LMFDB - Embedded newform 936.2.dg.d.829.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(829,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.829"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.dg (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.8607891481591137382656.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 5 x^{14} - 6 x^{13} + 6 x^{12} - 20 x^{10} + 48 x^{9} - 76 x^{8} + 96 x^{7} + \cdots + 256 $ x^16 - 3x^15 + 5x^14 - 6x^13 + 6x^12 - 20x^10 + 48x^9 - 76x^8 + 96x^7 - 80x^6 + 96x^4 - 192x^3 + 320x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			829.7
Root			$-0.741068 - 1.20450i$ of defining polynomial
Character	$\chi$	$=$	936.829
Dual form			936.2.dg.d.901.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.741068 - 1.20450i) q^{2} +(-0.901635 - 1.78523i) q^{4} -0.893415 q^{5} +(3.65473 + 2.11006i) q^{7} +(-2.81848 - 0.236960i) q^{8} +(-0.662082 + 1.07612i) q^{10} +(3.01779 + 5.22697i) q^{11} +(-0.579883 + 3.55861i) q^{13} +(5.24997 - 2.83842i) q^{14} +(-2.37411 + 3.21926i) q^{16} +(-1.00567 + 1.74186i) q^{17} +(1.59258 - 2.75843i) q^{19} +(0.805535 + 1.59495i) q^{20} +(8.53227 + 0.238614i) q^{22} +(2.65473 + 4.59813i) q^{23} -4.20181 q^{25} +(3.85661 + 3.33565i) q^{26} +(0.471712 - 8.42704i) q^{28} +(4.50378 - 2.60026i) q^{29} -2.51626i q^{31} +(2.11822 + 5.24530i) q^{32} +(1.35281 + 2.50216i) q^{34} +(-3.26519 - 1.88516i) q^{35} +(-1.00002 - 1.73208i) q^{37} +(-2.14232 - 3.96245i) q^{38} +(2.51808 + 0.211704i) q^{40} +(0.0169974 - 0.00981345i) q^{41} +(-3.45944 - 1.99731i) q^{43} +(6.61041 - 10.1003i) q^{44} +(7.50577 + 0.209907i) q^{46} -3.22446i q^{47} +(5.40470 + 9.36121i) q^{49} +(-3.11383 + 5.06107i) q^{50} +(6.87580 - 2.17335i) q^{52} -3.34691i q^{53} +(-2.69614 - 4.66986i) q^{55} +(-9.80079 - 6.81319i) q^{56} +(0.205600 - 7.35176i) q^{58} +(3.15097 - 5.45764i) q^{59} +(6.79553 + 3.92340i) q^{61} +(-3.03083 - 1.86472i) q^{62} +(7.88770 + 1.33574i) q^{64} +(0.518077 - 3.17932i) q^{65} +(1.53943 + 2.66638i) q^{67} +(4.01638 + 0.224820i) q^{68} +(-4.69040 + 2.53589i) q^{70} +(-2.22056 - 1.28204i) q^{71} -12.1386i q^{73} +(-2.82737 - 0.0790704i) q^{74} +(-6.36037 - 0.356028i) q^{76} +25.4709i q^{77} +3.01133 q^{79} +(2.12106 - 2.87613i) q^{80} +(0.000775941 - 0.0277458i) q^{82} -8.90367 q^{83} +(0.898477 - 1.55621i) q^{85} +(-4.96944 + 2.68675i) q^{86} +(-7.26702 - 15.4472i) q^{88} +(-7.52934 + 4.34707i) q^{89} +(-9.62820 + 11.7822i) q^{91} +(5.81512 - 8.88514i) q^{92} +(-3.88385 - 2.38954i) q^{94} +(-1.42284 + 2.46443i) q^{95} +(9.79132 + 5.65302i) q^{97} +(15.2808 + 0.427345i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} - q^{4} + 18 q^{7} - 9 q^{10} + 24 q^{14} - q^{16} - 8 q^{17} + 15 q^{20} + 22 q^{22} + 2 q^{23} - 12 q^{25} - 23 q^{26} + 27 q^{32} + 26 q^{40} - 24 q^{41} + 42 q^{46} - 14 q^{49} - 6 q^{50}+ \cdots + 93 q^{98}+O(q^{100}) $ 16 * q - 3 * q^2 - q^4 + 18 * q^7 - 9 * q^10 + 24 * q^14 - q^16 - 8 * q^17 + 15 * q^20 + 22 * q^22 + 2 * q^23 - 12 * q^25 - 23 * q^26 + 27 * q^32 + 26 * q^40 - 24 * q^41 + 42 * q^46 - 14 * q^49 - 6 * q^50 + 28 * q^52 + 4 * q^55 + 8 * q^56 - 33 * q^58 + 4 * q^62 + 50 * q^64 - 6 * q^65 - 5 * q^68 - 6 * q^71 + 29 * q^74 + 24 * q^76 + 32 * q^79 + 33 * q^80 + 9 * q^82 - 8 * q^88 + 30 * q^89 + 4 * q^92 - 24 * q^94 - 28 * q^95 - 30 * q^97 + 93 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.741068	−	1.20450i	0.524014	−	0.851709i
$2$	0.741068	−	1.20450i	0.524014	−	0.851709i
$3$		0			0
$3$		0			0
$4$	−0.901635	−	1.78523i	−0.450818	−	0.892616i
$5$	−0.893415			−0.399548			−0.199774	−	0.979842i	$-0.564021\pi$
$5$	−0.893415			−0.399548			−0.199774	+	0.979842i	$0.564021\pi$
$6$		0			0
$7$	3.65473	+	2.11006i	1.38136	+	0.797527i	0.992320	−	0.123695i	$-0.0394743\pi$
$7$	3.65473	+	2.11006i	1.38136	+	0.797527i	0.389037	+	0.921222i	$0.372808\pi$
$8$	−2.81848	−	0.236960i	−0.996484	−	0.0837781i
$9$		0			0
$10$	−0.662082	+	1.07612i	−0.209369	+	0.340298i
$11$	3.01779	+	5.22697i	0.909899	+	1.57599i	0.814203	+	0.580581i	$0.197174\pi$
$11$	3.01779	+	5.22697i	0.909899	+	1.57599i	0.0956963	+	0.995411i	$0.469492\pi$
$12$		0			0
$13$	−0.579883	+	3.55861i	−0.160831	+	0.986982i
$13$	−0.579883	+	3.55861i	−0.160831	+	0.986982i
$14$	5.24997	−	2.83842i	1.40311	−	0.758600i
$15$		0			0
$16$	−2.37411	+	3.21926i	−0.593527	+	0.804814i
$17$	−1.00567	+	1.74186i	−0.243910	+	0.422464i	−0.961825	−	0.273667i	$-0.911763\pi$
$17$	−1.00567	+	1.74186i	−0.243910	+	0.422464i	0.717915	+	0.696131i	$0.245097\pi$
$18$		0			0
$19$	1.59258	−	2.75843i	0.365364	−	0.632828i	−0.623471	−	0.781847i	$-0.714278\pi$
$19$	1.59258	−	2.75843i	0.365364	−	0.632828i	0.988834	+	0.149018i	$0.0476113\pi$
$20$	0.805535	+	1.59495i	0.180123	+	0.356643i
$21$		0			0
$22$	8.53227	+	0.238614i	1.81909	+	0.0508727i
$23$	2.65473	+	4.59813i	0.553549	+	0.958776i	0.998015	+	0.0629796i	$0.0200603\pi$
$23$	2.65473	+	4.59813i	0.553549	+	0.958776i	−0.444466	+	0.895796i	$0.646606\pi$
$24$		0			0
$25$	−4.20181			−0.840362
$26$	3.85661	+	3.33565i	0.756344	+	0.654174i
$27$		0			0
$28$	0.471712	−	8.42704i	0.0891452	−	1.59256i
$29$	4.50378	−	2.60026i	0.836330	−	0.482855i	−0.0196850	−	0.999806i	$-0.506266\pi$
$29$	4.50378	−	2.60026i	0.836330	−	0.482855i	0.856015	+	0.516951i	$0.172933\pi$
$30$		0			0
$31$		−	2.51626i		−	0.451934i	−0.974135	−	0.225967i	$-0.927446\pi$
$31$		−	2.51626i		−	0.451934i	0.974135	−	0.225967i	$-0.0725541\pi$
$32$	2.11822	+	5.24530i	0.374451	+	0.927247i
$33$		0			0
$34$	1.35281	+	2.50216i	0.232004	+	0.429118i
$35$	−3.26519	−	1.88516i	−0.551918	−	0.318650i
$36$		0			0
$37$	−1.00002	−	1.73208i	−0.164402	−	0.284752i	0.772041	−	0.635573i	$-0.219236\pi$
$37$	−1.00002	−	1.73208i	−0.164402	−	0.284752i	−0.936443	+	0.350821i	$0.885903\pi$
$38$	−2.14232	−	3.96245i	−0.347530	−	0.642795i
$39$		0			0
$40$	2.51808	+	0.211704i	0.398143	+	0.0334733i
$41$	0.0169974	−	0.00981345i	0.00265455	−	0.00153260i	−0.498672	−	0.866791i	$-0.666179\pi$
$41$	0.0169974	−	0.00981345i	0.00265455	−	0.00153260i	0.501327	+	0.865258i	$0.332845\pi$
$42$		0			0
$43$	−3.45944	−	1.99731i	−0.527560	−	0.304587i	0.212463	−	0.977169i	$-0.431852\pi$
$43$	−3.45944	−	1.99731i	−0.527560	−	0.304587i	−0.740022	+	0.672583i	$0.765185\pi$
$44$	6.61041	−	10.1003i	0.996557	−	1.52268i
$45$		0			0
$46$	7.50577	+	0.209907i	1.10667	+	0.0309491i
$47$		−	3.22446i		−	0.470335i	−0.971955	−	0.235168i	$-0.924436\pi$
$47$		−	3.22446i		−	0.470335i	0.971955	−	0.235168i	$-0.0755639\pi$
$48$		0			0
$49$	5.40470	+	9.36121i	0.772100	+	1.33732i
$50$	−3.11383	+	5.06107i	−0.440362	+	0.715744i
$51$		0			0
$52$	6.87580	−	2.17335i	0.953501	−	0.301389i
$53$		−	3.34691i		−	0.459733i	−0.973222	−	0.229867i	$-0.926171\pi$
$53$		−	3.34691i		−	0.459733i	0.973222	−	0.229867i	$-0.0738290\pi$
$54$		0			0
$55$	−2.69614	−	4.66986i	−0.363548	−	0.629683i
$56$	−9.80079	−	6.81319i	−1.30969	−	0.910451i
$57$		0			0
$58$	0.205600	−	7.35176i	0.0269966	−	0.965333i
$59$	3.15097	−	5.45764i	0.410221	−	0.710524i	−0.584692	−	0.811255i	$-0.698785\pi$
$59$	3.15097	−	5.45764i	0.410221	−	0.710524i	0.994914	+	0.100731i	$0.0321181\pi$
$60$		0			0
$61$	6.79553	+	3.92340i	0.870078	+	0.502340i	0.867374	−	0.497657i	$-0.165806\pi$
$61$	6.79553	+	3.92340i	0.870078	+	0.502340i	0.00270378	+	0.999996i	$0.499139\pi$
$62$	−3.03083	−	1.86472i	−0.384916	−	0.236820i
$63$		0			0
$64$	7.88770	+	1.33574i	0.985962	+	0.166967i
$65$	0.518077	−	3.17932i	0.0642595	−	0.394346i
$66$		0			0
$67$	1.53943	+	2.66638i	0.188072	+	0.325750i	0.944607	−	0.328203i	$-0.106443\pi$
$67$	1.53943	+	2.66638i	0.188072	+	0.325750i	−0.756536	+	0.653952i	$0.773110\pi$
$68$	4.01638	+	0.224820i	0.487057	+	0.0272635i
$69$		0			0
$70$	−4.69040	+	2.53589i	−0.560610	+	0.303097i
$71$	−2.22056	−	1.28204i	−0.263532	−	0.152150i	0.362413	−	0.932018i	$-0.381953\pi$
$71$	−2.22056	−	1.28204i	−0.263532	−	0.152150i	−0.625945	+	0.779867i	$0.715286\pi$
$72$		0			0
$73$		−	12.1386i		−	1.42072i	−0.703840	−	0.710359i	$-0.748533\pi$
$73$		−	12.1386i		−	1.42072i	0.703840	−	0.710359i	$-0.251467\pi$
$74$	−2.82737	−	0.0790704i	−0.328675	−	0.00919175i
$75$		0			0
$76$	−6.36037	−	0.356028i	−0.729585	−	0.0408392i
$77$			25.4709i			2.90268i
$78$		0			0
$79$	3.01133			0.338801			0.169401	−	0.985547i	$-0.445817\pi$
$79$	3.01133			0.338801			0.169401	+	0.985547i	$0.445817\pi$
$80$	2.12106	−	2.87613i	0.237142	−	0.321562i
$81$		0			0
$82$	0.000775941	−	0.0277458i	8.56884e−5	−	0.00306401i
$83$	−8.90367			−0.977304			−0.488652	−	0.872479i	$-0.662511\pi$
$83$	−8.90367			−0.977304			−0.488652	+	0.872479i	$0.662511\pi$
$84$		0			0
$85$	0.898477	−	1.55621i	0.0974535	−	0.168794i
$86$	−4.96944	+	2.68675i	−0.535868	+	0.289720i
$87$		0			0
$88$	−7.26702	−	15.4472i	−0.774667	−	1.64668i
$89$	−7.52934	+	4.34707i	−0.798109	+	0.460788i	−0.842809	−	0.538212i	$-0.819100\pi$
$89$	−7.52934	+	4.34707i	−0.798109	+	0.460788i	0.0447006	+	0.999000i	$0.485767\pi$
$90$		0			0
$91$	−9.62820	+	11.7822i	−1.00931	+	1.23511i
$92$	5.81512	−	8.88514i	0.606269	−	0.926340i
$93$		0			0
$94$	−3.88385	−	2.38954i	−0.400589	−	0.246462i
$95$	−1.42284	+	2.46443i	−0.145980	+	0.252845i
$96$		0			0
$97$	9.79132	+	5.65302i	0.994158	+	0.573977i	0.906514	−	0.422175i	$-0.138733\pi$
$97$	9.79132	+	5.65302i	0.994158	+	0.573977i	0.0876432	+	0.996152i	$0.472066\pi$
$98$	15.2808	+	0.427345i	1.54360	+	0.0431683i
$99$		0			0
$100$	3.78850	+	7.50120i	0.378850	+	0.750120i
$101$	11.0712	−	6.39194i	1.10162	−	0.636021i	0.164975	−	0.986298i	$-0.447246\pi$
$101$	11.0712	−	6.39194i	1.10162	−	0.636021i	0.936646	+	0.350276i	$0.113912\pi$
$102$		0			0
$103$	−6.35829			−0.626501			−0.313251	−	0.949671i	$-0.601418\pi$
$103$	−6.35829			−0.626501			−0.313251	+	0.949671i	$0.601418\pi$
$104$	2.47764	−	9.89249i	0.242953	−	0.970038i
$105$		0			0
$106$	−4.03135	−	2.48029i	−0.391559	−	0.240907i
$107$	−3.64486	+	2.10436i	−0.352362	+	0.203436i	−0.665725	−	0.746197i	$-0.731878\pi$
$107$	−3.64486	+	2.10436i	−0.352362	+	0.203436i	0.313363	+	0.949633i	$0.398544\pi$
$108$		0			0
$109$	15.3480			1.47007			0.735036	−	0.678028i	$-0.237165\pi$
$109$	15.3480			1.47007			0.735036	+	0.678028i	$0.237165\pi$
$110$	−7.62286	−	0.213182i	−0.726812	−	0.0203261i
$111$		0			0
$112$	−15.4695	+	6.75601i	−1.46173	+	0.638383i
$113$	−5.31512	+	9.20607i	−0.500005	+	0.866034i	0.499995	+	0.866028i	$0.333335\pi$
$113$	−5.31512	+	9.20607i	−0.500005	+	0.866034i	−1.00000		5.57645e-6i	$0.999998\pi$
$114$		0			0
$115$	−2.37178	−	4.10804i	−0.221169	−	0.383076i
$116$	−8.70282	−	5.69580i	−0.808037	−	0.528842i
$117$		0			0
$118$	−4.23864	−	7.83982i	−0.390198	−	0.721714i
$119$	−7.35087	+	4.24403i	−0.673853	+	0.389049i
$120$		0			0
$121$	−12.7142	+	22.0216i	−1.15583	+	2.00196i
$122$	9.76168	−	5.27770i	0.883781	−	0.477820i
$123$		0			0
$124$	−4.49211	+	2.26875i	−0.403403	+	0.203740i
$125$	8.22104			0.735312
$126$		0			0
$127$	−1.26804	−	2.19632i	−0.112521	−	0.194892i	0.804265	−	0.594271i	$-0.202559\pi$
$127$	−1.26804	−	2.19632i	−0.112521	−	0.194892i	−0.916786	+	0.399379i	$0.869226\pi$
$128$	7.45422	−	8.51085i	0.658866	−	0.752260i
$129$		0			0
$130$	−3.44556	−	2.98012i	−0.302195	−	0.261374i
$131$		−	2.01357i		−	0.175927i	−0.996124	−	0.0879633i	$-0.971964\pi$
$131$		−	2.01357i		−	0.175927i	0.996124	−	0.0879633i	$-0.0280358\pi$
$132$		0			0
$133$	11.6409	−	6.72089i	1.00940	−	0.582775i
$134$	4.35247	+	0.121722i	0.375996	+	0.0105151i
$135$		0			0
$136$	3.24721	−	4.67111i	0.278446	−	0.400545i
$137$	−11.8095	−	6.81819i	−1.00895	−	0.582518i	−0.0980660	−	0.995180i	$-0.531266\pi$
$137$	−11.8095	−	6.81819i	−1.00895	−	0.582518i	−0.910884	+	0.412662i	$0.864599\pi$
$138$		0			0
$139$	−15.6208	−	9.01865i	−1.32494	−	0.764952i	−0.340424	−	0.940272i	$-0.610571\pi$
$139$	−15.6208	−	9.01865i	−1.32494	−	0.764952i	−0.984512	+	0.175320i	$0.943904\pi$
$140$	−0.421435	+	7.52885i	−0.0356177	+	0.636304i
$141$		0			0
$142$	−3.18980	+	1.72458i	−0.267682	+	0.144724i
$143$	−20.3507	+	7.70813i	−1.70181	+	0.644586i
$144$		0			0
$145$	−4.02374	+	2.32311i	−0.334154	+	0.192924i
$146$	−14.6209	−	8.99554i	−1.21004	−	0.744476i
$147$		0			0
$148$	−2.19051	+	3.34696i	−0.180059	+	0.275119i
$149$	0.706789	−	1.22419i	0.0579024	−	0.100290i	−0.835621	−	0.549306i	$-0.814892\pi$
$149$	0.706789	−	1.22419i	0.0579024	−	0.100290i	0.893524	+	0.449016i	$0.148225\pi$
$150$		0			0
$151$			5.82833i			0.474303i	0.971473	+	0.237152i	$0.0762138\pi$
$151$			5.82833i			0.474303i	−0.971473	+	0.237152i	$0.923786\pi$
$152$	−5.14231	+	7.39722i	−0.417096	+	0.599994i
$153$		0			0
$154$	30.6797	+	18.8757i	2.47224	+	1.52104i
$155$			2.24807i			0.180569i
$156$		0			0
$157$			3.13281i			0.250025i	0.992155	+	0.125013i	$0.0398971\pi$
$157$			3.13281i			0.250025i	−0.992155	+	0.125013i	$0.960103\pi$
$158$	2.23160	−	3.62715i	0.177537	−	0.288560i
$159$		0			0
$160$	−1.89245	−	4.68623i	−0.149611	−	0.370479i
$161$			22.4065i			1.76588i
$162$		0			0
$163$	1.93896	−	3.35838i	0.151871	−	0.263048i	−0.780044	−	0.625724i	$-0.784803\pi$
$163$	1.93896	−	3.35838i	0.151871	−	0.263048i	0.931915	+	0.362676i	$0.118137\pi$
$164$	−0.0328448	−	0.0214962i	−0.00256474	−	0.00167857i
$165$		0			0
$166$	−6.59823	+	10.7245i	−0.512122	+	0.832379i
$167$	13.6659	−	7.89003i	1.05750	−	0.610549i	0.132761	−	0.991148i	$-0.457616\pi$
$167$	13.6659	−	7.89003i	1.05750	−	0.610549i	0.924740	+	0.380599i	$0.124282\pi$
$168$		0			0
$169$	−12.3275	−	4.12716i	−0.948267	−	0.317474i
$170$	−1.20862	−	2.23547i	−0.0926968	−	0.171453i
$171$		0			0
$172$	−0.446506	+	7.97675i	−0.0340458	+	0.608221i
$173$	0.538065	+	0.310652i	0.0409083	+	0.0236184i	0.520315	−	0.853975i	$-0.325815\pi$
$173$	0.538065	+	0.310652i	0.0409083	+	0.0236184i	−0.479406	+	0.877593i	$0.659148\pi$
$174$		0			0
$175$	−15.3565	−	8.86606i	−1.16084	−	0.670211i
$176$	−23.9915	−	2.69434i	−1.80843	−	0.203093i
$177$		0			0
$178$	−0.343719	+	12.2906i	−0.0257628	+	0.921217i
$179$	−9.39825	+	5.42608i	−0.702458	+	0.405564i	−0.808262	−	0.588823i	$-0.799592\pi$
$179$	−9.39825	+	5.42608i	−0.702458	+	0.405564i	0.105804	+	0.994387i	$0.466258\pi$
$180$		0			0
$181$			16.0515i			1.19310i	0.802577	+	0.596548i	$0.203461\pi$
$181$			16.0515i			1.19310i	−0.802577	+	0.596548i	$0.796539\pi$
$182$	7.05647	+	20.3286i	0.523060	+	1.50685i
$183$		0			0
$184$	−6.39274	−	13.5888i	−0.471279	−	1.00178i
$185$	0.893430	+	1.54747i	0.0656863	+	0.113772i
$186$		0			0
$187$	−12.1396			−0.887733
$188$	−5.75640	+	2.90728i	−0.419829	+	0.212035i
$189$		0			0
$190$	1.91398	+	3.54012i	0.138855	+	0.256827i
$191$	10.9755	−	19.0102i	0.794161	−	1.37553i	−0.129210	−	0.991617i	$-0.541244\pi$
$191$	10.9755	−	19.0102i	0.794161	−	1.37553i	0.923371	−	0.383909i	$-0.125423\pi$
$192$		0			0
$193$	−7.45812	+	4.30595i	−0.536847	+	0.309949i	−0.743800	−	0.668402i	$-0.766979\pi$
$193$	−7.45812	+	4.30595i	−0.536847	+	0.309949i	0.206953	+	0.978351i	$0.433645\pi$
$194$	14.0651	−	7.60436i	1.00981	−	0.545961i
$195$		0			0
$196$	11.8389	−	18.0890i	0.845633	−	1.29207i
$197$	−4.57874	−	7.93061i	−0.326222	−	0.565033i	0.655537	−	0.755163i	$-0.272442\pi$
$197$	−4.57874	−	7.93061i	−0.326222	−	0.565033i	−0.981759	+	0.190130i	$0.939109\pi$
$198$		0			0
$199$	7.83948	−	13.5784i	0.555726	−	0.962545i	−0.442121	−	0.896955i	$-0.645774\pi$
$199$	7.83948	−	13.5784i	0.555726	−	0.962545i	0.997847	−	0.0655898i	$-0.0208929\pi$
$200$	11.8427	+	0.995662i	0.837407	+	0.0704039i
$201$		0			0
$202$	0.505405	−	18.0721i	0.0355602	−	1.27155i
$203$	21.9468			1.54036
$204$		0			0
$205$	−0.0151857	+	0.00876749i	−0.00106062	+	0.000612348i
$206$	−4.71193	+	7.65856i	−0.328296	+	0.533597i
$207$		0			0
$208$	−10.0794	−	10.3153i	−0.698880	−	0.715239i
$209$	19.2243			1.32978
$210$		0			0
$211$	14.2765	−	8.24253i	0.982834	−	0.567439i	0.0797093	−	0.996818i	$-0.474601\pi$
$211$	14.2765	−	8.24253i	0.982834	−	0.567439i	0.903124	+	0.429379i	$0.141267\pi$
$212$	−5.97501	+	3.01769i	−0.410365	+	0.207256i
$213$		0			0
$214$	−0.166390	+	5.94970i	−0.0113742	+	0.406713i
$215$	3.09072	+	1.78443i	0.210785	+	0.121697i
$216$		0			0
$217$	5.30946	−	9.19625i	0.360430	−	0.624282i
$218$	11.3739	−	18.4866i	0.770339	−	1.25207i
$219$		0			0
$220$	−5.90584	+	9.02375i	−0.398172	+	0.608381i
$221$	−5.61545	−	4.58885i	−0.377736	−	0.308680i
$222$		0			0
$223$	4.14333	−	2.39215i	0.277458	−	0.160191i	−0.354814	−	0.934937i	$-0.615456\pi$
$223$	4.14333	−	2.39215i	0.277458	−	0.160191i	0.632272	+	0.774746i	$0.282122\pi$
$224$	−3.32639	+	23.6397i	−0.222254	+	1.57949i
$225$		0			0
$226$	7.14983	+	13.2244i	0.475599	+	0.879673i
$227$	−2.20440	+	3.81814i	−0.146311	+	0.253419i	−0.929861	−	0.367910i	$-0.880073\pi$
$227$	−2.20440	+	3.81814i	−0.146311	+	0.253419i	0.783550	+	0.621329i	$0.213407\pi$
$228$		0			0
$229$	18.9724			1.25373			0.626866	−	0.779127i	$-0.284338\pi$
$229$	18.9724			1.25373			0.626866	+	0.779127i	$0.284338\pi$
$230$	−6.70577	−	0.187534i	−0.442166	−	0.0123656i
$231$		0			0
$232$	−13.3100	+	6.26156i	−0.873843	+	0.411092i
$233$	16.2038			1.06155			0.530774	−	0.847513i	$-0.321901\pi$
$233$	16.2038			1.06155			0.530774	+	0.847513i	$0.321901\pi$
$234$		0			0
$235$			2.88078i			0.187921i
$236$	−12.5842	−	0.704411i	−0.819160	−	0.0458533i
$237$		0			0
$238$	−0.335572	+	11.9992i	−0.0217519	+	0.777795i
$239$			3.65538i			0.236447i	0.992987	+	0.118224i	$0.0377200\pi$
$239$			3.65538i			0.236447i	−0.992987	+	0.118224i	$0.962280\pi$
$240$		0			0
$241$	−19.7662	−	11.4120i	−1.27325	−	0.735114i	−0.297655	−	0.954673i	$-0.596205\pi$
$241$	−19.7662	−	11.4120i	−1.27325	−	0.735114i	−0.975599	+	0.219559i	$0.929538\pi$
$242$	17.1029	+	31.6337i	1.09942	+	2.03349i
$243$		0			0
$244$	0.877091	−	15.6691i	0.0561500	−	1.00311i
$245$	−4.82864	−	8.36345i	−0.308490	−	0.534321i
$246$		0			0
$247$	8.89269	+	7.26696i	0.565828	+	0.462385i
$248$	−0.596254	+	7.09204i	−0.0378621	+	0.450345i
$249$		0			0
$250$	6.09235	−	9.90223i	0.385314	−	0.626272i
$251$	5.22090	+	3.01429i	0.329540	+	0.190260i	0.655637	−	0.755076i	$-0.272400\pi$
$251$	5.22090	+	3.01429i	0.329540	+	0.190260i	−0.326097	+	0.945336i	$0.605733\pi$
$252$		0			0
$253$	−16.0228	+	27.7524i	−1.00735	+	1.74478i
$254$	−3.58517	−	0.100263i	−0.224954	−	0.00629107i
$255$		0			0
$256$	−4.72723	−	15.2857i	−0.295452	−	0.955358i
$257$	−11.6246	−	20.1344i	−0.725122	−	1.25595i	−0.958924	−	0.283663i	$-0.908450\pi$
$257$	−11.6246	−	20.1344i	−0.725122	−	1.25595i	0.233802	−	0.972284i	$-0.424883\pi$
$258$		0			0
$259$		−	8.44037i		−	0.524459i
$260$	−6.14294	+	1.94170i	−0.380969	+	0.120419i
$261$		0			0
$262$	−2.42535	−	1.49219i	−0.149838	−	0.0921881i
$263$	−1.34527	−	2.33008i	−0.0829529	−	0.143679i	0.821564	−	0.570116i	$-0.193102\pi$
$263$	−1.34527	−	2.33008i	−0.0829529	−	0.143679i	−0.904517	+	0.426437i	$0.859768\pi$
$264$		0			0
$265$			2.99018i			0.183685i
$266$	0.531415	−	19.0021i	0.0325831	−	1.16509i
$267$		0			0
$268$	3.37209	−	5.15234i	0.205983	−	0.314730i
$269$	10.8816	+	6.28249i	0.663462	+	0.383050i	0.793595	−	0.608447i	$-0.208207\pi$
$269$	10.8816	+	6.28249i	0.663462	+	0.383050i	−0.130133	+	0.991497i	$0.541540\pi$
$270$		0			0
$271$	0.248953	−	0.143733i	0.0151228	−	0.00873116i	−0.492420	−	0.870358i	$-0.663887\pi$
$271$	0.248953	−	0.143733i	0.0151228	−	0.00873116i	0.507542	+	0.861627i	$0.330554\pi$
$272$	−3.21995	−	7.37287i	−0.195238	−	0.447046i
$273$		0			0
$274$	−16.9641	+	9.17173i	−1.02484	+	0.554085i
$275$	−12.6802	−	21.9627i	−0.764644	−	1.32440i
$276$		0			0
$277$	−11.9899	−	6.92240i	−0.720406	−	0.415926i	0.0944963	−	0.995525i	$-0.469876\pi$
$277$	−11.9899	−	6.92240i	−0.720406	−	0.415926i	−0.814902	+	0.579599i	$0.803209\pi$
$278$	−22.4390	+	12.1318i	−1.34580	+	0.727614i
$279$		0			0
$280$	8.75618	+	6.08701i	0.523282	+	0.363768i
$281$		−	2.18634i		−	0.130426i	−0.997871	−	0.0652132i	$-0.979227\pi$
$281$		−	2.18634i		−	0.130426i	0.997871	−	0.0652132i	$-0.0207727\pi$
$282$		0			0
$283$	12.2639	−	7.08057i	0.729014	−	0.420896i	−0.0890474	−	0.996027i	$-0.528382\pi$
$283$	12.2639	−	7.08057i	0.729014	−	0.420896i	0.818061	+	0.575131i	$0.195049\pi$
$284$	−0.286605	+	5.12015i	−0.0170069	+	0.303825i
$285$		0			0
$286$	−5.79686	+	30.2247i	−0.342775	+	1.78722i
$287$	0.0828279			0.00488917
$288$		0			0
$289$	6.47727	+	11.2190i	0.381016	+	0.659939i
$290$	−0.183686	+	6.56818i	−0.0107864	+	0.385697i
$291$		0			0
$292$	−21.6702	+	10.9446i	−1.26815	+	0.640484i
$293$	−12.5394	+	21.7189i	−0.732559	+	1.26883i	0.223227	+	0.974767i	$0.428341\pi$
$293$	−12.5394	+	21.7189i	−0.732559	+	1.26883i	−0.955786	+	0.294063i	$0.904992\pi$
$294$		0			0
$295$	−2.81512	+	4.87594i	−0.163903	+	0.283888i
$296$	2.40810	+	5.11880i	0.139968	+	0.297524i
$297$		0			0
$298$	−0.950762	−	1.75854i	−0.0550762	−	0.101869i
$299$	−17.9024	+	6.78078i	−1.03532	+	0.392143i
$300$		0			0
$301$	−8.42888	−	14.5992i	−0.485832	−	0.841486i
$302$	7.02022	+	4.31919i	0.403968	+	0.248542i
$303$		0			0
$304$	5.09915	+	11.6758i	0.292456	+	0.669650i
$305$	−6.07123	−	3.50522i	−0.347637	−	0.200709i
$306$		0			0
$307$	−15.7714			−0.900120			−0.450060	−	0.892998i	$-0.648597\pi$
$307$	−15.7714			−0.900120			−0.450060	+	0.892998i	$0.648597\pi$
$308$	45.4714	−	22.9655i	2.59098	−	1.30858i
$309$		0			0
$310$	2.70779	+	1.66597i	0.153792	+	0.0946208i
$311$	−12.8116			−0.726477			−0.363238	−	0.931696i	$-0.618329\pi$
$311$	−12.8116			−0.726477			−0.363238	+	0.931696i	$0.618329\pi$
$312$		0			0
$313$	21.9885			1.24287			0.621433	−	0.783467i	$-0.286551\pi$
$313$	21.9885			1.24287			0.621433	+	0.783467i	$0.286551\pi$
$314$	3.77346	+	2.32162i	0.212949	+	0.131017i
$315$		0			0
$316$	−2.71512	−	5.37593i	−0.152738	−	0.302419i
$317$	−17.7840			−0.998846			−0.499423	−	0.866358i	$-0.666455\pi$
$317$	−17.7840			−0.998846			−0.499423	+	0.866358i	$0.666455\pi$
$318$		0			0
$319$	27.1829	+	15.6941i	1.52195	+	0.878699i
$320$	−7.04699	−	1.19337i	−0.393939	−	0.0667113i
$321$		0			0
$322$	26.9887	+	16.6048i	1.50402	+	0.925348i
$323$	3.20321	+	5.54813i	0.178231	+	0.308706i
$324$		0			0
$325$	2.43656	−	14.9526i	0.135156	−	0.829422i
$326$	−2.60826	−	4.82426i	−0.144458	−	0.267191i
$327$		0			0
$328$	−0.0502323	+	0.0236314i	−0.00277361	+	0.00130482i
$329$	6.80379	−	11.7845i	0.375105	−	0.649701i
$330$		0			0
$331$	−14.2386	+	24.6619i	−0.782623	+	1.35554i	0.147786	+	0.989019i	$0.452785\pi$
$331$	−14.2386	+	24.6619i	−0.782623	+	1.35554i	−0.930409	+	0.366523i	$0.880548\pi$
$332$	8.02786	+	15.8951i	0.440586	+	0.872358i
$333$		0			0
$334$	0.623858	−	22.3077i	0.0341360	−	1.22062i
$335$	−1.37535	−	2.38218i	−0.0751436	−	0.130152i
$336$		0			0
$337$	8.23580			0.448633			0.224316	−	0.974516i	$-0.427985\pi$
$337$	8.23580			0.448633			0.224316	+	0.974516i	$0.427985\pi$
$338$	−14.1067	+	11.7899i	−0.767301	+	0.641287i
$339$		0			0
$340$	−3.58829	−	0.200858i	−0.194602	−	0.0108931i
$341$	13.1524	−	7.59356i	0.712244	−	0.411214i
$342$		0			0
$343$			16.0761i			0.868027i
$344$	9.27709	+	6.44913i	0.500187	+	0.347714i
$345$		0			0
$346$	0.772923	−	0.417885i	0.0415526	−	0.0224656i
$347$	−16.9827	−	9.80497i	−0.911679	−	0.526358i	−0.0307081	−	0.999528i	$-0.509776\pi$
$347$	−16.9827	−	9.80497i	−0.911679	−	0.526358i	−0.880971	+	0.473170i	$0.843110\pi$
$348$		0			0
$349$	2.31326	+	4.00669i	0.123826	+	0.214473i	0.921273	−	0.388915i	$-0.127150\pi$
$349$	2.31326	+	4.00669i	0.123826	+	0.214473i	−0.797447	+	0.603389i	$0.793817\pi$
$350$	−22.0594	+	11.9265i	−1.17912	+	0.637498i
$351$		0			0
$352$	−21.0247	+	26.9011i	−1.12062	+	1.43383i
$353$	17.4284	−	10.0623i	0.927619	−	0.535561i	0.0415611	−	0.999136i	$-0.486767\pi$
$353$	17.4284	−	10.0623i	0.927619	−	0.535561i	0.886058	+	0.463575i	$0.153434\pi$
$354$		0			0
$355$	1.98388	+	1.14539i	0.105294	+	0.0607912i
$356$	14.5492	+	9.52216i	0.771109	+	0.504673i
$357$		0			0
$358$	−0.429035	+	15.3413i	−0.0226752	+	0.810812i
$359$		−	0.0956414i		−	0.00504776i	−0.999997	−	0.00252388i	$-0.999197\pi$
$359$		−	0.0956414i		−	0.00504776i	0.999997	−	0.00252388i	$-0.000803377\pi$
$360$		0			0
$361$	4.42736	+	7.66841i	0.233019	+	0.403601i
$362$	19.3340	+	11.8952i	1.01617	+	0.625199i
$363$		0			0
$364$	29.7151	+	6.56534i	1.55749	+	0.344117i
$365$			10.8448i			0.567644i
$366$		0			0
$367$	−15.7850	−	27.3405i	−0.823972	−	1.42716i	−0.902702	−	0.430266i	$-0.858420\pi$
$367$	−15.7850	−	27.3405i	−0.823972	−	1.42716i	0.0787296	−	0.996896i	$-0.474914\pi$
$368$	−21.1052	−	2.37019i	−1.10018	−	0.123555i
$369$		0			0
$370$	2.52601	+	0.0706427i	0.131321	+	0.00367254i
$371$	7.06218	−	12.2321i	0.366650	−	0.635056i
$372$		0			0
$373$	9.14193	+	5.27810i	0.473351	+	0.273290i	0.717642	−	0.696413i	$-0.245222\pi$
$373$	9.14193	+	5.27810i	0.473351	+	0.273290i	−0.244290	+	0.969702i	$0.578555\pi$
$374$	−8.99625	+	14.6221i	−0.465185	+	0.756091i
$375$		0			0
$376$	−0.764068	+	9.08808i	−0.0394038	+	0.468682i
$377$	6.64164	+	17.5350i	0.342062	+	0.903101i
$378$		0			0
$379$	−14.1854	−	24.5699i	−0.728657	−	1.26207i	−0.957451	−	0.288595i	$-0.906812\pi$
$379$	−14.1854	−	24.5699i	−0.728657	−	1.26207i	0.228795	−	0.973475i	$-0.426522\pi$
$380$	5.68246	+	0.318081i	0.291504	+	0.0163172i
$381$		0			0
$382$	−14.7641	−	27.3078i	−0.755397	−	1.39719i
$383$	21.8939	+	12.6405i	1.11873	+	0.645897i	0.941076	−	0.338196i	$-0.109817\pi$
$383$	21.8939	+	12.6405i	1.11873	+	0.645897i	0.177651	+	0.984094i	$0.443150\pi$
$384$		0			0
$385$		−	22.7561i		−	1.15976i
$386$	−0.340467	+	12.1743i	−0.0173293	+	0.619655i
$387$		0			0
$388$	1.26375	−	22.5767i	0.0641574	−	1.14616i
$389$		−	15.2123i		−	0.771294i	−0.922646	−	0.385647i	$-0.873978\pi$
$389$		−	15.2123i		−	0.771294i	0.922646	−	0.385647i	$-0.126022\pi$
$390$		0			0
$391$	−10.6791			−0.540064
$392$	−13.0148	−	27.6651i	−0.657347	−	1.39730i
$393$		0			0
$394$	−12.9456	−	0.362037i	−0.652188	−	0.0182392i
$395$	−2.69037			−0.135367
$396$		0			0
$397$	18.8616	−	32.6693i	0.946638	−	1.63963i	0.194202	−	0.980962i	$-0.437788\pi$
$397$	18.8616	−	32.6693i	0.946638	−	1.63963i	0.752437	−	0.658664i	$-0.228878\pi$
$398$	−10.5455	−	19.5051i	−0.528600	−	0.977704i
$399$		0			0
$400$	9.97555	−	13.5267i	0.498777	−	0.676335i
$401$	−28.2674	+	16.3202i	−1.41161	+	0.814991i	−0.995540	−	0.0943435i	$-0.969925\pi$
$401$	−28.2674	+	16.3202i	−1.41161	+	0.814991i	−0.416066	+	0.909334i	$0.636591\pi$
$402$		0			0
$403$	8.95440	+	1.45914i	0.446051	+	0.0726848i
$404$	−21.3932	−	14.0014i	−1.06435	−	0.696595i
$405$		0			0
$406$	16.2641	−	26.4349i	0.807172	−	1.31194i
$407$	6.03568	−	10.4541i	0.299178	−	0.518191i
$408$		0			0
$409$	3.01700	+	1.74186i	0.149181	+	0.0861296i	0.572732	−	0.819742i	$-0.305883\pi$
$409$	3.01700	+	1.74186i	0.149181	+	0.0861296i	−0.423552	+	0.905872i	$0.639217\pi$
$410$	−0.000693238		0.0247885i	−3.42366e−5		0.00122422i
$411$		0			0
$412$	5.73286	+	11.3510i	0.282438	+	0.559225i
$413$	23.0319	−	13.2975i	1.13332	−	0.654325i
$414$		0			0
$415$	7.95467			0.390480
$416$	−19.8943	+	4.49625i	−0.975399	+	0.220447i
$417$		0			0
$418$	14.2466	−	23.1557i	0.696822	−	1.13258i
$419$	27.5293	−	15.8940i	1.34489	−	0.776475i	0.357373	−	0.933962i	$-0.383672\pi$
$419$	27.5293	−	15.8940i	1.34489	−	0.776475i	0.987521	+	0.157487i	$0.0503391\pi$
$420$		0			0
$421$	−38.9188			−1.89679			−0.948394	−	0.317093i	$-0.897293\pi$
$421$	−38.9188			−1.89679			−0.948394	+	0.317093i	$0.897293\pi$
$422$	0.651730	−	23.3043i	0.0317257	−	1.13444i
$423$		0			0
$424$	−0.793085	+	9.43321i	−0.0385156	+	0.458117i
$425$	4.22562	−	7.31898i	0.204972	−	0.355023i
$426$		0			0
$427$	16.5572	+	28.6779i	0.801259	+	1.38782i
$428$	7.04310	+	4.60955i	0.340441	+	0.222811i
$429$		0			0
$430$	4.43977	−	2.40038i	0.214105	−	0.115757i
$431$	21.0414	−	12.1483i	1.01353	−	0.585161i	0.101306	−	0.994855i	$-0.467698\pi$
$431$	21.0414	−	12.1483i	1.01353	−	0.585161i	0.912223	+	0.409694i	$0.134364\pi$
$432$		0			0
$433$	11.5771	−	20.0521i	0.556360	−	0.963643i	−0.441437	−	0.897292i	$-0.645531\pi$
$433$	11.5771	−	20.0521i	0.556360	−	0.963643i	0.997796	−	0.0663510i	$-0.0211357\pi$
$434$	−7.14220	−	13.2103i	−0.342837	−	0.634114i
$435$		0			0
$436$	−13.8383	−	27.3997i	−0.662734	−	1.31221i
$437$	16.9115			0.808987
$438$		0			0
$439$	−14.7545	−	25.5555i	−0.704193	−	1.21970i	−0.966982	−	0.254845i	$-0.917975\pi$
$439$	−14.7545	−	25.5555i	−0.704193	−	1.21970i	0.262788	−	0.964853i	$-0.415358\pi$
$440$	6.49247	+	13.8008i	0.309516	+	0.657927i
$441$		0			0
$442$	−9.68871	+	3.36315i	−0.460845	+	0.159969i
$443$			8.91190i			0.423417i	0.977333	+	0.211709i	$0.0679028\pi$
$443$			8.91190i			0.423417i	−0.977333	+	0.211709i	$0.932097\pi$
$444$		0			0
$445$	6.72683	−	3.88374i	0.318882	−	0.184107i
$446$	0.189146	−	6.76339i	0.00895630	−	0.320256i
$447$		0			0
$448$	26.0089	+	21.5253i	1.22881	+	1.01697i
$449$	8.35715	+	4.82500i	0.394398	+	0.227706i	0.684064	−	0.729422i	$-0.260211\pi$
$449$	8.35715	+	4.82500i	0.394398	+	0.227706i	−0.289666	+	0.957128i	$0.593544\pi$
$450$		0			0
$451$	0.102589	+	0.0592300i	0.00483074	+	0.00278903i
$452$	21.2273	+	1.18822i	0.998447	+	0.0558890i
$453$		0			0
$454$	2.96533	+	5.48470i	0.139170	+	0.257410i
$455$	8.60198	−	10.5264i	0.403267	−	0.493485i
$456$		0			0
$457$	−6.30736	+	3.64156i	−0.295046	+	0.170345i	−0.640215	−	0.768196i	$-0.721155\pi$
$457$	−6.30736	+	3.64156i	−0.295046	+	0.170345i	0.345169	+	0.938540i	$0.387822\pi$
$458$	14.0598	−	22.8522i	0.656973	−	1.06781i
$459$		0			0
$460$	−5.19532	+	7.93812i	−0.242233	+	0.370117i
$461$	−14.1677	+	24.5391i	−0.659855	+	1.14290i	0.320798	+	0.947148i	$0.396049\pi$
$461$	−14.1677	+	24.5391i	−0.659855	+	1.14290i	−0.980653	+	0.195754i	$0.937284\pi$
$462$		0			0
$463$			34.4600i			1.60149i	0.599003	+	0.800747i	$0.295564\pi$
$463$			34.4600i			1.60149i	−0.599003	+	0.800747i	$0.704436\pi$
$464$	−2.32155	+	20.6721i	−0.107775	+	0.959678i
$465$		0			0
$466$	12.0082	−	19.5175i	0.556267	−	0.904131i
$467$		−	33.2473i		−	1.53850i	−0.638946	−	0.769252i	$-0.720629\pi$
$467$		−	33.2473i		−	1.53850i	0.638946	−	0.769252i	$-0.279371\pi$
$468$		0			0
$469$			12.9932i			0.599969i
$470$	3.46990	+	2.13485i	0.160054	+	0.0984735i
$471$		0			0
$472$	−10.1742	+	14.6356i	−0.468305	+	0.673659i
$473$		−	24.1099i		−	1.10857i
$474$		0			0
$475$	−6.69173	+	11.5904i	−0.307038	+	0.531805i
$476$	14.2044	+	9.29645i	0.651057	+	0.426102i
$477$		0			0
$478$	4.40291	+	2.70889i	0.201384	+	0.123902i
$479$	18.3155	−	10.5745i	0.836858	−	0.483160i	−0.0193371	−	0.999813i	$-0.506156\pi$
$479$	18.3155	−	10.5745i	0.836858	−	0.483160i	0.856195	+	0.516653i	$0.172822\pi$
$480$		0			0
$481$	6.74369	−	2.55427i	0.307486	−	0.116465i
$482$	−28.3939	+	15.3513i	−1.29331	+	0.699233i
$483$		0			0
$484$	50.7771	+	2.84230i	2.30805	+	0.129195i
$485$	−8.74771	−	5.05049i	−0.397213	−	0.229331i
$486$		0			0
$487$	15.5640	+	8.98589i	0.705273	+	0.407189i	0.809308	−	0.587384i	$-0.199842\pi$
$487$	15.5640	+	8.98589i	0.705273	+	0.407189i	−0.104035	+	0.994574i	$0.533176\pi$
$488$	−18.2234	−	12.6683i	−0.824934	−	0.573467i
$489$		0			0
$490$	−13.6521	−	0.381796i	−0.616740	−	0.0172478i
$491$	−4.43288	+	2.55932i	−0.200053	+	0.115501i	−0.596680	−	0.802479i	$-0.703514\pi$
$491$	−4.43288	+	2.55932i	−0.200053	+	0.115501i	0.396627	+	0.917980i	$0.370181\pi$
$492$		0			0
$493$			10.4600i			0.471093i
$494$	15.3431	−	5.32592i	0.690320	−	0.239625i
$495$		0			0
$496$	8.10049	+	5.97387i	0.363723	+	0.268235i
$497$	−5.41036	−	9.37102i	−0.242688	−	0.420348i
$498$		0			0
$499$	−19.2741			−0.862826			−0.431413	−	0.902155i	$-0.641985\pi$
$499$	−19.2741			−0.862826			−0.431413	+	0.902155i	$0.641985\pi$
$500$	−7.41238	−	14.6765i	−0.331492	−	0.656351i
$501$		0			0
$502$	7.49976	−	4.05478i	0.334730	−	0.180974i
$503$	−12.0244	+	20.8268i	−0.536139	+	0.928621i	0.462968	+	0.886375i	$0.346785\pi$
$503$	−12.0244	+	20.8268i	−0.536139	+	0.928621i	−0.999107	+	0.0422456i	$0.986549\pi$
$504$		0			0
$505$	−9.89114	+	5.71065i	−0.440150	+	0.254121i
$506$	21.5537	+	39.8659i	0.958179	+	1.77226i
$507$		0			0
$508$	−2.77762	+	4.24403i	−0.123237	+	0.188298i
$509$	−18.5759	−	32.1744i	−0.823362	−	1.42610i	−0.903165	−	0.429294i	$-0.858762\pi$
$509$	−18.5759	−	32.1744i	−0.823362	−	1.42610i	0.0798031	−	0.996811i	$-0.474571\pi$
$510$		0			0
$511$	25.6132	−	44.3633i	1.13306	−	1.96252i
$512$	−21.9148	−	5.63382i	−0.968508	−	0.248982i
$513$		0			0
$514$	−32.8664	−	0.919146i	−1.44968	−	0.0405418i
$515$	5.68060			0.250317
$516$		0			0
$517$	16.8541	−	9.73074i	0.741244	−	0.427958i
$518$	−10.1664	−	6.25489i	−0.446687	−	0.274824i
$519$		0			0
$520$	−2.21356	+	8.83810i	−0.0970712	+	0.387576i
$521$	9.09538			0.398476			0.199238	−	0.979951i	$-0.436153\pi$
$521$	9.09538			0.398476			0.199238	+	0.979951i	$0.436153\pi$
$522$		0			0
$523$	21.3438	−	12.3228i	0.933298	−	0.538840i	0.0454452	−	0.998967i	$-0.485529\pi$
$523$	21.3438	−	12.3228i	0.933298	−	0.538840i	0.887853	+	0.460127i	$0.152196\pi$
$524$	−3.59469	+	1.81551i	−0.157035	+	0.0793108i
$525$		0			0
$526$	−3.80351	−	0.106369i	−0.165841	−	0.00463793i
$527$	4.38298	+	2.53052i	0.190926	+	0.110231i
$528$		0			0
$529$	−2.59517	+	4.49497i	−0.112834	+	0.195434i
$530$	3.60167	+	2.21593i	0.156447	+	0.0962538i
$531$		0			0
$532$	−22.4942	−	14.7220i	−0.975248	−	0.638277i
$533$	0.0250658	+	0.0661779i	0.00108572	+	0.00286648i
$534$		0			0
$535$	3.25637	−	1.88007i	0.140785	−	0.0812824i
$536$	−3.70704	−	7.87992i	−0.160120	−	0.340361i
$537$		0			0
$538$	15.6312	−	8.45111i	0.673911	−	0.364353i
$539$	−32.6205	+	56.5004i	−1.40507	+	2.43364i
$540$		0			0
$541$	5.07378			0.218139			0.109069	−	0.994034i	$-0.465213\pi$
$541$	5.07378			0.218139			0.109069	+	0.994034i	$0.465213\pi$
$542$	0.0113648	−	0.406379i	0.000488162	−	0.0174555i
$543$		0			0
$544$	−11.2668	−	1.58537i	−0.483061	−	0.0679724i
$545$	−13.7121			−0.587363
$546$		0			0
$547$		−	0.158642i		−	0.00678304i	−0.999994	−	0.00339152i	$-0.998920\pi$
$547$		−	0.158642i		−	0.00678304i	0.999994	−	0.00339152i	$-0.00107956\pi$
$548$	−1.52423	+	27.2301i	−0.0651120	+	1.16321i
$549$		0			0
$550$	−35.8510	−	1.00261i	−1.52869	−	0.0427515i
$551$		−	16.5645i		−	0.705671i
$552$		0			0
$553$	11.0056	+	6.35409i	0.468006	+	0.270203i
$554$	−17.2234	+	9.31190i	−0.731751	+	0.395625i
$555$		0			0
$556$	−2.01615	+	36.0182i	−0.0855040	+	1.52751i
$557$	2.30308	+	3.98905i	0.0975847	+	0.169022i	0.910684	−	0.413103i	$-0.135555\pi$
$557$	2.30308	+	3.98905i	0.0975847	+	0.169022i	−0.813100	+	0.582124i	$0.802222\pi$
$558$		0			0
$559$	9.11372	−	11.1526i	0.385469	−	0.471705i
$560$	13.8207	−	6.03592i	0.584032	−	0.255064i
$561$		0			0
$562$	−2.63345	−	1.62023i	−0.111085	−	0.0683453i
$563$	−1.29014	−	0.744862i	−0.0543729	−	0.0313922i	0.472567	−	0.881295i	$-0.343327\pi$
$563$	−1.29014	−	0.744862i	−0.0543729	−	0.0313922i	−0.526940	+	0.849902i	$0.676661\pi$
$564$		0			0
$565$	4.74861	−	8.22484i	0.199776	−	0.346022i
$566$	0.559855	−	20.0191i	0.0235325	−	0.841464i
$567$		0			0
$568$	5.95482	+	4.13960i	0.249859	+	0.173694i
$569$	8.32754	+	14.4237i	0.349108	+	0.604674i	0.986091	−	0.166204i	$-0.0531512\pi$
$569$	8.32754	+	14.4237i	0.349108	+	0.604674i	−0.636983	+	0.770878i	$0.719818\pi$
$570$		0			0
$571$		−	21.2857i		−	0.890779i	−0.895337	−	0.445390i	$-0.853065\pi$
$571$		−	21.2857i		−	0.890779i	0.895337	−	0.445390i	$-0.146935\pi$
$572$	32.1098	+	29.3809i	1.34258	+	1.22848i
$573$		0			0
$574$	0.0613811	−	0.0997661i	0.00256200	−	0.00416416i
$575$	−11.1547	−	19.3204i	−0.465182	−	0.805718i
$576$		0			0
$577$			7.02758i			0.292562i	0.989243	+	0.146281i	$0.0467304\pi$
$577$			7.02758i			0.292562i	−0.989243	+	0.146281i	$0.953270\pi$
$578$	18.3133	+	0.512152i	0.761734	+	0.0213027i
$579$		0			0
$580$	7.77524	+	5.08872i	0.322849	+	0.211297i
$581$	−32.5405	−	18.7873i	−1.35001	−	0.779427i
$582$		0			0
$583$	17.4942	−	10.1003i	0.724536	−	0.418311i
$584$	−2.87637	+	34.2125i	−0.119025	+	1.41572i
$585$		0			0
$586$	16.8678	+	31.1989i	0.696803	+	1.28881i
$587$	−3.96345	−	6.86490i	−0.163589	−	0.283345i	0.772564	−	0.634937i	$-0.218974\pi$
$587$	−3.96345	−	6.86490i	−0.163589	−	0.283345i	−0.936153	+	0.351592i	$0.885640\pi$
$588$		0			0
$589$	−6.94094	−	4.00735i	−0.285996	−	0.165120i
$590$	3.78686	+	7.00422i	0.155903	+	0.288359i
$591$		0			0
$592$	7.95015	+	0.892832i	0.326749	+	0.0366952i
$593$		−	22.9984i		−	0.944430i	−0.881483	−	0.472215i	$-0.843455\pi$
$593$		−	22.9984i		−	0.944430i	0.881483	−	0.472215i	$-0.156545\pi$
$594$		0			0
$595$	6.56738	−	3.79168i	0.269236	−	0.155444i
$596$	−2.82274	−	0.158005i	−0.115624	−	0.00647215i
$597$		0			0
$598$	−5.09945	+	26.5884i	−0.208532	+	1.08728i
$599$	9.32430			0.380980			0.190490	−	0.981689i	$-0.438992\pi$
$599$	9.32430			0.380980			0.190490	+	0.981689i	$0.438992\pi$
$600$		0			0
$601$	−4.24363	−	7.35018i	−0.173101	−	0.299820i	0.766401	−	0.642362i	$-0.222045\pi$
$601$	−4.24363	−	7.35018i	−0.173101	−	0.299820i	−0.939503	+	0.342542i	$0.888712\pi$
$602$	−23.8311	−	0.666464i	−0.971285	−	0.0271630i
$603$		0			0
$604$	10.4049	−	5.25503i	0.423371	−	0.213824i
$605$	11.3590	−	19.6744i	0.461810	−	0.799878i
$606$		0			0
$607$	−10.3169	+	17.8694i	−0.418749	+	0.725295i	−0.995814	−	0.0914036i	$-0.970865\pi$
$607$	−10.3169	+	17.8694i	−0.418749	+	0.725295i	0.577065	+	0.816698i	$0.304198\pi$
$608$	17.8422	+	2.51061i	0.723599	+	0.101819i
$609$		0			0
$610$	−8.72123	+	4.71518i	−0.353112	+	0.190912i
$611$	11.4746	+	1.86981i	0.464212	+	0.0756443i
$612$		0			0
$613$	−18.0557	−	31.2734i	−0.729264	−	1.26312i	−0.957195	−	0.289445i	$-0.906529\pi$
$613$	−18.0557	−	31.2734i	−0.729264	−	1.26312i	0.227931	−	0.973677i	$-0.426804\pi$
$614$	−11.6877	+	18.9966i	−0.471676	+	0.766641i
$615$		0			0
$616$	6.03559	−	71.7893i	0.243181	−	2.89247i
$617$	29.2958	+	16.9139i	1.17940	+	0.680929i	0.955877	−	0.293769i	$-0.0949096\pi$
$617$	29.2958	+	16.9139i	1.17940	+	0.680929i	0.223527	+	0.974698i	$0.428243\pi$
$618$		0			0
$619$	−3.06121			−0.123040			−0.0615201	−	0.998106i	$-0.519595\pi$
$619$	−3.06121			−0.123040			−0.0615201	+	0.998106i	$0.519595\pi$
$620$	4.01332	−	2.02694i	0.161179	−	0.0814037i
$621$		0			0
$622$	−9.49424	+	15.4315i	−0.380684	+	0.618747i
$623$	−36.6903			−1.46997
$624$		0			0
$625$	13.6642			0.546570
$626$	16.2950	−	26.4852i	0.651280	−	1.05856i
$627$		0			0
$628$	5.59279	−	2.82465i	0.223177	−	0.112716i
$629$	4.02273			0.160397
$630$		0			0
$631$	−23.9926	−	13.8521i	−0.955130	−	0.551444i	−0.0604589	−	0.998171i	$-0.519256\pi$
$631$	−23.9926	−	13.8521i	−0.955130	−	0.551444i	−0.894671	+	0.446726i	$0.852590\pi$
$632$	−8.48739	−	0.713566i	−0.337610	−	0.0283841i
$633$		0			0
$634$	−13.1791	+	21.4208i	−0.523410	+	0.850727i
$635$	1.13289	+	1.96222i	0.0449574	+	0.0778685i
$636$		0			0
$637$	−36.4470	+	13.8048i	−1.44408	+	0.546967i
$638$	39.0479	−	21.1114i	1.54592	−	0.835810i
$639$		0			0
$640$	−6.65971	+	7.60373i	−0.263248	+	0.300564i
$641$	11.8526	−	20.5292i	0.468148	−	0.810856i	−0.531189	−	0.847253i	$-0.678255\pi$
$641$	11.8526	−	20.5292i	0.468148	−	0.810856i	0.999337	+	0.0363969i	$0.0115881\pi$
$642$		0			0
$643$	10.3454	−	17.9188i	0.407983	−	0.706648i	−0.586680	−	0.809819i	$-0.699565\pi$
$643$	10.3454	−	17.9188i	0.407983	−	0.706648i	0.994664	+	0.103171i	$0.0328988\pi$
$644$	40.0009	−	20.2025i	1.57626	−	0.796091i
$645$		0			0
$646$	9.05651	+	0.253275i	0.356324	+	0.00996498i
$647$	−0.671662	−	1.16335i	−0.0264058	−	0.0457361i	0.852521	−	0.522694i	$-0.175073\pi$
$647$	−0.671662	−	1.16335i	−0.0264058	−	0.0457361i	−0.878926	+	0.476958i	$0.841740\pi$
$648$		0			0
$649$	38.0359			1.49304
$650$	−16.2048	−	14.0157i	−0.635603	−	0.549743i
$651$		0			0
$652$	−7.74372	−	0.433462i	−0.303267	−	0.0169757i
$653$	−5.18453	+	2.99329i	−0.202887	+	0.117137i	−0.598001	−	0.801495i	$-0.704038\pi$
$653$	−5.18453	+	2.99329i	−0.202887	+	0.117137i	0.395115	+	0.918632i	$0.370705\pi$
$654$		0			0
$655$			1.79896i			0.0702910i
$656$	−0.00876163	+	0.0780172i	−0.000342084	+	0.00304606i
$657$		0			0
$658$	−9.15236	−	16.9283i	−0.356796	−	0.659934i
$659$	4.31253	+	2.48984i	0.167992	+	0.0969905i	0.581639	−	0.813447i	$-0.302412\pi$
$659$	4.31253	+	2.48984i	0.167992	+	0.0969905i	−0.413646	+	0.910438i	$0.635745\pi$
$660$		0			0
$661$	14.1524	+	24.5127i	0.550466	+	0.953435i	0.998241	+	0.0592889i	$0.0188833\pi$
$661$	14.1524	+	24.5127i	0.550466	+	0.953435i	−0.447775	+	0.894146i	$0.647783\pi$
$662$	19.1535	+	35.4265i	0.744423	+	1.37689i
$663$		0			0
$664$	25.0948	+	2.10981i	0.973869	+	0.0818767i
$665$	−10.4002	+	6.00454i	−0.403301	+	0.232846i
$666$		0			0
$667$	23.9126	+	13.8060i	0.925900	+	0.534569i
$668$	−26.4072	−	17.2829i	−1.02173	−	0.668697i
$669$		0			0
$670$	−3.88857	−	0.108748i	−0.150228	−	0.00420130i
$671$			47.3600i			1.82831i
$672$		0			0
$673$	−11.3696	−	19.6927i	−0.438264	−	0.759096i	0.559291	−	0.828971i	$-0.311073\pi$
$673$	−11.3696	−	19.6927i	−0.438264	−	0.759096i	−0.997556	+	0.0698751i	$0.977740\pi$
$674$	6.10329	−	9.92002i	0.235090	−	0.382105i
$675$		0			0
$676$	3.74694	+	25.7286i	0.144113	+	0.989561i
$677$			35.0768i			1.34811i	0.738681	+	0.674056i	$0.235449\pi$
$677$			35.0768i			1.34811i	−0.738681	+	0.674056i	$0.764551\pi$
$678$		0			0
$679$	23.8564	+	41.3205i	0.915525	+	1.58574i
$680$	−2.90110	+	4.17324i	−0.111252	+	0.160037i
$681$		0			0
$682$	0.600416	−	21.4694i	0.0229911	−	0.822107i
$683$	−24.6307	+	42.6617i	−0.942469	+	1.63240i	−0.181727	+	0.983349i	$0.558169\pi$
$683$	−24.6307	+	42.6617i	−0.942469	+	1.63240i	−0.760742	+	0.649055i	$0.775165\pi$
$684$		0			0
$685$	10.5508	+	6.09148i	0.403124	+	0.232743i
$686$	19.3636	+	11.9135i	0.739307	+	0.454859i
$687$		0			0
$688$	14.6429	−	6.39500i	0.558256	−	0.243807i
$689$	11.9104	+	1.94082i	0.453749	+	0.0739392i
$690$		0			0
$691$	−12.6649	−	21.9363i	−0.481797	−	0.834498i	0.517984	−	0.855390i	$-0.326683\pi$
$691$	−12.6649	−	21.9363i	−0.481797	−	0.834498i	−0.999782	+	0.0208926i	$0.993349\pi$
$692$	0.0694475	−	1.24067i	0.00264000	−	0.0471631i
$693$		0			0
$694$	−24.3954	+	13.1895i	−0.926037	+	0.500666i
$695$	13.9558	+	8.05740i	0.529375	+	0.305635i
$696$		0			0
$697$			0.0394762i			0.00149527i
$698$	6.54034	+	0.182908i	0.247555	+	0.00692316i
$699$		0			0
$700$	−1.98204	+	35.4088i	−0.0749142	+	1.33833i
$701$		−	37.7963i		−	1.42755i	−0.700377	−	0.713773i	$-0.746985\pi$
$701$		−	37.7963i		−	1.42755i	0.700377	−	0.713773i	$-0.253015\pi$
$702$		0			0
$703$	−6.37043			−0.240265
$704$	16.8216	+	45.2598i	0.633988	+	1.70579i
$705$		0			0
$706$	0.795615	−	28.4493i	0.0299434	−	1.07070i
$707$	53.9494			2.02898
$708$		0			0
$709$	−14.8681	+	25.7524i	−0.558385	+	0.967151i	0.439247	+	0.898367i	$0.355245\pi$
$709$	−14.8681	+	25.7524i	−0.558385	+	0.967151i	−0.997632	+	0.0687845i	$0.978088\pi$
$710$	2.84982	−	1.54077i	0.106952	−	0.0578240i
$711$		0			0
$712$	22.2514	−	10.4680i	0.833907	−	0.392304i
$713$	11.5701	−	6.67999i	0.433303	−	0.250168i
$714$		0			0
$715$	18.1817	−	6.88656i	0.679956	−	0.257543i
$716$	18.1606	+	11.8857i	0.678694	+	0.444190i
$717$		0			0
$718$	−0.115200	−	0.0708768i	−0.00429922	−	0.00264510i
$719$	12.2000	−	21.1310i	0.454983	−	0.788054i	−0.543704	−	0.839277i	$-0.682979\pi$
$719$	12.2000	−	21.1310i	0.454983	−	0.788054i	0.998687	+	0.0512233i	$0.0163120\pi$
$720$		0			0
$721$	−23.2378	−	13.4164i	−0.865422	−	0.499652i
$722$	12.5176	+	0.350068i	0.465856	+	0.0130282i
$723$		0			0
$724$	28.6556	−	14.4726i	1.06498	−	0.537869i
$725$	−18.9240	+	10.9258i	−0.702820	+	0.405773i
$726$		0			0
$727$	−44.0720			−1.63454			−0.817271	−	0.576254i	$-0.804514\pi$
$727$	−44.0720			−1.63454			−0.817271	+	0.576254i	$0.804514\pi$
$728$	29.9288	−	30.9264i	1.10924	−	1.14621i
$729$		0			0
$730$	13.0626	+	8.03676i	0.483468	+	0.297454i
$731$	6.95808	−	4.01725i	0.257354	−	0.148583i
$732$		0			0
$733$	−28.9063			−1.06768			−0.533839	−	0.845586i	$-0.679251\pi$
$733$	−28.9063			−1.06768			−0.533839	+	0.845586i	$0.679251\pi$
$734$	−44.6294	−	1.24811i	−1.64730	−	0.0460686i
$735$		0			0
$736$	−18.4953	+	23.6647i	−0.681744	+	0.872291i
$737$	−9.29138	+	16.0931i	−0.342252	+	0.592799i
$738$		0			0
$739$	12.3818	+	21.4460i	0.455474	+	0.788903i	0.998715	−	0.0506730i	$-0.0161366\pi$
$739$	12.3818	+	21.4460i	0.455474	+	0.788903i	−0.543242	+	0.839576i	$0.682803\pi$
$740$	1.95704	−	2.99023i	0.0719421	−	0.109923i
$741$		0			0
$742$	−9.49994	−	17.5712i	−0.348754	−	0.645058i
$743$	−44.5277	+	25.7081i	−1.63356	+	0.943139i	−0.650582	+	0.759436i	$0.725475\pi$
$743$	−44.5277	+	25.7081i	−1.63356	+	0.943139i	−0.982982	+	0.183703i	$0.941192\pi$
$744$		0			0
$745$	−0.631456	+	1.09371i	−0.0231348	+	0.0400706i
$746$	13.1323	−	7.10002i	0.480806	−	0.259950i
$747$		0			0
$748$	10.9455	+	21.6719i	0.400206	+	0.792405i
$749$	−17.7613			−0.648983
$750$		0			0
$751$	10.4756	+	18.1442i	0.382259	+	0.662093i	0.991385	−	0.130981i	$-0.0418127\pi$
$751$	10.4756	+	18.1442i	0.382259	+	0.662093i	−0.609125	+	0.793074i	$0.708479\pi$
$752$	10.3804	+	7.65521i	0.378533	+	0.279157i
$753$		0			0
$754$	26.0429	+	4.99481i	0.948425	+	0.181900i
$755$		−	5.20712i		−	0.189507i
$756$		0			0
$757$	−21.8620	+	12.6220i	−0.794587	+	0.458755i	−0.841575	−	0.540140i	$-0.818371\pi$
$757$	−21.8620	+	12.6220i	−0.794587	+	0.458755i	0.0469876	+	0.998895i	$0.485038\pi$
$758$	−40.1068	−	1.12163i	−1.45674	−	0.0407394i
$759$		0			0
$760$	4.59422	−	6.60879i	0.166650	−	0.239726i
$761$	5.11797	+	2.95486i	0.185526	+	0.107114i	0.589886	−	0.807486i	$-0.299172\pi$
$761$	5.11797	+	2.95486i	0.185526	+	0.107114i	−0.404360	+	0.914600i	$0.632506\pi$
$762$		0			0
$763$	56.0928	+	32.3852i	2.03069	+	1.17242i
$764$	−43.8335	−	2.45362i	−1.58584	−	0.0887688i
$765$		0			0
$766$	31.4503	−	17.0038i	1.13635	−	0.614370i
$767$	17.5944	+	14.3779i	0.635298	+	0.519155i
$768$		0			0
$769$	15.8579	−	9.15556i	0.571850	−	0.330158i	−0.186038	−	0.982543i	$-0.559565\pi$
$769$	15.8579	−	9.15556i	0.571850	−	0.330158i	0.757888	+	0.652385i	$0.226231\pi$
$770$	−27.4097	−	16.8638i	−0.987776	−	0.607730i
$771$		0			0
$772$	14.4116	+	9.43208i	0.518685	+	0.339468i
$773$	−9.59015	+	16.6106i	−0.344934	+	0.597443i	−0.985342	−	0.170592i	$-0.945432\pi$
$773$	−9.59015	+	16.6106i	−0.344934	+	0.597443i	0.640408	+	0.768035i	$0.278765\pi$
$774$		0			0
$775$			10.5728i			0.379788i
$776$	−26.2571	−	18.2531i	−0.942576	−	0.655248i
$777$		0			0
$778$	−18.3232	−	11.2734i	−0.656919	−	0.404169i
$779$		−	0.0625150i		−	0.00223983i
$780$		0			0
$781$		−	15.4757i		−	0.553765i
$782$	−7.91393	+	12.8629i	−0.283002	+	0.459978i
$783$		0			0
$784$	−42.9675	−	4.82541i	−1.53455	−	0.172336i
$785$		−	2.79890i		−	0.0998970i
$786$		0			0
$787$	−3.92375	+	6.79613i	−0.139867	+	0.242256i	−0.927446	−	0.373957i	$-0.878001\pi$
$787$	−3.92375	+	6.79613i	−0.139867	+	0.242256i	0.787579	+	0.616213i	$0.211334\pi$
$788$	−10.0296	+	15.3246i	−0.357291	+	0.545917i
$789$		0			0
$790$	−1.99375	+	3.24055i	−0.0709344	+	0.115294i
$791$	−38.8507	+	22.4305i	−1.38137	+	0.797535i
$792$		0			0
$793$	−17.9025	+	21.9075i	−0.635735	+	0.777960i
$794$	−25.3724	−	46.9290i	−0.900433	−	1.66545i
$795$		0			0
$796$	−31.3089	−	1.75255i	−1.10971	−	0.0621173i
$797$	22.6302	+	13.0656i	0.801605	+	0.462807i	0.844032	−	0.536293i	$-0.180176\pi$
$797$	22.6302	+	13.0656i	0.801605	+	0.462807i	−0.0424273	+	0.999100i	$0.513509\pi$
$798$		0			0
$799$	5.61657	+	3.24273i	0.198700	+	0.114719i
$800$	−8.90034	−	22.0397i	−0.314674	−	0.779223i
$801$		0			0
$802$	−1.29042	+	46.1424i	−0.0455664	+	1.62934i
$803$	63.4482	−	36.6318i	2.23904	−	1.29271i
$804$		0			0
$805$		−	20.0183i		−	0.705554i
$806$	8.39335	−	9.70425i	0.295643	−	0.341818i
$807$		0			0
$808$	−32.7185	+	15.3921i	−1.15103	+	0.541494i
$809$	−6.20747	−	10.7517i	−0.218243	−	0.378008i	0.736028	−	0.676951i	$-0.236699\pi$
$809$	−6.20747	−	10.7517i	−0.218243	−	0.378008i	−0.954271	+	0.298943i	$0.903366\pi$
$810$		0			0
$811$	15.9619			0.560499			0.280249	−	0.959927i	$-0.409583\pi$
$811$	15.9619			0.560499			0.280249	+	0.959927i	$0.409583\pi$
$812$	−19.7880	−	39.1801i	−0.694422	−	1.37495i
$813$		0			0
$814$	−8.11911	−	15.0172i	−0.284575	−	0.526352i
$815$	−1.73230	+	3.00043i	−0.0606797	+	0.105100i
$816$		0			0
$817$	−11.0189	+	6.36176i	−0.385502	+	0.222570i
$818$	4.33387	−	2.34313i	0.151530	−	0.0819256i
$819$		0			0
$820$	0.0293440	+	0.0192050i	0.00102474	+	0.000670667i
$821$	22.5254	+	39.0152i	0.786144	+	1.36164i	0.928314	+	0.371798i	$0.121259\pi$
$821$	22.5254	+	39.0152i	0.786144	+	1.36164i	−0.142170	+	0.989842i	$0.545408\pi$
$822$		0			0
$823$	−16.7658	+	29.0393i	−0.584420	+	1.01224i	0.410528	+	0.911848i	$0.365345\pi$
$823$	−16.7658	+	29.0393i	−0.584420	+	1.01224i	−0.994947	+	0.100397i	$0.967989\pi$
$824$	17.9207	+	1.50666i	0.624299	+	0.0524871i
$825$		0			0
$826$	1.05142	−	37.5962i	0.0365835	−	1.30814i
$827$	−51.5687			−1.79322			−0.896610	−	0.442820i	$-0.853978\pi$
$827$	−51.5687			−1.79322			−0.896610	+	0.442820i	$0.853978\pi$
$828$		0			0
$829$	−18.8521	+	10.8842i	−0.654759	+	0.378025i	−0.790277	−	0.612750i	$-0.790063\pi$
$829$	−18.8521	+	10.8842i	−0.654759	+	0.378025i	0.135518	+	0.990775i	$0.456730\pi$
$830$	5.89496	−	9.58140i	0.204617	−	0.332575i
$831$		0			0
$832$	−9.32732	+	27.2947i	−0.323367	+	0.946274i
$833$	−21.7413			−0.753291
$834$		0			0
$835$	−12.2094	+	7.04907i	−0.422522	+	0.243943i
$836$	−17.3333	−	34.3199i	−0.599486	−	1.18698i
$837$		0			0
$838$	1.25673	−	44.9376i	0.0434130	−	1.55234i
$839$	22.6729	+	13.0902i	0.782755	+	0.451924i	0.837406	−	0.546582i	$-0.184071\pi$
$839$	22.6729	+	13.0902i	0.782755	+	0.451924i	−0.0546509	+	0.998506i	$0.517405\pi$
$840$		0			0
$841$	−0.977337	+	1.69280i	−0.0337013	+	0.0583723i
$842$	−28.8415	+	46.8777i	−0.993945	+	1.61551i
$843$		0			0
$844$	−27.5870	−	18.0551i	−0.949584	−	0.621482i
$845$	11.0136	+	3.68727i	0.378878	+	0.126846i
$846$		0			0
$847$	−92.9336	+	53.6552i	−3.19324	+	1.84362i
$848$	10.7746	+	7.94592i	0.370000	+	0.272864i
$849$		0			0
$850$	−5.68423	−	10.5136i	−0.194968	−	0.360614i
$851$	5.30954	−	9.19640i	0.182009	−	0.315249i
$852$		0			0
$853$	−33.0664			−1.13217			−0.566086	−	0.824346i	$-0.691543\pi$
$853$	−33.0664			−1.13217			−0.566086	+	0.824346i	$0.691543\pi$
$854$	46.8125	+	1.30916i	1.60189	+	0.0447987i
$855$		0			0
$856$	10.7716	−	5.06742i	0.368166	−	0.173201i
$857$	−27.7866			−0.949172			−0.474586	−	0.880209i	$-0.657402\pi$
$857$	−27.7866			−0.949172			−0.474586	+	0.880209i	$0.657402\pi$
$858$		0			0
$859$			53.8754i			1.83820i	0.394020	+	0.919102i	$0.371084\pi$
$859$			53.8754i			1.83820i	−0.394020	+	0.919102i	$0.628916\pi$
$860$	0.398915	−	7.12655i	0.0136029	−	0.243013i
$861$		0			0
$862$	0.960553	−	34.3471i	0.0327166	−	1.16987i
$863$			48.6608i			1.65643i	0.560408	+	0.828217i	$0.310645\pi$
$863$			48.6608i			1.65643i	−0.560408	+	0.828217i	$0.689355\pi$
$864$		0			0
$865$	−0.480716	−	0.277541i	−0.0163448	−	0.00943669i
$866$	−15.5733	−	28.8046i	−0.529204	−	0.978820i
$867$		0			0
$868$	−21.2046	−	1.18695i	−0.719732	−	0.0402877i
$869$	9.08758	+	15.7401i	0.308275	+	0.533948i
$870$		0			0
$871$	−10.3813	+	3.93206i	−0.351757	+	0.133233i
$872$	−43.2581	−	3.63686i	−1.46490	−	0.123160i
$873$		0			0
$874$	12.5326	−	20.3699i	0.423921	−	0.689022i
$875$	30.0457	+	17.3469i	1.01573	+	0.586431i
$876$		0			0
$877$	1.83365	−	3.17598i	0.0619181	−	0.107245i	−0.833405	−	0.552663i	$-0.813612\pi$
$877$	1.83365	−	3.17598i	0.0619181	−	0.107245i	0.895323	+	0.445418i	$0.146945\pi$
$878$	−41.7157	−	1.16662i	−1.40784	−	0.0393717i
$879$		0			0
$880$	21.4344	+	2.40716i	0.722554	+	0.0811455i
$881$	0.624583	+	1.08181i	0.0210427	+	0.0364471i	0.876355	−	0.481666i	$-0.159968\pi$
$881$	0.624583	+	1.08181i	0.0210427	+	0.0364471i	−0.855312	+	0.518113i	$0.826635\pi$
$882$		0			0
$883$			4.46615i			0.150298i	0.997172	+	0.0751489i	$0.0239432\pi$
$883$			4.46615i			0.150298i	−0.997172	+	0.0751489i	$0.976057\pi$
$884$	−3.12908	+	14.1624i	−0.105242	+	0.476332i
$885$		0			0
$886$	10.7344	+	6.60433i	0.360628	+	0.221877i
$887$	6.70566	+	11.6145i	0.225154	+	0.389978i	0.956366	−	0.292173i	$-0.0943782\pi$
$887$	6.70566	+	11.6145i	0.225154	+	0.389978i	−0.731212	+	0.682151i	$0.761045\pi$
$888$		0			0
$889$		−	10.7026i		−	0.358953i
$890$	0.307084	−	10.9806i	0.0102935	−	0.368070i
$891$		0			0
$892$	−8.00633	−	5.23996i	−0.268072	−	0.175447i
$893$	−8.89445	−	5.13521i	−0.297641	−	0.171843i
$894$		0			0
$895$	8.39654	−	4.84774i	0.280665	−	0.162042i
$896$	45.2016	−	15.3760i	1.51008	−	0.513677i
$897$		0			0
$898$	12.0049	−	6.49052i	0.400610	−	0.216591i
$899$	−6.54292	−	11.3327i	−0.218219	−	0.377966i
$900$		0			0
$901$	5.82986	+	3.36587i	0.194221	+	0.112133i
$902$	0.147368	−	0.0796753i	0.00490682	−	0.00265290i
$903$		0			0
$904$	17.1621	−	24.6877i	0.570802	−	0.821100i
$905$		−	14.3406i		−	0.476698i
$906$		0			0
$907$	28.1142	−	16.2318i	0.933518	−	0.538967i	0.0455956	−	0.998960i	$-0.485481\pi$
$907$	28.1142	−	16.2318i	0.933518	−	0.538967i	0.887923	+	0.459993i	$0.152148\pi$
$908$	8.80383	+	0.492803i	0.292165	+	0.0163542i
$909$		0			0
$910$	−6.30436	−	18.1619i	−0.208988	−	0.602059i
$911$	−24.4263			−0.809279			−0.404639	−	0.914476i	$-0.632603\pi$
$911$	−24.4263			−0.809279			−0.404639	+	0.914476i	$0.632603\pi$
$912$		0			0
$913$	−26.8694	−	46.5392i	−0.889248	−	1.54022i
$914$	−0.287935	+	10.2959i	−0.00952404	+	0.340557i
$915$		0			0
$916$	−17.1062	−	33.8701i	−0.565204	−	1.11910i
$917$	4.24876	−	7.35906i	0.140306	−	0.243018i
$918$		0			0
$919$	22.1908	−	38.4356i	0.732008	−	1.26787i	−0.224016	−	0.974585i	$-0.571917\pi$
$919$	22.1908	−	38.4356i	0.732008	−	1.26787i	0.956024	−	0.293289i	$-0.0947498\pi$
$920$	5.71137	+	12.1404i	0.188298	+	0.400259i
$921$		0			0
$922$	19.0582	+	35.2501i	0.627647	+	1.16090i
$923$	5.84995	−	7.15868i	0.192554	−	0.235631i
$924$		0			0
$925$	4.20188	+	7.27786i	0.138157	+	0.239295i
$926$	41.5071	+	25.5372i	1.36401	+	0.839206i
$927$		0			0
$928$	23.1791	+	18.1157i	0.760891	+	0.594679i
$929$	21.9114	+	12.6505i	0.718889	+	0.415051i	0.814344	−	0.580383i	$-0.197097\pi$
$929$	21.9114	+	12.6505i	0.718889	+	0.415051i	−0.0954546	+	0.995434i	$0.530430\pi$
$930$		0			0
$931$	34.4297			1.12839
$932$	−14.6100	−	28.9276i	−0.478565	−	0.947555i
$933$		0			0
$934$	−40.0464	−	24.6386i	−1.31036	−	0.806198i
$935$	10.8457			0.354692
$936$		0			0
$937$	−41.0474			−1.34096			−0.670479	−	0.741928i	$-0.733912\pi$
$937$	−41.0474			−1.34096			−0.670479	+	0.741928i	$0.733912\pi$
$938$	15.6503	+	9.62883i	0.510999	+	0.314393i
$939$		0			0
$940$	5.14286	−	2.59741i	0.167742	−	0.0847182i
$941$	−36.6752			−1.19558			−0.597789	−	0.801653i	$-0.703954\pi$
$941$	−36.6752			−1.19558			−0.597789	+	0.801653i	$0.703954\pi$
$942$		0			0
$943$	0.0902470	+	0.0521041i	0.00293885	+	0.00169674i
$944$	10.0888	+	23.1008i	0.328363	+	0.751867i
$945$		0			0
$946$	−29.0403	−	17.8671i	−0.944181	−	0.580908i
$947$	−10.9465	−	18.9599i	−0.355714	−	0.616114i	0.631526	−	0.775355i	$-0.282429\pi$
$947$	−10.9465	−	18.9599i	−0.355714	−	0.616114i	−0.987240	+	0.159240i	$0.949096\pi$
$948$		0			0
$949$	43.1966	+	7.03898i	1.40222	+	0.228495i
$950$	9.00161	+	16.6495i	0.292051	+	0.540180i
$951$		0			0
$952$	21.7240	−	10.2199i	0.704078	−	0.331228i
$953$	−24.7900	+	42.9375i	−0.803026	+	1.39088i	0.114590	+	0.993413i	$0.463445\pi$
$953$	−24.7900	+	42.9375i	−0.803026	+	1.39088i	−0.917616	+	0.397469i	$0.869889\pi$
$954$		0			0
$955$	−9.80570	+	16.9840i	−0.317305	+	0.549588i
$956$	6.52571	−	3.29582i	0.211057	−	0.106595i
$957$		0			0
$958$	0.836115	−	29.8974i	0.0270136	−	0.965943i
$959$	−28.7736	−	49.8373i	−0.929147	−	1.60933i
$960$		0			0
$961$	24.6684			0.795756
$962$	1.92092	−	10.0157i	0.0619331	−	0.322918i
$963$		0			0
$964$	−2.55120	+	45.5768i	−0.0821688	+	1.46793i
$965$	6.66320	−	3.84700i	0.214496	−	0.123839i
$966$		0			0
$967$		−	31.4252i		−	1.01057i	−0.862953	−	0.505284i	$-0.831388\pi$
$967$		−	31.4252i		−	1.01057i	0.862953	−	0.505284i	$-0.168612\pi$
$968$	41.0529	−	59.0547i	1.31949	−	1.89809i
$969$		0			0
$970$	−12.5660	+	6.79385i	−0.403469	+	0.218137i
$971$	42.8554	+	24.7426i	1.37530	+	0.794028i	0.991589	−	0.129427i	$-0.0413139\pi$
$971$	42.8554	+	24.7426i	1.37530	+	0.794028i	0.383707	+	0.923455i	$0.374647\pi$
$972$		0			0
$973$	−38.0598	−	65.9215i	−1.22014	−	2.11334i
$974$	22.3575	−	12.0877i	0.716380	−	0.387314i
$975$		0			0
$976$	−28.7637	+	12.5620i	−0.920705	+	0.402099i
$977$	−34.7979	+	20.0906i	−1.11328	+	0.642754i	−0.939678	−	0.342061i	$-0.888875\pi$
$977$	−34.7979	+	20.0906i	−1.11328	+	0.642754i	−0.173605	+	0.984815i	$0.555542\pi$
$978$		0			0
$979$	−45.4440	−	26.2371i	−1.45240	−	0.838542i
$980$	−10.5770	+	16.1610i	−0.337871	+	0.516245i
$981$		0			0
$982$	−0.202364	+	7.23603i	−0.00645768	+	0.230911i
$983$		−	53.9410i		−	1.72045i	−0.509913	−	0.860226i	$-0.670323\pi$
$983$		−	53.9410i		−	1.72045i	0.509913	−	0.860226i	$-0.329677\pi$
$984$		0			0
$985$	4.09072	+	7.08533i	0.130341	+	0.225757i
$986$	12.5990	+	7.75154i	0.401234	+	0.246859i
$987$		0			0
$988$	4.95524	−	22.4277i	0.157647	−	0.713519i
$989$		−	21.2092i		−	0.674415i
$990$		0			0
$991$	21.4117	+	37.0862i	0.680166	+	1.17808i	0.974930	+	0.222512i	$0.0714255\pi$
$991$	21.4117	+	37.0862i	0.680166	+	1.17808i	−0.294764	+	0.955570i	$0.595241\pi$
$992$	13.1985	−	5.32998i	0.419054	−	0.169227i
$993$		0			0
$994$	−15.2968	−	0.427793i	−0.485186	−	0.0135688i
$995$	−7.00391	+	12.1311i	−0.222039	+	0.384583i
$996$		0			0
$997$	−38.5110	−	22.2343i	−1.21966	−	0.704168i	−0.254811	−	0.966991i	$-0.582013\pi$
$997$	−38.5110	−	22.2343i	−1.21966	−	0.704168i	−0.964844	+	0.262822i	$0.915347\pi$
$998$	−14.2834	+	23.2156i	−0.452133	+	0.734877i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.dg.d.829.7		16
3.2	odd	2		104.2.s.c.101.2	yes	16
8.5	even	2	inner	936.2.dg.d.829.8		16
12.11	even	2		416.2.ba.c.49.3		16
13.4	even	6	inner	936.2.dg.d.901.8		16
24.5	odd	2		104.2.s.c.101.1	yes	16
24.11	even	2		416.2.ba.c.49.6		16
39.17	odd	6		104.2.s.c.69.1	✓	16
104.69	even	6	inner	936.2.dg.d.901.7		16
156.95	even	6		416.2.ba.c.17.6		16
312.173	odd	6		104.2.s.c.69.2	yes	16
312.251	even	6		416.2.ba.c.17.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.s.c.69.1	✓	16	39.17	odd	6
104.2.s.c.69.2	yes	16	312.173	odd	6
104.2.s.c.101.1	yes	16	24.5	odd	2
104.2.s.c.101.2	yes	16	3.2	odd	2
416.2.ba.c.17.3		16	312.251	even	6
416.2.ba.c.17.6		16	156.95	even	6
416.2.ba.c.49.3		16	12.11	even	2
416.2.ba.c.49.6		16	24.11	even	2
936.2.dg.d.829.7		16	1.1	even	1	trivial
936.2.dg.d.829.8		16	8.5	even	2	inner
936.2.dg.d.901.7		16	104.69	even	6	inner
936.2.dg.d.901.8		16	13.4	even	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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.dg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.741068 - 1.20450i) q^{2} +(-0.901635 - 1.78523i) q^{4} -0.893415 q^{5} +(3.65473 + 2.11006i) q^{7} +(-2.81848 - 0.236960i) q^{8} +(-0.662082 + 1.07612i) q^{10} +(3.01779 + 5.22697i) q^{11} +(-0.579883 + 3.55861i) q^{13} +(5.24997 - 2.83842i) q^{14} +(-2.37411 + 3.21926i) q^{16} +(-1.00567 + 1.74186i) q^{17} +(1.59258 - 2.75843i) q^{19} +(0.805535 + 1.59495i) q^{20} +(8.53227 + 0.238614i) q^{22} +(2.65473 + 4.59813i) q^{23} -4.20181 q^{25} +(3.85661 + 3.33565i) q^{26} +(0.471712 - 8.42704i) q^{28} +(4.50378 - 2.60026i) q^{29} -2.51626i q^{31} +(2.11822 + 5.24530i) q^{32} +(1.35281 + 2.50216i) q^{34} +(-3.26519 - 1.88516i) q^{35} +(-1.00002 - 1.73208i) q^{37} +(-2.14232 - 3.96245i) q^{38} +(2.51808 + 0.211704i) q^{40} +(0.0169974 - 0.00981345i) q^{41} +(-3.45944 - 1.99731i) q^{43} +(6.61041 - 10.1003i) q^{44} +(7.50577 + 0.209907i) q^{46} -3.22446i q^{47} +(5.40470 + 9.36121i) q^{49} +(-3.11383 + 5.06107i) q^{50} +(6.87580 - 2.17335i) q^{52} -3.34691i q^{53} +(-2.69614 - 4.66986i) q^{55} +(-9.80079 - 6.81319i) q^{56} +(0.205600 - 7.35176i) q^{58} +(3.15097 - 5.45764i) q^{59} +(6.79553 + 3.92340i) q^{61} +(-3.03083 - 1.86472i) q^{62} +(7.88770 + 1.33574i) q^{64} +(0.518077 - 3.17932i) q^{65} +(1.53943 + 2.66638i) q^{67} +(4.01638 + 0.224820i) q^{68} +(-4.69040 + 2.53589i) q^{70} +(-2.22056 - 1.28204i) q^{71} -12.1386i q^{73} +(-2.82737 - 0.0790704i) q^{74} +(-6.36037 - 0.356028i) q^{76} +25.4709i q^{77} +3.01133 q^{79} +(2.12106 - 2.87613i) q^{80} +(0.000775941 - 0.0277458i) q^{82} -8.90367 q^{83} +(0.898477 - 1.55621i) q^{85} +(-4.96944 + 2.68675i) q^{86} +(-7.26702 - 15.4472i) q^{88} +(-7.52934 + 4.34707i) q^{89} +(-9.62820 + 11.7822i) q^{91} +(5.81512 - 8.88514i) q^{92} +(-3.88385 - 2.38954i) q^{94} +(-1.42284 + 2.46443i) q^{95} +(9.79132 + 5.65302i) q^{97} +(15.2808 + 0.427345i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} - q^{4} + 18 q^{7} - 9 q^{10} + 24 q^{14} - q^{16} - 8 q^{17} + 15 q^{20} + 22 q^{22} + 2 q^{23} - 12 q^{25} - 23 q^{26} + 27 q^{32} + 26 q^{40} - 24 q^{41} + 42 q^{46} - 14 q^{49} - 6 q^{50}+ \cdots + 93 q^{98}+O(q^{100}) \) 16 * q - 3 * q^2 - q^4 + 18 * q^7 - 9 * q^10 + 24 * q^14 - q^16 - 8 * q^17 + 15 * q^20 + 22 * q^22 + 2 * q^23 - 12 * q^25 - 23 * q^26 + 27 * q^32 + 26 * q^40 - 24 * q^41 + 42 * q^46 - 14 * q^49 - 6 * q^50 + 28 * q^52 + 4 * q^55 + 8 * q^56 - 33 * q^58 + 4 * q^62 + 50 * q^64 - 6 * q^65 - 5 * q^68 - 6 * q^71 + 29 * q^74 + 24 * q^76 + 32 * q^79 + 33 * q^80 + 9 * q^82 - 8 * q^88 + 30 * q^89 + 4 * q^92 - 24 * q^94 - 28 * q^95 - 30 * q^97 + 93 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more