LMFDB - Embedded newform 1050.2.d.a.1049.4

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			1049.4
Root			$-0.618034i$ of defining polynomial
Character	$\chi$	$=$	1050.1049
Dual form			1050.2.d.a.1049.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.618034 + 1.61803i) q^{3} +1.00000 q^{4} +(-0.618034 - 1.61803i) q^{6} +(0.381966 - 2.61803i) q^{7} -1.00000 q^{8} +(-2.23607 + 2.00000i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.618034 + 1.61803i) q^{3} +1.00000 q^{4} +(-0.618034 - 1.61803i) q^{6} +(0.381966 - 2.61803i) q^{7} -1.00000 q^{8} +(-2.23607 + 2.00000i) q^{9} -4.47214i q^{11} +(0.618034 + 1.61803i) q^{12} +1.23607 q^{13} +(-0.381966 + 2.61803i) q^{14} +1.00000 q^{16} +5.23607i q^{17} +(2.23607 - 2.00000i) q^{18} -8.47214i q^{19} +(4.47214 - 1.00000i) q^{21} +4.47214i q^{22} -4.00000 q^{23} +(-0.618034 - 1.61803i) q^{24} -1.23607 q^{26} +(-4.61803 - 2.38197i) q^{27} +(0.381966 - 2.61803i) q^{28} -7.70820i q^{29} -2.76393i q^{31} -1.00000 q^{32} +(7.23607 - 2.76393i) q^{33} -5.23607i q^{34} +(-2.23607 + 2.00000i) q^{36} -0.763932i q^{37} +8.47214i q^{38} +(0.763932 + 2.00000i) q^{39} +2.47214 q^{41} +(-4.47214 + 1.00000i) q^{42} -4.94427i q^{43} -4.47214i q^{44} +4.00000 q^{46} -6.47214i q^{47} +(0.618034 + 1.61803i) q^{48} +(-6.70820 - 2.00000i) q^{49} +(-8.47214 + 3.23607i) q^{51} +1.23607 q^{52} +0.472136 q^{53} +(4.61803 + 2.38197i) q^{54} +(-0.381966 + 2.61803i) q^{56} +(13.7082 - 5.23607i) q^{57} +7.70820i q^{58} +4.47214 q^{59} +7.23607i q^{61} +2.76393i q^{62} +(4.38197 + 6.61803i) q^{63} +1.00000 q^{64} +(-7.23607 + 2.76393i) q^{66} +12.0000i q^{67} +5.23607i q^{68} +(-2.47214 - 6.47214i) q^{69} +7.23607i q^{71} +(2.23607 - 2.00000i) q^{72} +11.2361 q^{73} +0.763932i q^{74} -8.47214i q^{76} +(-11.7082 - 1.70820i) q^{77} +(-0.763932 - 2.00000i) q^{78} +8.94427 q^{79} +(1.00000 - 8.94427i) q^{81} -2.47214 q^{82} -14.6525i q^{83} +(4.47214 - 1.00000i) q^{84} +4.94427i q^{86} +(12.4721 - 4.76393i) q^{87} +4.47214i q^{88} -5.52786 q^{89} +(0.472136 - 3.23607i) q^{91} -4.00000 q^{92} +(4.47214 - 1.70820i) q^{93} +6.47214i q^{94} +(-0.618034 - 1.61803i) q^{96} +0.763932 q^{97} +(6.70820 + 2.00000i) q^{98} +(8.94427 + 10.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.445167\pi$
$13$	1.23607			0.342824			0.171412	+	0.985199i	$0.445167\pi$
$14$	−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	$0.218986\pi$
$17$			5.23607i			1.26993i	−0.772540	+	0.634967i	$0.781014\pi$
$18$	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	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$	−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	$-0.979999\pi$
$37$		−	0.763932i		−	0.125590i	0.998026	−	0.0627948i	$-0.0200014\pi$
$38$			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	$-0.876957\pi$
$43$		−	4.94427i		−	0.753994i	0.926214	−	0.376997i	$-0.123043\pi$
$44$		−	4.47214i		−	0.674200i
$45$		0			0
$46$	4.00000			0.589768
$47$		−	6.47214i		−	0.944058i	−0.881583	−	0.472029i	$-0.843522\pi$
$47$		−	6.47214i		−	0.944058i	0.881583	−	0.472029i	$-0.156478\pi$
$48$	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	$-0.489677\pi$
$53$	0.472136			0.0648529			0.0324264	+	0.999474i	$0.489677\pi$
$54$	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	$0.261888\pi$
$67$			12.0000i			1.46603i	−0.680211	+	0.733017i	$0.738112\pi$
$68$			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	$-0.271597\pi$
$73$	11.2361			1.31508			0.657541	+	0.753419i	$0.271597\pi$
$74$			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	$-0.702616\pi$
$83$		−	14.6525i		−	1.60832i	0.594414	−	0.804159i	$-0.297384\pi$
$84$	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	$-0.487652\pi$
$97$	0.763932			0.0775655			0.0387828	+	0.999248i	$0.487652\pi$
$98$	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	$-0.243280\pi$
$103$	14.6525			1.44375			0.721876	+	0.692023i	$0.243280\pi$
$104$	−1.23607			−0.121206
$105$		0			0
$106$	−0.472136			−0.0458579
$107$	−11.4164			−1.10367			−0.551833	−	0.833955i	$-0.686071\pi$
$107$	−11.4164			−1.10367			−0.551833	+	0.833955i	$0.686071\pi$
$108$	−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	$-0.544224\pi$
$113$	−2.94427			−0.276974			−0.138487	+	0.990364i	$0.544224\pi$
$114$	−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	$0.00412107\pi$
$127$			0.291796i			0.0258927i	−0.999916	+	0.0129464i	$0.995879\pi$
$128$	−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	$-0.548154\pi$
$137$	−3.52786			−0.301406			−0.150703	+	0.988579i	$0.548154\pi$
$138$	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	$-0.620149\pi$
$157$	−9.23607			−0.737118			−0.368559	+	0.929604i	$0.620149\pi$
$158$	−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	$-0.865487\pi$
$163$		−	10.4721i		−	0.820241i	0.912031	−	0.410120i	$-0.134513\pi$
$164$	2.47214			0.193041
$165$		0			0
$166$			14.6525i			1.13725i
$167$		−	0.944272i		−	0.0730700i	−0.999332	−	0.0365350i	$-0.988368\pi$
$167$		−	0.944272i		−	0.0730700i	0.999332	−	0.0365350i	$-0.0116320\pi$
$168$	−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	$0.116527\pi$
$173$			9.41641i			0.715916i	−0.933738	+	0.357958i	$0.883473\pi$
$174$	−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	$-0.930717\pi$
$193$		−	6.00000i		−	0.431889i	0.976406	−	0.215945i	$-0.0692831\pi$
$194$	−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	$-0.540110\pi$
$197$	−3.52786			−0.251350			−0.125675	+	0.992071i	$0.540110\pi$
$198$	−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	$-0.702023\pi$
$223$	−17.7082			−1.18583			−0.592915	+	0.805265i	$0.702023\pi$
$224$	−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	$0.00807065\pi$
$227$			0.763932i			0.0507039i	−0.999679	+	0.0253520i	$0.991929\pi$
$228$	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	$-0.376747\pi$
$233$	11.5279			0.755215			0.377608	+	0.925966i	$0.376747\pi$
$234$	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	$0.145828\pi$
$257$			14.1803i			0.884545i	−0.896881	+	0.442273i	$0.854172\pi$
$258$	−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	$-0.630674\pi$
$263$	−12.9443			−0.798178			−0.399089	+	0.916912i	$0.630674\pi$
$264$	−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	$0.172007\pi$
$277$			17.1246i			1.02892i	−0.857515	+	0.514459i	$0.827993\pi$
$278$		−	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	$-0.628702\pi$
$283$	−13.2361			−0.786803			−0.393401	+	0.919367i	$0.628702\pi$
$284$			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	$0.0240449\pi$
$293$			2.58359i			0.150935i	−0.997148	+	0.0754675i	$0.975955\pi$
$294$	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	$-0.673622\pi$
$307$	−18.1803			−1.03761			−0.518803	+	0.854894i	$0.673622\pi$
$308$	−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	$-0.448424\pi$
$313$	5.70820			0.322647			0.161323	+	0.986902i	$0.448424\pi$
$314$	9.23607			0.521221
$315$		0			0
$316$	8.94427			0.503155
$317$	10.9443			0.614692			0.307346	−	0.951598i	$-0.400559\pi$
$317$	10.9443			0.614692			0.307346	+	0.951598i	$0.400559\pi$
$318$	−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	$-0.801756\pi$
$337$		−	21.4164i		−	1.16663i	0.812247	−	0.583313i	$-0.198244\pi$
$338$	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	$-0.521137\pi$
$347$	−2.47214			−0.132711			−0.0663556	+	0.997796i	$0.521137\pi$
$348$	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	$0.263937\pi$
$353$			27.7082i			1.47476i	−0.675479	+	0.737379i	$0.736063\pi$
$354$	−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	$-0.568488\pi$
$367$	−8.18034			−0.427010			−0.213505	+	0.976942i	$0.568488\pi$
$368$	−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	$-0.686554\pi$
$373$		−	32.1803i		−	1.66623i	0.553096	−	0.833117i	$-0.313446\pi$
$374$	−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	$0.115463\pi$
$383$			13.8885i			0.709671i	−0.934929	+	0.354836i	$0.884537\pi$
$384$	−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	$-0.302937\pi$
$397$	23.1246			1.16059			0.580295	+	0.814406i	$0.302937\pi$
$398$		−	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	$-0.721239\pi$
$433$	−26.6525			−1.28084			−0.640418	+	0.768026i	$0.721239\pi$
$434$	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	$-0.644603\pi$
$443$	−18.4721			−0.877638			−0.438819	+	0.898576i	$0.644603\pi$
$444$	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	$-0.782973\pi$
$457$		−	26.9443i		−	1.26040i	0.776433	−	0.630200i	$-0.217027\pi$
$458$		−	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	$-0.827642\pi$
$463$		−	22.1803i		−	1.03081i	0.856947	−	0.515404i	$-0.172358\pi$
$464$		−	7.70820i		−	0.357844i
$465$		0			0
$466$	−11.5279			−0.534018
$467$		−	33.7082i		−	1.55983i	−0.625886	−	0.779915i	$-0.715262\pi$
$467$		−	33.7082i		−	1.55983i	0.625886	−	0.779915i	$-0.284738\pi$
$468$	−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	$-0.869464\pi$
$487$		−	17.5967i		−	0.797385i	0.917085	−	0.398692i	$-0.130536\pi$
$488$		−	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	$0.217877\pi$
$503$			28.3607i			1.26454i	−0.774748	+	0.632270i	$0.782123\pi$
$504$	−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	$-0.119725\pi$
$523$	42.5410			1.86019			0.930094	+	0.367320i	$0.119725\pi$
$524$	−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	$0.273408\pi$
$547$			35.4164i			1.51430i	−0.653243	+	0.757148i	$0.726592\pi$
$548$	−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	$-0.449017\pi$
$557$	7.52786			0.318966			0.159483	+	0.987201i	$0.449017\pi$
$558$	−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	$-0.678586\pi$
$563$		−	40.1803i		−	1.69340i	0.532071	−	0.846700i	$-0.321414\pi$
$564$	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	$-0.554466\pi$
$577$	−8.18034			−0.340552			−0.170276	+	0.985396i	$0.554466\pi$
$578$	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	$-0.931874\pi$
$587$		−	10.2918i		−	0.424788i	0.977184	−	0.212394i	$-0.0681260\pi$
$588$	−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	$0.203131\pi$
$593$			29.0132i			1.19143i	−0.803197	+	0.595714i	$0.796869\pi$
$594$	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	$-0.627658\pi$
$607$	−19.2361			−0.780768			−0.390384	+	0.920652i	$0.627658\pi$
$608$			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	$0.279143\pi$
$613$			38.0689i			1.53759i	−0.639497	+	0.768794i	$0.720857\pi$
$614$	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	$-0.487182\pi$
$617$	2.00000			0.0805170			0.0402585	+	0.999189i	$0.487182\pi$
$618$	−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	$-0.422075\pi$
$643$	12.2918			0.484741			0.242371	+	0.970184i	$0.422075\pi$
$644$	−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	$0.240071\pi$
$647$			34.8328i			1.36942i	−0.728816	+	0.684710i	$0.759929\pi$
$648$	−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	$-0.345185\pi$
$653$	23.8885			0.934831			0.467415	+	0.884038i	$0.345185\pi$
$654$	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	$0.122829\pi$
$673$			19.5279i			0.752744i	−0.926469	+	0.376372i	$0.877171\pi$
$674$			21.4164i			0.824929i
$675$		0			0
$676$	−11.4721			−0.441236
$677$			18.0000i			0.691796i	0.938272	+	0.345898i	$0.112426\pi$
$677$			18.0000i			0.691796i	−0.938272	+	0.345898i	$0.887574\pi$
$678$	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	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$	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	$-0.337889\pi$
$727$	26.2918			0.975109			0.487554	+	0.873093i	$0.337889\pi$
$728$	−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	$-0.620858\pi$
$733$	−20.0689			−0.741261			−0.370631	+	0.928780i	$0.620858\pi$
$734$	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	$-0.438473\pi$
$743$	10.4721			0.384185			0.192093	+	0.981377i	$0.438473\pi$
$744$	−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	$0.0153494\pi$
$757$			2.65248i			0.0964059i	−0.998838	+	0.0482029i	$0.984651\pi$
$758$	−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	$-0.939043\pi$
$773$		−	10.5836i		−	0.380665i	0.981720	−	0.190333i	$-0.0609567\pi$
$774$	−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	$-0.276094\pi$
$787$	36.2918			1.29366			0.646831	+	0.762633i	$0.276094\pi$
$788$	−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	$0.123837\pi$
$797$			21.4164i			0.758608i	−0.925272	+	0.379304i	$0.876163\pi$
$798$	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	$-0.873657\pi$
$823$		−	22.1803i		−	0.773158i	0.922256	−	0.386579i	$-0.126343\pi$
$824$	−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	$-0.264068\pi$
$827$	38.8328			1.35035			0.675175	+	0.737658i	$0.264068\pi$
$828$	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	$-0.542128\pi$
$853$	−7.70820			−0.263924			−0.131962	+	0.991255i	$0.542128\pi$
$854$	−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	$-0.937915\pi$
$857$		−	11.3475i		−	0.387624i	0.981039	−	0.193812i	$-0.0620852\pi$
$858$	−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	$-0.326438\pi$
$863$	30.4721			1.03728			0.518642	+	0.854992i	$0.326438\pi$
$864$	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	$-0.773678\pi$
$877$		−	38.6525i		−	1.30520i	0.757702	−	0.652601i	$-0.226322\pi$
$878$			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	$-0.924919\pi$
$883$		−	13.8885i		−	0.467387i	0.972310	−	0.233693i	$-0.0750812\pi$
$884$			6.47214i			0.217681i
$885$		0			0
$886$	18.4721			0.620584
$887$		−	17.5279i		−	0.588528i	−0.955724	−	0.294264i	$-0.904925\pi$
$887$		−	17.5279i		−	0.588528i	0.955724	−	0.294264i	$-0.0950745\pi$
$888$	−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	$0.0939885\pi$
$907$			17.5279i			0.582003i	−0.956723	+	0.291002i	$0.906012\pi$
$908$			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	$-0.258855\pi$
$937$	42.0689			1.37433			0.687165	+	0.726501i	$0.258855\pi$
$938$	−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	$-0.937409\pi$
$947$	−60.3607			−1.96146			−0.980729	+	0.195372i	$0.937409\pi$
$948$	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	$-0.380803\pi$
$953$	22.5836			0.731554			0.365777	+	0.930702i	$0.380803\pi$
$954$	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	$0.218951\pi$
$967$			39.4853i			1.26976i	−0.772610	+	0.634881i	$0.781049\pi$
$968$	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	$-0.507213\pi$
$977$	−1.41641			−0.0453149			−0.0226575	+	0.999743i	$0.507213\pi$
$978$	−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	$0.0643142\pi$
$983$			12.5836i			0.401354i	−0.979657	+	0.200677i	$0.935686\pi$
$984$	−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	$-0.369143\pi$
$997$	25.2361			0.799234			0.399617	+	0.916682i	$0.369143\pi$
$998$	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.a.1049.4		4
3.2	odd	2		1050.2.d.d.1049.3		4
5.2	odd	4		210.2.b.b.41.2	yes	4
5.3	odd	4		1050.2.b.a.251.3		4
5.4	even	2		1050.2.d.f.1049.1		4
7.6	odd	2		1050.2.d.c.1049.1		4
15.2	even	4		210.2.b.a.41.3	yes	4
15.8	even	4		1050.2.b.c.251.2		4
15.14	odd	2		1050.2.d.c.1049.2		4
20.7	even	4		1680.2.f.e.881.2		4
21.20	even	2		1050.2.d.f.1049.2		4
35.13	even	4		1050.2.b.c.251.4		4
35.27	even	4		210.2.b.a.41.1	✓	4
35.34	odd	2		1050.2.d.d.1049.4		4
60.47	odd	4		1680.2.f.i.881.4		4
105.62	odd	4		210.2.b.b.41.4	yes	4
105.83	odd	4		1050.2.b.a.251.1		4
105.104	even	2	inner	1050.2.d.a.1049.3		4
140.27	odd	4		1680.2.f.i.881.3		4
420.167	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	35.27	even	4
210.2.b.a.41.3	yes	4	15.2	even	4
210.2.b.b.41.2	yes	4	5.2	odd	4
210.2.b.b.41.4	yes	4	105.62	odd	4
1050.2.b.a.251.1		4	105.83	odd	4
1050.2.b.a.251.3		4	5.3	odd	4
1050.2.b.c.251.2		4	15.8	even	4
1050.2.b.c.251.4		4	35.13	even	4
1050.2.d.a.1049.3		4	105.104	even	2	inner
1050.2.d.a.1049.4		4	1.1	even	1	trivial
1050.2.d.c.1049.1		4	7.6	odd	2
1050.2.d.c.1049.2		4	15.14	odd	2
1050.2.d.d.1049.3		4	3.2	odd	2
1050.2.d.d.1049.4		4	35.34	odd	2
1050.2.d.f.1049.1		4	5.4	even	2
1050.2.d.f.1049.2		4	21.20	even	2
1680.2.f.e.881.1		4	420.167	even	4
1680.2.f.e.881.2		4	20.7	even	4
1680.2.f.i.881.3		4	140.27	odd	4
1680.2.f.i.881.4		4	60.47	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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more