LMFDB - Embedded newform 1050.2.b.a.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			$-1.61803i$ of defining polynomial
Character	$\chi$	$=$	1050.251
Dual form			1050.2.b.a.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.618034 - 1.61803i) q^{3} -1.00000 q^{4} +(1.61803 + 0.618034i) q^{6} +(-0.381966 - 2.61803i) q^{7} -1.00000i q^{8} +(-2.23607 - 2.00000i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.618034 - 1.61803i) q^{3} -1.00000 q^{4} +(1.61803 + 0.618034i) q^{6} +(-0.381966 - 2.61803i) q^{7} -1.00000i q^{8} +(-2.23607 - 2.00000i) q^{9} +4.47214i q^{11} +(-0.618034 + 1.61803i) q^{12} -3.23607i q^{13} +(2.61803 - 0.381966i) q^{14} +1.00000 q^{16} +0.763932 q^{17} +(2.00000 - 2.23607i) q^{18} -0.472136i q^{19} +(-4.47214 - 1.00000i) q^{21} -4.47214 q^{22} -4.00000i q^{23} +(-1.61803 - 0.618034i) q^{24} +3.23607 q^{26} +(-4.61803 + 2.38197i) q^{27} +(0.381966 + 2.61803i) q^{28} -5.70820i q^{29} -7.23607i q^{31} +1.00000i q^{32} +(7.23607 + 2.76393i) q^{33} +0.763932i q^{34} +(2.23607 + 2.00000i) q^{36} -5.23607 q^{37} +0.472136 q^{38} +(-5.23607 - 2.00000i) q^{39} -6.47214 q^{41} +(1.00000 - 4.47214i) q^{42} -12.9443 q^{43} -4.47214i q^{44} +4.00000 q^{46} +2.47214 q^{47} +(0.618034 - 1.61803i) q^{48} +(-6.70820 + 2.00000i) q^{49} +(0.472136 - 1.23607i) q^{51} +3.23607i q^{52} -8.47214i q^{53} +(-2.38197 - 4.61803i) q^{54} +(-2.61803 + 0.381966i) q^{56} +(-0.763932 - 0.291796i) q^{57} +5.70820 q^{58} +4.47214 q^{59} +2.76393i q^{61} +7.23607 q^{62} +(-4.38197 + 6.61803i) q^{63} -1.00000 q^{64} +(-2.76393 + 7.23607i) q^{66} +12.0000 q^{67} -0.763932 q^{68} +(-6.47214 - 2.47214i) q^{69} +2.76393i q^{71} +(-2.00000 + 2.23607i) q^{72} +6.76393i q^{73} -5.23607i q^{74} +0.472136i q^{76} +(11.7082 - 1.70820i) q^{77} +(2.00000 - 5.23607i) q^{78} +8.94427 q^{79} +(1.00000 + 8.94427i) q^{81} -6.47214i q^{82} -16.6525 q^{83} +(4.47214 + 1.00000i) q^{84} -12.9443i q^{86} +(-9.23607 - 3.52786i) q^{87} +4.47214 q^{88} +14.4721 q^{89} +(-8.47214 + 1.23607i) q^{91} +4.00000i q^{92} +(-11.7082 - 4.47214i) q^{93} +2.47214i q^{94} +(1.61803 + 0.618034i) q^{96} -5.23607i q^{97} +(-2.00000 - 6.70820i) q^{98} +(8.94427 - 10.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 2 q^{24} + 4 q^{26} - 14 q^{27} + 6 q^{28} + 20 q^{33} - 12 q^{37} - 16 q^{38} - 12 q^{39} - 8 q^{41} + 4 q^{42} - 16 q^{43} + 16 q^{46} - 8 q^{47} - 2 q^{48} - 16 q^{51} - 14 q^{54} - 6 q^{56} - 12 q^{57} - 4 q^{58} + 20 q^{62} - 22 q^{63} - 4 q^{64} - 20 q^{66} + 48 q^{67} - 12 q^{68} - 8 q^{69} - 8 q^{72} + 20 q^{77} + 8 q^{78} + 4 q^{81} - 4 q^{83} - 28 q^{87} + 40 q^{89} - 16 q^{91} - 20 q^{93} + 2 q^{96} - 8 q^{98}+O(q^{100}) $ 4 * q - 2 * q^3 - 4 * q^4 + 2 * q^6 - 6 * q^7 + 2 * q^12 + 6 * q^14 + 4 * q^16 + 12 * q^17 + 8 * q^18 - 2 * q^24 + 4 * q^26 - 14 * q^27 + 6 * q^28 + 20 * q^33 - 12 * q^37 - 16 * q^38 - 12 * q^39 - 8 * q^41 + 4 * q^42 - 16 * q^43 + 16 * q^46 - 8 * q^47 - 2 * q^48 - 16 * q^51 - 14 * q^54 - 6 * q^56 - 12 * q^57 - 4 * q^58 + 20 * q^62 - 22 * q^63 - 4 * q^64 - 20 * q^66 + 48 * q^67 - 12 * q^68 - 8 * q^69 - 8 * q^72 + 20 * q^77 + 8 * q^78 + 4 * q^81 - 4 * q^83 - 28 * q^87 + 40 * q^89 - 16 * q^91 - 20 * q^93 + 2 * q^96 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	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	$-0.851865\pi$
$13$		−	3.23607i		−	0.897524i	0.893651	−	0.448762i	$-0.148135\pi$
$14$	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	$-0.470469\pi$
$17$	0.763932			0.185281			0.0926404	+	0.995700i	$0.470469\pi$
$18$	2.00000	−	2.23607i	0.471405	−	0.527046i
$19$		−	0.472136i		−	0.108315i	−0.998532	−	0.0541577i	$-0.982753\pi$
$19$		−	0.472136i		−	0.108315i	0.998532	−	0.0541577i	$-0.0172474\pi$
$20$		0			0
$21$	−4.47214	−	1.00000i	−0.975900	−	0.218218i
$22$	−4.47214			−0.953463
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$	−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	$-0.774845\pi$
$31$		−	7.23607i		−	1.29964i	0.760090	−	0.649818i	$-0.225155\pi$
$32$			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	$-0.668651\pi$
$41$	−6.47214			−1.01078			−0.505389	+	0.862892i	$0.668651\pi$
$42$	1.00000	−	4.47214i	0.154303	−	0.690066i
$43$	−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	$-0.442293\pi$
$47$	2.47214			0.360598			0.180299	+	0.983612i	$0.442293\pi$
$48$	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	$-0.405975\pi$
$59$	4.47214			0.582223			0.291111	+	0.956689i	$0.405975\pi$
$60$		0			0
$61$			2.76393i			0.353885i	0.984221	+	0.176943i	$0.0566207\pi$
$61$			2.76393i			0.353885i	−0.984221	+	0.176943i	$0.943379\pi$
$62$	7.23607			0.918982
$63$	−4.38197	+	6.61803i	−0.552076	+	0.833794i
$64$	−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	$0.129543\pi$
$73$			6.76393i			0.791658i	−0.918324	+	0.395829i	$0.870457\pi$
$74$		−	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	$-0.866963\pi$
$83$	−16.6525			−1.82785			−0.913923	+	0.405887i	$0.866963\pi$
$84$	4.47214	+	1.00000i	0.487950	+	0.109109i
$85$		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	$-0.221738\pi$
$89$	14.4721			1.53404			0.767022	+	0.641621i	$0.221738\pi$
$90$		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	$-0.914357\pi$
$97$		−	5.23607i		−	0.531642i	0.964022	−	0.265821i	$-0.0856430\pi$
$98$	−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	$-0.443840\pi$
$101$	3.52786			0.351036			0.175518	+	0.984476i	$0.443840\pi$
$102$	1.23607	+	0.472136i	0.122389	+	0.0467484i
$103$		−	16.6525i		−	1.64082i	−0.571778	−	0.820409i	$-0.693746\pi$
$103$		−	16.6525i		−	1.64082i	0.571778	−	0.820409i	$-0.306254\pi$
$104$	−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
$126$	−6.61803	−	4.38197i	−0.589581	−	0.390377i
$127$	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	$-0.114877\pi$
$131$	21.4164			1.87116			0.935580	+	0.353114i	$0.114877\pi$
$132$	−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	$-0.665269\pi$
$139$		−	20.4721i		−	1.73642i	0.496194	−	0.868212i	$-0.334731\pi$
$140$		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
$147$	−0.909830	+	12.0902i	−0.0750415	+	0.997180i
$148$	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	$0.0608817\pi$
$157$			4.76393i			0.380203i	−0.981764	+	0.190102i	$0.939118\pi$
$158$			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	$-0.272418\pi$
$167$	16.9443			1.31119			0.655594	+	0.755114i	$0.272418\pi$
$168$	−1.00000	+	4.47214i	−0.0771517	+	0.345033i
$169$	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	$-0.269677\pi$
$173$	17.4164			1.32414			0.662072	+	0.749440i	$0.269677\pi$
$174$	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	$0.0737714\pi$
$181$			6.18034i			0.459381i	−0.973264	+	0.229691i	$0.926229\pi$
$182$	−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
$189$	8.00000	+	11.1803i	0.581914	+	0.813250i
$190$		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	$0.00203464\pi$
$199$			0.180340i			0.0127840i	−0.999980	+	0.00639198i	$0.997965\pi$
$200$		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	$-0.954100\pi$
$223$		−	4.29180i		−	0.287400i	0.989621	−	0.143700i	$-0.0459000\pi$
$224$	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	$-0.444407\pi$
$227$	5.23607			0.347530			0.173765	+	0.984787i	$0.444407\pi$
$228$	0.763932	+	0.291796i	0.0505926	+	0.0193247i
$229$		−	13.2361i		−	0.874664i	−0.899300	−	0.437332i	$-0.855923\pi$
$229$		−	13.2361i		−	0.874664i	0.899300	−	0.437332i	$-0.144077\pi$
$230$		0			0
$231$	4.47214	−	20.0000i	0.294245	−	1.31590i
$232$	−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	$-0.804554\pi$
$241$		−	17.8885i		−	1.15230i	0.817343	−	0.576151i	$-0.195446\pi$
$242$		−	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	$-0.464486\pi$
$251$	3.52786			0.222677			0.111338	+	0.993783i	$0.464486\pi$
$252$	4.38197	−	6.61803i	0.276038	−	0.416897i
$253$	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	$-0.582121\pi$
$257$	−8.18034			−0.510276			−0.255138	+	0.966905i	$0.582121\pi$
$258$	−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	$-0.456467\pi$
$269$	4.47214			0.272671			0.136335	+	0.990663i	$0.456467\pi$
$270$		0			0
$271$			18.2918i			1.11115i	0.831467	+	0.555574i	$0.187501\pi$
$271$			18.2918i			1.11115i	−0.831467	+	0.555574i	$0.812499\pi$
$272$	0.763932			0.0463202
$273$	−3.23607	+	14.4721i	−0.195856	+	0.875894i
$274$	−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	$-0.916119\pi$
$283$		−	8.76393i		−	0.520962i	0.965479	−	0.260481i	$-0.0838811\pi$
$284$		−	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	$-0.829077\pi$
$293$	−29.4164			−1.71852			−0.859262	+	0.511535i	$0.829077\pi$
$294$	−12.0902	−	0.909830i	−0.705113	−	0.0530624i
$295$		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	$-0.961937\pi$
$307$		−	4.18034i		−	0.238585i	0.992859	−	0.119292i	$-0.0380626\pi$
$308$	−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	$-0.770211\pi$
$311$	−26.4721			−1.50110			−0.750549	+	0.660815i	$0.770211\pi$
$312$	−2.00000	+	5.23607i	−0.113228	+	0.296434i
$313$		−	7.70820i		−	0.435693i	−0.975983	−	0.217847i	$-0.930097\pi$
$313$		−	7.70820i		−	0.435693i	0.975983	−	0.217847i	$-0.0699033\pi$
$314$	−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
$336$	−4.47214	−	1.00000i	−0.243975	−	0.0545545i
$337$	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	$-0.981414\pi$
$349$		−	2.18034i		−	0.116711i	0.998296	−	0.0583555i	$-0.0185857\pi$
$350$		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	$-0.624192\pi$
$353$	−14.2918			−0.760676			−0.380338	+	0.924848i	$0.624192\pi$
$354$	7.23607	+	2.76393i	0.384593	+	0.146901i
$355$		0			0
$356$	−14.4721			−0.767022
$357$	−3.41641	−	0.763932i	−0.180815	−	0.0404316i
$358$	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	$-0.879322\pi$
$367$		−	14.1803i		−	0.740208i	0.928990	−	0.370104i	$-0.120678\pi$
$368$		−	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
$378$	−11.1803	+	8.00000i	−0.575055	+	0.411476i
$379$	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	$-0.311098\pi$
$383$	21.8885			1.11845			0.559226	+	0.829015i	$0.311098\pi$
$384$	−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	$0.141391\pi$
$397$			17.1246i			0.859460i	−0.902958	+	0.429730i	$0.858609\pi$
$398$	−0.180340			−0.00903962
$399$	−0.472136	+	2.11146i	−0.0236364	+	0.105705i
$400$		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	$-0.840622\pi$
$409$		−	19.4164i		−	0.960080i	0.877247	−	0.480040i	$-0.159378\pi$
$410$		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	$-0.365121\pi$
$419$	16.8328			0.822337			0.411168	+	0.911559i	$0.365121\pi$
$420$		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	$0.0356590\pi$
$433$			4.65248i			0.223584i	−0.993732	+	0.111792i	$0.964341\pi$
$434$	−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	$-0.906123\pi$
$439$		−	12.1803i		−	0.581336i	0.956824	−	0.290668i	$-0.0938775\pi$
$440$		0			0
$441$	19.0000	+	8.94427i	0.904762	+	0.425918i
$442$	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	$-0.582030\pi$
$461$	−10.9443			−0.509726			−0.254863	+	0.966977i	$0.582030\pi$
$462$	20.0000	+	4.47214i	0.930484	+	0.208063i
$463$	−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	$-0.655564\pi$
$467$	−20.2918			−0.938992			−0.469496	+	0.882935i	$0.655564\pi$
$468$	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	$-0.515360\pi$
$479$	−2.11146			−0.0964749			−0.0482374	+	0.998836i	$0.515360\pi$
$480$		0			0
$481$			16.9443i			0.772592i
$482$	17.8885			0.814801
$483$	−4.00000	+	17.8885i	−0.182006	+	0.813957i
$484$	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	$-0.381157\pi$
$503$	16.3607			0.729487			0.364743	+	0.931108i	$0.381157\pi$
$504$	6.61803	+	4.38197i	0.294791	+	0.195188i
$505$		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	$-0.682467\pi$
$509$	−24.4721			−1.08471			−0.542354	+	0.840150i	$0.682467\pi$
$510$		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	$-0.362933\pi$
$521$	19.0557			0.834847			0.417423	+	0.908712i	$0.362933\pi$
$522$	−12.7639	−	11.4164i	−0.558662	−	0.499683i
$523$		−	24.5410i		−	1.07310i	−0.843867	−	0.536552i	$-0.819727\pi$
$523$		−	24.5410i		−	1.07310i	0.843867	−	0.536552i	$-0.180273\pi$
$524$	−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
$546$	−14.4721	−	3.23607i	−0.619350	−	0.138491i
$547$	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	$-0.377469\pi$
$563$	17.8197			0.751009			0.375505	+	0.926821i	$0.377469\pi$
$564$	−1.52786	+	4.00000i	−0.0643347	+	0.168430i
$565$		0			0
$566$	8.76393			0.368376
$567$	23.0344	−	6.03444i	0.967356	−	0.253423i
$568$	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	$-0.904625\pi$
$577$		−	14.1803i		−	0.590335i	0.955445	−	0.295168i	$-0.0953755\pi$
$578$		−	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	$-0.662737\pi$
$587$	−23.7082			−0.978542			−0.489271	+	0.872132i	$0.662737\pi$
$588$	0.909830	−	12.0902i	0.0375208	−	0.498590i
$589$	−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	$-0.0841002\pi$
$593$	47.0132			1.93060			0.965299	+	0.261145i	$0.0841002\pi$
$594$	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	$0.0953747\pi$
$601$			14.4721i			0.590331i	−0.955446	+	0.295165i	$0.904625\pi$
$602$	−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	$0.0968615\pi$
$607$			14.7639i			0.599250i	−0.954057	+	0.299625i	$0.903139\pi$
$608$	0.472136			0.0191476
$609$	−5.70820	+	25.5279i	−0.231308	+	1.03444i
$610$		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	$0.0907834\pi$
$619$			14.0000i			0.562708i	−0.959604	+	0.281354i	$0.909217\pi$
$620$		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	$0.169215\pi$
$643$			25.7082i			1.01383i	−0.861995	+	0.506916i	$0.830785\pi$
$644$	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	$-0.620710\pi$
$647$	−18.8328			−0.740394			−0.370197	+	0.928953i	$0.620710\pi$
$648$	8.94427	−	1.00000i	0.351364	−	0.0392837i
$649$			20.0000i			0.785069i
$650$		0			0
$651$	−7.23607	+	32.3607i	−0.283604	+	1.26832i
$652$	−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	$0.211512\pi$
$661$			31.7082i			1.23331i	−0.787235	+	0.616653i	$0.788488\pi$
$662$			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
$672$	1.00000	−	4.47214i	0.0385758	−	0.172516i
$673$	−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	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$	−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	$-0.734468\pi$
$691$		−	38.9443i		−	1.48151i	0.671775	−	0.740755i	$-0.265532\pi$
$692$	−17.4164			−0.662072
$693$	−29.5967	−	19.5967i	−1.12429	−	0.744419i
$694$	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
$714$	0.763932	−	3.41641i	0.0285894	−	0.127856i
$715$		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	$-0.342081\pi$
$719$	25.5279			0.952029			0.476014	+	0.879438i	$0.342081\pi$
$720$		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	$-0.736549\pi$
$727$		−	39.7082i		−	1.47270i	0.676603	−	0.736348i	$-0.263451\pi$
$728$	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	$0.248180\pi$
$733$			38.0689i			1.40611i	−0.711137	+	0.703053i	$0.751820\pi$
$734$	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
$756$	−8.00000	−	11.1803i	−0.290957	−	0.406625i
$757$	−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	$-0.682230\pi$
$761$	−29.8885			−1.08346			−0.541729	+	0.840553i	$0.682230\pi$
$762$	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	$-0.775147\pi$
$769$		−	36.0000i		−	1.29819i	0.760706	−	0.649097i	$-0.224853\pi$
$770$		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	$-0.265054\pi$
$773$	37.4164			1.34577			0.672887	+	0.739745i	$0.265054\pi$
$774$	−25.8885	+	28.9443i	−0.930544	+	1.04038i
$775$		0			0
$776$	−5.23607			−0.187964
$777$	23.4164	+	5.23607i	0.840059	+	0.187843i
$778$	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	$-0.653505\pi$
$787$		−	49.7082i		−	1.77191i	0.463775	−	0.885953i	$-0.346495\pi$
$788$		−	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	$-0.530582\pi$
$797$	−5.41641			−0.191859			−0.0959295	+	0.995388i	$0.530582\pi$
$798$	−2.11146	−	0.472136i	−0.0747447	−	0.0167134i
$799$	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	$-0.904500\pi$
$811$		−	16.8328i		−	0.591080i	0.955330	−	0.295540i	$-0.0954996\pi$
$812$	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
$819$	21.4164	+	14.1803i	0.748350	+	0.495501i
$820$		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	$0.175599\pi$
$829$			30.1803i			1.04821i	−0.851655	+	0.524103i	$0.824401\pi$
$830$		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	$-0.580370\pi$
$839$	−14.4721			−0.499634			−0.249817	+	0.968293i	$0.580370\pi$
$840$		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	$0.0311558\pi$
$853$			5.70820i			0.195445i	−0.995214	+	0.0977226i	$0.968844\pi$
$854$	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	$-0.759778\pi$
$857$	−42.6525			−1.45698			−0.728490	+	0.685056i	$0.759778\pi$
$858$	23.4164	+	8.94427i	0.799423	+	0.305352i
$859$		−	34.9443i		−	1.19228i	−0.802879	−	0.596142i	$-0.796700\pi$
$859$		−	34.9443i		−	1.19228i	0.802879	−	0.596142i	$-0.203300\pi$
$860$		0			0
$861$	28.9443	+	6.47214i	0.986418	+	0.220570i
$862$	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	$-0.438401\pi$
$881$	11.4164			0.384629			0.192314	+	0.981333i	$0.438401\pi$
$882$	−8.94427	+	19.0000i	−0.301169	+	0.639763i
$883$	−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	$-0.646592\pi$
$887$	−26.4721			−0.888847			−0.444424	+	0.895817i	$0.646592\pi$
$888$	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
$903$	57.8885	+	12.9443i	1.92641	+	0.430758i
$904$	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
$924$	−4.47214	+	20.0000i	−0.147122	+	0.657952i
$925$		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	$-0.511028\pi$
$929$	−2.11146			−0.0692746			−0.0346373	+	0.999400i	$0.511028\pi$
$930$		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	$0.0845383\pi$
$937$			16.0689i			0.524948i	−0.964939	+	0.262474i	$0.915462\pi$
$938$	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	$-0.616742\pi$
$941$	−22.0000			−0.717180			−0.358590	+	0.933495i	$0.616742\pi$
$942$	−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
$966$	−17.8885	−	4.00000i	−0.575554	−	0.128698i
$967$	−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	$-0.119239\pi$
$971$	58.0000			1.86131			0.930654	+	0.365900i	$0.119239\pi$
$972$	−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	$-0.716369\pi$
$983$	−39.4164			−1.25719			−0.628594	+	0.777734i	$0.716369\pi$
$984$	10.4721	+	4.00000i	0.333840	+	0.127515i
$985$		0			0
$986$	4.36068			0.138872
$987$	−11.0557	−	2.47214i	−0.351908	−	0.0786890i
$988$	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	$-0.893356\pi$
$997$		−	20.7639i		−	0.657600i	0.944400	−	0.328800i	$-0.106644\pi$
$998$		−	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.a.251.4		4
3.2	odd	2		1050.2.b.c.251.1		4
5.2	odd	4		1050.2.d.a.1049.1		4
5.3	odd	4		1050.2.d.f.1049.4		4
5.4	even	2		210.2.b.b.41.1	yes	4
7.6	odd	2		1050.2.b.c.251.3		4
15.2	even	4		1050.2.d.d.1049.2		4
15.8	even	4		1050.2.d.c.1049.3		4
15.14	odd	2		210.2.b.a.41.4	yes	4
20.19	odd	2		1680.2.f.e.881.3		4
21.20	even	2	inner	1050.2.b.a.251.2		4
35.13	even	4		1050.2.d.d.1049.1		4
35.27	even	4		1050.2.d.c.1049.4		4
35.34	odd	2		210.2.b.a.41.2	✓	4
60.59	even	2		1680.2.f.i.881.1		4
105.62	odd	4		1050.2.d.f.1049.3		4
105.83	odd	4		1050.2.d.a.1049.2		4
105.104	even	2		210.2.b.b.41.3	yes	4
140.139	even	2		1680.2.f.i.881.2		4
420.419	odd	2		1680.2.f.e.881.4		4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.618034 - 1.61803i) q^{3} -1.00000 q^{4} +(1.61803 + 0.618034i) q^{6} +(-0.381966 - 2.61803i) q^{7} -1.00000i q^{8} +(-2.23607 - 2.00000i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.618034 - 1.61803i) q^{3} -1.00000 q^{4} +(1.61803 + 0.618034i) q^{6} +(-0.381966 - 2.61803i) q^{7} -1.00000i q^{8} +(-2.23607 - 2.00000i) q^{9} +4.47214i q^{11} +(-0.618034 + 1.61803i) q^{12} -3.23607i q^{13} +(2.61803 - 0.381966i) q^{14} +1.00000 q^{16} +0.763932 q^{17} +(2.00000 - 2.23607i) q^{18} -0.472136i q^{19} +(-4.47214 - 1.00000i) q^{21} -4.47214 q^{22} -4.00000i q^{23} +(-1.61803 - 0.618034i) q^{24} +3.23607 q^{26} +(-4.61803 + 2.38197i) q^{27} +(0.381966 + 2.61803i) q^{28} -5.70820i q^{29} -7.23607i q^{31} +1.00000i q^{32} +(7.23607 + 2.76393i) q^{33} +0.763932i q^{34} +(2.23607 + 2.00000i) q^{36} -5.23607 q^{37} +0.472136 q^{38} +(-5.23607 - 2.00000i) q^{39} -6.47214 q^{41} +(1.00000 - 4.47214i) q^{42} -12.9443 q^{43} -4.47214i q^{44} +4.00000 q^{46} +2.47214 q^{47} +(0.618034 - 1.61803i) q^{48} +(-6.70820 + 2.00000i) q^{49} +(0.472136 - 1.23607i) q^{51} +3.23607i q^{52} -8.47214i q^{53} +(-2.38197 - 4.61803i) q^{54} +(-2.61803 + 0.381966i) q^{56} +(-0.763932 - 0.291796i) q^{57} +5.70820 q^{58} +4.47214 q^{59} +2.76393i q^{61} +7.23607 q^{62} +(-4.38197 + 6.61803i) q^{63} -1.00000 q^{64} +(-2.76393 + 7.23607i) q^{66} +12.0000 q^{67} -0.763932 q^{68} +(-6.47214 - 2.47214i) q^{69} +2.76393i q^{71} +(-2.00000 + 2.23607i) q^{72} +6.76393i q^{73} -5.23607i q^{74} +0.472136i q^{76} +(11.7082 - 1.70820i) q^{77} +(2.00000 - 5.23607i) q^{78} +8.94427 q^{79} +(1.00000 + 8.94427i) q^{81} -6.47214i q^{82} -16.6525 q^{83} +(4.47214 + 1.00000i) q^{84} -12.9443i q^{86} +(-9.23607 - 3.52786i) q^{87} +4.47214 q^{88} +14.4721 q^{89} +(-8.47214 + 1.23607i) q^{91} +4.00000i q^{92} +(-11.7082 - 4.47214i) q^{93} +2.47214i q^{94} +(1.61803 + 0.618034i) q^{96} -5.23607i q^{97} +(-2.00000 - 6.70820i) q^{98} +(8.94427 - 10.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 4 q^{4} + 2 q^{6} - 6 q^{7}+O(q^{10}) \) 4 * q - 2 * q^3 - 4 * q^4 + 2 * q^6 - 6 * q^7	\( 4 q - 2 q^{3} - 4 q^{4} + 2 q^{6} - 6 q^{7} + 2 q^{12} + 6 q^{14} + 4 q^{16} + 12 q^{17} + 8 q^{18} - 2 q^{24} + 4 q^{26} - 14 q^{27} + 6 q^{28} + 20 q^{33} - 12 q^{37} - 16 q^{38} - 12 q^{39} - 8 q^{41} + 4 q^{42} - 16 q^{43} + 16 q^{46} - 8 q^{47} - 2 q^{48} - 16 q^{51} - 14 q^{54} - 6 q^{56} - 12 q^{57} - 4 q^{58} + 20 q^{62} - 22 q^{63} - 4 q^{64} - 20 q^{66} + 48 q^{67} - 12 q^{68} - 8 q^{69} - 8 q^{72} + 20 q^{77} + 8 q^{78} + 4 q^{81} - 4 q^{83} - 28 q^{87} + 40 q^{89} - 16 q^{91} - 20 q^{93} + 2 q^{96} - 8 q^{98}+O(q^{100}) \) 4 * q - 2 * q^3 - 4 * q^4 + 2 * q^6 - 6 * q^7 + 2 * q^12 + 6 * q^14 + 4 * q^16 + 12 * q^17 + 8 * q^18 - 2 * q^24 + 4 * q^26 - 14 * q^27 + 6 * q^28 + 20 * q^33 - 12 * q^37 - 16 * q^38 - 12 * q^39 - 8 * q^41 + 4 * q^42 - 16 * q^43 + 16 * q^46 - 8 * q^47 - 2 * q^48 - 16 * q^51 - 14 * q^54 - 6 * q^56 - 12 * q^57 - 4 * q^58 + 20 * q^62 - 22 * q^63 - 4 * q^64 - 20 * q^66 + 48 * q^67 - 12 * q^68 - 8 * q^69 - 8 * q^72 + 20 * q^77 + 8 * q^78 + 4 * q^81 - 4 * q^83 - 28 * q^87 + 40 * q^89 - 16 * q^91 - 20 * q^93 + 2 * q^96 - 8 * q^98

Introduction

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