LMFDB - Embedded newform 1458.2.c.g.973.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1458,2,Mod(487,1458)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1458, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("1458.487");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1458 = 2 \cdot 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1458.c (of order $3$, degree $2$, 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:	$11.6421886147$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
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} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			973.5
Root			$0.500000 + 1.74095i$ of defining polynomial
Character	$\chi$	$=$	1458.973
Dual form			1458.2.c.g.487.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.58406 - 2.74367i) q^{5} +(-1.84286 - 3.19193i) q^{7} -1.00000 q^{8} +3.16812 q^{10} +(-1.14253 - 1.97893i) q^{11} +(-1.55014 + 2.68492i) q^{13} +(1.84286 - 3.19193i) q^{14} +(-0.500000 - 0.866025i) q^{16} -1.72576 q^{17} -3.39480 q^{19} +(1.58406 + 2.74367i) q^{20} +(1.14253 - 1.97893i) q^{22} +(-1.67654 + 2.90386i) q^{23} +(-2.51848 - 4.36213i) q^{25} -3.10027 q^{26} +3.68572 q^{28} +(-0.292722 - 0.507009i) q^{29} +(2.31899 - 4.01660i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.862878 - 1.49455i) q^{34} -11.6768 q^{35} -7.30720 q^{37} +(-1.69740 - 2.93998i) q^{38} +(-1.58406 + 2.74367i) q^{40} +(-3.54026 + 6.13191i) q^{41} +(-0.828957 - 1.43580i) q^{43} +2.28507 q^{44} -3.35309 q^{46} +(-1.92599 - 3.33591i) q^{47} +(-3.29226 + 5.70237i) q^{49} +(2.51848 - 4.36213i) q^{50} +(-1.55014 - 2.68492i) q^{52} +2.58267 q^{53} -7.23936 q^{55} +(1.84286 + 3.19193i) q^{56} +(0.292722 - 0.507009i) q^{58} +(-4.83159 + 8.36857i) q^{59} +(-6.54567 - 11.3374i) q^{61} +4.63798 q^{62} +1.00000 q^{64} +(4.91101 + 8.50613i) q^{65} +(4.30438 - 7.45541i) q^{67} +(0.862878 - 1.49455i) q^{68} +(-5.83839 - 10.1124i) q^{70} -1.98746 q^{71} +10.6474 q^{73} +(-3.65360 - 6.32822i) q^{74} +(1.69740 - 2.93998i) q^{76} +(-4.21106 + 7.29377i) q^{77} +(-7.04660 - 12.2051i) q^{79} -3.16812 q^{80} -7.08052 q^{82} +(-1.54921 - 2.68331i) q^{83} +(-2.73370 + 4.73490i) q^{85} +(0.828957 - 1.43580i) q^{86} +(1.14253 + 1.97893i) q^{88} +17.3460 q^{89} +11.4267 q^{91} +(-1.67654 - 2.90386i) q^{92} +(1.92599 - 3.33591i) q^{94} +(-5.37755 + 9.31420i) q^{95} +(-4.59558 - 7.95978i) q^{97} -6.58452 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 12 q^{8} + 6 q^{10} + 3 q^{11} - 9 q^{13} + 6 q^{14} - 6 q^{16} - 12 q^{17} + 18 q^{19} + 3 q^{20} - 3 q^{22} - 3 q^{23} - 15 q^{25} - 18 q^{26} + 12 q^{28}+ \cdots - 24 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 12 * q^8 + 6 * q^10 + 3 * q^11 - 9 * q^13 + 6 * q^14 - 6 * q^16 - 12 * q^17 + 18 * q^19 + 3 * q^20 - 3 * q^22 - 3 * q^23 - 15 * q^25 - 18 * q^26 + 12 * q^28 + 3 * q^29 - 12 * q^31 + 6 * q^32 - 6 * q^34 + 6 * q^35 + 30 * q^37 + 9 * q^38 - 3 * q^40 + 3 * q^41 - 12 * q^43 - 6 * q^44 - 6 * q^46 - 9 * q^47 - 12 * q^49 + 15 * q^50 - 9 * q^52 + 12 * q^53 + 18 * q^55 + 6 * q^56 - 3 * q^58 - 3 * q^59 - 12 * q^61 - 24 * q^62 + 12 * q^64 - 3 * q^65 - 21 * q^67 + 6 * q^68 + 3 * q^70 + 24 * q^71 + 42 * q^73 + 15 * q^74 - 9 * q^76 - 3 * q^77 - 6 * q^80 + 6 * q^82 - 27 * q^83 + 12 * q^86 - 3 * q^88 + 24 * q^89 + 12 * q^91 - 3 * q^92 + 9 * q^94 - 30 * q^95 - 18 * q^97 - 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1458\mathbb{Z}\right)^\times$.

$n$	$731$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.58406	−	2.74367i	0.708412	−	1.22701i	−0.257034	−	0.966402i	$-0.582745\pi$
$5$	1.58406	−	2.74367i	0.708412	−	1.22701i	0.965446	−	0.260603i	$-0.0839215\pi$
$6$		0			0
$7$	−1.84286	−	3.19193i	−0.696535	−	1.20643i	−0.969660	−	0.244456i	$-0.921391\pi$
$7$	−1.84286	−	3.19193i	−0.696535	−	1.20643i	0.273125	−	0.961979i	$-0.411943\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	3.16812			1.00185
$11$	−1.14253	−	1.97893i	−0.344487	−	0.596669i	0.640774	−	0.767730i	$-0.278614\pi$
$11$	−1.14253	−	1.97893i	−0.344487	−	0.596669i	−0.985260	+	0.171061i	$0.945280\pi$
$12$		0			0
$13$	−1.55014	+	2.68492i	−0.429931	+	0.744662i	−0.996867	−	0.0791000i	$-0.974795\pi$
$13$	−1.55014	+	2.68492i	−0.429931	+	0.744662i	0.566936	+	0.823762i	$0.308129\pi$
$14$	1.84286	−	3.19193i	0.492525	−	0.853078i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.72576			−0.418557			−0.209279	−	0.977856i	$-0.567112\pi$
$17$	−1.72576			−0.418557			−0.209279	+	0.977856i	$0.567112\pi$
$18$		0			0
$19$	−3.39480			−0.778820			−0.389410	−	0.921065i	$-0.627321\pi$
$19$	−3.39480			−0.778820			−0.389410	+	0.921065i	$0.627321\pi$
$20$	1.58406	+	2.74367i	0.354206	+	0.613503i
$21$		0			0
$22$	1.14253	−	1.97893i	0.243589	−	0.421909i
$23$	−1.67654	+	2.90386i	−0.349584	+	0.605497i	−0.986175	−	0.165704i	$-0.947010\pi$
$23$	−1.67654	+	2.90386i	−0.349584	+	0.605497i	0.636592	+	0.771201i	$0.280344\pi$
$24$		0			0
$25$	−2.51848	−	4.36213i	−0.503695	−	0.872426i
$26$	−3.10027			−0.608014
$27$		0			0
$28$	3.68572			0.696535
$29$	−0.292722	−	0.507009i	−0.0543571	−	0.0941493i	0.837566	−	0.546335i	$-0.183978\pi$
$29$	−0.292722	−	0.507009i	−0.0543571	−	0.0941493i	−0.891924	+	0.452186i	$0.850644\pi$
$30$		0			0
$31$	2.31899	−	4.01660i	0.416502	−	0.721403i	−0.579082	−	0.815269i	$-0.696589\pi$
$31$	2.31899	−	4.01660i	0.416502	−	0.721403i	0.995585	+	0.0938656i	$0.0299224\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−0.862878	−	1.49455i	−0.147982	−	0.256313i
$35$	−11.6768			−1.97374
$36$		0			0
$37$	−7.30720			−1.20130			−0.600648	−	0.799514i	$-0.705091\pi$
$37$	−7.30720			−1.20130			−0.600648	+	0.799514i	$0.705091\pi$
$38$	−1.69740	−	2.93998i	−0.275354	−	0.476928i
$39$		0			0
$40$	−1.58406	+	2.74367i	−0.250462	+	0.433812i
$41$	−3.54026	+	6.13191i	−0.552895	+	0.957643i	0.445169	+	0.895447i	$0.353144\pi$
$41$	−3.54026	+	6.13191i	−0.552895	+	0.957643i	−0.998064	+	0.0621961i	$0.980190\pi$
$42$		0			0
$43$	−0.828957	−	1.43580i	−0.126415	−	0.218957i	0.795870	−	0.605467i	$-0.207014\pi$
$43$	−0.828957	−	1.43580i	−0.126415	−	0.218957i	−0.922285	+	0.386510i	$0.873680\pi$
$44$	2.28507			0.344487
$45$		0			0
$46$	−3.35309			−0.494386
$47$	−1.92599	−	3.33591i	−0.280935	−	0.486593i	0.690681	−	0.723160i	$-0.257311\pi$
$47$	−1.92599	−	3.33591i	−0.280935	−	0.486593i	−0.971615	+	0.236567i	$0.923978\pi$
$48$		0			0
$49$	−3.29226	+	5.70237i	−0.470323	+	0.814624i
$50$	2.51848	−	4.36213i	0.356166	−	0.616898i
$51$		0			0
$52$	−1.55014	−	2.68492i	−0.214965	−	0.372331i
$53$	2.58267			0.354757			0.177379	−	0.984143i	$-0.443238\pi$
$53$	2.58267			0.354757			0.177379	+	0.984143i	$0.443238\pi$
$54$		0			0
$55$	−7.23936			−0.976155
$56$	1.84286	+	3.19193i	0.246262	+	0.426539i
$57$		0			0
$58$	0.292722	−	0.507009i	0.0384363	−	0.0665736i
$59$	−4.83159	+	8.36857i	−0.629020	+	1.08949i	0.358729	+	0.933442i	$0.383210\pi$
$59$	−4.83159	+	8.36857i	−0.629020	+	1.08949i	−0.987749	+	0.156053i	$0.950123\pi$
$60$		0			0
$61$	−6.54567	−	11.3374i	−0.838087	−	1.45161i	−0.891492	−	0.453036i	$-0.850341\pi$
$61$	−6.54567	−	11.3374i	−0.838087	−	1.45161i	0.0534049	−	0.998573i	$-0.482993\pi$
$62$	4.63798			0.589023
$63$		0			0
$64$	1.00000			0.125000
$65$	4.91101	+	8.50613i	0.609136	+	1.05506i
$66$		0			0
$67$	4.30438	−	7.45541i	0.525864	−	0.910823i	−0.473682	−	0.880696i	$-0.657075\pi$
$67$	4.30438	−	7.45541i	0.525864	−	0.910823i	0.999546	−	0.0301270i	$-0.00959118\pi$
$68$	0.862878	−	1.49455i	0.104639	−	0.181241i
$69$		0			0
$70$	−5.83839	−	10.1124i	−0.697821	−	1.20866i
$71$	−1.98746			−0.235869			−0.117934	−	0.993021i	$-0.537627\pi$
$71$	−1.98746			−0.235869			−0.117934	+	0.993021i	$0.537627\pi$
$72$		0			0
$73$	10.6474			1.24619			0.623094	−	0.782147i	$-0.285876\pi$
$73$	10.6474			1.24619			0.623094	+	0.782147i	$0.285876\pi$
$74$	−3.65360	−	6.32822i	−0.424722	−	0.735640i
$75$		0			0
$76$	1.69740	−	2.93998i	0.194705	−	0.337239i
$77$	−4.21106	+	7.29377i	−0.479895	+	0.831202i
$78$		0			0
$79$	−7.04660	−	12.2051i	−0.792804	−	1.37318i	−0.924224	−	0.381850i	$-0.875287\pi$
$79$	−7.04660	−	12.2051i	−0.792804	−	1.37318i	0.131420	−	0.991327i	$-0.458046\pi$
$80$	−3.16812			−0.354206
$81$		0			0
$82$	−7.08052			−0.781912
$83$	−1.54921	−	2.68331i	−0.170048	−	0.294532i	0.768388	−	0.639984i	$-0.221059\pi$
$83$	−1.54921	−	2.68331i	−0.170048	−	0.294532i	−0.938436	+	0.345452i	$0.887726\pi$
$84$		0			0
$85$	−2.73370	+	4.73490i	−0.296511	+	0.513572i
$86$	0.828957	−	1.43580i	0.0893888	−	0.154826i
$87$		0			0
$88$	1.14253	+	1.97893i	0.121795	+	0.210954i
$89$	17.3460			1.83867			0.919336	−	0.393472i	$-0.128726\pi$
$89$	17.3460			1.83867			0.919336	+	0.393472i	$0.128726\pi$
$90$		0			0
$91$	11.4267			1.19785
$92$	−1.67654	−	2.90386i	−0.174792	−	0.302748i
$93$		0			0
$94$	1.92599	−	3.33591i	0.198651	−	0.344073i
$95$	−5.37755	+	9.31420i	−0.551725	+	0.955616i
$96$		0			0
$97$	−4.59558	−	7.95978i	−0.466611	−	0.808193i	0.532662	−	0.846328i	$-0.321192\pi$
$97$	−4.59558	−	7.95978i	−0.466611	−	0.808193i	−0.999273	+	0.0381347i	$0.987858\pi$
$98$	−6.58452			−0.665137
$99$		0			0
$100$	5.03695			0.503695
$101$	5.98009	+	10.3578i	0.595041	+	1.03064i	0.993541	+	0.113473i	$0.0361976\pi$
$101$	5.98009	+	10.3578i	0.595041	+	1.03064i	−0.398500	+	0.917168i	$0.630469\pi$
$102$		0			0
$103$	6.37324	−	11.0388i	0.627974	−	1.08768i	−0.359984	−	0.932958i	$-0.617218\pi$
$103$	6.37324	−	11.0388i	0.627974	−	1.08768i	0.987958	−	0.154724i	$-0.0494488\pi$
$104$	1.55014	−	2.68492i	0.152003	−	0.263278i
$105$		0			0
$106$	1.29134	+	2.23666i	0.125426	+	0.217244i
$107$	−6.09894			−0.589607			−0.294803	−	0.955558i	$-0.595254\pi$
$107$	−6.09894			−0.589607			−0.294803	+	0.955558i	$0.595254\pi$
$108$		0			0
$109$	11.2390			1.07650			0.538250	−	0.842785i	$-0.319086\pi$
$109$	11.2390			1.07650			0.538250	+	0.842785i	$0.319086\pi$
$110$	−3.61968	−	6.26947i	−0.345123	−	0.597770i
$111$		0			0
$112$	−1.84286	+	3.19193i	−0.174134	+	0.301609i
$113$	−3.51848	+	6.09418i	−0.330990	+	0.573292i	−0.982706	−	0.185171i	$-0.940716\pi$
$113$	−3.51848	+	6.09418i	−0.330990	+	0.573292i	0.651716	+	0.758463i	$0.274049\pi$
$114$		0			0
$115$	5.31149	+	9.19976i	0.495299	+	0.857882i
$116$	0.585444			0.0543571
$117$		0			0
$118$	−9.66319			−0.889568
$119$	3.18032	+	5.50848i	0.291540	+	0.504962i
$120$		0			0
$121$	2.88923	−	5.00430i	0.262658	−	0.454936i
$122$	6.54567	−	11.3374i	0.592617	−	1.02644i
$123$		0			0
$124$	2.31899	+	4.01660i	0.208251	+	0.360702i
$125$	−0.117076			−0.0104716
$126$		0			0
$127$	5.98500			0.531082			0.265541	−	0.964100i	$-0.414449\pi$
$127$	5.98500			0.531082			0.265541	+	0.964100i	$0.414449\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−4.91101	+	8.50613i	−0.430724	+	0.746037i
$131$	8.20752	−	14.2158i	0.717094	−	1.24204i	−0.245052	−	0.969510i	$-0.578805\pi$
$131$	8.20752	−	14.2158i	0.717094	−	1.24204i	0.962146	−	0.272533i	$-0.0878615\pi$
$132$		0			0
$133$	6.25613	+	10.8359i	0.542476	+	0.939595i
$134$	8.60876			0.743684
$135$		0			0
$136$	1.72576			0.147982
$137$	−0.105579	−	0.182869i	−0.00902025	−	0.0156235i	0.861480	−	0.507791i	$-0.169538\pi$
$137$	−0.105579	−	0.182869i	−0.00902025	−	0.0156235i	−0.870500	+	0.492168i	$0.836205\pi$
$138$		0			0
$139$	−1.83576	+	3.17962i	−0.155707	+	0.269692i	−0.933316	−	0.359056i	$-0.883099\pi$
$139$	−1.83576	+	3.17962i	−0.155707	+	0.269692i	0.777609	+	0.628748i	$0.216432\pi$
$140$	5.83839	−	10.1124i	0.493434	−	0.854653i
$141$		0			0
$142$	−0.993732	−	1.72119i	−0.0833921	−	0.144439i
$143$	7.08434			0.592422
$144$		0			0
$145$	−1.85475			−0.154029
$146$	5.32371	+	9.22094i	0.440594	+	0.763131i
$147$		0			0
$148$	3.65360	−	6.32822i	0.300324	−	0.520176i
$149$	7.73720	−	13.4012i	0.633856	−	1.09787i	−0.352900	−	0.935661i	$-0.614805\pi$
$149$	7.73720	−	13.4012i	0.633856	−	1.09787i	0.986756	−	0.162210i	$-0.0518621\pi$
$150$		0			0
$151$	−10.0729	−	17.4467i	−0.819718	−	1.41979i	−0.905890	−	0.423513i	$-0.860797\pi$
$151$	−10.0729	−	17.4467i	−0.819718	−	1.41979i	0.0861724	−	0.996280i	$-0.472536\pi$
$152$	3.39480			0.275354
$153$		0			0
$154$	−8.42212			−0.678673
$155$	−7.34682	−	12.7251i	−0.590111	−	1.02210i
$156$		0			0
$157$	−8.99872	+	15.5862i	−0.718176	+	1.24392i	0.243546	+	0.969889i	$0.421689\pi$
$157$	−8.99872	+	15.5862i	−0.718176	+	1.24392i	−0.961722	+	0.274028i	$0.911644\pi$
$158$	7.04660	−	12.2051i	0.560597	−	0.970983i
$159$		0			0
$160$	−1.58406	−	2.74367i	−0.125231	−	0.216906i
$161$	12.3585			0.973989
$162$		0			0
$163$	3.05289			0.239121			0.119560	−	0.992827i	$-0.461851\pi$
$163$	3.05289			0.239121			0.119560	+	0.992827i	$0.461851\pi$
$164$	−3.54026	−	6.13191i	−0.276448	−	0.478821i
$165$		0			0
$166$	1.54921	−	2.68331i	0.120242	−	0.208265i
$167$	−2.05060	+	3.55174i	−0.158680	+	0.274842i	−0.934393	−	0.356244i	$-0.884057\pi$
$167$	−2.05060	+	3.55174i	−0.158680	+	0.274842i	0.775713	+	0.631086i	$0.217390\pi$
$168$		0			0
$169$	1.69415	+	2.93435i	0.130319	+	0.225719i
$170$	−5.46739			−0.419330
$171$		0			0
$172$	1.65791			0.126415
$173$	−8.51355	−	14.7459i	−0.647273	−	1.12111i	−0.983771	−	0.179426i	$-0.942576\pi$
$173$	−8.51355	−	14.7459i	−0.647273	−	1.12111i	0.336498	−	0.941684i	$-0.390757\pi$
$174$		0			0
$175$	−9.28240	+	16.0776i	−0.701683	+	1.21535i
$176$	−1.14253	+	1.97893i	−0.0861217	+	0.149167i
$177$		0			0
$178$	8.67300	+	15.0221i	0.650069	+	1.12595i
$179$	14.5560			1.08797			0.543985	−	0.839095i	$-0.316915\pi$
$179$	14.5560			1.08797			0.543985	+	0.839095i	$0.316915\pi$
$180$		0			0
$181$	−13.0238			−0.968052			−0.484026	−	0.875054i	$-0.660826\pi$
$181$	−13.0238			−0.968052			−0.484026	+	0.875054i	$0.660826\pi$
$182$	5.71337	+	9.89585i	0.423503	+	0.733529i
$183$		0			0
$184$	1.67654	−	2.90386i	0.123596	−	0.214075i
$185$	−11.5750	+	20.0485i	−0.851013	+	1.47400i
$186$		0			0
$187$	1.97173	+	3.41514i	0.144187	+	0.249740i
$188$	3.85198			0.280935
$189$		0			0
$190$	−10.7551			−0.780258
$191$	1.80144	+	3.12018i	0.130347	+	0.225768i	0.923811	−	0.382850i	$-0.125057\pi$
$191$	1.80144	+	3.12018i	0.130347	+	0.225768i	−0.793463	+	0.608618i	$0.791724\pi$
$192$		0			0
$193$	−0.737435	+	1.27727i	−0.0530817	+	0.0919402i	−0.891345	−	0.453325i	$-0.850238\pi$
$193$	−0.737435	+	1.27727i	−0.0530817	+	0.0919402i	0.838264	+	0.545265i	$0.183571\pi$
$194$	4.59558	−	7.95978i	0.329944	−	0.571479i
$195$		0			0
$196$	−3.29226	−	5.70237i	−0.235162	−	0.407312i
$197$	−2.53862			−0.180869			−0.0904346	−	0.995902i	$-0.528826\pi$
$197$	−2.53862			−0.180869			−0.0904346	+	0.995902i	$0.528826\pi$
$198$		0			0
$199$	−1.85178			−0.131269			−0.0656347	−	0.997844i	$-0.520907\pi$
$199$	−1.85178			−0.131269			−0.0656347	+	0.997844i	$0.520907\pi$
$200$	2.51848	+	4.36213i	0.178083	+	0.308449i
$201$		0			0
$202$	−5.98009	+	10.3578i	−0.420758	+	0.728774i
$203$	−1.07889	+	1.86869i	−0.0757233	+	0.131157i
$204$		0			0
$205$	11.2159	+	19.4266i	0.783356	+	1.35681i
$206$	12.7465			0.888089
$207$		0			0
$208$	3.10027			0.214965
$209$	3.87867	+	6.71805i	0.268293	+	0.464697i
$210$		0			0
$211$	9.49415	−	16.4443i	0.653604	−	1.13208i	−0.328638	−	0.944456i	$-0.606590\pi$
$211$	9.49415	−	16.4443i	0.653604	−	1.13208i	0.982242	−	0.187619i	$-0.0600771\pi$
$212$	−1.29134	+	2.23666i	−0.0886893	+	0.153614i
$213$		0			0
$214$	−3.04947	−	5.28184i	−0.208457	−	0.361059i
$215$	−5.25247			−0.358215
$216$		0			0
$217$	−17.0943			−1.16043
$218$	5.61950	+	9.73326i	0.380600	+	0.659219i
$219$		0			0
$220$	3.61968	−	6.26947i	0.244039	−	0.422687i
$221$	2.67516	−	4.63351i	0.179951	−	0.311684i
$222$		0			0
$223$	3.62718	+	6.28246i	0.242894	+	0.420705i	0.961537	−	0.274674i	$-0.0885699\pi$
$223$	3.62718	+	6.28246i	0.242894	+	0.420705i	−0.718643	+	0.695379i	$0.755237\pi$
$224$	−3.68572			−0.246262
$225$		0			0
$226$	−7.03695			−0.468091
$227$	−14.2636	−	24.7053i	−0.946708	−	1.63975i	−0.752296	−	0.658825i	$-0.771054\pi$
$227$	−14.2636	−	24.7053i	−0.946708	−	1.63975i	−0.194412	−	0.980920i	$-0.562280\pi$
$228$		0			0
$229$	−0.927691	+	1.60681i	−0.0613036	+	0.106181i	−0.895048	−	0.445969i	$-0.852859\pi$
$229$	−0.927691	+	1.60681i	−0.0613036	+	0.106181i	0.833745	+	0.552150i	$0.186192\pi$
$230$	−5.31149	+	9.19976i	−0.350229	+	0.606614i
$231$		0			0
$232$	0.292722	+	0.507009i	0.0192181	+	0.0332868i
$233$	−8.53469			−0.559126			−0.279563	−	0.960127i	$-0.590190\pi$
$233$	−8.53469			−0.559126			−0.279563	+	0.960127i	$0.590190\pi$
$234$		0			0
$235$	−12.2035			−0.796070
$236$	−4.83159	−	8.36857i	−0.314510	−	0.544747i
$237$		0			0
$238$	−3.18032	+	5.50848i	−0.206150	+	0.357062i
$239$	−3.64398	+	6.31156i	−0.235710	+	0.408261i	−0.959479	−	0.281781i	$-0.909075\pi$
$239$	−3.64398	+	6.31156i	−0.235710	+	0.408261i	0.723769	+	0.690042i	$0.242408\pi$
$240$		0			0
$241$	0.667459	+	1.15607i	0.0429948	+	0.0744692i	0.886722	−	0.462303i	$-0.152977\pi$
$241$	0.667459	+	1.15607i	0.0429948	+	0.0744692i	−0.843727	+	0.536772i	$0.819643\pi$
$242$	5.77847			0.371454
$243$		0			0
$244$	13.0913			0.838087
$245$	10.4303	+	18.0657i	0.666365	+	1.15418i
$246$		0			0
$247$	5.26240	−	9.11475i	0.334839	−	0.579957i
$248$	−2.31899	+	4.01660i	−0.147256	+	0.255055i
$249$		0			0
$250$	−0.0585380	−	0.101391i	−0.00370227	−	0.00641251i
$251$	2.87856			0.181693			0.0908466	−	0.995865i	$-0.471043\pi$
$251$	2.87856			0.181693			0.0908466	+	0.995865i	$0.471043\pi$
$252$		0			0
$253$	7.66203			0.481708
$254$	2.99250	+	5.18316i	0.187766	+	0.325220i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.8890	+	22.3243i	−0.803991	+	1.39255i	0.112979	+	0.993597i	$0.463961\pi$
$257$	−12.8890	+	22.3243i	−0.803991	+	1.39255i	−0.916970	+	0.398956i	$0.869373\pi$
$258$		0			0
$259$	13.4661	+	23.3240i	0.836745	+	1.44929i
$260$	−9.82203			−0.609136
$261$		0			0
$262$	16.4150			1.01412
$263$	−7.53485	−	13.0507i	−0.464619	−	0.804743i	0.534566	−	0.845127i	$-0.320475\pi$
$263$	−7.53485	−	13.0507i	−0.464619	−	0.804743i	−0.999184	+	0.0403840i	$0.987142\pi$
$264$		0			0
$265$	4.09110	−	7.08599i	0.251314	−	0.435289i
$266$	−6.25613	+	10.8359i	−0.383588	+	0.664394i
$267$		0			0
$268$	4.30438	+	7.45541i	0.262932	+	0.455411i
$269$	−16.0615			−0.979286			−0.489643	−	0.871923i	$-0.662873\pi$
$269$	−16.0615			−0.979286			−0.489643	+	0.871923i	$0.662873\pi$
$270$		0			0
$271$	9.41446			0.571888			0.285944	−	0.958246i	$-0.407693\pi$
$271$	9.41446			0.571888			0.285944	+	0.958246i	$0.407693\pi$
$272$	0.862878	+	1.49455i	0.0523196	+	0.0906203i
$273$		0			0
$274$	0.105579	−	0.182869i	0.00637828	−	0.0110475i
$275$	−5.75489	+	9.96776i	−0.347033	+	0.601079i
$276$		0			0
$277$	−2.78738	−	4.82788i	−0.167477	−	0.290079i	0.770055	−	0.637978i	$-0.220229\pi$
$277$	−2.78738	−	4.82788i	−0.167477	−	0.290079i	−0.937532	+	0.347898i	$0.886895\pi$
$278$	−3.67151			−0.220203
$279$		0			0
$280$	11.6768			0.697821
$281$	14.0024	+	24.2529i	0.835313	+	1.44680i	0.893775	+	0.448515i	$0.148047\pi$
$281$	14.0024	+	24.2529i	0.835313	+	1.44680i	−0.0584622	+	0.998290i	$0.518620\pi$
$282$		0			0
$283$	−3.07761	+	5.33058i	−0.182945	+	0.316870i	−0.942882	−	0.333127i	$-0.891896\pi$
$283$	−3.07761	+	5.33058i	−0.182945	+	0.316870i	0.759937	+	0.649996i	$0.225230\pi$
$284$	0.993732	−	1.72119i	0.0589671	−	0.102134i
$285$		0			0
$286$	3.54217	+	6.13522i	0.209453	+	0.362783i
$287$	26.0968			1.54044
$288$		0			0
$289$	−14.0218			−0.824810
$290$	−0.927377	−	1.60626i	−0.0544575	−	0.0943231i
$291$		0			0
$292$	−5.32371	+	9.22094i	−0.311547	+	0.539615i
$293$	1.16755	−	2.02226i	0.0682090	−	0.118141i	−0.829904	−	0.557906i	$-0.811605\pi$
$293$	1.16755	−	2.02226i	0.0682090	−	0.118141i	0.898113	+	0.439765i	$0.144938\pi$
$294$		0			0
$295$	15.3070	+	26.5126i	0.891211	+	1.54362i
$296$	7.30720			0.424722
$297$		0			0
$298$	15.4744			0.896408
$299$	−5.19775	−	9.00276i	−0.300594	−	0.520643i
$300$		0			0
$301$	−3.05530	+	5.29194i	−0.176105	+	0.305022i
$302$	10.0729	−	17.4467i	0.579628	−	1.00395i
$303$		0			0
$304$	1.69740	+	2.93998i	0.0973525	+	0.168619i
$305$	−41.4749			−2.37484
$306$		0			0
$307$	6.82529			0.389540			0.194770	−	0.980849i	$-0.437604\pi$
$307$	6.82529			0.389540			0.194770	+	0.980849i	$0.437604\pi$
$308$	−4.21106	−	7.29377i	−0.239947	−	0.415601i
$309$		0			0
$310$	7.34682	−	12.7251i	0.417271	−	0.722735i
$311$	4.29761	−	7.44368i	0.243695	−	0.422092i	−0.718069	−	0.695972i	$-0.754974\pi$
$311$	4.29761	−	7.44368i	0.243695	−	0.422092i	0.961764	+	0.273880i	$0.0883071\pi$
$312$		0			0
$313$	10.8344	+	18.7658i	0.612399	+	1.06071i	0.990835	+	0.135079i	$0.0431288\pi$
$313$	10.8344	+	18.7658i	0.612399	+	1.06071i	−0.378436	+	0.925628i	$0.623538\pi$
$314$	−17.9974			−1.01565
$315$		0			0
$316$	14.0932			0.792804
$317$	17.6600	+	30.5880i	0.991883	+	1.71799i	0.606059	+	0.795420i	$0.292750\pi$
$317$	17.6600	+	30.5880i	0.991883	+	1.71799i	0.385824	+	0.922572i	$0.373917\pi$
$318$		0			0
$319$	−0.668890	+	1.15855i	−0.0374506	+	0.0648664i
$320$	1.58406	−	2.74367i	0.0885515	−	0.153376i
$321$		0			0
$322$	6.17927	+	10.7028i	0.344357	+	0.596444i
$323$	5.85859			0.325981
$324$		0			0
$325$	15.6159			0.866217
$326$	1.52645	+	2.64388i	0.0845420	+	0.146431i
$327$		0			0
$328$	3.54026	−	6.13191i	0.195478	−	0.338578i
$329$	−7.09866	+	12.2952i	−0.391362	+	0.677859i
$330$		0			0
$331$	12.9068	+	22.3553i	0.709423	+	1.22876i	0.965071	+	0.261987i	$0.0843778\pi$
$331$	12.9068	+	22.3553i	0.709423	+	1.22876i	−0.255648	+	0.966770i	$0.582289\pi$
$332$	3.09842			0.170048
$333$		0			0
$334$	−4.10119			−0.224407
$335$	−13.6368	−	23.6196i	−0.745057	−	1.29048i
$336$		0			0
$337$	1.69229	−	2.93114i	0.0921851	−	0.159669i	−0.816245	−	0.577706i	$-0.803948\pi$
$337$	1.69229	−	2.93114i	0.0921851	−	0.159669i	0.908430	+	0.418036i	$0.137282\pi$
$338$	−1.69415	+	2.93435i	−0.0921495	+	0.159608i
$339$		0			0
$340$	−2.73370	−	4.73490i	−0.148255	−	0.256786i
$341$	−10.5981			−0.573919
$342$		0			0
$343$	−1.53133			−0.0826839
$344$	0.828957	+	1.43580i	0.0446944	+	0.0774130i
$345$		0			0
$346$	8.51355	−	14.7459i	0.457691	−	0.792744i
$347$	−8.10001	+	14.0296i	−0.434831	+	0.753150i	−0.997282	−	0.0736809i	$-0.976525\pi$
$347$	−8.10001	+	14.0296i	−0.434831	+	0.753150i	0.562450	+	0.826831i	$0.309859\pi$
$348$		0			0
$349$	−2.24627	−	3.89065i	−0.120240	−	0.208261i	0.799622	−	0.600503i	$-0.205033\pi$
$349$	−2.24627	−	3.89065i	−0.120240	−	0.208261i	−0.919862	+	0.392242i	$0.871700\pi$
$350$	−18.5648			−0.992330
$351$		0			0
$352$	−2.28507			−0.121795
$353$	−11.6133	−	20.1149i	−0.618116	−	1.07061i	−0.989829	−	0.142260i	$-0.954563\pi$
$353$	−11.6133	−	20.1149i	−0.618116	−	1.07061i	0.371714	−	0.928347i	$-0.378770\pi$
$354$		0			0
$355$	−3.14826	+	5.45294i	−0.167092	+	0.289412i
$356$	−8.67300	+	15.0221i	−0.459668	+	0.796169i
$357$		0			0
$358$	7.27802	+	12.6059i	0.384656	+	0.666243i
$359$	11.5539			0.609794			0.304897	−	0.952385i	$-0.401378\pi$
$359$	11.5539			0.609794			0.304897	+	0.952385i	$0.401378\pi$
$360$		0			0
$361$	−7.47535			−0.393440
$362$	−6.51190	−	11.2789i	−0.342258	−	0.592808i
$363$		0			0
$364$	−5.71337	+	9.89585i	−0.299462	+	0.518683i
$365$	16.8661	−	29.2130i	0.882814	−	1.52908i
$366$		0			0
$367$	−7.78486	−	13.4838i	−0.406366	−	0.703847i	0.588113	−	0.808779i	$-0.299871\pi$
$367$	−7.78486	−	13.4838i	−0.406366	−	0.703847i	−0.994479	+	0.104932i	$0.966538\pi$
$368$	3.35309			0.174792
$369$		0			0
$370$	−23.1500			−1.20351
$371$	−4.75950	−	8.24370i	−0.247101	−	0.427991i
$372$		0			0
$373$	4.87863	−	8.45004i	0.252606	−	0.437526i	−0.711637	−	0.702548i	$-0.752046\pi$
$373$	4.87863	−	8.45004i	0.252606	−	0.437526i	0.964243	+	0.265021i	$0.0853790\pi$
$374$	−1.97173	+	3.41514i	−0.101956	+	0.176593i
$375$		0			0
$376$	1.92599	+	3.33591i	0.0993254	+	0.172037i
$377$	1.81504			0.0934792
$378$		0			0
$379$	−18.7904			−0.965197			−0.482599	−	0.875842i	$-0.660307\pi$
$379$	−18.7904			−0.965197			−0.482599	+	0.875842i	$0.660307\pi$
$380$	−5.37755	−	9.31420i	−0.275863	−	0.477808i
$381$		0			0
$382$	−1.80144	+	3.12018i	−0.0921695	+	0.159642i
$383$	15.3840	−	26.6459i	0.786086	−	1.36154i	−0.142262	−	0.989829i	$-0.545437\pi$
$383$	15.3840	−	26.6459i	0.786086	−	1.36154i	0.928348	−	0.371712i	$-0.121229\pi$
$384$		0			0
$385$	13.3411	+	23.1075i	0.679926	+	1.17767i
$386$	−1.47487			−0.0750689
$387$		0			0
$388$	9.19117			0.466611
$389$	14.8003	+	25.6349i	0.750407	+	1.29974i	0.947626	+	0.319383i	$0.103476\pi$
$389$	14.8003	+	25.6349i	0.750407	+	1.29974i	−0.197219	+	0.980359i	$0.563191\pi$
$390$		0			0
$391$	2.89330	−	5.01135i	0.146321	−	0.253435i
$392$	3.29226	−	5.70237i	0.166284	−	0.288013i
$393$		0			0
$394$	−1.26931	−	2.19851i	−0.0639469	−	0.110759i
$395$	−44.6489			−2.24653
$396$		0			0
$397$	16.1427			0.810178			0.405089	−	0.914277i	$-0.367241\pi$
$397$	16.1427			0.810178			0.405089	+	0.914277i	$0.367241\pi$
$398$	−0.925891	−	1.60369i	−0.0464107	−	0.0803858i
$399$		0			0
$400$	−2.51848	+	4.36213i	−0.125924	+	0.218107i
$401$	12.6812	−	21.9645i	0.633268	−	1.09685i	−0.353611	−	0.935393i	$-0.615046\pi$
$401$	12.6812	−	21.9645i	0.633268	−	1.09685i	0.986879	−	0.161460i	$-0.0516204\pi$
$402$		0			0
$403$	7.18950	+	12.4526i	0.358134	+	0.620307i
$404$	−11.9602			−0.595041
$405$		0			0
$406$	−2.15778			−0.107089
$407$	8.34872	+	14.4604i	0.413831	+	0.716776i
$408$		0			0
$409$	11.3857	−	19.7205i	0.562984	−	0.975118i	−0.434250	−	0.900793i	$-0.642986\pi$
$409$	11.3857	−	19.7205i	0.562984	−	0.975118i	0.997234	−	0.0743250i	$-0.0236802\pi$
$410$	−11.2159	+	19.4266i	−0.553916	+	0.959411i
$411$		0			0
$412$	6.37324	+	11.0388i	0.313987	+	0.543841i
$413$	35.6158			1.75254
$414$		0			0
$415$	−9.81616			−0.481856
$416$	1.55014	+	2.68492i	0.0760017	+	0.131639i
$417$		0			0
$418$	−3.87867	+	6.71805i	−0.189712	+	0.328591i
$419$	−2.46138	+	4.26323i	−0.120246	+	0.208273i	−0.919865	−	0.392236i	$-0.871702\pi$
$419$	−2.46138	+	4.26323i	−0.120246	+	0.208273i	0.799619	+	0.600508i	$0.205035\pi$
$420$		0			0
$421$	−9.85880	−	17.0759i	−0.480489	−	0.832231i	0.519261	−	0.854616i	$-0.326207\pi$
$421$	−9.85880	−	17.0759i	−0.480489	−	0.832231i	−0.999749	+	0.0223851i	$0.992874\pi$
$422$	18.9883			0.924336
$423$		0			0
$424$	−2.58267			−0.125426
$425$	4.34628	+	7.52797i	0.210825	+	0.365160i
$426$		0			0
$427$	−24.1255	+	41.7866i	−1.16751	+	2.02219i
$428$	3.04947	−	5.28184i	0.147402	−	0.255307i
$429$		0			0
$430$	−2.62623	−	4.54877i	−0.126648	−	0.219361i
$431$	6.16323			0.296873			0.148436	−	0.988922i	$-0.452576\pi$
$431$	6.16323			0.296873			0.148436	+	0.988922i	$0.452576\pi$
$432$		0			0
$433$	−14.7838			−0.710466			−0.355233	−	0.934778i	$-0.615599\pi$
$433$	−14.7838			−0.710466			−0.355233	+	0.934778i	$0.615599\pi$
$434$	−8.54714	−	14.8041i	−0.410276	−	0.710618i
$435$		0			0
$436$	−5.61950	+	9.73326i	−0.269125	+	0.466138i
$437$	5.69153	−	9.85801i	0.272263	−	0.471573i
$438$		0			0
$439$	−14.8835	−	25.7790i	−0.710352	−	1.23037i	−0.964725	−	0.263259i	$-0.915203\pi$
$439$	−14.8835	−	25.7790i	−0.710352	−	1.23037i	0.254374	−	0.967106i	$-0.418131\pi$
$440$	7.23936			0.345123
$441$		0			0
$442$	5.35032			0.254489
$443$	15.2372	+	26.3916i	0.723940	+	1.25390i	0.959409	+	0.282020i	$0.0910043\pi$
$443$	15.2372	+	26.3916i	0.723940	+	1.25390i	−0.235468	+	0.971882i	$0.575662\pi$
$444$		0			0
$445$	27.4771	−	47.5917i	1.30254	−	2.25606i
$446$	−3.62718	+	6.28246i	−0.171752	+	0.297483i
$447$		0			0
$448$	−1.84286	−	3.19193i	−0.0870669	−	0.150804i
$449$	−11.8411			−0.558816			−0.279408	−	0.960172i	$-0.590138\pi$
$449$	−11.8411			−0.558816			−0.279408	+	0.960172i	$0.590138\pi$
$450$		0			0
$451$	16.1795			0.761861
$452$	−3.51848	−	6.09418i	−0.165495	−	0.286646i
$453$		0			0
$454$	14.2636	−	24.7053i	0.669423	−	1.15948i
$455$	18.1006	−	31.3512i	0.848570	−	1.46977i
$456$		0			0
$457$	0.0931965	+	0.161421i	0.00435955	+	0.00755096i	0.868197	−	0.496220i	$-0.165279\pi$
$457$	0.0931965	+	0.161421i	0.00435955	+	0.00755096i	−0.863837	+	0.503771i	$0.831946\pi$
$458$	−1.85538			−0.0866963
$459$		0			0
$460$	−10.6230			−0.495299
$461$	5.20268	+	9.01130i	0.242313	+	0.419698i	0.961373	−	0.275250i	$-0.0887607\pi$
$461$	5.20268	+	9.01130i	0.242313	+	0.419698i	−0.719060	+	0.694948i	$0.755427\pi$
$462$		0			0
$463$	−12.8942	+	22.3334i	−0.599245	+	1.03792i	0.393688	+	0.919244i	$0.371199\pi$
$463$	−12.8942	+	22.3334i	−0.599245	+	1.03792i	−0.992933	+	0.118678i	$0.962134\pi$
$464$	−0.292722	+	0.507009i	−0.0135893	+	0.0235373i
$465$		0			0
$466$	−4.26735	−	7.39126i	−0.197681	−	0.342394i
$467$	−21.7011			−1.00421			−0.502104	−	0.864807i	$-0.667441\pi$
$467$	−21.7011			−1.00421			−0.502104	+	0.864807i	$0.667441\pi$
$468$		0			0
$469$	−31.7295			−1.46513
$470$	−6.10176	−	10.5686i	−0.281453	−	0.487491i
$471$		0			0
$472$	4.83159	−	8.36857i	0.222392	−	0.385194i
$473$	−1.89422	+	3.28089i	−0.0870965	+	0.150856i
$474$		0			0
$475$	8.54972	+	14.8085i	0.392288	+	0.679463i
$476$	−6.36065			−0.291540
$477$		0			0
$478$	−7.28796			−0.333344
$479$	−19.5606	−	33.8800i	−0.893747	−	1.54802i	−0.835348	−	0.549722i	$-0.814734\pi$
$479$	−19.5606	−	33.8800i	−0.893747	−	1.54802i	−0.0583996	−	0.998293i	$-0.518600\pi$
$480$		0			0
$481$	11.3272	−	19.6192i	0.516474	−	0.894559i
$482$	−0.667459	+	1.15607i	−0.0304019	+	0.0526577i
$483$		0			0
$484$	2.88923	+	5.00430i	0.131329	+	0.227468i
$485$	−29.1187			−1.32221
$486$		0			0
$487$	−10.4833			−0.475043			−0.237522	−	0.971382i	$-0.576335\pi$
$487$	−10.4833			−0.475043			−0.237522	+	0.971382i	$0.576335\pi$
$488$	6.54567	+	11.3374i	0.296309	+	0.513221i
$489$		0			0
$490$	−10.4303	+	18.0657i	−0.471191	+	0.816127i
$491$	3.42851	−	5.93835i	0.154727	−	0.267994i	−0.778233	−	0.627976i	$-0.783884\pi$
$491$	3.42851	−	5.93835i	0.154727	−	0.267994i	0.932959	+	0.359982i	$0.117217\pi$
$492$		0			0
$493$	0.505167	+	0.874974i	0.0227516	+	0.0394069i
$494$	10.5248			0.473533
$495$		0			0
$496$	−4.63798			−0.208251
$497$	3.66262	+	6.34384i	0.164291	+	0.284560i
$498$		0			0
$499$	−9.38685	+	16.2585i	−0.420213	+	0.727831i	−0.995960	−	0.0897973i	$-0.971378\pi$
$499$	−9.38685	+	16.2585i	−0.420213	+	0.727831i	0.575747	+	0.817628i	$0.304711\pi$
$500$	0.0585380	−	0.101391i	0.00261790	−	0.00453433i
$501$		0			0
$502$	1.43928	+	2.49291i	0.0642382	+	0.111264i
$503$	12.4270			0.554092			0.277046	−	0.960857i	$-0.410644\pi$
$503$	12.4270			0.554092			0.277046	+	0.960857i	$0.410644\pi$
$504$		0			0
$505$	37.8912			1.68614
$506$	3.83102	+	6.63552i	0.170309	+	0.294985i
$507$		0			0
$508$	−2.99250	+	5.18316i	−0.132771	+	0.229965i
$509$	16.4889	−	28.5595i	0.730856	−	1.26588i	−0.225662	−	0.974206i	$-0.572455\pi$
$509$	16.4889	−	28.5595i	0.730856	−	1.26588i	0.956518	−	0.291674i	$-0.0942121\pi$
$510$		0			0
$511$	−19.6217	−	33.9858i	−0.868014	−	1.50344i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−25.7779			−1.13702
$515$	−20.1912	−	34.9721i	−0.889728	−	1.54105i
$516$		0			0
$517$	−4.40102	+	7.62279i	−0.193557	+	0.335250i
$518$	−13.4661	+	23.3240i	−0.591668	+	1.02480i
$519$		0			0
$520$	−4.91101	−	8.50613i	−0.215362	−	0.373018i
$521$	−14.3320			−0.627895			−0.313947	−	0.949440i	$-0.601652\pi$
$521$	−14.3320			−0.627895			−0.313947	+	0.949440i	$0.601652\pi$
$522$		0			0
$523$	−5.70884			−0.249630			−0.124815	−	0.992180i	$-0.539834\pi$
$523$	−5.70884			−0.249630			−0.124815	+	0.992180i	$0.539834\pi$
$524$	8.20752	+	14.2158i	0.358547	+	0.621022i
$525$		0			0
$526$	7.53485	−	13.0507i	0.328535	−	0.569039i
$527$	−4.00200	+	6.93168i	−0.174330	+	0.301949i
$528$		0			0
$529$	5.87840	+	10.1817i	0.255583	+	0.442682i
$530$	8.18220			0.355412
$531$		0			0
$532$	−12.5123			−0.542476
$533$	−10.9758	−	19.0106i	−0.475413	−	0.823440i
$534$		0			0
$535$	−9.66107	+	16.7335i	−0.417685	+	0.723451i
$536$	−4.30438	+	7.45541i	−0.185921	+	0.322025i
$537$		0			0
$538$	−8.03074	−	13.9096i	−0.346230	−	0.599688i
$539$	15.0461			0.648081
$540$		0			0
$541$	18.0099			0.774305			0.387153	−	0.922016i	$-0.373459\pi$
$541$	18.0099			0.774305			0.387153	+	0.922016i	$0.373459\pi$
$542$	4.70723	+	8.15316i	0.202193	+	0.350208i
$543$		0			0
$544$	−0.862878	+	1.49455i	−0.0369956	+	0.0640782i
$545$	17.8032	−	30.8361i	0.762606	−	1.32087i
$546$		0			0
$547$	10.3139	+	17.8641i	0.440989	+	0.763815i	0.997763	−	0.0668489i	$-0.0212945\pi$
$547$	10.3139	+	17.8641i	0.440989	+	0.763815i	−0.556774	+	0.830664i	$0.687961\pi$
$548$	0.211159			0.00902025
$549$		0			0
$550$	−11.5098			−0.490779
$551$	0.993732	+	1.72119i	0.0423344	+	0.0733253i
$552$		0			0
$553$	−25.9718	+	44.9844i	−1.10443	+	1.91293i
$554$	2.78738	−	4.82788i	0.118424	−	0.205117i
$555$		0			0
$556$	−1.83576	−	3.17962i	−0.0778534	−	0.134846i
$557$	3.80418			0.161188			0.0805942	−	0.996747i	$-0.474318\pi$
$557$	3.80418			0.161188			0.0805942	+	0.996747i	$0.474318\pi$
$558$		0			0
$559$	5.13999			0.217398
$560$	5.83839	+	10.1124i	0.246717	+	0.427326i
$561$		0			0
$562$	−14.0024	+	24.2529i	−0.590656	+	1.02305i
$563$	−5.53568	+	9.58808i	−0.233301	+	0.404090i	−0.958778	−	0.284157i	$-0.908286\pi$
$563$	−5.53568	+	9.58808i	−0.233301	+	0.404090i	0.725476	+	0.688247i	$0.241619\pi$
$564$		0			0
$565$	11.1469	+	19.3071i	0.468955	+	0.812254i
$566$	−6.15522			−0.258723
$567$		0			0
$568$	1.98746			0.0833921
$569$	23.3576	+	40.4566i	0.979203	+	1.69603i	0.665302	+	0.746574i	$0.268303\pi$
$569$	23.3576	+	40.4566i	0.979203	+	1.69603i	0.313901	+	0.949456i	$0.398364\pi$
$570$		0			0
$571$	15.8431	−	27.4411i	0.663013	−	1.14837i	−0.316807	−	0.948490i	$-0.602611\pi$
$571$	15.8431	−	27.4411i	0.663013	−	1.14837i	0.979820	−	0.199883i	$-0.0640561\pi$
$572$	−3.54217	+	6.13522i	−0.148106	+	0.256526i
$573$		0			0
$574$	13.0484	+	22.6005i	0.544630	+	0.943326i
$575$	16.8894			0.704335
$576$		0			0
$577$	44.3284			1.84541			0.922707	−	0.385502i	$-0.125972\pi$
$577$	44.3284			1.84541			0.922707	+	0.385502i	$0.125972\pi$
$578$	−7.01088	−	12.1432i	−0.291614	−	0.505091i
$579$		0			0
$580$	0.927377	−	1.60626i	0.0385072	−	0.0666965i
$581$	−5.70996	+	9.88993i	−0.236889	+	0.410304i
$582$		0			0
$583$	−2.95079	−	5.11092i	−0.122209	−	0.211673i
$584$	−10.6474			−0.440594
$585$		0			0
$586$	2.33510			0.0964621
$587$	20.5223	+	35.5457i	0.847047	+	1.46713i	0.883831	+	0.467806i	$0.154955\pi$
$587$	20.5223	+	35.5457i	0.847047	+	1.46713i	−0.0367841	+	0.999323i	$0.511711\pi$
$588$		0			0
$589$	−7.87249	+	13.6356i	−0.324380	+	0.561843i
$590$	−15.3070	+	26.5126i	−0.630181	+	1.09151i
$591$		0			0
$592$	3.65360	+	6.32822i	0.150162	+	0.260088i
$593$	9.69265			0.398029			0.199015	−	0.979996i	$-0.436226\pi$
$593$	9.69265			0.398029			0.199015	+	0.979996i	$0.436226\pi$
$594$		0			0
$595$	20.1513			0.826121
$596$	7.73720	+	13.4012i	0.316928	+	0.548935i
$597$		0			0
$598$	5.19775	−	9.00276i	0.212552	−	0.368150i
$599$	−14.9190	+	25.8404i	−0.609572	+	1.05581i	0.381739	+	0.924270i	$0.375325\pi$
$599$	−14.9190	+	25.8404i	−0.609572	+	1.05581i	−0.991311	+	0.131539i	$0.958008\pi$
$600$		0			0
$601$	−6.27535	−	10.8692i	−0.255977	−	0.443365i	0.709184	−	0.705024i	$-0.249064\pi$
$601$	−6.27535	−	10.8692i	−0.255977	−	0.443365i	−0.965160	+	0.261659i	$0.915730\pi$
$602$	−6.11061			−0.249050
$603$		0			0
$604$	20.1457			0.819718
$605$	−9.15342	−	15.8542i	−0.372140	−	0.644565i
$606$		0			0
$607$	1.39007	−	2.40767i	0.0564211	−	0.0977242i	−0.836435	−	0.548066i	$-0.815364\pi$
$607$	1.39007	−	2.40767i	0.0564211	−	0.0977242i	0.892856	+	0.450341i	$0.148698\pi$
$608$	−1.69740	+	2.93998i	−0.0688386	+	0.119232i
$609$		0			0
$610$	−20.7374	−	35.9183i	−0.839634	−	1.45429i
$611$	11.9422			0.483130
$612$		0			0
$613$	−8.59291			−0.347064			−0.173532	−	0.984828i	$-0.555518\pi$
$613$	−8.59291			−0.347064			−0.173532	+	0.984828i	$0.555518\pi$
$614$	3.41265	+	5.91088i	0.137723	+	0.238544i
$615$		0			0
$616$	4.21106	−	7.29377i	0.169668	−	0.293874i
$617$	−10.0395	+	17.3890i	−0.404176	+	0.700053i	−0.994225	−	0.107314i	$-0.965775\pi$
$617$	−10.0395	+	17.3890i	−0.404176	+	0.700053i	0.590049	+	0.807367i	$0.299108\pi$
$618$		0			0
$619$	−4.19592	−	7.26755i	−0.168648	−	0.292108i	0.769296	−	0.638892i	$-0.220607\pi$
$619$	−4.19592	−	7.26755i	−0.168648	−	0.292108i	−0.937945	+	0.346784i	$0.887274\pi$
$620$	14.6936			0.590111
$621$		0			0
$622$	8.59522			0.344637
$623$	−31.9662	−	55.3672i	−1.28070	−	2.21824i
$624$		0			0
$625$	12.4069	−	21.4894i	0.496277	−	0.859577i
$626$	−10.8344	+	18.7658i	−0.433032	+	0.750033i
$627$		0			0
$628$	−8.99872	−	15.5862i	−0.359088	−	0.621959i
$629$	12.6104			0.502811
$630$		0			0
$631$	17.5631			0.699178			0.349589	−	0.936903i	$-0.386321\pi$
$631$	17.5631			0.699178			0.349589	+	0.936903i	$0.386321\pi$
$632$	7.04660	+	12.2051i	0.280299	+	0.485491i
$633$		0			0
$634$	−17.6600	+	30.5880i	−0.701367	+	1.21480i
$635$	9.48058	−	16.4208i	0.376225	−	0.651641i
$636$		0			0
$637$	−10.2069	−	17.6789i	−0.404413	−	0.700463i
$638$	−1.33778			−0.0529632
$639$		0			0
$640$	3.16812			0.125231
$641$	−6.70732	−	11.6174i	−0.264923	−	0.458860i	0.702620	−	0.711565i	$-0.252013\pi$
$641$	−6.70732	−	11.6174i	−0.264923	−	0.458860i	−0.967543	+	0.252705i	$0.918680\pi$
$642$		0			0
$643$	5.21755	−	9.03706i	0.205760	−	0.356387i	−0.744615	−	0.667495i	$-0.767367\pi$
$643$	5.21755	−	9.03706i	0.205760	−	0.356387i	0.950375	+	0.311108i	$0.100700\pi$
$644$	−6.17927	+	10.7028i	−0.243497	+	0.421750i
$645$		0			0
$646$	2.92929	+	5.07369i	0.115252	+	0.199622i
$647$	37.9585			1.49230			0.746152	−	0.665775i	$-0.231899\pi$
$647$	37.9585			1.49230			0.746152	+	0.665775i	$0.231899\pi$
$648$		0			0
$649$	22.0810			0.866756
$650$	7.80797	+	13.5238i	0.306254	+	0.530447i
$651$		0			0
$652$	−1.52645	+	2.64388i	−0.0597802	+	0.103542i
$653$	−13.6531	+	23.6479i	−0.534289	+	0.925415i	0.464909	+	0.885359i	$0.346087\pi$
$653$	−13.6531	+	23.6479i	−0.534289	+	0.925415i	−0.999197	+	0.0400567i	$0.987246\pi$
$654$		0			0
$655$	−26.0024	−	45.0374i	−1.01600	−	1.75976i
$656$	7.08052			0.276448
$657$		0			0
$658$	−14.1973			−0.553469
$659$	−17.1775	−	29.7522i	−0.669139	−	1.15898i	−0.978145	−	0.207922i	$-0.933330\pi$
$659$	−17.1775	−	29.7522i	−0.669139	−	1.15898i	0.309007	−	0.951060i	$-0.400003\pi$
$660$		0			0
$661$	12.2889	−	21.2849i	0.477981	−	0.827887i	−0.521700	−	0.853129i	$-0.674702\pi$
$661$	12.2889	−	21.2849i	0.477981	−	0.827887i	0.999681	+	0.0252414i	$0.00803544\pi$
$662$	−12.9068	+	22.3553i	−0.501638	+	0.868863i
$663$		0			0
$664$	1.54921	+	2.68331i	0.0601210	+	0.104133i
$665$	39.6403			1.53719
$666$		0			0
$667$	1.96305			0.0760094
$668$	−2.05060	−	3.55174i	−0.0793400	−	0.137421i
$669$		0			0
$670$	13.6368	−	23.6196i	0.526835	−	0.912504i
$671$	−14.9573	+	25.9068i	−0.577420	+	1.00012i
$672$		0			0
$673$	−21.4377	−	37.1312i	−0.826363	−	1.43130i	−0.900873	−	0.434083i	$-0.857072\pi$
$673$	−21.4377	−	37.1312i	−0.826363	−	1.43130i	0.0745094	−	0.997220i	$-0.476261\pi$
$674$	3.38459			0.130369
$675$		0			0
$676$	−3.38830			−0.130319
$677$	3.74371	+	6.48430i	0.143883	+	0.249212i	0.928956	−	0.370191i	$-0.120708\pi$
$677$	3.74371	+	6.48430i	0.143883	+	0.249212i	−0.785073	+	0.619403i	$0.787375\pi$
$678$		0			0
$679$	−16.9380	+	29.3375i	−0.650022	+	1.12587i
$680$	2.73370	−	4.73490i	0.104832	−	0.181575i
$681$		0			0
$682$	−5.29904	−	9.17821i	−0.202911	−	0.351452i
$683$	−16.7545			−0.641093			−0.320546	−	0.947233i	$-0.603866\pi$
$683$	−16.7545			−0.641093			−0.320546	+	0.947233i	$0.603866\pi$
$684$		0			0
$685$	−0.668975			−0.0255602
$686$	−0.765664	−	1.32617i	−0.0292332	−	0.0506334i
$687$		0			0
$688$	−0.828957	+	1.43580i	−0.0316037	+	0.0547392i
$689$	−4.00350	+	6.93426i	−0.152521	+	0.264174i
$690$		0			0
$691$	7.47672	+	12.9501i	0.284428	+	0.492644i	0.972470	−	0.233027i	$-0.0748630\pi$
$691$	7.47672	+	12.9501i	0.284428	+	0.492644i	−0.688042	+	0.725671i	$0.741530\pi$
$692$	17.0271			0.647273
$693$		0			0
$694$	−16.2000			−0.614945
$695$	5.81588	+	10.0734i	0.220609	+	0.382106i
$696$		0			0
$697$	6.10962	−	10.5822i	0.231418	−	0.400828i
$698$	2.24627	−	3.89065i	0.0850224	−	0.147263i
$699$		0			0
$700$	−9.28240	−	16.0776i	−0.350842	−	0.607676i
$701$	42.1025			1.59019			0.795094	−	0.606486i	$-0.207421\pi$
$701$	42.1025			1.59019			0.795094	+	0.606486i	$0.207421\pi$
$702$		0			0
$703$	24.8065			0.935593
$704$	−1.14253	−	1.97893i	−0.0430609	−	0.0745836i
$705$		0			0
$706$	11.6133	−	20.1149i	0.437074	−	0.757034i
$707$	22.0409	−	38.1760i	0.828934	−	1.43576i
$708$		0			0
$709$	−14.2428	−	24.6692i	−0.534899	−	0.926473i	−0.999168	−	0.0407786i	$-0.987016\pi$
$709$	−14.2428	−	24.6692i	−0.534899	−	0.926473i	0.464269	−	0.885694i	$-0.346317\pi$
$710$	−6.29651			−0.236304
$711$		0			0
$712$	−17.3460			−0.650069
$713$	7.77577	+	13.4680i	0.291205	+	0.504382i
$714$		0			0
$715$	11.2220	−	19.4371i	0.419679	−	0.726905i
$716$	−7.27802	+	12.6059i	−0.271993	+	0.471105i
$717$		0			0
$718$	5.77697	+	10.0060i	0.215595	+	0.373421i
$719$	−2.53487			−0.0945348			−0.0472674	−	0.998882i	$-0.515051\pi$
$719$	−2.53487			−0.0945348			−0.0472674	+	0.998882i	$0.515051\pi$
$720$		0			0
$721$	−46.9799			−1.74962
$722$	−3.73768	−	6.47385i	−0.139102	−	0.240932i
$723$		0			0
$724$	6.51190	−	11.2789i	0.242013	−	0.419179i
$725$	−1.47443	+	2.55378i	−0.0547589	+	0.0948451i
$726$		0			0
$727$	−9.94170	−	17.2195i	−0.368717	−	0.638637i	0.620648	−	0.784089i	$-0.286870\pi$
$727$	−9.94170	−	17.2195i	−0.368717	−	0.638637i	−0.989365	+	0.145452i	$0.953536\pi$
$728$	−11.4267			−0.423503
$729$		0			0
$730$	33.7323			1.24849
$731$	1.43058	+	2.47783i	0.0529118	+	0.0916460i
$732$		0			0
$733$	5.00553	−	8.66984i	0.184884	−	0.320228i	−0.758654	−	0.651494i	$-0.774143\pi$
$733$	5.00553	−	8.66984i	0.184884	−	0.320228i	0.943537	+	0.331266i	$0.107476\pi$
$734$	7.78486	−	13.4838i	0.287344	−	0.497695i
$735$		0			0
$736$	1.67654	+	2.90386i	0.0617982	+	0.107038i
$737$	−19.6716			−0.724613
$738$		0			0
$739$	−40.3914			−1.48582			−0.742911	−	0.669390i	$-0.766556\pi$
$739$	−40.3914			−1.48582			−0.742911	+	0.669390i	$0.766556\pi$
$740$	−11.5750	−	20.0485i	−0.425506	−	0.736998i
$741$		0			0
$742$	4.75950	−	8.24370i	0.174727	−	0.302636i
$743$	17.8251	−	30.8740i	0.653939	−	1.13266i	−0.328219	−	0.944602i	$-0.606449\pi$
$743$	17.8251	−	30.8740i	0.653939	−	1.13266i	0.982159	−	0.188054i	$-0.0602181\pi$
$744$		0			0
$745$	−24.5123	−	42.4566i	−0.898062	−	1.55549i
$746$	9.75726			0.357239
$747$		0			0
$748$	−3.94347			−0.144187
$749$	11.2395	+	19.4674i	0.410682	+	0.711322i
$750$		0			0
$751$	4.73436	−	8.20016i	0.172759	−	0.299228i	−0.766624	−	0.642096i	$-0.778065\pi$
$751$	4.73436	−	8.20016i	0.172759	−	0.299228i	0.939384	+	0.342868i	$0.111398\pi$
$752$	−1.92599	+	3.33591i	−0.0702337	+	0.121648i
$753$		0			0
$754$	0.907519	+	1.57187i	0.0330499	+	0.0572441i
$755$	−63.8240			−2.32279
$756$		0			0
$757$	−37.9651			−1.37987			−0.689933	−	0.723873i	$-0.742360\pi$
$757$	−37.9651			−1.37987			−0.689933	+	0.723873i	$0.742360\pi$
$758$	−9.39519	−	16.2730i	−0.341249	−	0.591060i
$759$		0			0
$760$	5.37755	−	9.31420i	0.195064	−	0.337861i
$761$	22.4429	−	38.8722i	0.813554	−	1.40912i	−0.0968081	−	0.995303i	$-0.530863\pi$
$761$	22.4429	−	38.8722i	0.813554	−	1.40912i	0.910362	−	0.413813i	$-0.135803\pi$
$762$		0			0
$763$	−20.7119	−	35.8740i	−0.749821	−	1.29873i
$764$	−3.60287			−0.130347
$765$		0			0
$766$	30.7680			1.11169
$767$	−14.9793	−	25.9449i	−0.540870	−	0.936814i
$768$		0			0
$769$	−22.8684	+	39.6093i	−0.824656	+	1.42835i	0.0775257	+	0.996990i	$0.475298\pi$
$769$	−22.8684	+	39.6093i	−0.824656	+	1.42835i	−0.902182	+	0.431356i	$0.858035\pi$
$770$	−13.3411	+	23.1075i	−0.480781	+	0.832736i
$771$		0			0
$772$	−0.737435	−	1.27727i	−0.0265409	−	0.0459701i
$773$	20.5707			0.739876			0.369938	−	0.929056i	$-0.379379\pi$
$773$	20.5707			0.739876			0.369938	+	0.929056i	$0.379379\pi$
$774$		0			0
$775$	−23.3613			−0.839162
$776$	4.59558	+	7.95978i	0.164972	+	0.285740i
$777$		0			0
$778$	−14.8003	+	25.6349i	−0.530618	+	0.919057i
$779$	12.0185	−	20.8166i	0.430606	−	0.745831i
$780$		0			0
$781$	2.27074	+	3.93304i	0.0812536	+	0.140735i
$782$	5.78661			0.206929
$783$		0			0
$784$	6.58452			0.235162
$785$	28.5090	+	49.3790i	1.01753	+	1.76241i
$786$		0			0
$787$	−22.2818	+	38.5931i	−0.794259	+	1.37570i	0.129050	+	0.991638i	$0.458807\pi$
$787$	−22.2818	+	38.5931i	−0.794259	+	1.37570i	−0.923309	+	0.384059i	$0.874526\pi$
$788$	1.26931	−	2.19851i	0.0452173	−	0.0783187i
$789$		0			0
$790$	−22.3244	−	38.6670i	−0.794267	−	1.37571i
$791$	25.9362			0.922186
$792$		0			0
$793$	40.5867			1.44128
$794$	8.07134	+	13.9800i	0.286441	+	0.496131i
$795$		0			0
$796$	0.925891	−	1.60369i	0.0328174	−	0.0568413i
$797$	21.9301	−	37.9840i	0.776803	−	1.34546i	−0.156973	−	0.987603i	$-0.550174\pi$
$797$	21.9301	−	37.9840i	0.776803	−	1.34546i	0.933776	−	0.357859i	$-0.116493\pi$
$798$		0			0
$799$	3.32379	+	5.75697i	0.117587	+	0.203667i
$800$	−5.03695			−0.178083
$801$		0			0
$802$	25.3624			0.895577
$803$	−12.1650	−	21.0705i	−0.429295	−	0.743561i
$804$		0			0
$805$	19.5766	−	33.9077i	0.689986	−	1.19509i
$806$	−7.18950	+	12.4526i	−0.253239	+	0.438623i
$807$		0			0
$808$	−5.98009	−	10.3578i	−0.210379	−	0.364387i
$809$	15.5821			0.547836			0.273918	−	0.961753i	$-0.411680\pi$
$809$	15.5821			0.547836			0.273918	+	0.961753i	$0.411680\pi$
$810$		0			0
$811$	−30.4691			−1.06992			−0.534958	−	0.844879i	$-0.679673\pi$
$811$	−30.4691			−1.06992			−0.534958	+	0.844879i	$0.679673\pi$
$812$	−1.07889	−	1.86869i	−0.0378617	−	0.0655783i
$813$		0			0
$814$	−8.34872	+	14.4604i	−0.292622	+	0.506837i
$815$	4.83596	−	8.37612i	0.169396	−	0.293403i
$816$		0			0
$817$	2.81414	+	4.87424i	0.0984544	+	0.170528i
$818$	22.7713			0.796180
$819$		0			0
$820$	−22.4319			−0.783356
$821$	−0.950509	−	1.64633i	−0.0331730	−	0.0574573i	0.848962	−	0.528453i	$-0.177228\pi$
$821$	−0.950509	−	1.64633i	−0.0331730	−	0.0574573i	−0.882135	+	0.470996i	$0.843895\pi$
$822$		0			0
$823$	11.0205	−	19.0881i	0.384151	−	0.665369i	−0.607500	−	0.794320i	$-0.707828\pi$
$823$	11.0205	−	19.0881i	0.384151	−	0.665369i	0.991651	+	0.128951i	$0.0411609\pi$
$824$	−6.37324	+	11.0388i	−0.222022	+	0.384554i
$825$		0			0
$826$	17.8079	+	30.8442i	0.619616	+	1.07321i
$827$	−48.4976			−1.68643			−0.843213	−	0.537579i	$-0.819339\pi$
$827$	−48.4976			−1.68643			−0.843213	+	0.537579i	$0.819339\pi$
$828$		0			0
$829$	−20.3186			−0.705693			−0.352846	−	0.935681i	$-0.614786\pi$
$829$	−20.3186			−0.705693			−0.352846	+	0.935681i	$0.614786\pi$
$830$	−4.90808	−	8.50104i	−0.170362	−	0.295075i
$831$		0			0
$832$	−1.55014	+	2.68492i	−0.0537413	+	0.0930827i
$833$	5.68164	−	9.84089i	0.196857	−	0.340966i
$834$		0			0
$835$	6.49653	+	11.2523i	0.224822	+	0.389403i
$836$	−7.75734			−0.268293
$837$		0			0
$838$	−4.92276			−0.170054
$839$	−2.53317	−	4.38759i	−0.0874549	−	0.151476i	0.818980	−	0.573822i	$-0.194540\pi$
$839$	−2.53317	−	4.38759i	−0.0874549	−	0.151476i	−0.906435	+	0.422346i	$0.861207\pi$
$840$		0			0
$841$	14.3286	−	24.8179i	0.494091	−	0.855790i
$842$	9.85880	−	17.0759i	0.339757	−	0.588476i
$843$		0			0
$844$	9.49415	+	16.4443i	0.326802	+	0.566038i
$845$	10.7345			0.369278
$846$		0			0
$847$	−21.2978			−0.731801
$848$	−1.29134	−	2.23666i	−0.0443446	−	0.0768072i
$849$		0			0
$850$	−4.34628	+	7.52797i	−0.149076	+	0.258207i
$851$	12.2508	−	21.2191i	0.419953	−	0.727381i
$852$		0			0
$853$	−13.2339	−	22.9218i	−0.453121	−	0.784829i	0.545457	−	0.838139i	$-0.316356\pi$
$853$	−13.2339	−	22.9218i	−0.453121	−	0.784829i	−0.998578	+	0.0533102i	$0.983023\pi$
$854$	−48.2510			−1.65112
$855$		0			0
$856$	6.09894			0.208457
$857$	−9.15582	−	15.8583i	−0.312757	−	0.541711i	0.666201	−	0.745772i	$-0.267919\pi$
$857$	−9.15582	−	15.8583i	−0.312757	−	0.541711i	−0.978958	+	0.204061i	$0.934586\pi$
$858$		0			0
$859$	4.71968	−	8.17473i	0.161034	−	0.278918i	−0.774206	−	0.632934i	$-0.781851\pi$
$859$	4.71968	−	8.17473i	0.161034	−	0.278918i	0.935240	+	0.354015i	$0.115184\pi$
$860$	2.62623	−	4.54877i	0.0895538	−	0.155112i
$861$		0			0
$862$	3.08162	+	5.33752i	0.104960	+	0.181797i
$863$	14.2154			0.483898			0.241949	−	0.970289i	$-0.422213\pi$
$863$	14.2154			0.483898			0.241949	+	0.970289i	$0.422213\pi$
$864$		0			0
$865$	−53.9438			−1.83414
$866$	−7.39192	−	12.8032i	−0.251188	−	0.435070i
$867$		0			0
$868$	8.54714	−	14.8041i	0.290109	−	0.502483i
$869$	−16.1019	+	27.8894i	−0.546221	+	0.946083i
$870$		0			0
$871$	13.3448	+	23.1138i	0.452170	+	0.783182i
$872$	−11.2390			−0.380600
$873$		0			0
$874$	11.3831			0.385038
$875$	0.215754	+	0.373698i	0.00729383	+	0.0126333i
$876$		0			0
$877$	−19.5527	+	33.8663i	−0.660248	+	1.14358i	0.320302	+	0.947316i	$0.396216\pi$
$877$	−19.5527	+	33.8663i	−0.660248	+	1.14358i	−0.980550	+	0.196268i	$0.937118\pi$
$878$	14.8835	−	25.7790i	0.502294	−	0.869999i
$879$		0			0
$880$	3.61968	+	6.26947i	0.122019	+	0.211344i
$881$	22.8938			0.771313			0.385657	−	0.922642i	$-0.373975\pi$
$881$	22.8938			0.771313			0.385657	+	0.922642i	$0.373975\pi$
$882$		0			0
$883$	−17.1509			−0.577174			−0.288587	−	0.957454i	$-0.593185\pi$
$883$	−17.1509			−0.577174			−0.288587	+	0.957454i	$0.593185\pi$
$884$	2.67516	+	4.63351i	0.0899753	+	0.155842i
$885$		0			0
$886$	−15.2372	+	26.3916i	−0.511903	+	0.886642i
$887$	9.12852	−	15.8111i	0.306506	−	0.530883i	−0.671090	−	0.741376i	$-0.734174\pi$
$887$	9.12852	−	15.8111i	0.306506	−	0.530883i	0.977595	+	0.210493i	$0.0675069\pi$
$888$		0			0
$889$	−11.0295	−	19.1037i	−0.369918	−	0.640716i
$890$	54.9541			1.84207
$891$		0			0
$892$	−7.25436			−0.242894
$893$	6.53835	+	11.3247i	0.218797	+	0.378968i
$894$		0			0
$895$	23.0576	−	39.9370i	0.770731	−	1.33495i
$896$	1.84286	−	3.19193i	0.0615656	−	0.106635i
$897$		0			0
$898$	−5.92055	−	10.2547i	−0.197571	−	0.342204i
$899$	−2.71527			−0.0905595
$900$		0			0
$901$	−4.45706			−0.148486
$902$	8.08973	+	14.0118i	0.269358	+	0.466543i
$903$		0			0
$904$	3.51848	−	6.09418i	0.117023	−	0.202689i
$905$	−20.6305	+	35.7330i	−0.685779	+	1.18780i
$906$		0			0
$907$	−14.5958	−	25.2807i	−0.484646	−	0.839432i	0.515198	−	0.857071i	$-0.327718\pi$
$907$	−14.5958	−	25.2807i	−0.484646	−	0.839432i	−0.999844	+	0.0176391i	$0.994385\pi$
$908$	28.5272			0.946708
$909$		0			0
$910$	36.2012			1.20006
$911$	27.3179	+	47.3161i	0.905084	+	1.56765i	0.820805	+	0.571209i	$0.193525\pi$
$911$	27.3179	+	47.3161i	0.905084	+	1.56765i	0.0842793	+	0.996442i	$0.473141\pi$
$912$		0			0
$913$	−3.54005	+	6.13155i	−0.117159	+	0.202925i
$914$	−0.0931965	+	0.161421i	−0.00308267	+	0.00533934i
$915$		0			0
$916$	−0.927691	−	1.60681i	−0.0306518	−	0.0530905i
$917$	−60.5012			−1.99793
$918$		0			0
$919$	41.0995			1.35575			0.677873	−	0.735179i	$-0.262902\pi$
$919$	41.0995			1.35575			0.677873	+	0.735179i	$0.262902\pi$
$920$	−5.31149	−	9.19976i	−0.175114	−	0.303307i
$921$		0			0
$922$	−5.20268	+	9.01130i	−0.171341	+	0.296771i
$923$	3.08084	−	5.33617i	0.101407	−	0.175642i
$924$		0			0
$925$	18.4030	+	31.8749i	0.605087	+	1.04804i
$926$	−25.7884			−0.847460
$927$		0			0
$928$	−0.585444			−0.0192181
$929$	7.29804	+	12.6406i	0.239441	+	0.414724i	0.960554	−	0.278094i	$-0.0897025\pi$
$929$	7.29804	+	12.6406i	0.239441	+	0.414724i	−0.721113	+	0.692817i	$0.756369\pi$
$930$		0			0
$931$	11.1766	−	19.3584i	0.366297	−	0.634445i
$932$	4.26735	−	7.39126i	0.139782	−	0.242109i
$933$		0			0
$934$	−10.8506	−	18.7937i	−0.355041	−	0.614950i
$935$	12.4934			0.408576
$936$		0			0
$937$	24.9282			0.814370			0.407185	−	0.913346i	$-0.366511\pi$
$937$	24.9282			0.814370			0.407185	+	0.913346i	$0.366511\pi$
$938$	−15.8647	−	27.4785i	−0.518002	−	0.897206i
$939$		0			0
$940$	6.10176	−	10.5686i	0.199017	−	0.344708i
$941$	10.4222	−	18.0517i	0.339753	−	0.588469i	−0.644633	−	0.764492i	$-0.722990\pi$
$941$	10.4222	−	18.0517i	0.339753	−	0.588469i	0.984386	+	0.176023i	$0.0563233\pi$
$942$		0			0
$943$	−11.8708	−	20.5608i	−0.386566	−	0.669553i
$944$	9.66319			0.314510
$945$		0			0
$946$	−3.78845			−0.123173
$947$	17.9565	+	31.1016i	0.583508	+	1.01067i	0.995060	+	0.0992789i	$0.0316536\pi$
$947$	17.9565	+	31.1016i	0.583508	+	1.01067i	−0.411552	+	0.911386i	$0.635013\pi$
$948$		0			0
$949$	−16.5050	+	28.5875i	−0.535774	+	0.927988i
$950$	−8.54972	+	14.8085i	−0.277390	+	0.480453i
$951$		0			0
$952$	−3.18032	−	5.50848i	−0.103075	−	0.178531i
$953$	−5.80207			−0.187947			−0.0939737	−	0.995575i	$-0.529957\pi$
$953$	−5.80207			−0.187947			−0.0939737	+	0.995575i	$0.529957\pi$
$954$		0			0
$955$	11.4143			0.369359
$956$	−3.64398	−	6.31156i	−0.117855	−	0.204131i
$957$		0			0
$958$	19.5606	−	33.8800i	0.631975	−	1.09461i
$959$	−0.389136	+	0.674003i	−0.0125658	+	0.0217647i
$960$		0			0
$961$	4.74459	+	8.21788i	0.153051	+	0.265093i
$962$	22.6543			0.730405
$963$		0			0
$964$	−1.33492			−0.0429948
$965$	2.33628	+	4.04655i	0.0752075	+	0.130263i
$966$		0			0
$967$	−14.8294	+	25.6854i	−0.476883	+	0.825986i	−0.999649	−	0.0264906i	$-0.991567\pi$
$967$	−14.8294	+	25.6854i	−0.476883	+	0.825986i	0.522766	+	0.852476i	$0.324900\pi$
$968$	−2.88923	+	5.00430i	−0.0928635	+	0.160844i
$969$		0			0
$970$	−14.5593	−	25.2175i	−0.467472	−	0.809685i
$971$	−47.1522			−1.51318			−0.756592	−	0.653887i	$-0.773137\pi$
$971$	−47.1522			−1.51318			−0.756592	+	0.653887i	$0.773137\pi$
$972$		0			0
$973$	13.5322			0.433821
$974$	−5.24165	−	9.07880i	−0.167953	−	0.290903i
$975$		0			0
$976$	−6.54567	+	11.3374i	−0.209522	+	0.362902i
$977$	−11.9015	+	20.6140i	−0.380762	+	0.659499i	−0.991171	−	0.132587i	$-0.957672\pi$
$977$	−11.9015	+	20.6140i	−0.380762	+	0.659499i	0.610410	+	0.792086i	$0.291005\pi$
$978$		0			0
$979$	−19.8184	−	34.3265i	−0.633399	−	1.09708i
$980$	−20.8605			−0.666365
$981$		0			0
$982$	6.85702			0.218816
$983$	5.54113	+	9.59751i	0.176734	+	0.306113i	0.940760	−	0.339073i	$-0.110113\pi$
$983$	5.54113	+	9.59751i	0.176734	+	0.306113i	−0.764026	+	0.645186i	$0.776780\pi$
$984$		0			0
$985$	−4.02132	+	6.96513i	−0.128130	+	0.221928i
$986$	−0.505167	+	0.874974i	−0.0160878	+	0.0278649i
$987$		0			0
$988$	5.26240	+	9.11475i	0.167419	+	0.289979i
$989$	5.55913			0.176770
$990$		0			0
$991$	11.4369			0.363306			0.181653	−	0.983363i	$-0.441855\pi$
$991$	11.4369			0.363306			0.181653	+	0.983363i	$0.441855\pi$
$992$	−2.31899	−	4.01660i	−0.0736279	−	0.127527i
$993$		0			0
$994$	−3.66262	+	6.34384i	−0.116171	+	0.201214i
$995$	−2.93333	+	5.08068i	−0.0929928	+	0.161068i
$996$		0			0
$997$	13.9473	+	24.1574i	0.441714	+	0.765071i	0.997817	−	0.0660422i	$-0.0210372\pi$
$997$	13.9473	+	24.1574i	0.441714	+	0.765071i	−0.556103	+	0.831114i	$0.687704\pi$
$998$	−18.7737			−0.594271
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1458.2.c.g.973.5		12
3.2	odd	2		1458.2.c.f.973.2		12
9.2	odd	6		1458.2.c.f.487.2		12
9.4	even	3		1458.2.a.f.1.2		6
9.5	odd	6		1458.2.a.g.1.5		6
9.7	even	3	inner	1458.2.c.g.487.5		12
27.2	odd	18		54.2.e.b.13.1	✓	12
27.4	even	9		162.2.e.b.73.1		12
27.5	odd	18		486.2.e.f.55.2		12
27.7	even	9		486.2.e.g.433.1		12
27.11	odd	18		486.2.e.h.109.1		12
27.13	even	9		486.2.e.e.379.2		12
27.14	odd	18		486.2.e.h.379.1		12
27.16	even	9		486.2.e.e.109.2		12
27.20	odd	18		486.2.e.f.433.2		12
27.22	even	9		486.2.e.g.55.1		12
27.23	odd	18		54.2.e.b.25.1	yes	12
27.25	even	9		162.2.e.b.91.1		12
108.23	even	18		432.2.u.b.241.2		12
108.83	even	18		432.2.u.b.337.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.13.1	✓	12	27.2	odd	18
54.2.e.b.25.1	yes	12	27.23	odd	18
162.2.e.b.73.1		12	27.4	even	9
162.2.e.b.91.1		12	27.25	even	9
432.2.u.b.241.2		12	108.23	even	18
432.2.u.b.337.2		12	108.83	even	18
486.2.e.e.109.2		12	27.16	even	9
486.2.e.e.379.2		12	27.13	even	9
486.2.e.f.55.2		12	27.5	odd	18
486.2.e.f.433.2		12	27.20	odd	18
486.2.e.g.55.1		12	27.22	even	9
486.2.e.g.433.1		12	27.7	even	9
486.2.e.h.109.1		12	27.11	odd	18
486.2.e.h.379.1		12	27.14	odd	18
1458.2.a.f.1.2		6	9.4	even	3
1458.2.a.g.1.5		6	9.5	odd	6
1458.2.c.f.487.2		12	9.2	odd	6
1458.2.c.f.973.2		12	3.2	odd	2
1458.2.c.g.487.5		12	9.7	even	3	inner
1458.2.c.g.973.5		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1458 = 2 \cdot 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1458.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.58406 - 2.74367i) q^{5} +(-1.84286 - 3.19193i) q^{7} -1.00000 q^{8} +3.16812 q^{10} +(-1.14253 - 1.97893i) q^{11} +(-1.55014 + 2.68492i) q^{13} +(1.84286 - 3.19193i) q^{14} +(-0.500000 - 0.866025i) q^{16} -1.72576 q^{17} -3.39480 q^{19} +(1.58406 + 2.74367i) q^{20} +(1.14253 - 1.97893i) q^{22} +(-1.67654 + 2.90386i) q^{23} +(-2.51848 - 4.36213i) q^{25} -3.10027 q^{26} +3.68572 q^{28} +(-0.292722 - 0.507009i) q^{29} +(2.31899 - 4.01660i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.862878 - 1.49455i) q^{34} -11.6768 q^{35} -7.30720 q^{37} +(-1.69740 - 2.93998i) q^{38} +(-1.58406 + 2.74367i) q^{40} +(-3.54026 + 6.13191i) q^{41} +(-0.828957 - 1.43580i) q^{43} +2.28507 q^{44} -3.35309 q^{46} +(-1.92599 - 3.33591i) q^{47} +(-3.29226 + 5.70237i) q^{49} +(2.51848 - 4.36213i) q^{50} +(-1.55014 - 2.68492i) q^{52} +2.58267 q^{53} -7.23936 q^{55} +(1.84286 + 3.19193i) q^{56} +(0.292722 - 0.507009i) q^{58} +(-4.83159 + 8.36857i) q^{59} +(-6.54567 - 11.3374i) q^{61} +4.63798 q^{62} +1.00000 q^{64} +(4.91101 + 8.50613i) q^{65} +(4.30438 - 7.45541i) q^{67} +(0.862878 - 1.49455i) q^{68} +(-5.83839 - 10.1124i) q^{70} -1.98746 q^{71} +10.6474 q^{73} +(-3.65360 - 6.32822i) q^{74} +(1.69740 - 2.93998i) q^{76} +(-4.21106 + 7.29377i) q^{77} +(-7.04660 - 12.2051i) q^{79} -3.16812 q^{80} -7.08052 q^{82} +(-1.54921 - 2.68331i) q^{83} +(-2.73370 + 4.73490i) q^{85} +(0.828957 - 1.43580i) q^{86} +(1.14253 + 1.97893i) q^{88} +17.3460 q^{89} +11.4267 q^{91} +(-1.67654 - 2.90386i) q^{92} +(1.92599 - 3.33591i) q^{94} +(-5.37755 + 9.31420i) q^{95} +(-4.59558 - 7.95978i) q^{97} -6.58452 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 12 q^{8} + 6 q^{10} + 3 q^{11} - 9 q^{13} + 6 q^{14} - 6 q^{16} - 12 q^{17} + 18 q^{19} + 3 q^{20} - 3 q^{22} - 3 q^{23} - 15 q^{25} - 18 q^{26} + 12 q^{28}+ \cdots - 24 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 12 * q^8 + 6 * q^10 + 3 * q^11 - 9 * q^13 + 6 * q^14 - 6 * q^16 - 12 * q^17 + 18 * q^19 + 3 * q^20 - 3 * q^22 - 3 * q^23 - 15 * q^25 - 18 * q^26 + 12 * q^28 + 3 * q^29 - 12 * q^31 + 6 * q^32 - 6 * q^34 + 6 * q^35 + 30 * q^37 + 9 * q^38 - 3 * q^40 + 3 * q^41 - 12 * q^43 - 6 * q^44 - 6 * q^46 - 9 * q^47 - 12 * q^49 + 15 * q^50 - 9 * q^52 + 12 * q^53 + 18 * q^55 + 6 * q^56 - 3 * q^58 - 3 * q^59 - 12 * q^61 - 24 * q^62 + 12 * q^64 - 3 * q^65 - 21 * q^67 + 6 * q^68 + 3 * q^70 + 24 * q^71 + 42 * q^73 + 15 * q^74 - 9 * q^76 - 3 * q^77 - 6 * q^80 + 6 * q^82 - 27 * q^83 + 12 * q^86 - 3 * q^88 + 24 * q^89 + 12 * q^91 - 3 * q^92 + 9 * q^94 - 30 * q^95 - 18 * q^97 - 24 * q^98

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