LMFDB - Embedded newform 729.2.e.t.82.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, 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("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			82.2
Root			$1.91182i$ of defining polynomial
Character	$\chi$	$=$	729.82
Dual form			729.2.e.t.649.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.426791 + 2.42045i) q^{2} +(-3.79704 + 1.38201i) q^{4} +(2.35962 + 1.97995i) q^{5} +(2.49833 + 0.909318i) q^{7} +(-2.50784 - 4.34371i) q^{8} +O(q^{10})$	\(q+(0.426791 + 2.42045i) q^{2} +(-3.79704 + 1.38201i) q^{4} +(2.35962 + 1.97995i) q^{5} +(2.49833 + 0.909318i) q^{7} +(-2.50784 - 4.34371i) q^{8} +(-3.78532 + 6.55636i) q^{10} +(2.63086 - 2.20755i) q^{11} +(-0.580672 + 3.29315i) q^{13} +(-1.13469 + 6.43517i) q^{14} +(3.25265 - 2.72930i) q^{16} +(1.28641 - 2.22813i) q^{17} +(1.04838 + 1.81585i) q^{19} +(-11.6959 - 4.25696i) q^{20} +(6.46609 + 5.42570i) q^{22} +(0.502213 - 0.182791i) q^{23} +(0.779336 + 4.41984i) q^{25} -8.21874 q^{26} -10.7430 q^{28} +(-0.439485 - 2.49244i) q^{29} +(-7.24945 + 2.63858i) q^{31} +(0.309858 + 0.260001i) q^{32} +(5.94209 + 2.16275i) q^{34} +(4.09470 + 7.09222i) q^{35} +(5.14783 - 8.91631i) q^{37} +(-3.94774 + 3.31254i) q^{38} +(2.68280 - 15.2149i) q^{40} +(0.848272 - 4.81079i) q^{41} +(2.10010 - 1.76220i) q^{43} +(-6.93862 + 12.0180i) q^{44} +(0.656775 + 1.13757i) q^{46} +(-5.31678 - 1.93515i) q^{47} +(0.0524824 + 0.0440380i) q^{49} +(-10.3654 + 3.77269i) q^{50} +(-2.34634 - 13.3067i) q^{52} -6.42657 q^{53} +10.5787 q^{55} +(-2.31560 - 13.1324i) q^{56} +(5.84527 - 2.12750i) q^{58} +(-1.26777 - 1.06378i) q^{59} +(-13.5055 - 4.91558i) q^{61} +(-9.48056 - 16.4208i) q^{62} +(3.74896 - 6.49338i) q^{64} +(-7.89046 + 6.62088i) q^{65} +(-1.02087 + 5.78967i) q^{67} +(-1.80526 + 10.2381i) q^{68} +(-15.4188 + 12.9379i) q^{70} +(7.40813 - 12.8313i) q^{71} +(-0.940699 - 1.62934i) q^{73} +(23.7785 + 8.65467i) q^{74} +(-6.49027 - 5.44599i) q^{76} +(8.58012 - 3.12291i) q^{77} +(2.98562 + 16.9323i) q^{79} +13.0789 q^{80} +12.0063 q^{82} +(-0.689172 - 3.90849i) q^{83} +(7.44702 - 2.71049i) q^{85} +(5.16161 + 4.33111i) q^{86} +(-16.1867 - 5.89149i) q^{88} +(2.54940 + 4.41569i) q^{89} +(-4.44523 + 7.69937i) q^{91} +(-1.65431 + 1.38813i) q^{92} +(2.41478 - 13.6949i) q^{94} +(-1.12152 + 6.36046i) q^{95} +(-8.14449 + 6.83404i) q^{97} +(-0.0841927 + 0.145826i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8} - 6 q^{10} - 15 q^{11} - 3 q^{13} - 21 q^{14} + 9 q^{16} - 9 q^{17} - 12 q^{19} - 3 q^{20} + 33 q^{22} + 15 q^{23} - 12 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} - 12 q^{31} - 27 q^{32} + 27 q^{34} + 30 q^{35} - 3 q^{37} - 39 q^{38} + 24 q^{40} - 39 q^{41} + 24 q^{43} - 33 q^{44} + 3 q^{46} - 42 q^{47} - 30 q^{49} - 15 q^{50} - 45 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} - 30 q^{58} + 15 q^{59} - 3 q^{61} - 30 q^{62} - 6 q^{64} - 6 q^{65} - 3 q^{67} + 36 q^{68} - 75 q^{70} - 12 q^{73} + 60 q^{74} + 30 q^{76} + 33 q^{77} + 33 q^{79} + 42 q^{80} - 42 q^{82} - 33 q^{83} - 18 q^{85} - 30 q^{86} - 42 q^{88} - 9 q^{89} - 18 q^{91} + 33 q^{92} - 66 q^{94} + 12 q^{95} + 15 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8 - 6 * q^10 - 15 * q^11 - 3 * q^13 - 21 * q^14 + 9 * q^16 - 9 * q^17 - 12 * q^19 - 3 * q^20 + 33 * q^22 + 15 * q^23 - 12 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 - 12 * q^31 - 27 * q^32 + 27 * q^34 + 30 * q^35 - 3 * q^37 - 39 * q^38 + 24 * q^40 - 39 * q^41 + 24 * q^43 - 33 * q^44 + 3 * q^46 - 42 * q^47 - 30 * q^49 - 15 * q^50 - 45 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 - 30 * q^58 + 15 * q^59 - 3 * q^61 - 30 * q^62 - 6 * q^64 - 6 * q^65 - 3 * q^67 + 36 * q^68 - 75 * q^70 - 12 * q^73 + 60 * q^74 + 30 * q^76 + 33 * q^77 + 33 * q^79 + 42 * q^80 - 42 * q^82 - 33 * q^83 - 18 * q^85 - 30 * q^86 - 42 * q^88 - 9 * q^89 - 18 * q^91 + 33 * q^92 - 66 * q^94 + 12 * q^95 + 15 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.426791	+	2.42045i	0.301787	+	1.71152i	0.638258	+	0.769823i	$0.279655\pi$
$2$	0.426791	+	2.42045i	0.301787	+	1.71152i	−0.336471	+	0.941694i	$0.609233\pi$
$3$		0			0
$3$		0			0
$4$	−3.79704	+	1.38201i	−1.89852	+	0.691005i
$5$	2.35962	+	1.97995i	1.05525	+	0.885463i	0.993636	−	0.112637i	$-0.0359298\pi$
$5$	2.35962	+	1.97995i	1.05525	+	0.885463i	0.0616172	+	0.998100i	$0.480374\pi$
$6$		0			0
$7$	2.49833	+	0.909318i	0.944280	+	0.343690i	0.767855	−	0.640624i	$-0.221324\pi$
$7$	2.49833	+	0.909318i	0.944280	+	0.343690i	0.176425	+	0.984314i	$0.443547\pi$
$8$	−2.50784	−	4.34371i	−0.886656	−	1.53573i
$9$		0			0
$10$	−3.78532	+	6.55636i	−1.19702	+	2.07330i
$11$	2.63086	−	2.20755i	0.793233	−	0.665602i	−0.153310	−	0.988178i	$-0.548993\pi$
$11$	2.63086	−	2.20755i	0.793233	−	0.665602i	0.946543	+	0.322576i	$0.104549\pi$
$12$		0			0
$13$	−0.580672	+	3.29315i	−0.161049	+	0.913357i	0.791995	+	0.610527i	$0.209042\pi$
$13$	−0.580672	+	3.29315i	−0.161049	+	0.913357i	−0.953045	+	0.302829i	$0.902069\pi$
$14$	−1.13469	+	6.43517i	−0.303260	+	1.71987i
$15$		0			0
$16$	3.25265	−	2.72930i	0.813162	−	0.682324i
$17$	1.28641	−	2.22813i	0.312000	−	0.540400i	−0.666795	−	0.745241i	$-0.732334\pi$
$17$	1.28641	−	2.22813i	0.312000	−	0.540400i	0.978795	+	0.204841i	$0.0656678\pi$
$18$		0			0
$19$	1.04838	+	1.81585i	0.240515	+	0.416585i	0.960861	−	0.277030i	$-0.0893503\pi$
$19$	1.04838	+	1.81585i	0.240515	+	0.416585i	−0.720346	+	0.693615i	$0.756017\pi$
$20$	−11.6959	−	4.25696i	−2.61528	−	0.951884i
$21$		0			0
$22$	6.46609	+	5.42570i	1.37858	+	1.15676i
$23$	0.502213	−	0.182791i	0.104719	−	0.0381145i	−0.289129	−	0.957290i	$-0.593366\pi$
$23$	0.502213	−	0.182791i	0.104719	−	0.0381145i	0.393848	+	0.919176i	$0.371144\pi$
$24$		0			0
$25$	0.779336	+	4.41984i	0.155867	+	0.883967i
$26$	−8.21874			−1.61183
$27$		0			0
$28$	−10.7430			−2.03023
$29$	−0.439485	−	2.49244i	−0.0816103	−	0.462835i	−0.998037	−	0.0626319i	$-0.980051\pi$
$29$	−0.439485	−	2.49244i	−0.0816103	−	0.462835i	0.916426	−	0.400203i	$-0.131061\pi$
$30$		0			0
$31$	−7.24945	+	2.63858i	−1.30204	+	0.473904i	−0.897660	−	0.440688i	$-0.854735\pi$
$31$	−7.24945	+	2.63858i	−1.30204	+	0.473904i	−0.404379	+	0.914592i	$0.632512\pi$
$32$	0.309858	+	0.260001i	0.0547756	+	0.0459622i
$33$		0			0
$34$	5.94209	+	2.16275i	1.01906	+	0.370908i
$35$	4.09470	+	7.09222i	0.692130	+	1.19880i
$36$		0			0
$37$	5.14783	−	8.91631i	0.846298	−	1.46583i	−0.0381907	−	0.999270i	$-0.512159\pi$
$37$	5.14783	−	8.91631i	0.846298	−	1.46583i	0.884489	−	0.466561i	$-0.154507\pi$
$38$	−3.94774	+	3.31254i	−0.640407	+	0.537365i
$39$		0			0
$40$	2.68280	−	15.2149i	0.424188	−	2.40569i
$41$	0.848272	−	4.81079i	0.132478	−	0.751320i	−0.844105	−	0.536178i	$-0.819868\pi$
$41$	0.848272	−	4.81079i	0.132478	−	0.751320i	0.976583	−	0.215142i	$-0.0690213\pi$
$42$		0			0
$43$	2.10010	−	1.76220i	0.320263	−	0.268732i	−0.468456	−	0.883487i	$-0.655189\pi$
$43$	2.10010	−	1.76220i	0.320263	−	0.268732i	0.788718	+	0.614755i	$0.210745\pi$
$44$	−6.93862	+	12.0180i	−1.04604	+	1.81179i
$45$		0			0
$46$	0.656775	+	1.13757i	0.0968363	+	0.167725i
$47$	−5.31678	−	1.93515i	−0.775532	−	0.282270i	−0.0762235	−	0.997091i	$-0.524286\pi$
$47$	−5.31678	−	1.93515i	−0.775532	−	0.282270i	−0.699308	+	0.714820i	$0.746508\pi$
$48$		0			0
$49$	0.0524824	+	0.0440380i	0.00749749	+	0.00629114i
$50$	−10.3654	+	3.77269i	−1.46589	+	0.533539i
$51$		0			0
$52$	−2.34634	−	13.3067i	−0.325379	−	1.84531i
$53$	−6.42657			−0.882758			−0.441379	−	0.897321i	$-0.645511\pi$
$53$	−6.42657			−0.882758			−0.441379	+	0.897321i	$0.645511\pi$
$54$		0			0
$55$	10.5787			1.42643
$56$	−2.31560	−	13.1324i	−0.309436	−	1.75490i
$57$		0			0
$58$	5.84527	−	2.12750i	0.767521	−	0.279355i
$59$	−1.26777	−	1.06378i	−0.165049	−	0.138493i	0.556522	−	0.830833i	$-0.312135\pi$
$59$	−1.26777	−	1.06378i	−0.165049	−	0.138493i	−0.721571	+	0.692340i	$0.756580\pi$
$60$		0			0
$61$	−13.5055	−	4.91558i	−1.72920	−	0.629376i	−0.730624	−	0.682780i	$-0.760771\pi$
$61$	−13.5055	−	4.91558i	−1.72920	−	0.629376i	−0.998573	+	0.0534042i	$0.982993\pi$
$62$	−9.48056	−	16.4208i	−1.20403	−	2.08544i
$63$		0			0
$64$	3.74896	−	6.49338i	0.468620	−	0.811673i
$65$	−7.89046	+	6.62088i	−0.978691	+	0.821219i
$66$		0			0
$67$	−1.02087	+	5.78967i	−0.124720	+	0.707320i	0.856754	+	0.515725i	$0.172477\pi$
$67$	−1.02087	+	5.78967i	−0.124720	+	0.707320i	−0.981474	+	0.191596i	$0.938634\pi$
$68$	−1.80526	+	10.2381i	−0.218920	+	1.24155i
$69$		0			0
$70$	−15.4188	+	12.9379i	−1.84290	+	1.54638i
$71$	7.40813	−	12.8313i	0.879184	−	1.52279i	0.0269456	−	0.999637i	$-0.491422\pi$
$71$	7.40813	−	12.8313i	0.879184	−	1.52279i	0.852238	−	0.523154i	$-0.175245\pi$
$72$		0			0
$73$	−0.940699	−	1.62934i	−0.110101	−	0.190700i	0.805710	−	0.592310i	$-0.201784\pi$
$73$	−0.940699	−	1.62934i	−0.110101	−	0.190700i	−0.915811	+	0.401610i	$0.868451\pi$
$74$	23.7785	+	8.65467i	2.76420	+	1.00609i
$75$		0			0
$76$	−6.49027	−	5.44599i	−0.744486	−	0.624698i
$77$	8.58012	−	3.12291i	0.977795	−	0.355888i
$78$		0			0
$79$	2.98562	+	16.9323i	0.335908	+	1.90503i	0.418076	+	0.908412i	$0.362704\pi$
$79$	2.98562	+	16.9323i	0.335908	+	1.90503i	−0.0821680	+	0.996618i	$0.526184\pi$
$80$	13.0789			1.46227
$81$		0			0
$82$	12.0063			1.32588
$83$	−0.689172	−	3.90849i	−0.0756465	−	0.429013i	−0.998986	−	0.0450274i	$-0.985662\pi$
$83$	−0.689172	−	3.90849i	−0.0756465	−	0.429013i	0.923339	−	0.383985i	$-0.125449\pi$
$84$		0			0
$85$	7.44702	−	2.71049i	0.807743	−	0.293994i
$86$	5.16161	+	4.33111i	0.556591	+	0.467035i
$87$		0			0
$88$	−16.1867	−	5.89149i	−1.72551	−	0.628035i
$89$	2.54940	+	4.41569i	0.270236	+	0.468062i	0.968922	−	0.247366i	$-0.0795651\pi$
$89$	2.54940	+	4.41569i	0.270236	+	0.468062i	−0.698686	+	0.715428i	$0.746232\pi$
$90$		0			0
$91$	−4.44523	+	7.69937i	−0.465987	+	0.807113i
$92$	−1.65431	+	1.38813i	−0.172473	+	0.144722i
$93$		0			0
$94$	2.41478	−	13.6949i	0.249066	−	1.41252i
$95$	−1.12152	+	6.36046i	−0.115066	+	0.652570i
$96$		0			0
$97$	−8.14449	+	6.83404i	−0.826948	+	0.693892i	−0.954588	−	0.297929i	$-0.903704\pi$
$97$	−8.14449	+	6.83404i	−0.826948	+	0.693892i	0.127640	+	0.991821i	$0.459260\pi$
$98$	−0.0841927	+	0.145826i	−0.00850475	+	0.0147307i
$99$		0			0
$100$	−9.06744	−	15.7053i	−0.906744	−	1.57053i
$101$	5.31686	+	1.93518i	0.529048	+	0.192558i	0.592713	−	0.805414i	$-0.298057\pi$
$101$	5.31686	+	1.93518i	0.529048	+	0.192558i	−0.0636653	+	0.997971i	$0.520279\pi$
$102$		0			0
$103$	7.94429	+	6.66605i	0.782775	+	0.656826i	0.943946	−	0.330101i	$-0.107083\pi$
$103$	7.94429	+	6.66605i	0.782775	+	0.656826i	−0.161171	+	0.986926i	$0.551527\pi$
$104$	15.7607	−	5.73644i	1.54547	−	0.562504i
$105$		0			0
$106$	−2.74280	−	15.5552i	−0.266404	−	1.51085i
$107$	14.2457			1.37719			0.688594	−	0.725147i	$-0.258228\pi$
$107$	14.2457			1.37719			0.688594	+	0.725147i	$0.258228\pi$
$108$		0			0
$109$	5.76064			0.551769			0.275884	−	0.961191i	$-0.411029\pi$
$109$	5.76064			0.551769			0.275884	+	0.961191i	$0.411029\pi$
$110$	4.51488	+	25.6051i	0.430477	+	2.44136i
$111$		0			0
$112$	10.6080	−	3.86099i	1.00236	−	0.364830i
$113$	8.74569	+	7.33851i	0.822726	+	0.690349i	0.953609	−	0.301049i	$-0.0973368\pi$
$113$	8.74569	+	7.33851i	0.822726	+	0.690349i	−0.130883	+	0.991398i	$0.541781\pi$
$114$		0			0
$115$	1.54695	+	0.563043i	0.144254	+	0.0525040i
$116$	5.11333	+	8.85654i	0.474761	+	0.822309i
$117$		0			0
$118$	2.03376	−	3.52257i	0.187223	−	0.324279i
$119$	5.23995	−	4.39684i	0.480345	−	0.403058i
$120$		0			0
$121$	0.137998	−	0.782623i	0.0125452	−	0.0711475i
$122$	6.13392	−	34.7872i	0.555339	−	3.14949i
$123$		0			0
$124$	23.8799	−	20.0376i	2.14448	−	1.79943i
$125$	0.788517	−	1.36575i	0.0705271	−	0.122157i
$126$		0			0
$127$	−1.29510	−	2.24317i	−0.114921	−	0.199049i	0.802827	−	0.596212i	$-0.203328\pi$
$127$	−1.29510	−	2.24317i	−0.114921	−	0.199049i	−0.917748	+	0.397163i	$0.869995\pi$
$128$	18.0771	+	6.57954i	1.59781	+	0.581554i
$129$		0			0
$130$	−19.3931	−	16.2727i	−1.70089	−	1.42721i
$131$	−4.14497	+	1.50865i	−0.362148	+	0.131811i	−0.516684	−	0.856176i	$-0.672834\pi$
$131$	−4.14497	+	1.50865i	−0.362148	+	0.131811i	0.154536	+	0.987987i	$0.450612\pi$
$132$		0			0
$133$	0.968018	+	5.48990i	0.0839378	+	0.476035i
$134$	−14.4493			−1.24823
$135$		0			0
$136$	−12.9044			−1.10655
$137$	−3.15479	−	17.8917i	−0.269531	−	1.52859i	−0.755813	−	0.654787i	$-0.772758\pi$
$137$	−3.15479	−	17.8917i	−0.269531	−	1.52859i	0.486282	−	0.873802i	$-0.338353\pi$
$138$		0			0
$139$	−1.83987	+	0.669656i	−0.156055	+	0.0567995i	−0.418867	−	0.908048i	$-0.637573\pi$
$139$	−1.83987	+	0.669656i	−0.156055	+	0.0567995i	0.262811	+	0.964847i	$0.415350\pi$
$140$	−25.3493	−	21.2706i	−2.14240	−	1.79769i
$141$		0			0
$142$	34.2192	+	12.4548i	2.87161	+	1.04518i
$143$	5.74214	+	9.94568i	0.480182	+	0.831700i
$144$		0			0
$145$	3.89791	−	6.75138i	0.323704	−	0.560671i
$146$	3.54225	−	2.97230i	0.293159	−	0.245989i
$147$		0			0
$148$	−7.22411	+	40.9700i	−0.593818	+	3.36771i
$149$	−1.27027	+	7.20405i	−0.104065	+	0.590179i	0.887525	+	0.460759i	$0.152423\pi$
$149$	−1.27027	+	7.20405i	−0.104065	+	0.590179i	−0.991590	+	0.129420i	$0.958688\pi$
$150$		0			0
$151$	3.71607	−	3.11815i	0.302410	−	0.253752i	−0.478937	−	0.877849i	$-0.658978\pi$
$151$	3.71607	−	3.11815i	0.302410	−	0.253752i	0.781346	+	0.624098i	$0.214533\pi$
$152$	5.25835	−	9.10773i	0.426508	−	0.738734i
$153$		0			0
$154$	11.2208	+	19.4349i	0.904194	+	1.56611i
$155$	−22.3302	−	8.12753i	−1.79361	−	0.652819i
$156$		0			0
$157$	1.13122	+	0.949206i	0.0902812	+	0.0757549i	0.686811	−	0.726836i	$-0.259010\pi$
$157$	1.13122	+	0.949206i	0.0902812	+	0.0757549i	−0.596530	+	0.802591i	$0.703454\pi$
$158$	−39.7095	+	14.4531i	−3.15912	+	1.14983i
$159$		0			0
$160$	0.216355	+	1.22701i	0.0171043	+	0.0970035i
$161$	1.42091			0.111983
$162$		0			0
$163$	−17.2536			−1.35141			−0.675703	−	0.737174i	$-0.736160\pi$
$163$	−17.2536			−1.35141			−0.675703	+	0.737174i	$0.736160\pi$
$164$	3.42764	+	19.4391i	0.267654	+	1.51794i
$165$		0			0
$166$	9.16617	−	3.33621i	0.711433	−	0.258940i
$167$	−5.24002	−	4.39690i	−0.405485	−	0.340242i	0.417124	−	0.908850i	$-0.363038\pi$
$167$	−5.24002	−	4.39690i	−0.405485	−	0.340242i	−0.822609	+	0.568607i	$0.807482\pi$
$168$		0			0
$169$	1.70832	+	0.621778i	0.131409	+	0.0478291i
$170$	9.73894	+	16.8683i	0.746942	+	1.29374i
$171$		0			0
$172$	−5.53881	+	9.59350i	−0.422330	+	0.731497i
$173$	18.3601	−	15.4059i	1.39589	−	1.17129i	0.433002	−	0.901393i	$-0.357454\pi$
$173$	18.3601	−	15.4059i	1.39589	−	1.17129i	0.962889	−	0.269899i	$-0.0869902\pi$
$174$		0			0
$175$	−2.07200	+	11.7509i	−0.156628	+	0.888283i
$176$	2.53219	−	14.3608i	0.190871	−	1.08248i
$177$		0			0
$178$	−9.59989	+	8.05527i	−0.719542	+	0.603768i
$179$	−10.2861	+	17.8161i	−0.768820	+	1.33163i	0.169384	+	0.985550i	$0.445822\pi$
$179$	−10.2861	+	17.8161i	−0.768820	+	1.33163i	−0.938203	+	0.346084i	$0.887511\pi$
$180$		0			0
$181$	7.73507	+	13.3975i	0.574943	+	0.995830i	0.996048	+	0.0888184i	$0.0283091\pi$
$181$	7.73507	+	13.3975i	0.574943	+	0.995830i	−0.421105	+	0.907012i	$0.638358\pi$
$182$	−20.5331	−	7.47345i	−1.52202	−	0.553969i
$183$		0			0
$184$	−2.05346	−	1.72306i	−0.151383	−	0.127025i
$185$	29.8008	−	10.8466i	2.19100	−	0.797458i
$186$		0			0
$187$	−1.53434	−	8.70170i	−0.112202	−	0.636331i
$188$	22.8624			1.66741
$189$		0			0
$190$	−15.8738			−1.15161
$191$	1.90159	+	10.7845i	0.137595	+	0.780338i	0.973018	+	0.230730i	$0.0741115\pi$
$191$	1.90159	+	10.7845i	0.137595	+	0.780338i	−0.835423	+	0.549607i	$0.814777\pi$
$192$		0			0
$193$	−1.07581	+	0.391562i	−0.0774384	+	0.0281853i	−0.380449	−	0.924802i	$-0.624230\pi$
$193$	−1.07581	+	0.391562i	−0.0774384	+	0.0281853i	0.303010	+	0.952987i	$0.402008\pi$
$194$	−20.0174	−	16.7966i	−1.43717	−	1.20593i
$195$		0			0
$196$	−0.260139	−	0.0946828i	−0.0185814	−	0.00676306i
$197$	−2.52097	−	4.36645i	−0.179612	−	0.311097i	0.762136	−	0.647417i	$-0.224151\pi$
$197$	−2.52097	−	4.36645i	−0.179612	−	0.311097i	−0.941748	+	0.336320i	$0.890818\pi$
$198$		0			0
$199$	−6.86291	+	11.8869i	−0.486499	+	0.842640i	−0.999880	−	0.0155206i	$-0.995059\pi$
$199$	−6.86291	+	11.8869i	−0.486499	+	0.842640i	0.513381	+	0.858161i	$0.328393\pi$
$200$	17.2440	−	14.4695i	1.21934	−	1.02315i
$201$		0			0
$202$	−2.41482	+	13.6951i	−0.169906	+	0.963585i
$203$	1.16844	−	6.62658i	0.0820087	−	0.465095i
$204$		0			0
$205$	11.5268	−	9.67209i	0.805063	−	0.675528i
$206$	−12.7443	+	22.0738i	−0.887938	+	1.53795i
$207$		0			0
$208$	7.09927	+	12.2963i	0.492246	+	0.852595i
$209$	6.76673	+	2.46289i	0.468064	+	0.170361i
$210$		0			0
$211$	−4.46997	−	3.75075i	−0.307725	−	0.258212i	0.475826	−	0.879540i	$-0.342149\pi$
$211$	−4.46997	−	3.75075i	−0.307725	−	0.258212i	−0.783551	+	0.621327i	$0.786594\pi$
$212$	24.4020	−	8.88159i	1.67593	−	0.609990i
$213$		0			0
$214$	6.07995	+	34.4811i	0.415617	+	2.35708i
$215$	8.44451			0.575911
$216$		0			0
$217$	−20.5108			−1.39237
$218$	2.45859	+	13.9433i	0.166516	+	0.944362i
$219$		0			0
$220$	−40.1677	+	14.6198i	−2.70810	+	0.985669i
$221$	6.59058	+	5.53015i	0.443330	+	0.371998i
$222$		0			0
$223$	−8.20228	−	2.98538i	−0.549265	−	0.199916i	0.0524549	−	0.998623i	$-0.483295\pi$
$223$	−8.20228	−	2.98538i	−0.549265	−	0.199916i	−0.601720	+	0.798707i	$0.705518\pi$
$224$	0.537703	+	0.931329i	0.0359268	+	0.0622270i
$225$		0			0
$226$	−14.0299	+	24.3005i	−0.933256	+	1.61645i
$227$	−18.6015	+	15.6085i	−1.23462	+	1.03597i	−0.236700	+	0.971583i	$0.576066\pi$
$227$	−18.6015	+	15.6085i	−1.23462	+	1.03597i	−0.997925	+	0.0643900i	$0.979490\pi$
$228$		0			0
$229$	3.15196	−	17.8757i	0.208288	−	1.18126i	−0.683894	−	0.729581i	$-0.739715\pi$
$229$	3.15196	−	17.8757i	0.208288	−	1.18126i	0.892182	−	0.451676i	$-0.149174\pi$
$230$	−0.702595	+	3.98461i	−0.0463277	+	0.262738i
$231$		0			0
$232$	−9.72429	+	8.15965i	−0.638431	+	0.535707i
$233$	5.26900	−	9.12617i	0.345183	−	0.597875i	−0.640204	−	0.768205i	$-0.721150\pi$
$233$	5.26900	−	9.12617i	0.345183	−	0.597875i	0.985387	+	0.170330i	$0.0544834\pi$
$234$		0			0
$235$	−8.71406	−	15.0932i	−0.568442	−	0.984571i
$236$	6.28392	+	2.28716i	0.409048	+	0.148881i
$237$		0			0
$238$	12.8787	+	10.8065i	0.834801	+	0.700482i
$239$	−8.96147	+	3.26171i	−0.579670	+	0.210982i	−0.615180	−	0.788387i	$-0.710917\pi$
$239$	−8.96147	+	3.26171i	−0.579670	+	0.210982i	0.0355102	+	0.999369i	$0.488694\pi$
$240$		0			0
$241$	−1.22201	−	6.93037i	−0.0787166	−	0.446424i	−0.998536	−	0.0540831i	$-0.982776\pi$
$241$	−1.22201	−	6.93037i	−0.0787166	−	0.446424i	0.919820	−	0.392341i	$-0.128335\pi$
$242$	1.95320			0.125556
$243$		0			0
$244$	58.0742			3.71782
$245$	0.0366453	+	0.207826i	0.00234118	+	0.0132775i
$246$		0			0
$247$	−6.58864	+	2.39807i	−0.419225	+	0.152585i
$248$	29.6417	+	24.8723i	1.88225	+	1.57940i
$249$		0			0
$250$	3.64227	+	1.32568i	0.230357	+	0.0838431i
$251$	−7.79350	−	13.4987i	−0.491921	−	0.852033i	0.508035	−	0.861336i	$-0.330372\pi$
$251$	−7.79350	−	13.4987i	−0.491921	−	0.852033i	−0.999957	+	0.00930331i	$0.997039\pi$
$252$		0			0
$253$	0.917731	−	1.58956i	0.0576973	−	0.0999346i
$254$	4.87676	−	4.09208i	0.305995	−	0.256760i
$255$		0			0
$256$	−5.60629	+	31.7949i	−0.350393	+	1.98718i
$257$	2.11673	−	12.0046i	0.132038	−	0.748825i	−0.844838	−	0.535021i	$-0.820304\pi$
$257$	2.11673	−	12.0046i	0.132038	−	0.748825i	0.976877	−	0.213804i	$-0.0685854\pi$
$258$		0			0
$259$	20.9687	−	17.5949i	1.30293	−	1.09329i
$260$	20.8103	−	36.0445i	1.29060	−	2.23538i
$261$		0			0
$262$	−5.42064	−	9.38882i	−0.334888	−	0.580043i
$263$	6.47414	+	2.35639i	0.399212	+	0.145301i	0.533821	−	0.845597i	$-0.320756\pi$
$263$	6.47414	+	2.35639i	0.399212	+	0.145301i	−0.134609	+	0.990899i	$0.542978\pi$
$264$		0			0
$265$	−15.1643	−	12.7243i	−0.931533	−	0.781649i
$266$	−12.8749	+	4.68608i	−0.789411	+	0.287322i
$267$		0			0
$268$	−4.12508	−	23.3945i	−0.251979	−	1.42905i
$269$	7.05875			0.430380			0.215190	−	0.976572i	$-0.430963\pi$
$269$	7.05875			0.430380			0.215190	+	0.976572i	$0.430963\pi$
$270$		0			0
$271$	23.7575			1.44316			0.721581	−	0.692330i	$-0.243416\pi$
$271$	23.7575			1.44316			0.721581	+	0.692330i	$0.243416\pi$
$272$	−1.89698	−	10.7583i	−0.115021	−	0.652318i
$273$		0			0
$274$	41.9595	−	15.2720i	2.53486	−	0.922615i
$275$	11.8073	+	9.90754i	0.712009	+	0.597447i
$276$		0			0
$277$	0.0981638	+	0.0357287i	0.00589809	+	0.00214673i	0.344968	−	0.938615i	$-0.387890\pi$
$277$	0.0981638	+	0.0357287i	0.00589809	+	0.00214673i	−0.339069	+	0.940761i	$0.610112\pi$
$278$	−2.40611	−	4.16750i	−0.144309	−	0.249950i
$279$		0			0
$280$	20.5377	−	35.5723i	1.22736	−	2.12585i
$281$	6.24495	−	5.24013i	0.372542	−	0.312600i	−0.437224	−	0.899353i	$-0.644038\pi$
$281$	6.24495	−	5.24013i	0.372542	−	0.312600i	0.809766	+	0.586753i	$0.199594\pi$
$282$		0			0
$283$	4.10087	−	23.2572i	0.243772	−	1.38250i	−0.579557	−	0.814932i	$-0.696774\pi$
$283$	4.10087	−	23.2572i	0.243772	−	1.38250i	0.823328	−	0.567565i	$-0.192115\pi$
$284$	−10.3961	+	58.9590i	−0.616893	+	3.49857i
$285$		0			0
$286$	−21.6223	+	18.1433i	−1.27856	+	1.07284i
$287$	6.49380	−	11.2476i	0.383317	−	0.663925i
$288$		0			0
$289$	5.19030	+	8.98987i	0.305312	+	0.528816i
$290$	18.0050	+	6.55327i	1.05729	+	0.384821i
$291$		0			0
$292$	5.82364	+	4.88661i	0.340803	+	0.285967i
$293$	−20.3216	+	7.39644i	−1.18720	+	0.432105i	−0.858739	−	0.512413i	$-0.828752\pi$
$293$	−20.3216	+	7.39644i	−1.18720	+	0.432105i	−0.328459	+	0.944518i	$0.606529\pi$
$294$		0			0
$295$	−0.885203	−	5.02024i	−0.0515385	−	0.292289i
$296$	−51.6398			−3.00150
$297$		0			0
$298$	−17.9792			−1.04151
$299$	0.310337	+	1.76001i	0.0179472	+	0.101784i
$300$		0			0
$301$	6.84915	−	2.49289i	0.394778	−	0.143688i
$302$	9.13332	+	7.66377i	0.525564	+	0.441000i
$303$		0			0
$304$	8.36601	+	3.04498i	0.479824	+	0.174642i
$305$	−22.1351	−	38.3391i	−1.26745	−	2.19529i
$306$		0			0
$307$	−8.17997	+	14.1681i	−0.466855	+	0.808617i	−0.999283	−	0.0378581i	$-0.987946\pi$
$307$	−8.17997	+	14.1681i	−0.466855	+	0.808617i	0.532428	+	0.846475i	$0.321280\pi$
$308$	−28.2632	+	23.7156i	−1.61044	+	1.35132i
$309$		0			0
$310$	10.1420	−	57.5179i	0.576025	−	3.26680i
$311$	1.34662	−	7.63705i	0.0763597	−	0.433057i	−0.922529	−	0.385928i	$-0.873881\pi$
$311$	1.34662	−	7.63705i	0.0763597	−	0.433057i	0.998889	−	0.0471298i	$-0.0150074\pi$
$312$		0			0
$313$	11.8109	−	9.91053i	0.667592	−	0.560177i	−0.244759	−	0.969584i	$-0.578709\pi$
$313$	11.8109	−	9.91053i	0.667592	−	0.560177i	0.912352	+	0.409407i	$0.134264\pi$
$314$	−1.81471	+	3.14317i	−0.102410	+	0.177380i
$315$		0			0
$316$	−34.7371	−	60.1664i	−1.95412	−	3.38463i
$317$	8.11538	+	2.95376i	0.455805	+	0.165899i	0.559711	−	0.828688i	$-0.310912\pi$
$317$	8.11538	+	2.95376i	0.455805	+	0.165899i	−0.103906	+	0.994587i	$0.533134\pi$
$318$		0			0
$319$	−6.65842	−	5.58708i	−0.372800	−	0.312816i
$320$	21.7027	−	7.89914i	1.21322	−	0.441575i
$321$		0			0
$322$	0.606431	+	3.43924i	0.0337951	+	0.191661i
$323$	5.39459			0.300163
$324$		0			0
$325$	−15.0077			−0.832480
$326$	−7.36368	−	41.7615i	−0.407836	−	2.31295i
$327$		0			0
$328$	−23.0240	+	8.38005i	−1.27129	+	0.462711i
$329$	−11.5234	−	9.66928i	−0.635306	−	0.533085i
$330$		0			0
$331$	−19.3055	−	7.02664i	−1.06113	−	0.386219i	−0.248276	−	0.968689i	$-0.579864\pi$
$331$	−19.3055	−	7.02664i	−1.06113	−	0.386219i	−0.812852	+	0.582470i	$0.802086\pi$
$332$	8.01839	+	13.8883i	0.440066	+	0.762217i
$333$		0			0
$334$	8.40609	−	14.5598i	0.459961	−	0.796675i
$335$	−13.8722	+	11.6401i	−0.757917	+	0.635968i
$336$		0			0
$337$	2.77459	−	15.7355i	0.151141	−	0.857165i	−0.811088	−	0.584924i	$-0.801124\pi$
$337$	2.77459	−	15.7355i	0.151141	−	0.857165i	0.962229	−	0.272241i	$-0.0877647\pi$
$338$	−0.775887	+	4.40028i	−0.0422027	+	0.239343i
$339$		0			0
$340$	−24.5307	+	20.5837i	−1.33037	+	1.11631i
$341$	−13.2475	+	22.9453i	−0.717390	+	1.24256i
$342$		0			0
$343$	−9.21426	−	15.9596i	−0.497523	−	0.861736i
$344$	−12.9212	−	4.70293i	−0.696664	−	0.253565i
$345$		0			0
$346$	45.1252	+	37.8645i	2.42595	+	2.03561i
$347$	−9.21300	+	3.35326i	−0.494580	+	0.180012i	−0.577255	−	0.816564i	$-0.695876\pi$
$347$	−9.21300	+	3.35326i	−0.494580	+	0.180012i	0.0826746	+	0.996577i	$0.473654\pi$
$348$		0			0
$349$	−1.63837	−	9.29164i	−0.0876997	−	0.497370i	−0.996741	−	0.0806644i	$-0.974296\pi$
$349$	−1.63837	−	9.29164i	−0.0876997	−	0.497370i	0.909042	−	0.416705i	$-0.136815\pi$
$350$	−29.3267			−1.56758
$351$		0			0
$352$	1.38916			0.0740424
$353$	0.587827	+	3.33374i	0.0312869	+	0.177437i	0.996447	−	0.0842237i	$-0.0268410\pi$
$353$	0.587827	+	3.33374i	0.0312869	+	0.177437i	−0.965160	+	0.261661i	$0.915730\pi$
$354$		0			0
$355$	42.8857	−	15.6091i	2.27614	−	0.828446i
$356$	−15.7827	−	13.2433i	−0.836482	−	0.701891i
$357$		0			0
$358$	−47.5129	−	17.2933i	−2.51113	−	0.913978i
$359$	17.6137	+	30.5078i	0.929614	+	1.61014i	0.783968	+	0.620801i	$0.213193\pi$
$359$	17.6137	+	30.5078i	0.929614	+	1.61014i	0.145646	+	0.989337i	$0.453474\pi$
$360$		0			0
$361$	7.30179	−	12.6471i	0.384305	−	0.665636i
$362$	−29.1268	+	24.4403i	−1.53087	+	1.28455i
$363$		0			0
$364$	6.23813	−	35.3782i	0.326967	−	1.85432i
$365$	1.00633	−	5.70716i	0.0526735	−	0.298726i
$366$		0			0
$367$	−24.1652	+	20.2770i	−1.26141	+	1.05845i	−0.265883	+	0.964005i	$0.585664\pi$
$367$	−24.1652	+	20.2770i	−1.26141	+	1.05845i	−0.995530	+	0.0944462i	$0.969892\pi$
$368$	1.13463	−	1.96524i	0.0591469	−	0.102445i
$369$		0			0
$370$	38.9724	+	67.5021i	2.02608	+	3.50927i
$371$	−16.0557	−	5.84380i	−0.833571	−	0.303395i
$372$		0			0
$373$	11.0635	+	9.28334i	0.572844	+	0.480673i	0.882588	−	0.470147i	$-0.155799\pi$
$373$	11.0635	+	9.28334i	0.572844	+	0.480673i	−0.309744	+	0.950820i	$0.600243\pi$
$374$	20.4072	−	7.42760i	1.05523	−	0.384072i
$375$		0			0
$376$	4.92791	+	27.9476i	0.254138	+	1.44129i
$377$	8.46320			0.435877
$378$		0			0
$379$	1.00099			0.0514176			0.0257088	−	0.999669i	$-0.491816\pi$
$379$	1.00099			0.0514176			0.0257088	+	0.999669i	$0.491816\pi$
$380$	−4.53176	−	25.7009i	−0.232474	−	1.31843i
$381$		0			0
$382$	−25.2917	+	9.20543i	−1.29404	+	0.470991i
$383$	−3.15407	−	2.64658i	−0.161165	−	0.135234i	0.558639	−	0.829411i	$-0.311324\pi$
$383$	−3.15407	−	2.64658i	−0.161165	−	0.135234i	−0.719804	+	0.694177i	$0.755768\pi$
$384$		0			0
$385$	26.4290	+	9.61937i	1.34695	+	0.490249i
$386$	−1.40690	−	2.43683i	−0.0716094	−	0.124031i
$387$		0			0
$388$	21.4803	−	37.2049i	1.09050	−	1.88879i
$389$	11.8889	−	9.97601i	0.602793	−	0.505804i	−0.289549	−	0.957163i	$-0.593505\pi$
$389$	11.8889	−	9.97601i	0.602793	−	0.505804i	0.892342	+	0.451359i	$0.149061\pi$
$390$		0			0
$391$	0.238771	−	1.35414i	0.0120752	−	0.0684817i
$392$	0.0596706	−	0.338409i	0.00301382	−	0.0170922i
$393$		0			0
$394$	9.49286	−	7.96545i	0.478243	−	0.401294i
$395$	−26.4802	+	45.8651i	−1.33237	+	2.30772i
$396$		0			0
$397$	0.774463	+	1.34141i	0.0388692	+	0.0673234i	0.884806	−	0.465960i	$-0.154291\pi$
$397$	0.774463	+	1.34141i	0.0388692	+	0.0673234i	−0.845936	+	0.533284i	$0.820958\pi$
$398$	−31.7007	−	11.5381i	−1.58901	−	0.578353i
$399$		0			0
$400$	14.5980	+	12.2491i	0.729898	+	0.612457i
$401$	7.46809	−	2.71816i	0.372939	−	0.135739i	−0.148749	−	0.988875i	$-0.547525\pi$
$401$	7.46809	−	2.71816i	0.372939	−	0.135739i	0.521688	+	0.853136i	$0.325303\pi$
$402$		0			0
$403$	−4.47971	−	25.4057i	−0.223150	−	1.26555i
$404$	−22.8628			−1.13747
$405$		0			0
$406$	16.5380			0.820766
$407$	−6.13999	−	34.8216i	−0.304348	−	1.72604i
$408$		0			0
$409$	−24.8599	+	9.04828i	−1.22925	+	0.447409i	−0.873339	−	0.487113i	$-0.838050\pi$
$409$	−24.8599	+	9.04828i	−1.22925	+	0.447409i	−0.355906	+	0.934522i	$0.615828\pi$
$410$	28.3303	+	23.7720i	1.39914	+	1.17401i
$411$		0			0
$412$	−39.3774	−	14.3322i	−1.93998	−	0.706097i
$413$	−2.19998	−	3.81048i	−0.108254	−	0.187501i
$414$		0			0
$415$	6.11245	−	10.5871i	0.300048	−	0.519699i
$416$	−1.03615	+	0.869434i	−0.0508015	+	0.0426275i
$417$		0			0
$418$	−3.07332	+	17.4297i	−0.150321	+	0.852512i
$419$	−6.65767	+	37.7575i	−0.325248	+	1.84458i	0.182675	+	0.983173i	$0.441524\pi$
$419$	−6.65767	+	37.7575i	−0.325248	+	1.84458i	−0.507923	+	0.861402i	$0.669587\pi$
$420$		0			0
$421$	5.62621	−	4.72095i	0.274205	−	0.230085i	−0.495307	−	0.868718i	$-0.664944\pi$
$421$	5.62621	−	4.72095i	0.274205	−	0.230085i	0.769511	+	0.638633i	$0.220500\pi$
$422$	7.17076	−	12.4201i	0.349067	−	0.604602i
$423$		0			0
$424$	16.1168	+	27.9152i	0.782702	+	1.35568i
$425$	10.8505	+	3.94926i	0.526326	+	0.191567i
$426$		0			0
$427$	−29.2713	−	24.5615i	−1.41654	−	1.18861i
$428$	−54.0917	+	19.6878i	−2.61462	+	0.951644i
$429$		0			0
$430$	3.60404	+	20.4395i	0.173802	+	0.985681i
$431$	15.8463			0.763289			0.381644	−	0.924309i	$-0.375358\pi$
$431$	15.8463			0.763289			0.381644	+	0.924309i	$0.375358\pi$
$432$		0			0
$433$	−23.8507			−1.14619			−0.573097	−	0.819488i	$-0.694258\pi$
$433$	−23.8507			−1.14619			−0.573097	+	0.819488i	$0.694258\pi$
$434$	−8.75383	−	49.6454i	−0.420197	−	2.38306i
$435$		0			0
$436$	−21.8734	+	7.96126i	−1.04755	+	0.381275i
$437$	0.858431	+	0.720309i	0.0410643	+	0.0344571i
$438$		0			0
$439$	20.1751	+	7.34315i	0.962907	+	0.350469i	0.775172	−	0.631750i	$-0.217663\pi$
$439$	20.1751	+	7.34315i	0.962907	+	0.350469i	0.187735	+	0.982220i	$0.439885\pi$
$440$	−26.5296	−	45.9507i	−1.26475	−	2.19061i
$441$		0			0
$442$	−10.5727	+	18.3124i	−0.502890	+	0.871031i
$443$	−24.1671	+	20.2786i	−1.14821	+	0.963466i	−0.999676	−	0.0254409i	$-0.991901\pi$
$443$	−24.1671	+	20.2786i	−1.14821	+	0.963466i	−0.148538	+	0.988907i	$0.547457\pi$
$444$		0			0
$445$	−2.72725	+	15.4670i	−0.129284	+	0.733208i
$446$	3.72532	−	21.1273i	0.176399	−	1.00041i
$447$		0			0
$448$	15.2707	−	12.8136i	0.721472	−	0.605387i
$449$	10.3949	−	18.0045i	0.490565	−	0.849684i	−0.509376	−	0.860544i	$-0.670124\pi$
$449$	10.3949	−	18.0045i	0.490565	−	0.849684i	0.999941	+	0.0108605i	$0.00345708\pi$
$450$		0			0
$451$	−8.38839	−	14.5291i	−0.394994	−	0.684149i
$452$	−43.3497	−	15.7780i	−2.03900	−	0.742134i
$453$		0			0
$454$	−45.7186	−	38.3624i	−2.14568	−	1.80044i
$455$	−25.7335	+	9.36621i	−1.20640	+	0.439095i
$456$		0			0
$457$	−3.02629	−	17.1630i	−0.141564	−	0.802850i	−0.970062	−	0.242858i	$-0.921915\pi$
$457$	−3.02629	−	17.1630i	−0.141564	−	0.802850i	0.828498	−	0.559992i	$-0.189196\pi$
$458$	44.6124			2.08460
$459$		0			0
$460$	−6.65196			−0.310149
$461$	5.38387	+	30.5334i	0.250752	+	1.42208i	0.806746	+	0.590898i	$0.201226\pi$
$461$	5.38387	+	30.5334i	0.250752	+	1.42208i	−0.555994	+	0.831186i	$0.687662\pi$
$462$		0			0
$463$	−6.09668	+	2.21901i	−0.283337	+	0.103126i	−0.479779	−	0.877389i	$-0.659283\pi$
$463$	−6.09668	+	2.21901i	−0.283337	+	0.103126i	0.196443	+	0.980515i	$0.437061\pi$
$464$	−8.23211	−	6.90756i	−0.382166	−	0.320676i
$465$		0			0
$466$	24.3382	+	8.85838i	1.12745	+	0.410357i
$467$	0.971950	+	1.68347i	0.0449765	+	0.0779016i	0.887637	−	0.460543i	$-0.152345\pi$
$467$	0.971950	+	1.68347i	0.0449765	+	0.0779016i	−0.842661	+	0.538445i	$0.819012\pi$
$468$		0			0
$469$	−7.81513	+	13.5362i	−0.360869	+	0.625044i
$470$	32.8132	−	27.5336i	1.51356	−	1.27003i
$471$		0			0
$472$	−1.44140	+	8.17460i	−0.0663459	+	0.376266i
$473$	1.63493	−	9.27217i	0.0751744	−	0.426335i
$474$		0			0
$475$	−7.20872	+	6.04883i	−0.330759	+	0.277540i
$476$	−13.8198	+	23.9367i	−0.633431	+	1.09713i
$477$		0			0
$478$	−11.7195	−	20.2987i	−0.536036	−	0.928442i
$479$	1.24922	+	0.454678i	0.0570783	+	0.0207748i	0.370402	−	0.928872i	$-0.379220\pi$
$479$	1.24922	+	0.454678i	0.0570783	+	0.0207748i	−0.313323	+	0.949647i	$0.601442\pi$
$480$		0			0
$481$	26.3736	+	22.1300i	1.20253	+	1.00904i
$482$	16.2531	−	5.91563i	0.740307	−	0.269450i
$483$		0			0
$484$	0.557611	+	3.16237i	0.0253459	+	0.143744i
$485$	−32.7490			−1.48705
$486$		0			0
$487$	21.2040			0.960844			0.480422	−	0.877037i	$-0.340484\pi$
$487$	21.2040			0.960844			0.480422	+	0.877037i	$0.340484\pi$
$488$	12.5177	+	70.9913i	0.566649	+	3.21362i
$489$		0			0
$490$	−0.487392	+	0.177396i	−0.0220181	+	0.00801394i
$491$	−20.6910	−	17.3618i	−0.933770	−	0.783526i	0.0427200	−	0.999087i	$-0.486398\pi$
$491$	−20.6910	−	17.3618i	−0.933770	−	0.783526i	−0.976490	+	0.215561i	$0.930842\pi$
$492$		0			0
$493$	−6.11884	−	2.22707i	−0.275578	−	0.100302i
$494$	−8.61638	−	14.9240i	−0.387669	−	0.671463i
$495$		0			0
$496$	−16.3784	+	28.3683i	−0.735414	+	1.27377i
$497$	30.1757	−	25.3204i	1.35356	−	1.13577i
$498$		0			0
$499$	2.61148	−	14.8104i	0.116906	−	0.663006i	−0.868883	−	0.495018i	$-0.835162\pi$
$499$	2.61148	−	14.8104i	0.116906	−	0.663006i	0.985789	−	0.167989i	$-0.0537273\pi$
$500$	−1.10655	+	6.27556i	−0.0494864	+	0.280651i
$501$		0			0
$502$	29.3468	−	24.6249i	1.30981	−	1.09906i
$503$	2.30325	−	3.98934i	0.102697	−	0.177876i	−0.810098	−	0.586294i	$-0.800586\pi$
$503$	2.30325	−	3.98934i	0.102697	−	0.177876i	0.912795	+	0.408418i	$0.133920\pi$
$504$		0			0
$505$	8.71420	+	15.0934i	0.387777	+	0.671649i
$506$	4.23912	+	1.54291i	0.188452	+	0.0685909i
$507$		0			0
$508$	8.01763	+	6.72759i	0.355725	+	0.298489i
$509$	27.9997	−	10.1911i	1.24106	−	0.451711i	0.363692	−	0.931519i	$-0.381516\pi$
$509$	27.9997	−	10.1911i	1.24106	−	0.451711i	0.877373	+	0.479809i	$0.159294\pi$
$510$		0			0
$511$	−0.868590	−	4.92602i	−0.0384242	−	0.217914i
$512$	−40.8760			−1.80648
$513$		0			0
$514$	29.9599			1.32147
$515$	5.54702	+	31.4587i	0.244431	+	1.38624i
$516$		0			0
$517$	−18.2596	+	6.64596i	−0.803057	+	0.292289i
$518$	51.5367	+	43.2445i	2.26439	+	1.90005i
$519$		0			0
$520$	48.5472	+	17.6697i	2.12894	+	0.774869i
$521$	−5.88104	−	10.1863i	−0.257653	−	0.446268i	0.707960	−	0.706253i	$-0.249616\pi$
$521$	−5.88104	−	10.1863i	−0.257653	−	0.446268i	−0.965613	+	0.259985i	$0.916283\pi$
$522$		0			0
$523$	−14.6926	+	25.4484i	−0.642464	+	1.11278i	0.342417	+	0.939548i	$0.388754\pi$
$523$	−14.6926	+	25.4484i	−0.642464	+	1.11278i	−0.984881	+	0.173232i	$0.944579\pi$
$524$	13.6537	−	11.4568i	0.596463	−	0.500492i
$525$		0			0
$526$	−2.94043	+	16.6760i	−0.128209	+	0.727109i
$527$	−3.44666	+	19.5470i	−0.150139	+	0.851480i
$528$		0			0
$529$	−17.4002	+	14.6005i	−0.756531	+	0.634805i
$530$	24.3266	−	42.1350i	1.05668	−	1.83023i
$531$		0			0
$532$	−11.2627	−	19.5076i	−0.488301	−	0.845761i
$533$	15.3501	+	5.58698i	0.664887	+	0.241999i
$534$		0			0
$535$	33.6145	+	28.2059i	1.45328	+	1.21945i
$536$	27.7088	−	10.0852i	1.19684	−	0.435614i
$537$		0			0
$538$	3.01261	+	17.0854i	0.129883	+	0.736602i
$539$	0.235290			0.0101347
$540$		0			0
$541$	−22.9116			−0.985046			−0.492523	−	0.870300i	$-0.663925\pi$
$541$	−22.9116			−0.985046			−0.492523	+	0.870300i	$0.663925\pi$
$542$	10.1395	+	57.5037i	0.435527	+	2.47000i
$543$		0			0
$544$	0.977920	−	0.355934i	0.0419280	−	0.0152605i
$545$	13.5929	+	11.4058i	0.582256	+	0.488571i
$546$		0			0
$547$	12.9280	+	4.70541i	0.552762	+	0.201189i	0.603273	−	0.797535i	$-0.293863\pi$
$547$	12.9280	+	4.70541i	0.552762	+	0.201189i	−0.0505115	+	0.998723i	$0.516085\pi$
$548$	36.7053	+	63.5755i	1.56797	+	2.71581i
$549$		0			0
$550$	−18.9414	+	32.8075i	−0.807665	+	1.39892i
$551$	4.06516	−	3.41107i	0.173181	−	0.145317i
$552$		0			0
$553$	−7.93776	+	45.0173i	−0.337548	+	1.91433i
$554$	−0.0445841	+	0.252849i	−0.00189420	+	0.0107425i
$555$		0			0
$556$	6.06058	−	5.08543i	0.257026	−	0.215670i
$557$	10.9520	−	18.9695i	0.464053	−	0.803763i	−0.535106	−	0.844785i	$-0.679728\pi$
$557$	10.9520	−	18.9695i	0.464053	−	0.803763i	0.999158	+	0.0410224i	$0.0130615\pi$
$558$		0			0
$559$	4.58371	+	7.93922i	0.193870	+	0.335793i
$560$	32.6754	+	11.8929i	1.38079	+	0.502566i
$561$		0			0
$562$	15.3488	+	12.8791i	0.647448	+	0.543274i
$563$	13.6898	−	4.98270i	0.576958	−	0.209996i	−0.0370255	−	0.999314i	$-0.511788\pi$
$563$	13.6898	−	4.98270i	0.576958	−	0.209996i	0.613984	+	0.789319i	$0.289566\pi$
$564$		0			0
$565$	6.10658	+	34.6322i	0.256906	+	1.45699i
$566$	58.0431			2.43973
$567$		0			0
$568$	−74.3137			−3.11813
$569$	3.88226	+	22.0174i	0.162753	+	0.923016i	0.951351	+	0.308108i	$0.0996958\pi$
$569$	3.88226	+	22.0174i	0.162753	+	0.923016i	−0.788599	+	0.614908i	$0.789193\pi$
$570$		0			0
$571$	14.4958	−	5.27605i	0.606632	−	0.220796i	−0.0203971	−	0.999792i	$-0.506493\pi$
$571$	14.4958	−	5.27605i	0.606632	−	0.220796i	0.627029	+	0.778996i	$0.284271\pi$
$572$	−35.5482	−	29.8285i	−1.48635	−	1.24719i
$573$		0			0
$574$	29.9957	+	10.9176i	1.25200	+	0.455690i
$575$	1.19930	+	2.07724i	0.0500142	+	0.0866271i
$576$		0			0
$577$	−16.4040	+	28.4126i	−0.682909	+	1.18283i	0.291180	+	0.956668i	$0.405952\pi$
$577$	−16.4040	+	28.4126i	−0.682909	+	1.18283i	−0.974089	+	0.226165i	$0.927381\pi$
$578$	−19.5444	+	16.3997i	−0.812938	+	0.682136i
$579$		0			0
$580$	−5.47005	+	31.0222i	−0.227132	+	1.28813i
$581$	1.83228	−	10.3914i	0.0760158	−	0.431107i
$582$		0			0
$583$	−16.9074	+	14.1870i	−0.700233	+	0.587565i
$584$	−4.71825	+	8.17225i	−0.195242	+	0.338170i
$585$		0			0
$586$	−26.5758	−	46.0306i	−1.09784	−	1.90151i
$587$	28.4109	+	10.3407i	1.17264	+	0.426807i	0.853598	−	0.520932i	$-0.174415\pi$
$587$	28.4109	+	10.3407i	1.17264	+	0.426807i	0.319046	+	0.947739i	$0.396638\pi$
$588$		0			0
$589$	−12.3915	−	10.3977i	−0.510581	−	0.428428i
$590$	11.7734	−	4.28518i	0.484705	−	0.176418i
$591$		0			0
$592$	−7.59116	−	43.0516i	−0.311995	−	1.76941i
$593$	−41.1023			−1.68787			−0.843935	−	0.536446i	$-0.819766\pi$
$593$	−41.1023			−1.68787			−0.843935	+	0.536446i	$0.819766\pi$
$594$		0			0
$595$	21.0698			0.863778
$596$	−5.13281	−	29.1096i	−0.210248	−	1.19238i
$597$		0			0
$598$	−4.12756	+	1.50231i	−0.168788	+	0.0614340i
$599$	−27.9993	−	23.4942i	−1.14402	−	0.959948i	−0.144458	−	0.989511i	$-0.546144\pi$
$599$	−27.9993	−	23.4942i	−1.14402	−	0.959948i	−0.999563	+	0.0295630i	$0.990588\pi$
$600$		0			0
$601$	−3.70784	−	1.34954i	−0.151246	−	0.0550491i	0.265288	−	0.964169i	$-0.414533\pi$
$601$	−3.70784	−	1.34954i	−0.151246	−	0.0550491i	−0.416534	+	0.909120i	$0.636755\pi$
$602$	8.95706	+	15.5141i	0.365062	+	0.632307i
$603$		0			0
$604$	−9.80076	+	16.9754i	−0.398787	+	0.690720i
$605$	1.87518	−	1.57346i	0.0762369	−	0.0639703i
$606$		0			0
$607$	1.73848	−	9.85942i	0.0705628	−	0.400182i	−0.928985	−	0.370117i	$-0.879318\pi$
$607$	1.73848	−	9.85942i	0.0705628	−	0.400182i	0.999548	−	0.0300646i	$-0.00957131\pi$
$608$	−0.147275	+	0.835236i	−0.00597277	+	0.0338733i
$609$		0			0
$610$	83.3508	−	69.9397i	3.37478	−	2.83177i
$611$	9.46005	−	16.3853i	0.382712	−	0.662877i
$612$		0			0
$613$	9.37838	+	16.2438i	0.378789	+	0.656082i	0.990886	−	0.134700i	$-0.0430072\pi$
$613$	9.37838	+	16.2438i	0.378789	+	0.656082i	−0.612097	+	0.790783i	$0.709674\pi$
$614$	−37.7844	−	13.7524i	−1.52485	−	0.555001i
$615$		0			0
$616$	−35.0826	−	29.4378i	−1.41352	−	1.18608i
$617$	−21.6224	+	7.86991i	−0.870485	+	0.316830i	−0.738363	−	0.674403i	$-0.764401\pi$
$617$	−21.6224	+	7.86991i	−0.870485	+	0.316830i	−0.132121	+	0.991234i	$0.542179\pi$
$618$		0			0
$619$	1.28743	+	7.30138i	0.0517462	+	0.293467i	0.999688	−	0.0249762i	$-0.00795098\pi$
$619$	1.28743	+	7.30138i	0.0517462	+	0.293467i	−0.947942	+	0.318444i	$0.896840\pi$
$620$	96.0211			3.85630
$621$		0			0
$622$	19.0598			0.764229
$623$	2.35398	+	13.3501i	0.0943100	+	0.534859i
$624$		0			0
$625$	25.6515	−	9.33639i	1.02606	−	0.373456i
$626$	29.0287	+	24.3580i	1.16022	+	0.973542i
$627$		0			0
$628$	−5.60710	−	2.04082i	−0.223748	−	0.0814376i
$629$	−13.2444	−	22.9400i	−0.528090	−	0.914679i
$630$		0			0
$631$	15.4962	−	26.8402i	0.616894	−	1.06849i	−0.373155	−	0.927769i	$-0.621724\pi$
$631$	15.4962	−	26.8402i	0.616894	−	1.06849i	0.990049	−	0.140723i	$-0.0449426\pi$
$632$	66.0614	−	55.4321i	2.62778	−	2.20497i
$633$		0			0
$634$	−3.68585	+	20.9035i	−0.146384	+	0.830184i
$635$	1.38545	−	7.85727i	0.0549798	−	0.311806i
$636$		0			0
$637$	−0.175499	+	0.147261i	−0.00695352	+	0.00583470i
$638$	10.6815	−	18.5009i	0.422884	−	0.732457i
$639$		0			0
$640$	29.6279	+	51.3171i	1.17115	+	2.02849i
$641$	−33.2145	−	12.0891i	−1.31189	−	0.477490i	−0.411042	−	0.911617i	$-0.634835\pi$
$641$	−33.2145	−	12.0891i	−1.31189	−	0.477490i	−0.900852	+	0.434126i	$0.857057\pi$
$642$		0			0
$643$	−15.0918	−	12.6635i	−0.595162	−	0.499400i	0.294724	−	0.955582i	$-0.404772\pi$
$643$	−15.0918	−	12.6635i	−0.595162	−	0.499400i	−0.889887	+	0.456182i	$0.849217\pi$
$644$	−5.39525	+	1.96371i	−0.212603	+	0.0773811i
$645$		0			0
$646$	2.30236	+	13.0573i	0.0905852	+	0.513734i
$647$	−46.8317			−1.84114			−0.920572	−	0.390572i	$-0.872277\pi$
$647$	−46.8317			−1.84114			−0.920572	+	0.390572i	$0.872277\pi$
$648$		0			0
$649$	−5.68366			−0.223103
$650$	−6.40516	−	36.3255i	−0.251231	−	1.42480i
$651$		0			0
$652$	65.5127	−	23.8447i	2.56567	−	0.933829i
$653$	−13.2730	−	11.1374i	−0.519414	−	0.435840i	0.345013	−	0.938598i	$-0.387874\pi$
$653$	−13.2730	−	11.1374i	−0.519414	−	0.435840i	−0.864427	+	0.502758i	$0.832319\pi$
$654$		0			0
$655$	−12.7676	−	4.64703i	−0.498871	−	0.181574i
$656$	−10.3709	−	17.9630i	−0.404918	−	0.701338i
$657$		0			0
$658$	18.4859	−	32.0186i	0.720657	−	1.24821i
$659$	−33.5023	+	28.1118i	−1.30507	+	1.09508i	−0.315820	+	0.948819i	$0.602279\pi$
$659$	−33.5023	+	28.1118i	−1.30507	+	1.09508i	−0.989246	+	0.146261i	$0.953276\pi$
$660$		0			0
$661$	−1.57792	+	8.94881i	−0.0613738	+	0.348068i	0.938621	+	0.344949i	$0.112104\pi$
$661$	−1.57792	+	8.94881i	−0.0613738	+	0.348068i	−0.999995	+	0.00311890i	$0.999007\pi$
$662$	8.76821	−	49.7270i	0.340786	−	1.93269i
$663$		0			0
$664$	−15.2490	+	12.7954i	−0.591776	+	0.496559i
$665$	−8.58561	+	14.8707i	−0.332936	+	0.576661i
$666$		0			0
$667$	−0.676311	−	1.17140i	−0.0261868	−	0.0453570i
$668$	25.9732	+	9.45346i	1.00493	+	0.365765i
$669$		0			0
$670$	−34.0948	−	28.6090i	−1.31720	−	1.10526i
$671$	−46.3823	+	16.8818i	−1.79057	+	0.651714i
$672$		0			0
$673$	1.30179	+	7.38279i	0.0501801	+	0.284586i	0.999564	−	0.0295331i	$-0.00940205\pi$
$673$	1.30179	+	7.38279i	0.0501801	+	0.284586i	−0.949384	+	0.314119i	$0.898291\pi$
$674$	39.2711			1.51266
$675$		0			0
$676$	−7.34587			−0.282534
$677$	−2.66768	−	15.1292i	−0.102527	−	0.581461i	−0.992179	−	0.124822i	$-0.960164\pi$
$677$	−2.66768	−	15.1292i	−0.102527	−	0.581461i	0.889652	−	0.456639i	$-0.150947\pi$
$678$		0			0
$679$	−26.5619	+	9.66776i	−1.01935	+	0.371014i
$680$	−30.4495	−	25.5502i	−1.16769	−	0.979806i
$681$		0			0
$682$	−61.1918	−	22.2720i	−2.34315	−	0.852838i
$683$	3.31079	+	5.73445i	0.126684	+	0.219423i	0.922390	−	0.386260i	$-0.126233\pi$
$683$	3.31079	+	5.73445i	0.126684	+	0.219423i	−0.795706	+	0.605683i	$0.792900\pi$
$684$		0			0
$685$	27.9806	−	48.4639i	1.06908	−	1.85171i
$686$	34.6968	−	29.1141i	1.32473	−	1.11158i
$687$		0			0
$688$	2.02134	−	11.4636i	0.0770630	−	0.437046i
$689$	3.73173	−	21.1637i	0.142168	−	0.806273i
$690$		0			0
$691$	−14.2920	+	11.9924i	−0.543693	+	0.456212i	−0.872798	−	0.488081i	$-0.837697\pi$
$691$	−14.2920	+	11.9924i	−0.543693	+	0.456212i	0.329106	+	0.944293i	$0.393253\pi$
$692$	−48.4228	+	83.8708i	−1.84076	+	3.18829i
$693$		0			0
$694$	−12.0484	−	20.8685i	−0.457352	−	0.792157i
$695$	−5.66727	−	2.06272i	−0.214972	−	0.0782433i
$696$		0			0
$697$	−9.62782	−	8.07870i	−0.364680	−	0.306003i
$698$	21.7907	−	7.93117i	0.824790	−	0.300199i
$699$		0			0
$700$	−8.37238	−	47.4821i	−0.316446	−	1.79465i
$701$	−24.8903			−0.940092			−0.470046	−	0.882642i	$-0.655763\pi$
$701$	−24.8903			−0.940092			−0.470046	+	0.882642i	$0.655763\pi$
$702$		0			0
$703$	21.5876			0.814190
$704$	−4.47151	−	25.3592i	−0.168526	−	0.955760i
$705$		0			0
$706$	−7.81826	+	2.84561i	−0.294244	+	0.107096i
$707$	11.5236	+	9.66944i	0.433389	+	0.363657i
$708$		0			0
$709$	24.6000	+	8.95366i	0.923871	+	0.336262i	0.759778	−	0.650183i	$-0.225308\pi$
$709$	24.6000	+	8.95366i	0.923871	+	0.336262i	0.164094	+	0.986445i	$0.447530\pi$
$710$	56.0843	+	97.1409i	2.10481	+	3.64563i
$711$		0			0
$712$	12.7870	−	22.1477i	0.479212	−	0.830020i
$713$	−3.15846	+	2.65026i	−0.118285	+	0.0992531i
$714$		0			0
$715$	−6.14274	+	34.8372i	−0.229725	+	1.30284i
$716$	14.4348	−	81.8638i	0.539454	−	3.05940i
$717$		0			0
$718$	−66.3252	+	55.6534i	−2.47523	+	2.07697i
$719$	10.5145	−	18.2117i	0.392125	−	0.679181i	−0.600604	−	0.799546i	$-0.705073\pi$
$719$	10.5145	−	18.2117i	0.392125	−	0.679181i	0.992730	+	0.120365i	$0.0384066\pi$
$720$		0			0
$721$	13.7859	+	23.8779i	0.513414	+	0.889259i
$722$	33.7280	+	12.2760i	1.25522	+	0.456864i
$723$		0			0
$724$	−47.8859	−	40.1810i	−1.77967	−	1.49332i
$725$	10.6737	−	3.88490i	0.396411	−	0.144282i
$726$		0			0
$727$	7.18828	+	40.7668i	0.266599	+	1.51196i	0.764444	+	0.644690i	$0.223014\pi$
$727$	7.18828	+	40.7668i	0.266599	+	1.51196i	−0.497845	+	0.867266i	$0.665875\pi$
$728$	44.5918			1.65268
$729$		0			0
$730$	14.2434			0.527171
$731$	−1.22480	−	6.94620i	−0.0453009	−	0.256914i
$732$		0			0
$733$	−31.5988	+	11.5010i	−1.16713	+	0.424800i	−0.851638	−	0.524130i	$-0.824391\pi$
$733$	−31.5988	+	11.5010i	−1.16713	+	0.424800i	−0.315489	+	0.948929i	$0.602169\pi$
$734$	−59.3930	−	49.8366i	−2.19223	−	1.83950i
$735$		0			0
$736$	0.203140	+	0.0739371i	0.00748786	+	0.00272536i
$737$	10.0952	+	17.4854i	0.371862	+	0.644084i
$738$		0			0
$739$	6.47268	−	11.2110i	0.238101	−	0.412403i	−0.722068	−	0.691822i	$-0.756808\pi$
$739$	6.47268	−	11.2110i	0.238101	−	0.412403i	0.960169	+	0.279418i	$0.0901417\pi$
$740$	−98.1648	+	82.3700i	−3.60861	+	3.02798i
$741$		0			0
$742$	7.29220	−	41.3561i	0.267705	−	1.51823i
$743$	0.0152687	−	0.0865933i	0.000560156	−	0.00317680i	−0.984526	−	0.175236i	$-0.943931\pi$
$743$	0.0152687	−	0.0865933i	0.000560156	−	0.00317680i	0.985087	+	0.172060i	$0.0550422\pi$
$744$		0			0
$745$	−17.2611	+	14.4837i	−0.632396	+	0.530643i
$746$	−17.7481	+	30.7406i	−0.649803	+	1.12549i
$747$		0			0
$748$	17.8518	+	30.9202i	0.652727	+	1.13056i
$749$	35.5906	+	12.9539i	1.30045	+	0.473325i
$750$		0			0
$751$	38.2226	+	32.0725i	1.39476	+	1.17034i	0.963369	+	0.268179i	$0.0864220\pi$
$751$	38.2226	+	32.0725i	1.39476	+	1.17034i	0.431392	+	0.902164i	$0.358022\pi$
$752$	−22.5752	+	8.21670i	−0.823233	+	0.299632i
$753$		0			0
$754$	3.61201	+	20.4847i	0.131542	+	0.746011i
$755$	14.9423			0.543806
$756$		0			0
$757$	−11.8679			−0.431348			−0.215674	−	0.976465i	$-0.569195\pi$
$757$	−11.8679			−0.431348			−0.215674	+	0.976465i	$0.569195\pi$
$758$	0.427214	+	2.42285i	0.0155171	+	0.0880020i
$759$		0			0
$760$	30.4406	−	11.0795i	1.10420	−	0.401894i
$761$	−2.90354	−	2.43636i	−0.105253	−	0.0883180i	0.588642	−	0.808394i	$-0.299663\pi$
$761$	−2.90354	−	2.43636i	−0.105253	−	0.0883180i	−0.693896	+	0.720076i	$0.744107\pi$
$762$		0			0
$763$	14.3920	+	5.23825i	0.521024	+	0.189637i
$764$	−22.1247	−	38.3211i	−0.800444	−	1.38641i
$765$		0			0
$766$	5.05978	−	8.76379i	0.182817	−	0.316649i
$767$	4.23935	−	3.55724i	0.153074	−	0.128444i
$768$		0			0
$769$	1.08869	−	6.17425i	0.0392591	−	0.222649i	−0.958866	−	0.283860i	$-0.908385\pi$
$769$	1.08869	−	6.17425i	0.0392591	−	0.222649i	0.998125	+	0.0612105i	$0.0194961\pi$
$770$	−12.0036	+	68.0756i	−0.432578	+	2.45327i
$771$		0			0
$772$	3.54375	−	2.97356i	0.127542	−	0.107021i
$773$	−0.647678	+	1.12181i	−0.0232954	+	0.0403487i	−0.877438	−	0.479690i	$-0.840749\pi$
$773$	−0.647678	+	1.12181i	−0.0232954	+	0.0403487i	0.854143	+	0.520039i	$0.174082\pi$
$774$		0			0
$775$	−17.3119	−	29.9850i	−0.621861	−	1.07709i
$776$	50.1102	+	18.2386i	1.79885	+	0.654728i
$777$		0			0
$778$	29.2205	+	24.5189i	1.04761	+	0.879046i
$779$	9.62499	−	3.50321i	0.344851	−	0.125516i
$780$		0			0

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.426791 + 2.42045i) q^{2} +(-3.79704 + 1.38201i) q^{4} +(2.35962 + 1.97995i) q^{5} +(2.49833 + 0.909318i) q^{7} +(-2.50784 - 4.34371i) q^{8} +O(q^{10})\)	\(q+(0.426791 + 2.42045i) q^{2} +(-3.79704 + 1.38201i) q^{4} +(2.35962 + 1.97995i) q^{5} +(2.49833 + 0.909318i) q^{7} +(-2.50784 - 4.34371i) q^{8} +(-3.78532 + 6.55636i) q^{10} +(2.63086 - 2.20755i) q^{11} +(-0.580672 + 3.29315i) q^{13} +(-1.13469 + 6.43517i) q^{14} +(3.25265 - 2.72930i) q^{16} +(1.28641 - 2.22813i) q^{17} +(1.04838 + 1.81585i) q^{19} +(-11.6959 - 4.25696i) q^{20} +(6.46609 + 5.42570i) q^{22} +(0.502213 - 0.182791i) q^{23} +(0.779336 + 4.41984i) q^{25} -8.21874 q^{26} -10.7430 q^{28} +(-0.439485 - 2.49244i) q^{29} +(-7.24945 + 2.63858i) q^{31} +(0.309858 + 0.260001i) q^{32} +(5.94209 + 2.16275i) q^{34} +(4.09470 + 7.09222i) q^{35} +(5.14783 - 8.91631i) q^{37} +(-3.94774 + 3.31254i) q^{38} +(2.68280 - 15.2149i) q^{40} +(0.848272 - 4.81079i) q^{41} +(2.10010 - 1.76220i) q^{43} +(-6.93862 + 12.0180i) q^{44} +(0.656775 + 1.13757i) q^{46} +(-5.31678 - 1.93515i) q^{47} +(0.0524824 + 0.0440380i) q^{49} +(-10.3654 + 3.77269i) q^{50} +(-2.34634 - 13.3067i) q^{52} -6.42657 q^{53} +10.5787 q^{55} +(-2.31560 - 13.1324i) q^{56} +(5.84527 - 2.12750i) q^{58} +(-1.26777 - 1.06378i) q^{59} +(-13.5055 - 4.91558i) q^{61} +(-9.48056 - 16.4208i) q^{62} +(3.74896 - 6.49338i) q^{64} +(-7.89046 + 6.62088i) q^{65} +(-1.02087 + 5.78967i) q^{67} +(-1.80526 + 10.2381i) q^{68} +(-15.4188 + 12.9379i) q^{70} +(7.40813 - 12.8313i) q^{71} +(-0.940699 - 1.62934i) q^{73} +(23.7785 + 8.65467i) q^{74} +(-6.49027 - 5.44599i) q^{76} +(8.58012 - 3.12291i) q^{77} +(2.98562 + 16.9323i) q^{79} +13.0789 q^{80} +12.0063 q^{82} +(-0.689172 - 3.90849i) q^{83} +(7.44702 - 2.71049i) q^{85} +(5.16161 + 4.33111i) q^{86} +(-16.1867 - 5.89149i) q^{88} +(2.54940 + 4.41569i) q^{89} +(-4.44523 + 7.69937i) q^{91} +(-1.65431 + 1.38813i) q^{92} +(2.41478 - 13.6949i) q^{94} +(-1.12152 + 6.36046i) q^{95} +(-8.14449 + 6.83404i) q^{97} +(-0.0841927 + 0.145826i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8} - 6 q^{10} - 15 q^{11} - 3 q^{13} - 21 q^{14} + 9 q^{16} - 9 q^{17} - 12 q^{19} - 3 q^{20} + 33 q^{22} + 15 q^{23} - 12 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} - 12 q^{31} - 27 q^{32} + 27 q^{34} + 30 q^{35} - 3 q^{37} - 39 q^{38} + 24 q^{40} - 39 q^{41} + 24 q^{43} - 33 q^{44} + 3 q^{46} - 42 q^{47} - 30 q^{49} - 15 q^{50} - 45 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} - 30 q^{58} + 15 q^{59} - 3 q^{61} - 30 q^{62} - 6 q^{64} - 6 q^{65} - 3 q^{67} + 36 q^{68} - 75 q^{70} - 12 q^{73} + 60 q^{74} + 30 q^{76} + 33 q^{77} + 33 q^{79} + 42 q^{80} - 42 q^{82} - 33 q^{83} - 18 q^{85} - 30 q^{86} - 42 q^{88} - 9 q^{89} - 18 q^{91} + 33 q^{92} - 66 q^{94} + 12 q^{95} + 15 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8 - 6 * q^10 - 15 * q^11 - 3 * q^13 - 21 * q^14 + 9 * q^16 - 9 * q^17 - 12 * q^19 - 3 * q^20 + 33 * q^22 + 15 * q^23 - 12 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 - 12 * q^31 - 27 * q^32 + 27 * q^34 + 30 * q^35 - 3 * q^37 - 39 * q^38 + 24 * q^40 - 39 * q^41 + 24 * q^43 - 33 * q^44 + 3 * q^46 - 42 * q^47 - 30 * q^49 - 15 * q^50 - 45 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 - 30 * q^58 + 15 * q^59 - 3 * q^61 - 30 * q^62 - 6 * q^64 - 6 * q^65 - 3 * q^67 + 36 * q^68 - 75 * q^70 - 12 * q^73 + 60 * q^74 + 30 * q^76 + 33 * q^77 + 33 * q^79 + 42 * q^80 - 42 * q^82 - 33 * q^83 - 18 * q^85 - 30 * q^86 - 42 * q^88 - 9 * q^89 - 18 * q^91 + 33 * q^92 - 66 * q^94 + 12 * q^95 + 15 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

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Database

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