LMFDB - Embedded newform 1040.2.da.b.881.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1040,2,Mod(641,1040)] 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("1040.641"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1040, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.da (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-2,0,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.3
Root			$0.665665 - 1.24775i$ of defining polynomial
Character	$\chi$	$=$	1040.881
Dual form			1040.2.da.b.641.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0473938 + 0.0820885i) q^{3} +1.00000i q^{5} +(4.18016 + 2.41342i) q^{7} +(1.49551 - 2.59030i) q^{9} +(0.926118 - 0.534695i) q^{11} +(0.331331 + 3.59030i) q^{13} +(-0.0820885 + 0.0473938i) q^{15} +(1.77944 - 3.08209i) q^{17} +(-4.96410 - 2.86603i) q^{19} +0.457524i q^{21} +(3.54290 + 6.13649i) q^{23} -1.00000 q^{25} +0.567874 q^{27} +(-0.736543 - 1.27573i) q^{29} -1.46410i q^{31} +(0.0877845 + 0.0506824i) q^{33} +(-2.41342 + 4.18016i) q^{35} +(-0.0219955 + 0.0126991i) q^{37} +(-0.279019 + 0.197356i) q^{39} +(-0.232051 + 0.133975i) q^{41} +(-1.77944 + 3.08209i) q^{43} +(2.59030 + 1.49551i) q^{45} -6.51793i q^{47} +(8.14918 + 14.1148i) q^{49} +0.337339 q^{51} +0.991015 q^{53} +(0.534695 + 0.926118i) q^{55} -0.543327i q^{57} +(7.55440 + 4.36153i) q^{59} +(-3.16867 + 5.48830i) q^{61} +(12.5029 - 7.21857i) q^{63} +(-3.59030 + 0.331331i) q^{65} +(4.48009 - 2.58658i) q^{67} +(-0.335823 + 0.581663i) q^{69} +(6.72458 + 3.88244i) q^{71} +10.1088i q^{73} +(-0.0473938 - 0.0820885i) q^{75} +5.16177 q^{77} -8.78347 q^{79} +(-4.45961 - 7.72427i) q^{81} -0.725474i q^{83} +(3.08209 + 1.77944i) q^{85} +(0.0698151 - 0.120923i) q^{87} +(11.6970 - 6.75327i) q^{89} +(-7.27987 + 15.8077i) q^{91} +(0.120186 - 0.0693893i) q^{93} +(2.86603 - 4.96410i) q^{95} +(-2.97800 - 1.71935i) q^{97} -3.19856i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9} + 6 q^{15} - 2 q^{17} - 12 q^{19} + 10 q^{23} - 8 q^{25} + 4 q^{27} - 8 q^{29} + 42 q^{33} - 10 q^{35} + 6 q^{37} + 12 q^{41} + 2 q^{43} + 12 q^{49} + 8 q^{51} - 24 q^{53}+ \cdots - 30 q^{97}+O(q^{100}) $ 8 * q - 2 * q^3 + 6 * q^7 - 4 * q^9 + 6 * q^15 - 2 * q^17 - 12 * q^19 + 10 * q^23 - 8 * q^25 + 4 * q^27 - 8 * q^29 + 42 * q^33 - 10 * q^35 + 6 * q^37 + 12 * q^41 + 2 * q^43 + 12 * q^49 + 8 * q^51 - 24 * q^53 + 12 * q^59 - 28 * q^61 + 24 * q^63 - 8 * q^65 - 6 * q^67 - 16 * q^69 + 2 * q^75 - 36 * q^77 + 16 * q^79 + 8 * q^81 + 18 * q^85 - 22 * q^87 + 24 * q^89 - 28 * q^91 + 16 * q^95 - 30 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	0.0473938	+	0.0820885i	0.0273628	+	0.0473938i	0.879383	−	0.476116i	$-0.157956\pi$
$3$	0.0473938	+	0.0820885i	0.0273628	+	0.0473938i	−0.852020	+	0.523510i	$0.824622\pi$
$4$		0			0
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	4.18016	+	2.41342i	1.57995	+	0.912187i	0.994864	+	0.101218i	$0.0322739\pi$
$7$	4.18016	+	2.41342i	1.57995	+	0.912187i	0.585089	+	0.810969i	$0.301059\pi$
$8$		0			0
$9$	1.49551	−	2.59030i	0.498503	−	0.863432i
$10$		0			0
$11$	0.926118	−	0.534695i	0.279235	−	0.161217i	−0.353842	−	0.935305i	$-0.615125\pi$
$11$	0.926118	−	0.534695i	0.279235	−	0.161217i	0.633077	+	0.774089i	$0.281792\pi$
$12$		0			0
$13$	0.331331	+	3.59030i	0.0918946	+	0.995769i
$13$	0.331331	+	3.59030i	0.0918946	+	0.995769i
$14$		0			0
$15$	−0.0820885	+	0.0473938i	−0.0211951	+	0.0122370i
$16$		0			0
$17$	1.77944	−	3.08209i	0.431579	−	0.747516i	−0.565431	−	0.824796i	$-0.691290\pi$
$17$	1.77944	−	3.08209i	0.431579	−	0.747516i	0.997009	+	0.0772795i	$0.0246234\pi$
$18$		0			0
$19$	−4.96410	−	2.86603i	−1.13884	−	0.657511i	−0.192699	−	0.981258i	$-0.561724\pi$
$19$	−4.96410	−	2.86603i	−1.13884	−	0.657511i	−0.946144	+	0.323747i	$0.895057\pi$
$20$		0			0
$21$			0.457524i			0.0998400i
$22$		0			0
$23$	3.54290	+	6.13649i	0.738746	+	1.27955i	0.953060	+	0.302781i	$0.0979150\pi$
$23$	3.54290	+	6.13649i	0.738746	+	1.27955i	−0.214314	+	0.976765i	$0.568752\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	0.567874			0.109287
$28$		0			0
$29$	−0.736543	−	1.27573i	−0.136773	−	0.236897i	0.789501	−	0.613750i	$-0.210340\pi$
$29$	−0.736543	−	1.27573i	−0.136773	−	0.236897i	−0.926273	+	0.376853i	$0.877006\pi$
$30$		0			0
$31$		−	1.46410i		−	0.262960i	−0.991319	−	0.131480i	$-0.958027\pi$
$31$		−	1.46410i		−	0.262960i	0.991319	−	0.131480i	$-0.0419730\pi$
$32$		0			0
$33$	0.0877845	+	0.0506824i	0.0152813	+	0.00882268i
$34$		0			0
$35$	−2.41342	+	4.18016i	−0.407942	+	0.706577i
$36$		0			0
$37$	−0.0219955	+	0.0126991i	−0.00361604	+	0.00208772i	−0.501807	−	0.864980i	$-0.667331\pi$
$37$	−0.0219955	+	0.0126991i	−0.00361604	+	0.00208772i	0.498191	+	0.867067i	$0.333998\pi$
$38$		0			0
$39$	−0.279019	+	0.197356i	−0.0446788	+	0.0316023i
$40$		0			0
$41$	−0.232051	+	0.133975i	−0.0362402	+	0.0209233i	−0.518011	−	0.855374i	$-0.673327\pi$
$41$	−0.232051	+	0.133975i	−0.0362402	+	0.0209233i	0.481770	+	0.876297i	$0.339994\pi$
$42$		0			0
$43$	−1.77944	+	3.08209i	−0.271363	+	0.470014i	−0.969211	−	0.246232i	$-0.920808\pi$
$43$	−1.77944	+	3.08209i	−0.271363	+	0.470014i	0.697848	+	0.716246i	$0.254141\pi$
$44$		0			0
$45$	2.59030	+	1.49551i	0.386138	+	0.222937i
$46$		0			0
$47$		−	6.51793i		−	0.950738i	−0.879787	−	0.475369i	$-0.842315\pi$
$47$		−	6.51793i		−	0.950738i	0.879787	−	0.475369i	$-0.157685\pi$
$48$		0			0
$49$	8.14918	+	14.1148i	1.16417	+	2.01640i
$50$		0			0
$51$	0.337339			0.0472368
$52$		0			0
$53$	0.991015			0.136126			0.0680632	−	0.997681i	$-0.478318\pi$
$53$	0.991015			0.136126			0.0680632	+	0.997681i	$0.478318\pi$
$54$		0			0
$55$	0.534695	+	0.926118i	0.0720982	+	0.124878i
$56$		0			0
$57$		−	0.543327i		−	0.0719655i
$58$		0			0
$59$	7.55440	+	4.36153i	0.983499	+	0.567823i	0.903325	−	0.428958i	$-0.141119\pi$
$59$	7.55440	+	4.36153i	0.983499	+	0.567823i	0.0801741	+	0.996781i	$0.474452\pi$
$60$		0			0
$61$	−3.16867	+	5.48830i	−0.405707	+	0.702704i	−0.994403	−	0.105650i	$-0.966308\pi$
$61$	−3.16867	+	5.48830i	−0.405707	+	0.702704i	0.588697	+	0.808354i	$0.299641\pi$
$62$		0			0
$63$	12.5029	−	7.21857i	1.57522	−	0.909455i
$64$		0			0
$65$	−3.59030	+	0.331331i	−0.445321	+	0.0410965i
$66$		0			0
$67$	4.48009	−	2.58658i	0.547330	−	0.316001i	−0.200714	−	0.979650i	$-0.564326\pi$
$67$	4.48009	−	2.58658i	0.547330	−	0.316001i	0.748044	+	0.663649i	$0.230993\pi$
$68$		0			0
$69$	−0.335823	+	0.581663i	−0.0404283	+	0.0700240i
$70$		0			0
$71$	6.72458	+	3.88244i	0.798061	+	0.460761i	0.842793	−	0.538238i	$-0.180910\pi$
$71$	6.72458	+	3.88244i	0.798061	+	0.460761i	−0.0447317	+	0.998999i	$0.514243\pi$
$72$		0			0
$73$			10.1088i			1.18314i	0.806252	+	0.591572i	$0.201493\pi$
$73$			10.1088i			1.18314i	−0.806252	+	0.591572i	$0.798507\pi$
$74$		0			0
$75$	−0.0473938	−	0.0820885i	−0.00547256	−	0.00947876i
$76$		0			0
$77$	5.16177			0.588238
$78$		0			0
$79$	−8.78347			−0.988218			−0.494109	−	0.869400i	$-0.664506\pi$
$79$	−8.78347			−0.988218			−0.494109	+	0.869400i	$0.664506\pi$
$80$		0			0
$81$	−4.45961	−	7.72427i	−0.495512	−	0.858252i
$82$		0			0
$83$		−	0.725474i		−	0.0796311i	−0.999207	−	0.0398155i	$-0.987323\pi$
$83$		−	0.725474i		−	0.0796311i	0.999207	−	0.0398155i	$-0.0126770\pi$
$84$		0			0
$85$	3.08209	+	1.77944i	0.334299	+	0.193008i
$86$		0			0
$87$	0.0698151	−	0.120923i	0.00748497	−	0.0129643i
$88$		0			0
$89$	11.6970	−	6.75327i	1.23988	−	0.715845i	0.270810	−	0.962633i	$-0.412708\pi$
$89$	11.6970	−	6.75327i	1.23988	−	0.715845i	0.969070	+	0.246788i	$0.0793750\pi$
$90$		0			0
$91$	−7.27987	+	15.8077i	−0.763138	+	1.65709i
$92$		0			0
$93$	0.120186	−	0.0693893i	0.0124627	−	0.00719534i
$94$		0			0
$95$	2.86603	−	4.96410i	0.294048	−	0.509306i
$96$		0			0
$97$	−2.97800	−	1.71935i	−0.302371	−	0.174574i	0.341137	−	0.940014i	$-0.389188\pi$
$97$	−2.97800	−	1.71935i	−0.302371	−	0.174574i	−0.643507	+	0.765440i	$0.722521\pi$
$98$		0			0
$99$		−	3.19856i		−	0.321467i
$100$		0			0
$101$	1.42763	+	2.47273i	0.142055	+	0.246046i	0.928270	−	0.371906i	$-0.121296\pi$
$101$	1.42763	+	2.47273i	0.142055	+	0.246046i	−0.786215	+	0.617953i	$0.787962\pi$
$102$		0			0
$103$	−5.54488			−0.546354			−0.273177	−	0.961964i	$-0.588074\pi$
$103$	−5.54488			−0.546354			−0.273177	+	0.961964i	$0.588074\pi$
$104$		0			0
$105$	−0.457524			−0.0446498
$106$		0			0
$107$	−2.22056	−	3.84611i	−0.214669	−	0.371818i	0.738501	−	0.674252i	$-0.235534\pi$
$107$	−2.22056	−	3.84611i	−0.214669	−	0.371818i	−0.953170	+	0.302434i	$0.902201\pi$
$108$		0			0
$109$		−	13.7804i		−	1.31993i	−0.751298	−	0.659963i	$-0.770572\pi$
$109$		−	13.7804i		−	1.31993i	0.751298	−	0.659963i	$-0.229428\pi$
$110$		0			0
$111$	−0.00208490	−	0.00120372i	−0.000197890	−	0.000114252i
$112$		0			0
$113$	4.02200	−	6.96630i	0.378358	−	0.655334i	−0.612466	−	0.790497i	$-0.709822\pi$
$113$	4.02200	−	6.96630i	0.378358	−	0.655334i	0.990823	+	0.135163i	$0.0431557\pi$
$114$		0			0
$115$	−6.13649	+	3.54290i	−0.572230	+	0.330377i
$116$		0			0
$117$	9.79543	+	4.51107i	0.905588	+	0.417049i
$118$		0			0
$119$	14.8767	−	8.58909i	1.36375	−	0.787361i
$120$		0			0
$121$	−4.92820	+	8.53590i	−0.448018	+	0.775991i
$122$		0			0
$123$	−0.0219955	−	0.0126991i	−0.00198327	−	0.00114504i
$124$		0			0
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	−0.353326	−	0.611979i	−0.0313526	−	0.0543044i	0.849923	−	0.526906i	$-0.176648\pi$
$127$	−0.353326	−	0.611979i	−0.0313526	−	0.0543044i	−0.881276	+	0.472602i	$0.843315\pi$
$128$		0			0
$129$	−0.337339			−0.0297010
$130$		0			0
$131$	−6.26554			−0.547423			−0.273711	−	0.961812i	$-0.588251\pi$
$131$	−6.26554			−0.547423			−0.273711	+	0.961812i	$0.588251\pi$
$132$		0			0
$133$	−13.8338	−	23.9609i	−1.19955	−	2.07767i
$134$		0			0
$135$			0.567874i			0.0488748i
$136$		0			0
$137$	−14.1212	−	8.15290i	−1.20646	−	0.696549i	−0.244475	−	0.969656i	$-0.578616\pi$
$137$	−14.1212	−	8.15290i	−1.20646	−	0.696549i	−0.961984	+	0.273107i	$0.911949\pi$
$138$		0			0
$139$	−3.41264	+	5.91087i	−0.289456	+	0.501353i	−0.973680	−	0.227919i	$-0.926808\pi$
$139$	−3.41264	+	5.91087i	−0.289456	+	0.501353i	0.684224	+	0.729272i	$0.260141\pi$
$140$		0			0
$141$	0.535047	−	0.308909i	0.0450591	−	0.0260149i
$142$		0			0
$143$	2.22656	+	3.14788i	0.186195	+	0.263239i
$144$		0			0
$145$	1.27573	−	0.736543i	0.105944	−	0.0611666i
$146$		0			0
$147$	−0.772442	+	1.33791i	−0.0637099	+	0.110349i
$148$		0			0
$149$	−7.30887	−	4.21978i	−0.598766	−	0.345698i	0.169790	−	0.985480i	$-0.445691\pi$
$149$	−7.30887	−	4.21978i	−0.598766	−	0.345698i	−0.768556	+	0.639783i	$0.779024\pi$
$150$		0			0
$151$			1.37017i			0.111503i	0.998445	+	0.0557513i	$0.0177554\pi$
$151$			1.37017i			0.111503i	−0.998445	+	0.0557513i	$0.982245\pi$
$152$		0			0
$153$	−5.32235	−	9.21857i	−0.430286	−	0.745278i
$154$		0			0
$155$	1.46410			0.117599
$156$		0			0
$157$	11.9700			0.955311			0.477656	−	0.878547i	$-0.341487\pi$
$157$	11.9700			0.955311			0.477656	+	0.878547i	$0.341487\pi$
$158$		0			0
$159$	0.0469680	+	0.0813509i	0.00372480	+	0.00645155i
$160$		0			0
$161$			34.2020i			2.69550i
$162$		0			0
$163$	−19.5474	−	11.2857i	−1.53107	−	0.883962i	−0.999313	−	0.0370630i	$-0.988200\pi$
$163$	−19.5474	−	11.2857i	−1.53107	−	0.883962i	−0.531754	−	0.846899i	$-0.678467\pi$
$164$		0			0
$165$	−0.0506824	+	0.0877845i	−0.00394562	+	0.00683402i
$166$		0			0
$167$	−7.09881	+	4.09850i	−0.549323	+	0.317152i	−0.748849	−	0.662741i	$-0.769393\pi$
$167$	−7.09881	+	4.09850i	−0.549323	+	0.317152i	0.199526	+	0.979893i	$0.436060\pi$
$168$		0			0
$169$	−12.7804	+	2.37915i	−0.983111	+	0.183012i
$170$		0			0
$171$	−14.8477	+	8.57233i	−1.13543	+	0.655542i
$172$		0			0
$173$	−4.58386	+	7.93948i	−0.348505	+	0.603628i	−0.985984	−	0.166840i	$-0.946644\pi$
$173$	−4.58386	+	7.93948i	−0.348505	+	0.603628i	0.637479	+	0.770467i	$0.279977\pi$
$174$		0			0
$175$	−4.18016	−	2.41342i	−0.315991	−	0.182437i
$176$		0			0
$177$			0.826838i			0.0621490i
$178$		0			0
$179$	5.01850	+	8.69229i	0.375100	+	0.649693i	0.990342	−	0.138646i	$-0.0442750\pi$
$179$	5.01850	+	8.69229i	0.375100	+	0.649693i	−0.615242	+	0.788338i	$0.710942\pi$
$180$		0			0
$181$	−17.0238			−1.26537			−0.632686	−	0.774408i	$-0.718048\pi$
$181$	−17.0238			−1.26537			−0.632686	+	0.774408i	$0.718048\pi$
$182$		0			0
$183$	−0.600701			−0.0444051
$184$		0			0
$185$	−0.0126991	−	0.0219955i	−0.000933659	−	0.00161714i
$186$		0			0
$187$		−	3.80584i		−	0.278310i
$188$		0			0
$189$	2.37381	+	1.37052i	0.172669	+	0.0996905i
$190$		0			0
$191$	−1.93870	+	3.35793i	−0.140280	+	0.242971i	−0.927602	−	0.373570i	$-0.878133\pi$
$191$	−1.93870	+	3.35793i	−0.140280	+	0.242971i	0.787322	+	0.616542i	$0.211467\pi$
$192$		0			0
$193$	1.08595	−	0.626972i	0.0781681	−	0.0451304i	−0.460406	−	0.887708i	$-0.652296\pi$
$193$	1.08595	−	0.626972i	0.0781681	−	0.0451304i	0.538575	+	0.842578i	$0.318963\pi$
$194$		0			0
$195$	−0.197356	−	0.279019i	−0.0141330	−	0.0199810i
$196$		0			0
$197$	13.2346	−	7.64098i	0.942923	−	0.544397i	0.0520479	−	0.998645i	$-0.483425\pi$
$197$	13.2346	−	7.64098i	0.942923	−	0.544397i	0.890876	+	0.454247i	$0.150092\pi$
$198$		0			0
$199$	6.61480	−	11.4572i	0.468911	−	0.812177i	−0.530458	−	0.847711i	$-0.677980\pi$
$199$	6.61480	−	11.4572i	0.468911	−	0.812177i	0.999368	+	0.0355340i	$0.0113132\pi$
$200$		0			0
$201$	0.424657	+	0.245176i	0.0299530	+	0.0172934i
$202$		0			0
$203$		−	7.11035i		−	0.499049i
$204$		0			0
$205$	−0.133975	−	0.232051i	−0.00935719	−	0.0162071i
$206$		0			0
$207$	21.1937			1.47307
$208$		0			0
$209$	−6.12979			−0.424007
$210$		0			0
$211$	−2.40521	−	4.16595i	−0.165582	−	0.286796i	0.771280	−	0.636496i	$-0.219617\pi$
$211$	−2.40521	−	4.16595i	−0.165582	−	0.286796i	−0.936862	+	0.349700i	$0.886283\pi$
$212$		0			0
$213$			0.736014i			0.0504309i
$214$		0			0
$215$	−3.08209	−	1.77944i	−0.210197	−	0.121357i
$216$		0			0
$217$	3.53349	−	6.12019i	0.239869	−	0.415465i
$218$		0			0
$219$	−0.829815	+	0.479094i	−0.0560737	+	0.0323742i
$220$		0			0
$221$	11.6552	+	5.36754i	0.784013	+	0.361060i
$222$		0			0
$223$	12.7420	−	7.35661i	0.853269	−	0.492635i	−0.00848317	−	0.999964i	$-0.502700\pi$
$223$	12.7420	−	7.35661i	0.853269	−	0.492635i	0.861753	+	0.507329i	$0.169367\pi$
$224$		0			0
$225$	−1.49551	+	2.59030i	−0.0997005	+	0.172686i
$226$		0			0
$227$	−12.9062	−	7.45140i	−0.856615	−	0.494567i	0.00626222	−	0.999980i	$-0.498007\pi$
$227$	−12.9062	−	7.45140i	−0.856615	−	0.494567i	−0.862877	+	0.505413i	$0.831340\pi$
$228$		0			0
$229$		−	19.3074i		−	1.27587i	−0.770092	−	0.637933i	$-0.779790\pi$
$229$		−	19.3074i		−	1.27587i	0.770092	−	0.637933i	$-0.220210\pi$
$230$		0			0
$231$	0.244636	+	0.423722i	0.0160959	+	0.0278788i
$232$		0			0
$233$	21.1937			1.38845			0.694224	−	0.719759i	$-0.255748\pi$
$233$	21.1937			1.38845			0.694224	+	0.719759i	$0.255748\pi$
$234$		0			0
$235$	6.51793			0.425183
$236$		0			0
$237$	−0.416282	−	0.721022i	−0.0270404	−	0.0468354i
$238$		0			0
$239$		−	14.8971i		−	0.963612i	−0.876278	−	0.481806i	$-0.839981\pi$
$239$		−	14.8971i		−	0.963612i	0.876278	−	0.481806i	$-0.160019\pi$
$240$		0			0
$241$	−8.13343	−	4.69584i	−0.523921	−	0.302486i	0.214617	−	0.976698i	$-0.431150\pi$
$241$	−8.13343	−	4.69584i	−0.523921	−	0.302486i	−0.738537	+	0.674213i	$0.764483\pi$
$242$		0			0
$243$	1.27453	−	2.20754i	0.0817609	−	0.141614i
$244$		0			0
$245$	−14.1148	+	8.14918i	−0.901762	+	0.520632i
$246$		0			0
$247$	8.64512	−	18.7722i	0.550076	−	1.19445i
$248$		0			0
$249$	0.0595530	−	0.0343829i	0.00377402	−	0.00217893i
$250$		0			0
$251$	−5.65817	+	9.80024i	−0.357140	+	0.618585i	−0.987482	−	0.157733i	$-0.949582\pi$
$251$	−5.65817	+	9.80024i	−0.357140	+	0.618585i	0.630341	+	0.776318i	$0.282915\pi$
$252$		0			0
$253$	6.56229	+	3.78874i	0.412568	+	0.238196i
$254$		0			0
$255$			0.337339i			0.0211250i
$256$		0			0
$257$	−13.2660	−	22.9773i	−0.827508	−	1.43329i	−0.899987	−	0.435917i	$-0.856424\pi$
$257$	−13.2660	−	22.9773i	−0.827508	−	1.43329i	0.0724788	−	0.997370i	$-0.476909\pi$
$258$		0			0
$259$	−0.122593			−0.00761758
$260$		0			0
$261$	−4.40602			−0.272726
$262$		0			0
$263$	−7.07038	−	12.2463i	−0.435979	−	0.755137i	0.561396	−	0.827547i	$-0.310264\pi$
$263$	−7.07038	−	12.2463i	−0.435979	−	0.755137i	−0.997375	+	0.0724100i	$0.976931\pi$
$264$		0			0
$265$			0.991015i			0.0608776i
$266$		0			0
$267$	1.10873	+	0.640126i	0.0678532	+	0.0391751i
$268$		0			0
$269$	−12.3872	+	21.4553i	−0.755264	+	1.30815i	0.189980	+	0.981788i	$0.439158\pi$
$269$	−12.3872	+	21.4553i	−0.755264	+	1.30815i	−0.945243	+	0.326367i	$0.894176\pi$
$270$		0			0
$271$	−16.2095	+	9.35856i	−0.984657	+	0.568492i	−0.903673	−	0.428224i	$-0.859140\pi$
$271$	−16.2095	+	9.35856i	−0.984657	+	0.568492i	−0.0809839	+	0.996715i	$0.525806\pi$
$272$		0			0
$273$	−1.64265	+	0.151592i	−0.0994176	+	0.00917476i
$274$		0			0
$275$	−0.926118	+	0.534695i	−0.0558470	+	0.0322433i
$276$		0			0
$277$	−11.3323	+	19.6282i	−0.680893	+	1.17934i	0.293815	+	0.955862i	$0.405075\pi$
$277$	−11.3323	+	19.6282i	−0.680893	+	1.17934i	−0.974709	+	0.223480i	$0.928258\pi$
$278$		0			0
$279$	−3.79246	−	2.18958i	−0.227048	−	0.131086i
$280$		0			0
$281$		−	27.8384i		−	1.66070i	−0.557241	−	0.830351i	$-0.688140\pi$
$281$		−	27.8384i		−	1.66070i	0.557241	−	0.830351i	$-0.311860\pi$
$282$		0			0
$283$	−3.96004	−	6.85898i	−0.235400	−	0.407724i	0.723989	−	0.689811i	$-0.242307\pi$
$283$	−3.96004	−	6.85898i	−0.235400	−	0.407724i	−0.959389	+	0.282087i	$0.908973\pi$
$284$		0			0
$285$	0.543327			0.0321839
$286$		0			0
$287$	−1.29335			−0.0763439
$288$		0			0
$289$	2.16715	+	3.75362i	0.127480	+	0.220801i
$290$		0			0
$291$		−	0.325946i		−	0.0191073i
$292$		0			0
$293$	0.236400	+	0.136485i	0.0138106	+	0.00797356i	0.506889	−	0.862011i	$-0.330795\pi$
$293$	0.236400	+	0.136485i	0.0138106	+	0.00797356i	−0.493079	+	0.869985i	$0.664129\pi$
$294$		0			0
$295$	−4.36153	+	7.55440i	−0.253938	+	0.439834i
$296$		0			0
$297$	0.525918	−	0.303639i	0.0305169	−	0.0176189i
$298$		0			0
$299$	−20.8579	+	14.7533i	−1.20624	+	0.853204i
$300$		0			0
$301$	−14.8767	+	8.58909i	−0.857481	+	0.495067i
$302$		0			0
$303$	−0.135322	+	0.234385i	−0.00777404	+	0.0134650i
$304$		0			0
$305$	−5.48830	−	3.16867i	−0.314259	−	0.181437i
$306$		0			0
$307$		−	6.85224i		−	0.391078i	−0.980696	−	0.195539i	$-0.937354\pi$
$307$		−	6.85224i		−	0.391078i	0.980696	−	0.195539i	$-0.0626456\pi$
$308$		0			0
$309$	−0.262793	−	0.455171i	−0.0149498	−	0.0258938i
$310$		0			0
$311$	10.6447			0.603605			0.301803	−	0.953370i	$-0.402412\pi$
$311$	10.6447			0.603605			0.301803	+	0.953370i	$0.402412\pi$
$312$		0			0
$313$	17.8236			1.00745			0.503724	−	0.863865i	$-0.331963\pi$
$313$	17.8236			1.00745			0.503724	+	0.863865i	$0.331963\pi$
$314$		0			0
$315$	7.21857	+	12.5029i	0.406721	+	0.704461i
$316$		0			0
$317$		−	8.17161i		−	0.458963i	−0.973313	−	0.229482i	$-0.926297\pi$
$317$		−	8.17161i		−	0.458963i	0.973313	−	0.229482i	$-0.0737031\pi$
$318$		0			0
$319$	−1.36425	−	0.787651i	−0.0763835	−	0.0441000i
$320$		0			0
$321$	0.210481	−	0.364564i	0.0117479	−	0.0203480i
$322$		0			0
$323$	−17.6667	+	10.1999i	−0.983001	+	0.567536i
$324$		0			0
$325$	−0.331331	−	3.59030i	−0.0183789	−	0.199154i
$326$		0			0
$327$	1.13122	−	0.653107i	0.0625563	−	0.0361169i
$328$		0			0
$329$	15.7305	−	27.2460i	0.867250	−	1.50212i
$330$		0			0
$331$	−21.5983	−	12.4698i	−1.18715	−	0.685400i	−0.229490	−	0.973311i	$-0.573706\pi$
$331$	−21.5983	−	12.4698i	−1.18715	−	0.685400i	−0.957657	+	0.287911i	$0.907039\pi$
$332$		0			0
$333$			0.0759666i			0.00416294i
$334$		0			0
$335$	2.58658	+	4.48009i	0.141320	+	0.244773i
$336$		0			0
$337$	19.6057			1.06799			0.533996	−	0.845487i	$-0.320690\pi$
$337$	19.6057			1.06799			0.533996	+	0.845487i	$0.320690\pi$
$338$		0			0
$339$	0.762471			0.0414117
$340$		0			0
$341$	−0.782847	−	1.35593i	−0.0423936	−	0.0734278i
$342$		0			0
$343$			44.8817i			2.42339i
$344$		0			0
$345$	−0.581663	−	0.335823i	−0.0313157	−	0.0180801i
$346$		0			0
$347$	8.54049	−	14.7926i	0.458478	−	0.794107i	−0.540403	−	0.841406i	$-0.681728\pi$
$347$	8.54049	−	14.7926i	0.458478	−	0.794107i	0.998881	+	0.0472996i	$0.0150615\pi$
$348$		0			0
$349$	−24.5708	+	14.1860i	−1.31525	+	0.759357i	−0.982960	−	0.183822i	$-0.941153\pi$
$349$	−24.5708	+	14.1860i	−1.31525	+	0.759357i	−0.332286	+	0.943179i	$0.607820\pi$
$350$		0			0
$351$	0.188154	+	2.03883i	0.0100429	+	0.108825i
$352$		0			0
$353$	−18.4047	+	10.6260i	−0.979586	+	0.565564i	−0.902145	−	0.431433i	$-0.858008\pi$
$353$	−18.4047	+	10.6260i	−0.979586	+	0.565564i	−0.0774407	+	0.996997i	$0.524675\pi$
$354$		0			0
$355$	−3.88244	+	6.72458i	−0.206058	+	0.356904i
$356$		0			0
$357$	1.41013	+	0.814139i	0.0746320	+	0.0430888i
$358$		0			0
$359$		−	32.6519i		−	1.72330i	−0.507502	−	0.861650i	$-0.669431\pi$
$359$		−	32.6519i		−	1.72330i	0.507502	−	0.861650i	$-0.330569\pi$
$360$		0			0
$361$	6.92820	+	12.0000i	0.364642	+	0.631579i
$362$		0			0
$363$	−0.934265			−0.0490362
$364$		0			0
$365$	−10.1088			−0.529118
$366$		0			0
$367$	−2.95918	−	5.12546i	−0.154468	−	0.267547i	0.778397	−	0.627772i	$-0.216033\pi$
$367$	−2.95918	−	5.12546i	−0.154468	−	0.267547i	−0.932865	+	0.360226i	$0.882700\pi$
$368$		0			0
$369$			0.801440i			0.0417213i
$370$		0			0
$371$	4.14261	+	2.39174i	0.215073	+	0.124173i
$372$		0			0
$373$	6.65926	−	11.5342i	0.344803	−	0.597217i	−0.640515	−	0.767946i	$-0.721279\pi$
$373$	6.65926	−	11.5342i	0.344803	−	0.597217i	0.985318	+	0.170729i	$0.0546123\pi$
$374$		0			0
$375$	0.0820885	−	0.0473938i	0.00423903	−	0.00244740i
$376$		0			0
$377$	4.33621	−	3.06710i	0.223326	−	0.157963i
$378$		0			0
$379$	22.0131	−	12.7093i	1.13074	−	0.652832i	0.186617	−	0.982433i	$-0.440248\pi$
$379$	22.0131	−	12.7093i	1.13074	−	0.652832i	0.944120	+	0.329601i	$0.106914\pi$
$380$		0			0
$381$	0.0334909	−	0.0580080i	0.00171579	−	0.00297184i
$382$		0			0
$383$	9.37632	+	5.41342i	0.479107	+	0.276613i	0.720044	−	0.693928i	$-0.244121\pi$
$383$	9.37632	+	5.41342i	0.479107	+	0.276613i	−0.240937	+	0.970541i	$0.577455\pi$
$384$		0			0
$385$			5.16177i			0.263068i
$386$		0			0
$387$	5.32235	+	9.21857i	0.270550	+	0.468606i
$388$		0			0
$389$	23.0370			1.16802			0.584011	−	0.811746i	$-0.301482\pi$
$389$	23.0370			1.16802			0.584011	+	0.811746i	$0.301482\pi$
$390$		0			0
$391$	25.2176			1.27531
$392$		0			0
$393$	−0.296948	−	0.514329i	−0.0149790	−	0.0259444i
$394$		0			0
$395$		−	8.78347i		−	0.441944i
$396$		0			0
$397$	−18.2614	−	10.5432i	−0.916512	−	0.529149i	−0.0339917	−	0.999422i	$-0.510822\pi$
$397$	−18.2614	−	10.5432i	−0.916512	−	0.529149i	−0.882521	+	0.470273i	$0.844155\pi$
$398$		0			0
$399$	1.31128	−	2.27120i	0.0656459	−	0.113702i
$400$		0			0
$401$	−17.1273	+	9.88845i	−0.855296	+	0.493805i	−0.862434	−	0.506169i	$-0.831061\pi$
$401$	−17.1273	+	9.88845i	−0.855296	+	0.493805i	0.00713812	+	0.999975i	$0.497728\pi$
$402$		0			0
$403$	5.25656	−	0.485102i	0.261848	−	0.0241646i
$404$		0			0
$405$	7.72427	−	4.45961i	0.383822	−	0.221600i
$406$		0			0
$407$	−0.0135803	+	0.0235218i	−0.000673151	+	0.00116593i
$408$		0			0
$409$	−27.6096	−	15.9404i	−1.36521	−	0.788204i	−0.374897	−	0.927066i	$-0.622322\pi$
$409$	−27.6096	−	15.9404i	−1.36521	−	0.788204i	−0.990312	+	0.138862i	$0.955655\pi$
$410$		0			0
$411$		−	1.54559i		−	0.0762382i
$412$		0			0
$413$	21.0524	+	36.4639i	1.03592	+	1.79427i
$414$		0			0
$415$	0.725474			0.0356121
$416$		0			0
$417$	−0.646952			−0.0316814
$418$		0			0
$419$	15.3648	+	26.6127i	0.750621	+	1.30011i	0.947522	+	0.319690i	$0.103579\pi$
$419$	15.3648	+	26.6127i	0.750621	+	1.30011i	−0.196902	+	0.980423i	$0.563088\pi$
$420$		0			0
$421$		−	17.9820i		−	0.876391i	−0.898880	−	0.438195i	$-0.855618\pi$
$421$		−	17.9820i		−	0.876391i	0.898880	−	0.438195i	$-0.144382\pi$
$422$		0			0
$423$	−16.8834	−	9.74761i	−0.820897	−	0.473945i
$424$		0			0
$425$	−1.77944	+	3.08209i	−0.0863157	+	0.149503i
$426$		0			0
$427$	−26.4911	+	15.2947i	−1.28200	+	0.740160i
$428$		0			0
$429$	−0.152879	+	0.331965i	−0.00738107	+	0.0160274i
$430$		0			0
$431$	4.24308	−	2.44974i	0.204382	−	0.118000i	−0.394316	−	0.918975i	$-0.629018\pi$
$431$	4.24308	−	2.44974i	0.204382	−	0.118000i	0.598698	+	0.800975i	$0.295685\pi$
$432$		0			0
$433$	−9.61972	+	16.6618i	−0.462294	+	0.800717i	−0.999075	−	0.0430048i	$-0.986307\pi$
$433$	−9.61972	+	16.6618i	−0.462294	+	0.800717i	0.536781	+	0.843722i	$0.319640\pi$
$434$		0			0
$435$	0.120923	+	0.0698151i	0.00579783	+	0.00334738i
$436$		0			0
$437$		−	40.6162i		−	1.94294i
$438$		0			0
$439$	4.27987	+	7.41295i	0.204267	+	0.353801i	0.949899	−	0.312557i	$-0.101186\pi$
$439$	4.27987	+	7.41295i	0.204267	+	0.353801i	−0.745632	+	0.666358i	$0.767852\pi$
$440$		0			0
$441$	48.7487			2.32137
$442$		0			0
$443$	37.9652			1.80378			0.901891	−	0.431965i	$-0.142179\pi$
$443$	37.9652			1.80378			0.901891	+	0.431965i	$0.142179\pi$
$444$		0			0
$445$	6.75327	+	11.6970i	0.320136	+	0.554491i
$446$		0			0
$447$		−	0.799965i		−	0.0378370i
$448$		0			0
$449$	23.1283	+	13.3531i	1.09149	+	0.630173i	0.933973	−	0.357344i	$-0.116317\pi$
$449$	23.1283	+	13.3531i	1.09149	+	0.630173i	0.157518	+	0.987516i	$0.449651\pi$
$450$		0			0
$451$	−0.143271	+	0.248153i	−0.00674637	+	0.0116851i
$452$		0			0
$453$	−0.112475	+	0.0649373i	−0.00528453	+	0.00305102i
$454$		0			0
$455$	−15.8077	−	7.27987i	−0.741075	−	0.341286i
$456$		0			0
$457$	3.69903	−	2.13563i	0.173033	−	0.0999007i	−0.410982	−	0.911643i	$-0.634814\pi$
$457$	3.69903	−	2.13563i	0.173033	−	0.0999007i	0.584015	+	0.811743i	$0.301481\pi$
$458$		0			0
$459$	1.01050	−	1.75024i	0.0471661	−	0.0816941i
$460$		0			0
$461$	17.8767	+	10.3211i	0.832603	+	0.480704i	0.854743	−	0.519051i	$-0.173715\pi$
$461$	17.8767	+	10.3211i	0.832603	+	0.480704i	−0.0221401	+	0.999755i	$0.507048\pi$
$462$		0			0
$463$			32.1040i			1.49200i	0.665947	+	0.745999i	$0.268028\pi$
$463$			32.1040i			1.49200i	−0.665947	+	0.745999i	$0.731972\pi$
$464$		0			0
$465$	0.0693893	+	0.120186i	0.00321785	+	0.00557349i
$466$		0			0
$467$	23.3774			1.08178			0.540888	−	0.841095i	$-0.318088\pi$
$467$	23.3774			1.08178			0.540888	+	0.841095i	$0.318088\pi$
$468$		0			0
$469$	24.9700			1.15301
$470$		0			0
$471$	0.567304	+	0.982600i	0.0261400	+	0.0452758i
$472$		0			0
$473$			3.80584i			0.174993i
$474$		0			0
$475$	4.96410	+	2.86603i	0.227769	+	0.131502i
$476$		0			0
$477$	1.48207	−	2.56702i	0.0678594	−	0.117536i
$478$		0			0
$479$	4.48198	−	2.58767i	0.204787	−	0.118234i	−0.394100	−	0.919068i	$-0.628943\pi$
$479$	4.48198	−	2.58767i	0.204787	−	0.118234i	0.598886	+	0.800834i	$0.295610\pi$
$480$		0			0
$481$	−0.0528814	−	0.0747629i	−0.00241119	−	0.00340889i
$482$		0			0
$483$	−2.80759	+	1.62096i	−0.127750	+	0.0737564i
$484$		0			0
$485$	1.71935	−	2.97800i	0.0780717	−	0.135224i
$486$		0			0
$487$	26.6501	+	15.3865i	1.20763	+	0.697227i	0.962242	−	0.272197i	$-0.0877502\pi$
$487$	26.6501	+	15.3865i	1.20763	+	0.697227i	0.245391	+	0.969424i	$0.421083\pi$
$488$		0			0
$489$		−	2.13948i		−	0.0967508i
$490$		0			0
$491$	−17.8992	−	31.0023i	−0.807778	−	1.39911i	−0.914400	−	0.404813i	$-0.867337\pi$
$491$	−17.8992	−	31.0023i	−0.807778	−	1.39911i	0.106622	−	0.994300i	$-0.465997\pi$
$492$		0			0
$493$	−5.24255			−0.236113
$494$		0			0
$495$	3.19856			0.143765
$496$		0			0
$497$	18.7399	+	32.4585i	0.840600	+	1.45596i
$498$		0			0
$499$			28.8971i			1.29361i	0.762655	+	0.646805i	$0.223895\pi$
$499$			28.8971i			1.29361i	−0.762655	+	0.646805i	$0.776105\pi$
$500$		0			0
$501$	−0.672879	−	0.388487i	−0.0300620	−	0.0173563i
$502$		0			0
$503$	−3.93161	+	6.80974i	−0.175302	+	0.303631i	−0.940266	−	0.340442i	$-0.889423\pi$
$503$	−3.93161	+	6.80974i	−0.175302	+	0.303631i	0.764964	+	0.644073i	$0.222757\pi$
$504$		0			0
$505$	−2.47273	+	1.42763i	−0.110035	+	0.0635289i
$506$		0			0
$507$	−0.801014	−	0.936370i	−0.0355743	−	0.0415856i
$508$		0			0
$509$	24.2585	−	14.0057i	1.07524	−	0.620790i	0.145631	−	0.989339i	$-0.453479\pi$
$509$	24.2585	−	14.0057i	1.07524	−	0.620790i	0.929608	+	0.368549i	$0.120145\pi$
$510$		0			0
$511$	−24.3968	+	42.2564i	−1.07925	+	1.86931i
$512$		0			0
$513$	−2.81898	−	1.62754i	−0.124461	−	0.0718577i
$514$		0			0
$515$		−	5.54488i		−	0.244337i
$516$		0			0
$517$	−3.48510	−	6.03637i	−0.153275	−	0.265479i
$518$		0			0
$519$	−0.868986			−0.0381443
$520$		0			0
$521$	−37.5609			−1.64557			−0.822786	−	0.568351i	$-0.807581\pi$
$521$	−37.5609			−1.64557			−0.822786	+	0.568351i	$0.807581\pi$
$522$		0			0
$523$	−22.6553	−	39.2401i	−0.990647	−	1.71585i	−0.613493	−	0.789700i	$-0.710236\pi$
$523$	−22.6553	−	39.2401i	−0.990647	−	1.71585i	−0.377154	−	0.926151i	$-0.623097\pi$
$524$		0			0
$525$		−	0.457524i		−	0.0199680i
$526$		0			0
$527$	−4.51249	−	2.60529i	−0.196567	−	0.113488i
$528$		0			0
$529$	−13.6043	+	23.5633i	−0.591491	+	1.02449i
$530$		0			0
$531$	22.5953	−	13.0454i	0.980553	−	0.566123i
$532$		0			0
$533$	−0.557894	−	0.788741i	−0.0241651	−	0.0341642i
$534$		0			0
$535$	3.84611	−	2.22056i	0.166282	−	0.0960030i
$536$		0			0
$537$	−0.475691	+	0.823922i	−0.0205276	+	0.0355548i
$538$		0			0
$539$	15.0942	+	8.71465i	0.650154	+	0.375367i
$540$		0			0
$541$			19.7445i			0.848882i	0.905456	+	0.424441i	$0.139529\pi$
$541$			19.7445i			0.848882i	−0.905456	+	0.424441i	$0.860471\pi$
$542$		0			0
$543$	−0.806824	−	1.39746i	−0.0346242	−	0.0599708i
$544$		0			0
$545$	13.7804			0.590289
$546$		0			0
$547$	11.8312			0.505867			0.252934	−	0.967484i	$-0.418605\pi$
$547$	11.8312			0.505867			0.252934	+	0.967484i	$0.418605\pi$
$548$		0			0
$549$	9.47754	+	16.4156i	0.404491	+	0.700600i
$550$		0			0
$551$			8.44381i			0.359718i
$552$		0			0
$553$	−36.7164	−	21.1982i	−1.56134	−	0.901439i
$554$		0			0
$555$	0.00120372	−	0.00208490i	5.10951e−5	−	8.84992e-5i
$556$		0			0
$557$	−3.50412	+	2.02310i	−0.148474	+	0.0857217i	−0.572397	−	0.819977i	$-0.693986\pi$
$557$	−3.50412	+	2.02310i	−0.148474	+	0.0857217i	0.423922	+	0.905699i	$0.360653\pi$
$558$		0			0
$559$	−11.6552	−	5.36754i	−0.492962	−	0.227023i
$560$		0			0
$561$	0.312415	−	0.180373i	0.0131902	−	0.00761536i
$562$		0			0
$563$	−1.94963	+	3.37686i	−0.0821671	+	0.142318i	−0.904181	−	0.427151i	$-0.859517\pi$
$563$	−1.94963	+	3.37686i	−0.0821671	+	0.142318i	0.822013	+	0.569468i	$0.192851\pi$
$564$		0			0
$565$	6.96630	+	4.02200i	0.293074	+	0.169207i
$566$		0			0
$567$		−	43.0516i		−	1.80800i
$568$		0			0
$569$	−8.66778	−	15.0130i	−0.363372	−	0.629379i	0.625141	−	0.780512i	$-0.285041\pi$
$569$	−8.66778	−	15.0130i	−0.363372	−	0.629379i	−0.988514	+	0.151133i	$0.951708\pi$
$570$		0			0
$571$	29.5118			1.23503			0.617515	−	0.786559i	$-0.288140\pi$
$571$	29.5118			1.23503			0.617515	+	0.786559i	$0.288140\pi$
$572$		0			0
$573$	−0.367530			−0.0153538
$574$		0			0
$575$	−3.54290	−	6.13649i	−0.147749	−	0.255909i
$576$		0			0
$577$			28.3684i			1.18099i	0.807041	+	0.590496i	$0.201068\pi$
$577$			28.3684i			1.18099i	−0.807041	+	0.590496i	$0.798932\pi$
$578$		0			0
$579$	0.102934	+	0.0594291i	0.00427780	+	0.00246979i
$580$		0			0
$581$	1.75087	−	3.03260i	0.0726384	−	0.125813i
$582$		0			0
$583$	0.917797	−	0.529891i	0.0380113	−	0.0219458i
$584$		0			0
$585$	−4.51107	+	9.79543i	−0.186510	+	0.404991i
$586$		0			0
$587$	−29.7806	+	17.1939i	−1.22918	+	0.709667i	−0.966858	−	0.255314i	$-0.917821\pi$
$587$	−29.7806	+	17.1939i	−1.22918	+	0.709667i	−0.262320	+	0.964981i	$0.584488\pi$
$588$		0			0
$589$	−4.19615	+	7.26795i	−0.172899	+	0.299471i
$590$		0			0
$591$	1.25447	+	0.724270i	0.0516021	+	0.0297925i
$592$		0			0
$593$		−	5.47612i		−	0.224877i	−0.993659	−	0.112439i	$-0.964134\pi$
$593$		−	5.47612i		−	0.224877i	0.993659	−	0.112439i	$-0.0358662\pi$
$594$		0			0
$595$	8.58909	+	14.8767i	0.352118	+	0.609887i
$596$		0			0
$597$	1.25400			0.0513229
$598$		0			0
$599$	−38.6039			−1.57731			−0.788657	−	0.614833i	$-0.789223\pi$
$599$	−38.6039			−1.57731			−0.788657	+	0.614833i	$0.789223\pi$
$600$		0			0
$601$	−3.28948	−	5.69754i	−0.134181	−	0.232408i	0.791104	−	0.611682i	$-0.209507\pi$
$601$	−3.28948	−	5.69754i	−0.134181	−	0.232408i	−0.925284	+	0.379275i	$0.876174\pi$
$602$		0			0
$603$		−	15.4730i		−	0.630109i
$604$		0			0
$605$	−8.53590	−	4.92820i	−0.347034	−	0.200360i
$606$		0			0
$607$	−8.38318	+	14.5201i	−0.340263	+	0.589352i	−0.984481	−	0.175489i	$-0.943849\pi$
$607$	−8.38318	+	14.5201i	−0.340263	+	0.589352i	0.644219	+	0.764841i	$0.277183\pi$
$608$		0			0
$609$	0.583678	−	0.336986i	0.0236518	−	0.0136554i
$610$		0			0
$611$	23.4013	−	2.15959i	0.946715	−	0.0873677i
$612$		0			0
$613$	24.9232	−	14.3894i	1.00664	−	0.581184i	0.0964341	−	0.995339i	$-0.469256\pi$
$613$	24.9232	−	14.3894i	1.00664	−	0.581184i	0.910206	+	0.414155i	$0.135923\pi$
$614$		0			0
$615$	0.0126991	−	0.0219955i	0.000512078	−	0.000886946i
$616$		0			0
$617$	32.3279	+	18.6645i	1.30147	+	0.751406i	0.980657	−	0.195735i	$-0.0627093\pi$
$617$	32.3279	+	18.6645i	1.30147	+	0.751406i	0.320817	+	0.947141i	$0.396043\pi$
$618$		0			0
$619$			12.7535i			0.512606i	0.966597	+	0.256303i	$0.0825045\pi$
$619$			12.7535i			0.512606i	−0.966597	+	0.256303i	$0.917496\pi$
$620$		0			0
$621$	2.01192	+	3.48475i	0.0807356	+	0.139838i
$622$		0			0
$623$	65.1939			2.61194
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−0.290514	−	0.503185i	−0.0116020	−	0.0200953i
$628$		0			0
$629$			0.0903896i			0.00360407i
$630$		0			0
$631$	−24.8759	−	14.3621i	−0.990294	−	0.571746i	−0.0849315	−	0.996387i	$-0.527067\pi$
$631$	−24.8759	−	14.3621i	−0.990294	−	0.571746i	−0.905362	+	0.424641i	$0.860400\pi$
$632$		0			0
$633$	0.227984	−	0.394880i	0.00906156	−	0.0156951i
$634$		0			0
$635$	0.611979	−	0.353326i	0.0242856	−	0.0140213i
$636$		0			0
$637$	−47.9762	+	33.9346i	−1.90089	+	1.34454i
$638$		0			0
$639$	20.1133	−	11.6124i	0.795671	−	0.459381i
$640$		0			0
$641$	−11.1985	+	19.3964i	−0.442315	+	0.766112i	−0.997861	−	0.0653739i	$-0.979176\pi$
$641$	−11.1985	+	19.3964i	−0.442315	+	0.766112i	0.555546	+	0.831486i	$0.312509\pi$
$642$		0			0
$643$	−12.2665	−	7.08209i	−0.483745	−	0.279290i	0.238231	−	0.971209i	$-0.423433\pi$
$643$	−12.2665	−	7.08209i	−0.483745	−	0.279290i	−0.721976	+	0.691918i	$0.756766\pi$
$644$		0			0
$645$		−	0.337339i		−	0.0132827i
$646$		0			0
$647$	11.8048	+	20.4466i	0.464096	+	0.803838i	0.999160	−	0.0409732i	$-0.0130458\pi$
$647$	11.8048	+	20.4466i	0.464096	+	0.803838i	−0.535064	+	0.844812i	$0.679713\pi$
$648$		0			0
$649$	9.32835			0.366170
$650$		0			0
$651$	0.669862			0.0262540
$652$		0			0
$653$	−16.6383	−	28.8183i	−0.651105	−	1.12775i	−0.982855	−	0.184380i	$-0.940972\pi$
$653$	−16.6383	−	28.8183i	−0.651105	−	1.12775i	0.331750	−	0.943367i	$-0.392361\pi$
$654$		0			0
$655$		−	6.26554i		−	0.244815i
$656$		0			0
$657$	26.1848	+	15.1178i	1.02156	+	0.589801i
$658$		0			0
$659$	11.5454	−	19.9972i	0.449745	−	0.778982i	−0.548624	−	0.836069i	$-0.684848\pi$
$659$	11.5454	−	19.9972i	0.449745	−	0.778982i	0.998369	+	0.0570875i	$0.0181814\pi$
$660$		0			0
$661$	11.6364	−	6.71826i	0.452602	−	0.261310i	−0.256326	−	0.966590i	$-0.582512\pi$
$661$	11.6364	−	6.71826i	0.452602	−	0.261310i	0.708929	+	0.705280i	$0.249179\pi$
$662$		0			0
$663$	0.111771	+	1.21114i	0.00434081	+	0.0470370i
$664$		0			0
$665$	23.9609	−	13.8338i	0.929164	−	0.536453i
$666$		0			0
$667$	5.21900	−	9.03957i	0.202080	−	0.350014i
$668$		0			0
$669$	1.20779	+	0.697316i	0.0466957	+	0.0269598i
$670$		0			0
$671$			6.77708i			0.261626i
$672$		0			0
$673$	−0.972620	−	1.68463i	−0.0374918	−	0.0649376i	0.846671	−	0.532117i	$-0.178603\pi$
$673$	−0.972620	−	1.68463i	−0.0374918	−	0.0649376i	−0.884162	+	0.467180i	$0.845270\pi$
$674$		0			0
$675$	−0.567874			−0.0218575
$676$		0			0
$677$	24.8683			0.955768			0.477884	−	0.878423i	$-0.341404\pi$
$677$	24.8683			0.955768			0.477884	+	0.878423i	$0.341404\pi$
$678$		0			0
$679$	−8.29903	−	14.3743i	−0.318488	−	0.551637i
$680$		0			0
$681$		−	1.41260i		−	0.0541310i
$682$		0			0
$683$	12.6631	+	7.31107i	0.484542	+	0.279750i	0.722307	−	0.691572i	$-0.243082\pi$
$683$	12.6631	+	7.31107i	0.484542	+	0.279750i	−0.237766	+	0.971323i	$0.576415\pi$
$684$		0			0
$685$	8.15290	−	14.1212i	0.311506	−	0.539545i
$686$		0			0
$687$	1.58491	−	0.915049i	0.0604681	−	0.0349113i
$688$		0			0
$689$	0.328354	+	3.55804i	0.0125093	+	0.135550i
$690$		0			0
$691$	3.05231	−	1.76225i	0.116115	−	0.0670393i	−0.440817	−	0.897597i	$-0.645311\pi$
$691$	3.05231	−	1.76225i	0.116115	−	0.0670393i	0.556933	+	0.830558i	$0.311978\pi$
$692$		0			0
$693$	7.71947	−	13.3705i	0.293238	−	0.507904i
$694$		0			0
$695$	−5.91087	−	3.41264i	−0.224212	−	0.129449i
$696$		0			0
$697$			0.953601i			0.0361202i
$698$		0			0
$699$	1.00445	+	1.73976i	0.0379919	+	0.0658038i
$700$		0			0
$701$	1.53457			0.0579599			0.0289800	−	0.999580i	$-0.490774\pi$
$701$	1.53457			0.0579599			0.0289800	+	0.999580i	$0.490774\pi$
$702$		0			0
$703$	0.145584			0.00549081
$704$		0			0
$705$	0.308909	+	0.535047i	0.0116342	+	0.0201510i
$706$		0			0
$707$			13.7819i			0.518322i
$708$		0			0
$709$	12.1289	+	7.00262i	0.455510	+	0.262989i	0.710155	−	0.704046i	$-0.248625\pi$
$709$	12.1289	+	7.00262i	0.455510	+	0.262989i	−0.254644	+	0.967035i	$0.581958\pi$
$710$		0			0
$711$	−13.1357	+	22.7518i	−0.492629	+	0.853259i
$712$		0			0
$713$	8.98444	−	5.18717i	0.336470	−	0.194261i
$714$		0			0
$715$	−3.14788	+	2.22656i	−0.117724	+	0.0832687i
$716$		0			0
$717$	1.22288	−	0.706029i	0.0456692	−	0.0263671i
$718$		0			0
$719$	−11.2381	+	19.4649i	−0.419109	+	0.725918i	−0.995850	−	0.0910091i	$-0.970991\pi$
$719$	−11.2381	+	19.4649i	−0.419109	+	0.725918i	0.576741	+	0.816927i	$0.304324\pi$
$720$		0			0
$721$	−23.1785	−	13.3821i	−0.863213	−	0.498376i
$722$		0			0
$723$		−	0.890215i		−	0.0331074i
$724$		0			0
$725$	0.736543	+	1.27573i	0.0273545	+	0.0473794i
$726$		0			0
$727$	−10.3421			−0.383566			−0.191783	−	0.981437i	$-0.561427\pi$
$727$	−10.3421			−0.383566			−0.191783	+	0.981437i	$0.561427\pi$
$728$		0			0
$729$	−26.5160			−0.982075
$730$		0			0
$731$	6.33285	+	10.9688i	0.234229	+	0.405696i
$732$		0			0
$733$			27.3533i			1.01032i	0.863026	+	0.505159i	$0.168566\pi$
$733$			27.3533i			1.01032i	−0.863026	+	0.505159i	$0.831434\pi$
$734$		0			0
$735$	−1.33791	−	0.772442i	−0.0493495	−	0.0284919i
$736$		0			0
$737$	2.76606	−	4.79096i	0.101889	−	0.176477i
$738$		0			0
$739$	−11.6495	+	6.72583i	−0.428533	+	0.247413i	−0.698721	−	0.715394i	$-0.746247\pi$
$739$	−11.6495	+	6.72583i	−0.428533	+	0.247413i	0.270189	+	0.962807i	$0.412914\pi$
$740$		0			0
$741$	1.95071	−	0.180021i	0.0716610	−	0.00661324i
$742$		0			0
$743$	−14.1964	+	8.19632i	−0.520817	+	0.300694i	−0.737269	−	0.675599i	$-0.763885\pi$
$743$	−14.1964	+	8.19632i	−0.520817	+	0.300694i	0.216452	+	0.976293i	$0.430552\pi$
$744$		0			0
$745$	4.21978	−	7.30887i	0.154601	−	0.267776i
$746$		0			0
$747$	−1.87919	−	1.08495i	−0.0687560	−	0.0396963i
$748$		0			0
$749$		−	21.4365i		−	0.783274i
$750$		0			0
$751$	13.8328	+	23.9590i	0.504764	+	0.874277i	0.999985	+	0.00551009i	$0.00175392\pi$
$751$	13.8328	+	23.9590i	0.504764	+	0.874277i	−0.495221	+	0.868767i	$0.664913\pi$
$752$		0			0
$753$	−1.07265			−0.0390895
$754$		0			0
$755$	−1.37017			−0.0498654
$756$		0			0
$757$	−11.4989	−	19.9167i	−0.417935	−	0.723885i	0.577797	−	0.816181i	$-0.303913\pi$
$757$	−11.4989	−	19.9167i	−0.417935	−	0.723885i	−0.995732	+	0.0922961i	$0.970579\pi$
$758$		0			0
$759$			0.718251i			0.0260709i
$760$		0			0
$761$	6.63759	+	3.83221i	0.240612	+	0.138918i	0.615458	−	0.788170i	$-0.288971\pi$
$761$	6.63759	+	3.83221i	0.240612	+	0.138918i	−0.374846	+	0.927087i	$0.622304\pi$
$762$		0			0
$763$	33.2580	−	57.6045i	1.20402	−	2.08542i
$764$		0			0
$765$	9.21857	−	5.32235i	0.333298	−	0.192430i
$766$		0			0
$767$	−13.1562	+	28.5676i	−0.475042	+	1.03152i
$768$		0			0
$769$	6.26219	−	3.61548i	0.225820	−	0.130377i	−0.382822	−	0.923822i	$-0.625048\pi$
$769$	6.26219	−	3.61548i	0.225820	−	0.130377i	0.608642	+	0.793445i	$0.291714\pi$
$770$		0			0
$771$	1.25745	−	2.17797i	0.0452859	−	0.0784375i
$772$		0			0
$773$	−29.0981	−	16.7998i	−1.04658	−	0.604246i	−0.124893	−	0.992170i	$-0.539859\pi$
$773$	−29.0981	−	16.7998i	−1.04658	−	0.604246i	−0.921691	+	0.387924i	$0.873192\pi$
$774$		0			0
$775$			1.46410i			0.0525921i
$776$		0			0
$777$	−0.00581016	−	0.0100635i	−0.000208438	−	0.000361026i
$778$		0			0
$779$	1.53590			0.0550293
$780$		0			0
$781$	8.30368			0.297129
$782$		0			0
$783$	−0.418264	−	0.724454i	−0.0149475	−	0.0258899i
$784$		0			0
$785$			11.9700i			0.427228i
$786$		0			0
$787$	−2.57355	−	1.48584i	−0.0917371	−	0.0529645i	0.453430	−	0.891292i	$-0.350200\pi$
$787$	−2.57355	−	1.48584i	−0.0917371	−	0.0529645i	−0.545167	+	0.838328i	$0.683534\pi$
$788$		0			0
$789$	0.670185	−	1.16079i	0.0238592	−	0.0413254i
$790$		0			0
$791$	33.6252	−	19.4135i	1.19557	−	0.690265i
$792$		0			0
$793$	−20.7545	−	9.55802i	−0.737013	−	0.339415i
$794$		0			0
$795$	−0.0813509	+	0.0469680i	−0.00288522	+	0.00166578i
$796$		0			0
$797$	−11.2875	+	19.5506i	−0.399825	+	0.692517i	−0.993704	−	0.112037i	$-0.964262\pi$
$797$	−11.2875	+	19.5506i	−0.399825	+	0.692517i	0.593879	+	0.804554i	$0.297596\pi$
$798$		0			0
$799$	−20.0888	−	11.5983i	−0.710692	−	0.410318i
$800$		0			0
$801$		−	40.3983i		−	1.42740i
$802$		0			0
$803$	5.40512	+	9.36194i	0.190742	+	0.330376i
$804$		0			0
$805$	−34.2020			−1.20546
$806$		0			0
$807$	−2.34831			−0.0826646
$808$		0			0
$809$	−6.82921	−	11.8285i	−0.240102	−	0.415869i	0.720641	−	0.693308i	$-0.243848\pi$
$809$	−6.82921	−	11.8285i	−0.240102	−	0.415869i	−0.960743	+	0.277439i	$0.910514\pi$
$810$		0			0
$811$			14.1147i			0.495636i	0.968807	+	0.247818i	$0.0797135\pi$
$811$			14.1147i			0.495636i	−0.968807	+	0.247818i	$0.920287\pi$
$812$		0			0
$813$	−1.53646	−	0.887075i	−0.0538860	−	0.0311111i
$814$		0			0
$815$	11.2857	−	19.5474i	0.395320	−	0.684714i
$816$		0			0
$817$	17.6667	−	10.1999i	0.618079	−	0.356848i
$818$		0			0
$819$	30.0594	+	42.4975i	1.05036	+	1.48498i
$820$		0			0
$821$	−1.37318	+	0.792808i	−0.0479244	+	0.0276692i	−0.523771	−	0.851859i	$-0.675475\pi$
$821$	−1.37318	+	0.792808i	−0.0479244	+	0.0276692i	0.475846	+	0.879528i	$0.342142\pi$
$822$		0			0
$823$	−9.28238	+	16.0776i	−0.323563	+	0.560428i	−0.981221	−	0.192889i	$-0.938214\pi$
$823$	−9.28238	+	16.0776i	−0.323563	+	0.560428i	0.657657	+	0.753317i	$0.271548\pi$
$824$		0			0
$825$	−0.0877845	−	0.0506824i	−0.00305626	−	0.00176454i
$826$		0			0
$827$		−	9.01023i		−	0.313316i	−0.987653	−	0.156658i	$-0.949928\pi$
$827$		−	9.01023i		−	0.313316i	0.987653	−	0.156658i	$-0.0500721\pi$
$828$		0			0
$829$	23.5588	+	40.8051i	0.818233	+	1.41722i	0.906983	+	0.421167i	$0.138379\pi$
$829$	23.5588	+	40.8051i	0.818233	+	1.41722i	−0.0887506	+	0.996054i	$0.528287\pi$
$830$		0			0
$831$	−2.14833			−0.0745247
$832$		0			0
$833$	58.0041			2.00972
$834$		0			0
$835$	−4.09850	−	7.09881i	−0.141835	−	0.245665i
$836$		0			0
$837$		−	0.831425i		−	0.0287383i
$838$		0			0
$839$	−46.3121	−	26.7383i	−1.59887	−	0.923108i	−0.991705	−	0.128531i	$-0.958974\pi$
$839$	−46.3121	−	26.7383i	−1.59887	−	0.923108i	−0.607164	−	0.794576i	$-0.707693\pi$
$840$		0			0
$841$	13.4150	−	23.2355i	0.462586	−	0.801223i
$842$		0			0
$843$	2.28521	−	1.31937i	0.0787070	−	0.0454415i
$844$		0			0
$845$	−2.37915	−	12.7804i	−0.0818453	−	0.439660i
$846$		0			0
$847$	−41.2014	+	23.7876i	−1.41570	+	0.817353i
$848$		0			0
$849$	0.375362	−	0.650146i	0.0128824	−	0.0223130i
$850$		0			0
$851$	−0.155856	−	0.0899835i	−0.00534268	−	0.00308460i
$852$		0			0
$853$			27.7756i			0.951019i	0.879711	+	0.475510i	$0.157736\pi$
$853$			27.7756i			0.951019i	−0.879711	+	0.475510i	$0.842264\pi$
$854$		0			0
$855$	−8.57233	−	14.8477i	−0.293167	−	0.507781i
$856$		0			0
$857$	−53.6917			−1.83407			−0.917037	−	0.398801i	$-0.869426\pi$
$857$	−53.6917			−1.83407			−0.917037	+	0.398801i	$0.869426\pi$
$858$		0			0
$859$	−2.08958			−0.0712955			−0.0356477	−	0.999364i	$-0.511349\pi$
$859$	−2.08958			−0.0712955			−0.0356477	+	0.999364i	$0.511349\pi$
$860$		0			0
$861$	−0.0612966	−	0.106169i	−0.00208898	−	0.00361823i
$862$		0			0
$863$			1.75413i			0.0597113i	0.999554	+	0.0298557i	$0.00950476\pi$
$863$			1.75413i			0.0597113i	−0.999554	+	0.0298557i	$0.990495\pi$
$864$		0			0
$865$	−7.93948	−	4.58386i	−0.269950	−	0.155856i
$866$		0			0
$867$	−0.205419	+	0.355797i	−0.00697640	+	0.0120835i
$868$		0			0
$869$	−8.13453	+	4.69647i	−0.275945	+	0.159317i
$870$		0			0
$871$	10.7710	+	15.2278i	0.364961	+	0.515975i
$872$		0			0
$873$	−8.90726	+	5.14261i	−0.301465	+	0.174051i
$874$		0			0
$875$	2.41342	−	4.18016i	0.0815885	−	0.141315i
$876$		0			0
$877$	−18.6777	−	10.7836i	−0.630702	−	0.364136i	0.150322	−	0.988637i	$-0.451969\pi$
$877$	−18.6777	−	10.7836i	−0.630702	−	0.364136i	−0.781024	+	0.624501i	$0.785302\pi$
$878$		0			0
$879$			0.0258742i			0.000872716i
$880$		0			0
$881$	12.5132	+	21.6734i	0.421579	+	0.730196i	0.996094	−	0.0882978i	$-0.0281427\pi$
$881$	12.5132	+	21.6734i	0.421579	+	0.730196i	−0.574515	+	0.818494i	$0.694809\pi$
$882$		0			0
$883$	−48.7832			−1.64169			−0.820843	−	0.571154i	$-0.806496\pi$
$883$	−48.7832			−1.64169			−0.820843	+	0.571154i	$0.806496\pi$
$884$		0			0
$885$	−0.826838			−0.0277939
$886$		0			0
$887$	−16.8967	−	29.2659i	−0.567334	−	0.982651i	−0.996828	−	0.0795819i	$-0.974641\pi$
$887$	−16.8967	−	29.2659i	−0.567334	−	0.982651i	0.429494	−	0.903070i	$-0.358692\pi$
$888$		0			0
$889$		−	3.41090i		−	0.114398i
$890$		0			0
$891$	−8.26025	−	4.76906i	−0.276729	−	0.159769i
$892$		0			0
$893$	−18.6806	+	32.3557i	−0.625121	+	1.08274i
$894$		0			0
$895$	−8.69229	+	5.01850i	−0.290551	+	0.167750i
$896$		0			0
$897$	−2.19961	−	1.01298i	−0.0734428	−	0.0338225i
$898$		0			0
$899$	−1.86780	+	1.07837i	−0.0622946	+	0.0359658i
$900$		0			0
$901$	1.76346	−	3.05440i	0.0587493	−	0.101757i
$902$		0			0
$903$	−1.41013	−	0.814139i	−0.0469262	−	0.0270929i
$904$		0			0
$905$		−	17.0238i		−	0.565892i
$906$		0			0
$907$	17.3135	+	29.9879i	0.574885	+	0.995731i	0.996054	+	0.0887485i	$0.0282867\pi$
$907$	17.3135	+	29.9879i	0.574885	+	0.995731i	−0.421169	+	0.906982i	$0.638380\pi$
$908$		0			0
$909$	8.54015			0.283259
$910$		0			0
$911$	−31.1865			−1.03326			−0.516628	−	0.856210i	$-0.672813\pi$
$911$	−31.1865			−1.03326			−0.516628	+	0.856210i	$0.672813\pi$
$912$		0			0
$913$	−0.387907	−	0.671874i	−0.0128378	−	0.0222358i
$914$		0			0
$915$		−	0.600701i		−	0.0198586i
$916$		0			0
$917$	−26.1910	−	15.1214i	−0.864903	−	0.499352i
$918$		0			0
$919$	−25.9610	+	44.9658i	−0.856374	+	1.48328i	0.0189904	+	0.999820i	$0.493955\pi$
$919$	−25.9610	+	44.9658i	−0.856374	+	1.48328i	−0.875364	+	0.483464i	$0.839379\pi$
$920$		0			0
$921$	0.562490	−	0.324753i	0.0185347	−	0.0107010i
$922$		0			0
$923$	−11.7110	+	25.4296i	−0.385474	+	0.837026i
$924$		0			0
$925$	0.0219955	−	0.0126991i	0.000723209	−	0.000417545i
$926$		0			0
$927$	−8.29242	+	14.3629i	−0.272359	+	0.471739i
$928$		0			0
$929$	−17.7462	−	10.2457i	−0.582232	−	0.336152i	0.179788	−	0.983705i	$-0.442459\pi$
$929$	−17.7462	−	10.2457i	−0.582232	−	0.336152i	−0.762020	+	0.647553i	$0.775792\pi$
$930$		0			0
$931$		−	93.4231i		−	3.06182i
$932$		0			0
$933$	0.504492	+	0.873806i	0.0165163	+	0.0286071i
$934$		0			0
$935$	3.80584			0.124464
$936$		0			0
$937$	−39.6806			−1.29631			−0.648154	−	0.761510i	$-0.724459\pi$
$937$	−39.6806			−1.29631			−0.648154	+	0.761510i	$0.724459\pi$
$938$		0			0
$939$	0.844727	+	1.46311i	0.0275666	+	0.0477468i
$940$		0			0
$941$		−	19.6189i		−	0.639557i	−0.947492	−	0.319779i	$-0.896391\pi$
$941$		−	19.6189i		−	0.639557i	0.947492	−	0.319779i	$-0.103609\pi$
$942$		0			0
$943$	−1.64427	−	0.949318i	−0.0535447	−	0.0309140i
$944$		0			0
$945$	−1.37052	+	2.37381i	−0.0445829	+	0.0772199i
$946$		0			0
$947$	49.5474	−	28.6062i	1.61007	−	0.929576i	0.620721	−	0.784032i	$-0.286840\pi$
$947$	49.5474	−	28.6062i	1.61007	−	0.929576i	0.989352	−	0.145544i	$-0.0464933\pi$
$948$		0			0
$949$	−36.2936	+	3.34935i	−1.17814	+	0.108725i
$950$		0			0
$951$	0.670795	−	0.387283i	0.0217520	−	0.0125585i
$952$		0			0
$953$	13.7385	−	23.7958i	0.445033	−	0.770820i	−0.553021	−	0.833167i	$-0.686525\pi$
$953$	13.7385	−	23.7958i	0.445033	−	0.770820i	0.998055	+	0.0623470i	$0.0198586\pi$
$954$		0			0
$955$	−3.35793	−	1.93870i	−0.108660	−	0.0627350i
$956$		0			0
$957$		−	0.149319i		−	0.00482680i
$958$		0			0
$959$	−39.3527	−	68.1609i	−1.27077	−	2.20103i
$960$		0			0
$961$	28.8564			0.930852
$962$		0			0
$963$	−13.2834			−0.428053
$964$		0			0
$965$	0.626972	+	1.08595i	0.0201829	+	0.0349579i
$966$		0			0
$967$			10.3643i			0.333293i	0.986017	+	0.166647i	$0.0532939\pi$
$967$			10.3643i			0.333293i	−0.986017	+	0.166647i	$0.946706\pi$
$968$		0			0
$969$	−1.67458	−	0.966821i	−0.0537953	−	0.0310588i
$970$		0			0
$971$	20.8758	−	36.1579i	0.669935	−	1.16036i	−0.307987	−	0.951391i	$-0.599655\pi$
$971$	20.8758	−	36.1579i	0.669935	−	1.16036i	0.977922	−	0.208971i	$-0.0670113\pi$
$972$		0			0
$973$	−28.5308	+	16.4723i	−0.914656	+	0.528077i
$974$		0			0
$975$	0.279019	−	0.197356i	0.00893575	−	0.00632045i
$976$		0			0
$977$	−11.9458	+	6.89691i	−0.382180	+	0.220652i	−0.678766	−	0.734354i	$-0.737485\pi$
$977$	−11.9458	+	6.89691i	−0.382180	+	0.220652i	0.296586	+	0.955006i	$0.404152\pi$
$978$		0			0
$979$	7.22187	−	12.5087i	0.230812	−	0.399778i
$980$		0			0
$981$	−35.6954	−	20.6088i	−1.13967	−	0.657987i
$982$		0			0
$983$			37.9997i			1.21200i	0.795463	+	0.606002i	$0.207227\pi$
$983$			37.9997i			1.21200i	−0.795463	+	0.606002i	$0.792773\pi$
$984$		0			0
$985$	7.64098	+	13.2346i	0.243462	+	0.421688i
$986$		0			0
$987$	2.98211			0.0949217
$988$		0			0
$989$	−25.2176			−0.801873
$990$		0			0
$991$	−26.2765	−	45.5122i	−0.834700	−	1.44574i	−0.894275	−	0.447519i	$-0.852308\pi$
$991$	−26.2765	−	45.5122i	−0.834700	−	1.44574i	0.0595748	−	0.998224i	$-0.481026\pi$
$992$		0			0
$993$		−	2.36396i		−	0.0750179i
$994$		0			0
$995$	11.4572	+	6.61480i	0.363217	+	0.209703i
$996$		0			0
$997$	−9.29497	+	16.0994i	−0.294375	+	0.509872i	−0.974839	−	0.222909i	$-0.928445\pi$
$997$	−9.29497	+	16.0994i	−0.294375	+	0.509872i	0.680465	+	0.732781i	$0.261778\pi$
$998$		0			0
$999$	−0.0124907	+	0.00721150i	−0.000395188	+	0.000228162i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.da.b.881.3		8
4.3	odd	2		65.2.m.a.36.4	✓	8
12.11	even	2		585.2.bu.c.361.1		8
13.4	even	6	inner	1040.2.da.b.641.3		8
20.3	even	4		325.2.m.c.49.1		8
20.7	even	4		325.2.m.b.49.4		8
20.19	odd	2		325.2.n.d.101.1		8
52.3	odd	6		845.2.c.g.506.7		8
52.7	even	12		845.2.e.m.191.4		8
52.11	even	12		845.2.a.m.1.1		4
52.15	even	12		845.2.a.l.1.4		4
52.19	even	12		845.2.e.n.191.1		8
52.23	odd	6		845.2.c.g.506.2		8
52.31	even	4		845.2.e.n.146.1		8
52.35	odd	6		845.2.m.g.316.1		8
52.43	odd	6		65.2.m.a.56.4	yes	8
52.47	even	4		845.2.e.m.146.4		8
52.51	odd	2		845.2.m.g.361.1		8
156.11	odd	12		7605.2.a.cf.1.4		4
156.95	even	6		585.2.bu.c.316.1		8
156.119	odd	12		7605.2.a.cj.1.1		4
260.43	even	12		325.2.m.b.199.4		8
260.119	even	12		4225.2.a.bl.1.1		4
260.147	even	12		325.2.m.c.199.1		8
260.199	odd	6		325.2.n.d.251.1		8
260.219	even	12		4225.2.a.bi.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.4	✓	8	4.3	odd	2
65.2.m.a.56.4	yes	8	52.43	odd	6
325.2.m.b.49.4		8	20.7	even	4
325.2.m.b.199.4		8	260.43	even	12
325.2.m.c.49.1		8	20.3	even	4
325.2.m.c.199.1		8	260.147	even	12
325.2.n.d.101.1		8	20.19	odd	2
325.2.n.d.251.1		8	260.199	odd	6
585.2.bu.c.316.1		8	156.95	even	6
585.2.bu.c.361.1		8	12.11	even	2
845.2.a.l.1.4		4	52.15	even	12
845.2.a.m.1.1		4	52.11	even	12
845.2.c.g.506.2		8	52.23	odd	6
845.2.c.g.506.7		8	52.3	odd	6
845.2.e.m.146.4		8	52.47	even	4
845.2.e.m.191.4		8	52.7	even	12
845.2.e.n.146.1		8	52.31	even	4
845.2.e.n.191.1		8	52.19	even	12
845.2.m.g.316.1		8	52.35	odd	6
845.2.m.g.361.1		8	52.51	odd	2
1040.2.da.b.641.3		8	13.4	even	6	inner
1040.2.da.b.881.3		8	1.1	even	1	trivial
4225.2.a.bi.1.4		4	260.219	even	12
4225.2.a.bl.1.1		4	260.119	even	12
7605.2.a.cf.1.4		4	156.11	odd	12
7605.2.a.cj.1.1		4	156.119	odd	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.da (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0473938 + 0.0820885i) q^{3} +1.00000i q^{5} +(4.18016 + 2.41342i) q^{7} +(1.49551 - 2.59030i) q^{9} +(0.926118 - 0.534695i) q^{11} +(0.331331 + 3.59030i) q^{13} +(-0.0820885 + 0.0473938i) q^{15} +(1.77944 - 3.08209i) q^{17} +(-4.96410 - 2.86603i) q^{19} +0.457524i q^{21} +(3.54290 + 6.13649i) q^{23} -1.00000 q^{25} +0.567874 q^{27} +(-0.736543 - 1.27573i) q^{29} -1.46410i q^{31} +(0.0877845 + 0.0506824i) q^{33} +(-2.41342 + 4.18016i) q^{35} +(-0.0219955 + 0.0126991i) q^{37} +(-0.279019 + 0.197356i) q^{39} +(-0.232051 + 0.133975i) q^{41} +(-1.77944 + 3.08209i) q^{43} +(2.59030 + 1.49551i) q^{45} -6.51793i q^{47} +(8.14918 + 14.1148i) q^{49} +0.337339 q^{51} +0.991015 q^{53} +(0.534695 + 0.926118i) q^{55} -0.543327i q^{57} +(7.55440 + 4.36153i) q^{59} +(-3.16867 + 5.48830i) q^{61} +(12.5029 - 7.21857i) q^{63} +(-3.59030 + 0.331331i) q^{65} +(4.48009 - 2.58658i) q^{67} +(-0.335823 + 0.581663i) q^{69} +(6.72458 + 3.88244i) q^{71} +10.1088i q^{73} +(-0.0473938 - 0.0820885i) q^{75} +5.16177 q^{77} -8.78347 q^{79} +(-4.45961 - 7.72427i) q^{81} -0.725474i q^{83} +(3.08209 + 1.77944i) q^{85} +(0.0698151 - 0.120923i) q^{87} +(11.6970 - 6.75327i) q^{89} +(-7.27987 + 15.8077i) q^{91} +(0.120186 - 0.0693893i) q^{93} +(2.86603 - 4.96410i) q^{95} +(-2.97800 - 1.71935i) q^{97} -3.19856i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9} + 6 q^{15} - 2 q^{17} - 12 q^{19} + 10 q^{23} - 8 q^{25} + 4 q^{27} - 8 q^{29} + 42 q^{33} - 10 q^{35} + 6 q^{37} + 12 q^{41} + 2 q^{43} + 12 q^{49} + 8 q^{51} - 24 q^{53}+ \cdots - 30 q^{97}+O(q^{100}) \) 8 * q - 2 * q^3 + 6 * q^7 - 4 * q^9 + 6 * q^15 - 2 * q^17 - 12 * q^19 + 10 * q^23 - 8 * q^25 + 4 * q^27 - 8 * q^29 + 42 * q^33 - 10 * q^35 + 6 * q^37 + 12 * q^41 + 2 * q^43 + 12 * q^49 + 8 * q^51 - 24 * q^53 + 12 * q^59 - 28 * q^61 + 24 * q^63 - 8 * q^65 - 6 * q^67 - 16 * q^69 + 2 * q^75 - 36 * q^77 + 16 * q^79 + 8 * q^81 + 18 * q^85 - 22 * q^87 + 24 * q^89 - 28 * q^91 + 16 * q^95 - 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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