LMFDB - Embedded newform 1008.2.cx.j.223.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(223,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.223"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cx (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,6,0,20,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			223.6
Character	$\chi$	$=$	1008.223
Dual form			1008.2.cx.j.895.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.940521 + 1.45445i) q^{3} +(-3.48918 + 2.01448i) q^{5} +(2.54444 + 0.725126i) q^{7} +(-1.23084 - 2.73588i) q^{9} +(-4.95331 - 2.85980i) q^{11} +(1.74224 - 1.00589i) q^{13} +(0.351689 - 6.96949i) q^{15} +4.18025i q^{17} -3.22849 q^{19} +(-3.44776 + 3.01877i) q^{21} +(-3.63065 + 2.09616i) q^{23} +(5.61625 - 9.72763i) q^{25} +(5.13683 + 0.782952i) q^{27} +(1.27096 - 2.20137i) q^{29} +(-3.10138 - 5.37176i) q^{31} +(8.81812 - 4.51464i) q^{33} +(-10.3388 + 2.59563i) q^{35} +3.21605 q^{37} +(-0.175608 + 3.48006i) q^{39} +(5.51107 - 3.18181i) q^{41} +(3.71365 + 2.14408i) q^{43} +(9.80600 + 7.06646i) q^{45} +(2.92547 - 5.06707i) q^{47} +(5.94838 + 3.69008i) q^{49} +(-6.07997 - 3.93161i) q^{51} +13.9105 q^{53} +23.0440 q^{55} +(3.03646 - 4.69567i) q^{57} +(-4.26142 - 7.38100i) q^{59} +(-10.9025 - 6.29455i) q^{61} +(-1.14795 - 7.85380i) q^{63} +(-4.05267 + 7.01943i) q^{65} +(-4.54387 + 2.62341i) q^{67} +(0.365949 - 7.25208i) q^{69} -12.5319i q^{71} +7.93971i q^{73} +(8.86614 + 17.3176i) q^{75} +(-10.5297 - 10.8684i) q^{77} +(-4.48851 - 2.59144i) q^{79} +(-5.97005 + 6.73487i) q^{81} +(-2.68950 + 4.65836i) q^{83} +(-8.42103 - 14.5857i) q^{85} +(2.00641 + 3.91898i) q^{87} -3.51148i q^{89} +(5.16244 - 1.29607i) q^{91} +(10.7299 + 0.541442i) q^{93} +(11.2648 - 6.50372i) q^{95} +(-9.29978 - 5.36923i) q^{97} +(-1.72731 + 17.0716i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{7} + 20 q^{9} - 24 q^{15} + 10 q^{21} - 18 q^{23} + 24 q^{25} - 6 q^{29} - 12 q^{37} + 12 q^{39} - 42 q^{43} + 12 q^{49} + 42 q^{51} + 96 q^{53} - 22 q^{57} - 18 q^{63} + 42 q^{65} - 36 q^{67}+ \cdots - 12 q^{99}+O(q^{100}) $ 24 * q + 6 * q^7 + 20 * q^9 - 24 * q^15 + 10 * q^21 - 18 * q^23 + 24 * q^25 - 6 * q^29 - 12 * q^37 + 12 * q^39 - 42 * q^43 + 12 * q^49 + 42 * q^51 + 96 * q^53 - 22 * q^57 - 18 * q^63 + 42 * q^65 - 36 * q^67 - 18 * q^77 + 60 * q^79 - 64 * q^81 - 6 * q^85 + 82 * q^93 + 126 * q^95 - 12 * 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
$3$	−0.940521	+	1.45445i	−0.543010	+	0.839726i
$3$	−0.940521	+	1.45445i	−0.543010	+	0.839726i
$4$		0			0
$5$	−3.48918	+	2.01448i	−1.56041	+	0.900902i	−0.563193	+	0.826325i	$0.690427\pi$
$5$	−3.48918	+	2.01448i	−1.56041	+	0.900902i	−0.997215	+	0.0745770i	$0.976239\pi$
$6$		0			0
$7$	2.54444	+	0.725126i	0.961709	+	0.274072i
$7$	2.54444	+	0.725126i	0.961709	+	0.274072i
$8$		0			0
$9$	−1.23084	−	2.73588i	−0.410281	−	0.911959i
$10$		0			0
$11$	−4.95331	−	2.85980i	−1.49348	−	0.862261i	−0.493508	−	0.869741i	$-0.664286\pi$
$11$	−4.95331	−	2.85980i	−1.49348	−	0.862261i	−0.999972	+	0.00747985i	$0.997619\pi$
$12$		0			0
$13$	1.74224	−	1.00589i	0.483212	−	0.278982i	−0.238542	−	0.971132i	$-0.576670\pi$
$13$	1.74224	−	1.00589i	0.483212	−	0.278982i	0.721754	+	0.692150i	$0.243336\pi$
$14$		0			0
$15$	0.351689	−	6.96949i	0.0908057	−	1.79951i
$16$		0			0
$17$			4.18025i			1.01386i	0.861987	+	0.506930i	$0.169220\pi$
$17$			4.18025i			1.01386i	−0.861987	+	0.506930i	$0.830780\pi$
$18$		0			0
$19$	−3.22849			−0.740666			−0.370333	−	0.928899i	$-0.620756\pi$
$19$	−3.22849			−0.740666			−0.370333	+	0.928899i	$0.620756\pi$
$20$		0			0
$21$	−3.44776	+	3.01877i	−0.752363	+	0.658749i
$22$		0			0
$23$	−3.63065	+	2.09616i	−0.757044	+	0.437079i	−0.828233	−	0.560383i	$-0.810654\pi$
$23$	−3.63065	+	2.09616i	−0.757044	+	0.437079i	0.0711897	+	0.997463i	$0.477320\pi$
$24$		0			0
$25$	5.61625	−	9.72763i	1.12325	−	1.94553i
$26$		0			0
$27$	5.13683	+	0.782952i	0.988583	+	0.150679i
$28$		0			0
$29$	1.27096	−	2.20137i	0.236011	−	0.408784i	−0.723555	−	0.690267i	$-0.757493\pi$
$29$	1.27096	−	2.20137i	0.236011	−	0.408784i	0.959566	+	0.281483i	$0.0908264\pi$
$30$		0			0
$31$	−3.10138	−	5.37176i	−0.557025	−	0.964796i	−0.997743	−	0.0671502i	$-0.978609\pi$
$31$	−3.10138	−	5.37176i	−0.557025	−	0.964796i	0.440718	−	0.897646i	$-0.354724\pi$
$32$		0			0
$33$	8.81812	−	4.51464i	1.53504	−	0.785898i
$34$		0			0
$35$	−10.3388	+	2.59563i	−1.74757	+	0.438742i
$36$		0			0
$37$	3.21605			0.528716			0.264358	−	0.964425i	$-0.414840\pi$
$37$	3.21605			0.528716			0.264358	+	0.964425i	$0.414840\pi$
$38$		0			0
$39$	−0.175608	+	3.48006i	−0.0281198	+	0.557256i
$40$		0			0
$41$	5.51107	−	3.18181i	0.860684	−	0.496916i	−0.00355743	−	0.999994i	$-0.501132\pi$
$41$	5.51107	−	3.18181i	0.860684	−	0.496916i	0.864241	+	0.503078i	$0.167799\pi$
$42$		0			0
$43$	3.71365	+	2.14408i	0.566327	+	0.326969i	0.755681	−	0.654940i	$-0.227306\pi$
$43$	3.71365	+	2.14408i	0.566327	+	0.326969i	−0.189354	+	0.981909i	$0.560639\pi$
$44$		0			0
$45$	9.80600	+	7.06646i	1.46179	+	1.05341i
$46$		0			0
$47$	2.92547	−	5.06707i	0.426724	−	0.739108i	−0.569855	−	0.821745i	$-0.693001\pi$
$47$	2.92547	−	5.06707i	0.426724	−	0.739108i	0.996580	+	0.0826368i	$0.0263342\pi$
$48$		0			0
$49$	5.94838	+	3.69008i	0.849769	+	0.527155i
$50$		0			0
$51$	−6.07997	−	3.93161i	−0.851365	−	0.550536i
$52$		0			0
$53$	13.9105			1.91076			0.955379	−	0.295383i	$-0.0954472\pi$
$53$	13.9105			1.91076			0.955379	+	0.295383i	$0.0954472\pi$
$54$		0			0
$55$	23.0440			3.10725
$56$		0			0
$57$	3.03646	−	4.69567i	0.402189	−	0.621957i
$58$		0			0
$59$	−4.26142	−	7.38100i	−0.554790	−	0.960925i	−0.997920	−	0.0644671i	$-0.979465\pi$
$59$	−4.26142	−	7.38100i	−0.554790	−	0.960925i	0.443130	−	0.896457i	$-0.353868\pi$
$60$		0			0
$61$	−10.9025	−	6.29455i	−1.39592	−	0.805934i	−0.401957	−	0.915659i	$-0.631670\pi$
$61$	−10.9025	−	6.29455i	−1.39592	−	0.805934i	−0.993962	+	0.109724i	$0.965003\pi$
$62$		0			0
$63$	−1.14795	−	7.85380i	−0.144628	−	0.989486i
$64$		0			0
$65$	−4.05267	+	7.01943i	−0.502672	+	0.870653i
$66$		0			0
$67$	−4.54387	+	2.62341i	−0.555122	+	0.320500i	−0.751185	−	0.660091i	$-0.770518\pi$
$67$	−4.54387	+	2.62341i	−0.555122	+	0.320500i	0.196063	+	0.980591i	$0.437184\pi$
$68$		0			0
$69$	0.365949	−	7.25208i	0.0440551	−	0.873048i
$70$		0			0
$71$		−	12.5319i		−	1.48727i	−0.668587	−	0.743634i	$-0.733101\pi$
$71$		−	12.5319i		−	1.48727i	0.668587	−	0.743634i	$-0.266899\pi$
$72$		0			0
$73$			7.93971i			0.929273i	0.885502	+	0.464636i	$0.153815\pi$
$73$			7.93971i			0.929273i	−0.885502	+	0.464636i	$0.846185\pi$
$74$		0			0
$75$	8.86614	+	17.3176i	1.02377	+	1.99966i
$76$		0			0
$77$	−10.5297	−	10.8684i	−1.19997	−	1.23857i
$78$		0			0
$79$	−4.48851	−	2.59144i	−0.504997	−	0.291560i	0.225778	−	0.974179i	$-0.427508\pi$
$79$	−4.48851	−	2.59144i	−0.504997	−	0.291560i	−0.730775	+	0.682619i	$0.760841\pi$
$80$		0			0
$81$	−5.97005	+	6.73487i	−0.663339	+	0.748319i
$82$		0			0
$83$	−2.68950	+	4.65836i	−0.295211	+	0.511321i	−0.975034	−	0.222055i	$-0.928723\pi$
$83$	−2.68950	+	4.65836i	−0.295211	+	0.511321i	0.679823	+	0.733377i	$0.262057\pi$
$84$		0			0
$85$	−8.42103	−	14.5857i	−0.913389	−	1.58204i
$86$		0			0
$87$	2.00641	+	3.91898i	0.215110	+	0.420159i
$88$		0			0
$89$		−	3.51148i		−	0.372216i	−0.982529	−	0.186108i	$-0.940413\pi$
$89$		−	3.51148i		−	0.372216i	0.982529	−	0.186108i	$-0.0595874\pi$
$90$		0			0
$91$	5.16244	−	1.29607i	0.541170	−	0.135865i
$92$		0			0
$93$	10.7299	+	0.541442i	1.11263	+	0.0561449i
$94$		0			0
$95$	11.2648	−	6.50372i	1.15574	−	0.667268i
$96$		0			0
$97$	−9.29978	−	5.36923i	−0.944250	−	0.545163i	−0.0529598	−	0.998597i	$-0.516866\pi$
$97$	−9.29978	−	5.36923i	−0.944250	−	0.545163i	−0.891290	+	0.453434i	$0.850199\pi$
$98$		0			0
$99$	−1.72731	+	17.0716i	−0.173601	+	1.71576i
$100$		0			0
$101$	2.98052	+	1.72080i	0.296573	+	0.171226i	0.640902	−	0.767623i	$-0.278560\pi$
$101$	2.98052	+	1.72080i	0.296573	+	0.171226i	−0.344330	+	0.938849i	$0.611894\pi$
$102$		0			0
$103$	−0.562042	−	0.973484i	−0.0553796	−	0.0959203i	0.837007	−	0.547193i	$-0.184304\pi$
$103$	−0.562042	−	0.973484i	−0.0553796	−	0.0959203i	−0.892386	+	0.451273i	$0.850970\pi$
$104$		0			0
$105$	5.94861	−	17.4785i	0.580525	−	1.70572i
$106$		0			0
$107$			2.50195i			0.241872i	0.992660	+	0.120936i	$0.0385897\pi$
$107$			2.50195i			0.241872i	−0.992660	+	0.120936i	$0.961410\pi$
$108$		0			0
$109$	−11.1266			−1.06573			−0.532867	−	0.846199i	$-0.678885\pi$
$109$	−11.1266			−1.06573			−0.532867	+	0.846199i	$0.678885\pi$
$110$		0			0
$111$	−3.02476	+	4.67758i	−0.287098	+	0.443976i
$112$		0			0
$113$	−0.599354	−	1.03811i	−0.0563825	−	0.0976574i	0.836457	−	0.548033i	$-0.184623\pi$
$113$	−0.599354	−	1.03811i	−0.0563825	−	0.0976574i	−0.892839	+	0.450376i	$0.851290\pi$
$114$		0			0
$115$	8.44533	−	14.6277i	0.787532	−	1.36404i
$116$		0			0
$117$	−4.89641	−	3.52848i	−0.452673	−	0.326208i
$118$		0			0
$119$	−3.03121	+	10.6364i	−0.277871	+	0.975039i
$120$		0			0
$121$	10.8569	+	18.8047i	0.986989	+	1.70951i
$122$		0			0
$123$	−0.555483	+	11.0081i	−0.0500862	+	0.992569i
$124$		0			0
$125$			25.1105i			2.24595i
$126$		0			0
$127$		−	3.48012i		−	0.308811i	−0.988008	−	0.154405i	$-0.950654\pi$
$127$		−	3.48012i		−	0.308811i	0.988008	−	0.154405i	$-0.0493462\pi$
$128$		0			0
$129$	−6.61122	+	3.38477i	−0.582085	+	0.298012i
$130$		0			0
$131$	−2.73241	−	4.73267i	−0.238732	−	0.413495i	0.721619	−	0.692290i	$-0.243398\pi$
$131$	−2.73241	−	4.73267i	−0.238732	−	0.413495i	−0.960351	+	0.278795i	$0.910065\pi$
$132$		0			0
$133$	−8.21471	−	2.34106i	−0.712306	−	0.202996i
$134$		0			0
$135$	−19.5005	+	7.61617i	−1.67834	+	0.655495i
$136$		0			0
$137$	−4.49760	+	7.79007i	−0.384256	+	0.665551i	−0.991666	−	0.128838i	$-0.958875\pi$
$137$	−4.49760	+	7.79007i	−0.384256	+	0.665551i	0.607410	+	0.794389i	$0.292209\pi$
$138$		0			0
$139$	−3.12779	−	5.41748i	−0.265295	−	0.459505i	0.702346	−	0.711836i	$-0.252136\pi$
$139$	−3.12779	−	5.41748i	−0.265295	−	0.459505i	−0.967641	+	0.252331i	$0.918803\pi$
$140$		0			0
$141$	4.61832	+	9.02064i	0.388933	+	0.759675i
$142$		0			0
$143$	−11.5065			−0.962223
$144$		0			0
$145$			10.2413i			0.850493i
$146$		0			0
$147$	−10.9616	+	5.18102i	−0.904099	+	0.427323i
$148$		0			0
$149$	−6.32221	−	10.9504i	−0.517936	−	0.897091i	−0.999783	−	0.0208358i	$-0.993367\pi$
$149$	−6.32221	−	10.9504i	−0.517936	−	0.897091i	0.481847	−	0.876255i	$-0.339966\pi$
$150$		0			0
$151$	−13.8107	−	7.97363i	−1.12390	−	0.648884i	−0.181507	−	0.983390i	$-0.558097\pi$
$151$	−13.8107	−	7.97363i	−1.12390	−	0.648884i	−0.942394	+	0.334505i	$0.891431\pi$
$152$		0			0
$153$	11.4367	−	5.14523i	0.924600	−	0.415967i
$154$		0			0
$155$	21.6426	+	12.4953i	1.73837	+	1.00365i
$156$		0			0
$157$	15.3782	−	8.87858i	1.22731	−	0.708588i	0.260844	−	0.965381i	$-0.415999\pi$
$157$	15.3782	−	8.87858i	1.22731	−	0.708588i	0.966467	+	0.256793i	$0.0826658\pi$
$158$		0			0
$159$	−13.0831	+	20.2322i	−1.03756	+	1.60451i
$160$		0			0
$161$	−10.7580	+	2.70088i	−0.847847	+	0.212859i
$162$		0			0
$163$			10.1287i			0.793339i	0.917962	+	0.396669i	$0.129834\pi$
$163$			10.1287i			0.793339i	−0.917962	+	0.396669i	$0.870166\pi$
$164$		0			0
$165$	−21.6734	+	33.5163i	−1.68727	+	2.60924i
$166$		0			0
$167$	−7.08298	−	12.2681i	−0.548098	−	0.949333i	−0.998405	−	0.0564595i	$-0.982019\pi$
$167$	−7.08298	−	12.2681i	−0.548098	−	0.949333i	0.450307	−	0.892874i	$-0.351315\pi$
$168$		0			0
$169$	−4.47639	+	7.75334i	−0.344338	+	0.596410i
$170$		0			0
$171$	3.97376	+	8.83275i	0.303881	+	0.675457i
$172$		0			0
$173$	−9.42612	−	5.44217i	−0.716654	−	0.413761i	0.0968656	−	0.995297i	$-0.469118\pi$
$173$	−9.42612	−	5.44217i	−0.716654	−	0.413761i	−0.813520	+	0.581537i	$0.802452\pi$
$174$		0			0
$175$	21.3440	−	20.6789i	1.61345	−	1.56318i
$176$		0			0
$177$	14.7432	+	0.743962i	1.10817	+	0.0559196i
$178$		0			0
$179$		−	11.7278i		−	0.876578i	−0.898834	−	0.438289i	$-0.855585\pi$
$179$		−	11.7278i		−	0.876578i	0.898834	−	0.438289i	$-0.144415\pi$
$180$		0			0
$181$		−	17.6522i		−	1.31208i	−0.754727	−	0.656039i	$-0.772231\pi$
$181$		−	17.6522i		−	1.31208i	0.754727	−	0.656039i	$-0.227769\pi$
$182$		0			0
$183$	19.4091	−	9.93694i	1.43476	−	0.734560i
$184$		0			0
$185$	−11.2214	+	6.47867i	−0.825012	+	0.476321i
$186$		0			0
$187$	11.9547	−	20.7061i	0.874213	−	1.51418i
$188$		0			0
$189$	12.5026	+	5.71702i	0.909432	+	0.415852i
$190$		0			0
$191$	0.581366	+	0.335652i	0.0420662	+	0.0242869i	0.520886	−	0.853626i	$-0.325602\pi$
$191$	0.581366	+	0.335652i	0.0420662	+	0.0242869i	−0.478819	+	0.877913i	$0.658935\pi$
$192$		0			0
$193$	−7.45526	−	12.9129i	−0.536642	−	0.929491i	−0.999082	−	0.0428402i	$-0.986359\pi$
$193$	−7.45526	−	12.9129i	−0.536642	−	0.929491i	0.462440	−	0.886650i	$-0.346974\pi$
$194$		0			0
$195$	−6.39778	−	12.4963i	−0.458154	−	0.894880i
$196$		0			0
$197$	8.84703			0.630325			0.315163	−	0.949038i	$-0.397941\pi$
$197$	8.84703			0.630325			0.315163	+	0.949038i	$0.397941\pi$
$198$		0			0
$199$	4.99197			0.353872			0.176936	−	0.984222i	$-0.443381\pi$
$199$	4.99197			0.353872			0.176936	+	0.984222i	$0.443381\pi$
$200$		0			0
$201$	0.457996	−	9.07619i	0.0323045	−	0.640185i
$202$		0			0
$203$	4.83016	−	4.67965i	0.339010	−	0.328447i
$204$		0			0
$205$	−12.8194	+	22.2038i	−0.895345	+	1.55078i
$206$		0			0
$207$	10.2036	+	7.35298i	0.709199	+	0.511068i
$208$		0			0
$209$	15.9917	+	9.23282i	1.10617	+	0.638648i
$210$		0			0
$211$	−1.47412	+	0.851085i	−0.101483	+	0.0585911i	−0.549882	−	0.835242i	$-0.685327\pi$
$211$	−1.47412	+	0.851085i	−0.101483	+	0.0585911i	0.448400	+	0.893833i	$0.351994\pi$
$212$		0			0
$213$	18.2271	+	11.7865i	1.24890	+	0.807601i
$214$		0			0
$215$	−17.2768			−1.17827
$216$		0			0
$217$	−3.99610	−	15.9170i	−0.271273	−	1.08052i
$218$		0			0
$219$	−11.5479	−	7.46746i	−0.780335	−	0.504604i
$220$		0			0
$221$	4.20486	+	7.28302i	0.282849	+	0.489909i
$222$		0			0
$223$	−10.0164	+	17.3488i	−0.670745	+	1.16176i	0.306948	+	0.951726i	$0.400692\pi$
$223$	−10.0164	+	17.3488i	−0.670745	+	1.16176i	−0.977693	+	0.210038i	$0.932641\pi$
$224$		0			0
$225$	−33.5263	−	3.39220i	−2.23509	−	0.226146i
$226$		0			0
$227$	−5.16212	+	8.94105i	−0.342622	+	0.593438i	−0.984919	−	0.173018i	$-0.944648\pi$
$227$	−5.16212	+	8.94105i	−0.342622	+	0.593438i	0.642297	+	0.766456i	$0.277982\pi$
$228$		0			0
$229$	2.90563	−	1.67756i	0.192009	−	0.110857i	−0.400914	−	0.916116i	$-0.631307\pi$
$229$	2.90563	−	1.67756i	0.192009	−	0.110857i	0.592923	+	0.805259i	$0.297974\pi$
$230$		0			0
$231$	25.7109	−	5.09301i	1.69165	−	0.335095i
$232$		0			0
$233$	−20.1788			−1.32196			−0.660978	−	0.750405i	$-0.729858\pi$
$233$	−20.1788			−1.32196			−0.660978	+	0.750405i	$0.729858\pi$
$234$		0			0
$235$			23.5732i			1.53775i
$236$		0			0
$237$	7.99066	−	4.09101i	0.519049	−	0.265739i
$238$		0			0
$239$	2.94777	−	1.70189i	0.190675	−	0.110086i	−0.401623	−	0.915805i	$-0.631554\pi$
$239$	2.94777	−	1.70189i	0.190675	−	0.110086i	0.592299	+	0.805719i	$0.298221\pi$
$240$		0			0
$241$	1.83067	+	1.05694i	0.117924	+	0.0680832i	0.557802	−	0.829974i	$-0.311645\pi$
$241$	1.83067	+	1.05694i	0.117924	+	0.0680832i	−0.439878	+	0.898058i	$0.644978\pi$
$242$		0			0
$243$	−4.18056	−	15.0174i	−0.268183	−	0.963368i
$244$		0			0
$245$	−28.1886	−	0.892469i	−1.80090	−	0.0570177i
$246$		0			0
$247$	−5.62482	+	3.24749i	−0.357899	+	0.206633i
$248$		0			0
$249$	−4.24581	−	8.29303i	−0.269067	−	0.525549i
$250$		0			0
$251$	−1.31087			−0.0827413			−0.0413707	−	0.999144i	$-0.513172\pi$
$251$	−1.31087			−0.0827413			−0.0413707	+	0.999144i	$0.513172\pi$
$252$		0			0
$253$	23.9784			1.50751
$254$		0			0
$255$	29.1342	+	1.47015i	1.82446	+	0.0920643i
$256$		0			0
$257$	9.71045	−	5.60633i	0.605721	−	0.349713i	−0.165568	−	0.986198i	$-0.552946\pi$
$257$	9.71045	−	5.60633i	0.605721	−	0.349713i	0.771289	+	0.636485i	$0.219612\pi$
$258$		0			0
$259$	8.18306	+	2.33204i	0.508471	+	0.144906i
$260$		0			0
$261$	−7.58703	−	0.767656i	−0.469625	−	0.0475167i
$262$		0			0
$263$	−1.54810	−	0.893798i	−0.0954601	−	0.0551139i	0.451510	−	0.892266i	$-0.350886\pi$
$263$	−1.54810	−	0.893798i	−0.0954601	−	0.0551139i	−0.546970	+	0.837152i	$0.684219\pi$
$264$		0			0
$265$	−48.5363	+	28.0225i	−2.98156	+	1.72141i
$266$		0			0
$267$	5.10726	+	3.30262i	0.312559	+	0.202117i
$268$		0			0
$269$		−	22.8546i		−	1.39347i	−0.717330	−	0.696734i	$-0.754636\pi$
$269$		−	22.8546i		−	1.39347i	0.717330	−	0.696734i	$-0.245364\pi$
$270$		0			0
$271$	−13.4933			−0.819657			−0.409828	−	0.912163i	$-0.634411\pi$
$271$	−13.4933			−0.819657			−0.409828	+	0.912163i	$0.634411\pi$
$272$		0			0
$273$	−2.97031	+	8.72748i	−0.179771	+	0.528211i
$274$		0			0
$275$	−55.6381	+	32.1227i	−3.35510	+	1.93707i
$276$		0			0
$277$	10.0276	−	17.3684i	0.602503	−	1.04357i	−0.389938	−	0.920841i	$-0.627504\pi$
$277$	10.0276	−	17.3684i	0.602503	−	1.04357i	0.992441	−	0.122724i	$-0.0391630\pi$
$278$		0			0
$279$	−10.8792	+	15.0968i	−0.651318	+	0.903821i
$280$		0			0
$281$	−7.99902	+	13.8547i	−0.477181	+	0.826502i	−0.999658	−	0.0261512i	$-0.991675\pi$
$281$	−7.99902	+	13.8547i	−0.477181	+	0.826502i	0.522477	+	0.852654i	$0.325008\pi$
$282$		0			0
$283$	9.43384	+	16.3399i	0.560783	+	0.971305i	0.997428	+	0.0716713i	$0.0228333\pi$
$283$	9.43384	+	16.3399i	0.560783	+	0.971305i	−0.436645	+	0.899634i	$0.643833\pi$
$284$		0			0
$285$	−1.13542	+	22.5009i	−0.0672567	+	1.33284i
$286$		0			0
$287$	16.3298	−	4.09973i	0.963918	−	0.242000i
$288$		0			0
$289$	−0.474525			−0.0279132
$290$		0			0
$291$	16.5559	−	8.47618i	0.970524	−	0.496883i
$292$		0			0
$293$	−13.2893	+	7.67260i	−0.776371	+	0.448238i	−0.835143	−	0.550034i	$-0.814615\pi$
$293$	−13.2893	+	7.67260i	−0.776371	+	0.448238i	0.0587718	+	0.998271i	$0.481282\pi$
$294$		0			0
$295$	29.7377	+	17.1691i	1.73140	+	0.999623i
$296$		0			0
$297$	−23.2052	−	18.5685i	−1.34650	−	1.07745i
$298$		0			0
$299$	−4.21699	+	7.30404i	−0.243875	+	0.422404i
$300$		0			0
$301$	7.89445	+	8.14835i	0.455029	+	0.469663i
$302$		0			0
$303$	−5.30606	+	2.71656i	−0.304825	+	0.156062i
$304$		0			0
$305$	50.7209			2.90427
$306$		0			0
$307$	−12.8290			−0.732192			−0.366096	−	0.930577i	$-0.619306\pi$
$307$	−12.8290			−0.732192			−0.366096	+	0.930577i	$0.619306\pi$
$308$		0			0
$309$	1.94449	+	0.0981216i	0.110618	+	0.00558194i
$310$		0			0
$311$	1.01728	+	1.76198i	0.0576846	+	0.0999127i	0.893426	−	0.449211i	$-0.148295\pi$
$311$	1.01728	+	1.76198i	0.0576846	+	0.0999127i	−0.835741	+	0.549124i	$0.814962\pi$
$312$		0			0
$313$	−8.42991	−	4.86701i	−0.476487	−	0.275100i	0.242465	−	0.970160i	$-0.422044\pi$
$313$	−8.42991	−	4.86701i	−0.476487	−	0.275100i	−0.718951	+	0.695061i	$0.755378\pi$
$314$		0			0
$315$	19.8267	+	25.0908i	1.11711	+	1.41371i
$316$		0			0
$317$	−11.5075	+	19.9315i	−0.646325	+	1.11947i	0.337669	+	0.941265i	$0.390361\pi$
$317$	−11.5075	+	19.9315i	−0.646325	+	1.11947i	−0.983994	+	0.178202i	$0.942972\pi$
$318$		0			0
$319$	−12.5909	+	7.26938i	−0.704957	+	0.407007i
$320$		0			0
$321$	−3.63895	−	2.35313i	−0.203107	−	0.131339i
$322$		0			0
$323$		−	13.4959i		−	0.750932i
$324$		0			0
$325$		−	22.5972i		−	1.25347i
$326$		0			0
$327$	10.4648	−	16.1830i	0.578703	−	0.894924i
$328$		0			0
$329$	11.1180	−	10.7715i	0.612953	−	0.593854i
$330$		0			0
$331$	18.3921	+	10.6187i	1.01092	+	0.583656i	0.911461	−	0.411386i	$-0.134955\pi$
$331$	18.3921	+	10.6187i	1.01092	+	0.583656i	0.0994598	+	0.995042i	$0.468289\pi$
$332$		0			0
$333$	−3.95845	−	8.79872i	−0.216922	−	0.482167i
$334$		0			0
$335$	10.5696	−	18.3071i	0.577478	−	1.00022i
$336$		0			0
$337$	−13.0884	−	22.6698i	−0.712971	−	1.23490i	−0.963737	−	0.266854i	$-0.914016\pi$
$337$	−13.0884	−	22.6698i	−0.712971	−	1.23490i	0.250766	−	0.968048i	$-0.419318\pi$
$338$		0			0
$339$	2.07359	+	0.104636i	0.112622	+	0.00568303i
$340$		0			0
$341$			35.4773i			1.92120i
$342$		0			0
$343$	12.4596	+	13.7025i	0.672753	+	0.739867i
$344$		0			0
$345$	13.3323	+	26.0410i	0.717787	+	1.40200i
$346$		0			0
$347$	−13.1001	+	7.56336i	−0.703251	+	0.406022i	−0.808557	−	0.588417i	$-0.799751\pi$
$347$	−13.1001	+	7.56336i	−0.703251	+	0.406022i	0.105306	+	0.994440i	$0.466418\pi$
$348$		0			0
$349$	18.8255	+	10.8689i	1.00771	+	0.581799i	0.910519	−	0.413467i	$-0.135682\pi$
$349$	18.8255	+	10.8689i	1.00771	+	0.581799i	0.0971868	+	0.995266i	$0.469016\pi$
$350$		0			0
$351$	9.73717	−	3.80296i	0.519731	−	0.202987i
$352$		0			0
$353$	−17.9454	−	10.3608i	−0.955136	−	0.551448i	−0.0604636	−	0.998170i	$-0.519258\pi$
$353$	−17.9454	−	10.3608i	−0.955136	−	0.551448i	−0.894673	+	0.446722i	$0.852591\pi$
$354$		0			0
$355$	25.2453	+	43.7262i	1.33988	+	2.32074i
$356$		0			0
$357$	−12.6192	−	14.4125i	−0.667880	−	0.762791i
$358$		0			0
$359$		−	8.70585i		−	0.459477i	−0.973252	−	0.229739i	$-0.926213\pi$
$359$		−	8.70585i		−	0.459477i	0.973252	−	0.229739i	$-0.0737871\pi$
$360$		0			0
$361$	−8.57686			−0.451414
$362$		0			0
$363$	−37.5615	−	1.89540i	−1.97147	−	0.0994827i
$364$		0			0
$365$	−15.9944	−	27.7031i	−0.837184	−	1.45005i
$366$		0			0
$367$	10.5062	−	18.1973i	0.548419	−	0.949890i	−0.449964	−	0.893047i	$-0.648563\pi$
$367$	10.5062	−	18.1973i	0.548419	−	0.949890i	0.998383	−	0.0568434i	$-0.0181036\pi$
$368$		0			0
$369$	−15.4883	−	11.1613i	−0.806289	−	0.581033i
$370$		0			0
$371$	35.3946	+	10.0869i	1.83759	+	0.523685i
$372$		0			0
$373$	6.05267	+	10.4835i	0.313395	+	0.542817i	0.979095	−	0.203403i	$-0.0652002\pi$
$373$	6.05267	+	10.4835i	0.313395	+	0.542817i	−0.665700	+	0.746220i	$0.731867\pi$
$374$		0			0
$375$	−36.5219	−	23.6169i	−1.88598	−	1.21957i
$376$		0			0
$377$		−	5.11376i		−	0.263372i
$378$		0			0
$379$		−	32.3259i		−	1.66047i	−0.557414	−	0.830234i	$-0.688206\pi$
$379$		−	32.3259i		−	1.66047i	0.557414	−	0.830234i	$-0.311794\pi$
$380$		0			0
$381$	5.06166	+	3.27312i	0.259316	+	0.167687i
$382$		0			0
$383$	2.70529	+	4.68571i	0.138234	+	0.239428i	0.926828	−	0.375486i	$-0.122524\pi$
$383$	2.70529	+	4.68571i	0.138234	+	0.239428i	−0.788594	+	0.614914i	$0.789191\pi$
$384$		0			0
$385$	58.6342	+	16.7098i	2.98827	+	0.851610i
$386$		0			0
$387$	1.29502	−	12.7991i	0.0658294	−	0.650616i
$388$		0			0
$389$	−8.74076	+	15.1394i	−0.443174	+	0.767600i	−0.997923	−	0.0644180i	$-0.979481\pi$
$389$	−8.74076	+	15.1394i	−0.443174	+	0.767600i	0.554749	+	0.832018i	$0.312814\pi$
$390$		0			0
$391$	−8.76248	−	15.1771i	−0.443138	−	0.767537i
$392$		0			0
$393$	9.45331	+	0.477026i	0.476857	+	0.0240628i
$394$		0			0
$395$	20.8816			1.05067
$396$		0			0
$397$		−	12.6177i		−	0.633264i	−0.948549	−	0.316632i	$-0.897448\pi$
$397$		−	12.6177i		−	0.633264i	0.948549	−	0.316632i	$-0.102552\pi$
$398$		0			0
$399$	11.1311	−	9.74606i	0.557250	−	0.487913i
$400$		0			0
$401$	5.40011	+	9.35327i	0.269669	+	0.467080i	0.968776	−	0.247937i	$-0.0797525\pi$
$401$	5.40011	+	9.35327i	0.269669	+	0.467080i	−0.699108	+	0.715017i	$0.746419\pi$
$402$		0			0
$403$	−10.8067	−	6.23927i	−0.538322	−	0.310800i
$404$		0			0
$405$	7.26335	−	35.5257i	0.360919	−	1.76529i
$406$		0			0
$407$	−15.9301	−	9.19725i	−0.789626	−	0.455891i
$408$		0			0
$409$	9.66191	−	5.57831i	0.477751	−	0.275830i	−0.241728	−	0.970344i	$-0.577714\pi$
$409$	9.66191	−	5.57831i	0.477751	−	0.275830i	0.719479	+	0.694515i	$0.244381\pi$
$410$		0			0
$411$	−7.10018	−	13.8683i	−0.350226	−	0.684071i
$412$		0			0
$413$	−5.49080	−	21.8706i	−0.270184	−	1.07618i
$414$		0			0
$415$		−	21.6718i		−	1.06383i
$416$		0			0
$417$	10.8212	+	0.546051i	0.529916	+	0.0267402i
$418$		0			0
$419$	−7.36007	−	12.7480i	−0.359563	−	0.622781i	0.628325	−	0.777951i	$-0.283741\pi$
$419$	−7.36007	−	12.7480i	−0.359563	−	0.622781i	−0.987888	+	0.155170i	$0.950408\pi$
$420$		0			0
$421$	7.90063	−	13.6843i	0.385053	−	0.666932i	−0.606723	−	0.794913i	$-0.707516\pi$
$421$	7.90063	−	13.6843i	0.385053	−	0.666932i	0.991777	+	0.127981i	$0.0408497\pi$
$422$		0			0
$423$	−17.4637	−	1.76698i	−0.849113	−	0.0859133i
$424$		0			0
$425$	40.6640	+	23.4773i	1.97249	+	1.13882i
$426$		0			0
$427$	−23.1764	−	23.9218i	−1.12158	−	1.15766i
$428$		0			0
$429$	10.8221	−	16.7356i	0.522496	−	0.808004i
$430$		0			0
$431$			0.798303i			0.0384529i	0.999815	+	0.0192265i	$0.00612035\pi$
$431$			0.798303i			0.0384529i	−0.999815	+	0.0192265i	$0.993880\pi$
$432$		0			0
$433$			31.2293i			1.50079i	0.660992	+	0.750393i	$0.270136\pi$
$433$			31.2293i			1.50079i	−0.660992	+	0.750393i	$0.729864\pi$
$434$		0			0
$435$	−14.8954	−	9.63214i	−0.714181	−	0.461826i
$436$		0			0
$437$	11.7215	−	6.76743i	0.560717	−	0.323730i
$438$		0			0
$439$	2.94795	−	5.10600i	0.140698	−	0.243696i	−0.787062	−	0.616874i	$-0.788399\pi$
$439$	2.94795	−	5.10600i	0.140698	−	0.243696i	0.927760	+	0.373178i	$0.121732\pi$
$440$		0			0
$441$	2.77409	−	20.8160i	0.132100	−	0.991236i
$442$		0			0
$443$	−2.02844	−	1.17112i	−0.0963742	−	0.0556417i	0.451038	−	0.892505i	$-0.351054\pi$
$443$	−2.02844	−	1.17112i	−0.0963742	−	0.0556417i	−0.547413	+	0.836863i	$0.684387\pi$
$444$		0			0
$445$	7.07379	+	12.2522i	0.335330	+	0.580809i
$446$		0			0
$447$	21.8730	+	1.10374i	1.03456	+	0.0522049i
$448$		0			0
$449$	23.9242			1.12905			0.564527	−	0.825415i	$-0.309059\pi$
$449$	23.9242			1.12905			0.564527	+	0.825415i	$0.309059\pi$
$450$		0			0
$451$	−36.3974			−1.71389
$452$		0			0
$453$	24.5865	−	12.5876i	1.15517	−	0.591419i
$454$		0			0
$455$	−15.4018	+	14.9218i	−0.722045	+	0.699547i
$456$		0			0
$457$	−7.24703	+	12.5522i	−0.339002	+	0.587168i	−0.984245	−	0.176809i	$-0.943423\pi$
$457$	−7.24703	+	12.5522i	−0.339002	+	0.587168i	0.645244	+	0.763977i	$0.276756\pi$
$458$		0			0
$459$	−3.27294	+	21.4732i	−0.152768	+	1.00229i
$460$		0			0
$461$	16.2137	+	9.36101i	0.755149	+	0.435986i	0.827551	−	0.561390i	$-0.189733\pi$
$461$	16.2137	+	9.36101i	0.755149	+	0.435986i	−0.0724022	+	0.997376i	$0.523067\pi$
$462$		0			0
$463$	1.88529	−	1.08847i	0.0876166	−	0.0505855i	−0.455552	−	0.890209i	$-0.650558\pi$
$463$	1.88529	−	1.08847i	0.0876166	−	0.0505855i	0.543168	+	0.839624i	$0.317225\pi$
$464$		0			0
$465$	−38.5291	+	19.7259i	−1.78675	+	0.914766i
$466$		0			0
$467$	20.8089			0.962923			0.481461	−	0.876467i	$-0.340106\pi$
$467$	20.8089			0.962923			0.481461	+	0.876467i	$0.340106\pi$
$468$		0			0
$469$	−13.4639	+	3.38023i	−0.621706	+	0.156084i
$470$		0			0
$471$	−1.55003	+	30.7172i	−0.0714216	+	1.41538i
$472$		0			0
$473$	−12.2633	−	21.2406i	−0.563865	−	0.976643i
$474$		0			0
$475$	−18.1320	+	31.4055i	−0.831953	+	1.44099i
$476$		0			0
$477$	−17.1217	−	38.0575i	−0.783947	−	1.74253i
$478$		0			0
$479$	−15.5470	+	26.9281i	−0.710359	+	1.23038i	0.254364	+	0.967109i	$0.418134\pi$
$479$	−15.5470	+	26.9281i	−0.710359	+	1.23038i	−0.964723	+	0.263269i	$0.915199\pi$
$480$		0			0
$481$	5.60315	−	3.23498i	0.255481	−	0.147502i
$482$		0			0
$483$	6.18981	−	18.1871i	0.281646	−	0.827544i
$484$		0			0
$485$	43.2648			1.96455
$486$		0			0
$487$		−	19.1545i		−	0.867972i	−0.900920	−	0.433986i	$-0.857107\pi$
$487$		−	19.1545i		−	0.867972i	0.900920	−	0.433986i	$-0.142893\pi$
$488$		0			0
$489$	−14.7316	−	9.52622i	−0.666187	−	0.430791i
$490$		0			0
$491$	33.4660	−	19.3216i	1.51030	−	0.871972i	0.510371	−	0.859954i	$-0.329508\pi$
$491$	33.4660	−	19.3216i	1.51030	−	0.871972i	0.999928	−	0.0120176i	$-0.00382540\pi$
$492$		0			0
$493$	9.20228	+	5.31294i	0.414450	+	0.239283i
$494$		0			0
$495$	−28.3635	−	63.0456i	−1.27485	−	2.83369i
$496$		0			0
$497$	9.08723	−	31.8868i	0.407618	−	1.43032i
$498$		0			0
$499$	−37.8146	+	21.8323i	−1.69281	+	0.977346i	−0.740584	+	0.671964i	$0.765451\pi$
$499$	−37.8146	+	21.8323i	−1.69281	+	0.977346i	−0.952230	+	0.305382i	$0.901216\pi$
$500$		0			0
$501$	24.5050	+	1.23655i	1.09480	+	0.0552451i
$502$		0			0
$503$	34.6828			1.54643			0.773215	−	0.634144i	$-0.218647\pi$
$503$	34.6828			1.54643			0.773215	+	0.634144i	$0.218647\pi$
$504$		0			0
$505$	−13.8661			−0.617032
$506$		0			0
$507$	−7.06669	−	13.8029i	−0.313843	−	0.613006i
$508$		0			0
$509$	−9.03205	+	5.21466i	−0.400339	+	0.231136i	−0.686630	−	0.727007i	$-0.740911\pi$
$509$	−9.03205	+	5.21466i	−0.400339	+	0.231136i	0.286291	+	0.958143i	$0.407577\pi$
$510$		0			0
$511$	−5.75729	+	20.2021i	−0.254688	+	0.893690i
$512$		0			0
$513$	−16.5842	−	2.52775i	−0.732210	−	0.111603i
$514$		0			0
$515$	3.92213	+	2.26444i	0.172830	+	0.0997832i
$516$		0			0
$517$	−28.9816	+	16.7325i	−1.27461	+	0.735896i
$518$		0			0
$519$	16.7808	−	8.59133i	0.736596	−	0.377118i
$520$		0			0
$521$		−	8.72877i		−	0.382414i	−0.981550	−	0.191207i	$-0.938760\pi$
$521$		−	8.72877i		−	0.382414i	0.981550	−	0.191207i	$-0.0612402\pi$
$522$		0			0
$523$	−10.6357			−0.465068			−0.232534	−	0.972588i	$-0.574702\pi$
$523$	−10.6357			−0.465068			−0.232534	+	0.972588i	$0.574702\pi$
$524$		0			0
$525$	10.0020	+	50.4927i	0.436521	+	2.20368i
$526$		0			0
$527$	22.4553	−	12.9646i	0.978169	−	0.564746i
$528$		0			0
$529$	−2.71224	+	4.69773i	−0.117923	+	0.204249i
$530$		0			0
$531$	−14.9484	+	20.7436i	−0.648704	+	0.900195i
$532$		0			0
$533$	6.40108	−	11.0870i	0.277262	−	0.480231i
$534$		0			0
$535$	−5.04012	−	8.72974i	−0.217903	−	0.377420i
$536$		0			0
$537$	17.0575	+	11.0303i	0.736086	+	0.475991i
$538$		0			0
$539$	−18.9113	−	35.2893i	−0.814569	−	1.52002i
$540$		0			0
$541$	35.8565			1.54159			0.770797	−	0.637081i	$-0.219858\pi$
$541$	35.8565			1.54159			0.770797	+	0.637081i	$0.219858\pi$
$542$		0			0
$543$	25.6742	+	16.6023i	1.10179	+	0.712471i
$544$		0			0
$545$	38.8226	−	22.4143i	1.66298	−	0.960121i
$546$		0			0
$547$	−35.5209	−	20.5080i	−1.51876	−	0.876859i	−0.999756	−	0.0220901i	$-0.992968\pi$
$547$	−35.5209	−	20.5080i	−1.51876	−	0.876859i	−0.519009	−	0.854769i	$-0.673699\pi$
$548$		0			0
$549$	−3.80189	+	37.5754i	−0.162261	+	1.60368i
$550$		0			0
$551$	−4.10328	+	7.10709i	−0.174806	+	0.302772i
$552$		0			0
$553$	−9.54165	−	9.84852i	−0.405752	−	0.418802i
$554$		0			0
$555$	1.13105	−	22.4142i	0.0480104	−	0.951432i
$556$		0			0
$557$	−33.8693			−1.43509			−0.717545	−	0.696512i	$-0.754734\pi$
$557$	−33.8693			−1.43509			−0.717545	+	0.696512i	$0.754734\pi$
$558$		0			0
$559$	8.62679			0.364874
$560$		0			0
$561$	18.8724	+	36.8620i	0.796791	+	1.55631i
$562$		0			0
$563$	14.7326	+	25.5176i	0.620904	+	1.07544i	0.989318	+	0.145775i	$0.0465676\pi$
$563$	14.7326	+	25.5176i	0.620904	+	1.07544i	−0.368414	+	0.929662i	$0.620099\pi$
$564$		0			0
$565$	4.18251	+	2.41477i	0.175960	+	0.101590i
$566$		0			0
$567$	−20.0741	+	12.8074i	−0.843033	+	0.537862i
$568$		0			0
$569$	9.11670	−	15.7906i	0.382192	−	0.661976i	−0.609183	−	0.793029i	$-0.708503\pi$
$569$	9.11670	−	15.7906i	0.382192	−	0.661976i	0.991375	+	0.131054i	$0.0418360\pi$
$570$		0			0
$571$	21.9710	−	12.6850i	0.919459	−	0.530850i	0.0359963	−	0.999352i	$-0.488540\pi$
$571$	21.9710	−	12.6850i	0.919459	−	0.530850i	0.883462	+	0.468502i	$0.155206\pi$
$572$		0			0
$573$	−1.03497	+	0.529880i	−0.0432367	+	0.0221360i
$574$		0			0
$575$			47.0902i			1.96380i
$576$		0			0
$577$		−	3.50461i		−	0.145899i	−0.997336	−	0.0729493i	$-0.976759\pi$
$577$		−	3.50461i		−	0.145899i	0.997336	−	0.0729493i	$-0.0232411\pi$
$578$		0			0
$579$	25.7930	+	1.30154i	1.07192	+	0.0540904i
$580$		0			0
$581$	−10.2212	+	9.90270i	−0.424046	+	0.410833i
$582$		0			0
$583$	−68.9032	−	39.7813i	−2.85368	−	1.64757i
$584$		0			0
$585$	24.1925	+	2.44780i	1.00024	+	0.101204i
$586$		0			0
$587$	20.1658	−	34.9282i	0.832332	−	1.44164i	−0.0638526	−	0.997959i	$-0.520339\pi$
$587$	20.1658	−	34.9282i	0.832332	−	1.44164i	0.896184	−	0.443682i	$-0.146328\pi$
$588$		0			0
$589$	10.0128	+	17.3427i	0.412570	+	0.714592i
$590$		0			0
$591$	−8.32082	+	12.8676i	−0.342273	+	0.529301i
$592$		0			0
$593$		−	9.30611i		−	0.382156i	−0.981575	−	0.191078i	$-0.938802\pi$
$593$		−	9.30611i		−	0.382156i	0.981575	−	0.191078i	$-0.0611984\pi$
$594$		0			0
$595$	−10.8504	−	43.2187i	−0.444823	−	1.77179i
$596$		0			0
$597$	−4.69505	+	7.26057i	−0.192156	+	0.297155i
$598$		0			0
$599$	−0.0337880	+	0.0195075i	−0.00138054	+	0.000797056i	−0.500690	−	0.865627i	$-0.666920\pi$
$599$	−0.0337880	+	0.0195075i	−0.00138054	+	0.000797056i	0.499310	+	0.866424i	$0.333587\pi$
$600$		0			0
$601$	−34.4552	−	19.8927i	−1.40546	−	0.811441i	−0.410511	−	0.911856i	$-0.634650\pi$
$601$	−34.4552	−	19.8927i	−1.40546	−	0.811441i	−0.994946	+	0.100415i	$0.967983\pi$
$602$		0			0
$603$	12.7701	+	9.20248i	0.520039	+	0.374754i
$604$		0			0
$605$	−75.7632	−	43.7419i	−3.08021	−	1.77836i
$606$		0			0
$607$	20.0081	+	34.6551i	0.812104	+	1.40661i	0.911389	+	0.411547i	$0.135011\pi$
$607$	20.0081	+	34.6551i	0.812104	+	1.40661i	−0.0992843	+	0.995059i	$0.531655\pi$
$608$		0			0
$609$	2.26345	+	11.4265i	0.0917196	+	0.463026i
$610$		0			0
$611$		−	11.7708i		−	0.476194i
$612$		0			0
$613$	5.49560			0.221965			0.110983	−	0.993822i	$-0.464600\pi$
$613$	5.49560			0.221965			0.110983	+	0.993822i	$0.464600\pi$
$614$		0			0
$615$	−20.2374	−	39.5283i	−0.816053	−	1.59394i
$616$		0			0
$617$	−18.1436	−	31.4256i	−0.730432	−	1.26515i	−0.956699	−	0.291080i	$-0.905985\pi$
$617$	−18.1436	−	31.4256i	−0.730432	−	1.26515i	0.226266	−	0.974065i	$-0.427348\pi$
$618$		0			0
$619$	−16.5285	+	28.6281i	−0.664335	+	1.15066i	0.315130	+	0.949048i	$0.397952\pi$
$619$	−16.5285	+	28.6281i	−0.664335	+	1.15066i	−0.979465	+	0.201613i	$0.935382\pi$
$620$		0			0
$621$	−20.2912	+	7.92498i	−0.814259	+	0.318018i
$622$		0			0
$623$	2.54626	−	8.93475i	0.102014	−	0.357963i
$624$		0			0
$625$	−22.5033	−	38.9768i	−0.900130	−	1.55907i
$626$		0			0
$627$	−28.4692	+	14.5755i	−1.13695	+	0.582088i
$628$		0			0
$629$			13.4439i			0.536044i
$630$		0			0
$631$			27.6502i			1.10074i	0.834921	+	0.550370i	$0.185513\pi$
$631$			27.6502i			1.10074i	−0.834921	+	0.550370i	$0.814487\pi$
$632$		0			0
$633$	0.148583	−	2.94450i	0.00590564	−	0.117033i
$634$		0			0
$635$	7.01063	+	12.1428i	0.278208	+	0.481871i
$636$		0			0
$637$	14.0753	+	0.445634i	0.557685	+	0.0176567i
$638$		0			0
$639$	−34.2859	+	15.4248i	−1.35633	+	0.610197i
$640$		0			0
$641$	−6.92939	+	12.0020i	−0.273694	+	0.474052i	−0.969805	−	0.243882i	$-0.921579\pi$
$641$	−6.92939	+	12.0020i	−0.273694	+	0.474052i	0.696111	+	0.717935i	$0.254912\pi$
$642$		0			0
$643$	18.7853	+	32.5370i	0.740819	+	1.28314i	0.952123	+	0.305715i	$0.0988956\pi$
$643$	18.7853	+	32.5370i	0.740819	+	1.28314i	−0.211304	+	0.977420i	$0.567771\pi$
$644$		0			0
$645$	16.2492	−	25.1282i	0.639811	−	0.989423i
$646$		0			0
$647$	−19.3733			−0.761641			−0.380821	−	0.924649i	$-0.624358\pi$
$647$	−19.3733			−0.761641			−0.380821	+	0.924649i	$0.624358\pi$
$648$		0			0
$649$			48.7472i			1.91350i
$650$		0			0
$651$	26.9089	+	9.15817i	1.05464	+	0.358937i
$652$		0			0
$653$	−4.26860	−	7.39344i	−0.167043	−	0.289328i	0.770336	−	0.637639i	$-0.220089\pi$
$653$	−4.26860	−	7.39344i	−0.167043	−	0.289328i	−0.937379	+	0.348311i	$0.886755\pi$
$654$		0			0
$655$	19.0677	+	11.0088i	0.745038	+	0.430148i
$656$		0			0
$657$	21.7221	−	9.77253i	0.847459	−	0.381263i
$658$		0			0
$659$	−4.61026	−	2.66174i	−0.179590	−	0.103687i	0.407510	−	0.913201i	$-0.366397\pi$
$659$	−4.61026	−	2.66174i	−0.179590	−	0.103687i	−0.587100	+	0.809514i	$0.699731\pi$
$660$		0			0
$661$	12.3847	−	7.15033i	0.481710	−	0.278115i	−0.239419	−	0.970916i	$-0.576957\pi$
$661$	12.3847	−	7.15033i	0.481710	−	0.278115i	0.721129	+	0.692801i	$0.243624\pi$
$662$		0			0
$663$	−14.5475	−	0.734086i	−0.564980	−	0.0285096i
$664$		0			0
$665$	33.3786	−	8.37997i	1.29437	−	0.324961i
$666$		0			0
$667$			10.6565i			0.412623i
$668$		0			0
$669$	−15.8124	−	30.8852i	−0.611343	−	1.19409i
$670$		0			0
$671$	36.0023	+	62.3577i	1.38985	+	2.40729i
$672$		0			0
$673$	−18.3816	+	31.8378i	−0.708558	+	1.22726i	0.256834	+	0.966456i	$0.417321\pi$
$673$	−18.3816	+	31.8378i	−0.708558	+	1.22726i	−0.965392	+	0.260803i	$0.916013\pi$
$674$		0			0
$675$	36.4660	−	45.5719i	1.40358	−	1.75406i
$676$		0			0
$677$	−7.71366	−	4.45348i	−0.296460	−	0.171161i	0.344391	−	0.938826i	$-0.388085\pi$
$677$	−7.71366	−	4.45348i	−0.296460	−	0.171161i	−0.640852	+	0.767665i	$0.721419\pi$
$678$		0			0
$679$	−19.7694	−	20.4052i	−0.758680	−	0.783080i
$680$		0			0
$681$	−8.14922	−	15.9173i	−0.312279	−	0.609951i
$682$		0			0
$683$			13.6622i			0.522768i	0.965235	+	0.261384i	$0.0841789\pi$
$683$			13.6622i			0.522768i	−0.965235	+	0.261384i	$0.915821\pi$
$684$		0			0
$685$		−	36.2413i		−	1.38471i
$686$		0			0
$687$	−0.292870	+	5.80387i	−0.0111737	+	0.221431i
$688$		0			0
$689$	24.2355	−	13.9924i	0.923300	−	0.533068i
$690$		0			0
$691$	17.2087	−	29.8063i	0.654648	−	1.13388i	−0.327334	−	0.944909i	$-0.606150\pi$
$691$	17.2087	−	29.8063i	0.654648	−	1.13388i	0.981982	−	0.188975i	$-0.0605166\pi$
$692$		0			0
$693$	−16.7741	+	42.1853i	−0.637196	+	1.60249i
$694$		0			0
$695$	21.8268	+	12.6017i	0.827938	+	0.478010i
$696$		0			0
$697$	13.3008	+	23.0377i	0.503804	+	0.872613i
$698$		0			0
$699$	18.9786	−	29.3490i	0.717835	−	1.11008i
$700$		0			0
$701$	18.0060			0.680078			0.340039	−	0.940411i	$-0.389560\pi$
$701$	18.0060			0.680078			0.340039	+	0.940411i	$0.389560\pi$
$702$		0			0
$703$	−10.3830			−0.391602
$704$		0			0
$705$	−34.2860	−	22.1711i	−1.29129	−	0.835012i
$706$		0			0
$707$	6.33596	+	6.53973i	0.238288	+	0.245952i
$708$		0			0
$709$	25.2917	−	43.8065i	0.949849	−	1.64519i	0.204111	−	0.978948i	$-0.434570\pi$
$709$	25.2917	−	43.8065i	0.949849	−	1.64519i	0.745738	−	0.666239i	$-0.232097\pi$
$710$		0			0
$711$	−1.56522	+	15.4697i	−0.0587005	+	0.580159i
$712$		0			0
$713$	22.5201	+	13.0020i	0.843385	+	0.486928i
$714$		0			0
$715$	40.1483	−	23.1796i	1.50146	−	0.866869i
$716$		0			0
$717$	−0.297118	+	5.88804i	−0.0110961	+	0.219893i
$718$		0			0
$719$	44.2317			1.64956			0.824782	−	0.565450i	$-0.191298\pi$
$719$	44.2317			1.64956			0.824782	+	0.565450i	$0.191298\pi$
$720$		0			0
$721$	−0.724184	−	2.88453i	−0.0269700	−	0.107425i
$722$		0			0
$723$	−3.25904	+	1.66854i	−0.121205	+	0.0620537i
$724$		0			0
$725$	−14.2761	−	24.7269i	−0.530200	−	0.918332i
$726$		0			0
$727$	−23.3313	+	40.4110i	−0.865310	+	1.49876i	0.00142913	+	0.999999i	$0.499545\pi$
$727$	−23.3313	+	40.4110i	−0.865310	+	1.49876i	−0.866739	+	0.498762i	$0.833788\pi$
$728$		0			0
$729$	25.7740	+	8.04378i	0.954592	+	0.297918i
$730$		0			0
$731$	−8.96279	+	15.5240i	−0.331501	+	0.574176i
$732$		0			0
$733$	29.4459	−	17.0006i	1.08761	−	0.627932i	0.154671	−	0.987966i	$-0.450568\pi$
$733$	29.4459	−	17.0006i	1.08761	−	0.627932i	0.932939	+	0.360034i	$0.117235\pi$
$734$		0			0
$735$	27.8100	−	40.1595i	1.02579	−	1.48130i
$736$		0			0
$737$	30.0096			1.10542
$738$		0			0
$739$		−	12.4853i		−	0.459279i	−0.973276	−	0.229640i	$-0.926245\pi$
$739$		−	12.4853i		−	0.459279i	0.973276	−	0.229640i	$-0.0737548\pi$
$740$		0			0
$741$	0.566949	−	11.2353i	0.0208274	−	0.412740i
$742$		0			0
$743$	−24.6313	+	14.2209i	−0.903636	+	0.521714i	−0.878378	−	0.477967i	$-0.841374\pi$
$743$	−24.6313	+	14.2209i	−0.903636	+	0.521714i	−0.0252578	+	0.999681i	$0.508041\pi$
$744$		0			0
$745$	44.1187	+	25.4719i	1.61638	+	0.933219i
$746$		0			0
$747$	16.0550	+	1.62445i	0.587424	+	0.0594356i
$748$		0			0
$749$	−1.81423	+	6.36606i	−0.0662904	+	0.232611i
$750$		0			0
$751$	3.91640	−	2.26113i	0.142911	−	0.0825100i	−0.426839	−	0.904327i	$-0.640373\pi$
$751$	3.91640	−	2.26113i	0.142911	−	0.0825100i	0.569751	+	0.821817i	$0.307040\pi$
$752$		0			0
$753$	1.23290	−	1.90659i	0.0449294	−	0.0694801i
$754$		0			0
$755$	64.2508			2.33833
$756$		0			0
$757$	−9.85242			−0.358092			−0.179046	−	0.983841i	$-0.557301\pi$
$757$	−9.85242			−0.358092			−0.179046	+	0.983841i	$0.557301\pi$
$758$		0			0
$759$	−22.5521	+	34.8753i	−0.818591	+	1.26589i
$760$		0			0
$761$	45.5417	−	26.2935i	1.65089	−	0.953139i	0.674176	−	0.738571i	$-0.264499\pi$
$761$	45.5417	−	26.2935i	1.65089	−	0.953139i	0.976709	−	0.214568i	$-0.0688345\pi$
$762$		0			0
$763$	−28.3110	−	8.06817i	−1.02493	−	0.292087i
$764$		0			0
$765$	−29.5396	+	40.9916i	−1.06801	+	1.48205i
$766$		0			0
$767$	−14.8489	−	8.57300i	−0.536162	−	0.309553i
$768$		0			0
$769$	9.80437	−	5.66055i	0.353555	−	0.204125i	−0.312695	−	0.949854i	$-0.601232\pi$
$769$	9.80437	−	5.66055i	0.353555	−	0.204125i	0.666250	+	0.745729i	$0.267899\pi$
$770$		0			0
$771$	−0.978757	+	19.3962i	−0.0352491	+	0.698538i
$772$		0			0
$773$			1.42526i			0.0512631i	0.999671	+	0.0256316i	$0.00815967\pi$
$773$			1.42526i			0.0512631i	−0.999671	+	0.0256316i	$0.991840\pi$
$774$		0			0
$775$	−69.6726			−2.50271
$776$		0			0
$777$	−11.0882	+	9.70851i	−0.397786	+	0.348291i
$778$		0			0
$779$	−17.7924	+	10.2725i	−0.637479	+	0.368049i
$780$		0			0
$781$	−35.8388	+	62.0746i	−1.28241	+	2.22120i
$782$		0			0
$783$	8.25227	−	10.3129i	0.294912	−	0.368555i
$784$		0			0
$785$	−35.7714	+	61.9579i	−1.27674	+	2.21137i
$786$		0			0
$787$	−20.9215	−	36.2370i	−0.745769	−	1.29171i	−0.949834	−	0.312753i	$-0.898749\pi$
$787$	−20.9215	−	36.2370i	−0.745769	−	1.29171i	0.204065	−	0.978957i	$-0.434585\pi$
$788$		0			0
$789$	2.75601	−	1.41100i	0.0981164	−	0.0502330i
$790$		0			0
$791$	−0.772261	−	3.07603i	−0.0274585	−	0.109371i
$792$		0			0
$793$	−25.3264			−0.899366
$794$		0			0
$795$	4.89218	−	96.9493i	0.173508	−	3.43844i
$796$		0			0
$797$	−7.85796	+	4.53679i	−0.278343	+	0.160701i	−0.632673	−	0.774419i	$-0.718042\pi$
$797$	−7.85796	+	4.53679i	−0.278343	+	0.160701i	0.354330	+	0.935120i	$0.384709\pi$
$798$		0			0
$799$	21.1816	+	12.2292i	0.749353	+	0.432639i
$800$		0			0
$801$	−9.60697	+	4.32207i	−0.339446	+	0.152713i
$802$		0			0
$803$	22.7060	−	39.3279i	0.801276	−	1.38785i
$804$		0			0
$805$	32.0956	−	31.0955i	1.13122	−	1.09597i
$806$		0			0
$807$	33.2408	+	21.4952i	1.17013	+	0.756667i
$808$		0			0
$809$	−18.6037			−0.654071			−0.327035	−	0.945012i	$-0.606050\pi$
$809$	−18.6037			−0.654071			−0.327035	+	0.945012i	$0.606050\pi$
$810$		0			0
$811$	43.7813			1.53737			0.768684	−	0.639628i	$-0.220912\pi$
$811$	43.7813			1.53737			0.768684	+	0.639628i	$0.220912\pi$
$812$		0			0
$813$	12.6907	−	19.6253i	0.445082	−	0.688288i
$814$		0			0
$815$	−20.4040	−	35.3407i	−0.714721	−	1.23793i
$816$		0			0
$817$	−11.9895	−	6.92213i	−0.419459	−	0.242175i
$818$		0			0
$819$	−9.90004	−	12.5285i	−0.345935	−	0.437782i
$820$		0			0
$821$	−11.8053	+	20.4474i	−0.412009	+	0.713620i	−0.995109	−	0.0987801i	$-0.968506\pi$
$821$	−11.8053	+	20.4474i	−0.412009	+	0.713620i	0.583101	+	0.812400i	$0.301839\pi$
$822$		0			0
$823$	−0.653789	+	0.377465i	−0.0227897	+	0.0131576i	−0.511352	−	0.859372i	$-0.670855\pi$
$823$	−0.653789	+	0.377465i	−0.0227897	+	0.0131576i	0.488562	+	0.872529i	$0.337522\pi$
$824$		0			0
$825$	5.60800	−	111.135i	0.195245	−	3.86922i
$826$		0			0
$827$		−	5.64456i		−	0.196281i	−0.995173	−	0.0981404i	$-0.968711\pi$
$827$		−	5.64456i		−	0.196281i	0.995173	−	0.0981404i	$-0.0312894\pi$
$828$		0			0
$829$			26.2077i			0.910230i	0.890433	+	0.455115i	$0.150402\pi$
$829$			26.2077i			0.910230i	−0.890433	+	0.455115i	$0.849598\pi$
$830$		0			0
$831$	15.8302	+	30.9200i	0.549144	+	1.07260i
$832$		0			0
$833$	−15.4255	+	24.8658i	−0.534461	+	0.861548i
$834$		0			0
$835$	49.4276	+	28.5370i	1.71051	+	0.987565i
$836$		0			0
$837$	−11.7254	−	30.0220i	−0.405291	−	1.03771i
$838$		0			0
$839$	10.5365	−	18.2498i	0.363761	−	0.630053i	−0.624815	−	0.780773i	$-0.714826\pi$
$839$	10.5365	−	18.2498i	0.363761	−	0.630053i	0.988577	+	0.150720i	$0.0481591\pi$
$840$		0			0
$841$	11.2693	+	19.5190i	0.388597	+	0.673070i
$842$		0			0
$843$	−12.6277	−	24.6648i	−0.434922	−	0.849501i
$844$		0			0
$845$		−	36.0704i		−	1.24086i
$846$		0			0
$847$	13.9890	+	55.7200i	0.480666	+	1.91456i
$848$		0			0
$849$	−32.6382	−	1.64697i	−1.12014	−	0.0565237i
$850$		0			0
$851$	−11.6764	+	6.74135i	−0.400261	+	0.231091i
$852$		0			0
$853$	−30.6601	−	17.7016i	−1.04978	−	0.606092i	−0.127193	−	0.991878i	$-0.540597\pi$
$853$	−30.6601	−	17.7016i	−1.04978	−	0.606092i	−0.922588	+	0.385786i	$0.873930\pi$
$854$		0			0
$855$	−31.6586	−	22.8140i	−1.08270	−	0.780222i
$856$		0			0
$857$	19.1852	+	11.0766i	0.655356	+	0.378370i	0.790505	−	0.612455i	$-0.209818\pi$
$857$	19.1852	+	11.0766i	0.655356	+	0.378370i	−0.135149	+	0.990825i	$0.543151\pi$
$858$		0			0
$859$	−2.32382	−	4.02497i	−0.0792876	−	0.137330i	0.823655	−	0.567091i	$-0.191931\pi$
$859$	−2.32382	−	4.02497i	−0.0792876	−	0.137330i	−0.902943	+	0.429761i	$0.858598\pi$
$860$		0			0
$861$	−9.39567	+	27.6068i	−0.320204	+	0.940836i
$862$		0			0
$863$		−	10.5090i		−	0.357732i	−0.983873	−	0.178866i	$-0.942757\pi$
$863$		−	10.5090i		−	0.357732i	0.983873	−	0.178866i	$-0.0572428\pi$
$864$		0			0
$865$	43.8526			1.49103
$866$		0			0
$867$	0.446300	−	0.690172i	0.0151572	−	0.0234395i
$868$		0			0
$869$	14.8220	+	25.6725i	0.502802	+	0.870879i
$870$		0			0
$871$	−5.27769	+	9.14122i	−0.178828	+	0.309739i
$872$		0			0
$873$	−3.24300	+	32.0517i	−0.109759	+	1.08479i
$874$		0			0
$875$	−18.2082	+	63.8922i	−0.615551	+	2.15995i
$876$		0			0
$877$	−3.60317	−	6.24087i	−0.121670	−	0.210739i	0.798756	−	0.601655i	$-0.205492\pi$
$877$	−3.60317	−	6.24087i	−0.121670	−	0.210739i	−0.920427	+	0.390916i	$0.872158\pi$
$878$		0			0
$879$	1.33949	−	26.5449i	0.0451798	−	0.895337i
$880$		0			0
$881$			47.4313i			1.59800i	0.601331	+	0.799000i	$0.294637\pi$
$881$			47.4313i			1.59800i	−0.601331	+	0.799000i	$0.705363\pi$
$882$		0			0
$883$			44.5341i			1.49869i	0.662178	+	0.749346i	$0.269632\pi$
$883$			44.5341i			1.49869i	−0.662178	+	0.749346i	$0.730368\pi$
$884$		0			0
$885$	−52.9405	+	27.1041i	−1.77958	+	0.911096i
$886$		0			0
$887$	−6.55039	−	11.3456i	−0.219941	−	0.380948i	0.734849	−	0.678231i	$-0.237253\pi$
$887$	−6.55039	−	11.3456i	−0.219941	−	0.380948i	−0.954790	+	0.297283i	$0.903920\pi$
$888$		0			0
$889$	2.52352	−	8.85497i	0.0846363	−	0.296986i
$890$		0			0
$891$	48.8319	−	16.2868i	1.63593	−	0.545627i
$892$		0			0
$893$	−9.44486	+	16.3590i	−0.316060	+	0.547432i
$894$		0			0
$895$	23.6254	+	40.9205i	0.789711	+	1.36782i
$896$		0			0
$897$	−6.65719	−	13.0030i	−0.222277	−	0.434157i
$898$		0			0
$899$	−15.7669			−0.525857
$900$		0			0
$901$			58.1495i			1.93724i
$902$		0			0
$903$	−19.2763	+	3.81838i	−0.641474	+	0.127068i
$904$		0			0
$905$	35.5600	+	61.5917i	1.18205	+	2.04738i
$906$		0			0
$907$	16.1687	+	9.33500i	0.536872	+	0.309963i	0.743810	−	0.668391i	$-0.233017\pi$
$907$	16.1687	+	9.33500i	0.536872	+	0.309963i	−0.206938	+	0.978354i	$0.566350\pi$
$908$		0			0
$909$	1.03936	−	10.2724i	0.0344734	−	0.340713i
$910$		0			0
$911$	−9.20898	−	5.31680i	−0.305107	−	0.176154i	0.339628	−	0.940560i	$-0.389699\pi$
$911$	−9.20898	−	5.31680i	−0.305107	−	0.176154i	−0.644735	+	0.764406i	$0.723032\pi$
$912$		0			0
$913$	26.6439	−	15.3829i	0.881785	−	0.509099i
$914$		0			0
$915$	−47.7041	+	73.7710i	−1.57705	+	2.43879i
$916$		0			0
$917$	−3.52068	−	14.0234i	−0.116263	−	0.463092i
$918$		0			0
$919$			25.9144i			0.854836i	0.904054	+	0.427418i	$0.140577\pi$
$919$			25.9144i			0.854836i	−0.904054	+	0.427418i	$0.859423\pi$
$920$		0			0
$921$	12.0660	−	18.6592i	0.397587	−	0.614841i
$922$		0			0
$923$	−12.6057	−	21.8337i	−0.414921	−	0.718665i
$924$		0			0
$925$	18.0621	−	31.2846i	0.593880	−	1.02863i
$926$		0			0
$927$	−1.97155	+	2.73588i	−0.0647542	+	0.0898582i
$928$		0			0
$929$	−44.4016	−	25.6353i	−1.45677	−	0.841066i	−0.457918	−	0.888994i	$-0.651405\pi$
$929$	−44.4016	−	25.6353i	−1.45677	−	0.841066i	−0.998851	+	0.0479287i	$0.984738\pi$
$930$		0			0
$931$	−19.2043	−	11.9134i	−0.629395	−	0.390446i
$932$		0			0
$933$	−3.51948	−	0.177597i	−0.115223	−	0.00581427i
$934$		0			0
$935$			96.3298i			3.15032i
$936$		0			0
$937$			47.7056i			1.55847i	0.626729	+	0.779237i	$0.284393\pi$
$937$			47.7056i			1.55847i	−0.626729	+	0.779237i	$0.715607\pi$
$938$		0			0
$939$	15.0073	−	7.68335i	0.489745	−	0.250736i
$940$		0			0
$941$	−49.3584	+	28.4971i	−1.60904	+	0.928978i	−0.619452	+	0.785035i	$0.712645\pi$
$941$	−49.3584	+	28.4971i	−1.60904	+	0.928978i	−0.989586	+	0.143944i	$0.954022\pi$
$942$		0			0
$943$	−13.3392	+	23.1041i	−0.434383	+	0.752374i
$944$		0			0
$945$	−55.1407	+	5.23855i	−1.79373	+	0.170410i
$946$		0			0
$947$	−4.86698	−	2.80995i	−0.158156	−	0.0913113i	0.418833	−	0.908063i	$-0.362439\pi$
$947$	−4.86698	−	2.80995i	−0.158156	−	0.0913113i	−0.576989	+	0.816752i	$0.695772\pi$
$948$		0			0
$949$	7.98644	+	13.8329i	0.259251	+	0.449035i
$950$		0			0
$951$	−18.1664	−	35.4831i	−0.589085	−	1.15062i
$952$		0			0
$953$	−39.6935			−1.28580			−0.642899	−	0.765951i	$-0.722269\pi$
$953$	−39.6935			−1.28580			−0.642899	+	0.765951i	$0.722269\pi$
$954$		0			0
$955$	−2.70465			−0.0875205
$956$		0			0
$957$	1.26909	−	25.1499i	0.0410239	−	0.812980i
$958$		0			0
$959$	−17.0927	+	16.5601i	−0.551951	+	0.534753i
$960$		0			0
$961$	−3.73718	+	6.47298i	−0.120554	+	0.208806i
$962$		0			0
$963$	6.84502	−	3.07950i	0.220578	−	0.0992356i
$964$		0			0
$965$	52.0255	+	30.0369i	1.67476	+	0.966923i
$966$		0			0
$967$	−23.3249	+	13.4666i	−0.750078	+	0.433058i	−0.825722	−	0.564077i	$-0.809232\pi$
$967$	−23.3249	+	13.4666i	−0.750078	+	0.433058i	0.0756442	+	0.997135i	$0.475899\pi$
$968$		0			0
$969$	19.6291	+	12.6932i	0.630578	+	0.407764i
$970$		0			0
$971$	−9.63591			−0.309231			−0.154616	−	0.987975i	$-0.549414\pi$
$971$	−9.63591			−0.309231			−0.154616	+	0.987975i	$0.549414\pi$
$972$		0			0
$973$	−4.03012	−	16.0525i	−0.129200	−	0.514620i
$974$		0			0
$975$	32.8665	+	21.2531i	1.05257	+	0.680645i
$976$		0			0
$977$	−25.0233	−	43.3417i	−0.800567	−	1.38662i	−0.919243	−	0.393690i	$-0.871198\pi$
$977$	−25.0233	−	43.3417i	−0.800567	−	1.38662i	0.118676	−	0.992933i	$-0.462135\pi$
$978$		0			0
$979$	−10.0421	+	17.3934i	−0.320947	+	0.555897i
$980$		0			0
$981$	13.6951	+	30.4410i	0.437250	+	0.971905i
$982$		0			0
$983$	20.3246	−	35.2032i	0.648254	−	1.12281i	−0.335286	−	0.942116i	$-0.608833\pi$
$983$	20.3246	−	35.2032i	0.648254	−	1.12281i	0.983540	−	0.180692i	$-0.0578337\pi$
$984$		0			0
$985$	−30.8689	+	17.8222i	−0.983564	+	0.567861i
$986$		0			0
$987$	5.20997	+	26.3014i	0.165835	+	0.837182i
$988$		0			0
$989$	−17.9773			−0.571645
$990$		0			0
$991$		−	7.45474i		−	0.236808i	−0.992966	−	0.118404i	$-0.962222\pi$
$991$		−	7.45474i		−	0.236808i	0.992966	−	0.118404i	$-0.0377777\pi$
$992$		0			0
$993$	−32.7425	+	16.7633i	−1.03905	+	0.531966i
$994$		0			0
$995$	−17.4179	+	10.0562i	−0.552184	+	0.318804i
$996$		0			0
$997$	−10.3529	−	5.97727i	−0.327881	−	0.189302i	0.327019	−	0.945018i	$-0.393956\pi$
$997$	−10.3529	−	5.97727i	−0.327881	−	0.189302i	−0.654900	+	0.755716i	$0.727289\pi$
$998$		0			0
$999$	16.5203	+	2.51802i	0.522679	+	0.0796665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cx.j.223.6	yes	24
3.2	odd	2		3024.2.cx.j.559.12		24
4.3	odd	2		1008.2.cx.i.223.7	yes	24
7.6	odd	2	inner	1008.2.cx.j.223.7	yes	24
9.4	even	3		1008.2.cx.i.895.6	yes	24
9.5	odd	6		3024.2.cx.i.2575.1		24
12.11	even	2		3024.2.cx.i.559.12		24
21.20	even	2		3024.2.cx.j.559.1		24
28.27	even	2		1008.2.cx.i.223.6	✓	24
36.23	even	6		3024.2.cx.j.2575.1		24
36.31	odd	6	inner	1008.2.cx.j.895.7	yes	24
63.13	odd	6		1008.2.cx.i.895.7	yes	24
63.41	even	6		3024.2.cx.i.2575.12		24
84.83	odd	2		3024.2.cx.i.559.1		24
252.139	even	6	inner	1008.2.cx.j.895.6	yes	24
252.167	odd	6		3024.2.cx.j.2575.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.cx.i.223.6	✓	24	28.27	even	2
1008.2.cx.i.223.7	yes	24	4.3	odd	2
1008.2.cx.i.895.6	yes	24	9.4	even	3
1008.2.cx.i.895.7	yes	24	63.13	odd	6
1008.2.cx.j.223.6	yes	24	1.1	even	1	trivial
1008.2.cx.j.223.7	yes	24	7.6	odd	2	inner
1008.2.cx.j.895.6	yes	24	252.139	even	6	inner
1008.2.cx.j.895.7	yes	24	36.31	odd	6	inner
3024.2.cx.i.559.1		24	84.83	odd	2
3024.2.cx.i.559.12		24	12.11	even	2
3024.2.cx.i.2575.1		24	9.5	odd	6
3024.2.cx.i.2575.12		24	63.41	even	6
3024.2.cx.j.559.1		24	21.20	even	2
3024.2.cx.j.559.12		24	3.2	odd	2
3024.2.cx.j.2575.1		24	36.23	even	6
3024.2.cx.j.2575.12		24	252.167	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.cx (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.940521 + 1.45445i) q^{3} +(-3.48918 + 2.01448i) q^{5} +(2.54444 + 0.725126i) q^{7} +(-1.23084 - 2.73588i) q^{9} +(-4.95331 - 2.85980i) q^{11} +(1.74224 - 1.00589i) q^{13} +(0.351689 - 6.96949i) q^{15} +4.18025i q^{17} -3.22849 q^{19} +(-3.44776 + 3.01877i) q^{21} +(-3.63065 + 2.09616i) q^{23} +(5.61625 - 9.72763i) q^{25} +(5.13683 + 0.782952i) q^{27} +(1.27096 - 2.20137i) q^{29} +(-3.10138 - 5.37176i) q^{31} +(8.81812 - 4.51464i) q^{33} +(-10.3388 + 2.59563i) q^{35} +3.21605 q^{37} +(-0.175608 + 3.48006i) q^{39} +(5.51107 - 3.18181i) q^{41} +(3.71365 + 2.14408i) q^{43} +(9.80600 + 7.06646i) q^{45} +(2.92547 - 5.06707i) q^{47} +(5.94838 + 3.69008i) q^{49} +(-6.07997 - 3.93161i) q^{51} +13.9105 q^{53} +23.0440 q^{55} +(3.03646 - 4.69567i) q^{57} +(-4.26142 - 7.38100i) q^{59} +(-10.9025 - 6.29455i) q^{61} +(-1.14795 - 7.85380i) q^{63} +(-4.05267 + 7.01943i) q^{65} +(-4.54387 + 2.62341i) q^{67} +(0.365949 - 7.25208i) q^{69} -12.5319i q^{71} +7.93971i q^{73} +(8.86614 + 17.3176i) q^{75} +(-10.5297 - 10.8684i) q^{77} +(-4.48851 - 2.59144i) q^{79} +(-5.97005 + 6.73487i) q^{81} +(-2.68950 + 4.65836i) q^{83} +(-8.42103 - 14.5857i) q^{85} +(2.00641 + 3.91898i) q^{87} -3.51148i q^{89} +(5.16244 - 1.29607i) q^{91} +(10.7299 + 0.541442i) q^{93} +(11.2648 - 6.50372i) q^{95} +(-9.29978 - 5.36923i) q^{97} +(-1.72731 + 17.0716i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{7} + 20 q^{9} - 24 q^{15} + 10 q^{21} - 18 q^{23} + 24 q^{25} - 6 q^{29} - 12 q^{37} + 12 q^{39} - 42 q^{43} + 12 q^{49} + 42 q^{51} + 96 q^{53} - 22 q^{57} - 18 q^{63} + 42 q^{65} - 36 q^{67}+ \cdots - 12 q^{99}+O(q^{100}) \) 24 * q + 6 * q^7 + 20 * q^9 - 24 * q^15 + 10 * q^21 - 18 * q^23 + 24 * q^25 - 6 * q^29 - 12 * q^37 + 12 * q^39 - 42 * q^43 + 12 * q^49 + 42 * q^51 + 96 * q^53 - 22 * q^57 - 18 * q^63 + 42 * q^65 - 36 * q^67 - 18 * q^77 + 60 * q^79 - 64 * q^81 - 6 * q^85 + 82 * q^93 + 126 * q^95 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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