LMFDB - Embedded newform 1050.2.b.c.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			$-1.61803i$ of defining polynomial
Character	$\chi$	$=$	1050.251
Dual form			1050.2.b.c.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.618034 + 1.61803i) q^{3} -1.00000 q^{4} +(-1.61803 - 0.618034i) q^{6} +(-0.381966 + 2.61803i) q^{7} -1.00000i q^{8} +(-2.23607 - 2.00000i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.618034 + 1.61803i) q^{3} -1.00000 q^{4} +(-1.61803 - 0.618034i) q^{6} +(-0.381966 + 2.61803i) q^{7} -1.00000i q^{8} +(-2.23607 - 2.00000i) q^{9} +4.47214i q^{11} +(0.618034 - 1.61803i) q^{12} +3.23607i q^{13} +(-2.61803 - 0.381966i) q^{14} +1.00000 q^{16} -0.763932 q^{17} +(2.00000 - 2.23607i) q^{18} +0.472136i q^{19} +(-4.00000 - 2.23607i) q^{21} -4.47214 q^{22} -4.00000i q^{23} +(1.61803 + 0.618034i) q^{24} -3.23607 q^{26} +(4.61803 - 2.38197i) q^{27} +(0.381966 - 2.61803i) q^{28} -5.70820i q^{29} +7.23607i q^{31} +1.00000i q^{32} +(-7.23607 - 2.76393i) q^{33} -0.763932i q^{34} +(2.23607 + 2.00000i) q^{36} -5.23607 q^{37} -0.472136 q^{38} +(-5.23607 - 2.00000i) q^{39} +6.47214 q^{41} +(2.23607 - 4.00000i) q^{42} -12.9443 q^{43} -4.47214i q^{44} +4.00000 q^{46} -2.47214 q^{47} +(-0.618034 + 1.61803i) q^{48} +(-6.70820 - 2.00000i) q^{49} +(0.472136 - 1.23607i) q^{51} -3.23607i q^{52} -8.47214i q^{53} +(2.38197 + 4.61803i) q^{54} +(2.61803 + 0.381966i) q^{56} +(-0.763932 - 0.291796i) q^{57} +5.70820 q^{58} -4.47214 q^{59} -2.76393i q^{61} -7.23607 q^{62} +(6.09017 - 5.09017i) q^{63} -1.00000 q^{64} +(2.76393 - 7.23607i) q^{66} +12.0000 q^{67} +0.763932 q^{68} +(6.47214 + 2.47214i) q^{69} +2.76393i q^{71} +(-2.00000 + 2.23607i) q^{72} -6.76393i q^{73} -5.23607i q^{74} -0.472136i q^{76} +(-11.7082 - 1.70820i) q^{77} +(2.00000 - 5.23607i) q^{78} +8.94427 q^{79} +(1.00000 + 8.94427i) q^{81} +6.47214i q^{82} +16.6525 q^{83} +(4.00000 + 2.23607i) q^{84} -12.9443i q^{86} +(9.23607 + 3.52786i) q^{87} +4.47214 q^{88} -14.4721 q^{89} +(-8.47214 - 1.23607i) q^{91} +4.00000i q^{92} +(-11.7082 - 4.47214i) q^{93} -2.47214i q^{94} +(-1.61803 - 0.618034i) q^{96} +5.23607i q^{97} +(2.00000 - 6.70820i) q^{98} +(8.94427 - 10.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.618034	+	1.61803i	−0.356822	+	0.934172i
$3$	−0.618034	+	1.61803i	−0.356822	+	0.934172i
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−1.61803	−	0.618034i	−0.660560	−	0.252311i
$7$	−0.381966	+	2.61803i	−0.144370	+	0.989524i
$7$	−0.381966	+	2.61803i	−0.144370	+	0.989524i
$8$		−	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	$0.235511\pi$
$11$			4.47214i			1.34840i	−0.738549	+	0.674200i	$0.764489\pi$
$12$	0.618034	−	1.61803i	0.178411	−	0.467086i
$13$			3.23607i			0.897524i	0.893651	+	0.448762i	$0.148135\pi$
$13$			3.23607i			0.897524i	−0.893651	+	0.448762i	$0.851865\pi$
$14$	−2.61803	−	0.381966i	−0.699699	−	0.102085i
$15$		0			0
$16$	1.00000			0.250000
$17$	−0.763932			−0.185281			−0.0926404	−	0.995700i	$-0.529531\pi$
$17$	−0.763932			−0.185281			−0.0926404	+	0.995700i	$0.529531\pi$
$18$	2.00000	−	2.23607i	0.471405	−	0.527046i
$19$			0.472136i			0.108315i	0.998532	+	0.0541577i	$0.0172474\pi$
$19$			0.472136i			0.108315i	−0.998532	+	0.0541577i	$0.982753\pi$
$20$		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	$-0.136929\pi$
$24$	1.61803	+	0.618034i	0.330280	+	0.126156i
$25$		0			0
$26$	−3.23607			−0.634645
$27$	4.61803	−	2.38197i	0.888741	−	0.458410i
$28$	0.381966	−	2.61803i	0.0721848	−	0.494762i
$29$		−	5.70820i		−	1.05999i	−0.848002	−	0.529993i	$-0.822194\pi$
$29$		−	5.70820i		−	1.05999i	0.848002	−	0.529993i	$-0.177806\pi$
$30$		0			0
$31$			7.23607i			1.29964i	0.760090	+	0.649818i	$0.225155\pi$
$31$			7.23607i			1.29964i	−0.760090	+	0.649818i	$0.774845\pi$
$32$			1.00000i			0.176777i
$33$	−7.23607	−	2.76393i	−1.25964	−	0.481139i
$34$		−	0.763932i		−	0.131013i
$35$		0			0
$36$	2.23607	+	2.00000i	0.372678	+	0.333333i
$37$	−5.23607			−0.860804			−0.430402	−	0.902637i	$-0.641628\pi$
$37$	−5.23607			−0.860804			−0.430402	+	0.902637i	$0.641628\pi$
$38$	−0.472136			−0.0765906
$39$	−5.23607	−	2.00000i	−0.838442	−	0.320256i
$40$		0			0
$41$	6.47214			1.01078			0.505389	−	0.862892i	$-0.331349\pi$
$41$	6.47214			1.01078			0.505389	+	0.862892i	$0.331349\pi$
$42$	2.23607	−	4.00000i	0.345033	−	0.617213i
$43$	−12.9443			−1.97398			−0.986991	−	0.160773i	$-0.948601\pi$
$43$	−12.9443			−1.97398			−0.986991	+	0.160773i	$0.948601\pi$
$44$		−	4.47214i		−	0.674200i
$45$		0			0
$46$	4.00000			0.589768
$47$	−2.47214			−0.360598			−0.180299	−	0.983612i	$-0.557707\pi$
$47$	−2.47214			−0.360598			−0.180299	+	0.983612i	$0.557707\pi$
$48$	−0.618034	+	1.61803i	−0.0892055	+	0.233543i
$49$	−6.70820	−	2.00000i	−0.958315	−	0.285714i
$50$		0			0
$51$	0.472136	−	1.23607i	0.0661123	−	0.173084i
$52$		−	3.23607i		−	0.448762i
$53$		−	8.47214i		−	1.16374i	−0.813283	−	0.581869i	$-0.802322\pi$
$53$		−	8.47214i		−	1.16374i	0.813283	−	0.581869i	$-0.197678\pi$
$54$	2.38197	+	4.61803i	0.324145	+	0.628435i
$55$		0			0
$56$	2.61803	+	0.381966i	0.349850	+	0.0510424i
$57$	−0.763932	−	0.291796i	−0.101185	−	0.0386493i
$58$	5.70820			0.749524
$59$	−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
$61$		−	2.76393i		−	0.353885i	−0.984221	−	0.176943i	$-0.943379\pi$
$61$		−	2.76393i		−	0.353885i	0.984221	−	0.176943i	$-0.0566207\pi$
$62$	−7.23607			−0.918982
$63$	6.09017	−	5.09017i	0.767289	−	0.641301i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	2.76393	−	7.23607i	0.340217	−	0.890698i
$67$	12.0000			1.46603			0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000			1.46603			0.733017	+	0.680211i	$0.238112\pi$
$68$	0.763932			0.0926404
$69$	6.47214	+	2.47214i	0.779154	+	0.297610i
$70$		0			0
$71$			2.76393i			0.328018i	0.986459	+	0.164009i	$0.0524427\pi$
$71$			2.76393i			0.328018i	−0.986459	+	0.164009i	$0.947557\pi$
$72$	−2.00000	+	2.23607i	−0.235702	+	0.263523i
$73$		−	6.76393i		−	0.791658i	−0.918324	−	0.395829i	$-0.870457\pi$
$73$		−	6.76393i		−	0.791658i	0.918324	−	0.395829i	$-0.129543\pi$
$74$		−	5.23607i		−	0.608681i
$75$		0			0
$76$		−	0.472136i		−	0.0541577i
$77$	−11.7082	−	1.70820i	−1.33427	−	0.194668i
$78$	2.00000	−	5.23607i	0.226455	−	0.592868i
$79$	8.94427			1.00631			0.503155	−	0.864196i	$-0.332173\pi$
$79$	8.94427			1.00631			0.503155	+	0.864196i	$0.332173\pi$
$80$		0			0
$81$	1.00000	+	8.94427i	0.111111	+	0.993808i
$82$			6.47214i			0.714728i
$83$	16.6525			1.82785			0.913923	−	0.405887i	$-0.133037\pi$
$83$	16.6525			1.82785			0.913923	+	0.405887i	$0.133037\pi$
$84$	4.00000	+	2.23607i	0.436436	+	0.243975i
$85$		0			0
$86$		−	12.9443i		−	1.39582i
$87$	9.23607	+	3.52786i	0.990210	+	0.378227i
$88$	4.47214			0.476731
$89$	−14.4721			−1.53404			−0.767022	−	0.641621i	$-0.778262\pi$
$89$	−14.4721			−1.53404			−0.767022	+	0.641621i	$0.778262\pi$
$90$		0			0
$91$	−8.47214	−	1.23607i	−0.888121	−	0.129575i
$92$			4.00000i			0.417029i
$93$	−11.7082	−	4.47214i	−1.21408	−	0.463739i
$94$		−	2.47214i		−	0.254981i
$95$		0			0
$96$	−1.61803	−	0.618034i	−0.165140	−	0.0630778i
$97$			5.23607i			0.531642i	0.964022	+	0.265821i	$0.0856430\pi$
$97$			5.23607i			0.531642i	−0.964022	+	0.265821i	$0.914357\pi$
$98$	2.00000	−	6.70820i	0.202031	−	0.677631i
$99$	8.94427	−	10.0000i	0.898933	−	1.00504i
$100$		0			0
$101$	−3.52786			−0.351036			−0.175518	−	0.984476i	$-0.556160\pi$
$101$	−3.52786			−0.351036			−0.175518	+	0.984476i	$0.556160\pi$
$102$	1.23607	+	0.472136i	0.122389	+	0.0467484i
$103$			16.6525i			1.64082i	0.571778	+	0.820409i	$0.306254\pi$
$103$			16.6525i			1.64082i	−0.571778	+	0.820409i	$0.693746\pi$
$104$	3.23607			0.317323
$105$		0			0
$106$	8.47214			0.822887
$107$		−	15.4164i		−	1.49036i	−0.666863	−	0.745180i	$-0.732363\pi$
$107$		−	15.4164i		−	1.49036i	0.666863	−	0.745180i	$-0.267637\pi$
$108$	−4.61803	+	2.38197i	−0.444371	+	0.229205i
$109$	−4.47214			−0.428353			−0.214176	−	0.976795i	$-0.568707\pi$
$109$	−4.47214			−0.428353			−0.214176	+	0.976795i	$0.568707\pi$
$110$		0			0
$111$	3.23607	−	8.47214i	0.307154	−	0.804140i
$112$	−0.381966	+	2.61803i	−0.0360924	+	0.247381i
$113$			14.9443i			1.40584i	0.711269	+	0.702919i	$0.248121\pi$
$113$			14.9443i			1.40584i	−0.711269	+	0.702919i	$0.751879\pi$
$114$	0.291796	−	0.763932i	0.0273292	−	0.0715488i
$115$		0			0
$116$			5.70820i			0.529993i
$117$	6.47214	−	7.23607i	0.598349	−	0.668975i
$118$		−	4.47214i		−	0.411693i
$119$	0.291796	−	2.00000i	0.0267489	−	0.183340i
$120$		0			0
$121$	−9.00000			−0.818182
$122$	2.76393			0.250235
$123$	−4.00000	+	10.4721i	−0.360668	+	0.944241i
$124$		−	7.23607i		−	0.649818i
$125$		0			0
$126$	5.09017	+	6.09017i	0.453468	+	0.542555i
$127$	13.7082			1.21641			0.608203	−	0.793781i	$-0.291891\pi$
$127$	13.7082			1.21641			0.608203	+	0.793781i	$0.291891\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	8.00000	−	20.9443i	0.704361	−	1.84404i
$130$		0			0
$131$	−21.4164			−1.87116			−0.935580	−	0.353114i	$-0.885123\pi$
$131$	−21.4164			−1.87116			−0.935580	+	0.353114i	$0.885123\pi$
$132$	7.23607	+	2.76393i	0.629819	+	0.240569i
$133$	−1.23607	−	0.180340i	−0.107181	−	0.0156375i
$134$			12.0000i			1.03664i
$135$		0			0
$136$			0.763932i			0.0655066i
$137$			12.4721i			1.06557i	0.846252	+	0.532783i	$0.178854\pi$
$137$			12.4721i			1.06557i	−0.846252	+	0.532783i	$0.821146\pi$
$138$	−2.47214	+	6.47214i	−0.210442	+	0.550945i
$139$			20.4721i			1.73642i	0.496194	+	0.868212i	$0.334731\pi$
$139$			20.4721i			1.73642i	−0.496194	+	0.868212i	$0.665269\pi$
$140$		0			0
$141$	1.52786	−	4.00000i	0.128669	−	0.336861i
$142$	−2.76393			−0.231944
$143$	−14.4721			−1.21022
$144$	−2.23607	−	2.00000i	−0.186339	−	0.166667i
$145$		0			0
$146$	6.76393			0.559787
$147$	7.38197	−	9.61803i	0.608854	−	0.793282i
$148$	5.23607			0.430402
$149$			17.7082i			1.45071i	0.688374	+	0.725356i	$0.258325\pi$
$149$			17.7082i			1.45071i	−0.688374	+	0.725356i	$0.741675\pi$
$150$		0			0
$151$	3.05573			0.248672			0.124336	−	0.992240i	$-0.460320\pi$
$151$	3.05573			0.248672			0.124336	+	0.992240i	$0.460320\pi$
$152$	0.472136			0.0382953
$153$	1.70820	+	1.52786i	0.138100	+	0.123520i
$154$	1.70820	−	11.7082i	0.137651	−	0.943474i
$155$		0			0
$156$	5.23607	+	2.00000i	0.419221	+	0.160128i
$157$		−	4.76393i		−	0.380203i	−0.981764	−	0.190102i	$-0.939118\pi$
$157$		−	4.76393i		−	0.380203i	0.981764	−	0.190102i	$-0.0608817\pi$
$158$			8.94427i			0.711568i
$159$	13.7082	+	5.23607i	1.08713	+	0.415247i
$160$		0			0
$161$	10.4721	+	1.52786i	0.825320	+	0.120413i
$162$	−8.94427	+	1.00000i	−0.702728	+	0.0785674i
$163$	1.52786			0.119672			0.0598358	−	0.998208i	$-0.480942\pi$
$163$	1.52786			0.119672			0.0598358	+	0.998208i	$0.480942\pi$
$164$	−6.47214			−0.505389
$165$		0			0
$166$			16.6525i			1.29248i
$167$	−16.9443			−1.31119			−0.655594	−	0.755114i	$-0.727582\pi$
$167$	−16.9443			−1.31119			−0.655594	+	0.755114i	$0.727582\pi$
$168$	−2.23607	+	4.00000i	−0.172516	+	0.308607i
$169$	2.52786			0.194451
$170$		0			0
$171$	0.944272	−	1.05573i	0.0722103	−	0.0807335i
$172$	12.9443			0.986991
$173$	−17.4164			−1.32414			−0.662072	−	0.749440i	$-0.730323\pi$
$173$	−17.4164			−1.32414			−0.662072	+	0.749440i	$0.730323\pi$
$174$	−3.52786	+	9.23607i	−0.267447	+	0.700185i
$175$		0			0
$176$			4.47214i			0.337100i
$177$	2.76393	−	7.23607i	0.207750	−	0.543896i
$178$		−	14.4721i		−	1.08473i
$179$		−	2.94427i		−	0.220065i	−0.993928	−	0.110033i	$-0.964904\pi$
$179$		−	2.94427i		−	0.220065i	0.993928	−	0.110033i	$-0.0350955\pi$
$180$		0			0
$181$		−	6.18034i		−	0.459381i	−0.973264	−	0.229691i	$-0.926229\pi$
$181$		−	6.18034i		−	0.459381i	0.973264	−	0.229691i	$-0.0737714\pi$
$182$	1.23607	−	8.47214i	0.0916235	−	0.627996i
$183$	4.47214	+	1.70820i	0.330590	+	0.126274i
$184$	−4.00000			−0.294884
$185$		0			0
$186$	4.47214	−	11.7082i	0.327913	−	0.858487i
$187$		−	3.41641i		−	0.249832i
$188$	2.47214			0.180299
$189$	4.47214	+	13.0000i	0.325300	+	0.945611i
$190$		0			0
$191$		−	2.76393i		−	0.199991i	−0.994988	−	0.0999956i	$-0.968117\pi$
$191$		−	2.76393i		−	0.199991i	0.994988	−	0.0999956i	$-0.0318829\pi$
$192$	0.618034	−	1.61803i	0.0446028	−	0.116772i
$193$	6.00000			0.431889			0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000			0.431889			0.215945	+	0.976406i	$0.430717\pi$
$194$	−5.23607			−0.375928
$195$		0			0
$196$	6.70820	+	2.00000i	0.479157	+	0.142857i
$197$			12.4721i			0.888603i	0.895877	+	0.444301i	$0.146548\pi$
$197$			12.4721i			0.888603i	−0.895877	+	0.444301i	$0.853452\pi$
$198$	10.0000	+	8.94427i	0.710669	+	0.635642i
$199$		−	0.180340i		−	0.0127840i	−0.999980	−	0.00639198i	$-0.997965\pi$
$199$		−	0.180340i		−	0.0127840i	0.999980	−	0.00639198i	$-0.00203464\pi$
$200$		0			0
$201$	−7.41641	+	19.4164i	−0.523113	+	1.36953i
$202$		−	3.52786i		−	0.248220i
$203$	14.9443	+	2.18034i	1.04888	+	0.153030i
$204$	−0.472136	+	1.23607i	−0.0330561	+	0.0865421i
$205$		0			0
$206$	−16.6525			−1.16023
$207$	−8.00000	+	8.94427i	−0.556038	+	0.621670i
$208$			3.23607i			0.224381i
$209$	−2.11146			−0.146052
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$			8.47214i			0.581869i
$213$	−4.47214	−	1.70820i	−0.306426	−	0.117044i
$214$	15.4164			1.05384
$215$		0			0
$216$	−2.38197	−	4.61803i	−0.162072	−	0.314217i
$217$	−18.9443	−	2.76393i	−1.28602	−	0.187628i
$218$		−	4.47214i		−	0.302891i
$219$	10.9443	+	4.18034i	0.739545	+	0.282481i
$220$		0			0
$221$		−	2.47214i		−	0.166294i
$222$	8.47214	+	3.23607i	0.568613	+	0.217191i
$223$			4.29180i			0.287400i	0.989621	+	0.143700i	$0.0459000\pi$
$223$			4.29180i			0.287400i	−0.989621	+	0.143700i	$0.954100\pi$
$224$	−2.61803	−	0.381966i	−0.174925	−	0.0255212i
$225$		0			0
$226$	−14.9443			−0.994078
$227$	−5.23607			−0.347530			−0.173765	−	0.984787i	$-0.555593\pi$
$227$	−5.23607			−0.347530			−0.173765	+	0.984787i	$0.555593\pi$
$228$	0.763932	+	0.291796i	0.0505926	+	0.0193247i
$229$			13.2361i			0.874664i	0.899300	+	0.437332i	$0.144077\pi$
$229$			13.2361i			0.874664i	−0.899300	+	0.437332i	$0.855923\pi$
$230$		0			0
$231$	10.0000	−	17.8885i	0.657952	−	1.17698i
$232$	−5.70820			−0.374762
$233$			20.4721i			1.34117i	0.741831	+	0.670587i	$0.233958\pi$
$233$			20.4721i			1.34117i	−0.741831	+	0.670587i	$0.766042\pi$
$234$	7.23607	+	6.47214i	0.473037	+	0.423097i
$235$		0			0
$236$	4.47214			0.291111
$237$	−5.52786	+	14.4721i	−0.359073	+	0.940066i
$238$	2.00000	+	0.291796i	0.129641	+	0.0189143i
$239$			22.1803i			1.43473i	0.696699	+	0.717363i	$0.254651\pi$
$239$			22.1803i			1.43473i	−0.696699	+	0.717363i	$0.745349\pi$
$240$		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
$243$	−15.0902	−	3.90983i	−0.968035	−	0.250816i
$244$			2.76393i			0.176943i
$245$		0			0
$246$	−10.4721	−	4.00000i	−0.667679	−	0.255031i
$247$	−1.52786			−0.0972157
$248$	7.23607			0.459491
$249$	−10.2918	+	26.9443i	−0.652216	+	1.70752i
$250$		0			0
$251$	−3.52786			−0.222677			−0.111338	−	0.993783i	$-0.535514\pi$
$251$	−3.52786			−0.222677			−0.111338	+	0.993783i	$0.535514\pi$
$252$	−6.09017	+	5.09017i	−0.383645	+	0.320651i
$253$	17.8885			1.12464
$254$			13.7082i			0.860129i
$255$		0			0
$256$	1.00000			0.0625000
$257$	8.18034			0.510276			0.255138	−	0.966905i	$-0.417879\pi$
$257$	8.18034			0.510276			0.255138	+	0.966905i	$0.417879\pi$
$258$	20.9443	+	8.00000i	1.30393	+	0.498058i
$259$	2.00000	−	13.7082i	0.124274	−	0.851786i
$260$		0			0
$261$	−11.4164	+	12.7639i	−0.706658	+	0.790068i
$262$		−	21.4164i		−	1.32311i
$263$			4.94427i			0.304877i	0.988313	+	0.152438i	$0.0487126\pi$
$263$			4.94427i			0.304877i	−0.988313	+	0.152438i	$0.951287\pi$
$264$	−2.76393	+	7.23607i	−0.170108	+	0.445349i
$265$		0			0
$266$	0.180340	−	1.23607i	0.0110573	−	0.0757882i
$267$	8.94427	−	23.4164i	0.547381	−	1.43306i
$268$	−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
$271$		−	18.2918i		−	1.11115i	−0.831467	−	0.555574i	$-0.812499\pi$
$271$		−	18.2918i		−	1.11115i	0.831467	−	0.555574i	$-0.187501\pi$
$272$	−0.763932			−0.0463202
$273$	7.23607	−	12.9443i	0.437947	−	0.783423i
$274$	−12.4721			−0.753469
$275$		0			0
$276$	−6.47214	−	2.47214i	−0.389577	−	0.148805i
$277$	−23.1246			−1.38942			−0.694712	−	0.719288i	$-0.744468\pi$
$277$	−23.1246			−1.38942			−0.694712	+	0.719288i	$0.744468\pi$
$278$	−20.4721			−1.22784
$279$	14.4721	−	16.1803i	0.866424	−	0.968692i
$280$		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	+	1.52786i	0.238197	+	0.0909830i
$283$			8.76393i			0.520962i	0.965479	+	0.260481i	$0.0838811\pi$
$283$			8.76393i			0.520962i	−0.965479	+	0.260481i	$0.916119\pi$
$284$		−	2.76393i		−	0.164009i
$285$		0			0
$286$		−	14.4721i		−	0.855755i
$287$	−2.47214	+	16.9443i	−0.145926	+	1.00019i
$288$	2.00000	−	2.23607i	0.117851	−	0.131762i
$289$	−16.4164			−0.965671
$290$		0			0
$291$	−8.47214	−	3.23607i	−0.496645	−	0.189702i
$292$			6.76393i			0.395829i
$293$	29.4164			1.71852			0.859262	−	0.511535i	$-0.170923\pi$
$293$	29.4164			1.71852			0.859262	+	0.511535i	$0.170923\pi$
$294$	9.61803	+	7.38197i	0.560935	+	0.430525i
$295$		0			0
$296$			5.23607i			0.304340i
$297$	10.6525	+	20.6525i	0.618119	+	1.19838i
$298$	−17.7082			−1.02581
$299$	12.9443			0.748587
$300$		0			0
$301$	4.94427	−	33.8885i	0.284983	−	1.95330i
$302$			3.05573i			0.175837i
$303$	2.18034	−	5.70820i	0.125257	−	0.327928i
$304$			0.472136i			0.0270789i
$305$		0			0
$306$	−1.52786	+	1.70820i	−0.0873422	+	0.0976515i
$307$			4.18034i			0.238585i	0.992859	+	0.119292i	$0.0380626\pi$
$307$			4.18034i			0.238585i	−0.992859	+	0.119292i	$0.961937\pi$
$308$	11.7082	+	1.70820i	0.667137	+	0.0973340i
$309$	−26.9443	−	10.2918i	−1.53281	−	0.585480i
$310$		0			0
$311$	26.4721			1.50110			0.750549	−	0.660815i	$-0.229789\pi$
$311$	26.4721			1.50110			0.750549	+	0.660815i	$0.229789\pi$
$312$	−2.00000	+	5.23607i	−0.113228	+	0.296434i
$313$			7.70820i			0.435693i	0.975983	+	0.217847i	$0.0699033\pi$
$313$			7.70820i			0.435693i	−0.975983	+	0.217847i	$0.930097\pi$
$314$	4.76393			0.268844
$315$		0			0
$316$	−8.94427			−0.503155
$317$			6.94427i			0.390029i	0.980800	+	0.195015i	$0.0624754\pi$
$317$			6.94427i			0.390029i	−0.980800	+	0.195015i	$0.937525\pi$
$318$	−5.23607	+	13.7082i	−0.293624	+	0.768718i
$319$	25.5279			1.42929
$320$		0			0
$321$	24.9443	+	9.52786i	1.39225	+	0.531794i
$322$	−1.52786	+	10.4721i	−0.0851445	+	0.583589i
$323$		−	0.360680i		−	0.0200688i
$324$	−1.00000	−	8.94427i	−0.0555556	−	0.496904i
$325$		0			0
$326$			1.52786i			0.0846206i
$327$	2.76393	−	7.23607i	0.152846	−	0.400155i
$328$		−	6.47214i		−	0.357364i
$329$	0.944272	−	6.47214i	0.0520594	−	0.356820i
$330$		0			0
$331$	20.9443			1.15120			0.575601	−	0.817731i	$-0.304768\pi$
$331$	20.9443			1.15120			0.575601	+	0.817731i	$0.304768\pi$
$332$	−16.6525			−0.913923
$333$	11.7082	+	10.4721i	0.641606	+	0.573870i
$334$		−	16.9443i		−	0.927149i
$335$		0			0
$336$	−4.00000	−	2.23607i	−0.218218	−	0.121988i
$337$	5.41641			0.295051			0.147525	−	0.989058i	$-0.452869\pi$
$337$	5.41641			0.295051			0.147525	+	0.989058i	$0.452869\pi$
$338$			2.52786i			0.137498i
$339$	−24.1803	−	9.23607i	−1.31330	−	0.501634i
$340$		0			0
$341$	−32.3607			−1.75243
$342$	1.05573	+	0.944272i	0.0570872	+	0.0510604i
$343$	7.79837	−	16.7984i	0.421073	−	0.907027i
$344$			12.9443i			0.697908i
$345$		0			0
$346$		−	17.4164i		−	0.936312i
$347$		−	6.47214i		−	0.347442i	−0.984795	−	0.173721i	$-0.944421\pi$
$347$		−	6.47214i		−	0.347442i	0.984795	−	0.173721i	$-0.0555792\pi$
$348$	−9.23607	−	3.52786i	−0.495105	−	0.189113i
$349$			2.18034i			0.116711i	0.998296	+	0.0583555i	$0.0185857\pi$
$349$			2.18034i			0.116711i	−0.998296	+	0.0583555i	$0.981414\pi$
$350$		0			0
$351$	7.70820	+	14.9443i	0.411433	+	0.797666i
$352$	−4.47214			−0.238366
$353$	14.2918			0.760676			0.380338	−	0.924848i	$-0.375808\pi$
$353$	14.2918			0.760676			0.380338	+	0.924848i	$0.375808\pi$
$354$	7.23607	+	2.76393i	0.384593	+	0.146901i
$355$		0			0
$356$	14.4721			0.767022
$357$	3.05573	+	1.70820i	0.161726	+	0.0904077i
$358$	2.94427			0.155610
$359$		−	10.1803i		−	0.537298i	−0.963238	−	0.268649i	$-0.913423\pi$
$359$		−	10.1803i		−	0.537298i	0.963238	−	0.268649i	$-0.0865771\pi$
$360$		0			0
$361$	18.7771			0.988268
$362$	6.18034			0.324831
$363$	5.56231	−	14.5623i	0.291945	−	0.764323i
$364$	8.47214	+	1.23607i	0.444061	+	0.0647876i
$365$		0			0
$366$	−1.70820	+	4.47214i	−0.0892892	+	0.233762i
$367$			14.1803i			0.740208i	0.928990	+	0.370104i	$0.120678\pi$
$367$			14.1803i			0.740208i	−0.928990	+	0.370104i	$0.879322\pi$
$368$		−	4.00000i		−	0.208514i
$369$	−14.4721	−	12.9443i	−0.753389	−	0.673852i
$370$		0			0
$371$	22.1803	+	3.23607i	1.15155	+	0.168008i
$372$	11.7082	+	4.47214i	0.607042	+	0.231869i
$373$	9.81966			0.508443			0.254221	−	0.967146i	$-0.418181\pi$
$373$	9.81966			0.508443			0.254221	+	0.967146i	$0.418181\pi$
$374$	3.41641			0.176658
$375$		0			0
$376$			2.47214i			0.127491i
$377$	18.4721			0.951363
$378$	−13.0000	+	4.47214i	−0.668648	+	0.230022i
$379$	17.8885			0.918873			0.459436	−	0.888211i	$-0.348051\pi$
$379$	17.8885			0.918873			0.459436	+	0.888211i	$0.348051\pi$
$380$		0			0
$381$	−8.47214	+	22.1803i	−0.434041	+	1.13633i
$382$	2.76393			0.141415
$383$	−21.8885			−1.11845			−0.559226	−	0.829015i	$-0.688902\pi$
$383$	−21.8885			−1.11845			−0.559226	+	0.829015i	$0.688902\pi$
$384$	1.61803	+	0.618034i	0.0825700	+	0.0315389i
$385$		0			0
$386$			6.00000i			0.305392i
$387$	28.9443	+	25.8885i	1.47132	+	1.31599i
$388$		−	5.23607i		−	0.265821i
$389$		−	7.81966i		−	0.396473i	−0.980154	−	0.198236i	$-0.936479\pi$
$389$		−	7.81966i		−	0.396473i	0.980154	−	0.198236i	$-0.0635213\pi$
$390$		0			0
$391$			3.05573i			0.154535i
$392$	−2.00000	+	6.70820i	−0.101015	+	0.338815i
$393$	13.2361	−	34.6525i	0.667671	−	1.74799i
$394$	−12.4721			−0.628337
$395$		0			0
$396$	−8.94427	+	10.0000i	−0.449467	+	0.502519i
$397$		−	17.1246i		−	0.859460i	−0.902958	−	0.429730i	$-0.858609\pi$
$397$		−	17.1246i		−	0.859460i	0.902958	−	0.429730i	$-0.141391\pi$
$398$	0.180340			0.00903962
$399$	1.05573	−	1.88854i	0.0528525	−	0.0945454i
$400$		0			0
$401$		−	5.52786i		−	0.276048i	−0.990429	−	0.138024i	$-0.955925\pi$
$401$		−	5.52786i		−	0.276048i	0.990429	−	0.138024i	$-0.0440752\pi$
$402$	−19.4164	−	7.41641i	−0.968402	−	0.369897i
$403$	−23.4164			−1.16645
$404$	3.52786			0.175518
$405$		0			0
$406$	−2.18034	+	14.9443i	−0.108208	+	0.741672i
$407$		−	23.4164i		−	1.16071i
$408$	−1.23607	−	0.472136i	−0.0611945	−	0.0233742i
$409$			19.4164i			0.960080i	0.877247	+	0.480040i	$0.159378\pi$
$409$			19.4164i			0.960080i	−0.877247	+	0.480040i	$0.840622\pi$
$410$		0			0
$411$	−20.1803	−	7.70820i	−0.995423	−	0.380218i
$412$		−	16.6525i		−	0.820409i
$413$	1.70820	−	11.7082i	0.0840552	−	0.576123i
$414$	−8.94427	−	8.00000i	−0.439587	−	0.393179i
$415$		0			0
$416$	−3.23607			−0.158661
$417$	−33.1246	−	12.6525i	−1.62212	−	0.619594i
$418$		−	2.11146i		−	0.103275i
$419$	−16.8328			−0.822337			−0.411168	−	0.911559i	$-0.634879\pi$
$419$	−16.8328			−0.822337			−0.411168	+	0.911559i	$0.634879\pi$
$420$		0			0
$421$	−12.4721			−0.607855			−0.303927	−	0.952695i	$-0.598298\pi$
$421$	−12.4721			−0.607855			−0.303927	+	0.952695i	$0.598298\pi$
$422$		−	8.00000i		−	0.389434i
$423$	5.52786	+	4.94427i	0.268774	+	0.240399i
$424$	−8.47214			−0.411443
$425$		0			0
$426$	1.70820	−	4.47214i	0.0827628	−	0.216676i
$427$	7.23607	+	1.05573i	0.350178	+	0.0510903i
$428$			15.4164i			0.745180i
$429$	8.94427	−	23.4164i	0.431834	−	1.13055i
$430$		0			0
$431$		−	9.59675i		−	0.462259i	−0.972923	−	0.231130i	$-0.925758\pi$
$431$		−	9.59675i		−	0.462259i	0.972923	−	0.231130i	$-0.0742421\pi$
$432$	4.61803	−	2.38197i	0.222185	−	0.114602i
$433$		−	4.65248i		−	0.223584i	−0.993732	−	0.111792i	$-0.964341\pi$
$433$		−	4.65248i		−	0.223584i	0.993732	−	0.111792i	$-0.0356590\pi$
$434$	2.76393	−	18.9443i	0.132673	−	0.909354i
$435$		0			0
$436$	4.47214			0.214176
$437$	1.88854			0.0903413
$438$	−4.18034	+	10.9443i	−0.199744	+	0.522938i
$439$			12.1803i			0.581336i	0.956824	+	0.290668i	$0.0938775\pi$
$439$			12.1803i			0.581336i	−0.956824	+	0.290668i	$0.906123\pi$
$440$		0			0
$441$	11.0000	+	17.8885i	0.523810	+	0.851835i
$442$	2.47214			0.117588
$443$		−	9.52786i		−	0.452682i	−0.974048	−	0.226341i	$-0.927324\pi$
$443$		−	9.52786i		−	0.452682i	0.974048	−	0.226341i	$-0.0726764\pi$
$444$	−3.23607	+	8.47214i	−0.153577	+	0.402070i
$445$		0			0
$446$	−4.29180			−0.203222
$447$	−28.6525	−	10.9443i	−1.35522	−	0.517646i
$448$	0.381966	−	2.61803i	0.0180462	−	0.123690i
$449$			1.52786i			0.0721044i	0.999350	+	0.0360522i	$0.0114783\pi$
$449$			1.52786i			0.0721044i	−0.999350	+	0.0360522i	$0.988522\pi$
$450$		0			0
$451$			28.9443i			1.36293i
$452$		−	14.9443i		−	0.702919i
$453$	−1.88854	+	4.94427i	−0.0887315	+	0.232302i
$454$		−	5.23607i		−	0.245741i
$455$		0			0
$456$	−0.291796	+	0.763932i	−0.0136646	+	0.0357744i
$457$	−9.05573			−0.423609			−0.211805	−	0.977312i	$-0.567934\pi$
$457$	−9.05573			−0.423609			−0.211805	+	0.977312i	$0.567934\pi$
$458$	−13.2361			−0.618481
$459$	−3.52786	+	1.81966i	−0.164667	+	0.0849345i
$460$		0			0
$461$	10.9443			0.509726			0.254863	−	0.966977i	$-0.417970\pi$
$461$	10.9443			0.509726			0.254863	+	0.966977i	$0.417970\pi$
$462$	17.8885	+	10.0000i	0.832250	+	0.465242i
$463$	−0.180340			−0.00838111			−0.00419055	−	0.999991i	$-0.501334\pi$
$463$	−0.180340			−0.00838111			−0.00419055	+	0.999991i	$0.501334\pi$
$464$		−	5.70820i		−	0.264997i
$465$		0			0
$466$	−20.4721			−0.948353
$467$	20.2918			0.938992			0.469496	−	0.882935i	$-0.344436\pi$
$467$	20.2918			0.938992			0.469496	+	0.882935i	$0.344436\pi$
$468$	−6.47214	+	7.23607i	−0.299175	+	0.334487i
$469$	−4.58359	+	31.4164i	−0.211651	+	1.45067i
$470$		0			0
$471$	7.70820	+	2.94427i	0.355175	+	0.135665i
$472$			4.47214i			0.205847i
$473$		−	57.8885i		−	2.66172i
$474$	−14.4721	−	5.52786i	−0.664727	−	0.253903i
$475$		0			0
$476$	−0.291796	+	2.00000i	−0.0133745	+	0.0916698i
$477$	−16.9443	+	18.9443i	−0.775825	+	0.867399i
$478$	−22.1803			−1.01451
$479$	2.11146			0.0964749			0.0482374	−	0.998836i	$-0.484640\pi$
$479$	2.11146			0.0964749			0.0482374	+	0.998836i	$0.484640\pi$
$480$		0			0
$481$		−	16.9443i		−	0.772592i
$482$	−17.8885			−0.814801
$483$	−8.94427	+	16.0000i	−0.406978	+	0.728025i
$484$	9.00000			0.409091
$485$		0			0
$486$	3.90983	−	15.0902i	0.177353	−	0.684504i
$487$	31.5967			1.43179			0.715893	−	0.698210i	$-0.246020\pi$
$487$	31.5967			1.43179			0.715893	+	0.698210i	$0.246020\pi$
$488$	−2.76393			−0.125117
$489$	−0.944272	+	2.47214i	−0.0427015	+	0.111794i
$490$		0			0
$491$			13.4164i			0.605474i	0.953074	+	0.302737i	$0.0979004\pi$
$491$			13.4164i			0.605474i	−0.953074	+	0.302737i	$0.902100\pi$
$492$	4.00000	−	10.4721i	0.180334	−	0.472120i
$493$			4.36068i			0.196395i
$494$		−	1.52786i		−	0.0687419i
$495$		0			0
$496$			7.23607i			0.324909i
$497$	−7.23607	−	1.05573i	−0.324582	−	0.0473559i
$498$	−26.9443	−	10.2918i	−1.20740	−	0.461186i
$499$	−17.8885			−0.800801			−0.400401	−	0.916340i	$-0.631129\pi$
$499$	−17.8885			−0.800801			−0.400401	+	0.916340i	$0.631129\pi$
$500$		0			0
$501$	10.4721	−	27.4164i	0.467861	−	1.22487i
$502$		−	3.52786i		−	0.157456i
$503$	−16.3607			−0.729487			−0.364743	−	0.931108i	$-0.618843\pi$
$503$	−16.3607			−0.729487			−0.364743	+	0.931108i	$0.618843\pi$
$504$	−5.09017	−	6.09017i	−0.226734	−	0.271278i
$505$		0			0
$506$			17.8885i			0.795243i
$507$	−1.56231	+	4.09017i	−0.0693844	+	0.181651i
$508$	−13.7082			−0.608203
$509$	24.4721			1.08471			0.542354	−	0.840150i	$-0.317533\pi$
$509$	24.4721			1.08471			0.542354	+	0.840150i	$0.317533\pi$
$510$		0			0
$511$	17.7082	+	2.58359i	0.783365	+	0.114291i
$512$			1.00000i			0.0441942i
$513$	1.12461	+	2.18034i	0.0496528	+	0.0962644i
$514$			8.18034i			0.360819i
$515$		0			0
$516$	−8.00000	+	20.9443i	−0.352180	+	0.922020i
$517$		−	11.0557i		−	0.486230i
$518$	13.7082	+	2.00000i	0.602304	+	0.0878750i
$519$	10.7639	−	28.1803i	0.472484	−	1.23698i
$520$		0			0
$521$	−19.0557			−0.834847			−0.417423	−	0.908712i	$-0.637067\pi$
$521$	−19.0557			−0.834847			−0.417423	+	0.908712i	$0.637067\pi$
$522$	−12.7639	−	11.4164i	−0.558662	−	0.499683i
$523$			24.5410i			1.07310i	0.843867	+	0.536552i	$0.180273\pi$
$523$			24.5410i			1.07310i	−0.843867	+	0.536552i	$0.819727\pi$
$524$	21.4164			0.935580
$525$		0			0
$526$	−4.94427			−0.215580
$527$		−	5.52786i		−	0.240798i
$528$	−7.23607	−	2.76393i	−0.314909	−	0.120285i
$529$	7.00000			0.304348
$530$		0			0
$531$	10.0000	+	8.94427i	0.433963	+	0.388148i
$532$	1.23607	+	0.180340i	0.0535903	+	0.00781873i
$533$			20.9443i			0.907197i
$534$	23.4164	+	8.94427i	1.01333	+	0.387056i
$535$		0			0
$536$		−	12.0000i		−	0.518321i
$537$	4.76393	+	1.81966i	0.205579	+	0.0785241i
$538$		−	4.47214i		−	0.192807i
$539$	8.94427	−	30.0000i	0.385257	−	1.29219i
$540$		0			0
$541$	13.0557			0.561310			0.280655	−	0.959809i	$-0.409448\pi$
$541$	13.0557			0.561310			0.280655	+	0.959809i	$0.409448\pi$
$542$	18.2918			0.785700
$543$	10.0000	+	3.81966i	0.429141	+	0.163917i
$544$		−	0.763932i		−	0.0327533i
$545$		0			0
$546$	12.9443	+	7.23607i	0.553964	+	0.309675i
$547$	8.58359			0.367008			0.183504	−	0.983019i	$-0.441256\pi$
$547$	8.58359			0.367008			0.183504	+	0.983019i	$0.441256\pi$
$548$		−	12.4721i		−	0.532783i
$549$	−5.52786	+	6.18034i	−0.235923	+	0.263770i
$550$		0			0
$551$	2.69505			0.114813
$552$	2.47214	−	6.47214i	0.105221	−	0.275472i
$553$	−3.41641	+	23.4164i	−0.145280	+	0.995767i
$554$		−	23.1246i		−	0.982471i
$555$		0			0
$556$		−	20.4721i		−	0.868212i
$557$		−	16.4721i		−	0.697947i	−0.937133	−	0.348973i	$-0.886530\pi$
$557$		−	16.4721i		−	0.697947i	0.937133	−	0.348973i	$-0.113470\pi$
$558$	16.1803	+	14.4721i	0.684968	+	0.612654i
$559$		−	41.8885i		−	1.77170i
$560$		0			0
$561$	5.52786	+	2.11146i	0.233387	+	0.0891457i
$562$	20.0000			0.843649
$563$	−17.8197			−0.751009			−0.375505	−	0.926821i	$-0.622531\pi$
$563$	−17.8197			−0.751009			−0.375505	+	0.926821i	$0.622531\pi$
$564$	−1.52786	+	4.00000i	−0.0643347	+	0.168430i
$565$		0			0
$566$	−8.76393			−0.368376
$567$	−23.7984	−	0.798374i	−0.999438	−	0.0335286i
$568$	2.76393			0.115972
$569$		−	18.4721i		−	0.774392i	−0.921997	−	0.387196i	$-0.873444\pi$
$569$		−	18.4721i		−	0.774392i	0.921997	−	0.387196i	$-0.126556\pi$
$570$		0			0
$571$	−34.8328			−1.45771			−0.728854	−	0.684669i	$-0.759947\pi$
$571$	−34.8328			−1.45771			−0.728854	+	0.684669i	$0.759947\pi$
$572$	14.4721			0.605110
$573$	4.47214	+	1.70820i	0.186826	+	0.0713612i
$574$	−16.9443	−	2.47214i	−0.707240	−	0.103185i
$575$		0			0
$576$	2.23607	+	2.00000i	0.0931695	+	0.0833333i
$577$			14.1803i			0.590335i	0.955445	+	0.295168i	$0.0953755\pi$
$577$			14.1803i			0.590335i	−0.955445	+	0.295168i	$0.904625\pi$
$578$		−	16.4164i		−	0.682833i
$579$	−3.70820	+	9.70820i	−0.154108	+	0.403459i
$580$		0			0
$581$	−6.36068	+	43.5967i	−0.263885	+	1.80870i
$582$	3.23607	−	8.47214i	0.134139	−	0.351181i
$583$	37.8885			1.56918
$584$	−6.76393			−0.279893
$585$		0			0
$586$			29.4164i			1.21518i
$587$	23.7082			0.978542			0.489271	−	0.872132i	$-0.337263\pi$
$587$	23.7082			0.978542			0.489271	+	0.872132i	$0.337263\pi$
$588$	−7.38197	+	9.61803i	−0.304427	+	0.396641i
$589$	−3.41641			−0.140771
$590$		0			0
$591$	−20.1803	−	7.70820i	−0.830108	−	0.317073i
$592$	−5.23607			−0.215201
$593$	−47.0132			−1.93060			−0.965299	−	0.261145i	$-0.915900\pi$
$593$	−47.0132			−1.93060			−0.965299	+	0.261145i	$0.915900\pi$
$594$	−20.6525	+	10.6525i	−0.847381	+	0.437076i
$595$		0			0
$596$		−	17.7082i		−	0.725356i
$597$	0.291796	+	0.111456i	0.0119424	+	0.00456160i
$598$			12.9443i			0.529331i
$599$		−	41.2361i		−	1.68486i	−0.538806	−	0.842430i	$-0.681124\pi$
$599$		−	41.2361i		−	1.68486i	0.538806	−	0.842430i	$-0.318876\pi$
$600$		0			0
$601$		−	14.4721i		−	0.590331i	−0.955446	−	0.295165i	$-0.904625\pi$
$601$		−	14.4721i		−	0.590331i	0.955446	−	0.295165i	$-0.0953747\pi$
$602$	33.8885	+	4.94427i	1.38119	+	0.201513i
$603$	−26.8328	−	24.0000i	−1.09272	−	0.977356i
$604$	−3.05573			−0.124336
$605$		0			0
$606$	5.70820	+	2.18034i	0.231880	+	0.0885703i
$607$		−	14.7639i		−	0.599250i	−0.954057	−	0.299625i	$-0.903139\pi$
$607$		−	14.7639i		−	0.599250i	0.954057	−	0.299625i	$-0.0968615\pi$
$608$	−0.472136			−0.0191476
$609$	−12.7639	+	22.8328i	−0.517221	+	0.925232i
$610$		0			0
$611$		−	8.00000i		−	0.323645i
$612$	−1.70820	−	1.52786i	−0.0690501	−	0.0617602i
$613$	20.0689			0.810575			0.405287	−	0.914189i	$-0.367171\pi$
$613$	20.0689			0.810575			0.405287	+	0.914189i	$0.367171\pi$
$614$	−4.18034			−0.168705
$615$		0			0
$616$	−1.70820	+	11.7082i	−0.0688255	+	0.471737i
$617$		−	2.00000i		−	0.0805170i	−0.999189	−	0.0402585i	$-0.987182\pi$
$617$		−	2.00000i		−	0.0805170i	0.999189	−	0.0402585i	$-0.0128181\pi$
$618$	10.2918	−	26.9443i	0.413997	−	1.08386i
$619$		−	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
$621$	−9.52786	−	18.4721i	−0.382340	−	0.741261i
$622$			26.4721i			1.06144i
$623$	5.52786	−	37.8885i	0.221469	−	1.51797i
$624$	−5.23607	−	2.00000i	−0.209610	−	0.0800641i
$625$		0			0
$626$	−7.70820			−0.308082
$627$	1.30495	−	3.41641i	0.0521148	−	0.136438i
$628$			4.76393i			0.190102i
$629$	4.00000			0.159490
$630$		0			0
$631$	29.8885			1.18984			0.594922	−	0.803783i	$-0.297183\pi$
$631$	29.8885			1.18984			0.594922	+	0.803783i	$0.297183\pi$
$632$		−	8.94427i		−	0.355784i
$633$	4.94427	−	12.9443i	0.196517	−	0.514489i
$634$	−6.94427			−0.275792
$635$		0			0
$636$	−13.7082	−	5.23607i	−0.543566	−	0.207624i
$637$	6.47214	−	21.7082i	0.256435	−	0.860110i
$638$			25.5279i			1.01066i
$639$	5.52786	−	6.18034i	0.218679	−	0.244490i
$640$		0			0
$641$			3.41641i			0.134940i	0.997721	+	0.0674700i	$0.0214927\pi$
$641$			3.41641i			0.134940i	−0.997721	+	0.0674700i	$0.978507\pi$
$642$	−9.52786	+	24.9443i	−0.376035	+	0.984472i
$643$		−	25.7082i		−	1.01383i	−0.861995	−	0.506916i	$-0.830785\pi$
$643$		−	25.7082i		−	1.01383i	0.861995	−	0.506916i	$-0.169215\pi$
$644$	−10.4721	−	1.52786i	−0.412660	−	0.0602063i
$645$		0			0
$646$	0.360680			0.0141908
$647$	18.8328			0.740394			0.370197	−	0.928953i	$-0.379290\pi$
$647$	18.8328			0.740394			0.370197	+	0.928953i	$0.379290\pi$
$648$	8.94427	−	1.00000i	0.351364	−	0.0392837i
$649$		−	20.0000i		−	0.785069i
$650$		0			0
$651$	16.1803	−	28.9443i	0.634158	−	1.13442i
$652$	−1.52786			−0.0598358
$653$		−	11.8885i		−	0.465235i	−0.972568	−	0.232617i	$-0.925271\pi$
$653$		−	11.8885i		−	0.465235i	0.972568	−	0.232617i	$-0.0747290\pi$
$654$	7.23607	+	2.76393i	0.282953	+	0.108078i
$655$		0			0
$656$	6.47214			0.252694
$657$	−13.5279	+	15.1246i	−0.527772	+	0.590067i
$658$	6.47214	+	0.944272i	0.252310	+	0.0368116i
$659$			40.4721i			1.57657i	0.615310	+	0.788285i	$0.289031\pi$
$659$			40.4721i			1.57657i	−0.615310	+	0.788285i	$0.710969\pi$
$660$		0			0
$661$		−	31.7082i		−	1.23331i	−0.787235	−	0.616653i	$-0.788488\pi$
$661$		−	31.7082i		−	1.23331i	0.787235	−	0.616653i	$-0.211512\pi$
$662$			20.9443i			0.814022i
$663$	4.00000	+	1.52786i	0.155347	+	0.0593373i
$664$		−	16.6525i		−	0.646241i
$665$		0			0
$666$	−10.4721	+	11.7082i	−0.405787	+	0.453684i
$667$	−22.8328			−0.884090
$668$	16.9443			0.655594
$669$	−6.94427	−	2.65248i	−0.268481	−	0.102551i
$670$		0			0
$671$	12.3607			0.477179
$672$	2.23607	−	4.00000i	0.0862582	−	0.154303i
$673$	−28.4721			−1.09752			−0.548760	−	0.835980i	$-0.684900\pi$
$673$	−28.4721			−1.09752			−0.548760	+	0.835980i	$0.684900\pi$
$674$			5.41641i			0.208632i
$675$		0			0
$676$	−2.52786			−0.0972255
$677$	−18.0000			−0.691796			−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000			−0.691796			−0.345898	+	0.938272i	$0.612426\pi$
$678$	9.23607	−	24.1803i	0.354709	−	0.928640i
$679$	−13.7082	−	2.00000i	−0.526073	−	0.0767530i
$680$		0			0
$681$	3.23607	−	8.47214i	0.124006	−	0.324653i
$682$		−	32.3607i		−	1.23915i
$683$			36.0000i			1.37750i	0.724998	+	0.688751i	$0.241841\pi$
$683$			36.0000i			1.37750i	−0.724998	+	0.688751i	$0.758159\pi$
$684$	−0.944272	+	1.05573i	−0.0361051	+	0.0403668i
$685$		0			0
$686$	16.7984	+	7.79837i	0.641365	+	0.297743i
$687$	−21.4164	−	8.18034i	−0.817087	−	0.312099i
$688$	−12.9443			−0.493496
$689$	27.4164			1.04448
$690$		0			0
$691$			38.9443i			1.48151i	0.671775	+	0.740755i	$0.265532\pi$
$691$			38.9443i			1.48151i	−0.671775	+	0.740755i	$0.734468\pi$
$692$	17.4164			0.662072
$693$	22.7639	+	27.2361i	0.864730	+	1.03461i
$694$	6.47214			0.245679
$695$		0			0
$696$	3.52786	−	9.23607i	0.133723	−	0.350092i
$697$	−4.94427			−0.187278
$698$	−2.18034			−0.0825271
$699$	−33.1246	−	12.6525i	−1.25289	−	0.478561i
$700$		0			0
$701$		−	14.0689i		−	0.531374i	−0.964059	−	0.265687i	$-0.914401\pi$
$701$		−	14.0689i		−	0.531374i	0.964059	−	0.265687i	$-0.0855988\pi$
$702$	−14.9443	+	7.70820i	−0.564035	+	0.290927i
$703$		−	2.47214i		−	0.0932384i
$704$		−	4.47214i		−	0.168550i
$705$		0			0
$706$			14.2918i			0.537879i
$707$	1.34752	−	9.23607i	0.0506789	−	0.347358i
$708$	−2.76393	+	7.23607i	−0.103875	+	0.271948i
$709$	−24.4721			−0.919070			−0.459535	−	0.888160i	$-0.651984\pi$
$709$	−24.4721			−0.919070			−0.459535	+	0.888160i	$0.651984\pi$
$710$		0			0
$711$	−20.0000	−	17.8885i	−0.750059	−	0.670873i
$712$			14.4721i			0.542366i
$713$	28.9443			1.08397
$714$	−1.70820	+	3.05573i	−0.0639279	+	0.114358i
$715$		0			0
$716$			2.94427i			0.110033i
$717$	−35.8885	−	13.7082i	−1.34028	−	0.511942i
$718$	10.1803			0.379927
$719$	−25.5279			−0.952029			−0.476014	−	0.879438i	$-0.657919\pi$
$719$	−25.5279			−0.952029			−0.476014	+	0.879438i	$0.657919\pi$
$720$		0			0
$721$	−43.5967	−	6.36068i	−1.62363	−	0.236884i
$722$			18.7771i			0.698811i
$723$	−28.9443	−	11.0557i	−1.07645	−	0.411167i
$724$			6.18034i			0.229691i
$725$		0			0
$726$	14.5623	+	5.56231i	0.540458	+	0.206437i
$727$			39.7082i			1.47270i	0.676603	+	0.736348i	$0.263451\pi$
$727$			39.7082i			1.47270i	−0.676603	+	0.736348i	$0.736549\pi$
$728$	−1.23607	+	8.47214i	−0.0458117	+	0.313998i
$729$	15.6525	−	22.0000i	0.579721	−	0.814815i
$730$		0			0
$731$	9.88854			0.365741
$732$	−4.47214	−	1.70820i	−0.165295	−	0.0631370i
$733$		−	38.0689i		−	1.40611i	−0.711137	−	0.703053i	$-0.751820\pi$
$733$		−	38.0689i		−	1.40611i	0.711137	−	0.703053i	$-0.248180\pi$
$734$	−14.1803			−0.523406
$735$		0			0
$736$	4.00000			0.147442
$737$			53.6656i			1.97680i
$738$	12.9443	−	14.4721i	0.476485	−	0.532727i
$739$	−8.94427			−0.329020			−0.164510	−	0.986375i	$-0.552604\pi$
$739$	−8.94427			−0.329020			−0.164510	+	0.986375i	$0.552604\pi$
$740$		0			0
$741$	0.944272	−	2.47214i	0.0346887	−	0.0908162i
$742$	−3.23607	+	22.1803i	−0.118800	+	0.814266i
$743$			1.52786i			0.0560519i	0.999607	+	0.0280259i	$0.00892210\pi$
$743$			1.52786i			0.0560519i	−0.999607	+	0.0280259i	$0.991078\pi$
$744$	−4.47214	+	11.7082i	−0.163956	+	0.429244i
$745$		0			0
$746$			9.81966i			0.359523i
$747$	−37.2361	−	33.3050i	−1.36240	−	1.21856i
$748$			3.41641i			0.124916i
$749$	40.3607	+	5.88854i	1.47475	+	0.215163i
$750$		0			0
$751$	35.4164			1.29236			0.646182	−	0.763184i	$-0.276365\pi$
$751$	35.4164			1.29236			0.646182	+	0.763184i	$0.276365\pi$
$752$	−2.47214			−0.0901495
$753$	2.18034	−	5.70820i	0.0794560	−	0.208019i
$754$			18.4721i			0.672716i
$755$		0			0
$756$	−4.47214	−	13.0000i	−0.162650	−	0.472805i
$757$	−28.6525			−1.04139			−0.520696	−	0.853742i	$-0.674327\pi$
$757$	−28.6525			−1.04139			−0.520696	+	0.853742i	$0.674327\pi$
$758$			17.8885i			0.649741i
$759$	−11.0557	+	28.9443i	−0.401298	+	1.05061i
$760$		0			0
$761$	29.8885			1.08346			0.541729	−	0.840553i	$-0.317770\pi$
$761$	29.8885			1.08346			0.541729	+	0.840553i	$0.317770\pi$
$762$	−22.1803	−	8.47214i	−0.803509	−	0.306913i
$763$	1.70820	−	11.7082i	0.0618411	−	0.423865i
$764$			2.76393i			0.0999956i
$765$		0			0
$766$		−	21.8885i		−	0.790865i
$767$		−	14.4721i		−	0.522559i
$768$	−0.618034	+	1.61803i	−0.0223014	+	0.0583858i
$769$			36.0000i			1.29819i	0.760706	+	0.649097i	$0.224853\pi$
$769$			36.0000i			1.29819i	−0.760706	+	0.649097i	$0.775147\pi$
$770$		0			0
$771$	−5.05573	+	13.2361i	−0.182078	+	0.476685i
$772$	−6.00000			−0.215945
$773$	−37.4164			−1.34577			−0.672887	−	0.739745i	$-0.734946\pi$
$773$	−37.4164			−1.34577			−0.672887	+	0.739745i	$0.734946\pi$
$774$	−25.8885	+	28.9443i	−0.930544	+	1.04038i
$775$		0			0
$776$	5.23607			0.187964
$777$	20.9443	+	11.7082i	0.751372	+	0.420029i
$778$	7.81966			0.280348
$779$			3.05573i			0.109483i
$780$		0			0
$781$	−12.3607			−0.442300
$782$	−3.05573			−0.109273
$783$	−13.5967	−	26.3607i	−0.485908	−	0.942054i
$784$	−6.70820	−	2.00000i	−0.239579	−	0.0714286i
$785$		0			0
$786$	34.6525	+	13.2361i	1.23601	+	0.472115i
$787$			49.7082i			1.77191i	0.463775	+	0.885953i	$0.346495\pi$
$787$			49.7082i			1.77191i	−0.463775	+	0.885953i	$0.653505\pi$
$788$		−	12.4721i		−	0.444301i
$789$	−8.00000	−	3.05573i	−0.284808	−	0.108787i
$790$		0			0
$791$	−39.1246	−	5.70820i	−1.39111	−	0.202960i
$792$	−10.0000	−	8.94427i	−0.355335	−	0.317821i
$793$	8.94427			0.317620
$794$	17.1246			0.607730
$795$		0			0
$796$			0.180340i			0.00639198i
$797$	5.41641			0.191859			0.0959295	−	0.995388i	$-0.469418\pi$
$797$	5.41641			0.191859			0.0959295	+	0.995388i	$0.469418\pi$
$798$	1.88854	+	1.05573i	0.0668537	+	0.0373724i
$799$	1.88854			0.0668119
$800$		0			0
$801$	32.3607	+	28.9443i	1.14341	+	1.02270i
$802$	5.52786			0.195196
$803$	30.2492			1.06747
$804$	7.41641	−	19.4164i	0.261557	−	0.684764i
$805$		0			0
$806$		−	23.4164i		−	0.824808i
$807$	2.76393	−	7.23607i	0.0972950	−	0.254722i
$808$			3.52786i			0.124110i
$809$			8.36068i			0.293946i	0.989141	+	0.146973i	$0.0469530\pi$
$809$			8.36068i			0.293946i	−0.989141	+	0.146973i	$0.953047\pi$
$810$		0			0
$811$			16.8328i			0.591080i	0.955330	+	0.295540i	$0.0954996\pi$
$811$			16.8328i			0.591080i	−0.955330	+	0.295540i	$0.904500\pi$
$812$	−14.9443	−	2.18034i	−0.524441	−	0.0765149i
$813$	29.5967	+	11.3050i	1.03800	+	0.396482i
$814$	23.4164			0.820745
$815$		0			0
$816$	0.472136	−	1.23607i	0.0165281	−	0.0432710i
$817$		−	6.11146i		−	0.213813i
$818$	−19.4164			−0.678879
$819$	16.4721	+	19.7082i	0.575583	+	0.688660i
$820$		0			0
$821$			18.2918i			0.638388i	0.947689	+	0.319194i	$0.103412\pi$
$821$			18.2918i			0.638388i	−0.947689	+	0.319194i	$0.896588\pi$
$822$	7.70820	−	20.1803i	0.268854	−	0.703870i
$823$	−0.180340			−0.00628625			−0.00314313	−	0.999995i	$-0.501000\pi$
$823$	−0.180340			−0.00628625			−0.00314313	+	0.999995i	$0.501000\pi$
$824$	16.6525			0.580116
$825$		0			0
$826$	11.7082	+	1.70820i	0.407381	+	0.0594360i
$827$			14.8328i			0.515788i	0.966173	+	0.257894i	$0.0830285\pi$
$827$			14.8328i			0.515788i	−0.966173	+	0.257894i	$0.916972\pi$
$828$	8.00000	−	8.94427i	0.278019	−	0.310835i
$829$		−	30.1803i		−	1.04821i	−0.851655	−	0.524103i	$-0.824401\pi$
$829$		−	30.1803i		−	1.04821i	0.851655	−	0.524103i	$-0.175599\pi$
$830$		0			0
$831$	14.2918	−	37.4164i	0.495777	−	1.29796i
$832$		−	3.23607i		−	0.112190i
$833$	5.12461	+	1.52786i	0.177557	+	0.0529374i
$834$	12.6525	−	33.1246i	0.438119	−	1.14701i
$835$		0			0
$836$	2.11146			0.0730262
$837$	17.2361	+	33.4164i	0.595766	+	1.15504i
$838$		−	16.8328i		−	0.581480i
$839$	14.4721			0.499634			0.249817	−	0.968293i	$-0.419630\pi$
$839$	14.4721			0.499634			0.249817	+	0.968293i	$0.419630\pi$
$840$		0			0
$841$	−3.58359			−0.123572
$842$		−	12.4721i		−	0.429818i
$843$	32.3607	+	12.3607i	1.11456	+	0.425724i
$844$	8.00000			0.275371
$845$		0			0
$846$	−4.94427	+	5.52786i	−0.169988	+	0.190052i
$847$	3.43769	−	23.5623i	0.118121	−	0.809610i
$848$		−	8.47214i		−	0.290934i
$849$	−14.1803	−	5.41641i	−0.486668	−	0.185891i
$850$		0			0
$851$			20.9443i			0.717960i
$852$	4.47214	+	1.70820i	0.153213	+	0.0585221i
$853$		−	5.70820i		−	0.195445i	−0.995214	−	0.0977226i	$-0.968844\pi$
$853$		−	5.70820i		−	0.195445i	0.995214	−	0.0977226i	$-0.0311558\pi$
$854$	−1.05573	+	7.23607i	−0.0361263	+	0.247613i
$855$		0			0
$856$	−15.4164			−0.526922
$857$	42.6525			1.45698			0.728490	−	0.685056i	$-0.240222\pi$
$857$	42.6525			1.45698			0.728490	+	0.685056i	$0.240222\pi$
$858$	23.4164	+	8.94427i	0.799423	+	0.305352i
$859$			34.9443i			1.19228i	0.802879	+	0.596142i	$0.203300\pi$
$859$			34.9443i			1.19228i	−0.802879	+	0.596142i	$0.796700\pi$
$860$		0			0
$861$	−25.8885	−	14.4721i	−0.882279	−	0.493209i
$862$	9.59675			0.326867
$863$			21.5279i			0.732817i	0.930454	+	0.366409i	$0.119413\pi$
$863$			21.5279i			0.732817i	−0.930454	+	0.366409i	$0.880587\pi$
$864$	2.38197	+	4.61803i	0.0810361	+	0.157109i
$865$		0			0
$866$	4.65248			0.158098
$867$	10.1459	−	26.5623i	0.344573	−	0.902103i
$868$	18.9443	+	2.76393i	0.643010	+	0.0938140i
$869$			40.0000i			1.35691i
$870$		0			0
$871$			38.8328i			1.31580i
$872$			4.47214i			0.151446i
$873$	10.4721	−	11.7082i	0.354428	−	0.396263i
$874$			1.88854i			0.0638809i
$875$		0			0
$876$	−10.9443	−	4.18034i	−0.369773	−	0.141241i
$877$	−7.34752			−0.248108			−0.124054	−	0.992275i	$-0.539590\pi$
$877$	−7.34752			−0.248108			−0.124054	+	0.992275i	$0.539590\pi$
$878$	−12.1803			−0.411067
$879$	−18.1803	+	47.5967i	−0.613208	+	1.60540i
$880$		0			0
$881$	−11.4164			−0.384629			−0.192314	−	0.981333i	$-0.561599\pi$
$881$	−11.4164			−0.384629			−0.192314	+	0.981333i	$0.561599\pi$
$882$	−17.8885	+	11.0000i	−0.602339	+	0.370389i
$883$	−21.8885			−0.736608			−0.368304	−	0.929705i	$-0.620061\pi$
$883$	−21.8885			−0.736608			−0.368304	+	0.929705i	$0.620061\pi$
$884$			2.47214i			0.0831469i
$885$		0			0
$886$	9.52786			0.320095
$887$	26.4721			0.888847			0.444424	−	0.895817i	$-0.353408\pi$
$887$	26.4721			0.888847			0.444424	+	0.895817i	$0.353408\pi$
$888$	−8.47214	−	3.23607i	−0.284306	−	0.108595i
$889$	−5.23607	+	35.8885i	−0.175612	+	1.20366i
$890$		0			0
$891$	−40.0000	+	4.47214i	−1.34005	+	0.149822i
$892$		−	4.29180i		−	0.143700i
$893$		−	1.16718i		−	0.0390583i
$894$	10.9443	−	28.6525i	0.366031	−	0.958282i
$895$		0			0
$896$	2.61803	+	0.381966i	0.0874624	+	0.0127606i
$897$	−8.00000	+	20.9443i	−0.267112	+	0.699309i
$898$	−1.52786			−0.0509855
$899$	41.3050			1.37760
$900$		0			0
$901$			6.47214i			0.215618i
$902$	−28.9443			−0.963739
$903$	51.7771	+	28.9443i	1.72303	+	0.963205i
$904$	14.9443			0.497039
$905$		0			0
$906$	−4.94427	−	1.88854i	−0.164262	−	0.0627427i
$907$	26.4721			0.878993			0.439496	−	0.898244i	$-0.355157\pi$
$907$	26.4721			0.878993			0.439496	+	0.898244i	$0.355157\pi$
$908$	5.23607			0.173765
$909$	7.88854	+	7.05573i	0.261646	+	0.234024i
$910$		0			0
$911$		−	19.3475i		−	0.641012i	−0.947246	−	0.320506i	$-0.896147\pi$
$911$		−	19.3475i		−	0.641012i	0.947246	−	0.320506i	$-0.103853\pi$
$912$	−0.763932	−	0.291796i	−0.0252963	−	0.00966233i
$913$			74.4721i			2.46467i
$914$		−	9.05573i		−	0.299537i
$915$		0			0
$916$		−	13.2361i		−	0.437332i
$917$	8.18034	−	56.0689i	0.270139	−	1.85156i
$918$	−1.81966	−	3.52786i	−0.0600577	−	0.116437i
$919$	44.7214			1.47522			0.737611	−	0.675226i	$-0.235954\pi$
$919$	44.7214			1.47522			0.737611	+	0.675226i	$0.235954\pi$
$920$		0			0
$921$	−6.76393	−	2.58359i	−0.222879	−	0.0851323i
$922$			10.9443i			0.360430i
$923$	−8.94427			−0.294404
$924$	−10.0000	+	17.8885i	−0.328976	+	0.588490i
$925$		0			0
$926$		−	0.180340i		−	0.00592634i
$927$	33.3050	−	37.2361i	1.09388	−	1.22299i
$928$	5.70820			0.187381
$929$	2.11146			0.0692746			0.0346373	−	0.999400i	$-0.488972\pi$
$929$	2.11146			0.0692746			0.0346373	+	0.999400i	$0.488972\pi$
$930$		0			0
$931$	0.944272	−	3.16718i	0.0309473	−	0.103800i
$932$		−	20.4721i		−	0.670587i
$933$	−16.3607	+	42.8328i	−0.535625	+	1.40228i
$934$			20.2918i			0.663968i
$935$		0			0
$936$	−7.23607	−	6.47214i	−0.236518	−	0.211548i
$937$		−	16.0689i		−	0.524948i	−0.964939	−	0.262474i	$-0.915462\pi$
$937$		−	16.0689i		−	0.524948i	0.964939	−	0.262474i	$-0.0845383\pi$
$938$	−31.4164	−	4.58359i	−1.02578	−	0.149660i
$939$	−12.4721	−	4.76393i	−0.407013	−	0.155465i
$940$		0			0
$941$	22.0000			0.717180			0.358590	−	0.933495i	$-0.383258\pi$
$941$	22.0000			0.717180			0.358590	+	0.933495i	$0.383258\pi$
$942$	−2.94427	+	7.70820i	−0.0959296	+	0.251147i
$943$		−	25.8885i		−	0.843047i
$944$	−4.47214			−0.145556
$945$		0			0
$946$	57.8885			1.88212
$947$			15.6393i			0.508210i	0.967177	+	0.254105i	$0.0817808\pi$
$947$			15.6393i			0.508210i	−0.967177	+	0.254105i	$0.918219\pi$
$948$	5.52786	−	14.4721i	0.179537	−	0.470033i
$949$	21.8885			0.710532
$950$		0			0
$951$	−11.2361	−	4.29180i	−0.364354	−	0.139171i
$952$	−2.00000	−	0.291796i	−0.0648204	−	0.00945716i
$953$			49.4164i			1.60075i	0.599497	+	0.800377i	$0.295367\pi$
$953$			49.4164i			1.60075i	−0.599497	+	0.800377i	$0.704633\pi$
$954$	−18.9443	−	16.9443i	−0.613343	−	0.548591i
$955$		0			0
$956$		−	22.1803i		−	0.717363i
$957$	−15.7771	+	41.3050i	−0.510001	+	1.33520i
$958$			2.11146i			0.0682181i
$959$	−32.6525	−	4.76393i	−1.05440	−	0.153835i
$960$		0			0
$961$	−21.3607			−0.689054
$962$	16.9443			0.546305
$963$	−30.8328	+	34.4721i	−0.993574	+	1.11085i
$964$		−	17.8885i		−	0.576151i
$965$		0			0
$966$	−16.0000	−	8.94427i	−0.514792	−	0.287777i
$967$	−45.4853			−1.46271			−0.731354	−	0.681998i	$-0.761111\pi$
$967$	−45.4853			−1.46271			−0.731354	+	0.681998i	$0.761111\pi$
$968$			9.00000i			0.289271i
$969$	0.583592	+	0.222912i	0.0187477	+	0.00716098i
$970$		0			0
$971$	−58.0000			−1.86131			−0.930654	−	0.365900i	$-0.880761\pi$
$971$	−58.0000			−1.86131			−0.930654	+	0.365900i	$0.880761\pi$
$972$	15.0902	+	3.90983i	0.484017	+	0.125408i
$973$	−53.5967	−	7.81966i	−1.71823	−	0.250687i
$974$			31.5967i			1.01243i
$975$		0			0
$976$		−	2.76393i		−	0.0884713i
$977$		−	25.4164i		−	0.813143i	−0.913619	−	0.406571i	$-0.866724\pi$
$977$		−	25.4164i		−	0.813143i	0.913619	−	0.406571i	$-0.133276\pi$
$978$	−2.47214	−	0.944272i	−0.0790502	−	0.0301945i
$979$		−	64.7214i		−	2.06850i
$980$		0			0
$981$	10.0000	+	8.94427i	0.319275	+	0.285569i
$982$	−13.4164			−0.428135
$983$	39.4164			1.25719			0.628594	−	0.777734i	$-0.283631\pi$
$983$	39.4164			1.25719			0.628594	+	0.777734i	$0.283631\pi$
$984$	10.4721	+	4.00000i	0.333840	+	0.127515i
$985$		0			0
$986$	−4.36068			−0.138872
$987$	9.88854	+	5.52786i	0.314756	+	0.175954i
$988$	1.52786			0.0486078
$989$			51.7771i			1.64642i
$990$		0			0
$991$	26.4721			0.840915			0.420458	−	0.907312i	$-0.361870\pi$
$991$	26.4721			0.840915			0.420458	+	0.907312i	$0.361870\pi$
$992$	−7.23607			−0.229745
$993$	−12.9443	+	33.8885i	−0.410774	+	1.07542i
$994$	1.05573	−	7.23607i	0.0334857	−	0.229514i
$995$		0			0
$996$	10.2918	−	26.9443i	0.326108	−	0.853762i
$997$			20.7639i			0.657600i	0.944400	+	0.328800i	$0.106644\pi$
$997$			20.7639i			0.657600i	−0.944400	+	0.328800i	$0.893356\pi$
$998$		−	17.8885i		−	0.566252i
$999$	−24.1803	+	12.4721i	−0.765032	+	0.394601i

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.618034 + 1.61803i) q^{3} -1.00000 q^{4} +(-1.61803 - 0.618034i) q^{6} +(-0.381966 + 2.61803i) q^{7} -1.00000i q^{8} +(-2.23607 - 2.00000i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.618034 + 1.61803i) q^{3} -1.00000 q^{4} +(-1.61803 - 0.618034i) q^{6} +(-0.381966 + 2.61803i) q^{7} -1.00000i q^{8} +(-2.23607 - 2.00000i) q^{9} +4.47214i q^{11} +(0.618034 - 1.61803i) q^{12} +3.23607i q^{13} +(-2.61803 - 0.381966i) q^{14} +1.00000 q^{16} -0.763932 q^{17} +(2.00000 - 2.23607i) q^{18} +0.472136i q^{19} +(-4.00000 - 2.23607i) q^{21} -4.47214 q^{22} -4.00000i q^{23} +(1.61803 + 0.618034i) q^{24} -3.23607 q^{26} +(4.61803 - 2.38197i) q^{27} +(0.381966 - 2.61803i) q^{28} -5.70820i q^{29} +7.23607i q^{31} +1.00000i q^{32} +(-7.23607 - 2.76393i) q^{33} -0.763932i q^{34} +(2.23607 + 2.00000i) q^{36} -5.23607 q^{37} -0.472136 q^{38} +(-5.23607 - 2.00000i) q^{39} +6.47214 q^{41} +(2.23607 - 4.00000i) q^{42} -12.9443 q^{43} -4.47214i q^{44} +4.00000 q^{46} -2.47214 q^{47} +(-0.618034 + 1.61803i) q^{48} +(-6.70820 - 2.00000i) q^{49} +(0.472136 - 1.23607i) q^{51} -3.23607i q^{52} -8.47214i q^{53} +(2.38197 + 4.61803i) q^{54} +(2.61803 + 0.381966i) q^{56} +(-0.763932 - 0.291796i) q^{57} +5.70820 q^{58} -4.47214 q^{59} -2.76393i q^{61} -7.23607 q^{62} +(6.09017 - 5.09017i) q^{63} -1.00000 q^{64} +(2.76393 - 7.23607i) q^{66} +12.0000 q^{67} +0.763932 q^{68} +(6.47214 + 2.47214i) q^{69} +2.76393i q^{71} +(-2.00000 + 2.23607i) q^{72} -6.76393i q^{73} -5.23607i q^{74} -0.472136i q^{76} +(-11.7082 - 1.70820i) q^{77} +(2.00000 - 5.23607i) q^{78} +8.94427 q^{79} +(1.00000 + 8.94427i) q^{81} +6.47214i q^{82} +16.6525 q^{83} +(4.00000 + 2.23607i) q^{84} -12.9443i q^{86} +(9.23607 + 3.52786i) q^{87} +4.47214 q^{88} -14.4721 q^{89} +(-8.47214 - 1.23607i) q^{91} +4.00000i q^{92} +(-11.7082 - 4.47214i) q^{93} -2.47214i q^{94} +(-1.61803 - 0.618034i) q^{96} +5.23607i q^{97} +(2.00000 - 6.70820i) q^{98} +(8.94427 - 10.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 4 q^{4} - 2 q^{6} - 6 q^{7}+O(q^{10}) \) 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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