LMFDB - Embedded newform 729.2.i.a.10.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(10,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(162))

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("729.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.i (of order $81$, degree $54$, 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:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			10.12
Character	$\chi$	$=$	729.10
Dual form			729.2.i.a.73.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.269146 - 0.0420937i) q^{2} +(-1.83383 - 0.587993i) q^{4} +(-0.567739 - 0.258069i) q^{5} +(-0.486494 - 3.56177i) q^{7} +(0.955700 + 0.479971i) q^{8} +O(q^{10})$	\(q+(-0.269146 - 0.0420937i) q^{2} +(-1.83383 - 0.587993i) q^{4} +(-0.567739 - 0.258069i) q^{5} +(-0.486494 - 3.56177i) q^{7} +(0.955700 + 0.479971i) q^{8} +(0.141942 + 0.0933565i) q^{10} +(-0.568575 + 0.0441932i) q^{11} +(-0.807583 - 2.36025i) q^{13} +(-0.0189899 + 0.979115i) q^{14} +(2.89644 + 2.07025i) q^{16} +(-2.48941 + 5.77111i) q^{17} +(-1.97451 + 2.65223i) q^{19} +(0.889392 + 0.807081i) q^{20} +(0.154890 + 0.0120390i) q^{22} +(4.42696 + 3.43116i) q^{23} +(-3.03188 - 3.47415i) q^{25} +(0.118006 + 0.669246i) q^{26} +(-1.20215 + 6.81773i) q^{28} +(-1.64506 + 0.992798i) q^{29} +(-6.69161 + 0.259665i) q^{31} +(-2.21945 - 2.17682i) q^{32} +(0.912943 - 1.44848i) q^{34} +(-0.642980 + 2.14770i) q^{35} +(-3.59976 + 3.81553i) q^{37} +(0.643074 - 0.630723i) q^{38} +(-0.418722 - 0.519134i) q^{40} +(1.62607 - 4.21162i) q^{41} +(0.935643 + 3.63239i) q^{43} +(1.06865 + 0.253276i) q^{44} +(-1.04707 - 1.10983i) q^{46} +(-10.8736 - 0.421946i) q^{47} +(-5.70593 + 1.58835i) q^{49} +(0.669779 + 1.06268i) q^{50} +(0.0931569 + 4.80314i) q^{52} +(-7.40900 + 2.69665i) q^{53} +(0.334207 + 0.121641i) q^{55} +(1.24460 - 3.63749i) q^{56} +(0.484552 - 0.197961i) q^{58} +(3.54618 + 7.41620i) q^{59} +(1.37755 - 0.441694i) q^{61} +(1.81195 + 0.211787i) q^{62} +(-3.74633 - 5.03219i) q^{64} +(-0.150611 + 1.54842i) q^{65} +(-0.745608 - 0.449977i) q^{67} +(7.95853 - 9.11946i) q^{68} +(0.263460 - 0.550981i) q^{70} +(-0.534202 + 9.17189i) q^{71} +(10.5992 - 6.97120i) q^{73} +(1.12947 - 0.875407i) q^{74} +(5.18041 - 3.70273i) q^{76} +(0.434015 + 2.00363i) q^{77} +(-5.66996 + 7.02965i) q^{79} +(-1.11015 - 1.92284i) q^{80} +(-0.614933 + 1.06510i) q^{82} +(-4.64147 - 12.0217i) q^{83} +(2.90268 - 2.63404i) q^{85} +(-0.0989240 - 1.01703i) q^{86} +(-0.564599 - 0.230664i) q^{88} +(0.0110750 + 0.190150i) q^{89} +(-8.01378 + 4.02467i) q^{91} +(-6.10079 - 8.89517i) q^{92} +(2.90883 + 0.571276i) q^{94} +(1.80547 - 0.996214i) q^{95} +(14.0870 - 6.40332i) q^{97} +(1.60259 - 0.187316i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{81}\right)$

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 $

$2$	−0.269146	−	0.0420937i	−0.190315	−	0.0297647i	0.0586429	−	0.998279i	$-0.481323\pi$
$2$	−0.269146	−	0.0420937i	−0.190315	−	0.0297647i	−0.248958	+	0.968514i	$0.580088\pi$
$3$		0			0
$3$		0			0
$4$	−1.83383	−	0.587993i	−0.916914	−	0.293997i
$5$	−0.567739	−	0.258069i	−0.253901	−	0.115412i	0.282817	−	0.959174i	$-0.408731\pi$
$5$	−0.567739	−	0.258069i	−0.253901	−	0.115412i	−0.536718	+	0.843762i	$0.680336\pi$
$6$		0			0
$7$	−0.486494	−	3.56177i	−0.183878	−	1.34622i	−0.818992	−	0.573804i	$-0.805467\pi$
$7$	−0.486494	−	3.56177i	−0.183878	−	1.34622i	0.635115	−	0.772418i	$-0.280953\pi$
$8$	0.955700	+	0.479971i	0.337891	+	0.169695i
$9$		0			0
$10$	0.141942	+	0.0933565i	0.0448859	+	0.0295219i
$11$	−0.568575	+	0.0441932i	−0.171432	+	0.0133247i	−0.162921	−	0.986639i	$-0.552092\pi$
$11$	−0.568575	+	0.0441932i	−0.171432	+	0.0133247i	−0.00851047	+	0.999964i	$0.502709\pi$
$12$		0			0
$13$	−0.807583	−	2.36025i	−0.223983	−	0.654615i	−0.999722	−	0.0235618i	$-0.992499\pi$
$13$	−0.807583	−	2.36025i	−0.223983	−	0.654615i	0.775739	−	0.631054i	$-0.217377\pi$
$14$	−0.0189899	+	0.979115i	−0.00507527	+	0.261679i
$15$		0			0
$16$	2.89644	+	2.07025i	0.724110	+	0.517563i
$17$	−2.48941	+	5.77111i	−0.603772	+	1.39970i	0.292531	+	0.956256i	$0.405503\pi$
$17$	−2.48941	+	5.77111i	−0.603772	+	1.39970i	−0.896302	+	0.443444i	$0.853757\pi$
$18$		0			0
$19$	−1.97451	+	2.65223i	−0.452984	+	0.608463i	−0.968681	−	0.248308i	$-0.920126\pi$
$19$	−1.97451	+	2.65223i	−0.452984	+	0.608463i	0.515697	+	0.856771i	$0.327533\pi$
$20$	0.889392	+	0.807081i	0.198874	+	0.180469i
$21$		0			0
$22$	0.154890	+	0.0120390i	0.0330227	+	0.00256673i
$23$	4.42696	+	3.43116i	0.923086	+	0.715445i	0.958849	−	0.283915i	$-0.0916333\pi$
$23$	4.42696	+	3.43116i	0.923086	+	0.715445i	−0.0357639	+	0.999360i	$0.511386\pi$
$24$		0			0
$25$	−3.03188	−	3.47415i	−0.606376	−	0.694830i
$26$	0.118006	+	0.669246i	0.0231429	+	0.131250i
$27$		0			0
$28$	−1.20215	+	6.81773i	−0.227185	+	1.28843i
$29$	−1.64506	+	0.992798i	−0.305480	+	0.184358i	−0.661150	−	0.750253i	$-0.729931\pi$
$29$	−1.64506	+	0.992798i	−0.305480	+	0.184358i	0.355671	+	0.934611i	$0.384252\pi$
$30$		0			0
$31$	−6.69161	+	0.259665i	−1.20185	+	0.0466372i	−0.631905	−	0.775046i	$-0.717727\pi$
$31$	−6.69161	+	0.259665i	−1.20185	+	0.0466372i	−0.569944	+	0.821683i	$0.693035\pi$
$32$	−2.21945	−	2.17682i	−0.392347	−	0.384812i
$33$		0			0
$34$	0.912943	−	1.44848i	0.156568	−	0.248413i
$35$	−0.642980	+	2.14770i	−0.108683	+	0.363028i
$36$		0			0
$37$	−3.59976	+	3.81553i	−0.591797	+	0.627268i	−0.952181	−	0.305536i	$-0.901164\pi$
$37$	−3.59976	+	3.81553i	−0.591797	+	0.627268i	0.360383	+	0.932804i	$0.382646\pi$
$38$	0.643074	−	0.630723i	0.104320	−	0.102317i
$39$		0			0
$40$	−0.418722	−	0.519134i	−0.0662058	−	0.0820823i
$41$	1.62607	−	4.21162i	0.253949	−	0.657745i	−0.746017	−	0.665927i	$-0.768036\pi$
$41$	1.62607	−	4.21162i	0.253949	−	0.657745i	0.999967	+	0.00818138i	$0.00260424\pi$
$42$		0			0
$43$	0.935643	+	3.63239i	0.142684	+	0.553934i	0.999280	+	0.0379457i	$0.0120814\pi$
$43$	0.935643	+	3.63239i	0.142684	+	0.553934i	−0.856596	+	0.515988i	$0.827425\pi$
$44$	1.06865	+	0.253276i	0.161106	+	0.0381828i
$45$		0			0
$46$	−1.04707	−	1.10983i	−0.154382	−	0.163635i
$47$	−10.8736	−	0.421946i	−1.58608	−	0.0615472i	−0.769450	−	0.638707i	$-0.779470\pi$
$47$	−10.8736	−	0.421946i	−1.58608	−	0.0615472i	−0.816631	+	0.577160i	$0.804161\pi$
$48$		0			0
$49$	−5.70593	+	1.58835i	−0.815132	+	0.226908i
$50$	0.669779	+	1.06268i	0.0947210	+	0.150285i
$51$		0			0
$52$	0.0931569	+	4.80314i	0.0129185	+	0.666076i
$53$	−7.40900	+	2.69665i	−1.01770	+	0.370414i	−0.796387	−	0.604788i	$-0.793258\pi$
$53$	−7.40900	+	2.69665i	−1.01770	+	0.370414i	−0.221317	+	0.975202i	$0.571036\pi$
$54$		0			0
$55$	0.334207	+	0.121641i	0.0450645	+	0.0164021i
$56$	1.24460	−	3.63749i	0.166317	−	0.486079i
$57$		0			0
$58$	0.484552	−	0.197961i	0.0636247	−	0.0259936i
$59$	3.54618	+	7.41620i	0.461673	+	0.965507i	0.992975	+	0.118325i	$0.0377524\pi$
$59$	3.54618	+	7.41620i	0.461673	+	0.965507i	−0.531302	+	0.847183i	$0.678297\pi$
$60$		0			0
$61$	1.37755	−	0.441694i	0.176377	−	0.0565531i	−0.215825	−	0.976432i	$-0.569244\pi$
$61$	1.37755	−	0.441694i	0.176377	−	0.0565531i	0.392202	+	0.919879i	$0.371713\pi$
$62$	1.81195	+	0.211787i	0.230118	+	0.0268969i
$63$		0			0
$64$	−3.74633	−	5.03219i	−0.468291	−	0.629024i
$65$	−0.150611	+	1.54842i	−0.0186810	+	0.192057i
$66$		0			0
$67$	−0.745608	−	0.449977i	−0.0910906	−	0.0549734i	0.470422	−	0.882441i	$-0.344102\pi$
$67$	−0.745608	−	0.449977i	−0.0910906	−	0.0549734i	−0.561513	+	0.827468i	$0.689781\pi$
$68$	7.95853	−	9.11946i	0.965114	−	1.10590i
$69$		0			0
$70$	0.263460	−	0.550981i	0.0314895	−	0.0658548i
$71$	−0.534202	+	9.17189i	−0.0633981	+	1.08850i	0.805206	+	0.592996i	$0.202055\pi$
$71$	−0.534202	+	9.17189i	−0.0633981	+	1.08850i	−0.868604	+	0.495507i	$0.834982\pi$
$72$		0			0
$73$	10.5992	−	6.97120i	1.24054	−	0.815917i	0.252127	−	0.967694i	$-0.418870\pi$
$73$	10.5992	−	6.97120i	1.24054	−	0.815917i	0.988415	+	0.151777i	$0.0484994\pi$
$74$	1.12947	−	0.875407i	0.131298	−	0.101764i
$75$		0			0
$76$	5.18041	−	3.70273i	0.594234	−	0.424733i
$77$	0.434015	+	2.00363i	0.0494606	+	0.228335i
$78$		0			0
$79$	−5.66996	+	7.02965i	−0.637921	+	0.790898i	−0.989387	−	0.145303i	$-0.953584\pi$
$79$	−5.66996	+	7.02965i	−0.637921	+	0.790898i	0.351467	+	0.936200i	$0.385683\pi$
$80$	−1.11015	−	1.92284i	−0.124119	−	0.214980i
$81$		0			0
$82$	−0.614933	+	1.06510i	−0.0679080	+	0.117620i
$83$	−4.64147	−	12.0217i	−0.509468	−	1.31955i	−0.914253	−	0.405143i	$-0.867222\pi$
$83$	−4.64147	−	12.0217i	−0.509468	−	1.31955i	0.404786	−	0.914412i	$-0.367346\pi$
$84$		0			0
$85$	2.90268	−	2.63404i	0.314840	−	0.285702i
$86$	−0.0989240	−	1.01703i	−0.0106672	−	0.109669i
$87$		0			0
$88$	−0.564599	−	0.230664i	−0.0601864	−	0.0245889i
$89$	0.0110750	+	0.190150i	0.00117394	+	0.0201558i	0.998844	−	0.0480640i	$-0.0153051\pi$
$89$	0.0110750	+	0.190150i	0.00117394	+	0.0201558i	−0.997670	+	0.0682198i	$0.978268\pi$
$90$		0			0
$91$	−8.01378	+	4.02467i	−0.840072	+	0.421900i
$92$	−6.10079	−	8.89517i	−0.636052	−	0.927386i
$93$		0			0
$94$	2.90883	+	0.571276i	0.300023	+	0.0589226i
$95$	1.80547	−	0.996214i	0.185237	−	0.102209i
$96$		0			0
$97$	14.0870	−	6.40332i	1.43032	−	0.650159i	0.459106	−	0.888381i	$-0.348170\pi$
$97$	14.0870	−	6.40332i	1.43032	−	0.650159i	0.971211	+	0.238223i	$0.0765648\pi$
$98$	1.60259	−	0.187316i	0.161886	−	0.0189217i
$99$		0			0
$100$	3.51717	+	8.15371i	0.351717	+	0.815371i
$101$	−2.39751	+	11.0681i	−0.238561	+	1.10132i	0.688156	+	0.725563i	$0.258420\pi$
$101$	−2.39751	+	11.0681i	−0.238561	+	1.10132i	−0.926717	+	0.375759i	$0.877382\pi$
$102$		0			0
$103$	−1.70326	+	2.48341i	−0.167827	+	0.244697i	−0.899462	−	0.436999i	$-0.856041\pi$
$103$	−1.70326	+	2.48341i	−0.167827	+	0.244697i	0.731635	+	0.681696i	$0.238757\pi$
$104$	0.361043	−	2.64331i	0.0354032	−	0.259197i
$105$		0			0
$106$	2.10761	−	0.413922i	0.204710	−	0.0402037i
$107$	2.52937	−	2.12240i	0.244524	−	0.205180i	−0.512286	−	0.858815i	$-0.671201\pi$
$107$	2.52937	−	2.12240i	0.244524	−	0.205180i	0.756810	+	0.653635i	$0.226757\pi$
$108$		0			0
$109$	3.88729	+	3.26182i	0.372335	+	0.312426i	0.809684	−	0.586866i	$-0.199638\pi$
$109$	3.88729	+	3.26182i	0.372335	+	0.312426i	−0.437350	+	0.899292i	$0.644083\pi$
$110$	−0.0848302	−	0.0468073i	−0.00808824	−	0.00446290i
$111$		0			0
$112$	5.96465	−	11.3236i	0.563607	−	1.06998i
$113$	3.75809	−	14.5898i	0.353532	−	1.37249i	−0.506494	−	0.862244i	$-0.669059\pi$
$113$	3.75809	−	14.5898i	0.353532	−	1.37249i	0.860026	−	0.510251i	$-0.170447\pi$
$114$		0			0
$115$	−1.62788	−	3.09046i	−0.151801	−	0.288187i
$116$	3.60051	−	0.853337i	0.334299	−	0.0792304i
$117$		0			0
$118$	−0.642265	−	2.14531i	−0.0591253	−	0.197492i
$119$	21.7664	+	6.05910i	1.99533	+	0.555437i
$120$		0			0
$121$	−10.5466	+	1.64945i	−0.958778	+	0.149950i
$122$	−0.389355	+	0.0608940i	−0.0352505	+	0.00551308i
$123$		0			0
$124$	12.4239	+	3.45844i	1.11570	+	0.310577i
$125$	1.71906	+	5.74205i	0.153757	+	0.513584i
$126$		0			0
$127$	−9.17684	+	2.17495i	−0.814313	+	0.192996i	−0.616613	−	0.787267i	$-0.711496\pi$
$127$	−9.17684	+	2.17495i	−0.814313	+	0.192996i	−0.197701	+	0.980262i	$0.563347\pi$
$128$	3.69414	+	7.01316i	0.326519	+	0.619881i
$129$		0			0
$130$	0.105715	−	0.410411i	0.00927181	−	0.0359954i
$131$	0.323128	−	0.613443i	0.0282318	−	0.0535968i	−0.870240	−	0.492628i	$-0.836036\pi$
$131$	0.323128	−	0.613443i	0.0282318	−	0.0535968i	0.898472	+	0.439031i	$0.144678\pi$
$132$		0			0
$133$	10.4072	+	5.74246i	0.902421	+	0.497935i
$134$	0.181736	+	0.152495i	0.0156996	+	0.0131736i
$135$		0			0
$136$	−5.14910	+	4.32060i	−0.441531	+	0.370489i
$137$	−20.4265	+	4.01163i	−1.74515	+	0.342737i	−0.960729	−	0.277490i	$-0.910497\pi$
$137$	−20.4265	+	4.01163i	−1.74515	+	0.342737i	−0.784423	+	0.620226i	$0.787041\pi$
$138$		0			0
$139$	1.54971	−	11.3459i	0.131445	−	0.962345i	−0.800394	−	0.599474i	$-0.795377\pi$
$139$	1.54971	−	11.3459i	0.131445	−	0.962345i	0.931839	−	0.362872i	$-0.118204\pi$
$140$	2.44195	−	3.56045i	0.206382	−	0.300913i
$141$		0			0
$142$	0.529857	−	2.44609i	0.0444646	−	0.205271i
$143$	0.563478	+	1.30629i	0.0471204	+	0.109237i
$144$		0			0
$145$	1.19017	−	0.139111i	0.0988385	−	0.0115526i
$146$	−3.14618	+	1.43011i	−0.260379	+	0.118357i
$147$		0			0
$148$	8.84485	−	4.88038i	0.727042	−	0.401165i
$149$	−10.7047	−	2.10233i	−0.876960	−	0.172229i	−0.266078	−	0.963951i	$-0.585728\pi$
$149$	−10.7047	−	2.10233i	−0.876960	−	0.172229i	−0.610881	+	0.791722i	$0.709185\pi$
$150$		0			0
$151$	−3.65809	−	5.33362i	−0.297691	−	0.434044i	0.646762	−	0.762692i	$-0.276123\pi$
$151$	−3.65809	−	5.33362i	−0.297691	−	0.434044i	−0.944452	+	0.328648i	$0.893407\pi$
$152$	−3.16003	+	1.58703i	−0.256313	+	0.128725i
$153$		0			0
$154$	−0.0324730	−	0.557540i	−0.00261675	−	0.0449278i
$155$	3.86610	+	1.57948i	0.310533	+	0.126867i
$156$		0			0
$157$	−2.17360	−	22.3466i	−0.173472	−	1.78345i	−0.528836	−	0.848724i	$-0.677371\pi$
$157$	−2.17360	−	22.3466i	−0.173472	−	1.78345i	0.355364	−	0.934728i	$-0.384357\pi$
$158$	1.82195	−	1.65333i	0.144947	−	0.131532i
$159$		0			0
$160$	0.698299	+	1.80864i	0.0552054	+	0.142985i
$161$	10.0673	−	17.4371i	0.793414	−	1.37423i
$162$		0			0
$163$	2.48880	+	4.31073i	0.194938	+	0.337642i	0.946880	−	0.321587i	$-0.104216\pi$
$163$	2.48880	+	4.31073i	0.194938	+	0.337642i	−0.751942	+	0.659229i	$0.770883\pi$
$164$	−5.45834	+	6.76728i	−0.426225	+	0.528436i
$165$		0			0
$166$	0.743196	+	3.43097i	0.0576832	+	0.266295i
$167$	−16.4767	+	11.7768i	−1.27501	+	0.911320i	−0.998761	−	0.0497672i	$-0.984152\pi$
$167$	−16.4767	+	11.7768i	−1.27501	+	0.911320i	−0.276246	+	0.961087i	$0.589090\pi$
$168$		0			0
$169$	5.35652	−	4.15162i	0.412040	−	0.319355i
$170$	−0.892122	+	0.586758i	−0.0684226	+	0.0450023i
$171$		0			0
$172$	0.420012	−	7.21133i	0.0320256	−	0.549858i
$173$	7.47798	−	15.6389i	0.568540	−	1.18900i	−0.394313	−	0.918976i	$-0.629017\pi$
$173$	7.47798	−	15.6389i	0.568540	−	1.18900i	0.962853	−	0.270025i	$-0.0870320\pi$
$174$		0			0
$175$	−10.8991	+	12.4890i	−0.823896	+	0.944080i
$176$	−1.73834	−	1.04909i	−0.131032	−	0.0790782i
$177$		0			0
$178$	0.00502332	−	0.0516442i	0.000376514	−	0.00387090i
$179$	−15.0823	−	20.2590i	−1.12730	−	1.51423i	−0.828563	−	0.559895i	$-0.810841\pi$
$179$	−15.0823	−	20.2590i	−1.12730	−	1.51423i	−0.298739	−	0.954335i	$-0.596566\pi$
$180$		0			0
$181$	7.57366	+	0.885234i	0.562946	+	0.0657990i	0.392807	−	0.919621i	$-0.371504\pi$
$181$	7.57366	+	0.885234i	0.562946	+	0.0657990i	0.170139	+	0.985420i	$0.445578\pi$
$182$	2.32629	−	0.745895i	0.172436	−	0.0552894i
$183$		0			0
$184$	2.58399	+	5.40397i	0.190495	+	0.398386i
$185$	3.02839	−	1.23723i	0.222652	−	0.0909633i
$186$		0			0
$187$	1.16038	−	3.39133i	0.0848551	−	0.247998i
$188$	19.6923	+	7.16740i	1.43621	+	0.522736i
$189$		0			0
$190$	−0.527868	+	0.192128i	−0.0382956	+	0.0139385i
$191$	−0.340376	−	17.5497i	−0.0246287	−	1.26985i	−0.784644	−	0.619946i	$-0.787154\pi$
$191$	−0.340376	−	17.5497i	−0.0246287	−	1.26985i	0.760016	−	0.649905i	$-0.225191\pi$
$192$		0			0
$193$	8.81341	+	13.9834i	0.634403	+	1.00655i	0.997207	+	0.0746839i	$0.0237948\pi$
$193$	8.81341	+	13.9834i	0.634403	+	1.00655i	−0.362804	+	0.931866i	$0.618181\pi$
$194$	−4.06100	+	1.13046i	−0.291563	+	0.0811620i
$195$		0			0
$196$	11.3976	+	0.442280i	0.814116	+	0.0315914i
$197$	16.7047	+	17.7060i	1.19016	+	1.26150i	0.957335	+	0.288980i	$0.0933162\pi$
$197$	16.7047	+	17.7060i	1.19016	+	1.26150i	0.232827	+	0.972518i	$0.425202\pi$
$198$		0			0
$199$	1.00166	+	0.237399i	0.0710061	+	0.0168287i	0.265965	−	0.963983i	$-0.414309\pi$
$199$	1.00166	+	0.237399i	0.0710061	+	0.0168287i	−0.194959	+	0.980811i	$0.562457\pi$
$200$	−1.23008	−	4.77546i	−0.0869796	−	0.337676i
$201$		0			0
$202$	1.11118	−	2.87803i	0.0781823	−	0.202497i
$203$	4.33643	+	5.37633i	0.304358	+	0.377344i
$204$		0			0
$205$	−2.01007	+	1.97146i	−0.140390	+	0.137693i
$206$	0.562961	−	0.596703i	0.0392233	−	0.0415743i
$207$		0			0
$208$	2.54719	−	8.50822i	0.176616	−	0.589939i
$209$	1.00545	−	1.59525i	0.0695483	−	0.110346i
$210$		0			0
$211$	−11.4612	−	11.2411i	−0.789022	−	0.773867i	0.189087	−	0.981960i	$-0.439447\pi$
$211$	−11.4612	−	11.2411i	−0.789022	−	0.773867i	−0.978109	+	0.208093i	$0.933274\pi$
$212$	15.1724	−	0.588760i	1.04205	−	0.0404362i
$213$		0			0
$214$	−0.770110	+	0.464764i	−0.0526437	+	0.0317706i
$215$	0.406206	−	2.30371i	0.0277030	−	0.157112i
$216$		0			0
$217$	4.18030	+	23.7077i	0.283777	+	1.60938i
$218$	−0.908947	−	1.04154i	−0.0615616	−	0.0705418i
$219$		0			0
$220$	−0.541354	−	0.419581i	−0.0364981	−	0.0282882i
$221$	15.6317	+	1.21499i	1.05150	+	0.0817290i
$222$		0			0
$223$	−6.11608	−	5.55004i	−0.409563	−	0.371658i	0.441022	−	0.897496i	$-0.354616\pi$
$223$	−6.11608	−	5.55004i	−0.409563	−	0.371658i	−0.850585	+	0.525838i	$0.823752\pi$
$224$	−6.67359	+	8.96419i	−0.445898	+	0.598945i
$225$		0			0
$226$	−1.62562	+	3.76860i	−0.108134	+	0.250684i
$227$	3.64692	+	2.60666i	0.242055	+	0.173010i	0.696049	−	0.717994i	$-0.254940\pi$
$227$	3.64692	+	2.60666i	0.242055	+	0.173010i	−0.453994	+	0.891005i	$0.650001\pi$
$228$		0			0
$229$	−0.395831	+	20.4090i	−0.0261573	+	1.34866i	0.725096	+	0.688648i	$0.241795\pi$
$229$	−0.395831	+	20.4090i	−0.0261573	+	1.34866i	−0.751253	+	0.660014i	$0.770550\pi$
$230$	0.308050	+	0.900309i	0.0203122	+	0.0593646i
$231$		0			0
$232$	−2.04870	+	0.159237i	−0.134503	+	0.0104544i
$233$	−11.5281	−	7.58212i	−0.755228	−	0.496721i	0.112567	−	0.993644i	$-0.464093\pi$
$233$	−11.5281	−	7.58212i	−0.755228	−	0.496721i	−0.867795	+	0.496923i	$0.834463\pi$
$234$		0			0
$235$	6.06449	+	3.04570i	0.395604	+	0.198680i
$236$	−2.14240	−	15.6852i	−0.139459	−	1.02102i
$237$		0			0
$238$	−5.60330	−	2.54701i	−0.363208	−	0.165098i
$239$	6.45105	+	2.06845i	0.417284	+	0.133797i	0.506549	−	0.862211i	$-0.330921\pi$
$239$	6.45105	+	2.06845i	0.417284	+	0.133797i	−0.0892652	+	0.996008i	$0.528452\pi$
$240$		0			0
$241$	−18.7775	−	2.93675i	−1.20957	−	0.189173i	−0.482597	−	0.875843i	$-0.660306\pi$
$241$	−18.7775	−	2.93675i	−1.20957	−	0.189173i	−0.726969	+	0.686670i	$0.759072\pi$
$242$	2.90800			0.186933
$243$		0			0
$244$	−2.78590			−0.178349
$245$	3.64938	+	0.570753i	0.233150	+	0.0364641i
$246$		0			0
$247$	7.85451	+	2.51845i	0.499770	+	0.160245i
$248$	−6.51981	−	2.96362i	−0.414008	−	0.188190i
$249$		0			0
$250$	−0.220973	−	1.61781i	−0.0139756	−	0.102319i
$251$	−7.49253	−	3.76289i	−0.472924	−	0.237512i	0.196340	−	0.980536i	$-0.437094\pi$
$251$	−7.49253	−	3.76289i	−0.472924	−	0.237512i	−0.669264	+	0.743024i	$0.733391\pi$
$252$		0			0
$253$	−2.66870	−	1.75523i	−0.167779	−	0.110350i
$254$	2.56146	−	0.199093i	0.160721	−	0.0124922i
$255$		0			0
$256$	3.36289	+	9.82843i	0.210181	+	0.614277i
$257$	0.346783	−	17.8801i	0.0216317	−	1.11533i	−0.819025	−	0.573758i	$-0.805485\pi$
$257$	0.346783	−	17.8801i	0.0216317	−	1.11533i	0.840656	−	0.541569i	$-0.182169\pi$
$258$		0			0
$259$	15.3413	+	10.9653i	0.953261	+	0.681350i
$260$	1.18665	−	2.75097i	0.0735931	−	0.170608i
$261$		0			0
$262$	−0.112791	+	0.151504i	−0.00696823	+	0.00935996i
$263$	0.0664281	+	0.0602803i	0.00409613	+	0.00371704i	0.674053	−	0.738683i	$-0.264552\pi$
$263$	0.0664281	+	0.0602803i	0.00409613	+	0.00371704i	−0.669957	+	0.742400i	$0.733688\pi$
$264$		0			0
$265$	4.90230	+	0.381037i	0.301146	+	0.0234069i
$266$	−2.55934	−	1.98364i	−0.156923	−	0.121625i
$267$		0			0
$268$	1.10273	+	1.26359i	0.0673602	+	0.0771862i
$269$	0.913509	+	5.18077i	0.0556976	+	0.315877i	0.999909	−	0.0134621i	$-0.00428525\pi$
$269$	0.913509	+	5.18077i	0.0556976	+	0.315877i	−0.944212	+	0.329339i	$0.893174\pi$
$270$		0			0
$271$	3.81482	−	21.6349i	0.231734	−	1.31423i	−0.617650	−	0.786453i	$-0.711915\pi$
$271$	3.81482	−	21.6349i	0.231734	−	1.31423i	0.849384	−	0.527776i	$-0.176974\pi$
$272$	−19.1581	+	11.5620i	−1.16163	+	0.701047i
$273$		0			0
$274$	5.66657	−	0.219889i	0.342330	−	0.0132840i
$275$	1.87739	+	1.84133i	0.113211	+	0.111036i
$276$		0			0
$277$	2.05530	−	3.26095i	0.123491	−	0.195932i	−0.778550	−	0.627583i	$-0.784044\pi$
$277$	2.05530	−	3.26095i	0.123491	−	0.195932i	0.902040	+	0.431652i	$0.142069\pi$
$278$	−0.894688	+	2.98847i	−0.0536598	+	0.179236i
$279$		0			0
$280$	−1.64533	+	1.74395i	−0.0983273	+	0.104221i
$281$	−0.334159	+	0.327741i	−0.0199343	+	0.0195514i	−0.710116	−	0.704084i	$-0.751358\pi$
$281$	−0.334159	+	0.327741i	−0.0199343	+	0.0195514i	0.690182	+	0.723636i	$0.257530\pi$
$282$		0			0
$283$	9.74101	+	12.0770i	0.579043	+	0.717901i	0.980178	−	0.198118i	$-0.0634829\pi$
$283$	9.74101	+	12.0770i	0.579043	+	0.717901i	−0.401135	+	0.916019i	$0.631384\pi$
$284$	6.37264	−	16.5056i	0.378147	−	0.979425i
$285$		0			0
$286$	−0.0966715	−	0.375302i	−0.00571630	−	0.0221921i
$287$	−15.7919	−	3.74275i	−0.932167	−	0.220928i
$288$		0			0
$289$	−15.4424	−	16.3680i	−0.908378	−	0.962824i
$290$	−0.326186	−	0.0126575i	−0.0191543	−	0.000743275i
$291$		0			0
$292$	−23.5361	+	6.55173i	−1.37735	+	0.383411i
$293$	1.37130	+	2.17572i	0.0801124	+	0.127107i	0.883652	−	0.468144i	$-0.155077\pi$
$293$	1.37130	+	2.17572i	0.0801124	+	0.127107i	−0.803540	+	0.595251i	$0.797053\pi$
$294$		0			0
$295$	−0.0994114	−	5.12562i	−0.00578795	−	0.298425i
$296$	−5.27163	+	1.91872i	−0.306407	+	0.111523i
$297$		0			0
$298$	2.79262	+	1.01643i	0.161772	+	0.0588803i
$299$	4.52324	−	13.2197i	0.261586	−	0.764514i
$300$		0			0
$301$	12.4825	−	5.09968i	0.719482	−	0.293941i
$302$	0.760048	+	1.58951i	0.0437358	+	0.0914657i
$303$		0			0
$304$	−11.2098	+	3.59429i	−0.642928	+	0.206147i
$305$	−0.896076	−	0.104736i	−0.0513092	−	0.00599718i
$306$		0			0
$307$	−1.93706	−	2.60193i	−0.110554	−	0.148500i	0.743402	−	0.668845i	$-0.233211\pi$
$307$	−1.93706	−	2.60193i	−0.110554	−	0.148500i	−0.853956	+	0.520345i	$0.825803\pi$
$308$	0.382216	−	3.92952i	0.0217787	−	0.223905i
$309$		0			0
$310$	−0.974060	−	0.587848i	−0.0553229	−	0.0333875i
$311$	−16.1655	+	18.5236i	−0.916663	+	1.05038i	0.0818921	+	0.996641i	$0.473904\pi$
$311$	−16.1655	+	18.5236i	−0.916663	+	1.05038i	−0.998555	+	0.0537380i	$0.982886\pi$
$312$		0			0
$313$	8.00531	−	16.7417i	0.452487	−	0.946295i	−0.541896	−	0.840446i	$-0.682293\pi$
$313$	8.00531	−	16.7417i	0.452487	−	0.946295i	0.994382	−	0.105850i	$-0.0337562\pi$
$314$	−0.355634	+	6.10599i	−0.0200696	+	0.344581i
$315$		0			0
$316$	14.5311	−	9.55727i	0.817440	−	0.537639i
$317$	−13.9030	+	10.7756i	−0.780869	+	0.605219i	−0.923076	−	0.384618i	$-0.874333\pi$
$317$	−13.9030	+	10.7756i	−0.780869	+	0.605219i	0.142207	+	0.989837i	$0.454580\pi$
$318$		0			0
$319$	0.891465	−	0.637181i	0.0499124	−	0.0356753i
$320$	0.828283	+	3.82378i	0.0463024	+	0.213756i
$321$		0			0
$322$	−3.44356	+	4.26935i	−0.191902	+	0.237921i
$323$	−10.3909	−	17.9976i	−0.578167	−	1.00141i
$324$		0			0
$325$	−5.75136	+	9.96165i	−0.319028	+	0.552573i
$326$	−0.488397	−	1.26498i	−0.0270498	−	0.0700607i
$327$		0			0
$328$	3.57549	−	3.24458i	0.197423	−	0.179152i
$329$	3.78708	+	38.9346i	0.208789	+	2.14654i
$330$		0			0
$331$	−12.7529	−	5.21014i	−0.700963	−	0.286375i	−0.000435194	−	1.00000i	$-0.500139\pi$
$331$	−12.7529	−	5.21014i	−0.700963	−	0.286375i	−0.700528	+	0.713625i	$0.747052\pi$
$332$	1.44297	+	24.7749i	0.0791935	+	1.35970i
$333$		0			0
$334$	4.93037	−	2.47613i	0.269778	−	0.135488i
$335$	0.307186	+	0.447888i	0.0167833	+	0.0244707i
$336$		0			0
$337$	−16.9071	−	3.32045i	−0.920988	−	0.180876i	−0.290321	−	0.956929i	$-0.593762\pi$
$337$	−16.9071	−	3.32045i	−0.920988	−	0.180876i	−0.630668	+	0.776053i	$0.717219\pi$
$338$	−1.61644	+	0.891915i	−0.0879229	+	0.0485138i
$339$		0			0
$340$	−6.87182	+	3.12362i	−0.372677	+	0.169402i
$341$	3.79321	−	0.443363i	0.205414	−	0.0240094i
$342$		0			0
$343$	−1.53366	−	3.55541i	−0.0828096	−	0.191974i
$344$	−0.849246	+	3.92055i	−0.0457882	+	0.211382i
$345$		0			0
$346$	−2.67097	+	3.89436i	−0.143592	+	0.209362i
$347$	−0.846889	+	6.20032i	−0.0454634	+	0.332851i	0.953991	+	0.299834i	$0.0969313\pi$
$347$	−0.846889	+	6.20032i	−0.0454634	+	0.332851i	−0.999455	+	0.0330169i	$0.989488\pi$
$348$		0			0
$349$	−26.7423	+	5.25202i	−1.43148	+	0.281134i	−0.847571	−	0.530682i	$-0.821936\pi$
$349$	−26.7423	+	5.25202i	−1.43148	+	0.281134i	−0.583913	+	0.811817i	$0.698479\pi$
$350$	3.45916	−	2.90258i	0.184900	−	0.155150i
$351$		0			0
$352$	1.35813	+	1.13960i	0.0723884	+	0.0607411i
$353$	25.0555	+	13.8251i	1.33357	+	0.735834i	0.979891	−	0.199532i	$-0.0639422\pi$
$353$	25.0555	+	13.8251i	1.33357	+	0.735834i	0.353681	+	0.935366i	$0.384930\pi$
$354$		0			0
$355$	2.67027	−	5.06938i	0.141723	−	0.269055i
$356$	0.0914972	−	0.355214i	0.00484934	−	0.0188263i
$357$		0			0
$358$	3.20656	+	6.08750i	0.169472	+	0.321735i
$359$	−16.9848	+	4.02548i	−0.896425	+	0.212457i	−0.652905	−	0.757439i	$-0.726450\pi$
$359$	−16.9848	+	4.02548i	−0.896425	+	0.212457i	−0.243519	+	0.969896i	$0.578302\pi$
$360$		0			0
$361$	2.31363	+	7.72808i	0.121770	+	0.406741i
$362$	−2.00116	−	0.557061i	−0.105179	−	0.0292785i
$363$		0			0
$364$	17.0624	−	2.66851i	0.894311	−	0.139868i
$365$	−7.81663	+	1.22250i	−0.409141	+	0.0639885i
$366$		0			0
$367$	−23.0437	−	6.41466i	−1.20287	−	0.334843i	−0.391945	−	0.919989i	$-0.628198\pi$
$367$	−23.0437	−	6.41466i	−1.20287	−	0.334843i	−0.810928	+	0.585146i	$0.801037\pi$
$368$	5.71908	+	19.1031i	0.298128	+	0.995816i
$369$		0			0
$370$	−0.867160	+	0.205521i	−0.0450815	+	0.0106845i
$371$	13.2093	+	25.0772i	0.685792	+	1.30194i
$372$		0			0
$373$	−1.54740	+	6.00737i	−0.0801213	+	0.311050i	−0.995880	−	0.0906783i	$-0.971097\pi$
$373$	−1.54740	+	6.00737i	−0.0801213	+	0.311050i	0.915759	+	0.401728i	$0.131590\pi$
$374$	−0.455064	+	0.863918i	−0.0235308	+	0.0446721i
$375$		0			0
$376$	−10.1894	−	5.62227i	−0.525478	−	0.289947i
$377$	3.67177	+	3.08098i	0.189106	+	0.158679i
$378$		0			0
$379$	14.1333	−	11.8592i	0.725978	−	0.609168i	−0.203054	−	0.979168i	$-0.565087\pi$
$379$	14.1333	−	11.8592i	0.725978	−	0.609168i	0.929032	+	0.370000i	$0.120642\pi$
$380$	−3.89668	+	0.765283i	−0.199895	+	0.0392582i
$381$		0			0
$382$	−0.647120	+	4.73776i	−0.0331095	+	0.242405i
$383$	−20.1573	+	29.3901i	−1.02999	+	1.50177i	−0.174021	+	0.984742i	$0.555676\pi$
$383$	−20.1573	+	29.3901i	−1.02999	+	1.50177i	−0.855971	+	0.517024i	$0.827040\pi$
$384$		0			0
$385$	0.270669	−	1.24955i	0.0137946	−	0.0636828i
$386$	−1.78348	−	4.13458i	−0.0907768	−	0.210444i
$387$		0			0
$388$	−29.5982	+	3.45954i	−1.50262	+	0.175631i
$389$	−5.56723	+	2.53062i	−0.282270	+	0.128307i	−0.549942	−	0.835203i	$-0.685350\pi$
$389$	−5.56723	+	2.53062i	−0.282270	+	0.128307i	0.267673	+	0.963510i	$0.413745\pi$
$390$		0			0
$391$	−30.8221	+	17.0069i	−1.55874	+	0.860077i
$392$	−6.21552	−	1.22069i	−0.313931	−	0.0616540i
$393$		0			0
$394$	−3.75070	−	5.46866i	−0.188958	−	0.275507i
$395$	5.03319	−	2.52776i	0.253247	−	0.127186i
$396$		0			0
$397$	−0.965187	−	16.5716i	−0.0484414	−	0.831706i	−0.931792	−	0.362993i	$-0.881755\pi$
$397$	−0.965187	−	16.5716i	−0.0484414	−	0.831706i	0.883351	−	0.468713i	$-0.155282\pi$
$398$	−0.259601	−	0.106059i	−0.0130126	−	0.00531624i
$399$		0			0
$400$	−1.58930	−	16.3394i	−0.0794649	−	0.816970i
$401$	3.44515	−	3.12631i	0.172043	−	0.156121i	−0.581437	−	0.813591i	$-0.697509\pi$
$401$	3.44515	−	3.12631i	0.172043	−	0.156121i	0.753480	+	0.657471i	$0.228374\pi$
$402$		0			0
$403$	6.01690	+	15.5842i	0.299723	+	0.776303i
$404$	10.9046	−	18.8874i	0.542525	−	0.939681i
$405$		0			0
$406$	−0.940823	−	1.62955i	−0.0466923	−	0.0808734i
$407$	1.87812	−	2.32850i	0.0930948	−	0.115419i
$408$		0			0
$409$	3.69831	+	17.0733i	0.182869	+	0.844219i	0.972914	+	0.231169i	$0.0742551\pi$
$409$	3.69831	+	17.0733i	0.182869	+	0.844219i	−0.790044	+	0.613050i	$0.789942\pi$
$410$	0.623989	−	0.446001i	0.0308166	−	0.0220264i
$411$		0			0
$412$	4.58371	−	3.55264i	0.225823	−	0.175026i
$413$	24.6896	−	16.2386i	1.21490	−	0.799050i
$414$		0			0
$415$	−0.467287	+	8.02301i	−0.0229382	+	0.393834i
$416$	−3.34545	+	6.99643i	−0.164024	+	0.343028i
$417$		0			0
$418$	−0.337763	+	0.387033i	−0.0165205	+	0.0189304i
$419$	−13.0358	−	7.86714i	−0.636840	−	0.384335i	0.161215	−	0.986919i	$-0.448459\pi$
$419$	−13.0358	−	7.86714i	−0.636840	−	0.384335i	−0.798055	+	0.602584i	$0.794138\pi$
$420$		0			0
$421$	−3.04350	+	31.2900i	−0.148331	+	1.52498i	0.565551	+	0.824713i	$0.308664\pi$
$421$	−3.04350	+	31.2900i	−0.148331	+	1.52498i	−0.713882	+	0.700266i	$0.753065\pi$
$422$	2.61156	+	3.50793i	0.127129	+	0.170764i
$423$		0			0
$424$	−8.37509	−	0.978908i	−0.406730	−	0.0475400i
$425$	27.5973	−	8.84872i	1.33867	−	0.429226i
$426$		0			0
$427$	−2.24338	−	4.69164i	−0.108565	−	0.227044i
$428$	−5.88639	+	2.40485i	−0.284529	+	0.116243i
$429$		0			0
$430$	−0.206300	+	0.602935i	−0.00994868	+	0.0290761i
$431$	−3.63913	−	1.32454i	−0.175291	−	0.0638007i	0.252884	−	0.967497i	$-0.418621\pi$
$431$	−3.63913	−	1.32454i	−0.175291	−	0.0638007i	−0.428175	+	0.903696i	$0.640843\pi$
$432$		0			0
$433$	23.7066	−	8.62851i	1.13927	−	0.414660i	0.297619	−	0.954685i	$-0.403807\pi$
$433$	23.7066	−	8.62851i	1.13927	−	0.414660i	0.841649	+	0.540025i	$0.181585\pi$
$434$	−0.127169	−	6.55679i	−0.00610430	−	0.314736i
$435$		0			0
$436$	−5.21069	−	8.26732i	−0.249547	−	0.395933i
$437$	−17.8413	+	4.96647i	−0.853465	+	0.237578i
$438$		0			0
$439$	−7.37917	−	0.286345i	−0.352189	−	0.0136665i	−0.137926	−	0.990443i	$-0.544044\pi$
$439$	−7.37917	−	0.286345i	−0.352189	−	0.0136665i	−0.214263	+	0.976776i	$0.568735\pi$
$440$	0.261017	+	0.276662i	0.0124435	+	0.0131894i
$441$		0			0
$442$	−4.15606	−	0.985004i	−0.197684	−	0.0468519i
$443$	9.34728	+	36.2884i	0.444103	+	1.72411i	0.663229	+	0.748416i	$0.269185\pi$
$443$	9.34728	+	36.2884i	0.444103	+	1.72411i	−0.219127	+	0.975696i	$0.570321\pi$
$444$		0			0
$445$	0.0427840	−	0.110813i	0.00202816	−	0.00525306i
$446$	1.41250	+	1.75122i	0.0668837	+	0.0829227i
$447$		0			0
$448$	−16.1009	+	15.7917i	−0.760698	+	0.746087i
$449$	6.92096	−	7.33579i	0.326620	−	0.346197i	−0.543167	−	0.839625i	$-0.682775\pi$
$449$	6.92096	−	7.33579i	0.326620	−	0.346197i	0.869787	+	0.493428i	$0.164256\pi$
$450$		0			0
$451$	−0.738418	+	2.46649i	−0.0347707	+	0.116142i
$452$	−15.4704	+	24.5455i	−0.727667	+	1.15452i
$453$		0			0
$454$	−0.871831	−	0.855086i	−0.0409171	−	0.0401312i
$455$	5.58838	−	0.216854i	0.261987	−	0.0101663i
$456$		0			0
$457$	0.732770	−	0.442229i	0.0342775	−	0.0206866i	−0.499457	−	0.866339i	$-0.666467\pi$
$457$	0.732770	−	0.442229i	0.0342775	−	0.0206866i	0.533735	+	0.845652i	$0.320788\pi$
$458$	0.965625	−	5.47633i	0.0451207	−	0.255892i
$459$		0			0
$460$	1.16809	+	6.62456i	0.0544624	+	0.308872i
$461$	19.2320	+	22.0374i	0.895724	+	1.02639i	0.999495	+	0.0317844i	$0.0101190\pi$
$461$	19.2320	+	22.0374i	0.895724	+	1.02639i	−0.103771	+	0.994601i	$0.533091\pi$
$462$		0			0
$463$	16.4665	+	12.7625i	0.765263	+	0.593124i	0.918664	−	0.395040i	$-0.129269\pi$
$463$	16.4665	+	12.7625i	0.765263	+	0.593124i	−0.153401	+	0.988164i	$0.549022\pi$
$464$	−6.82015	−	0.530104i	−0.316618	−	0.0246095i
$465$		0			0
$466$	2.78357	+	2.52596i	0.128946	+	0.117013i
$467$	−7.89341	+	10.6027i	−0.365264	+	0.490634i	−0.946321	−	0.323228i	$-0.895232\pi$
$467$	−7.89341	+	10.6027i	−0.365264	+	0.490634i	0.581057	+	0.813863i	$0.302639\pi$
$468$		0			0
$469$	−1.23998	+	2.87460i	−0.0572569	+	0.132737i
$470$	−1.50403	−	1.07502i	−0.0693757	−	0.0495868i
$471$		0			0
$472$	−0.170477	+	8.78972i	−0.00784682	+	0.404580i
$473$	−0.692510	−	2.02394i	−0.0318417	−	0.0930607i
$474$		0			0
$475$	15.2007	−	1.18149i	0.697457	−	0.0542107i
$476$	−36.3532	−	23.9099i	−1.66625	−	1.09591i
$477$		0			0
$478$	−1.64921	−	0.828262i	−0.0754329	−	0.0378838i
$479$	−1.77843	−	13.0204i	−0.0812586	−	0.594918i	−0.985724	−	0.168371i	$-0.946149\pi$
$479$	−1.77843	−	13.0204i	−0.0812586	−	0.594918i	0.904465	−	0.426548i	$-0.140270\pi$
$480$		0			0
$481$	11.9127	+	5.41498i	0.543172	+	0.246902i
$482$	4.93028	+	1.58083i	0.224568	+	0.0720048i
$483$		0			0
$484$	20.3105	+	3.17650i	0.923202	+	0.144386i
$485$	−9.65023			−0.438194
$486$		0			0
$487$	−7.94942			−0.360223			−0.180111	−	0.983646i	$-0.557646\pi$
$487$	−7.94942			−0.360223			−0.180111	+	0.983646i	$0.557646\pi$
$488$	1.52852	+	0.239057i	0.0691931	+	0.0108216i
$489$		0			0
$490$	−0.958192	−	0.307232i	−0.0432867	−	0.0138793i
$491$	−35.0142	−	15.9159i	−1.58017	−	0.718274i	−0.584512	−	0.811385i	$-0.698714\pi$
$491$	−35.0142	−	15.9159i	−1.58017	−	0.718274i	−0.995656	+	0.0931109i	$0.970319\pi$
$492$		0			0
$493$	−1.63431	−	11.9653i	−0.0736058	−	0.538890i
$494$	−2.00800	−	1.00846i	−0.0903442	−	0.0453725i
$495$		0			0
$496$	−19.9194	−	13.1012i	−0.894408	−	0.588262i
$497$	32.9280	−	2.55937i	1.47702	−	0.114803i
$498$		0			0
$499$	−7.76971	−	22.7078i	−0.347820	−	1.01654i	−0.971943	−	0.235216i	$-0.924420\pi$
$499$	−7.76971	−	22.7078i	−0.347820	−	1.01654i	0.624123	−	0.781326i	$-0.285456\pi$
$500$	0.223832	−	11.5407i	0.0100101	−	0.516117i
$501$		0			0
$502$	1.85819	+	1.32816i	0.0829352	+	0.0592785i
$503$	3.15916	−	7.32376i	0.140860	−	0.326551i	−0.833153	−	0.553043i	$-0.813467\pi$
$503$	3.15916	−	7.32376i	0.140860	−	0.326551i	0.974013	+	0.226492i	$0.0727258\pi$
$504$		0			0
$505$	4.21750	−	5.66509i	0.187676	−	0.252093i
$506$	0.644385	+	0.584748i	0.0286464	+	0.0259952i
$507$		0			0
$508$	18.1076	+	1.40743i	0.803395	+	0.0624448i
$509$	−3.09794	−	2.40108i	−0.137314	−	0.106426i	0.541628	−	0.840618i	$-0.317808\pi$
$509$	−3.09794	−	2.40108i	−0.137314	−	0.106426i	−0.678942	+	0.734192i	$0.737561\pi$
$510$		0			0
$511$	−29.9863	−	34.3604i	−1.32651	−	1.52002i
$512$	−3.24428	−	18.3992i	−0.143378	−	0.813137i
$513$		0			0
$514$	−0.845973	+	4.79775i	−0.0373143	+	0.211620i
$515$	1.60790	−	0.970370i	0.0708523	−	0.0427596i
$516$		0			0
$517$	6.20112	−	0.240632i	0.272725	−	0.0105830i
$518$	−3.66748	−	3.59704i	−0.161140	−	0.158045i
$519$		0			0
$520$	−0.887133	+	1.40753i	−0.0389034	+	0.0617244i
$521$	5.15555	−	17.2207i	0.225869	−	0.754454i	−0.767659	−	0.640859i	$-0.778578\pi$
$521$	5.15555	−	17.2207i	0.225869	−	0.754454i	0.993527	−	0.113595i	$-0.0362365\pi$
$522$		0			0
$523$	11.8103	−	12.5182i	0.516430	−	0.547384i	−0.415703	−	0.909501i	$-0.636464\pi$
$523$	11.8103	−	12.5182i	0.516430	−	0.547384i	0.932133	+	0.362116i	$0.117946\pi$
$524$	−0.953261	+	0.934952i	−0.0416434	+	0.0408436i
$525$		0			0
$526$	−0.0153415	−	0.0190204i	−0.000668919	−	0.000829330i
$527$	15.1596	−	39.2644i	0.660364	−	1.71039i
$528$		0			0
$529$	2.08803	+	8.10622i	0.0907838	+	0.352444i
$530$	−1.30339	−	0.308910i	−0.0566159	−	0.0134182i
$531$		0			0
$532$	−15.7085	−	16.6501i	−0.681051	−	0.721872i
$533$	−11.2537	−	0.436694i	−0.487451	−	0.0189153i
$534$		0			0
$535$	−1.98375	+	0.552214i	−0.0857649	+	0.0238743i
$536$	−0.496602	−	0.787913i	−0.0214499	−	0.0340327i
$537$		0			0
$538$	−0.0277898	−	1.43284i	−0.00119810	−	0.0617739i
$539$	3.17406	−	1.15526i	0.136716	−	0.0497606i
$540$		0			0
$541$	32.2402	+	11.7345i	1.38611	+	0.504504i	0.924026	−	0.382330i	$-0.124878\pi$
$541$	32.2402	+	11.7345i	1.38611	+	0.504504i	0.462088	+	0.886834i	$0.347101\pi$
$542$	−1.93744	+	5.66238i	−0.0832202	+	0.243220i
$543$		0			0
$544$	18.0878	−	7.38969i	0.775509	−	0.316830i
$545$	−1.36519	−	2.85505i	−0.0584783	−	0.122297i
$546$		0			0
$547$	16.5484	−	5.30603i	0.707558	−	0.226869i	0.0703070	−	0.997525i	$-0.477602\pi$
$547$	16.5484	−	5.30603i	0.707558	−	0.226869i	0.637251	+	0.770656i	$0.280071\pi$
$548$	39.8174	+	4.65399i	1.70092	+	0.198809i
$549$		0			0
$550$	−0.427783	−	0.574612i	−0.0182407	−	0.0245015i
$551$	0.615060	−	6.32336i	0.0262024	−	0.269384i
$552$		0			0
$553$	27.7964	+	16.7752i	1.18202	+	0.713355i
$554$	−0.690441	+	0.791157i	−0.0293340	+	0.0336130i
$555$		0			0
$556$	−9.51321	+	19.8952i	−0.403450	+	0.843744i
$557$	0.615660	−	10.5705i	0.0260863	−	0.447885i	−0.959823	−	0.280606i	$-0.909465\pi$
$557$	0.615660	−	10.5705i	0.0260863	−	0.447885i	0.985909	−	0.167280i	$-0.0534983\pi$
$558$		0			0
$559$	7.81773	−	5.14180i	0.330655	−	0.217475i
$560$	−6.30864	+	4.88956i	−0.266589	+	0.206622i
$561$		0			0
$562$	0.103733	−	0.0741442i	0.00437573	−	0.00312758i
$563$	6.87907	+	31.7573i	0.289918	+	1.33841i	0.857241	+	0.514916i	$0.172177\pi$
$563$	6.87907	+	31.7573i	0.289918	+	1.33841i	−0.567322	+	0.823496i	$0.692021\pi$
$564$		0			0
$565$	−5.89879	+	7.31336i	−0.248164	+	0.307675i
$566$	−2.11339	−	3.66050i	−0.0888325	−	0.153862i
$567$		0			0
$568$	−4.91277	+	8.50917i	−0.206135	+	0.357037i
$569$	−10.8363	−	28.0667i	−0.454281	−	1.17662i	−0.951133	−	0.308782i	$-0.900079\pi$
$569$	−10.8363	−	28.0667i	−0.454281	−	1.17662i	0.496852	−	0.867835i	$-0.334489\pi$
$570$		0			0
$571$	−27.4158	+	24.8785i	−1.14732	+	1.04113i	−0.148683	+	0.988885i	$0.547503\pi$
$571$	−27.4158	+	24.8785i	−1.14732	+	1.04113i	−0.998634	+	0.0522497i	$0.983361\pi$
$572$	−0.265233	−	2.72683i	−0.0110899	−	0.114015i
$573$		0			0
$574$	4.09278	+	1.67209i	0.170830	+	0.0697915i
$575$	−1.50168	−	25.7828i	−0.0626242	−	1.07522i
$576$		0			0
$577$	8.90642	−	4.47297i	0.370779	−	0.186212i	−0.253646	−	0.967297i	$-0.581630\pi$
$577$	8.90642	−	4.47297i	0.370779	−	0.186212i	0.624425	+	0.781085i	$0.285333\pi$
$578$	3.46728	+	5.05541i	0.144220	+	0.210278i
$579$		0			0
$580$	−2.26437	−	0.444708i	−0.0940229	−	0.0184655i
$581$	−40.5605	+	22.3803i	−1.68273	+	0.928493i
$582$		0			0
$583$	4.09340	−	1.86068i	0.169531	−	0.0770614i
$584$	13.4756	−	1.57507i	0.557625	−	0.0651770i
$585$		0			0
$586$	−0.277497	−	0.643310i	−0.0114633	−	0.0265749i
$587$	0.393361	−	1.81596i	0.0162357	−	0.0749525i	−0.968497	−	0.249024i	$-0.919890\pi$
$587$	0.393361	−	1.81596i	0.0162357	−	0.0749525i	0.984733	+	0.174072i	$0.0556925\pi$
$588$		0			0
$589$	12.5240	−	18.2604i	0.516042	−	0.752407i
$590$	−0.189000	+	1.38373i	−0.00778102	+	0.0569671i
$591$		0			0
$592$	−18.3256	+	3.59903i	−0.753177	+	0.147919i
$593$	24.8964	−	20.8906i	1.02237	−	0.857872i	0.0324484	−	0.999473i	$-0.489670\pi$
$593$	24.8964	−	20.8906i	1.02237	−	0.857872i	0.989924	+	0.141601i	$0.0452251\pi$
$594$		0			0
$595$	−10.7940	−	9.05723i	−0.442510	−	0.371310i
$596$	18.3943	+	10.1496i	0.753462	+	0.415743i
$597$		0			0
$598$	−1.77388	+	3.36762i	−0.0725393	+	0.137712i
$599$	3.07338	−	11.9316i	0.125575	−	0.487511i	−0.874423	−	0.485165i	$-0.838759\pi$
$599$	3.07338	−	11.9316i	0.125575	−	0.487511i	0.999997	−	0.00234582i	$-0.000746699\pi$
$600$		0			0
$601$	−15.5482	−	29.5175i	−0.634223	−	1.20404i	−0.965474	−	0.260500i	$-0.916113\pi$
$601$	−15.5482	−	29.5175i	−0.634223	−	1.20404i	0.331251	−	0.943543i	$-0.392529\pi$
$602$	−3.57429	+	0.847123i	−0.145677	+	0.0345261i
$603$		0			0
$604$	3.57217	+	11.9319i	0.145349	+	0.485501i
$605$	6.41337	+	1.78528i	0.260740	+	0.0725820i
$606$		0			0
$607$	36.4193	−	5.69587i	1.47821	−	0.231188i	0.636569	−	0.771220i	$-0.280353\pi$
$607$	36.4193	−	5.69587i	1.47821	−	0.231188i	0.841645	+	0.540032i	$0.181588\pi$
$608$	10.1558	−	1.58833i	0.411871	−	0.0644155i
$609$		0			0
$610$	0.236767	+	0.0659085i	0.00958640	+	0.00266856i
$611$	7.78545	+	26.0052i	0.314966	+	1.05206i
$612$		0			0
$613$	35.6746	−	8.45504i	1.44088	−	0.341496i	0.565430	−	0.824796i	$-0.308710\pi$
$613$	35.6746	−	8.45504i	1.44088	−	0.341496i	0.875455	+	0.483300i	$0.160562\pi$
$614$	0.411828	+	0.781836i	0.0166200	+	0.0315524i
$615$		0			0
$616$	−0.546898	+	2.12319i	−0.0220351	+	0.0855457i
$617$	20.7275	−	39.3501i	0.834457	−	1.58418i	0.0230208	−	0.999735i	$-0.492672\pi$
$617$	20.7275	−	39.3501i	0.834457	−	1.58418i	0.811436	−	0.584442i	$-0.198686\pi$
$618$		0			0
$619$	12.6054	+	6.95538i	0.506655	+	0.279560i	0.715777	−	0.698329i	$-0.246073\pi$
$619$	12.6054	+	6.95538i	0.506655	+	0.279560i	−0.209122	+	0.977890i	$0.567061\pi$
$620$	−6.16104	−	5.16973i	−0.247433	−	0.207621i
$621$		0			0
$622$	5.13062	−	4.30510i	0.205719	−	0.172619i
$623$	0.671881	−	0.131953i	0.0269184	−	0.00528659i
$624$		0			0
$625$	−2.61424	+	19.1396i	−0.104570	+	0.765586i
$626$	−2.85932	+	4.16898i	−0.114281	+	0.166626i
$627$		0			0
$628$	−9.15363	+	42.2579i	−0.365270	+	1.68627i
$629$	−13.0585	−	30.2730i	−0.520677	−	1.20707i
$630$		0			0
$631$	−2.07377	+	0.242389i	−0.0825557	+	0.00964937i	−0.157270	−	0.987556i	$-0.550269\pi$
$631$	−2.07377	+	0.242389i	−0.0825557	+	0.00964937i	0.0747148	+	0.997205i	$0.476195\pi$
$632$	−8.79281	+	3.99682i	−0.349759	+	0.158985i
$633$		0			0
$634$	4.19552	−	2.31499i	0.166625	−	0.0919400i
$635$	5.77134	+	1.13345i	0.229029	+	0.0449797i
$636$		0			0
$637$	8.35692	+	12.1847i	0.331113	+	0.482775i
$638$	−0.266756	+	0.133970i	−0.0105610	+	0.00530391i
$639$		0			0
$640$	−0.287430	−	4.93498i	−0.0113617	−	0.195072i
$641$	2.24184	+	0.915892i	0.0885473	+	0.0361756i	0.422041	−	0.906577i	$-0.361314\pi$
$641$	2.24184	+	0.915892i	0.0885473	+	0.0361756i	−0.333493	+	0.942752i	$0.608227\pi$
$642$		0			0
$643$	2.33172	+	23.9722i	0.0919542	+	0.945372i	0.921874	+	0.387489i	$0.126658\pi$
$643$	2.33172	+	23.9722i	0.0919542	+	0.945372i	−0.829920	+	0.557882i	$0.811614\pi$
$644$	−28.7146	+	26.0571i	−1.13151	+	1.02679i
$645$		0			0
$646$	2.03909	+	5.28138i	0.0802271	+	0.207793i
$647$	−19.1318	+	33.1372i	−0.752147	+	1.30276i	0.194633	+	0.980876i	$0.437648\pi$
$647$	−19.1318	+	33.1372i	−0.752147	+	1.30276i	−0.946780	+	0.321881i	$0.895685\pi$
$648$		0			0
$649$	−2.34402	−	4.05995i	−0.0920106	−	0.159367i
$650$	1.96728	−	2.43904i	0.0771630	−	0.0956672i
$651$		0			0
$652$	−2.02935	−	9.36854i	−0.0794756	−	0.366900i
$653$	2.85293	−	2.03915i	0.111644	−	0.0797982i	−0.524300	−	0.851534i	$-0.675673\pi$
$653$	2.85293	−	2.03915i	0.111644	−	0.0797982i	0.635943	+	0.771736i	$0.280611\pi$
$654$		0			0
$655$	−0.341763	+	0.264886i	−0.0133538	+	0.0103500i
$656$	13.4289	−	8.83235i	0.524312	−	0.344845i
$657$		0			0
$658$	0.619623	−	10.6385i	0.0241554	−	0.414733i
$659$	12.0578	−	25.2167i	0.469705	−	0.982304i	−0.521901	−	0.853006i	$-0.674777\pi$
$659$	12.0578	−	25.2167i	0.469705	−	0.982304i	0.991606	−	0.129298i	$-0.0412724\pi$
$660$		0			0
$661$	13.6897	−	15.6867i	0.532468	−	0.610141i	−0.422677	−	0.906281i	$-0.638909\pi$
$661$	13.6897	−	15.6867i	0.532468	−	0.610141i	0.955145	+	0.296140i	$0.0956995\pi$
$662$	3.21308	+	1.93910i	0.124880	+	0.0753654i
$663$		0			0
$664$	1.33421	−	13.7169i	0.0517775	−	0.532320i
$665$	−4.42663	−	5.94600i	−0.171657	−	0.230576i
$666$		0			0
$667$	−10.6891	−	1.24937i	−0.413882	−	0.0483758i
$668$	37.1402	−	11.9085i	1.43700	−	0.460754i
$669$		0			0
$670$	−0.0638246	−	0.133478i	−0.00246576	−	0.00515670i
$671$	−0.763721	+	0.312015i	−0.0294831	+	0.0120452i
$672$		0			0
$673$	−11.3834	+	33.2692i	−0.438797	+	1.28243i	0.476330	+	0.879267i	$0.341967\pi$
$673$	−11.3834	+	33.2692i	−0.438797	+	1.28243i	−0.915127	+	0.403166i	$0.867910\pi$
$674$	4.41071	+	1.60537i	0.169894	+	0.0618364i
$675$		0			0
$676$	−12.2641	+	4.46375i	−0.471694	+	0.171683i
$677$	−0.219765	−	11.3310i	−0.00844624	−	0.435486i	−0.980037	−	0.198817i	$-0.936290\pi$
$677$	−0.219765	−	11.3310i	−0.00844624	−	0.435486i	0.971590	−	0.236669i	$-0.0760557\pi$
$678$		0			0
$679$	−29.6604	−	47.0594i	−1.13826	−	1.80597i
$680$	4.03835	−	1.12415i	0.154864	−	0.0431093i
$681$		0			0
$682$	−1.03959	−	0.0403409i	−0.0398080	−	0.00154473i
$683$	19.7523	+	20.9362i	0.755801	+	0.801102i	0.985051	−	0.172266i	$-0.0551087\pi$
$683$	19.7523	+	20.9362i	0.755801	+	0.801102i	−0.229250	+	0.973368i	$0.573627\pi$
$684$		0			0
$685$	12.6322	+	2.99388i	0.482651	+	0.114390i
$686$	0.263117	+	1.02148i	0.0100458	+	0.0390004i
$687$		0			0
$688$	−4.80992	+	12.4580i	−0.183376	+	0.474957i
$689$	12.3482	+	15.3093i	0.470427	+	0.583238i
$690$		0			0
$691$	−0.943199	+	0.925083i	−0.0358810	+	0.0351918i	−0.717937	−	0.696108i	$-0.754913\pi$
$691$	−0.943199	+	0.925083i	−0.0358810	+	0.0351918i	0.682056	+	0.731300i	$0.261086\pi$
$692$	−22.9089	+	24.2820i	−0.870865	+	0.923063i
$693$		0			0
$694$	0.488931	−	1.63314i	0.0185596	−	0.0619933i
$695$	−3.80785	+	6.04157i	−0.144440	+	0.229170i
$696$		0			0
$697$	20.2578	+	19.8687i	0.767319	+	0.752581i
$698$	7.41867	−	0.287878i	0.280801	−	0.0108963i
$699$		0			0
$700$	27.3306	−	16.4941i	1.03300	−	0.623418i
$701$	−4.73515	+	26.8544i	−0.178844	+	1.01428i	0.754768	+	0.655991i	$0.227749\pi$
$701$	−4.73515	+	26.8544i	−0.178844	+	1.01428i	−0.933613	+	0.358284i	$0.883362\pi$
$702$		0			0
$703$	−3.01188	−	17.0812i	−0.113595	−	0.644230i
$704$	2.35246	+	2.69562i	0.0886616	+	0.101595i
$705$		0			0
$706$	−6.16165	−	4.77564i	−0.231897	−	0.179734i
$707$	40.5886	+	3.15479i	1.52649	+	0.118648i
$708$		0			0
$709$	−20.1021	−	18.2417i	−0.754950	−	0.685081i	0.200678	−	0.979657i	$-0.435686\pi$
$709$	−20.1021	−	18.2417i	−0.754950	−	0.685081i	−0.955628	+	0.294576i	$0.904821\pi$
$710$	−0.932080	+	1.25200i	−0.0349804	+	0.0469868i
$711$		0			0
$712$	−0.0806819	+	0.187042i	−0.00302368	+	0.00700968i
$713$	−30.5145	−	21.8104i	−1.14278	−	0.816807i
$714$		0			0
$715$	0.0172043	−	0.887048i	0.000643403	−	0.0331737i
$716$	15.7461	+	46.0198i	0.588461	+	1.71984i
$717$		0			0
$718$	4.74085	−	0.368488i	0.176927	−	0.0137518i
$719$	−37.8940	−	24.9233i	−1.41321	−	0.929481i	−0.999821	−	0.0189257i	$-0.993975\pi$
$719$	−37.8940	−	24.9233i	−1.41321	−	0.929481i	−0.413387	−	0.910556i	$-0.635654\pi$
$720$		0			0
$721$	9.67395	+	4.85844i	0.360277	+	0.180938i
$722$	−0.297402	−	2.17737i	−0.0110682	−	0.0810334i
$723$		0			0
$724$	−13.3683	−	6.07663i	−0.496828	−	0.225836i
$725$	8.43674	+	2.70513i	0.313333	+	0.100466i
$726$		0			0
$727$	5.62967	+	0.880464i	0.208793	+	0.0326546i	0.258050	−	0.966132i	$-0.416920\pi$
$727$	5.62967	+	0.880464i	0.208793	+	0.0326546i	−0.0492573	+	0.998786i	$0.515685\pi$
$728$	−9.59049			−0.355447
$729$		0			0
$730$	2.15527			0.0797703
$731$	−23.2921	−	3.64282i	−0.861490	−	0.134735i
$732$		0			0
$733$	42.6958	+	13.6899i	1.57701	+	0.505646i	0.959688	−	0.281068i	$-0.0906886\pi$
$733$	42.6958	+	13.6899i	1.57701	+	0.505646i	0.617317	+	0.786714i	$0.288219\pi$
$734$	5.93211	+	2.69648i	0.218958	+	0.0995288i
$735$		0			0
$736$	−2.35641	−	17.2520i	−0.0868586	−	0.635917i
$737$	0.443820	+	0.222895i	0.0163483	+	0.00821044i
$738$		0			0
$739$	5.27333	+	3.46832i	0.193983	+	0.127584i	0.642785	−	0.766047i	$-0.277779\pi$
$739$	5.27333	+	3.46832i	0.193983	+	0.127584i	−0.448802	+	0.893631i	$0.648149\pi$
$740$	−6.28104	+	0.488201i	−0.230896	+	0.0179466i
$741$		0			0
$742$	−2.49964	−	7.30547i	−0.0917646	−	0.268192i
$743$	0.217583	−	11.2185i	0.00798234	−	0.411568i	−0.974414	−	0.224760i	$-0.927840\pi$
$743$	0.217583	−	11.2185i	0.00798234	−	0.411568i	0.982397	−	0.186808i	$-0.0598141\pi$
$744$		0			0
$745$	5.53490	+	3.95611i	0.202783	+	0.144941i
$746$	0.669349	−	1.55172i	0.0245066	−	0.0568127i
$747$		0			0
$748$	−4.12201	+	5.53682i	−0.150715	+	0.202446i
$749$	−8.79001	−	7.97651i	−0.321180	−	0.291455i
$750$		0			0
$751$	−5.01298	−	0.389640i	−0.182926	−	0.0142182i	−0.0142975	−	0.999898i	$-0.504551\pi$
$751$	−5.01298	−	0.389640i	−0.182926	−	0.0142182i	−0.168629	+	0.985680i	$0.553934\pi$
$752$	−30.6213	−	23.7333i	−1.11664	−	0.865463i
$753$		0			0
$754$	−0.858553	−	0.983792i	−0.0312666	−	0.0358276i
$755$	0.700396	+	3.97214i	0.0254900	+	0.144561i
$756$		0			0
$757$	8.30919	−	47.1237i	0.302003	−	1.71274i	−0.335286	−	0.942116i	$-0.608833\pi$
$757$	8.30919	−	47.1237i	0.302003	−	1.71274i	0.637289	−	0.770625i	$-0.280056\pi$
$758$	−4.30312	+	2.59694i	−0.156296	+	0.0943253i
$759$		0			0
$760$	2.20364	−	0.0855111i	0.0799343	−	0.00310181i
$761$	11.3943	+	11.1755i	0.413043	+	0.405110i	0.876802	−	0.480852i	$-0.159672\pi$
$761$	11.3943	+	11.1755i	0.413043	+	0.405110i	−0.463759	+	0.885962i	$0.653500\pi$
$762$		0			0
$763$	9.72672	−	15.4325i	0.352131	−	0.558693i
$764$	−9.69491	+	32.3832i	−0.350749	+	1.17158i
$765$		0			0
$766$	6.66241	−	7.06174i	0.240723	−	0.255151i
$767$	14.6403	−	14.3591i	0.528629	−	0.518476i
$768$		0			0
$769$	2.75524	+	3.41596i	0.0993564	+	0.123183i	0.825602	−	0.564252i	$-0.190835\pi$
$769$	2.75524	+	3.41596i	0.0993564	+	0.123183i	−0.726246	+	0.687435i	$0.758737\pi$
$770$	−0.125448	+	0.324917i	−0.00452081	+	0.0117092i
$771$		0			0
$772$	−7.94012	−	30.8254i	−0.285771	−	1.10943i
$773$	15.5085	+	3.67557i	0.557801	+	0.132201i	0.499840	−	0.866118i	$-0.333392\pi$
$773$	15.5085	+	3.67557i	0.557801	+	0.132201i	0.0579606	+	0.998319i	$0.481540\pi$
$774$		0			0
$775$	21.1903	+	22.4604i	0.761177	+	0.806801i
$776$	16.5363	+	0.641685i	0.593620	+	0.0230352i
$777$		0			0
$778$	1.60492	−	0.446760i	0.0575392	−	0.0160171i
$779$	7.95951	+	12.6286i	0.285179	+	0.452467i
$780$		0			0
$781$	−0.101601	−	5.23852i	−0.00363557	−	0.187449i
$782$	9.01154	−	3.27993i	0.322252	−	0.117290i
$783$		0			0
$784$	−19.8152	−	7.21213i	−0.707684	−	0.257576i
$785$	−4.53292	+	13.2480i	−0.161787	+	0.472840i
$786$		0			0
$787$	13.5574	−	5.53880i	0.483268	−	0.197437i	−0.123455	−	0.992350i	$-0.539397\pi$
$787$	13.5574	−	5.53880i	0.483268	−	0.197437i	0.606723	+	0.794913i	$0.292484\pi$
$788$	−20.2226	−	42.2920i	−0.720400	−	1.50659i
$789$		0			0
$790$	−1.46107	+	0.468472i	−0.0519824	+	0.0166675i
$791$	−53.7939	−	6.28760i	−1.91269	−	0.223561i
$792$		0			0
$793$	−2.15499	−	2.89466i	−0.0765260	−	0.102792i
$794$	−0.437784	+	4.50082i	−0.0155364	+	0.159728i
$795$		0			0
$796$	−1.69729	−	1.02432i	−0.0601589	−	0.0363061i
$797$	24.3902	−	27.9481i	0.863946	−	0.989972i	−0.136054	−	0.990701i	$-0.543442\pi$
$797$	24.3902	−	27.9481i	0.863946	−	0.989972i	1.00000		0.000729105i	$0.000232081\pi$
$798$		0			0
$799$	29.5041	−	61.7025i	1.04378	−	2.18288i
$800$	−0.833496	+	14.3106i	−0.0294685	+	0.505955i
$801$		0			0
$802$	−1.05885	+	0.696415i	−0.0373892	+	0.0245913i
$803$	−5.71836	+	4.43207i	−0.201797	+	0.156404i
$804$		0			0
$805$	−10.2156	+	7.30164i	−0.360051	+	0.257349i
$806$	−0.963431	−	4.44769i	−0.0339354	−	0.156663i
$807$		0			0
$808$	−7.60368	+	9.42709i	−0.267497	+	0.331644i
$809$	−6.91226	−	11.9724i	−0.243022	−	0.420927i	0.718552	−	0.695474i	$-0.244805\pi$
$809$	−6.91226	−	11.9724i	−0.243022	−	0.420927i	−0.961574	+	0.274547i	$0.911472\pi$
$810$		0			0
$811$	−21.2251	+	36.7629i	−0.745312	+	1.29092i	0.204736	+	0.978817i	$0.434366\pi$
$811$	−21.2251	+	36.7629i	−0.745312	+	1.29092i	−0.950049	+	0.312102i	$0.898967\pi$
$812$	−4.79102	−	12.4090i	−0.168132	−	0.435472i
$813$		0			0
$814$	−0.603503	+	0.547650i	−0.0211528	+	0.0191951i
$815$	−0.300523	−	3.08965i	−0.0105269	−	0.108226i
$816$		0			0
$817$	−11.4814	−	4.69065i	−0.401682	−	0.164105i
$818$	−0.276707	−	4.75088i	−0.00967485	−	0.166111i
$819$		0			0
$820$	4.84533	−	2.43342i	0.169206	−	0.0849787i
$821$	−2.02743	−	2.95606i	−0.0707577	−	0.103167i	0.787681	−	0.616083i	$-0.211281\pi$
$821$	−2.02743	−	2.95606i	−0.0707577	−	0.103167i	−0.858439	+	0.512916i	$0.828565\pi$
$822$		0			0
$823$	−31.6745	−	6.22066i	−1.10410	−	0.216839i	−0.392730	−	0.919654i	$-0.628469\pi$
$823$	−31.6745	−	6.22066i	−1.10410	−	0.216839i	−0.711372	+	0.702815i	$0.751926\pi$
$824$	−2.81976	+	1.55588i	−0.0982311	+	0.0542017i
$825$		0			0
$826$	−7.32865	+	3.33128i	−0.254996	+	0.115910i
$827$	55.1787	−	6.44947i	1.91875	−	0.224270i	0.929321	−	0.369272i	$-0.120393\pi$
$827$	55.1787	−	6.44947i	1.91875	−	0.224270i	0.989431	+	0.145002i	$0.0463189\pi$
$828$		0			0
$829$	12.4694	+	28.9073i	0.433080	+	1.00399i	0.985384	+	0.170350i	$0.0544898\pi$
$829$	12.4694	+	28.9073i	0.433080	+	1.00399i	−0.552303	+	0.833643i	$0.686251\pi$
$830$	0.463487	−	2.13969i	0.0160879	−	0.0742698i
$831$		0			0
$832$	−8.85176	+	12.9062i	−0.306879	+	0.447441i
$833$	5.03785	−	36.8836i	0.174551	−	1.27794i
$834$		0			0
$835$	12.3937	−	2.43405i	0.428902	−	0.0842336i
$836$	−2.78182	+	2.33422i	−0.0962112	+	0.0807308i
$837$		0			0
$838$	3.17737	+	2.66613i	0.109761	+	0.0921001i
$839$	8.67597	+	4.78720i	0.299528	+	0.165272i	0.625757	−	0.780018i	$-0.284790\pi$
$839$	8.67597	+	4.78720i	0.299528	+	0.165272i	−0.326229	+	0.945291i	$0.605778\pi$
$840$		0			0
$841$	−11.7947	+	22.3917i	−0.406714	+	0.772127i
$842$	2.13626	−	8.29346i	0.0736203	−	0.285811i
$843$		0			0
$844$	14.4082	+	27.3533i	0.495951	+	0.941539i
$845$	−4.11251	+	0.974682i	−0.141475	+	0.0335301i
$846$		0			0
$847$	11.0058	+	36.7620i	0.378164	+	1.26316i
$848$	−27.0425	−	7.52778i	−0.928642	−	0.258505i
$849$		0			0
$850$	−7.80018	+	1.21993i	−0.267544	+	0.0418431i
$851$	−29.0277	+	4.53985i	−0.995056	+	0.155624i
$852$		0			0
$853$	−7.69351	−	2.14163i	−0.263421	−	0.0733282i	0.133944	−	0.990989i	$-0.457236\pi$
$853$	−7.69351	−	2.14163i	−0.263421	−	0.0733282i	−0.397365	+	0.917661i	$0.630075\pi$
$854$	0.406309	+	1.35717i	0.0139036	+	0.0464413i
$855$		0			0
$856$	3.43601	−	0.814349i	0.117440	−	0.0278339i
$857$	16.0447	+	30.4600i	0.548075	+	1.04049i	0.989681	+	0.143286i	$0.0457668\pi$
$857$	16.0447	+	30.4600i	0.548075	+	1.04049i	−0.441606	+	0.897209i	$0.645591\pi$
$858$		0			0
$859$	−3.83930	+	14.9051i	−0.130995	+	0.508555i	0.868912	+	0.494966i	$0.164819\pi$
$859$	−3.83930	+	14.9051i	−0.130995	+	0.508555i	−0.999908	+	0.0135889i	$0.995674\pi$
$860$	−2.09948	+	3.98576i	−0.0715915	+	0.135913i
$861$		0			0
$862$	0.923704	+	0.509678i	0.0314615	+	0.0173597i
$863$	17.1907	+	14.4247i	0.585177	+	0.491022i	0.886643	−	0.462455i	$-0.153031\pi$
$863$	17.1907	+	14.4247i	0.585177	+	0.491022i	−0.301465	+	0.953477i	$0.597476\pi$
$864$		0			0
$865$	−8.28145	+	6.94896i	−0.281578	+	0.236272i
$866$	−6.74376	+	1.32443i	−0.229162	+	0.0450060i
$867$		0			0
$868$	6.27399	−	45.9338i	0.212953	−	1.55909i
$869$	2.91314	−	4.24746i	0.0988215	−	0.144085i
$870$		0			0
$871$	−0.459917	+	2.12321i	−0.0155837	+	0.0719424i
$872$	2.14950	+	4.98311i	0.0727914	+	0.168749i
$873$		0			0
$874$	5.01098	−	0.585699i	0.169499	−	0.0198116i
$875$	19.6155	−	8.91635i	0.663126	−	0.301428i
$876$		0			0
$877$	−31.0868	+	17.1530i	−1.04973	+	0.579215i	−0.911549	−	0.411193i	$-0.865112\pi$
$877$	−31.0868	+	17.1530i	−1.04973	+	0.579215i	−0.138178	+	0.990407i	$0.544125\pi$
$878$	1.97402	+	0.387685i	0.0666200	+	0.0130837i
$879$		0			0
$880$	0.716183	+	1.04422i	0.0241425	+	0.0352006i
$881$	47.0238	−	23.6162i	1.58427	−	0.795651i	0.584396	−	0.811468i	$-0.301331\pi$
$881$	47.0238	−	23.6162i	1.58427	−	0.795651i	0.999875	+	0.0158175i	$0.00503508\pi$
$882$		0			0
$883$	3.04909	+	52.3509i	0.102610	+	1.76175i	0.521071	+	0.853514i	$0.325533\pi$
$883$	3.04909	+	52.3509i	0.102610	+	1.76175i	−0.418461	+	0.908235i	$0.637430\pi$
$884$	−27.9514	−	11.4194i	−0.940107	−	0.384076i
$885$		0			0
$886$	−0.988273	−	10.1603i	−0.0332017	−	0.341343i
$887$	−26.9748	+	24.4783i	−0.905724	+	0.821901i	−0.984571	−	0.174986i	$-0.944012\pi$
$887$	−26.9748	+	24.4783i	−0.905724	+	0.821901i	0.0788468	+	0.996887i	$0.474876\pi$
$888$		0			0
$889$	12.2112	+	31.6277i	0.409549	+	1.06076i
$890$	−0.0161797	+	0.0280241i	−0.000542345	+	0.000939369i
$891$		0			0
$892$	7.95245	+	13.7740i	0.266268	+	0.461189i
$893$	22.5892	−	28.0062i	0.755919	−	0.937193i
$894$		0			0
$895$	3.33457	+	15.3941i	0.111462	+	0.514568i
$896$	23.1821	−	16.5695i	0.774458	−	0.553550i
$897$		0			0
$898$	−2.17154	+	1.68307i	−0.0724652	+	0.0561648i
$899$	10.7503	−	7.07058i	0.358542	−	0.235817i
$900$		0			0
$901$	2.88137	−	49.4712i	0.0959924	−	1.64813i
$902$	0.302566	−	0.632763i	0.0100743	−	0.0210687i
$903$		0			0
$904$	10.5943	−	12.1397i	0.352361	−	0.403761i
$905$	−4.07141	−	2.45711i	−0.135338	−	0.0816771i
$906$		0			0
$907$	−2.92600	+	30.0819i	−0.0971561	+	0.998852i	0.812352	+	0.583167i	$0.198187\pi$
$907$	−2.92600	+	30.0819i	−0.0971561	+	0.998852i	−0.909509	+	0.415685i	$0.863542\pi$
$908$	−5.15513	−	6.92454i	−0.171079	−	0.229799i
$909$		0			0
$910$	−1.51322	−	0.176870i	−0.0501627	−	0.00586318i
$911$	−38.5972	+	12.3757i	−1.27878	+	0.410025i	−0.865652	−	0.500647i	$-0.833096\pi$
$911$	−38.5972	+	12.3757i	−1.27878	+	0.410025i	−0.413131	+	0.910672i	$0.635565\pi$
$912$		0			0
$913$	3.17030	+	6.63013i	0.104922	+	0.219425i
$914$	−0.215837	+	0.0881792i	−0.00713926	+	0.00291671i
$915$		0			0
$916$	12.7262	−	37.1938i	0.420486	−	1.22892i
$917$	−2.34214	−	0.852470i	−0.0773444	−	0.0281510i
$918$		0			0
$919$	−27.3298	+	9.94724i	−0.901527	+	0.328129i	−0.750865	−	0.660456i	$-0.770363\pi$
$919$	−27.3298	+	9.94724i	−0.901527	+	0.328129i	−0.150663	+	0.988585i	$0.548141\pi$
$920$	−0.0724381	−	3.73489i	−0.00238821	−	0.123136i
$921$		0			0
$922$	−4.24858	−	6.74084i	−0.139920	−	0.221998i
$923$	22.0794	−	6.14621i	0.726751	−	0.202305i
$924$		0			0
$925$	24.1697	+	0.937896i	0.794696	+	0.0308378i
$926$	−3.89467	−	4.12811i	−0.127987	−	0.135658i
$927$		0			0
$928$	5.81227	+	1.37753i	0.190797	+	0.0452198i
$929$	4.92208	+	19.1087i	0.161488	+	0.626936i	0.996996	+	0.0774569i	$0.0246800\pi$
$929$	4.92208	+	19.1087i	0.161488	+	0.626936i	−0.835507	+	0.549479i	$0.814826\pi$
$930$		0			0
$931$	7.05374	−	18.2697i	0.231177	−	0.598764i
$932$	16.6822	+	20.6827i	0.546445	+	0.677485i
$933$		0			0
$934$	2.57079	−	2.52141i	0.0841188	−	0.0825031i
$935$	−1.53399	+	1.62593i	−0.0501667	+	0.0531736i
$936$		0			0
$937$	2.75326	−	9.19652i	0.0899450	−	0.300437i	−0.901166	−	0.433474i	$-0.857288\pi$
$937$	2.75326	−	9.19652i	0.0899450	−	0.300437i	0.991111	+	0.133037i	$0.0424728\pi$
$938$	0.454738	−	0.721491i	0.0148477	−	0.0235575i
$939$		0			0
$940$	−9.33038	−	9.15117i	−0.304323	−	0.298478i
$941$	4.86424	−	0.188755i	0.158570	−	0.00615322i	0.0406317	−	0.999174i	$-0.487063\pi$
$941$	4.86424	−	0.188755i	0.158570	−	0.00615322i	0.117938	+	0.993021i	$0.462372\pi$
$942$		0			0
$943$	21.6493	−	13.0654i	0.704998	−	0.425468i
$944$	−5.08211	+	28.8221i	−0.165408	+	0.938078i
$945$		0			0
$946$	0.101191	+	0.573885i	0.00329002	+	0.0186586i
$947$	−27.4953	−	31.5062i	−0.893478	−	1.02381i	−0.999566	−	0.0294557i	$-0.990623\pi$
$947$	−27.4953	−	31.5062i	−0.893478	−	1.02381i	0.106088	−	0.994357i	$-0.466168\pi$
$948$		0			0
$949$	−25.0135	−	19.3869i	−0.811973	−	0.629326i
$950$	−4.14095	−	0.321860i	−0.134350	−	0.0104425i
$951$		0			0
$952$	17.8940	+	16.2379i	0.579948	+	0.526275i
$953$	−15.6772	+	21.0581i	−0.507833	+	0.682138i	−0.979915	−	0.199417i	$-0.936095\pi$
$953$	−15.6772	+	21.0581i	−0.507833	+	0.682138i	0.472082	+	0.881555i	$0.343503\pi$
$954$		0			0
$955$	−4.33578	+	10.0515i	−0.140303	+	0.325258i
$956$	−10.6139	−	7.58635i	−0.343277	−	0.245360i
$957$		0			0
$958$	−0.0694196	+	3.57926i	−0.00224285	+	0.115641i
$959$	24.2259	+	70.8027i	0.782294	+	2.28634i
$960$		0			0
$961$	13.8035	−	1.07289i	0.445273	−	0.0346094i
$962$	−2.97832	−	1.95887i	−0.0960249	−	0.0631565i
$963$		0			0
$964$	32.7079	+	16.4265i	1.05345	+	0.529064i
$965$	−1.39503	−	10.2134i	−0.0449075	−	0.328781i
$966$		0			0
$967$	−11.7884	−	5.35851i	−0.379091	−	0.172318i	0.215196	−	0.976571i	$-0.430961\pi$
$967$	−11.7884	−	5.35851i	−0.379091	−	0.172318i	−0.594287	+	0.804253i	$0.702566\pi$
$968$	−10.8710	−	3.48566i	−0.349408	−	0.112033i
$969$		0			0
$970$	2.59732	+	0.406214i	0.0833950	+	0.0130427i
$971$	−9.91271			−0.318114			−0.159057	−	0.987269i	$-0.550845\pi$
$971$	−9.91271			−0.318114			−0.159057	+	0.987269i	$0.550845\pi$
$972$		0			0
$973$	−41.1653			−1.31970
$974$	2.13956	+	0.334620i	0.0685558	+	0.0107219i
$975$		0			0
$976$	4.90441	+	1.57254i	0.156986	+	0.0503356i
$977$	−24.6300	−	11.1957i	−0.787983	−	0.358182i	−0.0209421	−	0.999781i	$-0.506667\pi$
$977$	−24.6300	−	11.1957i	−0.787983	−	0.358182i	−0.767041	+	0.641599i	$0.778272\pi$
$978$		0			0
$979$	−0.0147003	−	0.107625i	−0.000469823	−	0.00343971i
$980$	−6.35674	−	3.19247i	−0.203059	−	0.101980i
$981$		0			0
$982$	8.75397	+	5.75758i	0.279350	+	0.183732i
$983$	−6.17893	+	0.480264i	−0.197077	+	0.0153181i	−0.175652	−	0.984452i	$-0.556203\pi$
$983$	−6.17893	+	0.480264i	−0.197077	+	0.0153181i	−0.0214256	+	0.999770i	$0.506821\pi$
$984$		0			0
$985$	−4.91456	−	14.3633i	−0.156591	−	0.457654i
$986$	−0.0637941	+	3.28921i	−0.00203162	+	0.104750i
$987$		0			0
$988$	−12.9230	−	9.23679i	−0.411135	−	0.293862i
$989$	−8.32123	+	19.2908i	−0.264600	+	0.613411i
$990$		0			0
$991$	−10.3892	+	13.9552i	−0.330025	+	0.443301i	−0.935903	−	0.352257i	$-0.885414\pi$
$991$	−10.3892	+	13.9552i	−0.330025	+	0.443301i	0.605878	+	0.795557i	$0.292822\pi$
$992$	15.4170	+	13.9901i	0.489489	+	0.444188i
$993$		0			0
$994$	−8.97018	−	0.697218i	−0.284517	−	0.0221144i
$995$	−0.507418	−	0.393279i	−0.0160862	−	0.0124678i
$996$		0			0
$997$	35.9405	+	41.1832i	1.13825	+	1.30428i	0.946450	+	0.322850i	$0.104641\pi$
$997$	35.9405	+	41.1832i	1.13825	+	1.30428i	0.191796	+	0.981435i	$0.438569\pi$
$998$	1.13533	+	6.43878i	0.0359383	+	0.203816i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.i.a.10.12		1404
3.2	odd	2		243.2.i.a.13.15	✓	1404
243.56	odd	162		243.2.i.a.187.15	yes	1404
243.187	even	81	inner	729.2.i.a.73.12		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.13.15	✓	1404	3.2	odd	2
243.2.i.a.187.15	yes	1404	243.56	odd	162
729.2.i.a.10.12		1404	1.1	even	1	trivial
729.2.i.a.73.12		1404	243.187	even	81	inner

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.i (of order \(81\), degree \(54\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.269146 - 0.0420937i) q^{2} +(-1.83383 - 0.587993i) q^{4} +(-0.567739 - 0.258069i) q^{5} +(-0.486494 - 3.56177i) q^{7} +(0.955700 + 0.479971i) q^{8} +O(q^{10})\)	\(q+(-0.269146 - 0.0420937i) q^{2} +(-1.83383 - 0.587993i) q^{4} +(-0.567739 - 0.258069i) q^{5} +(-0.486494 - 3.56177i) q^{7} +(0.955700 + 0.479971i) q^{8} +(0.141942 + 0.0933565i) q^{10} +(-0.568575 + 0.0441932i) q^{11} +(-0.807583 - 2.36025i) q^{13} +(-0.0189899 + 0.979115i) q^{14} +(2.89644 + 2.07025i) q^{16} +(-2.48941 + 5.77111i) q^{17} +(-1.97451 + 2.65223i) q^{19} +(0.889392 + 0.807081i) q^{20} +(0.154890 + 0.0120390i) q^{22} +(4.42696 + 3.43116i) q^{23} +(-3.03188 - 3.47415i) q^{25} +(0.118006 + 0.669246i) q^{26} +(-1.20215 + 6.81773i) q^{28} +(-1.64506 + 0.992798i) q^{29} +(-6.69161 + 0.259665i) q^{31} +(-2.21945 - 2.17682i) q^{32} +(0.912943 - 1.44848i) q^{34} +(-0.642980 + 2.14770i) q^{35} +(-3.59976 + 3.81553i) q^{37} +(0.643074 - 0.630723i) q^{38} +(-0.418722 - 0.519134i) q^{40} +(1.62607 - 4.21162i) q^{41} +(0.935643 + 3.63239i) q^{43} +(1.06865 + 0.253276i) q^{44} +(-1.04707 - 1.10983i) q^{46} +(-10.8736 - 0.421946i) q^{47} +(-5.70593 + 1.58835i) q^{49} +(0.669779 + 1.06268i) q^{50} +(0.0931569 + 4.80314i) q^{52} +(-7.40900 + 2.69665i) q^{53} +(0.334207 + 0.121641i) q^{55} +(1.24460 - 3.63749i) q^{56} +(0.484552 - 0.197961i) q^{58} +(3.54618 + 7.41620i) q^{59} +(1.37755 - 0.441694i) q^{61} +(1.81195 + 0.211787i) q^{62} +(-3.74633 - 5.03219i) q^{64} +(-0.150611 + 1.54842i) q^{65} +(-0.745608 - 0.449977i) q^{67} +(7.95853 - 9.11946i) q^{68} +(0.263460 - 0.550981i) q^{70} +(-0.534202 + 9.17189i) q^{71} +(10.5992 - 6.97120i) q^{73} +(1.12947 - 0.875407i) q^{74} +(5.18041 - 3.70273i) q^{76} +(0.434015 + 2.00363i) q^{77} +(-5.66996 + 7.02965i) q^{79} +(-1.11015 - 1.92284i) q^{80} +(-0.614933 + 1.06510i) q^{82} +(-4.64147 - 12.0217i) q^{83} +(2.90268 - 2.63404i) q^{85} +(-0.0989240 - 1.01703i) q^{86} +(-0.564599 - 0.230664i) q^{88} +(0.0110750 + 0.190150i) q^{89} +(-8.01378 + 4.02467i) q^{91} +(-6.10079 - 8.89517i) q^{92} +(2.90883 + 0.571276i) q^{94} +(1.80547 - 0.996214i) q^{95} +(14.0870 - 6.40332i) q^{97} +(1.60259 - 0.187316i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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