LMFDB - Embedded newform 1008.2.r.g.673.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(337,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 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("1008.337"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.r (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,-2,0,3,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
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:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			673.3
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	1008.673
Dual form			1008.2.r.g.337.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.09097 + 1.34528i) q^{3} +(1.97141 + 3.41458i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-0.619562 + 2.93533i) q^{9} +(0.471410 - 0.816506i) q^{11} +(0.500000 + 0.866025i) q^{13} +(-2.44282 + 6.37731i) q^{15} +5.60301 q^{17} -1.28263 q^{19} +(1.71053 - 0.272169i) q^{21} +(-2.33009 - 4.03584i) q^{23} +(-5.27292 + 9.13296i) q^{25} +(-4.62476 + 2.36887i) q^{27} +(3.83009 - 6.63392i) q^{29} +(3.91423 + 6.77965i) q^{31} +(1.61273 - 0.256606i) q^{33} +3.94282 q^{35} -9.82846 q^{37} +(-0.619562 + 1.61745i) q^{39} +(-0.471410 - 0.816506i) q^{41} +(4.63160 - 8.02217i) q^{43} +(-11.2443 + 3.67119i) q^{45} +(-2.64132 + 4.57489i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(6.11273 + 7.53762i) q^{51} -9.22545 q^{53} +3.71737 q^{55} +(-1.39931 - 1.72550i) q^{57} +(-4.77292 - 8.26693i) q^{59} +(5.27292 - 9.13296i) q^{61} +(2.23229 + 2.00422i) q^{63} +(-1.97141 + 3.41458i) q^{65} +(-0.858685 - 1.48729i) q^{67} +(2.88727 - 7.53762i) q^{69} -3.54583 q^{71} +2.71737 q^{73} +(-18.0390 + 2.87024i) q^{75} +(-0.471410 - 0.816506i) q^{77} +(-8.18715 + 14.1806i) q^{79} +(-8.23229 - 3.63723i) q^{81} +(-0.198495 + 0.343803i) q^{83} +(11.0458 + 19.1319i) q^{85} +(13.1030 - 2.08486i) q^{87} +5.50808 q^{89} +1.00000 q^{91} +(-4.85021 + 12.6621i) q^{93} +(-2.52859 - 4.37965i) q^{95} +(6.77292 - 11.7310i) q^{97} +(2.10464 + 1.88962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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	−0.786165	−	0.618017i	$-0.787936\pi$
$11$	0.471410	−	0.816506i	0.142135	−	0.246186i	0.928301	+	0.371831i	$0.121270\pi$
$12$		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	$-0.547003\pi$
$19$	−1.28263			−0.294256			−0.147128	+	0.989117i	$0.547003\pi$
$20$		0			0
$21$	1.71053	−	0.272169i	0.373269	−	0.0593921i
$22$		0			0
$23$	−2.33009	−	4.03584i	−0.485858	−	0.841531i	0.514010	−	0.857784i	$-0.328160\pi$
$23$	−2.33009	−	4.03584i	−0.485858	−	0.841531i	−0.999868	+	0.0162531i	$0.994826\pi$
$24$		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	$0.0814973\pi$
$31$	3.91423	+	6.77965i	0.703016	+	1.21766i	−0.264386	+	0.964417i	$0.585169\pi$
$32$		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	$-0.583691\pi$
$43$	4.63160	−	8.02217i	0.706312	−	1.22337i	0.966216	−	0.257734i	$-0.0829759\pi$
$44$		0			0
$45$	−11.2443	+	3.67119i	−1.67621	+	0.547268i
$46$		0			0
$47$	−2.64132	+	4.57489i	−0.385275	+	0.667317i	−0.991807	−	0.127743i	$-0.959227\pi$
$47$	−2.64132	+	4.57489i	−0.385275	+	0.667317i	0.606532	+	0.795059i	$0.292560\pi$
$48$		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	$-0.953239\pi$
$59$	−4.77292	−	8.26693i	−0.621381	−	1.07626i	0.367848	−	0.929886i	$-0.380095\pi$
$60$		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	0.808794	−	0.588092i	$-0.200121\pi$
$67$	−0.858685	−	1.48729i	−0.104905	−	0.181701i	−0.913699	+	0.406391i	$0.866787\pi$
$68$		0			0
$69$	2.88727	−	7.53762i	0.347587	−	0.907423i
$70$		0			0
$71$	−3.54583			−0.420813			−0.210406	−	0.977614i	$-0.567479\pi$
$71$	−3.54583			−0.420813			−0.210406	+	0.977614i	$0.567479\pi$
$72$		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	$0.539396\pi$
$79$	−8.18715	+	14.1806i	−0.921126	+	1.59544i	−0.797676	+	0.603086i	$0.793938\pi$
$80$		0			0
$81$	−8.23229	−	3.63723i	−0.914699	−	0.404137i
$82$		0			0
$83$	−0.198495	+	0.343803i	−0.0217877	+	0.0377373i	−0.876714	−	0.481013i	$-0.840269\pi$
$83$	−0.198495	+	0.343803i	−0.0217877	+	0.0377373i	0.854926	+	0.518750i	$0.173602\pi$
$84$		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	$0.121858\pi$
$103$	7.99028	+	13.8396i	0.787306	+	1.36365i	−0.140305	+	0.990108i	$0.544808\pi$
$104$		0			0
$105$	4.30150	+	5.30420i	0.419784	+	0.517637i
$106$		0			0
$107$	10.8856			1.05235			0.526177	−	0.850375i	$-0.323625\pi$
$107$	10.8856			1.05235			0.526177	+	0.850375i	$0.323625\pi$
$108$		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	$-0.488297\pi$
$127$	0.828460			0.0735140			0.0367570	+	0.999324i	$0.488297\pi$
$128$		0			0
$129$	15.8450	−	2.52115i	1.39508	−	0.221975i
$130$		0			0
$131$	2.71574	+	4.70379i	0.237275	+	0.410972i	0.959931	−	0.280235i	$-0.0904125\pi$
$131$	2.71574	+	4.70379i	0.237275	+	0.410972i	−0.722656	+	0.691207i	$0.757079\pi$
$132$		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	0.824178	−	0.566331i	$-0.191638\pi$
$139$	−0.923945	−	1.60032i	−0.0783680	−	0.135737i	−0.902546	+	0.430594i	$0.858304\pi$
$140$		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	−0.988843	−	0.148965i	$-0.952406\pi$
$151$	−4.49028	+	7.77740i	−0.365414	+	0.632916i	0.623428	+	0.781880i	$0.285739\pi$
$152$		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	$-0.340265\pi$
$163$	12.2826			0.962050			0.481025	+	0.876707i	$0.340265\pi$
$164$		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	$-0.820502\pi$
$167$	−11.4428	−	19.8195i	−0.885472	−	1.53368i	−0.0403003	−	0.999188i	$-0.512831\pi$
$168$		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	$-0.442206\pi$
$179$	4.83173			0.361140			0.180570	+	0.983562i	$0.442206\pi$
$180$		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	$-0.654867\pi$
$191$	7.34897	−	12.7288i	0.531753	−	0.921023i	0.999313	−	0.0370616i	$-0.0117998\pi$
$192$		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	$-0.653842\pi$
$199$	−13.1111			−0.929421			−0.464710	+	0.885463i	$0.653842\pi$
$200$		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	0.900361	−	0.435143i	$-0.143302\pi$
$211$	1.06526	+	1.84509i	0.0733355	+	0.127021i	−0.827026	+	0.562164i	$0.809969\pi$
$212$		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	−0.999480	−	0.0322352i	$-0.989737\pi$
$223$	−7.04583	+	12.2037i	−0.471824	+	0.817223i	0.527657	+	0.849458i	$0.323071\pi$
$224$		0			0
$225$	−23.5413	−	21.1362i	−1.56942	−	1.40908i
$226$		0			0
$227$	2.39536	−	4.14888i	0.158985	−	0.275371i	−0.775518	−	0.631326i	$-0.782511\pi$
$227$	2.39536	−	4.14888i	0.158985	−	0.275371i	0.934503	+	0.355955i	$0.115844\pi$
$228$		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	0.595068	−	0.803676i	$-0.297125\pi$
$239$	−6.16019	−	10.6698i	−0.398470	−	0.690170i	−0.993537	+	0.113506i	$0.963792\pi$
$240$		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	$-0.477049\pi$
$251$	2.28263			0.144078			0.0720392	+	0.997402i	$0.477049\pi$
$252$		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	−0.657804	−	0.753189i	$-0.728514\pi$
$263$	5.24433	−	9.08344i	0.323379	−	0.560109i	0.981183	+	0.193080i	$0.0618478\pi$
$264$		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	$-0.114183\pi$
$271$	30.8285			1.87270			0.936348	+	0.351074i	$0.114183\pi$
$272$		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	$-0.923649\pi$
$283$	−11.6316	−	20.1465i	−0.691427	−	1.19759i	0.279944	−	0.960016i	$-0.409684\pi$
$284$		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	$-0.432511\pi$
$307$	7.37429			0.420873			0.210436	+	0.977608i	$0.432511\pi$
$308$		0			0
$309$	−9.90095	+	25.8478i	−0.563245	+	1.47043i
$310$		0			0
$311$	4.58577	+	7.94279i	0.260035	+	0.450394i	0.966251	−	0.257603i	$-0.0829325\pi$
$311$	4.58577	+	7.94279i	0.260035	+	0.450394i	−0.706216	+	0.707997i	$0.749599\pi$
$312$		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	−0.983973	−	0.178319i	$-0.942934\pi$
$331$	−6.14132	+	10.6371i	−0.337557	+	0.584666i	0.646415	+	0.762986i	$0.276267\pi$
$332$		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	$-0.970804\pi$
$347$	−10.7524	−	18.6237i	−0.577219	−	0.999773i	0.418577	−	0.908181i	$-0.362529\pi$
$348$		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	$-0.593417\pi$
$359$	−10.9623			−0.578565			−0.289283	+	0.957244i	$0.593417\pi$
$360$		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	−0.798183	−	0.602415i	$-0.794205\pi$
$367$	2.34897	−	4.06853i	0.122615	−	0.212376i	0.920798	+	0.390039i	$0.127539\pi$
$368$		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	$-0.386894\pi$
$379$	13.5458			0.695803			0.347901	+	0.937531i	$0.386894\pi$
$380$		0			0
$381$	0.903827	+	1.11451i	0.0463044	+	0.0570982i
$382$		0			0
$383$	6.13968	+	10.6342i	0.313723	+	0.543384i	0.979165	−	0.203065i	$-0.0650903\pi$
$383$	6.13968	+	10.6342i	0.313723	+	0.543384i	−0.665442	+	0.746449i	$0.731757\pi$
$384$		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	0.500928	−	0.865489i	$-0.332992\pi$
$419$	−10.2157	−	17.6942i	−0.499071	−	0.864417i	−0.999999	+	0.00107202i	$0.999659\pi$
$420$		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	$-0.277151\pi$
$431$	26.7518			1.28859			0.644296	+	0.764777i	$0.277151\pi$
$432$		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	$0.540140\pi$
$439$	−19.3187	+	33.4610i	−0.922033	+	1.59701i	−0.796264	+	0.604949i	$0.793193\pi$
$440$		0			0
$441$	2.85185	−	0.931107i	0.135802	−	0.0443384i
$442$		0			0
$443$	5.28263	−	9.14978i	0.250985	−	0.434719i	−0.712812	−	0.701355i	$-0.752579\pi$
$443$	5.28263	−	9.14978i	0.250985	−	0.434719i	0.963797	+	0.266636i	$0.0859121\pi$
$444$		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	0.936741	−	0.350024i	$-0.113827\pi$
$463$	3.55555	+	6.15838i	0.165240	+	0.286204i	−0.771500	+	0.636229i	$0.780493\pi$
$464$		0			0
$465$	−52.7977	+	8.40082i	−2.44843	+	0.389579i
$466$		0			0
$467$	−5.03448			−0.232968			−0.116484	−	0.993193i	$-0.537162\pi$
$467$	−5.03448			−0.232968			−0.116484	+	0.993193i	$0.537162\pi$
$468$		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	−0.785524	−	0.618831i	$-0.787607\pi$
$479$	3.13323	−	5.42692i	0.143161	−	0.247962i	0.928685	+	0.370869i	$0.120940\pi$
$480$		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	$-0.603292\pi$
$487$	−14.0722			−0.637674			−0.318837	+	0.947810i	$0.603292\pi$
$488$		0			0
$489$	13.4000	+	16.5236i	0.605969	+	0.747222i
$490$		0			0
$491$	1.97141	+	3.41458i	0.0889685	+	0.154098i	0.907075	−	0.420968i	$-0.138310\pi$
$491$	1.97141	+	3.41458i	0.0889685	+	0.154098i	−0.818107	+	0.575066i	$0.804976\pi$
$492$		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	0.997688	−	0.0679674i	$-0.0216514\pi$
$499$	9.82846	+	17.0234i	0.439982	+	0.762072i	−0.557705	+	0.830039i	$0.688318\pi$
$500$		0			0
$501$	14.1791	−	37.0164i	0.633474	−	1.65377i
$502$		0			0
$503$	10.2632			0.457613			0.228807	−	0.973472i	$-0.426518\pi$
$503$	10.2632			0.457613			0.228807	+	0.973472i	$0.426518\pi$
$504$		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	$-0.425008\pi$
$523$	10.6764			0.466844			0.233422	+	0.972376i	$0.425008\pi$
$524$		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	−0.649046	−	0.760749i	$-0.724832\pi$
$547$	7.81875	−	13.5425i	0.334305	−	0.579034i	0.983351	+	0.181715i	$0.0581650\pi$
$548$		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	0.980426	−	0.196889i	$-0.0630838\pi$
$563$	7.58577	+	13.1389i	0.319702	+	0.553740i	−0.660724	+	0.750629i	$0.729751\pi$
$564$		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	0.849400	−	0.527750i	$-0.176964\pi$
$571$	−0.772915	−	1.33873i	−0.0323455	−	0.0560240i	−0.881745	+	0.471726i	$0.843631\pi$
$572$		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	$0.469674\pi$
$587$	−19.7346	+	34.1813i	−0.814535	+	1.41082i	−0.909662	+	0.415350i	$0.863659\pi$
$588$		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	$0.209221\pi$
$599$	22.6375	+	39.2093i	0.924943	+	1.60205i	0.133290	+	0.991077i	$0.457446\pi$
$600$		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	0.612233	−	0.790678i	$-0.290272\pi$
$607$	−9.32846	−	16.1574i	−0.378631	−	0.655807i	−0.990863	+	0.134870i	$0.956938\pi$
$608$		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	−0.865830	−	0.500338i	$-0.833209\pi$
$619$	0.00971516	−	0.0168272i	0.000390485	−	0.000676340i	0.866221	+	0.499662i	$0.166542\pi$
$620$		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	$-0.691893\pi$
$631$	−28.4854			−1.13399			−0.566993	+	0.823723i	$0.691893\pi$
$632$		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	0.941142	−	0.338010i	$-0.109754\pi$
$643$	4.50972	+	7.81106i	0.177846	+	0.308038i	−0.763297	+	0.646048i	$0.776421\pi$
$644$		0			0
$645$	39.8457	+	49.1339i	1.56892	+	1.93464i
$646$		0			0
$647$	−42.8252			−1.68363			−0.841816	−	0.539765i	$-0.818513\pi$
$647$	−42.8252			−1.68363			−0.841816	+	0.539765i	$0.818513\pi$
$648$		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	−0.922567	−	0.385838i	$-0.873912\pi$
$659$	−3.26376	+	5.65299i	−0.127138	+	0.220209i	0.795429	+	0.606047i	$0.207246\pi$
$660$		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	$-0.413210\pi$
$683$	14.0755			0.538584			0.269292	+	0.963059i	$0.413210\pi$
$684$		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	$0.481431\pi$
$691$	−21.9601	+	38.0359i	−0.835400	+	1.44696i	−0.893704	+	0.448656i	$0.851903\pi$
$692$		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	$-0.484300\pi$
$719$	2.64403			0.0986056			0.0493028	+	0.998784i	$0.484300\pi$
$720$		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	−0.526908	−	0.849922i	$-0.676649\pi$
$727$	12.7427	−	22.0710i	0.472600	−	0.818568i	0.999508	+	0.0313547i	$0.00998214\pi$
$728$		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	$-0.890156\pi$
$739$	−51.1639			−1.88209			−0.941047	+	0.338276i	$0.890156\pi$
$740$		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	$-0.915137\pi$
$743$	−19.3668	−	33.5442i	−0.710498	−	1.23062i	0.254173	−	0.967159i	$-0.418197\pi$
$744$		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	0.916961	−	0.398977i	$-0.130635\pi$
$751$	3.09549	+	5.36154i	0.112956	+	0.195645i	−0.804005	+	0.594623i	$0.797301\pi$
$752$		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	$-0.753931\pi$
$787$	−27.0059	−	46.7756i	−0.962656	−	1.66737i	−0.246871	−	0.969048i	$-0.579402\pi$
$788$		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	$-0.488712\pi$
$811$	2.01943			0.0709118			0.0354559	+	0.999371i	$0.488712\pi$
$812$		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	0.728617	−	0.684921i	$-0.240163\pi$
$823$	−6.56526	−	11.3714i	−0.228851	−	0.396381i	−0.957468	+	0.288540i	$0.906830\pi$
$824$		0			0
$825$	−6.16019	+	16.0820i	−0.214470	+	0.559904i
$826$		0			0
$827$	11.3236			0.393762			0.196881	−	0.980427i	$-0.436919\pi$
$827$	11.3236			0.393762			0.196881	+	0.980427i	$0.436919\pi$
$828$		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	−0.760572	−	0.649254i	$-0.775081\pi$
$839$	5.27128	−	9.13013i	0.181985	−	0.315207i	0.942556	+	0.334047i	$0.108414\pi$
$840$		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	$-0.984476\pi$
$859$	−15.8743	−	27.4951i	−0.541624	−	0.938120i	0.457187	−	0.889370i	$-0.348857\pi$
$860$		0			0
$861$	−1.02859	−	1.26836i	−0.0350543	−	0.0432255i
$862$		0			0
$863$	27.8252			0.947181			0.473590	−	0.880745i	$-0.342958\pi$
$863$	27.8252			0.947181			0.473590	+	0.880745i	$0.342958\pi$
$864$		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	$-0.709785\pi$
$883$	−36.3937			−1.22475			−0.612373	+	0.790569i	$0.709785\pi$
$884$		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	$-0.906459\pi$
$887$	−21.7238	−	37.6268i	−0.729414	−	1.26338i	0.227717	−	0.973727i	$-0.426874\pi$
$888$		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	−0.619177	−	0.785252i	$-0.712534\pi$
$907$	11.1569	−	19.3244i	0.370459	−	0.641655i	0.989636	+	0.143597i	$0.0458669\pi$
$908$		0			0
$909$	5.81066	+	5.21700i	0.192728	+	0.173037i
$910$		0			0
$911$	−7.67799	+	13.2987i	−0.254383	+	0.440604i	−0.964728	−	0.263250i	$-0.915206\pi$
$911$	−7.67799	+	13.2987i	−0.254383	+	0.440604i	0.710345	+	0.703854i	$0.248539\pi$
$912$		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	$-0.292201\pi$
$919$	36.8285			1.21486			0.607429	+	0.794374i	$0.292201\pi$
$920$		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	$0.356120\pi$
$947$	−17.2535	+	29.8839i	−0.560663	+	0.971097i	−0.997439	+	0.0715263i	$0.977213\pi$
$948$		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	$0.0725741\pi$
$967$	21.2330	+	36.7766i	0.682806	+	1.18266i	−0.291314	+	0.956627i	$0.594093\pi$
$968$		0			0
$969$	−7.84037	−	9.66798i	−0.251869	−	0.310580i
$970$		0			0
$971$	−6.05391			−0.194279			−0.0971396	−	0.995271i	$-0.530969\pi$
$971$	−6.05391			−0.194279			−0.0971396	+	0.995271i	$0.530969\pi$
$972$		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	−0.899467	−	0.436988i	$-0.856045\pi$
$983$	−2.23517	+	3.87142i	−0.0712907	+	0.123479i	0.828177	+	0.560467i	$0.189378\pi$
$984$		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	$-0.333189\pi$
$991$	31.5048			1.00078			0.500392	+	0.865799i	$0.333189\pi$
$992$		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	1008.2.r.g.673.3		6
3.2	odd	2		3024.2.r.i.2017.1		6
4.3	odd	2		252.2.j.b.169.1	yes	6
9.2	odd	6		9072.2.a.bz.1.3		3
9.4	even	3	inner	1008.2.r.g.337.3		6
9.5	odd	6		3024.2.r.i.1009.1		6
9.7	even	3		9072.2.a.bt.1.1		3
12.11	even	2		756.2.j.a.505.1		6
28.3	even	6		1764.2.l.g.961.2		6
28.11	odd	6		1764.2.l.d.961.2		6
28.19	even	6		1764.2.i.e.1537.1		6
28.23	odd	6		1764.2.i.f.1537.3		6
28.27	even	2		1764.2.j.d.1177.3		6
36.7	odd	6		2268.2.a.g.1.1		3
36.11	even	6		2268.2.a.j.1.3		3
36.23	even	6		756.2.j.a.253.1		6
36.31	odd	6		252.2.j.b.85.1	✓	6
84.11	even	6		5292.2.l.g.3313.3		6
84.23	even	6		5292.2.i.d.2125.1		6
84.47	odd	6		5292.2.i.g.2125.3		6
84.59	odd	6		5292.2.l.d.3313.1		6
84.83	odd	2		5292.2.j.e.3529.3		6
252.23	even	6		5292.2.l.g.361.3		6
252.31	even	6		1764.2.i.e.373.1		6
252.59	odd	6		5292.2.i.g.1549.3		6
252.67	odd	6		1764.2.i.f.373.3		6
252.95	even	6		5292.2.i.d.1549.1		6
252.103	even	6		1764.2.l.g.949.2		6
252.131	odd	6		5292.2.l.d.361.1		6
252.139	even	6		1764.2.j.d.589.3		6
252.167	odd	6		5292.2.j.e.1765.3		6
252.247	odd	6		1764.2.l.d.949.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.j.b.85.1	✓	6	36.31	odd	6
252.2.j.b.169.1	yes	6	4.3	odd	2
756.2.j.a.253.1		6	36.23	even	6
756.2.j.a.505.1		6	12.11	even	2
1008.2.r.g.337.3		6	9.4	even	3	inner
1008.2.r.g.673.3		6	1.1	even	1	trivial
1764.2.i.e.373.1		6	252.31	even	6
1764.2.i.e.1537.1		6	28.19	even	6
1764.2.i.f.373.3		6	252.67	odd	6
1764.2.i.f.1537.3		6	28.23	odd	6
1764.2.j.d.589.3		6	252.139	even	6
1764.2.j.d.1177.3		6	28.27	even	2
1764.2.l.d.949.2		6	252.247	odd	6
1764.2.l.d.961.2		6	28.11	odd	6
1764.2.l.g.949.2		6	252.103	even	6
1764.2.l.g.961.2		6	28.3	even	6
2268.2.a.g.1.1		3	36.7	odd	6
2268.2.a.j.1.3		3	36.11	even	6
3024.2.r.i.1009.1		6	9.5	odd	6
3024.2.r.i.2017.1		6	3.2	odd	2
5292.2.i.d.1549.1		6	252.95	even	6
5292.2.i.d.2125.1		6	84.23	even	6
5292.2.i.g.1549.3		6	252.59	odd	6
5292.2.i.g.2125.3		6	84.47	odd	6
5292.2.j.e.1765.3		6	252.167	odd	6
5292.2.j.e.3529.3		6	84.83	odd	2
5292.2.l.d.361.1		6	252.131	odd	6
5292.2.l.d.3313.1		6	84.59	odd	6
5292.2.l.g.361.3		6	252.23	even	6
5292.2.l.g.3313.3		6	84.11	even	6
9072.2.a.bt.1.1		3	9.7	even	3
9072.2.a.bz.1.3		3	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.r (of order \(3\), degree \(2\), not 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

L-functions

Modular forms

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Database

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