LMFDB - Embedded newform 546.2.e.f.545.4

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			545.4
Root			$-0.420861 - 1.68014i$ of defining polynomial
Character	$\chi$	$=$	546.545
Dual form			546.2.e.f.545.3

$q$-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} +(0.955218 + 4.48191i) 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} +(-0.955218 - 4.48191i) 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} +(-7.93227 - 0.281364i) 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} +(0.955218 + 4.48191i) 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} +(-9.29360 - 2.15150i) 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	$-0.897319\pi$
$17$	−7.82087			−1.89684			−0.948420	+	0.317017i	$0.897319\pi$
$18$	2.64575	+	1.41421i	0.623610	+	0.333333i
$19$	−5.59388			−1.28332			−0.641662	−	0.766987i	$-0.721755\pi$
$19$	−5.59388			−1.28332			−0.641662	+	0.766987i	$0.721755\pi$
$20$		−	3.36028i		−	0.751382i
$21$	0.955218	+	4.48191i	0.208446	+	0.978034i
$22$		0			0
$23$			0.500983i			0.104462i	0.998635	+	0.0522311i	$0.0166333\pi$
$23$			0.500983i			0.104462i	−0.998635	+	0.0522311i	$0.983367\pi$
$24$	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	$0.158896\pi$
$29$			5.15587i			0.957421i	−0.877973	+	0.478711i	$0.841104\pi$
$30$	−5.64575	−	1.41421i	−1.03077	−	0.258199i
$31$	−3.06871			−0.551157			−0.275578	−	0.961279i	$-0.588869\pi$
$31$	−3.06871			−0.551157			−0.275578	+	0.961279i	$0.588869\pi$
$32$	−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	$-0.938725\pi$
$37$		−	2.32744i		−	0.382629i	0.981529	−	0.191315i	$-0.0612751\pi$
$38$	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	$-0.280102\pi$
$42$	−0.955218	−	4.48191i	−0.147393	−	0.691574i
$43$	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	$0.0109545\pi$
$53$			0.500983i			0.0688153i	−0.999408	+	0.0344077i	$0.989046\pi$
$54$	−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
$63$	−7.93227	−	0.281364i	−0.999372	−	0.0354486i
$64$	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	$-0.703415\pi$
$67$		−	13.1402i		−	1.60533i	0.596432	−	0.802664i	$-0.296585\pi$
$68$	−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	$-0.236815\pi$
$73$	12.5730			1.47156			0.735781	+	0.677220i	$0.236815\pi$
$74$			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	$0.787705\pi$
$84$	0.955218	+	4.48191i	0.104223	+	0.489017i
$85$			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
$91$	−9.29360	−	2.15150i	−0.974234	−	0.225539i
$92$			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	$-0.686454\pi$
$97$	−10.8896			−1.10567			−0.552835	+	0.833291i	$0.686454\pi$
$98$	−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	$-0.327890\pi$
$101$	10.3460			1.02947			0.514735	+	0.857350i	$0.327890\pi$
$102$	−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
$105$	15.0605	−	3.20980i	1.46975	−	0.313245i
$106$		−	0.500983i		−	0.0486598i
$107$		−	5.65685i		−	0.546869i	−0.961891	−	0.273434i	$-0.911840\pi$
$107$		−	5.65685i		−	0.546869i	0.961891	−	0.273434i	$-0.0881596\pi$
$108$	3.48957	−	3.85005i	0.335784	−	0.370471i
$109$			6.98233i			0.668786i	0.942434	+	0.334393i	$0.108531\pi$
$109$			6.98233i			0.668786i	−0.942434	+	0.334393i	$0.891469\pi$
$110$		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	$-0.768350\pi$
$113$		−	14.1421i		−	1.33038i	0.746674	−	0.665190i	$-0.231650\pi$
$114$	−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
$126$	7.93227	+	0.281364i	0.706662	+	0.0250659i
$127$	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	$-0.208191\pi$
$131$	18.1669			1.58725			0.793625	+	0.608407i	$0.208191\pi$
$132$		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
$147$	7.48537	+	9.53778i	0.617383	+	0.786662i
$148$		−	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	$-0.919386\pi$
$151$		−	6.15784i		−	0.501118i	0.968101	−	0.250559i	$-0.0806144\pi$
$152$	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	$0.107828\pi$
$163$			8.48528i			0.664619i	−0.943170	+	0.332309i	$0.892172\pi$
$164$		−	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	$0.916269\pi$
$168$	−0.955218	−	4.48191i	−0.0736966	−	0.345787i
$169$	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	$-0.564521\pi$
$173$	−5.29570			−0.402625			−0.201312	+	0.979527i	$0.564521\pi$
$174$	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	$0.138957\pi$
$179$			11.3137i			0.845626i	−0.906217	+	0.422813i	$0.861043\pi$
$180$	−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	$0.629460\pi$
$182$	9.29360	+	2.15150i	0.688888	+	0.159480i
$183$	−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
$189$	3.81112	−	13.2089i	0.277218	−	0.960807i
$190$		−	18.7970i		−	1.36368i
$191$		−	7.98430i		−	0.577724i	−0.957371	−	0.288862i	$-0.906723\pi$
$191$		−	7.98430i		−	0.577724i	0.957371	−	0.288862i	$-0.0932768\pi$
$192$	−0.420861	+	1.68014i	−0.0303731	+	0.121254i
$193$		−	8.48528i		−	0.610784i	−0.952227	−	0.305392i	$-0.901213\pi$
$193$		−	8.48528i		−	0.610784i	0.952227	−	0.305392i	$-0.0987875\pi$
$194$	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
$210$	−15.0605	+	3.20980i	−1.03927	+	0.221497i
$211$	−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	$-0.587634\pi$
$223$	−8.11905			−0.543692			−0.271846	+	0.962341i	$0.587634\pi$
$224$	−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	$-0.679604\pi$
$229$	−16.1853			−1.06955			−0.534777	+	0.844993i	$0.679604\pi$
$230$	−1.68345			−0.111003
$231$		0			0
$232$		−	5.15587i		−	0.338500i
$233$		−	22.6274i		−	1.48237i	−0.671300	−	0.741186i	$-0.734264\pi$
$233$		−	22.6274i		−	1.48237i	0.671300	−	0.741186i	$-0.265736\pi$
$234$	−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	$-0.479670\pi$
$241$	1.98162			0.127648			0.0638238	+	0.997961i	$0.479670\pi$
$242$	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	$-0.605875\pi$
$251$	−10.3460			−0.653036			−0.326518	+	0.945191i	$0.605875\pi$
$252$	−7.93227	−	0.281364i	−0.499686	−	0.0177243i
$253$		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	$-0.631491\pi$
$257$	−12.8712			−0.802884			−0.401442	+	0.915884i	$0.631491\pi$
$258$	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	$0.0893596\pi$
$263$			8.98626i			0.554117i	−0.960853	+	0.277058i	$0.910640\pi$
$264$		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	$-0.279642\pi$
$269$	20.9374			1.27658			0.638289	+	0.769797i	$0.279642\pi$
$270$	12.9373	+	11.7260i	0.787336	+	0.713619i
$271$	7.52269			0.456971			0.228485	−	0.973547i	$-0.426623\pi$
$271$	7.52269			0.456971			0.228485	+	0.973547i	$0.426623\pi$
$272$	−7.82087			−0.474210
$273$	7.52615	−	14.7091i	0.455503	−	0.890234i
$274$	−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	$0.815390\pi$
$294$	−7.48537	−	9.53778i	−0.436556	−	0.556254i
$295$	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	$-0.479758\pi$
$307$	2.22699			0.127101			0.0635505	+	0.997979i	$0.479758\pi$
$308$		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	$-0.200328\pi$
$311$	28.5129			1.61682			0.808410	+	0.588619i	$0.200328\pi$
$312$	−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
$315$	−0.945464	+	26.6547i	−0.0532709	+	1.50182i
$316$	−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	$0.0749186\pi$
$331$			8.48528i			0.466393i	−0.972430	+	0.233197i	$0.925081\pi$
$332$			11.2712i			0.618589i
$333$	−3.29150	+	6.15784i	−0.180373	+	0.337447i
$334$		−	6.72057i		−	0.367733i
$335$	−44.1547			−2.41243
$336$	0.955218	+	4.48191i	0.0521114	+	0.244508i
$337$	−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	$-0.672178\pi$
$347$		−	31.9372i		−	1.71448i	0.514918	−	0.857239i	$-0.327822\pi$
$348$	−8.66259	−	2.16991i	−0.464364	−	0.116319i
$349$	−0.543544			−0.0290952			−0.0145476	−	0.999894i	$-0.504631\pi$
$349$	−0.543544			−0.0290952			−0.0145476	+	0.999894i	$0.504631\pi$
$350$	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
$357$	−7.47063	−	35.0525i	−0.395388	−	1.85517i
$358$		−	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
$364$	−9.29360	−	2.15150i	−0.487117	−	0.112769i
$365$		−	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
$378$	−3.81112	+	13.2089i	−0.196023	+	0.679393i
$379$		−	30.1107i		−	1.54668i	−0.633989	−	0.773342i	$-0.718583\pi$
$379$		−	30.1107i		−	1.54668i	0.633989	−	0.773342i	$-0.281417\pi$
$380$			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	$0.0800075\pi$
$389$			9.81076i			0.497425i	−0.968577	+	0.248713i	$0.919993\pi$
$390$	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	$-0.729286\pi$
$397$	−26.2860			−1.31925			−0.659627	+	0.751593i	$0.729286\pi$
$398$			12.6724i			0.635212i
$399$	−5.34337	−	25.0713i	−0.267503	−	1.25513i
$400$	−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	$-0.462515\pi$
$409$	4.75216			0.234979			0.117490	+	0.993074i	$0.462515\pi$
$410$	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	$-0.622729\pi$
$419$	−15.3964			−0.752162			−0.376081	+	0.926587i	$0.622729\pi$
$420$	15.0605	−	3.20980i	0.734877	−	0.156622i
$421$			19.2980i			0.940527i	0.882526	+	0.470264i	$0.155841\pi$
$421$			19.2980i			0.940527i	−0.882526	+	0.470264i	$0.844159\pi$
$422$	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
$441$	−19.1751	+	8.56241i	−0.913101	+	0.407734i
$442$	−21.8745	−	17.7951i	−1.04046	−	0.846425i
$443$		−	5.65685i		−	0.268765i	−0.990930	−	0.134383i	$-0.957095\pi$
$443$		−	5.65685i		−	0.268765i	0.990930	−	0.134383i	$-0.0429051\pi$
$444$	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
$455$	−7.22966	+	31.2291i	−0.338931	+	1.46404i
$456$	−2.35425	+	9.39851i	−0.110248	+	0.440126i
$457$		−	17.7951i		−	0.832418i	−0.909269	−	0.416209i	$-0.863359\pi$
$457$		−	17.7951i		−	0.832418i	0.909269	−	0.416209i	$-0.136641\pi$
$458$	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	$0.0871605\pi$
$463$			11.6372i			0.540827i	−0.962744	+	0.270414i	$0.912840\pi$
$464$			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	$-0.214078\pi$
$467$	33.8086			1.56448			0.782239	+	0.622979i	$0.214078\pi$
$468$	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
$483$	−2.24536	+	0.478548i	−0.102168	+	0.0217747i
$484$	−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	$-0.849311\pi$
$487$		−	20.1225i		−	0.911838i	0.890021	−	0.455919i	$-0.150689\pi$
$488$		−	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	$0.0262671\pi$
$491$			3.65292i			0.164854i	−0.996597	+	0.0824270i	$0.973733\pi$
$492$	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	$-0.972676\pi$
$499$		−	3.83039i		−	0.171472i	0.996318	−	0.0857360i	$-0.0273242\pi$
$500$			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	$-0.386618\pi$
$503$	15.6417			0.697431			0.348715	+	0.937229i	$0.386618\pi$
$504$	7.93227	+	0.281364i	0.353331	+	0.0125330i
$505$		−	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	$-0.793005\pi$
$521$	−36.3338			−1.59181			−0.795907	+	0.605419i	$0.793005\pi$
$522$	−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
$525$	−6.00975	−	28.1980i	−0.262287	−	1.23066i
$526$		−	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	$0.303319\pi$
$541$			37.9176i			1.63020i	−0.579318	+	0.815102i	$0.696681\pi$
$542$	−7.52269			−0.323127
$543$	−41.5203	−	10.4005i	−1.78180	−	0.446327i
$544$	7.82087			0.335317
$545$	23.4626			1.00503
$546$	−7.52615	+	14.7091i	−0.322089	+	0.629491i
$547$	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	$-0.247594\pi$
$563$	33.8086			1.42486			0.712432	+	0.701741i	$0.247594\pi$
$564$	7.29150	+	1.82646i	0.307028	+	0.0769079i
$565$	−47.5216			−1.99925
$566$		−	12.0399i		−	0.506075i
$567$	20.5889	+	11.9623i	0.864652	+	0.502371i
$568$	6.58301			0.276217
$569$			15.1441i			0.634874i	0.948279	+	0.317437i	$0.102822\pi$
$569$			15.1441i			0.634874i	−0.948279	+	0.317437i	$0.897178\pi$
$570$	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	$-0.520346\pi$
$577$	−3.06871			−0.127752			−0.0638761	+	0.997958i	$0.520346\pi$
$578$	−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	$-0.135075\pi$
$588$	7.48537	+	9.53778i	0.308692	+	0.393331i
$589$	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	$-0.650564\pi$
$599$		−	43.5744i		−	1.78040i	0.455568	−	0.890201i	$-0.349436\pi$
$600$	−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
$609$	−23.1082	+	4.92498i	−0.936390	+	0.199570i
$610$	−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	$0.0646500\pi$
$613$			9.98823i			0.403421i	−0.979445	+	0.201710i	$0.935350\pi$
$614$	−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	$-0.264812\pi$
$619$	33.5105			1.34690			0.673450	+	0.739233i	$0.264812\pi$
$620$			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
$630$	0.945464	−	26.6547i	0.0376682	−	1.06195i
$631$		−	33.2627i		−	1.32417i	−0.749431	−	0.662083i	$-0.769673\pi$
$631$		−	33.2627i		−	1.32417i	0.749431	−	0.662083i	$-0.230327\pi$
$632$	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
$637$	−24.5861	+	5.70303i	−0.974136	+	0.225962i
$638$		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	$-0.988516\pi$
$641$		−	1.82646i		−	0.0721409i	0.999349	−	0.0360704i	$-0.0114841\pi$
$642$	−9.50432	−	2.38075i	−0.375105	−	0.0939608i
$643$	−5.59388			−0.220601			−0.110301	−	0.993898i	$-0.535181\pi$
$643$	−5.59388			−0.220601			−0.110301	+	0.993898i	$0.535181\pi$
$644$	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	$-0.753216\pi$
$647$	−36.3338			−1.42843			−0.714215	+	0.699926i	$0.753216\pi$
$648$	−5.00000	−	7.48331i	−0.196419	−	0.293972i
$649$		0			0
$650$	−17.5970	−	14.3152i	−0.690209	−	0.561490i
$651$	−2.93129	−	13.7537i	−0.114886	−	0.539050i
$652$			8.48528i			0.332309i
$653$		−	35.0891i		−	1.37314i	−0.727062	−	0.686572i	$-0.759115\pi$
$653$		−	35.0891i		−	1.37314i	0.727062	−	0.686572i	$-0.240885\pi$
$654$	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	$0.100672\pi$
$659$			15.9686i			0.622048i	−0.950402	+	0.311024i	$0.899328\pi$
$660$		0			0
$661$	12.3277			0.479491			0.239745	−	0.970836i	$-0.422936\pi$
$661$	12.3277			0.479491			0.239745	+	0.970836i	$0.422936\pi$
$662$		−	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
$672$	−0.955218	−	4.48191i	−0.0368483	−	0.172894i
$673$	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	$-0.598755\pi$
$677$	−15.8871			−0.610591			−0.305296	+	0.952258i	$0.598755\pi$
$678$	−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	$-0.503291\pi$
$691$	−0.543544			−0.0206774			−0.0103387	+	0.999947i	$0.503291\pi$
$692$	−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	$-0.899328\pi$
$701$		−	16.4696i		−	0.622047i	0.950402	−	0.311024i	$-0.100672\pi$
$702$	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	$-0.761525\pi$
$709$		−	36.2686i		−	1.36209i	0.732239	−	0.681047i	$-0.238475\pi$
$710$		−	22.1208i		−	0.830177i
$711$	1.87451	+	1.00197i	0.0702995	+	0.0375767i
$712$		−	3.14944i		−	0.118030i
$713$		−	1.53737i		−	0.0575751i
$714$	7.47063	+	35.0525i	0.279581	+	1.31181i
$715$		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	$-0.284752\pi$
$719$	33.5633			1.25170			0.625850	+	0.779944i	$0.284752\pi$
$720$	−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	$0.776772\pi$
$728$	9.29360	+	2.15150i	0.344444	+	0.0797400i
$729$	−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	$-0.172589\pi$
$733$	46.3817			1.71315			0.856573	+	0.516026i	$0.172589\pi$
$734$			14.6315i			0.540059i
$735$	32.0496	−	25.1530i	1.18217	−	0.927782i
$736$		−	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	$0.0224441\pi$
$739$			3.83039i			0.140903i	−0.997515	+	0.0704517i	$0.977556\pi$
$740$	−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
$756$	3.81112	−	13.2089i	0.138609	−	0.480404i
$757$	−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	$-0.729652\pi$
$769$	−36.6320			−1.32098			−0.660492	+	0.750833i	$0.729652\pi$
$770$		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
$777$	10.4314	−	2.22322i	0.374225	−	0.0797574i
$778$		−	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	$-0.0933440\pi$
$787$	53.7118			1.91462			0.957310	+	0.289064i	$0.0933440\pi$
$788$	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	$-0.809809\pi$
$797$	−46.6799			−1.65349			−0.826743	+	0.562580i	$0.809809\pi$
$798$	5.34337	+	25.0713i	0.189153	+	0.887514i
$799$			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	$-0.708822\pi$
$809$		−	45.0774i		−	1.58484i	0.609979	−	0.792418i	$-0.291178\pi$
$810$	−25.1461	+	16.8014i	−0.883542	+	0.590342i
$811$	38.5608			1.35405			0.677027	−	0.735959i	$-0.263268\pi$
$811$	38.5608			1.35405			0.677027	+	0.735959i	$0.263268\pi$
$812$	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
$819$	21.5459	+	18.8355i	0.752874	+	0.658165i
$820$	−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	$-0.108220\pi$
$840$	−15.0605	+	3.20980i	−0.519637	+	0.110749i
$841$	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	$-0.475416\pi$
$853$	4.50679			0.154310			0.0771548	+	0.997019i	$0.475416\pi$
$854$	−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	$-0.527491\pi$
$857$	−5.05034			−0.172516			−0.0862581	+	0.996273i	$0.527491\pi$
$858$		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
$861$	44.2365	−	9.42800i	1.50758	−	0.321305i
$862$	−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	$-0.911298\pi$
$877$		−	16.2921i		−	0.550145i	0.961423	−	0.275073i	$-0.0887019\pi$
$878$			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	$-0.514861\pi$
$881$	−2.77053			−0.0933416			−0.0466708	+	0.998910i	$0.514861\pi$
$882$	19.1751	−	8.56241i	0.645660	−	0.288311i
$883$	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	$-0.512186\pi$
$887$	−2.27980			−0.0765483			−0.0382742	+	0.999267i	$0.512186\pi$
$888$	−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
$903$	7.64174	+	35.8553i	0.254301	+	1.19319i
$904$			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
$910$	7.22966	−	31.2291i	0.239661	−	1.03524i
$911$			43.7519i			1.44956i	0.688978	+	0.724782i	$0.258060\pi$
$911$			43.7519i			1.44956i	−0.688978	+	0.724782i	$0.741940\pi$
$912$	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
$945$	−44.3857	−	12.8064i	−1.44387	−	0.416593i
$946$		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	$0.134270\pi$
$953$			25.2784i			0.818847i	−0.912345	+	0.409423i	$0.865730\pi$
$954$	−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
$966$	2.24536	−	0.478548i	0.0722434	−	0.0153970i
$967$			1.50295i			0.0483316i	0.999708	+	0.0241658i	$0.00769296\pi$
$967$			1.50295i			0.0483316i	−0.999708	+	0.0241658i	$0.992307\pi$
$968$	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	$-0.752407\pi$
$971$	−44.4001			−1.42487			−0.712433	+	0.701740i	$0.752407\pi$
$972$	−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
$987$	19.4507	−	4.14547i	0.619122	−	0.131952i
$988$	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.545.4	yes	8
3.2	odd	2		546.2.e.h.545.6	yes	8
7.6	odd	2	inner	546.2.e.f.545.5	yes	8
13.12	even	2		546.2.e.h.545.4	yes	8
21.20	even	2		546.2.e.h.545.3	yes	8
39.38	odd	2	inner	546.2.e.f.545.6	yes	8
91.90	odd	2		546.2.e.h.545.5	yes	8
273.272	even	2	inner	546.2.e.f.545.3	✓	8

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
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} +(0.955218 + 4.48191i) 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} +(-0.955218 - 4.48191i) 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} +(-7.93227 - 0.281364i) 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} +(0.955218 + 4.48191i) 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} +(-9.29360 - 2.15150i) 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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