LMFDB - Embedded newform 546.2.e.f.545.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(545,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("546.545");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.10070523904.11
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 10x^{4} + 81 $ x^8 - 10*x^4 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			545.6
Root			$0.420861 - 1.68014i$ of defining polynomial
Character	$\chi$	$=$	546.545
Dual form			546.2.e.f.545.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.420861 + 1.68014i) q^{3} +1.00000 q^{4} -3.36028i q^{5} +(-0.420861 - 1.68014i) q^{6} +(-2.37608 + 1.16372i) q^{7} -1.00000 q^{8} +(-2.64575 + 1.41421i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.420861 + 1.68014i) q^{3} +1.00000 q^{4} -3.36028i q^{5} +(-0.420861 - 1.68014i) q^{6} +(-2.37608 + 1.16372i) q^{7} -1.00000 q^{8} +(-2.64575 + 1.41421i) q^{9} +3.36028i q^{10} +(0.420861 + 1.68014i) q^{12} +(2.79694 - 2.27533i) q^{13} +(2.37608 - 1.16372i) q^{14} +(5.64575 - 1.41421i) q^{15} +1.00000 q^{16} +7.82087 q^{17} +(2.64575 - 1.41421i) q^{18} +5.59388 q^{19} -3.36028i q^{20} +(-2.95522 - 3.50238i) q^{21} -0.500983i q^{23} +(-0.420861 - 1.68014i) q^{24} -6.29150 q^{25} +(-2.79694 + 2.27533i) q^{26} +(-3.48957 - 3.85005i) q^{27} +(-2.37608 + 1.16372i) q^{28} -5.15587i q^{29} +(-5.64575 + 1.41421i) q^{30} +3.06871 q^{31} -1.00000 q^{32} -7.82087 q^{34} +(3.91044 + 7.98430i) q^{35} +(-2.64575 + 1.41421i) q^{36} +2.32744i q^{37} -5.59388 q^{38} +(5.00000 + 3.74166i) q^{39} +3.36028i q^{40} -9.87000i q^{41} +(2.95522 + 3.50238i) q^{42} +8.00000 q^{43} +(4.75216 + 8.89047i) q^{45} +0.500983i q^{46} -4.33981i q^{47} +(0.420861 + 1.68014i) q^{48} +(4.29150 - 5.53019i) q^{49} +6.29150 q^{50} +(3.29150 + 13.1402i) q^{51} +(2.79694 - 2.27533i) q^{52} -0.500983i q^{53} +(3.48957 + 3.85005i) q^{54} +(2.37608 - 1.16372i) q^{56} +(2.35425 + 9.39851i) q^{57} +5.15587i q^{58} +2.16991i q^{59} +(5.64575 - 1.41421i) q^{60} +4.55066i q^{61} -3.06871 q^{62} +(4.64076 - 6.43920i) q^{63} +1.00000 q^{64} +(-7.64575 - 9.39851i) q^{65} +13.1402i q^{67} +7.82087 q^{68} +(0.841723 - 0.210845i) q^{69} +(-3.91044 - 7.98430i) q^{70} -6.58301 q^{71} +(2.64575 - 1.41421i) q^{72} -12.5730 q^{73} -2.32744i q^{74} +(-2.64785 - 10.5706i) q^{75} +5.59388 q^{76} +(-5.00000 - 3.74166i) q^{78} -0.708497 q^{79} -3.36028i q^{80} +(5.00000 - 7.48331i) q^{81} +9.87000i q^{82} +11.2712i q^{83} +(-2.95522 - 3.50238i) q^{84} -26.2803i q^{85} -8.00000 q^{86} +(8.66259 - 2.16991i) q^{87} +3.14944i q^{89} +(-4.75216 - 8.89047i) q^{90} +(-3.99790 + 8.66122i) q^{91} -0.500983i q^{92} +(1.29150 + 5.15587i) q^{93} +4.33981i q^{94} -18.7970i q^{95} +(-0.420861 - 1.68014i) q^{96} +10.8896 q^{97} +(-4.29150 + 5.53019i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} + 24 q^{15} + 8 q^{16} - 8 q^{21} - 8 q^{25} - 24 q^{30} - 8 q^{32} + 40 q^{39} + 8 q^{42} + 64 q^{43} - 8 q^{49} + 8 q^{50} - 16 q^{51} + 40 q^{57} + 24 q^{60} + 8 q^{63} + 8 q^{64} - 40 q^{65} + 32 q^{71} - 40 q^{78} - 48 q^{79} + 40 q^{81} - 8 q^{84} - 64 q^{86} - 32 q^{91} - 32 q^{93} + 8 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 + 24 * q^15 + 8 * q^16 - 8 * q^21 - 8 * q^25 - 24 * q^30 - 8 * q^32 + 40 * q^39 + 8 * q^42 + 64 * q^43 - 8 * q^49 + 8 * q^50 - 16 * q^51 + 40 * q^57 + 24 * q^60 + 8 * q^63 + 8 * q^64 - 40 * q^65 + 32 * q^71 - 40 * q^78 - 48 * q^79 + 40 * q^81 - 8 * q^84 - 64 * q^86 - 32 * q^91 - 32 * q^93 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.420861	+	1.68014i	0.242984	+	0.970030i
$3$	0.420861	+	1.68014i	0.242984	+	0.970030i
$4$	1.00000			0.500000
$5$		−	3.36028i		−	1.50276i	−0.659867	−	0.751382i	$-0.729388\pi$
$5$		−	3.36028i		−	1.50276i	0.659867	−	0.751382i	$-0.270612\pi$
$6$	−0.420861	−	1.68014i	−0.171816	−	0.685915i
$7$	−2.37608	+	1.16372i	−0.898073	+	0.439846i
$7$	−2.37608	+	1.16372i	−0.898073	+	0.439846i
$8$	−1.00000			−0.353553
$9$	−2.64575	+	1.41421i	−0.881917	+	0.471405i
$10$			3.36028i			1.06261i
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	0.420861	+	1.68014i	0.121492	+	0.485015i
$13$	2.79694	−	2.27533i	0.775732	−	0.631063i
$13$	2.79694	−	2.27533i	0.775732	−	0.631063i
$14$	2.37608	−	1.16372i	0.635034	−	0.311018i
$15$	5.64575	−	1.41421i	1.45773	−	0.365148i
$16$	1.00000			0.250000
$17$	7.82087			1.89684			0.948420	−	0.317017i	$-0.102681\pi$
$17$	7.82087			1.89684			0.948420	+	0.317017i	$0.102681\pi$
$18$	2.64575	−	1.41421i	0.623610	−	0.333333i
$19$	5.59388			1.28332			0.641662	−	0.766987i	$-0.278245\pi$
$19$	5.59388			1.28332			0.641662	+	0.766987i	$0.278245\pi$
$20$		−	3.36028i		−	0.751382i
$21$	−2.95522	−	3.50238i	−0.644881	−	0.764283i
$22$		0			0
$23$		−	0.500983i		−	0.104462i	−0.998635	−	0.0522311i	$-0.983367\pi$
$23$		−	0.500983i		−	0.104462i	0.998635	−	0.0522311i	$-0.0166333\pi$
$24$	−0.420861	−	1.68014i	−0.0859080	−	0.342957i
$25$	−6.29150			−1.25830
$26$	−2.79694	+	2.27533i	−0.548525	+	0.446229i
$27$	−3.48957	−	3.85005i	−0.671569	−	0.740942i
$28$	−2.37608	+	1.16372i	−0.449037	+	0.219923i
$29$		−	5.15587i		−	0.957421i	−0.877973	−	0.478711i	$-0.841104\pi$
$29$		−	5.15587i		−	0.957421i	0.877973	−	0.478711i	$-0.158896\pi$
$30$	−5.64575	+	1.41421i	−1.03077	+	0.258199i
$31$	3.06871			0.551157			0.275578	−	0.961279i	$-0.411131\pi$
$31$	3.06871			0.551157			0.275578	+	0.961279i	$0.411131\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−7.82087			−1.34127
$35$	3.91044	+	7.98430i	0.660984	+	1.34959i
$36$	−2.64575	+	1.41421i	−0.440959	+	0.235702i
$37$			2.32744i			0.382629i	0.981529	+	0.191315i	$0.0612751\pi$
$37$			2.32744i			0.382629i	−0.981529	+	0.191315i	$0.938725\pi$
$38$	−5.59388			−0.907447
$39$	5.00000	+	3.74166i	0.800641	+	0.599145i
$40$			3.36028i			0.531307i
$41$		−	9.87000i		−	1.54144i	−0.637177	−	0.770718i	$-0.719898\pi$
$41$		−	9.87000i		−	1.54144i	0.637177	−	0.770718i	$-0.280102\pi$
$42$	2.95522	+	3.50238i	0.456000	+	0.540429i
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$	4.75216	+	8.89047i	0.708410	+	1.32531i
$46$			0.500983i			0.0738660i
$47$		−	4.33981i		−	0.633027i	−0.948588	−	0.316513i	$-0.897488\pi$
$47$		−	4.33981i		−	0.633027i	0.948588	−	0.316513i	$-0.102512\pi$
$48$	0.420861	+	1.68014i	0.0607461	+	0.242508i
$49$	4.29150	−	5.53019i	0.613072	−	0.790027i
$50$	6.29150			0.889753
$51$	3.29150	+	13.1402i	0.460903	+	1.83999i
$52$	2.79694	−	2.27533i	0.387866	−	0.315531i
$53$		−	0.500983i		−	0.0688153i	−0.999408	−	0.0344077i	$-0.989046\pi$
$53$		−	0.500983i		−	0.0688153i	0.999408	−	0.0344077i	$-0.0109545\pi$
$54$	3.48957	+	3.85005i	0.474871	+	0.523925i
$55$		0			0
$56$	2.37608	−	1.16372i	0.317517	−	0.155509i
$57$	2.35425	+	9.39851i	0.311828	+	1.24486i
$58$			5.15587i			0.676999i
$59$			2.16991i			0.282498i	0.989974	+	0.141249i	$0.0451118\pi$
$59$			2.16991i			0.282498i	−0.989974	+	0.141249i	$0.954888\pi$
$60$	5.64575	−	1.41421i	0.728863	−	0.182574i
$61$			4.55066i			0.582652i	0.956624	+	0.291326i	$0.0940965\pi$
$61$			4.55066i			0.582652i	−0.956624	+	0.291326i	$0.905904\pi$
$62$	−3.06871			−0.389727
$63$	4.64076	−	6.43920i	0.584681	−	0.811263i
$64$	1.00000			0.125000
$65$	−7.64575	−	9.39851i	−0.948339	−	1.16574i
$66$		0			0
$67$			13.1402i			1.60533i	0.596432	+	0.802664i	$0.296585\pi$
$67$			13.1402i			1.60533i	−0.596432	+	0.802664i	$0.703415\pi$
$68$	7.82087			0.948420
$69$	0.841723	−	0.210845i	0.101332	−	0.0253827i
$70$	−3.91044	−	7.98430i	−0.467386	−	0.954306i
$71$	−6.58301			−0.781259			−0.390629	−	0.920548i	$-0.627743\pi$
$71$	−6.58301			−0.781259			−0.390629	+	0.920548i	$0.627743\pi$
$72$	2.64575	−	1.41421i	0.311805	−	0.166667i
$73$	−12.5730			−1.47156			−0.735781	−	0.677220i	$-0.763185\pi$
$73$	−12.5730			−1.47156			−0.735781	+	0.677220i	$0.763185\pi$
$74$		−	2.32744i		−	0.270560i
$75$	−2.64785	−	10.5706i	−0.305747	−	1.22059i
$76$	5.59388			0.641662
$77$		0			0
$78$	−5.00000	−	3.74166i	−0.566139	−	0.423659i
$79$	−0.708497			−0.0797122			−0.0398561	−	0.999205i	$-0.512690\pi$
$79$	−0.708497			−0.0797122			−0.0398561	+	0.999205i	$0.512690\pi$
$80$		−	3.36028i		−	0.375691i
$81$	5.00000	−	7.48331i	0.555556	−	0.831479i
$82$			9.87000i			1.08996i
$83$			11.2712i			1.23718i	0.785715	+	0.618589i	$0.212295\pi$
$83$			11.2712i			1.23718i	−0.785715	+	0.618589i	$0.787705\pi$
$84$	−2.95522	−	3.50238i	−0.322441	−	0.382141i
$85$		−	26.2803i		−	2.85050i
$86$	−8.00000			−0.862662
$87$	8.66259	−	2.16991i	0.928727	−	0.232638i
$88$		0			0
$89$			3.14944i			0.333840i	0.985970	+	0.166920i	$0.0533821\pi$
$89$			3.14944i			0.333840i	−0.985970	+	0.166920i	$0.946618\pi$
$90$	−4.75216	−	8.89047i	−0.500921	−	0.937138i
$91$	−3.99790	+	8.66122i	−0.419094	+	0.907943i
$92$		−	0.500983i		−	0.0522311i
$93$	1.29150	+	5.15587i	0.133923	+	0.534639i
$94$			4.33981i			0.447618i
$95$		−	18.7970i		−	1.92853i
$96$	−0.420861	−	1.68014i	−0.0429540	−	0.171479i
$97$	10.8896			1.10567			0.552835	−	0.833291i	$-0.313546\pi$
$97$	10.8896			1.10567			0.552835	+	0.833291i	$0.313546\pi$
$98$	−4.29150	+	5.53019i	−0.433507	+	0.558634i
$99$		0			0
$100$	−6.29150			−0.629150
$101$	−10.3460			−1.02947			−0.514735	−	0.857350i	$-0.672110\pi$
$101$	−10.3460			−1.02947			−0.514735	+	0.857350i	$0.672110\pi$
$102$	−3.29150	−	13.1402i	−0.325907	−	1.30107i
$103$		−	16.5906i		−	1.63472i	−0.576129	−	0.817359i	$-0.695437\pi$
$103$		−	16.5906i		−	1.63472i	0.576129	−	0.817359i	$-0.304563\pi$
$104$	−2.79694	+	2.27533i	−0.274263	+	0.223114i
$105$	−11.7690	+	9.93037i	−1.14854	+	0.969105i
$106$			0.500983i			0.0486598i
$107$			5.65685i			0.546869i	0.961891	+	0.273434i	$0.0881596\pi$
$107$			5.65685i			0.546869i	−0.961891	+	0.273434i	$0.911840\pi$
$108$	−3.48957	−	3.85005i	−0.335784	−	0.370471i
$109$		−	6.98233i		−	0.668786i	−0.942434	−	0.334393i	$-0.891469\pi$
$109$		−	6.98233i		−	0.668786i	0.942434	−	0.334393i	$-0.108531\pi$
$110$		0			0
$111$	−3.91044	+	0.979531i	−0.371162	+	0.0929730i
$112$	−2.37608	+	1.16372i	−0.224518	+	0.109961i
$113$			14.1421i			1.33038i	0.746674	+	0.665190i	$0.231650\pi$
$113$			14.1421i			1.33038i	−0.746674	+	0.665190i	$0.768350\pi$
$114$	−2.35425	−	9.39851i	−0.220496	−	0.880251i
$115$	−1.68345			−0.156982
$116$		−	5.15587i		−	0.478711i
$117$	−4.18221	+	9.97543i	−0.386645	+	0.922229i
$118$		−	2.16991i		−	0.199756i
$119$	−18.5830	+	9.10132i	−1.70350	+	0.834316i
$120$	−5.64575	+	1.41421i	−0.515384	+	0.129099i
$121$	−11.0000			−1.00000
$122$		−	4.55066i		−	0.411997i
$123$	16.5830	−	4.15390i	1.49524	−	0.374545i
$124$	3.06871			0.275578
$125$			4.33981i			0.388165i
$126$	−4.64076	+	6.43920i	−0.413432	+	0.573650i
$127$	14.5830			1.29403			0.647016	−	0.762476i	$-0.276017\pi$
$127$	14.5830			1.29403			0.647016	+	0.762476i	$0.276017\pi$
$128$	−1.00000			−0.0883883
$129$	3.36689	+	13.4411i	0.296438	+	1.18343i
$130$	7.64575	+	9.39851i	0.670577	+	0.824304i
$131$	−18.1669			−1.58725			−0.793625	−	0.608407i	$-0.791809\pi$
$131$	−18.1669			−1.58725			−0.793625	+	0.608407i	$0.791809\pi$
$132$		0			0
$133$	−13.2915	+	6.50972i	−1.15252	+	0.564464i
$134$		−	13.1402i		−	1.13514i
$135$	−12.9373	+	11.7260i	−1.11346	+	1.00921i
$136$	−7.82087			−0.670634
$137$	9.29150			0.793827			0.396913	−	0.917856i	$-0.370081\pi$
$137$	9.29150			0.793827			0.396913	+	0.917856i	$0.370081\pi$
$138$	−0.841723	+	0.210845i	−0.0716522	+	0.0179483i
$139$		−	0.979531i		−	0.0830828i	−0.999137	−	0.0415414i	$-0.986773\pi$
$139$		−	0.979531i		−	0.0830828i	0.999137	−	0.0415414i	$-0.0132268\pi$
$140$	3.91044	+	7.98430i	0.330492	+	0.674796i
$141$	7.29150	−	1.82646i	0.614055	−	0.153816i
$142$	6.58301			0.552434
$143$		0			0
$144$	−2.64575	+	1.41421i	−0.220479	+	0.117851i
$145$	−17.3252			−1.43878
$146$	12.5730			1.04055
$147$	11.0976	+	4.88289i	0.915317	+	0.402734i
$148$			2.32744i			0.191315i
$149$	−6.00000			−0.491539			−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000			−0.491539			−0.245770	+	0.969328i	$0.579041\pi$
$150$	2.64785	+	10.5706i	0.216196	+	0.863087i
$151$			6.15784i			0.501118i	0.968101	+	0.250559i	$0.0806144\pi$
$151$			6.15784i			0.501118i	−0.968101	+	0.250559i	$0.919386\pi$
$152$	−5.59388			−0.453724
$153$	−20.6921	+	11.0604i	−1.67286	+	0.894179i
$154$		0			0
$155$		−	10.3117i		−	0.828259i
$156$	5.00000	+	3.74166i	0.400320	+	0.299572i
$157$		−	17.5701i		−	1.40225i	−0.713040	−	0.701123i	$-0.752682\pi$
$157$		−	17.5701i		−	1.40225i	0.713040	−	0.701123i	$-0.247318\pi$
$158$	0.708497			0.0563650
$159$	0.841723	−	0.210845i	0.0667530	−	0.0167211i
$160$			3.36028i			0.265654i
$161$	0.583005	+	1.19038i	0.0459472	+	0.0938148i
$162$	−5.00000	+	7.48331i	−0.392837	+	0.587945i
$163$		−	8.48528i		−	0.664619i	−0.943170	−	0.332309i	$-0.892172\pi$
$163$		−	8.48528i		−	0.664619i	0.943170	−	0.332309i	$-0.107828\pi$
$164$		−	9.87000i		−	0.770718i
$165$		0			0
$166$		−	11.2712i		−	0.874817i
$167$			6.72057i			0.520053i	0.965601	+	0.260027i	$0.0837313\pi$
$167$			6.72057i			0.520053i	−0.965601	+	0.260027i	$0.916269\pi$
$168$	2.95522	+	3.50238i	0.228000	+	0.270215i
$169$	2.64575	−	12.7279i	0.203519	−	0.979071i
$170$			26.2803i			2.01561i
$171$	−14.8000	+	7.91094i	−1.13179	+	0.604965i
$172$	8.00000			0.609994
$173$	5.29570			0.402625			0.201312	−	0.979527i	$-0.435479\pi$
$173$	5.29570			0.402625			0.201312	+	0.979527i	$0.435479\pi$
$174$	−8.66259	+	2.16991i	−0.656709	+	0.164500i
$175$	14.9491	−	7.32156i	1.13005	−	0.553458i
$176$		0			0
$177$	−3.64575	+	0.913230i	−0.274031	+	0.0686426i
$178$		−	3.14944i		−	0.236060i
$179$		−	11.3137i		−	0.845626i	−0.906217	−	0.422813i	$-0.861043\pi$
$179$		−	11.3137i		−	0.845626i	0.906217	−	0.422813i	$-0.138957\pi$
$180$	4.75216	+	8.89047i	0.354205	+	0.662657i
$181$			24.7124i			1.83686i	0.395589	+	0.918428i	$0.370540\pi$
$181$			24.7124i			1.83686i	−0.395589	+	0.918428i	$0.629460\pi$
$182$	3.99790	−	8.66122i	0.296344	−	0.642013i
$183$	−7.64575	+	1.91520i	−0.565190	+	0.141575i
$184$			0.500983i			0.0369330i
$185$	7.82087			0.575002
$186$	−1.29150	−	5.15587i	−0.0946976	−	0.378047i
$187$		0			0
$188$		−	4.33981i		−	0.316513i
$189$	12.7719	+	5.08713i	0.929018	+	0.370034i
$190$			18.7970i			1.36368i
$191$			7.98430i			0.577724i	0.957371	+	0.288862i	$0.0932768\pi$
$191$			7.98430i			0.577724i	−0.957371	+	0.288862i	$0.906723\pi$
$192$	0.420861	+	1.68014i	0.0303731	+	0.121254i
$193$			8.48528i			0.610784i	0.952227	+	0.305392i	$0.0987875\pi$
$193$			8.48528i			0.610784i	−0.952227	+	0.305392i	$0.901213\pi$
$194$	−10.8896			−0.781826
$195$	12.5730	−	16.8014i	0.900373	−	1.20317i
$196$	4.29150	−	5.53019i	0.306536	−	0.395014i
$197$	12.5830			0.896502			0.448251	−	0.893908i	$-0.352047\pi$
$197$	12.5830			0.896502			0.448251	+	0.893908i	$0.352047\pi$
$198$		0			0
$199$		−	12.6724i		−	0.898326i	−0.893450	−	0.449163i	$-0.851722\pi$
$199$		−	12.6724i		−	0.898326i	0.893450	−	0.449163i	$-0.148278\pi$
$200$	6.29150			0.444876
$201$	−22.0773	+	5.53019i	−1.55722	+	0.390070i
$202$	10.3460			0.727945
$203$	6.00000	+	12.2508i	0.421117	+	0.859835i
$204$	3.29150	+	13.1402i	0.230451	+	0.919996i
$205$	−33.1660			−2.31641
$206$			16.5906i			1.15592i
$207$	0.708497	+	1.32548i	0.0492440	+	0.0921270i
$208$	2.79694	−	2.27533i	0.193933	−	0.157766i
$209$		0			0
$210$	11.7690	−	9.93037i	0.812138	−	0.685260i
$211$	−10.5830			−0.728564			−0.364282	−	0.931289i	$-0.618686\pi$
$211$	−10.5830			−0.728564			−0.364282	+	0.931289i	$0.618686\pi$
$212$		−	0.500983i		−	0.0344077i
$213$	−2.77053	−	11.0604i	−0.189834	−	0.757845i
$214$		−	5.65685i		−	0.386695i
$215$		−	26.8823i		−	1.83336i
$216$	3.48957	+	3.85005i	0.237435	+	0.261963i
$217$	−7.29150	+	3.57113i	−0.494979	+	0.242424i
$218$			6.98233i			0.472903i
$219$	−5.29150	−	21.1245i	−0.357567	−	1.42746i
$220$		0			0
$221$	21.8745	−	17.7951i	1.47144	−	1.19703i
$222$	3.91044	−	0.979531i	0.262451	−	0.0657418i
$223$	8.11905			0.543692			0.271846	−	0.962341i	$-0.412366\pi$
$223$	8.11905			0.543692			0.271846	+	0.962341i	$0.412366\pi$
$224$	2.37608	−	1.16372i	0.158758	−	0.0777544i
$225$	16.6458	−	8.89753i	1.10972	−	0.593169i
$226$		−	14.1421i		−	0.940721i
$227$		−	17.9918i		−	1.19416i	−0.802183	−	0.597079i	$-0.796328\pi$
$227$		−	17.9918i		−	1.19416i	0.802183	−	0.597079i	$-0.203672\pi$
$228$	2.35425	+	9.39851i	0.155914	+	0.622432i
$229$	16.1853			1.06955			0.534777	−	0.844993i	$-0.320396\pi$
$229$	16.1853			1.06955			0.534777	+	0.844993i	$0.320396\pi$
$230$	1.68345			0.111003
$231$		0			0
$232$			5.15587i			0.338500i
$233$			22.6274i			1.48237i	0.671300	+	0.741186i	$0.265736\pi$
$233$			22.6274i			1.48237i	−0.671300	+	0.741186i	$0.734264\pi$
$234$	4.18221	−	9.97543i	0.273399	−	0.652114i
$235$	−14.5830			−0.951290
$236$			2.16991i			0.141249i
$237$	−0.298179	−	1.19038i	−0.0193688	−	0.0773232i
$238$	18.5830	−	9.10132i	1.20456	−	0.589951i
$239$	−9.87451			−0.638729			−0.319364	−	0.947632i	$-0.603469\pi$
$239$	−9.87451			−0.638729			−0.319364	+	0.947632i	$0.603469\pi$
$240$	5.64575	−	1.41421i	0.364432	−	0.0912871i
$241$	−1.98162			−0.127648			−0.0638238	−	0.997961i	$-0.520330\pi$
$241$	−1.98162			−0.127648			−0.0638238	+	0.997961i	$0.520330\pi$
$242$	11.0000			0.707107
$243$	14.6773	+	5.25127i	0.941551	+	0.336869i
$244$			4.55066i			0.291326i
$245$	−18.5830	−	14.4207i	−1.18722	−	0.921302i
$246$	−16.5830	+	4.15390i	−1.05729	+	0.264843i
$247$	15.6458	−	12.7279i	0.995515	−	0.809858i
$248$	−3.06871			−0.194863
$249$	−18.9373	+	4.74362i	−1.20010	+	0.300615i
$250$		−	4.33981i		−	0.274474i
$251$	10.3460			0.653036			0.326518	−	0.945191i	$-0.394125\pi$
$251$	10.3460			0.653036			0.326518	+	0.945191i	$0.394125\pi$
$252$	4.64076	−	6.43920i	0.292341	−	0.405632i
$253$		0			0
$254$	−14.5830			−0.915019
$255$	44.1547	−	11.0604i	2.76507	−	0.692628i
$256$	1.00000			0.0625000
$257$	12.8712			0.802884			0.401442	−	0.915884i	$-0.368509\pi$
$257$	12.8712			0.802884			0.401442	+	0.915884i	$0.368509\pi$
$258$	−3.36689	−	13.4411i	−0.209614	−	0.836808i
$259$	−2.70850	−	5.53019i	−0.168298	−	0.343629i
$260$	−7.64575	−	9.39851i	−0.474169	−	0.582871i
$261$	7.29150	+	13.6412i	0.451333	+	0.844366i
$262$	18.1669			1.12236
$263$		−	8.98626i		−	0.554117i	−0.960853	−	0.277058i	$-0.910640\pi$
$263$		−	8.98626i		−	0.554117i	0.960853	−	0.277058i	$-0.0893596\pi$
$264$		0			0
$265$	−1.68345			−0.103413
$266$	13.2915	−	6.50972i	0.814954	−	0.399137i
$267$	−5.29150	+	1.32548i	−0.323835	+	0.0811179i
$268$			13.1402i			0.802664i
$269$	−20.9374			−1.27658			−0.638289	−	0.769797i	$-0.720358\pi$
$269$	−20.9374			−1.27658			−0.638289	+	0.769797i	$0.720358\pi$
$270$	12.9373	−	11.7260i	0.787336	−	0.713619i
$271$	−7.52269			−0.456971			−0.228485	−	0.973547i	$-0.573377\pi$
$271$	−7.52269			−0.456971			−0.228485	+	0.973547i	$0.573377\pi$
$272$	7.82087			0.474210
$273$	−16.2346	−	3.07186i	−0.982565	−	0.185918i
$274$	−9.29150			−0.561320
$275$		0			0
$276$	0.841723	−	0.210845i	0.0506658	−	0.0126914i
$277$	−11.1660			−0.670901			−0.335450	−	0.942058i	$-0.608888\pi$
$277$	−11.1660			−0.670901			−0.335450	+	0.942058i	$0.608888\pi$
$278$			0.979531i			0.0587484i
$279$	−8.11905	+	4.33981i	−0.486075	+	0.259818i
$280$	−3.91044	−	7.98430i	−0.233693	−	0.477153i
$281$	−2.70850			−0.161575			−0.0807877	−	0.996731i	$-0.525744\pi$
$281$	−2.70850			−0.161575			−0.0807877	+	0.996731i	$0.525744\pi$
$282$	−7.29150	+	1.82646i	−0.434203	+	0.108764i
$283$			12.0399i			0.715698i	0.933779	+	0.357849i	$0.116490\pi$
$283$			12.0399i			0.715698i	−0.933779	+	0.357849i	$0.883510\pi$
$284$	−6.58301			−0.390629
$285$	31.5817	−	7.91094i	1.87074	−	0.468604i
$286$		0			0
$287$	11.4859	+	23.4519i	0.677994	+	1.38432i
$288$	2.64575	−	1.41421i	0.155902	−	0.0833333i
$289$	44.1660			2.59800
$290$	17.3252			1.01737
$291$	4.58301	+	18.2960i	0.268661	+	1.07253i
$292$	−12.5730			−0.735781
$293$			18.7605i			1.09600i	0.836479	+	0.547999i	$0.184610\pi$
$293$			18.7605i			1.09600i	−0.836479	+	0.547999i	$0.815390\pi$
$294$	−11.0976	−	4.88289i	−0.647227	−	0.284776i
$295$	7.29150			0.424528
$296$		−	2.32744i		−	0.135280i
$297$		0			0
$298$	6.00000			0.347571
$299$	−1.13990	−	1.40122i	−0.0659222	−	0.0810347i
$300$	−2.64785	−	10.5706i	−0.152874	−	0.610295i
$301$	−19.0086	+	9.30978i	−1.09564	+	0.536607i
$302$		−	6.15784i		−	0.354344i
$303$	−4.35425	−	17.3828i	−0.250145	−	0.998616i
$304$	5.59388			0.320831
$305$	15.2915			0.875589
$306$	20.6921	−	11.0604i	1.18289	−	0.632280i
$307$	−2.22699			−0.127101			−0.0635505	−	0.997979i	$-0.520242\pi$
$307$	−2.22699			−0.127101			−0.0635505	+	0.997979i	$0.520242\pi$
$308$		0			0
$309$	27.8745	−	6.98233i	1.58573	−	0.397211i
$310$			10.3117i			0.585668i
$311$	−28.5129			−1.61682			−0.808410	−	0.588619i	$-0.799672\pi$
$311$	−28.5129			−1.61682			−0.808410	+	0.588619i	$0.799672\pi$
$312$	−5.00000	−	3.74166i	−0.283069	−	0.211830i
$313$			27.3040i			1.54331i	0.636041	+	0.771655i	$0.280571\pi$
$313$			27.3040i			1.54331i	−0.636041	+	0.771655i	$0.719429\pi$
$314$			17.5701i			0.991538i
$315$	−21.6375	−	15.5943i	−1.21914	−	0.878638i
$316$	−0.708497			−0.0398561
$317$	6.00000			0.336994			0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000			0.336994			0.168497	+	0.985702i	$0.446109\pi$
$318$	−0.841723	+	0.210845i	−0.0472015	+	0.0118236i
$319$		0			0
$320$		−	3.36028i		−	0.187846i
$321$	−9.50432	+	2.38075i	−0.530479	+	0.132881i
$322$	−0.583005	−	1.19038i	−0.0324896	−	0.0663371i
$323$	43.7490			2.43426
$324$	5.00000	−	7.48331i	0.277778	−	0.415740i
$325$	−17.5970	+	14.3152i	−0.976104	+	0.794067i
$326$			8.48528i			0.469956i
$327$	11.7313	−	2.93859i	0.648743	−	0.162505i
$328$			9.87000i			0.544980i
$329$	5.05034	+	10.3117i	0.278434	+	0.568505i
$330$		0			0
$331$		−	8.48528i		−	0.466393i	−0.972430	−	0.233197i	$-0.925081\pi$
$331$		−	8.48528i		−	0.466393i	0.972430	−	0.233197i	$-0.0749186\pi$
$332$			11.2712i			0.618589i
$333$	−3.29150	−	6.15784i	−0.180373	−	0.337447i
$334$		−	6.72057i		−	0.367733i
$335$	44.1547			2.41243
$336$	−2.95522	−	3.50238i	−0.161220	−	0.191071i
$337$	−19.8745			−1.08263			−0.541317	−	0.840819i	$-0.682074\pi$
$337$	−19.8745			−1.08263			−0.541317	+	0.840819i	$0.682074\pi$
$338$	−2.64575	+	12.7279i	−0.143910	+	0.692308i
$339$	−23.7608	+	5.95188i	−1.29051	+	0.323262i
$340$		−	26.2803i		−	1.42525i
$341$		0			0
$342$	14.8000	−	7.91094i	0.800293	−	0.427775i
$343$	−3.76135	+	18.1343i	−0.203094	+	0.979159i
$344$	−8.00000			−0.431331
$345$	−0.708497	−	2.82843i	−0.0381442	−	0.152277i
$346$	−5.29570			−0.284699
$347$			31.9372i			1.71448i	0.514918	+	0.857239i	$0.327822\pi$
$347$			31.9372i			1.71448i	−0.514918	+	0.857239i	$0.672178\pi$
$348$	8.66259	−	2.16991i	0.464364	−	0.116319i
$349$	0.543544			0.0290952			0.0145476	−	0.999894i	$-0.495369\pi$
$349$	0.543544			0.0290952			0.0145476	+	0.999894i	$0.495369\pi$
$350$	−14.9491	+	7.32156i	−0.799063	+	0.391354i
$351$	−18.5203	−	2.82843i	−0.988538	−	0.150970i
$352$		0			0
$353$		−	30.0317i		−	1.59843i	−0.601048	−	0.799213i	$-0.705250\pi$
$353$		−	30.0317i		−	1.59843i	0.601048	−	0.799213i	$-0.294750\pi$
$354$	3.64575	−	0.913230i	0.193769	−	0.0485376i
$355$			22.1208i			1.17405i
$356$			3.14944i			0.166920i
$357$	−23.1124	−	27.3917i	−1.22324	−	1.44972i
$358$			11.3137i			0.597948i
$359$	27.2915			1.44039			0.720195	−	0.693771i	$-0.244052\pi$
$359$	27.2915			1.44039			0.720195	+	0.693771i	$0.244052\pi$
$360$	−4.75216	−	8.89047i	−0.250461	−	0.468569i
$361$	12.2915			0.646921
$362$		−	24.7124i		−	1.29885i
$363$	−4.62948	−	18.4816i	−0.242984	−	0.970030i
$364$	−3.99790	+	8.66122i	−0.209547	+	0.453971i
$365$			42.2489i			2.21141i
$366$	7.64575	−	1.91520i	0.399650	−	0.100109i
$367$		−	14.6315i		−	0.763759i	−0.924212	−	0.381879i	$-0.875277\pi$
$367$		−	14.6315i		−	0.763759i	0.924212	−	0.381879i	$-0.124723\pi$
$368$		−	0.500983i		−	0.0261156i
$369$	13.9583	+	26.1136i	0.726640	+	1.35942i
$370$	−7.82087			−0.406588
$371$	0.583005	+	1.19038i	0.0302681	+	0.0618012i
$372$	1.29150	+	5.15587i	0.0669613	+	0.267319i
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$		0			0
$375$	−7.29150	+	1.82646i	−0.376532	+	0.0943180i
$376$			4.33981i			0.223809i
$377$	−11.7313	−	14.4207i	−0.604193	−	0.742702i
$378$	−12.7719	−	5.08713i	−0.656915	−	0.261654i
$379$			30.1107i			1.54668i	0.633989	+	0.773342i	$0.281417\pi$
$379$			30.1107i			1.54668i	−0.633989	+	0.773342i	$0.718583\pi$
$380$		−	18.7970i		−	0.964267i
$381$	6.13742	+	24.5015i	0.314430	+	1.25525i
$382$		−	7.98430i		−	0.408512i
$383$			21.6991i			1.10877i	0.832260	+	0.554385i	$0.187047\pi$
$383$			21.6991i			1.10877i	−0.832260	+	0.554385i	$0.812953\pi$
$384$	−0.420861	−	1.68014i	−0.0214770	−	0.0857394i
$385$		0			0
$386$		−	8.48528i		−	0.431889i
$387$	−21.1660	+	11.3137i	−1.07593	+	0.575108i
$388$	10.8896			0.552835
$389$		−	9.81076i		−	0.497425i	−0.968577	−	0.248713i	$-0.919993\pi$
$389$		−	9.81076i		−	0.497425i	0.968577	−	0.248713i	$-0.0800075\pi$
$390$	−12.5730	+	16.8014i	−0.636660	+	0.850773i
$391$		−	3.91813i		−	0.198148i
$392$	−4.29150	+	5.53019i	−0.216754	+	0.279317i
$393$	−7.64575	−	30.5230i	−0.385677	−	1.53968i
$394$	−12.5830			−0.633923
$395$			2.38075i			0.119789i
$396$		0			0
$397$	26.2860			1.31925			0.659627	−	0.751593i	$-0.270714\pi$
$397$	26.2860			1.31925			0.659627	+	0.751593i	$0.270714\pi$
$398$			12.6724i			0.635212i
$399$	−16.5311	−	19.5919i	−0.827592	−	0.980823i
$400$	−6.29150			−0.314575
$401$	−6.00000			−0.299626			−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000			−0.299626			−0.149813	+	0.988714i	$0.547867\pi$
$402$	22.0773	−	5.53019i	1.10112	−	0.275821i
$403$	8.58301	−	6.98233i	0.427550	−	0.347815i
$404$	−10.3460			−0.514735
$405$	−25.1461	−	16.8014i	−1.24952	−	0.834869i
$406$	−6.00000	−	12.2508i	−0.297775	−	0.607995i
$407$		0			0
$408$	−3.29150	−	13.1402i	−0.162954	−	0.650535i
$409$	−4.75216			−0.234979			−0.117490	−	0.993074i	$-0.537485\pi$
$409$	−4.75216			−0.234979			−0.117490	+	0.993074i	$0.537485\pi$
$410$	33.1660			1.63795
$411$	3.91044	+	15.6110i	0.192888	+	0.770036i
$412$		−	16.5906i		−	0.817359i
$413$	−2.52517	−	5.15587i	−0.124255	−	0.253704i
$414$	−0.708497	−	1.32548i	−0.0348207	−	0.0651437i
$415$	37.8745			1.85919
$416$	−2.79694	+	2.27533i	−0.137131	+	0.111557i
$417$	1.64575	−	0.412247i	0.0805928	−	0.0201878i
$418$		0			0
$419$	15.3964			0.752162			0.376081	−	0.926587i	$-0.377271\pi$
$419$	15.3964			0.752162			0.376081	+	0.926587i	$0.377271\pi$
$420$	−11.7690	+	9.93037i	−0.574268	+	0.484552i
$421$		−	19.2980i		−	0.940527i	−0.882526	−	0.470264i	$-0.844159\pi$
$421$		−	19.2980i		−	0.940527i	0.882526	−	0.470264i	$-0.155841\pi$
$422$	10.5830			0.515173
$423$	6.13742	+	11.4821i	0.298412	+	0.558277i
$424$			0.500983i			0.0243299i
$425$	−49.2050			−2.38679
$426$	2.77053	+	11.0604i	0.134233	+	0.535877i
$427$	−5.29570	−	10.8127i	−0.256277	−	0.523264i
$428$			5.65685i			0.273434i
$429$		0			0
$430$			26.8823i			1.29638i
$431$	3.29150			0.158546			0.0792731	−	0.996853i	$-0.474740\pi$
$431$	3.29150			0.158546			0.0792731	+	0.996853i	$0.474740\pi$
$432$	−3.48957	−	3.85005i	−0.167892	−	0.185236i
$433$			1.95906i			0.0941465i	0.998891	+	0.0470733i	$0.0149894\pi$
$433$			1.95906i			0.0941465i	−0.998891	+	0.0470733i	$0.985011\pi$
$434$	7.29150	−	3.57113i	0.350003	−	0.171420i
$435$	−7.29150	−	29.1088i	−0.349601	−	1.39566i
$436$		−	6.98233i		−	0.334393i
$437$		−	2.80244i		−	0.134059i
$438$	5.29150	+	21.1245i	0.252838	+	1.00937i
$439$		−	14.6315i		−	0.698324i	−0.937062	−	0.349162i	$-0.886466\pi$
$439$		−	14.6315i		−	0.698324i	0.937062	−	0.349162i	$-0.113534\pi$
$440$		0			0
$441$	−3.53338	+	20.7006i	−0.168256	+	0.985743i
$442$	−21.8745	+	17.7951i	−1.04046	+	0.846425i
$443$			5.65685i			0.268765i	0.990930	+	0.134383i	$0.0429051\pi$
$443$			5.65685i			0.268765i	−0.990930	+	0.134383i	$0.957095\pi$
$444$	−3.91044	+	0.979531i	−0.185581	+	0.0464865i
$445$	10.5830			0.501683
$446$	−8.11905			−0.384448
$447$	−2.52517	−	10.0808i	−0.119436	−	0.476808i
$448$	−2.37608	+	1.16372i	−0.112259	+	0.0549807i
$449$	−22.4575			−1.05984			−0.529918	−	0.848049i	$-0.677777\pi$
$449$	−22.4575			−1.05984			−0.529918	+	0.848049i	$0.677777\pi$
$450$	−16.6458	+	8.89753i	−0.784688	+	0.419434i
$451$		0			0
$452$			14.1421i			0.665190i
$453$	−10.3460	+	2.59160i	−0.486099	+	0.121764i
$454$			17.9918i			0.844397i
$455$	29.1042	+	13.4341i	1.36442	+	0.629799i
$456$	−2.35425	−	9.39851i	−0.110248	−	0.440126i
$457$			17.7951i			0.832418i	0.909269	+	0.416209i	$0.136641\pi$
$457$			17.7951i			0.832418i	−0.909269	+	0.416209i	$0.863359\pi$
$458$	−16.1853			−0.756289
$459$	−27.2915	−	30.1107i	−1.27386	−	1.40545i
$460$	−1.68345			−0.0784911
$461$			25.9027i			1.20641i	0.797586	+	0.603205i	$0.206110\pi$
$461$			25.9027i			1.20641i	−0.797586	+	0.603205i	$0.793890\pi$
$462$		0			0
$463$		−	11.6372i		−	0.540827i	−0.962744	−	0.270414i	$-0.912840\pi$
$463$		−	11.6372i		−	0.540827i	0.962744	−	0.270414i	$-0.0871605\pi$
$464$		−	5.15587i		−	0.239355i
$465$	17.3252	−	4.33981i	0.803436	−	0.201254i
$466$		−	22.6274i		−	1.04819i
$467$	−33.8086			−1.56448			−0.782239	−	0.622979i	$-0.785922\pi$
$467$	−33.8086			−1.56448			−0.782239	+	0.622979i	$0.785922\pi$
$468$	−4.18221	+	9.97543i	−0.193323	+	0.461114i
$469$	−15.2915	−	31.2221i	−0.706096	−	1.44170i
$470$	14.5830			0.672664
$471$	29.5203	−	7.39458i	1.36022	−	0.340724i
$472$		−	2.16991i		−	0.0998781i
$473$		0			0
$474$	0.298179	+	1.19038i	0.0136958	+	0.0546758i
$475$	−35.1939			−1.61481
$476$	−18.5830	+	9.10132i	−0.851751	+	0.417158i
$477$	0.708497	+	1.32548i	0.0324399	+	0.0606894i
$478$	9.87451			0.451649
$479$			35.9836i			1.64413i	0.569392	+	0.822066i	$0.307179\pi$
$479$			35.9836i			1.64413i	−0.569392	+	0.822066i	$0.692821\pi$
$480$	−5.64575	+	1.41421i	−0.257692	+	0.0645497i
$481$	5.29570	+	6.50972i	0.241463	+	0.296818i
$482$	1.98162			0.0902605
$483$	−1.75464	+	1.48051i	−0.0798387	+	0.0673657i
$484$	−11.0000			−0.500000
$485$		−	36.5921i		−	1.66156i
$486$	−14.6773	−	5.25127i	−0.665777	−	0.238202i
$487$			20.1225i			0.911838i	0.890021	+	0.455919i	$0.150689\pi$
$487$			20.1225i			0.911838i	−0.890021	+	0.455919i	$0.849311\pi$
$488$		−	4.55066i		−	0.205999i
$489$	14.2565	−	3.57113i	0.644700	−	0.161492i
$490$	18.5830	+	14.4207i	0.839495	+	0.651459i
$491$		−	3.65292i		−	0.164854i	−0.996597	−	0.0824270i	$-0.973733\pi$
$491$		−	3.65292i		−	0.164854i	0.996597	−	0.0824270i	$-0.0262671\pi$
$492$	16.5830	−	4.15390i	0.747620	−	0.187272i
$493$		−	40.3234i		−	1.81607i
$494$	−15.6458	+	12.7279i	−0.703936	+	0.572656i
$495$		0			0
$496$	3.06871			0.137789
$497$	15.6417	−	7.66079i	0.701628	−	0.343633i
$498$	18.9373	−	4.74362i	0.848599	−	0.212567i
$499$			3.83039i			0.171472i	0.996318	+	0.0857360i	$0.0273242\pi$
$499$			3.83039i			0.171472i	−0.996318	+	0.0857360i	$0.972676\pi$
$500$			4.33981i			0.194082i
$501$	−11.2915	+	2.82843i	−0.504467	+	0.126365i
$502$	−10.3460			−0.461766
$503$	−15.6417			−0.697431			−0.348715	−	0.937229i	$-0.613382\pi$
$503$	−15.6417			−0.697431			−0.348715	+	0.937229i	$0.613382\pi$
$504$	−4.64076	+	6.43920i	−0.206716	+	0.286825i
$505$			34.7656i			1.54705i
$506$		0			0
$507$	22.4982	−	0.911455i	0.999180	−	0.0404791i
$508$	14.5830			0.647016
$509$			25.9027i			1.14812i	0.818814	+	0.574059i	$0.194632\pi$
$509$			25.9027i			1.14812i	−0.818814	+	0.574059i	$0.805368\pi$
$510$	−44.1547	+	11.0604i	−1.95520	+	0.489762i
$511$	29.8745	−	14.6315i	1.32157	−	0.647260i
$512$	−1.00000			−0.0441942
$513$	−19.5203	−	21.5367i	−0.861840	−	0.950869i
$514$	−12.8712			−0.567725
$515$	−55.7490			−2.45660
$516$	3.36689	+	13.4411i	0.148219	+	0.591713i
$517$		0			0
$518$	2.70850	+	5.53019i	0.119005	+	0.242983i
$519$	2.22876	+	8.89753i	0.0978316	+	0.390558i
$520$	7.64575	+	9.39851i	0.335288	+	0.412152i
$521$	36.3338			1.59181			0.795907	−	0.605419i	$-0.206995\pi$
$521$	36.3338			1.59181			0.795907	+	0.605419i	$0.206995\pi$
$522$	−7.29150	−	13.6412i	−0.319140	−	0.597057i
$523$			13.9990i			0.612132i	0.952010	+	0.306066i	$0.0990129\pi$
$523$			13.9990i			0.612132i	−0.952010	+	0.306066i	$0.900987\pi$
$524$	−18.1669			−0.793625
$525$	18.5928	+	22.0353i	0.811455	+	0.961697i
$526$			8.98626i			0.391820i
$527$	24.0000			1.04546
$528$		0			0
$529$	22.7490			0.989088
$530$	1.68345			0.0731242
$531$	−3.06871	−	5.74103i	−0.133171	−	0.249140i
$532$	−13.2915	+	6.50972i	−0.576260	+	0.282232i
$533$	−22.4575	−	27.6058i	−0.972743	−	1.19574i
$534$	5.29150	−	1.32548i	0.228986	−	0.0573590i
$535$	19.0086			0.821815
$536$		−	13.1402i		−	0.567569i
$537$	19.0086	−	4.76150i	0.820283	−	0.205474i
$538$	20.9374			0.902677
$539$		0			0
$540$	−12.9373	+	11.7260i	−0.556731	+	0.504605i
$541$		−	37.9176i		−	1.63020i	−0.579318	−	0.815102i	$-0.696681\pi$
$541$		−	37.9176i		−	1.63020i	0.579318	−	0.815102i	$-0.303319\pi$
$542$	7.52269			0.323127
$543$	−41.5203	+	10.4005i	−1.78180	+	0.446327i
$544$	−7.82087			−0.335317
$545$	−23.4626			−1.00503
$546$	16.2346	+	3.07186i	0.694779	+	0.131464i
$547$	14.5830			0.623524			0.311762	−	0.950160i	$-0.399081\pi$
$547$	14.5830			0.623524			0.311762	+	0.950160i	$0.399081\pi$
$548$	9.29150			0.396913
$549$	−6.43560	−	12.0399i	−0.274665	−	0.513851i
$550$		0			0
$551$		−	28.8413i		−	1.22868i
$552$	−0.841723	+	0.210845i	−0.0358261	+	0.00897414i
$553$	1.68345	−	0.824494i	0.0715874	−	0.0350610i
$554$	11.1660			0.474398
$555$	3.29150	+	13.1402i	0.139717	+	0.557769i
$556$		−	0.979531i		−	0.0415414i
$557$	−19.1660			−0.812090			−0.406045	−	0.913853i	$-0.633092\pi$
$557$	−19.1660			−0.812090			−0.406045	+	0.913853i	$0.633092\pi$
$558$	8.11905	−	4.33981i	0.343707	−	0.183719i
$559$	22.3755	−	18.2026i	0.946384	−	0.769889i
$560$	3.91044	+	7.98430i	0.165246	+	0.337398i
$561$		0			0
$562$	2.70850			0.114251
$563$	−33.8086			−1.42486			−0.712432	−	0.701741i	$-0.752406\pi$
$563$	−33.8086			−1.42486			−0.712432	+	0.701741i	$0.752406\pi$
$564$	7.29150	−	1.82646i	0.307028	−	0.0769079i
$565$	47.5216			1.99925
$566$		−	12.0399i		−	0.506075i
$567$	−3.17190	+	23.5996i	−0.133207	+	0.991088i
$568$	6.58301			0.276217
$569$		−	15.1441i		−	0.634874i	−0.948279	−	0.317437i	$-0.897178\pi$
$569$		−	15.1441i		−	0.634874i	0.948279	−	0.317437i	$-0.102822\pi$
$570$	−31.5817	+	7.91094i	−1.32281	+	0.331353i
$571$	−22.5830			−0.945069			−0.472535	−	0.881312i	$-0.656661\pi$
$571$	−22.5830			−0.945069			−0.472535	+	0.881312i	$0.656661\pi$
$572$		0			0
$573$	−13.4148	+	3.36028i	−0.560409	+	0.140378i
$574$	−11.4859	−	23.4519i	−0.479414	−	0.978864i
$575$			3.15194i			0.131445i
$576$	−2.64575	+	1.41421i	−0.110240	+	0.0589256i
$577$	3.06871			0.127752			0.0638761	−	0.997958i	$-0.479654\pi$
$577$	3.06871			0.127752			0.0638761	+	0.997958i	$0.479654\pi$
$578$	−44.1660			−1.83706
$579$	−14.2565	+	3.57113i	−0.592479	+	0.148411i
$580$	−17.3252			−0.719389
$581$	−13.1166	−	26.7813i	−0.544167	−	1.11108i
$582$	−4.58301	−	18.2960i	−0.189972	−	0.758395i
$583$		0			0
$584$	12.5730			0.520276
$585$	33.5203	+	14.0534i	1.38589	+	0.581037i
$586$		−	18.7605i		−	0.774988i
$587$		−	19.9509i		−	0.823460i	−0.911306	−	0.411730i	$-0.864925\pi$
$587$		−	19.9509i		−	0.823460i	0.911306	−	0.411730i	$-0.135075\pi$
$588$	11.0976	+	4.88289i	0.457659	+	0.201367i
$589$	17.1660			0.707313
$590$	−7.29150			−0.300186
$591$	5.29570	+	21.1412i	0.217836	+	0.869634i
$592$			2.32744i			0.0956574i
$593$		−	3.99282i		−	0.163965i	−0.996634	−	0.0819827i	$-0.973875\pi$
$593$		−	3.99282i		−	0.163965i	0.996634	−	0.0819827i	$-0.0261252\pi$
$594$		0			0
$595$	30.5830	+	62.4442i	1.25378	+	2.55996i
$596$	−6.00000			−0.245770
$597$	21.2915	−	5.33334i	0.871403	−	0.218279i
$598$	1.13990	+	1.40122i	0.0466141	+	0.0573002i
$599$			43.5744i			1.78040i	0.455568	+	0.890201i	$0.349436\pi$
$599$			43.5744i			1.78040i	−0.455568	+	0.890201i	$0.650564\pi$
$600$	2.64785	+	10.5706i	0.108098	+	0.431544i
$601$		−	18.2026i		−	0.742501i	−0.928533	−	0.371251i	$-0.878929\pi$
$601$		−	18.2026i		−	0.742501i	0.928533	−	0.371251i	$-0.121071\pi$
$602$	19.0086	−	9.30978i	0.774734	−	0.379438i
$603$	−18.5830	−	34.7656i	−0.756758	−	1.41577i
$604$			6.15784i			0.250559i
$605$			36.9631i			1.50276i
$606$	4.35425	+	17.3828i	0.176879	+	0.706128i
$607$		−	18.5496i		−	0.752906i	−0.926436	−	0.376453i	$-0.877144\pi$
$607$		−	18.5496i		−	0.752906i	0.926436	−	0.376453i	$-0.122856\pi$
$608$	−5.59388			−0.226862
$609$	−18.0578	+	15.2367i	−0.731740	+	0.617423i
$610$	−15.2915			−0.619135
$611$	−9.87451	−	12.1382i	−0.399480	−	0.491059i
$612$	−20.6921	+	11.0604i	−0.836428	+	0.447089i
$613$		−	9.98823i		−	0.403421i	−0.979445	−	0.201710i	$-0.935350\pi$
$613$		−	9.98823i		−	0.403421i	0.979445	−	0.201710i	$-0.0646500\pi$
$614$	2.22699			0.0898740
$615$	−13.9583	−	55.7236i	−0.562853	−	2.24699i
$616$		0			0
$617$	31.1660			1.25470			0.627348	−	0.778739i	$-0.284140\pi$
$617$	31.1660			1.25470			0.627348	+	0.778739i	$0.284140\pi$
$618$	−27.8745	+	6.98233i	−1.12128	+	0.280871i
$619$	−33.5105			−1.34690			−0.673450	−	0.739233i	$-0.735188\pi$
$619$	−33.5105			−1.34690			−0.673450	+	0.739233i	$0.735188\pi$
$620$		−	10.3117i		−	0.414130i
$621$	−1.92881	+	1.74822i	−0.0774005	+	0.0701536i
$622$	28.5129			1.14327
$623$	−3.66507	−	7.48331i	−0.146838	−	0.299813i
$624$	5.00000	+	3.74166i	0.200160	+	0.149786i
$625$	−16.8745			−0.674980
$626$		−	27.3040i		−	1.09129i
$627$		0			0
$628$		−	17.5701i		−	0.701123i
$629$			18.2026i			0.725787i
$630$	21.6375	+	15.5943i	0.862060	+	0.621291i
$631$			33.2627i			1.32417i	0.749431	+	0.662083i	$0.230327\pi$
$631$			33.2627i			1.32417i	−0.749431	+	0.662083i	$0.769673\pi$
$632$	0.708497			0.0281825
$633$	−4.45398	−	17.7809i	−0.177030	−	0.706729i
$634$	−6.00000			−0.238290
$635$		−	49.0030i		−	1.94463i
$636$	0.841723	−	0.210845i	0.0333765	−	0.00836053i
$637$	−0.579928	−	25.2322i	−0.0229776	−	0.999736i
$638$		0			0
$639$	17.4170	−	9.30978i	0.689006	−	0.368289i
$640$			3.36028i			0.132827i
$641$			1.82646i			0.0721409i	0.999349	+	0.0360704i	$0.0114841\pi$
$641$			1.82646i			0.0721409i	−0.999349	+	0.0360704i	$0.988516\pi$
$642$	9.50432	−	2.38075i	0.375105	−	0.0939608i
$643$	5.59388			0.220601			0.110301	−	0.993898i	$-0.464819\pi$
$643$	5.59388			0.220601			0.110301	+	0.993898i	$0.464819\pi$
$644$	0.583005	+	1.19038i	0.0229736	+	0.0469074i
$645$	45.1660	−	11.3137i	1.77841	−	0.445477i
$646$	−43.7490			−1.72128
$647$	36.3338			1.42843			0.714215	−	0.699926i	$-0.246784\pi$
$647$	36.3338			1.42843			0.714215	+	0.699926i	$0.246784\pi$
$648$	−5.00000	+	7.48331i	−0.196419	+	0.293972i
$649$		0			0
$650$	17.5970	−	14.3152i	0.690209	−	0.561490i
$651$	−9.06871	−	10.7478i	−0.355431	−	0.421240i
$652$		−	8.48528i		−	0.332309i
$653$			35.0891i			1.37314i	0.727062	+	0.686572i	$0.240885\pi$
$653$			35.0891i			1.37314i	−0.727062	+	0.686572i	$0.759115\pi$
$654$	−11.7313	+	2.93859i	−0.458730	+	0.114908i
$655$			61.0460i			2.38526i
$656$		−	9.87000i		−	0.385359i
$657$	33.2651	−	17.7809i	1.29780	−	0.693701i
$658$	−5.05034	−	10.3117i	−0.196883	−	0.401994i
$659$		−	15.9686i		−	0.622048i	−0.950402	−	0.311024i	$-0.899328\pi$
$659$		−	15.9686i		−	0.622048i	0.950402	−	0.311024i	$-0.100672\pi$
$660$		0			0
$661$	−12.3277			−0.479491			−0.239745	−	0.970836i	$-0.577064\pi$
$661$	−12.3277			−0.479491			−0.239745	+	0.970836i	$0.577064\pi$
$662$			8.48528i			0.329790i
$663$	39.1044	+	29.2630i	1.51869	+	1.13648i
$664$		−	11.2712i		−	0.437408i
$665$	21.8745	+	44.6632i	0.848257	+	1.73197i
$666$	3.29150	+	6.15784i	0.127543	+	0.238611i
$667$	−2.58301			−0.100014
$668$			6.72057i			0.260027i
$669$	3.41699	+	13.6412i	0.132109	+	0.527397i
$670$	−44.1547			−1.70584
$671$		0			0
$672$	2.95522	+	3.50238i	0.114000	+	0.135107i
$673$	2.00000			0.0770943			0.0385472	−	0.999257i	$-0.487727\pi$
$673$	2.00000			0.0770943			0.0385472	+	0.999257i	$0.487727\pi$
$674$	19.8745			0.765537
$675$	21.9547	+	24.2226i	0.845035	+	0.932328i
$676$	2.64575	−	12.7279i	0.101760	−	0.489535i
$677$	15.8871			0.610591			0.305296	−	0.952258i	$-0.401245\pi$
$677$	15.8871			0.610591			0.305296	+	0.952258i	$0.401245\pi$
$678$	23.7608	−	5.95188i	0.912528	−	0.228581i
$679$	−25.8745	+	12.6724i	−0.992972	+	0.486324i
$680$			26.2803i			1.00780i
$681$	30.2288	−	7.57205i	1.15837	−	0.290162i
$682$		0			0
$683$	−29.4170			−1.12561			−0.562805	−	0.826590i	$-0.690278\pi$
$683$	−29.4170			−1.12561			−0.562805	+	0.826590i	$0.690278\pi$
$684$	−14.8000	+	7.91094i	−0.565893	+	0.302482i
$685$		−	31.2221i		−	1.19293i
$686$	3.76135	−	18.1343i	0.143609	−	0.692370i
$687$	6.81176	+	27.1936i	0.259885	+	1.03750i
$688$	8.00000			0.304997
$689$	−1.13990	−	1.40122i	−0.0434268	−	0.0533822i
$690$	0.708497	+	2.82843i	0.0269720	+	0.107676i
$691$	0.543544			0.0206774			0.0103387	−	0.999947i	$-0.496709\pi$
$691$	0.543544			0.0206774			0.0103387	+	0.999947i	$0.496709\pi$
$692$	5.29570			0.201312
$693$		0			0
$694$		−	31.9372i		−	1.21232i
$695$	−3.29150			−0.124854
$696$	−8.66259	+	2.16991i	−0.328355	+	0.0822501i
$697$		−	77.1920i		−	2.92386i
$698$	−0.543544			−0.0205734
$699$	−38.0173	+	9.52301i	−1.43794	+	0.360193i
$700$	14.9491	−	7.32156i	0.565023	−	0.276729i
$701$			16.4696i			0.622047i	0.950402	+	0.311024i	$0.100672\pi$
$701$			16.4696i			0.622047i	−0.950402	+	0.311024i	$0.899328\pi$
$702$	18.5203	+	2.82843i	0.699002	+	0.106752i
$703$			13.0194i			0.491038i
$704$		0			0
$705$	−6.13742	−	24.5015i	−0.231149	−	0.922780i
$706$			30.0317i			1.13026i
$707$	24.5830	−	12.0399i	0.924539	−	0.452807i
$708$	−3.64575	+	0.913230i	−0.137016	+	0.0343213i
$709$			36.2686i			1.36209i	0.732239	+	0.681047i	$0.238475\pi$
$709$			36.2686i			1.36209i	−0.732239	+	0.681047i	$0.761525\pi$
$710$		−	22.1208i		−	0.830177i
$711$	1.87451	−	1.00197i	0.0702995	−	0.0375767i
$712$		−	3.14944i		−	0.118030i
$713$		−	1.53737i		−	0.0575751i
$714$	23.1124	+	27.3917i	0.864959	+	1.02511i
$715$		0			0
$716$		−	11.3137i		−	0.422813i
$717$	−4.15580	−	16.5906i	−0.155201	−	0.619586i
$718$	−27.2915			−1.01851
$719$	−33.5633			−1.25170			−0.625850	−	0.779944i	$-0.715248\pi$
$719$	−33.5633			−1.25170			−0.625850	+	0.779944i	$0.715248\pi$
$720$	4.75216	+	8.89047i	0.177102	+	0.331328i
$721$	19.3068	+	39.4205i	0.719023	+	1.46810i
$722$	−12.2915			−0.457442
$723$	−0.833990	−	3.32941i	−0.0310164	−	0.123822i
$724$			24.7124i			0.918428i
$725$			32.4382i			1.20472i
$726$	4.62948	+	18.4816i	0.171816	+	0.685915i
$727$			34.7932i			1.29041i	0.764010	+	0.645204i	$0.223228\pi$
$727$			34.7932i			1.29041i	−0.764010	+	0.645204i	$0.776772\pi$
$728$	3.99790	−	8.66122i	0.148172	−	0.321006i
$729$	−2.64575	+	26.8701i	−0.0979908	+	0.995187i
$730$		−	42.2489i		−	1.56370i
$731$	62.5670			2.31412
$732$	−7.64575	+	1.91520i	−0.282595	+	0.0707877i
$733$	−46.3817			−1.71315			−0.856573	−	0.516026i	$-0.827411\pi$
$733$	−46.3817			−1.71315			−0.856573	+	0.516026i	$0.827411\pi$
$734$			14.6315i			0.540059i
$735$	16.4079	−	37.2912i	0.605214	−	1.37551i
$736$			0.500983i			0.0184665i
$737$		0			0
$738$	−13.9583	−	26.1136i	−0.513812	−	0.961254i
$739$		−	3.83039i		−	0.140903i	−0.997515	−	0.0704517i	$-0.977556\pi$
$739$		−	3.83039i		−	0.140903i	0.997515	−	0.0704517i	$-0.0224441\pi$
$740$	7.82087			0.287501
$741$	27.9694	+	20.9304i	1.02748	+	0.768897i
$742$	−0.583005	−	1.19038i	−0.0214028	−	0.0437001i
$743$	−3.29150			−0.120754			−0.0603768	−	0.998176i	$-0.519230\pi$
$743$	−3.29150			−0.120754			−0.0603768	+	0.998176i	$0.519230\pi$
$744$	−1.29150	−	5.15587i	−0.0473488	−	0.189023i
$745$			20.1617i			0.738667i
$746$	22.0000			0.805477
$747$	−15.9399	−	29.8209i	−0.583211	−	1.09109i
$748$		0			0
$749$	−6.58301	−	13.4411i	−0.240538	−	0.491128i
$750$	7.29150	−	1.82646i	0.266248	−	0.0666929i
$751$	−29.1660			−1.06428			−0.532141	−	0.846655i	$-0.678613\pi$
$751$	−29.1660			−1.06428			−0.532141	+	0.846655i	$0.678613\pi$
$752$		−	4.33981i		−	0.158257i
$753$	4.35425	+	17.3828i	0.158678	+	0.633465i
$754$	11.7313	+	14.4207i	0.427229	+	0.525170i
$755$	20.6921			0.753062
$756$	12.7719	+	5.08713i	0.464509	+	0.185017i
$757$	−16.5830			−0.602720			−0.301360	−	0.953511i	$-0.597441\pi$
$757$	−16.5830			−0.602720			−0.301360	+	0.953511i	$0.597441\pi$
$758$		−	30.1107i		−	1.09367i
$759$		0			0
$760$			18.7970i			0.681840i
$761$		−	28.0726i		−	1.01763i	−0.860875	−	0.508816i	$-0.830083\pi$
$761$		−	28.0726i		−	1.01763i	0.860875	−	0.508816i	$-0.169917\pi$
$762$	−6.13742	−	24.5015i	−0.222335	−	0.887596i
$763$	8.12549	+	16.5906i	0.294163	+	0.600619i
$764$			7.98430i			0.288862i
$765$	37.1660	+	69.5312i	1.34374	+	2.51391i
$766$		−	21.6991i		−	0.784019i
$767$	4.93725	+	6.06910i	0.178274	+	0.219143i
$768$	0.420861	+	1.68014i	0.0151865	+	0.0606269i
$769$	36.6320			1.32098			0.660492	−	0.750833i	$-0.270348\pi$
$769$	36.6320			1.32098			0.660492	+	0.750833i	$0.270348\pi$
$770$		0			0
$771$	5.41699	+	21.6255i	0.195088	+	0.778822i
$772$			8.48528i			0.305392i
$773$			5.74103i			0.206491i	0.994656	+	0.103245i	$0.0329227\pi$
$773$			5.74103i			0.206491i	−0.994656	+	0.103245i	$0.967077\pi$
$774$	21.1660	−	11.3137i	0.760797	−	0.406663i
$775$	−19.3068			−0.693521
$776$	−10.8896			−0.390913
$777$	8.15160	−	6.87810i	0.292437	−	0.246751i
$778$			9.81076i			0.351733i
$779$		−	55.2116i		−	1.97816i
$780$	12.5730	−	16.8014i	0.450187	−	0.601587i
$781$		0			0
$782$			3.91813i			0.140112i
$783$	−19.8504	+	17.9918i	−0.709394	+	0.642974i
$784$	4.29150	−	5.53019i	0.153268	−	0.197507i
$785$	−59.0405			−2.10725
$786$	7.64575	+	30.5230i	0.272715	+	1.08872i
$787$	−53.7118			−1.91462			−0.957310	−	0.289064i	$-0.906656\pi$
$787$	−53.7118			−1.91462			−0.957310	+	0.289064i	$0.906656\pi$
$788$	12.5830			0.448251
$789$	15.0982	−	3.78197i	0.537510	−	0.134642i
$790$		−	2.38075i		−	0.0847033i
$791$	−16.4575	−	33.6028i	−0.585162	−	1.19478i
$792$		0			0
$793$	10.3542	+	12.7279i	0.367690	+	0.451982i
$794$	−26.2860			−0.932854
$795$	−0.708497	−	2.82843i	−0.0251278	−	0.100314i
$796$		−	12.6724i		−	0.449163i
$797$	46.6799			1.65349			0.826743	−	0.562580i	$-0.190191\pi$
$797$	46.6799			1.65349			0.826743	+	0.562580i	$0.190191\pi$
$798$	16.5311	+	19.5919i	0.585196	+	0.693546i
$799$		−	33.9411i		−	1.20075i
$800$	6.29150			0.222438
$801$	−4.45398	−	8.33263i	−0.157374	−	0.294419i
$802$	6.00000			0.211867
$803$		0			0
$804$	−22.0773	+	5.53019i	−0.778608	+	0.195035i
$805$	4.00000	−	1.95906i	0.140981	−	0.0690479i
$806$	−8.58301	+	6.98233i	−0.302323	+	0.245942i
$807$	−8.81176	−	35.1779i	−0.310189	−	1.23832i
$808$	10.3460			0.363972
$809$			45.0774i			1.58484i	0.609979	+	0.792418i	$0.291178\pi$
$809$			45.0774i			1.58484i	−0.609979	+	0.792418i	$0.708822\pi$
$810$	25.1461	+	16.8014i	0.883542	+	0.590342i
$811$	−38.5608			−1.35405			−0.677027	−	0.735959i	$-0.736732\pi$
$811$	−38.5608			−1.35405			−0.677027	+	0.735959i	$0.736732\pi$
$812$	6.00000	+	12.2508i	0.210559	+	0.429917i
$813$	−3.16601	−	12.6392i	−0.111037	−	0.443276i
$814$		0			0
$815$	−28.5129			−0.998765
$816$	3.29150	+	13.1402i	0.115226	+	0.459998i
$817$	44.7510			1.56564
$818$	4.75216			0.166155
$819$	−1.67137	−	28.5693i	−0.0584024	−	0.998293i
$820$	−33.1660			−1.15821
$821$	−42.0000			−1.46581			−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000			−1.46581			−0.732905	+	0.680331i	$0.761836\pi$
$822$	−3.91044	−	15.6110i	−0.136392	−	0.544498i
$823$	5.87451			0.204772			0.102386	−	0.994745i	$-0.467352\pi$
$823$	5.87451			0.204772			0.102386	+	0.994745i	$0.467352\pi$
$824$			16.5906i			0.577960i
$825$		0			0
$826$	2.52517	+	5.15587i	0.0878619	+	0.179396i
$827$	19.7490			0.686741			0.343370	−	0.939200i	$-0.388431\pi$
$827$	19.7490			0.686741			0.343370	+	0.939200i	$0.388431\pi$
$828$	0.708497	+	1.32548i	0.0246220	+	0.0460635i
$829$		−	39.6909i		−	1.37852i	−0.724514	−	0.689260i	$-0.757936\pi$
$829$		−	39.6909i		−	1.37852i	0.724514	−	0.689260i	$-0.242064\pi$
$830$	−37.8745			−1.31464
$831$	−4.69934	−	18.7605i	−0.163018	−	0.650794i
$832$	2.79694	−	2.27533i	0.0969665	−	0.0788829i
$833$	33.5633	−	43.2509i	1.16290	−	1.49855i
$834$	−1.64575	+	0.412247i	−0.0569877	+	0.0142749i
$835$	22.5830			0.781517
$836$		0			0
$837$	−10.7085	−	11.8147i	−0.370140	−	0.408375i
$838$	−15.3964			−0.531859
$839$		−	19.3183i		−	0.666942i	−0.942760	−	0.333471i	$-0.891780\pi$
$839$		−	19.3183i		−	0.666942i	0.942760	−	0.333471i	$-0.108220\pi$
$840$	11.7690	−	9.93037i	0.406069	−	0.342630i
$841$	2.41699			0.0833446
$842$			19.2980i			0.665053i
$843$	−1.13990	−	4.55066i	−0.0392603	−	0.156733i
$844$	−10.5830			−0.364282
$845$	−42.7694	−	8.89047i	−1.47131	−	0.305842i
$846$	−6.13742	−	11.4821i	−0.211009	−	0.394762i
$847$	26.1369	−	12.8009i	0.898073	−	0.439846i
$848$		−	0.500983i		−	0.0172038i
$849$	−20.2288	+	5.06713i	−0.694249	+	0.173904i
$850$	49.2050			1.68772
$851$	1.16601			0.0399703
$852$	−2.77053	−	11.0604i	−0.0949169	−	0.378922i
$853$	−4.50679			−0.154310			−0.0771548	−	0.997019i	$-0.524584\pi$
$853$	−4.50679			−0.154310			−0.0771548	+	0.997019i	$0.524584\pi$
$854$	5.29570	+	10.8127i	0.181215	+	0.370004i
$855$	26.5830	+	49.7322i	0.909120	+	1.70081i
$856$		−	5.65685i		−	0.193347i
$857$	5.05034			0.172516			0.0862581	−	0.996273i	$-0.472509\pi$
$857$	5.05034			0.172516			0.0862581	+	0.996273i	$0.472509\pi$
$858$		0			0
$859$			45.2211i			1.54292i	0.636276	+	0.771461i	$0.280474\pi$
$859$			45.2211i			1.54292i	−0.636276	+	0.771461i	$0.719526\pi$
$860$		−	26.8823i		−	0.916678i
$861$	−34.5685	+	29.1680i	−1.17809	+	0.994043i
$862$	−3.29150			−0.112109
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$	3.48957	+	3.85005i	0.118718	+	0.130981i
$865$		−	17.7951i		−	0.605050i
$866$		−	1.95906i		−	0.0665717i
$867$	18.5878	+	74.2051i	0.631274	+	2.52014i
$868$	−7.29150	+	3.57113i	−0.247490	+	0.121212i
$869$		0			0
$870$	7.29150	+	29.1088i	0.247205	+	0.986880i
$871$	29.8982	+	36.7523i	1.01306	+	1.24530i
$872$			6.98233i			0.236452i
$873$	−28.8111	+	15.4002i	−0.975109	+	0.521218i
$874$			2.80244i			0.0947940i
$875$	−5.05034	−	10.3117i	−0.170733	−	0.348601i
$876$	−5.29150	−	21.1245i	−0.178783	−	0.713730i
$877$			16.2921i			0.550145i	0.961423	+	0.275073i	$0.0887019\pi$
$877$			16.2921i			0.550145i	−0.961423	+	0.275073i	$0.911298\pi$
$878$			14.6315i			0.493789i
$879$	−31.5203	+	7.89556i	−1.06315	+	0.266311i
$880$		0			0
$881$	2.77053			0.0933416			0.0466708	−	0.998910i	$-0.485139\pi$
$881$	2.77053			0.0933416			0.0466708	+	0.998910i	$0.485139\pi$
$882$	3.53338	−	20.7006i	0.118975	−	0.697026i
$883$	14.5830			0.490757			0.245379	−	0.969427i	$-0.421088\pi$
$883$	14.5830			0.490757			0.245379	+	0.969427i	$0.421088\pi$
$884$	21.8745	−	17.7951i	0.735719	−	0.598513i
$885$	3.06871	+	12.2508i	0.103154	+	0.411805i
$886$		−	5.65685i		−	0.190046i
$887$	2.27980			0.0765483			0.0382742	−	0.999267i	$-0.487814\pi$
$887$	2.27980			0.0765483			0.0382742	+	0.999267i	$0.487814\pi$
$888$	3.91044	−	0.979531i	0.131226	−	0.0328709i
$889$	−34.6504	+	16.9706i	−1.16214	+	0.569174i
$890$	−10.5830			−0.354743
$891$		0			0
$892$	8.11905			0.271846
$893$		−	24.2764i		−	0.812379i
$894$	2.52517	+	10.0808i	0.0844543	+	0.337154i
$895$	−38.0173			−1.27078
$896$	2.37608	−	1.16372i	0.0793792	−	0.0388772i
$897$	1.87451	−	2.50492i	0.0625880	−	0.0836367i
$898$	22.4575			0.749417
$899$		−	15.8219i		−	0.527689i
$900$	16.6458	−	8.89753i	0.554858	−	0.296584i
$901$		−	3.91813i		−	0.130532i
$902$		0			0
$903$	−23.6417	−	28.0191i	−0.786748	−	0.932416i
$904$		−	14.1421i		−	0.470360i
$905$	83.0405			2.76036
$906$	10.3460	−	2.59160i	0.343724	−	0.0861000i
$907$	−4.00000			−0.132818			−0.0664089	−	0.997792i	$-0.521154\pi$
$907$	−4.00000			−0.132818			−0.0664089	+	0.997792i	$0.521154\pi$
$908$		−	17.9918i		−	0.597079i
$909$	27.3730	−	14.6315i	0.907907	−	0.485296i
$910$	−29.1042	−	13.4341i	−0.964794	−	0.445335i
$911$		−	43.7519i		−	1.44956i	−0.688978	−	0.724782i	$-0.741940\pi$
$911$		−	43.7519i		−	1.44956i	0.688978	−	0.724782i	$-0.258060\pi$
$912$	2.35425	+	9.39851i	0.0779570	+	0.311216i
$913$		0			0
$914$		−	17.7951i		−	0.588608i
$915$	6.43560	+	25.6919i	0.212754	+	0.849348i
$916$	16.1853			0.534777
$917$	43.1660	−	21.1412i	1.42547	−	0.698145i
$918$	27.2915	+	30.1107i	0.900754	+	0.993802i
$919$	29.8745			0.985469			0.492735	−	0.870180i	$-0.335997\pi$
$919$	29.8745			0.985469			0.492735	+	0.870180i	$0.335997\pi$
$920$	1.68345			0.0555016
$921$	−0.937254	−	3.74166i	−0.0308836	−	0.123292i
$922$		−	25.9027i		−	0.853061i
$923$	−18.4123	+	14.9785i	−0.606047	+	0.493024i
$924$		0			0
$925$		−	14.6431i		−	0.481463i
$926$			11.6372i			0.382423i
$927$	23.4626	+	43.8945i	0.770613	+	1.44169i
$928$			5.15587i			0.169250i
$929$		−	54.1115i		−	1.77534i	−0.460479	−	0.887671i	$-0.652322\pi$
$929$		−	54.1115i		−	1.77534i	0.460479	−	0.887671i	$-0.347678\pi$
$930$	−17.3252	+	4.33981i	−0.568115	+	0.142308i
$931$	24.0062	−	30.9352i	0.786770	−	1.01386i
$932$			22.6274i			0.741186i
$933$	−12.0000	−	47.9058i	−0.392862	−	1.56837i
$934$	33.8086			1.10625
$935$		0			0
$936$	4.18221	−	9.97543i	0.136700	−	0.326057i
$937$			14.9785i			0.489326i	0.969608	+	0.244663i	$0.0786774\pi$
$937$			14.9785i			0.489326i	−0.969608	+	0.244663i	$0.921323\pi$
$938$	15.2915	+	31.2221i	0.499285	+	1.01944i
$939$	−45.8745	+	11.4912i	−1.49706	+	0.375001i
$940$	−14.5830			−0.475645
$941$		−	43.6837i		−	1.42405i	−0.702155	−	0.712024i	$-0.747779\pi$
$941$		−	43.6837i		−	1.42405i	0.702155	−	0.712024i	$-0.252221\pi$
$942$	−29.5203	+	7.39458i	−0.961822	+	0.240928i
$943$	−4.94471			−0.161022
$944$			2.16991i			0.0706245i
$945$	17.0942	−	42.9172i	0.556074	−	1.39610i
$946$		0			0
$947$	−36.0000			−1.16984			−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000			−1.16984			−0.584921	+	0.811090i	$0.698875\pi$
$948$	−0.298179	−	1.19038i	−0.00968441	−	0.0386616i
$949$	−35.1660	+	28.6078i	−1.14154	+	0.928648i
$950$	35.1939			1.14184
$951$	2.52517	+	10.0808i	0.0818842	+	0.326894i
$952$	18.5830	−	9.10132i	0.602279	−	0.294975i
$953$		−	25.2784i		−	0.818847i	−0.912345	−	0.409423i	$-0.865730\pi$
$953$		−	25.2784i		−	0.818847i	0.912345	−	0.409423i	$-0.134270\pi$
$954$	−0.708497	−	1.32548i	−0.0229384	−	0.0429139i
$955$	26.8295			0.868182
$956$	−9.87451			−0.319364
$957$		0			0
$958$		−	35.9836i		−	1.16258i
$959$	−22.0773	+	10.8127i	−0.712915	+	0.349161i
$960$	5.64575	−	1.41421i	0.182216	−	0.0456435i
$961$	−21.5830			−0.696226
$962$	−5.29570	−	6.50972i	−0.170740	−	0.209882i
$963$	−8.00000	−	14.9666i	−0.257796	−	0.482293i
$964$	−1.98162			−0.0638238
$965$	28.5129			0.917864
$966$	1.75464	−	1.48051i	0.0564545	−	0.0476348i
$967$		−	1.50295i		−	0.0483316i	−0.999708	−	0.0241658i	$-0.992307\pi$
$967$		−	1.50295i		−	0.0483316i	0.999708	−	0.0241658i	$-0.00769296\pi$
$968$	11.0000			0.353553
$969$	18.4123	+	73.5045i	0.591487	+	2.36131i
$970$			36.5921i			1.17490i
$971$	44.4001			1.42487			0.712433	−	0.701740i	$-0.247593\pi$
$971$	44.4001			1.42487			0.712433	+	0.701740i	$0.247593\pi$
$972$	14.6773	+	5.25127i	0.470776	+	0.168435i
$973$	1.13990	+	2.32744i	0.0365436	+	0.0746144i
$974$		−	20.1225i		−	0.644767i
$975$	−31.4575	−	23.5406i	−1.00745	−	0.753904i
$976$			4.55066i			0.145663i
$977$	1.54249			0.0493485			0.0246743	−	0.999696i	$-0.492145\pi$
$977$	1.54249			0.0493485			0.0246743	+	0.999696i	$0.492145\pi$
$978$	−14.2565	+	3.57113i	−0.455872	+	0.114192i
$979$		0			0
$980$	−18.5830	−	14.4207i	−0.593612	−	0.460651i
$981$	9.87451	+	18.4735i	0.315269	+	0.589814i
$982$			3.65292i			0.116569i
$983$		−	55.7236i		−	1.77731i	−0.458580	−	0.888653i	$-0.651642\pi$
$983$		−	55.7236i		−	1.77731i	0.458580	−	0.888653i	$-0.348358\pi$
$984$	−16.5830	+	4.15390i	−0.528647	+	0.132422i
$985$		−	42.2825i		−	1.34723i
$986$			40.3234i			1.28416i
$987$	−15.1997	+	12.8251i	−0.483812	+	0.408227i
$988$	15.6458	−	12.7279i	0.497758	−	0.404929i
$989$		−	4.00787i		−	0.127443i
$990$		0			0
$991$	−0.708497			−0.0225062			−0.0112531	−	0.999937i	$-0.503582\pi$
$991$	−0.708497			−0.0225062			−0.0112531	+	0.999937i	$0.503582\pi$
$992$	−3.06871			−0.0974317
$993$	14.2565	−	3.57113i	0.452416	−	0.113326i
$994$	−15.6417	+	7.66079i	−0.496126	+	0.242985i
$995$	−42.5830			−1.34997
$996$	−18.9373	+	4.74362i	−0.600050	+	0.150307i
$997$			37.7318i			1.19498i	0.801877	+	0.597489i	$0.203835\pi$
$997$			37.7318i			1.19498i	−0.801877	+	0.597489i	$0.796165\pi$
$998$		−	3.83039i		−	0.121249i
$999$	8.96077	−	8.12179i	0.283506	−	0.256962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.e.f.545.6	yes	8
3.2	odd	2		546.2.e.h.545.4	yes	8
7.6	odd	2	inner	546.2.e.f.545.3	✓	8
13.12	even	2		546.2.e.h.545.6	yes	8
21.20	even	2		546.2.e.h.545.5	yes	8
39.38	odd	2	inner	546.2.e.f.545.4	yes	8
91.90	odd	2		546.2.e.h.545.3	yes	8
273.272	even	2	inner	546.2.e.f.545.5	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.e.f.545.3	✓	8	7.6	odd	2	inner
546.2.e.f.545.4	yes	8	39.38	odd	2	inner
546.2.e.f.545.5	yes	8	273.272	even	2	inner
546.2.e.f.545.6	yes	8	1.1	even	1	trivial
546.2.e.h.545.3	yes	8	91.90	odd	2
546.2.e.h.545.4	yes	8	3.2	odd	2
546.2.e.h.545.5	yes	8	21.20	even	2
546.2.e.h.545.6	yes	8	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.420861 + 1.68014i) q^{3} +1.00000 q^{4} -3.36028i q^{5} +(-0.420861 - 1.68014i) q^{6} +(-2.37608 + 1.16372i) q^{7} -1.00000 q^{8} +(-2.64575 + 1.41421i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.420861 + 1.68014i) q^{3} +1.00000 q^{4} -3.36028i q^{5} +(-0.420861 - 1.68014i) q^{6} +(-2.37608 + 1.16372i) q^{7} -1.00000 q^{8} +(-2.64575 + 1.41421i) q^{9} +3.36028i q^{10} +(0.420861 + 1.68014i) q^{12} +(2.79694 - 2.27533i) q^{13} +(2.37608 - 1.16372i) q^{14} +(5.64575 - 1.41421i) q^{15} +1.00000 q^{16} +7.82087 q^{17} +(2.64575 - 1.41421i) q^{18} +5.59388 q^{19} -3.36028i q^{20} +(-2.95522 - 3.50238i) q^{21} -0.500983i q^{23} +(-0.420861 - 1.68014i) q^{24} -6.29150 q^{25} +(-2.79694 + 2.27533i) q^{26} +(-3.48957 - 3.85005i) q^{27} +(-2.37608 + 1.16372i) q^{28} -5.15587i q^{29} +(-5.64575 + 1.41421i) q^{30} +3.06871 q^{31} -1.00000 q^{32} -7.82087 q^{34} +(3.91044 + 7.98430i) q^{35} +(-2.64575 + 1.41421i) q^{36} +2.32744i q^{37} -5.59388 q^{38} +(5.00000 + 3.74166i) q^{39} +3.36028i q^{40} -9.87000i q^{41} +(2.95522 + 3.50238i) q^{42} +8.00000 q^{43} +(4.75216 + 8.89047i) q^{45} +0.500983i q^{46} -4.33981i q^{47} +(0.420861 + 1.68014i) q^{48} +(4.29150 - 5.53019i) q^{49} +6.29150 q^{50} +(3.29150 + 13.1402i) q^{51} +(2.79694 - 2.27533i) q^{52} -0.500983i q^{53} +(3.48957 + 3.85005i) q^{54} +(2.37608 - 1.16372i) q^{56} +(2.35425 + 9.39851i) q^{57} +5.15587i q^{58} +2.16991i q^{59} +(5.64575 - 1.41421i) q^{60} +4.55066i q^{61} -3.06871 q^{62} +(4.64076 - 6.43920i) q^{63} +1.00000 q^{64} +(-7.64575 - 9.39851i) q^{65} +13.1402i q^{67} +7.82087 q^{68} +(0.841723 - 0.210845i) q^{69} +(-3.91044 - 7.98430i) q^{70} -6.58301 q^{71} +(2.64575 - 1.41421i) q^{72} -12.5730 q^{73} -2.32744i q^{74} +(-2.64785 - 10.5706i) q^{75} +5.59388 q^{76} +(-5.00000 - 3.74166i) q^{78} -0.708497 q^{79} -3.36028i q^{80} +(5.00000 - 7.48331i) q^{81} +9.87000i q^{82} +11.2712i q^{83} +(-2.95522 - 3.50238i) q^{84} -26.2803i q^{85} -8.00000 q^{86} +(8.66259 - 2.16991i) q^{87} +3.14944i q^{89} +(-4.75216 - 8.89047i) q^{90} +(-3.99790 + 8.66122i) q^{91} -0.500983i q^{92} +(1.29150 + 5.15587i) q^{93} +4.33981i q^{94} -18.7970i q^{95} +(-0.420861 - 1.68014i) q^{96} +10.8896 q^{97} +(-4.29150 + 5.53019i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} + 24 q^{15} + 8 q^{16} - 8 q^{21} - 8 q^{25} - 24 q^{30} - 8 q^{32} + 40 q^{39} + 8 q^{42} + 64 q^{43} - 8 q^{49} + 8 q^{50} - 16 q^{51} + 40 q^{57} + 24 q^{60} + 8 q^{63} + 8 q^{64} - 40 q^{65} + 32 q^{71} - 40 q^{78} - 48 q^{79} + 40 q^{81} - 8 q^{84} - 64 q^{86} - 32 q^{91} - 32 q^{93} + 8 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 + 24 * q^15 + 8 * q^16 - 8 * q^21 - 8 * q^25 - 24 * q^30 - 8 * q^32 + 40 * q^39 + 8 * q^42 + 64 * q^43 - 8 * q^49 + 8 * q^50 - 16 * q^51 + 40 * q^57 + 24 * q^60 + 8 * q^63 + 8 * q^64 - 40 * q^65 + 32 * q^71 - 40 * q^78 - 48 * q^79 + 40 * q^81 - 8 * q^84 - 64 * q^86 - 32 * q^91 - 32 * q^93 + 8 * q^98

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