LMFDB - Embedded newform 1050.2.b.a.251.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(251,1050)]

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, 0, 1]))

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

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

chi := DirichletCharacter("1050.251");

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.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.38429221223$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.3
Root			$0.618034i$ of defining polynomial
Character	$\chi$	$=$	1050.251
Dual form			1050.2.b.a.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.61803	+	0.618034i	−0.934172	+	0.356822i
$3$	−1.61803	+	0.618034i	−0.934172	+	0.356822i
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−0.618034	−	1.61803i	−0.252311	−	0.660560i
$7$	−2.61803	−	0.381966i	−0.989524	−	0.144370i
$7$	−2.61803	−	0.381966i	−0.989524	−	0.144370i
$8$		−	1.00000i		−	0.353553i
$9$	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	$-0.235511\pi$
$12$	1.61803	−	0.618034i	0.467086	−	0.178411i
$13$			1.23607i			0.342824i	0.985199	+	0.171412i	$0.0548329\pi$
$13$			1.23607i			0.342824i	−0.985199	+	0.171412i	$0.945167\pi$
$14$	0.381966	−	2.61803i	0.102085	−	0.699699i
$15$		0			0
$16$	1.00000			0.250000
$17$	5.23607			1.26993			0.634967	−	0.772540i	$-0.281014\pi$
$17$	5.23607			1.26993			0.634967	+	0.772540i	$0.281014\pi$
$18$	2.00000	+	2.23607i	0.471405	+	0.527046i
$19$			8.47214i			1.94364i	0.235722	+	0.971821i	$0.424255\pi$
$19$			8.47214i			1.94364i	−0.235722	+	0.971821i	$0.575745\pi$
$20$		0			0
$21$	4.47214	−	1.00000i	0.975900	−	0.218218i
$22$	4.47214			0.953463
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$	0.618034	+	1.61803i	0.126156	+	0.330280i
$25$		0			0
$26$	−1.23607			−0.242413
$27$	−2.38197	+	4.61803i	−0.458410	+	0.888741i
$28$	2.61803	+	0.381966i	0.494762	+	0.0721848i
$29$			7.70820i			1.43138i	0.698419	+	0.715689i	$0.253887\pi$
$29$			7.70820i			1.43138i	−0.698419	+	0.715689i	$0.746113\pi$
$30$		0			0
$31$		−	2.76393i		−	0.496417i	−0.968707	−	0.248208i	$-0.920158\pi$
$31$		−	2.76393i		−	0.496417i	0.968707	−	0.248208i	$-0.0798418\pi$
$32$			1.00000i			0.176777i
$33$	2.76393	+	7.23607i	0.481139	+	1.25964i
$34$			5.23607i			0.897978i
$35$		0			0
$36$	−2.23607	+	2.00000i	−0.372678	+	0.333333i
$37$	−0.763932			−0.125590			−0.0627948	−	0.998026i	$-0.520001\pi$
$37$	−0.763932			−0.125590			−0.0627948	+	0.998026i	$0.520001\pi$
$38$	−8.47214			−1.37436
$39$	−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	$0.438165\pi$
$42$	1.00000	+	4.47214i	0.154303	+	0.690066i
$43$	4.94427			0.753994			0.376997	−	0.926214i	$-0.376957\pi$
$43$	4.94427			0.753994			0.376997	+	0.926214i	$0.376957\pi$
$44$			4.47214i			0.674200i
$45$		0			0
$46$	4.00000			0.589768
$47$	−6.47214			−0.944058			−0.472029	−	0.881583i	$-0.656478\pi$
$47$	−6.47214			−0.944058			−0.472029	+	0.881583i	$0.656478\pi$
$48$	−1.61803	+	0.618034i	−0.233543	+	0.0892055i
$49$	6.70820	+	2.00000i	0.958315	+	0.285714i
$50$		0			0
$51$	−8.47214	+	3.23607i	−1.18634	+	0.453140i
$52$		−	1.23607i		−	0.171412i
$53$			0.472136i			0.0648529i	0.999474	+	0.0324264i	$0.0103235\pi$
$53$			0.472136i			0.0648529i	−0.999474	+	0.0324264i	$0.989677\pi$
$54$	−4.61803	−	2.38197i	−0.628435	−	0.324145i
$55$		0			0
$56$	−0.381966	+	2.61803i	−0.0510424	+	0.349850i
$57$	−5.23607	−	13.7082i	−0.693534	−	1.81570i
$58$	−7.70820			−1.01214
$59$	−4.47214			−0.582223			−0.291111	−	0.956689i	$-0.594025\pi$
$59$	−4.47214			−0.582223			−0.291111	+	0.956689i	$0.594025\pi$
$60$		0			0
$61$			7.23607i			0.926484i	0.886232	+	0.463242i	$0.153314\pi$
$61$			7.23607i			0.926484i	−0.886232	+	0.463242i	$0.846686\pi$
$62$	2.76393			0.351020
$63$	−6.61803	+	4.38197i	−0.833794	+	0.552076i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−7.23607	+	2.76393i	−0.890698	+	0.340217i
$67$	12.0000			1.46603			0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000			1.46603			0.733017	+	0.680211i	$0.238112\pi$
$68$	−5.23607			−0.634967
$69$	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	$0.858732\pi$
$72$	−2.00000	−	2.23607i	−0.235702	−	0.263523i
$73$			11.2361i			1.31508i	0.753419	+	0.657541i	$0.228403\pi$
$73$			11.2361i			1.31508i	−0.753419	+	0.657541i	$0.771597\pi$
$74$		−	0.763932i		−	0.0888053i
$75$		0			0
$76$		−	8.47214i		−	0.971821i
$77$	−1.70820	+	11.7082i	−0.194668	+	1.33427i
$78$	2.00000	−	0.763932i	0.226455	−	0.0864983i
$79$	−8.94427			−1.00631			−0.503155	−	0.864196i	$-0.667827\pi$
$79$	−8.94427			−1.00631			−0.503155	+	0.864196i	$0.667827\pi$
$80$		0			0
$81$	1.00000	−	8.94427i	0.111111	−	0.993808i
$82$			2.47214i			0.273002i
$83$	14.6525			1.60832			0.804159	−	0.594414i	$-0.202616\pi$
$83$	14.6525			1.60832			0.804159	+	0.594414i	$0.202616\pi$
$84$	−4.47214	+	1.00000i	−0.487950	+	0.109109i
$85$		0			0
$86$			4.94427i			0.533155i
$87$	−4.76393	−	12.4721i	−0.510747	−	1.33715i
$88$	−4.47214			−0.476731
$89$	5.52786			0.585952			0.292976	−	0.956120i	$-0.405354\pi$
$89$	5.52786			0.585952			0.292976	+	0.956120i	$0.405354\pi$
$90$		0			0
$91$	0.472136	−	3.23607i	0.0494933	−	0.339232i
$92$			4.00000i			0.417029i
$93$	1.70820	+	4.47214i	0.177132	+	0.463739i
$94$		−	6.47214i		−	0.667550i
$95$		0			0
$96$	−0.618034	−	1.61803i	−0.0630778	−	0.165140i
$97$		−	0.763932i		−	0.0775655i	−0.999248	−	0.0387828i	$-0.987652\pi$
$97$		−	0.763932i		−	0.0775655i	0.999248	−	0.0387828i	$-0.0123480\pi$
$98$	−2.00000	+	6.70820i	−0.202031	+	0.677631i
$99$	−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	$0.286925\pi$
$102$	−3.23607	−	8.47214i	−0.320418	−	0.838866i
$103$			14.6525i			1.44375i	0.692023	+	0.721876i	$0.256720\pi$
$103$			14.6525i			1.44375i	−0.692023	+	0.721876i	$0.743280\pi$
$104$	1.23607			0.121206
$105$		0			0
$106$	−0.472136			−0.0458579
$107$			11.4164i			1.10367i	0.833955	+	0.551833i	$0.186071\pi$
$107$			11.4164i			1.10367i	−0.833955	+	0.551833i	$0.813929\pi$
$108$	2.38197	−	4.61803i	0.229205	−	0.444371i
$109$	4.47214			0.428353			0.214176	−	0.976795i	$-0.431293\pi$
$109$	4.47214			0.428353			0.214176	+	0.976795i	$0.431293\pi$
$110$		0			0
$111$	1.23607	−	0.472136i	0.117322	−	0.0448132i
$112$	−2.61803	−	0.381966i	−0.247381	−	0.0360924i
$113$		−	2.94427i		−	0.276974i	−0.990364	−	0.138487i	$-0.955776\pi$
$113$		−	2.94427i		−	0.276974i	0.990364	−	0.138487i	$-0.0442239\pi$
$114$	13.7082	−	5.23607i	1.28389	−	0.490403i
$115$		0			0
$116$		−	7.70820i		−	0.715689i
$117$	2.47214	+	2.76393i	0.228549	+	0.255526i
$118$		−	4.47214i		−	0.411693i
$119$	−13.7082	−	2.00000i	−1.25663	−	0.183340i
$120$		0			0
$121$	−9.00000			−0.818182
$122$	−7.23607			−0.655123
$123$	−4.00000	+	1.52786i	−0.360668	+	0.137763i
$124$			2.76393i			0.248208i
$125$		0			0
$126$	−4.38197	−	6.61803i	−0.390377	−	0.589581i
$127$	0.291796			0.0258927			0.0129464	−	0.999916i	$-0.495879\pi$
$127$	0.291796			0.0258927			0.0129464	+	0.999916i	$0.495879\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−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	$0.576039\pi$
$132$	−2.76393	−	7.23607i	−0.240569	−	0.629819i
$133$	3.23607	−	22.1803i	0.280603	−	1.92328i
$134$			12.0000i			1.03664i
$135$		0			0
$136$		−	5.23607i		−	0.448989i
$137$			3.52786i			0.301406i	0.988579	+	0.150703i	$0.0481537\pi$
$137$			3.52786i			0.301406i	−0.988579	+	0.150703i	$0.951846\pi$
$138$	−6.47214	+	2.47214i	−0.550945	+	0.210442i
$139$		−	11.5279i		−	0.977781i	−0.872345	−	0.488890i	$-0.837402\pi$
$139$		−	11.5279i		−	0.977781i	0.872345	−	0.488890i	$-0.162598\pi$
$140$		0			0
$141$	10.4721	−	4.00000i	0.881913	−	0.336861i
$142$	−7.23607			−0.607237
$143$	5.52786			0.462263
$144$	2.23607	−	2.00000i	0.186339	−	0.166667i
$145$		0			0
$146$	−11.2361			−0.929904
$147$	−12.0902	+	0.909830i	−0.997180	+	0.0750415i
$148$	0.763932			0.0627948
$149$			4.29180i			0.351598i	0.984426	+	0.175799i	$0.0562508\pi$
$149$			4.29180i			0.351598i	−0.984426	+	0.175799i	$0.943749\pi$
$150$		0			0
$151$	20.9443			1.70442			0.852210	−	0.523199i	$-0.175262\pi$
$151$	20.9443			1.70442			0.852210	+	0.523199i	$0.175262\pi$
$152$	8.47214			0.687181
$153$	11.7082	−	10.4721i	0.946552	−	0.846622i
$154$	−11.7082	−	1.70820i	−0.943474	−	0.137651i
$155$		0			0
$156$	0.763932	+	2.00000i	0.0611635	+	0.160128i
$157$			9.23607i			0.737118i	0.929604	+	0.368559i	$0.120149\pi$
$157$			9.23607i			0.737118i	−0.929604	+	0.368559i	$0.879851\pi$
$158$		−	8.94427i		−	0.711568i
$159$	−0.291796	−	0.763932i	−0.0231409	−	0.0605838i
$160$		0			0
$161$	−1.52786	+	10.4721i	−0.120413	+	0.825320i
$162$	8.94427	+	1.00000i	0.702728	+	0.0785674i
$163$	10.4721			0.820241			0.410120	−	0.912031i	$-0.365487\pi$
$163$	10.4721			0.820241			0.410120	+	0.912031i	$0.365487\pi$
$164$	−2.47214			−0.193041
$165$		0			0
$166$			14.6525i			1.13725i
$167$	−0.944272			−0.0730700			−0.0365350	−	0.999332i	$-0.511632\pi$
$167$	−0.944272			−0.0730700			−0.0365350	+	0.999332i	$0.511632\pi$
$168$	−1.00000	−	4.47214i	−0.0771517	−	0.345033i
$169$	11.4721			0.882472
$170$		0			0
$171$	16.9443	+	18.9443i	1.29576	+	1.44870i
$172$	−4.94427			−0.376997
$173$	−9.41641			−0.715916			−0.357958	−	0.933738i	$-0.616527\pi$
$173$	−9.41641			−0.715916			−0.357958	+	0.933738i	$0.616527\pi$
$174$	12.4721	−	4.76393i	0.945510	−	0.361153i
$175$		0			0
$176$		−	4.47214i		−	0.337100i
$177$	7.23607	−	2.76393i	0.543896	−	0.207750i
$178$			5.52786i			0.414331i
$179$			14.9443i			1.11699i	0.829509	+	0.558494i	$0.188620\pi$
$179$			14.9443i			1.11699i	−0.829509	+	0.558494i	$0.811380\pi$
$180$		0			0
$181$		−	16.1803i		−	1.20268i	−0.798995	−	0.601338i	$-0.794635\pi$
$181$		−	16.1803i		−	1.20268i	0.798995	−	0.601338i	$-0.205365\pi$
$182$	3.23607	+	0.472136i	0.239873	+	0.0349970i
$183$	−4.47214	−	11.7082i	−0.330590	−	0.865495i
$184$	−4.00000			−0.294884
$185$		0			0
$186$	−4.47214	+	1.70820i	−0.327913	+	0.125252i
$187$		−	23.4164i		−	1.71238i
$188$	6.47214			0.472029
$189$	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	$-0.0843134\pi$
$192$	1.61803	−	0.618034i	0.116772	−	0.0446028i
$193$	6.00000			0.431889			0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000			0.431889			0.215945	+	0.976406i	$0.430717\pi$
$194$	0.763932			0.0548471
$195$		0			0
$196$	−6.70820	−	2.00000i	−0.479157	−	0.142857i
$197$			3.52786i			0.251350i	0.992071	+	0.125675i	$0.0401096\pi$
$197$			3.52786i			0.251350i	−0.992071	+	0.125675i	$0.959890\pi$
$198$	10.0000	−	8.94427i	0.710669	−	0.635642i
$199$		−	22.1803i		−	1.57232i	−0.618021	−	0.786161i	$-0.712065\pi$
$199$		−	22.1803i		−	1.57232i	0.618021	−	0.786161i	$-0.287935\pi$
$200$		0			0
$201$	−19.4164	+	7.41641i	−1.36953	+	0.523113i
$202$			12.4721i			0.877536i
$203$	2.94427	−	20.1803i	0.206647	−	1.41638i
$204$	8.47214	−	3.23607i	0.593168	−	0.226570i
$205$		0			0
$206$	−14.6525			−1.02089
$207$	−8.00000	−	8.94427i	−0.556038	−	0.621670i
$208$			1.23607i			0.0857059i
$209$	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	$0.588801\pi$
$212$		−	0.472136i		−	0.0324264i
$213$	−4.47214	−	11.7082i	−0.306426	−	0.802233i
$214$	−11.4164			−0.780410
$215$		0			0
$216$	4.61803	+	2.38197i	0.314217	+	0.162072i
$217$	−1.05573	+	7.23607i	−0.0716675	+	0.491216i
$218$			4.47214i			0.302891i
$219$	−6.94427	−	18.1803i	−0.469250	−	1.22851i
$220$		0			0
$221$			6.47214i			0.435363i
$222$	0.472136	+	1.23607i	0.0316877	+	0.0829595i
$223$		−	17.7082i		−	1.18583i	−0.805265	−	0.592915i	$-0.797977\pi$
$223$		−	17.7082i		−	1.18583i	0.805265	−	0.592915i	$-0.202023\pi$
$224$	0.381966	−	2.61803i	0.0255212	−	0.174925i
$225$		0			0
$226$	2.94427			0.195850
$227$	0.763932			0.0507039			0.0253520	−	0.999679i	$-0.491929\pi$
$227$	0.763932			0.0507039			0.0253520	+	0.999679i	$0.491929\pi$
$228$	5.23607	+	13.7082i	0.346767	+	0.907848i
$229$		−	8.76393i		−	0.579137i	−0.957157	−	0.289568i	$-0.906488\pi$
$229$		−	8.76393i		−	0.579137i	0.957157	−	0.289568i	$-0.0935118\pi$
$230$		0			0
$231$	−4.47214	−	20.0000i	−0.294245	−	1.31590i
$232$	7.70820			0.506068
$233$			11.5279i			0.755215i	0.925966	+	0.377608i	$0.123253\pi$
$233$			11.5279i			0.755215i	−0.925966	+	0.377608i	$0.876747\pi$
$234$	−2.76393	+	2.47214i	−0.180684	+	0.161609i
$235$		0			0
$236$	4.47214			0.291111
$237$	14.4721	−	5.52786i	0.940066	−	0.359073i
$238$	2.00000	−	13.7082i	0.129641	−	0.888571i
$239$		−	0.180340i		−	0.0116652i	−0.999983	−	0.00583261i	$-0.998143\pi$
$239$		−	0.180340i		−	0.0116652i	0.999983	−	0.00583261i	$-0.00185659\pi$
$240$		0			0
$241$			17.8885i			1.15230i	0.817343	+	0.576151i	$0.195446\pi$
$241$			17.8885i			1.15230i	−0.817343	+	0.576151i	$0.804554\pi$
$242$		−	9.00000i		−	0.578542i
$243$	3.90983	+	15.0902i	0.250816	+	0.968035i
$244$		−	7.23607i		−	0.463242i
$245$		0			0
$246$	−1.52786	−	4.00000i	−0.0974131	−	0.255031i
$247$	−10.4721			−0.666326
$248$	−2.76393			−0.175510
$249$	−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	$0.371224\pi$
$252$	6.61803	−	4.38197i	0.416897	−	0.276038i
$253$	−17.8885			−1.12464
$254$			0.291796i			0.0183089i
$255$		0			0
$256$	1.00000			0.0625000
$257$	14.1803			0.884545			0.442273	−	0.896881i	$-0.354172\pi$
$257$	14.1803			0.884545			0.442273	+	0.896881i	$0.354172\pi$
$258$	−3.05573	−	8.00000i	−0.190241	−	0.498058i
$259$	2.00000	+	0.291796i	0.124274	+	0.0181313i
$260$		0			0
$261$	15.4164	+	17.2361i	0.954252	+	1.06689i
$262$		−	5.41641i		−	0.334627i
$263$		−	12.9443i		−	0.798178i	−0.916912	−	0.399089i	$-0.869326\pi$
$263$		−	12.9443i		−	0.798178i	0.916912	−	0.399089i	$-0.130674\pi$
$264$	7.23607	−	2.76393i	0.445349	−	0.170108i
$265$		0			0
$266$	22.1803	+	3.23607i	1.35996	+	0.198416i
$267$	−8.94427	+	3.41641i	−0.547381	+	0.209081i
$268$	−12.0000			−0.733017
$269$	−4.47214			−0.272671			−0.136335	−	0.990663i	$-0.543533\pi$
$269$	−4.47214			−0.272671			−0.136335	+	0.990663i	$0.543533\pi$
$270$		0			0
$271$			31.7082i			1.92614i	0.269258	+	0.963068i	$0.413222\pi$
$271$			31.7082i			1.92614i	−0.269258	+	0.963068i	$0.586778\pi$
$272$	5.23607			0.317483
$273$	1.23607	+	5.52786i	0.0748102	+	0.334562i
$274$	−3.52786			−0.213126
$275$		0			0
$276$	−2.47214	−	6.47214i	−0.148805	−	0.389577i
$277$	17.1246			1.02892			0.514459	−	0.857515i	$-0.327993\pi$
$277$	17.1246			1.02892			0.514459	+	0.857515i	$0.327993\pi$
$278$	11.5279			0.691395
$279$	−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	$-0.203462\pi$
$282$	4.00000	+	10.4721i	0.238197	+	0.623607i
$283$		−	13.2361i		−	0.786803i	−0.919367	−	0.393401i	$-0.871298\pi$
$283$		−	13.2361i		−	0.786803i	0.919367	−	0.393401i	$-0.128702\pi$
$284$		−	7.23607i		−	0.429382i
$285$		0			0
$286$			5.52786i			0.326869i
$287$	−6.47214	−	0.944272i	−0.382038	−	0.0557386i
$288$	2.00000	+	2.23607i	0.117851	+	0.131762i
$289$	10.4164			0.612730
$290$		0			0
$291$	0.472136	+	1.23607i	0.0276771	+	0.0724596i
$292$		−	11.2361i		−	0.657541i
$293$	−2.58359			−0.150935			−0.0754675	−	0.997148i	$-0.524045\pi$
$293$	−2.58359			−0.150935			−0.0754675	+	0.997148i	$0.524045\pi$
$294$	−0.909830	−	12.0902i	−0.0530624	−	0.705113i
$295$		0			0
$296$			0.763932i			0.0444026i
$297$	20.6525	+	10.6525i	1.19838	+	0.618119i
$298$	−4.29180			−0.248617
$299$	4.94427			0.285935
$300$		0			0
$301$	−12.9443	−	1.88854i	−0.746095	−	0.108854i
$302$			20.9443i			1.20521i
$303$	−20.1803	+	7.70820i	−1.15933	+	0.442825i
$304$			8.47214i			0.485910i
$305$		0			0
$306$	10.4721	+	11.7082i	0.598652	+	0.669313i
$307$			18.1803i			1.03761i	0.854894	+	0.518803i	$0.173622\pi$
$307$			18.1803i			1.03761i	−0.854894	+	0.518803i	$0.826378\pi$
$308$	1.70820	−	11.7082i	0.0973340	−	0.667137i
$309$	−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	$0.665549\pi$
$312$	−2.00000	+	0.763932i	−0.113228	+	0.0432491i
$313$			5.70820i			0.322647i	0.986902	+	0.161323i	$0.0515762\pi$
$313$			5.70820i			0.322647i	−0.986902	+	0.161323i	$0.948424\pi$
$314$	−9.23607			−0.521221
$315$		0			0
$316$	8.94427			0.503155
$317$		−	10.9443i		−	0.614692i	−0.951598	−	0.307346i	$-0.900559\pi$
$317$		−	10.9443i		−	0.614692i	0.951598	−	0.307346i	$-0.0994408\pi$
$318$	0.763932	−	0.291796i	0.0428392	−	0.0163631i
$319$	34.4721			1.93007
$320$		0			0
$321$	−7.05573	−	18.4721i	−0.393812	−	1.03101i
$322$	−10.4721	−	1.52786i	−0.583589	−	0.0851445i
$323$			44.3607i			2.46829i
$324$	−1.00000	+	8.94427i	−0.0555556	+	0.496904i
$325$		0			0
$326$			10.4721i			0.579998i
$327$	−7.23607	+	2.76393i	−0.400155	+	0.152846i
$328$		−	2.47214i		−	0.136501i
$329$	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	$0.473237\pi$
$332$	−14.6525			−0.804159
$333$	−1.70820	+	1.52786i	−0.0936090	+	0.0837264i
$334$		−	0.944272i		−	0.0516683i
$335$		0			0
$336$	4.47214	−	1.00000i	0.243975	−	0.0545545i
$337$	−21.4164			−1.16663			−0.583313	−	0.812247i	$-0.698244\pi$
$337$	−21.4164			−1.16663			−0.583313	+	0.812247i	$0.698244\pi$
$338$			11.4721i			0.624002i
$339$	1.81966	+	4.76393i	0.0988304	+	0.258741i
$340$		0			0
$341$	−12.3607			−0.669368
$342$	−18.9443	+	16.9443i	−1.02439	+	0.916241i
$343$	−16.7984	−	7.79837i	−0.907027	−	0.421073i
$344$		−	4.94427i		−	0.266577i
$345$		0			0
$346$		−	9.41641i		−	0.506229i
$347$			2.47214i			0.132711i	0.997796	+	0.0663556i	$0.0211372\pi$
$347$			2.47214i			0.132711i	−0.997796	+	0.0663556i	$0.978863\pi$
$348$	4.76393	+	12.4721i	0.255374	+	0.668577i
$349$			20.1803i			1.08023i	0.841592	+	0.540114i	$0.181619\pi$
$349$			20.1803i			1.08023i	−0.841592	+	0.540114i	$0.818381\pi$
$350$		0			0
$351$	−5.70820	−	2.94427i	−0.304681	−	0.157154i
$352$	4.47214			0.238366
$353$	−27.7082			−1.47476			−0.737379	−	0.675479i	$-0.763937\pi$
$353$	−27.7082			−1.47476			−0.737379	+	0.675479i	$0.763937\pi$
$354$	2.76393	+	7.23607i	0.146901	+	0.384593i
$355$		0			0
$356$	−5.52786			−0.292976
$357$	23.4164	−	5.23607i	1.23933	−	0.277122i
$358$	−14.9443			−0.789829
$359$			12.1803i			0.642854i	0.946934	+	0.321427i	$0.104162\pi$
$359$			12.1803i			0.642854i	−0.946934	+	0.321427i	$0.895838\pi$
$360$		0			0
$361$	−52.7771			−2.77774
$362$	16.1803			0.850420
$363$	14.5623	−	5.56231i	0.764323	−	0.291945i
$364$	−0.472136	+	3.23607i	−0.0247466	+	0.169616i
$365$		0			0
$366$	11.7082	−	4.47214i	0.611998	−	0.233762i
$367$			8.18034i			0.427010i	0.976942	+	0.213505i	$0.0684880\pi$
$367$			8.18034i			0.427010i	−0.976942	+	0.213505i	$0.931512\pi$
$368$		−	4.00000i		−	0.208514i
$369$	5.52786	−	4.94427i	0.287769	−	0.257389i
$370$		0			0
$371$	0.180340	−	1.23607i	0.00936278	−	0.0641735i
$372$	−1.70820	−	4.47214i	−0.0885662	−	0.231869i
$373$	32.1803			1.66623			0.833117	−	0.553096i	$-0.186554\pi$
$373$	32.1803			1.66623			0.833117	+	0.553096i	$0.186554\pi$
$374$	23.4164			1.21083
$375$		0			0
$376$			6.47214i			0.333775i
$377$	−9.52786			−0.490710
$378$	11.1803	+	8.00000i	0.575055	+	0.411476i
$379$	−17.8885			−0.918873			−0.459436	−	0.888211i	$-0.651949\pi$
$379$	−17.8885			−0.918873			−0.459436	+	0.888211i	$0.651949\pi$
$380$		0			0
$381$	−0.472136	+	0.180340i	−0.0241883	+	0.00923909i
$382$	7.23607			0.370229
$383$	−13.8885			−0.709671			−0.354836	−	0.934929i	$-0.615463\pi$
$383$	−13.8885			−0.709671			−0.354836	+	0.934929i	$0.615463\pi$
$384$	0.618034	+	1.61803i	0.0315389	+	0.0825700i
$385$		0			0
$386$			6.00000i			0.305392i
$387$	11.0557	−	9.88854i	0.561994	−	0.502663i
$388$			0.763932i			0.0387828i
$389$		−	30.1803i		−	1.53020i	−0.643909	−	0.765102i	$-0.722689\pi$
$389$		−	30.1803i		−	1.53020i	0.643909	−	0.765102i	$-0.277311\pi$
$390$		0			0
$391$		−	20.9443i		−	1.05920i
$392$	2.00000	−	6.70820i	0.101015	−	0.338815i
$393$	8.76393	−	3.34752i	0.442082	−	0.168860i
$394$	−3.52786			−0.177731
$395$		0			0
$396$	8.94427	+	10.0000i	0.449467	+	0.502519i
$397$		−	23.1246i		−	1.16059i	−0.814406	−	0.580295i	$-0.802937\pi$
$397$		−	23.1246i		−	1.16059i	0.814406	−	0.580295i	$-0.197063\pi$
$398$	22.1803			1.11180
$399$	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	$-0.117685\pi$
$402$	−7.41641	−	19.4164i	−0.369897	−	0.968402i
$403$	3.41641			0.170183
$404$	−12.4721			−0.620512
$405$		0			0
$406$	20.1803	+	2.94427i	1.00153	+	0.146122i
$407$			3.41641i			0.169345i
$408$	3.23607	+	8.47214i	0.160209	+	0.419433i
$409$			7.41641i			0.366718i	0.983046	+	0.183359i	$0.0586970\pi$
$409$			7.41641i			0.366718i	−0.983046	+	0.183359i	$0.941303\pi$
$410$		0			0
$411$	−2.18034	−	5.70820i	−0.107548	−	0.281565i
$412$		−	14.6525i		−	0.721876i
$413$	11.7082	+	1.70820i	0.576123	+	0.0840552i
$414$	8.94427	−	8.00000i	0.439587	−	0.393179i
$415$		0			0
$416$	−1.23607			−0.0606032
$417$	7.12461	+	18.6525i	0.348894	+	0.913416i
$418$			37.8885i			1.85319i
$419$	−36.8328			−1.79940			−0.899700	−	0.436508i	$-0.856215\pi$
$419$	−36.8328			−1.79940			−0.899700	+	0.436508i	$0.856215\pi$
$420$		0			0
$421$	−3.52786			−0.171938			−0.0859688	−	0.996298i	$-0.527399\pi$
$421$	−3.52786			−0.171938			−0.0859688	+	0.996298i	$0.527399\pi$
$422$		−	8.00000i		−	0.389434i
$423$	−14.4721	+	12.9443i	−0.703659	+	0.629372i
$424$	0.472136			0.0229289
$425$		0			0
$426$	11.7082	−	4.47214i	0.567264	−	0.216676i
$427$	2.76393	−	18.9443i	0.133756	−	0.916778i
$428$		−	11.4164i		−	0.551833i
$429$	−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	$0.597289\pi$
$432$	−2.38197	+	4.61803i	−0.114602	+	0.222185i
$433$		−	26.6525i		−	1.28084i	−0.768026	−	0.640418i	$-0.778761\pi$
$433$		−	26.6525i		−	1.28084i	0.768026	−	0.640418i	$-0.221239\pi$
$434$	−7.23607	−	1.05573i	−0.347342	−	0.0506766i
$435$		0			0
$436$	−4.47214			−0.214176
$437$	33.8885			1.62111
$438$	18.1803	−	6.94427i	0.868690	−	0.331810i
$439$			10.1803i			0.485881i	0.970041	+	0.242941i	$0.0781120\pi$
$439$			10.1803i			0.485881i	−0.970041	+	0.242941i	$0.921888\pi$
$440$		0			0
$441$	19.0000	−	8.94427i	0.904762	−	0.425918i
$442$	−6.47214			−0.307848
$443$		−	18.4721i		−	0.877638i	−0.898576	−	0.438819i	$-0.855397\pi$
$443$		−	18.4721i		−	0.877638i	0.898576	−	0.438819i	$-0.144603\pi$
$444$	−1.23607	+	0.472136i	−0.0586612	+	0.0224066i
$445$		0			0
$446$	17.7082			0.838508
$447$	−2.65248	−	6.94427i	−0.125458	−	0.328453i
$448$	2.61803	+	0.381966i	0.123690	+	0.0180462i
$449$			10.4721i			0.494211i	0.968989	+	0.247105i	$0.0794794\pi$
$449$			10.4721i			0.494211i	−0.968989	+	0.247105i	$0.920521\pi$
$450$		0			0
$451$		−	11.0557i		−	0.520594i
$452$			2.94427i			0.138487i
$453$	−33.8885	+	12.9443i	−1.59222	+	0.608175i
$454$			0.763932i			0.0358531i
$455$		0			0
$456$	−13.7082	+	5.23607i	−0.641945	+	0.245201i
$457$	−26.9443			−1.26040			−0.630200	−	0.776433i	$-0.717027\pi$
$457$	−26.9443			−1.26040			−0.630200	+	0.776433i	$0.717027\pi$
$458$	8.76393			0.409512
$459$	−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	$0.448298\pi$
$462$	20.0000	−	4.47214i	0.930484	−	0.208063i
$463$	22.1803			1.03081			0.515404	−	0.856947i	$-0.327642\pi$
$463$	22.1803			1.03081			0.515404	+	0.856947i	$0.327642\pi$
$464$			7.70820i			0.357844i
$465$		0			0
$466$	−11.5279			−0.534018
$467$	−33.7082			−1.55983			−0.779915	−	0.625886i	$-0.784738\pi$
$467$	−33.7082			−1.55983			−0.779915	+	0.625886i	$0.784738\pi$
$468$	−2.47214	−	2.76393i	−0.114275	−	0.127763i
$469$	−31.4164	−	4.58359i	−1.45067	−	0.211651i
$470$		0			0
$471$	−5.70820	−	14.9443i	−0.263020	−	0.688596i
$472$			4.47214i			0.205847i
$473$		−	22.1115i		−	1.01669i
$474$	5.52786	+	14.4721i	0.253903	+	0.664727i
$475$		0			0
$476$	13.7082	+	2.00000i	0.628314	+	0.0916698i
$477$	0.944272	+	1.05573i	0.0432352	+	0.0483385i
$478$	0.180340			0.00824855
$479$	−37.8885			−1.73117			−0.865586	−	0.500761i	$-0.833054\pi$
$479$	−37.8885			−1.73117			−0.865586	+	0.500761i	$0.833054\pi$
$480$		0			0
$481$		−	0.944272i		−	0.0430551i
$482$	−17.8885			−0.814801
$483$	−4.00000	−	17.8885i	−0.182006	−	0.813957i
$484$	9.00000			0.409091
$485$		0			0
$486$	−15.0902	+	3.90983i	−0.684504	+	0.177353i
$487$	−17.5967			−0.797385			−0.398692	−	0.917085i	$-0.630536\pi$
$487$	−17.5967			−0.797385			−0.398692	+	0.917085i	$0.630536\pi$
$488$	7.23607			0.327561
$489$	−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	$-0.0979004\pi$
$492$	4.00000	−	1.52786i	0.180334	−	0.0688814i
$493$			40.3607i			1.81775i
$494$		−	10.4721i		−	0.471164i
$495$		0			0
$496$		−	2.76393i		−	0.124104i
$497$	2.76393	−	18.9443i	0.123979	−	0.849767i
$498$	−9.05573	−	23.7082i	−0.405797	−	1.06239i
$499$	17.8885			0.800801			0.400401	−	0.916340i	$-0.368871\pi$
$499$	17.8885			0.800801			0.400401	+	0.916340i	$0.368871\pi$
$500$		0			0
$501$	1.52786	−	0.583592i	0.0682599	−	0.0260730i
$502$			12.4721i			0.556659i
$503$	−28.3607			−1.26454			−0.632270	−	0.774748i	$-0.717877\pi$
$503$	−28.3607			−1.26454			−0.632270	+	0.774748i	$0.717877\pi$
$504$	4.38197	+	6.61803i	0.195188	+	0.294791i
$505$		0			0
$506$		−	17.8885i		−	0.795243i
$507$	−18.5623	+	7.09017i	−0.824381	+	0.314886i
$508$	−0.291796			−0.0129464
$509$	−15.5279			−0.688260			−0.344130	−	0.938922i	$-0.611826\pi$
$509$	−15.5279			−0.688260			−0.344130	+	0.938922i	$0.611826\pi$
$510$		0			0
$511$	4.29180	−	29.4164i	0.189858	−	1.30131i
$512$			1.00000i			0.0441942i
$513$	−39.1246	−	20.1803i	−1.72739	−	0.890984i
$514$			14.1803i			0.625468i
$515$		0			0
$516$	8.00000	−	3.05573i	0.352180	−	0.134521i
$517$			28.9443i			1.27297i
$518$	−0.291796	+	2.00000i	−0.0128208	+	0.0878750i
$519$	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	$0.199858\pi$
$522$	−17.2361	+	15.4164i	−0.754402	+	0.674758i
$523$			42.5410i			1.86019i	0.367320	+	0.930094i	$0.380275\pi$
$523$			42.5410i			1.86019i	−0.367320	+	0.930094i	$0.619725\pi$
$524$	5.41641			0.236617
$525$		0			0
$526$	12.9443			0.564397
$527$		−	14.4721i		−	0.630416i
$528$	2.76393	+	7.23607i	0.120285	+	0.314909i
$529$	7.00000			0.304348
$530$		0			0
$531$	−10.0000	+	8.94427i	−0.433963	+	0.388148i
$532$	−3.23607	+	22.1803i	−0.140301	+	0.961640i
$533$			3.05573i			0.132358i
$534$	−3.41641	−	8.94427i	−0.147842	−	0.387056i
$535$		0			0
$536$		−	12.0000i		−	0.518321i
$537$	−9.23607	−	24.1803i	−0.398566	−	1.04346i
$538$		−	4.47214i		−	0.192807i
$539$	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	$0.268347\pi$
$542$	−31.7082			−1.36198
$543$	10.0000	+	26.1803i	0.429141	+	1.12351i
$544$			5.23607i			0.224495i
$545$		0			0
$546$	−5.52786	+	1.23607i	−0.236571	+	0.0528988i
$547$	35.4164			1.51430			0.757148	−	0.653243i	$-0.226592\pi$
$547$	35.4164			1.51430			0.757148	+	0.653243i	$0.226592\pi$
$548$		−	3.52786i		−	0.150703i
$549$	14.4721	+	16.1803i	0.617656	+	0.690560i
$550$		0			0
$551$	−65.3050			−2.78208
$552$	6.47214	−	2.47214i	0.275472	−	0.105221i
$553$	23.4164	+	3.41641i	0.995767	+	0.145280i
$554$			17.1246i			0.727555i
$555$		0			0
$556$			11.5279i			0.488890i
$557$		−	7.52786i		−	0.318966i	−0.987201	−	0.159483i	$-0.949017\pi$
$557$		−	7.52786i		−	0.318966i	0.987201	−	0.159483i	$-0.0509827\pi$
$558$	6.18034	−	5.52786i	0.261635	−	0.234013i
$559$			6.11146i			0.258487i
$560$		0			0
$561$	14.4721	+	37.8885i	0.611014	+	1.59966i
$562$	20.0000			0.843649
$563$	40.1803			1.69340			0.846700	−	0.532071i	$-0.178586\pi$
$563$	40.1803			1.69340			0.846700	+	0.532071i	$0.178586\pi$
$564$	−10.4721	+	4.00000i	−0.440956	+	0.168430i
$565$		0			0
$566$	13.2361			0.556353
$567$	−6.03444	+	23.0344i	−0.253423	+	0.967356i
$568$	7.23607			0.303619
$569$		−	9.52786i		−	0.399429i	−0.979854	−	0.199714i	$-0.935999\pi$
$569$		−	9.52786i		−	0.399429i	0.979854	−	0.199714i	$-0.0640014\pi$
$570$		0			0
$571$	18.8328			0.788129			0.394064	−	0.919083i	$-0.371069\pi$
$571$	18.8328			0.788129			0.394064	+	0.919083i	$0.371069\pi$
$572$	−5.52786			−0.231132
$573$	4.47214	+	11.7082i	0.186826	+	0.489117i
$574$	0.944272	−	6.47214i	0.0394131	−	0.270142i
$575$		0			0
$576$	−2.23607	+	2.00000i	−0.0931695	+	0.0833333i
$577$			8.18034i			0.340552i	0.985396	+	0.170276i	$0.0544659\pi$
$577$			8.18034i			0.340552i	−0.985396	+	0.170276i	$0.945534\pi$
$578$			10.4164i			0.433265i
$579$	−9.70820	+	3.70820i	−0.403459	+	0.154108i
$580$		0			0
$581$	−38.3607	−	5.59675i	−1.59147	−	0.232192i
$582$	−1.23607	+	0.472136i	−0.0512367	+	0.0195707i
$583$	2.11146			0.0874476
$584$	11.2361			0.464952
$585$		0			0
$586$		−	2.58359i		−	0.106727i
$587$	−10.2918			−0.424788			−0.212394	−	0.977184i	$-0.568126\pi$
$587$	−10.2918			−0.424788			−0.212394	+	0.977184i	$0.568126\pi$
$588$	12.0902	−	0.909830i	0.498590	−	0.0375208i
$589$	23.4164			0.964856
$590$		0			0
$591$	−2.18034	−	5.70820i	−0.0896872	−	0.234804i
$592$	−0.763932			−0.0313974
$593$	−29.0132			−1.19143			−0.595714	−	0.803197i	$-0.703131\pi$
$593$	−29.0132			−1.19143			−0.595714	+	0.803197i	$0.703131\pi$
$594$	−10.6525	+	20.6525i	−0.437076	+	0.847381i
$595$		0			0
$596$		−	4.29180i		−	0.175799i
$597$	13.7082	+	35.8885i	0.561039	+	1.46882i
$598$			4.94427i			0.202186i
$599$		−	36.7639i		−	1.50213i	−0.660226	−	0.751067i	$-0.729540\pi$
$599$		−	36.7639i		−	1.50213i	0.660226	−	0.751067i	$-0.270460\pi$
$600$		0			0
$601$			5.52786i			0.225486i	0.993624	+	0.112743i	$0.0359637\pi$
$601$			5.52786i			0.225486i	−0.993624	+	0.112743i	$0.964036\pi$
$602$	1.88854	−	12.9443i	0.0769713	−	0.527569i
$603$	26.8328	−	24.0000i	1.09272	−	0.977356i
$604$	−20.9443			−0.852210
$605$		0			0
$606$	−7.70820	−	20.1803i	−0.313124	−	0.819770i
$607$			19.2361i			0.780768i	0.920652	+	0.390384i	$0.127658\pi$
$607$			19.2361i			0.780768i	−0.920652	+	0.390384i	$0.872342\pi$
$608$	−8.47214			−0.343590
$609$	7.70820	+	34.4721i	0.312352	+	1.39688i
$610$		0			0
$611$		−	8.00000i		−	0.323645i
$612$	−11.7082	+	10.4721i	−0.473276	+	0.423311i
$613$	−38.0689			−1.53759			−0.768794	−	0.639497i	$-0.779143\pi$
$613$	−38.0689			−1.53759			−0.768794	+	0.639497i	$0.779143\pi$
$614$	−18.1803			−0.733699
$615$		0			0
$616$	11.7082	+	1.70820i	0.471737	+	0.0688255i
$617$		−	2.00000i		−	0.0805170i	−0.999189	−	0.0402585i	$-0.987182\pi$
$617$		−	2.00000i		−	0.0805170i	0.999189	−	0.0402585i	$-0.0128181\pi$
$618$	23.7082	−	9.05573i	0.953684	−	0.364275i
$619$			14.0000i			0.562708i	0.959604	+	0.281354i	$0.0907834\pi$
$619$			14.0000i			0.562708i	−0.959604	+	0.281354i	$0.909217\pi$
$620$		0			0
$621$	18.4721	+	9.52786i	0.741261	+	0.382340i
$622$		−	17.5279i		−	0.702803i
$623$	−14.4721	−	2.11146i	−0.579814	−	0.0845937i
$624$	−0.763932	−	2.00000i	−0.0305818	−	0.0800641i
$625$		0			0
$626$	−5.70820			−0.228146
$627$	−61.3050	+	23.4164i	−2.44828	+	0.935161i
$628$		−	9.23607i		−	0.368559i
$629$	−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	$0.537395\pi$
$632$			8.94427i			0.355784i
$633$	12.9443	−	4.94427i	0.514489	−	0.196517i
$634$	10.9443			0.434653
$635$		0			0
$636$	0.291796	+	0.763932i	0.0115705	+	0.0302919i
$637$	−2.47214	+	8.29180i	−0.0979496	+	0.328533i
$638$			34.4721i			1.36476i
$639$	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	$-0.153028\pi$
$642$	18.4721	−	7.05573i	0.729037	−	0.278467i
$643$			12.2918i			0.484741i	0.970184	+	0.242371i	$0.0779250\pi$
$643$			12.2918i			0.484741i	−0.970184	+	0.242371i	$0.922075\pi$
$644$	1.52786	−	10.4721i	0.0602063	−	0.412660i
$645$		0			0
$646$	−44.3607			−1.74535
$647$	34.8328			1.36942			0.684710	−	0.728816i	$-0.259929\pi$
$647$	34.8328			1.36942			0.684710	+	0.728816i	$0.259929\pi$
$648$	−8.94427	−	1.00000i	−0.351364	−	0.0392837i
$649$			20.0000i			0.785069i
$650$		0			0
$651$	−2.76393	−	12.3607i	−0.108327	−	0.484453i
$652$	−10.4721			−0.410120
$653$			23.8885i			0.934831i	0.884038	+	0.467415i	$0.154815\pi$
$653$			23.8885i			0.934831i	−0.884038	+	0.467415i	$0.845185\pi$
$654$	−2.76393	−	7.23607i	−0.108078	−	0.282953i
$655$		0			0
$656$	2.47214			0.0965207
$657$	22.4721	+	25.1246i	0.876722	+	0.980204i
$658$	−2.47214	+	16.9443i	−0.0963739	+	0.660556i
$659$			31.5279i			1.22815i	0.789247	+	0.614076i	$0.210471\pi$
$659$			31.5279i			1.22815i	−0.789247	+	0.614076i	$0.789529\pi$
$660$		0			0
$661$			18.2918i			0.711468i	0.934587	+	0.355734i	$0.115769\pi$
$661$			18.2918i			0.711468i	−0.934587	+	0.355734i	$0.884231\pi$
$662$			3.05573i			0.118764i
$663$	−4.00000	−	10.4721i	−0.155347	−	0.406704i
$664$		−	14.6525i		−	0.568626i
$665$		0			0
$666$	−1.52786	−	1.70820i	−0.0592035	−	0.0661916i
$667$	30.8328			1.19385
$668$	0.944272			0.0365350
$669$	10.9443	+	28.6525i	0.423130	+	1.10777i
$670$		0			0
$671$	32.3607			1.24927
$672$	1.00000	+	4.47214i	0.0385758	+	0.172516i
$673$	−19.5279			−0.752744			−0.376372	−	0.926469i	$-0.622829\pi$
$673$	−19.5279			−0.752744			−0.376372	+	0.926469i	$0.622829\pi$
$674$		−	21.4164i		−	0.824929i
$675$		0			0
$676$	−11.4721			−0.441236
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$	−4.76393	+	1.81966i	−0.182958	+	0.0698836i
$679$	−0.291796	+	2.00000i	−0.0111981	+	0.0767530i
$680$		0			0
$681$	−1.23607	+	0.472136i	−0.0473662	+	0.0180923i
$682$		−	12.3607i		−	0.473315i
$683$			36.0000i			1.37750i	0.724998	+	0.688751i	$0.241841\pi$
$683$			36.0000i			1.37750i	−0.724998	+	0.688751i	$0.758159\pi$
$684$	−16.9443	−	18.9443i	−0.647880	−	0.724352i
$685$		0			0
$686$	7.79837	−	16.7984i	0.297743	−	0.641365i
$687$	5.41641	+	14.1803i	0.206649	+	0.541014i
$688$	4.94427			0.188499
$689$	−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	$-0.131163\pi$
$692$	9.41641			0.357958
$693$	19.5967	+	29.5967i	0.744419	+	1.12429i
$694$	−2.47214			−0.0938410
$695$		0			0
$696$	−12.4721	+	4.76393i	−0.472755	+	0.180576i
$697$	12.9443			0.490299
$698$	−20.1803			−0.763837
$699$	−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	$0.687064\pi$
$702$	2.94427	−	5.70820i	0.111124	−	0.215442i
$703$		−	6.47214i		−	0.244101i
$704$			4.47214i			0.168550i
$705$		0			0
$706$		−	27.7082i		−	1.04281i
$707$	−32.6525	−	4.76393i	−1.22802	−	0.179166i
$708$	−7.23607	+	2.76393i	−0.271948	+	0.103875i
$709$	−15.5279			−0.583161			−0.291581	−	0.956546i	$-0.594181\pi$
$709$	−15.5279			−0.583161			−0.291581	+	0.956546i	$0.594181\pi$
$710$		0			0
$711$	−20.0000	+	17.8885i	−0.750059	+	0.670873i
$712$		−	5.52786i		−	0.207165i
$713$	−11.0557			−0.414040
$714$	5.23607	+	23.4164i	0.195955	+	0.876337i
$715$		0			0
$716$		−	14.9443i		−	0.558494i
$717$	0.111456	+	0.291796i	0.00416241	+	0.0108973i
$718$	−12.1803			−0.454566
$719$	34.4721			1.28559			0.642797	−	0.766037i	$-0.277774\pi$
$719$	34.4721			1.28559			0.642797	+	0.766037i	$0.277774\pi$
$720$		0			0
$721$	5.59675	−	38.3607i	0.208434	−	1.42863i
$722$		−	52.7771i		−	1.96416i
$723$	−11.0557	−	28.9443i	−0.411167	−	1.07645i
$724$			16.1803i			0.601338i
$725$		0			0
$726$	5.56231	+	14.5623i	0.206437	+	0.540458i
$727$		−	26.2918i		−	0.975109i	−0.873093	−	0.487554i	$-0.837889\pi$
$727$		−	26.2918i		−	0.975109i	0.873093	−	0.487554i	$-0.162111\pi$
$728$	−3.23607	−	0.472136i	−0.119937	−	0.0174985i
$729$	−15.6525	−	22.0000i	−0.579721	−	0.814815i
$730$		0			0
$731$	25.8885			0.957522
$732$	4.47214	+	11.7082i	0.165295	+	0.432748i
$733$		−	20.0689i		−	0.741261i	−0.928780	−	0.370631i	$-0.879142\pi$
$733$		−	20.0689i		−	0.741261i	0.928780	−	0.370631i	$-0.120858\pi$
$734$	−8.18034			−0.301942
$735$		0			0
$736$	4.00000			0.147442
$737$		−	53.6656i		−	1.97680i
$738$	4.94427	+	5.52786i	0.182001	+	0.203483i
$739$	8.94427			0.329020			0.164510	−	0.986375i	$-0.447396\pi$
$739$	8.94427			0.329020			0.164510	+	0.986375i	$0.447396\pi$
$740$		0			0
$741$	16.9443	−	6.47214i	0.622463	−	0.237760i
$742$	1.23607	+	0.180340i	0.0453775	+	0.00662049i
$743$			10.4721i			0.384185i	0.981377	+	0.192093i	$0.0615274\pi$
$743$			10.4721i			0.384185i	−0.981377	+	0.192093i	$0.938473\pi$
$744$	4.47214	−	1.70820i	0.163956	−	0.0626258i
$745$		0			0
$746$			32.1803i			1.17821i
$747$	32.7639	−	29.3050i	1.19877	−	1.07221i
$748$			23.4164i			0.856189i
$749$	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	$0.449943\pi$
$752$	−6.47214			−0.236015
$753$	−20.1803	+	7.70820i	−0.735412	+	0.280903i
$754$		−	9.52786i		−	0.346984i
$755$		0			0
$756$	−8.00000	+	11.1803i	−0.290957	+	0.406625i
$757$	2.65248			0.0964059			0.0482029	−	0.998838i	$-0.484651\pi$
$757$	2.65248			0.0964059			0.0482029	+	0.998838i	$0.484651\pi$
$758$		−	17.8885i		−	0.649741i
$759$	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	$0.465962\pi$
$762$	−0.180340	−	0.472136i	−0.00653302	−	0.0171037i
$763$	−11.7082	−	1.70820i	−0.423865	−	0.0618411i
$764$			7.23607i			0.261792i
$765$		0			0
$766$		−	13.8885i		−	0.501813i
$767$		−	5.52786i		−	0.199600i
$768$	−1.61803	+	0.618034i	−0.0583858	+	0.0223014i
$769$		−	36.0000i		−	1.29819i	−0.760706	−	0.649097i	$-0.775147\pi$
$769$		−	36.0000i		−	1.29819i	0.760706	−	0.649097i	$-0.224853\pi$
$770$		0			0
$771$	−22.9443	+	8.76393i	−0.826318	+	0.315625i
$772$	−6.00000			−0.215945
$773$	10.5836			0.380665			0.190333	−	0.981720i	$-0.439043\pi$
$773$	10.5836			0.380665			0.190333	+	0.981720i	$0.439043\pi$
$774$	9.88854	+	11.0557i	0.355436	+	0.397390i
$775$		0			0
$776$	−0.763932			−0.0274236
$777$	−3.41641	+	0.763932i	−0.122563	+	0.0274059i
$778$	30.1803			1.08202
$779$			20.9443i			0.750406i
$780$		0			0
$781$	32.3607			1.15796
$782$	20.9443			0.748966
$783$	−35.5967	−	18.3607i	−1.27212	−	0.656157i
$784$	6.70820	+	2.00000i	0.239579	+	0.0714286i
$785$		0			0
$786$	3.34752	+	8.76393i	0.119402	+	0.312599i
$787$		−	36.2918i		−	1.29366i	−0.762633	−	0.646831i	$-0.776094\pi$
$787$		−	36.2918i		−	1.29366i	0.762633	−	0.646831i	$-0.223906\pi$
$788$		−	3.52786i		−	0.125675i
$789$	8.00000	+	20.9443i	0.284808	+	0.745636i
$790$		0			0
$791$	−1.12461	+	7.70820i	−0.0399866	+	0.274072i
$792$	−10.0000	+	8.94427i	−0.355335	+	0.317821i
$793$	−8.94427			−0.317620
$794$	23.1246			0.820662
$795$		0			0
$796$			22.1803i			0.786161i
$797$	21.4164			0.758608			0.379304	−	0.925272i	$-0.376163\pi$
$797$	21.4164			0.758608			0.379304	+	0.925272i	$0.376163\pi$
$798$	−37.8885	+	8.47214i	−1.34124	+	0.299910i
$799$	−33.8885			−1.19889
$800$		0			0
$801$	12.3607	−	11.0557i	0.436743	−	0.390635i
$802$	14.4721			0.511029
$803$	50.2492			1.77326
$804$	19.4164	−	7.41641i	0.684764	−	0.261557i
$805$		0			0
$806$			3.41641i			0.120338i
$807$	7.23607	−	2.76393i	0.254722	−	0.0972950i
$808$		−	12.4721i		−	0.438768i
$809$		−	36.3607i		−	1.27837i	−0.769052	−	0.639187i	$-0.779271\pi$
$809$		−	36.3607i		−	1.27837i	0.769052	−	0.639187i	$-0.220729\pi$
$810$		0			0
$811$			36.8328i			1.29338i	0.762755	+	0.646688i	$0.223846\pi$
$811$			36.8328i			1.29338i	−0.762755	+	0.646688i	$0.776154\pi$
$812$	−2.94427	+	20.1803i	−0.103324	+	0.708191i
$813$	−19.5967	−	51.3050i	−0.687288	−	1.79934i
$814$	−3.41641			−0.119745
$815$		0			0
$816$	−8.47214	+	3.23607i	−0.296584	+	0.113285i
$817$			41.8885i			1.46549i
$818$	−7.41641			−0.259309
$819$	−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	$0.813364\pi$
$822$	5.70820	−	2.18034i	0.199096	−	0.0760481i
$823$	22.1803			0.773158			0.386579	−	0.922256i	$-0.373657\pi$
$823$	22.1803			0.773158			0.386579	+	0.922256i	$0.373657\pi$
$824$	14.6525			0.510443
$825$		0			0
$826$	−1.70820	+	11.7082i	−0.0594360	+	0.407381i
$827$		−	38.8328i		−	1.35035i	−0.737658	−	0.675175i	$-0.764068\pi$
$827$		−	38.8328i		−	1.35035i	0.737658	−	0.675175i	$-0.235932\pi$
$828$	8.00000	+	8.94427i	0.278019	+	0.310835i
$829$			7.81966i			0.271588i	0.990737	+	0.135794i	$0.0433585\pi$
$829$			7.81966i			0.271588i	−0.990737	+	0.135794i	$0.956641\pi$
$830$		0			0
$831$	−27.7082	+	10.5836i	−0.961187	+	0.367141i
$832$		−	1.23607i		−	0.0428529i
$833$	35.1246	+	10.4721i	1.21700	+	0.362838i
$834$	−18.6525	+	7.12461i	−0.645882	+	0.246705i
$835$		0			0
$836$	−37.8885			−1.31040
$837$	12.7639	+	6.58359i	0.441186	+	0.227562i
$838$		−	36.8328i		−	1.27237i
$839$	−5.52786			−0.190843			−0.0954215	−	0.995437i	$-0.530420\pi$
$839$	−5.52786			−0.190843			−0.0954215	+	0.995437i	$0.530420\pi$
$840$		0			0
$841$	−30.4164			−1.04884
$842$		−	3.52786i		−	0.121578i
$843$	12.3607	+	32.3607i	0.425724	+	1.11456i
$844$	8.00000			0.275371
$845$		0			0
$846$	−12.9443	−	14.4721i	−0.445033	−	0.497562i
$847$	23.5623	+	3.43769i	0.809610	+	0.118121i
$848$			0.472136i			0.0162132i
$849$	8.18034	+	21.4164i	0.280749	+	0.735009i
$850$		0			0
$851$			3.05573i			0.104749i
$852$	4.47214	+	11.7082i	0.153213	+	0.401116i
$853$		−	7.70820i		−	0.263924i	−0.991255	−	0.131962i	$-0.957872\pi$
$853$		−	7.70820i		−	0.263924i	0.991255	−	0.131962i	$-0.0421277\pi$
$854$	18.9443	+	2.76393i	0.648260	+	0.0945798i
$855$		0			0
$856$	11.4164			0.390205
$857$	−11.3475			−0.387624			−0.193812	−	0.981039i	$-0.562085\pi$
$857$	−11.3475			−0.387624			−0.193812	+	0.981039i	$0.562085\pi$
$858$	−3.41641	−	8.94427i	−0.116634	−	0.305352i
$859$		−	17.0557i		−	0.581934i	−0.956733	−	0.290967i	$-0.906023\pi$
$859$		−	17.0557i		−	0.581934i	0.956733	−	0.290967i	$-0.0939770\pi$
$860$		0			0
$861$	11.0557	−	2.47214i	0.376778	−	0.0842502i
$862$	−39.5967			−1.34867
$863$			30.4721i			1.03728i	0.854992	+	0.518642i	$0.173562\pi$
$863$			30.4721i			1.03728i	−0.854992	+	0.518642i	$0.826438\pi$
$864$	−4.61803	−	2.38197i	−0.157109	−	0.0810361i
$865$		0			0
$866$	26.6525			0.905688
$867$	−16.8541	+	6.43769i	−0.572395	+	0.218636i
$868$	1.05573	−	7.23607i	0.0358337	−	0.245608i
$869$			40.0000i			1.35691i
$870$		0			0
$871$			14.8328i			0.502591i
$872$		−	4.47214i		−	0.151446i
$873$	−1.52786	−	1.70820i	−0.0517104	−	0.0578139i
$874$			33.8885i			1.14630i
$875$		0			0
$876$	6.94427	+	18.1803i	0.234625	+	0.614257i
$877$	−38.6525			−1.30520			−0.652601	−	0.757702i	$-0.726322\pi$
$877$	−38.6525			−1.30520			−0.652601	+	0.757702i	$0.726322\pi$
$878$	−10.1803			−0.343570
$879$	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	$0.583622\pi$
$882$	8.94427	+	19.0000i	0.301169	+	0.639763i
$883$	13.8885			0.467387			0.233693	−	0.972310i	$-0.424919\pi$
$883$	13.8885			0.467387			0.233693	+	0.972310i	$0.424919\pi$
$884$		−	6.47214i		−	0.217681i
$885$		0			0
$886$	18.4721			0.620584
$887$	−17.5279			−0.588528			−0.294264	−	0.955724i	$-0.595075\pi$
$887$	−17.5279			−0.588528			−0.294264	+	0.955724i	$0.595075\pi$
$888$	−0.472136	−	1.23607i	−0.0158438	−	0.0414797i
$889$	−0.763932	−	0.111456i	−0.0256215	−	0.00373812i
$890$		0			0
$891$	−40.0000	−	4.47214i	−1.34005	−	0.149822i
$892$			17.7082i			0.592915i
$893$		−	54.8328i		−	1.83491i
$894$	6.94427	−	2.65248i	0.232251	−	0.0887121i
$895$		0			0
$896$	−0.381966	+	2.61803i	−0.0127606	+	0.0874624i
$897$	−8.00000	+	3.05573i	−0.267112	+	0.102028i
$898$	−10.4721			−0.349460
$899$	21.3050			0.710560
$900$		0			0
$901$			2.47214i			0.0823588i
$902$	11.0557			0.368115
$903$	22.1115	−	4.94427i	0.735823	−	0.164535i
$904$	−2.94427			−0.0979250
$905$		0			0
$906$	−12.9443	−	33.8885i	−0.430045	−	1.12587i
$907$	17.5279			0.582003			0.291002	−	0.956723i	$-0.406012\pi$
$907$	17.5279			0.582003			0.291002	+	0.956723i	$0.406012\pi$
$908$	−0.763932			−0.0253520
$909$	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	$-0.316915\pi$
$912$	−5.23607	−	13.7082i	−0.173384	−	0.453924i
$913$		−	65.5279i		−	2.16866i
$914$		−	26.9443i		−	0.891237i
$915$		0			0
$916$			8.76393i			0.289568i
$917$	14.1803	+	2.06888i	0.468276	+	0.0683206i
$918$	−24.1803	−	12.4721i	−0.798070	−	0.411642i
$919$	−44.7214			−1.47522			−0.737611	−	0.675226i	$-0.764046\pi$
$919$	−44.7214			−1.47522			−0.737611	+	0.675226i	$0.764046\pi$
$920$		0			0
$921$	−11.2361	−	29.4164i	−0.370241	−	0.969304i
$922$			6.94427i			0.228697i
$923$	−8.94427			−0.294404
$924$	4.47214	+	20.0000i	0.147122	+	0.657952i
$925$		0			0
$926$			22.1803i			0.728891i
$927$	29.3050	+	32.7639i	0.962501	+	1.07611i
$928$	−7.70820			−0.253034
$929$	−37.8885			−1.24308			−0.621541	−	0.783381i	$-0.713493\pi$
$929$	−37.8885			−1.24308			−0.621541	+	0.783381i	$0.713493\pi$
$930$		0			0
$931$	−16.9443	+	56.8328i	−0.555326	+	1.86262i
$932$		−	11.5279i		−	0.377608i
$933$	28.3607	−	10.8328i	0.928487	−	0.354650i
$934$		−	33.7082i		−	1.10297i
$935$		0			0
$936$	2.76393	−	2.47214i	0.0903419	−	0.0808043i
$937$		−	42.0689i		−	1.37433i	−0.726501	−	0.687165i	$-0.758855\pi$
$937$		−	42.0689i		−	1.37433i	0.726501	−	0.687165i	$-0.241145\pi$
$938$	4.58359	−	31.4164i	0.149660	−	1.02578i
$939$	−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	$0.616742\pi$
$942$	14.9443	−	5.70820i	0.486911	−	0.185983i
$943$		−	9.88854i		−	0.322015i
$944$	−4.47214			−0.145556
$945$		0			0
$946$	22.1115			0.718905
$947$			60.3607i			1.96146i	0.195372	+	0.980729i	$0.437409\pi$
$947$			60.3607i			1.96146i	−0.195372	+	0.980729i	$0.562591\pi$
$948$	−14.4721	+	5.52786i	−0.470033	+	0.179537i
$949$	−13.8885			−0.450841
$950$		0			0
$951$	6.76393	+	17.7082i	0.219336	+	0.574228i
$952$	−2.00000	+	13.7082i	−0.0648204	+	0.444285i
$953$			22.5836i			0.731554i	0.930702	+	0.365777i	$0.119197\pi$
$953$			22.5836i			0.731554i	−0.930702	+	0.365777i	$0.880803\pi$
$954$	−1.05573	+	0.944272i	−0.0341805	+	0.0305719i
$955$		0			0
$956$			0.180340i			0.00583261i
$957$	−55.7771	+	21.3050i	−1.80302	+	0.688691i
$958$		−	37.8885i		−	1.22412i
$959$	1.34752	−	9.23607i	0.0435138	−	0.298248i
$960$		0			0
$961$	23.3607			0.753570
$962$	0.944272			0.0304445
$963$	22.8328	+	25.5279i	0.735777	+	0.822624i
$964$		−	17.8885i		−	0.576151i
$965$		0			0
$966$	17.8885	−	4.00000i	0.575554	−	0.128698i
$967$	39.4853			1.26976			0.634881	−	0.772610i	$-0.281049\pi$
$967$	39.4853			1.26976			0.634881	+	0.772610i	$0.281049\pi$
$968$			9.00000i			0.289271i
$969$	−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	$0.119239\pi$
$972$	−3.90983	−	15.0902i	−0.125408	−	0.484017i
$973$	−4.40325	+	30.1803i	−0.141162	+	0.967537i
$974$		−	17.5967i		−	0.563836i
$975$		0			0
$976$			7.23607i			0.231621i
$977$			1.41641i			0.0453149i	0.999743	+	0.0226575i	$0.00721271\pi$
$977$			1.41641i			0.0453149i	−0.999743	+	0.0226575i	$0.992787\pi$
$978$	−6.47214	−	16.9443i	−0.206956	−	0.541818i
$979$		−	24.7214i		−	0.790098i
$980$		0			0
$981$	10.0000	−	8.94427i	0.319275	−	0.285569i
$982$	13.4164			0.428135
$983$	−12.5836			−0.401354			−0.200677	−	0.979657i	$-0.564314\pi$
$983$	−12.5836			−0.401354			−0.200677	+	0.979657i	$0.564314\pi$
$984$	1.52786	+	4.00000i	0.0487065	+	0.127515i
$985$		0			0
$986$	−40.3607			−1.28535
$987$	−28.9443	+	6.47214i	−0.921306	+	0.206010i
$988$	10.4721			0.333163
$989$		−	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	$0.410197\pi$
$992$	2.76393			0.0877549
$993$	−4.94427	+	1.88854i	−0.156902	+	0.0599311i
$994$	18.9443	+	2.76393i	0.600876	+	0.0876666i
$995$		0			0
$996$	23.7082	−	9.05573i	0.751223	−	0.286942i
$997$		−	25.2361i		−	0.799234i	−0.916682	−	0.399617i	$-0.869143\pi$
$997$		−	25.2361i		−	0.799234i	0.916682	−	0.399617i	$-0.130857\pi$
$998$			17.8885i			0.566252i
$999$	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.b.a.251.3		4
3.2	odd	2		1050.2.b.c.251.2		4
5.2	odd	4		1050.2.d.a.1049.4		4
5.3	odd	4		1050.2.d.f.1049.1		4
5.4	even	2		210.2.b.b.41.2	yes	4
7.6	odd	2		1050.2.b.c.251.4		4
15.2	even	4		1050.2.d.d.1049.3		4
15.8	even	4		1050.2.d.c.1049.2		4
15.14	odd	2		210.2.b.a.41.3	yes	4
20.19	odd	2		1680.2.f.e.881.2		4
21.20	even	2	inner	1050.2.b.a.251.1		4
35.13	even	4		1050.2.d.d.1049.4		4
35.27	even	4		1050.2.d.c.1049.1		4
35.34	odd	2		210.2.b.a.41.1	✓	4
60.59	even	2		1680.2.f.i.881.4		4
105.62	odd	4		1050.2.d.f.1049.2		4
105.83	odd	4		1050.2.d.a.1049.3		4
105.104	even	2		210.2.b.b.41.4	yes	4
140.139	even	2		1680.2.f.i.881.3		4
420.419	odd	2		1680.2.f.e.881.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.b.a.41.1	✓	4	35.34	odd	2
210.2.b.a.41.3	yes	4	15.14	odd	2
210.2.b.b.41.2	yes	4	5.4	even	2
210.2.b.b.41.4	yes	4	105.104	even	2
1050.2.b.a.251.1		4	21.20	even	2	inner
1050.2.b.a.251.3		4	1.1	even	1	trivial
1050.2.b.c.251.2		4	3.2	odd	2
1050.2.b.c.251.4		4	7.6	odd	2
1050.2.d.a.1049.3		4	105.83	odd	4
1050.2.d.a.1049.4		4	5.2	odd	4
1050.2.d.c.1049.1		4	35.27	even	4
1050.2.d.c.1049.2		4	15.8	even	4
1050.2.d.d.1049.3		4	15.2	even	4
1050.2.d.d.1049.4		4	35.13	even	4
1050.2.d.f.1049.1		4	5.3	odd	4
1050.2.d.f.1049.2		4	105.62	odd	4
1680.2.f.e.881.1		4	420.419	odd	2
1680.2.f.e.881.2		4	20.19	odd	2
1680.2.f.i.881.3		4	140.139	even	2
1680.2.f.i.881.4		4	60.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.b (of order \(2\), degree \(1\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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