LMFDB - Embedded newform 1755.2.i.f.1171.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1755,2,Mod(586,1755)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1755, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1755.586");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1755 = 3^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1755.i (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:	$14.0137455547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 20 x^{14} - 44 x^{13} + 96 x^{12} - 107 x^{11} + 178 x^{10} - 19 x^{9} + 231 x^{8} + \cdots + 268 $ x^16 - 5x^15 + 20x^14 - 44x^13 + 96x^12 - 107x^11 + 178x^10 - 19x^9 + 231x^8 + 326x^7 + 551x^6 + 859x^5 + 1118x^4 + 1215x^3 + 1103x^2 + 770*x + 268
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 585)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1171.5
Root			$0.172467 + 1.52157i$ of defining polynomial
Character	$\chi$	$=$	1755.1171
Dual form			1755.2.i.f.586.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.327533 + 0.567303i) q^{2} +(0.785445 - 1.36043i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.388592 + 0.673061i) q^{7} +2.33917 q^{8} +O(q^{10})$	\(q+(0.327533 + 0.567303i) q^{2} +(0.785445 - 1.36043i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.388592 + 0.673061i) q^{7} +2.33917 q^{8} -0.655066 q^{10} +(-2.03399 - 3.52297i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-0.254553 + 0.440899i) q^{14} +(-0.804735 - 1.39384i) q^{16} -5.29154 q^{17} +6.65042 q^{19} +(0.785445 + 1.36043i) q^{20} +(1.33239 - 2.30778i) q^{22} +(1.15283 - 1.99677i) q^{23} +(-0.500000 - 0.866025i) q^{25} +0.655066 q^{26} +1.22087 q^{28} +(3.19008 + 5.52538i) q^{29} +(4.47259 - 7.74675i) q^{31} +(2.86632 - 4.96461i) q^{32} +(-1.73315 - 3.00191i) q^{34} -0.777184 q^{35} -2.80592 q^{37} +(2.17823 + 3.77280i) q^{38} +(-1.16958 + 2.02578i) q^{40} +(3.80493 - 6.59034i) q^{41} +(-4.42183 - 7.65883i) q^{43} -6.39034 q^{44} +1.51036 q^{46} +(-2.04391 - 3.54016i) q^{47} +(3.19799 - 5.53909i) q^{49} +(0.327533 - 0.567303i) q^{50} +(-0.785445 - 1.36043i) q^{52} +4.78025 q^{53} +4.06797 q^{55} +(0.908981 + 1.57440i) q^{56} +(-2.08971 + 3.61949i) q^{58} +(-2.37049 + 4.10581i) q^{59} +(7.18299 + 12.4413i) q^{61} +5.85967 q^{62} +0.536314 q^{64} +(0.500000 + 0.866025i) q^{65} +(-5.39353 + 9.34188i) q^{67} +(-4.15621 + 7.19877i) q^{68} +(-0.254553 - 0.440899i) q^{70} -0.307776 q^{71} -7.50636 q^{73} +(-0.919032 - 1.59181i) q^{74} +(5.22353 - 9.04743i) q^{76} +(1.58078 - 2.73799i) q^{77} +(-3.80949 - 6.59822i) q^{79} +1.60947 q^{80} +4.98496 q^{82} +(-6.26484 - 10.8510i) q^{83} +(2.64577 - 4.58261i) q^{85} +(2.89659 - 5.01704i) q^{86} +(-4.75783 - 8.24081i) q^{88} +11.7743 q^{89} +0.777184 q^{91} +(-1.81098 - 3.13670i) q^{92} +(1.33889 - 2.31903i) q^{94} +(-3.32521 + 5.75943i) q^{95} +(3.04268 + 5.27007i) q^{97} +4.18979 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8	$ 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8} - 6 q^{10} + 6 q^{11} + 8 q^{13} + 10 q^{14} - 11 q^{16} + 4 q^{17} - 20 q^{19} - 9 q^{20} - 3 q^{22} + 6 q^{23} - 8 q^{25} + 6 q^{26} - 68 q^{28} + 14 q^{29} + 31 q^{31} + q^{32} + 7 q^{34} - 22 q^{35} + 2 q^{37} + 9 q^{38} - 6 q^{40} - 12 q^{41} - 15 q^{43} - 32 q^{44} - 64 q^{46} - 18 q^{47} - 17 q^{49} + 3 q^{50} + 9 q^{52} - 4 q^{53} - 12 q^{55} + 16 q^{56} + 42 q^{58} + 24 q^{59} + 9 q^{61} + 40 q^{62} - 60 q^{64} + 8 q^{65} + 18 q^{67} - 14 q^{68} + 10 q^{70} - 20 q^{71} + 12 q^{73} - 37 q^{74} + 53 q^{76} - 34 q^{77} + 3 q^{79} + 22 q^{80} - 68 q^{82} - 10 q^{83} - 2 q^{85} + 60 q^{86} + 14 q^{88} + 26 q^{89} + 22 q^{91} + 5 q^{92} - 17 q^{94} + 10 q^{95} + 34 q^{97} + 60 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8 - 6 * q^10 + 6 * q^11 + 8 * q^13 + 10 * q^14 - 11 * q^16 + 4 * q^17 - 20 * q^19 - 9 * q^20 - 3 * q^22 + 6 * q^23 - 8 * q^25 + 6 * q^26 - 68 * q^28 + 14 * q^29 + 31 * q^31 + q^32 + 7 * q^34 - 22 * q^35 + 2 * q^37 + 9 * q^38 - 6 * q^40 - 12 * q^41 - 15 * q^43 - 32 * q^44 - 64 * q^46 - 18 * q^47 - 17 * q^49 + 3 * q^50 + 9 * q^52 - 4 * q^53 - 12 * q^55 + 16 * q^56 + 42 * q^58 + 24 * q^59 + 9 * q^61 + 40 * q^62 - 60 * q^64 + 8 * q^65 + 18 * q^67 - 14 * q^68 + 10 * q^70 - 20 * q^71 + 12 * q^73 - 37 * q^74 + 53 * q^76 - 34 * q^77 + 3 * q^79 + 22 * q^80 - 68 * q^82 - 10 * q^83 - 2 * q^85 + 60 * q^86 + 14 * q^88 + 26 * q^89 + 22 * q^91 + 5 * q^92 - 17 * q^94 + 10 * q^95 + 34 * q^97 + 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1755\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	0.327533	+	0.567303i	0.231601	+	0.401144i	0.958279	−	0.285833i	$-0.0922704\pi$
$2$	0.327533	+	0.567303i	0.231601	+	0.401144i	−0.726679	+	0.686978i	$0.758937\pi$
$3$		0			0
$3$		0			0
$4$	0.785445	−	1.36043i	0.392722	−	0.680215i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	0.388592	+	0.673061i	0.146874	+	0.254393i	0.930071	−	0.367381i	$-0.119746\pi$
$7$	0.388592	+	0.673061i	0.146874	+	0.254393i	−0.783197	+	0.621774i	$0.786412\pi$
$8$	2.33917			0.827020
$9$		0			0
$10$	−0.655066			−0.207150
$11$	−2.03399	−	3.52297i	−0.613270	−	1.06221i	−0.990685	−	0.136171i	$-0.956520\pi$
$11$	−2.03399	−	3.52297i	−0.613270	−	1.06221i	0.377415	−	0.926044i	$-0.376813\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	−0.254553	+	0.440899i	−0.0680322	+	0.117835i
$15$		0			0
$16$	−0.804735	−	1.39384i	−0.201184	−	0.348461i
$17$	−5.29154			−1.28339			−0.641693	−	0.766961i	$-0.721768\pi$
$17$	−5.29154			−1.28339			−0.641693	+	0.766961i	$0.721768\pi$
$18$		0			0
$19$	6.65042			1.52571			0.762855	−	0.646569i	$-0.223797\pi$
$19$	6.65042			1.52571			0.762855	+	0.646569i	$0.223797\pi$
$20$	0.785445	+	1.36043i	0.175631	+	0.304201i
$21$		0			0
$22$	1.33239	−	2.30778i	0.284067	−	0.492019i
$23$	1.15283	−	1.99677i	0.240383	−	0.416355i	−0.720441	−	0.693517i	$-0.756060\pi$
$23$	1.15283	−	1.99677i	0.240383	−	0.416355i	0.960823	+	0.277162i	$0.0893937\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.655066			0.128469
$27$		0			0
$28$	1.22087			0.230723
$29$	3.19008	+	5.52538i	0.592383	+	1.02604i	0.993910	+	0.110190i	$0.0351461\pi$
$29$	3.19008	+	5.52538i	0.592383	+	1.02604i	−0.401527	+	0.915847i	$0.631521\pi$
$30$		0			0
$31$	4.47259	−	7.74675i	0.803300	−	1.39136i	−0.114132	−	0.993466i	$-0.536409\pi$
$31$	4.47259	−	7.74675i	0.803300	−	1.39136i	0.917433	−	0.397891i	$-0.130258\pi$
$32$	2.86632	−	4.96461i	0.506699	−	0.877628i
$33$		0			0
$34$	−1.73315	−	3.00191i	−0.297233	−	0.514823i
$35$	−0.777184			−0.131368
$36$		0			0
$37$	−2.80592			−0.461291			−0.230645	−	0.973038i	$-0.574084\pi$
$37$	−2.80592			−0.461291			−0.230645	+	0.973038i	$0.574084\pi$
$38$	2.17823	+	3.77280i	0.353355	+	0.612030i
$39$		0			0
$40$	−1.16958	+	2.02578i	−0.184927	+	0.320304i
$41$	3.80493	−	6.59034i	0.594231	−	1.02924i	−0.399424	−	0.916766i	$-0.630790\pi$
$41$	3.80493	−	6.59034i	0.594231	−	1.02924i	0.993655	−	0.112471i	$-0.0358766\pi$
$42$		0			0
$43$	−4.42183	−	7.65883i	−0.674323	−	1.16796i	−0.976666	−	0.214762i	$-0.931102\pi$
$43$	−4.42183	−	7.65883i	−0.674323	−	1.16796i	0.302344	−	0.953199i	$-0.402231\pi$
$44$	−6.39034			−0.963379
$45$		0			0
$46$	1.51036			0.222691
$47$	−2.04391	−	3.54016i	−0.298135	−	0.516385i	0.677574	−	0.735454i	$-0.263031\pi$
$47$	−2.04391	−	3.54016i	−0.298135	−	0.516385i	−0.975709	+	0.219070i	$0.929698\pi$
$48$		0			0
$49$	3.19799	−	5.53909i	0.456856	−	0.791298i
$50$	0.327533	−	0.567303i	0.0463201	−	0.0802288i
$51$		0			0
$52$	−0.785445	−	1.36043i	−0.108922	−	0.188658i
$53$	4.78025			0.656618			0.328309	−	0.944570i	$-0.393521\pi$
$53$	4.78025			0.656618			0.328309	+	0.944570i	$0.393521\pi$
$54$		0			0
$55$	4.06797			0.548525
$56$	0.908981	+	1.57440i	0.121468	+	0.210388i
$57$		0			0
$58$	−2.08971	+	3.61949i	−0.274393	+	0.475262i
$59$	−2.37049	+	4.10581i	−0.308612	+	0.534532i	−0.978059	−	0.208328i	$-0.933198\pi$
$59$	−2.37049	+	4.10581i	−0.308612	+	0.534532i	0.669447	+	0.742860i	$0.266531\pi$
$60$		0			0
$61$	7.18299	+	12.4413i	0.919688	+	1.59295i	0.799889	+	0.600148i	$0.204891\pi$
$61$	7.18299	+	12.4413i	0.919688	+	1.59295i	0.119798	+	0.992798i	$0.461775\pi$
$62$	5.85967			0.744179
$63$		0			0
$64$	0.536314			0.0670393
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$		0			0
$67$	−5.39353	+	9.34188i	−0.658925	+	1.14129i	0.321969	+	0.946750i	$0.395655\pi$
$67$	−5.39353	+	9.34188i	−0.658925	+	1.14129i	−0.980894	+	0.194542i	$0.937678\pi$
$68$	−4.15621	+	7.19877i	−0.504015	+	0.872979i
$69$		0			0
$70$	−0.254553	−	0.440899i	−0.0304249	−	0.0526975i
$71$	−0.307776			−0.0365262			−0.0182631	−	0.999833i	$-0.505814\pi$
$71$	−0.307776			−0.0365262			−0.0182631	+	0.999833i	$0.505814\pi$
$72$		0			0
$73$	−7.50636			−0.878553			−0.439277	−	0.898352i	$-0.644765\pi$
$73$	−7.50636			−0.878553			−0.439277	+	0.898352i	$0.644765\pi$
$74$	−0.919032	−	1.59181i	−0.106835	−	0.185044i
$75$		0			0
$76$	5.22353	−	9.04743i	0.599180	−	1.03781i
$77$	1.58078	−	2.73799i	0.180147	−	0.312023i
$78$		0			0
$79$	−3.80949	−	6.59822i	−0.428601	−	0.742358i	0.568148	−	0.822926i	$-0.307660\pi$
$79$	−3.80949	−	6.59822i	−0.428601	−	0.742358i	−0.996749	+	0.0805679i	$0.974327\pi$
$80$	1.60947			0.179944
$81$		0			0
$82$	4.98496			0.550497
$83$	−6.26484	−	10.8510i	−0.687656	−	1.19105i	−0.972594	−	0.232509i	$-0.925307\pi$
$83$	−6.26484	−	10.8510i	−0.687656	−	1.19105i	0.284939	−	0.958546i	$-0.408027\pi$
$84$		0			0
$85$	2.64577	−	4.58261i	0.286974	−	0.497054i
$86$	2.89659	−	5.01704i	0.312347	−	0.541001i
$87$		0			0
$88$	−4.75783	−	8.24081i	−0.507187	−	0.878473i
$89$	11.7743			1.24807			0.624037	−	0.781394i	$-0.285491\pi$
$89$	11.7743			1.24807			0.624037	+	0.781394i	$0.285491\pi$
$90$		0			0
$91$	0.777184			0.0814710
$92$	−1.81098	−	3.13670i	−0.188807	−	0.327024i
$93$		0			0
$94$	1.33889	−	2.31903i	0.138096	−	0.239190i
$95$	−3.32521	+	5.75943i	−0.341159	+	0.590905i
$96$		0			0
$97$	3.04268	+	5.27007i	0.308937	+	0.535095i	0.978130	−	0.207994i	$-0.0666934\pi$
$97$	3.04268	+	5.27007i	0.308937	+	0.535095i	−0.669193	+	0.743089i	$0.733360\pi$
$98$	4.18979			0.423233
$99$		0			0
$100$	−1.57089			−0.157089
$101$	4.67604	+	8.09915i	0.465284	+	0.805895i	0.999214	−	0.0396332i	$-0.0126189\pi$
$101$	4.67604	+	8.09915i	0.465284	+	0.805895i	−0.533930	+	0.845528i	$0.679286\pi$
$102$		0			0
$103$	1.10733	−	1.91796i	0.109109	−	0.188982i	−0.806301	−	0.591506i	$-0.798534\pi$
$103$	1.10733	−	1.91796i	0.109109	−	0.188982i	0.915409	+	0.402524i	$0.131867\pi$
$104$	1.16958	−	2.02578i	0.114687	−	0.198644i
$105$		0			0
$106$	1.56569	+	2.71185i	0.152073	+	0.263399i
$107$	15.4985			1.49830			0.749148	−	0.662403i	$-0.230463\pi$
$107$	15.4985			1.49830			0.749148	+	0.662403i	$0.230463\pi$
$108$		0			0
$109$	−5.88278			−0.563468			−0.281734	−	0.959493i	$-0.590910\pi$
$109$	−5.88278			−0.563468			−0.281734	+	0.959493i	$0.590910\pi$
$110$	1.33239	+	2.30778i	0.127039	+	0.220038i
$111$		0			0
$112$	0.625427	−	1.08327i	0.0590973	−	0.102360i
$113$	5.28790	−	9.15892i	0.497444	−	0.861599i	−0.502551	−	0.864547i	$-0.667605\pi$
$113$	5.28790	−	9.15892i	0.497444	−	0.861599i	0.999996	+	0.00294864i	$0.000938584\pi$
$114$		0			0
$115$	1.15283	+	1.99677i	0.107502	+	0.186200i
$116$	10.0225			0.930568
$117$		0			0
$118$	−3.10566			−0.285899
$119$	−2.05625	−	3.56153i	−0.188496	−	0.326485i
$120$		0			0
$121$	−2.77420	+	4.80506i	−0.252200	+	0.436824i
$122$	−4.70533	+	8.14987i	−0.426001	+	0.737855i
$123$		0			0
$124$	−7.02594	−	12.1693i	−0.630948	−	1.09283i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−11.4873			−1.01934			−0.509668	−	0.860371i	$-0.670232\pi$
$127$	−11.4873			−1.01934			−0.509668	+	0.860371i	$0.670232\pi$
$128$	−5.55698	−	9.62497i	−0.491172	−	0.850736i
$129$		0			0
$130$	−0.327533	+	0.567303i	−0.0287265	+	0.0497558i
$131$	6.28967	−	10.8940i	0.549531	−	0.951815i	−0.448776	−	0.893644i	$-0.648140\pi$
$131$	6.28967	−	10.8940i	0.549531	−	0.951815i	0.998307	−	0.0581709i	$-0.0185268\pi$
$132$		0			0
$133$	2.58430	+	4.47613i	0.224087	+	0.388130i
$134$	−7.06624			−0.610430
$135$		0			0
$136$	−12.3778			−1.06139
$137$	−0.906022	−	1.56928i	−0.0774067	−	0.134072i	0.824724	−	0.565536i	$-0.191331\pi$
$137$	−0.906022	−	1.56928i	−0.0774067	−	0.134072i	−0.902130	+	0.431464i	$0.857997\pi$
$138$		0			0
$139$	10.2052	−	17.6760i	0.865597	−	1.49926i	−0.000855357	−	1.00000i	$-0.500272\pi$
$139$	10.2052	−	17.6760i	0.865597	−	1.49926i	0.866453	−	0.499259i	$-0.166394\pi$
$140$	−0.610435	+	1.05730i	−0.0515911	+	0.0893585i
$141$		0			0
$142$	−0.100807	−	0.174602i	−0.00845950	−	0.0146523i
$143$	−4.06797			−0.340181
$144$		0			0
$145$	−6.38016			−0.529843
$146$	−2.45858	−	4.25838i	−0.203473	−	0.352426i
$147$		0			0
$148$	−2.20390	+	3.81726i	−0.181159	+	0.313777i
$149$	−0.232060	+	0.401939i	−0.0190111	+	0.0329281i	−0.875374	−	0.483446i	$-0.839385\pi$
$149$	−0.232060	+	0.401939i	−0.0190111	+	0.0329281i	0.856363	+	0.516374i	$0.172718\pi$
$150$		0			0
$151$	4.98238	+	8.62973i	0.405460	+	0.702278i	0.994375	−	0.105917i	$-0.0337779\pi$
$151$	4.98238	+	8.62973i	0.405460	+	0.702278i	−0.588915	+	0.808195i	$0.700445\pi$
$152$	15.5564			1.26179
$153$		0			0
$154$	2.07103			0.166888
$155$	4.47259	+	7.74675i	0.359247	+	0.622234i
$156$		0			0
$157$	4.65985	−	8.07110i	0.371897	−	0.644144i	−0.617961	−	0.786209i	$-0.712041\pi$
$157$	4.65985	−	8.07110i	0.371897	−	0.644144i	0.989857	+	0.142065i	$0.0453742\pi$
$158$	2.49546	−	4.32227i	0.198528	−	0.343861i
$159$		0			0
$160$	2.86632	+	4.96461i	0.226603	+	0.392487i
$161$	1.79193			0.141224
$162$		0			0
$163$	8.93727			0.700021			0.350010	−	0.936746i	$-0.386178\pi$
$163$	8.93727			0.700021			0.350010	+	0.936746i	$0.386178\pi$
$164$	−5.97713	−	10.3527i	−0.466735	−	0.808409i
$165$		0			0
$166$	4.10388	−	7.10813i	0.318523	−	0.551698i
$167$	−8.17252	+	14.1552i	−0.632409	+	1.09536i	0.354649	+	0.935000i	$0.384600\pi$
$167$	−8.17252	+	14.1552i	−0.632409	+	1.09536i	−0.987058	+	0.160365i	$0.948733\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	3.46630			0.265853
$171$		0			0
$172$	−13.8924			−1.05929
$173$	5.50039	+	9.52696i	0.418187	+	0.724321i	0.995757	−	0.0920197i	$-0.0293323\pi$
$173$	5.50039	+	9.52696i	0.418187	+	0.724321i	−0.577570	+	0.816341i	$0.695999\pi$
$174$		0			0
$175$	0.388592	−	0.673061i	0.0293748	−	0.0508786i
$176$	−3.27364	+	5.67011i	−0.246760	+	0.427401i
$177$		0			0
$178$	3.85647	+	6.67961i	0.289055	+	0.500658i
$179$	2.87227			0.214683			0.107342	−	0.994222i	$-0.465766\pi$
$179$	2.87227			0.214683			0.107342	+	0.994222i	$0.465766\pi$
$180$		0			0
$181$	−10.8459			−0.806169			−0.403084	−	0.915163i	$-0.632062\pi$
$181$	−10.8459			−0.806169			−0.403084	+	0.915163i	$0.632062\pi$
$182$	0.254553	+	0.440899i	0.0188687	+	0.0326816i
$183$		0			0
$184$	2.69667	−	4.67077i	0.198801	−	0.344334i
$185$	1.40296	−	2.43000i	0.103148	−	0.178657i
$186$		0			0
$187$	10.7629	+	18.6419i	0.787063	+	1.36323i
$188$	−6.42151			−0.468337
$189$		0			0
$190$	−4.35646			−0.316051
$191$	6.94768	+	12.0337i	0.502716	+	0.870730i	0.999995	+	0.00313924i	$0.000999252\pi$
$191$	6.94768	+	12.0337i	0.502716	+	0.870730i	−0.497279	+	0.867591i	$0.665667\pi$
$192$		0			0
$193$	−10.8934	+	18.8679i	−0.784123	+	1.35814i	0.145399	+	0.989373i	$0.453553\pi$
$193$	−10.8934	+	18.8679i	−0.784123	+	1.35814i	−0.929522	+	0.368768i	$0.879780\pi$
$194$	−1.99315	+	3.45224i	−0.143100	+	0.247857i
$195$		0			0
$196$	−5.02369	−	8.70129i	−0.358835	−	0.621521i
$197$	3.29282			0.234604			0.117302	−	0.993096i	$-0.462575\pi$
$197$	3.29282			0.234604			0.117302	+	0.993096i	$0.462575\pi$
$198$		0			0
$199$	−19.7792			−1.40211			−0.701055	−	0.713107i	$-0.747287\pi$
$199$	−19.7792			−1.40211			−0.701055	+	0.713107i	$0.747287\pi$
$200$	−1.16958	−	2.02578i	−0.0827020	−	0.143244i
$201$		0			0
$202$	−3.06312	+	5.30547i	−0.215520	+	0.373292i
$203$	−2.47928	+	4.29424i	−0.174011	+	0.301396i
$204$		0			0
$205$	3.80493	+	6.59034i	0.265748	+	0.460289i
$206$	1.45075			0.101079
$207$		0			0
$208$	−1.60947			−0.111597
$209$	−13.5269	−	23.4292i	−0.935672	−	1.62063i
$210$		0			0
$211$	1.21405	−	2.10279i	0.0835783	−	0.144762i	−0.821206	−	0.570632i	$-0.806698\pi$
$211$	1.21405	−	2.10279i	0.0835783	−	0.144762i	0.904785	+	0.425870i	$0.140032\pi$
$212$	3.75462	−	6.50320i	0.257869	−	0.446642i
$213$		0			0
$214$	5.07626	+	8.79235i	0.347006	+	0.601033i
$215$	8.84366			0.603132
$216$		0			0
$217$	6.95204			0.471935
$218$	−1.92680	−	3.33732i	−0.130500	−	0.226032i
$219$		0			0
$220$	3.19517	−	5.53419i	0.215418	−	0.373115i
$221$	−2.64577	+	4.58261i	−0.177974	+	0.308260i
$222$		0			0
$223$	4.72863	+	8.19022i	0.316652	+	0.548458i	0.979787	−	0.200042i	$-0.0641078\pi$
$223$	4.72863	+	8.19022i	0.316652	+	0.548458i	−0.663135	+	0.748500i	$0.730774\pi$
$224$	4.45532			0.297683
$225$		0			0
$226$	6.92785			0.460834
$227$	12.0411	+	20.8557i	0.799193	+	1.38424i	0.920142	+	0.391585i	$0.128073\pi$
$227$	12.0411	+	20.8557i	0.799193	+	1.38424i	−0.120949	+	0.992659i	$0.538594\pi$
$228$		0			0
$229$	−4.98700	+	8.63774i	−0.329550	+	0.570798i	−0.982423	−	0.186670i	$-0.940230\pi$
$229$	−4.98700	+	8.63774i	−0.329550	+	0.570798i	0.652872	+	0.757468i	$0.273564\pi$
$230$	−0.755182	+	1.30801i	−0.0497953	+	0.0862479i
$231$		0			0
$232$	7.46213	+	12.9248i	0.489913	+	0.848554i
$233$	−18.2730			−1.19710			−0.598552	−	0.801084i	$-0.704257\pi$
$233$	−18.2730			−1.19710			−0.598552	+	0.801084i	$0.704257\pi$
$234$		0			0
$235$	4.08782			0.266660
$236$	3.72378	+	6.44978i	0.242398	+	0.419845i
$237$		0			0
$238$	1.34698	−	2.33303i	0.0873116	−	0.151228i
$239$	−13.2720	+	22.9878i	−0.858495	+	1.48696i	0.0148689	+	0.999889i	$0.495267\pi$
$239$	−13.2720	+	22.9878i	−0.858495	+	1.48696i	−0.873364	+	0.487068i	$0.838066\pi$
$240$		0			0
$241$	−7.20936	−	12.4870i	−0.464396	−	0.804357i	0.534778	−	0.844992i	$-0.320395\pi$
$241$	−7.20936	−	12.4870i	−0.464396	−	0.804357i	−0.999174	+	0.0406354i	$0.987062\pi$
$242$	−3.63457			−0.233639
$243$		0			0
$244$	22.5674			1.44473
$245$	3.19799	+	5.53909i	0.204312	+	0.353879i
$246$		0			0
$247$	3.32521	−	5.75943i	0.211578	−	0.366464i
$248$	10.4621	−	18.1209i	0.664346	−	1.15068i
$249$		0			0
$250$	0.327533	+	0.567303i	0.0207150	+	0.0358794i
$251$	−13.7541			−0.868148			−0.434074	−	0.900877i	$-0.642924\pi$
$251$	−13.7541			−0.868148			−0.434074	+	0.900877i	$0.642924\pi$
$252$		0			0
$253$	−9.37940			−0.589678
$254$	−3.76248	−	6.51681i	−0.236079	−	0.408901i
$255$		0			0
$256$	4.17650	−	7.23391i	0.261031	−	0.452120i
$257$	−2.45679	+	4.25528i	−0.153250	+	0.265437i	−0.932421	−	0.361375i	$-0.882307\pi$
$257$	−2.45679	+	4.25528i	−0.153250	+	0.265437i	0.779170	+	0.626812i	$0.215641\pi$
$258$		0			0
$259$	−1.09036	−	1.88856i	−0.0677516	−	0.117349i
$260$	1.57089			0.0974224
$261$		0			0
$262$	8.24029			0.509087
$263$	13.0361	+	22.5793i	0.803843	+	1.39230i	0.917069	+	0.398728i	$0.130548\pi$
$263$	13.0361	+	22.5793i	0.803843	+	1.39230i	−0.113226	+	0.993569i	$0.536118\pi$
$264$		0			0
$265$	−2.39013	+	4.13982i	−0.146824	+	0.254307i
$266$	−1.69288	+	2.93216i	−0.103797	+	0.179782i
$267$		0			0
$268$	8.47265	+	14.6751i	0.517549	+	0.896421i
$269$	−29.7277			−1.81253			−0.906263	−	0.422713i	$-0.861078\pi$
$269$	−29.7277			−1.81253			−0.906263	+	0.422713i	$0.861078\pi$
$270$		0			0
$271$	14.2980			0.868540			0.434270	−	0.900783i	$-0.357006\pi$
$271$	14.2980			0.868540			0.434270	+	0.900783i	$0.357006\pi$
$272$	4.25829	+	7.37557i	0.258197	+	0.447210i
$273$		0			0
$274$	0.593504	−	1.02798i	0.0358549	−	0.0621025i
$275$	−2.03399	+	3.52297i	−0.122654	+	0.212443i
$276$		0			0
$277$	−0.939303	−	1.62692i	−0.0564373	−	0.0977522i	0.836426	−	0.548079i	$-0.184641\pi$
$277$	−0.939303	−	1.62692i	−0.0564373	−	0.0977522i	−0.892864	+	0.450327i	$0.851307\pi$
$278$	13.3702			0.801892
$279$		0			0
$280$	−1.81796			−0.108644
$281$	1.78593	+	3.09331i	0.106539	+	0.184532i	0.914366	−	0.404888i	$-0.132690\pi$
$281$	1.78593	+	3.09331i	0.106539	+	0.184532i	−0.807827	+	0.589420i	$0.799356\pi$
$282$		0			0
$283$	6.87413	−	11.9063i	0.408625	−	0.707759i	−0.586111	−	0.810231i	$-0.699342\pi$
$283$	6.87413	−	11.9063i	0.408625	−	0.707759i	0.994736	+	0.102472i	$0.0326752\pi$
$284$	−0.241741	+	0.418707i	−0.0143447	+	0.0248457i
$285$		0			0
$286$	−1.33239	−	2.30778i	−0.0787861	−	0.136462i
$287$	5.91426			0.349108
$288$		0			0
$289$	11.0004			0.647081
$290$	−2.08971	−	3.61949i	−0.122712	−	0.212544i
$291$		0			0
$292$	−5.89583	+	10.2119i	−0.345027	+	0.597605i
$293$	−3.74904	+	6.49352i	−0.219021	+	0.379355i	−0.954509	−	0.298182i	$-0.903620\pi$
$293$	−3.74904	+	6.49352i	−0.219021	+	0.379355i	0.735488	+	0.677538i	$0.236953\pi$
$294$		0			0
$295$	−2.37049	−	4.10581i	−0.138015	−	0.239050i
$296$	−6.56352			−0.381497
$297$		0			0
$298$	−0.304028			−0.0176119
$299$	−1.15283	−	1.99677i	−0.0666702	−	0.115476i
$300$		0			0
$301$	3.43657	−	5.95232i	0.198081	−	0.343086i
$302$	−3.26379	+	5.65304i	−0.187810	+	0.325296i
$303$		0			0
$304$	−5.35183	−	9.26963i	−0.306948	−	0.531650i
$305$	−14.3660			−0.822594
$306$		0			0
$307$	−18.4113			−1.05079			−0.525395	−	0.850858i	$-0.676082\pi$
$307$	−18.4113			−1.05079			−0.525395	+	0.850858i	$0.676082\pi$
$308$	−2.48323	−	4.30108i	−0.141495	−	0.245077i
$309$		0			0
$310$	−2.92984	+	5.07463i	−0.166404	+	0.288219i
$311$	8.63239	−	14.9517i	0.489498	−	0.847835i	−0.510429	−	0.859920i	$-0.670513\pi$
$311$	8.63239	−	14.9517i	0.489498	−	0.847835i	0.999927	+	0.0120846i	$0.00384675\pi$
$312$		0			0
$313$	4.53031	+	7.84672i	0.256068	+	0.443523i	0.965185	−	0.261568i	$-0.0842396\pi$
$313$	4.53031	+	7.84672i	0.256068	+	0.443523i	−0.709117	+	0.705091i	$0.750906\pi$
$314$	6.10502			0.344526
$315$		0			0
$316$	−11.9686			−0.673284
$317$	4.01943	+	6.96187i	0.225754	+	0.391017i	0.956545	−	0.291584i	$-0.0941821\pi$
$317$	4.01943	+	6.96187i	0.225754	+	0.391017i	−0.730791	+	0.682601i	$0.760849\pi$
$318$		0			0
$319$	12.9772	−	22.4771i	0.726582	−	1.25848i
$320$	−0.268157	+	0.464462i	−0.0149904	+	0.0259642i
$321$		0			0
$322$	0.586916	+	1.01657i	0.0327075	+	0.0566511i
$323$	−35.1909			−1.95808
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	2.92725	+	5.07014i	0.162125	+	0.280809i
$327$		0			0
$328$	8.90037	−	15.4159i	0.491441	−	0.851200i
$329$	1.58849	−	2.75135i	0.0875765	−	0.151687i
$330$		0			0
$331$	14.9332	+	25.8651i	0.820803	+	1.42167i	0.905085	+	0.425230i	$0.139807\pi$
$331$	14.9332	+	25.8651i	0.820803	+	1.42167i	−0.0842828	+	0.996442i	$0.526860\pi$
$332$	−19.6827			−1.08023
$333$		0			0
$334$	−10.7071			−0.585865
$335$	−5.39353	−	9.34188i	−0.294680	−	0.510401i
$336$		0			0
$337$	−12.1043	+	20.9653i	−0.659366	+	1.14205i	0.321414	+	0.946939i	$0.395842\pi$
$337$	−12.1043	+	20.9653i	−0.659366	+	1.14205i	−0.980780	+	0.195116i	$0.937492\pi$
$338$	0.327533	−	0.567303i	0.0178154	−	0.0308572i
$339$		0			0
$340$	−4.15621	−	7.19877i	−0.225402	−	0.390408i
$341$	−36.3887			−1.97056
$342$		0			0
$343$	10.4111			0.562149
$344$	−10.3434	−	17.9153i	−0.557678	−	0.965927i
$345$		0			0
$346$	−3.60312	+	6.24078i	−0.193705	+	0.335507i
$347$	−11.4572	+	19.8444i	−0.615053	+	1.06530i	0.375323	+	0.926894i	$0.377532\pi$
$347$	−11.4572	+	19.8444i	−0.615053	+	1.06530i	−0.990375	+	0.138408i	$0.955801\pi$
$348$		0			0
$349$	6.17874	+	10.7019i	0.330740	+	0.572859i	0.982657	−	0.185431i	$-0.0593682\pi$
$349$	6.17874	+	10.7019i	0.330740	+	0.572859i	−0.651917	+	0.758291i	$0.726035\pi$
$350$	0.509106			0.0272129
$351$		0			0
$352$	−23.3202			−1.24297
$353$	−13.5190	−	23.4156i	−0.719544	−	1.24629i	−0.961181	−	0.275920i	$-0.911017\pi$
$353$	−13.5190	−	23.4156i	−0.719544	−	1.24629i	0.241636	−	0.970367i	$-0.422316\pi$
$354$		0			0
$355$	0.153888	−	0.266541i	0.00816751	−	0.0141465i
$356$	9.24807	−	16.0181i	0.490147	−	0.848959i
$357$		0			0
$358$	0.940762	+	1.62945i	0.0497208	+	0.0861190i
$359$	28.4894			1.50361			0.751806	−	0.659384i	$-0.229183\pi$
$359$	28.4894			1.50361			0.751806	+	0.659384i	$0.229183\pi$
$360$		0			0
$361$	25.2280			1.32779
$362$	−3.55238	−	6.15291i	−0.186709	−	0.323390i
$363$		0			0
$364$	0.610435	−	1.05730i	0.0319955	−	0.0554178i
$365$	3.75318	−	6.50070i	0.196450	−	0.340262i
$366$		0			0
$367$	15.1600	+	26.2579i	0.791347	+	1.37065i	0.925133	+	0.379643i	$0.123953\pi$
$367$	15.1600	+	26.2579i	0.791347	+	1.37065i	−0.133786	+	0.991010i	$0.542713\pi$
$368$	−3.71091			−0.193444
$369$		0			0
$370$	1.83806			0.0955563
$371$	1.85757	+	3.21740i	0.0964401	+	0.167039i
$372$		0			0
$373$	4.66810	−	8.08538i	0.241705	−	0.418645i	−0.719495	−	0.694498i	$-0.755627\pi$
$373$	4.66810	−	8.08538i	0.241705	−	0.418645i	0.961200	+	0.275852i	$0.0889600\pi$
$374$	−7.05042	+	12.2117i	−0.364568	+	0.631451i
$375$		0			0
$376$	−4.78104	−	8.28101i	−0.246564	−	0.427061i
$377$	6.38016			0.328595
$378$		0			0
$379$	−22.5156			−1.15655			−0.578274	−	0.815843i	$-0.696274\pi$
$379$	−22.5156			−1.15655			−0.578274	+	0.815843i	$0.696274\pi$
$380$	5.22353	+	9.04743i	0.267962	+	0.464123i
$381$		0			0
$382$	−4.55118	+	7.88288i	−0.232859	+	0.403323i
$383$	−1.51690	+	2.62735i	−0.0775100	+	0.134251i	−0.902175	−	0.431370i	$-0.858030\pi$
$383$	−1.51690	+	2.62735i	−0.0775100	+	0.134251i	0.824665	+	0.565621i	$0.191364\pi$
$384$		0			0
$385$	1.58078	+	2.73799i	0.0805641	+	0.139541i
$386$	−14.2718			−0.726413
$387$		0			0
$388$	9.55942			0.485306
$389$	−9.14936	−	15.8472i	−0.463891	−	0.803483i	0.535260	−	0.844687i	$-0.320214\pi$
$389$	−9.14936	−	15.8472i	−0.463891	−	0.803483i	−0.999151	+	0.0412048i	$0.986880\pi$
$390$		0			0
$391$	−6.10027	+	10.5660i	−0.308504	+	0.534345i
$392$	7.48064	−	12.9568i	0.377829	−	0.654419i
$393$		0			0
$394$	1.07851	+	1.86803i	0.0543344	+	0.0941100i
$395$	7.61897			0.383352
$396$		0			0
$397$	−29.4753			−1.47932			−0.739661	−	0.672980i	$-0.765014\pi$
$397$	−29.4753			−1.47932			−0.739661	+	0.672980i	$0.765014\pi$
$398$	−6.47834	−	11.2208i	−0.324730	−	0.562448i
$399$		0			0
$400$	−0.804735	+	1.39384i	−0.0402368	+	0.0696921i
$401$	−13.8838	+	24.0474i	−0.693322	+	1.20087i	0.277421	+	0.960748i	$0.410520\pi$
$401$	−13.8838	+	24.0474i	−0.693322	+	1.20087i	−0.970743	+	0.240121i	$0.922813\pi$
$402$		0			0
$403$	−4.47259	−	7.74675i	−0.222795	−	0.385893i
$404$	14.6911			0.730909
$405$		0			0
$406$	−3.24818			−0.161204
$407$	5.70721	+	9.88518i	0.282896	+	0.489990i
$408$		0			0
$409$	4.90416	−	8.49426i	0.242495	−	0.420014i	−0.718929	−	0.695083i	$-0.755367\pi$
$409$	4.90416	−	8.49426i	0.242495	−	0.420014i	0.961424	+	0.275069i	$0.0887008\pi$
$410$	−2.49248	+	4.31710i	−0.123095	+	0.213206i
$411$		0			0
$412$	−1.73950	−	3.01290i	−0.0856989	−	0.148435i
$413$	−3.68462			−0.181308
$414$		0			0
$415$	12.5297			0.615058
$416$	−2.86632	−	4.96461i	−0.140533	−	0.243410i
$417$		0			0
$418$	8.86098	−	15.3477i	0.433405	−	0.750679i
$419$	7.24144	−	12.5425i	0.353768	−	0.612744i	−0.633139	−	0.774038i	$-0.718234\pi$
$419$	7.24144	−	12.5425i	0.353768	−	0.612744i	0.986906	+	0.161295i	$0.0515670\pi$
$420$		0			0
$421$	17.9112	+	31.0231i	0.872937	+	1.51197i	0.858944	+	0.512070i	$0.171121\pi$
$421$	17.9112	+	31.0231i	0.872937	+	1.51197i	0.0139933	+	0.999902i	$0.495546\pi$
$422$	1.59056			0.0774272
$423$		0			0
$424$	11.1818			0.543037
$425$	2.64577	+	4.58261i	0.128339	+	0.222289i
$426$		0			0
$427$	−5.58250	+	9.66918i	−0.270156	+	0.467924i
$428$	12.1732	−	21.0846i	0.588414	−	1.01916i
$429$		0			0
$430$	2.89659	+	5.01704i	0.139686	+	0.241943i
$431$	−7.34712			−0.353898			−0.176949	−	0.984220i	$-0.556623\pi$
$431$	−7.34712			−0.353898			−0.176949	+	0.984220i	$0.556623\pi$
$432$		0			0
$433$	−6.55302			−0.314918			−0.157459	−	0.987526i	$-0.550330\pi$
$433$	−6.55302			−0.314918			−0.157459	+	0.987526i	$0.550330\pi$
$434$	2.27702	+	3.94392i	0.109301	+	0.189314i
$435$		0			0
$436$	−4.62060	+	8.00311i	−0.221286	+	0.383279i
$437$	7.66683	−	13.2793i	0.366754	−	0.635237i
$438$		0			0
$439$	0.855543	+	1.48184i	0.0408329	+	0.0707246i	0.885720	−	0.464221i	$-0.153666\pi$
$439$	0.855543	+	1.48184i	0.0408329	+	0.0707246i	−0.844887	+	0.534945i	$0.820332\pi$
$440$	9.51567			0.453642
$441$		0			0
$442$	−3.46630			−0.164875
$443$	−11.0458	−	19.1319i	−0.524801	−	0.908982i	−0.999583	−	0.0288783i	$-0.990806\pi$
$443$	−11.0458	−	19.1319i	−0.524801	−	0.908982i	0.474782	−	0.880103i	$-0.342527\pi$
$444$		0			0
$445$	−5.88716	+	10.1969i	−0.279078	+	0.483377i
$446$	−3.09756	+	5.36513i	−0.146674	+	0.254046i
$447$		0			0
$448$	0.208407	+	0.360972i	0.00984632	+	0.0170543i
$449$	−35.4082			−1.67102			−0.835508	−	0.549479i	$-0.814826\pi$
$449$	−35.4082			−1.67102			−0.835508	+	0.549479i	$0.814826\pi$
$450$		0			0
$451$	−30.9567			−1.45770
$452$	−8.30671	−	14.3876i	−0.390715	−	0.676738i
$453$		0			0
$454$	−7.88769	+	13.6619i	−0.370187	+	0.641183i
$455$	−0.388592	+	0.673061i	−0.0182175	+	0.0315536i
$456$		0			0
$457$	1.26715	+	2.19477i	0.0592748	+	0.102667i	0.894140	−	0.447787i	$-0.147788\pi$
$457$	1.26715	+	2.19477i	0.0592748	+	0.102667i	−0.834865	+	0.550454i	$0.814455\pi$
$458$	−6.53363			−0.305296
$459$		0			0
$460$	3.62195			0.168874
$461$	−1.09872	−	1.90304i	−0.0511724	−	0.0886332i	0.839305	−	0.543662i	$-0.182962\pi$
$461$	−1.09872	−	1.90304i	−0.0511724	−	0.0886332i	−0.890477	+	0.455028i	$0.849629\pi$
$462$		0			0
$463$	12.7269	−	22.0436i	0.591468	−	1.02445i	−0.402568	−	0.915390i	$-0.631882\pi$
$463$	12.7269	−	22.0436i	0.591468	−	1.02445i	0.994035	−	0.109061i	$-0.0347845\pi$
$464$	5.13434	−	8.89294i	0.238356	−	0.412844i
$465$		0			0
$466$	−5.98501	−	10.3663i	−0.277250	−	0.480211i
$467$	15.4769			0.716187			0.358093	−	0.933686i	$-0.383427\pi$
$467$	15.4769			0.716187			0.358093	+	0.933686i	$0.383427\pi$
$468$		0			0
$469$	−8.38353			−0.387116
$470$	1.33889	+	2.31903i	0.0617586	+	0.106969i
$471$		0			0
$472$	−5.54498	+	9.60418i	−0.255228	+	0.442068i
$473$	−17.9879	+	31.1559i	−0.827084	+	1.43255i
$474$		0			0
$475$	−3.32521	−	5.75943i	−0.152571	−	0.264261i
$476$	−6.46028			−0.296106
$477$		0			0
$478$	−17.3881			−0.795312
$479$	−4.81116	−	8.33317i	−0.219828	−	0.380752i	0.734928	−	0.678146i	$-0.237216\pi$
$479$	−4.81116	−	8.33317i	−0.219828	−	0.380752i	−0.954755	+	0.297393i	$0.903883\pi$
$480$		0			0
$481$	−1.40296	+	2.43000i	−0.0639695	+	0.110798i
$482$	4.72260	−	8.17979i	0.215109	−	0.372579i
$483$		0			0
$484$	4.35797	+	7.54822i	0.198089	+	0.343101i
$485$	−6.08536			−0.276322
$486$		0			0
$487$	−20.0963			−0.910649			−0.455325	−	0.890325i	$-0.650477\pi$
$487$	−20.0963			−0.910649			−0.455325	+	0.890325i	$0.650477\pi$
$488$	16.8022	+	29.1023i	0.760600	+	1.31740i
$489$		0			0
$490$	−2.09489	+	3.62846i	−0.0946377	+	0.163917i
$491$	1.48336	−	2.56925i	0.0669430	−	0.115949i	−0.830611	−	0.556853i	$-0.812009\pi$
$491$	1.48336	−	2.56925i	0.0669430	−	0.115949i	0.897554	+	0.440904i	$0.145342\pi$
$492$		0			0
$493$	−16.8804	−	29.2378i	−0.760256	−	1.31680i
$494$	4.35646			0.196006
$495$		0			0
$496$	−14.3970			−0.646444
$497$	−0.119599	−	0.207152i	−0.00536475	−	0.00929202i
$498$		0			0
$499$	−6.97206	+	12.0760i	−0.312112	+	0.540594i	−0.978819	−	0.204726i	$-0.934370\pi$
$499$	−6.97206	+	12.0760i	−0.312112	+	0.540594i	0.666707	+	0.745320i	$0.267703\pi$
$500$	0.785445	−	1.36043i	0.0351261	−	0.0608403i
$501$		0			0
$502$	−4.50490	−	7.80272i	−0.201064	−	0.348253i
$503$	25.1391			1.12090			0.560448	−	0.828190i	$-0.310629\pi$
$503$	25.1391			1.12090			0.560448	+	0.828190i	$0.310629\pi$
$504$		0			0
$505$	−9.35209			−0.416162
$506$	−3.07206	−	5.32097i	−0.136570	−	0.236546i
$507$		0			0
$508$	−9.02267	+	15.6277i	−0.400316	+	0.693368i
$509$	−1.04078	+	1.80269i	−0.0461320	+	0.0799029i	−0.888169	−	0.459516i	$-0.848023\pi$
$509$	−1.04078	+	1.80269i	−0.0461320	+	0.0799029i	0.842037	+	0.539419i	$0.181356\pi$
$510$		0			0
$511$	−2.91691	−	5.05224i	−0.129037	−	0.223498i
$512$	−16.7562			−0.740525
$513$		0			0
$514$	−3.21871			−0.141971
$515$	1.10733	+	1.91796i	0.0487949	+	0.0845153i
$516$		0			0
$517$	−8.31457	+	14.4013i	−0.365674	+	0.633367i
$518$	0.714256	−	1.23713i	0.0313826	−	0.0543563i
$519$		0			0
$520$	1.16958	+	2.02578i	0.0512896	+	0.0888362i
$521$	16.7112			0.732130			0.366065	−	0.930589i	$-0.380705\pi$
$521$	16.7112			0.732130			0.366065	+	0.930589i	$0.380705\pi$
$522$		0			0
$523$	39.1071			1.71003			0.855016	−	0.518602i	$-0.173547\pi$
$523$	39.1071			1.71003			0.855016	+	0.518602i	$0.173547\pi$
$524$	−9.88037	−	17.1133i	−0.431626	−	0.747598i
$525$		0			0
$526$	−8.53953	+	14.7909i	−0.372341	+	0.644914i
$527$	−23.6669	+	40.9922i	−1.03094	+	1.78565i
$528$		0			0
$529$	8.84194	+	15.3147i	0.384432	+	0.665856i
$530$	−3.13138			−0.136018
$531$		0			0
$532$	8.11929			0.352016
$533$	−3.80493	−	6.59034i	−0.164810	−	0.285459i
$534$		0			0
$535$	−7.74925	+	13.4221i	−0.335029	+	0.580288i
$536$	−12.6164	+	21.8522i	−0.544944	+	0.943871i
$537$		0			0
$538$	−9.73678	−	16.8646i	−0.419782	−	0.727084i
$539$	−26.0187			−1.12070
$540$		0			0
$541$	4.87732			0.209692			0.104846	−	0.994488i	$-0.466565\pi$
$541$	4.87732			0.209692			0.104846	+	0.994488i	$0.466565\pi$
$542$	4.68306	+	8.11129i	0.201154	+	0.348410i
$543$		0			0
$544$	−15.1672	+	26.2704i	−0.650290	+	1.12634i
$545$	2.94139	−	5.09464i	0.125995	−	0.218230i
$546$		0			0
$547$	7.47398	+	12.9453i	0.319564	+	0.553501i	0.980397	−	0.197032i	$-0.0631302\pi$
$547$	7.47398	+	12.9453i	0.319564	+	0.553501i	−0.660833	+	0.750533i	$0.729797\pi$
$548$	−2.84652			−0.121597
$549$		0			0
$550$	−2.66479			−0.113627
$551$	21.2154	+	36.7461i	0.903805	+	1.56544i
$552$		0			0
$553$	2.96067	−	5.12803i	0.125901	−	0.218066i
$554$	0.615305	−	1.06574i	0.0261418	−	0.0452789i
$555$		0			0
$556$	−16.0313	−	27.7670i	−0.679879	−	1.17758i
$557$	23.5505			0.997866			0.498933	−	0.866641i	$-0.333725\pi$
$557$	23.5505			0.997866			0.498933	+	0.866641i	$0.333725\pi$
$558$		0			0
$559$	−8.84366			−0.374047
$560$	0.625427	+	1.08327i	0.0264291	+	0.0457766i
$561$		0			0
$562$	−1.16990	+	2.02632i	−0.0493492	+	0.0854753i
$563$	−0.146577	+	0.253878i	−0.00617747	+	0.0106997i	−0.869098	−	0.494641i	$-0.835300\pi$
$563$	−0.146577	+	0.253878i	−0.00617747	+	0.0106997i	0.862920	+	0.505340i	$0.168633\pi$
$564$		0			0
$565$	5.28790	+	9.15892i	0.222464	+	0.385319i
$566$	9.00601			0.378551
$567$		0			0
$568$	−0.719938			−0.0302079
$569$	16.9315	+	29.3263i	0.709807	+	1.22942i	0.964928	+	0.262513i	$0.0845513\pi$
$569$	16.9315	+	29.3263i	0.709807	+	1.22942i	−0.255121	+	0.966909i	$0.582115\pi$
$570$		0			0
$571$	11.0154	−	19.0793i	0.460981	−	0.798443i	−0.538029	−	0.842926i	$-0.680831\pi$
$571$	11.0154	−	19.0793i	0.460981	−	0.798443i	0.999010	+	0.0444833i	$0.0141642\pi$
$572$	−3.19517	+	5.53419i	−0.133597	+	0.231396i
$573$		0			0
$574$	1.93711	+	3.35518i	0.0808536	+	0.140043i
$575$	−2.30567			−0.0961531
$576$		0			0
$577$	23.7846			0.990165			0.495083	−	0.868846i	$-0.335138\pi$
$577$	23.7846			0.990165			0.495083	+	0.868846i	$0.335138\pi$
$578$	3.60299	+	6.24055i	0.149864	+	0.259573i
$579$		0			0
$580$	−5.01126	+	8.67976i	−0.208081	+	0.360407i
$581$	4.86893	−	8.43324i	0.201997	−	0.349870i
$582$		0			0
$583$	−9.72297	−	16.8407i	−0.402684	−	0.697470i
$584$	−17.5586			−0.726581
$585$		0			0
$586$	−4.91173			−0.202902
$587$	5.84863	+	10.1301i	0.241399	+	0.418115i	0.961113	−	0.276155i	$-0.0890605\pi$
$587$	5.84863	+	10.1301i	0.241399	+	0.418115i	−0.719714	+	0.694271i	$0.755727\pi$
$588$		0			0
$589$	29.7446	−	51.5191i	1.22560	−	2.12281i
$590$	1.55283	−	2.68958i	0.0639289	−	0.110728i
$591$		0			0
$592$	2.25803	+	3.91101i	0.0928043	+	0.160742i
$593$	−14.5999			−0.599545			−0.299773	−	0.954011i	$-0.596911\pi$
$593$	−14.5999			−0.599545			−0.299773	+	0.954011i	$0.596911\pi$
$594$		0			0
$595$	4.11250			0.168596
$596$	0.364540	+	0.631402i	0.0149321	+	0.0258632i
$597$		0			0
$598$	0.755182	−	1.30801i	0.0308817	−	0.0534887i
$599$	8.74420	−	15.1454i	0.357278	−	0.618824i	−0.630227	−	0.776411i	$-0.717038\pi$
$599$	8.74420	−	15.1454i	0.357278	−	0.618824i	0.987505	+	0.157587i	$0.0503714\pi$
$600$		0			0
$601$	22.3969	+	38.7926i	0.913590	+	1.58238i	0.808952	+	0.587874i	$0.200035\pi$
$601$	22.3969	+	38.7926i	0.913590	+	1.58238i	0.104638	+	0.994510i	$0.466632\pi$
$602$	4.50236			0.183503
$603$		0			0
$604$	15.6535			0.636933
$605$	−2.77420	−	4.80506i	−0.112787	−	0.195354i
$606$		0			0
$607$	21.1894	−	36.7011i	0.860050	−	1.48965i	−0.0118293	−	0.999930i	$-0.503765\pi$
$607$	21.1894	−	36.7011i	0.860050	−	1.48965i	0.871879	−	0.489721i	$-0.162901\pi$
$608$	19.0622	−	33.0167i	0.773075	−	1.33901i
$609$		0			0
$610$	−4.70533	−	8.14987i	−0.190513	−	0.329979i
$611$	−4.08782			−0.165375
$612$		0			0
$613$	−6.73566			−0.272051			−0.136025	−	0.990705i	$-0.543433\pi$
$613$	−6.73566			−0.272051			−0.136025	+	0.990705i	$0.543433\pi$
$614$	−6.03031	−	10.4448i	−0.243364	−	0.421518i
$615$		0			0
$616$	3.69771	−	6.40462i	0.148985	−	0.258050i
$617$	7.39237	−	12.8040i	0.297606	−	0.515468i	−0.677982	−	0.735079i	$-0.737145\pi$
$617$	7.39237	−	12.8040i	0.297606	−	0.515468i	0.975588	+	0.219610i	$0.0704786\pi$
$618$		0			0
$619$	−13.6898	−	23.7114i	−0.550239	−	0.953041i	−0.998257	−	0.0590168i	$-0.981203\pi$
$619$	−13.6898	−	23.7114i	−0.550239	−	0.953041i	0.448018	−	0.894024i	$-0.352130\pi$
$620$	14.0519			0.564337
$621$		0			0
$622$	11.3096			0.453472
$623$	4.57540	+	7.92483i	0.183310	+	0.317502i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−2.96765	+	5.14011i	−0.118611	+	0.205440i
$627$		0			0
$628$	−7.32011	−	12.6788i	−0.292104	−	0.505940i
$629$	14.8476			0.592014
$630$		0			0
$631$	19.2458			0.766162			0.383081	−	0.923715i	$-0.374863\pi$
$631$	19.2458			0.766162			0.383081	+	0.923715i	$0.374863\pi$
$632$	−8.91102	−	15.4343i	−0.354461	−	0.613945i
$633$		0			0
$634$	−2.63299	+	4.56048i	−0.104570	+	0.181120i
$635$	5.74367	−	9.94833i	0.227931	−	0.394787i
$636$		0			0
$637$	−3.19799	−	5.53909i	−0.126709	−	0.219467i
$638$	17.0018			0.673107
$639$		0			0
$640$	11.1140			0.439318
$641$	−13.9581	−	24.1761i	−0.551310	−	0.954898i	−0.998180	−	0.0602987i	$-0.980795\pi$
$641$	−13.9581	−	24.1761i	−0.551310	−	0.954898i	0.446870	−	0.894599i	$-0.352539\pi$
$642$		0			0
$643$	−1.62382	+	2.81254i	−0.0640372	+	0.110916i	−0.896266	−	0.443516i	$-0.853731\pi$
$643$	−1.62382	+	2.81254i	−0.0640372	+	0.110916i	0.832229	+	0.554432i	$0.187064\pi$
$644$	1.40746	−	2.43779i	0.0554617	−	0.0960625i
$645$		0			0
$646$	−11.5262	−	19.9639i	−0.453492	−	0.785471i
$647$	1.47061			0.0578155			0.0289077	−	0.999582i	$-0.490797\pi$
$647$	1.47061			0.0578155			0.0289077	+	0.999582i	$0.490797\pi$
$648$		0			0
$649$	19.2862			0.757050
$650$	−0.327533	−	0.567303i	−0.0128469	−	0.0222515i
$651$		0			0
$652$	7.01973	−	12.1585i	0.274914	−	0.476165i
$653$	−1.19989	+	2.07827i	−0.0469554	+	0.0813291i	−0.888548	−	0.458784i	$-0.848285\pi$
$653$	−1.19989	+	2.07827i	−0.0469554	+	0.0813291i	0.841592	+	0.540113i	$0.181619\pi$
$654$		0			0
$655$	6.28967	+	10.8940i	0.245758	+	0.425665i
$656$	−12.2479			−0.478198
$657$		0			0
$658$	2.08113			0.0811311
$659$	−1.75372	−	3.03754i	−0.0683154	−	0.118326i	0.829844	−	0.557995i	$-0.188429\pi$
$659$	−1.75372	−	3.03754i	−0.0683154	−	0.118326i	−0.898160	+	0.439669i	$0.855096\pi$
$660$		0			0
$661$	10.1473	−	17.5757i	0.394685	−	0.683614i	−0.598376	−	0.801215i	$-0.704187\pi$
$661$	10.1473	−	17.5757i	0.394685	−	0.683614i	0.993061	+	0.117601i	$0.0375205\pi$
$662$	−9.78222	+	16.9433i	−0.380197	+	0.658520i
$663$		0			0
$664$	−14.6545	−	25.3823i	−0.568705	−	0.985026i
$665$	−5.16860			−0.200430
$666$		0			0
$667$	14.7105			0.569595
$668$	12.8381	+	22.2363i	0.496722	+	0.860348i
$669$		0			0
$670$	3.53312	−	6.11954i	0.136496	−	0.236419i
$671$	29.2202	−	50.6109i	1.12803	−	1.95381i
$672$		0			0
$673$	−4.94555	−	8.56594i	−0.190637	−	0.330193i	0.754825	−	0.655927i	$-0.227722\pi$
$673$	−4.94555	−	8.56594i	−0.190637	−	0.330193i	−0.945462	+	0.325734i	$0.894389\pi$
$674$	−15.8583			−0.610838
$675$		0			0
$676$	−1.57089			−0.0604188
$677$	4.01710	+	6.95783i	0.154390	+	0.267411i	0.932837	−	0.360300i	$-0.117326\pi$
$677$	4.01710	+	6.95783i	0.154390	+	0.267411i	−0.778447	+	0.627711i	$0.783992\pi$
$678$		0			0
$679$	−2.36472	+	4.09581i	−0.0907496	+	0.157183i
$680$	6.18889	−	10.7195i	0.237333	−	0.411073i
$681$		0			0
$682$	−11.9185	−	20.6434i	−0.456383	−	0.790478i
$683$	−0.652224			−0.0249567			−0.0124783	−	0.999922i	$-0.503972\pi$
$683$	−0.652224			−0.0249567			−0.0124783	+	0.999922i	$0.503972\pi$
$684$		0			0
$685$	1.81204			0.0692347
$686$	3.40999	+	5.90628i	0.130194	+	0.225503i
$687$		0			0
$688$	−7.11681	+	12.3267i	−0.271326	+	0.469950i
$689$	2.39013	−	4.13982i	0.0910566	−	0.157715i
$690$		0			0
$691$	−20.5644	−	35.6186i	−0.782308	−	1.35500i	−0.930594	−	0.366052i	$-0.880709\pi$
$691$	−20.5644	−	35.6186i	−0.782308	−	1.35500i	0.148286	−	0.988944i	$-0.452624\pi$
$692$	17.2810			0.656926
$693$		0			0
$694$	−15.0104			−0.569786
$695$	10.2052	+	17.6760i	0.387107	+	0.670489i
$696$		0			0
$697$	−20.1339	+	34.8730i	−0.762628	+	1.32091i
$698$	−4.04748	+	7.01044i	−0.153199	+	0.265349i
$699$		0			0
$700$	−0.610435	−	1.05730i	−0.0230723	−	0.0399623i
$701$	−28.9154			−1.09212			−0.546060	−	0.837746i	$-0.683873\pi$
$701$	−28.9154			−1.09212			−0.546060	+	0.837746i	$0.683873\pi$
$702$		0			0
$703$	−18.6606			−0.703796
$704$	−1.09086	−	1.88942i	−0.0411132	−	0.0712101i
$705$		0			0
$706$	8.85584	−	15.3388i	0.333294	−	0.577282i
$707$	−3.63415	+	6.29452i	−0.136676	+	0.236730i
$708$		0			0
$709$	19.1429	+	33.1565i	0.718927	+	1.24522i	0.961425	+	0.275066i	$0.0886998\pi$
$709$	19.1429	+	33.1565i	0.718927	+	1.24522i	−0.242498	+	0.970152i	$0.577967\pi$
$710$	0.201613			0.00756641
$711$		0			0
$712$	27.5421			1.03218
$713$	−10.3123	−	17.8614i	−0.386199	−	0.668916i
$714$		0			0
$715$	2.03399	−	3.52297i	0.0760668	−	0.131752i
$716$	2.25601	−	3.90752i	0.0843110	−	0.146031i
$717$		0			0
$718$	9.33121	+	16.1621i	0.348238	+	0.603165i
$719$	31.0939			1.15961			0.579803	−	0.814757i	$-0.303130\pi$
$719$	31.0939			1.15961			0.579803	+	0.814757i	$0.303130\pi$
$720$		0			0
$721$	1.72120			0.0641009
$722$	8.26301	+	14.3120i	0.307517	+	0.532636i
$723$		0			0
$724$	−8.51885	+	14.7551i	−0.316600	+	0.548368i
$725$	3.19008	−	5.52538i	0.118477	−	0.205207i
$726$		0			0
$727$	11.6752	+	20.2220i	0.433008	+	0.749992i	0.997131	−	0.0756988i	$-0.0241187\pi$
$727$	11.6752	+	20.2220i	0.433008	+	0.749992i	−0.564122	+	0.825691i	$0.690785\pi$
$728$	1.81796			0.0673782
$729$		0			0
$730$	4.91716			0.181992
$731$	23.3983	+	40.5270i	0.865417	+	1.49895i
$732$		0			0
$733$	−0.558131	+	0.966711i	−0.0206150	+	0.0357063i	−0.876149	−	0.482041i	$-0.839896\pi$
$733$	−0.558131	+	0.966711i	−0.0206150	+	0.0357063i	0.855534	+	0.517747i	$0.173229\pi$
$734$	−9.93081	+	17.2007i	−0.366553	+	0.634888i
$735$		0			0
$736$	−6.60879	−	11.4468i	−0.243603	−	0.421933i
$737$	43.8815			1.61640
$738$		0			0
$739$	1.73962			0.0639930			0.0319965	−	0.999488i	$-0.489813\pi$
$739$	1.73962			0.0639930			0.0319965	+	0.999488i	$0.489813\pi$
$740$	−2.20390	−	3.81726i	−0.0810168	−	0.140325i
$741$		0			0
$742$	−1.21683	+	2.10761i	−0.0446712	+	0.0773728i
$743$	−13.6377	+	23.6211i	−0.500317	+	0.866575i	0.499683	+	0.866209i	$0.333450\pi$
$743$	−13.6377	+	23.6211i	−0.500317	+	0.866575i	−1.00000		0.000366439i	$0.999883\pi$
$744$		0			0
$745$	−0.232060	−	0.401939i	−0.00850201	−	0.0147259i
$746$	6.11582			0.223916
$747$		0			0
$748$	33.8147			1.23639
$749$	6.02259	+	10.4314i	0.220061	+	0.381156i
$750$		0			0
$751$	−16.3324	+	28.2885i	−0.595977	+	1.03226i	0.397432	+	0.917632i	$0.369902\pi$
$751$	−16.3324	+	28.2885i	−0.595977	+	1.03226i	−0.993408	+	0.114630i	$0.963432\pi$
$752$	−3.28961	+	5.69778i	−0.119960	+	0.207777i
$753$		0			0
$754$	2.08971	+	3.61949i	0.0761028	+	0.131814i
$755$	−9.96476			−0.362655
$756$		0			0
$757$	43.4319			1.57856			0.789279	−	0.614035i	$-0.210455\pi$
$757$	43.4319			1.57856			0.789279	+	0.614035i	$0.210455\pi$
$758$	−7.37459	−	12.7732i	−0.267857	−	0.463942i
$759$		0			0
$760$	−7.77822	+	13.4723i	−0.282146	+	0.488690i
$761$	24.7445	−	42.8587i	0.896987	−	1.55363i	0.0656602	−	0.997842i	$-0.479085\pi$
$761$	24.7445	−	42.8587i	0.896987	−	1.55363i	0.831326	−	0.555784i	$-0.187582\pi$
$762$		0			0
$763$	−2.28600	−	3.95947i	−0.0827588	−	0.143342i
$764$	21.8281			0.789711
$765$		0			0
$766$	−1.98734			−0.0718055
$767$	2.37049	+	4.10581i	0.0855935	+	0.148252i
$768$		0			0
$769$	4.52027	−	7.82934i	0.163005	−	0.282333i	−0.772940	−	0.634479i	$-0.781215\pi$
$769$	4.52027	−	7.82934i	0.163005	−	0.282333i	0.935945	+	0.352146i	$0.114548\pi$
$770$	−1.03552	+	1.79357i	−0.0373174	+	0.0646356i
$771$		0			0
$772$	17.1123	+	29.6394i	0.615885	+	1.06674i
$773$	8.64817			0.311053			0.155527	−	0.987832i	$-0.450293\pi$
$773$	8.64817			0.311053			0.155527	+	0.987832i	$0.450293\pi$
$774$		0			0
$775$	−8.94517			−0.321320
$776$	7.11733	+	12.3276i	0.255497	+	0.442534i
$777$		0			0
$778$	5.99343	−	10.3809i	0.214875	−	0.372174i
$779$	25.3044	−	43.8285i	0.906624	−	1.57032i
$780$		0			0
$781$	0.626011	+	1.08428i	0.0224004	+	0.0387987i
$782$	−7.99215			−0.285799
$783$		0			0
$784$	−10.2942			−0.367648
$785$	4.65985	+	8.07110i	0.166317	+	0.288070i
$786$		0			0
$787$	−9.17712	+	15.8952i	−0.327129	+	0.566604i	−0.981941	−	0.189188i	$-0.939415\pi$
$787$	−9.17712	+	15.8952i	−0.327129	+	0.566604i	0.654812	+	0.755792i	$0.272748\pi$
$788$	2.58633	−	4.47965i	0.0921342	−	0.159581i
$789$		0			0
$790$	2.49546	+	4.32227i	0.0887846	+	0.153779i
$791$	8.21935			0.292246
$792$		0			0
$793$	14.3660			0.510151
$794$	−9.65412	−	16.7214i	−0.342612	−	0.593421i
$795$		0			0
$796$	−15.5355	+	26.9082i	−0.550640	+	0.953737i
$797$	7.12643	−	12.3433i	0.252431	−	0.437223i	−0.711764	−	0.702419i	$-0.752103\pi$
$797$	7.12643	−	12.3433i	0.252431	−	0.437223i	0.964195	+	0.265196i	$0.0854366\pi$
$798$		0			0
$799$	10.8154	+	18.7329i	0.382622	+	0.662721i
$800$	−5.73264			−0.202679
$801$		0			0
$802$	−18.1896			−0.642295
$803$	15.2678	+	26.4447i	0.538790	+	0.933212i
$804$		0			0
$805$	−0.895965	+	1.55186i	−0.0315786	+	0.0546957i
$806$	2.92984	−	5.07463i	0.103199	−	0.178746i
$807$		0			0
$808$	10.9380	+	18.9453i	0.384799	+	0.666492i
$809$	2.15221			0.0756676			0.0378338	−	0.999284i	$-0.487954\pi$
$809$	2.15221			0.0756676			0.0378338	+	0.999284i	$0.487954\pi$
$810$		0			0
$811$	−30.3748			−1.06660			−0.533302	−	0.845925i	$-0.679049\pi$
$811$	−30.3748			−1.06660			−0.533302	+	0.845925i	$0.679049\pi$
$812$	3.89467	+	6.74577i	0.136676	+	0.236730i
$813$		0			0
$814$	−3.73860	+	6.47544i	−0.131038	+	0.226964i
$815$	−4.46863	+	7.73990i	−0.156529	+	0.271117i
$816$		0			0
$817$	−29.4070	−	50.9344i	−1.02882	−	1.78197i
$818$	6.42510			0.224648
$819$		0			0
$820$	11.9543			0.417461
$821$	−5.98030	−	10.3582i	−0.208714	−	0.361503i	0.742596	−	0.669740i	$-0.233594\pi$
$821$	−5.98030	−	10.3582i	−0.208714	−	0.361503i	−0.951310	+	0.308237i	$0.900261\pi$
$822$		0			0
$823$	−1.94193	+	3.36352i	−0.0676914	+	0.117245i	−0.897885	−	0.440231i	$-0.854897\pi$
$823$	−1.94193	+	3.36352i	−0.0676914	+	0.117245i	0.830193	+	0.557476i	$0.188230\pi$
$824$	2.59024	−	4.48642i	0.0902352	−	0.156292i
$825$		0			0
$826$	−1.20683	−	2.09030i	−0.0419911	−	0.0727307i
$827$	30.4261			1.05802			0.529010	−	0.848615i	$-0.322563\pi$
$827$	30.4261			1.05802			0.529010	+	0.848615i	$0.322563\pi$
$828$		0			0
$829$	−23.8577			−0.828613			−0.414307	−	0.910137i	$-0.635976\pi$
$829$	−23.8577			−0.828613			−0.414307	+	0.910137i	$0.635976\pi$
$830$	4.10388	+	7.10813i	0.142448	+	0.246727i
$831$		0			0
$832$	0.268157	−	0.464462i	0.00929668	−	0.0161023i
$833$	−16.9223	+	29.3103i	−0.586323	+	1.01554i
$834$		0			0
$835$	−8.17252	−	14.1552i	−0.282822	−	0.489862i
$836$	−42.4984			−1.46984
$837$		0			0
$838$	9.48724			0.327731
$839$	−9.51666	−	16.4833i	−0.328552	−	0.569068i	0.653673	−	0.756777i	$-0.273227\pi$
$839$	−9.51666	−	16.4833i	−0.328552	−	0.569068i	−0.982225	+	0.187709i	$0.939894\pi$
$840$		0			0
$841$	−5.85322	+	10.1381i	−0.201835	+	0.349589i
$842$	−11.7330	+	20.3221i	−0.404346	+	0.700347i
$843$		0			0
$844$	−1.90713	−	3.30325i	−0.0656461	−	0.113702i
$845$	1.00000			0.0344010
$846$		0			0
$847$	−4.31213			−0.148167
$848$	−3.84684	−	6.66292i	−0.132101	−	0.228806i
$849$		0			0
$850$	−1.73315	+	3.00191i	−0.0594466	+	0.102965i
$851$	−3.23477	+	5.60278i	−0.110886	+	0.192061i
$852$		0			0
$853$	−10.5264	−	18.2322i	−0.360416	−	0.624259i	0.627613	−	0.778525i	$-0.284032\pi$
$853$	−10.5264	−	18.2322i	−0.360416	−	0.624259i	−0.988029	+	0.154266i	$0.950699\pi$
$854$	−7.31381			−0.250273
$855$		0			0
$856$	36.2536			1.23912
$857$	−4.94067	−	8.55749i	−0.168770	−	0.292318i	0.769218	−	0.638987i	$-0.220646\pi$
$857$	−4.94067	−	8.55749i	−0.168770	−	0.292318i	−0.937988	+	0.346669i	$0.887313\pi$
$858$		0			0
$859$	4.91195	−	8.50775i	0.167594	−	0.290281i	−0.769980	−	0.638068i	$-0.779734\pi$
$859$	4.91195	−	8.50775i	0.167594	−	0.290281i	0.937573	+	0.347788i	$0.113067\pi$
$860$	6.94620	−	12.0312i	0.236864	−	0.410260i
$861$		0			0
$862$	−2.40642	−	4.16805i	−0.0819631	−	0.141964i
$863$	−46.5764			−1.58548			−0.792739	−	0.609561i	$-0.791346\pi$
$863$	−46.5764			−1.58548			−0.792739	+	0.609561i	$0.791346\pi$
$864$		0			0
$865$	−11.0008			−0.374038
$866$	−2.14633	−	3.71755i	−0.0729352	−	0.126327i
$867$		0			0
$868$	5.46044	−	9.45777i	0.185340	−	0.321017i
$869$	−15.4969	+	26.8414i	−0.525696	+	0.910532i
$870$		0			0
$871$	5.39353	+	9.34188i	0.182753	+	0.316537i
$872$	−13.7608			−0.465999
$873$		0			0
$874$	10.0446			0.339762
$875$	0.388592	+	0.673061i	0.0131368	+	0.0227536i
$876$		0			0
$877$	27.9143	−	48.3489i	0.942598	−	1.63263i	0.182106	−	0.983279i	$-0.441709\pi$
$877$	27.9143	−	48.3489i	0.942598	−	1.63263i	0.760491	−	0.649348i	$-0.224958\pi$
$878$	−0.560437	+	0.970705i	−0.0189138	+	0.0327597i
$879$		0			0
$880$	−3.27364	−	5.67011i	−0.110354	−	0.191140i
$881$	−1.22939			−0.0414192			−0.0207096	−	0.999786i	$-0.506593\pi$
$881$	−1.22939			−0.0414192			−0.0207096	+	0.999786i	$0.506593\pi$
$882$		0			0
$883$	−5.89957			−0.198536			−0.0992681	−	0.995061i	$-0.531650\pi$
$883$	−5.89957			−0.198536			−0.0992681	+	0.995061i	$0.531650\pi$
$884$	4.15621	+	7.19877i	0.139788	+	0.242121i
$885$		0			0
$886$	7.23571	−	12.5326i	0.243088	−	0.421041i
$887$	−21.2331	+	36.7769i	−0.712939	+	1.23485i	0.250810	+	0.968036i	$0.419303\pi$
$887$	−21.2331	+	36.7769i	−0.712939	+	1.23485i	−0.963749	+	0.266810i	$0.914030\pi$
$888$		0			0
$889$	−4.46389	−	7.73168i	−0.149714	−	0.259312i
$890$	−7.71295			−0.258539
$891$		0			0
$892$	14.8563			0.497426
$893$	−13.5929	−	23.5435i	−0.454867	−	0.787853i
$894$		0			0
$895$	−1.43613	+	2.48746i	−0.0480047	+	0.0831465i
$896$	4.31880	−	7.48037i	0.144281	−	0.249902i
$897$		0			0
$898$	−11.5973	−	20.0872i	−0.387008	−	0.670318i
$899$	57.0716			1.90345
$900$		0			0
$901$	−25.2949			−0.842695
$902$	−10.1393	−	17.5619i	−0.337603	−	0.584746i
$903$		0			0
$904$	12.3693	−	21.4242i	0.411396	−	0.712560i
$905$	5.42295	−	9.39282i	0.180265	−	0.312228i
$906$		0			0
$907$	5.58861	+	9.67977i	0.185567	+	0.321411i	0.943767	−	0.330610i	$-0.107255\pi$
$907$	5.58861	+	9.67977i	0.185567	+	0.321411i	−0.758200	+	0.652021i	$0.773921\pi$
$908$	37.8304			1.25544
$909$		0			0
$910$	−0.509106			−0.0168767
$911$	−14.0144	−	24.2737i	−0.464319	−	0.804224i	0.534851	−	0.844946i	$-0.320368\pi$
$911$	−14.0144	−	24.2737i	−0.464319	−	0.804224i	−0.999171	+	0.0407218i	$0.987034\pi$
$912$		0			0
$913$	−25.4852	+	44.1417i	−0.843437	+	1.46088i
$914$	−0.830067	+	1.43772i	−0.0274562	+	0.0475555i
$915$		0			0
$916$	7.83403	+	13.5689i	0.258844	+	0.448330i
$917$	9.77645			0.322847
$918$		0			0
$919$	43.1860			1.42457			0.712287	−	0.701888i	$-0.247659\pi$
$919$	43.1860			1.42457			0.712287	+	0.701888i	$0.247659\pi$
$920$	2.69667	+	4.67077i	0.0889067	+	0.153991i
$921$		0			0
$922$	0.719732	−	1.24661i	0.0237031	−	0.0410550i
$923$	−0.153888	+	0.266541i	−0.00506528	+	0.00877332i
$924$		0			0
$925$	1.40296	+	2.43000i	0.0461291	+	0.0798979i
$926$	16.6739			0.547937
$927$		0			0
$928$	36.5752			1.20064
$929$	−9.19180	−	15.9207i	−0.301573	−	0.522340i	0.674919	−	0.737892i	$-0.264178\pi$
$929$	−9.19180	−	15.9207i	−0.301573	−	0.522340i	−0.976492	+	0.215551i	$0.930845\pi$
$930$		0			0
$931$	21.2680	−	36.8372i	0.697030	−	1.20729i
$932$	−14.3524	+	24.8591i	−0.470129	+	0.814288i
$933$		0			0
$934$	5.06920	+	8.78011i	0.165869	+	0.287294i
$935$	−21.5258			−0.703970
$936$		0			0
$937$	−13.2414			−0.432579			−0.216289	−	0.976329i	$-0.569395\pi$
$937$	−13.2414			−0.432579			−0.216289	+	0.976329i	$0.569395\pi$
$938$	−2.74588	−	4.75601i	−0.0896562	−	0.155289i
$939$		0			0
$940$	3.21076	−	5.56119i	0.104723	−	0.181386i
$941$	7.66547	−	13.2770i	0.249887	−	0.432817i	−0.713607	−	0.700546i	$-0.752940\pi$
$941$	7.66547	−	13.2770i	0.249887	−	0.432817i	0.963494	+	0.267729i	$0.0862731\pi$
$942$		0			0
$943$	−8.77292	−	15.1951i	−0.285685	−	0.494822i
$944$	7.63048			0.248351
$945$		0			0
$946$	−23.5665			−0.766213
$947$	22.0478	+	38.1879i	0.716457	+	1.24094i	0.962395	+	0.271654i	$0.0875707\pi$
$947$	22.0478	+	38.1879i	0.716457	+	1.24094i	−0.245938	+	0.969286i	$0.579096\pi$
$948$		0			0
$949$	−3.75318	+	6.50070i	−0.121833	+	0.211022i
$950$	2.17823	−	3.77280i	0.0706711	−	0.122406i
$951$		0			0
$952$	−4.80991	−	8.33101i	−0.155890	−	0.270009i
$953$	23.1623			0.750300			0.375150	−	0.926964i	$-0.377591\pi$
$953$	23.1623			0.750300			0.375150	+	0.926964i	$0.377591\pi$
$954$		0			0
$955$	−13.8954			−0.449643
$956$	20.8489	+	36.1113i	0.674300	+	1.16792i
$957$		0			0
$958$	3.15163	−	5.45878i	0.101824	−	0.176365i
$959$	0.704146	−	1.21962i	0.0227381	−	0.0393835i
$960$		0			0
$961$	−24.5081	−	42.4492i	−0.790582	−	1.36933i
$962$	−1.83806			−0.0592615
$963$		0			0
$964$	−22.6502			−0.729514
$965$	−10.8934	−	18.8679i	−0.350670	−	0.607379i
$966$		0			0
$967$	14.4178	−	24.9723i	0.463644	−	0.803056i	−0.535495	−	0.844539i	$-0.679875\pi$
$967$	14.4178	−	24.9723i	0.463644	−	0.803056i	0.999139	+	0.0414828i	$0.0132082\pi$
$968$	−6.48932	+	11.2398i	−0.208575	+	0.361262i
$969$		0			0
$970$	−1.99315	−	3.45224i	−0.0639963	−	0.110845i
$971$	1.72410			0.0553290			0.0276645	−	0.999617i	$-0.491193\pi$
$971$	1.72410			0.0553290			0.0276645	+	0.999617i	$0.491193\pi$
$972$		0			0
$973$	15.8627			0.508535
$974$	−6.58219	−	11.4007i	−0.210907	−	0.365302i
$975$		0			0
$976$	11.5608	−	20.0239i	0.370053	−	0.640950i
$977$	1.59192	−	2.75729i	0.0509301	−	0.0882135i	−0.839436	−	0.543458i	$-0.817115\pi$
$977$	1.59192	−	2.75729i	0.0509301	−	0.0882135i	0.890367	+	0.455244i	$0.150448\pi$
$978$		0			0
$979$	−23.9488	−	41.4805i	−0.765407	−	1.32572i
$980$	10.0474			0.320952
$981$		0			0
$982$	1.94339			0.0620162
$983$	5.85946	+	10.1489i	0.186888	+	0.323699i	0.944211	−	0.329341i	$-0.106827\pi$
$983$	5.85946	+	10.1489i	0.186888	+	0.323699i	−0.757323	+	0.653040i	$0.773493\pi$
$984$		0			0
$985$	−1.64641	+	2.85167i	−0.0524590	+	0.0908617i
$986$	11.0578	−	19.1527i	0.352152	−	0.609945i
$987$		0			0
$988$	−5.22353	−	9.04743i	−0.166183	−	0.287837i
$989$	−20.3906			−0.648382
$990$		0			0
$991$	45.8521			1.45654			0.728271	−	0.685290i	$-0.240324\pi$
$991$	45.8521			1.45654			0.728271	+	0.685290i	$0.240324\pi$
$992$	−25.6397	−	44.4093i	−0.814062	−	1.41000i
$993$		0			0
$994$	0.0783452	−	0.135698i	0.00248496	−	0.00430408i
$995$	9.88960	−	17.1293i	0.313521	−	0.543035i
$996$		0			0
$997$	12.0839	+	20.9299i	0.382701	+	0.662857i	0.991447	−	0.130508i	$-0.0416607\pi$
$997$	12.0839	+	20.9299i	0.382701	+	0.662857i	−0.608747	+	0.793365i	$0.708327\pi$
$998$	−9.13431			−0.289141
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1755.2.i.f.1171.5		16
3.2	odd	2		585.2.i.e.391.4	yes	16
9.2	odd	6		585.2.i.e.196.4	✓	16
9.4	even	3		5265.2.a.ba.1.4		8
9.5	odd	6		5265.2.a.bf.1.5		8
9.7	even	3	inner	1755.2.i.f.586.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.e.196.4	✓	16	9.2	odd	6
585.2.i.e.391.4	yes	16	3.2	odd	2
1755.2.i.f.586.5		16	9.7	even	3	inner
1755.2.i.f.1171.5		16	1.1	even	1	trivial
5265.2.a.ba.1.4		8	9.4	even	3
5265.2.a.bf.1.5		8	9.5	odd	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:	\( N \)	\(=\)	\( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1755.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.327533 + 0.567303i) q^{2} +(0.785445 - 1.36043i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.388592 + 0.673061i) q^{7} +2.33917 q^{8} +O(q^{10})\)	\(q+(0.327533 + 0.567303i) q^{2} +(0.785445 - 1.36043i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.388592 + 0.673061i) q^{7} +2.33917 q^{8} -0.655066 q^{10} +(-2.03399 - 3.52297i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-0.254553 + 0.440899i) q^{14} +(-0.804735 - 1.39384i) q^{16} -5.29154 q^{17} +6.65042 q^{19} +(0.785445 + 1.36043i) q^{20} +(1.33239 - 2.30778i) q^{22} +(1.15283 - 1.99677i) q^{23} +(-0.500000 - 0.866025i) q^{25} +0.655066 q^{26} +1.22087 q^{28} +(3.19008 + 5.52538i) q^{29} +(4.47259 - 7.74675i) q^{31} +(2.86632 - 4.96461i) q^{32} +(-1.73315 - 3.00191i) q^{34} -0.777184 q^{35} -2.80592 q^{37} +(2.17823 + 3.77280i) q^{38} +(-1.16958 + 2.02578i) q^{40} +(3.80493 - 6.59034i) q^{41} +(-4.42183 - 7.65883i) q^{43} -6.39034 q^{44} +1.51036 q^{46} +(-2.04391 - 3.54016i) q^{47} +(3.19799 - 5.53909i) q^{49} +(0.327533 - 0.567303i) q^{50} +(-0.785445 - 1.36043i) q^{52} +4.78025 q^{53} +4.06797 q^{55} +(0.908981 + 1.57440i) q^{56} +(-2.08971 + 3.61949i) q^{58} +(-2.37049 + 4.10581i) q^{59} +(7.18299 + 12.4413i) q^{61} +5.85967 q^{62} +0.536314 q^{64} +(0.500000 + 0.866025i) q^{65} +(-5.39353 + 9.34188i) q^{67} +(-4.15621 + 7.19877i) q^{68} +(-0.254553 - 0.440899i) q^{70} -0.307776 q^{71} -7.50636 q^{73} +(-0.919032 - 1.59181i) q^{74} +(5.22353 - 9.04743i) q^{76} +(1.58078 - 2.73799i) q^{77} +(-3.80949 - 6.59822i) q^{79} +1.60947 q^{80} +4.98496 q^{82} +(-6.26484 - 10.8510i) q^{83} +(2.64577 - 4.58261i) q^{85} +(2.89659 - 5.01704i) q^{86} +(-4.75783 - 8.24081i) q^{88} +11.7743 q^{89} +0.777184 q^{91} +(-1.81098 - 3.13670i) q^{92} +(1.33889 - 2.31903i) q^{94} +(-3.32521 + 5.75943i) q^{95} +(3.04268 + 5.27007i) q^{97} +4.18979 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8	\( 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8} - 6 q^{10} + 6 q^{11} + 8 q^{13} + 10 q^{14} - 11 q^{16} + 4 q^{17} - 20 q^{19} - 9 q^{20} - 3 q^{22} + 6 q^{23} - 8 q^{25} + 6 q^{26} - 68 q^{28} + 14 q^{29} + 31 q^{31} + q^{32} + 7 q^{34} - 22 q^{35} + 2 q^{37} + 9 q^{38} - 6 q^{40} - 12 q^{41} - 15 q^{43} - 32 q^{44} - 64 q^{46} - 18 q^{47} - 17 q^{49} + 3 q^{50} + 9 q^{52} - 4 q^{53} - 12 q^{55} + 16 q^{56} + 42 q^{58} + 24 q^{59} + 9 q^{61} + 40 q^{62} - 60 q^{64} + 8 q^{65} + 18 q^{67} - 14 q^{68} + 10 q^{70} - 20 q^{71} + 12 q^{73} - 37 q^{74} + 53 q^{76} - 34 q^{77} + 3 q^{79} + 22 q^{80} - 68 q^{82} - 10 q^{83} - 2 q^{85} + 60 q^{86} + 14 q^{88} + 26 q^{89} + 22 q^{91} + 5 q^{92} - 17 q^{94} + 10 q^{95} + 34 q^{97} + 60 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8 - 6 * q^10 + 6 * q^11 + 8 * q^13 + 10 * q^14 - 11 * q^16 + 4 * q^17 - 20 * q^19 - 9 * q^20 - 3 * q^22 + 6 * q^23 - 8 * q^25 + 6 * q^26 - 68 * q^28 + 14 * q^29 + 31 * q^31 + q^32 + 7 * q^34 - 22 * q^35 + 2 * q^37 + 9 * q^38 - 6 * q^40 - 12 * q^41 - 15 * q^43 - 32 * q^44 - 64 * q^46 - 18 * q^47 - 17 * q^49 + 3 * q^50 + 9 * q^52 - 4 * q^53 - 12 * q^55 + 16 * q^56 + 42 * q^58 + 24 * q^59 + 9 * q^61 + 40 * q^62 - 60 * q^64 + 8 * q^65 + 18 * q^67 - 14 * q^68 + 10 * q^70 - 20 * q^71 + 12 * q^73 - 37 * q^74 + 53 * q^76 - 34 * q^77 + 3 * q^79 + 22 * q^80 - 68 * q^82 - 10 * q^83 - 2 * q^85 + 60 * q^86 + 14 * q^88 + 26 * q^89 + 22 * q^91 + 5 * q^92 - 17 * q^94 + 10 * q^95 + 34 * q^97 + 60 * q^98

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