LMFDB - Embedded newform 252.2.i.b.25.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(25,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("252.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.i (of order $3$, degree $2$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.4
Root			$1.13119 + 1.31165i$ of defining polynomial
Character	$\chi$	$=$	252.25
Dual form			252.2.i.b.121.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.570327 - 1.63546i) q^{3} +(0.764702 - 1.32450i) q^{5} +(-1.91978 - 1.82056i) q^{7} +(-2.34945 - 1.86549i) q^{9} +O(q^{10})$	\(q+(0.570327 - 1.63546i) q^{3} +(0.764702 - 1.32450i) q^{5} +(-1.91978 - 1.82056i) q^{7} +(-2.34945 - 1.86549i) q^{9} +(-0.417818 - 0.723682i) q^{11} +(1.81222 + 3.13886i) q^{13} +(-1.73004 - 2.00604i) q^{15} +(0.301057 - 0.521446i) q^{17} +(0.846884 + 1.46685i) q^{19} +(-4.07236 + 2.10141i) q^{21} +(3.07202 - 5.32090i) q^{23} +(1.33046 + 2.30443i) q^{25} +(-4.39090 + 2.77849i) q^{27} +(4.99671 - 8.65455i) q^{29} -3.30841 q^{31} +(-1.42185 + 0.270589i) q^{33} +(-3.87940 + 1.15057i) q^{35} +(4.39846 + 7.61835i) q^{37} +(6.16704 - 1.17364i) q^{39} +(3.51718 + 6.09194i) q^{41} +(0.846884 - 1.46685i) q^{43} +(-4.26748 + 1.68531i) q^{45} +8.46401 q^{47} +(0.371118 + 6.99016i) q^{49} +(-0.681102 - 0.789761i) q^{51} +(-3.99616 + 6.92155i) q^{53} -1.27803 q^{55} +(2.88197 - 0.548462i) q^{57} +0.130428 q^{59} -4.76685 q^{61} +(1.11419 + 7.85866i) q^{63} +5.54324 q^{65} -2.24332 q^{67} +(-6.95006 - 8.05882i) q^{69} -9.39130 q^{71} +(-2.25454 + 3.90498i) q^{73} +(4.52759 - 0.861638i) q^{75} +(-0.515388 + 2.14997i) q^{77} +15.7424 q^{79} +(2.03987 + 8.76578i) q^{81} +(-3.16210 + 5.47692i) q^{83} +(-0.460438 - 0.797501i) q^{85} +(-11.3044 - 13.1078i) q^{87} +(-0.531180 - 0.920030i) q^{89} +(2.23542 - 9.32519i) q^{91} +(-1.88688 + 5.41077i) q^{93} +2.59046 q^{95} +(-7.76364 + 13.4470i) q^{97} +(-0.368380 + 2.47969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9}+O(q^{10}) $ 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9	$ 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9} + 2 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 11 q^{21} + 11 q^{23} - 9 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 4 q^{33} - 19 q^{35} + 10 q^{37} - 2 q^{39} - 33 q^{41} + 7 q^{43} - 10 q^{45} + 6 q^{47} - 4 q^{49} - 13 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} + 28 q^{59} + 20 q^{61} + 33 q^{63} - 30 q^{65} - 12 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} - 44 q^{75} - 47 q^{77} + 20 q^{79} - 29 q^{81} - 25 q^{83} + 8 q^{85} + 28 q^{87} - 6 q^{89} + 2 q^{91} + 22 q^{93} + 56 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) $ 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9 + 2 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 11 * q^21 + 11 * q^23 - 9 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 4 * q^33 - 19 * q^35 + 10 * q^37 - 2 * q^39 - 33 * q^41 + 7 * q^43 - 10 * q^45 + 6 * q^47 - 4 * q^49 - 13 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 + 28 * q^59 + 20 * q^61 + 33 * q^63 - 30 * q^65 - 12 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 - 44 * q^75 - 47 * q^77 + 20 * q^79 - 29 * q^81 - 25 * q^83 + 8 * q^85 + 28 * q^87 - 6 * q^89 + 2 * q^91 + 22 * q^93 + 56 * q^95 - 18 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.570327	−	1.63546i	0.329279	−	0.944233i
$3$	0.570327	−	1.63546i	0.329279	−	0.944233i
$4$		0			0
$5$	0.764702	−	1.32450i	0.341985	−	0.592336i	−0.642816	−	0.766021i	$-0.722234\pi$
$5$	0.764702	−	1.32450i	0.341985	−	0.592336i	0.984801	+	0.173685i	$0.0555674\pi$
$6$		0			0
$7$	−1.91978	−	1.82056i	−0.725609	−	0.688107i
$7$	−1.91978	−	1.82056i	−0.725609	−	0.688107i
$8$		0			0
$9$	−2.34945	−	1.86549i	−0.783151	−	0.621831i
$10$		0			0
$11$	−0.417818	−	0.723682i	−0.125977	−	0.218198i	0.796137	−	0.605116i	$-0.206873\pi$
$11$	−0.417818	−	0.723682i	−0.125977	−	0.218198i	−0.922114	+	0.386917i	$0.873540\pi$
$12$		0			0
$13$	1.81222	+	3.13886i	0.502620	+	0.870563i	0.999995	+	0.00302796i	$0.000963830\pi$
$13$	1.81222	+	3.13886i	0.502620	+	0.870563i	−0.497375	+	0.867535i	$0.665703\pi$
$14$		0			0
$15$	−1.73004	−	2.00604i	−0.446694	−	0.517957i
$16$		0			0
$17$	0.301057	−	0.521446i	0.0730170	−	0.126469i	−0.827205	−	0.561900i	$-0.810071\pi$
$17$	0.301057	−	0.521446i	0.0730170	−	0.126469i	0.900222	+	0.435431i	$0.143404\pi$
$18$		0			0
$19$	0.846884	+	1.46685i	0.194289	+	0.336518i	0.946667	−	0.322213i	$-0.104427\pi$
$19$	0.846884	+	1.46685i	0.194289	+	0.336518i	−0.752379	+	0.658731i	$0.771094\pi$
$20$		0			0
$21$	−4.07236	+	2.10141i	−0.888661	+	0.458565i
$22$		0			0
$23$	3.07202	−	5.32090i	0.640561	−	1.10948i	−0.344746	−	0.938696i	$-0.612035\pi$
$23$	3.07202	−	5.32090i	0.640561	−	1.10948i	0.985308	−	0.170789i	$-0.0546316\pi$
$24$		0			0
$25$	1.33046	+	2.30443i	0.266092	+	0.460885i
$26$		0			0
$27$	−4.39090	+	2.77849i	−0.845028	+	0.534721i
$28$		0			0
$29$	4.99671	−	8.65455i	0.927865	−	1.60711i	0.140977	−	0.990013i	$-0.454976\pi$
$29$	4.99671	−	8.65455i	0.927865	−	1.60711i	0.786888	−	0.617096i	$-0.211691\pi$
$30$		0			0
$31$	−3.30841			−0.594208			−0.297104	−	0.954845i	$-0.596021\pi$
$31$	−3.30841			−0.594208			−0.297104	+	0.954845i	$0.596021\pi$
$32$		0			0
$33$	−1.42185	+	0.270589i	−0.247512	+	0.0471035i
$34$		0			0
$35$	−3.87940	+	1.15057i	−0.655738	+	0.194482i
$36$		0			0
$37$	4.39846	+	7.61835i	0.723102	+	1.25245i	0.959751	+	0.280854i	$0.0906177\pi$
$37$	4.39846	+	7.61835i	0.723102	+	1.25245i	−0.236649	+	0.971595i	$0.576049\pi$
$38$		0			0
$39$	6.16704	−	1.17364i	0.987517	−	0.187932i
$40$		0			0
$41$	3.51718	+	6.09194i	0.549291	+	0.951401i	0.998323	+	0.0578850i	$0.0184357\pi$
$41$	3.51718	+	6.09194i	0.549291	+	0.951401i	−0.449032	+	0.893516i	$0.648231\pi$
$42$		0			0
$43$	0.846884	−	1.46685i	0.129149	−	0.223692i	−0.794198	−	0.607659i	$-0.792109\pi$
$43$	0.846884	−	1.46685i	0.129149	−	0.223692i	0.923347	+	0.383967i	$0.125442\pi$
$44$		0			0
$45$	−4.26748	+	1.68531i	−0.636159	+	0.251231i
$46$		0			0
$47$	8.46401			1.23460			0.617301	−	0.786727i	$-0.288226\pi$
$47$	8.46401			1.23460			0.617301	+	0.786727i	$0.288226\pi$
$48$		0			0
$49$	0.371118	+	6.99016i	0.0530168	+	0.998594i
$50$		0			0
$51$	−0.681102	−	0.789761i	−0.0953734	−	0.110589i
$52$		0			0
$53$	−3.99616	+	6.92155i	−0.548915	+	0.950748i	0.449434	+	0.893313i	$0.351626\pi$
$53$	−3.99616	+	6.92155i	−0.548915	+	0.950748i	−0.998349	+	0.0574350i	$0.981708\pi$
$54$		0			0
$55$	−1.27803			−0.172329
$56$		0			0
$57$	2.88197	−	0.548462i	0.381726	−	0.0726456i
$58$		0			0
$59$	0.130428			0.0169802			0.00849011	−	0.999964i	$-0.497297\pi$
$59$	0.130428			0.0169802			0.00849011	+	0.999964i	$0.497297\pi$
$60$		0			0
$61$	−4.76685			−0.610333			−0.305166	−	0.952299i	$-0.598712\pi$
$61$	−4.76685			−0.610333			−0.305166	+	0.952299i	$0.598712\pi$
$62$		0			0
$63$	1.11419	+	7.85866i	0.140375	+	0.990098i
$64$		0			0
$65$	5.54324			0.687554
$66$		0			0
$67$	−2.24332			−0.274066			−0.137033	−	0.990567i	$-0.543757\pi$
$67$	−2.24332			−0.274066			−0.137033	+	0.990567i	$0.543757\pi$
$68$		0			0
$69$	−6.95006	−	8.05882i	−0.836689	−	0.970168i
$70$		0			0
$71$	−9.39130			−1.11454			−0.557271	−	0.830331i	$-0.688152\pi$
$71$	−9.39130			−1.11454			−0.557271	+	0.830331i	$0.688152\pi$
$72$		0			0
$73$	−2.25454	+	3.90498i	−0.263874	+	0.457044i	−0.967268	−	0.253757i	$-0.918334\pi$
$73$	−2.25454	+	3.90498i	−0.263874	+	0.457044i	0.703394	+	0.710800i	$0.251667\pi$
$74$		0			0
$75$	4.52759	−	0.861638i	0.522801	−	0.0994934i
$76$		0			0
$77$	−0.515388	+	2.14997i	−0.0587339	+	0.245012i
$78$		0			0
$79$	15.7424			1.77116			0.885580	−	0.464488i	$-0.153761\pi$
$79$	15.7424			1.77116			0.885580	+	0.464488i	$0.153761\pi$
$80$		0			0
$81$	2.03987	+	8.76578i	0.226652	+	0.973976i
$82$		0			0
$83$	−3.16210	+	5.47692i	−0.347085	+	0.601170i	−0.985730	−	0.168332i	$-0.946162\pi$
$83$	−3.16210	+	5.47692i	−0.347085	+	0.601170i	0.638645	+	0.769502i	$0.279495\pi$
$84$		0			0
$85$	−0.460438	−	0.797501i	−0.0499415	−	0.0865011i
$86$		0			0
$87$	−11.3044	−	13.1078i	−1.21196	−	1.40531i
$88$		0			0
$89$	−0.531180	−	0.920030i	−0.0563049	−	0.0975230i	0.836499	−	0.547968i	$-0.184599\pi$
$89$	−0.531180	−	0.920030i	−0.0563049	−	0.0975230i	−0.892804	+	0.450445i	$0.851265\pi$
$90$		0			0
$91$	2.23542	−	9.32519i	0.234335	−	0.977545i
$92$		0			0
$93$	−1.88688	+	5.41077i	−0.195660	+	0.561071i
$94$		0			0
$95$	2.59046			0.265775
$96$		0			0
$97$	−7.76364	+	13.4470i	−0.788279	+	1.36534i	0.138742	+	0.990329i	$0.455694\pi$
$97$	−7.76364	+	13.4470i	−0.788279	+	1.36534i	−0.927021	+	0.375010i	$0.877639\pi$
$98$		0			0
$99$	−0.368380	+	2.47969i	−0.0370236	+	0.249219i
$100$		0			0
$101$	−9.75757	−	16.9006i	−0.970914	−	1.68167i	−0.692807	−	0.721123i	$-0.743626\pi$
$101$	−9.75757	−	16.9006i	−0.970914	−	1.68167i	−0.278107	−	0.960550i	$-0.589707\pi$
$102$		0			0
$103$	0.911770	−	1.57923i	0.0898394	−	0.155606i	−0.817604	−	0.575781i	$-0.804698\pi$
$103$	0.911770	−	1.57923i	0.0898394	−	0.155606i	0.907443	+	0.420175i	$0.138031\pi$
$104$		0			0
$105$	−0.330818	+	7.00080i	−0.0322845	+	0.683208i
$106$		0			0
$107$	−5.27078	−	9.12926i	−0.509546	−	0.882559i	−0.999939	−	0.0110578i	$-0.996480\pi$
$107$	−5.27078	−	9.12926i	−0.509546	−	0.882559i	0.490393	−	0.871501i	$-0.336853\pi$
$108$		0			0
$109$	6.30442	−	10.9196i	0.603854	−	1.04591i	−0.388377	−	0.921501i	$-0.626964\pi$
$109$	6.30442	−	10.9196i	0.603854	−	1.04591i	0.992231	−	0.124406i	$-0.0397025\pi$
$110$		0			0
$111$	14.9681	−	2.84854i	1.42071	−	0.270372i
$112$		0			0
$113$	7.76452	+	13.4485i	0.730424	+	1.26513i	0.956702	+	0.291069i	$0.0940110\pi$
$113$	7.76452	+	13.4485i	0.730424	+	1.26513i	−0.226278	+	0.974063i	$0.572656\pi$
$114$		0			0
$115$	−4.69837	−	8.13781i	−0.438125	−	0.758855i
$116$		0			0
$117$	1.59779	−	10.7553i	0.147716	−	0.994328i
$118$		0			0
$119$	−1.52729	+	0.452969i	−0.140006	+	0.0415236i
$120$		0			0
$121$	5.15086	−	8.92154i	0.468260	−	0.811050i
$122$		0			0
$123$	11.9691	−	2.27781i	1.07921	−	0.205383i
$124$		0			0
$125$	11.7166			1.04797
$126$		0			0
$127$	−10.8966			−0.966919			−0.483460	−	0.875367i	$-0.660620\pi$
$127$	−10.8966			−0.966919			−0.483460	+	0.875367i	$0.660620\pi$
$128$		0			0
$129$	−1.91597	−	2.22163i	−0.168691	−	0.195603i
$130$		0			0
$131$	−9.73088	+	16.8544i	−0.850191	+	1.47257i	0.0308446	+	0.999524i	$0.490180\pi$
$131$	−9.73088	+	16.8544i	−0.850191	+	1.47257i	−0.881036	+	0.473050i	$0.843153\pi$
$132$		0			0
$133$	1.04465	−	4.35783i	0.0905827	−	0.377872i
$134$		0			0
$135$	0.322395	+	7.94048i	0.0277474	+	0.683407i
$136$		0			0
$137$	−6.13833	−	10.6319i	−0.524433	−	0.908344i	−0.999595	−	0.0284461i	$-0.990944\pi$
$137$	−6.13833	−	10.6319i	−0.524433	−	0.908344i	0.475163	−	0.879898i	$-0.342389\pi$
$138$		0			0
$139$	−6.44692	−	11.1664i	−0.546821	−	0.947121i	−0.998490	−	0.0549357i	$-0.982505\pi$
$139$	−6.44692	−	11.1664i	−0.546821	−	0.947121i	0.451669	−	0.892185i	$-0.350829\pi$
$140$		0			0
$141$	4.82725	−	13.8425i	0.406528	−	1.16575i
$142$		0			0
$143$	1.51436	−	2.62295i	0.126637	−	0.219342i
$144$		0			0
$145$	−7.64198	−	13.2363i	−0.634632	−	1.09922i
$146$		0			0
$147$	11.6438	+	3.37973i	0.960362	+	0.278755i
$148$		0			0
$149$	9.03267	−	15.6451i	0.739986	−	1.28169i	−0.212516	−	0.977158i	$-0.568166\pi$
$149$	9.03267	−	15.6451i	0.739986	−	1.28169i	0.952501	−	0.304535i	$-0.0985010\pi$
$150$		0			0
$151$	−4.29891	−	7.44593i	−0.349840	−	0.605941i	0.636381	−	0.771375i	$-0.280431\pi$
$151$	−4.29891	−	7.44593i	−0.349840	−	0.605941i	−0.986221	+	0.165434i	$0.947097\pi$
$152$		0			0
$153$	−1.68007	+	0.663493i	−0.135826	+	0.0536402i
$154$		0			0
$155$	−2.52995	+	4.38200i	−0.203210	+	0.351971i
$156$		0			0
$157$	3.19366			0.254882			0.127441	−	0.991846i	$-0.459324\pi$
$157$	3.19366			0.254882			0.127441	+	0.991846i	$0.459324\pi$
$158$		0			0
$159$	9.04080	+	10.4831i	0.716982	+	0.831364i
$160$		0			0
$161$	−15.5846	+	4.62216i	−1.22824	+	0.364277i
$162$		0			0
$163$	2.04809	+	3.54740i	0.160419	+	0.277854i	0.935019	−	0.354598i	$-0.115382\pi$
$163$	2.04809	+	3.54740i	0.160419	+	0.277854i	−0.774600	+	0.632451i	$0.782049\pi$
$164$		0			0
$165$	−0.728893	+	2.09016i	−0.0567442	+	0.162719i
$166$		0			0
$167$	8.24859	+	14.2870i	0.638295	+	1.10556i	0.985807	+	0.167883i	$0.0536932\pi$
$167$	8.24859	+	14.2870i	0.638295	+	1.10556i	−0.347512	+	0.937676i	$0.612973\pi$
$168$		0			0
$169$	−0.0682984	+	0.118296i	−0.00525372	+	0.00909971i
$170$		0			0
$171$	0.746678	−	5.02614i	0.0570999	−	0.384359i
$172$		0			0
$173$	−12.8213			−0.974782			−0.487391	−	0.873184i	$-0.662051\pi$
$173$	−12.8213			−0.974782			−0.487391	+	0.873184i	$0.662051\pi$
$174$		0			0
$175$	1.64115	−	6.84618i	0.124060	−	0.517522i
$176$		0			0
$177$	0.0743864	−	0.213309i	0.00559122	−	0.0160333i
$178$		0			0
$179$	−11.8750	+	20.5680i	−0.887576	+	1.53733i	−0.0448441	+	0.998994i	$0.514279\pi$
$179$	−11.8750	+	20.5680i	−0.887576	+	1.53733i	−0.842732	+	0.538333i	$0.819054\pi$
$180$		0			0
$181$	−16.0244			−1.19108			−0.595542	−	0.803324i	$-0.703063\pi$
$181$	−16.0244			−1.19108			−0.595542	+	0.803324i	$0.703063\pi$
$182$		0			0
$183$	−2.71867	+	7.79599i	−0.200970	+	0.576296i
$184$		0			0
$185$	13.4540			0.989161
$186$		0			0
$187$	−0.503148			−0.0367938
$188$		0			0
$189$	13.4880	+	2.65979i	0.981106	+	0.193472i
$190$		0			0
$191$	−10.8095			−0.782148			−0.391074	−	0.920359i	$-0.627896\pi$
$191$	−10.8095			−0.782148			−0.391074	+	0.920359i	$0.627896\pi$
$192$		0			0
$193$	0.750260			0.0540049			0.0270025	−	0.999635i	$-0.491404\pi$
$193$	0.750260			0.0540049			0.0270025	+	0.999635i	$0.491404\pi$
$194$		0			0
$195$	3.16146	−	9.06574i	0.226397	−	0.649211i
$196$		0			0
$197$	10.3186			0.735169			0.367584	−	0.929990i	$-0.380185\pi$
$197$	10.3186			0.735169			0.367584	+	0.929990i	$0.380185\pi$
$198$		0			0
$199$	−2.85430	+	4.94379i	−0.202336	+	0.350456i	−0.949281	−	0.314430i	$-0.898187\pi$
$199$	−2.85430	+	4.94379i	−0.202336	+	0.350456i	0.746945	+	0.664886i	$0.231520\pi$
$200$		0			0
$201$	−1.27943	+	3.66886i	−0.0902439	+	0.258782i
$202$		0			0
$203$	−25.3487	+	7.51803i	−1.77913	+	0.527662i
$204$		0			0
$205$	10.7584			0.751398
$206$		0			0
$207$	−17.1437	+	6.77037i	−1.19157	+	0.470573i
$208$		0			0
$209$	0.707687	−	1.22575i	0.0489517	−	0.0847869i
$210$		0			0
$211$	2.73050	+	4.72937i	0.187976	+	0.325583i	0.944575	−	0.328295i	$-0.106474\pi$
$211$	2.73050	+	4.72937i	0.187976	+	0.325583i	−0.756600	+	0.653878i	$0.773141\pi$
$212$		0			0
$213$	−5.35611	+	15.3591i	−0.366995	+	1.05239i
$214$		0			0
$215$	−1.29523	−	2.24340i	−0.0883338	−	0.152999i
$216$		0			0
$217$	6.35143	+	6.02316i	0.431163	+	0.408879i
$218$		0			0
$219$	5.10062	+	5.91433i	0.344668	+	0.399654i
$220$		0			0
$221$	2.18233			0.146799
$222$		0			0
$223$	−9.00530	+	15.5976i	−0.603040	+	1.04450i	0.389318	+	0.921103i	$0.372711\pi$
$223$	−9.00530	+	15.5976i	−0.603040	+	1.04450i	−0.992358	+	0.123392i	$0.960623\pi$
$224$		0			0
$225$	1.17304	−	7.89611i	0.0782024	−	0.526407i
$226$		0			0
$227$	9.08699	+	15.7391i	0.603125	+	1.04464i	0.992345	+	0.123498i	$0.0394113\pi$
$227$	9.08699	+	15.7391i	0.603125	+	1.04464i	−0.389220	+	0.921145i	$0.627255\pi$
$228$		0			0
$229$	7.71391	−	13.3609i	0.509750	−	0.882912i	−0.490186	−	0.871618i	$-0.663071\pi$
$229$	7.71391	−	13.3609i	0.509750	−	0.882912i	0.999936	−	0.0112949i	$-0.00359534\pi$
$230$		0			0
$231$	3.22226	+	2.06908i	0.212009	+	0.136136i
$232$		0			0
$233$	−3.20892	−	5.55801i	−0.210223	−	0.364117i	0.741561	−	0.670885i	$-0.234086\pi$
$233$	−3.20892	−	5.55801i	−0.210223	−	0.364117i	−0.951784	+	0.306768i	$0.900752\pi$
$234$		0			0
$235$	6.47244	−	11.2106i	0.422216	−	0.731299i
$236$		0			0
$237$	8.97832	−	25.7461i	0.583205	−	1.67239i
$238$		0			0
$239$	−2.33317	−	4.04118i	−0.150920	−	0.261402i	0.780646	−	0.624974i	$-0.214890\pi$
$239$	−2.33317	−	4.04118i	−0.150920	−	0.261402i	−0.931566	+	0.363572i	$0.881557\pi$
$240$		0			0
$241$	9.42858	+	16.3308i	0.607348	+	1.05196i	0.991676	+	0.128761i	$0.0411000\pi$
$241$	9.42858	+	16.3308i	0.607348	+	1.05196i	−0.384327	+	0.923197i	$0.625567\pi$
$242$		0			0
$243$	15.4995	+	1.66325i	0.994292	+	0.106697i
$244$		0			0
$245$	9.54228	+	4.85384i	0.609634	+	0.310100i
$246$		0			0
$247$	−3.06948	+	5.31650i	−0.195307	+	0.338281i
$248$		0			0
$249$	7.15384	+	8.29512i	0.453356	+	0.525682i
$250$		0			0
$251$	15.7016			0.991074			0.495537	−	0.868587i	$-0.334971\pi$
$251$	15.7016			0.991074			0.495537	+	0.868587i	$0.334971\pi$
$252$		0			0
$253$	−5.13419			−0.322784
$254$		0			0
$255$	−1.56688	+	0.298190i	−0.0981219	+	0.0186734i
$256$		0			0
$257$	−4.60892	+	7.98289i	−0.287497	+	0.497959i	−0.973212	−	0.229911i	$-0.926156\pi$
$257$	−4.60892	+	7.98289i	−0.287497	+	0.497959i	0.685715	+	0.727870i	$0.259490\pi$
$258$		0			0
$259$	5.42560	−	22.6332i	0.337130	−	1.40636i
$260$		0			0
$261$	−27.8845	+	11.0121i	−1.72601	+	0.681634i
$262$		0			0
$263$	−0.241311	−	0.417962i	−0.0148799	−	0.0257727i	0.858490	−	0.512831i	$-0.171403\pi$
$263$	−0.241311	−	0.417962i	−0.0148799	−	0.0257727i	−0.873369	+	0.487058i	$0.838070\pi$
$264$		0			0
$265$	6.11174	+	10.5859i	0.375442	+	0.650284i
$266$		0			0
$267$	−1.80762	+	0.344004i	−0.110624	+	0.0210527i
$268$		0			0
$269$	−3.94288	+	6.82927i	−0.240402	+	0.416388i	−0.960829	−	0.277143i	$-0.910612\pi$
$269$	−3.94288	+	6.82927i	−0.240402	+	0.416388i	0.720427	+	0.693531i	$0.243946\pi$
$270$		0			0
$271$	12.7947	+	22.1610i	0.777220	+	1.34618i	0.933538	+	0.358478i	$0.116704\pi$
$271$	12.7947	+	22.1610i	0.777220	+	1.34618i	−0.156318	+	0.987707i	$0.549963\pi$
$272$		0			0
$273$	−13.9760	−	8.97434i	−0.845869	−	0.543152i
$274$		0			0
$275$	1.11178	−	1.92566i	0.0670429	−	0.116122i
$276$		0			0
$277$	−4.18466	−	7.24804i	−0.251432	−	0.435492i	0.712489	−	0.701684i	$-0.247568\pi$
$277$	−4.18466	−	7.24804i	−0.251432	−	0.435492i	−0.963920	+	0.266191i	$0.914235\pi$
$278$		0			0
$279$	7.77296	+	6.17182i	0.465355	+	0.369497i
$280$		0			0
$281$	−0.551848	+	0.955828i	−0.0329205	+	0.0570199i	−0.882016	−	0.471219i	$-0.843814\pi$
$281$	−0.551848	+	0.955828i	−0.0329205	+	0.0570199i	0.849096	+	0.528239i	$0.177147\pi$
$282$		0			0
$283$	2.90738			0.172826			0.0864128	−	0.996259i	$-0.472460\pi$
$283$	2.90738			0.172826			0.0864128	+	0.996259i	$0.472460\pi$
$284$		0			0
$285$	1.47741	−	4.23659i	0.0875141	−	0.250954i
$286$		0			0
$287$	4.33852	−	18.0984i	0.256095	−	1.06832i
$288$		0			0
$289$	8.31873	+	14.4085i	0.489337	+	0.847557i
$290$		0			0
$291$	17.5642	+	20.3663i	1.02963	+	1.19390i
$292$		0			0
$293$	−12.4381	−	21.5434i	−0.726642	−	1.25858i	−0.958295	−	0.285782i	$-0.907747\pi$
$293$	−12.4381	−	21.5434i	−0.726642	−	1.25858i	0.231653	−	0.972798i	$-0.425587\pi$
$294$		0			0
$295$	0.0997383	−	0.172752i	0.00580699	−	0.0100580i
$296$		0			0
$297$	3.84534	+	2.01671i	0.223129	+	0.117021i
$298$		0			0
$299$	22.2688			1.28784
$300$		0			0
$301$	−4.29631	+	1.27422i	−0.247635	+	0.0734448i
$302$		0			0
$303$	−33.2053	+	6.31923i	−1.90759	+	0.363030i
$304$		0			0
$305$	−3.64522	+	6.31371i	−0.208725	+	0.361522i
$306$		0			0
$307$	−23.7968			−1.35816			−0.679078	−	0.734066i	$-0.737620\pi$
$307$	−23.7968			−1.35816			−0.679078	+	0.734066i	$0.737620\pi$
$308$		0			0
$309$	−2.06276	−	2.39184i	−0.117346	−	0.136067i
$310$		0			0
$311$	18.7135			1.06115			0.530574	−	0.847639i	$-0.321976\pi$
$311$	18.7135			1.06115			0.530574	+	0.847639i	$0.321976\pi$
$312$		0			0
$313$	−19.3159			−1.09180			−0.545901	−	0.837850i	$-0.683812\pi$
$313$	−19.3159			−1.09180			−0.545901	+	0.837850i	$0.683812\pi$
$314$		0			0
$315$	11.2608	+	4.53379i	0.634477	+	0.255450i
$316$		0			0
$317$	−1.79508			−0.100822			−0.0504110	−	0.998729i	$-0.516053\pi$
$317$	−1.79508			−0.100822			−0.0504110	+	0.998729i	$0.516053\pi$
$318$		0			0
$319$	−8.35085			−0.467558
$320$		0			0
$321$	−17.9366	+	3.41348i	−1.00112	+	0.190522i
$322$		0			0
$323$	1.01984			0.0567455
$324$		0			0
$325$	−4.82218	+	8.35226i	−0.267487	+	0.463300i
$326$		0			0
$327$	−14.2629	−	16.5384i	−0.788743	−	0.914574i
$328$		0			0
$329$	−16.2490	−	15.4092i	−0.895838	−	0.849539i
$330$		0			0
$331$	−14.1367			−0.777021			−0.388511	−	0.921444i	$-0.627010\pi$
$331$	−14.1367			−0.777021			−0.388511	+	0.921444i	$0.627010\pi$
$332$		0			0
$333$	3.87802	−	26.1043i	0.212514	−	1.43050i
$334$		0			0
$335$	−1.71547	+	2.97129i	−0.0937264	+	0.162339i
$336$		0			0
$337$	−2.94072	−	5.09348i	−0.160191	−	0.277459i	0.774746	−	0.632273i	$-0.217878\pi$
$337$	−2.94072	−	5.09348i	−0.160191	−	0.277459i	−0.934937	+	0.354813i	$0.884544\pi$
$338$		0			0
$339$	26.4229	−	5.02848i	1.43509	−	0.273110i
$340$		0			0
$341$	1.38231	+	2.39424i	0.0748565	+	0.129655i
$342$		0			0
$343$	12.0135	−	14.0952i	0.648670	−	0.761070i
$344$		0			0
$345$	−15.9887	+	3.04277i	−0.860801	+	0.163817i
$346$		0			0
$347$	−6.35186			−0.340986			−0.170493	−	0.985359i	$-0.554536\pi$
$347$	−6.35186			−0.340986			−0.170493	+	0.985359i	$0.554536\pi$
$348$		0			0
$349$	10.4321	−	18.0689i	0.558416	−	0.967205i	−0.439213	−	0.898383i	$-0.644743\pi$
$349$	10.4321	−	18.0689i	0.558416	−	0.967205i	0.997629	−	0.0688222i	$-0.0219241\pi$
$350$		0			0
$351$	−16.6786	−	8.74717i	−0.890237	−	0.466889i
$352$		0			0
$353$	1.07115	+	1.85528i	0.0570114	+	0.0987466i	0.893123	−	0.449813i	$-0.148510\pi$
$353$	1.07115	+	1.85528i	0.0570114	+	0.0987466i	−0.836111	+	0.548560i	$0.815176\pi$
$354$		0			0
$355$	−7.18155	+	12.4388i	−0.381157	+	0.660183i
$356$		0			0
$357$	−0.130240	+	2.75616i	−0.00689305	+	0.145871i
$358$		0			0
$359$	−10.6198	−	18.3940i	−0.560492	−	0.970800i	−0.997454	−	0.0713198i	$-0.977279\pi$
$359$	−10.6198	−	18.3940i	−0.560492	−	0.970800i	0.436962	−	0.899480i	$-0.356054\pi$
$360$		0			0
$361$	8.06557	−	13.9700i	0.424504	−	0.735262i
$362$		0			0
$363$	−11.6531	−	13.5122i	−0.611632	−	0.709207i
$364$		0			0
$365$	3.44811	+	5.97230i	0.180482	+	0.312605i
$366$		0			0
$367$	16.2053	+	28.0685i	0.845912	+	1.46516i	0.884827	+	0.465919i	$0.154276\pi$
$367$	16.2053	+	28.0685i	0.845912	+	1.46516i	−0.0389156	+	0.999243i	$0.512390\pi$
$368$		0			0
$369$	3.10102	−	20.8740i	0.161432	−	1.08666i
$370$		0			0
$371$	20.2729	−	6.01261i	1.05251	−	0.312159i
$372$		0			0
$373$	−16.8101	+	29.1159i	−0.870393	+	1.50756i	−0.00880173	+	0.999961i	$0.502802\pi$
$373$	−16.8101	+	29.1159i	−0.870393	+	1.50756i	−0.861591	+	0.507603i	$0.830532\pi$
$374$		0			0
$375$	6.68232	−	19.1621i	0.345074	−	0.989527i
$376$		0			0
$377$	36.2206			1.86545
$378$		0			0
$379$	28.2829			1.45279			0.726396	−	0.687276i	$-0.241194\pi$
$379$	28.2829			1.45279			0.726396	+	0.687276i	$0.241194\pi$
$380$		0			0
$381$	−6.21464	+	17.8210i	−0.318386	+	0.912997i
$382$		0			0
$383$	5.09473	−	8.82434i	0.260329	−	0.450903i	−0.706001	−	0.708211i	$-0.749502\pi$
$383$	5.09473	−	8.82434i	0.260329	−	0.450903i	0.966329	+	0.257309i	$0.0828357\pi$
$384$		0			0
$385$	2.45353	+	2.32672i	0.125043	+	0.118581i
$386$		0			0
$387$	−4.72611	+	1.86643i	−0.240242	+	0.0948760i
$388$		0			0
$389$	−5.22525	−	9.05040i	−0.264931	−	0.458873i	0.702615	−	0.711570i	$-0.252016\pi$
$389$	−5.22525	−	9.05040i	−0.264931	−	0.458873i	−0.967545	+	0.252697i	$0.918682\pi$
$390$		0			0
$391$	−1.84971	−	3.20379i	−0.0935437	−	0.162022i
$392$		0			0
$393$	22.0149	+	25.5270i	1.11050	+	1.28767i
$394$		0			0
$395$	12.0383	−	20.8509i	0.605710	−	1.04912i
$396$		0			0
$397$	−7.25033	−	12.5579i	−0.363884	−	0.630265i	0.624713	−	0.780855i	$-0.285216\pi$
$397$	−7.25033	−	12.5579i	−0.363884	−	0.630265i	−0.988596	+	0.150590i	$0.951883\pi$
$398$		0			0
$399$	−6.53126	−	4.19387i	−0.326972	−	0.209956i
$400$		0			0
$401$	12.7071	−	22.0094i	0.634563	−	1.09909i	−0.352045	−	0.935983i	$-0.614514\pi$
$401$	12.7071	−	22.0094i	0.634563	−	1.09909i	0.986608	−	0.163112i	$-0.0521531\pi$
$402$		0			0
$403$	−5.99558	−	10.3846i	−0.298661	−	0.517296i
$404$		0			0
$405$	13.1702	+	4.00141i	0.654432	+	0.198831i
$406$		0			0
$407$	3.67551	−	6.36617i	0.182188	−	0.315559i
$408$		0			0
$409$	12.3907			0.612680			0.306340	−	0.951922i	$-0.400896\pi$
$409$	12.3907			0.612680			0.306340	+	0.951922i	$0.400896\pi$
$410$		0			0
$411$	−20.8889	+	3.97533i	−1.03037	+	0.196088i
$412$		0			0
$413$	−0.250392	−	0.237451i	−0.0123210	−	0.0116842i
$414$		0			0
$415$	4.83613	+	8.37642i	0.237396	+	0.411182i
$416$		0			0
$417$	−21.9390	+	4.17518i	−1.07436	+	0.204459i
$418$		0			0
$419$	−15.3596	−	26.6036i	−0.750365	−	1.29967i	−0.947646	−	0.319323i	$-0.896545\pi$
$419$	−15.3596	−	26.6036i	−0.750365	−	1.29967i	0.197281	−	0.980347i	$-0.436789\pi$
$420$		0			0
$421$	−2.88912	+	5.00410i	−0.140807	+	0.243885i	−0.927801	−	0.373076i	$-0.878303\pi$
$421$	−2.88912	+	5.00410i	−0.140807	+	0.243885i	0.786994	+	0.616961i	$0.211636\pi$
$422$		0			0
$423$	−19.8858	−	15.7896i	−0.966880	−	0.767714i
$424$		0			0
$425$	1.60218			0.0777170
$426$		0			0
$427$	9.15131	+	8.67834i	0.442863	+	0.419975i
$428$		0			0
$429$	−3.42604	−	3.97261i	−0.165411	−	0.191799i
$430$		0			0
$431$	−0.210278	+	0.364212i	−0.0101287	+	0.0175435i	−0.871045	−	0.491203i	$-0.836557\pi$
$431$	−0.210278	+	0.364212i	−0.0101287	+	0.0175435i	0.860917	+	0.508746i	$0.169891\pi$
$432$		0			0
$433$	30.8208			1.48115			0.740576	−	0.671972i	$-0.234553\pi$
$433$	30.8208			1.48115			0.740576	+	0.671972i	$0.234553\pi$
$434$		0			0
$435$	−26.0059	+	4.94913i	−1.24689	+	0.237293i
$436$		0			0
$437$	10.4066			0.497815
$438$		0			0
$439$	3.01181			0.143746			0.0718729	−	0.997414i	$-0.477102\pi$
$439$	3.01181			0.143746			0.0718729	+	0.997414i	$0.477102\pi$
$440$		0			0
$441$	12.1682	−	17.1154i	0.579437	−	0.815017i
$442$		0			0
$443$	−18.4428			−0.876245			−0.438122	−	0.898915i	$-0.644356\pi$
$443$	−18.4428			−0.876245			−0.438122	+	0.898915i	$0.644356\pi$
$444$		0			0
$445$	−1.62478			−0.0770218
$446$		0			0
$447$	−20.4353	−	23.6954i	−0.966555	−	1.12075i
$448$		0			0
$449$	−6.80998			−0.321383			−0.160691	−	0.987005i	$-0.551372\pi$
$449$	−6.80998			−0.321383			−0.160691	+	0.987005i	$0.551372\pi$
$450$		0			0
$451$	2.93908	−	5.09064i	0.138396	−	0.239709i
$452$		0			0
$453$	−14.6293	+	2.78407i	−0.687344	+	0.130807i
$454$		0			0
$455$	−10.6418	−	10.0918i	−0.498896	−	0.473111i
$456$		0			0
$457$	12.3657			0.578441			0.289220	−	0.957263i	$-0.406604\pi$
$457$	12.3657			0.578441			0.289220	+	0.957263i	$0.406604\pi$
$458$		0			0
$459$	0.126924	+	3.12610i	0.00592432	+	0.145914i
$460$		0			0
$461$	−16.3651	+	28.3453i	−0.762201	+	1.32017i	0.179513	+	0.983756i	$0.442548\pi$
$461$	−16.3651	+	28.3453i	−0.762201	+	1.32017i	−0.941714	+	0.336415i	$0.890786\pi$
$462$		0			0
$463$	9.61023	+	16.6454i	0.446625	+	0.773577i	0.998164	−	0.0605719i	$-0.0192924\pi$
$463$	9.61023	+	16.6454i	0.446625	+	0.773577i	−0.551539	+	0.834149i	$0.685959\pi$
$464$		0			0
$465$	5.72369	+	6.63680i	0.265430	+	0.307774i
$466$		0			0
$467$	1.50855	+	2.61289i	0.0698075	+	0.120910i	0.898816	−	0.438325i	$-0.144428\pi$
$467$	1.50855	+	2.61289i	0.0698075	+	0.120910i	−0.829009	+	0.559235i	$0.811095\pi$
$468$		0			0
$469$	4.30669	+	4.08411i	0.198864	+	0.188587i
$470$		0			0
$471$	1.82143	−	5.22310i	0.0839271	−	0.240668i
$472$		0			0
$473$	−1.41537			−0.0650790
$474$		0			0
$475$	−2.25349	+	3.90316i	−0.103397	+	0.179089i
$476$		0			0
$477$	22.3009	−	8.80705i	1.02109	−	0.403247i
$478$		0			0
$479$	12.9486	+	22.4276i	0.591635	+	1.02474i	0.994012	+	0.109269i	$0.0348509\pi$
$479$	12.9486	+	22.4276i	0.591635	+	1.02474i	−0.402377	+	0.915474i	$0.631816\pi$
$480$		0			0
$481$	−15.9420	+	27.6123i	−0.726891	+	1.25901i
$482$		0			0
$483$	−1.32899	+	28.1242i	−0.0604711	+	1.27969i
$484$		0			0
$485$	11.8738	+	20.5659i	0.539159	+	0.933851i
$486$		0			0
$487$	−20.8841	+	36.1724i	−0.946350	+	1.63913i	−0.193326	+	0.981135i	$0.561927\pi$
$487$	−20.8841	+	36.1724i	−0.946350	+	1.63913i	−0.753025	+	0.657992i	$0.771406\pi$
$488$		0			0
$489$	6.96970	−	1.32639i	0.315181	−	0.0599815i
$490$		0			0
$491$	−13.9879	−	24.2278i	−0.631265	−	1.09338i	−0.987293	−	0.158908i	$-0.949203\pi$
$491$	−13.9879	−	24.2278i	−0.631265	−	1.09338i	0.356028	−	0.934475i	$-0.384131\pi$
$492$		0			0
$493$	−3.00858	−	5.21102i	−0.135500	−	0.234693i
$494$		0			0
$495$	3.00266	+	2.38415i	0.134960	+	0.107160i
$496$		0			0
$497$	18.0292	+	17.0974i	0.808722	+	0.766924i
$498$		0			0
$499$	12.4748	−	21.6070i	0.558450	−	0.967264i	−0.439176	−	0.898401i	$-0.644730\pi$
$499$	12.4748	−	21.6070i	0.558450	−	0.967264i	0.997626	−	0.0688626i	$-0.0219370\pi$
$500$		0			0
$501$	28.0702	−	5.34198i	1.25408	−	0.238662i
$502$		0			0
$503$	34.1966			1.52475			0.762376	−	0.647135i	$-0.224033\pi$
$503$	34.1966			1.52475			0.762376	+	0.647135i	$0.224033\pi$
$504$		0			0
$505$	−29.8465			−1.32815
$506$		0			0
$507$	0.154516	+	0.179167i	0.00686231	+	0.00795708i
$508$		0			0
$509$	−6.84342	+	11.8532i	−0.303329	+	0.525382i	−0.976888	−	0.213752i	$-0.931432\pi$
$509$	−6.84342	+	11.8532i	−0.303329	+	0.525382i	0.673559	+	0.739134i	$0.264765\pi$
$510$		0			0
$511$	11.4375	−	3.39218i	0.505965	−	0.150061i
$512$		0			0
$513$	−7.79420	−	4.08771i	−0.344123	−	0.180477i
$514$		0			0
$515$	−1.39447	−	2.41528i	−0.0614475	−	0.106430i
$516$		0			0
$517$	−3.53641	−	6.12525i	−0.155531	−	0.269388i
$518$		0			0
$519$	−7.31231	+	20.9686i	−0.320975	+	0.920422i
$520$		0			0
$521$	−13.3748	+	23.1658i	−0.585960	+	1.01491i	0.408795	+	0.912626i	$0.365949\pi$
$521$	−13.3748	+	23.1658i	−0.585960	+	1.01491i	−0.994755	+	0.102286i	$0.967384\pi$
$522$		0			0
$523$	−10.6131	−	18.3824i	−0.464079	−	0.803808i	0.535081	−	0.844801i	$-0.320281\pi$
$523$	−10.6131	−	18.3824i	−0.464079	−	0.803808i	−0.999159	+	0.0409928i	$0.986948\pi$
$524$		0			0
$525$	−10.2607	−	6.58860i	−0.447812	−	0.287550i
$526$		0			0
$527$	−0.996020	+	1.72516i	−0.0433873	+	0.0751490i
$528$		0			0
$529$	−7.37466	−	12.7733i	−0.320637	−	0.555360i
$530$		0			0
$531$	−0.306434	−	0.243312i	−0.0132981	−	0.0105588i
$532$		0			0
$533$	−12.7478	+	22.0799i	−0.552170	+	0.956386i
$534$		0			0
$535$	−16.1223			−0.697029
$536$		0			0
$537$	26.8656	+	31.1515i	1.15933	+	1.34429i
$538$		0			0
$539$	4.90359	−	3.18918i	0.211213	−	0.137368i
$540$		0			0
$541$	10.1269	+	17.5402i	0.435388	+	0.754114i	0.997327	−	0.0730646i	$-0.0232779\pi$
$541$	10.1269	+	17.5402i	0.435388	+	0.754114i	−0.561939	+	0.827178i	$0.689945\pi$
$542$		0			0
$543$	−9.13915	+	26.2072i	−0.392198	+	1.12466i
$544$		0			0
$545$	−9.64201	−	16.7005i	−0.413019	−	0.715369i
$546$		0			0
$547$	−21.9668	+	38.0476i	−0.939233	+	1.62680i	−0.172327	+	0.985040i	$0.555129\pi$
$547$	−21.9668	+	38.0476i	−0.939233	+	1.62680i	−0.766906	+	0.641760i	$0.778205\pi$
$548$		0			0
$549$	11.1995	+	8.89253i	0.477983	+	0.379524i
$550$		0			0
$551$	16.9265			0.721094
$552$		0			0
$553$	−30.2220	−	28.6600i	−1.28517	−	1.21875i
$554$		0			0
$555$	7.67321	−	22.0035i	0.325709	−	0.933998i
$556$		0			0
$557$	−4.45483	+	7.71599i	−0.188757	+	0.326937i	−0.944836	−	0.327544i	$-0.893779\pi$
$557$	−4.45483	+	7.71599i	−0.188757	+	0.326937i	0.756079	+	0.654480i	$0.227113\pi$
$558$		0			0
$559$	6.13897			0.259651
$560$		0			0
$561$	−0.286959	+	0.822878i	−0.0121154	+	0.0347419i
$562$		0			0
$563$	−28.4193			−1.19773			−0.598865	−	0.800850i	$-0.704381\pi$
$563$	−28.4193			−1.19773			−0.598865	+	0.800850i	$0.704381\pi$
$564$		0			0
$565$	23.7502			0.999177
$566$		0			0
$567$	12.0425	−	20.5421i	0.505739	−	0.862686i
$568$		0			0
$569$	−8.57895			−0.359648			−0.179824	−	0.983699i	$-0.557553\pi$
$569$	−8.57895			−0.359648			−0.179824	+	0.983699i	$0.557553\pi$
$570$		0			0
$571$	19.3772			0.810912			0.405456	−	0.914115i	$-0.367113\pi$
$571$	19.3772			0.810912			0.405456	+	0.914115i	$0.367113\pi$
$572$		0			0
$573$	−6.16495	+	17.6785i	−0.257545	+	0.738530i
$574$		0			0
$575$	16.3488			0.681793
$576$		0			0
$577$	0.584441	−	1.01228i	0.0243306	−	0.0421418i	−0.853604	−	0.520923i	$-0.825588\pi$
$577$	0.584441	−	1.01228i	0.0243306	−	0.0421418i	0.877934	+	0.478781i	$0.158921\pi$
$578$		0			0
$579$	0.427894	−	1.22702i	0.0177827	−	0.0509932i
$580$		0			0
$581$	16.0416	−	4.75769i	0.665517	−	0.197382i
$582$		0			0
$583$	6.67867			0.276602
$584$		0			0
$585$	−13.0236	−	10.3409i	−0.538459	−	0.427543i
$586$		0			0
$587$	−15.5863	+	26.9963i	−0.643316	+	1.11426i	0.341372	+	0.939928i	$0.389108\pi$
$587$	−15.5863	+	26.9963i	−0.643316	+	1.11426i	−0.984688	+	0.174327i	$0.944225\pi$
$588$		0			0
$589$	−2.80184	−	4.85293i	−0.115448	−	0.199962i
$590$		0			0
$591$	5.88497	−	16.8756i	0.242075	−	0.694171i
$592$		0			0
$593$	−15.1887	−	26.3075i	−0.623724	−	1.08032i	−0.988786	−	0.149338i	$-0.952286\pi$
$593$	−15.1887	−	26.3075i	−0.623724	−	1.08032i	0.365062	−	0.930983i	$-0.381048\pi$
$594$		0			0
$595$	−0.567960	+	2.36928i	−0.0232841	+	0.0971311i
$596$		0			0
$597$	6.45748	+	7.48766i	0.264287	+	0.306450i
$598$		0			0
$599$	−7.30758			−0.298579			−0.149290	−	0.988793i	$-0.547699\pi$
$599$	−7.30758			−0.298579			−0.149290	+	0.988793i	$0.547699\pi$
$600$		0			0
$601$	4.61461	−	7.99274i	0.188234	−	0.326031i	−0.756428	−	0.654077i	$-0.773057\pi$
$601$	4.61461	−	7.99274i	0.188234	−	0.326031i	0.944661	+	0.328047i	$0.106390\pi$
$602$		0			0
$603$	5.27059	+	4.18491i	0.214635	+	0.170423i
$604$		0			0
$605$	−7.87774	−	13.6446i	−0.320276	−	0.554734i
$606$		0			0
$607$	8.53370	−	14.7808i	0.346372	−	0.599934i	−0.639230	−	0.769016i	$-0.720747\pi$
$607$	8.53370	−	14.7808i	0.346372	−	0.599934i	0.985602	+	0.169082i	$0.0540801\pi$
$608$		0			0
$609$	−2.16163	+	45.7445i	−0.0875935	+	1.85366i
$610$		0			0
$611$	15.3387	+	26.5673i	0.620536	+	1.07480i
$612$		0			0
$613$	−0.393059	+	0.680797i	−0.0158755	+	0.0274972i	−0.873854	−	0.486188i	$-0.838387\pi$
$613$	−0.393059	+	0.680797i	−0.0158755	+	0.0274972i	0.857979	+	0.513686i	$0.171720\pi$
$614$		0			0
$615$	6.13580	−	17.5949i	0.247419	−	0.709495i
$616$		0			0
$617$	23.7960	+	41.2159i	0.957991	+	1.65929i	0.727370	+	0.686246i	$0.240743\pi$
$617$	23.7960	+	41.2159i	0.957991	+	1.65929i	0.230621	+	0.973044i	$0.425924\pi$
$618$		0			0
$619$	−9.48717	−	16.4323i	−0.381321	−	0.660468i	0.609930	−	0.792455i	$-0.291198\pi$
$619$	−9.48717	−	16.4323i	−0.381321	−	0.660468i	−0.991251	+	0.131987i	$0.957864\pi$
$620$		0			0
$621$	1.29515	+	31.8991i	0.0519727	+	1.28007i
$622$		0			0
$623$	−0.655222	+	2.73330i	−0.0262509	+	0.109507i
$624$		0			0
$625$	2.30744	−	3.99660i	0.0922976	−	0.159864i
$626$		0			0
$627$	−1.60105	−	1.85647i	−0.0639398	−	0.0741403i
$628$		0			0
$629$	5.29674			0.211195
$630$		0			0
$631$	0.300343			0.0119565			0.00597823	−	0.999982i	$-0.498097\pi$
$631$	0.300343			0.0119565			0.00597823	+	0.999982i	$0.498097\pi$
$632$		0			0
$633$	9.29197	−	1.76834i	0.369323	−	0.0702851i
$634$		0			0
$635$	−8.33267	+	14.4326i	−0.330672	+	0.572741i
$636$		0			0
$637$	−21.2686	+	13.8326i	−0.842692	+	0.548068i
$638$		0			0
$639$	22.0644	+	17.5194i	0.872855	+	0.693057i
$640$		0			0
$641$	−14.0548	−	24.3436i	−0.555131	−	0.961514i	−0.997893	−	0.0648756i	$-0.979335\pi$
$641$	−14.0548	−	24.3436i	−0.555131	−	0.961514i	0.442763	−	0.896639i	$-0.353998\pi$
$642$		0			0
$643$	−1.55289	−	2.68968i	−0.0612399	−	0.106071i	0.833780	−	0.552097i	$-0.186172\pi$
$643$	−1.55289	−	2.68968i	−0.0612399	−	0.106071i	−0.895020	+	0.446026i	$0.852839\pi$
$644$		0			0
$645$	−4.40770	+	0.838820i	−0.173553	+	0.0330285i
$646$		0			0
$647$	23.3556	−	40.4532i	0.918205	−	1.59038i	0.116066	−	0.993242i	$-0.462972\pi$
$647$	23.3556	−	40.4532i	0.918205	−	1.59038i	0.802140	−	0.597137i	$-0.203695\pi$
$648$		0			0
$649$	−0.0544950	−	0.0943881i	−0.00213912	−	0.00370506i
$650$		0			0
$651$	13.4730	−	6.95232i	0.528050	−	0.272483i
$652$		0			0
$653$	0.998764	−	1.72991i	0.0390847	−	0.0676966i	−0.845821	−	0.533466i	$-0.820889\pi$
$653$	0.998764	−	1.72991i	0.0390847	−	0.0676966i	0.884906	+	0.465770i	$0.154222\pi$
$654$		0			0
$655$	14.8825	+	25.7772i	0.581506	+	1.00720i
$656$		0			0
$657$	12.5817	−	4.96874i	0.490858	−	0.193849i
$658$		0			0
$659$	8.37284	−	14.5022i	0.326160	−	0.564925i	−0.655587	−	0.755120i	$-0.727579\pi$
$659$	8.37284	−	14.5022i	0.326160	−	0.564925i	0.981746	+	0.190195i	$0.0609120\pi$
$660$		0			0
$661$	12.5774			0.489205			0.244602	−	0.969624i	$-0.421343\pi$
$661$	12.5774			0.489205			0.244602	+	0.969624i	$0.421343\pi$
$662$		0			0
$663$	1.24464	−	3.56911i	0.0483378	−	0.138613i
$664$		0			0
$665$	−4.97311	−	4.71608i	−0.192849	−	0.182882i
$666$		0			0
$667$	−30.7000	−	53.1740i	−1.18871	−	2.05890i
$668$		0			0
$669$	20.3733	+	23.6236i	0.787679	+	0.913340i
$670$		0			0
$671$	1.99168	+	3.44969i	0.0768878	+	0.133174i
$672$		0			0
$673$	23.8175	−	41.2531i	0.918096	−	1.59019i	0.115792	−	0.993273i	$-0.463059\pi$
$673$	23.8175	−	41.2531i	0.918096	−	1.59019i	0.802304	−	0.596916i	$-0.203607\pi$
$674$		0			0
$675$	−12.2448	−	6.42182i	−0.471301	−	0.247176i
$676$		0			0
$677$	−9.09327			−0.349483			−0.174741	−	0.984614i	$-0.555909\pi$
$677$	−9.09327			−0.349483			−0.174741	+	0.984614i	$0.555909\pi$
$678$		0			0
$679$	39.3856	−	11.6812i	1.51148	−	0.448282i
$680$		0			0
$681$	30.9233	−	5.88495i	1.18498	−	0.225512i
$682$		0			0
$683$	2.41674	−	4.18592i	0.0924741	−	0.160170i	−0.816078	−	0.577942i	$-0.803856\pi$
$683$	2.41674	−	4.18592i	0.0924741	−	0.160170i	0.908552	+	0.417773i	$0.137189\pi$
$684$		0			0
$685$	−18.7760			−0.717393
$686$		0			0
$687$	−17.4517	−	20.2359i	−0.665825	−	0.772047i
$688$		0			0
$689$	−28.9677			−1.10358
$690$		0			0
$691$	−10.7846			−0.410264			−0.205132	−	0.978734i	$-0.565762\pi$
$691$	−10.7846			−0.410264			−0.205132	+	0.978734i	$0.565762\pi$
$692$		0			0
$693$	5.22164	−	4.08981i	0.198354	−	0.155359i
$694$		0			0
$695$	−19.7199			−0.748018
$696$		0			0
$697$	4.23548			0.160430
$698$		0			0
$699$	−10.9200	+	2.07817i	−0.413033	+	0.0786036i
$700$		0			0
$701$	−31.8393			−1.20255			−0.601276	−	0.799041i	$-0.705341\pi$
$701$	−31.8393			−1.20255			−0.601276	+	0.799041i	$0.705341\pi$
$702$		0			0
$703$	−7.44997	+	12.9037i	−0.280981	+	0.486673i
$704$		0			0
$705$	−14.6431	−	16.9791i	−0.551490	−	0.639471i
$706$		0			0
$707$	−12.0362	+	50.2097i	−0.452667	+	1.88833i
$708$		0			0
$709$	−27.2064			−1.02176			−0.510879	−	0.859653i	$-0.670680\pi$
$709$	−27.2064			−1.02176			−0.510879	+	0.859653i	$0.670680\pi$
$710$		0			0
$711$	−36.9861	−	29.3674i	−1.38709	−	1.10136i
$712$		0			0
$713$	−10.1635	+	17.6037i	−0.380627	+	0.659265i
$714$		0			0
$715$	−2.31607	−	4.01154i	−0.0866160	−	0.150023i
$716$		0			0
$717$	−7.93985	+	1.51102i	−0.296519	+	0.0564300i
$718$		0			0
$719$	−14.4549	−	25.0366i	−0.539076	−	0.933707i	−0.998954	−	0.0457252i	$-0.985440\pi$
$719$	−14.4549	−	25.0366i	−0.539076	−	0.933707i	0.459878	−	0.887982i	$-0.347893\pi$
$720$		0			0
$721$	−4.62549	+	1.37185i	−0.172262	+	0.0510902i
$722$		0			0
$723$	32.0857	−	6.10617i	1.19328	−	0.227091i
$724$		0			0
$725$	26.5917			0.987591
$726$		0			0
$727$	4.29978	−	7.44744i	0.159470	−	0.276210i	−0.775208	−	0.631706i	$-0.782355\pi$
$727$	4.29978	−	7.44744i	0.159470	−	0.276210i	0.934678	+	0.355496i	$0.115688\pi$
$728$		0			0
$729$	11.5599	−	24.4002i	0.428146	−	0.903710i
$730$		0			0
$731$	−0.509920	−	0.883208i	−0.0188601	−	0.0326666i
$732$		0			0
$733$	22.7753	−	39.4480i	0.841225	−	1.45705i	−0.0476340	−	0.998865i	$-0.515168\pi$
$733$	22.7753	−	39.4480i	0.841225	−	1.45705i	0.888859	−	0.458180i	$-0.151499\pi$
$734$		0			0
$735$	13.3805	−	12.8377i	0.493546	−	0.473527i
$736$		0			0
$737$	0.937301	+	1.62345i	0.0345259	+	0.0598007i
$738$		0			0
$739$	6.34491	−	10.9897i	0.233401	−	0.404263i	−0.725405	−	0.688322i	$-0.758348\pi$
$739$	6.34491	−	10.9897i	0.233401	−	0.404263i	0.958807	+	0.284059i	$0.0916811\pi$
$740$		0			0
$741$	6.94431	+	8.05216i	0.255106	+	0.295804i
$742$		0			0
$743$	−5.04492	−	8.73806i	−0.185080	−	0.320568i	0.758523	−	0.651646i	$-0.225921\pi$
$743$	−5.04492	−	8.73806i	−0.185080	−	0.320568i	−0.943604	+	0.331078i	$0.892588\pi$
$744$		0			0
$745$	−13.8146	−	23.9276i	−0.506128	−	0.876640i
$746$		0			0
$747$	17.6464	−	6.96888i	0.645646	−	0.254978i
$748$		0			0
$749$	−6.50163	+	27.1220i	−0.237564	+	0.991015i
$750$		0			0
$751$	−2.50357	+	4.33631i	−0.0913565	+	0.158234i	−0.908082	−	0.418792i	$-0.862454\pi$
$751$	−2.50357	+	4.33631i	−0.0913565	+	0.158234i	0.816726	+	0.577026i	$0.195787\pi$
$752$		0			0
$753$	8.95503	−	25.6793i	0.326340	−	0.935805i
$754$		0			0
$755$	−13.1495			−0.478561
$756$		0			0
$757$	6.83620			0.248466			0.124233	−	0.992253i	$-0.460353\pi$
$757$	6.83620			0.248466			0.124233	+	0.992253i	$0.460353\pi$
$758$		0			0
$759$	−2.92817	+	8.39676i	−0.106286	+	0.304783i
$760$		0			0
$761$	−13.4377	+	23.2747i	−0.487115	+	0.843708i	−0.999890	−	0.0148147i	$-0.995284\pi$
$761$	−13.4377	+	23.2747i	−0.487115	+	0.843708i	0.512775	+	0.858523i	$0.328618\pi$
$762$		0			0
$763$	−31.9829	+	9.48562i	−1.15786	+	0.343403i
$764$		0			0
$765$	−0.405957	+	2.73264i	−0.0146774	+	0.0987986i
$766$		0			0
$767$	0.236364	+	0.409394i	0.00853460	+	0.0147824i
$768$		0			0
$769$	−2.00631	−	3.47503i	−0.0723493	−	0.125313i	0.827581	−	0.561346i	$-0.189716\pi$
$769$	−2.00631	−	3.47503i	−0.0723493	−	0.125313i	−0.899931	+	0.436033i	$0.856383\pi$
$770$		0			0
$771$	10.4271	+	12.0906i	0.375523	+	0.435431i
$772$		0			0
$773$	−13.6861	+	23.7051i	−0.492256	+	0.852612i	−0.999960	−	0.00891927i	$-0.997161\pi$
$773$	−13.6861	+	23.7051i	−0.492256	+	0.852612i	0.507704	+	0.861531i	$0.330494\pi$
$774$		0			0
$775$	−4.40171	−	7.62399i	−0.158114	−	0.273862i
$776$		0			0
$777$	−33.9214	−	21.7817i	−1.21692	−	0.781414i
$778$		0			0
$779$	−5.95729	+	10.3183i	−0.213442	+	0.369693i
$780$		0			0
$781$	3.92385	+	6.79631i	0.140407	+	0.243191i
$782$		0			0
$783$	2.10659	+	51.8845i	0.0752834	+	1.85420i
$784$		0			0
$785$	2.44220	−	4.23001i	0.0871658	−	0.150976i
$786$		0			0
$787$	−12.8727			−0.458863			−0.229432	−	0.973325i	$-0.573687\pi$
$787$	−12.8727			−0.458863			−0.229432	+	0.973325i	$0.573687\pi$
$788$		0			0
$789$	−0.821186	+	0.156278i	−0.0292350	+	0.00556366i
$790$		0			0
$791$	9.57771	−	39.9540i	0.340544	−	1.42060i
$792$		0			0
$793$	−8.63860	−	14.9625i	−0.306766	−	0.531334i
$794$		0			0
$795$	20.7984	−	3.95811i	0.737644	−	0.140380i
$796$		0			0
$797$	−8.71139	−	15.0886i	−0.308573	−	0.534465i	0.669477	−	0.742833i	$-0.266518\pi$
$797$	−8.71139	−	15.0886i	−0.308573	−	0.534465i	−0.978050	+	0.208368i	$0.933185\pi$
$798$		0			0
$799$	2.54815	−	4.41352i	0.0901469	−	0.156139i
$800$		0			0
$801$	−0.468328	+	3.15248i	−0.0165476	+	0.111387i
$802$		0			0
$803$	3.76796			0.132968
$804$		0			0
$805$	−5.79554	+	24.1765i	−0.204266	+	0.852109i
$806$		0			0
$807$	8.92026	+	10.3433i	0.314008	+	0.364103i
$808$		0			0
$809$	−3.04097	+	5.26712i	−0.106915	+	0.185182i	−0.914519	−	0.404543i	$-0.867431\pi$
$809$	−3.04097	+	5.26712i	−0.106915	+	0.185182i	0.807604	+	0.589725i	$0.200764\pi$
$810$		0			0
$811$	14.6219			0.513443			0.256722	−	0.966485i	$-0.417358\pi$
$811$	14.6219			0.513443			0.256722	+	0.966485i	$0.417358\pi$
$812$		0			0
$813$	43.5405	−	8.28612i	1.52703	−	0.290607i
$814$		0			0
$815$	6.26472			0.219443
$816$		0			0
$817$	2.86885			0.100368
$818$		0			0
$819$	−22.6481	+	17.7389i	−0.791388	+	0.619849i
$820$		0			0
$821$	−9.74323			−0.340041			−0.170021	−	0.985441i	$-0.554383\pi$
$821$	−9.74323			−0.340041			−0.170021	+	0.985441i	$0.554383\pi$
$822$		0			0
$823$	10.7797			0.375755			0.187878	−	0.982192i	$-0.439839\pi$
$823$	10.7797			0.375755			0.187878	+	0.982192i	$0.439839\pi$
$824$		0			0
$825$	−2.51526	−	2.91653i	−0.0875702	−	0.101541i
$826$		0			0
$827$	13.0521			0.453867			0.226933	−	0.973910i	$-0.427130\pi$
$827$	13.0521			0.453867			0.226933	+	0.973910i	$0.427130\pi$
$828$		0			0
$829$	24.5548	−	42.5301i	0.852822	−	1.47713i	−0.0258286	−	0.999666i	$-0.508222\pi$
$829$	24.5548	−	42.5301i	0.852822	−	1.47713i	0.878651	−	0.477465i	$-0.158444\pi$
$830$		0			0
$831$	−14.2405	+	2.71008i	−0.493997	+	0.0940117i
$832$		0			0
$833$	3.75671	+	1.91092i	0.130162	+	0.0662093i
$834$		0			0
$835$	25.2308			0.873149
$836$		0			0
$837$	14.5269	−	9.19240i	0.502123	−	0.317736i
$838$		0			0
$839$	−12.0830	+	20.9284i	−0.417151	+	0.722527i	−0.995652	−	0.0931549i	$-0.970305\pi$
$839$	−12.0830	+	20.9284i	−0.417151	+	0.722527i	0.578500	+	0.815682i	$0.303638\pi$
$840$		0			0
$841$	−35.4341	−	61.3737i	−1.22187	−	2.11633i
$842$		0			0
$843$	1.24848	+	1.44766i	0.0430001	+	0.0498600i
$844$		0			0
$845$	0.104456	+	0.180923i	0.00359339	+	0.00622393i
$846$		0			0
$847$	−26.1307	+	7.74997i	−0.897862	+	0.266292i
$848$		0			0
$849$	1.65816	−	4.75490i	0.0569078	−	0.163188i
$850$		0			0
$851$	54.0487			1.85276
$852$		0			0
$853$	2.72681	−	4.72297i	0.0933641	−	0.161711i	−0.815561	−	0.578672i	$-0.803571\pi$
$853$	2.72681	−	4.72297i	0.0933641	−	0.161711i	0.908925	+	0.416960i	$0.136905\pi$
$854$		0			0
$855$	−6.08616	−	4.83248i	−0.208142	−	0.165267i
$856$		0			0
$857$	−16.4194	−	28.4393i	−0.560876	−	0.971466i	−0.997420	−	0.0717835i	$-0.977131\pi$
$857$	−16.4194	−	28.4393i	−0.560876	−	0.971466i	0.436544	−	0.899683i	$-0.356202\pi$
$858$		0			0
$859$	−26.3299	+	45.6048i	−0.898365	+	1.55601i	−0.0687820	+	0.997632i	$0.521911\pi$
$859$	−26.3299	+	45.6048i	−0.898365	+	1.55601i	−0.829583	+	0.558383i	$0.811422\pi$
$860$		0			0
$861$	−27.1249	−	17.4175i	−0.924413	−	0.593587i
$862$		0			0
$863$	24.4095	+	42.2784i	0.830908	+	1.43917i	0.897319	+	0.441382i	$0.145512\pi$
$863$	24.4095	+	42.2784i	0.830908	+	1.43917i	−0.0664116	+	0.997792i	$0.521155\pi$
$864$		0			0
$865$	−9.80445	+	16.9818i	−0.333361	+	0.577398i
$866$		0			0
$867$	28.3089	−	5.38740i	0.961419	−	0.182966i
$868$		0			0
$869$	−6.57746	−	11.3925i	−0.223125	−	0.386464i
$870$		0			0
$871$	−4.06540	−	7.04148i	−0.137751	−	0.238591i
$872$		0			0
$873$	43.3257	−	17.1101i	1.46635	−	0.579090i
$874$		0			0
$875$	−22.4934	−	21.3309i	−0.760416	−	0.721115i
$876$		0			0
$877$	12.5373	−	21.7152i	0.423353	−	0.733269i	−0.572912	−	0.819617i	$-0.694186\pi$
$877$	12.5373	−	21.7152i	0.423353	−	0.733269i	0.996265	+	0.0863480i	$0.0275197\pi$
$878$		0			0
$879$	−42.3272	+	8.05521i	−1.42766	+	0.271695i
$880$		0			0
$881$	−16.2437			−0.547263			−0.273632	−	0.961835i	$-0.588225\pi$
$881$	−16.2437			−0.547263			−0.273632	+	0.961835i	$0.588225\pi$
$882$		0			0
$883$	29.7137			0.999945			0.499973	−	0.866041i	$-0.333343\pi$
$883$	29.7137			0.999945			0.499973	+	0.866041i	$0.333343\pi$
$884$		0			0
$885$	−0.225645	−	0.261643i	−0.00758497	−	0.00879503i
$886$		0			0
$887$	7.87353	−	13.6374i	0.264367	−	0.457897i	−0.703030	−	0.711160i	$-0.748170\pi$
$887$	7.87353	−	13.6374i	0.264367	−	0.457897i	0.967398	+	0.253262i	$0.0815036\pi$
$888$		0			0
$889$	20.9191	+	19.8380i	0.701605	+	0.665344i
$890$		0			0
$891$	5.49135	−	5.13872i	0.183967	−	0.172153i
$892$		0			0
$893$	7.16803	+	12.4154i	0.239869	+	0.415465i
$894$		0			0
$895$	18.1616	+	31.4568i	0.607076	+	1.05149i
$896$		0			0
$897$	12.7005	−	36.4196i	0.424057	−	1.21602i
$898$		0			0
$899$	−16.5312	+	28.6328i	−0.551345	+	0.954957i
$900$		0			0
$901$	2.40614	+	4.16756i	0.0801602	+	0.138842i
$902$		0			0
$903$	−0.366371	+	7.75317i	−0.0121921	+	0.258009i
$904$		0			0
$905$	−12.2539	+	21.2244i	−0.407333	+	0.705522i
$906$		0			0
$907$	1.29001	+	2.23437i	0.0428342	+	0.0741910i	0.886648	−	0.462446i	$-0.153028\pi$
$907$	1.29001	+	2.23437i	0.0428342	+	0.0741910i	−0.843813	+	0.536637i	$0.819695\pi$
$908$		0			0
$909$	−8.60302	+	57.9099i	−0.285344	+	1.92075i
$910$		0			0
$911$	23.2170	−	40.2130i	0.769214	−	1.33232i	−0.168776	−	0.985654i	$-0.553981\pi$
$911$	23.2170	−	40.2130i	0.769214	−	1.33232i	0.937990	−	0.346663i	$-0.112685\pi$
$912$		0			0
$913$	5.28473			0.174899
$914$		0			0
$915$	8.24685	+	9.56249i	0.272632	+	0.316126i
$916$		0			0
$917$	49.3656	−	14.6411i	1.63020	−	0.483490i
$918$		0			0
$919$	−2.84387	−	4.92572i	−0.0938106	−	0.162485i	0.815301	−	0.579037i	$-0.196571\pi$
$919$	−2.84387	−	4.92572i	−0.0938106	−	0.162485i	−0.909112	+	0.416553i	$0.863238\pi$
$920$		0			0
$921$	−13.5720	+	38.9187i	−0.447212	+	1.28242i
$922$		0			0
$923$	−17.0191	−	29.4780i	−0.560191	−	0.970279i
$924$		0			0
$925$	−11.7040	+	20.2718i	−0.384824	+	0.666534i
$926$		0			0
$927$	−5.08821	+	2.00943i	−0.167119	+	0.0659984i
$928$		0			0
$929$	47.9605			1.57353			0.786767	−	0.617251i	$-0.211754\pi$
$929$	47.9605			1.57353			0.786767	+	0.617251i	$0.211754\pi$
$930$		0			0
$931$	−9.93919	+	6.46422i	−0.325744	+	0.211856i
$932$		0			0
$933$	10.6728	−	30.6052i	0.349413	−	1.00197i
$934$		0			0
$935$	−0.384758	+	0.666421i	−0.0125829	+	0.0217943i
$936$		0			0
$937$	−25.3542			−0.828285			−0.414142	−	0.910212i	$-0.635918\pi$
$937$	−25.3542			−0.828285			−0.414142	+	0.910212i	$0.635918\pi$
$938$		0			0
$939$	−11.0164	+	31.5904i	−0.359507	+	1.03091i
$940$		0			0
$941$	2.51303			0.0819223			0.0409611	−	0.999161i	$-0.486958\pi$
$941$	2.51303			0.0819223			0.0409611	+	0.999161i	$0.486958\pi$
$942$		0			0
$943$	43.2195			1.40742
$944$		0			0
$945$	13.8372	−	15.8309i	0.450124	−	0.514980i
$946$		0			0
$947$	14.5307			0.472186			0.236093	−	0.971731i	$-0.424133\pi$
$947$	14.5307			0.472186			0.236093	+	0.971731i	$0.424133\pi$
$948$		0			0
$949$	−16.3429			−0.530514
$950$		0			0
$951$	−1.02379	+	2.93579i	−0.0331985	+	0.0951994i
$952$		0			0
$953$	−36.5564			−1.18418			−0.592089	−	0.805873i	$-0.701697\pi$
$953$	−36.5564			−1.18418			−0.592089	+	0.805873i	$0.701697\pi$
$954$		0			0
$955$	−8.26605	+	14.3172i	−0.267483	+	0.463294i
$956$		0			0
$957$	−4.76272	+	13.6575i	−0.153957	+	0.441484i
$958$		0			0
$959$	−7.57177	+	31.5861i	−0.244505	+	1.01997i
$960$		0			0
$961$	−20.0544			−0.646917
$962$		0			0
$963$	−4.64712	+	31.2814i	−0.149752	+	1.00803i
$964$		0			0
$965$	0.573726	−	0.993722i	0.0184689	−	0.0319890i
$966$		0			0
$967$	8.06111	+	13.9623i	0.259228	+	0.448996i	0.966035	−	0.258410i	$-0.0831986\pi$
$967$	8.06111	+	13.9623i	0.259228	+	0.448996i	−0.706807	+	0.707406i	$0.749865\pi$
$968$		0			0
$969$	0.581643	−	1.66791i	0.0186851	−	0.0535809i
$970$		0			0
$971$	8.60100	+	14.8974i	0.276019	+	0.478079i	0.970392	−	0.241537i	$-0.0776514\pi$
$971$	8.60100	+	14.8974i	0.276019	+	0.478079i	−0.694373	+	0.719616i	$0.744318\pi$
$972$		0			0
$973$	−7.95242	+	33.1740i	−0.254943	+	1.06351i
$974$		0			0
$975$	10.9096	+	12.6500i	0.349386	+	0.405124i
$976$		0			0
$977$	40.2450			1.28755			0.643776	−	0.765214i	$-0.277367\pi$
$977$	40.2450			1.28755			0.643776	+	0.765214i	$0.277367\pi$
$978$		0			0
$979$	−0.443873	+	0.768810i	−0.0141862	+	0.0245713i
$980$		0			0
$981$	−35.1824	+	13.8942i	−1.12329	+	0.443607i
$982$		0			0
$983$	−10.2760	−	17.7985i	−0.327753	−	0.567685i	0.654313	−	0.756224i	$-0.272958\pi$
$983$	−10.2760	−	17.7985i	−0.327753	−	0.567685i	−0.982066	+	0.188539i	$0.939625\pi$
$984$		0			0
$985$	7.89065	−	13.6670i	0.251417	−	0.435467i
$986$		0			0
$987$	−34.4684	+	17.7863i	−1.09714	+	0.566145i
$988$		0			0
$989$	−5.20330	−	9.01237i	−0.165455	−	0.286577i
$990$		0			0
$991$	−14.9872	+	25.9586i	−0.476083	+	0.824601i	−0.999625	−	0.0273998i	$-0.991277\pi$
$991$	−14.9872	+	25.9586i	−0.476083	+	0.824601i	0.523541	+	0.852000i	$0.324611\pi$
$992$		0			0
$993$	−8.06252	+	23.1199i	−0.255856	+	0.733689i
$994$		0			0
$995$	4.36537	+	7.56105i	0.138392	+	0.239701i
$996$		0			0
$997$	6.01944	+	10.4260i	0.190638	+	0.330194i	0.945462	−	0.325733i	$-0.105611\pi$
$997$	6.01944	+	10.4260i	0.190638	+	0.330194i	−0.754824	+	0.655927i	$0.772278\pi$
$998$		0			0
$999$	−40.4807	−	21.2303i	−1.28075	−	0.671697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.i.b.25.4	✓	14
3.2	odd	2		756.2.i.b.613.3		14
4.3	odd	2		1008.2.q.j.529.4		14
7.2	even	3		252.2.l.b.205.5	yes	14
7.3	odd	6		1764.2.j.h.1177.7		14
7.4	even	3		1764.2.j.g.1177.1		14
7.5	odd	6		1764.2.l.i.961.3		14
7.6	odd	2		1764.2.i.i.1537.4		14
9.2	odd	6		2268.2.k.f.1621.3		14
9.4	even	3		252.2.l.b.193.5	yes	14
9.5	odd	6		756.2.l.b.361.5		14
9.7	even	3		2268.2.k.e.1621.5		14
12.11	even	2		3024.2.q.j.2881.3		14
21.2	odd	6		756.2.l.b.289.5		14
21.5	even	6		5292.2.l.i.3313.3		14
21.11	odd	6		5292.2.j.h.3529.3		14
21.17	even	6		5292.2.j.g.3529.5		14
21.20	even	2		5292.2.i.i.2125.5		14
28.23	odd	6		1008.2.t.j.961.3		14
36.23	even	6		3024.2.t.j.1873.5		14
36.31	odd	6		1008.2.t.j.193.3		14
63.2	odd	6		2268.2.k.f.1297.3		14
63.4	even	3		1764.2.j.g.589.1		14
63.5	even	6		5292.2.i.i.1549.5		14
63.13	odd	6		1764.2.l.i.949.3		14
63.16	even	3		2268.2.k.e.1297.5		14
63.23	odd	6		756.2.i.b.37.3		14
63.31	odd	6		1764.2.j.h.589.7		14
63.32	odd	6		5292.2.j.h.1765.3		14
63.40	odd	6		1764.2.i.i.373.4		14
63.41	even	6		5292.2.l.i.361.3		14
63.58	even	3	inner	252.2.i.b.121.4	yes	14
63.59	even	6		5292.2.j.g.1765.5		14
84.23	even	6		3024.2.t.j.289.5		14
252.23	even	6		3024.2.q.j.2305.3		14
252.247	odd	6		1008.2.q.j.625.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.4	✓	14	1.1	even	1	trivial
252.2.i.b.121.4	yes	14	63.58	even	3	inner
252.2.l.b.193.5	yes	14	9.4	even	3
252.2.l.b.205.5	yes	14	7.2	even	3
756.2.i.b.37.3		14	63.23	odd	6
756.2.i.b.613.3		14	3.2	odd	2
756.2.l.b.289.5		14	21.2	odd	6
756.2.l.b.361.5		14	9.5	odd	6
1008.2.q.j.529.4		14	4.3	odd	2
1008.2.q.j.625.4		14	252.247	odd	6
1008.2.t.j.193.3		14	36.31	odd	6
1008.2.t.j.961.3		14	28.23	odd	6
1764.2.i.i.373.4		14	63.40	odd	6
1764.2.i.i.1537.4		14	7.6	odd	2
1764.2.j.g.589.1		14	63.4	even	3
1764.2.j.g.1177.1		14	7.4	even	3
1764.2.j.h.589.7		14	63.31	odd	6
1764.2.j.h.1177.7		14	7.3	odd	6
1764.2.l.i.949.3		14	63.13	odd	6
1764.2.l.i.961.3		14	7.5	odd	6
2268.2.k.e.1297.5		14	63.16	even	3
2268.2.k.e.1621.5		14	9.7	even	3
2268.2.k.f.1297.3		14	63.2	odd	6
2268.2.k.f.1621.3		14	9.2	odd	6
3024.2.q.j.2305.3		14	252.23	even	6
3024.2.q.j.2881.3		14	12.11	even	2
3024.2.t.j.289.5		14	84.23	even	6
3024.2.t.j.1873.5		14	36.23	even	6
5292.2.i.i.1549.5		14	63.5	even	6
5292.2.i.i.2125.5		14	21.20	even	2
5292.2.j.g.1765.5		14	63.59	even	6
5292.2.j.g.3529.5		14	21.17	even	6
5292.2.j.h.1765.3		14	63.32	odd	6
5292.2.j.h.3529.3		14	21.11	odd	6
5292.2.l.i.361.3		14	63.41	even	6
5292.2.l.i.3313.3		14	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.570327 - 1.63546i) q^{3} +(0.764702 - 1.32450i) q^{5} +(-1.91978 - 1.82056i) q^{7} +(-2.34945 - 1.86549i) q^{9} +O(q^{10})\)	\(q+(0.570327 - 1.63546i) q^{3} +(0.764702 - 1.32450i) q^{5} +(-1.91978 - 1.82056i) q^{7} +(-2.34945 - 1.86549i) q^{9} +(-0.417818 - 0.723682i) q^{11} +(1.81222 + 3.13886i) q^{13} +(-1.73004 - 2.00604i) q^{15} +(0.301057 - 0.521446i) q^{17} +(0.846884 + 1.46685i) q^{19} +(-4.07236 + 2.10141i) q^{21} +(3.07202 - 5.32090i) q^{23} +(1.33046 + 2.30443i) q^{25} +(-4.39090 + 2.77849i) q^{27} +(4.99671 - 8.65455i) q^{29} -3.30841 q^{31} +(-1.42185 + 0.270589i) q^{33} +(-3.87940 + 1.15057i) q^{35} +(4.39846 + 7.61835i) q^{37} +(6.16704 - 1.17364i) q^{39} +(3.51718 + 6.09194i) q^{41} +(0.846884 - 1.46685i) q^{43} +(-4.26748 + 1.68531i) q^{45} +8.46401 q^{47} +(0.371118 + 6.99016i) q^{49} +(-0.681102 - 0.789761i) q^{51} +(-3.99616 + 6.92155i) q^{53} -1.27803 q^{55} +(2.88197 - 0.548462i) q^{57} +0.130428 q^{59} -4.76685 q^{61} +(1.11419 + 7.85866i) q^{63} +5.54324 q^{65} -2.24332 q^{67} +(-6.95006 - 8.05882i) q^{69} -9.39130 q^{71} +(-2.25454 + 3.90498i) q^{73} +(4.52759 - 0.861638i) q^{75} +(-0.515388 + 2.14997i) q^{77} +15.7424 q^{79} +(2.03987 + 8.76578i) q^{81} +(-3.16210 + 5.47692i) q^{83} +(-0.460438 - 0.797501i) q^{85} +(-11.3044 - 13.1078i) q^{87} +(-0.531180 - 0.920030i) q^{89} +(2.23542 - 9.32519i) q^{91} +(-1.88688 + 5.41077i) q^{93} +2.59046 q^{95} +(-7.76364 + 13.4470i) q^{97} +(-0.368380 + 2.47969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9}+O(q^{10}) \) 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9	\( 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9} + 2 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 11 q^{21} + 11 q^{23} - 9 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 4 q^{33} - 19 q^{35} + 10 q^{37} - 2 q^{39} - 33 q^{41} + 7 q^{43} - 10 q^{45} + 6 q^{47} - 4 q^{49} - 13 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} + 28 q^{59} + 20 q^{61} + 33 q^{63} - 30 q^{65} - 12 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} - 44 q^{75} - 47 q^{77} + 20 q^{79} - 29 q^{81} - 25 q^{83} + 8 q^{85} + 28 q^{87} - 6 q^{89} + 2 q^{91} + 22 q^{93} + 56 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) \) 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9 + 2 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 11 * q^21 + 11 * q^23 - 9 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 4 * q^33 - 19 * q^35 + 10 * q^37 - 2 * q^39 - 33 * q^41 + 7 * q^43 - 10 * q^45 + 6 * q^47 - 4 * q^49 - 13 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 + 28 * q^59 + 20 * q^61 + 33 * q^63 - 30 * q^65 - 12 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 - 44 * q^75 - 47 * q^77 + 20 * q^79 - 29 * q^81 - 25 * q^83 + 8 * q^85 + 28 * q^87 - 6 * q^89 + 2 * q^91 + 22 * q^93 + 56 * q^95 - 18 * q^97 + 7 * q^99

Introduction

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