LMFDB - Embedded newform 135.2.e.b.91.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(46,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("135.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.e (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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			91.3
Root			$0.403374 + 1.68443i$ of defining polynomial
Character	$\chi$	$=$	135.91
Dual form			135.2.e.b.46.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25707 + 2.17731i) q^{2} +(-2.16044 + 3.74200i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.257068 + 0.445256i) q^{7} -5.83502 q^{8} +O(q^{10})$	\(q+(1.25707 + 2.17731i) q^{2} +(-2.16044 + 3.74200i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.257068 + 0.445256i) q^{7} -5.83502 q^{8} +2.51414 q^{10} +(-1.66044 - 2.87597i) q^{11} +(0.660442 - 1.14392i) q^{13} +(-0.646305 + 1.11943i) q^{14} +(-3.01414 - 5.22064i) q^{16} +3.32088 q^{17} -1.32088 q^{19} +(2.16044 + 3.74200i) q^{20} +(4.17458 - 7.23058i) q^{22} +(2.06382 - 3.57463i) q^{23} +(-0.500000 - 0.866025i) q^{25} +3.32088 q^{26} -2.22153 q^{28} +(-0.693252 - 1.20075i) q^{29} +(-4.36783 + 7.56531i) q^{31} +(1.74293 - 3.01885i) q^{32} +(4.17458 + 7.23058i) q^{34} +0.514137 q^{35} +0.292611 q^{37} +(-1.66044 - 2.87597i) q^{38} +(-2.91751 + 5.05328i) q^{40} +(-5.67458 + 9.82866i) q^{41} +(-5.17458 - 8.96263i) q^{43} +14.3492 q^{44} +10.3774 q^{46} +(-2.43165 - 4.21174i) q^{47} +(3.36783 - 5.83326i) q^{49} +(1.25707 - 2.17731i) q^{50} +(2.85369 + 4.94274i) q^{52} +5.02827 q^{53} -3.32088 q^{55} +(-1.50000 - 2.59808i) q^{56} +(1.74293 - 3.01885i) q^{58} +(-2.51414 + 4.35461i) q^{59} +(-3.67458 - 6.36456i) q^{61} -21.9627 q^{62} -3.29261 q^{64} +(-0.660442 - 1.14392i) q^{65} +(-4.72426 + 8.18266i) q^{67} +(-7.17458 + 12.4267i) q^{68} +(0.646305 + 1.11943i) q^{70} -8.99093 q^{71} +6.05655 q^{73} +(0.367832 + 0.637103i) q^{74} +(2.85369 - 4.94274i) q^{76} +(0.853695 - 1.47864i) q^{77} +(4.02827 + 6.97717i) q^{79} -6.02827 q^{80} -28.5333 q^{82} +(0.771205 + 1.33577i) q^{83} +(1.66044 - 2.87597i) q^{85} +(13.0096 - 22.5333i) q^{86} +(9.68872 + 16.7813i) q^{88} +3.00000 q^{89} +0.679116 q^{91} +(8.91751 + 15.4456i) q^{92} +(6.11350 - 10.5889i) q^{94} +(-0.660442 + 1.14392i) q^{95} +(6.12763 + 10.6134i) q^{97} +16.9344 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 5 q^{4} + 3 q^{5} - 5 q^{7} - 6 q^{8}+O(q^{10}) $ 6 * q + q^2 - 5 * q^4 + 3 * q^5 - 5 * q^7 - 6 * q^8	$ 6 q + q^{2} - 5 q^{4} + 3 q^{5} - 5 q^{7} - 6 q^{8} + 2 q^{10} - 2 q^{11} - 4 q^{13} - 9 q^{14} - 5 q^{16} + 4 q^{17} + 8 q^{19} + 5 q^{20} + 4 q^{22} + 3 q^{23} - 3 q^{25} + 4 q^{26} + 10 q^{28} - 7 q^{29} - 8 q^{31} + 17 q^{32} + 4 q^{34} - 10 q^{35} + 12 q^{37} - 2 q^{38} - 3 q^{40} - 13 q^{41} - 10 q^{43} + 44 q^{44} - 6 q^{46} + 13 q^{47} + 2 q^{49} + q^{50} + 12 q^{52} + 4 q^{53} - 4 q^{55} - 9 q^{56} + 17 q^{58} - 2 q^{59} - q^{61} - 84 q^{62} - 30 q^{64} + 4 q^{65} - 11 q^{67} - 22 q^{68} + 9 q^{70} + 20 q^{71} - 16 q^{73} - 16 q^{74} + 12 q^{76} - 2 q^{79} - 10 q^{80} - 58 q^{82} - 15 q^{83} + 2 q^{85} + 28 q^{86} + 24 q^{88} + 18 q^{89} + 20 q^{91} + 39 q^{92} + 31 q^{94} + 4 q^{95} + 18 q^{97} + 80 q^{98}+O(q^{100}) $ 6 * q + q^2 - 5 * q^4 + 3 * q^5 - 5 * q^7 - 6 * q^8 + 2 * q^10 - 2 * q^11 - 4 * q^13 - 9 * q^14 - 5 * q^16 + 4 * q^17 + 8 * q^19 + 5 * q^20 + 4 * q^22 + 3 * q^23 - 3 * q^25 + 4 * q^26 + 10 * q^28 - 7 * q^29 - 8 * q^31 + 17 * q^32 + 4 * q^34 - 10 * q^35 + 12 * q^37 - 2 * q^38 - 3 * q^40 - 13 * q^41 - 10 * q^43 + 44 * q^44 - 6 * q^46 + 13 * q^47 + 2 * q^49 + q^50 + 12 * q^52 + 4 * q^53 - 4 * q^55 - 9 * q^56 + 17 * q^58 - 2 * q^59 - q^61 - 84 * q^62 - 30 * q^64 + 4 * q^65 - 11 * q^67 - 22 * q^68 + 9 * q^70 + 20 * q^71 - 16 * q^73 - 16 * q^74 + 12 * q^76 - 2 * q^79 - 10 * q^80 - 58 * q^82 - 15 * q^83 + 2 * q^85 + 28 * q^86 + 24 * q^88 + 18 * q^89 + 20 * q^91 + 39 * q^92 + 31 * q^94 + 4 * q^95 + 18 * q^97 + 80 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.25707	+	2.17731i	0.888882	+	1.53959i	0.841199	+	0.540726i	$0.181850\pi$
$2$	1.25707	+	2.17731i	0.888882	+	1.53959i	0.0476826	+	0.998863i	$0.484816\pi$
$3$		0			0
$3$		0			0
$4$	−2.16044	+	3.74200i	−1.08022	+	1.87100i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	0.257068	+	0.445256i	0.0971627	+	0.168291i	0.910509	−	0.413489i	$-0.135690\pi$
$7$	0.257068	+	0.445256i	0.0971627	+	0.168291i	−0.813346	+	0.581780i	$0.802357\pi$
$8$	−5.83502			−2.06299
$9$		0			0
$10$	2.51414			0.795040
$11$	−1.66044	−	2.87597i	−0.500642	−	0.867138i	−1.00000		0.000741679i	$-0.999764\pi$
$11$	−1.66044	−	2.87597i	−0.500642	−	0.867138i	0.499358	−	0.866396i	$-0.333569\pi$
$12$		0			0
$13$	0.660442	−	1.14392i	0.183174	−	0.317266i	−0.759786	−	0.650173i	$-0.774696\pi$
$13$	0.660442	−	1.14392i	0.183174	−	0.317266i	0.942960	+	0.332907i	$0.108030\pi$
$14$	−0.646305	+	1.11943i	−0.172732	+	0.299181i
$15$		0			0
$16$	−3.01414	−	5.22064i	−0.753534	−	1.30516i
$17$	3.32088			0.805433			0.402716	−	0.915325i	$-0.368066\pi$
$17$	3.32088			0.805433			0.402716	+	0.915325i	$0.368066\pi$
$18$		0			0
$19$	−1.32088			−0.303032			−0.151516	−	0.988455i	$-0.548415\pi$
$19$	−1.32088			−0.303032			−0.151516	+	0.988455i	$0.548415\pi$
$20$	2.16044	+	3.74200i	0.483090	+	0.836736i
$21$		0			0
$22$	4.17458	−	7.23058i	0.890023	−	1.54157i
$23$	2.06382	−	3.57463i	0.430335	−	0.745363i	−0.566567	−	0.824016i	$-0.691729\pi$
$23$	2.06382	−	3.57463i	0.430335	−	0.745363i	0.996902	+	0.0786532i	$0.0250620\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	3.32088			0.651279
$27$		0			0
$28$	−2.22153			−0.419829
$29$	−0.693252	−	1.20075i	−0.128734	−	0.222973i	0.794453	−	0.607326i	$-0.207758\pi$
$29$	−0.693252	−	1.20075i	−0.128734	−	0.222973i	−0.923186	+	0.384353i	$0.874425\pi$
$30$		0			0
$31$	−4.36783	+	7.56531i	−0.784486	+	1.35877i	0.144820	+	0.989458i	$0.453740\pi$
$31$	−4.36783	+	7.56531i	−0.784486	+	1.35877i	−0.929306	+	0.369311i	$0.879594\pi$
$32$	1.74293	−	3.01885i	0.308110	−	0.533662i
$33$		0			0
$34$	4.17458	+	7.23058i	0.715934	+	1.24003i
$35$	0.514137			0.0869050
$36$		0			0
$37$	0.292611			0.0481049			0.0240524	−	0.999711i	$-0.492343\pi$
$37$	0.292611			0.0481049			0.0240524	+	0.999711i	$0.492343\pi$
$38$	−1.66044	−	2.87597i	−0.269359	−	0.466544i
$39$		0			0
$40$	−2.91751	+	5.05328i	−0.461299	+	0.798993i
$41$	−5.67458	+	9.82866i	−0.886220	+	1.53498i	−0.0419119	+	0.999121i	$0.513345\pi$
$41$	−5.67458	+	9.82866i	−0.886220	+	1.53498i	−0.844308	+	0.535857i	$0.819988\pi$
$42$		0			0
$43$	−5.17458	−	8.96263i	−0.789116	−	1.36679i	−0.926509	−	0.376272i	$-0.877206\pi$
$43$	−5.17458	−	8.96263i	−0.789116	−	1.36679i	0.137393	−	0.990517i	$-0.456128\pi$
$44$	14.3492			2.16322
$45$		0			0
$46$	10.3774			1.53007
$47$	−2.43165	−	4.21174i	−0.354692	−	0.614345i	0.632373	−	0.774664i	$-0.282081\pi$
$47$	−2.43165	−	4.21174i	−0.354692	−	0.614345i	−0.987065	+	0.160319i	$0.948748\pi$
$48$		0			0
$49$	3.36783	−	5.83326i	0.481119	−	0.833322i
$50$	1.25707	−	2.17731i	0.177776	−	0.307918i
$51$		0			0
$52$	2.85369	+	4.94274i	0.395736	+	0.685435i
$53$	5.02827			0.690687			0.345343	−	0.938476i	$-0.387762\pi$
$53$	5.02827			0.690687			0.345343	+	0.938476i	$0.387762\pi$
$54$		0			0
$55$	−3.32088			−0.447788
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$		0			0
$58$	1.74293	−	3.01885i	0.228858	−	0.396394i
$59$	−2.51414	+	4.35461i	−0.327313	+	0.566922i	−0.981978	−	0.188997i	$-0.939476\pi$
$59$	−2.51414	+	4.35461i	−0.327313	+	0.566922i	0.654665	+	0.755919i	$0.272810\pi$
$60$		0			0
$61$	−3.67458	−	6.36456i	−0.470482	−	0.814898i	0.528948	−	0.848654i	$-0.322586\pi$
$61$	−3.67458	−	6.36456i	−0.470482	−	0.814898i	−0.999430	+	0.0337558i	$0.989253\pi$
$62$	−21.9627			−2.78926
$63$		0			0
$64$	−3.29261			−0.411576
$65$	−0.660442	−	1.14392i	−0.0819178	−	0.141886i
$66$		0			0
$67$	−4.72426	+	8.18266i	−0.577160	+	0.999670i	0.418643	+	0.908151i	$0.362506\pi$
$67$	−4.72426	+	8.18266i	−0.577160	+	0.999670i	−0.995803	+	0.0915197i	$0.970828\pi$
$68$	−7.17458	+	12.4267i	−0.870046	+	1.50696i
$69$		0			0
$70$	0.646305	+	1.11943i	0.0772483	+	0.133798i
$71$	−8.99093			−1.06703			−0.533513	−	0.845792i	$-0.679129\pi$
$71$	−8.99093			−1.06703			−0.533513	+	0.845792i	$0.679129\pi$
$72$		0			0
$73$	6.05655			0.708865			0.354433	−	0.935082i	$-0.384674\pi$
$73$	6.05655			0.708865			0.354433	+	0.935082i	$0.384674\pi$
$74$	0.367832	+	0.637103i	0.0427596	+	0.0740617i
$75$		0			0
$76$	2.85369	−	4.94274i	0.327341	−	0.566972i
$77$	0.853695	−	1.47864i	0.0972875	−	0.168507i
$78$		0			0
$79$	4.02827	+	6.97717i	0.453216	+	0.784994i	0.998584	−	0.0532036i	$-0.0169432\pi$
$79$	4.02827	+	6.97717i	0.453216	+	0.784994i	−0.545367	+	0.838197i	$0.683610\pi$
$80$	−6.02827			−0.673982
$81$		0			0
$82$	−28.5333			−3.15098
$83$	0.771205	+	1.33577i	0.0846508	+	0.146619i	0.905242	−	0.424896i	$-0.139689\pi$
$83$	0.771205	+	1.33577i	0.0846508	+	0.146619i	−0.820592	+	0.571515i	$0.806356\pi$
$84$		0			0
$85$	1.66044	−	2.87597i	0.180100	−	0.311943i
$86$	13.0096	−	22.5333i	1.40286	−	2.42983i
$87$		0			0
$88$	9.68872	+	16.7813i	1.03282	+	1.78890i
$89$	3.00000			0.317999			0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000			0.317999			0.159000	+	0.987279i	$0.449173\pi$
$90$		0			0
$91$	0.679116			0.0711906
$92$	8.91751	+	15.4456i	0.929715	+	1.61031i
$93$		0			0
$94$	6.11350	−	10.5889i	0.630559	−	1.09216i
$95$	−0.660442	+	1.14392i	−0.0677599	+	0.117364i
$96$		0			0
$97$	6.12763	+	10.6134i	0.622167	+	1.07762i	0.989081	+	0.147370i	$0.0470808\pi$
$97$	6.12763	+	10.6134i	0.622167	+	1.07762i	−0.366915	+	0.930255i	$0.619586\pi$
$98$	16.9344			1.71063
$99$		0			0
$100$	4.32088			0.432088
$101$	5.83502	+	10.1066i	0.580606	+	1.00564i	0.995408	+	0.0957276i	$0.0305178\pi$
$101$	5.83502	+	10.1066i	0.580606	+	1.00564i	−0.414801	+	0.909912i	$0.636149\pi$
$102$		0			0
$103$	−0.146305	+	0.253408i	−0.0144159	+	0.0249691i	−0.873143	−	0.487464i	$-0.837922\pi$
$103$	−0.146305	+	0.253408i	−0.0144159	+	0.0249691i	0.858727	+	0.512433i	$0.171256\pi$
$104$	−3.85369	+	6.67479i	−0.377886	+	0.654517i
$105$		0			0
$106$	6.32088	+	10.9481i	0.613939	+	1.06337i
$107$	−1.87237			−0.181009			−0.0905043	−	0.995896i	$-0.528848\pi$
$107$	−1.87237			−0.181009			−0.0905043	+	0.995896i	$0.528848\pi$
$108$		0			0
$109$	5.54787			0.531390			0.265695	−	0.964057i	$-0.414399\pi$
$109$	5.54787			0.531390			0.265695	+	0.964057i	$0.414399\pi$
$110$	−4.17458	−	7.23058i	−0.398031	−	0.689409i
$111$		0			0
$112$	1.54968	−	2.68412i	0.146431	−	0.253626i
$113$	3.90064	−	6.75611i	0.366942	−	0.635561i	−0.622144	−	0.782903i	$-0.713738\pi$
$113$	3.90064	−	6.75611i	0.366942	−	0.635561i	0.989086	+	0.147341i	$0.0470716\pi$
$114$		0			0
$115$	−2.06382	−	3.57463i	−0.192452	−	0.333336i
$116$	5.99093			0.556244
$117$		0			0
$118$	−12.6418			−1.16377
$119$	0.853695	+	1.47864i	0.0782581	+	0.135547i
$120$		0			0
$121$	−0.0141369	+	0.0244859i	−0.00128518	+	0.00222599i
$122$	9.23840	−	16.0014i	0.836405	−	1.44870i
$123$		0			0
$124$	−18.8729	−	32.6888i	−1.69484	−	2.93554i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	17.8916			1.58762			0.793810	−	0.608166i	$-0.208094\pi$
$127$	17.8916			1.58762			0.793810	+	0.608166i	$0.208094\pi$
$128$	−7.62490	−	13.2067i	−0.673952	−	1.16732i
$129$		0			0
$130$	1.66044	−	2.87597i	0.145630	−	0.252239i
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	−0.966803	−	0.255524i	$-0.917752\pi$
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	0.704692	+	0.709514i	$0.251085\pi$
$132$		0			0
$133$	−0.339558	−	0.588131i	−0.0294434	−	0.0509974i
$134$	−23.7549			−2.05211
$135$		0			0
$136$	−19.3774			−1.66160
$137$	2.83502	+	4.91040i	0.242212	+	0.419524i	0.961344	−	0.275350i	$-0.0887936\pi$
$137$	2.83502	+	4.91040i	0.242212	+	0.419524i	−0.719132	+	0.694874i	$0.755460\pi$
$138$		0			0
$139$	−4.00000	+	6.92820i	−0.339276	+	0.587643i	−0.984297	−	0.176522i	$-0.943515\pi$
$139$	−4.00000	+	6.92820i	−0.339276	+	0.587643i	0.645021	+	0.764165i	$0.276849\pi$
$140$	−1.11076	+	1.92390i	−0.0938766	+	0.162599i
$141$		0			0
$142$	−11.3022	−	19.5760i	−0.948460	−	1.64278i
$143$	−4.38650			−0.366818
$144$		0			0
$145$	−1.38650			−0.115143
$146$	7.61350	+	13.1870i	0.630097	+	1.09136i
$147$		0			0
$148$	−0.632168	+	1.09495i	−0.0519639	+	0.0900042i
$149$	8.83049	−	15.2948i	0.723422	−	1.25300i	−0.236199	−	0.971705i	$-0.575902\pi$
$149$	8.83049	−	15.2948i	0.723422	−	1.25300i	0.959620	−	0.281298i	$-0.0907650\pi$
$150$		0			0
$151$	−0.632168	−	1.09495i	−0.0514451	−	0.0891056i	0.839156	−	0.543891i	$-0.183049\pi$
$151$	−0.632168	−	1.09495i	−0.0514451	−	0.0891056i	−0.890601	+	0.454785i	$0.849716\pi$
$152$	7.70739			0.625152
$153$		0			0
$154$	4.29261			0.345908
$155$	4.36783	+	7.56531i	0.350833	+	0.607660i
$156$		0			0
$157$	7.83502	−	13.5707i	0.625303	−	1.08306i	−0.363179	−	0.931719i	$-0.618309\pi$
$157$	7.83502	−	13.5707i	0.625303	−	1.08306i	0.988482	−	0.151337i	$-0.0483579\pi$
$158$	−10.1276	+	17.5416i	−0.805711	+	1.39553i
$159$		0			0
$160$	−1.74293	−	3.01885i	−0.137791	−	0.238661i
$161$	2.12217			0.167250
$162$		0			0
$163$	15.7074			1.23030			0.615149	−	0.788411i	$-0.289096\pi$
$163$	15.7074			1.23030			0.615149	+	0.788411i	$0.289096\pi$
$164$	−24.5192	−	42.4685i	−1.91463	−	3.31623i
$165$		0			0
$166$	−1.93892	+	3.35830i	−0.150489	+	0.260655i
$167$	3.08249	−	5.33903i	0.238530	−	0.413146i	−0.721763	−	0.692141i	$-0.756668\pi$
$167$	3.08249	−	5.33903i	0.238530	−	0.413146i	0.960293	+	0.278994i	$0.0900011\pi$
$168$		0			0
$169$	5.62763	+	9.74734i	0.432895	+	0.749796i
$170$	8.34916			0.640351
$171$		0			0
$172$	44.7175			3.40968
$173$	4.29261	+	7.43502i	0.326361	+	0.565274i	0.981787	−	0.189986i	$-0.0608441\pi$
$173$	4.29261	+	7.43502i	0.326361	+	0.565274i	−0.655426	+	0.755260i	$0.727511\pi$
$174$		0			0
$175$	0.257068	−	0.445256i	0.0194325	−	0.0336582i
$176$	−10.0096	+	17.3371i	−0.754502	+	1.30684i
$177$		0			0
$178$	3.77121	+	6.53192i	0.282664	+	0.489588i
$179$	1.06562			0.0796482			0.0398241	−	0.999207i	$-0.487320\pi$
$179$	1.06562			0.0796482			0.0398241	+	0.999207i	$0.487320\pi$
$180$		0			0
$181$	−12.6700			−0.941757			−0.470878	−	0.882198i	$-0.656063\pi$
$181$	−12.6700			−0.941757			−0.470878	+	0.882198i	$0.656063\pi$
$182$	0.853695	+	1.47864i	0.0632801	+	0.109604i
$183$		0			0
$184$	−12.0424	+	20.8581i	−0.887778	+	1.53768i
$185$	0.146305	−	0.253408i	0.0107566	−	0.0186309i
$186$		0			0
$187$	−5.51414	−	9.55077i	−0.403234	−	0.698421i
$188$	21.0137			1.53258
$189$		0			0
$190$	−3.32088			−0.240922
$191$	−8.46719	−	14.6656i	−0.612664	−	1.06117i	−0.990789	−	0.135411i	$-0.956764\pi$
$191$	−8.46719	−	14.6656i	−0.612664	−	1.06117i	0.378125	−	0.925754i	$-0.376569\pi$
$192$		0			0
$193$	−13.3588	+	23.1380i	−0.961585	+	1.66551i	−0.243060	+	0.970011i	$0.578151\pi$
$193$	−13.3588	+	23.1380i	−0.961585	+	1.66551i	−0.718524	+	0.695502i	$0.755182\pi$
$194$	−15.4057	+	26.6835i	−1.10607	+	1.91576i
$195$		0			0
$196$	14.5520	+	25.2048i	1.03943	+	1.80034i
$197$	14.2553			1.01565			0.507823	−	0.861462i	$-0.330450\pi$
$197$	14.2553			1.01565			0.507823	+	0.861462i	$0.330450\pi$
$198$		0			0
$199$	−24.6610			−1.74817			−0.874085	−	0.485773i	$-0.838538\pi$
$199$	−24.6610			−1.74817			−0.874085	+	0.485773i	$0.838538\pi$
$200$	2.91751	+	5.05328i	0.206299	+	0.357321i
$201$		0			0
$202$	−14.6700	+	25.4093i	−1.03218	+	1.78779i
$203$	0.356427	−	0.617349i	0.0250162	−	0.0433294i
$204$		0			0
$205$	5.67458	+	9.82866i	0.396330	+	0.686463i
$206$	−0.735663			−0.0512561
$207$		0			0
$208$	−7.96265			−0.552111
$209$	2.19325	+	3.79882i	0.151710	+	0.262770i
$210$		0			0
$211$	2.68872	−	4.65699i	0.185099	−	0.320601i	−0.758511	−	0.651660i	$-0.774073\pi$
$211$	2.68872	−	4.65699i	0.185099	−	0.320601i	0.943610	+	0.331060i	$0.107406\pi$
$212$	−10.8633	+	18.8158i	−0.746094	+	1.29227i
$213$		0			0
$214$	−2.35369	−	4.07672i	−0.160895	−	0.278679i
$215$	−10.3492			−0.705807
$216$		0			0
$217$	−4.49133			−0.304891
$218$	6.97406	+	12.0794i	0.472343	+	0.818122i
$219$		0			0
$220$	7.17458	−	12.4267i	0.483710	−	0.837810i
$221$	2.19325	−	3.79882i	0.147534	−	0.255537i
$222$		0			0
$223$	−4.33229	−	7.50375i	−0.290112	−	0.502488i	0.683724	−	0.729740i	$-0.260359\pi$
$223$	−4.33229	−	7.50375i	−0.290112	−	0.502488i	−0.973836	+	0.227252i	$0.927026\pi$
$224$	1.79221			0.119747
$225$		0			0
$226$	19.6135			1.30467
$227$	1.66044	+	2.87597i	0.110207	+	0.190885i	0.915854	−	0.401512i	$-0.131515\pi$
$227$	1.66044	+	2.87597i	0.110207	+	0.190885i	−0.805646	+	0.592397i	$0.798182\pi$
$228$		0			0
$229$	12.6559	−	21.9207i	0.836326	−	1.44856i	−0.0566206	−	0.998396i	$-0.518033\pi$
$229$	12.6559	−	21.9207i	0.836326	−	1.44856i	0.892946	−	0.450163i	$-0.148634\pi$
$230$	5.18872	−	8.98712i	0.342134	−	0.592593i
$231$		0			0
$232$	4.04514	+	7.00639i	0.265577	+	0.459992i
$233$	−27.6327			−1.81028			−0.905139	−	0.425116i	$-0.860233\pi$
$233$	−27.6327			−1.81028			−0.905139	+	0.425116i	$0.860233\pi$
$234$		0			0
$235$	−4.86330			−0.317246
$236$	−10.8633	−	18.8158i	−0.707140	−	1.22480i
$237$		0			0
$238$	−2.14631	+	3.71751i	−0.139124	+	0.240970i
$239$	−2.09936	+	3.63620i	−0.135796	+	0.235206i	−0.925901	−	0.377765i	$-0.876693\pi$
$239$	−2.09936	+	3.63620i	−0.135796	+	0.235206i	0.790105	+	0.612971i	$0.210026\pi$
$240$		0			0
$241$	−1.80221	−	3.12152i	−0.116091	−	0.201075i	0.802125	−	0.597157i	$-0.203703\pi$
$241$	−1.80221	−	3.12152i	−0.116091	−	0.201075i	−0.918215	+	0.396082i	$0.870370\pi$
$242$	−0.0710844			−0.00456948
$243$		0			0
$244$	31.7549			2.03290
$245$	−3.36783	−	5.83326i	−0.215163	−	0.372673i
$246$		0			0
$247$	−0.872368	+	1.51099i	−0.0555074	+	0.0961417i
$248$	25.4864	−	44.1437i	1.61839	−	2.80313i
$249$		0			0
$250$	−1.25707	−	2.17731i	−0.0795040	−	0.137705i
$251$	6.87783			0.434125			0.217062	−	0.976158i	$-0.430352\pi$
$251$	6.87783			0.434125			0.217062	+	0.976158i	$0.430352\pi$
$252$		0			0
$253$	−13.7074			−0.861776
$254$	22.4909	+	38.9554i	1.41121	+	2.44428i
$255$		0			0
$256$	15.8774	−	27.5005i	0.992340	−	1.71878i
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	0.435970	+	0.899961i	$0.356405\pi$
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	−0.997374	+	0.0724199i	$0.976928\pi$
$258$		0			0
$259$	0.0752210	+	0.130287i	0.00467400	+	0.00809561i
$260$	5.70739			0.353957
$261$		0			0
$262$	−15.0848			−0.931943
$263$	3.11803	+	5.40059i	0.192266	+	0.333015i	0.946001	−	0.324164i	$-0.105083\pi$
$263$	3.11803	+	5.40059i	0.192266	+	0.333015i	−0.753735	+	0.657179i	$0.771750\pi$
$264$		0			0
$265$	2.51414	−	4.35461i	0.154442	−	0.267502i
$266$	0.853695	−	1.47864i	0.0523434	−	0.0906614i
$267$		0			0
$268$	−20.4130	−	35.3563i	−1.24692	−	2.15973i
$269$	−9.92345			−0.605044			−0.302522	−	0.953142i	$-0.597828\pi$
$269$	−9.92345			−0.605044			−0.302522	+	0.953142i	$0.597828\pi$
$270$		0			0
$271$	6.60442			0.401190			0.200595	−	0.979674i	$-0.435712\pi$
$271$	6.60442			0.401190			0.200595	+	0.979674i	$0.435712\pi$
$272$	−10.0096	−	17.3371i	−0.606921	−	1.05122i
$273$		0			0
$274$	−7.12763	+	12.3454i	−0.430596	+	0.745814i
$275$	−1.66044	+	2.87597i	−0.100128	+	0.173428i
$276$		0			0
$277$	−11.3305	−	19.6250i	−0.680783	−	1.17915i	−0.974742	−	0.223333i	$-0.928306\pi$
$277$	−11.3305	−	19.6250i	−0.680783	−	1.17915i	0.293959	−	0.955818i	$-0.405027\pi$
$278$	−20.1131			−1.20630
$279$		0			0
$280$	−3.00000			−0.179284
$281$	−7.77394	−	13.4649i	−0.463754	−	0.803246i	0.535390	−	0.844605i	$-0.320165\pi$
$281$	−7.77394	−	13.4649i	−0.463754	−	0.803246i	−0.999144	+	0.0413590i	$0.986831\pi$
$282$		0			0
$283$	−0.322689	+	0.558913i	−0.0191819	+	0.0332240i	−0.875457	−	0.483296i	$-0.839439\pi$
$283$	−0.322689	+	0.558913i	−0.0191819	+	0.0332240i	0.856275	+	0.516520i	$0.172773\pi$
$284$	19.4244	−	33.6440i	1.15262	−	1.99640i
$285$		0			0
$286$	−5.51414	−	9.55077i	−0.326058	−	0.564749i
$287$	−5.83502			−0.344430
$288$		0			0
$289$	−5.97173			−0.351278
$290$	−1.74293	−	3.01885i	−0.102348	−	0.177273i
$291$		0			0
$292$	−13.0848	+	22.6636i	−0.765731	+	1.32629i
$293$	−0.688716	+	1.19289i	−0.0402352	+	0.0696895i	−0.885442	−	0.464750i	$-0.846144\pi$
$293$	−0.688716	+	1.19289i	−0.0402352	+	0.0696895i	0.845207	+	0.534440i	$0.179477\pi$
$294$		0			0
$295$	2.51414	+	4.35461i	0.146379	+	0.253535i
$296$	−1.70739			−0.0992400
$297$		0			0
$298$	44.4021			2.57214
$299$	−2.72606	−	4.72168i	−0.157652	−	0.273062i
$300$		0			0
$301$	2.66044	−	4.60802i	0.153345	−	0.265602i
$302$	1.58936	−	2.75285i	0.0914573	−	0.158409i
$303$		0			0
$304$	3.98133	+	6.89586i	0.228345	+	0.395505i
$305$	−7.34916			−0.420812
$306$		0			0
$307$	−7.98546			−0.455754			−0.227877	−	0.973690i	$-0.573178\pi$
$307$	−7.98546			−0.455754			−0.227877	+	0.973690i	$0.573178\pi$
$308$	3.68872	+	6.38904i	0.210184	+	0.364050i
$309$		0			0
$310$	−10.9813	+	19.0202i	−0.623697	+	1.08028i
$311$	4.81635	−	8.34216i	0.273110	−	0.473040i	−0.696547	−	0.717512i	$-0.745281\pi$
$311$	4.81635	−	8.34216i	0.273110	−	0.473040i	0.969657	+	0.244471i	$0.0786143\pi$
$312$		0			0
$313$	12.2685	+	21.2496i	0.693455	+	1.20110i	0.970699	+	0.240300i	$0.0772458\pi$
$313$	12.2685	+	21.2496i	0.693455	+	1.20110i	−0.277244	+	0.960800i	$0.589421\pi$
$314$	39.3966			2.22328
$315$		0			0
$316$	−34.8114			−1.95829
$317$	−10.1746	−	17.6229i	−0.571461	−	0.989800i	−0.996416	−	0.0845855i	$-0.973043\pi$
$317$	−10.1746	−	17.6229i	−0.571461	−	0.989800i	0.424955	−	0.905215i	$-0.360290\pi$
$318$		0			0
$319$	−2.30221	+	3.98755i	−0.128899	+	0.223260i
$320$	−1.64631	+	2.85148i	−0.0920313	+	0.159403i
$321$		0			0
$322$	2.66771	+	4.62061i	0.148666	+	0.257497i
$323$	−4.38650			−0.244072
$324$		0			0
$325$	−1.32088			−0.0732695
$326$	19.7453	+	34.1998i	1.09359	+	1.89415i
$327$		0			0
$328$	33.1113	−	57.3504i	1.82827	−	3.16665i
$329$	1.25020	−	2.16541i	0.0689257	−	0.119383i
$330$		0			0
$331$	−8.22153	−	14.2401i	−0.451896	−	0.782707i	0.546608	−	0.837389i	$-0.315919\pi$
$331$	−8.22153	−	14.2401i	−0.451896	−	0.782707i	−0.998504	+	0.0546819i	$0.982586\pi$
$332$	−6.66458			−0.365766
$333$		0			0
$334$	15.4996			0.848100
$335$	4.72426	+	8.18266i	0.258114	+	0.447066i
$336$		0			0
$337$	−2.44852	+	4.24096i	−0.133379	+	0.231020i	−0.924977	−	0.380023i	$-0.875916\pi$
$337$	−2.44852	+	4.24096i	−0.133379	+	0.231020i	0.791598	+	0.611042i	$0.209249\pi$
$338$	−14.1486	+	24.5062i	−0.769584	+	1.33296i
$339$		0			0
$340$	7.17458	+	12.4267i	0.389096	+	0.673934i
$341$	29.0101			1.57099
$342$		0			0
$343$	7.06201			0.381313
$344$	30.1938	+	52.2972i	1.62794	+	2.81967i
$345$		0			0
$346$	−10.7922	+	18.6927i	−0.580193	+	1.00492i
$347$	11.1372	−	19.2903i	0.597878	−	1.03556i	−0.395256	−	0.918571i	$-0.629344\pi$
$347$	11.1372	−	19.2903i	0.597878	−	1.03556i	0.993134	−	0.116984i	$-0.0373226\pi$
$348$		0			0
$349$	1.47173	+	2.54910i	0.0787797	+	0.136450i	0.902724	−	0.430221i	$-0.141564\pi$
$349$	1.47173	+	2.54910i	0.0787797	+	0.136450i	−0.823944	+	0.566671i	$0.808231\pi$
$350$	1.29261			0.0690929
$351$		0			0
$352$	−11.5761			−0.617011
$353$	9.41478	+	16.3069i	0.501098	+	0.867927i	0.999999	+	0.00126845i	$0.000403761\pi$
$353$	9.41478	+	16.3069i	0.501098	+	0.867927i	−0.498901	+	0.866659i	$0.666263\pi$
$354$		0			0
$355$	−4.49546	+	7.78637i	−0.238594	+	0.413258i
$356$	−6.48133	+	11.2260i	−0.343510	+	0.594976i
$357$		0			0
$358$	1.33956	+	2.32018i	0.0707978	+	0.122625i
$359$	31.8770			1.68241			0.841203	−	0.540720i	$-0.181848\pi$
$359$	31.8770			1.68241			0.841203	+	0.540720i	$0.181848\pi$
$360$		0			0
$361$	−17.2553			−0.908172
$362$	−15.9271	−	27.5866i	−0.837110	−	1.44992i
$363$		0			0
$364$	−1.46719	+	2.54125i	−0.0769016	+	0.133198i
$365$	3.02827	−	5.24512i	0.158507	−	0.274542i
$366$		0			0
$367$	9.17458	+	15.8908i	0.478909	+	0.829495i	0.999708	−	0.0241848i	$-0.00769900\pi$
$367$	9.17458	+	15.8908i	0.478909	+	0.829495i	−0.520798	+	0.853680i	$0.674366\pi$
$368$	−24.8825			−1.29709
$369$		0			0
$370$	0.735663			0.0382453
$371$	1.29261	+	2.23887i	0.0671090	+	0.116236i
$372$		0			0
$373$	1.09936	−	1.90414i	0.0569226	−	0.0985929i	−0.836160	−	0.548486i	$-0.815205\pi$
$373$	1.09936	−	1.90414i	0.0569226	−	0.0985929i	0.893083	+	0.449893i	$0.148538\pi$
$374$	13.8633	−	24.0119i	0.716854	−	1.24163i
$375$		0			0
$376$	14.1887	+	24.5756i	0.731727	+	1.26739i
$377$	−1.83141			−0.0943226
$378$		0			0
$379$	15.4713			0.794709			0.397354	−	0.917665i	$-0.369928\pi$
$379$	15.4713			0.794709			0.397354	+	0.917665i	$0.369928\pi$
$380$	−2.85369	−	4.94274i	−0.146391	−	0.253557i
$381$		0			0
$382$	21.2877	−	36.8713i	1.08917	−	1.88650i
$383$	3.85369	−	6.67479i	0.196915	−	0.341066i	−0.750612	−	0.660743i	$-0.770241\pi$
$383$	3.85369	−	6.67479i	0.196915	−	0.341066i	0.947526	+	0.319677i	$0.103574\pi$
$384$		0			0
$385$	−0.853695	−	1.47864i	−0.0435083	−	0.0753586i
$386$	−67.1715			−3.41894
$387$		0			0
$388$	−52.9536			−2.68831
$389$	−12.3163	−	21.3325i	−0.624464	−	1.08160i	−0.988644	−	0.150274i	$-0.951984\pi$
$389$	−12.3163	−	21.3325i	−0.624464	−	1.08160i	0.364181	−	0.931328i	$-0.381349\pi$
$390$		0			0
$391$	6.85369	−	11.8709i	0.346606	−	0.600340i
$392$	−19.6514	+	34.0372i	−0.992544	+	1.71914i
$393$		0			0
$394$	17.9198	+	31.0381i	0.902789	+	1.56368i
$395$	8.05655			0.405369
$396$		0			0
$397$	−6.77301			−0.339928			−0.169964	−	0.985450i	$-0.554365\pi$
$397$	−6.77301			−0.339928			−0.169964	+	0.985450i	$0.554365\pi$
$398$	−31.0005	−	53.6945i	−1.55392	−	2.69146i
$399$		0			0
$400$	−3.01414	+	5.22064i	−0.150707	+	0.261032i
$401$	−9.24980	+	16.0211i	−0.461913	+	0.800057i	−0.999056	−	0.0434343i	$-0.986170\pi$
$401$	−9.24980	+	16.0211i	−0.461913	+	0.800057i	0.537143	+	0.843491i	$0.319503\pi$
$402$		0			0
$403$	5.76940	+	9.99290i	0.287394	+	0.497782i
$404$	−50.4249			−2.50873
$405$		0			0
$406$	1.79221			0.0889459
$407$	−0.485863	−	0.841540i	−0.0240833	−	0.0417136i
$408$		0			0
$409$	6.70739	−	11.6175i	0.331659	−	0.574450i	−0.651178	−	0.758925i	$-0.725725\pi$
$409$	6.70739	−	11.6175i	0.331659	−	0.574450i	0.982837	+	0.184474i	$0.0590583\pi$
$410$	−14.2667	+	24.7106i	−0.704581	+	1.22037i
$411$		0			0
$412$	−0.632168	−	1.09495i	−0.0311447	−	0.0539442i
$413$	−2.58522			−0.127210
$414$		0			0
$415$	1.54241			0.0757140
$416$	−2.30221	−	3.98755i	−0.112875	−	0.195506i
$417$		0			0
$418$	−5.51414	+	9.55077i	−0.269705	+	0.467143i
$419$	−16.5575	+	28.6784i	−0.808886	+	1.40103i	0.104751	+	0.994499i	$0.466596\pi$
$419$	−16.5575	+	28.6784i	−0.808886	+	1.40103i	−0.913636	+	0.406532i	$0.866738\pi$
$420$		0			0
$421$	7.34916	+	12.7291i	0.358176	+	0.620379i	0.987656	−	0.156637i	$-0.0500654\pi$
$421$	7.34916	+	12.7291i	0.358176	+	0.620379i	−0.629480	+	0.777017i	$0.716732\pi$
$422$	13.5196			0.658124
$423$		0			0
$424$	−29.3401			−1.42488
$425$	−1.66044	−	2.87597i	−0.0805433	−	0.139505i
$426$		0			0
$427$	1.88924	−	3.27225i	0.0914266	−	0.158355i
$428$	4.04514	−	7.00639i	0.195529	−	0.338667i
$429$		0			0
$430$	−13.0096	−	22.5333i	−0.627379	−	1.08665i
$431$	32.7549			1.57775			0.788873	−	0.614556i	$-0.210665\pi$
$431$	32.7549			1.57775			0.788873	+	0.614556i	$0.210665\pi$
$432$		0			0
$433$	−11.8314			−0.568581			−0.284291	−	0.958738i	$-0.591758\pi$
$433$	−11.8314			−0.568581			−0.284291	+	0.958738i	$0.591758\pi$
$434$	−5.64591	−	9.77900i	−0.271012	−	0.469407i
$435$		0			0
$436$	−11.9859	+	20.7601i	−0.574019	+	0.994230i
$437$	−2.72606	+	4.72168i	−0.130405	+	0.225869i
$438$		0			0
$439$	−4.15591	−	7.19824i	−0.198351	−	0.343553i	0.749643	−	0.661842i	$-0.230225\pi$
$439$	−4.15591	−	7.19824i	−0.198351	−	0.343553i	−0.947994	+	0.318289i	$0.896892\pi$
$440$	19.3774			0.923783
$441$		0			0
$442$	11.0283			0.524561
$443$	−14.5876	−	25.2664i	−0.693076	−	1.20044i	−0.970825	−	0.239789i	$-0.922922\pi$
$443$	−14.5876	−	25.2664i	−0.693076	−	1.20044i	0.277750	−	0.960654i	$-0.410411\pi$
$444$		0			0
$445$	1.50000	−	2.59808i	0.0711068	−	0.123161i
$446$	10.8920	−	18.8654i	0.515750	−	0.893305i
$447$		0			0
$448$	−0.846426	−	1.46605i	−0.0399899	−	0.0692645i
$449$	−18.9717			−0.895331			−0.447666	−	0.894201i	$-0.647744\pi$
$449$	−18.9717			−0.895331			−0.447666	+	0.894201i	$0.647744\pi$
$450$		0			0
$451$	37.6892			1.77472
$452$	16.8542	+	29.1924i	0.792756	+	1.37309i
$453$		0			0
$454$	−4.17458	+	7.23058i	−0.195923	+	0.339348i
$455$	0.339558	−	0.588131i	0.0159187	−	0.0275720i
$456$		0			0
$457$	11.6176	+	20.1223i	0.543450	+	0.941283i	0.998703	+	0.0509206i	$0.0162155\pi$
$457$	11.6176	+	20.1223i	0.543450	+	0.941283i	−0.455253	+	0.890362i	$0.650451\pi$
$458$	63.6374			2.97358
$459$		0			0
$460$	17.8350			0.831562
$461$	2.21285	+	3.83277i	0.103063	+	0.178510i	0.912945	−	0.408082i	$-0.133802\pi$
$461$	2.21285	+	3.83277i	0.103063	+	0.178510i	−0.809882	+	0.586592i	$0.800469\pi$
$462$		0			0
$463$	9.75434	−	16.8950i	0.453322	−	0.785178i	−0.545268	−	0.838262i	$-0.683572\pi$
$463$	9.75434	−	16.8950i	0.453322	−	0.785178i	0.998590	+	0.0530845i	$0.0169053\pi$
$464$	−4.17912	+	7.23844i	−0.194011	+	0.336036i
$465$		0			0
$466$	−34.7362	−	60.1648i	−1.60912	−	2.78708i
$467$	24.5935			1.13805			0.569026	−	0.822320i	$-0.307321\pi$
$467$	24.5935			1.13805			0.569026	+	0.822320i	$0.307321\pi$
$468$		0			0
$469$	−4.85783			−0.224314
$470$	−6.11350	−	10.5889i	−0.281995	−	0.488429i
$471$		0			0
$472$	14.6700	−	25.4093i	0.675243	−	1.16956i
$473$	−17.1842	+	29.7639i	−0.790129	+	1.36854i
$474$		0			0
$475$	0.660442	+	1.14392i	0.0303032	+	0.0524866i
$476$	−7.37743			−0.338144
$477$		0			0
$478$	−10.5561			−0.482827
$479$	16.3774	+	28.3665i	0.748304	+	1.29610i	0.948635	+	0.316372i	$0.102465\pi$
$479$	16.3774	+	28.3665i	0.748304	+	1.29610i	−0.200331	+	0.979728i	$0.564202\pi$
$480$		0			0
$481$	0.193252	−	0.334723i	0.00881155	−	0.0152621i
$482$	4.53101	−	7.84793i	0.206382	−	0.357464i
$483$		0			0
$484$	−0.0610840	−	0.105801i	−0.00277655	−	0.00480912i
$485$	12.2553			0.556483
$486$		0			0
$487$	−6.03735			−0.273578			−0.136789	−	0.990600i	$-0.543678\pi$
$487$	−6.03735			−0.273578			−0.136789	+	0.990600i	$0.543678\pi$
$488$	21.4412	+	37.1373i	0.970600	+	1.68113i
$489$		0			0
$490$	8.46719	−	14.6656i	0.382509	−	0.662524i
$491$	7.22153	−	12.5081i	0.325903	−	0.564480i	−0.655792	−	0.754942i	$-0.727665\pi$
$491$	7.22153	−	12.5081i	0.325903	−	0.564480i	0.981695	+	0.190461i	$0.0609984\pi$
$492$		0			0
$493$	−2.30221	−	3.98755i	−0.103686	−	0.179590i
$494$	−4.38650			−0.197358
$495$		0			0
$496$	52.6610			2.36455
$497$	−2.31128	−	4.00326i	−0.103675	−	0.179571i
$498$		0			0
$499$	−10.4859	+	18.1620i	−0.469412	+	0.813045i	−0.999388	−	0.0349673i	$-0.988867\pi$
$499$	−10.4859	+	18.1620i	−0.469412	+	0.813045i	0.529977	+	0.848012i	$0.322201\pi$
$500$	2.16044	−	3.74200i	0.0966179	−	0.167347i
$501$		0			0
$502$	8.64591	+	14.9751i	0.385886	+	0.668374i
$503$	5.31728			0.237086			0.118543	−	0.992949i	$-0.462178\pi$
$503$	5.31728			0.237086			0.118543	+	0.992949i	$0.462178\pi$
$504$		0			0
$505$	11.6700			0.519310
$506$	−17.2311	−	29.8452i	−0.766017	−	1.32678i
$507$		0			0
$508$	−38.6537	+	66.9502i	−1.71498	+	2.97043i
$509$	9.11350	−	15.7850i	0.403949	−	0.699659i	−0.590250	−	0.807221i	$-0.700971\pi$
$509$	9.11350	−	15.7850i	0.403949	−	0.699659i	0.994198	+	0.107561i	$0.0343041\pi$
$510$		0			0
$511$	1.55695	+	2.69671i	0.0688753	+	0.119296i
$512$	49.3365			2.18038
$513$		0			0
$514$	−45.2545			−1.99609
$515$	0.146305	+	0.253408i	0.00644698	+	0.0111665i
$516$		0			0
$517$	−8.07522	+	13.9867i	−0.355148	+	0.615134i
$518$	−0.189116	+	0.327558i	−0.00830927	+	0.0143921i
$519$		0			0
$520$	3.85369	+	6.67479i	0.168996	+	0.292709i
$521$	−40.1232			−1.75783			−0.878915	−	0.476978i	$-0.841732\pi$
$521$	−40.1232			−1.75783			−0.878915	+	0.476978i	$0.841732\pi$
$522$		0			0
$523$	18.9873			0.830257			0.415129	−	0.909763i	$-0.363737\pi$
$523$	18.9873			0.830257			0.415129	+	0.909763i	$0.363737\pi$
$524$	−12.9627	−	22.4520i	−0.566276	−	0.980819i
$525$		0			0
$526$	−7.83916	+	13.5778i	−0.341804	+	0.592021i
$527$	−14.5051	+	25.1235i	−0.631851	+	1.09440i
$528$		0			0
$529$	2.98133	+	5.16381i	0.129623	+	0.224513i
$530$	12.6418			0.549123
$531$		0			0
$532$	2.93438			0.127221
$533$	7.49546	+	12.9825i	0.324665	+	0.562336i
$534$		0			0
$535$	−0.936184	+	1.62152i	−0.0404748	+	0.0701043i
$536$	27.5661	−	47.7460i	1.19068	−	2.06231i
$537$		0			0
$538$	−12.4745	−	21.6064i	−0.537812	−	0.931518i
$539$	−22.3684			−0.963473
$540$		0			0
$541$	16.5279			0.710589			0.355294	−	0.934754i	$-0.384381\pi$
$541$	16.5279			0.710589			0.355294	+	0.934754i	$0.384381\pi$
$542$	8.30221	+	14.3799i	0.356611	+	0.617668i
$543$		0			0
$544$	5.78807	−	10.0252i	0.248162	−	0.429829i
$545$	2.77394	−	4.80460i	0.118822	−	0.205806i
$546$		0			0
$547$	−8.83683	−	15.3058i	−0.377835	−	0.654430i	0.612912	−	0.790151i	$-0.289998\pi$
$547$	−8.83683	−	15.3058i	−0.377835	−	0.654430i	−0.990747	+	0.135721i	$0.956665\pi$
$548$	−24.4996			−1.04657
$549$		0			0
$550$	−8.34916			−0.356009
$551$	0.915706	+	1.58605i	0.0390104	+	0.0675680i
$552$		0			0
$553$	−2.07108	+	3.58722i	−0.0880715	+	0.152544i
$554$	28.4864	−	49.3399i	1.21027	−	2.09625i
$555$		0			0
$556$	−17.2835	−	29.9360i	−0.732985	−	1.26957i
$557$	−17.3401			−0.734723			−0.367362	−	0.930078i	$-0.619739\pi$
$557$	−17.3401			−0.734723			−0.367362	+	0.930078i	$0.619739\pi$
$558$		0			0
$559$	−13.6700			−0.578181
$560$	−1.54968	−	2.68412i	−0.0654859	−	0.113425i
$561$		0			0
$562$	19.5447	−	33.8525i	0.824445	−	1.42798i
$563$	6.49727	−	11.2536i	0.273827	−	0.474283i	−0.696011	−	0.718031i	$-0.745044\pi$
$563$	6.49727	−	11.2536i	0.273827	−	0.474283i	0.969839	+	0.243748i	$0.0783770\pi$
$564$		0			0
$565$	−3.90064	−	6.75611i	−0.164101	−	0.284232i
$566$	−1.62257			−0.0682016
$567$		0			0
$568$	52.4623			2.20127
$569$	−8.34009	−	14.4455i	−0.349635	−	0.605585i	0.636550	−	0.771236i	$-0.280361\pi$
$569$	−8.34009	−	14.4455i	−0.349635	−	0.605585i	−0.986184	+	0.165651i	$0.947028\pi$
$570$		0			0
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$	9.47679	−	16.4143i	0.396245	−	0.686316i
$573$		0			0
$574$	−7.33502	−	12.7046i	−0.306158	−	0.530281i
$575$	−4.12763			−0.172134
$576$		0			0
$577$	−23.5953			−0.982287			−0.491144	−	0.871079i	$-0.663421\pi$
$577$	−23.5953			−0.982287			−0.491144	+	0.871079i	$0.663421\pi$
$578$	−7.50687	−	13.0023i	−0.312245	−	0.540823i
$579$		0			0
$580$	2.99546	−	5.18830i	0.124380	−	0.215432i
$581$	−0.396505	+	0.686767i	−0.0164498	+	0.0284919i
$582$		0			0
$583$	−8.34916	−	14.4612i	−0.345787	−	0.598920i
$584$	−35.3401			−1.46238
$585$		0			0
$586$	−3.46305			−0.143057
$587$	14.0638	+	24.3592i	0.580476	+	1.00541i	0.995423	+	0.0955681i	$0.0304668\pi$
$587$	14.0638	+	24.3592i	0.580476	+	1.00541i	−0.414947	+	0.909846i	$0.636200\pi$
$588$		0			0
$589$	5.76940	−	9.99290i	0.237724	−	0.411750i
$590$	−6.32088	+	10.9481i	−0.260227	+	0.450726i
$591$		0			0
$592$	−0.881969	−	1.52761i	−0.0362487	−	0.0627846i
$593$	9.17872			0.376925			0.188462	−	0.982080i	$-0.439650\pi$
$593$	9.17872			0.376925			0.188462	+	0.982080i	$0.439650\pi$
$594$		0			0
$595$	1.70739			0.0699961
$596$	38.1555	+	66.0873i	1.56291	+	2.70704i
$597$		0			0
$598$	6.85369	−	11.8709i	0.280268	−	0.485439i
$599$	−15.7357	+	27.2550i	−0.642942	+	1.11361i	0.341831	+	0.939761i	$0.388953\pi$
$599$	−15.7357	+	27.2550i	−0.642942	+	1.11361i	−0.984773	+	0.173846i	$0.944380\pi$
$600$		0			0
$601$	14.6327	+	25.3446i	0.596880	+	1.03383i	0.993279	+	0.115748i	$0.0369265\pi$
$601$	14.6327	+	25.3446i	0.596880	+	1.03383i	−0.396398	+	0.918079i	$0.629740\pi$
$602$	13.3774			0.545223
$603$		0			0
$604$	5.46305			0.222288
$605$	0.0141369	+	0.0244859i	0.000574748	+	0.000995493i
$606$		0			0
$607$	22.1017	−	38.2813i	0.897080	−	1.55379i	0.0658708	−	0.997828i	$-0.479017\pi$
$607$	22.1017	−	38.2813i	0.897080	−	1.55379i	0.831209	−	0.555960i	$-0.187649\pi$
$608$	−2.30221	+	3.98755i	−0.0933670	+	0.161716i
$609$		0			0
$610$	−9.23840	−	16.0014i	−0.374052	−	0.647877i
$611$	−6.42385			−0.259881
$612$		0			0
$613$	−35.1715			−1.42056			−0.710282	−	0.703918i	$-0.751432\pi$
$613$	−35.1715			−1.42056			−0.710282	+	0.703918i	$0.751432\pi$
$614$	−10.0383	−	17.3868i	−0.405112	−	0.701674i
$615$		0			0
$616$	−4.98133	+	8.62791i	−0.200703	+	0.347628i
$617$	−3.71285	+	6.43085i	−0.149474	+	0.258896i	−0.931033	−	0.364935i	$-0.881091\pi$
$617$	−3.71285	+	6.43085i	−0.149474	+	0.258896i	0.781559	+	0.623831i	$0.214425\pi$
$618$		0			0
$619$	−4.27394	−	7.40268i	−0.171784	−	0.297539i	0.767260	−	0.641337i	$-0.221620\pi$
$619$	−4.27394	−	7.40268i	−0.171784	−	0.297539i	−0.939044	+	0.343798i	$0.888286\pi$
$620$	−37.7458			−1.51591
$621$		0			0
$622$	24.2179			0.971050
$623$	0.771205	+	1.33577i	0.0308977	+	0.0535164i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−30.8446	+	53.4245i	−1.23280	+	2.13527i
$627$		0			0
$628$	33.8542	+	58.6372i	1.35093	+	2.33988i
$629$	0.971726			0.0387453
$630$		0			0
$631$	−2.36836			−0.0942829			−0.0471415	−	0.998888i	$-0.515011\pi$
$631$	−2.36836			−0.0942829			−0.0471415	+	0.998888i	$0.515011\pi$
$632$	−23.5051	−	40.7120i	−0.934981	−	1.61944i
$633$		0			0
$634$	25.5803	−	44.3064i	1.01592	−	1.75963i
$635$	8.94578	−	15.4946i	0.355003	−	0.614883i
$636$		0			0
$637$	−4.44852	−	7.70506i	−0.176257	−	0.305285i
$638$	−11.5761			−0.458304
$639$		0			0
$640$	−15.2498			−0.602801
$641$	−0.0665480	−	0.115265i	−0.00262849	−	0.00455268i	0.864708	−	0.502275i	$-0.167503\pi$
$641$	−0.0665480	−	0.115265i	−0.00262849	−	0.00455268i	−0.867337	+	0.497722i	$0.834170\pi$
$642$		0			0
$643$	11.3232	−	19.6124i	0.446544	−	0.773437i	−0.551614	−	0.834099i	$-0.685988\pi$
$643$	11.3232	−	19.6124i	0.446544	−	0.773437i	0.998158	+	0.0606623i	$0.0193213\pi$
$644$	−4.58482	+	7.94114i	−0.180667	+	0.312925i
$645$		0			0
$646$	−5.51414	−	9.55077i	−0.216951	−	0.375770i
$647$	−46.3912			−1.82383			−0.911913	−	0.410385i	$-0.865394\pi$
$647$	−46.3912			−1.82383			−0.911913	+	0.410385i	$0.865394\pi$
$648$		0			0
$649$	16.6983			0.655466
$650$	−1.66044	−	2.87597i	−0.0651279	−	0.112805i
$651$		0			0
$652$	−33.9349	+	58.7770i	−1.32899	+	2.30188i
$653$	18.2029	−	31.5283i	0.712333	−	1.23380i	−0.251647	−	0.967819i	$-0.580972\pi$
$653$	18.2029	−	31.5283i	0.712333	−	1.23380i	0.963979	−	0.265977i	$-0.0856946\pi$
$654$		0			0
$655$	3.00000	+	5.19615i	0.117220	+	0.203030i
$656$	68.4158			2.67119
$657$		0			0
$658$	6.28635			0.245067
$659$	9.57068	+	16.5769i	0.372821	+	0.645745i	0.989998	−	0.141079i	$-0.0450572\pi$
$659$	9.57068	+	16.5769i	0.372821	+	0.645745i	−0.617177	+	0.786824i	$0.711724\pi$
$660$		0			0
$661$	−19.9536	+	34.5606i	−0.776104	+	1.34425i	0.158067	+	0.987428i	$0.449474\pi$
$661$	−19.9536	+	34.5606i	−0.776104	+	1.34425i	−0.934172	+	0.356824i	$0.883860\pi$
$662$	20.6700	−	35.8016i	0.803364	−	1.39147i
$663$		0			0
$664$	−4.50000	−	7.79423i	−0.174634	−	0.302475i
$665$	−0.679116			−0.0263350
$666$		0			0
$667$	−5.72298			−0.221595
$668$	13.3191	+	23.0693i	0.515331	+	0.892579i
$669$		0			0
$670$	−11.8774	+	20.5723i	−0.458865	+	0.794778i
$671$	−12.2029	+	21.1360i	−0.471086	+	0.815945i
$672$		0			0
$673$	−11.8254	−	20.4822i	−0.455836	−	0.789532i	0.542899	−	0.839798i	$-0.317326\pi$
$673$	−11.8254	−	20.4822i	−0.455836	−	0.789532i	−0.998736	+	0.0502658i	$0.983993\pi$
$674$	−12.3118			−0.474233
$675$		0			0
$676$	−48.6327			−1.87049
$677$	−7.40157	−	12.8199i	−0.284465	−	0.492709i	0.688014	−	0.725697i	$-0.258483\pi$
$677$	−7.40157	−	12.8199i	−0.284465	−	0.492709i	−0.972479	+	0.232989i	$0.925149\pi$
$678$		0			0
$679$	−3.15044	+	5.45673i	−0.120903	+	0.209410i
$680$	−9.68872	+	16.7813i	−0.371545	+	0.643535i
$681$		0			0
$682$	36.4677	+	63.1639i	1.39642	+	2.41867i
$683$	4.95252			0.189503			0.0947515	−	0.995501i	$-0.469794\pi$
$683$	4.95252			0.189503			0.0947515	+	0.995501i	$0.469794\pi$
$684$		0			0
$685$	5.67004			0.216641
$686$	8.87743	+	15.3762i	0.338942	+	0.587065i
$687$		0			0
$688$	−31.1938	+	54.0292i	−1.18925	+	2.05984i
$689$	3.32088	−	5.75194i	0.126516	−	0.219131i
$690$		0			0
$691$	9.60442	+	16.6353i	0.365369	+	0.632838i	0.988835	−	0.149012i	$-0.0476093\pi$
$691$	9.60442	+	16.6353i	0.365369	+	0.632838i	−0.623466	+	0.781851i	$0.714276\pi$
$692$	−37.0957			−1.41017
$693$		0			0
$694$	56.0011			2.12577
$695$	4.00000	+	6.92820i	0.151729	+	0.262802i
$696$		0			0
$697$	−18.8446	+	32.6398i	−0.713791	+	1.23632i
$698$	−3.70012	+	6.40880i	−0.140052	+	0.242577i
$699$		0			0
$700$	1.11076	+	1.92390i	0.0419829	+	0.0727165i
$701$	29.3492			1.10850			0.554251	−	0.832349i	$-0.313005\pi$
$701$	29.3492			1.10850			0.554251	+	0.832349i	$0.313005\pi$
$702$		0			0
$703$	−0.386505			−0.0145773
$704$	5.46719	+	9.46945i	0.206052	+	0.356893i
$705$		0			0
$706$	−23.6700	+	40.9977i	−0.890834	+	1.54297i
$707$	−3.00000	+	5.19615i	−0.112827	+	0.195421i
$708$		0			0
$709$	−19.3633	−	33.5382i	−0.727204	−	1.25955i	−0.958060	−	0.286566i	$-0.907486\pi$
$709$	−19.3633	−	33.5382i	−0.727204	−	1.25955i	0.230857	−	0.972988i	$-0.425847\pi$
$710$	−22.6044			−0.848329
$711$		0			0
$712$	−17.5051			−0.656030
$713$	18.0288	+	31.2268i	0.675184	+	1.16945i
$714$		0			0
$715$	−2.19325	+	3.79882i	−0.0820230	+	0.142068i
$716$	−2.30221	+	3.98755i	−0.0860377	+	0.149022i
$717$		0			0
$718$	40.0716	+	69.4061i	1.49546	+	2.59021i
$719$	15.0848			0.562569			0.281284	−	0.959624i	$-0.409240\pi$
$719$	15.0848			0.562569			0.281284	+	0.959624i	$0.409240\pi$
$720$		0			0
$721$	−0.150442			−0.00560275
$722$	−21.6910	−	37.5700i	−0.807257	−	1.39821i
$723$		0			0
$724$	27.3729	−	47.4112i	1.01731	−	1.76203i
$725$	−0.693252	+	1.20075i	−0.0257467	+	0.0445947i
$726$		0			0
$727$	−6.17277	−	10.6916i	−0.228936	−	0.396528i	0.728557	−	0.684985i	$-0.240191\pi$
$727$	−6.17277	−	10.6916i	−0.228936	−	0.396528i	−0.957493	+	0.288457i	$0.906858\pi$
$728$	−3.96265			−0.146866
$729$		0			0
$730$	15.2270			0.563576
$731$	−17.1842	−	29.7639i	−0.635580	−	1.10086i
$732$		0			0
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$	−23.0661	+	39.9517i	−0.851387	+	1.47465i
$735$		0			0
$736$	−7.19418	−	12.4607i	−0.265181	−	0.459307i
$737$	31.3774			1.15580
$738$		0			0
$739$	29.7266			1.09351			0.546755	−	0.837293i	$-0.315863\pi$
$739$	29.7266			1.09351			0.546755	+	0.837293i	$0.315863\pi$
$740$	0.632168	+	1.09495i	0.0232390	+	0.0402511i
$741$		0			0
$742$	−3.24980	+	5.62882i	−0.119304	+	0.206640i
$743$	24.1824	−	41.8851i	0.887165	−	1.53662i	0.0439537	−	0.999034i	$-0.486005\pi$
$743$	24.1824	−	41.8851i	0.887165	−	1.53662i	0.843212	−	0.537582i	$-0.180662\pi$
$744$		0			0
$745$	−8.83049	−	15.2948i	−0.323524	−	0.560360i
$746$	5.52787			0.202390
$747$		0			0
$748$	47.6519			1.74233
$749$	−0.481327	−	0.833682i	−0.0175873	−	0.0304621i
$750$		0			0
$751$	15.9102	−	27.5573i	0.580573	−	1.00558i	−0.414838	−	0.909895i	$-0.636162\pi$
$751$	15.9102	−	27.5573i	0.580573	−	1.00558i	0.995411	−	0.0956869i	$-0.0305047\pi$
$752$	−14.6586	+	25.3895i	−0.534546	+	0.925860i
$753$		0			0
$754$	−2.30221	−	3.98755i	−0.0838416	−	0.145218i
$755$	−1.26434			−0.0460139
$756$		0			0
$757$	4.94531			0.179740			0.0898701	−	0.995953i	$-0.471355\pi$
$757$	4.94531			0.179740			0.0898701	+	0.995953i	$0.471355\pi$
$758$	19.4485	+	33.6858i	0.706402	+	1.22352i
$759$		0			0
$760$	3.85369	−	6.67479i	0.139788	−	0.242120i
$761$	17.7125	−	30.6789i	0.642076	−	1.11211i	−0.342893	−	0.939375i	$-0.611407\pi$
$761$	17.7125	−	30.6789i	0.642076	−	1.11211i	0.984969	−	0.172734i	$-0.0552600\pi$
$762$		0			0
$763$	1.42618	+	2.47022i	0.0516313	+	0.0894281i
$764$	73.1715			2.64725
$765$		0			0
$766$	19.3774			0.700135
$767$	3.32088	+	5.75194i	0.119910	+	0.207691i
$768$		0			0
$769$	−24.7125	+	42.8032i	−0.891154	+	1.54352i	−0.0526602	+	0.998612i	$0.516770\pi$
$769$	−24.7125	+	42.8032i	−0.891154	+	1.54352i	−0.838494	+	0.544911i	$0.816563\pi$
$770$	2.14631	−	3.71751i	0.0773475	−	0.133970i
$771$		0			0
$772$	−57.7217	−	99.9768i	−2.07745	−	3.59825i
$773$	−12.6599			−0.455345			−0.227673	−	0.973738i	$-0.573112\pi$
$773$	−12.6599			−0.455345			−0.227673	+	0.973738i	$0.573112\pi$
$774$		0			0
$775$	8.73566			0.313794
$776$	−35.7549	−	61.9292i	−1.28352	−	2.22313i
$777$		0			0
$778$	30.9650	−	53.6329i	1.11015	−	1.92283i
$779$	7.49546	−	12.9825i	0.268553	−	0.465147i
$780$		0			0
$781$	14.9289	+	25.8576i	0.534199	+	0.925259i
$782$	34.4623			1.23237
$783$		0			0
$784$	−40.6044			−1.45016
$785$	−7.83502	−	13.5707i	−0.279644	−	0.484357i
$786$		0			0
$787$	−15.4672	+	26.7900i	−0.551346	+	0.954959i	0.446832	+	0.894618i	$0.352552\pi$
$787$	−15.4672	+	26.7900i	−0.551346	+	0.954959i	−0.998178	+	0.0603410i	$0.980781\pi$
$788$	−30.7977	+	53.3431i	−1.09712	+	1.90027i
$789$		0			0
$790$	10.1276	+	17.5416i	0.360325	+	0.624101i
$791$	4.01093			0.142612
$792$		0			0
$793$	−9.70739			−0.344720
$794$	−8.51414	−	14.7469i	−0.302155	−	0.523349i
$795$		0			0
$796$	53.2786	−	92.2812i	1.88841	−	3.27082i
$797$	−15.2967	+	26.4947i	−0.541839	+	0.938492i	0.456960	+	0.889487i	$0.348938\pi$
$797$	−15.2967	+	26.4947i	−0.541839	+	0.938492i	−0.998799	+	0.0490047i	$0.984395\pi$
$798$		0			0
$799$	−8.07522	−	13.9867i	−0.285681	−	0.494814i
$800$	−3.48586			−0.123244
$801$		0			0
$802$	−46.5105			−1.64234
$803$	−10.0565	−	17.4185i	−0.354888	−	0.614684i
$804$		0			0
$805$	1.06108	−	1.83785i	0.0373983	−	0.0647758i
$806$	−14.5051	+	25.1235i	−0.510919	+	0.884938i
$807$		0			0
$808$	−34.0475	−	58.9720i	−1.19779	−	2.07463i
$809$	2.89703			0.101854			0.0509271	−	0.998702i	$-0.483782\pi$
$809$	2.89703			0.101854			0.0509271	+	0.998702i	$0.483782\pi$
$810$		0			0
$811$	−14.8861			−0.522722			−0.261361	−	0.965241i	$-0.584171\pi$
$811$	−14.8861			−0.522722			−0.261361	+	0.965241i	$0.584171\pi$
$812$	1.54008	+	2.66749i	0.0540462	+	0.0936107i
$813$		0			0
$814$	1.22153	−	2.11575i	0.0428145	−	0.0741568i
$815$	7.85369	−	13.6030i	0.275103	−	0.476492i
$816$		0			0
$817$	6.83502	+	11.8386i	0.239127	+	0.414180i
$818$	33.7266			1.17922
$819$		0			0
$820$	−49.0384			−1.71250
$821$	−4.47586	−	7.75242i	−0.156209	−	0.270561i	0.777290	−	0.629143i	$-0.216594\pi$
$821$	−4.47586	−	7.75242i	−0.156209	−	0.270561i	−0.933498	+	0.358581i	$0.883261\pi$
$822$		0			0
$823$	−1.49727	+	2.59334i	−0.0521915	+	0.0903983i	−0.890941	−	0.454119i	$-0.849954\pi$
$823$	−1.49727	+	2.59334i	−0.0521915	+	0.0903983i	0.838749	+	0.544518i	$0.183287\pi$
$824$	0.853695	−	1.47864i	0.0297399	−	0.0515110i
$825$		0			0
$826$	−3.24980	−	5.62882i	−0.113075	−	0.195852i
$827$	−31.9663			−1.11158			−0.555788	−	0.831324i	$-0.687583\pi$
$827$	−31.9663			−1.11158			−0.555788	+	0.831324i	$0.687583\pi$
$828$		0			0
$829$	22.7458			0.789994			0.394997	−	0.918682i	$-0.370746\pi$
$829$	22.7458			0.789994			0.394997	+	0.918682i	$0.370746\pi$
$830$	1.93892	+	3.35830i	0.0673008	+	0.116568i
$831$		0			0
$832$	−2.17458	+	3.76648i	−0.0753900	+	0.130579i
$833$	11.1842	−	19.3716i	0.387509	−	0.671185i
$834$		0			0
$835$	−3.08249	−	5.33903i	−0.106674	−	0.184765i
$836$	−18.9536			−0.655523
$837$		0			0
$838$	−83.2555			−2.87601
$839$	−11.6322	−	20.1475i	−0.401587	−	0.695569i	0.592331	−	0.805695i	$-0.298208\pi$
$839$	−11.6322	−	20.1475i	−0.401587	−	0.695569i	−0.993918	+	0.110126i	$0.964875\pi$
$840$		0			0
$841$	13.5388	−	23.4499i	0.466855	−	0.808617i
$842$	−18.4768	+	32.0027i	−0.636752	+	1.10289i
$843$		0			0
$844$	11.6176	+	20.1223i	0.399895	+	0.692639i
$845$	11.2553			0.387193
$846$		0			0
$847$	−0.0145366			−0.000499485
$848$	−15.1559	−	26.2508i	−0.520456	−	0.901456i
$849$		0			0
$850$	4.17458	−	7.23058i	0.143187	−	0.248007i
$851$	0.603895	−	1.04598i	0.0207012	−	0.0358556i
$852$		0			0
$853$	−5.49546	−	9.51842i	−0.188161	−	0.325905i	0.756476	−	0.654021i	$-0.226919\pi$
$853$	−5.49546	−	9.51842i	−0.188161	−	0.325905i	−0.944637	+	0.328117i	$0.893586\pi$
$854$	9.49960			0.325070
$855$		0			0
$856$	10.9253			0.373419
$857$	−8.07522	−	13.9867i	−0.275844	−	0.477776i	0.694503	−	0.719489i	$-0.255624\pi$
$857$	−8.07522	−	13.9867i	−0.275844	−	0.477776i	−0.970348	+	0.241713i	$0.922291\pi$
$858$		0			0
$859$	−14.2594	+	24.6980i	−0.486524	+	0.842685i	−0.999880	−	0.0154909i	$-0.995069\pi$
$859$	−14.2594	+	24.6980i	−0.486524	+	0.842685i	0.513356	+	0.858176i	$0.328402\pi$
$860$	22.3588	−	38.7265i	0.762427	−	1.32056i
$861$		0			0
$862$	41.1751	+	71.3174i	1.40243	+	2.42908i
$863$	−12.2890			−0.418322			−0.209161	−	0.977881i	$-0.567073\pi$
$863$	−12.2890			−0.418322			−0.209161	+	0.977881i	$0.567073\pi$
$864$		0			0
$865$	8.58522			0.291906
$866$	−14.8729	−	25.7606i	−0.505402	−	0.875381i
$867$		0			0
$868$	9.70325	−	16.8065i	0.329350	−	0.570451i
$869$	13.3774	−	23.1704i	0.453798	−	0.786002i
$870$		0			0
$871$	6.24020	+	10.8083i	0.211441	+	0.366227i
$872$	−32.3720			−1.09625
$873$		0			0
$874$	−13.7074			−0.463659
$875$	−0.257068	−	0.445256i	−0.00869050	−	0.0150524i
$876$		0			0
$877$	19.8501	−	34.3814i	0.670290	−	1.16098i	−0.307532	−	0.951538i	$-0.599503\pi$
$877$	19.8501	−	34.3814i	0.670290	−	1.16098i	0.977822	−	0.209438i	$-0.0671635\pi$
$878$	10.4485	−	18.0974i	0.352620	−	0.610756i
$879$		0			0
$880$	10.0096	+	17.3371i	0.337424	+	0.584435i
$881$	−32.1040			−1.08161			−0.540806	−	0.841147i	$-0.681881\pi$
$881$	−32.1040			−1.08161			−0.540806	+	0.841147i	$0.681881\pi$
$882$		0			0
$883$	13.5051			0.454482			0.227241	−	0.973839i	$-0.427030\pi$
$883$	13.5051			0.454482			0.227241	+	0.973839i	$0.427030\pi$
$884$	9.47679	+	16.4143i	0.318739	+	0.552072i
$885$		0			0
$886$	36.6751	−	63.5231i	1.23212	−	2.13410i
$887$	17.5611	−	30.4167i	0.589643	−	1.02129i	−0.404635	−	0.914478i	$-0.632602\pi$
$887$	17.5611	−	30.4167i	0.589643	−	1.02129i	0.994279	−	0.106814i	$-0.0340651\pi$
$888$		0			0
$889$	4.59936	+	7.96632i	0.154258	+	0.267182i
$890$	7.54241			0.252822
$891$		0			0
$892$	37.4386			1.25354
$893$	3.21193	+	5.56322i	0.107483	+	0.186166i
$894$		0			0
$895$	0.532810	−	0.922854i	0.0178099	−	0.0308476i
$896$	3.92024	−	6.79006i	0.130966	−	0.226840i
$897$		0			0
$898$	−23.8488	−	41.3073i	−0.795843	−	1.37844i
$899$	12.1120			0.403959
$900$		0			0
$901$	16.6983			0.556302
$902$	47.3780	+	82.0610i	1.57751	+	2.73233i
$903$		0			0
$904$	−22.7603	+	39.4220i	−0.756997	+	1.31116i
$905$	−6.33502	+	10.9726i	−0.210583	+	0.364741i
$906$		0			0
$907$	−7.55928	−	13.0931i	−0.251002	−	0.434748i	0.712800	−	0.701367i	$-0.247427\pi$
$907$	−7.55928	−	13.0931i	−0.251002	−	0.434748i	−0.963802	+	0.266619i	$0.914093\pi$
$908$	−14.3492			−0.476194
$909$		0			0
$910$	1.70739			0.0565994
$911$	26.2781	+	45.5150i	0.870631	+	1.50798i	0.861345	+	0.508021i	$0.169623\pi$
$911$	26.2781	+	45.5150i	0.870631	+	1.50798i	0.00928675	+	0.999957i	$0.497044\pi$
$912$		0			0
$913$	2.56108	−	4.43593i	0.0847595	−	0.146808i
$914$	−29.2083	+	50.5903i	−0.966125	+	1.67338i
$915$		0			0
$916$	54.6847	+	94.7167i	1.80683	+	3.12953i
$917$	−3.08482			−0.101870
$918$		0			0
$919$	−54.5489			−1.79940			−0.899702	−	0.436505i	$-0.856216\pi$
$919$	−54.5489			−1.79940			−0.899702	+	0.436505i	$0.856216\pi$
$920$	12.0424	+	20.8581i	0.397027	+	0.687670i
$921$		0			0
$922$	−5.56342	+	9.63612i	−0.183221	+	0.317349i
$923$	−5.93799	+	10.2849i	−0.195451	+	0.338532i
$924$		0			0
$925$	−0.146305	−	0.253408i	−0.00481049	−	0.00833201i
$926$	49.0475			1.61180
$927$		0			0
$928$	−4.83317			−0.158656
$929$	10.1896	+	17.6490i	0.334311	+	0.579044i	0.983352	−	0.181709i	$-0.0581630\pi$
$929$	10.1896	+	17.6490i	0.334311	+	0.579044i	−0.649041	+	0.760753i	$0.724830\pi$
$930$		0			0
$931$	−4.44852	+	7.70506i	−0.145794	+	0.252523i
$932$	59.6988	−	103.401i	1.95550	−	3.38703i
$933$		0			0
$934$	30.9157	+	53.5476i	1.01159	+	1.75213i
$935$	−11.0283			−0.360663
$936$		0			0
$937$	49.1979			1.60723			0.803613	−	0.595152i	$-0.202908\pi$
$937$	49.1979			1.60723			0.803613	+	0.595152i	$0.202908\pi$
$938$	−6.10663	−	10.5770i	−0.199388	−	0.345351i
$939$		0			0
$940$	10.5069	−	18.1984i	0.342696	−	0.593567i
$941$	−11.6186	+	20.1239i	−0.378754	+	0.656022i	−0.990881	−	0.134738i	$-0.956981\pi$
$941$	−11.6186	+	20.1239i	−0.378754	+	0.656022i	0.612127	+	0.790759i	$0.290314\pi$
$942$		0			0
$943$	23.4226	+	40.5691i	0.762744	+	1.32111i
$944$	30.3118			0.986565
$945$		0			0
$946$	−86.4068			−2.80933
$947$	18.5821	+	32.1851i	0.603837	+	1.04588i	0.992234	+	0.124384i	$0.0396955\pi$
$947$	18.5821	+	32.1851i	0.603837	+	1.04588i	−0.388397	+	0.921492i	$0.626971\pi$
$948$		0			0
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$	−1.66044	+	2.87597i	−0.0538719	+	0.0933088i
$951$		0			0
$952$	−4.98133	−	8.62791i	−0.161446	−	0.279632i
$953$	23.5761			0.763706			0.381853	−	0.924223i	$-0.375286\pi$
$953$	23.5761			0.763706			0.381853	+	0.924223i	$0.375286\pi$
$954$		0			0
$955$	−16.9344			−0.547984
$956$	−9.07108	−	15.7116i	−0.293380	−	0.508149i
$957$		0			0
$958$	−41.1751	+	71.3174i	−1.33031	+	2.30416i
$959$	−1.45759	+	2.52462i	−0.0470680	+	0.0815242i
$960$		0			0
$961$	−22.6559	−	39.2412i	−0.730836	−	1.26584i
$962$	0.971726			0.0313297
$963$		0			0
$964$	15.5743			0.501614
$965$	13.3588	+	23.1380i	0.430034	+	0.744840i
$966$		0			0
$967$	−4.19145	+	7.25980i	−0.134788	+	0.233459i	−0.925516	−	0.378708i	$-0.876369\pi$
$967$	−4.19145	+	7.25980i	−0.134788	+	0.233459i	0.790729	+	0.612167i	$0.209702\pi$
$968$	0.0824893	−	0.142876i	0.00265131	−	0.00459220i
$969$		0			0
$970$	15.4057	+	26.6835i	0.494647	+	0.856754i
$971$	−13.2078			−0.423858			−0.211929	−	0.977285i	$-0.567975\pi$
$971$	−13.2078			−0.423858			−0.211929	+	0.977285i	$0.567975\pi$
$972$		0			0
$973$	−4.11310			−0.131860
$974$	−7.58936	−	13.1452i	−0.243179	−	0.421198i
$975$		0			0
$976$	−22.1514	+	38.3673i	−0.709048	+	1.22811i
$977$	−7.16551	+	12.4110i	−0.229245	+	0.397064i	−0.957585	−	0.288153i	$-0.906959\pi$
$977$	−7.16551	+	12.4110i	−0.229245	+	0.397064i	0.728340	+	0.685216i	$0.240292\pi$
$978$		0			0
$979$	−4.98133	−	8.62791i	−0.159204	−	0.275749i
$980$	29.1040			0.929694
$981$		0			0
$982$	36.3118			1.15876
$983$	−16.1541	−	27.9797i	−0.515236	−	0.892415i	−0.999844	−	0.0176831i	$-0.994371\pi$
$983$	−16.1541	−	27.9797i	−0.515236	−	0.892415i	0.484608	−	0.874732i	$-0.338962\pi$
$984$		0			0
$985$	7.12763	−	12.3454i	0.227105	−	0.393358i
$986$	5.78807	−	10.0252i	0.184330	−	0.319269i
$987$		0			0
$988$	−3.76940	−	6.52879i	−0.119921	−	0.207709i
$989$	−42.7175			−1.35834
$990$		0			0
$991$	−39.6700			−1.26016			−0.630080	−	0.776530i	$-0.716978\pi$
$991$	−39.6700			−1.26016			−0.630080	+	0.776530i	$0.716978\pi$
$992$	15.2257	+	26.3716i	0.483415	+	0.837300i
$993$		0			0
$994$	5.81088	−	10.0647i	0.184310	−	0.319234i
$995$	−12.3305	+	21.3570i	−0.390903	+	0.677063i
$996$		0			0
$997$	−19.3437	−	33.5043i	−0.612621	−	1.06109i	−0.990797	−	0.135357i	$-0.956782\pi$
$997$	−19.3437	−	33.5043i	−0.612621	−	1.06109i	0.378176	−	0.925734i	$-0.376551\pi$
$998$	−52.7258			−1.66901
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.e.b.91.3		6
3.2	odd	2		45.2.e.b.31.1	yes	6
4.3	odd	2		2160.2.q.k.1441.1		6
5.2	odd	4		675.2.k.b.199.1		12
5.3	odd	4		675.2.k.b.199.6		12
5.4	even	2		675.2.e.b.226.1		6
9.2	odd	6		45.2.e.b.16.1	✓	6
9.4	even	3		405.2.a.i.1.1		3
9.5	odd	6		405.2.a.j.1.3		3
9.7	even	3	inner	135.2.e.b.46.3		6
12.11	even	2		720.2.q.i.481.1		6
15.2	even	4		225.2.k.b.49.6		12
15.8	even	4		225.2.k.b.49.1		12
15.14	odd	2		225.2.e.b.76.3		6
36.7	odd	6		2160.2.q.k.721.1		6
36.11	even	6		720.2.q.i.241.1		6
36.23	even	6		6480.2.a.bv.1.3		3
36.31	odd	6		6480.2.a.bs.1.3		3
45.2	even	12		225.2.k.b.124.1		12
45.4	even	6		2025.2.a.o.1.3		3
45.7	odd	12		675.2.k.b.424.6		12
45.13	odd	12		2025.2.b.m.649.6		6
45.14	odd	6		2025.2.a.n.1.1		3
45.22	odd	12		2025.2.b.m.649.1		6
45.23	even	12		2025.2.b.l.649.1		6
45.29	odd	6		225.2.e.b.151.3		6
45.32	even	12		2025.2.b.l.649.6		6
45.34	even	6		675.2.e.b.451.1		6
45.38	even	12		225.2.k.b.124.6		12
45.43	odd	12		675.2.k.b.424.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.b.16.1	✓	6	9.2	odd	6
45.2.e.b.31.1	yes	6	3.2	odd	2
135.2.e.b.46.3		6	9.7	even	3	inner
135.2.e.b.91.3		6	1.1	even	1	trivial
225.2.e.b.76.3		6	15.14	odd	2
225.2.e.b.151.3		6	45.29	odd	6
225.2.k.b.49.1		12	15.8	even	4
225.2.k.b.49.6		12	15.2	even	4
225.2.k.b.124.1		12	45.2	even	12
225.2.k.b.124.6		12	45.38	even	12
405.2.a.i.1.1		3	9.4	even	3
405.2.a.j.1.3		3	9.5	odd	6
675.2.e.b.226.1		6	5.4	even	2
675.2.e.b.451.1		6	45.34	even	6
675.2.k.b.199.1		12	5.2	odd	4
675.2.k.b.199.6		12	5.3	odd	4
675.2.k.b.424.1		12	45.43	odd	12
675.2.k.b.424.6		12	45.7	odd	12
720.2.q.i.241.1		6	36.11	even	6
720.2.q.i.481.1		6	12.11	even	2
2025.2.a.n.1.1		3	45.14	odd	6
2025.2.a.o.1.3		3	45.4	even	6
2025.2.b.l.649.1		6	45.23	even	12
2025.2.b.l.649.6		6	45.32	even	12
2025.2.b.m.649.1		6	45.22	odd	12
2025.2.b.m.649.6		6	45.13	odd	12
2160.2.q.k.721.1		6	36.7	odd	6
2160.2.q.k.1441.1		6	4.3	odd	2
6480.2.a.bs.1.3		3	36.31	odd	6
6480.2.a.bv.1.3		3	36.23	even	6

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.25707 + 2.17731i) q^{2} +(-2.16044 + 3.74200i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.257068 + 0.445256i) q^{7} -5.83502 q^{8} +O(q^{10})\)	\(q+(1.25707 + 2.17731i) q^{2} +(-2.16044 + 3.74200i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.257068 + 0.445256i) q^{7} -5.83502 q^{8} +2.51414 q^{10} +(-1.66044 - 2.87597i) q^{11} +(0.660442 - 1.14392i) q^{13} +(-0.646305 + 1.11943i) q^{14} +(-3.01414 - 5.22064i) q^{16} +3.32088 q^{17} -1.32088 q^{19} +(2.16044 + 3.74200i) q^{20} +(4.17458 - 7.23058i) q^{22} +(2.06382 - 3.57463i) q^{23} +(-0.500000 - 0.866025i) q^{25} +3.32088 q^{26} -2.22153 q^{28} +(-0.693252 - 1.20075i) q^{29} +(-4.36783 + 7.56531i) q^{31} +(1.74293 - 3.01885i) q^{32} +(4.17458 + 7.23058i) q^{34} +0.514137 q^{35} +0.292611 q^{37} +(-1.66044 - 2.87597i) q^{38} +(-2.91751 + 5.05328i) q^{40} +(-5.67458 + 9.82866i) q^{41} +(-5.17458 - 8.96263i) q^{43} +14.3492 q^{44} +10.3774 q^{46} +(-2.43165 - 4.21174i) q^{47} +(3.36783 - 5.83326i) q^{49} +(1.25707 - 2.17731i) q^{50} +(2.85369 + 4.94274i) q^{52} +5.02827 q^{53} -3.32088 q^{55} +(-1.50000 - 2.59808i) q^{56} +(1.74293 - 3.01885i) q^{58} +(-2.51414 + 4.35461i) q^{59} +(-3.67458 - 6.36456i) q^{61} -21.9627 q^{62} -3.29261 q^{64} +(-0.660442 - 1.14392i) q^{65} +(-4.72426 + 8.18266i) q^{67} +(-7.17458 + 12.4267i) q^{68} +(0.646305 + 1.11943i) q^{70} -8.99093 q^{71} +6.05655 q^{73} +(0.367832 + 0.637103i) q^{74} +(2.85369 - 4.94274i) q^{76} +(0.853695 - 1.47864i) q^{77} +(4.02827 + 6.97717i) q^{79} -6.02827 q^{80} -28.5333 q^{82} +(0.771205 + 1.33577i) q^{83} +(1.66044 - 2.87597i) q^{85} +(13.0096 - 22.5333i) q^{86} +(9.68872 + 16.7813i) q^{88} +3.00000 q^{89} +0.679116 q^{91} +(8.91751 + 15.4456i) q^{92} +(6.11350 - 10.5889i) q^{94} +(-0.660442 + 1.14392i) q^{95} +(6.12763 + 10.6134i) q^{97} +16.9344 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 5 q^{4} + 3 q^{5} - 5 q^{7} - 6 q^{8}+O(q^{10}) \) 6 * q + q^2 - 5 * q^4 + 3 * q^5 - 5 * q^7 - 6 * q^8	\( 6 q + q^{2} - 5 q^{4} + 3 q^{5} - 5 q^{7} - 6 q^{8} + 2 q^{10} - 2 q^{11} - 4 q^{13} - 9 q^{14} - 5 q^{16} + 4 q^{17} + 8 q^{19} + 5 q^{20} + 4 q^{22} + 3 q^{23} - 3 q^{25} + 4 q^{26} + 10 q^{28} - 7 q^{29} - 8 q^{31} + 17 q^{32} + 4 q^{34} - 10 q^{35} + 12 q^{37} - 2 q^{38} - 3 q^{40} - 13 q^{41} - 10 q^{43} + 44 q^{44} - 6 q^{46} + 13 q^{47} + 2 q^{49} + q^{50} + 12 q^{52} + 4 q^{53} - 4 q^{55} - 9 q^{56} + 17 q^{58} - 2 q^{59} - q^{61} - 84 q^{62} - 30 q^{64} + 4 q^{65} - 11 q^{67} - 22 q^{68} + 9 q^{70} + 20 q^{71} - 16 q^{73} - 16 q^{74} + 12 q^{76} - 2 q^{79} - 10 q^{80} - 58 q^{82} - 15 q^{83} + 2 q^{85} + 28 q^{86} + 24 q^{88} + 18 q^{89} + 20 q^{91} + 39 q^{92} + 31 q^{94} + 4 q^{95} + 18 q^{97} + 80 q^{98}+O(q^{100}) \) 6 * q + q^2 - 5 * q^4 + 3 * q^5 - 5 * q^7 - 6 * q^8 + 2 * q^10 - 2 * q^11 - 4 * q^13 - 9 * q^14 - 5 * q^16 + 4 * q^17 + 8 * q^19 + 5 * q^20 + 4 * q^22 + 3 * q^23 - 3 * q^25 + 4 * q^26 + 10 * q^28 - 7 * q^29 - 8 * q^31 + 17 * q^32 + 4 * q^34 - 10 * q^35 + 12 * q^37 - 2 * q^38 - 3 * q^40 - 13 * q^41 - 10 * q^43 + 44 * q^44 - 6 * q^46 + 13 * q^47 + 2 * q^49 + q^50 + 12 * q^52 + 4 * q^53 - 4 * q^55 - 9 * q^56 + 17 * q^58 - 2 * q^59 - q^61 - 84 * q^62 - 30 * q^64 + 4 * q^65 - 11 * q^67 - 22 * q^68 + 9 * q^70 + 20 * q^71 - 16 * q^73 - 16 * q^74 + 12 * q^76 - 2 * q^79 - 10 * q^80 - 58 * q^82 - 15 * q^83 + 2 * q^85 + 28 * q^86 + 24 * q^88 + 18 * q^89 + 20 * q^91 + 39 * q^92 + 31 * q^94 + 4 * q^95 + 18 * q^97 + 80 * q^98

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