LMFDB - Embedded newform 1456.2.cc.f.225.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1456,2,Mod(225,1456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1456.225"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1456, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} + 38x^{14} + 587x^{12} + 4762x^{10} + 21849x^{8} + 56552x^{6} + 76456x^{4} + 42624x^{2} + 2704 $ x^16 + 38x^14 + 587x^12 + 4762x^10 + 21849x^8 + 56552x^6 + 76456x^4 + 42624*x^2 + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			225.4
Root			$0.268953i$ of defining polynomial
Character	$\chi$	$=$	1456.225
Dual form			1456.2.cc.f.673.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.134476 + 0.232920i) q^{3} -1.35585i q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.46383 + 2.53543i) q^{9} +(-2.42763 - 1.40159i) q^{11} +(0.303042 - 3.59279i) q^{13} +(0.315805 + 0.182330i) q^{15} +(-2.90934 - 5.03912i) q^{17} +(-2.75793 + 1.59229i) q^{19} -0.268953i q^{21} +(-3.77674 + 6.54150i) q^{23} +3.16167 q^{25} -1.59426 q^{27} +(-3.60830 + 6.24977i) q^{29} -8.04407i q^{31} +(0.652918 - 0.376962i) q^{33} +(0.677925 + 1.17420i) q^{35} +(-6.02532 - 3.47872i) q^{37} +(0.796082 + 0.553731i) q^{39} +(4.38164 + 2.52974i) q^{41} +(-3.13427 - 5.42872i) q^{43} +(3.43767 - 1.98474i) q^{45} -2.64315i q^{47} +(0.500000 - 0.866025i) q^{49} +1.56495 q^{51} -11.0887 q^{53} +(-1.90035 + 3.29150i) q^{55} -0.856503i q^{57} +(5.45213 - 3.14779i) q^{59} +(-6.40404 - 11.0921i) q^{61} +(-2.53543 - 1.46383i) q^{63} +(-4.87129 - 0.410880i) q^{65} +(-4.29803 - 2.48147i) q^{67} +(-1.01576 - 1.75936i) q^{69} +(14.2993 - 8.25572i) q^{71} +15.4351i q^{73} +(-0.425170 + 0.736416i) q^{75} +2.80318 q^{77} -14.7661 q^{79} +(-4.17711 + 7.23496i) q^{81} +9.79310i q^{83} +(-6.83230 + 3.94463i) q^{85} +(-0.970464 - 1.68089i) q^{87} +(-7.24707 - 4.18410i) q^{89} +(1.53395 + 3.26297i) q^{91} +(1.87363 + 1.08174i) q^{93} +(2.15891 + 3.73934i) q^{95} +(-10.5685 + 6.10170i) q^{97} -8.20678i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 14 q^{9} - 6 q^{11} + 10 q^{13} - 6 q^{15} + 2 q^{17} - 44 q^{25} + 12 q^{27} - 22 q^{29} + 42 q^{33} + 6 q^{35} + 12 q^{37} - 24 q^{39} + 36 q^{41} - 6 q^{43} - 30 q^{45} + 8 q^{49} + 4 q^{51} + 8 q^{53}+ \cdots - 42 q^{97}+O(q^{100}) $ 16 * q - 14 * q^9 - 6 * q^11 + 10 * q^13 - 6 * q^15 + 2 * q^17 - 44 * q^25 + 12 * q^27 - 22 * q^29 + 42 * q^33 + 6 * q^35 + 12 * q^37 - 24 * q^39 + 36 * q^41 - 6 * q^43 - 30 * q^45 + 8 * q^49 + 4 * q^51 + 8 * q^53 - 2 * q^55 + 18 * q^59 + 4 * q^61 + 12 * q^63 - 30 * q^65 - 24 * q^67 - 52 * q^69 - 36 * q^71 + 10 * q^75 - 24 * q^77 - 8 * q^79 + 42 * q^85 - 26 * q^87 - 36 * q^89 + 2 * q^91 - 42 * q^93 + 30 * q^95 - 42 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	−0.134476	+	0.232920i	−0.0776400	+	0.134476i	−0.902231	−	0.431252i	$-0.858072\pi$
$3$	−0.134476	+	0.232920i	−0.0776400	+	0.134476i	0.824591	+	0.565729i	$0.191405\pi$
$4$		0			0
$5$		−	1.35585i		−	0.606355i	−0.952934	−	0.303177i	$-0.901953\pi$
$5$		−	1.35585i		−	0.606355i	0.952934	−	0.303177i	$-0.0980475\pi$
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$		0			0
$9$	1.46383	+	2.53543i	0.487944	+	0.845144i
$10$		0			0
$11$	−2.42763	−	1.40159i	−0.731958	−	0.422596i	0.0871803	−	0.996193i	$-0.472214\pi$
$11$	−2.42763	−	1.40159i	−0.731958	−	0.422596i	−0.819138	+	0.573597i	$0.805548\pi$
$12$		0			0
$13$	0.303042	−	3.59279i	0.0840488	−	0.996462i
$13$	0.303042	−	3.59279i	0.0840488	−	0.996462i
$14$		0			0
$15$	0.315805	+	0.182330i	0.0815405	+	0.0470774i
$16$		0			0
$17$	−2.90934	−	5.03912i	−0.705618	−	1.22217i	−0.966468	−	0.256787i	$-0.917336\pi$
$17$	−2.90934	−	5.03912i	−0.705618	−	1.22217i	0.260850	−	0.965379i	$-0.415997\pi$
$18$		0			0
$19$	−2.75793	+	1.59229i	−0.632713	+	0.365297i	−0.781802	−	0.623527i	$-0.785699\pi$
$19$	−2.75793	+	1.59229i	−0.632713	+	0.365297i	0.149089	+	0.988824i	$0.452366\pi$
$20$		0			0
$21$		−	0.268953i		−	0.0586903i
$22$		0			0
$23$	−3.77674	+	6.54150i	−0.787504	+	1.36400i	0.139988	+	0.990153i	$0.455294\pi$
$23$	−3.77674	+	6.54150i	−0.787504	+	1.36400i	−0.927492	+	0.373843i	$0.878040\pi$
$24$		0			0
$25$	3.16167			0.632334
$26$		0			0
$27$	−1.59426			−0.306816
$28$		0			0
$29$	−3.60830	+	6.24977i	−0.670045	+	1.16055i	0.307845	+	0.951436i	$0.400392\pi$
$29$	−3.60830	+	6.24977i	−0.670045	+	1.16055i	−0.977891	+	0.209116i	$0.932941\pi$
$30$		0			0
$31$		−	8.04407i		−	1.44476i	−0.691498	−	0.722379i	$-0.743049\pi$
$31$		−	8.04407i		−	1.44476i	0.691498	−	0.722379i	$-0.256951\pi$
$32$		0			0
$33$	0.652918	−	0.376962i	0.113658	−	0.0656207i
$34$		0			0
$35$	0.677925	+	1.17420i	0.114590	+	0.198476i
$36$		0			0
$37$	−6.02532	−	3.47872i	−0.990557	−	0.571898i	−0.0851160	−	0.996371i	$-0.527126\pi$
$37$	−6.02532	−	3.47872i	−0.990557	−	0.571898i	−0.905441	+	0.424473i	$0.860459\pi$
$38$		0			0
$39$	0.796082	+	0.553731i	0.127475	+	0.0886679i
$40$		0			0
$41$	4.38164	+	2.52974i	0.684298	+	0.395079i	0.801472	−	0.598032i	$-0.204050\pi$
$41$	4.38164	+	2.52974i	0.684298	+	0.395079i	−0.117175	+	0.993111i	$0.537384\pi$
$42$		0			0
$43$	−3.13427	−	5.42872i	−0.477972	−	0.827872i	0.521709	−	0.853123i	$-0.325295\pi$
$43$	−3.13427	−	5.42872i	−0.477972	−	0.827872i	−0.999681	+	0.0252518i	$0.991961\pi$
$44$		0			0
$45$	3.43767	−	1.98474i	0.512457	−	0.295867i
$46$		0			0
$47$		−	2.64315i		−	0.385542i	−0.981244	−	0.192771i	$-0.938252\pi$
$47$		−	2.64315i		−	0.385542i	0.981244	−	0.192771i	$-0.0617475\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$		0			0
$51$	1.56495			0.219137
$52$		0			0
$53$	−11.0887			−1.52315			−0.761574	−	0.648079i	$-0.775573\pi$
$53$	−11.0887			−1.52315			−0.761574	+	0.648079i	$0.775573\pi$
$54$		0			0
$55$	−1.90035	+	3.29150i	−0.256243	+	0.443826i
$56$		0			0
$57$		−	0.856503i		−	0.113447i
$58$		0			0
$59$	5.45213	−	3.14779i	0.709807	−	0.409807i	−0.101183	−	0.994868i	$-0.532263\pi$
$59$	5.45213	−	3.14779i	0.709807	−	0.409807i	0.810989	+	0.585061i	$0.198929\pi$
$60$		0			0
$61$	−6.40404	−	11.0921i	−0.819953	−	1.42020i	−0.905716	−	0.423885i	$-0.860666\pi$
$61$	−6.40404	−	11.0921i	−0.819953	−	1.42020i	0.0857630	−	0.996316i	$-0.472667\pi$
$62$		0			0
$63$	−2.53543	−	1.46383i	−0.319434	−	0.184426i
$64$		0			0
$65$	−4.87129	−	0.410880i	−0.604209	−	0.0509634i
$66$		0			0
$67$	−4.29803	−	2.48147i	−0.525088	−	0.303160i	0.213926	−	0.976850i	$-0.431375\pi$
$67$	−4.29803	−	2.48147i	−0.525088	−	0.303160i	−0.739014	+	0.673690i	$0.764708\pi$
$68$		0			0
$69$	−1.01576	−	1.75936i	−0.122284	−	0.211801i
$70$		0			0
$71$	14.2993	−	8.25572i	1.69702	−	0.979773i	0.748453	−	0.663188i	$-0.230797\pi$
$71$	14.2993	−	8.25572i	1.69702	−	0.979773i	0.948564	−	0.316586i	$-0.102536\pi$
$72$		0			0
$73$			15.4351i			1.80654i	0.429071	+	0.903271i	$0.358841\pi$
$73$			15.4351i			1.80654i	−0.429071	+	0.903271i	$0.641159\pi$
$74$		0			0
$75$	−0.425170	+	0.736416i	−0.0490944	+	0.0850340i
$76$		0			0
$77$	2.80318			0.319452
$78$		0			0
$79$	−14.7661			−1.66131			−0.830656	−	0.556786i	$-0.812034\pi$
$79$	−14.7661			−1.66131			−0.830656	+	0.556786i	$0.812034\pi$
$80$		0			0
$81$	−4.17711	+	7.23496i	−0.464123	+	0.803884i
$82$		0			0
$83$			9.79310i			1.07493i	0.843285	+	0.537466i	$0.180618\pi$
$83$			9.79310i			1.07493i	−0.843285	+	0.537466i	$0.819382\pi$
$84$		0			0
$85$	−6.83230	+	3.94463i	−0.741067	+	0.427855i
$86$		0			0
$87$	−0.970464	−	1.68089i	−0.104045	−	0.180211i
$88$		0			0
$89$	−7.24707	−	4.18410i	−0.768188	−	0.443513i	0.0640399	−	0.997947i	$-0.479602\pi$
$89$	−7.24707	−	4.18410i	−0.768188	−	0.443513i	−0.832228	+	0.554434i	$0.812935\pi$
$90$		0			0
$91$	1.53395	+	3.26297i	0.160802	+	0.342052i
$92$		0			0
$93$	1.87363	+	1.08174i	0.194286	+	0.112171i
$94$		0			0
$95$	2.15891	+	3.73934i	0.221499	+	0.383648i
$96$		0			0
$97$	−10.5685	+	6.10170i	−1.07306	+	0.619534i	−0.929017	−	0.370037i	$-0.879345\pi$
$97$	−10.5685	+	6.10170i	−1.07306	+	0.619534i	−0.144047	+	0.989571i	$0.546012\pi$
$98$		0			0
$99$		−	8.20678i		−	0.824813i
$100$		0			0
$101$	−1.21143	+	2.09825i	−0.120541	+	0.208784i	−0.919981	−	0.391962i	$-0.871796\pi$
$101$	−1.21143	+	2.09825i	−0.120541	+	0.208784i	0.799440	+	0.600746i	$0.205130\pi$
$102$		0			0
$103$	−14.4909			−1.42783			−0.713917	−	0.700230i	$-0.753081\pi$
$103$	−14.4909			−1.42783			−0.713917	+	0.700230i	$0.753081\pi$
$104$		0			0
$105$	−0.364660			−0.0355872
$106$		0			0
$107$	3.24370	−	5.61826i	0.313581	−	0.543138i	−0.665554	−	0.746350i	$-0.731805\pi$
$107$	3.24370	−	5.61826i	0.313581	−	0.543138i	0.979135	+	0.203212i	$0.0651381\pi$
$108$		0			0
$109$		−	2.93644i		−	0.281260i	−0.990062	−	0.140630i	$-0.955087\pi$
$109$		−	2.93644i		−	0.281260i	0.990062	−	0.140630i	$-0.0449129\pi$
$110$		0			0
$111$	1.62053	−	0.935612i	0.153814	−	0.0888044i
$112$		0			0
$113$	1.66909	+	2.89095i	0.157015	+	0.271957i	0.933791	−	0.357819i	$-0.116480\pi$
$113$	1.66909	+	2.89095i	0.157015	+	0.271957i	−0.776776	+	0.629777i	$0.783146\pi$
$114$		0			0
$115$	8.86929	+	5.12069i	0.827066	+	0.477507i
$116$		0			0
$117$	9.55289	−	4.49090i	0.883165	−	0.415184i
$118$		0			0
$119$	5.03912	+	2.90934i	0.461936	+	0.266699i
$120$		0			0
$121$	−1.57108	−	2.72119i	−0.142825	−	0.247381i
$122$		0			0
$123$	−1.17846	+	0.680382i	−0.106258	+	0.0613480i
$124$		0			0
$125$		−	11.0660i		−	0.989773i
$126$		0			0
$127$	6.27512	−	10.8688i	0.556827	−	0.964452i	−0.440932	−	0.897540i	$-0.645352\pi$
$127$	6.27512	−	10.8688i	0.556827	−	0.964452i	0.997759	−	0.0669115i	$-0.0213145\pi$
$128$		0			0
$129$	1.68594			0.148439
$130$		0			0
$131$	−1.26001			−0.110087			−0.0550437	−	0.998484i	$-0.517530\pi$
$131$	−1.26001			−0.110087			−0.0550437	+	0.998484i	$0.517530\pi$
$132$		0			0
$133$	1.59229	−	2.75793i	0.138069	−	0.239143i
$134$		0			0
$135$			2.16158i			0.186039i
$136$		0			0
$137$	−7.20794	+	4.16151i	−0.615816	+	0.355542i	−0.775238	−	0.631669i	$-0.782370\pi$
$137$	−7.20794	+	4.16151i	−0.615816	+	0.355542i	0.159422	+	0.987211i	$0.449037\pi$
$138$		0			0
$139$	−2.89438	−	5.01322i	−0.245498	−	0.425216i	0.716773	−	0.697306i	$-0.245618\pi$
$139$	−2.89438	−	5.01322i	−0.245498	−	0.425216i	−0.962272	+	0.272091i	$0.912285\pi$
$140$		0			0
$141$	0.615642	+	0.355441i	0.0518464	+	0.0299335i
$142$		0			0
$143$	−5.77131	+	8.29723i	−0.482621	+	0.693849i
$144$		0			0
$145$	8.47375	+	4.89232i	0.703707	+	0.406285i
$146$		0			0
$147$	0.134476	+	0.232920i	0.0110914	+	0.0192109i
$148$		0			0
$149$	12.3009	−	7.10193i	1.00773	−	0.581812i	0.0972028	−	0.995265i	$-0.469010\pi$
$149$	12.3009	−	7.10193i	1.00773	−	0.581812i	0.910526	+	0.413452i	$0.135677\pi$
$150$		0			0
$151$		−	11.1509i		−	0.907451i	−0.891142	−	0.453725i	$-0.850095\pi$
$151$		−	11.1509i		−	0.907451i	0.891142	−	0.453725i	$-0.149905\pi$
$152$		0			0
$153$	8.51757	−	14.7529i	0.688605	−	1.19270i
$154$		0			0
$155$	−10.9066			−0.876036
$156$		0			0
$157$	4.04749			0.323025			0.161513	−	0.986871i	$-0.448363\pi$
$157$	4.04749			0.323025			0.161513	+	0.986871i	$0.448363\pi$
$158$		0			0
$159$	1.49117	−	2.58278i	0.118257	−	0.204827i
$160$		0			0
$161$		−	7.55347i		−	0.595297i
$162$		0			0
$163$	4.56675	−	2.63661i	0.357695	−	0.206515i	−0.310374	−	0.950615i	$-0.600454\pi$
$163$	4.56675	−	2.63661i	0.357695	−	0.206515i	0.668069	+	0.744099i	$0.267121\pi$
$164$		0			0
$165$	−0.511105	−	0.885259i	−0.0397894	−	0.0689173i
$166$		0			0
$167$	4.63307	+	2.67491i	0.358518	+	0.206990i	0.668430	−	0.743775i	$-0.266966\pi$
$167$	4.63307	+	2.67491i	0.358518	+	0.206990i	−0.309912	+	0.950765i	$0.600300\pi$
$168$		0			0
$169$	−12.8163	−	2.17754i	−0.985872	−	0.167503i
$170$		0			0
$171$	−8.07429	−	4.66170i	−0.617457	−	0.356489i
$172$		0			0
$173$	−4.87155	−	8.43777i	−0.370377	−	0.641511i	0.619247	−	0.785197i	$-0.287438\pi$
$173$	−4.87155	−	8.43777i	−0.370377	−	0.641511i	−0.989623	+	0.143685i	$0.954105\pi$
$174$		0			0
$175$	−2.73809	+	1.58083i	−0.206980	+	0.119500i
$176$		0			0
$177$			1.69321i			0.127270i
$178$		0			0
$179$	−5.70263	+	9.87724i	−0.426234	+	0.738259i	−0.996535	−	0.0831767i	$-0.973493\pi$
$179$	−5.70263	+	9.87724i	−0.426234	+	0.738259i	0.570301	+	0.821436i	$0.306827\pi$
$180$		0			0
$181$	25.4727			1.89337			0.946685	−	0.322160i	$-0.104409\pi$
$181$	25.4727			1.89337			0.946685	+	0.322160i	$0.104409\pi$
$182$		0			0
$183$	3.44477			0.254645
$184$		0			0
$185$	−4.71663	+	8.16943i	−0.346773	+	0.600629i
$186$		0			0
$187$			16.3108i			1.19277i
$188$		0			0
$189$	1.38067	−	0.797131i	0.100429	−	0.0579828i
$190$		0			0
$191$	8.18905	+	14.1838i	0.592539	+	1.02631i	0.993889	+	0.110382i	$0.0352075\pi$
$191$	8.18905	+	14.1838i	0.592539	+	1.02631i	−0.401351	+	0.915924i	$0.631459\pi$
$192$		0			0
$193$	8.28132	+	4.78122i	0.596103	+	0.344160i	0.767507	−	0.641041i	$-0.221497\pi$
$193$	8.28132	+	4.78122i	0.596103	+	0.344160i	−0.171404	+	0.985201i	$0.554830\pi$
$194$		0			0
$195$	0.750776	−	1.07937i	0.0537642	−	0.0772951i
$196$		0			0
$197$	2.60716	+	1.50525i	0.185753	+	0.107244i	0.589993	−	0.807409i	$-0.299131\pi$
$197$	2.60716	+	1.50525i	0.185753	+	0.107244i	−0.404240	+	0.914653i	$0.632464\pi$
$198$		0			0
$199$	2.30985	+	4.00077i	0.163741	+	0.283607i	0.936207	−	0.351448i	$-0.114311\pi$
$199$	2.30985	+	4.00077i	0.163741	+	0.283607i	−0.772467	+	0.635055i	$0.780977\pi$
$200$		0			0
$201$	1.15597	−	0.667399i	0.0815357	−	0.0470747i
$202$		0			0
$203$		−	7.21661i		−	0.506507i
$204$		0			0
$205$	3.42995	−	5.94085i	0.239558	−	0.414927i
$206$		0			0
$207$	−22.1140			−1.53703
$208$		0			0
$209$	8.92697			0.617492
$210$		0			0
$211$	1.16932	−	2.02533i	0.0804995	−	0.139429i	−0.822965	−	0.568092i	$-0.807682\pi$
$211$	1.16932	−	2.02533i	0.0804995	−	0.139429i	0.903465	+	0.428663i	$0.141015\pi$
$212$		0			0
$213$			4.44080i			0.304279i
$214$		0			0
$215$	−7.36053	+	4.24960i	−0.501984	+	0.289821i
$216$		0			0
$217$	4.02203	+	6.96637i	0.273033	+	0.472908i
$218$		0			0
$219$	−3.59515	−	2.07566i	−0.242937	−	0.140260i
$220$		0			0
$221$	−18.9862	+	8.92559i	−1.27715	+	0.600400i
$222$		0			0
$223$	4.21429	+	2.43312i	0.282210	+	0.162934i	0.634423	−	0.772986i	$-0.281238\pi$
$223$	4.21429	+	2.43312i	0.282210	+	0.162934i	−0.352214	+	0.935920i	$0.614571\pi$
$224$		0			0
$225$	4.62815	+	8.01620i	0.308544	+	0.534413i
$226$		0			0
$227$	24.3177	−	14.0398i	1.61402	−	0.931855i	0.625594	−	0.780149i	$-0.284857\pi$
$227$	24.3177	−	14.0398i	1.61402	−	0.931855i	0.988426	−	0.151706i	$-0.0484766\pi$
$228$		0			0
$229$		−	0.179280i		−	0.0118471i	−0.999982	−	0.00592357i	$-0.998114\pi$
$229$		−	0.179280i		−	0.0118471i	0.999982	−	0.00592357i	$-0.00188554\pi$
$230$		0			0
$231$	−0.376962	+	0.652918i	−0.0248023	+	0.0429588i
$232$		0			0
$233$	15.1384			0.991747			0.495873	−	0.868395i	$-0.334848\pi$
$233$	15.1384			0.991747			0.495873	+	0.868395i	$0.334848\pi$
$234$		0			0
$235$	−3.58371			−0.233775
$236$		0			0
$237$	1.98569	−	3.43931i	0.128984	−	0.223407i
$238$		0			0
$239$			12.8703i			0.832512i	0.909247	+	0.416256i	$0.136658\pi$
$239$			12.8703i			0.832512i	−0.909247	+	0.416256i	$0.863342\pi$
$240$		0			0
$241$	8.51452	−	4.91586i	0.548469	−	0.316659i	−0.200035	−	0.979789i	$-0.564106\pi$
$241$	8.51452	−	4.91586i	0.548469	−	0.316659i	0.748504	+	0.663130i	$0.230772\pi$
$242$		0			0
$243$	−3.51484	−	6.08788i	−0.225477	−	0.390538i
$244$		0			0
$245$	−1.17420	−	0.677925i	−0.0750170	−	0.0433111i
$246$		0			0
$247$	4.88501	+	10.3912i	0.310825	+	0.661177i
$248$		0			0
$249$	−2.28101	−	1.31694i	−0.144553	−	0.0834578i
$250$		0			0
$251$	8.66099	+	15.0013i	0.546677	+	0.946872i	0.998499	+	0.0547641i	$0.0174407\pi$
$251$	8.66099	+	15.0013i	0.546677	+	0.946872i	−0.451823	+	0.892108i	$0.649226\pi$
$252$		0			0
$253$	18.3370	−	10.5869i	1.15284	−	0.665592i
$254$		0			0
$255$		−	2.12184i		−	0.132875i
$256$		0			0
$257$	−5.35302	+	9.27170i	−0.333912	+	0.578353i	−0.983275	−	0.182126i	$-0.941702\pi$
$257$	−5.35302	+	9.27170i	−0.333912	+	0.578353i	0.649363	+	0.760478i	$0.275036\pi$
$258$		0			0
$259$	6.95744			0.432314
$260$		0			0
$261$	−21.1278			−1.30778
$262$		0			0
$263$	−7.03484	+	12.1847i	−0.433787	+	0.751341i	−0.997196	−	0.0748372i	$-0.976156\pi$
$263$	−7.03484	+	12.1847i	−0.433787	+	0.751341i	0.563409	+	0.826178i	$0.309490\pi$
$264$		0			0
$265$			15.0346i			0.923567i
$266$		0			0
$267$	1.94912	−	1.12533i	0.119284	−	0.0688688i
$268$		0			0
$269$	0.272011	+	0.471138i	0.0165848	+	0.0287258i	0.874199	−	0.485568i	$-0.161387\pi$
$269$	0.272011	+	0.471138i	0.0165848	+	0.0287258i	−0.857614	+	0.514294i	$0.828054\pi$
$270$		0			0
$271$	0.641910	+	0.370607i	0.0389933	+	0.0225128i	0.519370	−	0.854550i	$-0.326167\pi$
$271$	0.641910	+	0.370607i	0.0389933	+	0.0225128i	−0.480377	+	0.877062i	$0.659500\pi$
$272$		0			0
$273$	−0.966292	−	0.0815041i	−0.0584827	−	0.00493285i
$274$		0			0
$275$	−7.67536	−	4.43137i	−0.462842	−	0.267222i
$276$		0			0
$277$	−7.06675	−	12.2400i	−0.424600	−	0.735429i	0.571783	−	0.820405i	$-0.306252\pi$
$277$	−7.06675	−	12.2400i	−0.424600	−	0.735429i	−0.996383	+	0.0849763i	$0.972919\pi$
$278$		0			0
$279$	20.3952	−	11.7752i	1.22103	−	0.704961i
$280$		0			0
$281$			25.8051i			1.53940i	0.638404	+	0.769702i	$0.279595\pi$
$281$			25.8051i			1.53940i	−0.638404	+	0.769702i	$0.720405\pi$
$282$		0			0
$283$	−13.6409	+	23.6267i	−0.810865	+	1.40446i	0.101394	+	0.994846i	$0.467670\pi$
$283$	−13.6409	+	23.6267i	−0.810865	+	1.40446i	−0.912259	+	0.409613i	$0.865664\pi$
$284$		0			0
$285$	−1.16129			−0.0687889
$286$		0			0
$287$	−5.05949			−0.298652
$288$		0			0
$289$	−8.42851	+	14.5986i	−0.495795	+	0.858742i
$290$		0			0
$291$		−	3.28214i		−	0.192403i
$292$		0			0
$293$	−1.50010	+	0.866083i	−0.0876367	+	0.0505971i	−0.543178	−	0.839618i	$-0.682779\pi$
$293$	−1.50010	+	0.866083i	−0.0876367	+	0.0505971i	0.455541	+	0.890215i	$0.349446\pi$
$294$		0			0
$295$	−4.26793	−	7.39227i	−0.248489	−	0.430395i
$296$		0			0
$297$	3.87028	+	2.23451i	0.224576	+	0.129659i
$298$		0			0
$299$	22.3577	+	15.5514i	1.29298	+	0.899360i
$300$		0			0
$301$	5.42872	+	3.13427i	0.312906	+	0.180656i
$302$		0			0
$303$	−0.325817	−	0.564331i	−0.0187177	−	0.0324200i
$304$		0			0
$305$	−15.0393	+	8.68292i	−0.861145	+	0.497182i
$306$		0			0
$307$		−	21.4365i		−	1.22345i	−0.791072	−	0.611723i	$-0.790477\pi$
$307$		−	21.4365i		−	1.22345i	0.791072	−	0.611723i	$-0.209523\pi$
$308$		0			0
$309$	1.94869	−	3.37523i	0.110857	−	0.192010i
$310$		0			0
$311$	27.2724			1.54647			0.773237	−	0.634117i	$-0.218636\pi$
$311$	27.2724			1.54647			0.773237	+	0.634117i	$0.218636\pi$
$312$		0			0
$313$	7.28221			0.411615			0.205807	−	0.978593i	$-0.434018\pi$
$313$	7.28221			0.411615			0.205807	+	0.978593i	$0.434018\pi$
$314$		0			0
$315$	−1.98474	+	3.43767i	−0.111827	+	0.193691i
$316$		0			0
$317$		−	2.54836i		−	0.143130i	−0.997436	−	0.0715651i	$-0.977201\pi$
$317$		−	2.54836i		−	0.143130i	0.997436	−	0.0715651i	$-0.0227994\pi$
$318$		0			0
$319$	17.5192	−	10.1147i	0.980890	−	0.566317i
$320$		0			0
$321$	0.872404	+	1.51105i	0.0486928	+	0.0843384i
$322$		0			0
$323$	16.0475	+	9.26503i	0.892907	+	0.515520i
$324$		0			0
$325$	0.958120	−	11.3592i	0.0531469	−	0.630096i
$326$		0			0
$327$	0.683957	+	0.394883i	0.0378229	+	0.0218371i
$328$		0			0
$329$	1.32157	+	2.28903i	0.0728607	+	0.126198i
$330$		0			0
$331$	−0.169450	+	0.0978320i	−0.00931381	+	0.00537733i	−0.504650	−	0.863324i	$-0.668378\pi$
$331$	−0.169450	+	0.0978320i	−0.00931381	+	0.00537733i	0.495336	+	0.868702i	$0.335045\pi$
$332$		0			0
$333$		−	20.3691i		−	1.11622i
$334$		0			0
$335$	−3.36450	+	5.82749i	−0.183822	+	0.318390i
$336$		0			0
$337$	2.00900			0.109437			0.0547185	−	0.998502i	$-0.482574\pi$
$337$	2.00900			0.109437			0.0547185	+	0.998502i	$0.482574\pi$
$338$		0			0
$339$	−0.897813			−0.0487625
$340$		0			0
$341$	−11.2745	+	19.5280i	−0.610549	+	1.05750i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$	−2.38542	+	1.37722i	−0.128427	+	0.0741473i
$346$		0			0
$347$	2.27450	+	3.93956i	0.122102	+	0.211486i	0.920596	−	0.390516i	$-0.127703\pi$
$347$	2.27450	+	3.93956i	0.122102	+	0.211486i	−0.798495	+	0.602002i	$0.794370\pi$
$348$		0			0
$349$	4.65700	+	2.68872i	0.249284	+	0.143924i	0.619436	−	0.785047i	$-0.287361\pi$
$349$	4.65700	+	2.68872i	0.249284	+	0.143924i	−0.370153	+	0.928971i	$0.620695\pi$
$350$		0			0
$351$	−0.483129	+	5.72786i	−0.0257875	+	0.305730i
$352$		0			0
$353$	7.10223	+	4.10047i	0.378013	+	0.218246i	0.676954	−	0.736026i	$-0.263300\pi$
$353$	7.10223	+	4.10047i	0.378013	+	0.218246i	−0.298940	+	0.954272i	$0.596633\pi$
$354$		0			0
$355$	−11.1935	−	19.3877i	−0.594090	−	1.02899i
$356$		0			0
$357$	−1.35529	+	0.782475i	−0.0717294	+	0.0414130i
$358$		0			0
$359$		−	31.7664i		−	1.67657i	−0.545233	−	0.838284i	$-0.683559\pi$
$359$		−	31.7664i		−	1.67657i	0.545233	−	0.838284i	$-0.316441\pi$
$360$		0			0
$361$	−4.42921	+	7.67162i	−0.233117	+	0.403770i
$362$		0			0
$363$	0.845093			0.0443559
$364$		0			0
$365$	20.9277			1.09541
$366$		0			0
$367$	8.66870	−	15.0146i	0.452502	−	0.783757i	−0.546038	−	0.837760i	$-0.683865\pi$
$367$	8.66870	−	15.0146i	0.452502	−	0.783757i	0.998541	+	0.0540031i	$0.0171981\pi$
$368$		0			0
$369$			14.8125i			0.771107i
$370$		0			0
$371$	9.60308	−	5.54434i	0.498567	−	0.287848i
$372$		0			0
$373$	−8.04814	−	13.9398i	−0.416717	−	0.721775i	0.578890	−	0.815406i	$-0.303486\pi$
$373$	−8.04814	−	13.9398i	−0.416717	−	0.721775i	−0.995607	+	0.0936306i	$0.970153\pi$
$374$		0			0
$375$	2.57749	+	1.48812i	0.133101	+	0.0768460i
$376$		0			0
$377$	21.3607	+	14.8578i	1.10013	+	0.765218i
$378$		0			0
$379$	15.2907	+	8.82811i	0.785432	+	0.453470i	0.838352	−	0.545129i	$-0.183519\pi$
$379$	15.2907	+	8.82811i	0.785432	+	0.453470i	−0.0529197	+	0.998599i	$0.516853\pi$
$380$		0			0
$381$	1.68771	+	2.92320i	0.0864641	+	0.149760i
$382$		0			0
$383$	−7.12262	+	4.11225i	−0.363949	+	0.210126i	−0.670812	−	0.741628i	$-0.734054\pi$
$383$	−7.12262	+	4.11225i	−0.363949	+	0.210126i	0.306863	+	0.951754i	$0.400721\pi$
$384$		0			0
$385$		−	3.80070i		−	0.193702i
$386$		0			0
$387$	9.17609	−	15.8935i	0.466447	−	0.807910i
$388$		0			0
$389$	15.1688			0.769090			0.384545	−	0.923106i	$-0.374358\pi$
$389$	15.1688			0.769090			0.384545	+	0.923106i	$0.374358\pi$
$390$		0			0
$391$	43.9512			2.22271
$392$		0			0
$393$	0.169441	−	0.293481i	0.00854719	−	0.0148042i
$394$		0			0
$395$			20.0206i			1.00734i
$396$		0			0
$397$	−24.5139	+	14.1531i	−1.23032	+	0.710325i	−0.967096	−	0.254410i	$-0.918119\pi$
$397$	−24.5139	+	14.1531i	−1.23032	+	0.710325i	−0.263223	+	0.964735i	$0.584785\pi$
$398$		0			0
$399$	0.428252	+	0.741753i	0.0214394	+	0.0371341i
$400$		0			0
$401$	14.8257	+	8.55962i	0.740360	+	0.427447i	0.822200	−	0.569198i	$-0.192746\pi$
$401$	14.8257	+	8.55962i	0.740360	+	0.427447i	−0.0818403	+	0.996645i	$0.526080\pi$
$402$		0			0
$403$	−28.9007	−	2.43769i	−1.43965	−	0.121430i
$404$		0			0
$405$	9.80952	+	5.66353i	0.487439	+	0.281423i
$406$		0			0
$407$	9.75149	+	16.8901i	0.483364	+	0.837210i
$408$		0			0
$409$	9.82072	−	5.66999i	0.485603	−	0.280363i	−0.237145	−	0.971474i	$-0.576212\pi$
$409$	9.82072	−	5.66999i	0.485603	−	0.280363i	0.722749	+	0.691111i	$0.242878\pi$
$410$		0			0
$411$		−	2.23850i		−	0.110417i
$412$		0			0
$413$	−3.14779	+	5.45213i	−0.154893	+	0.268282i
$414$		0			0
$415$	13.2780			0.651790
$416$		0			0
$417$	1.55691			0.0762420
$418$		0			0
$419$	0.0694276	−	0.120252i	0.00339176	−	0.00587470i	−0.864325	−	0.502934i	$-0.832254\pi$
$419$	0.0694276	−	0.120252i	0.00339176	−	0.00587470i	0.867716	+	0.497060i	$0.165587\pi$
$420$		0			0
$421$		−	24.3258i		−	1.18557i	−0.805362	−	0.592783i	$-0.798029\pi$
$421$		−	24.3258i		−	1.18557i	0.805362	−	0.592783i	$-0.201971\pi$
$422$		0			0
$423$	6.70152	−	3.86912i	0.325839	−	0.188123i
$424$		0			0
$425$	−9.19837	−	15.9320i	−0.446186	−	0.772818i
$426$		0			0
$427$	11.0921	+	6.40404i	0.536785	+	0.309913i
$428$		0			0
$429$	−1.15649	−	2.46003i	−0.0558357	−	0.118772i
$430$		0			0
$431$	−24.9349	−	14.3962i	−1.20107	−	0.693440i	−0.240280	−	0.970704i	$-0.577239\pi$
$431$	−24.9349	−	14.3962i	−1.20107	−	0.693440i	−0.960794	+	0.277263i	$0.910573\pi$
$432$		0			0
$433$	−12.6367	−	21.8873i	−0.607279	−	1.05184i	−0.991687	−	0.128675i	$-0.958928\pi$
$433$	−12.6367	−	21.8873i	−0.607279	−	1.05184i	0.384408	−	0.923163i	$-0.374406\pi$
$434$		0			0
$435$	−2.27904	+	1.31580i	−0.109272	+	0.0630880i
$436$		0			0
$437$		−	24.0547i		−	1.15069i
$438$		0			0
$439$	−3.01512	+	5.22234i	−0.143904	+	0.249248i	−0.928963	−	0.370172i	$-0.879299\pi$
$439$	−3.01512	+	5.22234i	−0.143904	+	0.249248i	0.785060	+	0.619420i	$0.212632\pi$
$440$		0			0
$441$	2.92766			0.139413
$442$		0			0
$443$	−23.4988			−1.11646			−0.558230	−	0.829686i	$-0.688519\pi$
$443$	−23.4988			−1.11646			−0.558230	+	0.829686i	$0.688519\pi$
$444$		0			0
$445$	−5.67301	+	9.82594i	−0.268927	+	0.465794i
$446$		0			0
$447$			3.82017i			0.180688i
$448$		0			0
$449$	20.2543	−	11.6938i	0.955859	−	0.551865i	0.0609627	−	0.998140i	$-0.480583\pi$
$449$	20.2543	−	11.6938i	0.955859	−	0.551865i	0.894896	+	0.446275i	$0.147250\pi$
$450$		0			0
$451$	−7.09133	−	12.2826i	−0.333918	−	0.578363i
$452$		0			0
$453$	2.59728	+	1.49954i	0.122031	+	0.0704545i
$454$		0			0
$455$	4.42410	−	2.07981i	0.207405	−	0.0975031i
$456$		0			0
$457$	−22.6616	−	13.0837i	−1.06007	−	0.612030i	−0.134616	−	0.990898i	$-0.542980\pi$
$457$	−22.6616	−	13.0837i	−1.06007	−	0.612030i	−0.925451	+	0.378868i	$0.876313\pi$
$458$		0			0
$459$	4.63825	+	8.03369i	0.216495	+	0.374980i
$460$		0			0
$461$	−21.8524	+	12.6165i	−1.01777	+	0.587609i	−0.913457	−	0.406936i	$-0.866597\pi$
$461$	−21.8524	+	12.6165i	−1.01777	+	0.587609i	−0.104312	+	0.994545i	$0.533264\pi$
$462$		0			0
$463$			18.1600i			0.843968i	0.906603	+	0.421984i	$0.138666\pi$
$463$			18.1600i			0.843968i	−0.906603	+	0.421984i	$0.861334\pi$
$464$		0			0
$465$	1.46668	−	2.54036i	0.0680154	−	0.117806i
$466$		0			0
$467$	12.6328			0.584577			0.292289	−	0.956330i	$-0.405583\pi$
$467$	12.6328			0.584577			0.292289	+	0.956330i	$0.405583\pi$
$468$		0			0
$469$	4.96294			0.229167
$470$		0			0
$471$	−0.544293	+	0.942743i	−0.0250797	+	0.0434393i
$472$		0			0
$473$			17.5719i			0.807956i
$474$		0			0
$475$	−8.71966	+	5.03430i	−0.400086	+	0.230990i
$476$		0			0
$477$	−16.2320	−	28.1146i	−0.743211	−	1.28728i
$478$		0			0
$479$	−10.6585	−	6.15368i	−0.486999	−	0.281169i	0.236330	−	0.971673i	$-0.424055\pi$
$479$	−10.6585	−	6.15368i	−0.486999	−	0.281169i	−0.723329	+	0.690504i	$0.757389\pi$
$480$		0			0
$481$	−14.3243	+	20.5935i	−0.653130	+	0.938984i
$482$		0			0
$483$	1.75936	+	1.01576i	0.0800534	+	0.0462189i
$484$		0			0
$485$	8.27299	+	14.3292i	0.375657	+	0.650658i
$486$		0			0
$487$	−13.5393	+	7.81693i	−0.613525	+	0.354219i	−0.774344	−	0.632765i	$-0.781920\pi$
$487$	−13.5393	+	7.81693i	−0.613525	+	0.354219i	0.160819	+	0.986984i	$0.448587\pi$
$488$		0			0
$489$			1.41825i			0.0641355i
$490$		0			0
$491$	−5.10543	+	8.84286i	−0.230405	+	0.399073i	−0.957927	−	0.287011i	$-0.907338\pi$
$491$	−5.10543	+	8.84286i	−0.230405	+	0.399073i	0.727523	+	0.686084i	$0.240672\pi$
$492$		0			0
$493$	41.9911			1.89119
$494$		0			0
$495$	−11.1272			−0.500129
$496$		0			0
$497$	−8.25572	+	14.2993i	−0.370319	+	0.641412i
$498$		0			0
$499$			0.681003i			0.0304859i	0.999884	+	0.0152430i	$0.00485217\pi$
$499$			0.681003i			0.0304859i	−0.999884	+	0.0152430i	$0.995148\pi$
$500$		0			0
$501$	−1.24608	+	0.719424i	−0.0556707	+	0.0321415i
$502$		0			0
$503$	−17.6701	−	30.6056i	−0.787873	−	1.36464i	−0.927268	−	0.374399i	$-0.877849\pi$
$503$	−17.6701	−	30.6056i	−0.787873	−	1.36464i	0.139395	−	0.990237i	$-0.455484\pi$
$504$		0			0
$505$	2.84492	+	1.64251i	0.126597	+	0.0730909i
$506$		0			0
$507$	2.23069	−	2.69235i	0.0990683	−	0.119572i
$508$		0			0
$509$	14.5717	+	8.41300i	0.645881	+	0.372900i	0.786876	−	0.617111i	$-0.211697\pi$
$509$	14.5717	+	8.41300i	0.645881	+	0.372900i	−0.140995	+	0.990010i	$0.545030\pi$
$510$		0			0
$511$	−7.71755	−	13.3672i	−0.341404	−	0.591330i
$512$		0			0
$513$	4.39687	−	2.53853i	0.194126	−	0.112079i
$514$		0			0
$515$			19.6475i			0.865774i
$516$		0			0
$517$	−3.70461	+	6.41658i	−0.162929	+	0.282201i
$518$		0			0
$519$	2.62043			0.115024
$520$		0			0
$521$	4.76619			0.208811			0.104405	−	0.994535i	$-0.466706\pi$
$521$	4.76619			0.208811			0.104405	+	0.994535i	$0.466706\pi$
$522$		0			0
$523$	−0.319080	+	0.552662i	−0.0139524	+	0.0241662i	−0.872917	−	0.487868i	$-0.837775\pi$
$523$	−0.319080	+	0.552662i	−0.0139524	+	0.0241662i	0.858965	+	0.512034i	$0.171108\pi$
$524$		0			0
$525$		−	0.850340i		−	0.0371119i
$526$		0			0
$527$	−40.5351	+	23.4029i	−1.76573	+	1.01945i
$528$		0			0
$529$	−17.0275	−	29.4924i	−0.740325	−	1.28228i
$530$		0			0
$531$	15.9620	+	9.21567i	0.692692	+	0.399926i
$532$		0			0
$533$	10.4167	−	14.9757i	0.451196	−	0.648670i
$534$		0			0
$535$	−7.61752	−	4.39798i	−0.329334	−	0.190141i
$536$		0			0
$537$	−1.53374	−	2.65651i	−0.0661857	−	0.114637i
$538$		0			0
$539$	−2.42763	+	1.40159i	−0.104565	+	0.0603708i
$540$		0			0
$541$			22.2050i			0.954668i	0.878722	+	0.477334i	$0.158397\pi$
$541$			22.2050i			0.954668i	−0.878722	+	0.477334i	$0.841603\pi$
$542$		0			0
$543$	−3.42548	+	5.93310i	−0.147001	+	0.254614i
$544$		0			0
$545$	−3.98138			−0.170544
$546$		0			0
$547$	−16.2608			−0.695263			−0.347631	−	0.937631i	$-0.613014\pi$
$547$	−16.2608			−0.695263			−0.347631	+	0.937631i	$0.613014\pi$
$548$		0			0
$549$	18.7489	−	32.4740i	0.800182	−	1.38596i
$550$		0			0
$551$		−	22.9819i		−	0.979062i
$552$		0			0
$553$	12.7878	−	7.38303i	0.543792	−	0.313958i
$554$		0			0
$555$	−1.26855	−	2.19719i	−0.0538470	−	0.0932657i
$556$		0			0
$557$	−18.5915	−	10.7338i	−0.787747	−	0.454806i	0.0514219	−	0.998677i	$-0.483625\pi$
$557$	−18.5915	−	10.7338i	−0.787747	−	0.454806i	−0.839169	+	0.543871i	$0.816958\pi$
$558$		0			0
$559$	−20.4541	+	9.61566i	−0.865115	+	0.406699i
$560$		0			0
$561$	−3.79912	−	2.19342i	−0.160399	−	0.0926064i
$562$		0			0
$563$	5.59103	+	9.68395i	0.235634	+	0.408130i	0.959457	−	0.281856i	$-0.0909500\pi$
$563$	5.59103	+	9.68395i	0.235634	+	0.408130i	−0.723823	+	0.689986i	$0.757617\pi$
$564$		0			0
$565$	3.91969	−	2.26304i	0.164903	−	0.0952066i
$566$		0			0
$567$		−	8.35421i		−	0.350844i
$568$		0			0
$569$	−6.58165	+	11.3998i	−0.275917	+	0.477903i	−0.970366	−	0.241639i	$-0.922315\pi$
$569$	−6.58165	+	11.3998i	−0.275917	+	0.477903i	0.694449	+	0.719542i	$0.255648\pi$
$570$		0			0
$571$	17.4199			0.729001			0.364501	−	0.931203i	$-0.381240\pi$
$571$	17.4199			0.729001			0.364501	+	0.931203i	$0.381240\pi$
$572$		0			0
$573$	−4.40494			−0.184019
$574$		0			0
$575$	−11.9408	+	20.6821i	−0.497965	+	0.862501i
$576$		0			0
$577$		−	8.47023i		−	0.352620i	−0.984335	−	0.176310i	$-0.943584\pi$
$577$		−	8.47023i		−	0.352620i	0.984335	−	0.176310i	$-0.0564161\pi$
$578$		0			0
$579$	−2.22729	+	1.28592i	−0.0925629	+	0.0534412i
$580$		0			0
$581$	−4.89655	−	8.48107i	−0.203143	−	0.351854i
$582$		0			0
$583$	26.9192	+	15.5418i	1.11488	+	0.643676i
$584$		0			0
$585$	−6.08899	−	12.9523i	−0.251749	−	0.535511i
$586$		0			0
$587$	−18.2459	−	10.5342i	−0.753087	−	0.434795i	0.0737213	−	0.997279i	$-0.476512\pi$
$587$	−18.2459	−	10.5342i	−0.753087	−	0.434795i	−0.826808	+	0.562484i	$0.809846\pi$
$588$		0			0
$589$	12.8085	+	22.1850i	0.527765	+	0.914116i
$590$		0			0
$591$	−0.701205	+	0.404841i	−0.0288437	+	0.0166529i
$592$		0			0
$593$			13.2761i			0.545185i	0.962130	+	0.272593i	$0.0878811\pi$
$593$			13.2761i			0.545185i	−0.962130	+	0.272593i	$0.912119\pi$
$594$		0			0
$595$	3.94463	−	6.83230i	0.161714	−	0.280097i
$596$		0			0
$597$	−1.24248			−0.0508513
$598$		0			0
$599$	−5.39084			−0.220264			−0.110132	−	0.993917i	$-0.535127\pi$
$599$	−5.39084			−0.220264			−0.110132	+	0.993917i	$0.535127\pi$
$600$		0			0
$601$	12.2204	−	21.1663i	0.498480	−	0.863392i	−0.501519	−	0.865147i	$-0.667225\pi$
$601$	12.2204	−	21.1663i	0.498480	−	0.863392i	0.999998	+	0.00175467i	$0.000558528\pi$
$602$		0			0
$603$		−	14.5298i		−	0.591700i
$604$		0			0
$605$	−3.68953	+	2.13015i	−0.150001	+	0.0866029i
$606$		0			0
$607$	−12.9291	−	22.3939i	−0.524776	−	0.908939i	−0.999584	−	0.0288492i	$-0.990816\pi$
$607$	−12.9291	−	22.3939i	−0.524776	−	0.908939i	0.474808	−	0.880090i	$-0.342518\pi$
$608$		0			0
$609$	1.68089	+	0.970464i	0.0681132	+	0.0393252i
$610$		0			0
$611$	−9.49628	−	0.800985i	−0.384178	−	0.0324044i
$612$		0			0
$613$	12.2706	+	7.08441i	0.495603	+	0.286136i	0.726896	−	0.686748i	$-0.240962\pi$
$613$	12.2706	+	7.08441i	0.495603	+	0.286136i	−0.231293	+	0.972884i	$0.574296\pi$
$614$		0			0
$615$	0.922496	+	1.59781i	0.0371986	+	0.0644299i
$616$		0			0
$617$	39.8763	−	23.0226i	1.60536	−	0.926855i	0.614970	−	0.788550i	$-0.289168\pi$
$617$	39.8763	−	23.0226i	1.60536	−	0.926855i	0.990390	−	0.138305i	$-0.0441654\pi$
$618$		0			0
$619$			12.0284i			0.483464i	0.970343	+	0.241732i	$0.0777155\pi$
$619$			12.0284i			0.483464i	−0.970343	+	0.241732i	$0.922285\pi$
$620$		0			0
$621$	6.02111	−	10.4289i	0.241619	−	0.418496i
$622$		0			0
$623$	8.36820			0.335265
$624$		0			0
$625$	0.804500			0.0321800
$626$		0			0
$627$	−1.20047	+	2.07927i	−0.0479421	+	0.0830381i
$628$		0			0
$629$			40.4831i			1.61417i
$630$		0			0
$631$	−21.0476	+	12.1518i	−0.837890	+	0.483756i	−0.856546	−	0.516070i	$-0.827394\pi$
$631$	−21.0476	+	12.1518i	−0.837890	+	0.483756i	0.0186564	+	0.999826i	$0.494061\pi$
$632$		0			0
$633$	0.314493	+	0.544718i	0.0125000	+	0.0216506i
$634$		0			0
$635$	−14.7365	−	8.50812i	−0.584800	−	0.337634i
$636$		0			0
$637$	−2.95993	−	2.05884i	−0.117277	−	0.0815742i
$638$		0			0
$639$	41.8636	+	24.1700i	1.65610	+	0.956149i
$640$		0			0
$641$	−8.88276	−	15.3854i	−0.350848	−	0.607687i	0.635550	−	0.772060i	$-0.280773\pi$
$641$	−8.88276	−	15.3854i	−0.350848	−	0.607687i	−0.986398	+	0.164373i	$0.947440\pi$
$642$		0			0
$643$	37.3742	−	21.5780i	1.47389	−	0.850953i	0.474326	−	0.880349i	$-0.342692\pi$
$643$	37.3742	−	21.5780i	1.47389	−	0.850953i	0.999568	+	0.0293964i	$0.00935852\pi$
$644$		0			0
$645$		−	2.28589i		−	0.0900067i
$646$		0			0
$647$	5.39974	−	9.35262i	0.212286	−	0.367689i	−0.740144	−	0.672449i	$-0.765243\pi$
$647$	5.39974	−	9.35262i	0.212286	−	0.367689i	0.952429	+	0.304759i	$0.0985760\pi$
$648$		0			0
$649$	−17.6477			−0.692731
$650$		0			0
$651$	−2.16348			−0.0847933
$652$		0			0
$653$	1.53280	−	2.65489i	0.0599831	−	0.103894i	−0.834475	−	0.551047i	$-0.814229\pi$
$653$	1.53280	−	2.65489i	0.0599831	−	0.103894i	0.894458	+	0.447153i	$0.147562\pi$
$654$		0			0
$655$			1.70838i			0.0667520i
$656$		0			0
$657$	−39.1346	+	22.5944i	−1.52679	+	0.881491i
$658$		0			0
$659$	−1.82436	−	3.15988i	−0.0710670	−	0.123092i	0.828302	−	0.560282i	$-0.189307\pi$
$659$	−1.82436	−	3.15988i	−0.0710670	−	0.123092i	−0.899369	+	0.437190i	$0.855974\pi$
$660$		0			0
$661$	−23.5777	−	13.6126i	−0.917068	−	0.529469i	−0.0343693	−	0.999409i	$-0.510942\pi$
$661$	−23.5777	−	13.6126i	−0.917068	−	0.529469i	−0.882698	+	0.469940i	$0.844276\pi$
$662$		0			0
$663$	0.474246	−	5.62255i	0.0184182	−	0.218362i
$664$		0			0
$665$	−3.73934	−	2.15891i	−0.145005	−	0.0837189i
$666$		0			0
$667$	−27.2552	−	47.2074i	−1.05533	−	1.82788i
$668$		0			0
$669$	−1.13345	+	0.654396i	−0.0438216	+	0.0253004i
$670$		0			0
$671$			35.9034i			1.38604i
$672$		0			0
$673$	14.1485	−	24.5059i	0.545384	−	0.944633i	−0.453199	−	0.891410i	$-0.649717\pi$
$673$	14.1485	−	24.5059i	0.545384	−	0.944633i	0.998583	−	0.0532233i	$-0.0169495\pi$
$674$		0			0
$675$	−5.04053			−0.194010
$676$		0			0
$677$	−28.8361			−1.10826			−0.554131	−	0.832429i	$-0.686949\pi$
$677$	−28.8361			−1.10826			−0.554131	+	0.832429i	$0.686949\pi$
$678$		0			0
$679$	6.10170	−	10.5685i	0.234162	−	0.405580i
$680$		0			0
$681$			7.55209i			0.289397i
$682$		0			0
$683$	−35.4243	+	20.4522i	−1.35547	+	0.782583i	−0.989010	−	0.147849i	$-0.952765\pi$
$683$	−35.4243	+	20.4522i	−1.35547	+	0.782583i	−0.366464	+	0.930432i	$0.619432\pi$
$684$		0			0
$685$	5.64238	+	9.77290i	0.215584	+	0.373403i
$686$		0			0
$687$	0.0417579	+	0.0241089i	0.00159316	+	0.000919813i
$688$		0			0
$689$	−3.36034	+	39.8393i	−0.128019	+	1.51776i
$690$		0			0
$691$	36.5934	+	21.1272i	1.39208	+	0.803717i	0.993545	−	0.113436i	$-0.0361858\pi$
$691$	36.5934	+	21.1272i	1.39208	+	0.803717i	0.398534	+	0.917154i	$0.369519\pi$
$692$		0			0
$693$	4.10339	+	7.10728i	0.155875	+	0.269983i
$694$		0			0
$695$	−6.79717	+	3.92435i	−0.257831	+	0.148859i
$696$		0			0
$697$		−	29.4395i		−	1.11510i
$698$		0			0
$699$	−2.03575	+	3.52603i	−0.0769992	+	0.133367i
$700$		0			0
$701$	−30.3734			−1.14719			−0.573594	−	0.819140i	$-0.694451\pi$
$701$	−30.3734			−1.14719			−0.573594	+	0.819140i	$0.694451\pi$
$702$		0			0
$703$	22.1566			0.835650
$704$		0			0
$705$	0.481925	−	0.834718i	0.0181503	−	0.0314373i
$706$		0			0
$707$		−	2.42285i		−	0.0911208i
$708$		0			0
$709$	−20.2907	+	11.7148i	−0.762033	+	0.439960i	−0.830025	−	0.557726i	$-0.811674\pi$
$709$	−20.2907	+	11.7148i	−0.762033	+	0.439960i	0.0679919	+	0.997686i	$0.478341\pi$
$710$		0			0
$711$	−21.6150	−	37.4383i	−0.810627	−	1.40405i
$712$		0			0
$713$	52.6203	+	30.3803i	1.97064	+	1.13775i
$714$		0			0
$715$	11.2498	+	7.82503i	0.420719	+	0.292639i
$716$		0			0
$717$	−2.99776	−	1.73076i	−0.111953	−	0.0646363i
$718$		0			0
$719$	3.51491	+	6.08800i	0.131084	+	0.227044i	0.924095	−	0.382164i	$-0.124821\pi$
$719$	3.51491	+	6.08800i	0.131084	+	0.227044i	−0.793011	+	0.609208i	$0.791488\pi$
$720$		0			0
$721$	12.5495	−	7.24547i	0.467369	−	0.269835i
$722$		0			0
$723$			2.64427i			0.0983415i
$724$		0			0
$725$	−11.4083	+	19.7597i	−0.423692	+	0.733857i
$726$		0			0
$727$	20.6810			0.767015			0.383507	−	0.923538i	$-0.374716\pi$
$727$	20.6810			0.767015			0.383507	+	0.923538i	$0.374716\pi$
$728$		0			0
$729$	−23.1720			−0.858222
$730$		0			0
$731$	−18.2373	+	31.5880i	−0.674531	+	1.16832i
$732$		0			0
$733$		−	39.0035i		−	1.44063i	−0.693648	−	0.720314i	$-0.743998\pi$
$733$		−	39.0035i		−	1.44063i	0.693648	−	0.720314i	$-0.256002\pi$
$734$		0			0
$735$	0.315805	−	0.182330i	0.0116486	−	0.00672534i
$736$		0			0
$737$	6.95602	+	12.0482i	0.256228	+	0.443800i
$738$		0			0
$739$	−24.8910	−	14.3708i	−0.915629	−	0.528639i	−0.0333913	−	0.999442i	$-0.510631\pi$
$739$	−24.8910	−	14.3708i	−0.915629	−	0.528639i	−0.882238	+	0.470803i	$0.843964\pi$
$740$		0			0
$741$	−3.07724	−	0.259557i	−0.113045	−	0.00953505i
$742$		0			0
$743$	5.48059	+	3.16422i	0.201063	+	0.116084i	0.597151	−	0.802129i	$-0.296299\pi$
$743$	5.48059	+	3.16422i	0.201063	+	0.116084i	−0.396088	+	0.918213i	$0.629633\pi$
$744$		0			0
$745$	−9.62915	−	16.6782i	−0.352785	−	0.611041i
$746$		0			0
$747$	−24.8297	+	14.3355i	−0.908473	+	0.524507i
$748$		0			0
$749$			6.48741i			0.237045i
$750$		0			0
$751$	15.7203	−	27.2283i	0.573641	−	0.993575i	−0.422547	−	0.906341i	$-0.638864\pi$
$751$	15.7203	−	27.2283i	0.573641	−	0.993575i	0.996188	−	0.0872339i	$-0.0278028\pi$
$752$		0			0
$753$	−4.65880			−0.169776
$754$		0			0
$755$	−15.1190			−0.550237
$756$		0			0
$757$	−12.7212	+	22.0337i	−0.462358	+	0.800828i	−0.999078	−	0.0429328i	$-0.986330\pi$
$757$	−12.7212	+	22.0337i	−0.462358	+	0.800828i	0.536720	+	0.843760i	$0.319663\pi$
$758$		0			0
$759$			5.69475i			0.206706i
$760$		0			0
$761$	−17.8492	+	10.3053i	−0.647034	+	0.373565i	−0.787319	−	0.616546i	$-0.788531\pi$
$761$	−17.8492	+	10.3053i	−0.647034	+	0.373565i	0.140285	+	0.990111i	$0.455198\pi$
$762$		0			0
$763$	1.46822	+	2.54304i	0.0531532	+	0.0920641i
$764$		0			0
$765$	−20.0027	−	11.5485i	−0.723198	−	0.417539i
$766$		0			0
$767$	−9.65713	−	20.5423i	−0.348699	−	0.741739i
$768$		0			0
$769$	7.95173	+	4.59093i	0.286747	+	0.165553i	0.636474	−	0.771298i	$-0.280392\pi$
$769$	7.95173	+	4.59093i	0.286747	+	0.165553i	−0.349727	+	0.936852i	$0.613726\pi$
$770$		0			0
$771$	−1.43971	−	2.49365i	−0.0518499	−	0.0898066i
$772$		0			0
$773$	−7.35736	+	4.24777i	−0.264626	+	0.152782i	−0.626443	−	0.779467i	$-0.715490\pi$
$773$	−7.35736	+	4.24777i	−0.264626	+	0.152782i	0.361817	+	0.932249i	$0.382157\pi$
$774$		0			0
$775$		−	25.4327i		−	0.913569i
$776$		0			0
$777$	−0.935612	+	1.62053i	−0.0335649	+	0.0581361i
$778$		0			0
$779$	−16.1124			−0.577285
$780$		0			0
$781$	−46.2846			−1.65619
$782$		0			0
$783$	5.75259	−	9.96377i	0.205581	−	0.356076i
$784$		0			0
$785$		−	5.48780i		−	0.195868i
$786$		0			0
$787$	−1.70464	+	0.984173i	−0.0607638	+	0.0350820i	−0.530074	−	0.847951i	$-0.677836\pi$
$787$	−1.70464	+	0.984173i	−0.0607638	+	0.0350820i	0.469310	+	0.883033i	$0.344503\pi$
$788$		0			0
$789$	−1.89204	−	3.27711i	−0.0673585	−	0.116668i
$790$		0			0
$791$	−2.89095	−	1.66909i	−0.102790	−	0.0593460i
$792$		0			0
$793$	−41.7924	+	19.6470i	−1.48409	+	0.697686i
$794$		0			0
$795$	−3.50186	−	2.02180i	−0.124198	−	0.0717058i
$796$		0			0
$797$	−19.2449	−	33.3332i	−0.681690	−	1.18072i	−0.974465	−	0.224540i	$-0.927912\pi$
$797$	−19.2449	−	33.3332i	−0.681690	−	1.18072i	0.292775	−	0.956181i	$-0.405421\pi$
$798$		0			0
$799$	−13.3191	+	7.68981i	−0.471197	+	0.272046i
$800$		0			0
$801$		−	24.4993i		−	0.865639i
$802$		0			0
$803$	21.6337	−	37.4707i	0.763437	−	1.32231i
$804$		0			0
$805$	−10.2414			−0.360961
$806$		0			0
$807$	−0.146317			−0.00515059
$808$		0			0
$809$	−0.899878	+	1.55863i	−0.0316380	+	0.0547987i	−0.881411	−	0.472350i	$-0.843406\pi$
$809$	−0.899878	+	1.55863i	−0.0316380	+	0.0547987i	0.849773	+	0.527149i	$0.176739\pi$
$810$		0			0
$811$		−	49.9235i		−	1.75305i	−0.481357	−	0.876525i	$-0.659856\pi$
$811$		−	49.9235i		−	1.75305i	0.481357	−	0.876525i	$-0.340144\pi$
$812$		0			0
$813$	−0.172644	+	0.0996759i	−0.00605488	+	0.00349579i
$814$		0			0
$815$	−3.57485	−	6.19183i	−0.125222	−	0.216890i
$816$		0			0
$817$	17.2882	+	9.98135i	0.604838	+	0.349203i
$818$		0			0
$819$	−6.02759	+	8.66568i	−0.210621	+	0.302803i
$820$		0			0
$821$	3.65310	+	2.10912i	0.127494	+	0.0736087i	0.562391	−	0.826872i	$-0.309882\pi$
$821$	3.65310	+	2.10912i	0.127494	+	0.0736087i	−0.434897	+	0.900480i	$0.643215\pi$
$822$		0			0
$823$	−7.24912	−	12.5558i	−0.252688	−	0.437669i	0.711577	−	0.702608i	$-0.247981\pi$
$823$	−7.24912	−	12.5558i	−0.252688	−	0.437669i	−0.964265	+	0.264939i	$0.914648\pi$
$824$		0			0
$825$	2.06431	−	1.19183i	0.0718701	−	0.0414942i
$826$		0			0
$827$		−	26.2618i		−	0.913213i	−0.889669	−	0.456607i	$-0.849065\pi$
$827$		−	26.2618i		−	0.913213i	0.889669	−	0.456607i	$-0.150935\pi$
$828$		0			0
$829$	−27.5790	+	47.7682i	−0.957858	+	1.65906i	−0.230170	+	0.973150i	$0.573928\pi$
$829$	−27.5790	+	47.7682i	−0.957858	+	1.65906i	−0.727688	+	0.685909i	$0.759405\pi$
$830$		0			0
$831$	3.80125			0.131864
$832$		0			0
$833$	−5.81868			−0.201605
$834$		0			0
$835$	3.62677	−	6.28175i	0.125510	−	0.217389i
$836$		0			0
$837$			12.8244i			0.443275i
$838$		0			0
$839$	6.07974	−	3.51014i	0.209896	−	0.121184i	−0.391367	−	0.920235i	$-0.627998\pi$
$839$	6.07974	−	3.51014i	0.209896	−	0.121184i	0.601263	+	0.799051i	$0.294664\pi$
$840$		0			0
$841$	−11.5397	−	19.9874i	−0.397922	−	0.689221i
$842$		0			0
$843$	−6.01053	−	3.47018i	−0.207014	−	0.119519i
$844$		0			0
$845$	−2.95241	+	17.3770i	−0.101566	+	0.597788i
$846$		0			0
$847$	2.72119	+	1.57108i	0.0935012	+	0.0539829i
$848$		0			0
$849$	−3.66875	−	6.35446i	−0.125911	−	0.218085i
$850$		0			0
$851$	45.5121	−	26.2764i	1.56013	−	0.900744i
$852$		0			0
$853$		−	57.6508i		−	1.97393i	−0.160945	−	0.986963i	$-0.551454\pi$
$853$		−	57.6508i		−	1.97393i	0.160945	−	0.986963i	$-0.448546\pi$
$854$		0			0
$855$	−6.32056	+	10.9475i	−0.216159	+	0.374398i
$856$		0			0
$857$	−2.50654			−0.0856217			−0.0428109	−	0.999083i	$-0.513631\pi$
$857$	−2.50654			−0.0856217			−0.0428109	+	0.999083i	$0.513631\pi$
$858$		0			0
$859$	−17.1305			−0.584486			−0.292243	−	0.956344i	$-0.594402\pi$
$859$	−17.1305			−0.584486			−0.292243	+	0.956344i	$0.594402\pi$
$860$		0			0
$861$	0.680382	−	1.17846i	0.0231873	−	0.0401617i
$862$		0			0
$863$			55.6429i			1.89411i	0.321079	+	0.947053i	$0.395955\pi$
$863$			55.6429i			1.89411i	−0.321079	+	0.947053i	$0.604045\pi$
$864$		0			0
$865$	−11.4403	+	6.60509i	−0.388984	+	0.224580i
$866$		0			0
$867$	−2.26687	−	3.92634i	−0.0769870	−	0.133345i
$868$		0			0
$869$	35.8465	+	20.6960i	1.21601	+	0.702064i
$870$		0			0
$871$	−10.2179	+	14.6899i	−0.346220	+	0.497750i
$872$		0			0
$873$	−30.9409	−	17.8637i	−1.04719	−	0.604596i
$874$		0			0
$875$	5.53300	+	9.58344i	0.187050	+	0.323979i
$876$		0			0
$877$	34.7751	−	20.0774i	1.17427	−	0.677967i	0.219590	−	0.975592i	$-0.429528\pi$
$877$	34.7751	−	20.0774i	1.17427	−	0.677967i	0.954683	+	0.297626i	$0.0961947\pi$
$878$		0			0
$879$		−	0.465871i		−	0.0157134i
$880$		0			0
$881$	25.3837	−	43.9658i	0.855197	−	1.48124i	−0.0212650	−	0.999774i	$-0.506769\pi$
$881$	25.3837	−	43.9658i	0.855197	−	1.48124i	0.876462	−	0.481471i	$-0.159897\pi$
$882$		0			0
$883$	46.3312			1.55917			0.779585	−	0.626297i	$-0.215430\pi$
$883$	46.3312			1.55917			0.779585	+	0.626297i	$0.215430\pi$
$884$		0			0
$885$	2.29575			0.0771706
$886$		0			0
$887$	−5.12752	+	8.88113i	−0.172165	+	0.298199i	−0.939177	−	0.343435i	$-0.888410\pi$
$887$	−5.12752	+	8.88113i	−0.172165	+	0.298199i	0.767011	+	0.641634i	$0.221743\pi$
$888$		0			0
$889$			12.5502i			0.420921i
$890$		0			0
$891$	20.2809	−	11.7092i	0.679436	−	0.392273i
$892$		0			0
$893$	4.20866	+	7.28961i	0.140837	+	0.243938i
$894$		0			0
$895$	13.3921	+	7.73191i	0.447647	+	0.258449i
$896$		0			0
$897$	−6.62882	+	3.11627i	−0.221330	+	0.104049i
$898$		0			0
$899$	50.2736	+	29.0255i	1.67672	+	0.968053i
$900$		0			0
$901$	32.2607	+	55.8772i	1.07476	+	1.86154i
$902$		0			0
$903$	−1.46007	+	0.842971i	−0.0485881	+	0.0280523i
$904$		0			0
$905$		−	34.5372i		−	1.14805i
$906$		0			0
$907$	−26.1472	+	45.2883i	−0.868205	+	1.50377i	−0.00437495	+	0.999990i	$0.501393\pi$
$907$	−26.1472	+	45.2883i	−0.868205	+	1.50377i	−0.863830	+	0.503784i	$0.831941\pi$
$908$		0			0
$909$	−7.09330			−0.235270
$910$		0			0
$911$	−50.9172			−1.68696			−0.843481	−	0.537159i	$-0.819498\pi$
$911$	−50.9172			−1.68696			−0.843481	+	0.537159i	$0.819498\pi$
$912$		0			0
$913$	13.7259	−	23.7740i	0.454262	−	0.786805i
$914$		0			0
$915$		−	4.67059i		−	0.154405i
$916$		0			0
$917$	1.09120	−	0.630004i	0.0360346	−	0.0208046i
$918$		0			0
$919$	11.4323	+	19.8013i	0.377117	+	0.653186i	0.990641	−	0.136490i	$-0.0435821\pi$
$919$	11.4323	+	19.8013i	0.377117	+	0.653186i	−0.613524	+	0.789676i	$0.710249\pi$
$920$		0			0
$921$	4.99299	+	2.88270i	0.164525	+	0.0949884i
$922$		0			0
$923$	−25.3278	−	53.8763i	−0.833674	−	1.77336i
$924$		0			0
$925$	−19.0501	−	10.9986i	−0.626363	−	0.361631i
$926$		0			0
$927$	−21.2123	−	36.7408i	−0.696703	−	1.20673i
$928$		0			0
$929$	28.8090	−	16.6329i	0.945193	−	0.545708i	0.0536089	−	0.998562i	$-0.482928\pi$
$929$	28.8090	−	16.6329i	0.945193	−	0.545708i	0.891584	+	0.452854i	$0.149594\pi$
$930$		0			0
$931$			3.18458i			0.104371i
$932$		0			0
$933$	−3.66749	+	6.35228i	−0.120068	+	0.207964i
$934$		0			0
$935$	22.1150			0.723239
$936$		0			0
$937$	−51.2179			−1.67322			−0.836608	−	0.547802i	$-0.815465\pi$
$937$	−51.2179			−1.67322			−0.836608	+	0.547802i	$0.815465\pi$
$938$		0			0
$939$	−0.979286	+	1.69617i	−0.0319578	+	0.0553525i
$940$		0			0
$941$			10.2918i			0.335502i	0.985829	+	0.167751i	$0.0536504\pi$
$941$			10.2918i			0.335502i	−0.985829	+	0.167751i	$0.946350\pi$
$942$		0			0
$943$	−33.0966	+	19.1083i	−1.07777	+	0.622253i
$944$		0			0
$945$	−1.08079	−	1.87199i	−0.0351581	−	0.0608957i
$946$		0			0
$947$	−30.7341	−	17.7444i	−0.998725	−	0.576614i	−0.0908539	−	0.995864i	$-0.528960\pi$
$947$	−30.7341	−	17.7444i	−0.998725	−	0.576614i	−0.907871	+	0.419250i	$0.862293\pi$
$948$		0			0
$949$	55.4551	+	4.67749i	1.80015	+	0.151838i
$950$		0			0
$951$	0.593565	+	0.342695i	0.0192477	+	0.0111126i
$952$		0			0
$953$	16.6676	+	28.8691i	0.539916	+	0.935163i	0.998908	+	0.0467220i	$0.0148775\pi$
$953$	16.6676	+	28.8691i	0.539916	+	0.935163i	−0.458992	+	0.888441i	$0.651789\pi$
$954$		0			0
$955$	19.2312	−	11.1031i	0.622306	−	0.359289i
$956$		0			0
$957$			5.44078i			0.175875i
$958$		0			0
$959$	4.16151	−	7.20794i	0.134382	−	0.232757i
$960$		0			0
$961$	−33.7070			−1.08732
$962$		0			0
$963$	18.9929			0.612039
$964$		0			0
$965$	6.48263	−	11.2282i	0.208683	−	0.361450i
$966$		0			0
$967$		−	29.7131i		−	0.955509i	−0.878494	−	0.477754i	$-0.841451\pi$
$967$		−	29.7131i		−	0.955509i	0.878494	−	0.477754i	$-0.158549\pi$
$968$		0			0
$969$	−4.31602	+	2.49186i	−0.138651	+	0.0800500i
$970$		0			0
$971$	−4.41851	−	7.65308i	−0.141797	−	0.245599i	0.786377	−	0.617747i	$-0.211955\pi$
$971$	−4.41851	−	7.65308i	−0.141797	−	0.245599i	−0.928173	+	0.372148i	$0.878621\pi$
$972$		0			0
$973$	5.01322	+	2.89438i	0.160716	+	0.0927896i
$974$		0			0
$975$	2.51695	+	1.75071i	0.0806068	+	0.0560677i
$976$		0			0
$977$	−12.8437	−	7.41533i	−0.410907	−	0.237237i	0.280272	−	0.959921i	$-0.409575\pi$
$977$	−12.8437	−	7.41533i	−0.410907	−	0.237237i	−0.691180	+	0.722683i	$0.742909\pi$
$978$		0			0
$979$	11.7288	+	20.3149i	0.374854	+	0.649266i
$980$		0			0
$981$	7.44516	−	4.29846i	0.237706	−	0.137239i
$982$		0			0
$983$		−	20.3390i		−	0.648714i	−0.945935	−	0.324357i	$-0.894852\pi$
$983$		−	20.3390i		−	0.648714i	0.945935	−	0.324357i	$-0.105148\pi$
$984$		0			0
$985$	2.04089	−	3.53493i	0.0650282	−	0.112632i
$986$		0			0
$987$	−0.710882			−0.0226276
$988$		0			0
$989$	47.3493			1.50562
$990$		0			0
$991$	−25.4453	+	44.0726i	−0.808297	+	1.40001i	0.105745	+	0.994393i	$0.466277\pi$
$991$	−25.4453	+	44.0726i	−0.808297	+	1.40001i	−0.914042	+	0.405619i	$0.867056\pi$
$992$		0			0
$993$		−	0.0526244i		−	0.00166999i
$994$		0			0
$995$	5.42445	−	3.13181i	0.171967	−	0.0992849i
$996$		0			0
$997$	3.69697	+	6.40334i	0.117084	+	0.202796i	0.918611	−	0.395163i	$-0.129312\pi$
$997$	3.69697	+	6.40334i	0.117084	+	0.202796i	−0.801527	+	0.597959i	$0.795979\pi$
$998$		0			0
$999$	9.60595	+	5.54600i	0.303919	+	0.175468i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.f.225.4		16
4.3	odd	2		364.2.u.a.225.5	✓	16
12.11	even	2		3276.2.cf.c.2773.5		16
13.10	even	6	inner	1456.2.cc.f.673.4		16
28.3	even	6		2548.2.bq.c.1941.5		16
28.11	odd	6		2548.2.bq.e.1941.4		16
28.19	even	6		2548.2.bb.c.1733.4		16
28.23	odd	6		2548.2.bb.d.1733.5		16
28.27	even	2		2548.2.u.c.589.4		16
52.7	even	12		4732.2.a.t.1.4		8
52.19	even	12		4732.2.a.s.1.4		8
52.23	odd	6		364.2.u.a.309.5	yes	16
52.35	odd	6		4732.2.g.k.337.7		16
52.43	odd	6		4732.2.g.k.337.8		16
156.23	even	6		3276.2.cf.c.1765.4		16
364.23	odd	6		2548.2.bq.e.361.4		16
364.75	even	6		2548.2.bq.c.361.5		16
364.179	odd	6		2548.2.bb.d.569.5		16
364.283	even	6		2548.2.bb.c.569.4		16
364.335	even	6		2548.2.u.c.1765.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.u.a.225.5	✓	16	4.3	odd	2
364.2.u.a.309.5	yes	16	52.23	odd	6
1456.2.cc.f.225.4		16	1.1	even	1	trivial
1456.2.cc.f.673.4		16	13.10	even	6	inner
2548.2.u.c.589.4		16	28.27	even	2
2548.2.u.c.1765.4		16	364.335	even	6
2548.2.bb.c.569.4		16	364.283	even	6
2548.2.bb.c.1733.4		16	28.19	even	6
2548.2.bb.d.569.5		16	364.179	odd	6
2548.2.bb.d.1733.5		16	28.23	odd	6
2548.2.bq.c.361.5		16	364.75	even	6
2548.2.bq.c.1941.5		16	28.3	even	6
2548.2.bq.e.361.4		16	364.23	odd	6
2548.2.bq.e.1941.4		16	28.11	odd	6
3276.2.cf.c.1765.4		16	156.23	even	6
3276.2.cf.c.2773.5		16	12.11	even	2
4732.2.a.s.1.4		8	52.19	even	12
4732.2.a.t.1.4		8	52.7	even	12
4732.2.g.k.337.7		16	52.35	odd	6
4732.2.g.k.337.8		16	52.43	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.134476 + 0.232920i) q^{3} -1.35585i q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.46383 + 2.53543i) q^{9} +(-2.42763 - 1.40159i) q^{11} +(0.303042 - 3.59279i) q^{13} +(0.315805 + 0.182330i) q^{15} +(-2.90934 - 5.03912i) q^{17} +(-2.75793 + 1.59229i) q^{19} -0.268953i q^{21} +(-3.77674 + 6.54150i) q^{23} +3.16167 q^{25} -1.59426 q^{27} +(-3.60830 + 6.24977i) q^{29} -8.04407i q^{31} +(0.652918 - 0.376962i) q^{33} +(0.677925 + 1.17420i) q^{35} +(-6.02532 - 3.47872i) q^{37} +(0.796082 + 0.553731i) q^{39} +(4.38164 + 2.52974i) q^{41} +(-3.13427 - 5.42872i) q^{43} +(3.43767 - 1.98474i) q^{45} -2.64315i q^{47} +(0.500000 - 0.866025i) q^{49} +1.56495 q^{51} -11.0887 q^{53} +(-1.90035 + 3.29150i) q^{55} -0.856503i q^{57} +(5.45213 - 3.14779i) q^{59} +(-6.40404 - 11.0921i) q^{61} +(-2.53543 - 1.46383i) q^{63} +(-4.87129 - 0.410880i) q^{65} +(-4.29803 - 2.48147i) q^{67} +(-1.01576 - 1.75936i) q^{69} +(14.2993 - 8.25572i) q^{71} +15.4351i q^{73} +(-0.425170 + 0.736416i) q^{75} +2.80318 q^{77} -14.7661 q^{79} +(-4.17711 + 7.23496i) q^{81} +9.79310i q^{83} +(-6.83230 + 3.94463i) q^{85} +(-0.970464 - 1.68089i) q^{87} +(-7.24707 - 4.18410i) q^{89} +(1.53395 + 3.26297i) q^{91} +(1.87363 + 1.08174i) q^{93} +(2.15891 + 3.73934i) q^{95} +(-10.5685 + 6.10170i) q^{97} -8.20678i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 14 q^{9} - 6 q^{11} + 10 q^{13} - 6 q^{15} + 2 q^{17} - 44 q^{25} + 12 q^{27} - 22 q^{29} + 42 q^{33} + 6 q^{35} + 12 q^{37} - 24 q^{39} + 36 q^{41} - 6 q^{43} - 30 q^{45} + 8 q^{49} + 4 q^{51} + 8 q^{53}+ \cdots - 42 q^{97}+O(q^{100}) \) 16 * q - 14 * q^9 - 6 * q^11 + 10 * q^13 - 6 * q^15 + 2 * q^17 - 44 * q^25 + 12 * q^27 - 22 * q^29 + 42 * q^33 + 6 * q^35 + 12 * q^37 - 24 * q^39 + 36 * q^41 - 6 * q^43 - 30 * q^45 + 8 * q^49 + 4 * q^51 + 8 * q^53 - 2 * q^55 + 18 * q^59 + 4 * q^61 + 12 * q^63 - 30 * q^65 - 24 * q^67 - 52 * q^69 - 36 * q^71 + 10 * q^75 - 24 * q^77 - 8 * q^79 + 42 * q^85 - 26 * q^87 - 36 * q^89 + 2 * q^91 - 42 * q^93 + 30 * q^95 - 42 * q^97

Introduction

L-functions

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