LMFDB - Embedded newform 378.3.r.a.233.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(233,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 2])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.233"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			233.15
Character	$\chi$	$=$	378.233
Dual form			378.3.r.a.305.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.41421i q^{2} -2.00000 q^{4} +(7.20455 - 4.15955i) q^{5} +(5.54044 + 4.27827i) q^{7} -2.82843i q^{8} +(5.88249 + 10.1888i) q^{10} +(-9.13192 - 5.27232i) q^{11} +(1.24066 - 2.14889i) q^{13} +(-6.05038 + 7.83536i) q^{14} +4.00000 q^{16} +(27.5318 - 15.8955i) q^{17} +(6.85989 - 11.8817i) q^{19} +(-14.4091 + 8.31909i) q^{20} +(7.45618 - 12.9145i) q^{22} +(-27.8304 + 16.0679i) q^{23} +(22.1037 - 38.2847i) q^{25} +(3.03899 + 1.75456i) q^{26} +(-11.0809 - 8.55653i) q^{28} +(-2.05673 + 1.18745i) q^{29} +20.7685 q^{31} +5.65685i q^{32} +(22.4796 + 38.9358i) q^{34} +(57.7120 + 7.77726i) q^{35} +(5.23692 - 9.07061i) q^{37} +(16.8032 + 9.70134i) q^{38} +(-11.7650 - 20.3775i) q^{40} +(43.1999 + 24.9415i) q^{41} +(16.3930 + 28.3936i) q^{43} +(18.2638 + 10.5446i) q^{44} +(-22.7234 - 39.3581i) q^{46} +41.5702i q^{47} +(12.3929 + 47.4069i) q^{49} +(54.1427 + 31.2593i) q^{50} +(-2.48133 + 4.29779i) q^{52} +(-67.8875 + 39.1948i) q^{53} -87.7218 q^{55} +(12.1008 - 15.6707i) q^{56} +(-1.67931 - 2.90865i) q^{58} -71.7399i q^{59} +66.1453 q^{61} +29.3711i q^{62} -8.00000 q^{64} -20.6424i q^{65} -24.9448 q^{67} +(-55.0636 + 31.7910i) q^{68} +(-10.9987 + 81.6171i) q^{70} -23.3875i q^{71} +(19.5871 + 33.9258i) q^{73} +(12.8278 + 7.40612i) q^{74} +(-13.7198 + 23.7633i) q^{76} +(-28.0385 - 68.2797i) q^{77} -10.0737 q^{79} +(28.8182 - 16.6382i) q^{80} +(-35.2726 + 61.0939i) q^{82} +(-95.0843 + 54.8969i) q^{83} +(132.236 - 229.040i) q^{85} +(-40.1546 + 23.1833i) q^{86} +(-14.9124 + 25.8290i) q^{88} +(-36.4975 - 21.0718i) q^{89} +(16.0674 - 6.59792i) q^{91} +(55.6607 - 32.1357i) q^{92} -58.7892 q^{94} -114.136i q^{95} +(-37.7643 - 65.4097i) q^{97} +(-67.0435 + 17.5262i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 64 q^{4} + 2 q^{7} + 36 q^{11} + 10 q^{13} - 36 q^{14} + 128 q^{16} + 54 q^{17} + 28 q^{19} + 126 q^{23} + 80 q^{25} + 72 q^{26} - 4 q^{28} - 36 q^{29} + 16 q^{31} + 90 q^{35} + 22 q^{37} - 72 q^{41}+ \cdots - 288 q^{98}+O(q^{100}) $ 32 * q - 64 * q^4 + 2 * q^7 + 36 * q^11 + 10 * q^13 - 36 * q^14 + 128 * q^16 + 54 * q^17 + 28 * q^19 + 126 * q^23 + 80 * q^25 + 72 * q^26 - 4 * q^28 - 36 * q^29 + 16 * q^31 + 90 * q^35 + 22 * q^37 - 72 * q^41 + 16 * q^43 - 72 * q^44 - 12 * q^46 + 2 * q^49 + 288 * q^50 - 20 * q^52 + 72 * q^53 - 24 * q^55 + 72 * q^56 - 24 * q^58 + 124 * q^61 - 256 * q^64 - 140 * q^67 - 108 * q^68 + 72 * q^70 + 196 * q^73 - 216 * q^74 - 56 * q^76 - 486 * q^77 + 76 * q^79 + 60 * q^85 + 144 * q^86 + 486 * q^89 - 122 * q^91 - 252 * q^92 - 336 * q^94 - 38 * q^97 - 288 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$		0			0
$3$		0			0
$4$	−2.00000			−0.500000
$5$	7.20455	−	4.15955i	1.44091	−	0.831909i	0.442999	−	0.896522i	$-0.353915\pi$
$5$	7.20455	−	4.15955i	1.44091	−	0.831909i	0.997910	+	0.0646127i	$0.0205812\pi$
$6$		0			0
$7$	5.54044	+	4.27827i	0.791491	+	0.611181i
$7$	5.54044	+	4.27827i	0.791491	+	0.611181i
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	5.88249	+	10.1888i	0.588249	+	1.01888i
$11$	−9.13192	−	5.27232i	−0.830174	−	0.479301i	0.0237379	−	0.999718i	$-0.492443\pi$
$11$	−9.13192	−	5.27232i	−0.830174	−	0.479301i	−0.853912	+	0.520417i	$0.825777\pi$
$12$		0			0
$13$	1.24066	−	2.14889i	0.0954357	−	0.165300i	−0.814355	−	0.580368i	$-0.802909\pi$
$13$	1.24066	−	2.14889i	0.0954357	−	0.165300i	0.909790	+	0.415068i	$0.136242\pi$
$14$	−6.05038	+	7.83536i	−0.432170	+	0.559669i
$15$		0			0
$16$	4.00000			0.250000
$17$	27.5318	−	15.8955i	1.61952	−	0.935029i	0.632473	−	0.774582i	$-0.282040\pi$
$17$	27.5318	−	15.8955i	1.61952	−	0.935029i	0.987045	−	0.160446i	$-0.0512934\pi$
$18$		0			0
$19$	6.85989	−	11.8817i	0.361047	−	0.625351i	−0.627087	−	0.778949i	$-0.715753\pi$
$19$	6.85989	−	11.8817i	0.361047	−	0.625351i	0.988133	+	0.153598i	$0.0490862\pi$
$20$	−14.4091	+	8.31909i	−0.720455	+	0.415955i
$21$		0			0
$22$	7.45618	−	12.9145i	0.338917	−	0.587022i
$23$	−27.8304	+	16.0679i	−1.21002	+	0.698603i	−0.962763	−	0.270348i	$-0.912861\pi$
$23$	−27.8304	+	16.0679i	−1.21002	+	0.698603i	−0.247253	+	0.968951i	$0.579528\pi$
$24$		0			0
$25$	22.1037	−	38.2847i	0.884147	−	1.53139i
$26$	3.03899	+	1.75456i	0.116884	+	0.0674832i
$27$		0			0
$28$	−11.0809	−	8.55653i	−0.395746	−	0.305590i
$29$	−2.05673	+	1.18745i	−0.0709216	+	0.0409466i	−0.535041	−	0.844826i	$-0.679704\pi$
$29$	−2.05673	+	1.18745i	−0.0709216	+	0.0409466i	0.464120	+	0.885772i	$0.346371\pi$
$30$		0			0
$31$	20.7685			0.669952			0.334976	−	0.942227i	$-0.391272\pi$
$31$	20.7685			0.669952			0.334976	+	0.942227i	$0.391272\pi$
$32$			5.65685i			0.176777i
$33$		0			0
$34$	22.4796	+	38.9358i	0.661165	+	1.14517i
$35$	57.7120	+	7.77726i	1.64891	+	0.222207i
$36$		0			0
$37$	5.23692	−	9.07061i	0.141538	−	0.245152i	−0.786538	−	0.617542i	$-0.788128\pi$
$37$	5.23692	−	9.07061i	0.141538	−	0.245152i	0.928076	+	0.372391i	$0.121462\pi$
$38$	16.8032	+	9.70134i	0.442190	+	0.255298i
$39$		0			0
$40$	−11.7650	−	20.3775i	−0.294124	−	0.509438i
$41$	43.1999	+	24.9415i	1.05366	+	0.608329i	0.923671	−	0.383187i	$-0.125173\pi$
$41$	43.1999	+	24.9415i	1.05366	+	0.608329i	0.129986	+	0.991516i	$0.458507\pi$
$42$		0			0
$43$	16.3930	+	28.3936i	0.381234	+	0.660316i	0.991239	−	0.132081i	$-0.0421660\pi$
$43$	16.3930	+	28.3936i	0.381234	+	0.660316i	−0.610005	+	0.792397i	$0.708833\pi$
$44$	18.2638	+	10.5446i	0.415087	+	0.239651i
$45$		0			0
$46$	−22.7234	−	39.3581i	−0.493987	−	0.855610i
$47$			41.5702i			0.884473i	0.896899	+	0.442236i	$0.145815\pi$
$47$			41.5702i			0.884473i	−0.896899	+	0.442236i	$0.854185\pi$
$48$		0			0
$49$	12.3929	+	47.4069i	0.252916	+	0.967488i
$50$	54.1427	+	31.2593i	1.08285	+	0.625186i
$51$		0			0
$52$	−2.48133	+	4.29779i	−0.0477179	+	0.0826498i
$53$	−67.8875	+	39.1948i	−1.28090	+	0.739525i	−0.977012	−	0.213184i	$-0.931617\pi$
$53$	−67.8875	+	39.1948i	−1.28090	+	0.739525i	−0.303883	+	0.952709i	$0.598283\pi$
$54$		0			0
$55$	−87.7218			−1.59494
$56$	12.1008	−	15.6707i	0.216085	−	0.279834i
$57$		0			0
$58$	−1.67931	−	2.90865i	−0.0289536	−	0.0501491i
$59$		−	71.7399i		−	1.21593i	−0.793964	−	0.607965i	$-0.791986\pi$
$59$		−	71.7399i		−	1.21593i	0.793964	−	0.607965i	$-0.208014\pi$
$60$		0			0
$61$	66.1453			1.08435			0.542175	−	0.840266i	$-0.317601\pi$
$61$	66.1453			1.08435			0.542175	+	0.840266i	$0.317601\pi$
$62$			29.3711i			0.473728i
$63$		0			0
$64$	−8.00000			−0.125000
$65$		−	20.6424i		−	0.317575i
$66$		0			0
$67$	−24.9448			−0.372311			−0.186155	−	0.982520i	$-0.559603\pi$
$67$	−24.9448			−0.372311			−0.186155	+	0.982520i	$0.559603\pi$
$68$	−55.0636	+	31.7910i	−0.809759	+	0.467514i
$69$		0			0
$70$	−10.9987	+	81.6171i	−0.157124	+	1.16596i
$71$		−	23.3875i		−	0.329402i	−0.986344	−	0.164701i	$-0.947334\pi$
$71$		−	23.3875i		−	0.329402i	0.986344	−	0.164701i	$-0.0526659\pi$
$72$		0			0
$73$	19.5871	+	33.9258i	0.268316	+	0.464737i	0.968427	−	0.249297i	$-0.0801996\pi$
$73$	19.5871	+	33.9258i	0.268316	+	0.464737i	−0.700111	+	0.714034i	$0.746866\pi$
$74$	12.8278	+	7.40612i	0.173348	+	0.100083i
$75$		0			0
$76$	−13.7198	+	23.7633i	−0.180523	+	0.312676i
$77$	−28.0385	−	68.2797i	−0.364136	−	0.886750i
$78$		0			0
$79$	−10.0737			−0.127516			−0.0637579	−	0.997965i	$-0.520309\pi$
$79$	−10.0737			−0.127516			−0.0637579	+	0.997965i	$0.520309\pi$
$80$	28.8182	−	16.6382i	0.360227	−	0.207977i
$81$		0			0
$82$	−35.2726	+	61.0939i	−0.430154	+	0.745048i
$83$	−95.0843	+	54.8969i	−1.14559	+	0.661409i	−0.947810	−	0.318837i	$-0.896708\pi$
$83$	−95.0843	+	54.8969i	−1.14559	+	0.661409i	−0.197784	+	0.980246i	$0.563375\pi$
$84$		0			0
$85$	132.236	−	229.040i	1.55572	−	2.69458i
$86$	−40.1546	+	23.1833i	−0.466914	+	0.269573i
$87$		0			0
$88$	−14.9124	+	25.8290i	−0.169459	+	0.293511i
$89$	−36.4975	−	21.0718i	−0.410084	−	0.236762i	0.280742	−	0.959783i	$-0.409420\pi$
$89$	−36.4975	−	21.0718i	−0.410084	−	0.236762i	−0.690826	+	0.723021i	$0.742753\pi$
$90$		0			0
$91$	16.0674	−	6.59792i	0.176564	−	0.0725046i
$92$	55.6607	−	32.1357i	0.605008	−	0.349302i
$93$		0			0
$94$	−58.7892			−0.625417
$95$		−	114.136i		−	1.20143i
$96$		0			0
$97$	−37.7643	−	65.4097i	−0.389322	−	0.674326i	0.603036	−	0.797714i	$-0.293957\pi$
$97$	−37.7643	−	65.4097i	−0.389322	−	0.674326i	−0.992359	+	0.123388i	$0.960624\pi$
$98$	−67.0435	+	17.5262i	−0.684117	+	0.178839i
$99$		0			0
$100$	−44.2073	+	76.5693i	−0.442073	+	0.765693i
$101$	−113.453	−	65.5019i	−1.12329	−	0.648534i	−0.181054	−	0.983473i	$-0.557951\pi$
$101$	−113.453	−	65.5019i	−1.12329	−	0.648534i	−0.942240	+	0.334939i	$0.891284\pi$
$102$		0			0
$103$	16.6112	+	28.7715i	0.161274	+	0.279335i	0.935326	−	0.353788i	$-0.115106\pi$
$103$	16.6112	+	28.7715i	0.161274	+	0.279335i	−0.774052	+	0.633122i	$0.781773\pi$
$104$	−6.07799	−	3.50913i	−0.0584422	−	0.0337416i
$105$		0			0
$106$	−55.4299	−	96.0074i	−0.522923	−	0.905730i
$107$	−46.8532	−	27.0507i	−0.437881	−	0.252810i	0.264818	−	0.964299i	$-0.414688\pi$
$107$	−46.8532	−	27.0507i	−0.437881	−	0.252810i	−0.702698	+	0.711488i	$0.748022\pi$
$108$		0			0
$109$	−14.9320	−	25.8630i	−0.136991	−	0.237275i	0.789365	−	0.613924i	$-0.210410\pi$
$109$	−14.9320	−	25.8630i	−0.136991	−	0.237275i	−0.926356	+	0.376648i	$0.877076\pi$
$110$		−	124.057i		−	1.12779i
$111$		0			0
$112$	22.1617	+	17.1131i	0.197873	+	0.152795i
$113$	160.151	+	92.4632i	1.41726	+	0.818258i	0.996058	−	0.0887062i	$-0.0282732\pi$
$113$	160.151	+	92.4632i	1.41726	+	0.818258i	0.421207	+	0.906964i	$0.361607\pi$
$114$		0			0
$115$	−133.670	+	231.523i	−1.16235	+	2.01325i
$116$	4.11345	−	2.37490i	0.0354608	−	0.0204733i
$117$		0			0
$118$	101.455			0.859792
$119$	220.543	+	29.7204i	1.85331	+	0.249751i
$120$		0			0
$121$	−4.90537	−	8.49634i	−0.0405402	−	0.0702177i
$122$			93.5436i			0.766751i
$123$		0			0
$124$	−41.5370			−0.334976
$125$		−	159.788i		−	1.27830i
$126$		0			0
$127$	−111.511			−0.878041			−0.439020	−	0.898477i	$-0.644674\pi$
$127$	−111.511			−0.878041			−0.439020	+	0.898477i	$0.644674\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		0			0
$130$	29.1928			0.224560
$131$	−49.0008	+	28.2906i	−0.374052	+	0.215959i	−0.675227	−	0.737610i	$-0.735954\pi$
$131$	−49.0008	+	28.2906i	−0.374052	+	0.215959i	0.301175	+	0.953569i	$0.402621\pi$
$132$		0			0
$133$	88.8397	−	36.4812i	0.667968	−	0.274295i
$134$		−	35.2773i		−	0.263263i
$135$		0			0
$136$	−44.9592	−	77.8717i	−0.330583	−	0.572586i
$137$	−57.1869	−	33.0169i	−0.417423	−	0.240999i	0.276551	−	0.960999i	$-0.410808\pi$
$137$	−57.1869	−	33.0169i	−0.417423	−	0.240999i	−0.693974	+	0.720000i	$0.744142\pi$
$138$		0			0
$139$	45.2312	−	78.3427i	0.325404	−	0.563617i	−0.656190	−	0.754596i	$-0.727833\pi$
$139$	45.2312	−	78.3427i	0.325404	−	0.563617i	0.981594	+	0.190979i	$0.0611663\pi$
$140$	−115.424	−	15.5545i	−0.824457	−	0.111104i
$141$		0			0
$142$	33.0749			0.232922
$143$	−22.6593	+	13.0823i	−0.158457	+	0.0914850i
$144$		0			0
$145$	−9.87852	+	17.1101i	−0.0681277	+	0.118001i
$146$	−47.9783	+	27.7003i	−0.328618	+	0.189728i
$147$		0			0
$148$	−10.4738	+	18.1412i	−0.0707692	+	0.122576i
$149$	−85.3457	+	49.2744i	−0.572790	+	0.330701i	−0.758263	−	0.651949i	$-0.773952\pi$
$149$	−85.3457	+	49.2744i	−0.572790	+	0.330701i	0.185473	+	0.982649i	$0.440618\pi$
$150$		0			0
$151$	19.7972	−	34.2897i	0.131107	−	0.227084i	−0.792997	−	0.609226i	$-0.791480\pi$
$151$	19.7972	−	34.2897i	0.131107	−	0.227084i	0.924104	+	0.382142i	$0.124813\pi$
$152$	−33.6064	−	19.4027i	−0.221095	−	0.127649i
$153$		0			0
$154$	96.5621	−	39.6524i	0.627027	−	0.257483i
$155$	149.628	−	86.3876i	0.965341	−	0.557340i
$156$		0			0
$157$	−249.558			−1.58954			−0.794772	−	0.606909i	$-0.792409\pi$
$157$	−249.558			−1.58954			−0.794772	+	0.606909i	$0.792409\pi$
$158$		−	14.2464i		−	0.0901673i
$159$		0			0
$160$	23.5300	+	40.7551i	0.147062	+	0.254719i
$161$	−222.935	−	30.0427i	−1.38469	−	0.186600i
$162$		0			0
$163$	−121.137	+	209.816i	−0.743175	+	1.28722i	0.207868	+	0.978157i	$0.433348\pi$
$163$	−121.137	+	209.816i	−0.743175	+	1.28722i	−0.951043	+	0.309060i	$0.899986\pi$
$164$	−86.3999	−	49.8830i	−0.526828	−	0.304165i
$165$		0			0
$166$	−77.6360	−	134.469i	−0.467687	−	0.810057i
$167$	84.4167	+	48.7380i	0.505489	+	0.291844i	0.730977	−	0.682402i	$-0.239064\pi$
$167$	84.4167	+	48.7380i	0.505489	+	0.291844i	−0.225488	+	0.974246i	$0.572398\pi$
$168$		0			0
$169$	81.4215	+	141.026i	0.481784	+	0.834474i
$170$	323.911	+	187.010i	1.90536	+	1.10006i
$171$		0			0
$172$	−32.7861	−	56.7872i	−0.190617	−	0.330158i
$173$		−	53.6007i		−	0.309830i	−0.987928	−	0.154915i	$-0.950490\pi$
$173$		−	53.6007i		−	0.309830i	0.987928	−	0.154915i	$-0.0495104\pi$
$174$		0			0
$175$	286.256	−	117.548i	1.63575	−	0.671706i
$176$	−36.5277	−	21.0893i	−0.207544	−	0.119825i
$177$		0			0
$178$	29.8001	−	51.6152i	0.167416	−	0.289973i
$179$	−122.940	+	70.9794i	−0.686815	+	0.396533i	−0.802418	−	0.596763i	$-0.796453\pi$
$179$	−122.940	+	70.9794i	−0.686815	+	0.396533i	0.115603	+	0.993296i	$0.463120\pi$
$180$		0			0
$181$	−207.905			−1.14864			−0.574322	−	0.818629i	$-0.694734\pi$
$181$	−207.905			−1.14864			−0.574322	+	0.818629i	$0.694734\pi$
$182$	9.33087	+	22.7227i	0.0512685	+	0.124850i
$183$		0			0
$184$	45.4468	+	78.7162i	0.246993	+	0.427805i
$185$		−	87.1329i		−	0.470989i
$186$		0			0
$187$	−335.224			−1.79264
$188$		−	83.1404i		−	0.442236i
$189$		0			0
$190$	161.413			0.849541
$191$			307.887i			1.61197i	0.591934	+	0.805987i	$0.298365\pi$
$191$			307.887i			1.61197i	−0.591934	+	0.805987i	$0.701635\pi$
$192$		0			0
$193$	−165.134			−0.855617			−0.427808	−	0.903869i	$-0.640714\pi$
$193$	−165.134			−0.855617			−0.427808	+	0.903869i	$0.640714\pi$
$194$	92.5032	−	53.4068i	0.476821	−	0.275293i
$195$		0			0
$196$	−24.7858	−	94.8138i	−0.126458	−	0.483744i
$197$		−	86.2870i		−	0.438005i	−0.975724	−	0.219003i	$-0.929720\pi$
$197$		−	86.2870i		−	0.438005i	0.975724	−	0.219003i	$-0.0702803\pi$
$198$		0			0
$199$	−164.720	−	285.304i	−0.827739	−	1.43369i	−0.899808	−	0.436287i	$-0.856293\pi$
$199$	−164.720	−	285.304i	−0.827739	−	1.43369i	0.0720681	−	0.997400i	$-0.477040\pi$
$200$	−108.285	−	62.5186i	−0.541427	−	0.312593i
$201$		0			0
$202$	92.6337	−	160.446i	0.458583	−	0.794289i
$203$	−16.4754	−	2.22022i	−0.0811596	−	0.0109370i
$204$		0			0
$205$	414.981			2.02430
$206$	−40.6890	+	23.4918i	−0.197519	+	0.114038i
$207$		0			0
$208$	4.96266	−	8.59557i	0.0238589	−	0.0413249i
$209$	−125.288	+	72.3350i	−0.599463	+	0.346100i
$210$		0			0
$211$	−40.7068	+	70.5063i	−0.192923	+	0.334153i	−0.946218	−	0.323530i	$-0.895130\pi$
$211$	−40.7068	+	70.5063i	−0.192923	+	0.334153i	0.753294	+	0.657683i	$0.228464\pi$
$212$	135.775	−	78.3897i	0.640448	−	0.369763i
$213$		0			0
$214$	38.2555	−	66.2605i	0.178764	−	0.309628i
$215$	236.209	+	136.375i	1.09865	+	0.634304i
$216$		0			0
$217$	115.067	+	88.8533i	0.530261	+	0.409462i
$218$	36.5758	−	21.1171i	0.167779	−	0.0968673i
$219$		0			0
$220$	175.444			0.797471
$221$		−	78.8839i		−	0.356941i
$222$		0			0
$223$	93.2204	+	161.462i	0.418029	+	0.724047i	0.995741	−	0.0921934i	$-0.0293878\pi$
$223$	93.2204	+	161.462i	0.418029	+	0.724047i	−0.577712	+	0.816240i	$0.696054\pi$
$224$	−24.2015	+	31.3414i	−0.108043	+	0.139917i
$225$		0			0
$226$	−130.763	+	226.488i	−0.578596	+	1.00216i
$227$	−35.3648	−	20.4179i	−0.155792	−	0.0899465i	0.420077	−	0.907488i	$-0.362003\pi$
$227$	−35.3648	−	20.4179i	−0.155792	−	0.0899465i	−0.575869	+	0.817542i	$0.695336\pi$
$228$		0			0
$229$	35.6011	+	61.6629i	0.155463	+	0.269270i	0.933228	−	0.359286i	$-0.116980\pi$
$229$	35.6011	+	61.6629i	0.155463	+	0.269270i	−0.777764	+	0.628556i	$0.783646\pi$
$230$	−327.424	−	189.038i	−1.42358	−	0.821905i
$231$		0			0
$232$	3.35862	+	5.81730i	0.0144768	+	0.0250746i
$233$	6.66414	+	3.84755i	0.0286015	+	0.0165131i	0.514233	−	0.857651i	$-0.328077\pi$
$233$	6.66414	+	3.84755i	0.0286015	+	0.0165131i	−0.485631	+	0.874164i	$0.661410\pi$
$234$		0			0
$235$	172.913	+	299.495i	0.735801	+	1.27445i
$236$			143.480i			0.607965i
$237$		0			0
$238$	−42.0310	+	311.895i	−0.176601	+	1.31048i
$239$	204.678	+	118.171i	0.856392	+	0.494438i	0.862802	−	0.505541i	$-0.168707\pi$
$239$	204.678	+	118.171i	0.856392	+	0.494438i	−0.00641057	+	0.999979i	$0.502041\pi$
$240$		0			0
$241$	−63.2926	+	109.626i	−0.262625	+	0.454880i	−0.966939	−	0.255009i	$-0.917921\pi$
$241$	−63.2926	+	109.626i	−0.262625	+	0.454880i	0.704314	+	0.709889i	$0.251255\pi$
$242$	12.0156	−	6.93724i	0.0496514	−	0.0286663i
$243$		0			0
$244$	−132.291			−0.542175
$245$	286.476	+	289.997i	1.16929	+	1.18366i
$246$		0			0
$247$	−17.0216	−	29.4823i	−0.0689135	−	0.119362i
$248$		−	58.7423i		−	0.236864i
$249$		0			0
$250$	225.974			0.903895
$251$			318.476i			1.26883i	0.772993	+	0.634414i	$0.218759\pi$
$251$			318.476i			1.26883i	−0.772993	+	0.634414i	$0.781241\pi$
$252$		0			0
$253$	338.860			1.33937
$254$		−	157.701i		−	0.620869i
$255$		0			0
$256$	16.0000			0.0625000
$257$	421.007	−	243.069i	1.63816	−	0.945792i	0.656694	−	0.754157i	$-0.271954\pi$
$257$	421.007	−	243.069i	1.63816	−	0.945792i	0.981466	−	0.191635i	$-0.0613789\pi$
$258$		0			0
$259$	67.8213	−	27.8502i	0.261858	−	0.107530i
$260$			41.2848i			0.158788i
$261$		0			0
$262$	−40.0090	−	69.2976i	−0.152706	−	0.264495i
$263$	302.149	+	174.446i	1.14885	+	0.663291i	0.948608	−	0.316454i	$-0.102492\pi$
$263$	302.149	+	174.446i	1.14885	+	0.663291i	0.200247	+	0.979746i	$0.435826\pi$
$264$		0			0
$265$	−326.066	+	564.762i	−1.23044	+	2.13118i
$266$	51.5923	+	125.638i	0.193956	+	0.472324i
$267$		0			0
$268$	49.8896			0.186155
$269$	−335.922	+	193.945i	−1.24878	+	0.720985i	−0.970867	−	0.239621i	$-0.922977\pi$
$269$	−335.922	+	193.945i	−1.24878	+	0.720985i	−0.277916	+	0.960606i	$0.589644\pi$
$270$		0			0
$271$	118.336	−	204.964i	0.436664	−	0.756324i	−0.560766	−	0.827974i	$-0.689493\pi$
$271$	118.336	−	204.964i	0.436664	−	0.756324i	0.997430	+	0.0716504i	$0.0228266\pi$
$272$	110.127	−	63.5820i	0.404879	−	0.233757i
$273$		0			0
$274$	46.6929	−	80.8745i	0.170412	−	0.295162i
$275$	−403.698	+	233.075i	−1.46799	+	0.847546i
$276$		0			0
$277$	101.755	−	176.246i	0.367348	−	0.636266i	−0.621802	−	0.783175i	$-0.713599\pi$
$277$	101.755	−	176.246i	0.367348	−	0.636266i	0.989150	+	0.146909i	$0.0469324\pi$
$278$	110.793	+	63.9665i	0.398537	+	0.230095i
$279$		0			0
$280$	21.9974	−	163.234i	0.0785621	−	0.582979i
$281$	−45.9455	+	26.5266i	−0.163507	+	0.0944008i	−0.579521	−	0.814958i	$-0.696760\pi$
$281$	−45.9455	+	26.5266i	−0.163507	+	0.0944008i	0.416014	+	0.909358i	$0.363427\pi$
$282$		0			0
$283$	−47.8110			−0.168944			−0.0844718	−	0.996426i	$-0.526920\pi$
$283$	−47.8110			−0.168944			−0.0844718	+	0.996426i	$0.526920\pi$
$284$			46.7750i			0.164701i
$285$		0			0
$286$	−18.5012	−	32.0451i	−0.0646896	−	0.112046i
$287$	132.640	+	323.008i	0.462161	+	1.12546i
$288$		0			0
$289$	360.833	−	624.982i	1.24856	−	2.16257i
$290$	−24.1973	−	13.9703i	−0.0834391	−	0.0481736i
$291$		0			0
$292$	−39.1741	−	67.8515i	−0.134158	−	0.232368i
$293$	10.7293	+	6.19459i	0.0366189	+	0.0211419i	0.518198	−	0.855261i	$-0.326603\pi$
$293$	10.7293	+	6.19459i	0.0366189	+	0.0211419i	−0.481579	+	0.876403i	$0.659936\pi$
$294$		0			0
$295$	−298.405	−	516.853i	−1.01154	−	1.75204i
$296$	−25.6556	−	14.8122i	−0.0866742	−	0.0500414i
$297$		0			0
$298$	−69.6845	−	120.697i	−0.233841	−	0.405024i
$299$			79.7393i			0.266687i
$300$		0			0
$301$	−30.6507	+	227.447i	−0.101829	+	0.755637i
$302$	48.4930	+	27.9974i	0.160573	+	0.0927067i
$303$		0			0
$304$	27.4395	−	47.5267i	0.0902616	−	0.156338i
$305$	476.547	−	275.135i	1.56245	−	0.902081i
$306$		0			0
$307$	420.839			1.37081			0.685406	−	0.728161i	$-0.259625\pi$
$307$	420.839			1.37081			0.685406	+	0.728161i	$0.259625\pi$
$308$	56.0769	+	136.559i	0.182068	+	0.443375i
$309$		0			0
$310$	122.171	+	211.606i	0.394099	+	0.682599i
$311$		−	465.113i		−	1.49554i	−0.663957	−	0.747771i	$-0.731124\pi$
$311$		−	465.113i		−	1.49554i	0.663957	−	0.747771i	$-0.268876\pi$
$312$		0			0
$313$	−364.970			−1.16604			−0.583019	−	0.812459i	$-0.698129\pi$
$313$	−364.970			−1.16604			−0.583019	+	0.812459i	$0.698129\pi$
$314$		−	352.929i		−	1.12398i
$315$		0			0
$316$	20.1475			0.0637579
$317$		−	23.8488i		−	0.0752329i	−0.999292	−	0.0376164i	$-0.988023\pi$
$317$		−	23.8488i		−	0.0752329i	0.999292	−	0.0376164i	$-0.0119765\pi$
$318$		0			0
$319$	25.0425			0.0785030
$320$	−57.6364	+	33.2764i	−0.180114	+	0.103989i
$321$		0			0
$322$	42.4868	−	315.278i	0.131946	−	0.979123i
$323$		−	436.165i		−	1.35036i
$324$		0			0
$325$	−54.8465	−	94.9969i	−0.168758	−	0.292298i
$326$	−296.725	−	171.314i	−0.910200	−	0.525504i
$327$		0			0
$328$	70.5452	−	122.188i	0.215077	−	0.372524i
$329$	−177.848	+	230.317i	−0.540573	+	0.700052i
$330$		0			0
$331$	226.135			0.683188			0.341594	−	0.939848i	$-0.389033\pi$
$331$	226.135			0.683188			0.341594	+	0.939848i	$0.389033\pi$
$332$	190.169	−	109.794i	0.572797	−	0.330704i
$333$		0			0
$334$	−68.9259	+	119.383i	−0.206365	+	0.357435i
$335$	−179.716	+	103.759i	−0.536466	+	0.309729i
$336$		0			0
$337$	151.164	−	261.824i	0.448558	−	0.776926i	−0.549734	−	0.835340i	$-0.685271\pi$
$337$	151.164	−	261.824i	0.448558	−	0.776926i	0.998292	+	0.0584139i	$0.0186043\pi$
$338$	−199.441	+	115.147i	−0.590063	+	0.340673i
$339$		0			0
$340$	−264.472	+	458.079i	−0.777859	+	1.34729i
$341$	−189.656	−	109.498i	−0.556177	−	0.321109i
$342$		0			0
$343$	−134.157	+	315.675i	−0.391129	+	0.920336i
$344$	80.3092	−	46.3665i	0.233457	−	0.134786i
$345$		0			0
$346$	75.8028			0.219083
$347$			176.421i			0.508417i	0.967149	+	0.254209i	$0.0818150\pi$
$347$			176.421i			0.508417i	−0.967149	+	0.254209i	$0.918185\pi$
$348$		0			0
$349$	−87.3168	−	151.237i	−0.250191	−	0.433344i	0.713387	−	0.700770i	$-0.247160\pi$
$349$	−87.3168	−	151.237i	−0.250191	−	0.433344i	−0.963578	+	0.267426i	$0.913827\pi$
$350$	166.239	+	404.827i	0.474968	+	1.15665i
$351$		0			0
$352$	29.8247	−	51.6579i	0.0847293	−	0.146756i
$353$	123.536	+	71.3235i	0.349960	+	0.202050i	0.664668	−	0.747139i	$-0.268573\pi$
$353$	123.536	+	71.3235i	0.349960	+	0.202050i	−0.314708	+	0.949189i	$0.601906\pi$
$354$		0			0
$355$	−97.2815	−	168.496i	−0.274032	−	0.474638i
$356$	72.9950	+	42.1437i	0.205042	+	0.118381i
$357$		0			0
$358$	−100.380	−	173.863i	−0.280391	−	0.485652i
$359$	−529.406	−	305.653i	−1.47467	−	0.851401i	−0.475077	−	0.879944i	$-0.657580\pi$
$359$	−529.406	−	305.653i	−1.47467	−	0.851401i	−0.999593	+	0.0285432i	$0.990913\pi$
$360$		0			0
$361$	86.3839	+	149.621i	0.239291	+	0.414464i
$362$		−	294.022i		−	0.812215i
$363$		0			0
$364$	−32.1347	+	13.1958i	−0.0882822	+	0.0362523i
$365$	282.232	+	162.947i	0.773238	+	0.446429i
$366$		0			0
$367$	−84.4264	+	146.231i	−0.230045	+	0.398449i	−0.957821	−	0.287365i	$-0.907221\pi$
$367$	−84.4264	+	146.231i	−0.230045	+	0.398449i	0.727776	+	0.685815i	$0.240554\pi$
$368$	−111.321	+	64.2715i	−0.302504	+	0.174651i
$369$		0			0
$370$	123.224			0.333039
$371$	−543.812	−	73.2840i	−1.46580	−	0.197531i
$372$		0			0
$373$	−162.732	−	281.861i	−0.436280	−	0.755659i	0.561119	−	0.827735i	$-0.310371\pi$
$373$	−162.732	−	281.861i	−0.436280	−	0.755659i	−0.997399	+	0.0720763i	$0.977037\pi$
$374$		−	474.079i		−	1.26759i
$375$		0			0
$376$	117.578			0.312708
$377$			5.89291i			0.0156311i
$378$		0			0
$379$	7.72342			0.0203784			0.0101892	−	0.999948i	$-0.496757\pi$
$379$	7.72342			0.0203784			0.0101892	+	0.999948i	$0.496757\pi$
$380$			228.272i			0.600716i
$381$		0			0
$382$	−435.418			−1.13984
$383$	−561.085	+	323.943i	−1.46498	+	0.845804i	−0.999235	−	0.0391176i	$-0.987545\pi$
$383$	−561.085	+	323.943i	−1.46498	+	0.845804i	−0.465740	+	0.884921i	$0.654212\pi$
$384$		0			0
$385$	−486.017	−	375.297i	−1.26238	−	0.974798i
$386$		−	233.535i		−	0.605012i
$387$		0			0
$388$	75.5286	+	130.819i	0.194661	+	0.337163i
$389$	−129.356	−	74.6840i	−0.332536	−	0.191990i	0.324431	−	0.945910i	$-0.394827\pi$
$389$	−129.356	−	74.6840i	−0.332536	−	0.191990i	−0.656966	+	0.753920i	$0.728161\pi$
$390$		0			0
$391$	−510.813	+	884.755i	−1.30643	+	2.26280i
$392$	134.087	−	35.0524i	0.342059	−	0.0894193i
$393$		0			0
$394$	122.028			0.309716
$395$	−72.5768	+	41.9022i	−0.183739	+	0.106082i
$396$		0			0
$397$	47.6251	−	82.4890i	0.119962	−	0.207781i	−0.799790	−	0.600280i	$-0.795056\pi$
$397$	47.6251	−	82.4890i	0.119962	−	0.207781i	0.919753	+	0.392499i	$0.128389\pi$
$398$	403.480	−	232.949i	1.01377	−	0.585300i
$399$		0			0
$400$	88.4147	−	153.139i	0.221037	−	0.382847i
$401$	315.630	−	182.229i	0.787108	−	0.454437i	−0.0518355	−	0.998656i	$-0.516507\pi$
$401$	315.630	−	182.229i	0.787108	−	0.454437i	0.838943	+	0.544219i	$0.183174\pi$
$402$		0			0
$403$	25.7668	−	44.6293i	0.0639374	−	0.110743i
$404$	226.905	+	131.004i	0.561647	+	0.324267i
$405$		0			0
$406$	3.13987	−	23.2997i	0.00773366	−	0.0573885i
$407$	−95.6463	+	55.2214i	−0.235003	+	0.135679i
$408$		0			0
$409$	781.333			1.91035			0.955174	−	0.296044i	$-0.0956675\pi$
$409$	781.333			1.91035			0.955174	+	0.296044i	$0.0956675\pi$
$410$			586.872i			1.43140i
$411$		0			0
$412$	−33.2224	−	57.5429i	−0.0806369	−	0.139667i
$413$	306.922	−	397.470i	0.743153	−	0.962398i
$414$		0			0
$415$	−456.693	+	791.015i	−1.10046	+	1.90606i
$416$	12.1560	+	7.01826i	0.0292211	+	0.0168708i
$417$		0			0
$418$	−102.297	−	177.184i	−0.244730	−	0.423885i
$419$	401.472	+	231.790i	0.958167	+	0.553198i	0.895608	−	0.444843i	$-0.146741\pi$
$419$	401.472	+	231.790i	0.958167	+	0.553198i	0.0625584	+	0.998041i	$0.480074\pi$
$420$		0			0
$421$	299.652	+	519.012i	0.711762	+	1.23281i	0.964195	+	0.265194i	$0.0854359\pi$
$421$	299.652	+	519.012i	0.711762	+	1.23281i	−0.252433	+	0.967614i	$0.581231\pi$
$422$	−99.7110	−	57.5682i	−0.236282	−	0.136417i
$423$		0			0
$424$	110.860	+	192.015i	0.261462	+	0.452865i
$425$		−	1405.39i		−	3.30681i
$426$		0			0
$427$	366.474	+	282.987i	0.858253	+	0.662734i
$428$	93.7064	+	54.1014i	0.218940	+	0.126405i
$429$		0			0
$430$	−192.864	+	334.050i	−0.448520	+	0.776860i
$431$	261.400	−	150.919i	0.606496	−	0.350161i	−0.165097	−	0.986277i	$-0.552794\pi$
$431$	261.400	−	150.919i	0.606496	−	0.350161i	0.771593	+	0.636117i	$0.219460\pi$
$432$		0			0
$433$	582.634			1.34557			0.672787	−	0.739836i	$-0.265097\pi$
$433$	582.634			1.34557			0.672787	+	0.739836i	$0.265097\pi$
$434$	−125.657	+	162.729i	−0.289533	+	0.374951i
$435$		0			0
$436$	29.8640	+	51.7260i	0.0684955	+	0.118638i
$437$			440.895i			1.00891i
$438$		0			0
$439$	56.3737			0.128414			0.0642069	−	0.997937i	$-0.479548\pi$
$439$	56.3737			0.128414			0.0642069	+	0.997937i	$0.479548\pi$
$440$			248.115i			0.563897i
$441$		0			0
$442$	111.559			0.252395
$443$		−	190.861i		−	0.430838i	−0.976522	−	0.215419i	$-0.930888\pi$
$443$		−	190.861i		−	0.430838i	0.976522	−	0.215419i	$-0.0691116\pi$
$444$		0			0
$445$	−350.597			−0.787859
$446$	−228.342	+	131.834i	−0.511979	+	0.295591i
$447$		0			0
$448$	−44.3235	−	34.2261i	−0.0989364	−	0.0763976i
$449$			4.42392i			0.00985283i	0.999988	+	0.00492642i	$0.00156813\pi$
$449$			4.42392i			0.00985283i	−0.999988	+	0.00492642i	$0.998432\pi$
$450$		0			0
$451$	−262.999	−	455.527i	−0.583146	−	1.01004i
$452$	−320.302	−	184.926i	−0.708632	−	0.409129i
$453$		0			0
$454$	28.8752	−	50.0133i	0.0636018	−	0.110162i
$455$	88.3137	−	114.368i	0.194096	−	0.251358i
$456$		0			0
$457$	−674.875			−1.47675			−0.738375	−	0.674390i	$-0.764407\pi$
$457$	−674.875			−1.47675			−0.738375	+	0.674390i	$0.764407\pi$
$458$	−87.2045	+	50.3475i	−0.190403	+	0.109929i
$459$		0			0
$460$	267.340	−	463.047i	0.581174	−	1.00662i
$461$	−365.804	+	211.197i	−0.793501	+	0.458128i	−0.841194	−	0.540734i	$-0.818147\pi$
$461$	−365.804	+	211.197i	−0.793501	+	0.458128i	0.0476924	+	0.998862i	$0.484813\pi$
$462$		0			0
$463$	40.8889	−	70.8216i	0.0883129	−	0.152962i	−0.818485	−	0.574528i	$-0.805186\pi$
$463$	40.8889	−	70.8216i	0.0883129	−	0.152962i	0.906798	+	0.421565i	$0.138519\pi$
$464$	−8.22690	+	4.74980i	−0.0177304	+	0.0102366i
$465$		0			0
$466$	−5.44125	+	9.42452i	−0.0116765	+	0.0202243i
$467$	484.152	+	279.525i	1.03673	+	0.598555i	0.918905	−	0.394480i	$-0.129075\pi$
$467$	484.152	+	279.525i	1.03673	+	0.598555i	0.117823	+	0.993035i	$0.462409\pi$
$468$		0			0
$469$	−138.205	−	106.721i	−0.294681	−	0.227549i
$470$	−423.549	+	244.536i	−0.901169	+	0.520290i
$471$		0			0
$472$	−202.911			−0.429896
$473$		−	345.717i		−	0.730903i
$474$		0			0
$475$	−303.257	−	525.257i	−0.638436	−	1.10580i
$476$	−441.087	−	59.4407i	−0.926653	−	0.124876i
$477$		0			0
$478$	−167.119	+	289.458i	−0.349620	+	0.605560i
$479$	−69.6614	−	40.2190i	−0.145431	−	0.0839646i	0.425519	−	0.904950i	$-0.360092\pi$
$479$	−69.6614	−	40.2190i	−0.145431	−	0.0839646i	−0.570950	+	0.820985i	$0.693425\pi$
$480$		0			0
$481$	−12.9945	−	22.5072i	−0.0270156	−	0.0467925i
$482$	−155.035	−	89.5092i	−0.321648	−	0.185704i
$483$		0			0
$484$	9.81073	+	16.9927i	0.0202701	+	0.0351089i
$485$	−544.149	−	314.165i	−1.12196	−	0.647762i
$486$		0			0
$487$	201.883	+	349.672i	0.414544	+	0.718011i	0.995380	−	0.0960090i	$-0.0306078\pi$
$487$	201.883	+	349.672i	0.414544	+	0.718011i	−0.580836	+	0.814020i	$0.697274\pi$
$488$		−	187.087i		−	0.383376i
$489$		0			0
$490$	−410.117	+	405.139i	−0.836974	+	0.826814i
$491$	−708.736	−	409.189i	−1.44345	−	0.833378i	−0.445375	−	0.895344i	$-0.646930\pi$
$491$	−708.736	−	409.189i	−1.44345	−	0.833378i	−0.998078	+	0.0619657i	$0.980263\pi$
$492$		0			0
$493$	−37.7502	+	65.3853i	−0.0765725	+	0.132627i
$494$	41.6943	−	24.0722i	0.0844014	−	0.0487292i
$495$		0			0
$496$	83.0741			0.167488
$497$	100.058	−	129.577i	0.201324	−	0.260718i
$498$		0			0
$499$	−187.514	−	324.785i	−0.375780	−	0.650871i	0.614663	−	0.788790i	$-0.289292\pi$
$499$	−187.514	−	324.785i	−0.375780	−	0.650871i	−0.990444	+	0.137919i	$0.955959\pi$
$500$			319.575i			0.639150i
$501$		0			0
$502$	−450.393			−0.897197
$503$			434.043i			0.862909i	0.902135	+	0.431454i	$0.141999\pi$
$503$			434.043i			0.862909i	−0.902135	+	0.431454i	$0.858001\pi$
$504$		0			0
$505$	−1089.83			−2.15809
$506$			479.220i			0.947075i
$507$		0			0
$508$	223.022			0.439020
$509$	156.206	−	90.1855i	0.306888	−	0.177182i	−0.338645	−	0.940914i	$-0.609969\pi$
$509$	156.206	−	90.1855i	0.306888	−	0.177182i	0.645533	+	0.763732i	$0.276635\pi$
$510$		0			0
$511$	−36.6226	+	271.762i	−0.0716685	+	0.531824i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	343.751	+	595.394i	0.668776	+	1.15835i
$515$	239.352	+	138.190i	0.464762	+	0.268331i
$516$		0			0
$517$	219.171	−	379.616i	0.423929	−	0.734267i
$518$	39.3862	+	95.9138i	0.0760351	+	0.185162i
$519$		0			0
$520$	−58.3855			−0.112280
$521$	−296.089	+	170.947i	−0.568310	+	0.328114i	−0.756474	−	0.654024i	$-0.773080\pi$
$521$	−296.089	+	170.947i	−0.568310	+	0.328114i	0.188164	+	0.982138i	$0.439746\pi$
$522$		0			0
$523$	−189.342	+	327.951i	−0.362031	+	0.627057i	−0.988295	−	0.152555i	$-0.951250\pi$
$523$	−189.342	+	327.951i	−0.362031	+	0.627057i	0.626264	+	0.779611i	$0.284583\pi$
$524$	98.0016	−	56.5812i	0.187026	−	0.107979i
$525$		0			0
$526$	−246.703	+	427.303i	−0.469018	+	0.812363i
$527$	571.795	−	330.126i	1.08500	−	0.626425i
$528$		0			0
$529$	251.853	−	436.222i	0.476092	−	0.824616i
$530$	−798.694	−	461.126i	−1.50697	−	0.870050i
$531$		0			0
$532$	−177.679	+	72.9625i	−0.333984	+	0.137147i
$533$	107.193	−	61.8880i	0.201113	−	0.116113i
$534$		0			0
$535$	−450.075			−0.841262
$536$			70.5546i			0.131632i
$537$		0			0
$538$	−274.279	−	475.066i	−0.509813	−	0.883022i
$539$	136.773	−	498.255i	0.253754	−	0.924407i
$540$		0			0
$541$	143.032	−	247.739i	0.264385	−	0.457928i	−0.703017	−	0.711173i	$-0.748164\pi$
$541$	143.032	−	247.739i	0.264385	−	0.457928i	0.967402	+	0.253244i	$0.0814977\pi$
$542$	289.863	+	167.352i	0.534802	+	0.308768i
$543$		0			0
$544$	89.9185	+	155.743i	0.165291	+	0.286293i
$545$	−215.157	−	124.221i	−0.394783	−	0.227928i
$546$		0			0
$547$	−318.027	−	550.839i	−0.581402	−	1.00702i	−0.995313	−	0.0967009i	$-0.969171\pi$
$547$	−318.027	−	550.839i	−0.581402	−	1.00702i	0.413911	−	0.910317i	$-0.364162\pi$
$548$	114.374	+	66.0338i	0.208711	+	0.120500i
$549$		0			0
$550$	−329.618	−	570.915i	−0.599305	−	1.03803i
$551$			32.5831i			0.0591345i
$552$		0			0
$553$	−55.8130	−	43.0982i	−0.100928	−	0.0779352i
$554$	249.249	+	143.904i	0.449908	+	0.259754i
$555$		0			0
$556$	−90.4624	+	156.685i	−0.162702	+	0.281808i
$557$	−2.15468	+	1.24401i	−0.00386837	+	0.00223341i	−0.501933	−	0.864907i	$-0.667378\pi$
$557$	−2.15468	+	1.24401i	−0.00386837	+	0.00223341i	0.498065	+	0.867140i	$0.334044\pi$
$558$		0			0
$559$	81.3531			0.145533
$560$	230.848	+	31.1090i	0.412228	+	0.0555518i
$561$		0			0
$562$	−37.5143	−	64.9767i	−0.0667515	−	0.115617i
$563$		−	346.115i		−	0.614769i	−0.951585	−	0.307385i	$-0.900546\pi$
$563$		−	346.115i		−	0.614769i	0.951585	−	0.307385i	$-0.0994538\pi$
$564$		0			0
$565$	1538.42			2.72287
$566$		−	67.6150i		−	0.119461i
$567$		0			0
$568$	−66.1499			−0.116461
$569$			965.866i			1.69748i	0.528810	+	0.848740i	$0.322638\pi$
$569$			965.866i			1.69748i	−0.528810	+	0.848740i	$0.677362\pi$
$570$		0			0
$571$	165.110			0.289159			0.144579	−	0.989493i	$-0.453817\pi$
$571$	165.110			0.289159			0.144579	+	0.989493i	$0.453817\pi$
$572$	45.3186	−	26.1647i	0.0792283	−	0.0457425i
$573$		0			0
$574$	−456.802	+	187.582i	−0.795822	+	0.326797i
$575$			1420.64i			2.47067i
$576$		0			0
$577$	−449.998	−	779.419i	−0.779892	−	1.35081i	−0.932004	−	0.362449i	$-0.881941\pi$
$577$	−449.998	−	779.419i	−0.779892	−	1.35081i	0.152112	−	0.988363i	$-0.451393\pi$
$578$	883.857	+	510.295i	1.52916	+	0.882864i
$579$		0			0
$580$	19.7570	−	34.2202i	0.0340639	−	0.0590003i
$581$	−761.672	−	102.643i	−1.31097	−	0.176666i
$582$		0			0
$583$	826.590			1.41782
$584$	95.9566	−	55.4006i	0.164309	−	0.0948640i
$585$		0			0
$586$	−8.76047	+	15.1736i	−0.0149496	+	0.0258935i
$587$	829.734	−	479.047i	1.41352	−	0.816094i	0.417799	−	0.908540i	$-0.362802\pi$
$587$	829.734	−	479.047i	1.41352	−	0.816094i	0.995718	+	0.0924455i	$0.0294684\pi$
$588$		0			0
$589$	142.470	−	246.765i	0.241884	−	0.418955i
$590$	730.941	−	422.009i	1.23888	−	0.715269i
$591$		0			0
$592$	20.9477	−	36.2825i	0.0353846	−	0.0612879i
$593$	362.413	+	209.239i	0.611151	+	0.352848i	0.773416	−	0.633899i	$-0.218547\pi$
$593$	362.413	+	209.239i	0.611151	+	0.352848i	−0.162265	+	0.986747i	$0.551880\pi$
$594$		0			0
$595$	1712.54	−	703.239i	2.87822	−	1.18191i
$596$	170.691	−	98.5488i	0.286395	−	0.165350i
$597$		0			0
$598$	−112.768			−0.188576
$599$		−	12.6522i		−	0.0211222i	−0.999944	−	0.0105611i	$-0.996638\pi$
$599$		−	12.6522i		−	0.0211222i	0.999944	−	0.0105611i	$-0.00336176\pi$
$600$		0			0
$601$	77.9185	+	134.959i	0.129648	+	0.224557i	0.923540	−	0.383502i	$-0.125282\pi$
$601$	77.9185	+	134.959i	0.129648	+	0.224557i	−0.793892	+	0.608059i	$0.791949\pi$
$602$	−321.658	−	43.3466i	−0.534316	−	0.0720043i
$603$		0			0
$604$	−39.5943	+	68.5794i	−0.0655535	+	0.113542i
$605$	−70.6819	−	40.8082i	−0.116830	−	0.0674516i
$606$		0			0
$607$	215.508	+	373.270i	0.355037	+	0.614943i	0.987124	−	0.159955i	$-0.0511348\pi$
$607$	215.508	+	373.270i	0.355037	+	0.614943i	−0.632087	+	0.774897i	$0.717801\pi$
$608$	67.2129	+	38.8054i	0.110547	+	0.0638246i
$609$		0			0
$610$	389.099	+	673.939i	0.637867	+	1.10482i
$611$	89.3300	+	51.5747i	0.146203	+	0.0844103i
$612$		0			0
$613$	438.082	+	758.781i	0.714653	+	1.23781i	0.963093	+	0.269168i	$0.0867486\pi$
$613$	438.082	+	758.781i	0.714653	+	1.23781i	−0.248441	+	0.968647i	$0.579918\pi$
$614$			595.157i			0.969310i
$615$		0			0
$616$	−193.124	+	79.3047i	−0.313513	+	0.128741i
$617$	311.826	+	180.033i	0.505390	+	0.291787i	0.730937	−	0.682445i	$-0.239083\pi$
$617$	311.826	+	180.033i	0.505390	+	0.291787i	−0.225546	+	0.974232i	$0.572417\pi$
$618$		0			0
$619$	−28.2684	+	48.9623i	−0.0456679	+	0.0790991i	−0.887956	−	0.459929i	$-0.847875\pi$
$619$	−28.2684	+	48.9623i	−0.0456679	+	0.0790991i	0.842288	+	0.539028i	$0.181208\pi$
$620$	−299.256	+	172.775i	−0.482670	+	0.278670i
$621$		0			0
$622$	657.770			1.05751
$623$	−112.061	−	272.893i	−0.179873	−	0.438031i
$624$		0			0
$625$	−112.052	−	194.080i	−0.179284	−	0.310529i
$626$		−	516.145i		−	0.824513i
$627$		0			0
$628$	499.117			0.794772
$629$		−	332.974i		−	0.529370i
$630$		0			0
$631$	−632.353			−1.00214			−0.501072	−	0.865406i	$-0.667061\pi$
$631$	−632.353			−1.00214			−0.501072	+	0.865406i	$0.667061\pi$
$632$			28.4929i			0.0450836i
$633$		0			0
$634$	33.7273			0.0531977
$635$	−803.388	+	463.836i	−1.26518	+	0.730450i
$636$		0			0
$637$	117.248	+	32.1851i	0.184063	+	0.0505260i
$638$			35.4154i			0.0555100i
$639$		0			0
$640$	−47.0599	−	81.5101i	−0.0735311	−	0.127360i
$641$	−446.899	−	258.017i	−0.697191	−	0.402523i	0.109109	−	0.994030i	$-0.465200\pi$
$641$	−446.899	−	258.017i	−0.697191	−	0.402523i	−0.806300	+	0.591506i	$0.798533\pi$
$642$		0			0
$643$	273.812	−	474.257i	0.425836	−	0.737569i	−0.570662	−	0.821185i	$-0.693313\pi$
$643$	273.812	−	474.257i	0.425836	−	0.737569i	0.996498	+	0.0836157i	$0.0266468\pi$
$644$	445.870	+	60.0854i	0.692345	+	0.0933002i
$645$		0			0
$646$	616.830			0.954846
$647$	−186.510	+	107.681i	−0.288268	+	0.166432i	−0.637161	−	0.770731i	$-0.719891\pi$
$647$	−186.510	+	107.681i	−0.288268	+	0.166432i	0.348892	+	0.937163i	$0.386558\pi$
$648$		0			0
$649$	−378.235	+	655.123i	−0.582797	+	1.00943i
$650$	134.346	−	77.5646i	0.206686	−	0.119330i
$651$		0			0
$652$	242.275	−	419.633i	0.371587	−	0.643608i
$653$	278.235	−	160.639i	0.426088	−	0.246002i	−0.271591	−	0.962413i	$-0.587550\pi$
$653$	278.235	−	160.639i	0.426088	−	0.246002i	0.697679	+	0.716411i	$0.254216\pi$
$654$		0			0
$655$	−235.352	+	407.642i	−0.359317	+	0.622355i
$656$	172.800	+	99.7660i	0.263414	+	0.152082i
$657$		0			0
$658$	−325.718	−	251.516i	−0.495012	−	0.382243i
$659$	346.818	−	200.235i	0.526279	−	0.303847i	−0.213221	−	0.977004i	$-0.568395\pi$
$659$	346.818	−	200.235i	0.526279	−	0.303847i	0.739500	+	0.673157i	$0.235062\pi$
$660$		0			0
$661$	575.452			0.870577			0.435289	−	0.900291i	$-0.356646\pi$
$661$	575.452			0.870577			0.435289	+	0.900291i	$0.356646\pi$
$662$			319.803i			0.483087i
$663$		0			0
$664$	155.272	+	268.939i	0.233843	+	0.405029i
$665$	488.304	−	632.364i	0.734292	−	0.950923i
$666$		0			0
$667$	38.1596	−	66.0944i	0.0572108	−	0.0990921i
$668$	−168.833	−	97.4760i	−0.252744	−	0.145922i
$669$		0			0
$670$	−146.738	−	254.157i	−0.219011	−	0.379339i
$671$	−604.034	−	348.739i	−0.900199	−	0.519730i
$672$		0			0
$673$	473.931	+	820.873i	0.704207	+	1.21972i	0.966977	+	0.254864i	$0.0820307\pi$
$673$	473.931	+	820.873i	0.704207	+	1.21972i	−0.262770	+	0.964859i	$0.584636\pi$
$674$	370.275	+	213.778i	0.549369	+	0.317179i
$675$		0			0
$676$	−162.843	−	282.052i	−0.240892	−	0.417237i
$677$			1306.26i			1.92948i	0.263203	+	0.964741i	$0.415221\pi$
$677$			1306.26i			1.92948i	−0.263203	+	0.964741i	$0.584779\pi$
$678$		0			0
$679$	70.6092	−	523.964i	0.103990	−	0.771670i
$680$	−647.822	−	374.020i	−0.952679	−	0.550030i
$681$		0			0
$682$	154.854	−	268.215i	0.227058	−	0.393277i
$683$	617.670	−	356.612i	0.904349	−	0.522126i	0.0257402	−	0.999669i	$-0.491806\pi$
$683$	617.670	−	356.612i	0.904349	−	0.522126i	0.878609	+	0.477543i	$0.158472\pi$
$684$		0			0
$685$	−549.341			−0.801958
$686$	−446.432	−	189.727i	−0.650776	−	0.276570i
$687$		0			0
$688$	65.5722	+	113.574i	0.0953084	+	0.165079i
$689$			194.511i			0.282309i
$690$		0			0
$691$	364.791			0.527918			0.263959	−	0.964534i	$-0.414972\pi$
$691$	364.791			0.527918			0.263959	+	0.964534i	$0.414972\pi$
$692$			107.201i			0.154915i
$693$		0			0
$694$	−249.497			−0.359505
$695$		−	752.565i		−	1.08283i
$696$		0			0
$697$	1585.83			2.27522
$698$	213.882	−	123.485i	0.306421	−	0.176912i
$699$		0			0
$700$	−572.512	+	235.097i	−0.817874	+	0.335853i
$701$			944.475i			1.34732i	0.739039	+	0.673662i	$0.235280\pi$
$701$			944.475i			1.34732i	−0.739039	+	0.673662i	$0.764720\pi$
$702$		0			0
$703$	−71.8494	−	124.447i	−0.102204	−	0.177022i
$704$	73.0554	+	42.1785i	0.103772	+	0.0599127i
$705$		0			0
$706$	−100.867	+	174.706i	−0.142871	+	0.247459i
$707$	−348.343	−	848.290i	−0.492706	−	1.19984i
$708$		0			0
$709$	−1031.54			−1.45493			−0.727464	−	0.686146i	$-0.759301\pi$
$709$	−1031.54			−1.45493			−0.727464	+	0.686146i	$0.759301\pi$
$710$	238.290	−	137.577i	0.335620	−	0.193770i
$711$		0			0
$712$	−59.6001	+	103.230i	−0.0837081	+	0.144987i
$713$	−577.996	+	333.706i	−0.810653	+	0.468031i
$714$		0			0
$715$	−108.833	+	188.505i	−0.152214	+	0.263643i
$716$	245.880	−	141.959i	0.343408	−	0.198266i
$717$		0			0
$718$	432.259	−	748.694i	0.602031	−	1.04275i
$719$	27.9770	+	16.1525i	0.0389109	+	0.0224652i	0.519329	−	0.854574i	$-0.326182\pi$
$719$	27.9770	+	16.1525i	0.0389109	+	0.0224652i	−0.480418	+	0.877039i	$0.659515\pi$
$720$		0			0
$721$	−31.0586	+	230.474i	−0.0430771	+	0.319658i
$722$	−211.597	+	122.165i	−0.293070	+	0.169204i
$723$		0			0
$724$	415.809			0.574322
$725$			104.988i			0.144811i
$726$		0			0
$727$	−102.737	−	177.945i	−0.141316	−	0.244767i	0.786676	−	0.617366i	$-0.211800\pi$
$727$	−102.737	−	177.945i	−0.141316	−	0.244767i	−0.927992	+	0.372599i	$0.878467\pi$
$728$	−18.6617	−	45.4454i	−0.0256342	−	0.0624249i
$729$		0			0
$730$	−230.441	+	399.136i	−0.315673	+	0.546762i
$731$	902.660	+	521.151i	1.23483	+	0.712929i
$732$		0			0
$733$	293.871	+	509.000i	0.400916	+	0.694407i	0.993837	−	0.110854i	$-0.0353587\pi$
$733$	293.871	+	509.000i	0.400916	+	0.694407i	−0.592921	+	0.805261i	$0.702025\pi$
$734$	−206.802	−	119.397i	−0.281746	−	0.162666i
$735$		0			0
$736$	−90.8936	−	157.432i	−0.123497	−	0.213903i
$737$	227.794	+	131.517i	0.309083	+	0.178449i
$738$		0			0
$739$	−395.335	−	684.741i	−0.534960	−	0.926578i	−0.999165	−	0.0408504i	$-0.986993\pi$
$739$	−395.335	−	684.741i	−0.534960	−	0.926578i	0.464205	−	0.885728i	$-0.346340\pi$
$740$			174.266i			0.235494i
$741$		0			0
$742$	103.639	−	769.066i	0.139676	−	1.03648i
$743$	15.5592	+	8.98312i	0.0209411	+	0.0120903i	0.510434	−	0.859917i	$-0.329485\pi$
$743$	15.5592	+	8.98312i	0.0209411	+	0.0120903i	−0.489493	+	0.872007i	$0.662818\pi$
$744$		0			0
$745$	−409.918	+	709.999i	−0.550226	+	0.953019i
$746$	398.611	−	230.138i	0.534331	−	0.308496i
$747$		0			0
$748$	670.448			0.896321
$749$	−143.857	−	350.323i	−0.192066	−	0.467721i
$750$		0			0
$751$	−397.119	−	687.830i	−0.528787	−	0.915886i	−0.999437	−	0.0335656i	$-0.989314\pi$
$751$	−397.119	−	687.830i	−0.528787	−	0.915886i	0.470650	−	0.882320i	$-0.344020\pi$
$752$			166.281i			0.221118i
$753$		0			0
$754$	−8.33384			−0.0110528
$755$		−	329.389i		−	0.436277i
$756$		0			0
$757$	99.2649			0.131129			0.0655647	−	0.997848i	$-0.479115\pi$
$757$	99.2649			0.131129			0.0655647	+	0.997848i	$0.479115\pi$
$758$			10.9226i			0.0144097i
$759$		0			0
$760$	−322.826			−0.424770
$761$	−636.996	+	367.770i	−0.837051	+	0.483272i	−0.856261	−	0.516544i	$-0.827218\pi$
$761$	−636.996	+	367.770i	−0.837051	+	0.483272i	0.0192098	+	0.999815i	$0.493885\pi$
$762$		0			0
$763$	27.9189	−	207.176i	0.0365910	−	0.271528i
$764$		−	615.774i		−	0.805987i
$765$		0			0
$766$	−458.124	−	793.495i	−0.598074	−	1.03589i
$767$	−154.161	−	89.0051i	−0.200993	−	0.116043i
$768$		0			0
$769$	−239.582	+	414.969i	−0.311550	+	0.539621i	−0.978698	−	0.205304i	$-0.934182\pi$
$769$	−239.582	+	414.969i	−0.311550	+	0.539621i	0.667148	+	0.744925i	$0.267515\pi$
$770$	530.750	−	687.332i	0.689286	−	0.892639i
$771$		0			0
$772$	330.268			0.427808
$773$	100.386	−	57.9577i	0.129865	−	0.0749776i	−0.433660	−	0.901077i	$-0.642778\pi$
$773$	100.386	−	57.9577i	0.129865	−	0.0749776i	0.563525	+	0.826099i	$0.309445\pi$
$774$		0			0
$775$	459.060	−	795.116i	0.592336	−	1.02596i
$776$	−185.006	+	106.814i	−0.238410	+	0.137646i
$777$		0			0
$778$	105.619	−	182.938i	0.135757	−	0.235138i
$779$	592.693	−	342.192i	0.760838	−	0.439270i
$780$		0			0
$781$	−123.306	+	213.573i	−0.157883	+	0.273461i
$782$	−1251.23	−	722.399i	−1.60004	−	0.923784i
$783$		0			0
$784$	49.5716	+	189.628i	0.0632290	+	0.241872i
$785$	−1797.95	+	1038.05i	−2.29039	+	1.32236i
$786$		0			0
$787$	977.438			1.24198			0.620990	−	0.783818i	$-0.286731\pi$
$787$	977.438			1.24198			0.620990	+	0.783818i	$0.286731\pi$
$788$			172.574i			0.219003i
$789$		0			0
$790$	−59.2587	−	102.639i	−0.0750110	−	0.129923i
$791$	491.724	+	1197.45i	0.621649	+	1.51385i
$792$		0			0
$793$	82.0642	−	142.139i	0.103486	−	0.179242i
$794$	116.657	+	67.3520i	0.146923	+	0.0848262i
$795$		0			0
$796$	329.440	+	570.607i	0.413870	+	0.716843i
$797$	982.477	+	567.234i	1.23272	+	0.711711i	0.967596	−	0.252503i	$-0.0812539\pi$
$797$	982.477	+	567.234i	1.23272	+	0.711711i	0.265124	+	0.964214i	$0.414587\pi$
$798$		0			0
$799$	660.779	+	1144.50i	0.827008	+	1.43242i
$800$	216.571	+	125.037i	0.270714	+	0.156297i
$801$		0			0
$802$	257.711	+	446.369i	0.321335	+	0.556569i
$803$		−	413.077i		−	0.514417i
$804$		0			0
$805$	−1731.11	+	710.865i	−2.15045	+	0.883062i
$806$	63.1154	+	36.4397i	0.0783070	+	0.0452106i
$807$		0			0
$808$	−185.267	+	320.893i	−0.229291	+	0.397144i
$809$	−751.325	+	433.778i	−0.928708	+	0.536190i	−0.886403	−	0.462915i	$-0.846804\pi$
$809$	−751.325	+	433.778i	−0.928708	+	0.536190i	−0.0423053	+	0.999105i	$0.513470\pi$
$810$		0			0
$811$	−329.692			−0.406525			−0.203263	−	0.979124i	$-0.565155\pi$
$811$	−329.692			−0.406525			−0.203263	+	0.979124i	$0.565155\pi$
$812$	32.9508	+	4.44044i	0.0405798	+	0.00546852i
$813$		0			0
$814$	−78.0949	−	135.264i	−0.0959396	−	0.166172i
$815$			2015.51i			2.47302i
$816$		0			0
$817$	449.818			0.550572
$818$			1104.97i			1.35082i
$819$		0			0
$820$	−829.963			−1.01215
$821$		−	1028.55i		−	1.25281i	−0.779500	−	0.626403i	$-0.784527\pi$
$821$		−	1028.55i		−	1.25281i	0.779500	−	0.626403i	$-0.215473\pi$
$822$		0			0
$823$	−1250.00			−1.51883			−0.759415	−	0.650607i	$-0.774515\pi$
$823$	−1250.00			−1.51883			−0.759415	+	0.650607i	$0.774515\pi$
$824$	81.3780	−	46.9836i	0.0987597	−	0.0570189i
$825$		0			0
$826$	562.108	+	434.054i	0.680518	+	0.525489i
$827$		−	1582.29i		−	1.91329i	−0.291248	−	0.956647i	$-0.594071\pi$
$827$		−	1582.29i		−	1.91329i	0.291248	−	0.956647i	$-0.405929\pi$
$828$		0			0
$829$	−275.656	−	477.450i	−0.332516	−	0.575935i	0.650488	−	0.759516i	$-0.274564\pi$
$829$	−275.656	−	477.450i	−0.332516	−	0.575935i	−0.983004	+	0.183581i	$0.941231\pi$
$830$	−1118.66	−	645.861i	−1.34779	−	0.778146i
$831$		0			0
$832$	−9.92531	+	17.1911i	−0.0119295	+	0.0206624i
$833$	1094.75	+	1108.21i	1.31423	+	1.33038i
$834$		0			0
$835$	810.912			0.971152
$836$	250.576	−	144.670i	0.299732	−	0.173050i
$837$		0			0
$838$	−327.800	+	567.767i	−0.391170	+	0.677526i
$839$	1220.53	−	704.672i	1.45474	−	0.839895i	0.455997	−	0.889981i	$-0.349283\pi$
$839$	1220.53	−	704.672i	1.45474	−	0.839895i	0.998745	+	0.0500860i	$0.0159495\pi$
$840$		0			0
$841$	−417.680	+	723.443i	−0.496647	+	0.860217i
$842$	−733.994	+	423.772i	−0.871727	+	0.503292i
$843$		0			0
$844$	81.4137	−	141.013i	0.0964617	−	0.167077i
$845$	1173.21	+	677.353i	1.38841	+	0.801601i
$846$		0			0
$847$	9.17174	−	68.0599i	0.0108285	−	0.0803541i
$848$	−271.550	+	156.779i	−0.320224	+	0.184881i
$849$		0			0
$850$	1987.53			2.33827
$851$			336.585i			0.395517i
$852$		0			0
$853$	−305.025	−	528.318i	−0.357590	−	0.619365i	0.629967	−	0.776622i	$-0.283068\pi$
$853$	−305.025	−	528.318i	−0.357590	−	0.619365i	−0.987558	+	0.157257i	$0.949735\pi$
$854$	−400.204	+	518.273i	−0.468624	+	0.606877i
$855$		0			0
$856$	−76.5110	+	132.521i	−0.0893820	+	0.154814i
$857$	938.243	+	541.695i	1.09480	+	0.632083i	0.934850	−	0.355043i	$-0.115534\pi$
$857$	938.243	+	541.695i	1.09480	+	0.632083i	0.159949	+	0.987125i	$0.448867\pi$
$858$		0			0
$859$	−698.024	−	1209.01i	−0.812601	−	1.40747i	−0.911038	−	0.412322i	$-0.864718\pi$
$859$	−698.024	−	1209.01i	−0.812601	−	1.40747i	0.0984373	−	0.995143i	$-0.468616\pi$
$860$	−472.418	−	272.751i	−0.549323	−	0.317152i
$861$		0			0
$862$	213.432	+	369.675i	0.247601	+	0.428857i
$863$	−33.5922	−	19.3944i	−0.0389249	−	0.0224733i	0.480411	−	0.877043i	$-0.340487\pi$
$863$	−33.5922	−	19.3944i	−0.0389249	−	0.0224733i	−0.519336	+	0.854570i	$0.673821\pi$
$864$		0			0
$865$	−222.954	−	386.168i	−0.257751	−	0.446438i
$866$			823.969i			0.951465i
$867$		0			0
$868$	−230.133	−	177.707i	−0.265131	−	0.204731i
$869$	91.9926	+	53.1120i	0.105860	+	0.0611185i
$870$		0			0
$871$	−30.9481	+	53.6038i	−0.0355317	+	0.0615428i
$872$	−73.1517	+	42.2341i	−0.0838895	+	0.0484336i
$873$		0			0
$874$	−623.520			−0.713409
$875$	683.614	−	885.293i	0.781273	−	1.01176i
$876$		0			0
$877$	−625.286	−	1083.03i	−0.712982	−	1.23492i	−0.963733	−	0.266870i	$-0.914011\pi$
$877$	−625.286	−	1083.03i	−0.712982	−	1.23492i	0.250750	−	0.968052i	$-0.419323\pi$
$878$			79.7244i			0.0908023i
$879$		0			0
$880$	−350.887			−0.398735
$881$		−	844.579i		−	0.958659i	−0.877635	−	0.479329i	$-0.840880\pi$
$881$		−	844.579i		−	0.958659i	0.877635	−	0.479329i	$-0.159120\pi$
$882$		0			0
$883$	−378.496			−0.428648			−0.214324	−	0.976763i	$-0.568755\pi$
$883$	−378.496			−0.428648			−0.214324	+	0.976763i	$0.568755\pi$
$884$			157.768i			0.178470i
$885$		0			0
$886$	269.918			0.304648
$887$	1003.41	−	579.319i	1.13124	−	0.653121i	0.186993	−	0.982361i	$-0.440126\pi$
$887$	1003.41	−	579.319i	1.13124	−	0.653121i	0.944246	+	0.329240i	$0.106792\pi$
$888$		0			0
$889$	−617.821	−	477.074i	−0.694961	−	0.536642i
$890$		−	495.819i		−	0.557100i
$891$		0			0
$892$	−186.441	−	322.925i	−0.209014	−	0.362023i
$893$	493.924	+	285.167i	0.553106	+	0.319336i
$894$		0			0
$895$	−590.484	+	1022.75i	−0.659759	+	1.14274i
$896$	48.4030	−	62.6829i	0.0540213	−	0.0699586i
$897$		0			0
$898$	−6.25637			−0.00696700
$899$	−42.7152	+	24.6616i	−0.0475141	+	0.0274323i
$900$		0			0
$901$	−1246.04	+	2158.21i	−1.38296	+	2.39535i
$902$	644.213	−	371.937i	0.714205	−	0.412347i
$903$		0			0
$904$	261.525	−	452.975i	0.289298	−	0.501079i
$905$	−1497.86	+	864.789i	−1.65509	+	0.955568i
$906$		0			0
$907$	140.650	−	243.613i	0.155072	−	0.268593i	−0.778013	−	0.628248i	$-0.783772\pi$
$907$	140.650	−	243.613i	0.155072	−	0.268593i	0.933085	+	0.359655i	$0.117106\pi$
$908$	70.7295	+	40.8357i	0.0778960	+	0.0449733i
$909$		0			0
$910$	161.741	+	124.894i	0.177737	+	0.137247i
$911$	−176.629	+	101.977i	−0.193885	+	0.111939i	−0.593800	−	0.804613i	$-0.702373\pi$
$911$	−176.629	+	101.977i	−0.193885	+	0.111939i	0.399915	+	0.916552i	$0.369040\pi$
$912$		0			0
$913$	1157.74			1.26806
$914$		−	954.417i		−	1.04422i
$915$		0			0
$916$	−71.2022	−	123.326i	−0.0777316	−	0.134635i
$917$	−392.521	−	52.8960i	−0.428049	−	0.0576838i
$918$		0			0
$919$	−499.667	+	865.449i	−0.543708	+	0.941730i	0.454979	+	0.890502i	$0.349647\pi$
$919$	−499.667	+	865.449i	−0.543708	+	0.941730i	−0.998687	+	0.0512275i	$0.983687\pi$
$920$	654.847	+	378.076i	0.711790	+	0.410952i
$921$		0			0
$922$	−298.678	−	517.325i	−0.323946	−	0.561090i
$923$	−50.2573	−	29.0161i	−0.0544499	−	0.0314367i
$924$		0			0
$925$	−231.510	−	400.988i	−0.250281	−	0.433500i
$926$	100.157	+	57.8256i	0.108161	+	0.0624466i
$927$		0			0
$928$	−6.71724	−	11.6346i	−0.00723840	−	0.0125373i
$929$			61.1046i			0.0657746i	0.999459	+	0.0328873i	$0.0104702\pi$
$929$			61.1046i			0.0657746i	−0.999459	+	0.0328873i	$0.989530\pi$
$930$		0			0
$931$	648.287	+	177.958i	0.696334	+	0.191147i
$932$	−13.3283	−	7.69509i	−0.0143007	−	0.00825653i
$933$		0			0
$934$	−395.308	+	684.694i	−0.423242	+	0.733077i
$935$	−2415.14	+	1394.38i	−2.58304	+	1.49132i
$936$		0			0
$937$	−233.228			−0.248909			−0.124455	−	0.992225i	$-0.539718\pi$
$937$	−233.228			−0.248909			−0.124455	+	0.992225i	$0.539718\pi$
$938$	150.926	−	195.452i	0.160902	−	0.208371i
$939$		0			0
$940$	−345.827	−	598.989i	−0.367901	−	0.637223i
$941$		−	822.293i		−	0.873851i	−0.899498	−	0.436925i	$-0.856067\pi$
$941$		−	822.293i		−	0.873851i	0.899498	−	0.436925i	$-0.143933\pi$
$942$		0			0
$943$	−1603.03			−1.69992
$944$		−	286.959i		−	0.303982i
$945$		0			0
$946$	488.918			0.516827
$947$		−	1566.48i		−	1.65415i	−0.562092	−	0.827075i	$-0.690003\pi$
$947$		−	1566.48i		−	1.65415i	0.562092	−	0.827075i	$-0.309997\pi$
$948$		0			0
$949$	97.2038			0.102428
$950$	742.825	−	428.870i	0.781922	−	0.451443i
$951$		0			0
$952$	84.0619	−	623.791i	0.0883003	−	0.655242i
$953$		−	852.327i		−	0.894362i	−0.894443	−	0.447181i	$-0.852428\pi$
$953$		−	852.327i		−	0.894362i	0.894443	−	0.447181i	$-0.147572\pi$
$954$		0			0
$955$	1280.67	+	2218.19i	1.34102	+	2.32271i
$956$	−409.355	−	236.341i	−0.428196	−	0.247219i
$957$		0			0
$958$	56.8783	−	98.5161i	0.0593719	−	0.102835i
$959$	−175.586	−	427.589i	−0.183092	−	0.445869i
$960$		0			0
$961$	−529.668			−0.551164
$962$	31.8299	−	18.3770i	0.0330873	−	0.0191029i
$963$		0			0
$964$	126.585	−	219.252i	0.131312	−	0.227440i
$965$	−1189.72	+	686.883i	−1.23287	+	0.711796i
$966$		0			0
$967$	−553.241	+	958.241i	−0.572121	+	0.990942i	0.424227	+	0.905556i	$0.360546\pi$
$967$	−553.241	+	958.241i	−0.572121	+	0.990942i	−0.996348	+	0.0853865i	$0.972787\pi$
$968$	−24.0313	+	13.8745i	−0.0248257	+	0.0143331i
$969$		0			0
$970$	444.296	−	769.543i	0.458037	−	0.793343i
$971$	−479.817	−	277.023i	−0.494148	−	0.285296i	0.232146	−	0.972681i	$-0.425425\pi$
$971$	−479.817	−	277.023i	−0.494148	−	0.285296i	−0.726293	+	0.687385i	$0.758759\pi$
$972$		0			0
$973$	585.771	−	240.542i	0.602026	−	0.247217i
$974$	−494.510	+	285.506i	−0.507711	+	0.293127i
$975$		0			0
$976$	264.581			0.271087
$977$		−	173.601i		−	0.177688i	−0.996046	−	0.0888439i	$-0.971683\pi$
$977$		−	173.601i		−	0.177688i	0.996046	−	0.0888439i	$-0.0283172\pi$
$978$		0			0
$979$	222.195	+	384.853i	0.226961	+	0.393108i
$980$	−572.953	−	579.993i	−0.584646	−	0.591830i
$981$		0			0
$982$	578.680	−	1002.30i	0.589287	−	1.02068i
$983$	−1189.13	−	686.542i	−1.20969	−	0.698415i	−0.246999	−	0.969016i	$-0.579444\pi$
$983$	−1189.13	−	686.542i	−1.20969	−	0.698415i	−0.962692	+	0.270600i	$0.912778\pi$
$984$		0			0
$985$	−358.915	−	621.659i	−0.364381	−	0.631126i
$986$	−92.4688	−	53.3869i	−0.0937818	−	0.0541449i
$987$		0			0
$988$	34.0433	+	58.9647i	0.0344567	+	0.0596808i
$989$	−912.449	−	526.803i	−0.922597	−	0.532662i
$990$		0			0
$991$	−523.608	−	906.916i	−0.528364	−	0.915153i	−0.999453	−	0.0330672i	$-0.989472\pi$
$991$	−523.608	−	906.916i	−0.528364	−	0.915153i	0.471090	−	0.882085i	$-0.343861\pi$
$992$			117.485i			0.118432i
$993$		0			0
$994$	183.250	+	141.503i	0.184356	+	0.142358i
$995$	−2373.47	−	1370.32i	−2.38540	−	1.37721i
$996$		0			0
$997$	−94.6794	+	163.990i	−0.0949643	+	0.164483i	−0.909594	−	0.415499i	$-0.863607\pi$
$997$	−94.6794	+	163.990i	−0.0949643	+	0.164483i	0.814629	+	0.579982i	$0.196940\pi$
$998$	459.315	−	265.185i	0.460235	−	0.265717i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.r.a.233.15		32
3.2	odd	2		126.3.r.a.23.7	yes	32
7.4	even	3		378.3.i.a.179.7		32
9.2	odd	6		378.3.i.a.359.2		32
9.7	even	3		126.3.i.a.65.13	✓	32
21.11	odd	6		126.3.i.a.95.13	yes	32
63.11	odd	6	inner	378.3.r.a.305.7		32
63.25	even	3		126.3.r.a.11.15	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.i.a.65.13	✓	32	9.7	even	3
126.3.i.a.95.13	yes	32	21.11	odd	6
126.3.r.a.11.15	yes	32	63.25	even	3
126.3.r.a.23.7	yes	32	3.2	odd	2
378.3.i.a.179.7		32	7.4	even	3
378.3.i.a.359.2		32	9.2	odd	6
378.3.r.a.233.15		32	1.1	even	1	trivial
378.3.r.a.305.7		32	63.11	odd	6	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -2.00000 q^{4} +(7.20455 - 4.15955i) q^{5} +(5.54044 + 4.27827i) q^{7} -2.82843i q^{8} +(5.88249 + 10.1888i) q^{10} +(-9.13192 - 5.27232i) q^{11} +(1.24066 - 2.14889i) q^{13} +(-6.05038 + 7.83536i) q^{14} +4.00000 q^{16} +(27.5318 - 15.8955i) q^{17} +(6.85989 - 11.8817i) q^{19} +(-14.4091 + 8.31909i) q^{20} +(7.45618 - 12.9145i) q^{22} +(-27.8304 + 16.0679i) q^{23} +(22.1037 - 38.2847i) q^{25} +(3.03899 + 1.75456i) q^{26} +(-11.0809 - 8.55653i) q^{28} +(-2.05673 + 1.18745i) q^{29} +20.7685 q^{31} +5.65685i q^{32} +(22.4796 + 38.9358i) q^{34} +(57.7120 + 7.77726i) q^{35} +(5.23692 - 9.07061i) q^{37} +(16.8032 + 9.70134i) q^{38} +(-11.7650 - 20.3775i) q^{40} +(43.1999 + 24.9415i) q^{41} +(16.3930 + 28.3936i) q^{43} +(18.2638 + 10.5446i) q^{44} +(-22.7234 - 39.3581i) q^{46} +41.5702i q^{47} +(12.3929 + 47.4069i) q^{49} +(54.1427 + 31.2593i) q^{50} +(-2.48133 + 4.29779i) q^{52} +(-67.8875 + 39.1948i) q^{53} -87.7218 q^{55} +(12.1008 - 15.6707i) q^{56} +(-1.67931 - 2.90865i) q^{58} -71.7399i q^{59} +66.1453 q^{61} +29.3711i q^{62} -8.00000 q^{64} -20.6424i q^{65} -24.9448 q^{67} +(-55.0636 + 31.7910i) q^{68} +(-10.9987 + 81.6171i) q^{70} -23.3875i q^{71} +(19.5871 + 33.9258i) q^{73} +(12.8278 + 7.40612i) q^{74} +(-13.7198 + 23.7633i) q^{76} +(-28.0385 - 68.2797i) q^{77} -10.0737 q^{79} +(28.8182 - 16.6382i) q^{80} +(-35.2726 + 61.0939i) q^{82} +(-95.0843 + 54.8969i) q^{83} +(132.236 - 229.040i) q^{85} +(-40.1546 + 23.1833i) q^{86} +(-14.9124 + 25.8290i) q^{88} +(-36.4975 - 21.0718i) q^{89} +(16.0674 - 6.59792i) q^{91} +(55.6607 - 32.1357i) q^{92} -58.7892 q^{94} -114.136i q^{95} +(-37.7643 - 65.4097i) q^{97} +(-67.0435 + 17.5262i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} + 2 q^{7} + 36 q^{11} + 10 q^{13} - 36 q^{14} + 128 q^{16} + 54 q^{17} + 28 q^{19} + 126 q^{23} + 80 q^{25} + 72 q^{26} - 4 q^{28} - 36 q^{29} + 16 q^{31} + 90 q^{35} + 22 q^{37} - 72 q^{41}+ \cdots - 288 q^{98}+O(q^{100}) \) 32 * q - 64 * q^4 + 2 * q^7 + 36 * q^11 + 10 * q^13 - 36 * q^14 + 128 * q^16 + 54 * q^17 + 28 * q^19 + 126 * q^23 + 80 * q^25 + 72 * q^26 - 4 * q^28 - 36 * q^29 + 16 * q^31 + 90 * q^35 + 22 * q^37 - 72 * q^41 + 16 * q^43 - 72 * q^44 - 12 * q^46 + 2 * q^49 + 288 * q^50 - 20 * q^52 + 72 * q^53 - 24 * q^55 + 72 * q^56 - 24 * q^58 + 124 * q^61 - 256 * q^64 - 140 * q^67 - 108 * q^68 + 72 * q^70 + 196 * q^73 - 216 * q^74 - 56 * q^76 - 486 * q^77 + 76 * q^79 + 60 * q^85 + 144 * q^86 + 486 * q^89 - 122 * q^91 - 252 * q^92 - 336 * q^94 - 38 * q^97 - 288 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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