LMFDB - Embedded newform 243.2.e.a.28.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(28,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("243.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			28.2
Root			$0.500000 - 2.22827i$ of defining polynomial
Character	$\chi$	$=$	243.28
Dual form			243.2.e.a.217.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.367548 + 2.08447i) q^{2} +(-2.33052 + 0.848241i) q^{4} +(2.05537 + 1.72466i) q^{5} +(-0.913694 - 0.332557i) q^{7} +(-0.508086 - 0.880031i) q^{8} +O(q^{10})$	\(q+(0.367548 + 2.08447i) q^{2} +(-2.33052 + 0.848241i) q^{4} +(2.05537 + 1.72466i) q^{5} +(-0.913694 - 0.332557i) q^{7} +(-0.508086 - 0.880031i) q^{8} +(-2.83955 + 4.91825i) q^{10} +(0.242761 - 0.203701i) q^{11} +(-0.262909 + 1.49103i) q^{13} +(0.357379 - 2.02679i) q^{14} +(-2.15207 + 1.80580i) q^{16} +(0.587342 - 1.01731i) q^{17} +(-3.11040 - 5.38737i) q^{19} +(-6.25302 - 2.27591i) q^{20} +(0.513834 + 0.431158i) q^{22} +(2.03231 - 0.739701i) q^{23} +(0.381855 + 2.16561i) q^{25} -3.20463 q^{26} +2.41147 q^{28} +(0.764905 + 4.33799i) q^{29} +(8.15017 - 2.96642i) q^{31} +(-6.11199 - 5.12857i) q^{32} +(2.33642 + 0.850386i) q^{34} +(-1.30443 - 2.25934i) q^{35} +(2.23332 - 3.86823i) q^{37} +(10.0866 - 8.46364i) q^{38} +(0.473450 - 2.68507i) q^{40} +(-1.01501 + 5.75638i) q^{41} +(4.28295 - 3.59382i) q^{43} +(-0.392973 + 0.680649i) q^{44} +(2.28885 + 3.96441i) q^{46} +(-2.32674 - 0.846865i) q^{47} +(-4.63807 - 3.89180i) q^{49} +(-4.37378 + 1.59193i) q^{50} +(-0.652037 - 3.69789i) q^{52} +10.8920 q^{53} +0.850279 q^{55} +(0.171574 + 0.973047i) q^{56} +(-8.76126 + 3.18884i) q^{58} +(1.32082 + 1.10830i) q^{59} +(-0.953579 - 0.347074i) q^{61} +(9.17898 + 15.8985i) q^{62} +(5.63455 - 9.75933i) q^{64} +(-3.11190 + 2.61119i) q^{65} +(0.148739 - 0.843538i) q^{67} +(-0.505893 + 2.86906i) q^{68} +(4.23008 - 3.54946i) q^{70} +(-4.79788 + 8.31018i) q^{71} +(7.62091 + 13.1998i) q^{73} +(8.88405 + 3.23353i) q^{74} +(11.8187 + 9.91703i) q^{76} +(-0.289552 + 0.105388i) q^{77} +(-1.94725 - 11.0434i) q^{79} -7.53771 q^{80} -12.3721 q^{82} +(-0.813530 - 4.61376i) q^{83} +(2.96172 - 1.07798i) q^{85} +(9.06538 + 7.60676i) q^{86} +(-0.302607 - 0.110140i) q^{88} +(-7.74976 - 13.4230i) q^{89} +(0.736071 - 1.27491i) q^{91} +(-4.10891 + 3.44778i) q^{92} +(0.910073 - 5.16128i) q^{94} +(2.89837 - 16.4375i) q^{95} +(-4.25115 + 3.56714i) q^{97} +(6.40762 - 11.0983i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 6 * q^8	$ 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} + 6 q^{11} + 3 q^{13} + 21 q^{14} + 9 q^{16} - 9 q^{17} - 3 q^{19} - 24 q^{20} + 12 q^{22} + 12 q^{23} + 12 q^{25} + 30 q^{26} - 12 q^{28} + 24 q^{29} + 12 q^{31} - 27 q^{32} - 12 q^{35} - 3 q^{37} + 30 q^{38} - 15 q^{40} - 6 q^{41} - 15 q^{43} - 3 q^{44} - 3 q^{46} - 12 q^{47} - 33 q^{49} - 21 q^{50} - 45 q^{52} + 18 q^{53} - 12 q^{55} - 30 q^{56} - 51 q^{58} + 3 q^{59} - 33 q^{61} + 12 q^{62} + 12 q^{64} - 21 q^{65} - 6 q^{67} - 9 q^{68} - 15 q^{70} - 27 q^{71} + 6 q^{73} + 21 q^{74} + 6 q^{76} + 12 q^{77} + 21 q^{79} - 42 q^{80} - 12 q^{82} + 6 q^{83} + 36 q^{85} + 21 q^{86} + 42 q^{88} - 9 q^{89} + 6 q^{91} + 3 q^{92} + 48 q^{94} - 3 q^{95} + 39 q^{97} + 45 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^10 + 6 * q^11 + 3 * q^13 + 21 * q^14 + 9 * q^16 - 9 * q^17 - 3 * q^19 - 24 * q^20 + 12 * q^22 + 12 * q^23 + 12 * q^25 + 30 * q^26 - 12 * q^28 + 24 * q^29 + 12 * q^31 - 27 * q^32 - 12 * q^35 - 3 * q^37 + 30 * q^38 - 15 * q^40 - 6 * q^41 - 15 * q^43 - 3 * q^44 - 3 * q^46 - 12 * q^47 - 33 * q^49 - 21 * q^50 - 45 * q^52 + 18 * q^53 - 12 * q^55 - 30 * q^56 - 51 * q^58 + 3 * q^59 - 33 * q^61 + 12 * q^62 + 12 * q^64 - 21 * q^65 - 6 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 + 21 * q^74 + 6 * q^76 + 12 * q^77 + 21 * q^79 - 42 * q^80 - 12 * q^82 + 6 * q^83 + 36 * q^85 + 21 * q^86 + 42 * q^88 - 9 * q^89 + 6 * q^91 + 3 * q^92 + 48 * q^94 - 3 * q^95 + 39 * q^97 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	0.367548	+	2.08447i	0.259895	+	1.47394i	0.783187	+	0.621786i	$0.213593\pi$
$2$	0.367548	+	2.08447i	0.259895	+	1.47394i	−0.523291	+	0.852154i	$0.675296\pi$
$3$		0			0
$3$		0			0
$4$	−2.33052	+	0.848241i	−1.16526	+	0.424121i
$5$	2.05537	+	1.72466i	0.919190	+	0.771292i	0.973845	−	0.227213i	$-0.0729614\pi$
$5$	2.05537	+	1.72466i	0.919190	+	0.771292i	−0.0546547	+	0.998505i	$0.517406\pi$
$6$		0			0
$7$	−0.913694	−	0.332557i	−0.345344	−	0.125695i	0.163524	−	0.986539i	$-0.447714\pi$
$7$	−0.913694	−	0.332557i	−0.345344	−	0.125695i	−0.508868	+	0.860844i	$0.669936\pi$
$8$	−0.508086	−	0.880031i	−0.179636	−	0.311138i
$9$		0			0
$10$	−2.83955	+	4.91825i	−0.897945	+	1.55529i
$11$	0.242761	−	0.203701i	0.0731952	−	0.0614181i	−0.605456	−	0.795879i	$-0.707009\pi$
$11$	0.242761	−	0.203701i	0.0731952	−	0.0614181i	0.678651	+	0.734461i	$0.262565\pi$
$12$		0			0
$13$	−0.262909	+	1.49103i	−0.0729177	+	0.413537i	0.926398	+	0.376546i	$0.122888\pi$
$13$	−0.262909	+	1.49103i	−0.0729177	+	0.413537i	−0.999316	+	0.0369909i	$0.988223\pi$
$14$	0.357379	−	2.02679i	0.0955135	−	0.541684i
$15$		0			0
$16$	−2.15207	+	1.80580i	−0.538018	+	0.451451i
$17$	0.587342	−	1.01731i	0.142451	−	0.246733i	−0.785968	−	0.618267i	$-0.787835\pi$
$17$	0.587342	−	1.01731i	0.142451	−	0.246733i	0.928419	+	0.371534i	$0.121168\pi$
$18$		0			0
$19$	−3.11040	−	5.38737i	−0.713575	−	1.23595i	−0.963507	−	0.267685i	$-0.913741\pi$
$19$	−3.11040	−	5.38737i	−0.713575	−	1.23595i	0.249931	−	0.968264i	$-0.419592\pi$
$20$	−6.25302	−	2.27591i	−1.39822	−	0.508910i
$21$		0			0
$22$	0.513834	+	0.431158i	0.109550	+	0.0919231i
$23$	2.03231	−	0.739701i	0.423766	−	0.154238i	−0.121329	−	0.992612i	$-0.538716\pi$
$23$	2.03231	−	0.739701i	0.423766	−	0.154238i	0.545095	+	0.838374i	$0.316493\pi$
$24$		0			0
$25$	0.381855	+	2.16561i	0.0763710	+	0.433121i
$26$	−3.20463			−0.628480
$27$		0			0
$28$	2.41147			0.455726
$29$	0.764905	+	4.33799i	0.142039	+	0.805545i	0.969697	+	0.244311i	$0.0785618\pi$
$29$	0.764905	+	4.33799i	0.142039	+	0.805545i	−0.827658	+	0.561233i	$0.810327\pi$
$30$		0			0
$31$	8.15017	−	2.96642i	1.46381	−	0.532784i	0.517400	−	0.855743i	$-0.326900\pi$
$31$	8.15017	−	2.96642i	1.46381	−	0.532784i	0.946413	+	0.322959i	$0.104678\pi$
$32$	−6.11199	−	5.12857i	−1.08046	−	0.906611i
$33$		0			0
$34$	2.33642	+	0.850386i	0.400692	+	0.145840i
$35$	−1.30443	−	2.25934i	−0.220489	−	0.381899i
$36$		0			0
$37$	2.23332	−	3.86823i	0.367156	−	0.635933i	−0.621964	−	0.783046i	$-0.713665\pi$
$37$	2.23332	−	3.86823i	0.367156	−	0.635933i	0.989120	+	0.147113i	$0.0469982\pi$
$38$	10.0866	−	8.46364i	1.63626	−	1.37298i
$39$		0			0
$40$	0.473450	−	2.68507i	0.0748590	−	0.424547i
$41$	−1.01501	+	5.75638i	−0.158517	+	0.898996i	0.796982	+	0.604003i	$0.206428\pi$
$41$	−1.01501	+	5.75638i	−0.158517	+	0.898996i	−0.955499	+	0.294993i	$0.904683\pi$
$42$		0			0
$43$	4.28295	−	3.59382i	0.653143	−	0.548052i	−0.254880	−	0.966973i	$-0.582036\pi$
$43$	4.28295	−	3.59382i	0.653143	−	0.548052i	0.908023	+	0.418920i	$0.137591\pi$
$44$	−0.392973	+	0.680649i	−0.0592429	+	0.102612i
$45$		0			0
$46$	2.28885	+	3.96441i	0.337473	+	0.584521i
$47$	−2.32674	−	0.846865i	−0.339390	−	0.123528i	0.166702	−	0.986007i	$-0.446688\pi$
$47$	−2.32674	−	0.846865i	−0.339390	−	0.123528i	−0.506092	+	0.862479i	$0.668910\pi$
$48$		0			0
$49$	−4.63807	−	3.89180i	−0.662581	−	0.555972i
$50$	−4.37378	+	1.59193i	−0.618546	+	0.225132i
$51$		0			0
$52$	−0.652037	−	3.69789i	−0.0904213	−	0.512805i
$53$	10.8920			1.49613			0.748063	−	0.663628i	$-0.230984\pi$
$53$	10.8920			1.49613			0.748063	+	0.663628i	$0.230984\pi$
$54$		0			0
$55$	0.850279			0.114652
$56$	0.171574	+	0.973047i	0.0229276	+	0.130029i
$57$		0			0
$58$	−8.76126	+	3.18884i	−1.15041	+	0.418715i
$59$	1.32082	+	1.10830i	0.171956	+	0.144289i	0.724704	−	0.689060i	$-0.241976\pi$
$59$	1.32082	+	1.10830i	0.171956	+	0.144289i	−0.552748	+	0.833348i	$0.686421\pi$
$60$		0			0
$61$	−0.953579	−	0.347074i	−0.122093	−	0.0444383i	0.280251	−	0.959927i	$-0.409582\pi$
$61$	−0.953579	−	0.347074i	−0.122093	−	0.0444383i	−0.402344	+	0.915488i	$0.631805\pi$
$62$	9.17898	+	15.8985i	1.16573	+	2.01911i
$63$		0			0
$64$	5.63455	−	9.75933i	0.704319	−	1.21992i
$65$	−3.11190	+	2.61119i	−0.385983	+	0.323878i
$66$		0			0
$67$	0.148739	−	0.843538i	0.0181713	−	0.103055i	−0.974373	−	0.224938i	$-0.927782\pi$
$67$	0.148739	−	0.843538i	0.0181713	−	0.103055i	0.992544	+	0.121883i	$0.0388933\pi$
$68$	−0.505893	+	2.86906i	−0.0613486	+	0.347925i
$69$		0			0
$70$	4.23008	−	3.54946i	0.505592	−	0.424242i
$71$	−4.79788	+	8.31018i	−0.569404	+	0.986237i	0.427221	+	0.904147i	$0.359493\pi$
$71$	−4.79788	+	8.31018i	−0.569404	+	0.986237i	−0.996625	+	0.0820894i	$0.973841\pi$
$72$		0			0
$73$	7.62091	+	13.1998i	0.891960	+	1.54492i	0.837522	+	0.546404i	$0.184004\pi$
$73$	7.62091	+	13.1998i	0.891960	+	1.54492i	0.0544385	+	0.998517i	$0.482663\pi$
$74$	8.88405	+	3.23353i	1.03275	+	0.375890i
$75$		0			0
$76$	11.8187	+	9.91703i	1.35569	+	1.13756i
$77$	−0.289552	+	0.105388i	−0.0329975	+	0.0120101i
$78$		0			0
$79$	−1.94725	−	11.0434i	−0.219083	−	1.24248i	−0.873680	−	0.486502i	$-0.838273\pi$
$79$	−1.94725	−	11.0434i	−0.219083	−	1.24248i	0.654597	−	0.755978i	$-0.272838\pi$
$80$	−7.53771			−0.842741
$81$		0			0
$82$	−12.3721			−1.36626
$83$	−0.813530	−	4.61376i	−0.0892965	−	0.506425i	−0.996347	−	0.0854026i	$-0.972782\pi$
$83$	−0.813530	−	4.61376i	−0.0892965	−	0.506425i	0.907050	−	0.421023i	$-0.138329\pi$
$84$		0			0
$85$	2.96172	−	1.07798i	0.321243	−	0.116923i
$86$	9.06538	+	7.60676i	0.977546	+	0.820258i
$87$		0			0
$88$	−0.302607	−	0.110140i	−0.0322580	−	0.0117409i
$89$	−7.74976	−	13.4230i	−0.821473	−	1.42283i	−0.904586	−	0.426292i	$-0.859820\pi$
$89$	−7.74976	−	13.4230i	−0.821473	−	1.42283i	0.0831130	−	0.996540i	$-0.473514\pi$
$90$		0			0
$91$	0.736071	−	1.27491i	0.0771612	−	0.133647i
$92$	−4.10891	+	3.44778i	−0.428383	+	0.359456i
$93$		0			0
$94$	0.910073	−	5.16128i	0.0938669	−	0.532346i
$95$	2.89837	−	16.4375i	0.297366	−	1.68645i
$96$		0			0
$97$	−4.25115	+	3.56714i	−0.431639	+	0.362188i	−0.832570	−	0.553920i	$-0.813131\pi$
$97$	−4.25115	+	3.56714i	−0.431639	+	0.362188i	0.400931	+	0.916108i	$0.368687\pi$
$98$	6.40762	−	11.0983i	0.647267	−	1.12110i
$99$		0			0
$100$	−2.72688	−	4.72309i	−0.272688	−	0.472309i
$101$	−9.52759	−	3.46776i	−0.948030	−	0.345055i	−0.178698	−	0.983904i	$-0.557189\pi$
$101$	−9.52759	−	3.46776i	−0.948030	−	0.345055i	−0.769332	+	0.638849i	$0.779411\pi$
$102$		0			0
$103$	−7.54806	−	6.33357i	−0.743732	−	0.624065i	0.190105	−	0.981764i	$-0.439117\pi$
$103$	−7.54806	−	6.33357i	−0.743732	−	0.624065i	−0.933837	+	0.357698i	$0.883562\pi$
$104$	1.44573	−	0.526203i	0.141766	−	0.0515985i
$105$		0			0
$106$	4.00331	+	22.7039i	0.388836	+	2.20520i
$107$	−5.17080			−0.499880			−0.249940	−	0.968261i	$-0.580411\pi$
$107$	−5.17080			−0.499880			−0.249940	+	0.968261i	$0.580411\pi$
$108$		0			0
$109$	−7.31065			−0.700234			−0.350117	−	0.936706i	$-0.613858\pi$
$109$	−7.31065			−0.700234			−0.350117	+	0.936706i	$0.613858\pi$
$110$	0.312518	+	1.77238i	0.0297974	+	0.168990i
$111$		0			0
$112$	2.56687	−	0.934263i	0.242546	−	0.0882796i
$113$	−7.94820	−	6.66933i	−0.747704	−	0.627398i	0.187191	−	0.982324i	$-0.440062\pi$
$113$	−7.94820	−	6.66933i	−0.747704	−	0.627398i	−0.934895	+	0.354925i	$0.884506\pi$
$114$		0			0
$115$	5.45289	+	1.98469i	0.508485	+	0.185073i
$116$	−5.46229	−	9.46096i	−0.507161	−	0.878428i
$117$		0			0
$118$	−1.82475	+	3.16056i	−0.167982	+	0.290953i
$119$	−0.874964	+	0.734182i	−0.0802078	+	0.0673023i
$120$		0			0
$121$	−1.89269	+	10.7340i	−0.172063	+	0.975817i
$122$	0.372979	−	2.11527i	0.0337680	−	0.191508i
$123$		0			0
$124$	−16.4779	+	13.8266i	−1.47976	+	1.24167i
$125$	3.75766	−	6.50846i	0.336095	−	0.582134i
$126$		0			0
$127$	−2.61372	−	4.52709i	−0.231930	−	0.401714i	0.726446	−	0.687223i	$-0.241171\pi$
$127$	−2.61372	−	4.52709i	−0.231930	−	0.401714i	−0.958376	+	0.285509i	$0.907837\pi$
$128$	7.41903	+	2.70031i	0.655756	+	0.238676i
$129$		0			0
$130$	−6.58671	−	5.52691i	−0.577693	−	0.484742i
$131$	−6.79802	+	2.47428i	−0.593946	+	0.216179i	−0.621464	−	0.783443i	$-0.713462\pi$
$131$	−6.79802	+	2.47428i	−0.593946	+	0.216179i	0.0275183	+	0.999621i	$0.491240\pi$
$132$		0			0
$133$	1.05034	+	5.95680i	0.0910764	+	0.516520i
$134$	1.81300			0.156619
$135$		0			0
$136$	−1.19368			−0.102357
$137$	−1.95342	−	11.0784i	−0.166892	−	0.946493i	−0.947092	−	0.320962i	$-0.895994\pi$
$137$	−1.95342	−	11.0784i	−0.166892	−	0.946493i	0.780200	−	0.625531i	$-0.215117\pi$
$138$		0			0
$139$	−8.81447	+	3.20820i	−0.747634	+	0.272116i	−0.687610	−	0.726081i	$-0.741340\pi$
$139$	−8.81447	+	3.20820i	−0.747634	+	0.272116i	−0.0600240	+	0.998197i	$0.519118\pi$
$140$	4.95648	+	4.15898i	0.418899	+	0.351498i
$141$		0			0
$142$	−19.0857	−	6.94664i	−1.60164	−	0.582949i
$143$	0.239900	+	0.415518i	0.0200614	+	0.0347474i
$144$		0			0
$145$	−5.90940	+	10.2354i	−0.490749	+	0.850003i
$146$	−24.7135	+	20.7371i	−2.04530	+	1.71621i
$147$		0			0
$148$	−1.92362	+	10.9094i	−0.158121	+	0.896747i
$149$	−3.30821	+	18.7618i	−0.271019	+	1.53703i	0.480309	+	0.877099i	$0.340525\pi$
$149$	−3.30821	+	18.7618i	−0.271019	+	1.53703i	−0.751328	+	0.659928i	$0.770587\pi$
$150$		0			0
$151$	3.07490	−	2.58015i	0.250232	−	0.209970i	−0.509040	−	0.860743i	$-0.670000\pi$
$151$	3.07490	−	2.58015i	0.250232	−	0.209970i	0.759272	+	0.650773i	$0.225555\pi$
$152$	−3.16070	+	5.47450i	−0.256367	+	0.444041i
$153$		0			0
$154$	−0.326102	−	0.564825i	−0.0262780	−	0.0455149i
$155$	21.8677	+	7.95919i	1.75646	+	0.639298i
$156$		0			0
$157$	5.57368	+	4.67687i	0.444828	+	0.373255i	0.837512	−	0.546418i	$-0.184009\pi$
$157$	5.57368	+	4.67687i	0.444828	+	0.373255i	−0.392685	+	0.919673i	$0.628454\pi$
$158$	22.3039	−	8.11795i	1.77440	−	0.645830i
$159$		0			0
$160$	−3.71737	−	21.0822i	−0.293884	−	1.66670i
$161$	−2.10290			−0.165732
$162$		0			0
$163$	12.4492			0.975094			0.487547	−	0.873097i	$-0.337892\pi$
$163$	12.4492			0.975094			0.487547	+	0.873097i	$0.337892\pi$
$164$	−2.51731	−	14.2764i	−0.196569	−	1.11480i
$165$		0			0
$166$	9.31821	−	3.39155i	0.723233	−	0.263235i
$167$	1.78633	+	1.49891i	0.138230	+	0.115989i	0.709281	−	0.704926i	$-0.249020\pi$
$167$	1.78633	+	1.49891i	0.138230	+	0.115989i	−0.571051	+	0.820915i	$0.693464\pi$
$168$		0			0
$169$	10.0620	+	3.66225i	0.773997	+	0.281712i
$170$	3.33558	+	5.77739i	0.255827	+	0.443106i
$171$		0			0
$172$	−6.93308	+	12.0085i	−0.528643	+	0.915636i
$173$	2.74418	−	2.30264i	0.208636	−	0.175066i	−0.532482	−	0.846442i	$-0.678740\pi$
$173$	2.74418	−	2.30264i	0.208636	−	0.175066i	0.741118	+	0.671375i	$0.234296\pi$
$174$		0			0
$175$	0.371290	−	2.10569i	0.0280669	−	0.159175i
$176$	−0.154596	+	0.876757i	−0.0116531	+	0.0660880i
$177$		0			0
$178$	25.1313	−	21.0877i	1.88367	−	1.58059i
$179$	−9.99785	+	17.3168i	−0.747275	+	1.29432i	0.201850	+	0.979416i	$0.435305\pi$
$179$	−9.99785	+	17.3168i	−0.747275	+	1.29432i	−0.949124	+	0.314901i	$0.898029\pi$
$180$		0			0
$181$	−4.86616	−	8.42844i	−0.361699	−	0.626481i	0.626542	−	0.779388i	$-0.284470\pi$
$181$	−4.86616	−	8.42844i	−0.361699	−	0.626481i	−0.988241	+	0.152907i	$0.951136\pi$
$182$	2.92805	+	1.06572i	0.217042	+	0.0789967i
$183$		0			0
$184$	−1.68355	−	1.41267i	−0.124113	−	0.104143i
$185$	11.2617	−	4.09892i	0.827976	−	0.301359i
$186$		0			0
$187$	−0.0646422	−	0.366604i	−0.00472711	−	0.0268088i
$188$	6.14088			0.447869
$189$		0			0
$190$	35.3286			2.56301
$191$	3.08339	+	17.4868i	0.223106	+	1.26530i	0.866273	+	0.499571i	$0.166509\pi$
$191$	3.08339	+	17.4868i	0.223106	+	1.26530i	−0.643167	+	0.765726i	$0.722380\pi$
$192$		0			0
$193$	−9.94602	+	3.62006i	−0.715930	+	0.260577i	−0.674197	−	0.738551i	$-0.735510\pi$
$193$	−9.94602	+	3.62006i	−0.715930	+	0.260577i	−0.0417333	+	0.999129i	$0.513288\pi$
$194$	−8.99809	−	7.55029i	−0.646025	−	0.542079i
$195$		0			0
$196$	14.1103	+	5.13574i	1.00788	+	0.366838i
$197$	7.07945	+	12.2620i	0.504390	+	0.873628i	0.999987	+	0.00507615i	$0.00161579\pi$
$197$	7.07945	+	12.2620i	0.504390	+	0.873628i	−0.495597	+	0.868552i	$0.665051\pi$
$198$		0			0
$199$	−3.77010	+	6.53000i	−0.267255	+	0.462899i	−0.968152	−	0.250363i	$-0.919450\pi$
$199$	−3.77010	+	6.53000i	−0.267255	+	0.462899i	0.700897	+	0.713263i	$0.252783\pi$
$200$	1.71179	−	1.43636i	0.121042	−	0.101566i
$201$		0			0
$202$	3.72658	−	21.1345i	0.262201	−	1.48702i
$203$	0.743742	−	4.21797i	0.0522004	−	0.296043i
$204$		0			0
$205$	−12.0140	+	10.0810i	−0.839096	+	0.704085i
$206$	10.4278	−	18.0616i	0.726543	−	1.25841i
$207$		0			0
$208$	−2.12670	−	3.68356i	−0.147460	−	0.255409i
$209$	−1.85250	−	0.674254i	−0.128140	−	0.0466391i
$210$		0			0
$211$	3.99388	+	3.35126i	0.274950	+	0.230710i	0.769827	−	0.638253i	$-0.220342\pi$
$211$	3.99388	+	3.35126i	0.274950	+	0.230710i	−0.494877	+	0.868963i	$0.664787\pi$
$212$	−25.3840	+	9.23901i	−1.74338	+	0.634538i
$213$		0			0
$214$	−1.90052	−	10.7784i	−0.129917	−	0.736794i
$215$	15.0012			1.02307
$216$		0			0
$217$	−8.43326			−0.572487
$218$	−2.68701	−	15.2388i	−0.181988	−	1.03210i
$219$		0			0
$220$	−1.98160	+	0.721242i	−0.133599	+	0.0486261i
$221$	1.36242	+	1.14320i	0.0916460	+	0.0769001i
$222$		0			0
$223$	−16.6267	−	6.05164i	−1.11341	−	0.405248i	−0.281166	−	0.959659i	$-0.590721\pi$
$223$	−16.6267	−	6.05164i	−1.11341	−	0.405248i	−0.832243	+	0.554412i	$0.812943\pi$
$224$	3.87894	+	6.71853i	0.259173	+	0.448901i
$225$		0			0
$226$	10.9807	−	19.0191i	0.730423	−	1.26513i
$227$	12.0820	−	10.1380i	0.801913	−	0.672885i	−0.146750	−	0.989174i	$-0.546881\pi$
$227$	12.0820	−	10.1380i	0.801913	−	0.672885i	0.948663	+	0.316289i	$0.102437\pi$
$228$		0			0
$229$	−0.306813	+	1.74002i	−0.0202748	+	0.114984i	−0.993266	−	0.115860i	$-0.963038\pi$
$229$	−0.306813	+	1.74002i	−0.0202748	+	0.114984i	0.972991	+	0.230844i	$0.0741487\pi$
$230$	−2.13282	+	12.0958i	−0.140634	+	0.797576i
$231$		0			0
$232$	3.42893	−	2.87721i	0.225120	−	0.188898i
$233$	−6.94920	+	12.0364i	−0.455257	+	0.788529i	−0.998703	−	0.0509157i	$-0.983786\pi$
$233$	−6.94920	+	12.0364i	−0.455257	+	0.788529i	0.543446	+	0.839444i	$0.317119\pi$
$234$		0			0
$235$	−3.32177	−	5.75347i	−0.216688	−	0.375315i
$236$	−4.01831	−	1.46255i	−0.261570	−	0.0952037i
$237$		0			0
$238$	−1.85197	−	1.55399i	−0.120045	−	0.100730i
$239$	−18.6366	+	6.78318i	−1.20550	+	0.438767i	−0.865142	−	0.501527i	$-0.832772\pi$
$239$	−18.6366	+	6.78318i	−1.20550	+	0.438767i	−0.340362	+	0.940295i	$0.610549\pi$
$240$		0			0
$241$	3.36438	+	19.0804i	0.216719	+	1.22907i	0.877899	+	0.478846i	$0.158945\pi$
$241$	3.36438	+	19.0804i	0.216719	+	1.22907i	−0.661180	+	0.750227i	$0.729944\pi$
$242$	−23.0703			−1.48301
$243$		0			0
$244$	2.51674			0.161118
$245$	−2.82091	−	15.9982i	−0.180222	−	1.02209i
$246$		0			0
$247$	8.85048	−	3.22131i	0.563143	−	0.204967i
$248$	−6.75153	−	5.66521i	−0.428723	−	0.359741i
$249$		0			0
$250$	14.9478	+	5.44055i	0.945381	+	0.344090i
$251$	−2.73786	−	4.74212i	−0.172812	−	0.299320i	0.766590	−	0.642137i	$-0.221952\pi$
$251$	−2.73786	−	4.74212i	−0.172812	−	0.299320i	−0.939402	+	0.342818i	$0.888619\pi$
$252$		0			0
$253$	0.342689	−	0.593554i	0.0215447	−	0.0373164i
$254$	8.47590	−	7.11212i	0.531825	−	0.446254i
$255$		0			0
$256$	1.01187	−	5.73859i	0.0632418	−	0.358662i
$257$	2.00827	−	11.3895i	0.125272	−	0.710455i	−0.855873	−	0.517186i	$-0.826980\pi$
$257$	2.00827	−	11.3895i	0.125272	−	0.710455i	0.981146	−	0.193270i	$-0.0619092\pi$
$258$		0			0
$259$	−3.32698	+	2.79167i	−0.206729	+	0.173466i
$260$	5.03743	−	8.72508i	0.312408	−	0.541107i
$261$		0			0
$262$	−7.65614	−	13.2608i	−0.472998	−	0.819257i
$263$	6.08727	+	2.21558i	0.375357	+	0.136619i	0.522808	−	0.852451i	$-0.324885\pi$
$263$	6.08727	+	2.21558i	0.375357	+	0.136619i	−0.147451	+	0.989069i	$0.547107\pi$
$264$		0			0
$265$	22.3870	+	18.7849i	1.37522	+	1.15395i
$266$	−12.0307	+	4.37881i	−0.737649	+	0.268482i
$267$		0			0
$268$	0.368885	+	2.09205i	0.0225332	+	0.127792i
$269$	13.8387			0.843758			0.421879	−	0.906652i	$-0.361371\pi$
$269$	13.8387			0.843758			0.421879	+	0.906652i	$0.361371\pi$
$270$		0			0
$271$	1.94536			0.118172			0.0590860	−	0.998253i	$-0.481181\pi$
$271$	1.94536			0.118172			0.0590860	+	0.998253i	$0.481181\pi$
$272$	0.573052	+	3.24994i	0.0347464	+	0.197057i
$273$		0			0
$274$	22.3746	−	8.14369i	1.35170	−	0.491978i
$275$	0.533835	+	0.447941i	0.0321915	+	0.0270118i
$276$		0			0
$277$	−11.7205	−	4.26591i	−0.704216	−	0.256314i	−0.0350062	−	0.999387i	$-0.511145\pi$
$277$	−11.7205	−	4.26591i	−0.704216	−	0.256314i	−0.669210	+	0.743073i	$0.733367\pi$
$278$	−9.92713	−	17.1943i	−0.595390	−	1.03125i
$279$		0			0
$280$	−1.32553	+	2.29588i	−0.0792154	+	0.137205i
$281$	−7.47343	+	6.27095i	−0.445827	+	0.374094i	−0.837885	−	0.545847i	$-0.816208\pi$
$281$	−7.47343	+	6.27095i	−0.445827	+	0.374094i	0.392057	+	0.919941i	$0.371763\pi$
$282$		0			0
$283$	4.61405	−	26.1676i	0.274277	−	1.55550i	−0.466974	−	0.884271i	$-0.654656\pi$
$283$	4.61405	−	26.1676i	0.274277	−	1.55550i	0.741250	−	0.671229i	$-0.234233\pi$
$284$	4.13255	−	23.4368i	0.245221	−	1.39072i
$285$		0			0
$286$	−0.777960	+	0.652786i	−0.0460017	+	0.0386000i
$287$	2.84173	−	4.92202i	0.167742	−	0.290538i
$288$		0			0
$289$	7.81006	+	13.5274i	0.459415	+	0.795730i
$290$	−23.5073	−	8.55596i	−1.38040	−	0.502423i
$291$		0			0
$292$	−28.9573	−	24.2981i	−1.69460	−	1.42194i
$293$	11.5182	−	4.19230i	0.672903	−	0.244917i	0.0171059	−	0.999854i	$-0.494555\pi$
$293$	11.5182	−	4.19230i	0.672903	−	0.244917i	0.655797	+	0.754937i	$0.272333\pi$
$294$		0			0
$295$	0.803336	+	4.55594i	0.0467720	+	0.265257i
$296$	−4.53888			−0.263817
$297$		0			0
$298$	−40.3243			−2.33592
$299$	0.568603	+	3.22471i	0.0328832	+	0.186490i
$300$		0			0
$301$	−5.10845	+	1.85933i	−0.294446	+	0.107170i
$302$	6.50841	+	5.46121i	0.374517	+	0.314257i
$303$		0			0
$304$	16.4223	+	5.97724i	0.941886	+	0.342818i
$305$	−1.36137	−	2.35797i	−0.0779521	−	0.135017i
$306$		0			0
$307$	13.2370	−	22.9271i	0.755475	−	1.30852i	−0.189663	−	0.981849i	$-0.560740\pi$
$307$	13.2370	−	22.9271i	0.755475	−	1.30852i	0.945138	−	0.326671i	$-0.105927\pi$
$308$	0.585412	−	0.491219i	0.0333569	−	0.0279898i
$309$		0			0
$310$	−8.55325	+	48.5079i	−0.485792	+	2.75506i
$311$	3.06654	−	17.3912i	0.173887	−	0.986164i	−0.765533	−	0.643397i	$-0.777525\pi$
$311$	3.06654	−	17.3912i	0.173887	−	0.986164i	0.939420	−	0.342768i	$-0.111364\pi$
$312$		0			0
$313$	7.39019	−	6.20111i	0.417718	−	0.350507i	−0.409576	−	0.912276i	$-0.634323\pi$
$313$	7.39019	−	6.20111i	0.417718	−	0.350507i	0.827294	+	0.561769i	$0.189879\pi$
$314$	−7.70019	+	13.3371i	−0.434547	+	0.752657i
$315$		0			0
$316$	13.9056	+	24.0852i	0.782250	+	1.35490i
$317$	−3.48672	−	1.26906i	−0.195834	−	0.0712777i	0.242241	−	0.970216i	$-0.422117\pi$
$317$	−3.48672	−	1.26906i	−0.195834	−	0.0712777i	−0.438075	+	0.898938i	$0.644340\pi$
$318$		0			0
$319$	1.06934	+	0.897284i	0.0598716	+	0.0502382i
$320$	28.4126	−	10.3414i	1.58831	−	0.578099i
$321$		0			0
$322$	−0.772918	−	4.38343i	−0.0430730	−	0.244279i
$323$	−7.30748			−0.406599
$324$		0			0
$325$	−3.32937			−0.184680
$326$	4.57566	+	25.9499i	0.253422	+	1.43723i
$327$		0			0
$328$	5.58151	−	2.03150i	0.308187	−	0.112171i
$329$	1.84430	+	1.54755i	0.101680	+	0.0853193i
$330$		0			0
$331$	1.32759	+	0.483205i	0.0729712	+	0.0265593i	0.378248	−	0.925704i	$-0.376527\pi$
$331$	1.32759	+	0.483205i	0.0729712	+	0.0265593i	−0.305277	+	0.952264i	$0.598749\pi$
$332$	5.80953	+	10.0624i	0.318839	+	0.552246i
$333$		0			0
$334$	−2.46786	+	4.27446i	−0.135035	+	0.233888i
$335$	1.76053	−	1.47726i	0.0961881	−	0.0807114i
$336$		0			0
$337$	−2.25570	+	12.7927i	−0.122876	+	0.696864i	0.859671	+	0.510848i	$0.170669\pi$
$337$	−2.25570	+	12.7927i	−0.122876	+	0.696864i	−0.982547	+	0.186016i	$0.940442\pi$
$338$	−3.93559	+	22.3199i	−0.214068	+	1.21404i
$339$		0			0
$340$	−5.98797	+	5.02450i	−0.324743	+	0.272492i
$341$	1.37428	−	2.38033i	0.0744215	−	0.128902i
$342$		0			0
$343$	6.34669	+	10.9928i	0.342689	+	0.593555i
$344$	−5.33878	−	1.94316i	−0.287848	−	0.104768i
$345$		0			0
$346$	5.80839	+	4.87382i	0.312261	+	0.262018i
$347$	−4.51096	+	1.64185i	−0.242161	+	0.0881394i	−0.460250	−	0.887790i	$-0.652240\pi$
$347$	−4.51096	+	1.64185i	−0.242161	+	0.0881394i	0.218089	+	0.975929i	$0.430018\pi$
$348$		0			0
$349$	−3.92055	−	22.2346i	−0.209862	−	1.19019i	−0.889602	−	0.456736i	$-0.849018\pi$
$349$	−3.92055	−	22.2346i	−0.209862	−	1.19019i	0.679740	−	0.733453i	$-0.262093\pi$
$350$	4.52571			0.241909
$351$		0			0
$352$	−2.52845			−0.134767
$353$	5.15849	+	29.2553i	0.274559	+	1.55710i	0.740360	+	0.672211i	$0.234655\pi$
$353$	5.15849	+	29.2553i	0.274559	+	1.55710i	−0.465801	+	0.884889i	$0.654234\pi$
$354$		0			0
$355$	−24.1937	+	8.80578i	−1.28407	+	0.467362i
$356$	29.4469	+	24.7089i	1.56068	+	1.30957i
$357$		0			0
$358$	−39.7710	−	14.4754i	−2.10196	−	0.765051i
$359$	6.70991	+	11.6219i	0.354136	+	0.613381i	0.986970	−	0.160906i	$-0.0514418\pi$
$359$	6.70991	+	11.6219i	0.354136	+	0.613381i	−0.632834	+	0.774288i	$0.718108\pi$
$360$		0			0
$361$	−9.84920	+	17.0593i	−0.518379	+	0.897858i
$362$	15.7802	−	13.2412i	0.829392	−	0.695942i
$363$		0			0
$364$	−0.633997	+	3.59558i	−0.0332305	+	0.188459i
$365$	−7.10140	+	40.2740i	−0.371704	+	2.10804i
$366$		0			0
$367$	−6.09004	+	5.11015i	−0.317897	+	0.266748i	−0.787747	−	0.615999i	$-0.788753\pi$
$367$	−6.09004	+	5.11015i	−0.317897	+	0.266748i	0.469850	+	0.882746i	$0.344308\pi$
$368$	−3.03793	+	5.26184i	−0.158363	+	0.274293i
$369$		0			0
$370$	12.6833	+	21.9681i	0.659372	+	1.14207i
$371$	−9.95192	−	3.62220i	−0.516678	−	0.188055i
$372$		0			0
$373$	−8.74862	−	7.34096i	−0.452986	−	0.380101i	0.387556	−	0.921846i	$-0.373319\pi$
$373$	−8.74862	−	7.34096i	−0.452986	−	0.380101i	−0.840543	+	0.541745i	$0.817764\pi$
$374$	0.740415	−	0.269489i	0.0382860	−	0.0139350i
$375$		0			0
$376$	0.436918	+	2.47789i	0.0225323	+	0.127787i
$377$	−6.66917			−0.343480
$378$		0			0
$379$	−24.1705			−1.24155			−0.620777	−	0.783987i	$-0.713183\pi$
$379$	−24.1705			−1.24155			−0.620777	+	0.783987i	$0.713183\pi$
$380$	7.18821	+	40.7664i	0.368748	+	2.09127i
$381$		0			0
$382$	−35.3173	+	12.8544i	−1.80699	+	0.657690i
$383$	−7.23397	−	6.07003i	−0.369639	−	0.310164i	0.438980	−	0.898497i	$-0.355340\pi$
$383$	−7.23397	−	6.07003i	−0.369639	−	0.310164i	−0.808619	+	0.588333i	$0.799784\pi$
$384$		0			0
$385$	−0.776895	−	0.282767i	−0.0395942	−	0.0144111i
$386$	−11.2015	−	19.4016i	−0.570143	−	0.987516i
$387$		0			0
$388$	6.88162	−	11.9193i	0.349361	−	0.605111i
$389$	1.95166	−	1.63763i	0.0989529	−	0.0830314i	−0.591969	−	0.805961i	$-0.701649\pi$
$389$	1.95166	−	1.63763i	0.0989529	−	0.0830314i	0.690922	+	0.722929i	$0.257205\pi$
$390$		0			0
$391$	0.441160	−	2.50194i	0.0223104	−	0.126529i
$392$	−1.06837	+	6.05902i	−0.0539607	+	0.306027i
$393$		0			0
$394$	−22.9576	+	19.2637i	−1.15659	+	0.970492i
$395$	15.0438	−	26.0567i	0.756937	−	1.31105i
$396$		0			0
$397$	−1.83759	−	3.18279i	−0.0922258	−	0.159740i	0.816222	−	0.577739i	$-0.196065\pi$
$397$	−1.83759	−	3.18279i	−0.0922258	−	0.159740i	−0.908447	+	0.417999i	$0.862731\pi$
$398$	−14.9973	−	5.45855i	−0.751744	−	0.273613i
$399$		0			0
$400$	−4.73244	−	3.97098i	−0.236622	−	0.198549i
$401$	15.1748	−	5.52319i	0.757795	−	0.275815i	0.0659131	−	0.997825i	$-0.479004\pi$
$401$	15.1748	−	5.52319i	0.757795	−	0.275815i	0.691882	+	0.722010i	$0.256782\pi$
$402$		0			0
$403$	2.28027	+	12.9320i	0.113588	+	0.644190i
$404$	25.1458			1.25105
$405$		0			0
$406$	9.06558			0.449917
$407$	−0.245797	−	1.39399i	−0.0121837	−	0.0690973i
$408$		0			0
$409$	−8.62823	+	3.14042i	−0.426639	+	0.155284i	−0.546410	−	0.837518i	$-0.684006\pi$
$409$	−8.62823	+	3.14042i	−0.426639	+	0.155284i	0.119772	+	0.992801i	$0.461784\pi$
$410$	−25.4292	−	21.3376i	−1.25586	−	1.05379i
$411$		0			0
$412$	22.9633	+	8.35797i	1.13132	+	0.411767i
$413$	−0.838253	−	1.45190i	−0.0412477	−	0.0714432i
$414$		0			0
$415$	6.28506	−	10.8860i	0.308522	−	0.534375i
$416$	9.25374	−	7.76481i	0.453702	−	0.380701i
$417$		0			0
$418$	0.724578	−	4.10929i	0.0354403	−	0.200992i
$419$	1.21187	−	6.87285i	0.0592037	−	0.335761i	−0.940791	−	0.338987i	$-0.889916\pi$
$419$	1.21187	−	6.87285i	0.0592037	−	0.335761i	0.999995	+	0.00322608i	$0.00102690\pi$
$420$		0			0
$421$	23.6023	−	19.8047i	1.15031	−	0.965221i	0.150579	−	0.988598i	$-0.451886\pi$
$421$	23.6023	−	19.8047i	1.15031	−	0.965221i	0.999727	+	0.0233767i	$0.00744170\pi$
$422$	−5.51765	+	9.55686i	−0.268595	+	0.465221i
$423$		0			0
$424$	−5.53405	−	9.58526i	−0.268757	−	0.465502i
$425$	2.42736	+	0.883488i	0.117744	+	0.0428555i
$426$		0			0
$427$	0.755857	+	0.634240i	0.0365785	+	0.0306930i
$428$	12.0507	−	4.38609i	0.582491	−	0.212010i
$429$		0			0
$430$	5.51365	+	31.2694i	0.265892	+	1.50795i
$431$	−27.8971			−1.34376			−0.671879	−	0.740661i	$-0.734513\pi$
$431$	−27.8971			−1.34376			−0.671879	+	0.740661i	$0.734513\pi$
$432$		0			0
$433$	19.1706			0.921278			0.460639	−	0.887588i	$-0.347620\pi$
$433$	19.1706			0.921278			0.460639	+	0.887588i	$0.347620\pi$
$434$	−3.09963	−	17.5789i	−0.148787	−	0.843812i
$435$		0			0
$436$	17.0377	−	6.20120i	0.815956	−	0.296984i
$437$	−10.3064	−	8.64806i	−0.493020	−	0.413693i
$438$		0			0
$439$	22.3167	+	8.12263i	1.06512	+	0.387672i	0.814350	−	0.580375i	$-0.197094\pi$
$439$	22.3167	+	8.12263i	1.06512	+	0.387672i	0.250770	+	0.968047i	$0.419316\pi$
$440$	−0.432015	−	0.748272i	−0.0205955	−	0.0356725i
$441$		0			0
$442$	−1.88221	+	3.26009i	−0.0895278	+	0.155067i
$443$	−17.8935	+	15.0144i	−0.850144	+	0.713356i	−0.959821	−	0.280612i	$-0.909463\pi$
$443$	−17.8935	+	15.0144i	−0.850144	+	0.713356i	0.109677	+	0.993967i	$0.465018\pi$
$444$		0			0
$445$	7.22146	−	40.9549i	0.342330	−	1.94145i
$446$	6.50332	−	36.8821i	0.307941	−	1.74642i
$447$		0			0
$448$	−8.39379	+	7.04323i	−0.396569	+	0.332761i
$449$	2.40953	−	4.17343i	0.113713	−	0.196956i	−0.803552	−	0.595235i	$-0.797059\pi$
$449$	2.40953	−	4.17343i	0.113713	−	0.196956i	0.917264	+	0.398279i	$0.130392\pi$
$450$		0			0
$451$	0.926176	+	1.60418i	0.0436119	+	0.0755380i
$452$	24.1807	+	8.80105i	1.13736	+	0.413966i
$453$		0			0
$454$	25.5731	+	21.4584i	1.20021	+	1.00709i
$455$	3.71169	−	1.35095i	0.174007	−	0.0633333i
$456$		0			0
$457$	−0.849765	−	4.81926i	−0.0397503	−	0.225435i	0.958461	−	0.285225i	$-0.0920682\pi$
$457$	−0.849765	−	4.81926i	−0.0397503	−	0.225435i	−0.998211	+	0.0597894i	$0.980957\pi$
$458$	−3.73978			−0.174749
$459$		0			0
$460$	−14.3916			−0.671012
$461$	−4.86049	−	27.5652i	−0.226376	−	1.28384i	−0.860038	−	0.510230i	$-0.829560\pi$
$461$	−4.86049	−	27.5652i	−0.226376	−	1.28384i	0.633662	−	0.773610i	$-0.281551\pi$
$462$		0			0
$463$	25.8184	−	9.39712i	1.19988	−	0.436721i	0.336699	−	0.941612i	$-0.390690\pi$
$463$	25.8184	−	9.39712i	1.19988	−	0.436721i	0.863183	+	0.504891i	$0.168467\pi$
$464$	−9.47968	−	7.95440i	−0.440083	−	0.369274i
$465$		0			0
$466$	−27.6436	−	10.0614i	−1.28056	−	0.466087i
$467$	−10.6232	−	18.4000i	−0.491585	−	0.851450i	0.508368	−	0.861140i	$-0.330249\pi$
$467$	−10.6232	−	18.4000i	−0.491585	−	0.851450i	−0.999953	+	0.00968963i	$0.996916\pi$
$468$		0			0
$469$	−0.416426	+	0.721272i	−0.0192288	+	0.0333052i
$470$	10.7720	−	9.03879i	0.496876	−	0.416928i
$471$		0			0
$472$	0.304248	−	1.72548i	0.0140042	−	0.0794215i
$473$	0.307669	−	1.74488i	0.0141466	−	0.0802296i
$474$		0			0
$475$	10.4792	−	8.79310i	0.480819	−	0.403455i
$476$	1.41636	−	2.45321i	0.0649188	−	0.112443i
$477$		0			0
$478$	−20.9892	−	36.3543i	−0.960022	−	1.66281i
$479$	−39.1653	−	14.2550i	−1.78951	−	0.651328i	−0.999257	−	0.0385448i	$-0.987728\pi$
$479$	−39.1653	−	14.2550i	−1.78951	−	0.651328i	−0.790251	−	0.612783i	$-0.790050\pi$
$480$		0			0
$481$	5.18048	+	4.34694i	0.236210	+	0.198203i
$482$	−38.5358	+	14.0259i	−1.75526	+	0.638861i
$483$		0			0
$484$	−4.69405	−	26.6213i	−0.213366	−	1.21006i
$485$	−14.8898			−0.676112
$486$		0			0
$487$	4.02801			0.182527			0.0912634	−	0.995827i	$-0.470909\pi$
$487$	4.02801			0.182527			0.0912634	+	0.995827i	$0.470909\pi$
$488$	0.179064	+	1.01552i	0.00810585	+	0.0459706i
$489$		0			0
$490$	32.3109	−	11.7602i	1.45966	−	0.531272i
$491$	29.5857	+	24.8253i	1.33518	+	1.12035i	0.982836	+	0.184482i	$0.0590607\pi$
$491$	29.5857	+	24.8253i	1.33518	+	1.12035i	0.352347	+	0.935869i	$0.385384\pi$
$492$		0			0
$493$	4.86233	+	1.76974i	0.218988	+	0.0797052i
$494$	9.96769	+	17.2645i	0.448468	+	0.776769i
$495$		0			0
$496$	−12.1830	+	21.1015i	−0.547032	+	0.947487i
$497$	7.14741	−	5.99739i	0.320605	−	0.269020i
$498$		0			0
$499$	−0.707071	+	4.01000i	−0.0316528	+	0.179512i	−0.996535	−	0.0831694i	$-0.973496\pi$
$499$	−0.707071	+	4.01000i	−0.0316528	+	0.179512i	0.964883	+	0.262682i	$0.0846069\pi$
$500$	−3.23657	+	18.3555i	−0.144744	+	0.820884i
$501$		0			0
$502$	8.87849	−	7.44994i	0.396266	−	0.332507i
$503$	−1.71297	+	2.96695i	−0.0763775	+	0.132290i	−0.901684	−	0.432395i	$-0.857669\pi$
$503$	−1.71297	+	2.96695i	−0.0763775	+	0.132290i	0.825307	+	0.564684i	$0.191002\pi$
$504$		0			0
$505$	−13.6020	−	23.5594i	−0.605282	−	1.04838i
$506$	1.36320	+	0.496164i	0.0606016	+	0.0220572i
$507$		0			0
$508$	9.93139	+	8.33343i	0.440634	+	0.369736i
$509$	−11.5238	+	4.19434i	−0.510785	+	0.185911i	−0.584539	−	0.811366i	$-0.698724\pi$
$509$	−11.5238	+	4.19434i	−0.510785	+	0.185911i	0.0737534	+	0.997277i	$0.476502\pi$
$510$		0			0
$511$	−2.57349	−	14.5950i	−0.113844	−	0.645644i
$512$	28.1241			1.24292
$513$		0			0
$514$	24.4791			1.07973
$515$	−4.59080	−	26.0357i	−0.202295	−	1.14727i
$516$		0			0
$517$	−0.737350	+	0.268373i	−0.0324286	+	0.0118030i
$518$	−7.04196	−	5.90891i	−0.309406	−	0.259623i
$519$		0			0
$520$	3.87904	+	1.41186i	0.170107	+	0.0619140i
$521$	7.04117	+	12.1957i	0.308479	+	0.534302i	0.978030	−	0.208465i	$-0.0668466\pi$
$521$	7.04117	+	12.1957i	0.308479	+	0.534302i	−0.669551	+	0.742766i	$0.733513\pi$
$522$		0			0
$523$	−4.88956	+	8.46897i	−0.213806	+	0.370322i	−0.952902	−	0.303277i	$-0.901919\pi$
$523$	−4.88956	+	8.46897i	−0.213806	+	0.370322i	0.739097	+	0.673599i	$0.235253\pi$
$524$	13.7442	−	11.5327i	0.600416	−	0.503809i
$525$		0			0
$526$	−2.38095	+	13.5030i	−0.103814	+	0.588761i
$527$	1.76918	−	10.0335i	0.0770667	−	0.437067i
$528$		0			0
$529$	−14.0359	+	11.7775i	−0.610256	+	0.512065i
$530$	−30.9283	+	53.5694i	−1.34344	+	2.32691i
$531$		0			0
$532$	−7.50065	−	12.9915i	−0.325195	−	0.563254i
$533$	−8.31608	−	3.02681i	−0.360209	−	0.131105i
$534$		0			0
$535$	−10.6279	−	8.91789i	−0.459485	−	0.385554i
$536$	−0.817912	+	0.297696i	−0.0353284	+	0.0128585i
$537$		0			0
$538$	5.08637	+	28.8462i	0.219289	+	1.24365i
$539$	−1.91871			−0.0826445
$540$		0			0
$541$	40.9454			1.76038			0.880189	−	0.474623i	$-0.157416\pi$
$541$	40.9454			1.76038			0.880189	+	0.474623i	$0.157416\pi$
$542$	0.715012	+	4.05503i	0.0307124	+	0.174179i
$543$		0			0
$544$	−8.80715	+	3.20554i	−0.377604	+	0.137436i
$545$	−15.0261	−	12.6084i	−0.643648	−	0.540085i
$546$		0			0
$547$	−1.04332	−	0.379737i	−0.0446091	−	0.0162364i	0.319619	−	0.947546i	$-0.396445\pi$
$547$	−1.04332	−	0.379737i	−0.0446091	−	0.0162364i	−0.364228	+	0.931310i	$0.618667\pi$
$548$	13.9497	+	24.1615i	0.595900	+	1.03213i
$549$		0			0
$550$	−0.737508	+	1.27740i	−0.0314474	+	0.0544686i
$551$	20.9912	−	17.6137i	0.894256	−	0.750370i
$552$		0			0
$553$	−1.89338	+	10.7379i	−0.0805145	+	0.456620i
$554$	4.58431	−	25.9989i	0.194769	−	1.10459i
$555$		0			0
$556$	17.8210	−	14.9536i	0.755779	−	0.634174i
$557$	17.5201	−	30.3458i	0.742352	−	1.28579i	−0.209070	−	0.977901i	$-0.567044\pi$
$557$	17.5201	−	30.3458i	0.742352	−	1.28579i	0.951422	−	0.307890i	$-0.0996230\pi$
$558$		0			0
$559$	4.23247	+	7.33084i	0.179014	+	0.310062i
$560$	6.88716	+	2.50672i	0.291035	+	0.105928i
$561$		0			0
$562$	−15.8184	−	13.2732i	−0.667260	−	0.559898i
$563$	−36.4330	+	13.2605i	−1.53547	+	0.558865i	−0.964953	−	0.262423i	$-0.915479\pi$
$563$	−36.4330	+	13.2605i	−1.53547	+	0.558865i	−0.570515	+	0.821287i	$0.693256\pi$
$564$		0			0
$565$	−4.83417	−	27.4159i	−0.203375	−	1.15340i
$566$	56.2413			2.36400
$567$		0			0
$568$	9.75095			0.409141
$569$	5.89854	+	33.4523i	0.247280	+	1.40239i	0.815138	+	0.579266i	$0.196661\pi$
$569$	5.89854	+	33.4523i	0.247280	+	1.40239i	−0.567859	+	0.823126i	$0.692228\pi$
$570$		0			0
$571$	−9.48043	+	3.45060i	−0.396744	+	0.144403i	−0.532684	−	0.846314i	$-0.678817\pi$
$571$	−9.48043	+	3.45060i	−0.396744	+	0.144403i	0.135940	+	0.990717i	$0.456594\pi$
$572$	−0.911552	−	0.764883i	−0.0381139	−	0.0319814i
$573$		0			0
$574$	11.3043	+	4.11442i	0.471831	+	0.171732i
$575$	2.37795	+	4.11873i	0.0991674	+	0.171763i
$576$		0			0
$577$	6.06615	−	10.5069i	0.252537	−	0.437407i	−0.711687	−	0.702497i	$-0.752068\pi$
$577$	6.06615	−	10.5069i	0.252537	−	0.437407i	0.964224	+	0.265090i	$0.0854017\pi$
$578$	−25.3269	+	21.2518i	−1.05346	+	0.883957i
$579$		0			0
$580$	5.08993	−	28.8664i	0.211348	−	1.19861i
$581$	−0.791021	+	4.48611i	−0.0328171	+	0.186115i
$582$		0			0
$583$	2.64414	−	2.21870i	0.109509	−	0.0918892i
$584$	7.74416	−	13.4133i	0.320456	−	0.555046i
$585$		0			0
$586$	12.9722	+	22.4685i	0.535877	+	0.928167i
$587$	29.8345	+	10.8589i	1.23140	+	0.448193i	0.874077	−	0.485787i	$-0.161467\pi$
$587$	29.8345	+	10.8589i	1.23140	+	0.448193i	0.357324	+	0.933981i	$0.383689\pi$
$588$		0			0
$589$	−41.3315	−	34.6812i	−1.70303	−	1.42902i
$590$	−9.20145	+	3.34905i	−0.378818	+	0.137878i
$591$		0			0
$592$	2.17899	+	12.3576i	0.0895558	+	0.507896i
$593$	−13.4906			−0.553993			−0.276996	−	0.960871i	$-0.589339\pi$
$593$	−13.4906			−0.553993			−0.276996	+	0.960871i	$0.589339\pi$
$594$		0			0
$595$	−3.06459			−0.125636
$596$	−8.20467	−	46.5310i	−0.336077	−	1.90598i
$597$		0			0
$598$	−6.51281	+	2.37047i	−0.266329	+	0.0969357i
$599$	32.5036	+	27.2737i	1.32806	+	1.11437i	0.984527	+	0.175233i	$0.0560679\pi$
$599$	32.5036	+	27.2737i	1.32806	+	1.11437i	0.343532	+	0.939141i	$0.388377\pi$
$600$		0			0
$601$	18.6104	+	6.77362i	0.759133	+	0.276302i	0.692444	−	0.721472i	$-0.256534\pi$
$601$	18.6104	+	6.77362i	0.759133	+	0.276302i	0.0666892	+	0.997774i	$0.478756\pi$
$602$	−5.75330	−	9.96501i	−0.234487	−	0.406144i
$603$		0			0
$604$	−4.97755	+	8.62136i	−0.202533	+	0.350798i
$605$	−22.4027	+	18.7981i	−0.910798	+	0.764251i
$606$		0			0
$607$	−6.25117	+	35.4521i	−0.253727	+	1.43896i	0.545592	+	0.838051i	$0.316305\pi$
$607$	−6.25117	+	35.4521i	−0.253727	+	1.43896i	−0.799319	+	0.600906i	$0.794806\pi$
$608$	−8.61877	+	48.8795i	−0.349537	+	1.98232i
$609$		0			0
$610$	4.41474	−	3.70441i	0.178748	−	0.149987i
$611$	1.87442	−	3.24659i	0.0758310	−	0.131343i
$612$		0			0
$613$	−13.2314	−	22.9175i	−0.534411	−	0.925627i	−0.999192	−	0.0402013i	$-0.987200\pi$
$613$	−13.2314	−	22.9175i	−0.534411	−	0.925627i	0.464780	−	0.885426i	$-0.346133\pi$
$614$	52.6561	+	19.1652i	2.12503	+	0.773446i
$615$		0			0
$616$	0.239862	+	0.201268i	0.00966431	+	0.00810932i
$617$	46.1546	−	16.7989i	1.85812	−	0.676299i	0.877747	−	0.479124i	$-0.159045\pi$
$617$	46.1546	−	16.7989i	1.85812	−	0.676299i	0.980368	−	0.197175i	$-0.0631768\pi$
$618$		0			0
$619$	−4.20336	−	23.8385i	−0.168947	−	0.958149i	−0.944900	−	0.327358i	$-0.893842\pi$
$619$	−4.20336	−	23.8385i	−0.168947	−	0.958149i	0.775953	−	0.630791i	$-0.217269\pi$
$620$	−57.7145			−2.31787
$621$		0			0
$622$	37.3785			1.49874
$623$	2.61700	+	14.8417i	0.104848	+	0.594621i
$624$		0			0
$625$	29.2803	−	10.6571i	1.17121	−	0.426286i
$626$	15.6422	+	13.1254i	0.625190	+	0.524597i
$627$		0			0
$628$	−16.9567	−	6.17173i	−0.676646	−	0.246279i
$629$	−2.62345	−	4.54395i	−0.104604	−	0.181179i
$630$		0			0
$631$	−8.84842	+	15.3259i	−0.352250	+	0.610115i	−0.986643	−	0.162895i	$-0.947917\pi$
$631$	−8.84842	+	15.3259i	−0.352250	+	0.610115i	0.634393	+	0.773010i	$0.281250\pi$
$632$	−8.72917	+	7.32464i	−0.347228	+	0.291359i
$633$		0			0
$634$	1.36378	−	7.73439i	0.0541627	−	0.307172i
$635$	2.43554	−	13.8126i	0.0966514	−	0.548137i
$636$		0			0
$637$	7.02218	−	5.89231i	0.278229	−	0.233462i
$638$	−1.47732	+	2.55880i	−0.0584878	+	0.101304i
$639$		0			0
$640$	10.5917	+	18.3454i	0.418676	+	0.725167i
$641$	35.7557	+	13.0140i	1.41226	+	0.514022i	0.931794	−	0.362988i	$-0.118243\pi$
$641$	35.7557	+	13.0140i	1.41226	+	0.514022i	0.480471	+	0.877011i	$0.340466\pi$
$642$		0			0
$643$	35.9600	+	30.1741i	1.41813	+	1.18995i	0.952335	+	0.305053i	$0.0986743\pi$
$643$	35.9600	+	30.1741i	1.41813	+	1.18995i	0.465790	+	0.884895i	$0.345770\pi$
$644$	4.90087	−	1.78377i	0.193121	−	0.0702904i
$645$		0			0
$646$	−2.68585	−	15.2322i	−0.105673	−	0.599303i
$647$	28.2333			1.10997			0.554983	−	0.831862i	$-0.312725\pi$
$647$	28.2333			1.10997			0.554983	+	0.831862i	$0.312725\pi$
$648$		0			0
$649$	0.546406			0.0214483
$650$	−1.22370	−	6.93997i	−0.0479976	−	0.272208i
$651$		0			0
$652$	−29.0131	+	10.5599i	−1.13624	+	0.413557i
$653$	−27.0469	−	22.6950i	−1.05843	−	0.888125i	−0.0644721	−	0.997920i	$-0.520536\pi$
$653$	−27.0469	−	22.6950i	−1.05843	−	0.888125i	−0.993954	+	0.109794i	$0.964981\pi$
$654$		0			0
$655$	−18.2398	−	6.63873i	−0.712686	−	0.259397i
$656$	−8.21052	−	14.2210i	−0.320567	−	0.555239i
$657$		0			0
$658$	−2.54795	+	4.41318i	−0.0993295	+	0.172044i
$659$	−31.9392	+	26.8002i	−1.24418	+	1.04399i	−0.246990	+	0.969018i	$0.579442\pi$
$659$	−31.9392	+	26.8002i	−1.24418	+	1.04399i	−0.997186	+	0.0749700i	$0.976114\pi$
$660$		0			0
$661$	0.221213	−	1.25456i	0.00860418	−	0.0487967i	−0.980203	−	0.197993i	$-0.936558\pi$
$661$	0.221213	−	1.25456i	0.00860418	−	0.0487967i	0.988808	+	0.149197i	$0.0476687\pi$
$662$	−0.519270	+	2.94493i	−0.0201820	+	0.114458i
$663$		0			0
$664$	−3.64691	+	3.06012i	−0.141527	+	0.118756i
$665$	−8.11461	+	14.0549i	−0.314671	+	0.545027i
$666$		0			0
$667$	4.76334	+	8.25035i	0.184437	+	0.319455i
$668$	−5.43452	−	1.97800i	−0.210268	−	0.0765312i
$669$		0			0
$670$	3.72638	+	3.12680i	0.143963	+	0.120799i
$671$	−0.302191	+	0.109989i	−0.0116660	+	0.00424606i
$672$		0			0
$673$	6.18756	+	35.0914i	0.238513	+	1.35267i	0.835088	+	0.550117i	$0.185417\pi$
$673$	6.18756	+	35.0914i	0.238513	+	1.35267i	−0.596575	+	0.802558i	$0.703472\pi$
$674$	−27.4951			−1.05907
$675$		0			0
$676$	−26.5561			−1.02139
$677$	−3.12600	−	17.7284i	−0.120142	−	0.681358i	−0.984075	−	0.177752i	$-0.943118\pi$
$677$	−3.12600	−	17.7284i	−0.120142	−	0.681358i	0.863934	−	0.503606i	$-0.167994\pi$
$678$		0			0
$679$	5.07053	−	1.84552i	0.194589	−	0.0708246i
$680$	−2.45346	−	2.05870i	−0.0940859	−	0.0789474i
$681$		0			0
$682$	5.46682	+	1.98976i	0.209336	+	0.0761919i
$683$	19.8807	+	34.4344i	0.760715	+	1.31760i	0.942483	+	0.334255i	$0.108485\pi$
$683$	19.8807	+	34.4344i	0.760715	+	1.31760i	−0.181768	+	0.983341i	$0.558182\pi$
$684$		0			0
$685$	15.0915	−	26.1393i	0.576617	−	0.998730i
$686$	−20.5814	+	17.2698i	−0.785801	+	0.659366i
$687$		0			0
$688$	−2.72748	+	15.4683i	−0.103984	+	0.589724i
$689$	−2.86359	+	16.2402i	−0.109094	+	0.618703i
$690$		0			0
$691$	−12.9007	+	10.8250i	−0.490767	+	0.411802i	−0.854301	−	0.519779i	$-0.826014\pi$
$691$	−12.9007	+	10.8250i	−0.490767	+	0.411802i	0.363534	+	0.931581i	$0.381570\pi$
$692$	−4.44218	+	7.69408i	−0.168866	+	0.292485i
$693$		0			0
$694$	−5.08038	−	8.79948i	−0.192849	−	0.334024i
$695$	−23.6501	−	8.60793i	−0.897099	−	0.326517i
$696$		0			0
$697$	5.25985	+	4.41354i	0.199231	+	0.167175i
$698$	44.9062	−	16.3445i	1.69973	−	0.618649i
$699$		0			0
$700$	0.920833	+	5.22230i	0.0348042	+	0.197385i
$701$	8.96921			0.338762			0.169381	−	0.985551i	$-0.445823\pi$
$701$	8.96921			0.338762			0.169381	+	0.985551i	$0.445823\pi$
$702$		0			0
$703$	−27.7861			−1.04797
$704$	−0.620133	−	3.51695i	−0.0233721	−	0.132550i
$705$		0			0
$706$	−59.0856	+	21.5054i	−2.22372	+	0.809366i
$707$	7.55207	+	6.33694i	0.284025	+	0.238325i
$708$		0			0
$709$	−17.0476	−	6.20480i	−0.640235	−	0.233026i	0.00144523	−	0.999999i	$-0.499540\pi$
$709$	−17.0476	−	6.20480i	−0.640235	−	0.233026i	−0.641680	+	0.766973i	$0.721762\pi$
$710$	−27.2477	−	47.1944i	−1.02259	−	1.77117i
$711$		0			0
$712$	−7.87509	+	13.6401i	−0.295131	+	0.511183i
$713$	14.3694	−	12.0574i	0.538139	−	0.451552i
$714$		0			0
$715$	−0.223546	+	1.26779i	−0.00836014	+	0.0474127i
$716$	8.61142	−	48.8378i	0.321824	−	1.82515i
$717$		0			0
$718$	−21.7593	+	18.2582i	−0.812049	+	0.681390i
$719$	15.7860	−	27.3421i	0.588718	−	1.01969i	−0.405683	−	0.914014i	$-0.632966\pi$
$719$	15.7860	−	27.3421i	0.588718	−	1.01969i	0.994401	−	0.105675i	$-0.0337004\pi$
$720$		0			0
$721$	4.79034	+	8.29711i	0.178402	+	0.309001i
$722$	−39.1796	−	14.2602i	−1.45811	−	0.530710i
$723$		0			0
$724$	18.4901	+	15.5150i	0.687177	+	0.576610i
$725$	−9.10230	+	3.31296i	−0.338051	+	0.123040i
$726$		0			0
$727$	6.66970	+	37.8257i	0.247365	+	1.40288i	0.814934	+	0.579553i	$0.196773\pi$
$727$	6.66970	+	37.8257i	0.247365	+	1.40288i	−0.567569	+	0.823326i	$0.692116\pi$
$728$	−1.49595			−0.0554436
$729$		0			0
$730$	−86.5599			−3.20373
$731$	−1.14046	−	6.46787i	−0.0421814	−	0.239223i
$732$		0			0
$733$	28.5012	−	10.3736i	1.05271	−	0.383157i	0.243028	−	0.970019i	$-0.421859\pi$
$733$	28.5012	−	10.3736i	1.05271	−	0.383157i	0.809686	+	0.586863i	$0.199637\pi$
$734$	−12.8903	−	10.8163i	−0.475790	−	0.399235i
$735$		0			0
$736$	−16.2151	−	5.90181i	−0.597696	−	0.217543i
$737$	−0.135721	−	0.235076i	−0.00499936	−	0.00865915i
$738$		0			0
$739$	−5.00127	+	8.66245i	−0.183975	+	0.318653i	−0.943230	−	0.332139i	$-0.892230\pi$
$739$	−5.00127	+	8.66245i	−0.183975	+	0.318653i	0.759256	+	0.650792i	$0.225563\pi$
$740$	−22.7688	+	19.1053i	−0.836997	+	0.702324i
$741$		0			0
$742$	3.89255	−	22.0758i	0.142900	−	0.810427i
$743$	−6.29888	+	35.7227i	−0.231083	+	1.31054i	0.619624	+	0.784899i	$0.287285\pi$
$743$	−6.29888	+	35.7227i	−0.231083	+	1.31054i	−0.850707	+	0.525640i	$0.823826\pi$
$744$		0			0
$745$	−39.1574	+	32.8570i	−1.43462	+	1.20379i
$746$	12.0865	−	20.9344i	0.442517	−	0.766461i
$747$		0			0
$748$	0.461619	+	0.799548i	0.0168785	+	0.0292344i
$749$	4.72453	+	1.71959i	0.172631	+	0.0628324i
$750$		0			0
$751$	−11.1493	−	9.35536i	−0.406843	−	0.341382i	0.416288	−	0.909233i	$-0.363331\pi$
$751$	−11.1493	−	9.35536i	−0.406843	−	0.341382i	−0.823132	+	0.567851i	$0.807775\pi$
$752$	6.53659	−	2.37912i	0.238365	−	0.0867577i
$753$		0			0
$754$	−2.45124	−	13.9017i	−0.0892688	−	0.506268i
$755$	10.7700			0.391959
$756$		0			0
$757$	−45.5754			−1.65646			−0.828232	−	0.560385i	$-0.810653\pi$
$757$	−45.5754			−1.65646			−0.828232	+	0.560385i	$0.810653\pi$
$758$	−8.88380	−	50.3826i	−0.322674	−	1.82998i
$759$		0			0
$760$	−15.9381	+	5.80099i	−0.578135	+	0.210424i
$761$	−17.0411	−	14.2992i	−0.617739	−	0.518344i	0.279353	−	0.960188i	$-0.409880\pi$
$761$	−17.0411	−	14.2992i	−0.617739	−	0.518344i	−0.897092	+	0.441844i	$0.854324\pi$
$762$		0			0
$763$	6.67970	+	2.43121i	0.241821	+	0.0880158i
$764$	−22.0189	−	38.1379i	−0.796616	−	1.37978i
$765$		0			0
$766$	9.99393	−	17.3100i	0.361096	−	0.625436i
$767$	−1.99976	+	1.67800i	−0.0722073	+	0.0605891i
$768$		0			0
$769$	2.37289	−	13.4573i	0.0855686	−	0.485284i	−0.911664	−	0.410937i	$-0.865202\pi$
$769$	2.37289	−	13.4573i	0.0855686	−	0.485284i	0.997232	−	0.0743470i	$-0.0236872\pi$
$770$	0.303872	−	1.72334i	0.0109508	−	0.0621049i
$771$		0			0
$772$	20.1088	−	16.8733i	0.723730	−	0.607282i
$773$	−10.3270	+	17.8869i	−0.371436	+	0.643345i	−0.989787	−	0.142557i	$-0.954468\pi$
$773$	−10.3270	+	17.8869i	−0.371436	+	0.643345i	0.618351	+	0.785902i	$0.287801\pi$
$774$		0			0
$775$	9.53628	+	16.5173i	0.342553	+	0.593319i
$776$	5.29915	+	1.92873i	0.190228	+	0.0692374i
$777$		0			0
$778$	4.13092	+	3.46625i	0.148101	+	0.124271i
$779$	34.1689	−	12.4364i	1.22423	−	0.445582i

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.367548 + 2.08447i) q^{2} +(-2.33052 + 0.848241i) q^{4} +(2.05537 + 1.72466i) q^{5} +(-0.913694 - 0.332557i) q^{7} +(-0.508086 - 0.880031i) q^{8} +O(q^{10})\)	\(q+(0.367548 + 2.08447i) q^{2} +(-2.33052 + 0.848241i) q^{4} +(2.05537 + 1.72466i) q^{5} +(-0.913694 - 0.332557i) q^{7} +(-0.508086 - 0.880031i) q^{8} +(-2.83955 + 4.91825i) q^{10} +(0.242761 - 0.203701i) q^{11} +(-0.262909 + 1.49103i) q^{13} +(0.357379 - 2.02679i) q^{14} +(-2.15207 + 1.80580i) q^{16} +(0.587342 - 1.01731i) q^{17} +(-3.11040 - 5.38737i) q^{19} +(-6.25302 - 2.27591i) q^{20} +(0.513834 + 0.431158i) q^{22} +(2.03231 - 0.739701i) q^{23} +(0.381855 + 2.16561i) q^{25} -3.20463 q^{26} +2.41147 q^{28} +(0.764905 + 4.33799i) q^{29} +(8.15017 - 2.96642i) q^{31} +(-6.11199 - 5.12857i) q^{32} +(2.33642 + 0.850386i) q^{34} +(-1.30443 - 2.25934i) q^{35} +(2.23332 - 3.86823i) q^{37} +(10.0866 - 8.46364i) q^{38} +(0.473450 - 2.68507i) q^{40} +(-1.01501 + 5.75638i) q^{41} +(4.28295 - 3.59382i) q^{43} +(-0.392973 + 0.680649i) q^{44} +(2.28885 + 3.96441i) q^{46} +(-2.32674 - 0.846865i) q^{47} +(-4.63807 - 3.89180i) q^{49} +(-4.37378 + 1.59193i) q^{50} +(-0.652037 - 3.69789i) q^{52} +10.8920 q^{53} +0.850279 q^{55} +(0.171574 + 0.973047i) q^{56} +(-8.76126 + 3.18884i) q^{58} +(1.32082 + 1.10830i) q^{59} +(-0.953579 - 0.347074i) q^{61} +(9.17898 + 15.8985i) q^{62} +(5.63455 - 9.75933i) q^{64} +(-3.11190 + 2.61119i) q^{65} +(0.148739 - 0.843538i) q^{67} +(-0.505893 + 2.86906i) q^{68} +(4.23008 - 3.54946i) q^{70} +(-4.79788 + 8.31018i) q^{71} +(7.62091 + 13.1998i) q^{73} +(8.88405 + 3.23353i) q^{74} +(11.8187 + 9.91703i) q^{76} +(-0.289552 + 0.105388i) q^{77} +(-1.94725 - 11.0434i) q^{79} -7.53771 q^{80} -12.3721 q^{82} +(-0.813530 - 4.61376i) q^{83} +(2.96172 - 1.07798i) q^{85} +(9.06538 + 7.60676i) q^{86} +(-0.302607 - 0.110140i) q^{88} +(-7.74976 - 13.4230i) q^{89} +(0.736071 - 1.27491i) q^{91} +(-4.10891 + 3.44778i) q^{92} +(0.910073 - 5.16128i) q^{94} +(2.89837 - 16.4375i) q^{95} +(-4.25115 + 3.56714i) q^{97} +(6.40762 - 11.0983i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 6 * q^8	\( 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} + 6 q^{11} + 3 q^{13} + 21 q^{14} + 9 q^{16} - 9 q^{17} - 3 q^{19} - 24 q^{20} + 12 q^{22} + 12 q^{23} + 12 q^{25} + 30 q^{26} - 12 q^{28} + 24 q^{29} + 12 q^{31} - 27 q^{32} - 12 q^{35} - 3 q^{37} + 30 q^{38} - 15 q^{40} - 6 q^{41} - 15 q^{43} - 3 q^{44} - 3 q^{46} - 12 q^{47} - 33 q^{49} - 21 q^{50} - 45 q^{52} + 18 q^{53} - 12 q^{55} - 30 q^{56} - 51 q^{58} + 3 q^{59} - 33 q^{61} + 12 q^{62} + 12 q^{64} - 21 q^{65} - 6 q^{67} - 9 q^{68} - 15 q^{70} - 27 q^{71} + 6 q^{73} + 21 q^{74} + 6 q^{76} + 12 q^{77} + 21 q^{79} - 42 q^{80} - 12 q^{82} + 6 q^{83} + 36 q^{85} + 21 q^{86} + 42 q^{88} - 9 q^{89} + 6 q^{91} + 3 q^{92} + 48 q^{94} - 3 q^{95} + 39 q^{97} + 45 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^10 + 6 * q^11 + 3 * q^13 + 21 * q^14 + 9 * q^16 - 9 * q^17 - 3 * q^19 - 24 * q^20 + 12 * q^22 + 12 * q^23 + 12 * q^25 + 30 * q^26 - 12 * q^28 + 24 * q^29 + 12 * q^31 - 27 * q^32 - 12 * q^35 - 3 * q^37 + 30 * q^38 - 15 * q^40 - 6 * q^41 - 15 * q^43 - 3 * q^44 - 3 * q^46 - 12 * q^47 - 33 * q^49 - 21 * q^50 - 45 * q^52 + 18 * q^53 - 12 * q^55 - 30 * q^56 - 51 * q^58 + 3 * q^59 - 33 * q^61 + 12 * q^62 + 12 * q^64 - 21 * q^65 - 6 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 + 21 * q^74 + 6 * q^76 + 12 * q^77 + 21 * q^79 - 42 * q^80 - 12 * q^82 + 6 * q^83 + 36 * q^85 + 21 * q^86 + 42 * q^88 - 9 * q^89 + 6 * q^91 + 3 * q^92 + 48 * q^94 - 3 * q^95 + 39 * q^97 + 45 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more