LMFDB - Embedded newform 1050.2.d.f.1049.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(1049,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, 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("1050.1049");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.d (of order $2$, degree $1$, not 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1049.1
Root			$-0.618034i$ of defining polynomial
Character	$\chi$	$=$	1050.1049
Dual form			1050.2.d.f.1049.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.618034 - 1.61803i) q^{3} +1.00000 q^{4} +(-0.618034 - 1.61803i) q^{6} +(-0.381966 + 2.61803i) q^{7} +1.00000 q^{8} +(-2.23607 + 2.00000i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.618034 - 1.61803i) q^{3} +1.00000 q^{4} +(-0.618034 - 1.61803i) q^{6} +(-0.381966 + 2.61803i) q^{7} +1.00000 q^{8} +(-2.23607 + 2.00000i) q^{9} -4.47214i q^{11} +(-0.618034 - 1.61803i) q^{12} -1.23607 q^{13} +(-0.381966 + 2.61803i) q^{14} +1.00000 q^{16} -5.23607i q^{17} +(-2.23607 + 2.00000i) q^{18} -8.47214i q^{19} +(4.47214 - 1.00000i) q^{21} -4.47214i q^{22} +4.00000 q^{23} +(-0.618034 - 1.61803i) q^{24} -1.23607 q^{26} +(4.61803 + 2.38197i) q^{27} +(-0.381966 + 2.61803i) q^{28} -7.70820i q^{29} -2.76393i q^{31} +1.00000 q^{32} +(-7.23607 + 2.76393i) q^{33} -5.23607i q^{34} +(-2.23607 + 2.00000i) q^{36} +0.763932i q^{37} -8.47214i q^{38} +(0.763932 + 2.00000i) q^{39} +2.47214 q^{41} +(4.47214 - 1.00000i) q^{42} +4.94427i q^{43} -4.47214i q^{44} +4.00000 q^{46} +6.47214i q^{47} +(-0.618034 - 1.61803i) q^{48} +(-6.70820 - 2.00000i) q^{49} +(-8.47214 + 3.23607i) q^{51} -1.23607 q^{52} -0.472136 q^{53} +(4.61803 + 2.38197i) q^{54} +(-0.381966 + 2.61803i) q^{56} +(-13.7082 + 5.23607i) q^{57} -7.70820i q^{58} +4.47214 q^{59} +7.23607i q^{61} -2.76393i q^{62} +(-4.38197 - 6.61803i) q^{63} +1.00000 q^{64} +(-7.23607 + 2.76393i) q^{66} -12.0000i q^{67} -5.23607i q^{68} +(-2.47214 - 6.47214i) q^{69} +7.23607i q^{71} +(-2.23607 + 2.00000i) q^{72} -11.2361 q^{73} +0.763932i q^{74} -8.47214i q^{76} +(11.7082 + 1.70820i) q^{77} +(0.763932 + 2.00000i) q^{78} +8.94427 q^{79} +(1.00000 - 8.94427i) q^{81} +2.47214 q^{82} +14.6525i q^{83} +(4.47214 - 1.00000i) q^{84} +4.94427i q^{86} +(-12.4721 + 4.76393i) q^{87} -4.47214i q^{88} -5.52786 q^{89} +(0.472136 - 3.23607i) q^{91} +4.00000 q^{92} +(-4.47214 + 1.70820i) q^{93} +6.47214i q^{94} +(-0.618034 - 1.61803i) q^{96} -0.763932 q^{97} +(-6.70820 - 2.00000i) q^{98} +(8.94427 + 10.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 2 q^{6} - 6 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 2 * q^6 - 6 * q^7 + 4 * q^8	$ 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 2 q^{6} - 6 q^{7} + 4 q^{8} + 2 q^{12} + 4 q^{13} - 6 q^{14} + 4 q^{16} + 16 q^{23} + 2 q^{24} + 4 q^{26} + 14 q^{27} - 6 q^{28} + 4 q^{32} - 20 q^{33} + 12 q^{39} - 8 q^{41} + 16 q^{46} + 2 q^{48} - 16 q^{51} + 4 q^{52} + 16 q^{53} + 14 q^{54} - 6 q^{56} - 28 q^{57} - 22 q^{63} + 4 q^{64} - 20 q^{66} + 8 q^{69} - 36 q^{73} + 20 q^{77} + 12 q^{78} + 4 q^{81} - 8 q^{82} - 32 q^{87} - 40 q^{89} - 16 q^{91} + 16 q^{92} + 2 q^{96} - 12 q^{97}+O(q^{100}) $ 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 2 * q^6 - 6 * q^7 + 4 * q^8 + 2 * q^12 + 4 * q^13 - 6 * q^14 + 4 * q^16 + 16 * q^23 + 2 * q^24 + 4 * q^26 + 14 * q^27 - 6 * q^28 + 4 * q^32 - 20 * q^33 + 12 * q^39 - 8 * q^41 + 16 * q^46 + 2 * q^48 - 16 * q^51 + 4 * q^52 + 16 * q^53 + 14 * q^54 - 6 * q^56 - 28 * q^57 - 22 * q^63 + 4 * q^64 - 20 * q^66 + 8 * q^69 - 36 * q^73 + 20 * q^77 + 12 * q^78 + 4 * q^81 - 8 * q^82 - 32 * q^87 - 40 * q^89 - 16 * q^91 + 16 * q^92 + 2 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$-1$	$-1$

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
$3$	−0.618034	−	1.61803i	−0.356822	−	0.934172i
$3$	−0.618034	−	1.61803i	−0.356822	−	0.934172i
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−0.618034	−	1.61803i	−0.252311	−	0.660560i
$7$	−0.381966	+	2.61803i	−0.144370	+	0.989524i
$7$	−0.381966	+	2.61803i	−0.144370	+	0.989524i
$8$	1.00000			0.353553
$9$	−2.23607	+	2.00000i	−0.745356	+	0.666667i
$10$		0			0
$11$		−	4.47214i		−	1.34840i	−0.738549	−	0.674200i	$-0.764489\pi$
$11$		−	4.47214i		−	1.34840i	0.738549	−	0.674200i	$-0.235511\pi$
$12$	−0.618034	−	1.61803i	−0.178411	−	0.467086i
$13$	−1.23607			−0.342824			−0.171412	−	0.985199i	$-0.554833\pi$
$13$	−1.23607			−0.342824			−0.171412	+	0.985199i	$0.554833\pi$
$14$	−0.381966	+	2.61803i	−0.102085	+	0.699699i
$15$		0			0
$16$	1.00000			0.250000
$17$		−	5.23607i		−	1.26993i	−0.772540	−	0.634967i	$-0.781014\pi$
$17$		−	5.23607i		−	1.26993i	0.772540	−	0.634967i	$-0.218986\pi$
$18$	−2.23607	+	2.00000i	−0.527046	+	0.471405i
$19$		−	8.47214i		−	1.94364i	−0.235722	−	0.971821i	$-0.575745\pi$
$19$		−	8.47214i		−	1.94364i	0.235722	−	0.971821i	$-0.424255\pi$
$20$		0			0
$21$	4.47214	−	1.00000i	0.975900	−	0.218218i
$22$		−	4.47214i		−	0.953463i
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$	−0.618034	−	1.61803i	−0.126156	−	0.330280i
$25$		0			0
$26$	−1.23607			−0.242413
$27$	4.61803	+	2.38197i	0.888741	+	0.458410i
$28$	−0.381966	+	2.61803i	−0.0721848	+	0.494762i
$29$		−	7.70820i		−	1.43138i	−0.698419	−	0.715689i	$-0.746113\pi$
$29$		−	7.70820i		−	1.43138i	0.698419	−	0.715689i	$-0.253887\pi$
$30$		0			0
$31$		−	2.76393i		−	0.496417i	−0.968707	−	0.248208i	$-0.920158\pi$
$31$		−	2.76393i		−	0.496417i	0.968707	−	0.248208i	$-0.0798418\pi$
$32$	1.00000			0.176777
$33$	−7.23607	+	2.76393i	−1.25964	+	0.481139i
$34$		−	5.23607i		−	0.897978i
$35$		0			0
$36$	−2.23607	+	2.00000i	−0.372678	+	0.333333i
$37$			0.763932i			0.125590i	0.998026	+	0.0627948i	$0.0200014\pi$
$37$			0.763932i			0.125590i	−0.998026	+	0.0627948i	$0.979999\pi$
$38$		−	8.47214i		−	1.37436i
$39$	0.763932	+	2.00000i	0.122327	+	0.320256i
$40$		0			0
$41$	2.47214			0.386083			0.193041	−	0.981191i	$-0.438165\pi$
$41$	2.47214			0.386083			0.193041	+	0.981191i	$0.438165\pi$
$42$	4.47214	−	1.00000i	0.690066	−	0.154303i
$43$			4.94427i			0.753994i	0.926214	+	0.376997i	$0.123043\pi$
$43$			4.94427i			0.753994i	−0.926214	+	0.376997i	$0.876957\pi$
$44$		−	4.47214i		−	0.674200i
$45$		0			0
$46$	4.00000			0.589768
$47$			6.47214i			0.944058i	0.881583	+	0.472029i	$0.156478\pi$
$47$			6.47214i			0.944058i	−0.881583	+	0.472029i	$0.843522\pi$
$48$	−0.618034	−	1.61803i	−0.0892055	−	0.233543i
$49$	−6.70820	−	2.00000i	−0.958315	−	0.285714i
$50$		0			0
$51$	−8.47214	+	3.23607i	−1.18634	+	0.453140i
$52$	−1.23607			−0.171412
$53$	−0.472136			−0.0648529			−0.0324264	−	0.999474i	$-0.510323\pi$
$53$	−0.472136			−0.0648529			−0.0324264	+	0.999474i	$0.510323\pi$
$54$	4.61803	+	2.38197i	0.628435	+	0.324145i
$55$		0			0
$56$	−0.381966	+	2.61803i	−0.0510424	+	0.349850i
$57$	−13.7082	+	5.23607i	−1.81570	+	0.693534i
$58$		−	7.70820i		−	1.01214i
$59$	4.47214			0.582223			0.291111	−	0.956689i	$-0.405975\pi$
$59$	4.47214			0.582223			0.291111	+	0.956689i	$0.405975\pi$
$60$		0			0
$61$			7.23607i			0.926484i	0.886232	+	0.463242i	$0.153314\pi$
$61$			7.23607i			0.926484i	−0.886232	+	0.463242i	$0.846686\pi$
$62$		−	2.76393i		−	0.351020i
$63$	−4.38197	−	6.61803i	−0.552076	−	0.833794i
$64$	1.00000			0.125000
$65$		0			0
$66$	−7.23607	+	2.76393i	−0.890698	+	0.340217i
$67$		−	12.0000i		−	1.46603i	−0.680211	−	0.733017i	$-0.738112\pi$
$67$		−	12.0000i		−	1.46603i	0.680211	−	0.733017i	$-0.261888\pi$
$68$		−	5.23607i		−	0.634967i
$69$	−2.47214	−	6.47214i	−0.297610	−	0.779154i
$70$		0			0
$71$			7.23607i			0.858763i	0.903123	+	0.429382i	$0.141268\pi$
$71$			7.23607i			0.858763i	−0.903123	+	0.429382i	$0.858732\pi$
$72$	−2.23607	+	2.00000i	−0.263523	+	0.235702i
$73$	−11.2361			−1.31508			−0.657541	−	0.753419i	$-0.728403\pi$
$73$	−11.2361			−1.31508			−0.657541	+	0.753419i	$0.728403\pi$
$74$			0.763932i			0.0888053i
$75$		0			0
$76$		−	8.47214i		−	0.971821i
$77$	11.7082	+	1.70820i	1.33427	+	0.194668i
$78$	0.763932	+	2.00000i	0.0864983	+	0.226455i
$79$	8.94427			1.00631			0.503155	−	0.864196i	$-0.332173\pi$
$79$	8.94427			1.00631			0.503155	+	0.864196i	$0.332173\pi$
$80$		0			0
$81$	1.00000	−	8.94427i	0.111111	−	0.993808i
$82$	2.47214			0.273002
$83$			14.6525i			1.60832i	0.594414	+	0.804159i	$0.297384\pi$
$83$			14.6525i			1.60832i	−0.594414	+	0.804159i	$0.702616\pi$
$84$	4.47214	−	1.00000i	0.487950	−	0.109109i
$85$		0			0
$86$			4.94427i			0.533155i
$87$	−12.4721	+	4.76393i	−1.33715	+	0.510747i
$88$		−	4.47214i		−	0.476731i
$89$	−5.52786			−0.585952			−0.292976	−	0.956120i	$-0.594646\pi$
$89$	−5.52786			−0.585952			−0.292976	+	0.956120i	$0.594646\pi$
$90$		0			0
$91$	0.472136	−	3.23607i	0.0494933	−	0.339232i
$92$	4.00000			0.417029
$93$	−4.47214	+	1.70820i	−0.463739	+	0.177132i
$94$			6.47214i			0.667550i
$95$		0			0
$96$	−0.618034	−	1.61803i	−0.0630778	−	0.165140i
$97$	−0.763932			−0.0775655			−0.0387828	−	0.999248i	$-0.512348\pi$
$97$	−0.763932			−0.0775655			−0.0387828	+	0.999248i	$0.512348\pi$
$98$	−6.70820	−	2.00000i	−0.677631	−	0.202031i
$99$	8.94427	+	10.0000i	0.898933	+	1.00504i
$100$		0			0
$101$	12.4721			1.24102			0.620512	−	0.784197i	$-0.286925\pi$
$101$	12.4721			1.24102			0.620512	+	0.784197i	$0.286925\pi$
$102$	−8.47214	+	3.23607i	−0.838866	+	0.320418i
$103$	−14.6525			−1.44375			−0.721876	−	0.692023i	$-0.756720\pi$
$103$	−14.6525			−1.44375			−0.721876	+	0.692023i	$0.756720\pi$
$104$	−1.23607			−0.121206
$105$		0			0
$106$	−0.472136			−0.0458579
$107$	11.4164			1.10367			0.551833	−	0.833955i	$-0.313929\pi$
$107$	11.4164			1.10367			0.551833	+	0.833955i	$0.313929\pi$
$108$	4.61803	+	2.38197i	0.444371	+	0.229205i
$109$	−4.47214			−0.428353			−0.214176	−	0.976795i	$-0.568707\pi$
$109$	−4.47214			−0.428353			−0.214176	+	0.976795i	$0.568707\pi$
$110$		0			0
$111$	1.23607	−	0.472136i	0.117322	−	0.0448132i
$112$	−0.381966	+	2.61803i	−0.0360924	+	0.247381i
$113$	2.94427			0.276974			0.138487	−	0.990364i	$-0.455776\pi$
$113$	2.94427			0.276974			0.138487	+	0.990364i	$0.455776\pi$
$114$	−13.7082	+	5.23607i	−1.28389	+	0.490403i
$115$		0			0
$116$		−	7.70820i		−	0.715689i
$117$	2.76393	−	2.47214i	0.255526	−	0.228549i
$118$	4.47214			0.411693
$119$	13.7082	+	2.00000i	1.25663	+	0.183340i
$120$		0			0
$121$	−9.00000			−0.818182
$122$			7.23607i			0.655123i
$123$	−1.52786	−	4.00000i	−0.137763	−	0.360668i
$124$		−	2.76393i		−	0.248208i
$125$		0			0
$126$	−4.38197	−	6.61803i	−0.390377	−	0.589581i
$127$		−	0.291796i		−	0.0258927i	−0.999916	−	0.0129464i	$-0.995879\pi$
$127$		−	0.291796i		−	0.0258927i	0.999916	−	0.0129464i	$-0.00412107\pi$
$128$	1.00000			0.0883883
$129$	8.00000	−	3.05573i	0.704361	−	0.269042i
$130$		0			0
$131$	−5.41641			−0.473234			−0.236617	−	0.971603i	$-0.576039\pi$
$131$	−5.41641			−0.473234			−0.236617	+	0.971603i	$0.576039\pi$
$132$	−7.23607	+	2.76393i	−0.629819	+	0.240569i
$133$	22.1803	+	3.23607i	1.92328	+	0.280603i
$134$		−	12.0000i		−	1.03664i
$135$		0			0
$136$		−	5.23607i		−	0.448989i
$137$	3.52786			0.301406			0.150703	−	0.988579i	$-0.451846\pi$
$137$	3.52786			0.301406			0.150703	+	0.988579i	$0.451846\pi$
$138$	−2.47214	−	6.47214i	−0.210442	−	0.550945i
$139$			11.5279i			0.977781i	0.872345	+	0.488890i	$0.162598\pi$
$139$			11.5279i			0.977781i	−0.872345	+	0.488890i	$0.837402\pi$
$140$		0			0
$141$	10.4721	−	4.00000i	0.881913	−	0.336861i
$142$			7.23607i			0.607237i
$143$			5.52786i			0.462263i
$144$	−2.23607	+	2.00000i	−0.186339	+	0.166667i
$145$		0			0
$146$	−11.2361			−0.929904
$147$	0.909830	+	12.0902i	0.0750415	+	0.997180i
$148$			0.763932i			0.0627948i
$149$		−	4.29180i		−	0.351598i	−0.984426	−	0.175799i	$-0.943749\pi$
$149$		−	4.29180i		−	0.351598i	0.984426	−	0.175799i	$-0.0562508\pi$
$150$		0			0
$151$	20.9443			1.70442			0.852210	−	0.523199i	$-0.175262\pi$
$151$	20.9443			1.70442			0.852210	+	0.523199i	$0.175262\pi$
$152$		−	8.47214i		−	0.687181i
$153$	10.4721	+	11.7082i	0.846622	+	0.946552i
$154$	11.7082	+	1.70820i	0.943474	+	0.137651i
$155$		0			0
$156$	0.763932	+	2.00000i	0.0611635	+	0.160128i
$157$	9.23607			0.737118			0.368559	−	0.929604i	$-0.379851\pi$
$157$	9.23607			0.737118			0.368559	+	0.929604i	$0.379851\pi$
$158$	8.94427			0.711568
$159$	0.291796	+	0.763932i	0.0231409	+	0.0605838i
$160$		0			0
$161$	−1.52786	+	10.4721i	−0.120413	+	0.825320i
$162$	1.00000	−	8.94427i	0.0785674	−	0.702728i
$163$			10.4721i			0.820241i	0.912031	+	0.410120i	$0.134513\pi$
$163$			10.4721i			0.820241i	−0.912031	+	0.410120i	$0.865487\pi$
$164$	2.47214			0.193041
$165$		0			0
$166$			14.6525i			1.13725i
$167$			0.944272i			0.0730700i	0.999332	+	0.0365350i	$0.0116320\pi$
$167$			0.944272i			0.0730700i	−0.999332	+	0.0365350i	$0.988368\pi$
$168$	4.47214	−	1.00000i	0.345033	−	0.0771517i
$169$	−11.4721			−0.882472
$170$		0			0
$171$	16.9443	+	18.9443i	1.29576	+	1.44870i
$172$			4.94427i			0.376997i
$173$		−	9.41641i		−	0.715916i	−0.933738	−	0.357958i	$-0.883473\pi$
$173$		−	9.41641i		−	0.715916i	0.933738	−	0.357958i	$-0.116527\pi$
$174$	−12.4721	+	4.76393i	−0.945510	+	0.361153i
$175$		0			0
$176$		−	4.47214i		−	0.337100i
$177$	−2.76393	−	7.23607i	−0.207750	−	0.543896i
$178$	−5.52786			−0.414331
$179$		−	14.9443i		−	1.11699i	−0.829509	−	0.558494i	$-0.811380\pi$
$179$		−	14.9443i		−	1.11699i	0.829509	−	0.558494i	$-0.188620\pi$
$180$		0			0
$181$		−	16.1803i		−	1.20268i	−0.798995	−	0.601338i	$-0.794635\pi$
$181$		−	16.1803i		−	1.20268i	0.798995	−	0.601338i	$-0.205365\pi$
$182$	0.472136	−	3.23607i	0.0349970	−	0.239873i
$183$	11.7082	−	4.47214i	0.865495	−	0.330590i
$184$	4.00000			0.294884
$185$		0			0
$186$	−4.47214	+	1.70820i	−0.327913	+	0.125252i
$187$	−23.4164			−1.71238
$188$			6.47214i			0.472029i
$189$	−8.00000	+	11.1803i	−0.581914	+	0.813250i
$190$		0			0
$191$		−	7.23607i		−	0.523584i	−0.965124	−	0.261792i	$-0.915687\pi$
$191$		−	7.23607i		−	0.523584i	0.965124	−	0.261792i	$-0.0843134\pi$
$192$	−0.618034	−	1.61803i	−0.0446028	−	0.116772i
$193$			6.00000i			0.431889i	0.976406	+	0.215945i	$0.0692831\pi$
$193$			6.00000i			0.431889i	−0.976406	+	0.215945i	$0.930717\pi$
$194$	−0.763932			−0.0548471
$195$		0			0
$196$	−6.70820	−	2.00000i	−0.479157	−	0.142857i
$197$	3.52786			0.251350			0.125675	−	0.992071i	$-0.459890\pi$
$197$	3.52786			0.251350			0.125675	+	0.992071i	$0.459890\pi$
$198$	8.94427	+	10.0000i	0.635642	+	0.710669i
$199$			22.1803i			1.57232i	0.618021	+	0.786161i	$0.287935\pi$
$199$			22.1803i			1.57232i	−0.618021	+	0.786161i	$0.712065\pi$
$200$		0			0
$201$	−19.4164	+	7.41641i	−1.36953	+	0.523113i
$202$	12.4721			0.877536
$203$	20.1803	+	2.94427i	1.41638	+	0.206647i
$204$	−8.47214	+	3.23607i	−0.593168	+	0.226570i
$205$		0			0
$206$	−14.6525			−1.02089
$207$	−8.94427	+	8.00000i	−0.621670	+	0.556038i
$208$	−1.23607			−0.0857059
$209$	−37.8885			−2.62081
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	−0.472136			−0.0324264
$213$	11.7082	−	4.47214i	0.802233	−	0.306426i
$214$	11.4164			0.780410
$215$		0			0
$216$	4.61803	+	2.38197i	0.314217	+	0.162072i
$217$	7.23607	+	1.05573i	0.491216	+	0.0716675i
$218$	−4.47214			−0.302891
$219$	6.94427	+	18.1803i	0.469250	+	1.22851i
$220$		0			0
$221$			6.47214i			0.435363i
$222$	1.23607	−	0.472136i	0.0829595	−	0.0316877i
$223$	17.7082			1.18583			0.592915	−	0.805265i	$-0.297977\pi$
$223$	17.7082			1.18583			0.592915	+	0.805265i	$0.297977\pi$
$224$	−0.381966	+	2.61803i	−0.0255212	+	0.174925i
$225$		0			0
$226$	2.94427			0.195850
$227$		−	0.763932i		−	0.0507039i	−0.999679	−	0.0253520i	$-0.991929\pi$
$227$		−	0.763932i		−	0.0507039i	0.999679	−	0.0253520i	$-0.00807065\pi$
$228$	−13.7082	+	5.23607i	−0.907848	+	0.346767i
$229$			8.76393i			0.579137i	0.957157	+	0.289568i	$0.0935118\pi$
$229$			8.76393i			0.579137i	−0.957157	+	0.289568i	$0.906488\pi$
$230$		0			0
$231$	−4.47214	−	20.0000i	−0.294245	−	1.31590i
$232$		−	7.70820i		−	0.506068i
$233$	−11.5279			−0.755215			−0.377608	−	0.925966i	$-0.623253\pi$
$233$	−11.5279			−0.755215			−0.377608	+	0.925966i	$0.623253\pi$
$234$	2.76393	−	2.47214i	0.180684	−	0.161609i
$235$		0			0
$236$	4.47214			0.291111
$237$	−5.52786	−	14.4721i	−0.359073	−	0.940066i
$238$	13.7082	+	2.00000i	0.888571	+	0.129641i
$239$			0.180340i			0.0116652i	0.999983	+	0.00583261i	$0.00185659\pi$
$239$			0.180340i			0.0116652i	−0.999983	+	0.00583261i	$0.998143\pi$
$240$		0			0
$241$			17.8885i			1.15230i	0.817343	+	0.576151i	$0.195446\pi$
$241$			17.8885i			1.15230i	−0.817343	+	0.576151i	$0.804554\pi$
$242$	−9.00000			−0.578542
$243$	−15.0902	+	3.90983i	−0.968035	+	0.250816i
$244$			7.23607i			0.463242i
$245$		0			0
$246$	−1.52786	−	4.00000i	−0.0974131	−	0.255031i
$247$			10.4721i			0.666326i
$248$		−	2.76393i		−	0.175510i
$249$	23.7082	−	9.05573i	1.50245	−	0.573883i
$250$		0			0
$251$	12.4721			0.787234			0.393617	−	0.919274i	$-0.371224\pi$
$251$	12.4721			0.787234			0.393617	+	0.919274i	$0.371224\pi$
$252$	−4.38197	−	6.61803i	−0.276038	−	0.416897i
$253$		−	17.8885i		−	1.12464i
$254$		−	0.291796i		−	0.0183089i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	14.1803i		−	0.884545i	−0.896881	−	0.442273i	$-0.854172\pi$
$257$		−	14.1803i		−	0.884545i	0.896881	−	0.442273i	$-0.145828\pi$
$258$	8.00000	−	3.05573i	0.498058	−	0.190241i
$259$	−2.00000	−	0.291796i	−0.124274	−	0.0181313i
$260$		0			0
$261$	15.4164	+	17.2361i	0.954252	+	1.06689i
$262$	−5.41641			−0.334627
$263$	12.9443			0.798178			0.399089	−	0.916912i	$-0.369326\pi$
$263$	12.9443			0.798178			0.399089	+	0.916912i	$0.369326\pi$
$264$	−7.23607	+	2.76393i	−0.445349	+	0.170108i
$265$		0			0
$266$	22.1803	+	3.23607i	1.35996	+	0.198416i
$267$	3.41641	+	8.94427i	0.209081	+	0.547381i
$268$		−	12.0000i		−	0.733017i
$269$	4.47214			0.272671			0.136335	−	0.990663i	$-0.456467\pi$
$269$	4.47214			0.272671			0.136335	+	0.990663i	$0.456467\pi$
$270$		0			0
$271$			31.7082i			1.92614i	0.269258	+	0.963068i	$0.413222\pi$
$271$			31.7082i			1.92614i	−0.269258	+	0.963068i	$0.586778\pi$
$272$		−	5.23607i		−	0.317483i
$273$	−5.52786	+	1.23607i	−0.334562	+	0.0748102i
$274$	3.52786			0.213126
$275$		0			0
$276$	−2.47214	−	6.47214i	−0.148805	−	0.389577i
$277$		−	17.1246i		−	1.02892i	−0.857515	−	0.514459i	$-0.827993\pi$
$277$		−	17.1246i		−	1.02892i	0.857515	−	0.514459i	$-0.172007\pi$
$278$			11.5279i			0.691395i
$279$	5.52786	+	6.18034i	0.330945	+	0.370007i
$280$		0			0
$281$		−	20.0000i		−	1.19310i	−0.802576	−	0.596550i	$-0.796538\pi$
$281$		−	20.0000i		−	1.19310i	0.802576	−	0.596550i	$-0.203462\pi$
$282$	10.4721	−	4.00000i	0.623607	−	0.238197i
$283$	13.2361			0.786803			0.393401	−	0.919367i	$-0.371298\pi$
$283$	13.2361			0.786803			0.393401	+	0.919367i	$0.371298\pi$
$284$			7.23607i			0.429382i
$285$		0			0
$286$			5.52786i			0.326869i
$287$	−0.944272	+	6.47214i	−0.0557386	+	0.382038i
$288$	−2.23607	+	2.00000i	−0.131762	+	0.117851i
$289$	−10.4164			−0.612730
$290$		0			0
$291$	0.472136	+	1.23607i	0.0276771	+	0.0724596i
$292$	−11.2361			−0.657541
$293$		−	2.58359i		−	0.150935i	−0.997148	−	0.0754675i	$-0.975955\pi$
$293$		−	2.58359i		−	0.150935i	0.997148	−	0.0754675i	$-0.0240449\pi$
$294$	0.909830	+	12.0902i	0.0530624	+	0.705113i
$295$		0			0
$296$			0.763932i			0.0444026i
$297$	10.6525	−	20.6525i	0.618119	−	1.19838i
$298$		−	4.29180i		−	0.248617i
$299$	−4.94427			−0.285935
$300$		0			0
$301$	−12.9443	−	1.88854i	−0.746095	−	0.108854i
$302$	20.9443			1.20521
$303$	−7.70820	−	20.1803i	−0.442825	−	1.15933i
$304$		−	8.47214i		−	0.485910i
$305$		0			0
$306$	10.4721	+	11.7082i	0.598652	+	0.669313i
$307$	18.1803			1.03761			0.518803	−	0.854894i	$-0.326378\pi$
$307$	18.1803			1.03761			0.518803	+	0.854894i	$0.326378\pi$
$308$	11.7082	+	1.70820i	0.667137	+	0.0973340i
$309$	9.05573	+	23.7082i	0.515162	+	1.34871i
$310$		0			0
$311$	−17.5279			−0.993914			−0.496957	−	0.867775i	$-0.665549\pi$
$311$	−17.5279			−0.993914			−0.496957	+	0.867775i	$0.665549\pi$
$312$	0.763932	+	2.00000i	0.0432491	+	0.113228i
$313$	−5.70820			−0.322647			−0.161323	−	0.986902i	$-0.551576\pi$
$313$	−5.70820			−0.322647			−0.161323	+	0.986902i	$0.551576\pi$
$314$	9.23607			0.521221
$315$		0			0
$316$	8.94427			0.503155
$317$	−10.9443			−0.614692			−0.307346	−	0.951598i	$-0.599441\pi$
$317$	−10.9443			−0.614692			−0.307346	+	0.951598i	$0.599441\pi$
$318$	0.291796	+	0.763932i	0.0163631	+	0.0428392i
$319$	−34.4721			−1.93007
$320$		0			0
$321$	−7.05573	−	18.4721i	−0.393812	−	1.03101i
$322$	−1.52786	+	10.4721i	−0.0851445	+	0.583589i
$323$	−44.3607			−2.46829
$324$	1.00000	−	8.94427i	0.0555556	−	0.496904i
$325$		0			0
$326$			10.4721i			0.579998i
$327$	2.76393	+	7.23607i	0.152846	+	0.400155i
$328$	2.47214			0.136501
$329$	−16.9443	−	2.47214i	−0.934168	−	0.136293i
$330$		0			0
$331$	3.05573			0.167958			0.0839790	−	0.996468i	$-0.473237\pi$
$331$	3.05573			0.167958			0.0839790	+	0.996468i	$0.473237\pi$
$332$			14.6525i			0.804159i
$333$	−1.52786	−	1.70820i	−0.0837264	−	0.0936090i
$334$			0.944272i			0.0516683i
$335$		0			0
$336$	4.47214	−	1.00000i	0.243975	−	0.0545545i
$337$			21.4164i			1.16663i	0.812247	+	0.583313i	$0.198244\pi$
$337$			21.4164i			1.16663i	−0.812247	+	0.583313i	$0.801756\pi$
$338$	−11.4721			−0.624002
$339$	−1.81966	−	4.76393i	−0.0988304	−	0.258741i
$340$		0			0
$341$	−12.3607			−0.669368
$342$	16.9443	+	18.9443i	0.916241	+	1.02439i
$343$	7.79837	−	16.7984i	0.421073	−	0.907027i
$344$			4.94427i			0.266577i
$345$		0			0
$346$		−	9.41641i		−	0.506229i
$347$	2.47214			0.132711			0.0663556	−	0.997796i	$-0.478863\pi$
$347$	2.47214			0.132711			0.0663556	+	0.997796i	$0.478863\pi$
$348$	−12.4721	+	4.76393i	−0.668577	+	0.255374i
$349$		−	20.1803i		−	1.08023i	−0.841592	−	0.540114i	$-0.818381\pi$
$349$		−	20.1803i		−	1.08023i	0.841592	−	0.540114i	$-0.181619\pi$
$350$		0			0
$351$	−5.70820	−	2.94427i	−0.304681	−	0.157154i
$352$		−	4.47214i		−	0.238366i
$353$		−	27.7082i		−	1.47476i	−0.675479	−	0.737379i	$-0.736063\pi$
$353$		−	27.7082i		−	1.47476i	0.675479	−	0.737379i	$-0.263937\pi$
$354$	−2.76393	−	7.23607i	−0.146901	−	0.384593i
$355$		0			0
$356$	−5.52786			−0.292976
$357$	−5.23607	−	23.4164i	−0.277122	−	1.23933i
$358$		−	14.9443i		−	0.789829i
$359$		−	12.1803i		−	0.642854i	−0.946934	−	0.321427i	$-0.895838\pi$
$359$		−	12.1803i		−	0.642854i	0.946934	−	0.321427i	$-0.104162\pi$
$360$		0			0
$361$	−52.7771			−2.77774
$362$		−	16.1803i		−	0.850420i
$363$	5.56231	+	14.5623i	0.291945	+	0.764323i
$364$	0.472136	−	3.23607i	0.0247466	−	0.169616i
$365$		0			0
$366$	11.7082	−	4.47214i	0.611998	−	0.233762i
$367$	8.18034			0.427010			0.213505	−	0.976942i	$-0.431512\pi$
$367$	8.18034			0.427010			0.213505	+	0.976942i	$0.431512\pi$
$368$	4.00000			0.208514
$369$	−5.52786	+	4.94427i	−0.287769	+	0.257389i
$370$		0			0
$371$	0.180340	−	1.23607i	0.00936278	−	0.0641735i
$372$	−4.47214	+	1.70820i	−0.231869	+	0.0885662i
$373$			32.1803i			1.66623i	0.553096	+	0.833117i	$0.313446\pi$
$373$			32.1803i			1.66623i	−0.553096	+	0.833117i	$0.686554\pi$
$374$	−23.4164			−1.21083
$375$		0			0
$376$			6.47214i			0.333775i
$377$			9.52786i			0.490710i
$378$	−8.00000	+	11.1803i	−0.411476	+	0.575055i
$379$	17.8885			0.918873			0.459436	−	0.888211i	$-0.348051\pi$
$379$	17.8885			0.918873			0.459436	+	0.888211i	$0.348051\pi$
$380$		0			0
$381$	−0.472136	+	0.180340i	−0.0241883	+	0.00923909i
$382$		−	7.23607i		−	0.370229i
$383$		−	13.8885i		−	0.709671i	−0.934929	−	0.354836i	$-0.884537\pi$
$383$		−	13.8885i		−	0.709671i	0.934929	−	0.354836i	$-0.115463\pi$
$384$	−0.618034	−	1.61803i	−0.0315389	−	0.0825700i
$385$		0			0
$386$			6.00000i			0.305392i
$387$	−9.88854	−	11.0557i	−0.502663	−	0.561994i
$388$	−0.763932			−0.0387828
$389$			30.1803i			1.53020i	0.643909	+	0.765102i	$0.277311\pi$
$389$			30.1803i			1.53020i	−0.643909	+	0.765102i	$0.722689\pi$
$390$		0			0
$391$		−	20.9443i		−	1.05920i
$392$	−6.70820	−	2.00000i	−0.338815	−	0.101015i
$393$	3.34752	+	8.76393i	0.168860	+	0.442082i
$394$	3.52786			0.177731
$395$		0			0
$396$	8.94427	+	10.0000i	0.449467	+	0.502519i
$397$	−23.1246			−1.16059			−0.580295	−	0.814406i	$-0.697063\pi$
$397$	−23.1246			−1.16059			−0.580295	+	0.814406i	$0.697063\pi$
$398$			22.1803i			1.11180i
$399$	−8.47214	−	37.8885i	−0.424137	−	1.89680i
$400$		0			0
$401$		−	14.4721i		−	0.722704i	−0.932429	−	0.361352i	$-0.882315\pi$
$401$		−	14.4721i		−	0.722704i	0.932429	−	0.361352i	$-0.117685\pi$
$402$	−19.4164	+	7.41641i	−0.968402	+	0.369897i
$403$			3.41641i			0.170183i
$404$	12.4721			0.620512
$405$		0			0
$406$	20.1803	+	2.94427i	1.00153	+	0.146122i
$407$	3.41641			0.169345
$408$	−8.47214	+	3.23607i	−0.419433	+	0.160209i
$409$		−	7.41641i		−	0.366718i	−0.983046	−	0.183359i	$-0.941303\pi$
$409$		−	7.41641i		−	0.366718i	0.983046	−	0.183359i	$-0.0586970\pi$
$410$		0			0
$411$	−2.18034	−	5.70820i	−0.107548	−	0.281565i
$412$	−14.6525			−0.721876
$413$	−1.70820	+	11.7082i	−0.0840552	+	0.576123i
$414$	−8.94427	+	8.00000i	−0.439587	+	0.393179i
$415$		0			0
$416$	−1.23607			−0.0606032
$417$	18.6525	−	7.12461i	0.913416	−	0.348894i
$418$	−37.8885			−1.85319
$419$	36.8328			1.79940			0.899700	−	0.436508i	$-0.143785\pi$
$419$	36.8328			1.79940			0.899700	+	0.436508i	$0.143785\pi$
$420$		0			0
$421$	−3.52786			−0.171938			−0.0859688	−	0.996298i	$-0.527399\pi$
$421$	−3.52786			−0.171938			−0.0859688	+	0.996298i	$0.527399\pi$
$422$	−8.00000			−0.389434
$423$	−12.9443	−	14.4721i	−0.629372	−	0.703659i
$424$	−0.472136			−0.0229289
$425$		0			0
$426$	11.7082	−	4.47214i	0.567264	−	0.216676i
$427$	−18.9443	−	2.76393i	−0.916778	−	0.133756i
$428$	11.4164			0.551833
$429$	8.94427	−	3.41641i	0.431834	−	0.164946i
$430$		0			0
$431$			39.5967i			1.90731i	0.300905	+	0.953654i	$0.402711\pi$
$431$			39.5967i			1.90731i	−0.300905	+	0.953654i	$0.597289\pi$
$432$	4.61803	+	2.38197i	0.222185	+	0.114602i
$433$	26.6525			1.28084			0.640418	−	0.768026i	$-0.278761\pi$
$433$	26.6525			1.28084			0.640418	+	0.768026i	$0.278761\pi$
$434$	7.23607	+	1.05573i	0.347342	+	0.0506766i
$435$		0			0
$436$	−4.47214			−0.214176
$437$		−	33.8885i		−	1.62111i
$438$	6.94427	+	18.1803i	0.331810	+	0.868690i
$439$		−	10.1803i		−	0.485881i	−0.970041	−	0.242941i	$-0.921888\pi$
$439$		−	10.1803i		−	0.485881i	0.970041	−	0.242941i	$-0.0781120\pi$
$440$		0			0
$441$	19.0000	−	8.94427i	0.904762	−	0.425918i
$442$			6.47214i			0.307848i
$443$	18.4721			0.877638			0.438819	−	0.898576i	$-0.355397\pi$
$443$	18.4721			0.877638			0.438819	+	0.898576i	$0.355397\pi$
$444$	1.23607	−	0.472136i	0.0586612	−	0.0224066i
$445$		0			0
$446$	17.7082			0.838508
$447$	−6.94427	+	2.65248i	−0.328453	+	0.125458i
$448$	−0.381966	+	2.61803i	−0.0180462	+	0.123690i
$449$		−	10.4721i		−	0.494211i	−0.968989	−	0.247105i	$-0.920521\pi$
$449$		−	10.4721i		−	0.494211i	0.968989	−	0.247105i	$-0.0794794\pi$
$450$		0			0
$451$		−	11.0557i		−	0.520594i
$452$	2.94427			0.138487
$453$	−12.9443	−	33.8885i	−0.608175	−	1.59222i
$454$		−	0.763932i		−	0.0358531i
$455$		0			0
$456$	−13.7082	+	5.23607i	−0.641945	+	0.245201i
$457$			26.9443i			1.26040i	0.776433	+	0.630200i	$0.217027\pi$
$457$			26.9443i			1.26040i	−0.776433	+	0.630200i	$0.782973\pi$
$458$			8.76393i			0.409512i
$459$	12.4721	−	24.1803i	0.582149	−	1.12864i
$460$		0			0
$461$	6.94427			0.323427			0.161713	−	0.986838i	$-0.448298\pi$
$461$	6.94427			0.323427			0.161713	+	0.986838i	$0.448298\pi$
$462$	−4.47214	−	20.0000i	−0.208063	−	0.930484i
$463$			22.1803i			1.03081i	0.856947	+	0.515404i	$0.172358\pi$
$463$			22.1803i			1.03081i	−0.856947	+	0.515404i	$0.827642\pi$
$464$		−	7.70820i		−	0.357844i
$465$		0			0
$466$	−11.5279			−0.534018
$467$			33.7082i			1.55983i	0.625886	+	0.779915i	$0.284738\pi$
$467$			33.7082i			1.55983i	−0.625886	+	0.779915i	$0.715262\pi$
$468$	2.76393	−	2.47214i	0.127763	−	0.114275i
$469$	31.4164	+	4.58359i	1.45067	+	0.211651i
$470$		0			0
$471$	−5.70820	−	14.9443i	−0.263020	−	0.688596i
$472$	4.47214			0.205847
$473$	22.1115			1.01669
$474$	−5.52786	−	14.4721i	−0.253903	−	0.664727i
$475$		0			0
$476$	13.7082	+	2.00000i	0.628314	+	0.0916698i
$477$	1.05573	−	0.944272i	0.0483385	−	0.0432352i
$478$			0.180340i			0.00824855i
$479$	37.8885			1.73117			0.865586	−	0.500761i	$-0.166946\pi$
$479$	37.8885			1.73117			0.865586	+	0.500761i	$0.166946\pi$
$480$		0			0
$481$		−	0.944272i		−	0.0430551i
$482$			17.8885i			0.814801i
$483$	17.8885	−	4.00000i	0.813957	−	0.182006i
$484$	−9.00000			−0.409091
$485$		0			0
$486$	−15.0902	+	3.90983i	−0.684504	+	0.177353i
$487$			17.5967i			0.797385i	0.917085	+	0.398692i	$0.130536\pi$
$487$			17.5967i			0.797385i	−0.917085	+	0.398692i	$0.869464\pi$
$488$			7.23607i			0.327561i
$489$	16.9443	−	6.47214i	0.766246	−	0.292680i
$490$		0			0
$491$		−	13.4164i		−	0.605474i	−0.953074	−	0.302737i	$-0.902100\pi$
$491$		−	13.4164i		−	0.605474i	0.953074	−	0.302737i	$-0.0979004\pi$
$492$	−1.52786	−	4.00000i	−0.0688814	−	0.180334i
$493$	−40.3607			−1.81775
$494$			10.4721i			0.471164i
$495$		0			0
$496$		−	2.76393i		−	0.124104i
$497$	−18.9443	−	2.76393i	−0.849767	−	0.123979i
$498$	23.7082	−	9.05573i	1.06239	−	0.405797i
$499$	−17.8885			−0.800801			−0.400401	−	0.916340i	$-0.631129\pi$
$499$	−17.8885			−0.800801			−0.400401	+	0.916340i	$0.631129\pi$
$500$		0			0
$501$	1.52786	−	0.583592i	0.0682599	−	0.0260730i
$502$	12.4721			0.556659
$503$		−	28.3607i		−	1.26454i	−0.774748	−	0.632270i	$-0.782123\pi$
$503$		−	28.3607i		−	1.26454i	0.774748	−	0.632270i	$-0.217877\pi$
$504$	−4.38197	−	6.61803i	−0.195188	−	0.294791i
$505$		0			0
$506$		−	17.8885i		−	0.795243i
$507$	7.09017	+	18.5623i	0.314886	+	0.824381i
$508$		−	0.291796i		−	0.0129464i
$509$	15.5279			0.688260			0.344130	−	0.938922i	$-0.388174\pi$
$509$	15.5279			0.688260			0.344130	+	0.938922i	$0.388174\pi$
$510$		0			0
$511$	4.29180	−	29.4164i	0.189858	−	1.30131i
$512$	1.00000			0.0441942
$513$	20.1803	−	39.1246i	0.890984	−	1.72739i
$514$		−	14.1803i		−	0.625468i
$515$		0			0
$516$	8.00000	−	3.05573i	0.352180	−	0.134521i
$517$	28.9443			1.27297
$518$	−2.00000	−	0.291796i	−0.0878750	−	0.0128208i
$519$	−15.2361	+	5.81966i	−0.668789	+	0.255455i
$520$		0			0
$521$	36.9443			1.61856			0.809279	−	0.587425i	$-0.199858\pi$
$521$	36.9443			1.61856			0.809279	+	0.587425i	$0.199858\pi$
$522$	15.4164	+	17.2361i	0.674758	+	0.754402i
$523$	−42.5410			−1.86019			−0.930094	−	0.367320i	$-0.880275\pi$
$523$	−42.5410			−1.86019			−0.930094	+	0.367320i	$0.880275\pi$
$524$	−5.41641			−0.236617
$525$		0			0
$526$	12.9443			0.564397
$527$	−14.4721			−0.630416
$528$	−7.23607	+	2.76393i	−0.314909	+	0.120285i
$529$	−7.00000			−0.304348
$530$		0			0
$531$	−10.0000	+	8.94427i	−0.433963	+	0.388148i
$532$	22.1803	+	3.23607i	0.961640	+	0.140301i
$533$	−3.05573			−0.132358
$534$	3.41641	+	8.94427i	0.147842	+	0.387056i
$535$		0			0
$536$		−	12.0000i		−	0.518321i
$537$	−24.1803	+	9.23607i	−1.04346	+	0.398566i
$538$	4.47214			0.192807
$539$	−8.94427	+	30.0000i	−0.385257	+	1.29219i
$540$		0			0
$541$	30.9443			1.33040			0.665199	−	0.746666i	$-0.268347\pi$
$541$	30.9443			1.33040			0.665199	+	0.746666i	$0.268347\pi$
$542$			31.7082i			1.36198i
$543$	−26.1803	+	10.0000i	−1.12351	+	0.429141i
$544$		−	5.23607i		−	0.224495i
$545$		0			0
$546$	−5.52786	+	1.23607i	−0.236571	+	0.0528988i
$547$		−	35.4164i		−	1.51430i	−0.653243	−	0.757148i	$-0.726592\pi$
$547$		−	35.4164i		−	1.51430i	0.653243	−	0.757148i	$-0.273408\pi$
$548$	3.52786			0.150703
$549$	−14.4721	−	16.1803i	−0.617656	−	0.690560i
$550$		0			0
$551$	−65.3050			−2.78208
$552$	−2.47214	−	6.47214i	−0.105221	−	0.275472i
$553$	−3.41641	+	23.4164i	−0.145280	+	0.995767i
$554$		−	17.1246i		−	0.727555i
$555$		0			0
$556$			11.5279i			0.488890i
$557$	−7.52786			−0.318966			−0.159483	−	0.987201i	$-0.550983\pi$
$557$	−7.52786			−0.318966			−0.159483	+	0.987201i	$0.550983\pi$
$558$	5.52786	+	6.18034i	0.234013	+	0.261635i
$559$		−	6.11146i		−	0.258487i
$560$		0			0
$561$	14.4721	+	37.8885i	0.611014	+	1.59966i
$562$		−	20.0000i		−	0.843649i
$563$			40.1803i			1.69340i	0.532071	+	0.846700i	$0.321414\pi$
$563$			40.1803i			1.69340i	−0.532071	+	0.846700i	$0.678586\pi$
$564$	10.4721	−	4.00000i	0.440956	−	0.168430i
$565$		0			0
$566$	13.2361			0.556353
$567$	23.0344	+	6.03444i	0.967356	+	0.253423i
$568$			7.23607i			0.303619i
$569$			9.52786i			0.399429i	0.979854	+	0.199714i	$0.0640014\pi$
$569$			9.52786i			0.399429i	−0.979854	+	0.199714i	$0.935999\pi$
$570$		0			0
$571$	18.8328			0.788129			0.394064	−	0.919083i	$-0.371069\pi$
$571$	18.8328			0.788129			0.394064	+	0.919083i	$0.371069\pi$
$572$			5.52786i			0.231132i
$573$	−11.7082	+	4.47214i	−0.489117	+	0.186826i
$574$	−0.944272	+	6.47214i	−0.0394131	+	0.270142i
$575$		0			0
$576$	−2.23607	+	2.00000i	−0.0931695	+	0.0833333i
$577$	8.18034			0.340552			0.170276	−	0.985396i	$-0.445534\pi$
$577$	8.18034			0.340552			0.170276	+	0.985396i	$0.445534\pi$
$578$	−10.4164			−0.433265
$579$	9.70820	−	3.70820i	0.403459	−	0.154108i
$580$		0			0
$581$	−38.3607	−	5.59675i	−1.59147	−	0.232192i
$582$	0.472136	+	1.23607i	0.0195707	+	0.0512367i
$583$			2.11146i			0.0874476i
$584$	−11.2361			−0.464952
$585$		0			0
$586$		−	2.58359i		−	0.106727i
$587$			10.2918i			0.424788i	0.977184	+	0.212394i	$0.0681260\pi$
$587$			10.2918i			0.424788i	−0.977184	+	0.212394i	$0.931874\pi$
$588$	0.909830	+	12.0902i	0.0375208	+	0.498590i
$589$	−23.4164			−0.964856
$590$		0			0
$591$	−2.18034	−	5.70820i	−0.0896872	−	0.234804i
$592$			0.763932i			0.0313974i
$593$		−	29.0132i		−	1.19143i	−0.803197	−	0.595714i	$-0.796869\pi$
$593$		−	29.0132i		−	1.19143i	0.803197	−	0.595714i	$-0.203131\pi$
$594$	10.6525	−	20.6525i	0.437076	−	0.847381i
$595$		0			0
$596$		−	4.29180i		−	0.175799i
$597$	35.8885	−	13.7082i	1.46882	−	0.561039i
$598$	−4.94427			−0.202186
$599$			36.7639i			1.50213i	0.660226	+	0.751067i	$0.270460\pi$
$599$			36.7639i			1.50213i	−0.660226	+	0.751067i	$0.729540\pi$
$600$		0			0
$601$			5.52786i			0.225486i	0.993624	+	0.112743i	$0.0359637\pi$
$601$			5.52786i			0.225486i	−0.993624	+	0.112743i	$0.964036\pi$
$602$	−12.9443	−	1.88854i	−0.527569	−	0.0769713i
$603$	24.0000	+	26.8328i	0.977356	+	1.09272i
$604$	20.9443			0.852210
$605$		0			0
$606$	−7.70820	−	20.1803i	−0.313124	−	0.819770i
$607$	19.2361			0.780768			0.390384	−	0.920652i	$-0.372342\pi$
$607$	19.2361			0.780768			0.390384	+	0.920652i	$0.372342\pi$
$608$		−	8.47214i		−	0.343590i
$609$	−7.70820	−	34.4721i	−0.312352	−	1.39688i
$610$		0			0
$611$		−	8.00000i		−	0.323645i
$612$	10.4721	+	11.7082i	0.423311	+	0.473276i
$613$		−	38.0689i		−	1.53759i	−0.639497	−	0.768794i	$-0.720857\pi$
$613$		−	38.0689i		−	1.53759i	0.639497	−	0.768794i	$-0.279143\pi$
$614$	18.1803			0.733699
$615$		0			0
$616$	11.7082	+	1.70820i	0.471737	+	0.0688255i
$617$	−2.00000			−0.0805170			−0.0402585	−	0.999189i	$-0.512818\pi$
$617$	−2.00000			−0.0805170			−0.0402585	+	0.999189i	$0.512818\pi$
$618$	9.05573	+	23.7082i	0.364275	+	0.953684i
$619$		−	14.0000i		−	0.562708i	−0.959604	−	0.281354i	$-0.909217\pi$
$619$		−	14.0000i		−	0.562708i	0.959604	−	0.281354i	$-0.0907834\pi$
$620$		0			0
$621$	18.4721	+	9.52786i	0.741261	+	0.382340i
$622$	−17.5279			−0.702803
$623$	2.11146	−	14.4721i	0.0845937	−	0.579814i
$624$	0.763932	+	2.00000i	0.0305818	+	0.0800641i
$625$		0			0
$626$	−5.70820			−0.228146
$627$	23.4164	+	61.3050i	0.935161	+	2.44828i
$628$	9.23607			0.368559
$629$	4.00000			0.159490
$630$		0			0
$631$	−5.88854			−0.234419			−0.117210	−	0.993107i	$-0.537395\pi$
$631$	−5.88854			−0.234419			−0.117210	+	0.993107i	$0.537395\pi$
$632$	8.94427			0.355784
$633$	4.94427	+	12.9443i	0.196517	+	0.514489i
$634$	−10.9443			−0.434653
$635$		0			0
$636$	0.291796	+	0.763932i	0.0115705	+	0.0302919i
$637$	8.29180	+	2.47214i	0.328533	+	0.0979496i
$638$	−34.4721			−1.36476
$639$	−14.4721	−	16.1803i	−0.572509	−	0.640084i
$640$		0			0
$641$		−	23.4164i		−	0.924893i	−0.886647	−	0.462446i	$-0.846972\pi$
$641$		−	23.4164i		−	0.924893i	0.886647	−	0.462446i	$-0.153028\pi$
$642$	−7.05573	−	18.4721i	−0.278467	−	0.729037i
$643$	−12.2918			−0.484741			−0.242371	−	0.970184i	$-0.577925\pi$
$643$	−12.2918			−0.484741			−0.242371	+	0.970184i	$0.577925\pi$
$644$	−1.52786	+	10.4721i	−0.0602063	+	0.412660i
$645$		0			0
$646$	−44.3607			−1.74535
$647$		−	34.8328i		−	1.36942i	−0.728816	−	0.684710i	$-0.759929\pi$
$647$		−	34.8328i		−	1.36942i	0.728816	−	0.684710i	$-0.240071\pi$
$648$	1.00000	−	8.94427i	0.0392837	−	0.351364i
$649$		−	20.0000i		−	0.785069i
$650$		0			0
$651$	−2.76393	−	12.3607i	−0.108327	−	0.484453i
$652$			10.4721i			0.410120i
$653$	−23.8885			−0.934831			−0.467415	−	0.884038i	$-0.654815\pi$
$653$	−23.8885			−0.934831			−0.467415	+	0.884038i	$0.654815\pi$
$654$	2.76393	+	7.23607i	0.108078	+	0.282953i
$655$		0			0
$656$	2.47214			0.0965207
$657$	25.1246	−	22.4721i	0.980204	−	0.876722i
$658$	−16.9443	−	2.47214i	−0.660556	−	0.0963739i
$659$		−	31.5279i		−	1.22815i	−0.789247	−	0.614076i	$-0.789529\pi$
$659$		−	31.5279i		−	1.22815i	0.789247	−	0.614076i	$-0.210471\pi$
$660$		0			0
$661$			18.2918i			0.711468i	0.934587	+	0.355734i	$0.115769\pi$
$661$			18.2918i			0.711468i	−0.934587	+	0.355734i	$0.884231\pi$
$662$	3.05573			0.118764
$663$	10.4721	−	4.00000i	0.406704	−	0.155347i
$664$			14.6525i			0.568626i
$665$		0			0
$666$	−1.52786	−	1.70820i	−0.0592035	−	0.0661916i
$667$		−	30.8328i		−	1.19385i
$668$			0.944272i			0.0365350i
$669$	−10.9443	−	28.6525i	−0.423130	−	1.10777i
$670$		0			0
$671$	32.3607			1.24927
$672$	4.47214	−	1.00000i	0.172516	−	0.0385758i
$673$		−	19.5279i		−	0.752744i	−0.926469	−	0.376372i	$-0.877171\pi$
$673$		−	19.5279i		−	0.752744i	0.926469	−	0.376372i	$-0.122829\pi$
$674$			21.4164i			0.824929i
$675$		0			0
$676$	−11.4721			−0.441236
$677$		−	18.0000i		−	0.691796i	−0.938272	−	0.345898i	$-0.887574\pi$
$677$		−	18.0000i		−	0.691796i	0.938272	−	0.345898i	$-0.112426\pi$
$678$	−1.81966	−	4.76393i	−0.0698836	−	0.182958i
$679$	0.291796	−	2.00000i	0.0111981	−	0.0767530i
$680$		0			0
$681$	−1.23607	+	0.472136i	−0.0473662	+	0.0180923i
$682$	−12.3607			−0.473315
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$	16.9443	+	18.9443i	0.647880	+	0.724352i
$685$		0			0
$686$	7.79837	−	16.7984i	0.297743	−	0.641365i
$687$	14.1803	−	5.41641i	0.541014	−	0.206649i
$688$			4.94427i			0.188499i
$689$	0.583592			0.0222331
$690$		0			0
$691$		−	21.0557i		−	0.800998i	−0.916297	−	0.400499i	$-0.868837\pi$
$691$		−	21.0557i		−	0.800998i	0.916297	−	0.400499i	$-0.131163\pi$
$692$		−	9.41641i		−	0.357958i
$693$	−29.5967	+	19.5967i	−1.12429	+	0.744419i
$694$	2.47214			0.0938410
$695$		0			0
$696$	−12.4721	+	4.76393i	−0.472755	+	0.180576i
$697$		−	12.9443i		−	0.490299i
$698$		−	20.1803i		−	0.763837i
$699$	7.12461	+	18.6525i	0.269478	+	0.705501i
$700$		0			0
$701$			44.0689i			1.66446i	0.554431	+	0.832229i	$0.312936\pi$
$701$			44.0689i			1.66446i	−0.554431	+	0.832229i	$0.687064\pi$
$702$	−5.70820	−	2.94427i	−0.215442	−	0.111124i
$703$	6.47214			0.244101
$704$		−	4.47214i		−	0.168550i
$705$		0			0
$706$		−	27.7082i		−	1.04281i
$707$	−4.76393	+	32.6525i	−0.179166	+	1.22802i
$708$	−2.76393	−	7.23607i	−0.103875	−	0.271948i
$709$	15.5279			0.583161			0.291581	−	0.956546i	$-0.405819\pi$
$709$	15.5279			0.583161			0.291581	+	0.956546i	$0.405819\pi$
$710$		0			0
$711$	−20.0000	+	17.8885i	−0.750059	+	0.670873i
$712$	−5.52786			−0.207165
$713$		−	11.0557i		−	0.414040i
$714$	−5.23607	−	23.4164i	−0.195955	−	0.876337i
$715$		0			0
$716$		−	14.9443i		−	0.558494i
$717$	0.291796	−	0.111456i	0.0108973	−	0.00416241i
$718$		−	12.1803i		−	0.454566i
$719$	−34.4721			−1.28559			−0.642797	−	0.766037i	$-0.722226\pi$
$719$	−34.4721			−1.28559			−0.642797	+	0.766037i	$0.722226\pi$
$720$		0			0
$721$	5.59675	−	38.3607i	0.208434	−	1.42863i
$722$	−52.7771			−1.96416
$723$	28.9443	−	11.0557i	1.07645	−	0.411167i
$724$		−	16.1803i		−	0.601338i
$725$		0			0
$726$	5.56231	+	14.5623i	0.206437	+	0.540458i
$727$	−26.2918			−0.975109			−0.487554	−	0.873093i	$-0.662111\pi$
$727$	−26.2918			−0.975109			−0.487554	+	0.873093i	$0.662111\pi$
$728$	0.472136	−	3.23607i	0.0174985	−	0.119937i
$729$	15.6525	+	22.0000i	0.579721	+	0.814815i
$730$		0			0
$731$	25.8885			0.957522
$732$	11.7082	−	4.47214i	0.432748	−	0.165295i
$733$	20.0689			0.741261			0.370631	−	0.928780i	$-0.379142\pi$
$733$	20.0689			0.741261			0.370631	+	0.928780i	$0.379142\pi$
$734$	8.18034			0.301942
$735$		0			0
$736$	4.00000			0.147442
$737$	−53.6656			−1.97680
$738$	−5.52786	+	4.94427i	−0.203483	+	0.182001i
$739$	−8.94427			−0.329020			−0.164510	−	0.986375i	$-0.552604\pi$
$739$	−8.94427			−0.329020			−0.164510	+	0.986375i	$0.552604\pi$
$740$		0			0
$741$	16.9443	−	6.47214i	0.622463	−	0.237760i
$742$	0.180340	−	1.23607i	0.00662049	−	0.0453775i
$743$	−10.4721			−0.384185			−0.192093	−	0.981377i	$-0.561527\pi$
$743$	−10.4721			−0.384185			−0.192093	+	0.981377i	$0.561527\pi$
$744$	−4.47214	+	1.70820i	−0.163956	+	0.0626258i
$745$		0			0
$746$			32.1803i			1.17821i
$747$	−29.3050	−	32.7639i	−1.07221	−	1.19877i
$748$	−23.4164			−0.856189
$749$	−4.36068	+	29.8885i	−0.159336	+	1.09210i
$750$		0			0
$751$	8.58359			0.313220			0.156610	−	0.987661i	$-0.449943\pi$
$751$	8.58359			0.313220			0.156610	+	0.987661i	$0.449943\pi$
$752$			6.47214i			0.236015i
$753$	−7.70820	−	20.1803i	−0.280903	−	0.735412i
$754$			9.52786i			0.346984i
$755$		0			0
$756$	−8.00000	+	11.1803i	−0.290957	+	0.406625i
$757$		−	2.65248i		−	0.0964059i	−0.998838	−	0.0482029i	$-0.984651\pi$
$757$		−	2.65248i		−	0.0964059i	0.998838	−	0.0482029i	$-0.0153494\pi$
$758$	17.8885			0.649741
$759$	−28.9443	+	11.0557i	−1.05061	+	0.401298i
$760$		0			0
$761$	5.88854			0.213460			0.106730	−	0.994288i	$-0.465962\pi$
$761$	5.88854			0.213460			0.106730	+	0.994288i	$0.465962\pi$
$762$	−0.472136	+	0.180340i	−0.0171037	+	0.00653302i
$763$	1.70820	−	11.7082i	0.0618411	−	0.423865i
$764$		−	7.23607i		−	0.261792i
$765$		0			0
$766$		−	13.8885i		−	0.501813i
$767$	−5.52786			−0.199600
$768$	−0.618034	−	1.61803i	−0.0223014	−	0.0583858i
$769$			36.0000i			1.29819i	0.760706	+	0.649097i	$0.224853\pi$
$769$			36.0000i			1.29819i	−0.760706	+	0.649097i	$0.775147\pi$
$770$		0			0
$771$	−22.9443	+	8.76393i	−0.826318	+	0.315625i
$772$			6.00000i			0.215945i
$773$			10.5836i			0.380665i	0.981720	+	0.190333i	$0.0609567\pi$
$773$			10.5836i			0.380665i	−0.981720	+	0.190333i	$0.939043\pi$
$774$	−9.88854	−	11.0557i	−0.355436	−	0.397390i
$775$		0			0
$776$	−0.763932			−0.0274236
$777$	0.763932	+	3.41641i	0.0274059	+	0.122563i
$778$			30.1803i			1.08202i
$779$		−	20.9443i		−	0.750406i
$780$		0			0
$781$	32.3607			1.15796
$782$		−	20.9443i		−	0.748966i
$783$	18.3607	−	35.5967i	0.656157	−	1.27212i
$784$	−6.70820	−	2.00000i	−0.239579	−	0.0714286i
$785$		0			0
$786$	3.34752	+	8.76393i	0.119402	+	0.312599i
$787$	−36.2918			−1.29366			−0.646831	−	0.762633i	$-0.723906\pi$
$787$	−36.2918			−1.29366			−0.646831	+	0.762633i	$0.723906\pi$
$788$	3.52786			0.125675
$789$	−8.00000	−	20.9443i	−0.284808	−	0.745636i
$790$		0			0
$791$	−1.12461	+	7.70820i	−0.0399866	+	0.274072i
$792$	8.94427	+	10.0000i	0.317821	+	0.355335i
$793$		−	8.94427i		−	0.317620i
$794$	−23.1246			−0.820662
$795$		0			0
$796$			22.1803i			0.786161i
$797$		−	21.4164i		−	0.758608i	−0.925272	−	0.379304i	$-0.876163\pi$
$797$		−	21.4164i		−	0.758608i	0.925272	−	0.379304i	$-0.123837\pi$
$798$	−8.47214	−	37.8885i	−0.299910	−	1.34124i
$799$	33.8885			1.19889
$800$		0			0
$801$	12.3607	−	11.0557i	0.436743	−	0.390635i
$802$		−	14.4721i		−	0.511029i
$803$			50.2492i			1.77326i
$804$	−19.4164	+	7.41641i	−0.684764	+	0.261557i
$805$		0			0
$806$			3.41641i			0.120338i
$807$	−2.76393	−	7.23607i	−0.0972950	−	0.254722i
$808$	12.4721			0.438768
$809$			36.3607i			1.27837i	0.769052	+	0.639187i	$0.220729\pi$
$809$			36.3607i			1.27837i	−0.769052	+	0.639187i	$0.779271\pi$
$810$		0			0
$811$			36.8328i			1.29338i	0.762755	+	0.646688i	$0.223846\pi$
$811$			36.8328i			1.29338i	−0.762755	+	0.646688i	$0.776154\pi$
$812$	20.1803	+	2.94427i	0.708191	+	0.103324i
$813$	51.3050	−	19.5967i	1.79934	−	0.687288i
$814$	3.41641			0.119745
$815$		0			0
$816$	−8.47214	+	3.23607i	−0.296584	+	0.113285i
$817$	41.8885			1.46549
$818$		−	7.41641i		−	0.259309i
$819$	5.41641	+	8.18034i	0.189265	+	0.285844i
$820$		0			0
$821$			31.7082i			1.10662i	0.832974	+	0.553312i	$0.186636\pi$
$821$			31.7082i			1.10662i	−0.832974	+	0.553312i	$0.813364\pi$
$822$	−2.18034	−	5.70820i	−0.0760481	−	0.199096i
$823$			22.1803i			0.773158i	0.922256	+	0.386579i	$0.126343\pi$
$823$			22.1803i			0.773158i	−0.922256	+	0.386579i	$0.873657\pi$
$824$	−14.6525			−0.510443
$825$		0			0
$826$	−1.70820	+	11.7082i	−0.0594360	+	0.407381i
$827$	−38.8328			−1.35035			−0.675175	−	0.737658i	$-0.735932\pi$
$827$	−38.8328			−1.35035			−0.675175	+	0.737658i	$0.735932\pi$
$828$	−8.94427	+	8.00000i	−0.310835	+	0.278019i
$829$		−	7.81966i		−	0.271588i	−0.990737	−	0.135794i	$-0.956641\pi$
$829$		−	7.81966i		−	0.271588i	0.990737	−	0.135794i	$-0.0433585\pi$
$830$		0			0
$831$	−27.7082	+	10.5836i	−0.961187	+	0.367141i
$832$	−1.23607			−0.0428529
$833$	−10.4721	+	35.1246i	−0.362838	+	1.21700i
$834$	18.6525	−	7.12461i	0.645882	−	0.246705i
$835$		0			0
$836$	−37.8885			−1.31040
$837$	6.58359	−	12.7639i	0.227562	−	0.441186i
$838$	36.8328			1.27237
$839$	5.52786			0.190843			0.0954215	−	0.995437i	$-0.469580\pi$
$839$	5.52786			0.190843			0.0954215	+	0.995437i	$0.469580\pi$
$840$		0			0
$841$	−30.4164			−1.04884
$842$	−3.52786			−0.121578
$843$	−32.3607	+	12.3607i	−1.11456	+	0.425724i
$844$	−8.00000			−0.275371
$845$		0			0
$846$	−12.9443	−	14.4721i	−0.445033	−	0.497562i
$847$	3.43769	−	23.5623i	0.118121	−	0.809610i
$848$	−0.472136			−0.0162132
$849$	−8.18034	−	21.4164i	−0.280749	−	0.735009i
$850$		0			0
$851$			3.05573i			0.104749i
$852$	11.7082	−	4.47214i	0.401116	−	0.153213i
$853$	7.70820			0.263924			0.131962	−	0.991255i	$-0.457872\pi$
$853$	7.70820			0.263924			0.131962	+	0.991255i	$0.457872\pi$
$854$	−18.9443	−	2.76393i	−0.648260	−	0.0945798i
$855$		0			0
$856$	11.4164			0.390205
$857$			11.3475i			0.387624i	0.981039	+	0.193812i	$0.0620852\pi$
$857$			11.3475i			0.387624i	−0.981039	+	0.193812i	$0.937915\pi$
$858$	8.94427	−	3.41641i	0.305352	−	0.116634i
$859$			17.0557i			0.581934i	0.956733	+	0.290967i	$0.0939770\pi$
$859$			17.0557i			0.581934i	−0.956733	+	0.290967i	$0.906023\pi$
$860$		0			0
$861$	11.0557	−	2.47214i	0.376778	−	0.0842502i
$862$			39.5967i			1.34867i
$863$	−30.4721			−1.03728			−0.518642	−	0.854992i	$-0.673562\pi$
$863$	−30.4721			−1.03728			−0.518642	+	0.854992i	$0.673562\pi$
$864$	4.61803	+	2.38197i	0.157109	+	0.0810361i
$865$		0			0
$866$	26.6525			0.905688
$867$	6.43769	+	16.8541i	0.218636	+	0.572395i
$868$	7.23607	+	1.05573i	0.245608	+	0.0358337i
$869$		−	40.0000i		−	1.35691i
$870$		0			0
$871$			14.8328i			0.502591i
$872$	−4.47214			−0.151446
$873$	1.70820	−	1.52786i	0.0578139	−	0.0517104i
$874$		−	33.8885i		−	1.14630i
$875$		0			0
$876$	6.94427	+	18.1803i	0.234625	+	0.614257i
$877$			38.6525i			1.30520i	0.757702	+	0.652601i	$0.226322\pi$
$877$			38.6525i			1.30520i	−0.757702	+	0.652601i	$0.773678\pi$
$878$		−	10.1803i		−	0.343570i
$879$	−4.18034	+	1.59675i	−0.140999	+	0.0538570i
$880$		0			0
$881$	−15.4164			−0.519392			−0.259696	−	0.965690i	$-0.583622\pi$
$881$	−15.4164			−0.519392			−0.259696	+	0.965690i	$0.583622\pi$
$882$	19.0000	−	8.94427i	0.639763	−	0.301169i
$883$			13.8885i			0.467387i	0.972310	+	0.233693i	$0.0750812\pi$
$883$			13.8885i			0.467387i	−0.972310	+	0.233693i	$0.924919\pi$
$884$			6.47214i			0.217681i
$885$		0			0
$886$	18.4721			0.620584
$887$			17.5279i			0.588528i	0.955724	+	0.294264i	$0.0950745\pi$
$887$			17.5279i			0.588528i	−0.955724	+	0.294264i	$0.904925\pi$
$888$	1.23607	−	0.472136i	0.0414797	−	0.0158438i
$889$	0.763932	+	0.111456i	0.0256215	+	0.00373812i
$890$		0			0
$891$	−40.0000	−	4.47214i	−1.34005	−	0.149822i
$892$	17.7082			0.592915
$893$	54.8328			1.83491
$894$	−6.94427	+	2.65248i	−0.232251	+	0.0887121i
$895$		0			0
$896$	−0.381966	+	2.61803i	−0.0127606	+	0.0874624i
$897$	3.05573	+	8.00000i	0.102028	+	0.267112i
$898$		−	10.4721i		−	0.349460i
$899$	−21.3050			−0.710560
$900$		0			0
$901$			2.47214i			0.0823588i
$902$		−	11.0557i		−	0.368115i
$903$	4.94427	+	22.1115i	0.164535	+	0.735823i
$904$	2.94427			0.0979250
$905$		0			0
$906$	−12.9443	−	33.8885i	−0.430045	−	1.12587i
$907$		−	17.5279i		−	0.582003i	−0.956723	−	0.291002i	$-0.906012\pi$
$907$		−	17.5279i		−	0.582003i	0.956723	−	0.291002i	$-0.0939885\pi$
$908$		−	0.763932i		−	0.0253520i
$909$	−27.8885	+	24.9443i	−0.925005	+	0.827349i
$910$		0			0
$911$		−	50.6525i		−	1.67819i	−0.543984	−	0.839096i	$-0.683085\pi$
$911$		−	50.6525i		−	1.67819i	0.543984	−	0.839096i	$-0.316915\pi$
$912$	−13.7082	+	5.23607i	−0.453924	+	0.173384i
$913$	65.5279			2.16866
$914$			26.9443i			0.891237i
$915$		0			0
$916$			8.76393i			0.289568i
$917$	2.06888	−	14.1803i	0.0683206	−	0.468276i
$918$	12.4721	−	24.1803i	0.411642	−	0.798070i
$919$	44.7214			1.47522			0.737611	−	0.675226i	$-0.235954\pi$
$919$	44.7214			1.47522			0.737611	+	0.675226i	$0.235954\pi$
$920$		0			0
$921$	−11.2361	−	29.4164i	−0.370241	−	0.969304i
$922$	6.94427			0.228697
$923$		−	8.94427i		−	0.294404i
$924$	−4.47214	−	20.0000i	−0.147122	−	0.657952i
$925$		0			0
$926$			22.1803i			0.728891i
$927$	32.7639	−	29.3050i	1.07611	−	0.962501i
$928$		−	7.70820i		−	0.253034i
$929$	37.8885			1.24308			0.621541	−	0.783381i	$-0.286507\pi$
$929$	37.8885			1.24308			0.621541	+	0.783381i	$0.286507\pi$
$930$		0			0
$931$	−16.9443	+	56.8328i	−0.555326	+	1.86262i
$932$	−11.5279			−0.377608
$933$	10.8328	+	28.3607i	0.354650	+	0.928487i
$934$			33.7082i			1.10297i
$935$		0			0
$936$	2.76393	−	2.47214i	0.0903419	−	0.0808043i
$937$	−42.0689			−1.37433			−0.687165	−	0.726501i	$-0.741145\pi$
$937$	−42.0689			−1.37433			−0.687165	+	0.726501i	$0.741145\pi$
$938$	31.4164	+	4.58359i	1.02578	+	0.149660i
$939$	3.52786	+	9.23607i	0.115127	+	0.301408i
$940$		0			0
$941$	−22.0000			−0.717180			−0.358590	−	0.933495i	$-0.616742\pi$
$941$	−22.0000			−0.717180			−0.358590	+	0.933495i	$0.616742\pi$
$942$	−5.70820	−	14.9443i	−0.185983	−	0.486911i
$943$	9.88854			0.322015
$944$	4.47214			0.145556
$945$		0			0
$946$	22.1115			0.718905
$947$	60.3607			1.96146			0.980729	−	0.195372i	$-0.0625913\pi$
$947$	60.3607			1.96146			0.980729	+	0.195372i	$0.0625913\pi$
$948$	−5.52786	−	14.4721i	−0.179537	−	0.470033i
$949$	13.8885			0.450841
$950$		0			0
$951$	6.76393	+	17.7082i	0.219336	+	0.574228i
$952$	13.7082	+	2.00000i	0.444285	+	0.0648204i
$953$	−22.5836			−0.731554			−0.365777	−	0.930702i	$-0.619197\pi$
$953$	−22.5836			−0.731554			−0.365777	+	0.930702i	$0.619197\pi$
$954$	1.05573	−	0.944272i	0.0341805	−	0.0305719i
$955$		0			0
$956$			0.180340i			0.00583261i
$957$	21.3050	+	55.7771i	0.688691	+	1.80302i
$958$	37.8885			1.22412
$959$	−1.34752	+	9.23607i	−0.0435138	+	0.298248i
$960$		0			0
$961$	23.3607			0.753570
$962$		−	0.944272i		−	0.0304445i
$963$	−25.5279	+	22.8328i	−0.822624	+	0.735777i
$964$			17.8885i			0.576151i
$965$		0			0
$966$	17.8885	−	4.00000i	0.575554	−	0.128698i
$967$		−	39.4853i		−	1.26976i	−0.772610	−	0.634881i	$-0.781049\pi$
$967$		−	39.4853i		−	1.26976i	0.772610	−	0.634881i	$-0.218951\pi$
$968$	−9.00000			−0.289271
$969$	27.4164	+	71.7771i	0.880742	+	2.30581i
$970$		0			0
$971$	58.0000			1.86131			0.930654	−	0.365900i	$-0.119239\pi$
$971$	58.0000			1.86131			0.930654	+	0.365900i	$0.119239\pi$
$972$	−15.0902	+	3.90983i	−0.484017	+	0.125408i
$973$	−30.1803	−	4.40325i	−0.967537	−	0.141162i
$974$			17.5967i			0.563836i
$975$		0			0
$976$			7.23607i			0.231621i
$977$	1.41641			0.0453149			0.0226575	−	0.999743i	$-0.492787\pi$
$977$	1.41641			0.0453149			0.0226575	+	0.999743i	$0.492787\pi$
$978$	16.9443	−	6.47214i	0.541818	−	0.206956i
$979$			24.7214i			0.790098i
$980$		0			0
$981$	10.0000	−	8.94427i	0.319275	−	0.285569i
$982$		−	13.4164i		−	0.428135i
$983$		−	12.5836i		−	0.401354i	−0.979657	−	0.200677i	$-0.935686\pi$
$983$		−	12.5836i		−	0.401354i	0.979657	−	0.200677i	$-0.0643142\pi$
$984$	−1.52786	−	4.00000i	−0.0487065	−	0.127515i
$985$		0			0
$986$	−40.3607			−1.28535
$987$	6.47214	+	28.9443i	0.206010	+	0.921306i
$988$			10.4721i			0.333163i
$989$			19.7771i			0.628875i
$990$		0			0
$991$	17.5279			0.556791			0.278395	−	0.960467i	$-0.410197\pi$
$991$	17.5279			0.556791			0.278395	+	0.960467i	$0.410197\pi$
$992$		−	2.76393i		−	0.0877549i
$993$	−1.88854	−	4.94427i	−0.0599311	−	0.156902i
$994$	−18.9443	−	2.76393i	−0.600876	−	0.0876666i
$995$		0			0
$996$	23.7082	−	9.05573i	0.751223	−	0.286942i
$997$	−25.2361			−0.799234			−0.399617	−	0.916682i	$-0.630857\pi$
$997$	−25.2361			−0.799234			−0.399617	+	0.916682i	$0.630857\pi$
$998$	−17.8885			−0.566252
$999$	−1.81966	+	3.52786i	−0.0575715	+	0.111617i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.d.f.1049.1		4
3.2	odd	2		1050.2.d.c.1049.2		4
5.2	odd	4		1050.2.b.a.251.3		4
5.3	odd	4		210.2.b.b.41.2	yes	4
5.4	even	2		1050.2.d.a.1049.4		4
7.6	odd	2		1050.2.d.d.1049.4		4
15.2	even	4		1050.2.b.c.251.2		4
15.8	even	4		210.2.b.a.41.3	yes	4
15.14	odd	2		1050.2.d.d.1049.3		4
20.3	even	4		1680.2.f.e.881.2		4
21.20	even	2		1050.2.d.a.1049.3		4
35.13	even	4		210.2.b.a.41.1	✓	4
35.27	even	4		1050.2.b.c.251.4		4
35.34	odd	2		1050.2.d.c.1049.1		4
60.23	odd	4		1680.2.f.i.881.4		4
105.62	odd	4		1050.2.b.a.251.1		4
105.83	odd	4		210.2.b.b.41.4	yes	4
105.104	even	2	inner	1050.2.d.f.1049.2		4
140.83	odd	4		1680.2.f.i.881.3		4
420.83	even	4		1680.2.f.e.881.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.b.a.41.1	✓	4	35.13	even	4
210.2.b.a.41.3	yes	4	15.8	even	4
210.2.b.b.41.2	yes	4	5.3	odd	4
210.2.b.b.41.4	yes	4	105.83	odd	4
1050.2.b.a.251.1		4	105.62	odd	4
1050.2.b.a.251.3		4	5.2	odd	4
1050.2.b.c.251.2		4	15.2	even	4
1050.2.b.c.251.4		4	35.27	even	4
1050.2.d.a.1049.3		4	21.20	even	2
1050.2.d.a.1049.4		4	5.4	even	2
1050.2.d.c.1049.1		4	35.34	odd	2
1050.2.d.c.1049.2		4	3.2	odd	2
1050.2.d.d.1049.3		4	15.14	odd	2
1050.2.d.d.1049.4		4	7.6	odd	2
1050.2.d.f.1049.1		4	1.1	even	1	trivial
1050.2.d.f.1049.2		4	105.104	even	2	inner
1680.2.f.e.881.1		4	420.83	even	4
1680.2.f.e.881.2		4	20.3	even	4
1680.2.f.i.881.3		4	140.83	odd	4
1680.2.f.i.881.4		4	60.23	odd	4

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.618034 - 1.61803i) q^{3} +1.00000 q^{4} +(-0.618034 - 1.61803i) q^{6} +(-0.381966 + 2.61803i) q^{7} +1.00000 q^{8} +(-2.23607 + 2.00000i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.618034 - 1.61803i) q^{3} +1.00000 q^{4} +(-0.618034 - 1.61803i) q^{6} +(-0.381966 + 2.61803i) q^{7} +1.00000 q^{8} +(-2.23607 + 2.00000i) q^{9} -4.47214i q^{11} +(-0.618034 - 1.61803i) q^{12} -1.23607 q^{13} +(-0.381966 + 2.61803i) q^{14} +1.00000 q^{16} -5.23607i q^{17} +(-2.23607 + 2.00000i) q^{18} -8.47214i q^{19} +(4.47214 - 1.00000i) q^{21} -4.47214i q^{22} +4.00000 q^{23} +(-0.618034 - 1.61803i) q^{24} -1.23607 q^{26} +(4.61803 + 2.38197i) q^{27} +(-0.381966 + 2.61803i) q^{28} -7.70820i q^{29} -2.76393i q^{31} +1.00000 q^{32} +(-7.23607 + 2.76393i) q^{33} -5.23607i q^{34} +(-2.23607 + 2.00000i) q^{36} +0.763932i q^{37} -8.47214i q^{38} +(0.763932 + 2.00000i) q^{39} +2.47214 q^{41} +(4.47214 - 1.00000i) q^{42} +4.94427i q^{43} -4.47214i q^{44} +4.00000 q^{46} +6.47214i q^{47} +(-0.618034 - 1.61803i) q^{48} +(-6.70820 - 2.00000i) q^{49} +(-8.47214 + 3.23607i) q^{51} -1.23607 q^{52} -0.472136 q^{53} +(4.61803 + 2.38197i) q^{54} +(-0.381966 + 2.61803i) q^{56} +(-13.7082 + 5.23607i) q^{57} -7.70820i q^{58} +4.47214 q^{59} +7.23607i q^{61} -2.76393i q^{62} +(-4.38197 - 6.61803i) q^{63} +1.00000 q^{64} +(-7.23607 + 2.76393i) q^{66} -12.0000i q^{67} -5.23607i q^{68} +(-2.47214 - 6.47214i) q^{69} +7.23607i q^{71} +(-2.23607 + 2.00000i) q^{72} -11.2361 q^{73} +0.763932i q^{74} -8.47214i q^{76} +(11.7082 + 1.70820i) q^{77} +(0.763932 + 2.00000i) q^{78} +8.94427 q^{79} +(1.00000 - 8.94427i) q^{81} +2.47214 q^{82} +14.6525i q^{83} +(4.47214 - 1.00000i) q^{84} +4.94427i q^{86} +(-12.4721 + 4.76393i) q^{87} -4.47214i q^{88} -5.52786 q^{89} +(0.472136 - 3.23607i) q^{91} +4.00000 q^{92} +(-4.47214 + 1.70820i) q^{93} +6.47214i q^{94} +(-0.618034 - 1.61803i) q^{96} -0.763932 q^{97} +(-6.70820 - 2.00000i) q^{98} +(8.94427 + 10.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 2 q^{6} - 6 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 2 * q^6 - 6 * q^7 + 4 * q^8	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 2 q^{6} - 6 q^{7} + 4 q^{8} + 2 q^{12} + 4 q^{13} - 6 q^{14} + 4 q^{16} + 16 q^{23} + 2 q^{24} + 4 q^{26} + 14 q^{27} - 6 q^{28} + 4 q^{32} - 20 q^{33} + 12 q^{39} - 8 q^{41} + 16 q^{46} + 2 q^{48} - 16 q^{51} + 4 q^{52} + 16 q^{53} + 14 q^{54} - 6 q^{56} - 28 q^{57} - 22 q^{63} + 4 q^{64} - 20 q^{66} + 8 q^{69} - 36 q^{73} + 20 q^{77} + 12 q^{78} + 4 q^{81} - 8 q^{82} - 32 q^{87} - 40 q^{89} - 16 q^{91} + 16 q^{92} + 2 q^{96} - 12 q^{97}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 2 * q^6 - 6 * q^7 + 4 * q^8 + 2 * q^12 + 4 * q^13 - 6 * q^14 + 4 * q^16 + 16 * q^23 + 2 * q^24 + 4 * q^26 + 14 * q^27 - 6 * q^28 + 4 * q^32 - 20 * q^33 + 12 * q^39 - 8 * q^41 + 16 * q^46 + 2 * q^48 - 16 * q^51 + 4 * q^52 + 16 * q^53 + 14 * q^54 - 6 * q^56 - 28 * q^57 - 22 * q^63 + 4 * q^64 - 20 * q^66 + 8 * q^69 - 36 * q^73 + 20 * q^77 + 12 * q^78 + 4 * q^81 - 8 * q^82 - 32 * q^87 - 40 * q^89 - 16 * q^91 + 16 * q^92 + 2 * q^96 - 12 * q^97

Introduction

L-functions

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