LMFDB - Embedded newform 416.2.i.g.321.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [416,2,Mod(289,416)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("416.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.6927565824.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 23x^{4} + 10x^{2} + 4 $ x^8 + 5x^6 + 23x^4 + 10*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			321.4
Root			$-0.331077 - 0.573442i$ of defining polynomial
Character	$\chi$	$=$	416.321
Dual form			416.2.i.g.289.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.17915 - 2.04234i) q^{3} -2.56155 q^{5} +(-1.84130 - 3.18923i) q^{7} +(-1.28078 - 2.21837i) q^{9} +(-0.516994 + 0.895460i) q^{11} +(-2.84233 + 2.21837i) q^{13} +(-3.02045 + 5.23157i) q^{15} +(-3.06155 - 5.30277i) q^{17} +(2.50345 + 4.33611i) q^{19} -8.68466 q^{21} +(3.53744 - 6.12703i) q^{23} +1.56155 q^{25} +1.03399 q^{27} +(2.50000 - 4.33013i) q^{29} -3.39228 q^{31} +(1.21922 + 2.11176i) q^{33} +(4.71659 + 8.16937i) q^{35} +(-1.06155 + 1.83866i) q^{37} +(1.17915 + 8.42080i) q^{39} +(2.06155 - 3.57071i) q^{41} +(-4.19960 - 7.27391i) q^{43} +(3.28078 + 5.68247i) q^{45} +10.7575 q^{47} +(-3.28078 + 5.68247i) q^{49} -14.4401 q^{51} -2.56155 q^{53} +(1.32431 - 2.29377i) q^{55} +11.8078 q^{57} +(-5.23358 - 9.06483i) q^{59} +(5.62311 + 9.73950i) q^{61} +(-4.71659 + 8.16937i) q^{63} +(7.28078 - 5.68247i) q^{65} +(4.86175 - 8.42080i) q^{67} +(-8.34233 - 14.4493i) q^{69} +(-2.50345 - 4.33611i) q^{71} -4.31534 q^{73} +(1.84130 - 3.18923i) q^{75} +3.80776 q^{77} +11.5012 q^{79} +(5.06155 - 8.76687i) q^{81} -2.64861 q^{83} +(7.84233 + 13.5833i) q^{85} +(-5.89574 - 10.2117i) q^{87} +(-5.34233 + 9.25319i) q^{89} +(12.3085 + 4.98015i) q^{91} +(-4.00000 + 6.92820i) q^{93} +(-6.41273 - 11.1072i) q^{95} +(4.90388 + 8.49377i) q^{97} +2.64861 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} - 2 q^{9} + 2 q^{13} - 8 q^{17} - 20 q^{21} - 4 q^{25} + 20 q^{29} + 18 q^{33} + 8 q^{37} + 18 q^{45} - 18 q^{49} - 4 q^{53} + 12 q^{57} + 12 q^{61} + 50 q^{65} - 42 q^{69} - 84 q^{73} - 52 q^{77}+ \cdots - 2 q^{97}+O(q^{100}) $ 8 * q - 4 * q^5 - 2 * q^9 + 2 * q^13 - 8 * q^17 - 20 * q^21 - 4 * q^25 + 20 * q^29 + 18 * q^33 + 8 * q^37 + 18 * q^45 - 18 * q^49 - 4 * q^53 + 12 * q^57 + 12 * q^61 + 50 * q^65 - 42 * q^69 - 84 * q^73 - 52 * q^77 + 24 * q^81 + 38 * q^85 - 18 * q^89 - 32 * q^93 - 2 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.17915	−	2.04234i	0.680781	−	1.17915i	−0.293962	−	0.955817i	$-0.594974\pi$
$3$	1.17915	−	2.04234i	0.680781	−	1.17915i	0.974743	−	0.223330i	$-0.0716928\pi$
$4$		0			0
$5$	−2.56155			−1.14556			−0.572781	−	0.819709i	$-0.694135\pi$
$5$	−2.56155			−1.14556			−0.572781	+	0.819709i	$0.694135\pi$
$6$		0			0
$7$	−1.84130	−	3.18923i	−0.695946	−	1.20541i	−0.969861	−	0.243660i	$-0.921652\pi$
$7$	−1.84130	−	3.18923i	−0.695946	−	1.20541i	0.273914	−	0.961754i	$-0.411681\pi$
$8$		0			0
$9$	−1.28078	−	2.21837i	−0.426925	−	0.739457i
$10$		0			0
$11$	−0.516994	+	0.895460i	−0.155879	+	0.269991i	−0.933379	−	0.358892i	$-0.883154\pi$
$11$	−0.516994	+	0.895460i	−0.155879	+	0.269991i	0.777499	+	0.628884i	$0.216488\pi$
$12$		0			0
$13$	−2.84233	+	2.21837i	−0.788320	+	0.615265i
$13$	−2.84233	+	2.21837i	−0.788320	+	0.615265i
$14$		0			0
$15$	−3.02045	+	5.23157i	−0.779876	+	1.35079i
$16$		0			0
$17$	−3.06155	−	5.30277i	−0.742536	−	1.28611i	−0.951337	−	0.308151i	$-0.900290\pi$
$17$	−3.06155	−	5.30277i	−0.742536	−	1.28611i	0.208802	−	0.977958i	$-0.433044\pi$
$18$		0			0
$19$	2.50345	+	4.33611i	0.574332	+	0.994772i	0.996114	+	0.0880746i	$0.0280714\pi$
$19$	2.50345	+	4.33611i	0.574332	+	0.994772i	−0.421782	+	0.906697i	$0.638595\pi$
$20$		0			0
$21$	−8.68466			−1.89515
$22$		0			0
$23$	3.53744	−	6.12703i	0.737608	−	1.27757i	−0.215962	−	0.976402i	$-0.569289\pi$
$23$	3.53744	−	6.12703i	0.737608	−	1.27757i	0.953570	−	0.301172i	$-0.0973779\pi$
$24$		0			0
$25$	1.56155			0.312311
$26$		0			0
$27$	1.03399			0.198991
$28$		0			0
$29$	2.50000	−	4.33013i	0.464238	−	0.804084i	−0.534928	−	0.844897i	$-0.679661\pi$
$29$	2.50000	−	4.33013i	0.464238	−	0.804084i	0.999167	+	0.0408130i	$0.0129948\pi$
$30$		0			0
$31$	−3.39228			−0.609272			−0.304636	−	0.952469i	$-0.598535\pi$
$31$	−3.39228			−0.609272			−0.304636	+	0.952469i	$0.598535\pi$
$32$		0			0
$33$	1.21922	+	2.11176i	0.212240	+	0.367610i
$34$		0			0
$35$	4.71659	+	8.16937i	0.797249	+	1.38088i
$36$		0			0
$37$	−1.06155	+	1.83866i	−0.174518	+	0.302274i	−0.939994	−	0.341190i	$-0.889170\pi$
$37$	−1.06155	+	1.83866i	−0.174518	+	0.302274i	0.765476	+	0.643464i	$0.222503\pi$
$38$		0			0
$39$	1.17915	+	8.42080i	0.188815	+	1.34841i
$40$		0			0
$41$	2.06155	−	3.57071i	0.321960	−	0.557652i	−0.658932	−	0.752202i	$-0.728992\pi$
$41$	2.06155	−	3.57071i	0.321960	−	0.557652i	0.980892	+	0.194551i	$0.0623249\pi$
$42$		0			0
$43$	−4.19960	−	7.27391i	−0.640432	−	1.10926i	−0.985336	−	0.170623i	$-0.945422\pi$
$43$	−4.19960	−	7.27391i	−0.640432	−	1.10926i	0.344904	−	0.938638i	$-0.387911\pi$
$44$		0			0
$45$	3.28078	+	5.68247i	0.489069	+	0.847093i
$46$		0			0
$47$	10.7575			1.56914			0.784570	−	0.620040i	$-0.212884\pi$
$47$	10.7575			1.56914			0.784570	+	0.620040i	$0.212884\pi$
$48$		0			0
$49$	−3.28078	+	5.68247i	−0.468682	+	0.811782i
$50$		0			0
$51$	−14.4401			−2.02202
$52$		0			0
$53$	−2.56155			−0.351856			−0.175928	−	0.984403i	$-0.556293\pi$
$53$	−2.56155			−0.351856			−0.175928	+	0.984403i	$0.556293\pi$
$54$		0			0
$55$	1.32431	−	2.29377i	0.178570	−	0.309291i
$56$		0			0
$57$	11.8078			1.56398
$58$		0			0
$59$	−5.23358	−	9.06483i	−0.681354	−	1.18014i	−0.974568	−	0.224093i	$-0.928058\pi$
$59$	−5.23358	−	9.06483i	−0.681354	−	1.18014i	0.293213	−	0.956047i	$-0.405275\pi$
$60$		0			0
$61$	5.62311	+	9.73950i	0.719965	+	1.24702i	0.961013	+	0.276503i	$0.0891755\pi$
$61$	5.62311	+	9.73950i	0.719965	+	1.24702i	−0.241048	+	0.970513i	$0.577491\pi$
$62$		0			0
$63$	−4.71659	+	8.16937i	−0.594234	+	1.02924i
$64$		0			0
$65$	7.28078	−	5.68247i	0.903069	−	0.704824i
$66$		0			0
$67$	4.86175	−	8.42080i	0.593957	−	1.02876i	−0.399736	−	0.916630i	$-0.630898\pi$
$67$	4.86175	−	8.42080i	0.593957	−	1.02876i	0.993693	−	0.112134i	$-0.0357685\pi$
$68$		0			0
$69$	−8.34233	−	14.4493i	−1.00430	−	1.73950i
$70$		0			0
$71$	−2.50345	−	4.33611i	−0.297105	−	0.514602i	0.678367	−	0.734723i	$-0.262688\pi$
$71$	−2.50345	−	4.33611i	−0.297105	−	0.514602i	−0.975472	+	0.220122i	$0.929355\pi$
$72$		0			0
$73$	−4.31534			−0.505073			−0.252536	−	0.967587i	$-0.581265\pi$
$73$	−4.31534			−0.505073			−0.252536	+	0.967587i	$0.581265\pi$
$74$		0			0
$75$	1.84130	−	3.18923i	0.212615	−	0.368260i
$76$		0			0
$77$	3.80776			0.433935
$78$		0			0
$79$	11.5012			1.29398			0.646990	−	0.762498i	$-0.276027\pi$
$79$	11.5012			1.29398			0.646990	+	0.762498i	$0.276027\pi$
$80$		0			0
$81$	5.06155	−	8.76687i	0.562395	−	0.974096i
$82$		0			0
$83$	−2.64861			−0.290723			−0.145362	−	0.989379i	$-0.546435\pi$
$83$	−2.64861			−0.290723			−0.145362	+	0.989379i	$0.546435\pi$
$84$		0			0
$85$	7.84233	+	13.5833i	0.850620	+	1.47332i
$86$		0			0
$87$	−5.89574	−	10.2117i	−0.632089	−	1.09481i
$88$		0			0
$89$	−5.34233	+	9.25319i	−0.566286	+	0.980836i	0.430643	+	0.902522i	$0.358287\pi$
$89$	−5.34233	+	9.25319i	−0.566286	+	0.980836i	−0.996929	+	0.0783134i	$0.975047\pi$
$90$		0			0
$91$	12.3085	+	4.98015i	1.29028	+	0.522061i
$92$		0			0
$93$	−4.00000	+	6.92820i	−0.414781	+	0.718421i
$94$		0			0
$95$	−6.41273	−	11.1072i	−0.657932	−	1.13957i
$96$		0			0
$97$	4.90388	+	8.49377i	0.497914	+	0.862412i	0.999997	−	0.00240728i	$-0.000766263\pi$
$97$	4.90388	+	8.49377i	0.497914	+	0.862412i	−0.502083	+	0.864819i	$0.667433\pi$
$98$		0			0
$99$	2.64861			0.266196
$100$		0			0
$101$	0.0615528	−	0.106613i	0.00612473	−	0.0106084i	−0.862947	−	0.505295i	$-0.831384\pi$
$101$	0.0615528	−	0.106613i	0.00612473	−	0.0106084i	0.869072	+	0.494686i	$0.164717\pi$
$102$		0			0
$103$	8.68951			0.856203			0.428101	−	0.903731i	$-0.359183\pi$
$103$	8.68951			0.856203			0.428101	+	0.903731i	$0.359183\pi$
$104$		0			0
$105$	22.2462			2.17101
$106$		0			0
$107$	−4.86175	+	8.42080i	−0.470003	+	0.814069i	−0.999412	−	0.0342979i	$-0.989080\pi$
$107$	−4.86175	+	8.42080i	−0.470003	+	0.814069i	0.529409	+	0.848367i	$0.322414\pi$
$108$		0			0
$109$	1.12311			0.107574			0.0537870	−	0.998552i	$-0.482871\pi$
$109$	1.12311			0.107574			0.0537870	+	0.998552i	$0.482871\pi$
$110$		0			0
$111$	2.50345	+	4.33611i	0.237617	+	0.411565i
$112$		0			0
$113$	−8.18466	−	14.1762i	−0.769948	−	1.33359i	−0.937591	−	0.347741i	$-0.886949\pi$
$113$	−8.18466	−	14.1762i	−0.769948	−	1.33359i	0.167643	−	0.985848i	$-0.446385\pi$
$114$		0			0
$115$	−9.06134	+	15.6947i	−0.844975	+	1.46354i
$116$		0			0
$117$	8.56155	+	3.46410i	0.791516	+	0.320256i
$118$		0			0
$119$	−11.2745	+	19.5280i	−1.03353	+	1.79013i
$120$		0			0
$121$	4.96543	+	8.60039i	0.451403	+	0.781853i
$122$		0			0
$123$	−4.86175	−	8.42080i	−0.438369	−	0.759278i
$124$		0			0
$125$	8.80776			0.787790
$126$		0			0
$127$	−0.145160	+	0.251424i	−0.0128808	+	0.0223103i	−0.872394	−	0.488803i	$-0.837434\pi$
$127$	−0.145160	+	0.251424i	−0.0128808	+	0.0223103i	0.859513	+	0.511114i	$0.170767\pi$
$128$		0			0
$129$	−19.8078			−1.74398
$130$		0			0
$131$	11.3381			0.990616			0.495308	−	0.868717i	$-0.335055\pi$
$131$	11.3381			0.990616			0.495308	+	0.868717i	$0.335055\pi$
$132$		0			0
$133$	9.21922	−	15.9682i	0.799408	−	1.38462i
$134$		0			0
$135$	−2.64861			−0.227956
$136$		0			0
$137$	8.50000	+	14.7224i	0.726204	+	1.25782i	0.958477	+	0.285171i	$0.0920506\pi$
$137$	8.50000	+	14.7224i	0.726204	+	1.25782i	−0.232273	+	0.972651i	$0.574616\pi$
$138$		0			0
$139$	10.2405	+	17.7371i	0.868587	+	1.50444i	0.863441	+	0.504450i	$0.168305\pi$
$139$	10.2405	+	17.7371i	0.868587	+	1.50444i	0.00514635	+	0.999987i	$0.498362\pi$
$140$		0			0
$141$	12.6847	−	21.9705i	1.06824	−	1.85025i
$142$		0			0
$143$	−0.516994	−	3.69207i	−0.0432332	−	0.308747i
$144$		0			0
$145$	−6.40388	+	11.0918i	−0.531813	+	0.921128i
$146$		0			0
$147$	7.73704	+	13.4009i	0.638140	+	1.10529i
$148$		0			0
$149$	3.37689	+	5.84895i	0.276646	+	0.479165i	0.970549	−	0.240904i	$-0.0774437\pi$
$149$	3.37689	+	5.84895i	0.276646	+	0.479165i	−0.693903	+	0.720068i	$0.744110\pi$
$150$		0			0
$151$	−20.7713			−1.69034			−0.845172	−	0.534494i	$-0.820502\pi$
$151$	−20.7713			−1.69034			−0.845172	+	0.534494i	$0.820502\pi$
$152$		0			0
$153$	−7.84233	+	13.5833i	−0.634015	+	1.09815i
$154$		0			0
$155$	8.68951			0.697958
$156$		0			0
$157$	−0.315342			−0.0251670			−0.0125835	−	0.999921i	$-0.504006\pi$
$157$	−0.315342			−0.0251670			−0.0125835	+	0.999921i	$0.504006\pi$
$158$		0			0
$159$	−3.02045	+	5.23157i	−0.239537	+	0.414890i
$160$		0			0
$161$	−26.0540			−2.05334
$162$		0			0
$163$	−10.2405	−	17.7371i	−0.802097	−	1.38927i	−0.918233	−	0.396040i	$-0.870384\pi$
$163$	−10.2405	−	17.7371i	−0.802097	−	1.38927i	0.116136	−	0.993233i	$-0.462949\pi$
$164$		0			0
$165$	−3.12311	−	5.40938i	−0.243133	−	0.421119i
$166$		0			0
$167$	5.23358	−	9.06483i	0.404987	−	0.701458i	−0.589333	−	0.807890i	$-0.700609\pi$
$167$	5.23358	−	9.06483i	0.404987	−	0.701458i	0.994320	+	0.106432i	$0.0339428\pi$
$168$		0			0
$169$	3.15767	−	12.6107i	0.242898	−	0.970052i
$170$		0			0
$171$	6.41273	−	11.1072i	0.490394	−	0.849387i
$172$		0			0
$173$	−4.21922	−	7.30791i	−0.320782	−	0.555610i	0.659868	−	0.751382i	$-0.270612\pi$
$173$	−4.21922	−	7.30791i	−0.320782	−	0.555610i	−0.980650	+	0.195772i	$0.937279\pi$
$174$		0			0
$175$	−2.87529	−	4.98015i	−0.217351	−	0.376464i
$176$		0			0
$177$	−24.6847			−1.85541
$178$		0			0
$179$	2.87529	−	4.98015i	0.214909	−	0.372234i	−0.738335	−	0.674434i	$-0.764388\pi$
$179$	2.87529	−	4.98015i	0.214909	−	0.372234i	0.953244	+	0.302200i	$0.0977211\pi$
$180$		0			0
$181$	−20.8078			−1.54663			−0.773314	−	0.634023i	$-0.781403\pi$
$181$	−20.8078			−1.54663			−0.773314	+	0.634023i	$0.781403\pi$
$182$		0			0
$183$	26.5219			1.96055
$184$		0			0
$185$	2.71922	−	4.70983i	0.199921	−	0.346274i
$186$		0			0
$187$	6.33122			0.462984
$188$		0			0
$189$	−1.90388	−	3.29762i	−0.138487	−	0.239867i
$190$		0			0
$191$	−6.18606	−	10.7146i	−0.447607	−	0.775279i	0.550622	−	0.834754i	$-0.314390\pi$
$191$	−6.18606	−	10.7146i	−0.447607	−	0.775279i	−0.998230	+	0.0594759i	$0.981057\pi$
$192$		0			0
$193$	0.938447	−	1.62544i	0.0675509	−	0.117002i	−0.830272	−	0.557359i	$-0.811815\pi$
$193$	0.938447	−	1.62544i	0.0675509	−	0.117002i	0.897823	+	0.440357i	$0.145148\pi$
$194$		0			0
$195$	−3.02045	−	21.5703i	−0.216299	−	1.54468i
$196$		0			0
$197$	2.90388	−	5.02967i	0.206893	−	0.358349i	−0.743841	−	0.668356i	$-0.766998\pi$
$197$	2.90388	−	5.02967i	0.206893	−	0.358349i	0.950734	+	0.310007i	$0.100331\pi$
$198$		0			0
$199$	3.53744	+	6.12703i	0.250763	+	0.434334i	0.963736	−	0.266858i	$-0.0859853\pi$
$199$	3.53744	+	6.12703i	0.250763	+	0.434334i	−0.712973	+	0.701191i	$0.752652\pi$
$200$		0			0
$201$	−11.4654	−	19.8587i	−0.808709	−	1.40073i
$202$		0			0
$203$	−18.4130			−1.29234
$204$		0			0
$205$	−5.28078	+	9.14657i	−0.368825	+	0.638824i
$206$		0			0
$207$	−18.1227			−1.25961
$208$		0			0
$209$	−5.17708			−0.358106
$210$		0			0
$211$	1.17915	−	2.04234i	0.0811758	−	0.140601i	−0.822579	−	0.568650i	$-0.807466\pi$
$211$	1.17915	−	2.04234i	0.0811758	−	0.140601i	0.903755	+	0.428050i	$0.140799\pi$
$212$		0			0
$213$	−11.8078			−0.809055
$214$		0			0
$215$	10.7575	+	18.6325i	0.733654	+	1.27073i
$216$		0			0
$217$	6.24621	+	10.8188i	0.424020	+	0.734425i
$218$		0			0
$219$	−5.08842	+	8.81341i	−0.343844	+	0.595555i
$220$		0			0
$221$	20.4654	+	8.28055i	1.37665	+	0.557010i
$222$		0			0
$223$	6.18606	−	10.7146i	0.414249	−	0.717500i	−0.581100	−	0.813832i	$-0.697378\pi$
$223$	6.18606	−	10.7146i	0.414249	−	0.717500i	0.995349	+	0.0963317i	$0.0307110\pi$
$224$		0			0
$225$	−2.00000	−	3.46410i	−0.133333	−	0.230940i
$226$		0			0
$227$	3.24712	+	5.62418i	0.215519	+	0.373290i	0.953433	−	0.301605i	$-0.0975223\pi$
$227$	3.24712	+	5.62418i	0.215519	+	0.373290i	−0.737914	+	0.674895i	$0.764189\pi$
$228$		0			0
$229$	−19.3693			−1.27996			−0.639980	−	0.768391i	$-0.721057\pi$
$229$	−19.3693			−1.27996			−0.639980	+	0.768391i	$0.721057\pi$
$230$		0			0
$231$	4.48991	−	7.77676i	0.295415	−	0.511673i
$232$		0			0
$233$	−15.3693			−1.00688			−0.503439	−	0.864031i	$-0.667932\pi$
$233$	−15.3693			−1.00688			−0.503439	+	0.864031i	$0.667932\pi$
$234$		0			0
$235$	−27.5559			−1.79755
$236$		0			0
$237$	13.5616	−	23.4893i	0.880918	−	1.52579i
$238$		0			0
$239$	−6.78456			−0.438857			−0.219428	−	0.975629i	$-0.570419\pi$
$239$	−6.78456			−0.438857			−0.219428	+	0.975629i	$0.570419\pi$
$240$		0			0
$241$	8.93845	+	15.4818i	0.575776	+	0.997273i	0.995957	+	0.0898329i	$0.0286333\pi$
$241$	8.93845	+	15.4818i	0.575776	+	0.997273i	−0.420181	+	0.907440i	$0.638033\pi$
$242$		0			0
$243$	−10.3857	−	17.9885i	−0.666240	−	1.15396i
$244$		0			0
$245$	8.40388	−	14.5560i	0.536904	−	0.929946i
$246$		0			0
$247$	−16.7347	−	6.77106i	−1.06481	−	0.430833i
$248$		0			0
$249$	−3.12311	+	5.40938i	−0.197919	+	0.342805i
$250$		0			0
$251$	0.145160	+	0.251424i	0.00916240	+	0.0158697i	0.870570	−	0.492044i	$-0.163750\pi$
$251$	0.145160	+	0.251424i	0.00916240	+	0.0158697i	−0.861408	+	0.507914i	$0.830417\pi$
$252$		0			0
$253$	3.65767	+	6.33527i	0.229956	+	0.398295i
$254$		0			0
$255$	36.9890			2.31634
$256$		0			0
$257$	2.06155	−	3.57071i	0.128596	−	0.222735i	−0.794537	−	0.607216i	$-0.792286\pi$
$257$	2.06155	−	3.57071i	0.128596	−	0.222735i	0.923133	+	0.384481i	$0.125620\pi$
$258$		0			0
$259$	7.81855			0.485821
$260$		0			0
$261$	−12.8078			−0.792781
$262$		0			0
$263$	−3.45593	+	5.98584i	−0.213102	+	0.369103i	−0.952684	−	0.303964i	$-0.901690\pi$
$263$	−3.45593	+	5.98584i	−0.213102	+	0.369103i	0.739582	+	0.673066i	$0.235023\pi$
$264$		0			0
$265$	6.56155			0.403073
$266$		0			0
$267$	12.5988	+	21.8217i	0.771033	+	1.33547i
$268$		0			0
$269$	9.34233	+	16.1814i	0.569612	+	0.986597i	0.996604	+	0.0823414i	$0.0262398\pi$
$269$	9.34233	+	16.1814i	0.569612	+	0.986597i	−0.426992	+	0.904255i	$0.640427\pi$
$270$		0			0
$271$	5.23358	−	9.06483i	0.317918	−	0.550649i	−0.662136	−	0.749384i	$-0.730350\pi$
$271$	5.23358	−	9.06483i	0.317918	−	0.550649i	0.980053	+	0.198735i	$0.0636832\pi$
$272$		0			0
$273$	24.6847	−	19.2658i	1.49398	−	1.16602i
$274$		0			0
$275$	−0.807313	+	1.39831i	−0.0486828	+	0.0843211i
$276$		0			0
$277$	−0.815342	−	1.41221i	−0.0489891	−	0.0848517i	0.840491	−	0.541825i	$-0.182267\pi$
$277$	−0.815342	−	1.41221i	−0.0489891	−	0.0848517i	−0.889480	+	0.456974i	$0.848933\pi$
$278$		0			0
$279$	4.34475	+	7.52534i	0.260114	+	0.450530i
$280$		0			0
$281$	−12.3153			−0.734672			−0.367336	−	0.930088i	$-0.619730\pi$
$281$	−12.3153			−0.734672			−0.367336	+	0.930088i	$0.619730\pi$
$282$		0			0
$283$	−12.5988	+	21.8217i	−0.748920	+	1.29717i	0.199421	+	0.979914i	$0.436094\pi$
$283$	−12.5988	+	21.8217i	−0.748920	+	1.29717i	−0.948341	+	0.317254i	$0.897239\pi$
$284$		0			0
$285$	−30.2462			−1.79163
$286$		0			0
$287$	−15.1838			−0.896269
$288$		0			0
$289$	−10.2462	+	17.7470i	−0.602718	+	1.04394i
$290$		0			0
$291$	23.1296			1.35588
$292$		0			0
$293$	0.500000	+	0.866025i	0.0292103	+	0.0505937i	0.880261	−	0.474490i	$-0.157367\pi$
$293$	0.500000	+	0.866025i	0.0292103	+	0.0505937i	−0.851051	+	0.525084i	$0.824034\pi$
$294$		0			0
$295$	13.4061	+	23.2200i	0.780533	+	1.35192i
$296$		0			0
$297$	−0.534565	+	0.925894i	−0.0310186	+	0.0537258i
$298$		0			0
$299$	3.53744	+	25.2624i	0.204576	+	1.46096i
$300$		0			0
$301$	−15.4654	+	26.7869i	−0.891413	+	1.54397i
$302$		0			0
$303$	−0.145160	−	0.251424i	−0.00833920	−	0.0144439i
$304$		0			0
$305$	−14.4039	−	24.9483i	−0.824764	−	1.42853i
$306$		0			0
$307$	−19.6100			−1.11920			−0.559602	−	0.828762i	$-0.689046\pi$
$307$	−19.6100			−1.11920			−0.559602	+	0.828762i	$0.689046\pi$
$308$		0			0
$309$	10.2462	−	17.7470i	0.582887	−	1.00959i
$310$		0			0
$311$	10.1768			0.577076			0.288538	−	0.957468i	$-0.406831\pi$
$311$	10.1768			0.577076			0.288538	+	0.957468i	$0.406831\pi$
$312$		0			0
$313$	13.1231			0.741762			0.370881	−	0.928680i	$-0.379056\pi$
$313$	13.1231			0.741762			0.370881	+	0.928680i	$0.379056\pi$
$314$		0			0
$315$	12.0818	−	20.9263i	0.680732	−	1.17906i
$316$		0			0
$317$	2.80776			0.157700			0.0788499	−	0.996887i	$-0.474875\pi$
$317$	2.80776			0.157700			0.0788499	+	0.996887i	$0.474875\pi$
$318$		0			0
$319$	2.58497	+	4.47730i	0.144730	+	0.250681i
$320$		0			0
$321$	11.4654	+	19.8587i	0.639938	+	1.10841i
$322$		0			0
$323$	15.3289	−	26.5505i	0.852924	−	1.47731i
$324$		0			0
$325$	−4.43845	+	3.46410i	−0.246201	+	0.192154i
$326$		0			0
$327$	1.32431	−	2.29377i	0.0732343	−	0.126846i
$328$		0			0
$329$	−19.8078	−	34.3081i	−1.09204	−	1.89146i
$330$		0			0
$331$	−7.59188	−	13.1495i	−0.417287	−	0.722763i	0.578378	−	0.815769i	$-0.303686\pi$
$331$	−7.59188	−	13.1495i	−0.417287	−	0.722763i	−0.995666	+	0.0930059i	$0.970352\pi$
$332$		0			0
$333$	5.43845			0.298025
$334$		0			0
$335$	−12.4536	+	21.5703i	−0.680414	+	1.17851i
$336$		0			0
$337$	34.4233			1.87516			0.937578	−	0.347775i	$-0.113063\pi$
$337$	34.4233			1.87516			0.937578	+	0.347775i	$0.113063\pi$
$338$		0			0
$339$	−38.6037			−2.09666
$340$		0			0
$341$	1.75379	−	3.03765i	0.0949730	−	0.164498i
$342$		0			0
$343$	−1.61463			−0.0871816
$344$		0			0
$345$	21.3693	+	37.0127i	1.15049	+	1.99270i
$346$		0			0
$347$	−2.50345	−	4.33611i	−0.134392	−	0.232775i	0.790973	−	0.611851i	$-0.209575\pi$
$347$	−2.50345	−	4.33611i	−0.134392	−	0.232775i	−0.925365	+	0.379077i	$0.876242\pi$
$348$		0			0
$349$	14.2192	−	24.6284i	0.761138	−	1.31833i	−0.181127	−	0.983460i	$-0.557975\pi$
$349$	14.2192	−	24.6284i	0.761138	−	1.31833i	0.942265	−	0.334869i	$-0.108692\pi$
$350$		0			0
$351$	−2.93893	+	2.29377i	−0.156869	+	0.122432i
$352$		0			0
$353$	6.74621	−	11.6848i	0.359065	−	0.621918i	−0.628740	−	0.777615i	$-0.716429\pi$
$353$	6.74621	−	11.6848i	0.359065	−	0.621918i	0.987805	+	0.155697i	$0.0497624\pi$
$354$		0			0
$355$	6.41273	+	11.1072i	0.340352	+	0.589508i
$356$		0			0
$357$	26.5885	+	46.0527i	1.40721	+	2.43737i
$358$		0			0
$359$	−1.48734			−0.0784986			−0.0392493	−	0.999229i	$-0.512497\pi$
$359$	−1.48734			−0.0784986			−0.0392493	+	0.999229i	$0.512497\pi$
$360$		0			0
$361$	−3.03457	+	5.25602i	−0.159714	+	0.276633i
$362$		0			0
$363$	23.4199			1.22923
$364$		0			0
$365$	11.0540			0.578592
$366$		0			0
$367$	−3.24712	+	5.62418i	−0.169498	+	0.293580i	−0.938244	−	0.345975i	$-0.887548\pi$
$367$	−3.24712	+	5.62418i	−0.169498	+	0.293580i	0.768745	+	0.639555i	$0.220881\pi$
$368$		0			0
$369$	−10.5616			−0.549812
$370$		0			0
$371$	4.71659	+	8.16937i	0.244873	+	0.424133i
$372$		0			0
$373$	−12.1847	−	21.1044i	−0.630898	−	1.09275i	−0.987369	−	0.158440i	$-0.949353\pi$
$373$	−12.1847	−	21.1044i	−0.630898	−	1.09275i	0.356471	−	0.934306i	$-0.383980\pi$
$374$		0			0
$375$	10.3857	−	17.9885i	0.536313	−	0.928921i
$376$		0			0
$377$	2.50000	+	17.8536i	0.128757	+	0.919506i
$378$		0			0
$379$	1.17915	−	2.04234i	0.0605687	−	0.104908i	−0.834151	−	0.551536i	$-0.814042\pi$
$379$	1.17915	−	2.04234i	0.0605687	−	0.104908i	0.894720	+	0.446628i	$0.147375\pi$
$380$		0			0
$381$	0.342329	+	0.592932i	0.0175381	+	0.0303768i
$382$		0			0
$383$	6.84821	+	11.8614i	0.349927	+	0.606092i	0.986236	−	0.165343i	$-0.0528730\pi$
$383$	6.84821	+	11.8614i	0.349927	+	0.606092i	−0.636309	+	0.771434i	$0.719540\pi$
$384$		0			0
$385$	−9.75379			−0.497099
$386$		0			0
$387$	−10.7575	+	18.6325i	−0.546834	+	0.947144i
$388$		0			0
$389$	6.80776			0.345167			0.172584	−	0.984995i	$-0.444788\pi$
$389$	6.80776			0.345167			0.172584	+	0.984995i	$0.444788\pi$
$390$		0			0
$391$	−43.3203			−2.19080
$392$		0			0
$393$	13.3693	−	23.1563i	0.674393	−	1.16808i
$394$		0			0
$395$	−29.4608			−1.48233
$396$		0			0
$397$	9.34233	+	16.1814i	0.468878	+	0.812121i	0.999367	−	0.0355711i	$-0.0113250\pi$
$397$	9.34233	+	16.1814i	0.468878	+	0.812121i	−0.530489	+	0.847692i	$0.677992\pi$
$398$		0			0
$399$	−21.7416	−	37.6576i	−1.08844	−	1.88524i
$400$		0			0
$401$	7.18466	−	12.4442i	0.358785	−	0.621433i	−0.628973	−	0.777427i	$-0.716525\pi$
$401$	7.18466	−	12.4442i	0.358785	−	0.621433i	0.987758	+	0.155993i	$0.0498579\pi$
$402$		0			0
$403$	9.64198	−	7.52534i	0.480301	−	0.374864i
$404$		0			0
$405$	−12.9654	+	22.4568i	−0.644258	+	1.11589i
$406$		0			0
$407$	−1.09763	−	1.90116i	−0.0544076	−	0.0942368i
$408$		0			0
$409$	2.06155	+	3.57071i	0.101937	+	0.176560i	0.912483	−	0.409115i	$-0.134163\pi$
$409$	2.06155	+	3.57071i	0.101937	+	0.176560i	−0.810546	+	0.585676i	$0.800829\pi$
$410$		0			0
$411$	40.0910			1.97754
$412$		0			0
$413$	−19.2732	+	33.3822i	−0.948372	+	1.64263i
$414$		0			0
$415$	6.78456			0.333041
$416$		0			0
$417$	48.3002			2.36527
$418$		0			0
$419$	13.5513	−	23.4715i	0.662022	−	1.14666i	−0.318061	−	0.948070i	$-0.603032\pi$
$419$	13.5513	−	23.4715i	0.662022	−	1.14666i	0.980083	−	0.198586i	$-0.0636349\pi$
$420$		0			0
$421$	15.6847			0.764423			0.382212	−	0.924075i	$-0.375162\pi$
$421$	15.6847			0.764423			0.382212	+	0.924075i	$0.375162\pi$
$422$		0			0
$423$	−13.7779	−	23.8641i	−0.669906	−	1.16031i
$424$		0			0
$425$	−4.78078	−	8.28055i	−0.231902	−	0.401666i
$426$		0			0
$427$	20.7077	−	35.8667i	1.00211	−	1.73571i
$428$		0			0
$429$	−8.15009	−	3.29762i	−0.393490	−	0.159211i
$430$		0			0
$431$	10.9842	−	19.0251i	0.529088	−	0.916408i	−0.470336	−	0.882487i	$-0.655867\pi$
$431$	10.9842	−	19.0251i	0.529088	−	0.916408i	0.999425	−	0.0339206i	$-0.0107993\pi$
$432$		0			0
$433$	19.1847	+	33.2288i	0.921956	+	1.59687i	0.796385	+	0.604790i	$0.206743\pi$
$433$	19.1847	+	33.2288i	0.921956	+	1.59687i	0.125571	+	0.992085i	$0.459924\pi$
$434$		0			0
$435$	15.1022	+	26.1578i	0.724097	+	1.25417i
$436$		0			0
$437$	35.4233			1.69453
$438$		0			0
$439$	7.59188	−	13.1495i	0.362341	−	0.627592i	−0.626005	−	0.779819i	$-0.715311\pi$
$439$	7.59188	−	13.1495i	0.362341	−	0.627592i	0.988346	+	0.152227i	$0.0486444\pi$
$440$		0			0
$441$	16.8078			0.800370
$442$		0			0
$443$	2.64861			0.125839			0.0629197	−	0.998019i	$-0.479959\pi$
$443$	2.64861			0.125839			0.0629197	+	0.998019i	$0.479959\pi$
$444$		0			0
$445$	13.6847	−	23.7025i	0.648715	−	1.12361i
$446$		0			0
$447$	15.9274			0.753341
$448$		0			0
$449$	4.21922	+	7.30791i	0.199117	+	0.344882i	0.948243	−	0.317547i	$-0.102859\pi$
$449$	4.21922	+	7.30791i	0.199117	+	0.344882i	−0.749125	+	0.662429i	$0.769526\pi$
$450$		0			0
$451$	2.13162	+	3.69207i	0.100374	+	0.173853i
$452$		0			0
$453$	−24.4924	+	42.4221i	−1.15075	+	1.99317i
$454$		0			0
$455$	−31.5288	−	12.7569i	−1.47809	−	0.598053i
$456$		0			0
$457$	18.7462	−	32.4694i	0.876911	−	1.51885i	0.0221975	−	0.999754i	$-0.492934\pi$
$457$	18.7462	−	32.4694i	0.876911	−	1.51885i	0.854713	−	0.519100i	$-0.173733\pi$
$458$		0			0
$459$	−3.16561	−	5.48299i	−0.147758	−	0.255924i
$460$		0			0
$461$	−3.06155	−	5.30277i	−0.142591	−	0.246974i	0.785881	−	0.618378i	$-0.212210\pi$
$461$	−3.06155	−	5.30277i	−0.142591	−	0.246974i	−0.928471	+	0.371404i	$0.878877\pi$
$462$		0			0
$463$	−6.78456			−0.315305			−0.157653	−	0.987495i	$-0.550393\pi$
$463$	−6.78456			−0.315305			−0.157653	+	0.987495i	$0.550393\pi$
$464$		0			0
$465$	10.2462	−	17.7470i	0.475157	−	0.822995i
$466$		0			0
$467$	−11.5012			−0.532210			−0.266105	−	0.963944i	$-0.585737\pi$
$467$	−11.5012			−0.532210			−0.266105	+	0.963944i	$0.585737\pi$
$468$		0			0
$469$	−35.8078			−1.65345
$470$		0			0
$471$	−0.371834	+	0.644036i	−0.0171332	+	0.0296756i
$472$		0			0
$473$	8.68466			0.399321
$474$		0			0
$475$	3.90928	+	6.77106i	0.179370	+	0.310678i
$476$		0			0
$477$	3.28078	+	5.68247i	0.150216	+	0.260182i
$478$		0			0
$479$	5.89574	−	10.2117i	0.269383	−	0.466585i	−0.699320	−	0.714809i	$-0.746514\pi$
$479$	5.89574	−	10.2117i	0.269383	−	0.466585i	0.968703	+	0.248224i	$0.0798469\pi$
$480$		0			0
$481$	−1.06155	−	7.58100i	−0.0484026	−	0.345664i
$482$		0			0
$483$	−30.7215	+	53.2112i	−1.39788	+	2.42119i
$484$		0			0
$485$	−12.5616	−	21.7572i	−0.570391	−	0.987946i
$486$		0			0
$487$	18.0590	+	31.2792i	0.818333	+	1.41739i	0.906909	+	0.421326i	$0.138435\pi$
$487$	18.0590	+	31.2792i	0.818333	+	1.41739i	−0.0885761	+	0.996069i	$0.528232\pi$
$488$		0			0
$489$	−48.3002			−2.18421
$490$		0			0
$491$	2.42194	−	4.19492i	0.109301	−	0.189314i	−0.806187	−	0.591661i	$-0.798472\pi$
$491$	2.42194	−	4.19492i	0.109301	−	0.189314i	0.915487	+	0.402347i	$0.131806\pi$
$492$		0			0
$493$	−30.6155			−1.37885
$494$		0			0
$495$	−6.78456			−0.304943
$496$		0			0
$497$	−9.21922	+	15.9682i	−0.413539	+	0.716270i
$498$		0			0
$499$	31.6918			1.41872			0.709360	−	0.704846i	$-0.248984\pi$
$499$	31.6918			1.41872			0.709360	+	0.704846i	$0.248984\pi$
$500$		0			0
$501$	−12.3423	−	21.3775i	−0.551415	−	0.955078i
$502$		0			0
$503$	16.2814	+	28.2002i	0.725951	+	1.25738i	0.958581	+	0.284819i	$0.0919335\pi$
$503$	16.2814	+	28.2002i	0.725951	+	1.25738i	−0.232630	+	0.972565i	$0.574733\pi$
$504$		0			0
$505$	−0.157671	+	0.273094i	−0.00701626	+	0.0121525i
$506$		0			0
$507$	−22.0320	−	21.3189i	−0.978474	−	0.946805i
$508$		0			0
$509$	5.18466	−	8.98009i	0.229806	−	0.398036i	−0.727945	−	0.685636i	$-0.759524\pi$
$509$	5.18466	−	8.98009i	0.229806	−	0.398036i	0.957750	+	0.287600i	$0.0928575\pi$
$510$		0			0
$511$	7.94584	+	13.7626i	0.351503	+	0.608822i
$512$		0			0
$513$	2.58854	+	4.48348i	0.114287	+	0.197951i
$514$		0			0
$515$	−22.2586			−0.980833
$516$		0			0
$517$	−5.56155	+	9.63289i	−0.244597	+	0.423654i
$518$		0			0
$519$	−19.9003			−0.873528
$520$		0			0
$521$	33.4384			1.46496			0.732482	−	0.680786i	$-0.238362\pi$
$521$	33.4384			1.46496			0.732482	+	0.680786i	$0.238362\pi$
$522$		0			0
$523$	−14.9571	+	25.9064i	−0.654027	+	1.13281i	0.328109	+	0.944640i	$0.393589\pi$
$523$	−14.9571	+	25.9064i	−0.654027	+	1.13281i	−0.982137	+	0.188169i	$0.939745\pi$
$524$		0			0
$525$	−13.5616			−0.591875
$526$		0			0
$527$	10.3857	+	17.9885i	0.452406	+	0.783590i
$528$		0			0
$529$	−13.5270	−	23.4294i	−0.588130	−	1.01867i
$530$		0			0
$531$	−13.4061	+	23.2200i	−0.581775	+	1.00766i
$532$		0			0
$533$	2.06155	+	14.7224i	0.0892958	+	0.637699i
$534$		0			0
$535$	12.4536	−	21.5703i	0.538417	−	0.932566i
$536$		0			0
$537$	−6.78078	−	11.7446i	−0.292612	−	0.506819i
$538$		0			0
$539$	−3.39228	−	5.87560i	−0.146116	−	0.253080i
$540$		0			0
$541$	−10.1771			−0.437547			−0.218773	−	0.975776i	$-0.570206\pi$
$541$	−10.1771			−0.437547			−0.218773	+	0.975776i	$0.570206\pi$
$542$		0			0
$543$	−24.5354	+	42.4966i	−1.05292	+	1.82370i
$544$		0			0
$545$	−2.87689			−0.123233
$546$		0			0
$547$	19.6100			0.838464			0.419232	−	0.907879i	$-0.362299\pi$
$547$	19.6100			0.838464			0.419232	+	0.907879i	$0.362299\pi$
$548$		0			0
$549$	14.4039	−	24.9483i	0.614743	−	1.06477i
$550$		0			0
$551$	25.0345			1.06651
$552$		0			0
$553$	−21.1771	−	36.6798i	−0.900541	−	1.55978i
$554$		0			0
$555$	−6.41273	−	11.1072i	−0.272205	−	0.471473i
$556$		0			0
$557$	−17.9924	+	31.1638i	−0.762363	+	1.32045i	0.179266	+	0.983801i	$0.442628\pi$
$557$	−17.9924	+	31.1638i	−0.762363	+	1.32045i	−0.941629	+	0.336651i	$0.890706\pi$
$558$		0			0
$559$	28.0729	+	11.3586i	1.18736	+	0.480418i
$560$		0			0
$561$	7.46543	−	12.9305i	0.315191	−	0.545927i
$562$		0			0
$563$	10.2405	+	17.7371i	0.431585	+	0.747528i	0.997010	−	0.0772723i	$-0.0246211\pi$
$563$	10.2405	+	17.7371i	0.431585	+	0.747528i	−0.565425	+	0.824800i	$0.691288\pi$
$564$		0			0
$565$	20.9654	+	36.3132i	0.882022	+	1.52771i
$566$		0			0
$567$	−37.2794			−1.56559
$568$		0			0
$569$	−17.8348	+	30.8907i	−0.747672	+	1.29501i	0.201264	+	0.979537i	$0.435495\pi$
$569$	−17.8348	+	30.8907i	−0.747672	+	1.29501i	−0.948936	+	0.315468i	$0.897838\pi$
$570$		0			0
$571$	−13.2431			−0.554205			−0.277103	−	0.960840i	$-0.589374\pi$
$571$	−13.2431			−0.554205			−0.277103	+	0.960840i	$0.589374\pi$
$572$		0			0
$573$	−29.1771			−1.21889
$574$		0			0
$575$	5.52390	−	9.56768i	0.230363	−	0.399000i
$576$		0			0
$577$	13.9309			0.579950			0.289975	−	0.957034i	$-0.406353\pi$
$577$	13.9309			0.579950			0.289975	+	0.957034i	$0.406353\pi$
$578$		0			0
$579$	−2.21313	−	3.83326i	−0.0919747	−	0.159305i
$580$		0			0
$581$	4.87689	+	8.44703i	0.202328	+	0.350442i
$582$		0			0
$583$	1.32431	−	2.29377i	0.0548472	−	0.0949981i
$584$		0			0
$585$	−21.9309	−	8.87348i	−0.906730	−	0.366873i
$586$		0			0
$587$	21.2883	−	36.8724i	0.878662	−	1.52189i	0.0258520	−	0.999666i	$-0.491770\pi$
$587$	21.2883	−	36.8724i	0.878662	−	1.52189i	0.852810	−	0.522221i	$-0.174897\pi$
$588$		0			0
$589$	−8.49242	−	14.7093i	−0.349924	−	0.606086i
$590$		0			0
$591$	−6.84821	−	11.8614i	−0.281698	−	0.487915i
$592$		0			0
$593$	−11.0540			−0.453932			−0.226966	−	0.973903i	$-0.572881\pi$
$593$	−11.0540			−0.453932			−0.226966	+	0.973903i	$0.572881\pi$
$594$		0			0
$595$	28.8802	−	50.0219i	1.18397	−	2.05070i
$596$		0			0
$597$	16.6847			0.682858
$598$		0			0
$599$	−1.32431			−0.0541097			−0.0270549	−	0.999634i	$-0.508613\pi$
$599$	−1.32431			−0.0541097			−0.0270549	+	0.999634i	$0.508613\pi$
$600$		0			0
$601$	−3.06155	+	5.30277i	−0.124883	+	0.216304i	−0.921687	−	0.387934i	$-0.873189\pi$
$601$	−3.06155	+	5.30277i	−0.124883	+	0.216304i	0.796804	+	0.604238i	$0.206522\pi$
$602$		0			0
$603$	−24.9073			−1.01430
$604$		0			0
$605$	−12.7192	−	22.0303i	−0.517110	−	0.895661i
$606$		0			0
$607$	13.7143	+	23.7538i	0.556646	+	0.964139i	0.997773	+	0.0666944i	$0.0212453\pi$
$607$	13.7143	+	23.7538i	0.556646	+	0.964139i	−0.441128	+	0.897444i	$0.645421\pi$
$608$		0			0
$609$	−21.7116	+	37.6057i	−0.879800	+	1.52386i
$610$		0			0
$611$	−30.5763	+	23.8641i	−1.23699	+	0.965437i
$612$		0			0
$613$	13.1847	−	22.8365i	0.532523	−	0.922357i	−0.466755	−	0.884386i	$-0.654577\pi$
$613$	13.1847	−	22.8365i	0.532523	−	0.922357i	0.999279	−	0.0379711i	$-0.0120895\pi$
$614$		0			0
$615$	12.4536	+	21.5703i	0.502179	+	0.869799i
$616$		0			0
$617$	−4.62311	−	8.00745i	−0.186119	−	0.322368i	0.757834	−	0.652448i	$-0.226258\pi$
$617$	−4.62311	−	8.00745i	−0.186119	−	0.322368i	−0.943953	+	0.330080i	$0.892924\pi$
$618$		0			0
$619$	−2.64861			−0.106457			−0.0532284	−	0.998582i	$-0.516951\pi$
$619$	−2.64861			−0.106457			−0.0532284	+	0.998582i	$0.516951\pi$
$620$		0			0
$621$	3.65767	−	6.33527i	0.146777	−	0.254226i
$622$		0			0
$623$	39.3473			1.57642
$624$		0			0
$625$	−30.3693			−1.21477
$626$		0			0
$627$	−6.10454	+	10.5734i	−0.243792	+	0.422260i
$628$		0			0
$629$	13.0000			0.518344
$630$		0			0
$631$	10.5308	+	18.2399i	0.419225	+	0.726119i	0.995862	−	0.0908818i	$-0.0289685\pi$
$631$	10.5308	+	18.2399i	0.419225	+	0.726119i	−0.576637	+	0.817001i	$0.695635\pi$
$632$		0			0
$633$	−2.78078	−	4.81645i	−0.110526	−	0.191437i
$634$		0			0
$635$	0.371834	−	0.644036i	0.0147558	−	0.0255578i
$636$		0			0
$637$	−3.28078	−	23.4294i	−0.129989	−	0.928308i
$638$		0			0
$639$	−6.41273	+	11.1072i	−0.253684	+	0.439393i
$640$		0			0
$641$	−5.30776	−	9.19332i	−0.209644	−	0.363114i	0.741958	−	0.670446i	$-0.233897\pi$
$641$	−5.30776	−	9.19332i	−0.209644	−	0.363114i	−0.951602	+	0.307332i	$0.900564\pi$
$642$		0			0
$643$	−16.2814	−	28.2002i	−0.642075	−	1.11211i	−0.984969	−	0.172733i	$-0.944740\pi$
$643$	−16.2814	−	28.2002i	−0.642075	−	1.11211i	0.342894	−	0.939374i	$-0.388593\pi$
$644$		0			0
$645$	50.7386			1.99783
$646$		0			0
$647$	24.7621	−	42.8892i	0.973498	−	1.68615i	0.288694	−	0.957421i	$-0.406779\pi$
$647$	24.7621	−	42.8892i	0.973498	−	1.68615i	0.684804	−	0.728727i	$-0.259888\pi$
$648$		0			0
$649$	10.8229			0.424837
$650$		0			0
$651$	29.4608			1.15466
$652$		0			0
$653$	−1.78078	+	3.08440i	−0.0696872	+	0.120702i	−0.898764	−	0.438434i	$-0.855533\pi$
$653$	−1.78078	+	3.08440i	−0.0696872	+	0.120702i	0.829076	+	0.559135i	$0.188867\pi$
$654$		0			0
$655$	−29.0432			−1.13481
$656$		0			0
$657$	5.52699	+	9.57302i	0.215628	+	0.373479i
$658$		0			0
$659$	−18.9300	−	32.7877i	−0.737408	−	1.27723i	−0.953659	−	0.300890i	$-0.902716\pi$
$659$	−18.9300	−	32.7877i	−0.737408	−	1.27723i	0.216251	−	0.976338i	$-0.430617\pi$
$660$		0			0
$661$	12.0616	−	20.8912i	0.469140	−	0.812574i	−0.530238	−	0.847849i	$-0.677897\pi$
$661$	12.0616	−	20.8912i	0.469140	−	0.812574i	0.999378	+	0.0352747i	$0.0112306\pi$
$662$		0			0
$663$	41.0435	−	32.0335i	1.59400	−	1.24408i
$664$		0			0
$665$	−23.6155	+	40.9033i	−0.915771	+	1.58616i
$666$		0			0
$667$	−17.6872	−	30.6351i	−0.684851	−	1.18620i
$668$		0			0
$669$	−14.5885	−	25.2681i	−0.564026	−	0.976921i
$670$		0			0
$671$	−11.6284			−0.448911
$672$		0			0
$673$	11.8693	−	20.5583i	0.457529	−	0.792463i	−0.541301	−	0.840829i	$-0.682068\pi$
$673$	11.8693	−	20.5583i	0.457529	−	0.792463i	0.998830	+	0.0483661i	$0.0154014\pi$
$674$		0			0
$675$	1.61463			0.0621470
$676$		0			0
$677$	−14.8769			−0.571765			−0.285883	−	0.958265i	$-0.592287\pi$
$677$	−14.8769			−0.571765			−0.285883	+	0.958265i	$0.592287\pi$
$678$		0			0
$679$	18.0590	−	31.2792i	0.693042	−	1.20038i
$680$		0			0
$681$	15.3153			0.586885
$682$		0			0
$683$	3.24712	+	5.62418i	0.124248	+	0.215203i	0.921439	−	0.388524i	$-0.127015\pi$
$683$	3.24712	+	5.62418i	0.124248	+	0.215203i	−0.797191	+	0.603727i	$0.793682\pi$
$684$		0			0
$685$	−21.7732	−	37.7123i	−0.831911	−	1.44091i
$686$		0			0
$687$	−22.8393	+	39.5588i	−0.871373	+	1.50926i
$688$		0			0
$689$	7.28078	−	5.68247i	0.277375	−	0.216485i
$690$		0			0
$691$	−4.65294	+	8.05914i	−0.177006	+	0.306584i	−0.940854	−	0.338813i	$-0.889975\pi$
$691$	−4.65294	+	8.05914i	−0.177006	+	0.306584i	0.763847	+	0.645397i	$0.223308\pi$
$692$		0			0
$693$	−4.87689	−	8.44703i	−0.185258	−	0.320876i
$694$		0			0
$695$	−26.2316	−	45.4344i	−0.995020	−	1.72342i
$696$		0			0
$697$	−25.2462			−0.956268
$698$		0			0
$699$	−18.1227	+	31.3894i	−0.685463	+	1.18726i
$700$		0			0
$701$	−14.8769			−0.561893			−0.280946	−	0.959723i	$-0.590648\pi$
$701$	−14.8769			−0.561893			−0.280946	+	0.959723i	$0.590648\pi$
$702$		0			0
$703$	−10.6302			−0.400925
$704$		0			0
$705$	−32.4924	+	56.2785i	−1.22374	+	2.11957i
$706$		0			0
$707$	−0.453349			−0.0170499
$708$		0			0
$709$	10.0616	+	17.4271i	0.377870	+	0.654489i	0.990752	−	0.135685i	$-0.0433234\pi$
$709$	10.0616	+	17.4271i	0.377870	+	0.654489i	−0.612883	+	0.790174i	$0.709990\pi$
$710$		0			0
$711$	−14.7304	−	25.5138i	−0.552433	−	0.956843i
$712$		0			0
$713$	−12.0000	+	20.7846i	−0.449404	+	0.778390i
$714$		0			0
$715$	1.32431	+	9.45744i	0.0495263	+	0.353688i
$716$		0			0
$717$	−8.00000	+	13.8564i	−0.298765	+	0.517477i
$718$		0			0
$719$	−7.13853	−	12.3643i	−0.266222	−	0.461110i	0.701661	−	0.712511i	$-0.252442\pi$
$719$	−7.13853	−	12.3643i	−0.266222	−	0.461110i	−0.967883	+	0.251401i	$0.919109\pi$
$720$		0			0
$721$	−16.0000	−	27.7128i	−0.595871	−	1.03208i
$722$		0			0
$723$	42.1590			1.56791
$724$		0			0
$725$	3.90388	−	6.76172i	0.144987	−	0.251124i
$726$		0			0
$727$	−25.6509			−0.951340			−0.475670	−	0.879624i	$-0.657794\pi$
$727$	−25.6509			−0.951340			−0.475670	+	0.879624i	$0.657794\pi$
$728$		0			0
$729$	−18.6155			−0.689464
$730$		0			0
$731$	−25.7146	+	44.5389i	−0.951088	+	1.64733i
$732$		0			0
$733$	−11.9309			−0.440677			−0.220338	−	0.975424i	$-0.570716\pi$
$733$	−11.9309			−0.440677			−0.220338	+	0.975424i	$0.570716\pi$
$734$		0			0
$735$	−19.8188	−	34.3272i	−0.731029	−	1.26618i
$736$		0			0
$737$	5.02699	+	8.70700i	0.185171	+	0.320726i
$738$		0			0
$739$	−3.61896	+	6.26822i	−0.133125	+	0.230580i	−0.924880	−	0.380260i	$-0.875835\pi$
$739$	−3.61896	+	6.26822i	−0.133125	+	0.230580i	0.791754	+	0.610840i	$0.209168\pi$
$740$		0			0
$741$	−33.5616	+	26.1940i	−1.23291	+	0.962260i
$742$		0			0
$743$	−13.9231	+	24.1155i	−0.510789	+	0.884712i	0.489133	+	0.872209i	$0.337313\pi$
$743$	−13.9231	+	24.1155i	−0.510789	+	0.884712i	−0.999922	+	0.0125029i	$0.996020\pi$
$744$		0			0
$745$	−8.65009	−	14.9824i	−0.316915	−	0.548913i
$746$		0			0
$747$	3.39228	+	5.87560i	0.124117	+	0.214977i
$748$		0			0
$749$	35.8078			1.30839
$750$		0			0
$751$	−10.9842	+	19.0251i	−0.400818	+	0.694237i	−0.993825	−	0.110961i	$-0.964607\pi$
$751$	−10.9842	+	19.0251i	−0.400818	+	0.694237i	0.593007	+	0.805197i	$0.297941\pi$
$752$		0			0
$753$	0.684658			0.0249503
$754$		0			0
$755$	53.2068			1.93639
$756$		0			0
$757$	6.71165	−	11.6249i	0.243939	−	0.422515i	−0.717894	−	0.696153i	$-0.754894\pi$
$757$	6.71165	−	11.6249i	0.243939	−	0.422515i	0.961833	+	0.273638i	$0.0882270\pi$
$758$		0			0
$759$	17.2517			0.626198
$760$		0			0
$761$	−1.53457	−	2.65794i	−0.0556279	−	0.0963504i	0.836870	−	0.547401i	$-0.184383\pi$
$761$	−1.53457	−	2.65794i	−0.0556279	−	0.0963504i	−0.892498	+	0.451051i	$0.851049\pi$
$762$		0			0
$763$	−2.06798	−	3.58184i	−0.0748657	−	0.129671i
$764$		0			0
$765$	20.0885	−	34.7944i	0.726303	−	1.25799i
$766$		0			0
$767$	34.9847	+	14.1552i	1.26322	+	0.511115i
$768$		0			0
$769$	−2.02699	+	3.51085i	−0.0730950	+	0.126604i	−0.900256	−	0.435360i	$-0.856621\pi$
$769$	−2.02699	+	3.51085i	−0.0730950	+	0.126604i	0.827161	+	0.561965i	$0.189954\pi$
$770$		0			0
$771$	−4.86175	−	8.42080i	−0.175092	−	0.303268i
$772$		0			0
$773$	9.34233	+	16.1814i	0.336020	+	0.582004i	0.983680	−	0.179925i	$-0.0575856\pi$
$773$	9.34233	+	16.1814i	0.336020	+	0.582004i	−0.647660	+	0.761929i	$0.724252\pi$
$774$		0			0
$775$	−5.29723			−0.190282
$776$		0			0
$777$	9.21922	−	15.9682i	0.330738	−	0.572855i
$778$		0			0
$779$	20.6440			0.739648
$780$		0			0
$781$	5.17708			0.185251
$782$		0			0
$783$	2.58497	−	4.47730i	0.0923793	−	0.160006i
$784$		0			0
$785$	0.807764			0.0288303
$786$		0			0
$787$	8.83467	+	15.3021i	0.314922	+	0.545461i	0.979421	−	0.201828i	$-0.0646883\pi$
$787$	8.83467	+	15.3021i	0.314922	+	0.545461i	−0.664499	+	0.747289i	$0.731355\pi$
$788$		0			0
$789$	8.15009	+	14.1164i	0.290151	+	0.502556i
$790$		0			0
$791$	−30.1408	+	52.2055i	−1.07168	+	1.85621i
$792$		0			0
$793$	−37.5885	−	15.2088i	−1.33481	−	0.540079i
$794$		0			0
$795$	7.73704	−	13.4009i	0.274404	−	0.475282i
$796$		0			0
$797$	26.0270	+	45.0801i	0.921923	+	1.59682i	0.796436	+	0.604723i	$0.206716\pi$
$797$	26.0270	+	45.0801i	0.921923	+	1.59682i	0.125487	+	0.992095i	$0.459951\pi$
$798$		0			0
$799$	−32.9346	−	57.0444i	−1.16514	−	2.01809i
$800$		0			0
$801$	27.3693			0.967047
$802$		0			0
$803$	2.23100	−	3.86421i	0.0787304	−	0.136365i
$804$		0			0
$805$	66.7386			2.35223
$806$		0			0
$807$	44.0639			1.55112
$808$		0			0
$809$	−16.1847	+	28.0327i	−0.569022	+	0.985576i	0.427641	+	0.903949i	$0.359345\pi$
$809$	−16.1847	+	28.0327i	−0.569022	+	0.985576i	−0.996663	+	0.0816267i	$0.973988\pi$
$810$		0			0
$811$	−14.8934			−0.522979			−0.261490	−	0.965206i	$-0.584214\pi$
$811$	−14.8934			−0.522979			−0.261490	+	0.965206i	$0.584214\pi$
$812$		0			0
$813$	−12.3423	−	21.3775i	−0.432864	−	0.749743i
$814$		0			0
$815$	26.2316	+	45.4344i	0.918851	+	1.59150i
$816$		0			0
$817$	21.0270	−	36.4198i	0.735641	−	1.27417i
$818$		0			0
$819$	−4.71659	−	33.6832i	−0.164811	−	1.17699i
$820$		0			0
$821$	10.9039	−	18.8861i	0.380548	−	0.659129i	−0.610593	−	0.791945i	$-0.709069\pi$
$821$	10.9039	−	18.8861i	0.380548	−	0.659129i	0.991141	+	0.132816i	$0.0424020\pi$
$822$		0			0
$823$	−1.55098	−	2.68638i	−0.0540638	−	0.0936413i	0.837727	−	0.546089i	$-0.183884\pi$
$823$	−1.55098	−	2.68638i	−0.0540638	−	0.0936413i	−0.891791	+	0.452448i	$0.850551\pi$
$824$		0			0
$825$	1.90388	+	3.29762i	0.0662847	+	0.114808i
$826$		0			0
$827$	38.8940			1.35248			0.676238	−	0.736683i	$-0.263609\pi$
$827$	38.8940			1.35248			0.676238	+	0.736683i	$0.263609\pi$
$828$		0			0
$829$	22.9924	−	39.8240i	0.798560	−	1.38315i	−0.121994	−	0.992531i	$-0.538929\pi$
$829$	22.9924	−	39.8240i	0.798560	−	1.38315i	0.920554	−	0.390615i	$-0.127738\pi$
$830$		0			0
$831$	−3.84563			−0.133403
$832$		0			0
$833$	40.1771			1.39205
$834$		0			0
$835$	−13.4061	+	23.2200i	−0.463937	+	0.803563i
$836$		0			0
$837$	−3.50758			−0.121240
$838$		0			0
$839$	−21.3698	−	37.0136i	−0.737768	−	1.27785i	−0.953498	−	0.301398i	$-0.902547\pi$
$839$	−21.3698	−	37.0136i	−0.737768	−	1.27785i	0.215731	−	0.976453i	$-0.430787\pi$
$840$		0			0
$841$	2.00000	+	3.46410i	0.0689655	+	0.119452i
$842$		0			0
$843$	−14.5216	+	25.1522i	−0.500151	+	0.866286i
$844$		0			0
$845$	−8.08854	+	32.3029i	−0.278254	+	1.11125i
$846$		0			0
$847$	18.2857	−	31.6718i	0.628305	−	1.08826i
$848$		0			0
$849$	29.7116	+	51.4621i	1.01970	+	1.76617i
$850$		0			0
$851$	7.51036	+	13.0083i	0.257452	+	0.445920i
$852$		0			0
$853$	−23.0540			−0.789353			−0.394677	−	0.918820i	$-0.629143\pi$
$853$	−23.0540			−0.789353			−0.394677	+	0.918820i	$0.629143\pi$
$854$		0			0
$855$	−16.4265	+	28.4516i	−0.561776	+	0.973025i
$856$		0			0
$857$	17.4384			0.595686			0.297843	−	0.954615i	$-0.403733\pi$
$857$	17.4384			0.595686			0.297843	+	0.954615i	$0.403733\pi$
$858$		0			0
$859$	23.4199			0.799077			0.399539	−	0.916716i	$-0.369170\pi$
$859$	23.4199			0.799077			0.399539	+	0.916716i	$0.369170\pi$
$860$		0			0
$861$	−17.9039	+	31.0104i	−0.610163	+	1.05683i
$862$		0			0
$863$	−10.5945			−0.360639			−0.180320	−	0.983608i	$-0.557713\pi$
$863$	−10.5945			−0.360639			−0.180320	+	0.983608i	$0.557713\pi$
$864$		0			0
$865$	10.8078	+	18.7196i	0.367475	+	0.636485i
$866$		0			0
$867$	24.1636	+	41.8526i	0.820638	+	1.42139i
$868$		0			0
$869$	−5.94602	+	10.2988i	−0.201705	+	0.349363i
$870$		0			0
$871$	4.86175	+	34.7198i	0.164734	+	1.17644i
$872$		0			0
$873$	12.5616	−	21.7572i	0.425144	−	0.736371i
$874$		0			0
$875$	−16.2177	−	28.0900i	−0.548260	−	0.949614i
$876$		0			0
$877$	−4.62311	−	8.00745i	−0.156111	−	0.270393i	0.777352	−	0.629066i	$-0.216562\pi$
$877$	−4.62311	−	8.00745i	−0.156111	−	0.270393i	−0.933463	+	0.358673i	$0.883229\pi$
$878$		0			0
$879$	2.35829			0.0795433
$880$		0			0
$881$	−14.4309	+	24.9950i	−0.486188	+	0.842103i	−0.999874	−	0.0158756i	$-0.994946\pi$
$881$	−14.4309	+	24.9950i	−0.486188	+	0.842103i	0.513686	+	0.857978i	$0.328280\pi$
$882$		0			0
$883$	16.6354			0.559824			0.279912	−	0.960026i	$-0.409695\pi$
$883$	16.6354			0.559824			0.279912	+	0.960026i	$0.409695\pi$
$884$		0			0
$885$	63.2311			2.12549
$886$		0			0
$887$	−18.0590	+	31.2792i	−0.606363	+	1.05025i	0.385471	+	0.922720i	$0.374039\pi$
$887$	−18.0590	+	31.2792i	−0.606363	+	1.05025i	−0.991834	+	0.127532i	$0.959294\pi$
$888$		0			0
$889$	1.06913			0.0358575
$890$		0			0
$891$	5.23358	+	9.06483i	0.175332	+	0.303683i
$892$		0			0
$893$	26.9309	+	46.6456i	0.901207	+	1.56094i
$894$		0			0
$895$	−7.36520	+	12.7569i	−0.246192	+	0.426416i
$896$		0			0
$897$	55.7656	+	22.5634i	1.86196	+	0.753370i
$898$		0			0
$899$	−8.48071	+	14.6890i	−0.282847	+	0.489906i
$900$		0			0
$901$	7.84233	+	13.5833i	0.261266	+	0.452526i
$902$		0			0
$903$	36.4720	+	63.1714i	1.21371	+	2.10221i
$904$		0			0
$905$	53.3002			1.77176
$906$		0			0
$907$	12.3085	−	21.3189i	0.408696	−	0.707882i	−0.586048	−	0.810276i	$-0.699317\pi$
$907$	12.3085	−	21.3189i	0.408696	−	0.707882i	0.994744	+	0.102394i	$0.0326503\pi$
$908$		0			0
$909$	−0.315342			−0.0104592
$910$		0			0
$911$	−15.8917			−0.526515			−0.263257	−	0.964726i	$-0.584797\pi$
$911$	−15.8917			−0.526515			−0.263257	+	0.964726i	$0.584797\pi$
$912$		0			0
$913$	1.36932	−	2.37173i	0.0453178	−	0.0784927i
$914$		0			0
$915$	−67.9372			−2.24593
$916$		0			0
$917$	−20.8769	−	36.1598i	−0.689416	−	1.19410i
$918$		0			0
$919$	3.99079	+	6.91225i	0.131644	+	0.228014i	0.924310	−	0.381641i	$-0.124641\pi$
$919$	3.99079	+	6.91225i	0.131644	+	0.228014i	−0.792666	+	0.609656i	$0.791308\pi$
$920$		0			0
$921$	−23.1231	+	40.0504i	−0.761932	+	1.31971i
$922$		0			0
$923$	16.7347	+	6.77106i	0.550831	+	0.222872i
$924$		0			0
$925$	−1.65767	+	2.87117i	−0.0545039	+	0.0944035i
$926$		0			0
$927$	−11.1293	−	19.2765i	−0.365535	−	0.633125i
$928$		0			0
$929$	−15.0616	−	26.0874i	−0.494154	−	0.855899i	0.505824	−	0.862637i	$-0.331189\pi$
$929$	−15.0616	−	26.0874i	−0.494154	−	0.855899i	−0.999977	+	0.00673783i	$0.997855\pi$
$930$		0			0
$931$	−32.8531			−1.07672
$932$		0			0
$933$	12.0000	−	20.7846i	0.392862	−	0.680458i
$934$		0			0
$935$	−16.2177			−0.530377
$936$		0			0
$937$	−48.8078			−1.59448			−0.797240	−	0.603662i	$-0.793708\pi$
$937$	−48.8078			−1.59448			−0.797240	+	0.603662i	$0.793708\pi$
$938$		0			0
$939$	15.4741	−	26.8019i	0.504977	−	0.874646i
$940$		0			0
$941$	−2.00000			−0.0651981			−0.0325991	−	0.999469i	$-0.510378\pi$
$941$	−2.00000			−0.0651981			−0.0325991	+	0.999469i	$0.510378\pi$
$942$		0			0
$943$	−14.5852	−	25.2624i	−0.474961	−	0.822657i
$944$		0			0
$945$	4.87689	+	8.44703i	0.158645	+	0.274782i
$946$		0			0
$947$	15.9096	−	27.5562i	0.516991	−	0.895455i	−0.482814	−	0.875723i	$-0.660385\pi$
$947$	15.9096	−	27.5562i	0.516991	−	0.895455i	0.999805	−	0.0197319i	$-0.00628127\pi$
$948$		0			0
$949$	12.2656	−	9.57302i	0.398159	−	0.310753i
$950$		0			0
$951$	3.31077	−	5.73442i	0.107359	−	0.185951i
$952$		0			0
$953$	17.3963	+	30.1313i	0.563522	+	0.976048i	0.997186	+	0.0749733i	$0.0238872\pi$
$953$	17.3963	+	30.1313i	0.563522	+	0.976048i	−0.433664	+	0.901075i	$0.642780\pi$
$954$		0			0
$955$	15.8459	+	27.4459i	0.512762	+	0.888129i
$956$		0			0
$957$	12.1922			0.394119
$958$		0			0
$959$	31.3021	−	54.2168i	1.01080	−	1.75075i
$960$		0			0
$961$	−19.4924			−0.628788
$962$		0			0
$963$	24.9073			0.802625
$964$		0			0
$965$	−2.40388	+	4.16365i	−0.0773837	+	0.134033i
$966$		0			0
$967$	−8.68951			−0.279436			−0.139718	−	0.990191i	$-0.544620\pi$
$967$	−8.68951			−0.279436			−0.139718	+	0.990191i	$0.544620\pi$
$968$		0			0
$969$	−36.1501	−	62.6138i	−1.16131	−	2.01144i
$970$		0			0
$971$	−9.28802	−	16.0873i	−0.298067	−	0.516267i	0.677627	−	0.735406i	$-0.263008\pi$
$971$	−9.28802	−	16.0873i	−0.298067	−	0.516267i	−0.975694	+	0.219139i	$0.929675\pi$
$972$		0			0
$973$	37.7116	−	65.3185i	1.20898	−	2.09401i
$974$		0			0
$975$	1.84130	+	13.1495i	0.0589688	+	0.421122i
$976$		0			0
$977$	7.86932	−	13.6301i	0.251762	−	0.436064i	−0.712249	−	0.701927i	$-0.752323\pi$
$977$	7.86932	−	13.6301i	0.251762	−	0.436064i	0.964011	+	0.265863i	$0.0856567\pi$
$978$		0			0
$979$	−5.52390	−	9.56768i	−0.176545	−	0.305784i
$980$		0			0
$981$	−1.43845	−	2.49146i	−0.0459261	−	0.0795463i
$982$		0			0
$983$	−30.5305			−0.973773			−0.486886	−	0.873465i	$-0.661867\pi$
$983$	−30.5305			−0.973773			−0.486886	+	0.873465i	$0.661867\pi$
$984$		0			0
$985$	−7.43845	+	12.8838i	−0.237009	+	0.410511i
$986$		0			0
$987$	−93.4251			−2.97375
$988$		0			0
$989$	−59.4233			−1.88955
$990$		0			0
$991$	8.54435	−	14.7992i	0.271420	−	0.470114i	−0.697806	−	0.716287i	$-0.745840\pi$
$991$	8.54435	−	14.7992i	0.271420	−	0.470114i	0.969226	+	0.246174i	$0.0791734\pi$
$992$		0			0
$993$	−35.8078			−1.13633
$994$		0			0
$995$	−9.06134	−	15.6947i	−0.287264	−	0.497556i
$996$		0			0
$997$	14.1155	+	24.4488i	0.447043	+	0.774302i	0.998192	−	0.0601053i	$-0.0191437\pi$
$997$	14.1155	+	24.4488i	0.447043	+	0.774302i	−0.551149	+	0.834407i	$0.685810\pi$
$998$		0			0
$999$	−1.09763	+	1.90116i	−0.0347276	+	0.0601499i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.i.g.321.4	yes	8
4.3	odd	2	inner	416.2.i.g.321.1	yes	8
8.3	odd	2		832.2.i.q.321.4		8
8.5	even	2		832.2.i.q.321.1		8
13.3	even	3	inner	416.2.i.g.289.4	yes	8
13.4	even	6		5408.2.a.bi.1.1		4
13.9	even	3		5408.2.a.bh.1.1		4
52.3	odd	6	inner	416.2.i.g.289.1	✓	8
52.35	odd	6		5408.2.a.bh.1.4		4
52.43	odd	6		5408.2.a.bi.1.4		4
104.3	odd	6		832.2.i.q.705.4		8
104.29	even	6		832.2.i.q.705.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.i.g.289.1	✓	8	52.3	odd	6	inner
416.2.i.g.289.4	yes	8	13.3	even	3	inner
416.2.i.g.321.1	yes	8	4.3	odd	2	inner
416.2.i.g.321.4	yes	8	1.1	even	1	trivial
832.2.i.q.321.1		8	8.5	even	2
832.2.i.q.321.4		8	8.3	odd	2
832.2.i.q.705.1		8	104.29	even	6
832.2.i.q.705.4		8	104.3	odd	6
5408.2.a.bh.1.1		4	13.9	even	3
5408.2.a.bh.1.4		4	52.35	odd	6
5408.2.a.bi.1.1		4	13.4	even	6
5408.2.a.bi.1.4		4	52.43	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17915 - 2.04234i) q^{3} -2.56155 q^{5} +(-1.84130 - 3.18923i) q^{7} +(-1.28078 - 2.21837i) q^{9} +(-0.516994 + 0.895460i) q^{11} +(-2.84233 + 2.21837i) q^{13} +(-3.02045 + 5.23157i) q^{15} +(-3.06155 - 5.30277i) q^{17} +(2.50345 + 4.33611i) q^{19} -8.68466 q^{21} +(3.53744 - 6.12703i) q^{23} +1.56155 q^{25} +1.03399 q^{27} +(2.50000 - 4.33013i) q^{29} -3.39228 q^{31} +(1.21922 + 2.11176i) q^{33} +(4.71659 + 8.16937i) q^{35} +(-1.06155 + 1.83866i) q^{37} +(1.17915 + 8.42080i) q^{39} +(2.06155 - 3.57071i) q^{41} +(-4.19960 - 7.27391i) q^{43} +(3.28078 + 5.68247i) q^{45} +10.7575 q^{47} +(-3.28078 + 5.68247i) q^{49} -14.4401 q^{51} -2.56155 q^{53} +(1.32431 - 2.29377i) q^{55} +11.8078 q^{57} +(-5.23358 - 9.06483i) q^{59} +(5.62311 + 9.73950i) q^{61} +(-4.71659 + 8.16937i) q^{63} +(7.28078 - 5.68247i) q^{65} +(4.86175 - 8.42080i) q^{67} +(-8.34233 - 14.4493i) q^{69} +(-2.50345 - 4.33611i) q^{71} -4.31534 q^{73} +(1.84130 - 3.18923i) q^{75} +3.80776 q^{77} +11.5012 q^{79} +(5.06155 - 8.76687i) q^{81} -2.64861 q^{83} +(7.84233 + 13.5833i) q^{85} +(-5.89574 - 10.2117i) q^{87} +(-5.34233 + 9.25319i) q^{89} +(12.3085 + 4.98015i) q^{91} +(-4.00000 + 6.92820i) q^{93} +(-6.41273 - 11.1072i) q^{95} +(4.90388 + 8.49377i) q^{97} +2.64861 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} - 2 q^{9} + 2 q^{13} - 8 q^{17} - 20 q^{21} - 4 q^{25} + 20 q^{29} + 18 q^{33} + 8 q^{37} + 18 q^{45} - 18 q^{49} - 4 q^{53} + 12 q^{57} + 12 q^{61} + 50 q^{65} - 42 q^{69} - 84 q^{73} - 52 q^{77}+ \cdots - 2 q^{97}+O(q^{100}) \) 8 * q - 4 * q^5 - 2 * q^9 + 2 * q^13 - 8 * q^17 - 20 * q^21 - 4 * q^25 + 20 * q^29 + 18 * q^33 + 8 * q^37 + 18 * q^45 - 18 * q^49 - 4 * q^53 + 12 * q^57 + 12 * q^61 + 50 * q^65 - 42 * q^69 - 84 * q^73 - 52 * q^77 + 24 * q^81 + 38 * q^85 - 18 * q^89 - 32 * q^93 - 2 * q^97

Introduction

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