LMFDB - Embedded newform 224.2.u.a.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(29,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("224.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.u (of order $8$, degree $4$, 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:	$1.78864900528$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			85.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	224.85
Dual form			224.2.u.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-1.00000 + 0.414214i) q^{3} -2.00000i q^{4} +(-0.585786 + 1.41421i) q^{5} +(0.585786 - 1.41421i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.29289 + 1.29289i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.00000 + 0.414214i) q^{3} -2.00000i q^{4} +(-0.585786 + 1.41421i) q^{5} +(0.585786 - 1.41421i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.29289 + 1.29289i) q^{9} +(-0.828427 - 2.00000i) q^{10} +(-3.70711 - 1.53553i) q^{11} +(0.828427 + 2.00000i) q^{12} +(-1.41421 - 3.41421i) q^{13} +1.41421 q^{14} -1.65685i q^{15} -4.00000 q^{16} -2.58579i q^{18} +(-2.41421 - 5.82843i) q^{19} +(2.82843 + 1.17157i) q^{20} +(1.00000 + 0.414214i) q^{21} +(5.24264 - 2.17157i) q^{22} +(-1.00000 + 1.00000i) q^{23} +(-2.82843 - 1.17157i) q^{24} +(1.87868 + 1.87868i) q^{25} +(4.82843 + 2.00000i) q^{26} +(2.00000 - 4.82843i) q^{27} +(-1.41421 + 1.41421i) q^{28} +(-4.70711 + 1.94975i) q^{29} +(1.65685 + 1.65685i) q^{30} -3.17157 q^{31} +(4.00000 - 4.00000i) q^{32} +4.34315 q^{33} +(1.41421 - 0.585786i) q^{35} +(2.58579 + 2.58579i) q^{36} +(-3.29289 + 7.94975i) q^{37} +(8.24264 + 3.41421i) q^{38} +(2.82843 + 2.82843i) q^{39} +(-4.00000 + 1.65685i) q^{40} +(-0.585786 + 0.585786i) q^{41} +(-1.41421 + 0.585786i) q^{42} +(-6.12132 - 2.53553i) q^{43} +(-3.07107 + 7.41421i) q^{44} +(-1.07107 - 2.58579i) q^{45} -2.00000i q^{46} +3.17157i q^{47} +(4.00000 - 1.65685i) q^{48} +1.00000i q^{49} -3.75736 q^{50} +(-6.82843 + 2.82843i) q^{52} +(9.94975 + 4.12132i) q^{53} +(2.82843 + 6.82843i) q^{54} +(4.34315 - 4.34315i) q^{55} -2.82843i q^{56} +(4.82843 + 4.82843i) q^{57} +(2.75736 - 6.65685i) q^{58} +(-5.00000 + 12.0711i) q^{59} -3.31371 q^{60} +(-6.82843 + 2.82843i) q^{61} +(3.17157 - 3.17157i) q^{62} +1.82843 q^{63} +8.00000i q^{64} +5.65685 q^{65} +(-4.34315 + 4.34315i) q^{66} +(3.29289 - 1.36396i) q^{67} +(0.585786 - 1.41421i) q^{69} +(-0.828427 + 2.00000i) q^{70} +(4.24264 + 4.24264i) q^{71} -5.17157 q^{72} +(8.82843 - 8.82843i) q^{73} +(-4.65685 - 11.2426i) q^{74} +(-2.65685 - 1.10051i) q^{75} +(-11.6569 + 4.82843i) q^{76} +(1.53553 + 3.70711i) q^{77} -5.65685 q^{78} +9.89949i q^{79} +(2.34315 - 5.65685i) q^{80} +0.171573i q^{81} -1.17157i q^{82} +(-5.24264 - 12.6569i) q^{83} +(0.828427 - 2.00000i) q^{84} +(8.65685 - 3.58579i) q^{86} +(3.89949 - 3.89949i) q^{87} +(-4.34315 - 10.4853i) q^{88} +(-10.8284 - 10.8284i) q^{89} +(3.65685 + 1.51472i) q^{90} +(-1.41421 + 3.41421i) q^{91} +(2.00000 + 2.00000i) q^{92} +(3.17157 - 1.31371i) q^{93} +(-3.17157 - 3.17157i) q^{94} +9.65685 q^{95} +(-2.34315 + 5.65685i) q^{96} +6.82843 q^{97} +(-1.00000 - 1.00000i) q^{98} +(6.77817 - 2.80761i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} - 8 q^{5} + 8 q^{6} + 8 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 + 8 * q^6 + 8 * q^8 - 8 * q^9	$ 4 q - 4 q^{2} - 4 q^{3} - 8 q^{5} + 8 q^{6} + 8 q^{8} - 8 q^{9} + 8 q^{10} - 12 q^{11} - 8 q^{12} - 16 q^{16} - 4 q^{19} + 4 q^{21} + 4 q^{22} - 4 q^{23} + 16 q^{25} + 8 q^{26} + 8 q^{27} - 16 q^{29} - 16 q^{30} - 24 q^{31} + 16 q^{32} + 40 q^{33} + 16 q^{36} - 16 q^{37} + 16 q^{38} - 16 q^{40} - 8 q^{41} - 16 q^{43} + 16 q^{44} + 24 q^{45} + 16 q^{48} - 32 q^{50} - 16 q^{52} + 20 q^{53} + 40 q^{55} + 8 q^{57} + 28 q^{58} - 20 q^{59} + 32 q^{60} - 16 q^{61} + 24 q^{62} - 4 q^{63} - 40 q^{66} + 16 q^{67} + 8 q^{69} + 8 q^{70} - 32 q^{72} + 24 q^{73} + 4 q^{74} + 12 q^{75} - 24 q^{76} - 8 q^{77} + 32 q^{80} - 4 q^{83} - 8 q^{84} + 12 q^{86} - 24 q^{87} - 40 q^{88} - 32 q^{89} - 8 q^{90} + 8 q^{92} + 24 q^{93} - 24 q^{94} + 16 q^{95} - 32 q^{96} + 16 q^{97} - 4 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 + 8 * q^6 + 8 * q^8 - 8 * q^9 + 8 * q^10 - 12 * q^11 - 8 * q^12 - 16 * q^16 - 4 * q^19 + 4 * q^21 + 4 * q^22 - 4 * q^23 + 16 * q^25 + 8 * q^26 + 8 * q^27 - 16 * q^29 - 16 * q^30 - 24 * q^31 + 16 * q^32 + 40 * q^33 + 16 * q^36 - 16 * q^37 + 16 * q^38 - 16 * q^40 - 8 * q^41 - 16 * q^43 + 16 * q^44 + 24 * q^45 + 16 * q^48 - 32 * q^50 - 16 * q^52 + 20 * q^53 + 40 * q^55 + 8 * q^57 + 28 * q^58 - 20 * q^59 + 32 * q^60 - 16 * q^61 + 24 * q^62 - 4 * q^63 - 40 * q^66 + 16 * q^67 + 8 * q^69 + 8 * q^70 - 32 * q^72 + 24 * q^73 + 4 * q^74 + 12 * q^75 - 24 * q^76 - 8 * q^77 + 32 * q^80 - 4 * q^83 - 8 * q^84 + 12 * q^86 - 24 * q^87 - 40 * q^88 - 32 * q^89 - 8 * q^90 + 8 * q^92 + 24 * q^93 - 24 * q^94 + 16 * q^95 - 32 * q^96 + 16 * q^97 - 4 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{8}\right)$

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$3$	−1.00000	+	0.414214i	−0.577350	+	0.239146i	−0.652198	−	0.758049i	$-0.726153\pi$
$3$	−1.00000	+	0.414214i	−0.577350	+	0.239146i	0.0748477	+	0.997195i	$0.476153\pi$
$4$		−	2.00000i		−	1.00000i
$5$	−0.585786	+	1.41421i	−0.261972	+	0.632456i	−0.999060	−	0.0433405i	$-0.986200\pi$
$5$	−0.585786	+	1.41421i	−0.261972	+	0.632456i	0.737089	+	0.675796i	$0.236200\pi$
$6$	0.585786	−	1.41421i	0.239146	−	0.577350i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	−1.29289	+	1.29289i	−0.430964	+	0.430964i
$10$	−0.828427	−	2.00000i	−0.261972	−	0.632456i
$11$	−3.70711	−	1.53553i	−1.11773	−	0.462981i	−0.254140	−	0.967167i	$-0.581792\pi$
$11$	−3.70711	−	1.53553i	−1.11773	−	0.462981i	−0.863595	+	0.504187i	$0.831792\pi$
$12$	0.828427	+	2.00000i	0.239146	+	0.577350i
$13$	−1.41421	−	3.41421i	−0.392232	−	0.946932i	−0.989453	−	0.144855i	$-0.953728\pi$
$13$	−1.41421	−	3.41421i	−0.392232	−	0.946932i	0.597221	−	0.802077i	$-0.296272\pi$
$14$	1.41421			0.377964
$15$		−	1.65685i		−	0.427798i
$16$	−4.00000			−1.00000
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$		−	2.58579i		−	0.609476i
$19$	−2.41421	−	5.82843i	−0.553859	−	1.33713i	−0.914560	−	0.404451i	$-0.867462\pi$
$19$	−2.41421	−	5.82843i	−0.553859	−	1.33713i	0.360701	−	0.932682i	$-0.382538\pi$
$20$	2.82843	+	1.17157i	0.632456	+	0.261972i
$21$	1.00000	+	0.414214i	0.218218	+	0.0903888i
$22$	5.24264	−	2.17157i	1.11773	−	0.462981i
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	0.595121	+	0.803636i	$0.297104\pi$
$24$	−2.82843	−	1.17157i	−0.577350	−	0.239146i
$25$	1.87868	+	1.87868i	0.375736	+	0.375736i
$26$	4.82843	+	2.00000i	0.946932	+	0.392232i
$27$	2.00000	−	4.82843i	0.384900	−	0.929231i
$28$	−1.41421	+	1.41421i	−0.267261	+	0.267261i
$29$	−4.70711	+	1.94975i	−0.874088	+	0.362059i	−0.774201	−	0.632940i	$-0.781848\pi$
$29$	−4.70711	+	1.94975i	−0.874088	+	0.362059i	−0.0998868	+	0.994999i	$0.531848\pi$
$30$	1.65685	+	1.65685i	0.302499	+	0.302499i
$31$	−3.17157			−0.569631			−0.284816	−	0.958582i	$-0.591932\pi$
$31$	−3.17157			−0.569631			−0.284816	+	0.958582i	$0.591932\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$	4.34315			0.756045
$34$		0			0
$35$	1.41421	−	0.585786i	0.239046	−	0.0990160i
$36$	2.58579	+	2.58579i	0.430964	+	0.430964i
$37$	−3.29289	+	7.94975i	−0.541348	+	1.30693i	0.382424	+	0.923987i	$0.375090\pi$
$37$	−3.29289	+	7.94975i	−0.541348	+	1.30693i	−0.923772	+	0.382943i	$0.874910\pi$
$38$	8.24264	+	3.41421i	1.33713	+	0.553859i
$39$	2.82843	+	2.82843i	0.452911	+	0.452911i
$40$	−4.00000	+	1.65685i	−0.632456	+	0.261972i
$41$	−0.585786	+	0.585786i	−0.0914845	+	0.0914845i	−0.751368	−	0.659883i	$-0.770606\pi$
$41$	−0.585786	+	0.585786i	−0.0914845	+	0.0914845i	0.659883	+	0.751368i	$0.270606\pi$
$42$	−1.41421	+	0.585786i	−0.218218	+	0.0903888i
$43$	−6.12132	−	2.53553i	−0.933493	−	0.386665i	−0.136490	−	0.990641i	$-0.543582\pi$
$43$	−6.12132	−	2.53553i	−0.933493	−	0.386665i	−0.797002	+	0.603976i	$0.793582\pi$
$44$	−3.07107	+	7.41421i	−0.462981	+	1.11773i
$45$	−1.07107	−	2.58579i	−0.159665	−	0.385466i
$46$		−	2.00000i		−	0.294884i
$47$			3.17157i			0.462621i	0.972880	+	0.231311i	$0.0743014\pi$
$47$			3.17157i			0.462621i	−0.972880	+	0.231311i	$0.925699\pi$
$48$	4.00000	−	1.65685i	0.577350	−	0.239146i
$49$			1.00000i			0.142857i
$50$	−3.75736			−0.531371
$51$		0			0
$52$	−6.82843	+	2.82843i	−0.946932	+	0.392232i
$53$	9.94975	+	4.12132i	1.36670	+	0.566107i	0.940892	−	0.338705i	$-0.109989\pi$
$53$	9.94975	+	4.12132i	1.36670	+	0.566107i	0.425810	+	0.904812i	$0.359989\pi$
$54$	2.82843	+	6.82843i	0.384900	+	0.929231i
$55$	4.34315	−	4.34315i	0.585630	−	0.585630i
$56$		−	2.82843i		−	0.377964i
$57$	4.82843	+	4.82843i	0.639541	+	0.639541i
$58$	2.75736	−	6.65685i	0.362059	−	0.874088i
$59$	−5.00000	+	12.0711i	−0.650945	+	1.57152i	0.160465	+	0.987041i	$0.448701\pi$
$59$	−5.00000	+	12.0711i	−0.650945	+	1.57152i	−0.811410	+	0.584478i	$0.801299\pi$
$60$	−3.31371			−0.427798
$61$	−6.82843	+	2.82843i	−0.874291	+	0.362143i	−0.774280	−	0.632843i	$-0.781888\pi$
$61$	−6.82843	+	2.82843i	−0.874291	+	0.362143i	−0.100011	+	0.994986i	$0.531888\pi$
$62$	3.17157	−	3.17157i	0.402790	−	0.402790i
$63$	1.82843			0.230360
$64$			8.00000i			1.00000i
$65$	5.65685			0.701646
$66$	−4.34315	+	4.34315i	−0.534604	+	0.534604i
$67$	3.29289	−	1.36396i	0.402291	−	0.166634i	−0.172358	−	0.985034i	$-0.555139\pi$
$67$	3.29289	−	1.36396i	0.402291	−	0.166634i	0.574649	+	0.818400i	$0.305139\pi$
$68$		0			0
$69$	0.585786	−	1.41421i	0.0705204	−	0.170251i
$70$	−0.828427	+	2.00000i	−0.0990160	+	0.239046i
$71$	4.24264	+	4.24264i	0.503509	+	0.503509i	0.912526	−	0.409018i	$-0.134129\pi$
$71$	4.24264	+	4.24264i	0.503509	+	0.503509i	−0.409018	+	0.912526i	$0.634129\pi$
$72$	−5.17157			−0.609476
$73$	8.82843	−	8.82843i	1.03329	−	1.03329i	0.0338627	−	0.999426i	$-0.489219\pi$
$73$	8.82843	−	8.82843i	1.03329	−	1.03329i	0.999426	−	0.0338627i	$-0.0107809\pi$
$74$	−4.65685	−	11.2426i	−0.541348	−	1.30693i
$75$	−2.65685	−	1.10051i	−0.306787	−	0.127075i
$76$	−11.6569	+	4.82843i	−1.33713	+	0.553859i
$77$	1.53553	+	3.70711i	0.174990	+	0.422464i
$78$	−5.65685			−0.640513
$79$			9.89949i			1.11378i	0.830586	+	0.556890i	$0.188006\pi$
$79$			9.89949i			1.11378i	−0.830586	+	0.556890i	$0.811994\pi$
$80$	2.34315	−	5.65685i	0.261972	−	0.632456i
$81$			0.171573i			0.0190637i
$82$		−	1.17157i		−	0.129379i
$83$	−5.24264	−	12.6569i	−0.575455	−	1.38927i	−0.896854	−	0.442327i	$-0.854153\pi$
$83$	−5.24264	−	12.6569i	−0.575455	−	1.38927i	0.321399	−	0.946944i	$-0.395847\pi$
$84$	0.828427	−	2.00000i	0.0903888	−	0.218218i
$85$		0			0
$86$	8.65685	−	3.58579i	0.933493	−	0.386665i
$87$	3.89949	−	3.89949i	0.418070	−	0.418070i
$88$	−4.34315	−	10.4853i	−0.462981	−	1.11773i
$89$	−10.8284	−	10.8284i	−1.14781	−	1.14781i	−0.986982	−	0.160829i	$-0.948583\pi$
$89$	−10.8284	−	10.8284i	−1.14781	−	1.14781i	−0.160829	−	0.986982i	$-0.551417\pi$
$90$	3.65685	+	1.51472i	0.385466	+	0.159665i
$91$	−1.41421	+	3.41421i	−0.148250	+	0.357907i
$92$	2.00000	+	2.00000i	0.208514	+	0.208514i
$93$	3.17157	−	1.31371i	0.328877	−	0.136225i
$94$	−3.17157	−	3.17157i	−0.327123	−	0.327123i
$95$	9.65685			0.990772
$96$	−2.34315	+	5.65685i	−0.239146	+	0.577350i
$97$	6.82843			0.693322			0.346661	−	0.937991i	$-0.387315\pi$
$97$	6.82843			0.693322			0.346661	+	0.937991i	$0.387315\pi$
$98$	−1.00000	−	1.00000i	−0.101015	−	0.101015i
$99$	6.77817	−	2.80761i	0.681232	−	0.282176i
$100$	3.75736	−	3.75736i	0.375736	−	0.375736i
$101$	−0.585786	+	1.41421i	−0.0582879	+	0.140720i	−0.950340	−	0.311212i	$-0.899265\pi$
$101$	−0.585786	+	1.41421i	−0.0582879	+	0.140720i	0.892052	+	0.451932i	$0.149265\pi$
$102$		0			0
$103$	−1.75736	−	1.75736i	−0.173158	−	0.173158i	0.615207	−	0.788365i	$-0.289072\pi$
$103$	−1.75736	−	1.75736i	−0.173158	−	0.173158i	−0.788365	+	0.615207i	$0.789072\pi$
$104$	4.00000	−	9.65685i	0.392232	−	0.946932i
$105$	−1.17157	+	1.17157i	−0.114334	+	0.114334i
$106$	−14.0711	+	5.82843i	−1.36670	+	0.566107i
$107$	10.3640	+	4.29289i	1.00192	+	0.415010i	0.822502	−	0.568763i	$-0.192578\pi$
$107$	10.3640	+	4.29289i	1.00192	+	0.415010i	0.179420	+	0.983773i	$0.442578\pi$
$108$	−9.65685	−	4.00000i	−0.929231	−	0.384900i
$109$	−1.46447	−	3.53553i	−0.140270	−	0.338643i	0.838096	−	0.545523i	$-0.183669\pi$
$109$	−1.46447	−	3.53553i	−0.140270	−	0.338643i	−0.978366	+	0.206880i	$0.933669\pi$
$110$			8.68629i			0.828205i
$111$		−	9.31371i		−	0.884018i
$112$	2.82843	+	2.82843i	0.267261	+	0.267261i
$113$		−	14.5858i		−	1.37212i	−0.727547	−	0.686058i	$-0.759340\pi$
$113$		−	14.5858i		−	1.37212i	0.727547	−	0.686058i	$-0.240660\pi$
$114$	−9.65685			−0.904447
$115$	−0.828427	−	2.00000i	−0.0772512	−	0.186501i
$116$	3.89949	+	9.41421i	0.362059	+	0.874088i
$117$	6.24264	+	2.58579i	0.577132	+	0.239056i
$118$	−7.07107	−	17.0711i	−0.650945	−	1.57152i
$119$		0			0
$120$	3.31371	−	3.31371i	0.302499	−	0.302499i
$121$	3.60660	+	3.60660i	0.327873	+	0.327873i
$122$	4.00000	−	9.65685i	0.362143	−	0.874291i
$123$	0.343146	−	0.828427i	0.0309404	−	0.0746968i
$124$			6.34315i			0.569631i
$125$	−10.8284	+	4.48528i	−0.968524	+	0.401176i
$126$	−1.82843	+	1.82843i	−0.162889	+	0.162889i
$127$	−18.9706			−1.68337			−0.841683	−	0.539973i	$-0.818435\pi$
$127$	−18.9706			−1.68337			−0.841683	+	0.539973i	$0.818435\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$	7.17157			0.631422
$130$	−5.65685	+	5.65685i	−0.496139	+	0.496139i
$131$	−0.414214	+	0.171573i	−0.0361900	+	0.0149904i	−0.400705	−	0.916207i	$-0.631235\pi$
$131$	−0.414214	+	0.171573i	−0.0361900	+	0.0149904i	0.364515	+	0.931198i	$0.381235\pi$
$132$		−	8.68629i		−	0.756045i
$133$	−2.41421	+	5.82843i	−0.209339	+	0.505389i
$134$	−1.92893	+	4.65685i	−0.166634	+	0.402291i
$135$	5.65685	+	5.65685i	0.486864	+	0.486864i
$136$		0			0
$137$	−13.1421	+	13.1421i	−1.12281	+	1.12281i	−0.131491	+	0.991317i	$0.541976\pi$
$137$	−13.1421	+	13.1421i	−1.12281	+	1.12281i	−0.991317	+	0.131491i	$0.958024\pi$
$138$	0.828427	+	2.00000i	0.0705204	+	0.170251i
$139$	−5.24264	−	2.17157i	−0.444675	−	0.184190i	0.149099	−	0.988822i	$-0.452363\pi$
$139$	−5.24264	−	2.17157i	−0.444675	−	0.184190i	−0.593774	+	0.804632i	$0.702363\pi$
$140$	−1.17157	−	2.82843i	−0.0990160	−	0.239046i
$141$	−1.31371	−	3.17157i	−0.110634	−	0.267095i
$142$	−8.48528			−0.712069
$143$			14.8284i			1.24002i
$144$	5.17157	−	5.17157i	0.430964	−	0.430964i
$145$		−	7.79899i		−	0.647671i
$146$			17.6569i			1.46129i
$147$	−0.414214	−	1.00000i	−0.0341638	−	0.0824786i
$148$	15.8995	+	6.58579i	1.30693	+	0.541348i
$149$	−9.94975	−	4.12132i	−0.815115	−	0.337632i	−0.0641222	−	0.997942i	$-0.520425\pi$
$149$	−9.94975	−	4.12132i	−0.815115	−	0.337632i	−0.750993	+	0.660310i	$0.770425\pi$
$150$	3.75736	−	1.55635i	0.306787	−	0.127075i
$151$	−3.00000	+	3.00000i	−0.244137	+	0.244137i	−0.818559	−	0.574422i	$-0.805227\pi$
$151$	−3.00000	+	3.00000i	−0.244137	+	0.244137i	0.574422	+	0.818559i	$0.305227\pi$
$152$	6.82843	−	16.4853i	0.553859	−	1.33713i
$153$		0			0
$154$	−5.24264	−	2.17157i	−0.422464	−	0.174990i
$155$	1.85786	−	4.48528i	0.149227	−	0.360266i
$156$	5.65685	−	5.65685i	0.452911	−	0.452911i
$157$	14.4853	−	6.00000i	1.15605	−	0.478852i	0.279493	−	0.960148i	$-0.409834\pi$
$157$	14.4853	−	6.00000i	1.15605	−	0.478852i	0.876558	+	0.481296i	$0.159834\pi$
$158$	−9.89949	−	9.89949i	−0.787562	−	0.787562i
$159$	−11.6569			−0.924449
$160$	3.31371	+	8.00000i	0.261972	+	0.632456i
$161$	1.41421			0.111456
$162$	−0.171573	−	0.171573i	−0.0134800	−	0.0134800i
$163$	11.9497	−	4.94975i	0.935976	−	0.387694i	0.138034	−	0.990428i	$-0.455922\pi$
$163$	11.9497	−	4.94975i	0.935976	−	0.387694i	0.797943	+	0.602733i	$0.205922\pi$
$164$	1.17157	+	1.17157i	0.0914845	+	0.0914845i
$165$	−2.54416	+	6.14214i	−0.198062	+	0.478165i
$166$	17.8995	+	7.41421i	1.38927	+	0.575455i
$167$	14.2426	+	14.2426i	1.10213	+	1.10213i	0.994154	+	0.107975i	$0.0344367\pi$
$167$	14.2426	+	14.2426i	1.10213	+	1.10213i	0.107975	+	0.994154i	$0.465563\pi$
$168$	1.17157	+	2.82843i	0.0903888	+	0.218218i
$169$	−0.464466	+	0.464466i	−0.0357282	+	0.0357282i
$170$		0			0
$171$	10.6569	+	4.41421i	0.814950	+	0.337563i
$172$	−5.07107	+	12.2426i	−0.386665	+	0.933493i
$173$	−4.24264	−	10.2426i	−0.322562	−	0.778734i	−0.999104	−	0.0423292i	$-0.986522\pi$
$173$	−4.24264	−	10.2426i	−0.322562	−	0.778734i	0.676542	−	0.736404i	$-0.263478\pi$
$174$			7.79899i			0.591240i
$175$		−	2.65685i		−	0.200839i
$176$	14.8284	+	6.14214i	1.11773	+	0.462981i
$177$		−	14.1421i		−	1.06299i
$178$	21.6569			1.62325
$179$	−3.46447	−	8.36396i	−0.258946	−	0.625152i	0.739923	−	0.672692i	$-0.234862\pi$
$179$	−3.46447	−	8.36396i	−0.258946	−	0.625152i	−0.998869	+	0.0475398i	$0.984862\pi$
$180$	−5.17157	+	2.14214i	−0.385466	+	0.159665i
$181$	−2.58579	−	1.07107i	−0.192200	−	0.0796118i	0.284508	−	0.958674i	$-0.408170\pi$
$181$	−2.58579	−	1.07107i	−0.192200	−	0.0796118i	−0.476708	+	0.879062i	$0.658170\pi$
$182$	−2.00000	−	4.82843i	−0.148250	−	0.357907i
$183$	5.65685	−	5.65685i	0.418167	−	0.418167i
$184$	−4.00000			−0.294884
$185$	−9.31371	−	9.31371i	−0.684757	−	0.684757i
$186$	−1.85786	+	4.48528i	−0.136225	+	0.328877i
$187$		0			0
$188$	6.34315			0.462621
$189$	−4.82843	+	2.00000i	−0.351216	+	0.145479i
$190$	−9.65685	+	9.65685i	−0.700582	+	0.700582i
$191$	−11.0711			−0.801074			−0.400537	−	0.916281i	$-0.631176\pi$
$191$	−11.0711			−0.801074			−0.400537	+	0.916281i	$0.631176\pi$
$192$	−3.31371	−	8.00000i	−0.239146	−	0.577350i
$193$	−1.41421			−0.101797			−0.0508987	−	0.998704i	$-0.516209\pi$
$193$	−1.41421			−0.101797			−0.0508987	+	0.998704i	$0.516209\pi$
$194$	−6.82843	+	6.82843i	−0.490252	+	0.490252i
$195$	−5.65685	+	2.34315i	−0.405096	+	0.167796i
$196$	2.00000			0.142857
$197$	−8.60660	+	20.7782i	−0.613195	+	1.48038i	0.246276	+	0.969200i	$0.420793\pi$
$197$	−8.60660	+	20.7782i	−0.613195	+	1.48038i	−0.859471	+	0.511184i	$0.829207\pi$
$198$	−3.97056	+	9.58579i	−0.282176	+	0.681232i
$199$	15.0711	+	15.0711i	1.06836	+	1.06836i	0.997485	+	0.0708744i	$0.0225790\pi$
$199$	15.0711	+	15.0711i	1.06836	+	1.06836i	0.0708744	+	0.997485i	$0.477421\pi$
$200$			7.51472i			0.531371i
$201$	−2.72792	+	2.72792i	−0.192413	+	0.192413i
$202$	−0.828427	−	2.00000i	−0.0582879	−	0.140720i
$203$	4.70711	+	1.94975i	0.330374	+	0.136845i
$204$		0			0
$205$	−0.485281	−	1.17157i	−0.0338935	−	0.0818262i
$206$	3.51472			0.244882
$207$		−	2.58579i		−	0.179725i
$208$	5.65685	+	13.6569i	0.392232	+	0.946932i
$209$			25.3137i			1.75099i
$210$		−	2.34315i		−	0.161692i
$211$	0.121320	+	0.292893i	0.00835204	+	0.0201636i	0.928001	−	0.372579i	$-0.121526\pi$
$211$	0.121320	+	0.292893i	0.00835204	+	0.0201636i	−0.919649	+	0.392742i	$0.871526\pi$
$212$	8.24264	−	19.8995i	0.566107	−	1.36670i
$213$	−6.00000	−	2.48528i	−0.411113	−	0.170289i
$214$	−14.6569	+	6.07107i	−1.00192	+	0.415010i
$215$	7.17157	−	7.17157i	0.489097	−	0.489097i
$216$	13.6569	−	5.65685i	0.929231	−	0.384900i
$217$	2.24264	+	2.24264i	0.152240	+	0.152240i
$218$	5.00000	+	2.07107i	0.338643	+	0.140270i
$219$	−5.17157	+	12.4853i	−0.349463	+	0.843677i
$220$	−8.68629	−	8.68629i	−0.585630	−	0.585630i
$221$		0			0
$222$	9.31371	+	9.31371i	0.625095	+	0.625095i
$223$	−0.686292			−0.0459575			−0.0229787	−	0.999736i	$-0.507315\pi$
$223$	−0.686292			−0.0459575			−0.0229787	+	0.999736i	$0.507315\pi$
$224$	−5.65685			−0.377964
$225$	−4.85786			−0.323858
$226$	14.5858	+	14.5858i	0.970232	+	0.970232i
$227$	−11.0000	+	4.55635i	−0.730096	+	0.302416i	−0.716591	−	0.697493i	$-0.754299\pi$
$227$	−11.0000	+	4.55635i	−0.730096	+	0.302416i	−0.0135043	+	0.999909i	$0.504299\pi$
$228$	9.65685	−	9.65685i	0.639541	−	0.639541i
$229$	8.00000	−	19.3137i	0.528655	−	1.27629i	−0.403750	−	0.914869i	$-0.632293\pi$
$229$	8.00000	−	19.3137i	0.528655	−	1.27629i	0.932405	−	0.361416i	$-0.117707\pi$
$230$	2.82843	+	1.17157i	0.186501	+	0.0772512i
$231$	−3.07107	−	3.07107i	−0.202061	−	0.202061i
$232$	−13.3137	−	5.51472i	−0.874088	−	0.362059i
$233$	3.82843	−	3.82843i	0.250809	−	0.250809i	−0.570494	−	0.821302i	$-0.693248\pi$
$233$	3.82843	−	3.82843i	0.250809	−	0.250809i	0.821302	+	0.570494i	$0.193248\pi$
$234$	−8.82843	+	3.65685i	−0.577132	+	0.239056i
$235$	−4.48528	−	1.85786i	−0.292587	−	0.121194i
$236$	24.1421	+	10.0000i	1.57152	+	0.650945i
$237$	−4.10051	−	9.89949i	−0.266356	−	0.643041i
$238$		0			0
$239$		−	6.00000i		−	0.388108i	−0.980991	−	0.194054i	$-0.937836\pi$
$239$		−	6.00000i		−	0.388108i	0.980991	−	0.194054i	$-0.0621637\pi$
$240$			6.62742i			0.427798i
$241$		−	15.7990i		−	1.01770i	−0.860854	−	0.508851i	$-0.830070\pi$
$241$		−	15.7990i		−	1.01770i	0.860854	−	0.508851i	$-0.169930\pi$
$242$	−7.21320			−0.463682
$243$	5.92893	+	14.3137i	0.380341	+	0.918225i
$244$	5.65685	+	13.6569i	0.362143	+	0.874291i
$245$	−1.41421	−	0.585786i	−0.0903508	−	0.0374245i
$246$	0.485281	+	1.17157i	0.0309404	+	0.0746968i
$247$	−16.4853	+	16.4853i	−1.04893	+	1.04893i
$248$	−6.34315	−	6.34315i	−0.402790	−	0.402790i
$249$	10.4853	+	10.4853i	0.664478	+	0.664478i
$250$	6.34315	−	15.3137i	0.401176	−	0.968524i
$251$	−8.65685	+	20.8995i	−0.546416	+	1.31916i	0.373711	+	0.927545i	$0.378085\pi$
$251$	−8.65685	+	20.8995i	−0.546416	+	1.31916i	−0.920127	+	0.391619i	$0.871915\pi$
$252$		−	3.65685i		−	0.230360i
$253$	5.24264	−	2.17157i	0.329602	−	0.136526i
$254$	18.9706	−	18.9706i	1.19032	−	1.19032i
$255$		0			0
$256$	16.0000			1.00000
$257$	0.142136			0.00886618			0.00443309	−	0.999990i	$-0.498589\pi$
$257$	0.142136			0.00886618			0.00443309	+	0.999990i	$0.498589\pi$
$258$	−7.17157	+	7.17157i	−0.446483	+	0.446483i
$259$	7.94975	−	3.29289i	0.493973	−	0.204610i
$260$		−	11.3137i		−	0.701646i
$261$	3.56497	−	8.60660i	0.220666	−	0.532735i
$262$	0.242641	−	0.585786i	0.0149904	−	0.0361900i
$263$	1.65685	+	1.65685i	0.102166	+	0.102166i	0.756342	−	0.654176i	$-0.226985\pi$
$263$	1.65685	+	1.65685i	0.102166	+	0.102166i	−0.654176	+	0.756342i	$0.726985\pi$
$264$	8.68629	+	8.68629i	0.534604	+	0.534604i
$265$	−11.6569	+	11.6569i	−0.716075	+	0.716075i
$266$	−3.41421	−	8.24264i	−0.209339	−	0.505389i
$267$	15.3137	+	6.34315i	0.937184	+	0.388194i
$268$	−2.72792	−	6.58579i	−0.166634	−	0.402291i
$269$	−5.75736	−	13.8995i	−0.351032	−	0.847467i	−0.996493	−	0.0836738i	$-0.973335\pi$
$269$	−5.75736	−	13.8995i	−0.351032	−	0.847467i	0.645461	−	0.763793i	$-0.276665\pi$
$270$	−11.3137			−0.688530
$271$		−	28.4853i		−	1.73036i	−0.501463	−	0.865179i	$-0.667205\pi$
$271$		−	28.4853i		−	1.73036i	0.501463	−	0.865179i	$-0.332795\pi$
$272$		0			0
$273$		−	4.00000i		−	0.242091i
$274$		−	26.2843i		−	1.58789i
$275$	−4.07969	−	9.84924i	−0.246015	−	0.593932i
$276$	−2.82843	−	1.17157i	−0.170251	−	0.0705204i
$277$	4.36396	+	1.80761i	0.262205	+	0.108609i	0.509913	−	0.860226i	$-0.329677\pi$
$277$	4.36396	+	1.80761i	0.262205	+	0.108609i	−0.247708	+	0.968835i	$0.579677\pi$
$278$	7.41421	−	3.07107i	0.444675	−	0.184190i
$279$	4.10051	−	4.10051i	0.245491	−	0.245491i
$280$	4.00000	+	1.65685i	0.239046	+	0.0990160i
$281$	−12.6569	−	12.6569i	−0.755045	−	0.755045i	0.220371	−	0.975416i	$-0.429273\pi$
$281$	−12.6569	−	12.6569i	−0.755045	−	0.755045i	−0.975416	+	0.220371i	$0.929273\pi$
$282$	4.48528	+	1.85786i	0.267095	+	0.110634i
$283$	−6.89949	+	16.6569i	−0.410132	+	0.990147i	0.574969	+	0.818175i	$0.305014\pi$
$283$	−6.89949	+	16.6569i	−0.410132	+	0.990147i	−0.985102	+	0.171972i	$0.944986\pi$
$284$	8.48528	−	8.48528i	0.503509	−	0.503509i
$285$	−9.65685	+	4.00000i	−0.572023	+	0.236940i
$286$	−14.8284	−	14.8284i	−0.876823	−	0.876823i
$287$	0.828427			0.0489005
$288$			10.3431i			0.609476i
$289$	17.0000			1.00000
$290$	7.79899	+	7.79899i	0.457972	+	0.457972i
$291$	−6.82843	+	2.82843i	−0.400289	+	0.165805i
$292$	−17.6569	−	17.6569i	−1.03329	−	1.03329i
$293$	9.17157	−	22.1421i	0.535809	−	1.29356i	−0.391816	−	0.920044i	$-0.628153\pi$
$293$	9.17157	−	22.1421i	0.535809	−	1.29356i	0.927625	−	0.373514i	$-0.121847\pi$
$294$	1.41421	+	0.585786i	0.0824786	+	0.0341638i
$295$	−14.1421	−	14.1421i	−0.823387	−	0.823387i
$296$	−22.4853	+	9.31371i	−1.30693	+	0.541348i
$297$	−14.8284	+	14.8284i	−0.860433	+	0.860433i
$298$	14.0711	−	5.82843i	0.815115	−	0.337632i
$299$	4.82843	+	2.00000i	0.279235	+	0.115663i
$300$	−2.20101	+	5.31371i	−0.127075	+	0.306787i
$301$	2.53553	+	6.12132i	0.146146	+	0.352827i
$302$		−	6.00000i		−	0.345261i
$303$		−	1.65685i		−	0.0951838i
$304$	9.65685	+	23.3137i	0.553859	+	1.33713i
$305$		−	11.3137i		−	0.647821i
$306$		0			0
$307$	−0.857864	−	2.07107i	−0.0489609	−	0.118202i	0.897507	−	0.441001i	$-0.145376\pi$
$307$	−0.857864	−	2.07107i	−0.0489609	−	0.118202i	−0.946468	+	0.322799i	$0.895376\pi$
$308$	7.41421	−	3.07107i	0.422464	−	0.174990i
$309$	2.48528	+	1.02944i	0.141383	+	0.0585626i
$310$	2.62742	+	6.34315i	0.149227	+	0.360266i
$311$	−3.31371	+	3.31371i	−0.187903	+	0.187903i	−0.794789	−	0.606886i	$-0.792419\pi$
$311$	−3.31371	+	3.31371i	−0.187903	+	0.187903i	0.606886	+	0.794789i	$0.292419\pi$
$312$			11.3137i			0.640513i
$313$	−19.0711	−	19.0711i	−1.07796	−	1.07796i	−0.996692	−	0.0812682i	$-0.974103\pi$
$313$	−19.0711	−	19.0711i	−1.07796	−	1.07796i	−0.0812682	−	0.996692i	$-0.525897\pi$
$314$	−8.48528	+	20.4853i	−0.478852	+	1.15605i
$315$	−1.07107	+	2.58579i	−0.0603478	+	0.145693i
$316$	19.7990			1.11378
$317$	−8.36396	+	3.46447i	−0.469767	+	0.194584i	−0.604993	−	0.796231i	$-0.706824\pi$
$317$	−8.36396	+	3.46447i	−0.469767	+	0.194584i	0.135226	+	0.990815i	$0.456824\pi$
$318$	11.6569	−	11.6569i	0.653684	−	0.653684i
$319$	20.4437			1.14462
$320$	−11.3137	−	4.68629i	−0.632456	−	0.261972i
$321$	−12.1421			−0.677708
$322$	−1.41421	+	1.41421i	−0.0788110	+	0.0788110i
$323$		0			0
$324$	0.343146			0.0190637
$325$	3.75736	−	9.07107i	0.208421	−	0.503172i
$326$	−7.00000	+	16.8995i	−0.387694	+	0.935976i
$327$	2.92893	+	2.92893i	0.161970	+	0.161970i
$328$	−2.34315			−0.129379
$329$	2.24264	−	2.24264i	0.123641	−	0.123641i
$330$	−3.59798	−	8.68629i	−0.198062	−	0.478165i
$331$	0.878680	+	0.363961i	0.0482966	+	0.0200051i	0.406701	−	0.913561i	$-0.366679\pi$
$331$	0.878680	+	0.363961i	0.0482966	+	0.0200051i	−0.358404	+	0.933566i	$0.616679\pi$
$332$	−25.3137	+	10.4853i	−1.38927	+	0.575455i
$333$	−6.02082	−	14.5355i	−0.329939	−	0.796542i
$334$	−28.4853			−1.55865
$335$			5.45584i			0.298085i
$336$	−4.00000	−	1.65685i	−0.218218	−	0.0903888i
$337$			32.7279i			1.78280i	0.453214	+	0.891402i	$0.350277\pi$
$337$			32.7279i			1.78280i	−0.453214	+	0.891402i	$0.649723\pi$
$338$		−	0.928932i		−	0.0505272i
$339$	6.04163	+	14.5858i	0.328136	+	0.792191i
$340$		0			0
$341$	11.7574	+	4.87006i	0.636697	+	0.263728i
$342$	−15.0711	+	6.24264i	−0.814950	+	0.337563i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−7.17157	−	17.3137i	−0.386665	−	0.933493i
$345$	1.65685	+	1.65685i	0.0892020	+	0.0892020i
$346$	14.4853	+	6.00000i	0.778734	+	0.322562i
$347$	2.12132	−	5.12132i	0.113878	−	0.274927i	−0.856657	−	0.515887i	$-0.827462\pi$
$347$	2.12132	−	5.12132i	0.113878	−	0.274927i	0.970535	+	0.240960i	$0.0774624\pi$
$348$	−7.79899	−	7.79899i	−0.418070	−	0.418070i
$349$	19.3137	−	8.00000i	1.03384	−	0.428230i	0.199742	−	0.979848i	$-0.435989\pi$
$349$	19.3137	−	8.00000i	1.03384	−	0.428230i	0.834097	+	0.551618i	$0.185989\pi$
$350$	2.65685	+	2.65685i	0.142015	+	0.142015i
$351$	−19.3137			−1.03089
$352$	−20.9706	+	8.68629i	−1.11773	+	0.462981i
$353$	−23.4558			−1.24843			−0.624214	−	0.781253i	$-0.714581\pi$
$353$	−23.4558			−1.24843			−0.624214	+	0.781253i	$0.714581\pi$
$354$	14.1421	+	14.1421i	0.751646	+	0.751646i
$355$	−8.48528	+	3.51472i	−0.450352	+	0.186542i
$356$	−21.6569	+	21.6569i	−1.14781	+	1.14781i
$357$		0			0
$358$	11.8284	+	4.89949i	0.625152	+	0.258946i
$359$	−21.9706	−	21.9706i	−1.15956	−	1.15956i	−0.984570	−	0.174992i	$-0.944010\pi$
$359$	−21.9706	−	21.9706i	−1.15956	−	1.15956i	−0.174992	−	0.984570i	$-0.555990\pi$
$360$	3.02944	−	7.31371i	0.159665	−	0.385466i
$361$	−14.7071	+	14.7071i	−0.774058	+	0.774058i
$362$	3.65685	−	1.51472i	0.192200	−	0.0796118i
$363$	−5.10051	−	2.11270i	−0.267707	−	0.110888i
$364$	6.82843	+	2.82843i	0.357907	+	0.148250i
$365$	7.31371	+	17.6569i	0.382817	+	0.924202i
$366$			11.3137i			0.591377i
$367$			4.48528i			0.234130i	0.993124	+	0.117065i	$0.0373486\pi$
$367$			4.48528i			0.234130i	−0.993124	+	0.117065i	$0.962651\pi$
$368$	4.00000	−	4.00000i	0.208514	−	0.208514i
$369$		−	1.51472i		−	0.0788531i
$370$	18.6274			0.968393
$371$	−4.12132	−	9.94975i	−0.213968	−	0.516565i
$372$	−2.62742	−	6.34315i	−0.136225	−	0.328877i
$373$	28.6066	+	11.8492i	1.48119	+	0.613531i	0.969380	−	0.245566i	$-0.0789738\pi$
$373$	28.6066	+	11.8492i	1.48119	+	0.613531i	0.511814	+	0.859096i	$0.328974\pi$
$374$		0			0
$375$	8.97056	−	8.97056i	0.463238	−	0.463238i
$376$	−6.34315	+	6.34315i	−0.327123	+	0.327123i
$377$	13.3137	+	13.3137i	0.685691	+	0.685691i
$378$	2.82843	−	6.82843i	0.145479	−	0.351216i
$379$	13.2635	−	32.0208i	0.681298	−	1.64480i	−0.0803173	−	0.996769i	$-0.525593\pi$
$379$	13.2635	−	32.0208i	0.681298	−	1.64480i	0.761615	−	0.648029i	$-0.224407\pi$
$380$		−	19.3137i		−	0.990772i
$381$	18.9706	−	7.85786i	0.971891	−	0.402571i
$382$	11.0711	−	11.0711i	0.566445	−	0.566445i
$383$	−7.17157			−0.366450			−0.183225	−	0.983071i	$-0.558654\pi$
$383$	−7.17157			−0.366450			−0.183225	+	0.983071i	$0.558654\pi$
$384$	11.3137	+	4.68629i	0.577350	+	0.239146i
$385$	−6.14214			−0.313032
$386$	1.41421	−	1.41421i	0.0719816	−	0.0719816i
$387$	11.1924	−	4.63604i	0.568941	−	0.235663i
$388$		−	13.6569i		−	0.693322i
$389$	−12.0208	+	29.0208i	−0.609480	+	1.47141i	0.254088	+	0.967181i	$0.418225\pi$
$389$	−12.0208	+	29.0208i	−0.609480	+	1.47141i	−0.863568	+	0.504233i	$0.831775\pi$
$390$	3.31371	−	8.00000i	0.167796	−	0.405096i
$391$		0			0
$392$	−2.00000	+	2.00000i	−0.101015	+	0.101015i
$393$	0.343146	−	0.343146i	0.0173094	−	0.0173094i
$394$	−12.1716	−	29.3848i	−0.613195	−	1.48038i
$395$	−14.0000	−	5.79899i	−0.704416	−	0.291779i
$396$	−5.61522	−	13.5563i	−0.282176	−	0.681232i
$397$	9.65685	+	23.3137i	0.484664	+	1.17008i	0.957371	+	0.288862i	$0.0932768\pi$
$397$	9.65685	+	23.3137i	0.484664	+	1.17008i	−0.472707	+	0.881220i	$0.656723\pi$
$398$	−30.1421			−1.51089
$399$		−	6.82843i		−	0.341849i
$400$	−7.51472	−	7.51472i	−0.375736	−	0.375736i
$401$		−	23.7574i		−	1.18639i	−0.805060	−	0.593193i	$-0.797867\pi$
$401$		−	23.7574i		−	1.18639i	0.805060	−	0.593193i	$-0.202133\pi$
$402$		−	5.45584i		−	0.272113i
$403$	4.48528	+	10.8284i	0.223428	+	0.539402i
$404$	2.82843	+	1.17157i	0.140720	+	0.0582879i
$405$	−0.242641	−	0.100505i	−0.0120569	−	0.00499414i
$406$	−6.65685	+	2.75736i	−0.330374	+	0.136845i
$407$	24.4142	−	24.4142i	1.21017	−	1.21017i
$408$		0			0
$409$	24.2426	+	24.2426i	1.19872	+	1.19872i	0.974550	+	0.224172i	$0.0719677\pi$
$409$	24.2426	+	24.2426i	1.19872	+	1.19872i	0.224172	+	0.974550i	$0.428032\pi$
$410$	1.65685	+	0.686292i	0.0818262	+	0.0338935i
$411$	7.69848	−	18.5858i	0.379738	−	0.916769i
$412$	−3.51472	+	3.51472i	−0.173158	+	0.173158i
$413$	12.0711	−	5.00000i	0.593978	−	0.246034i
$414$	2.58579	+	2.58579i	0.127084	+	0.127084i
$415$	20.9706			1.02940
$416$	−19.3137	−	8.00000i	−0.946932	−	0.392232i
$417$	6.14214			0.300782
$418$	−25.3137	−	25.3137i	−1.23813	−	1.23813i
$419$	−7.24264	+	3.00000i	−0.353826	+	0.146560i	−0.552515	−	0.833503i	$-0.686332\pi$
$419$	−7.24264	+	3.00000i	−0.353826	+	0.146560i	0.198689	+	0.980063i	$0.436332\pi$
$420$	2.34315	+	2.34315i	0.114334	+	0.114334i
$421$	2.39340	−	5.77817i	0.116647	−	0.281611i	−0.854763	−	0.519018i	$-0.826298\pi$
$421$	2.39340	−	5.77817i	0.116647	−	0.281611i	0.971410	+	0.237407i	$0.0762976\pi$
$422$	−0.414214	−	0.171573i	−0.0201636	−	0.00835204i
$423$	−4.10051	−	4.10051i	−0.199373	−	0.199373i
$424$	11.6569	+	28.1421i	0.566107	+	1.36670i
$425$		0			0
$426$	8.48528	−	3.51472i	0.411113	−	0.170289i
$427$	6.82843	+	2.82843i	0.330451	+	0.136877i
$428$	8.58579	−	20.7279i	0.415010	−	1.00192i
$429$	−6.14214	−	14.8284i	−0.296545	−	0.715923i
$430$			14.3431i			0.691688i
$431$		−	10.3431i		−	0.498212i	−0.968476	−	0.249106i	$-0.919863\pi$
$431$		−	10.3431i		−	0.498212i	0.968476	−	0.249106i	$-0.0801367\pi$
$432$	−8.00000	+	19.3137i	−0.384900	+	0.929231i
$433$			32.2843i			1.55148i	0.631051	+	0.775742i	$0.282624\pi$
$433$			32.2843i			1.55148i	−0.631051	+	0.775742i	$0.717376\pi$
$434$	−4.48528			−0.215300
$435$	3.23045	+	7.79899i	0.154888	+	0.373933i
$436$	−7.07107	+	2.92893i	−0.338643	+	0.140270i
$437$	8.24264	+	3.41421i	0.394299	+	0.163324i
$438$	−7.31371	−	17.6569i	−0.349463	−	0.843677i
$439$	−18.0000	+	18.0000i	−0.859093	+	0.859093i	−0.991231	−	0.132138i	$-0.957816\pi$
$439$	−18.0000	+	18.0000i	−0.859093	+	0.859093i	0.132138	+	0.991231i	$0.457816\pi$
$440$	17.3726			0.828205
$441$	−1.29289	−	1.29289i	−0.0615663	−	0.0615663i
$442$		0			0
$443$	−4.19239	+	10.1213i	−0.199186	+	0.480878i	−0.991637	−	0.129057i	$-0.958805\pi$
$443$	−4.19239	+	10.1213i	−0.199186	+	0.480878i	0.792451	+	0.609936i	$0.208805\pi$
$444$	−18.6274			−0.884018
$445$	21.6569	−	8.97056i	1.02663	−	0.425245i
$446$	0.686292	−	0.686292i	0.0324968	−	0.0324968i
$447$	11.6569			0.551350
$448$	5.65685	−	5.65685i	0.267261	−	0.267261i
$449$	17.4558			0.823792			0.411896	−	0.911231i	$-0.364867\pi$
$449$	17.4558			0.823792			0.411896	+	0.911231i	$0.364867\pi$
$450$	4.85786	−	4.85786i	0.229002	−	0.229002i
$451$	3.07107	−	1.27208i	0.144611	−	0.0598998i
$452$	−29.1716			−1.37212
$453$	1.75736	−	4.24264i	0.0825679	−	0.199337i
$454$	6.44365	−	15.5563i	0.302416	−	0.730096i
$455$	−4.00000	−	4.00000i	−0.187523	−	0.187523i
$456$			19.3137i			0.904447i
$457$	8.00000	−	8.00000i	0.374224	−	0.374224i	−0.494789	−	0.869013i	$-0.664755\pi$
$457$	8.00000	−	8.00000i	0.374224	−	0.374224i	0.869013	+	0.494789i	$0.164755\pi$
$458$	11.3137	+	27.3137i	0.528655	+	1.27629i
$459$		0			0
$460$	−4.00000	+	1.65685i	−0.186501	+	0.0772512i
$461$	8.48528	+	20.4853i	0.395199	+	0.954095i	0.988788	+	0.149326i	$0.0477105\pi$
$461$	8.48528	+	20.4853i	0.395199	+	0.954095i	−0.593589	+	0.804768i	$0.702290\pi$
$462$	6.14214			0.285758
$463$		−	20.0416i		−	0.931414i	−0.884939	−	0.465707i	$-0.845800\pi$
$463$		−	20.0416i		−	0.931414i	0.884939	−	0.465707i	$-0.154200\pi$
$464$	18.8284	−	7.79899i	0.874088	−	0.362059i
$465$			5.25483i			0.243687i
$466$			7.65685i			0.354697i
$467$	14.6569	+	35.3848i	0.678238	+	1.63741i	0.767224	+	0.641379i	$0.221637\pi$
$467$	14.6569	+	35.3848i	0.678238	+	1.63741i	−0.0889857	+	0.996033i	$0.528363\pi$
$468$	5.17157	−	12.4853i	0.239056	−	0.577132i
$469$	−3.29289	−	1.36396i	−0.152052	−	0.0629819i
$470$	6.34315	−	2.62742i	0.292587	−	0.121194i
$471$	−12.0000	+	12.0000i	−0.552931	+	0.552931i
$472$	−34.1421	+	14.1421i	−1.57152	+	0.650945i
$473$	18.7990	+	18.7990i	0.864378	+	0.864378i
$474$	14.0000	+	5.79899i	0.643041	+	0.266356i
$475$	6.41421	−	15.4853i	0.294304	−	0.710513i
$476$		0			0
$477$	−18.1924	+	7.53553i	−0.832972	+	0.345028i
$478$	6.00000	+	6.00000i	0.274434	+	0.274434i
$479$	−6.68629			−0.305504			−0.152752	−	0.988265i	$-0.548814\pi$
$479$	−6.68629			−0.305504			−0.152752	+	0.988265i	$0.548814\pi$
$480$	−6.62742	−	6.62742i	−0.302499	−	0.302499i
$481$	31.7990			1.44991
$482$	15.7990	+	15.7990i	0.719624	+	0.719624i
$483$	−1.41421	+	0.585786i	−0.0643489	+	0.0266542i
$484$	7.21320	−	7.21320i	0.327873	−	0.327873i
$485$	−4.00000	+	9.65685i	−0.181631	+	0.438495i
$486$	−20.2426	−	8.38478i	−0.918225	−	0.380341i
$487$	−29.1421	−	29.1421i	−1.32056	−	1.32056i	−0.913325	−	0.407231i	$-0.866494\pi$
$487$	−29.1421	−	29.1421i	−1.32056	−	1.32056i	−0.407231	−	0.913325i	$-0.633506\pi$
$488$	−19.3137	−	8.00000i	−0.874291	−	0.362143i
$489$	−9.89949	+	9.89949i	−0.447671	+	0.447671i
$490$	2.00000	−	0.828427i	0.0903508	−	0.0374245i
$491$	13.5355	+	5.60660i	0.610850	+	0.253022i	0.666592	−	0.745423i	$-0.267752\pi$
$491$	13.5355	+	5.60660i	0.610850	+	0.253022i	−0.0557418	+	0.998445i	$0.517752\pi$
$492$	−1.65685	−	0.686292i	−0.0746968	−	0.0309404i
$493$		0			0
$494$		−	32.9706i		−	1.48342i
$495$			11.2304i			0.504771i
$496$	12.6863			0.569631
$497$		−	6.00000i		−	0.269137i
$498$	−20.9706			−0.939713
$499$	7.46447	+	18.0208i	0.334155	+	0.806722i	0.998253	+	0.0590770i	$0.0188157\pi$
$499$	7.46447	+	18.0208i	0.334155	+	0.806722i	−0.664098	+	0.747646i	$0.731184\pi$
$500$	8.97056	+	21.6569i	0.401176	+	0.968524i
$501$	−20.1421	−	8.34315i	−0.899884	−	0.372744i
$502$	−12.2426	−	29.5563i	−0.546416	−	1.31916i
$503$	10.8284	−	10.8284i	0.482816	−	0.482816i	−0.423214	−	0.906030i	$-0.639098\pi$
$503$	10.8284	−	10.8284i	0.482816	−	0.482816i	0.906030	+	0.423214i	$0.139098\pi$
$504$	3.65685	+	3.65685i	0.162889	+	0.162889i
$505$	−1.65685	−	1.65685i	−0.0737290	−	0.0737290i
$506$	−3.07107	+	7.41421i	−0.136526	+	0.329602i
$507$	0.272078	−	0.656854i	0.0120834	−	0.0291719i
$508$			37.9411i			1.68337i
$509$	−19.3137	+	8.00000i	−0.856065	+	0.354594i	−0.767167	−	0.641447i	$-0.778334\pi$
$509$	−19.3137	+	8.00000i	−0.856065	+	0.354594i	−0.0888977	+	0.996041i	$0.528334\pi$
$510$		0			0
$511$	−12.4853			−0.552316
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	−32.9706			−1.45569
$514$	−0.142136	+	0.142136i	−0.00626933	+	0.00626933i
$515$	3.51472	−	1.45584i	0.154877	−	0.0641522i
$516$		−	14.3431i		−	0.631422i
$517$	4.87006	−	11.7574i	0.214185	−	0.517088i
$518$	−4.65685	+	11.2426i	−0.204610	+	0.493973i
$519$	8.48528	+	8.48528i	0.372463	+	0.372463i
$520$	11.3137	+	11.3137i	0.496139	+	0.496139i
$521$	8.72792	−	8.72792i	0.382377	−	0.382377i	−0.489581	−	0.871958i	$-0.662850\pi$
$521$	8.72792	−	8.72792i	0.382377	−	0.382377i	0.871958	+	0.489581i	$0.162850\pi$
$522$	5.04163	+	12.1716i	0.220666	+	0.532735i
$523$	−1.00000	−	0.414214i	−0.0437269	−	0.0181123i	0.360713	−	0.932677i	$-0.382533\pi$
$523$	−1.00000	−	0.414214i	−0.0437269	−	0.0181123i	−0.404440	+	0.914565i	$0.632533\pi$
$524$	0.343146	+	0.828427i	0.0149904	+	0.0361900i
$525$	1.10051	+	2.65685i	0.0480300	+	0.115955i
$526$	−3.31371			−0.144485
$527$		0			0
$528$	−17.3726			−0.756045
$529$			21.0000i			0.913043i
$530$		−	23.3137i		−	1.01268i
$531$	−9.14214	−	22.0711i	−0.396735	−	0.957803i
$532$	11.6569	+	4.82843i	0.505389	+	0.209339i
$533$	2.82843	+	1.17157i	0.122513	+	0.0507465i
$534$	−21.6569	+	8.97056i	−0.937184	+	0.388194i
$535$	−12.1421	+	12.1421i	−0.524950	+	0.524950i
$536$	9.31371	+	3.85786i	0.402291	+	0.166634i
$537$	6.92893	+	6.92893i	0.299005	+	0.299005i
$538$	19.6569	+	8.14214i	0.847467	+	0.351032i
$539$	1.53553	−	3.70711i	0.0661401	−	0.159676i
$540$	11.3137	−	11.3137i	0.486864	−	0.486864i
$541$	9.12132	−	3.77817i	0.392156	−	0.162436i	−0.177887	−	0.984051i	$-0.556926\pi$
$541$	9.12132	−	3.77817i	0.392156	−	0.162436i	0.570044	+	0.821614i	$0.306926\pi$
$542$	28.4853	+	28.4853i	1.22355	+	1.22355i
$543$	3.02944			0.130006
$544$		0			0
$545$	5.85786			0.250923
$546$	4.00000	+	4.00000i	0.171184	+	0.171184i
$547$	8.77817	−	3.63604i	0.375328	−	0.155466i	−0.187042	−	0.982352i	$-0.559890\pi$
$547$	8.77817	−	3.63604i	0.375328	−	0.155466i	0.562369	+	0.826886i	$0.309890\pi$
$548$	26.2843	+	26.2843i	1.12281	+	1.12281i
$549$	5.17157	−	12.4853i	0.220717	−	0.532859i
$550$	13.9289	+	5.76955i	0.593932	+	0.246015i
$551$	22.7279	+	22.7279i	0.968242	+	0.968242i
$552$	4.00000	−	1.65685i	0.170251	−	0.0705204i
$553$	7.00000	−	7.00000i	0.297670	−	0.297670i
$554$	−6.17157	+	2.55635i	−0.262205	+	0.108609i
$555$	13.1716	+	5.45584i	0.559102	+	0.231588i
$556$	−4.34315	+	10.4853i	−0.184190	+	0.444675i
$557$	1.80761	+	4.36396i	0.0765910	+	0.184907i	0.957537	−	0.288309i	$-0.0930930\pi$
$557$	1.80761	+	4.36396i	0.0765910	+	0.184907i	−0.880946	+	0.473216i	$0.843093\pi$
$558$			8.20101i			0.347176i
$559$			24.4853i			1.03562i
$560$	−5.65685	+	2.34315i	−0.239046	+	0.0990160i
$561$		0			0
$562$	25.3137			1.06779
$563$	−8.31371	−	20.0711i	−0.350381	−	0.845895i	−0.996573	−	0.0827196i	$-0.973639\pi$
$563$	−8.31371	−	20.0711i	−0.350381	−	0.845895i	0.646192	−	0.763175i	$-0.276361\pi$
$564$	−6.34315	+	2.62742i	−0.267095	+	0.110634i
$565$	20.6274	+	8.54416i	0.867802	+	0.359455i
$566$	−9.75736	−	23.5563i	−0.410132	−	0.990147i
$567$	0.121320	−	0.121320i	0.00509498	−	0.00509498i
$568$			16.9706i			0.712069i
$569$	−19.7990	−	19.7990i	−0.830017	−	0.830017i	0.157502	−	0.987519i	$-0.449656\pi$
$569$	−19.7990	−	19.7990i	−0.830017	−	0.830017i	−0.987519	+	0.157502i	$0.949656\pi$
$570$	5.65685	−	13.6569i	0.236940	−	0.572023i
$571$	−12.1213	+	29.2635i	−0.507261	+	1.22464i	0.438192	+	0.898881i	$0.355619\pi$
$571$	−12.1213	+	29.2635i	−0.507261	+	1.22464i	−0.945454	+	0.325756i	$0.894381\pi$
$572$	29.6569			1.24002
$573$	11.0711	−	4.58579i	0.462500	−	0.191574i
$574$	−0.828427	+	0.828427i	−0.0345779	+	0.0345779i
$575$	−3.75736			−0.156693
$576$	−10.3431	−	10.3431i	−0.430964	−	0.430964i
$577$	−24.1421			−1.00505			−0.502525	−	0.864563i	$-0.667596\pi$
$577$	−24.1421			−1.00505			−0.502525	+	0.864563i	$0.667596\pi$
$578$	−17.0000	+	17.0000i	−0.707107	+	0.707107i
$579$	1.41421	−	0.585786i	0.0587727	−	0.0243445i
$580$	−15.5980			−0.647671
$581$	−5.24264	+	12.6569i	−0.217501	+	0.525095i
$582$	4.00000	−	9.65685i	0.165805	−	0.400289i
$583$	−30.5563	−	30.5563i	−1.26551	−	1.26551i
$584$	35.3137			1.46129
$585$	−7.31371	+	7.31371i	−0.302385	+	0.302385i
$586$	12.9706	+	31.3137i	0.535809	+	1.29356i
$587$	−23.2426	−	9.62742i	−0.959326	−	0.397366i	−0.152598	−	0.988288i	$-0.548764\pi$
$587$	−23.2426	−	9.62742i	−0.959326	−	0.397366i	−0.806728	+	0.590922i	$0.798764\pi$
$588$	−2.00000	+	0.828427i	−0.0824786	+	0.0341638i
$589$	7.65685	+	18.4853i	0.315495	+	0.761673i
$590$	28.2843			1.16445
$591$		−	24.3431i		−	1.00134i
$592$	13.1716	−	31.7990i	0.541348	−	1.30693i
$593$			28.8284i			1.18384i	0.805996	+	0.591921i	$0.201630\pi$
$593$			28.8284i			1.18384i	−0.805996	+	0.591921i	$0.798370\pi$
$594$		−	29.6569i		−	1.21684i
$595$		0			0
$596$	−8.24264	+	19.8995i	−0.337632	+	0.815115i
$597$	−21.3137	−	8.82843i	−0.872312	−	0.361323i
$598$	−6.82843	+	2.82843i	−0.279235	+	0.115663i
$599$	3.31371	−	3.31371i	0.135394	−	0.135394i	−0.636161	−	0.771556i	$-0.719479\pi$
$599$	3.31371	−	3.31371i	0.135394	−	0.135394i	0.771556	+	0.636161i	$0.219479\pi$
$600$	−3.11270	−	7.51472i	−0.127075	−	0.306787i
$601$	−21.3137	−	21.3137i	−0.869404	−	0.869404i	0.123002	−	0.992406i	$-0.460748\pi$
$601$	−21.3137	−	21.3137i	−0.869404	−	0.869404i	−0.992406	+	0.123002i	$0.960748\pi$
$602$	−8.65685	−	3.58579i	−0.352827	−	0.146146i
$603$	−2.49390	+	6.02082i	−0.101560	+	0.245187i
$604$	6.00000	+	6.00000i	0.244137	+	0.244137i
$605$	−7.21320	+	2.98781i	−0.293258	+	0.121472i
$606$	1.65685	+	1.65685i	0.0673051	+	0.0673051i
$607$	−37.6569			−1.52844			−0.764222	−	0.644953i	$-0.776877\pi$
$607$	−37.6569			−1.52844			−0.764222	+	0.644953i	$0.776877\pi$
$608$	−32.9706	−	13.6569i	−1.33713	−	0.553859i
$609$	−5.51472			−0.223468
$610$	11.3137	+	11.3137i	0.458079	+	0.458079i
$611$	10.8284	−	4.48528i	0.438071	−	0.181455i
$612$		0			0
$613$	15.7487	−	38.0208i	0.636086	−	1.53565i	−0.195768	−	0.980650i	$-0.562720\pi$
$613$	15.7487	−	38.0208i	0.636086	−	1.53565i	0.831853	−	0.554996i	$-0.187280\pi$
$614$	2.92893	+	1.21320i	0.118202	+	0.0489609i
$615$	0.970563	+	0.970563i	0.0391369	+	0.0391369i
$616$	−4.34315	+	10.4853i	−0.174990	+	0.422464i
$617$	26.9706	−	26.9706i	1.08579	−	1.08579i	0.0898375	−	0.995956i	$-0.471365\pi$
$617$	26.9706	−	26.9706i	1.08579	−	1.08579i	0.995956	−	0.0898375i	$-0.0286348\pi$
$618$	−3.51472	+	1.45584i	−0.141383	+	0.0585626i
$619$	−16.8995	−	7.00000i	−0.679248	−	0.281354i	0.0162645	−	0.999868i	$-0.494823\pi$
$619$	−16.8995	−	7.00000i	−0.679248	−	0.281354i	−0.695513	+	0.718514i	$0.744823\pi$
$620$	−8.97056	−	3.71573i	−0.360266	−	0.149227i
$621$	2.82843	+	6.82843i	0.113501	+	0.274015i
$622$		−	6.62742i		−	0.265735i
$623$			15.3137i			0.613531i
$624$	−11.3137	−	11.3137i	−0.452911	−	0.452911i
$625$		−	4.65685i		−	0.186274i
$626$	38.1421			1.52447
$627$	−10.4853	−	25.3137i	−0.418742	−	1.01093i
$628$	−12.0000	−	28.9706i	−0.478852	−	1.15605i
$629$		0			0
$630$	−1.51472	−	3.65685i	−0.0603478	−	0.145693i
$631$	−20.2426	+	20.2426i	−0.805847	+	0.805847i	−0.984002	−	0.178156i	$-0.942987\pi$
$631$	−20.2426	+	20.2426i	−0.805847	+	0.805847i	0.178156	+	0.984002i	$0.442987\pi$
$632$	−19.7990	+	19.7990i	−0.787562	+	0.787562i
$633$	−0.242641	−	0.242641i	−0.00964410	−	0.00964410i
$634$	4.89949	−	11.8284i	0.194584	−	0.469767i
$635$	11.1127	−	26.8284i	0.440994	−	1.06465i
$636$			23.3137i			0.924449i
$637$	3.41421	−	1.41421i	0.135276	−	0.0560332i
$638$	−20.4437	+	20.4437i	−0.809372	+	0.809372i
$639$	−10.9706			−0.433989
$640$	16.0000	−	6.62742i	0.632456	−	0.261972i
$641$	−38.1838			−1.50817			−0.754084	−	0.656778i	$-0.771919\pi$
$641$	−38.1838			−1.50817			−0.754084	+	0.656778i	$0.771919\pi$
$642$	12.1421	−	12.1421i	0.479212	−	0.479212i
$643$	−18.5563	+	7.68629i	−0.731791	+	0.303118i	−0.717288	−	0.696777i	$-0.754617\pi$
$643$	−18.5563	+	7.68629i	−0.731791	+	0.303118i	−0.0145032	+	0.999895i	$0.504617\pi$
$644$		−	2.82843i		−	0.111456i
$645$	−4.20101	+	10.1421i	−0.165415	+	0.399346i
$646$		0			0
$647$	−11.5563	−	11.5563i	−0.454327	−	0.454327i	0.442461	−	0.896788i	$-0.354106\pi$
$647$	−11.5563	−	11.5563i	−0.454327	−	0.454327i	−0.896788	+	0.442461i	$0.854106\pi$
$648$	−0.343146	+	0.343146i	−0.0134800	+	0.0134800i
$649$	37.0711	−	37.0711i	1.45517	−	1.45517i
$650$	5.31371	+	12.8284i	0.208421	+	0.503172i
$651$	−3.17157	−	1.31371i	−0.124304	−	0.0514883i
$652$	−9.89949	−	23.8995i	−0.387694	−	0.935976i
$653$	6.77817	+	16.3640i	0.265250	+	0.640371i	0.999248	−	0.0387812i	$-0.0123475\pi$
$653$	6.77817	+	16.3640i	0.265250	+	0.640371i	−0.733997	+	0.679152i	$0.762348\pi$
$654$	−5.85786			−0.229061
$655$		−	0.686292i		−	0.0268156i
$656$	2.34315	−	2.34315i	0.0914845	−	0.0914845i
$657$			22.8284i			0.890622i
$658$			4.48528i			0.174854i
$659$	1.43503	+	3.46447i	0.0559008	+	0.134956i	0.949362	−	0.314183i	$-0.101731\pi$
$659$	1.43503	+	3.46447i	0.0559008	+	0.134956i	−0.893462	+	0.449140i	$0.851731\pi$
$660$	12.2843	+	5.08831i	0.478165	+	0.198062i
$661$	−40.8701	−	16.9289i	−1.58966	−	0.658459i	−0.599755	−	0.800184i	$-0.704735\pi$
$661$	−40.8701	−	16.9289i	−1.58966	−	0.658459i	−0.989906	+	0.141725i	$0.954735\pi$
$662$	−1.24264	+	0.514719i	−0.0482966	+	0.0200051i
$663$		0			0
$664$	14.8284	−	35.7990i	0.575455	−	1.38927i
$665$	−6.82843	−	6.82843i	−0.264795	−	0.264795i
$666$	20.5563	+	8.51472i	0.796542	+	0.329939i
$667$	2.75736	−	6.65685i	0.106765	−	0.257754i
$668$	28.4853	−	28.4853i	1.10213	−	1.10213i
$669$	0.686292	−	0.284271i	0.0265336	−	0.0109906i
$670$	−5.45584	−	5.45584i	−0.210778	−	0.210778i
$671$	29.6569			1.14489
$672$	5.65685	−	2.34315i	0.218218	−	0.0903888i
$673$	−25.4558			−0.981251			−0.490625	−	0.871371i	$-0.663232\pi$
$673$	−25.4558			−0.981251			−0.490625	+	0.871371i	$0.663232\pi$
$674$	−32.7279	−	32.7279i	−1.26063	−	1.26063i
$675$	12.8284	−	5.31371i	0.493766	−	0.204525i
$676$	0.928932	+	0.928932i	0.0357282	+	0.0357282i
$677$	−0.627417	+	1.51472i	−0.0241136	+	0.0582154i	−0.935478	−	0.353386i	$-0.885030\pi$
$677$	−0.627417	+	1.51472i	−0.0241136	+	0.0582154i	0.911364	+	0.411601i	$0.135030\pi$
$678$	−20.6274	−	8.54416i	−0.792191	−	0.328136i
$679$	−4.82843	−	4.82843i	−0.185298	−	0.185298i
$680$		0			0
$681$	9.11270	−	9.11270i	0.349199	−	0.349199i
$682$	−16.6274	+	6.88730i	−0.636697	+	0.263728i
$683$	−16.3640	−	6.77817i	−0.626150	−	0.259360i	0.0469665	−	0.998896i	$-0.485045\pi$
$683$	−16.3640	−	6.77817i	−0.626150	−	0.259360i	−0.673116	+	0.739537i	$0.735045\pi$
$684$	8.82843	−	21.3137i	0.337563	−	0.814950i
$685$	−10.8873	−	26.2843i	−0.415982	−	1.00427i
$686$			1.41421i			0.0539949i
$687$			22.6274i			0.863290i
$688$	24.4853	+	10.1421i	0.933493	+	0.386665i
$689$		−	39.7990i		−	1.51622i
$690$	−3.31371			−0.126151
$691$	16.8995	+	40.7990i	0.642887	+	1.55207i	0.822767	+	0.568378i	$0.192429\pi$
$691$	16.8995	+	40.7990i	0.642887	+	1.55207i	−0.179880	+	0.983689i	$0.557571\pi$
$692$	−20.4853	+	8.48528i	−0.778734	+	0.322562i
$693$	−6.77817	−	2.80761i	−0.257482	−	0.106652i
$694$	3.00000	+	7.24264i	0.113878	+	0.274927i
$695$	6.14214	−	6.14214i	0.232984	−	0.232984i
$696$	15.5980			0.591240
$697$		0			0
$698$	−11.3137	+	27.3137i	−0.428230	+	1.03384i
$699$	−2.24264	+	5.41421i	−0.0848245	+	0.204784i
$700$	−5.31371			−0.200839
$701$	−18.7782	+	7.77817i	−0.709242	+	0.293778i	−0.707991	−	0.706222i	$-0.750398\pi$
$701$	−18.7782	+	7.77817i	−0.709242	+	0.293778i	−0.00125103	+	0.999999i	$0.500398\pi$
$702$	19.3137	−	19.3137i	0.728949	−	0.728949i
$703$	54.2843			2.04737
$704$	12.2843	−	29.6569i	0.462981	−	1.11773i
$705$	5.25483			0.197908
$706$	23.4558	−	23.4558i	0.882772	−	0.882772i
$707$	1.41421	−	0.585786i	0.0531870	−	0.0220308i
$708$	−28.2843			−1.06299
$709$	−16.5355	+	39.9203i	−0.621005	+	1.49924i	0.229520	+	0.973304i	$0.426284\pi$
$709$	−16.5355	+	39.9203i	−0.621005	+	1.49924i	−0.850525	+	0.525935i	$0.823716\pi$
$710$	4.97056	−	12.0000i	0.186542	−	0.450352i
$711$	−12.7990	−	12.7990i	−0.480000	−	0.480000i
$712$		−	43.3137i		−	1.62325i
$713$	3.17157	−	3.17157i	0.118776	−	0.118776i
$714$		0			0
$715$	−20.9706	−	8.68629i	−0.784255	−	0.324849i
$716$	−16.7279	+	6.92893i	−0.625152	+	0.258946i
$717$	2.48528	+	6.00000i	0.0928145	+	0.224074i
$718$	43.9411			1.63987
$719$			33.3137i			1.24239i	0.783655	+	0.621196i	$0.213353\pi$
$719$			33.3137i			1.24239i	−0.783655	+	0.621196i	$0.786647\pi$
$720$	4.28427	+	10.3431i	0.159665	+	0.385466i
$721$			2.48528i			0.0925567i
$722$		−	29.4142i		−	1.09468i
$723$	6.54416	+	15.7990i	0.243380	+	0.587571i
$724$	−2.14214	+	5.17157i	−0.0796118	+	0.192200i
$725$	−12.5061	−	5.18019i	−0.464465	−	0.192388i
$726$	7.21320	−	2.98781i	0.267707	−	0.110888i
$727$	19.2132	−	19.2132i	0.712578	−	0.712578i	−0.254496	−	0.967074i	$-0.581909\pi$
$727$	19.2132	−	19.2132i	0.712578	−	0.712578i	0.967074	+	0.254496i	$0.0819095\pi$
$728$	−9.65685	+	4.00000i	−0.357907	+	0.148250i
$729$	−12.2218	−	12.2218i	−0.452660	−	0.452660i
$730$	−24.9706	−	10.3431i	−0.924202	−	0.382817i
$731$		0			0
$732$	−11.3137	−	11.3137i	−0.418167	−	0.418167i
$733$	−32.1421	+	13.3137i	−1.18720	+	0.491753i	−0.886841	−	0.462074i	$-0.847105\pi$
$733$	−32.1421	+	13.3137i	−1.18720	+	0.491753i	−0.300356	+	0.953827i	$0.597105\pi$
$734$	−4.48528	−	4.48528i	−0.165555	−	0.165555i
$735$	1.65685			0.0611140
$736$			8.00000i			0.294884i
$737$	−14.3015			−0.526803
$738$	1.51472	+	1.51472i	0.0557576	+	0.0557576i
$739$	2.19239	−	0.908117i	0.0806483	−	0.0334056i	−0.341995	−	0.939702i	$-0.611102\pi$
$739$	2.19239	−	0.908117i	0.0806483	−	0.0334056i	0.422643	+	0.906296i	$0.361102\pi$
$740$	−18.6274	+	18.6274i	−0.684757	+	0.684757i
$741$	9.65685	−	23.3137i	0.354753	−	0.856450i
$742$	14.0711	+	5.82843i	0.516565	+	0.213968i
$743$	15.4853	+	15.4853i	0.568100	+	0.568100i	0.931596	−	0.363496i	$-0.118417\pi$
$743$	15.4853	+	15.4853i	0.568100	+	0.568100i	−0.363496	+	0.931596i	$0.618417\pi$
$744$	8.97056	+	3.71573i	0.328877	+	0.136225i
$745$	11.6569	−	11.6569i	0.427074	−	0.427074i
$746$	−40.4558	+	16.7574i	−1.48119	+	0.613531i
$747$	23.1421	+	9.58579i	0.846726	+	0.350726i
$748$		0			0
$749$	−4.29289	−	10.3640i	−0.156859	−	0.378691i
$750$			17.9411i			0.655117i
$751$		−	30.2843i		−	1.10509i	−0.833483	−	0.552544i	$-0.813657\pi$
$751$		−	30.2843i		−	1.10509i	0.833483	−	0.552544i	$-0.186343\pi$
$752$		−	12.6863i		−	0.462621i
$753$		−	24.4853i		−	0.892293i
$754$	−26.6274			−0.969713
$755$	−2.48528	−	6.00000i	−0.0904487	−	0.218362i
$756$	4.00000	+	9.65685i	0.145479	+	0.351216i
$757$	10.5355	+	4.36396i	0.382920	+	0.158611i	0.565836	−	0.824518i	$-0.308554\pi$
$757$	10.5355	+	4.36396i	0.382920	+	0.158611i	−0.182916	+	0.983129i	$0.558554\pi$
$758$	18.7574	+	45.2843i	0.681298	+	1.64480i
$759$	−4.34315	+	4.34315i	−0.157646	+	0.157646i
$760$	19.3137	+	19.3137i	0.700582	+	0.700582i
$761$	−4.58579	−	4.58579i	−0.166235	−	0.166235i	0.619087	−	0.785322i	$-0.287503\pi$
$761$	−4.58579	−	4.58579i	−0.166235	−	0.166235i	−0.785322	+	0.619087i	$0.787503\pi$
$762$	−11.1127	+	26.8284i	−0.402571	+	0.971891i
$763$	−1.46447	+	3.53553i	−0.0530172	+	0.127995i
$764$			22.1421i			0.801074i
$765$		0			0
$766$	7.17157	−	7.17157i	0.259119	−	0.259119i
$767$	48.2843			1.74344
$768$	−16.0000	+	6.62742i	−0.577350	+	0.239146i
$769$	−21.9411			−0.791217			−0.395609	−	0.918419i	$-0.629466\pi$
$769$	−21.9411			−0.791217			−0.395609	+	0.918419i	$0.629466\pi$
$770$	6.14214	−	6.14214i	0.221347	−	0.221347i
$771$	−0.142136	+	0.0588745i	−0.00511889	+	0.00212031i
$772$			2.82843i			0.101797i
$773$	4.82843	−	11.6569i	0.173666	−	0.419268i	−0.812948	−	0.582336i	$-0.802139\pi$
$773$	4.82843	−	11.6569i	0.173666	−	0.419268i	0.986615	+	0.163068i	$0.0521389\pi$
$774$	−6.55635	+	15.8284i	−0.235663	+	0.568941i
$775$	−5.95837	−	5.95837i	−0.214031	−	0.214031i
$776$	13.6569	+	13.6569i	0.490252	+	0.490252i
$777$	−6.58579	+	6.58579i	−0.236264	+	0.236264i
$778$	−17.0000	−	41.0416i	−0.609480	−	1.47141i
$779$	4.82843	+	2.00000i	0.172996	+	0.0716574i
$780$	4.68629	+	11.3137i	0.167796	+	0.405096i
$781$	−9.21320	−	22.2426i	−0.329674	−	0.795904i
$782$		0			0
$783$			26.6274i			0.951586i
$784$		−	4.00000i		−	0.142857i
$785$			24.0000i			0.856597i
$786$			0.686292i			0.0244792i
$787$	−3.24264	−	7.82843i	−0.115588	−	0.279053i	0.855489	−	0.517821i	$-0.173257\pi$
$787$	−3.24264	−	7.82843i	−0.115588	−	0.279053i	−0.971077	+	0.238768i	$0.923257\pi$
$788$	41.5563	+	17.2132i	1.48038	+	0.613195i
$789$	−2.34315	−	0.970563i	−0.0834182	−	0.0345529i
$790$	19.7990	−	8.20101i	0.704416	−	0.291779i
$791$	−10.3137	+	10.3137i	−0.366713	+	0.366713i
$792$	19.1716	+	7.94113i	0.681232	+	0.282176i
$793$	19.3137	+	19.3137i	0.685850	+	0.685850i
$794$	−32.9706	−	13.6569i	−1.17008	−	0.484664i
$795$	6.82843	−	16.4853i	0.242179	−	0.584673i
$796$	30.1421	−	30.1421i	1.06836	−	1.06836i
$797$	11.5563	−	4.78680i	0.409347	−	0.169557i	−0.168501	−	0.985701i	$-0.553893\pi$
$797$	11.5563	−	4.78680i	0.409347	−	0.169557i	0.577848	+	0.816144i	$0.303893\pi$
$798$	6.82843	+	6.82843i	0.241724	+	0.241724i
$799$		0			0
$800$	15.0294			0.531371
$801$	28.0000			0.989331
$802$	23.7574	+	23.7574i	0.838902	+	0.838902i
$803$	−46.2843	+	19.1716i	−1.63334	+	0.676550i
$804$	5.45584	+	5.45584i	0.192413	+	0.192413i
$805$	−0.828427	+	2.00000i	−0.0291982	+	0.0704907i
$806$	−15.3137	−	6.34315i	−0.539402	−	0.223428i
$807$	11.5147	+	11.5147i	0.405337	+	0.405337i
$808$	−4.00000	+	1.65685i	−0.140720	+	0.0582879i
$809$	25.4558	−	25.4558i	0.894980	−	0.894980i	−0.100007	−	0.994987i	$-0.531886\pi$
$809$	25.4558	−	25.4558i	0.894980	−	0.894980i	0.994987	+	0.100007i	$0.0318865\pi$
$810$	0.343146	−	0.142136i	0.0120569	−	0.00499414i
$811$	−17.3848	−	7.20101i	−0.610462	−	0.252862i	0.0559640	−	0.998433i	$-0.482177\pi$
$811$	−17.3848	−	7.20101i	−0.610462	−	0.252862i	−0.666426	+	0.745571i	$0.732177\pi$
$812$	3.89949	−	9.41421i	0.136845	−	0.330374i
$813$	11.7990	+	28.4853i	0.413809	+	0.999022i
$814$			48.8284i			1.71144i
$815$			19.7990i			0.693528i
$816$		0			0
$817$			41.7990i			1.46236i
$818$	−48.4853			−1.69525
$819$	−2.58579	−	6.24264i	−0.0903547	−	0.218136i
$820$	−2.34315	+	0.970563i	−0.0818262	+	0.0338935i
$821$	−12.6066	−	5.22183i	−0.439973	−	0.182243i	0.151690	−	0.988428i	$-0.451529\pi$
$821$	−12.6066	−	5.22183i	−0.439973	−	0.182243i	−0.591663	+	0.806185i	$0.701529\pi$
$822$	10.8873	+	26.2843i	0.379738	+	0.916769i
$823$	−35.1127	+	35.1127i	−1.22395	+	1.22395i	−0.257736	+	0.966215i	$0.582977\pi$
$823$	−35.1127	+	35.1127i	−1.22395	+	1.22395i	−0.966215	+	0.257736i	$0.917023\pi$
$824$		−	7.02944i		−	0.244882i
$825$	8.15938	+	8.15938i	0.284073	+	0.284073i
$826$	−7.07107	+	17.0711i	−0.246034	+	0.593978i
$827$	−2.53553	+	6.12132i	−0.0881692	+	0.212859i	−0.961813	−	0.273706i	$-0.911750\pi$
$827$	−2.53553	+	6.12132i	−0.0881692	+	0.212859i	0.873644	+	0.486565i	$0.161750\pi$
$828$	−5.17157			−0.179725
$829$	3.07107	−	1.27208i	0.106663	−	0.0441811i	−0.328714	−	0.944430i	$-0.606615\pi$
$829$	3.07107	−	1.27208i	0.106663	−	0.0441811i	0.435377	+	0.900248i	$0.356615\pi$
$830$	−20.9706	+	20.9706i	−0.727899	+	0.727899i
$831$	−5.11270			−0.177358
$832$	27.3137	−	11.3137i	0.946932	−	0.392232i
$833$		0			0
$834$	−6.14214	+	6.14214i	−0.212685	+	0.212685i
$835$	−28.4853	+	11.7990i	−0.985774	+	0.408321i
$836$	50.6274			1.75099
$837$	−6.34315	+	15.3137i	−0.219251	+	0.529319i
$838$	4.24264	−	10.2426i	0.146560	−	0.353826i
$839$	31.4142	+	31.4142i	1.08454	+	1.08454i	0.996080	+	0.0884593i	$0.0281943\pi$
$839$	31.4142	+	31.4142i	1.08454	+	1.08454i	0.0884593	+	0.996080i	$0.471806\pi$
$840$	−4.68629			−0.161692
$841$	−2.15076	+	2.15076i	−0.0741641	+	0.0741641i
$842$	3.38478	+	8.17157i	0.116647	+	0.281611i
$843$	17.8995	+	7.41421i	0.616491	+	0.255359i
$844$	0.585786	−	0.242641i	0.0201636	−	0.00835204i
$845$	−0.384776	−	0.928932i	−0.0132367	−	0.0319562i
$846$	8.20101			0.281957
$847$		−	5.10051i		−	0.175255i
$848$	−39.7990	−	16.4853i	−1.36670	−	0.566107i
$849$		−	19.5147i		−	0.669743i
$850$		0			0
$851$	−4.65685	−	11.2426i	−0.159635	−	0.385393i
$852$	−4.97056	+	12.0000i	−0.170289	+	0.411113i
$853$	−43.3137	−	17.9411i	−1.48303	−	0.614292i	−0.513245	−	0.858242i	$-0.671557\pi$
$853$	−43.3137	−	17.9411i	−1.48303	−	0.614292i	−0.969788	+	0.243950i	$0.921557\pi$
$854$	−9.65685	+	4.00000i	−0.330451	+	0.136877i
$855$	−12.4853	+	12.4853i	−0.426988	+	0.426988i
$856$	12.1421	+	29.3137i	0.415010	+	1.00192i
$857$	4.38478	+	4.38478i	0.149781	+	0.149781i	0.778020	−	0.628239i	$-0.216224\pi$
$857$	4.38478	+	4.38478i	0.149781	+	0.149781i	−0.628239	+	0.778020i	$0.716224\pi$
$858$	20.9706	+	8.68629i	0.715923	+	0.296545i
$859$	16.4142	−	39.6274i	0.560046	−	1.35207i	−0.349683	−	0.936868i	$-0.613711\pi$
$859$	16.4142	−	39.6274i	0.560046	−	1.35207i	0.909729	−	0.415202i	$-0.136289\pi$
$860$	−14.3431	−	14.3431i	−0.489097	−	0.489097i
$861$	−0.828427	+	0.343146i	−0.0282327	+	0.0116944i
$862$	10.3431	+	10.3431i	0.352289	+	0.352289i
$863$	29.6985			1.01095			0.505474	−	0.862842i	$-0.331318\pi$
$863$	29.6985			1.01095			0.505474	+	0.862842i	$0.331318\pi$
$864$	−11.3137	−	27.3137i	−0.384900	−	0.929231i
$865$	16.9706			0.577016
$866$	−32.2843	−	32.2843i	−1.09706	−	1.09706i
$867$	−17.0000	+	7.04163i	−0.577350	+	0.239146i
$868$	4.48528	−	4.48528i	0.152240	−	0.152240i
$869$	15.2010	−	36.6985i	0.515659	−	1.24491i
$870$	−11.0294	−	4.56854i	−0.373933	−	0.154888i
$871$	−9.31371	−	9.31371i	−0.315583	−	0.315583i
$872$	4.14214	−	10.0000i	0.140270	−	0.338643i
$873$	−8.82843	+	8.82843i	−0.298797	+	0.298797i
$874$	−11.6569	+	4.82843i	−0.394299	+	0.163324i
$875$	10.8284	+	4.48528i	0.366068	+	0.151630i
$876$	24.9706	+	10.3431i	0.843677	+	0.349463i
$877$	15.1924	+	36.6777i	0.513010	+	1.23852i	0.942123	+	0.335266i	$0.108826\pi$
$877$	15.1924	+	36.6777i	0.513010	+	1.23852i	−0.429113	+	0.903251i	$0.641174\pi$
$878$		−	36.0000i		−	1.21494i
$879$			25.9411i			0.874972i
$880$	−17.3726	+	17.3726i	−0.585630	+	0.585630i
$881$		−	27.4558i		−	0.925011i	−0.886616	−	0.462505i	$-0.846951\pi$
$881$		−	27.4558i		−	0.925011i	0.886616	−	0.462505i	$-0.153049\pi$
$882$	2.58579			0.0870680
$883$	15.3345	+	37.0208i	0.516048	+	1.24585i	0.940313	+	0.340312i	$0.110533\pi$
$883$	15.3345	+	37.0208i	0.516048	+	1.24585i	−0.424265	+	0.905538i	$0.639467\pi$
$884$		0			0
$885$	20.0000	+	8.28427i	0.672293	+	0.278473i
$886$	−5.92893	−	14.3137i	−0.199186	−	0.480878i
$887$	40.7279	−	40.7279i	1.36751	−	1.36751i	0.503535	−	0.863975i	$-0.332033\pi$
$887$	40.7279	−	40.7279i	1.36751	−	1.36751i	0.863975	−	0.503535i	$-0.167967\pi$
$888$	18.6274	−	18.6274i	0.625095	−	0.625095i
$889$	13.4142	+	13.4142i	0.449898	+	0.449898i
$890$	−12.6863	+	30.6274i	−0.425245	+	1.02663i
$891$	0.263456	−	0.636039i	0.00882611	−	0.0213081i
$892$			1.37258i			0.0459575i
$893$	18.4853	−	7.65685i	0.618586	−	0.256227i
$894$	−11.6569	+	11.6569i	−0.389864	+	0.389864i
$895$	13.8579			0.463217
$896$			11.3137i			0.377964i
$897$	−5.65685			−0.188877
$898$	−17.4558	+	17.4558i	−0.582509	+	0.582509i
$899$	14.9289	−	6.18377i	0.497908	−	0.206240i
$900$			9.71573i			0.323858i
$901$		0			0
$902$	−1.79899	+	4.34315i	−0.0598998	+	0.144611i
$903$	−5.07107	−	5.07107i	−0.168755	−	0.168755i
$904$	29.1716	−	29.1716i	0.970232	−	0.970232i
$905$	3.02944	−	3.02944i	0.100702	−	0.100702i
$906$	2.48528	+	6.00000i	0.0825679	+	0.199337i
$907$	−8.77817	−	3.63604i	−0.291475	−	0.120733i	0.232155	−	0.972679i	$-0.425422\pi$
$907$	−8.77817	−	3.63604i	−0.291475	−	0.120733i	−0.523629	+	0.851946i	$0.675422\pi$
$908$	9.11270	+	22.0000i	0.302416	+	0.730096i
$909$	−1.07107	−	2.58579i	−0.0355251	−	0.0857651i
$910$	8.00000			0.265197
$911$			18.6863i			0.619104i	0.950882	+	0.309552i	$0.100179\pi$
$911$			18.6863i			0.619104i	−0.950882	+	0.309552i	$0.899821\pi$
$912$	−19.3137	−	19.3137i	−0.639541	−	0.639541i
$913$			54.9706i			1.81926i
$914$			16.0000i			0.529233i
$915$	4.68629	+	11.3137i	0.154924	+	0.374020i
$916$	−38.6274	−	16.0000i	−1.27629	−	0.528655i
$917$	0.414214	+	0.171573i	0.0136785	+	0.00566584i
$918$		0			0
$919$	−8.92893	+	8.92893i	−0.294538	+	0.294538i	−0.838870	−	0.544332i	$-0.816783\pi$
$919$	−8.92893	+	8.92893i	−0.294538	+	0.294538i	0.544332	+	0.838870i	$0.316783\pi$
$920$	2.34315	−	5.65685i	0.0772512	−	0.186501i
$921$	1.71573	+	1.71573i	0.0565352	+	0.0565352i
$922$	−28.9706	−	12.0000i	−0.954095	−	0.395199i
$923$	8.48528	−	20.4853i	0.279296	−	0.674281i
$924$	−6.14214	+	6.14214i	−0.202061	+	0.202061i
$925$	−21.1213	+	8.74874i	−0.694465	+	0.287657i
$926$	20.0416	+	20.0416i	0.658609	+	0.658609i
$927$	4.54416			0.149250
$928$	−11.0294	+	26.6274i	−0.362059	+	0.874088i
$929$	41.9411			1.37604			0.688022	−	0.725690i	$-0.258479\pi$
$929$	41.9411			1.37604			0.688022	+	0.725690i	$0.258479\pi$
$930$	−5.25483	−	5.25483i	−0.172313	−	0.172313i
$931$	5.82843	−	2.41421i	0.191019	−	0.0791227i
$932$	−7.65685	−	7.65685i	−0.250809	−	0.250809i
$933$	1.94113	−	4.68629i	0.0635496	−	0.153422i
$934$	−50.0416	−	20.7279i	−1.63741	−	0.678238i
$935$		0			0
$936$	7.31371	+	17.6569i	0.239056	+	0.577132i
$937$	20.1421	−	20.1421i	0.658015	−	0.658015i	−0.296895	−	0.954910i	$-0.595951\pi$
$937$	20.1421	−	20.1421i	0.658015	−	0.658015i	0.954910	+	0.296895i	$0.0959512\pi$
$938$	4.65685	−	1.92893i	0.152052	−	0.0629819i
$939$	26.9706	+	11.1716i	0.880151	+	0.364571i
$940$	−3.71573	+	8.97056i	−0.121194	+	0.292587i
$941$	0.970563	+	2.34315i	0.0316394	+	0.0763844i	0.938910	−	0.344164i	$-0.111838\pi$
$941$	0.970563	+	2.34315i	0.0316394	+	0.0763844i	−0.907270	+	0.420548i	$0.861838\pi$
$942$		−	24.0000i		−	0.781962i
$943$		−	1.17157i		−	0.0381517i
$944$	20.0000	−	48.2843i	0.650945	−	1.57152i
$945$		−	8.00000i		−	0.260240i
$946$	−37.5980			−1.22242
$947$	−10.7487	−	25.9497i	−0.349287	−	0.843253i	−0.996705	−	0.0811179i	$-0.974151\pi$
$947$	−10.7487	−	25.9497i	−0.349287	−	0.843253i	0.647417	−	0.762136i	$-0.275849\pi$
$948$	−19.7990	+	8.20101i	−0.643041	+	0.266356i
$949$	−42.6274	−	17.6569i	−1.38374	−	0.573166i
$950$	9.07107	+	21.8995i	0.294304	+	0.710513i
$951$	6.92893	−	6.92893i	0.224686	−	0.224686i
$952$		0			0
$953$	−5.97056	−	5.97056i	−0.193405	−	0.193405i	0.603760	−	0.797166i	$-0.293668\pi$
$953$	−5.97056	−	5.97056i	−0.193405	−	0.193405i	−0.797166	+	0.603760i	$0.793668\pi$
$954$	10.6569	−	25.7279i	0.345028	−	0.832972i
$955$	6.48528	−	15.6569i	0.209859	−	0.506644i
$956$	−12.0000			−0.388108
$957$	−20.4437	+	8.46804i	−0.660849	+	0.273733i
$958$	6.68629	−	6.68629i	0.216024	−	0.216024i
$959$	18.5858			0.600166
$960$	13.2548			0.427798
$961$	−20.9411			−0.675520
$962$	−31.7990	+	31.7990i	−1.02524	+	1.02524i
$963$	−18.9497	+	7.84924i	−0.610647	+	0.252938i
$964$	−31.5980			−1.01770
$965$	0.828427	−	2.00000i	0.0266680	−	0.0643823i
$966$	0.828427	−	2.00000i	0.0266542	−	0.0643489i
$967$	7.34315	+	7.34315i	0.236140	+	0.236140i	0.815250	−	0.579110i	$-0.196600\pi$
$967$	7.34315	+	7.34315i	0.236140	+	0.236140i	−0.579110	+	0.815250i	$0.696600\pi$
$968$			14.4264i			0.463682i
$969$		0			0
$970$	−5.65685	−	13.6569i	−0.181631	−	0.438495i
$971$	−26.5563	−	11.0000i	−0.852234	−	0.353007i	−0.0865684	−	0.996246i	$-0.527590\pi$
$971$	−26.5563	−	11.0000i	−0.852234	−	0.353007i	−0.765665	+	0.643239i	$0.777590\pi$
$972$	28.6274	−	11.8579i	0.918225	−	0.380341i
$973$	2.17157	+	5.24264i	0.0696174	+	0.168071i
$974$	58.2843			1.86755
$975$			10.6274i			0.340350i
$976$	27.3137	−	11.3137i	0.874291	−	0.362143i
$977$		−	53.1716i		−	1.70111i	−0.525887	−	0.850555i	$-0.676266\pi$
$977$		−	53.1716i		−	1.70111i	0.525887	−	0.850555i	$-0.323734\pi$
$978$		−	19.7990i		−	0.633102i
$979$	23.5147	+	56.7696i	0.751534	+	1.81436i
$980$	−1.17157	+	2.82843i	−0.0374245	+	0.0903508i
$981$	6.46447	+	2.67767i	0.206395	+	0.0854914i
$982$	−19.1421	+	7.92893i	−0.610850	+	0.253022i
$983$	−0.585786	+	0.585786i	−0.0186837	+	0.0186837i	−0.716387	−	0.697703i	$-0.754205\pi$
$983$	−0.585786	+	0.585786i	−0.0186837	+	0.0186837i	0.697703	+	0.716387i	$0.254205\pi$
$984$	2.34315	−	0.970563i	0.0746968	−	0.0309404i
$985$	−24.3431	−	24.3431i	−0.775637	−	0.775637i
$986$		0			0
$987$	−1.31371	+	3.17157i	−0.0418158	+	0.100952i
$988$	32.9706	+	32.9706i	1.04893	+	1.04893i
$989$	8.65685	−	3.58579i	0.275272	−	0.114021i
$990$	−11.2304	−	11.2304i	−0.356927	−	0.356927i
$991$	50.1838			1.59414			0.797070	−	0.603887i	$-0.206382\pi$
$991$	50.1838			1.59414			0.797070	+	0.603887i	$0.206382\pi$
$992$	−12.6863	+	12.6863i	−0.402790	+	0.402790i
$993$	−1.02944			−0.0326682
$994$	6.00000	+	6.00000i	0.190308	+	0.190308i
$995$	−30.1421	+	12.4853i	−0.955570	+	0.395810i
$996$	20.9706	−	20.9706i	0.664478	−	0.664478i
$997$	−14.7279	+	35.5563i	−0.466438	+	1.12608i	0.499269	+	0.866447i	$0.333602\pi$
$997$	−14.7279	+	35.5563i	−0.466438	+	1.12608i	−0.965707	+	0.259634i	$0.916398\pi$
$998$	−25.4853	−	10.5563i	−0.806722	−	0.334155i
$999$	31.7990	+	31.7990i	1.00608	+	1.00608i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.u.a.85.1	yes	4
4.3	odd	2		896.2.u.a.561.1		4
32.3	odd	8		896.2.u.a.337.1		4
32.29	even	8	inner	224.2.u.a.29.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.a.29.1	✓	4	32.29	even	8	inner
224.2.u.a.85.1	yes	4	1.1	even	1	trivial
896.2.u.a.337.1		4	32.3	odd	8
896.2.u.a.561.1		4	4.3	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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.00000 + 0.414214i) q^{3} -2.00000i q^{4} +(-0.585786 + 1.41421i) q^{5} +(0.585786 - 1.41421i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.29289 + 1.29289i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.00000 + 0.414214i) q^{3} -2.00000i q^{4} +(-0.585786 + 1.41421i) q^{5} +(0.585786 - 1.41421i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.29289 + 1.29289i) q^{9} +(-0.828427 - 2.00000i) q^{10} +(-3.70711 - 1.53553i) q^{11} +(0.828427 + 2.00000i) q^{12} +(-1.41421 - 3.41421i) q^{13} +1.41421 q^{14} -1.65685i q^{15} -4.00000 q^{16} -2.58579i q^{18} +(-2.41421 - 5.82843i) q^{19} +(2.82843 + 1.17157i) q^{20} +(1.00000 + 0.414214i) q^{21} +(5.24264 - 2.17157i) q^{22} +(-1.00000 + 1.00000i) q^{23} +(-2.82843 - 1.17157i) q^{24} +(1.87868 + 1.87868i) q^{25} +(4.82843 + 2.00000i) q^{26} +(2.00000 - 4.82843i) q^{27} +(-1.41421 + 1.41421i) q^{28} +(-4.70711 + 1.94975i) q^{29} +(1.65685 + 1.65685i) q^{30} -3.17157 q^{31} +(4.00000 - 4.00000i) q^{32} +4.34315 q^{33} +(1.41421 - 0.585786i) q^{35} +(2.58579 + 2.58579i) q^{36} +(-3.29289 + 7.94975i) q^{37} +(8.24264 + 3.41421i) q^{38} +(2.82843 + 2.82843i) q^{39} +(-4.00000 + 1.65685i) q^{40} +(-0.585786 + 0.585786i) q^{41} +(-1.41421 + 0.585786i) q^{42} +(-6.12132 - 2.53553i) q^{43} +(-3.07107 + 7.41421i) q^{44} +(-1.07107 - 2.58579i) q^{45} -2.00000i q^{46} +3.17157i q^{47} +(4.00000 - 1.65685i) q^{48} +1.00000i q^{49} -3.75736 q^{50} +(-6.82843 + 2.82843i) q^{52} +(9.94975 + 4.12132i) q^{53} +(2.82843 + 6.82843i) q^{54} +(4.34315 - 4.34315i) q^{55} -2.82843i q^{56} +(4.82843 + 4.82843i) q^{57} +(2.75736 - 6.65685i) q^{58} +(-5.00000 + 12.0711i) q^{59} -3.31371 q^{60} +(-6.82843 + 2.82843i) q^{61} +(3.17157 - 3.17157i) q^{62} +1.82843 q^{63} +8.00000i q^{64} +5.65685 q^{65} +(-4.34315 + 4.34315i) q^{66} +(3.29289 - 1.36396i) q^{67} +(0.585786 - 1.41421i) q^{69} +(-0.828427 + 2.00000i) q^{70} +(4.24264 + 4.24264i) q^{71} -5.17157 q^{72} +(8.82843 - 8.82843i) q^{73} +(-4.65685 - 11.2426i) q^{74} +(-2.65685 - 1.10051i) q^{75} +(-11.6569 + 4.82843i) q^{76} +(1.53553 + 3.70711i) q^{77} -5.65685 q^{78} +9.89949i q^{79} +(2.34315 - 5.65685i) q^{80} +0.171573i q^{81} -1.17157i q^{82} +(-5.24264 - 12.6569i) q^{83} +(0.828427 - 2.00000i) q^{84} +(8.65685 - 3.58579i) q^{86} +(3.89949 - 3.89949i) q^{87} +(-4.34315 - 10.4853i) q^{88} +(-10.8284 - 10.8284i) q^{89} +(3.65685 + 1.51472i) q^{90} +(-1.41421 + 3.41421i) q^{91} +(2.00000 + 2.00000i) q^{92} +(3.17157 - 1.31371i) q^{93} +(-3.17157 - 3.17157i) q^{94} +9.65685 q^{95} +(-2.34315 + 5.65685i) q^{96} +6.82843 q^{97} +(-1.00000 - 1.00000i) q^{98} +(6.77817 - 2.80761i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} - 8 q^{5} + 8 q^{6} + 8 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 + 8 * q^6 + 8 * q^8 - 8 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} - 8 q^{5} + 8 q^{6} + 8 q^{8} - 8 q^{9} + 8 q^{10} - 12 q^{11} - 8 q^{12} - 16 q^{16} - 4 q^{19} + 4 q^{21} + 4 q^{22} - 4 q^{23} + 16 q^{25} + 8 q^{26} + 8 q^{27} - 16 q^{29} - 16 q^{30} - 24 q^{31} + 16 q^{32} + 40 q^{33} + 16 q^{36} - 16 q^{37} + 16 q^{38} - 16 q^{40} - 8 q^{41} - 16 q^{43} + 16 q^{44} + 24 q^{45} + 16 q^{48} - 32 q^{50} - 16 q^{52} + 20 q^{53} + 40 q^{55} + 8 q^{57} + 28 q^{58} - 20 q^{59} + 32 q^{60} - 16 q^{61} + 24 q^{62} - 4 q^{63} - 40 q^{66} + 16 q^{67} + 8 q^{69} + 8 q^{70} - 32 q^{72} + 24 q^{73} + 4 q^{74} + 12 q^{75} - 24 q^{76} - 8 q^{77} + 32 q^{80} - 4 q^{83} - 8 q^{84} + 12 q^{86} - 24 q^{87} - 40 q^{88} - 32 q^{89} - 8 q^{90} + 8 q^{92} + 24 q^{93} - 24 q^{94} + 16 q^{95} - 32 q^{96} + 16 q^{97} - 4 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 + 8 * q^6 + 8 * q^8 - 8 * q^9 + 8 * q^10 - 12 * q^11 - 8 * q^12 - 16 * q^16 - 4 * q^19 + 4 * q^21 + 4 * q^22 - 4 * q^23 + 16 * q^25 + 8 * q^26 + 8 * q^27 - 16 * q^29 - 16 * q^30 - 24 * q^31 + 16 * q^32 + 40 * q^33 + 16 * q^36 - 16 * q^37 + 16 * q^38 - 16 * q^40 - 8 * q^41 - 16 * q^43 + 16 * q^44 + 24 * q^45 + 16 * q^48 - 32 * q^50 - 16 * q^52 + 20 * q^53 + 40 * q^55 + 8 * q^57 + 28 * q^58 - 20 * q^59 + 32 * q^60 - 16 * q^61 + 24 * q^62 - 4 * q^63 - 40 * q^66 + 16 * q^67 + 8 * q^69 + 8 * q^70 - 32 * q^72 + 24 * q^73 + 4 * q^74 + 12 * q^75 - 24 * q^76 - 8 * q^77 + 32 * q^80 - 4 * q^83 - 8 * q^84 + 12 * q^86 - 24 * q^87 - 40 * q^88 - 32 * q^89 - 8 * q^90 + 8 * q^92 + 24 * q^93 - 24 * q^94 + 16 * q^95 - 32 * q^96 + 16 * q^97 - 4 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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