LMFDB - Embedded newform 108.2.h.a.71.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,2,Mod(35,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("108.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	108.h (of order $6$, degree $2$, not minimal)

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:	no
Analytic conductor:	$0.862384341830$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.170772624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 $ x^8 - 3x^7 + 5x^6 - 6x^5 + 6x^4 - 12x^3 + 20x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.4
Root			$1.41203 - 0.0786378i$ of defining polynomial
Character	$\chi$	$=$	108.71
Dual form			108.2.h.a.35.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41203 - 0.0786378i) q^{2} +(1.98763 - 0.222077i) q^{4} +(-0.686141 - 0.396143i) q^{5} +(-2.35143 + 1.35760i) q^{7} +(2.78912 - 0.469882i) q^{8} +O(q^{10})$	\(q+(1.41203 - 0.0786378i) q^{2} +(1.98763 - 0.222077i) q^{4} +(-0.686141 - 0.396143i) q^{5} +(-2.35143 + 1.35760i) q^{7} +(2.78912 - 0.469882i) q^{8} +(-1.00000 - 0.505408i) q^{10} +(-1.71352 - 2.96790i) q^{11} +(-1.68614 + 2.92048i) q^{13} +(-3.21352 + 2.10187i) q^{14} +(3.90136 - 0.882816i) q^{16} +2.52434i q^{17} -2.20979i q^{19} +(-1.45177 - 0.635011i) q^{20} +(-2.65292 - 4.05600i) q^{22} +(-1.07561 + 1.86301i) q^{23} +(-2.18614 - 3.78651i) q^{25} +(-2.15121 + 4.25639i) q^{26} +(-4.37228 + 3.22060i) q^{28} +(0.686141 - 0.396143i) q^{29} +(1.47603 + 0.852189i) q^{31} +(5.43940 - 1.55335i) q^{32} +(0.198508 + 3.56443i) q^{34} +2.15121 q^{35} +4.74456 q^{37} +(-0.173773 - 3.12027i) q^{38} +(-2.09987 - 0.782488i) q^{40} +(-0.127719 - 0.0737384i) q^{41} +(6.01594 - 3.47331i) q^{43} +(-4.06494 - 5.51856i) q^{44} +(-1.37228 + 2.71519i) q^{46} +(5.77846 + 10.0086i) q^{47} +(0.186141 - 0.322405i) q^{49} +(-3.38465 - 5.17473i) q^{50} +(-2.70285 + 6.17930i) q^{52} -8.51278i q^{53} +2.71519i q^{55} +(-5.92051 + 4.89140i) q^{56} +(0.937696 - 0.613321i) q^{58} +(2.58891 - 4.48412i) q^{59} +(-1.68614 - 2.92048i) q^{61} +(2.15121 + 1.08724i) q^{62} +(7.55842 - 2.62112i) q^{64} +(2.31386 - 1.33591i) q^{65} +(6.01594 + 3.47331i) q^{67} +(0.560598 + 5.01746i) q^{68} +(3.03757 - 0.169167i) q^{70} -1.75079 q^{71} -2.37228 q^{73} +(6.69944 - 0.373102i) q^{74} +(-0.490743 - 4.39224i) q^{76} +(8.05842 + 4.65253i) q^{77} +(-8.80507 + 5.08361i) q^{79} +(-3.02661 - 0.939764i) q^{80} +(-0.186141 - 0.0940770i) q^{82} +(-3.62725 - 6.28258i) q^{83} +(1.00000 - 1.73205i) q^{85} +(8.22153 - 5.37748i) q^{86} +(-6.17377 - 7.47269i) q^{88} +5.34363i q^{89} -9.15640i q^{91} +(-1.72418 + 3.94184i) q^{92} +(8.94639 + 13.6780i) q^{94} +(-0.875393 + 1.51622i) q^{95} +(6.24456 + 10.8159i) q^{97} +(0.237482 - 0.469882i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) $ 8 * q + 3 * q^2 - q^4 + 6 * q^5	$ 8 q + 3 q^{2} - q^{4} + 6 q^{5} - 8 q^{10} - 2 q^{13} - 12 q^{14} - q^{16} - 18 q^{20} + 3 q^{22} - 6 q^{25} - 12 q^{28} - 6 q^{29} + 33 q^{32} + 7 q^{34} - 8 q^{37} + 27 q^{38} + 10 q^{40} - 24 q^{41} + 12 q^{46} - 10 q^{49} - 21 q^{50} + 16 q^{52} - 18 q^{56} + 4 q^{58} - 2 q^{61} + 26 q^{64} + 30 q^{65} + 15 q^{68} - 6 q^{70} + 4 q^{73} + 30 q^{74} - 3 q^{76} + 30 q^{77} + 10 q^{82} + 8 q^{85} - 21 q^{86} - 21 q^{88} - 24 q^{92} - 18 q^{94} + 4 q^{97}+O(q^{100}) $ 8 * q + 3 * q^2 - q^4 + 6 * q^5 - 8 * q^10 - 2 * q^13 - 12 * q^14 - q^16 - 18 * q^20 + 3 * q^22 - 6 * q^25 - 12 * q^28 - 6 * q^29 + 33 * q^32 + 7 * q^34 - 8 * q^37 + 27 * q^38 + 10 * q^40 - 24 * q^41 + 12 * q^46 - 10 * q^49 - 21 * q^50 + 16 * q^52 - 18 * q^56 + 4 * q^58 - 2 * q^61 + 26 * q^64 + 30 * q^65 + 15 * q^68 - 6 * q^70 + 4 * q^73 + 30 * q^74 - 3 * q^76 + 30 * q^77 + 10 * q^82 + 8 * q^85 - 21 * q^86 - 21 * q^88 - 24 * q^92 - 18 * q^94 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.41203	−	0.0786378i	0.998453	−	0.0556054i
$2$	1.41203	−	0.0786378i	0.998453	−	0.0556054i
$3$		0			0
$3$		0			0
$4$	1.98763	−	0.222077i	0.993816	−	0.111039i
$5$	−0.686141	−	0.396143i	−0.306851	−	0.177161i	0.338665	−	0.940907i	$-0.390025\pi$
$5$	−0.686141	−	0.396143i	−0.306851	−	0.177161i	−0.645517	+	0.763746i	$0.723358\pi$
$6$		0			0
$7$	−2.35143	+	1.35760i	−0.888756	+	0.513124i	−0.873535	−	0.486761i	$-0.838178\pi$
$7$	−2.35143	+	1.35760i	−0.888756	+	0.513124i	−0.0152206	+	0.999884i	$0.504845\pi$
$8$	2.78912	−	0.469882i	0.986104	−	0.166128i
$9$		0			0
$10$	−1.00000	−	0.505408i	−0.316228	−	0.159824i
$11$	−1.71352	−	2.96790i	−0.516645	−	0.894855i	−0.999813	−	0.0193276i	$-0.993847\pi$
$11$	−1.71352	−	2.96790i	−0.516645	−	0.894855i	0.483168	−	0.875527i	$-0.339486\pi$
$12$		0			0
$13$	−1.68614	+	2.92048i	−0.467651	+	0.809996i	−0.999317	−	0.0369586i	$-0.988233\pi$
$13$	−1.68614	+	2.92048i	−0.467651	+	0.809996i	0.531666	+	0.846954i	$0.321566\pi$
$14$	−3.21352	+	2.10187i	−0.858849	+	0.561749i
$15$		0			0
$16$	3.90136	−	0.882816i	0.975341	−	0.220704i
$17$			2.52434i			0.612242i	0.951993	+	0.306121i	$0.0990312\pi$
$17$			2.52434i			0.612242i	−0.951993	+	0.306121i	$0.900969\pi$
$18$		0			0
$19$		−	2.20979i		−	0.506960i	−0.967341	−	0.253480i	$-0.918425\pi$
$19$		−	2.20979i		−	0.506960i	0.967341	−	0.253480i	$-0.0815752\pi$
$20$	−1.45177	−	0.635011i	−0.324626	−	0.141993i
$21$		0			0
$22$	−2.65292	−	4.05600i	−0.565604	−	0.864742i
$23$	−1.07561	+	1.86301i	−0.224279	+	0.388463i	−0.956103	−	0.293031i	$-0.905336\pi$
$23$	−1.07561	+	1.86301i	−0.224279	+	0.388463i	0.731824	+	0.681494i	$0.238670\pi$
$24$		0			0
$25$	−2.18614	−	3.78651i	−0.437228	−	0.757301i
$26$	−2.15121	+	4.25639i	−0.421888	+	0.834746i
$27$		0			0
$28$	−4.37228	+	3.22060i	−0.826284	+	0.608637i
$29$	0.686141	−	0.396143i	0.127413	−	0.0735620i	−0.434939	−	0.900460i	$-0.643230\pi$
$29$	0.686141	−	0.396143i	0.127413	−	0.0735620i	0.562352	+	0.826898i	$0.309897\pi$
$30$		0			0
$31$	1.47603	+	0.852189i	0.265104	+	0.153058i	0.626660	−	0.779292i	$-0.284421\pi$
$31$	1.47603	+	0.852189i	0.265104	+	0.153058i	−0.361557	+	0.932350i	$0.617755\pi$
$32$	5.43940	−	1.55335i	0.961559	−	0.274597i
$33$		0			0
$34$	0.198508	+	3.56443i	0.0340439	+	0.611295i
$35$	2.15121			0.363621
$36$		0			0
$37$	4.74456			0.780001			0.390001	−	0.920815i	$-0.372475\pi$
$37$	4.74456			0.780001			0.390001	+	0.920815i	$0.372475\pi$
$38$	−0.173773	−	3.12027i	−0.0281897	−	0.506175i
$39$		0			0
$40$	−2.09987	−	0.782488i	−0.332019	−	0.123722i
$41$	−0.127719	−	0.0737384i	−0.0199463	−	0.0115160i	0.489994	−	0.871726i	$-0.336999\pi$
$41$	−0.127719	−	0.0737384i	−0.0199463	−	0.0115160i	−0.509940	+	0.860210i	$0.670332\pi$
$42$		0			0
$43$	6.01594	−	3.47331i	0.917423	−	0.529674i	0.0346108	−	0.999401i	$-0.488981\pi$
$43$	6.01594	−	3.47331i	0.917423	−	0.529674i	0.882812	+	0.469727i	$0.155647\pi$
$44$	−4.06494	−	5.51856i	−0.612813	−	0.831954i
$45$		0			0
$46$	−1.37228	+	2.71519i	−0.202332	+	0.400334i
$47$	5.77846	+	10.0086i	0.842875	+	1.45990i	0.887454	+	0.460897i	$0.152472\pi$
$47$	5.77846	+	10.0086i	0.842875	+	1.45990i	−0.0445785	+	0.999006i	$0.514194\pi$
$48$		0			0
$49$	0.186141	−	0.322405i	0.0265915	−	0.0460579i
$50$	−3.38465	−	5.17473i	−0.478662	−	0.731817i
$51$		0			0
$52$	−2.70285	+	6.17930i	−0.374819	+	0.856914i
$53$		−	8.51278i		−	1.16932i	−0.811278	−	0.584660i	$-0.801228\pi$
$53$		−	8.51278i		−	1.16932i	0.811278	−	0.584660i	$-0.198772\pi$
$54$		0			0
$55$			2.71519i			0.366117i
$56$	−5.92051	+	4.89140i	−0.791162	+	0.653641i
$57$		0			0
$58$	0.937696	−	0.613321i	0.123126	−	0.0805330i
$59$	2.58891	−	4.48412i	0.337047	−	0.583783i	−0.646829	−	0.762635i	$-0.723905\pi$
$59$	2.58891	−	4.48412i	0.337047	−	0.583783i	0.983876	+	0.178852i	$0.0572384\pi$
$60$		0			0
$61$	−1.68614	−	2.92048i	−0.215888	−	0.373929i	0.737659	−	0.675174i	$-0.235931\pi$
$61$	−1.68614	−	2.92048i	−0.215888	−	0.373929i	−0.953547	+	0.301244i	$0.902598\pi$
$62$	2.15121	+	1.08724i	0.273204	+	0.138080i
$63$		0			0
$64$	7.55842	−	2.62112i	0.944803	−	0.327640i
$65$	2.31386	−	1.33591i	0.286999	−	0.165699i
$66$		0			0
$67$	6.01594	+	3.47331i	0.734964	+	0.424332i	0.820236	−	0.572026i	$-0.193842\pi$
$67$	6.01594	+	3.47331i	0.734964	+	0.424332i	−0.0852711	+	0.996358i	$0.527176\pi$
$68$	0.560598	+	5.01746i	0.0679825	+	0.608456i
$69$		0			0
$70$	3.03757	−	0.169167i	0.363059	−	0.0202193i
$71$	−1.75079			−0.207780			−0.103890	−	0.994589i	$-0.533129\pi$
$71$	−1.75079			−0.207780			−0.103890	+	0.994589i	$0.533129\pi$
$72$		0			0
$73$	−2.37228			−0.277655			−0.138827	−	0.990317i	$-0.544333\pi$
$73$	−2.37228			−0.277655			−0.138827	+	0.990317i	$0.544333\pi$
$74$	6.69944	−	0.373102i	0.778794	−	0.0433722i
$75$		0			0
$76$	−0.490743	−	4.39224i	−0.0562921	−	0.503825i
$77$	8.05842	+	4.65253i	0.918342	+	0.530205i
$78$		0			0
$79$	−8.80507	+	5.08361i	−0.990647	+	0.571951i	−0.905468	−	0.424415i	$-0.860480\pi$
$79$	−8.80507	+	5.08361i	−0.990647	+	0.571951i	−0.0851797	+	0.996366i	$0.527146\pi$
$80$	−3.02661	−	0.939764i	−0.338385	−	0.105069i
$81$		0			0
$82$	−0.186141	−	0.0940770i	−0.0205558	−	0.0103891i
$83$	−3.62725	−	6.28258i	−0.398142	−	0.689603i	0.595355	−	0.803463i	$-0.297012\pi$
$83$	−3.62725	−	6.28258i	−0.398142	−	0.689603i	−0.993497	+	0.113861i	$0.963678\pi$
$84$		0			0
$85$	1.00000	−	1.73205i	0.108465	−	0.187867i
$86$	8.22153	−	5.37748i	0.886551	−	0.579868i
$87$		0			0
$88$	−6.17377	−	7.47269i	−0.658126	−	0.796591i
$89$			5.34363i			0.566424i	0.959057	+	0.283212i	$0.0913999\pi$
$89$			5.34363i			0.566424i	−0.959057	+	0.283212i	$0.908600\pi$
$90$		0			0
$91$		−	9.15640i		−	0.959852i
$92$	−1.72418	+	3.94184i	−0.179758	+	0.410965i
$93$		0			0
$94$	8.94639	+	13.6780i	0.922750	+	1.41078i
$95$	−0.875393	+	1.51622i	−0.0898134	+	0.155561i
$96$		0			0
$97$	6.24456	+	10.8159i	0.634039	+	1.09819i	0.986718	+	0.162444i	$0.0519376\pi$
$97$	6.24456	+	10.8159i	0.634039	+	1.09819i	−0.352679	+	0.935745i	$0.614729\pi$
$98$	0.237482	−	0.469882i	0.0239893	−	0.0474652i
$99$		0			0
$100$	−5.18614	−	7.04069i	−0.518614	−	0.704069i
$101$	−15.4307	+	8.90892i	−1.53541	+	0.886471i	−0.536314	+	0.844019i	$0.680184\pi$
$101$	−15.4307	+	8.90892i	−1.53541	+	0.886471i	−0.999099	+	0.0424521i	$0.986483\pi$
$102$		0			0
$103$	−12.6325	−	7.29339i	−1.24472	−	0.718640i	−0.274669	−	0.961539i	$-0.588568\pi$
$103$	−12.6325	−	7.29339i	−1.24472	−	0.718640i	−0.970051	+	0.242899i	$0.921901\pi$
$104$	−3.33057	+	8.93787i	−0.326590	+	0.876430i
$105$		0			0
$106$	−0.669426	−	12.0203i	−0.0650204	−	1.16751i
$107$	−13.2332			−1.27930			−0.639650	−	0.768667i	$-0.720920\pi$
$107$	−13.2332			−1.27930			−0.639650	+	0.768667i	$0.720920\pi$
$108$		0			0
$109$	−9.48913			−0.908893			−0.454447	−	0.890774i	$-0.650163\pi$
$109$	−9.48913			−0.908893			−0.454447	+	0.890774i	$0.650163\pi$
$110$	0.213517	+	3.83392i	0.0203581	+	0.365550i
$111$		0			0
$112$	−7.97526	+	7.37236i	−0.753592	+	0.696622i
$113$	−13.8030	−	7.96916i	−1.29848	−	0.749675i	−0.318335	−	0.947978i	$-0.603124\pi$
$113$	−13.8030	−	7.96916i	−1.29848	−	0.749675i	−0.980141	+	0.198303i	$0.936457\pi$
$114$		0			0
$115$	1.47603	−	0.852189i	0.137641	−	0.0794670i
$116$	1.27582	−	0.939764i	0.118457	−	0.0872549i
$117$		0			0
$118$	3.30298	−	6.53528i	0.304064	−	0.601621i
$119$	−3.42703	−	5.93580i	−0.314156	−	0.544134i
$120$		0			0
$121$	−0.372281	+	0.644810i	−0.0338438	+	0.0586191i
$122$	−2.61053	−	3.99120i	−0.236347	−	0.361346i
$123$		0			0
$124$	3.12307	+	1.36604i	0.280460	+	0.122674i
$125$			7.42554i			0.664160i
$126$		0			0
$127$			16.2912i			1.44561i	0.691053	+	0.722804i	$0.257147\pi$
$127$			16.2912i			1.44561i	−0.691053	+	0.722804i	$0.742853\pi$
$128$	10.4666	−	4.29546i	0.925122	−	0.379669i
$129$		0			0
$130$	3.16218	−	2.06829i	0.277341	−	0.181401i
$131$	3.62725	−	6.28258i	0.316914	−	0.548911i	−0.662928	−	0.748683i	$-0.730687\pi$
$131$	3.62725	−	6.28258i	0.316914	−	0.548911i	0.979843	+	0.199771i	$0.0640200\pi$
$132$		0			0
$133$	3.00000	+	5.19615i	0.260133	+	0.450564i
$134$	8.76780	+	4.43132i	0.757423	+	0.382807i
$135$		0			0
$136$	1.18614	+	7.04069i	0.101711	+	0.603734i
$137$	16.2446	−	9.37880i	1.38787	−	0.801285i	0.394792	−	0.918771i	$-0.370817\pi$
$137$	16.2446	−	9.37880i	1.38787	−	0.801285i	0.993075	+	0.117485i	$0.0374833\pi$
$138$		0			0
$139$	−8.09262	−	4.67228i	−0.686407	−	0.396297i	0.115858	−	0.993266i	$-0.463038\pi$
$139$	−8.09262	−	4.67228i	−0.686407	−	0.396297i	−0.802265	+	0.596968i	$0.796372\pi$
$140$	4.27582	−	0.477736i	0.361373	−	0.0403760i
$141$		0			0
$142$	−2.47215	+	0.137678i	−0.207458	+	0.0115537i
$143$	11.5569			0.966438
$144$		0			0
$145$	−0.627719			−0.0521292
$146$	−3.34972	+	0.186551i	−0.277225	+	0.0154391i
$147$		0			0
$148$	9.43045	−	1.05366i	0.775178	−	0.0866103i
$149$	8.31386	+	4.80001i	0.681098	+	0.393232i	0.800269	−	0.599642i	$-0.204690\pi$
$149$	8.31386	+	4.80001i	0.681098	+	0.393232i	−0.119171	+	0.992874i	$0.538024\pi$
$150$		0			0
$151$	7.92967	−	4.57820i	0.645308	−	0.372569i	−0.141348	−	0.989960i	$-0.545144\pi$
$151$	7.92967	−	4.57820i	0.645308	−	0.372569i	0.786656	+	0.617391i	$0.211810\pi$
$152$	−1.03834	−	6.16337i	−0.0842204	−	0.499915i
$153$		0			0
$154$	11.7446	+	5.93580i	0.946404	+	0.478320i
$155$	−0.675178	−	1.16944i	−0.0542316	−	0.0939319i
$156$		0			0
$157$	8.43070	−	14.6024i	0.672843	−	1.16540i	−0.304251	−	0.952592i	$-0.598406\pi$
$157$	8.43070	−	14.6024i	0.672843	−	1.16540i	0.977094	−	0.212807i	$-0.0682605\pi$
$158$	−12.0332	+	7.87060i	−0.957311	+	0.626151i
$159$		0			0
$160$	−4.34755	−	1.08896i	−0.343704	−	0.0860902i
$161$		−	5.84096i		−	0.460332i
$162$		0			0
$163$			11.8716i			0.929855i	0.885349	+	0.464928i	$0.153920\pi$
$163$			11.8716i			0.929855i	−0.885349	+	0.464928i	$0.846080\pi$
$164$	−0.270233	−	0.118201i	−0.0211017	−	0.00922998i
$165$		0			0
$166$	−5.61582	−	8.58592i	−0.435872	−	0.666397i
$167$	−9.60592	+	16.6379i	−0.743329	+	1.28748i	0.207643	+	0.978205i	$0.433421\pi$
$167$	−9.60592	+	16.6379i	−0.743329	+	1.28748i	−0.950972	+	0.309278i	$0.899913\pi$
$168$		0			0
$169$	0.813859	+	1.40965i	0.0626046	+	0.108434i
$170$	1.27582	−	2.52434i	0.0978510	−	0.193608i
$171$		0			0
$172$	11.1861	−	8.23966i	0.852935	−	0.628268i
$173$	4.80298	−	2.77300i	0.365164	−	0.210828i	−0.306180	−	0.951974i	$-0.599051\pi$
$173$	4.80298	−	2.77300i	0.365164	−	0.210828i	0.671344	+	0.741146i	$0.265717\pi$
$174$		0			0
$175$	10.2811	+	5.93580i	0.777178	+	0.448704i
$176$	−9.30516	−	10.0661i	−0.701403	−	0.758763i
$177$		0			0
$178$	0.420211	+	7.54534i	0.0314962	+	0.565547i
$179$	18.8114			1.40603			0.703016	−	0.711174i	$-0.251836\pi$
$179$	18.8114			1.40603			0.703016	+	0.711174i	$0.251836\pi$
$180$		0			0
$181$	−4.00000			−0.297318			−0.148659	−	0.988889i	$-0.547496\pi$
$181$	−4.00000			−0.297318			−0.148659	+	0.988889i	$0.547496\pi$
$182$	−0.720040	−	12.9291i	−0.0533729	−	0.958366i
$183$		0			0
$184$	−2.12461	+	5.70156i	−0.156628	+	0.420325i
$185$	−3.25544	−	1.87953i	−0.239345	−	0.138186i
$186$		0			0
$187$	7.49198	−	4.32550i	0.547868	−	0.316312i
$188$	13.7081	+	18.6101i	0.999769	+	1.35728i
$189$		0			0
$190$	−1.11684	+	2.20979i	−0.0810244	+	0.160315i
$191$	1.95100	+	3.37923i	0.141169	+	0.244512i	0.927937	−	0.372736i	$-0.121580\pi$
$191$	1.95100	+	3.37923i	0.141169	+	0.244512i	−0.786768	+	0.617249i	$0.788247\pi$
$192$		0			0
$193$	1.87228	−	3.24289i	0.134770	−	0.233428i	−0.790740	−	0.612153i	$-0.790304\pi$
$193$	1.87228	−	3.24289i	0.134770	−	0.233428i	0.925509	+	0.378724i	$0.123637\pi$
$194$	9.66802	+	14.7813i	0.694123	+	1.06123i
$195$		0			0
$196$	0.298380	−	0.682160i	0.0213129	−	0.0487257i
$197$		−	10.6873i		−	0.761436i	−0.924691	−	0.380718i	$-0.875677\pi$
$197$		−	10.6873i		−	0.761436i	0.924691	−	0.380718i	$-0.124323\pi$
$198$		0			0
$199$		−	19.3236i		−	1.36981i	−0.728630	−	0.684907i	$-0.759843\pi$
$199$		−	19.3236i		−	1.36981i	0.728630	−	0.684907i	$-0.240157\pi$
$200$	−7.87663	−	9.53381i	−0.556962	−	0.674142i
$201$		0			0
$202$	−21.0880	+	13.7931i	−1.48374	+	0.970476i
$203$	−1.07561	+	1.86301i	−0.0754928	+	0.130757i
$204$		0			0
$205$	0.0584220	+	0.101190i	0.00408037	+	0.00706741i
$206$	−18.4110	−	9.30506i	−1.28275	−	0.648315i
$207$		0			0
$208$	−4.00000	+	12.8824i	−0.277350	+	0.893234i
$209$	−6.55842	+	3.78651i	−0.453656	+	0.261918i
$210$		0			0
$211$	5.30350	+	3.06198i	0.365108	+	0.210795i	0.671319	−	0.741169i	$-0.265728\pi$
$211$	5.30350	+	3.06198i	0.365108	+	0.210795i	−0.306211	+	0.951964i	$0.599061\pi$
$212$	−1.89049	−	16.9203i	−0.129840	−	1.16209i
$213$		0			0
$214$	−18.6856	+	1.04063i	−1.27732	+	0.0711359i
$215$	−5.50371			−0.375350
$216$		0			0
$217$	−4.62772			−0.314150
$218$	−13.3989	+	0.746204i	−0.907487	+	0.0505393i
$219$		0			0
$220$	0.602983	+	5.39681i	0.0406531	+	0.363853i
$221$	−7.37228	−	4.25639i	−0.495913	−	0.286316i
$222$		0			0
$223$	1.47603	−	0.852189i	0.0988426	−	0.0570668i	−0.449764	−	0.893147i	$-0.648492\pi$
$223$	1.47603	−	0.852189i	0.0988426	−	0.0570668i	0.548606	+	0.836081i	$0.315159\pi$
$224$	−10.6815	+	11.0371i	−0.713690	+	0.737448i
$225$		0			0
$226$	−20.1168	−	10.1672i	−1.33815	−	0.676313i
$227$	9.44298	+	16.3557i	0.626752	+	1.08557i	0.988199	+	0.153174i	$0.0489496\pi$
$227$	9.44298	+	16.3557i	0.626752	+	1.08557i	−0.361447	+	0.932393i	$0.617717\pi$
$228$		0			0
$229$	−4.68614	+	8.11663i	−0.309669	+	0.536362i	−0.978290	−	0.207241i	$-0.933552\pi$
$229$	−4.68614	+	8.11663i	−0.309669	+	0.536362i	0.668621	+	0.743603i	$0.266885\pi$
$230$	2.01718	−	1.31939i	0.133009	−	0.0869977i
$231$		0			0
$232$	1.72759	−	1.42730i	0.113422	−	0.0937067i
$233$			28.0627i			1.83845i	0.393737	+	0.919223i	$0.371182\pi$
$233$			28.0627i			1.83845i	−0.393737	+	0.919223i	$0.628818\pi$
$234$		0			0
$235$		−	9.15640i		−	0.597298i
$236$	4.14998	−	9.48772i	0.270141	−	0.617598i
$237$		0			0
$238$	−5.30584	−	8.11200i	−0.343926	−	0.525823i
$239$	8.33010	−	14.4282i	0.538830	−	0.933280i	−0.460138	−	0.887847i	$-0.652200\pi$
$239$	8.33010	−	14.4282i	0.538830	−	0.933280i	0.998967	−	0.0454327i	$-0.0144667\pi$
$240$		0			0
$241$	−8.24456	−	14.2800i	−0.531079	−	0.919856i	−0.999342	−	0.0362667i	$-0.988453\pi$
$241$	−8.24456	−	14.2800i	−0.531079	−	0.919856i	0.468263	−	0.883589i	$-0.344880\pi$
$242$	−0.474964	+	0.939764i	−0.0305319	+	0.0604103i
$243$		0			0
$244$	−4.00000	−	5.43039i	−0.256074	−	0.347645i
$245$	−0.255437	+	0.147477i	−0.0163193	+	0.00942195i
$246$		0			0
$247$	6.45364	+	3.72601i	0.410635	+	0.237080i
$248$	4.51727	+	1.68330i	0.286847	+	0.106890i
$249$		0			0
$250$	0.583928	+	10.4850i	0.0369309	+	0.663133i
$251$	−16.7347			−1.05629			−0.528144	−	0.849155i	$-0.677112\pi$
$251$	−16.7347			−1.05629			−0.528144	+	0.849155i	$0.677112\pi$
$252$		0			0
$253$	7.37228			0.463491
$254$	1.28110	+	23.0035i	0.0803835	+	1.44337i
$255$		0			0
$256$	14.4413	−	6.88837i	0.902580	−	0.430523i
$257$	9.98913	+	5.76722i	0.623105	+	0.359750i	0.778077	−	0.628169i	$-0.216195\pi$
$257$	9.98913	+	5.76722i	0.623105	+	0.359750i	−0.154972	+	0.987919i	$0.549529\pi$
$258$		0			0
$259$	−11.1565	+	6.44121i	−0.693231	+	0.400237i
$260$	4.30243	−	3.16915i	0.266825	−	0.196542i
$261$		0			0
$262$	4.62772	−	9.15640i	0.285901	−	0.565684i
$263$	−6.25343	−	10.8313i	−0.385603	−	0.667884i	0.606250	−	0.795274i	$-0.292673\pi$
$263$	−6.25343	−	10.8313i	−0.385603	−	0.667884i	−0.991853	+	0.127391i	$0.959340\pi$
$264$		0			0
$265$	−3.37228	+	5.84096i	−0.207158	+	0.358807i
$266$	4.64469	+	7.10119i	0.284784	+	0.435402i
$267$		0			0
$268$	12.7288	+	5.56765i	0.777537	+	0.340098i
$269$		−	24.9484i		−	1.52113i	−0.649260	−	0.760566i	$-0.724921\pi$
$269$		−	24.9484i		−	1.52113i	0.649260	−	0.760566i	$-0.275079\pi$
$270$		0			0
$271$		−	1.38712i		−	0.0842618i	−0.999112	−	0.0421309i	$-0.986585\pi$
$271$		−	1.38712i		−	0.0842618i	0.999112	−	0.0421309i	$-0.0134147\pi$
$272$	2.22853	+	9.84836i	0.135124	+	0.597144i
$273$		0			0
$274$	22.2002	−	14.5205i	1.34116	−	0.877218i
$275$	−7.49198	+	12.9765i	−0.451783	+	0.782512i
$276$		0			0
$277$	−0.313859	−	0.543620i	−0.0188580	−	0.0326630i	0.856442	−	0.516243i	$-0.172670\pi$
$277$	−0.313859	−	0.543620i	−0.0188580	−	0.0326630i	−0.875300	+	0.483580i	$0.839336\pi$
$278$	−11.7944	−	5.96099i	−0.707381	−	0.357516i
$279$		0			0
$280$	6.00000	−	1.01082i	0.358569	−	0.0604078i
$281$	5.56930	−	3.21543i	0.332236	−	0.191817i	−0.324597	−	0.945852i	$-0.605229\pi$
$281$	5.56930	−	3.21543i	0.332236	−	0.191817i	0.656834	+	0.754036i	$0.271895\pi$
$282$		0			0
$283$	−8.80507	−	5.08361i	−0.523407	−	0.302189i	0.214921	−	0.976632i	$-0.431051\pi$
$283$	−8.80507	−	5.08361i	−0.523407	−	0.302189i	−0.738327	+	0.674442i	$0.764384\pi$
$284$	−3.47992	+	0.388810i	−0.206495	+	0.0230716i
$285$		0			0
$286$	16.3187	−	0.908812i	0.964943	−	0.0537392i
$287$	0.400428			0.0236365
$288$		0			0
$289$	10.6277			0.625160
$290$	−0.886355	+	0.0493624i	−0.0520485	+	0.00289866i
$291$		0			0
$292$	−4.71522	+	0.526830i	−0.275938	+	0.0308304i
$293$	17.3139	+	9.99616i	1.01149	+	0.583982i	0.911627	−	0.411020i	$-0.134827\pi$
$293$	17.3139	+	9.99616i	1.01149	+	0.583982i	0.0998599	+	0.995002i	$0.468161\pi$
$294$		0			0
$295$	−3.55271	+	2.05116i	−0.206847	+	0.119423i
$296$	13.2332	−	2.22938i	0.769163	−	0.129580i
$297$		0			0
$298$	12.1168	+	6.12395i	0.701910	+	0.354751i
$299$	−3.62725	−	6.28258i	−0.209769	−	0.363331i
$300$		0			0
$301$	−9.43070	+	16.3345i	−0.543577	+	0.941502i
$302$	10.8369	−	7.08811i	0.623593	−	0.407875i
$303$		0			0
$304$	−1.95083	−	8.62118i	−0.111888	−	0.494459i
$305$			2.67181i			0.152988i
$306$		0			0
$307$			25.9530i			1.48121i	0.671938	+	0.740607i	$0.265462\pi$
$307$			25.9530i			1.48121i	−0.671938	+	0.740607i	$0.734538\pi$
$308$	17.0504	+	7.45793i	0.971537	+	0.424955i
$309$		0			0
$310$	−1.04533	−	1.59819i	−0.0593708	−	0.0907710i
$311$	15.6591	−	27.1224i	0.887948	−	1.53797i	0.0456512	−	0.998957i	$-0.485464\pi$
$311$	15.6591	−	27.1224i	0.887948	−	1.53797i	0.842297	−	0.539014i	$-0.181203\pi$
$312$		0			0
$313$	−2.24456	−	3.88770i	−0.126870	−	0.219746i	0.795592	−	0.605832i	$-0.207160\pi$
$313$	−2.24456	−	3.88770i	−0.126870	−	0.219746i	−0.922462	+	0.386087i	$0.873826\pi$
$314$	10.7561	−	21.2819i	0.607000	−	1.20101i
$315$		0			0
$316$	−16.3723	+	12.0597i	−0.921013	+	0.678414i
$317$	−20.6644	+	11.9306i	−1.16063	+	0.670089i	−0.951454	−	0.307790i	$-0.900411\pi$
$317$	−20.6644	+	11.9306i	−1.16063	+	0.670089i	−0.209173	+	0.977879i	$0.567077\pi$
$318$		0			0
$319$	−2.35143	−	1.35760i	−0.131655	−	0.0760109i
$320$	−6.22448	−	1.19576i	−0.347959	−	0.0668453i
$321$		0			0
$322$	−0.459321	−	8.24759i	−0.0255969	−	0.459620i
$323$	5.57825			0.310382
$324$		0			0
$325$	14.7446			0.817881
$326$	0.933557	+	16.7630i	0.0517049	+	0.928416i
$327$		0			0
$328$	−0.390872	−	0.145653i	−0.0215823	−	0.00804233i
$329$	−27.1753	−	15.6896i	−1.49822	−	0.864998i
$330$		0			0
$331$	−24.1149	+	13.9228i	−1.32548	+	0.765264i	−0.984596	−	0.174843i	$-0.944058\pi$
$331$	−24.1149	+	13.9228i	−1.32548	+	0.765264i	−0.340879	+	0.940107i	$0.610725\pi$
$332$	−8.60485	−	11.6819i	−0.472253	−	0.641129i
$333$		0			0
$334$	−12.2554	+	24.2486i	−0.670588	+	1.32682i
$335$	−2.75186	−	4.76635i	−0.150350	−	0.260414i
$336$		0			0
$337$	2.12772	−	3.68532i	0.115904	−	0.200752i	−0.802237	−	0.597006i	$-0.796357\pi$
$337$	2.12772	−	3.68532i	0.115904	−	0.200752i	0.918141	+	0.396254i	$0.129690\pi$
$338$	1.26004	+	1.92646i	0.0685372	+	0.104785i
$339$		0			0
$340$	1.60298	−	3.66476i	0.0869340	−	0.198749i
$341$		−	5.84096i		−	0.316306i
$342$		0			0
$343$		−	17.9955i		−	0.971668i
$344$	15.1472	−	12.5143i	0.816681	−	0.674724i
$345$		0			0
$346$	6.56387	−	4.29325i	0.352876	−	0.230807i
$347$	−3.86473	+	6.69391i	−0.207470	+	0.359348i	−0.950917	−	0.309447i	$-0.899856\pi$
$347$	−3.86473	+	6.69391i	−0.207470	+	0.359348i	0.743447	+	0.668795i	$0.233189\pi$
$348$		0			0
$349$	5.68614	+	9.84868i	0.304372	+	0.527188i	0.977121	−	0.212683i	$-0.0682200\pi$
$349$	5.68614	+	9.84868i	0.304372	+	0.527188i	−0.672749	+	0.739871i	$0.734887\pi$
$350$	14.9840	+	7.57301i	0.800926	+	0.404795i
$351$		0			0
$352$	−13.9307	−	13.4819i	−0.742509	−	0.718587i
$353$	4.24456	−	2.45060i	0.225915	−	0.130432i	−0.382771	−	0.923843i	$-0.625030\pi$
$353$	4.24456	−	2.45060i	0.225915	−	0.130432i	0.608686	+	0.793411i	$0.291697\pi$
$354$		0			0
$355$	1.20128	+	0.693562i	0.0637576	+	0.0368105i
$356$	1.18670	+	10.6212i	0.0628949	+	0.562921i
$357$		0			0
$358$	26.5622	−	1.47929i	1.40386	−	0.0781829i
$359$	−29.9679			−1.58165			−0.790823	−	0.612045i	$-0.790347\pi$
$359$	−29.9679			−1.58165			−0.790823	+	0.612045i	$0.790347\pi$
$360$		0			0
$361$	14.1168			0.742992
$362$	−5.64810	+	0.314551i	−0.296858	+	0.0165325i
$363$		0			0
$364$	−2.03343	−	18.1996i	−0.106581	−	0.953916i
$365$	1.62772	+	0.939764i	0.0851987	+	0.0491895i
$366$		0			0
$367$	11.7571	−	6.78799i	0.613718	−	0.354330i	−0.160701	−	0.987003i	$-0.551376\pi$
$367$	11.7571	−	6.78799i	0.613718	−	0.354330i	0.774419	+	0.632673i	$0.218042\pi$
$368$	−2.55164	+	8.21782i	−0.133014	+	0.428384i
$369$		0			0
$370$	−4.74456	−	2.39794i	−0.246658	−	0.124663i
$371$	11.5569	+	20.0172i	0.600006	+	1.03924i
$372$		0			0
$373$	−4.43070	+	7.67420i	−0.229413	+	0.397355i	−0.957634	−	0.287987i	$-0.907014\pi$
$373$	−4.43070	+	7.67420i	−0.229413	+	0.397355i	0.728221	+	0.685342i	$0.240347\pi$
$374$	10.2387	−	6.69686i	0.529431	−	0.346287i
$375$		0			0
$376$	20.8197	+	25.2000i	1.07369	+	1.29959i
$377$			2.67181i			0.137605i
$378$		0			0
$379$		−	9.66181i		−	0.496294i	−0.968722	−	0.248147i	$-0.920178\pi$
$379$		−	9.66181i		−	0.496294i	0.968722	−	0.248147i	$-0.0798216\pi$
$380$	−1.40324	+	3.20810i	−0.0719847	+	0.164572i
$381$		0			0
$382$	3.02060	+	4.61814i	0.154547	+	0.236284i
$383$	−0.200214	+	0.346781i	−0.0102305	+	0.0177197i	−0.871095	−	0.491114i	$-0.836590\pi$
$383$	−0.200214	+	0.346781i	−0.0102305	+	0.0177197i	0.860865	+	0.508834i	$0.169923\pi$
$384$		0			0
$385$	−3.68614	−	6.38458i	−0.187863	−	0.325388i
$386$	2.38870	−	4.72627i	0.121581	−	0.240561i
$387$		0			0
$388$	14.8139	+	20.1113i	0.752060	+	1.02099i
$389$	−7.19702	+	4.15520i	−0.364903	+	0.210677i	−0.671229	−	0.741250i	$-0.734233\pi$
$389$	−7.19702	+	4.15520i	−0.364903	+	0.210677i	0.306326	+	0.951927i	$0.400900\pi$
$390$		0			0
$391$	−4.70285	−	2.71519i	−0.237834	−	0.137313i
$392$	0.367677	−	0.986692i	0.0185705	−	0.0498355i
$393$		0			0
$394$	−0.840423	−	15.0907i	−0.0423399	−	0.760258i
$395$	8.05535			0.405309
$396$		0			0
$397$	−7.25544			−0.364140			−0.182070	−	0.983286i	$-0.558280\pi$
$397$	−7.25544			−0.364140			−0.182070	+	0.983286i	$0.558280\pi$
$398$	−1.51957	−	27.2854i	−0.0761690	−	1.36770i
$399$		0			0
$400$	−11.8717	−	12.8426i	−0.593586	−	0.642129i
$401$	18.9891	+	10.9634i	0.948272	+	0.547485i	0.892544	−	0.450961i	$-0.148919\pi$
$401$	18.9891	+	10.9634i	0.948272	+	0.547485i	0.0557281	+	0.998446i	$0.482252\pi$
$402$		0			0
$403$	−4.97760	+	2.87382i	−0.247952	+	0.143155i
$404$	−28.6921	+	21.1345i	−1.42749	+	1.05148i
$405$		0			0
$406$	−1.37228	+	2.71519i	−0.0681052	+	0.134753i
$407$	−8.12989	−	14.0814i	−0.402984	−	0.697988i
$408$		0			0
$409$	−1.12772	+	1.95327i	−0.0557621	+	0.0965828i	−0.892559	−	0.450931i	$-0.851092\pi$
$409$	−1.12772	+	1.95327i	−0.0557621	+	0.0965828i	0.836797	+	0.547513i	$0.184426\pi$
$410$	0.0904507	+	0.138288i	0.00446704	+	0.00682958i
$411$		0			0
$412$	−26.7285	−	11.6912i	−1.31682	−	0.575983i
$413$			14.0588i			0.691788i
$414$		0			0
$415$			5.74764i			0.282141i
$416$	−4.63506	+	18.5048i	−0.227252	+	0.907275i
$417$		0			0
$418$	−8.96290	+	5.86238i	−0.438390	+	0.286739i
$419$	−2.82639	+	4.89545i	−0.138078	+	0.239159i	−0.926769	−	0.375631i	$-0.877426\pi$
$419$	−2.82639	+	4.89545i	−0.138078	+	0.239159i	0.788691	+	0.614790i	$0.210759\pi$
$420$		0			0
$421$	−14.8030	−	25.6395i	−0.721453	−	1.24959i	−0.960417	−	0.278565i	$-0.910141\pi$
$421$	−14.8030	−	25.6395i	−0.721453	−	1.24959i	0.238964	−	0.971028i	$-0.423192\pi$
$422$	7.72946	+	3.90653i	0.376264	+	0.190167i
$423$		0			0
$424$	−4.00000	−	23.7432i	−0.194257	−	1.15307i
$425$	9.55842	−	5.51856i	0.463652	−	0.267689i
$426$		0			0
$427$	7.92967	+	4.57820i	0.383744	+	0.221555i
$428$	−26.3027	+	2.93879i	−1.27139	+	0.142052i
$429$		0			0
$430$	−7.77138	+	0.432800i	−0.374769	+	0.0208715i
$431$	14.6581			0.706054			0.353027	−	0.935613i	$-0.385152\pi$
$431$	14.6581			0.706054			0.353027	+	0.935613i	$0.385152\pi$
$432$		0			0
$433$	−14.3723			−0.690688			−0.345344	−	0.938476i	$-0.612238\pi$
$433$	−14.3723			−0.690688			−0.345344	+	0.938476i	$0.612238\pi$
$434$	−6.53446	+	0.363914i	−0.313664	+	0.0174684i
$435$		0			0
$436$	−18.8609	+	2.10732i	−0.903273	+	0.100922i
$437$	4.11684	+	2.37686i	0.196935	+	0.113701i
$438$		0			0
$439$	28.4919	−	16.4498i	1.35984	−	0.785106i	0.370241	−	0.928936i	$-0.379275\pi$
$439$	28.4919	−	16.4498i	1.35984	−	0.785106i	0.989602	+	0.143830i	$0.0459418\pi$
$440$	1.27582	+	7.57301i	0.0608224	+	0.361029i
$441$		0			0
$442$	−10.7446	−	5.43039i	−0.511067	−	0.258297i
$443$	−2.58891	−	4.48412i	−0.123003	−	0.213047i	0.797948	−	0.602727i	$-0.205919\pi$
$443$	−2.58891	−	4.48412i	−0.123003	−	0.213047i	−0.920950	+	0.389680i	$0.872586\pi$
$444$		0			0
$445$	2.11684	−	3.66648i	0.100348	−	0.173808i
$446$	2.01718	−	1.31939i	0.0955165	−	0.0624747i
$447$		0			0
$448$	−14.2147	+	16.4247i	−0.671580	+	0.775992i
$449$			3.81396i			0.179992i	0.995942	+	0.0899959i	$0.0286854\pi$
$449$			3.81396i			0.179992i	−0.995942	+	0.0899959i	$0.971315\pi$
$450$		0			0
$451$			0.505408i			0.0237987i
$452$	−29.2050	−	12.7744i	−1.37369	−	0.600858i
$453$		0			0
$454$	14.6199	+	22.3521i	0.686146	+	1.04904i
$455$	−3.62725	+	6.28258i	−0.170048	+	0.294532i
$456$		0			0
$457$	2.98913	+	5.17732i	0.139825	+	0.242185i	0.927430	−	0.373996i	$-0.122013\pi$
$457$	2.98913	+	5.17732i	0.139825	+	0.242185i	−0.787605	+	0.616180i	$0.788679\pi$
$458$	−5.97868	+	11.8294i	−0.279365	+	0.552752i
$459$		0			0
$460$	2.74456	−	2.02163i	0.127966	−	0.0942591i
$461$	19.8030	−	11.4333i	0.922317	−	0.532500i	0.0379435	−	0.999280i	$-0.487919\pi$
$461$	19.8030	−	11.4333i	0.922317	−	0.532500i	0.884373	+	0.466780i	$0.154586\pi$
$462$		0			0
$463$	18.2108	+	10.5140i	0.846327	+	0.488627i	0.859410	−	0.511288i	$-0.170831\pi$
$463$	18.2108	+	10.5140i	0.846327	+	0.488627i	−0.0130831	+	0.999914i	$0.504165\pi$
$464$	2.32716	−	2.15124i	0.108036	−	0.0998686i
$465$		0			0
$466$	2.20679	+	39.6252i	0.102227	+	1.83560i
$467$	24.3897			1.12862			0.564310	−	0.825563i	$-0.309142\pi$
$467$	24.3897			1.12862			0.564310	+	0.825563i	$0.309142\pi$
$468$		0			0
$469$	−18.8614			−0.870939
$470$	−0.720040	−	12.9291i	−0.0332129	−	0.596374i
$471$		0			0
$472$	5.11378	−	13.7233i	0.235381	−	0.631664i
$473$	−20.6168	−	11.9031i	−0.947963	−	0.547307i
$474$		0			0
$475$	−8.36737	+	4.83090i	−0.383921	+	0.221657i
$476$	−8.12989	−	11.0371i	−0.372633	−	0.505885i
$477$		0			0
$478$	10.6277	−	21.0280i	0.486101	−	0.961798i
$479$	4.90307	+	8.49236i	0.224027	+	0.388026i	0.956027	−	0.293278i	$-0.0947463\pi$
$479$	4.90307	+	8.49236i	0.224027	+	0.388026i	−0.732000	+	0.681304i	$0.761413\pi$
$480$		0			0
$481$	−8.00000	+	13.8564i	−0.364769	+	0.631798i
$482$	−12.7645	−	19.5154i	−0.581406	−	0.888902i
$483$		0			0
$484$	−0.596761	+	1.36432i	−0.0271255	+	0.0620146i
$485$		−	9.89497i		−	0.449308i
$486$		0			0
$487$		−	17.9365i		−	0.812780i	−0.913700	−	0.406390i	$-0.866787\pi$
$487$		−	17.9365i		−	0.812780i	0.913700	−	0.406390i	$-0.133213\pi$
$488$	−6.07514	−	7.35330i	−0.275008	−	0.332868i
$489$		0			0
$490$	−0.349087	+	0.228328i	−0.0157701	+	0.0103148i
$491$	−12.3950	+	21.4689i	−0.559381	+	0.968876i	0.438168	+	0.898893i	$0.355628\pi$
$491$	−12.3950	+	21.4689i	−0.559381	+	0.968876i	−0.997548	+	0.0699824i	$0.977706\pi$
$492$		0			0
$493$	1.00000	+	1.73205i	0.0450377	+	0.0780076i
$494$	9.40571	+	4.75372i	0.423183	+	0.213880i
$495$		0			0
$496$	6.51087	+	2.02163i	0.292347	+	0.0907740i
$497$	4.11684	−	2.37686i	0.184666	−	0.106617i
$498$		0			0
$499$	−0.437696	−	0.252704i	−0.0195940	−	0.0113126i	0.490171	−	0.871626i	$-0.336934\pi$
$499$	−0.437696	−	0.252704i	−0.0195940	−	0.0113126i	−0.509765	+	0.860314i	$0.670268\pi$
$500$	1.64904	+	14.7592i	0.0737474	+	0.660053i
$501$		0			0
$502$	−23.6299	+	1.31598i	−1.05465	+	0.0587352i
$503$	12.9073			0.575507			0.287754	−	0.957704i	$-0.407092\pi$
$503$	12.9073			0.575507			0.287754	+	0.957704i	$0.407092\pi$
$504$		0			0
$505$	14.1168			0.628191
$506$	10.4098	−	0.579740i	0.462774	−	0.0257726i
$507$		0			0
$508$	3.61790	+	32.3808i	0.160518	+	1.43667i
$509$	−15.6861	−	9.05640i	−0.695276	−	0.401418i	0.110310	−	0.993897i	$-0.464816\pi$
$509$	−15.6861	−	9.05640i	−0.695276	−	0.401418i	−0.805586	+	0.592480i	$0.798149\pi$
$510$		0			0
$511$	5.57825	−	3.22060i	0.246767	−	0.142471i
$512$	19.8498	−	10.8622i	0.877244	−	0.480045i
$513$		0			0
$514$	14.5584	+	7.35794i	0.642144	+	0.324545i
$515$	5.77846	+	10.0086i	0.254629	+	0.441031i
$516$		0			0
$517$	19.8030	−	34.2998i	0.870934	−	1.50850i
$518$	−15.2467	+	9.97247i	−0.669903	+	0.438165i
$519$		0			0
$520$	5.82592	−	4.81325i	0.255484	−	0.211075i
$521$		−	10.4472i		−	0.457700i	−0.973462	−	0.228850i	$-0.926503\pi$
$521$		−	10.4472i		−	0.457700i	0.973462	−	0.228850i	$-0.0734966\pi$
$522$		0			0
$523$			4.41957i			0.193254i	0.995321	+	0.0966272i	$0.0308055\pi$
$523$			4.41957i			0.193254i	−0.995321	+	0.0966272i	$0.969195\pi$
$524$	5.81442	−	13.2930i	0.254004	−	0.580707i
$525$		0			0
$526$	−9.68174	−	14.8022i	−0.422144	−	0.645409i
$527$	−2.15121	+	3.72601i	−0.0937083	+	0.162308i
$528$		0			0
$529$	9.18614	+	15.9109i	0.399397	+	0.691777i
$530$	−4.30243	+	8.51278i	−0.186885	+	0.369771i
$531$		0			0
$532$	7.11684	+	9.66181i	0.308554	+	0.418892i
$533$	0.430703	−	0.248667i	0.0186558	−	0.0107709i
$534$		0			0
$535$	9.07982	+	5.24224i	0.392555	+	0.226642i
$536$	18.4113	+	6.86070i	0.795245	+	0.296337i
$537$		0			0
$538$	−1.96189	−	35.2278i	−0.0845831	−	1.51878i
$539$	−1.27582			−0.0549535
$540$		0			0
$541$	36.9783			1.58982			0.794910	−	0.606728i	$-0.207518\pi$
$541$	36.9783			1.58982			0.794910	+	0.606728i	$0.207518\pi$
$542$	−0.109080	−	1.95865i	−0.00468541	−	0.0841314i
$543$		0			0
$544$	3.92119	+	13.7309i	0.168120	+	0.588707i
$545$	6.51087	+	3.75906i	0.278895	+	0.161020i
$546$		0			0
$547$	7.21723	−	4.16687i	0.308586	−	0.178162i	−0.337707	−	0.941251i	$-0.609651\pi$
$547$	7.21723	−	4.16687i	0.308586	−	0.178162i	0.646294	+	0.763089i	$0.276318\pi$
$548$	30.2054	−	22.2492i	1.29031	−	0.950437i
$549$		0			0
$550$	−9.55842	+	18.9123i	−0.407572	+	0.806423i
$551$	−0.875393	−	1.51622i	−0.0372930	−	0.0645933i
$552$		0			0
$553$	13.8030	−	23.9075i	0.586963	−	1.01665i
$554$	−0.485927	−	0.742925i	−0.0206450	−	0.0315638i
$555$		0			0
$556$	−17.1228	−	7.48958i	−0.726167	−	0.317629i
$557$			20.4897i			0.868175i	0.900871	+	0.434087i	$0.142929\pi$
$557$			20.4897i			0.868175i	−0.900871	+	0.434087i	$0.857071\pi$
$558$		0			0
$559$			23.4259i			0.990811i
$560$	8.39266	−	1.89913i	0.354655	−	0.0802527i
$561$		0			0
$562$	7.61113	−	4.97823i	0.321056	−	0.209994i
$563$	5.54098	−	9.59726i	0.233524	−	0.404476i	−0.725318	−	0.688414i	$-0.758307\pi$
$563$	5.54098	−	9.59726i	0.233524	−	0.404476i	0.958843	+	0.283937i	$0.0916408\pi$
$564$		0			0
$565$	6.31386	+	10.9359i	0.265626	+	0.460078i
$566$	−12.8327	−	6.48577i	−0.539400	−	0.272617i
$567$		0			0
$568$	−4.88316	+	0.822662i	−0.204893	+	0.0345181i
$569$	−0.989125	+	0.571072i	−0.0414663	+	0.0239406i	−0.520590	−	0.853807i	$-0.674288\pi$
$569$	−0.989125	+	0.571072i	−0.0414663	+	0.0239406i	0.479124	+	0.877747i	$0.340955\pi$
$570$		0			0
$571$	−14.5463	−	8.39829i	−0.608742	−	0.351457i	0.163731	−	0.986505i	$-0.447647\pi$
$571$	−14.5463	−	8.39829i	−0.608742	−	0.351457i	−0.772473	+	0.635048i	$0.780980\pi$
$572$	22.9709	−	2.56653i	0.960462	−	0.107312i
$573$		0			0
$574$	0.565415	−	0.0314888i	0.0236000	−	0.00131432i
$575$	9.40571			0.392245
$576$		0			0
$577$	−42.8397			−1.78344			−0.891719	−	0.452589i	$-0.850500\pi$
$577$	−42.8397			−1.78344			−0.891719	+	0.452589i	$0.850500\pi$
$578$	15.0066	−	0.835741i	0.624193	−	0.0347622i
$579$		0			0
$580$	−1.24767	+	0.139402i	−0.0518068	+	0.00578836i
$581$	17.0584	+	9.84868i	0.707703	+	0.408592i
$582$		0			0
$583$	−25.2651	+	14.5868i	−1.04637	+	0.604123i
$584$	−6.61659	+	1.11469i	−0.273796	+	0.0461263i
$585$		0			0
$586$	25.2337	+	12.7533i	1.04239	+	0.526834i
$587$	−6.41637	−	11.1135i	−0.264832	−	0.458702i	0.702688	−	0.711499i	$-0.251983\pi$
$587$	−6.41637	−	11.1135i	−0.264832	−	0.458702i	−0.967520	+	0.252796i	$0.918650\pi$
$588$		0			0
$589$	1.88316	−	3.26172i	0.0775941	−	0.134397i
$590$	−4.85522	+	3.17567i	−0.199886	+	0.130740i
$591$		0			0
$592$	18.5103	−	4.18858i	0.760767	−	0.172149i
$593$		−	15.4410i		−	0.634085i	−0.948411	−	0.317043i	$-0.897310\pi$
$593$		−	15.4410i		−	0.634085i	0.948411	−	0.317043i	$-0.102690\pi$
$594$		0			0
$595$			5.43039i			0.222624i
$596$	17.5909	+	7.69433i	0.720550	+	0.315172i
$597$		0			0
$598$	−5.61582	−	8.58592i	−0.229648	−	0.351104i
$599$	9.20550	−	15.9444i	0.376126	−	0.651470i	−0.614369	−	0.789019i	$-0.710589\pi$
$599$	9.20550	−	15.9444i	0.376126	−	0.651470i	0.990495	+	0.137549i	$0.0439225\pi$
$600$		0			0
$601$	14.9891	+	25.9619i	0.611419	+	1.05901i	0.991001	+	0.133851i	$0.0427344\pi$
$601$	14.9891	+	25.9619i	0.611419	+	1.05901i	−0.379582	+	0.925158i	$0.623932\pi$
$602$	−12.0319	+	23.8063i	−0.490383	+	0.970272i
$603$		0			0
$604$	14.7446	−	10.8608i	0.599948	−	0.441919i
$605$	0.510875	−	0.294954i	0.0207700	−	0.0119916i
$606$		0			0
$607$	−33.1947	−	19.1650i	−1.34733	−	0.777883i	−0.359462	−	0.933160i	$-0.617040\pi$
$607$	−33.1947	−	19.1650i	−1.34733	−	0.777883i	−0.987871	+	0.155277i	$0.950373\pi$
$608$	−3.43258	−	12.0199i	−0.139209	−	0.487472i
$609$		0			0
$610$	0.210106	+	3.77267i	0.00850693	+	0.152751i
$611$	−38.9732			−1.57669
$612$		0			0
$613$	−30.2337			−1.22113			−0.610564	−	0.791967i	$-0.709057\pi$
$613$	−30.2337			−1.22113			−0.610564	+	0.791967i	$0.709057\pi$
$614$	2.04089	+	36.6463i	0.0823635	+	1.47892i
$615$		0			0
$616$	24.6621	+	9.18998i	0.993663	+	0.370275i
$617$	−7.24456	−	4.18265i	−0.291655	−	0.168387i	0.347033	−	0.937853i	$-0.387189\pi$
$617$	−7.24456	−	4.18265i	−0.291655	−	0.168387i	−0.638688	+	0.769466i	$0.720523\pi$
$618$		0			0
$619$	23.9520	−	13.8287i	0.962711	−	0.555821i	0.0657046	−	0.997839i	$-0.479070\pi$
$619$	23.9520	−	13.8287i	0.962711	−	0.555821i	0.897006	+	0.442018i	$0.145737\pi$
$620$	−1.60171	−	2.17448i	−0.0643263	−	0.0873293i
$621$		0			0
$622$	19.9783	−	39.5289i	0.801055	−	1.58497i
$623$	−7.25450	−	12.5652i	−0.290645	−	0.503412i
$624$		0			0
$625$	−7.98913	+	13.8376i	−0.319565	+	0.553503i
$626$	−3.47510	−	5.31302i	−0.138893	−	0.212351i
$627$		0			0
$628$	13.5143	−	30.8965i	0.539278	−	1.23290i
$629$			11.9769i			0.477549i
$630$		0			0
$631$			17.9365i			0.714040i	0.934097	+	0.357020i	$0.116207\pi$
$631$			17.9365i			0.714040i	−0.934097	+	0.357020i	$0.883793\pi$
$632$	−22.1697	+	18.3162i	−0.881864	+	0.728577i
$633$		0			0
$634$	−28.2405	+	18.4713i	−1.12157	+	0.733589i
$635$	6.45364	−	11.1780i	0.256105	−	0.443587i
$636$		0			0
$637$	0.627719	+	1.08724i	0.0248711	+	0.0430780i
$638$	−3.42703	−	1.73205i	−0.135678	−	0.0685725i
$639$		0			0
$640$	−8.88316	−	1.19897i	−0.351138	−	0.0473935i
$641$	−23.8723	+	13.7827i	−0.942898	+	0.544383i	−0.890868	−	0.454263i	$-0.849903\pi$
$641$	−23.8723	+	13.7827i	−0.942898	+	0.544383i	−0.0520307	+	0.998645i	$0.516569\pi$
$642$		0			0
$643$	−5.46644	−	3.15605i	−0.215575	−	0.124463i	0.388324	−	0.921523i	$-0.373054\pi$
$643$	−5.46644	−	3.15605i	−0.215575	−	0.124463i	−0.603900	+	0.797060i	$0.706387\pi$
$644$	−1.29715	−	11.6097i	−0.0511147	−	0.457486i
$645$		0			0
$646$	7.87663	−	0.438661i	0.309902	−	0.0172589i
$647$	−36.9711			−1.45348			−0.726741	−	0.686912i	$-0.758966\pi$
$647$	−36.9711			−1.45348			−0.726741	+	0.686912i	$0.758966\pi$
$648$		0			0
$649$	−17.7446			−0.696535
$650$	20.8197	−	1.15948i	0.816616	−	0.0454786i
$651$		0			0
$652$	2.63641	+	23.5964i	0.103250	+	0.924105i
$653$	−6.68614	−	3.86025i	−0.261649	−	0.151063i	0.363438	−	0.931619i	$-0.381603\pi$
$653$	−6.68614	−	3.86025i	−0.261649	−	0.151063i	−0.625087	+	0.780555i	$0.714936\pi$
$654$		0			0
$655$	−4.97760	+	2.87382i	−0.194491	+	0.112290i
$656$	−0.563374	−	0.174928i	−0.0219961	−	0.00682980i
$657$		0			0
$658$	−39.6060	−	20.0172i	−1.54400	−	0.780351i
$659$	−8.33010	−	14.4282i	−0.324495	−	0.562041i	0.656915	−	0.753964i	$-0.271861\pi$
$659$	−8.33010	−	14.4282i	−0.324495	−	0.562041i	−0.981410	+	0.191923i	$0.938528\pi$
$660$		0			0
$661$	−10.6861	+	18.5089i	−0.415643	+	0.719914i	−0.995496	−	0.0948069i	$-0.969777\pi$
$661$	−10.6861	+	18.5089i	−0.415643	+	0.719914i	0.579853	+	0.814721i	$0.303110\pi$
$662$	−32.9560	+	21.5556i	−1.28087	+	0.837783i
$663$		0			0
$664$	−13.0689	−	15.8185i	−0.507172	−	0.613877i
$665$		−	4.75372i		−	0.184341i
$666$		0			0
$667$			1.70438i			0.0659938i
$668$	−15.3981	+	35.2034i	−0.595772	+	1.36206i
$669$		0			0
$670$	−4.26051	−	6.51381i	−0.164598	−	0.251651i
$671$	−5.77846	+	10.0086i	−0.223075	+	0.386377i
$672$		0			0
$673$	−0.569297	−	0.986051i	−0.0219448	−	0.0380095i	0.854844	−	0.518884i	$-0.173652\pi$
$673$	−0.569297	−	0.986051i	−0.0219448	−	0.0380095i	−0.876789	+	0.480875i	$0.840319\pi$
$674$	2.71459	−	5.37108i	0.104562	−	0.206886i
$675$		0			0
$676$	1.93070	+	2.62112i	0.0742578	+	0.100812i
$677$	−28.5475	+	16.4819i	−1.09717	+	0.633452i	−0.935477	−	0.353389i	$-0.885029\pi$
$677$	−28.5475	+	16.4819i	−1.09717	+	0.633452i	−0.161695	+	0.986841i	$0.551696\pi$
$678$		0			0
$679$	−29.3673	−	16.9552i	−1.12701	−	0.650681i
$680$	1.97526	−	5.30079i	0.0757479	−	0.203276i
$681$		0			0
$682$	−0.459321	−	8.24759i	−0.0175883	−	0.315816i
$683$	−2.07668			−0.0794618			−0.0397309	−	0.999210i	$-0.512650\pi$
$683$	−2.07668			−0.0794618			−0.0397309	+	0.999210i	$0.512650\pi$
$684$		0			0
$685$	−14.8614			−0.567825
$686$	−1.41513	−	25.4102i	−0.0540299	−	0.970165i
$687$		0			0
$688$	20.4041	−	18.8616i	0.777899	−	0.719092i
$689$	24.8614	+	14.3537i	0.947144	+	0.546834i
$690$		0			0
$691$	−10.0064	+	5.77717i	−0.380660	+	0.219774i	−0.678105	−	0.734965i	$-0.737199\pi$
$691$	−10.0064	+	5.77717i	−0.380660	+	0.219774i	0.297446	+	0.954739i	$0.403865\pi$
$692$	8.93075	−	6.57835i	0.339496	−	0.250071i
$693$		0			0
$694$	−4.93070	+	9.75588i	−0.187167	+	0.370328i
$695$	3.70178	+	6.41168i	0.140417	+	0.243209i
$696$		0			0
$697$	0.186141	−	0.322405i	0.00705058	−	0.0122120i
$698$	8.80346	+	13.4594i	0.333216	+	0.509448i
$699$		0			0
$700$	21.7533	+	9.51498i	0.822196	+	0.359633i
$701$			26.1282i			0.986850i	0.869788	+	0.493425i	$0.164255\pi$
$701$			26.1282i			0.986850i	−0.869788	+	0.493425i	$0.835745\pi$
$702$		0			0
$703$		−	10.4845i		−	0.395429i
$704$	−20.7307	−	17.9413i	−0.781317	−	0.676188i
$705$		0			0
$706$	5.80072	−	3.79409i	0.218313	−	0.142793i
$707$	24.1895	−	41.8974i	0.909738	−	1.57571i
$708$		0			0
$709$	2.43070	+	4.21010i	0.0912870	+	0.158114i	0.908053	−	0.418855i	$-0.137569\pi$
$709$	2.43070	+	4.21010i	0.0912870	+	0.158114i	−0.816766	+	0.576969i	$0.804235\pi$
$710$	1.75079	+	0.884861i	0.0657058	+	0.0332082i
$711$		0			0
$712$	2.51087	+	14.9040i	0.0940990	+	0.558553i
$713$	−3.17527	+	1.83324i	−0.118915	+	0.0686554i
$714$		0			0
$715$	−7.92967	−	4.57820i	−0.296553	−	0.171215i
$716$	37.3902	−	4.17759i	1.39734	−	0.156124i
$717$		0			0
$718$	−42.3155	+	2.35661i	−1.57920	+	0.0879480i
$719$	7.65492			0.285481			0.142740	−	0.989760i	$-0.454409\pi$
$719$	7.65492			0.285481			0.142740	+	0.989760i	$0.454409\pi$
$720$		0			0
$721$	39.6060			1.47500
$722$	19.9333	−	1.11012i	0.741842	−	0.0413143i
$723$		0			0
$724$	−7.95053	+	0.888309i	−0.295479	+	0.0330137i
$725$	−3.00000	−	1.73205i	−0.111417	−	0.0643268i
$726$		0			0
$727$	2.67732	−	1.54575i	0.0992963	−	0.0573287i	−0.449530	−	0.893265i	$-0.648408\pi$
$727$	2.67732	−	1.54575i	0.0992963	−	0.0573287i	0.548826	+	0.835937i	$0.315075\pi$
$728$	−4.30243	−	25.5383i	−0.159459	−	0.946514i
$729$		0			0
$730$	2.37228	+	1.19897i	0.0878021	+	0.0443759i
$731$	8.76780	+	15.1863i	0.324289	+	0.561685i
$732$		0			0
$733$	2.68614	−	4.65253i	0.0992149	−	0.171845i	−0.812145	−	0.583456i	$-0.801700\pi$
$733$	2.68614	−	4.65253i	0.0992149	−	0.171845i	0.911360	+	0.411610i	$0.135034\pi$
$734$	16.0676	−	10.5094i	0.593065	−	0.387908i
$735$		0			0
$736$	−2.95675	+	11.8044i	−0.108987	+	0.435117i
$737$		−	23.8063i		−	0.876916i
$738$		0			0
$739$			9.66181i			0.355415i	0.984083	+	0.177708i	$0.0568681\pi$
$739$			9.66181i			0.355415i	−0.984083	+	0.177708i	$0.943132\pi$
$740$	−6.88801	−	3.01285i	−0.253208	−	0.110755i
$741$		0			0
$742$	17.8928	+	27.3560i	0.656865	+	1.00427i
$743$	−22.5132	+	38.9940i	−0.825929	+	1.43055i	0.0752776	+	0.997163i	$0.476016\pi$
$743$	−22.5132	+	38.9940i	−0.825929	+	1.43055i	−0.901207	+	0.433389i	$0.857318\pi$
$744$		0			0
$745$	−3.80298	−	6.58696i	−0.139331	−	0.241328i
$746$	−5.65278	+	11.1846i	−0.206963	+	0.409497i
$747$		0			0
$748$	13.9307	−	10.2613i	0.509357	−	0.375190i
$749$	31.1168	−	17.9653i	1.13698	−	0.656438i
$750$		0			0
$751$	39.9743	+	23.0792i	1.45868	+	0.842170i	0.998947	−	0.0458859i	$-0.0146111\pi$
$751$	39.9743	+	23.0792i	1.45868	+	0.842170i	0.459735	+	0.888056i	$0.347944\pi$
$752$	31.3796	+	33.9458i	1.14430	+	1.23788i
$753$		0			0
$754$	0.210106	+	3.77267i	0.00765160	+	0.137393i
$755$	−7.25450			−0.264018
$756$		0			0
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$	−0.759784	−	13.6427i	−0.0275966	−	0.495526i
$759$		0			0
$760$	−1.72913	+	4.64027i	−0.0627222	+	0.168320i
$761$	16.5475	+	9.55373i	0.599848	+	0.346322i	0.768982	−	0.639271i	$-0.220764\pi$
$761$	16.5475	+	9.55373i	0.599848	+	0.346322i	−0.169134	+	0.985593i	$0.554097\pi$
$762$		0			0
$763$	22.3130	−	12.8824i	0.807784	−	0.466375i
$764$	4.62832	+	6.28339i	0.167447	+	0.227325i
$765$		0			0
$766$	−0.255437	+	0.505408i	−0.00922933	+	0.0182611i
$767$	8.73053	+	15.1217i	0.315241	+	0.546014i
$768$		0			0
$769$	27.5475	−	47.7138i	0.993390	−	1.72060i	0.397285	−	0.917695i	$-0.369952\pi$
$769$	27.5475	−	47.7138i	0.993390	−	1.72060i	0.596105	−	0.802907i	$-0.296714\pi$
$770$	−5.70699	−	8.72532i	−0.205666	−	0.314439i
$771$		0			0
$772$	3.00124	−	6.86146i	0.108017	−	0.246949i
$773$		−	45.7330i		−	1.64490i	−0.568835	−	0.822451i	$-0.692606\pi$
$773$		−	45.7330i		−	1.64490i	0.568835	−	0.822451i	$-0.307394\pi$
$774$		0			0
$775$		−	7.45202i		−	0.267685i
$776$	22.4991	+	27.2327i	0.807669	+	0.977596i
$777$		0			0
$778$	−9.83561	+	6.43320i	−0.352624	+	0.230642i
$779$	−0.162946	+	0.282231i	−0.00583815	+	0.0101120i
$780$		0			0
$781$	3.00000	+	5.19615i	0.107348	+	0.185933i
$782$	−6.85407	−	3.46410i	−0.245101	−	0.123876i
$783$		0			0
$784$	0.441578	−	1.42215i	0.0157706	−	0.0507910i
$785$	−11.5693	+	6.67954i	−0.412926	+	0.238403i
$786$		0			0
$787$	17.0095	+	9.82043i	0.606323	+	0.350061i	0.771525	−	0.636199i	$-0.219494\pi$
$787$	17.0095	+	9.82043i	0.606323	+	0.350061i	−0.165202	+	0.986260i	$0.552828\pi$
$788$	−2.37340	−	21.2423i	−0.0845488	−	0.756727i
$789$		0			0
$790$	11.3744	−	0.633456i	0.404682	−	0.0225373i
$791$	43.2756			1.53870
$792$		0			0
$793$	11.3723			0.403842
$794$	−10.2449	+	0.570552i	−0.363577	+	0.0202481i
$795$		0			0
$796$	−4.29134	−	38.4082i	−0.152102	−	1.36134i
$797$	−40.8030	−	23.5576i	−1.44532	−	0.834454i	−0.447119	−	0.894475i	$-0.647550\pi$
$797$	−40.8030	−	23.5576i	−1.44532	−	0.834454i	−0.998197	+	0.0600211i	$0.980883\pi$
$798$		0			0
$799$	−25.2651	+	14.5868i	−0.893814	+	0.516043i
$800$	−17.7731	−	17.2005i	−0.628373	−	0.608129i
$801$		0			0
$802$	27.6753	+	13.9873i	0.977248	+	0.493909i
$803$	4.06494	+	7.04069i	0.143449	+	0.248461i
$804$		0			0
$805$	−2.31386	+	4.00772i	−0.0815528	+	0.141254i
$806$	−6.80251	+	4.44934i	−0.239608	+	0.156721i
$807$		0			0
$808$	−38.8520	+	32.0987i	−1.36681	+	1.12923i
$809$			27.1778i			0.955521i	0.878490	+	0.477760i	$0.158551\pi$
$809$			27.1778i			0.955521i	−0.878490	+	0.477760i	$0.841449\pi$
$810$		0			0
$811$		−	25.9530i		−	0.911332i	−0.890151	−	0.455666i	$-0.849401\pi$
$811$		−	25.9530i		−	0.911332i	0.890151	−	0.455666i	$-0.150599\pi$
$812$	−1.72418	+	3.94184i	−0.0605068	+	0.138331i
$813$		0			0
$814$	−12.5869	−	19.2440i	−0.441172	−	0.674500i
$815$	4.70285	−	8.14558i	0.164734	−	0.285327i
$816$		0			0
$817$	−7.67527	−	13.2940i	−0.268524	−	0.465096i
$818$	−1.43877	+	2.84674i	−0.0503053	+	0.0995340i
$819$		0			0
$820$	0.138593	+	0.188154i	0.00483989	+	0.00657062i
$821$	18.6861	−	10.7884i	0.652151	−	0.376519i	−0.137129	−	0.990553i	$-0.543787\pi$
$821$	18.6861	−	10.7884i	0.652151	−	0.376519i	0.789280	+	0.614034i	$0.210454\pi$
$822$		0			0
$823$	25.8657	+	14.9336i	0.901622	+	0.520552i	0.877726	−	0.479163i	$-0.159060\pi$
$823$	25.8657	+	14.9336i	0.901622	+	0.520552i	0.0238957	+	0.999714i	$0.492393\pi$
$824$	−38.6607	−	14.4064i	−1.34681	−	0.501870i
$825$		0			0
$826$	1.10555	+	19.8514i	0.0384671	+	0.690717i
$827$	7.00314			0.243523			0.121762	−	0.992559i	$-0.461146\pi$
$827$	7.00314			0.243523			0.121762	+	0.992559i	$0.461146\pi$
$828$		0			0
$829$	−13.7663			−0.478124			−0.239062	−	0.971004i	$-0.576840\pi$
$829$	−13.7663			−0.478124			−0.239062	+	0.971004i	$0.576840\pi$
$830$	0.451982	+	8.11582i	0.0156885	+	0.281704i
$831$		0			0
$832$	−5.08964	+	26.4938i	−0.176451	+	0.918507i
$833$	0.813859	+	0.469882i	0.0281986	+	0.0162804i
$834$		0			0
$835$	13.1820	−	7.61065i	0.456183	−	0.263377i
$836$	−12.1948	+	8.98266i	−0.421767	+	0.310672i
$837$		0			0
$838$	−3.60597	+	7.13477i	−0.124566	+	0.246466i
$839$	22.8391	+	39.5585i	0.788493	+	1.36571i	0.926890	+	0.375333i	$0.122472\pi$
$839$	22.8391	+	39.5585i	0.788493	+	1.36571i	−0.138397	+	0.990377i	$0.544195\pi$
$840$		0			0
$841$	−14.1861	+	24.5711i	−0.489177	+	0.847280i
$842$	−22.9184	−	35.0396i	−0.789821	−	1.20754i
$843$		0			0
$844$	11.2214	+	4.90829i	0.386256	+	0.168950i
$845$		−	1.28962i		−	0.0443643i
$846$		0			0
$847$		−	2.02163i		−	0.0694641i
$848$	−7.51522	−	33.2114i	−0.258074	−	1.14049i
$849$		0			0
$850$	13.0628	−	8.54400i	0.448049	−	0.293057i
$851$	−5.10328	+	8.83915i	−0.174938	+	0.303002i
$852$		0			0
$853$	−2.19702	−	3.80534i	−0.0752244	−	0.130292i	0.825959	−	0.563730i	$-0.190634\pi$
$853$	−2.19702	−	3.80534i	−0.0752244	−	0.130292i	−0.901184	+	0.433437i	$0.857301\pi$
$854$	11.5569	+	5.84096i	0.395470	+	0.199874i
$855$		0			0
$856$	−36.9090	+	6.21803i	−1.26152	+	0.212528i
$857$	22.0367	−	12.7229i	0.752758	−	0.434605i	−0.0739313	−	0.997263i	$-0.523555\pi$
$857$	22.0367	−	12.7229i	0.752758	−	0.434605i	0.826690	+	0.562658i	$0.190221\pi$
$858$		0			0
$859$	30.4056	+	17.5547i	1.03743	+	0.598958i	0.919103	−	0.394017i	$-0.128915\pi$
$859$	30.4056	+	17.5547i	1.03743	+	0.598958i	0.118323	+	0.992975i	$0.462248\pi$
$860$	−10.9394	+	1.22225i	−0.373029	+	0.0416784i
$861$		0			0
$862$	20.6976	−	1.15268i	0.704962	−	0.0392604i
$863$	4.15335			0.141382			0.0706909	−	0.997498i	$-0.477480\pi$
$863$	4.15335			0.141382			0.0706909	+	0.997498i	$0.477480\pi$
$864$		0			0
$865$	−4.39403			−0.149402
$866$	−20.2940	+	1.13021i	−0.689619	+	0.0384059i
$867$		0			0
$868$	−9.19820	+	1.02771i	−0.312207	+	0.0348828i
$869$	30.1753	+	17.4217i	1.02363	+	0.590991i
$870$		0			0
$871$	−20.2875	+	11.7130i	−0.687414	+	0.396879i
$872$	−26.4663	+	4.45877i	−0.896264	+	0.150993i
$873$		0			0
$874$	6.00000	+	3.03245i	0.202953	+	0.102574i
$875$	−10.0809	−	17.4606i	−0.340796	−	0.590276i
$876$		0			0
$877$	−13.6861	+	23.7051i	−0.462148	+	0.800464i	−0.999068	−	0.0431693i	$-0.986254\pi$
$877$	−13.6861	+	23.7051i	−0.462148	+	0.800464i	0.536920	+	0.843633i	$0.319588\pi$
$878$	38.9377	−	25.4681i	1.31408	−	0.859506i
$879$		0			0
$880$	2.39702	+	10.5930i	0.0808034	+	0.357089i
$881$		−	19.7899i		−	0.666740i	−0.942796	−	0.333370i	$-0.891814\pi$
$881$		−	19.7899i		−	0.666740i	0.942796	−	0.333370i	$-0.108186\pi$
$882$		0			0
$883$		−	34.7921i		−	1.17085i	−0.810727	−	0.585424i	$-0.800928\pi$
$883$		−	34.7921i		−	1.17085i	0.810727	−	0.585424i	$-0.199072\pi$
$884$	−15.5986	−	6.82292i	−0.524639	−	0.229480i
$885$		0			0
$886$	−4.00823	−	6.12811i	−0.134659	−	0.205878i
$887$	2.75186	−	4.76635i	0.0923983	−	0.160039i	−0.816122	−	0.577880i	$-0.803880\pi$
$887$	2.75186	−	4.76635i	0.0923983	−	0.160039i	0.908520	+	0.417842i	$0.137213\pi$
$888$		0			0
$889$	−22.1168	−	38.3075i	−0.741775	−	1.28479i
$890$	2.70071	−	5.34363i	0.0905281	−	0.179119i
$891$		0			0
$892$	2.74456	−	2.02163i	0.0918948	−	0.0676893i
$893$	22.1168	−	12.7692i	0.740112	−	0.427304i
$894$		0			0
$895$	−12.9073	−	7.45202i	−0.431443	−	0.249094i
$896$	−18.7799	+	24.3099i	−0.627391	+	0.812135i
$897$		0			0
$898$	0.299921	+	5.38541i	0.0100085	+	0.179713i
$899$	1.35036			0.0450369
$900$		0			0
$901$	21.4891			0.715907
$902$	0.0397442	+	0.713649i	0.00132334	+	0.0237619i
$903$		0			0
$904$	−42.2428	−	15.7412i	−1.40497	−	0.523544i
$905$	2.74456	+	1.58457i	0.0912323	+	0.0526730i
$906$		0			0
$907$	21.3258	−	12.3125i	0.708111	−	0.408828i	−0.102250	−	0.994759i	$-0.532604\pi$
$907$	21.3258	−	12.3125i	0.708111	−	0.408828i	0.810361	+	0.585930i	$0.199271\pi$
$908$	22.4014	+	30.4121i	0.743417	+	1.00926i
$909$		0			0
$910$	−4.62772	+	9.15640i	−0.153407	+	0.303532i
$911$	−6.57932	−	11.3957i	−0.217983	−	0.377557i	0.736209	−	0.676755i	$-0.236614\pi$
$911$	−6.57932	−	11.3957i	−0.217983	−	0.377557i	−0.954191	+	0.299198i	$0.903281\pi$
$912$		0			0
$913$	−12.4307	+	21.5306i	−0.411396	+	0.712559i
$914$	4.62785	+	7.07545i	0.153076	+	0.234035i
$915$		0			0
$916$	−7.51180	+	17.1736i	−0.248197	+	0.567431i
$917$			19.6974i			0.650464i
$918$		0			0
$919$			46.0993i			1.52067i	0.649529	+	0.760337i	$0.274966\pi$
$919$			46.0993i			1.52067i	−0.649529	+	0.760337i	$0.725034\pi$
$920$	3.71642	−	3.07042i	0.122527	−	0.101229i
$921$		0			0
$922$	27.0632	−	17.7013i	0.891280	−	0.582962i
$923$	2.95207	−	5.11313i	0.0971686	−	0.168301i
$924$		0			0
$925$	−10.3723	−	17.9653i	−0.341039	−	0.590696i
$926$	26.5409	+	13.4140i	0.872187	+	0.440811i
$927$		0			0
$928$	3.11684	−	3.22060i	0.102315	−	0.105721i
$929$	−30.4307	+	17.5692i	−0.998399	+	0.576426i	−0.907774	−	0.419459i	$-0.862220\pi$
$929$	−30.4307	+	17.5692i	−0.998399	+	0.576426i	−0.0906248	+	0.995885i	$0.528886\pi$
$930$		0			0
$931$	−0.712446	−	0.411331i	−0.0233495	−	0.0134808i
$932$	6.23208	+	55.7783i	0.204139	+	1.82708i
$933$		0			0
$934$	34.4388	−	1.91795i	1.12687	−	0.0627573i
$935$	−6.85407			−0.224152
$936$		0			0
$937$	−11.7228			−0.382968			−0.191484	−	0.981496i	$-0.561330\pi$
$937$	−11.7228			−0.382968			−0.191484	+	0.981496i	$0.561330\pi$
$938$	−26.6328	+	1.48322i	−0.869591	+	0.0484289i
$939$		0			0
$940$	−2.03343	−	18.1996i	−0.0663231	−	0.593604i
$941$	−31.8030	−	18.3615i	−1.03675	−	0.598567i	−0.117837	−	0.993033i	$-0.537596\pi$
$941$	−31.8030	−	18.3615i	−1.03675	−	0.598567i	−0.918910	+	0.394466i	$0.870929\pi$
$942$		0			0
$943$	0.274750	−	0.158627i	0.00894709	−	0.00516561i
$944$	6.14162	−	19.7797i	0.199893	−	0.643775i
$945$		0			0
$946$	−30.0475	−	15.1863i	−0.976930	−	0.493748i
$947$	−22.2757	−	38.5827i	−0.723864	−	1.25377i	−0.959440	−	0.281913i	$-0.909031\pi$
$947$	−22.2757	−	38.5827i	−0.723864	−	1.25377i	0.235576	−	0.971856i	$-0.424302\pi$
$948$		0			0
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$	−11.4350	+	7.47935i	−0.371002	+	0.242662i
$951$		0			0
$952$	−12.3475	−	14.9454i	−0.400186	−	0.484382i
$953$			32.8164i			1.06303i	0.847050	+	0.531514i	$0.178377\pi$
$953$			32.8164i			1.06303i	−0.847050	+	0.531514i	$0.821623\pi$
$954$		0			0
$955$		−	3.09150i		−	0.100039i
$956$	13.3530	−	30.5278i	0.431867	−	0.987340i
$957$		0			0
$958$	7.59108	+	11.6059i	0.245257	+	0.374969i
$959$	−25.4653	+	44.1071i	−0.822317	+	1.42429i
$960$		0			0
$961$	−14.0475	−	24.3311i	−0.453147	−	0.784873i
$962$	−10.2066	+	20.1947i	−0.329073	+	0.651103i
$963$		0			0
$964$	−19.5584	−	26.5525i	−0.629934	−	0.855197i
$965$	−2.56930	+	1.48338i	−0.0827086	+	0.0477518i
$966$		0			0
$967$	−48.7282	−	28.1332i	−1.56699	−	0.904704i	−0.996517	−	0.0833895i	$-0.973425\pi$
$967$	−48.7282	−	28.1332i	−1.56699	−	0.904704i	−0.570476	−	0.821314i	$-0.693241\pi$
$968$	−0.735354	+	1.97338i	−0.0236352	+	0.0634270i
$969$		0			0
$970$	−0.778119	−	13.9720i	−0.0249839	−	0.448612i
$971$	24.7156			0.793160			0.396580	−	0.918000i	$-0.370197\pi$
$971$	24.7156			0.793160			0.396580	+	0.918000i	$0.370197\pi$
$972$		0			0
$973$	25.3723			0.813398
$974$	−1.41049	−	25.3268i	−0.0451949	−	0.811523i
$975$		0			0
$976$	−9.15649	−	9.90531i	−0.293092	−	0.317061i
$977$	18.6386	+	10.7610i	0.596301	+	0.344275i	0.767585	−	0.640947i	$-0.221458\pi$
$977$	18.6386	+	10.7610i	0.596301	+	0.344275i	−0.171284	+	0.985222i	$0.554791\pi$
$978$		0			0
$979$	15.8593	−	9.15640i	0.506867	−	0.292640i
$980$	−0.474964	+	0.349857i	−0.0151722	+	0.0111758i
$981$		0			0
$982$	−15.8139	+	31.2893i	−0.504641	+	0.998481i
$983$	8.40464	+	14.5573i	0.268066	+	0.464305i	0.968362	−	0.249548i	$-0.0802820\pi$
$983$	8.40464	+	14.5573i	0.268066	+	0.464305i	−0.700296	+	0.713852i	$0.746949\pi$
$984$		0			0
$985$	−4.23369	+	7.33296i	−0.134897	+	0.233648i
$986$	1.54823	+	2.36706i	0.0493057	+	0.0753826i
$987$		0			0
$988$	13.6549	+	5.97273i	0.434421	+	0.190018i
$989$			14.9436i			0.475180i
$990$		0			0
$991$		−	16.2912i		−	0.517506i	−0.965944	−	0.258753i	$-0.916688\pi$
$991$		−	16.2912i		−	0.517506i	0.965944	−	0.258753i	$-0.0833116\pi$
$992$	9.35250	+	2.34260i	0.296942	+	0.0743775i
$993$		0			0
$994$	5.62618	−	3.67993i	0.178452	−	0.116720i
$995$	−7.65492	+	13.2587i	−0.242677	+	0.420330i
$996$		0			0
$997$	26.4307	+	45.7793i	0.837069	+	1.44985i	0.892335	+	0.451374i	$0.149066\pi$
$997$	26.4307	+	45.7793i	0.837069	+	1.44985i	−0.0552661	+	0.998472i	$0.517601\pi$
$998$	−0.637910	−	0.322405i	−0.0201927	−	0.0102056i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.2.h.a.71.4		8
3.2	odd	2		36.2.h.a.23.1	yes	8
4.3	odd	2	inner	108.2.h.a.71.3		8
8.3	odd	2		1728.2.s.f.1151.4		8
8.5	even	2		1728.2.s.f.1151.3		8
9.2	odd	6	inner	108.2.h.a.35.3		8
9.4	even	3		324.2.b.b.323.4		8
9.5	odd	6		324.2.b.b.323.5		8
9.7	even	3		36.2.h.a.11.2	yes	8
12.11	even	2		36.2.h.a.23.2	yes	8
15.2	even	4		900.2.o.a.599.4		16
15.8	even	4		900.2.o.a.599.5		16
15.14	odd	2		900.2.r.c.851.4		8
24.5	odd	2		576.2.s.f.383.2		8
24.11	even	2		576.2.s.f.383.3		8
36.7	odd	6		36.2.h.a.11.1	✓	8
36.11	even	6	inner	108.2.h.a.35.4		8
36.23	even	6		324.2.b.b.323.3		8
36.31	odd	6		324.2.b.b.323.6		8
45.7	odd	12		900.2.o.a.299.7		16
45.34	even	6		900.2.r.c.551.3		8
45.43	odd	12		900.2.o.a.299.2		16
60.23	odd	4		900.2.o.a.599.7		16
60.47	odd	4		900.2.o.a.599.2		16
60.59	even	2		900.2.r.c.851.3		8
72.5	odd	6		5184.2.c.j.5183.5		8
72.11	even	6		1728.2.s.f.575.3		8
72.13	even	6		5184.2.c.j.5183.3		8
72.29	odd	6		1728.2.s.f.575.4		8
72.43	odd	6		576.2.s.f.191.2		8
72.59	even	6		5184.2.c.j.5183.6		8
72.61	even	6		576.2.s.f.191.3		8
72.67	odd	6		5184.2.c.j.5183.4		8
180.7	even	12		900.2.o.a.299.5		16
180.43	even	12		900.2.o.a.299.4		16
180.79	odd	6		900.2.r.c.551.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.2.h.a.11.1	✓	8	36.7	odd	6
36.2.h.a.11.2	yes	8	9.7	even	3
36.2.h.a.23.1	yes	8	3.2	odd	2
36.2.h.a.23.2	yes	8	12.11	even	2
108.2.h.a.35.3		8	9.2	odd	6	inner
108.2.h.a.35.4		8	36.11	even	6	inner
108.2.h.a.71.3		8	4.3	odd	2	inner
108.2.h.a.71.4		8	1.1	even	1	trivial
324.2.b.b.323.3		8	36.23	even	6
324.2.b.b.323.4		8	9.4	even	3
324.2.b.b.323.5		8	9.5	odd	6
324.2.b.b.323.6		8	36.31	odd	6
576.2.s.f.191.2		8	72.43	odd	6
576.2.s.f.191.3		8	72.61	even	6
576.2.s.f.383.2		8	24.5	odd	2
576.2.s.f.383.3		8	24.11	even	2
900.2.o.a.299.2		16	45.43	odd	12
900.2.o.a.299.4		16	180.43	even	12
900.2.o.a.299.5		16	180.7	even	12
900.2.o.a.299.7		16	45.7	odd	12
900.2.o.a.599.2		16	60.47	odd	4
900.2.o.a.599.4		16	15.2	even	4
900.2.o.a.599.5		16	15.8	even	4
900.2.o.a.599.7		16	60.23	odd	4
900.2.r.c.551.3		8	45.34	even	6
900.2.r.c.551.4		8	180.79	odd	6
900.2.r.c.851.3		8	60.59	even	2
900.2.r.c.851.4		8	15.14	odd	2
1728.2.s.f.575.3		8	72.11	even	6
1728.2.s.f.575.4		8	72.29	odd	6
1728.2.s.f.1151.3		8	8.5	even	2
1728.2.s.f.1151.4		8	8.3	odd	2
5184.2.c.j.5183.3		8	72.13	even	6
5184.2.c.j.5183.4		8	72.67	odd	6
5184.2.c.j.5183.5		8	72.5	odd	6
5184.2.c.j.5183.6		8	72.59	even	6

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	108.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.41203 - 0.0786378i) q^{2} +(1.98763 - 0.222077i) q^{4} +(-0.686141 - 0.396143i) q^{5} +(-2.35143 + 1.35760i) q^{7} +(2.78912 - 0.469882i) q^{8} +O(q^{10})\)	\(q+(1.41203 - 0.0786378i) q^{2} +(1.98763 - 0.222077i) q^{4} +(-0.686141 - 0.396143i) q^{5} +(-2.35143 + 1.35760i) q^{7} +(2.78912 - 0.469882i) q^{8} +(-1.00000 - 0.505408i) q^{10} +(-1.71352 - 2.96790i) q^{11} +(-1.68614 + 2.92048i) q^{13} +(-3.21352 + 2.10187i) q^{14} +(3.90136 - 0.882816i) q^{16} +2.52434i q^{17} -2.20979i q^{19} +(-1.45177 - 0.635011i) q^{20} +(-2.65292 - 4.05600i) q^{22} +(-1.07561 + 1.86301i) q^{23} +(-2.18614 - 3.78651i) q^{25} +(-2.15121 + 4.25639i) q^{26} +(-4.37228 + 3.22060i) q^{28} +(0.686141 - 0.396143i) q^{29} +(1.47603 + 0.852189i) q^{31} +(5.43940 - 1.55335i) q^{32} +(0.198508 + 3.56443i) q^{34} +2.15121 q^{35} +4.74456 q^{37} +(-0.173773 - 3.12027i) q^{38} +(-2.09987 - 0.782488i) q^{40} +(-0.127719 - 0.0737384i) q^{41} +(6.01594 - 3.47331i) q^{43} +(-4.06494 - 5.51856i) q^{44} +(-1.37228 + 2.71519i) q^{46} +(5.77846 + 10.0086i) q^{47} +(0.186141 - 0.322405i) q^{49} +(-3.38465 - 5.17473i) q^{50} +(-2.70285 + 6.17930i) q^{52} -8.51278i q^{53} +2.71519i q^{55} +(-5.92051 + 4.89140i) q^{56} +(0.937696 - 0.613321i) q^{58} +(2.58891 - 4.48412i) q^{59} +(-1.68614 - 2.92048i) q^{61} +(2.15121 + 1.08724i) q^{62} +(7.55842 - 2.62112i) q^{64} +(2.31386 - 1.33591i) q^{65} +(6.01594 + 3.47331i) q^{67} +(0.560598 + 5.01746i) q^{68} +(3.03757 - 0.169167i) q^{70} -1.75079 q^{71} -2.37228 q^{73} +(6.69944 - 0.373102i) q^{74} +(-0.490743 - 4.39224i) q^{76} +(8.05842 + 4.65253i) q^{77} +(-8.80507 + 5.08361i) q^{79} +(-3.02661 - 0.939764i) q^{80} +(-0.186141 - 0.0940770i) q^{82} +(-3.62725 - 6.28258i) q^{83} +(1.00000 - 1.73205i) q^{85} +(8.22153 - 5.37748i) q^{86} +(-6.17377 - 7.47269i) q^{88} +5.34363i q^{89} -9.15640i q^{91} +(-1.72418 + 3.94184i) q^{92} +(8.94639 + 13.6780i) q^{94} +(-0.875393 + 1.51622i) q^{95} +(6.24456 + 10.8159i) q^{97} +(0.237482 - 0.469882i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) 8 * q + 3 * q^2 - q^4 + 6 * q^5	\( 8 q + 3 q^{2} - q^{4} + 6 q^{5} - 8 q^{10} - 2 q^{13} - 12 q^{14} - q^{16} - 18 q^{20} + 3 q^{22} - 6 q^{25} - 12 q^{28} - 6 q^{29} + 33 q^{32} + 7 q^{34} - 8 q^{37} + 27 q^{38} + 10 q^{40} - 24 q^{41} + 12 q^{46} - 10 q^{49} - 21 q^{50} + 16 q^{52} - 18 q^{56} + 4 q^{58} - 2 q^{61} + 26 q^{64} + 30 q^{65} + 15 q^{68} - 6 q^{70} + 4 q^{73} + 30 q^{74} - 3 q^{76} + 30 q^{77} + 10 q^{82} + 8 q^{85} - 21 q^{86} - 21 q^{88} - 24 q^{92} - 18 q^{94} + 4 q^{97}+O(q^{100}) \) 8 * q + 3 * q^2 - q^4 + 6 * q^5 - 8 * q^10 - 2 * q^13 - 12 * q^14 - q^16 - 18 * q^20 + 3 * q^22 - 6 * q^25 - 12 * q^28 - 6 * q^29 + 33 * q^32 + 7 * q^34 - 8 * q^37 + 27 * q^38 + 10 * q^40 - 24 * q^41 + 12 * q^46 - 10 * q^49 - 21 * q^50 + 16 * q^52 - 18 * q^56 + 4 * q^58 - 2 * q^61 + 26 * q^64 + 30 * q^65 + 15 * q^68 - 6 * q^70 + 4 * q^73 + 30 * q^74 - 3 * q^76 + 30 * q^77 + 10 * q^82 + 8 * q^85 - 21 * q^86 - 21 * q^88 - 24 * q^92 - 18 * q^94 + 4 * q^97

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