LMFDB - Embedded newform 729.2.g.d.28.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, 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:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			28.6
Character	$\chi$	$=$	729.28
Dual form			729.2.g.d.703.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.890910 - 0.585961i) q^{2} +(-0.341789 + 0.792356i) q^{4} +(0.585850 - 0.620965i) q^{5} +(0.284505 + 0.0332539i) q^{7} +(0.530120 + 3.00646i) q^{8} +O(q^{10})$	\(q+(0.890910 - 0.585961i) q^{2} +(-0.341789 + 0.792356i) q^{4} +(0.585850 - 0.620965i) q^{5} +(0.284505 + 0.0332539i) q^{7} +(0.530120 + 3.00646i) q^{8} +(0.158079 - 0.896509i) q^{10} +(-0.519011 + 1.73362i) q^{11} +(-0.325075 + 5.58132i) q^{13} +(0.272954 - 0.137083i) q^{14} +(1.04960 + 1.11251i) q^{16} +(4.42908 - 1.61205i) q^{17} +(-1.75427 - 0.638503i) q^{19} +(0.291788 + 0.676441i) q^{20} +(0.553440 + 1.84862i) q^{22} +(1.34612 - 0.157339i) q^{23} +(0.248347 + 4.26396i) q^{25} +(2.98082 + 5.16294i) q^{26} +(-0.123590 + 0.214064i) q^{28} +(5.35083 + 2.68729i) q^{29} +(-2.54206 - 3.41458i) q^{31} +(-4.35412 - 1.03194i) q^{32} +(3.00131 - 4.03146i) q^{34} +(0.187327 - 0.157186i) q^{35} +(-5.46107 - 4.58238i) q^{37} +(-1.93704 + 0.459086i) q^{38} +(2.17748 + 1.43215i) q^{40} +(9.58849 + 6.30645i) q^{41} +(12.3767 - 2.93332i) q^{43} +(-1.19625 - 1.00377i) q^{44} +(1.10708 - 0.928949i) q^{46} +(-1.22397 + 1.64408i) q^{47} +(-6.73148 - 1.59539i) q^{49} +(2.71977 + 3.65328i) q^{50} +(-4.31129 - 2.16521i) q^{52} +(-1.54131 + 2.66962i) q^{53} +(0.772454 + 1.33793i) q^{55} +(0.0508455 + 0.872983i) q^{56} +(6.34175 - 0.741244i) q^{58} +(0.361763 + 1.20837i) q^{59} +(1.09744 + 2.54416i) q^{61} +(-4.26556 - 1.55254i) q^{62} +(-7.35831 + 2.67821i) q^{64} +(3.27536 + 3.47168i) q^{65} +(-5.61273 + 2.81882i) q^{67} +(-0.236491 + 4.06039i) q^{68} +(0.0747867 - 0.249805i) q^{70} +(2.24048 - 12.7064i) q^{71} +(-1.11508 - 6.32396i) q^{73} +(-7.55042 - 0.882517i) q^{74} +(1.10551 - 1.17178i) q^{76} +(-0.205311 + 0.475965i) q^{77} +(-5.95312 + 3.91543i) q^{79} +1.30574 q^{80} +12.2378 q^{82} +(11.3260 - 7.44925i) q^{83} +(1.59375 - 3.69472i) q^{85} +(9.30768 - 9.86557i) q^{86} +(-5.48720 - 0.641362i) q^{88} +(-0.0750415 - 0.425581i) q^{89} +(-0.278086 + 1.57711i) q^{91} +(-0.335421 + 1.12038i) q^{92} +(-0.127083 + 2.18193i) q^{94} +(-1.42423 + 0.715275i) q^{95} +(-6.92494 - 7.34001i) q^{97} +(-6.93197 + 2.52303i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{22}{27}\right)$

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 $

$2$	0.890910	−	0.585961i	0.629968	−	0.414337i	−0.193977	−	0.981006i	$-0.562139\pi$
$2$	0.890910	−	0.585961i	0.629968	−	0.414337i	0.823945	+	0.566669i	$0.191768\pi$
$3$		0			0
$3$		0			0
$4$	−0.341789	+	0.792356i	−0.170894	+	0.396178i
$5$	0.585850	−	0.620965i	0.262000	−	0.277704i	−0.582998	−	0.812474i	$-0.698120\pi$
$5$	0.585850	−	0.620965i	0.262000	−	0.277704i	0.844998	+	0.534770i	$0.179602\pi$
$6$		0			0
$7$	0.284505	+	0.0332539i	0.107533	+	0.0125688i	0.169689	−	0.985498i	$-0.445724\pi$
$7$	0.284505	+	0.0332539i	0.107533	+	0.0125688i	−0.0621562	+	0.998066i	$0.519798\pi$
$8$	0.530120	+	3.00646i	0.187426	+	1.06295i
$9$		0			0
$10$	0.158079	−	0.896509i	0.0499889	−	0.283501i
$11$	−0.519011	+	1.73362i	−0.156488	+	0.522706i	−0.999894	−	0.0145710i	$-0.995362\pi$
$11$	−0.519011	+	1.73362i	−0.156488	+	0.522706i	0.843406	+	0.537277i	$0.180547\pi$
$12$		0			0
$13$	−0.325075	+	5.58132i	−0.0901596	+	1.54798i	0.585443	+	0.810714i	$0.300921\pi$
$13$	−0.325075	+	5.58132i	−0.0901596	+	1.54798i	−0.675602	+	0.737266i	$0.736116\pi$
$14$	0.272954	−	0.137083i	0.0729501	−	0.0366369i
$15$		0			0
$16$	1.04960	+	1.11251i	0.262400	+	0.278128i
$17$	4.42908	−	1.61205i	1.07421	−	0.390980i	0.256460	−	0.966555i	$-0.417444\pi$
$17$	4.42908	−	1.61205i	1.07421	−	0.390980i	0.817749	+	0.575574i	$0.195222\pi$
$18$		0			0
$19$	−1.75427	−	0.638503i	−0.402458	−	0.146483i	0.132857	−	0.991135i	$-0.457585\pi$
$19$	−1.75427	−	0.638503i	−0.402458	−	0.146483i	−0.535315	+	0.844652i	$0.679807\pi$
$20$	0.291788	+	0.676441i	0.0652458	+	0.151257i
$21$		0			0
$22$	0.553440	+	1.84862i	0.117994	+	0.394127i
$23$	1.34612	−	0.157339i	0.280686	−	0.0328074i	0.0254146	−	0.999677i	$-0.491909\pi$
$23$	1.34612	−	0.157339i	0.280686	−	0.0328074i	0.255271	+	0.966870i	$0.417835\pi$
$24$		0			0
$25$	0.248347	+	4.26396i	0.0496694	+	0.852791i
$26$	2.98082	+	5.16294i	0.584587	+	1.01254i
$27$		0			0
$28$	−0.123590	+	0.214064i	−0.0233563	+	0.0404542i
$29$	5.35083	+	2.68729i	0.993624	+	0.499017i	0.869862	−	0.493295i	$-0.164208\pi$
$29$	5.35083	+	2.68729i	0.993624	+	0.499017i	0.123762	+	0.992312i	$0.460504\pi$
$30$		0			0
$31$	−2.54206	−	3.41458i	−0.456568	−	0.613277i	0.512914	−	0.858440i	$-0.328566\pi$
$31$	−2.54206	−	3.41458i	−0.456568	−	0.613277i	−0.969482	+	0.245163i	$0.921159\pi$
$32$	−4.35412	−	1.03194i	−0.769706	−	0.182424i
$33$		0			0
$34$	3.00131	−	4.03146i	0.514721	−	0.691390i
$35$	0.187327	−	0.157186i	0.0316641	−	0.0265693i
$36$		0			0
$37$	−5.46107	−	4.58238i	−0.897794	−	0.753339i	0.0719637	−	0.997407i	$-0.477073\pi$
$37$	−5.46107	−	4.58238i	−0.897794	−	0.753339i	−0.969758	+	0.244068i	$0.921518\pi$
$38$	−1.93704	+	0.459086i	−0.314229	+	0.0744736i
$39$		0			0
$40$	2.17748	+	1.43215i	0.344290	+	0.226443i
$41$	9.58849	+	6.30645i	1.49747	+	0.984902i	0.992563	+	0.121728i	$0.0388437\pi$
$41$	9.58849	+	6.30645i	1.49747	+	0.984902i	0.504907	+	0.863174i	$0.331527\pi$
$42$		0			0
$43$	12.3767	−	2.93332i	1.88742	−	0.447328i	0.887514	−	0.460780i	$-0.152430\pi$
$43$	12.3767	−	2.93332i	1.88742	−	0.447328i	0.999910	+	0.0134525i	$0.00428219\pi$
$44$	−1.19625	−	1.00377i	−0.180342	−	0.151325i
$45$		0			0
$46$	1.10708	−	0.928949i	0.163230	−	0.136966i
$47$	−1.22397	+	1.64408i	−0.178535	+	0.239814i	−0.882378	−	0.470542i	$-0.844059\pi$
$47$	−1.22397	+	1.64408i	−0.178535	+	0.239814i	0.703843	+	0.710356i	$0.251466\pi$
$48$		0			0
$49$	−6.73148	−	1.59539i	−0.961640	−	0.227913i
$50$	2.71977	+	3.65328i	0.384633	+	0.516652i
$51$		0			0
$52$	−4.31129	−	2.16521i	−0.597868	−	0.300261i
$53$	−1.54131	+	2.66962i	−0.211715	+	0.366701i	−0.952251	−	0.305315i	$-0.901238\pi$
$53$	−1.54131	+	2.66962i	−0.211715	+	0.366701i	0.740537	+	0.672016i	$0.234571\pi$
$54$		0			0
$55$	0.772454	+	1.33793i	0.104158	+	0.180406i
$56$	0.0508455	+	0.872983i	0.00679452	+	0.116657i
$57$		0			0
$58$	6.34175	−	0.741244i	0.832713	−	0.0973301i
$59$	0.361763	+	1.20837i	0.0470975	+	0.157317i	0.978304	−	0.207177i	$-0.0664275\pi$
$59$	0.361763	+	1.20837i	0.0470975	+	0.157317i	−0.931206	+	0.364493i	$0.881242\pi$
$60$		0			0
$61$	1.09744	+	2.54416i	0.140513	+	0.325747i	0.973912	−	0.226926i	$-0.0728674\pi$
$61$	1.09744	+	2.54416i	0.140513	+	0.325747i	−0.833399	+	0.552672i	$0.813608\pi$
$62$	−4.26556	−	1.55254i	−0.541726	−	0.197172i
$63$		0			0
$64$	−7.35831	+	2.67821i	−0.919789	+	0.334776i
$65$	3.27536	+	3.47168i	0.406258	+	0.430609i
$66$		0			0
$67$	−5.61273	+	2.81882i	−0.685705	+	0.344374i	−0.757307	−	0.653060i	$-0.773485\pi$
$67$	−5.61273	+	2.81882i	−0.685705	+	0.344374i	0.0716021	+	0.997433i	$0.477189\pi$
$68$	−0.236491	+	4.06039i	−0.0286787	+	0.492395i
$69$		0			0
$70$	0.0747867	−	0.249805i	0.00893872	−	0.0298574i
$71$	2.24048	−	12.7064i	0.265896	−	1.50797i	−0.500576	−	0.865693i	$-0.666878\pi$
$71$	2.24048	−	12.7064i	0.265896	−	1.50797i	0.766472	−	0.642278i	$-0.222011\pi$
$72$		0			0
$73$	−1.11508	−	6.32396i	−0.130511	−	0.740164i	−0.977881	−	0.209161i	$-0.932927\pi$
$73$	−1.11508	−	6.32396i	−0.130511	−	0.740164i	0.847370	−	0.531002i	$-0.178184\pi$
$74$	−7.55042	−	0.882517i	−0.877718	−	0.102591i
$75$		0			0
$76$	1.10551	−	1.17178i	0.126811	−	0.134412i
$77$	−0.205311	+	0.475965i	−0.0233974	+	0.0542412i
$78$		0			0
$79$	−5.95312	+	3.91543i	−0.669778	+	0.440520i	−0.838323	−	0.545174i	$-0.816464\pi$
$79$	−5.95312	+	3.91543i	−0.669778	+	0.440520i	0.168545	+	0.985694i	$0.446093\pi$
$80$	1.30574			0.145986
$81$		0			0
$82$	12.2378			1.35144
$83$	11.3260	−	7.44925i	1.24319	−	0.817661i	0.254421	−	0.967094i	$-0.418115\pi$
$83$	11.3260	−	7.44925i	1.24319	−	0.817661i	0.988772	+	0.149433i	$0.0477447\pi$
$84$		0			0
$85$	1.59375	−	3.69472i	0.172866	−	0.400749i
$86$	9.30768	−	9.86557i	1.00367	−	1.06383i
$87$		0			0
$88$	−5.48720	−	0.641362i	−0.584937	−	0.0683694i
$89$	−0.0750415	−	0.425581i	−0.00795438	−	0.0451115i	0.980572	−	0.196158i	$-0.0628467\pi$
$89$	−0.0750415	−	0.425581i	−0.00795438	−	0.0451115i	−0.988527	+	0.151047i	$0.951736\pi$
$90$		0			0
$91$	−0.278086	+	1.57711i	−0.0291514	+	0.165326i
$92$	−0.335421	+	1.12038i	−0.0349700	+	0.116808i
$93$		0			0
$94$	−0.127083	+	2.18193i	−0.0131076	+	0.225049i
$95$	−1.42423	+	0.715275i	−0.146123	+	0.0733857i
$96$		0			0
$97$	−6.92494	−	7.34001i	−0.703121	−	0.745265i	0.273114	−	0.961982i	$-0.411947\pi$
$97$	−6.92494	−	7.34001i	−0.703121	−	0.745265i	−0.976234	+	0.216717i	$0.930465\pi$
$98$	−6.93197	+	2.52303i	−0.700235	+	0.254865i
$99$		0			0
$100$	−3.46345	−	1.26059i	−0.346345	−	0.126059i
$101$	−3.67502	−	8.51965i	−0.365678	−	0.847737i	−0.997367	−	0.0725151i	$-0.976897\pi$
$101$	−3.67502	−	8.51965i	−0.365678	−	0.847737i	0.631689	−	0.775222i	$-0.282362\pi$
$102$		0			0
$103$	−4.20365	−	14.0412i	−0.414198	−	1.38352i	−0.869831	−	0.493349i	$-0.835772\pi$
$103$	−4.20365	−	14.0412i	−0.414198	−	1.38352i	0.455634	−	0.890167i	$-0.349413\pi$
$104$	−16.9524	+	1.98145i	−1.66232	+	0.194297i
$105$		0			0
$106$	0.191128	+	3.28154i	0.0185640	+	0.318731i
$107$	0.0376376	+	0.0651902i	0.00363856	+	0.00630218i	0.867839	−	0.496846i	$-0.165508\pi$
$107$	0.0376376	+	0.0651902i	0.00363856	+	0.00630218i	−0.864200	+	0.503148i	$0.832175\pi$
$108$		0			0
$109$	−2.64599	+	4.58298i	−0.253440	+	0.438970i	−0.964470	−	0.264191i	$-0.914895\pi$
$109$	−2.64599	+	4.58298i	−0.253440	+	0.438970i	0.711031	+	0.703161i	$0.248229\pi$
$110$	1.47216	+	0.739347i	0.140365	+	0.0704939i
$111$		0			0
$112$	0.261622	+	0.351419i	0.0247210	+	0.0332060i
$113$	−18.0181	−	4.27037i	−1.69500	−	0.401722i	−0.734193	−	0.678941i	$-0.762439\pi$
$113$	−18.0181	−	4.27037i	−1.69500	−	0.401722i	−0.960807	+	0.277219i	$0.910587\pi$
$114$		0			0
$115$	0.690923	−	0.928071i	0.0644289	−	0.0865430i
$116$	−3.95814	+	3.32128i	−0.367504	+	0.308373i
$117$		0			0
$118$	1.03036	+	0.864571i	0.0948520	+	0.0795903i
$119$	1.31370	−	0.311354i	0.120427	−	0.0285417i
$120$		0			0
$121$	6.45430	+	4.24506i	0.586755	+	0.385915i
$122$	2.46850	+	1.62356i	0.223488	+	0.146990i
$123$		0			0
$124$	3.57441	−	0.847151i	0.320992	−	0.0760764i
$125$	6.06315	+	5.08759i	0.542305	+	0.455048i
$126$		0			0
$127$	8.52895	−	7.15664i	0.756822	−	0.635049i	−0.180476	−	0.983579i	$-0.557764\pi$
$127$	8.52895	−	7.15664i	0.756822	−	0.635049i	0.937297	+	0.348531i	$0.113319\pi$
$128$	0.357982	−	0.480853i	0.0316414	−	0.0425018i
$129$		0			0
$130$	4.95232	+	1.17372i	0.434347	+	0.102942i
$131$	0.164790	+	0.221351i	0.0143977	+	0.0193395i	0.809264	−	0.587445i	$-0.199866\pi$
$131$	0.164790	+	0.221351i	0.0143977	+	0.0193395i	−0.794866	+	0.606785i	$0.792459\pi$
$132$		0			0
$133$	−0.477868	−	0.239994i	−0.0414364	−	0.0208101i
$134$	−3.34872	+	5.80016i	−0.289285	+	0.501057i
$135$		0			0
$136$	7.19452	+	12.4613i	0.616925	+	1.06855i
$137$	−0.612702	−	10.5197i	−0.0523466	−	0.898757i	−0.917621	−	0.397458i	$-0.869893\pi$
$137$	−0.612702	−	10.5197i	−0.0523466	−	0.898757i	0.865274	−	0.501299i	$-0.167144\pi$
$138$		0			0
$139$	−0.538250	+	0.0629124i	−0.0456537	+	0.00533616i	−0.138889	−	0.990308i	$-0.544353\pi$
$139$	−0.538250	+	0.0629124i	−0.0456537	+	0.00533616i	0.0932354	+	0.995644i	$0.470279\pi$
$140$	0.0605210	+	0.202154i	0.00511496	+	0.0170851i
$141$		0			0
$142$	−5.44938	−	12.6331i	−0.457302	−	1.06014i
$143$	−9.50717	−	3.46033i	−0.795029	−	0.289367i
$144$		0			0
$145$	4.80349	−	1.74833i	0.398908	−	0.145191i
$146$	−4.69903	−	4.98068i	−0.388895	−	0.412204i
$147$		0			0
$148$	5.49741	−	2.76090i	0.451884	−	0.226945i
$149$	1.14216	−	19.6101i	0.0935693	−	1.60652i	−0.545997	−	0.837787i	$-0.683849\pi$
$149$	1.14216	−	19.6101i	0.0935693	−	1.60652i	0.639566	−	0.768736i	$-0.279114\pi$
$150$		0			0
$151$	−4.25389	+	14.2090i	−0.346177	+	1.15631i	0.590770	+	0.806840i	$0.298824\pi$
$151$	−4.25389	+	14.2090i	−0.346177	+	1.15631i	−0.936947	+	0.349471i	$0.886361\pi$
$152$	0.989660	−	5.61264i	0.0802720	−	0.455245i
$153$		0			0
$154$	0.0959829	+	0.544346i	0.00773452	+	0.0438647i
$155$	−3.60960	−	0.421902i	−0.289930	−	0.0338880i
$156$		0			0
$157$	−4.00801	+	4.24824i	−0.319874	+	0.339047i	−0.867280	−	0.497820i	$-0.834134\pi$
$157$	−4.00801	+	4.24824i	−0.319874	+	0.339047i	0.547406	+	0.836867i	$0.315615\pi$
$158$	−3.00941	+	6.97659i	−0.239415	+	0.555027i
$159$		0			0
$160$	−3.19166	+	2.09919i	−0.252323	+	0.165955i
$161$	0.388211			0.0305953
$162$		0			0
$163$	−6.88988			−0.539657			−0.269828	−	0.962908i	$-0.586967\pi$
$163$	−6.88988			−0.539657			−0.269828	+	0.962908i	$0.586967\pi$
$164$	−8.27419	+	5.44202i	−0.646106	+	0.424951i
$165$		0			0
$166$	5.72551	−	13.2732i	0.444385	−	1.03020i
$167$	12.1766	−	12.9064i	0.942252	−	0.998728i	−0.0577483	−	0.998331i	$-0.518392\pi$
$167$	12.1766	−	12.9064i	0.942252	−	0.998728i	1.00000		0.000397221i	$-0.000126439\pi$
$168$		0			0
$169$	−18.1334	−	2.11949i	−1.39488	−	0.163038i
$170$	−0.745077	−	4.22554i	−0.0571448	−	0.324084i
$171$		0			0
$172$	−1.90597	+	10.8093i	−0.145329	+	0.824202i
$173$	−4.01157	+	13.3996i	−0.304994	+	1.01875i	0.658848	+	0.752276i	$0.271044\pi$
$173$	−4.01157	+	13.3996i	−0.304994	+	1.01875i	−0.963842	+	0.266474i	$0.914141\pi$
$174$		0			0
$175$	−0.0711371	+	1.22138i	−0.00537746	+	0.0923274i
$176$	−2.47343	+	1.24220i	−0.186442	+	0.0936345i
$177$		0			0
$178$	−0.316229	−	0.335183i	−0.0237024	−	0.0251230i
$179$	9.85261	−	3.58606i	0.736418	−	0.268034i	0.0535392	−	0.998566i	$-0.482950\pi$
$179$	9.85261	−	3.58606i	0.736418	−	0.268034i	0.682879	+	0.730531i	$0.260728\pi$
$180$		0			0
$181$	11.6610	+	4.24426i	0.866755	+	0.315473i	0.736852	−	0.676054i	$-0.236311\pi$
$181$	11.6610	+	4.24426i	0.866755	+	0.315473i	0.129903	+	0.991527i	$0.458533\pi$
$182$	0.676372	+	1.56801i	0.0501361	+	0.116228i
$183$		0			0
$184$	1.18664	+	3.96365i	0.0874803	+	0.292204i
$185$	−6.04487	+	0.706543i	−0.444427	+	0.0519461i
$186$		0			0
$187$	0.495943	+	8.51501i	0.0362669	+	0.622679i
$188$	−0.884358	−	1.53175i	−0.0644984	−	0.111715i
$189$		0			0
$190$	−0.849737	+	1.47179i	−0.0616464	+	0.106775i
$191$	−12.6284	−	6.34222i	−0.913759	−	0.458907i	−0.0711702	−	0.997464i	$-0.522673\pi$
$191$	−12.6284	−	6.34222i	−0.913759	−	0.458907i	−0.842589	+	0.538557i	$0.818970\pi$
$192$		0			0
$193$	13.1675	+	17.6871i	0.947820	+	1.27314i	0.961945	+	0.273243i	$0.0880965\pi$
$193$	13.1675	+	17.6871i	0.947820	+	1.27314i	−0.0141245	+	0.999900i	$0.504496\pi$
$194$	−10.4705	−	2.48154i	−0.751735	−	0.178164i
$195$		0			0
$196$	3.56486	−	4.78844i	0.254633	−	0.342031i
$197$	−1.28639	+	1.07941i	−0.0916516	+	0.0769049i	−0.687462	−	0.726220i	$-0.741275\pi$
$197$	−1.28639	+	1.07941i	−0.0916516	+	0.0769049i	0.595811	+	0.803125i	$0.296831\pi$
$198$		0			0
$199$	8.18059	+	6.86433i	0.579906	+	0.486599i	0.884916	−	0.465750i	$-0.154215\pi$
$199$	8.18059	+	6.86433i	0.579906	+	0.486599i	−0.305010	+	0.952349i	$0.598660\pi$
$200$	−12.6878	+	3.00706i	−0.897161	+	0.212631i
$201$		0			0
$202$	−8.26629	−	5.43682i	−0.581614	−	0.382534i
$203$	1.43298	+	0.942484i	0.100575	+	0.0661494i
$204$		0			0
$205$	9.53350	−	2.25948i	0.665849	−	0.157809i
$206$	−11.9726	−	10.0462i	−0.834173	−	0.699954i
$207$		0			0
$208$	−6.55049	+	5.49652i	−0.454195	+	0.381115i
$209$	2.01741	−	2.70985i	0.139547	−	0.187444i
$210$		0			0
$211$	−10.1652	−	2.40919i	−0.699798	−	0.165855i	−0.134709	−	0.990885i	$-0.543010\pi$
$211$	−10.1652	−	2.40919i	−0.699798	−	0.165855i	−0.565089	+	0.825030i	$0.691158\pi$
$212$	−1.58849	−	2.13371i	−0.109098	−	0.146544i
$213$		0			0
$214$	0.0717306	+	0.0360245i	0.00490341	+	0.00246258i
$215$	5.42938	−	9.40396i	0.370281	−	0.641345i
$216$		0			0
$217$	−0.609682	−	1.05600i	−0.0413879	−	0.0716860i
$218$	0.328112	+	5.63347i	0.0222226	+	0.381547i
$219$		0			0
$220$	−1.32413	+	0.154769i	−0.0892730	+	0.0104345i
$221$	7.55761	+	25.2442i	0.508380	+	1.69811i
$222$		0			0
$223$	5.39966	+	12.5178i	0.361588	+	0.838256i	0.997772	+	0.0667182i	$0.0212528\pi$
$223$	5.39966	+	12.5178i	0.361588	+	0.838256i	−0.636184	+	0.771538i	$0.719488\pi$
$224$	−1.20445	−	0.438385i	−0.0804759	−	0.0292908i
$225$		0			0
$226$	−18.5548	+	6.75338i	−1.23424	+	0.449228i
$227$	8.98971	+	9.52854i	0.596668	+	0.632431i	0.953376	−	0.301785i	$-0.0975824\pi$
$227$	8.98971	+	9.52854i	0.596668	+	0.632431i	−0.356708	+	0.934216i	$0.616101\pi$
$228$		0			0
$229$	1.54142	−	0.774128i	0.101860	−	0.0511559i	−0.397140	−	0.917758i	$-0.629997\pi$
$229$	1.54142	−	0.774128i	0.101860	−	0.0511559i	0.499000	+	0.866602i	$0.333701\pi$
$230$	0.0717373	−	1.23168i	0.00473021	−	0.0812146i
$231$		0			0
$232$	−5.24264	+	17.5116i	−0.344196	+	1.14970i
$233$	−4.21198	+	23.8873i	−0.275936	+	1.56491i	0.460036	+	0.887900i	$0.347836\pi$
$233$	−4.21198	+	23.8873i	−0.275936	+	1.56491i	−0.735972	+	0.677011i	$0.763275\pi$
$234$		0			0
$235$	0.303852	+	1.72323i	0.0198211	+	0.112411i
$236$	−1.08111	−	0.126363i	−0.0703741	−	0.00822555i
$237$		0			0
$238$	0.987951	−	1.04717i	0.0640394	−	0.0678778i
$239$	8.77100	−	20.3335i	0.567349	−	1.31526i	−0.357139	−	0.934051i	$-0.616248\pi$
$239$	8.77100	−	20.3335i	0.567349	−	1.31526i	0.924488	−	0.381211i	$-0.124493\pi$
$240$		0			0
$241$	15.1000	−	9.93144i	0.972677	−	0.639740i	0.0395241	−	0.999219i	$-0.487416\pi$
$241$	15.1000	−	9.93144i	0.972677	−	0.639740i	0.933153	+	0.359479i	$0.117045\pi$
$242$	8.23764			0.529536
$243$		0			0
$244$	−2.39098			−0.153067
$245$	−4.93432	+	3.24535i	−0.315242	+	0.207338i
$246$		0			0
$247$	4.13396	−	9.58361i	0.263038	−	0.609790i
$248$	8.91821	−	9.45275i	0.566307	−	0.600250i
$249$		0			0
$250$	8.38285	+	0.979815i	0.530178	+	0.0619689i
$251$	−1.74420	−	9.89185i	−0.110093	−	0.624368i	−0.989063	−	0.147492i	$-0.952880\pi$
$251$	−1.74420	−	9.89185i	−0.110093	−	0.624368i	0.878970	−	0.476876i	$-0.158231\pi$
$252$		0			0
$253$	−0.425886	+	2.41532i	−0.0267752	+	0.151850i
$254$	3.40502	−	11.3735i	0.213650	−	0.713640i
$255$		0			0
$256$	0.947781	−	16.2728i	0.0592363	−	1.01705i
$257$	−8.19846	+	4.11742i	−0.511406	+	0.256838i	−0.685737	−	0.727849i	$-0.740520\pi$
$257$	−8.19846	+	4.11742i	−0.511406	+	0.256838i	0.174331	+	0.984687i	$0.444224\pi$
$258$		0			0
$259$	−1.40132	−	1.48531i	−0.0870739	−	0.0922929i
$260$	−3.87029	+	1.40867i	−0.240025	+	0.0873620i
$261$		0			0
$262$	0.276516	+	0.100643i	0.0170832	+	0.00621777i
$263$	−9.41306	−	21.8219i	−0.580434	−	1.34560i	−0.915087	−	0.403257i	$-0.867878\pi$
$263$	−9.41306	−	21.8219i	−0.580434	−	1.34560i	0.334653	−	0.942342i	$-0.391381\pi$
$264$		0			0
$265$	0.754766	+	2.52109i	0.0463649	+	0.154870i
$266$	−0.566364	+	0.0661985i	−0.0347260	+	0.00405889i
$267$		0			0
$268$	−0.315139	−	5.41072i	−0.0192502	−	0.330513i
$269$	3.35091	+	5.80395i	0.204309	+	0.353873i	0.949912	−	0.312517i	$-0.101172\pi$
$269$	3.35091	+	5.80395i	0.204309	+	0.353873i	−0.745604	+	0.666390i	$0.767839\pi$
$270$		0			0
$271$	4.74494	−	8.21848i	0.288235	−	0.499237i	−0.685154	−	0.728398i	$-0.740265\pi$
$271$	4.74494	−	8.21848i	0.288235	−	0.499237i	0.973388	+	0.229161i	$0.0735984\pi$
$272$	6.44220	+	3.23539i	0.390616	+	0.196175i
$273$		0			0
$274$	−6.70998	−	9.01307i	−0.405365	−	0.544499i
$275$	−7.52097	−	1.78250i	−0.453532	−	0.107489i
$276$		0			0
$277$	−0.827868	+	1.11202i	−0.0497418	+	0.0668148i	−0.826298	−	0.563233i	$-0.809557\pi$
$277$	−0.827868	+	1.11202i	−0.0497418	+	0.0668148i	0.776556	+	0.630048i	$0.216965\pi$
$278$	−0.442668	+	0.371442i	−0.0265494	+	0.0222776i
$279$		0			0
$280$	0.571880	+	0.479864i	0.0341764	+	0.0286774i
$281$	15.5815	−	3.69287i	0.929512	−	0.220298i	0.262146	−	0.965028i	$-0.415570\pi$
$281$	15.5815	−	3.69287i	0.929512	−	0.220298i	0.667366	+	0.744730i	$0.267422\pi$
$282$		0			0
$283$	0.262449	+	0.172616i	0.0156010	+	0.0102609i	0.557286	−	0.830321i	$-0.311843\pi$
$283$	0.262449	+	0.172616i	0.0156010	+	0.0102609i	−0.541685	+	0.840582i	$0.682213\pi$
$284$	9.30221	+	6.11816i	0.551985	+	0.363046i
$285$		0			0
$286$	−10.4976	+	2.48799i	−0.620739	+	0.147118i
$287$	2.51826	+	2.11307i	0.148648	+	0.124731i
$288$		0			0
$289$	3.99528	−	3.35244i	0.235016	−	0.197202i
$290$	3.25503	−	4.37226i	0.191142	−	0.256748i
$291$		0			0
$292$	5.39195	+	1.27792i	0.315540	+	0.0747844i
$293$	11.1446	+	14.9698i	0.651076	+	0.874547i	0.997991	−	0.0633491i	$-0.0201782\pi$
$293$	11.1446	+	14.9698i	0.651076	+	0.874547i	−0.346915	+	0.937897i	$0.612771\pi$
$294$		0			0
$295$	0.962295	+	0.483283i	0.0560270	+	0.0281378i
$296$	10.8817	−	18.8477i	0.632488	−	1.09550i
$297$		0			0
$298$	−10.4732	−	18.1401i	−0.606696	−	1.05083i
$299$	0.440569	+	7.56428i	0.0254788	+	0.437454i
$300$		0			0
$301$	3.61877	−	0.422974i	0.208583	−	0.0243798i
$302$	4.53607	+	15.1515i	0.261022	+	0.871873i
$303$		0			0
$304$	−1.13095	−	2.62183i	−0.0648642	−	0.150372i
$305$	2.22277	+	0.809023i	0.127276	+	0.0463245i
$306$		0			0
$307$	25.4414	−	9.25992i	1.45202	−	0.528491i	0.508864	−	0.860847i	$-0.330066\pi$
$307$	25.4414	−	9.25992i	1.45202	−	0.528491i	0.943154	+	0.332356i	$0.107843\pi$
$308$	−0.306960	−	0.325359i	−0.0174907	−	0.0185391i
$309$		0			0
$310$	−3.46305	+	1.73921i	−0.196688	+	0.0987804i
$311$	0.719941	−	12.3609i	0.0408241	−	0.700923i	−0.914359	−	0.404906i	$-0.867304\pi$
$311$	0.719941	−	12.3609i	0.0408241	−	0.700923i	0.955183	−	0.296017i	$-0.0956586\pi$
$312$		0			0
$313$	6.15560	−	20.5611i	0.347935	−	1.16218i	−0.587660	−	0.809108i	$-0.699951\pi$
$313$	6.15560	−	20.5611i	0.347935	−	1.16218i	0.935595	−	0.353076i	$-0.114864\pi$
$314$	−1.08147	+	6.13334i	−0.0610311	+	0.346124i
$315$		0			0
$316$	−1.06770	−	6.05524i	−0.0600629	−	0.340634i
$317$	23.4460	+	2.74044i	1.31686	+	0.153919i	0.745348	−	0.666676i	$-0.232283\pi$
$317$	23.4460	+	2.74044i	1.31686	+	0.153919i	0.571511	+	0.820595i	$0.306358\pi$
$318$		0			0
$319$	−7.43587	+	7.88156i	−0.416329	+	0.441283i
$320$	−2.64780	+	6.13828i	−0.148016	+	0.343140i
$321$		0			0
$322$	0.345861	−	0.227476i	0.0192741	−	0.0126768i
$323$	−8.79912			−0.489596
$324$		0			0
$325$	−23.8792			−1.32458
$326$	−6.13826	+	4.03720i	−0.339967	+	0.223600i
$327$		0			0
$328$	−13.8770	+	32.1706i	−0.766232	+	1.77633i
$329$	−0.402900	+	0.427049i	−0.0222126	+	0.0235439i
$330$		0			0
$331$	0.842076	+	0.0984246i	0.0462847	+	0.00540990i	0.139204	−	0.990264i	$-0.455546\pi$
$331$	0.842076	+	0.0984246i	0.0462847	+	0.00540990i	−0.0929190	+	0.995674i	$0.529620\pi$
$332$	2.03134	+	11.5203i	0.111484	+	0.632259i
$333$		0			0
$334$	3.28558	−	18.6334i	0.179779	−	1.01958i
$335$	−1.53783	+	5.13672i	−0.0840207	+	0.280649i
$336$		0			0
$337$	−0.118835	+	2.04032i	−0.00647336	+	0.111143i	−0.999997	−	0.00248306i	$-0.999210\pi$
$337$	−0.118835	+	2.04032i	−0.00647336	+	0.111143i	0.993524	+	0.113626i	$0.0362467\pi$
$338$	−17.3971	+	8.73718i	−0.946280	+	0.475240i
$339$		0			0
$340$	2.38281	+	2.52563i	0.129226	+	0.136972i
$341$	7.23894	−	2.63476i	0.392011	−	0.142680i
$342$		0			0
$343$	−3.74626	−	1.36353i	−0.202279	−	0.0736236i
$344$	15.3801	+	35.6550i	0.829237	+	1.92239i
$345$		0			0
$346$	4.27767	+	14.2884i	0.229969	+	0.768151i
$347$	6.45936	−	0.754991i	0.346757	−	0.0405300i	0.0590678	−	0.998254i	$-0.481187\pi$
$347$	6.45936	−	0.754991i	0.346757	−	0.0405300i	0.287689	+	0.957724i	$0.407113\pi$
$348$		0			0
$349$	−0.384965	−	6.60959i	−0.0206067	−	0.353803i	−0.992813	−	0.119677i	$-0.961814\pi$
$349$	−0.384965	−	6.60959i	−0.0206067	−	0.353803i	0.972206	−	0.234126i	$-0.0752229\pi$
$350$	0.652302	+	1.12982i	0.0348670	+	0.0603914i
$351$		0			0
$352$	4.04883	−	7.01279i	0.215804	−	0.373783i
$353$	−0.270111	−	0.135655i	−0.0143765	−	0.00722017i	0.441596	−	0.897214i	$-0.354412\pi$
$353$	−0.270111	−	0.135655i	−0.0143765	−	0.00722017i	−0.455973	+	0.889994i	$0.650709\pi$
$354$		0			0
$355$	−6.57763	−	8.83530i	−0.349105	−	0.468929i
$356$	0.362860	+	0.0859995i	0.0192316	+	0.00455796i
$357$		0			0
$358$	6.67650	−	8.96809i	0.352864	−	0.473978i
$359$	3.14494	−	2.63892i	0.165984	−	0.139277i	−0.556012	−	0.831174i	$-0.687669\pi$
$359$	3.14494	−	2.63892i	0.165984	−	0.139277i	0.721996	+	0.691897i	$0.243225\pi$
$360$		0			0
$361$	−11.8851	−	9.97274i	−0.625529	−	0.524881i
$362$	12.8759	−	3.05164i	0.676740	−	0.160390i
$363$		0			0
$364$	−1.15458	−	0.759381i	−0.0605166	−	0.0398024i
$365$	−4.58023	−	3.01246i	−0.239740	−	0.157680i
$366$		0			0
$367$	−8.75239	+	2.07435i	−0.456871	+	0.108280i	−0.452606	−	0.891711i	$-0.649506\pi$
$367$	−8.75239	+	2.07435i	−0.456871	+	0.108280i	−0.00426466	+	0.999991i	$0.501357\pi$
$368$	1.58793	+	1.33243i	0.0827767	+	0.0694579i
$369$		0			0
$370$	−4.97142	+	4.17152i	−0.258452	+	0.216867i
$371$	−0.527285	+	0.708267i	−0.0273753	+	0.0367714i
$372$		0			0
$373$	5.11858	+	1.21313i	0.265030	+	0.0628133i	0.360982	−	0.932573i	$-0.382441\pi$
$373$	5.11858	+	1.21313i	0.265030	+	0.0628133i	−0.0959522	+	0.995386i	$0.530590\pi$
$374$	5.43130	+	7.29550i	0.280846	+	0.377242i
$375$		0			0
$376$	−5.59173	−	2.80827i	−0.288371	−	0.144826i
$377$	−16.7380	+	28.9911i	−0.862053	+	1.49312i
$378$		0			0
$379$	−3.76722	−	6.52502i	−0.193509	−	0.335168i	0.752902	−	0.658133i	$-0.228654\pi$
$379$	−3.76722	−	6.52502i	−0.193509	−	0.335168i	−0.946411	+	0.322965i	$0.895320\pi$
$380$	−0.0799664	−	1.37297i	−0.00410219	−	0.0704319i
$381$		0			0
$382$	−14.9671	+	1.74940i	−0.765782	+	0.0895070i
$383$	10.2165	+	34.1256i	0.522040	+	1.74374i	0.657996	+	0.753022i	$0.271404\pi$
$383$	10.2165	+	34.1256i	0.522040	+	1.74374i	−0.135955	+	0.990715i	$0.543410\pi$
$384$		0			0
$385$	0.175276	+	0.406335i	0.00893288	+	0.0207088i
$386$	22.0950	+	8.04193i	1.12461	+	0.409324i
$387$		0			0
$388$	8.18276	−	2.97828i	0.415417	−	0.151199i
$389$	−8.68991	−	9.21077i	−0.440596	−	0.467005i	0.468577	−	0.883423i	$-0.344767\pi$
$389$	−8.68991	−	9.21077i	−0.440596	−	0.467005i	−0.909173	+	0.416418i	$0.863285\pi$
$390$		0			0
$391$	5.70844	−	2.86689i	0.288688	−	0.144985i
$392$	1.22798	−	21.0837i	0.0620226	−	1.06489i
$393$		0			0
$394$	−0.513567	+	1.71543i	−0.0258731	+	0.0864223i
$395$	−1.05629	+	5.99053i	−0.0531478	+	0.301416i
$396$		0			0
$397$	1.88601	+	10.6961i	0.0946564	+	0.536823i	0.994852	+	0.101337i	$0.0323122\pi$
$397$	1.88601	+	10.6961i	0.0946564	+	0.536823i	−0.900196	+	0.435486i	$0.856577\pi$
$398$	11.3104	+	1.32200i	0.566939	+	0.0662656i
$399$		0			0
$400$	−4.48304	+	4.75175i	−0.224152	+	0.237587i
$401$	2.27311	−	5.26965i	0.113514	−	0.263154i	−0.851983	−	0.523569i	$-0.824600\pi$
$401$	2.27311	−	5.26965i	0.113514	−	0.263154i	0.965497	+	0.260415i	$0.0838594\pi$
$402$		0			0
$403$	19.8842	−	13.0781i	0.990505	−	0.651465i
$404$	8.00667			0.398347
$405$		0			0
$406$	1.82891			0.0907674
$407$	10.7785	−	7.08910i	0.534268	−	0.351394i
$408$		0			0
$409$	−11.7085	+	27.1434i	−0.578948	+	1.34215i	0.337245	+	0.941417i	$0.390505\pi$
$409$	−11.7085	+	27.1434i	−0.578948	+	1.34215i	−0.916193	+	0.400737i	$0.868754\pi$
$410$	7.16952	−	7.59925i	0.354078	−	0.375300i
$411$		0			0
$412$	12.5624	+	1.46833i	0.618903	+	0.0723394i
$413$	0.0627404	+	0.355818i	0.00308725	+	0.0175087i
$414$		0			0
$415$	2.00964	−	11.3972i	0.0986491	−	0.559467i
$416$	7.17503	−	23.9663i	0.351785	−	1.17504i
$417$		0			0
$418$	0.209464	−	3.59636i	0.0102452	−	0.175904i
$419$	−7.98438	+	4.00990i	−0.390062	+	0.195897i	−0.633012	−	0.774142i	$-0.718181\pi$
$419$	−7.98438	+	4.00990i	−0.390062	+	0.195897i	0.242949	+	0.970039i	$0.421885\pi$
$420$		0			0
$421$	−1.73759	−	1.84173i	−0.0846848	−	0.0897606i	0.683645	−	0.729814i	$-0.260394\pi$
$421$	−1.73759	−	1.84173i	−0.0846848	−	0.0897606i	−0.768330	+	0.640054i	$0.778912\pi$
$422$	−10.4679	+	3.81001i	−0.509570	+	0.185468i
$423$		0			0
$424$	−8.84319	−	3.21866i	−0.429463	−	0.156312i
$425$	7.97367	+	18.4851i	0.386780	+	0.896657i
$426$		0			0
$427$	0.227626	+	0.760322i	0.0110156	+	0.0367946i
$428$	−0.0645180	+	0.00754107i	−0.00311860	+	0.000364511i
$429$		0			0
$430$	−0.673263	−	11.5595i	−0.0324676	−	0.557448i
$431$	−14.8594	−	25.7372i	−0.715750	−	1.23972i	−0.962669	−	0.270680i	$-0.912751\pi$
$431$	−14.8594	−	25.7372i	−0.715750	−	1.23972i	0.246919	−	0.969036i	$-0.420582\pi$
$432$		0			0
$433$	0.612994	−	1.06174i	0.0294586	−	0.0510238i	−0.850920	−	0.525295i	$-0.823955\pi$
$433$	0.612994	−	1.06174i	0.0294586	−	0.0510238i	0.880379	+	0.474271i	$0.157288\pi$
$434$	−1.16195	−	0.583551i	−0.0557752	−	0.0280114i
$435$		0			0
$436$	−2.72698	−	3.66298i	−0.130599	−	0.175425i
$437$	−2.46193	−	0.583487i	−0.117770	−	0.0279120i
$438$		0			0
$439$	−10.3661	+	13.9241i	−0.494748	+	0.664562i	−0.977436	−	0.211231i	$-0.932253\pi$
$439$	−10.3661	+	13.9241i	−0.494748	+	0.664562i	0.482689	+	0.875792i	$0.339660\pi$
$440$	−3.61294	+	3.03162i	−0.172240	+	0.144527i
$441$		0			0
$442$	21.5252	+	18.0618i	1.02385	+	0.859113i
$443$	−11.6619	+	2.76392i	−0.554073	+	0.131318i	−0.498108	−	0.867115i	$-0.665972\pi$
$443$	−11.6619	+	2.76392i	−0.554073	+	0.131318i	−0.0559651	+	0.998433i	$0.517824\pi$
$444$		0			0
$445$	−0.308234	−	0.202729i	−0.0146117	−	0.00961027i
$446$	12.1456	+	7.98827i	0.575109	+	0.378255i
$447$		0			0
$448$	−2.18254	+	0.517271i	−0.103115	+	0.0244388i
$449$	15.0015	+	12.5878i	0.707965	+	0.594053i	0.924027	−	0.382327i	$-0.124877\pi$
$449$	15.0015	+	12.5878i	0.707965	+	0.594053i	−0.216063	+	0.976380i	$0.569322\pi$
$450$		0			0
$451$	−15.9095	+	13.3497i	−0.749150	+	0.628611i
$452$	9.54203	−	12.8172i	0.448820	−	0.602869i
$453$		0			0
$454$	13.5924	+	3.22145i	0.637921	+	0.151190i
$455$	0.816411	+	1.09663i	0.0382739	+	0.0514108i
$456$		0			0
$457$	21.4625	+	10.7789i	1.00397	+	0.504215i	0.873286	−	0.487208i	$-0.161985\pi$
$457$	21.4625	+	10.7789i	1.00397	+	0.504215i	0.130689	+	0.991423i	$0.458281\pi$
$458$	0.919654	−	1.59289i	0.0429726	−	0.0744308i
$459$		0			0
$460$	0.499212	+	0.864661i	0.0232759	+	0.0403150i
$461$	0.823736	+	14.1430i	0.0383652	+	0.658705i	0.961598	+	0.274463i	$0.0885001\pi$
$461$	0.823736	+	14.1430i	0.0383652	+	0.658705i	−0.923232	+	0.384242i	$0.874463\pi$
$462$		0			0
$463$	10.9340	−	1.27800i	0.508147	−	0.0593938i	0.141843	−	0.989889i	$-0.454697\pi$
$463$	10.9340	−	1.27800i	0.508147	−	0.0593938i	0.366304	+	0.930495i	$0.380623\pi$
$464$	2.62660	+	8.77345i	0.121937	+	0.407297i
$465$		0			0
$466$	10.2445	+	23.7495i	0.474569	+	1.10018i
$467$	36.6170	+	13.3275i	1.69443	+	0.616723i	0.995172	−	0.0981436i	$-0.0312904\pi$
$467$	36.6170	+	13.3275i	1.69443	+	0.616723i	0.699261	+	0.714867i	$0.253513\pi$
$468$		0			0
$469$	−1.69059	+	0.615324i	−0.0780642	+	0.0284130i
$470$	1.28045	+	1.35720i	0.0590628	+	0.0626029i
$471$		0			0
$472$	−3.44115	+	1.72821i	−0.158392	+	0.0795472i
$473$	−1.33837	+	22.9789i	−0.0615381	+	1.05657i
$474$		0			0
$475$	2.28688	−	7.63872i	0.104929	−	0.350488i
$476$	−0.202307	+	1.14734i	−0.00927272	+	0.0525882i
$477$		0			0
$478$	−4.10044	−	23.2547i	−0.187550	−	1.06365i
$479$	−14.0251	−	1.63930i	−0.640825	−	0.0749017i	−0.210526	−	0.977588i	$-0.567518\pi$
$479$	−14.0251	−	1.63930i	−0.640825	−	0.0749017i	−0.430299	+	0.902686i	$0.641592\pi$
$480$		0			0
$481$	27.3510	−	28.9904i	1.24710	−	1.32185i
$482$	7.63332	−	17.6960i	0.347688	−	0.806032i
$483$		0			0
$484$	−5.56961	+	3.66319i	−0.253164	+	0.166509i
$485$	−8.61486			−0.391181
$486$		0			0
$487$	−11.6224			−0.526663			−0.263332	−	0.964705i	$-0.584821\pi$
$487$	−11.6224			−0.526663			−0.263332	+	0.964705i	$0.584821\pi$
$488$	−7.06715	+	4.64814i	−0.319915	+	0.210411i
$489$		0			0
$490$	−2.49438	+	5.78263i	−0.112685	+	0.261233i
$491$	3.60508	−	3.82116i	0.162695	−	0.172447i	−0.640898	−	0.767626i	$-0.721438\pi$
$491$	3.60508	−	3.82116i	0.162695	−	0.172447i	0.803593	+	0.595180i	$0.202919\pi$
$492$		0			0
$493$	28.0313	+	3.27639i	1.26247	+	0.147561i
$494$	−1.93263	−	10.9605i	−0.0869530	−	0.493135i
$495$		0			0
$496$	1.13061	−	6.41203i	0.0507660	−	0.287909i
$497$	1.05997	−	3.54053i	0.0475460	−	0.158815i
$498$		0			0
$499$	−0.320759	+	5.50722i	−0.0143592	+	0.246537i	0.983489	+	0.180968i	$0.0579232\pi$
$499$	−0.320759	+	5.50722i	−0.0143592	+	0.246537i	−0.997848	+	0.0655687i	$0.979114\pi$
$500$	−6.10350	+	3.06529i	−0.272957	+	0.137084i
$501$		0			0
$502$	−7.35016	−	7.79071i	−0.328054	−	0.347717i
$503$	−31.2754	+	11.3833i	−1.39450	+	0.507557i	−0.926541	−	0.376193i	$-0.877233\pi$
$503$	−31.2754	+	11.3833i	−1.39450	+	0.507557i	−0.467959	+	0.883750i	$0.655011\pi$
$504$		0			0
$505$	−7.44341	−	2.70918i	−0.331227	−	0.120557i
$506$	1.03586	+	2.40139i	0.0460495	+	0.106755i
$507$		0			0
$508$	2.75550	+	9.20402i	0.122256	+	0.408362i
$509$	21.9142	−	2.56140i	0.971328	−	0.113532i	0.384396	−	0.923168i	$-0.374410\pi$
$509$	21.9142	−	2.56140i	0.971328	−	0.113532i	0.586932	+	0.809636i	$0.300336\pi$
$510$		0			0
$511$	−0.106951	−	1.83628i	−0.00473124	−	0.0812323i
$512$	−8.09134	−	14.0146i	−0.357590	−	0.619364i
$513$		0			0
$514$	−4.89144	+	8.47222i	−0.215752	+	0.373694i
$515$	−11.1818	−	5.61570i	−0.492728	−	0.247457i
$516$		0			0
$517$	−2.21496	−	2.97520i	−0.0974137	−	0.130849i
$518$	−2.11879	−	0.502162i	−0.0930942	−	0.0220637i
$519$		0			0
$520$	−8.70114	+	11.6877i	−0.381570	+	0.512538i
$521$	21.4866	−	18.0294i	0.941345	−	0.789882i	−0.0364742	−	0.999335i	$-0.511613\pi$
$521$	21.4866	−	18.0294i	0.941345	−	0.789882i	0.977819	+	0.209453i	$0.0671682\pi$
$522$		0			0
$523$	−6.29841	−	5.28500i	−0.275410	−	0.231097i	0.494612	−	0.869114i	$-0.335310\pi$
$523$	−6.29841	−	5.28500i	−0.275410	−	0.231097i	−0.770022	+	0.638017i	$0.779755\pi$
$524$	−0.231712	+	0.0549167i	−0.0101224	+	0.00239905i
$525$		0			0
$526$	−21.1730	−	13.9257i	−0.923186	−	0.607189i
$527$	−16.7635	−	11.0255i	−0.730229	−	0.480279i
$528$		0			0
$529$	−20.5927	+	4.88057i	−0.895337	+	0.212199i
$530$	2.14969	+	1.80381i	0.0933766	+	0.0783523i
$531$		0			0
$532$	0.353491	−	0.296614i	0.0153258	−	0.0128598i
$533$	−38.3153	+	51.4664i	−1.65962	+	2.22926i
$534$		0			0
$535$	0.0625308	+	0.0148201i	0.00270344	+	0.000640728i
$536$	−11.4501	−	15.3802i	−0.494569	−	0.664322i
$537$		0			0
$538$	6.38625	+	3.20729i	0.275331	+	0.138276i
$539$	6.25951	−	10.8418i	0.269616	−	0.466989i
$540$		0			0
$541$	0.833782	+	1.44415i	0.0358471	+	0.0620889i	0.883392	−	0.468634i	$-0.155254\pi$
$541$	0.833782	+	1.44415i	0.0358471	+	0.0620889i	−0.847545	+	0.530723i	$0.821920\pi$
$542$	−0.588390	−	10.1023i	−0.0252735	−	0.433930i
$543$		0			0
$544$	−20.9483	+	2.44850i	−0.898150	+	0.104979i
$545$	1.29572	+	4.32801i	0.0555025	+	0.185391i
$546$		0			0
$547$	7.06785	+	16.3851i	0.302199	+	0.700577i	0.999875	−	0.0158373i	$-0.00504139\pi$
$547$	7.06785	+	16.3851i	0.302199	+	0.700577i	−0.697675	+	0.716414i	$0.745782\pi$
$548$	8.54475	+	3.11003i	0.365013	+	0.132854i
$549$		0			0
$550$	−7.74498	+	2.81894i	−0.330247	+	0.120200i
$551$	−7.67098	−	8.13076i	−0.326795	−	0.346382i
$552$		0			0
$553$	−1.82390	+	0.915996i	−0.0775600	+	0.0389521i
$554$	−0.0859560	+	1.47581i	−0.00365192	+	0.0627010i
$555$		0			0
$556$	0.134119	−	0.447988i	0.00568790	−	0.0189989i
$557$	3.03540	−	17.2146i	0.128614	−	0.729407i	−0.850481	−	0.526005i	$-0.823689\pi$
$557$	3.03540	−	17.2146i	0.128614	−	0.729407i	0.979095	−	0.203402i	$-0.0651997\pi$
$558$		0			0
$559$	12.3485	+	70.0317i	0.522285	+	2.96203i
$560$	0.371490	+	0.0434210i	0.0156983	+	0.00183487i
$561$		0			0
$562$	11.7178	−	12.4201i	0.494285	−	0.523912i
$563$	13.6909	−	31.7390i	0.577002	−	1.33764i	−0.340626	−	0.940199i	$-0.610639\pi$
$563$	13.6909	−	31.7390i	0.577002	−	1.33764i	0.917628	−	0.397441i	$-0.130102\pi$
$564$		0			0
$565$	−13.2076	+	8.68681i	−0.555650	+	0.365457i
$566$	0.334965			0.0140796
$567$		0			0
$568$	39.3890			1.65273
$569$	−21.3130	+	14.0178i	−0.893489	+	0.587657i	−0.911099	−	0.412188i	$-0.864765\pi$
$569$	−21.3130	+	14.0178i	−0.893489	+	0.587657i	0.0176099	+	0.999845i	$0.494394\pi$
$570$		0			0
$571$	8.79169	−	20.3814i	0.367921	−	0.852936i	−0.629210	−	0.777235i	$-0.716621\pi$
$571$	8.79169	−	20.3814i	0.367921	−	0.852936i	0.997131	−	0.0757007i	$-0.0241194\pi$
$572$	5.99126	−	6.35036i	0.250507	−	0.265522i
$573$		0			0
$574$	3.48172	+	0.406955i	0.145324	+	0.0169860i
$575$	1.00519	+	5.70073i	0.0419194	+	0.237737i
$576$		0			0
$577$	−3.76924	+	21.3764i	−0.156915	+	0.889911i	0.800098	+	0.599869i	$0.204781\pi$
$577$	−3.76924	+	21.3764i	−0.156915	+	0.889911i	−0.957014	+	0.290042i	$0.906331\pi$
$578$	1.59504	−	5.32779i	0.0663448	−	0.221607i
$579$		0			0
$580$	−0.256483	+	4.40364i	−0.0106499	+	0.182851i
$581$	3.47003	−	1.74272i	0.143961	−	0.0723000i
$582$		0			0
$583$	−3.82815	−	4.05760i	−0.158546	−	0.168049i
$584$	18.4216	−	6.70492i	0.762292	−	0.277452i
$585$		0			0
$586$	18.7006	+	6.80646i	0.772515	+	0.281172i
$587$	−8.05782	−	18.6801i	−0.332582	−	0.771012i	−0.999661	−	0.0260249i	$-0.991715\pi$
$587$	−8.05782	−	18.6801i	−0.332582	−	0.771012i	0.667079	−	0.744987i	$-0.267544\pi$
$588$		0			0
$589$	2.27925	+	7.61323i	0.0939149	+	0.313698i
$590$	1.14050	−	0.133306i	0.0469538	−	0.00548811i
$591$		0			0
$592$	−0.633990	−	10.8852i	−0.0260568	−	0.447378i
$593$	0.579087	+	1.00301i	0.0237803	+	0.0411886i	0.877671	−	0.479264i	$-0.159096\pi$
$593$	0.579087	+	1.00301i	0.0237803	+	0.0411886i	−0.853890	+	0.520453i	$0.825763\pi$
$594$		0			0
$595$	0.576294	−	0.998171i	0.0236258	−	0.0409210i
$596$	15.1478	+	7.60752i	0.620479	+	0.311616i
$597$		0			0
$598$	4.82488	+	6.48094i	0.197304	+	0.265025i
$599$	−44.1467	−	10.4629i	−1.80378	−	0.427505i	−0.815326	−	0.579002i	$-0.803442\pi$
$599$	−44.1467	−	10.4629i	−1.80378	−	0.427505i	−0.988458	+	0.151498i	$0.951590\pi$
$600$		0			0
$601$	−19.5190	+	26.2185i	−0.796195	+	1.06948i	0.199780	+	0.979841i	$0.435977\pi$
$601$	−19.5190	+	26.2185i	−0.796195	+	1.06948i	−0.995975	+	0.0896345i	$0.971430\pi$
$602$	2.97615	−	2.49729i	0.121299	−	0.101782i
$603$		0			0
$604$	−9.80464	−	8.22707i	−0.398945	−	0.334755i
$605$	6.41729	−	1.52093i	0.260900	−	0.0618344i
$606$		0			0
$607$	−0.512985	−	0.337395i	−0.0208214	−	0.0136945i	0.539056	−	0.842270i	$-0.318781\pi$
$607$	−0.512985	−	0.337395i	−0.0208214	−	0.0136945i	−0.559877	+	0.828576i	$0.689152\pi$
$608$	6.97941	+	4.59043i	0.283052	+	0.186167i
$609$		0			0
$610$	2.45435	−	0.581691i	0.0993736	−	0.0235520i
$611$	−8.77827	−	7.36585i	−0.355131	−	0.297990i
$612$		0			0
$613$	−15.6352	+	13.1195i	−0.631499	+	0.529891i	−0.901394	−	0.432999i	$-0.857455\pi$
$613$	−15.6352	+	13.1195i	−0.631499	+	0.529891i	0.269895	+	0.962890i	$0.413011\pi$
$614$	17.2401	−	23.1574i	0.695752	−	0.934557i
$615$		0			0
$616$	−1.53981	−	0.364942i	−0.0620407	−	0.0147039i
$617$	5.77352	+	7.75518i	0.232433	+	0.312212i	0.903003	−	0.429635i	$-0.141358\pi$
$617$	5.77352	+	7.75518i	0.232433	+	0.312212i	−0.670570	+	0.741847i	$0.733950\pi$
$618$		0			0
$619$	−24.0046	−	12.0556i	−0.964828	−	0.484555i	−0.104628	−	0.994511i	$-0.533365\pi$
$619$	−24.0046	−	12.0556i	−0.964828	−	0.484555i	−0.860200	+	0.509957i	$0.829661\pi$
$620$	1.56802	−	2.71589i	0.0629732	−	0.109073i
$621$		0			0
$622$	−6.60160	−	11.4343i	−0.264700	−	0.458474i
$623$	−0.00719746	−	0.123576i	−0.000288360	−	0.00495095i
$624$		0			0
$625$	−14.5002	+	1.69483i	−0.580008	+	0.0677932i
$626$	−6.56393	−	21.9251i	−0.262347	−	0.876302i
$627$		0			0
$628$	−1.99623	−	4.62778i	−0.0796581	−	0.184668i
$629$	−31.5746	−	11.4922i	−1.25896	−	0.458224i
$630$		0			0
$631$	29.6208	−	10.7811i	1.17918	−	0.429188i	0.323270	−	0.946307i	$-0.395218\pi$
$631$	29.6208	−	10.7811i	1.17918	−	0.429188i	0.855914	+	0.517119i	$0.172996\pi$
$632$	−14.9275	−	15.8222i	−0.593782	−	0.629372i
$633$		0			0
$634$	22.4941	−	11.2969i	0.893354	−	0.448659i
$635$	0.552665	−	9.48889i	0.0219318	−	0.376555i
$636$		0			0
$637$	11.0926	−	37.0519i	0.439505	−	1.46805i
$638$	−2.00641	+	11.3789i	−0.0794344	+	0.450495i
$639$		0			0
$640$	−0.0888692	−	0.504002i	−0.00351286	−	0.0199224i
$641$	11.2656	+	1.31676i	0.444965	+	0.0520089i	0.335625	−	0.941996i	$-0.391052\pi$
$641$	11.2656	+	1.31676i	0.444965	+	0.0520089i	0.109339	+	0.994004i	$0.465126\pi$
$642$		0			0
$643$	−9.07210	+	9.61586i	−0.357769	+	0.379213i	−0.881111	−	0.472910i	$-0.843204\pi$
$643$	−9.07210	+	9.61586i	−0.357769	+	0.379213i	0.523342	+	0.852123i	$0.324685\pi$
$644$	−0.132686	+	0.307601i	−0.00522857	+	0.0121212i
$645$		0			0
$646$	−7.83922	+	5.15594i	−0.308430	+	0.202858i
$647$	−36.5943			−1.43867			−0.719336	−	0.694663i	$-0.755554\pi$
$647$	−36.5943			−1.43867			−0.719336	+	0.694663i	$0.755554\pi$
$648$		0			0
$649$	−2.28261			−0.0896005
$650$	−21.2743	+	13.9923i	−0.834445	+	0.548823i
$651$		0			0
$652$	2.35488	−	5.45923i	0.0922244	−	0.213800i
$653$	−18.7327	+	19.8555i	−0.733069	+	0.777008i	−0.981463	−	0.191651i	$-0.938616\pi$
$653$	−18.7327	+	19.8555i	−0.733069	+	0.777008i	0.248394	+	0.968659i	$0.420097\pi$
$654$		0			0
$655$	0.233993	+	0.0273499i	0.00914287	+	0.00106865i
$656$	3.04809	+	17.2866i	0.119008	+	0.674928i
$657$		0			0
$658$	−0.108714	+	0.616545i	−0.00423809	+	0.0240354i
$659$	4.23303	−	14.1393i	0.164895	−	0.550789i	−0.835104	−	0.550091i	$-0.814593\pi$
$659$	4.23303	−	14.1393i	0.164895	−	0.550789i	1.00000		0.000697383i	$-0.000221984\pi$
$660$		0			0
$661$	1.61762	−	27.7734i	0.0629181	−	1.08026i	−0.808111	−	0.589030i	$-0.799510\pi$
$661$	1.61762	−	27.7734i	0.0629181	−	1.08026i	0.871029	−	0.491232i	$-0.163453\pi$
$662$	0.807887	−	0.405736i	0.0313994	−	0.0157694i
$663$		0			0
$664$	28.4000	+	30.1023i	1.10214	+	1.16820i
$665$	−0.428987	+	0.156138i	−0.0166354	+	0.00605479i
$666$		0			0
$667$	7.62568	+	2.77552i	0.295267	+	0.107469i
$668$	6.06466	+	14.0595i	0.234649	+	0.543977i
$669$		0			0
$670$	1.63984	+	5.47746i	0.0633527	+	0.211613i
$671$	−4.98019	+	0.582101i	−0.192258	+	0.0224718i
$672$		0			0
$673$	−1.91225	−	32.8321i	−0.0737118	−	1.26558i	−0.808992	−	0.587820i	$-0.799986\pi$
$673$	−1.91225	−	32.8321i	−0.0737118	−	1.26558i	0.735280	−	0.677763i	$-0.237051\pi$
$674$	1.08967	+	1.88737i	0.0419727	+	0.0726989i
$675$		0			0
$676$	7.87718	−	13.6437i	0.302968	−	0.524757i
$677$	−21.5460	−	10.8208i	−0.828081	−	0.415878i	−0.0163192	−	0.999867i	$-0.505195\pi$
$677$	−21.5460	−	10.8208i	−0.828081	−	0.415878i	−0.811762	+	0.583989i	$0.801491\pi$
$678$		0			0
$679$	−1.72610	−	2.31855i	−0.0662416	−	0.0889779i
$680$	11.9529	+	2.83290i	0.458374	+	0.108637i
$681$		0			0
$682$	4.90538	−	6.58907i	0.187837	−	0.252308i
$683$	−10.1873	+	8.54816i	−0.389806	+	0.327086i	−0.816538	−	0.577292i	$-0.804109\pi$
$683$	−10.1873	+	8.54816i	−0.389806	+	0.327086i	0.426731	+	0.904378i	$0.359665\pi$
$684$		0			0
$685$	−6.89130	−	5.78249i	−0.263303	−	0.220938i
$686$	−4.13656	+	0.980382i	−0.157934	+	0.0374311i
$687$		0			0
$688$	16.2539	+	10.6904i	0.619675	+	0.407567i
$689$	−14.3990	−	9.47035i	−0.548557	−	0.360792i
$690$		0			0
$691$	−42.6555	+	10.1095i	−1.62269	+	0.384585i	−0.938654	−	0.344862i	$-0.887926\pi$
$691$	−42.6555	+	10.1095i	−1.62269	+	0.384585i	−0.684038	+	0.729447i	$0.739778\pi$
$692$	−9.24612	−	7.75841i	−0.351485	−	0.294931i
$693$		0			0
$694$	5.31231	−	4.45756i	0.201653	−	0.169207i
$695$	−0.276267	+	0.371091i	−0.0104794	+	0.0140763i
$696$		0			0
$697$	52.6345	+	12.4746i	1.99367	+	0.472510i
$698$	−4.21593	−	5.66297i	−0.159575	−	0.214347i
$699$		0			0
$700$	−0.943452	−	0.473819i	−0.0356591	−	0.0179087i
$701$	−3.65194	+	6.32534i	−0.137932	+	0.238905i	−0.926714	−	0.375768i	$-0.877379\pi$
$701$	−3.65194	+	6.32534i	−0.137932	+	0.238905i	0.788782	+	0.614673i	$0.210712\pi$
$702$		0			0
$703$	6.65434	+	11.5257i	0.250973	+	0.434699i
$704$	−0.823941	−	14.1465i	−0.0310535	−	0.533167i
$705$		0			0
$706$	−0.320133	+	0.0374181i	−0.0120484	+	0.00140825i
$707$	−0.762251	−	2.54609i	−0.0286674	−	0.0957558i
$708$		0			0
$709$	−17.3188	−	40.1494i	−0.650420	−	1.50784i	−0.849350	−	0.527829i	$-0.823006\pi$
$709$	−17.3188	−	40.1494i	−0.650420	−	1.50784i	0.198931	−	0.980014i	$-0.436253\pi$
$710$	−11.0372	−	4.01722i	−0.414219	−	0.150764i
$711$		0			0
$712$	1.23971	−	0.451219i	0.0464602	−	0.0169101i
$713$	−3.95917	−	4.19647i	−0.148272	−	0.157159i
$714$		0			0
$715$	−7.71852	+	3.87638i	−0.288656	+	0.144969i
$716$	−0.526080	+	9.03245i	−0.0196605	+	0.337558i
$717$		0			0
$718$	1.25556	−	4.19385i	0.0468569	−	0.156513i
$719$	−1.93615	+	10.9804i	−0.0722061	+	0.409501i	0.927185	+	0.374604i	$0.122221\pi$
$719$	−1.93615	+	10.9804i	−0.0722061	+	0.409501i	−0.999391	+	0.0348968i	$0.988890\pi$
$720$		0			0
$721$	−0.729037	−	4.13457i	−0.0271508	−	0.153980i
$722$	−16.4321	−	1.92064i	−0.611541	−	0.0714789i
$723$		0			0
$724$	−7.34856	+	7.78902i	−0.273107	+	0.289477i
$725$	−10.1296	+	23.4831i	−0.376204	+	0.872140i
$726$		0			0
$727$	−24.3067	+	15.9867i	−0.901484	+	0.592916i	−0.913422	−	0.407013i	$-0.866570\pi$
$727$	−24.3067	+	15.9867i	−0.901484	+	0.592916i	0.0119379	+	0.999929i	$0.496200\pi$
$728$	−4.88893			−0.181196
$729$		0			0
$730$	−5.84576			−0.216361
$731$	50.0886	−	32.9438i	1.85259	−	1.21847i
$732$		0			0
$733$	6.87604	−	15.9405i	0.253972	−	0.588774i	−0.742759	−	0.669559i	$-0.766483\pi$
$733$	6.87604	−	15.9405i	0.253972	−	0.588774i	0.996732	+	0.0807844i	$0.0257425\pi$
$734$	−6.58210	+	6.97662i	−0.242950	+	0.257512i
$735$		0			0
$736$	−6.02353	−	0.704050i	−0.222030	−	0.0259516i
$737$	−1.97369	−	11.1933i	−0.0727017	−	0.412312i
$738$		0			0
$739$	3.59215	−	20.3721i	0.132139	−	0.749400i	−0.844670	−	0.535288i	$-0.820203\pi$
$739$	3.59215	−	20.3721i	0.132139	−	0.749400i	0.976809	−	0.214112i	$-0.0686857\pi$
$740$	1.50623	−	5.03117i	0.0553703	−	0.184950i
$741$		0			0
$742$	−0.0547471	+	0.939971i	−0.00200983	+	0.0345074i
$743$	−34.0508	+	17.1009i	−1.24920	+	0.627373i	−0.945571	−	0.325417i	$-0.894495\pi$
$743$	−34.0508	+	17.1009i	−1.24920	+	0.627373i	−0.303632	+	0.952790i	$0.598199\pi$
$744$		0			0
$745$	−11.5081	−	12.1978i	−0.421623	−	0.446894i
$746$	5.27104	−	1.91850i	0.192986	−	0.0702413i
$747$		0			0
$748$	−6.91643	−	2.51737i	−0.252890	−	0.0920443i
$749$	0.00854027	+	0.0197986i	0.000312055	+	0.000723424i
$750$		0			0
$751$	−9.82318	−	32.8117i	−0.358453	−	1.19732i	−0.927125	−	0.374752i	$-0.877728\pi$
$751$	−9.82318	−	32.8117i	−0.358453	−	1.19732i	0.568672	−	0.822564i	$-0.307457\pi$
$752$	−3.11375	+	0.363945i	−0.113547	+	0.0132717i
$753$		0			0
$754$	2.07558	+	35.6363i	0.0755881	+	1.29780i
$755$	6.33114	+	10.9659i	0.230414	+	0.399088i
$756$		0			0
$757$	−14.5877	+	25.2666i	−0.530198	+	0.918330i	0.469181	+	0.883102i	$0.344549\pi$
$757$	−14.5877	+	25.2666i	−0.530198	+	0.918330i	−0.999379	+	0.0352284i	$0.988784\pi$
$758$	−7.17966	−	3.60576i	−0.260777	−	0.130967i
$759$		0			0
$760$	−2.90546	−	3.90271i	−0.105392	−	0.141566i
$761$	12.0070	+	2.84572i	0.435255	+	0.103157i	0.442401	−	0.896817i	$-0.354127\pi$
$761$	12.0070	+	2.84572i	0.435255	+	0.103157i	−0.00714662	+	0.999974i	$0.502275\pi$
$762$		0			0
$763$	−0.905200	+	1.21589i	−0.0327704	+	0.0440183i
$764$	9.34155	−	7.83849i	0.337965	−	0.283587i
$765$		0			0
$766$	29.0983	+	24.4163i	1.05136	+	0.882198i
$767$	−6.86191	+	1.62630i	−0.247769	+	0.0587224i
$768$		0			0
$769$	−2.31777	−	1.52442i	−0.0835810	−	0.0549721i	0.507031	−	0.861928i	$-0.330743\pi$
$769$	−2.31777	−	1.52442i	−0.0835810	−	0.0549721i	−0.590612	+	0.806956i	$0.701113\pi$
$770$	0.394251	+	0.259303i	0.0142078	+	0.00934464i
$771$		0			0
$772$	−18.5150	+	4.38813i	−0.666369	+	0.157932i
$773$	−21.3606	−	17.9237i	−0.768287	−	0.644669i	0.171983	−	0.985100i	$-0.444983\pi$
$773$	−21.3606	−	17.9237i	−0.768287	−	0.644669i	−0.940270	+	0.340431i	$0.889427\pi$
$774$		0			0
$775$	13.9283	−	11.6872i	0.500320	−	0.419818i
$776$	18.3964	−	24.7107i	0.660392	−	0.887061i
$777$		0			0
$778$	−13.1391	−	3.11402i	−0.471059	−	0.111643i
$779$	−12.7941	−	17.1855i	−0.458398	−	0.615735i
$780$		0			0
$781$	20.8652	+	10.4789i	0.746616	+	0.374964i
$782$	3.40582	−	5.89906i	0.121792	−	0.210950i
$783$		0

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.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.890910 - 0.585961i) q^{2} +(-0.341789 + 0.792356i) q^{4} +(0.585850 - 0.620965i) q^{5} +(0.284505 + 0.0332539i) q^{7} +(0.530120 + 3.00646i) q^{8} +O(q^{10})\)	\(q+(0.890910 - 0.585961i) q^{2} +(-0.341789 + 0.792356i) q^{4} +(0.585850 - 0.620965i) q^{5} +(0.284505 + 0.0332539i) q^{7} +(0.530120 + 3.00646i) q^{8} +(0.158079 - 0.896509i) q^{10} +(-0.519011 + 1.73362i) q^{11} +(-0.325075 + 5.58132i) q^{13} +(0.272954 - 0.137083i) q^{14} +(1.04960 + 1.11251i) q^{16} +(4.42908 - 1.61205i) q^{17} +(-1.75427 - 0.638503i) q^{19} +(0.291788 + 0.676441i) q^{20} +(0.553440 + 1.84862i) q^{22} +(1.34612 - 0.157339i) q^{23} +(0.248347 + 4.26396i) q^{25} +(2.98082 + 5.16294i) q^{26} +(-0.123590 + 0.214064i) q^{28} +(5.35083 + 2.68729i) q^{29} +(-2.54206 - 3.41458i) q^{31} +(-4.35412 - 1.03194i) q^{32} +(3.00131 - 4.03146i) q^{34} +(0.187327 - 0.157186i) q^{35} +(-5.46107 - 4.58238i) q^{37} +(-1.93704 + 0.459086i) q^{38} +(2.17748 + 1.43215i) q^{40} +(9.58849 + 6.30645i) q^{41} +(12.3767 - 2.93332i) q^{43} +(-1.19625 - 1.00377i) q^{44} +(1.10708 - 0.928949i) q^{46} +(-1.22397 + 1.64408i) q^{47} +(-6.73148 - 1.59539i) q^{49} +(2.71977 + 3.65328i) q^{50} +(-4.31129 - 2.16521i) q^{52} +(-1.54131 + 2.66962i) q^{53} +(0.772454 + 1.33793i) q^{55} +(0.0508455 + 0.872983i) q^{56} +(6.34175 - 0.741244i) q^{58} +(0.361763 + 1.20837i) q^{59} +(1.09744 + 2.54416i) q^{61} +(-4.26556 - 1.55254i) q^{62} +(-7.35831 + 2.67821i) q^{64} +(3.27536 + 3.47168i) q^{65} +(-5.61273 + 2.81882i) q^{67} +(-0.236491 + 4.06039i) q^{68} +(0.0747867 - 0.249805i) q^{70} +(2.24048 - 12.7064i) q^{71} +(-1.11508 - 6.32396i) q^{73} +(-7.55042 - 0.882517i) q^{74} +(1.10551 - 1.17178i) q^{76} +(-0.205311 + 0.475965i) q^{77} +(-5.95312 + 3.91543i) q^{79} +1.30574 q^{80} +12.2378 q^{82} +(11.3260 - 7.44925i) q^{83} +(1.59375 - 3.69472i) q^{85} +(9.30768 - 9.86557i) q^{86} +(-5.48720 - 0.641362i) q^{88} +(-0.0750415 - 0.425581i) q^{89} +(-0.278086 + 1.57711i) q^{91} +(-0.335421 + 1.12038i) q^{92} +(-0.127083 + 2.18193i) q^{94} +(-1.42423 + 0.715275i) q^{95} +(-6.92494 - 7.34001i) q^{97} +(-6.93197 + 2.52303i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Introduction

L-functions

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