LMFDB - Embedded newform 820.2.u.b.201.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(141,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.141"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.u (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.8
Character	$\chi$	$=$	820.201
Dual form			820.2.u.b.461.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.33542 q^{3} +(-0.309017 + 0.951057i) q^{5} +(-1.68976 - 1.22768i) q^{7} +8.12504 q^{9} +(1.44022 + 4.43255i) q^{11} +(3.98542 - 2.89558i) q^{13} +(-1.03070 + 3.17218i) q^{15} +(0.947354 + 2.91566i) q^{17} +(-4.36981 - 3.17485i) q^{19} +(-5.63605 - 4.09483i) q^{21} +(-6.90892 + 5.01963i) q^{23} +(-0.809017 - 0.587785i) q^{25} +17.0942 q^{27} +(3.25893 - 10.0300i) q^{29} +(0.826547 + 2.54385i) q^{31} +(4.80375 + 14.7844i) q^{33} +(1.68976 - 1.22768i) q^{35} +(0.690770 - 2.12597i) q^{37} +(13.2931 - 9.65798i) q^{39} +(-4.00305 + 4.99756i) q^{41} +(6.50654 - 4.72728i) q^{43} +(-2.51078 + 7.72738i) q^{45} +(-1.29163 + 0.938421i) q^{47} +(-0.815042 - 2.50844i) q^{49} +(3.15983 + 9.72494i) q^{51} +(-1.46112 + 4.49688i) q^{53} -4.66066 q^{55} +(-14.5752 - 10.5895i) q^{57} +(0.728491 - 0.529280i) q^{59} +(-6.48509 - 4.71170i) q^{61} +(-13.7293 - 9.97495i) q^{63} +(1.52230 + 4.68515i) q^{65} +(0.657405 - 2.02328i) q^{67} +(-23.0442 + 16.7426i) q^{69} +(1.11976 + 3.44626i) q^{71} +2.17713 q^{73} +(-2.69841 - 1.96051i) q^{75} +(3.00813 - 9.25806i) q^{77} -4.97360 q^{79} +32.6412 q^{81} -14.4597 q^{83} -3.06570 q^{85} +(10.8699 - 33.4541i) q^{87} +(-2.85465 - 2.07402i) q^{89} -10.2892 q^{91} +(2.75688 + 8.48482i) q^{93} +(4.36981 - 3.17485i) q^{95} +(-5.37460 + 16.5413i) q^{97} +(11.7019 + 36.0147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 8 q^{5} - 5 q^{7} + 46 q^{9} + q^{11} + q^{13} - 2 q^{15} + 7 q^{17} - 13 q^{19} - 6 q^{21} + 4 q^{23} - 8 q^{25} - 28 q^{27} + 3 q^{29} - q^{31} + 14 q^{33} + 5 q^{35} - 25 q^{37} + 26 q^{41}+ \cdots + 30 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 8 * q^5 - 5 * q^7 + 46 * q^9 + q^11 + q^13 - 2 * q^15 + 7 * q^17 - 13 * q^19 - 6 * q^21 + 4 * q^23 - 8 * q^25 - 28 * q^27 + 3 * q^29 - q^31 + 14 * q^33 + 5 * q^35 - 25 * q^37 + 26 * q^41 + 8 * q^43 + 19 * q^45 + q^47 - 15 * q^49 + 29 * q^51 - 33 * q^53 + 4 * q^55 - 29 * q^57 + 20 * q^59 - 24 * q^61 - 66 * q^63 - q^65 - 48 * q^67 - 16 * q^69 + 5 * q^71 + 4 * q^73 - 3 * q^75 - 16 * q^77 - 102 * q^79 + 200 * q^81 - 110 * q^83 + 8 * q^85 + 25 * q^87 - 34 * q^89 - 10 * q^91 - 18 * q^93 + 13 * q^95 - 36 * q^97 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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
$3$	3.33542			1.92571			0.962854	−	0.270024i	$-0.0870316\pi$
$3$	3.33542			1.92571			0.962854	+	0.270024i	$0.0870316\pi$
$4$		0			0
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$		0			0
$7$	−1.68976	−	1.22768i	−0.638667	−	0.464019i	0.220725	−	0.975336i	$-0.429158\pi$
$7$	−1.68976	−	1.22768i	−0.638667	−	0.464019i	−0.859392	+	0.511317i	$0.829158\pi$
$8$		0			0
$9$	8.12504			2.70835
$10$		0			0
$11$	1.44022	+	4.43255i	0.434244	+	1.33646i	0.893860	+	0.448347i	$0.147987\pi$
$11$	1.44022	+	4.43255i	0.434244	+	1.33646i	−0.459616	+	0.888118i	$0.652013\pi$
$12$		0			0
$13$	3.98542	−	2.89558i	1.10536	−	0.803089i	0.123431	−	0.992353i	$-0.460610\pi$
$13$	3.98542	−	2.89558i	1.10536	−	0.803089i	0.981926	+	0.189264i	$0.0606101\pi$
$14$		0			0
$15$	−1.03070	+	3.17218i	−0.266126	+	0.819052i
$16$		0			0
$17$	0.947354	+	2.91566i	0.229767	+	0.707150i	0.997773	+	0.0667071i	$0.0212493\pi$
$17$	0.947354	+	2.91566i	0.229767	+	0.707150i	−0.768006	+	0.640443i	$0.778751\pi$
$18$		0			0
$19$	−4.36981	−	3.17485i	−1.00250	−	0.728361i	−0.0398800	−	0.999204i	$-0.512698\pi$
$19$	−4.36981	−	3.17485i	−1.00250	−	0.728361i	−0.962624	+	0.270843i	$0.912698\pi$
$20$		0			0
$21$	−5.63605	−	4.09483i	−1.22989	−	0.893565i
$22$		0			0
$23$	−6.90892	+	5.01963i	−1.44061	+	1.04666i	−0.452695	+	0.891665i	$0.649537\pi$
$23$	−6.90892	+	5.01963i	−1.44061	+	1.04666i	−0.987915	+	0.154999i	$0.950463\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$		0			0
$27$	17.0942			3.28978
$28$		0			0
$29$	3.25893	−	10.0300i	0.605168	−	1.86252i	0.109538	−	0.993983i	$-0.465063\pi$
$29$	3.25893	−	10.0300i	0.605168	−	1.86252i	0.495630	−	0.868534i	$-0.334937\pi$
$30$		0			0
$31$	0.826547	+	2.54385i	0.148452	+	0.456889i	0.997439	−	0.0715254i	$-0.0227867\pi$
$31$	0.826547	+	2.54385i	0.148452	+	0.456889i	−0.848986	+	0.528415i	$0.822787\pi$
$32$		0			0
$33$	4.80375	+	14.7844i	0.836226	+	2.57364i
$34$		0			0
$35$	1.68976	−	1.22768i	0.285621	−	0.207516i
$36$		0			0
$37$	0.690770	−	2.12597i	0.113562	−	0.349508i	−0.878082	−	0.478509i	$-0.841177\pi$
$37$	0.690770	−	2.12597i	0.113562	−	0.349508i	0.991644	+	0.129002i	$0.0411773\pi$
$38$		0			0
$39$	13.2931	−	9.65798i	2.12860	−	1.54652i
$40$		0			0
$41$	−4.00305	+	4.99756i	−0.625171	+	0.780488i
$41$	−4.00305	+	4.99756i	−0.625171	+	0.780488i
$42$		0			0
$43$	6.50654	−	4.72728i	0.992239	−	0.720904i	0.0318284	−	0.999493i	$-0.489867\pi$
$43$	6.50654	−	4.72728i	0.992239	−	0.720904i	0.960410	+	0.278590i	$0.0898670\pi$
$44$		0			0
$45$	−2.51078	+	7.72738i	−0.374285	+	1.15193i
$46$		0			0
$47$	−1.29163	+	0.938421i	−0.188403	+	0.136883i	−0.677988	−	0.735073i	$-0.737148\pi$
$47$	−1.29163	+	0.938421i	−0.188403	+	0.136883i	0.489586	+	0.871955i	$0.337148\pi$
$48$		0			0
$49$	−0.815042	−	2.50844i	−0.116435	−	0.358349i
$50$		0			0
$51$	3.15983	+	9.72494i	0.442464	+	1.36176i
$52$		0			0
$53$	−1.46112	+	4.49688i	−0.200701	+	0.617693i	0.799162	+	0.601116i	$0.205277\pi$
$53$	−1.46112	+	4.49688i	−0.200701	+	0.617693i	−0.999863	+	0.0165775i	$0.994723\pi$
$54$		0			0
$55$	−4.66066			−0.628443
$56$		0			0
$57$	−14.5752	−	10.5895i	−1.93053	−	1.40261i
$58$		0			0
$59$	0.728491	−	0.529280i	0.0948415	−	0.0689064i	−0.539354	−	0.842079i	$-0.681331\pi$
$59$	0.728491	−	0.529280i	0.0948415	−	0.0689064i	0.634195	+	0.773173i	$0.281331\pi$
$60$		0			0
$61$	−6.48509	−	4.71170i	−0.830331	−	0.603271i	0.0893219	−	0.996003i	$-0.471530\pi$
$61$	−6.48509	−	4.71170i	−0.830331	−	0.603271i	−0.919653	+	0.392732i	$0.871530\pi$
$62$		0			0
$63$	−13.7293	−	9.97495i	−1.72973	−	1.25673i
$64$		0			0
$65$	1.52230	+	4.68515i	0.188818	+	0.581121i
$66$		0			0
$67$	0.657405	−	2.02328i	0.0803148	−	0.247183i	−0.902834	−	0.429988i	$-0.858518\pi$
$67$	0.657405	−	2.02328i	0.0803148	−	0.247183i	0.983149	+	0.182805i	$0.0585177\pi$
$68$		0			0
$69$	−23.0442	+	16.7426i	−2.77419	+	2.01557i
$70$		0			0
$71$	1.11976	+	3.44626i	0.132891	+	0.408996i	0.995256	−	0.0972906i	$-0.0310176\pi$
$71$	1.11976	+	3.44626i	0.132891	+	0.408996i	−0.862365	+	0.506287i	$0.831018\pi$
$72$		0			0
$73$	2.17713			0.254814			0.127407	−	0.991851i	$-0.459335\pi$
$73$	2.17713			0.254814			0.127407	+	0.991851i	$0.459335\pi$
$74$		0			0
$75$	−2.69841	−	1.96051i	−0.311586	−	0.226380i
$76$		0			0
$77$	3.00813	−	9.25806i	0.342808	−	1.05505i
$78$		0			0
$79$	−4.97360			−0.559573			−0.279787	−	0.960062i	$-0.590264\pi$
$79$	−4.97360			−0.559573			−0.279787	+	0.960062i	$0.590264\pi$
$80$		0			0
$81$	32.6412			3.62680
$82$		0			0
$83$	−14.4597			−1.58716			−0.793582	−	0.608464i	$-0.791786\pi$
$83$	−14.4597			−1.58716			−0.793582	+	0.608464i	$0.791786\pi$
$84$		0			0
$85$	−3.06570			−0.332522
$86$		0			0
$87$	10.8699	−	33.4541i	1.16538	−	3.58666i
$88$		0			0
$89$	−2.85465	−	2.07402i	−0.302592	−	0.219846i	0.426119	−	0.904667i	$-0.359880\pi$
$89$	−2.85465	−	2.07402i	−0.302592	−	0.219846i	−0.728711	+	0.684821i	$0.759880\pi$
$90$		0			0
$91$	−10.2892			−1.07860
$92$		0			0
$93$	2.75688	+	8.48482i	0.285876	+	0.879835i
$94$		0			0
$95$	4.36981	−	3.17485i	0.448333	−	0.325733i
$96$		0			0
$97$	−5.37460	+	16.5413i	−0.545707	+	1.67951i	0.173594	+	0.984817i	$0.444462\pi$
$97$	−5.37460	+	16.5413i	−0.545707	+	1.67951i	−0.719302	+	0.694698i	$0.755538\pi$
$98$		0			0
$99$	11.7019	+	36.0147i	1.17608	+	3.61961i
$100$		0			0
$101$	−6.38013	−	4.63543i	−0.634846	−	0.461243i	0.223230	−	0.974766i	$-0.428340\pi$
$101$	−6.38013	−	4.63543i	−0.634846	−	0.461243i	−0.858076	+	0.513523i	$0.828340\pi$
$102$		0			0
$103$	−5.79954	−	4.21361i	−0.571446	−	0.415180i	0.264184	−	0.964472i	$-0.414897\pi$
$103$	−5.79954	−	4.21361i	−0.571446	−	0.415180i	−0.835630	+	0.549292i	$0.814897\pi$
$104$		0			0
$105$	5.63605	−	4.09483i	0.550022	−	0.399614i
$106$		0			0
$107$	8.80188	+	6.39494i	0.850910	+	0.618222i	0.925397	−	0.379000i	$-0.123732\pi$
$107$	8.80188	+	6.39494i	0.850910	+	0.618222i	−0.0744871	+	0.997222i	$0.523732\pi$
$108$		0			0
$109$	−13.6586			−1.30826			−0.654130	−	0.756383i	$-0.726965\pi$
$109$	−13.6586			−1.30826			−0.654130	+	0.756383i	$0.726965\pi$
$110$		0			0
$111$	2.30401	−	7.09102i	0.218687	−	0.673049i
$112$		0			0
$113$	−6.00712	−	18.4880i	−0.565103	−	1.73921i	−0.667646	−	0.744479i	$-0.732698\pi$
$113$	−6.00712	−	18.4880i	−0.565103	−	1.73921i	0.102544	−	0.994729i	$-0.467302\pi$
$114$		0			0
$115$	−2.63897	−	8.12192i	−0.246086	−	0.757373i
$116$		0			0
$117$	32.3817	−	23.5267i	2.99369	−	2.17505i
$118$		0			0
$119$	1.97869	−	6.08979i	0.181386	−	0.558250i
$120$		0			0
$121$	−8.67408	+	6.30209i	−0.788553	+	0.572917i
$122$		0			0
$123$	−13.3518	+	16.6690i	−1.20390	+	1.50299i
$124$		0			0
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$		0			0
$127$	−1.82706	+	5.62312i	−0.162126	+	0.498971i	−0.998813	−	0.0487095i	$-0.984489\pi$
$127$	−1.82706	+	5.62312i	−0.162126	+	0.498971i	0.836687	+	0.547681i	$0.184489\pi$
$128$		0			0
$129$	21.7021	−	15.7675i	1.91076	−	1.38825i
$130$		0			0
$131$	−0.0873182	−	0.268738i	−0.00762903	−	0.0234797i	0.947170	−	0.320733i	$-0.103929\pi$
$131$	−0.0873182	−	0.268738i	−0.00762903	−	0.0234797i	−0.954799	+	0.297254i	$0.903929\pi$
$132$		0			0
$133$	3.48621	+	10.7295i	0.302293	+	0.930361i
$134$		0			0
$135$	−5.28240	+	16.2575i	−0.454636	+	1.39923i
$136$		0			0
$137$	1.29862			0.110949			0.0554745	−	0.998460i	$-0.482333\pi$
$137$	1.29862			0.110949			0.0554745	+	0.998460i	$0.482333\pi$
$138$		0			0
$139$	12.1357	+	8.81709i	1.02933	+	0.747856i	0.968175	−	0.250272i	$-0.0805202\pi$
$139$	12.1357	+	8.81709i	1.02933	+	0.747856i	0.0611594	+	0.998128i	$0.480520\pi$
$140$		0			0
$141$	−4.30812	+	3.13003i	−0.362809	+	0.263596i
$142$		0			0
$143$	18.5747	+	13.4953i	1.55329	+	1.12853i
$144$		0			0
$145$	8.53199	+	6.19885i	0.708543	+	0.514787i
$146$		0			0
$147$	−2.71851	−	8.36671i	−0.224219	−	0.690075i
$148$		0			0
$149$	5.21209	−	16.0412i	0.426991	−	1.31414i	−0.474084	−	0.880479i	$-0.657221\pi$
$149$	5.21209	−	16.0412i	0.426991	−	1.31414i	0.901075	−	0.433663i	$-0.142779\pi$
$150$		0			0
$151$	5.73818	−	4.16903i	0.466966	−	0.339271i	−0.329291	−	0.944228i	$-0.606810\pi$
$151$	5.73818	−	4.16903i	0.466966	−	0.339271i	0.796258	+	0.604957i	$0.206810\pi$
$152$		0			0
$153$	7.69729	+	23.6898i	0.622289	+	1.91521i
$154$		0			0
$155$	−2.67476			−0.214842
$156$		0			0
$157$	−0.158957	−	0.115489i	−0.0126862	−	0.00921704i	0.581424	−	0.813601i	$-0.302496\pi$
$157$	−0.158957	−	0.115489i	−0.0126862	−	0.00921704i	−0.594110	+	0.804384i	$0.702496\pi$
$158$		0			0
$159$	−4.87346	+	14.9990i	−0.386491	+	1.18950i
$160$		0			0
$161$	17.8369			1.40574
$162$		0			0
$163$	−17.7761			−1.39234			−0.696168	−	0.717879i	$-0.745113\pi$
$163$	−17.7761			−1.39234			−0.696168	+	0.717879i	$0.745113\pi$
$164$		0			0
$165$	−15.5453			−1.21020
$166$		0			0
$167$	−2.70930			−0.209652			−0.104826	−	0.994491i	$-0.533429\pi$
$167$	−2.70930			−0.209652			−0.104826	+	0.994491i	$0.533429\pi$
$168$		0			0
$169$	3.48200	−	10.7165i	0.267846	−	0.824346i
$170$		0			0
$171$	−35.5049	−	25.7958i	−2.71513	−	1.97266i
$172$		0			0
$173$	11.8388			0.900084			0.450042	−	0.893007i	$-0.351409\pi$
$173$	11.8388			0.900084			0.450042	+	0.893007i	$0.351409\pi$
$174$		0			0
$175$	0.645429	+	1.98643i	0.0487898	+	0.150160i
$176$		0			0
$177$	2.42983	−	1.76537i	0.182637	−	0.132694i
$178$		0			0
$179$	−4.68596	+	14.4219i	−0.350245	+	1.07794i	0.608470	+	0.793577i	$0.291783\pi$
$179$	−4.68596	+	14.4219i	−0.350245	+	1.07794i	−0.958715	+	0.284367i	$0.908217\pi$
$180$		0			0
$181$	−2.67735	−	8.24004i	−0.199006	−	0.612477i	−0.999906	−	0.0136798i	$-0.995645\pi$
$181$	−2.67735	−	8.24004i	−0.199006	−	0.612477i	0.800901	−	0.598797i	$-0.204355\pi$
$182$		0			0
$183$	−21.6305	−	15.7155i	−1.59897	−	1.16172i
$184$		0			0
$185$	1.80846	+	1.31392i	0.132961	+	0.0966015i
$186$		0			0
$187$	−11.5594	+	8.39839i	−0.845306	+	0.614151i
$188$		0			0
$189$	−28.8850	−	20.9862i	−2.10107	−	1.52652i
$190$		0			0
$191$	−13.9269			−1.00772			−0.503859	−	0.863786i	$-0.668087\pi$
$191$	−13.9269			−1.00772			−0.503859	+	0.863786i	$0.668087\pi$
$192$		0			0
$193$	−0.708923	+	2.18184i	−0.0510294	+	0.157052i	−0.973324	−	0.229436i	$-0.926312\pi$
$193$	−0.708923	+	2.18184i	−0.0510294	+	0.157052i	0.922294	+	0.386488i	$0.126312\pi$
$194$		0			0
$195$	5.07750	+	15.6269i	0.363607	+	1.11907i
$196$		0			0
$197$	−0.684485	−	2.10663i	−0.0487675	−	0.150091i	0.923707	−	0.383099i	$-0.125143\pi$
$197$	−0.684485	−	2.10663i	−0.0487675	−	0.150091i	−0.972475	+	0.233008i	$0.925143\pi$
$198$		0			0
$199$	−5.30006	+	3.85072i	−0.375711	+	0.272970i	−0.759575	−	0.650419i	$-0.774593\pi$
$199$	−5.30006	+	3.85072i	−0.375711	+	0.272970i	0.383864	+	0.923390i	$0.374593\pi$
$200$		0			0
$201$	2.19272	−	6.74851i	0.154663	−	0.476003i
$202$		0			0
$203$	−17.8204	+	12.9473i	−1.25074	+	0.908719i
$204$		0			0
$205$	−3.51596	−	5.35145i	−0.245565	−	0.373762i
$206$		0			0
$207$	−56.1353	+	40.7847i	−3.90167	+	2.83473i
$208$		0			0
$209$	7.77920	−	23.9419i	0.538098	−	1.65610i
$210$		0			0
$211$	20.2500	−	14.7125i	1.39407	−	1.01285i	0.398661	−	0.917098i	$-0.369475\pi$
$211$	20.2500	−	14.7125i	1.39407	−	1.01285i	0.995405	−	0.0957498i	$-0.0305249\pi$
$212$		0			0
$213$	3.73487	+	11.4947i	0.255909	+	0.787607i
$214$		0			0
$215$	2.48528	+	7.64890i	0.169495	+	0.521651i
$216$		0			0
$217$	1.72637	−	5.31322i	0.117194	−	0.360685i
$218$		0			0
$219$	7.26166			0.490698
$220$		0			0
$221$	12.2181	+	8.87698i	0.821880	+	0.597131i
$222$		0			0
$223$	5.11803	−	3.71846i	0.342728	−	0.249007i	−0.403084	−	0.915163i	$-0.632062\pi$
$223$	5.11803	−	3.71846i	0.342728	−	0.249007i	0.745812	+	0.666156i	$0.232062\pi$
$224$		0			0
$225$	−6.57330	−	4.77578i	−0.438220	−	0.318385i
$226$		0			0
$227$	8.07829	+	5.86922i	0.536175	+	0.389554i	0.822663	−	0.568530i	$-0.192488\pi$
$227$	8.07829	+	5.86922i	0.536175	+	0.389554i	−0.286487	+	0.958084i	$0.592488\pi$
$228$		0			0
$229$	−3.35428	−	10.3234i	−0.221657	−	0.682190i	−0.998614	−	0.0526362i	$-0.983238\pi$
$229$	−3.35428	−	10.3234i	−0.221657	−	0.682190i	0.776957	−	0.629554i	$-0.216762\pi$
$230$		0			0
$231$	10.0334	−	30.8795i	0.660147	−	2.03172i
$232$		0			0
$233$	−4.64205	+	3.37265i	−0.304111	+	0.220949i	−0.729365	−	0.684124i	$-0.760185\pi$
$233$	−4.64205	+	3.37265i	−0.304111	+	0.220949i	0.425255	+	0.905074i	$0.360185\pi$
$234$		0			0
$235$	−0.493357	−	1.51840i	−0.0321831	−	0.0990493i
$236$		0			0
$237$	−16.5890			−1.07757
$238$		0			0
$239$	4.43359	+	3.22119i	0.286785	+	0.208362i	0.721872	−	0.692027i	$-0.243282\pi$
$239$	4.43359	+	3.22119i	0.286785	+	0.208362i	−0.435086	+	0.900389i	$0.643282\pi$
$240$		0			0
$241$	3.21806	−	9.90416i	0.207293	−	0.637983i	−0.792318	−	0.610108i	$-0.791126\pi$
$241$	3.21806	−	9.90416i	0.207293	−	0.637983i	0.999611	−	0.0278749i	$-0.00887401\pi$
$242$		0			0
$243$	57.5897			3.69438
$244$		0			0
$245$	2.63753			0.168506
$246$		0			0
$247$	−26.6086			−1.69306
$248$		0			0
$249$	−48.2294			−3.05641
$250$		0			0
$251$	3.57057	−	10.9891i	0.225372	−	0.693625i	−0.772881	−	0.634551i	$-0.781185\pi$
$251$	3.57057	−	10.9891i	0.225372	−	0.693625i	0.998254	−	0.0590742i	$-0.0188149\pi$
$252$		0			0
$253$	−32.2001	−	23.3948i	−2.02441	−	1.47082i
$254$		0			0
$255$	−10.2254			−0.640340
$256$		0			0
$257$	3.98181	+	12.2547i	0.248378	+	0.764430i	0.995062	+	0.0992512i	$0.0316447\pi$
$257$	3.98181	+	12.2547i	0.248378	+	0.764430i	−0.746684	+	0.665179i	$0.768355\pi$
$258$		0			0
$259$	−3.77724	+	2.74433i	−0.234707	+	0.170524i
$260$		0			0
$261$	26.4790	−	81.4938i	1.63901	−	5.04434i
$262$		0			0
$263$	3.80885	+	11.7224i	0.234864	+	0.722837i	0.997139	+	0.0755840i	$0.0240821\pi$
$263$	3.80885	+	11.7224i	0.234864	+	0.722837i	−0.762276	+	0.647253i	$0.775918\pi$
$264$		0			0
$265$	−3.82527	−	2.77922i	−0.234985	−	0.170726i
$266$		0			0
$267$	−9.52146	−	6.91775i	−0.582704	−	0.423359i
$268$		0			0
$269$	22.4571	−	16.3160i	1.36923	−	0.994806i	0.371436	−	0.928459i	$-0.378865\pi$
$269$	22.4571	−	16.3160i	1.36923	−	0.994806i	0.997797	−	0.0663473i	$-0.0211345\pi$
$270$		0			0
$271$	7.89280	+	5.73446i	0.479453	+	0.348343i	0.801114	−	0.598512i	$-0.204241\pi$
$271$	7.89280	+	5.73446i	0.479453	+	0.348343i	−0.321661	+	0.946855i	$0.604241\pi$
$272$		0			0
$273$	−34.3189			−2.07708
$274$		0			0
$275$	1.44022	−	4.43255i	0.0868487	−	0.267293i
$276$		0			0
$277$	1.76931	+	5.44537i	0.106307	+	0.327181i	0.990035	−	0.140821i	$-0.0449742\pi$
$277$	1.76931	+	5.44537i	0.106307	+	0.327181i	−0.883728	+	0.468002i	$0.844974\pi$
$278$		0			0
$279$	6.71573	+	20.6689i	0.402060	+	1.23741i
$280$		0			0
$281$	4.23818	−	3.07922i	0.252828	−	0.183691i	−0.454151	−	0.890925i	$-0.650057\pi$
$281$	4.23818	−	3.07922i	0.252828	−	0.183691i	0.706979	+	0.707234i	$0.250057\pi$
$282$		0			0
$283$	−6.29412	+	19.3713i	−0.374146	+	1.15150i	0.569906	+	0.821710i	$0.306980\pi$
$283$	−6.29412	+	19.3713i	−0.374146	+	1.15150i	−0.944053	+	0.329795i	$0.893020\pi$
$284$		0			0
$285$	14.5752	−	10.5895i	0.863359	−	0.627267i
$286$		0			0
$287$	12.8996	−	3.53020i	0.761437	−	0.208381i
$288$		0			0
$289$	6.14972	−	4.46803i	0.361748	−	0.262825i
$290$		0			0
$291$	−17.9265	+	55.1722i	−1.05087	+	3.23425i
$292$		0			0
$293$	1.22346	−	0.888896i	0.0714753	−	0.0519299i	−0.551474	−	0.834192i	$-0.685934\pi$
$293$	1.22346	−	0.888896i	0.0714753	−	0.0519299i	0.622949	+	0.782262i	$0.285934\pi$
$294$		0			0
$295$	0.278259	+	0.856393i	0.0162009	+	0.0498611i
$296$		0			0
$297$	24.6194	+	75.7709i	1.42857	+	4.39667i
$298$		0			0
$299$	−13.0003	+	40.0107i	−0.751824	+	2.31388i
$300$		0			0
$301$	−16.7980			−0.968223
$302$		0			0
$303$	−21.2804	−	15.4611i	−1.22253	−	0.888218i
$304$		0			0
$305$	6.48509	−	4.71170i	0.371335	−	0.269791i
$306$		0			0
$307$	−3.43825	−	2.49803i	−0.196231	−	0.142570i	0.485331	−	0.874331i	$-0.338699\pi$
$307$	−3.43825	−	2.49803i	−0.196231	−	0.142570i	−0.681562	+	0.731760i	$0.738699\pi$
$308$		0			0
$309$	−19.3439	−	14.0542i	−1.10044	−	0.799515i
$310$		0			0
$311$	1.28745	+	3.96238i	0.0730048	+	0.224686i	0.980900	−	0.194511i	$-0.0623119\pi$
$311$	1.28745	+	3.96238i	0.0730048	+	0.224686i	−0.907896	+	0.419196i	$0.862312\pi$
$312$		0			0
$313$	−5.62796	+	17.3211i	−0.318111	+	0.979045i	0.656344	+	0.754462i	$0.272102\pi$
$313$	−5.62796	+	17.3211i	−0.318111	+	0.979045i	−0.974455	+	0.224583i	$0.927898\pi$
$314$		0			0
$315$	13.7293	−	9.97495i	0.773560	−	0.562025i
$316$		0			0
$317$	8.24654	+	25.3802i	0.463172	+	1.42550i	0.861268	+	0.508152i	$0.169671\pi$
$317$	8.24654	+	25.3802i	0.463172	+	1.42550i	−0.398096	+	0.917344i	$0.630329\pi$
$318$		0			0
$319$	49.1519			2.75198
$320$		0			0
$321$	29.3580	+	21.3298i	1.63860	+	1.19051i
$322$		0			0
$323$	5.11702	−	15.7486i	0.284719	−	0.876274i
$324$		0			0
$325$	−4.92625			−0.273259
$326$		0			0
$327$	−45.5573			−2.51932
$328$		0			0
$329$	3.33461			0.183843
$330$		0			0
$331$	12.3659			0.679690			0.339845	−	0.940481i	$-0.389625\pi$
$331$	12.3659			0.679690			0.339845	+	0.940481i	$0.389625\pi$
$332$		0			0
$333$	5.61254	−	17.2736i	0.307565	−	0.946588i
$334$		0			0
$335$	1.72111	+	1.25046i	0.0940342	+	0.0683198i
$336$		0			0
$337$	−3.83903			−0.209125			−0.104563	−	0.994518i	$-0.533344\pi$
$337$	−3.83903			−0.209125			−0.104563	+	0.994518i	$0.533344\pi$
$338$		0			0
$339$	−20.0363	−	61.6654i	−1.08822	−	3.34920i
$340$		0			0
$341$	−10.0853	+	7.32743i	−0.546152	+	0.396802i
$342$		0			0
$343$	−6.22034	+	19.1442i	−0.335867	+	1.03369i
$344$		0			0
$345$	−8.80209	−	27.0901i	−0.473889	−	1.45848i
$346$		0			0
$347$	−10.9230	−	7.93602i	−0.586377	−	0.426028i	0.254640	−	0.967036i	$-0.418043\pi$
$347$	−10.9230	−	7.93602i	−0.586377	−	0.426028i	−0.841018	+	0.541008i	$0.818043\pi$
$348$		0			0
$349$	13.5471	+	9.84254i	0.725159	+	0.526859i	0.888028	−	0.459789i	$-0.152075\pi$
$349$	13.5471	+	9.84254i	0.725159	+	0.526859i	−0.162869	+	0.986648i	$0.552075\pi$
$350$		0			0
$351$	68.1276	−	49.4976i	3.63638	−	2.64199i
$352$		0			0
$353$	17.8128	+	12.9418i	0.948080	+	0.688821i	0.950352	−	0.311177i	$-0.100723\pi$
$353$	17.8128	+	12.9418i	0.948080	+	0.688821i	−0.00227162	+	0.999997i	$0.500723\pi$
$354$		0			0
$355$	−3.62362			−0.192322
$356$		0			0
$357$	6.59978	−	20.3120i	0.349297	−	1.07503i
$358$		0			0
$359$	1.51736	+	4.66996i	0.0800833	+	0.246471i	0.983080	−	0.183176i	$-0.0586379\pi$
$359$	1.51736	+	4.66996i	0.0800833	+	0.246471i	−0.902997	+	0.429647i	$0.858638\pi$
$360$		0			0
$361$	3.14423	+	9.67696i	0.165486	+	0.509314i
$362$		0			0
$363$	−28.9317	+	21.0201i	−1.51852	+	1.10327i
$364$		0			0
$365$	−0.672772	+	2.07058i	−0.0352145	+	0.108379i
$366$		0			0
$367$	2.57292	−	1.86933i	0.134305	−	0.0975784i	−0.518604	−	0.855014i	$-0.673548\pi$
$367$	2.57292	−	1.86933i	0.134305	−	0.0975784i	0.652909	+	0.757436i	$0.273548\pi$
$368$		0			0
$369$	−32.5249	+	40.6054i	−1.69318	+	2.11383i
$370$		0			0
$371$	7.98966	−	5.80483i	0.414803	−	0.301372i
$372$		0			0
$373$	−9.49473	+	29.2218i	−0.491619	+	1.51305i	0.330542	+	0.943791i	$0.392768\pi$
$373$	−9.49473	+	29.2218i	−0.491619	+	1.51305i	−0.822161	+	0.569255i	$0.807232\pi$
$374$		0			0
$375$	2.69841	−	1.96051i	0.139345	−	0.101240i
$376$		0			0
$377$	−16.0543	−	49.4101i	−0.826840	−	2.54475i
$378$		0			0
$379$	−3.81262	−	11.7340i	−0.195841	−	0.602737i	−0.999966	−	0.00827636i	$-0.997366\pi$
$379$	−3.81262	−	11.7340i	−0.195841	−	0.602737i	0.804125	−	0.594461i	$-0.202634\pi$
$380$		0			0
$381$	−6.09403	+	18.7555i	−0.312206	+	0.960872i
$382$		0			0
$383$	29.2716			1.49571			0.747855	−	0.663862i	$-0.231084\pi$
$383$	29.2716			1.49571			0.747855	+	0.663862i	$0.231084\pi$
$384$		0			0
$385$	7.87537	+	5.72179i	0.401366	+	0.291610i
$386$		0			0
$387$	52.8660	−	38.4094i	2.68733	−	1.95246i
$388$		0			0
$389$	12.4093	+	9.01588i	0.629176	+	0.457123i	0.856115	−	0.516786i	$-0.172872\pi$
$389$	12.4093	+	9.01588i	0.629176	+	0.457123i	−0.226938	+	0.973909i	$0.572872\pi$
$390$		0			0
$391$	−21.1807	−	15.3887i	−1.07115	−	0.778239i
$392$		0			0
$393$	−0.291243	−	0.896354i	−0.0146913	−	0.0452151i
$394$		0			0
$395$	1.53693	−	4.73017i	0.0773311	−	0.238001i
$396$		0			0
$397$	9.72585	−	7.06624i	0.488126	−	0.354644i	−0.316337	−	0.948647i	$-0.602453\pi$
$397$	9.72585	−	7.06624i	0.488126	−	0.354644i	0.804463	+	0.594002i	$0.202453\pi$
$398$		0			0
$399$	11.6280	+	35.7873i	0.582127	+	1.79160i
$400$		0			0
$401$	8.26601			0.412785			0.206392	−	0.978469i	$-0.433828\pi$
$401$	8.26601			0.412785			0.206392	+	0.978469i	$0.433828\pi$
$402$		0			0
$403$	10.6601	+	7.74499i	0.531016	+	0.385805i
$404$		0			0
$405$	−10.0867	+	31.0436i	−0.501212	+	1.54257i
$406$		0			0
$407$	10.4183			0.516418
$408$		0			0
$409$	−3.64646			−0.180306			−0.0901529	−	0.995928i	$-0.528736\pi$
$409$	−3.64646			−0.180306			−0.0901529	+	0.995928i	$0.528736\pi$
$410$		0			0
$411$	4.33146			0.213655
$412$		0			0
$413$	−1.88076			−0.0925461
$414$		0			0
$415$	4.46831	−	13.7520i	0.219341	−	0.675061i
$416$		0			0
$417$	40.4776	+	29.4087i	1.98220	+	1.44015i
$418$		0			0
$419$	0.224533			0.0109692			0.00548459	−	0.999985i	$-0.498254\pi$
$419$	0.224533			0.0109692			0.00548459	+	0.999985i	$0.498254\pi$
$420$		0			0
$421$	6.99199	+	21.5191i	0.340769	+	1.04878i	0.963810	+	0.266589i	$0.0858967\pi$
$421$	6.99199	+	21.5191i	0.340769	+	1.04878i	−0.623042	+	0.782189i	$0.714103\pi$
$422$		0			0
$423$	−10.4945	+	7.62471i	−0.510261	+	0.370726i
$424$		0			0
$425$	0.947354	−	2.91566i	0.0459534	−	0.141430i
$426$		0			0
$427$	5.17377	+	15.9232i	0.250376	+	0.770579i
$428$		0			0
$429$	61.9545	+	45.0126i	2.99119	+	2.17323i
$430$		0			0
$431$	9.86774	+	7.16933i	0.475312	+	0.345335i	0.799508	−	0.600655i	$-0.205094\pi$
$431$	9.86774	+	7.16933i	0.475312	+	0.345335i	−0.324196	+	0.945990i	$0.605094\pi$
$432$		0			0
$433$	28.4081	−	20.6397i	1.36521	−	0.991880i	0.367112	−	0.930177i	$-0.380347\pi$
$433$	28.4081	−	20.6397i	1.36521	−	0.991880i	0.998095	−	0.0617035i	$-0.0196533\pi$
$434$		0			0
$435$	28.4578	+	20.6758i	1.36445	+	0.991329i
$436$		0			0
$437$	46.1273			2.20657
$438$		0			0
$439$	6.67042	−	20.5295i	0.318362	−	0.979817i	−0.655986	−	0.754773i	$-0.727747\pi$
$439$	6.67042	−	20.5295i	0.318362	−	0.979817i	0.974348	−	0.225045i	$-0.0722528\pi$
$440$		0			0
$441$	−6.62225	−	20.3812i	−0.315345	−	0.970533i
$442$		0			0
$443$	−8.73195	−	26.8742i	−0.414867	−	1.27683i	−0.912370	−	0.409368i	$-0.865749\pi$
$443$	−8.73195	−	26.8742i	−0.414867	−	1.27683i	0.497502	−	0.867463i	$-0.334251\pi$
$444$		0			0
$445$	2.85465	−	2.07402i	0.135323	−	0.0983182i
$446$		0			0
$447$	17.3845	−	53.5040i	0.822259	−	2.53065i
$448$		0			0
$449$	−16.8159	+	12.2175i	−0.793593	+	0.576579i	−0.909028	−	0.416736i	$-0.863174\pi$
$449$	−16.8159	+	12.2175i	−0.793593	+	0.576579i	0.115435	+	0.993315i	$0.463174\pi$
$450$		0			0
$451$	−27.9172	−	10.5461i	−1.31457	−	0.496596i
$452$		0			0
$453$	19.1393	−	13.9055i	0.899240	−	0.653336i
$454$		0			0
$455$	3.17955	−	9.78564i	0.149060	−	0.458758i
$456$		0			0
$457$	5.49369	−	3.99140i	0.256984	−	0.186710i	−0.451833	−	0.892103i	$-0.649230\pi$
$457$	5.49369	−	3.99140i	0.256984	−	0.186710i	0.708816	+	0.705393i	$0.249230\pi$
$458$		0			0
$459$	16.1942	+	49.8408i	0.755883	+	2.32637i
$460$		0			0
$461$	7.67147	+	23.6103i	0.357296	+	1.09964i	0.954666	+	0.297678i	$0.0962122\pi$
$461$	7.67147	+	23.6103i	0.357296	+	1.09964i	−0.597371	+	0.801965i	$0.703788\pi$
$462$		0			0
$463$	0.862331	−	2.65398i	0.0400759	−	0.123341i	−0.929017	−	0.370037i	$-0.879345\pi$
$463$	0.862331	−	2.65398i	0.0400759	−	0.123341i	0.969093	+	0.246696i	$0.0793449\pi$
$464$		0			0
$465$	−8.92147			−0.413723
$466$		0			0
$467$	9.45879	+	6.87221i	0.437700	+	0.318008i	0.784721	−	0.619850i	$-0.212806\pi$
$467$	9.45879	+	6.87221i	0.437700	+	0.318008i	−0.347020	+	0.937858i	$0.612806\pi$
$468$		0			0
$469$	−3.59480	+	2.61177i	−0.165992	+	0.120600i
$470$		0			0
$471$	−0.530189	−	0.385205i	−0.0244298	−	0.0177493i
$472$		0			0
$473$	30.3248	+	22.0322i	1.39434	+	1.01304i
$474$		0			0
$475$	1.66912	+	5.13702i	0.0765845	+	0.235703i
$476$		0			0
$477$	−11.8717	+	36.5373i	−0.543567	+	1.67293i
$478$		0			0
$479$	−3.85685	+	2.80216i	−0.176224	+	0.128034i	−0.672401	−	0.740187i	$-0.734737\pi$
$479$	−3.85685	+	2.80216i	−0.176224	+	0.128034i	0.496177	+	0.868221i	$0.334737\pi$
$480$		0			0
$481$	−3.40291	−	10.4731i	−0.155159	−	0.477531i
$482$		0			0
$483$	59.4935			2.70705
$484$		0			0
$485$	−14.0709	−	10.2231i	−0.638925	−	0.464206i
$486$		0			0
$487$	−10.1656	+	31.2864i	−0.460646	+	1.41772i	0.403730	+	0.914878i	$0.367713\pi$
$487$	−10.1656	+	31.2864i	−0.460646	+	1.41772i	−0.864376	+	0.502845i	$0.832287\pi$
$488$		0			0
$489$	−59.2910			−2.68123
$490$		0			0
$491$	−5.26471			−0.237593			−0.118796	−	0.992919i	$-0.537904\pi$
$491$	−5.26471			−0.237593			−0.118796	+	0.992919i	$0.537904\pi$
$492$		0			0
$493$	32.3313			1.45613
$494$		0			0
$495$	−37.8681			−1.70204
$496$		0			0
$497$	2.33879	−	7.19805i	0.104909	−	0.322877i
$498$		0			0
$499$	−9.14446	−	6.64384i	−0.409362	−	0.297419i	0.363981	−	0.931406i	$-0.381417\pi$
$499$	−9.14446	−	6.64384i	−0.409362	−	0.297419i	−0.773343	+	0.633987i	$0.781417\pi$
$500$		0			0
$501$	−9.03665			−0.403728
$502$		0			0
$503$	8.44803	+	26.0004i	0.376679	+	1.15930i	0.942339	+	0.334660i	$0.108622\pi$
$503$	8.44803	+	26.0004i	0.376679	+	1.15930i	−0.565660	+	0.824639i	$0.691378\pi$
$504$		0			0
$505$	6.38013	−	4.63543i	0.283912	−	0.206274i
$506$		0			0
$507$	11.6139	−	35.7440i	0.515793	−	1.58745i
$508$		0			0
$509$	3.45003	+	10.6181i	0.152920	+	0.470639i	0.997944	−	0.0640886i	$-0.0204140\pi$
$509$	3.45003	+	10.6181i	0.152920	+	0.470639i	−0.845024	+	0.534728i	$0.820414\pi$
$510$		0			0
$511$	−3.67882	−	2.67282i	−0.162742	−	0.118239i
$512$		0			0
$513$	−74.6984	−	54.2716i	−3.29801	−	2.39615i
$514$		0			0
$515$	5.79954	−	4.21361i	0.255558	−	0.185674i
$516$		0			0
$517$	−6.01983	−	4.37366i	−0.264752	−	0.192353i
$518$		0			0
$519$	39.4873			1.73330
$520$		0			0
$521$	7.87727	−	24.2438i	0.345110	−	1.06214i	−0.616416	−	0.787421i	$-0.711416\pi$
$521$	7.87727	−	24.2438i	0.345110	−	1.06214i	0.961525	−	0.274717i	$-0.0885842\pi$
$522$		0			0
$523$	−3.68459	−	11.3400i	−0.161116	−	0.495864i	0.837613	−	0.546264i	$-0.183950\pi$
$523$	−3.68459	−	11.3400i	−0.161116	−	0.495864i	−0.998729	+	0.0504001i	$0.983950\pi$
$524$		0			0
$525$	2.15278	+	6.62557i	0.0939550	+	0.289164i
$526$		0			0
$527$	−6.63396	+	4.81985i	−0.288980	+	0.209956i
$528$		0			0
$529$	15.4292	−	47.4861i	0.670833	−	2.06461i
$530$		0			0
$531$	5.91903	−	4.30042i	0.256864	−	0.186622i
$532$		0			0
$533$	−1.48299	+	31.5085i	−0.0642355	+	1.36479i
$534$		0			0
$535$	−8.80188	+	6.39494i	−0.380538	+	0.276477i
$536$		0			0
$537$	−15.6297	+	48.1031i	−0.674470	+	2.07580i
$538$		0			0
$539$	9.94495	−	7.22543i	0.428360	−	0.311221i
$540$		0			0
$541$	2.25833	+	6.95043i	0.0970933	+	0.298823i	0.987794	−	0.155769i	$-0.0497854\pi$
$541$	2.25833	+	6.95043i	0.0970933	+	0.298823i	−0.890700	+	0.454591i	$0.849785\pi$
$542$		0			0
$543$	−8.93010	−	27.4840i	−0.383227	−	1.17945i
$544$		0			0
$545$	4.22075	−	12.9901i	0.180797	−	0.556436i
$546$		0			0
$547$	9.80378			0.419179			0.209590	−	0.977789i	$-0.432787\pi$
$547$	9.80378			0.419179			0.209590	+	0.977789i	$0.432787\pi$
$548$		0			0
$549$	−52.6917	−	38.2827i	−2.24883	−	1.63387i
$550$		0			0
$551$	−46.0846	+	33.4824i	−1.96327	+	1.42640i
$552$		0			0
$553$	8.40416	+	6.10598i	0.357381	+	0.259653i
$554$		0			0
$555$	6.03198	+	4.38249i	0.256043	+	0.186026i
$556$		0			0
$557$	−10.2160	−	31.4416i	−0.432865	−	1.33222i	−0.895258	−	0.445548i	$-0.853009\pi$
$557$	−10.2160	−	31.4416i	−0.432865	−	1.33222i	0.462393	−	0.886675i	$-0.346991\pi$
$558$		0			0
$559$	12.2431	−	37.6804i	0.517829	−	1.59371i
$560$		0			0
$561$	−38.5555	+	28.0122i	−1.62781	+	1.18268i
$562$		0			0
$563$	−0.534193	−	1.64408i	−0.0225135	−	0.0692896i	0.939169	−	0.343457i	$-0.111598\pi$
$563$	−0.534193	−	1.64408i	−0.0225135	−	0.0692896i	−0.961682	+	0.274167i	$0.911598\pi$
$564$		0			0
$565$	19.4395			0.817824
$566$		0			0
$567$	−55.1557	−	40.0729i	−2.31632	−	1.68290i
$568$		0			0
$569$	6.71066	−	20.6533i	0.281325	−	0.865830i	−0.706151	−	0.708062i	$-0.749570\pi$
$569$	6.71066	−	20.6533i	0.281325	−	0.865830i	0.987476	−	0.157769i	$-0.0504301\pi$
$570$		0			0
$571$	−26.1499			−1.09434			−0.547169	−	0.837022i	$-0.684295\pi$
$571$	−26.1499			−1.09434			−0.547169	+	0.837022i	$0.684295\pi$
$572$		0			0
$573$	−46.4522			−1.94057
$574$		0			0
$575$	8.53990			0.356138
$576$		0			0
$577$	−36.1356			−1.50434			−0.752172	−	0.658967i	$-0.770994\pi$
$577$	−36.1356			−1.50434			−0.752172	+	0.658967i	$0.770994\pi$
$578$		0			0
$579$	−2.36456	+	7.27736i	−0.0982676	+	0.302437i
$580$		0			0
$581$	24.4334	+	17.7519i	1.01367	+	0.736474i
$582$		0			0
$583$	−22.0370			−0.912678
$584$		0			0
$585$	12.3687	+	38.0670i	0.511384	+	1.57388i
$586$		0			0
$587$	−2.43422	+	1.76856i	−0.100471	+	0.0729964i	−0.636886	−	0.770958i	$-0.719778\pi$
$587$	−2.43422	+	1.76856i	−0.100471	+	0.0729964i	0.536416	+	0.843954i	$0.319778\pi$
$588$		0			0
$589$	4.46450	−	13.7403i	0.183957	−	0.566160i
$590$		0			0
$591$	−2.28305	−	7.02649i	−0.0939119	−	0.289031i
$592$		0			0
$593$	−15.7878	−	11.4705i	−0.648327	−	0.471037i	0.214374	−	0.976752i	$-0.431229\pi$
$593$	−15.7878	−	11.4705i	−0.648327	−	0.471037i	−0.862701	+	0.505715i	$0.831229\pi$
$594$		0			0
$595$	5.18029	+	3.76370i	0.212371	+	0.154297i
$596$		0			0
$597$	−17.6779	+	12.8438i	−0.723510	+	0.525661i
$598$		0			0
$599$	−35.6648	−	25.9120i	−1.45722	−	1.05873i	−0.984075	−	0.177752i	$-0.943118\pi$
$599$	−35.6648	−	25.9120i	−1.45722	−	1.05873i	−0.473148	−	0.880983i	$-0.656882\pi$
$600$		0			0
$601$	38.2332			1.55956			0.779782	−	0.626051i	$-0.215330\pi$
$601$	38.2332			1.55956			0.779782	+	0.626051i	$0.215330\pi$
$602$		0			0
$603$	5.34144	−	16.4393i	0.217520	−	0.669459i
$604$		0			0
$605$	−3.31320	−	10.1970i	−0.134701	−	0.414567i
$606$		0			0
$607$	2.57731	+	7.93214i	0.104610	+	0.321956i	0.989639	−	0.143580i	$-0.0458616\pi$
$607$	2.57731	+	7.93214i	0.104610	+	0.321956i	−0.885029	+	0.465536i	$0.845862\pi$
$608$		0			0
$609$	−59.4384	+	43.1846i	−2.40857	+	1.74993i
$610$		0			0
$611$	−2.43040	+	7.48001i	−0.0983235	+	0.302609i
$612$		0			0
$613$	−2.05084	+	1.49002i	−0.0828325	+	0.0601814i	−0.628431	−	0.777866i	$-0.716302\pi$
$613$	−2.05084	+	1.49002i	−0.0828325	+	0.0601814i	0.545598	+	0.838047i	$0.316302\pi$
$614$		0			0
$615$	−11.7272	−	17.8494i	−0.472886	−	0.719756i
$616$		0			0
$617$	−5.81819	+	4.22716i	−0.234232	+	0.170179i	−0.698710	−	0.715405i	$-0.746242\pi$
$617$	−5.81819	+	4.22716i	−0.234232	+	0.170179i	0.464478	+	0.885585i	$0.346242\pi$
$618$		0			0
$619$	−2.01414	+	6.19889i	−0.0809552	+	0.249154i	−0.983340	−	0.181777i	$-0.941815\pi$
$619$	−2.01414	+	6.19889i	−0.0809552	+	0.249154i	0.902385	+	0.430932i	$0.141815\pi$
$620$		0			0
$621$	−118.102	+	85.8064i	−4.73929	+	3.44329i
$622$		0			0
$623$	2.27742	+	7.00918i	0.0912430	+	0.280817i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$		0			0
$627$	25.9469	−	79.8564i	1.03622	−	3.18916i
$628$		0			0
$629$	6.85301			0.273247
$630$		0			0
$631$	16.6157	+	12.0720i	0.661461	+	0.480580i	0.867156	−	0.498037i	$-0.165945\pi$
$631$	16.6157	+	12.0720i	0.661461	+	0.480580i	−0.205695	+	0.978616i	$0.565945\pi$
$632$		0			0
$633$	67.5422	−	49.0723i	2.68456	−	1.95045i
$634$		0			0
$635$	−4.78331	−	3.47528i	−0.189820	−	0.137912i
$636$		0			0
$637$	−10.5117	−	7.63718i	−0.416488	−	0.302596i
$638$		0			0
$639$	9.09809	+	28.0011i	0.359915	+	1.10770i
$640$		0			0
$641$	−9.92677	+	30.5514i	−0.392084	+	1.20671i	0.539126	+	0.842225i	$0.318755\pi$
$641$	−9.92677	+	30.5514i	−0.392084	+	1.20671i	−0.931210	+	0.364484i	$0.881245\pi$
$642$		0			0
$643$	−10.1087	+	7.34438i	−0.398647	+	0.289634i	−0.768990	−	0.639261i	$-0.779240\pi$
$643$	−10.1087	+	7.34438i	−0.398647	+	0.289634i	0.370343	+	0.928895i	$0.379240\pi$
$644$		0			0
$645$	8.28945	+	25.5123i	0.326397	+	1.00455i
$646$		0			0
$647$	−25.7019			−1.01045			−0.505223	−	0.862989i	$-0.668590\pi$
$647$	−25.7019			−1.01045			−0.505223	+	0.862989i	$0.668590\pi$
$648$		0			0
$649$	3.39525	+	2.46679i	0.133275	+	0.0968301i
$650$		0			0
$651$	5.75817	−	17.7218i	0.225681	−	0.694573i
$652$		0			0
$653$	−29.9489			−1.17199			−0.585995	−	0.810315i	$-0.699296\pi$
$653$	−29.9489			−1.17199			−0.585995	+	0.810315i	$0.699296\pi$
$654$		0			0
$655$	0.282568			0.0110408
$656$		0			0
$657$	17.6893			0.690126
$658$		0			0
$659$	43.5367			1.69595			0.847974	−	0.530038i	$-0.177822\pi$
$659$	43.5367			1.69595			0.847974	+	0.530038i	$0.177822\pi$
$660$		0			0
$661$	−11.8803	+	36.5639i	−0.462092	+	1.42217i	0.400512	+	0.916292i	$0.368832\pi$
$661$	−11.8803	+	36.5639i	−0.462092	+	1.42217i	−0.862603	+	0.505881i	$0.831168\pi$
$662$		0			0
$663$	40.7526	+	29.6085i	1.58270	+	1.14990i
$664$		0			0
$665$	−11.2816			−0.437482
$666$		0			0
$667$	27.8309	+	85.6548i	1.07762	+	3.31657i
$668$		0			0
$669$	17.0708	−	12.4026i	0.659995	−	0.479514i
$670$		0			0
$671$	11.5449	−	35.5314i	0.445684	−	1.37167i
$672$		0			0
$673$	1.77591	+	5.46570i	0.0684564	+	0.210687i	0.979433	−	0.201772i	$-0.0646700\pi$
$673$	1.77591	+	5.46570i	0.0684564	+	0.210687i	−0.910976	+	0.412459i	$0.864670\pi$
$674$		0			0
$675$	−13.8295	−	10.0477i	−0.532297	−	0.386737i
$676$		0			0
$677$	14.9671	+	10.8743i	0.575233	+	0.417931i	0.837003	−	0.547199i	$-0.184306\pi$
$677$	14.9671	+	10.8743i	0.575233	+	0.417931i	−0.261769	+	0.965131i	$0.584306\pi$
$678$		0			0
$679$	29.3892	−	21.3525i	1.12785	−	0.819433i
$680$		0			0
$681$	26.9445	+	19.5763i	1.03252	+	0.750167i
$682$		0			0
$683$	11.7416			0.449280			0.224640	−	0.974442i	$-0.427879\pi$
$683$	11.7416			0.449280			0.224640	+	0.974442i	$0.427879\pi$
$684$		0			0
$685$	−0.401297	+	1.23506i	−0.0153328	+	0.0471894i
$686$		0			0
$687$	−11.1879	−	34.4329i	−0.426847	−	1.31370i
$688$		0			0
$689$	7.19787	+	22.1528i	0.274217	+	0.843953i
$690$		0			0
$691$	17.2683	−	12.5461i	0.656915	−	0.477277i	−0.208705	−	0.977979i	$-0.566925\pi$
$691$	17.2683	−	12.5461i	0.656915	−	0.477277i	0.865620	+	0.500702i	$0.166925\pi$
$692$		0			0
$693$	24.4412	−	75.2221i	0.928443	−	2.85745i
$694$		0			0
$695$	−12.1357	+	8.81709i	−0.460333	+	0.334451i
$696$		0			0
$697$	−18.3635	−	6.93704i	−0.695566	−	0.262759i
$698$		0			0
$699$	−15.4832	+	11.2492i	−0.585628	+	0.425484i
$700$		0			0
$701$	14.8791	−	45.7931i	0.561975	−	1.72958i	−0.114798	−	0.993389i	$-0.536622\pi$
$701$	14.8791	−	45.7931i	0.561975	−	1.72958i	0.676773	−	0.736192i	$-0.263378\pi$
$702$		0			0
$703$	−9.76819	+	7.09700i	−0.368414	+	0.267669i
$704$		0			0
$705$	−1.64555	−	5.06449i	−0.0619751	−	0.190740i
$706$		0			0
$707$	5.09003	+	15.6655i	0.191430	+	0.589161i
$708$		0			0
$709$	7.32742	−	22.5515i	0.275187	−	0.846939i	−0.713983	−	0.700163i	$-0.753111\pi$
$709$	7.32742	−	22.5515i	0.275187	−	0.846939i	0.989170	−	0.146775i	$-0.0468895\pi$
$710$		0			0
$711$	−40.4107			−1.51552
$712$		0			0
$713$	−18.4797	−	13.4263i	−0.692071	−	0.502819i
$714$		0			0
$715$	−18.5747	+	13.4953i	−0.694655	+	0.504696i
$716$		0			0
$717$	14.7879	+	10.7440i	0.552265	+	0.401244i
$718$		0			0
$719$	30.0373	+	21.8233i	1.12020	+	0.813874i	0.984240	−	0.176841i	$-0.0565877\pi$
$719$	30.0373	+	21.8233i	1.12020	+	0.813874i	0.135961	+	0.990714i	$0.456588\pi$
$720$		0			0
$721$	4.62684	+	14.2400i	0.172313	+	0.530324i
$722$		0			0
$723$	10.7336	−	33.0346i	0.399186	−	1.22857i
$724$		0			0
$725$	−8.53199	+	6.19885i	−0.316870	+	0.230220i
$726$		0			0
$727$	4.23471	+	13.0331i	0.157057	+	0.483370i	0.998363	−	0.0571873i	$-0.0182132\pi$
$727$	4.23471	+	13.0331i	0.157057	+	0.483370i	−0.841307	+	0.540558i	$0.818213\pi$
$728$		0			0
$729$	94.1623			3.48749
$730$		0			0
$731$	19.9471	+	14.4924i	0.737771	+	0.536022i
$732$		0			0
$733$	−5.12741	+	15.7805i	−0.189385	+	0.582867i	−0.999996	−	0.00271745i	$-0.999135\pi$
$733$	−5.12741	+	15.7805i	−0.189385	+	0.582867i	0.810611	+	0.585585i	$0.199135\pi$
$734$		0			0
$735$	8.79728			0.324493
$736$		0			0
$737$	9.91512			0.365228
$738$		0			0
$739$	5.19391			0.191061			0.0955305	−	0.995427i	$-0.469545\pi$
$739$	5.19391			0.191061			0.0955305	+	0.995427i	$0.469545\pi$
$740$		0			0
$741$	−88.7509			−3.26035
$742$		0			0
$743$	−3.13542	+	9.64982i	−0.115027	+	0.354018i	−0.991953	−	0.126609i	$-0.959591\pi$
$743$	−3.13542	+	9.64982i	−0.115027	+	0.354018i	0.876925	+	0.480627i	$0.159591\pi$
$744$		0			0
$745$	13.6454	+	9.91398i	0.499929	+	0.363220i
$746$		0			0
$747$	−117.486			−4.29859
$748$		0			0
$749$	−7.02209	−	21.6118i	−0.256581	−	0.789677i
$750$		0			0
$751$	−39.5434	+	28.7300i	−1.44296	+	1.04837i	−0.455547	+	0.890212i	$0.650556\pi$
$751$	−39.5434	+	28.7300i	−1.44296	+	1.04837i	−0.987413	+	0.158160i	$0.949444\pi$
$752$		0			0
$753$	11.9094	−	36.6532i	0.434001	−	1.33572i
$754$		0			0
$755$	2.19179	+	6.74563i	0.0797674	+	0.245499i
$756$		0			0
$757$	30.2686	+	21.9914i	1.10013	+	0.799292i	0.981081	−	0.193596i	$-0.0620151\pi$
$757$	30.2686	+	21.9914i	1.10013	+	0.799292i	0.119050	+	0.992888i	$0.462015\pi$
$758$		0			0
$759$	−107.401	−	78.0314i	−3.89841	−	2.83236i
$760$		0			0
$761$	5.24832	−	3.81313i	0.190251	−	0.138226i	−0.488582	−	0.872518i	$-0.662486\pi$
$761$	5.24832	−	3.81313i	0.190251	−	0.138226i	0.678834	+	0.734292i	$0.262486\pi$
$762$		0			0
$763$	23.0797	+	16.7684i	0.835542	+	0.607057i
$764$		0			0
$765$	−24.9090			−0.900585
$766$		0			0
$767$	1.37077	−	4.21881i	0.0494958	−	0.152332i
$768$		0			0
$769$	−13.0012	−	40.0136i	−0.468835	−	1.44293i	−0.854094	−	0.520119i	$-0.825888\pi$
$769$	−13.0012	−	40.0136i	−0.468835	−	1.44293i	0.385259	−	0.922809i	$-0.374112\pi$
$770$		0			0
$771$	13.2810	+	40.8748i	0.478304	+	1.47207i
$772$		0			0
$773$	−28.7605	+	20.8957i	−1.03444	+	0.751567i	−0.969193	−	0.246301i	$-0.920785\pi$
$773$	−28.7605	+	20.8957i	−1.03444	+	0.751567i	−0.0652506	+	0.997869i	$0.520785\pi$
$774$		0			0
$775$	0.826547	−	2.54385i	0.0296905	−	0.0913778i
$776$		0			0
$777$	−12.5987	+	9.15349i	−0.451976	+	0.328380i
$778$		0			0
$779$	33.3591	−	9.12932i	1.19521	−	0.327092i
$780$		0			0
$781$	−13.6630	+	9.92678i	−0.488902	+	0.355208i
$782$		0			0
$783$	55.7088	−	171.454i	1.99087	−	6.12727i
$784$		0			0
$785$	0.158957	−	0.115489i	0.00567343	−	0.00412198i
$786$		0			0
$787$	−5.65684	−	17.4100i	−0.201645	−	0.620598i	−0.999835	−	0.0181924i	$-0.994209\pi$
$787$	−5.65684	−	17.4100i	−0.201645	−	0.620598i	0.798190	−	0.602406i	$-0.205791\pi$
$788$		0			0
$789$	12.7041	+	39.0993i	0.452279	+	1.39197i
$790$		0			0
$791$	−12.5468	+	38.6151i	−0.446113	+	1.37299i
$792$		0			0
$793$	−39.4889			−1.40229
$794$		0			0
$795$	−12.7589	−	9.26988i	−0.452511	−	0.328769i
$796$		0			0
$797$	5.86018	−	4.25767i	0.207578	−	0.150814i	−0.479139	−	0.877739i	$-0.659051\pi$
$797$	5.86018	−	4.25767i	0.207578	−	0.150814i	0.686717	+	0.726925i	$0.259051\pi$
$798$		0			0
$799$	−3.95974	−	2.87692i	−0.140085	−	0.101778i
$800$		0			0
$801$	−23.1941	−	16.8515i	−0.819525	−	0.595420i
$802$		0			0
$803$	3.13556	+	9.65026i	0.110651	+	0.340550i
$804$		0			0
$805$	−5.51190	+	16.9639i	−0.194269	+	0.597898i
$806$		0			0
$807$	74.9039	−	54.4209i	2.63674	−	1.91570i
$808$		0			0
$809$	3.50044	+	10.7732i	0.123069	+	0.378767i	0.993544	−	0.113445i	$-0.0361886\pi$
$809$	3.50044	+	10.7732i	0.123069	+	0.378767i	−0.870475	+	0.492212i	$0.836189\pi$
$810$		0			0
$811$	54.3313			1.90783			0.953916	−	0.300074i	$-0.0970115\pi$
$811$	54.3313			1.90783			0.953916	+	0.300074i	$0.0970115\pi$
$812$		0			0
$813$	26.3258	+	19.1268i	0.923287	+	0.670807i
$814$		0			0
$815$	5.49313	−	16.9061i	0.192416	−	0.592196i
$816$		0			0
$817$	−43.4408			−1.51980
$818$		0			0
$819$	−83.6005			−2.92124
$820$		0			0
$821$	21.8549			0.762742			0.381371	−	0.924422i	$-0.375452\pi$
$821$	21.8549			0.762742			0.381371	+	0.924422i	$0.375452\pi$
$822$		0			0
$823$	32.2458			1.12402			0.562009	−	0.827131i	$-0.310029\pi$
$823$	32.2458			1.12402			0.562009	+	0.827131i	$0.310029\pi$
$824$		0			0
$825$	4.80375	−	14.7844i	0.167245	−	0.514728i
$826$		0			0
$827$	21.5312	+	15.6433i	0.748714	+	0.543972i	0.895428	−	0.445207i	$-0.146870\pi$
$827$	21.5312	+	15.6433i	0.748714	+	0.543972i	−0.146714	+	0.989179i	$0.546870\pi$
$828$		0			0
$829$	25.6128			0.889570			0.444785	−	0.895637i	$-0.353280\pi$
$829$	25.6128			0.889570			0.444785	+	0.895637i	$0.353280\pi$
$830$		0			0
$831$	5.90139	+	18.1626i	0.204717	+	0.630054i
$832$		0			0
$833$	6.54162	−	4.75276i	0.226654	−	0.164674i
$834$		0			0
$835$	0.837219	−	2.57669i	0.0289732	−	0.0891702i
$836$		0			0
$837$	14.1292	+	43.4851i	0.488375	+	1.50306i
$838$		0			0
$839$	−18.0619	−	13.1227i	−0.623565	−	0.453047i	0.230600	−	0.973049i	$-0.425931\pi$
$839$	−18.0619	−	13.1227i	−0.623565	−	0.453047i	−0.854165	+	0.520002i	$0.825931\pi$
$840$		0			0
$841$	−66.5179	−	48.3281i	−2.29372	−	1.66649i
$842$		0			0
$843$	14.1361	−	10.2705i	0.486873	−	0.353734i
$844$		0			0
$845$	9.11599	+	6.62316i	0.313600	+	0.227844i
$846$		0			0
$847$	22.3940			0.769467
$848$		0			0
$849$	−20.9935	+	64.6115i	−0.720497	+	2.21746i
$850$		0			0
$851$	5.89911	+	18.1556i	0.202219	+	0.622365i
$852$		0			0
$853$	−1.07527	−	3.30936i	−0.0368167	−	0.113310i	0.930959	−	0.365123i	$-0.118973\pi$
$853$	−1.07527	−	3.30936i	−0.0368167	−	0.113310i	−0.967776	+	0.251813i	$0.918973\pi$
$854$		0			0
$855$	35.5049	−	25.7958i	1.21424	−	0.882199i
$856$		0			0
$857$	17.0710	−	52.5390i	0.583133	−	1.79470i	−0.0235106	−	0.999724i	$-0.507484\pi$
$857$	17.0710	−	52.5390i	0.583133	−	1.79470i	0.606643	−	0.794974i	$-0.292516\pi$
$858$		0			0
$859$	1.03047	−	0.748680i	0.0351591	−	0.0255446i	−0.570067	−	0.821598i	$-0.693083\pi$
$859$	1.03047	−	0.748680i	0.0351591	−	0.0255446i	0.605226	+	0.796054i	$0.293083\pi$
$860$		0			0
$861$	43.0255	−	11.7747i	1.46631	−	0.401281i
$862$		0			0
$863$	−31.8678	+	23.1533i	−1.08479	+	0.788147i	−0.978512	−	0.206189i	$-0.933894\pi$
$863$	−31.8678	+	23.1533i	−1.08479	+	0.788147i	−0.106279	+	0.994336i	$0.533894\pi$
$864$		0			0
$865$	−3.65838	+	11.2593i	−0.124389	+	0.382829i
$866$		0			0
$867$	20.5119	−	14.9028i	0.696621	−	0.506125i
$868$		0			0
$869$	−7.16309	−	22.0457i	−0.242991	−	0.747850i
$870$		0			0
$871$	−3.23854	−	9.96721i	−0.109734	−	0.337726i
$872$		0			0
$873$	−43.6688	+	134.399i	−1.47797	+	4.54871i
$874$		0			0
$875$	−2.08865			−0.0706093
$876$		0			0
$877$	−6.61692	−	4.80748i	−0.223438	−	0.162337i	0.470435	−	0.882435i	$-0.344097\pi$
$877$	−6.61692	−	4.80748i	−0.223438	−	0.162337i	−0.693873	+	0.720098i	$0.744097\pi$
$878$		0			0
$879$	4.08076	−	2.96484i	0.137641	−	0.100002i
$880$		0			0
$881$	20.3449	+	14.7814i	0.685436	+	0.497999i	0.875157	−	0.483840i	$-0.160758\pi$
$881$	20.3449	+	14.7814i	0.685436	+	0.497999i	−0.189720	+	0.981838i	$0.560758\pi$
$882$		0			0
$883$	−36.7804	−	26.7225i	−1.23776	−	0.899285i	−0.240312	−	0.970696i	$-0.577250\pi$
$883$	−36.7804	−	26.7225i	−1.23776	−	0.899285i	−0.997447	+	0.0714110i	$0.977250\pi$
$884$		0			0
$885$	0.928111	+	2.85643i	0.0311981	+	0.0960179i
$886$		0			0
$887$	−2.90142	+	8.92964i	−0.0974201	+	0.299828i	−0.987877	−	0.155240i	$-0.950385\pi$
$887$	−2.90142	+	8.92964i	−0.0974201	+	0.299828i	0.890457	+	0.455068i	$0.150385\pi$
$888$		0			0
$889$	9.99067	−	7.25865i	0.335076	−	0.243447i
$890$		0			0
$891$	47.0106	+	144.684i	1.57492	+	4.84709i
$892$		0			0
$893$	8.62351			0.288575
$894$		0			0
$895$	−12.2680	−	8.91323i	−0.410074	−	0.297936i
$896$		0			0
$897$	−43.3613	+	133.452i	−1.44779	+	4.45585i
$898$		0			0
$899$	28.2084			0.940802
$900$		0			0
$901$	−14.4955			−0.482917
$902$		0			0
$903$	−56.0286			−1.86451
$904$		0			0
$905$	8.66409			0.288004
$906$		0			0
$907$	5.34193	−	16.4408i	0.177376	−	0.545907i	−0.822358	−	0.568970i	$-0.807342\pi$
$907$	5.34193	−	16.4408i	0.177376	−	0.545907i	0.999734	+	0.0230633i	$0.00734192\pi$
$908$		0			0
$909$	−51.8388	−	37.6631i	−1.71938	−	1.24921i
$910$		0			0
$911$	−54.5483			−1.80727			−0.903633	−	0.428307i	$-0.859110\pi$
$911$	−54.5483			−1.80727			−0.903633	+	0.428307i	$0.859110\pi$
$912$		0			0
$913$	−20.8253	−	64.0936i	−0.689216	−	2.12119i
$914$		0			0
$915$	21.6305	−	15.7155i	0.715083	−	0.519538i
$916$		0			0
$917$	−0.182377	+	0.561300i	−0.00602263	+	0.0185357i
$918$		0			0
$919$	−2.65635	−	8.17539i	−0.0876248	−	0.269681i	0.897637	−	0.440736i	$-0.145283\pi$
$919$	−2.65635	−	8.17539i	−0.0876248	−	0.269681i	−0.985262	+	0.171055i	$0.945283\pi$
$920$		0			0
$921$	−11.4680	−	8.33200i	−0.377884	−	0.274549i
$922$		0			0
$923$	14.4417	+	10.4925i	0.475353	+	0.345364i
$924$		0			0
$925$	−1.80846	+	1.31392i	−0.0594618	+	0.0432015i
$926$		0			0
$927$	−47.1215	−	34.2358i	−1.54767	−	1.12445i
$928$		0			0
$929$	29.4749			0.967041			0.483520	−	0.875333i	$-0.339358\pi$
$929$	29.4749			0.967041			0.483520	+	0.875333i	$0.339358\pi$
$930$		0			0
$931$	−4.40236	+	13.5491i	−0.144281	+	0.444052i
$932$		0			0
$933$	4.29420	+	13.2162i	0.140586	+	0.432679i
$934$		0			0
$935$	−4.41529	−	13.5889i	−0.144396	−	0.444404i
$936$		0			0
$937$	42.0020	−	30.5162i	1.37215	−	0.996922i	0.374579	−	0.927195i	$-0.377787\pi$
$937$	42.0020	−	30.5162i	1.37215	−	0.996922i	0.997566	−	0.0697268i	$-0.0222128\pi$
$938$		0			0
$939$	−18.7716	+	57.7731i	−0.612589	+	1.88535i
$940$		0			0
$941$	22.9438	−	16.6697i	0.747947	−	0.543416i	−0.147243	−	0.989100i	$-0.547040\pi$
$941$	22.9438	−	16.6697i	0.747947	−	0.543416i	0.895190	+	0.445685i	$0.147040\pi$
$942$		0			0
$943$	2.57083	−	54.6216i	0.0837179	−	1.77872i
$944$		0			0
$945$	28.8850	−	20.9862i	0.939629	−	0.682680i
$946$		0			0
$947$	2.34187	−	7.20753i	0.0761005	−	0.234213i	−0.905769	−	0.423772i	$-0.860706\pi$
$947$	2.34187	−	7.20753i	0.0761005	−	0.234213i	0.981869	+	0.189559i	$0.0607057\pi$
$948$		0			0
$949$	8.67680	−	6.30407i	0.281661	−	0.204639i
$950$		0			0
$951$	27.5057	+	84.6538i	0.891933	+	2.74509i
$952$		0			0
$953$	3.17955	+	9.78565i	0.102996	+	0.316988i	0.989255	−	0.146202i	$-0.0467048\pi$
$953$	3.17955	+	9.78565i	0.102996	+	0.316988i	−0.886259	+	0.463190i	$0.846705\pi$
$954$		0			0
$955$	4.30366	−	13.2453i	0.139263	−	0.428608i
$956$		0			0
$957$	163.942			5.29950
$958$		0			0
$959$	−2.19436	−	1.59429i	−0.0708594	−	0.0514824i
$960$		0			0
$961$	19.2915	−	14.0161i	0.622307	−	0.452133i
$962$		0			0
$963$	71.5156	+	51.9592i	2.30456	+	1.67436i
$964$		0			0
$965$	−1.85598	−	1.34845i	−0.0597462	−	0.0434082i
$966$		0			0
$967$	−3.28081	−	10.0973i	−0.105504	−	0.324707i	0.884345	−	0.466835i	$-0.154606\pi$
$967$	−3.28081	−	10.0973i	−0.105504	−	0.324707i	−0.989848	+	0.142128i	$0.954606\pi$
$968$		0			0
$969$	17.0674	−	52.5282i	0.548285	−	1.68745i
$970$		0			0
$971$	−36.4545	+	26.4858i	−1.16988	+	0.849969i	−0.990995	−	0.133901i	$-0.957250\pi$
$971$	−36.4545	+	26.4858i	−1.16988	+	0.849969i	−0.178887	+	0.983870i	$0.557250\pi$
$972$		0			0
$973$	−9.68177	−	29.7974i	−0.310383	−	0.955262i
$974$		0			0
$975$	−16.4311			−0.526218
$976$		0			0
$977$	−47.2187	−	34.3064i	−1.51066	−	1.09756i	−0.965883	−	0.258979i	$-0.916614\pi$
$977$	−47.2187	−	34.3064i	−1.51066	−	1.09756i	−0.544778	−	0.838580i	$-0.683386\pi$
$978$		0			0
$979$	5.08188	−	15.6404i	0.162418	−	0.499870i
$980$		0			0
$981$	−110.977			−3.54322
$982$		0			0
$983$	0.907982			0.0289601			0.0144801	−	0.999895i	$-0.495391\pi$
$983$	0.907982			0.0289601			0.0144801	+	0.999895i	$0.495391\pi$
$984$		0			0
$985$	2.21504			0.0705770
$986$		0			0
$987$	11.1223			0.354028
$988$		0			0
$989$	−21.2240	+	65.3208i	−0.674885	+	2.07708i
$990$		0			0
$991$	33.8655	+	24.6047i	1.07577	+	0.781595i	0.976941	−	0.213509i	$-0.0684892\pi$
$991$	33.8655	+	24.6047i	1.07577	+	0.781595i	0.0988324	+	0.995104i	$0.468489\pi$
$992$		0			0
$993$	41.2454			1.30888
$994$		0			0
$995$	−2.02444	−	6.23060i	−0.0641792	−	0.197523i
$996$		0			0
$997$	−37.0372	+	26.9091i	−1.17298	+	0.852219i	−0.991363	−	0.131150i	$-0.958133\pi$
$997$	−37.0372	+	26.9091i	−1.17298	+	0.852219i	−0.181617	+	0.983369i	$0.558133\pi$
$998$		0			0
$999$	11.8082	−	36.3418i	0.373594	−	1.14980i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.u.b.201.8	✓	32
41.10	even	5	inner	820.2.u.b.461.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.u.b.201.8	✓	32	1.1	even	1	trivial
820.2.u.b.461.8	yes	32	41.10	even	5	inner

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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.u (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+3.33542 q^{3} +(-0.309017 + 0.951057i) q^{5} +(-1.68976 - 1.22768i) q^{7} +8.12504 q^{9} +(1.44022 + 4.43255i) q^{11} +(3.98542 - 2.89558i) q^{13} +(-1.03070 + 3.17218i) q^{15} +(0.947354 + 2.91566i) q^{17} +(-4.36981 - 3.17485i) q^{19} +(-5.63605 - 4.09483i) q^{21} +(-6.90892 + 5.01963i) q^{23} +(-0.809017 - 0.587785i) q^{25} +17.0942 q^{27} +(3.25893 - 10.0300i) q^{29} +(0.826547 + 2.54385i) q^{31} +(4.80375 + 14.7844i) q^{33} +(1.68976 - 1.22768i) q^{35} +(0.690770 - 2.12597i) q^{37} +(13.2931 - 9.65798i) q^{39} +(-4.00305 + 4.99756i) q^{41} +(6.50654 - 4.72728i) q^{43} +(-2.51078 + 7.72738i) q^{45} +(-1.29163 + 0.938421i) q^{47} +(-0.815042 - 2.50844i) q^{49} +(3.15983 + 9.72494i) q^{51} +(-1.46112 + 4.49688i) q^{53} -4.66066 q^{55} +(-14.5752 - 10.5895i) q^{57} +(0.728491 - 0.529280i) q^{59} +(-6.48509 - 4.71170i) q^{61} +(-13.7293 - 9.97495i) q^{63} +(1.52230 + 4.68515i) q^{65} +(0.657405 - 2.02328i) q^{67} +(-23.0442 + 16.7426i) q^{69} +(1.11976 + 3.44626i) q^{71} +2.17713 q^{73} +(-2.69841 - 1.96051i) q^{75} +(3.00813 - 9.25806i) q^{77} -4.97360 q^{79} +32.6412 q^{81} -14.4597 q^{83} -3.06570 q^{85} +(10.8699 - 33.4541i) q^{87} +(-2.85465 - 2.07402i) q^{89} -10.2892 q^{91} +(2.75688 + 8.48482i) q^{93} +(4.36981 - 3.17485i) q^{95} +(-5.37460 + 16.5413i) q^{97} +(11.7019 + 36.0147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 8 q^{5} - 5 q^{7} + 46 q^{9} + q^{11} + q^{13} - 2 q^{15} + 7 q^{17} - 13 q^{19} - 6 q^{21} + 4 q^{23} - 8 q^{25} - 28 q^{27} + 3 q^{29} - q^{31} + 14 q^{33} + 5 q^{35} - 25 q^{37} + 26 q^{41}+ \cdots + 30 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 8 * q^5 - 5 * q^7 + 46 * q^9 + q^11 + q^13 - 2 * q^15 + 7 * q^17 - 13 * q^19 - 6 * q^21 + 4 * q^23 - 8 * q^25 - 28 * q^27 + 3 * q^29 - q^31 + 14 * q^33 + 5 * q^35 - 25 * q^37 + 26 * q^41 + 8 * q^43 + 19 * q^45 + q^47 - 15 * q^49 + 29 * q^51 - 33 * q^53 + 4 * q^55 - 29 * q^57 + 20 * q^59 - 24 * q^61 - 66 * q^63 - q^65 - 48 * q^67 - 16 * q^69 + 5 * q^71 + 4 * q^73 - 3 * q^75 - 16 * q^77 - 102 * q^79 + 200 * q^81 - 110 * q^83 + 8 * q^85 + 25 * q^87 - 34 * q^89 - 10 * q^91 - 18 * q^93 + 13 * q^95 - 36 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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