129728	0.0648639	−	0.997894i	$-0.479339\pi$
$787$	3.63932	0.129728	0.0648639	+	0.997894i	$0.479339\pi$
$788$	90.8115	3.23503
$789$	−57.2361	−2.03766
$790$	−35.1246	−1.24968
$791$	19.4164	0.690368
$792$	89.6656	3.18613
$793$	35.1246	1.24731
$794$	−1.09017	−0.0386887
$795$	−29.5967	−1.04969
$796$	−123.374	−4.37287
$797$	10.9443	0.387666	0.193833	−	0.981035i	$-0.437908\pi$
$797$	10.9443	0.387666	0.193833	+	0.981035i	$0.437908\pi$
$798$	−2.76393	−0.0978421
$799$	0.763932	0.0270260
$800$	10.8541	0.383750
$801$	−9.52786	−0.336651
$802$	−35.5967	−1.25696
$803$	54.0000	1.90562
$804$	13.4164	0.473160
$805$	1.00000	0.0352454
$806$	27.2705	0.960563
$807$	−15.0000	−0.528025
$808$	−81.7771	−2.87691
$809$	−0.111456	−0.00391859	−0.00195930	−	0.999998i	$-0.500624\pi$
$809$	−0.111456	−0.00391859	−0.00195930	+	0.999998i	$0.500624\pi$
$810$	28.7984	1.01187
$811$	9.00000	0.316033	0.158016	−	0.987436i	$-0.449490\pi$
$811$	9.00000	0.316033	0.158016	+	0.987436i	$0.449490\pi$
$812$	7.14590	0.250772
$813$	59.1935	2.07601
$814$	−43.4164	−1.52174
$815$	17.0000	0.595484
$816$	−71.3050	−2.49617
$817$	4.58359	0.160360
$818$	97.3394	3.40339
$819$	−6.00000	−0.209657
$820$	32.5623	1.13713
$821$	−10.3607	−0.361590	−0.180795	−	0.983521i	$-0.557867\pi$
$821$	−10.3607	−0.361590	−0.180795	+	0.983521i	$0.557867\pi$
$822$	18.9443	0.660757
$823$	19.8328	0.691328	0.345664	−	0.938358i	$-0.387654\pi$
$823$	19.8328	0.691328	0.345664	+	0.938358i	$0.387654\pi$
$824$	−126.610	−4.41066
$825$	−13.4164	−0.467099
$826$	−6.47214	−0.225194
$827$	29.3050	1.01903	0.509517	−	0.860461i	$-0.329824\pi$
$827$	29.3050	1.01903	0.509517	+	0.860461i	$0.329824\pi$
$828$	9.70820	0.337383
$829$	−30.0000	−1.04194	−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000	−1.04194	−0.520972	+	0.853574i	$0.674430\pi$
$830$	25.4164	0.882216
$831$	73.9443	2.56510
$832$	26.1246	0.905708
$833$	3.23607	0.112123
$834$	14.7984	0.512426
$835$	0.944272	0.0326779
$836$	−13.7508	−0.475581
$837$	7.76393	0.268361
$838$	−38.3607	−1.32515
$839$	6.87539	0.237365	0.118682	−	0.992932i	$-0.462133\pi$
$839$	6.87539	0.237365	0.118682	+	0.992932i	$0.462133\pi$
$840$	−16.7082	−0.576488
$841$	−26.8328	−0.925270
$842$	83.7771	2.88715
$843$	18.2918	0.630003
$844$	4.58359	0.157774
$845$	4.00000	0.137604
$846$	1.23607	0.0424969
$847$	−25.0000	−0.859010
$848$	−130.430	−4.47897
$849$	−24.8754	−0.853721
$850$	8.47214	0.290592
$851$	−2.76393	−0.0947464
$852$	−2.56231	−0.0877832
$853$	23.3050	0.797946	0.398973	−	0.916963i	$-0.369367\pi$
$853$	23.3050	0.797946	0.398973	+	0.916963i	$0.369367\pi$
$854$	−30.6525	−1.04891
$855$	0.944272	0.0322934
$856$	148.610	5.07938
$857$	−17.9443	−0.612965	−0.306482	−	0.951876i	$-0.599152\pi$
$857$	−17.9443	−0.612965	−0.306482	+	0.951876i	$0.599152\pi$
$858$	−105.374	−3.59740
$859$	−29.4721	−1.00558	−0.502788	−	0.864410i	$-0.667692\pi$
$859$	−29.4721	−1.00558	−0.502788	+	0.864410i	$0.667692\pi$
$860$	47.1246	1.60694
$861$	−15.0000	−0.511199
$862$	8.00000	0.272481
$863$	−17.3607	−0.590964	−0.295482	−	0.955348i	$-0.595480\pi$
$863$	−17.3607	−0.590964	−0.295482	+	0.955348i	$0.595480\pi$
$864$	24.2705	0.825700
$865$	−14.9443	−0.508120
$866$	11.2361	0.381817
$867$	14.5967	0.495732
$868$	−16.8541	−0.572065
$869$	80.4984	2.73072
$870$	−8.61803	−0.292179
$871$	−3.70820	−0.125648
$872$	−12.7639	−0.432241
$873$	−27.4164	−0.927905
$874$	−1.23607	−0.0418106
$875$	1.00000	0.0338062
$876$	−97.6869	−3.30054
$877$	33.4164	1.12839	0.564196	−	0.825641i	$-0.309186\pi$
$877$	33.4164	1.12839	0.564196	+	0.825641i	$0.309186\pi$
$878$	−23.5623	−0.795189
$879$	71.9574	2.42706
$880$	−59.1246	−1.99309
$881$	−38.8328	−1.30831	−0.654155	−	0.756360i	$-0.726976\pi$
$881$	−38.8328	−1.30831	−0.654155	+	0.756360i	$0.726976\pi$
$882$	5.23607	0.176308
$883$	2.11146	0.0710562	0.0355281	−	0.999369i	$-0.488689\pi$
$883$	2.11146	0.0710562	0.0355281	+	0.999369i	$0.488689\pi$
$884$	47.1246	1.58497
$885$	5.52786	0.185817
$886$	−19.2705	−0.647405
$887$	−34.0132	−1.14205	−0.571025	−	0.820933i	$-0.693454\pi$
$887$	−34.0132	−1.14205	−0.571025	+	0.820933i	$0.693454\pi$
$888$	46.1803	1.54971
$889$	−3.00000	−0.100617
$890$	12.4721	0.418067
$891$	−66.0000	−2.21108
$892$	24.0000	0.803579
$893$	−0.111456	−0.00372974
$894$	−54.0689	−1.80833
$895$	−5.29180	−0.176885
$896$	−1.09017	−0.0364200
$897$	−6.70820	−0.223980
$898$	−66.5410	−2.22050
$899$	−5.11146	−0.170477
$900$	9.70820	0.323607
$901$	−42.8328	−1.42697
$902$	−105.374	−3.50856
$903$	−21.7082	−0.722404
$904$	−145.082	−4.82536
$905$	10.0000	0.332411
$906$	−103.992	−3.45490
$907$	36.2492	1.20364	0.601818	−	0.798633i	$-0.294443\pi$
$907$	36.2492	1.20364	0.601818	+	0.798633i	$0.294443\pi$
$908$	36.0000	1.19470
$909$	−21.8885	−0.725997
$910$	7.85410	0.260361
$911$	15.7082	0.520436	0.260218	−	0.965550i	$-0.416206\pi$
$911$	15.7082	0.520436	0.260218	+	0.965550i	$0.416206\pi$
$912$	10.4033	0.344486
$913$	−58.2492	−1.92777
$914$	−75.3050	−2.49087
$915$	26.1803	0.865495
$916$	−58.2492	−1.92461
$917$	−19.4721	−0.643027
$918$	18.9443	0.625254
$919$	−5.12461	−0.169045	−0.0845227	−	0.996422i	$-0.526937\pi$
$919$	−5.12461	−0.169045	−0.0845227	+	0.996422i	$0.526937\pi$
$920$	−7.47214	−0.246349
$921$	−43.4164	−1.43062
$922$	9.56231	0.314918
$923$	0.708204	0.0233108
$924$	65.1246	2.14244
$925$	−2.76393	−0.0908775
$926$	91.1935	2.99680
$927$	−33.8885	−1.11305
$928$	−15.9787	−0.524527
$929$	46.9574	1.54062	0.770312	−	0.637668i	$-0.220101\pi$
$929$	46.9574	1.54062	0.770312	+	0.637668i	$0.220101\pi$
$930$	20.3262	0.666524
$931$	−0.472136	−0.0154736
$932$	−32.5623	−1.06661
$933$	23.2918	0.762539
$934$	23.7082	0.775756
$935$	−19.4164	−0.634984
$936$	44.8328	1.46541
$937$	28.6525	0.936036	0.468018	−	0.883719i	$-0.344968\pi$
$937$	28.6525	0.936036	0.468018	+	0.883719i	$0.344968\pi$
$938$	3.23607	0.105661
$939$	14.0689	0.459121
$940$	−1.14590	−0.0373751
$941$	41.3050	1.34650	0.673251	−	0.739414i	$-0.264897\pi$
$941$	41.3050	1.34650	0.673251	+	0.739414i	$0.264897\pi$
$942$	112.610	3.66903
$943$	−6.70820	−0.218449
$944$	24.3607	0.792873
$945$	2.23607	0.0727393
$946$	−152.498	−4.95815
$947$	4.41641	0.143514	0.0717570	−	0.997422i	$-0.477139\pi$
$947$	4.41641	0.143514	0.0717570	+	0.997422i	$0.477139\pi$
$948$	−145.623	−4.72962
$949$	27.0000	0.876457
$950$	−1.23607	−0.0401033
$951$	7.88854	0.255804
$952$	−24.1803	−0.783689
$953$	−14.9443	−0.484092	−0.242046	−	0.970265i	$-0.577819\pi$
$953$	−14.9443	−0.484092	−0.242046	+	0.970265i	$0.577819\pi$
$954$	−69.3050	−2.24383
$955$	8.47214	0.274152
$956$	−66.2705	−2.14334
$957$	19.7508	0.638452
$958$	−70.2492	−2.26965
$959$	3.23607	0.104498
$960$	19.4721	0.628460
$961$	−18.9443	−0.611106
$962$	−21.7082	−0.699901
$963$	39.7771	1.28180
$964$	54.0000	1.73922
$965$	6.23607	0.200746
$966$	5.85410	0.188353
$967$	17.1115	0.550267	0.275134	−	0.961406i	$-0.411278\pi$
$967$	17.1115	0.550267	0.275134	+	0.961406i	$0.411278\pi$
$968$	186.803	6.00409
$969$	3.41641	0.109751
$970$	35.8885	1.15231
$971$	2.18034	0.0699704	0.0349852	−	0.999388i	$-0.488862\pi$
$971$	2.18034	0.0699704	0.0349852	+	0.999388i	$0.488862\pi$
$972$	86.8328	2.78516
$973$	2.52786	0.0810396
$974$	−105.812	−3.39042
$975$	−6.70820	−0.214834
$976$	115.374	3.69303
$977$	45.2361	1.44723	0.723615	−	0.690204i	$-0.242479\pi$
$977$	45.2361	1.44723	0.723615	+	0.690204i	$0.242479\pi$
$978$	99.5197	3.18229
$979$	−28.5836	−0.913536
$980$	−4.85410	−0.155059
$981$	−3.41641	−0.109078
$982$	−24.0344	−0.766970
$983$	25.0132	0.797796	0.398898	−	0.916995i	$-0.369393\pi$
$983$	25.0132	0.797796	0.398898	+	0.916995i	$0.369393\pi$
$984$	112.082	3.57304
$985$	−18.7082	−0.596093
$986$	−12.4721	−0.397194
$987$	0.527864	0.0168021
$988$	−6.87539	−0.218735
$989$	−9.70820	−0.308703
$990$	−31.4164	−0.998479
$991$	4.00000	0.127064	0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000	0.127064	0.0635321	+	0.997980i	$0.479763\pi$
$992$	37.6869	1.19656
$993$	−45.0000	−1.42803
$994$	−0.618034	−0.0196028
$995$	25.4164	0.805754
$996$	105.374	3.33890
$997$	48.8328	1.54655	0.773275	−	0.634070i	$-0.218617\pi$
$997$	48.8328	1.54655	0.773275	+	0.634070i	$0.218617\pi$
$998$	−22.7984	−0.721670
$999$	−6.18034	−0.195537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.a.e.1.2	✓	2
3.2	odd	2		7245.2.a.v.1.1		2
5.4	even	2		4025.2.a.h.1.1		2
7.6	odd	2		5635.2.a.q.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.e.1.2	✓	2	1.1	even	1	trivial
4025.2.a.h.1.1		2	5.4	even	2
5635.2.a.q.1.2		2	7.6	odd	2
7245.2.a.v.1.1		2	3.2	odd	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:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.a (trivial)

\(f(q)\)	\(=\)	\(q+2.61803 q^{2} -2.23607 q^{3} +4.85410 q^{4} -1.00000 q^{5} -5.85410 q^{6} -1.00000 q^{7} +7.47214 q^{8} +2.00000 q^{9} +O(q^{10})\)	\(q+2.61803 q^{2} -2.23607 q^{3} +4.85410 q^{4} -1.00000 q^{5} -5.85410 q^{6} -1.00000 q^{7} +7.47214 q^{8} +2.00000 q^{9} -2.61803 q^{10} +6.00000 q^{11} -10.8541 q^{12} +3.00000 q^{13} -2.61803 q^{14} +2.23607 q^{15} +9.85410 q^{16} +3.23607 q^{17} +5.23607 q^{18} -0.472136 q^{19} -4.85410 q^{20} +2.23607 q^{21} +15.7082 q^{22} +1.00000 q^{23} -16.7082 q^{24} +1.00000 q^{25} +7.85410 q^{26} +2.23607 q^{27} -4.85410 q^{28} -1.47214 q^{29} +5.85410 q^{30} +3.47214 q^{31} +10.8541 q^{32} -13.4164 q^{33} +8.47214 q^{34} +1.00000 q^{35} +9.70820 q^{36} -2.76393 q^{37} -1.23607 q^{38} -6.70820 q^{39} -7.47214 q^{40} -6.70820 q^{41} +5.85410 q^{42} -9.70820 q^{43} +29.1246 q^{44} -2.00000 q^{45} +2.61803 q^{46} +0.236068 q^{47} -22.0344 q^{48} +1.00000 q^{49} +2.61803 q^{50} -7.23607 q^{51} +14.5623 q^{52} -13.2361 q^{53} +5.85410 q^{54} -6.00000 q^{55} -7.47214 q^{56} +1.05573 q^{57} -3.85410 q^{58} +2.47214 q^{59} +10.8541 q^{60} +11.7082 q^{61} +9.09017 q^{62} -2.00000 q^{63} +8.70820 q^{64} -3.00000 q^{65} -35.1246 q^{66} -1.23607 q^{67} +15.7082 q^{68} -2.23607 q^{69} +2.61803 q^{70} +0.236068 q^{71} +14.9443 q^{72} +9.00000 q^{73} -7.23607 q^{74} -2.23607 q^{75} -2.29180 q^{76} -6.00000 q^{77} -17.5623 q^{78} +13.4164 q^{79} -9.85410 q^{80} -11.0000 q^{81} -17.5623 q^{82} -9.70820 q^{83} +10.8541 q^{84} -3.23607 q^{85} -25.4164 q^{86} +3.29180 q^{87} +44.8328 q^{88} -4.76393 q^{89} -5.23607 q^{90} -3.00000 q^{91} +4.85410 q^{92} -7.76393 q^{93} +0.618034 q^{94} +0.472136 q^{95} -24.2705 q^{96} -13.7082 q^{97} +2.61803 q^{98} +12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + 3 q^{4} - 2 q^{5} - 5 q^{6} - 2 q^{7} + 6 q^{8} + 4 q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 + 3 * q^4 - 2 * q^5 - 5 * q^6 - 2 * q^7 + 6 * q^8 + 4 * q^9	\( 2 q + 3 q^{2} + 3 q^{4} - 2 q^{5} - 5 q^{6} - 2 q^{7} + 6 q^{8} + 4 q^{9} - 3 q^{10} + 12 q^{11} - 15 q^{12} + 6 q^{13} - 3 q^{14} + 13 q^{16} + 2 q^{17} + 6 q^{18} + 8 q^{19} - 3 q^{20} + 18 q^{22} + 2 q^{23} - 20 q^{24} + 2 q^{25} + 9 q^{26} - 3 q^{28} + 6 q^{29} + 5 q^{30} - 2 q^{31} + 15 q^{32} + 8 q^{34} + 2 q^{35} + 6 q^{36} - 10 q^{37} + 2 q^{38} - 6 q^{40} + 5 q^{42} - 6 q^{43} + 18 q^{44} - 4 q^{45} + 3 q^{46} - 4 q^{47} - 15 q^{48} + 2 q^{49} + 3 q^{50} - 10 q^{51} + 9 q^{52} - 22 q^{53} + 5 q^{54} - 12 q^{55} - 6 q^{56} + 20 q^{57} - q^{58} - 4 q^{59} + 15 q^{60} + 10 q^{61} + 7 q^{62} - 4 q^{63} + 4 q^{64} - 6 q^{65} - 30 q^{66} + 2 q^{67} + 18 q^{68} + 3 q^{70} - 4 q^{71} + 12 q^{72} + 18 q^{73} - 10 q^{74} - 18 q^{76} - 12 q^{77} - 15 q^{78} - 13 q^{80} - 22 q^{81} - 15 q^{82} - 6 q^{83} + 15 q^{84} - 2 q^{85} - 24 q^{86} + 20 q^{87} + 36 q^{88} - 14 q^{89} - 6 q^{90} - 6 q^{91} + 3 q^{92} - 20 q^{93} - q^{94} - 8 q^{95} - 15 q^{96} - 14 q^{97} + 3 q^{98} + 24 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 + 3 * q^4 - 2 * q^5 - 5 * q^6 - 2 * q^7 + 6 * q^8 + 4 * q^9 - 3 * q^10 + 12 * q^11 - 15 * q^12 + 6 * q^13 - 3 * q^14 + 13 * q^16 + 2 * q^17 + 6 * q^18 + 8 * q^19 - 3 * q^20 + 18 * q^22 + 2 * q^23 - 20 * q^24 + 2 * q^25 + 9 * q^26 - 3 * q^28 + 6 * q^29 + 5 * q^30 - 2 * q^31 + 15 * q^32 + 8 * q^34 + 2 * q^35 + 6 * q^36 - 10 * q^37 + 2 * q^38 - 6 * q^40 + 5 * q^42 - 6 * q^43 + 18 * q^44 - 4 * q^45 + 3 * q^46 - 4 * q^47 - 15 * q^48 + 2 * q^49 + 3 * q^50 - 10 * q^51 + 9 * q^52 - 22 * q^53 + 5 * q^54 - 12 * q^55 - 6 * q^56 + 20 * q^57 - q^58 - 4 * q^59 + 15 * q^60 + 10 * q^61 + 7 * q^62 - 4 * q^63 + 4 * q^64 - 6 * q^65 - 30 * q^66 + 2 * q^67 + 18 * q^68 + 3 * q^70 - 4 * q^71 + 12 * q^72 + 18 * q^73 - 10 * q^74 - 18 * q^76 - 12 * q^77 - 15 * q^78 - 13 * q^80 - 22 * q^81 - 15 * q^82 - 6 * q^83 + 15 * q^84 - 2 * q^85 - 24 * q^86 + 20 * q^87 + 36 * q^88 - 14 * q^89 - 6 * q^90 - 6 * q^91 + 3 * q^92 - 20 * q^93 - q^94 - 8 * q^95 - 15 * q^96 - 14 * q^97 + 3 * q^98 + 24 * q^99

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