LMFDB - Embedded newform 650.2.o.h.549.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(399,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.399"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$650 = 2 \cdot 5^{2} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	650.o (of order $6$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,4,0,2,0,0,2,0,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.592240896.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - 7x^{6} + 40x^{4} - 63x^{2} + 81$ x^8 - 7x^6 + 40x^4 - 63*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			549.2
Root			$-1.12824 + 0.651388i$ of defining polynomial
Character	$\chi$	$=$	650.549
Dual form			650.2.o.h.399.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(1.12824 - 0.651388i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.651388 + 1.12824i) q^{6} +(3.72631 + 2.15139i) q^{7} +1.00000i q^{8} +(-0.651388 + 1.12824i) q^{9} +(2.15139 + 3.72631i) q^{11} -1.30278i q^{12} +(3.12250 - 1.80278i) q^{13} -4.30278 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-6.84881 - 3.95416i) q^{17} -1.30278i q^{18} +(-3.80278 + 6.58660i) q^{19} +5.60555 q^{21} +(-3.72631 - 2.15139i) q^{22} +(1.39045 - 0.802776i) q^{23} +(0.651388 + 1.12824i) q^{24} +(-1.80278 + 3.12250i) q^{26} +5.60555i q^{27} +(3.72631 - 2.15139i) q^{28} +(-0.151388 - 0.262211i) q^{29} -1.39445 q^{31} +(0.866025 + 0.500000i) q^{32} +(4.85455 + 2.80278i) q^{33} +7.90833 q^{34} +(0.651388 + 1.12824i) q^{36} +(6.32439 - 3.65139i) q^{37} -7.60555i q^{38} +(2.34861 - 4.06792i) q^{39} +(-0.500000 - 0.866025i) q^{41} +(-4.85455 + 2.80278i) q^{42} +(8.23926 + 4.75694i) q^{43} +4.30278 q^{44} +(-0.802776 + 1.39045i) q^{46} -6.69722i q^{47} +(-1.12824 - 0.651388i) q^{48} +(5.75694 + 9.97131i) q^{49} -10.3028 q^{51} -3.60555i q^{52} +2.21110i q^{53} +(-2.80278 - 4.85455i) q^{54} +(-2.15139 + 3.72631i) q^{56} +9.90833i q^{57} +(0.262211 + 0.151388i) q^{58} +(2.10555 - 3.64692i) q^{59} +(5.10555 - 8.84307i) q^{61} +(1.20763 - 0.697224i) q^{62} +(-4.85455 + 2.80278i) q^{63} -1.00000 q^{64} -5.60555 q^{66} +(1.39045 - 0.802776i) q^{67} +(-6.84881 + 3.95416i) q^{68} +(1.04584 - 1.81144i) q^{69} +(1.69722 - 2.93968i) q^{71} +(-1.12824 - 0.651388i) q^{72} -8.00000i q^{73} +(-3.65139 + 6.32439i) q^{74} +(3.80278 + 6.58660i) q^{76} +18.5139i q^{77} +4.69722i q^{78} -5.69722 q^{79} +(1.69722 + 2.93968i) q^{81} +(0.866025 + 0.500000i) q^{82} -4.81665i q^{83} +(2.80278 - 4.85455i) q^{84} -9.51388 q^{86} +(-0.341603 - 0.197224i) q^{87} +(-3.72631 + 2.15139i) q^{88} +(5.45416 + 9.44689i) q^{89} +15.5139 q^{91} -1.60555i q^{92} +(-1.57327 + 0.908327i) q^{93} +(3.34861 + 5.79997i) q^{94} +1.30278 q^{96} +(-13.2526 - 7.65139i) q^{97} +(-9.97131 - 5.75694i) q^{98} -5.60555 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 4 q^{4} + 2 q^{6} + 2 q^{9} + 10 q^{11} - 20 q^{14} - 4 q^{16} - 16 q^{19} + 16 q^{21} - 2 q^{24} + 6 q^{29} - 40 q^{31} + 20 q^{34} - 2 q^{36} + 26 q^{39} - 4 q^{41} + 20 q^{44} + 8 q^{46} + 10 q^{49}+ \cdots - 16 q^{99}+O(q^{100})$ 8 * q + 4 * q^4 + 2 * q^6 + 2 * q^9 + 10 * q^11 - 20 * q^14 - 4 * q^16 - 16 * q^19 + 16 * q^21 - 2 * q^24 + 6 * q^29 - 40 * q^31 + 20 * q^34 - 2 * q^36 + 26 * q^39 - 4 * q^41 + 20 * q^44 + 8 * q^46 + 10 * q^49 - 68 * q^51 - 8 * q^54 - 10 * q^56 - 12 * q^59 + 12 * q^61 - 8 * q^64 - 16 * q^66 + 30 * q^69 + 28 * q^71 - 22 * q^74 + 16 * q^76 - 60 * q^79 + 28 * q^81 + 8 * q^84 - 4 * q^86 + 22 * q^89 + 52 * q^91 + 34 * q^94 - 4 * q^96 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$ .

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	1.12824	−	0.651388i	0.651388	−	0.376079i	−0.137600	−	0.990488i	$-0.543939\pi$
$3$	1.12824	−	0.651388i	0.651388	−	0.376079i	0.788988	+	0.614409i	$0.210605\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.651388	+	1.12824i	−0.265928	+	0.460601i
$7$	3.72631	+	2.15139i	1.40841	+	0.813148i	0.995235	−	0.0975019i	$-0.0310852\pi$
$7$	3.72631	+	2.15139i	1.40841	+	0.813148i	0.413179	+	0.910650i	$0.364419\pi$
$8$			1.00000i			0.353553i
$9$	−0.651388	+	1.12824i	−0.217129	+	0.376079i
$10$		0			0
$11$	2.15139	+	3.72631i	0.648668	+	1.12353i	0.983441	+	0.181227i	$0.0580069\pi$
$11$	2.15139	+	3.72631i	0.648668	+	1.12353i	−0.334773	+	0.942299i	$0.608660\pi$
$12$		−	1.30278i		−	0.376079i
$13$	3.12250	−	1.80278i	0.866025	−	0.500000i
$13$	3.12250	−	1.80278i	0.866025	−	0.500000i
$14$	−4.30278			−1.14997
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−6.84881	−	3.95416i	−1.66108	−	0.959026i	−0.972200	−	0.234151i	$-0.924769\pi$
$17$	−6.84881	−	3.95416i	−1.66108	−	0.959026i	−0.688881	−	0.724875i	$-0.741898\pi$
$18$		−	1.30278i		−	0.307067i
$19$	−3.80278	+	6.58660i	−0.872417	+	1.51107i	−0.0129270	+	0.999916i	$0.504115\pi$
$19$	−3.80278	+	6.58660i	−0.872417	+	1.51107i	−0.859490	+	0.511153i	$0.829218\pi$
$20$		0			0
$21$	5.60555			1.22323
$22$	−3.72631	−	2.15139i	−0.794453	−	0.458677i
$23$	1.39045	−	0.802776i	0.289928	−	0.167390i	−0.347981	−	0.937502i	$-0.613133\pi$
$23$	1.39045	−	0.802776i	0.289928	−	0.167390i	0.637910	+	0.770111i	$0.279799\pi$
$24$	0.651388	+	1.12824i	0.132964	+	0.230300i
$25$		0			0
$26$	−1.80278	+	3.12250i	−0.353553	+	0.612372i
$27$			5.60555i			1.07879i
$28$	3.72631	−	2.15139i	0.704207	−	0.406574i
$29$	−0.151388	−	0.262211i	−0.0281120	−	0.0486914i	0.851627	−	0.524148i	$-0.175616\pi$
$29$	−0.151388	−	0.262211i	−0.0281120	−	0.0486914i	−0.879739	+	0.475457i	$0.842283\pi$
$30$		0			0
$31$	−1.39445			−0.250450			−0.125225	−	0.992128i	$-0.539965\pi$
$31$	−1.39445			−0.250450			−0.125225	+	0.992128i	$0.539965\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	4.85455	+	2.80278i	0.845069	+	0.487901i
$34$	7.90833			1.35627
$35$		0			0
$36$	0.651388	+	1.12824i	0.108565	+	0.188039i
$37$	6.32439	−	3.65139i	1.03972	−	0.600284i	0.119968	−	0.992778i	$-0.461721\pi$
$37$	6.32439	−	3.65139i	1.03972	−	0.600284i	0.919755	+	0.392493i	$0.128387\pi$
$38$		−	7.60555i		−	1.23378i
$39$	2.34861	−	4.06792i	0.376079	−	0.651388i
$40$		0			0
$41$	−0.500000	−	0.866025i	−0.0780869	−	0.135250i	0.824338	−	0.566099i	$-0.191548\pi$
$41$	−0.500000	−	0.866025i	−0.0780869	−	0.135250i	−0.902424	+	0.430848i	$0.858214\pi$
$42$	−4.85455	+	2.80278i	−0.749073	+	0.432478i
$43$	8.23926	+	4.75694i	1.25648	+	0.725426i	0.972388	−	0.233372i	$-0.0749759\pi$
$43$	8.23926	+	4.75694i	1.25648	+	0.725426i	0.284088	+	0.958798i	$0.408309\pi$
$44$	4.30278			0.648668
$45$		0			0
$46$	−0.802776	+	1.39045i	−0.118363	+	0.205010i
$47$		−	6.69722i		−	0.976891i	−0.872595	−	0.488445i	$-0.837564\pi$
$47$		−	6.69722i		−	0.976891i	0.872595	−	0.488445i	$-0.162436\pi$
$48$	−1.12824	−	0.651388i	−0.162847	−	0.0940197i
$49$	5.75694	+	9.97131i	0.822420	+	1.42447i
$50$		0			0
$51$	−10.3028			−1.44268
$52$		−	3.60555i		−	0.500000i
$53$			2.21110i			0.303718i	0.988402	+	0.151859i	$0.0485260\pi$
$53$			2.21110i			0.303718i	−0.988402	+	0.151859i	$0.951474\pi$
$54$	−2.80278	−	4.85455i	−0.381409	−	0.660621i
$55$		0			0
$56$	−2.15139	+	3.72631i	−0.287491	+	0.497950i
$57$			9.90833i			1.31239i
$58$	0.262211	+	0.151388i	0.0344300	+	0.0198782i
$59$	2.10555	−	3.64692i	0.274119	−	0.474789i	−0.695793	−	0.718242i	$-0.744947\pi$
$59$	2.10555	−	3.64692i	0.274119	−	0.474789i	0.969913	+	0.243453i	$0.0782803\pi$
$60$		0			0
$61$	5.10555	−	8.84307i	0.653699	−	1.13224i	−0.328519	−	0.944497i	$-0.606550\pi$
$61$	5.10555	−	8.84307i	0.653699	−	1.13224i	0.982218	−	0.187742i	$-0.0601170\pi$
$62$	1.20763	−	0.697224i	0.153369	−	0.0885476i
$63$	−4.85455	+	2.80278i	−0.611616	+	0.353117i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−5.60555			−0.689996
$67$	1.39045	−	0.802776i	0.169870	−	0.0980747i	−0.412654	−	0.910888i	$-0.635398\pi$
$67$	1.39045	−	0.802776i	0.169870	−	0.0980747i	0.582525	+	0.812813i	$0.302065\pi$
$68$	−6.84881	+	3.95416i	−0.830540	+	0.479513i
$69$	1.04584	−	1.81144i	0.125904	−	0.218072i
$70$		0			0
$71$	1.69722	−	2.93968i	0.201423	−	0.348876i	−0.747564	−	0.664190i	$-0.768777\pi$
$71$	1.69722	−	2.93968i	0.201423	−	0.348876i	0.948987	+	0.315314i	$0.102110\pi$
$72$	−1.12824	−	0.651388i	−0.132964	−	0.0767668i
$73$		−	8.00000i		−	0.936329i	−0.883641	−	0.468165i	$-0.844915\pi$
$73$		−	8.00000i		−	0.936329i	0.883641	−	0.468165i	$-0.155085\pi$
$74$	−3.65139	+	6.32439i	−0.424465	+	0.735195i
$75$		0			0
$76$	3.80278	+	6.58660i	0.436208	+	0.755535i
$77$			18.5139i			2.10985i
$78$			4.69722i			0.531856i
$79$	−5.69722			−0.640988			−0.320494	−	0.947251i	$-0.603849\pi$
$79$	−5.69722			−0.640988			−0.320494	+	0.947251i	$0.603849\pi$
$80$		0			0
$81$	1.69722	+	2.93968i	0.188580	+	0.326631i
$82$	0.866025	+	0.500000i	0.0956365	+	0.0552158i
$83$		−	4.81665i		−	0.528696i	−0.964427	−	0.264348i	$-0.914843\pi$
$83$		−	4.81665i		−	0.528696i	0.964427	−	0.264348i	$-0.0851568\pi$
$84$	2.80278	−	4.85455i	0.305808	−	0.529675i
$85$		0			0
$86$	−9.51388			−1.02591
$87$	−0.341603	−	0.197224i	−0.0366236	−	0.0211447i
$88$	−3.72631	+	2.15139i	−0.397226	+	0.229339i
$89$	5.45416	+	9.44689i	0.578140	+	1.00137i	0.995693	+	0.0927153i	$0.0295547\pi$
$89$	5.45416	+	9.44689i	0.578140	+	1.00137i	−0.417552	+	0.908653i	$0.637112\pi$
$90$		0			0
$91$	15.5139			1.62630
$92$		−	1.60555i		−	0.167390i
$93$	−1.57327	+	0.908327i	−0.163140	+	0.0941891i
$94$	3.34861	+	5.79997i	0.345383	+	0.598221i
$95$		0			0
$96$	1.30278			0.132964
$97$	−13.2526	−	7.65139i	−1.34560	−	0.776881i	−0.357975	−	0.933731i	$-0.616533\pi$
$97$	−13.2526	−	7.65139i	−1.34560	−	0.776881i	−0.987622	+	0.156851i	$0.949866\pi$
$98$	−9.97131	−	5.75694i	−1.00725	−	0.581539i
$99$	−5.60555			−0.563379
$100$		0			0
$101$	−4.10555	−	7.11102i	−0.408518	−	0.707573i	0.586206	−	0.810162i	$-0.300621\pi$
$101$	−4.10555	−	7.11102i	−0.408518	−	0.707573i	−0.994724	+	0.102589i	$0.967287\pi$
$102$	8.92247	−	5.15139i	0.883456	−	0.510063i
$103$			13.6056i			1.34059i	0.742093	+	0.670297i	$0.233833\pi$
$103$			13.6056i			1.34059i	−0.742093	+	0.670297i	$0.766167\pi$
$104$	1.80278	+	3.12250i	0.176777	+	0.306186i
$105$		0			0
$106$	−1.10555	−	1.91487i	−0.107381	−	0.185989i
$107$	6.76942	−	3.90833i	0.654425	−	0.377832i	−0.135725	−	0.990747i	$-0.543336\pi$
$107$	6.76942	−	3.90833i	0.654425	−	0.377832i	0.790149	+	0.612914i	$0.210003\pi$
$108$	4.85455	+	2.80278i	0.467129	+	0.269697i
$109$	−4.39445			−0.420912			−0.210456	−	0.977603i	$-0.567495\pi$
$109$	−4.39445			−0.420912			−0.210456	+	0.977603i	$0.567495\pi$
$110$		0			0
$111$	4.75694	−	8.23926i	0.451509	−	0.782036i
$112$		−	4.30278i		−	0.406574i
$113$	−6.50721	−	3.75694i	−0.612147	−	0.353423i	0.161658	−	0.986847i	$-0.448316\pi$
$113$	−6.50721	−	3.75694i	−0.612147	−	0.353423i	−0.773805	+	0.633424i	$0.781649\pi$
$114$	−4.95416	−	8.58086i	−0.464000	−	0.803671i
$115$		0			0
$116$	−0.302776			−0.0281120
$117$			4.69722i			0.434259i
$118$			4.21110i			0.387663i
$119$	−17.0139	−	29.4689i	−1.55966	−	2.70141i
$120$		0			0
$121$	−3.75694	+	6.50721i	−0.341540	+	0.591564i
$122$			10.2111i			0.924470i
$123$	−1.12824	−	0.651388i	−0.101730	−	0.0587337i
$124$	−0.697224	+	1.20763i	−0.0626126	+	0.108448i
$125$		0			0
$126$	2.80278	−	4.85455i	0.249691	−	0.432478i
$127$	5.11676	−	2.95416i	0.454039	−	0.262140i	−0.255495	−	0.966810i	$-0.582239\pi$
$127$	5.11676	−	2.95416i	0.454039	−	0.262140i	0.709535	+	0.704671i	$0.248905\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	12.3944			1.09127
$130$		0			0
$131$	−12.8167			−1.11980			−0.559898	−	0.828561i	$-0.689160\pi$
$131$	−12.8167			−1.11980			−0.559898	+	0.828561i	$0.689160\pi$
$132$	4.85455	−	2.80278i	0.422534	−	0.243950i
$133$	−28.3407	+	16.3625i	−2.45745	+	1.41881i
$134$	−0.802776	+	1.39045i	−0.0693493	+	0.120116i
$135$		0			0
$136$	3.95416	−	6.84881i	0.339067	−	0.587281i
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$			2.09167i			0.178055i
$139$	5.90833	−	10.2335i	0.501138	−	0.867996i	−0.498861	−	0.866682i	$-0.666248\pi$
$139$	5.90833	−	10.2335i	0.501138	−	0.867996i	0.999999	−	0.00131426i	$-0.000418341\pi$
$140$		0			0
$141$	−4.36249	−	7.55605i	−0.367388	−	0.636335i
$142$			3.39445i			0.284856i
$143$	13.4354	+	7.75694i	1.12353	+	0.648668i
$144$	1.30278			0.108565
$145$		0			0
$146$	4.00000	+	6.92820i	0.331042	+	0.573382i
$147$	12.9904	+	7.50000i	1.07143	+	0.618590i
$148$		−	7.30278i		−	0.600284i
$149$	−2.34861	+	4.06792i	−0.192406	+	0.333257i	−0.946047	−	0.324029i	$-0.894962\pi$
$149$	−2.34861	+	4.06792i	−0.192406	+	0.333257i	0.753641	+	0.657286i	$0.228296\pi$
$150$		0			0
$151$	13.1194			1.06764			0.533822	−	0.845597i	$-0.320755\pi$
$151$	13.1194			1.06764			0.533822	+	0.845597i	$0.320755\pi$
$152$	−6.58660	−	3.80278i	−0.534244	−	0.308446i
$153$	8.92247	−	5.15139i	0.721339	−	0.416465i
$154$	−9.25694	−	16.0335i	−0.745945	−	1.29202i
$155$		0			0
$156$	−2.34861	−	4.06792i	−0.188039	−	0.325694i
$157$		−	4.42221i		−	0.352930i	−0.984307	−	0.176465i	$-0.943534\pi$
$157$		−	4.42221i		−	0.352930i	0.984307	−	0.176465i	$-0.0564663\pi$
$158$	4.93394	−	2.84861i	0.392523	−	0.226623i
$159$	1.44029	+	2.49465i	0.114222	+	0.197838i
$160$		0			0
$161$	6.90833			0.544452
$162$	−2.93968	−	1.69722i	−0.230963	−	0.133347i
$163$	−7.71484	−	4.45416i	−0.604273	−	0.348877i	0.166448	−	0.986050i	$-0.446770\pi$
$163$	−7.71484	−	4.45416i	−0.604273	−	0.348877i	−0.770721	+	0.637173i	$0.780104\pi$
$164$	−1.00000			−0.0780869
$165$		0			0
$166$	2.40833	+	4.17134i	0.186922	+	0.323759i
$167$	−3.12250	+	1.80278i	−0.241626	+	0.139503i	−0.615924	−	0.787806i	$-0.711217\pi$
$167$	−3.12250	+	1.80278i	−0.241626	+	0.139503i	0.374298	+	0.927309i	$0.377884\pi$
$168$			5.60555i			0.432478i
$169$	6.50000	−	11.2583i	0.500000	−	0.866025i
$170$		0			0
$171$	−4.95416	−	8.58086i	−0.378854	−	0.656195i
$172$	8.23926	−	4.75694i	0.628238	−	0.362713i
$173$	−21.2296	−	12.2569i	−1.61406	−	0.931878i	−0.988416	−	0.151769i	$-0.951503\pi$
$173$	−21.2296	−	12.2569i	−1.61406	−	0.931878i	−0.625644	−	0.780109i	$-0.715164\pi$
$174$	0.394449			0.0299031
$175$		0			0
$176$	2.15139	−	3.72631i	0.162167	−	0.280881i
$177$		−	5.48612i		−	0.412362i
$178$	−9.44689	−	5.45416i	−0.708074	−	0.408807i
$179$	−3.60555	−	6.24500i	−0.269492	−	0.466773i	0.699239	−	0.714888i	$-0.253522\pi$
$179$	−3.60555	−	6.24500i	−0.269492	−	0.466773i	−0.968731	+	0.248115i	$0.920189\pi$
$180$		0			0
$181$	−7.09167			−0.527120			−0.263560	−	0.964643i	$-0.584897\pi$
$181$	−7.09167			−0.527120			−0.263560	+	0.964643i	$0.584897\pi$
$182$	−13.4354	+	7.75694i	−0.995899	+	0.574983i
$183$		−	13.3028i		−	0.983369i
$184$	0.802776	+	1.39045i	0.0591814	+	0.102505i
$185$		0			0
$186$	0.908327	−	1.57327i	0.0666018	−	0.115358i
$187$		−	34.0278i		−	2.48836i
$188$	−5.79997	−	3.34861i	−0.423006	−	0.244223i
$189$	−12.0597	+	20.8880i	−0.877215	+	1.51938i
$190$		0			0
$191$	−5.40833	+	9.36750i	−0.391333	+	0.677808i	−0.992626	−	0.121220i	$-0.961319\pi$
$191$	−5.40833	+	9.36750i	−0.391333	+	0.677808i	0.601293	+	0.799029i	$0.294653\pi$
$192$	−1.12824	+	0.651388i	−0.0814235	+	0.0470099i
$193$	−0.445032	+	0.256939i	−0.0320341	+	0.0184949i	−0.515932	−	0.856630i	$-0.672554\pi$
$193$	−0.445032	+	0.256939i	−0.0320341	+	0.0184949i	0.483897	+	0.875125i	$0.339221\pi$
$194$	15.3028			1.09868
$195$		0			0
$196$	11.5139			0.822420
$197$	16.1923	−	9.34861i	1.15365	−	0.666061i	0.203877	−	0.978996i	$-0.434646\pi$
$197$	16.1923	−	9.34861i	1.15365	−	0.666061i	0.949774	+	0.312935i	$0.101312\pi$
$198$	4.85455	−	2.80278i	0.344998	−	0.199185i
$199$	−3.45416	+	5.98279i	−0.244859	+	0.424108i	−0.962092	−	0.272725i	$-0.912075\pi$
$199$	−3.45416	+	5.98279i	−0.244859	+	0.424108i	0.717233	+	0.696834i	$0.245408\pi$
$200$		0			0
$201$	1.04584	−	1.81144i	0.0737676	−	0.127769i
$202$	7.11102	+	4.10555i	0.500330	+	0.288866i
$203$		−	1.30278i		−	0.0914369i
$204$	−5.15139	+	8.92247i	−0.360669	+	0.624698i
$205$		0			0
$206$	−6.80278	−	11.7828i	−0.473972	−	0.820943i
$207$			2.09167i			0.145381i
$208$	−3.12250	−	1.80278i	−0.216506	−	0.125000i
$209$	−32.7250			−2.26363
$210$		0			0
$211$	−7.40833	−	12.8316i	−0.510010	−	0.883364i	−0.999933	−	0.0115977i	$-0.996308\pi$
$211$	−7.40833	−	12.8316i	−0.510010	−	0.883364i	0.489922	−	0.871766i	$-0.337025\pi$
$212$	1.91487	+	1.10555i	0.131514	+	0.0759296i
$213$		−	4.42221i		−	0.303005i
$214$	−3.90833	+	6.76942i	−0.267168	+	0.462748i
$215$		0			0
$216$	−5.60555			−0.381409
$217$	−5.19615	−	3.00000i	−0.352738	−	0.203653i
$218$	3.80570	−	2.19722i	0.257755	−	0.148815i
$219$	−5.21110	−	9.02589i	−0.352134	−	0.609913i
$220$		0			0
$221$	−28.5139			−1.91805
$222$			9.51388i			0.638530i
$223$	4.48891	−	2.59167i	0.300600	−	0.173551i	−0.342113	−	0.939659i	$-0.611142\pi$
$223$	4.48891	−	2.59167i	0.300600	−	0.173551i	0.642712	+	0.766108i	$0.277809\pi$
$224$	2.15139	+	3.72631i	0.143746	+	0.248975i
$225$		0			0
$226$	7.51388			0.499816
$227$	−16.4545	−	9.50000i	−1.09212	−	0.630537i	−0.157982	−	0.987442i	$-0.550499\pi$
$227$	−16.4545	−	9.50000i	−1.09212	−	0.630537i	−0.934141	+	0.356905i	$0.883832\pi$
$228$	8.58086	+	4.95416i	0.568282	+	0.328097i
$229$	10.5139			0.694777			0.347388	−	0.937721i	$-0.387069\pi$
$229$	10.5139			0.694777			0.347388	+	0.937721i	$0.387069\pi$
$230$		0			0
$231$	12.0597	+	20.8880i	0.793471	+	1.37433i
$232$	0.262211	−	0.151388i	0.0172150	−	0.00993910i
$233$			21.0000i			1.37576i	0.725826	+	0.687878i	$0.241458\pi$
$233$			21.0000i			1.37576i	−0.725826	+	0.687878i	$0.758542\pi$
$234$	−2.34861	−	4.06792i	−0.153534	−	0.265928i
$235$		0			0
$236$	−2.10555	−	3.64692i	−0.137060	−	0.237394i
$237$	−6.42782	+	3.71110i	−0.417532	+	0.241062i
$238$	29.4689	+	17.0139i	1.91019	+	1.10285i
$239$	29.4222			1.90316			0.951582	−	0.307395i	$-0.0994572\pi$
$239$	29.4222			1.90316			0.951582	+	0.307395i	$0.0994572\pi$
$240$		0			0
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	−0.935242	−	0.354010i	$-0.884818\pi$
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	0.774202	+	0.632938i	$0.218151\pi$
$242$		−	7.51388i		−	0.483010i
$243$	−10.7339	−	6.19722i	−0.688580	−	0.397552i
$244$	−5.10555	−	8.84307i	−0.326849	−	0.566120i
$245$		0			0
$246$	1.30278			0.0830619
$247$			27.4222i			1.74483i
$248$		−	1.39445i		−	0.0885476i
$249$	−3.13751	−	5.43433i	−0.198832	−	0.344386i
$250$		0			0
$251$	−11.1653	+	19.3388i	−0.704745	+	1.22065i	0.262038	+	0.965058i	$0.415605\pi$
$251$	−11.1653	+	19.3388i	−0.704745	+	1.22065i	−0.966783	+	0.255597i	$0.917728\pi$
$252$			5.60555i			0.353117i
$253$	5.98279	+	3.45416i	0.376135	+	0.217161i
$254$	−2.95416	+	5.11676i	−0.185361	+	0.321054i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.39045	+	0.802776i	−0.0867338	+	0.0500758i	−0.542740	−	0.839901i	$-0.682613\pi$
$257$	−1.39045	+	0.802776i	−0.0867338	+	0.0500758i	0.456006	+	0.889977i	$0.349280\pi$
$258$	−10.7339	+	6.19722i	−0.668264	+	0.385822i
$259$	31.4222			1.95248
$260$		0			0
$261$	0.394449			0.0244158
$262$	11.0995	−	6.40833i	0.685732	−	0.395908i
$263$	11.8862	−	6.86249i	0.732933	−	0.423159i	−0.0865610	−	0.996247i	$-0.527588\pi$
$263$	11.8862	−	6.86249i	0.732933	−	0.423159i	0.819494	+	0.573087i	$0.194254\pi$
$264$	−2.80278	+	4.85455i	−0.172499	+	0.298777i
$265$		0			0
$266$	16.3625	−	28.3407i	1.00325	−	1.73768i
$267$	12.3072	+	7.10555i	0.753187	+	0.434853i
$268$		−	1.60555i		−	0.0980747i
$269$	−3.59167	+	6.22096i	−0.218988	+	0.379299i	−0.954499	−	0.298214i	$-0.903609\pi$
$269$	−3.59167	+	6.22096i	−0.218988	+	0.379299i	0.735511	+	0.677513i	$0.236942\pi$
$270$		0			0
$271$	13.2111	+	22.8823i	0.802517	+	1.39000i	0.917954	+	0.396686i	$0.129840\pi$
$271$	13.2111	+	22.8823i	0.802517	+	1.39000i	−0.115437	+	0.993315i	$0.536827\pi$
$272$			7.90833i			0.479513i
$273$	17.5033	−	10.1056i	1.05935	−	0.611616i
$274$		0			0
$275$		0			0
$276$	−1.04584	−	1.81144i	−0.0629520	−	0.109036i
$277$	5.95875	+	3.44029i	0.358027	+	0.206707i	0.668215	−	0.743968i	$-0.267059\pi$
$277$	5.95875	+	3.44029i	0.358027	+	0.206707i	−0.310188	+	0.950675i	$0.600392\pi$
$278$			11.8167i			0.708716i
$279$	0.908327	−	1.57327i	0.0543801	−	0.0941891i
$280$		0			0
$281$	9.69722			0.578488			0.289244	−	0.957255i	$-0.406596\pi$
$281$	9.69722			0.578488			0.289244	+	0.957255i	$0.406596\pi$
$282$	7.55605	+	4.36249i	0.449957	+	0.259783i
$283$	−3.88510	+	2.24306i	−0.230945	+	0.133336i	−0.611008	−	0.791624i	$-0.709236\pi$
$283$	−3.88510	+	2.24306i	−0.230945	+	0.133336i	0.380063	+	0.924961i	$0.375902\pi$
$284$	−1.69722	−	2.93968i	−0.100712	−	0.174438i
$285$		0			0
$286$	−15.5139			−0.917355
$287$		−	4.30278i		−	0.253985i
$288$	−1.12824	+	0.651388i	−0.0664820	+	0.0383834i
$289$	22.7708	+	39.4402i	1.33946	+	2.32001i
$290$		0			0
$291$	−19.9361			−1.16867
$292$	−6.92820	−	4.00000i	−0.405442	−	0.234082i
$293$	−13.4354	−	7.75694i	−0.784905	−	0.453165i	0.0532607	−	0.998581i	$-0.483039\pi$
$293$	−13.4354	−	7.75694i	−0.784905	−	0.453165i	−0.838166	+	0.545415i	$0.816372\pi$
$294$	−15.0000			−0.874818
$295$		0			0
$296$	3.65139	+	6.32439i	0.212233	+	0.367598i
$297$	−20.8880	+	12.0597i	−1.21205	+	0.699776i
$298$		−	4.69722i		−	0.272103i
$299$	2.89445	−	5.01333i	0.167390	−	0.289928i
$300$		0			0
$301$	20.4680	+	35.4517i	1.17976	+	2.04340i
$302$	−11.3618	+	6.55971i	−0.653796	+	0.377469i
$303$	−9.26407	−	5.34861i	−0.532207	−	0.307270i
$304$	7.60555			0.436208
$305$		0			0
$306$	−5.15139	+	8.92247i	−0.294485	+	0.510063i
$307$		−	3.21110i		−	0.183267i	−0.995793	−	0.0916337i	$-0.970791\pi$
$307$		−	3.21110i		−	0.183267i	0.995793	−	0.0916337i	$-0.0292089\pi$
$308$	16.0335	+	9.25694i	0.913593	+	0.527463i
$309$	8.86249	+	15.3503i	0.504169	+	0.873247i
$310$		0			0
$311$	0.908327			0.0515065			0.0257532	−	0.999668i	$-0.491802\pi$
$311$	0.908327			0.0515065			0.0257532	+	0.999668i	$0.491802\pi$
$312$	4.06792	+	2.34861i	0.230300	+	0.132964i
$313$			5.09167i			0.287798i	0.989592	+	0.143899i	$0.0459641\pi$
$313$			5.09167i			0.287798i	−0.989592	+	0.143899i	$0.954036\pi$
$314$	2.21110	+	3.82974i	0.124780	+	0.216125i
$315$		0			0
$316$	−2.84861	+	4.93394i	−0.160247	+	0.277556i
$317$			29.5139i			1.65766i	0.559497	+	0.828832i	$0.310994\pi$
$317$			29.5139i			1.65766i	−0.559497	+	0.828832i	$0.689006\pi$
$318$	−2.49465	−	1.44029i	−0.139893	−	0.0807672i
$319$	0.651388	−	1.12824i	0.0364707	−	0.0631691i
$320$		0			0
$321$	5.09167	−	8.81904i	0.284189	−	0.492231i
$322$	−5.98279	+	3.45416i	−0.333408	+	0.192493i
$323$	52.0890	−	30.0736i	2.89831	−	1.67334i
$324$	3.39445			0.188580
$325$		0			0
$326$	8.90833			0.493387
$327$	−4.95798	+	2.86249i	−0.274177	+	0.158296i
$328$	0.866025	−	0.500000i	0.0478183	−	0.0276079i
$329$	14.4083	−	24.9560i	0.794357	−	1.37587i
$330$		0			0
$331$	5.04584	−	8.73965i	0.277344	−	0.480374i	−0.693380	−	0.720572i	$-0.743879\pi$
$331$	5.04584	−	8.73965i	0.277344	−	0.480374i	0.970724	+	0.240198i	$0.0772124\pi$
$332$	−4.17134	−	2.40833i	−0.228932	−	0.132174i
$333$			9.51388i			0.521357i
$334$	1.80278	−	3.12250i	0.0986435	−	0.170856i
$335$		0			0
$336$	−2.80278	−	4.85455i	−0.152904	−	0.264837i
$337$		−	22.0278i		−	1.19993i	−0.800027	−	0.599964i	$-0.795181\pi$
$337$		−	22.0278i		−	1.19993i	0.800027	−	0.599964i	$-0.204819\pi$
$338$			13.0000i			0.707107i
$339$	−9.78890			−0.531660
$340$		0			0
$341$	−3.00000	−	5.19615i	−0.162459	−	0.281387i
$342$	8.58086	+	4.95416i	0.464000	+	0.267890i
$343$			19.4222i			1.04870i
$344$	−4.75694	+	8.23926i	−0.256477	+	0.444231i
$345$		0			0
$346$	24.5139			1.31787
$347$	−10.5751	−	6.10555i	−0.567702	−	0.327763i	0.188529	−	0.982068i	$-0.439628\pi$
$347$	−10.5751	−	6.10555i	−0.567702	−	0.327763i	−0.756231	+	0.654305i	$0.772961\pi$
$348$	−0.341603	+	0.197224i	−0.0183118	+	0.0105723i
$349$	−0.637510	−	1.10420i	−0.0341251	−	0.0591064i	0.848458	−	0.529262i	$-0.177531\pi$
$349$	−0.637510	−	1.10420i	−0.0341251	−	0.0591064i	−0.882584	+	0.470156i	$0.844198\pi$
$350$		0			0
$351$	10.1056	+	17.5033i	0.539394	+	0.934259i
$352$			4.30278i			0.229339i
$353$	−2.15304	+	1.24306i	−0.114595	+	0.0661615i	−0.556202	−	0.831047i	$-0.687742\pi$
$353$	−2.15304	+	1.24306i	−0.114595	+	0.0661615i	0.441607	+	0.897209i	$0.354409\pi$
$354$	2.74306	+	4.75112i	0.145792	+	0.252519i
$355$		0			0
$356$	10.9083			0.578140
$357$	−38.3914	−	22.1653i	−2.03189	−	1.17311i
$358$	6.24500	+	3.60555i	0.330058	+	0.190559i
$359$	−23.9361			−1.26330			−0.631649	−	0.775254i	$-0.717622\pi$
$359$	−23.9361			−1.26330			−0.631649	+	0.775254i	$0.717622\pi$
$360$		0			0
$361$	−19.4222	−	33.6402i	−1.02222	−	1.77054i
$362$	6.14157	−	3.54584i	0.322794	−	0.186365i
$363$			9.78890i			0.513784i
$364$	7.75694	−	13.4354i	0.406574	−	0.704207i
$365$		0			0
$366$	6.65139	+	11.5205i	0.347674	+	0.602188i
$367$	−3.62288	+	2.09167i	−0.189113	+	0.109184i	−0.591567	−	0.806256i	$-0.701491\pi$
$367$	−3.62288	+	2.09167i	−0.189113	+	0.109184i	0.402454	+	0.915440i	$0.368157\pi$
$368$	−1.39045	−	0.802776i	−0.0724821	−	0.0418476i
$369$	1.30278			0.0678198
$370$		0			0
$371$	−4.75694	+	8.23926i	−0.246968	+	0.427761i
$372$			1.81665i			0.0941891i
$373$	−0.683205	−	0.394449i	−0.0353750	−	0.0204238i	0.482208	−	0.876057i	$-0.339835\pi$
$373$	−0.683205	−	0.394449i	−0.0353750	−	0.0204238i	−0.517583	+	0.855633i	$0.673168\pi$
$374$	17.0139	+	29.4689i	0.879767	+	1.52380i
$375$		0			0
$376$	6.69722			0.345383
$377$	−0.945417	−	0.545837i	−0.0486914	−	0.0281120i
$378$		−	24.1194i		−	1.24057i
$379$	−6.59167	−	11.4171i	−0.338592	−	0.586458i	0.645577	−	0.763696i	$-0.276617\pi$
$379$	−6.59167	−	11.4171i	−0.338592	−	0.586458i	−0.984168	+	0.177238i	$0.943284\pi$
$380$		0			0
$381$	3.84861	−	6.66599i	0.197170	−	0.341509i
$382$		−	10.8167i		−	0.553428i
$383$	3.80570	+	2.19722i	0.194462	+	0.112273i	0.594070	−	0.804413i	$-0.297520\pi$
$383$	3.80570	+	2.19722i	0.194462	+	0.112273i	−0.399608	+	0.916686i	$0.630854\pi$
$384$	0.651388	−	1.12824i	0.0332410	−	0.0575751i
$385$		0			0
$386$	0.256939	−	0.445032i	0.0130779	−	0.0226515i
$387$	−10.7339	+	6.19722i	−0.545635	+	0.315023i
$388$	−13.2526	+	7.65139i	−0.672798	+	0.388440i
$389$	−5.21110			−0.264213			−0.132107	−	0.991236i	$-0.542174\pi$
$389$	−5.21110			−0.264213			−0.132107	+	0.991236i	$0.542174\pi$
$390$		0			0
$391$	−12.6972			−0.642126
$392$	−9.97131	+	5.75694i	−0.503627	+	0.290769i
$393$	−14.4602	+	8.34861i	−0.729422	+	0.421132i
$394$	−9.34861	+	16.1923i	−0.470976	+	0.815755i
$395$		0			0
$396$	−2.80278	+	4.85455i	−0.140845	+	0.243950i
$397$	−25.4010	−	14.6653i	−1.27484	−	0.736029i	−0.298944	−	0.954271i	$-0.596634\pi$
$397$	−25.4010	−	14.6653i	−1.27484	−	0.736029i	−0.975895	+	0.218242i	$0.929968\pi$
$398$		−	6.90833i		−	0.346283i
$399$	−21.3167	+	36.9215i	−1.06717	+	1.84839i
$400$		0			0
$401$	8.86249	+	15.3503i	0.442572	+	0.766557i	0.997880	−	0.0650883i	$-0.0207329\pi$
$401$	8.86249	+	15.3503i	0.442572	+	0.766557i	−0.555308	+	0.831645i	$0.687400\pi$
$402$			2.09167i			0.104323i
$403$	−4.35416	+	2.51388i	−0.216896	+	0.125225i
$404$	−8.21110			−0.408518
$405$		0			0
$406$	0.651388	+	1.12824i	0.0323278	+	0.0559935i
$407$	27.2124	+	15.7111i	1.34887	+	0.778770i
$408$		−	10.3028i		−	0.510063i
$409$	−9.89445	+	17.1377i	−0.489249	+	0.847404i	−0.999923	−	0.0123700i	$-0.996062\pi$
$409$	−9.89445	+	17.1377i	−0.489249	+	0.847404i	0.510674	+	0.859774i	$0.329396\pi$
$410$		0			0
$411$		0			0
$412$	11.7828	+	6.80278i	0.580495	+	0.335149i
$413$	15.6919	−	9.05971i	0.772147	−	0.445799i
$414$	−1.04584	−	1.81144i	−0.0514001	−	0.0890275i
$415$		0			0
$416$	3.60555			0.176777
$417$		−	15.3944i		−	0.753869i
$418$	28.3407	−	16.3625i	1.38619	−	0.800316i
$419$	6.84861	+	11.8621i	0.334577	+	0.579504i	0.983403	−	0.181432i	$-0.0580734\pi$
$419$	6.84861	+	11.8621i	0.334577	+	0.579504i	−0.648827	+	0.760936i	$0.724740\pi$
$420$		0			0
$421$	−19.0917			−0.930471			−0.465236	−	0.885187i	$-0.654030\pi$
$421$	−19.0917			−0.930471			−0.465236	+	0.885187i	$0.654030\pi$
$422$	12.8316	+	7.40833i	0.624632	+	0.360632i
$423$	7.55605	+	4.36249i	0.367388	+	0.212112i
$424$	−2.21110			−0.107381
$425$		0			0
$426$	2.21110	+	3.82974i	0.107128	+	0.185552i
$427$	38.0498	−	21.9680i	1.84136	−	1.06311i
$428$		−	7.81665i		−	0.377832i
$429$	20.2111			0.975801
$430$		0			0
$431$	4.95416	+	8.58086i	0.238634	+	0.413326i	0.960322	−	0.278892i	$-0.0899672\pi$
$431$	4.95416	+	8.58086i	0.238634	+	0.413326i	−0.721689	+	0.692218i	$0.756634\pi$
$432$	4.85455	−	2.80278i	0.233565	−	0.134849i
$433$	13.1492	+	7.59167i	0.631908	+	0.364833i	0.781491	−	0.623917i	$-0.214460\pi$
$433$	13.1492	+	7.59167i	0.631908	+	0.364833i	−0.149582	+	0.988749i	$0.547793\pi$
$434$	6.00000			0.288009
$435$		0			0
$436$	−2.19722	+	3.80570i	−0.105228	+	0.182260i
$437$			12.2111i			0.584136i
$438$	9.02589	+	5.21110i	0.431274	+	0.248996i
$439$	−12.5139	−	21.6747i	−0.597255	−	1.03448i	−0.993224	−	0.116212i	$-0.962925\pi$
$439$	−12.5139	−	21.6747i	−0.597255	−	1.03448i	0.395970	−	0.918264i	$-0.370409\pi$
$440$		0			0
$441$	−15.0000			−0.714286
$442$	24.6937	−	14.2569i	1.17456	−	0.678133i
$443$		−	33.1194i		−	1.57355i	−0.617239	−	0.786776i	$-0.711749\pi$
$443$		−	33.1194i		−	1.57355i	0.617239	−	0.786776i	$-0.288251\pi$
$444$	−4.75694	−	8.23926i	−0.225754	−	0.391018i
$445$		0			0
$446$	−2.59167	+	4.48891i	−0.122719	+	0.212556i
$447$			6.11943i			0.289439i
$448$	−3.72631	−	2.15139i	−0.176052	−	0.101644i
$449$	13.0458	−	22.5961i	0.615671	−	1.06637i	−0.374595	−	0.927188i	$-0.622218\pi$
$449$	13.0458	−	22.5961i	0.615671	−	1.06637i	0.990266	−	0.139185i	$-0.0444483\pi$
$450$		0			0
$451$	2.15139	−	3.72631i	0.101305	−	0.175465i
$452$	−6.50721	+	3.75694i	−0.306073	+	0.176712i
$453$	14.8018	−	8.54584i	0.695450	−	0.401518i
$454$	19.0000			0.891714
$455$		0			0
$456$	−9.90833			−0.464000
$457$	−6.50721	+	3.75694i	−0.304394	+	0.175742i	−0.644415	−	0.764676i	$-0.722899\pi$
$457$	−6.50721	+	3.75694i	−0.304394	+	0.175742i	0.340021	+	0.940418i	$0.389566\pi$
$458$	−9.10529	+	5.25694i	−0.425462	+	0.245641i
$459$	22.1653	−	38.3914i	1.03459	−	1.79196i
$460$		0			0
$461$	−13.2569	+	22.9617i	−0.617437	+	1.06943i	0.372514	+	0.928026i	$0.378496\pi$
$461$	−13.2569	+	22.9617i	−0.617437	+	1.06943i	−0.989952	+	0.141406i	$0.954838\pi$
$462$	−20.8880	−	12.0597i	−0.971800	−	0.561069i
$463$		−	28.5139i		−	1.32515i	−0.748995	−	0.662576i	$-0.769463\pi$
$463$		−	28.5139i		−	1.32515i	0.748995	−	0.662576i	$-0.230537\pi$
$464$	−0.151388	+	0.262211i	−0.00702800	+	0.0121729i
$465$		0			0
$466$	−10.5000	−	18.1865i	−0.486403	−	0.842475i
$467$			34.5139i			1.59711i	0.601921	+	0.798556i	$0.294402\pi$
$467$			34.5139i			1.59711i	−0.601921	+	0.798556i	$0.705598\pi$
$468$	4.06792	+	2.34861i	0.188039	+	0.108565i
$469$	6.90833			0.318997
$470$		0			0
$471$	−2.88057	−	4.98929i	−0.132730	−	0.229895i
$472$	3.64692	+	2.10555i	0.167863	+	0.0969159i
$473$			40.9361i			1.88224i
$474$	3.71110	−	6.42782i	0.170457	−	0.295239i
$475$		0			0
$476$	−34.0278			−1.55966
$477$	−2.49465	−	1.44029i	−0.114222	−	0.0659461i
$478$	−25.4804	+	14.7111i	−1.16545	+	0.672870i
$479$	−0.362490	−	0.627852i	−0.0165626	−	0.0286873i	0.857625	−	0.514275i	$-0.171939\pi$
$479$	−0.362490	−	0.627852i	−0.0165626	−	0.0286873i	−0.874188	+	0.485588i	$0.838606\pi$
$480$		0			0
$481$	13.1653	−	22.8029i	0.600284	−	1.03972i
$482$		−	5.00000i		−	0.227744i
$483$	7.79423	−	4.50000i	0.354650	−	0.204757i
$484$	3.75694	+	6.50721i	0.170770	+	0.295782i
$485$		0			0
$486$	12.3944			0.562224
$487$	−2.86029	−	1.65139i	−0.129612	−	0.0748315i	0.433792	−	0.901013i	$-0.357175\pi$
$487$	−2.86029	−	1.65139i	−0.129612	−	0.0748315i	−0.563404	+	0.826181i	$0.690509\pi$
$488$	8.84307	+	5.10555i	0.400307	+	0.231117i
$489$	−11.6056			−0.524821
$490$		0			0
$491$	4.28890	+	7.42859i	0.193555	+	0.335247i	0.946426	−	0.322921i	$-0.104665\pi$
$491$	4.28890	+	7.42859i	0.193555	+	0.335247i	−0.752871	+	0.658168i	$0.771331\pi$
$492$	−1.12824	+	0.651388i	−0.0508648	+	0.0293668i
$493$			2.39445i			0.107841i
$494$	−13.7111	−	23.7483i	−0.616892	−	1.06849i
$495$		0			0
$496$	0.697224	+	1.20763i	0.0313063	+	0.0542241i
$497$	12.6488	−	7.30278i	0.567375	−	0.327574i
$498$	5.43433	+	3.13751i	0.243518	+	0.140595i
$499$	−14.6333			−0.655077			−0.327538	−	0.944838i	$-0.606219\pi$
$499$	−14.6333			−0.655077			−0.327538	+	0.944838i	$0.606219\pi$
$500$		0			0
$501$	−2.34861	+	4.06792i	−0.104928	+	0.181741i
$502$		−	22.3305i		−	0.996660i
$503$	−15.0640	−	8.69722i	−0.671672	−	0.387790i	0.125038	−	0.992152i	$-0.460095\pi$
$503$	−15.0640	−	8.69722i	−0.671672	−	0.387790i	−0.796710	+	0.604362i	$0.793428\pi$
$504$	−2.80278	−	4.85455i	−0.124846	−	0.216239i
$505$		0			0
$506$	−6.90833			−0.307113
$507$		−	16.9361i		−	0.752158i
$508$		−	5.90833i		−	0.262140i
$509$	−12.9083	−	22.3579i	−0.572152	−	0.990996i	−0.996345	−	0.0854238i	$-0.972776\pi$
$509$	−12.9083	−	22.3579i	−0.572152	−	0.990996i	0.424193	−	0.905572i	$-0.360558\pi$
$510$		0			0
$511$	17.2111	−	29.8105i	0.761374	−	1.31874i
$512$		−	1.00000i		−	0.0441942i
$513$	−36.9215	−	21.3167i	−1.63013	−	0.941153i
$514$	0.802776	−	1.39045i	0.0354089	−	0.0613300i
$515$		0			0
$516$	6.19722	−	10.7339i	0.272818	−	0.472534i
$517$	24.9560	−	14.4083i	1.09756	−	0.633677i
$518$	−27.2124	+	15.7111i	−1.19565	+	0.690306i
$519$	−31.9361			−1.40184
$520$		0			0
$521$	34.8444			1.52656			0.763281	−	0.646067i	$-0.223587\pi$
$521$	34.8444			1.52656			0.763281	+	0.646067i	$0.223587\pi$
$522$	−0.341603	+	0.197224i	−0.0149515	+	0.00863228i
$523$	−7.61141	+	4.39445i	−0.332824	+	0.192156i	−0.657094	−	0.753809i	$-0.728215\pi$
$523$	−7.61141	+	4.39445i	−0.332824	+	0.192156i	0.324270	+	0.945964i	$0.394881\pi$
$524$	−6.40833	+	11.0995i	−0.279949	+	0.484886i
$525$		0			0
$526$	−6.86249	+	11.8862i	−0.299219	+	0.518262i
$527$	9.55032	+	5.51388i	0.416018	+	0.240188i
$528$		−	5.60555i		−	0.243950i
$529$	−10.2111	+	17.6861i	−0.443961	+	0.768963i
$530$		0			0
$531$	2.74306	+	4.75112i	0.119039	+	0.206181i
$532$			32.7250i			1.41881i
$533$	−3.12250	−	1.80278i	−0.135250	−	0.0780869i
$534$	−14.2111			−0.614975
$535$		0			0
$536$	0.802776	+	1.39045i	0.0346746	+	0.0600582i
$537$	−8.13583	−	4.69722i	−0.351087	−	0.202700i
$538$		−	7.18335i		−	0.309696i
$539$	−24.7708	+	42.9043i	−1.06695	+	1.84802i
$540$		0			0
$541$	−3.81665			−0.164091			−0.0820454	−	0.996629i	$-0.526145\pi$
$541$	−3.81665			−0.164091			−0.0820454	+	0.996629i	$0.526145\pi$
$542$	−22.8823	−	13.2111i	−0.982879	−	0.567465i
$543$	−8.00109	+	4.61943i	−0.343359	+	0.198239i
$544$	−3.95416	−	6.84881i	−0.169533	−	0.293640i
$545$		0			0
$546$	−10.1056	+	17.5033i	−0.432478	+	0.749073i
$547$		−	14.3944i		−	0.615462i	−0.951473	−	0.307731i	$-0.900430\pi$
$547$		−	14.3944i		−	0.615462i	0.951473	−	0.307731i	$-0.0995697\pi$
$548$		0			0
$549$	6.65139	+	11.5205i	0.283874	+	0.491685i
$550$		0			0
$551$	2.30278			0.0981015
$552$	1.81144	+	1.04584i	0.0771001	+	0.0445138i
$553$	−21.2296	−	12.2569i	−0.902776	−	0.521218i
$554$	−6.88057			−0.292327
$555$		0			0
$556$	−5.90833	−	10.2335i	−0.250569	−	0.433998i
$557$	10.2335	−	5.90833i	0.433608	−	0.250344i	−0.267274	−	0.963620i	$-0.586123\pi$
$557$	10.2335	−	5.90833i	0.433608	−	0.250344i	0.700883	+	0.713277i	$0.252790\pi$
$558$			1.81665i			0.0769051i
$559$	34.3028			1.45085
$560$		0			0
$561$	−22.1653	−	38.3914i	−0.935818	−	1.62088i
$562$	−8.39804	+	4.84861i	−0.354250	+	0.204526i
$563$	−10.1541	−	5.86249i	−0.427946	−	0.247075i	0.270525	−	0.962713i	$-0.412803\pi$
$563$	−10.1541	−	5.86249i	−0.427946	−	0.247075i	−0.698471	+	0.715638i	$0.746136\pi$
$564$	−8.72498			−0.367388
$565$		0			0
$566$	2.24306	−	3.88510i	0.0942829	−	0.163303i
$567$			14.6056i			0.613375i
$568$	2.93968	+	1.69722i	0.123346	+	0.0712140i
$569$	−16.5736	−	28.7063i	−0.694801	−	1.20343i	−0.970248	−	0.242115i	$-0.922159\pi$
$569$	−16.5736	−	28.7063i	−0.694801	−	1.20343i	0.275447	−	0.961316i	$-0.411174\pi$
$570$		0			0
$571$	−4.51388			−0.188900			−0.0944500	−	0.995530i	$-0.530109\pi$
$571$	−4.51388			−0.188900			−0.0944500	+	0.995530i	$0.530109\pi$
$572$	13.4354	−	7.75694i	0.561763	−	0.324334i
$573$			14.0917i			0.588688i
$574$	2.15139	+	3.72631i	0.0897972	+	0.155533i
$575$		0			0
$576$	0.651388	−	1.12824i	0.0271412	−	0.0470099i
$577$			16.3944i			0.682510i	0.939971	+	0.341255i	$0.110852\pi$
$577$			16.3944i			0.682510i	−0.939971	+	0.341255i	$0.889148\pi$
$578$	−39.4402	−	22.7708i	−1.64050	−	0.947141i
$579$	−0.334734	+	0.579776i	−0.0139111	+	0.0240947i
$580$		0			0
$581$	10.3625	−	17.9484i	0.429909	−	0.744623i
$582$	17.2652	−	9.96804i	0.715664	−	0.413189i
$583$	−8.23926	+	4.75694i	−0.341235	+	0.197012i
$584$	8.00000			0.331042
$585$		0			0
$586$	15.5139			0.640872
$587$	28.1578	−	16.2569i	1.16220	−	0.670996i	0.210369	−	0.977622i	$-0.432534\pi$
$587$	28.1578	−	16.2569i	1.16220	−	0.670996i	0.951830	+	0.306626i	$0.0992002\pi$
$588$	12.9904	−	7.50000i	0.535714	−	0.309295i
$589$	5.30278	−	9.18468i	0.218497	−	0.378448i
$590$		0			0
$591$	12.1791	−	21.0949i	0.500983	−	0.867728i
$592$	−6.32439	−	3.65139i	−0.259931	−	0.150071i
$593$			36.6611i			1.50549i	0.658313	+	0.752745i	$0.271271\pi$
$593$			36.6611i			1.50549i	−0.658313	+	0.752745i	$0.728729\pi$
$594$	12.0597	−	20.8880i	0.494816	−	0.857047i
$595$		0			0
$596$	2.34861	+	4.06792i	0.0962029	+	0.166628i
$597$			9.00000i			0.368345i
$598$			5.78890i			0.236726i
$599$	41.6611			1.70222			0.851112	−	0.524983i	$-0.175928\pi$
$599$	41.6611			1.70222			0.851112	+	0.524983i	$0.175928\pi$
$600$		0			0
$601$	7.80278	+	13.5148i	0.318282	+	0.551280i	0.980130	−	0.198358i	$-0.0635608\pi$
$601$	7.80278	+	13.5148i	0.318282	+	0.551280i	−0.661848	+	0.749638i	$0.730227\pi$
$602$	−35.4517	−	20.4680i	−1.44490	−	0.834215i
$603$			2.09167i			0.0851795i
$604$	6.55971	−	11.3618i	0.266911	−	0.462303i
$605$		0			0
$606$	10.6972			0.434545
$607$	−35.5551	−	20.5278i	−1.44314	−	0.833196i	−0.445080	−	0.895491i	$-0.646825\pi$
$607$	−35.5551	−	20.5278i	−1.44314	−	0.833196i	−0.998058	+	0.0622949i	$0.980158\pi$
$608$	−6.58660	+	3.80278i	−0.267122	+	0.154223i
$609$	−0.848612	−	1.46984i	−0.0343875	−	0.0595609i
$610$		0			0
$611$	−12.0736	−	20.9121i	−0.488445	−	0.846012i
$612$		−	10.3028i		−	0.416465i
$613$	37.6288	−	21.7250i	1.51981	−	0.877464i	0.520084	−	0.854115i	$-0.325901\pi$
$613$	37.6288	−	21.7250i	1.51981	−	0.877464i	0.999727	−	0.0233488i	$-0.00743283\pi$
$614$	1.60555	+	2.78090i	0.0647948	+	0.112228i
$615$		0			0
$616$	−18.5139			−0.745945
$617$	42.4833	+	24.5278i	1.71031	+	0.987450i	0.934122	+	0.356954i	$0.116185\pi$
$617$	42.4833	+	24.5278i	1.71031	+	0.987450i	0.776192	+	0.630497i	$0.217149\pi$
$618$	−15.3503	−	8.86249i	−0.617479	−	0.356502i
$619$	32.3305			1.29947			0.649737	−	0.760159i	$-0.274879\pi$
$619$	32.3305			1.29947			0.649737	+	0.760159i	$0.274879\pi$
$620$		0			0
$621$	4.50000	+	7.79423i	0.180579	+	0.312772i
$622$	−0.786634	+	0.454163i	−0.0315412	+	0.0182103i
$623$			46.9361i			1.88045i
$624$	−4.69722			−0.188039
$625$		0			0
$626$	−2.54584	−	4.40952i	−0.101752	−	0.176240i
$627$	−36.9215	+	21.3167i	−1.47450	+	0.851305i
$628$	−3.82974	−	2.21110i	−0.152823	−	0.0882326i
$629$	−57.7527			−2.30275
$630$		0			0
$631$	7.95416	−	13.7770i	0.316650	−	0.548454i	−0.663137	−	0.748498i	$-0.730775\pi$
$631$	7.95416	−	13.7770i	0.316650	−	0.548454i	0.979787	+	0.200044i	$0.0641085\pi$
$632$		−	5.69722i		−	0.226623i
$633$	−16.7167	−	9.65139i	−0.664429	−	0.383608i
$634$	−14.7569	−	25.5598i	−0.586073	−	1.01511i
$635$		0			0
$636$	2.88057			0.114222
$637$	35.9521	+	20.7569i	1.42447	+	0.822420i
$638$			1.30278i			0.0515774i
$639$	2.21110	+	3.82974i	0.0874699	+	0.151502i
$640$		0			0
$641$	25.0875	−	43.4528i	0.990896	−	1.71628i	0.378852	−	0.925457i	$-0.376319\pi$
$641$	25.0875	−	43.4528i	0.990896	−	1.71628i	0.612043	−	0.790824i	$-0.290348\pi$
$642$			10.1833i			0.401905i
$643$	5.69654	+	3.28890i	0.224650	+	0.129701i	0.608101	−	0.793859i	$-0.291931\pi$
$643$	5.69654	+	3.28890i	0.224650	+	0.129701i	−0.383452	+	0.923561i	$0.625265\pi$
$644$	3.45416	−	5.98279i	0.136113	−	0.235755i
$645$		0			0
$646$	−30.0736	+	52.0890i	−1.18323	+	2.04941i
$647$	−10.9961	+	6.34861i	−0.432302	+	0.249590i	−0.700327	−	0.713822i	$-0.746962\pi$
$647$	−10.9961	+	6.34861i	−0.432302	+	0.249590i	0.268025	+	0.963412i	$0.413629\pi$
$648$	−2.93968	+	1.69722i	−0.115481	+	0.0666733i
$649$	18.1194			0.711250
$650$		0			0
$651$	−7.81665			−0.306359
$652$	−7.71484	+	4.45416i	−0.302136	+	0.174439i
$653$	5.37897	−	3.10555i	0.210495	−	0.121530i	−0.391046	−	0.920371i	$-0.627887\pi$
$653$	5.37897	−	3.10555i	0.210495	−	0.121530i	0.601542	+	0.798841i	$0.294553\pi$
$654$	2.86249	−	4.95798i	0.111932	−	0.193872i
$655$		0			0
$656$	−0.500000	+	0.866025i	−0.0195217	+	0.0338126i
$657$	9.02589	+	5.21110i	0.352134	+	0.203304i
$658$			28.8167i			1.12339i
$659$	2.60555	−	4.51295i	0.101498	−	0.175799i	−0.810804	−	0.585318i	$-0.800970\pi$
$659$	2.60555	−	4.51295i	0.101498	−	0.175799i	0.912302	+	0.409518i	$0.134303\pi$
$660$		0			0
$661$	12.3486	+	21.3884i	0.480305	+	0.831913i	0.999745	−	0.0225940i	$-0.00719252\pi$
$661$	12.3486	+	21.3884i	0.480305	+	0.831913i	−0.519439	+	0.854507i	$0.673859\pi$
$662$			10.0917i			0.392224i
$663$	−32.1704	+	18.5736i	−1.24940	+	0.721339i
$664$	4.81665			0.186922
$665$		0			0
$666$	−4.75694	−	8.23926i	−0.184328	−	0.319265i
$667$	−0.420994	−	0.243061i	−0.0163009	−	0.00941136i
$668$			3.60555i			0.139503i
$669$	3.37637	−	5.84804i	0.130538	−	0.226098i
$670$		0			0
$671$	43.9361			1.69613
$672$	4.85455	+	2.80278i	0.187268	+	0.108119i
$673$	−18.2106	+	10.5139i	−0.701966	+	0.405280i	−0.808079	−	0.589074i	$-0.799493\pi$
$673$	−18.2106	+	10.5139i	−0.701966	+	0.405280i	0.106113	+	0.994354i	$0.466159\pi$
$674$	11.0139	+	19.0766i	0.424239	+	0.734803i
$675$		0			0
$676$	−6.50000	−	11.2583i	−0.250000	−	0.433013i
$677$			21.4222i			0.823322i	0.911337	+	0.411661i	$0.135051\pi$
$677$			21.4222i			0.823322i	−0.911337	+	0.411661i	$0.864949\pi$
$678$	8.47743	−	4.89445i	0.325574	−	0.187970i
$679$	−32.9222	−	57.0229i	−1.26344	−	2.18834i
$680$		0			0
$681$	−24.7527			−0.948527
$682$	5.19615	+	3.00000i	0.198971	+	0.114876i
$683$	23.0651	+	13.3167i	0.882562	+	0.509548i	0.871502	−	0.490391i	$-0.163146\pi$
$683$	23.0651	+	13.3167i	0.882562	+	0.509548i	0.0110599	+	0.999939i	$0.496479\pi$
$684$	−9.90833			−0.378854
$685$		0			0
$686$	−9.71110	−	16.8201i	−0.370772	−	0.642195i
$687$	11.8621	−	6.84861i	0.452569	−	0.261291i
$688$		−	9.51388i		−	0.362713i
$689$	3.98612	+	6.90417i	0.151859	+	0.263028i
$690$		0			0
$691$	15.3028	+	26.5052i	0.582145	+	1.00830i	0.995225	+	0.0976099i	$0.0311197\pi$
$691$	15.3028	+	26.5052i	0.582145	+	1.00830i	−0.413080	+	0.910695i	$0.635547\pi$
$692$	−21.2296	+	12.2569i	−0.807030	+	0.465939i
$693$	−20.8880	−	12.0597i	−0.793471	−	0.458111i
$694$	12.2111			0.463527
$695$		0			0
$696$	0.197224	−	0.341603i	0.00747577	−	0.0129484i
$697$			7.90833i			0.299549i
$698$	1.10420	+	0.637510i	0.0417946	+	0.0241301i
$699$	13.6791	+	23.6930i	0.517393	+	0.896151i
$700$		0			0
$701$	−13.9083			−0.525310			−0.262655	−	0.964890i	$-0.584598\pi$
$701$	−13.9083			−0.525310			−0.262655	+	0.964890i	$0.584598\pi$
$702$	−17.5033	−	10.1056i	−0.660621	−	0.381409i
$703$			55.5416i			2.09479i
$704$	−2.15139	−	3.72631i	−0.0810835	−	0.140441i
$705$		0			0
$706$	1.24306	−	2.15304i	0.0467832	−	0.0810309i
$707$		−	35.3305i		−	1.32874i
$708$	−4.75112	−	2.74306i	−0.178558	−	0.103091i
$709$	−23.7708	+	41.1723i	−0.892732	+	1.54626i	−0.0561448	+	0.998423i	$0.517881\pi$
$709$	−23.7708	+	41.1723i	−0.892732	+	1.54626i	−0.836587	+	0.547834i	$0.815452\pi$
$710$		0			0
$711$	3.71110	−	6.42782i	0.139177	−	0.241062i
$712$	−9.44689	+	5.45416i	−0.354037	+	0.204403i
$713$	−1.93891	+	1.11943i	−0.0726127	+	0.0419230i
$714$	44.3305			1.65903
$715$		0			0
$716$	−7.21110			−0.269492
$717$	33.1952	−	19.1653i	1.23970	−	0.715740i
$718$	20.7293	−	11.9680i	0.773609	−	0.446643i
$719$	19.4680	−	33.7196i	0.726035	−	1.25753i	−0.232511	−	0.972594i	$-0.574694\pi$
$719$	19.4680	−	33.7196i	0.726035	−	1.25753i	0.958546	−	0.284936i	$-0.0919725\pi$
$720$		0			0
$721$	−29.2708	+	50.6985i	−1.09010	+	1.88811i
$722$	33.6402	+	19.4222i	1.25196	+	0.722820i
$723$			6.51388i			0.242254i
$724$	−3.54584	+	6.14157i	−0.131780	+	0.228250i
$725$		0			0
$726$	−4.89445	−	8.47743i	−0.181650	−	0.314627i
$727$			30.0555i			1.11470i	0.830279	+	0.557349i	$0.188181\pi$
$727$			30.0555i			1.11470i	−0.830279	+	0.557349i	$0.811819\pi$
$728$			15.5139i			0.574983i
$729$	−26.3305			−0.975205
$730$		0			0
$731$	−37.6194	−	65.1588i	−1.39140	−	2.40998i
$732$	−11.5205	−	6.65139i	−0.425811	−	0.245842i
$733$			12.5416i			0.463236i	0.972807	+	0.231618i	$0.0744019\pi$
$733$			12.5416i			0.463236i	−0.972807	+	0.231618i	$0.925598\pi$
$734$	2.09167	−	3.62288i	0.0772051	−	0.133723i
$735$		0			0
$736$	1.60555			0.0591814
$737$	5.98279	+	3.45416i	0.220379	+	0.127236i
$738$	−1.12824	+	0.651388i	−0.0415310	+	0.0239779i
$739$	8.86249	+	15.3503i	0.326012	+	0.564669i	0.981717	−	0.190348i	$-0.0609617\pi$
$739$	8.86249	+	15.3503i	0.326012	+	0.564669i	−0.655705	+	0.755017i	$0.727628\pi$
$740$		0			0
$741$	17.8625	+	30.9387i	0.656195	+	1.13656i
$742$		−	9.51388i		−	0.349265i
$743$	−18.0037	+	10.3944i	−0.660492	+	0.381335i	−0.792464	−	0.609918i	$-0.791202\pi$
$743$	−18.0037	+	10.3944i	−0.660492	+	0.381335i	0.131972	+	0.991253i	$0.457869\pi$
$744$	−0.908327	−	1.57327i	−0.0333009	−	0.0576788i
$745$		0			0
$746$	0.788897			0.0288836
$747$	5.43433	+	3.13751i	0.198832	+	0.114795i
$748$	−29.4689	−	17.0139i	−1.07749	−	0.622089i
$749$	33.6333			1.22893
$750$		0			0
$751$	5.31665	+	9.20871i	0.194007	+	0.336031i	0.946575	−	0.322485i	$-0.104518\pi$
$751$	5.31665	+	9.20871i	0.194007	+	0.336031i	−0.752567	+	0.658515i	$0.771185\pi$
$752$	−5.79997	+	3.34861i	−0.211503	+	0.122111i
$753$			29.0917i			1.06016i
$754$	1.09167			0.0397564
$755$		0			0
$756$	12.0597	+	20.8880i	0.438608	+	0.759691i
$757$	−20.9674	+	12.1056i	−0.762074	+	0.439984i	−0.830040	−	0.557704i	$-0.811682\pi$
$757$	−20.9674	+	12.1056i	−0.762074	+	0.439984i	0.0679658	+	0.997688i	$0.478349\pi$
$758$	11.4171	+	6.59167i	0.414688	+	0.239420i
$759$	9.00000			0.326679
$760$		0			0
$761$	6.19722	−	10.7339i	0.224649	−	0.389104i	−0.731565	−	0.681772i	$-0.761210\pi$
$761$	6.19722	−	10.7339i	0.224649	−	0.389104i	0.956214	+	0.292668i	$0.0945430\pi$
$762$			7.69722i			0.278841i
$763$	−16.3751	−	9.45416i	−0.592818	−	0.342264i
$764$	5.40833	+	9.36750i	0.195666	+	0.338904i
$765$		0			0
$766$	−4.39445			−0.158778
$767$		−	15.1833i		−	0.548239i
$768$			1.30278i			0.0470099i
$769$	−21.7250	−	37.6288i	−0.783423	−	1.35693i	−0.929937	−	0.367720i	$-0.880139\pi$
$769$	−21.7250	−	37.6288i	−0.783423	−	1.35693i	0.146514	−	0.989209i	$-0.453195\pi$
$770$		0			0
$771$	−1.04584	+	1.81144i	−0.0376649	+	0.0652375i
$772$			0.513878i			0.0184949i
$773$	14.5877	+	8.42221i	0.524683	+	0.302926i	0.738848	−	0.673872i	$-0.235370\pi$
$773$	14.5877	+	8.42221i	0.524683	+	0.302926i	−0.214166	+	0.976797i	$0.568703\pi$
$774$	6.19722	−	10.7339i	0.222755	−	0.385822i
$775$		0			0
$776$	7.65139	−	13.2526i	0.274669	−	0.475740i
$777$	35.4517	−	20.4680i	1.27182	−	0.734287i
$778$	4.51295	−	2.60555i	0.161797	−	0.0934135i
$779$	7.60555			0.272497
$780$		0			0
$781$	14.6056			0.522628
$782$	10.9961	−	6.34861i	0.393220	−	0.227026i
$783$	1.46984	−	0.848612i	0.0525278	−	0.0303269i
$784$	5.75694	−	9.97131i	0.205605	−	0.356118i
$785$		0			0
$786$	8.34861	−	14.4602i	0.297785	−	0.515779i
$787$	−12.7282	−	7.34861i	−0.453710	−	0.261950i	0.255686	−	0.966760i	$-0.417699\pi$
$787$	−12.7282	−	7.34861i	−0.453710	−	0.261950i	−0.709396	+	0.704810i	$0.751032\pi$
$788$		−	18.6972i		−	0.666061i
$789$	8.94029	−	15.4850i	0.318283	−	0.551282i
$790$		0			0
$791$	−16.1653	−	27.9991i	−0.574771	−	0.995532i
$792$		−	5.60555i		−	0.199185i
$793$		−	36.8167i		−	1.30740i
$794$	29.3305			1.04090
$795$		0			0
$796$	3.45416	+	5.98279i	0.122430	+	0.212054i
$797$	−0.866025	−	0.500000i	−0.0306762	−	0.0177109i	0.484583	−	0.874745i	$-0.338971\pi$
$797$	−0.866025	−	0.500000i	−0.0306762	−	0.0177109i	−0.515260	+	0.857034i	$0.672305\pi$
$798$		−	42.6333i		−	1.50920i
$799$	−26.4819	+	45.8680i	−0.936863	+	1.62269i
$800$		0			0
$801$	−14.2111			−0.502125
$802$	−15.3503	−	8.86249i	−0.542037	−	0.312945i
$803$	29.8105	−	17.2111i	1.05199	−	0.607367i
$804$	−1.04584	−	1.81144i	−0.0368838	−	0.0638846i
$805$		0			0
$806$	2.51388	−	4.35416i	0.0885476	−	0.153369i
$807$			9.35829i			0.329427i
$808$	7.11102	−	4.10555i	0.250165	−	0.144433i
$809$	14.8167	+	25.6632i	0.520926	+	0.902270i	0.999704	+	0.0243340i	$0.00774652\pi$
$809$	14.8167	+	25.6632i	0.520926	+	0.902270i	−0.478778	+	0.877936i	$0.658920\pi$
$810$		0			0
$811$	−25.3028			−0.888501			−0.444250	−	0.895903i	$-0.646530\pi$
$811$	−25.3028			−0.888501			−0.444250	+	0.895903i	$0.646530\pi$
$812$	−1.12824	−	0.651388i	−0.0395933	−	0.0228592i
$813$	29.8105	+	17.2111i	1.04550	+	0.603620i
$814$	−31.4222			−1.10135
$815$		0			0
$816$	5.15139	+	8.92247i	0.180335	+	0.312349i
$817$	−62.6641	+	36.1791i	−2.19234	+	1.26575i
$818$		−	19.7889i		−	0.691903i
$819$	−10.1056	+	17.5033i	−0.353117	+	0.611616i
$820$		0			0
$821$	−5.28890	−	9.16064i	−0.184584	−	0.319709i	0.758852	−	0.651263i	$-0.225760\pi$
$821$	−5.28890	−	9.16064i	−0.184584	−	0.319709i	−0.943436	+	0.331554i	$0.892427\pi$
$822$		0			0
$823$	−29.2861	−	16.9083i	−1.02085	−	0.589387i	−0.106499	−	0.994313i	$-0.533964\pi$
$823$	−29.2861	−	16.9083i	−1.02085	−	0.589387i	−0.914350	+	0.404926i	$0.867297\pi$
$824$	−13.6056			−0.473972
$825$		0			0
$826$	−9.05971	+	15.6919i	−0.315228	+	0.545991i
$827$		−	14.4500i		−	0.502474i	−0.967926	−	0.251237i	$-0.919163\pi$
$827$		−	14.4500i		−	0.502474i	0.967926	−	0.251237i	$-0.0808374\pi$
$828$	1.81144	+	1.04584i	0.0629520	+	0.0363453i
$829$	14.0458	+	24.3281i	0.487832	+	0.844950i	0.999902	−	0.0139938i	$-0.00445451\pi$
$829$	14.0458	+	24.3281i	0.487832	+	0.844950i	−0.512070	+	0.858944i	$0.671121\pi$
$830$		0			0
$831$	8.96384			0.310952
$832$	−3.12250	+	1.80278i	−0.108253	+	0.0625000i
$833$		−	91.0555i		−	3.15489i
$834$	7.69722	+	13.3320i	0.266533	+	0.461649i
$835$		0			0
$836$	−16.3625	+	28.3407i	−0.565909	+	0.980182i
$837$		−	7.81665i		−	0.270183i
$838$	−11.8621	−	6.84861i	−0.409771	−	0.236581i
$839$	−16.9680	+	29.3895i	−0.585802	+	1.01464i	0.408973	+	0.912546i	$0.365887\pi$
$839$	−16.9680	+	29.3895i	−0.585802	+	1.01464i	−0.994775	+	0.102092i	$0.967446\pi$
$840$		0			0
$841$	14.4542	−	25.0353i	0.498419	−	0.863288i
$842$	16.5339	−	9.54584i	0.569795	−	0.328971i
$843$	10.9408	−	6.31665i	0.376820	−	0.217557i
$844$	−14.8167			−0.510010
$845$		0			0
$846$	−8.72498			−0.299971
$847$	−27.9991	+	16.1653i	−0.962059	+	0.555445i
$848$	1.91487	−	1.10555i	0.0657569	−	0.0379648i
$849$	−2.92221	+	5.06141i	−0.100290	+	0.173707i
$850$		0			0
$851$	5.86249	−	10.1541i	0.200964	−	0.348079i
$852$	−3.82974	−	2.21110i	−0.131205	−	0.0757511i
$853$		−	40.7250i		−	1.39440i	−0.716878	−	0.697198i	$-0.754430\pi$
$853$		−	40.7250i		−	1.39440i	0.716878	−	0.697198i	$-0.245570\pi$
$854$	−21.9680	+	38.0498i	−0.751731	+	1.30204i
$855$		0			0
$856$	3.90833	+	6.76942i	0.133584	+	0.231374i
$857$		−	49.4222i		−	1.68823i	−0.536162	−	0.844115i	$-0.680126\pi$
$857$		−	49.4222i		−	1.68823i	0.536162	−	0.844115i	$-0.319874\pi$
$858$	−17.5033	+	10.1056i	−0.597554	+	0.344998i
$859$	10.1194			0.345270			0.172635	−	0.984986i	$-0.444772\pi$
$859$	10.1194			0.345270			0.172635	+	0.984986i	$0.444772\pi$
$860$		0			0
$861$	−2.80278	−	4.85455i	−0.0955183	−	0.165443i
$862$	−8.58086	−	4.95416i	−0.292265	−	0.168739i
$863$			32.0278i			1.09024i	0.838359	+	0.545119i	$0.183515\pi$
$863$			32.0278i			1.09024i	−0.838359	+	0.545119i	$0.816485\pi$
$864$	−2.80278	+	4.85455i	−0.0953524	+	0.165155i
$865$		0			0
$866$	−15.1833			−0.515951
$867$	51.3817	+	29.6653i	1.74502	+	1.00749i
$868$	−5.19615	+	3.00000i	−0.176369	+	0.101827i
$869$	−12.2569	−	21.2296i	−0.415788	−	0.720166i
$870$		0			0
$871$	2.89445	−	5.01333i	0.0980747	−	0.169870i
$872$		−	4.39445i		−	0.148815i
$873$	17.2652	−	9.96804i	0.584337	−	0.337367i
$874$	−6.10555	−	10.5751i	−0.206523	−	0.357709i
$875$		0			0
$876$	−10.4222			−0.352134
$877$	46.3131	+	26.7389i	1.56388	+	0.902907i	0.996858	+	0.0792049i	$0.0252381\pi$
$877$	46.3131	+	26.7389i	1.56388	+	0.902907i	0.567023	+	0.823702i	$0.308095\pi$
$878$	21.6747	+	12.5139i	0.731485	+	0.422323i
$879$	−20.2111			−0.681704
$880$		0			0
$881$	28.7847	+	49.8566i	0.969781	+	1.67971i	0.696181	+	0.717867i	$0.254881\pi$
$881$	28.7847	+	49.8566i	0.969781	+	1.67971i	0.273600	+	0.961843i	$0.411785\pi$
$882$	12.9904	−	7.50000i	0.437409	−	0.252538i
$883$		−	23.1194i		−	0.778031i	−0.921231	−	0.389015i	$-0.872815\pi$
$883$		−	23.1194i		−	0.778031i	0.921231	−	0.389015i	$-0.127185\pi$
$884$	−14.2569	+	24.6937i	−0.479513	+	0.830540i
$885$		0			0
$886$	16.5597	+	28.6823i	0.556334	+	0.963600i
$887$	−8.29461	+	4.78890i	−0.278506	+	0.160795i	−0.632747	−	0.774359i	$-0.718073\pi$
$887$	−8.29461	+	4.78890i	−0.278506	+	0.160795i	0.354241	+	0.935154i	$0.384739\pi$
$888$	8.23926	+	4.75694i	0.276491	+	0.159632i
$889$	25.4222			0.852633
$890$		0			0
$891$	−7.30278	+	12.6488i	−0.244652	+	0.423750i
$892$		−	5.18335i		−	0.173551i
$893$	44.1119	+	25.4680i	1.47615	+	0.852256i
$894$	−3.05971	−	5.29958i	−0.102332	−	0.177245i
$895$		0			0
$896$	4.30278			0.143746
$897$		−	7.54163i		−	0.251808i
$898$			26.0917i			0.870690i
$899$	0.211103	+	0.365640i	0.00704066	+	0.0121948i
$900$		0			0
$901$	8.74306	−	15.1434i	0.291274	−	0.504501i
$902$			4.30278i			0.143267i
$903$	46.1856	+	26.6653i	1.53696	+	0.887364i
$904$	3.75694	−	6.50721i	0.124954	−	0.216427i
$905$		0			0
$906$	−8.54584	+	14.8018i	−0.283916	+	0.491758i
$907$	−29.1513	+	16.8305i	−0.967954	+	0.558849i	−0.898612	−	0.438744i	$-0.855423\pi$
$907$	−29.1513	+	16.8305i	−0.967954	+	0.558849i	−0.0693423	+	0.997593i	$0.522090\pi$
$908$	−16.4545	+	9.50000i	−0.546061	+	0.315269i
$909$	10.6972			0.354805
$910$		0			0
$911$	37.4222			1.23985			0.619926	−	0.784660i	$-0.287162\pi$
$911$	37.4222			1.23985			0.619926	+	0.784660i	$0.287162\pi$
$912$	8.58086	−	4.95416i	0.284141	−	0.164049i
$913$	17.9484	−	10.3625i	0.594004	−	0.342948i
$914$	3.75694	−	6.50721i	0.124269	−	0.215239i
$915$		0			0
$916$	5.25694	−	9.10529i	0.173694	−	0.300847i
$917$	−47.7589	−	27.5736i	−1.57714	−	0.910560i
$918$			44.3305i			1.46313i
$919$	−11.1194	+	19.2594i	−0.366796	+	0.635310i	−0.989063	−	0.147496i	$-0.952879\pi$
$919$	−11.1194	+	19.2594i	−0.366796	+	0.635310i	0.622267	+	0.782805i	$0.286212\pi$
$920$		0			0
$921$	−2.09167	−	3.62288i	−0.0689230	−	0.119378i
$922$		−	26.5139i		−	0.873188i
$923$		−	12.2389i		−	0.402847i
$924$	24.1194			0.793471
$925$		0			0
$926$	14.2569	+	24.6937i	0.468512	+	0.811487i
$927$	−15.3503	−	8.86249i	−0.504169	−	0.291082i
$928$		−	0.302776i		−	0.00993910i
$929$	19.3305	−	33.4815i	0.634214	−	1.09849i	−0.352467	−	0.935824i	$-0.614657\pi$
$929$	19.3305	−	33.4815i	0.634214	−	1.09849i	0.986681	−	0.162667i	$-0.0520096\pi$
$930$		0			0
$931$	−87.5694			−2.86997
$932$	18.1865	+	10.5000i	0.595720	+	0.343939i
$933$	1.02481	−	0.591673i	0.0335507	−	0.0193705i
$934$	−17.2569	−	29.8899i	−0.564664	−	0.978027i
$935$		0			0
$936$	−4.69722			−0.153534
$937$		−	1.33053i		−	0.0434666i	−0.999764	−	0.0217333i	$-0.993082\pi$
$937$		−	1.33053i		−	0.0434666i	0.999764	−	0.0217333i	$-0.00691847\pi$
$938$	−5.98279	+	3.45416i	−0.195345	+	0.112782i
$939$	3.31665	+	5.74461i	0.108235	+	0.187468i
$940$		0			0
$941$	47.5694			1.55072			0.775359	−	0.631521i	$-0.217569\pi$
$941$	47.5694			1.55072			0.775359	+	0.631521i	$0.217569\pi$
$942$	4.98929	+	2.88057i	0.162560	+	0.0938541i
$943$	−1.39045	−	0.802776i	−0.0452792	−	0.0261420i
$944$	−4.21110			−0.137060
$945$		0			0
$946$	−20.4680	−	35.4517i	−0.665473	−	1.15263i
$947$	−10.1061	+	5.83473i	−0.328403	+	0.189603i	−0.655132	−	0.755515i	$-0.727387\pi$
$947$	−10.1061	+	5.83473i	−0.328403	+	0.189603i	0.326729	+	0.945118i	$0.394054\pi$
$948$			7.42221i			0.241062i
$949$	−14.4222	−	24.9800i	−0.468165	−	0.810885i
$950$		0			0
$951$	19.2250	+	33.2986i	0.623413	+	1.07978i
$952$	29.4689	−	17.0139i	0.955093	−	0.551423i
$953$	37.6528	+	21.7389i	1.21969	+	0.704191i	0.964852	−	0.262792i	$-0.0846433\pi$
$953$	37.6528	+	21.7389i	1.21969	+	0.704191i	0.254842	+	0.966983i	$0.417977\pi$
$954$	2.88057			0.0932619
$955$		0			0
$956$	14.7111	−	25.4804i	0.475791	−	0.824094i
$957$		−	1.69722i		−	0.0548635i
$958$	0.627852	+	0.362490i	0.0202850	+	0.0117115i
$959$		0			0
$960$		0			0
$961$	−29.0555			−0.937275
$962$			26.3305i			0.848930i
$963$			10.1833i			0.328154i
$964$	2.50000	+	4.33013i	0.0805196	+	0.139464i
$965$		0			0
$966$	−4.50000	+	7.79423i	−0.144785	+	0.250775i
$967$		−	4.97224i		−	0.159897i	−0.996799	−	0.0799483i	$-0.974524\pi$
$967$		−	4.97224i		−	0.159897i	0.996799	−	0.0799483i	$-0.0254755\pi$
$968$	−6.50721	−	3.75694i	−0.209150	−	0.120753i
$969$	39.1791	−	67.8603i	1.25862	−	2.17999i
$970$		0			0
$971$	−23.2250	+	40.2268i	−0.745325	+	1.29094i	0.204718	+	0.978821i	$0.434372\pi$
$971$	−23.2250	+	40.2268i	−0.745325	+	1.29094i	−0.950043	+	0.312120i	$0.898961\pi$
$972$	−10.7339	+	6.19722i	−0.344290	+	0.198776i
$973$	44.0326	−	25.4222i	1.41162	−	0.814998i
$974$	3.30278			0.105828
$975$		0			0
$976$	−10.2111			−0.326849
$977$	4.17134	−	2.40833i	0.133453	−	0.0770492i	−0.431787	−	0.901976i	$-0.642117\pi$
$977$	4.17134	−	2.40833i	0.133453	−	0.0770492i	0.565240	+	0.824926i	$0.308783\pi$
$978$	10.0507	−	5.80278i	0.321386	−	0.185552i
$979$	−23.4680	+	40.6478i	−0.750042	+	1.29911i
$980$		0			0
$981$	2.86249	−	4.95798i	0.0913923	−	0.158296i
$982$	−7.42859	−	4.28890i	−0.237056	−	0.136864i
$983$		−	53.9638i		−	1.72118i	−0.509299	−	0.860590i	$-0.670095\pi$
$983$		−	53.9638i		−	1.72118i	0.509299	−	0.860590i	$-0.329905\pi$
$984$	0.651388	−	1.12824i	0.0207655	−	0.0359669i
$985$		0			0
$986$	−1.19722	−	2.07365i	−0.0381274	−	0.0660386i
$987$		−	37.5416i		−	1.19496i
$988$	23.7483	+	13.7111i	0.755535	+	0.436208i
$989$	15.2750			0.485717
$990$		0			0
$991$	27.4222	+	47.4967i	0.871095	+	1.50878i	0.860865	+	0.508833i	$0.169923\pi$
$991$	27.4222	+	47.4967i	0.871095	+	1.50878i	0.0102299	+	0.999948i	$0.496744\pi$
$992$	−1.20763	−	0.697224i	−0.0383422	−	0.0221369i
$993$		−	13.1472i		−	0.417213i
$994$	−7.30278	+	12.6488i	−0.231630	+	0.401195i
$995$		0			0
$996$	−6.27502			−0.198832
$997$	−10.3129	−	5.95416i	−0.326613	−	0.188570i	0.327723	−	0.944774i	$-0.393719\pi$
$997$	−10.3129	−	5.95416i	−0.326613	−	0.188570i	−0.654336	+	0.756204i	$0.727052\pi$
$998$	12.6728	−	7.31665i	0.401151	−	0.231605i
$999$	20.4680	+	35.4517i	0.647580	+	1.12164i

Display

a_p

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p

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a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.o.h.549.2		8
5.2	odd	4		650.2.e.e.601.1	yes	4
5.3	odd	4		650.2.e.g.601.2	yes	4
5.4	even	2	inner	650.2.o.h.549.3		8
13.9	even	3	inner	650.2.o.h.399.3		8
65.3	odd	12		8450.2.a.bd.1.1		2
65.9	even	6	inner	650.2.o.h.399.2		8
65.22	odd	12		650.2.e.e.451.1	✓	4
65.23	odd	12		8450.2.a.bl.1.1		2
65.42	odd	12		8450.2.a.bi.1.2		2
65.48	odd	12		650.2.e.g.451.2	yes	4
65.62	odd	12		8450.2.a.ba.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.e.e.451.1	✓	4	65.22	odd	12
650.2.e.e.601.1	yes	4	5.2	odd	4
650.2.e.g.451.2	yes	4	65.48	odd	12
650.2.e.g.601.2	yes	4	5.3	odd	4
650.2.o.h.399.2		8	65.9	even	6	inner
650.2.o.h.399.3		8	13.9	even	3	inner
650.2.o.h.549.2		8	1.1	even	1	trivial
650.2.o.h.549.3		8	5.4	even	2	inner
8450.2.a.ba.1.2		2	65.62	odd	12
8450.2.a.bd.1.1		2	65.3	odd	12
8450.2.a.bi.1.2		2	65.42	odd	12
8450.2.a.bl.1.1		2	65.23	odd	12

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	650.2.o.h.549.2

Level	$650$
Weight	$2$
Character	650.549
Analytic conductor	$5.190$
Analytic rank	$0$
Dimension	$8$
Inner twists	$4$