LMFDB - Embedded newform 768.2.n.b.481.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(97,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("768.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.n (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			481.6
Character	$\chi$	$=$	768.481
Dual form			768.2.n.b.289.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.382683 + 0.923880i) q^{3} +(-0.825824 - 0.342068i) q^{5} +(-1.17750 - 1.17750i) q^{7} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(0.382683 + 0.923880i) q^{3} +(-0.825824 - 0.342068i) q^{5} +(-1.17750 - 1.17750i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(-1.46490 + 3.53657i) q^{11} +(-3.01061 + 1.24703i) q^{13} -0.893866i q^{15} -4.58215i q^{17} +(-3.29978 + 1.36681i) q^{19} +(0.637258 - 1.53848i) q^{21} +(-5.41196 + 5.41196i) q^{23} +(-2.97056 - 2.97056i) q^{25} +(-0.923880 - 0.382683i) q^{27} +(2.46490 + 5.95078i) q^{29} +5.25495 q^{31} -3.82796 q^{33} +(0.569623 + 1.37519i) q^{35} +(-7.33917 - 3.03998i) q^{37} +(-2.30422 - 2.30422i) q^{39} +(-1.35921 + 1.35921i) q^{41} +(-2.95781 + 7.14079i) q^{43} +(0.825824 - 0.342068i) q^{45} +8.16360i q^{47} -4.22699i q^{49} +(4.23336 - 1.75351i) q^{51} +(3.13863 - 7.57731i) q^{53} +(2.41949 - 2.41949i) q^{55} +(-2.52554 - 2.52554i) q^{57} +(0.221996 + 0.0919539i) q^{59} +(-2.66861 - 6.44260i) q^{61} +1.66523 q^{63} +2.91280 q^{65} +(-5.52539 - 13.3395i) q^{67} +(-7.07107 - 2.92893i) q^{69} +(-1.51271 - 1.51271i) q^{71} +(-9.62682 + 9.62682i) q^{73} +(1.60765 - 3.88122i) q^{75} +(5.88923 - 2.43940i) q^{77} +5.34497i q^{79} -1.00000i q^{81} +(5.64233 - 2.33713i) q^{83} +(-1.56741 + 3.78405i) q^{85} +(-4.55453 + 4.55453i) q^{87} +(5.09017 + 5.09017i) q^{89} +(5.01337 + 2.07660i) q^{91} +(2.01098 + 4.85494i) q^{93} +3.19258 q^{95} +19.0146 q^{97} +(-1.46490 - 3.53657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 16 q^{23} + 48 q^{31} - 48 q^{35} - 16 q^{43} + 16 q^{51} + 32 q^{53} - 32 q^{55} + 64 q^{59} + 32 q^{61} - 16 q^{63} + 16 q^{67} + 32 q^{69} - 64 q^{71} + 32 q^{75} + 32 q^{77} - 48 q^{91}+O(q^{100}) $ 32 * q + 16 * q^23 + 48 * q^31 - 48 * q^35 - 16 * q^43 + 16 * q^51 + 32 * q^53 - 32 * q^55 + 64 * q^59 + 32 * q^61 - 16 * q^63 + 16 * q^67 + 32 * q^69 - 64 * q^71 + 32 * q^75 + 32 * q^77 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{8}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	0.382683	+	0.923880i	0.220942	+	0.533402i
$3$	0.382683	+	0.923880i	0.220942	+	0.533402i
$4$		0			0
$5$	−0.825824	−	0.342068i	−0.369320	−	0.152977i	0.190302	−	0.981726i	$-0.439053\pi$
$5$	−0.825824	−	0.342068i	−0.369320	−	0.152977i	−0.559621	+	0.828748i	$0.689053\pi$
$6$		0			0
$7$	−1.17750	−	1.17750i	−0.445053	−	0.445053i	0.448653	−	0.893706i	$-0.351904\pi$
$7$	−1.17750	−	1.17750i	−0.445053	−	0.445053i	−0.893706	+	0.448653i	$0.851904\pi$
$8$		0			0
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$		0			0
$11$	−1.46490	+	3.53657i	−0.441683	+	1.06632i	0.533675	+	0.845690i	$0.320811\pi$
$11$	−1.46490	+	3.53657i	−0.441683	+	1.06632i	−0.975358	+	0.220627i	$0.929189\pi$
$12$		0			0
$13$	−3.01061	+	1.24703i	−0.834992	+	0.345865i	−0.758877	−	0.651234i	$-0.774252\pi$
$13$	−3.01061	+	1.24703i	−0.834992	+	0.345865i	−0.0761151	+	0.997099i	$0.524252\pi$
$14$		0			0
$15$		−	0.893866i		−	0.230795i
$16$		0			0
$17$		−	4.58215i		−	1.11134i	−0.831404	−	0.555668i	$-0.812463\pi$
$17$		−	4.58215i		−	1.11134i	0.831404	−	0.555668i	$-0.187537\pi$
$18$		0			0
$19$	−3.29978	+	1.36681i	−0.757021	+	0.313568i	−0.727602	−	0.685999i	$-0.759365\pi$
$19$	−3.29978	+	1.36681i	−0.757021	+	0.313568i	−0.0294181	+	0.999567i	$0.509365\pi$
$20$		0			0
$21$	0.637258	−	1.53848i	0.139061	−	0.335723i
$22$		0			0
$23$	−5.41196	+	5.41196i	−1.12847	+	1.12847i	−0.138046	+	0.990426i	$0.544082\pi$
$23$	−5.41196	+	5.41196i	−1.12847	+	1.12847i	−0.990426	+	0.138046i	$0.955918\pi$
$24$		0			0
$25$	−2.97056	−	2.97056i	−0.594112	−	0.594112i
$26$		0			0
$27$	−0.923880	−	0.382683i	−0.177801	−	0.0736475i
$28$		0			0
$29$	2.46490	+	5.95078i	0.457720	+	1.10503i	0.969318	+	0.245808i	$0.0790534\pi$
$29$	2.46490	+	5.95078i	0.457720	+	1.10503i	−0.511599	+	0.859224i	$0.670947\pi$
$30$		0			0
$31$	5.25495			0.943816			0.471908	−	0.881648i	$-0.343565\pi$
$31$	5.25495			0.943816			0.471908	+	0.881648i	$0.343565\pi$
$32$		0			0
$33$	−3.82796			−0.666362
$34$		0			0
$35$	0.569623	+	1.37519i	0.0962838	+	0.232450i
$36$		0			0
$37$	−7.33917	−	3.03998i	−1.20655	−	0.499770i	−0.313442	−	0.949607i	$-0.601482\pi$
$37$	−7.33917	−	3.03998i	−1.20655	−	0.499770i	−0.893111	+	0.449837i	$0.851482\pi$
$38$		0			0
$39$	−2.30422	−	2.30422i	−0.368970	−	0.368970i
$40$		0			0
$41$	−1.35921	+	1.35921i	−0.212273	+	0.212273i	−0.805232	−	0.592959i	$-0.797959\pi$
$41$	−1.35921	+	1.35921i	−0.212273	+	0.212273i	0.592959	+	0.805232i	$0.297959\pi$
$42$		0			0
$43$	−2.95781	+	7.14079i	−0.451062	+	1.08896i	0.520856	+	0.853644i	$0.325613\pi$
$43$	−2.95781	+	7.14079i	−0.451062	+	1.08896i	−0.971919	+	0.235317i	$0.924387\pi$
$44$		0			0
$45$	0.825824	−	0.342068i	0.123107	−	0.0509924i
$46$		0			0
$47$			8.16360i			1.19078i	0.803436	+	0.595391i	$0.203003\pi$
$47$			8.16360i			1.19078i	−0.803436	+	0.595391i	$0.796997\pi$
$48$		0			0
$49$		−	4.22699i		−	0.603856i
$50$		0			0
$51$	4.23336	−	1.75351i	0.592789	−	0.245541i
$52$		0			0
$53$	3.13863	−	7.57731i	0.431123	−	1.04082i	−0.547802	−	0.836608i	$-0.684535\pi$
$53$	3.13863	−	7.57731i	0.431123	−	1.04082i	0.978926	−	0.204216i	$-0.0654646\pi$
$54$		0			0
$55$	2.41949	−	2.41949i	0.326244	−	0.326244i
$56$		0			0
$57$	−2.52554	−	2.52554i	−0.334516	−	0.334516i
$58$		0			0
$59$	0.221996	+	0.0919539i	0.0289014	+	0.0119714i	0.397087	−	0.917781i	$-0.370021\pi$
$59$	0.221996	+	0.0919539i	0.0289014	+	0.0119714i	−0.368186	+	0.929752i	$0.620021\pi$
$60$		0			0
$61$	−2.66861	−	6.44260i	−0.341681	−	0.824891i	−0.997546	−	0.0700128i	$-0.977696\pi$
$61$	−2.66861	−	6.44260i	−0.341681	−	0.824891i	0.655865	−	0.754878i	$-0.272304\pi$
$62$		0			0
$63$	1.66523			0.209800
$64$		0			0
$65$	2.91280			0.361289
$66$		0			0
$67$	−5.52539	−	13.3395i	−0.675033	−	1.62968i	−0.772940	−	0.634479i	$-0.781215\pi$
$67$	−5.52539	−	13.3395i	−0.675033	−	1.62968i	0.0979063	−	0.995196i	$-0.468785\pi$
$68$		0			0
$69$	−7.07107	−	2.92893i	−0.851257	−	0.352602i
$70$		0			0
$71$	−1.51271	−	1.51271i	−0.179526	−	0.179526i	0.611623	−	0.791149i	$-0.290517\pi$
$71$	−1.51271	−	1.51271i	−0.179526	−	0.179526i	−0.791149	+	0.611623i	$0.790517\pi$
$72$		0			0
$73$	−9.62682	+	9.62682i	−1.12673	+	1.12673i	−0.136029	+	0.990705i	$0.543434\pi$
$73$	−9.62682	+	9.62682i	−1.12673	+	1.12673i	−0.990705	+	0.136029i	$0.956566\pi$
$74$		0			0
$75$	1.60765	−	3.88122i	0.185636	−	0.448165i
$76$		0			0
$77$	5.88923	−	2.43940i	0.671140	−	0.277995i
$78$		0			0
$79$			5.34497i			0.601356i	0.953726	+	0.300678i	$0.0972129\pi$
$79$			5.34497i			0.601356i	−0.953726	+	0.300678i	$0.902787\pi$
$80$		0			0
$81$		−	1.00000i		−	0.111111i
$82$		0			0
$83$	5.64233	−	2.33713i	0.619327	−	0.256533i	−0.0508839	−	0.998705i	$-0.516204\pi$
$83$	5.64233	−	2.33713i	0.619327	−	0.256533i	0.670210	+	0.742171i	$0.266204\pi$
$84$		0			0
$85$	−1.56741	+	3.78405i	−0.170009	+	0.410438i
$86$		0			0
$87$	−4.55453	+	4.55453i	−0.488297	+	0.488297i
$88$		0			0
$89$	5.09017	+	5.09017i	0.539557	+	0.539557i	0.923399	−	0.383842i	$-0.125399\pi$
$89$	5.09017	+	5.09017i	0.539557	+	0.539557i	−0.383842	+	0.923399i	$0.625399\pi$
$90$		0			0
$91$	5.01337	+	2.07660i	0.525544	+	0.217687i
$92$		0			0
$93$	2.01098	+	4.85494i	0.208529	+	0.503434i
$94$		0			0
$95$	3.19258			0.327551
$96$		0			0
$97$	19.0146			1.93064			0.965319	−	0.261072i	$-0.0840761\pi$
$97$	19.0146			1.93064			0.965319	+	0.261072i	$0.0840761\pi$
$98$		0			0
$99$	−1.46490	−	3.53657i	−0.147228	−	0.355439i
$100$		0			0
$101$	3.55331	+	1.47183i	0.353567	+	0.146452i	0.552396	−	0.833582i	$-0.313714\pi$
$101$	3.55331	+	1.47183i	0.353567	+	0.146452i	−0.198828	+	0.980034i	$0.563714\pi$
$102$		0			0
$103$	−3.30552	−	3.30552i	−0.325703	−	0.325703i	0.525247	−	0.850950i	$-0.323973\pi$
$103$	−3.30552	−	3.30552i	−0.325703	−	0.325703i	−0.850950	+	0.525247i	$0.823973\pi$
$104$		0			0
$105$	−1.05253	+	1.05253i	−0.102716	+	0.102716i
$106$		0			0
$107$	−4.98987	+	12.0466i	−0.482389	+	1.16459i	0.476082	+	0.879401i	$0.342057\pi$
$107$	−4.98987	+	12.0466i	−0.482389	+	1.16459i	−0.958471	+	0.285190i	$0.907943\pi$
$108$		0			0
$109$	4.16532	−	1.72533i	0.398966	−	0.165257i	−0.174174	−	0.984715i	$-0.555725\pi$
$109$	4.16532	−	1.72533i	0.398966	−	0.165257i	0.573139	+	0.819458i	$0.305725\pi$
$110$		0			0
$111$		−	7.94386i		−	0.753998i
$112$		0			0
$113$			15.7676i			1.48329i	0.670792	+	0.741645i	$0.265954\pi$
$113$			15.7676i			1.48329i	−0.670792	+	0.741645i	$0.734046\pi$
$114$		0			0
$115$	6.32059	−	2.61807i	0.589398	−	0.244137i
$116$		0			0
$117$	1.24703	−	3.01061i	0.115288	−	0.278331i
$118$		0			0
$119$	−5.39548	+	5.39548i	−0.494603	+	0.494603i
$120$		0			0
$121$	−2.58325	−	2.58325i	−0.234841	−	0.234841i
$122$		0			0
$123$	−1.77589	−	0.735600i	−0.160127	−	0.0663268i
$124$		0			0
$125$	3.14736	+	7.59841i	0.281509	+	0.679623i
$126$		0			0
$127$	−5.62550			−0.499182			−0.249591	−	0.968351i	$-0.580296\pi$
$127$	−5.62550			−0.499182			−0.249591	+	0.968351i	$0.580296\pi$
$128$		0			0
$129$	−7.72914			−0.680513
$130$		0			0
$131$	2.77061	+	6.68884i	0.242069	+	0.584407i	0.997488	−	0.0708355i	$-0.0225665\pi$
$131$	2.77061	+	6.68884i	0.242069	+	0.584407i	−0.755419	+	0.655242i	$0.772567\pi$
$132$		0			0
$133$	5.49490	+	2.27606i	0.476468	+	0.197360i
$134$		0			0
$135$	0.632058	+	0.632058i	0.0543989	+	0.0543989i
$136$		0			0
$137$	3.13785	−	3.13785i	0.268085	−	0.268085i	−0.560243	−	0.828328i	$-0.689292\pi$
$137$	3.13785	−	3.13785i	0.268085	−	0.268085i	0.828328	+	0.560243i	$0.189292\pi$
$138$		0			0
$139$	3.60636	−	8.70653i	0.305888	−	0.738478i	−0.693942	−	0.720031i	$-0.744128\pi$
$139$	3.60636	−	8.70653i	0.305888	−	0.738478i	0.999830	−	0.0184473i	$-0.00587229\pi$
$140$		0			0
$141$	−7.54218	+	3.12407i	−0.635166	+	0.263094i
$142$		0			0
$143$		−	12.4740i		−	1.04313i
$144$		0			0
$145$		−	5.75746i		−	0.478131i
$146$		0			0
$147$	3.90523	−	1.61760i	0.322098	−	0.133417i
$148$		0			0
$149$	1.00661	−	2.43018i	0.0824648	−	0.199088i	−0.877269	−	0.479999i	$-0.840637\pi$
$149$	1.00661	−	2.43018i	0.0824648	−	0.199088i	0.959734	+	0.280912i	$0.0906368\pi$
$150$		0			0
$151$	14.3784	−	14.3784i	1.17010	−	1.17010i	0.187914	−	0.982186i	$-0.439827\pi$
$151$	14.3784	−	14.3784i	1.17010	−	1.17010i	0.982186	−	0.187914i	$-0.0601726\pi$
$152$		0			0
$153$	3.24007	+	3.24007i	0.261944	+	0.261944i
$154$		0			0
$155$	−4.33966	−	1.79755i	−0.348570	−	0.144382i
$156$		0			0
$157$	2.10034	+	5.07067i	0.167625	+	0.404684i	0.985262	−	0.171051i	$-0.0547162\pi$
$157$	2.10034	+	5.07067i	0.167625	+	0.404684i	−0.817637	+	0.575734i	$0.804716\pi$
$158$		0			0
$159$	8.20163			0.650431
$160$		0			0
$161$	12.7452			1.00446
$162$		0			0
$163$	−4.14645	−	10.0104i	−0.324775	−	0.784076i	−0.998964	−	0.0455168i	$-0.985507\pi$
$163$	−4.14645	−	10.0104i	−0.324775	−	0.784076i	0.674189	−	0.738559i	$-0.264493\pi$
$164$		0			0
$165$	3.16122	+	1.30942i	0.246101	+	0.101938i
$166$		0			0
$167$	5.38194	+	5.38194i	0.416467	+	0.416467i	0.883984	−	0.467517i	$-0.154851\pi$
$167$	5.38194	+	5.38194i	0.416467	+	0.416467i	−0.467517	+	0.883984i	$0.654851\pi$
$168$		0			0
$169$	−1.68373	+	1.68373i	−0.129518	+	0.129518i
$170$		0			0
$171$	1.36681	−	3.29978i	0.104523	−	0.252340i
$172$		0			0
$173$	9.62485	−	3.98675i	0.731764	−	0.303107i	0.0144874	−	0.999895i	$-0.495388\pi$
$173$	9.62485	−	3.98675i	0.731764	−	0.303107i	0.717277	+	0.696788i	$0.245388\pi$
$174$		0			0
$175$			6.99566i			0.528822i
$176$		0			0
$177$			0.240287i			0.0180611i
$178$		0			0
$179$	−12.7809	+	5.29402i	−0.955288	+	0.395693i	−0.805216	−	0.592982i	$-0.797951\pi$
$179$	−12.7809	+	5.29402i	−0.955288	+	0.395693i	−0.150072	+	0.988675i	$0.547951\pi$
$180$		0			0
$181$	−8.21217	+	19.8259i	−0.610406	+	1.47365i	0.252150	+	0.967688i	$0.418862\pi$
$181$	−8.21217	+	19.8259i	−0.610406	+	1.47365i	−0.862556	+	0.505962i	$0.831138\pi$
$182$		0			0
$183$	4.93096	−	4.93096i	0.364507	−	0.364507i
$184$		0			0
$185$	5.02098	+	5.02098i	0.369150	+	0.369150i
$186$		0			0
$187$	16.2051	+	6.71238i	1.18504	+	0.490858i
$188$		0			0
$189$	0.637258	+	1.53848i	0.0463537	+	0.111908i
$190$		0			0
$191$	10.3772			0.750866			0.375433	−	0.926850i	$-0.377494\pi$
$191$	10.3772			0.750866			0.375433	+	0.926850i	$0.377494\pi$
$192$		0			0
$193$	−8.76090			−0.630623			−0.315312	−	0.948988i	$-0.602109\pi$
$193$	−8.76090			−0.630623			−0.315312	+	0.948988i	$0.602109\pi$
$194$		0			0
$195$	1.11468	+	2.69108i	0.0798240	+	0.192712i
$196$		0			0
$197$	4.35045	+	1.80201i	0.309956	+	0.128388i	0.532239	−	0.846594i	$-0.321351\pi$
$197$	4.35045	+	1.80201i	0.309956	+	0.128388i	−0.222283	+	0.974982i	$0.571351\pi$
$198$		0			0
$199$	−3.47990	−	3.47990i	−0.246684	−	0.246684i	0.572925	−	0.819608i	$-0.305809\pi$
$199$	−3.47990	−	3.47990i	−0.246684	−	0.246684i	−0.819608	+	0.572925i	$0.805809\pi$
$200$		0			0
$201$	10.2096	−	10.2096i	0.720129	−	0.720129i
$202$		0			0
$203$	4.10463	−	9.90945i	0.288088	−	0.695507i
$204$		0			0
$205$	1.58741	−	0.657527i	0.110870	−	0.0459237i
$206$		0			0
$207$		−	7.65367i		−	0.531967i
$208$		0			0
$209$		−	13.6721i		−	0.945722i
$210$		0			0
$211$	−4.76129	+	1.97219i	−0.327781	+	0.135771i	−0.540505	−	0.841341i	$-0.681767\pi$
$211$	−4.76129	+	1.97219i	−0.327781	+	0.135771i	0.212724	+	0.977112i	$0.431767\pi$
$212$		0			0
$213$	0.818674	−	1.97645i	0.0560946	−	0.135424i
$214$		0			0
$215$	4.88527	−	4.88527i	0.333173	−	0.333173i
$216$		0			0
$217$	−6.18769	−	6.18769i	−0.420048	−	0.420048i
$218$		0			0
$219$	−12.5780	−	5.21000i	−0.849946	−	0.352059i
$220$		0			0
$221$	5.71410	+	13.7951i	0.384372	+	0.927956i
$222$		0			0
$223$	−12.6045			−0.844059			−0.422029	−	0.906582i	$-0.638682\pi$
$223$	−12.6045			−0.844059			−0.422029	+	0.906582i	$0.638682\pi$
$224$		0			0
$225$	4.20100			0.280067
$226$		0			0
$227$	1.84453	+	4.45310i	0.122426	+	0.295563i	0.973197	−	0.229975i	$-0.0738644\pi$
$227$	1.84453	+	4.45310i	0.122426	+	0.295563i	−0.850771	+	0.525537i	$0.823864\pi$
$228$		0			0
$229$	19.3957	+	8.03395i	1.28170	+	0.530898i	0.916502	−	0.400031i	$-0.131001\pi$
$229$	19.3957	+	8.03395i	1.28170	+	0.530898i	0.365200	+	0.930929i	$0.381001\pi$
$230$		0			0
$231$	4.50742	+	4.50742i	0.296566	+	0.296566i
$232$		0			0
$233$	13.4162	−	13.4162i	0.878921	−	0.878921i	−0.114502	−	0.993423i	$-0.536527\pi$
$233$	13.4162	−	13.4162i	0.878921	−	0.878921i	0.993423	+	0.114502i	$0.0365271\pi$
$234$		0			0
$235$	2.79250	−	6.74169i	0.182163	−	0.439780i
$236$		0			0
$237$	−4.93811	+	2.04543i	−0.320765	+	0.132865i
$238$		0			0
$239$		−	4.57889i		−	0.296184i	−0.988974	−	0.148092i	$-0.952687\pi$
$239$		−	4.57889i		−	0.296184i	0.988974	−	0.148092i	$-0.0473131\pi$
$240$		0			0
$241$			14.5911i			0.939895i	0.882694	+	0.469948i	$0.155727\pi$
$241$			14.5911i			0.939895i	−0.882694	+	0.469948i	$0.844273\pi$
$242$		0			0
$243$	0.923880	−	0.382683i	0.0592669	−	0.0245492i
$244$		0			0
$245$	−1.44592	+	3.49075i	−0.0923763	+	0.223016i
$246$		0			0
$247$	8.22987	−	8.22987i	0.523654	−	0.523654i
$248$		0			0
$249$	4.31845	+	4.31845i	0.273671	+	0.273671i
$250$		0			0
$251$	−1.91315	−	0.792453i	−0.120757	−	0.0500192i	0.321487	−	0.946914i	$-0.395817\pi$
$251$	−1.91315	−	0.792453i	−0.120757	−	0.0500192i	−0.442244	+	0.896895i	$0.645817\pi$
$252$		0			0
$253$	−11.2118	−	27.0678i	−0.704882	−	1.70174i
$254$		0			0
$255$	−4.09583			−0.256491
$256$		0			0
$257$	−21.4012			−1.33497			−0.667485	−	0.744624i	$-0.732629\pi$
$257$	−21.4012			−1.33497			−0.667485	+	0.744624i	$0.732629\pi$
$258$		0			0
$259$	5.06229	+	12.2214i	0.314555	+	0.759403i
$260$		0			0
$261$	−5.95078	−	2.46490i	−0.368344	−	0.152573i
$262$		0			0
$263$	−4.14877	−	4.14877i	−0.255824	−	0.255824i	0.567529	−	0.823353i	$-0.307899\pi$
$263$	−4.14877	−	4.14877i	−0.255824	−	0.255824i	−0.823353	+	0.567529i	$0.807899\pi$
$264$		0			0
$265$	−5.18391	+	5.18391i	−0.318445	+	0.318445i
$266$		0			0
$267$	−2.75478	+	6.65062i	−0.168590	+	0.407011i
$268$		0			0
$269$	−28.0039	+	11.5996i	−1.70743	+	0.707241i	−0.707430	+	0.706783i	$0.750146\pi$
$269$	−28.0039	+	11.5996i	−1.70743	+	0.707241i	−1.00000		0.000457143i	$0.999854\pi$
$270$		0			0
$271$		−	10.3370i		−	0.627930i	−0.949435	−	0.313965i	$-0.898343\pi$
$271$		−	10.3370i		−	0.627930i	0.949435	−	0.313965i	$-0.101657\pi$
$272$		0			0
$273$			5.42643i			0.328422i
$274$		0			0
$275$	14.8572	−	6.15404i	0.895920	−	0.371102i
$276$		0			0
$277$	6.39508	−	15.4391i	0.384243	−	0.927645i	−0.606892	−	0.794785i	$-0.707584\pi$
$277$	6.39508	−	15.4391i	0.384243	−	0.927645i	0.991135	−	0.132860i	$-0.0424162\pi$
$278$		0			0
$279$	−3.71581	+	3.71581i	−0.222460	+	0.222460i
$280$		0			0
$281$	7.85631	+	7.85631i	0.468668	+	0.468668i	0.901483	−	0.432815i	$-0.142480\pi$
$281$	7.85631	+	7.85631i	0.468668	+	0.468668i	−0.432815	+	0.901483i	$0.642480\pi$
$282$		0			0
$283$	6.76840	+	2.80356i	0.402340	+	0.166655i	0.574671	−	0.818385i	$-0.305130\pi$
$283$	6.76840	+	2.80356i	0.402340	+	0.166655i	−0.172331	+	0.985039i	$0.555130\pi$
$284$		0			0
$285$	1.22175	+	2.94956i	0.0723700	+	0.174717i
$286$		0			0
$287$	3.20094			0.188945
$288$		0			0
$289$	−3.99613			−0.235067
$290$		0			0
$291$	7.27657	+	17.5672i	0.426560	+	1.02981i
$292$		0			0
$293$	−12.3397	−	5.11128i	−0.720895	−	0.298604i	−0.00809031	−	0.999967i	$-0.502575\pi$
$293$	−12.3397	−	5.11128i	−0.720895	−	0.298604i	−0.712804	+	0.701363i	$0.752575\pi$
$294$		0			0
$295$	−0.151875	−	0.151875i	−0.00884253	−	0.00884253i
$296$		0			0
$297$	2.70678	−	2.70678i	0.157063	−	0.157063i
$298$		0			0
$299$	9.54439	−	23.0422i	0.551966	−	1.33256i
$300$		0			0
$301$	11.8911	−	4.92545i	0.685392	−	0.283898i
$302$		0			0
$303$			3.84607i			0.220951i
$304$		0			0
$305$			6.23330i			0.356918i
$306$		0			0
$307$	−7.47343	+	3.09560i	−0.426531	+	0.176675i	−0.585614	−	0.810590i	$-0.699146\pi$
$307$	−7.47343	+	3.09560i	−0.426531	+	0.176675i	0.159082	+	0.987265i	$0.449146\pi$
$308$		0			0
$309$	1.78894	−	4.31887i	0.101769	−	0.245692i
$310$		0			0
$311$	−12.5179	+	12.5179i	−0.709823	+	0.709823i	−0.966498	−	0.256675i	$-0.917373\pi$
$311$	−12.5179	+	12.5179i	−0.709823	+	0.709823i	0.256675	+	0.966498i	$0.417373\pi$
$312$		0			0
$313$	2.11020	+	2.11020i	0.119276	+	0.119276i	0.764225	−	0.644950i	$-0.223122\pi$
$313$	2.11020	+	2.11020i	0.119276	+	0.119276i	−0.644950	+	0.764225i	$0.723122\pi$
$314$		0			0
$315$	−1.37519	−	0.569623i	−0.0774832	−	0.0320946i
$316$		0			0
$317$	−13.3122	−	32.1384i	−0.747686	−	1.80507i	−0.571278	−	0.820756i	$-0.693552\pi$
$317$	−13.3122	−	32.1384i	−0.747686	−	1.80507i	−0.176408	−	0.984317i	$-0.556448\pi$
$318$		0			0
$319$	−24.6562			−1.38048
$320$		0			0
$321$	−13.0392			−0.727776
$322$		0			0
$323$	6.26294	+	15.1201i	0.348479	+	0.841304i
$324$		0			0
$325$	12.6476	+	5.23880i	0.701561	+	0.290596i
$326$		0			0
$327$	3.18800	+	3.18800i	0.176297	+	0.176297i
$328$		0			0
$329$	9.61262	−	9.61262i	0.529961	−	0.529961i
$330$		0			0
$331$	−1.26744	+	3.05988i	−0.0696650	+	0.168186i	−0.954877	−	0.297002i	$-0.904013\pi$
$331$	−1.26744	+	3.05988i	−0.0696650	+	0.168186i	0.885212	+	0.465188i	$0.154013\pi$
$332$		0			0
$333$	7.33917	−	3.03998i	0.402184	−	0.166590i
$334$		0			0
$335$			12.9061i			0.705136i
$336$		0			0
$337$		−	10.1534i		−	0.553088i	−0.961001	−	0.276544i	$-0.910811\pi$
$337$		−	10.1534i		−	0.553088i	0.961001	−	0.276544i	$-0.0891892\pi$
$338$		0			0
$339$	−14.5674	+	6.03400i	−0.791190	+	0.327722i
$340$		0			0
$341$	−7.69795	+	18.5845i	−0.416868	+	1.00641i
$342$		0			0
$343$	−13.2198	+	13.2198i	−0.713801	+	0.713801i
$344$		0			0
$345$	4.83757	+	4.83757i	0.260446	+	0.260446i
$346$		0			0
$347$	−25.9794	−	10.7610i	−1.39465	−	0.577681i	−0.446289	−	0.894889i	$-0.647255\pi$
$347$	−25.9794	−	10.7610i	−1.39465	−	0.577681i	−0.948356	+	0.317208i	$0.897255\pi$
$348$		0			0
$349$	−5.71239	−	13.7909i	−0.305777	−	0.738212i	−0.999833	−	0.0182903i	$-0.994178\pi$
$349$	−5.71239	−	13.7909i	−0.305777	−	0.738212i	0.694055	−	0.719922i	$-0.255822\pi$
$350$		0			0
$351$	3.25866			0.173934
$352$		0			0
$353$	−18.8434			−1.00293			−0.501467	−	0.865177i	$-0.667206\pi$
$353$	−18.8434			−1.00293			−0.501467	+	0.865177i	$0.667206\pi$
$354$		0			0
$355$	0.731784	+	1.76668i	0.0388391	+	0.0937658i
$356$		0			0
$357$	−7.04954	−	2.92001i	−0.373101	−	0.154543i
$358$		0			0
$359$	18.8776	+	18.8776i	0.996324	+	0.996324i	0.999993	−	0.00366976i	$-0.00116812\pi$
$359$	18.8776	+	18.8776i	0.996324	+	0.996324i	−0.00366976	+	0.999993i	$0.501168\pi$
$360$		0			0
$361$	−4.41468	+	4.41468i	−0.232352	+	0.232352i
$362$		0			0
$363$	1.39805	−	3.37519i	0.0733785	−	0.177151i
$364$		0			0
$365$	11.2431	−	4.65704i	0.588490	−	0.243760i
$366$		0			0
$367$			25.6668i			1.33980i	0.742453	+	0.669898i	$0.233662\pi$
$367$			25.6668i			1.33980i	−0.742453	+	0.669898i	$0.766338\pi$
$368$		0			0
$369$		−	1.92221i		−	0.100066i
$370$		0			0
$371$	−12.6180	+	5.22655i	−0.655094	+	0.271349i
$372$		0			0
$373$	−3.11418	+	7.51829i	−0.161246	+	0.389282i	−0.983767	−	0.179453i	$-0.942567\pi$
$373$	−3.11418	+	7.51829i	−0.161246	+	0.389282i	0.822521	+	0.568735i	$0.192567\pi$
$374$		0			0
$375$	−5.81557	+	5.81557i	−0.300315	+	0.300315i
$376$		0			0
$377$	−14.8417	−	14.8417i	−0.764384	−	0.764384i
$378$		0			0
$379$	−5.17051	−	2.14170i	−0.265591	−	0.110012i	0.245914	−	0.969292i	$-0.420912\pi$
$379$	−5.17051	−	2.14170i	−0.265591	−	0.110012i	−0.511505	+	0.859280i	$0.670912\pi$
$380$		0			0
$381$	−2.15278	−	5.19728i	−0.110290	−	0.266265i
$382$		0			0
$383$	−33.8865			−1.73152			−0.865758	−	0.500462i	$-0.833163\pi$
$383$	−33.8865			−1.73152			−0.865758	+	0.500462i	$0.833163\pi$
$384$		0			0
$385$	−5.69790			−0.290392
$386$		0			0
$387$	−2.95781	−	7.14079i	−0.150354	−	0.362987i
$388$		0			0
$389$	3.06573	+	1.26987i	0.155439	+	0.0643847i	0.459046	−	0.888412i	$-0.348191\pi$
$389$	3.06573	+	1.26987i	0.155439	+	0.0643847i	−0.303608	+	0.952797i	$0.598191\pi$
$390$		0			0
$391$	24.7984	+	24.7984i	1.25411	+	1.25411i
$392$		0			0
$393$	−5.11942	+	5.11942i	−0.258240	+	0.258240i
$394$		0			0
$395$	1.82834	−	4.41400i	0.0919938	−	0.222093i
$396$		0			0
$397$	−21.9201	+	9.07961i	−1.10014	+	0.455693i	−0.857531	−	0.514432i	$-0.828003\pi$
$397$	−21.9201	+	9.07961i	−1.10014	+	0.455693i	−0.242608	+	0.970124i	$0.578003\pi$
$398$		0			0
$399$			5.94764i			0.297754i
$400$		0			0
$401$			7.03254i			0.351188i	0.984463	+	0.175594i	$0.0561846\pi$
$401$			7.03254i			0.351188i	−0.984463	+	0.175594i	$0.943815\pi$
$402$		0			0
$403$	−15.8206	+	6.55310i	−0.788079	+	0.326433i
$404$		0			0
$405$	−0.342068	+	0.825824i	−0.0169975	+	0.0410355i
$406$		0			0
$407$	21.5023	−	21.5023i	1.06583	−	1.06583i
$408$		0			0
$409$	−5.52966	−	5.52966i	−0.273424	−	0.273424i	0.557053	−	0.830477i	$-0.311932\pi$
$409$	−5.52966	−	5.52966i	−0.273424	−	0.273424i	−0.830477	+	0.557053i	$0.811932\pi$
$410$		0			0
$411$	4.09980	+	1.69819i	0.202228	+	0.0837657i
$412$		0			0
$413$	−0.153125	−	0.369676i	−0.00753478	−	0.0181906i
$414$		0			0
$415$	−5.45903			−0.267973
$416$		0			0
$417$	9.42388			0.461489
$418$		0			0
$419$	−7.37792	−	17.8119i	−0.360435	−	0.870167i	−0.995236	−	0.0974917i	$-0.968918\pi$
$419$	−7.37792	−	17.8119i	−0.360435	−	0.870167i	0.634801	−	0.772675i	$-0.281082\pi$
$420$		0			0
$421$	5.73622	+	2.37602i	0.279566	+	0.115800i	0.518061	−	0.855344i	$-0.326654\pi$
$421$	5.73622	+	2.37602i	0.279566	+	0.115800i	−0.238495	+	0.971144i	$0.576654\pi$
$422$		0			0
$423$	−5.77253	−	5.77253i	−0.280670	−	0.280670i
$424$		0			0
$425$	−13.6116	+	13.6116i	−0.660257	+	0.660257i
$426$		0			0
$427$	−4.44387	+	10.7284i	−0.215054	+	0.519186i
$428$		0			0
$429$	11.5245	−	4.77360i	0.556407	−	0.230471i
$430$		0			0
$431$		−	16.9436i		−	0.816146i	−0.912949	−	0.408073i	$-0.866201\pi$
$431$		−	16.9436i		−	0.816146i	0.912949	−	0.408073i	$-0.133799\pi$
$432$		0			0
$433$			26.4587i			1.27152i	0.771886	+	0.635761i	$0.219314\pi$
$433$			26.4587i			1.27152i	−0.771886	+	0.635761i	$0.780686\pi$
$434$		0			0
$435$	5.31920	−	2.20328i	0.255036	−	0.105639i
$436$		0			0
$437$	10.4611	−	25.2554i	0.500424	−	1.20813i
$438$		0			0
$439$	−9.68299	+	9.68299i	−0.462144	+	0.462144i	−0.899358	−	0.437214i	$-0.855965\pi$
$439$	−9.68299	+	9.68299i	−0.462144	+	0.462144i	0.437214	+	0.899358i	$0.355965\pi$
$440$		0			0
$441$	2.98894	+	2.98894i	0.142330	+	0.142330i
$442$		0			0
$443$	10.4314	+	4.32084i	0.495612	+	0.205289i	0.616467	−	0.787381i	$-0.288563\pi$
$443$	10.4314	+	4.32084i	0.495612	+	0.205289i	−0.120855	+	0.992670i	$0.538563\pi$
$444$		0			0
$445$	−2.46240	−	5.94476i	−0.116729	−	0.281809i
$446$		0			0
$447$	2.63040			0.124414
$448$		0			0
$449$	−23.6353			−1.11542			−0.557708	−	0.830037i	$-0.688319\pi$
$449$	−23.6353			−1.11542			−0.557708	+	0.830037i	$0.688319\pi$
$450$		0			0
$451$	−2.81585	−	6.79805i	−0.132593	−	0.320108i
$452$		0			0
$453$	18.7863	+	7.78155i	0.882658	+	0.365609i
$454$		0			0
$455$	−3.42982	−	3.42982i	−0.160792	−	0.160792i
$456$		0			0
$457$	23.4812	−	23.4812i	1.09840	−	1.09840i	0.103807	−	0.994597i	$-0.466898\pi$
$457$	23.4812	−	23.4812i	1.09840	−	1.09840i	0.994597	−	0.103807i	$-0.0331025\pi$
$458$		0			0
$459$	−1.75351	+	4.23336i	−0.0818470	+	0.197596i
$460$		0			0
$461$	−25.8692	+	10.7154i	−1.20485	+	0.499064i	−0.892562	−	0.450924i	$-0.851095\pi$
$461$	−25.8692	+	10.7154i	−1.20485	+	0.499064i	−0.312286	+	0.949988i	$0.601095\pi$
$462$		0			0
$463$			19.5222i			0.907272i	0.891187	+	0.453636i	$0.149873\pi$
$463$			19.5222i			0.907272i	−0.891187	+	0.453636i	$0.850127\pi$
$464$		0			0
$465$		−	4.69722i		−	0.217828i
$466$		0			0
$467$	−5.42932	+	2.24890i	−0.251239	+	0.104067i	−0.504749	−	0.863266i	$-0.668415\pi$
$467$	−5.42932	+	2.24890i	−0.251239	+	0.104067i	0.253510	+	0.967333i	$0.418415\pi$
$468$		0			0
$469$	−9.20107	+	22.2133i	−0.424866	+	1.02572i
$470$		0			0
$471$	−3.88092	+	3.88092i	−0.178824	+	0.178824i
$472$		0			0
$473$	−20.9211	−	20.9211i	−0.961951	−	0.961951i
$474$		0			0
$475$	13.8624	+	5.74198i	0.636049	+	0.263460i
$476$		0			0
$477$	3.13863	+	7.57731i	0.143708	+	0.346941i
$478$		0			0
$479$	−14.2300			−0.650187			−0.325094	−	0.945682i	$-0.605396\pi$
$479$	−14.2300			−0.650187			−0.325094	+	0.945682i	$0.605396\pi$
$480$		0			0
$481$	25.8863			1.18031
$482$		0			0
$483$	4.87736	+	11.7750i	0.221928	+	0.535781i
$484$		0			0
$485$	−15.7027	−	6.50427i	−0.713023	−	0.295344i
$486$		0			0
$487$	−17.2727	−	17.2727i	−0.782700	−	0.782700i	0.197586	−	0.980286i	$-0.436690\pi$
$487$	−17.2727	−	17.2727i	−0.782700	−	0.782700i	−0.980286	+	0.197586i	$0.936690\pi$
$488$		0			0
$489$	7.66164	−	7.66164i	0.346471	−	0.346471i
$490$		0			0
$491$	−2.16195	+	5.21940i	−0.0975673	+	0.235548i	−0.965126	−	0.261787i	$-0.915688\pi$
$491$	−2.16195	+	5.21940i	−0.0975673	+	0.235548i	0.867558	+	0.497335i	$0.165688\pi$
$492$		0			0
$493$	27.2674	−	11.2945i	1.22806	−	0.508680i
$494$		0			0
$495$			3.42168i			0.153793i
$496$		0			0
$497$			3.56243i			0.159797i
$498$		0			0
$499$	−14.2581	+	5.90591i	−0.638281	+	0.264385i	−0.678267	−	0.734816i	$-0.737269\pi$
$499$	−14.2581	+	5.90591i	−0.638281	+	0.264385i	0.0399860	+	0.999200i	$0.487269\pi$
$500$		0			0
$501$	−2.91268	+	7.03184i	−0.130129	+	0.314159i
$502$		0			0
$503$	9.06568	−	9.06568i	0.404219	−	0.404219i	−0.475498	−	0.879717i	$-0.657732\pi$
$503$	9.06568	−	9.06568i	0.404219	−	0.404219i	0.879717	+	0.475498i	$0.157732\pi$
$504$		0			0
$505$	−2.43094	−	2.43094i	−0.108176	−	0.108176i
$506$		0			0
$507$	−2.19990	−	0.911227i	−0.0977008	−	0.0404690i
$508$		0			0
$509$	−8.46300	−	20.4315i	−0.375116	−	0.905610i	−0.992866	−	0.119236i	$-0.961956\pi$
$509$	−8.46300	−	20.4315i	−0.375116	−	0.905610i	0.617750	−	0.786375i	$-0.288044\pi$
$510$		0			0
$511$	22.6711			1.00291
$512$		0			0
$513$	3.57165			0.157692
$514$		0			0
$515$	1.59907	+	3.86049i	0.0704633	+	0.170114i
$516$		0			0
$517$	−28.8712	−	11.9588i	−1.26975	−	0.525949i
$518$		0			0
$519$	7.36654	+	7.36654i	0.323355	+	0.323355i
$520$		0			0
$521$	−6.25345	+	6.25345i	−0.273969	+	0.273969i	−0.830696	−	0.556727i	$-0.812057\pi$
$521$	−6.25345	+	6.25345i	−0.273969	+	0.273969i	0.556727	+	0.830696i	$0.312057\pi$
$522$		0			0
$523$	0.570636	−	1.37764i	0.0249522	−	0.0602399i	−0.910912	−	0.412600i	$-0.864621\pi$
$523$	0.570636	−	1.37764i	0.0249522	−	0.0602399i	0.935865	+	0.352360i	$0.114621\pi$
$524$		0			0
$525$	−6.46315	+	2.67712i	−0.282075	+	0.116839i
$526$		0			0
$527$		−	24.0790i		−	1.04890i
$528$		0			0
$529$		−	35.5787i		−	1.54690i
$530$		0			0
$531$	−0.221996	+	0.0919539i	−0.00963382	+	0.00399046i
$532$		0			0
$533$	2.39707	−	5.78703i	0.103829	−	0.250664i
$534$		0			0
$535$	8.24152	−	8.24152i	0.356312	−	0.356312i
$536$		0			0
$537$	−9.78207	−	9.78207i	−0.422127	−	0.422127i
$538$		0			0
$539$	14.9491	+	6.19211i	0.643902	+	0.266713i
$540$		0			0
$541$	12.3150	+	29.7310i	0.529463	+	1.27824i	0.931876	+	0.362778i	$0.118172\pi$
$541$	12.3150	+	29.7310i	0.529463	+	1.27824i	−0.402413	+	0.915458i	$0.631828\pi$
$542$		0			0
$543$	−21.4594			−0.920912
$544$		0			0
$545$	−4.03000			−0.172626
$546$		0			0
$547$	12.9326	+	31.2221i	0.552959	+	1.33496i	0.915246	+	0.402895i	$0.131996\pi$
$547$	12.9326	+	31.2221i	0.552959	+	1.33496i	−0.362287	+	0.932067i	$0.618004\pi$
$548$		0			0
$549$	6.44260	+	2.66861i	0.274964	+	0.113894i
$550$		0			0
$551$	−16.2672	−	16.2672i	−0.693006	−	0.693006i
$552$		0			0
$553$	6.29369	−	6.29369i	0.267635	−	0.267635i
$554$		0			0
$555$	−2.71734	+	6.56023i	−0.115345	+	0.278466i
$556$		0			0
$557$	2.78310	−	1.15280i	0.117924	−	0.0488456i	−0.322941	−	0.946419i	$-0.604672\pi$
$557$	2.78310	−	1.15280i	0.117924	−	0.0488456i	0.440865	+	0.897573i	$0.354672\pi$
$558$		0			0
$559$		−	25.1866i		−	1.06528i
$560$		0			0
$561$			17.5403i			0.740552i
$562$		0			0
$563$	35.0055	−	14.4998i	1.47531	−	0.611092i	0.507245	−	0.861802i	$-0.330664\pi$
$563$	35.0055	−	14.4998i	1.47531	−	0.611092i	0.968062	+	0.250709i	$0.0806638\pi$
$564$		0			0
$565$	5.39358	−	13.0213i	0.226910	−	0.547808i
$566$		0			0
$567$	−1.17750	+	1.17750i	−0.0494503	+	0.0494503i
$568$		0			0
$569$	11.2443	+	11.2443i	0.471387	+	0.471387i	0.902363	−	0.430976i	$-0.141831\pi$
$569$	11.2443	+	11.2443i	0.471387	+	0.471387i	−0.430976	+	0.902363i	$0.641831\pi$
$570$		0			0
$571$	−17.4655	−	7.23445i	−0.730909	−	0.302752i	−0.0139834	−	0.999902i	$-0.504451\pi$
$571$	−17.4655	−	7.23445i	−0.730909	−	0.302752i	−0.716925	+	0.697150i	$0.754451\pi$
$572$		0			0
$573$	3.97117	+	9.58726i	0.165898	+	0.400514i
$574$		0			0
$575$	32.1531			1.34088
$576$		0			0
$577$	−1.06924			−0.0445129			−0.0222564	−	0.999752i	$-0.507085\pi$
$577$	−1.06924			−0.0445129			−0.0222564	+	0.999752i	$0.507085\pi$
$578$		0			0
$579$	−3.35265	−	8.09401i	−0.139331	−	0.336376i
$580$		0			0
$581$	−9.39581	−	3.89187i	−0.389804	−	0.161462i
$582$		0			0
$583$	22.2000	+	22.2000i	0.919429	+	0.919429i
$584$		0			0
$585$	−2.05966	+	2.05966i	−0.0851565	+	0.0851565i
$586$		0			0
$587$	−5.82611	+	14.0655i	−0.240469	+	0.580544i	−0.997330	−	0.0730327i	$-0.976732\pi$
$587$	−5.82611	+	14.0655i	−0.240469	+	0.580544i	0.756860	+	0.653577i	$0.226732\pi$
$588$		0			0
$589$	−17.3402	+	7.18253i	−0.714488	+	0.295951i
$590$		0			0
$591$			4.70889i			0.193698i
$592$		0			0
$593$		−	41.5874i		−	1.70779i	−0.520447	−	0.853894i	$-0.674235\pi$
$593$		−	41.5874i		−	1.70779i	0.520447	−	0.853894i	$-0.325765\pi$
$594$		0			0
$595$	6.30134	−	2.61010i	0.258330	−	0.107004i
$596$		0			0
$597$	1.88331	−	4.54671i	0.0770787	−	0.186084i
$598$		0			0
$599$	−2.97009	+	2.97009i	−0.121354	+	0.121354i	−0.765176	−	0.643821i	$-0.777348\pi$
$599$	−2.97009	+	2.97009i	−0.121354	+	0.121354i	0.643821	+	0.765176i	$0.277348\pi$
$600$		0			0
$601$	24.7211	+	24.7211i	1.00840	+	1.00840i	0.999964	+	0.00843176i	$0.00268394\pi$
$601$	24.7211	+	24.7211i	1.00840	+	1.00840i	0.00843176	+	0.999964i	$0.497316\pi$
$602$		0			0
$603$	13.3395	+	5.52539i	0.543225	+	0.225011i
$604$		0			0
$605$	1.24967	+	3.01696i	0.0508062	+	0.122657i
$606$		0			0
$607$	6.96020			0.282506			0.141253	−	0.989974i	$-0.454887\pi$
$607$	6.96020			0.282506			0.141253	+	0.989974i	$0.454887\pi$
$608$		0			0
$609$	10.7259			0.434636
$610$		0			0
$611$	−10.1803	−	24.5774i	−0.411850	−	0.994294i
$612$		0			0
$613$	−7.35571	−	3.04684i	−0.297094	−	0.123061i	0.229157	−	0.973389i	$-0.426403\pi$
$613$	−7.35571	−	3.04684i	−0.297094	−	0.123061i	−0.526252	+	0.850329i	$0.676403\pi$
$614$		0			0
$615$	1.21495	+	1.21495i	0.0489916	+	0.0489916i
$616$		0			0
$617$	−9.81719	+	9.81719i	−0.395225	+	0.395225i	−0.876545	−	0.481320i	$-0.840158\pi$
$617$	−9.81719	+	9.81719i	−0.395225	+	0.395225i	0.481320	+	0.876545i	$0.340158\pi$
$618$		0			0
$619$	−4.68397	+	11.3081i	−0.188265	+	0.454511i	−0.989626	−	0.143670i	$-0.954110\pi$
$619$	−4.68397	+	11.3081i	−0.188265	+	0.454511i	0.801361	+	0.598181i	$0.204110\pi$
$620$		0			0
$621$	7.07107	−	2.92893i	0.283752	−	0.117534i
$622$		0			0
$623$		−	11.9873i		−	0.480262i
$624$		0			0
$625$			13.6535i			0.546138i
$626$		0			0
$627$	12.6314	−	5.23210i	0.504450	−	0.208950i
$628$		0			0
$629$	−13.9297	+	33.6292i	−0.555412	+	1.34088i
$630$		0			0
$631$	29.7384	−	29.7384i	1.18387	−	1.18387i	0.205130	−	0.978735i	$-0.434238\pi$
$631$	29.7384	−	29.7384i	1.18387	−	1.18387i	0.978735	−	0.205130i	$-0.0657619\pi$
$632$		0			0
$633$	−3.64414	−	3.64414i	−0.144841	−	0.144841i
$634$		0			0
$635$	4.64567	+	1.92430i	0.184358	+	0.0763635i
$636$		0			0
$637$	5.27121	+	12.7258i	0.208853	+	0.504215i
$638$		0			0
$639$	2.13930			0.0846293
$640$		0			0
$641$	10.7253			0.423623			0.211811	−	0.977311i	$-0.432064\pi$
$641$	10.7253			0.423623			0.211811	+	0.977311i	$0.432064\pi$
$642$		0			0
$643$	−6.96903	−	16.8247i	−0.274832	−	0.663502i	0.724846	−	0.688911i	$-0.241911\pi$
$643$	−6.96903	−	16.8247i	−0.274832	−	0.663502i	−0.999677	+	0.0254092i	$0.991911\pi$
$644$		0			0
$645$	6.38291	+	2.64389i	0.251327	+	0.104103i
$646$		0			0
$647$	−33.4123	−	33.4123i	−1.31357	−	1.31357i	−0.918764	−	0.394808i	$-0.870811\pi$
$647$	−33.4123	−	33.4123i	−1.31357	−	1.31357i	−0.394808	−	0.918764i	$-0.629189\pi$
$648$		0			0
$649$	−0.650403	+	0.650403i	−0.0255306	+	0.0255306i
$650$		0			0
$651$	3.34876	−	8.08461i	0.131248	−	0.316861i
$652$		0			0
$653$	10.9408	−	4.53181i	0.428145	−	0.177343i	−0.158196	−	0.987408i	$-0.550568\pi$
$653$	10.9408	−	4.53181i	0.428145	−	0.177343i	0.586341	+	0.810064i	$0.300568\pi$
$654$		0			0
$655$		−	6.47154i		−	0.252864i
$656$		0			0
$657$		−	13.6144i		−	0.531148i
$658$		0			0
$659$	−0.739338	+	0.306244i	−0.0288005	+	0.0119296i	−0.397037	−	0.917803i	$-0.629962\pi$
$659$	−0.739338	+	0.306244i	−0.0288005	+	0.0119296i	0.368237	+	0.929732i	$0.379962\pi$
$660$		0			0
$661$	−3.14127	+	7.58370i	−0.122181	+	0.294972i	−0.973122	−	0.230290i	$-0.926033\pi$
$661$	−3.14127	+	7.58370i	−0.122181	+	0.294972i	0.850941	+	0.525262i	$0.176033\pi$
$662$		0			0
$663$	−10.5583	+	10.5583i	−0.410050	+	0.410050i
$664$		0			0
$665$	−3.75926	−	3.75926i	−0.145778	−	0.145778i
$666$		0			0
$667$	−45.5453	−	18.8655i	−1.76352	−	0.730475i
$668$		0			0
$669$	−4.82353	−	11.6450i	−0.186488	−	0.450223i
$670$		0			0
$671$	26.6940			1.03051
$672$		0			0
$673$	32.0221			1.23436			0.617180	−	0.786822i	$-0.288275\pi$
$673$	32.0221			1.23436			0.617180	+	0.786822i	$0.288275\pi$
$674$		0			0
$675$	1.60765	+	3.88122i	0.0618787	+	0.149388i
$676$		0			0
$677$	22.8528	+	9.46594i	0.878304	+	0.363805i	0.775839	−	0.630931i	$-0.217327\pi$
$677$	22.8528	+	9.46594i	0.878304	+	0.363805i	0.102465	+	0.994737i	$0.467327\pi$
$678$		0			0
$679$	−22.3897	−	22.3897i	−0.859236	−	0.859236i
$680$		0			0
$681$	−3.40825	+	3.40825i	−0.130605	+	0.130605i
$682$		0			0
$683$	6.46834	−	15.6160i	0.247504	−	0.597528i	−0.750487	−	0.660885i	$-0.770181\pi$
$683$	6.46834	−	15.6160i	0.247504	−	0.597528i	0.997991	+	0.0633577i	$0.0201809\pi$
$684$		0			0
$685$	−3.66467	+	1.51796i	−0.140020	+	0.0579981i
$686$		0			0
$687$			20.9937i			0.800960i
$688$		0			0
$689$			26.7263i			1.01819i
$690$		0			0
$691$	23.6307	−	9.78817i	0.898955	−	0.372359i	0.115137	−	0.993350i	$-0.463269\pi$
$691$	23.6307	−	9.78817i	0.898955	−	0.372359i	0.783818	+	0.620990i	$0.213269\pi$
$692$		0			0
$693$	−2.43940	+	5.88923i	−0.0926650	+	0.223713i
$694$		0			0
$695$	−5.95644	+	5.95644i	−0.225941	+	0.225941i
$696$		0			0
$697$	6.22811	+	6.22811i	0.235907	+	0.235907i
$698$		0			0
$699$	17.5290	+	7.26077i	0.663009	+	0.274628i
$700$		0			0
$701$	9.69117	+	23.3965i	0.366030	+	0.883675i	0.994392	+	0.105754i	$0.0337257\pi$
$701$	9.69117	+	23.3965i	0.366030	+	0.883675i	−0.628362	+	0.777921i	$0.716274\pi$
$702$		0			0
$703$	28.3727			1.07010
$704$		0			0
$705$	7.29716			0.274827
$706$		0			0
$707$	−2.45094	−	5.91709i	−0.0921771	−	0.222535i
$708$		0			0
$709$	11.9720	+	4.95898i	0.449619	+	0.186238i	0.595991	−	0.802991i	$-0.296760\pi$
$709$	11.9720	+	4.95898i	0.449619	+	0.186238i	−0.146372	+	0.989230i	$0.546760\pi$
$710$		0			0
$711$	−3.77946	−	3.77946i	−0.141741	−	0.141741i
$712$		0			0
$713$	−28.4396	+	28.4396i	−1.06507	+	1.06507i
$714$		0			0
$715$	−4.26695	+	10.3013i	−0.159575	+	0.385248i
$716$		0			0
$717$	4.23034	−	1.75226i	0.157985	−	0.0654395i
$718$		0			0
$719$			18.7152i			0.697960i	0.937130	+	0.348980i	$0.113472\pi$
$719$			18.7152i			0.697960i	−0.937130	+	0.348980i	$0.886528\pi$
$720$		0			0
$721$			7.78449i			0.289910i
$722$		0			0
$723$	−13.4804	+	5.58377i	−0.501342	+	0.207663i
$724$		0			0
$725$	10.3550	−	24.9993i	0.384576	−	0.928449i
$726$		0			0
$727$	−37.4952	+	37.4952i	−1.39062	+	1.39062i	−0.566690	+	0.823931i	$0.691776\pi$
$727$	−37.4952	+	37.4952i	−1.39062	+	1.39062i	−0.823931	+	0.566690i	$0.808224\pi$
$728$		0			0
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$		0			0
$731$	32.7202	+	13.5532i	1.21020	+	0.501282i
$732$		0			0
$733$	11.1057	+	26.8115i	0.410198	+	0.990305i	0.985084	+	0.172072i	$0.0550461\pi$
$733$	11.1057	+	26.8115i	0.410198	+	0.990305i	−0.574887	+	0.818233i	$0.694954\pi$
$734$		0			0
$735$	−3.77836			−0.139367
$736$		0			0
$737$	55.2701			2.03590
$738$		0			0
$739$	0.383327	+	0.925433i	0.0141009	+	0.0340426i	0.930773	−	0.365597i	$-0.119135\pi$
$739$	0.383327	+	0.925433i	0.0141009	+	0.0340426i	−0.916672	+	0.399640i	$0.869135\pi$
$740$		0			0
$741$	10.7528	+	4.45397i	0.395015	+	0.163621i
$742$		0			0
$743$	34.4148	+	34.4148i	1.26256	+	1.26256i	0.949849	+	0.312708i	$0.101236\pi$
$743$	34.4148	+	34.4148i	1.26256	+	1.26256i	0.312708	+	0.949849i	$0.398764\pi$
$744$		0			0
$745$	−1.66257	+	1.66257i	−0.0609118	+	0.0609118i
$746$		0			0
$747$	−2.33713	+	5.64233i	−0.0855111	+	0.206442i
$748$		0			0
$749$	20.0605	−	8.30931i	0.732993	−	0.303616i
$750$		0			0
$751$		−	20.2742i		−	0.739816i	−0.929068	−	0.369908i	$-0.879389\pi$
$751$		−	20.2742i		−	0.739816i	0.929068	−	0.369908i	$-0.120611\pi$
$752$		0			0
$753$		−	2.07078i		−	0.0754634i
$754$		0			0
$755$	−16.7924	+	6.95566i	−0.611139	+	0.253142i
$756$		0			0
$757$	18.5068	−	44.6794i	0.672641	−	1.62390i	−0.104465	−	0.994529i	$-0.533313\pi$
$757$	18.5068	−	44.6794i	0.672641	−	1.62390i	0.777106	−	0.629370i	$-0.216687\pi$
$758$		0			0
$759$	20.7168	−	20.7168i	0.751971	−	0.751971i
$760$		0			0
$761$	13.1682	+	13.1682i	0.477345	+	0.477345i	0.904282	−	0.426936i	$-0.140407\pi$
$761$	13.1682	+	13.1682i	0.477345	+	0.477345i	−0.426936	+	0.904282i	$0.640407\pi$
$762$		0			0
$763$	−6.93624	−	2.87308i	−0.251109	−	0.104013i
$764$		0			0
$765$	−1.56741	−	3.78405i	−0.0566697	−	0.136813i
$766$		0			0
$767$	−0.783013			−0.0282730
$768$		0			0
$769$	−40.4343			−1.45810			−0.729049	−	0.684461i	$-0.760037\pi$
$769$	−40.4343			−1.45810			−0.729049	+	0.684461i	$0.760037\pi$
$770$		0			0
$771$	−8.18988	−	19.7721i	−0.294951	−	0.712075i
$772$		0			0
$773$	−2.36151	−	0.978168i	−0.0849375	−	0.0351823i	0.339810	−	0.940494i	$-0.389637\pi$
$773$	−2.36151	−	0.978168i	−0.0849375	−	0.0351823i	−0.424748	+	0.905312i	$0.639637\pi$
$774$		0			0
$775$	−15.6101	−	15.6101i	−0.560732	−	0.560732i
$776$		0			0
$777$	−9.35389	+	9.35389i	−0.335569	+	0.335569i
$778$		0			0
$779$	2.62731	−	6.34288i	0.0941330	−	0.227257i
$780$		0			0
$781$	7.56578	−	3.13385i	0.270725	−	0.112138i
$782$		0			0
$783$		−	6.44108i		−	0.230185i
$784$		0			0
$785$		−	4.90594i		−	0.175101i
$786$		0			0
$787$	27.5997	−	11.4322i	0.983825	−	0.407514i	0.167984	−	0.985790i	$-0.446274\pi$
$787$	27.5997	−	11.4322i	0.983825	−	0.407514i	0.815841	+	0.578276i	$0.196274\pi$
$788$		0			0
$789$	2.24530	−	5.42063i	0.0799348	−	0.192980i
$790$		0			0
$791$	18.5663	−	18.5663i	0.660142	−	0.660142i
$792$		0			0
$793$	16.0683	+	16.0683i	0.570602	+	0.570602i
$794$		0			0
$795$	−6.77310	−	2.80551i	−0.240217	−	0.0995012i
$796$		0			0
$797$	21.0345	+	50.7818i	0.745080	+	1.79878i	0.583842	+	0.811867i	$0.301549\pi$
$797$	21.0345	+	50.7818i	0.745080	+	1.79878i	0.161238	+	0.986916i	$0.448451\pi$
$798$		0			0
$799$	37.4069			1.32336
$800$		0			0
$801$	−7.19858			−0.254349
$802$		0			0
$803$	−19.9437	−	48.1483i	−0.703796	−	1.69911i
$804$		0			0
$805$	−10.5253	−	4.35971i	−0.370967	−	0.153659i
$806$		0			0
$807$	−21.4333	−	21.4333i	−0.754487	−	0.754487i
$808$		0			0
$809$	10.8210	−	10.8210i	0.380446	−	0.380446i	−0.490817	−	0.871263i	$-0.663302\pi$
$809$	10.8210	−	10.8210i	0.380446	−	0.380446i	0.871263	+	0.490817i	$0.163302\pi$
$810$		0			0
$811$	9.28572	−	22.4177i	0.326066	−	0.787192i	−0.672811	−	0.739814i	$-0.734913\pi$
$811$	9.28572	−	22.4177i	0.326066	−	0.787192i	0.998877	−	0.0473779i	$-0.0150865\pi$
$812$		0			0
$813$	9.55017	−	3.95581i	0.334939	−	0.138736i
$814$		0			0
$815$			9.68520i			0.339258i
$816$		0			0
$817$		−	27.6058i		−	0.965805i
$818$		0			0
$819$	−5.01337	+	2.07660i	−0.175181	+	0.0725624i
$820$		0			0
$821$	−2.83930	+	6.85468i	−0.0990924	+	0.239230i	−0.965650	−	0.259847i	$-0.916328\pi$
$821$	−2.83930	+	6.85468i	−0.0990924	+	0.239230i	0.866557	+	0.499078i	$0.166328\pi$
$822$		0			0
$823$	−25.2545	+	25.2545i	−0.880317	+	0.880317i	−0.993567	−	0.113250i	$-0.963874\pi$
$823$	−25.2545	+	25.2545i	−0.880317	+	0.880317i	0.113250	+	0.993567i	$0.463874\pi$
$824$		0			0
$825$	11.3712	+	11.3712i	0.395894	+	0.395894i
$826$		0			0
$827$	−30.9624	−	12.8251i	−1.07667	−	0.445971i	−0.227330	−	0.973818i	$-0.572999\pi$
$827$	−30.9624	−	12.8251i	−1.07667	−	0.445971i	−0.849339	+	0.527847i	$0.822999\pi$
$828$		0			0
$829$	9.26963	+	22.3789i	0.321948	+	0.777251i	0.999141	+	0.0414451i	$0.0131962\pi$
$829$	9.26963	+	22.3789i	0.321948	+	0.777251i	−0.677193	+	0.735805i	$0.736804\pi$
$830$		0			0
$831$	16.7112			0.579703
$832$		0			0
$833$	−19.3687			−0.671087
$834$		0			0
$835$	−2.60355	−	6.28552i	−0.0900994	−	0.217519i
$836$		0			0
$837$	−4.85494	−	2.01098i	−0.167811	−	0.0695097i
$838$		0			0
$839$	−23.7415	−	23.7415i	−0.819648	−	0.819648i	0.166409	−	0.986057i	$-0.446783\pi$
$839$	−23.7415	−	23.7415i	−0.819648	−	0.819648i	−0.986057	+	0.166409i	$0.946783\pi$
$840$		0			0
$841$	−8.83001	+	8.83001i	−0.304483	+	0.304483i
$842$		0			0
$843$	−4.25181	+	10.2648i	−0.146440	+	0.353537i
$844$		0			0
$845$	1.96641	−	0.814514i	0.0676466	−	0.0280201i
$846$		0			0
$847$			6.08356i			0.209034i
$848$		0			0
$849$			7.32606i			0.251430i
$850$		0			0
$851$	56.1716	−	23.2670i	1.92554	−	0.797584i
$852$		0			0
$853$	7.82863	−	18.9000i	0.268047	−	0.647123i	−0.731344	−	0.682009i	$-0.761107\pi$
$853$	7.82863	−	18.9000i	0.268047	−	0.647123i	0.999391	+	0.0348853i	$0.0111066\pi$
$854$		0			0
$855$	−2.25749	+	2.25749i	−0.0772046	+	0.0772046i
$856$		0			0
$857$	−19.1000	−	19.1000i	−0.652445	−	0.652445i	0.301136	−	0.953581i	$-0.402634\pi$
$857$	−19.1000	−	19.1000i	−0.652445	−	0.652445i	−0.953581	+	0.301136i	$0.902634\pi$
$858$		0			0
$859$	23.7460	+	9.83590i	0.810202	+	0.335597i	0.749035	−	0.662531i	$-0.230518\pi$
$859$	23.7460	+	9.83590i	0.810202	+	0.335597i	0.0611672	+	0.998128i	$0.480518\pi$
$860$		0			0
$861$	1.22495	+	2.95728i	0.0417460	+	0.100784i
$862$		0			0
$863$	−7.14216			−0.243122			−0.121561	−	0.992584i	$-0.538790\pi$
$863$	−7.14216			−0.243122			−0.121561	+	0.992584i	$0.538790\pi$
$864$		0			0
$865$	−9.31217			−0.316623
$866$		0			0
$867$	−1.52925	−	3.69195i	−0.0519362	−	0.125385i
$868$		0			0
$869$	−18.9029	−	7.82983i	−0.641236	−	0.265609i
$870$		0			0
$871$	33.2695	+	33.2695i	1.12730	+	1.12730i
$872$		0			0
$873$	−13.4453	+	13.4453i	−0.455056	+	0.455056i
$874$		0			0
$875$	5.24110	−	12.6531i	0.177182	−	0.427754i
$876$		0			0
$877$	−13.2121	+	5.47264i	−0.446141	+	0.184798i	−0.594432	−	0.804146i	$-0.702623\pi$
$877$	−13.2121	+	5.47264i	−0.446141	+	0.184798i	0.148290	+	0.988944i	$0.452623\pi$
$878$		0			0
$879$		−	13.3564i		−	0.450501i
$880$		0			0
$881$			8.29862i			0.279588i	0.990181	+	0.139794i	$0.0446440\pi$
$881$			8.29862i			0.279588i	−0.990181	+	0.139794i	$0.955356\pi$
$882$		0			0
$883$	23.1211	−	9.57707i	0.778087	−	0.322294i	0.0419435	−	0.999120i	$-0.486645\pi$
$883$	23.1211	−	9.57707i	0.778087	−	0.322294i	0.736143	+	0.676826i	$0.236645\pi$
$884$		0			0
$885$	0.0821944	−	0.198435i	0.00276293	−	0.00667031i
$886$		0			0
$887$	−27.8541	+	27.8541i	−0.935249	+	0.935249i	−0.998027	−	0.0627784i	$-0.980004\pi$
$887$	−27.8541	+	27.8541i	−0.935249	+	0.935249i	0.0627784	+	0.998027i	$0.480004\pi$
$888$		0			0
$889$	6.62401	+	6.62401i	0.222162	+	0.222162i
$890$		0			0
$891$	3.53657	+	1.46490i	0.118480	+	0.0490759i
$892$		0			0
$893$	−11.1581	−	26.9380i	−0.373392	−	0.901447i
$894$		0			0
$895$	12.3657			0.413339
$896$		0			0
$897$	24.9407			0.832745
$898$		0			0
$899$	12.9529	+	31.2711i	0.432003	+	1.04295i
$900$		0			0
$901$	−34.7204	−	14.3817i	−1.15670	−	0.479123i
$902$		0			0
$903$	9.10105	+	9.10105i	0.302864	+	0.302864i
$904$		0			0
$905$	13.5636	−	13.5636i	0.450870	−	0.450870i
$906$		0			0
$907$	−5.14391	+	12.4185i	−0.170801	+	0.412349i	−0.985981	−	0.166858i	$-0.946638\pi$
$907$	−5.14391	+	12.4185i	−0.170801	+	0.412349i	0.815180	+	0.579207i	$0.196638\pi$
$908$		0			0
$909$	−3.55331	+	1.47183i	−0.117856	+	0.0488175i
$910$		0			0
$911$			43.4302i			1.43891i	0.694541	+	0.719454i	$0.255608\pi$
$911$			43.4302i			1.43891i	−0.694541	+	0.719454i	$0.744392\pi$
$912$		0			0
$913$			23.3782i			0.773705i
$914$		0			0
$915$	−5.75882	+	2.38538i	−0.190381	+	0.0788583i
$916$		0			0
$917$	4.61371	−	11.1385i	0.152358	−	0.367825i
$918$		0			0
$919$	−13.6438	+	13.6438i	−0.450068	+	0.450068i	−0.895377	−	0.445309i	$-0.853094\pi$
$919$	−13.6438	+	13.6438i	−0.450068	+	0.450068i	0.445309	+	0.895377i	$0.353094\pi$
$920$		0			0
$921$	−5.71992	−	5.71992i	−0.188478	−	0.188478i
$922$		0			0
$923$	6.44058	+	2.66778i	0.211994	+	0.0878110i
$924$		0			0
$925$	12.7710	+	30.8319i	0.419907	+	1.01375i
$926$		0			0
$927$	4.67471			0.153538
$928$		0			0
$929$	52.3939			1.71899			0.859494	−	0.511146i	$-0.170779\pi$
$929$	52.3939			1.71899			0.859494	+	0.511146i	$0.170779\pi$
$930$		0			0
$931$	5.77751	+	13.9481i	0.189350	+	0.457132i
$932$		0			0
$933$	−16.3554	−	6.77462i	−0.535451	−	0.221791i
$934$		0			0
$935$	−11.0865	−	11.0865i	−0.362567	−	0.362567i
$936$		0			0
$937$	−18.9484	+	18.9484i	−0.619017	+	0.619017i	−0.945279	−	0.326262i	$-0.894211\pi$
$937$	−18.9484	+	18.9484i	−0.619017	+	0.619017i	0.326262	+	0.945279i	$0.394211\pi$
$938$		0			0
$939$	−1.14203	+	2.75711i	−0.0372688	+	0.0899748i
$940$		0			0
$941$	3.46272	−	1.43430i	0.112881	−	0.0467570i	−0.325528	−	0.945532i	$-0.605542\pi$
$941$	3.46272	−	1.43430i	0.112881	−	0.0467570i	0.438409	+	0.898775i	$0.355542\pi$
$942$		0			0
$943$		−	14.7120i		−	0.479088i
$944$		0			0
$945$		−	1.48850i		−	0.0484208i
$946$		0			0
$947$	−52.3991	+	21.7044i	−1.70274	+	0.705298i	−0.999981	−	0.00612896i	$-0.998049\pi$
$947$	−52.3991	+	21.7044i	−1.70274	+	0.705298i	−0.702760	+	0.711427i	$0.748049\pi$
$948$		0			0
$949$	16.9776	−	40.9875i	0.551116	−	1.33051i
$950$		0			0
$951$	24.5977	−	24.5977i	0.797635	−	0.797635i
$952$		0			0
$953$	−10.0461	−	10.0461i	−0.325424	−	0.325424i	0.525419	−	0.850843i	$-0.323908\pi$
$953$	−10.0461	−	10.0461i	−0.325424	−	0.325424i	−0.850843	+	0.525419i	$0.823908\pi$
$954$		0			0
$955$	−8.56972	−	3.54970i	−0.277310	−	0.114865i
$956$		0			0
$957$	−9.43552	−	22.7794i	−0.305007	−	0.736352i
$958$		0			0
$959$	−7.38963			−0.238624
$960$		0			0
$961$	−3.38553			−0.109211
$962$		0			0
$963$	−4.98987	−	12.0466i	−0.160796	−	0.388197i
$964$		0			0
$965$	7.23496	+	2.99682i	0.232902	+	0.0964710i
$966$		0			0
$967$	−34.5937	−	34.5937i	−1.11246	−	1.11246i	−0.992817	−	0.119640i	$-0.961826\pi$
$967$	−34.5937	−	34.5937i	−1.11246	−	1.11246i	−0.119640	−	0.992817i	$-0.538174\pi$
$968$		0			0
$969$	−11.5724	+	11.5724i	−0.371759	+	0.371759i
$970$		0			0
$971$	−11.4425	+	27.6245i	−0.367206	+	0.886513i	0.627000	+	0.779019i	$0.284283\pi$
$971$	−11.4425	+	27.6245i	−0.367206	+	0.886513i	−0.994206	+	0.107494i	$0.965717\pi$
$972$		0			0
$973$	−14.4984	+	6.00544i	−0.464798	+	0.192526i
$974$		0			0
$975$			13.6896i			0.438419i
$976$		0			0
$977$			7.83370i			0.250622i	0.992117	+	0.125311i	$0.0399929\pi$
$977$			7.83370i			0.250622i	−0.992117	+	0.125311i	$0.960007\pi$
$978$		0			0
$979$	−25.4583	+	10.5452i	−0.813651	+	0.337025i
$980$		0			0
$981$	−1.72533	+	4.16532i	−0.0550857	+	0.132989i
$982$		0			0
$983$	13.3719	−	13.3719i	0.426497	−	0.426497i	−0.460937	−	0.887433i	$-0.652486\pi$
$983$	13.3719	−	13.3719i	0.426497	−	0.426497i	0.887433	+	0.460937i	$0.152486\pi$
$984$		0			0
$985$	−2.97629	−	2.97629i	−0.0948326	−	0.0948326i
$986$		0			0
$987$	12.5595	+	5.20232i	0.399773	+	0.165592i
$988$		0			0
$989$	−22.6381	−	54.6533i	−0.719851	−	1.73787i
$990$		0			0
$991$	−42.1375			−1.33854			−0.669270	−	0.743019i	$-0.733393\pi$
$991$	−42.1375			−1.33854			−0.669270	+	0.743019i	$0.733393\pi$
$992$		0			0
$993$	−3.31199			−0.105103
$994$		0			0
$995$	1.68342	+	4.06415i	0.0533681	+	0.128842i
$996$		0			0
$997$	−6.17091	−	2.55607i	−0.195435	−	0.0809517i	0.282820	−	0.959173i	$-0.408730\pi$
$997$	−6.17091	−	2.55607i	−0.195435	−	0.0809517i	−0.478254	+	0.878221i	$0.658730\pi$
$998$		0			0
$999$	5.61716	+	5.61716i	0.177719	+	0.177719i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.n.b.481.6		32
4.3	odd	2		768.2.n.a.481.2		32
8.3	odd	2		96.2.n.a.37.1	yes	32
8.5	even	2		384.2.n.a.241.3		32
24.5	odd	2		1152.2.v.c.1009.4		32
24.11	even	2		288.2.v.d.37.8		32
32.3	odd	8		96.2.n.a.13.1	✓	32
32.13	even	8	inner	768.2.n.b.289.6		32
32.19	odd	8		768.2.n.a.289.2		32
32.29	even	8		384.2.n.a.145.3		32
96.29	odd	8		1152.2.v.c.145.4		32
96.35	even	8		288.2.v.d.109.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.1	✓	32	32.3	odd	8
96.2.n.a.37.1	yes	32	8.3	odd	2
288.2.v.d.37.8		32	24.11	even	2
288.2.v.d.109.8		32	96.35	even	8
384.2.n.a.145.3		32	32.29	even	8
384.2.n.a.241.3		32	8.5	even	2
768.2.n.a.289.2		32	32.19	odd	8
768.2.n.a.481.2		32	4.3	odd	2
768.2.n.b.289.6		32	32.13	even	8	inner
768.2.n.b.481.6		32	1.1	even	1	trivial
1152.2.v.c.145.4		32	96.29	odd	8
1152.2.v.c.1009.4		32	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.382683 + 0.923880i) q^{3} +(-0.825824 - 0.342068i) q^{5} +(-1.17750 - 1.17750i) q^{7} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(0.382683 + 0.923880i) q^{3} +(-0.825824 - 0.342068i) q^{5} +(-1.17750 - 1.17750i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(-1.46490 + 3.53657i) q^{11} +(-3.01061 + 1.24703i) q^{13} -0.893866i q^{15} -4.58215i q^{17} +(-3.29978 + 1.36681i) q^{19} +(0.637258 - 1.53848i) q^{21} +(-5.41196 + 5.41196i) q^{23} +(-2.97056 - 2.97056i) q^{25} +(-0.923880 - 0.382683i) q^{27} +(2.46490 + 5.95078i) q^{29} +5.25495 q^{31} -3.82796 q^{33} +(0.569623 + 1.37519i) q^{35} +(-7.33917 - 3.03998i) q^{37} +(-2.30422 - 2.30422i) q^{39} +(-1.35921 + 1.35921i) q^{41} +(-2.95781 + 7.14079i) q^{43} +(0.825824 - 0.342068i) q^{45} +8.16360i q^{47} -4.22699i q^{49} +(4.23336 - 1.75351i) q^{51} +(3.13863 - 7.57731i) q^{53} +(2.41949 - 2.41949i) q^{55} +(-2.52554 - 2.52554i) q^{57} +(0.221996 + 0.0919539i) q^{59} +(-2.66861 - 6.44260i) q^{61} +1.66523 q^{63} +2.91280 q^{65} +(-5.52539 - 13.3395i) q^{67} +(-7.07107 - 2.92893i) q^{69} +(-1.51271 - 1.51271i) q^{71} +(-9.62682 + 9.62682i) q^{73} +(1.60765 - 3.88122i) q^{75} +(5.88923 - 2.43940i) q^{77} +5.34497i q^{79} -1.00000i q^{81} +(5.64233 - 2.33713i) q^{83} +(-1.56741 + 3.78405i) q^{85} +(-4.55453 + 4.55453i) q^{87} +(5.09017 + 5.09017i) q^{89} +(5.01337 + 2.07660i) q^{91} +(2.01098 + 4.85494i) q^{93} +3.19258 q^{95} +19.0146 q^{97} +(-1.46490 - 3.53657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 16 q^{23} + 48 q^{31} - 48 q^{35} - 16 q^{43} + 16 q^{51} + 32 q^{53} - 32 q^{55} + 64 q^{59} + 32 q^{61} - 16 q^{63} + 16 q^{67} + 32 q^{69} - 64 q^{71} + 32 q^{75} + 32 q^{77} - 48 q^{91}+O(q^{100}) \) 32 * q + 16 * q^23 + 48 * q^31 - 48 * q^35 - 16 * q^43 + 16 * q^51 + 32 * q^53 - 32 * q^55 + 64 * q^59 + 32 * q^61 - 16 * q^63 + 16 * q^67 + 32 * q^69 - 64 * q^71 + 32 * q^75 + 32 * q^77 - 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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