LMFDB - Embedded newform 1050.2.b.c.251.4

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			251.4
Root			$0.618034i$ of defining polynomial
Character	$\chi$	$=$	1050.251
Dual form			1050.2.b.c.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.61803 - 0.618034i) q^{3} -1.00000 q^{4} +(0.618034 + 1.61803i) q^{6} +(-2.61803 + 0.381966i) q^{7} -1.00000i q^{8} +(2.23607 - 2.00000i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.61803 - 0.618034i) q^{3} -1.00000 q^{4} +(0.618034 + 1.61803i) q^{6} +(-2.61803 + 0.381966i) q^{7} -1.00000i q^{8} +(2.23607 - 2.00000i) q^{9} -4.47214i q^{11} +(-1.61803 + 0.618034i) q^{12} -1.23607i q^{13} +(-0.381966 - 2.61803i) q^{14} +1.00000 q^{16} -5.23607 q^{17} +(2.00000 + 2.23607i) q^{18} -8.47214i q^{19} +(-4.00000 + 2.23607i) q^{21} +4.47214 q^{22} -4.00000i q^{23} +(-0.618034 - 1.61803i) q^{24} +1.23607 q^{26} +(2.38197 - 4.61803i) q^{27} +(2.61803 - 0.381966i) q^{28} +7.70820i q^{29} +2.76393i q^{31} +1.00000i q^{32} +(-2.76393 - 7.23607i) q^{33} -5.23607i q^{34} +(-2.23607 + 2.00000i) q^{36} -0.763932 q^{37} +8.47214 q^{38} +(-0.763932 - 2.00000i) q^{39} -2.47214 q^{41} +(-2.23607 - 4.00000i) q^{42} +4.94427 q^{43} +4.47214i q^{44} +4.00000 q^{46} +6.47214 q^{47} +(1.61803 - 0.618034i) q^{48} +(6.70820 - 2.00000i) q^{49} +(-8.47214 + 3.23607i) q^{51} +1.23607i q^{52} +0.472136i q^{53} +(4.61803 + 2.38197i) q^{54} +(0.381966 + 2.61803i) q^{56} +(-5.23607 - 13.7082i) q^{57} -7.70820 q^{58} +4.47214 q^{59} -7.23607i q^{61} -2.76393 q^{62} +(-5.09017 + 6.09017i) q^{63} -1.00000 q^{64} +(7.23607 - 2.76393i) q^{66} +12.0000 q^{67} +5.23607 q^{68} +(-2.47214 - 6.47214i) q^{69} +7.23607i q^{71} +(-2.00000 - 2.23607i) q^{72} -11.2361i q^{73} -0.763932i q^{74} +8.47214i q^{76} +(1.70820 + 11.7082i) q^{77} +(2.00000 - 0.763932i) q^{78} -8.94427 q^{79} +(1.00000 - 8.94427i) q^{81} -2.47214i q^{82} -14.6525 q^{83} +(4.00000 - 2.23607i) q^{84} +4.94427i q^{86} +(4.76393 + 12.4721i) q^{87} -4.47214 q^{88} -5.52786 q^{89} +(0.472136 + 3.23607i) q^{91} +4.00000i q^{92} +(1.70820 + 4.47214i) q^{93} +6.47214i q^{94} +(0.618034 + 1.61803i) q^{96} +0.763932i q^{97} +(2.00000 + 6.70820i) q^{98} +(-8.94427 - 10.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 16 q^{21} + 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} - 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} + 2 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} + 16 q^{84} + 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 - 16 * q^21 + 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 - 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 + 2 * 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 + 16 * q^84 + 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	$-0.945167\pi$
$13$		−	1.23607i		−	0.342824i	0.985199	−	0.171412i	$-0.0548329\pi$
$14$	−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	$-0.718986\pi$
$17$	−5.23607			−1.26993			−0.634967	+	0.772540i	$0.718986\pi$
$18$	2.00000	+	2.23607i	0.471405	+	0.527046i
$19$		−	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
$21$	−4.00000	+	2.23607i	−0.872872	+	0.487950i
$22$	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	$0.0798418\pi$
$31$			2.76393i			0.496417i	−0.968707	+	0.248208i	$0.920158\pi$
$32$			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	$-0.561835\pi$
$41$	−2.47214			−0.386083			−0.193041	+	0.981191i	$0.561835\pi$
$42$	−2.23607	−	4.00000i	−0.345033	−	0.617213i
$43$	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	$-0.343522\pi$
$47$	6.47214			0.944058			0.472029	+	0.881583i	$0.343522\pi$
$48$	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	$-0.405975\pi$
$59$	4.47214			0.582223			0.291111	+	0.956689i	$0.405975\pi$
$60$		0			0
$61$		−	7.23607i		−	0.926484i	−0.886232	−	0.463242i	$-0.846686\pi$
$61$		−	7.23607i		−	0.926484i	0.886232	−	0.463242i	$-0.153314\pi$
$62$	−2.76393			−0.351020
$63$	−5.09017	+	6.09017i	−0.641301	+	0.767289i
$64$	−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	$-0.771597\pi$
$73$		−	11.2361i		−	1.31508i	0.753419	−	0.657541i	$-0.228403\pi$
$74$		−	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	$-0.797384\pi$
$83$	−14.6525			−1.60832			−0.804159	+	0.594414i	$0.797384\pi$
$84$	4.00000	−	2.23607i	0.436436	−	0.243975i
$85$		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	$-0.594646\pi$
$89$	−5.52786			−0.585952			−0.292976	+	0.956120i	$0.594646\pi$
$90$		0			0
$91$	0.472136	+	3.23607i	0.0494933	+	0.339232i
$92$			4.00000i			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	$0.0123480\pi$
$97$			0.763932i			0.0775655i	−0.999248	+	0.0387828i	$0.987652\pi$
$98$	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	$-0.713075\pi$
$101$	−12.4721			−1.24102			−0.620512	+	0.784197i	$0.713075\pi$
$102$	−3.23607	−	8.47214i	−0.320418	−	0.838866i
$103$		−	14.6525i		−	1.44375i	−0.692023	−	0.721876i	$-0.743280\pi$
$103$		−	14.6525i		−	1.44375i	0.692023	−	0.721876i	$-0.256720\pi$
$104$	−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
$126$	−6.09017	−	5.09017i	−0.542555	−	0.453468i
$127$	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	$-0.423961\pi$
$131$	5.41641			0.473234			0.236617	+	0.971603i	$0.423961\pi$
$132$	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	$0.162598\pi$
$139$			11.5279i			0.977781i	−0.872345	+	0.488890i	$0.837402\pi$
$140$		0			0
$141$	10.4721	−	4.00000i	0.881913	−	0.336861i
$142$	−7.23607			−0.607237
$143$	−5.52786			−0.462263
$144$	2.23607	−	2.00000i	0.186339	−	0.166667i
$145$		0			0
$146$	11.2361			0.929904
$147$	9.61803	−	7.38197i	0.793282	−	0.608854i
$148$	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	$-0.879851\pi$
$157$		−	9.23607i		−	0.737118i	0.929604	−	0.368559i	$-0.120149\pi$
$158$		−	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	$-0.488368\pi$
$167$	0.944272			0.0730700			0.0365350	+	0.999332i	$0.488368\pi$
$168$	2.23607	+	4.00000i	0.172516	+	0.308607i
$169$	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	$-0.383473\pi$
$173$	9.41641			0.715916			0.357958	+	0.933738i	$0.383473\pi$
$174$	−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	$0.205365\pi$
$181$			16.1803i			1.20268i	−0.798995	+	0.601338i	$0.794635\pi$
$182$	−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
$189$	−4.47214	+	13.0000i	−0.325300	+	0.945611i
$190$		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	$0.287935\pi$
$199$			22.1803i			1.57232i	−0.618021	+	0.786161i	$0.712065\pi$
$200$		0			0
$201$	19.4164	−	7.41641i	1.36953	−	0.523113i
$202$		−	12.4721i		−	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	$0.202023\pi$
$223$			17.7082i			1.18583i	−0.805265	+	0.592915i	$0.797977\pi$
$224$	−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	$-0.508071\pi$
$227$	−0.763932			−0.0507039			−0.0253520	+	0.999679i	$0.508071\pi$
$228$	5.23607	+	13.7082i	0.346767	+	0.907848i
$229$			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
$231$	10.0000	+	17.8885i	0.657952	+	1.17698i
$232$	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	$-0.804554\pi$
$241$		−	17.8885i		−	1.15230i	0.817343	−	0.576151i	$-0.195446\pi$
$242$		−	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	$-0.628776\pi$
$251$	−12.4721			−0.787234			−0.393617	+	0.919274i	$0.628776\pi$
$252$	5.09017	−	6.09017i	0.320651	−	0.383645i
$253$	−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	$-0.645828\pi$
$257$	−14.1803			−0.884545			−0.442273	+	0.896881i	$0.645828\pi$
$258$	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	$-0.456467\pi$
$269$	4.47214			0.272671			0.136335	+	0.990663i	$0.456467\pi$
$270$		0			0
$271$		−	31.7082i		−	1.92614i	−0.269258	−	0.963068i	$-0.586778\pi$
$271$		−	31.7082i		−	1.92614i	0.269258	−	0.963068i	$-0.413222\pi$
$272$	−5.23607			−0.317483
$273$	2.76393	+	4.94427i	0.167281	+	0.299241i
$274$	−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	$0.128702\pi$
$283$			13.2361i			0.786803i	−0.919367	+	0.393401i	$0.871298\pi$
$284$		−	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	$-0.475955\pi$
$293$	2.58359			0.150935			0.0754675	+	0.997148i	$0.475955\pi$
$294$	7.38197	+	9.61803i	0.430525	+	0.560935i
$295$		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	$-0.826378\pi$
$307$		−	18.1803i		−	1.03761i	0.854894	−	0.518803i	$-0.173622\pi$
$308$	−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	$-0.334451\pi$
$311$	17.5279			0.993914			0.496957	+	0.867775i	$0.334451\pi$
$312$	−2.00000	+	0.763932i	−0.113228	+	0.0432491i
$313$		−	5.70820i		−	0.322647i	−0.986902	−	0.161323i	$-0.948424\pi$
$313$		−	5.70820i		−	0.322647i	0.986902	−	0.161323i	$-0.0515762\pi$
$314$	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
$336$	−4.00000	+	2.23607i	−0.218218	+	0.121988i
$337$	−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	$-0.818381\pi$
$349$		−	20.1803i		−	1.08023i	0.841592	−	0.540114i	$-0.181619\pi$
$350$		0			0
$351$	−5.70820	−	2.94427i	−0.304681	−	0.157154i
$352$	4.47214			0.238366
$353$	27.7082			1.47476			0.737379	−	0.675479i	$-0.236063\pi$
$353$	27.7082			1.47476			0.737379	+	0.675479i	$0.236063\pi$
$354$	2.76393	+	7.23607i	0.146901	+	0.384593i
$355$		0			0
$356$	5.52786			0.292976
$357$	20.9443	−	11.7082i	1.10849	−	0.619664i
$358$	−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	$-0.931512\pi$
$367$		−	8.18034i		−	0.427010i	0.976942	−	0.213505i	$-0.0684880\pi$
$368$		−	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
$378$	−13.0000	−	4.47214i	−0.668648	−	0.230022i
$379$	−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	$-0.384537\pi$
$383$	13.8885			0.709671			0.354836	+	0.934929i	$0.384537\pi$
$384$	−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	$0.197063\pi$
$397$			23.1246i			1.16059i	−0.814406	+	0.580295i	$0.802937\pi$
$398$	−22.1803			−1.11180
$399$	18.9443	+	33.8885i	0.948400	+	1.69655i
$400$		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	$-0.941303\pi$
$409$		−	7.41641i		−	0.366718i	0.983046	−	0.183359i	$-0.0586970\pi$
$410$		0			0
$411$	2.18034	+	5.70820i	0.107548	+	0.281565i
$412$			14.6525i			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	$-0.143785\pi$
$419$	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	$0.527399\pi$
$422$		−	8.00000i		−	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	$0.221239\pi$
$433$			26.6525i			1.28084i	−0.768026	+	0.640418i	$0.778761\pi$
$434$	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	$-0.921888\pi$
$439$		−	10.1803i		−	0.485881i	0.970041	−	0.242941i	$-0.0781120\pi$
$440$		0			0
$441$	11.0000	−	17.8885i	0.523810	−	0.851835i
$442$	−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	$-0.551702\pi$
$461$	−6.94427			−0.323427			−0.161713	+	0.986838i	$0.551702\pi$
$462$	−17.8885	+	10.0000i	−0.832250	+	0.465242i
$463$	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	$-0.215262\pi$
$467$	33.7082			1.55983			0.779915	+	0.625886i	$0.215262\pi$
$468$	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	$-0.166946\pi$
$479$	37.8885			1.73117			0.865586	+	0.500761i	$0.166946\pi$
$480$		0			0
$481$			0.944272i			0.0430551i
$482$	17.8885			0.814801
$483$	8.94427	+	16.0000i	0.406978	+	0.728025i
$484$	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	$-0.282123\pi$
$503$	28.3607			1.26454			0.632270	+	0.774748i	$0.282123\pi$
$504$	6.09017	+	5.09017i	0.271278	+	0.226734i
$505$		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	$-0.388174\pi$
$509$	15.5279			0.688260			0.344130	+	0.938922i	$0.388174\pi$
$510$		0			0
$511$	4.29180	+	29.4164i	0.189858	+	1.30131i
$512$			1.00000i			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	$-0.800142\pi$
$521$	−36.9443			−1.61856			−0.809279	+	0.587425i	$0.800142\pi$
$522$	−17.2361	+	15.4164i	−0.754402	+	0.674758i
$523$		−	42.5410i		−	1.86019i	−0.367320	−	0.930094i	$-0.619725\pi$
$523$		−	42.5410i		−	1.86019i	0.367320	−	0.930094i	$-0.380275\pi$
$524$	−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
$546$	−4.94427	+	2.76393i	−0.211595	+	0.118285i
$547$	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	$-0.821414\pi$
$563$	−40.1803			−1.69340			−0.846700	+	0.532071i	$0.821414\pi$
$564$	−10.4721	+	4.00000i	−0.440956	+	0.168430i
$565$		0			0
$566$	−13.2361			−0.556353
$567$	0.798374	+	23.7984i	0.0335286	+	0.999438i
$568$	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	$-0.945534\pi$
$577$		−	8.18034i		−	0.340552i	0.985396	−	0.170276i	$-0.0544659\pi$
$578$			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	$-0.431874\pi$
$587$	10.2918			0.424788			0.212394	+	0.977184i	$0.431874\pi$
$588$	−9.61803	+	7.38197i	−0.396641	+	0.304427i
$589$	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	$-0.296869\pi$
$593$	29.0132			1.19143			0.595714	+	0.803197i	$0.296869\pi$
$594$	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	$-0.964036\pi$
$601$		−	5.52786i		−	0.225486i	0.993624	−	0.112743i	$-0.0359637\pi$
$602$	−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	$-0.872342\pi$
$607$		−	19.2361i		−	0.780768i	0.920652	−	0.390384i	$-0.127658\pi$
$608$	8.47214			0.343590
$609$	−17.2361	−	30.8328i	−0.698441	−	1.24941i
$610$		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	$-0.909217\pi$
$619$		−	14.0000i		−	0.562708i	0.959604	−	0.281354i	$-0.0907834\pi$
$620$		0			0
$621$	−18.4721	−	9.52786i	−0.741261	−	0.382340i
$622$			17.5279i			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	$-0.922075\pi$
$643$		−	12.2918i		−	0.484741i	0.970184	−	0.242371i	$-0.0779250\pi$
$644$	−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	$-0.740071\pi$
$647$	−34.8328			−1.36942			−0.684710	+	0.728816i	$0.740071\pi$
$648$	−8.94427	−	1.00000i	−0.351364	−	0.0392837i
$649$		−	20.0000i		−	0.785069i
$650$		0			0
$651$	−6.18034	−	11.0557i	−0.242227	−	0.433308i
$652$	−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	$-0.884231\pi$
$661$		−	18.2918i		−	0.711468i	0.934587	−	0.355734i	$-0.115769\pi$
$662$			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
$672$	−2.23607	−	4.00000i	−0.0862582	−	0.154303i
$673$	−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	$-0.612426\pi$
$677$	−18.0000			−0.691796			−0.345898	+	0.938272i	$0.612426\pi$
$678$	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	$0.131163\pi$
$691$			21.0557i			0.800998i	−0.916297	+	0.400499i	$0.868837\pi$
$692$	−9.41641			−0.357958
$693$	27.2361	+	22.7639i	1.03461	+	0.864730i
$694$	−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
$714$	11.7082	+	20.9443i	0.438169	+	0.783820i
$715$		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	$-0.722226\pi$
$719$	−34.4721			−1.28559			−0.642797	+	0.766037i	$0.722226\pi$
$720$		0			0
$721$	5.59675	+	38.3607i	0.208434	+	1.42863i
$722$		−	52.7771i		−	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	$0.162111\pi$
$727$			26.2918i			0.975109i	−0.873093	+	0.487554i	$0.837889\pi$
$728$	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	$0.120858\pi$
$733$			20.0689i			0.741261i	−0.928780	+	0.370631i	$0.879142\pi$
$734$	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
$756$	4.47214	−	13.0000i	0.162650	−	0.472805i
$757$	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	$-0.534038\pi$
$761$	−5.88854			−0.213460			−0.106730	+	0.994288i	$0.534038\pi$
$762$	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	$0.224853\pi$
$769$			36.0000i			1.29819i	−0.760706	+	0.649097i	$0.775147\pi$
$770$		0			0
$771$	−22.9443	+	8.76393i	−0.826318	+	0.315625i
$772$	−6.00000			−0.215945
$773$	−10.5836			−0.380665			−0.190333	−	0.981720i	$-0.560957\pi$
$773$	−10.5836			−0.380665			−0.190333	+	0.981720i	$0.560957\pi$
$774$	9.88854	+	11.0557i	0.355436	+	0.397390i
$775$		0			0
$776$	0.763932			0.0274236
$777$	3.05573	−	1.70820i	0.109624	−	0.0612815i
$778$	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	$0.223906\pi$
$787$			36.2918i			1.29366i	−0.762633	+	0.646831i	$0.776094\pi$
$788$		−	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	$-0.623837\pi$
$797$	−21.4164			−0.758608			−0.379304	+	0.925272i	$0.623837\pi$
$798$	−33.8885	+	18.9443i	−1.19964	+	0.670620i
$799$	−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	$-0.776154\pi$
$811$		−	36.8328i		−	1.29338i	0.762755	−	0.646688i	$-0.223846\pi$
$812$	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
$819$	7.52786	+	6.29180i	0.263045	+	0.219853i
$820$		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	$-0.956641\pi$
$829$		−	7.81966i		−	0.271588i	0.990737	−	0.135794i	$-0.0433585\pi$
$830$		0			0
$831$	27.7082	−	10.5836i	0.961187	−	0.367141i
$832$			1.23607i			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	$-0.469580\pi$
$839$	5.52786			0.190843			0.0954215	+	0.995437i	$0.469580\pi$
$840$		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	$0.0421277\pi$
$853$			7.70820i			0.263924i	−0.991255	+	0.131962i	$0.957872\pi$
$854$	−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	$-0.437915\pi$
$857$	11.3475			0.387624			0.193812	+	0.981039i	$0.437915\pi$
$858$	−3.41641	−	8.94427i	−0.116634	−	0.305352i
$859$			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
$861$	9.88854	−	5.52786i	0.337001	−	0.188389i
$862$	−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	$-0.416378\pi$
$881$	15.4164			0.519392			0.259696	+	0.965690i	$0.416378\pi$
$882$	17.8885	+	11.0000i	0.602339	+	0.370389i
$883$	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	$-0.404925\pi$
$887$	17.5279			0.588528			0.294264	+	0.955724i	$0.404925\pi$
$888$	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
$903$	−19.7771	+	11.0557i	−0.658140	+	0.367912i
$904$	−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
$924$	−10.0000	−	17.8885i	−0.328976	−	0.588490i
$925$		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	$-0.286507\pi$
$929$	37.8885			1.24308			0.621541	+	0.783381i	$0.286507\pi$
$930$		0			0
$931$	−16.9443	−	56.8328i	−0.555326	−	1.86262i
$932$		−	11.5279i		−	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	$0.241145\pi$
$937$			42.0689i			1.37433i	−0.726501	+	0.687165i	$0.758855\pi$
$938$	−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	$-0.383258\pi$
$941$	22.0000			0.717180			0.358590	+	0.933495i	$0.383258\pi$
$942$	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
$966$	−16.0000	+	8.94427i	−0.514792	+	0.287777i
$967$	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	$-0.880761\pi$
$971$	−58.0000			−1.86131			−0.930654	+	0.365900i	$0.880761\pi$
$972$	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	$-0.435686\pi$
$983$	12.5836			0.401354			0.200677	+	0.979657i	$0.435686\pi$
$984$	1.52786	+	4.00000i	0.0487065	+	0.127515i
$985$		0			0
$986$	40.3607			1.28535
$987$	−25.8885	+	14.4721i	−0.824041	+	0.460653i
$988$	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	$0.130857\pi$
$997$			25.2361i			0.799234i	−0.916682	+	0.399617i	$0.869143\pi$
$998$			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.c.251.4		4
3.2	odd	2		1050.2.b.a.251.1		4
5.2	odd	4		1050.2.d.c.1049.1		4
5.3	odd	4		1050.2.d.d.1049.4		4
5.4	even	2		210.2.b.a.41.1	✓	4
7.6	odd	2		1050.2.b.a.251.3		4
15.2	even	4		1050.2.d.f.1049.2		4
15.8	even	4		1050.2.d.a.1049.3		4
15.14	odd	2		210.2.b.b.41.4	yes	4
20.19	odd	2		1680.2.f.i.881.3		4
21.20	even	2	inner	1050.2.b.c.251.2		4
35.13	even	4		1050.2.d.f.1049.1		4
35.27	even	4		1050.2.d.a.1049.4		4
35.34	odd	2		210.2.b.b.41.2	yes	4
60.59	even	2		1680.2.f.e.881.1		4
105.62	odd	4		1050.2.d.d.1049.3		4
105.83	odd	4		1050.2.d.c.1049.2		4
105.104	even	2		210.2.b.a.41.3	yes	4
140.139	even	2		1680.2.f.e.881.2		4
420.419	odd	2		1680.2.f.i.881.4		4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.61803 - 0.618034i) q^{3} -1.00000 q^{4} +(0.618034 + 1.61803i) q^{6} +(-2.61803 + 0.381966i) q^{7} -1.00000i q^{8} +(2.23607 - 2.00000i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.61803 - 0.618034i) q^{3} -1.00000 q^{4} +(0.618034 + 1.61803i) q^{6} +(-2.61803 + 0.381966i) q^{7} -1.00000i q^{8} +(2.23607 - 2.00000i) q^{9} -4.47214i q^{11} +(-1.61803 + 0.618034i) q^{12} -1.23607i q^{13} +(-0.381966 - 2.61803i) q^{14} +1.00000 q^{16} -5.23607 q^{17} +(2.00000 + 2.23607i) q^{18} -8.47214i q^{19} +(-4.00000 + 2.23607i) q^{21} +4.47214 q^{22} -4.00000i q^{23} +(-0.618034 - 1.61803i) q^{24} +1.23607 q^{26} +(2.38197 - 4.61803i) q^{27} +(2.61803 - 0.381966i) q^{28} +7.70820i q^{29} +2.76393i q^{31} +1.00000i q^{32} +(-2.76393 - 7.23607i) q^{33} -5.23607i q^{34} +(-2.23607 + 2.00000i) q^{36} -0.763932 q^{37} +8.47214 q^{38} +(-0.763932 - 2.00000i) q^{39} -2.47214 q^{41} +(-2.23607 - 4.00000i) q^{42} +4.94427 q^{43} +4.47214i q^{44} +4.00000 q^{46} +6.47214 q^{47} +(1.61803 - 0.618034i) q^{48} +(6.70820 - 2.00000i) q^{49} +(-8.47214 + 3.23607i) q^{51} +1.23607i q^{52} +0.472136i q^{53} +(4.61803 + 2.38197i) q^{54} +(0.381966 + 2.61803i) q^{56} +(-5.23607 - 13.7082i) q^{57} -7.70820 q^{58} +4.47214 q^{59} -7.23607i q^{61} -2.76393 q^{62} +(-5.09017 + 6.09017i) q^{63} -1.00000 q^{64} +(7.23607 - 2.76393i) q^{66} +12.0000 q^{67} +5.23607 q^{68} +(-2.47214 - 6.47214i) q^{69} +7.23607i q^{71} +(-2.00000 - 2.23607i) q^{72} -11.2361i q^{73} -0.763932i q^{74} +8.47214i q^{76} +(1.70820 + 11.7082i) q^{77} +(2.00000 - 0.763932i) q^{78} -8.94427 q^{79} +(1.00000 - 8.94427i) q^{81} -2.47214i q^{82} -14.6525 q^{83} +(4.00000 - 2.23607i) q^{84} +4.94427i q^{86} +(4.76393 + 12.4721i) q^{87} -4.47214 q^{88} -5.52786 q^{89} +(0.472136 + 3.23607i) q^{91} +4.00000i q^{92} +(1.70820 + 4.47214i) q^{93} +6.47214i q^{94} +(0.618034 + 1.61803i) q^{96} +0.763932i q^{97} +(2.00000 + 6.70820i) q^{98} +(-8.94427 - 10.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 4 q^{4} - 2 q^{6} - 6 q^{7}+O(q^{10}) \) 4 * q + 2 * q^3 - 4 * q^4 - 2 * q^6 - 6 * q^7	\( 4 q + 2 q^{3} - 4 q^{4} - 2 q^{6} - 6 q^{7} - 2 q^{12} - 6 q^{14} + 4 q^{16} - 12 q^{17} + 8 q^{18} - 16 q^{21} + 2 q^{24} - 4 q^{26} + 14 q^{27} + 6 q^{28} - 20 q^{33} - 12 q^{37} + 16 q^{38} - 12 q^{39} + 8 q^{41} - 16 q^{43} + 16 q^{46} + 8 q^{47} + 2 q^{48} - 16 q^{51} + 14 q^{54} + 6 q^{56} - 12 q^{57} - 4 q^{58} - 20 q^{62} + 2 q^{63} - 4 q^{64} + 20 q^{66} + 48 q^{67} + 12 q^{68} + 8 q^{69} - 8 q^{72} - 20 q^{77} + 8 q^{78} + 4 q^{81} + 4 q^{83} + 16 q^{84} + 28 q^{87} - 40 q^{89} - 16 q^{91} - 20 q^{93} - 2 q^{96} + 8 q^{98}+O(q^{100}) \) 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 - 16 * q^21 + 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 - 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 + 2 * 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 + 16 * q^84 + 28 * q^87 - 40 * q^89 - 16 * q^91 - 20 * q^93 - 2 * q^96 + 8 * q^98

Introduction

L-functions

Modular forms

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