LMFDB - Embedded newform 252.2.j.b.169.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [252,2,Mod(85,252)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(252, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("252.85"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [6,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			169.1
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	252.169
Dual form			252.2.j.b.85.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.09097 - 1.34528i) q^{3} +(1.97141 + 3.41458i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.619562 + 2.93533i) q^{9} +(-0.471410 + 0.816506i) q^{11} +(0.500000 + 0.866025i) q^{13} +(2.44282 - 6.37731i) q^{15} +5.60301 q^{17} +1.28263 q^{19} +(1.71053 - 0.272169i) q^{21} +(2.33009 + 4.03584i) q^{23} +(-5.27292 + 9.13296i) q^{25} +(4.62476 - 2.36887i) q^{27} +(3.83009 - 6.63392i) q^{29} +(-3.91423 - 6.77965i) q^{31} +(1.61273 - 0.256606i) q^{33} -3.94282 q^{35} -9.82846 q^{37} +(0.619562 - 1.61745i) q^{39} +(-0.471410 - 0.816506i) q^{41} +(-4.63160 + 8.02217i) q^{43} +(-11.2443 + 3.67119i) q^{45} +(2.64132 - 4.57489i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-6.11273 - 7.53762i) q^{51} -9.22545 q^{53} -3.71737 q^{55} +(-1.39931 - 1.72550i) q^{57} +(4.77292 + 8.26693i) q^{59} +(5.27292 - 9.13296i) q^{61} +(-2.23229 - 2.00422i) q^{63} +(-1.97141 + 3.41458i) q^{65} +(0.858685 + 1.48729i) q^{67} +(2.88727 - 7.53762i) q^{69} +3.54583 q^{71} +2.71737 q^{73} +(18.0390 - 2.87024i) q^{75} +(-0.471410 - 0.816506i) q^{77} +(8.18715 - 14.1806i) q^{79} +(-8.23229 - 3.63723i) q^{81} +(0.198495 - 0.343803i) q^{83} +(11.0458 + 19.1319i) q^{85} +(-13.1030 + 2.08486i) q^{87} +5.50808 q^{89} -1.00000 q^{91} +(-4.85021 + 12.6621i) q^{93} +(2.52859 + 4.37965i) q^{95} +(6.77292 - 11.7310i) q^{97} +(-2.10464 - 1.88962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{3} + 3 q^{5} - 3 q^{7} - 4 q^{9} + 6 q^{11} + 3 q^{13} - 3 q^{15} + 6 q^{19} + 2 q^{21} + 6 q^{23} - 6 q^{25} - 7 q^{27} + 15 q^{29} + 3 q^{31} - 6 q^{35} - 6 q^{37} + 4 q^{39} + 6 q^{41} - 3 q^{43}+ \cdots - 24 q^{99}+O(q^{100}) $ 6 * q + 2 * q^3 + 3 * q^5 - 3 * q^7 - 4 * q^9 + 6 * q^11 + 3 * q^13 - 3 * q^15 + 6 * q^19 + 2 * q^21 + 6 * q^23 - 6 * q^25 - 7 * q^27 + 15 * q^29 + 3 * q^31 - 6 * q^35 - 6 * q^37 + 4 * q^39 + 6 * q^41 - 3 * q^43 - 33 * q^45 + 15 * q^47 - 3 * q^49 - 27 * q^51 - 36 * q^53 - 24 * q^55 + 7 * q^57 + 3 * q^59 + 6 * q^61 - 4 * q^63 - 3 * q^65 + 6 * q^67 + 27 * q^69 - 30 * q^71 + 18 * q^73 + 47 * q^75 + 6 * q^77 - 3 * q^79 - 40 * q^81 + 18 * q^83 + 15 * q^85 - 45 * q^87 + 12 * q^89 - 6 * q^91 + 25 * q^93 + 24 * q^95 + 15 * q^97 - 24 * q^99

Character values

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

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

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
$3$	−1.09097	−	1.34528i	−0.629873	−	0.776698i
$3$	−1.09097	−	1.34528i	−0.629873	−	0.776698i
$4$		0			0
$5$	1.97141	+	3.41458i	0.881641	+	1.52705i	0.849515	+	0.527564i	$0.176894\pi$
$5$	1.97141	+	3.41458i	0.881641	+	1.52705i	0.0321260	+	0.999484i	$0.489772\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$		0			0
$9$	−0.619562	+	2.93533i	−0.206521	+	0.978442i
$10$		0			0
$11$	−0.471410	+	0.816506i	−0.142135	+	0.246186i	−0.928301	−	0.371831i	$-0.878730\pi$
$11$	−0.471410	+	0.816506i	−0.142135	+	0.246186i	0.786165	+	0.618017i	$0.212064\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	0.926995	−	0.375073i	$-0.122382\pi$
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	−0.788320	+	0.615265i	$0.789049\pi$
$14$		0			0
$15$	2.44282	−	6.37731i	0.630733	−	1.64662i
$16$		0			0
$17$	5.60301			1.35893			0.679465	−	0.733708i	$-0.262212\pi$
$17$	5.60301			1.35893			0.679465	+	0.733708i	$0.262212\pi$
$18$		0			0
$19$	1.28263			0.294256			0.147128	−	0.989117i	$-0.452997\pi$
$19$	1.28263			0.294256			0.147128	+	0.989117i	$0.452997\pi$
$20$		0			0
$21$	1.71053	−	0.272169i	0.373269	−	0.0593921i
$22$		0			0
$23$	2.33009	+	4.03584i	0.485858	+	0.841531i	0.999868	−	0.0162531i	$-0.00517374\pi$
$23$	2.33009	+	4.03584i	0.485858	+	0.841531i	−0.514010	+	0.857784i	$0.671840\pi$
$24$		0			0
$25$	−5.27292	+	9.13296i	−1.05458	+	1.82659i
$26$		0			0
$27$	4.62476	−	2.36887i	0.890036	−	0.455890i
$28$		0			0
$29$	3.83009	−	6.63392i	0.711231	−	1.23189i	−0.253165	−	0.967423i	$-0.581471\pi$
$29$	3.83009	−	6.63392i	0.711231	−	1.23189i	0.964395	−	0.264465i	$-0.0851952\pi$
$30$		0			0
$31$	−3.91423	−	6.77965i	−0.703016	−	1.21766i	−0.967403	−	0.253243i	$-0.918503\pi$
$31$	−3.91423	−	6.77965i	−0.703016	−	1.21766i	0.264386	−	0.964417i	$-0.414831\pi$
$32$		0			0
$33$	1.61273	−	0.256606i	0.280739	−	0.0446694i
$34$		0			0
$35$	−3.94282			−0.666458
$36$		0			0
$37$	−9.82846			−1.61579			−0.807894	−	0.589327i	$-0.799393\pi$
$37$	−9.82846			−1.61579			−0.807894	+	0.589327i	$0.799393\pi$
$38$		0			0
$39$	0.619562	−	1.61745i	0.0992093	−	0.258999i
$40$		0			0
$41$	−0.471410	−	0.816506i	−0.0736219	−	0.127517i	0.826864	−	0.562402i	$-0.190122\pi$
$41$	−0.471410	−	0.816506i	−0.0736219	−	0.127517i	−0.900486	+	0.434885i	$0.856789\pi$
$42$		0			0
$43$	−4.63160	+	8.02217i	−0.706312	+	1.22337i	0.259903	+	0.965635i	$0.416309\pi$
$43$	−4.63160	+	8.02217i	−0.706312	+	1.22337i	−0.966216	+	0.257734i	$0.917024\pi$
$44$		0			0
$45$	−11.2443	+	3.67119i	−1.67621	+	0.547268i
$46$		0			0
$47$	2.64132	−	4.57489i	0.385275	−	0.667317i	−0.606532	−	0.795059i	$-0.707440\pi$
$47$	2.64132	−	4.57489i	0.385275	−	0.667317i	0.991807	+	0.127743i	$0.0407731\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$	−6.11273	−	7.53762i	−0.855953	−	1.05548i
$52$		0			0
$53$	−9.22545			−1.26721			−0.633607	−	0.773655i	$-0.718426\pi$
$53$	−9.22545			−1.26721			−0.633607	+	0.773655i	$0.718426\pi$
$54$		0			0
$55$	−3.71737			−0.501250
$56$		0			0
$57$	−1.39931	−	1.72550i	−0.185344	−	0.228548i
$58$		0			0
$59$	4.77292	+	8.26693i	0.621381	+	1.07626i	0.989229	+	0.146377i	$0.0467612\pi$
$59$	4.77292	+	8.26693i	0.621381	+	1.07626i	−0.367848	+	0.929886i	$0.619905\pi$
$60$		0			0
$61$	5.27292	−	9.13296i	0.675128	−	1.16936i	−0.301304	−	0.953528i	$-0.597422\pi$
$61$	5.27292	−	9.13296i	0.675128	−	1.16936i	0.976432	−	0.215827i	$-0.0692448\pi$
$62$		0			0
$63$	−2.23229	−	2.00422i	−0.281242	−	0.252508i
$64$		0			0
$65$	−1.97141	+	3.41458i	−0.244523	+	0.423527i
$66$		0			0
$67$	0.858685	+	1.48729i	0.104905	+	0.181701i	0.913699	−	0.406391i	$-0.133213\pi$
$67$	0.858685	+	1.48729i	0.104905	+	0.181701i	−0.808794	+	0.588092i	$0.799879\pi$
$68$		0			0
$69$	2.88727	−	7.53762i	0.347587	−	0.907423i
$70$		0			0
$71$	3.54583			0.420813			0.210406	−	0.977614i	$-0.432521\pi$
$71$	3.54583			0.420813			0.210406	+	0.977614i	$0.432521\pi$
$72$		0			0
$73$	2.71737			0.318044			0.159022	−	0.987275i	$-0.449166\pi$
$73$	2.71737			0.318044			0.159022	+	0.987275i	$0.449166\pi$
$74$		0			0
$75$	18.0390	−	2.87024i	2.08296	−	0.331427i
$76$		0			0
$77$	−0.471410	−	0.816506i	−0.0537222	−	0.0930495i
$78$		0			0
$79$	8.18715	−	14.1806i	0.921126	−	1.59544i	0.123449	−	0.992351i	$-0.460604\pi$
$79$	8.18715	−	14.1806i	0.921126	−	1.59544i	0.797676	−	0.603086i	$-0.206062\pi$
$80$		0			0
$81$	−8.23229	−	3.63723i	−0.914699	−	0.404137i
$82$		0			0
$83$	0.198495	−	0.343803i	0.0217877	−	0.0377373i	−0.854926	−	0.518750i	$-0.826398\pi$
$83$	0.198495	−	0.343803i	0.0217877	−	0.0377373i	0.876714	+	0.481013i	$0.159731\pi$
$84$		0			0
$85$	11.0458	+	19.1319i	1.19809	+	2.07515i
$86$		0			0
$87$	−13.1030	+	2.08486i	−1.40479	+	0.223521i
$88$		0			0
$89$	5.50808			0.583855			0.291928	−	0.956440i	$-0.405703\pi$
$89$	5.50808			0.583855			0.291928	+	0.956440i	$0.405703\pi$
$90$		0			0
$91$	−1.00000			−0.104828
$92$		0			0
$93$	−4.85021	+	12.6621i	−0.502944	+	1.31300i
$94$		0			0
$95$	2.52859	+	4.37965i	0.259428	+	0.449342i
$96$		0			0
$97$	6.77292	−	11.7310i	0.687685	−	1.19111i	−0.284899	−	0.958557i	$-0.591960\pi$
$97$	6.77292	−	11.7310i	0.687685	−	1.19111i	0.972585	−	0.232549i	$-0.0747064\pi$
$98$		0			0
$99$	−2.10464	−	1.88962i	−0.211525	−	0.189914i
$100$		0			0
$101$	1.30150	−	2.25427i	0.129505	−	0.224309i	−0.793980	−	0.607944i	$-0.791995\pi$
$101$	1.30150	−	2.25427i	0.129505	−	0.224309i	0.923485	+	0.383635i	$0.125328\pi$
$102$		0			0
$103$	−7.99028	−	13.8396i	−0.787306	−	1.36365i	−0.927612	−	0.373546i	$-0.878142\pi$
$103$	−7.99028	−	13.8396i	−0.787306	−	1.36365i	0.140305	−	0.990108i	$-0.455192\pi$
$104$		0			0
$105$	4.30150	+	5.30420i	0.419784	+	0.517637i
$106$		0			0
$107$	−10.8856			−1.05235			−0.526177	−	0.850375i	$-0.676375\pi$
$107$	−10.8856			−1.05235			−0.526177	+	0.850375i	$0.676375\pi$
$108$		0			0
$109$	−3.28263			−0.314419			−0.157209	−	0.987565i	$-0.550250\pi$
$109$	−3.28263			−0.314419			−0.157209	+	0.987565i	$0.550250\pi$
$110$		0			0
$111$	10.7226	+	13.2220i	1.01774	+	1.25498i
$112$		0			0
$113$	3.22545	+	5.58664i	0.303425	+	0.525547i	0.976909	−	0.213654i	$-0.0685365\pi$
$113$	3.22545	+	5.58664i	0.303425	+	0.525547i	−0.673485	+	0.739201i	$0.735203\pi$
$114$		0			0
$115$	−9.18715	+	15.9126i	−0.856706	+	1.48386i
$116$		0			0
$117$	−2.85185	+	0.931107i	−0.263653	+	0.0860809i
$118$		0			0
$119$	−2.80150	+	4.85235i	−0.256814	+	0.444814i
$120$		0			0
$121$	5.05555	+	8.75646i	0.459595	+	0.796042i
$122$		0			0
$123$	−0.584135	+	1.52496i	−0.0526697	+	0.137501i
$124$		0			0
$125$	−21.8662			−1.95577
$126$		0			0
$127$	−0.828460			−0.0735140			−0.0367570	−	0.999324i	$-0.511703\pi$
$127$	−0.828460			−0.0735140			−0.0367570	+	0.999324i	$0.511703\pi$
$128$		0			0
$129$	15.8450	−	2.52115i	1.39508	−	0.221975i
$130$		0			0
$131$	−2.71574	−	4.70379i	−0.237275	−	0.410972i	0.722656	−	0.691207i	$-0.242921\pi$
$131$	−2.71574	−	4.70379i	−0.237275	−	0.410972i	−0.959931	+	0.280235i	$0.909588\pi$
$132$		0			0
$133$	−0.641315	+	1.11079i	−0.0556091	+	0.0963177i
$134$		0			0
$135$	17.2060	+	11.1216i	1.48086	+	0.957196i
$136$		0			0
$137$	10.5744	−	18.3154i	0.903434	−	1.56479i	0.0804276	−	0.996760i	$-0.474371\pi$
$137$	10.5744	−	18.3154i	0.903434	−	1.56479i	0.823006	−	0.568033i	$-0.192295\pi$
$138$		0			0
$139$	0.923945	+	1.60032i	0.0783680	+	0.135737i	0.902546	−	0.430594i	$-0.141696\pi$
$139$	0.923945	+	1.60032i	0.0783680	+	0.135737i	−0.824178	+	0.566331i	$0.808362\pi$
$140$		0			0
$141$	−9.03611	+	1.43777i	−0.760978	+	0.121082i
$142$		0			0
$143$	−0.942820			−0.0788426
$144$		0			0
$145$	30.2028			2.50820
$146$		0			0
$147$	−0.619562	+	1.61745i	−0.0511006	+	0.133405i
$148$		0			0
$149$	−6.07442	−	10.5212i	−0.497636	−	0.861931i	0.502360	−	0.864658i	$-0.332465\pi$
$149$	−6.07442	−	10.5212i	−0.497636	−	0.861931i	−0.999996	+	0.00272771i	$0.999132\pi$
$150$		0			0
$151$	4.49028	−	7.77740i	0.365414	−	0.632916i	−0.623428	−	0.781880i	$-0.714261\pi$
$151$	4.49028	−	7.77740i	0.365414	−	0.632916i	0.988843	+	0.148965i	$0.0475940\pi$
$152$		0			0
$153$	−3.47141	+	16.4467i	−0.280647	+	1.32963i
$154$		0			0
$155$	15.4331	−	26.7309i	1.23962	−	2.14708i
$156$		0			0
$157$	5.90451	+	10.2269i	0.471232	+	0.816197i	0.999458	−	0.0329062i	$-0.0104763\pi$
$157$	5.90451	+	10.2269i	0.471232	+	0.816197i	−0.528227	+	0.849103i	$0.677143\pi$
$158$		0			0
$159$	10.0647	+	12.4108i	0.798183	+	0.984242i
$160$		0			0
$161$	−4.66019			−0.367274
$162$		0			0
$163$	−12.2826			−0.962050			−0.481025	−	0.876707i	$-0.659735\pi$
$163$	−12.2826			−0.962050			−0.481025	+	0.876707i	$0.659735\pi$
$164$		0			0
$165$	4.05555	+	5.00091i	0.315724	+	0.389320i
$166$		0			0
$167$	11.4428	+	19.8195i	0.885472	+	1.53368i	0.845172	+	0.534495i	$0.179498\pi$
$167$	11.4428	+	19.8195i	0.885472	+	1.53368i	0.0403003	+	0.999188i	$0.487169\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$	−0.794668	+	3.76494i	−0.0607698	+	0.287912i
$172$		0			0
$173$	−9.63160	+	16.6824i	−0.732277	+	1.26834i	0.223631	+	0.974674i	$0.428209\pi$
$173$	−9.63160	+	16.6824i	−0.732277	+	1.26834i	−0.955908	+	0.293667i	$0.905124\pi$
$174$		0			0
$175$	−5.27292	−	9.13296i	−0.398595	−	0.690387i
$176$		0			0
$177$	5.91423	−	15.4399i	0.444541	−	1.16053i
$178$		0			0
$179$	−4.83173			−0.361140			−0.180570	−	0.983562i	$-0.557794\pi$
$179$	−4.83173			−0.361140			−0.180570	+	0.983562i	$0.557794\pi$
$180$		0			0
$181$	3.26320			0.242552			0.121276	−	0.992619i	$-0.461301\pi$
$181$	3.26320			0.242552			0.121276	+	0.992619i	$0.461301\pi$
$182$		0			0
$183$	−18.0390	+	2.87024i	−1.33348	+	0.212175i
$184$		0			0
$185$	−19.3759	−	33.5601i	−1.42455	−	2.46739i
$186$		0			0
$187$	−2.64132	+	4.57489i	−0.193152	+	0.334549i
$188$		0			0
$189$	−0.260877	+	5.18960i	−0.0189760	+	0.377488i
$190$		0			0
$191$	−7.34897	+	12.7288i	−0.531753	+	0.921023i	0.467560	+	0.883961i	$0.345133\pi$
$191$	−7.34897	+	12.7288i	−0.531753	+	0.921023i	−0.999313	+	0.0370616i	$0.988200\pi$
$192$		0			0
$193$	−5.05555	−	8.75646i	−0.363906	−	0.630304i	0.624694	−	0.780870i	$-0.285224\pi$
$193$	−5.05555	−	8.75646i	−0.363906	−	0.630304i	−0.988600	+	0.150566i	$0.951890\pi$
$194$		0			0
$195$	6.74433	−	1.07311i	0.482971	−	0.0768472i
$196$		0			0
$197$	16.6375			1.18537			0.592686	−	0.805434i	$-0.298067\pi$
$197$	16.6375			1.18537			0.592686	+	0.805434i	$0.298067\pi$
$198$		0			0
$199$	13.1111			0.929421			0.464710	−	0.885463i	$-0.346158\pi$
$199$	13.1111			0.929421			0.464710	+	0.885463i	$0.346158\pi$
$200$		0			0
$201$	1.06402	−	2.77776i	0.0750499	−	0.195928i
$202$		0			0
$203$	3.83009	+	6.63392i	0.268820	+	0.465610i
$204$		0			0
$205$	1.85868	−	3.21934i	0.129816	−	0.224848i
$206$		0			0
$207$	−13.2902	+	4.33914i	−0.923730	+	0.301591i
$208$		0			0
$209$	−0.604645	+	1.04728i	−0.0418242	+	0.0724416i
$210$		0			0
$211$	−1.06526	−	1.84509i	−0.0733355	−	0.127021i	0.827026	−	0.562164i	$-0.190031\pi$
$211$	−1.06526	−	1.84509i	−0.0733355	−	0.127021i	−0.900361	+	0.435143i	$0.856698\pi$
$212$		0			0
$213$	−3.86840	−	4.77014i	−0.265058	−	0.326844i
$214$		0			0
$215$	−36.5231			−2.49086
$216$		0			0
$217$	7.82846			0.531431
$218$		0			0
$219$	−2.96457	−	3.65563i	−0.200327	−	0.247024i
$220$		0			0
$221$	2.80150	+	4.85235i	0.188450	+	0.326404i
$222$		0			0
$223$	7.04583	−	12.2037i	0.471824	−	0.817223i	−0.527657	−	0.849458i	$-0.676929\pi$
$223$	7.04583	−	12.2037i	0.471824	−	0.817223i	0.999480	+	0.0322352i	$0.0102626\pi$
$224$		0			0
$225$	−23.5413	−	21.1362i	−1.56942	−	1.40908i
$226$		0			0
$227$	−2.39536	+	4.14888i	−0.158985	+	0.275371i	−0.934503	−	0.355955i	$-0.884156\pi$
$227$	−2.39536	+	4.14888i	−0.158985	+	0.275371i	0.775518	+	0.631326i	$0.217489\pi$
$228$		0			0
$229$	−9.04583	−	15.6678i	−0.597765	−	1.03536i	−0.993150	−	0.116844i	$-0.962722\pi$
$229$	−9.04583	−	15.6678i	−0.597765	−	1.03536i	0.395385	−	0.918516i	$-0.370611\pi$
$230$		0			0
$231$	−0.584135	+	1.52496i	−0.0384333	+	0.100335i
$232$		0			0
$233$	−3.14884			−0.206287			−0.103144	−	0.994666i	$-0.532890\pi$
$233$	−3.14884			−0.206287			−0.103144	+	0.994666i	$0.532890\pi$
$234$		0			0
$235$	20.8285			1.35870
$236$		0			0
$237$	−28.0088	+	4.45657i	−1.81937	+	0.289485i
$238$		0			0
$239$	6.16019	+	10.6698i	0.398470	+	0.690170i	0.993537	−	0.113506i	$-0.0362081\pi$
$239$	6.16019	+	10.6698i	0.398470	+	0.690170i	−0.595068	+	0.803676i	$0.702875\pi$
$240$		0			0
$241$	−7.27292	+	12.5971i	−0.468490	+	0.811448i	−0.999351	−	0.0360106i	$-0.988535\pi$
$241$	−7.27292	+	12.5971i	−0.468490	+	0.811448i	0.530862	+	0.847458i	$0.321868\pi$
$242$		0			0
$243$	4.08809	+	15.0429i	0.262251	+	0.965000i
$244$		0			0
$245$	1.97141	−	3.41458i	0.125949	−	0.218150i
$246$		0			0
$247$	0.641315	+	1.11079i	0.0408059	+	0.0706779i
$248$		0			0
$249$	−0.679065	+	0.108048i	−0.0430340	+	0.00684728i
$250$		0			0
$251$	−2.28263			−0.144078			−0.0720392	−	0.997402i	$-0.522951\pi$
$251$	−2.28263			−0.144078			−0.0720392	+	0.997402i	$0.522951\pi$
$252$		0			0
$253$	−4.39372			−0.276231
$254$		0			0
$255$	13.6871	−	35.7321i	0.857122	−	2.23763i
$256$		0			0
$257$	−0.396990	−	0.687607i	−0.0247636	−	0.0428917i	0.853378	−	0.521293i	$-0.174550\pi$
$257$	−0.396990	−	0.687607i	−0.0247636	−	0.0428917i	−0.878142	+	0.478401i	$0.841217\pi$
$258$		0			0
$259$	4.91423	−	8.51170i	0.305355	−	0.528891i
$260$		0			0
$261$	17.0997	+	15.3527i	1.05845	+	0.950308i
$262$		0			0
$263$	−5.24433	+	9.08344i	−0.323379	+	0.560109i	−0.981183	−	0.193080i	$-0.938152\pi$
$263$	−5.24433	+	9.08344i	−0.323379	+	0.560109i	0.657804	+	0.753189i	$0.271486\pi$
$264$		0			0
$265$	−18.1871	−	31.5011i	−1.11723	−	1.93509i
$266$		0			0
$267$	−6.00916	−	7.40992i	−0.367755	−	0.453479i
$268$		0			0
$269$	10.3398			0.630429			0.315215	−	0.949020i	$-0.397923\pi$
$269$	10.3398			0.630429			0.315215	+	0.949020i	$0.397923\pi$
$270$		0			0
$271$	−30.8285			−1.87270			−0.936348	−	0.351074i	$-0.885817\pi$
$271$	−30.8285			−1.87270			−0.936348	+	0.351074i	$0.885817\pi$
$272$		0			0
$273$	1.09097	+	1.34528i	0.0660286	+	0.0814201i
$274$		0			0
$275$	−4.97141	−	8.61073i	−0.299787	−	0.519247i
$276$		0			0
$277$	−7.12188	+	12.3355i	−0.427913	+	0.741166i	−0.996687	−	0.0813269i	$-0.974084\pi$
$277$	−7.12188	+	12.3355i	−0.427913	+	0.741166i	0.568775	+	0.822493i	$0.307418\pi$
$278$		0			0
$279$	22.3256	−	7.28914i	1.33660	−	0.436389i
$280$		0			0
$281$	4.46169	−	7.72788i	0.266162	−	0.461007i	−0.701705	−	0.712468i	$-0.747578\pi$
$281$	4.46169	−	7.72788i	0.266162	−	0.461007i	0.967868	+	0.251461i	$0.0809109\pi$
$282$		0			0
$283$	11.6316	+	20.1465i	0.691427	+	1.19759i	0.971370	+	0.237570i	$0.0763509\pi$
$283$	11.6316	+	20.1465i	0.691427	+	1.19759i	−0.279944	+	0.960016i	$0.590316\pi$
$284$		0			0
$285$	3.13323	−	8.17973i	0.185597	−	0.484526i
$286$		0			0
$287$	0.942820			0.0556529
$288$		0			0
$289$	14.3937			0.846689
$290$		0			0
$291$	−23.1706	+	3.68675i	−1.35828	+	0.216121i
$292$		0			0
$293$	−11.9412	−	20.6827i	−0.697611	−	1.20830i	−0.969292	−	0.245911i	$-0.920913\pi$
$293$	−11.9412	−	20.6827i	−0.697611	−	1.20830i	0.271681	−	0.962387i	$-0.412420\pi$
$294$		0			0
$295$	−18.8187	+	32.5950i	−1.09567	+	1.89776i
$296$		0			0
$297$	−0.245960	+	4.89286i	−0.0142720	+	0.283912i
$298$		0			0
$299$	−2.33009	+	4.03584i	−0.134753	+	0.233399i
$300$		0			0
$301$	−4.63160	−	8.02217i	−0.266961	−	0.462390i
$302$		0			0
$303$	−4.45254	+	0.708458i	−0.255791	+	0.0406998i
$304$		0			0
$305$	41.5803			2.38088
$306$		0			0
$307$	−7.37429			−0.420873			−0.210436	−	0.977608i	$-0.567489\pi$
$307$	−7.37429			−0.420873			−0.210436	+	0.977608i	$0.567489\pi$
$308$		0			0
$309$	−9.90095	+	25.8478i	−0.563245	+	1.47043i
$310$		0			0
$311$	−4.58577	−	7.94279i	−0.260035	−	0.450394i	0.706216	−	0.707997i	$-0.250401\pi$
$311$	−4.58577	−	7.94279i	−0.260035	−	0.450394i	−0.966251	+	0.257603i	$0.917067\pi$
$312$		0			0
$313$	−8.05555	+	13.9526i	−0.455326	+	0.788648i	−0.998707	−	0.0508381i	$-0.983811\pi$
$313$	−8.05555	+	13.9526i	−0.455326	+	0.788648i	0.543381	+	0.839486i	$0.317144\pi$
$314$		0			0
$315$	2.44282	−	11.5735i	0.137637	−	0.652091i
$316$		0			0
$317$	2.13160	−	3.69204i	0.119723	−	0.207366i	−0.799935	−	0.600086i	$-0.795133\pi$
$317$	2.13160	−	3.69204i	0.119723	−	0.207366i	0.919658	+	0.392721i	$0.128466\pi$
$318$		0			0
$319$	3.61109	+	6.25459i	0.202182	+	0.350190i
$320$		0			0
$321$	11.8759	+	14.6442i	0.662849	+	0.817362i
$322$		0			0
$323$	7.18659			0.399873
$324$		0			0
$325$	−10.5458			−0.584977
$326$		0			0
$327$	3.58126	+	4.41606i	0.198044	+	0.244209i
$328$		0			0
$329$	2.64132	+	4.57489i	0.145620	+	0.252222i
$330$		0			0
$331$	6.14132	−	10.6371i	0.337557	−	0.584666i	−0.646415	−	0.762986i	$-0.723733\pi$
$331$	6.14132	−	10.6371i	0.337557	−	0.584666i	0.983973	+	0.178319i	$0.0570660\pi$
$332$		0			0
$333$	6.08934	−	28.8497i	0.333694	−	1.58096i
$334$		0			0
$335$	−3.38564	+	5.86410i	−0.184977	+	0.320390i
$336$		0			0
$337$	13.4903	+	23.3659i	0.734863	+	1.27282i	0.954784	+	0.297302i	$0.0960867\pi$
$337$	13.4903	+	23.3659i	0.734863	+	1.27282i	−0.219921	+	0.975518i	$0.570580\pi$
$338$		0			0
$339$	3.99673	−	10.4340i	0.217073	−	0.566697i
$340$		0			0
$341$	7.38083			0.399694
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	31.4298	−	5.00091i	1.69213	−	0.269240i
$346$		0			0
$347$	10.7524	+	18.6237i	0.577219	+	0.999773i	0.995797	+	0.0915921i	$0.0291956\pi$
$347$	10.7524	+	18.6237i	0.577219	+	0.999773i	−0.418577	+	0.908181i	$0.637471\pi$
$348$		0			0
$349$	2.54583	−	4.40951i	0.136275	−	0.236035i	−0.789809	−	0.613353i	$-0.789820\pi$
$349$	2.54583	−	4.40951i	0.136275	−	0.236035i	0.926084	+	0.377318i	$0.123154\pi$
$350$		0			0
$351$	4.36389	+	2.82073i	0.232927	+	0.150559i
$352$		0			0
$353$	−4.78426	+	8.28659i	−0.254641	+	0.441051i	−0.964798	−	0.262993i	$-0.915291\pi$
$353$	−4.78426	+	8.28659i	−0.254641	+	0.441051i	0.710157	+	0.704043i	$0.248624\pi$
$354$		0			0
$355$	6.99028	+	12.1075i	0.371006	+	0.642601i
$356$		0			0
$357$	9.58414	−	1.52496i	0.507246	−	0.0807097i
$358$		0			0
$359$	10.9623			0.578565			0.289283	−	0.957244i	$-0.406583\pi$
$359$	10.9623			0.578565			0.289283	+	0.957244i	$0.406583\pi$
$360$		0			0
$361$	−17.3549			−0.913414
$362$		0			0
$363$	6.26444	−	16.3542i	0.328798	−	0.858372i
$364$		0			0
$365$	5.35705	+	9.27868i	0.280401	+	0.485668i
$366$		0			0
$367$	−2.34897	+	4.06853i	−0.122615	+	0.212376i	−0.920798	−	0.390039i	$-0.872461\pi$
$367$	−2.34897	+	4.06853i	−0.122615	+	0.212376i	0.798183	+	0.602415i	$0.205795\pi$
$368$		0			0
$369$	2.68878	−	0.877867i	0.139972	−	0.0456999i
$370$		0			0
$371$	4.61273	−	7.98947i	0.239481	−	0.414793i
$372$		0			0
$373$	−4.63160	−	8.02217i	−0.239815	−	0.415372i	0.720846	−	0.693095i	$-0.243754\pi$
$373$	−4.63160	−	8.02217i	−0.239815	−	0.415372i	−0.960661	+	0.277723i	$0.910420\pi$
$374$		0			0
$375$	23.8554	+	29.4162i	1.23189	+	1.51905i
$376$		0			0
$377$	7.66019			0.394520
$378$		0			0
$379$	−13.5458			−0.695803			−0.347901	−	0.937531i	$-0.613106\pi$
$379$	−13.5458			−0.695803			−0.347901	+	0.937531i	$0.613106\pi$
$380$		0			0
$381$	0.903827	+	1.11451i	0.0463044	+	0.0570982i
$382$		0			0
$383$	−6.13968	−	10.6342i	−0.313723	−	0.543384i	0.665442	−	0.746449i	$-0.268243\pi$
$383$	−6.13968	−	10.6342i	−0.313723	−	0.543384i	−0.979165	+	0.203065i	$0.934910\pi$
$384$		0			0
$385$	1.85868	−	3.21934i	0.0947274	−	0.164073i
$386$		0			0
$387$	−20.6781	−	18.5655i	−1.05113	−	0.943737i
$388$		0			0
$389$	3.75567	−	6.50502i	0.190420	−	0.329818i	−0.754969	−	0.655760i	$-0.772348\pi$
$389$	3.75567	−	6.50502i	0.190420	−	0.329818i	0.945390	+	0.325943i	$0.105682\pi$
$390$		0			0
$391$	13.0555	+	22.6129i	0.660247	+	1.14358i
$392$		0			0
$393$	−3.36513	+	8.78513i	−0.169748	+	0.443151i
$394$		0			0
$395$	64.5609			3.24841
$396$		0			0
$397$	−22.9201			−1.15033			−0.575164	−	0.818038i	$-0.695062\pi$
$397$	−22.9201			−1.15033			−0.575164	+	0.818038i	$0.695062\pi$
$398$		0			0
$399$	2.19398	−	0.349092i	0.109836	−	0.0174764i
$400$		0			0
$401$	10.5631	+	18.2958i	0.527495	+	0.913647i	0.999486	+	0.0320445i	$0.0102018\pi$
$401$	10.5631	+	18.2958i	0.527495	+	0.913647i	−0.471992	+	0.881603i	$0.656465\pi$
$402$		0			0
$403$	3.91423	−	6.77965i	0.194982	−	0.337718i
$404$		0			0
$405$	−3.80959	−	35.2803i	−0.189300	−	1.75309i
$406$		0			0
$407$	4.63323	−	8.02500i	0.229661	−	0.397784i
$408$		0			0
$409$	−1.71737	−	2.97457i	−0.0849185	−	0.147083i	0.820438	−	0.571736i	$-0.193730\pi$
$409$	−1.71737	−	2.97457i	−0.0849185	−	0.147083i	−0.905356	+	0.424652i	$0.860396\pi$
$410$		0			0
$411$	−36.1758	+	5.75605i	−1.78442	+	0.283925i
$412$		0			0
$413$	−9.54583			−0.469720
$414$		0			0
$415$	1.56526			0.0768356
$416$		0			0
$417$	1.14488	−	2.98887i	0.0560651	−	0.146366i
$418$		0			0
$419$	10.2157	+	17.6942i	0.499071	+	0.864417i	0.999999	−	0.00107202i	$-0.000341235\pi$
$419$	10.2157	+	17.6942i	0.499071	+	0.864417i	−0.500928	+	0.865489i	$0.667008\pi$
$420$		0			0
$421$	−7.90451	+	13.6910i	−0.385242	+	0.667260i	−0.991803	−	0.127778i	$-0.959216\pi$
$421$	−7.90451	+	13.6910i	−0.385242	+	0.667260i	0.606560	+	0.795037i	$0.292549\pi$
$422$		0			0
$423$	11.7923	+	10.5876i	0.573363	+	0.514784i
$424$		0			0
$425$	−29.5442	+	51.1720i	−1.43310	+	2.48221i
$426$		0			0
$427$	5.27292	+	9.13296i	0.255174	+	0.441975i
$428$		0			0
$429$	1.02859	+	1.26836i	0.0496608	+	0.0612369i
$430$		0			0
$431$	−26.7518			−1.28859			−0.644296	−	0.764777i	$-0.722849\pi$
$431$	−26.7518			−1.28859			−0.644296	+	0.764777i	$0.722849\pi$
$432$		0			0
$433$	−14.4347			−0.693689			−0.346845	−	0.937923i	$-0.612747\pi$
$433$	−14.4347			−0.693689			−0.346845	+	0.937923i	$0.612747\pi$
$434$		0			0
$435$	−32.9503	−	40.6312i	−1.57985	−	1.94812i
$436$		0			0
$437$	2.98865	+	5.17649i	0.142967	+	0.247625i
$438$		0			0
$439$	19.3187	−	33.4610i	0.922033	−	1.59701i	0.125769	−	0.992060i	$-0.459860\pi$
$439$	19.3187	−	33.4610i	0.922033	−	1.59701i	0.796264	−	0.604949i	$-0.206807\pi$
$440$		0			0
$441$	2.85185	−	0.931107i	0.135802	−	0.0443384i
$442$		0			0
$443$	−5.28263	+	9.14978i	−0.250985	+	0.434719i	−0.963797	−	0.266636i	$-0.914088\pi$
$443$	−5.28263	+	9.14978i	−0.250985	+	0.434719i	0.712812	+	0.701355i	$0.247421\pi$
$444$		0			0
$445$	10.8587	+	18.8078i	0.514751	+	0.891575i
$446$		0			0
$447$	−7.52696	+	19.6501i	−0.356013	+	0.929420i
$448$		0			0
$449$	−9.37429			−0.442400			−0.221200	−	0.975228i	$-0.570997\pi$
$449$	−9.37429			−0.442400			−0.221200	+	0.975228i	$0.570997\pi$
$450$		0			0
$451$	0.888910			0.0418571
$452$		0			0
$453$	−15.3616	+	2.44423i	−0.721749	+	0.114840i
$454$		0			0
$455$	−1.97141	−	3.41458i	−0.0924211	−	0.160078i
$456$		0			0
$457$	−10.3587	+	17.9418i	−0.484559	+	0.839281i	−0.999843	−	0.0177391i	$-0.994353\pi$
$457$	−10.3587	+	17.9418i	−0.484559	+	0.839281i	0.515284	+	0.857020i	$0.327687\pi$
$458$		0			0
$459$	25.9126	−	13.2728i	1.20950	−	0.619522i
$460$		0			0
$461$	−17.6300	+	30.5360i	−0.821109	+	1.42220i	0.0837475	+	0.996487i	$0.473311\pi$
$461$	−17.6300	+	30.5360i	−0.821109	+	1.42220i	−0.904857	+	0.425716i	$0.860022\pi$
$462$		0			0
$463$	−3.55555	−	6.15838i	−0.165240	−	0.286204i	0.771500	−	0.636229i	$-0.219507\pi$
$463$	−3.55555	−	6.15838i	−0.165240	−	0.286204i	−0.936741	+	0.350024i	$0.886173\pi$
$464$		0			0
$465$	−52.7977	+	8.40082i	−2.44843	+	0.389579i
$466$		0			0
$467$	5.03448			0.232968			0.116484	−	0.993193i	$-0.462838\pi$
$467$	5.03448			0.232968			0.116484	+	0.993193i	$0.462838\pi$
$468$		0			0
$469$	−1.71737			−0.0793008
$470$		0			0
$471$	7.31642	−	19.1005i	0.337123	−	0.880105i
$472$		0			0
$473$	−4.36677	−	7.56346i	−0.200784	−	0.347768i
$474$		0			0
$475$	−6.76320	+	11.7142i	−0.310317	+	0.537485i
$476$		0			0
$477$	5.71574	−	27.0797i	0.261706	−	1.23989i
$478$		0			0
$479$	−3.13323	+	5.42692i	−0.143161	+	0.247962i	−0.928685	−	0.370869i	$-0.879060\pi$
$479$	−3.13323	+	5.42692i	−0.143161	+	0.247962i	0.785524	+	0.618831i	$0.212393\pi$
$480$		0			0
$481$	−4.91423	−	8.51170i	−0.224070	−	0.388100i
$482$		0			0
$483$	5.08414	+	6.26926i	0.231336	+	0.285261i
$484$		0			0
$485$	53.4088			2.42517
$486$		0			0
$487$	14.0722			0.637674			0.318837	−	0.947810i	$-0.396708\pi$
$487$	14.0722			0.637674			0.318837	+	0.947810i	$0.396708\pi$
$488$		0			0
$489$	13.4000	+	16.5236i	0.605969	+	0.747222i
$490$		0			0
$491$	−1.97141	−	3.41458i	−0.0889685	−	0.154098i	0.818107	−	0.575066i	$-0.195024\pi$
$491$	−1.97141	−	3.41458i	−0.0889685	−	0.154098i	−0.907075	+	0.420968i	$0.861690\pi$
$492$		0			0
$493$	21.4601	−	37.1699i	0.966512	−	1.67405i
$494$		0			0
$495$	2.30314	−	10.9117i	0.103518	−	0.490444i
$496$		0			0
$497$	−1.77292	+	3.07078i	−0.0795261	+	0.137743i
$498$		0			0
$499$	−9.82846	−	17.0234i	−0.439982	−	0.762072i	0.557705	−	0.830039i	$-0.311682\pi$
$499$	−9.82846	−	17.0234i	−0.439982	−	0.762072i	−0.997688	+	0.0679674i	$0.978349\pi$
$500$		0			0
$501$	14.1791	−	37.0164i	0.633474	−	1.65377i
$502$		0			0
$503$	−10.2632			−0.457613			−0.228807	−	0.973472i	$-0.573482\pi$
$503$	−10.2632			−0.457613			−0.228807	+	0.973472i	$0.573482\pi$
$504$		0			0
$505$	10.2632			0.456706
$506$		0			0
$507$	−20.5264	+	3.26602i	−0.911609	+	0.145049i
$508$		0			0
$509$	−0.669905	−	1.16031i	−0.0296930	−	0.0514298i	0.850797	−	0.525494i	$-0.176120\pi$
$509$	−0.669905	−	1.16031i	−0.0296930	−	0.0514298i	−0.880490	+	0.474065i	$0.842786\pi$
$510$		0			0
$511$	−1.35868	+	2.35331i	−0.0601047	+	0.104104i
$512$		0			0
$513$	5.93186	−	3.03839i	0.261898	−	0.134148i
$514$		0			0
$515$	31.5043	−	54.5670i	1.38824	−	2.40451i
$516$		0			0
$517$	2.49028	+	4.31330i	0.109523	+	0.189699i
$518$		0			0
$519$	32.9503	−	5.24284i	1.44636	−	0.230135i
$520$		0			0
$521$	15.7940			0.691947			0.345973	−	0.938244i	$-0.387549\pi$
$521$	15.7940			0.691947			0.345973	+	0.938244i	$0.387549\pi$
$522$		0			0
$523$	−10.6764			−0.466844			−0.233422	−	0.972376i	$-0.574992\pi$
$523$	−10.6764			−0.466844			−0.233422	+	0.972376i	$0.574992\pi$
$524$		0			0
$525$	−6.53379	+	17.0573i	−0.285158	+	0.744444i
$526$		0			0
$527$	−21.9315	−	37.9864i	−0.955350	−	1.65471i
$528$		0			0
$529$	0.641315	−	1.11079i	0.0278833	−	0.0482952i
$530$		0			0
$531$	−27.2233	+	8.88819i	−1.18139	+	0.385715i
$532$		0			0
$533$	0.471410	−	0.816506i	0.0204190	−	0.0353668i
$534$		0			0
$535$	−21.4601	−	37.1699i	−0.927799	−	1.60700i
$536$		0			0
$537$	5.27128	+	6.50003i	0.227473	+	0.280497i
$538$		0			0
$539$	0.942820			0.0406101
$540$		0			0
$541$	16.6569			0.716137			0.358068	−	0.933695i	$-0.383435\pi$
$541$	16.6569			0.716137			0.358068	+	0.933695i	$0.383435\pi$
$542$		0			0
$543$	−3.56006	−	4.38992i	−0.152777	−	0.188390i
$544$		0			0
$545$	−6.47141	−	11.2088i	−0.277205	−	0.480133i
$546$		0			0
$547$	−7.81875	+	13.5425i	−0.334305	+	0.579034i	−0.983351	−	0.181715i	$-0.941835\pi$
$547$	−7.81875	+	13.5425i	−0.334305	+	0.579034i	0.649046	+	0.760749i	$0.275168\pi$
$548$		0			0
$549$	23.5413	+	21.1362i	1.00472	+	0.902069i
$550$		0			0
$551$	4.91260	−	8.50886i	0.209284	−	0.362490i
$552$		0			0
$553$	8.18715	+	14.1806i	0.348153	+	0.603018i
$554$		0			0
$555$	−24.0092	+	62.6792i	−1.01913	+	2.66058i
$556$		0			0
$557$	−16.7907			−0.711445			−0.355723	−	0.934592i	$-0.615765\pi$
$557$	−16.7907			−0.711445			−0.355723	+	0.934592i	$0.615765\pi$
$558$		0			0
$559$	−9.26320			−0.391792
$560$		0			0
$561$	9.03611	−	1.43777i	0.381505	−	0.0607026i
$562$		0			0
$563$	−7.58577	−	13.1389i	−0.319702	−	0.553740i	0.660724	−	0.750629i	$-0.270249\pi$
$563$	−7.58577	−	13.1389i	−0.319702	−	0.553740i	−0.980426	+	0.196889i	$0.936916\pi$
$564$		0			0
$565$	−12.7174	+	22.0271i	−0.535024	+	0.926688i
$566$		0			0
$567$	7.26608	−	5.31075i	0.305147	−	0.223031i
$568$		0			0
$569$	−17.7632	+	30.7668i	−0.744672	+	1.28981i	0.205676	+	0.978620i	$0.434061\pi$
$569$	−17.7632	+	30.7668i	−0.744672	+	1.28981i	−0.950348	+	0.311190i	$0.899273\pi$
$570$		0			0
$571$	0.772915	+	1.33873i	0.0323455	+	0.0560240i	0.881745	−	0.471726i	$-0.156369\pi$
$571$	0.772915	+	1.33873i	0.0323455	+	0.0560240i	−0.849400	+	0.527750i	$0.823036\pi$
$572$		0			0
$573$	25.1413	−	4.00032i	1.05029	−	0.167116i
$574$		0			0
$575$	−49.1456			−2.04951
$576$		0			0
$577$	−1.67635			−0.0697874			−0.0348937	−	0.999391i	$-0.511109\pi$
$577$	−1.67635			−0.0697874			−0.0348937	+	0.999391i	$0.511109\pi$
$578$		0			0
$579$	−6.26444	+	16.3542i	−0.260341	+	0.679657i
$580$		0			0
$581$	0.198495	+	0.343803i	0.00823496	+	0.0142634i
$582$		0			0
$583$	4.34897	−	7.53264i	0.180116	−	0.311970i
$584$		0			0
$585$	−8.80150	−	7.90228i	−0.363897	−	0.326719i
$586$		0			0
$587$	19.7346	−	34.1813i	0.814535	−	1.41082i	−0.0951271	−	0.995465i	$-0.530326\pi$
$587$	19.7346	−	34.1813i	0.814535	−	1.41082i	0.909662	−	0.415350i	$-0.136341\pi$
$588$		0			0
$589$	−5.02051	−	8.69578i	−0.206866	−	0.358303i
$590$		0			0
$591$	−18.1510	−	22.3821i	−0.746634	−	0.920677i
$592$		0			0
$593$	22.8317			0.937587			0.468793	−	0.883308i	$-0.344689\pi$
$593$	22.8317			0.937587			0.468793	+	0.883308i	$0.344689\pi$
$594$		0			0
$595$	−22.0917			−0.905670
$596$		0			0
$597$	−14.3038	−	17.6381i	−0.585417	−	0.721879i
$598$		0			0
$599$	−22.6375	−	39.2093i	−0.924943	−	1.60205i	−0.791653	−	0.610971i	$-0.790779\pi$
$599$	−22.6375	−	39.2093i	−0.924943	−	1.60205i	−0.133290	−	0.991077i	$-0.542554\pi$
$600$		0			0
$601$	−13.5253	+	23.4265i	−0.551709	+	0.955589i	0.446442	+	0.894813i	$0.352691\pi$
$601$	−13.5253	+	23.4265i	−0.551709	+	0.955589i	−0.998151	+	0.0607761i	$0.980642\pi$
$602$		0			0
$603$	−4.89768	+	1.59906i	−0.199449	+	0.0651186i
$604$		0			0
$605$	−19.9331	+	34.5252i	−0.810396	+	1.40365i
$606$		0			0
$607$	9.32846	+	16.1574i	0.378631	+	0.655807i	0.990863	−	0.134870i	$-0.0430618\pi$
$607$	9.32846	+	16.1574i	0.378631	+	0.655807i	−0.612233	+	0.790678i	$0.709728\pi$
$608$		0			0
$609$	4.74596	−	12.3900i	0.192316	−	0.502067i
$610$		0			0
$611$	5.28263			0.213712
$612$		0			0
$613$	−28.9611			−1.16973			−0.584865	−	0.811131i	$-0.698852\pi$
$613$	−28.9611			−1.16973			−0.584865	+	0.811131i	$0.698852\pi$
$614$		0			0
$615$	−6.35868	+	1.01175i	−0.256407	+	0.0407978i
$616$		0			0
$617$	−18.8457	−	32.6417i	−0.758699	−	1.31411i	−0.943514	−	0.331332i	$-0.892502\pi$
$617$	−18.8457	−	32.6417i	−0.758699	−	1.31411i	0.184815	−	0.982773i	$-0.440831\pi$
$618$		0			0
$619$	−0.00971516	+	0.0168272i	−0.000390485	+	0.000676340i	−0.866221	−	0.499662i	$-0.833458\pi$
$619$	−0.00971516	+	0.0168272i	−0.000390485	+	0.000676340i	0.865830	+	0.500338i	$0.166791\pi$
$620$		0			0
$621$	20.3365	+	13.1451i	0.816077	+	0.527495i
$622$		0			0
$623$	−2.75404	+	4.77014i	−0.110338	+	0.191112i
$624$		0			0
$625$	−16.7427	−	28.9992i	−0.669708	−	1.15997i
$626$		0			0
$627$	2.06853	−	0.329131i	0.0826091	−	0.0131442i
$628$		0			0
$629$	−55.0690			−2.19574
$630$		0			0
$631$	28.4854			1.13399			0.566993	−	0.823723i	$-0.308107\pi$
$631$	28.4854			1.13399			0.566993	+	0.823723i	$0.308107\pi$
$632$		0			0
$633$	−1.31999	+	3.44601i	−0.0524648	+	0.136967i
$634$		0			0
$635$	−1.63323	−	2.82885i	−0.0648129	−	0.112259i
$636$		0			0
$637$	0.500000	−	0.866025i	0.0198107	−	0.0343132i
$638$		0			0
$639$	−2.19686	+	10.4082i	−0.0869064	+	0.411741i
$640$		0			0
$641$	−22.2696	+	38.5722i	−0.879598	+	1.52351i	−0.0278156	+	0.999613i	$0.508855\pi$
$641$	−22.2696	+	38.5722i	−0.879598	+	1.52351i	−0.851783	+	0.523896i	$0.824478\pi$
$642$		0			0
$643$	−4.50972	−	7.81106i	−0.177846	−	0.308038i	0.763297	−	0.646048i	$-0.223579\pi$
$643$	−4.50972	−	7.81106i	−0.177846	−	0.308038i	−0.941142	+	0.338010i	$0.890246\pi$
$644$		0			0
$645$	39.8457	+	49.1339i	1.56892	+	1.93464i
$646$		0			0
$647$	42.8252			1.68363			0.841816	−	0.539765i	$-0.181487\pi$
$647$	42.8252			1.68363			0.841816	+	0.539765i	$0.181487\pi$
$648$		0			0
$649$	−9.00000			−0.353281
$650$		0			0
$651$	−8.54063	−	10.5315i	−0.334734	−	0.412761i
$652$		0			0
$653$	−2.80150	−	4.85235i	−0.109631	−	0.189887i	0.805990	−	0.591930i	$-0.201634\pi$
$653$	−2.80150	−	4.85235i	−0.109631	−	0.189887i	−0.915621	+	0.402043i	$0.868300\pi$
$654$		0			0
$655$	10.7077	−	18.5462i	0.418383	−	0.724660i
$656$		0			0
$657$	−1.68358	+	7.97637i	−0.0656826	+	0.311188i
$658$		0			0
$659$	3.26376	−	5.65299i	0.127138	−	0.220209i	−0.795429	−	0.606047i	$-0.792754\pi$
$659$	3.26376	−	5.65299i	0.127138	−	0.220209i	0.922567	+	0.385838i	$0.126088\pi$
$660$		0			0
$661$	5.50972	+	9.54311i	0.214303	+	0.371184i	0.953057	−	0.302792i	$-0.0979186\pi$
$661$	5.50972	+	9.54311i	0.214303	+	0.371184i	−0.738754	+	0.673976i	$0.764585\pi$
$662$		0			0
$663$	3.47141	−	9.06259i	0.134818	−	0.351962i
$664$		0			0
$665$	−5.05718			−0.196109
$666$		0			0
$667$	35.6979			1.38223
$668$		0			0
$669$	−24.1043	+	3.83531i	−0.931924	+	0.148282i
$670$		0			0
$671$	4.97141	+	8.61073i	0.191919	+	0.332414i
$672$		0			0
$673$	1.67743	−	2.90539i	0.0646602	−	0.111995i	−0.831883	−	0.554951i	$-0.812737\pi$
$673$	1.67743	−	2.90539i	0.0646602	−	0.111995i	0.896543	+	0.442956i	$0.146070\pi$
$674$		0			0
$675$	−2.75116	+	54.7286i	−0.105892	+	2.10651i
$676$		0			0
$677$	20.3187	−	35.1931i	0.780913	−	1.35258i	−0.150498	−	0.988610i	$-0.548088\pi$
$677$	20.3187	−	35.1931i	0.780913	−	1.35258i	0.931411	−	0.363970i	$-0.118579\pi$
$678$		0			0
$679$	6.77292	+	11.7310i	0.259921	+	0.450196i
$680$		0			0
$681$	8.19467	−	1.30388i	0.314020	−	0.0499648i
$682$		0			0
$683$	−14.0755			−0.538584			−0.269292	−	0.963059i	$-0.586790\pi$
$683$	−14.0755			−0.538584			−0.269292	+	0.963059i	$0.586790\pi$
$684$		0			0
$685$	83.3861			3.18602
$686$		0			0
$687$	−11.2089	+	29.2623i	−0.427646	+	1.11643i
$688$		0			0
$689$	−4.61273	−	7.98947i	−0.175731	−	0.304375i
$690$		0			0
$691$	21.9601	−	38.0359i	0.835400	−	1.44696i	−0.0583042	−	0.998299i	$-0.518569\pi$
$691$	21.9601	−	38.0359i	0.835400	−	1.44696i	0.893704	−	0.448656i	$-0.148097\pi$
$692$		0			0
$693$	2.68878	−	0.877867i	0.102138	−	0.0333474i
$694$		0			0
$695$	−3.64295	+	6.30977i	−0.138185	+	0.239343i
$696$		0			0
$697$	−2.64132	−	4.57489i	−0.100047	−	0.173286i
$698$		0			0
$699$	3.43530	+	4.23607i	0.129935	+	0.160223i
$700$		0			0
$701$	7.69578			0.290666			0.145333	−	0.989383i	$-0.453575\pi$
$701$	7.69578			0.290666			0.145333	+	0.989383i	$0.453575\pi$
$702$		0			0
$703$	−12.6063			−0.475455
$704$		0			0
$705$	−22.7233	−	28.0201i	−0.855807	−	1.05530i
$706$		0			0
$707$	1.30150	+	2.25427i	0.0489481	+	0.0847807i
$708$		0			0
$709$	−0.111090	+	0.192414i	−0.00417209	+	0.00722626i	−0.868104	−	0.496383i	$-0.834661\pi$
$709$	−0.111090	+	0.192414i	−0.00417209	+	0.00722626i	0.863932	+	0.503609i	$0.167995\pi$
$710$		0			0
$711$	36.5521	+	32.8177i	1.37081	+	1.23076i
$712$		0			0
$713$	18.2411	−	31.5944i	0.683133	−	1.18322i
$714$		0			0
$715$	−1.85868	−	3.21934i	−0.0695109	−	0.120396i
$716$		0			0
$717$	7.63323	−	19.9276i	0.285068	−	0.744210i
$718$		0			0
$719$	−2.64403			−0.0986056			−0.0493028	−	0.998784i	$-0.515700\pi$
$719$	−2.64403			−0.0986056			−0.0493028	+	0.998784i	$0.515700\pi$
$720$		0			0
$721$	15.9806			0.595148
$722$		0			0
$723$	24.8811	−	3.95892i	0.925339	−	0.147234i
$724$		0			0
$725$	40.3915	+	69.9602i	1.50010	+	2.59826i
$726$		0			0
$727$	−12.7427	+	22.0710i	−0.472600	+	0.818568i	−0.999508	−	0.0313547i	$-0.990018\pi$
$727$	−12.7427	+	22.0710i	−0.472600	+	0.818568i	0.526908	+	0.849922i	$0.323351\pi$
$728$		0			0
$729$	15.7769	−	21.9110i	0.584329	−	0.811517i
$730$		0			0
$731$	−25.9509	+	44.9483i	−0.959829	+	1.66247i
$732$		0			0
$733$	−0.934740	−	1.61902i	−0.0345254	−	0.0597997i	0.848246	−	0.529602i	$-0.177659\pi$
$733$	−0.934740	−	1.61902i	−0.0345254	−	0.0597997i	−0.882772	+	0.469802i	$0.844325\pi$
$734$		0			0
$735$	−6.74433	+	1.07311i	−0.248768	+	0.0395823i
$736$		0			0
$737$	−1.61917			−0.0596429
$738$		0			0
$739$	51.1639			1.88209			0.941047	−	0.338276i	$-0.109844\pi$
$739$	51.1639			1.88209			0.941047	+	0.338276i	$0.109844\pi$
$740$		0			0
$741$	0.794668	−	2.07459i	0.0291929	−	0.0762120i
$742$		0			0
$743$	19.3668	+	33.5442i	0.710498	+	1.23062i	0.964671	+	0.263459i	$0.0848635\pi$
$743$	19.3668	+	33.5442i	0.710498	+	1.23062i	−0.254173	+	0.967159i	$0.581803\pi$
$744$		0			0
$745$	23.9503	−	41.4832i	0.877473	−	1.51983i
$746$		0			0
$747$	0.886196	+	0.795655i	0.0324242	+	0.0291115i
$748$		0			0
$749$	5.44282	−	9.42724i	0.198876	−	0.344464i
$750$		0			0
$751$	−3.09549	−	5.36154i	−0.112956	−	0.195645i	0.804005	−	0.594623i	$-0.202699\pi$
$751$	−3.09549	−	5.36154i	−0.112956	−	0.195645i	−0.916961	+	0.398977i	$0.869365\pi$
$752$		0			0
$753$	2.49028	+	3.07078i	0.0907510	+	0.111905i
$754$		0			0
$755$	35.4088			1.28866
$756$		0			0
$757$	−13.7174			−0.498566			−0.249283	−	0.968431i	$-0.580195\pi$
$757$	−13.7174			−0.498566			−0.249283	+	0.968431i	$0.580195\pi$
$758$		0			0
$759$	4.79342	+	5.91079i	0.173990	+	0.214548i
$760$		0			0
$761$	−19.6602	−	34.0524i	−0.712681	−	1.23440i	−0.963847	−	0.266456i	$-0.914147\pi$
$761$	−19.6602	−	34.0524i	−0.712681	−	1.23440i	0.251166	−	0.967944i	$-0.419186\pi$
$762$		0			0
$763$	1.64132	−	2.84284i	0.0594196	−	0.102918i
$764$		0			0
$765$	−63.0021	+	20.5697i	−2.27784	+	0.743699i
$766$		0			0
$767$	−4.77292	+	8.26693i	−0.172340	+	0.298502i
$768$		0			0
$769$	−11.3646	−	19.6840i	−0.409817	−	0.709824i	0.585052	−	0.810996i	$-0.301074\pi$
$769$	−11.3646	−	19.6840i	−0.409817	−	0.709824i	−0.994869	+	0.101172i	$0.967741\pi$
$770$		0			0
$771$	−0.491920	+	1.28422i	−0.0177161	+	0.0462502i
$772$		0			0
$773$	−28.7324			−1.03343			−0.516717	−	0.856156i	$-0.672846\pi$
$773$	−28.7324			−1.03343			−0.516717	+	0.856156i	$0.672846\pi$
$774$		0			0
$775$	82.5576			2.96556
$776$		0			0
$777$	−16.8119	+	2.67500i	−0.603124	+	0.0959651i
$778$		0			0
$779$	−0.604645	−	1.04728i	−0.0216636	−	0.0375225i
$780$		0			0
$781$	−1.67154	+	2.89519i	−0.0598124	+	0.103598i
$782$		0			0
$783$	1.99837	−	39.7533i	0.0714157	−	1.42067i
$784$		0			0
$785$	−23.2804	+	40.3229i	−0.830915	+	1.43919i
$786$		0			0
$787$	27.0059	+	46.7756i	0.962656	+	1.66737i	0.715785	+	0.698321i	$0.246069\pi$
$787$	27.0059	+	46.7756i	0.962656	+	1.66737i	0.246871	+	0.969048i	$0.420598\pi$
$788$		0			0
$789$	17.9412	−	2.85468i	0.638723	−	0.101629i
$790$		0			0
$791$	−6.45090			−0.229368
$792$		0			0
$793$	10.5458			0.374493
$794$		0			0
$795$	−22.5361	+	58.8336i	−0.799274	+	2.08661i
$796$		0			0
$797$	0.103565	+	0.179381i	0.00366848	+	0.00635399i	0.867854	−	0.496820i	$-0.165499\pi$
$797$	0.103565	+	0.179381i	0.00366848	+	0.00635399i	−0.864185	+	0.503174i	$0.832166\pi$
$798$		0			0
$799$	14.7993	−	25.6332i	0.523562	−	0.906836i
$800$		0			0
$801$	−3.41260	+	16.1680i	−0.120578	+	0.571269i
$802$		0			0
$803$	−1.28100	+	2.21875i	−0.0452053	+	0.0782980i
$804$		0			0
$805$	−9.18715	−	15.9126i	−0.323804	−	0.560846i
$806$		0			0
$807$	−11.2804	−	13.9099i	−0.397090	−	0.489653i
$808$		0			0
$809$	−36.0539			−1.26759			−0.633794	−	0.773502i	$-0.718503\pi$
$809$	−36.0539			−1.26759			−0.633794	+	0.773502i	$0.718503\pi$
$810$		0			0
$811$	−2.01943			−0.0709118			−0.0354559	−	0.999371i	$-0.511288\pi$
$811$	−2.01943			−0.0709118			−0.0354559	+	0.999371i	$0.511288\pi$
$812$		0			0
$813$	33.6330	+	41.4729i	1.17956	+	1.45452i
$814$		0			0
$815$	−24.2141	−	41.9401i	−0.848183	−	1.46910i
$816$		0			0
$817$	−5.94063	+	10.2895i	−0.207836	+	0.359983i
$818$		0			0
$819$	0.619562	−	2.93533i	0.0216492	−	0.102569i
$820$		0			0
$821$	15.1871	−	26.3049i	0.530035	−	0.918048i	−0.469351	−	0.883012i	$-0.655512\pi$
$821$	15.1871	−	26.3049i	0.530035	−	0.918048i	0.999386	−	0.0350359i	$-0.0111546\pi$
$822$		0			0
$823$	6.56526	+	11.3714i	0.228851	+	0.396381i	0.957468	−	0.288540i	$-0.0931699\pi$
$823$	6.56526	+	11.3714i	0.228851	+	0.396381i	−0.728617	+	0.684921i	$0.759837\pi$
$824$		0			0
$825$	−6.16019	+	16.0820i	−0.214470	+	0.559904i
$826$		0			0
$827$	−11.3236			−0.393762			−0.196881	−	0.980427i	$-0.563081\pi$
$827$	−11.3236			−0.393762			−0.196881	+	0.980427i	$0.563081\pi$
$828$		0			0
$829$	−11.0604			−0.384145			−0.192073	−	0.981381i	$-0.561521\pi$
$829$	−11.0604			−0.384145			−0.192073	+	0.981381i	$0.561521\pi$
$830$		0			0
$831$	24.3644	−	3.87671i	0.845193	−	0.134482i
$832$		0			0
$833$	−2.80150	−	4.85235i	−0.0970664	−	0.168124i
$834$		0			0
$835$	−45.1170	+	78.1449i	−1.56134	+	2.70432i
$836$		0			0
$837$	−34.1625	−	22.0819i	−1.18083	−	0.763263i
$838$		0			0
$839$	−5.27128	+	9.13013i	−0.181985	+	0.315207i	−0.942556	−	0.334047i	$-0.891586\pi$
$839$	−5.27128	+	9.13013i	−0.181985	+	0.315207i	0.760572	+	0.649254i	$0.224919\pi$
$840$		0			0
$841$	−14.8393	−	25.7023i	−0.511698	−	0.886288i
$842$		0			0
$843$	−15.2638	+	2.42867i	−0.525712	+	0.0836478i
$844$		0			0
$845$	47.3138			1.62765
$846$		0			0
$847$	−10.1111			−0.347421
$848$		0			0
$849$	14.4130	−	37.6271i	0.494652	−	1.29136i
$850$		0			0
$851$	−22.9012	−	39.6661i	−0.785045	−	1.35974i
$852$		0			0
$853$	13.6413	−	23.6275i	0.467070	−	0.808989i	−0.532223	−	0.846604i	$-0.678643\pi$
$853$	13.6413	−	23.6275i	0.467070	−	0.808989i	0.999292	+	0.0376160i	$0.0119764\pi$
$854$		0			0
$855$	−14.4223	+	4.70878i	−0.493233	+	0.161037i
$856$		0			0
$857$	1.21574	−	2.10571i	0.0415287	−	0.0719299i	−0.844514	−	0.535534i	$-0.820111\pi$
$857$	1.21574	−	2.10571i	0.0415287	−	0.0719299i	0.886043	+	0.463604i	$0.153444\pi$
$858$		0			0
$859$	15.8743	+	27.4951i	0.541624	+	0.938120i	0.998811	+	0.0487495i	$0.0155236\pi$
$859$	15.8743	+	27.4951i	0.541624	+	0.938120i	−0.457187	+	0.889370i	$0.651143\pi$
$860$		0			0
$861$	−1.02859	−	1.26836i	−0.0350543	−	0.0432255i
$862$		0			0
$863$	−27.8252			−0.947181			−0.473590	−	0.880745i	$-0.657042\pi$
$863$	−27.8252			−0.947181			−0.473590	+	0.880745i	$0.657042\pi$
$864$		0			0
$865$	−75.9513			−2.58242
$866$		0			0
$867$	−15.7031	−	19.3636i	−0.533307	−	0.657622i
$868$		0			0
$869$	7.71900	+	13.3697i	0.261849	+	0.453536i
$870$		0			0
$871$	−0.858685	+	1.48729i	−0.0290954	+	0.0503948i
$872$		0			0
$873$	30.2382	+	27.1488i	1.02341	+	0.918848i
$874$		0			0
$875$	10.9331	−	18.9367i	0.369606	−	0.640177i
$876$		0			0
$877$	2.29342	+	3.97233i	0.0774434	+	0.134136i	0.902146	−	0.431430i	$-0.141991\pi$
$877$	2.29342	+	3.97233i	0.0774434	+	0.134136i	−0.824703	+	0.565566i	$0.808658\pi$
$878$		0			0
$879$	−14.7966	+	38.6285i	−0.499077	+	1.30291i
$880$		0			0
$881$	57.4465			1.93542			0.967711	−	0.252062i	$-0.0811085\pi$
$881$	57.4465			1.93542			0.967711	+	0.252062i	$0.0811085\pi$
$882$		0			0
$883$	36.3937			1.22475			0.612373	−	0.790569i	$-0.290215\pi$
$883$	36.3937			1.22475			0.612373	+	0.790569i	$0.290215\pi$
$884$		0			0
$885$	64.3802	−	10.2437i	2.16412	−	0.344340i
$886$		0			0
$887$	21.7238	+	37.6268i	0.729414	+	1.26338i	0.957131	+	0.289655i	$0.0935407\pi$
$887$	21.7238	+	37.6268i	0.729414	+	1.26338i	−0.227717	+	0.973727i	$0.573126\pi$
$888$		0			0
$889$	0.414230	−	0.717468i	0.0138928	−	0.0240631i
$890$		0			0
$891$	6.85060	−	5.00708i	0.229504	−	0.167744i
$892$		0			0
$893$	3.38783	−	5.86789i	0.113369	−	0.196362i
$894$		0			0
$895$	−9.52532	−	16.4983i	−0.318396	−	0.551479i
$896$		0			0
$897$	7.97141	−	1.26836i	0.266158	−	0.0423492i
$898$		0			0
$899$	−59.9675			−2.00003
$900$		0			0
$901$	−51.6903			−1.72205
$902$		0			0
$903$	−5.73912	+	14.9828i	−0.190986	+	0.498595i
$904$		0			0
$905$	6.43310	+	11.1425i	0.213844	+	0.370388i
$906$		0			0
$907$	−11.1569	+	19.3244i	−0.370459	+	0.641655i	−0.989636	−	0.143597i	$-0.954133\pi$
$907$	−11.1569	+	19.3244i	−0.370459	+	0.641655i	0.619177	+	0.785252i	$0.287466\pi$
$908$		0			0
$909$	5.81066	+	5.21700i	0.192728	+	0.173037i
$910$		0			0
$911$	7.67799	−	13.2987i	0.254383	−	0.440604i	−0.710345	−	0.703854i	$-0.751461\pi$
$911$	7.67799	−	13.2987i	0.254383	−	0.440604i	0.964728	+	0.263250i	$0.0847943\pi$
$912$		0			0
$913$	0.187145	+	0.324145i	0.00619360	+	0.0107276i
$914$		0			0
$915$	−45.3629	−	55.9372i	−1.49965	−	1.84923i
$916$		0			0
$917$	5.43147			0.179363
$918$		0			0
$919$	−36.8285			−1.21486			−0.607429	−	0.794374i	$-0.707799\pi$
$919$	−36.8285			−1.21486			−0.607429	+	0.794374i	$0.707799\pi$
$920$		0			0
$921$	8.04514	+	9.92049i	0.265096	+	0.326891i
$922$		0			0
$923$	1.77292	+	3.07078i	0.0583562	+	0.101076i
$924$		0			0
$925$	51.8246	−	89.7629i	1.70398	−	2.95139i
$926$		0			0
$927$	45.5742	−	14.8796i	1.49685	−	0.488711i
$928$		0			0
$929$	20.8646	−	36.1385i	0.684545	−	1.18567i	−0.289035	−	0.957318i	$-0.593334\pi$
$929$	20.8646	−	36.1385i	0.684545	−	1.18567i	0.973580	−	0.228347i	$-0.0733322\pi$
$930$		0			0
$931$	−0.641315	−	1.11079i	−0.0210183	−	0.0364047i
$932$		0			0
$933$	−5.68233	+	14.8345i	−0.186031	+	0.485660i
$934$		0			0
$935$	−20.8285			−0.681163
$936$		0			0
$937$	−25.3743			−0.828942			−0.414471	−	0.910063i	$-0.636033\pi$
$937$	−25.3743			−0.828942			−0.414471	+	0.910063i	$0.636033\pi$
$938$		0			0
$939$	27.5586	−	4.38493i	0.899340	−	0.143097i
$940$		0			0
$941$	−23.5712	−	40.8264i	−0.768398	−	1.33090i	−0.938431	−	0.345465i	$-0.887721\pi$
$941$	−23.5712	−	40.8264i	−0.768398	−	1.33090i	0.170034	−	0.985438i	$-0.445612\pi$
$942$		0			0
$943$	2.19686	−	3.80507i	0.0715396	−	0.123910i
$944$		0			0
$945$	−18.2346	+	9.34004i	−0.593172	+	0.303832i
$946$		0			0
$947$	17.2535	−	29.8839i	0.560663	−	0.971097i	−0.436776	−	0.899570i	$-0.643880\pi$
$947$	17.2535	−	29.8839i	0.560663	−	0.971097i	0.997439	−	0.0715263i	$-0.0227870\pi$
$948$		0			0
$949$	1.35868	+	2.35331i	0.0441048	+	0.0763917i
$950$		0			0
$951$	−7.29235	+	1.16031i	−0.236470	+	0.0376256i
$952$		0			0
$953$	−44.1833			−1.43124			−0.715619	−	0.698491i	$-0.753855\pi$
$953$	−44.1833			−1.43124			−0.715619	+	0.698491i	$0.753855\pi$
$954$		0			0
$955$	−57.9513			−1.87526
$956$		0			0
$957$	4.47459	−	11.6815i	0.144643	−	0.377610i
$958$		0			0
$959$	10.5744	+	18.3154i	0.341466	+	0.591436i
$960$		0			0
$961$	−15.1424	+	26.2274i	−0.488464	+	0.846045i
$962$		0			0
$963$	6.74433	−	31.9529i	0.217333	−	1.02967i
$964$		0			0
$965$	19.9331	−	34.5252i	0.641669	−	1.11140i
$966$		0			0
$967$	−21.2330	−	36.7766i	−0.682806	−	1.18266i	−0.974121	−	0.226028i	$-0.927426\pi$
$967$	−21.2330	−	36.7766i	−0.682806	−	1.18266i	0.291314	−	0.956627i	$-0.405907\pi$
$968$		0			0
$969$	−7.84037	−	9.66798i	−0.251869	−	0.310580i
$970$		0			0
$971$	6.05391			0.194279			0.0971396	−	0.995271i	$-0.469031\pi$
$971$	6.05391			0.194279			0.0971396	+	0.995271i	$0.469031\pi$
$972$		0			0
$973$	−1.84789			−0.0592406
$974$		0			0
$975$	11.5052	+	14.1871i	0.368461	+	0.454351i
$976$		0			0
$977$	22.0264	+	38.1508i	0.704687	+	1.22055i	0.966804	+	0.255518i	$0.0822459\pi$
$977$	22.0264	+	38.1508i	0.704687	+	1.22055i	−0.262117	+	0.965036i	$0.584421\pi$
$978$		0			0
$979$	−2.59656	+	4.49738i	−0.0829866	+	0.143737i
$980$		0			0
$981$	2.03379	−	9.63559i	0.0649340	−	0.307641i
$982$		0			0
$983$	2.23517	−	3.87142i	0.0712907	−	0.123479i	−0.828177	−	0.560467i	$-0.810622\pi$
$983$	2.23517	−	3.87142i	0.0712907	−	0.123479i	0.899467	+	0.436988i	$0.143955\pi$
$984$		0			0
$985$	32.7993	+	56.8101i	1.04507	+	1.81012i
$986$		0			0
$987$	3.27292	−	8.54439i	0.104178	−	0.271971i
$988$		0			0
$989$	−43.1683			−1.37267
$990$		0			0
$991$	−31.5048			−1.00078			−0.500392	−	0.865799i	$-0.666811\pi$
$991$	−31.5048			−1.00078			−0.500392	+	0.865799i	$0.666811\pi$
$992$		0			0
$993$	−21.0098	+	3.34295i	−0.666727	+	0.106085i
$994$		0			0
$995$	25.8473	+	44.7689i	0.819416	+	1.41927i
$996$		0			0
$997$	−13.0000	+	22.5167i	−0.411714	+	0.713110i	−0.995077	−	0.0991016i	$-0.968403\pi$
$997$	−13.0000	+	22.5167i	−0.411714	+	0.713110i	0.583363	+	0.812211i	$0.301736\pi$
$998$		0			0
$999$	−45.4543	+	23.2824i	−1.43811	+	0.736622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.j.b.169.1	yes	6
3.2	odd	2		756.2.j.a.505.1		6
4.3	odd	2		1008.2.r.g.673.3		6
7.2	even	3		1764.2.i.f.1537.3		6
7.3	odd	6		1764.2.l.g.961.2		6
7.4	even	3		1764.2.l.d.961.2		6
7.5	odd	6		1764.2.i.e.1537.1		6
7.6	odd	2		1764.2.j.d.1177.3		6
9.2	odd	6		2268.2.a.j.1.3		3
9.4	even	3	inner	252.2.j.b.85.1	✓	6
9.5	odd	6		756.2.j.a.253.1		6
9.7	even	3		2268.2.a.g.1.1		3
12.11	even	2		3024.2.r.i.2017.1		6
21.2	odd	6		5292.2.i.d.2125.1		6
21.5	even	6		5292.2.i.g.2125.3		6
21.11	odd	6		5292.2.l.g.3313.3		6
21.17	even	6		5292.2.l.d.3313.1		6
21.20	even	2		5292.2.j.e.3529.3		6
36.7	odd	6		9072.2.a.bt.1.1		3
36.11	even	6		9072.2.a.bz.1.3		3
36.23	even	6		3024.2.r.i.1009.1		6
36.31	odd	6		1008.2.r.g.337.3		6
63.4	even	3		1764.2.i.f.373.3		6
63.5	even	6		5292.2.l.d.361.1		6
63.13	odd	6		1764.2.j.d.589.3		6
63.23	odd	6		5292.2.l.g.361.3		6
63.31	odd	6		1764.2.i.e.373.1		6
63.32	odd	6		5292.2.i.d.1549.1		6
63.40	odd	6		1764.2.l.g.949.2		6
63.41	even	6		5292.2.j.e.1765.3		6
63.58	even	3		1764.2.l.d.949.2		6
63.59	even	6		5292.2.i.g.1549.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.j.b.85.1	✓	6	9.4	even	3	inner
252.2.j.b.169.1	yes	6	1.1	even	1	trivial
756.2.j.a.253.1		6	9.5	odd	6
756.2.j.a.505.1		6	3.2	odd	2
1008.2.r.g.337.3		6	36.31	odd	6
1008.2.r.g.673.3		6	4.3	odd	2
1764.2.i.e.373.1		6	63.31	odd	6
1764.2.i.e.1537.1		6	7.5	odd	6
1764.2.i.f.373.3		6	63.4	even	3
1764.2.i.f.1537.3		6	7.2	even	3
1764.2.j.d.589.3		6	63.13	odd	6
1764.2.j.d.1177.3		6	7.6	odd	2
1764.2.l.d.949.2		6	63.58	even	3
1764.2.l.d.961.2		6	7.4	even	3
1764.2.l.g.949.2		6	63.40	odd	6
1764.2.l.g.961.2		6	7.3	odd	6
2268.2.a.g.1.1		3	9.7	even	3
2268.2.a.j.1.3		3	9.2	odd	6
3024.2.r.i.1009.1		6	36.23	even	6
3024.2.r.i.2017.1		6	12.11	even	2
5292.2.i.d.1549.1		6	63.32	odd	6
5292.2.i.d.2125.1		6	21.2	odd	6
5292.2.i.g.1549.3		6	63.59	even	6
5292.2.i.g.2125.3		6	21.5	even	6
5292.2.j.e.1765.3		6	63.41	even	6
5292.2.j.e.3529.3		6	21.20	even	2
5292.2.l.d.361.1		6	63.5	even	6
5292.2.l.d.3313.1		6	21.17	even	6
5292.2.l.g.361.3		6	63.23	odd	6
5292.2.l.g.3313.3		6	21.11	odd	6
9072.2.a.bt.1.1		3	36.7	odd	6
9072.2.a.bz.1.3		3	36.11	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.09097 - 1.34528i) q^{3} +(1.97141 + 3.41458i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.619562 + 2.93533i) q^{9} +(-0.471410 + 0.816506i) q^{11} +(0.500000 + 0.866025i) q^{13} +(2.44282 - 6.37731i) q^{15} +5.60301 q^{17} +1.28263 q^{19} +(1.71053 - 0.272169i) q^{21} +(2.33009 + 4.03584i) q^{23} +(-5.27292 + 9.13296i) q^{25} +(4.62476 - 2.36887i) q^{27} +(3.83009 - 6.63392i) q^{29} +(-3.91423 - 6.77965i) q^{31} +(1.61273 - 0.256606i) q^{33} -3.94282 q^{35} -9.82846 q^{37} +(0.619562 - 1.61745i) q^{39} +(-0.471410 - 0.816506i) q^{41} +(-4.63160 + 8.02217i) q^{43} +(-11.2443 + 3.67119i) q^{45} +(2.64132 - 4.57489i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-6.11273 - 7.53762i) q^{51} -9.22545 q^{53} -3.71737 q^{55} +(-1.39931 - 1.72550i) q^{57} +(4.77292 + 8.26693i) q^{59} +(5.27292 - 9.13296i) q^{61} +(-2.23229 - 2.00422i) q^{63} +(-1.97141 + 3.41458i) q^{65} +(0.858685 + 1.48729i) q^{67} +(2.88727 - 7.53762i) q^{69} +3.54583 q^{71} +2.71737 q^{73} +(18.0390 - 2.87024i) q^{75} +(-0.471410 - 0.816506i) q^{77} +(8.18715 - 14.1806i) q^{79} +(-8.23229 - 3.63723i) q^{81} +(0.198495 - 0.343803i) q^{83} +(11.0458 + 19.1319i) q^{85} +(-13.1030 + 2.08486i) q^{87} +5.50808 q^{89} -1.00000 q^{91} +(-4.85021 + 12.6621i) q^{93} +(2.52859 + 4.37965i) q^{95} +(6.77292 - 11.7310i) q^{97} +(-2.10464 - 1.88962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{3} + 3 q^{5} - 3 q^{7} - 4 q^{9} + 6 q^{11} + 3 q^{13} - 3 q^{15} + 6 q^{19} + 2 q^{21} + 6 q^{23} - 6 q^{25} - 7 q^{27} + 15 q^{29} + 3 q^{31} - 6 q^{35} - 6 q^{37} + 4 q^{39} + 6 q^{41} - 3 q^{43}+ \cdots - 24 q^{99}+O(q^{100}) \) 6 * q + 2 * q^3 + 3 * q^5 - 3 * q^7 - 4 * q^9 + 6 * q^11 + 3 * q^13 - 3 * q^15 + 6 * q^19 + 2 * q^21 + 6 * q^23 - 6 * q^25 - 7 * q^27 + 15 * q^29 + 3 * q^31 - 6 * q^35 - 6 * q^37 + 4 * q^39 + 6 * q^41 - 3 * q^43 - 33 * q^45 + 15 * q^47 - 3 * q^49 - 27 * q^51 - 36 * q^53 - 24 * q^55 + 7 * q^57 + 3 * q^59 + 6 * q^61 - 4 * q^63 - 3 * q^65 + 6 * q^67 + 27 * q^69 - 30 * q^71 + 18 * q^73 + 47 * q^75 + 6 * q^77 - 3 * q^79 - 40 * q^81 + 18 * q^83 + 15 * q^85 - 45 * q^87 + 12 * q^89 - 6 * q^91 + 25 * q^93 + 24 * q^95 + 15 * q^97 - 24 * q^99

Introduction

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