LMFDB - Embedded newform 2548.2.bq.e.1941.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2548,2,Mod(361,2548)] 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("2548.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2548, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.bq (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,28,0,0,0,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 38x^{14} + 587x^{12} + 4762x^{10} + 21849x^{8} + 56552x^{6} + 76456x^{4} + 42624x^{2} + 2704 $ x^16 + 38x^14 + 587x^12 + 4762x^10 + 21849x^8 + 56552x^6 + 76456x^4 + 42624*x^2 + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1941.6
Root			$1.75101i$ of defining polynomial
Character	$\chi$	$=$	2548.1941
Dual form			2548.2.bq.e.361.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.75101 q^{3} +(-1.19976 - 0.692682i) q^{5} +0.0660200 q^{9} -1.15290i q^{11} +(-1.65348 + 3.20406i) q^{13} +(-2.10079 - 1.21289i) q^{15} +(-0.781246 + 1.35316i) q^{17} -8.38917i q^{19} +(-1.11067 - 1.92374i) q^{23} +(-1.54038 - 2.66802i) q^{25} -5.13741 q^{27} +(-1.43491 + 2.48533i) q^{29} +(-5.75927 + 3.32512i) q^{31} -2.01874i q^{33} +(-3.01436 + 1.74034i) q^{37} +(-2.89525 + 5.61033i) q^{39} +(10.8758 + 6.27917i) q^{41} +(-3.07841 - 5.33196i) q^{43} +(-0.0792081 - 0.0457308i) q^{45} +(-6.41233 - 3.70216i) q^{47} +(-1.36797 + 2.36939i) q^{51} +(-5.61504 - 9.72553i) q^{53} +(-0.798593 + 1.38320i) q^{55} -14.6895i q^{57} +(-6.97634 - 4.02779i) q^{59} +1.65841 q^{61} +(4.20317 - 2.69877i) q^{65} +3.71128i q^{67} +(-1.94479 - 3.36848i) q^{69} +(8.60538 - 4.96832i) q^{71} +(2.85962 - 1.65100i) q^{73} +(-2.69722 - 4.67173i) q^{75} +(-2.32405 + 4.02538i) q^{79} -9.19370 q^{81} -1.82551i q^{83} +(1.87462 - 1.08231i) q^{85} +(-2.51253 + 4.35183i) q^{87} +(-2.05837 + 1.18840i) q^{89} +(-10.0845 + 5.82230i) q^{93} +(-5.81102 + 10.0650i) q^{95} +(-6.53519 + 3.77309i) q^{97} -0.0761145i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 28 q^{9} + 10 q^{13} + 6 q^{15} + 2 q^{17} + 22 q^{25} - 12 q^{27} - 22 q^{29} - 30 q^{31} - 12 q^{37} - 6 q^{39} + 36 q^{41} + 6 q^{43} + 30 q^{45} + 18 q^{47} + 2 q^{51} - 4 q^{53} + 2 q^{55} + 18 q^{59}+ \cdots - 42 q^{97}+O(q^{100}) $ 16 * q + 28 * q^9 + 10 * q^13 + 6 * q^15 + 2 * q^17 + 22 * q^25 - 12 * q^27 - 22 * q^29 - 30 * q^31 - 12 * q^37 - 6 * q^39 + 36 * q^41 + 6 * q^43 + 30 * q^45 + 18 * q^47 + 2 * q^51 - 4 * q^53 + 2 * q^55 + 18 * q^59 - 8 * q^61 - 52 * q^69 + 36 * q^71 + 12 * q^73 - 10 * q^75 - 4 * q^79 + 42 * q^85 + 26 * q^87 + 36 * q^89 + 42 * q^93 - 30 * q^95 - 42 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.75101			1.01094			0.505472	−	0.862843i	$-0.331318\pi$
$3$	1.75101			1.01094			0.505472	+	0.862843i	$0.331318\pi$
$4$		0			0
$5$	−1.19976	−	0.692682i	−0.536549	−	0.309777i	0.207130	−	0.978313i	$-0.433588\pi$
$5$	−1.19976	−	0.692682i	−0.536549	−	0.309777i	−0.743679	+	0.668537i	$0.766921\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	0.0660200			0.0220067
$10$		0			0
$11$		−	1.15290i		−	0.347613i	−0.984780	−	0.173806i	$-0.944393\pi$
$11$		−	1.15290i		−	0.347613i	0.984780	−	0.173806i	$-0.0556067\pi$
$12$		0			0
$13$	−1.65348	+	3.20406i	−0.458593	+	0.888647i
$13$	−1.65348	+	3.20406i	−0.458593	+	0.888647i
$14$		0			0
$15$	−2.10079	−	1.21289i	−0.542420	−	0.313167i
$16$		0			0
$17$	−0.781246	+	1.35316i	−0.189480	+	0.328189i	−0.945077	−	0.326848i	$-0.894014\pi$
$17$	−0.781246	+	1.35316i	−0.189480	+	0.328189i	0.755597	+	0.655037i	$0.227347\pi$
$18$		0			0
$19$		−	8.38917i		−	1.92461i	−0.271978	−	0.962303i	$-0.587678\pi$
$19$		−	8.38917i		−	1.92461i	0.271978	−	0.962303i	$-0.412322\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.11067	−	1.92374i	−0.231591	−	0.401127i	0.726685	−	0.686970i	$-0.241060\pi$
$23$	−1.11067	−	1.92374i	−0.231591	−	0.401127i	−0.958276	+	0.285843i	$0.907726\pi$
$24$		0			0
$25$	−1.54038	−	2.66802i	−0.308077	−	0.533605i
$26$		0			0
$27$	−5.13741			−0.988696
$28$		0			0
$29$	−1.43491	+	2.48533i	−0.266455	+	0.461514i	−0.967944	−	0.251167i	$-0.919186\pi$
$29$	−1.43491	+	2.48533i	−0.266455	+	0.461514i	0.701489	+	0.712681i	$0.252519\pi$
$30$		0			0
$31$	−5.75927	+	3.32512i	−1.03440	+	0.597209i	−0.918241	−	0.396022i	$-0.870390\pi$
$31$	−5.75927	+	3.32512i	−1.03440	+	0.597209i	−0.116155	+	0.993231i	$0.537057\pi$
$32$		0			0
$33$		−	2.01874i		−	0.351417i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.01436	+	1.74034i	−0.495557	+	0.286110i	−0.726877	−	0.686768i	$-0.759029\pi$
$37$	−3.01436	+	1.74034i	−0.495557	+	0.286110i	0.231320	+	0.972878i	$0.425696\pi$
$38$		0			0
$39$	−2.89525	+	5.61033i	−0.463611	+	0.898371i
$40$		0			0
$41$	10.8758	+	6.27917i	1.69852	+	0.980641i	0.947167	+	0.320740i	$0.103932\pi$
$41$	10.8758	+	6.27917i	1.69852	+	0.980641i	0.751353	+	0.659901i	$0.229402\pi$
$42$		0			0
$43$	−3.07841	−	5.33196i	−0.469453	−	0.813116i	0.529937	−	0.848037i	$-0.322215\pi$
$43$	−3.07841	−	5.33196i	−0.469453	−	0.813116i	−0.999390	+	0.0349208i	$0.988882\pi$
$44$		0			0
$45$	−0.0792081	−	0.0457308i	−0.0118076	−	0.00681715i
$46$		0			0
$47$	−6.41233	−	3.70216i	−0.935334	−	0.540015i	−0.0468394	−	0.998902i	$-0.514915\pi$
$47$	−6.41233	−	3.70216i	−0.935334	−	0.540015i	−0.888495	+	0.458887i	$0.848248\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1.36797	+	2.36939i	−0.191554	+	0.331781i
$52$		0			0
$53$	−5.61504	−	9.72553i	−0.771285	−	1.33590i	−0.936859	−	0.349707i	$-0.886281\pi$
$53$	−5.61504	−	9.72553i	−0.771285	−	1.33590i	0.165574	−	0.986197i	$-0.447052\pi$
$54$		0			0
$55$	−0.798593	+	1.38320i	−0.107682	+	0.186511i
$56$		0			0
$57$		−	14.6895i		−	1.94567i
$58$		0			0
$59$	−6.97634	−	4.02779i	−0.908243	−	0.524374i	−0.0283773	−	0.999597i	$-0.509034\pi$
$59$	−6.97634	−	4.02779i	−0.908243	−	0.524374i	−0.879865	+	0.475223i	$0.842367\pi$
$60$		0			0
$61$	1.65841			0.212338			0.106169	−	0.994348i	$-0.466142\pi$
$61$	1.65841			0.212338			0.106169	+	0.994348i	$0.466142\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.20317	−	2.69877i	0.521339	−	0.334741i
$66$		0			0
$67$			3.71128i			0.453405i	0.973964	+	0.226702i	$0.0727945\pi$
$67$			3.71128i			0.453405i	−0.973964	+	0.226702i	$0.927206\pi$
$68$		0			0
$69$	−1.94479	−	3.36848i	−0.234125	−	0.405517i
$70$		0			0
$71$	8.60538	−	4.96832i	1.02127	−	0.589631i	0.106799	−	0.994281i	$-0.465940\pi$
$71$	8.60538	−	4.96832i	1.02127	−	0.589631i	0.914472	+	0.404650i	$0.132607\pi$
$72$		0			0
$73$	2.85962	−	1.65100i	0.334693	−	0.193235i	−0.323230	−	0.946320i	$-0.604769\pi$
$73$	2.85962	−	1.65100i	0.334693	−	0.193235i	0.657923	+	0.753086i	$0.271435\pi$
$74$		0			0
$75$	−2.69722	−	4.67173i	−0.311448	−	0.539444i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−2.32405	+	4.02538i	−0.261477	+	0.452891i	−0.966635	−	0.256160i	$-0.917543\pi$
$79$	−2.32405	+	4.02538i	−0.261477	+	0.452891i	0.705158	+	0.709050i	$0.250876\pi$
$80$		0			0
$81$	−9.19370			−1.02152
$82$		0			0
$83$		−	1.82551i		−	0.200376i	−0.994969	−	0.100188i	$-0.968056\pi$
$83$		−	1.82551i		−	0.200376i	0.994969	−	0.100188i	$-0.0319445\pi$
$84$		0			0
$85$	1.87462	−	1.08231i	0.203331	−	0.117393i
$86$		0			0
$87$	−2.51253	+	4.35183i	−0.269371	+	0.466565i
$88$		0			0
$89$	−2.05837	+	1.18840i	−0.218187	+	0.125970i	−0.605111	−	0.796141i	$-0.706871\pi$
$89$	−2.05837	+	1.18840i	−0.218187	+	0.125970i	0.386923	+	0.922112i	$0.373538\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−10.0845	+	5.82230i	−1.04572	+	0.603744i
$94$		0			0
$95$	−5.81102	+	10.0650i	−0.596198	+	1.03265i
$96$		0			0
$97$	−6.53519	+	3.77309i	−0.663548	+	0.383099i	−0.793627	−	0.608404i	$-0.791810\pi$
$97$	−6.53519	+	3.77309i	−0.663548	+	0.383099i	0.130080	+	0.991504i	$0.458477\pi$
$98$		0			0
$99$		−	0.0761145i		−	0.00764980i
$100$		0			0
$101$	−13.2005			−1.31350			−0.656751	−	0.754108i	$-0.728070\pi$
$101$	−13.2005			−1.31350			−0.656751	+	0.754108i	$0.728070\pi$
$102$		0			0
$103$	−2.95060	+	5.11059i	−0.290731	+	0.503562i	−0.973983	−	0.226621i	$-0.927232\pi$
$103$	−2.95060	+	5.11059i	−0.290731	+	0.503562i	0.683251	+	0.730183i	$0.260565\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.09634	−	8.82712i	−0.492682	−	0.853350i	0.507283	−	0.861780i	$-0.330650\pi$
$107$	−5.09634	−	8.82712i	−0.492682	−	0.853350i	−0.999964	+	0.00842995i	$0.997317\pi$
$108$		0			0
$109$	5.32481	−	3.07428i	0.510024	−	0.294463i	−0.222819	−	0.974860i	$-0.571526\pi$
$109$	5.32481	−	3.07428i	0.510024	−	0.294463i	0.732844	+	0.680397i	$0.238193\pi$
$110$		0			0
$111$	−5.27816	+	3.04734i	−0.500980	+	0.289241i
$112$		0			0
$113$	−7.29876	−	12.6418i	−0.686609	−	1.18924i	−0.972928	−	0.231108i	$-0.925765\pi$
$113$	−7.29876	−	12.6418i	−0.686609	−	1.18924i	0.286319	−	0.958134i	$-0.407568\pi$
$114$		0			0
$115$			3.07737i			0.286966i
$116$		0			0
$117$	−0.109163	+	0.211532i	−0.0100921	+	0.0195561i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	9.67082			0.879165
$122$		0			0
$123$	19.0436	+	10.9949i	1.71711	+	0.991373i
$124$		0			0
$125$			11.1948i			1.00129i
$126$		0			0
$127$	4.36114	−	7.55372i	0.386989	−	0.670284i	−0.605054	−	0.796184i	$-0.706849\pi$
$127$	4.36114	−	7.55372i	0.386989	−	0.670284i	0.992043	+	0.125900i	$0.0401818\pi$
$128$		0			0
$129$	−5.39031	−	9.33629i	−0.474590	−	0.822014i
$130$		0			0
$131$	−9.72166	+	16.8384i	−0.849385	+	1.47118i	0.0323725	+	0.999476i	$0.489694\pi$
$131$	−9.72166	+	16.8384i	−0.849385	+	1.47118i	−0.881758	+	0.471703i	$0.843640\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	6.16366	+	3.55859i	0.530484	+	0.306275i
$136$		0			0
$137$	−2.90516	−	1.67730i	−0.248205	−	0.143301i	0.370737	−	0.928738i	$-0.379105\pi$
$137$	−2.90516	−	1.67730i	−0.248205	−	0.143301i	−0.618942	+	0.785437i	$0.712438\pi$
$138$		0			0
$139$	3.95629	+	6.85250i	0.335568	+	0.581222i	0.983594	−	0.180397i	$-0.0577383\pi$
$139$	3.95629	+	6.85250i	0.335568	+	0.581222i	−0.648025	+	0.761619i	$0.724405\pi$
$140$		0			0
$141$	−11.2280	−	6.48250i	−0.945570	−	0.545925i
$142$		0			0
$143$	3.69397	+	1.90630i	0.308905	+	0.159413i
$144$		0			0
$145$	3.44308	−	1.98787i	0.285933	−	0.165083i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			2.36432i			0.193693i	0.995299	+	0.0968464i	$0.0308755\pi$
$149$			2.36432i			0.193693i	−0.995299	+	0.0968464i	$0.969124\pi$
$150$		0			0
$151$	10.0357	−	5.79414i	0.816697	−	0.471520i	−0.0325791	−	0.999469i	$-0.510372\pi$
$151$	10.0357	−	5.79414i	0.816697	−	0.471520i	0.849276	+	0.527949i	$0.177039\pi$
$152$		0			0
$153$	−0.0515779	+	0.0893355i	−0.00416982	+	0.00722235i
$154$		0			0
$155$	9.21299			0.740005
$156$		0			0
$157$	4.51821	+	7.82577i	0.360592	+	0.624564i	0.988058	−	0.154080i	$-0.0492413\pi$
$157$	4.51821	+	7.82577i	0.360592	+	0.624564i	−0.627466	+	0.778644i	$0.715908\pi$
$158$		0			0
$159$	−9.83196	−	17.0295i	−0.779725	−	1.35052i
$160$		0			0
$161$		0			0
$162$		0			0
$163$		−	21.3556i		−	1.67270i	−0.548195	−	0.836351i	$-0.684685\pi$
$163$		−	21.3556i		−	1.67270i	0.548195	−	0.836351i	$-0.315315\pi$
$164$		0			0
$165$	−1.39834	+	2.42200i	−0.108861	+	0.188552i
$166$		0			0
$167$	−2.75508	−	1.59065i	−0.213194	−	0.123088i	0.389601	−	0.920984i	$-0.372613\pi$
$167$	−2.75508	−	1.59065i	−0.213194	−	0.123088i	−0.602795	+	0.797896i	$0.705946\pi$
$168$		0			0
$169$	−7.53201	−	10.5957i	−0.579385	−	0.815054i
$170$		0			0
$171$		−	0.553853i		−	0.0423542i
$172$		0			0
$173$	−5.33904			−0.405920			−0.202960	−	0.979187i	$-0.565056\pi$
$173$	−5.33904			−0.405920			−0.202960	+	0.979187i	$0.565056\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−12.2156	−	7.05269i	−0.918182	−	0.530113i
$178$		0			0
$179$	−9.84558			−0.735893			−0.367947	−	0.929847i	$-0.619939\pi$
$179$	−9.84558			−0.735893			−0.367947	+	0.929847i	$0.619939\pi$
$180$		0			0
$181$	15.1253			1.12425			0.562127	−	0.827051i	$-0.309983\pi$
$181$	15.1253			1.12425			0.562127	+	0.827051i	$0.309983\pi$
$182$		0			0
$183$	2.90389			0.214662
$184$		0			0
$185$	4.82200			0.354521
$186$		0			0
$187$	1.56006	+	0.900700i	0.114083	+	0.0658657i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−22.1800			−1.60489			−0.802443	−	0.596729i	$-0.796467\pi$
$191$	−22.1800			−1.60489			−0.802443	+	0.596729i	$0.796467\pi$
$192$		0			0
$193$			6.97186i			0.501846i	0.968007	+	0.250923i	$0.0807340\pi$
$193$			6.97186i			0.501846i	−0.968007	+	0.250923i	$0.919266\pi$
$194$		0			0
$195$	7.35978	−	4.72556i	0.527045	−	0.338404i
$196$		0			0
$197$	17.0895	+	9.86660i	1.21757	+	0.702966i	0.964398	−	0.264455i	$-0.0851919\pi$
$197$	17.0895	+	9.86660i	1.21757	+	0.702966i	0.253175	+	0.967421i	$0.418525\pi$
$198$		0			0
$199$	−6.90193	+	11.9545i	−0.489265	+	0.847431i	−0.999924	−	0.0123521i	$-0.996068\pi$
$199$	−6.90193	+	11.9545i	−0.489265	+	0.847431i	0.510659	+	0.859783i	$0.329401\pi$
$200$		0			0
$201$			6.49847i			0.458367i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−8.69892	−	15.0670i	−0.607559	−	1.05232i
$206$		0			0
$207$	−0.0733265	−	0.127005i	−0.00509655	−	0.00882748i
$208$		0			0
$209$	−9.67188			−0.669018
$210$		0			0
$211$	4.73718	−	8.20504i	0.326121	−	0.564859i	−0.655617	−	0.755093i	$-0.727592\pi$
$211$	4.73718	−	8.20504i	0.326121	−	0.564859i	0.981739	+	0.190235i	$0.0609249\pi$
$212$		0			0
$213$	15.0681	−	8.69955i	1.03245	−	0.596083i
$214$		0			0
$215$			8.52942i			0.581702i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	5.00720	−	2.89091i	0.338355	−	0.195350i
$220$		0			0
$221$	−3.04383	−	4.74058i	−0.204750	−	0.318886i
$222$		0			0
$223$	12.6335	+	7.29395i	0.846001	+	0.488439i	0.859300	−	0.511473i	$-0.170900\pi$
$223$	12.6335	+	7.29395i	0.846001	+	0.488439i	−0.0132984	+	0.999912i	$0.504233\pi$
$224$		0			0
$225$	−0.101696	−	0.176143i	−0.00677974	−	0.0117429i
$226$		0			0
$227$	6.20380	+	3.58176i	0.411760	+	0.237730i	0.691546	−	0.722333i	$-0.256930\pi$
$227$	6.20380	+	3.58176i	0.411760	+	0.237730i	−0.279785	+	0.960063i	$0.590263\pi$
$228$		0			0
$229$	−10.6525	−	6.15024i	−0.703939	−	0.406420i	0.104874	−	0.994486i	$-0.466556\pi$
$229$	−10.6525	−	6.15024i	−0.703939	−	0.406420i	−0.808813	+	0.588066i	$0.799890\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.40185	−	16.2845i	0.615936	−	1.06683i	−0.374284	−	0.927314i	$-0.622111\pi$
$233$	9.40185	−	16.2845i	0.615936	−	1.06683i	0.990220	−	0.139518i	$-0.0445553\pi$
$234$		0			0
$235$	5.12883	+	8.88340i	0.334568	+	0.579489i
$236$		0			0
$237$	−4.06943	+	7.04846i	−0.264338	+	0.457847i
$238$		0			0
$239$			1.60295i			0.103686i	0.998655	+	0.0518432i	$0.0165096\pi$
$239$			1.60295i			0.103686i	−0.998655	+	0.0518432i	$0.983490\pi$
$240$		0			0
$241$	15.9051	+	9.18284i	1.02454	+	0.591519i	0.915416	−	0.402509i	$-0.131862\pi$
$241$	15.9051	+	9.18284i	1.02454	+	0.591519i	0.109125	+	0.994028i	$0.465195\pi$
$242$		0			0
$243$	−0.685976			−0.0440054
$244$		0			0
$245$		0			0
$246$		0			0
$247$	26.8794	+	13.8713i	1.71030	+	0.882611i
$248$		0			0
$249$		−	3.19649i		−	0.202569i
$250$		0			0
$251$	−7.18228	−	12.4401i	−0.453341	−	0.785210i	0.545250	−	0.838274i	$-0.316435\pi$
$251$	−7.18228	−	12.4401i	−0.453341	−	0.785210i	−0.998591	+	0.0530634i	$0.983101\pi$
$252$		0			0
$253$	−2.21788	+	1.28049i	−0.139437	+	0.0805040i
$254$		0			0
$255$	3.28246	−	1.89513i	0.205556	−	0.118678i
$256$		0			0
$257$	8.68283	+	15.0391i	0.541620	+	0.938113i	0.998811	+	0.0487448i	$0.0155221\pi$
$257$	8.68283	+	15.0391i	0.541620	+	0.938113i	−0.457191	+	0.889368i	$0.651145\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.0947325	+	0.164081i	−0.00586379	+	0.0101564i
$262$		0			0
$263$	16.7419			1.03235			0.516175	−	0.856483i	$-0.327355\pi$
$263$	16.7419			1.03235			0.516175	+	0.856483i	$0.327355\pi$
$264$		0			0
$265$			15.5577i			0.955704i
$266$		0			0
$267$	−3.60422	+	2.08090i	−0.220575	+	0.127349i
$268$		0			0
$269$	−12.3957	+	21.4700i	−0.755781	+	1.30905i	0.189204	+	0.981938i	$0.439409\pi$
$269$	−12.3957	+	21.4700i	−0.755781	+	1.30905i	−0.944985	+	0.327114i	$0.893924\pi$
$270$		0			0
$271$	17.5211	−	10.1158i	1.06433	−	0.614493i	0.137706	−	0.990473i	$-0.456027\pi$
$271$	17.5211	−	10.1158i	1.06433	−	0.614493i	0.926628	+	0.375980i	$0.122694\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.07597	+	1.77591i	−0.185488	+	0.107091i
$276$		0			0
$277$	5.52664	−	9.57242i	0.332064	−	0.575151i	−0.650853	−	0.759204i	$-0.725588\pi$
$277$	5.52664	−	9.57242i	0.332064	−	0.575151i	0.982916	+	0.184053i	$0.0589218\pi$
$278$		0			0
$279$	−0.380227	+	0.219524i	−0.0227636	+	0.0131426i
$280$		0			0
$281$		−	3.18955i		−	0.190273i	−0.995464	−	0.0951363i	$-0.969671\pi$
$281$		−	3.18955i		−	0.190273i	0.995464	−	0.0951363i	$-0.0303287\pi$
$282$		0			0
$283$	−17.9296			−1.06581			−0.532903	−	0.846177i	$-0.678899\pi$
$283$	−17.9296			−1.06581			−0.532903	+	0.846177i	$0.678899\pi$
$284$		0			0
$285$	−10.1751	+	17.6238i	−0.602723	+	1.04395i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.27931	+	12.6081i	0.428195	+	0.741655i
$290$		0			0
$291$	−11.4431	+	6.60670i	−0.670809	+	0.387292i
$292$		0			0
$293$	−14.6945	+	8.48385i	−0.858460	+	0.495632i	−0.863496	−	0.504355i	$-0.831730\pi$
$293$	−14.6945	+	8.48385i	−0.858460	+	0.495632i	0.00503646	+	0.999987i	$0.498397\pi$
$294$		0			0
$295$	5.57996	+	9.66477i	0.324878	+	0.562705i
$296$		0			0
$297$			5.92293i			0.343683i
$298$		0			0
$299$	8.00025	−	0.377794i	0.462666	−	0.0218484i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−23.1142			−1.32788
$304$		0			0
$305$	−1.98970	−	1.14875i	−0.113930	−	0.0657774i
$306$		0			0
$307$		−	26.9884i		−	1.54031i	−0.637857	−	0.770155i	$-0.720179\pi$
$307$		−	26.9884i		−	1.54031i	0.637857	−	0.770155i	$-0.279821\pi$
$308$		0			0
$309$	−5.16652	+	8.94868i	−0.293913	+	0.509072i
$310$		0			0
$311$	−14.1891	−	24.5762i	−0.804588	−	1.39359i	−0.916569	−	0.399876i	$-0.869053\pi$
$311$	−14.1891	−	24.5762i	−0.804588	−	1.39359i	0.111981	−	0.993710i	$-0.464280\pi$
$312$		0			0
$313$	8.33368	−	14.4344i	0.471047	−	0.815878i	−0.528404	−	0.848993i	$-0.677209\pi$
$313$	8.33368	−	14.4344i	0.471047	−	0.815878i	0.999452	+	0.0331150i	$0.0105428\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	24.8919	+	14.3713i	1.39807	+	0.807175i	0.994190	−	0.107638i	$-0.0343287\pi$
$317$	24.8919	+	14.3713i	1.39807	+	0.807175i	0.403878	+	0.914813i	$0.367662\pi$
$318$		0			0
$319$	2.86534	+	1.65430i	0.160428	+	0.0926233i
$320$		0			0
$321$	−8.92372	−	15.4563i	−0.498073	−	0.862688i
$322$		0			0
$323$	11.3519	+	6.55401i	0.631635	+	0.364675i
$324$		0			0
$325$	11.0955	−	0.523961i	0.615468	−	0.0290641i
$326$		0			0
$327$	9.32377	−	5.38308i	0.515606	−	0.297685i
$328$		0			0
$329$		0			0
$330$		0			0
$331$			26.1917i			1.43963i	0.694167	+	0.719814i	$0.255773\pi$
$331$			26.1917i			1.43963i	−0.694167	+	0.719814i	$0.744227\pi$
$332$		0			0
$333$	−0.199008	+	0.114897i	−0.0109056	+	0.00629633i
$334$		0			0
$335$	2.57073	−	4.45264i	0.140454	−	0.243274i
$336$		0			0
$337$	4.47831			0.243949			0.121975	−	0.992533i	$-0.461077\pi$
$337$	4.47831			0.243949			0.121975	+	0.992533i	$0.461077\pi$
$338$		0			0
$339$	−12.7802	−	22.1359i	−0.694123	−	1.20226i
$340$		0			0
$341$	3.83353	+	6.63988i	0.207597	+	0.359569i
$342$		0			0
$343$		0			0
$344$		0			0
$345$			5.38849i			0.290106i
$346$		0			0
$347$	13.4606	−	23.3144i	0.722602	−	1.25158i	−0.237351	−	0.971424i	$-0.576279\pi$
$347$	13.4606	−	23.3144i	0.722602	−	1.25158i	0.959953	−	0.280160i	$-0.0903874\pi$
$348$		0			0
$349$	17.9560	+	10.3669i	0.961164	+	0.554928i	0.896531	−	0.442981i	$-0.146079\pi$
$349$	17.9560	+	10.3669i	0.961164	+	0.554928i	0.0646328	+	0.997909i	$0.479412\pi$
$350$		0			0
$351$	8.49461	−	16.4606i	0.453409	−	0.878601i
$352$		0			0
$353$			11.3041i			0.601655i	0.953679	+	0.300828i	$0.0972629\pi$
$353$			11.3041i			0.601655i	−0.953679	+	0.300828i	$0.902737\pi$
$354$		0			0
$355$	−13.7658			−0.730615
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−15.3678	−	8.87263i	−0.811084	−	0.468279i	0.0362484	−	0.999343i	$-0.488459\pi$
$359$	−15.3678	−	8.87263i	−0.811084	−	0.468279i	−0.847332	+	0.531063i	$0.821793\pi$
$360$		0			0
$361$	−51.3781			−2.70411
$362$		0			0
$363$	16.9337			0.888786
$364$		0			0
$365$	−4.57447			−0.239439
$366$		0			0
$367$	9.56310			0.499190			0.249595	−	0.968350i	$-0.419703\pi$
$367$	9.56310			0.499190			0.249595	+	0.968350i	$0.419703\pi$
$368$		0			0
$369$	0.718022	+	0.414550i	0.0373788	+	0.0215806i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	11.8835			0.615306			0.307653	−	0.951499i	$-0.400456\pi$
$373$	11.8835			0.615306			0.307653	+	0.951499i	$0.400456\pi$
$374$		0			0
$375$			19.6022i			1.01225i
$376$		0			0
$377$	−5.59056	−	8.70697i	−0.287928	−	0.448432i
$378$		0			0
$379$	−14.9391	−	8.62512i	−0.767372	−	0.443042i	0.0645643	−	0.997914i	$-0.479434\pi$
$379$	−14.9391	−	8.62512i	−0.767372	−	0.443042i	−0.831936	+	0.554871i	$0.812768\pi$
$380$		0			0
$381$	7.63639	−	13.2266i	0.391224	−	0.677620i
$382$		0			0
$383$		−	13.0300i		−	0.665800i	−0.942962	−	0.332900i	$-0.891973\pi$
$383$		−	13.0300i		−	0.665800i	0.942962	−	0.332900i	$-0.108027\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.203236	−	0.352016i	−0.0103311	−	0.0178940i
$388$		0			0
$389$	−12.0792	−	20.9218i	−0.612442	−	1.06078i	−0.990828	−	0.135132i	$-0.956854\pi$
$389$	−12.0792	−	20.9218i	−0.612442	−	1.06078i	0.378386	−	0.925648i	$-0.376479\pi$
$390$		0			0
$391$	3.47083			0.175528
$392$		0			0
$393$	−17.0227	+	29.4841i	−0.858680	+	1.48728i
$394$		0			0
$395$	5.57661	−	3.21966i	0.280590	−	0.161999i
$396$		0			0
$397$			4.81535i			0.241675i	0.992672	+	0.120838i	$0.0385581\pi$
$397$			4.81535i			0.241675i	−0.992672	+	0.120838i	$0.961442\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.94702	−	4.01086i	0.346918	−	0.200293i	−0.316409	−	0.948623i	$-0.602477\pi$
$401$	6.94702	−	4.01086i	0.346918	−	0.200293i	0.663327	+	0.748330i	$0.269144\pi$
$402$		0			0
$403$	−1.13104	−	23.9511i	−0.0563410	−	1.19309i
$404$		0			0
$405$	11.0302	+	6.36831i	0.548097	+	0.316444i
$406$		0			0
$407$	2.00644	+	3.47526i	0.0994555	+	0.172262i
$408$		0			0
$409$	8.63206	+	4.98372i	0.426828	+	0.246429i	0.697994	−	0.716103i	$-0.254076\pi$
$409$	8.63206	+	4.98372i	0.426828	+	0.246429i	−0.271166	+	0.962532i	$0.587409\pi$
$410$		0			0
$411$	−5.08696	−	2.93696i	−0.250921	−	0.144869i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1.26450	+	2.19018i	−0.0620719	+	0.107512i
$416$		0			0
$417$	6.92749	+	11.9988i	0.339241	+	0.587582i
$418$		0			0
$419$	14.8442	−	25.7109i	0.725187	−	1.25606i	−0.233710	−	0.972306i	$-0.575087\pi$
$419$	14.8442	−	25.7109i	0.725187	−	1.25606i	0.958897	−	0.283754i	$-0.0915800\pi$
$420$		0			0
$421$			13.1380i			0.640305i	0.947366	+	0.320152i	$0.103734\pi$
$421$			13.1380i			0.640305i	−0.947366	+	0.320152i	$0.896266\pi$
$422$		0			0
$423$	−0.423342	−	0.244416i	−0.0205836	−	0.0118839i
$424$		0			0
$425$	4.81368			0.233498
$426$		0			0
$427$		0			0
$428$		0			0
$429$	6.46815	+	3.33794i	0.312285	+	0.161157i
$430$		0			0
$431$			14.4025i			0.693745i	0.937912	+	0.346872i	$0.112756\pi$
$431$			14.4025i			0.693745i	−0.937912	+	0.346872i	$0.887244\pi$
$432$		0			0
$433$	−18.1596	−	31.4534i	−0.872695	−	1.51155i	−0.859198	−	0.511643i	$-0.829037\pi$
$433$	−18.1596	−	31.4534i	−0.872695	−	1.51155i	−0.0134964	−	0.999909i	$-0.504296\pi$
$434$		0			0
$435$	6.02886	−	3.48076i	0.289062	−	0.166890i
$436$		0			0
$437$	−16.1386	+	9.31761i	−0.772013	+	0.445722i
$438$		0			0
$439$	10.2722	+	17.7920i	0.490266	+	0.849166i	0.999937	−	0.0112036i	$-0.00356630\pi$
$439$	10.2722	+	17.7920i	0.490266	+	0.849166i	−0.509671	+	0.860369i	$0.670233\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	12.6606	−	21.9287i	0.601521	−	1.04187i	−0.391070	−	0.920361i	$-0.627895\pi$
$443$	12.6606	−	21.9287i	0.601521	−	1.04187i	0.992591	−	0.121504i	$-0.0387719\pi$
$444$		0			0
$445$	3.29274			0.156091
$446$		0			0
$447$			4.13994i			0.195812i
$448$		0			0
$449$	−29.0997	+	16.8007i	−1.37330	+	0.792876i	−0.991342	−	0.131303i	$-0.958084\pi$
$449$	−29.0997	+	16.8007i	−1.37330	+	0.792876i	−0.381959	+	0.924179i	$0.624751\pi$
$450$		0			0
$451$	7.23926	−	12.5388i	0.340883	−	0.590427i
$452$		0			0
$453$	17.5726	−	10.1456i	0.825635	−	0.476680i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−32.9050	+	18.9977i	−1.53923	+	0.888677i	−0.540350	+	0.841441i	$0.681708\pi$
$457$	−32.9050	+	18.9977i	−1.53923	+	0.888677i	−0.998884	+	0.0472361i	$0.984959\pi$
$458$		0			0
$459$	4.01359	−	6.95174i	0.187338	−	0.324479i
$460$		0			0
$461$	−31.4812	+	18.1757i	−1.46623	+	0.846525i	−0.999287	−	0.0377645i	$-0.987976\pi$
$461$	−31.4812	+	18.1757i	−1.46623	+	0.846525i	−0.466938	+	0.884290i	$0.654643\pi$
$462$		0			0
$463$			35.3400i			1.64239i	0.570649	+	0.821194i	$0.306692\pi$
$463$			35.3400i			1.64239i	−0.570649	+	0.821194i	$0.693308\pi$
$464$		0			0
$465$	16.1320			0.748104
$466$		0			0
$467$	14.7859	−	25.6099i	0.684208	−	1.18508i	−0.289476	−	0.957185i	$-0.593481\pi$
$467$	14.7859	−	25.6099i	0.684208	−	1.18508i	0.973685	−	0.227899i	$-0.0731855\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	7.91141	+	13.7030i	0.364538	+	0.631399i
$472$		0			0
$473$	−6.14722	+	3.54910i	−0.282650	+	0.163188i
$474$		0			0
$475$	−22.3825	+	12.9225i	−1.02698	+	0.592927i
$476$		0			0
$477$	−0.370705	−	0.642079i	−0.0169734	−	0.0293988i
$478$		0			0
$479$		−	21.7476i		−	0.993672i	−0.867845	−	0.496836i	$-0.834495\pi$
$479$		−	21.7476i		−	0.993672i	0.867845	−	0.496836i	$-0.165505\pi$
$480$		0			0
$481$	−0.591976	−	12.5358i	−0.0269918	−	0.571583i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	10.4542			0.474701
$486$		0			0
$487$	26.0217	+	15.0236i	1.17916	+	0.680786i	0.955819	−	0.293955i	$-0.0949716\pi$
$487$	26.0217	+	15.0236i	1.17916	+	0.680786i	0.223337	+	0.974741i	$0.428305\pi$
$488$		0			0
$489$		−	37.3938i		−	1.69101i
$490$		0			0
$491$	−20.0899	+	34.7967i	−0.906643	+	1.57035i	−0.0879471	+	0.996125i	$0.528031\pi$
$491$	−20.0899	+	34.7967i	−0.906643	+	1.57035i	−0.818696	+	0.574227i	$0.805303\pi$
$492$		0			0
$493$	−2.24203	−	3.88331i	−0.100976	−	0.174895i
$494$		0			0
$495$	−0.0527231	+	0.0913191i	−0.00236973	+	0.00410449i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	10.1671	+	5.86999i	0.455143	+	0.262777i	0.710000	−	0.704202i	$-0.248695\pi$
$499$	10.1671	+	5.86999i	0.455143	+	0.262777i	−0.254857	+	0.966979i	$0.582028\pi$
$500$		0			0
$501$	−4.82416	−	2.78523i	−0.215528	−	0.124435i
$502$		0			0
$503$	16.6965	+	28.9191i	0.744459	+	1.28944i	0.950447	+	0.310886i	$0.100626\pi$
$503$	16.6965	+	28.9191i	0.744459	+	1.28944i	−0.205989	+	0.978554i	$0.566041\pi$
$504$		0			0
$505$	15.8375	+	9.14376i	0.704758	+	0.406892i
$506$		0			0
$507$	−13.1886	−	18.5531i	−0.585726	−	0.823973i
$508$		0			0
$509$	17.9983	−	10.3913i	0.797759	−	0.460586i	−0.0449282	−	0.998990i	$-0.514306\pi$
$509$	17.9983	−	10.3913i	0.797759	−	0.460586i	0.842687	+	0.538404i	$0.180973\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$			43.0986i			1.90285i
$514$		0			0
$515$	7.08003	−	4.08766i	0.311983	−	0.180124i
$516$		0			0
$517$	−4.26822	+	7.39278i	−0.187716	+	0.325134i
$518$		0			0
$519$	−9.34869			−0.410362
$520$		0			0
$521$	−3.75119	−	6.49726i	−0.164343	−	0.284650i	0.772079	−	0.635527i	$-0.219217\pi$
$521$	−3.75119	−	6.49726i	−0.164343	−	0.284650i	−0.936422	+	0.350877i	$0.885884\pi$
$522$		0			0
$523$	−3.66289	−	6.34431i	−0.160167	−	0.277417i	0.774762	−	0.632254i	$-0.217870\pi$
$523$	−3.66289	−	6.34431i	−0.160167	−	0.277417i	−0.934928	+	0.354836i	$0.884537\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	10.3909i		−	0.452637i
$528$		0			0
$529$	9.03282	−	15.6453i	0.392731	−	0.680230i
$530$		0			0
$531$	−0.460578	−	0.265915i	−0.0199874	−	0.0115397i
$532$		0			0
$533$	−38.1018	+	24.4644i	−1.65037	+	1.05967i
$534$		0			0
$535$			14.1206i			0.610485i
$536$		0			0
$537$	−17.2397			−0.743947
$538$		0			0
$539$		0			0
$540$		0			0
$541$	10.1260	+	5.84622i	0.435349	+	0.251349i	0.701623	−	0.712549i	$-0.252459\pi$
$541$	10.1260	+	5.84622i	0.435349	+	0.251349i	−0.266274	+	0.963897i	$0.585793\pi$
$542$		0			0
$543$	26.4844			1.13656
$544$		0			0
$545$	−8.51799			−0.364871
$546$		0			0
$547$	5.10513			0.218280			0.109140	−	0.994026i	$-0.465190\pi$
$547$	5.10513			0.218280			0.109140	+	0.994026i	$0.465190\pi$
$548$		0			0
$549$	0.109488			0.00467285
$550$		0			0
$551$	20.8498	+	12.0377i	0.888233	+	0.512822i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	8.44336			0.358401
$556$		0			0
$557$		−	12.5336i		−	0.531065i	−0.964102	−	0.265532i	$-0.914452\pi$
$557$		−	12.5336i		−	0.531065i	0.964102	−	0.265532i	$-0.0855477\pi$
$558$		0			0
$559$	22.1740	−	1.04712i	0.937860	−	0.0442884i
$560$		0			0
$561$	2.73167	+	1.57713i	0.115331	+	0.0665865i
$562$		0			0
$563$	1.95315	−	3.38296i	0.0823155	−	0.142575i	−0.821929	−	0.569590i	$-0.807102\pi$
$563$	1.95315	−	3.38296i	0.0823155	−	0.142575i	0.904244	+	0.427016i	$0.140435\pi$
$564$		0			0
$565$			20.2229i			0.850782i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−23.0664	−	39.9523i	−0.966996	−	1.67489i	−0.704155	−	0.710046i	$-0.748674\pi$
$569$	−23.0664	−	39.9523i	−0.966996	−	1.67489i	−0.262841	−	0.964839i	$-0.584659\pi$
$570$		0			0
$571$	15.0580	+	26.0812i	0.630157	+	1.09146i	0.987519	+	0.157499i	$0.0503430\pi$
$571$	15.0580	+	26.0812i	0.630157	+	1.09146i	−0.357362	+	0.933966i	$0.616324\pi$
$572$		0			0
$573$	−38.8372			−1.62245
$574$		0			0
$575$	−3.42172	+	5.92660i	−0.142696	+	0.247156i
$576$		0			0
$577$	22.1962	−	12.8150i	0.924042	−	0.533496i	0.0391195	−	0.999235i	$-0.487545\pi$
$577$	22.1962	−	12.8150i	0.924042	−	0.533496i	0.884922	+	0.465739i	$0.154211\pi$
$578$		0			0
$579$			12.2078i			0.507338i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−11.2126	+	6.47358i	−0.464377	+	0.268108i
$584$		0			0
$585$	0.277493	−	0.178173i	0.0114729	−	0.00736653i
$586$		0			0
$587$	11.4147	+	6.59025i	0.471133	+	0.272009i	0.716714	−	0.697367i	$-0.245645\pi$
$587$	11.4147	+	6.59025i	0.471133	+	0.272009i	−0.245581	+	0.969376i	$0.578979\pi$
$588$		0			0
$589$	27.8950	+	48.3155i	1.14939	+	1.99081i
$590$		0			0
$591$	29.9237	+	17.2765i	1.23090	+	0.710659i
$592$		0			0
$593$	−5.66124	−	3.26852i	−0.232479	−	0.134222i	0.379236	−	0.925300i	$-0.376187\pi$
$593$	−5.66124	−	3.26852i	−0.232479	−	0.134222i	−0.611715	+	0.791078i	$0.709520\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−12.0853	+	20.9324i	−0.494619	+	0.856705i
$598$		0			0
$599$	−6.21222	−	10.7599i	−0.253824	−	0.439637i	0.710751	−	0.703444i	$-0.248355\pi$
$599$	−6.21222	−	10.7599i	−0.253824	−	0.439637i	−0.964576	+	0.263807i	$0.915022\pi$
$600$		0			0
$601$	9.27019	−	16.0564i	0.378139	−	0.654956i	−0.612653	−	0.790352i	$-0.709898\pi$
$601$	9.27019	−	16.0564i	0.378139	−	0.654956i	0.990791	+	0.135397i	$0.0432309\pi$
$602$		0			0
$603$			0.245018i			0.00997792i
$604$		0			0
$605$	−11.6027	−	6.69880i	−0.471715	−	0.272345i
$606$		0			0
$607$	15.7445			0.639050			0.319525	−	0.947578i	$-0.396477\pi$
$607$	15.7445			0.639050			0.319525	+	0.947578i	$0.396477\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	22.4646	−	14.4240i	0.908820	−	0.583534i
$612$		0			0
$613$		−	19.2599i		−	0.777901i	−0.921259	−	0.388950i	$-0.872838\pi$
$613$		−	19.2599i		−	0.777901i	0.921259	−	0.388950i	$-0.127162\pi$
$614$		0			0
$615$	−15.2319	−	26.3824i	−0.614208	−	1.06384i
$616$		0			0
$617$	37.5872	−	21.7010i	1.51320	−	0.873649i	0.513323	−	0.858195i	$-0.328414\pi$
$617$	37.5872	−	21.7010i	1.51320	−	0.873649i	0.999881	−	0.0154532i	$-0.00491911\pi$
$618$		0			0
$619$	11.5943	−	6.69400i	0.466016	−	0.269054i	−0.248555	−	0.968618i	$-0.579956\pi$
$619$	11.5943	−	6.69400i	0.466016	−	0.269054i	0.714570	+	0.699564i	$0.246622\pi$
$620$		0			0
$621$	5.70598	+	9.88305i	0.228973	+	0.396593i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.0525074	−	0.0909454i	0.00210029	−	0.00363782i
$626$		0			0
$627$	−16.9355			−0.676339
$628$		0			0
$629$		−	5.43854i		−	0.216849i
$630$		0			0
$631$	13.1568	−	7.59606i	0.523762	−	0.302394i	−0.214710	−	0.976678i	$-0.568881\pi$
$631$	13.1568	−	7.59606i	0.523762	−	0.302394i	0.738473	+	0.674283i	$0.235547\pi$
$632$		0			0
$633$	8.29484	−	14.3671i	0.329690	−	0.571040i
$634$		0			0
$635$	−10.4646	+	6.04177i	−0.415277	+	0.239760i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	0.568127	−	0.328008i	0.0224747	−	0.0129758i
$640$		0			0
$641$	−17.9671	+	31.1199i	−0.709658	+	1.22916i	0.255326	+	0.966855i	$0.417817\pi$
$641$	−17.9671	+	31.1199i	−0.709658	+	1.22916i	−0.964984	+	0.262309i	$0.915516\pi$
$642$		0			0
$643$	7.72476	−	4.45989i	0.304635	−	0.175881i	−0.339888	−	0.940466i	$-0.610389\pi$
$643$	7.72476	−	4.45989i	0.304635	−	0.175881i	0.644523	+	0.764585i	$0.277056\pi$
$644$		0			0
$645$			14.9351i			0.588068i
$646$		0			0
$647$	−9.76721			−0.383989			−0.191994	−	0.981396i	$-0.561495\pi$
$647$	−9.76721			−0.383989			−0.191994	+	0.981396i	$0.561495\pi$
$648$		0			0
$649$	−4.64365	+	8.04304i	−0.182279	+	0.315717i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8.26858	−	14.3216i	−0.323575	−	0.560448i	0.657648	−	0.753325i	$-0.271551\pi$
$653$	−8.26858	−	14.3216i	−0.323575	−	0.560448i	−0.981223	+	0.192877i	$0.938218\pi$
$654$		0			0
$655$	23.3273	−	13.4680i	0.911473	−	0.526239i
$656$		0			0
$657$	0.188792	−	0.108999i	0.00736547	−	0.00425245i
$658$		0			0
$659$	−7.82010	−	13.5448i	−0.304628	−	0.527631i	0.672550	−	0.740051i	$-0.265199\pi$
$659$	−7.82010	−	13.5448i	−0.304628	−	0.527631i	−0.977178	+	0.212420i	$0.931865\pi$
$660$		0			0
$661$			25.3249i			0.985024i	0.870306	+	0.492512i	$0.163921\pi$
$661$			25.3249i			0.985024i	−0.870306	+	0.492512i	$0.836079\pi$
$662$		0			0
$663$	−5.32976	−	8.30078i	−0.206991	−	0.322376i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	6.37484			0.246835
$668$		0			0
$669$	22.1213	+	12.7717i	0.855259	+	0.493784i
$670$		0			0
$671$		−	1.91199i		−	0.0738114i
$672$		0			0
$673$	−4.08919	+	7.08268i	−0.157627	+	0.273017i	−0.934012	−	0.357241i	$-0.883718\pi$
$673$	−4.08919	+	7.08268i	−0.157627	+	0.273017i	0.776386	+	0.630258i	$0.217051\pi$
$674$		0			0
$675$	7.91359	+	13.7067i	0.304594	+	0.527573i
$676$		0			0
$677$	−22.4808	+	38.9379i	−0.864007	+	1.49650i	0.00402279	+	0.999992i	$0.498720\pi$
$677$	−22.4808	+	38.9379i	−0.864007	+	1.49650i	−0.868030	+	0.496512i	$0.834614\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	10.8629	+	6.27169i	0.416267	+	0.240332i
$682$		0			0
$683$	−17.7090	−	10.2243i	−0.677616	−	0.391222i	0.121340	−	0.992611i	$-0.461281\pi$
$683$	−17.7090	−	10.2243i	−0.677616	−	0.391222i	−0.798956	+	0.601389i	$0.794614\pi$
$684$		0			0
$685$	2.32367	+	4.02471i	0.0887827	+	0.153776i
$686$		0			0
$687$	−18.6526	−	10.7691i	−0.711643	−	0.410867i
$688$		0			0
$689$	40.4455	−	1.90995i	1.54085	−	0.0727634i
$690$		0			0
$691$	29.1943	−	16.8554i	1.11061	−	0.641208i	0.171619	−	0.985163i	$-0.445100\pi$
$691$	29.1943	−	16.8554i	1.11061	−	0.641208i	0.938986	+	0.343955i	$0.111767\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	10.9618i		−	0.415805i
$696$		0			0
$697$	−16.9934	+	9.81115i	−0.643671	+	0.371624i
$698$		0			0
$699$	16.4627	−	28.5142i	0.622676	−	1.07851i
$700$		0			0
$701$	−29.6172			−1.11862			−0.559312	−	0.828957i	$-0.688935\pi$
$701$	−29.6172			−1.11862			−0.559312	+	0.828957i	$0.688935\pi$
$702$		0			0
$703$	14.6000	+	25.2879i	0.550649	+	0.953753i
$704$		0			0
$705$	8.98062	+	15.5549i	0.338230	+	0.585831i
$706$		0			0
$707$		0			0
$708$		0			0
$709$			9.92641i			0.372794i	0.982474	+	0.186397i	$0.0596811\pi$
$709$			9.92641i			0.372794i	−0.982474	+	0.186397i	$0.940319\pi$
$710$		0			0
$711$	−0.153434	+	0.265756i	−0.00575423	+	0.00996661i
$712$		0			0
$713$	12.7933	+	7.38623i	0.479114	+	0.276616i
$714$		0			0
$715$	−3.11141	−	4.84584i	−0.116360	−	0.181224i
$716$		0			0
$717$			2.80678i			0.104821i
$718$		0			0
$719$	20.6850			0.771422			0.385711	−	0.922620i	$-0.373956\pi$
$719$	20.6850			0.771422			0.385711	+	0.922620i	$0.373956\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	27.8500	+	16.0792i	1.03575	+	0.597992i
$724$		0			0
$725$	8.84123			0.328355
$726$		0			0
$727$	4.83449			0.179301			0.0896506	−	0.995973i	$-0.471425\pi$
$727$	4.83449			0.179301			0.0896506	+	0.995973i	$0.471425\pi$
$728$		0			0
$729$	26.3800			0.977035
$730$		0			0
$731$	9.61998			0.355808
$732$		0			0
$733$	−11.0018	−	6.35187i	−0.406359	−	0.234612i	0.282865	−	0.959160i	$-0.408715\pi$
$733$	−11.0018	−	6.35187i	−0.406359	−	0.234612i	−0.689224	+	0.724548i	$0.742049\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.27874			0.157609
$738$		0			0
$739$			2.58482i			0.0950840i	0.998869	+	0.0475420i	$0.0151388\pi$
$739$			2.58482i			0.0950840i	−0.998869	+	0.0475420i	$0.984861\pi$
$740$		0			0
$741$	47.0660	+	24.2888i	1.72901	+	0.892270i
$742$		0			0
$743$	9.98318	+	5.76379i	0.366247	+	0.211453i	0.671818	−	0.740717i	$-0.265514\pi$
$743$	9.98318	+	5.76379i	0.366247	+	0.211453i	−0.305570	+	0.952169i	$0.598847\pi$
$744$		0			0
$745$	1.63772	−	2.83662i	0.0600015	−	0.103926i
$746$		0			0
$747$		−	0.120520i		−	0.00440961i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−3.50269	−	6.06684i	−0.127815	−	0.221382i	0.795015	−	0.606590i	$-0.207463\pi$
$751$	−3.50269	−	6.06684i	−0.127815	−	0.221382i	−0.922830	+	0.385208i	$0.874130\pi$
$752$		0			0
$753$	−12.5762	−	21.7826i	−0.458302	−	0.793803i
$754$		0			0
$755$	−16.0540			−0.584264
$756$		0			0
$757$	8.60091	−	14.8972i	0.312605	−	0.541449i	−0.666320	−	0.745666i	$-0.732132\pi$
$757$	8.60091	−	14.8972i	0.312605	−	0.541449i	0.978926	+	0.204217i	$0.0654649\pi$
$758$		0			0
$759$	−3.88352	+	2.24215i	−0.140963	+	0.0813850i
$760$		0			0
$761$			34.5530i			1.25255i	0.779603	+	0.626274i	$0.215421\pi$
$761$			34.5530i			1.25255i	−0.779603	+	0.626274i	$0.784579\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.123762	−	0.0714541i	0.00447463	−	0.00258343i
$766$		0			0
$767$	24.4405	−	15.6928i	0.882497	−	0.566632i
$768$		0			0
$769$	9.48253	+	5.47474i	0.341949	+	0.197424i	0.661133	−	0.750268i	$-0.270076\pi$
$769$	9.48253	+	5.47474i	0.341949	+	0.197424i	−0.319185	+	0.947693i	$0.603409\pi$
$770$		0			0
$771$	15.2037	+	26.3335i	0.547547	+	0.948379i
$772$		0			0
$773$	−19.0556	−	11.0018i	−0.685384	−	0.395707i	0.116496	−	0.993191i	$-0.462834\pi$
$773$	−19.0556	−	11.0018i	−0.685384	−	0.395707i	−0.801880	+	0.597484i	$0.796167\pi$
$774$		0			0
$775$	17.7430	+	10.2439i	0.637347	+	0.367973i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	52.6770	−	91.2392i	1.88735	−	3.26898i
$780$		0			0
$781$	−5.72798	−	9.92115i	−0.204963	−	0.355007i
$782$		0			0
$783$	7.37171	−	12.7682i	0.263443	−	0.456297i
$784$		0			0
$785$		−	12.5187i		−	0.446812i
$786$		0			0
$787$	−34.0548	−	19.6616i	−1.21392	−	0.700859i	−0.250312	−	0.968165i	$-0.580533\pi$
$787$	−34.0548	−	19.6616i	−1.21392	−	0.700859i	−0.963612	+	0.267306i	$0.913866\pi$
$788$		0			0
$789$	29.3152			1.04365
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−2.74215	+	5.31366i	−0.0973767	+	0.188693i
$794$		0			0
$795$			27.2417i			0.966162i
$796$		0			0
$797$	−27.2620	−	47.2192i	−0.965669	−	1.67259i	−0.707806	−	0.706407i	$-0.750315\pi$
$797$	−27.2620	−	47.2192i	−0.965669	−	1.67259i	−0.257863	−	0.966181i	$-0.583018\pi$
$798$		0			0
$799$	10.0192	−	5.78460i	0.354454	−	0.204644i
$800$		0			0
$801$	−0.135894	+	0.0784583i	−0.00480157	+	0.00277219i
$802$		0			0
$803$	−1.90344	−	3.29685i	−0.0671709	−	0.116343i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−21.7050	+	37.5942i	−0.764052	+	1.32338i
$808$		0			0
$809$	3.12637			0.109917			0.0549586	−	0.998489i	$-0.482497\pi$
$809$	3.12637			0.109917			0.0549586	+	0.998489i	$0.482497\pi$
$810$		0			0
$811$		−	4.48741i		−	0.157574i	−0.996891	−	0.0787872i	$-0.974895\pi$
$811$		−	4.48741i		−	0.157574i	0.996891	−	0.0787872i	$-0.0251048\pi$
$812$		0			0
$813$	30.6796	−	17.7129i	1.07598	−	0.621218i
$814$		0			0
$815$	−14.7926	+	25.6216i	−0.518164	+	0.897486i
$816$		0			0
$817$	−44.7307	+	25.8253i	−1.56493	+	0.903512i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	21.3797	−	12.3436i	0.746158	−	0.430795i	−0.0781459	−	0.996942i	$-0.524900\pi$
$821$	21.3797	−	12.3436i	0.746158	−	0.430795i	0.824304	+	0.566147i	$0.191567\pi$
$822$		0			0
$823$	−5.50672	+	9.53791i	−0.191952	+	0.332471i	−0.945897	−	0.324467i	$-0.894815\pi$
$823$	−5.50672	+	9.53791i	−0.191952	+	0.332471i	0.753945	+	0.656938i	$0.228148\pi$
$824$		0			0
$825$	−5.38604	+	3.10963i	−0.187518	+	0.108263i
$826$		0			0
$827$			23.8575i			0.829605i	0.909911	+	0.414803i	$0.136149\pi$
$827$			23.8575i			0.829605i	−0.909911	+	0.414803i	$0.863851\pi$
$828$		0			0
$829$	−20.4314			−0.709611			−0.354806	−	0.934940i	$-0.615453\pi$
$829$	−20.4314			−0.709611			−0.354806	+	0.934940i	$0.615453\pi$
$830$		0			0
$831$	9.67718	−	16.7614i	0.335697	−	0.581445i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	2.20362	+	3.81679i	0.0762595	+	0.132085i
$836$		0			0
$837$	29.5878	−	17.0825i	1.02270	−	0.590458i
$838$		0			0
$839$	21.0080	−	12.1290i	0.725276	−	0.418738i	−0.0914153	−	0.995813i	$-0.529139\pi$
$839$	21.0080	−	12.1290i	0.725276	−	0.418738i	0.816692	+	0.577074i	$0.195806\pi$
$840$		0			0
$841$	10.3821	+	17.9823i	0.358003	+	0.620080i
$842$		0			0
$843$		−	5.58492i		−	0.192355i
$844$		0			0
$845$	1.69715	+	17.9296i	0.0583839	+	0.616796i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−31.3949			−1.07747
$850$		0			0
$851$	6.69592	+	3.86589i	0.229533	+	0.132521i
$852$		0			0
$853$		−	51.8470i		−	1.77521i	−0.460608	−	0.887604i	$-0.652369\pi$
$853$		−	51.8470i		−	1.77521i	0.460608	−	0.887604i	$-0.347631\pi$
$854$		0			0
$855$	−0.383643	+	0.664490i	−0.0131203	+	0.0227251i
$856$		0			0
$857$	13.4527	+	23.3008i	0.459536	+	0.795939i	0.998936	−	0.0461102i	$-0.0146825\pi$
$857$	13.4527	+	23.3008i	0.459536	+	0.795939i	−0.539401	+	0.842049i	$0.681349\pi$
$858$		0			0
$859$	−16.7255	+	28.9694i	−0.570665	+	0.988422i	0.425832	+	0.904802i	$0.359981\pi$
$859$	−16.7255	+	28.9694i	−0.570665	+	0.988422i	−0.996498	+	0.0836195i	$0.973352\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	5.14724	+	2.97176i	0.175214	+	0.101160i	0.585042	−	0.811003i	$-0.301078\pi$
$863$	5.14724	+	2.97176i	0.175214	+	0.101160i	−0.409828	+	0.912163i	$0.634411\pi$
$864$		0			0
$865$	6.40557	+	3.69825i	0.217796	+	0.125744i
$866$		0			0
$867$	12.7461	+	22.0769i	0.432881	+	0.749771i
$868$		0			0
$869$	4.64087	+	2.67941i	0.157431	+	0.0908926i
$870$		0			0
$871$	−11.8912	−	6.13652i	−0.402917	−	0.207928i
$872$		0			0
$873$	−0.431453	+	0.249099i	−0.0146025	+	0.00843074i
$874$		0			0
$875$		0			0
$876$		0			0
$877$			49.6605i			1.67692i	0.544966	+	0.838458i	$0.316542\pi$
$877$			49.6605i			1.67692i	−0.544966	+	0.838458i	$0.683458\pi$
$878$		0			0
$879$	−25.7301	+	14.8553i	−0.867854	+	0.501056i
$880$		0			0
$881$	−10.6452	+	18.4381i	−0.358647	+	0.621195i	−0.987735	−	0.156139i	$-0.950095\pi$
$881$	−10.6452	+	18.4381i	−0.358647	+	0.621195i	0.629088	+	0.777334i	$0.283428\pi$
$882$		0			0
$883$	−32.8053			−1.10399			−0.551993	−	0.833848i	$-0.686133\pi$
$883$	−32.8053			−1.10399			−0.551993	+	0.833848i	$0.686133\pi$
$884$		0			0
$885$	9.77054	+	16.9231i	0.328433	+	0.568863i
$886$		0			0
$887$	8.61790	+	14.9266i	0.289361	+	0.501187i	0.973657	−	0.228016i	$-0.0732240\pi$
$887$	8.61790	+	14.9266i	0.289361	+	0.501187i	−0.684297	+	0.729204i	$0.739891\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$			10.5994i			0.355094i
$892$		0			0
$893$	−31.0580	+	53.7941i	−1.03932	+	1.80015i
$894$		0			0
$895$	11.8123	+	6.81985i	0.394843	+	0.227963i
$896$		0			0
$897$	14.0085	−	0.661520i	0.467730	−	0.0220875i
$898$		0			0
$899$		−	19.0849i		−	0.636518i
$900$		0			0
$901$	17.5469			0.584572
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−18.1467	−	10.4770i	−0.603217	−	0.348267i
$906$		0			0
$907$	34.6356			1.15006			0.575028	−	0.818134i	$-0.304991\pi$
$907$	34.6356			1.15006			0.575028	+	0.818134i	$0.304991\pi$
$908$		0			0
$909$	−0.871499			−0.0289058
$910$		0			0
$911$	−7.85153			−0.260133			−0.130066	−	0.991505i	$-0.541519\pi$
$911$	−7.85153			−0.260133			−0.130066	+	0.991505i	$0.541519\pi$
$912$		0			0
$913$	−2.10464			−0.0696533
$914$		0			0
$915$	−3.48397	−	2.01147i	−0.115177	−	0.0664972i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−36.7317			−1.21167			−0.605834	−	0.795591i	$-0.707160\pi$
$919$	−36.7317			−1.21167			−0.605834	+	0.795591i	$0.707160\pi$
$920$		0			0
$921$		−	47.2568i		−	1.55717i
$922$		0			0
$923$	1.68997	+	35.7872i	0.0556260	+	1.17795i
$924$		0			0
$925$	9.28654	+	5.36159i	0.305339	+	0.176288i
$926$		0			0
$927$	−0.194799	+	0.337401i	−0.00639803	+	0.0110817i
$928$		0			0
$929$			33.0655i			1.08484i	0.840107	+	0.542421i	$0.182492\pi$
$929$			33.0655i			1.08484i	−0.840107	+	0.542421i	$0.817508\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−24.8451	−	43.0330i	−0.813393	−	1.40884i
$934$		0			0
$935$	−1.24780	−	2.16125i	−0.0408073	−	0.0706803i
$936$		0			0
$937$	−45.8626			−1.49826			−0.749132	−	0.662421i	$-0.769529\pi$
$937$	−45.8626			−1.49826			−0.749132	+	0.662421i	$0.769529\pi$
$938$		0			0
$939$	14.5923	−	25.2746i	0.476202	−	0.824806i
$940$		0			0
$941$	−5.00328	+	2.88864i	−0.163102	+	0.0941671i	−0.579329	−	0.815094i	$-0.696685\pi$
$941$	−5.00328	+	2.88864i	−0.163102	+	0.0941671i	0.416227	+	0.909261i	$0.363352\pi$
$942$		0			0
$943$		−	27.8964i		−	0.908431i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.0487521	−	0.0281471i	0.00158423	−	0.000914656i	−0.499208	−	0.866482i	$-0.666376\pi$
$947$	0.0487521	−	0.0281471i	0.00158423	−	0.000914656i	0.500792	+	0.865568i	$0.333042\pi$
$948$		0			0
$949$	0.561587	+	11.8923i	0.0182299	+	0.386040i
$950$		0			0
$951$	43.5858	+	25.1643i	1.41337	+	0.816008i
$952$		0			0
$953$	−20.0778	−	34.7758i	−0.650385	−	1.12650i	−0.983030	−	0.183447i	$-0.941274\pi$
$953$	−20.0778	−	34.7758i	−0.650385	−	1.12650i	0.332645	−	0.943052i	$-0.392059\pi$
$954$		0			0
$955$	26.6106	+	15.3636i	0.861099	+	0.497156i
$956$		0			0
$957$	5.01723	+	2.89670i	0.162184	+	0.0936369i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	6.61283	−	11.4538i	0.213317	−	0.369476i
$962$		0			0
$963$	−0.336460	−	0.582766i	−0.0108423	−	0.0187794i
$964$		0			0
$965$	4.82928	−	8.36456i	0.155460	−	0.269265i
$966$		0			0
$967$		−	32.3647i		−	1.04078i	−0.853929	−	0.520390i	$-0.825787\pi$
$967$		−	32.3647i		−	1.04078i	0.853929	−	0.520390i	$-0.174213\pi$
$968$		0			0
$969$	19.8772	+	11.4761i	0.638547	+	0.368665i
$970$		0			0
$971$	−30.6918			−0.984947			−0.492473	−	0.870328i	$-0.663907\pi$
$971$	−30.6918			−0.984947			−0.492473	+	0.870328i	$0.663907\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	19.4283	−	0.917458i	0.622203	−	0.0293822i
$976$		0			0
$977$		−	5.62992i		−	0.180117i	−0.995936	−	0.0900585i	$-0.971295\pi$
$977$		−	5.62992i		−	0.180117i	0.995936	−	0.0900585i	$-0.0287054\pi$
$978$		0			0
$979$	1.37011	+	2.37310i	0.0437890	+	0.0758447i
$980$		0			0
$981$	0.351544	−	0.202964i	0.0112239	−	0.00648014i
$982$		0			0
$983$	−5.77088	+	3.33182i	−0.184062	+	0.106268i	−0.589200	−	0.807987i	$-0.700557\pi$
$983$	−5.77088	+	3.33182i	−0.184062	+	0.106268i	0.405138	+	0.914256i	$0.367224\pi$
$984$		0			0
$985$	−13.6688	−	23.6751i	−0.435525	−	0.754351i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−6.83820	+	11.8441i	−0.217442	+	0.376621i
$990$		0			0
$991$	−52.8312			−1.67824			−0.839120	−	0.543946i	$-0.816929\pi$
$991$	−52.8312			−1.67824			−0.839120	+	0.543946i	$0.816929\pi$
$992$		0			0
$993$			45.8618i			1.45538i
$994$		0			0
$995$	16.5613	−	9.56167i	0.525029	−	0.303125i
$996$		0			0
$997$	7.31833	−	12.6757i	0.231774	−	0.401444i	−0.726556	−	0.687107i	$-0.758880\pi$
$997$	7.31833	−	12.6757i	0.231774	−	0.401444i	0.958330	+	0.285663i	$0.0922137\pi$
$998$		0			0
$999$	15.4860	−	8.94085i	0.489955	−	0.282876i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.bq.e.1941.6		16
7.2	even	3		364.2.u.a.225.3	✓	16
7.3	odd	6		2548.2.bb.c.1733.6		16
7.4	even	3		2548.2.bb.d.1733.3		16
7.5	odd	6		2548.2.u.c.589.6		16
7.6	odd	2		2548.2.bq.c.1941.3		16
13.10	even	6		2548.2.bb.d.569.3		16
21.2	odd	6		3276.2.cf.c.2773.3		16
28.23	odd	6		1456.2.cc.f.225.6		16
91.9	even	3		4732.2.g.k.337.12		16
91.10	odd	6		2548.2.bq.c.361.3		16
91.23	even	6		364.2.u.a.309.3	yes	16
91.30	even	6		4732.2.g.k.337.11		16
91.58	odd	12		4732.2.a.s.1.6		8
91.62	odd	6		2548.2.bb.c.569.6		16
91.72	odd	12		4732.2.a.t.1.6		8
91.75	odd	6		2548.2.u.c.1765.6		16
91.88	even	6	inner	2548.2.bq.e.361.6		16
273.23	odd	6		3276.2.cf.c.1765.6		16
364.23	odd	6		1456.2.cc.f.673.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.u.a.225.3	✓	16	7.2	even	3
364.2.u.a.309.3	yes	16	91.23	even	6
1456.2.cc.f.225.6		16	28.23	odd	6
1456.2.cc.f.673.6		16	364.23	odd	6
2548.2.u.c.589.6		16	7.5	odd	6
2548.2.u.c.1765.6		16	91.75	odd	6
2548.2.bb.c.569.6		16	91.62	odd	6
2548.2.bb.c.1733.6		16	7.3	odd	6
2548.2.bb.d.569.3		16	13.10	even	6
2548.2.bb.d.1733.3		16	7.4	even	3
2548.2.bq.c.361.3		16	91.10	odd	6
2548.2.bq.c.1941.3		16	7.6	odd	2
2548.2.bq.e.361.6		16	91.88	even	6	inner
2548.2.bq.e.1941.6		16	1.1	even	1	trivial
3276.2.cf.c.1765.6		16	273.23	odd	6
3276.2.cf.c.2773.3		16	21.2	odd	6
4732.2.a.s.1.6		8	91.58	odd	12
4732.2.a.t.1.6		8	91.72	odd	12
4732.2.g.k.337.11		16	91.30	even	6
4732.2.g.k.337.12		16	91.9	even	3

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:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.bq (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.75101 q^{3} +(-1.19976 - 0.692682i) q^{5} +0.0660200 q^{9} -1.15290i q^{11} +(-1.65348 + 3.20406i) q^{13} +(-2.10079 - 1.21289i) q^{15} +(-0.781246 + 1.35316i) q^{17} -8.38917i q^{19} +(-1.11067 - 1.92374i) q^{23} +(-1.54038 - 2.66802i) q^{25} -5.13741 q^{27} +(-1.43491 + 2.48533i) q^{29} +(-5.75927 + 3.32512i) q^{31} -2.01874i q^{33} +(-3.01436 + 1.74034i) q^{37} +(-2.89525 + 5.61033i) q^{39} +(10.8758 + 6.27917i) q^{41} +(-3.07841 - 5.33196i) q^{43} +(-0.0792081 - 0.0457308i) q^{45} +(-6.41233 - 3.70216i) q^{47} +(-1.36797 + 2.36939i) q^{51} +(-5.61504 - 9.72553i) q^{53} +(-0.798593 + 1.38320i) q^{55} -14.6895i q^{57} +(-6.97634 - 4.02779i) q^{59} +1.65841 q^{61} +(4.20317 - 2.69877i) q^{65} +3.71128i q^{67} +(-1.94479 - 3.36848i) q^{69} +(8.60538 - 4.96832i) q^{71} +(2.85962 - 1.65100i) q^{73} +(-2.69722 - 4.67173i) q^{75} +(-2.32405 + 4.02538i) q^{79} -9.19370 q^{81} -1.82551i q^{83} +(1.87462 - 1.08231i) q^{85} +(-2.51253 + 4.35183i) q^{87} +(-2.05837 + 1.18840i) q^{89} +(-10.0845 + 5.82230i) q^{93} +(-5.81102 + 10.0650i) q^{95} +(-6.53519 + 3.77309i) q^{97} -0.0761145i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 28 q^{9} + 10 q^{13} + 6 q^{15} + 2 q^{17} + 22 q^{25} - 12 q^{27} - 22 q^{29} - 30 q^{31} - 12 q^{37} - 6 q^{39} + 36 q^{41} + 6 q^{43} + 30 q^{45} + 18 q^{47} + 2 q^{51} - 4 q^{53} + 2 q^{55} + 18 q^{59}+ \cdots - 42 q^{97}+O(q^{100}) \) 16 * q + 28 * q^9 + 10 * q^13 + 6 * q^15 + 2 * q^17 + 22 * q^25 - 12 * q^27 - 22 * q^29 - 30 * q^31 - 12 * q^37 - 6 * q^39 + 36 * q^41 + 6 * q^43 + 30 * q^45 + 18 * q^47 + 2 * q^51 - 4 * q^53 + 2 * q^55 + 18 * q^59 - 8 * q^61 - 52 * q^69 + 36 * q^71 + 12 * q^73 - 10 * q^75 - 4 * q^79 + 42 * q^85 + 26 * q^87 + 36 * q^89 + 42 * q^93 - 30 * q^95 - 42 * q^97

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