LMFDB - Embedded newform 243.2.e.d.217.2

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			217.2
Root			$0.500000 - 0.258654i$ of defining polynomial
Character	$\chi$	$=$	243.217
Dual form			243.2.e.d.28.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0721450 + 0.409154i) q^{2} +(1.71718 + 0.625003i) q^{4} +(1.69693 - 1.42389i) q^{5} +(1.24005 - 0.451340i) q^{7} +(-0.795075 + 1.37711i) q^{8} +O(q^{10})$	\(q+(-0.0721450 + 0.409154i) q^{2} +(1.71718 + 0.625003i) q^{4} +(1.69693 - 1.42389i) q^{5} +(1.24005 - 0.451340i) q^{7} +(-0.795075 + 1.37711i) q^{8} +(0.460168 + 0.797034i) q^{10} +(-3.99506 - 3.35226i) q^{11} +(-0.00313583 - 0.0177842i) q^{13} +(0.0952046 + 0.539932i) q^{14} +(2.29363 + 1.92458i) q^{16} +(1.56640 + 2.71308i) q^{17} +(-0.208676 + 0.361438i) q^{19} +(3.80388 - 1.38450i) q^{20} +(1.65981 - 1.39275i) q^{22} +(0.972005 + 0.353781i) q^{23} +(-0.0161402 + 0.0915354i) q^{25} +0.00750270 q^{26} +2.41147 q^{28} +(-1.35571 + 7.68861i) q^{29} +(-3.50474 - 1.27562i) q^{31} +(-3.38918 + 2.84386i) q^{32} +(-1.22308 + 0.445163i) q^{34} +(1.46161 - 2.53159i) q^{35} +(-2.21238 - 3.83195i) q^{37} +(-0.132829 - 0.111457i) q^{38} +(0.611672 + 3.46897i) q^{40} +(-0.638147 - 3.61911i) q^{41} +(-6.36420 - 5.34020i) q^{43} +(-4.76508 - 8.25337i) q^{44} +(-0.214876 + 0.372177i) q^{46} +(6.66985 - 2.42763i) q^{47} +(-4.02831 + 3.38015i) q^{49} +(-0.0362877 - 0.0132076i) q^{50} +(0.00573038 - 0.0324986i) q^{52} -1.30057 q^{53} -11.5526 q^{55} +(-0.364385 + 2.06653i) q^{56} +(-3.04802 - 1.10939i) q^{58} +(-2.83575 + 2.37948i) q^{59} +(-6.49726 + 2.36481i) q^{61} +(0.774775 - 1.34195i) q^{62} +(2.07506 + 3.59410i) q^{64} +(-0.0306441 - 0.0257134i) q^{65} +(-1.91478 - 10.8593i) q^{67} +(0.994107 + 5.63786i) q^{68} +(0.930362 + 0.780666i) q^{70} +(3.04214 + 5.26914i) q^{71} +(0.273486 - 0.473692i) q^{73} +(1.72747 - 0.628748i) q^{74} +(-0.584235 + 0.490231i) q^{76} +(-6.46707 - 2.35382i) q^{77} +(0.0849390 - 0.481713i) q^{79} +6.63254 q^{80} +1.52681 q^{82} +(0.801155 - 4.54358i) q^{83} +(6.52121 + 2.37353i) q^{85} +(2.64411 - 2.21867i) q^{86} +(7.79281 - 2.83635i) q^{88} +(1.68653 - 2.92116i) q^{89} +(-0.0119153 - 0.0206379i) q^{91} +(1.44800 + 1.21501i) q^{92} +(0.512078 + 2.90414i) q^{94} +(0.160540 + 0.910468i) q^{95} +(7.61552 + 6.39018i) q^{97} +(-1.09238 - 1.89206i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.0721450	+	0.409154i	−0.0510142	+	0.289316i	−0.999633	−	0.0271067i	$-0.991371\pi$
$2$	−0.0721450	+	0.409154i	−0.0510142	+	0.289316i	0.948618	+	0.316423i	$0.102482\pi$
$3$		0			0
$3$		0			0
$4$	1.71718	+	0.625003i	0.858591	+	0.312502i
$5$	1.69693	−	1.42389i	0.758891	−	0.636785i	−0.178947	−	0.983859i	$-0.557269\pi$
$5$	1.69693	−	1.42389i	0.758891	−	0.636785i	0.937838	+	0.347074i	$0.112825\pi$
$6$		0			0
$7$	1.24005	−	0.451340i	0.468693	−	0.170590i	−0.0968671	−	0.995297i	$-0.530882\pi$
$7$	1.24005	−	0.451340i	0.468693	−	0.170590i	0.565560	+	0.824707i	$0.308660\pi$
$8$	−0.795075	+	1.37711i	−0.281102	+	0.486882i
$9$		0			0
$10$	0.460168	+	0.797034i	0.145518	+	0.252044i
$11$	−3.99506	−	3.35226i	−1.20456	−	1.01074i	−0.999488	−	0.0319962i	$-0.989814\pi$
$11$	−3.99506	−	3.35226i	−1.20456	−	1.01074i	−0.205069	−	0.978747i	$-0.565742\pi$
$12$		0			0
$13$	−0.00313583	−	0.0177842i	−0.000869722	−	0.00493244i	0.984370	−	0.176114i	$-0.0563527\pi$
$13$	−0.00313583	−	0.0177842i	−0.000869722	−	0.00493244i	−0.985240	+	0.171181i	$0.945242\pi$
$14$	0.0952046	+	0.539932i	0.0254445	+	0.144303i
$15$		0			0
$16$	2.29363	+	1.92458i	0.573408	+	0.481146i
$17$	1.56640	+	2.71308i	0.379907	+	0.658019i	0.991048	−	0.133503i	$-0.0426226\pi$
$17$	1.56640	+	2.71308i	0.379907	+	0.658019i	−0.611141	+	0.791522i	$0.709289\pi$
$18$		0			0
$19$	−0.208676	+	0.361438i	−0.0478736	+	0.0829195i	−0.888969	−	0.457967i	$-0.848578\pi$
$19$	−0.208676	+	0.361438i	−0.0478736	+	0.0829195i	0.841096	+	0.540886i	$0.181911\pi$
$20$	3.80388	−	1.38450i	0.850574	−	0.309583i
$21$		0			0
$22$	1.65981	−	1.39275i	0.353874	−	0.296935i
$23$	0.972005	+	0.353781i	0.202677	+	0.0737684i	0.441364	−	0.897328i	$-0.354495\pi$
$23$	0.972005	+	0.353781i	0.202677	+	0.0737684i	−0.238687	+	0.971097i	$0.576717\pi$
$24$		0			0
$25$	−0.0161402	+	0.0915354i	−0.00322803	+	0.0183071i
$26$	0.00750270			0.00147140
$27$		0			0
$28$	2.41147			0.455726
$29$	−1.35571	+	7.68861i	−0.251749	+	1.42774i	0.552533	+	0.833491i	$0.313662\pi$
$29$	−1.35571	+	7.68861i	−0.251749	+	1.42774i	−0.804282	+	0.594248i	$0.797450\pi$
$30$		0			0
$31$	−3.50474	−	1.27562i	−0.629470	−	0.229108i	0.00753084	−	0.999972i	$-0.497603\pi$
$31$	−3.50474	−	1.27562i	−0.629470	−	0.229108i	−0.637000	+	0.770863i	$0.719825\pi$
$32$	−3.38918	+	2.84386i	−0.599128	+	0.502728i
$33$		0			0
$34$	−1.22308	+	0.445163i	−0.209756	+	0.0763449i
$35$	1.46161	−	2.53159i	0.247058	−	0.427916i
$36$		0			0
$37$	−2.21238	−	3.83195i	−0.363713	−	0.629969i	0.624856	−	0.780740i	$-0.285158\pi$
$37$	−2.21238	−	3.83195i	−0.363713	−	0.629969i	−0.988569	+	0.150771i	$0.951824\pi$
$38$	−0.132829	−	0.111457i	−0.0215477	−	0.0180807i
$39$		0			0
$40$	0.611672	+	3.46897i	0.0967139	+	0.548492i
$41$	−0.638147	−	3.61911i	−0.0996618	−	0.565210i	−0.993219	−	0.116260i	$-0.962909\pi$
$41$	−0.638147	−	3.61911i	−0.0996618	−	0.565210i	0.893557	−	0.448950i	$-0.148202\pi$
$42$		0			0
$43$	−6.36420	−	5.34020i	−0.970531	−	0.814373i	0.0121027	−	0.999927i	$-0.496148\pi$
$43$	−6.36420	−	5.34020i	−0.970531	−	0.814373i	−0.982634	+	0.185554i	$0.940592\pi$
$44$	−4.76508	−	8.25337i	−0.718363	−	1.24424i
$45$		0			0
$46$	−0.214876	+	0.372177i	−0.0316818	+	0.0548745i
$47$	6.66985	−	2.42763i	0.972898	−	0.354106i	0.193823	−	0.981037i	$-0.437911\pi$
$47$	6.66985	−	2.42763i	0.972898	−	0.354106i	0.779075	+	0.626931i	$0.215689\pi$
$48$		0			0
$49$	−4.02831	+	3.38015i	−0.575472	+	0.482878i
$50$	−0.0362877	−	0.0132076i	−0.00513185	−	0.00186784i
$51$		0			0
$52$	0.00573038	−	0.0324986i	0.000794660	−	0.00450674i
$53$	−1.30057			−0.178648			−0.0893238	−	0.996003i	$-0.528471\pi$
$53$	−1.30057			−0.178648			−0.0893238	+	0.996003i	$0.528471\pi$
$54$		0			0
$55$	−11.5526			−1.55775
$56$	−0.364385	+	2.06653i	−0.0486930	+	0.276152i
$57$		0			0
$58$	−3.04802	−	1.10939i	−0.400225	−	0.145670i
$59$	−2.83575	+	2.37948i	−0.369183	+	0.309782i	−0.808438	−	0.588581i	$-0.799687\pi$
$59$	−2.83575	+	2.37948i	−0.369183	+	0.309782i	0.439255	+	0.898362i	$0.355242\pi$
$60$		0			0
$61$	−6.49726	+	2.36481i	−0.831889	+	0.302783i	−0.722634	−	0.691231i	$-0.757069\pi$
$61$	−6.49726	+	2.36481i	−0.831889	+	0.302783i	−0.109255	+	0.994014i	$0.534846\pi$
$62$	0.774775	−	1.34195i	0.0983965	−	0.170428i
$63$		0			0
$64$	2.07506	+	3.59410i	0.259382	+	0.449263i
$65$	−0.0306441	−	0.0257134i	−0.00380093	−	0.00318936i
$66$		0			0
$67$	−1.91478	−	10.8593i	−0.233928	−	1.32667i	−0.844860	−	0.534988i	$-0.820316\pi$
$67$	−1.91478	−	10.8593i	−0.233928	−	1.32667i	0.610932	−	0.791683i	$-0.290795\pi$
$68$	0.994107	+	5.63786i	0.120553	+	0.683691i
$69$		0			0
$70$	0.930362	+	0.780666i	0.111200	+	0.0933075i
$71$	3.04214	+	5.26914i	0.361035	+	0.625332i	0.988132	−	0.153610i	$-0.0490900\pi$
$71$	3.04214	+	5.26914i	0.361035	+	0.625332i	−0.627096	+	0.778942i	$0.715757\pi$
$72$		0			0
$73$	0.273486	−	0.473692i	0.0320092	−	0.0554415i	−0.849577	−	0.527465i	$-0.823143\pi$
$73$	0.273486	−	0.473692i	0.0320092	−	0.0554415i	0.881586	+	0.472023i	$0.156476\pi$
$74$	1.72747	−	0.628748i	0.200815	−	0.0730905i
$75$		0			0
$76$	−0.584235	+	0.490231i	−0.0670163	+	0.0562334i
$77$	−6.46707	−	2.35382i	−0.736991	−	0.268243i
$78$		0			0
$79$	0.0849390	−	0.481713i	0.00955638	−	0.0541969i	−0.979657	−	0.200681i	$-0.935685\pi$
$79$	0.0849390	−	0.481713i	0.00955638	−	0.0541969i	0.989213	+	0.146484i	$0.0467957\pi$
$80$	6.63254			0.741540
$81$		0			0
$82$	1.52681			0.168608
$83$	0.801155	−	4.54358i	0.0879382	−	0.498722i	−0.908746	−	0.417351i	$-0.862959\pi$
$83$	0.801155	−	4.54358i	0.0879382	−	0.498722i	0.996684	−	0.0813719i	$-0.0259302\pi$
$84$		0			0
$85$	6.52121	+	2.37353i	0.707324	+	0.257445i
$86$	2.64411	−	2.21867i	0.285122	−	0.239246i
$87$		0			0
$88$	7.79281	−	2.83635i	0.830716	−	0.302356i
$89$	1.68653	−	2.92116i	0.178772	−	0.309642i	−0.762688	−	0.646766i	$-0.776121\pi$
$89$	1.68653	−	2.92116i	0.178772	−	0.309642i	0.941460	+	0.337124i	$0.109454\pi$
$90$		0			0
$91$	−0.0119153	−	0.0206379i	−0.00124906	−	0.00216344i
$92$	1.44800	+	1.21501i	0.150964	+	0.126674i
$93$		0			0
$94$	0.512078	+	2.90414i	0.0528168	+	0.299539i
$95$	0.160540	+	0.910468i	0.0164711	+	0.0934120i
$96$		0			0
$97$	7.61552	+	6.39018i	0.773239	+	0.648825i	0.941536	−	0.336912i	$-0.109382\pi$
$97$	7.61552	+	6.39018i	0.773239	+	0.648825i	−0.168297	+	0.985736i	$0.553827\pi$
$98$	−1.09238	−	1.89206i	−0.110347	−	0.191127i
$99$		0			0
$100$	−0.0849256	+	0.147095i	−0.00849256	+	0.0147095i
$101$	−12.9673	+	4.71970i	−1.29029	+	0.469628i	−0.893823	−	0.448420i	$-0.851987\pi$
$101$	−12.9673	+	4.71970i	−1.29029	+	0.469628i	−0.396469	+	0.918048i	$0.629765\pi$
$102$		0			0
$103$	3.49708	−	2.93440i	0.344578	−	0.289135i	−0.454031	−	0.890986i	$-0.650014\pi$
$103$	3.49708	−	2.93440i	0.344578	−	0.289135i	0.798608	+	0.601851i	$0.205570\pi$
$104$	0.0269840	+	0.00982137i	0.00264600	+	0.000963064i
$105$		0			0
$106$	0.0938299	−	0.532136i	0.00911356	−	0.0516856i
$107$	−11.2965			−1.09207			−0.546035	−	0.837762i	$-0.683864\pi$
$107$	−11.2965			−1.09207			−0.546035	+	0.837762i	$0.683864\pi$
$108$		0			0
$109$	14.5032			1.38915			0.694577	−	0.719419i	$-0.255592\pi$
$109$	14.5032			1.38915			0.694577	+	0.719419i	$0.255592\pi$
$110$	0.833463	−	4.72680i	0.0794676	−	0.450683i
$111$		0			0
$112$	3.71285	+	1.35137i	0.350831	+	0.127692i
$113$	9.62031	−	8.07240i	0.905003	−	0.759388i	−0.0661589	−	0.997809i	$-0.521074\pi$
$113$	9.62031	−	8.07240i	0.905003	−	0.759388i	0.971162	+	0.238422i	$0.0766300\pi$
$114$		0			0
$115$	2.15317	−	0.783691i	0.200784	−	0.0730796i
$116$	−7.13341	+	12.3554i	−0.662321	+	1.14717i
$117$		0			0
$118$	−0.768989	−	1.33193i	−0.0707912	−	0.122614i
$119$	3.16693	+	2.65737i	0.290312	+	0.243600i
$120$		0			0
$121$	2.81278	+	15.9521i	0.255708	+	1.45019i
$122$	−0.498827	−	2.82899i	−0.0451617	−	0.256125i
$123$		0			0
$124$	−5.22101	−	4.38095i	−0.468860	−	0.393421i
$125$	5.64092	+	9.77035i	0.504539	+	0.873887i
$126$		0			0
$127$	4.19749	−	7.27027i	0.372467	−	0.645132i	−0.617477	−	0.786589i	$-0.711845\pi$
$127$	4.19749	−	7.27027i	0.372467	−	0.645132i	0.989944	+	0.141456i	$0.0451785\pi$
$128$	−9.93513	+	3.61609i	−0.878150	+	0.319620i
$129$		0			0
$130$	0.0127316	−	0.0106831i	0.00111663	−	0.000936966i
$131$	14.5980	+	5.31325i	1.27544	+	0.464221i	0.888920	−	0.458062i	$-0.151456\pi$
$131$	14.5980	+	5.31325i	1.27544	+	0.464221i	0.386516	+	0.922283i	$0.373679\pi$
$132$		0			0
$133$	−0.0956368	+	0.542383i	−0.00829276	+	0.0470306i
$134$	4.58126			0.395761
$135$		0			0
$136$	−4.98162			−0.427170
$137$	2.08506	−	11.8250i	0.178139	−	1.01028i	−0.756319	−	0.654203i	$-0.773004\pi$
$137$	2.08506	−	11.8250i	0.178139	−	1.01028i	0.934458	−	0.356073i	$-0.115885\pi$
$138$		0			0
$139$	−5.77452	−	2.10175i	−0.489789	−	0.178268i	0.0853069	−	0.996355i	$-0.472813\pi$
$139$	−5.77452	−	2.10175i	−0.489789	−	0.178268i	−0.575096	+	0.818086i	$0.695035\pi$
$140$	4.09211	−	3.43369i	0.345846	−	0.290199i
$141$		0			0
$142$	−2.37537	+	0.864563i	−0.199336	+	0.0725525i
$143$	−0.0470893	+	0.0815610i	−0.00393780	+	0.00682047i
$144$		0			0
$145$	8.64723	+	14.9774i	0.718113	+	1.24381i
$146$	0.174083	+	0.146073i	0.0144072	+	0.0120891i
$147$		0			0
$148$	−1.40408	−	7.96291i	−0.115414	−	0.654547i
$149$	0.153300	+	0.869408i	0.0125588	+	0.0712247i	0.990443	−	0.137922i	$-0.0440424\pi$
$149$	0.153300	+	0.869408i	0.0125588	+	0.0712247i	−0.977884	+	0.209147i	$0.932931\pi$
$150$		0			0
$151$	6.30108	+	5.28723i	0.512774	+	0.430269i	0.862104	−	0.506731i	$-0.169146\pi$
$151$	6.30108	+	5.28723i	0.512774	+	0.430269i	−0.349330	+	0.937000i	$0.613591\pi$
$152$	−0.331826	−	0.574740i	−0.0269147	−	0.0466176i
$153$		0			0
$154$	1.42964	−	2.47621i	0.115204	−	0.199539i
$155$	−7.76365	+	2.82574i	−0.623591	+	0.226969i
$156$		0			0
$157$	9.62138	−	8.07330i	0.767870	−	0.644319i	−0.172293	−	0.985046i	$-0.555117\pi$
$157$	9.62138	−	8.07330i	0.767870	−	0.644319i	0.940162	+	0.340726i	$0.110673\pi$
$158$	0.190967	+	0.0695063i	0.0151925	+	0.00552962i
$159$		0			0
$160$	−1.70185	+	9.65166i	−0.134543	+	0.763031i
$161$	1.36501			0.107578
$162$		0			0
$163$	3.31466			0.259624			0.129812	−	0.991539i	$-0.458563\pi$
$163$	3.31466			0.259624			0.129812	+	0.991539i	$0.458563\pi$
$164$	1.16614	−	6.61352i	0.0910603	−	0.516429i
$165$		0			0
$166$	1.80123	+	0.655592i	0.139802	+	0.0508838i
$167$	−15.7522	+	13.2176i	−1.21894	+	1.02281i	−0.220059	+	0.975487i	$0.570625\pi$
$167$	−15.7522	+	13.2176i	−1.21894	+	1.02281i	−0.998880	+	0.0473242i	$0.984931\pi$
$168$		0			0
$169$	12.2157	−	4.44615i	0.939669	−	0.342012i
$170$	−1.44161	+	2.49694i	−0.110567	+	0.191507i
$171$		0			0
$172$	−7.59085	−	13.1477i	−0.578797	−	1.00251i
$173$	10.7501	+	9.02041i	0.817316	+	0.685809i	0.952342	−	0.305033i	$-0.0986674\pi$
$173$	10.7501	+	9.02041i	0.817316	+	0.685809i	−0.135026	+	0.990842i	$0.543112\pi$
$174$		0			0
$175$	0.0212990	+	0.120793i	0.00161006	+	0.00913108i
$176$	−2.71150	−	15.3777i	−0.204387	−	1.15914i
$177$		0			0
$178$	1.07353	+	0.900799i	0.0804645	+	0.0675177i
$179$	−5.09500	−	8.82479i	−0.380818	−	0.659596i	0.610361	−	0.792123i	$-0.291024\pi$
$179$	−5.09500	−	8.82479i	−0.380818	−	0.659596i	−0.991179	+	0.132527i	$0.957691\pi$
$180$		0			0
$181$	−12.0274	+	20.8320i	−0.893987	+	1.54843i	−0.0589331	+	0.998262i	$0.518770\pi$
$181$	−12.0274	+	20.8320i	−0.893987	+	1.54843i	−0.835054	+	0.550169i	$0.814563\pi$
$182$	0.00930370	−	0.00338627i	0.000689636	−	0.000251007i
$183$		0			0
$184$	−1.26001	+	1.05728i	−0.0928894	+	0.0779434i
$185$	−9.21055	−	3.35237i	−0.677173	−	0.246471i
$186$		0			0
$187$	2.83708	−	16.0899i	0.207468	−	1.17661i
$188$	12.9706			0.945981
$189$		0			0
$190$	−0.384104			−0.0278658
$191$	1.90082	−	10.7801i	0.137538	−	0.780018i	−0.835520	−	0.549460i	$-0.814834\pi$
$191$	1.90082	−	10.7801i	0.137538	−	0.780018i	0.973058	−	0.230559i	$-0.0740554\pi$
$192$		0			0
$193$	10.1543	+	3.69586i	0.730922	+	0.266034i	0.680555	−	0.732697i	$-0.261739\pi$
$193$	10.1543	+	3.69586i	0.730922	+	0.266034i	0.0503667	+	0.998731i	$0.483961\pi$
$194$	−3.16399	+	2.65490i	−0.227161	+	0.190611i
$195$		0			0
$196$	−9.02994	+	3.28663i	−0.644996	+	0.234759i
$197$	11.0367	−	19.1161i	0.786331	−	1.36196i	−0.141870	−	0.989885i	$-0.545311\pi$
$197$	11.0367	−	19.1161i	0.786331	−	1.36196i	0.928201	−	0.372080i	$-0.121355\pi$
$198$		0			0
$199$	−6.44338	−	11.1603i	−0.456759	−	0.791130i	0.542028	−	0.840360i	$-0.317657\pi$
$199$	−6.44338	−	11.1603i	−0.456759	−	0.791130i	−0.998787	+	0.0492301i	$0.984323\pi$
$200$	−0.113222	−	0.0950043i	−0.00800599	−	0.00671782i
$201$		0			0
$202$	−0.995564	−	5.64612i	−0.0700476	−	0.397260i
$203$	1.78903	+	10.1461i	0.125566	+	0.712118i
$204$		0			0
$205$	−6.23612	−	5.23273i	−0.435550	−	0.365470i
$206$	0.948326	+	1.64255i	0.0660730	+	0.114442i
$207$		0			0
$208$	0.0270347	−	0.0468255i	0.00187452	−	0.00324676i
$209$	2.04531	−	0.744431i	0.141477	−	0.0514934i
$210$		0			0
$211$	−18.3817	+	15.4241i	−1.26545	+	1.06184i	−0.270371	+	0.962756i	$0.587146\pi$
$211$	−18.3817	+	15.4241i	−1.26545	+	1.06184i	−0.995079	+	0.0990822i	$0.968409\pi$
$212$	−2.23332	−	0.812863i	−0.153385	−	0.0558277i
$213$		0			0
$214$	0.814983	−	4.62200i	0.0557111	−	0.315953i
$215$	−18.4035			−1.25511
$216$		0			0
$217$	−4.92177			−0.334112
$218$	−1.04633	+	5.93404i	−0.0708665	+	0.401904i
$219$		0			0
$220$	−19.8379	−	7.22042i	−1.33747	−	0.486801i
$221$	0.0433379	−	0.0363648i	0.00291522	−	0.00244616i
$222$		0			0
$223$	−20.3558	+	7.40890i	−1.36312	+	0.496137i	−0.917019	−	0.398844i	$-0.869411\pi$
$223$	−20.3558	+	7.40890i	−1.36312	+	0.496137i	−0.446105	+	0.894981i	$0.647189\pi$
$224$	−2.91919	+	5.05618i	−0.195047	+	0.337831i
$225$		0			0
$226$	2.60880	+	4.51858i	0.173535	+	0.300571i
$227$	16.5786	+	13.9111i	1.10036	+	0.923314i	0.997449	−	0.0713762i	$-0.0227391\pi$
$227$	16.5786	+	13.9111i	1.10036	+	0.923314i	0.102913	+	0.994690i	$0.467184\pi$
$228$		0			0
$229$	−1.87633	−	10.6412i	−0.123991	−	0.703190i	−0.981902	−	0.189391i	$-0.939349\pi$
$229$	−1.87633	−	10.6412i	−0.123991	−	0.703190i	0.857910	−	0.513799i	$-0.171762\pi$
$230$	0.165310	+	0.937520i	0.0109002	+	0.0618182i
$231$		0			0
$232$	−9.51018	−	7.97999i	−0.624374	−	0.523912i
$233$	−3.81950	−	6.61557i	−0.250224	−	0.433400i	0.713364	−	0.700794i	$-0.247171\pi$
$233$	−3.81950	−	6.61557i	−0.250224	−	0.433400i	−0.963587	+	0.267394i	$0.913838\pi$
$234$		0			0
$235$	7.86160	−	13.6167i	0.512834	−	0.888255i
$236$	−6.35669	+	2.31364i	−0.413785	+	0.150605i
$237$		0			0
$238$	−1.31575	+	1.10405i	−0.0852874	+	0.0715647i
$239$	3.03661	+	1.10524i	0.196422	+	0.0714917i	0.438358	−	0.898800i	$-0.355560\pi$
$239$	3.03661	+	1.10524i	0.196422	+	0.0714917i	−0.241936	+	0.970292i	$0.577782\pi$
$240$		0			0
$241$	−4.60948	+	26.1417i	−0.296923	+	1.68393i	0.362360	+	0.932038i	$0.381971\pi$
$241$	−4.60948	+	26.1417i	−0.296923	+	1.68393i	−0.659283	+	0.751895i	$0.729140\pi$
$242$	−6.72979			−0.432608
$243$		0			0
$244$	−12.6350			−0.808873
$245$	−2.02278	+	11.4718i	−0.129231	+	0.732904i
$246$		0			0
$247$	0.00708224	+	0.00257773i	0.000450632	+	0.000164017i
$248$	4.54320	−	3.81220i	0.288494	−	0.242075i
$249$		0			0
$250$	−4.40455	+	1.60312i	−0.278568	+	0.101390i
$251$	2.24965	−	3.89651i	0.141997	−	0.245945i	−0.786252	−	0.617906i	$-0.787981\pi$
$251$	2.24965	−	3.89651i	0.141997	−	0.245945i	0.928248	+	0.371961i	$0.121314\pi$
$252$		0			0
$253$	−2.69726	−	4.67179i	−0.169575	−	0.293713i
$254$	2.67184	+	2.24194i	0.167646	+	0.140672i
$255$		0			0
$256$	0.678549	+	3.84824i	0.0424093	+	0.240515i
$257$	2.38513	+	13.5267i	0.148780	+	0.843775i	0.964254	+	0.264981i	$0.0853655\pi$
$257$	2.38513	+	13.5267i	0.148780	+	0.843775i	−0.815473	+	0.578794i	$0.803523\pi$
$258$		0			0
$259$	−4.47296	−	3.75326i	−0.277936	−	0.233216i
$260$	−0.0365505	−	0.0633073i	−0.00226677	−	0.00392615i
$261$		0			0
$262$	−3.22711	+	5.58952i	−0.199372	+	0.345322i
$263$	22.7430	−	8.27776i	1.40239	−	0.510429i	0.473504	−	0.880792i	$-0.342989\pi$
$263$	22.7430	−	8.27776i	1.40239	−	0.510429i	0.928887	+	0.370363i	$0.120767\pi$
$264$		0			0
$265$	−2.20699	+	1.85188i	−0.135574	+	0.113760i
$266$	−0.215019	−	0.0782604i	−0.0131836	−	0.00479845i
$267$		0			0
$268$	3.49905	−	19.8441i	0.213739	−	1.21217i
$269$	12.0062			0.732032			0.366016	−	0.930609i	$-0.380722\pi$
$269$	12.0062			0.732032			0.366016	+	0.930609i	$0.380722\pi$
$270$		0			0
$271$	3.71777			0.225839			0.112919	−	0.993604i	$-0.463980\pi$
$271$	3.71777			0.225839			0.112919	+	0.993604i	$0.463980\pi$
$272$	−1.62881	+	9.23747i	−0.0987614	+	0.560104i
$273$		0			0
$274$	4.68781	+	1.70622i	0.283201	+	0.103077i
$275$	0.371331	−	0.311584i	0.0223921	−	0.0187892i
$276$		0			0
$277$	22.0669	−	8.03170i	1.32587	−	0.482578i	0.420537	−	0.907275i	$-0.361842\pi$
$277$	22.0669	−	8.03170i	1.32587	−	0.482578i	0.905335	+	0.424697i	$0.139620\pi$
$278$	1.27654	−	2.21104i	0.0765621	−	0.132609i
$279$		0			0
$280$	2.32418	+	4.02560i	0.138897	+	0.240576i
$281$	−15.6057	−	13.0947i	−0.930955	−	0.781164i	0.0450333	−	0.998985i	$-0.485661\pi$
$281$	−15.6057	−	13.0947i	−0.930955	−	0.781164i	−0.975989	+	0.217821i	$0.930105\pi$
$282$		0			0
$283$	2.01431	+	11.4237i	0.119738	+	0.679069i	0.984295	+	0.176533i	$0.0564884\pi$
$283$	2.01431	+	11.4237i	0.119738	+	0.679069i	−0.864556	+	0.502536i	$0.832401\pi$
$284$	1.93068	+	10.9494i	0.114565	+	0.649729i
$285$		0			0
$286$	−0.0299738	−	0.0251510i	−0.00177239	−	0.00148721i
$287$	−2.42478	−	4.19984i	−0.143130	−	0.247909i
$288$		0			0
$289$	3.59280	−	6.22291i	0.211341	−	0.366053i
$290$	−6.75194	+	2.45750i	−0.396488	+	0.144310i
$291$		0			0
$292$	0.765686	−	0.642487i	0.0448084	−	0.0375987i
$293$	−29.6700	−	10.7990i	−1.73334	−	0.630884i	−0.734481	−	0.678630i	$-0.762574\pi$
$293$	−29.6700	−	10.7990i	−1.73334	−	0.630884i	−0.998860	+	0.0477455i	$0.984796\pi$
$294$		0			0
$295$	−1.42395	+	8.07562i	−0.0829056	+	0.470181i
$296$	7.03603			0.408961
$297$		0			0
$298$	−0.366782			−0.0212471
$299$	0.00324366	−	0.0183957i	0.000187586	−	0.00106385i
$300$		0			0
$301$	−10.3021	−	3.74967i	−0.593806	−	0.216128i
$302$	−2.61789	+	2.19667i	−0.150642	+	0.126404i
$303$		0			0
$304$	−1.17424	+	0.427390i	−0.0673475	+	0.0245125i
$305$	−7.65816	+	13.2643i	−0.438505	+	0.759513i
$306$		0			0
$307$	4.06027	+	7.03259i	0.231732	+	0.401371i	0.958318	−	0.285704i	$-0.0922275\pi$
$307$	4.06027	+	7.03259i	0.231732	+	0.401371i	−0.726586	+	0.687075i	$0.758894\pi$
$308$	−9.63400	−	8.08388i	−0.548948	−	0.460622i
$309$		0			0
$310$	−0.596055	−	3.38039i	−0.0338536	−	0.191993i
$311$	−4.14126	−	23.4862i	−0.234829	−	1.33178i	−0.842973	−	0.537956i	$-0.819197\pi$
$311$	−4.14126	−	23.4862i	−0.234829	−	1.33178i	0.608144	−	0.793827i	$-0.291914\pi$
$312$		0			0
$313$	20.6146	+	17.2977i	1.16521	+	0.977725i	0.999964	−	0.00852816i	$-0.00271463\pi$
$313$	20.6146	+	17.2977i	1.16521	+	0.977725i	0.165243	+	0.986253i	$0.447159\pi$
$314$	2.60909	+	4.51908i	0.147240	+	0.255026i
$315$		0			0
$316$	0.446928	−	0.774102i	0.0251417	−	0.0435466i
$317$	7.82983	−	2.84983i	0.439767	−	0.160062i	−0.112641	−	0.993636i	$-0.535931\pi$
$317$	7.82983	−	2.84983i	0.439767	−	0.160062i	0.552408	+	0.833574i	$0.313709\pi$
$318$		0			0
$319$	31.1904	−	26.1718i	1.74633	−	1.46534i
$320$	8.63886	+	3.14429i	0.482927	+	0.175771i
$321$		0			0
$322$	−0.0984783	+	0.558498i	−0.00548798	+	0.0311239i
$323$	−1.30748			−0.0727501
$324$		0			0
$325$	0.00167849			9.31061e−5
$326$	−0.239136	+	1.35621i	−0.0132445	+	0.0751134i
$327$		0			0
$328$	5.49129	+	1.99867i	0.303206	+	0.110358i
$329$	7.17524	−	6.02074i	0.395584	−	0.331934i
$330$		0			0
$331$	6.03307	−	2.19586i	0.331607	−	0.120695i	−0.170850	−	0.985297i	$-0.554651\pi$
$331$	6.03307	−	2.19586i	0.331607	−	0.120695i	0.502458	+	0.864602i	$0.332429\pi$
$332$	4.21548	−	7.30143i	0.231355	−	0.400718i
$333$		0			0
$334$	−4.27161	−	7.39865i	−0.233732	−	0.404836i
$335$	−18.7117	−	15.7010i	−1.02233	−	0.857837i
$336$		0			0
$337$	1.29800	+	7.36133i	0.0707066	+	0.400997i	0.999535	+	0.0304874i	$0.00970594\pi$
$337$	1.29800	+	7.36133i	0.0707066	+	0.400997i	−0.928829	+	0.370510i	$0.879183\pi$
$338$	0.937861	+	5.31887i	0.0510129	+	0.289309i
$339$		0			0
$340$	9.71465	+	8.15156i	0.526851	+	0.442080i
$341$	9.72545	+	16.8450i	0.526663	+	0.912206i
$342$		0			0
$343$	−8.08839	+	14.0095i	−0.436732	+	0.756442i
$344$	12.4141	−	4.51835i	0.669321	−	0.243613i
$345$		0			0
$346$	−4.46631	+	3.74768i	−0.240110	+	0.201476i
$347$	29.5576	+	10.7581i	1.58673	+	0.577524i	0.976654	−	0.214817i	$-0.0689156\pi$
$347$	29.5576	+	10.7581i	1.58673	+	0.577524i	0.610079	+	0.792341i	$0.291138\pi$
$348$		0			0
$349$	2.05824	−	11.6729i	0.110175	−	0.624835i	−0.878851	−	0.477096i	$-0.841689\pi$
$349$	2.05824	−	11.6729i	0.110175	−	0.624835i	0.989026	−	0.147739i	$-0.0471994\pi$
$350$	−0.0509595			−0.00272390
$351$		0			0
$352$	23.0733			1.22981
$353$	−1.42515	+	8.08240i	−0.0758528	+	0.430183i	0.923105	+	0.384547i	$0.125642\pi$
$353$	−1.42515	+	8.08240i	−0.0758528	+	0.430183i	−0.998958	+	0.0456355i	$0.985469\pi$
$354$		0			0
$355$	12.6650	+	4.60968i	0.672188	+	0.244657i
$356$	4.72182	−	3.96208i	0.250256	−	0.209990i
$357$		0			0
$358$	3.97828	−	1.44798i	0.210259	−	0.0765279i
$359$	−8.86365	+	15.3523i	−0.467806	+	0.810263i	−0.999323	−	0.0367840i	$-0.988289\pi$
$359$	−8.86365	+	15.3523i	−0.467806	+	0.810263i	0.531517	+	0.847047i	$0.321622\pi$
$360$		0			0
$361$	9.41291	+	16.3036i	0.495416	+	0.858086i
$362$	−7.65579	−	6.42397i	−0.402379	−	0.337636i
$363$		0			0
$364$	−0.00756197	−	0.0428861i	−0.000396355	−	0.00224784i
$365$	−0.210400	−	1.19324i	−0.0110129	−	0.0624570i
$366$		0			0
$367$	−15.5657	−	13.0611i	−0.812521	−	0.681786i	0.138687	−	0.990336i	$-0.455712\pi$
$367$	−15.5657	−	13.0611i	−0.812521	−	0.681786i	−0.951208	+	0.308550i	$0.900156\pi$
$368$	1.54854	+	2.68215i	0.0807232	+	0.139817i
$369$		0			0
$370$	2.03613	−	3.52668i	0.105853	−	0.183343i
$371$	−1.61277	+	0.587001i	−0.0837309	+	0.0304756i
$372$		0			0
$373$	−7.41641	+	6.22311i	−0.384007	+	0.322220i	−0.814273	−	0.580482i	$-0.802864\pi$
$373$	−7.41641	+	6.22311i	−0.384007	+	0.322220i	0.430266	+	0.902702i	$0.358420\pi$
$374$	6.37857	+	2.32161i	0.329828	+	0.120048i
$375$		0			0
$376$	−1.95992	+	11.1153i	−0.101075	+	0.573226i
$377$	0.140987			0.00726119
$378$		0			0
$379$	−4.12905			−0.212095			−0.106048	−	0.994361i	$-0.533820\pi$
$379$	−4.12905			−0.212095			−0.106048	+	0.994361i	$0.533820\pi$
$380$	−0.293369	+	1.66378i	−0.0150495	+	0.0853500i
$381$		0			0
$382$	4.27358	+	1.55546i	0.218655	+	0.0795840i
$383$	3.63885	−	3.05336i	0.185937	−	0.156019i	−0.545068	−	0.838392i	$-0.683496\pi$
$383$	3.63885	−	3.05336i	0.185937	−	0.156019i	0.731005	+	0.682372i	$0.239052\pi$
$384$		0			0
$385$	−14.3258	+	5.21415i	−0.730109	+	0.265738i
$386$	−2.24476	+	3.88803i	−0.114255	+	0.197896i
$387$		0			0
$388$	9.08336	+	15.7328i	0.461138	+	0.798714i
$389$	−16.7100	−	14.0213i	−0.847229	−	0.710910i	0.111949	−	0.993714i	$-0.464291\pi$
$389$	−16.7100	−	14.0213i	−0.847229	−	0.710910i	−0.959178	+	0.282804i	$0.908735\pi$
$390$		0			0
$391$	0.562710	+	3.19129i	0.0284575	+	0.161390i
$392$	−1.45203	−	8.23490i	−0.0733388	−	0.415925i
$393$		0			0
$394$	7.02519	+	5.89483i	0.353924	+	0.296977i
$395$	−0.541773	−	0.938378i	−0.0272595	−	0.0472149i
$396$		0			0
$397$	17.4245	−	30.1802i	0.874512	−	1.51470i	0.0172294	−	0.999852i	$-0.494515\pi$
$397$	17.4245	−	30.1802i	0.874512	−	1.51470i	0.857282	−	0.514847i	$-0.172151\pi$
$398$	5.03113	−	1.83118i	0.252188	−	0.0917888i
$399$		0			0
$400$	−0.213187	+	0.178885i	−0.0106594	+	0.00894427i
$401$	17.6907	+	6.43890i	0.883433	+	0.321543i	0.743594	−	0.668631i	$-0.233119\pi$
$401$	17.6907	+	6.43890i	0.883433	+	0.321543i	0.139839	+	0.990174i	$0.455342\pi$
$402$		0			0
$403$	−0.0116956	+	0.0663290i	−0.000582599	+	0.00330408i
$404$	−25.2170			−1.25459
$405$		0			0
$406$	−4.28040			−0.212433
$407$	−4.00709	+	22.7254i	−0.198624	+	1.12645i
$408$		0			0
$409$	5.97640	+	2.17523i	0.295514	+	0.107558i	0.485523	−	0.874224i	$-0.338629\pi$
$409$	5.97640	+	2.17523i	0.295514	+	0.107558i	−0.190008	+	0.981782i	$0.560852\pi$
$410$	2.59090	−	2.17402i	0.127955	−	0.107367i
$411$		0			0
$412$	7.83914	−	2.85322i	0.386207	−	0.140568i
$413$	−2.44251	+	4.23055i	−0.120188	+	0.208172i
$414$		0			0
$415$	−5.11007	−	8.85090i	−0.250843	−	0.434474i
$416$	0.0612035	+	0.0513559i	0.00300075	+	0.00251793i
$417$		0			0
$418$	0.157029	+	0.890553i	0.00768052	+	0.0435584i
$419$	−4.22277	−	23.9485i	−0.206296	−	1.16996i	−0.895388	−	0.445288i	$-0.853101\pi$
$419$	−4.22277	−	23.9485i	−0.206296	−	1.16996i	0.689092	−	0.724674i	$-0.258010\pi$
$420$		0			0
$421$	−6.12072	−	5.13590i	−0.298306	−	0.250308i	0.481333	−	0.876538i	$-0.340153\pi$
$421$	−6.12072	−	5.13590i	−0.298306	−	0.250308i	−0.779639	+	0.626230i	$0.784597\pi$
$422$	−4.98469	−	8.63373i	−0.242651	−	0.420283i
$423$		0			0
$424$	1.03405	−	1.79103i	0.0502181	−	0.0869803i
$425$	−0.273625	+	0.0995913i	−0.0132728	+	0.00483089i
$426$		0			0
$427$	−6.98956	+	5.86494i	−0.338249	+	0.283824i
$428$	−19.3981	−	7.06033i	−0.937643	−	0.341274i
$429$		0			0
$430$	1.32772	−	7.52987i	0.0640283	−	0.363122i
$431$	9.87124			0.475481			0.237740	−	0.971329i	$-0.423593\pi$
$431$	9.87124			0.475481			0.237740	+	0.971329i	$0.423593\pi$
$432$		0			0
$433$	−6.10369			−0.293325			−0.146662	−	0.989187i	$-0.546853\pi$
$433$	−6.10369			−0.293325			−0.146662	+	0.989187i	$0.546853\pi$
$434$	0.355081	−	2.01377i	0.0170444	−	0.0966638i
$435$		0			0
$436$	24.9046	+	9.06454i	1.19272	+	0.434113i
$437$	−0.330704	+	0.277494i	−0.0158197	+	0.0132743i
$438$		0			0
$439$	14.2213	−	5.17614i	0.678747	−	0.247044i	0.0204376	−	0.999791i	$-0.493494\pi$
$439$	14.2213	−	5.17614i	0.678747	−	0.247044i	0.658309	+	0.752747i	$0.271272\pi$
$440$	9.18520	−	15.9092i	0.437887	−	0.758443i
$441$		0			0
$442$	0.0117522	+	0.0203554i	0.000558996	+	0.000968210i
$443$	−0.553692	−	0.464603i	−0.0263067	−	0.0220739i	0.629539	−	0.776968i	$-0.283244\pi$
$443$	−0.553692	−	0.464603i	−0.0263067	−	0.0220739i	−0.655846	+	0.754895i	$0.727688\pi$
$444$		0			0
$445$	−1.29749	−	7.35845i	−0.0615071	−	0.348824i
$446$	−1.56282	−	8.86317i	−0.0740015	−	0.419683i
$447$		0			0
$448$	4.19533	+	3.52030i	0.198211	+	0.166318i
$449$	−0.834224	−	1.44492i	−0.0393695	−	0.0681899i	0.845669	−	0.533707i	$-0.179202\pi$
$449$	−0.834224	−	1.44492i	−0.0393695	−	0.0681899i	−0.885039	+	0.465517i	$0.845868\pi$
$450$		0			0
$451$	−9.58275	+	16.5978i	−0.451234	+	0.781560i
$452$	21.5651	−	7.84906i	1.01434	−	0.369189i
$453$		0			0
$454$	−6.88786	+	5.77960i	−0.323263	+	0.271250i
$455$	−0.0496055	−	0.0180549i	−0.00232554	−	0.000846429i
$456$		0			0
$457$	1.92462	−	10.9151i	0.0900299	−	0.510585i	−0.906128	−	0.423005i	$-0.860975\pi$
$457$	1.92462	−	10.9151i	0.0900299	−	0.510585i	0.996157	−	0.0875805i	$-0.0279135\pi$
$458$	4.48926			0.209769
$459$		0			0
$460$	4.18720			0.195229
$461$	−3.80018	+	21.5519i	−0.176992	+	1.00377i	0.758827	+	0.651292i	$0.225773\pi$
$461$	−3.80018	+	21.5519i	−0.176992	+	1.00377i	−0.935819	+	0.352480i	$0.885338\pi$
$462$		0			0
$463$	−23.3530	−	8.49979i	−1.08531	−	0.395019i	−0.263426	−	0.964680i	$-0.584852\pi$
$463$	−23.3530	−	8.49979i	−1.08531	−	0.395019i	−0.821880	+	0.569661i	$0.807075\pi$
$464$	−17.9069	+	15.0257i	−0.831306	+	0.697549i
$465$		0			0
$466$	2.98235	−	1.08549i	0.138154	−	0.0502841i
$467$	5.91777	−	10.2499i	0.273842	−	0.474308i	−0.696001	−	0.718041i	$-0.745039\pi$
$467$	5.91777	−	10.2499i	0.273842	−	0.474308i	0.969842	+	0.243734i	$0.0783722\pi$
$468$		0			0
$469$	−7.27564	−	12.6018i	−0.335958	−	0.581896i
$470$	5.00415	+	4.19898i	0.230824	+	0.193685i
$471$		0			0
$472$	−1.02217	−	5.79701i	−0.0470491	−	0.266829i
$473$	7.52367	+	42.6689i	0.345939	+	1.96192i
$474$		0			0
$475$	−0.0297163	−	0.0249349i	−0.00136348	−	0.00114409i
$476$	3.77733	+	6.54252i	0.173134	+	0.299876i
$477$		0			0
$478$	−0.671288	+	1.16270i	−0.0307040	+	0.0531809i
$479$	−2.71322	+	0.987532i	−0.123970	+	0.0451215i	−0.403260	−	0.915085i	$-0.632123\pi$
$479$	−2.71322	+	0.987532i	−0.123970	+	0.0451215i	0.279290	+	0.960207i	$0.409901\pi$
$480$		0			0
$481$	−0.0612104	+	0.0513617i	−0.00279096	+	0.00234189i
$482$	−10.3634	−	3.77198i	−0.472041	−	0.171809i
$483$		0			0
$484$	−5.14005	+	29.1506i	−0.233638	+	1.32503i
$485$	22.0220			0.999966
$486$		0			0
$487$	8.75903			0.396910			0.198455	−	0.980110i	$-0.436408\pi$
$487$	8.75903			0.396910			0.198455	+	0.980110i	$0.436408\pi$
$488$	1.90921	−	10.8276i	0.0864257	−	0.490144i
$489$		0			0
$490$	−4.54779	−	1.65526i	−0.205448	−	0.0747770i
$491$	−17.2920	+	14.5097i	−0.780375	+	0.654812i	−0.943343	−	0.331819i	$-0.892338\pi$
$491$	−17.2920	+	14.5097i	−0.780375	+	0.654812i	0.162968	+	0.986631i	$0.447893\pi$
$492$		0			0
$493$	−22.9834	+	8.36528i	−1.03512	+	0.376753i
$494$	−0.00156564	+	0.00271176i	−7.04413e−5	+	0.000122008i
$495$		0			0
$496$	−5.58354	−	9.67097i	−0.250708	−	0.434239i
$497$	6.15056	+	5.16094i	0.275890	+	0.231500i
$498$		0			0
$499$	−4.39900	−	24.9479i	−0.196926	−	1.11682i	−0.909649	−	0.415378i	$-0.863649\pi$
$499$	−4.39900	−	24.9479i	−0.196926	−	1.11682i	0.712723	−	0.701446i	$-0.247462\pi$
$500$	3.57998	+	20.3031i	0.160102	+	0.907981i
$501$		0			0
$502$	1.43197	+	1.20157i	0.0639120	+	0.0536286i
$503$	−1.87207	−	3.24252i	−0.0834714	−	0.144577i	0.821267	−	0.570543i	$-0.193267\pi$
$503$	−1.87207	−	3.24252i	−0.0834714	−	0.144577i	−0.904739	+	0.425967i	$0.859934\pi$
$504$		0			0
$505$	−15.2842	+	26.4731i	−0.680139	+	1.17804i
$506$	2.10608	−	0.766549i	0.0936265	−	0.0340773i
$507$		0			0
$508$	11.7518	−	9.86094i	0.521402	−	0.437508i
$509$	−22.8814	−	8.32815i	−1.01420	−	0.369139i	−0.219156	−	0.975690i	$-0.570330\pi$
$509$	−22.8814	−	8.32815i	−1.01420	−	0.369139i	−0.795045	+	0.606551i	$0.792553\pi$
$510$		0			0
$511$	0.125340	−	0.710836i	0.00554469	−	0.0314455i
$512$	−22.7690			−1.00626
$513$		0			0
$514$	−5.70660			−0.251707
$515$	1.75603	−	9.95896i	0.0773801	−	0.438844i
$516$		0			0
$517$	−34.7845	−	12.6605i	−1.52982	−	0.556810i
$518$	1.85836	−	1.55935i	0.0816519	−	0.0685141i
$519$		0			0
$520$	0.0597746	−	0.0217562i	0.00262129	−	0.000954071i
$521$	−9.81046	+	16.9922i	−0.429804	+	0.744443i	−0.996856	−	0.0792397i	$-0.974751\pi$
$521$	−9.81046	+	16.9922i	−0.429804	+	0.744443i	0.567051	+	0.823682i	$0.308084\pi$
$522$		0			0
$523$	−10.4077	−	18.0267i	−0.455097	−	0.788251i	0.543597	−	0.839346i	$-0.317062\pi$
$523$	−10.4077	−	18.0267i	−0.455097	−	0.788251i	−0.998694	+	0.0510956i	$0.983729\pi$
$524$	21.7467	+	18.2476i	0.950008	+	0.797152i
$525$		0			0
$526$	1.74609	+	9.90258i	0.0761333	+	0.431773i
$527$	−2.02895	−	11.5068i	−0.0883826	−	0.501243i
$528$		0			0
$529$	−16.7994	−	14.0964i	−0.730408	−	0.612885i
$530$	−0.598482	−	1.03660i	−0.0259964	−	0.0450271i
$531$		0			0
$532$	−0.503217	+	0.871598i	−0.0218172	+	0.0377886i
$533$	−0.0623617	+	0.0226978i	−0.00270119	+	0.000983152i
$534$		0			0
$535$	−19.1693	+	16.0850i	−0.828763	+	0.695414i
$536$	16.4768	+	5.99707i	0.711690	+	0.259034i
$537$		0			0
$538$	−0.866188	+	4.91240i	−0.0373440	+	0.211788i
$539$	27.4245			1.18126
$540$		0			0
$541$	−30.6272			−1.31676			−0.658382	−	0.752684i	$-0.728759\pi$
$541$	−30.6272			−1.31676			−0.658382	+	0.752684i	$0.728759\pi$
$542$	−0.268219	+	1.52114i	−0.0115210	+	0.0653387i
$543$		0			0
$544$	−13.0244	−	4.74050i	−0.558417	−	0.203247i
$545$	24.6109	−	20.6510i	1.05422	−	0.884592i
$546$		0			0
$547$	−21.2819	+	7.74596i	−0.909946	+	0.331193i	−0.754231	−	0.656609i	$-0.771990\pi$
$547$	−21.2819	+	7.74596i	−0.909946	+	0.331193i	−0.155715	+	0.987802i	$0.549768\pi$
$548$	10.9711	−	19.0025i	0.468661	−	0.811745i
$549$		0			0
$550$	0.100696	+	0.174411i	0.00429370	+	0.00743691i
$551$	−2.49605	−	2.09444i	−0.106335	−	0.0892259i
$552$		0			0
$553$	−0.112088	−	0.635682i	−0.00476646	−	0.0270320i
$554$	1.69419	+	9.60822i	0.0719792	+	0.408214i
$555$		0			0
$556$	−8.60231	−	7.21819i	−0.364819	−	0.306120i
$557$	−18.2259	−	31.5682i	−0.772256	−	1.33759i	−0.936324	−	0.351138i	$-0.885795\pi$
$557$	−18.2259	−	31.5682i	−0.772256	−	1.33759i	0.164067	−	0.986449i	$-0.447539\pi$
$558$		0			0
$559$	−0.0750139	+	0.129928i	−0.00317275	+	0.00549537i
$560$	8.22465	−	2.99353i	0.347555	−	0.126500i
$561$		0			0
$562$	6.48362	−	5.44041i	0.273495	−	0.229490i
$563$	−24.9171	−	9.06909i	−1.05013	−	0.382216i	−0.241419	−	0.970421i	$-0.577613\pi$
$563$	−24.9171	−	9.06909i	−1.05013	−	0.382216i	−0.808712	+	0.588205i	$0.799835\pi$
$564$		0			0
$565$	4.83076	−	27.3966i	0.203232	−	1.15258i
$566$	−4.81938			−0.202574
$567$		0			0
$568$	−9.67492			−0.405950
$569$	3.98825	−	22.6185i	0.167196	−	0.948216i	−0.779575	−	0.626309i	$-0.784565\pi$
$569$	3.98825	−	22.6185i	0.167196	−	0.948216i	0.946771	−	0.321907i	$-0.104324\pi$
$570$		0			0
$571$	4.50865	+	1.64101i	0.188681	+	0.0686743i	0.434633	−	0.900608i	$-0.356878\pi$
$571$	4.50865	+	1.64101i	0.188681	+	0.0686743i	−0.245952	+	0.969282i	$0.579100\pi$
$572$	−0.131837	+	0.110624i	−0.00551237	+	0.00462543i
$573$		0			0
$574$	1.89332	−	0.689112i	0.0790256	−	0.0287630i
$575$	−0.0480718	+	0.0832628i	−0.00200473	+	0.00347230i
$576$		0			0
$577$	2.15666	+	3.73545i	0.0897831	+	0.155509i	0.907419	−	0.420226i	$-0.138049\pi$
$577$	2.15666	+	3.73545i	0.0897831	+	0.155509i	−0.817636	+	0.575735i	$0.804716\pi$
$578$	2.28693	+	1.91896i	0.0951237	+	0.0798182i
$579$		0			0
$580$	5.48792	+	31.1236i	0.227874	+	1.29234i
$581$	−1.05723	−	5.99584i	−0.0438612	−	0.248749i
$582$		0			0
$583$	5.19588	+	4.35986i	0.215191	+	0.180567i
$584$	0.434885	+	0.753242i	0.0179957	+	0.0311694i
$585$		0			0
$586$	6.55900	−	11.3605i	0.270950	−	0.469299i
$587$	−39.3000	+	14.3040i	−1.62209	+	0.590391i	−0.983778	−	0.179391i	$-0.942587\pi$
$587$	−39.3000	+	14.3040i	−1.62209	+	0.590391i	−0.638308	+	0.769781i	$0.720365\pi$
$588$		0			0
$589$	1.19241	−	1.00055i	0.0491325	−	0.0412271i
$590$	−3.20145	−	1.16523i	−0.131801	−	0.0479718i
$591$		0			0
$592$	2.30054	−	13.0470i	0.0945515	−	0.536228i
$593$	−31.5370			−1.29507			−0.647536	−	0.762035i	$-0.724200\pi$
$593$	−31.5370			−1.29507			−0.647536	+	0.762035i	$0.724200\pi$
$594$		0			0
$595$	9.15786			0.375436
$596$	−0.280139	+	1.58875i	−0.0114749	+	0.0650776i
$597$		0			0
$598$	0.00729267	+	0.00265431i	0.000298219	+	0.000108543i
$599$	−9.67537	+	8.11860i	−0.395325	+	0.331717i	−0.818683	−	0.574245i	$-0.805296\pi$
$599$	−9.67537	+	8.11860i	−0.395325	+	0.331717i	0.423358	+	0.905962i	$0.360851\pi$
$600$		0			0
$601$	−19.3041	+	7.02611i	−0.787430	+	0.286601i	−0.704267	−	0.709935i	$-0.748724\pi$
$601$	−19.3041	+	7.02611i	−0.787430	+	0.286601i	−0.0831627	+	0.996536i	$0.526502\pi$
$602$	2.27744	−	3.94465i	0.0928216	−	0.160772i
$603$		0			0
$604$	7.51556	+	13.0173i	0.305804	+	0.529668i
$605$	27.4872	+	23.0645i	1.11751	+	0.937705i
$606$		0			0
$607$	2.24224	+	12.7164i	0.0910098	+	0.516142i	0.995897	+	0.0904914i	$0.0288437\pi$
$607$	2.24224	+	12.7164i	0.0910098	+	0.516142i	−0.904887	+	0.425651i	$0.860045\pi$
$608$	−0.320637	−	1.81842i	−0.0130035	−	0.0737467i
$609$		0			0
$610$	−4.87466	−	4.09033i	−0.197369	−	0.165612i
$611$	−0.0640889	−	0.111005i	−0.00259276	−	0.00449079i
$612$		0			0
$613$	15.5799	−	26.9851i	0.629265	−	1.08992i	−0.358434	−	0.933555i	$-0.616689\pi$
$613$	15.5799	−	26.9851i	0.629265	−	1.08992i	0.987699	−	0.156364i	$-0.0499774\pi$
$614$	−3.17034	+	1.15391i	−0.127945	+	0.0465680i
$615$		0			0
$616$	8.38328	−	7.03441i	0.337772	−	0.283424i
$617$	6.71014	+	2.44229i	0.270140	+	0.0983230i	0.473539	−	0.880773i	$-0.342976\pi$
$617$	6.71014	+	2.44229i	0.270140	+	0.0983230i	−0.203398	+	0.979096i	$0.565199\pi$
$618$		0			0
$619$	−1.74185	+	9.87851i	−0.0700108	+	0.397051i	0.929585	+	0.368609i	$0.120166\pi$
$619$	−1.74185	+	9.87851i	−0.0700108	+	0.397051i	−0.999595	+	0.0284422i	$0.990945\pi$
$620$	−15.0977			−0.606338
$621$		0			0
$622$	9.90827			0.397285
$623$	0.772942	−	4.38357i	0.0309673	−	0.175624i
$624$		0			0
$625$	23.0475	+	8.38860i	0.921899	+	0.335544i
$626$	−8.56468	+	7.18662i	−0.342313	+	0.287235i
$627$		0			0
$628$	21.5675	−	7.84993i	0.860637	−	0.313246i
$629$	6.93093	−	12.0047i	0.276354	−	0.478660i
$630$		0			0
$631$	3.53780	+	6.12765i	0.140838	+	0.243938i	0.927812	−	0.373047i	$-0.121687\pi$
$631$	3.53780	+	6.12765i	0.140838	+	0.243938i	−0.786975	+	0.616985i	$0.788354\pi$
$632$	0.595839	+	0.499968i	0.0237012	+	0.0198877i
$633$		0			0
$634$	0.601136	+	3.40921i	0.0238741	+	0.135397i
$635$	−3.22924	−	18.3139i	−0.128149	−	0.726767i
$636$		0			0
$637$	0.0727452	+	0.0610405i	0.00288227	+	0.00241851i
$638$	8.45809	+	14.6498i	0.334859	+	0.579993i
$639$		0			0
$640$	−11.7103	+	20.2828i	−0.462890	+	0.801750i
$641$	4.70900	−	1.71394i	0.185994	−	0.0676964i	−0.247344	−	0.968928i	$-0.579558\pi$
$641$	4.70900	−	1.71394i	0.185994	−	0.0676964i	0.433338	+	0.901231i	$0.357336\pi$
$642$		0			0
$643$	1.25509	−	1.05315i	0.0494959	−	0.0415320i	−0.617704	−	0.786411i	$-0.711937\pi$
$643$	1.25509	−	1.05315i	0.0494959	−	0.0415320i	0.667200	+	0.744879i	$0.267493\pi$
$644$	2.34397	+	0.853134i	0.0923652	+	0.0336182i
$645$		0			0
$646$	0.0943280	−	0.534961i	0.00371129	−	0.0210478i
$647$	34.4927			1.35605			0.678024	−	0.735040i	$-0.262836\pi$
$647$	34.4927			1.35605			0.678024	+	0.735040i	$0.262836\pi$
$648$		0			0
$649$	19.3056			0.757813
$650$	−0.000121095	0	0.000686763i	−4.74973e−6	0	2.69371e-5i
$651$		0			0
$652$	5.69188	+	2.07167i	0.222911	+	0.0811330i
$653$	29.6923	−	24.9148i	1.16195	−	0.974993i	0.162021	−	0.986787i	$-0.448199\pi$
$653$	29.6923	−	24.9148i	1.16195	−	0.974993i	0.999930	+	0.0117946i	$0.00375443\pi$
$654$		0			0
$655$	32.3374	−	11.7698i	1.26353	−	0.459886i
$656$	5.50161	−	9.52907i	0.214802	−	0.372048i
$657$		0			0
$658$	1.94575	+	3.37015i	0.0758534	+	0.131382i
$659$	7.19463	+	6.03701i	0.280263	+	0.235169i	0.772073	−	0.635534i	$-0.219220\pi$
$659$	7.19463	+	6.03701i	0.280263	+	0.235169i	−0.491810	+	0.870703i	$0.663664\pi$
$660$		0			0
$661$	−4.19316	−	23.7806i	−0.163095	−	0.924957i	−0.951007	−	0.309169i	$-0.899949\pi$
$661$	−4.19316	−	23.7806i	−0.163095	−	0.924957i	0.787912	−	0.615788i	$-0.211162\pi$
$662$	0.463189	+	2.62688i	0.0180024	+	0.102096i
$663$		0			0
$664$	5.62003	+	4.71577i	0.218100	+	0.183007i
$665$	0.610007	+	1.05656i	0.0236551	+	0.0409718i
$666$		0			0
$667$	−4.03784	+	6.99375i	−0.156346	+	0.270799i
$668$	−35.3104	+	12.8519i	−1.36620	+	0.497256i
$669$		0			0
$670$	7.77409	−	6.52323i	0.300339	−	0.252014i
$671$	33.8844	+	12.3329i	1.30809	+	0.476107i
$672$		0			0
$673$	−4.59580	+	26.0641i	−0.177155	+	1.00470i	0.758472	+	0.651705i	$0.225946\pi$
$673$	−4.59580	+	26.0641i	−0.177155	+	1.00470i	−0.935627	+	0.352990i	$0.885165\pi$
$674$	−3.10557			−0.119622
$675$		0			0
$676$	23.7554			0.913671
$677$	5.39470	−	30.5949i	0.207335	−	1.17586i	−0.686387	−	0.727236i	$-0.740804\pi$
$677$	5.39470	−	30.5949i	0.207335	−	1.17586i	0.893723	−	0.448620i	$-0.148084\pi$
$678$		0			0
$679$	12.3277	+	4.48693i	0.473095	+	0.172193i
$680$	−8.45346	+	7.09330i	−0.324175	+	0.272015i
$681$		0			0
$682$	−7.59384	+	2.76393i	−0.290783	+	0.105836i
$683$	−19.0681	+	33.0268i	−0.729619	+	1.26374i	0.227425	+	0.973796i	$0.426969\pi$
$683$	−19.0681	+	33.0268i	−0.729619	+	1.26374i	−0.957044	+	0.289942i	$0.906364\pi$
$684$		0			0
$685$	−13.2993	−	23.0351i	−0.508140	−	0.880125i
$686$	−5.14851	−	4.32011i	−0.196571	−	0.164943i
$687$		0			0
$688$	−4.31946	−	24.4969i	−0.164678	−	0.933935i
$689$	0.00407838	+	0.0231296i	0.000155374	+	0.000881169i
$690$		0			0
$691$	25.2255	+	21.1667i	0.959623	+	0.805219i	0.980892	−	0.194555i	$-0.0623262\pi$
$691$	25.2255	+	21.1667i	0.959623	+	0.805219i	−0.0212689	+	0.999774i	$0.506771\pi$
$692$	12.8221	+	22.2085i	0.487424	+	0.844242i
$693$		0			0
$694$	−6.53414	+	11.3175i	−0.248033	+	0.429605i
$695$	−12.7916	+	4.65578i	−0.485215	+	0.176604i
$696$		0			0
$697$	8.81934	−	7.40031i	0.334056	−	0.280307i
$698$	4.62751	+	1.68428i	0.175154	+	0.0637509i
$699$		0			0
$700$	−0.0389216	+	0.220735i	−0.00147110	+	0.00834301i
$701$	−2.30710			−0.0871381			−0.0435690	−	0.999050i	$-0.513873\pi$
$701$	−2.30710			−0.0871381			−0.0435690	+	0.999050i	$0.513873\pi$
$702$		0			0
$703$	1.84668			0.0696490
$704$	3.75838	−	21.3148i	0.141649	−	0.803332i
$705$		0			0
$706$	−3.20413	−	1.16621i	−0.120589	−	0.0438908i
$707$	−13.9498	+	11.7053i	−0.524637	+	0.440223i
$708$		0			0
$709$	10.4795	−	3.81423i	0.393566	−	0.143246i	−0.137653	−	0.990480i	$-0.543956\pi$
$709$	10.4795	−	3.81423i	0.393566	−	0.143246i	0.531220	+	0.847234i	$0.321734\pi$
$710$	−2.79979	+	4.84937i	−0.105074	+	0.181994i
$711$		0			0
$712$	2.68184	+	4.64508i	0.100506	+	0.174082i
$713$	−2.95533	−	2.47982i	−0.110678	−	0.0928700i
$714$		0			0
$715$	0.0362270	+	0.205454i	0.00135481	+	0.00768353i
$716$	−3.23351	−	18.3382i	−0.120842	−	0.685330i
$717$		0			0
$718$	−5.64199	−	4.73419i	−0.210557	−	0.176679i
$719$	16.0850	+	27.8600i	0.599869	+	1.03900i	0.992840	+	0.119453i	$0.0381140\pi$
$719$	16.0850	+	27.8600i	0.599869	+	1.03900i	−0.392971	+	0.919551i	$0.628553\pi$
$720$		0			0
$721$	3.01213	−	5.21717i	0.112178	−	0.194297i
$722$	−7.34980	+	2.67511i	−0.273531	+	0.0995572i
$723$		0			0
$724$	−33.6733	+	28.2552i	−1.25146	+	1.05010i
$725$	−0.681899	−	0.248191i	−0.0253251	−	0.00921758i
$726$		0			0
$727$	−0.931711	+	5.28399i	−0.0345552	+	0.195973i	−0.997199	−	0.0748002i	$-0.976168\pi$
$727$	−0.931711	+	5.28399i	−0.0345552	+	0.195973i	0.962643	+	0.270773i	$0.0872792\pi$
$728$	0.0378942			0.00140445
$729$		0			0
$730$	0.503399			0.0186316
$731$	4.51952	−	25.6315i	0.167160	−	0.948014i
$732$		0			0
$733$	13.7161	+	4.99225i	0.506615	+	0.184393i	0.582667	−	0.812711i	$-0.302009\pi$
$733$	13.7161	+	4.99225i	0.506615	+	0.184393i	−0.0760518	+	0.997104i	$0.524231\pi$
$734$	6.46701	−	5.42646i	0.238702	−	0.200294i
$735$		0			0
$736$	−4.30040	+	1.56522i	−0.158515	+	0.0576947i
$737$	−28.7534	+	49.8023i	−1.05915	+	1.83449i
$738$		0			0
$739$	21.6083	+	37.4266i	0.794873	+	1.37676i	0.922920	+	0.384992i	$0.125796\pi$
$739$	21.6083	+	37.4266i	0.794873	+	1.37676i	−0.128047	+	0.991768i	$0.540871\pi$
$740$	−13.7210	−	11.5133i	−0.504392	−	0.423236i
$741$		0			0
$742$	−0.123821	−	0.702222i	−0.00454560	−	0.0257794i
$743$	1.40867	+	7.98896i	0.0516791	+	0.293087i	0.999683	−	0.0251716i	$-0.00801320\pi$
$743$	1.40867	+	7.98896i	0.0516791	+	0.293087i	−0.948004	+	0.318258i	$0.896902\pi$
$744$		0			0
$745$	1.49809	+	1.25704i	0.0548856	+	0.0460545i
$746$	−2.01116	−	3.48342i	−0.0736336	−	0.127537i
$747$		0			0
$748$	14.9280	−	25.8561i	0.545823	−	0.945393i
$749$	−14.0081	+	5.09855i	−0.511846	+	0.186297i
$750$		0			0
$751$	6.70707	−	5.62790i	0.244744	−	0.205365i	−0.512161	−	0.858890i	$-0.671155\pi$
$751$	6.70707	−	5.62790i	0.244744	−	0.205365i	0.756905	+	0.653525i	$0.226710\pi$
$752$	19.9704	+	7.26861i	0.728244	+	0.265059i
$753$		0			0
$754$	−0.0101715	+	0.0576854i	−0.000370424	+	0.00210078i
$755$	18.2210			0.663129
$756$		0			0
$757$	−32.1511			−1.16855			−0.584276	−	0.811555i	$-0.698622\pi$
$757$	−32.1511			−1.16855			−0.584276	+	0.811555i	$0.698622\pi$
$758$	0.297890	−	1.68942i	0.0108199	−	0.0613625i
$759$		0			0
$760$	−1.38146	−	0.502809i	−0.0501107	−	0.0182388i
$761$	−18.8033	+	15.7778i	−0.681618	+	0.571945i	−0.916479	−	0.400084i	$-0.868981\pi$
$761$	−18.8033	+	15.7778i	−0.681618	+	0.571945i	0.234861	+	0.972029i	$0.424537\pi$
$762$		0			0
$763$	17.9846	−	6.54586i	0.651087	−	0.236976i
$764$	10.0016	−	17.3233i	0.361846	−	0.626736i
$765$		0			0
$766$	0.986770	+	1.70914i	0.0356535	+	0.0617536i
$767$	0.0512095	+	0.0429699i	0.00184907	+	0.00155155i
$768$		0			0
$769$	5.45505	+	30.9371i	0.196714	+	1.11562i	0.909956	+	0.414704i	$0.136115\pi$
$769$	5.45505	+	30.9371i	0.196714	+	1.11562i	−0.713242	+	0.700918i	$0.752774\pi$
$770$	−1.09986	−	6.23763i	−0.0396363	−	0.224788i
$771$		0			0
$772$	15.1268	+	12.6929i	0.544427	+	0.456828i
$773$	−14.3573	−	24.8675i	−0.516395	−	0.894422i	−0.999819	−	0.0190355i	$-0.993940\pi$
$773$	−14.3573	−	24.8675i	−0.516395	−	0.894422i	0.483424	−	0.875386i	$-0.339393\pi$
$774$		0			0
$775$	0.173332	−	0.300219i	0.00622625	−	0.0107842i
$776$	−14.8549	+	5.40674i	−0.533260	+	0.194091i
$777$		0			0
$778$	6.94243	−	5.82539i	0.248898	−	0.208850i
$779$	1.44125	+	0.524572i	0.0516381	+	0.0187947i

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)

\(f(q)\)	\(=\)	\(q+(-0.0721450 + 0.409154i) q^{2} +(1.71718 + 0.625003i) q^{4} +(1.69693 - 1.42389i) q^{5} +(1.24005 - 0.451340i) q^{7} +(-0.795075 + 1.37711i) q^{8} +O(q^{10})\)	\(q+(-0.0721450 + 0.409154i) q^{2} +(1.71718 + 0.625003i) q^{4} +(1.69693 - 1.42389i) q^{5} +(1.24005 - 0.451340i) q^{7} +(-0.795075 + 1.37711i) q^{8} +(0.460168 + 0.797034i) q^{10} +(-3.99506 - 3.35226i) q^{11} +(-0.00313583 - 0.0177842i) q^{13} +(0.0952046 + 0.539932i) q^{14} +(2.29363 + 1.92458i) q^{16} +(1.56640 + 2.71308i) q^{17} +(-0.208676 + 0.361438i) q^{19} +(3.80388 - 1.38450i) q^{20} +(1.65981 - 1.39275i) q^{22} +(0.972005 + 0.353781i) q^{23} +(-0.0161402 + 0.0915354i) q^{25} +0.00750270 q^{26} +2.41147 q^{28} +(-1.35571 + 7.68861i) q^{29} +(-3.50474 - 1.27562i) q^{31} +(-3.38918 + 2.84386i) q^{32} +(-1.22308 + 0.445163i) q^{34} +(1.46161 - 2.53159i) q^{35} +(-2.21238 - 3.83195i) q^{37} +(-0.132829 - 0.111457i) q^{38} +(0.611672 + 3.46897i) q^{40} +(-0.638147 - 3.61911i) q^{41} +(-6.36420 - 5.34020i) q^{43} +(-4.76508 - 8.25337i) q^{44} +(-0.214876 + 0.372177i) q^{46} +(6.66985 - 2.42763i) q^{47} +(-4.02831 + 3.38015i) q^{49} +(-0.0362877 - 0.0132076i) q^{50} +(0.00573038 - 0.0324986i) q^{52} -1.30057 q^{53} -11.5526 q^{55} +(-0.364385 + 2.06653i) q^{56} +(-3.04802 - 1.10939i) q^{58} +(-2.83575 + 2.37948i) q^{59} +(-6.49726 + 2.36481i) q^{61} +(0.774775 - 1.34195i) q^{62} +(2.07506 + 3.59410i) q^{64} +(-0.0306441 - 0.0257134i) q^{65} +(-1.91478 - 10.8593i) q^{67} +(0.994107 + 5.63786i) q^{68} +(0.930362 + 0.780666i) q^{70} +(3.04214 + 5.26914i) q^{71} +(0.273486 - 0.473692i) q^{73} +(1.72747 - 0.628748i) q^{74} +(-0.584235 + 0.490231i) q^{76} +(-6.46707 - 2.35382i) q^{77} +(0.0849390 - 0.481713i) q^{79} +6.63254 q^{80} +1.52681 q^{82} +(0.801155 - 4.54358i) q^{83} +(6.52121 + 2.37353i) q^{85} +(2.64411 - 2.21867i) q^{86} +(7.79281 - 2.83635i) q^{88} +(1.68653 - 2.92116i) q^{89} +(-0.0119153 - 0.0206379i) q^{91} +(1.44800 + 1.21501i) q^{92} +(0.512078 + 2.90414i) q^{94} +(0.160540 + 0.910468i) q^{95} +(7.61552 + 6.39018i) q^{97} +(-1.09238 - 1.89206i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 6 q^{8}+O(q^{10}) \) 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

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