LMFDB - Embedded newform 378.3.i.a.179.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(179,378)] 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, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.179"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.i (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			179.7
Character	$\chi$	$=$	378.179
Dual form			378.3.i.a.359.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +8.31909i q^{5} +(0.934868 + 6.93729i) q^{7} -2.82843i q^{8} +(5.88249 - 10.1888i) q^{10} +10.5446i q^{11} +(1.24066 - 2.14889i) q^{13} +(3.76043 - 9.15746i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-27.5318 - 15.8955i) q^{17} +(6.85989 + 11.8817i) q^{19} +(-14.4091 + 8.31909i) q^{20} +(7.45618 - 12.9145i) q^{22} -32.1357i q^{23} -44.2073 q^{25} +(-3.03899 + 1.75456i) q^{26} +(-11.0809 + 8.55653i) q^{28} +(-2.05673 + 1.18745i) q^{29} +(-10.3843 - 17.9861i) q^{31} +(4.89898 - 2.82843i) q^{32} +(22.4796 + 38.9358i) q^{34} +(-57.7120 + 7.77726i) q^{35} +(5.23692 + 9.07061i) q^{37} -19.4027i q^{38} +23.5300 q^{40} +(43.1999 + 24.9415i) q^{41} +(16.3930 + 28.3936i) q^{43} +(-18.2638 + 10.5446i) q^{44} +(-22.7234 + 39.3581i) q^{46} +(-36.0009 - 20.7851i) q^{47} +(-47.2520 + 12.9709i) q^{49} +(54.1427 + 31.2593i) q^{50} +4.96266 q^{52} +(67.8875 + 39.1948i) q^{53} -87.7218 q^{55} +(19.6216 - 2.64421i) q^{56} +3.35862 q^{58} +(-62.1285 + 35.8699i) q^{59} +(-33.0727 + 57.2835i) q^{61} +29.3711i q^{62} -8.00000 q^{64} +(17.8768 + 10.3212i) q^{65} +(12.4724 + 21.6028i) q^{67} -63.5820i q^{68} +(76.1818 + 31.2834i) q^{70} -23.3875i q^{71} +(19.5871 - 33.9258i) q^{73} -14.8122i q^{74} +(-13.7198 + 23.7633i) q^{76} +(-73.1512 + 9.85784i) q^{77} +(5.03687 - 8.72412i) q^{79} +(-28.8182 - 16.6382i) q^{80} +(-35.2726 - 61.0939i) q^{82} +(-95.0843 + 54.8969i) q^{83} +(132.236 - 229.040i) q^{85} -46.3665i q^{86} +29.8247 q^{88} +(36.4975 - 21.0718i) q^{89} +(16.0674 + 6.59792i) q^{91} +(55.6607 - 32.1357i) q^{92} +(29.3946 + 50.9129i) q^{94} +(-98.8447 + 57.0680i) q^{95} +(-37.7643 - 65.4097i) q^{97} +(67.0435 + 17.5262i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} + 2 q^{7} + 10 q^{13} - 36 q^{14} - 64 q^{16} - 54 q^{17} + 28 q^{19} - 160 q^{25} - 72 q^{26} - 4 q^{28} - 36 q^{29} - 8 q^{31} - 90 q^{35} + 22 q^{37} - 72 q^{41} + 16 q^{43} + 72 q^{44}+ \cdots + 288 q^{98}+O(q^{100}) $ 32 * q + 32 * q^4 + 2 * q^7 + 10 * q^13 - 36 * q^14 - 64 * q^16 - 54 * q^17 + 28 * q^19 - 160 * q^25 - 72 * q^26 - 4 * q^28 - 36 * q^29 - 8 * q^31 - 90 * q^35 + 22 * q^37 - 72 * q^41 + 16 * q^43 + 72 * q^44 - 12 * q^46 + 108 * q^47 + 74 * q^49 + 288 * q^50 + 40 * q^52 - 72 * q^53 - 24 * q^55 + 48 * q^58 + 90 * q^59 - 62 * q^61 - 256 * q^64 - 378 * q^65 + 70 * q^67 - 108 * q^70 + 196 * q^73 - 56 * q^76 - 630 * q^77 - 38 * q^79 + 60 * q^85 - 486 * q^89 - 122 * q^91 - 252 * q^92 + 168 * q^94 + 72 * q^95 - 38 * q^97 + 288 * q^98

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$			8.31909i			1.66382i	0.554911	+	0.831909i	$0.312752\pi$
$5$			8.31909i			1.66382i	−0.554911	+	0.831909i	$0.687248\pi$
$6$		0			0
$7$	0.934868	+	6.93729i	0.133553	+	0.991042i
$7$	0.934868	+	6.93729i	0.133553	+	0.991042i
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	5.88249	−	10.1888i	0.588249	−	1.01888i
$11$			10.5446i			0.958603i	0.877650	+	0.479301i	$0.159110\pi$
$11$			10.5446i			0.958603i	−0.877650	+	0.479301i	$0.840890\pi$
$12$		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	$0.136242\pi$
$14$	3.76043	−	9.15746i	0.268602	−	0.654105i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−27.5318	−	15.8955i	−1.61952	−	0.935029i	−0.987045	−	0.160446i	$-0.948707\pi$
$17$	−27.5318	−	15.8955i	−1.61952	−	0.935029i	−0.632473	−	0.774582i	$-0.717960\pi$
$18$		0			0
$19$	6.85989	+	11.8817i	0.361047	+	0.625351i	0.988133	−	0.153598i	$-0.0490862\pi$
$19$	6.85989	+	11.8817i	0.361047	+	0.625351i	−0.627087	+	0.778949i	$0.715753\pi$
$20$	−14.4091	+	8.31909i	−0.720455	+	0.415955i
$21$		0			0
$22$	7.45618	−	12.9145i	0.338917	−	0.587022i
$23$		−	32.1357i		−	1.39721i	−0.715509	−	0.698603i	$-0.753805\pi$
$23$		−	32.1357i		−	1.39721i	0.715509	−	0.698603i	$-0.246195\pi$
$24$		0			0
$25$	−44.2073			−1.76829
$26$	−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
$31$	−10.3843	−	17.9861i	−0.334976	−	0.580196i	0.648504	−	0.761211i	$-0.275395\pi$
$31$	−10.3843	−	17.9861i	−0.334976	−	0.580196i	−0.983480	+	0.181015i	$0.942062\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$		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	0.928076	−	0.372391i	$-0.121462\pi$
$37$	5.23692	+	9.07061i	0.141538	+	0.245152i	−0.786538	+	0.617542i	$0.788128\pi$
$38$		−	19.4027i		−	0.510597i
$39$		0			0
$40$	23.5300			0.588249
$41$	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
$47$	−36.0009	−	20.7851i	−0.765976	−	0.442236i	0.0654613	−	0.997855i	$-0.479148\pi$
$47$	−36.0009	−	20.7851i	−0.765976	−	0.442236i	−0.831437	+	0.555619i	$0.812481\pi$
$48$		0			0
$49$	−47.2520	+	12.9709i	−0.964327	+	0.264712i
$50$	54.1427	+	31.2593i	1.08285	+	0.625186i
$51$		0			0
$52$	4.96266			0.0954357
$53$	67.8875	+	39.1948i	1.28090	+	0.739525i	0.977012	−	0.213184i	$-0.0683834\pi$
$53$	67.8875	+	39.1948i	1.28090	+	0.739525i	0.303883	+	0.952709i	$0.401717\pi$
$54$		0			0
$55$	−87.7218			−1.59494
$56$	19.6216	−	2.64421i	0.350386	−	0.0472180i
$57$		0			0
$58$	3.35862			0.0579072
$59$	−62.1285	+	35.8699i	−1.05303	+	0.607965i	−0.923495	−	0.383610i	$-0.874681\pi$
$59$	−62.1285	+	35.8699i	−1.05303	+	0.607965i	−0.129531	+	0.991575i	$0.541347\pi$
$60$		0			0
$61$	−33.0727	+	57.2835i	−0.542175	+	0.939074i	0.456604	+	0.889670i	$0.349066\pi$
$61$	−33.0727	+	57.2835i	−0.542175	+	0.939074i	−0.998779	+	0.0494044i	$0.984268\pi$
$62$			29.3711i			0.473728i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	17.8768	+	10.3212i	0.275028	+	0.158788i
$66$		0			0
$67$	12.4724	+	21.6028i	0.186155	+	0.322431i	0.943965	−	0.330045i	$-0.107064\pi$
$67$	12.4724	+	21.6028i	0.186155	+	0.322431i	−0.757810	+	0.652475i	$0.773731\pi$
$68$		−	63.5820i		−	0.935029i
$69$		0			0
$70$	76.1818	+	31.2834i	1.08831	+	0.446905i
$71$		−	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	−0.700111	−	0.714034i	$-0.746866\pi$
$73$	19.5871	−	33.9258i	0.268316	−	0.464737i	0.968427	+	0.249297i	$0.0801996\pi$
$74$		−	14.8122i		−	0.200166i
$75$		0			0
$76$	−13.7198	+	23.7633i	−0.180523	+	0.312676i
$77$	−73.1512	+	9.85784i	−0.950015	+	0.128024i
$78$		0			0
$79$	5.03687	−	8.72412i	0.0637579	−	0.110432i	−0.832384	−	0.554199i	$-0.813025\pi$
$79$	5.03687	−	8.72412i	0.0637579	−	0.110432i	0.896142	+	0.443767i	$0.146358\pi$
$80$	−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
$86$		−	46.3665i		−	0.539146i
$87$		0			0
$88$	29.8247			0.338917
$89$	36.4975	−	21.0718i	0.410084	−	0.236762i	−0.280742	−	0.959783i	$-0.590580\pi$
$89$	36.4975	−	21.0718i	0.410084	−	0.236762i	0.690826	+	0.723021i	$0.257247\pi$
$90$		0			0
$91$	16.0674	+	6.59792i	0.176564	+	0.0725046i
$92$	55.6607	−	32.1357i	0.605008	−	0.349302i
$93$		0			0
$94$	29.3946	+	50.9129i	0.312708	+	0.541627i
$95$	−98.8447	+	57.0680i	−1.04047	+	0.600716i
$96$		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
$101$			131.004i			1.29707i	0.761186	+	0.648534i	$0.224618\pi$
$101$			131.004i			1.29707i	−0.761186	+	0.648534i	$0.775382\pi$
$102$		0			0
$103$	−33.2224			−0.322548			−0.161274	−	0.986910i	$-0.551560\pi$
$103$	−33.2224			−0.322548			−0.161274	+	0.986910i	$0.551560\pi$
$104$	−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	$-0.585312\pi$
$107$	46.8532	−	27.0507i	0.437881	−	0.252810i	0.702698	+	0.711488i	$0.251978\pi$
$108$		0			0
$109$	−14.9320	+	25.8630i	−0.136991	+	0.237275i	−0.926356	−	0.376648i	$-0.877076\pi$
$109$	−14.9320	+	25.8630i	−0.136991	+	0.237275i	0.789365	+	0.613924i	$0.210410\pi$
$110$	107.437	+	62.0287i	0.976698	+	0.563897i
$111$		0			0
$112$	−25.9012	−	10.6361i	−0.231261	−	0.0949652i
$113$	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
$115$	267.340			2.32470
$116$	−4.11345	−	2.37490i	−0.0354608	−	0.0204733i
$117$		0			0
$118$	101.455			0.859792
$119$	84.5331	−	205.856i	0.710362	−	1.72988i
$120$		0			0
$121$	9.81073			0.0810804
$122$	81.0112	−	46.7718i	0.664026	−	0.383376i
$123$		0			0
$124$	20.7685	−	35.9721i	0.167488	−	0.290098i
$125$		−	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	$0.644674\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−14.5964	−	25.2817i	−0.112280	−	0.194474i
$131$		−	56.5812i		−	0.431918i	−0.976402	−	0.215959i	$-0.930712\pi$
$131$		−	56.5812i		−	0.431918i	0.976402	−	0.215959i	$-0.0692877\pi$
$132$		0			0
$133$	−76.0135	+	58.6968i	−0.571530	+	0.441329i
$134$		−	35.2773i		−	0.263263i
$135$		0			0
$136$	−44.9592	+	77.8717i	−0.330583	+	0.572586i
$137$			66.0338i			0.481998i	0.970525	+	0.240999i	$0.0774751\pi$
$137$			66.0338i			0.481998i	−0.970525	+	0.240999i	$0.922525\pi$
$138$		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	$0.0611663\pi$
$140$	−71.1826	−	92.1828i	−0.508447	−	0.658449i
$141$		0			0
$142$	−16.5375	+	28.6437i	−0.116461	+	0.201717i
$143$	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
$149$		−	98.5488i		−	0.661401i	−0.943736	−	0.330701i	$-0.892715\pi$
$149$		−	98.5488i		−	0.661401i	0.943736	−	0.330701i	$-0.107285\pi$
$150$		0			0
$151$	−39.5943			−0.262214			−0.131107	−	0.991368i	$-0.541853\pi$
$151$	−39.5943			−0.262214			−0.131107	+	0.991368i	$0.541853\pi$
$152$	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
$157$	124.779	+	216.124i	0.794772	+	1.37658i	0.922984	+	0.384838i	$0.125743\pi$
$157$	124.779	+	216.124i	0.794772	+	1.37658i	−0.128213	+	0.991747i	$0.540924\pi$
$158$	−12.3378	+	7.12321i	−0.0780872	+	0.0450836i
$159$		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	−0.951043	−	0.309060i	$-0.899986\pi$
$163$	−121.137	−	209.816i	−0.743175	−	1.28722i	0.207868	−	0.978157i	$-0.433348\pi$
$164$			99.7660i			0.608329i
$165$		0			0
$166$	155.272			0.935373
$167$	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
$173$	46.4195	+	26.8003i	0.268321	+	0.154915i	0.628124	−	0.778113i	$-0.283823\pi$
$173$	46.4195	+	26.8003i	0.268321	+	0.154915i	−0.359803	+	0.933028i	$0.617156\pi$
$174$		0			0
$175$	−41.3280	−	306.679i	−0.236160	−	1.75245i
$176$	−36.5277	−	21.0893i	−0.207544	−	0.119825i
$177$		0			0
$178$	−59.6001			−0.334832
$179$	122.940	+	70.9794i	0.686815	+	0.396533i	0.802418	−	0.596763i	$-0.203547\pi$
$179$	122.940	+	70.9794i	0.686815	+	0.396533i	−0.115603	+	0.993296i	$0.536880\pi$
$180$		0			0
$181$	−207.905			−1.14864			−0.574322	−	0.818629i	$-0.694734\pi$
$181$	−207.905			−1.14864			−0.574322	+	0.818629i	$0.694734\pi$
$182$	−15.0130	−	19.4421i	−0.0824889	−	0.106825i
$183$		0			0
$184$	−90.8936			−0.493987
$185$	−75.4593	+	43.5664i	−0.407888	+	0.235494i
$186$		0			0
$187$	167.612	−	290.313i	0.896321	−	1.55247i
$188$		−	83.1404i		−	0.442236i
$189$		0			0
$190$	161.413			0.849541
$191$	−266.638	−	153.943i	−1.39601	−	0.805987i	−0.402038	−	0.915623i	$-0.631698\pi$
$191$	−266.638	−	153.943i	−1.39601	−	0.805987i	−0.993972	+	0.109637i	$0.965031\pi$
$192$		0			0
$193$	82.5670	+	143.010i	0.427808	+	0.740986i	0.996678	−	0.0814418i	$-0.0259525\pi$
$193$	82.5670	+	143.010i	0.427808	+	0.740986i	−0.568870	+	0.822428i	$0.692619\pi$
$194$			106.814i			0.550585i
$195$		0			0
$196$	−69.7183	−	68.8720i	−0.355706	−	0.351388i
$197$		−	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	0.0720681	+	0.997400i	$0.477040\pi$
$199$	−164.720	+	285.304i	−0.827739	+	1.43369i	−0.899808	+	0.436287i	$0.856293\pi$
$200$			125.037i			0.625186i
$201$		0			0
$202$	92.6337	−	160.446i	0.458583	−	0.794289i
$203$	−10.1605	−	13.1580i	−0.0500515	−	0.0648177i
$204$		0			0
$205$	−207.491	+	359.384i	−1.01215	+	1.75309i
$206$	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	$0.228464\pi$
$212$			156.779i			0.739525i
$213$		0			0
$214$	−76.5110			−0.357528
$215$	−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
$220$	−87.7218	−	151.939i	−0.398735	−	0.690630i
$221$	−68.3154	+	39.4419i	−0.309120	+	0.178470i
$222$		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
$227$			40.8357i			0.179893i	0.995947	+	0.0899465i	$0.0286696\pi$
$227$			40.8357i			0.179893i	−0.995947	+	0.0899465i	$0.971330\pi$
$228$		0			0
$229$	−71.2022			−0.310926			−0.155463	−	0.987842i	$-0.549687\pi$
$229$	−71.2022			−0.310926			−0.155463	+	0.987842i	$0.549687\pi$
$230$	−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	$-0.671923\pi$
$233$	−6.66414	+	3.84755i	−0.0286015	+	0.0165131i	0.485631	+	0.874164i	$0.338590\pi$
$234$		0			0
$235$	172.913	−	299.495i	0.735801	−	1.27445i
$236$	−124.257	−	71.7399i	−0.526513	−	0.303982i
$237$		0			0
$238$	−249.094	+	192.348i	−1.04661	+	0.808183i
$239$	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
$241$	126.585			0.525250			0.262625	−	0.964898i	$-0.415412\pi$
$241$	126.585			0.525250			0.262625	+	0.964898i	$0.415412\pi$
$242$	−12.0156	−	6.93724i	−0.0496514	−	0.0286663i
$243$		0			0
$244$	−132.291			−0.542175
$245$	−107.906	−	393.094i	−0.440433	−	1.60447i
$246$		0			0
$247$	34.0433			0.137827
$248$	−50.8723	+	29.3711i	−0.205130	+	0.118432i
$249$		0			0
$250$	−112.987	+	195.699i	−0.451948	+	0.782796i
$251$			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
$254$	136.573	+	78.8503i	0.537688	+	0.310434i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$			486.137i			1.89158i	0.324773	+	0.945792i	$0.394712\pi$
$257$			486.137i			1.89158i	−0.324773	+	0.945792i	$0.605288\pi$
$258$		0			0
$259$	−58.0297	+	44.8099i	−0.224053	+	0.173011i
$260$			41.2848i			0.158788i
$261$		0			0
$262$	−40.0090	+	69.2976i	−0.152706	+	0.264495i
$263$		−	348.891i		−	1.32658i	−0.748361	−	0.663291i	$-0.769159\pi$
$263$		−	348.891i		−	1.32658i	0.748361	−	0.663291i	$-0.230841\pi$
$264$		0			0
$265$	−326.066	+	564.762i	−1.23044	+	2.13118i
$266$	134.602	−	18.1390i	0.506023	−	0.0681915i
$267$		0			0
$268$	−24.9448	+	43.2057i	−0.0930777	+	0.161215i
$269$	335.922	+	193.945i	1.24878	+	0.720985i	0.970867	−	0.239621i	$-0.0770231\pi$
$269$	335.922	+	193.945i	1.24878	+	0.720985i	0.277916	+	0.960606i	$0.410356\pi$
$270$		0			0
$271$	118.336	+	204.964i	0.436664	+	0.756324i	0.997430	−	0.0716504i	$-0.0228266\pi$
$271$	118.336	+	204.964i	0.436664	+	0.756324i	−0.560766	+	0.827974i	$0.689493\pi$
$272$	110.127	−	63.5820i	0.404879	−	0.233757i
$273$		0			0
$274$	46.6929	−	80.8745i	0.170412	−	0.295162i
$275$		−	466.150i		−	1.69509i
$276$		0			0
$277$	−203.511			−0.734697			−0.367348	−	0.930083i	$-0.619734\pi$
$277$	−203.511			−0.734697			−0.367348	+	0.930083i	$0.619734\pi$
$278$	−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
$283$	23.9055	+	41.4056i	0.0844718	+	0.146309i	0.905166	−	0.425058i	$-0.139746\pi$
$283$	23.9055	+	41.4056i	0.0844718	+	0.146309i	−0.820694	+	0.571368i	$0.806413\pi$
$284$	40.5084	−	23.3875i	0.142635	−	0.0823504i
$285$		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
$290$			27.9407i			0.0963471i
$291$		0			0
$292$	78.3482			0.268316
$293$	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
$299$	−69.0563	−	39.8697i	−0.230957	−	0.133343i
$300$		0			0
$301$	−181.649	+	140.268i	−0.603486	+	0.466005i
$302$	48.4930	+	27.9974i	0.160573	+	0.0927067i
$303$		0			0
$304$	−54.8791			−0.180523
$305$	−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	$0.259625\pi$
$308$	−90.2255	−	116.844i	−0.292940	−	0.379363i
$309$		0			0
$310$	−244.341			−0.788197
$311$	−402.800	+	232.557i	−1.29518	+	0.747771i	−0.979567	−	0.201118i	$-0.935542\pi$
$311$	−402.800	+	232.557i	−1.29518	+	0.747771i	−0.315610	+	0.948889i	$0.602209\pi$
$312$		0			0
$313$	182.485	−	316.073i	0.583019	−	1.00982i	−0.412100	−	0.911139i	$-0.635205\pi$
$313$	182.485	−	316.073i	0.583019	−	1.00982i	0.995119	−	0.0986800i	$-0.0314620\pi$
$314$		−	352.929i		−	1.12398i
$315$		0			0
$316$	20.1475			0.0637579
$317$	20.6537	+	11.9244i	0.0651536	+	0.0376164i	0.532223	−	0.846604i	$-0.321357\pi$
$317$	20.6537	+	11.9244i	0.0651536	+	0.0376164i	−0.467069	+	0.884221i	$0.654690\pi$
$318$		0			0
$319$	−12.5212	−	21.6874i	−0.0392515	−	0.0679856i
$320$		−	66.5528i		−	0.207977i
$321$		0			0
$322$	−294.282	−	120.844i	−0.913919	−	0.375293i
$323$		−	436.165i		−	1.35036i
$324$		0			0
$325$	−54.8465	+	94.9969i	−0.168758	+	0.292298i
$326$			342.629i			1.05101i
$327$		0			0
$328$	70.5452	−	122.188i	0.215077	−	0.372524i
$329$	110.536	−	269.180i	0.335977	−	0.818176i
$330$		0			0
$331$	−113.068	+	195.839i	−0.341594	+	0.591658i	−0.984729	−	0.174095i	$-0.944300\pi$
$331$	−113.068	+	195.839i	−0.341594	+	0.591658i	0.643135	+	0.765753i	$0.277633\pi$
$332$	−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	$0.0186043\pi$
$338$		−	230.295i		−	0.681346i
$339$		0			0
$340$	528.944			1.55572
$341$	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
$346$	−37.9014	−	65.6471i	−0.109542	−	0.189732i
$347$	152.785	−	88.2104i	0.440302	−	0.254209i	−0.263423	−	0.964680i	$-0.584852\pi$
$347$	152.785	−	88.2104i	0.440302	−	0.254209i	0.703726	+	0.710472i	$0.251518\pi$
$348$		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
$353$		−	142.647i		−	0.404099i	−0.979375	−	0.202050i	$-0.935240\pi$
$353$		−	142.647i		−	0.404099i	0.979375	−	0.202050i	$-0.0647602\pi$
$354$		0			0
$355$	194.563			0.548065
$356$	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	$-0.342420\pi$
$359$	529.406	−	305.653i	1.47467	−	0.851401i	0.999593	+	0.0285432i	$0.00908683\pi$
$360$		0			0
$361$	86.3839	−	149.621i	0.239291	−	0.414464i
$362$	254.630	+	147.011i	0.703398	+	0.406107i
$363$		0			0
$364$	4.63943	+	34.4274i	0.0127457	+	0.0945808i
$365$	282.232	+	162.947i	0.773238	+	0.446429i
$366$		0			0
$367$	168.853			0.460090			0.230045	−	0.973180i	$-0.426113\pi$
$367$	168.853			0.460090			0.230045	+	0.973180i	$0.426113\pi$
$368$	111.321	+	64.2715i	0.302504	+	0.174651i
$369$		0			0
$370$	123.224			0.333039
$371$	−208.440	+	507.597i	−0.561834	+	1.36819i
$372$		0			0
$373$	325.465			0.872559			0.436280	−	0.899811i	$-0.356296\pi$
$373$	325.465			0.872559			0.436280	+	0.899811i	$0.356296\pi$
$374$	−410.564	+	237.039i	−1.09777	+	0.633795i
$375$		0			0
$376$	−58.7892	+	101.826i	−0.156354	+	0.270813i
$377$			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	$0.496757\pi$
$380$	−197.689	−	114.136i	−0.520235	−	0.300358i
$381$		0			0
$382$	217.709	+	377.083i	0.569919	+	0.987128i
$383$		−	647.886i		−	1.69161i	−0.533494	−	0.845804i	$-0.679121\pi$
$383$		−	647.886i		−	1.69161i	0.533494	−	0.845804i	$-0.320879\pi$
$384$		0			0
$385$	−82.0083	−	608.552i	−0.213009	−	1.58065i
$386$		−	233.535i		−	0.605012i
$387$		0			0
$388$	75.5286	−	130.819i	0.194661	−	0.337163i
$389$			149.368i			0.383979i	0.981397	+	0.191990i	$0.0614940\pi$
$389$			149.368i			0.383979i	−0.981397	+	0.191990i	$0.938506\pi$
$390$		0			0
$391$	−510.813	+	884.755i	−1.30643	+	2.26280i
$392$	36.6873	+	133.649i	0.0935900	+	0.340941i
$393$		0			0
$394$	−61.0141	+	105.680i	−0.154858	+	0.268222i
$395$	72.5768	+	41.9022i	0.183739	+	0.106082i
$396$		0			0
$397$	47.6251	+	82.4890i	0.119962	+	0.207781i	0.919753	−	0.392499i	$-0.128389\pi$
$397$	47.6251	+	82.4890i	0.119962	+	0.207781i	−0.799790	+	0.600280i	$0.795056\pi$
$398$	403.480	−	232.949i	1.01377	−	0.585300i
$399$		0			0
$400$	88.4147	−	153.139i	0.221037	−	0.382847i
$401$			364.458i			0.908874i	0.890779	+	0.454437i	$0.150160\pi$
$401$			364.458i			0.908874i	−0.890779	+	0.454437i	$0.849840\pi$
$402$		0			0
$403$	−51.5335			−0.127875
$404$	−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
$409$	−390.666	−	676.654i	−0.955174	−	1.65441i	−0.733969	−	0.679183i	$-0.762334\pi$
$409$	−390.666	−	676.654i	−0.955174	−	1.65441i	−0.221206	−	0.975227i	$-0.570999\pi$
$410$	508.246	−	293.436i	1.23962	−	0.715698i
$411$		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
$416$		−	14.0365i		−	0.0337416i
$417$		0			0
$418$	204.594			0.489460
$419$	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
$425$	1217.11	+	702.697i	2.86378	+	1.65341i
$426$		0			0
$427$	−428.311	−	175.882i	−1.00307	−	0.411902i
$428$	93.7064	+	54.1014i	0.218940	+	0.126405i
$429$		0			0
$430$	385.728			0.897041
$431$	−261.400	−	150.919i	−0.606496	−	0.350161i	0.165097	−	0.986277i	$-0.447206\pi$
$431$	−261.400	−	150.919i	−0.606496	−	0.350161i	−0.771593	+	0.636117i	$0.780540\pi$
$432$		0			0
$433$	582.634			1.34557			0.672787	−	0.739836i	$-0.265097\pi$
$433$	582.634			1.34557			0.672787	+	0.739836i	$0.265097\pi$
$434$	−203.756	+	27.4581i	−0.469484	+	0.0632676i
$435$		0			0
$436$	−59.7281			−0.136991
$437$	381.826	−	220.447i	0.873744	−	0.504456i
$438$		0			0
$439$	−28.1868	+	48.8210i	−0.0642069	+	0.111210i	−0.896342	−	0.443363i	$-0.853785\pi$
$439$	−28.1868	+	48.8210i	−0.0642069	+	0.111210i	0.832135	+	0.554573i	$0.187118\pi$
$440$			248.115i			0.563897i
$441$		0			0
$442$	111.559			0.252395
$443$	165.291	+	95.4305i	0.373116	+	0.215419i	0.674819	−	0.737983i	$-0.264222\pi$
$443$	165.291	+	95.4305i	0.373116	+	0.215419i	−0.301703	+	0.953402i	$0.597555\pi$
$444$		0			0
$445$	175.299	+	303.626i	0.393929	+	0.682306i
$446$		−	263.667i		−	0.591182i
$447$		0			0
$448$	−7.47894	−	55.4983i	−0.0166941	−	0.123880i
$449$			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
$452$			369.853i			0.818258i
$453$		0			0
$454$	28.8752	−	50.0133i	0.0636018	−	0.110162i
$455$	−54.8887	+	133.666i	−0.120635	+	0.293771i
$456$		0			0
$457$	337.437	−	584.459i	0.738375	−	1.27890i	−0.214851	−	0.976647i	$-0.568927\pi$
$457$	337.437	−	584.459i	0.738375	−	1.27890i	0.953227	−	0.302257i	$-0.0977400\pi$
$458$	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	$0.138519\pi$
$464$		−	9.49961i		−	0.0204733i
$465$		0			0
$466$	10.8825			0.0233530
$467$	−484.152	+	279.525i	−1.03673	+	0.598555i	−0.918905	−	0.394480i	$-0.870925\pi$
$467$	−484.152	+	279.525i	−1.03673	+	0.598555i	−0.117823	+	0.993035i	$0.537591\pi$
$468$		0			0
$469$	−138.205	+	106.721i	−0.294681	+	0.227549i
$470$	−423.549	+	244.536i	−0.901169	+	0.520290i
$471$		0			0
$472$	101.455	+	175.726i	0.214948	+	0.372301i
$473$	−299.400	+	172.859i	−0.632981	+	0.365452i
$474$		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
$479$			80.4381i			0.167929i	0.996469	+	0.0839646i	$0.0267583\pi$
$479$			80.4381i			0.167929i	−0.996469	+	0.0839646i	$0.973242\pi$
$480$		0			0
$481$	25.9890			0.0540313
$482$	−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	−0.580836	−	0.814020i	$-0.697274\pi$
$487$	201.883	−	349.672i	0.414544	−	0.718011i	0.995380	+	0.0960090i	$0.0306078\pi$
$488$	162.022	+	93.5436i	0.332013	+	0.191688i
$489$		0			0
$490$	−145.802	+	557.741i	−0.297555	+	1.13825i
$491$	−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
$493$	75.5005			0.153145
$494$	−41.6943	−	24.0722i	−0.0844014	−	0.0487292i
$495$		0			0
$496$	83.0741			0.167488
$497$	162.246	−	21.8642i	0.326451	−	0.0439924i
$498$		0			0
$499$	375.029			0.751561			0.375780	−	0.926709i	$-0.377375\pi$
$499$	375.029			0.751561			0.375780	+	0.926709i	$0.377375\pi$
$500$	276.760	−	159.788i	0.553520	−	0.319575i
$501$		0			0
$502$	225.196	−	390.052i	0.448599	−	0.776995i
$503$			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
$506$	−415.016	−	239.610i	−0.820191	−	0.473537i
$507$		0			0
$508$	−111.511	−	193.143i	−0.219510	−	0.380203i
$509$			180.371i			0.354364i	0.984178	+	0.177182i	$0.0566980\pi$
$509$			180.371i			0.354364i	−0.984178	+	0.177182i	$0.943302\pi$
$510$		0			0
$511$	253.664	+	104.165i	0.496408	+	0.203845i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	343.751	−	595.394i	0.668776	−	1.15835i
$515$		−	276.380i		−	0.536661i
$516$		0			0
$517$	219.171	−	379.616i	0.423929	−	0.734267i
$518$	102.757	−	13.8475i	0.198372	−	0.0267326i
$519$		0			0
$520$	29.1928	−	50.5634i	0.0561399	−	0.0972372i
$521$	296.089	+	170.947i	0.568310	+	0.328114i	0.756474	−	0.654024i	$-0.226920\pi$
$521$	296.089	+	170.947i	0.568310	+	0.328114i	−0.188164	+	0.982138i	$0.560254\pi$
$522$		0			0
$523$	−189.342	−	327.951i	−0.362031	−	0.627057i	0.626264	−	0.779611i	$-0.284583\pi$
$523$	−189.342	−	327.951i	−0.362031	−	0.627057i	−0.988295	+	0.152555i	$0.951250\pi$
$524$	98.0016	−	56.5812i	0.187026	−	0.107979i
$525$		0			0
$526$	−246.703	+	427.303i	−0.469018	+	0.812363i
$527$			660.252i			1.25285i
$528$		0			0
$529$	−503.706			−0.952185
$530$	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
$535$	225.037	+	389.776i	0.420631	+	0.728554i
$536$	61.1021	−	35.2773i	0.113996	−	0.0658159i
$537$		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	0.967402	−	0.253244i	$-0.0814977\pi$
$541$	143.032	+	247.739i	0.264385	+	0.457928i	−0.703017	+	0.711173i	$0.748164\pi$
$542$		−	334.704i		−	0.617536i
$543$		0			0
$544$	−179.837			−0.330583
$545$	−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
$551$	−28.2178	−	16.2916i	−0.0512120	−	0.0295673i
$552$		0			0
$553$	65.2306	+	26.7864i	0.117958	+	0.0484383i
$554$	249.249	+	143.904i	0.449908	+	0.259754i
$555$		0			0
$556$	180.925			0.325404
$557$	2.15468	+	1.24401i	0.00386837	+	0.00223341i	0.501933	−	0.864907i	$-0.332622\pi$
$557$	2.15468	+	1.24401i	0.00386837	+	0.00223341i	−0.498065	+	0.867140i	$0.665956\pi$
$558$		0			0
$559$	81.3531			0.145533
$560$	88.4828	−	215.475i	0.158005	−	0.384776i
$561$		0			0
$562$	75.0286			0.133503
$563$	−299.745	+	173.058i	−0.532406	+	0.307385i	−0.741996	−	0.670405i	$-0.766121\pi$
$563$	−299.745	+	173.058i	−0.532406	+	0.307385i	0.209590	+	0.977789i	$0.432787\pi$
$564$		0			0
$565$	−769.210	+	1332.31i	−1.36143	+	2.35807i
$566$		−	67.6150i		−	0.119461i
$567$		0			0
$568$	−66.1499			−0.116461
$569$	−836.465	−	482.933i	−1.47006	−	0.848740i	−0.470626	−	0.882333i	$-0.655972\pi$
$569$	−836.465	−	482.933i	−1.47006	−	0.848740i	−0.999436	+	0.0335928i	$0.989305\pi$
$570$		0			0
$571$	−82.5549	−	142.989i	−0.144579	−	0.250419i	0.784637	−	0.619956i	$-0.212850\pi$
$571$	−82.5549	−	142.989i	−0.144579	−	0.250419i	−0.929216	+	0.369537i	$0.879516\pi$
$572$			52.3294i			0.0914850i
$573$		0			0
$574$	390.851	−	301.811i	0.680925	−	0.525803i
$575$			1420.64i			2.47067i
$576$		0			0
$577$	−449.998	+	779.419i	−0.779892	+	1.35081i	0.152112	+	0.988363i	$0.451393\pi$
$577$	−449.998	+	779.419i	−0.779892	+	1.35081i	−0.932004	+	0.362449i	$0.881941\pi$
$578$		−	1020.59i		−	1.76573i
$579$		0			0
$580$	19.7570	−	34.2202i	0.0340639	−	0.0590003i
$581$	−469.727	−	608.306i	−0.808481	−	1.04700i
$582$		0			0
$583$	−413.295	+	715.848i	−0.708911	+	1.22787i
$584$	−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
$590$			844.018i			1.43054i
$591$		0			0
$592$	−41.8954			−0.0707692
$593$	−362.413	+	209.239i	−0.611151	+	0.352848i	−0.773416	−	0.633899i	$-0.781453\pi$
$593$	−362.413	+	209.239i	−0.611151	+	0.352848i	0.162265	+	0.986747i	$0.448120\pi$
$594$		0			0
$595$	1712.54	+	703.239i	2.87822	+	1.18191i
$596$	170.691	−	98.5488i	0.286395	−	0.165350i
$597$		0			0
$598$	56.3842	+	97.6603i	0.0942880	+	0.163312i
$599$	−10.9571	+	6.32609i	−0.0182923	+	0.0105611i	−0.509118	−	0.860697i	$-0.670028\pi$
$599$	−10.9571	+	6.32609i	−0.0182923	+	0.0105611i	0.490826	+	0.871258i	$0.336695\pi$
$600$		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
$605$			81.6164i			0.134903i
$606$		0			0
$607$	−431.015			−0.710075			−0.355037	−	0.934852i	$-0.615532\pi$
$607$	−431.015			−0.710075			−0.355037	+	0.934852i	$0.615532\pi$
$608$	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	−0.248441	−	0.968647i	$-0.579918\pi$
$613$	438.082	−	758.781i	0.714653	−	1.23781i	0.963093	−	0.269168i	$-0.0867486\pi$
$614$	−515.421	−	297.578i	−0.839447	−	0.484655i
$615$		0			0
$616$	27.8822	+	206.903i	0.0452633	+	0.335881i
$617$	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
$619$	56.5368			0.0913357			0.0456679	−	0.998957i	$-0.485458\pi$
$619$	56.5368			0.0913357			0.0456679	+	0.998957i	$0.485458\pi$
$620$	299.256	+	172.775i	0.482670	+	0.278670i
$621$		0			0
$622$	657.770			1.05751
$623$	180.302	+	233.494i	0.289409	+	0.374790i
$624$		0			0
$625$	224.105			0.358568
$626$	−446.995	+	258.073i	−0.714050	+	0.412257i
$627$		0			0
$628$	−249.558	+	432.248i	−0.397386	+	0.688292i
$629$		−	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	$0.667061\pi$
$632$	−24.6755	−	14.2464i	−0.0390436	−	0.0225418i
$633$		0			0
$634$	−16.8637	−	29.2087i	−0.0265988	−	0.0460705i
$635$		−	927.672i		−	1.46090i
$636$		0			0
$637$	−30.7508	+	117.632i	−0.0482745	+	0.184666i
$638$			35.4154i			0.0555100i
$639$		0			0
$640$	−47.0599	+	81.5101i	−0.0735311	+	0.127360i
$641$			516.035i			0.805047i	0.915410	+	0.402523i	$0.131867\pi$
$641$			516.035i			0.805047i	−0.915410	+	0.402523i	$0.868133\pi$
$642$		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	$0.0266468\pi$
$644$	274.970	+	356.092i	0.426973	+	0.552938i
$645$		0			0
$646$	−308.415	+	534.191i	−0.477423	+	0.826921i
$647$	186.510	+	107.681i	0.288268	+	0.166432i	0.637161	−	0.770731i	$-0.280109\pi$
$647$	186.510	+	107.681i	0.288268	+	0.166432i	−0.348892	+	0.937163i	$0.613442\pi$
$648$		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
$653$			321.278i			0.492004i	0.969269	+	0.246002i	$0.0791169\pi$
$653$			321.278i			0.492004i	−0.969269	+	0.246002i	$0.920883\pi$
$654$		0			0
$655$	470.705			0.718633
$656$	−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
$661$	−287.726	−	498.356i	−0.435289	−	0.753942i	0.562030	−	0.827117i	$-0.310020\pi$
$661$	−287.726	−	498.356i	−0.435289	−	0.753942i	−0.997319	+	0.0731743i	$0.976687\pi$
$662$	276.958	−	159.902i	0.418365	−	0.241543i
$663$		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
$668$			194.952i			0.291844i
$669$		0			0
$670$	293.475			0.438023
$671$	−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
$677$	−1131.25	−	653.129i	−1.67098	−	0.964741i	−0.967091	−	0.254430i	$-0.918112\pi$
$677$	−1131.25	−	653.129i	−1.67098	−	0.964741i	−0.703889	−	0.710310i	$-0.748555\pi$
$678$		0			0
$679$	418.461	−	323.131i	0.616290	−	0.475893i
$680$	−647.822	−	374.020i	−0.952679	−	0.550030i
$681$		0			0
$682$	−309.708			−0.454117
$683$	−617.670	−	356.612i	−0.904349	−	0.522126i	−0.0257402	−	0.999669i	$-0.508194\pi$
$683$	−617.670	−	356.612i	−0.904349	−	0.522126i	−0.878609	+	0.477543i	$0.841528\pi$
$684$		0			0
$685$	−549.341			−0.801958
$686$	−58.9075	+	481.485i	−0.0858709	+	0.701873i
$687$		0			0
$688$	−131.144			−0.190617
$689$	168.451	−	97.2553i	0.244486	−	0.141154i
$690$		0			0
$691$	−182.396	+	315.919i	−0.263959	+	0.457191i	−0.967290	−	0.253672i	$-0.918362\pi$
$691$	−182.396	+	315.919i	−0.263959	+	0.457191i	0.703331	+	0.710862i	$0.251695\pi$
$692$			107.201i			0.154915i
$693$		0			0
$694$	−249.497			−0.359505
$695$	651.740	+	376.282i	0.937756	+	0.541414i
$696$		0			0
$697$	−792.915	−	1373.37i	−1.13761	−	1.97040i
$698$			246.969i			0.353824i
$699$		0			0
$700$	489.856	−	378.261i	0.699794	−	0.540373i
$701$			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
$704$		−	84.3571i		−	0.119825i
$705$		0			0
$706$	−100.867	+	174.706i	−0.142871	+	0.247459i
$707$	−908.812	+	122.471i	−1.28545	+	0.173227i
$708$		0			0
$709$	515.772	−	893.343i	0.727464	−	1.26000i	−0.230488	−	0.973075i	$-0.574032\pi$
$709$	515.772	−	893.343i	0.727464	−	1.26000i	0.957952	−	0.286929i	$-0.0926345\pi$
$710$	−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
$716$			283.918i			0.396533i
$717$		0			0
$718$	−864.517			−1.20406
$719$	−27.9770	+	16.1525i	−0.0389109	+	0.0224652i	−0.519329	−	0.854574i	$-0.673818\pi$
$719$	−27.9770	+	16.1525i	−0.0389109	+	0.0224652i	0.480418	+	0.877039i	$0.340485\pi$
$720$		0			0
$721$	−31.0586	−	230.474i	−0.0430771	−	0.319658i
$722$	−211.597	+	122.165i	−0.293070	+	0.169204i
$723$		0			0
$724$	−207.905	−	360.102i	−0.287161	−	0.497378i
$725$	90.9224	−	52.4940i	0.125410	−	0.0724056i
$726$		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
$731$		−	1042.30i		−	1.42586i
$732$		0			0
$733$	−587.743			−0.801832			−0.400916	−	0.916115i	$-0.631308\pi$
$733$	−587.743			−0.801832			−0.400916	+	0.916115i	$0.631308\pi$
$734$	−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	0.464205	+	0.885728i	$0.346340\pi$
$739$	−395.335	+	684.741i	−0.534960	+	0.926578i	−0.999165	+	0.0408504i	$0.986993\pi$
$740$	−150.919	−	87.1329i	−0.203944	−	0.117747i
$741$		0			0
$742$	614.211	−	474.287i	0.827778	−	0.639201i
$743$	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
$745$	819.836			1.10045
$746$	−398.611	−	230.138i	−0.534331	−	0.308496i
$747$		0			0
$748$	670.448			0.896321
$749$	231.460	+	299.746i	0.309026	+	0.400194i
$750$		0			0
$751$	794.238			1.05757			0.528787	−	0.848755i	$-0.322647\pi$
$751$	794.238			1.05757			0.528787	+	0.848755i	$0.322647\pi$
$752$	144.003	−	83.1404i	0.191494	−	0.110559i
$753$		0			0
$754$	4.16692	−	7.21731i	0.00552642	−	0.00957204i
$755$		−	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	$0.479115\pi$
$758$	−9.45922	−	5.46129i	−0.0124792	−	0.00720486i
$759$		0			0
$760$	161.413	+	279.575i	0.212385	+	0.367862i
$761$		−	735.539i		−	0.966543i	−0.875471	−	0.483272i	$-0.839448\pi$
$761$		−	735.539i		−	0.966543i	0.875471	−	0.483272i	$-0.160552\pi$
$762$		0			0
$763$	−193.379	−	79.4093i	−0.253445	−	0.104075i
$764$		−	615.774i		−	0.805987i
$765$		0			0
$766$	−458.124	+	793.495i	−0.598074	+	1.03589i
$767$			178.010i			0.232086i
$768$		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	$0.267515\pi$
$770$	−329.872	+	803.309i	−0.428405	+	1.04326i
$771$		0			0
$772$	−165.134	+	286.021i	−0.213904	+	0.370493i
$773$	−100.386	−	57.9577i	−0.129865	−	0.0749776i	0.433660	−	0.901077i	$-0.357222\pi$
$773$	−100.386	−	57.9577i	−0.129865	−	0.0749776i	−0.563525	+	0.826099i	$0.690555\pi$
$774$		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
$779$			684.383i			0.878541i
$780$		0			0
$781$	246.613			0.315765
$782$	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
$787$	−488.719	−	846.487i	−0.620990	−	1.07559i	−0.989302	−	0.145884i	$-0.953397\pi$
$787$	−488.719	−	846.487i	−0.620990	−	1.07559i	0.368312	−	0.929702i	$-0.379936\pi$
$788$	149.453	−	86.2870i	0.189662	−	0.109501i
$789$		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
$794$		−	134.704i		−	0.169652i
$795$		0			0
$796$	−658.881			−0.827739
$797$	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
$803$	357.735	+	206.538i	0.445498	+	0.257208i
$804$		0			0
$805$	249.928	+	1854.62i	0.310469	+	2.30387i
$806$	63.1154	+	36.4397i	0.0783070	+	0.0452106i
$807$		0			0
$808$	370.535			0.458583
$809$	751.325	+	433.778i	0.928708	+	0.536190i	0.886403	−	0.462915i	$-0.153196\pi$
$809$	751.325	+	433.778i	0.928708	+	0.536190i	0.0423053	+	0.999105i	$0.486530\pi$
$810$		0			0
$811$	−329.692			−0.406525			−0.203263	−	0.979124i	$-0.565155\pi$
$811$	−329.692			−0.406525			−0.203263	+	0.979124i	$0.565155\pi$
$812$	12.6299	−	30.7564i	0.0155540	−	0.0378774i
$813$		0			0
$814$	156.190			0.191879
$815$	1745.48	−	1007.75i	2.14170	−	1.23651i
$816$		0			0
$817$	−224.909	+	389.553i	−0.275286	+	0.476810i
$818$			1104.97i			1.35082i
$819$		0			0
$820$	−829.963			−1.01215
$821$	890.753	+	514.277i	1.08496	+	0.626403i	0.932230	−	0.361865i	$-0.117860\pi$
$821$	890.753	+	514.277i	1.08496	+	0.626403i	0.152731	+	0.988268i	$0.451193\pi$
$822$		0			0
$823$	624.999	+	1082.53i	0.759415	+	1.31535i	0.943149	+	0.332369i	$0.107848\pi$
$823$	624.999	+	1082.53i	0.759415	+	1.31535i	−0.183734	+	0.982976i	$0.558819\pi$
$824$			93.9672i			0.114038i
$825$		0			0
$826$	94.8475	+	703.826i	0.114827	+	0.852090i
$827$		−	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	−0.983004	−	0.183581i	$-0.941231\pi$
$829$	−275.656	+	477.450i	−0.332516	+	0.575935i	0.650488	+	0.759516i	$0.274564\pi$
$830$			1291.72i			1.55629i
$831$		0			0
$832$	−9.92531	+	17.1911i	−0.0119295	+	0.0206624i
$833$	1507.11	+	393.982i	1.80926	+	0.472968i
$834$		0			0
$835$	−405.456	+	702.270i	−0.485576	+	0.841042i
$836$	−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
$842$		−	847.543i		−	1.00658i
$843$		0			0
$844$	−162.827			−0.192923
$845$	−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
$850$	−993.764	−	1721.25i	−1.16913	−	2.02500i
$851$	291.491	−	168.292i	0.342527	−	0.197758i
$852$		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
$857$		−	1083.39i		−	1.26417i	−0.774901	−	0.632083i	$-0.782200\pi$
$857$		−	1083.39i		−	1.26417i	0.774901	−	0.632083i	$-0.217800\pi$
$858$		0			0
$859$	1396.05			1.62520			0.812601	−	0.582821i	$-0.198051\pi$
$859$	1396.05			1.62520			0.812601	+	0.582821i	$0.198051\pi$
$860$	−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	$-0.659513\pi$
$863$	33.5922	−	19.3944i	0.0389249	−	0.0224733i	0.519336	+	0.854570i	$0.326179\pi$
$864$		0			0
$865$	−222.954	+	386.168i	−0.257751	+	0.446438i
$866$	−713.578	−	411.984i	−0.823993	−	0.475733i
$867$		0			0
$868$	268.965	+	110.448i	0.309868	+	0.127244i
$869$	91.9926	+	53.1120i	0.105860	+	0.0611185i
$870$		0			0
$871$	61.8963			0.0710635
$872$	73.1517	+	42.2341i	0.0838895	+	0.0484336i
$873$		0			0
$874$	−623.520			−0.713409
$875$	1108.49	−	149.380i	1.26685	−	0.170720i
$876$		0			0
$877$	1250.57			1.42596			0.712982	−	0.701182i	$-0.247344\pi$
$877$	1250.57			1.42596			0.712982	+	0.701182i	$0.247344\pi$
$878$	69.0434	−	39.8622i	0.0786371	−	0.0454011i
$879$		0			0
$880$	175.444	−	303.877i	0.199368	−	0.345315i
$881$		−	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	$0.568755\pi$
$884$	−136.631	−	78.8839i	−0.154560	−	0.0892352i
$885$		0			0
$886$	−134.959	−	233.756i	−0.152324	−	0.263833i
$887$			1158.64i			1.30624i	0.757253	+	0.653121i	$0.226541\pi$
$887$			1158.64i			1.30624i	−0.757253	+	0.653121i	$0.773459\pi$
$888$		0			0
$889$	−104.248	−	773.586i	−0.117265	−	0.870175i
$890$		−	495.819i		−	0.557100i
$891$		0			0
$892$	−186.441	+	322.925i	−0.209014	+	0.362023i
$893$		−	570.334i		−	0.638672i
$894$		0			0
$895$	−590.484	+	1022.75i	−0.659759	+	1.14274i
$896$	−30.0835	+	73.2597i	−0.0335753	+	0.0817631i
$897$		0			0
$898$	3.12818	−	5.41817i	0.00348350	−	0.00603360i
$899$	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
$905$		−	1729.58i		−	1.91114i
$906$		0			0
$907$	−281.301			−0.310144			−0.155072	−	0.987903i	$-0.549561\pi$
$907$	−281.301			−0.310144			−0.155072	+	0.987903i	$0.549561\pi$
$908$	−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
$913$	−578.868	−	1002.63i	−0.634029	−	1.09817i
$914$	−826.550	+	477.209i	−0.904321	+	0.522110i
$915$		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	−0.998687	−	0.0512275i	$-0.983687\pi$
$919$	−499.667	−	865.449i	−0.543708	−	0.941730i	0.454979	−	0.890502i	$-0.349647\pi$
$920$		−	756.152i		−	0.821905i
$921$		0			0
$922$	597.356			0.647891
$923$	−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
$929$	−52.9181	−	30.5523i	−0.0569625	−	0.0328873i	0.471248	−	0.882001i	$-0.343804\pi$
$929$	−52.9181	−	30.5523i	−0.0569625	−	0.0328873i	−0.528211	+	0.849113i	$0.677137\pi$
$930$		0			0
$931$	−478.260	−	472.454i	−0.513705	−	0.507470i
$932$	−13.3283	−	7.69509i	−0.0143007	−	0.00825653i
$933$		0			0
$934$	790.616			0.846484
$935$	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	$0.539718\pi$
$938$	244.729	−	32.9796i	0.260905	−	0.0351595i
$939$		0			0
$940$	691.653			0.735801
$941$	−712.127	+	411.147i	−0.756777	+	0.436925i	−0.828137	−	0.560525i	$-0.810599\pi$
$941$	−712.127	+	411.147i	−0.756777	+	0.436925i	0.0713605	+	0.997451i	$0.477266\pi$
$942$		0			0
$943$	801.513	−	1388.26i	0.849961	−	1.47218i
$944$		−	286.959i		−	0.303982i
$945$		0			0
$946$	488.918			0.516827
$947$	1356.61	+	783.240i	1.43254	+	0.827075i	0.997314	−	0.0732485i	$-0.0233366\pi$
$947$	1356.61	+	783.240i	1.43254	+	0.827075i	0.435222	+	0.900323i	$0.356670\pi$
$948$		0			0
$949$	−48.6019	−	84.1810i	−0.0512138	−	0.0887049i
$950$			857.741i			0.902885i
$951$		0			0
$952$	−582.250	−	239.096i	−0.611607	−	0.251151i
$953$		−	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
$956$			472.683i			0.494438i
$957$		0			0
$958$	56.8783	−	98.5161i	0.0593719	−	0.102835i
$959$	−458.096	+	61.7329i	−0.477680	+	0.0643721i
$960$		0			0
$961$	264.834	−	458.706i	0.275582	−	0.477322i
$962$	−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	$0.972787\pi$
$968$		−	27.7489i		−	0.0286663i
$969$		0			0
$970$	−888.592			−0.916074
$971$	479.817	−	277.023i	0.494148	−	0.285296i	−0.232146	−	0.972681i	$-0.574575\pi$
$971$	479.817	−	277.023i	0.494148	−	0.285296i	0.726293	+	0.687385i	$0.241241\pi$
$972$		0			0
$973$	585.771	+	240.542i	0.602026	+	0.247217i
$974$	−494.510	+	285.506i	−0.507711	+	0.293127i
$975$		0			0
$976$	−132.291	−	229.134i	−0.135544	−	0.234769i
$977$	−150.343	+	86.8005i	−0.153882	+	0.0888439i	−0.574964	−	0.818179i	$-0.694984\pi$
$977$	−150.343	+	86.8005i	−0.153882	+	0.0888439i	0.421082	+	0.907023i	$0.361651\pi$
$978$		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
$983$			1373.08i			1.39683i	0.715693	+	0.698415i	$0.246111\pi$
$983$			1373.08i			1.39683i	−0.715693	+	0.698415i	$0.753889\pi$
$984$		0			0
$985$	717.830			0.728761
$986$	−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	0.471090	+	0.882085i	$0.343861\pi$
$991$	−523.608	+	906.916i	−0.528364	+	0.915153i	−0.999453	+	0.0330672i	$0.989472\pi$
$992$	−101.745	−	58.7423i	−0.102565	−	0.0592160i
$993$		0			0
$994$	−214.170	−	87.9472i	−0.215463	−	0.0884780i
$995$	−2373.47	−	1370.32i	−2.38540	−	1.37721i
$996$		0			0
$997$	189.359			0.189929			0.0949643	−	0.995481i	$-0.469726\pi$
$997$	189.359			0.189929			0.0949643	+	0.995481i	$0.469726\pi$
$998$	−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.i.a.179.7		32
3.2	odd	2		126.3.i.a.95.13	yes	32
7.2	even	3		378.3.r.a.233.15		32
9.2	odd	6		378.3.r.a.305.7		32
9.7	even	3		126.3.r.a.11.15	yes	32
21.2	odd	6		126.3.r.a.23.7	yes	32
63.2	odd	6	inner	378.3.i.a.359.2		32
63.16	even	3		126.3.i.a.65.13	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.i.a.65.13	✓	32	63.16	even	3
126.3.i.a.95.13	yes	32	3.2	odd	2
126.3.r.a.11.15	yes	32	9.7	even	3
126.3.r.a.23.7	yes	32	21.2	odd	6
378.3.i.a.179.7		32	1.1	even	1	trivial
378.3.i.a.359.2		32	63.2	odd	6	inner
378.3.r.a.233.15		32	7.2	even	3
378.3.r.a.305.7		32	9.2	odd	6

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.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +8.31909i q^{5} +(0.934868 + 6.93729i) q^{7} -2.82843i q^{8} +(5.88249 - 10.1888i) q^{10} +10.5446i q^{11} +(1.24066 - 2.14889i) q^{13} +(3.76043 - 9.15746i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-27.5318 - 15.8955i) q^{17} +(6.85989 + 11.8817i) q^{19} +(-14.4091 + 8.31909i) q^{20} +(7.45618 - 12.9145i) q^{22} -32.1357i q^{23} -44.2073 q^{25} +(-3.03899 + 1.75456i) q^{26} +(-11.0809 + 8.55653i) q^{28} +(-2.05673 + 1.18745i) q^{29} +(-10.3843 - 17.9861i) q^{31} +(4.89898 - 2.82843i) q^{32} +(22.4796 + 38.9358i) q^{34} +(-57.7120 + 7.77726i) q^{35} +(5.23692 + 9.07061i) q^{37} -19.4027i q^{38} +23.5300 q^{40} +(43.1999 + 24.9415i) q^{41} +(16.3930 + 28.3936i) q^{43} +(-18.2638 + 10.5446i) q^{44} +(-22.7234 + 39.3581i) q^{46} +(-36.0009 - 20.7851i) q^{47} +(-47.2520 + 12.9709i) q^{49} +(54.1427 + 31.2593i) q^{50} +4.96266 q^{52} +(67.8875 + 39.1948i) q^{53} -87.7218 q^{55} +(19.6216 - 2.64421i) q^{56} +3.35862 q^{58} +(-62.1285 + 35.8699i) q^{59} +(-33.0727 + 57.2835i) q^{61} +29.3711i q^{62} -8.00000 q^{64} +(17.8768 + 10.3212i) q^{65} +(12.4724 + 21.6028i) q^{67} -63.5820i q^{68} +(76.1818 + 31.2834i) q^{70} -23.3875i q^{71} +(19.5871 - 33.9258i) q^{73} -14.8122i q^{74} +(-13.7198 + 23.7633i) q^{76} +(-73.1512 + 9.85784i) q^{77} +(5.03687 - 8.72412i) q^{79} +(-28.8182 - 16.6382i) q^{80} +(-35.2726 - 61.0939i) q^{82} +(-95.0843 + 54.8969i) q^{83} +(132.236 - 229.040i) q^{85} -46.3665i q^{86} +29.8247 q^{88} +(36.4975 - 21.0718i) q^{89} +(16.0674 + 6.59792i) q^{91} +(55.6607 - 32.1357i) q^{92} +(29.3946 + 50.9129i) q^{94} +(-98.8447 + 57.0680i) q^{95} +(-37.7643 - 65.4097i) q^{97} +(67.0435 + 17.5262i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} + 2 q^{7} + 10 q^{13} - 36 q^{14} - 64 q^{16} - 54 q^{17} + 28 q^{19} - 160 q^{25} - 72 q^{26} - 4 q^{28} - 36 q^{29} - 8 q^{31} - 90 q^{35} + 22 q^{37} - 72 q^{41} + 16 q^{43} + 72 q^{44}+ \cdots + 288 q^{98}+O(q^{100}) \) 32 * q + 32 * q^4 + 2 * q^7 + 10 * q^13 - 36 * q^14 - 64 * q^16 - 54 * q^17 + 28 * q^19 - 160 * q^25 - 72 * q^26 - 4 * q^28 - 36 * q^29 - 8 * q^31 - 90 * q^35 + 22 * q^37 - 72 * q^41 + 16 * q^43 + 72 * q^44 - 12 * q^46 + 108 * q^47 + 74 * q^49 + 288 * q^50 + 40 * q^52 - 72 * q^53 - 24 * q^55 + 48 * q^58 + 90 * q^59 - 62 * q^61 - 256 * q^64 - 378 * q^65 + 70 * q^67 - 108 * q^70 + 196 * q^73 - 56 * q^76 - 630 * q^77 - 38 * q^79 + 60 * q^85 - 486 * q^89 - 122 * q^91 - 252 * q^92 + 168 * q^94 + 72 * q^95 - 38 * q^97 + 288 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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