LMFDB - Embedded newform 243.2.e.a.217.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(28,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [12,-3,0,3,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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			217.1
Root			$0.500000 - 0.258654i$ of defining polynomial
Character	$\chi$	$=$	243.217
Dual form			243.2.e.a.28.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

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	−0.948618	−	0.316423i	$-0.897518\pi$
$2$	0.0721450	−	0.409154i	0.0510142	−	0.289316i	0.999633	+	0.0271067i	$0.00862938\pi$
$3$		0			0
$3$		0			0
$4$	1.71718	+	0.625003i	0.858591	+	0.312502i
$5$	−1.69693	+	1.42389i	−0.758891	+	0.636785i	−0.937838	−	0.347074i	$-0.887175\pi$
$5$	−1.69693	+	1.42389i	−0.758891	+	0.636785i	0.178947	+	0.983859i	$0.442731\pi$
$6$		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	$0.0101864\pi$
$11$	3.99506	+	3.35226i	1.20456	+	1.01074i	0.205069	+	0.978747i	$0.434258\pi$
$12$		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	0.611141	−	0.791522i	$-0.290711\pi$
$17$	−1.56640	−	2.71308i	−0.379907	−	0.658019i	−0.991048	+	0.133503i	$0.957377\pi$
$18$		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	0.238687	−	0.971097i	$-0.423283\pi$
$23$	−0.972005	−	0.353781i	−0.202677	−	0.0737684i	−0.441364	+	0.897328i	$0.645505\pi$
$24$		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	$-0.686338\pi$
$29$	1.35571	−	7.68861i	0.251749	−	1.42774i	0.804282	−	0.594248i	$-0.202550\pi$
$30$		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	$0.0370907\pi$
$41$	0.638147	+	3.61911i	0.0996618	+	0.565210i	−0.893557	+	0.448950i	$0.851798\pi$
$42$		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	−0.779075	−	0.626931i	$-0.784311\pi$
$47$	−6.66985	+	2.42763i	−0.972898	+	0.354106i	−0.193823	+	0.981037i	$0.562089\pi$
$48$		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	$-0.471529\pi$
$53$	1.30057			0.178648			0.0893238	+	0.996003i	$0.471529\pi$
$54$		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	−0.439255	−	0.898362i	$-0.644758\pi$
$59$	2.83575	−	2.37948i	0.369183	−	0.309782i	0.808438	+	0.588581i	$0.200313\pi$
$60$		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	0.627096	−	0.778942i	$-0.284243\pi$
$71$	−3.04214	−	5.26914i	−0.361035	−	0.625332i	−0.988132	+	0.153610i	$0.950910\pi$
$72$		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	$0.137041\pi$
$83$	−0.801155	+	4.54358i	−0.0879382	+	0.498722i	−0.996684	+	0.0813719i	$0.974070\pi$
$84$		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	−0.941460	−	0.337124i	$-0.890546\pi$
$89$	−1.68653	+	2.92116i	−0.178772	+	0.309642i	0.762688	+	0.646766i	$0.223879\pi$
$90$		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	0.396469	−	0.918048i	$-0.370235\pi$
$101$	12.9673	−	4.71970i	1.29029	−	0.469628i	0.893823	+	0.448420i	$0.148013\pi$
$102$		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	$-0.316136\pi$
$107$	11.2965			1.09207			0.546035	+	0.837762i	$0.316136\pi$
$108$		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	−0.971162	−	0.238422i	$-0.923370\pi$
$113$	−9.62031	+	8.07240i	−0.905003	+	0.759388i	0.0661589	+	0.997809i	$0.478926\pi$
$114$		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	−0.386516	−	0.922283i	$-0.626321\pi$
$131$	−14.5980	−	5.31325i	−1.27544	−	0.464221i	−0.888920	+	0.458062i	$0.848544\pi$
$132$		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	$0.226996\pi$
$137$	−2.08506	+	11.8250i	−0.178139	+	1.01028i	−0.934458	+	0.356073i	$0.884115\pi$
$138$		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	0.977884	−	0.209147i	$-0.0670687\pi$
$149$	−0.153300	−	0.869408i	−0.0125588	−	0.0712247i	−0.990443	+	0.137922i	$0.955958\pi$
$150$		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	$-0.429375\pi$
$167$	15.7522	−	13.2176i	1.21894	−	1.02281i	0.998880	−	0.0473242i	$-0.0150694\pi$
$168$		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	0.135026	−	0.990842i	$-0.456888\pi$
$173$	−10.7501	−	9.02041i	−0.817316	−	0.685809i	−0.952342	+	0.305033i	$0.901333\pi$
$174$		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	0.991179	−	0.132527i	$-0.0423091\pi$
$179$	5.09500	+	8.82479i	0.380818	+	0.659596i	−0.610361	+	0.792123i	$0.708976\pi$
$180$		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	$0.185166\pi$
$191$	−1.90082	+	10.7801i	−0.137538	+	0.780018i	−0.973058	+	0.230559i	$0.925945\pi$
$192$		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	$0.454689\pi$
$197$	−11.0367	+	19.1161i	−0.786331	+	1.36196i	−0.928201	+	0.372080i	$0.878645\pi$
$198$		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	−0.102913	−	0.994690i	$-0.532816\pi$
$227$	−16.5786	−	13.9111i	−1.10036	−	0.923314i	−0.997449	+	0.0713762i	$0.977261\pi$
$228$		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	0.963587	−	0.267394i	$-0.0861625\pi$
$233$	3.81950	+	6.61557i	0.250224	+	0.433400i	−0.713364	+	0.700794i	$0.752829\pi$
$234$		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	0.241936	−	0.970292i	$-0.422218\pi$
$239$	−3.03661	−	1.10524i	−0.196422	−	0.0714917i	−0.438358	+	0.898800i	$0.644440\pi$
$240$		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	−0.928248	−	0.371961i	$-0.878686\pi$
$251$	−2.24965	+	3.89651i	−0.141997	+	0.245945i	0.786252	+	0.617906i	$0.212019\pi$
$252$		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	$-0.914634\pi$
$257$	−2.38513	−	13.5267i	−0.148780	−	0.843775i	0.815473	−	0.578794i	$-0.196477\pi$
$258$		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	−0.928887	−	0.370363i	$-0.879233\pi$
$263$	−22.7430	+	8.27776i	−1.40239	+	0.510429i	−0.473504	+	0.880792i	$0.657011\pi$
$264$		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	$-0.619278\pi$
$269$	−12.0062			−0.732032			−0.366016	+	0.930609i	$0.619278\pi$
$270$		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	0.975989	−	0.217821i	$-0.0698950\pi$
$281$	15.6057	+	13.0947i	0.930955	+	0.781164i	−0.0450333	+	0.998985i	$0.514339\pi$
$282$		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	0.998860	−	0.0477455i	$-0.0152036\pi$
$293$	29.6700	+	10.7990i	1.73334	+	0.630884i	0.734481	+	0.678630i	$0.237426\pi$
$294$		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	$0.180803\pi$
$311$	4.14126	+	23.4862i	0.234829	+	1.33178i	−0.608144	+	0.793827i	$0.708086\pi$
$312$		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	−0.552408	−	0.833574i	$-0.686291\pi$
$317$	−7.82983	+	2.84983i	−0.439767	+	0.160062i	0.112641	+	0.993636i	$0.464069\pi$
$318$		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	−0.610079	−	0.792341i	$-0.708862\pi$
$347$	−29.5576	−	10.7581i	−1.58673	−	0.577524i	−0.976654	+	0.214817i	$0.931084\pi$
$348$		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	$-0.874358\pi$
$353$	1.42515	−	8.08240i	0.0758528	−	0.430183i	0.998958	−	0.0456355i	$-0.0145313\pi$
$354$		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	−0.531517	−	0.847047i	$-0.678378\pi$
$359$	8.86365	−	15.3523i	0.467806	−	0.810263i	0.999323	+	0.0367840i	$0.0117114\pi$
$360$		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	−0.731005	−	0.682372i	$-0.760948\pi$
$383$	−3.63885	+	3.05336i	−0.185937	+	0.156019i	0.545068	+	0.838392i	$0.316504\pi$
$384$		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	0.959178	−	0.282804i	$-0.0912647\pi$
$389$	16.7100	+	14.0213i	0.847229	+	0.710910i	−0.111949	+	0.993714i	$0.535709\pi$
$390$		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	−0.139839	−	0.990174i	$-0.544658\pi$
$401$	−17.6907	−	6.43890i	−0.883433	−	0.321543i	−0.743594	+	0.668631i	$0.766881\pi$
$402$		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	$0.146899\pi$
$419$	4.22277	+	23.9485i	0.206296	+	1.16996i	−0.689092	+	0.724674i	$0.741990\pi$
$420$		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	$-0.576407\pi$
$431$	−9.87124			−0.475481			−0.237740	+	0.971329i	$0.576407\pi$
$432$		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	0.655846	−	0.754895i	$-0.272312\pi$
$443$	0.553692	+	0.464603i	0.0263067	+	0.0220739i	−0.629539	+	0.776968i	$0.716756\pi$
$444$		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	0.885039	−	0.465517i	$-0.154132\pi$
$449$	0.834224	+	1.44492i	0.0393695	+	0.0681899i	−0.845669	+	0.533707i	$0.820798\pi$
$450$		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	$-0.774227\pi$
$461$	3.80018	−	21.5519i	0.176992	−	1.00377i	0.935819	−	0.352480i	$-0.114662\pi$
$462$		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	−0.969842	−	0.243734i	$-0.921628\pi$
$467$	−5.91777	+	10.2499i	−0.273842	+	0.474308i	0.696001	+	0.718041i	$0.254961\pi$
$468$		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	−0.279290	−	0.960207i	$-0.590099\pi$
$479$	2.71322	−	0.987532i	0.123970	−	0.0451215i	0.403260	+	0.915085i	$0.367877\pi$
$480$		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	−0.162968	−	0.986631i	$-0.552107\pi$
$491$	17.2920	−	14.5097i	0.780375	−	0.654812i	0.943343	+	0.331819i	$0.107662\pi$
$492$		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	0.904739	−	0.425967i	$-0.140066\pi$
$503$	1.87207	+	3.24252i	0.0834714	+	0.144577i	−0.821267	+	0.570543i	$0.806733\pi$
$504$		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	0.795045	−	0.606551i	$-0.207447\pi$
$509$	22.8814	+	8.32815i	1.01420	+	0.369139i	0.219156	+	0.975690i	$0.429670\pi$
$510$		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	−0.567051	−	0.823682i	$-0.691916\pi$
$521$	9.81046	−	16.9922i	0.429804	−	0.744443i	0.996856	+	0.0792397i	$0.0252492\pi$
$522$		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	$0.114205\pi$
$557$	18.2259	+	31.5682i	0.772256	+	1.33759i	−0.164067	+	0.986449i	$0.552461\pi$
$558$		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	0.808712	−	0.588205i	$-0.200165\pi$
$563$	24.9171	+	9.06909i	1.05013	+	0.382216i	0.241419	+	0.970421i	$0.422387\pi$
$564$		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	$0.215435\pi$
$569$	−3.98825	+	22.6185i	−0.167196	+	0.948216i	−0.946771	+	0.321907i	$0.895676\pi$
$570$		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	0.638308	−	0.769781i	$-0.279635\pi$
$587$	39.3000	−	14.3040i	1.62209	−	0.590391i	0.983778	+	0.179391i	$0.0574126\pi$
$588$		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	$-0.275800\pi$
$593$	31.5370			1.29507			0.647536	+	0.762035i	$0.275800\pi$
$594$		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	−0.423358	−	0.905962i	$-0.639149\pi$
$599$	9.67537	−	8.11860i	0.395325	−	0.331717i	0.818683	+	0.574245i	$0.194704\pi$
$600$		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	0.203398	−	0.979096i	$-0.434801\pi$
$617$	−6.71014	−	2.44229i	−0.270140	−	0.0983230i	−0.473539	+	0.880773i	$0.657024\pi$
$618$		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	−0.433338	−	0.901231i	$-0.642664\pi$
$641$	−4.70900	+	1.71394i	−0.185994	+	0.0676964i	0.247344	+	0.968928i	$0.420442\pi$
$642$		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	$-0.737164\pi$
$647$	−34.4927			−1.35605			−0.678024	+	0.735040i	$0.737164\pi$
$648$		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	−0.999930	−	0.0117946i	$-0.996246\pi$
$653$	−29.6923	+	24.9148i	−1.16195	+	0.974993i	−0.162021	+	0.986787i	$0.551801\pi$
$654$		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	0.491810	−	0.870703i	$-0.336336\pi$
$659$	−7.19463	−	6.03701i	−0.280263	−	0.235169i	−0.772073	+	0.635534i	$0.780780\pi$
$660$		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	$0.259196\pi$
$677$	−5.39470	+	30.5949i	−0.207335	+	1.17586i	−0.893723	+	0.448620i	$0.851916\pi$
$678$		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	$-0.573031\pi$
$683$	19.0681	−	33.0268i	0.729619	−	1.26374i	0.957044	−	0.289942i	$-0.0936359\pi$
$684$		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	$-0.486127\pi$
$701$	2.30710			0.0871381			0.0435690	+	0.999050i	$0.486127\pi$
$702$		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	$-0.961886\pi$
$719$	−16.0850	−	27.8600i	−0.599869	−	1.03900i	0.392971	−	0.919551i	$-0.371447\pi$
$720$		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	0.948004	−	0.318258i	$-0.103098\pi$
$743$	−1.40867	−	7.98896i	−0.0516791	−	0.293087i	−0.999683	+	0.0251716i	$0.991987\pi$
$744$		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	−0.234861	−	0.972029i	$-0.575463\pi$
$761$	18.8033	−	15.7778i	0.681618	−	0.571945i	0.916479	+	0.400084i	$0.131019\pi$
$762$		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	$0.00605954\pi$
$773$	14.3573	+	24.8675i	0.516395	+	0.894422i	−0.483424	+	0.875386i	$0.660607\pi$
$774$		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
$780$		0			0
$781$	5.50997	−	31.2486i	0.197162	−	1.11816i
$782$	1.34633			0.0481446
$783$		0			0
$784$	−15.7448			−0.562315
$785$	−4.83130	+	27.3997i	−0.172437	+	0.977936i
$786$		0			0
$787$	36.4751	+	13.2759i	1.30020	+	0.473233i	0.897061	−	0.441906i	$-0.145698\pi$
$787$	36.4751	+	13.2759i	1.30020	+	0.473233i	0.403137	+	0.915140i	$0.367920\pi$
$788$	−30.8996	+	25.9279i	−1.10075	+	0.923642i
$789$		0			0
$790$	0.423028	−	0.153969i	0.0150506	−	0.00547799i
$791$	−8.28623	+	14.3522i	−0.294625	+	0.510305i
$792$		0			0
$793$	0.0624304	+	0.108133i	0.00221697	+	0.00383990i
$794$	−11.0913	−	9.30666i	−0.393614	−	0.330281i
$795$		0			0
$796$	−4.08926	−	23.1913i	−0.144940	−	0.821996i
$797$	0.700514	+	3.97281i	0.0248135	+	0.140724i	0.994698	−	0.102842i	$-0.0327937\pi$
$797$	0.700514	+	3.97281i	0.0248135	+	0.140724i	−0.969884	+	0.243567i	$0.921683\pi$
$798$		0			0
$799$	17.0340	+	14.2932i	0.602619	+	0.505658i
$800$	0.205612	+	0.356130i	0.00726948	+	0.0125911i
$801$		0			0
$802$	−3.91080	+	6.77371i	−0.138095	+	0.239188i
$803$	2.68054	−	0.975635i	0.0945940	−	0.0344294i
$804$		0			0
$805$	2.31632	−	1.94363i	0.0816396	−	0.0685038i
$806$	0.0262950	+	0.00957060i	0.000926202	+	0.000337110i
$807$		0			0
$808$	3.81041	−	21.6099i	0.134050	−	0.760233i
$809$	29.9454			1.05283			0.526413	−	0.850229i	$-0.323537\pi$
$809$	29.9454			1.05283			0.526413	+	0.850229i	$0.323537\pi$
$810$		0			0
$811$	20.2173			0.709927			0.354963	−	0.934880i	$-0.384493\pi$
$811$	20.2173			0.709927			0.354963	+	0.934880i	$0.384493\pi$
$812$	3.26926	−	18.5409i	0.114729	−	0.650658i
$813$		0			0
$814$	−9.00909	−	3.27904i	−0.315768	−	0.114930i
$815$	−5.62475	+	4.71973i	−0.197026	+	0.165325i
$816$		0			0
$817$	3.25821	−	1.18589i	0.113990	−	0.0414890i
$818$	1.32117	−	2.28834i	0.0461938	−	0.0800099i
$819$		0			0
$820$	−7.43809	−	12.8831i	−0.259749	−	0.449899i
$821$	−20.5864	−	17.2740i	−0.718470	−	0.602868i	0.208491	−	0.978024i	$-0.433145\pi$
$821$	−20.5864	−	17.2740i	−0.718470	−	0.602868i	−0.926962	+	0.375156i	$0.877589\pi$
$822$		0			0
$823$	4.00334	+	22.7041i	0.139548	+	0.791414i	0.971584	+	0.236694i	$0.0760638\pi$
$823$	4.00334	+	22.7041i	0.139548	+	0.791414i	−0.832037	+	0.554721i	$0.812825\pi$
$824$	−1.26055	−	7.14894i	−0.0439134	−	0.249045i
$825$		0			0
$826$	−1.55473	−	1.30458i	−0.0540961	−	0.0453920i
$827$	−2.55476	−	4.42498i	−0.0888378	−	0.153872i	0.818182	−	0.574959i	$-0.194982\pi$
$827$	−2.55476	−	4.42498i	−0.0888378	−	0.153872i	−0.907020	+	0.421087i	$0.861649\pi$
$828$		0			0
$829$	15.2991	−	26.4988i	0.531360	−	0.920343i	−0.467970	−	0.883744i	$-0.655014\pi$
$829$	15.2991	−	26.4988i	0.531360	−	0.920343i	0.999330	−	0.0365985i	$-0.0116523\pi$
$830$	−3.99005	+	1.45226i	−0.138497	+	0.0504087i
$831$		0			0
$832$	0.0574111	−	0.0481737i	0.00199037	−	0.00167012i
$833$	15.4805	+	5.63446i	0.536369	+	0.195222i
$834$		0			0
$835$	−7.90982	+	44.8588i	−0.273731	+	1.55240i
$836$	−3.97744			−0.137563
$837$		0			0
$838$	10.1033			0.349013
$839$	9.77790	−	55.4532i	0.337571	−	1.91446i	−0.0626417	−	0.998036i	$-0.519953\pi$
$839$	9.77790	−	55.4532i	0.337571	−	1.91446i	0.400212	−	0.916422i	$-0.368936\pi$
$840$		0			0
$841$	−30.0257	−	10.9285i	−1.03537	−	0.376844i
$842$	−2.54295	+	2.13379i	−0.0876360	+	0.0735353i
$843$		0			0
$844$	−41.2049	+	14.9974i	−1.41833	+	0.516230i
$845$	−14.3984	+	24.9387i	−0.495318	+	0.857917i
$846$		0			0
$847$	10.6878	+	18.5118i	0.367237	+	0.636073i
$848$	2.98304	+	2.50306i	0.102438	+	0.0859556i
$849$		0			0
$850$	−0.0210076	−	0.119140i	−0.000720553	−	0.00408646i
$851$	0.794772	+	4.50737i	0.0272444	+	0.154511i
$852$		0			0
$853$	−34.8895	−	29.2758i	−1.19459	−	1.00238i	−0.999768	−	0.0215447i	$-0.993142\pi$
$853$	−34.8895	−	29.2758i	−1.19459	−	1.00238i	−0.194825	−	0.980838i	$-0.562414\pi$
$854$	1.89540	+	3.28294i	0.0648594	+	0.112340i
$855$		0			0
$856$	8.98154	−	15.5565i	0.306983	−	0.531710i
$857$	−16.4345	+	5.98165i	−0.561390	+	0.204329i	−0.607100	−	0.794625i	$-0.707667\pi$
$857$	−16.4345	+	5.98165i	−0.561390	+	0.204329i	0.0457098	+	0.998955i	$0.485445\pi$
$858$		0			0
$859$	14.0539	−	11.7926i	0.479512	−	0.402358i	−0.370738	−	0.928737i	$-0.620895\pi$
$859$	14.0539	−	11.7926i	0.479512	−	0.402358i	0.850250	+	0.526379i	$0.176451\pi$
$860$	31.6022	+	11.5022i	1.07762	+	0.392223i
$861$		0			0
$862$	−0.712160	+	4.03886i	−0.0242563	+	0.137564i
$863$	−4.65373			−0.158415			−0.0792073	−	0.996858i	$-0.525239\pi$
$863$	−4.65373			−0.158415			−0.0792073	+	0.996858i	$0.525239\pi$
$864$		0			0
$865$	31.0863			1.05697
$866$	−0.440350	+	2.49735i	−0.0149637	+	0.0848634i
$867$		0			0
$868$	−8.45159	−	3.07613i	−0.286866	−	0.104411i
$869$	1.95416	−	1.63974i	0.0662904	−	0.0556243i
$870$		0			0
$871$	−0.187119	+	0.0681056i	−0.00634028	+	0.00230767i
$872$	11.5311	−	19.9725i	0.390493	−	0.676354i
$873$		0			0
$874$	−0.0896791	−	0.155329i	−0.00303344	−	0.00525407i
$875$	−11.4047	−	9.56971i	−0.385551	−	0.323515i
$876$		0			0
$877$	−0.636784	−	3.61138i	−0.0215027	−	0.121948i	0.972167	−	0.234289i	$-0.0752762\pi$
$877$	−0.636784	−	3.61138i	−0.0215027	−	0.121948i	−0.993670	+	0.112341i	$0.964165\pi$
$878$	−1.09184	−	6.19215i	−0.0368479	−	0.208975i
$879$		0			0
$880$	−26.4974	−	22.2340i	−0.893228	−	0.749507i
$881$	19.1504	+	33.1694i	0.645193	+	1.11751i	0.984257	+	0.176744i	$0.0565564\pi$
$881$	19.1504	+	33.1694i	0.645193	+	1.11751i	−0.339064	+	0.940763i	$0.610110\pi$
$882$		0			0
$883$	−11.3071	+	19.5844i	−0.380513	+	0.659069i	−0.991136	−	0.132853i	$-0.957586\pi$
$883$	−11.3071	+	19.5844i	−0.380513	+	0.659069i	0.610622	+	0.791922i	$0.290919\pi$
$884$	−0.0971473	+	0.0353587i	−0.00326742	+	0.00118924i
$885$		0			0
$886$	0.230040	−	0.193027i	0.00772835	−	0.00648486i
$887$	−1.78218	−	0.648661i	−0.0598398	−	0.0217799i	0.311927	−	0.950106i	$-0.399026\pi$
$887$	−1.78218	−	0.648661i	−0.0598398	−	0.0217799i	−0.371767	+	0.928326i	$0.621248\pi$
$888$		0			0
$889$	1.92372	−	10.9100i	0.0645195	−	0.365909i
$890$	−3.10435			−0.104058
$891$		0			0
$892$	−39.5852			−1.32541
$893$	0.514403	−	2.91732i	0.0172138	−	0.0976245i
$894$		0			0
$895$	−21.2114	−	7.72033i	−0.709020	−	0.258062i
$896$	10.6879	−	8.96824i	0.357059	−	0.299608i
$897$		0			0
$898$	0.651379	−	0.237083i	0.0217368	−	0.00791155i
$899$	−14.5592	+	25.2172i	−0.485575	+	0.841041i
$900$		0			0
$901$	−2.03722	−	3.52856i	−0.0678695	−	0.117553i
$902$	6.09972	+	5.11827i	0.203098	+	0.170420i
$903$		0			0
$904$	3.46772	+	19.6664i	0.115335	+	0.654095i
$905$	−9.25297	−	52.4762i	−0.307579	−	1.74437i
$906$		0			0
$907$	5.00299	+	4.19801i	0.166122	+	0.139393i	0.722059	−	0.691832i	$-0.243196\pi$
$907$	5.00299	+	4.19801i	0.166122	+	0.139393i	−0.555937	+	0.831224i	$0.687640\pi$
$908$	−19.7740	−	34.2497i	−0.656225	−	1.13661i
$909$		0			0
$910$	0.0109660	−	0.0189938i	0.000363521	−	0.000629637i
$911$	−40.4417	+	14.7196i	−1.33989	+	0.487681i	−0.909779	−	0.415094i	$-0.863749\pi$
$911$	−40.4417	+	14.7196i	−1.33989	+	0.487681i	−0.430114	+	0.902775i	$0.641526\pi$
$912$		0			0
$913$	−18.4319	+	15.4662i	−0.610007	+	0.511857i
$914$	−4.32709	−	1.57493i	−0.143128	−	0.0520942i
$915$		0			0
$916$	3.42878	−	19.4456i	0.113290	−	0.642501i
$917$	−20.5003			−0.676980
$918$		0			0
$919$	−16.7911			−0.553887			−0.276943	−	0.960886i	$-0.589321\pi$
$919$	−16.7911			−0.553887			−0.276943	+	0.960886i	$0.589321\pi$
$920$	0.632705	−	3.58825i	0.0208597	−	0.118301i
$921$		0			0
$922$	−8.54390	−	3.10972i	−0.281378	−	0.102413i
$923$	−0.0841676	+	0.0706250i	−0.00277041	+	0.00232465i
$924$		0			0
$925$	0.386467	−	0.140663i	0.0127070	−	0.00462496i
$926$	−5.16253	+	8.94176i	−0.169651	+	0.293844i
$927$		0			0
$928$	−17.2706	−	29.9135i	−0.566935	−	0.981960i
$929$	8.88612	+	7.45634i	0.291544	+	0.244635i	0.776814	−	0.629730i	$-0.216834\pi$
$929$	8.88612	+	7.45634i	0.291544	+	0.244635i	−0.485270	+	0.874364i	$0.661279\pi$
$930$		0			0
$931$	−0.381102	−	2.16134i	−0.0124901	−	0.0708350i
$932$	2.42403	+	13.7473i	0.0794016	+	0.450309i
$933$		0			0
$934$	3.76684	+	3.16076i	0.123255	+	0.103423i
$935$	18.0960	+	31.3432i	0.591802	+	1.02503i
$936$		0			0
$937$	−23.8976	+	41.3919i	−0.780702	+	1.35222i	0.150832	+	0.988559i	$0.451805\pi$
$937$	−23.8976	+	41.3919i	−0.780702	+	1.35222i	−0.931533	+	0.363656i	$0.881528\pi$
$938$	−5.68097	+	2.06771i	−0.185490	+	0.0675130i
$939$		0			0
$940$	22.0103	−	18.4688i	0.717896	−	0.602386i
$941$	10.5813	+	3.85127i	0.344940	+	0.125548i	0.508680	−	0.860956i	$-0.330134\pi$
$941$	10.5813	+	3.85127i	0.344940	+	0.125548i	−0.163740	+	0.986503i	$0.552356\pi$
$942$		0			0
$943$	0.660090	−	3.74356i	0.0214955	−	0.121907i
$944$	11.0837			0.360743
$945$		0			0
$946$	−18.0010			−0.585261
$947$	−1.27317	+	7.22051i	−0.0413725	+	0.234635i	−0.998481	−	0.0550942i	$-0.982454\pi$
$947$	−1.27317	+	7.22051i	−0.0413725	+	0.234635i	0.957109	+	0.289729i	$0.0935652\pi$
$948$		0			0
$949$	−0.00928183	−	0.00337831i	−0.000301301	−	0.000109665i
$950$	−0.0123461	+	0.0103596i	−0.000400561	+	0.000336110i
$951$		0			0
$952$	−6.17743	+	2.24840i	−0.200212	+	0.0728711i
$953$	−12.4377	+	21.5427i	−0.402895	+	0.697835i	−0.994074	−	0.108705i	$-0.965329\pi$
$953$	−12.4377	+	21.5427i	−0.402895	+	0.697835i	0.591179	+	0.806541i	$0.298663\pi$
$954$		0			0
$955$	−12.1241	−	20.9996i	−0.392328	−	0.679531i
$956$	−4.52364	−	3.79578i	−0.146305	−	0.122764i
$957$		0			0
$958$	−0.208308	−	1.18137i	−0.00673012	−	0.0381684i
$959$	2.75151	+	15.6046i	0.0888508	+	0.503898i
$960$		0			0
$961$	−13.0914	−	10.9850i	−0.422303	−	0.354354i
$962$	0.0165988	+	0.0287500i	0.000535168	+	0.000926937i
$963$		0			0
$964$	−24.2540	+	42.0091i	−0.781167	+	1.35302i
$965$	−22.4936	+	8.18702i	−0.724096	+	0.263549i
$966$		0			0
$967$	−26.0685	+	21.8740i	−0.838306	+	0.703422i	−0.957182	−	0.289487i	$-0.906515\pi$
$967$	−26.0685	+	21.8740i	−0.838306	+	0.703422i	0.118876	+	0.992909i	$0.462071\pi$
$968$	24.2042	+	8.80959i	0.777951	+	0.283151i
$969$		0			0
$970$	−1.58877	+	9.01038i	−0.0510125	+	0.289306i
$971$	34.2476			1.09906			0.549530	−	0.835474i	$-0.314807\pi$
$971$	34.2476			1.09906			0.549530	+	0.835474i	$0.314807\pi$
$972$		0			0
$973$	−8.10928			−0.259971
$974$	0.631920	−	3.58380i	0.0202480	−	0.114832i
$975$		0			0
$976$	−19.4536	−	7.08052i	−0.622694	−	0.226642i
$977$	17.9387	−	15.0524i	0.573910	−	0.481567i	−0.309031	−	0.951052i	$-0.600005\pi$
$977$	17.9387	−	15.0524i	0.573910	−	0.481567i	0.882941	+	0.469485i	$0.155560\pi$
$978$		0			0
$979$	−16.5303	+	6.01653i	−0.528310	+	0.192289i
$980$	10.6434	−	18.4349i	0.339990	−	0.588880i
$981$		0			0
$982$	−4.68917	−	8.12188i	−0.149637	−	0.259180i
$983$	25.4351	+	21.3426i	0.811253	+	0.680722i	0.950906	−	0.309479i	$-0.100154\pi$
$983$	25.4351	+	21.3426i	0.811253	+	0.680722i	−0.139654	+	0.990200i	$0.544599\pi$
$984$		0			0
$985$	−8.49081	−	48.1538i	−0.270540	−	1.53431i
$986$	1.76455	+	10.0073i	0.0561948	+	0.318697i
$987$		0			0
$988$	0.0105504	+	0.00885285i	0.000335653	+	0.000281647i
$989$	4.29678	+	7.44223i	0.136630	+	0.236649i
$990$		0			0
$991$	14.0903	−	24.4051i	0.447594	−	0.775255i	−0.550635	−	0.834746i	$-0.685614\pi$
$991$	14.0903	−	24.4051i	0.447594	−	0.775255i	0.998229	+	0.0594912i	$0.0189478\pi$
$992$	−15.5059	+	5.64367i	−0.492312	+	0.179187i
$993$		0			0
$994$	−2.55535	+	2.14419i	−0.0810508	+	0.0680097i
$995$	26.8250	+	9.76351i	0.850410	+	0.309524i
$996$		0			0
$997$	−7.80561	+	44.2678i	−0.247206	+	1.40198i	0.568107	+	0.822955i	$0.307676\pi$
$997$	−7.80561	+	44.2678i	−0.247206	+	1.40198i	−0.815313	+	0.579021i	$0.803435\pi$
$998$	−10.5249			−0.333161
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.e.a.217.1		12
3.2	odd	2		243.2.e.d.217.2		12
9.2	odd	6		243.2.e.c.55.1		12
9.4	even	3		81.2.e.a.46.1		12
9.5	odd	6		27.2.e.a.16.2	✓	12
9.7	even	3		243.2.e.b.55.2		12
27.2	odd	18		729.2.c.e.487.3		12
27.4	even	9		81.2.e.a.37.1		12
27.5	odd	18		243.2.e.c.190.1		12
27.7	even	9		729.2.c.b.244.4		12
27.11	odd	18		729.2.a.a.1.4		6
27.13	even	9	inner	243.2.e.a.28.1		12
27.14	odd	18		243.2.e.d.28.2		12
27.16	even	9		729.2.a.d.1.3		6
27.20	odd	18		729.2.c.e.244.3		12
27.22	even	9		243.2.e.b.190.2		12
27.23	odd	18		27.2.e.a.22.2	yes	12
27.25	even	9		729.2.c.b.487.4		12
36.23	even	6		432.2.u.c.97.1		12
45.14	odd	6		675.2.l.c.151.1		12
45.23	even	12		675.2.u.b.124.2		24
45.32	even	12		675.2.u.b.124.3		24
108.23	even	18		432.2.u.c.49.1		12
135.23	even	36		675.2.u.b.49.3		24
135.77	even	36		675.2.u.b.49.2		24
135.104	odd	18		675.2.l.c.76.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.16.2	✓	12	9.5	odd	6
27.2.e.a.22.2	yes	12	27.23	odd	18
81.2.e.a.37.1		12	27.4	even	9
81.2.e.a.46.1		12	9.4	even	3
243.2.e.a.28.1		12	27.13	even	9	inner
243.2.e.a.217.1		12	1.1	even	1	trivial
243.2.e.b.55.2		12	9.7	even	3
243.2.e.b.190.2		12	27.22	even	9
243.2.e.c.55.1		12	9.2	odd	6
243.2.e.c.190.1		12	27.5	odd	18
243.2.e.d.28.2		12	27.14	odd	18
243.2.e.d.217.2		12	3.2	odd	2
432.2.u.c.49.1		12	108.23	even	18
432.2.u.c.97.1		12	36.23	even	6
675.2.l.c.76.1		12	135.104	odd	18
675.2.l.c.151.1		12	45.14	odd	6
675.2.u.b.49.2		24	135.77	even	36
675.2.u.b.49.3		24	135.23	even	36
675.2.u.b.124.2		24	45.23	even	12
675.2.u.b.124.3		24	45.32	even	12
729.2.a.a.1.4		6	27.11	odd	18
729.2.a.d.1.3		6	27.16	even	9
729.2.c.b.244.4		12	27.7	even	9
729.2.c.b.487.4		12	27.25	even	9
729.2.c.e.244.3		12	27.20	odd	18
729.2.c.e.487.3		12	27.2	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.0721450 - 0.409154i) q^{2} +(1.71718 + 0.625003i) q^{4} +(-1.69693 + 1.42389i) q^{5} +(1.24005 - 0.451340i) q^{7} +(0.795075 - 1.37711i) q^{8} +(0.460168 + 0.797034i) q^{10} +(3.99506 + 3.35226i) q^{11} +(-0.00313583 - 0.0177842i) q^{13} +(-0.0952046 - 0.539932i) q^{14} +(2.29363 + 1.92458i) q^{16} +(-1.56640 - 2.71308i) q^{17} +(-0.208676 + 0.361438i) q^{19} +(-3.80388 + 1.38450i) q^{20} +(1.65981 - 1.39275i) q^{22} +(-0.972005 - 0.353781i) q^{23} +(-0.0161402 + 0.0915354i) q^{25} -0.00750270 q^{26} +2.41147 q^{28} +(1.35571 - 7.68861i) q^{29} +(-3.50474 - 1.27562i) q^{31} +(3.38918 - 2.84386i) q^{32} +(-1.22308 + 0.445163i) q^{34} +(-1.46161 + 2.53159i) q^{35} +(-2.21238 - 3.83195i) q^{37} +(0.132829 + 0.111457i) q^{38} +(0.611672 + 3.46897i) q^{40} +(0.638147 + 3.61911i) q^{41} +(-6.36420 - 5.34020i) q^{43} +(4.76508 + 8.25337i) q^{44} +(-0.214876 + 0.372177i) q^{46} +(-6.66985 + 2.42763i) q^{47} +(-4.02831 + 3.38015i) q^{49} +(0.0362877 + 0.0132076i) q^{50} +(0.00573038 - 0.0324986i) q^{52} +1.30057 q^{53} -11.5526 q^{55} +(0.364385 - 2.06653i) q^{56} +(-3.04802 - 1.10939i) q^{58} +(2.83575 - 2.37948i) q^{59} +(-6.49726 + 2.36481i) q^{61} +(-0.774775 + 1.34195i) q^{62} +(2.07506 + 3.59410i) q^{64} +(0.0306441 + 0.0257134i) q^{65} +(-1.91478 - 10.8593i) q^{67} +(-0.994107 - 5.63786i) q^{68} +(0.930362 + 0.780666i) q^{70} +(-3.04214 - 5.26914i) q^{71} +(0.273486 - 0.473692i) q^{73} +(-1.72747 + 0.628748i) q^{74} +(-0.584235 + 0.490231i) q^{76} +(6.46707 + 2.35382i) q^{77} +(0.0849390 - 0.481713i) q^{79} -6.63254 q^{80} +1.52681 q^{82} +(-0.801155 + 4.54358i) q^{83} +(6.52121 + 2.37353i) q^{85} +(-2.64411 + 2.21867i) q^{86} +(7.79281 - 2.83635i) q^{88} +(-1.68653 + 2.92116i) q^{89} +(-0.0119153 - 0.0206379i) q^{91} +(-1.44800 - 1.21501i) q^{92} +(0.512078 + 2.90414i) q^{94} +(-0.160540 - 0.910468i) q^{95} +(7.61552 + 6.39018i) q^{97} +(1.09238 + 1.89206i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} + 6 q^{11} + 3 q^{13} + 21 q^{14} + 9 q^{16} - 9 q^{17} - 3 q^{19} - 24 q^{20} + 12 q^{22} + 12 q^{23} + 12 q^{25} + 30 q^{26} - 12 q^{28}+ \cdots + 45 q^{98}+O(q^{100}) \) 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

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Database

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