LMFDB - Embedded newform 1008.2.cx.i.223.7

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			223.7
Character	$\chi$	$=$	1008.223
Dual form			1008.2.cx.i.895.7

$q$-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	0.999972	−	0.00747985i	$-0.00238093\pi$
$11$	4.95331	+	2.85980i	1.49348	+	0.862261i	0.493508	+	0.869741i	$0.335714\pi$
$12$		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	$-0.379244\pi$
$19$	3.22849			0.740666			0.370333	+	0.928899i	$0.379244\pi$
$20$		0			0
$21$	−3.44776	+	3.01877i	−0.752363	+	0.658749i
$22$		0			0
$23$	3.63065	−	2.09616i	0.757044	−	0.437079i	−0.0711897	−	0.997463i	$-0.522680\pi$
$23$	3.63065	−	2.09616i	0.757044	−	0.437079i	0.828233	+	0.560383i	$0.189346\pi$
$24$		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	$0.0213907\pi$
$31$	3.10138	+	5.37176i	0.557025	+	0.964796i	−0.440718	+	0.897646i	$0.645276\pi$
$32$		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	0.189354	−	0.981909i	$-0.439361\pi$
$43$	−3.71365	−	2.14408i	−0.566327	−	0.326969i	−0.755681	+	0.654940i	$0.772694\pi$
$44$		0			0
$45$	9.80600	+	7.06646i	1.46179	+	1.05341i
$46$		0			0
$47$	−2.92547	+	5.06707i	−0.426724	+	0.739108i	−0.996580	−	0.0826368i	$-0.973666\pi$
$47$	−2.92547	+	5.06707i	−0.426724	+	0.739108i	0.569855	+	0.821745i	$0.306999\pi$
$48$		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	$0.0205348\pi$
$59$	4.26142	+	7.38100i	0.554790	+	0.960925i	−0.443130	+	0.896457i	$0.646132\pi$
$60$		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	−0.196063	−	0.980591i	$-0.562816\pi$
$67$	4.54387	−	2.62341i	0.555122	−	0.320500i	0.751185	+	0.660091i	$0.229482\pi$
$68$		0			0
$69$	0.365949	−	7.25208i	0.0440551	−	0.873048i
$70$		0			0
$71$			12.5319i			1.48727i	0.668587	+	0.743634i	$0.266899\pi$
$71$			12.5319i			1.48727i	−0.668587	+	0.743634i	$0.733101\pi$
$72$		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	0.730775	−	0.682619i	$-0.239159\pi$
$79$	4.48851	+	2.59144i	0.504997	+	0.291560i	−0.225778	+	0.974179i	$0.572492\pi$
$80$		0			0
$81$	−5.97005	+	6.73487i	−0.663339	+	0.748319i
$82$		0			0
$83$	2.68950	−	4.65836i	0.295211	−	0.511321i	−0.679823	−	0.733377i	$-0.737943\pi$
$83$	2.68950	−	4.65836i	0.295211	−	0.511321i	0.975034	+	0.222055i	$0.0712766\pi$
$84$		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	0.892386	−	0.451273i	$-0.149030\pi$
$103$	0.562042	+	0.973484i	0.0553796	+	0.0959203i	−0.837007	+	0.547193i	$0.815696\pi$
$104$		0			0
$105$	5.94861	−	17.4785i	0.580525	−	1.70572i
$106$		0			0
$107$		−	2.50195i		−	0.241872i	−0.992660	−	0.120936i	$-0.961410\pi$
$107$		−	2.50195i		−	0.241872i	0.992660	−	0.120936i	$-0.0385897\pi$
$108$		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	$0.0493462\pi$
$127$			3.48012i			0.308811i	−0.988008	+	0.154405i	$0.950654\pi$
$128$		0			0
$129$	−6.61122	+	3.38477i	−0.582085	+	0.298012i
$130$		0			0
$131$	2.73241	+	4.73267i	0.238732	+	0.413495i	0.960351	−	0.278795i	$-0.0899350\pi$
$131$	2.73241	+	4.73267i	0.238732	+	0.413495i	−0.721619	+	0.692290i	$0.756602\pi$
$132$		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	0.967641	−	0.252331i	$-0.0811972\pi$
$139$	3.12779	+	5.41748i	0.265295	+	0.459505i	−0.702346	+	0.711836i	$0.747864\pi$
$140$		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	0.942394	−	0.334505i	$-0.108569\pi$
$151$	13.8107	+	7.97363i	1.12390	+	0.648884i	0.181507	+	0.983390i	$0.441903\pi$
$152$		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	$-0.870166\pi$
$163$		−	10.1287i		−	0.793339i	0.917962	−	0.396669i	$-0.129834\pi$
$164$		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	$0.0179812\pi$
$167$	7.08298	+	12.2681i	0.548098	+	0.949333i	−0.450307	+	0.892874i	$0.648685\pi$
$168$		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	$0.144415\pi$
$179$			11.7278i			0.876578i	−0.898834	+	0.438289i	$0.855585\pi$
$180$		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	0.478819	−	0.877913i	$-0.341065\pi$
$191$	−0.581366	−	0.335652i	−0.0420662	−	0.0242869i	−0.520886	+	0.853626i	$0.674398\pi$
$192$		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	$-0.556619\pi$
$199$	−4.99197			−0.353872			−0.176936	+	0.984222i	$0.556619\pi$
$200$		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	−0.448400	−	0.893833i	$-0.648006\pi$
$211$	1.47412	−	0.851085i	0.101483	−	0.0585911i	0.549882	+	0.835242i	$0.314673\pi$
$212$		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	$-0.599308\pi$
$223$	10.0164	−	17.3488i	0.670745	−	1.16176i	0.977693	−	0.210038i	$-0.0673588\pi$
$224$		0			0
$225$	−33.5263	−	3.39220i	−2.23509	−	0.226146i
$226$		0			0
$227$	5.16212	−	8.94105i	0.342622	−	0.593438i	−0.642297	−	0.766456i	$-0.722018\pi$
$227$	5.16212	−	8.94105i	0.342622	−	0.593438i	0.984919	+	0.173018i	$0.0553517\pi$
$228$		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	−0.592299	−	0.805719i	$-0.701779\pi$
$239$	−2.94777	+	1.70189i	−0.190675	+	0.110086i	0.401623	+	0.915805i	$0.368446\pi$
$240$		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	$-0.486828\pi$
$251$	1.31087			0.0827413			0.0413707	+	0.999144i	$0.486828\pi$
$252$		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	0.546970	−	0.837152i	$-0.315781\pi$
$263$	1.54810	+	0.893798i	0.0954601	+	0.0551139i	−0.451510	+	0.892266i	$0.649114\pi$
$264$		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	$-0.365589\pi$
$271$	13.4933			0.819657			0.409828	+	0.912163i	$0.365589\pi$
$272$		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	$-0.977167\pi$
$283$	−9.43384	−	16.3399i	−0.560783	−	0.971305i	0.436645	−	0.899634i	$-0.356167\pi$
$284$		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	$-0.380694\pi$
$307$	12.8290			0.732192			0.366096	+	0.930577i	$0.380694\pi$
$308$		0			0
$309$	1.94449	+	0.0981216i	0.110618	+	0.00558194i
$310$		0			0
$311$	−1.01728	−	1.76198i	−0.0576846	−	0.0999127i	0.835741	−	0.549124i	$-0.185038\pi$
$311$	−1.01728	−	1.76198i	−0.0576846	−	0.0999127i	−0.893426	+	0.449211i	$0.851705\pi$
$312$		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	−0.0994598	−	0.995042i	$-0.531711\pi$
$331$	−18.3921	−	10.6187i	−1.01092	−	0.583656i	−0.911461	+	0.411386i	$0.865045\pi$
$332$		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	−0.105306	−	0.994440i	$-0.533582\pi$
$347$	13.1001	−	7.56336i	0.703251	−	0.406022i	0.808557	+	0.588417i	$0.200249\pi$
$348$		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	$0.0737871\pi$
$359$			8.70585i			0.459477i	−0.973252	+	0.229739i	$0.926213\pi$
$360$		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	$0.351437\pi$
$367$	−10.5062	+	18.1973i	−0.548419	+	0.949890i	−0.998383	+	0.0568434i	$0.981896\pi$
$368$		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	$0.311794\pi$
$379$			32.3259i			1.66047i	−0.557414	+	0.830234i	$0.688206\pi$
$380$		0			0
$381$	5.06166	+	3.27312i	0.259316	+	0.167687i
$382$		0			0
$383$	−2.70529	−	4.68571i	−0.138234	−	0.239428i	0.788594	−	0.614914i	$-0.210809\pi$
$383$	−2.70529	−	4.68571i	−0.138234	−	0.239428i	−0.926828	+	0.375486i	$0.877476\pi$
$384$		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	0.987888	−	0.155170i	$-0.0495925\pi$
$419$	7.36007	+	12.7480i	0.359563	+	0.622781i	−0.628325	+	0.777951i	$0.716259\pi$
$420$		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	$-0.993880\pi$
$431$		−	0.798303i		−	0.0384529i	0.999815	−	0.0192265i	$-0.00612035\pi$
$432$		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	−0.927760	−	0.373178i	$-0.878268\pi$
$439$	−2.94795	+	5.10600i	−0.140698	+	0.243696i	0.787062	+	0.616874i	$0.211601\pi$
$440$		0			0
$441$	2.77409	−	20.8160i	0.132100	−	0.991236i
$442$		0			0
$443$	2.02844	+	1.17112i	0.0963742	+	0.0556417i	0.547413	−	0.836863i	$-0.315613\pi$
$443$	2.02844	+	1.17112i	0.0963742	+	0.0556417i	−0.451038	+	0.892505i	$0.648946\pi$
$444$		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	−0.543168	−	0.839624i	$-0.682775\pi$
$463$	−1.88529	+	1.08847i	−0.0876166	+	0.0505855i	0.455552	+	0.890209i	$0.349442\pi$
$464$		0			0
$465$	−38.5291	+	19.7259i	−1.78675	+	0.914766i
$466$		0			0
$467$	−20.8089			−0.962923			−0.481461	−	0.876467i	$-0.659894\pi$
$467$	−20.8089			−0.962923			−0.481461	+	0.876467i	$0.659894\pi$
$468$		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	$-0.581866\pi$
$479$	15.5470	−	26.9281i	0.710359	−	1.23038i	0.964723	−	0.263269i	$-0.0848005\pi$
$480$		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	$0.142893\pi$
$487$			19.1545i			0.867972i	−0.900920	+	0.433986i	$0.857107\pi$
$488$		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	$0.670492\pi$
$491$	−33.4660	+	19.3216i	−1.51030	+	0.871972i	−0.999928	+	0.0120176i	$0.996175\pi$
$492$		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	$-0.234549\pi$
$499$	37.8146	−	21.8323i	1.69281	−	0.977346i	0.952230	−	0.305382i	$-0.0987843\pi$
$500$		0			0
$501$	24.5050	+	1.23655i	1.09480	+	0.0552451i
$502$		0			0
$503$	−34.6828			−1.54643			−0.773215	−	0.634144i	$-0.781353\pi$
$503$	−34.6828			−1.54643			−0.773215	+	0.634144i	$0.781353\pi$
$504$		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	$-0.425298\pi$
$523$	10.6357			0.465068			0.232534	+	0.972588i	$0.425298\pi$
$524$		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	$0.00703206\pi$
$547$	35.5209	+	20.5080i	1.51876	+	0.876859i	0.519009	+	0.854769i	$0.326301\pi$
$548$		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	$-0.953432\pi$
$563$	−14.7326	−	25.5176i	−0.620904	−	1.07544i	0.368414	−	0.929662i	$-0.379901\pi$
$564$		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	−0.883462	−	0.468502i	$-0.844794\pi$
$571$	−21.9710	+	12.6850i	−0.919459	+	0.530850i	−0.0359963	+	0.999352i	$0.511460\pi$
$572$		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	$0.479661\pi$
$587$	−20.1658	+	34.9282i	−0.832332	+	1.44164i	−0.896184	+	0.443682i	$0.853672\pi$
$588$		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	−0.499310	−	0.866424i	$-0.666413\pi$
$599$	0.0337880	−	0.0195075i	0.00138054	−	0.000797056i	0.500690	+	0.865627i	$0.333080\pi$
$600$		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	$-0.864989\pi$
$607$	−20.0081	−	34.6551i	−0.812104	−	1.40661i	0.0992843	−	0.995059i	$-0.468345\pi$
$608$		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	$-0.602048\pi$
$619$	16.5285	−	28.6281i	0.664335	−	1.15066i	0.979465	−	0.201613i	$-0.0646185\pi$
$620$		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	$-0.814487\pi$
$631$		−	27.6502i		−	1.10074i	0.834921	−	0.550370i	$-0.185513\pi$
$632$		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	$-0.901104\pi$
$643$	−18.7853	−	32.5370i	−0.740819	−	1.28314i	0.211304	−	0.977420i	$-0.432229\pi$
$644$		0			0
$645$	16.2492	−	25.1282i	0.639811	−	0.989423i
$646$		0			0
$647$	19.3733			0.761641			0.380821	−	0.924649i	$-0.375642\pi$
$647$	19.3733			0.761641			0.380821	+	0.924649i	$0.375642\pi$
$648$		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	0.587100	−	0.809514i	$-0.300269\pi$
$659$	4.61026	+	2.66174i	0.179590	+	0.103687i	−0.407510	+	0.913201i	$0.633603\pi$
$660$		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	$-0.915821\pi$
$683$		−	13.6622i		−	0.522768i	0.965235	−	0.261384i	$-0.0841789\pi$
$684$		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	$0.393850\pi$
$691$	−17.2087	+	29.8063i	−0.654648	+	1.13388i	−0.981982	+	0.188975i	$0.939483\pi$
$692$		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	$-0.808702\pi$
$719$	−44.2317			−1.64956			−0.824782	+	0.565450i	$0.808702\pi$
$720$		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	$-0.500455\pi$
$727$	23.3313	−	40.4110i	0.865310	−	1.49876i	0.866739	−	0.498762i	$-0.166212\pi$
$728$		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	$0.0737548\pi$
$739$			12.4853i			0.459279i	−0.973276	+	0.229640i	$0.926245\pi$
$740$		0			0
$741$	0.566949	−	11.2353i	0.0208274	−	0.412740i
$742$		0			0
$743$	24.6313	−	14.2209i	0.903636	−	0.521714i	0.0252578	−	0.999681i	$-0.491959\pi$
$743$	24.6313	−	14.2209i	0.903636	−	0.521714i	0.878378	+	0.477967i	$0.158626\pi$
$744$		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	−0.569751	−	0.821817i	$-0.692960\pi$
$751$	−3.91640	+	2.26113i	−0.142911	+	0.0825100i	0.426839	+	0.904327i	$0.359627\pi$
$752$		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	$0.101251\pi$
$787$	20.9215	+	36.2370i	0.745769	+	1.29171i	−0.204065	+	0.978957i	$0.565415\pi$
$788$		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	$-0.779088\pi$
$811$	−43.7813			−1.53737			−0.768684	+	0.639628i	$0.779088\pi$
$812$		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	−0.488562	−	0.872529i	$-0.662478\pi$
$823$	0.653789	−	0.377465i	0.0227897	−	0.0131576i	0.511352	+	0.859372i	$0.329145\pi$
$824$		0			0
$825$	5.60800	−	111.135i	0.195245	−	3.86922i
$826$		0			0
$827$			5.64456i			0.196281i	0.995173	+	0.0981404i	$0.0312894\pi$
$827$			5.64456i			0.196281i	−0.995173	+	0.0981404i	$0.968711\pi$
$828$		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	−0.988577	−	0.150720i	$-0.951841\pi$
$839$	−10.5365	+	18.2498i	−0.363761	+	0.630053i	0.624815	+	0.780773i	$0.285174\pi$
$840$		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	0.902943	−	0.429761i	$-0.141402\pi$
$859$	2.32382	+	4.02497i	0.0792876	+	0.137330i	−0.823655	+	0.567091i	$0.808069\pi$
$860$		0			0
$861$	−9.39567	+	27.6068i	−0.320204	+	0.940836i
$862$		0			0
$863$			10.5090i			0.357732i	0.983873	+	0.178866i	$0.0572428\pi$
$863$			10.5090i			0.357732i	−0.983873	+	0.178866i	$0.942757\pi$
$864$		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	$-0.730368\pi$
$883$		−	44.5341i		−	1.49869i	0.662178	−	0.749346i	$-0.269632\pi$
$884$		0			0
$885$	−52.9405	+	27.1041i	−1.77958	+	0.911096i
$886$		0			0
$887$	6.55039	+	11.3456i	0.219941	+	0.380948i	0.954790	−	0.297283i	$-0.0960803\pi$
$887$	6.55039	+	11.3456i	0.219941	+	0.380948i	−0.734849	+	0.678231i	$0.762747\pi$
$888$		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	0.206938	−	0.978354i	$-0.433650\pi$
$907$	−16.1687	−	9.33500i	−0.536872	−	0.309963i	−0.743810	+	0.668391i	$0.766983\pi$
$908$		0			0
$909$	1.03936	−	10.2724i	0.0344734	−	0.340713i
$910$		0			0
$911$	9.20898	+	5.31680i	0.305107	+	0.176154i	0.644735	−	0.764406i	$-0.276968\pi$
$911$	9.20898	+	5.31680i	0.305107	+	0.176154i	−0.339628	+	0.940560i	$0.610301\pi$
$912$		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	$-0.859423\pi$
$919$		−	25.9144i		−	0.854836i	0.904054	−	0.427418i	$-0.140577\pi$
$920$		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	0.576989	−	0.816752i	$-0.304228\pi$
$947$	4.86698	+	2.80995i	0.158156	+	0.0913113i	−0.418833	+	0.908063i	$0.637561\pi$
$948$		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	−0.0756442	−	0.997135i	$-0.524101\pi$
$967$	23.3249	−	13.4666i	0.750078	−	0.433058i	0.825722	+	0.564077i	$0.190768\pi$
$968$		0			0
$969$	19.6291	+	12.6932i	0.630578	+	0.407764i
$970$		0			0
$971$	9.63591			0.309231			0.154616	−	0.987975i	$-0.450586\pi$
$971$	9.63591			0.309231			0.154616	+	0.987975i	$0.450586\pi$
$972$		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	$0.391167\pi$
$983$	−20.3246	+	35.2032i	−0.648254	+	1.12281i	−0.983540	+	0.180692i	$0.942166\pi$
$984$		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	$0.0377777\pi$
$991$			7.45474i			0.236808i	−0.992966	+	0.118404i	$0.962222\pi$
$992$		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.i.223.7	yes	24
3.2	odd	2		3024.2.cx.i.559.12		24
4.3	odd	2		1008.2.cx.j.223.6	yes	24
7.6	odd	2	inner	1008.2.cx.i.223.6	✓	24
9.4	even	3		1008.2.cx.j.895.7	yes	24
9.5	odd	6		3024.2.cx.j.2575.1		24
12.11	even	2		3024.2.cx.j.559.12		24
21.20	even	2		3024.2.cx.i.559.1		24
28.27	even	2		1008.2.cx.j.223.7	yes	24
36.23	even	6		3024.2.cx.i.2575.1		24
36.31	odd	6	inner	1008.2.cx.i.895.6	yes	24
63.13	odd	6		1008.2.cx.j.895.6	yes	24
63.41	even	6		3024.2.cx.j.2575.12		24
84.83	odd	2		3024.2.cx.j.559.1		24
252.139	even	6	inner	1008.2.cx.i.895.7	yes	24
252.167	odd	6		3024.2.cx.i.2575.12		24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
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

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Database

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