LMFDB - Embedded newform 1040.2.da.b.641.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(641,1040)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			641.3
Root			$0.665665 + 1.24775i$ of defining polynomial
Character	$\chi$	$=$	1040.641
Dual form			1040.2.da.b.881.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.852020	−	0.523510i	$-0.824622\pi$
$3$	0.0473938	−	0.0820885i	0.0273628	−	0.0473938i	0.879383	+	0.476116i	$0.157956\pi$
$4$		0			0
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	4.18016	−	2.41342i	1.57995	−	0.912187i	0.585089	−	0.810969i	$-0.301059\pi$
$7$	4.18016	−	2.41342i	1.57995	−	0.912187i	0.994864	−	0.101218i	$-0.0322739\pi$
$8$		0			0
$9$	1.49551	+	2.59030i	0.498503	+	0.863432i
$10$		0			0
$11$	0.926118	+	0.534695i	0.279235	+	0.161217i	0.633077	−	0.774089i	$-0.281792\pi$
$11$	0.926118	+	0.534695i	0.279235	+	0.161217i	−0.353842	+	0.935305i	$0.615125\pi$
$12$		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	0.997009	−	0.0772795i	$-0.0246234\pi$
$17$	1.77944	+	3.08209i	0.431579	+	0.747516i	−0.565431	+	0.824796i	$0.691290\pi$
$18$		0			0
$19$	−4.96410	+	2.86603i	−1.13884	+	0.657511i	−0.946144	−	0.323747i	$-0.895057\pi$
$19$	−4.96410	+	2.86603i	−1.13884	+	0.657511i	−0.192699	+	0.981258i	$0.561724\pi$
$20$		0			0
$21$		−	0.457524i		−	0.0998400i
$22$		0			0
$23$	3.54290	−	6.13649i	0.738746	−	1.27955i	−0.214314	−	0.976765i	$-0.568752\pi$
$23$	3.54290	−	6.13649i	0.738746	−	1.27955i	0.953060	−	0.302781i	$-0.0979150\pi$
$24$		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	−0.926273	−	0.376853i	$-0.877006\pi$
$29$	−0.736543	+	1.27573i	−0.136773	+	0.236897i	0.789501	+	0.613750i	$0.210340\pi$
$30$		0			0
$31$			1.46410i			0.262960i	0.991319	+	0.131480i	$0.0419730\pi$
$31$			1.46410i			0.262960i	−0.991319	+	0.131480i	$0.958027\pi$
$32$		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	0.498191	−	0.867067i	$-0.333998\pi$
$37$	−0.0219955	−	0.0126991i	−0.00361604	−	0.00208772i	−0.501807	+	0.864980i	$0.667331\pi$
$38$		0			0
$39$	−0.279019	−	0.197356i	−0.0446788	−	0.0316023i
$40$		0			0
$41$	−0.232051	−	0.133975i	−0.0362402	−	0.0209233i	0.481770	−	0.876297i	$-0.339994\pi$
$41$	−0.232051	−	0.133975i	−0.0362402	−	0.0209233i	−0.518011	+	0.855374i	$0.673327\pi$
$42$		0			0
$43$	−1.77944	−	3.08209i	−0.271363	−	0.470014i	0.697848	−	0.716246i	$-0.254141\pi$
$43$	−1.77944	−	3.08209i	−0.271363	−	0.470014i	−0.969211	+	0.246232i	$0.920808\pi$
$44$		0			0
$45$	2.59030	−	1.49551i	0.386138	−	0.222937i
$46$		0			0
$47$			6.51793i			0.950738i	0.879787	+	0.475369i	$0.157685\pi$
$47$			6.51793i			0.950738i	−0.879787	+	0.475369i	$0.842315\pi$
$48$		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	0.0801741	−	0.996781i	$-0.474452\pi$
$59$	7.55440	−	4.36153i	0.983499	−	0.567823i	0.903325	+	0.428958i	$0.141119\pi$
$60$		0			0
$61$	−3.16867	−	5.48830i	−0.405707	−	0.702704i	0.588697	−	0.808354i	$-0.299641\pi$
$61$	−3.16867	−	5.48830i	−0.405707	−	0.702704i	−0.994403	+	0.105650i	$0.966308\pi$
$62$		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	0.748044	−	0.663649i	$-0.230993\pi$
$67$	4.48009	+	2.58658i	0.547330	+	0.316001i	−0.200714	+	0.979650i	$0.564326\pi$
$68$		0			0
$69$	−0.335823	−	0.581663i	−0.0404283	−	0.0700240i
$70$		0			0
$71$	6.72458	−	3.88244i	0.798061	−	0.460761i	−0.0447317	−	0.998999i	$-0.514243\pi$
$71$	6.72458	−	3.88244i	0.798061	−	0.460761i	0.842793	+	0.538238i	$0.180910\pi$
$72$		0			0
$73$		−	10.1088i		−	1.18314i	−0.806252	−	0.591572i	$-0.798507\pi$
$73$		−	10.1088i		−	1.18314i	0.806252	−	0.591572i	$-0.201493\pi$
$74$		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	$0.0126770\pi$
$83$			0.725474i			0.0796311i	−0.999207	+	0.0398155i	$0.987323\pi$
$84$		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	0.969070	−	0.246788i	$-0.0793750\pi$
$89$	11.6970	+	6.75327i	1.23988	+	0.715845i	0.270810	+	0.962633i	$0.412708\pi$
$90$		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	−0.643507	−	0.765440i	$-0.722521\pi$
$97$	−2.97800	+	1.71935i	−0.302371	+	0.174574i	0.341137	+	0.940014i	$0.389188\pi$
$98$		0			0
$99$			3.19856i			0.321467i
$100$		0			0
$101$	1.42763	−	2.47273i	0.142055	−	0.246046i	−0.786215	−	0.617953i	$-0.787962\pi$
$101$	1.42763	−	2.47273i	0.142055	−	0.246046i	0.928270	+	0.371906i	$0.121296\pi$
$102$		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	−0.953170	−	0.302434i	$-0.902201\pi$
$107$	−2.22056	+	3.84611i	−0.214669	+	0.371818i	0.738501	+	0.674252i	$0.235534\pi$
$108$		0			0
$109$			13.7804i			1.31993i	0.751298	+	0.659963i	$0.229428\pi$
$109$			13.7804i			1.31993i	−0.751298	+	0.659963i	$0.770572\pi$
$110$		0			0
$111$	−0.00208490	+	0.00120372i	−0.000197890	+	0.000114252i
$112$		0			0
$113$	4.02200	+	6.96630i	0.378358	+	0.655334i	0.990823	−	0.135163i	$-0.0431557\pi$
$113$	4.02200	+	6.96630i	0.378358	+	0.655334i	−0.612466	+	0.790497i	$0.709822\pi$
$114$		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	−0.881276	−	0.472602i	$-0.843315\pi$
$127$	−0.353326	+	0.611979i	−0.0313526	+	0.0543044i	0.849923	+	0.526906i	$0.176648\pi$
$128$		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	−0.961984	−	0.273107i	$-0.911949\pi$
$137$	−14.1212	+	8.15290i	−1.20646	+	0.696549i	−0.244475	+	0.969656i	$0.578616\pi$
$138$		0			0
$139$	−3.41264	−	5.91087i	−0.289456	−	0.501353i	0.684224	−	0.729272i	$-0.260141\pi$
$139$	−3.41264	−	5.91087i	−0.289456	−	0.501353i	−0.973680	+	0.227919i	$0.926808\pi$
$140$		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	−0.768556	−	0.639783i	$-0.779024\pi$
$149$	−7.30887	+	4.21978i	−0.598766	+	0.345698i	0.169790	+	0.985480i	$0.445691\pi$
$150$		0			0
$151$		−	1.37017i		−	0.111503i	−0.998445	−	0.0557513i	$-0.982245\pi$
$151$		−	1.37017i		−	0.111503i	0.998445	−	0.0557513i	$-0.0177554\pi$
$152$		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	−0.531754	+	0.846899i	$0.678467\pi$
$163$	−19.5474	+	11.2857i	−1.53107	+	0.883962i	−0.999313	+	0.0370630i	$0.988200\pi$
$164$		0			0
$165$	−0.0506824	−	0.0877845i	−0.00394562	−	0.00683402i
$166$		0			0
$167$	−7.09881	−	4.09850i	−0.549323	−	0.317152i	0.199526	−	0.979893i	$-0.436060\pi$
$167$	−7.09881	−	4.09850i	−0.549323	−	0.317152i	−0.748849	+	0.662741i	$0.769393\pi$
$168$		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	0.637479	−	0.770467i	$-0.279977\pi$
$173$	−4.58386	−	7.93948i	−0.348505	−	0.603628i	−0.985984	+	0.166840i	$0.946644\pi$
$174$		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	−0.615242	−	0.788338i	$-0.710942\pi$
$179$	5.01850	−	8.69229i	0.375100	−	0.649693i	0.990342	+	0.138646i	$0.0442750\pi$
$180$		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	0.787322	−	0.616542i	$-0.211467\pi$
$191$	−1.93870	−	3.35793i	−0.140280	−	0.242971i	−0.927602	+	0.373570i	$0.878133\pi$
$192$		0			0
$193$	1.08595	+	0.626972i	0.0781681	+	0.0451304i	0.538575	−	0.842578i	$-0.318963\pi$
$193$	1.08595	+	0.626972i	0.0781681	+	0.0451304i	−0.460406	+	0.887708i	$0.652296\pi$
$194$		0			0
$195$	−0.197356	+	0.279019i	−0.0141330	+	0.0199810i
$196$		0			0
$197$	13.2346	+	7.64098i	0.942923	+	0.544397i	0.890876	−	0.454247i	$-0.150092\pi$
$197$	13.2346	+	7.64098i	0.942923	+	0.544397i	0.0520479	+	0.998645i	$0.483425\pi$
$198$		0			0
$199$	6.61480	+	11.4572i	0.468911	+	0.812177i	0.999368	−	0.0355340i	$-0.0113132\pi$
$199$	6.61480	+	11.4572i	0.468911	+	0.812177i	−0.530458	+	0.847711i	$0.677980\pi$
$200$		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	−0.936862	−	0.349700i	$-0.886283\pi$
$211$	−2.40521	+	4.16595i	−0.165582	+	0.286796i	0.771280	+	0.636496i	$0.219617\pi$
$212$		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	0.861753	−	0.507329i	$-0.169367\pi$
$223$	12.7420	+	7.35661i	0.853269	+	0.492635i	−0.00848317	+	0.999964i	$0.502700\pi$
$224$		0			0
$225$	−1.49551	−	2.59030i	−0.0997005	−	0.172686i
$226$		0			0
$227$	−12.9062	+	7.45140i	−0.856615	+	0.494567i	−0.862877	−	0.505413i	$-0.831340\pi$
$227$	−12.9062	+	7.45140i	−0.856615	+	0.494567i	0.00626222	+	0.999980i	$0.498007\pi$
$228$		0			0
$229$			19.3074i			1.27587i	0.770092	+	0.637933i	$0.220210\pi$
$229$			19.3074i			1.27587i	−0.770092	+	0.637933i	$0.779790\pi$
$230$		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	$0.160019\pi$
$239$			14.8971i			0.963612i	−0.876278	+	0.481806i	$0.839981\pi$
$240$		0			0
$241$	−8.13343	+	4.69584i	−0.523921	+	0.302486i	−0.738537	−	0.674213i	$-0.764483\pi$
$241$	−8.13343	+	4.69584i	−0.523921	+	0.302486i	0.214617	+	0.976698i	$0.431150\pi$
$242$		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	0.630341	−	0.776318i	$-0.282915\pi$
$251$	−5.65817	−	9.80024i	−0.357140	−	0.618585i	−0.987482	+	0.157733i	$0.949582\pi$
$252$		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	0.0724788	+	0.997370i	$0.476909\pi$
$257$	−13.2660	+	22.9773i	−0.827508	+	1.43329i	−0.899987	+	0.435917i	$0.856424\pi$
$258$		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	−0.997375	−	0.0724100i	$-0.976931\pi$
$263$	−7.07038	+	12.2463i	−0.435979	+	0.755137i	0.561396	+	0.827547i	$0.310264\pi$
$264$		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	−0.945243	−	0.326367i	$-0.894176\pi$
$269$	−12.3872	−	21.4553i	−0.755264	−	1.30815i	0.189980	−	0.981788i	$-0.439158\pi$
$270$		0			0
$271$	−16.2095	−	9.35856i	−0.984657	−	0.568492i	−0.0809839	−	0.996715i	$-0.525806\pi$
$271$	−16.2095	−	9.35856i	−0.984657	−	0.568492i	−0.903673	+	0.428224i	$0.859140\pi$
$272$		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	−0.974709	−	0.223480i	$-0.928258\pi$
$277$	−11.3323	−	19.6282i	−0.680893	−	1.17934i	0.293815	−	0.955862i	$-0.405075\pi$
$278$		0			0
$279$	−3.79246	+	2.18958i	−0.227048	+	0.131086i
$280$		0			0
$281$			27.8384i			1.66070i	0.557241	+	0.830351i	$0.311860\pi$
$281$			27.8384i			1.66070i	−0.557241	+	0.830351i	$0.688140\pi$
$282$		0			0
$283$	−3.96004	+	6.85898i	−0.235400	+	0.407724i	−0.959389	−	0.282087i	$-0.908973\pi$
$283$	−3.96004	+	6.85898i	−0.235400	+	0.407724i	0.723989	+	0.689811i	$0.242307\pi$
$284$		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	−0.493079	−	0.869985i	$-0.664129\pi$
$293$	0.236400	−	0.136485i	0.0138106	−	0.00797356i	0.506889	+	0.862011i	$0.330795\pi$
$294$		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	$0.0626456\pi$
$307$			6.85224i			0.391078i	−0.980696	+	0.195539i	$0.937354\pi$
$308$		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	$0.0737031\pi$
$317$			8.17161i			0.458963i	−0.973313	+	0.229482i	$0.926297\pi$
$318$		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	−0.957657	−	0.287911i	$-0.907039\pi$
$331$	−21.5983	+	12.4698i	−1.18715	+	0.685400i	−0.229490	+	0.973311i	$0.573706\pi$
$332$		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	0.998881	−	0.0472996i	$-0.0150615\pi$
$347$	8.54049	+	14.7926i	0.458478	+	0.794107i	−0.540403	+	0.841406i	$0.681728\pi$
$348$		0			0
$349$	−24.5708	−	14.1860i	−1.31525	−	0.759357i	−0.332286	−	0.943179i	$-0.607820\pi$
$349$	−24.5708	−	14.1860i	−1.31525	−	0.759357i	−0.982960	+	0.183822i	$0.941153\pi$
$350$		0			0
$351$	0.188154	−	2.03883i	0.0100429	−	0.108825i
$352$		0			0
$353$	−18.4047	−	10.6260i	−0.979586	−	0.565564i	−0.0774407	−	0.996997i	$-0.524675\pi$
$353$	−18.4047	−	10.6260i	−0.979586	−	0.565564i	−0.902145	+	0.431433i	$0.858008\pi$
$354$		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	$0.330569\pi$
$359$			32.6519i			1.72330i	−0.507502	+	0.861650i	$0.669431\pi$
$360$		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	−0.932865	−	0.360226i	$-0.882700\pi$
$367$	−2.95918	+	5.12546i	−0.154468	+	0.267547i	0.778397	+	0.627772i	$0.216033\pi$
$368$		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	0.985318	−	0.170729i	$-0.0546123\pi$
$373$	6.65926	+	11.5342i	0.344803	+	0.597217i	−0.640515	+	0.767946i	$0.721279\pi$
$374$		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	0.944120	−	0.329601i	$-0.106914\pi$
$379$	22.0131	+	12.7093i	1.13074	+	0.652832i	0.186617	+	0.982433i	$0.440248\pi$
$380$		0			0
$381$	0.0334909	+	0.0580080i	0.00171579	+	0.00297184i
$382$		0			0
$383$	9.37632	−	5.41342i	0.479107	−	0.276613i	−0.240937	−	0.970541i	$-0.577455\pi$
$383$	9.37632	−	5.41342i	0.479107	−	0.276613i	0.720044	+	0.693928i	$0.244121\pi$
$384$		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	−0.882521	−	0.470273i	$-0.844155\pi$
$397$	−18.2614	+	10.5432i	−0.916512	+	0.529149i	−0.0339917	+	0.999422i	$0.510822\pi$
$398$		0			0
$399$	1.31128	+	2.27120i	0.0656459	+	0.113702i
$400$		0			0
$401$	−17.1273	−	9.88845i	−0.855296	−	0.493805i	0.00713812	−	0.999975i	$-0.497728\pi$
$401$	−17.1273	−	9.88845i	−0.855296	−	0.493805i	−0.862434	+	0.506169i	$0.831061\pi$
$402$		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	−0.990312	−	0.138862i	$-0.955655\pi$
$409$	−27.6096	+	15.9404i	−1.36521	+	0.788204i	−0.374897	+	0.927066i	$0.622322\pi$
$410$		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	−0.196902	−	0.980423i	$-0.563088\pi$
$419$	15.3648	−	26.6127i	0.750621	−	1.30011i	0.947522	−	0.319690i	$-0.103579\pi$
$420$		0			0
$421$			17.9820i			0.876391i	0.898880	+	0.438195i	$0.144382\pi$
$421$			17.9820i			0.876391i	−0.898880	+	0.438195i	$0.855618\pi$
$422$		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	0.598698	−	0.800975i	$-0.295685\pi$
$431$	4.24308	+	2.44974i	0.204382	+	0.118000i	−0.394316	+	0.918975i	$0.629018\pi$
$432$		0			0
$433$	−9.61972	−	16.6618i	−0.462294	−	0.800717i	0.536781	−	0.843722i	$-0.319640\pi$
$433$	−9.61972	−	16.6618i	−0.462294	−	0.800717i	−0.999075	+	0.0430048i	$0.986307\pi$
$434$		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	−0.745632	−	0.666358i	$-0.767852\pi$
$439$	4.27987	−	7.41295i	0.204267	−	0.353801i	0.949899	+	0.312557i	$0.101186\pi$
$440$		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	0.157518	−	0.987516i	$-0.449651\pi$
$449$	23.1283	−	13.3531i	1.09149	−	0.630173i	0.933973	+	0.357344i	$0.116317\pi$
$450$		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	0.584015	−	0.811743i	$-0.301481\pi$
$457$	3.69903	+	2.13563i	0.173033	+	0.0999007i	−0.410982	+	0.911643i	$0.634814\pi$
$458$		0			0
$459$	1.01050	+	1.75024i	0.0471661	+	0.0816941i
$460$		0			0
$461$	17.8767	−	10.3211i	0.832603	−	0.480704i	−0.0221401	−	0.999755i	$-0.507048\pi$
$461$	17.8767	−	10.3211i	0.832603	−	0.480704i	0.854743	+	0.519051i	$0.173715\pi$
$462$		0			0
$463$		−	32.1040i		−	1.49200i	−0.665947	−	0.745999i	$-0.731972\pi$
$463$		−	32.1040i		−	1.49200i	0.665947	−	0.745999i	$-0.268028\pi$
$464$		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	0.598886	−	0.800834i	$-0.295610\pi$
$479$	4.48198	+	2.58767i	0.204787	+	0.118234i	−0.394100	+	0.919068i	$0.628943\pi$
$480$		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	0.245391	−	0.969424i	$-0.421083\pi$
$487$	26.6501	−	15.3865i	1.20763	−	0.697227i	0.962242	+	0.272197i	$0.0877502\pi$
$488$		0			0
$489$			2.13948i			0.0967508i
$490$		0			0
$491$	−17.8992	+	31.0023i	−0.807778	+	1.39911i	0.106622	+	0.994300i	$0.465997\pi$
$491$	−17.8992	+	31.0023i	−0.807778	+	1.39911i	−0.914400	+	0.404813i	$0.867337\pi$
$492$		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	$-0.776105\pi$
$499$		−	28.8971i		−	1.29361i	0.762655	−	0.646805i	$-0.223895\pi$
$500$		0			0
$501$	−0.672879	+	0.388487i	−0.0300620	+	0.0173563i
$502$		0			0
$503$	−3.93161	−	6.80974i	−0.175302	−	0.303631i	0.764964	−	0.644073i	$-0.222757\pi$
$503$	−3.93161	−	6.80974i	−0.175302	−	0.303631i	−0.940266	+	0.340442i	$0.889423\pi$
$504$		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	0.929608	−	0.368549i	$-0.120145\pi$
$509$	24.2585	+	14.0057i	1.07524	+	0.620790i	0.145631	+	0.989339i	$0.453479\pi$
$510$		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	−0.377154	+	0.926151i	$0.623097\pi$
$523$	−22.6553	+	39.2401i	−0.990647	+	1.71585i	−0.613493	+	0.789700i	$0.710236\pi$
$524$		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	$-0.860471\pi$
$541$		−	19.7445i		−	0.848882i	0.905456	−	0.424441i	$-0.139529\pi$
$542$		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	0.423922	−	0.905699i	$-0.360653\pi$
$557$	−3.50412	−	2.02310i	−0.148474	−	0.0857217i	−0.572397	+	0.819977i	$0.693986\pi$
$558$		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	0.822013	−	0.569468i	$-0.192851\pi$
$563$	−1.94963	−	3.37686i	−0.0821671	−	0.142318i	−0.904181	+	0.427151i	$0.859517\pi$
$564$		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	−0.988514	−	0.151133i	$-0.951708\pi$
$569$	−8.66778	+	15.0130i	−0.363372	+	0.629379i	0.625141	+	0.780512i	$0.285041\pi$
$570$		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	$-0.798932\pi$
$577$		−	28.3684i		−	1.18099i	0.807041	−	0.590496i	$-0.201068\pi$
$578$		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	−0.262320	−	0.964981i	$-0.584488\pi$
$587$	−29.7806	−	17.1939i	−1.22918	−	0.709667i	−0.966858	+	0.255314i	$0.917821\pi$
$588$		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	$0.0358662\pi$
$593$			5.47612i			0.224877i	−0.993659	+	0.112439i	$0.964134\pi$
$594$		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	−0.925284	−	0.379275i	$-0.876174\pi$
$601$	−3.28948	+	5.69754i	−0.134181	+	0.232408i	0.791104	+	0.611682i	$0.209507\pi$
$602$		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	0.644219	−	0.764841i	$-0.277183\pi$
$607$	−8.38318	−	14.5201i	−0.340263	−	0.589352i	−0.984481	+	0.175489i	$0.943849\pi$
$608$		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	0.910206	−	0.414155i	$-0.135923\pi$
$613$	24.9232	+	14.3894i	1.00664	+	0.581184i	0.0964341	+	0.995339i	$0.469256\pi$
$614$		0			0
$615$	0.0126991	+	0.0219955i	0.000512078	+	0.000886946i
$616$		0			0
$617$	32.3279	−	18.6645i	1.30147	−	0.751406i	0.320817	−	0.947141i	$-0.396043\pi$
$617$	32.3279	−	18.6645i	1.30147	−	0.751406i	0.980657	+	0.195735i	$0.0627093\pi$
$618$		0			0
$619$		−	12.7535i		−	0.512606i	−0.966597	−	0.256303i	$-0.917496\pi$
$619$		−	12.7535i		−	0.512606i	0.966597	−	0.256303i	$-0.0825045\pi$
$620$		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	−0.905362	−	0.424641i	$-0.860400\pi$
$631$	−24.8759	+	14.3621i	−0.990294	+	0.571746i	−0.0849315	+	0.996387i	$0.527067\pi$
$632$		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	0.555546	−	0.831486i	$-0.312509\pi$
$641$	−11.1985	−	19.3964i	−0.442315	−	0.766112i	−0.997861	+	0.0653739i	$0.979176\pi$
$642$		0			0
$643$	−12.2665	+	7.08209i	−0.483745	+	0.279290i	−0.721976	−	0.691918i	$-0.756766\pi$
$643$	−12.2665	+	7.08209i	−0.483745	+	0.279290i	0.238231	+	0.971209i	$0.423433\pi$
$644$		0			0
$645$			0.337339i			0.0132827i
$646$		0			0
$647$	11.8048	−	20.4466i	0.464096	−	0.803838i	−0.535064	−	0.844812i	$-0.679713\pi$
$647$	11.8048	−	20.4466i	0.464096	−	0.803838i	0.999160	+	0.0409732i	$0.0130458\pi$
$648$		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	0.331750	+	0.943367i	$0.392361\pi$
$653$	−16.6383	+	28.8183i	−0.651105	+	1.12775i	−0.982855	+	0.184380i	$0.940972\pi$
$654$		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	0.998369	−	0.0570875i	$-0.0181814\pi$
$659$	11.5454	+	19.9972i	0.449745	+	0.778982i	−0.548624	+	0.836069i	$0.684848\pi$
$660$		0			0
$661$	11.6364	+	6.71826i	0.452602	+	0.261310i	0.708929	−	0.705280i	$-0.249179\pi$
$661$	11.6364	+	6.71826i	0.452602	+	0.261310i	−0.256326	+	0.966590i	$0.582512\pi$
$662$		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	−0.884162	−	0.467180i	$-0.845270\pi$
$673$	−0.972620	+	1.68463i	−0.0374918	+	0.0649376i	0.846671	+	0.532117i	$0.178603\pi$
$674$		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	−0.237766	−	0.971323i	$-0.576415\pi$
$683$	12.6631	−	7.31107i	0.484542	−	0.279750i	0.722307	+	0.691572i	$0.243082\pi$
$684$		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	0.556933	−	0.830558i	$-0.311978\pi$
$691$	3.05231	+	1.76225i	0.116115	+	0.0670393i	−0.440817	+	0.897597i	$0.645311\pi$
$692$		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	−0.254644	−	0.967035i	$-0.581958\pi$
$709$	12.1289	−	7.00262i	0.455510	−	0.262989i	0.710155	+	0.704046i	$0.248625\pi$
$710$		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	0.576741	−	0.816927i	$-0.304324\pi$
$719$	−11.2381	−	19.4649i	−0.419109	−	0.725918i	−0.995850	+	0.0910091i	$0.970991\pi$
$720$		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	$-0.831434\pi$
$733$		−	27.3533i		−	1.01032i	0.863026	−	0.505159i	$-0.168566\pi$
$734$		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	0.270189	−	0.962807i	$-0.412914\pi$
$739$	−11.6495	−	6.72583i	−0.428533	−	0.247413i	−0.698721	+	0.715394i	$0.746247\pi$
$740$		0			0
$741$	1.95071	+	0.180021i	0.0716610	+	0.00661324i
$742$		0			0
$743$	−14.1964	−	8.19632i	−0.520817	−	0.300694i	0.216452	−	0.976293i	$-0.430552\pi$
$743$	−14.1964	−	8.19632i	−0.520817	−	0.300694i	−0.737269	+	0.675599i	$0.763885\pi$
$744$		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	−0.495221	−	0.868767i	$-0.664913\pi$
$751$	13.8328	−	23.9590i	0.504764	−	0.874277i	0.999985	−	0.00551009i	$-0.00175392\pi$
$752$		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	−0.995732	−	0.0922961i	$-0.970579\pi$
$757$	−11.4989	+	19.9167i	−0.417935	+	0.723885i	0.577797	+	0.816181i	$0.303913\pi$
$758$		0			0
$759$		−	0.718251i		−	0.0260709i
$760$		0			0
$761$	6.63759	−	3.83221i	0.240612	−	0.138918i	−0.374846	−	0.927087i	$-0.622304\pi$
$761$	6.63759	−	3.83221i	0.240612	−	0.138918i	0.615458	+	0.788170i	$0.288971\pi$
$762$		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	0.608642	−	0.793445i	$-0.291714\pi$
$769$	6.26219	+	3.61548i	0.225820	+	0.130377i	−0.382822	+	0.923822i	$0.625048\pi$
$770$		0			0
$771$	1.25745	+	2.17797i	0.0452859	+	0.0784375i
$772$		0			0
$773$	−29.0981	+	16.7998i	−1.04658	+	0.604246i	−0.921691	−	0.387924i	$-0.873192\pi$
$773$	−29.0981	+	16.7998i	−1.04658	+	0.604246i	−0.124893	+	0.992170i	$0.539859\pi$
$774$		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	−0.545167	−	0.838328i	$-0.683534\pi$
$787$	−2.57355	+	1.48584i	−0.0917371	+	0.0529645i	0.453430	+	0.891292i	$0.350200\pi$
$788$		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	0.593879	−	0.804554i	$-0.297596\pi$
$797$	−11.2875	−	19.5506i	−0.399825	−	0.692517i	−0.993704	+	0.112037i	$0.964262\pi$
$798$		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	−0.960743	−	0.277439i	$-0.910514\pi$
$809$	−6.82921	+	11.8285i	−0.240102	+	0.415869i	0.720641	+	0.693308i	$0.243848\pi$
$810$		0			0
$811$		−	14.1147i		−	0.495636i	−0.968807	−	0.247818i	$-0.920287\pi$
$811$		−	14.1147i		−	0.495636i	0.968807	−	0.247818i	$-0.0797135\pi$
$812$		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	0.475846	−	0.879528i	$-0.342142\pi$
$821$	−1.37318	−	0.792808i	−0.0479244	−	0.0276692i	−0.523771	+	0.851859i	$0.675475\pi$
$822$		0			0
$823$	−9.28238	−	16.0776i	−0.323563	−	0.560428i	0.657657	−	0.753317i	$-0.271548\pi$
$823$	−9.28238	−	16.0776i	−0.323563	−	0.560428i	−0.981221	+	0.192889i	$0.938214\pi$
$824$		0			0
$825$	−0.0877845	+	0.0506824i	−0.00305626	+	0.00176454i
$826$		0			0
$827$			9.01023i			0.313316i	0.987653	+	0.156658i	$0.0500721\pi$
$827$			9.01023i			0.313316i	−0.987653	+	0.156658i	$0.949928\pi$
$828$		0			0
$829$	23.5588	−	40.8051i	0.818233	−	1.41722i	−0.0887506	−	0.996054i	$-0.528287\pi$
$829$	23.5588	−	40.8051i	0.818233	−	1.41722i	0.906983	−	0.421167i	$-0.138379\pi$
$830$		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	−0.607164	+	0.794576i	$0.707693\pi$
$839$	−46.3121	+	26.7383i	−1.59887	+	0.923108i	−0.991705	+	0.128531i	$0.958974\pi$
$840$		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	$-0.842264\pi$
$853$		−	27.7756i		−	0.951019i	0.879711	−	0.475510i	$-0.157736\pi$
$854$		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	$-0.990495\pi$
$863$		−	1.75413i		−	0.0597113i	0.999554	−	0.0298557i	$-0.00950476\pi$
$864$		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	−0.781024	−	0.624501i	$-0.785302\pi$
$877$	−18.6777	+	10.7836i	−0.630702	+	0.364136i	0.150322	+	0.988637i	$0.451969\pi$
$878$		0			0
$879$		−	0.0258742i		−	0.000872716i
$880$		0			0
$881$	12.5132	−	21.6734i	0.421579	−	0.730196i	−0.574515	−	0.818494i	$-0.694809\pi$
$881$	12.5132	−	21.6734i	0.421579	−	0.730196i	0.996094	+	0.0882978i	$0.0281427\pi$
$882$		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	0.429494	+	0.903070i	$0.358692\pi$
$887$	−16.8967	+	29.2659i	−0.567334	+	0.982651i	−0.996828	+	0.0795819i	$0.974641\pi$
$888$		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	−0.421169	−	0.906982i	$-0.638380\pi$
$907$	17.3135	−	29.9879i	0.574885	−	0.995731i	0.996054	−	0.0887485i	$-0.0282867\pi$
$908$		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	−0.875364	−	0.483464i	$-0.839379\pi$
$919$	−25.9610	−	44.9658i	−0.856374	−	1.48328i	0.0189904	−	0.999820i	$-0.493955\pi$
$920$		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	−0.762020	−	0.647553i	$-0.775792\pi$
$929$	−17.7462	+	10.2457i	−0.582232	+	0.336152i	0.179788	+	0.983705i	$0.442459\pi$
$930$		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	$0.103609\pi$
$941$			19.6189i			0.639557i	−0.947492	+	0.319779i	$0.896391\pi$
$942$		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	0.989352	+	0.145544i	$0.0464933\pi$
$947$	49.5474	+	28.6062i	1.61007	+	0.929576i	0.620721	+	0.784032i	$0.286840\pi$
$948$		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	0.998055	−	0.0623470i	$-0.0198586\pi$
$953$	13.7385	+	23.7958i	0.445033	+	0.770820i	−0.553021	+	0.833167i	$0.686525\pi$
$954$		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	$-0.946706\pi$
$967$		−	10.3643i		−	0.333293i	0.986017	−	0.166647i	$-0.0532939\pi$
$968$		0			0
$969$	−1.67458	+	0.966821i	−0.0537953	+	0.0310588i
$970$		0			0
$971$	20.8758	+	36.1579i	0.669935	+	1.16036i	0.977922	+	0.208971i	$0.0670113\pi$
$971$	20.8758	+	36.1579i	0.669935	+	1.16036i	−0.307987	+	0.951391i	$0.599655\pi$
$972$		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	0.296586	−	0.955006i	$-0.404152\pi$
$977$	−11.9458	−	6.89691i	−0.382180	−	0.220652i	−0.678766	+	0.734354i	$0.737485\pi$
$978$		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	$-0.792773\pi$
$983$		−	37.9997i		−	1.21200i	0.795463	−	0.606002i	$-0.207227\pi$
$984$		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	0.0595748	+	0.998224i	$0.481026\pi$
$991$	−26.2765	+	45.5122i	−0.834700	+	1.44574i	−0.894275	+	0.447519i	$0.852308\pi$
$992$		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	0.680465	−	0.732781i	$-0.261778\pi$
$997$	−9.29497	−	16.0994i	−0.294375	−	0.509872i	−0.974839	+	0.222909i	$0.928445\pi$
$998$		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.641.3		8
4.3	odd	2		65.2.m.a.56.4	yes	8
12.11	even	2		585.2.bu.c.316.1		8
13.10	even	6	inner	1040.2.da.b.881.3		8
20.3	even	4		325.2.m.b.199.4		8
20.7	even	4		325.2.m.c.199.1		8
20.19	odd	2		325.2.n.d.251.1		8
52.3	odd	6		845.2.m.g.361.1		8
52.7	even	12		845.2.a.l.1.4		4
52.11	even	12		845.2.e.n.146.1		8
52.15	even	12		845.2.e.m.146.4		8
52.19	even	12		845.2.a.m.1.1		4
52.23	odd	6		65.2.m.a.36.4	✓	8
52.31	even	4		845.2.e.m.191.4		8
52.35	odd	6		845.2.c.g.506.2		8
52.43	odd	6		845.2.c.g.506.7		8
52.47	even	4		845.2.e.n.191.1		8
52.51	odd	2		845.2.m.g.316.1		8
156.23	even	6		585.2.bu.c.361.1		8
156.59	odd	12		7605.2.a.cj.1.1		4
156.71	odd	12		7605.2.a.cf.1.4		4
260.19	even	12		4225.2.a.bi.1.4		4
260.23	even	12		325.2.m.c.49.1		8
260.59	even	12		4225.2.a.bl.1.1		4
260.127	even	12		325.2.m.b.49.4		8
260.179	odd	6		325.2.n.d.101.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.4	✓	8	52.23	odd	6
65.2.m.a.56.4	yes	8	4.3	odd	2
325.2.m.b.49.4		8	260.127	even	12
325.2.m.b.199.4		8	20.3	even	4
325.2.m.c.49.1		8	260.23	even	12
325.2.m.c.199.1		8	20.7	even	4
325.2.n.d.101.1		8	260.179	odd	6
325.2.n.d.251.1		8	20.19	odd	2
585.2.bu.c.316.1		8	12.11	even	2
585.2.bu.c.361.1		8	156.23	even	6
845.2.a.l.1.4		4	52.7	even	12
845.2.a.m.1.1		4	52.19	even	12
845.2.c.g.506.2		8	52.35	odd	6
845.2.c.g.506.7		8	52.43	odd	6
845.2.e.m.146.4		8	52.15	even	12
845.2.e.m.191.4		8	52.31	even	4
845.2.e.n.146.1		8	52.11	even	12
845.2.e.n.191.1		8	52.47	even	4
845.2.m.g.316.1		8	52.51	odd	2
845.2.m.g.361.1		8	52.3	odd	6
1040.2.da.b.641.3		8	1.1	even	1	trivial
1040.2.da.b.881.3		8	13.10	even	6	inner
4225.2.a.bi.1.4		4	260.19	even	12
4225.2.a.bl.1.1		4	260.59	even	12
7605.2.a.cf.1.4		4	156.71	odd	12
7605.2.a.cj.1.1		4	156.59	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 $\F_{q}$

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

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

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Database

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