LMFDB - Embedded newform 729.2.e.b.649.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			649.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	729.649
Dual form			729.2.e.b.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.439693 - 2.49362i) q^{2} +(-4.14543 - 1.50881i) q^{4} +(0.358441 - 0.300767i) q^{5} +(3.03209 - 1.10359i) q^{7} +(-3.05303 + 5.28801i) q^{8} +O(q^{10})$	\(q+(0.439693 - 2.49362i) q^{2} +(-4.14543 - 1.50881i) q^{4} +(0.358441 - 0.300767i) q^{5} +(3.03209 - 1.10359i) q^{7} +(-3.05303 + 5.28801i) q^{8} +(-0.592396 - 1.02606i) q^{10} +(-2.37939 - 1.99654i) q^{11} +(-0.379385 - 2.15160i) q^{13} +(-1.41875 - 8.04612i) q^{14} +(5.08512 + 4.26692i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(-0.0209445 + 0.0362770i) q^{19} +(-1.93969 + 0.705990i) q^{20} +(-6.02481 + 5.05542i) q^{22} +(-5.73783 - 2.08840i) q^{23} +(-0.830222 + 4.70842i) q^{25} -5.53209 q^{26} -14.2344 q^{28} +(1.14156 - 6.47410i) q^{29} +(5.85117 + 2.12965i) q^{31} +(3.52094 - 2.95442i) q^{32} +(-7.13816 + 2.59808i) q^{34} +(0.754900 - 1.30753i) q^{35} +(-1.79813 - 3.11446i) q^{37} +(0.0812519 + 0.0681784i) q^{38} +(0.496130 + 2.81369i) q^{40} +(1.33750 + 7.58532i) q^{41} +(-0.450837 - 0.378297i) q^{43} +(6.85117 + 11.8666i) q^{44} +(-7.73055 + 13.3897i) q^{46} +(9.07785 - 3.30407i) q^{47} +(2.61334 - 2.19285i) q^{49} +(11.3760 + 4.14052i) q^{50} +(-1.67365 + 9.49173i) q^{52} +4.95811 q^{53} -1.45336 q^{55} +(-3.42127 + 19.4030i) q^{56} +(-15.6420 - 5.69323i) q^{58} +(-6.53596 + 5.48432i) q^{59} +(1.19207 - 0.433877i) q^{61} +(7.88326 - 13.6542i) q^{62} +(0.819078 + 1.41868i) q^{64} +(-0.783119 - 0.657115i) q^{65} +(1.73783 + 9.85570i) q^{67} +(2.29813 + 13.0334i) q^{68} +(-2.92855 - 2.45734i) q^{70} +(-5.91534 - 10.2457i) q^{71} +(4.11721 - 7.13122i) q^{73} +(-8.55690 + 3.11446i) q^{74} +(0.141559 - 0.118782i) q^{76} +(-9.41787 - 3.42782i) q^{77} +(1.91875 - 10.8818i) q^{79} +3.10607 q^{80} +19.5030 q^{82} +(-0.262174 + 1.48686i) q^{83} +(-1.31908 - 0.480105i) q^{85} +(-1.14156 + 0.957882i) q^{86} +(17.8221 - 6.48670i) q^{88} +(7.93629 - 13.7461i) q^{89} +(-3.52481 - 6.10516i) q^{91} +(20.6348 + 17.3146i) q^{92} +(-4.24763 - 24.0895i) q^{94} +(0.00340357 + 0.0193026i) q^{95} +(14.2836 + 11.9854i) q^{97} +(-4.31908 - 7.48086i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 9 q^{4} - 6 q^{5} + 9 q^{7} - 6 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 9 * q^4 - 6 * q^5 + 9 * q^7 - 6 * q^8	$ 6 q - 3 q^{2} - 9 q^{4} - 6 q^{5} + 9 q^{7} - 6 q^{8} - 3 q^{11} + 9 q^{13} - 6 q^{14} + 9 q^{16} - 9 q^{17} + 3 q^{19} - 6 q^{20} - 9 q^{22} - 15 q^{23} + 18 q^{25} - 24 q^{26} - 24 q^{28} + 15 q^{29} + 9 q^{31} + 18 q^{32} - 9 q^{34} + 6 q^{35} + 3 q^{37} + 3 q^{38} + 27 q^{40} + 3 q^{41} + 9 q^{43} + 15 q^{44} - 9 q^{46} + 15 q^{47} + 9 q^{49} + 15 q^{50} - 9 q^{52} + 36 q^{53} + 18 q^{55} - 3 q^{56} - 36 q^{58} - 6 q^{59} + 18 q^{61} + 12 q^{62} - 12 q^{64} - 21 q^{65} - 9 q^{67} - 18 q^{70} + 9 q^{71} - 6 q^{73} - 15 q^{74} + 9 q^{76} + 3 q^{77} + 9 q^{79} - 6 q^{80} + 36 q^{82} - 21 q^{83} + 9 q^{85} - 15 q^{86} + 9 q^{88} + 6 q^{91} + 48 q^{92} - 9 q^{94} + 42 q^{95} + 36 q^{97} - 9 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 - 9 * q^4 - 6 * q^5 + 9 * q^7 - 6 * q^8 - 3 * q^11 + 9 * q^13 - 6 * q^14 + 9 * q^16 - 9 * q^17 + 3 * q^19 - 6 * q^20 - 9 * q^22 - 15 * q^23 + 18 * q^25 - 24 * q^26 - 24 * q^28 + 15 * q^29 + 9 * q^31 + 18 * q^32 - 9 * q^34 + 6 * q^35 + 3 * q^37 + 3 * q^38 + 27 * q^40 + 3 * q^41 + 9 * q^43 + 15 * q^44 - 9 * q^46 + 15 * q^47 + 9 * q^49 + 15 * q^50 - 9 * q^52 + 36 * q^53 + 18 * q^55 - 3 * q^56 - 36 * q^58 - 6 * q^59 + 18 * q^61 + 12 * q^62 - 12 * q^64 - 21 * q^65 - 9 * q^67 - 18 * q^70 + 9 * q^71 - 6 * q^73 - 15 * q^74 + 9 * q^76 + 3 * q^77 + 9 * q^79 - 6 * q^80 + 36 * q^82 - 21 * q^83 + 9 * q^85 - 15 * q^86 + 9 * q^88 + 6 * q^91 + 48 * q^92 - 9 * q^94 + 42 * q^95 + 36 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	0.439693	−	2.49362i	0.310910	−	1.76326i	−0.283383	−	0.959007i	$-0.591457\pi$
$2$	0.439693	−	2.49362i	0.310910	−	1.76326i	0.594292	−	0.804249i	$-0.297432\pi$
$3$		0			0
$3$		0			0
$4$	−4.14543	−	1.50881i	−2.07271	−	0.754407i
$5$	0.358441	−	0.300767i	0.160300	−	0.134507i	−0.559110	−	0.829094i	$-0.688857\pi$
$5$	0.358441	−	0.300767i	0.160300	−	0.134507i	0.719409	+	0.694586i	$0.244413\pi$
$6$		0			0
$7$	3.03209	−	1.10359i	1.14602	−	0.417118i	0.301937	−	0.953328i	$-0.402367\pi$
$7$	3.03209	−	1.10359i	1.14602	−	0.417118i	0.844085	+	0.536210i	$0.180144\pi$
$8$	−3.05303	+	5.28801i	−1.07941	+	1.86959i
$9$		0			0
$10$	−0.592396	−	1.02606i	−0.187332	−	0.324469i
$11$	−2.37939	−	1.99654i	−0.717412	−	0.601980i	0.209256	−	0.977861i	$-0.432896\pi$
$11$	−2.37939	−	1.99654i	−0.717412	−	0.601980i	−0.926668	+	0.375881i	$0.877340\pi$
$12$		0			0
$13$	−0.379385	−	2.15160i	−0.105223	−	0.596747i	−0.991131	−	0.132887i	$-0.957575\pi$
$13$	−0.379385	−	2.15160i	−0.105223	−	0.596747i	0.885909	−	0.463860i	$-0.153536\pi$
$14$	−1.41875	−	8.04612i	−0.379176	−	2.15042i
$15$		0			0
$16$	5.08512	+	4.26692i	1.27128	+	1.06673i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$		0			0
$19$	−0.0209445	+	0.0362770i	−0.00480501	+	0.00832251i	−0.868418	−	0.495833i	$-0.834863\pi$
$19$	−0.0209445	+	0.0362770i	−0.00480501	+	0.00832251i	0.863613	+	0.504155i	$0.168196\pi$
$20$	−1.93969	+	0.705990i	−0.433728	+	0.157864i
$21$		0			0
$22$	−6.02481	+	5.05542i	−1.28449	+	1.07782i
$23$	−5.73783	−	2.08840i	−1.19642	−	0.435461i	−0.334446	−	0.942415i	$-0.608549\pi$
$23$	−5.73783	−	2.08840i	−1.19642	−	0.435461i	−0.861973	+	0.506954i	$0.830771\pi$
$24$		0			0
$25$	−0.830222	+	4.70842i	−0.166044	+	0.941685i
$26$	−5.53209			−1.08493
$27$		0			0
$28$	−14.2344			−2.69005
$29$	1.14156	−	6.47410i	0.211982	−	1.20221i	−0.674085	−	0.738654i	$-0.735462\pi$
$29$	1.14156	−	6.47410i	0.211982	−	1.20221i	0.886067	−	0.463557i	$-0.153427\pi$
$30$		0			0
$31$	5.85117	+	2.12965i	1.05090	+	0.382497i	0.809003	−	0.587805i	$-0.200008\pi$
$31$	5.85117	+	2.12965i	1.05090	+	0.382497i	0.241898	+	0.970302i	$0.422230\pi$
$32$	3.52094	−	2.95442i	0.622421	−	0.522273i
$33$		0			0
$34$	−7.13816	+	2.59808i	−1.22418	+	0.445566i
$35$	0.754900	−	1.30753i	0.127601	−	0.221012i
$36$		0			0
$37$	−1.79813	−	3.11446i	−0.295611	−	0.512014i	0.679516	−	0.733661i	$-0.262190\pi$
$37$	−1.79813	−	3.11446i	−0.295611	−	0.512014i	−0.975127	+	0.221647i	$0.928857\pi$
$38$	0.0812519	+	0.0681784i	0.0131808	+	0.0110600i
$39$		0			0
$40$	0.496130	+	2.81369i	0.0784450	+	0.444884i
$41$	1.33750	+	7.58532i	0.208882	+	1.18463i	0.891213	+	0.453585i	$0.149855\pi$
$41$	1.33750	+	7.58532i	0.208882	+	1.18463i	−0.682331	+	0.731043i	$0.739034\pi$
$42$		0			0
$43$	−0.450837	−	0.378297i	−0.0687520	−	0.0576898i	0.607764	−	0.794118i	$-0.292067\pi$
$43$	−0.450837	−	0.378297i	−0.0687520	−	0.0576898i	−0.676516	+	0.736428i	$0.736511\pi$
$44$	6.85117	+	11.8666i	1.03285	+	1.78895i
$45$		0			0
$46$	−7.73055	+	13.3897i	−1.13981	+	1.97420i
$47$	9.07785	−	3.30407i	1.32414	−	0.481948i	0.419358	−	0.907821i	$-0.362255\pi$
$47$	9.07785	−	3.30407i	1.32414	−	0.481948i	0.904783	+	0.425874i	$0.140033\pi$
$48$		0			0
$49$	2.61334	−	2.19285i	0.373334	−	0.313265i
$50$	11.3760	+	4.14052i	1.60881	+	0.585558i
$51$		0			0
$52$	−1.67365	+	9.49173i	−0.232093	+	1.31627i
$53$	4.95811			0.681049			0.340524	−	0.940236i	$-0.389395\pi$
$53$	4.95811			0.681049			0.340524	+	0.940236i	$0.389395\pi$
$54$		0			0
$55$	−1.45336			−0.195971
$56$	−3.42127	+	19.4030i	−0.457187	+	2.59284i
$57$		0			0
$58$	−15.6420	−	5.69323i	−2.05390	−	0.747558i
$59$	−6.53596	+	5.48432i	−0.850909	+	0.713998i	−0.959990	−	0.280035i	$-0.909654\pi$
$59$	−6.53596	+	5.48432i	−0.850909	+	0.713998i	0.109080	+	0.994033i	$0.465209\pi$
$60$		0			0
$61$	1.19207	−	0.433877i	0.152628	−	0.0555522i	−0.264576	−	0.964365i	$-0.585232\pi$
$61$	1.19207	−	0.433877i	0.152628	−	0.0555522i	0.417205	+	0.908813i	$0.363010\pi$
$62$	7.88326	−	13.6542i	1.00117	−	1.73409i
$63$		0			0
$64$	0.819078	+	1.41868i	0.102385	+	0.177336i
$65$	−0.783119	−	0.657115i	−0.0971339	−	0.0815050i
$66$		0			0
$67$	1.73783	+	9.85570i	0.212309	+	1.20407i	0.885515	+	0.464610i	$0.153806\pi$
$67$	1.73783	+	9.85570i	0.212309	+	1.20407i	−0.673206	+	0.739455i	$0.735083\pi$
$68$	2.29813	+	13.0334i	0.278690	+	1.58053i
$69$		0			0
$70$	−2.92855	−	2.45734i	−0.350028	−	0.293709i
$71$	−5.91534	−	10.2457i	−0.702022	−	1.21594i	−0.967755	−	0.251892i	$-0.918947\pi$
$71$	−5.91534	−	10.2457i	−0.702022	−	1.21594i	0.265733	−	0.964047i	$-0.414386\pi$
$72$		0			0
$73$	4.11721	−	7.13122i	0.481883	−	0.834646i	−0.517901	−	0.855441i	$-0.673286\pi$
$73$	4.11721	−	7.13122i	0.481883	−	0.834646i	0.999784	+	0.0207947i	$0.00661964\pi$
$74$	−8.55690	+	3.11446i	−0.994720	+	0.362048i
$75$		0			0
$76$	0.141559	−	0.118782i	0.0162380	−	0.0136253i
$77$	−9.41787	−	3.42782i	−1.07327	−	0.390637i
$78$		0			0
$79$	1.91875	−	10.8818i	0.215876	−	1.22429i	−0.663504	−	0.748173i	$-0.730931\pi$
$79$	1.91875	−	10.8818i	0.215876	−	1.22429i	0.879380	−	0.476121i	$-0.157958\pi$
$80$	3.10607			0.347269
$81$		0			0
$82$	19.5030			2.15375
$83$	−0.262174	+	1.48686i	−0.0287773	+	0.163204i	−0.995810	−	0.0914488i	$-0.970850\pi$
$83$	−0.262174	+	1.48686i	−0.0287773	+	0.163204i	0.967032	+	0.254653i	$0.0819613\pi$
$84$		0			0
$85$	−1.31908	−	0.480105i	−0.143074	−	0.0520747i
$86$	−1.14156	+	0.957882i	−0.123098	+	0.103291i
$87$		0			0
$88$	17.8221	−	6.48670i	1.89984	−	0.691485i
$89$	7.93629	−	13.7461i	0.841245	−	1.45708i	−0.0475978	−	0.998867i	$-0.515157\pi$
$89$	7.93629	−	13.7461i	0.841245	−	1.45708i	0.888843	−	0.458212i	$-0.151510\pi$
$90$		0			0
$91$	−3.52481	−	6.10516i	−0.369501	−	0.639995i
$92$	20.6348	+	17.3146i	2.15132	+	1.80517i
$93$		0			0
$94$	−4.24763	−	24.0895i	−0.438109	−	2.48464i
$95$	0.00340357	+	0.0193026i	0.000349199	+	0.00198040i
$96$		0			0
$97$	14.2836	+	11.9854i	1.45028	+	1.21693i	0.932377	+	0.361488i	$0.117731\pi$
$97$	14.2836	+	11.9854i	1.45028	+	1.21693i	0.517902	+	0.855440i	$0.326713\pi$
$98$	−4.31908	−	7.48086i	−0.436293	−	0.755681i
$99$		0			0
$100$	10.5458	−	18.2658i	1.05458	−	1.82658i
$101$	−8.53849	+	3.10775i	−0.849611	+	0.309233i	−0.729882	−	0.683573i	$-0.760425\pi$
$101$	−8.53849	+	3.10775i	−0.849611	+	0.309233i	−0.119729	+	0.992807i	$0.538203\pi$
$102$		0			0
$103$	0.199807	−	0.167658i	0.0196876	−	0.0165199i	−0.632891	−	0.774241i	$-0.718132\pi$
$103$	0.199807	−	0.167658i	0.0196876	−	0.0165199i	0.652578	+	0.757721i	$0.273687\pi$
$104$	12.5360	+	4.56272i	1.22925	+	0.447411i
$105$		0			0
$106$	2.18004	−	12.3636i	0.211745	−	1.20086i
$107$	4.04189			0.390744			0.195372	−	0.980729i	$-0.437409\pi$
$107$	4.04189			0.390744			0.195372	+	0.980729i	$0.437409\pi$
$108$		0			0
$109$	−5.40373			−0.517584			−0.258792	−	0.965933i	$-0.583324\pi$
$109$	−5.40373			−0.517584			−0.258792	+	0.965933i	$0.583324\pi$
$110$	−0.639033	+	3.62414i	−0.0609294	+	0.345548i
$111$		0			0
$112$	20.1275	+	7.32580i	1.90187	+	0.692223i
$113$	1.06031	−	0.889704i	0.0997453	−	0.0836963i	−0.591551	−	0.806267i	$-0.701484\pi$
$113$	1.06031	−	0.889704i	0.0997453	−	0.0836963i	0.691297	+	0.722571i	$0.257040\pi$
$114$		0			0
$115$	−2.68479	+	0.977185i	−0.250358	+	0.0911229i
$116$	−14.5005	+	25.1155i	−1.34633	+	2.33192i
$117$		0			0
$118$	10.8020	+	18.7096i	0.994405	+	1.72236i
$119$	−7.41534	−	6.22221i	−0.679764	−	0.570389i
$120$		0			0
$121$	−0.234833	−	1.33180i	−0.0213484	−	0.121073i
$122$	−0.557781	−	3.16333i	−0.0504991	−	0.286395i
$123$		0			0
$124$	−21.0424	−	17.6566i	−1.88966	−	1.58561i
$125$	2.28833	+	3.96351i	0.204675	+	0.354507i
$126$		0			0
$127$	3.31908	−	5.74881i	0.294521	−	0.510125i	−0.680353	−	0.732885i	$-0.738173\pi$
$127$	3.31908	−	5.74881i	0.294521	−	0.510125i	0.974873	+	0.222760i	$0.0715067\pi$
$128$	12.5360	−	4.56272i	1.10803	−	0.403291i
$129$		0			0
$130$	−1.98293	+	1.66387i	−0.173914	+	0.145931i
$131$	11.8785	+	4.32342i	1.03783	+	0.377739i	0.804057	−	0.594552i	$-0.202671\pi$
$131$	11.8785	+	4.32342i	1.03783	+	0.377739i	0.233773	+	0.972291i	$0.424893\pi$
$132$		0			0
$133$	−0.0234708	+	0.133109i	−0.00203517	+	0.0115420i
$134$	25.3405			2.18908
$135$		0			0
$136$	18.3182			1.57077
$137$	1.84343	−	10.4546i	0.157495	−	0.893196i	−0.798975	−	0.601364i	$-0.794624\pi$
$137$	1.84343	−	10.4546i	0.157495	−	0.893196i	0.956470	−	0.291832i	$-0.0942647\pi$
$138$		0			0
$139$	7.01114	+	2.55185i	0.594678	+	0.216445i	0.621785	−	0.783188i	$-0.286408\pi$
$139$	7.01114	+	2.55185i	0.594678	+	0.216445i	−0.0271080	+	0.999633i	$0.508630\pi$
$140$	−5.10220	+	4.28125i	−0.431214	+	0.361832i
$141$		0			0
$142$	−28.1498	+	10.2457i	−2.36228	+	0.859798i
$143$	−3.39306	+	5.87695i	−0.283742	+	0.491455i
$144$		0			0
$145$	−1.53802	−	2.66393i	−0.127725	−	0.221227i
$146$	−15.9722	−	13.4023i	−1.32187	−	1.10918i
$147$		0			0
$148$	2.75490	+	15.6238i	0.226451	+	1.28427i
$149$	−0.738703	−	4.18939i	−0.0605169	−	0.343209i	−1.00000		0.000612725i	$-0.999805\pi$
$149$	−0.738703	−	4.18939i	−0.0605169	−	0.343209i	0.939483	−	0.342596i	$-0.111306\pi$
$150$		0			0
$151$	0.103541	+	0.0868809i	0.00842602	+	0.00707027i	0.646991	−	0.762498i	$-0.276027\pi$
$151$	0.103541	+	0.0868809i	0.00842602	+	0.00707027i	−0.638565	+	0.769568i	$0.720472\pi$
$152$	−0.127889	−	0.221510i	−0.0103731	−	0.0179668i
$153$		0			0
$154$	−12.6887	+	21.9774i	−1.02248	+	1.77099i
$155$	2.73783	−	0.996487i	0.219907	−	0.0800398i
$156$		0			0
$157$	10.2083	−	8.56575i	0.814708	−	0.683621i	−0.137018	−	0.990568i	$-0.543752\pi$
$157$	10.2083	−	8.56575i	0.814708	−	0.683621i	0.951727	+	0.306947i	$0.0993075\pi$
$158$	−26.2913	−	9.56926i	−2.09163	−	0.761289i
$159$		0			0
$160$	0.373455	−	2.11797i	0.0295242	−	0.167440i
$161$	−19.7023			−1.55276
$162$		0			0
$163$	−9.76382			−0.764762			−0.382381	−	0.924005i	$-0.624896\pi$
$163$	−9.76382			−0.764762			−0.382381	+	0.924005i	$0.624896\pi$
$164$	5.90033	−	33.4624i	0.460738	−	2.61298i
$165$		0			0
$166$	3.59240	+	1.30753i	0.278824	+	0.101484i
$167$	−2.73783	+	2.29731i	−0.211859	+	0.177771i	−0.742542	−	0.669799i	$-0.766380\pi$
$167$	−2.73783	+	2.29731i	−0.211859	+	0.177771i	0.530683	+	0.847571i	$0.321936\pi$
$168$		0			0
$169$	7.73055	−	2.81369i	0.594658	−	0.216438i
$170$	−1.77719	+	3.07818i	−0.136304	+	0.236086i
$171$		0			0
$172$	1.29813	+	2.24843i	0.0989817	+	0.171441i
$173$	14.3760	+	12.0629i	1.09299	+	0.917124i	0.996934	−	0.0782525i	$-0.0249340\pi$
$173$	14.3760	+	12.0629i	1.09299	+	0.917124i	0.0960521	+	0.995376i	$0.469378\pi$
$174$		0			0
$175$	2.67886	+	15.1926i	0.202503	+	1.14845i
$176$	−3.58037	−	20.3053i	−0.269881	−	1.53057i
$177$		0			0
$178$	−30.7879	−	25.8341i	−2.30765	−	1.93635i
$179$	2.54189	+	4.40268i	0.189990	+	0.329072i	0.945247	−	0.326357i	$-0.105821\pi$
$179$	2.54189	+	4.40268i	0.189990	+	0.329072i	−0.755257	+	0.655429i	$0.772488\pi$
$180$		0			0
$181$	−3.57532	+	6.19264i	−0.265752	+	0.460295i	−0.967760	−	0.251873i	$-0.918953\pi$
$181$	−3.57532	+	6.19264i	−0.265752	+	0.460295i	0.702009	+	0.712168i	$0.252287\pi$
$182$	−16.7738	+	6.10516i	−1.24336	+	0.452544i
$183$		0			0
$184$	28.5612	−	23.9657i	2.10556	−	1.76678i
$185$	−1.58125	−	0.575529i	−0.116256	−	0.0423137i
$186$		0			0
$187$	−1.61809	+	9.17664i	−0.118326	+	0.671062i
$188$	−42.6168			−3.10815
$189$		0			0
$190$	0.0496299			0.00360053
$191$	−1.82501	+	10.3501i	−0.132053	+	0.748909i	0.844814	+	0.535060i	$0.179711\pi$
$191$	−1.82501	+	10.3501i	−0.132053	+	0.748909i	−0.976867	+	0.213849i	$0.931400\pi$
$192$		0			0
$193$	9.53121	+	3.46908i	0.686072	+	0.249710i	0.661452	−	0.749987i	$-0.269940\pi$
$193$	9.53121	+	3.46908i	0.686072	+	0.249710i	0.0246193	+	0.999697i	$0.492163\pi$
$194$	36.1673	−	30.3480i	2.59666	−	2.17886i
$195$		0			0
$196$	−14.1420	+	5.14728i	−1.01014	+	0.367663i
$197$	−7.04189	+	12.1969i	−0.501714	+	0.868994i	0.498284	+	0.867014i	$0.333964\pi$
$197$	−7.04189	+	12.1969i	−0.501714	+	0.868994i	−0.999998	+	0.00198008i	$0.999370\pi$
$198$		0			0
$199$	−5.13816	−	8.89955i	−0.364234	−	0.630872i	0.624419	−	0.781090i	$-0.285336\pi$
$199$	−5.13816	−	8.89955i	−0.364234	−	0.630872i	−0.988653	+	0.150218i	$0.952003\pi$
$200$	−22.3635	−	18.7652i	−1.58134	−	1.32690i
$201$		0			0
$202$	3.99525	+	22.6582i	0.281105	+	1.59423i
$203$	−3.68345	−	20.8899i	−0.258527	−	1.46618i
$204$		0			0
$205$	2.76083	+	2.31661i	0.192825	+	0.161799i
$206$	−0.330222	−	0.571962i	−0.0230077	−	0.0398505i
$207$		0			0
$208$	7.25150	−	12.5600i	0.502801	−	0.870877i
$209$	0.122264	−	0.0445003i	0.00845715	−	0.00307815i
$210$		0			0
$211$	−5.47178	+	4.59137i	−0.376693	+	0.316083i	−0.811403	−	0.584488i	$-0.801295\pi$
$211$	−5.47178	+	4.59137i	−0.376693	+	0.316083i	0.434710	+	0.900571i	$0.356851\pi$
$212$	−20.5535	−	7.48086i	−1.41162	−	0.513788i
$213$		0			0
$214$	1.77719	−	10.0789i	0.121486	−	0.688982i
$215$	−0.275378			−0.0187806
$216$		0			0
$217$	20.0915			1.36390
$218$	−2.37598	+	13.4749i	−0.160922	+	0.912633i
$219$		0			0
$220$	6.02481	+	2.19285i	0.406193	+	0.147842i
$221$	−5.02094	+	4.21307i	−0.337745	+	0.283402i
$222$		0			0
$223$	9.71213	−	3.53493i	0.650373	−	0.236716i	0.00429825	−	0.999991i	$-0.498632\pi$
$223$	9.71213	−	3.53493i	0.650373	−	0.236716i	0.646074	+	0.763275i	$0.276410\pi$
$224$	7.41534	−	12.8438i	0.495459	−	0.858159i
$225$		0			0
$226$	−1.75237	−	3.03520i	−0.116566	−	0.201899i
$227$	−9.97565	−	8.37057i	−0.662107	−	0.555574i	0.248610	−	0.968604i	$-0.420026\pi$
$227$	−9.97565	−	8.37057i	−0.662107	−	0.555574i	−0.910718	+	0.413030i	$0.864471\pi$
$228$		0			0
$229$	−4.87939	−	27.6724i	−0.322439	−	1.82864i	−0.527093	−	0.849807i	$-0.676718\pi$
$229$	−4.87939	−	27.6724i	−0.322439	−	1.82864i	0.204655	−	0.978834i	$-0.434393\pi$
$230$	1.25624	+	7.12452i	0.0828343	+	0.469777i
$231$		0			0
$232$	30.7499	+	25.8022i	2.01883	+	1.69400i
$233$	6.95723	+	12.0503i	0.455784	+	0.789440i	0.998733	−	0.0503252i	$-0.0160258\pi$
$233$	6.95723	+	12.0503i	0.455784	+	0.789440i	−0.542949	+	0.839765i	$0.682692\pi$
$234$		0			0
$235$	2.26011	−	3.91463i	0.147434	−	0.255363i
$236$	35.3692	−	12.8733i	2.30234	−	0.837982i
$237$		0			0
$238$	−18.7763	+	15.7552i	−1.21709	+	1.02126i
$239$	14.1138	+	5.13701i	0.912946	+	0.332285i	0.755429	−	0.655231i	$-0.227429\pi$
$239$	14.1138	+	5.13701i	0.912946	+	0.332285i	0.157518	+	0.987516i	$0.449651\pi$
$240$		0			0
$241$	−2.25284	+	12.7765i	−0.145118	+	0.823006i	0.822154	+	0.569265i	$0.192772\pi$
$241$	−2.25284	+	12.7765i	−0.145118	+	0.823006i	−0.967272	+	0.253741i	$0.918339\pi$
$242$	−3.42427			−0.220120
$243$		0			0
$244$	−5.59627			−0.358264
$245$	0.277189	−	1.57202i	0.0177089	−	0.100432i
$246$		0			0
$247$	0.0859997	+	0.0313013i	0.00547203	+	0.00199165i
$248$	−29.1254	+	24.4391i	−1.84947	+	1.55189i
$249$		0			0
$250$	10.8897	−	3.96351i	0.688722	−	0.250674i
$251$	−0.436289	+	0.755675i	−0.0275383	+	0.0476978i	−0.879466	−	0.475961i	$-0.842100\pi$
$251$	−0.436289	+	0.755675i	−0.0275383	+	0.0476978i	0.851928	+	0.523659i	$0.175433\pi$
$252$		0			0
$253$	9.48293	+	16.4249i	0.596186	+	1.03263i
$254$	−12.8760	−	10.8042i	−0.807911	−	0.677918i
$255$		0			0
$256$	−5.29679	−	30.0396i	−0.331049	−	1.87747i
$257$	0.794730	+	4.50714i	0.0495739	+	0.281147i	0.999510	−	0.0312963i	$-0.00996354\pi$
$257$	0.794730	+	4.50714i	0.0495739	+	0.281147i	−0.949936	+	0.312444i	$0.898852\pi$
$258$		0			0
$259$	−8.88919	−	7.45891i	−0.552347	−	0.463474i
$260$	2.25490	+	3.90560i	0.139843	+	0.242215i
$261$		0			0
$262$	16.0039	−	27.7195i	0.988722	−	1.71252i
$263$	−4.03849	+	1.46989i	−0.249024	+	0.0906372i	−0.463516	−	0.886088i	$-0.653412\pi$
$263$	−4.03849	+	1.46989i	−0.249024	+	0.0906372i	0.214493	+	0.976726i	$0.431190\pi$
$264$		0			0
$265$	1.77719	−	1.49124i	0.109172	−	0.0916061i
$266$	0.321604	+	0.117054i	0.0197188	+	0.00717706i
$267$		0			0
$268$	7.66637	−	43.4782i	0.468298	−	2.65585i
$269$	12.1257			0.739315			0.369657	−	0.929168i	$-0.379475\pi$
$269$	12.1257			0.739315			0.369657	+	0.929168i	$0.379475\pi$
$270$		0			0
$271$	−0.319955			−0.0194359			−0.00971795	−	0.999953i	$-0.503093\pi$
$271$	−0.319955			−0.0194359			−0.00971795	+	0.999953i	$0.503093\pi$
$272$	3.45811	−	19.6119i	0.209679	−	1.18915i
$273$		0			0
$274$	−25.2592	−	9.19361i	−1.52597	−	0.555406i
$275$	11.3760	−	9.54558i	0.685998	−	0.575620i
$276$		0			0
$277$	25.2037	−	9.17339i	1.51434	−	0.551175i	0.554615	−	0.832107i	$-0.312866\pi$
$277$	25.2037	−	9.17339i	1.51434	−	0.551175i	0.959728	+	0.280932i	$0.0906435\pi$
$278$	9.44609	−	16.3611i	0.566539	−	0.981274i
$279$		0			0
$280$	4.60947	+	7.98384i	0.275469	+	0.477126i
$281$	20.4388	+	17.1502i	1.21928	+	1.02310i	0.998862	+	0.0476892i	$0.0151857\pi$
$281$	20.4388	+	17.1502i	1.21928	+	1.02310i	0.220415	+	0.975406i	$0.429259\pi$
$282$		0			0
$283$	−1.61381	−	9.15236i	−0.0959309	−	0.544051i	−0.994458	−	0.105133i	$-0.966473\pi$
$283$	−1.61381	−	9.15236i	−0.0959309	−	0.544051i	0.898527	−	0.438918i	$-0.144638\pi$
$284$	9.06283	+	51.3979i	0.537780	+	3.04990i
$285$		0			0
$286$	13.1630	+	11.0450i	0.778343	+	0.653107i
$287$	12.4265	+	21.5233i	0.733512	+	1.27048i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	−7.31908	+	2.66393i	−0.429791	+	0.156431i
$291$		0			0
$292$	−27.8273	+	23.3499i	−1.62847	+	1.36645i
$293$	18.4547	+	6.71696i	1.07814	+	0.392409i	0.819213	−	0.573489i	$-0.194410\pi$
$293$	18.4547	+	6.71696i	1.07814	+	0.392409i	0.258922	+	0.965898i	$0.416633\pi$
$294$		0			0
$295$	−0.693249	+	3.93161i	−0.0403625	+	0.228907i
$296$	21.9590			1.27634
$297$		0			0
$298$	−10.7716			−0.623980
$299$	−2.31655	+	13.1378i	−0.133970	+	0.759780i
$300$		0			0
$301$	−1.78446	−	0.649491i	−0.102855	−	0.0374361i
$302$	0.262174	−	0.219990i	0.0150864	−	0.0126590i
$303$		0			0
$304$	−0.261297	+	0.0951042i	−0.0149864	+	0.00545460i
$305$	0.296789	−	0.514054i	0.0169941	−	0.0294346i
$306$		0			0
$307$	−14.1716	−	24.5459i	−0.808815	−	1.40091i	−0.913685	−	0.406423i	$-0.866776\pi$
$307$	−14.1716	−	24.5459i	−0.808815	−	1.40091i	0.104870	−	0.994486i	$-0.466557\pi$
$308$	33.8692	+	28.4196i	1.92988	+	1.61936i
$309$		0			0
$310$	−1.28106	−	7.26525i	−0.0727593	−	0.412638i
$311$	−0.355037	−	2.01352i	−0.0201323	−	0.114176i	0.973086	−	0.230444i	$-0.0740179\pi$
$311$	−0.355037	−	2.01352i	−0.0201323	−	0.114176i	−0.993218	+	0.116268i	$0.962907\pi$
$312$		0			0
$313$	6.44356	+	5.40679i	0.364212	+	0.305610i	0.806467	−	0.591279i	$-0.201377\pi$
$313$	6.44356	+	5.40679i	0.364212	+	0.305610i	−0.442255	+	0.896889i	$0.645821\pi$
$314$	−16.8712	−	29.2218i	−0.952099	−	1.64908i
$315$		0			0
$316$	−24.3726	+	42.2145i	−1.37106	+	2.37475i
$317$	−29.2511	+	10.6465i	−1.64290	+	0.597968i	−0.987543	−	0.157347i	$-0.949706\pi$
$317$	−29.2511	+	10.6465i	−1.64290	+	0.597968i	−0.655361	+	0.755316i	$0.727484\pi$
$318$		0			0
$319$	−15.6420	+	13.1252i	−0.875785	+	0.734871i
$320$	0.720285	+	0.262162i	0.0402652	+	0.0146553i
$321$		0			0
$322$	−8.66297	+	49.1301i	−0.482768	+	2.73792i
$323$	0.125667			0.00699231
$324$		0			0
$325$	10.4456			0.579419
$326$	−4.29308	+	24.3473i	−0.237772	+	1.34847i
$327$		0			0
$328$	−44.1946	−	16.0855i	−2.44024	−	0.888175i
$329$	23.8785	−	20.0364i	1.31646	−	1.10465i
$330$		0			0
$331$	−29.1596	+	10.6132i	−1.60275	+	0.583355i	−0.979989	−	0.199053i	$-0.936213\pi$
$331$	−29.1596	+	10.6132i	−1.60275	+	0.583355i	−0.622766	+	0.782408i	$0.713991\pi$
$332$	3.33022	−	5.76811i	0.182770	−	0.316566i
$333$		0			0
$334$	4.52481	+	7.83721i	0.247587	+	0.428833i
$335$	3.58718	+	3.01000i	0.195989	+	0.164454i
$336$		0			0
$337$	4.12061	+	23.3692i	0.224464	+	1.27300i	0.863707	+	0.503995i	$0.168137\pi$
$337$	4.12061	+	23.3692i	0.224464	+	1.27300i	−0.639243	+	0.769005i	$0.720752\pi$
$338$	−3.61721	−	20.5142i	−0.196750	−	1.11583i
$339$		0			0
$340$	4.74376	+	3.98048i	0.257266	+	0.215872i
$341$	−9.67024	−	16.7494i	−0.523673	−	0.907028i
$342$		0			0
$343$	−5.78952	+	10.0277i	−0.312604	+	0.541447i
$344$	3.37686	−	1.22908i	0.182068	−	0.0662673i
$345$		0			0
$346$	36.4013	−	30.5443i	1.95694	−	1.64207i
$347$	1.69934	+	0.618509i	0.0912254	+	0.0332033i	0.387230	−	0.921983i	$-0.373432\pi$
$347$	1.69934	+	0.618509i	0.0912254	+	0.0332033i	−0.296004	+	0.955187i	$0.595654\pi$
$348$		0			0
$349$	2.65002	−	15.0290i	0.141852	−	0.804483i	−0.827989	−	0.560744i	$-0.810515\pi$
$349$	2.65002	−	15.0290i	0.141852	−	0.804483i	0.969841	−	0.243739i	$-0.0783739\pi$
$350$	39.0624			2.08797
$351$		0			0
$352$	−14.2763			−0.760930
$353$	−5.62314	+	31.8904i	−0.299290	+	1.69736i	0.349947	+	0.936769i	$0.386199\pi$
$353$	−5.62314	+	31.8904i	−0.299290	+	1.69736i	−0.649237	+	0.760586i	$0.724912\pi$
$354$		0			0
$355$	−5.20187	−	1.89332i	−0.276086	−	0.100487i
$356$	−53.6396	+	45.0089i	−2.84289	+	2.38547i
$357$		0			0
$358$	12.0963	−	4.40268i	0.639308	−	0.232689i
$359$	0.957234	−	1.65798i	0.0505209	−	0.0875047i	−0.839659	−	0.543114i	$-0.817245\pi$
$359$	0.957234	−	1.65798i	0.0505209	−	0.0875047i	0.890180	+	0.455609i	$0.150579\pi$
$360$		0			0
$361$	9.49912	+	16.4530i	0.499954	+	0.865945i
$362$	13.8701	+	11.6384i	0.728994	+	0.611698i
$363$		0			0
$364$	5.40033	+	30.6268i	0.283054	+	1.60528i
$365$	−0.669063	−	3.79444i	−0.0350203	−	0.198610i
$366$		0			0
$367$	−20.5797	−	17.2684i	−1.07425	−	0.901402i	−0.0788188	−	0.996889i	$-0.525115\pi$
$367$	−20.5797	−	17.2684i	−1.07425	−	0.901402i	−0.995431	+	0.0954866i	$0.969559\pi$
$368$	−20.2665	−	35.1026i	−1.05646	−	1.82985i
$369$		0			0
$370$	−2.13041	+	3.68999i	−0.110755	+	0.191833i
$371$	15.0334	−	5.47172i	0.780497	−	0.284078i
$372$		0			0
$373$	11.3682	−	9.53909i	0.588625	−	0.493915i	−0.299142	−	0.954209i	$-0.596700\pi$
$373$	11.3682	−	9.53909i	0.588625	−	0.493915i	0.887767	+	0.460294i	$0.152256\pi$
$374$	22.1716	+	8.06980i	1.14647	+	0.417279i
$375$		0			0
$376$	−10.2430	+	58.0912i	−0.528244	+	2.99582i
$377$	−14.3628			−0.739721
$378$		0			0
$379$	−33.7870			−1.73552			−0.867762	−	0.496980i	$-0.834442\pi$
$379$	−33.7870			−1.73552			−0.867762	+	0.496980i	$0.834442\pi$
$380$	0.0150147	−	0.0851529i	0.000770240	−	0.00436825i
$381$		0			0
$382$	25.0069	+	9.10175i	1.27946	+	0.465686i
$383$	−7.10813	+	5.96443i	−0.363208	+	0.304768i	−0.806068	−	0.591823i	$-0.798408\pi$
$383$	−7.10813	+	5.96443i	−0.363208	+	0.304768i	0.442860	+	0.896591i	$0.353964\pi$
$384$		0			0
$385$	−4.40673	+	1.60392i	−0.224588	+	0.0817432i
$386$	12.8414	−	22.2419i	0.653608	−	1.13208i
$387$		0			0
$388$	−41.1279	−	71.2357i	−2.08796	−	3.61644i
$389$	−12.2404	−	10.2709i	−0.620610	−	0.520754i	0.277385	−	0.960759i	$-0.410532\pi$
$389$	−12.2404	−	10.2709i	−0.620610	−	0.520754i	−0.897995	+	0.440005i	$0.854977\pi$
$390$		0			0
$391$	3.18092	+	18.0399i	0.160866	+	0.912317i
$392$	3.61721	+	20.5142i	0.182697	+	1.03612i
$393$		0			0
$394$	27.3182	+	22.9227i	1.37627	+	1.15483i
$395$	−2.58512	−	4.47756i	−0.130072	−	0.225291i
$396$		0			0
$397$	−9.85251	+	17.0650i	−0.494483	+	0.856470i	−0.999980	−	0.00635841i	$-0.997976\pi$
$397$	−9.85251	+	17.0650i	−0.494483	+	0.856470i	0.505496	+	0.862829i	$0.331309\pi$
$398$	−24.4513	+	8.89955i	−1.22563	+	0.446094i
$399$		0			0
$400$	−24.3123	+	20.4004i	−1.21561	+	1.02002i
$401$	−1.07873	−	0.392624i	−0.0538690	−	0.0196067i	0.314945	−	0.949110i	$-0.398014\pi$
$401$	−1.07873	−	0.392624i	−0.0538690	−	0.0196067i	−0.368814	+	0.929503i	$0.620236\pi$
$402$		0			0
$403$	2.36231	−	13.3973i	0.117675	−	0.667369i
$404$	40.0847			1.99429
$405$		0			0
$406$	−53.7110			−2.66563
$407$	−1.93969	+	11.0005i	−0.0961470	+	0.545277i
$408$		0			0
$409$	2.91400	+	1.06061i	0.144088	+	0.0524438i	0.413057	−	0.910705i	$-0.364461\pi$
$409$	2.91400	+	1.06061i	0.144088	+	0.0524438i	−0.268969	+	0.963149i	$0.586683\pi$
$410$	6.99067	−	5.86587i	0.345244	−	0.289694i
$411$		0			0
$412$	−1.08125	+	0.393544i	−0.0532695	+	0.0193885i
$413$	−13.7652	+	23.8420i	−0.677340	+	1.17319i
$414$		0			0
$415$	0.353226	+	0.611806i	0.0173392	+	0.0300324i
$416$	−7.69253	−	6.45480i	−0.377157	−	0.316473i
$417$		0			0
$418$	−0.0572085	−	0.324446i	−0.00279816	−	0.0158692i
$419$	6.15570	+	34.9107i	0.300725	+	1.70550i	0.642973	+	0.765889i	$0.277701\pi$
$419$	6.15570	+	34.9107i	0.300725	+	1.70550i	−0.342247	+	0.939610i	$0.611188\pi$
$420$		0			0
$421$	7.06077	+	5.92469i	0.344121	+	0.288752i	0.798424	−	0.602095i	$-0.205667\pi$
$421$	7.06077	+	5.92469i	0.344121	+	0.288752i	−0.454303	+	0.890847i	$0.650112\pi$
$422$	9.04323	+	15.6633i	0.440218	+	0.762479i
$423$		0			0
$424$	−15.1373	+	26.2185i	−0.735131	+	1.27328i
$425$	13.4782	−	4.90566i	0.653788	−	0.237959i
$426$		0			0
$427$	3.13563	−	2.63111i	0.151744	−	0.127328i
$428$	−16.7554	−	6.09845i	−0.809901	−	0.294780i
$429$		0			0
$430$	−0.121082	+	0.686688i	−0.00583907	+	0.0331150i
$431$	11.5794			0.557758			0.278879	−	0.960326i	$-0.410037\pi$
$431$	11.5794			0.557758			0.278879	+	0.960326i	$0.410037\pi$
$432$		0			0
$433$	6.06511			0.291471			0.145735	−	0.989324i	$-0.453445\pi$
$433$	6.06511			0.291471			0.145735	+	0.989324i	$0.453445\pi$
$434$	8.83409	−	50.1006i	0.424050	−	2.40491i
$435$		0			0
$436$	22.4008	+	8.15322i	1.07280	+	0.390469i
$437$	0.195937	−	0.164411i	0.00937293	−	0.00786482i
$438$		0			0
$439$	−27.2567	+	9.92063i	−1.30089	+	0.473486i	−0.897287	−	0.441448i	$-0.854465\pi$
$439$	−27.2567	+	9.92063i	−1.30089	+	0.473486i	−0.403605	+	0.914933i	$0.632243\pi$
$440$	4.43717	−	7.68540i	0.211534	−	0.366387i
$441$		0			0
$442$	8.29813	+	14.3728i	0.394702	+	0.683644i
$443$	23.6648	+	19.8571i	1.12435	+	0.943440i	0.998816	−	0.0486498i	$-0.0154918\pi$
$443$	23.6648	+	19.8571i	1.12435	+	0.943440i	0.125532	+	0.992090i	$0.459936\pi$
$444$		0			0
$445$	−1.28968	−	7.31412i	−0.0611366	−	0.346723i
$446$	−4.54442	−	25.7727i	−0.215184	−	1.22037i
$447$		0			0
$448$	4.04916	+	3.39765i	0.191305	+	0.160524i
$449$	19.5410	+	33.8460i	0.922197	+	1.59729i	0.796008	+	0.605287i	$0.206941\pi$
$449$	19.5410	+	33.8460i	0.922197	+	1.59729i	0.126190	+	0.992006i	$0.459725\pi$
$450$		0			0
$451$	11.9620	−	20.7188i	0.563268	−	0.975608i
$452$	−5.73783	+	2.08840i	−0.269885	+	0.0982300i
$453$		0			0
$454$	−25.2592	+	21.1950i	−1.18547	+	0.994731i
$455$	−3.09967	−	1.12819i	−0.145315	−	0.0528903i
$456$		0			0
$457$	−0.261297	+	1.48189i	−0.0122229	+	0.0693198i	−0.990309	−	0.138881i	$-0.955650\pi$
$457$	−0.261297	+	1.48189i	−0.0122229	+	0.0693198i	0.978086	+	0.208200i	$0.0667606\pi$
$458$	−71.1498			−3.32461
$459$		0			0
$460$	12.6040			0.587665
$461$	4.55603	−	25.8385i	0.212195	−	1.20342i	−0.673512	−	0.739176i	$-0.735215\pi$
$461$	4.55603	−	25.8385i	0.212195	−	1.20342i	0.885708	−	0.464243i	$-0.153674\pi$
$462$		0			0
$463$	−6.34895	−	2.31083i	−0.295061	−	0.107393i	0.190248	−	0.981736i	$-0.439071\pi$
$463$	−6.34895	−	2.31083i	−0.295061	−	0.107393i	−0.485309	+	0.874343i	$0.661293\pi$
$464$	33.4295	−	28.0507i	1.55192	−	1.30222i
$465$		0			0
$466$	33.1079	−	12.0503i	1.53369	−	0.558219i
$467$	−16.8735	+	29.2257i	−0.780810	+	1.35240i	0.150660	+	0.988586i	$0.451860\pi$
$467$	−16.8735	+	29.2257i	−0.780810	+	1.35240i	−0.931470	+	0.363818i	$0.881473\pi$
$468$		0			0
$469$	16.1459	+	27.9655i	0.745548	+	1.29133i
$470$	−8.76786	−	7.35710i	−0.404431	−	0.339358i
$471$		0			0
$472$	−9.04664	−	51.3060i	−0.416405	−	2.36155i
$473$	0.317429	+	1.80023i	0.0145954	+	0.0827746i
$474$		0			0
$475$	−0.153419	−	0.128734i	−0.00703934	−	0.00590671i
$476$	21.3516	+	36.9821i	0.978651	+	1.69507i
$477$		0			0
$478$	19.0155	−	32.9358i	0.869748	−	1.50645i
$479$	−10.4556	+	3.80552i	−0.477728	+	0.173879i	−0.569650	−	0.821887i	$-0.692921\pi$
$479$	−10.4556	+	3.80552i	−0.477728	+	0.173879i	0.0919220	+	0.995766i	$0.470699\pi$
$480$		0			0
$481$	−6.01889	+	5.05044i	−0.274438	+	0.230280i
$482$	30.8692	+	11.2355i	1.40605	+	0.511761i
$483$		0			0
$484$	−1.03596	+	5.87522i	−0.0470891	+	0.267055i
$485$	8.72462			0.396165
$486$		0			0
$487$	−4.74691			−0.215103			−0.107552	−	0.994200i	$-0.534301\pi$
$487$	−4.74691			−0.215103			−0.107552	+	0.994200i	$0.534301\pi$
$488$	−1.34507	+	7.62830i	−0.0608887	+	0.345317i
$489$		0			0
$490$	−3.79813	−	1.38241i	−0.171582	−	0.0624508i
$491$	17.1138	−	14.3602i	0.772335	−	0.648066i	−0.168971	−	0.985621i	$-0.554044\pi$
$491$	17.1138	−	14.3602i	0.772335	−	0.648066i	0.941306	+	0.337555i	$0.109600\pi$
$492$		0			0
$493$	−18.5326	+	6.74530i	−0.834664	+	0.303793i
$494$	0.115867	−	0.200688i	0.00521310	−	0.00902936i
$495$		0			0
$496$	20.6668	+	35.7960i	0.927969	+	1.60729i
$497$	−29.2429	−	24.5377i	−1.31172	−	1.10067i
$498$		0			0
$499$	−1.81655	−	10.3022i	−0.0813200	−	0.461189i	−0.998090	−	0.0617736i	$-0.980324\pi$
$499$	−1.81655	−	10.3022i	−0.0813200	−	0.461189i	0.916770	−	0.399415i	$-0.130787\pi$
$500$	−3.50593	−	19.8831i	−0.156790	−	0.889200i
$501$		0			0
$502$	1.69253	+	1.42020i	0.0755415	+	0.0633868i
$503$	−12.5209	−	21.6869i	−0.558281	−	0.966972i	−0.997640	−	0.0686600i	$-0.978128\pi$
$503$	−12.5209	−	21.6869i	−0.558281	−	0.966972i	0.439359	−	0.898312i	$-0.355206\pi$
$504$		0			0
$505$	−2.12583	+	3.68204i	−0.0945982	+	0.163849i
$506$	45.1271	−	16.4249i	2.00614	−	0.730176i
$507$		0			0
$508$	−22.4329	+	18.8234i	−0.995298	+	0.835154i
$509$	−16.9731	−	6.17771i	−0.752321	−	0.273822i	−0.0627387	−	0.998030i	$-0.519983\pi$
$509$	−16.9731	−	6.17771i	−0.752321	−	0.273822i	−0.689582	+	0.724208i	$0.742206\pi$
$510$		0			0
$511$	4.61381	−	26.1662i	0.204103	−	1.15752i
$512$	−50.5553			−2.23425
$513$		0			0
$514$	11.5885			0.511148
$515$	0.0211929	−	0.120191i	0.000933872	−	0.00529625i
$516$		0			0
$517$	−28.1964	−	10.2627i	−1.24008	−	0.451351i
$518$	−22.5082	+	18.8866i	−0.988954	+	0.829831i
$519$		0			0
$520$	5.86571	−	2.13495i	0.257229	−	0.0936236i
$521$	12.9791	−	22.4804i	0.568623	−	0.984883i	−0.428080	−	0.903741i	$-0.640810\pi$
$521$	12.9791	−	22.4804i	0.568623	−	0.984883i	0.996703	−	0.0811425i	$-0.0258569\pi$
$522$		0			0
$523$	−12.7973	−	22.1655i	−0.559585	−	0.969230i	−0.997531	−	0.0702283i	$-0.977627\pi$
$523$	−12.7973	−	22.1655i	−0.559585	−	0.969230i	0.437946	−	0.899001i	$-0.355706\pi$
$524$	−42.7183	−	35.8449i	−1.86616	−	1.56589i
$525$		0			0
$526$	1.88965	+	10.7168i	0.0823928	+	0.467273i
$527$	−3.24376	−	18.3963i	−0.141300	−	0.801353i
$528$		0			0
$529$	10.9422	+	9.18161i	0.475749	+	0.399201i
$530$	−2.93717	−	5.08732i	−0.127582	−	0.220979i
$531$		0			0
$532$	0.298133	−	0.516382i	0.0129257	−	0.0223880i
$533$	15.8131	−	5.75552i	0.684943	−	0.249299i
$534$		0			0
$535$	1.44878	−	1.21567i	0.0626361	−	0.0525579i
$536$	−57.4227	−	20.9001i	−2.48028	−	0.902749i
$537$		0			0
$538$	5.33157	−	30.2368i	0.229860	−	1.30360i
$539$	−10.5963			−0.456414
$540$		0			0
$541$	27.8476			1.19726			0.598631	−	0.801025i	$-0.295712\pi$
$541$	27.8476			1.19726			0.598631	+	0.801025i	$0.295712\pi$
$542$	−0.140682	+	0.797847i	−0.00604281	+	0.0342705i
$543$		0			0
$544$	−12.9572	−	4.71605i	−0.555537	−	0.202199i
$545$	−1.93692	+	1.62527i	−0.0829685	+	0.0696188i
$546$		0			0
$547$	5.55216	−	2.02082i	0.237393	−	0.0864040i	−0.220584	−	0.975368i	$-0.570796\pi$
$547$	5.55216	−	2.02082i	0.237393	−	0.0864040i	0.457977	+	0.888964i	$0.348574\pi$
$548$	−23.4158	+	40.5574i	−1.00027	+	1.73253i
$549$		0			0
$550$	−18.8011	−	32.5645i	−0.801683	−	1.38856i
$551$	0.210952	+	0.177009i	0.00898684	+	0.00754086i
$552$		0			0
$553$	−6.19119	−	35.1120i	−0.263276	−	1.49311i
$554$	−11.7931	−	66.8819i	−0.501040	−	2.84154i
$555$		0			0
$556$	−25.2139	−	21.1570i	−1.06931	−	0.897257i
$557$	−13.3525	−	23.1272i	−0.565764	−	0.979932i	−0.996978	−	0.0776824i	$-0.975248\pi$
$557$	−13.3525	−	23.1272i	−0.565764	−	0.979932i	0.431214	−	0.902250i	$-0.358085\pi$
$558$		0			0
$559$	−0.642903	+	1.11354i	−0.0271919	+	0.0470978i
$560$	9.41787	−	3.42782i	0.397978	−	0.144852i
$561$		0			0
$562$	51.7529	−	43.4258i	2.18306	−	1.83181i
$563$	−33.8876	−	12.3341i	−1.42819	−	0.519819i	−0.491779	−	0.870720i	$-0.663653\pi$
$563$	−33.8876	−	12.3341i	−1.42819	−	0.519819i	−0.936413	+	0.350901i	$0.885875\pi$
$564$		0			0
$565$	0.112463	−	0.637812i	0.00473137	−	0.0268329i
$566$	−23.5321			−0.989127
$567$		0			0
$568$	72.2390			3.03108
$569$	−1.57104	+	8.90982i	−0.0658615	+	0.373519i	0.934006	+	0.357257i	$0.116288\pi$
$569$	−1.57104	+	8.90982i	−0.0658615	+	0.373519i	−0.999868	+	0.0162624i	$0.994823\pi$
$570$		0			0
$571$	−28.7349	−	10.4586i	−1.20252	−	0.437681i	−0.338415	−	0.940997i	$-0.609891\pi$
$571$	−28.7349	−	10.4586i	−1.20252	−	0.437681i	−0.864102	+	0.503316i	$0.832113\pi$
$572$	22.9329	−	19.2430i	0.958872	−	0.804589i
$573$		0			0
$574$	59.1348	−	21.5233i	2.46824	−	0.898366i
$575$	14.5967	−	25.2823i	0.608726	−	1.05434i
$576$		0			0
$577$	12.5744	+	21.7796i	0.523481	+	0.906696i	0.999626	+	0.0273292i	$0.00870022\pi$
$577$	12.5744	+	21.7796i	0.523481	+	0.906696i	−0.476146	+	0.879367i	$0.657966\pi$
$578$	−15.5175	−	13.0208i	−0.645445	−	0.541592i
$579$		0			0
$580$	2.35638	+	13.3637i	0.0978434	+	0.554898i
$581$	0.845952	+	4.79763i	0.0350960	+	0.199039i
$582$		0			0
$583$	−11.7973	−	9.89907i	−0.488592	−	0.409978i
$584$	25.1400	+	43.5437i	1.04030	+	1.80185i
$585$		0			0
$586$	24.8640	−	43.0656i	1.02712	−	1.77903i
$587$	−19.6147	+	7.13916i	−0.809585	+	0.294665i	−0.713452	−	0.700704i	$-0.752869\pi$
$587$	−19.6147	+	7.13916i	−0.809585	+	0.294665i	−0.0961324	+	0.995369i	$0.530647\pi$
$588$		0			0
$589$	−0.199807	+	0.167658i	−0.00823292	+	0.00690824i
$590$	9.49912	+	3.45740i	0.391073	+	0.142339i
$591$		0			0
$592$	4.14543	−	23.5099i	0.170376	−	0.966251i
$593$	15.6212			0.641488			0.320744	−	0.947166i	$-0.396067\pi$
$593$	15.6212			0.641488			0.320744	+	0.947166i	$0.396067\pi$
$594$		0			0
$595$	−4.52940			−0.185687
$596$	−3.25877	+	18.4814i	−0.133484	+	0.757028i
$597$		0			0
$598$	31.7422	+	11.5532i	1.29803	+	0.472446i
$599$	−0.343426	+	0.288169i	−0.0140320	+	0.0117742i	−0.649777	−	0.760125i	$-0.725138\pi$
$599$	−0.343426	+	0.288169i	−0.0140320	+	0.0117742i	0.635745	+	0.771899i	$0.280693\pi$
$600$		0			0
$601$	16.6065	−	6.04428i	0.677395	−	0.246551i	0.0196662	−	0.999807i	$-0.493740\pi$
$601$	16.6065	−	6.04428i	0.677395	−	0.246551i	0.657728	+	0.753255i	$0.271517\pi$
$602$	−2.40420	+	4.16420i	−0.0979879	+	0.169720i
$603$		0			0
$604$	−0.298133	−	0.516382i	−0.0121309	−	0.0210113i
$605$	−0.484737	−	0.406743i	−0.0197074	−	0.0165364i
$606$		0			0
$607$	4.54933	+	25.8005i	0.184651	+	1.04721i	0.926402	+	0.376535i	$0.122884\pi$
$607$	4.54933	+	25.8005i	0.184651	+	1.04721i	−0.741751	+	0.670675i	$0.766004\pi$
$608$	0.0334331	+	0.189608i	0.00135589	+	0.00768963i
$609$		0			0
$610$	−1.15136	−	0.966105i	−0.0466172	−	0.0391165i
$611$	−10.5530	−	18.2784i	−0.426930	−	0.739465i
$612$		0			0
$613$	−7.27719	+	12.6045i	−0.293923	+	0.509089i	−0.974734	−	0.223370i	$-0.928294\pi$
$613$	−7.27719	+	12.6045i	−0.293923	+	0.509089i	0.680811	+	0.732459i	$0.261628\pi$
$614$	−67.4393	+	24.5459i	−2.72163	+	0.990592i
$615$		0			0
$616$	46.8794	−	39.3365i	1.88883	−	1.58491i
$617$	−13.1750	−	4.79531i	−0.530405	−	0.193052i	0.0629140	−	0.998019i	$-0.479961\pi$
$617$	−13.1750	−	4.79531i	−0.530405	−	0.193052i	−0.593319	+	0.804967i	$0.702183\pi$
$618$		0			0
$619$	−5.50681	+	31.2307i	−0.221337	+	1.25527i	0.648227	+	0.761447i	$0.275511\pi$
$619$	−5.50681	+	31.2307i	−0.221337	+	1.25527i	−0.869565	+	0.493819i	$0.835600\pi$
$620$	−12.8530			−0.516188
$621$		0			0
$622$	−5.17705			−0.207581
$623$	8.89352	−	50.4377i	0.356311	−	2.02074i
$624$		0			0
$625$	−20.4513	−	7.44367i	−0.818052	−	0.297747i
$626$	16.3157	−	13.6905i	0.652105	−	0.547181i
$627$		0			0
$628$	−55.2418	+	20.1064i	−2.20439	+	0.802331i
$629$	−5.39440	+	9.34337i	−0.215089	+	0.372545i
$630$		0			0
$631$	19.2879	+	33.4077i	0.767840	+	1.32994i	0.938732	+	0.344648i	$0.112002\pi$
$631$	19.2879	+	33.4077i	0.767840	+	1.32994i	−0.170892	+	0.985290i	$0.554665\pi$
$632$	51.6848	+	43.3687i	2.05591	+	1.72512i
$633$		0			0
$634$	13.6869	+	77.6223i	0.543577	+	3.08278i
$635$	−0.539363	−	3.05888i	−0.0214040	−	0.121388i
$636$		0			0
$637$	−5.70961	−	4.79093i	−0.226223	−	0.189824i
$638$	25.8516	+	44.7763i	1.02348	+	1.77271i
$639$		0			0
$640$	3.12108	−	5.40587i	0.123372	−	0.213686i
$641$	28.7704	−	10.4716i	1.13636	−	0.413602i	0.295764	−	0.955261i	$-0.404426\pi$
$641$	28.7704	−	10.4716i	1.13636	−	0.413602i	0.840598	+	0.541659i	$0.182204\pi$
$642$		0			0
$643$	−26.2178	+	21.9994i	−1.03393	+	0.867570i	−0.991313	−	0.131521i	$-0.958014\pi$
$643$	−26.2178	+	21.9994i	−1.03393	+	0.867570i	−0.0426164	+	0.999092i	$0.513569\pi$
$644$	81.6746	+	29.7271i	3.21843	+	1.17141i
$645$		0			0
$646$	0.0552549	−	0.313366i	0.00217398	−	0.0123292i
$647$	−12.8726			−0.506073			−0.253037	−	0.967457i	$-0.581429\pi$
$647$	−12.8726			−0.506073			−0.253037	+	0.967457i	$0.581429\pi$
$648$		0			0
$649$	26.5012			1.04026
$650$	4.59286	−	26.0474i	0.180147	−	1.02166i
$651$		0			0
$652$	40.4752	+	14.7318i	1.58513	+	0.576941i
$653$	−8.67096	+	7.27580i	−0.339321	+	0.284724i	−0.796485	−	0.604658i	$-0.793310\pi$
$653$	−8.67096	+	7.27580i	−0.339321	+	0.284724i	0.457164	+	0.889382i	$0.348865\pi$
$654$		0			0
$655$	5.55809	−	2.02298i	0.217172	−	0.0790443i
$656$	−25.5646	+	44.2793i	−0.998132	+	1.72881i
$657$		0			0
$658$	−39.4641	−	68.3538i	−1.53847	−	2.66471i
$659$	−10.5478	−	8.85067i	−0.410885	−	0.344773i	0.413798	−	0.910369i	$-0.364202\pi$
$659$	−10.5478	−	8.85067i	−0.410885	−	0.344773i	−0.824683	+	0.565595i	$0.808646\pi$
$660$		0			0
$661$	−3.51930	−	19.9589i	−0.136885	−	0.776312i	−0.973529	−	0.228565i	$-0.926597\pi$
$661$	−3.51930	−	19.9589i	−0.136885	−	0.776312i	0.836644	−	0.547747i	$-0.184514\pi$
$662$	13.6441	+	77.3795i	0.530292	+	3.00744i
$663$		0			0
$664$	−7.06212	−	5.92582i	−0.274063	−	0.229966i
$665$	0.0316221	+	0.0547710i	0.00122625	+	0.00212393i
$666$		0			0
$667$	−20.0706	+	34.7633i	−0.777136	+	1.34604i
$668$	14.8157	−	5.39246i	0.573236	−	0.208641i
$669$		0			0
$670$	9.08306	−	7.62159i	0.350909	−	0.294448i
$671$	−3.70264	−	1.34765i	−0.142939	−	0.0520255i
$672$		0			0
$673$	−5.30406	+	30.0808i	−0.204457	+	1.15953i	0.693836	+	0.720133i	$0.255919\pi$
$673$	−5.30406	+	30.0808i	−0.204457	+	1.15953i	−0.898293	+	0.439398i	$0.855192\pi$
$674$	60.0856			2.31441
$675$		0			0
$676$	−36.2918			−1.39584
$677$	−0.645840	+	3.66274i	−0.0248217	+	0.140771i	−0.994700	−	0.102819i	$-0.967214\pi$
$677$	−0.645840	+	3.66274i	−0.0248217	+	0.140771i	0.969878	+	0.243589i	$0.0783249\pi$
$678$		0			0
$679$	56.5360	+	20.5774i	2.16965	+	0.789689i
$680$	6.56599	−	5.50952i	0.251794	−	0.211280i
$681$		0			0
$682$	−46.0185	+	16.7494i	−1.76214	+	0.641366i
$683$	10.8735	−	18.8334i	0.416061	−	0.720639i	−0.579478	−	0.814988i	$-0.696744\pi$
$683$	10.8735	−	18.8334i	0.416061	−	0.720639i	0.995539	+	0.0943487i	$0.0300769\pi$
$684$		0			0
$685$	−2.48364	−	4.30179i	−0.0948950	−	0.164363i
$686$	22.4598	+	18.8460i	0.857518	+	0.719543i
$687$		0			0
$688$	−0.678396	−	3.84737i	−0.0258636	−	0.146680i
$689$	−1.88103	−	10.6679i	−0.0716617	−	0.406414i
$690$		0			0
$691$	−28.7993	−	24.1655i	−1.09558	−	0.919299i	−0.0984578	−	0.995141i	$-0.531391\pi$
$691$	−28.7993	−	24.1655i	−1.09558	−	0.919299i	−0.997120	+	0.0758425i	$0.975835\pi$
$692$	−41.3940	−	71.6965i	−1.57356	−	2.72549i
$693$		0			0
$694$	2.28952	−	3.96556i	0.0869088	−	0.150530i
$695$	3.28059	−	1.19404i	0.124440	−	0.0452924i
$696$		0			0
$697$	17.7010	−	14.8529i	0.670473	−	0.562593i
$698$	−36.3114	−	13.2163i	−1.37441	−	0.500243i
$699$		0			0
$700$	11.8177	−	67.0217i	0.446668	−	2.53318i
$701$	23.3351			0.881355			0.440678	−	0.897665i	$-0.354738\pi$
$701$	23.3351			0.881355			0.440678	+	0.897665i	$0.354738\pi$
$702$		0			0
$703$	0.150644			0.00568166
$704$	0.883560	−	5.01092i	0.0333004	−	0.188856i
$705$		0			0
$706$	77.0502	+	28.0440i	2.89982	+	1.05545i
$707$	−22.4598	+	18.8460i	−0.844686	+	0.708776i
$708$		0			0
$709$	−6.18227	+	2.25016i	−0.232180	+	0.0845066i	−0.455490	−	0.890241i	$-0.650536\pi$
$709$	−6.18227	+	2.25016i	−0.232180	+	0.0845066i	0.223310	+	0.974747i	$0.428314\pi$
$710$	−7.00846	+	12.1390i	−0.263023	+	0.455569i
$711$		0			0
$712$	48.4595	+	83.9343i	1.81610	+	3.14557i
$713$	−29.1254	−	24.4391i	−1.09076	−	0.915253i
$714$		0			0
$715$	0.551385	+	3.12706i	0.0206206	+	0.116945i
$716$	−3.89440	−	22.0862i	−0.145541	−	0.825402i
$717$		0			0
$718$	−3.71348	−	3.11598i	−0.138586	−	0.116287i
$719$	8.41622	+	14.5773i	0.313872	+	0.543642i	0.979197	−	0.202911i	$-0.0650403\pi$
$719$	8.41622	+	14.5773i	0.313872	+	0.543642i	−0.665325	+	0.746554i	$0.731707\pi$
$720$		0			0
$721$	0.420807	−	0.728860i	0.0156717	−	0.0271442i
$722$	45.2041	−	16.4530i	1.68232	−	0.612316i
$723$		0			0
$724$	24.1648	−	20.2767i	0.898077	−	0.753576i
$725$	29.5351	+	10.7499i	1.09691	+	0.399241i
$726$		0			0
$727$	4.43882	−	25.1738i	0.164627	−	0.933644i	−0.784822	−	0.619721i	$-0.787246\pi$
$727$	4.43882	−	25.1738i	0.164627	−	0.933644i	0.949449	−	0.313922i	$-0.101643\pi$
$728$	43.0455			1.59537
$729$		0			0
$730$	−9.75608			−0.361089
$731$	−0.306589	+	1.73875i	−0.0113396	+	0.0643102i
$732$		0			0
$733$	13.9055	+	5.06120i	0.513613	+	0.186940i	0.585807	−	0.810451i	$-0.300778\pi$
$733$	13.9055	+	5.06120i	0.513613	+	0.186940i	−0.0721937	+	0.997391i	$0.523000\pi$
$734$	−52.1095	+	43.7251i	−1.92340	+	1.61392i
$735$		0			0
$736$	−26.3726	+	9.59883i	−0.972106	+	0.353818i
$737$	15.5424	−	26.9202i	0.572510	−	0.991616i
$738$		0			0
$739$	−4.59539	−	7.95945i	−0.169044	−	0.292793i	0.769040	−	0.639201i	$-0.220735\pi$
$739$	−4.59539	−	7.95945i	−0.169044	−	0.292793i	−0.938084	+	0.346408i	$0.887401\pi$
$740$	5.68660	+	4.77163i	0.209044	+	0.175408i
$741$		0			0
$742$	−7.03431	−	39.8936i	−0.258238	−	1.46454i
$743$	7.71853	+	43.7740i	0.283165	+	1.60591i	0.711766	+	0.702417i	$0.247896\pi$
$743$	7.71853	+	43.7740i	0.283165	+	1.60591i	−0.428600	+	0.903494i	$0.640993\pi$
$744$		0			0
$745$	−1.52481	−	1.27947i	−0.0558649	−	0.0468762i
$746$	−18.7883	−	32.5423i	−0.687890	−	1.19146i
$747$		0			0
$748$	20.5535	−	35.5997i	0.751510	−	1.30165i
$749$	12.2554	−	4.46059i	0.447801	−	0.162986i
$750$		0			0
$751$	−27.4290	+	23.0157i	−1.00090	+	0.839854i	−0.987109	−	0.160051i	$-0.948834\pi$
$751$	−27.4290	+	23.0157i	−1.00090	+	0.839854i	−0.0137902	+	0.999905i	$0.504390\pi$
$752$	60.2602	+	21.9329i	2.19746	+	0.799811i
$753$		0			0
$754$	−6.31521	+	35.8153i	−0.229986	+	1.30432i
$755$	0.0632441			0.00230169
$756$		0			0
$757$	−45.8976			−1.66818			−0.834088	−	0.551632i	$-0.814005\pi$
$757$	−45.8976			−1.66818			−0.834088	+	0.551632i	$0.814005\pi$
$758$	−14.8559	+	84.2521i	−0.539591	+	3.06017i
$759$		0			0
$760$	−0.112463	−	0.0409333i	−0.00407948	−	0.00148481i
$761$	−28.4932	+	23.9086i	−1.03288	+	0.866687i	−0.991191	−	0.132444i	$-0.957718\pi$
$761$	−28.4932	+	23.9086i	−1.03288	+	0.866687i	−0.0416869	+	0.999131i	$0.513273\pi$
$762$		0			0
$763$	−16.3846	+	5.96351i	−0.593162	+	0.215893i
$764$	23.1819	−	40.1522i	0.838690	−	1.45265i
$765$		0			0
$766$	11.7476	+	20.3475i	0.424459	+	0.735185i
$767$	14.2797	+	11.9821i	0.515611	+	0.432649i
$768$		0			0
$769$	−6.65657	−	37.7513i	−0.240042	−	1.36135i	−0.831730	−	0.555180i	$-0.812649\pi$
$769$	−6.65657	−	37.7513i	−0.240042	−	1.36135i	0.591688	−	0.806167i	$-0.298462\pi$
$770$	2.06196	+	11.6939i	0.0743077	+	0.421420i
$771$		0			0
$772$	−34.2768	−	28.7616i	−1.23365	−	1.03515i
$773$	−26.4136	−	45.7497i	−0.950031	−	1.64550i	−0.745351	−	0.666673i	$-0.767718\pi$
$773$	−26.4136	−	45.7497i	−0.950031	−	1.64550i	−0.204680	−	0.978829i	$-0.565615\pi$
$774$		0			0
$775$	−14.8851	+	25.7817i	−0.534687	+	0.926106i
$776$	−106.987	+	38.9401i	−3.84061	+	1.39787i
$777$		0			0
$778$	−30.9937	+	26.0068i	−1.11118	+	0.932388i
$779$	−0.303186	−	0.110351i	−0.0108628	−	0.00395372i
$780$		0			0
$781$	−6.38103	+	36.1886i	−0.228331	+	1.29493i
$782$	46.3833			1.65866
$783$		0			0
$784$	22.6459			0.808782
$785$	1.08276	−	6.14063i	0.0386453	−	0.219168i
$786$		0			0
$787$	−42.5121	−	15.4731i	−1.51539	−	0.551558i	−0.555400	−	0.831584i	$-0.687435\pi$
$787$	−42.5121	−	15.4731i	−1.51539	−	0.551558i	−0.959992	+	0.280026i	$0.909657\pi$
$788$	47.5945	−	39.9365i	1.69548	−	1.42268i
$789$		0			0
$790$	−12.3020	+	4.47756i	−0.437686	+	0.159305i
$791$	2.23308	−	3.86780i	0.0793991	−	0.137523i
$792$		0			0
$793$	−1.38578	−	2.40024i	−0.0492106	−	0.0852352i
$794$	38.2217	+	32.0718i	1.35644	+	1.13819i
$795$		0			0
$796$	7.87211	+	44.6450i	0.279020	+	1.58240i
$797$	−2.93794	−	16.6619i	−0.104067	−	0.590194i	−0.991589	−	0.129428i	$-0.958686\pi$
$797$	−2.93794	−	16.6619i	−0.104067	−	0.590194i	0.887522	−	0.460766i	$-0.152425\pi$
$798$		0			0
$799$	−22.2010	−	18.6288i	−0.785415	−	0.659041i
$800$	10.9875	+	19.0309i	0.388467	+	0.672845i
$801$		0			0
$802$	−1.45336	+	2.51730i	−0.0513200	+	0.0888889i
$803$	−24.0342	+	8.74774i	−0.848149	+	0.308701i
$804$		0			0
$805$	−7.06212	+	5.92582i	−0.248907	+	0.208858i
$806$	−32.3692	−	11.7814i	−1.14016	−	0.414983i
$807$		0			0
$808$	9.63445	−	54.6397i	0.338939	−	1.92222i
$809$	−34.9145			−1.22753			−0.613764	−	0.789490i	$-0.710345\pi$
$809$	−34.9145			−1.22753			−0.613764	+	0.789490i	$0.710345\pi$
$810$		0			0
$811$	18.0419			0.633536			0.316768	−	0.948503i	$-0.397402\pi$
$811$	18.0419			0.633536			0.316768	+	0.948503i	$0.397402\pi$
$812$	−16.2494	+	92.1551i	−0.570243	+	3.23401i
$813$		0			0
$814$	26.5783	+	9.67372i	0.931569	+	0.339064i
$815$	−3.49975	+	2.93664i	−0.122591	+	0.102866i
$816$		0			0
$817$	0.0231661	−	0.00843175i	0.000810478	−	0.000294990i
$818$	3.92602	−	6.80007i	0.137270	−	0.237759i
$819$		0			0
$820$	−7.94949	−	13.7689i	−0.277608	−	0.480832i
$821$	31.1313	+	26.1223i	1.08649	+	0.911675i	0.996444	−	0.0842628i	$-0.0268535\pi$
$821$	31.1313	+	26.1223i	1.08649	+	0.911675i	0.0900480	+	0.995937i	$0.471298\pi$
$822$		0			0
$823$	4.52347	+	25.6539i	0.157678	+	0.894238i	0.956296	+	0.292400i	$0.0944537\pi$
$823$	4.52347	+	25.6539i	0.157678	+	0.894238i	−0.798618	+	0.601838i	$0.794435\pi$
$824$	0.276560	+	1.56845i	0.00963442	+	0.0546395i
$825$		0			0
$826$	53.4004	+	44.8082i	1.85804	+	1.55908i
$827$	18.8097	+	32.5794i	0.654079	+	1.13290i	0.982124	+	0.188236i	$0.0602769\pi$
$827$	18.8097	+	32.5794i	0.654079	+	1.13290i	−0.328045	+	0.944662i	$0.606390\pi$
$828$		0			0
$829$	17.5107	−	30.3295i	0.608173	−	1.05339i	−0.383368	−	0.923595i	$-0.625236\pi$
$829$	17.5107	−	30.3295i	0.608173	−	1.05339i	0.991541	−	0.129791i	$-0.0414306\pi$
$830$	1.68092	−	0.611806i	0.0583457	−	0.0212361i
$831$		0			0
$832$	2.74170	−	2.30056i	0.0950512	−	0.0797574i
$833$	−9.61721	−	3.50038i	−0.333217	−	0.121281i
$834$		0			0
$835$	−0.290393	+	1.64690i	−0.0100494	+	0.0569933i
$836$	−0.573978			−0.0198514
$837$		0			0
$838$	89.7606			3.10073
$839$	4.62149	−	26.2098i	0.159552	−	0.904862i	−0.794954	−	0.606670i	$-0.792505\pi$
$839$	4.62149	−	26.2098i	0.159552	−	0.904862i	0.954506	−	0.298193i	$-0.0963838\pi$
$840$		0			0
$841$	−13.3598	−	4.86256i	−0.460682	−	0.167675i
$842$	17.8785	−	15.0018i	0.616134	−	0.516998i
$843$		0			0
$844$	29.6104	−	10.7773i	1.01923	−	0.370970i
$845$	1.92468	−	3.33364i	0.0662109	−	0.114681i
$846$		0			0
$847$	−2.18180	−	3.77899i	−0.0749675	−	0.129848i
$848$	25.2126	+	21.1559i	0.865804	+	0.726496i
$849$		0			0
$850$	−6.30659	−	35.7664i	−0.216314	−	1.22678i
$851$	3.81315	+	21.6254i	0.130713	+	0.741310i
$852$		0			0
$853$	1.88073	+	1.57812i	0.0643949	+	0.0540338i	0.674417	−	0.738351i	$-0.264395\pi$
$853$	1.88073	+	1.57812i	0.0643949	+	0.0540338i	−0.610022	+	0.792384i	$0.708839\pi$
$854$	−5.18227	−	8.97595i	−0.177334	−	0.307151i
$855$		0			0
$856$	−12.3400	+	21.3735i	−0.421773	+	0.730533i
$857$	9.23695	−	3.36197i	0.315528	−	0.114843i	−0.179401	−	0.983776i	$-0.557416\pi$
$857$	9.23695	−	3.36197i	0.315528	−	0.114843i	0.494930	+	0.868933i	$0.335194\pi$
$858$		0			0
$859$	6.75418	−	5.66743i	0.230450	−	0.193370i	−0.520250	−	0.854014i	$-0.674161\pi$
$859$	6.75418	−	5.66743i	0.230450	−	0.193370i	0.750699	+	0.660644i	$0.229717\pi$
$860$	1.14156	+	0.415494i	0.0389268	+	0.0141682i
$861$		0			0
$862$	5.09136	−	28.8745i	0.173412	−	0.983470i
$863$	−6.62124			−0.225390			−0.112695	−	0.993630i	$-0.535948\pi$
$863$	−6.62124			−0.225390			−0.112695	+	0.993630i	$0.535948\pi$
$864$		0			0
$865$	8.78106			0.298565
$866$	2.66678	−	15.1241i	0.0906210	−	0.513937i
$867$		0			0
$868$	−83.2880	−	30.3143i	−2.82698	−	1.02894i
$869$	−26.2913	+	22.0610i	−0.891872	+	0.748370i
$870$		0			0
$871$	20.5462	−	7.47821i	0.696182	−	0.253390i
$872$	16.4978	−	28.5750i	0.558685	−	0.967671i
$873$		0			0
$874$	−0.323826	−	0.560882i	−0.0109536	−	0.0189721i
$875$	11.3125	+	9.49233i	0.382433	+	0.320899i
$876$		0			0
$877$	−0.707796	−	4.01411i	−0.0239006	−	0.135547i	0.970523	−	0.241010i	$-0.0774787\pi$
$877$	−0.707796	−	4.01411i	−0.0239006	−	0.135547i	−0.994423	+	0.105463i	$0.966368\pi$
$878$	12.7537	+	72.3299i	0.430417	+	2.44102i
$879$		0			0
$880$	−7.39053	−	6.20139i	−0.249135	−	0.209049i
$881$	−4.62567	−	8.01189i	−0.155843	−	0.269927i	0.777523	−	0.628855i	$-0.216476\pi$
$881$	−4.62567	−	8.01189i	−0.155843	−	0.269927i	−0.933366	+	0.358927i	$0.883143\pi$
$882$		0			0
$883$	18.8851	−	32.7099i	0.635533	−	1.10078i	−0.350869	−	0.936425i	$-0.614114\pi$
$883$	18.8851	−	32.7099i	0.635533	−	1.10078i	0.986402	−	0.164351i	$-0.0525530\pi$
$884$	27.1707	−	9.88933i	0.913850	−	0.332614i
$885$		0			0
$886$	59.9213	−	50.2800i	2.01310	−	1.68919i
$887$	−17.8341	−	6.49108i	−0.598810	−	0.217949i	0.0247898	−	0.999693i	$-0.492108\pi$
$887$	−17.8341	−	6.49108i	−0.598810	−	0.217949i	−0.623600	+	0.781744i	$0.714331\pi$
$888$		0			0
$889$	3.71941	−	21.0938i	0.124745	−	0.707464i
$890$	−18.8057			−0.630369
$891$		0			0
$892$	−45.5945			−1.52662
$893$	−0.0702697	+	0.398519i	−0.00235149	+	0.0133359i
$894$		0			0
$895$	2.23530	+	0.813583i	0.0747178	+	0.0271951i
$896$	32.9748	−	27.6691i	1.10161	−	0.924360i
$897$		0			0
$898$	92.9912	−	33.8460i	3.10316	−	1.12946i
$899$	20.4670	−	35.4499i	0.682614	−	1.18232i
$900$		0			0
$901$	−7.43717	−	12.8816i	−0.247768	−	0.429147i
$902$	−46.4051	−	38.9385i	−1.54512	−	1.29651i
$903$		0			0
$904$	1.46761	+	8.32321i	0.0488119	+	0.276826i
$905$	0.581004	+	3.29503i	0.0193132	+	0.109531i
$906$		0			0
$907$	7.38919	+	6.20026i	0.245354	+	0.205876i	0.757169	−	0.653220i	$-0.226582\pi$
$907$	7.38919	+	6.20026i	0.245354	+	0.205876i	−0.511815	+	0.859096i	$0.671027\pi$
$908$	28.7237	+	49.7510i	0.953231	+	1.65104i
$909$		0			0
$910$	−4.17617	+	7.23335i	−0.138439	+	0.239783i
$911$	6.14068	−	2.23503i	0.203450	−	0.0740497i	−0.238285	−	0.971195i	$-0.576585\pi$
$911$	6.14068	−	2.23503i	0.203450	−	0.0740497i	0.441735	+	0.897146i	$0.354363\pi$
$912$		0			0
$913$	3.59240	−	3.01438i	0.118891	−	0.0997614i
$914$	3.58037	+	1.30315i	0.118428	+	0.0431044i
$915$		0			0
$916$	−21.5253	+	122.076i	−0.711215	+	4.03350i
$917$	40.7880			1.34694
$918$		0			0
$919$	3.89124			0.128360			0.0641802	−	0.997938i	$-0.479557\pi$
$919$	3.89124			0.128360			0.0641802	+	0.997938i	$0.479557\pi$
$920$	3.02940	−	17.1806i	0.0998764	−	0.566427i
$921$		0			0
$922$	−62.4282	−	22.7220i	−2.05596	−	0.748309i
$923$	−19.8004	+	16.6145i	−0.651738	+	0.546874i
$924$		0			0
$925$	16.1570	−	5.88068i	0.531240	−	0.193356i
$926$	−8.55391	+	14.8158i	−0.281099	+	0.486878i
$927$		0			0
$928$	−15.1079	−	26.1676i	−0.495940	−	0.858994i
$929$	−30.5292	−	25.6170i	−1.00163	−	0.840467i	−0.0144197	−	0.999896i	$-0.504590\pi$
$929$	−30.5292	−	25.6170i	−1.00163	−	0.840467i	−0.987209	+	0.159430i	$0.949035\pi$
$930$		0			0
$931$	0.0248149	+	0.140732i	0.000813276	+	0.00461232i
$932$	−10.6591	−	60.4508i	−0.349150	−	1.98013i
$933$		0			0
$934$	65.4586	+	54.9263i	2.14187	+	1.79724i
$935$	2.18004	+	3.77595i	0.0712951	+	0.123487i
$936$		0			0
$937$	−16.5326	+	28.6352i	−0.540095	+	0.935472i	0.458803	+	0.888538i	$0.348278\pi$
$937$	−16.5326	+	28.6352i	−0.540095	+	0.935472i	−0.998898	+	0.0469340i	$0.985055\pi$
$938$	76.8346	−	27.9655i	2.50874	−	0.913106i
$939$		0			0
$940$	−15.2756	+	12.8177i	−0.498235	+	0.418069i
$941$	50.5617	+	18.4030i	1.64826	+	0.599919i	0.988455	−	0.151514i	$-0.0484148\pi$
$941$	50.5617	+	18.4030i	1.64826	+	0.599919i	0.659809	+	0.751433i	$0.270637\pi$
$942$		0			0
$943$	8.16684	−	46.3165i	0.265949	−	1.50827i
$944$	−56.6373			−1.84339
$945$		0			0
$946$	4.62866			0.150491
$947$	7.33409	−	41.5937i	0.238326	−	1.35161i	−0.597169	−	0.802116i	$-0.703708\pi$
$947$	7.33409	−	41.5937i	0.238326	−	1.35161i	0.835495	−	0.549498i	$-0.185181\pi$
$948$		0			0
$949$	−16.9055	−	6.15311i	−0.548777	−	0.199739i
$950$	−0.388470	+	0.325965i	−0.0126036	+	0.0105757i
$951$		0			0
$952$	55.5424	−	20.2158i	1.80014	−	0.655197i
$953$	−12.2888	+	21.2848i	−0.398073	+	0.689483i	−0.993488	−	0.113935i	$-0.963654\pi$
$953$	−12.2888	+	21.2848i	−0.398073	+	0.689483i	0.595415	+	0.803418i	$0.296988\pi$
$954$		0			0
$955$	2.45883	+	4.25881i	0.0795657	+	0.137812i
$956$	−50.7570	−	42.5902i	−1.64160	−	1.37747i
$957$		0			0
$958$	4.89228	+	27.7455i	0.158063	+	0.896417i
$959$	−5.94815	−	33.7336i	−0.192076	−	1.08932i
$960$		0			0
$961$	5.95336	+	4.99546i	0.192044	+	0.161144i
$962$	9.94743	+	17.2295i	0.320718	+	0.555500i
$963$		0			0
$964$	28.6163	−	49.5649i	0.921670	−	1.59638i
$965$	4.45976	−	1.62322i	0.143565	−	0.0522533i
$966$		0			0
$967$	3.42577	−	2.87457i	0.110165	−	0.0924398i	−0.586041	−	0.810281i	$-0.699314\pi$
$967$	3.42577	−	2.87457i	0.110165	−	0.0924398i	0.696206	+	0.717842i	$0.254870\pi$
$968$	7.75954	+	2.82424i	0.249401	+	0.0907746i
$969$		0			0
$970$	3.83615	−	21.7559i	0.123171	−	0.698540i
$971$	−4.61949			−0.148246			−0.0741232	−	0.997249i	$-0.523616\pi$
$971$	−4.61949			−0.148246			−0.0741232	+	0.997249i	$0.523616\pi$
$972$		0			0
$973$	24.0746			0.771796
$974$	−2.08718	+	11.8370i	−0.0668776	+	0.379282i
$975$		0			0
$976$	7.91312	+	2.88014i	0.253293	+	0.0921911i
$977$	−8.64156	+	7.25113i	−0.276468	+	0.231984i	−0.770470	−	0.637477i	$-0.779978\pi$
$977$	−8.64156	+	7.25113i	−0.276468	+	0.231984i	0.494002	+	0.869461i	$0.335534\pi$
$978$		0			0
$979$	−46.3281	+	16.8620i	−1.48065	+	0.538913i
$980$	−3.52094	+	6.09845i	−0.112472	+	0.194808i
$981$		0			0
$982$	−28.2841	−	48.9894i	−0.902580	−	1.56332i
$983$	−13.0719	−	10.9686i	−0.416929	−	0.349845i	0.410064	−	0.912057i	$-0.365506\pi$
$983$	−13.0719	−	10.9686i	−0.416929	−	0.349845i	−0.826994	+	0.562211i	$0.809951\pi$
$984$		0			0
$985$	1.14433	+	6.48984i	0.0364615	+	0.206783i
$986$	8.67159	+	49.1790i	0.276160	+	1.56618i
$987$		0			0
$988$	−0.309278	−	0.259515i	−0.00983943	−	0.00825627i
$989$	1.79679	+	3.11213i	0.0571346	+	0.0989600i
$990$		0			0
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	−0.881471	−	0.472237i	$-0.843446\pi$
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	0.849705	+	0.527258i	$0.176780\pi$
$992$	26.8935	−	9.78844i	0.853870	−	0.310783i
$993$		0			0
$994$	−74.0456	+	62.1316i	−2.34858	+	1.97069i
$995$	−4.51842	−	1.64457i	−0.143243	−	0.0521364i
$996$		0			0
$997$	3.88707	−	22.0447i	0.123105	−	0.698162i	−0.859311	−	0.511454i	$-0.829107\pi$
$997$	3.88707	−	22.0447i	0.123105	−	0.698162i	0.982415	−	0.186708i	$-0.0597818\pi$
$998$	−26.4884			−0.838477
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.b.649.1		6
3.2	odd	2		729.2.e.g.649.1		6
9.2	odd	6		729.2.e.h.163.1		6
9.4	even	3		729.2.e.i.406.1		6
9.5	odd	6		729.2.e.a.406.1		6
9.7	even	3		729.2.e.c.163.1		6
27.2	odd	18		243.2.c.f.163.3		6
27.4	even	9		729.2.e.i.325.1		6
27.5	odd	18		729.2.e.h.568.1		6
27.7	even	9		243.2.c.e.82.1		6
27.11	odd	18		243.2.a.e.1.1	✓	3
27.13	even	9	inner	729.2.e.b.82.1		6
27.14	odd	18		729.2.e.g.82.1		6
27.16	even	9		243.2.a.f.1.3	yes	3
27.20	odd	18		243.2.c.f.82.3		6
27.22	even	9		729.2.e.c.568.1		6
27.23	odd	18		729.2.e.a.325.1		6
27.25	even	9		243.2.c.e.163.1		6
108.11	even	18		3888.2.a.bd.1.3		3
108.43	odd	18		3888.2.a.bk.1.1		3
135.119	odd	18		6075.2.a.bv.1.3		3
135.124	even	18		6075.2.a.bq.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.a.e.1.1	✓	3	27.11	odd	18
243.2.a.f.1.3	yes	3	27.16	even	9
243.2.c.e.82.1		6	27.7	even	9
243.2.c.e.163.1		6	27.25	even	9
243.2.c.f.82.3		6	27.20	odd	18
243.2.c.f.163.3		6	27.2	odd	18
729.2.e.a.325.1		6	27.23	odd	18
729.2.e.a.406.1		6	9.5	odd	6
729.2.e.b.82.1		6	27.13	even	9	inner
729.2.e.b.649.1		6	1.1	even	1	trivial
729.2.e.c.163.1		6	9.7	even	3
729.2.e.c.568.1		6	27.22	even	9
729.2.e.g.82.1		6	27.14	odd	18
729.2.e.g.649.1		6	3.2	odd	2
729.2.e.h.163.1		6	9.2	odd	6
729.2.e.h.568.1		6	27.5	odd	18
729.2.e.i.325.1		6	27.4	even	9
729.2.e.i.406.1		6	9.4	even	3
3888.2.a.bd.1.3		3	108.11	even	18
3888.2.a.bk.1.1		3	108.43	odd	18
6075.2.a.bq.1.1		3	135.124	even	18
6075.2.a.bv.1.3		3	135.119	odd	18

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.439693 - 2.49362i) q^{2} +(-4.14543 - 1.50881i) q^{4} +(0.358441 - 0.300767i) q^{5} +(3.03209 - 1.10359i) q^{7} +(-3.05303 + 5.28801i) q^{8} +O(q^{10})\)	\(q+(0.439693 - 2.49362i) q^{2} +(-4.14543 - 1.50881i) q^{4} +(0.358441 - 0.300767i) q^{5} +(3.03209 - 1.10359i) q^{7} +(-3.05303 + 5.28801i) q^{8} +(-0.592396 - 1.02606i) q^{10} +(-2.37939 - 1.99654i) q^{11} +(-0.379385 - 2.15160i) q^{13} +(-1.41875 - 8.04612i) q^{14} +(5.08512 + 4.26692i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(-0.0209445 + 0.0362770i) q^{19} +(-1.93969 + 0.705990i) q^{20} +(-6.02481 + 5.05542i) q^{22} +(-5.73783 - 2.08840i) q^{23} +(-0.830222 + 4.70842i) q^{25} -5.53209 q^{26} -14.2344 q^{28} +(1.14156 - 6.47410i) q^{29} +(5.85117 + 2.12965i) q^{31} +(3.52094 - 2.95442i) q^{32} +(-7.13816 + 2.59808i) q^{34} +(0.754900 - 1.30753i) q^{35} +(-1.79813 - 3.11446i) q^{37} +(0.0812519 + 0.0681784i) q^{38} +(0.496130 + 2.81369i) q^{40} +(1.33750 + 7.58532i) q^{41} +(-0.450837 - 0.378297i) q^{43} +(6.85117 + 11.8666i) q^{44} +(-7.73055 + 13.3897i) q^{46} +(9.07785 - 3.30407i) q^{47} +(2.61334 - 2.19285i) q^{49} +(11.3760 + 4.14052i) q^{50} +(-1.67365 + 9.49173i) q^{52} +4.95811 q^{53} -1.45336 q^{55} +(-3.42127 + 19.4030i) q^{56} +(-15.6420 - 5.69323i) q^{58} +(-6.53596 + 5.48432i) q^{59} +(1.19207 - 0.433877i) q^{61} +(7.88326 - 13.6542i) q^{62} +(0.819078 + 1.41868i) q^{64} +(-0.783119 - 0.657115i) q^{65} +(1.73783 + 9.85570i) q^{67} +(2.29813 + 13.0334i) q^{68} +(-2.92855 - 2.45734i) q^{70} +(-5.91534 - 10.2457i) q^{71} +(4.11721 - 7.13122i) q^{73} +(-8.55690 + 3.11446i) q^{74} +(0.141559 - 0.118782i) q^{76} +(-9.41787 - 3.42782i) q^{77} +(1.91875 - 10.8818i) q^{79} +3.10607 q^{80} +19.5030 q^{82} +(-0.262174 + 1.48686i) q^{83} +(-1.31908 - 0.480105i) q^{85} +(-1.14156 + 0.957882i) q^{86} +(17.8221 - 6.48670i) q^{88} +(7.93629 - 13.7461i) q^{89} +(-3.52481 - 6.10516i) q^{91} +(20.6348 + 17.3146i) q^{92} +(-4.24763 - 24.0895i) q^{94} +(0.00340357 + 0.0193026i) q^{95} +(14.2836 + 11.9854i) q^{97} +(-4.31908 - 7.48086i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 9 q^{4} - 6 q^{5} + 9 q^{7} - 6 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 9 * q^4 - 6 * q^5 + 9 * q^7 - 6 * q^8	\( 6 q - 3 q^{2} - 9 q^{4} - 6 q^{5} + 9 q^{7} - 6 q^{8} - 3 q^{11} + 9 q^{13} - 6 q^{14} + 9 q^{16} - 9 q^{17} + 3 q^{19} - 6 q^{20} - 9 q^{22} - 15 q^{23} + 18 q^{25} - 24 q^{26} - 24 q^{28} + 15 q^{29} + 9 q^{31} + 18 q^{32} - 9 q^{34} + 6 q^{35} + 3 q^{37} + 3 q^{38} + 27 q^{40} + 3 q^{41} + 9 q^{43} + 15 q^{44} - 9 q^{46} + 15 q^{47} + 9 q^{49} + 15 q^{50} - 9 q^{52} + 36 q^{53} + 18 q^{55} - 3 q^{56} - 36 q^{58} - 6 q^{59} + 18 q^{61} + 12 q^{62} - 12 q^{64} - 21 q^{65} - 9 q^{67} - 18 q^{70} + 9 q^{71} - 6 q^{73} - 15 q^{74} + 9 q^{76} + 3 q^{77} + 9 q^{79} - 6 q^{80} + 36 q^{82} - 21 q^{83} + 9 q^{85} - 15 q^{86} + 9 q^{88} + 6 q^{91} + 48 q^{92} - 9 q^{94} + 42 q^{95} + 36 q^{97} - 9 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 - 9 * q^4 - 6 * q^5 + 9 * q^7 - 6 * q^8 - 3 * q^11 + 9 * q^13 - 6 * q^14 + 9 * q^16 - 9 * q^17 + 3 * q^19 - 6 * q^20 - 9 * q^22 - 15 * q^23 + 18 * q^25 - 24 * q^26 - 24 * q^28 + 15 * q^29 + 9 * q^31 + 18 * q^32 - 9 * q^34 + 6 * q^35 + 3 * q^37 + 3 * q^38 + 27 * q^40 + 3 * q^41 + 9 * q^43 + 15 * q^44 - 9 * q^46 + 15 * q^47 + 9 * q^49 + 15 * q^50 - 9 * q^52 + 36 * q^53 + 18 * q^55 - 3 * q^56 - 36 * q^58 - 6 * q^59 + 18 * q^61 + 12 * q^62 - 12 * q^64 - 21 * q^65 - 9 * q^67 - 18 * q^70 + 9 * q^71 - 6 * q^73 - 15 * q^74 + 9 * q^76 + 3 * q^77 + 9 * q^79 - 6 * q^80 + 36 * q^82 - 21 * q^83 + 9 * q^85 - 15 * q^86 + 9 * q^88 + 6 * q^91 + 48 * q^92 - 9 * q^94 + 42 * q^95 + 36 * q^97 - 9 * q^98

Introduction

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